LMFDB - Embedded newform 570.2.i.g.391.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.2
Root			$-1.88600 - 3.26665i$ of defining polynomial
Character	$\chi$	$=$	570.391
Dual form			570.2.i.g.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +3.77200 q^{11} +1.00000 q^{12} +(2.38600 + 4.13267i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{18} +(2.88600 + 3.26665i) q^{19} +1.00000 q^{20} +(0.500000 - 0.866025i) q^{21} +(1.88600 - 3.26665i) q^{22} +(1.88600 + 3.26665i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.77200 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} -1.00000 q^{30} +2.77200 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.88600 + 3.26665i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.00000 q^{37} +(4.27200 - 0.866025i) q^{38} -4.77200 q^{39} +(0.500000 - 0.866025i) q^{40} +(1.88600 - 3.26665i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.38600 + 7.59678i) q^{43} +(-1.88600 - 3.26665i) q^{44} +1.00000 q^{45} +3.77200 q^{46} +(-0.500000 - 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(2.38600 - 4.13267i) q^{52} +(-4.88600 - 8.46280i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.88600 + 3.26665i) q^{55} +1.00000 q^{56} +(-4.27200 + 0.866025i) q^{57} +6.00000 q^{58} +(6.77200 - 11.7295i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-1.38600 - 2.40062i) q^{61} +(1.38600 - 2.40062i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} -4.77200 q^{65} +(1.88600 + 3.26665i) q^{66} +(5.38600 + 9.32883i) q^{67} -3.77200 q^{69} +(-0.500000 - 0.866025i) q^{70} +(3.77200 - 6.53330i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.61400 - 2.79553i) q^{73} +(-0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(1.38600 - 4.13267i) q^{76} -3.77200 q^{77} +(-2.38600 + 4.13267i) q^{78} +(-5.15800 + 8.93392i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.88600 - 3.26665i) q^{82} +6.00000 q^{83} -1.00000 q^{84} +(4.38600 + 7.59678i) q^{86} -6.00000 q^{87} -3.77200 q^{88} +(-8.65800 - 14.9961i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-2.38600 - 4.13267i) q^{91} +(1.88600 - 3.26665i) q^{92} +(-1.38600 + 2.40062i) q^{93} +(-4.27200 + 0.866025i) q^{95} -1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(-1.88600 - 3.26665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} - 2 q^{14} - 2 q^{15} - 2 q^{16} - 4 q^{18} + 3 q^{19} + 4 q^{20} + 2 q^{21} - q^{22} - q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} + 4 q^{27} + 2 q^{28} + 12 q^{29} - 4 q^{30} - 6 q^{31} + 2 q^{32} + q^{33} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 2 q^{39} + 2 q^{40} - q^{41} - 2 q^{42} - 9 q^{43} + q^{44} + 4 q^{45} - 2 q^{46} - 2 q^{48} - 24 q^{49} - 4 q^{50} + q^{52} - 11 q^{53} + 2 q^{54} + q^{55} + 4 q^{56} + 24 q^{58} + 10 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{65} - q^{66} + 13 q^{67} + 2 q^{69} - 2 q^{70} - 2 q^{71} + 2 q^{72} + 15 q^{73} - 2 q^{74} + 4 q^{75} - 3 q^{76} + 2 q^{77} - q^{78} + 5 q^{79} - 2 q^{80} - 2 q^{81} + q^{82} + 24 q^{83} - 4 q^{84} + 9 q^{86} - 24 q^{87} + 2 q^{88} - 9 q^{89} + 2 q^{90} - q^{91} - q^{92} + 3 q^{93} - 4 q^{96} + 20 q^{97} - 12 q^{98} + q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 + q^13 - 2 * q^14 - 2 * q^15 - 2 * q^16 - 4 * q^18 + 3 * q^19 + 4 * q^20 + 2 * q^21 - q^22 - q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 + 4 * q^27 + 2 * q^28 + 12 * q^29 - 4 * q^30 - 6 * q^31 + 2 * q^32 + q^33 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 2 * q^39 + 2 * q^40 - q^41 - 2 * q^42 - 9 * q^43 + q^44 + 4 * q^45 - 2 * q^46 - 2 * q^48 - 24 * q^49 - 4 * q^50 + q^52 - 11 * q^53 + 2 * q^54 + q^55 + 4 * q^56 + 24 * q^58 + 10 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^62 + 2 * q^63 + 4 * q^64 - 2 * q^65 - q^66 + 13 * q^67 + 2 * q^69 - 2 * q^70 - 2 * q^71 + 2 * q^72 + 15 * q^73 - 2 * q^74 + 4 * q^75 - 3 * q^76 + 2 * q^77 - q^78 + 5 * q^79 - 2 * q^80 - 2 * q^81 + q^82 + 24 * q^83 - 4 * q^84 + 9 * q^86 - 24 * q^87 + 2 * q^88 - 9 * q^89 + 2 * q^90 - q^91 - q^92 + 3 * q^93 - 4 * q^96 + 20 * q^97 - 12 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	3.77200			1.13730			0.568651	−	0.822579i	$-0.307466\pi$
$11$	3.77200			1.13730			0.568651	+	0.822579i	$0.307466\pi$
$12$	1.00000			0.288675
$13$	2.38600	+	4.13267i	0.661758	+	1.14620i	0.980154	+	0.198240i	$0.0635225\pi$
$13$	2.38600	+	4.13267i	0.661758	+	1.14620i	−0.318396	+	0.947958i	$0.603144\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−1.00000			−0.235702
$19$	2.88600	+	3.26665i	0.662094	+	0.749421i
$19$	2.88600	+	3.26665i	0.662094	+	0.749421i
$20$	1.00000			0.223607
$21$	0.500000	−	0.866025i	0.109109	−	0.188982i
$22$	1.88600	−	3.26665i	0.402097	−	0.696452i
$23$	1.88600	+	3.26665i	0.393258	+	0.681143i	0.992877	−	0.119142i	$-0.0380145\pi$
$23$	1.88600	+	3.26665i	0.393258	+	0.681143i	−0.599619	+	0.800286i	$0.704681\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.77200			0.935867
$27$	1.00000			0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$	−1.00000			−0.182574
$31$	2.77200			0.497866			0.248933	−	0.968521i	$-0.419920\pi$
$31$	2.77200			0.497866			0.248933	+	0.968521i	$0.419920\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.88600	+	3.26665i	−0.328311	+	0.568651i
$34$		0			0
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	−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	$0.526194\pi$
$38$	4.27200	−	0.866025i	0.693010	−	0.140488i
$39$	−4.77200			−0.764132
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	1.88600	−	3.26665i	0.294544	−	0.510165i	−0.680335	−	0.732901i	$-0.738166\pi$
$41$	1.88600	−	3.26665i	0.294544	−	0.510165i	0.974879	+	0.222737i	$0.0714990\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−4.38600	+	7.59678i	−0.668859	+	1.15850i	0.309365	+	0.950943i	$0.399884\pi$
$43$	−4.38600	+	7.59678i	−0.668859	+	1.15850i	−0.978224	+	0.207554i	$0.933450\pi$
$44$	−1.88600	−	3.26665i	−0.284325	−	0.492466i
$45$	1.00000			0.149071
$46$	3.77200			0.556151
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−6.00000			−0.857143
$50$	−1.00000			−0.141421
$51$		0			0
$52$	2.38600	−	4.13267i	0.330879	−	0.573099i
$53$	−4.88600	−	8.46280i	−0.671144	−	1.16246i	−0.977580	−	0.210564i	$-0.932470\pi$
$53$	−4.88600	−	8.46280i	−0.671144	−	1.16246i	0.306436	−	0.951891i	$-0.400863\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−1.88600	+	3.26665i	−0.254308	+	0.440475i
$56$	1.00000			0.133631
$57$	−4.27200	+	0.866025i	−0.565840	+	0.114708i
$58$	6.00000			0.787839
$59$	6.77200	−	11.7295i	0.881640	−	1.52704i	0.0321221	−	0.999484i	$-0.489773\pi$
$59$	6.77200	−	11.7295i	0.881640	−	1.52704i	0.849517	−	0.527561i	$-0.176893\pi$
$60$	−0.500000	+	0.866025i	−0.0645497	+	0.111803i
$61$	−1.38600	−	2.40062i	−0.177459	−	0.307368i	0.763550	−	0.645748i	$-0.223454\pi$
$61$	−1.38600	−	2.40062i	−0.177459	−	0.307368i	−0.941010	+	0.338380i	$0.890121\pi$
$62$	1.38600	−	2.40062i	0.176022	−	0.304880i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	−4.77200			−0.591894
$66$	1.88600	+	3.26665i	0.232151	+	0.402097i
$67$	5.38600	+	9.32883i	0.658005	+	1.13970i	0.981131	+	0.193342i	$0.0619327\pi$
$67$	5.38600	+	9.32883i	0.658005	+	1.13970i	−0.323127	+	0.946356i	$0.604734\pi$
$68$		0			0
$69$	−3.77200			−0.454096
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	3.77200	−	6.53330i	0.447654	−	0.775360i	−0.550579	−	0.834783i	$-0.685593\pi$
$71$	3.77200	−	6.53330i	0.447654	−	0.775360i	0.998233	+	0.0594234i	$0.0189262\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	1.61400	−	2.79553i	0.188904	−	0.327192i	−0.755981	−	0.654594i	$-0.772840\pi$
$73$	1.61400	−	2.79553i	0.188904	−	0.327192i	0.944885	+	0.327402i	$0.106173\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	1.00000			0.115470
$76$	1.38600	−	4.13267i	0.158985	−	0.474050i
$77$	−3.77200			−0.429860
