LMFDB - Embedded newform 770.2.n.f.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$0.476925 - 1.46782i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.f.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.167908 + 0.516768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.439589 + 0.319380i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.18820 - 1.58982i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.167908 + 0.516768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.439589 + 0.319380i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.18820 - 1.58982i) q^{9} -1.00000 q^{10} +(2.31504 - 2.37499i) q^{11} +0.543362 q^{12} +(1.34184 - 0.974905i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.167908 - 0.516768i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.65537 - 1.20270i) q^{17} +(0.835816 - 2.57238i) q^{18} +(1.14483 + 3.52343i) q^{19} +(-0.809017 + 0.587785i) q^{20} -0.543362 q^{21} +(0.476925 - 3.28216i) q^{22} -4.99442 q^{23} +(0.439589 - 0.319380i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.512538 - 1.57743i) q^{26} +(2.50775 + 1.82199i) q^{27} +(0.809017 + 0.587785i) q^{28} +(2.20524 - 6.78704i) q^{29} +(-0.167908 - 0.516768i) q^{30} +(8.23652 - 5.98418i) q^{31} -1.00000 q^{32} +(1.61603 + 0.797560i) q^{33} -2.04615 q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.835816 - 2.57238i) q^{36} +(2.82328 - 8.68916i) q^{37} +(2.99721 + 2.17760i) q^{38} +(0.729106 + 0.529726i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(1.55935 + 4.79917i) q^{41} +(-0.439589 + 0.319380i) q^{42} +5.78688 q^{43} +(-1.54336 - 2.93565i) q^{44} -2.70476 q^{45} +(-4.04057 + 2.93565i) q^{46} +(-1.41049 - 4.34104i) q^{47} +(0.167908 - 0.516768i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.343565 - 1.05738i) q^{51} +(-0.512538 - 1.57743i) q^{52} +(-7.18619 + 5.22108i) q^{53} +3.09975 q^{54} +(-3.26889 + 0.560659i) q^{55} +1.00000 q^{56} +(-1.62857 + 1.18323i) q^{57} +(-2.20524 - 6.78704i) q^{58} +(-4.35238 + 13.3952i) q^{59} +(-0.439589 - 0.319380i) q^{60} +(2.67393 + 1.94273i) q^{61} +(3.14607 - 9.68261i) q^{62} +(0.835816 + 2.57238i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.65861 q^{65} +(1.77619 - 0.304641i) q^{66} -3.18992 q^{67} +(-1.65537 + 1.20270i) q^{68} +(-0.838604 - 2.58096i) q^{69} +(0.309017 - 0.951057i) q^{70} +(6.31677 + 4.58940i) q^{71} +(-2.18820 - 1.58982i) q^{72} +(-3.36971 + 10.3709i) q^{73} +(-2.82328 - 8.68916i) q^{74} +(-0.439589 + 0.319380i) q^{75} +3.70476 q^{76} +(1.54336 + 2.93565i) q^{77} +0.901224 q^{78} +(-9.06537 + 6.58638i) q^{79} +(0.309017 + 0.951057i) q^{80} +(1.98698 - 6.11528i) q^{81} +(4.08242 + 2.96605i) q^{82} +(-3.29927 - 2.39706i) q^{83} +(-0.167908 + 0.516768i) q^{84} +(0.632295 + 1.94600i) q^{85} +(4.68168 - 3.40144i) q^{86} +3.87760 q^{87} +(-2.97414 - 1.46782i) q^{88} -3.32679 q^{89} +(-2.18820 + 1.58982i) q^{90} +(0.512538 + 1.57743i) q^{91} +(-1.54336 + 4.74998i) q^{92} +(4.47541 + 3.25158i) q^{93} +(-3.69271 - 2.68291i) q^{94} +(1.14483 - 3.52343i) q^{95} +(-0.167908 - 0.516768i) q^{96} +(-7.44004 + 5.40550i) q^{97} -1.00000 q^{98} +(1.28997 - 8.87743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.167908	+	0.516768i	0.0969418	+	0.298356i	0.987755	−	0.156014i	$-0.0498644\pi$
$3$	0.167908	+	0.516768i	0.0969418	+	0.298356i	−0.890813	+	0.454370i	$0.849864\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	0.439589	+	0.319380i	0.179461	+	0.130386i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	2.18820	−	1.58982i	0.729398	−	0.529939i
$10$	−1.00000			−0.316228
$11$	2.31504	−	2.37499i	0.698012	−	0.716086i
$11$	2.31504	−	2.37499i	0.698012	−	0.716086i
$12$	0.543362			0.156855
$13$	1.34184	−	0.974905i	0.372160	−	0.270390i	−0.385946	−	0.922521i	$-0.626125\pi$
$13$	1.34184	−	0.974905i	0.372160	−	0.270390i	0.758106	+	0.652131i	$0.226125\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.167908	−	0.516768i	0.0433537	−	0.133429i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.65537	−	1.20270i	−0.401486	−	0.291697i	0.368660	−	0.929564i	$-0.379817\pi$
$17$	−1.65537	−	1.20270i	−0.401486	−	0.291697i	−0.770146	+	0.637868i	$0.779817\pi$
$18$	0.835816	−	2.57238i	0.197004	−	0.606315i
$19$	1.14483	+	3.52343i	0.262643	+	0.808331i	0.992227	+	0.124440i	$0.0397136\pi$
$19$	1.14483	+	3.52343i	0.262643	+	0.808331i	−0.729584	+	0.683891i	$0.760286\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	−0.543362			−0.118571
$22$	0.476925	−	3.28216i	0.101681	−	0.699758i
$23$	−4.99442			−1.04141			−0.520705	−	0.853737i	$-0.674331\pi$
$23$	−4.99442			−1.04141			−0.520705	+	0.853737i	$0.674331\pi$
$24$	0.439589	−	0.319380i	0.0897307	−	0.0651932i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.512538	−	1.57743i	0.100517	−	0.309359i
$27$	2.50775	+	1.82199i	0.482617	+	0.350641i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	2.20524	−	6.78704i	0.409504	−	1.26032i	−0.507572	−	0.861609i	$-0.669457\pi$
$29$	2.20524	−	6.78704i	0.409504	−	1.26032i	0.917076	−	0.398713i	$-0.130543\pi$
$30$	−0.167908	−	0.516768i	−0.0306557	−	0.0943485i
$31$	8.23652	−	5.98418i	1.47932	−	1.07479i	0.501548	−	0.865130i	$-0.332764\pi$
$31$	8.23652	−	5.98418i	1.47932	−	1.07479i	0.977774	−	0.209661i	$-0.0672360\pi$
$32$	−1.00000			−0.176777
$33$	1.61603	+	0.797560i	0.281315	+	0.138837i
$34$	−2.04615			−0.350912
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	−0.835816	−	2.57238i	−0.139303	−	0.428730i
$37$	2.82328	−	8.68916i	0.464144	−	1.42849i	−0.395912	−	0.918289i	$-0.629571\pi$
$37$	2.82328	−	8.68916i	0.464144	−	1.42849i	0.860056	−	0.510200i	$-0.170429\pi$
$38$	2.99721	+	2.17760i	0.486212	+	0.353254i
$39$	0.729106	+	0.529726i	0.116750	+	0.0848241i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	1.55935	+	4.79917i	0.243529	+	0.749505i	0.995875	+	0.0907368i	$0.0289222\pi$
$41$	1.55935	+	4.79917i	0.243529	+	0.749505i	−0.752346	+	0.658768i	$0.771078\pi$
$42$	−0.439589	+	0.319380i	−0.0678301	+	0.0492814i
$43$	5.78688			0.882491			0.441245	−	0.897387i	$-0.354537\pi$
$43$	5.78688			0.882491			0.441245	+	0.897387i	$0.354537\pi$
$44$	−1.54336	−	2.93565i	−0.232671	−	0.442566i
$45$	−2.70476			−0.403201
$46$	−4.04057	+	2.93565i	−0.595750	+	0.432838i
$47$	−1.41049	−	4.34104i	−0.205741	−	0.633205i	−0.999682	−	0.0252108i	$-0.991974\pi$
$47$	−1.41049	−	4.34104i	−0.205741	−	0.633205i	0.793941	−	0.607994i	$-0.208026\pi$
$48$	0.167908	−	0.516768i	0.0242354	−	0.0745890i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	0.343565	−	1.05738i	0.0481087	−	0.148063i
$52$	−0.512538	−	1.57743i	−0.0710762	−	0.218750i
$53$	−7.18619	+	5.22108i	−0.987100	+	0.717170i	−0.959284	−	0.282443i	$-0.908855\pi$
$53$	−7.18619	+	5.22108i	−0.987100	+	0.717170i	−0.0278156	+	0.999613i	$0.508855\pi$
$54$	3.09975			0.421822
$55$	−3.26889	+	0.560659i	−0.440777	+	0.0755992i
$56$	1.00000			0.133631
$57$	−1.62857	+	1.18323i	−0.215709	+	0.156722i
$58$	−2.20524	−	6.78704i	−0.289563	−	0.891182i
$59$	−4.35238	+	13.3952i	−0.566631	+	1.74391i	0.0964222	+	0.995341i	$0.469260\pi$
$59$	−4.35238	+	13.3952i	−0.566631	+	1.74391i	−0.663054	+	0.748572i	$0.730740\pi$
$60$	−0.439589	−	0.319380i	−0.0567507	−	0.0412318i
$61$	2.67393	+	1.94273i	0.342362	+	0.248741i	0.745658	−	0.666329i	$-0.232135\pi$
$61$	2.67393	+	1.94273i	0.342362	+	0.248741i	−0.403296	+	0.915070i	$0.632135\pi$
$62$	3.14607	−	9.68261i	0.399551	−	1.22969i
$63$	0.835816	+	2.57238i	0.105303	+	0.324089i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.65861			−0.205725
$66$	1.77619	−	0.304641i	0.218634	−	0.0374987i
$67$	−3.18992			−0.389711			−0.194855	−	0.980832i	$-0.562424\pi$
$67$	−3.18992			−0.389711			−0.194855	+	0.980832i	$0.562424\pi$
$68$	−1.65537	+	1.20270i	−0.200743	+	0.145848i
$69$	−0.838604	−	2.58096i	−0.100956	−	0.310711i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	6.31677	+	4.58940i	0.749662	+	0.544661i	0.895722	−	0.444614i	$-0.146659\pi$
$71$	6.31677	+	4.58940i	0.749662	+	0.544661i	−0.146060	+	0.989276i	$0.546659\pi$
$72$	−2.18820	−	1.58982i	−0.257881	−	0.187362i
$73$	−3.36971	+	10.3709i	−0.394394	+	1.21382i	0.535038	+	0.844828i	$0.320297\pi$
$73$	−3.36971	+	10.3709i	−0.394394	+	1.21382i	−0.929432	+	0.368993i	$0.879703\pi$
$74$	−2.82328	−	8.68916i	−0.328199	−	1.01009i
$75$	−0.439589	+	0.319380i	−0.0507594	+	0.0368788i
$76$	3.70476			0.424965
$77$	1.54336	+	2.93565i	0.175882	+	0.334548i
$78$	0.901224			0.102044
$79$	−9.06537	+	6.58638i	−1.01993	+	0.741025i	−0.966269	−	0.257534i	$-0.917090\pi$
$79$	−9.06537	+	6.58638i	−1.01993	+	0.741025i	−0.0536647	+	0.998559i	$0.517090\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	1.98698	−	6.11528i	0.220775	−	0.679476i
$82$	4.08242	+	2.96605i	0.450828	+	0.327546i
$83$	−3.29927	−	2.39706i	−0.362142	−	0.263111i	0.391803	−	0.920049i	$-0.371851\pi$
