LMFDB - Embedded newform 430.2.e.f.221.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(221,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("430.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.27870912.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} + 2x^{3} + 38x^{2} - 12x + 4 $ x^6 - x^5 + 7x^4 + 2x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.3
Root			$-1.08870 + 1.88569i$ of defining polynomial
Character	$\chi$	$=$	430.221
Dual form			430.2.e.f.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.58870 - 2.75172i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.58870 - 2.75172i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-3.54797 - 6.14526i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.58870 - 2.75172i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.58870 - 2.75172i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-3.54797 - 6.14526i) q^{9} +(-0.500000 + 0.866025i) q^{10} +2.17741 q^{11} +(1.58870 - 2.75172i) q^{12} +(-1.45926 - 2.52751i) q^{13} +(1.00000 + 1.73205i) q^{14} +(1.58870 + 2.75172i) q^{15} +1.00000 q^{16} +(-0.629444 - 1.09023i) q^{17} +(-3.54797 - 6.14526i) q^{18} +(-2.82982 + 4.90139i) q^{19} +(-0.500000 + 0.866025i) q^{20} +6.35482 q^{21} +2.17741 q^{22} +(-1.17741 + 2.03933i) q^{23} +(1.58870 - 2.75172i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.45926 - 2.52751i) q^{26} -13.0145 q^{27} +(1.00000 + 1.73205i) q^{28} +(3.32982 + 5.76741i) q^{29} +(1.58870 + 2.75172i) q^{30} +(0.459261 - 0.795464i) q^{31} +1.00000 q^{32} +(3.45926 - 5.99162i) q^{33} +(-0.629444 - 1.09023i) q^{34} -2.00000 q^{35} +(-3.54797 - 6.14526i) q^{36} +(-2.71815 + 4.70797i) q^{37} +(-2.82982 + 4.90139i) q^{38} -9.27334 q^{39} +(-0.500000 + 0.866025i) q^{40} -11.7096 q^{41} +6.35482 q^{42} +(5.31408 - 3.84195i) q^{43} +2.17741 q^{44} +7.09593 q^{45} +(-1.17741 + 2.03933i) q^{46} +1.74111 q^{47} +(1.58870 - 2.75172i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} -4.00000 q^{51} +(-1.45926 - 2.52751i) q^{52} +(1.74111 - 3.01570i) q^{53} -13.0145 q^{54} +(-1.08870 + 1.88569i) q^{55} +(1.00000 + 1.73205i) q^{56} +(8.99149 + 15.5737i) q^{57} +(3.32982 + 5.76741i) q^{58} -9.45075 q^{59} +(1.58870 + 2.75172i) q^{60} +(7.27334 + 12.5978i) q^{61} +(0.459261 - 0.795464i) q^{62} +(7.09593 - 12.2905i) q^{63} +1.00000 q^{64} +2.91852 q^{65} +(3.45926 - 5.99162i) q^{66} +(5.87778 - 10.1806i) q^{67} +(-0.629444 - 1.09023i) q^{68} +(3.74111 + 6.47980i) q^{69} -2.00000 q^{70} +(4.63667 + 8.03095i) q^{71} +(-3.54797 - 6.14526i) q^{72} +(7.26611 + 12.5853i) q^{73} +(-2.71815 + 4.70797i) q^{74} -3.17741 q^{75} +(-2.82982 + 4.90139i) q^{76} +(2.17741 + 3.77138i) q^{77} -9.27334 q^{78} +(-4.35482 - 7.54277i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-10.0322 + 17.3763i) q^{81} -11.7096 q^{82} +(-2.50723 + 4.34265i) q^{83} +6.35482 q^{84} +1.25889 q^{85} +(5.31408 - 3.84195i) q^{86} +21.1604 q^{87} +2.17741 q^{88} +(0.758887 - 1.31443i) q^{89} +7.09593 q^{90} +(2.91852 - 5.05503i) q^{91} +(-1.17741 + 2.03933i) q^{92} +(-1.45926 - 2.52751i) q^{93} +1.74111 q^{94} +(-2.82982 - 4.90139i) q^{95} +(1.58870 - 2.75172i) q^{96} +12.9330 q^{97} +(1.50000 - 2.59808i) q^{98} +(-7.72538 - 13.3807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 3 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 3 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 - 5 * q^9	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 3 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} - 5 q^{9} - 3 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 6 q^{16} - 5 q^{17} - 5 q^{18} - 7 q^{19} - 3 q^{20} + 8 q^{21} - 2 q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 28 q^{27} + 6 q^{28} + 10 q^{29} + 2 q^{30} - 6 q^{31} + 6 q^{32} + 12 q^{33} - 5 q^{34} - 12 q^{35} - 5 q^{36} - 10 q^{37} - 7 q^{38} - 8 q^{39} - 3 q^{40} - 10 q^{41} + 8 q^{42} - 7 q^{43} - 2 q^{44} + 10 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 9 q^{49} - 3 q^{50} - 24 q^{51} + 8 q^{53} - 28 q^{54} + q^{55} + 6 q^{56} + 10 q^{58} + 6 q^{59} + 2 q^{60} - 4 q^{61} - 6 q^{62} + 10 q^{63} + 6 q^{64} + 12 q^{66} + 9 q^{67} - 5 q^{68} + 20 q^{69} - 12 q^{70} + 4 q^{71} - 5 q^{72} + 21 q^{73} - 10 q^{74} - 4 q^{75} - 7 q^{76} - 2 q^{77} - 8 q^{78} + 4 q^{79} - 3 q^{80} - 15 q^{81} - 10 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 7 q^{86} + 4 q^{87} - 2 q^{88} + 7 q^{89} + 10 q^{90} + 8 q^{92} + 8 q^{94} - 7 q^{95} + 2 q^{96} + 10 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 3 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 - 5 * q^9 - 3 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 6 * q^16 - 5 * q^17 - 5 * q^18 - 7 * q^19 - 3 * q^20 + 8 * q^21 - 2 * q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 28 * q^27 + 6 * q^28 + 10 * q^29 + 2 * q^30 - 6 * q^31 + 6 * q^32 + 12 * q^33 - 5 * q^34 - 12 * q^35 - 5 * q^36 - 10 * q^37 - 7 * q^38 - 8 * q^39 - 3 * q^40 - 10 * q^41 + 8 * q^42 - 7 * q^43 - 2 * q^44 + 10 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 9 * q^49 - 3 * q^50 - 24 * q^51 + 8 * q^53 - 28 * q^54 + q^55 + 6 * q^56 + 10 * q^58 + 6 * q^59 + 2 * q^60 - 4 * q^61 - 6 * q^62 + 10 * q^63 + 6 * q^64 + 12 * q^66 + 9 * q^67 - 5 * q^68 + 20 * q^69 - 12 * q^70 + 4 * q^71 - 5 * q^72 + 21 * q^73 - 10 * q^74 - 4 * q^75 - 7 * q^76 - 2 * q^77 - 8 * q^78 + 4 * q^79 - 3 * q^80 - 15 * q^81 - 10 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 7 * q^86 + 4 * q^87 - 2 * q^88 + 7 * q^89 + 10 * q^90 + 8 * q^92 + 8 * q^94 - 7 * q^95 + 2 * q^96 + 10 * q^97 + 9 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.58870	−	2.75172i	0.917239	−	1.58870i	0.113650	−	0.993521i	$-0.463746\pi$
$3$	1.58870	−	2.75172i	0.917239	−	1.58870i	0.803589	−	0.595184i	$-0.202921\pi$
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.58870	−	2.75172i	0.648586	−	1.12338i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	1.00000			0.353553
$9$	−3.54797	−	6.14526i	−1.18266	−	2.04842i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.17741			0.656514			0.328257	−	0.944588i	$-0.393539\pi$
$11$	2.17741			0.656514			0.328257	+	0.944588i	$0.393539\pi$
$12$	1.58870	−	2.75172i	0.458620	−	0.794352i
$13$	−1.45926	−	2.52751i	−0.404726	−	0.701006i	0.589563	−	0.807722i	$-0.299300\pi$
$13$	−1.45926	−	2.52751i	−0.404726	−	0.701006i	−0.994290	+	0.106716i	$0.965967\pi$
$14$	1.00000	+	1.73205i	0.267261	+	0.462910i
$15$	1.58870	+	2.75172i	0.410202	+	0.710490i
$16$	1.00000			0.250000
$17$	−0.629444	−	1.09023i	−0.152662	−	0.264419i	0.779543	−	0.626349i	$-0.215451\pi$
$17$	−0.629444	−	1.09023i	−0.152662	−	0.264419i	−0.932205	+	0.361930i	$0.882118\pi$
$18$	−3.54797	−	6.14526i	−0.836264	−	1.44845i
$19$	−2.82982	+	4.90139i	−0.649205	+	1.12446i	0.334108	+	0.942535i	$0.391565\pi$
$19$	−2.82982	+	4.90139i	−0.649205	+	1.12446i	−0.983313	+	0.181921i	$0.941769\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	6.35482			1.38674
$22$	2.17741			0.464225
$23$	−1.17741	+	2.03933i	−0.245507	+	0.425230i	−0.962274	−	0.272082i	$-0.912288\pi$
$23$	−1.17741	+	2.03933i	−0.245507	+	0.425230i	0.716767	+	0.697313i	$0.245621\pi$
$24$	1.58870	−	2.75172i	0.324293	−	0.561692i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.45926	−	2.52751i	−0.286185	−	0.495686i
$27$	−13.0145			−2.50463
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	3.32982	+	5.76741i	0.618332	+	1.07098i	0.989790	+	0.142532i	$0.0455245\pi$
$29$	3.32982	+	5.76741i	0.618332	+	1.07098i	−0.371459	+	0.928450i	$0.621142\pi$
$30$	1.58870	+	2.75172i	0.290056	+	0.502393i
$31$	0.459261	−	0.795464i	0.0824858	−	0.142870i	−0.821831	−	0.569731i	$-0.807047\pi$
$31$	0.459261	−	0.795464i	0.0824858	−	0.142870i	0.904317	+	0.426861i	$0.140381\pi$
$32$	1.00000			0.176777
$33$	3.45926	−	5.99162i	0.602180	−	1.04301i
$34$	−0.629444	−	1.09023i	−0.107949	−	0.186973i
$35$	−2.00000			−0.338062
$36$	−3.54797	−	6.14526i	−0.591328	−	1.02421i
$37$	−2.71815	+	4.70797i	−0.446861	+	0.773986i	−0.998180	−	0.0603089i	$-0.980791\pi$
$37$	−2.71815	+	4.70797i	−0.446861	+	0.773986i	0.551319	+	0.834295i	$0.314125\pi$
$38$	−2.82982	+	4.90139i	−0.459057	+	0.795110i
$39$	−9.27334			−1.48492
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−11.7096			−1.82874			−0.914369	−	0.404882i	$-0.867313\pi$
$41$	−11.7096			−1.82874			−0.914369	+	0.404882i	$0.867313\pi$
$42$	6.35482			0.980570
$43$	5.31408	−	3.84195i	0.810390	−	0.585891i
$43$	5.31408	−	3.84195i	0.810390	−	0.585891i
$44$	2.17741			0.328257
$45$	7.09593			1.05780
$46$	−1.17741	+	2.03933i	−0.173600	+	0.300683i
$47$	1.74111			0.253967			0.126984	−	0.991905i	$-0.459470\pi$
$47$	1.74111			0.253967			0.126984	+	0.991905i	$0.459470\pi$
$48$	1.58870	−	2.75172i	0.229310	−	0.397176i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−4.00000			−0.560112