$78$	−2.38600	+	4.13267i	−0.270161	+	0.467933i
$79$	−5.15800	+	8.93392i	−0.580321	+	1.00514i	0.415120	+	0.909766i	$0.363739\pi$
$79$	−5.15800	+	8.93392i	−0.580321	+	1.00514i	−0.995441	+	0.0953784i	$0.969594\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.88600	−	3.26665i	−0.208274	−	0.360741i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000			−0.109109
$85$		0			0
$86$	4.38600	+	7.59678i	0.472955	+	0.819181i
$87$	−6.00000			−0.643268
$88$	−3.77200			−0.402097
$89$	−8.65800	−	14.9961i	−0.917746	−	1.58958i	−0.802830	−	0.596208i	$-0.796673\pi$
$89$	−8.65800	−	14.9961i	−0.917746	−	1.58958i	−0.114917	−	0.993375i	$-0.536660\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	−2.38600	−	4.13267i	−0.250121	−	0.433222i
$92$	1.88600	−	3.26665i	0.196629	−	0.340572i
$93$	−1.38600	+	2.40062i	−0.143722	+	0.248933i
$94$		0			0
$95$	−4.27200	+	0.866025i	−0.438298	+	0.0888523i
$96$	−1.00000			−0.102062
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	−1.88600	−	3.26665i	−0.189550	−	0.328311i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	−2.38600	−	4.13267i	−0.233967	−	0.405242i
$105$	0.500000	+	0.866025i	0.0487950	+	0.0845154i
$106$	−9.77200			−0.949141
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−4.77200	+	8.26535i	−0.457075	+	0.791677i	−0.998805	−	0.0488756i	$-0.984436\pi$
$109$	−4.77200	+	8.26535i	−0.457075	+	0.791677i	0.541730	+	0.840553i	$0.317770\pi$
$110$	1.88600	+	3.26665i	0.179823	+	0.311463i
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−13.5440			−1.27411			−0.637056	−	0.770817i	$-0.719848\pi$
$113$	−13.5440			−1.27411			−0.637056	+	0.770817i	$0.719848\pi$
$114$	−1.38600	+	4.13267i	−0.129811	+	0.387060i
$115$	−3.77200			−0.351741
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	2.38600	−	4.13267i	0.220586	−	0.382066i
$118$	−6.77200	−	11.7295i	−0.623413	−	1.07978i
$119$		0			0
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	3.22800			0.293454
$122$	−2.77200			−0.250965
$123$	1.88600	+	3.26665i	0.170055	+	0.294544i
$124$	−1.38600	−	2.40062i	−0.124467	−	0.215582i
$125$	1.00000			0.0894427
$126$	1.00000			0.0890871
$127$	4.65800	+	8.06790i	0.413331	+	0.715910i	0.995252	−	0.0973354i	$-0.0310319\pi$
$127$	4.65800	+	8.06790i	0.413331	+	0.715910i	−0.581921	+	0.813246i	$0.697699\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.38600	−	7.59678i	−0.386166	−	0.668859i
$130$	−2.38600	+	4.13267i	−0.209266	+	0.362460i
$131$	5.65800	−	9.79995i	0.494342	−	0.856225i	−0.505637	−	0.862746i	$-0.668742\pi$
$131$	5.65800	−	9.79995i	0.494342	−	0.856225i	0.999979	+	0.00652102i	$0.00207572\pi$
$132$	3.77200			0.328311
$133$	−2.88600	−	3.26665i	−0.250248	−	0.283254i
$134$	10.7720			0.930559
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	0.772002	+	1.33715i	0.0659566	+	0.114240i	0.897118	−	0.441791i	$-0.145657\pi$
$137$	0.772002	+	1.33715i	0.0659566	+	0.114240i	−0.831161	+	0.556031i	$0.812323\pi$
$138$	−1.88600	+	3.26665i	−0.160547	+	0.278076i
$139$	5.38600	+	9.32883i	0.456835	+	0.791261i	0.998792	−	0.0491454i	$-0.0156498\pi$
$139$	5.38600	+	9.32883i	0.456835	+	0.791261i	−0.541957	+	0.840406i	$0.682316\pi$
$140$	−1.00000			−0.0845154
$141$		0			0
$142$	−3.77200	−	6.53330i	−0.316539	−	0.548262i
$143$	9.00000	+	15.5885i	0.752618	+	1.30357i
$144$	1.00000			0.0833333
$145$	−6.00000			−0.498273
$146$	−1.61400	−	2.79553i	−0.133576	−	0.231360i
$147$	3.00000	−	5.19615i	0.247436	−	0.428571i
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	6.77200	−	11.7295i	0.554784	−	0.960914i	−0.443136	−	0.896454i	$-0.646134\pi$
$149$	6.77200	−	11.7295i	0.554784	−	0.960914i	0.997920	−	0.0644598i	$-0.0205324\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−2.88600	−	3.26665i	−0.234086	−	0.264960i
$153$		0			0
$154$	−1.88600	+	3.26665i	−0.151978	+	0.263234i
$155$	−1.38600	+	2.40062i	−0.111326	+	0.192823i
$156$	2.38600	+	4.13267i	0.191033	+	0.330879i
$157$	−1.72800	+	2.99298i	−0.137909	+	0.238866i	−0.926705	−	0.375790i	$-0.877372\pi$
$157$	−1.72800	+	2.99298i	−0.137909	+	0.238866i	0.788796	+	0.614655i	$0.210705\pi$
$158$	5.15800	+	8.93392i	0.410349	+	0.710745i
$159$	9.77200			0.774970
$160$	−1.00000			−0.0790569
$161$	−1.88600	−	3.26665i	−0.148638	−	0.257448i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−18.3160			−1.43462			−0.717310	−	0.696754i	$-0.754627\pi$
$163$	−18.3160			−1.43462			−0.717310	+	0.696754i	$0.754627\pi$
$164$	−3.77200			−0.294544
$165$	−1.88600	−	3.26665i	−0.146825	−	0.254308i
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	5.65800	+	9.79995i	0.437829	+	0.758343i	0.997522	−	0.0703577i	$-0.0224141\pi$
$167$	5.65800	+	9.79995i	0.437829	+	0.758343i	−0.559692	+	0.828700i	$0.689081\pi$
$168$	−0.500000	+	0.866025i	−0.0385758	+	0.0668153i
$169$	−4.88600	+	8.46280i	−0.375846	+	0.650985i
$170$		0			0
$171$	1.38600	−	4.13267i	0.105990	−	0.316034i
$172$	8.77200			0.668859
$173$	−5.65800	+	9.79995i	−0.430170	+	0.745076i	−0.996888	−	0.0788358i	$-0.974880\pi$
$173$	−5.65800	+	9.79995i	−0.430170	+	0.745076i	0.566718	+	0.823912i	$0.308213\pi$
$174$	−3.00000	+	5.19615i	−0.227429	+	0.393919i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−1.88600	+	3.26665i	−0.142163	+	0.246233i
$177$	6.77200	+	11.7295i	0.509015	+	0.881640i
$178$	−17.3160			−1.29789
$179$	−0.683994			−0.0511241			−0.0255621	−	0.999673i	$-0.508138\pi$
$179$	−0.683994			−0.0511241			−0.0255621	+	0.999673i	$0.508138\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−8.54400	−	14.7986i	−0.635071	−	1.09997i	−0.986500	−	0.163760i	$-0.947638\pi$
$181$	−8.54400	−	14.7986i	−0.635071	−	1.09997i	0.351429	−	0.936214i	$-0.385696\pi$
$182$	−4.77200			−0.353724
$183$	2.77200			0.204912
$184$	−1.88600	−	3.26665i	−0.139038	−	0.240821i
$185$	0.500000	−	0.866025i	0.0367607	−	0.0636715i
$186$	1.38600	+	2.40062i	0.101627	+	0.176022i
$187$		0			0
$188$		0			0
$189$	−1.00000			−0.0727393
$190$	−1.38600	+	4.13267i	−0.100551	+	0.299816i
$191$	7.54400			0.545865			0.272932	−	0.962033i	$-0.412006\pi$
$191$	7.54400			0.545865			0.272932	+	0.962033i	$0.412006\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.38600	+	2.40062i	−0.0997665	+	0.172801i	−0.911588	−	0.411105i	$-0.865143\pi$
$193$	−1.38600	+	2.40062i	−0.0997665	+	0.172801i	0.811821	+	0.583906i	$0.198476\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$	2.38600	−	4.13267i	0.170865	−	0.295947i
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	−11.3160			−0.806232			−0.403116	−	0.915149i	$-0.632073\pi$
$197$	−11.3160			−0.806232			−0.403116	+	0.915149i	$0.632073\pi$
$198$	−3.77200			−0.268065
$199$	0.158003	+	0.273669i	0.0112005	+	0.0193999i	0.871571	−	0.490269i	$-0.163101\pi$
$199$	0.158003	+	0.273669i	0.0112005	+	0.0193999i	−0.860371	+	0.509669i	$0.829768\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−10.7720			−0.759798
$202$	6.00000			0.422159
$203$	−3.00000	−	5.19615i	−0.210559	−	0.364698i
$204$		0			0
$205$	1.88600	+	3.26665i	0.131724	+	0.228153i
$206$	−6.50000	+	11.2583i	−0.452876	+	0.784405i
$207$	1.88600	−	3.26665i	0.131086	−	0.227048i
$208$	−4.77200			−0.330879
$209$	10.8860	+	12.3218i	0.753000	+	0.852317i
$210$	1.00000			0.0690066
$211$	10.2720	−	17.7916i	0.707154	−	1.22483i	−0.258755	−	0.965943i	$-0.583312\pi$
$211$	10.2720	−	17.7916i	0.707154	−	1.22483i	0.965909	−	0.258883i	$-0.0833545\pi$
$212$	−4.88600	+	8.46280i	−0.335572	+	0.581228i
$213$	3.77200	+	6.53330i	0.258453	+	0.447654i
$214$		0			0
$215$	−4.38600	−	7.59678i	−0.299123	−	0.518096i
$216$	−1.00000			−0.0680414
$217$	−2.77200			−0.188176
$218$	4.77200	+	8.26535i	0.323201	+	0.559800i
$219$	1.61400	+	2.79553i	0.109064	+	0.188904i
$220$	3.77200			0.254308
$221$		0			0
$222$	−0.500000	−	0.866025i	−0.0335578	−	0.0581238i
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	−0.0552786	−	0.998471i	$-0.517605\pi$
