LMFDB - Embedded newform 121.3.d.e.118.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,3,Mod(40,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("121.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	121.d (of order $10$, degree $4$, 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:	$3.29701119876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			118.1
Root			$-0.831254 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	121.118
Dual form			121.3.d.e.40.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831254 - 1.14412i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.618034 - 1.90211i) q^{4} +(5.66312 + 4.11450i) q^{5} +(-0.831254 + 1.14412i) q^{6} +(6.72499 + 2.18508i) q^{7} +(-8.06998 + 2.62210i) q^{8} +(6.47214 - 4.70228i) q^{9} +O(q^{10})$	\(q+(-0.831254 - 1.14412i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.618034 - 1.90211i) q^{4} +(5.66312 + 4.11450i) q^{5} +(-0.831254 + 1.14412i) q^{6} +(6.72499 + 2.18508i) q^{7} +(-8.06998 + 2.62210i) q^{8} +(6.47214 - 4.70228i) q^{9} -9.89949i q^{10} -2.00000 q^{12} +(-9.97505 - 13.7295i) q^{13} +(-3.09017 - 9.51057i) q^{14} +(2.16312 - 6.65740i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-2.49376 + 3.43237i) q^{17} +(-10.7600 - 3.49613i) q^{18} +(16.1400 - 5.24419i) q^{19} +(11.3262 - 8.22899i) q^{20} -7.07107i q^{21} -9.00000 q^{23} +(4.98752 + 6.86474i) q^{24} +(7.41641 + 22.8254i) q^{25} +(-7.41641 + 22.8254i) q^{26} +(-13.7533 - 9.99235i) q^{27} +(8.31254 - 11.4412i) q^{28} +(21.5200 + 6.99226i) q^{29} +(-9.41498 + 3.05911i) q^{30} +(-39.6418 + 28.8015i) q^{31} +28.2843i q^{32} +6.00000 q^{34} +(29.0939 + 40.0443i) q^{35} +(-4.94427 - 15.2169i) q^{36} +(5.25329 - 16.1680i) q^{37} +(-19.4164 - 14.1068i) q^{38} +(-9.97505 + 13.7295i) q^{39} +(-56.4899 - 18.3547i) q^{40} +(16.1400 - 5.24419i) q^{41} +(-8.09017 + 5.87785i) q^{42} +46.6690i q^{43} +56.0000 q^{45} +(7.48128 + 10.2971i) q^{46} +(9.88854 + 30.4338i) q^{47} +(1.23607 - 3.80423i) q^{48} +(0.809017 + 0.587785i) q^{49} +(19.9501 - 27.4589i) q^{50} +(4.03499 + 1.31105i) q^{51} +(-32.2799 + 10.4884i) q^{52} +(-12.9443 + 9.40456i) q^{53} +24.0416i q^{54} -60.0000 q^{56} +(-9.97505 - 13.7295i) q^{57} +(-9.88854 - 30.4338i) q^{58} +(-21.9402 + 67.5250i) q^{59} +(-11.3262 - 8.22899i) q^{60} +(6.65003 - 9.15298i) q^{61} +(65.9049 + 21.4138i) q^{62} +(53.7999 - 17.4806i) q^{63} +(45.3050 - 32.9160i) q^{64} -118.794i q^{65} -31.0000 q^{67} +(4.98752 + 6.86474i) q^{68} +(2.78115 + 8.55951i) q^{69} +(21.6312 - 66.5740i) q^{70} +(59.0582 + 42.9083i) q^{71} +(-39.9002 + 54.9179i) q^{72} +(-37.6599 - 12.2364i) q^{73} +(-22.8649 + 7.42927i) q^{74} +(19.4164 - 14.1068i) q^{75} -33.9411i q^{76} +24.0000 q^{78} +(-92.2692 - 126.998i) q^{79} +(8.65248 + 26.6296i) q^{80} +(16.9959 - 52.3081i) q^{81} +(-19.4164 - 14.1068i) q^{82} +(-20.7813 + 28.6031i) q^{83} +(-13.4500 - 4.37016i) q^{84} +(-28.2449 + 9.17734i) q^{85} +(53.3951 - 38.7938i) q^{86} -22.6274i q^{87} -9.00000 q^{89} +(-46.5502 - 64.0709i) q^{90} +(-37.0820 - 114.127i) q^{91} +(-5.56231 + 17.1190i) q^{92} +(39.6418 + 28.8015i) q^{93} +(26.6001 - 36.6119i) q^{94} +(112.980 + 36.7093i) q^{95} +(26.8999 - 8.74032i) q^{96} +(13.7533 - 9.99235i) q^{97} -1.41421i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9	$ 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9} - 16 q^{12} + 20 q^{14} - 14 q^{15} + 8 q^{16} + 28 q^{20} - 72 q^{23} - 48 q^{25} + 48 q^{26} - 34 q^{27} - 98 q^{31} + 48 q^{34} + 32 q^{36} - 34 q^{37} - 48 q^{38} - 20 q^{42} + 448 q^{45} - 64 q^{47} - 8 q^{48} + 2 q^{49} - 32 q^{53} - 480 q^{56} + 64 q^{58} + 142 q^{59} - 28 q^{60} + 112 q^{64} - 248 q^{67} - 18 q^{69} - 140 q^{70} + 146 q^{71} + 48 q^{75} + 192 q^{78} - 56 q^{80} - 110 q^{81} - 48 q^{82} + 132 q^{86} - 72 q^{89} + 240 q^{91} + 36 q^{92} + 98 q^{93} + 34 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9 - 16 * q^12 + 20 * q^14 - 14 * q^15 + 8 * q^16 + 28 * q^20 - 72 * q^23 - 48 * q^25 + 48 * q^26 - 34 * q^27 - 98 * q^31 + 48 * q^34 + 32 * q^36 - 34 * q^37 - 48 * q^38 - 20 * q^42 + 448 * q^45 - 64 * q^47 - 8 * q^48 + 2 * q^49 - 32 * q^53 - 480 * q^56 + 64 * q^58 + 142 * q^59 - 28 * q^60 + 112 * q^64 - 248 * q^67 - 18 * q^69 - 140 * q^70 + 146 * q^71 + 48 * q^75 + 192 * q^78 - 56 * q^80 - 110 * q^81 - 48 * q^82 + 132 * q^86 - 72 * q^89 + 240 * q^91 + 36 * q^92 + 98 * q^93 + 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i	0.548953	−	0.835853i	$-0.315027\pi$
$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i	−0.964580	+	0.263792i	$0.915027\pi$
$3$	−0.309017	−	0.951057i	−0.103006	−	0.317019i	0.886252	−	0.463204i	$-0.153300\pi$
$3$	−0.309017	−	0.951057i	−0.103006	−	0.317019i	−0.989257	+	0.146185i	$0.953300\pi$
$4$	0.618034	−	1.90211i	0.154508	−	0.475528i
$5$	5.66312	+	4.11450i	1.13262	+	0.822899i	0.986075	−	0.166304i	$-0.0531833\pi$
$5$	5.66312	+	4.11450i	1.13262	+	0.822899i	0.146549	+	0.989203i	$0.453183\pi$
$6$	−0.831254	+	1.14412i	−0.138542	+	0.190687i
$7$	6.72499	+	2.18508i	0.960712	+	0.312154i	0.747061	−	0.664756i	$-0.231464\pi$
$7$	6.72499	+	2.18508i	0.960712	+	0.312154i	0.213651	+	0.976910i	$0.431464\pi$
$8$	−8.06998	+	2.62210i	−1.00875	+	0.327762i
$9$	6.47214	−	4.70228i	0.719126	−	0.522476i
$10$		−	9.89949i		−	0.989949i
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.166667
$13$	−9.97505	−	13.7295i	−0.767311	−	1.05611i	−0.996571	−	0.0827480i	$-0.973630\pi$
$13$	−9.97505	−	13.7295i	−0.767311	−	1.05611i	0.229259	−	0.973365i	$-0.426370\pi$
$14$	−3.09017	−	9.51057i	−0.220726	−	0.679326i
$15$	2.16312	−	6.65740i	0.144208	−	0.443826i
$16$	3.23607	+	2.35114i	0.202254	+	0.146946i
$17$	−2.49376	+	3.43237i	−0.146692	+	0.201904i	−0.876040	−	0.482239i	$-0.839824\pi$
$17$	−2.49376	+	3.43237i	−0.146692	+	0.201904i	0.729348	+	0.684143i	$0.239824\pi$
$18$	−10.7600	−	3.49613i	−0.597776	−	0.194229i
$19$	16.1400	−	5.24419i	0.849472	−	0.276010i	0.148247	−	0.988950i	$-0.452637\pi$
$19$	16.1400	−	5.24419i	0.849472	−	0.276010i	0.701225	+	0.712940i	$0.252637\pi$
$20$	11.3262	−	8.22899i	0.566312	−	0.411450i
$21$		−	7.07107i		−	0.336718i
$22$		0			0
$23$	−9.00000			−0.391304			−0.195652	−	0.980673i	$-0.562682\pi$
$23$	−9.00000			−0.391304			−0.195652	+	0.980673i	$0.562682\pi$
$24$	4.98752	+	6.86474i	0.207813	+	0.286031i
$25$	7.41641	+	22.8254i	0.296656	+	0.913014i
$26$	−7.41641	+	22.8254i	−0.285246	+	0.877898i
$27$	−13.7533	−	9.99235i	−0.509381	−	0.370087i
$28$	8.31254	−	11.4412i	0.296876	−	0.408615i
$29$	21.5200	+	6.99226i	0.742067	+	0.241112i	0.655564	−	0.755139i	$-0.272431\pi$
$29$	21.5200	+	6.99226i	0.742067	+	0.241112i	0.0865030	+	0.996252i	$0.472431\pi$
$30$	−9.41498	+	3.05911i	−0.313833	+	0.101970i
$31$	−39.6418	+	28.8015i	−1.27877	+	0.929080i	−0.999515	−	0.0311374i	$-0.990087\pi$
$31$	−39.6418	+	28.8015i	−1.27877	+	0.929080i	−0.279254	+	0.960217i	$0.590087\pi$
$32$			28.2843i			0.883883i
$33$		0			0
$34$	6.00000			0.176471
$35$	29.0939	+	40.0443i	0.831254	+	1.14412i
$36$	−4.94427	−	15.2169i	−0.137341	−	0.422692i
$37$	5.25329	−	16.1680i	0.141981	−	0.436972i	−0.854630	−	0.519238i	$-0.826216\pi$
$37$	5.25329	−	16.1680i	0.141981	−	0.436972i	0.996610	+	0.0822662i	$0.0262158\pi$
$38$	−19.4164	−	14.1068i	−0.510958	−	0.371233i
$39$	−9.97505	+	13.7295i	−0.255770	+	0.352038i
$40$	−56.4899	−	18.3547i	−1.41225	−	0.458867i
$41$	16.1400	−	5.24419i	0.393658	−	0.127907i	−0.105498	−	0.994420i	$-0.533644\pi$
$41$	16.1400	−	5.24419i	0.393658	−	0.127907i	0.499156	+	0.866512i	$0.333644\pi$
$42$	−8.09017	+	5.87785i	−0.192623	+	0.139949i
$43$			46.6690i			1.08533i	0.839950	+	0.542663i	$0.182584\pi$
$43$			46.6690i			1.08533i	−0.839950	+	0.542663i	$0.817416\pi$
$44$		0			0
$45$	56.0000			1.24444
$46$	7.48128	+	10.2971i	0.162637	+	0.223850i
$47$	9.88854	+	30.4338i	0.210395	+	0.647528i	0.999449	+	0.0332041i	$0.0105711\pi$
$47$	9.88854	+	30.4338i	0.210395	+	0.647528i	−0.789054	+	0.614324i	$0.789429\pi$
$48$	1.23607	−	3.80423i	0.0257514	−	0.0792547i
$49$	0.809017	+	0.587785i	0.0165106	+	0.0119956i
$50$	19.9501	−	27.4589i	0.399002	−	0.549179i
$51$	4.03499	+	1.31105i	0.0791175	+	0.0257068i
$52$	−32.2799	+	10.4884i	−0.620768	+	0.201700i
$53$	−12.9443	+	9.40456i	−0.244232	+	0.177445i	−0.703166	−	0.711025i	$-0.748231\pi$
$53$	−12.9443	+	9.40456i	−0.244232	+	0.177445i	0.458935	+	0.888470i	$0.348231\pi$
$54$			24.0416i			0.445215i
$55$		0			0
$56$	−60.0000			−1.07143
$57$	−9.97505	−	13.7295i	−0.175001	−	0.240868i
$58$	−9.88854	−	30.4338i	−0.170492	−	0.524721i
$59$	−21.9402	+	67.5250i	−0.371868	+	1.14449i	0.573700	+	0.819066i	$0.305508\pi$
$59$	−21.9402	+	67.5250i	−0.371868	+	1.14449i	−0.945568	+	0.325426i	$0.894492\pi$
$60$	−11.3262	−	8.22899i	−0.188771	−	0.137150i
$61$	6.65003	−	9.15298i	0.109017	−	0.150049i	−0.751022	−	0.660277i	$-0.770439\pi$