$52$	−1.45926	−	2.52751i	−0.202363	−	0.350503i
$53$	1.74111	−	3.01570i	0.239160	−	0.414238i	−0.721313	−	0.692609i	$-0.756461\pi$
$53$	1.74111	−	3.01570i	0.239160	−	0.414238i	0.960474	+	0.278371i	$0.0897945\pi$
$54$	−13.0145			−1.77104
$55$	−1.08870	+	1.88569i	−0.146801	+	0.254267i
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$	8.99149	+	15.5737i	1.19095	+	2.06279i
$58$	3.32982	+	5.76741i	0.437226	+	0.757298i
$59$	−9.45075			−1.23038			−0.615192	−	0.788378i	$-0.710921\pi$
$59$	−9.45075			−1.23038			−0.615192	+	0.788378i	$0.710921\pi$
$60$	1.58870	+	2.75172i	0.205101	+	0.355245i
$61$	7.27334	+	12.5978i	0.931256	+	1.61298i	0.781178	+	0.624309i	$0.214619\pi$
$61$	7.27334	+	12.5978i	0.931256	+	1.61298i	0.150078	+	0.988674i	$0.452047\pi$
$62$	0.459261	−	0.795464i	0.0583262	−	0.101024i
$63$	7.09593	−	12.2905i	0.894003	−	1.54846i
$64$	1.00000			0.125000
$65$	2.91852			0.361998
$66$	3.45926	−	5.99162i	0.425806	−	0.737517i
$67$	5.87778	−	10.1806i	0.718086	−	1.24376i	−0.243672	−	0.969858i	$-0.578352\pi$
$67$	5.87778	−	10.1806i	0.718086	−	1.24376i	0.961757	−	0.273903i	$-0.0883147\pi$
$68$	−0.629444	−	1.09023i	−0.0763312	−	0.132210i
$69$	3.74111	+	6.47980i	0.450377	+	0.780076i
$70$	−2.00000			−0.239046
$71$	4.63667	+	8.03095i	0.550272	+	0.953098i	0.998255	+	0.0590563i	$0.0188092\pi$
$71$	4.63667	+	8.03095i	0.550272	+	0.953098i	−0.447983	+	0.894042i	$0.647858\pi$
$72$	−3.54797	−	6.14526i	−0.418132	−	0.724226i
$73$	7.26611	+	12.5853i	0.850434	+	1.47300i	0.880817	+	0.473457i	$0.156994\pi$
$73$	7.26611	+	12.5853i	0.850434	+	1.47300i	−0.0303824	+	0.999538i	$0.509673\pi$
$74$	−2.71815	+	4.70797i	−0.315978	+	0.547291i
$75$	−3.17741			−0.366896
$76$	−2.82982	+	4.90139i	−0.324602	+	0.562228i
$77$	2.17741	+	3.77138i	0.248139	+	0.429789i
$78$	−9.27334			−1.05000
$79$	−4.35482	−	7.54277i	−0.489955	−	0.848628i	0.509978	−	0.860188i	$-0.329654\pi$
$79$	−4.35482	−	7.54277i	−0.489955	−	0.848628i	−0.999933	+	0.0115599i	$0.996320\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−10.0322	+	17.3763i	−1.11469	+	1.93070i
$82$	−11.7096			−1.29311
$83$	−2.50723	+	4.34265i	−0.275204	+	0.476667i	−0.970187	−	0.242359i	$-0.922079\pi$
$83$	−2.50723	+	4.34265i	−0.275204	+	0.476667i	0.694983	+	0.719027i	$0.255412\pi$
$84$	6.35482			0.693368
$85$	1.25889			0.136545
$86$	5.31408	−	3.84195i	0.573032	−	0.414288i
$87$	21.1604			2.26863
$88$	2.17741			0.232113
$89$	0.758887	−	1.31443i	0.0804419	−	0.139329i	−0.822998	−	0.568044i	$-0.807700\pi$
$89$	0.758887	−	1.31443i	0.0804419	−	0.139329i	0.903440	+	0.428715i	$0.141034\pi$
$90$	7.09593			0.747977
$91$	2.91852	−	5.05503i	0.305944	−	0.529911i
$92$	−1.17741	+	2.03933i	−0.122753	+	0.212615i
$93$	−1.45926	−	2.52751i	−0.151318	−	0.262091i
$94$	1.74111			0.179582
$95$	−2.82982	−	4.90139i	−0.290333	−	0.502872i
$96$	1.58870	−	2.75172i	0.162147	−	0.280846i
$97$	12.9330			1.31314			0.656572	−	0.754263i	$-0.272006\pi$
$97$	12.9330			1.31314			0.656572	+	0.754263i	$0.272006\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	−7.72538	−	13.3807i	−0.776429	−	1.34482i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.94352	−	13.7586i	−0.790410	−	1.36903i	−0.925713	−	0.378226i	$-0.876534\pi$
$101$	−7.94352	−	13.7586i	−0.790410	−	1.36903i	0.135303	−	0.990804i	$-0.456799\pi$
$102$	−4.00000			−0.396059
$103$	−4.30685	−	7.45969i	−0.424367	−	0.735025i	0.571994	−	0.820258i	$-0.306170\pi$
$103$	−4.30685	−	7.45969i	−0.424367	−	0.735025i	−0.996361	+	0.0852327i	$0.972837\pi$
$104$	−1.45926	−	2.52751i	−0.143092	−	0.247843i
$105$	−3.17741	+	5.50344i	−0.310083	+	0.537080i
$106$	1.74111	−	3.01570i	0.169112	−	0.292910i
$107$	−2.27334			−0.219772			−0.109886	−	0.993944i	$-0.535049\pi$
$107$	−2.27334			−0.219772			−0.109886	+	0.993944i	$0.535049\pi$
$108$	−13.0145			−1.25232
$109$	4.15241	−	7.19218i	0.397729	−	0.688886i	−0.595717	−	0.803195i	$-0.703132\pi$
$109$	4.15241	−	7.19218i	0.397729	−	0.688886i	0.993445	+	0.114309i	$0.0364652\pi$
$110$	−1.08870	+	1.88569i	−0.103804	+	0.179794i
$111$	8.63667	+	14.9592i	0.819757	+	1.41986i
$112$	1.00000	+	1.73205i	0.0944911	+	0.163663i
$113$	−11.0500			−1.03950			−0.519748	−	0.854319i	$-0.673974\pi$
$113$	−11.0500			−1.03950			−0.519748	+	0.854319i	$0.673974\pi$
$114$	8.99149	+	15.5737i	0.842130	+	1.45861i
$115$	−1.17741	−	2.03933i	−0.109794	−	0.190169i
$116$	3.32982	+	5.76741i	0.309166	+	0.535491i
$117$	−10.3548	+	17.9351i	−0.957303	+	1.65810i
$118$	−9.45075			−0.870012
$119$	1.25889	−	2.18046i	0.115402	−	0.199882i
$120$	1.58870	+	2.75172i	0.145028	+	0.251196i
$121$	−6.25889			−0.568990
$122$	7.27334	+	12.5978i	0.658497	+	1.14055i
$123$	−18.6032	+	32.2216i	−1.67739	+	2.90533i
$124$	0.459261	−	0.795464i	0.0412429	−	0.0714348i
$125$	1.00000			0.0894427
$126$	7.09593	−	12.2905i	0.632156	−	1.09493i
$127$	10.9685			0.973299			0.486650	−	0.873597i	$-0.338219\pi$
$127$	10.9685			0.973299			0.486650	+	0.873597i	$0.338219\pi$
$128$	1.00000			0.0883883
$129$	−2.12944	−	20.7266i	−0.187487	−	1.82487i
$130$	2.91852			0.255971
$131$	−8.22334			−0.718476			−0.359238	−	0.933246i	$-0.616963\pi$
$131$	−8.22334			−0.718476			−0.359238	+	0.933246i	$0.616963\pi$
$132$	3.45926	−	5.99162i	0.301090	−	0.521503i
$133$	−11.3193			−0.981505
$134$	5.87778	−	10.1806i	0.507763	−	0.879472i
$135$	6.50723	−	11.2708i	0.560053	−	0.970040i
$136$	−0.629444	−	1.09023i	−0.0539743	−	0.0934863i
$137$	−11.0815			−0.946755			−0.473377	−	0.880860i	$-0.656965\pi$
$137$	−11.0815			−0.946755			−0.473377	+	0.880860i	$0.656965\pi$
$138$	3.74111	+	6.47980i	0.318465	+	0.551597i
$139$	−8.20760	+	14.2160i	−0.696160	+	1.20578i	0.273629	+	0.961835i	$0.411776\pi$
$139$	−8.20760	+	14.2160i	−0.696160	+	1.20578i	−0.969788	+	0.243948i	$0.921557\pi$
$140$	−2.00000			−0.169031
$141$	2.76611	−	4.79105i	0.232949	−	0.403479i
$142$	4.63667	+	8.03095i	0.389101	+	0.673942i
$143$	−3.17741	−	5.50344i	−0.265708	−	0.460220i
$144$	−3.54797	−	6.14526i	−0.295664	−	0.512105i
$145$	−6.65964			−0.553053
$146$	7.26611	+	12.5853i	0.601348	+	1.04157i
$147$	−4.76611	−	8.25515i	−0.393103	−	0.680874i
$148$	−2.71815	+	4.70797i	−0.223430	+	0.386993i
$149$	11.0250	−	19.0959i	0.903203	−	1.56439i	0.0798923	−	0.996803i	$-0.474542\pi$
$149$	11.0250	−	19.0959i	0.903203	−	1.56439i	0.823311	−	0.567591i	$-0.192124\pi$
$150$	−3.17741			−0.259434
$151$	−9.88297			−0.804265			−0.402133	−	0.915581i	$-0.631731\pi$
$151$	−9.88297			−0.804265			−0.402133	+	0.915581i	$0.631731\pi$
$152$	−2.82982	+	4.90139i	−0.229529	+	0.397555i
$153$	−4.46649	+	7.73619i	−0.361094	+	0.625434i
$154$	2.17741	+	3.77138i	0.175461	+	0.303907i
$155$	0.459261	+	0.795464i	0.0368888	+	0.0638932i
$156$	−9.27334			−0.742462
$157$	0.718148	+	1.24387i	0.0573145	+	0.0992716i	0.893259	−	0.449542i	$-0.148413\pi$
$157$	0.718148	+	1.24387i	0.0573145	+	0.0992716i	−0.835945	+	0.548814i	$0.815080\pi$
$158$	−4.35482	−	7.54277i	−0.346451	−	0.600070i
$159$	−5.53223	−	9.58210i	−0.438734	−	0.759910i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−4.70964			−0.371172
$162$	−10.0322	+	17.3763i	−0.788206	+	1.36521i
$163$	−12.1511	−	21.0464i	−0.951750	−	1.64848i	−0.741637	−	0.670802i	$-0.765950\pi$
$163$	−12.1511	−	21.0464i	−0.951750	−	1.64848i	−0.210113	−	0.977677i	$-0.567383\pi$
$164$	−11.7096			−0.914369
$165$	3.45926	+	5.99162i	0.269303	+	0.466447i
$166$	−2.50723	+	4.34265i	−0.194599	+	0.337055i
$167$	0.789079	−	1.36673i	0.0610608	−	0.105760i	−0.833879	−	0.551947i	$-0.813885\pi$
$167$	0.789079	−	1.36673i	0.0610608	−	0.105760i	0.894940	+	0.446187i	$0.147218\pi$
$168$	6.35482			0.490285
$169$	2.24111	−	3.88172i	0.172393	−	0.298594i
$170$	1.25889			0.0965522
$171$	40.1604			3.07114
$172$	5.31408	−	3.84195i	0.405195	−	0.292946i
$173$	−12.0000			−0.912343			−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000			−0.912343			−0.456172	+	0.889892i	$0.650780\pi$
$174$	21.1604			1.60417
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	2.17741			0.164128
$177$	−15.0145	+	26.0058i	−1.12856	+	1.95472i
$178$	0.758887	−	1.31443i	0.0568810	−	0.0985208i
$179$	−4.64390	−	8.04347i	−0.347101	−	0.601197i	0.638632	−	0.769512i	$-0.279501\pi$
$179$	−4.64390	−	8.04347i	−0.347101	−	0.601197i	−0.985733	+	0.168315i	$0.946167\pi$
$180$	7.09593			0.528900
$181$	5.91852	+	10.2512i	0.439920	+	0.761964i	0.997683	−	0.0680362i	$-0.0216733\pi$
$181$	5.91852	+	10.2512i	0.439920	+	0.761964i	−0.557763	+	0.830001i	$0.688340\pi$
$182$	2.91852	−	5.05503i	0.216335	−	0.374704i
$183$	46.2208			3.41674
$184$	−1.17741	+	2.03933i	−0.0867998	+	0.150342i
$185$	−2.71815	−	4.70797i	−0.199842	−	0.346137i
$186$	−1.45926	−	2.52751i	−0.106998	−	0.185326i
$187$	−1.37056	−	2.37387i	−0.100225	−	0.173595i
$188$	1.74111			0.126984
$189$	−13.0145	−	22.5417i	−0.946662	−	1.63967i
$190$	−2.82982	−	4.90139i	−0.205297	−	0.355584i
