LMFDB - Embedded newform 570.2.i.j.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.i (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29654208.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 12 $ x^6 + 14x^4 + 49x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$2.86514i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.2.i.j.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.75353 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.75353 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -2.20905 q^{11} +1.00000 q^{12} +(1.60452 - 2.77912i) q^{13} +(-0.876763 - 1.51860i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.58581 - 6.21081i) q^{17} +1.00000 q^{18} +(0.727762 - 4.29772i) q^{19} +1.00000 q^{20} +(-0.876763 - 1.51860i) q^{21} +(1.10452 + 1.91309i) q^{22} +(-1.10452 + 1.91309i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -3.20905 q^{26} +1.00000 q^{27} +(-0.876763 + 1.51860i) q^{28} +(-3.83229 + 6.63772i) q^{29} +1.00000 q^{30} -3.20905 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.10452 + 1.91309i) q^{33} +(-3.58581 + 6.21081i) q^{34} +(-0.876763 - 1.51860i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(-4.08581 + 1.51860i) q^{38} -3.20905 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.23481 - 9.06696i) q^{41} +(-0.876763 + 1.51860i) q^{42} +(1.35805 + 2.35221i) q^{43} +(1.10452 - 1.91309i) q^{44} +1.00000 q^{45} +2.20905 q^{46} +(4.96257 - 8.59543i) q^{47} +(-0.500000 + 0.866025i) q^{48} -3.92515 q^{49} +1.00000 q^{50} +(-3.58581 + 6.21081i) q^{51} +(1.60452 + 2.77912i) q^{52} +(-5.48129 + 9.49387i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.10452 + 1.91309i) q^{55} +1.75353 q^{56} +(-4.08581 + 1.51860i) q^{57} +7.66457 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(2.98129 - 5.16374i) q^{61} +(1.60452 + 2.77912i) q^{62} +(-0.876763 + 1.51860i) q^{63} +1.00000 q^{64} -3.20905 q^{65} +(1.10452 - 1.91309i) q^{66} +(-0.0187126 + 0.0324111i) q^{67} +7.17162 q^{68} +2.20905 q^{69} +(-0.876763 + 1.51860i) q^{70} +(-3.58581 - 6.21081i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.98129 + 10.3599i) q^{73} +(0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(3.35805 + 2.77912i) q^{76} -3.87362 q^{77} +(1.60452 + 2.77912i) q^{78} +(-0.604525 - 1.04707i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.23481 + 9.06696i) q^{82} +14.8362 q^{83} +1.75353 q^{84} +(-3.58581 + 6.21081i) q^{85} +(1.35805 - 2.35221i) q^{86} +7.66457 q^{87} -2.20905 q^{88} +(5.48129 - 9.49387i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(2.81357 - 4.87325i) q^{91} +(-1.10452 - 1.91309i) q^{92} +(1.60452 + 2.77912i) q^{93} -9.92515 q^{94} +(-4.08581 + 1.51860i) q^{95} +1.00000 q^{96} +(-5.62324 - 9.73973i) q^{97} +(1.96257 + 3.39928i) q^{98} +(1.10452 - 1.91309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} + 6 q^{12} - q^{13} - q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{20} - q^{21} - 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} + 6 q^{27} - q^{28} - 6 q^{29} + 6 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 4 q^{34} - q^{35} - 3 q^{36} - 6 q^{37} + q^{38} + 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} - 11 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} - 3 q^{48} + 36 q^{49} + 6 q^{50} + 4 q^{51} - q^{52} - 18 q^{53} - 3 q^{54} - 4 q^{55} + 2 q^{56} + q^{57} + 12 q^{58} - 18 q^{59} - 3 q^{60} + 3 q^{61} - q^{62} - q^{63} + 6 q^{64} + 2 q^{65} - 4 q^{66} - 15 q^{67} - 8 q^{68} - 8 q^{69} - q^{70} + 4 q^{71} - 3 q^{72} + 21 q^{73} + 3 q^{74} + 6 q^{75} + q^{76} + 32 q^{77} - q^{78} + 7 q^{79} - 3 q^{80} - 3 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 4 q^{85} - 11 q^{86} + 12 q^{87} + 8 q^{88} + 18 q^{89} - 3 q^{90} - 15 q^{91} + 4 q^{92} - q^{93} + q^{95} + 6 q^{96} - 38 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 + 6 * q^12 - q^13 - q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^20 - q^21 - 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 + 6 * q^27 - q^28 - 6 * q^29 + 6 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 4 * q^34 - q^35 - 3 * q^36 - 6 * q^37 + q^38 + 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 - 11 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 + 36 * q^49 + 6 * q^50 + 4 * q^51 - q^52 - 18 * q^53 - 3 * q^54 - 4 * q^55 + 2 * q^56 + q^57 + 12 * q^58 - 18 * q^59 - 3 * q^60 + 3 * q^61 - q^62 - q^63 + 6 * q^64 + 2 * q^65 - 4 * q^66 - 15 * q^67 - 8 * q^68 - 8 * q^69 - q^70 + 4 * q^71 - 3 * q^72 + 21 * q^73 + 3 * q^74 + 6 * q^75 + q^76 + 32 * q^77 - q^78 + 7 * q^79 - 3 * q^80 - 3 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 4 * q^85 - 11 * q^86 + 12 * q^87 + 8 * q^88 + 18 * q^89 - 3 * q^90 - 15 * q^91 + 4 * q^92 - q^93 + q^95 + 6 * q^96 - 38 * q^97 - 18 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.75353			0.662770			0.331385	−	0.943496i	$-0.392484\pi$
$7$	1.75353			0.662770			0.331385	+	0.943496i	$0.392484\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.20905			−0.666054			−0.333027	−	0.942917i	$-0.608070\pi$
$11$	−2.20905			−0.666054			−0.333027	+	0.942917i	$0.608070\pi$
$12$	1.00000			0.288675
$13$	1.60452	−	2.77912i	0.445015	−	0.770789i	−0.553038	−	0.833156i	$-0.686532\pi$
$13$	1.60452	−	2.77912i	0.445015	−	0.770789i	0.998053	+	0.0623671i	$0.0198650\pi$
$14$	−0.876763	−	1.51860i	−0.234325	−	0.405862i
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.58581	−	6.21081i	−0.869687	−	1.50634i	−0.862317	−	0.506370i	$-0.830987\pi$
$17$	−3.58581	−	6.21081i	−0.869687	−	1.50634i	−0.00737071	−	0.999973i	$-0.502346\pi$
$18$	1.00000			0.235702
$19$	0.727762	−	4.29772i	0.166960	−	0.985964i
$19$	0.727762	−	4.29772i	0.166960	−	0.985964i
$20$	1.00000			0.223607
$21$	−0.876763	−	1.51860i	−0.191325	−	0.331385i
$22$	1.10452	+	1.91309i	0.235485	+	0.407873i
$23$	−1.10452	+	1.91309i	−0.230309	+	0.398908i	−0.957899	−	0.287105i	$-0.907307\pi$
$23$	−1.10452	+	1.91309i	−0.230309	+	0.398908i	0.727590	+	0.686012i	$0.240640\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.20905			−0.629346
$27$	1.00000			0.192450
$28$	−0.876763	+	1.51860i	−0.165693	+	0.286988i
$29$	−3.83229	+	6.63772i	−0.711638	+	1.23259i	0.252604	+	0.967570i	$0.418713\pi$
$29$	−3.83229	+	6.63772i	−0.711638	+	1.23259i	−0.964242	+	0.265023i	$0.914620\pi$
$30$	1.00000			0.182574
$31$	−3.20905			−0.576362			−0.288181	−	0.957576i	$-0.593051\pi$
$31$	−3.20905			−0.576362			−0.288181	+	0.957576i	$0.593051\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.10452	+	1.91309i	0.192273	+	0.333027i
$34$	−3.58581	+	6.21081i	−0.614962	+	1.06514i
$35$	−0.876763	−	1.51860i	−0.148200	−	0.256690i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−4.08581	+	1.51860i	−0.662806	+	0.246349i
$39$	−3.20905			−0.513859
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−5.23481	−	9.06696i	−0.817540	−	1.41602i	−0.907489	−	0.420075i	$-0.862004\pi$
$41$	−5.23481	−	9.06696i	−0.817540	−	1.41602i	0.0899490	−	0.995946i	$-0.471330\pi$
$42$	−0.876763	+	1.51860i	−0.135287	+	0.234325i
$43$	1.35805	+	2.35221i	0.207101	+	0.358709i	0.950800	−	0.309805i	$-0.100264\pi$
$43$	1.35805	+	2.35221i	0.207101	+	0.358709i	−0.743699	+	0.668514i	$0.766931\pi$
$44$	1.10452	−	1.91309i	0.166513	−	0.288410i
$45$	1.00000			0.149071
$46$	2.20905			0.325707
$47$	4.96257	−	8.59543i	0.723866	−	1.25377i	−0.235573	−	0.971857i	$-0.575697\pi$
$47$	4.96257	−	8.59543i	0.723866	−	1.25377i	0.959439	−	0.281916i	$-0.0909699\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−3.92515			−0.560736
$50$	1.00000			0.141421
$51$	−3.58581	+	6.21081i	−0.502114	+	0.869687i
$52$	1.60452	+	2.77912i	0.222508	+	0.385394i
$53$	−5.48129	+	9.49387i	−0.752913	+	1.30408i	0.193493	+	0.981102i	$0.438018\pi$
$53$	−5.48129	+	9.49387i	−0.752913	+	1.30408i	−0.946405	+	0.322981i	$0.895315\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.10452	+	1.91309i	0.148934	+	0.257961i
$56$	1.75353			0.234325
$57$	−4.08581	+	1.51860i	−0.541179	+	0.201143i
$58$	7.66457			1.00641
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	2.98129	−	5.16374i	0.381715	−	0.661149i	−0.609593	−	0.792715i	$-0.708667\pi$
$61$	2.98129	−	5.16374i	0.381715	−	0.661149i	0.991307	+	0.131565i	$0.0420003\pi$
$62$	1.60452	+	2.77912i	0.203775	+	0.352948i
$63$	−0.876763	+	1.51860i	−0.110462	+	0.191325i
$64$	1.00000			0.125000
$65$	−3.20905			−0.398034
$66$	1.10452	−	1.91309i	0.135958	−	0.235485i
$67$	−0.0187126	+	0.0324111i	−0.00228610	+	0.00395965i	−0.867166	−	0.498019i	$-0.834061\pi$
$67$	−0.0187126	+	0.0324111i	−0.00228610	+	0.00395965i	0.864880	+	0.501979i	$0.167394\pi$
