LMFDB - Embedded newform 121.3.d.e.40.1

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			40.1
Root			$-0.831254 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	121.40
Dual form			121.3.d.e.118.1

$q$-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 $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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	−0.964580	−	0.263792i	$-0.915027\pi$
$2$	−0.831254	+	1.14412i	−0.415627	+	0.572061i	0.548953	+	0.835853i	$0.315027\pi$
$3$	−0.309017	+	0.951057i	−0.103006	+	0.317019i	−0.989257	−	0.146185i	$-0.953300\pi$
$3$	−0.309017	+	0.951057i	−0.103006	+	0.317019i	0.886252	+	0.463204i	$0.153300\pi$
$4$	0.618034	+	1.90211i	0.154508	+	0.475528i
$5$	5.66312	−	4.11450i	1.13262	−	0.822899i	0.146549	−	0.989203i	$-0.453183\pi$
$5$	5.66312	−	4.11450i	1.13262	−	0.822899i	0.986075	+	0.166304i	$0.0531833\pi$
$6$	−0.831254	−	1.14412i	−0.138542	−	0.190687i
$7$	6.72499	−	2.18508i	0.960712	−	0.312154i	0.213651	−	0.976910i	$-0.431464\pi$
$7$	6.72499	−	2.18508i	0.960712	−	0.312154i	0.747061	+	0.664756i	$0.231464\pi$
$8$	−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	0.229259	+	0.973365i	$0.426370\pi$
$13$	−9.97505	+	13.7295i	−0.767311	+	1.05611i	−0.996571	+	0.0827480i	$0.973630\pi$
$14$	−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	0.729348	−	0.684143i	$-0.239824\pi$
$17$	−2.49376	−	3.43237i	−0.146692	−	0.201904i	−0.876040	+	0.482239i	$0.839824\pi$
$18$	−10.7600	+	3.49613i	−0.597776	+	0.194229i
$19$	16.1400	+	5.24419i	0.849472	+	0.276010i	0.701225	−	0.712940i	$-0.252637\pi$
$19$	16.1400	+	5.24419i	0.849472	+	0.276010i	0.148247	+	0.988950i	$0.452637\pi$
$20$	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	0.0865030	−	0.996252i	$-0.472431\pi$
$29$	21.5200	−	6.99226i	0.742067	−	0.241112i	0.655564	+	0.755139i	$0.272431\pi$
$30$	−9.41498	−	3.05911i	−0.313833	−	0.101970i
$31$	−39.6418	−	28.8015i	−1.27877	−	0.929080i	−0.279254	−	0.960217i	$-0.590087\pi$
$31$	−39.6418	−	28.8015i	−1.27877	−	0.929080i	−0.999515	+	0.0311374i	$0.990087\pi$
$32$		−	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	0.996610	−	0.0822662i	$-0.0262158\pi$
$37$	5.25329	+	16.1680i	0.141981	+	0.436972i	−0.854630	+	0.519238i	$0.826216\pi$
$38$	−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	0.499156	−	0.866512i	$-0.333644\pi$
$41$	16.1400	+	5.24419i	0.393658	+	0.127907i	−0.105498	+	0.994420i	$0.533644\pi$
$42$	−8.09017	−	5.87785i	−0.192623	−	0.139949i
$43$		−	46.6690i		−	1.08533i	−0.839950	−	0.542663i	$-0.817416\pi$
$43$		−	46.6690i		−	1.08533i	0.839950	−	0.542663i	$-0.182584\pi$
$44$		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	−0.789054	−	0.614324i	$-0.789429\pi$
$47$	9.88854	−	30.4338i	0.210395	−	0.647528i	0.999449	−	0.0332041i	$-0.0105711\pi$
$48$	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	0.458935	−	0.888470i	$-0.348231\pi$
$53$	−12.9443	−	9.40456i	−0.244232	−	0.177445i	−0.703166	+	0.711025i	$0.748231\pi$
$54$		−	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	−0.945568	−	0.325426i	$-0.894492\pi$
$59$	−21.9402	−	67.5250i	−0.371868	−	1.14449i	0.573700	−	0.819066i	$-0.305508\pi$
$60$	−11.3262	+	8.22899i	−0.188771	+	0.137150i
$61$	6.65003	+	9.15298i	0.109017	+	0.150049i	0.860039	−	0.510228i	$-0.170439\pi$
$61$	6.65003	+	9.15298i	0.109017	+	0.150049i	−0.751022	+	0.660277i	$0.770439\pi$
$62$	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	−0.0882635	−	0.996097i	$-0.528132\pi$
$71$	59.0582	−	42.9083i	0.831806	−	0.604343i	0.920070	+	0.391755i	$0.128132\pi$
$72$	−39.9002	−	54.9179i	−0.554169	−	0.762749i
$73$	−37.6599	+	12.2364i	−0.515889	+	0.167623i	−0.555379	−	0.831597i	$-0.687427\pi$