$83$	−3.29927	−	2.39706i	−0.362142	−	0.263111i	−0.753945	+	0.656938i	$0.771851\pi$
$84$	−0.167908	+	0.516768i	−0.0183203	+	0.0563840i
$85$	0.632295	+	1.94600i	0.0685820	+	0.211074i
$86$	4.68168	−	3.40144i	0.504839	−	0.366787i
$87$	3.87760			0.415723
$88$	−2.97414	−	1.46782i	−0.317044	−	0.156471i
$89$	−3.32679			−0.352639			−0.176320	−	0.984333i	$-0.556419\pi$
$89$	−3.32679			−0.352639			−0.176320	+	0.984333i	$0.556419\pi$
$90$	−2.18820	+	1.58982i	−0.230656	+	0.167581i
$91$	0.512538	+	1.57743i	0.0537286	+	0.165360i
$92$	−1.54336	+	4.74998i	−0.160907	+	0.495220i
$93$	4.47541	+	3.25158i	0.464078	+	0.337173i
$94$	−3.69271	−	2.68291i	−0.380874	−	0.276721i
$95$	1.14483	−	3.52343i	0.117457	−	0.361497i
$96$	−0.167908	−	0.516768i	−0.0171370	−	0.0527424i
$97$	−7.44004	+	5.40550i	−0.755422	+	0.548846i	−0.897503	−	0.441009i	$-0.854621\pi$
$97$	−7.44004	+	5.40550i	−0.755422	+	0.548846i	0.142081	+	0.989855i	$0.454621\pi$
$98$	−1.00000			−0.101015
$99$	1.28997	−	8.87743i	0.129647	−	0.892216i
$100$	1.00000			0.100000
$101$	−2.21127	+	1.60658i	−0.220030	+	0.159861i	−0.692340	−	0.721571i	$-0.743420\pi$
$101$	−2.21127	+	1.60658i	−0.220030	+	0.159861i	0.472310	+	0.881432i	$0.343420\pi$
$102$	−0.343565	−	1.05738i	−0.0340180	−	0.104697i
$103$	−0.478162	+	1.47163i	−0.0471147	+	0.145004i	−0.971846	−	0.235616i	$-0.924289\pi$
$103$	−0.478162	+	1.47163i	−0.0471147	+	0.145004i	0.924732	+	0.380620i	$0.124289\pi$
$104$	−1.34184	−	0.974905i	−0.131578	−	0.0955973i
$105$	0.439589	+	0.319380i	0.0428995	+	0.0311683i
$106$	−2.74488	+	8.44788i	−0.266606	+	0.820530i
$107$	3.77275	+	11.6113i	0.364725	+	1.12251i	0.950153	+	0.311784i	$0.100927\pi$
$107$	3.77275	+	11.6113i	0.364725	+	1.12251i	−0.585428	+	0.810724i	$0.699073\pi$
$108$	2.50775	−	1.82199i	0.241308	−	0.175321i
$109$	−1.32376			−0.126794			−0.0633968	−	0.997988i	$-0.520193\pi$
$109$	−1.32376			−0.126794			−0.0633968	+	0.997988i	$0.520193\pi$
$110$	−2.31504	+	2.37499i	−0.220731	+	0.226446i
$111$	4.96433			0.471193
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	1.06874	+	3.28924i	0.100538	+	0.309426i	0.988657	−	0.150188i	$-0.0479879\pi$
$113$	1.06874	+	3.28924i	0.100538	+	0.309426i	−0.888119	+	0.459614i	$0.847988\pi$
$114$	−0.622059	+	1.91450i	−0.0582611	+	0.179309i
$115$	4.04057	+	2.93565i	0.376785	+	0.273751i
$116$	−5.77340	−	4.19462i	−0.536047	−	0.389461i
$117$	1.38629	−	4.26657i	0.128163	−	0.394444i
$118$	4.35238	+	13.3952i	0.400669	+	1.23313i
$119$	1.65537	−	1.20270i	0.151748	−	0.110251i
$120$	−0.543362			−0.0496019
$121$	−0.281153	−	10.9964i	−0.0255594	−	0.999673i
$122$	3.30516			0.299236
$123$	−2.21823	+	1.61164i	−0.200011	+	0.145317i
$124$	−3.14607	−	9.68261i	−0.282525	−	0.869524i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	2.18820	+	1.58982i	0.194940	+	0.141632i
$127$	14.7435	+	10.7118i	1.30827	+	0.950515i	1.00000		0.000782596i	$-0.000249108\pi$
$127$	14.7435	+	10.7118i	1.30827	+	0.950515i	0.308273	+	0.951298i	$0.400249\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	0.971664	+	2.99047i	0.0855502	+	0.263296i
$130$	−1.34184	+	0.974905i	−0.117687	+	0.0855049i
$131$	−9.47001			−0.827398			−0.413699	−	0.910414i	$-0.635763\pi$
$131$	−9.47001			−0.827398			−0.413699	+	0.910414i	$0.635763\pi$
$132$	1.25791	−	1.29048i	0.109487	−	0.112322i
$133$	−3.70476			−0.321243
$134$	−2.58070	+	1.87499i	−0.222938	+	0.161974i
$135$	−0.957875	−	2.94804i	−0.0824407	−	0.253727i
$136$	−0.632295	+	1.94600i	−0.0542189	+	0.166868i
$137$	−9.28812	−	6.74821i	−0.793537	−	0.576539i	0.115474	−	0.993311i	$-0.463161\pi$
$137$	−9.28812	−	6.74821i	−0.793537	−	0.576539i	−0.909011	+	0.416772i	$0.863161\pi$
$138$	−2.19549	−	1.59512i	−0.186893	−	0.135786i
$139$	−1.50279	+	4.62511i	−0.127465	+	0.392296i	−0.994342	−	0.106225i	$-0.966124\pi$
$139$	−1.50279	+	4.62511i	−0.127465	+	0.392296i	0.866877	+	0.498522i	$0.166124\pi$
$140$	−0.309017	−	0.951057i	−0.0261167	−	0.0803789i
$141$	2.00648	−	1.45779i	0.168976	−	0.122768i
$142$	7.80795			0.655229
$143$	0.791032	−	5.44381i	0.0661494	−	0.455234i
$144$	−2.70476			−0.225396
$145$	−5.77340	+	4.19462i	−0.479455	+	0.348345i
$146$	3.36971	+	10.3709i	0.278879	+	0.858301i
$147$	0.167908	−	0.516768i	0.0138488	−	0.0426223i
$148$	−7.39144	−	5.37019i	−0.607572	−	0.441427i
$149$	−6.15582	−	4.47247i	−0.504304	−	0.366399i	0.306354	−	0.951918i	$-0.400891\pi$
$149$	−6.15582	−	4.47247i	−0.504304	−	0.366399i	−0.810659	+	0.585519i	$0.800891\pi$
$150$	−0.167908	+	0.516768i	−0.0137096	+	0.0421939i
$151$	3.35717	+	10.3323i	0.273202	+	0.840831i	0.989689	+	0.143230i	$0.0457489\pi$
$151$	3.35717	+	10.3323i	0.273202	+	0.840831i	−0.716487	+	0.697601i	$0.754251\pi$
$152$	2.99721	−	2.17760i	0.243106	−	0.176627i
$153$	−5.53434			−0.447425
$154$	2.97414	+	1.46782i	0.239663	+	0.118281i
$155$	−10.1809			−0.817749
$156$	0.729106	−	0.529726i	0.0583752	−	0.0424121i
$157$	2.99070	+	9.20443i	0.238684	+	0.734593i	0.996611	+	0.0822545i	$0.0262120\pi$
$157$	2.99070	+	9.20443i	0.238684	+	0.734593i	−0.757928	+	0.652339i	$0.773788\pi$
$158$	−3.46266	+	10.6570i	−0.275475	+	0.847824i
$159$	−3.90470	−	2.83693i	−0.309663	−	0.224983i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	1.54336	−	4.74998i	0.121634	−	0.374351i
$162$	−1.98698	−	6.11528i	−0.156112	−	0.480462i
$163$	−13.1932	+	9.58539i	−1.03337	+	0.750786i	−0.968980	−	0.247139i	$-0.920509\pi$
$163$	−13.1932	+	9.58539i	−1.03337	+	0.750786i	−0.0643878	+	0.997925i	$0.520509\pi$
$164$	5.04615			0.394038
$165$	−0.838604	−	1.59512i	−0.0652852	−	0.124180i
$166$	−4.07812			−0.316523
$167$	7.68041	−	5.58014i	0.594328	−	0.431805i	−0.249533	−	0.968366i	$-0.580277\pi$
$167$	7.68041	−	5.58014i	0.594328	−	0.431805i	0.843861	+	0.536562i	$0.180277\pi$
$168$	0.167908	+	0.516768i	0.0129544	+	0.0398695i
$169$	−3.16712	+	9.74740i	−0.243625	+	0.749800i
$170$	1.65537	+	1.20270i	0.126961	+	0.0922426i
$171$	8.10673	+	5.88989i	0.619937	+	0.450411i
$172$	1.78824	−	5.50365i	0.136352	−	0.419649i
$173$	0.445036	+	1.36968i	0.0338355	+	0.104135i	0.966548	−	0.256486i	$-0.0825648\pi$
$173$	0.445036	+	1.36968i	0.0338355	+	0.104135i	−0.932712	+	0.360621i	$0.882565\pi$
$174$	3.13705	−	2.27920i	0.237819	−	0.172786i
$175$	−1.00000			−0.0755929
$176$	−3.26889	+	0.560659i	−0.246402	+	0.0422613i
$177$	−7.65303			−0.575237
$178$	−2.69143	+	1.95544i	−0.201731	+	0.146566i
$179$	−2.94446	−	9.06211i	−0.220079	−	0.677334i	−0.998754	−	0.0499061i	$-0.984108\pi$
$179$	−2.94446	−	9.06211i	−0.220079	−	0.677334i	0.778675	−	0.627428i	$-0.215892\pi$
$180$	−0.835816	+	2.57238i	−0.0622981	+	0.191734i
$181$	9.33857	+	6.78487i	0.694130	+	0.504315i	0.878015	−	0.478633i	$-0.158867\pi$
$181$	9.33857	+	6.78487i	0.694130	+	0.504315i	−0.183885	+	0.982948i	$0.558867\pi$
$182$	1.34184	+	0.974905i	0.0994639	+	0.0722648i
$183$	−0.554964	+	1.70800i	−0.0410241	+	0.126259i
$184$	1.54336	+	4.74998i	0.113778	+	0.350173i
$185$	−7.39144	+	5.37019i	−0.543429	+	0.394825i
$186$	5.53191			0.405619
$187$	−6.68865	+	1.14719i	−0.489122	+	0.0838910i
$188$	−4.56444			−0.332896
$189$	−2.50775	+	1.82199i	−0.182412	+	0.132530i
$190$	−1.14483	−	3.52343i	−0.0830549	−	0.255617i
$191$	7.98857	−	24.5863i	0.578033	−	1.77900i	−0.0475797	−	0.998867i	$-0.515151\pi$
$191$	7.98857	−	24.5863i	0.578033	−	1.77900i	0.625612	−	0.780134i	$-0.284849\pi$
$192$	−0.439589	−	0.319380i	−0.0317246	−	0.0230493i
$193$	−20.7342	−	15.0643i	−1.49248	−	1.08435i	−0.973259	−	0.229708i	$-0.926223\pi$
$193$	−20.7342	−	15.0643i	−1.49248	−	1.08435i	−0.519219	−	0.854641i	$-0.673777\pi$
$194$	−2.84184	+	8.74629i	−0.204032	+	0.627947i
$195$	−0.278494	−	0.857115i	−0.0199433	−	0.0613793i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	10.5223			0.749682			0.374841	−	0.927089i	$-0.377697\pi$
$197$	10.5223			0.749682			0.374841	+	0.927089i	$0.377697\pi$
$198$	−4.17442	−	7.94022i	−0.296663	−	0.564287i
$199$	18.3423			1.30025			0.650125	−	0.759827i	$-0.274716\pi$
$199$	18.3423			1.30025			0.650125	+	0.759827i	$0.274716\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	−0.535613	−	1.64845i	−0.0377792	−	0.116273i
$202$	−0.844630	+	2.59950i	−0.0594280	+	0.182900i
$203$	5.77340	+	4.19462i	0.405214	+	0.294405i
$204$	−0.899465	−	0.653500i	−0.0629751	−	0.0457541i
$205$	1.55935	−	4.79917i	0.108909	−	0.335189i
$206$	0.478162	+	1.47163i	0.0333151	+	0.102533i
$207$	−10.9288	+	7.94022i	−0.759602	+	0.551883i
$208$	−1.65861			−0.115004
$209$	11.0185	+	5.43793i	0.762163	+	0.376150i
$210$	0.543362			0.0374955
$211$	19.1174	−	13.8896i	1.31610	−	0.956201i	0.316125	−	0.948717i	$-0.397618\pi$
$211$	19.1174	−	13.8896i	1.31610	−	0.956201i	0.999972	−	0.00748332i	$-0.00238204\pi$
$212$	2.74488	+	8.44788i	0.188519	+	0.580203i
$213$	−1.31102	+	4.03490i	−0.0898295	+	0.276467i
$214$	9.87718	+	7.17619i	0.675190	+	0.490554i