$68$	7.17162			0.869687
$69$	2.20905			0.265938
$70$	−0.876763	+	1.51860i	−0.104793	+	0.181507i
$71$	−3.58581	−	6.21081i	−0.425558	−	0.737087i	0.570915	−	0.821009i	$-0.306589\pi$
$71$	−3.58581	−	6.21081i	−0.425558	−	0.737087i	−0.996472	+	0.0839219i	$0.973255\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	5.98129	+	10.3599i	0.700057	+	1.21253i	0.968446	+	0.249223i	$0.0801753\pi$
$73$	5.98129	+	10.3599i	0.700057	+	1.21253i	−0.268389	+	0.963311i	$0.586491\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$	1.00000			0.115470
$76$	3.35805	+	2.77912i	0.385195	+	0.318787i
$77$	−3.87362			−0.441440
$78$	1.60452	+	2.77912i	0.181677	+	0.314673i
$79$	−0.604525	−	1.04707i	−0.0680144	−	0.117804i	0.830013	−	0.557744i	$-0.188333\pi$
$79$	−0.604525	−	1.04707i	−0.0680144	−	0.117804i	−0.898027	+	0.439940i	$0.855000\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.23481	+	9.06696i	−0.578088	+	1.00128i
$83$	14.8362			1.62848			0.814242	−	0.580525i	$-0.197153\pi$
$83$	14.8362			1.62848			0.814242	+	0.580525i	$0.197153\pi$
$84$	1.75353			0.191325
$85$	−3.58581	+	6.21081i	−0.388936	+	0.673657i
$86$	1.35805	−	2.35221i	0.146442	−	0.253645i
$87$	7.66457			0.821729
$88$	−2.20905			−0.235485
$89$	5.48129	−	9.49387i	0.581015	−	1.00635i	−0.414344	−	0.910120i	$-0.635989\pi$
$89$	5.48129	−	9.49387i	0.581015	−	1.00635i	0.995359	−	0.0962277i	$-0.0306777\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	2.81357	−	4.87325i	0.294943	−	0.510856i
$92$	−1.10452	−	1.91309i	−0.115155	−	0.199454i
$93$	1.60452	+	2.77912i	0.166381	+	0.288181i
$94$	−9.92515			−1.02370
$95$	−4.08581	+	1.51860i	−0.419195	+	0.155805i
$96$	1.00000			0.102062
$97$	−5.62324	−	9.73973i	−0.570953	−	0.988920i	−0.996468	−	0.0839687i	$-0.973240\pi$
$97$	−5.62324	−	9.73973i	−0.570953	−	0.988920i	0.425515	−	0.904951i	$-0.360093\pi$
$98$	1.96257	+	3.39928i	0.198250	+	0.343379i
$99$	1.10452	−	1.91309i	0.111009	−	0.192273i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−0.246475	+	0.426907i	−0.0245252	+	0.0424788i	−0.878027	−	0.478610i	$-0.841141\pi$
$101$	−0.246475	+	0.426907i	−0.0245252	+	0.0424788i	0.853502	+	0.521089i	$0.174474\pi$
$102$	7.17162			0.710097
$103$	11.6787			1.15073			0.575367	−	0.817895i	$-0.304859\pi$
$103$	11.6787			1.15073			0.575367	+	0.817895i	$0.304859\pi$
$104$	1.60452	−	2.77912i	0.157337	−	0.272515i
$105$	−0.876763	+	1.51860i	−0.0855633	+	0.148200i
$106$	10.9626			1.06478
$107$	8.26058			0.798580			0.399290	−	0.916825i	$-0.369257\pi$
$107$	8.26058			0.798580			0.399290	+	0.916825i	$0.369257\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	2.58581	+	4.47876i	0.247676	+	0.428987i	0.962881	−	0.269928i	$-0.0869999\pi$
$109$	2.58581	+	4.47876i	0.247676	+	0.428987i	−0.715205	+	0.698915i	$0.753667\pi$
$110$	1.10452	−	1.91309i	0.105312	−	0.182406i
$111$	0.500000	+	0.866025i	0.0474579	+	0.0821995i
$112$	−0.876763	−	1.51860i	−0.0828463	−	0.143494i
$113$	−2.26058			−0.212657			−0.106329	−	0.994331i	$-0.533910\pi$
$113$	−2.26058			−0.212657			−0.106329	+	0.994331i	$0.533910\pi$
$114$	3.35805	+	2.77912i	0.314510	+	0.260288i
$115$	2.20905			0.205995
$116$	−3.83229	−	6.63772i	−0.355819	−	0.616296i
$117$	1.60452	+	2.77912i	0.148338	+	0.256930i
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	−6.28781	−	10.8908i	−0.576403	−	0.998359i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−6.12010			−0.556373
$122$	−5.96257			−0.539826
$123$	−5.23481	+	9.06696i	−0.472007	+	0.817540i
$124$	1.60452	−	2.77912i	0.144091	−	0.249572i
$125$	1.00000			0.0894427
$126$	1.75353			0.156216
$127$	6.44386	−	11.1611i	0.571800	−	0.990387i	−0.424581	−	0.905390i	$-0.639579\pi$
$127$	6.44386	−	11.1611i	0.571800	−	0.990387i	0.996381	−	0.0849972i	$-0.0270881\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.35805	−	2.35221i	0.119570	−	0.207101i
$130$	1.60452	+	2.77912i	0.140726	+	0.243745i
$131$	6.61158	+	11.4516i	0.577656	+	1.00053i	0.995747	+	0.0921246i	$0.0293658\pi$
$131$	6.61158	+	11.4516i	0.577656	+	1.00053i	−0.418091	+	0.908405i	$0.637301\pi$
$132$	−2.20905			−0.192273
$133$	1.27615	−	7.53615i	0.110656	−	0.653467i
$134$	0.0374251			0.00323304
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−3.58581	−	6.21081i	−0.307481	−	0.532572i
$137$	10.7161	−	18.5608i	0.915538	−	1.58576i	0.109427	−	0.993995i	$-0.465098\pi$
$137$	10.7161	−	18.5608i	0.915538	−	1.58576i	0.806111	−	0.591764i	$-0.201568\pi$
$138$	−1.10452	−	1.91309i	−0.0940234	−	0.162853i
$139$	−3.60452	+	6.24322i	−0.305732	+	0.529543i	−0.977424	−	0.211287i	$-0.932234\pi$
$139$	−3.60452	+	6.24322i	−0.305732	+	0.529543i	0.671692	+	0.740830i	$0.265568\pi$
$140$	1.75353			0.148200
$141$	−9.92515			−0.835848
$142$	−3.58581	+	6.21081i	−0.300915	+	0.521200i
$143$	−3.54448	+	6.13921i	−0.296404	+	0.513387i
$144$	1.00000			0.0833333
$145$	7.66457			0.636508
$146$	5.98129	−	10.3599i	0.495015	−	0.857391i
$147$	1.96257	+	3.39928i	0.161870	+	0.280368i
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	4.37676	+	7.58078i	0.358558	+	0.621041i	0.987720	−	0.156233i	$-0.0499351\pi$
$149$	4.37676	+	7.58078i	0.358558	+	0.621041i	−0.629162	+	0.777274i	$0.716602\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	8.67867			0.706261			0.353130	−	0.935574i	$-0.385117\pi$
$151$	8.67867			0.706261			0.353130	+	0.935574i	$0.385117\pi$
$152$	0.727762	−	4.29772i	0.0590293	−	0.348591i
$153$	7.17162			0.579791
$154$	1.93681	+	3.35466i	0.156073	+	0.270326i
$155$	1.60452	+	2.77912i	0.128879	+	0.223224i
$156$	1.60452	−	2.77912i	0.128465	−	0.222508i
$157$	−2.25353	−	3.90322i	−0.179851	−	0.311511i	0.761978	−	0.647602i	$-0.224228\pi$
$157$	−2.25353	−	3.90322i	−0.179851	−	0.311511i	−0.941829	+	0.336092i	$0.890895\pi$
$158$	−0.604525	+	1.04707i	−0.0480934	+	0.0833002i
$159$	10.9626			0.869389
$160$	1.00000			0.0790569
$161$	−1.93681	+	3.35466i	−0.152642	+	0.264384i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	23.6271			1.85062			0.925311	−	0.379210i	$-0.123804\pi$
$163$	23.6271			1.85062			0.925311	+	0.379210i	$0.123804\pi$
$164$	10.4696			0.817540
$165$	1.10452	−	1.91309i	0.0859871	−	0.148934i
$166$	−7.41810	−	12.8485i	−0.575756	−	0.997239i
$167$	−4.89548	+	8.47921i	−0.378823	+	0.656141i	−0.990891	−	0.134664i	$-0.957005\pi$
$167$	−4.89548	+	8.47921i	−0.378823	+	0.656141i	0.612068	+	0.790805i	$0.290338\pi$
$168$	−0.876763	−	1.51860i	−0.0676437	−	0.117162i
$169$	1.35100	+	2.34000i	0.103923	+	0.180000i
$170$	7.17162			0.550039
$171$	3.35805	+	2.77912i	0.256797	+	0.212525i
$172$	−2.71610			−0.207101
$173$	−5.72776	−	9.92078i	−0.435474	−	0.754263i	0.561860	−	0.827232i	$-0.310086\pi$
$173$	−5.72776	−	9.92078i	−0.435474	−	0.754263i	−0.997334	+	0.0729694i	$0.976752\pi$
$174$	−3.83229	−	6.63772i	−0.290525	−	0.503204i
$175$	−0.876763	+	1.51860i	−0.0662770	+	0.114795i
$176$	1.10452	+	1.91309i	0.0832567	+	0.144205i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	−10.9626			−0.821680
$179$	6.62715			0.495336			0.247668	−	0.968845i	$-0.420336\pi$
$179$	6.62715			0.495336			0.247668	+	0.968845i	$0.420336\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−5.13029	+	8.88592i	−0.381331	+	0.660485i	−0.991253	−	0.131977i	$-0.957868\pi$
$181$	−5.13029	+	8.88592i	−0.381331	+	0.660485i	0.609922	+	0.792462i	$0.291201\pi$
$182$	−5.62715			−0.417112
$183$	−5.96257			−0.440766
$184$	−1.10452	+	1.91309i	−0.0814267	+	0.141035i
$185$	0.500000	+	0.866025i	0.0367607	+	0.0636715i
$186$	1.60452	−	2.77912i	0.117649	−	0.203775i
$187$	7.92124	+	13.7200i	0.579258	+	1.00330i
$188$	4.96257	+	8.59543i	0.361933	+	0.626886i
$189$	1.75353			0.127550
$190$	3.35805	+	2.77912i	0.243619	+	0.201618i
$191$	25.2543			1.82734			0.913668	−	0.406460i	$-0.133237\pi$
$191$	25.2543			1.82734			0.913668	+	0.406460i	$0.133237\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−1.43681	−	2.48863i	−0.103424	−	0.179136i	0.809669	−	0.586886i	$-0.199647\pi$
$193$	−1.43681	−	2.48863i	−0.103424	−	0.179136i	−0.913093	+	0.407751i	$0.866313\pi$
$194$	−5.62324	+	9.73973i	−0.403725	+	0.699272i
$195$	1.60452	+	2.77912i	0.114902	+	0.199017i
$196$	1.96257	−	3.39928i	0.140184	−	0.242806i
$197$	−14.8877			−1.06071			−0.530353	−	0.847777i	$-0.677941\pi$
$197$	−14.8877			−1.06071			−0.530353	+	0.847777i	$0.677941\pi$
$198$	−2.20905			−0.156990
$199$	0.772238	−	1.33755i	0.0547425	−	0.0948168i	−0.837356	−	0.546659i	$-0.815900\pi$
$199$	0.772238	−	1.33755i	0.0547425	−	0.0948168i	0.892098	+	0.451842i	$0.149233\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	0.0374251			0.00263977
$202$	0.492950			0.0346838
$203$	−6.72001	+	11.6394i	−0.471652	+	0.816926i
$204$	−3.58581	−	6.21081i	−0.251057	−	0.434844i