$73$	−37.6599	+	12.2364i	−0.515889	+	0.167623i	0.0394897	+	0.999220i	$0.487427\pi$
$74$	−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	−0.492101	+	0.870538i	$0.663771\pi$
$79$	−92.2692	+	126.998i	−1.16796	+	1.60756i	−0.675864	+	0.737027i	$0.736229\pi$
$80$	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	0.665266	−	0.746607i	$-0.268318\pi$
$83$	−20.7813	−	28.6031i	−0.250378	−	0.344615i	−0.915643	+	0.401991i	$0.868318\pi$
$84$	−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	0.656417	−	0.754398i	$-0.272071\pi$
$97$	13.7533	+	9.99235i	0.141786	+	0.103014i	−0.514631	+	0.857412i	$0.672071\pi$
$98$			1.41421i			0.0144308i
$99$		0			0
$100$	48.0000			0.480000
$101$	90.6067	−	124.709i	0.897096	−	1.23475i	−0.0742894	−	0.997237i	$-0.523669\pi$
$101$	90.6067	−	124.709i	0.897096	−	1.23475i	0.971385	−	0.237510i	$-0.0763311\pi$
$102$	−1.85410	+	5.70634i	−0.0181775	+	0.0559445i
$103$	−4.94427	−	15.2169i	−0.0480026	−	0.147737i	0.924182	−	0.381952i	$-0.124748\pi$
$103$	−4.94427	−	15.2169i	−0.0480026	−	0.147737i	−0.972185	+	0.234215i	$0.924748\pi$
$104$	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	−0.668662	−	0.743566i	$-0.733133\pi$
$107$	−176.195	−	57.2491i	−1.64668	−	0.535038i	−0.978016	+	0.208528i	$0.933133\pi$
$108$	−27.5066	−	19.9847i	−0.254691	−	0.185044i
$109$		−	46.6690i		−	0.428156i	−0.976817	−	0.214078i	$-0.931325\pi$
$109$		−	46.6690i		−	0.428156i	0.976817	−	0.214078i	$-0.0686747\pi$
$110$		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	−0.821995	−	0.569494i	$-0.807139\pi$
$113$	20.0861	−	61.8187i	0.177753	−	0.547068i	0.999748	+	0.0224263i	$0.00713910\pi$
$114$	−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	−0.991072	−	0.133330i	$-0.957433\pi$
$127$	−103.075	−	141.871i	−0.811618	−	1.11710i	0.179454	−	0.983766i	$-0.442567\pi$
$128$	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	$-0.820546\pi$
$131$		−	140.007i		−	1.06876i	0.845245	−	0.534378i	$-0.179454\pi$
$132$		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	−0.555006	+	0.831846i	$0.687284\pi$
$137$	−207.917	+	151.061i	−1.51765	+	1.10263i	−0.962639	+	0.270787i	$0.912716\pi$
$138$	7.48128	+	10.2971i	0.0542122	+	0.0746167i
$139$	−82.0448	+	26.6580i	−0.590250	+	0.191784i	−0.588887	−	0.808215i	$-0.700434\pi$
$139$	−82.0448	+	26.6580i	−0.590250	+	0.191784i	−0.00136305	+	0.999999i	$0.500434\pi$
$140$	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	0.850536	+	0.525917i	$0.176278\pi$
$149$	162.095	+	223.104i	1.08788	+	1.49734i	0.237347	+	0.971425i	$0.423722\pi$
$150$	−32.2799	+	10.4884i	−0.215200	+	0.0699226i
$151$	149.295	+	48.5088i	0.988706	+	0.321250i	0.758344	−	0.651855i	$-0.226009\pi$
$151$	149.295	+	48.5088i	0.988706	+	0.321250i	0.230363	+	0.973105i	$0.426009\pi$
$152$	−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	−0.617434	−	0.786623i	$-0.711828\pi$
$157$	54.0780	−	166.435i	0.344446	−	1.06009i	0.961880	−	0.273472i	$-0.0881722\pi$
$158$	−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	0.909185	−	0.416392i	$-0.136705\pi$
$163$	129.443	+	94.0456i	0.794127	+	0.576967i	−0.115058	+	0.993359i	$0.536705\pi$
$164$			33.9411i			0.206958i
$165$		0			0
$166$	50.0000			0.301205
$167$	−9.97505	+	13.7295i	−0.0597308	+	0.0822124i	−0.837837	−	0.545920i	$-0.816180\pi$
$167$	−9.97505	+	13.7295i	−0.0597308	+	0.0822124i	0.778107	+	0.628132i	$0.216180\pi$
$168$	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	−0.0493734	−	0.998780i	$-0.515722\pi$
$173$	−117.015	−	38.0204i	−0.676386	−	0.219771i	−0.627012	+	0.779009i	$0.715722\pi$
$174$	−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	0.618815	+	0.785537i	$0.287613\pi$