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	0.892341	−	0.451363i	$-0.149062\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−6.77200	+	11.7295i	−0.450467	+	0.780231i
$227$	9.08801			0.603192			0.301596	−	0.953436i	$-0.402481\pi$
$227$	9.08801			0.603192			0.301596	+	0.953436i	$0.402481\pi$
$228$	2.88600	+	3.26665i	0.191130	+	0.216339i
$229$	23.8600			1.57671			0.788357	−	0.615218i	$-0.210932\pi$
$229$	23.8600			1.57671			0.788357	+	0.615218i	$0.210932\pi$
$230$	−1.88600	+	3.26665i	−0.124359	+	0.215396i
$231$	1.88600	−	3.26665i	0.124090	−	0.214930i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	2.22800	−	3.85901i	0.145961	−	0.252812i	−0.783770	−	0.621051i	$-0.786706\pi$
$233$	2.22800	−	3.85901i	0.145961	−	0.252812i	0.929731	+	0.368239i	$0.120039\pi$
$234$	−2.38600	−	4.13267i	−0.155978	−	0.270161i
$235$		0			0
$236$	−13.5440			−0.881640
$237$	−5.15800	−	8.93392i	−0.335048	−	0.580321i
$238$		0			0
$239$	13.5440			0.876089			0.438044	−	0.898953i	$-0.355671\pi$
$239$	13.5440			0.876089			0.438044	+	0.898953i	$0.355671\pi$
$240$	1.00000			0.0645497
$241$	−11.1580	−	19.3262i	−0.718750	−	1.24491i	−0.961495	−	0.274822i	$-0.911381\pi$
$241$	−11.1580	−	19.3262i	−0.718750	−	1.24491i	0.242745	−	0.970090i	$-0.421952\pi$
$242$	1.61400	−	2.79553i	0.103752	−	0.179703i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.38600	+	2.40062i	−0.0887296	+	0.153684i
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$	3.77200			0.240494
$247$	−6.61400	+	19.7211i	−0.420839	+	1.25483i
$248$	−2.77200			−0.176022
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−0.772002	−	1.33715i	−0.0487283	−	0.0843999i	0.840632	−	0.541606i	$-0.182184\pi$
$251$	−0.772002	−	1.33715i	−0.0487283	−	0.0843999i	−0.889361	+	0.457206i	$0.848850\pi$
$252$	0.500000	−	0.866025i	0.0314970	−	0.0545545i
$253$	7.11400	+	12.3218i	0.447253	+	0.774665i
$254$	9.31601			0.584538
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.773427	+	0.633885i	$0.218541\pi$
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.162247	+	0.986750i	$0.448126\pi$
$258$	−8.77200			−0.546121
$259$	1.00000			0.0621370
$260$	2.38600	+	4.13267i	0.147973	+	0.256298i
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−5.65800	−	9.79995i	−0.349553	−	0.605443i
$263$	−7.88600	+	13.6590i	−0.486272	+	0.842247i	−0.999875	−	0.0157802i	$-0.994977\pi$
$263$	−7.88600	+	13.6590i	−0.486272	+	0.842247i	0.513604	+	0.858027i	$0.328310\pi$
$264$	1.88600	−	3.26665i	0.116075	−	0.201048i
$265$	9.77200			0.600289
$266$	−4.27200	+	0.866025i	−0.261933	+	0.0530994i
$267$	17.3160			1.05972
$268$	5.38600	−	9.32883i	0.329002	−	0.569849i
$269$	12.7720	−	22.1218i	0.778723	−	1.34879i	−0.153956	−	0.988078i	$-0.549201\pi$
$269$	12.7720	−	22.1218i	0.778723	−	1.34879i	0.932678	−	0.360709i	$-0.117465\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	−6.22800	+	10.7872i	−0.378324	+	0.655276i	−0.990819	−	0.135198i	$-0.956833\pi$
$271$	−6.22800	+	10.7872i	−0.378324	+	0.655276i	0.612495	+	0.790475i	$0.290166\pi$
$272$		0			0
$273$	4.77200			0.288815
$274$	1.54400			0.0932767
$275$	−1.88600	−	3.26665i	−0.113730	−	0.196986i
$276$	1.88600	+	3.26665i	0.113524	+	0.196629i
$277$	5.08801			0.305709			0.152854	−	0.988249i	$-0.451153\pi$
$277$	5.08801			0.305709			0.152854	+	0.988249i	$0.451153\pi$
$278$	10.7720			0.646062
$279$	−1.38600	−	2.40062i	−0.0829777	−	0.143722i
$280$	−0.500000	+	0.866025i	−0.0298807	+	0.0517549i
$281$	−13.8860	−	24.0513i	−0.828369	−	1.43478i	−0.899317	−	0.437298i	$-0.855936\pi$
$281$	−13.8860	−	24.0513i	−0.828369	−	1.43478i	0.0709474	−	0.997480i	$-0.477398\pi$
$282$		0			0
$283$	13.3160	−	23.0640i	0.791554	−	1.37101i	−0.133450	−	0.991056i	$-0.542606\pi$
$283$	13.3160	−	23.0640i	0.791554	−	1.37101i	0.925004	−	0.379957i	$-0.124061\pi$
$284$	−7.54400			−0.447654
$285$	1.38600	−	4.13267i	0.0820996	−	0.244799i
$286$	18.0000			1.06436
$287$	−1.88600	+	3.26665i	−0.111327	+	0.192824i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−3.22800			−0.188904
$293$	−20.2280			−1.18173			−0.590866	−	0.806770i	$-0.701214\pi$
$293$	−20.2280			−1.18173			−0.590866	+	0.806770i	$0.701214\pi$
$294$	−3.00000	−	5.19615i	−0.174964	−	0.303046i
$295$	6.77200	+	11.7295i	0.394281	+	0.682915i
$296$	1.00000			0.0581238
$297$	3.77200			0.218874
$298$	−6.77200	−	11.7295i	−0.392292	−	0.679469i
$299$	−9.00000	+	15.5885i	−0.520483	+	0.901504i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	4.38600	−	7.59678i	0.252805	−	0.437871i
$302$	4.00000	−	6.92820i	0.230174	−	0.398673i
$303$	−6.00000			−0.344691
$304$	−4.27200	+	0.866025i	−0.245016	+	0.0496700i
$305$	2.77200			0.158724
$306$		0			0
$307$	11.7720	−	20.3897i	0.671864	−	1.16370i	−0.305511	−	0.952188i	$-0.598827\pi$
$307$	11.7720	−	20.3897i	0.671864	−	1.16370i	0.977375	−	0.211514i	$-0.0678392\pi$
$308$	1.88600	+	3.26665i	0.107465	+	0.186135i
$309$	6.50000	−	11.2583i	0.369772	−	0.640464i
$310$	1.38600	+	2.40062i	0.0787196	+	0.136346i
$311$	25.5440			1.44847			0.724234	−	0.689555i	$-0.242194\pi$
$311$	25.5440			1.44847			0.724234	+	0.689555i	$0.242194\pi$
$312$	4.77200			0.270161
$313$	1.22800	+	2.12696i	0.0694106	+	0.120223i	0.898642	−	0.438683i	$-0.144555\pi$
$313$	1.22800	+	2.12696i	0.0694106	+	0.120223i	−0.829231	+	0.558905i	$0.811221\pi$
$314$	1.72800	+	2.99298i	0.0975166	+	0.168904i
$315$	−1.00000			−0.0563436
$316$	10.3160			0.580321
$317$	−10.1140	−	17.5180i	−0.568059	−	0.983907i	−0.996758	−	0.0804593i	$-0.974361\pi$
$317$	−10.1140	−	17.5180i	−0.568059	−	0.983907i	0.428699	−	0.903447i	$-0.358972\pi$
$318$	4.88600	−	8.46280i	0.273993	−	0.474570i
$319$	11.3160	+	19.5999i	0.633575	+	1.09738i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−3.77200			−0.210205
$323$		0			0
$324$	1.00000			0.0555556
$325$	2.38600	−	4.13267i	0.132352	−	0.229240i
$326$	−9.15800	+	15.8621i	−0.507215	+	0.878522i
$327$	−4.77200	−	8.26535i	−0.263892	−	0.457075i
$328$	−1.88600	+	3.26665i	−0.104137	+	0.180371i
$329$		0			0
$330$	−3.77200			−0.207642
$331$	−26.5440			−1.45899			−0.729495	−	0.683986i	$-0.760245\pi$
$331$	−26.5440			−1.45899			−0.729495	+	0.683986i	$0.760245\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	0.500000	+	0.866025i	0.0273998	+	0.0474579i
$334$	11.3160			0.619184
$335$	−10.7720			−0.588537
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	15.1580	−	26.2544i	0.825709	−	1.43017i	−0.0756672	−	0.997133i	$-0.524109\pi$
$337$	15.1580	−	26.2544i	0.825709	−	1.43017i	0.901376	−	0.433037i	$-0.142558\pi$
$338$	4.88600	+	8.46280i	0.265763	+	0.460316i
$339$	6.77200	−	11.7295i	0.367805	−	0.637056i
$340$		0			0
$341$	10.4560			0.566224
$342$	−2.88600	−	3.26665i	−0.156057	−	0.176640i
$343$	13.0000			0.701934
$344$	4.38600	−	7.59678i	0.236477	−	0.409591i
$345$	1.88600	−	3.26665i	0.101539	−	0.175870i
$346$	5.65800	+	9.79995i	0.304176	+	0.526848i
$347$	3.77200	−	6.53330i	0.202492	−	0.350726i	−0.746839	−	0.665005i	$-0.768429\pi$
$347$	3.77200	−	6.53330i	0.202492	−	0.350726i	0.949331	+	0.314279i	$0.101763\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−9.22800			−0.493963			−0.246982	−	0.969020i	$-0.579439\pi$
$349$	−9.22800			−0.493963			−0.246982	+	0.969020i	$0.579439\pi$
$350$	1.00000			0.0534522
$351$	2.38600	+	4.13267i	0.127355	+	0.220586i
$352$	1.88600	+	3.26665i	0.100524	+	0.174113i
$353$	−13.5440			−0.720875			−0.360437	−	0.932783i	$-0.617373\pi$
$353$	−13.5440			−0.720875			−0.360437	+	0.932783i	$0.617373\pi$
$354$	13.5440			0.719856
$355$	3.77200	+	6.53330i	0.200197	+	0.346752i
$356$	−8.65800	+	14.9961i	−0.458873	+	0.794792i
$357$		0			0
$358$	−0.341997	+	0.592357i	−0.0180751	+	0.0313070i
$359$	−10.5440	+	18.2628i	−0.556491	+	0.963871i	0.441295	+	0.897362i	$0.354519\pi$
$359$	−10.5440	+	18.2628i	−0.556491	+	0.963871i	−0.997786	+	0.0665088i	$0.978814\pi$
$360$	−1.00000			−0.0527046
$361$	−2.34200	+	18.8551i	−0.123263	+	0.992374i
$362$	−17.0880			−0.898126
$363$	−1.61400	+	2.79553i	−0.0847130	+	0.146727i