$205$	−5.23481	+	9.06696i	−0.365615	+	0.633264i
$206$	−5.83934	−	10.1140i	−0.406846	−	0.704678i
$207$	−1.10452	−	1.91309i	−0.0767698	−	0.132969i
$208$	−3.20905			−0.222508
$209$	−1.60766	+	9.49387i	−0.111204	+	0.656705i
$210$	1.75353			0.121005
$211$	−6.38381	−	11.0571i	−0.439480	−	0.761201i	0.558170	−	0.829727i	$-0.311504\pi$
$211$	−6.38381	−	11.0571i	−0.439480	−	0.761201i	−0.997649	+	0.0685256i	$0.978171\pi$
$212$	−5.48129	−	9.49387i	−0.376456	−	0.652042i
$213$	−3.58581	+	6.21081i	−0.245696	+	0.425558i
$214$	−4.13029	−	7.15387i	−0.282341	−	0.489028i
$215$	1.35805	−	2.35221i	0.0926182	−	0.160419i
$216$	1.00000			0.0680414
$217$	−5.62715			−0.381996
$218$	2.58581	−	4.47876i	0.175133	−	0.303340i
$219$	5.98129	−	10.3599i	0.404178	−	0.700057i
$220$	−2.20905			−0.148934
$221$	−23.0141			−1.54810
$222$	0.500000	−	0.866025i	0.0335578	−	0.0581238i
$223$	−3.57876	−	6.19860i	−0.239652	−	0.415089i	0.720963	−	0.692974i	$-0.243700\pi$
$223$	−3.57876	−	6.19860i	−0.239652	−	0.415089i	−0.960614	+	0.277885i	$0.910367\pi$
$224$	−0.876763	+	1.51860i	−0.0585812	+	0.101466i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	1.13029	+	1.95772i	0.0751856	+	0.130225i
$227$	−14.2606			−0.946508			−0.473254	−	0.880926i	$-0.656921\pi$
$227$	−14.2606			−0.946508			−0.473254	+	0.880926i	$0.656921\pi$
$228$	0.727762	−	4.29772i	0.0481972	−	0.284623i
$229$	−21.2090			−1.40153			−0.700767	−	0.713390i	$-0.747159\pi$
$229$	−21.2090			−1.40153			−0.700767	+	0.713390i	$0.747159\pi$
$230$	−1.10452	−	1.91309i	−0.0728302	−	0.126146i
$231$	1.93681	+	3.35466i	0.127433	+	0.220720i
$232$	−3.83229	+	6.63772i	−0.251602	+	0.435787i
$233$	2.70200	+	4.68000i	0.177014	+	0.306597i	0.940856	−	0.338806i	$-0.110023\pi$
$233$	2.70200	+	4.68000i	0.177014	+	0.306597i	−0.763842	+	0.645403i	$0.776690\pi$
$234$	1.60452	−	2.77912i	0.104891	−	0.181677i
$235$	−9.92515			−0.647445
$236$	6.00000			0.390567
$237$	−0.604525	+	1.04707i	−0.0392681	+	0.0680144i
$238$	−6.28781	+	10.8908i	−0.407578	+	0.705946i
$239$	21.4322			1.38633			0.693167	−	0.720777i	$-0.256215\pi$
$239$	21.4322			1.38633			0.693167	+	0.720777i	$0.256215\pi$
$240$	1.00000			0.0645497
$241$	3.18643	−	5.51905i	0.205256	−	0.355513i	−0.744958	−	0.667111i	$-0.767531\pi$
$241$	3.18643	−	5.51905i	0.205256	−	0.355513i	0.950214	+	0.311598i	$0.100864\pi$
$242$	3.06005	+	5.30016i	0.196707	+	0.340707i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.98129	+	5.16374i	0.190857	+	0.330575i
$245$	1.96257	+	3.39928i	0.125384	+	0.217172i
$246$	10.4696			0.667519
$247$	−10.7761	−	8.91833i	−0.685670	−	0.567460i
$248$	−3.20905			−0.203775
$249$	−7.41810	−	12.8485i	−0.470103	−	0.814242i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−9.13420	+	15.8209i	−0.576546	+	0.998606i	0.419326	+	0.907836i	$0.362266\pi$
$251$	−9.13420	+	15.8209i	−0.576546	+	0.998606i	−0.995872	+	0.0907706i	$0.971067\pi$
$252$	−0.876763	−	1.51860i	−0.0552308	−	0.0956626i
$253$	2.43995	−	4.22612i	0.153398	−	0.265694i
$254$	−12.8877			−0.808648
$255$	7.17162			0.449105
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	−2.71610			−0.169097
$259$	−1.75353			−0.108959
$260$	1.60452	−	2.77912i	0.0995084	−	0.172354i
$261$	−3.83229	−	6.63772i	−0.237213	−	0.410864i
$262$	6.61158	−	11.4516i	0.408464	−	0.707481i
$263$	15.3136	+	26.5239i	0.944275	+	1.63553i	0.757195	+	0.653188i	$0.226569\pi$
$263$	15.3136	+	26.5239i	0.944275	+	1.63553i	0.187080	+	0.982345i	$0.440098\pi$
$264$	1.10452	+	1.91309i	0.0679788	+	0.117743i
$265$	10.9626			0.673426
$266$	−7.16457	+	2.66290i	−0.439288	+	0.163273i
$267$	−10.9626			−0.670899
$268$	−0.0187126	−	0.0324111i	−0.00114305	−	0.00197982i
$269$	8.79486	+	15.2331i	0.536232	+	0.928781i	0.999103	+	0.0423555i	$0.0134862\pi$
$269$	8.79486	+	15.2331i	0.536232	+	0.928781i	−0.462870	+	0.886426i	$0.653180\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−9.45552	−	16.3774i	−0.574382	−	0.994859i	−0.996108	−	0.0881360i	$-0.971909\pi$
$271$	−9.45552	−	16.3774i	−0.574382	−	0.994859i	0.421726	−	0.906723i	$-0.361424\pi$
$272$	−3.58581	+	6.21081i	−0.217422	+	0.376586i
$273$	−5.62715			−0.340571
$274$	−21.4322			−1.29477
$275$	1.10452	−	1.91309i	0.0666054	−	0.115364i
$276$	−1.10452	+	1.91309i	−0.0664846	+	0.115155i
$277$	24.9110			1.49676			0.748380	−	0.663270i	$-0.230832\pi$
$277$	24.9110			1.49676			0.748380	+	0.663270i	$0.230832\pi$
$278$	7.20905			0.432370
$279$	1.60452	−	2.77912i	0.0960604	−	0.166381i
$280$	−0.876763	−	1.51860i	−0.0523966	−	0.0907535i
$281$	−13.4439	+	23.2855i	−0.801994	+	1.38909i	0.116308	+	0.993213i	$0.462894\pi$
$281$	−13.4439	+	23.2855i	−0.801994	+	1.38909i	−0.918302	+	0.395880i	$0.870439\pi$
$282$	4.96257	+	8.59543i	0.295517	+	0.511851i
$283$	−12.8877	−	22.3222i	−0.766096	−	1.32692i	−0.939665	−	0.342095i	$-0.888864\pi$
$283$	−12.8877	−	22.3222i	−0.766096	−	1.32692i	0.173570	−	0.984822i	$-0.444470\pi$
$284$	7.17162			0.425558
$285$	3.35805	+	2.77912i	0.198914	+	0.164621i
$286$	7.08895			0.419178
$287$	−9.17938	−	15.8991i	−0.541841	−	0.938497i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−17.2161	+	29.8192i	−1.01271	+	1.75407i
$290$	−3.83229	−	6.63772i	−0.225040	−	0.389780i
$291$	−5.62324	+	9.73973i	−0.329640	+	0.570953i
$292$	−11.9626			−0.700057
$293$	1.53037			0.0894055			0.0447027	−	0.999000i	$-0.485766\pi$
$293$	1.53037			0.0894055			0.0447027	+	0.999000i	$0.485766\pi$
$294$	1.96257	−	3.39928i	0.114460	−	0.198250i
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$	−1.00000			−0.0581238
$297$	−2.20905			−0.128182
$298$	4.37676	−	7.58078i	0.253539	−	0.439143i
$299$	3.54448	+	6.13921i	0.204982	+	0.355040i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	2.38137	+	4.12466i	0.137260	+	0.237742i
$302$	−4.33934	−	7.51595i	−0.249701	−	0.432494i
$303$	0.492950			0.0283192
$304$	−4.08581	+	1.51860i	−0.234337	+	0.0870975i
$305$	−5.96257			−0.341416
$306$	−3.58581	−	6.21081i	−0.204987	−	0.355048i
$307$	8.88381	+	15.3872i	0.507026	+	0.878195i	0.999967	+	0.00813199i	$0.00258852\pi$
$307$	8.88381	+	15.3872i	0.507026	+	0.878195i	−0.492941	+	0.870063i	$0.664078\pi$
$308$	1.93681	−	3.35466i	0.110360	−	0.191149i
$309$	−5.83934	−	10.1140i	−0.332188	−	0.575367i
$310$	1.60452	−	2.77912i	0.0911309	−	0.157843i
$311$	11.4040			0.646661			0.323331	−	0.946286i	$-0.395197\pi$
$311$	11.4040			0.646661			0.323331	+	0.946286i	$0.395197\pi$
$312$	−3.20905			−0.181677
$313$	5.13420	−	8.89269i	0.290202	−	0.502645i	−0.683655	−	0.729805i	$-0.739611\pi$
$313$	5.13420	−	8.89269i	0.290202	−	0.502645i	0.973857	+	0.227160i	$0.0729441\pi$
$314$	−2.25353	+	3.90322i	−0.127174	+	0.220271i
$315$	1.75353			0.0987999
$316$	1.20905			0.0680144
$317$	12.4064	−	21.4886i	0.696815	−	1.20692i	−0.272750	−	0.962085i	$-0.587933\pi$
$317$	12.4064	−	21.4886i	0.696815	−	1.20692i	0.969565	−	0.244834i	$-0.0787334\pi$
$318$	−5.48129	−	9.49387i	−0.307375	−	0.532390i
$319$	8.46571	−	14.6630i	0.473989	−	0.820973i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−4.13029	−	7.15387i	−0.230530	−	0.399290i
$322$	3.87362			0.215869
$323$	−29.3019	+	10.8908i	−1.63040	+	0.605981i
$324$	1.00000			0.0555556
$325$	1.60452	+	2.77912i	0.0890030	+	0.154158i
$326$	−11.8136	−	20.4617i	−0.654293	−	1.13327i
$327$	2.58581	−	4.47876i	0.142996	−	0.247676i
$328$	−5.23481	−	9.06696i	−0.289044	−	0.500639i
$329$	8.70200	−	15.0723i	0.479757	−	0.830963i
$330$	−2.20905			−0.121604
$331$	−9.75353			−0.536102			−0.268051	−	0.963405i	$-0.586380\pi$
$331$	−9.75353			−0.536102			−0.268051	+	0.963405i	$0.586380\pi$
$332$	−7.41810	+	12.8485i	−0.407121	+	0.705154i
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$	9.79095			0.535737
$335$	0.0374251			0.00204475
$336$	−0.876763	+	1.51860i	−0.0478313	+	0.0828463i
$337$	−11.3206	−	19.6079i	−0.616674	−	1.06811i	−0.990088	−	0.140446i	$-0.955146\pi$
$337$	−11.3206	−	19.6079i	−0.616674	−	1.06811i	0.373415	−	0.927665i	$-0.378187\pi$
$338$	1.35100	−	2.34000i	0.0734847	−	0.127279i
$339$	1.13029	+	1.95772i	0.0613888	+	0.106329i
$340$	−3.58581	−	6.21081i	−0.194468	−	0.336828i
$341$	7.08895			0.383888
$342$	0.727762	−	4.29772i	0.0393529	−	0.232394i
$343$	−19.1575			−1.03441
$344$	1.35805	+	2.35221i	0.0732211	+	0.126823i
$345$	−1.10452	−	1.91309i	−0.0594656	−	0.102997i
$346$	−5.72776	+	9.92078i	−0.307926	+	0.533344i
$347$	12.6271	+	21.8709i	0.677861	+	1.17409i	0.975624	+	0.219450i	$0.0704262\pi$
$347$	12.6271	+	21.8709i	0.677861	+	1.17409i	−0.297763	+	0.954640i	$0.596240\pi$
$348$	−3.83229	+	6.63772i	−0.205432	+	0.355819i
$349$	29.2169			1.56394			0.781972	−	0.623314i	$-0.214214\pi$
$349$	29.2169			1.56394			0.781972	+	0.623314i	$0.214214\pi$
$350$	1.75353			0.0937299