$215$	−4.68168	−	3.40144i	−0.319288	−	0.231976i
$216$	0.957875	−	2.94804i	0.0651751	−	0.200588i
$217$	3.14607	+	9.68261i	0.213569	+	0.657298i
$218$	−1.07095	+	0.778089i	−0.0725337	+	0.0526988i
$219$	−5.92514			−0.400384
$220$	−0.476925	+	3.28216i	−0.0321543	+	0.221283i
$221$	−3.39376			−0.228289
$222$	4.01623	−	2.91796i	0.269551	−	0.195841i
$223$	0.855524	+	2.63303i	0.0572902	+	0.176321i	0.975607	−	0.219526i	$-0.0704511\pi$
$223$	0.855524	+	2.63303i	0.0572902	+	0.176321i	−0.918316	+	0.395847i	$0.870451\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	2.18820	+	1.58982i	0.145880	+	0.105988i
$226$	2.79799	+	2.03286i	0.186120	+	0.135224i
$227$	0.492251	−	1.51499i	0.0326719	−	0.100554i	−0.933391	−	0.358862i	$-0.883165\pi$
$227$	0.492251	−	1.51499i	0.0326719	−	0.100554i	0.966063	+	0.258308i	$0.0831650\pi$
$228$	0.622059	+	1.91450i	0.0411968	+	0.126791i
$229$	−19.0723	+	13.8568i	−1.26033	+	0.915685i	−0.998774	−	0.0495021i	$-0.984237\pi$
$229$	−19.0723	+	13.8568i	−1.26033	+	0.915685i	−0.261559	+	0.965188i	$0.584237\pi$
$230$	4.99442			0.329323
$231$	−1.25791	+	1.29048i	−0.0827641	+	0.0849073i
$232$	−7.13632			−0.468522
$233$	−3.01147	+	2.18796i	−0.197288	+	0.143338i	−0.682044	−	0.731311i	$-0.738909\pi$
$233$	−3.01147	+	2.18796i	−0.197288	+	0.143338i	0.484755	+	0.874650i	$0.338909\pi$
$234$	−1.38629	−	4.26657i	−0.0906247	−	0.278914i
$235$	−1.41049	+	4.34104i	−0.0920101	+	0.283178i
$236$	11.3947	+	8.27872i	0.741730	+	0.538899i
$237$	−4.92578	−	3.57879i	−0.319964	−	0.232467i
$238$	0.632295	−	1.94600i	0.0409856	−	0.126141i
$239$	4.63796	+	14.2742i	0.300005	+	0.923320i	0.981494	+	0.191492i	$0.0613326\pi$
$239$	4.63796	+	14.2742i	0.300005	+	0.923320i	−0.681489	+	0.731828i	$0.738667\pi$
$240$	−0.439589	+	0.319380i	−0.0283753	+	0.0206159i
$241$	23.4709			1.51189			0.755947	−	0.654633i	$-0.227177\pi$
$241$	23.4709			1.51189			0.755947	+	0.654633i	$0.227177\pi$
$242$	−6.69098	−	8.73102i	−0.430113	−	0.561251i
$243$	12.7931			0.820675
$244$	2.67393	−	1.94273i	0.171181	−	0.124370i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	−0.847289	+	2.60769i	−0.0540212	+	0.166260i
$247$	4.97120	+	3.61179i	0.316310	+	0.229813i
$248$	−8.23652	−	5.98418i	−0.523019	−	0.379996i
$249$	0.684749	−	2.10744i	0.0433942	−	0.133554i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−19.3116	+	14.0307i	−1.21894	+	0.885612i	−0.996012	−	0.0892232i	$-0.971562\pi$
$251$	−19.3116	+	14.0307i	−1.21894	+	0.885612i	−0.222928	+	0.974835i	$0.571562\pi$
$252$	2.70476			0.170384
$253$	−11.5623	+	11.8617i	−0.726916	+	0.745739i
$254$	18.2239			1.14347
$255$	−0.899465	+	0.653500i	−0.0563267	+	0.0409237i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	0.970112	−	2.98570i	0.0605139	−	0.186243i	−0.916230	−	0.400654i	$-0.868783\pi$
$257$	0.970112	−	2.98570i	0.0605139	−	0.186243i	0.976744	+	0.214411i	$0.0687831\pi$
$258$	2.54385	+	1.84821i	0.158373	+	0.115065i
$259$	7.39144	+	5.37019i	0.459282	+	0.333688i
$260$	−0.512538	+	1.57743i	−0.0317863	+	0.0978280i
$261$	−5.96465	−	18.3573i	−0.369203	−	1.13629i
$262$	−7.66140	+	5.56633i	−0.473323	+	0.343889i
$263$	18.0997			1.11608			0.558039	−	0.829815i	$-0.311554\pi$
$263$	18.0997			1.11608			0.558039	+	0.829815i	$0.311554\pi$
$264$	0.259143	−	1.78340i	0.0159491	−	0.109761i
$265$	8.88262			0.545655
$266$	−2.99721	+	2.17760i	−0.183771	+	0.133517i
$267$	−0.558596	−	1.71918i	−0.0341855	−	0.105212i
$268$	−0.985739	+	3.03379i	−0.0602136	+	0.185318i
$269$	4.57718	+	3.32552i	0.279076	+	0.202760i	0.718514	−	0.695512i	$-0.244823\pi$
$269$	4.57718	+	3.32552i	0.279076	+	0.202760i	−0.439438	+	0.898273i	$0.644823\pi$
$270$	−2.50775	−	1.82199i	−0.152617	−	0.110883i
$271$	9.82018	−	30.2234i	0.596533	−	1.83594i	0.0495917	−	0.998770i	$-0.484208\pi$
$271$	9.82018	−	30.2234i	0.596533	−	1.83594i	0.546942	−	0.837171i	$-0.315792\pi$
$272$	0.632295	+	1.94600i	0.0383385	+	0.117994i
$273$	−0.729106	+	0.529726i	−0.0441275	+	0.0320605i
$274$	−11.4807			−0.693577
$275$	2.97414	+	1.46782i	0.179347	+	0.0885131i
$276$	−2.71378			−0.163350
$277$	1.94713	−	1.41467i	0.116992	−	0.0849994i	−0.527751	−	0.849399i	$-0.676965\pi$
$277$	1.94713	−	1.41467i	0.116992	−	0.0849994i	0.644743	+	0.764400i	$0.276965\pi$
$278$	1.50279	+	4.62511i	0.0901312	+	0.277395i
$279$	8.50936	−	26.1891i	0.509442	−	1.56790i
$280$	−0.809017	−	0.587785i	−0.0483480	−	0.0351269i
$281$	−9.07942	−	6.59659i	−0.541633	−	0.393519i	0.283058	−	0.959103i	$-0.408651\pi$
$281$	−9.07942	−	6.59659i	−0.541633	−	0.393519i	−0.824691	+	0.565583i	$0.808651\pi$
$282$	0.766406	−	2.35875i	0.0456388	−	0.140462i
$283$	9.65861	+	29.7261i	0.574145	+	1.76704i	0.639074	+	0.769146i	$0.279318\pi$
$283$	9.65861	+	29.7261i	0.574145	+	1.76704i	−0.0649289	+	0.997890i	$0.520682\pi$
$284$	6.31677	−	4.58940i	0.374831	−	0.272331i
$285$	2.01302			0.119241
$286$	−2.55983	−	4.86909i	−0.151366	−	0.287915i
$287$	−5.04615			−0.297865
$288$	−2.18820	+	1.58982i	−0.128941	+	0.0936809i
$289$	−3.95952	−	12.1861i	−0.232913	−	0.716832i
$290$	−2.20524	+	6.78704i	−0.129496	+	0.398549i
$291$	−4.04263	−	2.93715i	−0.236983	−	0.172179i
$292$	8.82201	+	6.40956i	0.516269	+	0.375091i
$293$	0.702178	−	2.16108i	0.0410217	−	0.126252i	−0.928448	−	0.371461i	$-0.878857\pi$
$293$	0.702178	−	2.16108i	0.0410217	−	0.126252i	0.969470	+	0.245210i	$0.0788568\pi$
$294$	−0.167908	−	0.516768i	−0.00979260	−	0.0301385i
$295$	11.3947	−	8.27872i	0.663424	−	0.482006i
$296$	−9.13632			−0.531038
$297$	10.1327	−	1.73790i	0.587962	−	0.100843i
$298$	−7.60901			−0.440778
$299$	−6.70173	+	4.86909i	−0.387571	+	0.281587i
$300$	0.167908	+	0.516768i	0.00969418	+	0.0298356i
$301$	−1.78824	+	5.50365i	−0.103073	+	0.317225i
$302$	8.78918	+	6.38571i	0.505760	+	0.367456i
$303$	−1.20152	−	0.872955i	−0.0690255	−	0.0501500i
$304$	1.14483	−	3.52343i	0.0656607	−	0.202083i
$305$	−1.02135	−	3.14340i	−0.0584824	−	0.179990i
$306$	−4.47738	+	3.25300i	−0.255954	+	0.185962i
$307$	5.55583			0.317088			0.158544	−	0.987352i	$-0.449320\pi$
$307$	5.55583			0.317088			0.158544	+	0.987352i	$0.449320\pi$
$308$	3.26889	−	0.560659i	0.186262	−	0.0319465i
$309$	−0.840779			−0.0478302
$310$	−8.23652	+	5.98418i	−0.467803	+	0.339879i
$311$	−6.28682	−	19.3488i	−0.356493	−	1.09717i	−0.955139	−	0.296159i	$-0.904294\pi$
$311$	−6.28682	−	19.3488i	−0.356493	−	1.09717i	0.598646	−	0.801014i	$-0.295706\pi$
$312$	0.278494	−	0.857115i	0.0157666	−	0.0485246i
$313$	−22.7254	−	16.5109i	−1.28451	−	0.933254i	−0.284834	−	0.958577i	$-0.591939\pi$
$313$	−22.7254	−	16.5109i	−1.28451	−	0.933254i	−0.999679	+	0.0253230i	$0.991939\pi$
$314$	7.82975	+	5.68865i	0.441859	+	0.321029i
$315$	0.835816	−	2.57238i	0.0470929	−	0.144937i
$316$	3.46266	+	10.6570i	0.194790	+	0.599502i
$317$	−6.16185	+	4.47684i	−0.346084	+	0.251445i	−0.747224	−	0.664572i	$-0.768614\pi$
$317$	−6.16185	+	4.47684i	−0.346084	+	0.251445i	0.401141	+	0.916017i	$0.368614\pi$
$318$	−4.82648			−0.270656
$319$	−11.0139	−	20.9497i	−0.616661	−	1.17296i
$320$	1.00000			0.0559017
$321$	−5.36688	+	3.89927i	−0.299550	+	0.217636i
$322$	−1.54336	−	4.74998i	−0.0860082	−	0.264706i
$323$	2.34250	−	7.20947i	0.130340	−	0.401146i
$324$	−5.20197	−	3.77945i	−0.288998	−	0.209970i
$325$	1.34184	+	0.974905i	0.0744320	+	0.0540780i
$326$	−5.03934	+	15.5095i	−0.279103	+	0.858991i
$327$	−0.222271	−	0.684079i	−0.0122916	−	0.0378297i
$328$	4.08242	−	2.96605i	0.225414	−	0.163773i
$329$	4.56444			0.251645
$330$	−1.61603	−	0.797560i	−0.0889597	−	0.0439042i
$331$	9.86518			0.542239			0.271120	−	0.962546i	$-0.412606\pi$
$331$	9.86518			0.542239			0.271120	+	0.962546i	$0.412606\pi$
$332$	−3.29927	+	2.39706i	−0.181071	+	0.131556i
$333$	−7.63628	−	23.5021i	−0.418466	−	1.28791i
$334$	2.93366	−	9.02886i	0.160522	−	0.494037i
$335$	2.58070	+	1.87499i	0.140999	+	0.102441i
$336$	0.439589	+	0.319380i	0.0239815	+	0.0174236i
$337$	−7.07406	+	21.7717i	−0.385348	+	1.18598i	0.550879	+	0.834585i	$0.314293\pi$
$337$	−7.07406	+	21.7717i	−0.385348	+	1.18598i	−0.936227	+	0.351395i	$0.885707\pi$
$338$	3.16712	+	9.74740i	0.172269	+	0.530188i
$339$	−1.52032	+	1.10458i	−0.0825726	+	0.0599925i
$340$	2.04615			0.110968
$341$	4.85552	−	33.4153i	0.262941	−	1.80954i
$342$	10.0205			0.541845
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−1.78824	−	5.50365i	−0.0964156	−	0.296737i
$345$	−0.838604	+	2.58096i	−0.0451489	+	0.138954i
$346$	1.16512	+	0.846509i	0.0626372	+	0.0455086i
$347$	6.53455	+	4.74763i	0.350793	+	0.254866i	0.749202	−	0.662342i	$-0.230437\pi$
$347$	6.53455	+	4.74763i	0.350793	+	0.254866i	−0.398409	+	0.917208i	$0.630437\pi$
$348$	1.19825	−	3.68782i	0.0642327	−	0.197688i
$349$	5.05607	+	15.5610i	0.270645	+	0.832961i	0.990339	+	0.138669i	$0.0442823\pi$
$349$	5.05607	+	15.5610i	0.270645	+	0.832961i	−0.719694	+	0.694292i	$0.755718\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	5.14127			0.274421