$191$	2.91852	−	5.05503i	0.211177	−	0.365769i	−0.740906	−	0.671608i	$-0.765604\pi$
$191$	2.91852	−	5.05503i	0.211177	−	0.365769i	0.952083	+	0.305839i	$0.0989371\pi$
$192$	1.58870	−	2.75172i	0.114655	−	0.198588i
$193$	12.0289			0.865860			0.432930	−	0.901428i	$-0.357480\pi$
$193$	12.0289			0.865860			0.432930	+	0.901428i	$0.357480\pi$
$194$	12.9330			0.928534
$195$	4.63667	−	8.03095i	0.332039	−	0.575108i
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	6.25889	+	10.8407i	0.445927	+	0.772369i	0.998116	−	0.0613503i	$-0.0195407\pi$
$197$	6.25889	+	10.8407i	0.445927	+	0.772369i	−0.552189	+	0.833719i	$0.686207\pi$
$198$	−7.72538	−	13.3807i	−0.549019	−	0.950928i
$199$	−3.27334			−0.232041			−0.116021	−	0.993247i	$-0.537014\pi$
$199$	−3.27334			−0.232041			−0.116021	+	0.993247i	$0.537014\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−18.6761	−	32.3480i	−1.31731	−	2.28165i
$202$	−7.94352	−	13.7586i	−0.558904	−	0.968051i
$203$	−6.65964	+	11.5348i	−0.467415	+	0.809586i
$204$	−4.00000			−0.280056
$205$	5.85482	−	10.1408i	0.408918	−	0.708267i
$206$	−4.30685	−	7.45969i	−0.300073	−	0.519741i
$207$	16.7096			1.16140
$208$	−1.45926	−	2.52751i	−0.101182	−	0.175252i
$209$	−6.16167	+	10.6723i	−0.426212	+	0.738221i
$210$	−3.17741	+	5.50344i	−0.219262	+	0.379773i
$211$	−21.7911			−1.50016			−0.750081	−	0.661346i	$-0.769986\pi$
$211$	−21.7911			−1.50016			−0.750081	+	0.661346i	$0.769986\pi$
$212$	1.74111	−	3.01570i	0.119580	−	0.207119i
$213$	29.4652			2.01892
$214$	−2.27334			−0.155402
$215$	0.670182	+	6.52310i	0.0457060	+	0.444872i
$216$	−13.0145			−0.885521
$217$	1.83705			0.124707
$218$	4.15241	−	7.19218i	0.281237	−	0.487116i
$219$	46.1748			3.12021
$220$	−1.08870	+	1.88569i	−0.0734005	+	0.127133i
$221$	−1.83705	+	3.18186i	−0.123573	+	0.214035i
$222$	8.63667	+	14.9592i	0.579655	+	1.00399i
$223$	25.3233			1.69578			0.847888	−	0.530175i	$-0.177874\pi$
$223$	25.3233			1.69578			0.847888	+	0.530175i	$0.177874\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$	−3.54797	+	6.14526i	−0.236531	+	0.409684i
$226$	−11.0500			−0.735035
$227$	3.60444	−	6.24308i	0.239235	−	0.414368i	−0.721260	−	0.692665i	$-0.756437\pi$
$227$	3.60444	−	6.24308i	0.239235	−	0.414368i	0.960495	+	0.278297i	$0.0897700\pi$
$228$	8.99149	+	15.5737i	0.595476	+	1.03139i
$229$	−2.68464	−	4.64993i	−0.177406	−	0.307276i	0.763585	−	0.645707i	$-0.223437\pi$
$229$	−2.68464	−	4.64993i	−0.177406	−	0.307276i	−0.940991	+	0.338431i	$0.890104\pi$
$230$	−1.17741	−	2.03933i	−0.0776361	−	0.134470i
$231$	13.8370			0.910411
$232$	3.32982	+	5.76741i	0.218613	+	0.378649i
$233$	9.08020	+	15.7274i	0.594863	+	1.03033i	0.993566	+	0.113253i	$0.0361272\pi$
$233$	9.08020	+	15.7274i	0.594863	+	1.03033i	−0.398703	+	0.917080i	$0.630539\pi$
$234$	−10.3548	+	17.9351i	−0.676916	+	1.17245i
$235$	−0.870556	+	1.50785i	−0.0567888	+	0.0983612i
$236$	−9.45075			−0.615192
$237$	−27.6741			−1.79763
$238$	1.25889	−	2.18046i	0.0816015	−	0.141338i
$239$	11.4278	−	19.7935i	0.739202	−	1.28034i	−0.213653	−	0.976910i	$-0.568536\pi$
$239$	11.4278	−	19.7935i	0.739202	−	1.28034i	0.952855	−	0.303426i	$-0.0981305\pi$
$240$	1.58870	+	2.75172i	0.102550	+	0.177623i
$241$	1.03351	+	1.79009i	0.0665743	+	0.115310i	0.897391	−	0.441236i	$-0.145460\pi$
$241$	1.03351	+	1.79009i	0.0665743	+	0.115310i	−0.830817	+	0.556546i	$0.812126\pi$
$242$	−6.25889			−0.402336
$243$	12.3548	+	21.3992i	0.792562	+	1.37276i
$244$	7.27334	+	12.5978i	0.465628	+	0.806491i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$	−18.6032	+	32.2216i	−1.18609	+	2.05438i
$247$	16.5178			1.05100
$248$	0.459261	−	0.795464i	0.0291631	−	0.0505120i
$249$	7.96649	+	13.7984i	0.504856	+	0.874436i
$250$	1.00000			0.0632456
$251$	−10.7024	−	18.5371i	−0.675530	−	1.17005i	−0.976314	−	0.216360i	$-0.930581\pi$
$251$	−10.7024	−	18.5371i	−0.675530	−	1.17005i	0.300783	−	0.953692i	$-0.402752\pi$
$252$	7.09593	−	12.2905i	0.447002	−	0.774230i
$253$	−2.56370	+	4.44046i	−0.161179	+	0.279170i
$254$	10.9685			0.688227
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$	1.00000			0.0625000
$257$	12.0145			0.749441			0.374721	−	0.927138i	$-0.377739\pi$
$257$	12.0145			0.749441			0.374721	+	0.927138i	$0.377739\pi$
$258$	−2.12944	−	20.7266i	−0.132573	−	1.29038i
$259$	−10.8726			−0.675590
$260$	2.91852			0.180999
$261$	23.6282	−	40.9252i	1.46255	−	2.53320i
$262$	−8.22334			−0.508040
$263$	−12.9206	+	22.3791i	−0.796716	+	1.37995i	0.125028	+	0.992153i	$0.460098\pi$
$263$	−12.9206	+	22.3791i	−0.796716	+	1.37995i	−0.921744	+	0.387799i	$0.873235\pi$
$264$	3.45926	−	5.99162i	0.212903	−	0.368758i
$265$	1.74111	+	3.01570i	0.106956	+	0.185253i
$266$	−11.3193			−0.694029
$267$	−2.41130	−	4.17649i	−0.147569	−	0.255597i
$268$	5.87778	−	10.1806i	0.359043	−	0.621880i
$269$	−23.8160			−1.45208			−0.726042	−	0.687650i	$-0.758642\pi$
$269$	−23.8160			−1.45208			−0.726042	+	0.687650i	$0.758642\pi$
$270$	6.50723	−	11.2708i	0.396017	−	0.685922i
$271$	1.82259	+	3.15682i	0.110714	+	0.191763i	0.916059	−	0.401045i	$-0.131353\pi$
$271$	1.82259	+	3.15682i	0.110714	+	0.191763i	−0.805344	+	0.592808i	$0.798019\pi$
$272$	−0.629444	−	1.09023i	−0.0381656	−	0.0661048i
$273$	−9.27334	−	16.0619i	−0.561248	−	0.972110i
$274$	−11.0815			−0.669457
$275$	−1.08870	−	1.88569i	−0.0656514	−	0.113712i
$276$	3.74111	+	6.47980i	0.225189	+	0.390038i
$277$	8.53223	−	14.7783i	0.512652	−	0.887939i	−0.487240	−	0.873268i	$-0.661996\pi$
$277$	8.53223	−	14.7783i	0.512652	−	0.887939i	0.999892	−	0.0146714i	$-0.00467021\pi$
$278$	−8.20760	+	14.2160i	−0.492259	+	0.852618i
$279$	−6.51777			−0.390209
$280$	−2.00000			−0.119523
$281$	−11.8213	+	20.4751i	−0.705200	+	1.22144i	0.261419	+	0.965225i	$0.415810\pi$
$281$	−11.8213	+	20.4751i	−0.705200	+	1.22144i	−0.966619	+	0.256217i	$0.917524\pi$
$282$	2.76611	−	4.79105i	0.164720	−	0.285303i
$283$	−5.77130	−	9.99619i	−0.343068	−	0.594212i	0.641932	−	0.766761i	$-0.278133\pi$
$283$	−5.77130	−	9.99619i	−0.343068	−	0.594212i	−0.985001	+	0.172549i	$0.944800\pi$
$284$	4.63667	+	8.03095i	0.275136	+	0.476549i
$285$	−17.9830			−1.06522
$286$	−3.17741	−	5.50344i	−0.187884	−	0.325425i
$287$	−11.7096	−	20.2817i	−0.691198	−	1.19719i
$288$	−3.54797	−	6.14526i	−0.209066	−	0.362113i
$289$	7.70760	−	13.3500i	0.453388	−	0.785292i
$290$	−6.65964			−0.391067
$291$	20.5467	−	35.5879i	1.20447	−	2.08620i
$292$	7.26611	+	12.5853i	0.425217	+	0.736498i
$293$	−19.0645			−1.11376			−0.556879	−	0.830594i	$-0.688001\pi$
$293$	−19.0645			−1.11376			−0.556879	+	0.830594i	$0.688001\pi$
$294$	−4.76611	−	8.25515i	−0.277965	−	0.481450i
$295$	4.72538	−	8.18459i	0.275122	−	0.476525i
$296$	−2.71815	+	4.70797i	−0.157989	+	0.273645i
$297$	−28.3378			−1.64433
$298$	11.0250	−	19.0959i	0.638661	−	1.10619i
$299$	6.87259			0.397452
$300$	−3.17741			−0.183448
$301$	11.9685	+	5.36231i	0.689854	+	0.309079i
$302$	−9.88297			−0.568701
$303$	−50.4797			−2.89998
$304$	−2.82982	+	4.90139i	−0.162301	+	0.281114i
$305$	−14.5467			−0.832941
$306$	−4.46649	+	7.73619i	−0.255332	+	0.442248i
$307$	13.9278	−	24.1236i	0.794901	−	1.37681i	−0.128001	−	0.991774i	$-0.540856\pi$
$307$	13.9278	−	24.1236i	0.794901	−	1.37681i	0.922902	−	0.385035i	$-0.125810\pi$
$308$	2.17741	+	3.77138i	0.124069	+	0.214895i
$309$	−27.3693			−1.55698
$310$	0.459261	+	0.795464i	0.0260843	+	0.0451793i
$311$	−6.70964	+	11.6214i	−0.380469	+	0.658991i	−0.991129	−	0.132901i	$-0.957571\pi$
$311$	−6.70964	+	11.6214i	−0.380469	+	0.658991i	0.610661	+	0.791892i	$0.290904\pi$
$312$	−9.27334			−0.525000
$313$	5.07297	−	8.78664i	0.286741	−	0.496650i	−0.686289	−	0.727329i	$-0.740761\pi$
$313$	5.07297	−	8.78664i	0.286741	−	0.496650i	0.973030	+	0.230679i	$0.0740947\pi$
$314$	0.718148	+	1.24387i	0.0405275	+	0.0701956i
$315$	7.09593	+	12.2905i	0.399810	+	0.692492i
$316$	−4.35482	−	7.54277i	−0.244978	−	0.424314i
$317$	14.4007			0.808827			0.404413	−	0.914576i	$-0.367476\pi$
$317$	14.4007			0.808827			0.404413	+	0.914576i	$0.367476\pi$
$318$	−5.53223	−	9.58210i	−0.310232	−	0.537338i
$319$	7.25038	+	12.5580i	0.405943	+	0.703114i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−3.61167	+	6.25559i	−0.201584	+	0.349153i
$322$	−4.70964			−0.262458
$323$	7.12484			0.396437
$324$	−10.0322	+	17.3763i	−0.557346	+	0.965352i
$325$	−1.45926	+	2.52751i	−0.0809453	+	0.140201i
$326$	−12.1511	−	21.0464i	−0.672989	−	1.16565i
$327$	−13.1939	−	22.8525i	−0.729624	−	1.26375i
$328$	−11.7096			−0.646557
$329$	1.74111	+	3.01570i	0.0959907	+	0.166261i
$330$	3.45926	+	5.99162i	0.190426	+	0.329828i
$331$	0.243150	+	0.421148i	0.0133647	+	0.0231484i	0.872630	−	0.488381i	$-0.162412\pi$
$331$	0.243150	+	0.421148i	0.0133647	+	0.0231484i	−0.859266	+	0.511530i	$0.829079\pi$
$332$	−2.50723	+	4.34265i	−0.137602	+	0.238334i
$333$	38.5756			2.11393
$334$	0.789079	−	1.36673i	0.0431765	−	0.0747839i
$335$	5.87778	+	10.1806i	0.321138	+	0.556227i