$351$	1.60452	−	2.77912i	0.0856432	−	0.148338i
$352$	1.10452	−	1.91309i	0.0588714	−	0.101968i
$353$	−32.9189			−1.75209			−0.876047	−	0.482225i	$-0.839829\pi$
$353$	−32.9189			−1.75209			−0.876047	+	0.482225i	$0.839829\pi$
$354$	6.00000			0.318896
$355$	−3.58581	+	6.21081i	−0.190315	+	0.329636i
$356$	5.48129	+	9.49387i	0.290508	+	0.503174i
$357$	−6.28781	+	10.8908i	−0.332786	+	0.576403i
$358$	−3.31357	−	5.73928i	−0.175128	−	0.303330i
$359$	1.62324	+	2.81153i	0.0856712	+	0.148387i	0.905677	−	0.423968i	$-0.139363\pi$
$359$	1.62324	+	2.81153i	0.0856712	+	0.148387i	−0.820006	+	0.572355i	$0.806030\pi$
$360$	1.00000			0.0527046
$361$	−17.9407	−	6.25543i	−0.944249	−	0.329233i
$362$	10.2606			0.539284
$363$	3.06005	+	5.30016i	0.160611	+	0.278186i
$364$	2.81357	+	4.87325i	0.147471	+	0.255428i
$365$	5.98129	−	10.3599i	0.313075	−	0.542262i
$366$	2.98129	+	5.16374i	0.155834	+	0.269913i
$367$	6.02262	−	10.4315i	0.314378	−	0.544519i	−0.664927	−	0.746909i	$-0.731537\pi$
$367$	6.02262	−	10.4315i	0.314378	−	0.544519i	0.979305	+	0.202389i	$0.0648706\pi$
$368$	2.20905			0.115155
$369$	10.4696			0.545027
$370$	0.500000	−	0.866025i	0.0259938	−	0.0450225i
$371$	−9.61158	+	16.6477i	−0.499008	+	0.864307i
$372$	−3.20905			−0.166381
$373$	−3.86580			−0.200164			−0.100082	−	0.994979i	$-0.531910\pi$
$373$	−3.86580			−0.200164			−0.100082	+	0.994979i	$0.531910\pi$
$374$	7.92124	−	13.7200i	0.409597	−	0.709444i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	4.96257	−	8.59543i	0.255925	−	0.443276i
$377$	12.2980	+	21.3008i	0.633379	+	1.09705i
$378$	−0.876763	−	1.51860i	−0.0450958	−	0.0781082i
$379$	−23.0593			−1.18448			−0.592240	−	0.805762i	$-0.701756\pi$
$379$	−23.0593			−1.18448			−0.592240	+	0.805762i	$0.701756\pi$
$380$	0.727762	−	4.29772i	0.0373334	−	0.220468i
$381$	−12.8877			−0.660258
$382$	−12.6271	−	21.8709i	−0.646061	−	1.11901i
$383$	−1.03743	−	1.79687i	−0.0530099	−	0.0918159i	0.838303	−	0.545205i	$-0.183548\pi$
$383$	−1.03743	−	1.79687i	−0.0530099	−	0.0918159i	−0.891313	+	0.453389i	$0.850215\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	1.93681	+	3.35466i	0.0987091	+	0.170969i
$386$	−1.43681	+	2.48863i	−0.0731318	+	0.126668i
$387$	−2.71610			−0.138067
$388$	11.2465			0.570953
$389$	9.83229	−	17.0300i	0.498517	−	0.863456i	−0.501482	−	0.865168i	$-0.667212\pi$
$389$	9.83229	−	17.0300i	0.498517	−	0.863456i	0.999999	+	0.00171186i	$0.000544903\pi$
$390$	1.60452	−	2.77912i	0.0812483	−	0.140726i
$391$	15.8425			0.801188
$392$	−3.92515			−0.198250
$393$	6.61158	−	11.4516i	0.333510	−	0.577656i
$394$	7.44386	+	12.8931i	0.375016	+	0.649547i
$395$	−0.604525	+	1.04707i	−0.0304169	+	0.0526837i
$396$	1.10452	+	1.91309i	0.0555045	+	0.0961366i
$397$	4.42515	+	7.66458i	0.222092	+	0.384674i	0.955443	−	0.295176i	$-0.0953782\pi$
$397$	4.42515	+	7.66458i	0.222092	+	0.384674i	−0.733351	+	0.679850i	$0.762045\pi$
$398$	−1.54448			−0.0774176
$399$	−7.16457	+	2.66290i	−0.358677	+	0.133312i
$400$	1.00000			0.0500000
$401$	0.925150	+	1.60241i	0.0461998	+	0.0800204i	0.888201	−	0.459456i	$-0.151956\pi$
$401$	0.925150	+	1.60241i	0.0461998	+	0.0800204i	−0.842001	+	0.539476i	$0.818622\pi$
$402$	−0.0187126	−	0.0324111i	−0.000933298	−	0.00161652i
$403$	−5.14900	+	8.91833i	−0.256490	+	0.444254i
$404$	−0.246475	−	0.426907i	−0.0122626	−	0.0212394i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	13.4400			0.667017
$407$	2.20905			0.109499
$408$	−3.58581	+	6.21081i	−0.177524	+	0.307481i
$409$	−9.02967	+	15.6399i	−0.446489	+	0.773341i	−0.998155	−	0.0607241i	$-0.980659\pi$
$409$	−9.02967	+	15.6399i	−0.446489	+	0.773341i	0.551666	+	0.834065i	$0.313992\pi$
$410$	10.4696			0.517058
$411$	−21.4322			−1.05717
$412$	−5.83934	+	10.1140i	−0.287684	+	0.498282i
$413$	−5.26058	−	9.11158i	−0.258856	−	0.448352i
$414$	−1.10452	+	1.91309i	−0.0542844	+	0.0940234i
$415$	−7.41810	−	12.8485i	−0.364140	−	0.630709i
$416$	1.60452	+	2.77912i	0.0786683	+	0.136258i
$417$	7.20905			0.353029
$418$	9.02576	−	3.35466i	0.441464	−	0.164082i
$419$	−1.44770			−0.0707248			−0.0353624	−	0.999375i	$-0.511259\pi$
$419$	−1.44770			−0.0707248			−0.0353624	+	0.999375i	$0.511259\pi$
$420$	−0.876763	−	1.51860i	−0.0427816	−	0.0741000i
$421$	8.58581	+	14.8711i	0.418447	+	0.724771i	0.995783	−	0.0917350i	$-0.0292413\pi$
$421$	8.58581	+	14.8711i	0.418447	+	0.724771i	−0.577337	+	0.816506i	$0.695908\pi$
$422$	−6.38381	+	11.0571i	−0.310759	+	0.538251i
$423$	4.96257	+	8.59543i	0.241289	+	0.417924i
$424$	−5.48129	+	9.49387i	−0.266195	+	0.461063i
$425$	7.17162			0.347875
$426$	7.17162			0.347466
$427$	5.22776	−	9.05475i	0.252989	−	0.438190i
$428$	−4.13029	+	7.15387i	−0.199645	+	0.345795i
$429$	7.08895			0.342258
$430$	−2.71610			−0.130982
$431$	9.53429	−	16.5139i	0.459250	−	0.795445i	−0.539671	−	0.841876i	$-0.681451\pi$
$431$	9.53429	−	16.5139i	0.459250	−	0.795445i	0.998922	+	0.0464309i	$0.0147847\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	7.94386	−	13.7592i	0.381758	−	0.661224i	−0.609556	−	0.792743i	$-0.708652\pi$
$433$	7.94386	−	13.7592i	0.381758	−	0.661224i	0.991314	+	0.131519i	$0.0419856\pi$
$434$	2.81357	+	4.87325i	0.135056	+	0.233924i
$435$	−3.83229	−	6.63772i	−0.183744	−	0.318254i
$436$	−5.17162			−0.247676
$437$	7.41810	+	6.13921i	0.354856	+	0.293678i
$438$	−11.9626			−0.571594
$439$	−1.68329	−	2.91554i	−0.0803389	−	0.139151i	0.823057	−	0.567959i	$-0.192267\pi$
$439$	−1.68329	−	2.91554i	−0.0803389	−	0.139151i	−0.903396	+	0.428808i	$0.858934\pi$
$440$	1.10452	+	1.91309i	0.0526562	+	0.0912031i
$441$	1.96257	−	3.39928i	0.0934559	−	0.161870i
$442$	11.5071	+	19.9308i	0.547335	+	0.948011i
$443$	11.7949	−	20.4293i	0.560391	−	0.970625i	−0.437071	−	0.899427i	$-0.643984\pi$
$443$	11.7949	−	20.4293i	0.560391	−	0.970625i	0.997462	−	0.0711985i	$-0.0226824\pi$
$444$	−1.00000			−0.0474579
$445$	−10.9626			−0.519676
$446$	−3.57876	+	6.19860i	−0.169459	+	0.293512i
$447$	4.37676	−	7.58078i	0.207014	−	0.358558i
$448$	1.75353			0.0828463
$449$	−10.9626			−0.517356			−0.258678	−	0.965964i	$-0.583287\pi$
$449$	−10.9626			−0.517356			−0.258678	+	0.965964i	$0.583287\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	11.5640	+	20.0294i	0.544526	+	0.943146i
$452$	1.13029	−	1.95772i	0.0531643	−	0.0920832i
$453$	−4.33934	−	7.51595i	−0.203880	−	0.353130i
$454$	7.13029	+	12.3500i	0.334641	+	0.579615i
$455$	−5.62715			−0.263805
$456$	−4.08581	+	1.51860i	−0.191336	+	0.0711148i
$457$	26.6491			1.24659			0.623296	−	0.781986i	$-0.285793\pi$
$457$	26.6491			1.24659			0.623296	+	0.781986i	$0.285793\pi$
$458$	10.6045	+	18.3676i	0.495517	+	0.858260i
$459$	−3.58581	−	6.21081i	−0.167371	−	0.289896i
$460$	−1.10452	+	1.91309i	−0.0514987	+	0.0891984i
$461$	−2.20905	−	3.82619i	−0.102886	−	0.178203i	0.809987	−	0.586448i	$-0.199474\pi$
$461$	−2.20905	−	3.82619i	−0.102886	−	0.178203i	−0.912872	+	0.408245i	$0.866141\pi$
$462$	1.93681	−	3.35466i	0.0901087	−	0.156073i
$463$	−7.67867			−0.356858			−0.178429	−	0.983953i	$-0.557102\pi$
$463$	−7.67867			−0.356858			−0.178429	+	0.983953i	$0.557102\pi$
$464$	7.66457			0.355819
$465$	1.60452	−	2.77912i	0.0744081	−	0.128879i
$466$	2.70200	−	4.68000i	0.125168	−	0.216797i
$467$	24.0827			1.11441			0.557207	−	0.830374i	$-0.311873\pi$
$467$	24.0827			1.11441			0.557207	+	0.830374i	$0.311873\pi$
$468$	−3.20905			−0.148338
$469$	−0.0328130	+	0.0568337i	−0.00151516	+	0.00262434i
$470$	4.96257	+	8.59543i	0.228907	+	0.396478i
$471$	−2.25353	+	3.90322i	−0.103837	+	0.179851i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−3.00000	−	5.19615i	−0.137940	−	0.238919i
$474$	1.20905			0.0555335
$475$	3.35805	+	2.77912i	0.154078	+	0.127515i
$476$	12.5756			0.576403
$477$	−5.48129	−	9.49387i	−0.250971	−	0.434694i
$478$	−10.7161	−	18.5608i	−0.490143	−	0.848953i
$479$	−0.451613	+	0.782216i	−0.0206347	+	0.0357404i	−0.876158	−	0.482023i	$-0.839902\pi$
$479$	−0.451613	+	0.782216i	−0.0206347	+	0.0357404i	0.855524	+	0.517764i	$0.173235\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−1.60452	+	2.77912i	−0.0731600	+	0.126717i
$482$	−6.37285			−0.290275
$483$	3.87362			0.176256
$484$	3.06005	−	5.30016i	0.139093	−	0.240916i
$485$	−5.62324	+	9.73973i	−0.255338	+	0.442258i
$486$	1.00000			0.0453609
$487$	12.5727			0.569722			0.284861	−	0.958569i	$-0.408052\pi$
$487$	12.5727			0.569722			0.284861	+	0.958569i	$0.408052\pi$
$488$	2.98129	−	5.16374i	0.134957	−	0.233752i
$489$	−11.8136	−	20.4617i	−0.534228	−	0.925311i
$490$	1.96257	−	3.39928i	0.0886601	−	0.153564i
$491$	14.5226	+	25.1539i	0.655397	+	1.13518i	0.981794	+	0.189948i	$0.0608319\pi$
$491$	14.5226	+	25.1539i	0.655397	+	1.13518i	−0.326397	+	0.945233i	$0.605835\pi$