$179$	−61.4944	+	189.260i	−0.343544	+	1.05732i	−0.962359	+	0.271783i	$0.912387\pi$
$180$	34.6099	+	106.518i	0.192277	+	0.591768i
$181$	59.0582	−	42.9083i	0.326289	−	0.237063i	−0.412566	−	0.910928i	$-0.635367\pi$
$181$	59.0582	−	42.9083i	0.326289	−	0.237063i	0.738854	+	0.673865i	$0.235367\pi$
$182$	−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	0.960042	+	0.279855i	$0.0902864\pi$
$191$	66.4387	+	204.477i	0.347846	+	1.07056i	−0.612196	+	0.790706i	$0.709714\pi$
$192$	−45.3050	+	32.9160i	−0.235963	+	0.171437i
$193$	79.8004	+	109.836i	0.413473	+	0.569097i	0.964061	−	0.265680i	$-0.0855964\pi$
$193$	79.8004	+	109.836i	0.413473	+	0.569097i	−0.550588	+	0.834777i	$0.685596\pi$
$194$	−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	$0.171570\pi$
$197$			202.233i			1.02656i	−0.858221	+	0.513281i	$0.828430\pi$
$198$		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	−0.904951	−	0.425515i	$-0.860093\pi$
$211$	−46.5502	+	64.0709i	−0.220617	+	0.303653i	0.684334	+	0.729168i	$0.260093\pi$
$212$	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	−0.998039	−	0.0625957i	$-0.980062\pi$
$223$	−34.3009	+	105.567i	−0.153816	+	0.473396i	0.844223	+	0.535992i	$0.180062\pi$
$224$	−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	−0.0202490	−	0.999795i	$-0.506446\pi$
$227$	125.085	−	40.6425i	0.551034	−	0.179042i	0.571283	+	0.820753i	$0.306446\pi$
$228$	−32.2799	−	10.4884i	−0.141579	−	0.0460017i
$229$	245.132	+	178.099i	1.07045	+	0.777725i	0.975992	−	0.217805i	$-0.0698896\pi$
$229$	245.132	+	178.099i	1.07045	+	0.777725i	0.0944537	+	0.995529i	$0.469890\pi$
$230$		−	89.0955i		−	0.387372i
$231$		0			0
$232$	−192.000			−0.827586
$233$	−46.5502	+	64.0709i	−0.199786	+	0.274982i	−0.897141	−	0.441744i	$-0.854360\pi$
$233$	−46.5502	+	64.0709i	−0.199786	+	0.274982i	0.697355	+	0.716726i	$0.254360\pi$
$234$	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	0.809727	−	0.586807i	$-0.199615\pi$
$239$	267.654	+	86.9662i	1.11989	+	0.363875i	0.310166	+	0.950682i	$0.399615\pi$
$240$	22.6525	+	16.4580i	0.0943853	+	0.0685749i
$241$			373.352i			1.54918i	0.632464	+	0.774590i	$0.282044\pi$
$241$			373.352i			1.54918i	−0.632464	+	0.774590i	$0.717956\pi$
$242$		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	0.162831	−	0.986654i	$-0.447937\pi$
$251$	−182.029	−	132.252i	−0.725214	−	0.526899i	−0.888046	+	0.459755i	$0.847937\pi$
$252$			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	0.792517	+	0.609850i	$0.208770\pi$
$257$	131.023	+	403.248i	0.509818	+	1.56906i	−0.282699	+	0.959209i	$0.591230\pi$
$258$	−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	$-0.914241\pi$
$263$		−	140.007i		−	0.532347i	0.963925	−	0.266173i	$-0.0857593\pi$
$264$		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	−0.773205	−	0.634156i	$-0.781348\pi$
$269$	−110.026	+	79.9388i	−0.409020	+	0.297170i	0.364185	+	0.931327i	$0.381348\pi$
$270$	−98.9192	−	136.151i	−0.366367	−	0.504262i
$271$	−274.379	+	89.1513i	−1.01247	+	0.328971i	−0.767838	−	0.640644i	$-0.778667\pi$
$271$	−274.379	+	89.1513i	−1.01247	+	0.328971i	−0.244632	+	0.969616i	$0.578667\pi$
$272$	−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	−0.658273	−	0.752779i	$-0.728713\pi$
$277$	72.3191	−	99.5387i	0.261080	−	0.359345i	0.919353	+	0.393434i	$0.128713\pi$
$278$	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	0.400602	−	0.916252i	$-0.368801\pi$
$281$	−167.082	−	229.969i	−0.594598	−	0.818394i	−0.995200	+	0.0978581i	$0.968801\pi$
$282$	−43.0399	+	13.9845i	−0.152624	+	0.0495905i
$283$	75.3198	+	24.4729i	0.266148	+	0.0864767i	0.439051	−	0.898462i	$-0.355315\pi$
$283$	75.3198	+	24.4729i	0.266148	+	0.0864767i	−0.172903	+	0.984939i	$0.555315\pi$