$336$	6.35482			0.346684
$337$	15.0572	+	26.0799i	0.820220	+	1.42066i	0.905519	+	0.424307i	$0.139482\pi$
$337$	15.0572	+	26.0799i	0.820220	+	1.42066i	−0.0852989	+	0.996355i	$0.527185\pi$
$338$	2.24111	−	3.88172i	0.121900	−	0.211138i
$339$	−17.5552	+	30.4065i	−0.953467	+	1.65145i
$340$	1.25889			0.0682727
$341$	1.00000	−	1.73205i	0.0541530	−	0.0937958i
$342$	40.1604			2.17163
$343$	20.0000			1.07990
$344$	5.31408	−	3.84195i	0.286516	−	0.207144i
$345$	−7.48223			−0.402829
$346$	−12.0000			−0.645124
$347$	8.87778	−	15.3768i	0.476584	−	0.825468i	−0.523056	−	0.852299i	$-0.675208\pi$
$347$	8.87778	−	15.3768i	0.476584	−	0.825468i	0.999640	+	0.0268302i	$0.00854133\pi$
$348$	21.1604			1.13432
$349$	−16.4258	+	28.4502i	−0.879250	+	1.52291i	−0.0270851	+	0.999633i	$0.508623\pi$
$349$	−16.4258	+	28.4502i	−0.879250	+	1.52291i	−0.852165	+	0.523273i	$0.824711\pi$
$350$	1.00000	−	1.73205i	0.0534522	−	0.0925820i
$351$	18.9915	+	32.8942i	1.01369	+	1.75576i
$352$	2.17741			0.116056
$353$	6.53946	+	11.3267i	0.348060	+	0.602858i	0.985905	−	0.167307i	$-0.0535072\pi$
$353$	6.53946	+	11.3267i	0.348060	+	0.602858i	−0.637845	+	0.770165i	$0.720174\pi$
$354$	−15.0145	+	26.0058i	−0.798009	+	1.38219i
$355$	−9.27334			−0.492178
$356$	0.758887	−	1.31443i	0.0402209	−	0.0696647i
$357$	−4.00000	−	6.92820i	−0.211702	−	0.366679i
$358$	−4.64390	−	8.04347i	−0.245438	−	0.425110i
$359$	2.02296	+	3.50388i	0.106768	+	0.184928i	0.914459	−	0.404678i	$-0.132616\pi$
$359$	2.02296	+	3.50388i	0.106768	+	0.184928i	−0.807691	+	0.589606i	$0.799283\pi$
$360$	7.09593			0.373988
$361$	−6.51574	−	11.2856i	−0.342934	−	0.593978i
$362$	5.91852	+	10.2512i	0.311071	+	0.538790i
$363$	−9.94352	+	17.2227i	−0.521900	+	0.903957i
$364$	2.91852	−	5.05503i	0.152972	−	0.264956i
$365$	−14.5322			−0.760652
$366$	46.2208			2.41600
$367$	2.38629	−	4.13318i	0.124564	−	0.215750i	−0.796999	−	0.603981i	$-0.793580\pi$
$367$	2.38629	−	4.13318i	0.124564	−	0.215750i	0.921562	+	0.388231i	$0.126914\pi$
$368$	−1.17741	+	2.03933i	−0.0613767	+	0.106308i
$369$	41.5454	+	71.9587i	2.16277	+	3.74602i
$370$	−2.71815	−	4.70797i	−0.141310	−	0.244756i
$371$	6.96445			0.361576
$372$	−1.45926	−	2.52751i	−0.0756592	−	0.131046i
$373$	−0.223339	−	0.386834i	−0.0115640	−	0.0200295i	0.860185	−	0.509981i	$-0.170348\pi$
$373$	−0.223339	−	0.386834i	−0.0115640	−	0.0200295i	−0.871750	+	0.489952i	$0.837014\pi$
$374$	−1.37056	−	2.37387i	−0.0708698	−	0.122750i
$375$	1.58870	−	2.75172i	0.0820404	−	0.142098i
$376$	1.74111			0.0897910
$377$	9.71815	−	16.8323i	0.500510	−	0.866909i
$378$	−13.0145	−	22.5417i	−0.669391	−	1.15942i
$379$	13.0789			0.671819			0.335909	−	0.941894i	$-0.390956\pi$
$379$	13.0789			0.671819			0.335909	+	0.941894i	$0.390956\pi$
$380$	−2.82982	−	4.90139i	−0.145167	−	0.251436i
$381$	17.4258	−	30.1823i	0.892748	−	1.54629i
$382$	2.91852	−	5.05503i	0.149325	−	0.258638i
$383$	−17.6782			−0.903312			−0.451656	−	0.892192i	$-0.649167\pi$
$383$	−17.6782			−0.903312			−0.451656	+	0.892192i	$0.649167\pi$
$384$	1.58870	−	2.75172i	0.0810733	−	0.140423i
$385$	−4.35482			−0.221942
$386$	12.0289			0.612255
$387$	−42.4639	−	19.0253i	−2.15856	−	0.967110i
$388$	12.9330			0.656572
$389$	11.1563			0.565648			0.282824	−	0.959172i	$-0.408729\pi$
$389$	11.1563			0.565648			0.282824	+	0.959172i	$0.408729\pi$
$390$	4.63667	−	8.03095i	0.234787	−	0.406663i
$391$	2.96445			0.149919
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$	−13.0645	+	22.6283i	−0.659015	+	1.14145i
$394$	6.25889	+	10.8407i	0.315318	+	0.546147i
$395$	8.70964			0.438229
$396$	−7.72538	−	13.3807i	−0.388215	−	0.672408i
$397$	−10.4363	+	18.0762i	−0.523783	+	0.907218i	0.475834	+	0.879535i	$0.342146\pi$
$397$	−10.4363	+	18.0762i	−0.523783	+	0.907218i	−0.999617	+	0.0276832i	$0.991187\pi$
$398$	−3.27334			−0.164078
$399$	−17.9830	+	31.1474i	−0.900275	+	1.55932i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−1.82259	−	3.15682i	−0.0910158	−	0.157644i	0.816923	−	0.576747i	$-0.195678\pi$
$401$	−1.82259	−	3.15682i	−0.0910158	−	0.157644i	−0.907939	+	0.419103i	$0.862345\pi$
$402$	−18.6761	−	32.3480i	−0.931481	−	1.61337i
$403$	−2.68073			−0.133537
$404$	−7.94352	−	13.7586i	−0.395205	−	0.684515i
$405$	−10.0322	−	17.3763i	−0.498505	−	0.863437i
$406$	−6.65964	+	11.5348i	−0.330512	+	0.572464i
$407$	−5.91852	+	10.2512i	−0.293370	+	0.508132i
$408$	−4.00000			−0.198030
$409$	37.7675			1.86748			0.933740	−	0.357951i	$-0.116525\pi$
$409$	37.7675			1.86748			0.933740	+	0.357951i	$0.116525\pi$
$410$	5.85482	−	10.1408i	0.289149	−	0.500821i
$411$	−17.6052	+	30.4931i	−0.868400	+	1.50411i
$412$	−4.30685	−	7.45969i	−0.212183	−	0.367512i
$413$	−9.45075	−	16.3692i	−0.465041	−	0.805475i
$414$	16.7096			0.821234
$415$	−2.50723	−	4.34265i	−0.123075	−	0.213172i
$416$	−1.45926	−	2.52751i	−0.0715462	−	0.123922i
$417$	26.0789	+	45.1700i	1.27709	+	2.21198i
$418$	−6.16167	+	10.6723i	−0.301377	+	0.522001i
$419$	−31.9660			−1.56164			−0.780820	−	0.624756i	$-0.785198\pi$
$419$	−31.9660			−1.56164			−0.780820	+	0.624756i	$0.785198\pi$
$420$	−3.17741	+	5.50344i	−0.155042	+	0.268540i
$421$	−2.42575	−	4.20152i	−0.118224	−	0.204770i	0.800840	−	0.598878i	$-0.204387\pi$
$421$	−2.42575	−	4.20152i	−0.118224	−	0.204770i	−0.919064	+	0.394109i	$0.871053\pi$
$422$	−21.7911			−1.06077
$423$	−6.17741	−	10.6996i	−0.300356	−	0.520232i
$424$	1.74111	−	3.01570i	0.0845559	−	0.146455i
$425$	−0.629444	+	1.09023i	−0.0305325	+	0.0528838i
$426$	29.4652			1.42759
$427$	−14.5467	+	25.1956i	−0.703963	+	1.21930i
$428$	−2.27334			−0.109886
$429$	−20.1919			−0.974872
$430$	0.670182	+	6.52310i	0.0323191	+	0.314572i
$431$	−15.2444			−0.734298			−0.367149	−	0.930162i	$-0.619666\pi$
$431$	−15.2444			−0.734298			−0.367149	+	0.930162i	$0.619666\pi$
$432$	−13.0145			−0.626158
$433$	−3.02296	+	5.23593i	−0.145274	+	0.251623i	−0.929475	−	0.368884i	$-0.879740\pi$
$433$	−3.02296	+	5.23593i	−0.145274	+	0.251623i	0.784201	+	0.620507i	$0.213073\pi$
$434$	1.83705			0.0881810
$435$	−10.5802	+	18.3254i	−0.507282	+	0.878637i
$436$	4.15241	−	7.19218i	0.198864	−	0.344443i
$437$	−6.66371	−	11.5419i	−0.318768	−	0.552123i
$438$	46.1748			2.20632
$439$	9.54668	+	16.5353i	0.455638	+	0.789189i	0.998725	−	0.0504881i	$-0.0160777\pi$
$439$	9.54668	+	16.5353i	0.455638	+	0.789189i	−0.543086	+	0.839677i	$0.682744\pi$
$440$	−1.08870	+	1.88569i	−0.0519020	+	0.0898968i
$441$	−21.2878			−1.01370
$442$	−1.83705	+	3.18186i	−0.0873793	+	0.151345i
$443$	10.1354	+	17.5550i	0.481547	+	0.834064i	0.999776	−	0.0211784i	$-0.00674179\pi$
$443$	10.1354	+	17.5550i	0.481547	+	0.834064i	−0.518229	+	0.855242i	$0.673408\pi$
$444$	8.63667	+	14.9592i	0.409878	+	0.709930i
$445$	0.758887	+	1.31443i	0.0359747	+	0.0623100i
$446$	25.3233			1.19910
$447$	−35.0309	−	60.6754i	−1.65691	−	2.86985i
$448$	1.00000	+	1.73205i	0.0472456	+	0.0818317i
$449$	2.15964	−	3.74060i	0.101920	−	0.176530i	−0.810556	−	0.585661i	$-0.800835\pi$
$449$	2.15964	−	3.74060i	0.101920	−	0.176530i	0.912475	+	0.409131i	$0.134168\pi$
$450$	−3.54797	+	6.14526i	−0.167253	+	0.289690i
$451$	−25.4967			−1.20059
$452$	−11.0500			−0.519748
$453$	−15.7011	+	27.1952i	−0.737703	+	1.27774i
$454$	3.60444	−	6.24308i	0.169165	−	0.293002i
$455$	2.91852	+	5.05503i	0.136822	+	0.236983i
$456$	8.99149	+	15.5737i	0.421065	+	0.729306i
$457$	32.4152			1.51632			0.758160	−	0.652069i	$-0.226099\pi$
$457$	32.4152			1.51632			0.758160	+	0.652069i	$0.226099\pi$
$458$	−2.68464	−	4.64993i	−0.125445	−	0.217277i
$459$	8.19186	+	14.1887i	0.382363	+	0.662273i
$460$	−1.17741	−	2.03933i	−0.0548970	−	0.0950844i
$461$	3.78057	−	6.54814i	0.176079	−	0.304977i	−0.764455	−	0.644677i	$-0.776992\pi$
$461$	3.78057	−	6.54814i	0.176079	−	0.304977i	0.940534	+	0.339699i	$0.110325\pi$
$462$	13.8370			0.643758
$463$	4.56574	−	7.90809i	0.212188	−	0.367520i	−0.740211	−	0.672375i	$-0.765274\pi$
$463$	4.56574	−	7.90809i	0.212188	−	0.367520i	0.952399	+	0.304854i	$0.0986078\pi$
$464$	3.32982	+	5.76741i	0.154583	+	0.267745i
$465$	2.91852			0.135343
$466$	9.08020	+	15.7274i	0.420632	+	0.728556i
$467$	4.96981	−	8.60796i	0.229975	−	0.398329i	−0.727825	−	0.685763i	$-0.759469\pi$
$467$	4.96981	−	8.60796i	0.229975	−	0.398329i	0.957801	+	0.287434i	$0.0928021\pi$
$468$	−10.3548	+	17.9351i	−0.478652	+	0.829049i
$469$	23.5111			1.08564
$470$	−0.870556	+	1.50785i	−0.0401558	+	0.0695518i
$471$	4.56370			0.210284
$472$	−9.45075			−0.435006
$473$	11.5709	−	8.36549i	0.532032	−	0.384646i
$474$	−27.6741			−1.27111
$475$	5.65964			0.259682
$476$	1.25889	−	2.18046i	0.0577010	−	0.0999411i
$477$	−24.7096			−1.13138
$478$	11.4278	−	19.7935i	0.522695	−	0.905334i
$479$	16.6741	−	28.8804i	0.761859	−	1.31958i	−0.180033	−	0.983661i	$-0.557620\pi$
$479$	16.6741	−	28.8804i	0.761859	−	1.31958i	0.941891	−	0.335917i	$-0.109046\pi$
$480$	1.58870	+	2.75172i	0.0725141	+	0.125598i
$481$	15.8660			0.723425