$492$	−5.23481	−	9.06696i	−0.236004	−	0.408770i
$493$	54.9675			2.47561
$494$	−2.33543	+	13.7916i	−0.105076	+	0.620513i
$495$	−2.20905			−0.0992894
$496$	1.60452	+	2.77912i	0.0720453	+	0.124786i
$497$	−6.28781	−	10.8908i	−0.282047	−	0.488520i
$498$	−7.41810	+	12.8485i	−0.332413	+	0.575756i
$499$	−9.63029	−	16.6801i	−0.431111	−	0.746706i	0.565858	−	0.824502i	$-0.308545\pi$
$499$	−9.63029	−	16.6801i	−0.431111	−	0.746706i	−0.996969	+	0.0777965i	$0.975212\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	9.79095			0.437427
$502$	18.2684			0.815359
$503$	−8.52262	+	14.7616i	−0.380005	+	0.658188i	−0.991063	−	0.133398i	$-0.957411\pi$
$503$	−8.52262	+	14.7616i	−0.380005	+	0.658188i	0.611057	+	0.791586i	$0.290744\pi$
$504$	−0.876763	+	1.51860i	−0.0390541	+	0.0676437i
$505$	0.492950			0.0219360
$506$	−4.87990			−0.216938
$507$	1.35100	−	2.34000i	0.0600000	−	0.103923i
$508$	6.44386	+	11.1611i	0.285900	+	0.495194i
$509$	9.38067	−	16.2478i	0.415791	−	0.720171i	−0.579720	−	0.814816i	$-0.696838\pi$
$509$	9.38067	−	16.2478i	0.415791	−	0.720171i	0.995511	+	0.0946444i	$0.0301714\pi$
$510$	−3.58581	−	6.21081i	−0.158782	−	0.275019i
$511$	10.4883	+	18.1663i	0.463977	+	0.803631i
$512$	1.00000			0.0441942
$513$	0.727762	−	4.29772i	0.0321315	−	0.189749i
$514$	6.00000			0.264649
$515$	−5.83934	−	10.1140i	−0.257312	−	0.445677i
$516$	1.35805	+	2.35221i	0.0597848	+	0.103550i
$517$	−10.9626	+	18.9877i	−0.482133	+	0.835080i
$518$	0.876763	+	1.51860i	0.0385227	+	0.0667233i
$519$	−5.72776	+	9.92078i	−0.251421	+	0.435474i
$520$	−3.20905			−0.140726
$521$	1.08895			0.0477078			0.0238539	−	0.999715i	$-0.492406\pi$
$521$	1.08895			0.0477078			0.0238539	+	0.999715i	$0.492406\pi$
$522$	−3.83229	+	6.63772i	−0.167735	+	0.290525i
$523$	15.6600	−	27.1239i	0.684762	−	1.18604i	−0.288749	−	0.957405i	$-0.593239\pi$
$523$	15.6600	−	27.1239i	0.684762	−	1.18604i	0.973511	−	0.228638i	$-0.0734273\pi$
$524$	−13.2232			−0.577656
$525$	1.75353			0.0765301
$526$	15.3136	−	26.5239i	0.667704	−	1.15650i
$527$	11.5071	+	19.9308i	0.501255	+	0.868199i
$528$	1.10452	−	1.91309i	0.0480683	−	0.0832567i
$529$	9.06005	+	15.6925i	0.393915	+	0.682281i
$530$	−5.48129	−	9.49387i	−0.238092	−	0.412387i
$531$	6.00000			0.260378
$532$	5.88842	+	4.87325i	0.255296	+	0.211282i
$533$	−33.5975			−1.45527
$534$	5.48129	+	9.49387i	0.237199	+	0.410840i
$535$	−4.13029	−	7.15387i	−0.178568	−	0.309289i
$536$	−0.0187126	+	0.0324111i	−0.000808260	+	0.00139995i
$537$	−3.31357	−	5.73928i	−0.142991	−	0.247668i
$538$	8.79486	−	15.2331i	0.379173	−	0.656748i
$539$	8.67085			0.373480
$540$	1.00000			0.0430331
$541$	11.7246	−	20.3076i	0.504081	−	0.873094i	−0.495908	−	0.868375i	$-0.665165\pi$
$541$	11.7246	−	20.3076i	0.504081	−	0.873094i	0.999989	−	0.00471871i	$-0.00150202\pi$
$542$	−9.45552	+	16.3774i	−0.406150	+	0.703472i
$543$	10.2606			0.440323
$544$	7.17162			0.307481
$545$	2.58581	−	4.47876i	0.110764	−	0.191849i
$546$	2.81357	+	4.87325i	0.120410	+	0.208556i
$547$	4.60452	−	7.97527i	0.196875	−	0.340998i	−0.750638	−	0.660713i	$-0.770254\pi$
$547$	4.60452	−	7.97527i	0.196875	−	0.340998i	0.947514	+	0.319715i	$0.103587\pi$
$548$	10.7161	+	18.5608i	0.457769	+	0.792879i
$549$	2.98129	+	5.16374i	0.127238	+	0.220383i
$550$	−2.20905			−0.0941942
$551$	25.7380	+	21.3008i	1.09648	+	0.907443i
$552$	2.20905			0.0940234
$553$	−1.06005	−	1.83606i	−0.0450779	−	0.0780772i
$554$	−12.4555	−	21.5736i	−0.529185	−	0.916575i
$555$	0.500000	−	0.866025i	0.0212238	−	0.0367607i
$556$	−3.60452	−	6.24322i	−0.152866	−	0.264772i
$557$	1.55614	−	2.69531i	0.0659357	−	0.114204i	−0.831173	−	0.556014i	$-0.812330\pi$
$557$	1.55614	−	2.69531i	0.0659357	−	0.114204i	0.897109	+	0.441810i	$0.145663\pi$
$558$	−3.20905			−0.135850
$559$	8.71610			0.368652
$560$	−0.876763	+	1.51860i	−0.0370500	+	0.0641724i
$561$	7.92124	−	13.7200i	0.334435	−	0.579258i
$562$	26.8877			1.13419
$563$	−30.2684			−1.27566			−0.637830	−	0.770177i	$-0.720168\pi$
$563$	−30.2684			−1.27566			−0.637830	+	0.770177i	$0.720168\pi$
$564$	4.96257	−	8.59543i	0.208962	−	0.361933i
$565$	1.13029	+	1.95772i	0.0475516	+	0.0823617i
$566$	−12.8877	+	22.3222i	−0.541711	+	0.938272i
$567$	−0.876763	−	1.51860i	−0.0368206	−	0.0637751i
$568$	−3.58581	−	6.21081i	−0.150457	−	0.260600i
$569$	−4.36657			−0.183056			−0.0915282	−	0.995802i	$-0.529175\pi$
$569$	−4.36657			−0.183056			−0.0915282	+	0.995802i	$0.529175\pi$
$570$	0.727762	−	4.29772i	0.0304826	−	0.180012i
$571$	−43.4026			−1.81634			−0.908171	−	0.418599i	$-0.862521\pi$
$571$	−43.4026			−1.81634			−0.908171	+	0.418599i	$0.862521\pi$
$572$	−3.54448	−	6.13921i	−0.148202	−	0.256693i
$573$	−12.6271	−	21.8709i	−0.527507	−	0.913668i
$574$	−9.17938	+	15.8991i	−0.383140	+	0.663617i
$575$	−1.10452	−	1.91309i	−0.0460619	−	0.0797815i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−20.3354			−0.846575			−0.423287	−	0.905995i	$-0.639124\pi$
$577$	−20.3354			−0.846575			−0.423287	+	0.905995i	$0.639124\pi$
$578$	34.4322			1.43219
$579$	−1.43681	+	2.48863i	−0.0597119	+	0.103424i
$580$	−3.83229	+	6.63772i	−0.159127	+	0.275616i
$581$	26.0156			1.07931
$582$	11.2465			0.466181
$583$	12.1084	−	20.9724i	0.501480	−	0.868589i
$584$	5.98129	+	10.3599i	0.247507	+	0.428695i
$585$	1.60452	−	2.77912i	0.0663389	−	0.114902i
$586$	−0.765187	−	1.32534i	−0.0316096	−	0.0547494i
$587$	6.38067	+	11.0517i	0.263359	+	0.456151i	0.967132	−	0.254274i	$-0.0818364\pi$
$587$	6.38067	+	11.0517i	0.263359	+	0.456151i	−0.703774	+	0.710424i	$0.748503\pi$
$588$	−3.92515			−0.161870
$589$	−2.33543	+	13.7916i	−0.0962295	+	0.568272i
$590$	6.00000			0.247016
$591$	7.44386	+	12.8931i	0.306200	+	0.530353i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	18.4735	−	31.9971i	0.758617	−	1.31396i	−0.184939	−	0.982750i	$-0.559209\pi$
$593$	18.4735	−	31.9971i	0.758617	−	1.31396i	0.943556	−	0.331214i	$-0.107458\pi$
$594$	1.10452	+	1.91309i	0.0453192	+	0.0784952i
$595$	−6.28781	+	10.8908i	−0.257775	+	0.446480i
$596$	−8.75353			−0.358558
$597$	−1.54448			−0.0632112
$598$	3.54448	−	6.13921i	0.144944	−	0.251051i
$599$	10.8090	−	18.7217i	0.441642	−	0.764947i	−0.556169	−	0.831069i	$-0.687729\pi$
$599$	10.8090	−	18.7217i	0.441642	−	0.764947i	0.997812	+	0.0661222i	$0.0210627\pi$
$600$	1.00000			0.0408248
$601$	−36.0141			−1.46905			−0.734523	−	0.678584i	$-0.762594\pi$
$601$	−36.0141			−1.46905			−0.734523	+	0.678584i	$0.762594\pi$
$602$	2.38137	−	4.12466i	0.0970576	−	0.168109i
$603$	−0.0187126	−	0.0324111i	−0.000762035	−	0.00131988i
$604$	−4.33934	+	7.51595i	−0.176565	+	0.305820i
$605$	3.06005	+	5.30016i	0.124409	+	0.215482i
$606$	−0.246475	−	0.426907i	−0.0100124	−	0.0173419i
$607$	1.65047			0.0669907			0.0334953	−	0.999439i	$-0.489336\pi$
$607$	1.65047			0.0669907			0.0334953	+	0.999439i	$0.489336\pi$
$608$	3.35805	+	2.77912i	0.136187	+	0.112708i
$609$	13.4400			0.544617
$610$	2.98129	+	5.16374i	0.120709	+	0.209074i
$611$	−15.9251	−	27.5832i	−0.644263	−	1.11590i
$612$	−3.58581	+	6.21081i	−0.144948	+	0.251057i
$613$	−12.7691	−	22.1167i	−0.515739	−	0.893286i	−0.999833	−	0.0182703i	$-0.994184\pi$
$613$	−12.7691	−	22.1167i	−0.515739	−	0.893286i	0.484094	−	0.875016i	$-0.339149\pi$
$614$	8.88381	−	15.3872i	0.358522	−	0.620977i
$615$	10.4696			0.422176
$616$	−3.87362			−0.156073
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	−0.719605	−	0.694383i	$-0.755677\pi$
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	0.961156	+	0.276005i	$0.0890106\pi$
$618$	−5.83934	+	10.1140i	−0.234893	+	0.406846i
$619$	14.7394			0.592427			0.296214	−	0.955122i	$-0.404276\pi$
$619$	14.7394			0.592427			0.296214	+	0.955122i	$0.404276\pi$
$620$	−3.20905			−0.128879
$621$	−1.10452	+	1.91309i	−0.0443231	+	0.0767698i
$622$	−5.70200	−	9.87615i	−0.228629	−	0.395998i
$623$	9.61158	−	16.6477i	0.385080	−	0.666977i
$624$	1.60452	+	2.77912i	0.0642324	+	0.111254i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.2684			−0.410408
$627$	9.02576	−	3.35466i	0.360454	−	0.133972i
$628$	4.50705			0.179851
$629$	3.58581	+	6.21081i	0.142976	+	0.247641i
$630$	−0.876763	−	1.51860i	−0.0349311	−	0.0605024i
$631$	10.6459	−	18.4392i	0.423805	−	0.734052i	−0.572503	−	0.819903i	$-0.694027\pi$
$631$	10.6459	−	18.4392i	0.423805	−	0.734052i	0.996308	+	0.0858508i	$0.0273608\pi$
$632$	−0.604525	−	1.04707i	−0.0240467	−	0.0416501i
$633$	−6.38381	+	11.0571i	−0.253734	+	0.439480i
$634$	−24.8129			−0.985445
$635$	−12.8877			−0.511434
$636$	−5.48129	+	9.49387i	−0.217347	+	0.376456i
$637$	−6.29800	+	10.9085i	−0.249536	+	0.432209i
$638$	−16.9314			−0.670322
$639$	7.17162			0.283705
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	19.3058	+	33.4387i	0.762534	+	1.32075i	0.941540	+	0.336900i	$0.109378\pi$