$352$	−2.31504	+	2.37499i	−0.123392	+	0.126587i
$353$	−18.5642			−0.988072			−0.494036	−	0.869442i	$-0.664479\pi$
$353$	−18.5642			−0.988072			−0.494036	+	0.869442i	$0.664479\pi$
$354$	−6.19143	+	4.49834i	−0.329071	+	0.239084i
$355$	−2.41279	−	7.42580i	−0.128058	−	0.394121i
$356$	−1.02804	+	3.16397i	−0.0544858	+	0.167690i
$357$	0.899465	+	0.653500i	0.0476047	+	0.0345869i
$358$	−7.70869	−	5.60069i	−0.407417	−	0.296006i
$359$	1.41854	−	4.36581i	0.0748676	−	0.230419i	−0.906619	−	0.421951i	$-0.861346\pi$
$359$	1.41854	−	4.36581i	0.0748676	−	0.230419i	0.981486	+	0.191532i	$0.0613456\pi$
$360$	0.835816	+	2.57238i	0.0440514	+	0.135576i
$361$	4.26738	−	3.10043i	0.224599	−	0.163181i
$362$	11.5431			0.606692
$363$	5.63538	−	1.99168i	0.295781	−	0.104536i
$364$	1.65861			0.0869347
$365$	8.82201	−	6.40956i	0.461765	−	0.335492i
$366$	0.554964	+	1.70800i	0.0290084	+	0.0892787i
$367$	3.94597	−	12.1445i	0.205978	−	0.633935i	−0.793694	−	0.608318i	$-0.791845\pi$
$367$	3.94597	−	12.1445i	0.205978	−	0.633935i	0.999672	−	0.0256178i	$-0.00815529\pi$
$368$	4.04057	+	2.93565i	0.210629	+	0.153031i
$369$	11.0420	+	8.02245i	0.574821	+	0.417632i
$370$	−2.82328	+	8.68916i	−0.146775	+	0.451728i
$371$	−2.74488	−	8.44788i	−0.142507	−	0.438592i
$372$	4.47541	−	3.25158i	0.232039	−	0.168586i
$373$	−22.4340			−1.16159			−0.580795	−	0.814050i	$-0.697258\pi$
$373$	−22.4340			−1.16159			−0.580795	+	0.814050i	$0.697258\pi$
$374$	−4.73692	+	4.85959i	−0.244941	+	0.251283i
$375$	0.543362			0.0280591
$376$	−3.69271	+	2.68291i	−0.190437	+	0.138360i
$377$	−3.65764	−	11.2570i	−0.188378	−	0.579767i
$378$	−0.957875	+	2.94804i	−0.0492678	+	0.151631i
$379$	24.3795	+	17.7127i	1.25229	+	0.909841i	0.998352	−	0.0573798i	$-0.0182746\pi$
$379$	24.3795	+	17.7127i	1.25229	+	0.909841i	0.253936	+	0.967221i	$0.418275\pi$
$380$	−2.99721	−	2.17760i	−0.153754	−	0.111709i
$381$	−3.05995	+	9.41755i	−0.156766	+	0.482476i
$382$	−7.98857	−	24.5863i	−0.408731	−	1.25794i
$383$	−22.6164	+	16.4317i	−1.15564	+	0.839623i	−0.989221	−	0.146432i	$-0.953221\pi$
$383$	−22.6164	+	16.4317i	−1.15564	+	0.839623i	−0.166421	+	0.986055i	$0.553221\pi$
$384$	−0.543362			−0.0277283
$385$	0.476925	−	3.28216i	0.0243064	−	0.167274i
$386$	−25.6289			−1.30447
$387$	12.6628	−	9.20008i	0.643687	−	0.467666i
$388$	2.84184	+	8.74629i	0.144273	+	0.444026i
$389$	1.41421	−	4.35250i	0.0717034	−	0.220680i	−0.908782	−	0.417270i	$-0.862987\pi$
$389$	1.41421	−	4.35250i	0.0717034	−	0.220680i	0.980486	+	0.196590i	$0.0629868\pi$
$390$	−0.729106	−	0.529726i	−0.0369197	−	0.0268237i
$391$	8.26762	+	6.00678i	0.418112	+	0.303776i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	−1.59009	−	4.89380i	−0.0802095	−	0.246859i
$394$	8.51271	−	6.18485i	0.428864	−	0.311588i
$395$	11.2054			0.563806
$396$	−8.04432	−	3.97011i	−0.404242	−	0.199506i
$397$	−37.9390			−1.90411			−0.952053	−	0.305933i	$-0.901032\pi$
$397$	−37.9390			−1.90411			−0.952053	+	0.305933i	$0.901032\pi$
$398$	14.8392	−	10.7813i	0.743823	−	0.540419i
$399$	−0.622059	−	1.91450i	−0.0311419	−	0.0958449i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−12.9085	−	9.37854i	−0.644617	−	0.468342i	0.216816	−	0.976212i	$-0.430433\pi$
$401$	−12.9085	−	9.37854i	−0.644617	−	0.468342i	−0.861433	+	0.507871i	$0.830433\pi$
$402$	−1.40225	−	1.01880i	−0.0699380	−	0.0508129i
$403$	5.21810	−	16.0596i	0.259932	−	0.799988i
$404$	0.844630	+	2.59950i	0.0420219	+	0.129330i
$405$	−5.20197	+	3.77945i	−0.258488	+	0.187802i
$406$	7.13632			0.354170
$407$	−14.1006	−	26.8210i	−0.698943	−	1.32947i
$408$	−1.11180			−0.0550423
$409$	19.6335	−	14.2646i	0.970816	−	0.705339i	0.0151783	−	0.999885i	$-0.495168\pi$
$409$	19.6335	−	14.2646i	0.970816	−	0.705339i	0.955637	+	0.294546i	$0.0951684\pi$
$410$	−1.55935	−	4.79917i	−0.0770106	−	0.237014i
$411$	1.92771	−	5.93288i	0.0950869	−	0.292647i
$412$	1.25184	+	0.909518i	0.0616739	+	0.0448087i
$413$	−11.3947	−	8.27872i	−0.560695	−	0.407369i
$414$	−4.17442	+	12.8475i	−0.205162	+	0.631422i
$415$	1.26021	+	3.87852i	0.0618612	+	0.190389i
$416$	−1.34184	+	0.974905i	−0.0657892	+	0.0477987i
$417$	−2.64244			−0.129401
$418$	12.1105	−	2.07711i	0.592342	−	0.101595i
$419$	−25.6838			−1.25473			−0.627367	−	0.778724i	$-0.715867\pi$
$419$	−25.6838			−1.25473			−0.627367	+	0.778724i	$0.715867\pi$
$420$	0.439589	−	0.319380i	0.0214497	−	0.0155842i
$421$	−2.89352	−	8.90533i	−0.141021	−	0.434019i	0.855456	−	0.517875i	$-0.173277\pi$
$421$	−2.89352	−	8.90533i	−0.141021	−	0.434019i	−0.996478	+	0.0838553i	$0.973277\pi$
$422$	7.30220	−	22.4739i	0.355466	−	1.09401i
$423$	−9.98788	−	7.25662i	−0.485627	−	0.352829i
$424$	7.18619	+	5.22108i	0.348992	+	0.253558i
$425$	0.632295	−	1.94600i	0.0306708	−	0.0943951i
$426$	1.31102	+	4.03490i	0.0635190	+	0.195491i
$427$	−2.67393	+	1.94273i	−0.129401	+	0.0940151i
$428$	12.2089			0.590138
$429$	2.94601	−	0.505280i	0.142235	−	0.0243951i
$430$	−5.78688			−0.279068
$431$	−13.7453	+	9.98657i	−0.662089	+	0.481036i	−0.867368	−	0.497668i	$-0.834190\pi$
$431$	−13.7453	+	9.98657i	−0.662089	+	0.481036i	0.205279	+	0.978704i	$0.434190\pi$
$432$	−0.957875	−	2.94804i	−0.0460858	−	0.141837i
$433$	2.07246	−	6.37838i	0.0995962	−	0.306526i	−0.888828	−	0.458241i	$-0.848480\pi$
$433$	2.07246	−	6.37838i	0.0995962	−	0.306526i	0.988424	+	0.151715i	$0.0484797\pi$
$434$	8.23652	+	5.98418i	0.395366	+	0.287250i
$435$	−3.13705	−	2.27920i	−0.150410	−	0.109279i
$436$	−0.409066	+	1.25897i	−0.0195907	+	0.0602940i
$437$	−5.71778	−	17.5975i	−0.273519	−	0.841804i
$438$	−4.79354	+	3.48271i	−0.229044	+	0.166410i
$439$	12.8474			0.613171			0.306586	−	0.951843i	$-0.400813\pi$
$439$	12.8474			0.613171			0.306586	+	0.951843i	$0.400813\pi$
$440$	1.54336	+	2.93565i	0.0735769	+	0.139952i
$441$	−2.70476			−0.128798
$442$	−2.74561	+	1.99480i	−0.130595	+	0.0948831i
$443$	0.209626	+	0.645164i	0.00995965	+	0.0306527i	0.955913	−	0.293651i	$-0.0948702\pi$
$443$	0.209626	+	0.645164i	0.00995965	+	0.0306527i	−0.945953	+	0.324303i	$0.894870\pi$
$444$	1.53406	−	4.72136i	0.0728034	−	0.224066i
$445$	2.69143	+	1.95544i	0.127586	+	0.0926968i
$446$	2.23979	+	1.62730i	0.106057	+	0.0770551i
$447$	1.27761	−	3.93209i	0.0604291	−	0.185982i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	−6.14468	+	4.46437i	−0.289986	+	0.210687i	−0.723261	−	0.690575i	$-0.757358\pi$
$449$	−6.14468	+	4.46437i	−0.289986	+	0.210687i	0.433276	+	0.901261i	$0.357358\pi$
$450$	2.70476			0.127504
$451$	15.0079	+	7.40686i	0.706696	+	0.348776i
$452$	3.45851			0.162675
$453$	−4.77571	+	3.46975i	−0.224382	+	0.163023i
$454$	−0.492251	−	1.51499i	−0.0231025	−	0.0711021i
$455$	0.512538	−	1.57743i	0.0240282	−	0.0739511i
$456$	1.62857	+	1.18323i	0.0762648	+	0.0554096i
$457$	26.7382	+	19.4264i	1.25076	+	0.908731i	0.998266	−	0.0588676i	$-0.0187490\pi$
$457$	26.7382	+	19.4264i	1.25076	+	0.908731i	0.252495	+	0.967598i	$0.418749\pi$
$458$	−7.28497	+	22.4208i	−0.340404	+	1.04766i
$459$	−1.95996	−	6.03212i	−0.0914829	−	0.281555i
$460$	4.04057	−	2.93565i	0.188393	−	0.136875i
$461$	20.2500			0.943136			0.471568	−	0.881830i	$-0.343688\pi$
$461$	20.2500			0.943136			0.471568	+	0.881830i	$0.343688\pi$
$462$	−0.259143	+	1.78340i	−0.0120564	+	0.0829712i
$463$	39.3213			1.82742			0.913708	−	0.406371i	$-0.133206\pi$
$463$	39.3213			1.82742			0.913708	+	0.406371i	$0.133206\pi$
$464$	−5.77340	+	4.19462i	−0.268024	+	0.194731i
$465$	−1.70945	−	5.26116i	−0.0792741	−	0.243980i
$466$	−1.15028	+	3.54020i	−0.0532857	+	0.163997i
$467$	15.2230	+	11.0602i	0.704438	+	0.511804i	0.881375	−	0.472418i	$-0.156619\pi$
$467$	15.2230	+	11.0602i	0.704438	+	0.511804i	−0.176936	+	0.984222i	$0.556619\pi$
$468$	−3.62936	−	2.63688i	−0.167767	−	0.121890i
$469$	0.985739	−	3.03379i	0.0455172	−	0.140088i
$470$	1.41049	+	4.34104i	0.0650610	+	0.200237i
$471$	−4.25439	+	3.09100i	−0.196032	+	0.142426i
$472$	14.0846			0.648296
$473$	13.3969	−	13.7438i	0.615989	−	0.631940i
$474$	−6.08860			−0.279658
$475$	−2.99721	+	2.17760i	−0.137522	+	0.0999152i
$476$	−0.632295	−	1.94600i	−0.0289812	−	0.0891950i
$477$	−7.42424	+	22.8495i	−0.339933	+	1.04621i
$478$	12.1423	+	8.82193i	0.555378	+	0.403506i
$479$	6.12127	+	4.44736i	0.279688	+	0.203205i	0.718781	−	0.695236i	$-0.244700\pi$
$479$	6.12127	+	4.44736i	0.279688	+	0.203205i	−0.439093	+	0.898441i	$0.644700\pi$
$480$	−0.167908	+	0.516768i	−0.00766392	+	0.0235871i
$481$	−4.68271	−	14.4119i	−0.213513	−	0.657126i
$482$	18.9884	−	13.7959i	0.864896	−	0.628384i
$483$	2.71378			0.123481
$484$	−10.5451	−	3.13068i	−0.479322	−	0.142304i
$485$	9.19639			0.417587
$486$	10.3498	−	7.51957i	0.469476	−	0.341095i
$487$	2.44850	+	7.53569i	0.110952	+	0.341475i	0.991081	−	0.133259i	$-0.0425443\pi$
$487$	2.44850	+	7.53569i	0.110952	+	0.341475i	−0.880129	+	0.474734i	$0.842544\pi$
$488$	1.02135	−	3.14340i	0.0462344	−	0.142295i