$482$	1.03351	+	1.79009i	0.0470751	+	0.0815365i
$483$	−7.48223	+	12.9596i	−0.340453	+	0.589682i
$484$	−6.25889			−0.284495
$485$	−6.46649	+	11.2003i	−0.293628	+	0.508579i
$486$	12.3548	+	21.3992i	0.560426	+	0.970686i
$487$	2.61167	+	4.52354i	0.118346	+	0.204981i	0.919112	−	0.393996i	$-0.128907\pi$
$487$	2.61167	+	4.52354i	0.118346	+	0.204981i	−0.800766	+	0.598977i	$0.795574\pi$
$488$	7.27334	+	12.5978i	0.329249	+	0.570276i
$489$	−77.2182			−3.49193
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	5.96130	+	10.3253i	0.269030	+	0.465973i	0.968612	−	0.248579i	$-0.0799637\pi$
$491$	5.96130	+	10.3253i	0.269030	+	0.465973i	−0.699582	+	0.714552i	$0.746630\pi$
$492$	−18.6032	+	32.2216i	−0.838695	+	1.45266i
$493$	4.19186	−	7.26052i	0.188792	−	0.326997i
$494$	16.5178			0.743170
$495$	15.4508			0.694460
$496$	0.459261	−	0.795464i	0.0206214	−	0.0357174i
$497$	−9.27334	+	16.0619i	−0.415966	+	0.720475i
$498$	7.96649	+	13.7984i	0.356987	+	0.618319i
$499$	5.60648	+	9.71071i	0.250980	+	0.434711i	0.963796	−	0.266641i	$-0.0859137\pi$
$499$	5.60648	+	9.71071i	0.250980	+	0.434711i	−0.712816	+	0.701352i	$0.752580\pi$
$500$	1.00000			0.0447214
$501$	−2.50723	−	4.34265i	−0.112015	−	0.194015i
$502$	−10.7024	−	18.5371i	−0.477672	−	0.827352i
$503$	−1.43426	−	2.48421i	−0.0639505	−	0.110765i	0.832277	−	0.554359i	$-0.187037\pi$
$503$	−1.43426	−	2.48421i	−0.0639505	−	0.110765i	−0.896228	+	0.443594i	$0.853703\pi$
$504$	7.09593	−	12.2905i	0.316078	−	0.547463i
$505$	15.8870			0.706964
$506$	−2.56370	+	4.44046i	−0.113971	+	0.197403i
$507$	−7.12093	−	12.3338i	−0.316252	−	0.547764i
$508$	10.9685			0.486650
$509$	−5.42575	−	9.39767i	−0.240492	−	0.416545i	0.720362	−	0.693598i	$-0.243975\pi$
$509$	−5.42575	−	9.39767i	−0.240492	−	0.416545i	−0.960855	+	0.277053i	$0.910642\pi$
$510$	2.00000	−	3.46410i	0.0885615	−	0.153393i
$511$	−14.5322	+	25.1706i	−0.642868	+	1.11348i
$512$	1.00000			0.0441942
$513$	36.8285	−	63.7889i	1.62602	−	2.81635i
$514$	12.0145			0.529935
$515$	8.61371			0.379565
$516$	−2.12944	−	20.7266i	−0.0937435	−	0.912436i
$517$	3.79112			0.166733
$518$	−10.8726			−0.477714
$519$	−19.0645	+	33.0206i	−0.836837	+	1.44944i
$520$	2.91852			0.127986
$521$	−10.2576	+	17.7667i	−0.449394	+	0.778373i	−0.998347	−	0.0574804i	$-0.981693\pi$
$521$	−10.2576	+	17.7667i	−0.449394	+	0.778373i	0.548953	+	0.835853i	$0.315027\pi$
$522$	23.6282	−	40.9252i	1.03418	−	1.79125i
$523$	−12.1867	−	21.1079i	−0.532886	−	0.922986i	−0.999262	−	0.0383994i	$-0.987774\pi$
$523$	−12.1867	−	21.1079i	−0.532886	−	0.922986i	0.466376	−	0.884586i	$-0.345559\pi$
$524$	−8.22334			−0.359238
$525$	−3.17741	−	5.50344i	−0.138674	−	0.240190i
$526$	−12.9206	+	22.3791i	−0.563363	+	0.975774i
$527$	−1.15632			−0.0503699
$528$	3.45926	−	5.99162i	0.150545	−	0.260752i
$529$	8.72741	+	15.1163i	0.379453	+	0.657231i
$530$	1.74111	+	3.01570i	0.0756291	+	0.130993i
$531$	33.5309	+	58.0773i	1.45512	+	2.52034i
$532$	−11.3193			−0.490753
$533$	17.0874	+	29.5963i	0.740138	+	1.28196i
$534$	−2.41130	−	4.17649i	−0.104347	−	0.180734i
$535$	1.13667	−	1.96877i	0.0491426	−	0.0851174i
$536$	5.87778	−	10.1806i	0.253882	−	0.439736i
$537$	−29.5111			−1.27350
$538$	−23.8160			−1.02678
$539$	3.26611	−	5.65708i	0.140682	−	0.243668i
$540$	6.50723	−	11.2708i	0.280026	−	0.485020i
$541$	4.63463	+	8.02742i	0.199258	+	0.345126i	0.948288	−	0.317411i	$-0.102813\pi$
$541$	4.63463	+	8.02742i	0.199258	+	0.345126i	−0.749030	+	0.662536i	$0.769480\pi$
$542$	1.82259	+	3.15682i	0.0782870	+	0.135597i
$543$	37.6111			1.61405
$544$	−0.629444	−	1.09023i	−0.0269872	−	0.0467431i
$545$	4.15241	+	7.19218i	0.177870	+	0.308079i
$546$	−9.27334	−	16.0619i	−0.396862	−	0.687386i
$547$	−11.4258	+	19.7900i	−0.488530	+	0.846158i	−0.999913	−	0.0131944i	$-0.995800\pi$
$547$	−11.4258	+	19.7900i	−0.488530	+	0.846158i	0.511383	+	0.859353i	$0.329133\pi$
$548$	−11.0815			−0.473377
$549$	51.6111	−	89.3931i	2.20271	−	3.81521i
$550$	−1.08870	−	1.88569i	−0.0464225	−	0.0804062i
$551$	−37.6911			−1.60570
$552$	3.74111	+	6.47980i	0.159232	+	0.275799i
$553$	8.70964	−	15.0855i	0.370372	−	0.641502i
$554$	8.53223	−	14.7783i	0.362500	−	0.627868i
$555$	−17.2733			−0.733213
$556$	−8.20760	+	14.2160i	−0.348080	+	0.602892i
$557$	33.5822			1.42292			0.711462	−	0.702724i	$-0.248033\pi$
$557$	33.5822			1.42292			0.711462	+	0.702724i	$0.248033\pi$
$558$	−6.51777			−0.275919
$559$	−17.4652	−	7.82501i	−0.738700	−	0.330963i
$560$	−2.00000			−0.0845154
$561$	−8.70964			−0.367721
$562$	−11.8213	+	20.4751i	−0.498652	+	0.863690i
$563$	19.3693			0.816318			0.408159	−	0.912911i	$-0.366171\pi$
$563$	19.3693			0.816318			0.408159	+	0.912911i	$0.366171\pi$
$564$	2.76611	−	4.79105i	0.116474	−	0.201740i
$565$	5.52500	−	9.56958i	0.232439	−	0.402595i
$566$	−5.77130	−	9.99619i	−0.242586	−	0.420171i
$567$	−40.1289			−1.68526
$568$	4.63667	+	8.03095i	0.194550	+	0.336971i
$569$	7.43298	−	12.8743i	0.311607	−	0.539719i	−0.667104	−	0.744965i	$-0.732466\pi$
$569$	7.43298	−	12.8743i	0.311607	−	0.539719i	0.978710	+	0.205246i	$0.0657996\pi$
$570$	−17.9830			−0.753224
$571$	5.03742	−	8.72507i	0.210809	−	0.365133i	−0.741159	−	0.671330i	$-0.765723\pi$
$571$	5.03742	−	8.72507i	0.210809	−	0.365133i	0.951968	+	0.306197i	$0.0990567\pi$
$572$	−3.17741	−	5.50344i	−0.132854	−	0.230110i
$573$	−9.27334	−	16.0619i	−0.387399	−	0.670995i
$574$	−11.7096	−	20.2817i	−0.488751	−	0.846541i
$575$	2.35482			0.0982028
$576$	−3.54797	−	6.14526i	−0.147832	−	0.256052i
$577$	−19.5237	−	33.8161i	−0.812783	−	1.40778i	−0.910909	−	0.412608i	$-0.864618\pi$
$577$	−19.5237	−	33.8161i	−0.812783	−	1.40778i	0.0981258	−	0.995174i	$-0.468715\pi$
$578$	7.70760	−	13.3500i	0.320594	−	0.555285i
$579$	19.1104	−	33.1002i	0.794201	−	1.37560i
$580$	−6.65964			−0.276526
$581$	−10.0289			−0.416069
$582$	20.5467	−	35.5879i	0.851687	−	1.47517i
$583$	3.79112	−	6.56641i	0.157012	−	0.271953i
$584$	7.26611	+	12.5853i	0.300674	+	0.520783i
$585$	−10.3548	−	17.9351i	−0.428119	−	0.741524i
$586$	−19.0645			−0.787546
$587$	5.04074	+	8.73082i	0.208054	+	0.360359i	0.951101	−	0.308879i	$-0.0999538\pi$
$587$	5.04074	+	8.73082i	0.208054	+	0.360359i	−0.743048	+	0.669238i	$0.766621\pi$
$588$	−4.76611	−	8.25515i	−0.196551	−	0.340437i
$589$	2.59925	+	4.50204i	0.107100	+	0.185503i
$590$	4.72538	−	8.18459i	0.194541	−	0.336954i
$591$	39.7741			1.63609
$592$	−2.71815	+	4.70797i	−0.111715	+	0.193496i
$593$	18.8672	+	32.6790i	0.774785	+	1.34197i	0.934915	+	0.354870i	$0.115475\pi$
$593$	18.8672	+	32.6790i	0.774785	+	1.34197i	−0.160131	+	0.987096i	$0.551192\pi$
$594$	−28.3378			−1.16271
$595$	1.25889	+	2.18046i	0.0516093	+	0.0893900i
$596$	11.0250	−	19.0959i	0.451602	−	0.782197i
$597$	−5.20037	+	9.00731i	−0.212837	+	0.368645i
$598$	6.87259			0.281041
$599$	−18.2963	+	31.6901i	−0.747567	+	1.29482i	0.201419	+	0.979505i	$0.435445\pi$
$599$	−18.2963	+	31.6901i	−0.747567	+	1.29482i	−0.948986	+	0.315319i	$0.897889\pi$
$600$	−3.17741			−0.129717
$601$	−25.5756			−1.04325			−0.521625	−	0.853175i	$-0.674674\pi$
$601$	−25.5756			−1.04325			−0.521625	+	0.853175i	$0.674674\pi$
$602$	11.9685	+	5.36231i	0.487801	+	0.218552i
$603$	−83.4167			−3.39699
$604$	−9.88297			−0.402133
$605$	3.12944	−	5.42036i	0.127230	−	0.220369i
$606$	−50.4797			−2.05060
$607$	4.58020	−	7.93313i	0.185904	−	0.321996i	−0.757977	−	0.652282i	$-0.773812\pi$
$607$	4.58020	−	7.93313i	0.185904	−	0.321996i	0.943881	+	0.330286i	$0.107145\pi$
$608$	−2.82982	+	4.90139i	−0.114764	+	0.198778i
$609$	21.1604	+	36.6509i	0.857462	+	1.48517i
$610$	−14.5467			−0.588978
$611$	−2.54074	−	4.40069i	−0.102787	−	0.178033i
$612$	−4.46649	+	7.73619i	−0.180547	+	0.312717i
$613$	47.2274			1.90750			0.953749	−	0.300605i	$-0.0971887\pi$
$613$	47.2274			1.90750			0.953749	+	0.300605i	$0.0971887\pi$
$614$	13.9278	−	24.1236i	0.562080	−	0.973551i
$615$	−18.6032	−	32.2216i	−0.750152	−	1.29930i
$616$	2.17741	+	3.77138i	0.0877303	+	0.151953i
$617$	2.10444	+	3.64500i	0.0847216	+	0.146742i	0.905273	−	0.424831i	$-0.139667\pi$
$617$	2.10444	+	3.64500i	0.0847216	+	0.146742i	−0.820551	+	0.571573i	$0.806333\pi$
$618$	−27.3693			−1.10095
$619$	−1.36333	−	2.36136i	−0.0547968	−	0.0949109i	0.837326	−	0.546704i	$-0.184118\pi$
$619$	−1.36333	−	2.36136i	−0.0547968	−	0.0949109i	−0.892123	+	0.451793i	$0.850784\pi$
$620$	0.459261	+	0.795464i	0.0184444	+	0.0319466i
$621$	15.3233	−	26.5408i	0.614905	−	1.06505i
$622$	−6.70964	+	11.6214i	−0.269032	+	0.465977i
$623$	3.03555			0.121617
$624$	−9.27334			−0.371231
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.07297	−	8.78664i	0.202757	−	0.351185i
$627$	19.5782	+	33.9104i	0.781876	+	1.35425i
$628$	0.718148	+	1.24387i	0.0286572	+	0.0496358i
$629$	6.84368			0.272876
$630$	7.09593	+	12.2905i	0.282709	+	0.489666i
$631$	10.2878	+	17.8190i	0.409551	+	0.709363i	0.994839	−	0.101462i	$-0.0323521\pi$
