LMFDB - Embedded newform 546.2.j.b.529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
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			529.4
Root			$-0.186817 - 0.323577i$ of defining polynomial
Character	$\chi$	$=$	546.529
Dual form			546.2.j.b.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 + 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 + 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.651388 - 1.12824i) q^{10} +(-3.04616 - 5.27610i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.61985 + 2.47718i) q^{13} +(-2.21184 + 1.45181i) q^{14} +(0.651388 - 1.12824i) q^{15} +1.00000 q^{16} +3.48676 q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.835374 + 1.44691i) q^{19} +(0.651388 + 1.12824i) q^{20} +(-2.36323 - 1.18960i) q^{21} +(3.04616 + 5.27610i) q^{22} -0.816013 q^{23} +(0.500000 + 0.866025i) q^{24} +(1.65139 - 2.86029i) q^{25} +(-2.61985 - 2.47718i) q^{26} +1.00000 q^{27} +(2.21184 - 1.45181i) q^{28} +(-0.243381 + 0.421549i) q^{29} +(-0.651388 + 1.12824i) q^{30} +(0.256619 - 0.444477i) q^{31} -1.00000 q^{32} +(-3.04616 + 5.27610i) q^{33} -3.48676 q^{34} +(3.07876 + 1.54979i) q^{35} +(-0.500000 + 0.866025i) q^{36} +10.7631 q^{37} +(0.835374 - 1.44691i) q^{38} +(0.835374 - 3.50744i) q^{39} +(-0.651388 - 1.12824i) q^{40} +(4.81845 - 8.34580i) q^{41} +(2.36323 + 1.18960i) q^{42} +(-6.00032 - 10.3929i) q^{43} +(-3.04616 - 5.27610i) q^{44} -1.30278 q^{45} +0.816013 q^{46} +(-6.57401 - 11.3865i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(2.78447 - 6.42236i) q^{49} +(-1.65139 + 2.86029i) q^{50} +(-1.74338 - 3.01962i) q^{51} +(2.61985 + 2.47718i) q^{52} +(-6.24476 + 10.8162i) q^{53} -1.00000 q^{54} +(3.96846 - 6.87357i) q^{55} +(-2.21184 + 1.45181i) q^{56} +1.67075 q^{57} +(0.243381 - 0.421549i) q^{58} +9.15014 q^{59} +(0.651388 - 1.12824i) q^{60} +(1.11879 - 1.93780i) q^{61} +(-0.256619 + 0.444477i) q^{62} +(0.151388 + 2.64142i) q^{63} +1.00000 q^{64} +(-1.08831 + 4.56941i) q^{65} +(3.04616 - 5.27610i) q^{66} +(1.07770 + 1.86663i) q^{67} +3.48676 q^{68} +(0.408007 + 0.706688i) q^{69} +(-3.07876 - 1.54979i) q^{70} +(5.44093 + 9.42396i) q^{71} +(0.500000 - 0.866025i) q^{72} +(2.44198 - 4.22964i) q^{73} -10.7631 q^{74} -3.30278 q^{75} +(-0.835374 + 1.44691i) q^{76} +(-14.3975 - 7.24743i) q^{77} +(-0.835374 + 3.50744i) q^{78} +(5.95628 + 10.3166i) q^{79} +(0.651388 + 1.12824i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.81845 + 8.34580i) q^{82} -0.486762 q^{83} +(-2.36323 - 1.18960i) q^{84} +(2.27123 + 3.93389i) q^{85} +(6.00032 + 10.3929i) q^{86} +0.486762 q^{87} +(3.04616 + 5.27610i) q^{88} -7.69998 q^{89} +1.30278 q^{90} +(9.39108 + 1.67559i) q^{91} -0.816013 q^{92} -0.513238 q^{93} +(6.57401 + 11.3865i) q^{94} -2.17661 q^{95} +(0.500000 + 0.866025i) q^{96} +(-7.84999 - 13.5966i) q^{97} +(-2.78447 + 6.42236i) q^{98} +6.09231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} + 12 q^{17} + 4 q^{18} + 2 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} - 7 q^{26} + 8 q^{27} + 3 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} - 8 q^{32} - 2 q^{33} - 12 q^{34} + 