$641$	19.3058	+	33.4387i	0.762534	+	1.32075i	−0.179006	+	0.983848i	$0.557288\pi$
$642$	−4.13029	+	7.15387i	−0.163009	+	0.282341i
$643$	6.27929	+	10.8760i	0.247631	+	0.428909i	0.962868	−	0.269973i	$-0.0870146\pi$
$643$	6.27929	+	10.8760i	0.247631	+	0.428909i	−0.715237	+	0.698882i	$0.753681\pi$
$644$	−1.93681	−	3.35466i	−0.0763211	−	0.132192i
$645$	−2.71610			−0.106946
$646$	24.0827	+	19.9308i	0.947520	+	0.784167i
$647$	−24.2373			−0.952865			−0.476432	−	0.879211i	$-0.658070\pi$
$647$	−24.2373			−0.952865			−0.476432	+	0.879211i	$0.658070\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	6.62715	+	11.4786i	0.260138	+	0.450573i
$650$	1.60452	−	2.77912i	0.0629346	−	0.109006i
$651$	2.81357	+	4.87325i	0.110273	+	0.190998i
$652$	−11.8136	+	20.4617i	−0.462655	+	0.801342i
$653$	−5.35247			−0.209458			−0.104729	−	0.994501i	$-0.533398\pi$
$653$	−5.35247			−0.209458			−0.104729	+	0.994501i	$0.533398\pi$
$654$	−5.17162			−0.202227
$655$	6.61158	−	11.4516i	0.258336	−	0.447450i
$656$	−5.23481	+	9.06696i	−0.204385	+	0.354005i
$657$	−11.9626			−0.466704
$658$	−17.4040			−0.678479
$659$	−1.59747	+	2.76691i	−0.0622288	+	0.107783i	−0.895461	−	0.445139i	$-0.853154\pi$
$659$	−1.59747	+	2.76691i	−0.0622288	+	0.107783i	0.833233	+	0.552923i	$0.186488\pi$
$660$	1.10452	+	1.91309i	0.0429936	+	0.0744671i
$661$	−18.6412	+	32.2876i	−0.725061	+	1.25584i	0.233888	+	0.972263i	$0.424855\pi$
$661$	−18.6412	+	32.2876i	−0.725061	+	1.25584i	−0.958949	+	0.283578i	$0.908478\pi$
$662$	4.87676	+	8.44680i	0.189541	+	0.328294i
$663$	11.5071	+	19.9308i	0.446897	+	0.774048i
$664$	14.8362			0.575756
$665$	−7.16457	+	2.66290i	−0.277830	+	0.103263i
$666$	−1.00000			−0.0387492
$667$	−8.46571	−	14.6630i	−0.327794	−	0.567755i
$668$	−4.89548	−	8.47921i	−0.189412	−	0.328071i
$669$	−3.57876	+	6.19860i	−0.138363	+	0.239652i
$670$	−0.0187126	−	0.0324111i	−0.000722930	−	0.00125215i
$671$	−6.58581	+	11.4070i	−0.254242	+	0.440361i
$672$	1.75353			0.0676437
$673$	0.940651			0.0362594			0.0181297	−	0.999836i	$-0.494229\pi$
$673$	0.940651			0.0362594			0.0181297	+	0.999836i	$0.494229\pi$
$674$	−11.3206	+	19.6079i	−0.436054	+	0.755268i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−2.70200			−0.103923
$677$	30.8129			1.18423			0.592117	−	0.805852i	$-0.298292\pi$
$677$	30.8129			1.18423			0.592117	+	0.805852i	$0.298292\pi$
$678$	1.13029	−	1.95772i	0.0434084	−	0.0751856i
$679$	−9.86049	−	17.0789i	−0.378411	−	0.655427i
$680$	−3.58581	+	6.21081i	−0.137510	+	0.238174i
$681$	7.13029	+	12.3500i	0.273233	+	0.473254i
$682$	−3.54448	−	6.13921i	−0.135725	−	0.235083i
$683$	−8.26058			−0.316082			−0.158041	−	0.987433i	$-0.550518\pi$
$683$	−8.26058			−0.316082			−0.158041	+	0.987433i	$0.550518\pi$
$684$	−4.08581	+	1.51860i	−0.156225	+	0.0580650i
$685$	−21.4322			−0.818882
$686$	9.57876	+	16.5909i	0.365719	+	0.633444i
$687$	10.6045	+	18.3676i	0.404588	+	0.700767i
$688$	1.35805	−	2.35221i	0.0517752	−	0.0896772i
$689$	17.5897	+	30.4663i	0.670115	+	1.16067i
$690$	−1.10452	+	1.91309i	−0.0420485	+	0.0728302i
$691$	5.97668			0.227363			0.113682	−	0.993517i	$-0.463736\pi$
$691$	5.97668			0.227363			0.113682	+	0.993517i	$0.463736\pi$
$692$	11.4555			0.435474
$693$	1.93681	−	3.35466i	0.0735734	−	0.127433i
$694$	12.6271	−	21.8709i	0.479320	−	0.830207i
$695$	7.20905			0.273455
$696$	7.66457			0.290525
$697$	−37.5421	+	65.0248i	−1.42201	+	2.46299i
$698$	−14.6084	−	25.3026i	−0.552937	−	0.957716i
$699$	2.70200	−	4.68000i	0.102199	−	0.177014i
$700$	−0.876763	−	1.51860i	−0.0331385	−	0.0573976i
$701$	−22.0593	−	38.2079i	−0.833170	−	1.44309i	−0.895512	−	0.445038i	$-0.853190\pi$
$701$	−22.0593	−	38.2079i	−0.833170	−	1.44309i	0.0623415	−	0.998055i	$-0.480143\pi$
$702$	−3.20905			−0.121118
$703$	−0.727762	+	4.29772i	−0.0274481	+	0.162091i
$704$	−2.20905			−0.0832567
$705$	4.96257	+	8.59543i	0.186901	+	0.323723i
$706$	16.4594	+	28.5086i	0.619459	+	1.07293i
$707$	−0.432200	+	0.748592i	−0.0162546	+	0.0281537i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	−14.4135	+	24.9649i	−0.541310	+	0.937576i	0.457519	+	0.889200i	$0.348738\pi$
$709$	−14.4135	+	24.9649i	−0.541310	+	0.937576i	−0.998829	+	0.0483765i	$0.984595\pi$
$710$	7.17162			0.269146
$711$	1.20905			0.0453429
$712$	5.48129	−	9.49387i	0.205420	−	0.355798i
$713$	3.54448	−	6.13921i	0.132742	−	0.229915i
$714$	12.5756			0.470631
$715$	7.08895			0.265112
$716$	−3.31357	+	5.73928i	−0.123834	+	0.214487i
$717$	−10.7161	−	18.5608i	−0.400200	−	0.693167i
$718$	1.62324	−	2.81153i	0.0605787	−	0.104925i
$719$	−22.7988	−	39.4886i	−0.850251	−	1.47268i	−0.880982	−	0.473150i	$-0.843117\pi$
$719$	−22.7988	−	39.4886i	−0.850251	−	1.47268i	0.0307311	−	0.999528i	$-0.490216\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	20.4788			0.762672
$722$	3.55300	+	18.6648i	0.132229	+	0.694633i
$723$	−6.37285			−0.237009
$724$	−5.13029	−	8.88592i	−0.190666	−	0.330243i
$725$	−3.83229	−	6.63772i	−0.142328	−	0.246519i
$726$	3.06005	−	5.30016i	0.113569	−	0.196707i
$727$	−2.56710	−	4.44635i	−0.0952085	−	0.164906i	0.814487	−	0.580182i	$-0.197018\pi$
$727$	−2.56710	−	4.44635i	−0.0952085	−	0.164906i	−0.909696	+	0.415276i	$0.863685\pi$
$728$	2.81357	−	4.87325i	0.104278	−	0.180615i
$729$	1.00000			0.0370370
$730$	−11.9626			−0.442755
$731$	9.73942	−	16.8692i	0.360226	−	0.623929i
$732$	2.98129	−	5.16374i	0.110192	−	0.190857i
$733$	17.7910			0.657124			0.328562	−	0.944482i	$-0.393436\pi$
$733$	17.7910			0.657124			0.328562	+	0.944482i	$0.393436\pi$
$734$	−12.0452			−0.444598
$735$	1.96257	−	3.39928i	0.0723907	−	0.125384i
$736$	−1.10452	−	1.91309i	−0.0407133	−	0.0705176i
$737$	0.0413370	−	0.0715978i	0.00152267	−	0.00263734i
$738$	−5.23481	−	9.06696i	−0.192696	−	0.333759i
$739$	5.36971	+	9.30061i	0.197528	+	0.342129i	0.947726	−	0.319084i	$-0.103375\pi$
$739$	5.36971	+	9.30061i	0.197528	+	0.342129i	−0.750198	+	0.661213i	$0.770042\pi$
$740$	−1.00000			−0.0367607
$741$	−2.33543	+	13.7916i	−0.0857940	+	0.506647i
$742$	19.2232			0.705704
$743$	−16.5367	−	28.6424i	−0.606674	−	1.05079i	−0.991785	−	0.127919i	$-0.959170\pi$
$743$	−16.5367	−	28.6424i	−0.606674	−	1.05079i	0.385111	−	0.922870i	$-0.374163\pi$
$744$	1.60452	+	2.77912i	0.0588247	+	0.101887i
$745$	4.37676	−	7.58078i	0.160352	−	0.277738i
$746$	1.93290	+	3.34788i	0.0707685	+	0.122575i
$747$	−7.41810	+	12.8485i	−0.271414	+	0.470103i
$748$	−15.8425			−0.579258
$749$	14.4851			0.529275
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−12.0600	+	20.8886i	−0.440077	+	0.762237i	−0.997695	−	0.0678616i	$-0.978382\pi$
$751$	−12.0600	+	20.8886i	−0.440077	+	0.762237i	0.557617	+	0.830098i	$0.311716\pi$
$752$	−9.92515			−0.361933
$753$	18.2684			0.665737
$754$	12.2980	−	21.3008i	0.447867	−	0.775728i
$755$	−4.33934	−	7.51595i	−0.157925	−	0.273534i
$756$	−0.876763	+	1.51860i	−0.0318875	+	0.0552308i
$757$	15.5827	+	26.9900i	0.566362	+	0.980968i	0.996922	+	0.0784055i	$0.0249829\pi$
$757$	15.5827	+	26.9900i	0.566362	+	0.980968i	−0.430560	+	0.902562i	$0.641684\pi$
$758$	11.5297	+	19.9700i	0.418777	+	0.725342i
$759$	−4.87990			−0.177129
$760$	−4.08581	+	1.51860i	−0.148208	+	0.0550853i
$761$	11.5586			0.418998			0.209499	−	0.977809i	$-0.432817\pi$
$761$	11.5586			0.418998			0.209499	+	0.977809i	$0.432817\pi$
$762$	6.44386	+	11.1611i	0.233437	+	0.404324i
$763$	4.53429	+	7.85362i	0.164152	+	0.284320i
$764$	−12.6271	+	21.8709i	−0.456834	+	0.791260i
$765$	−3.58581	−	6.21081i	−0.129645	−	0.224552i
$766$	−1.03743	+	1.79687i	−0.0374837	+	0.0649237i
$767$	−19.2543			−0.695232
$768$	1.00000			0.0360844
$769$	7.22385	−	12.5121i	0.260499	−	0.451197i	−0.705876	−	0.708336i	$-0.749446\pi$
$769$	7.22385	−	12.5121i	0.260499	−	0.451197i	0.966375	+	0.257139i	$0.0827797\pi$
$770$	1.93681	−	3.35466i	0.0697979	−	0.120893i
$771$	6.00000			0.216085
$772$	2.87362			0.103424
$773$	18.9509	−	32.8239i	0.681617	−	1.18060i	−0.292870	−	0.956152i	$-0.594610\pi$
$773$	18.9509	−	32.8239i	0.681617	−	1.18060i	0.974487	−	0.224443i	$-0.0720563\pi$
$774$	1.35805	+	2.35221i	0.0488141	+	0.0845485i
$775$	1.60452	−	2.77912i	0.0576362	−	0.0998289i
$776$	−5.62324	−	9.73973i	−0.201862	−	0.349636i
$777$	0.876763	+	1.51860i	0.0314537	+	0.0544794i
$778$	−19.6646			−0.705009
$779$	−42.7769	+	15.8991i	−1.53264	+	0.569646i
$780$	−3.20905			−0.114902
$781$	7.92124	+	13.7200i	0.283444	+	0.490940i
$782$	−7.92124	−	13.7200i	−0.283263	−	0.490626i
$783$	−3.83229	+	6.63772i	−0.136955	+	0.237213i
$784$	1.96257	+	3.39928i	0.0700920	+	0.121403i
$785$	−2.25353	+	3.90322i	−0.0804318	+	0.139312i
$786$	−13.2232			−0.471654
$787$	−46.6491			−1.66286			−0.831430	−	0.555630i	$-0.812477\pi$