$61$	6.65003	−	9.15298i	0.109017	−	0.150049i	0.860039	+	0.510228i	$0.170439\pi$
$62$	65.9049	+	21.4138i	1.06298	+	0.345384i
$63$	53.7999	−	17.4806i	0.853966	−	0.277470i
$64$	45.3050	−	32.9160i	0.707890	−	0.514312i
$65$		−	118.794i		−	1.82760i
$66$		0			0
$67$	−31.0000			−0.462687			−0.231343	−	0.972872i	$-0.574312\pi$
$67$	−31.0000			−0.462687			−0.231343	+	0.972872i	$0.574312\pi$
$68$	4.98752	+	6.86474i	0.0733459	+	0.100952i
$69$	2.78115	+	8.55951i	0.0403066	+	0.124051i
$70$	21.6312	−	66.5740i	0.309017	−	0.951057i
$71$	59.0582	+	42.9083i	0.831806	+	0.604343i	0.920070	−	0.391755i	$-0.128132\pi$
$71$	59.0582	+	42.9083i	0.831806	+	0.604343i	−0.0882635	+	0.996097i	$0.528132\pi$
$72$	−39.9002	+	54.9179i	−0.554169	+	0.762749i
$73$	−37.6599	−	12.2364i	−0.515889	−	0.167623i	0.0394897	−	0.999220i	$-0.487427\pi$
$73$	−37.6599	−	12.2364i	−0.515889	−	0.167623i	−0.555379	+	0.831597i	$0.687427\pi$
$74$	−22.8649	+	7.42927i	−0.308986	+	0.100396i
$75$	19.4164	−	14.1068i	0.258885	−	0.188091i
$76$		−	33.9411i		−	0.446594i
$77$		0			0
$78$	24.0000			0.307692
$79$	−92.2692	−	126.998i	−1.16796	−	1.60756i	−0.675864	−	0.737027i	$-0.736229\pi$
$79$	−92.2692	−	126.998i	−1.16796	−	1.60756i	−0.492101	−	0.870538i	$-0.663771\pi$
$80$	8.65248	+	26.6296i	0.108156	+	0.332870i
$81$	16.9959	−	52.3081i	0.209826	−	0.645779i
$82$	−19.4164	−	14.1068i	−0.236785	−	0.172035i
$83$	−20.7813	+	28.6031i	−0.250378	+	0.344615i	−0.915643	−	0.401991i	$-0.868318\pi$
$83$	−20.7813	+	28.6031i	−0.250378	+	0.344615i	0.665266	+	0.746607i	$0.268318\pi$
$84$	−13.4500	−	4.37016i	−0.160119	−	0.0520257i
$85$	−28.2449	+	9.17734i	−0.332293	+	0.107969i
$86$	53.3951	−	38.7938i	0.620874	−	0.451091i
$87$		−	22.6274i		−	0.260085i
$88$		0			0
$89$	−9.00000			−0.101124			−0.0505618	−	0.998721i	$-0.516101\pi$
$89$	−9.00000			−0.101124			−0.0505618	+	0.998721i	$0.516101\pi$
$90$	−46.5502	−	64.0709i	−0.517225	−	0.711899i
$91$	−37.0820	−	114.127i	−0.407495	−	1.25414i
$92$	−5.56231	+	17.1190i	−0.0604598	+	0.186076i
$93$	39.6418	+	28.8015i	0.426256	+	0.309693i
$94$	26.6001	−	36.6119i	0.282980	−	0.389489i
$95$	112.980	+	36.7093i	1.18926	+	0.386414i
$96$	26.8999	−	8.74032i	0.280208	−	0.0910450i
$97$	13.7533	−	9.99235i	0.141786	−	0.103014i	−0.514631	−	0.857412i	$-0.672071\pi$
$97$	13.7533	−	9.99235i	0.141786	−	0.103014i	0.656417	+	0.754398i	$0.272071\pi$
$98$		−	1.41421i		−	0.0144308i
$99$		0			0
$100$	48.0000			0.480000
$101$	90.6067	+	124.709i	0.897096	+	1.23475i	0.971385	+	0.237510i	$0.0763311\pi$
$101$	90.6067	+	124.709i	0.897096	+	1.23475i	−0.0742894	+	0.997237i	$0.523669\pi$
$102$	−1.85410	−	5.70634i	−0.0181775	−	0.0559445i
$103$	−4.94427	+	15.2169i	−0.0480026	+	0.147737i	−0.972185	−	0.234215i	$-0.924748\pi$
$103$	−4.94427	+	15.2169i	−0.0480026	+	0.147737i	0.924182	+	0.381952i	$0.124748\pi$
$104$	116.498	+	84.6411i	1.12018	+	0.813857i
$105$	29.0939	−	40.0443i	0.277085	−	0.381374i
$106$	21.5200	+	6.99226i	0.203018	+	0.0659647i
$107$	−176.195	+	57.2491i	−1.64668	+	0.535038i	−0.978016	−	0.208528i	$-0.933133\pi$
$107$	−176.195	+	57.2491i	−1.64668	+	0.535038i	−0.668662	+	0.743566i	$0.733133\pi$
$108$	−27.5066	+	19.9847i	−0.254691	+	0.185044i
$109$			46.6690i			0.428156i	0.976817	+	0.214078i	$0.0686747\pi$
$109$			46.6690i			0.428156i	−0.976817	+	0.214078i	$0.931325\pi$
$110$		0			0
$111$	−17.0000			−0.153153
$112$	16.6251	+	22.8825i	0.148438	+	0.204308i
$113$	20.0861	+	61.8187i	0.177753	+	0.547068i	0.999748	−	0.0224263i	$-0.00713910\pi$
$113$	20.0861	+	61.8187i	0.177753	+	0.547068i	−0.821995	+	0.569494i	$0.807139\pi$
$114$	−7.41641	+	22.8254i	−0.0650562	+	0.200222i
$115$	−50.9681	−	37.0305i	−0.443201	−	0.322004i
$116$	26.6001	−	36.6119i	0.229311	−	0.315620i
$117$	−129.120	−	41.9535i	−1.10359	−	0.358577i
$118$	95.4948	−	31.0281i	0.809278	−	0.262950i
$119$	−24.2705	+	17.6336i	−0.203954	+	0.148181i
$120$			59.3970i			0.494975i
$121$		0			0
$122$	−16.0000			−0.131148
$123$	−9.97505	−	13.7295i	−0.0810979	−	0.111622i
$124$	30.2837	+	93.2035i	0.244223	+	0.751641i
$125$	2.16312	−	6.65740i	0.0173050	−	0.0532592i
$126$	−64.7214	−	47.0228i	−0.513662	−	0.373197i
$127$	−103.075	+	141.871i	−0.811618	+	1.11710i	0.179454	+	0.983766i	$0.442567\pi$
$127$	−103.075	+	141.871i	−0.811618	+	1.11710i	−0.991072	+	0.133330i	$0.957433\pi$
$128$	32.2799	+	10.4884i	0.252187	+	0.0819405i
$129$	44.3849	−	14.4215i	0.344069	−	0.111795i
$130$	−135.915	+	98.7479i	−1.04550	+	0.759599i
$131$			140.007i			1.06876i	0.845245	+	0.534378i	$0.179454\pi$
$131$			140.007i			1.06876i	−0.845245	+	0.534378i	$0.820546\pi$
$132$		0			0
$133$	120.000			0.902256
$134$	25.7689	+	35.4678i	0.192305	+	0.264685i
$135$	−36.7730	−	113.176i	−0.272393	−	0.838339i
$136$	11.1246	−	34.2380i	0.0817986	−	0.251750i
$137$	−207.917	−	151.061i	−1.51765	−	1.10263i	−0.962639	−	0.270787i	$-0.912716\pi$
$137$	−207.917	−	151.061i	−1.51765	−	1.10263i	−0.555006	−	0.831846i	$-0.687284\pi$
$138$	7.48128	−	10.2971i	0.0542122	−	0.0746167i
$139$	−82.0448	−	26.6580i	−0.590250	−	0.191784i	−0.00136305	−	0.999999i	$-0.500434\pi$
$139$	−82.0448	−	26.6580i	−0.590250	−	0.191784i	−0.588887	+	0.808215i	$0.700434\pi$
$140$	94.1498	−	30.5911i	0.672499	−	0.218508i
$141$	25.8885	−	18.8091i	0.183607	−	0.133398i
$142$		−	103.238i		−	0.727025i
$143$		0			0
$144$	32.0000			0.222222
$145$	93.1004	+	128.142i	0.642072	+	0.883736i
$146$	17.3050	+	53.2592i	0.118527	+	0.364789i
$147$	0.309017	−	0.951057i	0.00210216	−	0.00646977i
$148$	−27.5066	−	19.9847i	−0.185855	−	0.135032i
$149$	162.095	−	223.104i	1.08788	−	1.49734i	0.237347	−	0.971425i	$-0.423722\pi$
$149$	162.095	−	223.104i	1.08788	−	1.49734i	0.850536	−	0.525917i	$-0.176278\pi$
$150$	−32.2799	−	10.4884i	−0.215200	−	0.0699226i
$151$	149.295	−	48.5088i	0.988706	−	0.321250i	0.230363	−	0.973105i	$-0.426009\pi$
$151$	149.295	−	48.5088i	0.988706	−	0.321250i	0.758344	+	0.651855i	$0.226009\pi$
$152$	−116.498	+	84.6411i	−0.766437	+	0.556849i
$153$			33.9411i			0.221837i
$154$		0			0
$155$	−343.000			−2.21290
$156$	19.9501	+	27.4589i	0.127885	+	0.176019i
$157$	54.0780	+	166.435i	0.344446	+	1.06009i	0.961880	+	0.273472i	$0.0881722\pi$
$157$	54.0780	+	166.435i	0.344446	+	1.06009i	−0.617434	+	0.786623i	$0.711828\pi$
$158$	−68.6018	+	211.135i	−0.434188	+	1.33629i
$159$	12.9443	+	9.40456i	0.0814105	+	0.0591482i
$160$	−116.376	+	160.177i	−0.727347	+	1.00111i
$161$	−60.5249	−	19.6657i	−0.375931	−	0.122147i
$162$	−73.9748	+	24.0359i	−0.456635	+	0.148370i
$163$	129.443	−	94.0456i	0.794127	−	0.576967i	−0.115058	−	0.993359i	$-0.536705\pi$
$163$	129.443	−	94.0456i	0.794127	−	0.576967i	0.909185	+	0.416392i	$0.136705\pi$
$164$		−	33.9411i		−	0.206958i
$165$		0			0
$166$	50.0000			0.301205
$167$	−9.97505	−	13.7295i	−0.0597308	−	0.0822124i	0.778107	−	0.628132i	$-0.216180\pi$
$167$	−9.97505	−	13.7295i	−0.0597308	−	0.0822124i	−0.837837	+	0.545920i	$0.816180\pi$
$168$	18.5410	+	57.0634i	0.110363	+	0.339663i
$169$	−36.7730	+	113.176i	−0.217592	+	0.669679i
$170$	33.9787	+	24.6870i	0.199875	+	0.145218i
$171$	79.8004	−	109.836i	0.466669	−	0.642315i
$172$	88.7698	+	28.8431i	0.516104	+	0.167692i
$173$	−117.015	+	38.0204i	−0.676386	+	0.219771i	−0.627012	−	0.779009i	$-0.715722\pi$
$173$	−117.015	+	38.0204i	−0.676386	+	0.219771i	−0.0493734	+	0.998780i	$0.515722\pi$
$174$	−25.8885	+	18.8091i	−0.148785	+	0.108098i
$175$			169.706i			0.969746i
$176$		0			0
$177$	71.0000			0.401130
$178$	7.48128	+	10.2971i	0.0420297	+	0.0578489i
$179$	−61.4944	−	189.260i	−0.343544	−	1.05732i	−0.962359	−	0.271783i	$-0.912387\pi$
$179$	−61.4944	−	189.260i	−0.343544	−	1.05732i	0.618815	−	0.785537i	$-0.287613\pi$
$180$	34.6099	−	106.518i	0.192277	−	0.591768i
$181$	59.0582	+	42.9083i	0.326289	+	0.237063i	0.738854	−	0.673865i	$-0.235367\pi$
$181$	59.0582	+	42.9083i	0.326289	+	0.237063i	−0.412566	+	0.910928i	$0.635367\pi$
$182$	−99.7505	+	137.295i	−0.548079	+	0.754367i
$183$	−10.7600	−	3.49613i	−0.0587977	−	0.0191045i
$184$	72.6298	−	23.5989i	0.394727	−	0.128255i
$185$	96.2730	−	69.9464i	0.520395	−	0.378089i
$186$		−	69.2965i		−	0.372562i
$187$		0			0
$188$	64.0000			0.340426
$189$	−70.6566	−	97.2504i	−0.373844	−	0.514553i
$190$	−51.9149	−	159.777i	−0.273236	−	0.840934i
$191$	66.4387	−	204.477i	0.347846	−	1.07056i	−0.612196	−	0.790706i	$-0.709714\pi$
$191$	66.4387	−	204.477i	0.347846	−	1.07056i	0.960042	−	0.279855i	$-0.0902864\pi$
$192$	−45.3050	−	32.9160i	−0.235963	−	0.171437i
$193$	79.8004	−	109.836i	0.413473	−	0.569097i	−0.550588	−	0.834777i	$-0.685596\pi$
$193$	79.8004	−	109.836i	0.413473	−	0.569097i	0.964061	+	0.265680i	$0.0855964\pi$
$194$	−22.8649	−	7.42927i	−0.117861	−	0.0382952i
$195$	−112.980	+	36.7093i	−0.579383	+	0.188253i
$196$	1.61803	−	1.17557i	0.00825528	−	0.00599781i
$197$		−	202.233i		−	1.02656i	−0.858221	−	0.513281i	$-0.828430\pi$