$284$	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	−0.562906	−	0.826521i	$-0.690317\pi$
$293$	−156.020	+	50.6939i	−0.532490	+	0.173017i	0.0304160	+	0.999537i	$0.490317\pi$
$294$	−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	$-0.901667\pi$
$307$		−	186.676i		−	0.608066i	0.952662	−	0.304033i	$-0.0983333\pi$
$308$		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	−0.855394	−	0.517979i	$-0.826685\pi$
$311$	43.8804	−	135.050i	0.141095	−	0.434244i	0.996488	+	0.0837342i	$0.0266847\pi$
$312$	44.4984	+	136.952i	0.142623	+	0.438949i
$313$	361.631	−	262.740i	1.15537	−	0.839425i	0.166184	−	0.986095i	$-0.446855\pi$
$313$	361.631	−	262.740i	1.15537	−	0.839425i	0.989186	+	0.146670i	$0.0468555\pi$
$314$	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	−0.101937	−	0.994791i	$-0.532504\pi$
$317$	−342.214	−	248.633i	−1.07954	−	0.784332i	−0.977603	+	0.210459i	$0.932504\pi$
$318$			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	0.0753293	−	0.997159i	$-0.475999\pi$
$337$	243.444	−	79.0999i	0.722387	−	0.234718i	0.647058	+	0.762441i	$0.275999\pi$
$338$	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	−0.960065	−	0.279775i	$-0.909740\pi$
$347$	−322.527	−	443.920i	−0.929471	−	1.27931i	0.0305943	−	0.999532i	$-0.490260\pi$
$348$	−43.0399	+	13.9845i	−0.123678	+	0.0401854i
$349$	415.604	+	135.038i	1.19084	+	0.386928i	0.836384	−	0.548144i	$-0.184665\pi$
$349$	415.604	+	135.038i	1.19084	+	0.386928i	0.354458	+	0.935072i	$0.384665\pi$
$350$	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	−0.799783	−	0.600289i	$-0.795052\pi$
$359$	−392.739	+	127.609i	−1.09398	+	0.355456i	−0.294197	+	0.955745i	$0.595052\pi$
$360$	−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	0.866502	+	0.499174i	$0.166363\pi$
$367$	168.414	+	518.326i	0.458894	+	1.41233i	−0.407607	+	0.913157i	$0.633637\pi$
$368$	−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	$0.101265\pi$
$373$			233.345i			0.625590i	−0.949821	+	0.312795i	$0.898735\pi$
$374$		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	0.00238088	−	0.999997i	$-0.499242\pi$
$379$	361.631	−	262.740i	0.954170	−	0.693245i	0.951790	+	0.306752i	$0.0992421\pi$
$380$	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	0.988642	−	0.150292i	$-0.0480215\pi$
$383$	440.914	+	320.343i	1.15121	+	0.836405i	0.162571	+	0.986697i	$0.448021\pi$
$384$			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	0.999416	−	0.0341589i	$-0.0108752\pi$
$389$	66.4387	+	204.477i	0.170793	+	0.525648i	−0.828623	+	0.559807i	$0.810875\pi$
$390$	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	−0.958719	−	0.284357i	$-0.908220\pi$
$401$	−394.800	+	286.839i	−0.984539	+	0.715310i	−0.0258209	+	0.999667i	$0.508220\pi$
$402$	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	−0.906779	−	0.421607i	$-0.861466\pi$
$409$	−92.2692	+	126.998i	−0.225597	+	0.310508i	0.681182	+	0.732114i	$0.261466\pi$
$410$	−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	−0.845244	−	0.534380i	$-0.820545\pi$
$421$	64.2755	−	197.820i	0.152673	−	0.469881i	0.997918	+	0.0644995i	$0.0205451\pi$
$422$	−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	0.231041	+	0.972944i	$0.425787\pi$
$431$	−330.008	+	454.217i	−0.765679	+	1.05387i	−0.996720	+	0.0809232i	$0.974213\pi$
$432$	−21.0132	+	64.6718i	−0.0486416	+	0.149703i
$433$	12.0517	+	37.0912i	0.0278329	+	0.0856610i	0.964008	−	0.265873i	$-0.0856602\pi$
$433$	12.0517	+	37.0912i	0.0278329	+	0.0856610i	−0.936175	+	0.351534i	$0.885660\pi$
$434$	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	$0.0914913\pi$
$439$			248.902i			0.566974i	−0.958976	+	0.283487i	$0.908509\pi$