$787$	−46.6491			−1.66286			−0.831430	+	0.555630i	$0.812477\pi$
$788$	7.44386	−	12.8931i	0.265177	−	0.459299i
$789$	15.3136	−	26.5239i	0.545178	−	0.944275i
$790$	1.20905			0.0430161
$791$	−3.96398			−0.140943
$792$	1.10452	−	1.91309i	0.0392476	−	0.0679788i
$793$	−9.56710	−	16.5707i	−0.339738	−	0.588443i
$794$	4.42515	−	7.66458i	0.157043	−	0.272006i
$795$	−5.48129	−	9.49387i	−0.194401	−	0.336713i
$796$	0.772238	+	1.33755i	0.0273712	+	0.0474084i
$797$	1.79877			0.0637158			0.0318579	−	0.999492i	$-0.489858\pi$
$797$	1.79877			0.0637158			0.0318579	+	0.999492i	$0.489858\pi$
$798$	5.88842	+	4.87325i	0.208448	+	0.172511i
$799$	−71.1794			−2.51815
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	5.48129	+	9.49387i	0.193672	+	0.335449i
$802$	0.925150	−	1.60241i	0.0326682	−	0.0565829i
$803$	−13.2130	−	22.8855i	−0.466275	−	0.807612i
$804$	−0.0187126	+	0.0324111i	−0.000659941	+	0.00114305i
$805$	3.87362			0.136527
$806$	10.2980			0.362732
$807$	8.79486	−	15.2331i	0.309594	−	0.536232i
$808$	−0.246475	+	0.426907i	−0.00867096	+	0.0150185i
$809$	−39.9251			−1.40369			−0.701847	−	0.712328i	$-0.747641\pi$
$809$	−39.9251			−1.40369			−0.701847	+	0.712328i	$0.747641\pi$
$810$	1.00000			0.0351364
$811$	6.98834	−	12.1042i	0.245394	−	0.425034i	−0.716849	−	0.697229i	$-0.754416\pi$
$811$	6.98834	−	12.1042i	0.245394	−	0.425034i	0.962242	+	0.272195i	$0.0877494\pi$
$812$	−6.72001	−	11.6394i	−0.235826	−	0.408463i
$813$	−9.45552	+	16.3774i	−0.331620	+	0.574382i
$814$	−1.10452	−	1.91309i	−0.0387136	−	0.0670539i
$815$	−11.8136	−	20.4617i	−0.413811	−	0.716742i
$816$	7.17162			0.251057
$817$	11.0975	−	4.12466i	0.388251	−	0.144304i
$818$	18.0593			0.631430
$819$	2.81357	+	4.87325i	0.0983143	+	0.170285i
$820$	−5.23481	−	9.06696i	−0.182808	−	0.316632i
$821$	10.5819	−	18.3284i	0.369311	−	0.639665i	−0.620147	−	0.784486i	$-0.712927\pi$
$821$	10.5819	−	18.3284i	0.369311	−	0.639665i	0.989458	+	0.144820i	$0.0462604\pi$
$822$	10.7161	+	18.5608i	0.373767	+	0.647383i
$823$	17.8994	−	31.0026i	0.623933	−	1.08068i	−0.364813	−	0.931081i	$-0.618867\pi$
$823$	17.8994	−	31.0026i	0.623933	−	1.08068i	0.988746	−	0.149603i	$-0.0477997\pi$
$824$	11.6787			0.406846
$825$	−2.20905			−0.0769092
$826$	−5.26058	+	9.11158i	−0.183039	+	0.317033i
$827$	−15.2878	+	26.4793i	−0.531609	+	0.920774i	0.467710	+	0.883882i	$0.345079\pi$
$827$	−15.2878	+	26.4793i	−0.531609	+	0.920774i	−0.999319	+	0.0368923i	$0.988254\pi$
$828$	2.20905			0.0767698
$829$	−54.3136			−1.88639			−0.943195	−	0.332238i	$-0.892196\pi$
$829$	−54.3136			−1.88639			−0.943195	+	0.332238i	$0.892196\pi$
$830$	−7.41810	+	12.8485i	−0.257486	+	0.445979i
$831$	−12.4555	−	21.5736i	−0.432077	−	0.748380i
$832$	1.60452	−	2.77912i	0.0556269	−	0.0963486i
$833$	14.0749	+	24.3784i	0.487665	+	0.844660i
$834$	−3.60452	−	6.24322i	−0.124814	−	0.216185i
$835$	9.79095			0.338830
$836$	−7.41810	−	6.13921i	−0.256560	−	0.212329i
$837$	−3.20905			−0.110921
$838$	0.723850	+	1.25375i	0.0250050	+	0.0433099i
$839$	−19.7988	−	34.2925i	−0.683530	−	1.18391i	−0.973896	−	0.226993i	$-0.927111\pi$
$839$	−19.7988	−	34.2925i	−0.683530	−	1.18391i	0.290367	−	0.956915i	$-0.406223\pi$
$840$	−0.876763	+	1.51860i	−0.0302512	+	0.0523966i
$841$	−14.8729	−	25.7605i	−0.512857	−	0.888294i
$842$	8.58581	−	14.8711i	0.295887	−	0.512491i
$843$	26.8877			0.926062
$844$	12.7676			0.439480
$845$	1.35100	−	2.34000i	0.0464758	−	0.0804985i
$846$	4.96257	−	8.59543i	0.170617	−	0.295517i
$847$	−10.7317			−0.368747
$848$	10.9626			0.376456
$849$	−12.8877	+	22.3222i	−0.442306	+	0.766096i
$850$	−3.58581	−	6.21081i	−0.122992	−	0.213029i
$851$	1.10452	−	1.91309i	0.0378626	−	0.0655800i
$852$	−3.58581	−	6.21081i	−0.122848	−	0.212779i
$853$	11.7761	+	20.3969i	0.403208	+	0.698376i	0.994111	−	0.108366i	$-0.0345619\pi$
$853$	11.7761	+	20.3969i	0.403208	+	0.698376i	−0.590903	+	0.806742i	$0.701229\pi$
$854$	−10.4555			−0.357781
$855$	0.727762	−	4.29772i	0.0248889	−	0.146979i
$856$	8.26058			0.282341
$857$	−27.9251	−	48.3678i	−0.953905	−	1.65221i	−0.736854	−	0.676051i	$-0.763690\pi$
$857$	−27.9251	−	48.3678i	−0.953905	−	1.65221i	−0.217051	−	0.976160i	$-0.569644\pi$
$858$	−3.54448	−	6.13921i	−0.121006	−	0.209589i
$859$	−14.2949	+	24.7594i	−0.487734	+	0.844781i	−0.999901	−	0.0141057i	$-0.995510\pi$
$859$	−14.2949	+	24.7594i	−0.487734	+	0.844781i	0.512166	+	0.858886i	$0.328843\pi$
$860$	1.35805	+	2.35221i	0.0463091	+	0.0802097i
$861$	−9.17938	+	15.8991i	−0.312832	+	0.541841i
$862$	−19.0686			−0.649478
$863$	2.31210			0.0787048			0.0393524	−	0.999225i	$-0.487471\pi$
$863$	2.31210			0.0787048			0.0393524	+	0.999225i	$0.487471\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−5.72776	+	9.92078i	−0.194750	+	0.337316i
$866$	−15.8877			−0.539887
$867$	34.4322			1.16938
$868$	2.81357	−	4.87325i	0.0954989	−	0.165409i
$869$	1.33543	+	2.31302i	0.0453012	+	0.0784640i
$870$	−3.83229	+	6.63772i	−0.129927	+	0.225040i
$871$	0.0600496	+	0.104009i	0.00203470	+	0.00352421i
$872$	2.58581	+	4.47876i	0.0875667	+	0.151670i
$873$	11.2465			0.380636
$874$	1.60766	−	9.49387i	0.0543800	−	0.321135i
$875$	1.75353			0.0592800
$876$	5.98129	+	10.3599i	0.202089	+	0.350028i
$877$	4.78390	+	8.28596i	0.161541	+	0.279797i	0.935421	−	0.353535i	$-0.115020\pi$
$877$	4.78390	+	8.28596i	0.161541	+	0.279797i	−0.773881	+	0.633331i	$0.781687\pi$
$878$	−1.68329	+	2.91554i	−0.0568082	+	0.0983947i
$879$	−0.765187	−	1.32534i	−0.0258091	−	0.0447027i
$880$	1.10452	−	1.91309i	0.0372335	−	0.0644904i
$881$	23.5586			0.793709			0.396854	−	0.917882i	$-0.370102\pi$
$881$	23.5586			0.793709			0.396854	+	0.917882i	$0.370102\pi$
$882$	−3.92515			−0.132167
$883$	−28.5195	+	49.3972i	−0.959757	+	1.66235i	−0.236671	+	0.971590i	$0.576056\pi$
$883$	−28.5195	+	49.3972i	−0.959757	+	1.66235i	−0.723086	+	0.690758i	$0.757277\pi$
$884$	11.5071	−	19.9308i	0.387024	−	0.670345i
$885$	6.00000			0.201688
$886$	−23.5897			−0.792512
$887$	−18.6271	+	32.2632i	−0.625438	+	1.08329i	0.363017	+	0.931782i	$0.381747\pi$
$887$	−18.6271	+	32.2632i	−0.625438	+	1.08329i	−0.988456	+	0.151509i	$0.951587\pi$
$888$	0.500000	+	0.866025i	0.0167789	+	0.0290619i
$889$	11.2995	−	19.5713i	0.378972	−	0.656399i
$890$	5.48129	+	9.49387i	0.183733	+	0.318235i
$891$	1.10452	+	1.91309i	0.0370030	+	0.0640910i
$892$	7.15752			0.239652
$893$	−33.3291	−	27.5832i	−1.11532	−	0.923036i
$894$	−8.75353			−0.292762
$895$	−3.31357	−	5.73928i	−0.110761	−	0.191843i
$896$	−0.876763	−	1.51860i	−0.0292906	−	0.0507328i
$897$	3.54448	−	6.13921i	0.118347	−	0.204982i
$898$	5.48129	+	9.49387i	0.182913	+	0.316814i
$899$	12.2980	−	21.3008i	0.410161	−	0.710420i
$900$	1.00000			0.0333333
$901$	78.6195			2.61919
$902$	11.5640	−	20.0294i	0.385038	−	0.666905i
$903$	2.38137	−	4.12466i	0.0792472	−	0.137260i
$904$	−2.26058			−0.0751856
$905$	10.2606			0.341073
$906$	−4.33934	+	7.51595i	−0.144165	+	0.249701i
$907$	−22.1342	−	38.3376i	−0.734954	−	1.27298i	−0.954744	−	0.297430i	$-0.903870\pi$
$907$	−22.1342	−	38.3376i	−0.734954	−	1.27298i	0.219789	−	0.975547i	$-0.429463\pi$
$908$	7.13029	−	12.3500i	0.236627	−	0.409850i
$909$	−0.246475	−	0.426907i	−0.00817506	−	0.0141596i
$910$	2.81357	+	4.87325i	0.0932691	+	0.161547i
$911$	52.1935			1.72925			0.864625	−	0.502418i	$-0.167556\pi$
$911$	52.1935			1.72925			0.864625	+	0.502418i	$0.167556\pi$
$912$	3.35805	+	2.77912i	0.111196	+	0.0920258i
$913$	−32.7739			−1.08466
$914$	−13.3245	−	23.0788i	−0.440737	−	0.763378i
$915$	2.98129	+	5.16374i	0.0985583	+	0.170708i
$916$	10.6045	−	18.3676i	0.350383	−	0.606882i
$917$	11.5936	+	20.0806i	0.382853	+	0.663121i
$918$	−3.58581	+	6.21081i	−0.118349	+	0.204987i
$919$	−4.38067			−0.144505			−0.0722526	−	0.997386i	$-0.523019\pi$
$919$	−4.38067			−0.144505			−0.0722526	+	0.997386i	$0.523019\pi$
$920$	2.20905			0.0728302
$921$	8.88381	−	15.3872i	0.292732	−	0.507026i
$922$	−2.20905	+	3.82619i	−0.0727512	+	0.126009i
$923$	−23.0141			−0.757518
$924$	−3.87362			−0.127433
$925$	0.500000	−	0.866025i	0.0164399	−	0.0284747i
$926$	3.83934	+	6.64993i	0.126168	+	0.218530i
$927$	−5.83934	+	10.1140i	−0.191789	+	0.332188i
$928$	−3.83229	−	6.63772i	−0.125801	−	0.217894i
$929$	4.88529	+	8.46156i	0.160281	+	0.277615i	0.934969	−	0.354728i	$-0.115427\pi$
$929$	4.88529	+	8.46156i	0.160281	+	0.277615i	−0.774688	+	0.632343i	$0.782093\pi$
$930$	−3.20905			−0.105229
$931$	−2.85658	+	16.8692i	−0.0936205	+	0.552865i
$932$	−5.40400			−0.177014
$933$	−5.70200	−	9.87615i	−0.186675	−	0.323331i
$934$	−12.0413	−	20.8562i	−0.394005	−	0.682436i
$935$	7.92124	−	13.7200i	0.259052	−	0.448692i
$936$	1.60452	+	2.77912i	0.0524455	+	0.0908383i