$197$		−	202.233i		−	1.02656i	0.858221	−	0.513281i	$-0.171570\pi$
$198$		0			0
$199$	200.000			1.00503			0.502513	−	0.864570i	$-0.332409\pi$
$199$	200.000			1.00503			0.502513	+	0.864570i	$0.332409\pi$
$200$	−119.701	−	164.754i	−0.598503	−	0.823768i
$201$	9.57953	+	29.4828i	0.0476593	+	0.146680i
$202$	67.3657	−	207.330i	0.333494	−	1.02639i
$203$	129.443	+	94.0456i	0.637649	+	0.463279i
$204$	4.98752	−	6.86474i	0.0244486	−	0.0336507i
$205$	112.980	+	36.7093i	0.551121	+	0.179070i
$206$	21.5200	−	6.99226i	0.104466	−	0.0339430i
$207$	−58.2492	+	42.3205i	−0.281397	+	0.204447i
$208$		−	67.8823i		−	0.326357i
$209$		0			0
$210$	−70.0000			−0.333333
$211$	−46.5502	−	64.0709i	−0.220617	−	0.303653i	0.684334	−	0.729168i	$-0.260093\pi$
$211$	−46.5502	−	64.0709i	−0.220617	−	0.303653i	−0.904951	+	0.425515i	$0.860093\pi$
$212$	9.88854	+	30.4338i	0.0466441	+	0.143556i
$213$	22.5582	−	69.4271i	0.105907	−	0.325949i
$214$	211.962	+	154.000i	0.990479	+	0.719625i
$215$	−192.020	+	264.292i	−0.893115	+	1.22927i
$216$	137.190	+	44.5756i	0.635137	+	0.206369i
$217$	−329.524	+	107.069i	−1.51855	+	0.493405i
$218$	53.3951	−	38.7938i	0.244932	−	0.177953i
$219$			39.5980i			0.180813i
$220$		0			0
$221$	72.0000			0.325792
$222$	14.1313	+	19.4501i	0.0636546	+	0.0876130i
$223$	−34.3009	−	105.567i	−0.153816	−	0.473396i	0.844223	−	0.535992i	$-0.180062\pi$
$223$	−34.3009	−	105.567i	−0.153816	−	0.473396i	−0.998039	+	0.0625957i	$0.980062\pi$
$224$	−61.8034	+	190.211i	−0.275908	+	0.849158i
$225$	155.331	+	112.855i	0.690361	+	0.501577i
$226$	54.0315	−	74.3680i	0.239077	−	0.329062i
$227$	125.085	+	40.6425i	0.551034	+	0.179042i	0.571283	−	0.820753i	$-0.306446\pi$
$227$	125.085	+	40.6425i	0.551034	+	0.179042i	−0.0202490	+	0.999795i	$0.506446\pi$
$228$	−32.2799	+	10.4884i	−0.141579	+	0.0460017i
$229$	245.132	−	178.099i	1.07045	−	0.777725i	0.0944537	−	0.995529i	$-0.469890\pi$
$229$	245.132	−	178.099i	1.07045	−	0.777725i	0.975992	+	0.217805i	$0.0698896\pi$
$230$			89.0955i			0.387372i
$231$		0			0
$232$	−192.000			−0.827586
$233$	−46.5502	−	64.0709i	−0.199786	−	0.274982i	0.697355	−	0.716726i	$-0.254360\pi$
$233$	−46.5502	−	64.0709i	−0.199786	−	0.274982i	−0.897141	+	0.441744i	$0.854360\pi$
$234$	59.3313	+	182.603i	0.253552	+	0.780354i
$235$	−69.2198	+	213.037i	−0.294552	+	0.906539i
$236$	114.880	+	83.4655i	0.486781	+	0.353667i
$237$	−92.2692	+	126.998i	−0.389321	+	0.535855i
$238$	40.3499	+	13.1105i	0.169537	+	0.0550861i
$239$	267.654	−	86.9662i	1.11989	−	0.363875i	0.310166	−	0.950682i	$-0.399615\pi$
$239$	267.654	−	86.9662i	1.11989	−	0.363875i	0.809727	+	0.586807i	$0.199615\pi$
$240$	22.6525	−	16.4580i	0.0943853	−	0.0685749i
$241$		−	373.352i		−	1.54918i	−0.632464	−	0.774590i	$-0.717956\pi$
$241$		−	373.352i		−	1.54918i	0.632464	−	0.774590i	$-0.282044\pi$
$242$		0			0
$243$	−208.000			−0.855967
$244$	−13.3001	−	18.3060i	−0.0545085	−	0.0750244i
$245$	2.16312	+	6.65740i	0.00882906	+	0.0271730i
$246$	−7.41641	+	22.8254i	−0.0301480	+	0.0927860i
$247$	−232.997	−	169.282i	−0.943307	−	0.685353i
$248$	244.389	−	336.372i	0.985438	−	1.35634i
$249$	33.6249	+	10.9254i	0.135040	+	0.0438771i
$250$	−9.41498	+	3.05911i	−0.0376599	+	0.0122364i
$251$	−182.029	+	132.252i	−0.725214	+	0.526899i	−0.888046	−	0.459755i	$-0.847937\pi$
$251$	−182.029	+	132.252i	−0.725214	+	0.526899i	0.162831	+	0.986654i	$0.447937\pi$
$252$		−	113.137i		−	0.448957i
$253$		0			0
$254$	248.000			0.976378
$255$	17.4563	+	24.0266i	0.0684562	+	0.0942219i
$256$	−84.0526	−	258.687i	−0.328331	−	1.01050i
$257$	131.023	−	403.248i	0.509818	−	1.56906i	−0.282699	−	0.959209i	$-0.591230\pi$
$257$	131.023	−	403.248i	0.509818	−	1.56906i	0.792517	−	0.609850i	$-0.208770\pi$
$258$	−53.3951	−	38.7938i	−0.206958	−	0.150364i
$259$	70.6566	−	97.2504i	0.272805	−	0.375484i
$260$	−225.960	−	73.4187i	−0.869075	−	0.282380i
$261$	172.160	−	55.9381i	0.659615	−	0.214322i
$262$	160.185	−	116.381i	0.611395	−	0.444204i
$263$			140.007i			0.532347i	0.963925	+	0.266173i	$0.0857593\pi$
$263$			140.007i			0.532347i	−0.963925	+	0.266173i	$0.914241\pi$
$264$		0			0
$265$	−112.000			−0.422642
$266$	−99.7505	−	137.295i	−0.375002	−	0.516146i
$267$	2.78115	+	8.55951i	0.0104163	+	0.0320581i
$268$	−19.1591	+	58.9655i	−0.0714890	+	0.220021i
$269$	−110.026	−	79.9388i	−0.409020	−	0.297170i	0.364185	−	0.931327i	$-0.381348\pi$
$269$	−110.026	−	79.9388i	−0.409020	−	0.297170i	−0.773205	+	0.634156i	$0.781348\pi$
$270$	−98.9192	+	136.151i	−0.366367	+	0.504262i
$271$	−274.379	−	89.1513i	−1.01247	−	0.328971i	−0.244632	−	0.969616i	$-0.578667\pi$
$271$	−274.379	−	89.1513i	−1.01247	−	0.328971i	−0.767838	+	0.640644i	$0.778667\pi$
$272$	−16.1400	+	5.24419i	−0.0593381	+	0.0192801i
$273$	−97.0820	+	70.5342i	−0.355612	+	0.258367i
$274$			363.453i			1.32647i
$275$		0			0
$276$	18.0000			0.0652174
$277$	72.3191	+	99.5387i	0.261080	+	0.359345i	0.919353	−	0.393434i	$-0.128713\pi$
$277$	72.3191	+	99.5387i	0.261080	+	0.359345i	−0.658273	+	0.752779i	$0.728713\pi$
$278$	37.7001	+	116.029i	0.135612	+	0.417370i
$279$	−121.135	+	372.814i	−0.434174	+	1.33625i
$280$	−339.787	−	246.870i	−1.21353	−	0.881678i
$281$	−167.082	+	229.969i	−0.594598	+	0.818394i	−0.995200	−	0.0978581i	$-0.968801\pi$
$281$	−167.082	+	229.969i	−0.594598	+	0.818394i	0.400602	+	0.916252i	$0.368801\pi$
$282$	−43.0399	−	13.9845i	−0.152624	−	0.0495905i
$283$	75.3198	−	24.4729i	0.266148	−	0.0864767i	−0.172903	−	0.984939i	$-0.555315\pi$
$283$	75.3198	−	24.4729i	0.266148	−	0.0864767i	0.439051	+	0.898462i	$0.355315\pi$
$284$	118.116	−	85.8166i	0.415903	−	0.302171i
$285$		−	118.794i		−	0.416821i
$286$		0			0
$287$	120.000			0.418118
$288$	133.001	+	183.060i	0.461808	+	0.635624i
$289$	83.7436	+	257.736i	0.289770	+	0.891821i
$290$	69.2198	−	213.037i	0.238689	−	0.734609i
$291$	−13.7533	−	9.99235i	−0.0472622	−	0.0343380i
$292$	−46.5502	+	64.0709i	−0.159419	+	0.219421i
$293$	−156.020	−	50.6939i	−0.532490	−	0.173017i	0.0304160	−	0.999537i	$-0.490317\pi$
$293$	−156.020	−	50.6939i	−0.532490	−	0.173017i	−0.562906	+	0.826521i	$0.690317\pi$
$294$	−1.34500	+	0.437016i	−0.00457482	+	0.00148645i
$295$	−402.081	+	292.129i	−1.36299	+	0.990269i
$296$			144.250i			0.487330i
$297$		0			0
$298$	−390.000			−1.30872
$299$	89.7754	+	123.565i	0.300252	+	0.413262i
$300$	−14.8328	−	45.6507i	−0.0494427	−	0.152169i
$301$	−101.976	+	313.849i	−0.338789	+	1.04269i
$302$	−179.602	−	130.488i	−0.594708	−	0.432081i
$303$	90.6067	−	124.709i	0.299032	−	0.411582i
$304$	64.5599	+	20.9768i	0.212368	+	0.0690025i
$305$	75.3198	−	24.4729i	0.246950	−	0.0802390i
$306$	38.8328	−	28.2137i	0.126905	−	0.0922016i
$307$			186.676i			0.608066i	0.952662	+	0.304033i	$0.0983333\pi$
$307$			186.676i			0.608066i	−0.952662	+	0.304033i	$0.901667\pi$
$308$		0			0
$309$	16.0000			0.0517799
$310$	285.120	+	392.434i	0.919742	+	1.26592i
$311$	43.8804	+	135.050i	0.141095	+	0.434244i	0.996488	−	0.0837342i	$-0.0266847\pi$
$311$	43.8804	+	135.050i	0.141095	+	0.434244i	−0.855394	+	0.517979i	$0.826685\pi$
$312$	44.4984	−	136.952i	0.142623	−	0.438949i
$313$	361.631	+	262.740i	1.15537	+	0.839425i	0.989186	−	0.146670i	$-0.0468555\pi$
$313$	361.631	+	262.740i	1.15537	+	0.839425i	0.166184	+	0.986095i	$0.446855\pi$
$314$	145.469	−	200.221i	0.463278	−	0.637648i
$315$	376.599	+	122.364i	1.19555	+	0.388459i
$316$	−298.589	+	97.0176i	−0.944903	+	0.307018i
$317$	−342.214	+	248.633i	−1.07954	+	0.784332i	−0.977603	−	0.210459i	$-0.932504\pi$
$317$	−342.214	+	248.633i	−1.07954	+	0.784332i	−0.101937	+	0.994791i	$0.532504\pi$
$318$		−	22.6274i		−	0.0711554i
$319$		0			0
$320$	392.000			1.22500
$321$	108.894	+	149.880i	0.339234	+	0.466916i
$322$	27.8115	+	85.5951i	0.0863712	+	0.265823i
$323$	−22.2492	+	68.4761i	−0.0688830	+	0.212000i
$324$	−88.9919	−	64.6564i	−0.274666	−	0.199557i
$325$	239.401	−	329.507i	0.736619	−	1.01387i
$326$	−215.200	−	69.9226i	−0.660121	−	0.214486i
$327$	44.3849	−	14.4215i	0.135734	−	0.0441025i
$328$	−116.498	+	84.6411i	−0.355178	+	0.258052i
$329$			226.274i			0.687763i
$330$		0			0
$331$	145.000			0.438066			0.219033	−	0.975717i	$-0.429710\pi$
$331$	145.000			0.438066			0.219033	+	0.975717i	$0.429710\pi$
$332$	41.5627	+	57.2061i	0.125189	+	0.172308i
$333$	−42.0263	−	129.344i	−0.126205	−	0.388419i
$334$	−7.41641	+	22.8254i	−0.0222048	+	0.0683394i
$335$	−175.557	−	127.549i	−0.524050	−	0.380744i
$336$	16.6251	−	22.8825i	0.0494794	−	0.0681025i
$337$	243.444	+	79.0999i	0.722387	+	0.234718i	0.647058	−	0.762441i	$-0.275999\pi$
$337$	243.444	+	79.0999i	0.722387	+	0.234718i	0.0753293	+	0.997159i	$0.475999\pi$
$338$	160.055	−	52.0049i	0.473534	−	0.153861i
$339$	52.5861	−	38.2060i	0.155121	−	0.112702i
$340$			59.3970i			0.174697i
$341$		0			0
$342$	−192.000			−0.561404
$343$	−199.501	−	274.589i	−0.581635	−	0.800552i
$344$	−122.371	−	376.618i	−0.355729	−	1.09482i