$489$	−7.16866	−	5.20834i	−0.324178	−	0.235529i
$490$	0.809017	+	0.587785i	0.0365477	+	0.0265534i
$491$	−4.66927	+	14.3705i	−0.210721	+	0.648534i	0.788708	+	0.614767i	$0.210750\pi$
$491$	−4.66927	+	14.3705i	−0.210721	+	0.648534i	−0.999430	+	0.0337662i	$0.989250\pi$
$492$	0.847289	+	2.60769i	0.0381988	+	0.117564i
$493$	−11.8132	+	8.58283i	−0.532042	+	0.386551i
$494$	6.14474			0.276465
$495$	−6.26163	+	6.42377i	−0.281439	+	0.288727i
$496$	−10.1809			−0.457136
$497$	−6.31677	+	4.58940i	−0.283346	+	0.205863i
$498$	−0.684749	−	2.10744i	−0.0306843	−	0.0944367i
$499$	−1.84344	+	5.67351i	−0.0825235	+	0.253981i	−0.983802	−	0.179259i	$-0.942630\pi$
$499$	−1.84344	+	5.67351i	−0.0825235	+	0.253981i	0.901278	+	0.433241i	$0.142630\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	4.17324	+	3.03204i	0.186447	+	0.135461i
$502$	−7.37639	+	22.7022i	−0.329224	+	1.01325i
$503$	−7.88663	−	24.2725i	−0.351647	−	1.08226i	−0.957928	−	0.287008i	$-0.907339\pi$
$503$	−7.88663	−	24.2725i	−0.351647	−	1.08226i	0.606281	−	0.795251i	$-0.292661\pi$
$504$	2.18820	−	1.58982i	0.0974700	−	0.0708161i
$505$	2.73328			0.121629
$506$	−2.38197	+	16.3925i	−0.105891	+	0.728734i
$507$	−5.56893			−0.247325
$508$	14.7435	−	10.7118i	0.654136	−	0.475258i
$509$	−8.57950	−	26.4050i	−0.380280	−	1.17038i	−0.939847	−	0.341596i	$-0.889033\pi$
$509$	−8.57950	−	26.4050i	−0.380280	−	1.17038i	0.559567	−	0.828785i	$-0.310967\pi$
$510$	−0.343565	+	1.05738i	−0.0152133	+	0.0468218i
$511$	−8.82201	−	6.40956i	−0.390263	−	0.283542i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−3.54869	+	10.9218i	−0.156679	+	0.482207i
$514$	−0.970112	−	2.98570i	−0.0427898	−	0.131694i
$515$	1.25184	−	0.909518i	0.0551628	−	0.0400781i
$516$	3.14437			0.138423
$517$	−13.5753	−	6.69979i	−0.597039	−	0.294656i
$518$	9.13632			0.401427
$519$	−0.633082	+	0.459961i	−0.0277892	+	0.0201900i
$520$	0.512538	+	1.57743i	0.0224763	+	0.0691749i
$521$	7.37620	−	22.7016i	0.323157	−	0.994576i	−0.649108	−	0.760696i	$-0.724858\pi$
$521$	7.37620	−	22.7016i	0.323157	−	0.994576i	0.972265	−	0.233880i	$-0.0751423\pi$
$522$	−15.6157	−	11.3454i	−0.683479	−	0.496576i
$523$	−1.93184	−	1.40356i	−0.0844735	−	0.0613736i	0.544747	−	0.838600i	$-0.316626\pi$
$523$	−1.93184	−	1.40356i	−0.0844735	−	0.0613736i	−0.629220	+	0.777227i	$0.716626\pi$
$524$	−2.92639	+	9.00651i	−0.127840	+	0.393451i
$525$	−0.167908	−	0.516768i	−0.00732811	−	0.0225536i
$526$	14.6430	−	10.6388i	0.638465	−	0.463872i
$527$	−20.8316			−0.907440
$528$	−0.838604	−	1.59512i	−0.0364956	−	0.0694187i
$529$	1.94427			0.0845336
$530$	7.18619	−	5.22108i	0.312148	−	0.226789i
$531$	11.7721	+	36.2309i	0.510867	+	1.57229i
$532$	−1.14483	+	3.52343i	−0.0496348	+	0.152760i
$533$	6.77114	+	4.91952i	0.293290	+	0.213088i
$534$	−1.46242	−	1.06251i	−0.0632852	−	0.0459794i
$535$	3.77275	−	11.6113i	0.163110	−	0.502001i
$536$	0.985739	+	3.03379i	0.0425774	+	0.131040i
$537$	4.18861	−	3.04320i	0.180752	−	0.131324i
$538$	5.65771			0.243921
$539$	−3.26889	+	0.560659i	−0.140801	+	0.0241493i
$540$	−3.09975			−0.133392
$541$	−20.1027	+	14.6054i	−0.864281	+	0.627937i	−0.929046	−	0.369963i	$-0.879370\pi$
$541$	−20.1027	+	14.6054i	−0.864281	+	0.627937i	0.0647650	+	0.997901i	$0.479370\pi$
$542$	−9.82018	−	30.2234i	−0.421813	−	1.29821i
$543$	−1.93818	+	5.96511i	−0.0831753	+	0.255987i
$544$	1.65537	+	1.20270i	0.0709734	+	0.0515652i
$545$	1.07095	+	0.778089i	0.0458744	+	0.0333297i
$546$	−0.278494	+	0.857115i	−0.0119184	+	0.0366812i
$547$	10.2440	+	31.5279i	0.438003	+	1.34804i	0.889977	+	0.456005i	$0.150720\pi$
$547$	10.2440	+	31.5279i	0.438003	+	1.34804i	−0.451974	+	0.892031i	$0.649280\pi$
$548$	−9.28812	+	6.74821i	−0.396769	+	0.288269i
$549$	8.93967			0.381536
$550$	3.26889	−	0.560659i	0.139386	−	0.0239066i
$551$	26.4383			1.12631
$552$	−2.19549	+	1.59512i	−0.0934464	+	0.0678928i
$553$	−3.46266	−	10.6570i	−0.147247	−	0.453181i
$554$	0.743737	−	2.28899i	0.0315984	−	0.0972498i
$555$	−4.01623	−	2.91796i	−0.170479	−	0.123860i
$556$	3.93435	+	2.85847i	0.166854	+	0.121226i
$557$	8.66037	−	26.6539i	0.366952	−	1.12936i	−0.581798	−	0.813333i	$-0.697651\pi$
$557$	8.66037	−	26.6539i	0.366952	−	1.12936i	0.948750	−	0.316028i	$-0.102349\pi$
$558$	−8.50936	−	26.1891i	−0.360230	−	1.10867i
$559$	7.76508	−	5.64166i	0.328428	−	0.238617i
$560$	−1.00000			−0.0422577
$561$	−1.71591	−	3.26385i	−0.0724458	−	0.137800i
$562$	−11.2228			−0.473405
$563$	−2.57033	+	1.86746i	−0.108327	+	0.0787039i	−0.640630	−	0.767850i	$-0.721327\pi$
$563$	−2.57033	+	1.86746i	−0.108327	+	0.0787039i	0.532303	+	0.846554i	$0.321327\pi$
$564$	−0.766406	−	2.35875i	−0.0322715	−	0.0993215i
$565$	1.06874	−	3.28924i	0.0449622	−	0.138379i
$566$	25.2866	+	18.3718i	1.06287	+	0.772223i
$567$	5.20197	+	3.77945i	0.218462	+	0.158722i
$568$	2.41279	−	7.42580i	0.101238	−	0.311580i
$569$	5.79599	+	17.8382i	0.242981	+	0.747818i	0.995962	+	0.0897757i	$0.0286150\pi$
$569$	5.79599	+	17.8382i	0.242981	+	0.747818i	−0.752981	+	0.658042i	$0.771385\pi$
$570$	1.62857	−	1.18323i	0.0682133	−	0.0495599i
$571$	−20.5329			−0.859276			−0.429638	−	0.903001i	$-0.641359\pi$
$571$	−20.5329			−0.859276			−0.429638	+	0.903001i	$0.641359\pi$
$572$	−4.93293	−	2.43455i	−0.206256	−	0.101793i
$573$	14.0468			0.586811
$574$	−4.08242	+	2.96605i	−0.170397	+	0.123801i
$575$	−1.54336	−	4.74998i	−0.0643626	−	0.198088i
$576$	−0.835816	+	2.57238i	−0.0348257	+	0.107182i
$577$	−13.5695	−	9.85885i	−0.564908	−	0.410429i	0.268344	−	0.963323i	$-0.413524\pi$
$577$	−13.5695	−	9.85885i	−0.564908	−	0.410429i	−0.833252	+	0.552894i	$0.813524\pi$
$578$	−10.3662	−	7.53145i	−0.431175	−	0.313267i
$579$	4.30329	−	13.2442i	0.178839	−	0.550409i
$580$	2.20524	+	6.78704i	0.0915678	+	0.281817i
$581$	3.29927	−	2.39706i	0.136877	−	0.0994467i
$582$	−4.99697			−0.207131
$583$	−4.23635	+	29.1542i	−0.175452	+	1.20744i
$584$	10.9046			0.451235
$585$	−3.62936	+	2.63688i	−0.150055	+	0.109022i
$586$	−0.702178	−	2.16108i	−0.0290067	−	0.0892735i
$587$	7.74382	−	23.8330i	0.319622	−	0.983694i	−0.654189	−	0.756331i	$-0.726990\pi$
$587$	7.74382	−	23.8330i	0.319622	−	0.983694i	0.973810	−	0.227363i	$-0.0730102\pi$
$588$	−0.439589	−	0.319380i	−0.0181283	−	0.0131710i
$589$	30.5143	+	22.1699i	1.25732	+	0.913496i
$590$	4.35238	−	13.3952i	0.179185	−	0.551474i
$591$	1.76678	+	5.43758i	0.0726755	+	0.223672i
$592$	−7.39144	+	5.37019i	−0.303786	+	0.220714i
$593$	44.2586			1.81748			0.908741	−	0.417360i	$-0.137044\pi$
$593$	44.2586			1.81748			0.908741	+	0.417360i	$0.137044\pi$
$594$	7.17605	−	7.36187i	0.294437	−	0.302061i
$595$	−2.04615			−0.0838840
$596$	−6.15582	+	4.47247i	−0.252152	+	0.183199i
$597$	3.07982	+	9.47871i	0.126049	+	0.387938i
$598$	−2.55983	+	7.87835i	−0.104679	+	0.322170i
$599$	−1.93463	−	1.40559i	−0.0790468	−	0.0574308i	0.547560	−	0.836766i	$-0.315557\pi$
$599$	−1.93463	−	1.40559i	−0.0790468	−	0.0574308i	−0.626607	+	0.779336i	$0.715557\pi$
$600$	0.439589	+	0.319380i	0.0179461	+	0.0130386i
$601$	−10.7117	+	32.9673i	−0.436940	+	1.34476i	0.454145	+	0.890928i	$0.349945\pi$
$601$	−10.7117	+	32.9673i	−0.436940	+	1.34476i	−0.891085	+	0.453836i	$0.850055\pi$
$602$	1.78824	+	5.50365i	0.0728834	+	0.224312i
$603$	−6.98016	+	5.07139i	−0.284254	+	0.206523i
$604$	10.8640			0.442051
$605$	−6.23607	+	9.06154i	−0.253532	+	0.368404i
$606$	−1.48516			−0.0603305
$607$	−22.0600	+	16.0275i	−0.895386	+	0.650536i	−0.937277	−	0.348586i	$-0.886662\pi$
$607$	−22.0600	+	16.0275i	−0.895386	+	0.650536i	0.0418904	+	0.999122i	$0.486662\pi$
$608$	−1.14483	−	3.52343i	−0.0464291	−	0.142894i
$609$	−1.19825	+	3.68782i	−0.0485554	+	0.149438i
$610$	−2.67393	−	1.94273i	−0.108264	−	0.0786587i
$611$	−6.12475	−	4.44989i	−0.247781	−	0.180023i
$612$	−1.71021	+	5.26347i	−0.0691309	+	0.212763i
$613$	0.140216	+	0.431540i	0.00566327	+	0.0174297i	0.953848	−	0.300289i	$-0.0970832\pi$
$613$	0.140216	+	0.431540i	0.00566327	+	0.0174297i	−0.948185	+	0.317719i	$0.897083\pi$
$614$	4.49476	−	3.26563i	0.181394	−	0.131790i
$615$	2.74189			0.110564
$616$	2.31504	−	2.37499i	0.0932757	−	0.0956911i
$617$	35.9399			1.44688			0.723442	−	0.690385i	$-0.242559\pi$
$617$	35.9399			1.44688			0.723442	+	0.690385i	$0.242559\pi$
$618$	−0.680204	+	0.494197i	−0.0273618	+	0.0198795i
$619$	−13.7452	−	42.3035i	−0.552468	−	1.70032i	−0.702538	−	0.711646i	$-0.747950\pi$
$619$	−13.7452	−	42.3035i	−0.552468	−	1.70032i	0.150071	−	0.988675i	$-0.452050\pi$
$620$	−3.14607	+	9.68261i	−0.126349	+	0.388863i
$621$	−12.5248	−	9.09977i	−0.502601	−	0.365161i
$622$	−16.4591	−	11.9582i	−0.659950	−	0.479482i
$623$	1.02804	−	3.16397i	0.0411874	−	0.126762i
$624$	−0.278494	−	0.857115i	−0.0111487	−	0.0343121i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−28.0901			−1.12271
$627$	−0.960062	+	6.60706i	−0.0383412	+	0.263860i
$628$	9.67811			0.386199
$629$	−15.1240	+	10.9882i	−0.603033	+	0.438129i