$364$	−2.38600	+	4.13267i	−0.125060	+	0.216611i
$365$	1.61400	+	2.79553i	0.0844806	+	0.146325i
$366$	1.38600	−	2.40062i	0.0724474	−	0.125483i
$367$	4.61400	+	7.99168i	0.240849	+	0.417162i	0.960956	−	0.276700i	$-0.0892409\pi$
$367$	4.61400	+	7.99168i	0.240849	+	0.417162i	−0.720108	+	0.693862i	$0.755908\pi$
$368$	−3.77200			−0.196629
$369$	−3.77200			−0.196363
$370$	−0.500000	−	0.866025i	−0.0259938	−	0.0450225i
$371$	4.88600	+	8.46280i	0.253669	+	0.439367i
$372$	2.77200			0.143722
$373$	−0.227998			−0.0118053			−0.00590265	−	0.999983i	$-0.501879\pi$
$373$	−0.227998			−0.0118053			−0.00590265	+	0.999983i	$0.501879\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−14.3160	+	24.7960i	−0.737312	+	1.27706i
$378$	−0.500000	+	0.866025i	−0.0257172	+	0.0445435i
$379$	−9.22800			−0.474010			−0.237005	−	0.971508i	$-0.576166\pi$
$379$	−9.22800			−0.474010			−0.237005	+	0.971508i	$0.576166\pi$
$380$	2.88600	+	3.26665i	0.148049	+	0.167576i
$381$	−9.31601			−0.477273
$382$	3.77200	−	6.53330i	0.192992	−	0.334273i
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	1.88600	−	3.26665i	0.0961195	−	0.166484i
$386$	1.38600	+	2.40062i	0.0705456	+	0.122189i
$387$	8.77200			0.445906
$388$	−10.0000			−0.507673
$389$	4.54400	+	7.87045i	0.230390	+	0.399047i	0.957923	−	0.287025i	$-0.0926664\pi$
$389$	4.54400	+	7.87045i	0.230390	+	0.399047i	−0.727533	+	0.686073i	$0.759333\pi$
$390$	−2.38600	−	4.13267i	−0.120820	−	0.209266i
$391$		0			0
$392$	6.00000			0.303046
$393$	5.65800	+	9.79995i	0.285408	+	0.494342i
$394$	−5.65800	+	9.79995i	−0.285046	+	0.493714i
$395$	−5.15800	−	8.93392i	−0.259527	−	0.449514i
$396$	−1.88600	+	3.26665i	−0.0947751	+	0.164155i
$397$	−1.04400	+	1.80827i	−0.0523970	+	0.0907543i	−0.891034	−	0.453936i	$-0.850019\pi$
$397$	−1.04400	+	1.80827i	−0.0523970	+	0.0907543i	0.838637	+	0.544690i	$0.183353\pi$
$398$	0.316006			0.0158399
$399$	4.27200	−	0.866025i	0.213868	−	0.0433555i
$400$	1.00000			0.0500000
$401$	−4.54400	+	7.87045i	−0.226917	+	0.393031i	−0.956893	−	0.290441i	$-0.906198\pi$
$401$	−4.54400	+	7.87045i	−0.226917	+	0.393031i	0.729976	+	0.683473i	$0.239531\pi$
$402$	−5.38600	+	9.32883i	−0.268629	+	0.465280i
$403$	6.61400	+	11.4558i	0.329467	+	0.570653i
$404$	3.00000	−	5.19615i	0.149256	−	0.258518i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−6.00000			−0.297775
$407$	−3.77200			−0.186971
$408$		0			0
$409$	15.2020	+	26.3306i	0.751691	+	1.30197i	0.947003	+	0.321226i	$0.104095\pi$
$409$	15.2020	+	26.3306i	0.751691	+	1.30197i	−0.195312	+	0.980741i	$0.562572\pi$
$410$	3.77200			0.186286
$411$	−1.54400			−0.0761601
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$	−6.77200	+	11.7295i	−0.333228	+	0.577169i
$414$	−1.88600	−	3.26665i	−0.0926919	−	0.160547i
$415$	−3.00000	+	5.19615i	−0.147264	+	0.255069i
$416$	−2.38600	+	4.13267i	−0.116983	+	0.202621i
$417$	−10.7720			−0.527507
$418$	16.1140	−	3.26665i	0.788161	−	0.159777i
$419$	−24.8600			−1.21449			−0.607245	−	0.794514i	$-0.707726\pi$
$419$	−24.8600			−1.21449			−0.607245	+	0.794514i	$0.707726\pi$
$420$	0.500000	−	0.866025i	0.0243975	−	0.0422577i
$421$	8.77200	−	15.1936i	0.427521	−	0.740488i	−0.569131	−	0.822247i	$-0.692720\pi$
$421$	8.77200	−	15.1936i	0.427521	−	0.740488i	0.996652	+	0.0817584i	$0.0260536\pi$
$422$	−10.2720	−	17.7916i	−0.500033	−	0.866083i
$423$		0			0
$424$	4.88600	+	8.46280i	0.237285	+	0.410990i
$425$		0			0
$426$	7.54400			0.365508
$427$	1.38600	+	2.40062i	0.0670733	+	0.116174i
$428$		0			0
$429$	−18.0000			−0.869048
$430$	−8.77200			−0.423023
$431$	1.54400	+	2.67429i	0.0743720	+	0.128816i	0.900813	−	0.434207i	$-0.142971\pi$
$431$	1.54400	+	2.67429i	0.0743720	+	0.128816i	−0.826441	+	0.563023i	$0.809638\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−5.15800	−	8.93392i	−0.247878	−	0.429337i	0.715059	−	0.699064i	$-0.246400\pi$
$433$	−5.15800	−	8.93392i	−0.247878	−	0.429337i	−0.962937	+	0.269727i	$0.913066\pi$
$434$	−1.38600	+	2.40062i	−0.0665302	+	0.115234i
$435$	3.00000	−	5.19615i	0.143839	−	0.249136i
$436$	9.54400			0.457075
$437$	−5.22800	+	15.5885i	−0.250089	+	0.745697i
$438$	3.22800			0.154240
$439$	−2.15800	+	3.73777i	−0.102996	+	0.178394i	−0.912918	−	0.408144i	$-0.866176\pi$
$439$	−2.15800	+	3.73777i	−0.102996	+	0.178394i	0.809922	+	0.586538i	$0.199510\pi$
$440$	1.88600	−	3.26665i	0.0899116	−	0.155731i
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$		0			0
$443$	−19.5440	−	33.8512i	−0.928564	−	1.60832i	−0.785727	−	0.618573i	$-0.787711\pi$
$443$	−19.5440	−	33.8512i	−0.928564	−	1.60832i	−0.142836	−	0.989746i	$-0.545622\pi$
$444$	−1.00000			−0.0474579
$445$	17.3160			0.820857
$446$	−12.5000	−	21.6506i	−0.591892	−	1.02519i
$447$	6.77200	+	11.7295i	0.320305	+	0.554784i
$448$	−1.00000			−0.0472456
$449$	2.22800			0.105146			0.0525729	−	0.998617i	$-0.483258\pi$
$449$	2.22800			0.105146			0.0525729	+	0.998617i	$0.483258\pi$
$450$	0.500000	+	0.866025i	0.0235702	+	0.0408248i
$451$	7.11400	−	12.3218i	0.334985	−	0.580211i
$452$	6.77200	+	11.7295i	0.318528	+	0.551707i
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	4.54400	−	7.87045i	0.213261	−	0.369378i
$455$	4.77200			0.223715
$456$	4.27200	−	0.866025i	0.200055	−	0.0405554i
$457$	−25.8600			−1.20968			−0.604840	−	0.796347i	$-0.706763\pi$
$457$	−25.8600			−1.20968			−0.604840	+	0.796347i	$0.706763\pi$
$458$	11.9300	−	20.6634i	0.557453	−	0.965536i
$459$		0			0
$460$	1.88600	+	3.26665i	0.0879352	+	0.152308i
$461$	−17.3160	+	29.9922i	−0.806487	+	1.39688i	0.108796	+	0.994064i	$0.465300\pi$
$461$	−17.3160	+	29.9922i	−0.806487	+	1.39688i	−0.915283	+	0.402812i	$0.868033\pi$
$462$	−1.88600	−	3.26665i	−0.0877447	−	0.151978i
$463$	27.6320			1.28417			0.642084	−	0.766634i	$-0.278070\pi$
$463$	27.6320			1.28417			0.642084	+	0.766634i	$0.278070\pi$
$464$	−6.00000			−0.278543
$465$	−1.38600	−	2.40062i	−0.0642743	−	0.111326i
$466$	−2.22800	−	3.85901i	−0.103210	−	0.178765i
$467$	−9.08801			−0.420543			−0.210271	−	0.977643i	$-0.567435\pi$
$467$	−9.08801			−0.420543			−0.210271	+	0.977643i	$0.567435\pi$
$468$	−4.77200			−0.220586
$469$	−5.38600	−	9.32883i	−0.248702	−	0.430765i
$470$		0			0
$471$	−1.72800	−	2.99298i	−0.0796220	−	0.137909i
$472$	−6.77200	+	11.7295i	−0.311707	+	0.539892i
$473$	−16.5440	+	28.6551i	−0.760694	+	1.31756i
$474$	−10.3160			−0.473830
$475$	1.38600	−	4.13267i	0.0635941	−	0.189620i
$476$		0			0
$477$	−4.88600	+	8.46280i	−0.223715	+	0.387485i
$478$	6.77200	−	11.7295i	0.309744	−	0.536493i
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$	0.500000	−	0.866025i	0.0228218	−	0.0395285i
$481$	−2.38600	−	4.13267i	−0.108792	−	0.188434i
$482$	−22.3160			−1.01647
$483$	3.77200			0.171632
$484$	−1.61400	−	2.79553i	−0.0733636	−	0.127069i
$485$	5.00000	+	8.66025i	0.227038	+	0.393242i
$486$	−1.00000			−0.0453609
$487$	−9.31601			−0.422149			−0.211074	−	0.977470i	$-0.567696\pi$
$487$	−9.31601			−0.422149			−0.211074	+	0.977470i	$0.567696\pi$
$488$	1.38600	+	2.40062i	0.0627413	+	0.108671i
$489$	9.15800	−	15.8621i	0.414139	−	0.717310i
$490$	−3.00000	−	5.19615i	−0.135526	−	0.234738i
$491$	−3.34200	+	5.78851i	−0.150822	+	0.261232i	−0.931530	−	0.363665i	$-0.881525\pi$
$491$	−3.34200	+	5.78851i	−0.150822	+	0.261232i	0.780708	+	0.624896i	$0.214859\pi$
$492$	1.88600	−	3.26665i	0.0850275	−	0.147272i
$493$		0			0
$494$	13.7720	+	15.5885i	0.619632	+	0.701358i
$495$	3.77200			0.169539
$496$	−1.38600	+	2.40062i	−0.0622333	+	0.107791i
$497$	−3.77200	+	6.53330i	−0.169197	+	0.293059i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$	−10.8160	+	18.7339i	−0.484191	+	0.838643i	−0.999835	−	0.0181596i	$-0.994219\pi$
$499$	−10.8160	+	18.7339i	−0.484191	+	0.838643i	0.515644	+	0.856803i	$0.327553\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−11.3160			−0.505562
$502$	−1.54400			−0.0689123
$503$	−8.65800	−	14.9961i	−0.386041	−	0.668643i	0.605872	−	0.795562i	$-0.292824\pi$