$345$	−19.4681	+	59.9166i	−0.0564292	+	0.173671i
$346$	140.769	+	102.275i	0.406847	+	0.295591i
$347$	−322.527	+	443.920i	−0.929471	+	1.27931i	0.0305943	+	0.999532i	$0.490260\pi$
$347$	−322.527	+	443.920i	−0.929471	+	1.27931i	−0.960065	+	0.279775i	$0.909740\pi$
$348$	−43.0399	−	13.9845i	−0.123678	−	0.0401854i
$349$	415.604	−	135.038i	1.19084	−	0.386928i	0.354458	−	0.935072i	$-0.384665\pi$
$349$	415.604	−	135.038i	1.19084	−	0.386928i	0.836384	+	0.548144i	$0.184665\pi$
$350$	194.164	−	141.068i	0.554755	−	0.403053i
$351$			288.500i			0.821936i
$352$		0			0
$353$	585.000			1.65722			0.828612	−	0.559823i	$-0.189131\pi$
$353$	585.000			1.65722			0.828612	+	0.559823i	$0.189131\pi$
$354$	−59.0190	−	81.2327i	−0.166720	−	0.229471i
$355$	157.908	+	485.990i	0.444810	+	1.36899i
$356$	−5.56231	+	17.1190i	−0.0156245	+	0.0480871i
$357$	24.2705	+	17.6336i	0.0679846	+	0.0493937i
$358$	−165.420	+	227.680i	−0.462066	+	0.635979i
$359$	−392.739	−	127.609i	−1.09398	−	0.355456i	−0.294197	−	0.955745i	$-0.595052\pi$
$359$	−392.739	−	127.609i	−1.09398	−	0.355456i	−0.799783	+	0.600289i	$0.795052\pi$
$360$	−451.919	+	146.837i	−1.25533	+	0.407882i
$361$	−59.0582	+	42.9083i	−0.163596	+	0.118860i
$362$		−	103.238i		−	0.285187i
$363$		0			0
$364$	−240.000			−0.659341
$365$	−162.926	−	224.248i	−0.446372	−	0.614378i
$366$	4.94427	+	15.2169i	0.0135089	+	0.0415762i
$367$	168.414	−	518.326i	0.458894	−	1.41233i	−0.407607	−	0.913157i	$-0.633637\pi$
$367$	168.414	−	518.326i	0.458894	−	1.41233i	0.866502	−	0.499174i	$-0.166363\pi$
$368$	−29.1246	−	21.1603i	−0.0791430	−	0.0575007i
$369$	79.8004	−	109.836i	0.216261	−	0.297658i
$370$	−160.055	−	52.0049i	−0.432580	−	0.140554i
$371$	−107.600	+	34.9613i	−0.290026	+	0.0942353i
$372$	79.2837	−	57.6030i	0.213128	−	0.154847i
$373$		−	233.345i		−	0.625590i	−0.949821	−	0.312795i	$-0.898735\pi$
$373$		−	233.345i		−	0.625590i	0.949821	−	0.312795i	$-0.101265\pi$
$374$		0			0
$375$	−7.00000			−0.0186667
$376$	−159.601	−	219.672i	−0.424470	−	0.584233i
$377$	−118.663	−	365.206i	−0.314755	−	0.968715i
$378$	−52.5329	+	161.680i	−0.138976	+	0.427724i
$379$	361.631	+	262.740i	0.954170	+	0.693245i	0.951790	−	0.306752i	$-0.0992421\pi$
$379$	361.631	+	262.740i	0.954170	+	0.693245i	0.00238088	+	0.999997i	$0.499242\pi$
$380$	139.651	−	192.213i	0.367502	−	0.505823i
$381$	166.780	+	54.1900i	0.437742	+	0.142231i
$382$	−289.174	+	93.9584i	−0.757001	+	0.245965i
$383$	440.914	−	320.343i	1.15121	−	0.836405i	0.162571	−	0.986697i	$-0.448021\pi$
$383$	440.914	−	320.343i	1.15121	−	0.836405i	0.988642	+	0.150292i	$0.0480215\pi$
$384$		−	33.9411i		−	0.0883883i
$385$		0			0
$386$	−192.000			−0.497409
$387$	219.451	+	302.048i	0.567057	+	0.780487i
$388$	−10.5066	−	32.3359i	−0.0270788	−	0.0833400i
$389$	66.4387	−	204.477i	0.170793	−	0.525648i	−0.828623	−	0.559807i	$-0.810875\pi$
$389$	66.4387	−	204.477i	0.170793	−	0.525648i	0.999416	+	0.0341589i	$0.0108752\pi$
$390$	135.915	+	98.7479i	0.348500	+	0.253200i
$391$	22.4439	−	30.8913i	0.0574012	−	0.0790059i
$392$	−8.06998	−	2.62210i	−0.0205867	−	0.00668902i
$393$	133.155	−	43.2646i	0.338816	−	0.110088i
$394$	−231.379	+	168.107i	−0.587256	+	0.426666i
$395$		−	1098.84i		−	2.78188i
$396$		0			0
$397$	−592.000			−1.49118			−0.745592	−	0.666403i	$-0.767833\pi$
$397$	−592.000			−1.49118			−0.745592	+	0.666403i	$0.767833\pi$
$398$	−166.251	−	228.825i	−0.417716	−	0.574936i
$399$	−37.0820	−	114.127i	−0.0929374	−	0.286032i
$400$	−29.6656	+	91.3014i	−0.0741641	+	0.228254i
$401$	−394.800	−	286.839i	−0.984539	−	0.715310i	−0.0258209	−	0.999667i	$-0.508220\pi$
$401$	−394.800	−	286.839i	−0.984539	−	0.715310i	−0.958719	+	0.284357i	$0.908220\pi$
$402$	25.7689	−	35.4678i	0.0641017	−	0.0882284i
$403$	790.858	+	256.965i	1.96243	+	0.637631i
$404$	293.209	−	95.2695i	0.725766	−	0.235816i
$405$	311.472	−	226.297i	0.769066	−	0.558759i
$406$		−	226.274i		−	0.557326i
$407$		0			0
$408$	−36.0000			−0.0882353
$409$	−92.2692	−	126.998i	−0.225597	−	0.310508i	0.681182	−	0.732114i	$-0.261466\pi$
$409$	−92.2692	−	126.998i	−0.225597	−	0.310508i	−0.906779	+	0.421607i	$0.861466\pi$
$410$	−51.9149	−	159.777i	−0.126622	−	0.389701i
$411$	−79.4174	+	244.422i	−0.193230	+	0.594700i
$412$	25.8885	+	18.8091i	0.0628363	+	0.0456532i
$413$	−295.095	+	406.164i	−0.714516	+	0.983447i
$414$	96.8398	+	31.4652i	0.233913	+	0.0760028i
$415$	−235.374	+	76.4778i	−0.567167	+	0.184284i
$416$	388.328	−	282.137i	0.933481	−	0.678214i
$417$			86.2670i			0.206875i
$418$		0			0
$419$	−328.000			−0.782816			−0.391408	−	0.920217i	$-0.628012\pi$
$419$	−328.000			−0.782816			−0.391408	+	0.920217i	$0.628012\pi$
$420$	−58.1878	−	80.0886i	−0.138542	−	0.190687i
$421$	64.2755	+	197.820i	0.152673	+	0.469881i	0.997918	−	0.0644995i	$-0.0205451\pi$
$421$	64.2755	+	197.820i	0.152673	+	0.469881i	−0.845244	+	0.534380i	$0.820545\pi$
$422$	−34.6099	+	106.518i	−0.0820140	+	0.252413i
$423$	207.108	+	150.473i	0.489618	+	0.355728i
$424$	79.8004	−	109.836i	0.188208	−	0.259047i
$425$	−96.8398	−	31.4652i	−0.227858	−	0.0740357i
$426$	−98.1848	+	31.9022i	−0.230481	+	0.0748877i
$427$	64.7214	−	47.0228i	0.151572	−	0.110124i
$428$			370.524i			0.865710i
$429$		0			0
$430$	462.000			1.07442
$431$	−330.008	−	454.217i	−0.765679	−	1.05387i	−0.996720	−	0.0809232i	$-0.974213\pi$
$431$	−330.008	−	454.217i	−0.765679	−	1.05387i	0.231041	−	0.972944i	$-0.425787\pi$
$432$	−21.0132	−	64.6718i	−0.0486416	−	0.149703i
$433$	12.0517	−	37.0912i	0.0278329	−	0.0856610i	−0.936175	−	0.351534i	$-0.885660\pi$
$433$	12.0517	−	37.0912i	0.0278329	−	0.0856610i	0.964008	+	0.265873i	$0.0856602\pi$
$434$	396.418	+	288.015i	0.913406	+	0.663629i
$435$	93.1004	−	128.142i	0.214024	−	0.294579i
$436$	88.7698	+	28.8431i	0.203600	+	0.0661538i
$437$	−145.260	+	47.1977i	−0.332402	+	0.108004i
$438$	45.3050	−	32.9160i	0.103436	−	0.0751506i
$439$		−	248.902i		−	0.566974i	−0.958976	−	0.283487i	$-0.908509\pi$
$439$		−	248.902i		−	0.566974i	0.958976	−	0.283487i	$-0.0914913\pi$
$440$		0			0
$441$	8.00000			0.0181406
$442$	−59.8503	−	82.3768i	−0.135408	−	0.186373i
$443$	54.0780	+	166.435i	0.122072	+	0.375700i	0.993356	−	0.115079i	$-0.0367123\pi$
$443$	54.0780	+	166.435i	0.122072	+	0.375700i	−0.871284	+	0.490779i	$0.836712\pi$
$444$	−10.5066	+	32.3359i	−0.0236635	+	0.0728287i
$445$	−50.9681	−	37.0305i	−0.114535	−	0.0832145i
$446$	−92.2692	+	126.998i	−0.206882	+	0.284748i
$447$	−262.274	−	85.2181i	−0.586744	−	0.190645i
$448$	376.599	−	122.364i	0.840623	−	0.273135i
$449$	−253.222	+	183.977i	−0.563970	+	0.409748i	−0.832910	−	0.553409i	$-0.813327\pi$
$449$	−253.222	+	183.977i	−0.563970	+	0.409748i	0.268940	+	0.963157i	$0.413327\pi$
$450$		−	271.529i		−	0.603398i
$451$		0			0
$452$	130.000			0.287611
$453$	−92.2692	−	126.998i	−0.203685	−	0.280348i
$454$	−57.4772	−	176.897i	−0.126602	−	0.389640i
$455$	259.574	−	798.887i	0.570493	−	1.75580i
$456$	116.498	+	84.6411i	0.255479	+	0.185616i
$457$	6.65003	−	9.15298i	0.0145515	−	0.0200284i	−0.801679	−	0.597754i	$-0.796060\pi$
$457$	6.65003	−	9.15298i	0.0145515	−	0.0200284i	0.816231	+	0.577726i	$0.196060\pi$
$458$	−407.534	−	132.416i	−0.889812	−	0.289118i
$459$	68.5948	−	22.2878i	0.149444	−	0.0485573i
$460$	−101.936	+	74.0609i	−0.221600	+	0.161002i
$461$			871.156i			1.88971i	0.327491	+	0.944854i	$0.393797\pi$
$461$			871.156i			1.88971i	−0.327491	+	0.944854i	$0.606203\pi$
$462$		0			0
$463$	321.000			0.693305			0.346652	−	0.937994i	$-0.387318\pi$
$463$	321.000			0.693305			0.346652	+	0.937994i	$0.387318\pi$
$464$	53.2002	+	73.2239i	0.114656	+	0.157810i
$465$	105.993	+	326.212i	0.227942	+	0.701532i
$466$	−34.6099	+	106.518i	−0.0742702	+	0.228580i
$467$	130.252	+	94.6334i	0.278912	+	0.202641i	0.718443	−	0.695586i	$-0.244855\pi$
$467$	130.252	+	94.6334i	0.278912	+	0.202641i	−0.439531	+	0.898227i	$0.644855\pi$
$468$	−159.601	+	219.672i	−0.341027	+	0.469384i
$469$	−208.475	−	67.7375i	−0.444509	−	0.144430i
$470$	301.279	−	97.8916i	0.641020	−	0.208280i
$471$	141.578	−	102.862i	0.300590	−	0.218392i
$472$		−	602.455i		−	1.27639i
$473$		0			0
$474$	222.000			0.468354
$475$	239.401	+	329.507i	0.504002	+	0.693700i
$476$	18.5410	+	57.0634i	0.0389517	+	0.119881i
$477$	−39.5542	+	121.735i	−0.0829228	+	0.255210i
$478$	−321.989	−	233.939i	−0.673617	−	0.489411i
$479$	262.676	−	361.543i	0.548385	−	0.754787i	−0.441407	−	0.897307i	$-0.645521\pi$
$479$	262.676	−	361.543i	0.548385	−	0.754787i	0.989792	+	0.142520i	$0.0455206\pi$
$480$	188.300	+	61.1822i	0.392291	+	0.127463i
$481$	−274.379	+	89.1513i	−0.570435	+	0.185346i
$482$	−427.161	+	310.351i	−0.886226	+	0.643881i
$483$			63.6396i			0.131759i
$484$		0			0
$485$	119.000			0.245361
$486$	172.901	+	237.978i	0.355763	+	0.489666i
$487$	−224.655	−	691.418i	−0.461305	−	1.41975i	−0.863571	−	0.504227i	$-0.831777\pi$