$440$		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	−0.871284	−	0.490779i	$-0.836712\pi$
$443$	54.0780	−	166.435i	0.122072	−	0.375700i	0.993356	+	0.115079i	$0.0367123\pi$
$444$	−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	0.268940	−	0.963157i	$-0.413327\pi$
$449$	−253.222	−	183.977i	−0.563970	−	0.409748i	−0.832910	+	0.553409i	$0.813327\pi$
$450$			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	0.816231	−	0.577726i	$-0.196060\pi$
$457$	6.65003	+	9.15298i	0.0145515	+	0.0200284i	−0.801679	+	0.597754i	$0.796060\pi$
$458$	−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	$-0.606203\pi$
$461$		−	871.156i		−	1.88971i	0.327491	−	0.944854i	$-0.393797\pi$
$462$		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	−0.439531	−	0.898227i	$-0.644855\pi$
$467$	130.252	−	94.6334i	0.278912	−	0.202641i	0.718443	+	0.695586i	$0.244855\pi$
$468$	−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	0.989792	−	0.142520i	$-0.0455206\pi$
$479$	262.676	+	361.543i	0.548385	+	0.754787i	−0.441407	+	0.897307i	$0.645521\pi$
$480$	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	0.402266	+	0.915523i	$0.368223\pi$
$487$	−224.655	+	691.418i	−0.461305	+	1.41975i	−0.863571	+	0.504227i	$0.831777\pi$
$488$	−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	0.241980	−	0.970281i	$-0.422203\pi$
$491$	494.959	−	160.822i	1.00806	−	0.327540i	0.766083	+	0.642742i	$0.222203\pi$
$492$	−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	−0.997985	−	0.0634485i	$-0.979790\pi$
$499$	−113.718	−	349.989i	−0.227892	−	0.701380i	0.770093	−	0.637932i	$-0.220210\pi$
$500$	−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	−0.165885	−	0.986145i	$-0.553048\pi$
$503$	−442.504	−	143.778i	−0.879730	−	0.285841i	−0.713845	+	0.700304i	$0.753048\pi$
$504$	−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	−0.979080	−	0.203474i	$-0.934777\pi$
$509$	−34.3009	+	105.567i	−0.0673888	+	0.207401i	0.911692	+	0.410875i	$0.134777\pi$
$510$	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	−0.980385	−	0.197094i	$-0.936850\pi$
$521$	−157.908	−	485.990i	−0.303086	−	0.932802i	0.677299	−	0.735708i	$-0.263150\pi$
$522$	−207.108	+	150.473i	−0.396759	+	0.288262i
$523$	408.977	+	562.908i	0.781983	+	1.07631i	0.995060	+	0.0992715i	$0.0316512\pi$
$523$	408.977	+	562.908i	0.781983	+	1.07631i	−0.213078	+	0.977035i	$0.568349\pi$
$524$	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	−0.664218	−	0.747539i	$-0.731235\pi$
$541$	136.326	−	187.636i	0.251988	−	0.346832i	0.916206	+	0.400707i	$0.131235\pi$
$542$	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	0.846934	−	0.531697i	$-0.178446\pi$
$547$	667.119	+	216.760i	1.21960	+	0.396270i	0.372661	+	0.927968i	$0.378446\pi$
$548$	−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	−0.483335	−	0.875436i	$-0.660575\pi$
$557$	−200.405	+	65.1154i	−0.359793	+	0.116904i	0.123542	+	0.992339i	$0.460575\pi$
$558$	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	−0.425226	−	0.905087i	$-0.639805\pi$
$563$	319.201	−	439.343i	0.566965	−	0.780361i	0.992191	+	0.124726i	$0.0398053\pi$
$564$	−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	0.374454	−	0.927246i	$-0.377830\pi$
$569$	75.3198	+	24.4729i	0.132372	+	0.0430104i	−0.242082	+	0.970256i	$0.577830\pi$
$570$	−135.915	−	98.7479i	−0.238447	−	0.173242i
$571$		−	124.451i		−	0.217952i	−0.994044	−	0.108976i	$-0.965243\pi$
$571$		−	124.451i		−	0.217952i	0.994044	−	0.108976i	$-0.0347572\pi$
$572$		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	−0.657648	−	0.753325i	$-0.728449\pi$
$577$	−83.3288	+	60.5419i	−0.144417	+	0.104925i	0.513231	+	0.858251i	$0.328449\pi$