$503$	−8.65800	−	14.9961i	−0.386041	−	0.668643i	−0.991913	+	0.126919i	$0.959491\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$	−6.00000			−0.266996
$506$	14.2280			0.632512
$507$	−4.88600	−	8.46280i	−0.216995	−	0.375846i
$508$	4.65800	−	8.06790i	0.206665	−	0.357955i
$509$	−17.3160	−	29.9922i	−0.767518	−	1.32938i	−0.938905	−	0.344177i	$-0.888158\pi$
$509$	−17.3160	−	29.9922i	−0.767518	−	1.32938i	0.171386	−	0.985204i	$-0.445175\pi$
$510$		0			0
$511$	−1.61400	+	2.79553i	−0.0713991	+	0.123667i
$512$	−1.00000			−0.0441942
$513$	2.88600	+	3.26665i	0.127420	+	0.144226i
$514$	30.0000			1.32324
$515$	6.50000	−	11.2583i	0.286424	−	0.496101i
$516$	−4.38600	+	7.59678i	−0.193083	+	0.334429i
$517$		0			0
$518$	0.500000	−	0.866025i	0.0219687	−	0.0380510i
$519$	−5.65800	−	9.79995i	−0.248359	−	0.430170i
$520$	4.77200			0.209266
$521$	−16.4560			−0.720950			−0.360475	−	0.932769i	$-0.617385\pi$
$521$	−16.4560			−0.720950			−0.360475	+	0.932769i	$0.617385\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	−11.1580	−	19.3262i	−0.487905	−	0.845077i	0.511998	−	0.858987i	$-0.328906\pi$
$523$	−11.1580	−	19.3262i	−0.487905	−	0.845077i	−0.999903	+	0.0139098i	$0.995572\pi$
$524$	−11.3160			−0.494342
$525$	−1.00000			−0.0436436
$526$	7.88600	+	13.6590i	0.343846	+	0.595559i
$527$		0			0
$528$	−1.88600	−	3.26665i	−0.0820777	−	0.142163i
$529$	4.38600	−	7.59678i	0.190696	−	0.330295i
$530$	4.88600	−	8.46280i	0.212234	−	0.367601i
$531$	−13.5440			−0.587760
$532$	−1.38600	+	4.13267i	−0.0600908	+	0.179174i
$533$	18.0000			0.779667
$534$	8.65800	−	14.9961i	0.374668	−	0.648945i
$535$		0			0
$536$	−5.38600	−	9.32883i	−0.232640	−	0.402944i
$537$	0.341997	−	0.592357i	0.0147583	−	0.0255621i
$538$	−12.7720	−	22.1218i	−0.550640	−	0.953737i
$539$	−22.6320			−0.974830
$540$	1.00000			0.0430331
$541$	−8.15800	−	14.1301i	−0.350740	−	0.607499i	0.635639	−	0.771986i	$-0.280737\pi$
$541$	−8.15800	−	14.1301i	−0.350740	−	0.607499i	−0.986379	+	0.164487i	$0.947403\pi$
$542$	6.22800	+	10.7872i	0.267515	+	0.463350i
$543$	17.0880			0.733317
$544$		0			0
$545$	−4.77200	−	8.26535i	−0.204410	−	0.354049i
$546$	2.38600	−	4.13267i	0.102111	−	0.176862i
$547$	−5.93000	−	10.2711i	−0.253549	−	0.439159i	0.710952	−	0.703241i	$-0.248264\pi$
$547$	−5.93000	−	10.2711i	−0.253549	−	0.439159i	−0.964500	+	0.264082i	$0.914931\pi$
$548$	0.772002	−	1.33715i	0.0329783	−	0.0571201i
$549$	−1.38600	+	2.40062i	−0.0591531	+	0.102456i
$550$	−3.77200			−0.160839
$551$	−8.31601	+	24.7960i	−0.354274	+	1.05635i
$552$	3.77200			0.160547
$553$	5.15800	−	8.93392i	0.219341	−	0.379909i
$554$	2.54400	−	4.40634i	0.108084	−	0.187208i
$555$	0.500000	+	0.866025i	0.0212238	+	0.0367607i
$556$	5.38600	−	9.32883i	0.228417	−	0.395630i
$557$	−1.11400	−	1.92950i	−0.0472017	−	0.0817557i	0.841459	−	0.540321i	$-0.181697\pi$
$557$	−1.11400	−	1.92950i	−0.0472017	−	0.0817557i	−0.888661	+	0.458565i	$0.848364\pi$
$558$	−2.77200			−0.117348
$559$	−41.8600			−1.77049
$560$	0.500000	+	0.866025i	0.0211289	+	0.0365963i
$561$		0			0
$562$	−27.7720			−1.17149
$563$	37.5440			1.58229			0.791146	−	0.611628i	$-0.209485\pi$
$563$	37.5440			1.58229			0.791146	+	0.611628i	$0.209485\pi$
$564$		0			0
$565$	6.77200	−	11.7295i	0.284900	−	0.493462i
$566$	−13.3160	−	23.0640i	−0.559713	−	0.969452i
$567$	0.500000	−	0.866025i	0.0209980	−	0.0363696i
$568$	−3.77200	+	6.53330i	−0.158270	+	0.274131i
$569$	2.22800			0.0934025			0.0467013	−	0.998909i	$-0.485129\pi$
$569$	2.22800			0.0934025			0.0467013	+	0.998909i	$0.485129\pi$
$570$	−2.88600	−	3.26665i	−0.120881	−	0.136825i
$571$	−1.86001			−0.0778390			−0.0389195	−	0.999242i	$-0.512392\pi$
$571$	−1.86001			−0.0778390			−0.0389195	+	0.999242i	$0.512392\pi$
$572$	9.00000	−	15.5885i	0.376309	−	0.651786i
$573$	−3.77200	+	6.53330i	−0.157578	+	0.272932i
$574$	1.88600	+	3.26665i	0.0787202	+	0.136347i
$575$	1.88600	−	3.26665i	0.0786517	−	0.136229i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	9.54400			0.397322			0.198661	−	0.980068i	$-0.436341\pi$
$577$	9.54400			0.397322			0.198661	+	0.980068i	$0.436341\pi$
$578$	17.0000			0.707107
$579$	−1.38600	−	2.40062i	−0.0576002	−	0.0997665i
$580$	3.00000	+	5.19615i	0.124568	+	0.215758i
$581$	−6.00000			−0.248922
$582$	10.0000			0.414513
$583$	−18.4300	−	31.9217i	−0.763293	−	1.32206i
$584$	−1.61400	+	2.79553i	−0.0667878	+	0.115680i
$585$	2.38600	+	4.13267i	0.0986490	+	0.170865i
$586$	−10.1140	+	17.5180i	−0.417805	+	0.723660i
$587$	12.7720	−	22.1218i	0.527157	−	0.913063i	−0.472342	−	0.881415i	$-0.656591\pi$
$587$	12.7720	−	22.1218i	0.527157	−	0.913063i	0.999499	−	0.0316473i	$-0.0100753\pi$
$588$	−6.00000			−0.247436
$589$	8.00000	+	9.05516i	0.329634	+	0.373111i
$590$	13.5440			0.557598
$591$	5.65800	−	9.79995i	0.232739	−	0.403116i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−3.77200	−	6.53330i	−0.154898	−	0.268290i	0.778124	−	0.628110i	$-0.216171\pi$
$593$	−3.77200	−	6.53330i	−0.154898	−	0.268290i	−0.933022	+	0.359820i	$0.882838\pi$
$594$	1.88600	−	3.26665i	0.0773836	−	0.134032i
$595$		0			0
$596$	−13.5440			−0.554784
$597$	−0.316006			−0.0129332
$598$	9.00000	+	15.5885i	0.368037	+	0.637459i
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$	−1.00000			−0.0408248
$601$	−35.6320			−1.45346			−0.726730	−	0.686923i	$-0.758961\pi$
$601$	−35.6320			−1.45346			−0.726730	+	0.686923i	$0.758961\pi$
$602$	−4.38600	−	7.59678i	−0.178760	−	0.309621i
$603$	5.38600	−	9.32883i	0.219335	−	0.379899i
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	−1.61400	+	2.79553i	−0.0656184	+	0.113654i
$606$	−3.00000	+	5.19615i	−0.121867	+	0.211079i
$607$	−40.0880			−1.62712			−0.813561	−	0.581480i	$-0.802474\pi$
$607$	−40.0880			−1.62712			−0.813561	+	0.581480i	$0.802474\pi$
$608$	−1.38600	+	4.13267i	−0.0562098	+	0.167602i
$609$	6.00000			0.243132
$610$	1.38600	−	2.40062i	0.0561175	−	0.0971984i
$611$		0			0
$612$		0			0
$613$	17.4300	−	30.1897i	0.703991	−	1.21935i	−0.263063	−	0.964779i	$-0.584733\pi$
$613$	17.4300	−	30.1897i	0.703991	−	1.21935i	0.967054	−	0.254570i	$-0.0819339\pi$
$614$	−11.7720	−	20.3897i	−0.475079	−	0.822862i
$615$	−3.77200			−0.152102
$616$	3.77200			0.151978
$617$	1.54400	+	2.67429i	0.0621593	+	0.107663i	0.895430	−	0.445202i	$-0.146868\pi$
$617$	1.54400	+	2.67429i	0.0621593	+	0.107663i	−0.833271	+	0.552865i	$0.813535\pi$
$618$	−6.50000	−	11.2583i	−0.261468	−	0.452876i
$619$	−31.1760			−1.25307			−0.626535	−	0.779393i	$-0.715527\pi$
$619$	−31.1760			−1.25307			−0.626535	+	0.779393i	$0.715527\pi$
$620$	2.77200			0.111326
$621$	1.88600	+	3.26665i	0.0756826	+	0.131086i
$622$	12.7720	−	22.1218i	0.512111	−	0.887002i
$623$	8.65800	+	14.9961i	0.346876	+	0.600806i
$624$	2.38600	−	4.13267i	0.0955165	−	0.165439i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.45600			0.0981614
$627$	−16.1140	+	3.26665i	−0.643531	+	0.130457i
$628$	3.45600			0.137909
$629$		0			0
$630$	−0.500000	+	0.866025i	−0.0199205	+	0.0345033i
$631$	21.9300	+	37.9839i	0.873020	+	1.51211i	0.858857	+	0.512215i	$0.171175\pi$
$631$	21.9300	+	37.9839i	0.873020	+	1.51211i	0.0141623	+	0.999900i	$0.495492\pi$
$632$	5.15800	−	8.93392i	0.205174	−	0.355372i
$633$	10.2720	+	17.7916i	0.408275	+	0.707154i
$634$	−20.2280			−0.803356
$635$	−9.31601			−0.369694
$636$	−4.88600	−	8.46280i	−0.193743	−	0.335572i
$637$	−14.3160	−	24.7960i	−0.567221	−	0.982455i
$638$	22.6320			0.896010
$639$	−7.54400			−0.298436
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−9.77200	+	16.9256i	−0.385971	+	0.668521i	−0.991903	−	0.126995i	$-0.959467\pi$
$641$	−9.77200	+	16.9256i	−0.385971	+	0.668521i	0.605933	+	0.795516i	$0.292800\pi$
$642$		0			0
$643$	0.158003	−	0.273669i	0.00623102	−	0.0107924i	−0.862893	−	0.505387i	$-0.831350\pi$
$643$	0.158003	−	0.273669i	0.00623102	−	0.0107924i	0.869124	+	0.494594i	$0.164683\pi$
$644$	−1.88600	+	3.26665i	−0.0743188	+	0.128724i
$645$	8.77200			0.345397
$646$		0			0