$487$	−224.655	−	691.418i	−0.461305	−	1.41975i	0.402266	−	0.915523i	$-0.368223\pi$
$488$	−29.6656	+	91.3014i	−0.0607902	+	0.187093i
$489$	−129.443	−	94.0456i	−0.264709	−	0.192322i
$490$	5.81878	−	8.00886i	0.0118751	−	0.0163446i
$491$	494.959	+	160.822i	1.00806	+	0.327540i	0.766083	−	0.642742i	$-0.222203\pi$
$491$	494.959	+	160.822i	1.00806	+	0.327540i	0.241980	+	0.970281i	$0.422203\pi$
$492$	−32.2799	+	10.4884i	−0.0656096	+	0.0213179i
$493$	−77.6656	+	56.4274i	−0.157537	+	0.114457i
$494$			407.294i			0.824481i
$495$		0			0
$496$	−196.000			−0.395161
$497$	303.408	+	417.605i	0.610478	+	0.840251i
$498$	−15.4508	−	47.5528i	−0.0310258	−	0.0954876i
$499$	−113.718	+	349.989i	−0.227892	+	0.701380i	0.770093	+	0.637932i	$0.220210\pi$
$499$	−113.718	+	349.989i	−0.227892	+	0.701380i	−0.997985	+	0.0634485i	$0.979790\pi$
$500$	−11.3262	−	8.22899i	−0.0226525	−	0.0164580i
$501$	−9.97505	+	13.7295i	−0.0199103	+	0.0274041i
$502$	302.624	+	98.3286i	0.602837	+	0.195874i
$503$	−442.504	+	143.778i	−0.879730	+	0.285841i	−0.713845	−	0.700304i	$-0.753048\pi$
$503$	−442.504	+	143.778i	−0.879730	+	0.285841i	−0.165885	+	0.986145i	$0.553048\pi$
$504$	−388.328	+	282.137i	−0.770492	+	0.559795i
$505$			1079.04i			2.13672i
$506$		0			0
$507$	119.000			0.234714
$508$	206.151	+	283.742i	0.405809	+	0.558548i
$509$	−34.3009	−	105.567i	−0.0673888	−	0.207401i	0.911692	−	0.410875i	$-0.134777\pi$
$509$	−34.3009	−	105.567i	−0.0673888	−	0.207401i	−0.979080	+	0.203474i	$0.934777\pi$
$510$	12.9787	−	39.9444i	0.0254485	−	0.0783223i
$511$	−226.525	−	164.580i	−0.443297	−	0.322074i
$512$	−146.301	+	201.366i	−0.285744	+	0.393292i
$513$	−274.379	−	89.1513i	−0.534853	−	0.173784i
$514$	−570.279	+	185.295i	−1.10949	+	0.360496i
$515$	−90.6099	+	65.8319i	−0.175942	+	0.127829i
$516$		−	93.3381i		−	0.180888i
$517$		0			0
$518$	−170.000			−0.328185
$519$	72.3191	+	99.5387i	0.139343	+	0.191789i
$520$	311.489	+	958.665i	0.599018	+	1.84359i
$521$	−157.908	+	485.990i	−0.303086	+	0.932802i	0.677299	+	0.735708i	$0.263150\pi$
$521$	−157.908	+	485.990i	−0.303086	+	0.932802i	−0.980385	+	0.197094i	$0.936850\pi$
$522$	−207.108	−	150.473i	−0.396759	−	0.288262i
$523$	408.977	−	562.908i	0.781983	−	1.07631i	−0.213078	−	0.977035i	$-0.568349\pi$
$523$	408.977	−	562.908i	0.781983	−	1.07631i	0.995060	−	0.0992715i	$-0.0316512\pi$
$524$	266.309	+	86.5292i	0.508224	+	0.165132i
$525$	161.400	−	52.4419i	0.307428	−	0.0998894i
$526$	160.185	−	116.381i	0.304535	−	0.221258i
$527$		−	207.889i		−	0.394477i
$528$		0			0
$529$	−448.000			−0.846881
$530$	93.1004	+	128.142i	0.175661	+	0.241777i
$531$	175.522	+	540.200i	0.330549	+	1.01733i
$532$	74.1641	−	228.254i	0.139406	−	0.429048i
$533$	−232.997	−	169.282i	−0.437142	−	0.317603i
$534$	7.48128	−	10.2971i	0.0140099	−	0.0192830i
$535$	−1233.36	−	400.744i	−2.30535	−	0.749054i
$536$	250.169	−	81.2850i	0.466734	−	0.151651i
$537$	−160.994	+	116.969i	−0.299803	+	0.217820i
$538$			192.333i			0.357496i
$539$		0			0
$540$	−238.000			−0.440741
$541$	136.326	+	187.636i	0.251988	+	0.346832i	0.916206	−	0.400707i	$-0.131235\pi$
$541$	136.326	+	187.636i	0.251988	+	0.346832i	−0.664218	+	0.747539i	$0.731235\pi$
$542$	126.079	+	388.031i	0.232618	+	0.715924i
$543$	22.5582	−	69.4271i	0.0415437	−	0.127858i
$544$	−97.0820	−	70.5342i	−0.178460	−	0.129659i
$545$	−192.020	+	264.292i	−0.352330	+	0.484940i
$546$	161.400	+	52.4419i	0.295604	+	0.0960475i
$547$	667.119	−	216.760i	1.21960	−	0.396270i	0.372661	−	0.927968i	$-0.378446\pi$
$547$	667.119	−	216.760i	1.21960	−	0.396270i	0.846934	+	0.531697i	$0.178446\pi$
$548$	−415.835	+	302.122i	−0.758823	+	0.551317i
$549$		−	90.5097i		−	0.164863i
$550$		0			0
$551$	384.000			0.696915
$552$	−44.8877	−	61.7826i	−0.0813183	−	0.111925i
$553$	−343.009	−	1055.67i	−0.620269	−	1.90899i
$554$	53.7690	−	165.484i	0.0970559	−	0.298707i
$555$	−96.2730	−	69.9464i	−0.173465	−	0.126030i
$556$	−101.413	+	139.583i	−0.182397	+	0.251049i
$557$	−200.405	−	65.1154i	−0.359793	−	0.116904i	0.123542	−	0.992339i	$-0.460575\pi$
$557$	−200.405	−	65.1154i	−0.359793	−	0.116904i	−0.483335	+	0.875436i	$0.660575\pi$
$558$	527.239	−	171.310i	0.944872	−	0.307008i
$559$	640.741	−	465.526i	1.14623	−	0.832783i
$560$			197.990i			0.353553i
$561$		0			0
$562$	402.000			0.715302
$563$	319.201	+	439.343i	0.566965	+	0.780361i	0.992191	−	0.124726i	$-0.0398053\pi$
$563$	319.201	+	439.343i	0.566965	+	0.780361i	−0.425226	+	0.905087i	$0.639805\pi$
$564$	−19.7771	−	60.8676i	−0.0350658	−	0.107921i
$565$	−140.603	+	432.731i	−0.248854	+	0.765895i
$566$	−90.6099	−	65.8319i	−0.160088	−	0.116311i
$567$	228.595	−	314.634i	0.403165	−	0.554910i
$568$	−589.109	−	191.413i	−1.03716	−	0.336995i
$569$	75.3198	−	24.4729i	0.132372	−	0.0430104i	−0.242082	−	0.970256i	$-0.577830\pi$
$569$	75.3198	−	24.4729i	0.132372	−	0.0430104i	0.374454	+	0.927246i	$0.377830\pi$
$570$	−135.915	+	98.7479i	−0.238447	+	0.173242i
$571$			124.451i			0.217952i	0.994044	+	0.108976i	$0.0347572\pi$
$571$			124.451i			0.217952i	−0.994044	+	0.108976i	$0.965243\pi$
$572$		0			0
$573$	−215.000			−0.375218
$574$	−99.7505	−	137.295i	−0.173781	−	0.239189i
$575$	−66.7477	−	205.428i	−0.116083	−	0.357266i
$576$	138.440	−	426.073i	0.240347	−	0.739711i
$577$	−83.3288	−	60.5419i	−0.144417	−	0.104925i	0.513231	−	0.858251i	$-0.328449\pi$
$577$	−83.3288	−	60.5419i	−0.144417	−	0.104925i	−0.657648	+	0.753325i	$0.728449\pi$
$578$	225.270	−	310.057i	0.389740	−	0.536431i
$579$	−129.120	−	41.9535i	−0.223005	−	0.0724586i
$580$	301.279	−	97.8916i	0.519447	−	0.168779i
$581$	−202.254	+	146.946i	−0.348114	+	0.252920i
$582$			24.0416i			0.0413086i
$583$		0			0
$584$	336.000			0.575342
$585$	−558.603	−	768.851i	−0.954876	−	1.31427i
$586$	71.6919	+	220.645i	0.122341	+	0.376527i
$587$	−195.299	+	601.068i	−0.332707	+	1.02397i	0.635134	+	0.772402i	$0.280945\pi$
$587$	−195.299	+	601.068i	−0.332707	+	1.02397i	−0.967841	+	0.251564i	$0.919055\pi$
$588$	−1.61803	−	1.17557i	−0.00275176	−	0.00199927i
$589$	−488.777	+	672.744i	−0.829843	+	1.14218i
$590$	668.464	+	217.197i	1.13299	+	0.368130i
$591$	−192.335	+	62.4933i	−0.325439	+	0.105742i
$592$	55.0132	−	39.9694i	0.0929276	−	0.0675159i
$593$		−	497.803i		−	0.839466i	−0.907648	−	0.419733i	$-0.862124\pi$
$593$		−	497.803i		−	0.839466i	0.907648	−	0.419733i	$-0.137876\pi$
$594$		0			0
$595$	−210.000			−0.352941
$596$	−324.189	−	446.208i	−0.543941	−	0.748671i
$597$	−61.8034	−	190.211i	−0.103523	−	0.318612i
$598$	66.7477	−	205.428i	0.111618	−	0.343525i
$599$	−252.413	−	183.389i	−0.421391	−	0.306159i	0.356806	−	0.934178i	$-0.383866\pi$
$599$	−252.413	−	183.389i	−0.421391	−	0.306159i	−0.778197	+	0.628020i	$0.783866\pi$
$600$	−119.701	+	164.754i	−0.199501	+	0.274589i
$601$	391.394	+	127.172i	0.651238	+	0.211600i	0.615960	−	0.787777i	$-0.288768\pi$
$601$	391.394	+	127.172i	0.651238	+	0.211600i	0.0352782	+	0.999378i	$0.488768\pi$
$602$	443.849	−	144.215i	0.737291	−	0.239560i
$603$	−200.636	+	145.771i	−0.332730	+	0.241743i
$604$		−	313.955i		−	0.519794i
$605$		0			0
$606$	−218.000			−0.359736
$607$	72.3191	+	99.5387i	0.119142	+	0.163985i	0.864422	−	0.502766i	$-0.167684\pi$
$607$	72.3191	+	99.5387i	0.119142	+	0.163985i	−0.745280	+	0.666751i	$0.767684\pi$
$608$	148.328	+	456.507i	0.243961	+	0.750834i
$609$	49.4427	−	152.169i	0.0811867	−	0.249867i
$610$	−90.6099	−	65.8319i	−0.148541	−	0.107921i
$611$	319.201	−	439.343i	0.522425	−	0.719056i
$612$	64.5599	+	20.9768i	0.105490	+	0.0342758i
$613$	−516.479	+	167.814i	−0.842543	+	0.273759i	−0.698319	−	0.715786i	$-0.746068\pi$
$613$	−516.479	+	167.814i	−0.842543	+	0.273759i	−0.144224	+	0.989545i	$0.546068\pi$
$614$	213.580	−	155.175i	0.347851	−	0.252729i
$615$		−	118.794i		−	0.193161i
$616$		0			0
$617$	−1120.00			−1.81524			−0.907618	−	0.419798i	$-0.862101\pi$
$617$	−1120.00			−1.81524			−0.907618	+	0.419798i	$0.862101\pi$
$618$	−13.3001	−	18.3060i	−0.0215211	−	0.0296213i
$619$	217.239	+	668.593i	0.350951	+	1.08012i	0.958320	+	0.285697i	$0.0922252\pi$
$619$	217.239	+	668.593i	0.350951	+	1.08012i	−0.607368	+	0.794420i	$0.707775\pi$
$620$	−211.986	+	652.425i	−0.341912	+	1.05230i
$621$	123.780	+	89.9311i	0.199323	+	0.144817i
$622$	118.038	−	162.465i	0.189772	−	0.261198i
$623$	−60.5249	−	19.6657i	−0.0971507	−	0.0315662i
$624$	−64.5599	+	20.9768i	−0.103461	+	0.0336166i
$625$	525.052	−	381.473i	0.840083	−	0.610356i
$626$		−	632.153i		−	1.00983i
$627$		0			0
$628$	350.000			0.557325
$629$	42.3939	+	58.3503i	0.0673990	+	0.0927667i
$630$	−173.050	−	532.592i	−0.274682	−	0.845384i
$631$	120.826	−	371.863i	0.191483	−	0.589323i	−0.808517	−	0.588473i	$-0.799729\pi$
$631$	120.826	−	371.863i	0.191483	−	0.589323i	1.00000		0.000850413i	$-0.000270695\pi$
$632$	1077.61	+	782.930i	1.70508	+	1.23881i
$633$	−46.5502	+	64.0709i	−0.0735390	+	0.101218i
$634$	568.934	+	184.858i	0.897372	+	0.291574i