$631$	10.2878	+	17.8190i	0.409551	+	0.709363i	−0.585289	+	0.810825i	$0.699019\pi$
$632$	−4.35482	−	7.54277i	−0.173225	−	0.300035i
$633$	−34.6197	+	59.9630i	−1.37601	+	2.38332i
$634$	14.4007			0.571927
$635$	−5.48426	+	9.49902i	−0.217636	+	0.376957i
$636$	−5.53223	−	9.58210i	−0.219367	−	0.379955i
$637$	−8.75557			−0.346908
$638$	7.25038	+	12.5580i	0.287045	+	0.497177i
$639$	32.9015	−	56.9871i	1.30156	−	2.25437i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	24.5822			0.970940			0.485470	−	0.874253i	$-0.338649\pi$
$641$	24.5822			0.970940			0.485470	+	0.874253i	$0.338649\pi$
$642$	−3.61167	+	6.25559i	−0.142541	+	0.246889i
$643$	6.24443			0.246256			0.123128	−	0.992391i	$-0.460707\pi$
$643$	6.24443			0.246256			0.123128	+	0.992391i	$0.460707\pi$
$644$	−4.70964			−0.185586
$645$	19.0145	+	8.51913i	0.748693	+	0.335440i
$646$	7.12484			0.280323
$647$	15.3233			0.602423			0.301211	−	0.953557i	$-0.402609\pi$
$647$	15.3233			0.602423			0.301211	+	0.953557i	$0.402609\pi$
$648$	−10.0322	+	17.3763i	−0.394103	+	0.682607i
$649$	−20.5782			−0.807763
$650$	−1.45926	+	2.52751i	−0.0572369	+	0.0991373i
$651$	2.91852	−	5.05503i	0.114386	−	0.198122i
$652$	−12.1511	−	21.0464i	−0.475875	−	0.824239i
$653$	−35.0934			−1.37331			−0.686655	−	0.726984i	$-0.740922\pi$
$653$	−35.0934			−1.37331			−0.686655	+	0.726984i	$0.740922\pi$
$654$	−13.1939	−	22.8525i	−0.515922	−	0.893604i
$655$	4.11167	−	7.12162i	0.160656	−	0.278265i
$656$	−11.7096			−0.457185
$657$	51.5599	−	89.3043i	2.01154	−	3.48409i
$658$	1.74111	+	3.01570i	0.0678756	+	0.117564i
$659$	−1.74111	−	3.01570i	−0.0678241	−	0.117475i	0.830119	−	0.557586i	$-0.188272\pi$
$659$	−1.74111	−	3.01570i	−0.0678241	−	0.117475i	−0.897943	+	0.440111i	$0.854939\pi$
$660$	3.45926	+	5.99162i	0.134652	+	0.233223i
$661$	14.5467			0.565800			0.282900	−	0.959149i	$-0.408703\pi$
$661$	14.5467			0.565800			0.282900	+	0.959149i	$0.408703\pi$
$662$	0.243150	+	0.421148i	0.00945029	+	0.0163684i
$663$	5.83705	+	10.1101i	0.226692	+	0.392642i
$664$	−2.50723	+	4.34265i	−0.0972993	+	0.168527i
$665$	5.65964	−	9.80278i	0.219471	−	0.380135i
$666$	38.5756			1.49477
$667$	−15.6822			−0.607219
$668$	0.789079	−	1.36673i	0.0305304	−	0.0528802i
$669$	40.2313	−	69.6827i	1.55543	−	2.69409i
$670$	5.87778	+	10.1806i	0.227079	+	0.393312i
$671$	15.8370	+	27.4306i	0.611382	+	1.05895i
$672$	6.35482			0.245142
$673$	−18.4495	−	31.9554i	−0.711175	−	1.23179i	−0.964416	−	0.264388i	$-0.914830\pi$
$673$	−18.4495	−	31.9554i	−0.711175	−	1.23179i	0.253242	−	0.967403i	$-0.418503\pi$
$674$	15.0572	+	26.0799i	0.579983	+	1.00456i
$675$	6.50723	+	11.2708i	0.250463	+	0.433815i
$676$	2.24111	−	3.88172i	0.0861967	−	0.149297i
$677$	26.2459			1.00871			0.504357	−	0.863495i	$-0.331730\pi$
$677$	26.2459			1.00871			0.504357	+	0.863495i	$0.331730\pi$
$678$	−17.5552	+	30.4065i	−0.674203	+	1.16775i
$679$	12.9330	+	22.4006i	0.496322	+	0.859655i
$680$	1.25889			0.0482761
$681$	−11.4528	−	19.8368i	−0.438872	−	0.760148i
$682$	1.00000	−	1.73205i	0.0382920	−	0.0663237i
$683$	2.75557	−	4.77278i	0.105439	−	0.182625i	−0.808479	−	0.588526i	$-0.799709\pi$
$683$	2.75557	−	4.77278i	0.105439	−	0.182625i	0.913917	+	0.405900i	$0.133042\pi$
$684$	40.1604			1.53557
$685$	5.54074	−	9.59684i	0.211701	−	0.366676i
$686$	20.0000			0.763604
$687$	−17.0604			−0.650894
$688$	5.31408	−	3.84195i	0.202597	−	0.146473i
$689$	−10.1630			−0.387178
$690$	−7.48223			−0.284843
$691$	25.2661	−	43.7622i	0.961168	−	1.66479i	0.241593	−	0.970378i	$-0.422330\pi$
$691$	25.2661	−	43.7622i	0.961168	−	1.66479i	0.719575	−	0.694415i	$-0.244337\pi$
$692$	−12.0000			−0.456172
$693$	15.4508	−	26.7615i	0.586926	−	1.01658i
$694$	8.87778	−	15.3768i	0.336996	−	0.583694i
$695$	−8.20760	−	14.2160i	−0.311332	−	0.539243i
$696$	21.1604			0.802083
$697$	7.37056	+	12.7662i	0.279180	+	0.483553i
$698$	−16.4258	+	28.4502i	−0.621724	+	1.07686i
$699$	57.7030			2.18253
$700$	1.00000	−	1.73205i	0.0377964	−	0.0654654i
$701$	18.9895	+	32.8907i	0.717222	+	1.24226i	0.962096	+	0.272710i	$0.0879199\pi$
$701$	18.9895	+	32.8907i	0.717222	+	1.24226i	−0.244875	+	0.969555i	$0.578747\pi$
$702$	18.9915	+	32.8942i	0.716788	+	1.24151i
$703$	−15.3837	−	26.6454i	−0.580208	−	1.00495i
$704$	2.17741			0.0820642
$705$	2.76611	+	4.79105i	0.104178	+	0.180441i
$706$	6.53946	+	11.3267i	0.246116	+	0.426285i
$707$	15.8870	−	27.5172i	0.597494	−	1.03489i
$708$	−15.0145	+	26.0058i	−0.564278	+	0.977358i
$709$	−38.5967			−1.44953			−0.724765	−	0.688997i	$-0.758051\pi$
$709$	−38.5967			−1.44953			−0.724765	+	0.688997i	$0.758051\pi$
$710$	−9.27334			−0.348022
$711$	−30.9015	+	53.5230i	−1.15890	+	2.00727i
$712$	0.758887	−	1.31443i	0.0284405	−	0.0492604i
$713$	1.08148	+	1.87317i	0.0405016	+	0.0701509i
$714$	−4.00000	−	6.92820i	−0.149696	−	0.259281i
$715$	6.35482			0.237657
$716$	−4.64390	−	8.04347i	−0.173551	−	0.300599i
$717$	−36.3108	−	62.8921i	−1.35605	−	2.34875i
$718$	2.02296	+	3.50388i	0.0754964	+	0.130764i
$719$	−11.3548	+	19.6671i	−0.423463	+	0.733460i	−0.996276	−	0.0862266i	$-0.972519\pi$
$719$	−11.3548	+	19.6671i	−0.423463	+	0.733460i	0.572812	+	0.819687i	$0.305852\pi$
$720$	7.09593			0.264450
$721$	8.61371	−	14.9194i	0.320791	−	0.555627i
$722$	−6.51574	−	11.2856i	−0.242491	−	0.420006i
$723$	6.56778			0.244258
$724$	5.91852	+	10.2512i	0.219960	+	0.380982i
$725$	3.32982	−	5.76741i	0.123666	−	0.214196i
$726$	−9.94352	+	17.2227i	−0.369039	+	0.639194i
$727$	−29.9371			−1.11030			−0.555152	−	0.831749i	$-0.687340\pi$
$727$	−29.9371			−1.11030			−0.555152	+	0.831749i	$0.687340\pi$
$728$	2.91852	−	5.05503i	0.108168	−	0.187352i
$729$	18.3193			0.678492
$730$	−14.5322			−0.537862
$731$	−7.53351	−	3.37527i	−0.278637	−	0.124839i
$732$	46.2208			1.70837
$733$	6.30889			0.233024			0.116512	−	0.993189i	$-0.462829\pi$
$733$	6.30889			0.233024			0.116512	+	0.993189i	$0.462829\pi$
$734$	2.38629	−	4.13318i	0.0880797	−	0.152559i
$735$	9.53223			0.351602
$736$	−1.17741	+	2.03933i	−0.0433999	+	0.0751708i
$737$	12.7983	−	22.1674i	0.471433	−	0.816546i
$738$	41.5454	+	71.9587i	1.52931	+	2.64884i
$739$	−37.1393			−1.36619			−0.683096	−	0.730329i	$-0.739367\pi$
$739$	−37.1393			−1.36619			−0.683096	+	0.730329i	$0.739367\pi$
$740$	−2.71815	−	4.70797i	−0.0999211	−	0.173068i
$741$	26.2419	−	45.4522i	0.964019	−	1.66973i
$742$	6.96445			0.255673
$743$	−8.32335	+	14.4165i	−0.305354	+	0.528889i	−0.977340	−	0.211675i	$-0.932108\pi$
$743$	−8.32335	+	14.4165i	−0.305354	+	0.528889i	0.671986	+	0.740564i	$0.265441\pi$
$744$	−1.45926	−	2.52751i	−0.0534991	−	0.0926632i
$745$	11.0250	+	19.0959i	0.403925	+	0.699618i
$746$	−0.223339	−	0.386834i	−0.00817701	−	0.0141630i
$747$	35.5822			1.30189
$748$	−1.37056	−	2.37387i	−0.0501125	−	0.0867974i
$749$	−2.27334	−	3.93754i	−0.0830661	−	0.143875i
$750$	1.58870	−	2.75172i	0.0580113	−	0.100479i
$751$	−17.4737	+	30.2654i	−0.637625	+	1.10440i	0.348328	+	0.937373i	$0.386750\pi$
$751$	−17.4737	+	30.2654i	−0.637625	+	1.10440i	−0.985953	+	0.167026i	$0.946584\pi$
$752$	1.74111			0.0634919
$753$	−68.0119			−2.47849
$754$	9.71815	−	16.8323i	0.353914	−	0.612997i
$755$	4.94149	−	8.55891i	0.179839	−	0.311491i
$756$	−13.0145	−	22.5417i	−0.473331	−	0.819834i
$757$	14.2819	+	24.7369i	0.519083	+	0.899078i	0.999754	+	0.0221768i	$0.00705968\pi$
$757$	14.2819	+	24.7369i	0.519083	+	0.899078i	−0.480671	+	0.876901i	$0.659607\pi$
$758$	13.0789			0.475048
$759$	8.14594	+	14.1092i	0.295679	+	0.512131i
$760$	−2.82982	−	4.90139i	−0.102648	−	0.177792i
$761$	3.99796	+	6.92467i	0.144926	+	0.251019i	0.929345	−	0.369212i	$-0.120372\pi$
$761$	3.99796	+	6.92467i	0.144926	+	0.251019i	−0.784419	+	0.620231i	$0.787039\pi$
$762$	17.4258	−	30.1823i	0.631268	−	1.09339i
$763$	16.6096			0.601309
$764$	2.91852	−	5.05503i	0.105588	−	0.182885i
$765$	−4.46649	−	7.73619i	−0.161486	−	0.279702i
$766$	−17.6782			−0.638738
$767$	13.7911	+	23.8869i	0.497968	+	0.862506i
$768$	1.58870	−	2.75172i	0.0573274	−	0.0992941i
$769$	4.64390	−	8.04347i	0.167463	−	0.290055i	−0.770064	−	0.637967i	$-0.779776\pi$
$769$	4.64390	−	8.04347i	0.167463	−	0.290055i	0.937527	+	0.347912i	$0.113109\pi$
$770$	−4.35482			−0.156937
$771$	19.0874	−	33.0604i	0.687417	−	1.19064i
$772$	12.0289			0.432930
$773$	−2.88961			−0.103932			−0.0519661	−	0.998649i	$-0.516549\pi$
$773$	−2.88961			−0.103932			−0.0519661	+	0.998649i	$0.516549\pi$
$774$	−42.4639	−	19.0253i	−1.52633	−	0.683850i
$775$	−0.918523			−0.0329943
$776$	12.9330			0.464267
$777$	−17.2733	+	29.9183i	−0.619678	+	1.07331i
$778$	11.1563			0.399973
$779$	33.1361	−	57.3935i	1.18723	−	2.05633i
$780$	4.63667	−	8.03095i	0.166019	−	0.287554i
$781$	10.0959	+	17.4867i	0.361261	+	0.625722i
$782$	2.96445			0.106009
$783$	−43.3358	−	75.0597i	−1.54869	−	2.68242i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	−1.43630			−0.0512636
$786$	−13.0645	+	22.6283i	−0.465994	+	0.807125i