$937$	22.2871	−	38.6024i	0.728088	−	1.26109i	−0.229602	−	0.973285i	$-0.573742\pi$
$937$	22.2871	−	38.6024i	0.728088	−	1.26109i	0.957690	−	0.287801i	$-0.0929242\pi$
$938$	0.0656259			0.00214276
$939$	−10.2684			−0.335097
$940$	4.96257	−	8.59543i	0.161861	−	0.280352i
$941$	1.26449	−	2.19016i	0.0412211	−	0.0713970i	−0.844679	−	0.535274i	$-0.820209\pi$
$941$	1.26449	−	2.19016i	0.0412211	−	0.0713970i	0.885900	+	0.463877i	$0.153542\pi$
$942$	4.50705			0.146848
$943$	23.1279			0.753149
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$	−0.876763	−	1.51860i	−0.0285211	−	0.0494000i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	2.66066	+	4.60840i	0.0864599	+	0.149753i	0.906012	−	0.423251i	$-0.139111\pi$
$947$	2.66066	+	4.60840i	0.0864599	+	0.149753i	−0.819552	+	0.573004i	$0.805778\pi$
$948$	−0.604525	−	1.04707i	−0.0196341	−	0.0340072i
$949$	38.3885			1.24614
$950$	0.727762	−	4.29772i	0.0236117	−	0.139436i
$951$	−24.8129			−0.804613
$952$	−6.28781	−	10.8908i	−0.203789	−	0.352973i
$953$	−5.01410	−	8.68468i	−0.162423	−	0.281324i	0.773314	−	0.634023i	$-0.218597\pi$
$953$	−5.01410	−	8.68468i	−0.162423	−	0.281324i	−0.935737	+	0.352699i	$0.885264\pi$
$954$	−5.48129	+	9.49387i	−0.177463	+	0.307375i
$955$	−12.6271	−	21.8709i	−0.408605	−	0.707725i
$956$	−10.7161	+	18.5608i	−0.346583	+	0.600300i
$957$	−16.9314			−0.547315
$958$	0.903226			0.0291819
$959$	18.7910	−	32.5469i	0.606791	−	1.05099i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	−20.7020			−0.667806
$962$	3.20905			0.103464
$963$	−4.13029	+	7.15387i	−0.133097	+	0.230530i
$964$	3.18643	+	5.51905i	0.102628	+	0.177757i
$965$	−1.43681	+	2.48863i	−0.0462526	+	0.0801119i
$966$	−1.93681	−	3.35466i	−0.0623159	−	0.107934i
$967$	−16.3955	−	28.3978i	−0.527243	−	0.913212i	−0.999496	−	0.0317485i	$-0.989892\pi$
$967$	−16.3955	−	28.3978i	−0.527243	−	0.913212i	0.472253	−	0.881463i	$-0.343441\pi$
$968$	−6.12010			−0.196707
$969$	24.0827	+	19.9308i	0.773647	+	0.640269i
$970$	11.2465			0.361103
$971$	−14.8877	−	25.7863i	−0.477770	−	0.827522i	0.521905	−	0.853003i	$-0.325221\pi$
$971$	−14.8877	−	25.7863i	−0.477770	−	0.827522i	−0.999675	+	0.0254817i	$0.991888\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−6.32062	+	10.9476i	−0.202630	+	0.350965i
$974$	−6.28634	−	10.8883i	−0.201427	−	0.348882i
$975$	1.60452	−	2.77912i	0.0513859	−	0.0890030i
$976$	−5.96257			−0.190857
$977$	49.7084			1.59031			0.795157	−	0.606404i	$-0.207389\pi$
$977$	49.7084			1.59031			0.795157	+	0.606404i	$0.207389\pi$
$978$	−11.8136	+	20.4617i	−0.377756	+	0.654293i
$979$	−12.1084	+	20.9724i	−0.386987	+	0.670282i
$980$	−3.92515			−0.125384
$981$	−5.17162			−0.165117
$982$	14.5226	−	25.1539i	0.463436	−	0.802694i
$983$	13.3510	+	23.1246i	0.425831	+	0.737561i	0.996498	−	0.0836212i	$-0.0266486\pi$
$983$	13.3510	+	23.1246i	0.425831	+	0.737561i	−0.570667	+	0.821182i	$0.693315\pi$
$984$	−5.23481	+	9.06696i	−0.166880	+	0.289044i
$985$	7.44386	+	12.8931i	0.237181	+	0.410810i
$986$	−27.4837	−	47.6032i	−0.875260	−	1.51600i
$987$	−17.4040			−0.553975
$988$	13.1116	−	4.87325i	0.417135	−	0.155039i
$989$	−6.00000			−0.190789
$990$	1.10452	+	1.91309i	0.0351041	+	0.0608021i
$991$	21.9580	+	38.0323i	0.697518	+	1.20814i	0.969325	+	0.245784i	$0.0790455\pi$
$991$	21.9580	+	38.0323i	0.697518	+	1.20814i	−0.271807	+	0.962352i	$0.587621\pi$
$992$	1.60452	−	2.77912i	0.0509437	−	0.0882371i
$993$	4.87676	+	8.44680i	0.154759	+	0.268051i
$994$	−6.28781	+	10.8908i	−0.199437	+	0.345436i
$995$	−1.54448			−0.0489632
$996$	14.8362			0.470103
$997$	−29.2239	+	50.6173i	−0.925531	+	1.60307i	−0.134826	+	0.990869i	$0.543048\pi$
$997$	−29.2239	+	50.6173i	−0.925531	+	1.60307i	−0.790705	+	0.612197i	$0.790286\pi$
$998$	−9.63029	+	16.6801i	−0.304841	+	0.528001i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.j.121.2	✓	6
3.2	odd	2		1710.2.l.q.1261.2		6
19.11	even	3	inner	570.2.i.j.391.2	yes	6
57.11	odd	6		1710.2.l.q.1531.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.j.121.2	✓	6	1.1	even	1	trivial
570.2.i.j.391.2	yes	6	19.11	even	3	inner
1710.2.l.q.1261.2		6	3.2	odd	2
1710.2.l.q.1531.2		6	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.75353 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.75353 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -2.20905 q^{11} +1.00000 q^{12} +(1.60452 - 2.77912i) q^{13} +(-0.876763 - 1.51860i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.58581 - 6.21081i) q^{17} +1.00000 q^{18} +(0.727762 - 4.29772i) q^{19} +1.00000 q^{20} +(-0.876763 - 1.51860i) q^{21} +(1.10452 + 1.91309i) q^{22} +(-1.10452 + 1.91309i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -3.20905 q^{26} +1.00000 q^{27} +(-0.876763 + 1.51860i) q^{28} +(-3.83229 + 6.63772i) q^{29} +1.00000 q^{30} -3.20905 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.10452 + 1.91309i) q^{33} +(-3.58581 + 6.21081i) q^{34} +(-0.876763 - 1.51860i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(-4.08581 + 1.51860i) q^{38} -3.20905 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-5.23481 - 9.06696i) q^{41} +(-0.876763 + 1.51860i) q^{42} +(1.35805 + 2.35221i) q^{43} +(1.10452 - 1.91309i) q^{44} +1.00000 q^{45} +2.20905 q^{46} +(4.96257 - 8.59543i) q^{47} +(-0.500000 + 0.866025i) q^{48} -3.92515 q^{49} +1.00000 q^{50} +(-3.58581 + 6.21081i) q^{51} +(1.60452 + 2.77912i) q^{52} +(-5.48129 + 9.49387i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.10452 + 1.91309i) q^{55} +1.75353 q^{56} +(-4.08581 + 1.51860i) q^{57} +7.66457 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(2.98129 - 5.16374i) q^{61} +(1.60452 + 2.77912i) q^{62} +(-0.876763 + 1.51860i) q^{63} +1.00000 q^{64} -3.20905 q^{65} +(1.10452 - 1.91309i) q^{66} +(-0.0187126 + 0.0324111i) q^{67} +7.17162 q^{68} +2.20905 q^{69} +(-0.876763 + 1.51860i) q^{70} +(-3.58581 - 6.21081i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.98129 + 10.3599i) q^{73} +(0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(3.35805 + 2.77912i) q^{76} -3.87362 q^{77} +(1.60452 + 2.77912i) q^{78} +(-0.604525 - 1.04707i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.23481 + 9.06696i) q^{82} +14.8362 q^{83} +1.75353 q^{84} +(-3.58581 + 6.21081i) q^{85} +(1.35805 - 2.35221i) q^{86} +7.66457 q^{87} -2.20905 q^{88} +(5.48129 - 9.49387i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(2.81357 - 4.87325i) q^{91} +(-1.10452 - 1.91309i) q^{92} +(1.60452 + 2.77912i) q^{93} -9.92515 q^{94} +(-4.08581 + 1.51860i) q^{95} +1.00000 q^{96} +(-5.62324 - 9.73973i) q^{97} +(1.96257 + 3.39928i) q^{98} +(1.10452 - 1.91309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} + 6 q^{12} - q^{13} - q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{20} - q^{21} - 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} + 6 q^{27} - q^{28} - 6 q^{29} + 6 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 4 q^{34} - q^{35} - 3 q^{36} - 6 q^{37} + q^{38} + 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} - 11 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} - 3 q^{48} + 36 q^{49} + 6 q^{50} + 4 q^{51} - q^{52} - 18 q^{53} - 3 q^{54} - 4 q^{55} + 2 q^{56} + q^{57} + 12 q^{58} - 18 q^{59} - 3 q^{60} + 3 q^{61} - q^{62} - q^{63} + 6 q^{64} + 2 q^{65} - 4 q^{66} - 15 q^{67} - 8 q^{68} - 8 q^{69} - q^{70} + 4 q^{71} - 3 q^{72} + 21 q^{73} + 3 q^{74} + 6 q^{75} + q^{76} + 32 q^{77} - q^{78} + 7 q^{79} - 3 q^{80} - 3 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 4 q^{85} - 11 q^{86} + 12 q^{87} + 8 q^{88} + 18 q^{89} - 3 q^{90} - 15 q^{91} + 4 q^{92} - q^{93} + q^{95} + 6 q^{96} - 38 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 + 6 * q^12 - q^13 - q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^20 - q^21 - 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 + 6 * q^27 - q^28 - 6 * q^29 + 6 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 4 * q^34 - q^35 - 3 * q^36 - 6 * q^37 + q^38 + 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 - 11 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 + 36 * q^49 + 6 * q^50 + 4 * q^51 - q^52 - 18 * q^53 - 3 * q^54 - 4 * q^55 + 2 * q^56 + q^57 + 12 * q^58 - 18 * q^59 - 3 * q^60 + 3 * q^61 - q^62 - q^63 + 6 * q^64 + 2 * q^65 - 4 * q^66 - 15 * q^67 - 8 * q^68 - 8 * q^69 - q^70 + 4 * q^71 - 3 * q^72 + 21 * q^73 + 3 * q^74 + 6 * q^75 + q^76 + 32 * q^77 - q^78 + 7 * q^79 - 3 * q^80 - 3 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 4 * q^85 - 11 * q^86 + 12 * q^87 + 8 * q^88 + 18 * q^89 - 3 * q^90 - 15 * q^91 + 4 * q^92 - q^93 + q^95 + 6 * q^96 - 38 * q^97 - 18 * q^98 - 4 * q^99

Introduction

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