$635$	−1167.46	+	379.330i	−1.83852	+	0.597370i
$636$	25.8885	−	18.8091i	0.0407053	−	0.0295741i
$637$		−	16.9706i		−	0.0266414i
$638$		0			0
$639$	584.000			0.913928
$640$	139.651	+	192.213i	0.218204	+	0.300332i
$641$	−7.10739	−	21.8743i	−0.0110880	−	0.0341253i	0.945359	−	0.326030i	$-0.105711\pi$
$641$	−7.10739	−	21.8743i	−0.0110880	−	0.0341253i	−0.956447	+	0.291905i	$0.905711\pi$
$642$	80.9625	−	249.177i	0.126110	−	0.388126i
$643$	361.631	+	262.740i	0.562412	+	0.408616i	0.832341	−	0.554264i	$-0.187000\pi$
$643$	361.631	+	262.740i	0.562412	+	0.408616i	−0.269929	+	0.962880i	$0.587000\pi$
$644$	−74.8128	+	102.971i	−0.116169	+	0.159893i
$645$	310.694	+	100.951i	0.481697	+	0.156513i
$646$	96.8398	−	31.4652i	0.149907	−	0.0487077i
$647$	387.519	−	281.549i	0.598948	−	0.435161i	−0.246558	−	0.969128i	$-0.579299\pi$
$647$	387.519	−	281.549i	0.598948	−	0.435161i	0.845505	+	0.533967i	$0.179299\pi$
$648$			466.690i			0.720201i
$649$		0			0
$650$	−576.000			−0.886154
$651$	203.657	+	280.310i	0.312837	+	0.430584i
$652$	−98.8854	−	304.338i	−0.151665	−	0.466776i
$653$	222.801	−	685.712i	0.341196	−	1.05009i	−0.622392	−	0.782705i	$-0.713839\pi$
$653$	222.801	−	685.712i	0.341196	−	1.05009i	0.963589	−	0.267389i	$-0.0861609\pi$
$654$	−53.3951	−	38.7938i	−0.0816439	−	0.0593178i
$655$	−576.059	+	792.877i	−0.879479	+	1.21050i
$656$	64.5599	+	20.9768i	0.0984144	+	0.0319768i
$657$	−301.279	+	97.8916i	−0.458568	+	0.148998i
$658$	258.885	−	188.091i	0.393443	−	0.285853i
$659$		−	700.036i		−	1.06227i	−0.847287	−	0.531135i	$-0.821766\pi$
$659$		−	700.036i		−	1.06227i	0.847287	−	0.531135i	$-0.178234\pi$
$660$		0			0
$661$	607.000			0.918306			0.459153	−	0.888357i	$-0.348153\pi$
$661$	607.000			0.918306			0.459153	+	0.888357i	$0.348153\pi$
$662$	−120.532	−	165.898i	−0.182072	−	0.250601i
$663$	−22.2492	−	68.4761i	−0.0335584	−	0.103282i
$664$	92.7051	−	285.317i	0.139616	−	0.429694i
$665$	679.574	+	493.740i	1.02192	+	0.742466i
$666$	−113.051	+	155.601i	−0.169746	+	0.233635i
$667$	−193.680	−	62.9303i	−0.290374	−	0.0943483i
$668$	−32.2799	+	10.4884i	−0.0483232	+	0.0157012i
$669$	−89.8009	+	65.2442i	−0.134232	+	0.0975249i
$670$			306.884i			0.458036i
$671$		0			0
$672$	200.000			0.297619
$673$	−586.034	−	806.607i	−0.870779	−	1.19852i	−0.978891	−	0.204385i	$-0.934481\pi$
$673$	−586.034	−	806.607i	−0.870779	−	1.19852i	0.108112	−	0.994139i	$-0.465519\pi$
$674$	−111.864	−	344.282i	−0.165971	−	0.510805i
$675$	126.079	−	388.031i	0.186784	−	0.574861i
$676$	192.546	+	139.893i	0.284831	+	0.206942i
$677$	454.696	−	625.835i	0.671633	−	0.924424i	−0.328163	−	0.944621i	$-0.606429\pi$
$677$	454.696	−	625.835i	0.671633	−	0.924424i	0.999796	+	0.0201971i	$0.00642937\pi$
$678$	−87.4248	−	28.4060i	−0.128945	−	0.0418968i
$679$	114.325	−	37.1464i	0.168372	−	0.0547075i
$680$	203.872	−	148.122i	0.299812	−	0.217826i
$681$		−	131.522i		−	0.193130i
$682$		0			0
$683$	−218.000			−0.319180			−0.159590	−	0.987183i	$-0.551017\pi$
$683$	−218.000			−0.319180			−0.159590	+	0.987183i	$0.551017\pi$
$684$	−159.601	−	219.672i	−0.233334	−	0.321157i
$685$	−555.922	−	1710.95i	−0.811564	−	2.49774i
$686$	−148.328	+	456.507i	−0.216222	+	0.665462i
$687$	−245.132	−	178.099i	−0.356815	−	0.259242i
$688$	−109.726	+	151.024i	−0.159485	+	0.219512i
$689$	258.239	+	83.9071i	0.374803	+	0.121781i
$690$	84.7348	−	27.5320i	0.122804	−	0.0399015i
$691$	−698.182	+	507.259i	−1.01039	+	0.734094i	−0.964292	−	0.264843i	$-0.914680\pi$
$691$	−698.182	+	507.259i	−1.01039	+	0.734094i	−0.0461016	+	0.998937i	$0.514680\pi$
$692$			246.073i			0.355597i
$693$		0			0
$694$	776.000			1.11816
$695$	−354.945	−	488.540i	−0.510713	−	0.702936i
$696$	59.3313	+	182.603i	0.0852461	+	0.262360i
$697$	−22.2492	+	68.4761i	−0.0319214	+	0.0982440i
$698$	−499.973	−	363.251i	−0.716293	−	0.520417i
$699$	−46.5502	+	64.0709i	−0.0665954	+	0.0916608i
$700$	322.799	+	104.884i	0.461142	+	0.149834i
$701$	−383.324	+	124.550i	−0.546825	+	0.177674i	−0.569384	−	0.822071i	$-0.692818\pi$
$701$	−383.324	+	124.550i	−0.546825	+	0.177674i	0.0225597	+	0.999745i	$0.492818\pi$
$702$	330.079	−	239.816i	0.470198	−	0.341619i
$703$		−	288.500i		−	0.410383i
$704$		0			0
$705$	224.000			0.317730
$706$	−486.284	−	669.312i	−0.688787	−	0.948034i
$707$	336.829	+	1036.65i	0.476419	+	1.46627i
$708$	43.8804	−	135.050i	0.0619780	−	0.190749i
$709$	504.018	+	366.190i	0.710885	+	0.516488i	0.883459	−	0.468508i	$-0.155208\pi$
$709$	504.018	+	366.190i	0.710885	+	0.516488i	−0.172574	+	0.984997i	$0.555208\pi$
$710$	424.771	−	584.647i	0.598269	−	0.823446i
$711$	−1194.36	−	388.070i	−1.67983	−	0.545809i
$712$	72.6298	−	23.5989i	0.102008	−	0.0331445i
$713$	356.776	−	259.213i	0.500388	−	0.363553i
$714$		−	42.4264i		−	0.0594207i
$715$		0			0
$716$	−398.000			−0.555866
$717$	−165.420	−	227.680i	−0.230711	−	0.317546i
$718$	180.466	+	555.417i	0.251345	+	0.773561i
$719$	86.8338	−	267.247i	0.120770	−	0.371692i	−0.872337	−	0.488906i	$-0.837396\pi$
$719$	86.8338	−	267.247i	0.120770	−	0.371692i	0.993107	+	0.117213i	$0.0373962\pi$
$720$	181.220	+	131.664i	0.251694	+	0.182867i
$721$	−66.5003	+	91.5298i	−0.0922334	+	0.126948i
$722$	98.1848	+	31.9022i	0.135990	+	0.0441858i
$723$	−355.079	+	115.372i	−0.491119	+	0.159574i
$724$	118.116	−	85.8166i	0.163144	−	0.118531i
$725$			543.058i			0.749046i
$726$		0			0
$727$	1223.00			1.68226			0.841128	−	0.540836i	$-0.181892\pi$
$727$	1223.00			1.68226			0.841128	+	0.540836i	$0.181892\pi$
$728$	598.503	+	823.768i	0.822119	+	1.13155i
$729$	−88.6879	−	272.953i	−0.121657	−	0.374421i
$730$	−121.135	+	372.814i	−0.165938	+	0.510704i
$731$	−160.185	−	116.381i	−0.219132	−	0.159209i
$732$	−13.3001	+	18.3060i	−0.0181695	+	0.0250081i
$733$	850.038	+	276.194i	1.15967	+	0.376800i	0.824778	−	0.565457i	$-0.191300\pi$
$733$	850.038	+	276.194i	1.15967	+	0.376800i	0.334892	+	0.942256i	$0.391300\pi$
$734$	−733.023	+	238.174i	−0.998669	+	0.324487i
$735$	5.66312	−	4.11450i	0.00770492	−	0.00559795i
$736$		−	254.558i		−	0.345867i
$737$		0			0
$738$	−192.000			−0.260163
$739$	566.084	+	779.148i	0.766013	+	1.05433i	0.996690	+	0.0812965i	$0.0259061\pi$
$739$	566.084	+	779.148i	0.766013	+	1.05433i	−0.230677	+	0.973030i	$0.574094\pi$
$740$	−73.5460	−	226.351i	−0.0993865	−	0.305880i
$741$	−88.9969	+	273.904i	−0.120104	+	0.369641i
$742$	129.443	+	94.0456i	0.174451	+	0.126746i
$743$	6.65003	−	9.15298i	0.00895024	−	0.0123190i	−0.804518	−	0.593928i	$-0.797577\pi$
$743$	6.65003	−	9.15298i	0.00895024	−	0.0123190i	0.813469	+	0.581609i	$0.197577\pi$
$744$	−395.429	−	128.483i	−0.531491	−	0.172692i
$745$	1835.92	−	596.527i	2.46432	−	0.800707i
$746$	−266.976	+	193.969i	−0.357876	+	0.260012i
$747$			282.843i			0.378638i
$748$		0			0
$749$	−1310.00			−1.74900
$750$	5.81878	+	8.00886i	0.00775837	+	0.0106785i
$751$	162.852	+	501.207i	0.216847	+	0.667386i	0.999017	+	0.0443214i	$0.0141126\pi$
$751$	162.852	+	501.207i	0.216847	+	0.667386i	−0.782171	+	0.623064i	$0.785887\pi$
$752$	−39.5542	+	121.735i	−0.0525986	+	0.161882i
$753$	182.029	+	132.252i	0.241738	+	0.175633i
$754$	−319.201	+	439.343i	−0.423344	+	0.582683i
$755$	1045.06	+	339.561i	1.38419	+	0.449750i
$756$	−228.649	+	74.2927i	−0.302446	+	0.0982708i
$757$	−30.7426	+	22.3358i	−0.0406112	+	0.0295057i	−0.607906	−	0.794009i	$-0.707990\pi$
$757$	−30.7426	+	22.3358i	−0.0406112	+	0.0295057i	0.567295	+	0.823515i	$0.307990\pi$
$758$		−	632.153i		−	0.833976i
$759$		0			0
$760$	−1008.00			−1.32632
$761$	721.528	+	993.099i	0.948132	+	1.30499i	0.952352	+	0.305000i	$0.0986566\pi$
$761$	721.528	+	993.099i	0.948132	+	1.30499i	−0.00422031	+	0.999991i	$0.501343\pi$
$762$	−76.6362	−	235.862i	−0.100572	−	0.309530i
$763$	−101.976	+	313.849i	−0.133651	+	0.411335i
$764$	−347.877	−	252.748i	−0.455337	−	0.330822i
$765$	−139.651	+	192.213i	−0.182550	+	0.251258i
$766$	−733.023	−	238.174i	−0.956950	−	0.310932i
$767$	1145.94	−	372.338i	1.49405	−	0.485447i
$768$	−220.053	+	159.878i	−0.286527	+	0.208174i
$769$		−	311.127i		−	0.404586i	−0.979325	−	0.202293i	$-0.935161\pi$
$769$		−	311.127i		−	0.404586i	0.979325	−	0.202293i	$-0.0648394\pi$
$770$		0			0
$771$	−424.000			−0.549935
$772$	−159.601	−	219.672i	−0.206737	−	0.284549i
$773$	363.404	+	1118.44i	0.470122	+	1.44689i	0.852425	+	0.522849i	$0.175131\pi$
$773$	363.404	+	1118.44i	0.470122	+	1.44689i	−0.382304	+	0.924037i	$0.624869\pi$
$774$	163.161	−	502.158i	0.210802	−	0.648783i
$775$	−951.404	−	691.235i	−1.22762	−	0.891917i
$776$	−84.7879	+	116.701i	−0.109263	+	0.150387i
$777$	−114.325	−	37.1464i	−0.147136	−	0.0478074i
$778$	−289.174	+	93.9584i	−0.371689	+	0.120769i
$779$	232.997	−	169.282i	0.299097	−	0.217307i
$780$			237.588i			0.304600i
$781$		0			0
$782$	−54.0000			−0.0690537
$783$	−226.101	−	311.201i	−0.288763	−	0.397448i
$784$	1.23607	+	3.80423i	0.00157662	+	0.00485233i
$785$	−378.546	+	1165.04i	−0.482224	+	1.48413i