$787$	−3.04202	−	5.26893i	−0.108436	−	0.187817i	0.806701	−	0.590960i	$-0.201251\pi$
$787$	−3.04202	−	5.26893i	−0.108436	−	0.187817i	−0.915137	+	0.403143i	$0.867918\pi$
$788$	6.25889	+	10.8407i	0.222964	+	0.386184i
$789$	41.0539	+	71.1075i	1.46156	+	2.53149i
$790$	8.70964			0.309875
$791$	−11.0500	−	19.1392i	−0.392893	−	0.680510i
$792$	−7.72538	−	13.3807i	−0.274509	−	0.475464i
$793$	21.2274	−	36.7670i	0.753808	−	1.30563i
$794$	−10.4363	+	18.0762i	−0.370370	+	0.641500i
$795$	11.0645			0.392416
$796$	−3.27334			−0.116021
$797$	8.93111	−	15.4691i	0.316356	−	0.547945i	−0.663369	−	0.748293i	$-0.730874\pi$
$797$	8.93111	−	15.4691i	0.316356	−	0.547945i	0.979725	+	0.200348i	$0.0642073\pi$
$798$	−17.9830	+	31.1474i	−0.636591	+	1.10261i
$799$	−1.09593	−	1.89821i	−0.0387713	−	0.0671539i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−10.7700			−0.380540
$802$	−1.82259	−	3.15682i	−0.0643579	−	0.111471i
$803$	15.8213	+	27.4033i	0.558322	+	0.967042i
$804$	−18.6761	−	32.3480i	−0.658656	−	1.14083i
$805$	2.35482	−	4.07867i	0.0829965	−	0.143754i
$806$	−2.68073			−0.0944247
$807$	−37.8365	+	65.5348i	−1.33191	+	2.30693i
$808$	−7.94352	−	13.7586i	−0.279452	−	0.484025i
$809$	29.8989			1.05119			0.525595	−	0.850735i	$-0.323843\pi$
$809$	29.8989			1.05119			0.525595	+	0.850735i	$0.323843\pi$
$810$	−10.0322	−	17.3763i	−0.352497	−	0.610542i
$811$	−21.6269	+	37.4589i	−0.759422	+	1.31536i	0.183723	+	0.982978i	$0.441185\pi$
$811$	−21.6269	+	37.4589i	−0.759422	+	1.31536i	−0.943145	+	0.332380i	$0.892148\pi$
$812$	−6.65964	+	11.5348i	−0.233707	+	0.404793i
$813$	11.5822			0.406207
$814$	−5.91852	+	10.2512i	−0.207444	+	0.359304i
$815$	24.3023			0.851271
$816$	−4.00000			−0.140028
$817$	3.79299	+	36.9184i	0.132700	+	1.29161i
$818$	37.7675			1.32051
$819$	−41.4193			−1.44731
$820$	5.85482	−	10.1408i	0.204459	−	0.354134i
$821$	0.134045			0.00467820			0.00233910	−	0.999997i	$-0.499255\pi$
$821$	0.134045			0.00467820			0.00233910	+	0.999997i	$0.499255\pi$
$822$	−17.6052	+	30.4931i	−0.614052	+	1.06357i
$823$	−19.2398	+	33.3244i	−0.670658	+	1.16161i	0.307059	+	0.951690i	$0.400655\pi$
$823$	−19.2398	+	33.3244i	−0.670658	+	1.16161i	−0.977718	+	0.209924i	$0.932678\pi$
$824$	−4.30685	−	7.45969i	−0.150036	−	0.259871i
$825$	−6.91852			−0.240872
$826$	−9.45075	−	16.3692i	−0.328834	−	0.569557i
$827$	−1.43758	+	2.48996i	−0.0499895	+	0.0865844i	−0.889937	−	0.456083i	$-0.849252\pi$
$827$	−1.43758	+	2.48996i	−0.0499895	+	0.0865844i	0.839948	+	0.542667i	$0.182585\pi$
$828$	16.7096			0.580700
$829$	−21.7135	+	37.6090i	−0.754143	+	1.30621i	0.191657	+	0.981462i	$0.438614\pi$
$829$	−21.7135	+	37.6090i	−0.754143	+	1.30621i	−0.945799	+	0.324751i	$0.894719\pi$
$830$	−2.50723	−	4.34265i	−0.0870271	−	0.150735i
$831$	−27.1104	−	46.9566i	−0.940449	−	1.62891i
$832$	−1.45926	−	2.52751i	−0.0505908	−	0.0876258i
$833$	−3.77666			−0.130854
$834$	26.0789	+	45.1700i	0.903039	+	1.56411i
$835$	0.789079	+	1.36673i	0.0273072	+	0.0472975i
$836$	−6.16167	+	10.6723i	−0.213106	+	0.369110i
$837$	−5.97704	+	10.3525i	−0.206597	+	0.357836i
$838$	−31.9660			−1.10425
$839$	−4.84743			−0.167352			−0.0836759	−	0.996493i	$-0.526666\pi$
$839$	−4.84743			−0.167352			−0.0836759	+	0.996493i	$0.526666\pi$
$840$	−3.17741	+	5.50344i	−0.109631	+	0.189887i
$841$	−7.67537	+	13.2941i	−0.264668	+	0.458418i
$842$	−2.42575	−	4.20152i	−0.0835969	−	0.144794i
$843$	37.5611	+	65.0578i	1.29367	+	2.24071i
$844$	−21.7911			−0.750081
$845$	2.24111	+	3.88172i	0.0770966	+	0.133535i
$846$	−6.17741	−	10.6996i	−0.212384	−	0.367859i
$847$	−6.25889	−	10.8407i	−0.215058	−	0.372491i
$848$	1.74111	−	3.01570i	0.0597901	−	0.103559i
$849$	−36.6756			−1.25870
$850$	−0.629444	+	1.09023i	−0.0215897	+	0.0373945i
$851$	−6.40075	−	11.0864i	−0.219415	−	0.380038i
$852$	29.4652			1.00946
$853$	9.03742	+	15.6533i	0.309435	+	0.535958i	0.978239	−	0.207481i	$-0.0665266\pi$
$853$	9.03742	+	15.6533i	0.309435	+	0.535958i	−0.668804	+	0.743439i	$0.733193\pi$
$854$	−14.5467	+	25.1956i	−0.497777	+	0.862176i
$855$	−20.0802	+	34.7799i	−0.686728	+	1.18945i
$856$	−2.27334			−0.0777012
$857$	−19.3819	+	33.5704i	−0.662072	+	1.14674i	0.317999	+	0.948091i	$0.396989\pi$
$857$	−19.3819	+	33.5704i	−0.662072	+	1.14674i	−0.980070	+	0.198651i	$0.936344\pi$
$858$	−20.1919			−0.689339
$859$	−13.5218			−0.461360			−0.230680	−	0.973030i	$-0.574095\pi$
$859$	−13.5218			−0.461360			−0.230680	+	0.973030i	$0.574095\pi$
$860$	0.670182	+	6.52310i	0.0228530	+	0.222436i
$861$	−74.4126			−2.53598
$862$	−15.2444			−0.519227
$863$	14.7911	−	25.6190i	0.503495	−	0.872080i	−0.496496	−	0.868039i	$-0.665380\pi$
$863$	14.7911	−	25.6190i	0.503495	−	0.872080i	0.999992	−	0.00404091i	$-0.00128627\pi$
$864$	−13.0145			−0.442761
$865$	6.00000	−	10.3923i	0.204006	−	0.353349i
$866$	−3.02296	+	5.23593i	−0.102725	+	0.177924i
$867$	−24.4902	−	42.4183i	−0.831731	−	1.44060i
$868$	1.83705			0.0623534
$869$	−9.48223	−	16.4237i	−0.321662	−	0.557136i
$870$	−10.5802	+	18.3254i	−0.358702	+	0.621290i
$871$	−34.3089			−1.16251
$872$	4.15241	−	7.19218i	0.140618	−	0.243558i
$873$	−45.8858	−	79.4765i	−1.55300	−	2.68987i
$874$	−6.66371	−	11.5419i	−0.225403	−	0.390410i
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$	46.1748			1.56010
$877$	16.3378	+	28.2979i	0.551688	+	0.955552i	0.998153	+	0.0607509i	$0.0193495\pi$
$877$	16.3378	+	28.2979i	0.551688	+	0.955552i	−0.446465	+	0.894801i	$0.647317\pi$
$878$	9.54668	+	16.5353i	0.322185	+	0.558041i
$879$	−30.2878	+	52.4600i	−1.02158	+	1.76943i
$880$	−1.08870	+	1.88569i	−0.0367002	+	0.0635667i
$881$	30.3482			1.02246			0.511228	−	0.859445i	$-0.329191\pi$
$881$	30.3482			1.02246			0.511228	+	0.859445i	$0.329191\pi$
$882$	−21.2878			−0.716797
$883$	6.10648	−	10.5767i	0.205499	−	0.355935i	−0.744792	−	0.667296i	$-0.767451\pi$
$883$	6.10648	−	10.5767i	0.205499	−	0.355935i	0.950292	+	0.311361i	$0.100785\pi$
$884$	−1.83705	+	3.18186i	−0.0617865	+	0.107017i
$885$	−15.0145	−	26.0058i	−0.504705	−	0.874175i
$886$	10.1354	+	17.5550i	0.340505	+	0.589772i
$887$	10.2630			0.344597			0.172298	−	0.985045i	$-0.444881\pi$
$887$	10.2630			0.344597			0.172298	+	0.985045i	$0.444881\pi$
$888$	8.63667	+	14.9592i	0.289828	+	0.501996i
$889$	10.9685	+	18.9980i	0.367873	+	0.637174i
$890$	0.758887	+	1.31443i	0.0254380	+	0.0440598i
$891$	−21.8443	+	37.8354i	−0.731811	+	1.26753i
$892$	25.3233			0.847888
$893$	−4.92703	+	8.53387i	−0.164877	+	0.285575i
$894$	−35.0309	−	60.6754i	−1.17161	−	2.02929i
$895$	9.28780			0.310457
$896$	1.00000	+	1.73205i	0.0334077	+	0.0578638i
$897$	10.9185	−	18.9114i	0.364559	−	0.631434i
$898$	2.15964	−	3.74060i	0.0720680	−	0.124825i
$899$	6.11703			0.204014
$900$	−3.54797	+	6.14526i	−0.118266	+	0.204842i
$901$	−4.38373			−0.146043
$902$	−25.4967			−0.848947
$903$	33.7700	−	24.4149i	1.12380	−	0.812476i
$904$	−11.0500			−0.367518
$905$	−11.8370			−0.393477
$906$	−15.7011	+	27.1952i	−0.521635	+	0.903498i
$907$	−34.6152			−1.14938			−0.574690	−	0.818371i	$-0.694877\pi$
$907$	−34.6152			−1.14938			−0.574690	+	0.818371i	$0.694877\pi$
$908$	3.60444	−	6.24308i	0.119618	−	0.207184i
$909$	−56.3667	+	97.6300i	−1.86957	+	3.23818i
$910$	2.91852	+	5.05503i	0.0967481	+	0.167573i
$911$	40.9134			1.35552			0.677761	−	0.735283i	$-0.262951\pi$
$911$	40.9134			1.35552			0.677761	+	0.735283i	$0.262951\pi$
$912$	8.99149	+	15.5737i	0.297738	+	0.515697i
$913$	−5.45926	+	9.45572i	−0.180675	+	0.312939i
$914$	32.4152			1.07220
$915$	−23.1104	+	40.0284i	−0.764006	+	1.32330i
$916$	−2.68464	−	4.64993i	−0.0887029	−	0.153638i
$917$	−8.22334	−	14.2432i	−0.271559	−	0.470353i
$918$	8.19186	+	14.1887i	0.270372	+	0.468298i
$919$	−33.8452			−1.11645			−0.558225	−	0.829690i	$-0.688517\pi$
$919$	−33.8452			−1.11645			−0.558225	+	0.829690i	$0.688517\pi$
$920$	−1.17741	−	2.03933i	−0.0388180	−	0.0672348i
$921$	−44.2543	−	76.6507i	−1.45823	−	2.52573i
$922$	3.78057	−	6.54814i	0.124506	−	0.215651i
$923$	13.5322	−	23.4385i	0.445419	−	0.771488i
$924$	13.8370			0.455205
$925$	5.43630			0.178744
$926$	4.56574	−	7.90809i	0.150040	−	0.259876i
$927$	−30.5611	+	52.9334i	−1.00376	+	1.73856i
$928$	3.32982	+	5.76741i	0.109307	+	0.189325i
$929$	27.3076	+	47.2982i	0.895934	+	1.55180i	0.832645	+	0.553807i	$0.186826\pi$
$929$	27.3076	+	47.2982i	0.895934	+	1.55180i	0.0632886	+	0.997995i	$0.479841\pi$
$930$	2.91852			0.0957021
$931$	8.48945	+	14.7042i	0.278231	+	0.481910i
$932$	9.08020	+	15.7274i	0.297432	+	0.515167i
$933$	21.3193	+	36.9261i	0.697962	+	1.20890i
$934$	4.96981	−	8.60796i	0.162617	−	0.281661i
$935$	2.74111			0.0896440
$936$	−10.3548	+	17.9351i	−0.338458	+	0.586226i
$937$	−0.143144	−	0.247932i	−0.00467630	−	0.00809958i	0.863678	−	0.504044i	$-0.168155\pi$
$937$	−0.143144	−	0.247932i	−0.00467630	−	0.00809958i	−0.868354	+	0.495945i	$0.834822\pi$
$938$	23.5111			0.767666
$939$	−16.1189	−	27.9187i	−0.526020	−	0.911094i