$578$	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	−0.967841	−	0.251564i	$-0.919055\pi$
$587$	−195.299	−	601.068i	−0.332707	−	1.02397i	0.635134	−	0.772402i	$-0.280945\pi$
$588$	−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	$0.137876\pi$
$593$			497.803i			0.839466i	−0.907648	+	0.419733i	$0.862124\pi$
$594$		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	−0.778197	−	0.628020i	$-0.783866\pi$
$599$	−252.413	+	183.389i	−0.421391	+	0.306159i	0.356806	+	0.934178i	$0.383866\pi$
$600$	−119.701	−	164.754i	−0.199501	−	0.274589i
$601$	391.394	−	127.172i	0.651238	−	0.211600i	0.0352782	−	0.999378i	$-0.488768\pi$
$601$	391.394	−	127.172i	0.651238	−	0.211600i	0.615960	+	0.787777i	$0.288768\pi$
$602$	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	−0.745280	−	0.666751i	$-0.767684\pi$
$607$	72.3191	−	99.5387i	0.119142	−	0.163985i	0.864422	+	0.502766i	$0.167684\pi$
$608$	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	−0.144224	−	0.989545i	$-0.546068\pi$
$613$	−516.479	−	167.814i	−0.842543	−	0.273759i	−0.698319	+	0.715786i	$0.746068\pi$
$614$	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	−0.607368	−	0.794420i	$-0.707775\pi$
$619$	217.239	−	668.593i	0.350951	−	1.08012i	0.958320	−	0.285697i	$-0.0922252\pi$
$620$	−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	1.00000		0.000850413i	$0.000270695\pi$
$631$	120.826	+	371.863i	0.191483	+	0.589323i	−0.808517	+	0.588473i	$0.799729\pi$
$632$	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	−0.956447	−	0.291905i	$-0.905711\pi$
$641$	−7.10739	+	21.8743i	−0.0110880	+	0.0341253i	0.945359	+	0.326030i	$0.105711\pi$
$642$	80.9625	+	249.177i	0.126110	+	0.388126i
$643$	361.631	−	262.740i	0.562412	−	0.408616i	−0.269929	−	0.962880i	$-0.587000\pi$
$643$	361.631	−	262.740i	0.562412	−	0.408616i	0.832341	+	0.554264i	$0.187000\pi$
$644$	−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	0.845505	−	0.533967i	$-0.179299\pi$
$647$	387.519	+	281.549i	0.598948	+	0.435161i	−0.246558	+	0.969128i	$0.579299\pi$
$648$		−	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	0.963589	+	0.267389i	$0.0861609\pi$
$653$	222.801	+	685.712i	0.341196	+	1.05009i	−0.622392	+	0.782705i	$0.713839\pi$
$654$	−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	$0.178234\pi$
$659$			700.036i			1.06227i	−0.847287	+	0.531135i	$0.821766\pi$
$660$		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	0.108112	+	0.994139i	$0.465519\pi$
$673$	−586.034	+	806.607i	−0.870779	+	1.19852i	−0.978891	+	0.204385i	$0.934481\pi$
$674$	−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	0.999796	−	0.0201971i	$-0.00642937\pi$
$677$	454.696	+	625.835i	0.671633	+	0.924424i	−0.328163	+	0.944621i	$0.606429\pi$
$678$	−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	−0.0461016	−	0.998937i	$-0.514680\pi$
$691$	−698.182	−	507.259i	−1.01039	−	0.734094i	−0.964292	+	0.264843i	$0.914680\pi$
$692$		−	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	0.0225597	−	0.999745i	$-0.492818\pi$
$701$	−383.324	−	124.550i	−0.546825	−	0.177674i	−0.569384	+	0.822071i	$0.692818\pi$
$702$	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	−0.172574	−	0.984997i	$-0.555208\pi$
$709$	504.018	−	366.190i	0.710885	−	0.516488i	0.883459	+	0.468508i	$0.155208\pi$
$710$	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	0.993107	−	0.117213i	$-0.0373962\pi$
$719$	86.8338	+	267.247i	0.120770	+	0.371692i	−0.872337	+	0.488906i	$0.837396\pi$
$720$	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	0.334892	−	0.942256i	$-0.391300\pi$
$733$	850.038	−	276.194i	1.15967	−	0.376800i	0.824778	+	0.565457i	$0.191300\pi$