8 q^{35} - 4 q^{36} + 24 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} + 4 q^{45} + 8 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} - 8 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} + 12 q^{65} + 2 q^{66} - 7 q^{67} + 12 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 4 q^{72} - 19 q^{73} - 24 q^{74} - 12 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} - 2 q^{80} - 4 q^{81} + 6 q^{82} + 12 q^{83} + 3 q^{84} - 3 q^{85} + 4 q^{86} - 12 q^{87} + 2 q^{88} + 14 q^{89} - 4 q^{90} + 40 q^{91} - 8 q^{92} - 20 q^{93} + 17 q^{94} + 24 q^{95} + 4 q^{96} - 25 q^{97} - 17 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 + 12 * q^17 + 4 * q^18 + 2 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 - 7 * q^26 + 8 * q^27 + 3 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 - 8 * q^32 - 2 * q^33 - 12 * q^34 + 8 * q^35 - 4 * q^36 + 24 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 + 4 * q^45 + 8 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 - 8 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 + 12 * q^65 + 2 * q^66 - 7 * q^67 + 12 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 4 * q^72 - 19 * q^73 - 24 * q^74 - 12 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 - 2 * q^80 - 4 * q^81 + 6 * q^82 + 12 * q^83 + 3 * q^84 - 3 * q^85 + 4 * q^86 - 12 * q^87 + 2 * q^88 + 14 * q^89 - 4 * q^90 + 40 * q^91 - 8 * q^92 - 20 * q^93 + 17 * q^94 + 24 * q^95 + 4 * q^96 - 25 * q^97 - 17 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	0.651388	+	1.12824i	0.291309	+	0.504563i	0.974120	−	0.226033i	$-0.0725757\pi$
$5$	0.651388	+	1.12824i	0.291309	+	0.504563i	−0.682810	+	0.730596i	$0.739242\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	2.21184	−	1.45181i	0.835997	−	0.548734i
$7$	2.21184	−	1.45181i	0.835997	−	0.548734i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.651388	−	1.12824i	−0.205987	−	0.356780i
$11$	−3.04616	−	5.27610i	−0.918451	−	1.59080i	−0.801769	−	0.597634i	$-0.796108\pi$
$11$	−3.04616	−	5.27610i	−0.918451	−	1.59080i	−0.116682	−	0.993169i	$-0.537226\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.61985	+	2.47718i	0.726615	+	0.687045i
$13$	2.61985	+	2.47718i	0.726615	+	0.687045i
$14$	−2.21184	+	1.45181i	−0.591139	+	0.388014i
$15$	0.651388	−	1.12824i	0.168188	−	0.291309i
$16$	1.00000			0.250000
$17$	3.48676			0.845664			0.422832	−	0.906208i	$-0.361036\pi$
$17$	3.48676			0.845664			0.422832	+	0.906208i	$0.361036\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−0.835374	+	1.44691i	−0.191648	+	0.331944i	−0.945797	−	0.324760i	$-0.894717\pi$
$19$	−0.835374	+	1.44691i	−0.191648	+	0.331944i	0.754148	+	0.656704i	$0.228050\pi$
$20$	0.651388	+	1.12824i	0.145655	+	0.252281i
$21$	−2.36323	−	1.18960i	−0.515699	−	0.259593i
$22$	3.04616	+	5.27610i	0.649443	+	1.12487i
$23$	−0.816013			−0.170151			−0.0850753	−	0.996375i	$-0.527113\pi$
$23$	−0.816013			−0.170151			−0.0850753	+	0.996375i	$0.527113\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.65139	−	2.86029i	0.330278	−	0.572058i
$26$	−2.61985	−	2.47718i	−0.513794	−	0.485814i
$27$	1.00000			0.192450