$647$	−12.6840			−0.498659			−0.249330	−	0.968419i	$-0.580210\pi$
$647$	−12.6840			−0.498659			−0.249330	+	0.968419i	$0.580210\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	25.5440	−	44.2435i	1.00269	−	1.73671i
$650$	−2.38600	−	4.13267i	−0.0935867	−	0.162097i
$651$	1.38600	−	2.40062i	0.0543217	−	0.0940879i
$652$	9.15800	+	15.8621i	0.358655	+	0.621209i
$653$	29.3160			1.14722			0.573612	−	0.819127i	$-0.305542\pi$
$653$	29.3160			1.14722			0.573612	+	0.819127i	$0.305542\pi$
$654$	−9.54400			−0.373200
$655$	5.65800	+	9.79995i	0.221076	+	0.382916i
$656$	1.88600	+	3.26665i	0.0736360	+	0.127541i
$657$	−3.22800			−0.125936
$658$		0			0
$659$	−6.34200	−	10.9847i	−0.247049	−	0.427902i	0.715657	−	0.698452i	$-0.246128\pi$
$659$	−6.34200	−	10.9847i	−0.247049	−	0.427902i	−0.962706	+	0.270551i	$0.912794\pi$
$660$	−1.88600	+	3.26665i	−0.0734125	+	0.127154i
$661$	22.3160	+	38.6525i	0.867992	+	1.50341i	0.864045	+	0.503414i	$0.167923\pi$
$661$	22.3160	+	38.6525i	0.867992	+	1.50341i	0.00394672	+	0.999992i	$0.498744\pi$
$662$	−13.2720	+	22.9878i	−0.515831	+	0.893446i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	4.27200	−	0.866025i	0.165661	−	0.0335830i
$666$	1.00000			0.0387492
$667$	−11.3160	+	19.5999i	−0.438157	+	0.758911i
$668$	5.65800	−	9.79995i	0.218915	−	0.379171i
$669$	12.5000	+	21.6506i	0.483278	+	0.837062i
$670$	−5.38600	+	9.32883i	−0.208079	+	0.360404i
$671$	−5.22800	−	9.05516i	−0.201825	−	0.349571i
$672$	1.00000			0.0385758
$673$	−21.2280			−0.818279			−0.409140	−	0.912472i	$-0.634171\pi$
$673$	−21.2280			−0.818279			−0.409140	+	0.912472i	$0.634171\pi$
$674$	−15.1580	−	26.2544i	−0.583864	−	1.01128i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	9.77200			0.375846
$677$	17.3160			0.665508			0.332754	−	0.943014i	$-0.392022\pi$
$677$	17.3160			0.665508			0.332754	+	0.943014i	$0.392022\pi$
$678$	−6.77200	−	11.7295i	−0.260077	−	0.450467i
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$		0			0
$681$	−4.54400	+	7.87045i	−0.174127	+	0.301596i
$682$	5.22800	−	9.05516i	0.200190	−	0.346740i
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$	−4.27200	+	0.866025i	−0.163344	+	0.0331133i
$685$	−1.54400			−0.0589934
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	−11.9300	+	20.6634i	−0.455158	+	0.788357i
$688$	−4.38600	−	7.59678i	−0.167215	−	0.289624i
$689$	23.3160	−	40.3845i	0.888269	−	1.53853i
$690$	−1.88600	−	3.26665i	−0.0717988	−	0.124359i
$691$	7.13999			0.271618			0.135809	−	0.990735i	$-0.456637\pi$
$691$	7.13999			0.271618			0.135809	+	0.990735i	$0.456637\pi$
$692$	11.3160			0.430170
$693$	1.88600	+	3.26665i	0.0716433	+	0.124090i
$694$	−3.77200	−	6.53330i	−0.143183	−	0.248001i
$695$	−10.7720			−0.408605
$696$	6.00000			0.227429
$697$		0			0
$698$	−4.61400	+	7.99168i	−0.174642	+	0.302490i
$699$	2.22800	+	3.85901i	0.0842706	+	0.145961i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−17.3160	+	29.9922i	−0.654017	+	1.13279i	0.328123	+	0.944635i	$0.393584\pi$
$701$	−17.3160	+	29.9922i	−0.654017	+	1.13279i	−0.982139	+	0.188155i	$0.939749\pi$
$702$	4.77200			0.180108
$703$	−2.88600	−	3.26665i	−0.108848	−	0.123204i
$704$	3.77200			0.142163
$705$		0			0
$706$	−6.77200	+	11.7295i	−0.254868	+	0.441444i
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$	6.77200	−	11.7295i	0.254507	−	0.440820i
$709$	17.3860	+	30.1134i	0.652945	+	1.13093i	0.982405	+	0.186764i	$0.0598001\pi$
$709$	17.3860	+	30.1134i	0.652945	+	1.13093i	−0.329460	+	0.944170i	$0.606867\pi$
$710$	7.54400			0.283121
$711$	10.3160			0.386880
$712$	8.65800	+	14.9961i	0.324472	+	0.562003i
$713$	5.22800	+	9.05516i	0.195790	+	0.339118i
$714$		0			0
$715$	−18.0000			−0.673162
$716$	0.341997	+	0.592357i	0.0127810	+	0.0221374i
$717$	−6.77200	+	11.7295i	−0.252905	+	0.438044i
$718$	10.5440	+	18.2628i	0.393499	+	0.681560i
$719$	−14.3160	+	24.7960i	−0.533897	+	0.924737i	0.465319	+	0.885143i	$0.345940\pi$
$719$	−14.3160	+	24.7960i	−0.533897	+	0.924737i	−0.999216	+	0.0395935i	$0.987394\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	13.0000			0.484145
$722$	15.1580	+	11.4558i	0.564122	+	0.426340i
$723$	22.3160			0.829941
$724$	−8.54400	+	14.7986i	−0.317535	+	0.549987i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	1.61400	+	2.79553i	0.0599011	+	0.103752i
$727$	−21.7020	+	37.5890i	−0.804883	+	1.39410i	0.111487	+	0.993766i	$0.464439\pi$
$727$	−21.7020	+	37.5890i	−0.804883	+	1.39410i	−0.916370	+	0.400332i	$0.868895\pi$
$728$	2.38600	+	4.13267i	0.0884311	+	0.153167i
$729$	1.00000			0.0370370
$730$	3.22800			0.119474
$731$		0			0
$732$	−1.38600	−	2.40062i	−0.0512281	−	0.0887296i
$733$	22.4040			0.827511			0.413756	−	0.910388i	$-0.364217\pi$
$733$	22.4040			0.827511			0.413756	+	0.910388i	$0.364217\pi$
$734$	9.22800			0.340612
$735$	3.00000	+	5.19615i	0.110657	+	0.191663i
$736$	−1.88600	+	3.26665i	−0.0695189	+	0.120410i
$737$	20.3160	+	35.1884i	0.748350	+	1.29618i
$738$	−1.88600	+	3.26665i	−0.0694247	+	0.120247i
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$	−1.00000			−0.0367607
$741$	−13.7720	−	15.5885i	−0.505927	−	0.572656i
$742$	9.77200			0.358741
$743$	−10.1140	+	17.5180i	−0.371047	+	0.642672i	−0.989727	−	0.142971i	$-0.954334\pi$
$743$	−10.1140	+	17.5180i	−0.371047	+	0.642672i	0.618680	+	0.785643i	$0.287668\pi$
$744$	1.38600	−	2.40062i	0.0508133	−	0.0880111i
$745$	6.77200	+	11.7295i	0.248107	+	0.429734i
$746$	−0.113999	+	0.197452i	−0.00417380	+	0.00722924i
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$		0			0
$749$		0			0
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−25.3860	−	43.9698i	−0.926348	−	1.60448i	−0.789378	−	0.613907i	$-0.789597\pi$
$751$	−25.3860	−	43.9698i	−0.926348	−	1.60448i	−0.136970	−	0.990575i	$-0.543736\pi$
$752$		0			0
$753$	1.54400			0.0562666
$754$	14.3160	+	24.7960i	0.521358	+	0.903019i
$755$	−4.00000	+	6.92820i	−0.145575	+	0.252143i
$756$	0.500000	+	0.866025i	0.0181848	+	0.0314970i
$757$	14.8160	−	25.6621i	0.538497	−	0.932704i	−0.460488	−	0.887666i	$-0.652326\pi$
$757$	14.8160	−	25.6621i	0.538497	−	0.932704i	0.998985	−	0.0450382i	$-0.0143410\pi$
$758$	−4.61400	+	7.99168i	−0.167588	+	0.290271i
$759$	−14.2280			−0.516444
$760$	4.27200	−	0.866025i	0.154962	−	0.0314140i
$761$	21.9480			0.795615			0.397807	−	0.917469i	$-0.369771\pi$
$761$	21.9480			0.795615			0.397807	+	0.917469i	$0.369771\pi$
$762$	−4.65800	+	8.06790i	−0.168742	+	0.292269i
$763$	4.77200	−	8.26535i	0.172758	−	0.299226i
$764$	−3.77200	−	6.53330i	−0.136466	−	0.236366i
$765$		0			0
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	64.6320			2.33373
$768$	1.00000			0.0360844
$769$	−17.9300	−	31.0557i	−0.646573	−	1.11990i	−0.983936	−	0.178522i	$-0.942868\pi$
$769$	−17.9300	−	31.0557i	−0.646573	−	1.11990i	0.337363	−	0.941374i	$-0.390465\pi$
$770$	−1.88600	−	3.26665i	−0.0679668	−	0.117722i
$771$	−30.0000			−1.08042
$772$	2.77200			0.0997665
$773$	1.88600	+	3.26665i	0.0678347	+	0.117493i	0.897948	−	0.440102i	$-0.145058\pi$
$773$	1.88600	+	3.26665i	0.0678347	+	0.117493i	−0.830113	+	0.557595i	$0.811724\pi$
$774$	4.38600	−	7.59678i	0.157652	−	0.273060i
$775$	−1.38600	−	2.40062i	−0.0497866	−	0.0862330i
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$	−0.500000	+	0.866025i	−0.0179374	+	0.0310685i
$778$	9.08801			0.325821
$779$	16.1140	−	3.26665i	0.577344	−	0.117040i
$780$	−4.77200			−0.170865
$781$	14.2280	−	24.6436i	0.509118	−	0.881818i
$782$		0			0
$783$	3.00000	+	5.19615i	0.107211	+	0.185695i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	−1.72800	−	2.99298i	−0.0616749	−	0.106824i
$786$	11.3160			0.403629
$787$	34.3160			1.22323			0.611617	−	0.791154i	$-0.290519\pi$
$787$	34.3160			1.22323			0.611617	+	0.791154i	$0.290519\pi$
$788$	5.65800	+	9.79995i	0.201558	+	0.349109i
$789$	−7.88600	−	13.6590i	−0.280749	−	0.486272i
$790$	−10.3160			−0.367027
$791$	13.5440			0.481569
$792$	1.88600	+	3.26665i	0.0670161	+	0.116075i