$630$	−0.835816	−	2.57238i	−0.0332997	−	0.102486i
$631$	5.98293	−	18.4136i	0.238177	−	0.733032i	−0.758508	−	0.651664i	$-0.774071\pi$
$631$	5.98293	−	18.4136i	0.238177	−	0.733032i	0.996684	−	0.0813680i	$-0.0259289\pi$
$632$	9.06537	+	6.58638i	0.360601	+	0.261992i
$633$	10.3877	+	7.54709i	0.412873	+	0.299970i
$634$	−2.35362	+	7.24368i	−0.0934740	+	0.287683i
$635$	−5.63151	−	17.3320i	−0.223480	−	0.687799i
$636$	−3.90470	+	2.83693i	−0.154832	+	0.112492i
$637$	−1.65861			−0.0657164
$638$	−21.2244	−	10.4749i	−0.840282	−	0.414704i
$639$	21.1186			0.835440
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	7.43409	+	22.8798i	0.293629	+	0.903697i	0.983679	+	0.179935i	$0.0575887\pi$
$641$	7.43409	+	22.8798i	0.293629	+	0.903697i	−0.690050	+	0.723762i	$0.742411\pi$
$642$	−2.04997	+	6.30915i	−0.0809057	+	0.249002i
$643$	11.6787	+	8.48506i	0.460562	+	0.334618i	0.793752	−	0.608242i	$-0.208125\pi$
$643$	11.6787	+	8.48506i	0.460562	+	0.334618i	−0.333189	+	0.942860i	$0.608125\pi$
$644$	−4.04057	−	2.93565i	−0.159221	−	0.115681i
$645$	0.971664	−	2.99047i	0.0382592	−	0.117750i
$646$	−2.34250	−	7.20947i	−0.0921644	−	0.283653i
$647$	11.8594	−	8.61636i	0.466241	−	0.338744i	−0.329733	−	0.944074i	$-0.606959\pi$
$647$	11.8594	−	8.61636i	0.466241	−	0.338744i	0.795975	+	0.605330i	$0.206959\pi$
$648$	−6.42999			−0.252594
$649$	21.7376	+	41.3474i	0.853276	+	1.62303i
$650$	1.65861			0.0650560
$651$	−4.47541	+	3.25158i	−0.175405	+	0.127439i
$652$	5.03934	+	15.5095i	0.197356	+	0.607398i
$653$	7.45965	−	22.9584i	0.291919	−	0.898433i	−0.692321	−	0.721590i	$-0.743412\pi$
$653$	7.45965	−	22.9584i	0.291919	−	0.898433i	0.984239	−	0.176843i	$-0.0565884\pi$
$654$	−0.581912	−	0.422784i	−0.0227546	−	0.0165322i
$655$	7.66140	+	5.56633i	0.299356	+	0.217495i
$656$	1.55935	−	4.79917i	0.0608822	−	0.187376i
$657$	9.11424	+	28.0507i	0.355580	+	1.09436i
$658$	3.69271	−	2.68291i	0.143957	−	0.104591i
$659$	−25.1109			−0.978182			−0.489091	−	0.872233i	$-0.662671\pi$
$659$	−25.1109			−0.978182			−0.489091	+	0.872233i	$0.662671\pi$
$660$	−1.77619	+	0.304641i	−0.0691382	+	0.0118581i
$661$	−29.7048			−1.15538			−0.577692	−	0.816255i	$-0.696047\pi$
$661$	−29.7048			−1.15538			−0.577692	+	0.816255i	$0.696047\pi$
$662$	7.98110	−	5.79861i	0.310194	−	0.225369i
$663$	−0.569840	−	1.75379i	−0.0221307	−	0.0681114i
$664$	−1.26021	+	3.87852i	−0.0489055	+	0.150516i
$665$	2.99721	+	2.17760i	0.116227	+	0.0844438i
$666$	−19.9920	−	14.5251i	−0.774676	−	0.562835i
$667$	−11.0139	+	33.8974i	−0.426461	+	1.31251i
$668$	−2.93366	−	9.02886i	−0.113507	−	0.349337i
$669$	−1.21702	+	0.884215i	−0.0470526	+	0.0341857i
$670$	3.18992			0.123237
$671$	10.8042	−	1.85307i	0.417093	−	0.0715370i
$672$	0.543362			0.0209606
$673$	39.6880	−	28.8350i	1.52986	−	1.11151i	0.573543	−	0.819175i	$-0.305569\pi$
$673$	39.6880	−	28.8350i	1.52986	−	1.11151i	0.956317	−	0.292333i	$-0.0944315\pi$
$674$	7.07406	+	21.7717i	0.272482	+	0.838615i
$675$	−0.957875	+	2.94804i	−0.0368686	+	0.113470i
$676$	8.29163	+	6.02422i	0.318909	+	0.231701i
$677$	−22.3487	−	16.2373i	−0.858932	−	0.624050i	0.0686625	−	0.997640i	$-0.478127\pi$
$677$	−22.3487	−	16.2373i	−0.858932	−	0.624050i	−0.927594	+	0.373590i	$0.878127\pi$
$678$	−0.580712	+	1.78725i	−0.0223021	+	0.0686388i
$679$	−2.84184	−	8.74629i	−0.109060	−	0.335652i
$680$	1.65537	−	1.20270i	0.0634805	−	0.0461213i
$681$	0.865553			0.0331681
$682$	−15.7128	−	29.8875i	−0.601674	−	1.14445i
$683$	6.50934			0.249073			0.124536	−	0.992215i	$-0.460256\pi$
$683$	6.50934			0.249073			0.124536	+	0.992215i	$0.460256\pi$
$684$	8.10673	−	5.88989i	0.309969	−	0.225205i
$685$	3.54774	+	10.9188i	0.135552	+	0.417187i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−10.3632	−	7.52928i	−0.395379	−	0.287260i
$688$	−4.68168	−	3.40144i	−0.178487	−	0.129679i
$689$	−4.55268	+	14.0117i	−0.173443	+	0.533804i
$690$	0.838604	+	2.58096i	0.0319251	+	0.0982554i
$691$	−16.0552	+	11.6648i	−0.610767	+	0.443748i	−0.849684	−	0.527292i	$-0.823207\pi$
$691$	−16.0552	+	11.6648i	−0.610767	+	0.443748i	0.238917	+	0.971040i	$0.423207\pi$
$692$	1.44017			0.0547470
$693$	8.04432	+	3.97011i	0.305578	+	0.150812i
$694$	8.07715			0.306604
$695$	3.93435	−	2.85847i	0.149238	−	0.108428i
$696$	−1.19825	−	3.68782i	−0.0454194	−	0.139786i
$697$	3.19066	−	9.81983i	0.120855	−	0.371953i
$698$	13.2370	+	9.61722i	0.501027	+	0.364017i
$699$	−1.63632	−	1.18886i	−0.0618913	−	0.0449667i
$700$	−0.309017	+	0.951057i	−0.0116797	+	0.0359466i
$701$	−2.90529	−	8.94157i	−0.109731	−	0.337718i	0.881080	−	0.472967i	$-0.156817\pi$
$701$	−2.90529	−	8.94157i	−0.109731	−	0.337718i	−0.990812	+	0.135248i	$0.956817\pi$
$702$	4.15937	−	3.02196i	0.156985	−	0.114057i
$703$	33.8479			1.27660
$704$	−0.476925	+	3.28216i	−0.0179748	+	0.123701i
$705$	−2.48014			−0.0934075
$706$	−15.0187	+	10.9118i	−0.565238	+	0.410669i
$707$	−0.844630	−	2.59950i	−0.0317656	−	0.0977644i
$708$	−2.36492	+	7.27847i	−0.0888790	+	0.273542i
$709$	21.8262	+	15.8577i	0.819700	+	0.595547i	0.916627	−	0.399744i	$-0.130901\pi$
$709$	21.8262	+	15.8577i	0.819700	+	0.595547i	−0.0969264	+	0.995292i	$0.530901\pi$
$710$	−6.31677	−	4.58940i	−0.237064	−	0.172237i
$711$	−9.36567	+	28.8246i	−0.351240	+	1.08101i
$712$	1.02804	+	3.16397i	0.0385273	+	0.118575i
$713$	−41.1367	+	29.8875i	−1.54058	+	1.11930i
$714$	1.11180			0.0416081
$715$	−3.83975	+	3.93918i	−0.143598	+	0.147317i
$716$	−9.52847			−0.356095
$717$	−6.59769	+	4.79350i	−0.246395	+	0.179017i
$718$	−1.41854	−	4.36581i	−0.0529394	−	0.162931i
$719$	−7.32536	+	22.5451i	−0.273190	+	0.840792i	0.716503	+	0.697584i	$0.245742\pi$
$719$	−7.32536	+	22.5451i	−0.273190	+	0.840792i	−0.989693	+	0.143208i	$0.954258\pi$
$720$	2.18820	+	1.58982i	0.0815492	+	0.0592490i
$721$	−1.25184	−	0.909518i	−0.0466211	−	0.0338722i
$722$	1.62999	−	5.01660i	0.0606621	−	0.186699i
$723$	3.94095	+	12.1290i	0.146566	+	0.451083i
$724$	9.33857	−	6.78487i	0.347065	−	0.252158i
$725$	7.13632			0.265036
$726$	3.38844	−	4.92369i	0.125757	−	0.182735i
$727$	−42.5192			−1.57695			−0.788475	−	0.615066i	$-0.789129\pi$
$727$	−42.5192			−1.57695			−0.788475	+	0.615066i	$0.789129\pi$
$728$	1.34184	−	0.974905i	0.0497320	−	0.0361324i
$729$	−3.81287	−	11.7348i	−0.141217	−	0.434622i
$730$	3.36971	−	10.3709i	0.124718	−	0.383844i
$731$	−9.57942	−	6.95986i	−0.354308	−	0.257420i
$732$	1.45291	+	1.05560i	0.0537012	+	0.0390162i
$733$	−1.39878	+	4.30500i	−0.0516651	+	0.159009i	−0.973560	−	0.228431i	$-0.926641\pi$
$733$	−1.39878	+	4.30500i	−0.0516651	+	0.159009i	0.921895	+	0.387440i	$0.126641\pi$
$734$	−3.94597	−	12.1445i	−0.145649	−	0.448260i
$735$	−0.439589	+	0.319380i	−0.0162145	+	0.0117805i
$736$	4.99442			0.184097
$737$	−7.38480	+	7.57602i	−0.272023	+	0.279066i
$738$	13.6486			0.502412
$739$	−25.4069	+	18.4592i	−0.934608	+	0.679032i	−0.947117	−	0.320889i	$-0.896018\pi$
$739$	−25.4069	+	18.4592i	−0.934608	+	0.679032i	0.0125088	+	0.999922i	$0.496018\pi$
$740$	2.82328	+	8.68916i	0.103786	+	0.319420i
$741$	−1.03175	+	3.17540i	−0.0379023	+	0.116651i
$742$	−7.18619	−	5.22108i	−0.263813	−	0.191672i
$743$	−7.29469	−	5.29990i	−0.267616	−	0.194434i	0.445882	−	0.895092i	$-0.352890\pi$
$743$	−7.29469	−	5.29990i	−0.267616	−	0.194434i	−0.713498	+	0.700657i	$0.752890\pi$
$744$	1.70945	−	5.26116i	0.0626716	−	0.192883i
$745$	2.35131	+	7.23660i	0.0861455	+	0.265129i
$746$	−18.1495	+	13.1864i	−0.664501	+	0.482788i
$747$	−11.0303			−0.403578
$748$	−0.975860	+	6.71578i	−0.0356810	+	0.245553i
$749$	−12.2089			−0.446102
$750$	0.439589	−	0.319380i	0.0160515	−	0.0116621i
$751$	2.63468	+	8.10870i	0.0961407	+	0.295891i	0.987549	−	0.157310i	$-0.0502821\pi$
$751$	2.63468	+	8.10870i	0.0961407	+	0.295891i	−0.891409	+	0.453201i	$0.850282\pi$
$752$	−1.41049	+	4.34104i	−0.0514352	+	0.158301i
$753$	−10.4932	−	7.62376i	−0.382394	−	0.277825i
$754$	−9.57581	−	6.95724i	−0.348731	−	0.253368i
$755$	3.35717	−	10.3323i	0.122180	−	0.376031i
$756$	0.957875	+	2.94804i	0.0348376	+	0.107219i
$757$	−25.4450	+	18.4868i	−0.924813	+	0.671916i	−0.944717	−	0.327886i	$-0.893664\pi$
$757$	−25.4450	+	18.4868i	−0.924813	+	0.671916i	0.0199044	+	0.999802i	$0.493664\pi$
$758$	30.1347			1.09454
$759$	−8.07115	−	3.98335i	−0.292964	−	0.144587i
$760$	−3.70476			−0.134386
$761$	−40.0423	+	29.0924i	−1.45153	+	1.05460i	−0.466062	+	0.884752i	$0.654328\pi$
$761$	−40.0423	+	29.0924i	−1.45153	+	1.05460i	−0.985470	+	0.169848i	$0.945672\pi$
$762$	3.05995	+	9.41755i	0.110850	+	0.341162i
$763$	0.409066	−	1.25897i	0.0148092	−	0.0455779i
$764$	−20.9143	−	15.1952i	−0.756655	−	0.549742i
$765$	4.47738	+	3.25300i	0.161880	+	0.117613i
$766$	−8.63868	+	26.5871i	−0.312128	+	0.960632i
$767$	7.21889	+	22.2175i	0.260659	+	0.802226i
$768$	−0.439589	+	0.319380i	−0.0158623	+	0.0115246i
$769$	−32.2787			−1.16400			−0.582000	−	0.813189i	$-0.697730\pi$