$28$	2.21184	−	1.45181i	0.417998	−	0.274367i
$29$	−0.243381	+	0.421549i	−0.0451947	+	0.0782796i	−0.887738	−	0.460349i	$-0.847724\pi$
$29$	−0.243381	+	0.421549i	−0.0451947	+	0.0782796i	0.842543	+	0.538629i	$0.181058\pi$
$30$	−0.651388	+	1.12824i	−0.118927	+	0.205987i
$31$	0.256619	−	0.444477i	0.0460901	−	0.0798304i	−0.842060	−	0.539384i	$-0.818657\pi$
$31$	0.256619	−	0.444477i	0.0460901	−	0.0798304i	0.888150	+	0.459553i	$0.151991\pi$
$32$	−1.00000			−0.176777
$33$	−3.04616	+	5.27610i	−0.530268	+	0.918451i
$34$	−3.48676			−0.597975
$35$	3.07876	+	1.54979i	0.520405	+	0.261962i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	10.7631			1.76944			0.884718	−	0.466126i	$-0.154351\pi$
$37$	10.7631			1.76944			0.884718	+	0.466126i	$0.154351\pi$
$38$	0.835374	−	1.44691i	0.135516	−	0.234720i
$39$	0.835374	−	3.50744i	0.133767	−	0.561640i
$40$	−0.651388	−	1.12824i	−0.102993	−	0.178390i
$41$	4.81845	−	8.34580i	0.752515	−	1.30339i	−0.194085	−	0.980985i	$-0.562174\pi$
$41$	4.81845	−	8.34580i	0.752515	−	1.30339i	0.946600	−	0.322410i	$-0.104493\pi$
$42$	2.36323	+	1.18960i	0.364654	+	0.183560i
$43$	−6.00032	−	10.3929i	−0.915040	−	1.58490i	−0.806842	−	0.590767i	$-0.798825\pi$
$43$	−6.00032	−	10.3929i	−0.915040	−	1.58490i	−0.108198	−	0.994129i	$-0.534508\pi$
$44$	−3.04616	−	5.27610i	−0.459225	−	0.795402i
$45$	−1.30278			−0.194206
$46$	0.816013			0.120315
$47$	−6.57401	−	11.3865i	−0.958918	−	1.66089i	−0.725136	−	0.688605i	$-0.758223\pi$
$47$	−6.57401	−	11.3865i	−0.958918	−	1.66089i	−0.233782	−	0.972289i	$-0.575110\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	2.78447	−	6.42236i	0.397782	−	0.917480i
$50$	−1.65139	+	2.86029i	−0.233542	+	0.404506i
$51$	−1.74338	−	3.01962i	−0.244122	−	0.422832i
$52$	2.61985	+	2.47718i	0.363307	+	0.343523i
$53$	−6.24476	+	10.8162i	−0.857784	+	1.48572i	0.0162547	+	0.999868i	$0.494826\pi$
$53$	−6.24476	+	10.8162i	−0.857784	+	1.48572i	−0.874038	+	0.485857i	$0.838508\pi$
$54$	−1.00000			−0.136083
$55$	3.96846	−	6.87357i	0.535107	−	0.926832i
$56$	−2.21184	+	1.45181i	−0.295570	+	0.194007i
$57$	1.67075			0.221296
$58$	0.243381	−	0.421549i	0.0319575	−	0.0553520i
$59$	9.15014			1.19125			0.595623	−	0.803264i	$-0.296905\pi$
$59$	9.15014			1.19125			0.595623	+	0.803264i	$0.296905\pi$
$60$	0.651388	−	1.12824i	0.0840938	−	0.145655i
$61$	1.11879	−	1.93780i	0.143246	−	0.248110i	−0.785471	−	0.618898i	$-0.787579\pi$
$61$	1.11879	−	1.93780i	0.143246	−	0.248110i	0.928717	+	0.370789i	$0.120913\pi$
$62$	−0.256619	+	0.444477i	−0.0325906	+	0.0564486i
$63$	0.151388	+	2.64142i	0.0190731	+	0.332787i
$64$	1.00000			0.125000
$65$	−1.08831	+	4.56941i	−0.134988	+	0.566766i
$66$	3.04616	−	5.27610i	0.374956	−	0.649443i
$67$	1.07770	+	1.86663i	0.131662	+	0.228045i	0.924317	−	0.381625i	$-0.124635\pi$
$67$	1.07770	+	1.86663i	0.131662	+	0.228045i	−0.792656	+	0.609670i	$0.791302\pi$
$68$	3.48676			0.422832
$69$	0.408007	+	0.706688i	0.0491182	+	0.0850753i
$70$	−3.07876	−	1.54979i	−0.367982	−	0.185235i
$71$	5.44093	+	9.42396i	0.645719	+	1.11842i	0.984135	+	0.177422i	$0.0567756\pi$