$786$	−160.185	−	116.381i	−0.203798	−	0.148068i
$787$	738.153	−	1015.98i	0.937933	−	1.29095i	−0.0187502	−	0.999824i	$-0.505969\pi$
$787$	738.153	−	1015.98i	0.937933	−	1.29095i	0.956683	−	0.291130i	$-0.0940313\pi$
$788$	−384.669	−	124.987i	−0.488159	−	0.158612i
$789$	133.155	−	43.2646i	0.168764	−	0.0548347i
$790$	−1257.21	+	913.418i	−1.59141	+	1.15623i
$791$			459.619i			0.581061i
$792$		0			0
$793$	−192.000			−0.242119
$794$	492.102	+	677.321i	0.619776	+	0.853049i
$795$	34.6099	+	106.518i	0.0435345	+	0.133985i
$796$	123.607	−	380.423i	0.155285	−	0.477918i
$797$	−154.522	−	112.267i	−0.193880	−	0.140862i	0.486610	−	0.873619i	$-0.338233\pi$
$797$	−154.522	−	112.267i	−0.193880	−	0.140862i	−0.680490	+	0.732757i	$0.738233\pi$
$798$	−99.7505	+	137.295i	−0.125001	+	0.172049i
$799$	−129.120	−	41.9535i	−0.161602	−	0.0525076i
$800$	−645.599	+	209.768i	−0.806998	+	0.262210i
$801$	−58.2492	+	42.3205i	−0.0727206	+	0.0528346i
$802$			690.136i			0.860519i
$803$		0			0
$804$	62.0000			0.0771144
$805$	−261.845	−	360.399i	−0.325273	−	0.447700i
$806$	−363.404	−	1118.44i	−0.450873	−	1.38765i
$807$	−42.0263	+	129.344i	−0.0520772	+	0.160277i
$808$	−1058.19	−	768.823i	−1.30965	−	0.951514i
$809$	−322.527	+	443.920i	−0.398673	+	0.548726i	−0.960410	−	0.278589i	$-0.910133\pi$
$809$	−322.527	+	443.920i	−0.398673	+	0.548726i	0.561737	+	0.827316i	$0.310133\pi$
$810$	−517.824	−	168.251i	−0.639289	−	0.207717i
$811$	386.014	−	125.424i	0.475973	−	0.154653i	−0.0611992	−	0.998126i	$-0.519492\pi$
$811$	386.014	−	125.424i	0.475973	−	0.154653i	0.537172	+	0.843473i	$0.319492\pi$
$812$	258.885	−	188.091i	0.318824	−	0.231640i
$813$			288.500i			0.354858i
$814$		0			0
$815$	1120.00			1.37423
$816$	9.97505	+	13.7295i	0.0122243	+	0.0168253i
$817$	244.741	+	753.237i	0.299561	+	0.921954i
$818$	−68.6018	+	211.135i	−0.0838652	+	0.258111i
$819$	−776.656	−	564.274i	−0.948298	−	0.688979i
$820$	139.651	−	192.213i	0.170306	−	0.234406i
$821$	−52.4549	−	17.0436i	−0.0638915	−	0.0207596i	0.276897	−	0.960900i	$-0.410694\pi$
$821$	−52.4549	−	17.0436i	−0.0638915	−	0.0207596i	−0.340788	+	0.940140i	$0.610694\pi$
$822$	345.664	−	112.313i	0.420516	−	0.136634i
$823$	−555.795	+	403.808i	−0.675328	+	0.490654i	−0.871804	−	0.489854i	$-0.837050\pi$
$823$	−555.795	+	403.808i	−0.675328	+	0.490654i	0.196477	+	0.980508i	$0.437050\pi$
$824$		−	135.765i		−	0.164763i
$825$		0			0
$826$	710.000			0.859564
$827$	−9.97505	−	13.7295i	−0.0120617	−	0.0166015i	0.802944	−	0.596055i	$-0.203266\pi$
$827$	−9.97505	−	13.7295i	−0.0120617	−	0.0166015i	−0.815005	+	0.579454i	$0.803266\pi$
$828$	44.4984	+	136.952i	0.0537421	+	0.165401i
$829$	304.382	−	936.791i	0.367167	−	1.13002i	−0.581445	−	0.813585i	$-0.697513\pi$
$829$	304.382	−	936.791i	0.367167	−	1.13002i	0.948613	−	0.316439i	$-0.102487\pi$
$830$	283.156	+	205.725i	0.341152	+	0.247861i
$831$	72.3191	−	99.5387i	0.0870266	−	0.119782i
$832$	−903.838	−	293.675i	−1.08634	−	0.352974i
$833$	−4.03499	+	1.31105i	−0.00484393	+	0.00157389i
$834$	98.7001	−	71.7098i	0.118345	−	0.0859830i
$835$		−	118.794i		−	0.142268i
$836$		0			0
$837$	833.000			0.995221
$838$	272.651	+	375.272i	0.325360	+	0.447819i
$839$	26.8845	+	82.7419i	0.0320435	+	0.0986197i	0.965799	−	0.259292i	$-0.0834890\pi$
$839$	26.8845	+	82.7419i	0.0320435	+	0.0986197i	−0.933756	+	0.357911i	$0.883489\pi$
$840$	−129.787	+	399.444i	−0.154508	+	0.475528i
$841$	−266.167	−	193.381i	−0.316488	−	0.229942i
$842$	172.901	−	237.978i	0.205345	−	0.282634i
$843$	270.344	+	87.8402i	0.320693	+	0.104200i
$844$	−150.640	+	48.9458i	−0.178483	+	0.0579926i
$845$	−673.911	+	489.625i	−0.797528	+	0.579438i
$846$		−	362.039i		−	0.427942i
$847$		0			0
$848$	−64.0000			−0.0754717
$849$	−46.5502	−	64.0709i	−0.0548295	−	0.0754663i
$850$	44.4984	+	136.952i	0.0523511	+	0.161120i
$851$	−47.2796	+	145.512i	−0.0555577	+	0.170989i
$852$	−118.116	−	85.8166i	−0.138634	−	0.100724i
$853$	−313.383	+	431.334i	−0.367389	+	0.505667i	−0.952189	−	0.305510i	$-0.901173\pi$
$853$	−313.383	+	431.334i	−0.367389	+	0.505667i	0.584800	+	0.811178i	$0.301173\pi$
$854$	−107.600	−	34.9613i	−0.125995	−	0.0409383i
$855$	903.838	−	293.675i	1.05712	−	0.343479i
$856$	1271.77	−	923.998i	1.48572	−	1.07944i
$857$			1368.96i			1.59738i	0.601740	+	0.798692i	$0.294475\pi$
$857$			1368.96i			1.59738i	−0.601740	+	0.798692i	$0.705525\pi$
$858$		0			0
$859$	−977.000			−1.13737			−0.568685	−	0.822556i	$-0.692547\pi$
$859$	−977.000			−1.13737			−0.568685	+	0.822556i	$0.692547\pi$
$860$	384.039	+	528.585i	0.446557	+	0.614633i
$861$	−37.0820	−	114.127i	−0.0430686	−	0.132551i
$862$	−245.359	+	755.139i	−0.284640	+	0.876031i
$863$	1029.07	+	747.663i	1.19243	+	0.866353i	0.993519	−	0.113664i	$-0.0362587\pi$
$863$	1029.07	+	747.663i	1.19243	+	0.866353i	0.198914	+	0.980017i	$0.436259\pi$
$864$	282.626	−	389.002i	0.327114	−	0.450234i
$865$	−819.103	−	266.143i	−0.946940	−	0.307679i
$866$	−52.4549	+	17.0436i	−0.0605715	+	0.0196809i
$867$	219.244	−	159.290i	0.252876	−	0.183725i
$868$			692.965i			0.798346i
$869$		0			0
$870$	−224.000			−0.257471
$871$	309.226	+	425.614i	0.355025	+	0.488649i
$872$	−122.371	−	376.618i	−0.140333	−	0.431902i
$873$	42.0263	−	129.344i	0.0481401	−	0.148160i
$874$	174.748	+	126.962i	0.199940	+	0.145265i
$875$	29.0939	−	40.0443i	0.0332502	−	0.0457649i
$876$	75.3198	+	24.4729i	0.0859815	+	0.0279371i
$877$	−575.659	+	187.043i	−0.656395	+	0.213276i	−0.618232	−	0.785996i	$-0.712151\pi$
$877$	−575.659	+	187.043i	−0.656395	+	0.213276i	−0.0381634	+	0.999272i	$0.512151\pi$
$878$	−284.774	+	206.900i	−0.324344	+	0.235650i
$879$			164.049i			0.186631i
$880$		0			0
$881$	−295.000			−0.334847			−0.167423	−	0.985885i	$-0.553545\pi$
$881$	−295.000			−0.334847			−0.167423	+	0.985885i	$0.553545\pi$
$882$	−6.65003	−	9.15298i	−0.00753972	−	0.0103775i
$883$	−180.466	−	555.417i	−0.204378	−	0.629011i	−0.999738	−	0.0228742i	$-0.992718\pi$
$883$	−180.466	−	555.417i	−0.204378	−	0.629011i	0.795360	−	0.606137i	$-0.207282\pi$
$884$	44.4984	−	136.952i	0.0503376	−	0.154923i
$885$	402.081	+	292.129i	0.454329	+	0.330090i
$886$	145.469	−	200.221i	0.164187	−	0.225984i
$887$	924.013	+	300.230i	1.04173	+	0.338478i	0.779417	−	0.626505i	$-0.215515\pi$
$887$	924.013	+	300.230i	1.04173	+	0.338478i	0.262311	+	0.964983i	$0.415515\pi$
$888$	137.190	−	44.5756i	0.154493	−	0.0501978i
$889$	−1003.18	+	728.854i	−1.12844	+	0.819858i
$890$			89.0955i			0.100107i
$891$		0			0
$892$	−222.000			−0.248879
$893$	319.201	+	439.343i	0.357448	+	0.491986i
$894$	120.517	+	370.912i	0.134806	+	0.414890i
$895$	430.461	−	1324.82i	0.480962	−	1.48025i
$896$	194.164	+	141.068i	0.216701	+	0.157442i
$897$	89.7754	−	123.565i	0.100084	−	0.137754i
$898$	420.984	+	136.786i	0.468802	+	0.152323i
$899$	−1054.48	+	342.621i	−1.17295	+	0.381113i
$900$	310.663	−	225.710i	0.345181	−	0.250788i
$901$		−	67.8823i		−	0.0753410i
$902$		0			0
$903$	330.000			0.365449
$904$	−324.189	−	446.208i	−0.358616	−	0.493593i
$905$	157.908	+	485.990i	0.174484	+	0.537005i
$906$	−68.6018	+	211.135i	−0.0757194	+	0.233040i
$907$	1242.65	+	902.838i	1.37007	+	0.995411i	0.997732	+	0.0673127i	$0.0214425\pi$
$907$	1242.65	+	902.838i	1.37007	+	0.995411i	0.372334	+	0.928099i	$0.378557\pi$
$908$	154.613	−	212.807i	0.170279	−	0.234369i
$909$	1172.84	+	381.078i	1.29025	+	0.419228i
$910$	−1129.80	+	367.093i	−1.24154	+	0.403399i
$911$	−671.484	+	487.862i	−0.737085	+	0.535523i	−0.891797	−	0.452436i	$-0.850555\pi$
$911$	−671.484	+	487.862i	−0.737085	+	0.535523i	0.154712	+	0.987960i	$0.450555\pi$
$912$		−	67.8823i		−	0.0744323i
$913$		0			0
$914$	−16.0000			−0.0175055
$915$	−46.5502	−	64.0709i	−0.0508746	−	0.0700228i
$916$	−187.264	−	576.340i	−0.204437	−	0.629192i
$917$	−305.927	+	941.546i	−0.333617	+	1.02677i
$918$	−82.5197	−	59.9541i	−0.0898908	−	0.0653095i
$919$	−331.670	+	456.505i	−0.360903	+	0.496741i	−0.950400	−	0.311030i	$-0.899326\pi$
$919$	−331.670	+	456.505i	−0.360903	+	0.496741i	0.589497	+	0.807771i	$0.299326\pi$
$920$	508.409	+	165.192i	0.552618	+	0.179557i
$921$	177.540	−	57.6861i	0.192768	−	0.0626342i
$922$	996.709	−	724.151i	1.08103	−	0.785414i
$923$		−	1238.85i		−	1.34220i
$924$		0			0
$925$	408.000			0.441081
$926$	−266.832	−	367.263i	−0.288156	−	0.396613i
$927$	39.5542	+	121.735i	0.0426690	+	0.131322i
$928$	−197.771	+	608.676i	−0.213115	+	0.655901i
$929$	−1249.12	−	907.540i	−1.34459	−	0.976900i	−0.999262	−	0.0384176i	$-0.987768\pi$
$929$	−1249.12	−	907.540i	−1.34459	−	0.976900i	−0.345326	−	0.938483i	$-0.612232\pi$
$930$	285.120	−	392.434i	0.306581	−	0.421972i
$931$	16.1400	+	5.24419i	0.0173362	+	0.00563286i
$932$	−150.640	+	48.9458i	−0.161631	+	0.0525169i
$933$	114.880	−	83.4655i	0.123130	−	0.0894593i
$934$		−	227.688i		−	0.243778i
$935$		0			0
$936$	1152.00			1.23077
$937$	−522.027	−	718.509i	−0.557126	−	0.766819i	0.433831	−	0.900994i	$-0.357161\pi$