$734$	−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	−0.230677	−	0.973030i	$-0.574094\pi$
$739$	566.084	−	779.148i	0.766013	−	1.05433i	0.996690	−	0.0812965i	$-0.0259061\pi$
$740$	−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	0.813469	−	0.581609i	$-0.197577\pi$
$743$	6.65003	+	9.15298i	0.00895024	+	0.0123190i	−0.804518	+	0.593928i	$0.797577\pi$
$744$	−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	−0.782171	−	0.623064i	$-0.785887\pi$
$751$	162.852	−	501.207i	0.216847	−	0.667386i	0.999017	−	0.0443214i	$-0.0141126\pi$
$752$	−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	0.567295	−	0.823515i	$-0.307990\pi$
$757$	−30.7426	−	22.3358i	−0.0406112	−	0.0295057i	−0.607906	+	0.794009i	$0.707990\pi$
$758$			632.153i			0.833976i
$759$		0			0
$760$	−1008.00			−1.32632
$761$	721.528	−	993.099i	0.948132	−	1.30499i	−0.00422031	−	0.999991i	$-0.501343\pi$
$761$	721.528	−	993.099i	0.948132	−	1.30499i	0.952352	−	0.305000i	$-0.0986566\pi$
$762$	−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	$0.0648394\pi$
$769$			311.127i			0.404586i	−0.979325	+	0.202293i	$0.935161\pi$
$770$		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	−0.382304	−	0.924037i	$-0.624869\pi$
$773$	363.404	−	1118.44i	0.470122	−	1.44689i	0.852425	−	0.522849i	$-0.175131\pi$
$774$	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	0.956683	+	0.291130i	$0.0940313\pi$
$787$	738.153	+	1015.98i	0.937933	+	1.29095i	−0.0187502	+	0.999824i	$0.505969\pi$
$788$	−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	−0.680490	−	0.732757i	$-0.738233\pi$
$797$	−154.522	+	112.267i	−0.193880	+	0.140862i	0.486610	+	0.873619i	$0.338233\pi$
$798$	−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	0.561737	−	0.827316i	$-0.310133\pi$
$809$	−322.527	−	443.920i	−0.398673	−	0.548726i	−0.960410	+	0.278589i	$0.910133\pi$
$810$	−517.824	+	168.251i	−0.639289	+	0.207717i
$811$	386.014	+	125.424i	0.475973	+	0.154653i	0.537172	−	0.843473i	$-0.319492\pi$
$811$	386.014	+	125.424i	0.475973	+	0.154653i	−0.0611992	+	0.998126i	$0.519492\pi$
$812$	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	−0.340788	−	0.940140i	$-0.610694\pi$
$821$	−52.4549	+	17.0436i	−0.0638915	+	0.0207596i	0.276897	+	0.960900i	$0.410694\pi$
$822$	345.664	+	112.313i	0.420516	+	0.136634i
$823$	−555.795	−	403.808i	−0.675328	−	0.490654i	0.196477	−	0.980508i	$-0.437050\pi$
$823$	−555.795	−	403.808i	−0.675328	−	0.490654i	−0.871804	+	0.489854i	$0.837050\pi$
$824$			135.765i			0.164763i
$825$		0			0
$826$	710.000			0.859564
$827$	−9.97505	+	13.7295i	−0.0120617	+	0.0166015i	−0.815005	−	0.579454i	$-0.803266\pi$
$827$	−9.97505	+	13.7295i	−0.0120617	+	0.0166015i	0.802944	+	0.596055i	$0.203266\pi$
$828$	44.4984	−	136.952i	0.0537421	−	0.165401i
$829$	304.382	+	936.791i	0.367167	+	1.13002i	0.948613	+	0.316439i	$0.102487\pi$
$829$	304.382	+	936.791i	0.367167	+	1.13002i	−0.581445	+	0.813585i	$0.697513\pi$
$830$	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	−0.933756	−	0.357911i	$-0.883489\pi$
$839$	26.8845	−	82.7419i	0.0320435	−	0.0986197i	0.965799	+	0.259292i	$0.0834890\pi$
$840$	−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	0.584800	−	0.811178i	$-0.301173\pi$
$853$	−313.383	−	431.334i	−0.367389	−	0.505667i	−0.952189	+	0.305510i	$0.901173\pi$
$854$	−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	$-0.705525\pi$
$857$		−	1368.96i		−	1.59738i	0.601740	−	0.798692i	$-0.294475\pi$
$858$		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	0.198914	−	0.980017i	$-0.436259\pi$
$863$	1029.07	−	747.663i	1.19243	−	0.866353i	0.993519	+	0.113664i	$0.0362587\pi$
$864$	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	−0.0381634	−	0.999272i	$-0.512151\pi$