$940$	−0.870556	+	1.50785i	−0.0283944	+	0.0491806i
$941$	−25.4652	+	44.1070i	−0.830142	+	1.43785i	0.0677832	+	0.997700i	$0.478407\pi$
$941$	−25.4652	+	44.1070i	−0.830142	+	1.43785i	−0.897925	+	0.440148i	$0.854926\pi$
$942$	4.56370			0.148693
$943$	13.7870	−	23.8799i	0.448968	−	0.777635i
$944$	−9.45075			−0.307596
$945$	26.0289			0.846720
$946$	11.5709	−	8.36549i	0.376203	−	0.271986i
$947$	−27.7767			−0.902620			−0.451310	−	0.892367i	$-0.649043\pi$
$947$	−27.7767			−0.902620			−0.451310	+	0.892367i	$0.649043\pi$
$948$	−27.6741			−0.898813
$949$	21.2063	−	36.7304i	0.688386	−	1.19232i
$950$	5.65964			0.183623
$951$	22.8785	−	39.6268i	0.741887	−	1.28499i
$952$	1.25889	−	2.18046i	0.0408008	−	0.0706690i
$953$	−11.6826	−	20.2349i	−0.378437	−	0.655471i	0.612398	−	0.790549i	$-0.290205\pi$
$953$	−11.6826	−	20.2349i	−0.378437	−	0.655471i	−0.990835	+	0.135078i	$0.956872\pi$
$954$	−24.7096			−0.800004
$955$	2.91852	+	5.05503i	0.0944412	+	0.163577i
$956$	11.4278	−	19.7935i	0.369601	−	0.640168i
$957$	46.0748			1.48939
$958$	16.6741	−	28.8804i	0.538715	−	0.933082i
$959$	−11.0815	−	19.1937i	−0.357840	−	0.619796i
$960$	1.58870	+	2.75172i	0.0512752	+	0.0888113i
$961$	15.0782	+	26.1161i	0.486392	+	0.842456i
$962$	15.8660			0.511539
$963$	8.06574	+	13.9703i	0.259915	+	0.450186i
$964$	1.03351	+	1.79009i	0.0332872	+	0.0576550i
$965$	−6.01445	+	10.4173i	−0.193612	+	0.335346i
$966$	−7.48223	+	12.9596i	−0.240737	+	0.416968i
$967$	−10.2341			−0.329105			−0.164552	−	0.986368i	$-0.552618\pi$
$967$	−10.2341			−0.329105			−0.164552	+	0.986368i	$0.552618\pi$
$968$	−6.25889			−0.201168
$969$	11.3193	−	19.6056i	0.363627	−	0.629821i
$970$	−6.46649	+	11.2003i	−0.207626	+	0.359620i
$971$	−6.51965	−	11.2924i	−0.209225	−	0.362389i	0.742245	−	0.670128i	$-0.233761\pi$
$971$	−6.51965	−	11.2924i	−0.209225	−	0.362389i	−0.951471	+	0.307739i	$0.900428\pi$
$972$	12.3548	+	21.3992i	0.396281	+	0.686379i
$973$	−32.8304			−1.05249
$974$	2.61167	+	4.52354i	0.0836833	+	0.144944i
$975$	4.63667	+	8.03095i	0.148492	+	0.257196i
$976$	7.27334	+	12.5978i	0.232814	+	0.403246i
$977$	14.9087	−	25.8227i	0.476973	−	0.826141i	−0.522679	−	0.852529i	$-0.675067\pi$
$977$	14.9087	−	25.8227i	0.476973	−	0.826141i	0.999652	+	0.0263887i	$0.00840077\pi$
$978$	−77.2182			−2.46917
$979$	1.65241	−	2.86205i	0.0528112	−	0.0914717i
$980$	1.50000	+	2.59808i	0.0479157	+	0.0829925i
$981$	−58.9304			−1.88150
$982$	5.96130	+	10.3253i	0.190233	+	0.329493i
$983$	4.65760	−	8.06720i	0.148554	−	0.257304i	−0.782139	−	0.623104i	$-0.785871\pi$
$983$	4.65760	−	8.06720i	0.148554	−	0.257304i	0.930693	+	0.365800i	$0.119205\pi$
$984$	−18.6032	+	32.2216i	−0.593047	+	1.02719i
$985$	−12.5178			−0.398849
$986$	4.19186	−	7.26052i	0.133496	−	0.231222i
$987$	11.0645			0.352186
$988$	16.5178			0.525500
$989$	1.57816	+	15.3607i	0.0501825	+	0.488443i
$990$	15.4508			0.491057
$991$	−48.4837			−1.54014			−0.770068	−	0.637961i	$-0.779778\pi$
$991$	−48.4837			−1.54014			−0.770068	+	0.637961i	$0.779778\pi$
$992$	0.459261	−	0.795464i	0.0145816	−	0.0252560i
$993$	1.54517			0.0490346
$994$	−9.27334	+	16.0619i	−0.294133	+	0.509453i
$995$	1.63667	−	2.83480i	0.0518860	−	0.0898691i
$996$	7.96649	+	13.7984i	0.252428	+	0.437218i
$997$	21.8660			0.692502			0.346251	−	0.938142i	$-0.387455\pi$
$997$	21.8660			0.692502			0.346251	+	0.938142i	$0.387455\pi$
$998$	5.60648	+	9.71071i	0.177470	+	0.307387i
$999$	35.3752	−	61.2717i	1.11922	−	1.93855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.f.221.3	✓	6
43.36	even	3	inner	430.2.e.f.251.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.f.221.3	✓	6	1.1	even	1	trivial
430.2.e.f.251.3	yes	6	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.58870 - 2.75172i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.58870 - 2.75172i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-3.54797 - 6.14526i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.58870 - 2.75172i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.58870 - 2.75172i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-3.54797 - 6.14526i) q^{9} +(-0.500000 + 0.866025i) q^{10} +2.17741 q^{11} +(1.58870 - 2.75172i) q^{12} +(-1.45926 - 2.52751i) q^{13} +(1.00000 + 1.73205i) q^{14} +(1.58870 + 2.75172i) q^{15} +1.00000 q^{16} +(-0.629444 - 1.09023i) q^{17} +(-3.54797 - 6.14526i) q^{18} +(-2.82982 + 4.90139i) q^{19} +(-0.500000 + 0.866025i) q^{20} +6.35482 q^{21} +2.17741 q^{22} +(-1.17741 + 2.03933i) q^{23} +(1.58870 - 2.75172i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.45926 - 2.52751i) q^{26} -13.0145 q^{27} +(1.00000 + 1.73205i) q^{28} +(3.32982 + 5.76741i) q^{29} +(1.58870 + 2.75172i) q^{30} +(0.459261 - 0.795464i) q^{31} +1.00000 q^{32} +(3.45926 - 5.99162i) q^{33} +(-0.629444 - 1.09023i) q^{34} -2.00000 q^{35} +(-3.54797 - 6.14526i) q^{36} +(-2.71815 + 4.70797i) q^{37} +(-2.82982 + 4.90139i) q^{38} -9.27334 q^{39} +(-0.500000 + 0.866025i) q^{40} -11.7096 q^{41} +6.35482 q^{42} +(5.31408 - 3.84195i) q^{43} +2.17741 q^{44} +7.09593 q^{45} +(-1.17741 + 2.03933i) q^{46} +1.74111 q^{47} +(1.58870 - 2.75172i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} -4.00000 q^{51} +(-1.45926 - 2.52751i) q^{52} +(1.74111 - 3.01570i) q^{53} -13.0145 q^{54} +(-1.08870 + 1.88569i) q^{55} +(1.00000 + 1.73205i) q^{56} +(8.99149 + 15.5737i) q^{57} +(3.32982 + 5.76741i) q^{58} -9.45075 q^{59} +(1.58870 + 2.75172i) q^{60} +(7.27334 + 12.5978i) q^{61} +(0.459261 - 0.795464i) q^{62} +(7.09593 - 12.2905i) q^{63} +1.00000 q^{64} +2.91852 q^{65} +(3.45926 - 5.99162i) q^{66} +(5.87778 - 10.1806i) q^{67} +(-0.629444 - 1.09023i) q^{68} +(3.74111 + 6.47980i) q^{69} -2.00000 q^{70} +(4.63667 + 8.03095i) q^{71} +(-3.54797 - 6.14526i) q^{72} +(7.26611 + 12.5853i) q^{73} +(-2.71815 + 4.70797i) q^{74} -3.17741 q^{75} +(-2.82982 + 4.90139i) q^{76} +(2.17741 + 3.77138i) q^{77} -9.27334 q^{78} +(-4.35482 - 7.54277i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-10.0322 + 17.3763i) q^{81} -11.7096 q^{82} +(-2.50723 + 4.34265i) q^{83} +6.35482 q^{84} +1.25889 q^{85} +(5.31408 - 3.84195i) q^{86} +21.1604 q^{87} +2.17741 q^{88} +(0.758887 - 1.31443i) q^{89} +7.09593 q^{90} +(2.91852 - 5.05503i) q^{91} +(-1.17741 + 2.03933i) q^{92} +(-1.45926 - 2.52751i) q^{93} +1.74111 q^{94} +(-2.82982 - 4.90139i) q^{95} +(1.58870 - 2.75172i) q^{96} +12.9330 q^{97} +(1.50000 - 2.59808i) q^{98} +(-7.72538 - 13.3807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 3 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 3 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 - 5 * q^9	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 3 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} - 5 q^{9} - 3 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 6 q^{16} - 5 q^{17} - 5 q^{18} - 7 q^{19} - 3 q^{20} + 8 q^{21} - 2 q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 28 q^{27} + 6 q^{28} + 10 q^{29} + 2 q^{30} - 6 q^{31} + 6 q^{32} + 12 q^{33} - 5 q^{34} - 12 q^{35} - 5 q^{36} - 10 q^{37} - 7 q^{38} - 8 q^{39} - 3 q^{40} - 10 q^{41} + 8 q^{42} - 7 q^{43} - 2 q^{44} + 10 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 9 q^{49} - 3 q^{50} - 24 q^{51} + 8 q^{53} - 28 q^{54} + q^{55} + 6 q^{56} + 10 q^{58} + 6 q^{59} + 2 q^{60} - 4 q^{61} - 6 q^{62} + 10 q^{63} + 6 q^{64} + 12 q^{66} + 9 q^{67} - 5 q^{68} + 20 q^{69} - 12 q^{70} + 4 q^{71} - 5 q^{72} + 21 q^{73} - 10 q^{74} - 4 q^{75} - 7 q^{76} - 2 q^{77} - 8 q^{78} + 4 q^{79} - 3 q^{80} - 15 q^{81} - 10 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 7 q^{86} + 4 q^{87} - 2 q^{88} + 7 q^{89} + 10 q^{90} + 8 q^{92} + 8 q^{94} - 7 q^{95} + 2 q^{96} + 10 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 3 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 - 5 * q^9 - 3 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 6 * q^16 - 5 * q^17 - 5 * q^18 - 7 * q^19 - 3 * q^20 + 8 * q^21 - 2 * q^22 + 8 * q^23 + 2 * q^24 - 3 * q^25 - 28 * q^27 + 6 * q^28 + 10 * q^29 + 2 * q^30 - 6 * q^31 + 6 * q^32 + 12 * q^33 - 5 * q^34 - 12 * q^35 - 5 * q^36 - 10 * q^37 - 7 * q^38 - 8 * q^39 - 3 * q^40 - 10 * q^41 + 8 * q^42 - 7 * q^43 - 2 * q^44 + 10 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 9 * q^49 - 3 * q^50 - 24 * q^51 + 8 * q^53 - 28 * q^54 + q^55 + 6 * q^56 + 10 * q^58 + 6 * q^59 + 2 * q^60 - 4 * q^61 - 6 * q^62 + 10 * q^63 + 6 * q^64 + 12 * q^66 + 9 * q^67 - 5 * q^68 + 20 * q^69 - 12 * q^70 + 4 * q^71 - 5 * q^72 + 21 * q^73 - 10 * q^74 - 4 * q^75 - 7 * q^76 - 2 * q^77 - 8 * q^78 + 4 * q^79 - 3 * q^80 - 15 * q^81 - 10 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 7 * q^86 + 4 * q^87 - 2 * q^88 + 7 * q^89 + 10 * q^90 + 8 * q^92 + 8 * q^94 - 7 * q^95 + 2 * q^96 + 10 * q^97 + 9 * q^98 - 15 * q^99

Introduction

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