$937$	−522.027	−	718.509i	−0.557126	−	0.766819i	−0.990958	+	0.134175i	$0.957161\pi$
$938$	95.7953	+	294.828i	0.102127	+	0.314315i
$939$	138.131	−	425.122i	0.147104	−	0.452739i
$940$	362.440	+	263.328i	0.385574	+	0.280136i
$941$	−477.971	+	657.871i	−0.507939	+	0.699119i	−0.983570	−	0.180526i	$-0.942220\pi$
$941$	−477.971	+	657.871i	−0.507939	+	0.699119i	0.475631	+	0.879645i	$0.342220\pi$
$942$	−235.374	−	76.4778i	−0.249867	−	0.0811866i
$943$	−145.260	+	47.1977i	−0.154040	+	0.0500506i
$944$	−229.761	+	166.931i	−0.243391	+	0.176834i
$945$		−	841.457i		−	0.890431i
$946$		0			0
$947$	145.000			0.153115			0.0765576	−	0.997065i	$-0.475607\pi$
$947$	145.000			0.153115			0.0765576	+	0.997065i	$0.475607\pi$
$948$	184.538	+	253.995i	0.194661	+	0.267927i
$949$	207.659	+	639.110i	0.218819	+	0.673456i
$950$	177.994	−	547.809i	0.187362	−	0.576641i
$951$	342.214	+	248.633i	0.359847	+	0.261444i
$952$	149.626	−	205.942i	0.157170	−	0.216326i
$953$	598.524	+	194.472i	0.628042	+	0.204063i	0.605707	−	0.795687i	$-0.292890\pi$
$953$	598.524	+	194.472i	0.628042	+	0.204063i	0.0223342	+	0.999751i	$0.492890\pi$
$954$	172.160	−	55.9381i	0.180461	−	0.0586353i
$955$	1217.57	−	884.617i	1.27494	−	0.926300i
$956$		−	562.857i		−	0.588763i
$957$		0			0
$958$	−632.000			−0.659708
$959$	−1068.16	−	1470.20i	−1.11383	−	1.53305i
$960$	−121.135	−	372.814i	−0.126182	−	0.388348i
$961$	444.984	−	1369.52i	0.463043	−	1.42510i
$962$	330.079	+	239.816i	0.343117	+	0.249289i
$963$	−871.154	+	1199.04i	−0.904625	+	1.24511i
$964$	−710.158	−	230.744i	−0.736679	−	0.239361i
$965$	903.838	−	293.675i	0.936620	−	0.304326i
$966$	72.8115	−	52.9007i	0.0753743	−	0.0547626i
$967$		−	373.352i		−	0.386093i	−0.981190	−	0.193047i	$-0.938163\pi$
$967$		−	373.352i		−	0.386093i	0.981190	−	0.193047i	$-0.0618369\pi$
$968$		0			0
$969$	72.0000			0.0743034
$970$	−98.9192	−	136.151i	−0.101979	−	0.140361i
$971$	−523.784	−	1612.04i	−0.539427	−	1.66019i	−0.733884	−	0.679275i	$-0.762294\pi$
$971$	−523.784	−	1612.04i	−0.539427	−	1.66019i	0.194457	−	0.980911i	$-0.437706\pi$
$972$	−128.551	+	395.640i	−0.132254	+	0.407037i
$973$	−493.500	−	358.549i	−0.507195	−	0.368498i
$974$	−604.322	+	831.777i	−0.620453	+	0.853981i
$975$	−387.359	−	125.861i	−0.397291	−	0.129088i
$976$	43.0399	−	13.9845i	0.0440983	−	0.0143284i
$977$	298.527	−	216.893i	0.305555	−	0.221999i	−0.424432	−	0.905460i	$-0.639526\pi$
$977$	298.527	−	216.893i	0.305555	−	0.221999i	0.729987	+	0.683461i	$0.239526\pi$
$978$			226.274i			0.231364i
$979$		0			0
$980$	14.0000			0.0142857
$981$	219.451	+	302.048i	0.223701	+	0.307898i
$982$	−227.437	−	699.978i	−0.231605	−	0.712808i
$983$	141.221	−	434.633i	0.143663	−	0.442149i	−0.853174	−	0.521627i	$-0.825325\pi$
$983$	141.221	−	434.633i	0.143663	−	0.442149i	0.996837	+	0.0794777i	$0.0253252\pi$
$984$	116.498	+	84.6411i	0.118393	+	0.0860174i
$985$	832.085	−	1145.27i	0.844756	−	1.16271i
$986$	129.120	+	41.9535i	0.130953	+	0.0425492i
$987$	215.200	−	69.9226i	0.218034	−	0.0708435i
$988$	−465.994	+	338.564i	−0.471654	+	0.342676i
$989$		−	420.021i		−	0.424693i
$990$		0			0
$991$	−1032.00			−1.04137			−0.520686	−	0.853748i	$-0.674324\pi$
$991$	−1032.00			−1.04137			−0.520686	+	0.853748i	$0.674324\pi$
$992$	−814.629	−	1121.24i	−0.821198	−	1.13028i
$993$	−44.8075	−	137.903i	−0.0451233	−	0.138875i
$994$	225.582	−	694.271i	0.226944	−	0.698462i
$995$	1132.62	+	822.899i	1.13832	+	0.827035i
$996$	41.5627	−	57.2061i	0.0417296	−	0.0574359i
$997$	−673.844	−	218.945i	−0.675871	−	0.219604i	−0.0490843	−	0.998795i	$-0.515630\pi$
$997$	−673.844	−	218.945i	−0.675871	−	0.219604i	−0.626787	+	0.779191i	$0.715630\pi$
$998$	494.959	−	160.822i	0.495951	−	0.161144i
$999$	−233.806	+	169.870i	−0.234040	+	0.170040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.3.d.e.118.1		8
11.2	odd	10		121.3.b.a.120.1	✓	2
11.3	even	5	inner	121.3.d.e.94.1		8
11.4	even	5	inner	121.3.d.e.40.2		8
11.5	even	5	inner	121.3.d.e.112.2		8
11.6	odd	10	inner	121.3.d.e.112.1		8
11.7	odd	10	inner	121.3.d.e.40.1		8
11.8	odd	10	inner	121.3.d.e.94.2		8
11.9	even	5		121.3.b.a.120.2	yes	2
11.10	odd	2	inner	121.3.d.e.118.2		8
33.2	even	10		1089.3.c.a.604.2		2
33.20	odd	10		1089.3.c.a.604.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.3.b.a.120.1	✓	2	11.2	odd	10
121.3.b.a.120.2	yes	2	11.9	even	5
121.3.d.e.40.1		8	11.7	odd	10	inner
121.3.d.e.40.2		8	11.4	even	5	inner
121.3.d.e.94.1		8	11.3	even	5	inner
121.3.d.e.94.2		8	11.8	odd	10	inner
121.3.d.e.112.1		8	11.6	odd	10	inner
121.3.d.e.112.2		8	11.5	even	5	inner
121.3.d.e.118.1		8	1.1	even	1	trivial
121.3.d.e.118.2		8	11.10	odd	2	inner
1089.3.c.a.604.1		2	33.20	odd	10
1089.3.c.a.604.2		2	33.2	even	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	121.d (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.831254 - 1.14412i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.618034 - 1.90211i) q^{4} +(5.66312 + 4.11450i) q^{5} +(-0.831254 + 1.14412i) q^{6} +(6.72499 + 2.18508i) q^{7} +(-8.06998 + 2.62210i) q^{8} +(6.47214 - 4.70228i) q^{9} +O(q^{10})\)	\(q+(-0.831254 - 1.14412i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.618034 - 1.90211i) q^{4} +(5.66312 + 4.11450i) q^{5} +(-0.831254 + 1.14412i) q^{6} +(6.72499 + 2.18508i) q^{7} +(-8.06998 + 2.62210i) q^{8} +(6.47214 - 4.70228i) q^{9} -9.89949i q^{10} -2.00000 q^{12} +(-9.97505 - 13.7295i) q^{13} +(-3.09017 - 9.51057i) q^{14} +(2.16312 - 6.65740i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-2.49376 + 3.43237i) q^{17} +(-10.7600 - 3.49613i) q^{18} +(16.1400 - 5.24419i) q^{19} +(11.3262 - 8.22899i) q^{20} -7.07107i q^{21} -9.00000 q^{23} +(4.98752 + 6.86474i) q^{24} +(7.41641 + 22.8254i) q^{25} +(-7.41641 + 22.8254i) q^{26} +(-13.7533 - 9.99235i) q^{27} +(8.31254 - 11.4412i) q^{28} +(21.5200 + 6.99226i) q^{29} +(-9.41498 + 3.05911i) q^{30} +(-39.6418 + 28.8015i) q^{31} +28.2843i q^{32} +6.00000 q^{34} +(29.0939 + 40.0443i) q^{35} +(-4.94427 - 15.2169i) q^{36} +(5.25329 - 16.1680i) q^{37} +(-19.4164 - 14.1068i) q^{38} +(-9.97505 + 13.7295i) q^{39} +(-56.4899 - 18.3547i) q^{40} +(16.1400 - 5.24419i) q^{41} +(-8.09017 + 5.87785i) q^{42} +46.6690i q^{43} +56.0000 q^{45} +(7.48128 + 10.2971i) q^{46} +(9.88854 + 30.4338i) q^{47} +(1.23607 - 3.80423i) q^{48} +(0.809017 + 0.587785i) q^{49} +(19.9501 - 27.4589i) q^{50} +(4.03499 + 1.31105i) q^{51} +(-32.2799 + 10.4884i) q^{52} +(-12.9443 + 9.40456i) q^{53} +24.0416i q^{54} -60.0000 q^{56} +(-9.97505 - 13.7295i) q^{57} +(-9.88854 - 30.4338i) q^{58} +(-21.9402 + 67.5250i) q^{59} +(-11.3262 - 8.22899i) q^{60} +(6.65003 - 9.15298i) q^{61} +(65.9049 + 21.4138i) q^{62} +(53.7999 - 17.4806i) q^{63} +(45.3050 - 32.9160i) q^{64} -118.794i q^{65} -31.0000 q^{67} +(4.98752 + 6.86474i) q^{68} +(2.78115 + 8.55951i) q^{69} +(21.6312 - 66.5740i) q^{70} +(59.0582 + 42.9083i) q^{71} +(-39.9002 + 54.9179i) q^{72} +(-37.6599 - 12.2364i) q^{73} +(-22.8649 + 7.42927i) q^{74} +(19.4164 - 14.1068i) q^{75} -33.9411i q^{76} +24.0000 q^{78} +(-92.2692 - 126.998i) q^{79} +(8.65248 + 26.6296i) q^{80} +(16.9959 - 52.3081i) q^{81} +(-19.4164 - 14.1068i) q^{82} +(-20.7813 + 28.6031i) q^{83} +(-13.4500 - 4.37016i) q^{84} +(-28.2449 + 9.17734i) q^{85} +(53.3951 - 38.7938i) q^{86} -22.6274i q^{87} -9.00000 q^{89} +(-46.5502 - 64.0709i) q^{90} +(-37.0820 - 114.127i) q^{91} +(-5.56231 + 17.1190i) q^{92} +(39.6418 + 28.8015i) q^{93} +(26.6001 - 36.6119i) q^{94} +(112.980 + 36.7093i) q^{95} +(26.8999 - 8.74032i) q^{96} +(13.7533 - 9.99235i) q^{97} -1.41421i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9	\( 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9} - 16 q^{12} + 20 q^{14} - 14 q^{15} + 8 q^{16} + 28 q^{20} - 72 q^{23} - 48 q^{25} + 48 q^{26} - 34 q^{27} - 98 q^{31} + 48 q^{34} + 32 q^{36} - 34 q^{37} - 48 q^{38} - 20 q^{42} + 448 q^{45} - 64 q^{47} - 8 q^{48} + 2 q^{49} - 32 q^{53} - 480 q^{56} + 64 q^{58} + 142 q^{59} - 28 q^{60} + 112 q^{64} - 248 q^{67} - 18 q^{69} - 140 q^{70} + 146 q^{71} + 48 q^{75} + 192 q^{78} - 56 q^{80} - 110 q^{81} - 48 q^{82} + 132 q^{86} - 72 q^{89} + 240 q^{91} + 36 q^{92} + 98 q^{93} + 34 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9 - 16 * q^12 + 20 * q^14 - 14 * q^15 + 8 * q^16 + 28 * q^20 - 72 * q^23 - 48 * q^25 + 48 * q^26 - 34 * q^27 - 98 * q^31 + 48 * q^34 + 32 * q^36 - 34 * q^37 - 48 * q^38 - 20 * q^42 + 448 * q^45 - 64 * q^47 - 8 * q^48 + 2 * q^49 - 32 * q^53 - 480 * q^56 + 64 * q^58 + 142 * q^59 - 28 * q^60 + 112 * q^64 - 248 * q^67 - 18 * q^69 - 140 * q^70 + 146 * q^71 + 48 * q^75 + 192 * q^78 - 56 * q^80 - 110 * q^81 - 48 * q^82 + 132 * q^86 - 72 * q^89 + 240 * q^91 + 36 * q^92 + 98 * q^93 + 34 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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