$877$	−575.659	−	187.043i	−0.656395	−	0.213276i	−0.618232	+	0.785996i	$0.712151\pi$
$878$	−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	0.795360	+	0.606137i	$0.207282\pi$
$883$	−180.466	+	555.417i	−0.204378	+	0.629011i	−0.999738	+	0.0228742i	$0.992718\pi$
$884$	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	0.262311	−	0.964983i	$-0.415515\pi$
$887$	924.013	−	300.230i	1.04173	−	0.338478i	0.779417	+	0.626505i	$0.215515\pi$
$888$	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	0.372334	−	0.928099i	$-0.378557\pi$
$907$	1242.65	−	902.838i	1.37007	−	0.995411i	0.997732	−	0.0673127i	$-0.0214425\pi$
$908$	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	0.154712	−	0.987960i	$-0.450555\pi$
$911$	−671.484	−	487.862i	−0.737085	−	0.535523i	−0.891797	+	0.452436i	$0.850555\pi$
$912$			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	0.589497	−	0.807771i	$-0.299326\pi$
$919$	−331.670	−	456.505i	−0.360903	−	0.496741i	−0.950400	+	0.311030i	$0.899326\pi$
$920$	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	−0.345326	+	0.938483i	$0.612232\pi$
$929$	−1249.12	+	907.540i	−1.34459	+	0.976900i	−0.999262	+	0.0384176i	$0.987768\pi$
$930$	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	−0.990958	−	0.134175i	$-0.957161\pi$
$937$	−522.027	+	718.509i	−0.557126	+	0.766819i	0.433831	+	0.900994i	$0.357161\pi$
$938$	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	0.475631	−	0.879645i	$-0.342220\pi$
$941$	−477.971	−	657.871i	−0.507939	−	0.699119i	−0.983570	+	0.180526i	$0.942220\pi$
$942$	−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	0.0223342	−	0.999751i	$-0.492890\pi$
$953$	598.524	−	194.472i	0.628042	−	0.204063i	0.605707	+	0.795687i	$0.292890\pi$
$954$	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	$0.0618369\pi$
$967$			373.352i			0.386093i	−0.981190	+	0.193047i	$0.938163\pi$
$968$		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	0.194457	+	0.980911i	$0.437706\pi$
$971$	−523.784	+	1612.04i	−0.539427	+	1.66019i	−0.733884	+	0.679275i	$0.762294\pi$
$972$	−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	0.729987	−	0.683461i	$-0.239526\pi$
$977$	298.527	+	216.893i	0.305555	+	0.221999i	−0.424432	+	0.905460i	$0.639526\pi$
$978$		−	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	0.996837	−	0.0794777i	$-0.0253252\pi$
$983$	141.221	+	434.633i	0.143663	+	0.442149i	−0.853174	+	0.521627i	$0.825325\pi$
$984$	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	−0.626787	−	0.779191i	$-0.715630\pi$
$997$	−673.844	+	218.945i	−0.675871	+	0.219604i	−0.0490843	+	0.998795i	$0.515630\pi$
$998$	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.40.1		8
11.2	odd	10	inner	121.3.d.e.94.1		8
11.3	even	5	inner	121.3.d.e.118.2		8
11.4	even	5	inner	121.3.d.e.112.1		8
11.5	even	5		121.3.b.a.120.1	✓	2
11.6	odd	10		121.3.b.a.120.2	yes	2
11.7	odd	10	inner	121.3.d.e.112.2		8
11.8	odd	10	inner	121.3.d.e.118.1		8
11.9	even	5	inner	121.3.d.e.94.2		8
11.10	odd	2	inner	121.3.d.e.40.2		8
33.5	odd	10		1089.3.c.a.604.2		2
33.17	even	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	11.5	even	5
121.3.b.a.120.2	yes	2	11.6	odd	10
121.3.d.e.40.1		8	1.1	even	1	trivial
121.3.d.e.40.2		8	11.10	odd	2	inner
121.3.d.e.94.1		8	11.2	odd	10	inner
121.3.d.e.94.2		8	11.9	even	5	inner
121.3.d.e.112.1		8	11.4	even	5	inner
121.3.d.e.112.2		8	11.7	odd	10	inner
121.3.d.e.118.1		8	11.8	odd	10	inner
121.3.d.e.118.2		8	11.3	even	5	inner
1089.3.c.a.604.1		2	33.17	even	10
1089.3.c.a.604.2		2	33.5	odd	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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