$769$	−32.2787			−1.16400			−0.582000	+	0.813189i	$0.697730\pi$
$770$	−1.54336	−	2.93565i	−0.0556189	−	0.105793i
$771$	1.70580			0.0614330
$772$	−20.7342	+	15.0643i	−0.746239	+	0.542175i
$773$	1.59580	+	4.91135i	0.0573968	+	0.176649i	0.975645	−	0.219357i	$-0.0703959\pi$
$773$	1.59580	+	4.91135i	0.0573968	+	0.176649i	−0.918248	+	0.396006i	$0.870396\pi$
$774$	4.83677	−	14.8860i	0.173854	−	0.535068i
$775$	8.23652	+	5.98418i	0.295864	+	0.214958i
$776$	7.44004	+	5.40550i	0.267082	+	0.194046i
$777$	−1.53406	+	4.72136i	−0.0550342	+	0.169378i
$778$	−1.41421	−	4.35250i	−0.0507020	−	0.156045i
$779$	−15.1244	+	10.9885i	−0.541887	+	0.393704i
$780$	−0.901224			−0.0322690
$781$	25.5234	−	4.37760i	0.913298	−	0.156643i
$782$	10.2193			0.365443
$783$	17.8961	−	13.0023i	0.639554	−	0.464663i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	2.99070	−	9.20443i	0.106743	−	0.328520i
$786$	−4.16291	−	3.02453i	−0.148486	−	0.107881i
$787$	11.8390	+	8.60153i	0.422014	+	0.306611i	0.778448	−	0.627709i	$-0.216007\pi$
$787$	11.8390	+	8.60153i	0.422014	+	0.306611i	−0.356434	+	0.934321i	$0.616007\pi$
$788$	3.25157	−	10.0073i	0.115832	−	0.356495i
$789$	3.03909	+	9.35337i	0.108195	+	0.332989i
$790$	9.06537	−	6.58638i	0.322531	−	0.234333i
$791$	−3.45851			−0.122970
$792$	−8.84156	+	1.51645i	−0.314171	+	0.0538846i
$793$	5.48197			0.194671
$794$	−30.6933	+	22.3000i	−1.08927	+	0.791398i
$795$	1.49146	+	4.59025i	0.0528968	+	0.162800i
$796$	5.66808	−	17.4446i	0.200900	−	0.618306i
$797$	−23.5435	−	17.1054i	−0.833955	−	0.605904i	0.0867207	−	0.996233i	$-0.472361\pi$
$797$	−23.5435	−	17.1054i	−0.833955	−	0.605904i	−0.920675	+	0.390329i	$0.872361\pi$
$798$	−1.62857	−	1.18323i	−0.0576508	−	0.0418857i
$799$	−2.88607	+	8.88241i	−0.102102	+	0.314237i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$	−7.27967	+	5.28899i	−0.257215	+	0.186877i
$802$	−15.9557			−0.563416
$803$	16.8297	+	32.0121i	0.593909	+	1.12968i
$804$	−1.73328			−0.0611281
$805$	−4.04057	+	2.93565i	−0.142412	+	0.103468i
$806$	−5.21810	−	16.0596i	−0.183800	−	0.565677i
$807$	−0.949975	+	2.92372i	−0.0334407	+	0.102920i
$808$	2.21127	+	1.60658i	0.0777922	+	0.0565193i
$809$	23.7664	+	17.2673i	0.835582	+	0.607086i	0.921133	−	0.389248i	$-0.127265\pi$
$809$	23.7664	+	17.2673i	0.835582	+	0.607086i	−0.0855512	+	0.996334i	$0.527265\pi$
$810$	−1.98698	+	6.11528i	−0.0698152	+	0.214869i
$811$	8.61596	+	26.5172i	0.302547	+	0.931145i	0.980581	+	0.196114i	$0.0628323\pi$
$811$	8.61596	+	26.5172i	0.302547	+	0.931145i	−0.678034	+	0.735031i	$0.737168\pi$
$812$	5.77340	−	4.19462i	0.202607	−	0.147202i
$813$	17.2674			0.605593
$814$	−27.1727	−	13.4105i	−0.952402	−	0.470038i
$815$	16.3076			0.571232
$816$	−0.899465	+	0.653500i	−0.0314876	+	0.0228771i
$817$	6.62501	+	20.3897i	0.231780	+	0.713345i
$818$	7.49934	−	23.0806i	0.262208	−	0.806994i
$819$	3.62936	+	2.63688i	0.126820	+	0.0921401i
$820$	−4.08242	−	2.96605i	−0.142564	−	0.103579i
$821$	1.76267	−	5.42494i	0.0615176	−	0.189332i	−0.915575	−	0.402148i	$-0.868264\pi$
$821$	1.76267	−	5.42494i	0.0615176	−	0.189332i	0.977092	+	0.212817i	$0.0682637\pi$
$822$	−1.92771	−	5.93288i	−0.0672366	−	0.206933i
$823$	9.12217	−	6.62765i	0.317979	−	0.231025i	−0.417334	−	0.908753i	$-0.637035\pi$
$823$	9.12217	−	6.62765i	0.317979	−	0.231025i	0.735313	+	0.677728i	$0.237035\pi$
$824$	1.54736			0.0539050
$825$	−0.259143	+	1.78340i	−0.00902220	+	0.0620900i
$826$	−14.0846			−0.490066
$827$	−8.84342	+	6.42512i	−0.307516	+	0.223423i	−0.730830	−	0.682560i	$-0.760867\pi$
$827$	−8.84342	+	6.42512i	−0.307516	+	0.223423i	0.423314	+	0.905983i	$0.360867\pi$
$828$	4.17442	+	12.8475i	0.145071	+	0.446483i
$829$	0.235896	−	0.726014i	0.00819301	−	0.0252155i	−0.946876	−	0.321598i	$-0.895780\pi$
$829$	0.235896	−	0.726014i	0.00819301	−	0.0252155i	0.955069	+	0.296382i	$0.0957802\pi$
$830$	3.29927	+	2.39706i	0.114519	+	0.0832031i
$831$	1.05800	+	0.768679i	0.0367015	+	0.0266652i
$832$	−0.512538	+	1.57743i	−0.0177691	+	0.0546875i
$833$	0.632295	+	1.94600i	0.0219077	+	0.0674250i
$834$	−2.13778	+	1.55319i	−0.0740251	+	0.0537824i
$835$	−9.49351			−0.328536
$836$	8.57667	−	8.79876i	0.296630	−	0.304312i
$837$	31.5582			1.09081
$838$	−20.7786	+	15.0965i	−0.717785	+	0.521501i
$839$	−8.45621	−	26.0255i	−0.291941	−	0.898501i	−0.984232	−	0.176883i	$-0.943399\pi$
$839$	−8.45621	−	26.0255i	−0.291941	−	0.898501i	0.692291	−	0.721618i	$-0.256601\pi$
$840$	0.167908	−	0.516768i	0.00579338	−	0.0178302i
$841$	−17.7394	−	12.8884i	−0.611702	−	0.444428i
$842$	−7.57533	−	5.50380i	−0.261063	−	0.189673i
$843$	1.88440	−	5.79958i	0.0649021	−	0.199748i
$844$	−7.30220	−	22.4739i	−0.251352	−	0.773583i
$845$	8.29163	−	6.02422i	0.285241	−	0.207240i
$846$	−12.3457			−0.424454
$847$	10.5451	+	3.13068i	0.362333	+	0.107572i
$848$	8.88262			0.305031
$849$	−13.7398	+	9.98252i	−0.471547	+	0.342599i
$850$	−0.632295	−	1.94600i	−0.0216875	−	0.0667474i
$851$	−14.1006	+	43.3973i	−0.483364	+	1.48764i
$852$	3.43229	+	2.49370i	0.117588	+	0.0854329i
$853$	−29.3691	−	21.3379i	−1.00558	−	0.730596i	−0.0423020	−	0.999105i	$-0.513469\pi$
$853$	−29.3691	−	21.3379i	−1.00558	−	0.730596i	−0.963277	+	0.268509i	$0.913469\pi$
$854$	−1.02135	+	3.14340i	−0.0349499	+	0.107565i
$855$	−3.09650	−	9.53004i	−0.105898	−	0.325920i
$856$	9.87718	−	7.17619i	0.337595	−	0.245277i
$857$	30.3248			1.03587			0.517937	−	0.855419i	$-0.326700\pi$
$857$	30.3248			1.03587			0.517937	+	0.855419i	$0.326700\pi$
$858$	2.08637	−	2.14040i	0.0712276	−	0.0730720i
$859$	−45.7487			−1.56093			−0.780463	−	0.625202i	$-0.785017\pi$
$859$	−45.7487			−1.56093			−0.780463	+	0.625202i	$0.785017\pi$
$860$	−4.68168	+	3.40144i	−0.159644	+	0.115988i
$861$	−0.847289	−	2.60769i	−0.0288755	−	0.0888698i
$862$	−5.25025	+	16.1586i	−0.178824	+	0.550364i
$863$	3.88176	+	2.82026i	0.132137	+	0.0960028i	0.651890	−	0.758313i	$-0.273976\pi$
$863$	3.88176	+	2.82026i	0.132137	+	0.0960028i	−0.519754	+	0.854316i	$0.673976\pi$
$864$	−2.50775	−	1.82199i	−0.0853154	−	0.0619852i
$865$	0.445036	−	1.36968i	0.0151317	−	0.0465705i
$866$	−2.07246	−	6.37838i	−0.0704252	−	0.216746i
$867$	5.63257	−	4.09230i	0.191292	−	0.138982i
$868$	10.1809			0.345562
$869$	−5.34414	+	36.7779i	−0.181288	+	1.24761i
$870$	−3.87760			−0.131463
$871$	−4.28037	+	3.10987i	−0.145035	+	0.105374i
$872$	0.409066	+	1.25897i	0.0138527	+	0.0426343i
$873$	−7.68649	+	23.6566i	−0.260148	+	0.800655i
$874$	−14.9693	−	10.8759i	−0.506346	−	0.367882i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−1.83097	+	5.63515i	−0.0618627	+	0.190394i
$877$	10.0447	+	30.9146i	0.339187	+	1.04391i	0.964623	+	0.263635i	$0.0849213\pi$
$877$	10.0447	+	30.9146i	0.339187	+	1.04391i	−0.625436	+	0.780276i	$0.715079\pi$
$878$	10.3937	−	7.55149i	0.350772	−	0.254851i
$879$	1.23468			0.0416447
$880$	2.97414	+	1.46782i	0.100258	+	0.0494804i
$881$	−45.5066			−1.53316			−0.766578	−	0.642151i	$-0.778042\pi$
$881$	−45.5066			−1.53316			−0.766578	+	0.642151i	$0.778042\pi$
$882$	−2.18820	+	1.58982i	−0.0736804	+	0.0535319i
$883$	−5.23470	−	16.1108i	−0.176162	−	0.542170i	0.823523	−	0.567283i	$-0.192005\pi$
$883$	−5.23470	−	16.1108i	−0.176162	−	0.542170i	−0.999685	+	0.0251129i	$0.992005\pi$
$884$	−1.04873	+	3.22766i	−0.0352726	+	0.108558i
$885$	6.19143	+	4.49834i	0.208123	+	0.151210i
$886$	0.548809	+	0.398733i	0.0184376	+	0.0133957i
$887$	−0.556108	+	1.71152i	−0.0186723	+	0.0574674i	−0.959959	−	0.280142i	$-0.909618\pi$
$887$	−0.556108	+	1.71152i	−0.0186723	+	0.0574674i	0.941286	+	0.337610i	$0.109618\pi$
$888$	−1.53406	−	4.72136i	−0.0514797	−	0.158438i
$889$	−14.7435	+	10.7118i	−0.494480	+	0.359261i
$890$	3.32679			0.111514
$891$	−9.92380	−	18.8762i	−0.332460	−	0.632376i
$892$	2.76854			0.0926974
$893$	13.6806	−	9.93952i	0.457803	−	0.332614i
$894$	−1.27761	−	3.93209i	−0.0427298	−	0.131509i
$895$	−2.94446	+	9.06211i	−0.0984224	+	0.302913i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	−3.64146	−	2.64568i	−0.121585	−	0.0883366i
$898$	−2.34706	+	7.22351i	−0.0783224	+	0.241052i
$899$	−22.4514	−	69.0982i	−0.748795	−	2.30455i
$900$	2.18820	−	1.58982i	0.0729398	−	0.0529939i
$901$	18.1752			0.605503
$902$	16.4953	−	2.82917i	0.549234	−	0.0942010i
$903$	−3.14437			−0.104638
$904$	2.79799	−	2.03286i	0.0930599	−	0.0676120i
$905$	−3.56702	−	10.9781i	−0.118572	−	0.364926i
$906$	−1.82416	+	5.61418i	−0.0606036	+	0.186519i
$907$	−14.6333	−	10.6317i	−0.485892	−	0.353021i	0.317711	−	0.948188i	$-0.397086\pi$
$907$	−14.6333	−	10.6317i	−0.485892	−	0.353021i	−0.803602	+	0.595167i	$0.797086\pi$
$908$	−1.28873	−	0.936317i	−0.0427680	−	0.0310728i
$909$	−2.28452	+	7.03103i	−0.0757727	+	0.233204i
$910$	−0.512538	−	1.57743i	−0.0169905	−	0.0522913i
$911$	−16.5169	+	12.0002i	−0.547229	+	0.397585i	−0.826763	−	0.562551i	$-0.809820\pi$
$911$	−16.5169	+	12.0002i	−0.547229	+	0.397585i	0.279534	+	0.960136i	$0.409820\pi$