$793$	6.61400	−	11.4558i	0.234870	−	0.406807i
$794$	1.04400	+	1.80827i	0.0370503	+	0.0641730i
$795$	−4.88600	+	8.46280i	−0.173289	+	0.300145i
$796$	0.158003	−	0.273669i	0.00560026	−	0.00969994i
$797$	−15.7720			−0.558673			−0.279336	−	0.960193i	$-0.590114\pi$
$797$	−15.7720			−0.558673			−0.279336	+	0.960193i	$0.590114\pi$
$798$	1.38600	−	4.13267i	0.0490639	−	0.146295i
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−8.65800	+	14.9961i	−0.305915	+	0.529861i
$802$	4.54400	+	7.87045i	0.160454	+	0.277915i
$803$	6.08801	−	10.5447i	0.214841	−	0.372116i
$804$	5.38600	+	9.32883i	0.189950	+	0.329002i
$805$	3.77200			0.132946
$806$	13.2280			0.465936
$807$	12.7720	+	22.1218i	0.449596	+	0.778723i
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	−18.0000			−0.632846			−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000			−0.632846			−0.316423	+	0.948618i	$0.602482\pi$
$810$	−1.00000			−0.0351364
$811$	−20.8860	−	36.1756i	−0.733407	−	1.27030i	−0.955419	−	0.295254i	$-0.904596\pi$
$811$	−20.8860	−	36.1756i	−0.733407	−	1.27030i	0.222012	−	0.975044i	$-0.428738\pi$
$812$	−3.00000	+	5.19615i	−0.105279	+	0.182349i
$813$	−6.22800	−	10.7872i	−0.218425	−	0.378324i
$814$	−1.88600	+	3.26665i	−0.0661043	+	0.114496i
$815$	9.15800	−	15.8621i	0.320791	−	0.555626i
$816$		0			0
$817$	−37.4740	+	7.59678i	−1.31105	+	0.265778i
$818$	30.4040			1.06305
$819$	−2.38600	+	4.13267i	−0.0833736	+	0.144407i
$820$	1.88600	−	3.26665i	0.0658620	−	0.114076i
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$	−0.772002	+	1.33715i	−0.0269267	+	0.0466383i
$823$	20.4300	+	35.3858i	0.712145	+	1.23347i	0.964050	+	0.265720i	$0.0856096\pi$
$823$	20.4300	+	35.3858i	0.712145	+	1.23347i	−0.251905	+	0.967752i	$0.581057\pi$
$824$	13.0000			0.452876
$825$	3.77200			0.131324
$826$	6.77200	+	11.7295i	0.235628	+	0.408120i
$827$	21.0000	+	36.3731i	0.730242	+	1.26482i	0.956780	+	0.290813i	$0.0939258\pi$
$827$	21.0000	+	36.3731i	0.730242	+	1.26482i	−0.226538	+	0.974002i	$0.572741\pi$
$828$	−3.77200			−0.131086
$829$	31.4040			1.09071			0.545353	−	0.838206i	$-0.316396\pi$
$829$	31.4040			1.09071			0.545353	+	0.838206i	$0.316396\pi$
$830$	3.00000	+	5.19615i	0.104132	+	0.180361i
$831$	−2.54400	+	4.40634i	−0.0882505	+	0.152854i
$832$	2.38600	+	4.13267i	0.0827197	+	0.143275i
$833$		0			0
$834$	−5.38600	+	9.32883i	−0.186502	+	0.323031i
$835$	−11.3160			−0.391607
$836$	5.22800	−	15.5885i	0.180814	−	0.539138i
$837$	2.77200			0.0958144
$838$	−12.4300	+	21.5294i	−0.429387	+	0.743721i
$839$	0.683994	−	1.18471i	0.0236141	−	0.0409008i	−0.853977	−	0.520311i	$-0.825816\pi$
$839$	0.683994	−	1.18471i	0.0236141	−	0.0409008i	0.877591	+	0.479410i	$0.159149\pi$
$840$	−0.500000	−	0.866025i	−0.0172516	−	0.0298807i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−8.77200	−	15.1936i	−0.302303	−	0.523604i
$843$	27.7720			0.956519
$844$	−20.5440			−0.707154
$845$	−4.88600	−	8.46280i	−0.168084	−	0.291129i
$846$		0			0
$847$	−3.22800			−0.110915
$848$	9.77200			0.335572
$849$	13.3160	+	23.0640i	0.457004	+	0.791554i
$850$		0			0
$851$	−1.88600	−	3.26665i	−0.0646513	−	0.111979i
$852$	3.77200	−	6.53330i	0.129227	−	0.223827i
$853$	3.15800	−	5.46982i	0.108128	−	0.187283i	−0.806884	−	0.590710i	$-0.798848\pi$
$853$	3.15800	−	5.46982i	0.108128	−	0.187283i	0.915012	+	0.403427i	$0.132181\pi$
$854$	2.77200			0.0948560
$855$	2.88600	+	3.26665i	0.0986991	+	0.111717i
$856$		0			0
$857$	22.6320	−	39.1998i	0.773095	−	1.33904i	−0.162764	−	0.986665i	$-0.552041\pi$
$857$	22.6320	−	39.1998i	0.773095	−	1.33904i	0.935859	−	0.352374i	$-0.114626\pi$
$858$	−9.00000	+	15.5885i	−0.307255	+	0.532181i
$859$	25.2720	+	43.7724i	0.862270	+	1.49349i	0.869733	+	0.493523i	$0.164291\pi$
$859$	25.2720	+	43.7724i	0.862270	+	1.49349i	−0.00746341	+	0.999972i	$0.502376\pi$
$860$	−4.38600	+	7.59678i	−0.149561	+	0.259048i
$861$	−1.88600	−	3.26665i	−0.0642747	−	0.111327i
$862$	3.08801			0.105178
$863$	−24.6840			−0.840253			−0.420126	−	0.907466i	$-0.638014\pi$
$863$	−24.6840			−0.840253			−0.420126	+	0.907466i	$0.638014\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−5.65800	−	9.79995i	−0.192378	−	0.333208i
$866$	−10.3160			−0.350552
$867$	−17.0000			−0.577350
$868$	1.38600	+	2.40062i	0.0470439	+	0.0814825i
$869$	−19.4560	+	33.6988i	−0.659999	+	1.14315i
$870$	−3.00000	−	5.19615i	−0.101710	−	0.176166i
$871$	−25.7020	+	44.5172i	−0.870879	+	1.50841i
$872$	4.77200	−	8.26535i	0.161600	−	0.279900i
$873$	−10.0000			−0.338449
$874$	10.8860	+	12.3218i	0.368224	+	0.416791i
$875$	−1.00000			−0.0338062
$876$	1.61400	−	2.79553i	0.0545320	−	0.0944522i
$877$	−3.27200	+	5.66727i	−0.110488	+	0.191370i	−0.915967	−	0.401254i	$-0.868575\pi$
$877$	−3.27200	+	5.66727i	−0.110488	+	0.191370i	0.805479	+	0.592624i	$0.201908\pi$
$878$	2.15800	+	3.73777i	0.0728291	+	0.126144i
$879$	10.1140	−	17.5180i	0.341137	−	0.590866i
$880$	−1.88600	−	3.26665i	−0.0635771	−	0.110119i
$881$	42.8600			1.44399			0.721995	−	0.691898i	$-0.243225\pi$
$881$	42.8600			1.44399			0.721995	+	0.691898i	$0.243225\pi$
$882$	6.00000			0.202031
$883$	3.84200	+	6.65453i	0.129293	+	0.223943i	0.923403	−	0.383832i	$-0.125396\pi$
$883$	3.84200	+	6.65453i	0.129293	+	0.223943i	−0.794110	+	0.607775i	$0.792062\pi$
$884$		0			0
$885$	−13.5440			−0.455277
$886$	−39.0880			−1.31319
$887$	−27.0880	−	46.9178i	−0.909526	−	1.57535i	−0.814724	−	0.579850i	$-0.803111\pi$
$887$	−27.0880	−	46.9178i	−0.909526	−	1.57535i	−0.0948028	−	0.995496i	$-0.530222\pi$
$888$	−0.500000	+	0.866025i	−0.0167789	+	0.0290619i
$889$	−4.65800	−	8.06790i	−0.156224	−	0.270589i
$890$	8.65800	−	14.9961i	0.290217	−	0.502670i
$891$	−1.88600	+	3.26665i	−0.0631834	+	0.109437i
$892$	−25.0000			−0.837062
$893$		0			0
$894$	13.5440			0.452979
$895$	0.341997	−	0.592357i	0.0114317	−	0.0198003i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	−9.00000	−	15.5885i	−0.300501	−	0.520483i
$898$	1.11400	−	1.92950i	0.0371746	−	0.0643883i
$899$	8.31601	+	14.4037i	0.277354	+	0.480392i
$900$	1.00000			0.0333333
$901$		0			0
$902$	−7.11400	−	12.3218i	−0.236870	−	0.410271i
$903$	4.38600	+	7.59678i	0.145957	+	0.252805i
$904$	13.5440			0.450467
$905$	17.0880			0.568025
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	10.2280	−	17.7154i	0.339615	−	0.588231i	−0.644745	−	0.764398i	$-0.723037\pi$
$907$	10.2280	−	17.7154i	0.339615	−	0.588231i	0.984360	+	0.176167i	$0.0563699\pi$
$908$	−4.54400	−	7.87045i	−0.150798	−	0.261190i
$909$	3.00000	−	5.19615i	0.0995037	−	0.172345i
$910$	2.38600	−	4.13267i	0.0790952	−	0.136997i
$911$	36.1760			1.19856			0.599282	−	0.800538i	$-0.295453\pi$
$911$	36.1760			1.19856			0.599282	+	0.800538i	$0.295453\pi$
$912$	1.38600	−	4.13267i	0.0458951	−	0.136847i
$913$	22.6320			0.749010
$914$	−12.9300	+	22.3954i	−0.427687	+	0.740775i
$915$	−1.38600	+	2.40062i	−0.0458198	+	0.0793622i
$916$	−11.9300	−	20.6634i	−0.394178	−	0.682737i
$917$	−5.65800	+	9.79995i	−0.186844	+	0.323623i
$918$		0			0
$919$	−33.4040			−1.10190			−0.550948	−	0.834539i	$-0.685734\pi$
$919$	−33.4040			−1.10190			−0.550948	+	0.834539i	$0.685734\pi$
$920$	3.77200			0.124359
$921$	11.7720	+	20.3897i	0.387901	+	0.671864i
$922$	17.3160	+	29.9922i	0.570272	+	0.987741i
$923$	36.0000			1.18495
$924$	−3.77200			−0.124090
$925$	0.500000	+	0.866025i	0.0164399	+	0.0284747i
$926$	13.8160	−	23.9300i	0.454022	−	0.786389i
$927$	6.50000	+	11.2583i	0.213488	+	0.369772i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	27.5180	−	47.6626i	0.902837	−	1.56376i	0.0790416	−	0.996871i	$-0.474814\pi$
$929$	27.5180	−	47.6626i	0.902837	−	1.56376i	0.823795	−	0.566888i	$-0.191853\pi$
$930$	−2.77200			−0.0908975
$931$	−17.3160	−	19.5999i	−0.567509	−	0.642361i
$932$	−4.45600			−0.145961
$933$	−12.7720	+	22.1218i	−0.418137	+	0.724234i
$934$	−4.54400	+	7.87045i	−0.148684	+	0.257529i
$935$		0			0
$936$	−2.38600	+	4.13267i	−0.0779889	+	0.135081i