$912$	2.01302			0.0666579
$913$	−13.3309	+	2.28643i	−0.441189	+	0.0756699i
$914$	33.0502			1.09320
$915$	1.45291	−	1.05560i	0.0480319	−	0.0348972i
$916$	7.28497	+	22.4208i	0.240702	+	0.740805i
$917$	2.92639	−	9.00651i	0.0966380	−	0.297421i
$918$	−5.13123	−	3.72806i	−0.169356	−	0.123044i
$919$	−33.5273	−	24.3590i	−1.10596	−	0.803529i	−0.123939	−	0.992290i	$-0.539553\pi$
$919$	−33.5273	−	24.3590i	−1.10596	−	0.803529i	−0.982023	+	0.188761i	$0.939553\pi$
$920$	1.54336	−	4.74998i	0.0508831	−	0.156602i
$921$	0.932869	+	2.87107i	0.0307391	+	0.0946051i
$922$	16.3826	−	11.9026i	0.539532	−	0.391993i
$923$	12.9503			0.426265
$924$	0.838604	+	1.59512i	0.0275880	+	0.0524756i
$925$	9.13632			0.300400
$926$	31.8116	−	23.1125i	1.04539	−	0.759523i
$927$	1.29331	+	3.98040i	0.0424779	+	0.130734i
$928$	−2.20524	+	6.78704i	−0.0723907	+	0.222796i
$929$	36.7721	+	26.7165i	1.20645	+	0.876541i	0.994904	−	0.100826i	$-0.0321487\pi$
$929$	36.7721	+	26.7165i	1.20645	+	0.876541i	0.211551	+	0.977367i	$0.432149\pi$
$930$	−4.47541	−	3.25158i	−0.146754	−	0.106623i
$931$	1.14483	−	3.52343i	0.0375204	−	0.115476i
$932$	1.15028	+	3.54020i	0.0376787	+	0.115963i
$933$	8.94325	−	6.49765i	0.292789	−	0.212724i
$934$	18.8167			0.615702
$935$	6.08553	+	3.00339i	0.199018	+	0.0982213i
$936$	−4.48613			−0.146634
$937$	19.6439	−	14.2721i	0.641739	−	0.466251i	−0.218708	−	0.975790i	$-0.570184\pi$
$937$	19.6439	−	14.2721i	0.641739	−	0.466251i	0.860447	+	0.509540i	$0.170184\pi$
$938$	−0.985739	−	3.03379i	−0.0321855	−	0.0990568i
$939$	4.71655	−	14.5161i	0.153919	−	0.473714i
$940$	3.69271	+	2.68291i	0.120443	+	0.0875068i
$941$	23.2130	+	16.8652i	0.756723	+	0.549791i	0.897903	−	0.440193i	$-0.145090\pi$
$941$	23.2130	+	16.8652i	0.756723	+	0.549791i	−0.141181	+	0.989984i	$0.545090\pi$
$942$	−1.62503	+	5.00134i	−0.0529464	+	0.162952i
$943$	−7.78804	−	23.9691i	−0.253613	−	0.780542i
$944$	11.3947	−	8.27872i	0.370865	−	0.269449i
$945$	3.09975			0.100835
$946$	2.75991	−	18.9934i	0.0897323	−	0.617530i
$947$	50.0233			1.62554			0.812770	−	0.582585i	$-0.197959\pi$
$947$	50.0233			1.62554			0.812770	+	0.582585i	$0.197959\pi$
$948$	−4.92578	+	3.57879i	−0.159982	+	0.116234i
$949$	5.58902	+	17.2012i	0.181427	+	0.558376i
$950$	−1.14483	+	3.52343i	−0.0371433	+	0.114315i
$951$	−3.34811	−	2.43255i	−0.108570	−	0.0788807i
$952$	−1.65537	−	1.20270i	−0.0536509	−	0.0389796i
$953$	18.4578	−	56.8071i	0.597905	−	1.84016i	0.0582085	−	0.998304i	$-0.481461\pi$
$953$	18.4578	−	56.8071i	0.597905	−	1.84016i	0.539697	−	0.841859i	$-0.318539\pi$
$954$	7.42424	+	22.8495i	0.240369	+	0.739779i
$955$	−20.9143	+	15.1952i	−0.676772	+	0.491704i
$956$	15.0088			0.485418
$957$	8.97682	−	9.20927i	0.290179	−	0.297693i
$958$	7.56631			0.244456
$959$	9.28812	−	6.74821i	0.299929	−	0.217911i
$960$	0.167908	+	0.516768i	0.00541921	+	0.0166786i
$961$	22.4503	−	69.0949i	0.724203	−	2.22887i
$962$	−12.2595	−	8.90705i	−0.395262	−	0.287175i
$963$	26.7154	+	19.4099i	0.860891	+	0.625474i
$964$	7.25291	−	22.3222i	0.233600	−	0.718948i
$965$	7.91975	+	24.3745i	0.254946	+	0.784643i
$966$	2.19549	−	1.59512i	0.0706389	−	0.0513221i
$967$	−14.2933			−0.459640			−0.229820	−	0.973233i	$-0.573814\pi$
$967$	−14.2933			−0.459640			−0.229820	+	0.973233i	$0.573814\pi$
$968$	−10.3713	+	3.66547i	−0.333347	+	0.117813i
$969$	4.11895			0.132320
$970$	7.44004	−	5.40550i	0.238885	−	0.173560i
$971$	5.47214	+	16.8415i	0.175609	+	0.540470i	0.999661	−	0.0260453i	$-0.00829140\pi$
$971$	5.47214	+	16.8415i	0.175609	+	0.540470i	−0.824052	+	0.566515i	$0.808291\pi$
$972$	3.95327	−	12.1669i	0.126801	−	0.390254i
$973$	−3.93435	−	2.85847i	−0.126129	−	0.0916384i
$974$	6.41024	+	4.65731i	0.205397	+	0.149230i
$975$	−0.278494	+	0.857115i	−0.00891893	+	0.0274497i
$976$	−1.02135	−	3.14340i	−0.0326927	−	0.100618i
$977$	20.1732	−	14.6567i	0.645398	−	0.468909i	−0.216303	−	0.976326i	$-0.569400\pi$
$977$	20.1732	−	14.6567i	0.645398	−	0.468909i	0.861700	+	0.507418i	$0.169400\pi$
$978$	−8.86095			−0.283342
$979$	−7.70167	+	7.90110i	−0.246146	+	0.252520i
$980$	1.00000			0.0319438
$981$	−2.89665	+	2.10454i	−0.0924831	+	0.0671929i
$982$	4.66927	+	14.3705i	0.149003	+	0.458583i
$983$	−15.4988	+	47.7004i	−0.494335	+	1.52141i	0.323655	+	0.946175i	$0.395088\pi$
$983$	−15.4988	+	47.7004i	−0.494335	+	1.52141i	−0.817990	+	0.575232i	$0.804912\pi$
$984$	2.21823	+	1.61164i	0.0707147	+	0.0513772i
$985$	−8.51271	−	6.18485i	−0.271237	−	0.197066i
$986$	−4.51226	+	13.8873i	−0.143700	+	0.442262i
$987$	0.766406	+	2.35875i	0.0243950	+	0.0750800i
$988$	4.97120	−	3.61179i	0.158155	−	0.114906i
$989$	−28.9021			−0.919034
$990$	−1.28997	+	8.87743i	−0.0409978	+	0.282143i
$991$	−5.56911			−0.176909			−0.0884543	−	0.996080i	$-0.528193\pi$
$991$	−5.56911			−0.176909			−0.0884543	+	0.996080i	$0.528193\pi$
$992$	−8.23652	+	5.98418i	−0.261510	+	0.189998i
$993$	1.65644	+	5.09801i	0.0525656	+	0.161780i
$994$	−2.41279	+	7.42580i	−0.0765290	+	0.235532i
$995$	−14.8392	−	10.7813i	−0.470435	−	0.341791i
$996$	−1.79270	−	1.30247i	−0.0568037	−	0.0412703i
$997$	−3.77323	+	11.6128i	−0.119499	+	0.367782i	−0.992859	−	0.119295i	$-0.961937\pi$
$997$	−3.77323	+	11.6128i	−0.119499	+	0.367782i	0.873359	+	0.487076i	$0.161937\pi$
$998$	1.84344	+	5.67351i	0.0583530	+	0.179592i
$999$	22.9116	−	16.6462i	0.724891	−	0.526664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.f.421.2	✓	8
11.2	odd	10		8470.2.a.cs.1.3		4
11.4	even	5	inner	770.2.n.f.631.2	yes	8
11.9	even	5		8470.2.a.co.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.f.421.2	✓	8	1.1	even	1	trivial
770.2.n.f.631.2	yes	8	11.4	even	5	inner
8470.2.a.co.1.3		4	11.9	even	5
8470.2.a.cs.1.3		4	11.2	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.167908 + 0.516768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.439589 + 0.319380i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.18820 - 1.58982i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.167908 + 0.516768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.439589 + 0.319380i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.18820 - 1.58982i) q^{9} -1.00000 q^{10} +(2.31504 - 2.37499i) q^{11} +0.543362 q^{12} +(1.34184 - 0.974905i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.167908 - 0.516768i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.65537 - 1.20270i) q^{17} +(0.835816 - 2.57238i) q^{18} +(1.14483 + 3.52343i) q^{19} +(-0.809017 + 0.587785i) q^{20} -0.543362 q^{21} +(0.476925 - 3.28216i) q^{22} -4.99442 q^{23} +(0.439589 - 0.319380i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.512538 - 1.57743i) q^{26} +(2.50775 + 1.82199i) q^{27} +(0.809017 + 0.587785i) q^{28} +(2.20524 - 6.78704i) q^{29} +(-0.167908 - 0.516768i) q^{30} +(8.23652 - 5.98418i) q^{31} -1.00000 q^{32} +(1.61603 + 0.797560i) q^{33} -2.04615 q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.835816 - 2.57238i) q^{36} +(2.82328 - 8.68916i) q^{37} +(2.99721 + 2.17760i) q^{38} +(0.729106 + 0.529726i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(1.55935 + 4.79917i) q^{41} +(-0.439589 + 0.319380i) q^{42} +5.78688 q^{43} +(-1.54336 - 2.93565i) q^{44} -2.70476 q^{45} +(-4.04057 + 2.93565i) q^{46} +(-1.41049 - 4.34104i) q^{47} +(0.167908 - 0.516768i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.343565 - 1.05738i) q^{51} +(-0.512538 - 1.57743i) q^{52} +(-7.18619 + 5.22108i) q^{53} +3.09975 q^{54} +(-3.26889 + 0.560659i) q^{55} +1.00000 q^{56} +(-1.62857 + 1.18323i) q^{57} +(-2.20524 - 6.78704i) q^{58} +(-4.35238 + 13.3952i) q^{59} +(-0.439589 - 0.319380i) q^{60} +(2.67393 + 1.94273i) q^{61} +(3.14607 - 9.68261i) q^{62} +(0.835816 + 2.57238i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.65861 q^{65} +(1.77619 - 0.304641i) q^{66} -3.18992 q^{67} +(-1.65537 + 1.20270i) q^{68} +(-0.838604 - 2.58096i) q^{69} +(0.309017 - 0.951057i) q^{70} +(6.31677 + 4.58940i) q^{71} +(-2.18820 - 1.58982i) q^{72} +(-3.36971 + 10.3709i) q^{73} +(-2.82328 - 8.68916i) q^{74} +(-0.439589 + 0.319380i) q^{75} +3.70476 q^{76} +(1.54336 + 2.93565i) q^{77} +0.901224 q^{78} +(-9.06537 + 6.58638i) q^{79} +(0.309017 + 0.951057i) q^{80} +(1.98698 - 6.11528i) q^{81} +(4.08242 + 2.96605i) q^{82} +(-3.29927 - 2.39706i) q^{83} +(-0.167908 + 0.516768i) q^{84} +(0.632295 + 1.94600i) q^{85} +(4.68168 - 3.40144i) q^{86} +3.87760 q^{87} +(-2.97414 - 1.46782i) q^{88} -3.32679 q^{89} +(-2.18820 + 1.58982i) q^{90} +(0.512538 + 1.57743i) q^{91} +(-1.54336 + 4.74998i) q^{92} +(4.47541 + 3.25158i) q^{93} +(-3.69271 - 2.68291i) q^{94} +(1.14483 - 3.52343i) q^{95} +(-0.167908 - 0.516768i) q^{96} +(-7.44004 + 5.40550i) q^{97} -1.00000 q^{98} +(1.28997 - 8.87743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * q^99

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