$937$	26.3860	+	45.7019i	0.861993	+	1.49302i	0.870002	+	0.493048i	$0.164117\pi$
$937$	26.3860	+	45.7019i	0.861993	+	1.49302i	−0.00800910	+	0.999968i	$0.502549\pi$
$938$	−10.7720			−0.351718
$939$	−2.45600			−0.0801484
$940$		0			0
$941$	4.54400	+	7.87045i	0.148130	+	0.256569i	0.930536	−	0.366199i	$-0.119341\pi$
$941$	4.54400	+	7.87045i	0.148130	+	0.256569i	−0.782406	+	0.622769i	$0.786008\pi$
$942$	−3.45600			−0.112602
$943$	14.2280			0.463327
$944$	6.77200	+	11.7295i	0.220410	+	0.381761i
$945$	0.500000	−	0.866025i	0.0162650	−	0.0281718i
$946$	16.5440	+	28.6551i	0.537892	+	0.931656i
$947$	2.31601	−	4.01144i	0.0752601	−	0.130354i	−0.825939	−	0.563759i	$-0.809355\pi$
$947$	2.31601	−	4.01144i	0.0752601	−	0.130354i	0.901199	+	0.433405i	$0.142688\pi$
$948$	−5.15800	+	8.93392i	−0.167524	+	0.290160i
$949$	15.4040			0.500035
$950$	−2.88600	−	3.26665i	−0.0936342	−	0.105984i
$951$	20.2280			0.655938
$952$		0			0
$953$	30.0000	−	51.9615i	0.971795	−	1.68320i	0.281666	−	0.959512i	$-0.409113\pi$
$953$	30.0000	−	51.9615i	0.971795	−	1.68320i	0.690129	−	0.723686i	$-0.257554\pi$
$954$	4.88600	+	8.46280i	0.158190	+	0.273993i
$955$	−3.77200	+	6.53330i	−0.122059	+	0.211413i
$956$	−6.77200	−	11.7295i	−0.219022	−	0.379358i
$957$	−22.6320			−0.731589
$958$	18.0000			0.581554
$959$	−0.772002	−	1.33715i	−0.0249292	−	0.0431787i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	−23.3160			−0.752129
$962$	−4.77200			−0.153856
$963$		0			0
$964$	−11.1580	+	19.3262i	−0.359375	+	0.622456i
$965$	−1.38600	−	2.40062i	−0.0446169	−	0.0772788i
$966$	1.88600	−	3.26665i	0.0606811	−	0.105103i
$967$	22.6140	−	39.1686i	0.727217	−	1.25958i	−0.230838	−	0.972992i	$-0.574147\pi$
$967$	22.6140	−	39.1686i	0.727217	−	1.25958i	0.958055	−	0.286585i	$-0.0925200\pi$
$968$	−3.22800			−0.103752
$969$		0			0
$970$	10.0000			0.321081
$971$	19.5440	−	33.8512i	0.627197	−	1.08634i	−0.360915	−	0.932599i	$-0.617535\pi$
$971$	19.5440	−	33.8512i	0.627197	−	1.08634i	0.988112	−	0.153738i	$-0.0491312\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−5.38600	−	9.32883i	−0.172667	−	0.299068i
$974$	−4.65800	+	8.06790i	−0.149252	+	0.258512i
$975$	2.38600	+	4.13267i	0.0764132	+	0.132352i
$976$	2.77200			0.0887296
$977$	60.1760			1.92520			0.962601	−	0.270924i	$-0.0873293\pi$
$977$	60.1760			1.92520			0.962601	+	0.270924i	$0.0873293\pi$
$978$	−9.15800	−	15.8621i	−0.292841	−	0.507215i
$979$	−32.6580	−	56.5653i	−1.04375	−	1.80784i
$980$	−6.00000			−0.191663
$981$	9.54400			0.304717
$982$	3.34200	+	5.78851i	0.106647	+	0.184719i
$983$	2.65800	−	4.60380i	0.0847771	−	0.146838i	−0.820519	−	0.571619i	$-0.806316\pi$
$983$	2.65800	−	4.60380i	0.0847771	−	0.146838i	0.905296	+	0.424781i	$0.139649\pi$
$984$	−1.88600	−	3.26665i	−0.0601235	−	0.104137i
$985$	5.65800	−	9.79995i	0.180279	−	0.312252i
$986$		0			0
$987$		0			0
$988$	20.3860	−	4.13267i	0.648565	−	0.131478i
$989$	−33.0880			−1.05214
$990$	1.88600	−	3.26665i	0.0599410	−	0.103821i
$991$	−16.3860	+	28.3814i	−0.520518	+	0.901564i	0.479197	+	0.877707i	$0.340928\pi$
$991$	−16.3860	+	28.3814i	−0.520518	+	0.901564i	−0.999715	+	0.0238570i	$0.992405\pi$
$992$	1.38600	+	2.40062i	0.0440056	+	0.0762199i
$993$	13.2720	−	22.9878i	0.421174	−	0.729495i
$994$	3.77200	+	6.53330i	0.119641	+	0.207224i
$995$	−0.316006			−0.0100181
$996$	6.00000			0.190117
$997$	10.2720	+	17.7916i	0.325318	+	0.563467i	0.981577	−	0.191069i	$-0.0611955\pi$
$997$	10.2720	+	17.7916i	0.325318	+	0.563467i	−0.656259	+	0.754536i	$0.727862\pi$
$998$	10.8160	+	18.7339i	0.342375	+	0.593010i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.g.391.2	yes	4
3.2	odd	2		1710.2.l.l.1531.1		4
19.7	even	3	inner	570.2.i.g.121.2	✓	4
57.26	odd	6		1710.2.l.l.1261.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.g.121.2	✓	4	19.7	even	3	inner
570.2.i.g.391.2	yes	4	1.1	even	1	trivial
1710.2.l.l.1261.1		4	57.26	odd	6
1710.2.l.l.1531.1		4	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +3.77200 q^{11} +1.00000 q^{12} +(2.38600 + 4.13267i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{18} +(2.88600 + 3.26665i) q^{19} +1.00000 q^{20} +(0.500000 - 0.866025i) q^{21} +(1.88600 - 3.26665i) q^{22} +(1.88600 + 3.26665i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.77200 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} -1.00000 q^{30} +2.77200 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.88600 + 3.26665i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.00000 q^{37} +(4.27200 - 0.866025i) q^{38} -4.77200 q^{39} +(0.500000 - 0.866025i) q^{40} +(1.88600 - 3.26665i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.38600 + 7.59678i) q^{43} +(-1.88600 - 3.26665i) q^{44} +1.00000 q^{45} +3.77200 q^{46} +(-0.500000 - 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(2.38600 - 4.13267i) q^{52} +(-4.88600 - 8.46280i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.88600 + 3.26665i) q^{55} +1.00000 q^{56} +(-4.27200 + 0.866025i) q^{57} +6.00000 q^{58} +(6.77200 - 11.7295i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-1.38600 - 2.40062i) q^{61} +(1.38600 - 2.40062i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} -4.77200 q^{65} +(1.88600 + 3.26665i) q^{66} +(5.38600 + 9.32883i) q^{67} -3.77200 q^{69} +(-0.500000 - 0.866025i) q^{70} +(3.77200 - 6.53330i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.61400 - 2.79553i) q^{73} +(-0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(1.38600 - 4.13267i) q^{76} -3.77200 q^{77} +(-2.38600 + 4.13267i) q^{78} +(-5.15800 + 8.93392i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.88600 - 3.26665i) q^{82} +6.00000 q^{83} -1.00000 q^{84} +(4.38600 + 7.59678i) q^{86} -6.00000 q^{87} -3.77200 q^{88} +(-8.65800 - 14.9961i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-2.38600 - 4.13267i) q^{91} +(1.88600 - 3.26665i) q^{92} +(-1.38600 + 2.40062i) q^{93} +(-4.27200 + 0.866025i) q^{95} -1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(-1.88600 - 3.26665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} - 2 q^{14} - 2 q^{15} - 2 q^{16} - 4 q^{18} + 3 q^{19} + 4 q^{20} + 2 q^{21} - q^{22} - q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} + 4 q^{27} + 2 q^{28} + 12 q^{29} - 4 q^{30} - 6 q^{31} + 2 q^{32} + q^{33} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 2 q^{39} + 2 q^{40} - q^{41} - 2 q^{42} - 9 q^{43} + q^{44} + 4 q^{45} - 2 q^{46} - 2 q^{48} - 24 q^{49} - 4 q^{50} + q^{52} - 11 q^{53} + 2 q^{54} + q^{55} + 4 q^{56} + 24 q^{58} + 10 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{65} - q^{66} + 13 q^{67} + 2 q^{69} - 2 q^{70} - 2 q^{71} + 2 q^{72} + 15 q^{73} - 2 q^{74} + 4 q^{75} - 3 q^{76} + 2 q^{77} - q^{78} + 5 q^{79} - 2 q^{80} - 2 q^{81} + q^{82} + 24 q^{83} - 4 q^{84} + 9 q^{86} - 24 q^{87} + 2 q^{88} - 9 q^{89} + 2 q^{90} - q^{91} - q^{92} + 3 q^{93} - 4 q^{96} + 20 q^{97} - 12 q^{98} + q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 + q^13 - 2 * q^14 - 2 * q^15 - 2 * q^16 - 4 * q^18 + 3 * q^19 + 4 * q^20 + 2 * q^21 - q^22 - q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 + 4 * q^27 + 2 * q^28 + 12 * q^29 - 4 * q^30 - 6 * q^31 + 2 * q^32 + q^33 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 2 * q^39 + 2 * q^40 - q^41 - 2 * q^42 - 9 * q^43 + q^44 + 4 * q^45 - 2 * q^46 - 2 * q^48 - 24 * q^49 - 4 * q^50 + q^52 - 11 * q^53 + 2 * q^54 + q^55 + 4 * q^56 + 24 * q^58 + 10 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^62 + 2 * q^63 + 4 * q^64 - 2 * q^65 - q^66 + 13 * q^67 + 2 * q^69 - 2 * q^70 - 2 * q^71 + 2 * q^72 + 15 * q^73 - 2 * q^74 + 4 * q^75 - 3 * q^76 + 2 * q^77 - q^78 + 5 * q^79 - 2 * q^80 - 2 * q^81 + q^82 + 24 * q^83 - 4 * q^84 + 9 * q^86 - 24 * q^87 + 2 * q^88 - 9 * q^89 + 2 * q^90 - q^91 - q^92 + 3 * q^93 - 4 * q^96 + 20 * q^97 - 12 * q^98 + q^99

Introduction

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