$71$	5.44093	+	9.42396i	0.645719	+	1.11842i	−0.338416	+	0.940997i	$0.609891\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.44198	−	4.22964i	0.285813	−	0.495042i	−0.686993	−	0.726664i	$-0.741070\pi$
$73$	2.44198	−	4.22964i	0.285813	−	0.495042i	0.972806	+	0.231622i	$0.0744032\pi$
$74$	−10.7631			−1.25118
$75$	−3.30278			−0.381372
$76$	−0.835374	+	1.44691i	−0.0958240	+	0.165972i
$77$	−14.3975	−	7.24743i	−1.64075	−	0.825922i
$78$	−0.835374	+	3.50744i	−0.0945875	+	0.397140i
$79$	5.95628	+	10.3166i	0.670134	+	1.16071i	0.977866	+	0.209233i	$0.0670966\pi$
$79$	5.95628	+	10.3166i	0.670134	+	1.16071i	−0.307732	+	0.951473i	$0.599570\pi$
$80$	0.651388	+	1.12824i	0.0728274	+	0.126141i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.81845	+	8.34580i	−0.532109	+	0.921639i
$83$	−0.486762			−0.0534291			−0.0267146	−	0.999643i	$-0.508505\pi$
$83$	−0.486762			−0.0534291			−0.0267146	+	0.999643i	$0.508505\pi$
$84$	−2.36323	−	1.18960i	−0.257849	−	0.129796i
$85$	2.27123	+	3.93389i	0.246350	+	0.426691i
$86$	6.00032	+	10.3929i	0.647031	+	1.12069i
$87$	0.486762			0.0521864
$88$	3.04616	+	5.27610i	0.324721	+	0.562434i
$89$	−7.69998			−0.816196			−0.408098	−	0.912938i	$-0.633808\pi$
$89$	−7.69998			−0.816196			−0.408098	+	0.912938i	$0.633808\pi$
$90$	1.30278			0.137325
$91$	9.39108	+	1.67559i	0.984453	+	0.175649i
$92$	−0.816013			−0.0850753
$93$	−0.513238			−0.0532203
$94$	6.57401	+	11.3865i	0.678057	+	1.17443i
$95$	−2.17661			−0.223316
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−7.84999	−	13.5966i	−0.797046	−	1.38052i	−0.921532	−	0.388302i	$-0.873062\pi$
$97$	−7.84999	−	13.5966i	−0.797046	−	1.38052i	0.124486	−	0.992221i	$-0.460272\pi$
$98$	−2.78447	+	6.42236i	−0.281274	+	0.648756i
$99$	6.09231			0.612301
$100$	1.65139	−	2.86029i	0.165139	−	0.286029i
$101$	8.19386	+	14.1922i	0.815319	+	1.41217i	0.909098	+	0.416581i	$0.136772\pi$
$101$	8.19386	+	14.1922i	0.815319	+	1.41217i	−0.0937792	+	0.995593i	$0.529895\pi$
$102$	1.74338	+	3.01962i	0.172620	+	0.298987i
$103$	2.45785	+	4.25712i	0.242179	+	0.419467i	0.961335	−	0.275382i	$-0.0888044\pi$
$103$	2.45785	+	4.25712i	0.242179	+	0.419467i	−0.719155	+	0.694849i	$0.755471\pi$
$104$	−2.61985	−	2.47718i	−0.256897	−	0.242907i
$105$	−0.197224	−	3.44117i	−0.0192471	−	0.335824i
$106$	6.24476	−	10.8162i	0.606545	−	1.05057i
$107$	−4.87910			−0.471680			−0.235840	−	0.971792i	$-0.575784\pi$
$107$	−4.87910			−0.471680			−0.235840	+	0.971792i	$0.575784\pi$
$108$	1.00000			0.0962250
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$	−3.96846	+	6.87357i	−0.378378	+	0.655369i
$111$	−5.38153	−	9.32109i	−0.510792	−	0.884718i
$112$	2.21184	−	1.45181i	0.208999	−	0.137184i
$113$	−6.36829	−	11.0302i	−0.599079	−	1.03763i	−0.992957	−	0.118472i	$-0.962200\pi$
$113$	−6.36829	−	11.0302i	−0.599079	−	1.03763i	0.393879	−	0.919162i	$-0.371133\pi$
$114$	−1.67075			−0.156480
$115$	−0.531541	−	0.920656i	−0.0495665	−	0.0858516i
$116$	−0.243381	+	0.421549i	−0.0225974	+	0.0391398i
$117$	−3.45522	+	1.03027i	−0.319435	+	0.0952481i
$118$	−9.15014			−0.842338
$119$	7.71216	−	5.06213i	0.706973	−	0.464045i
$120$	−0.651388	+	1.12824i	−0.0594633	+	0.102993i
$121$	−13.0581	+	22.6174i	−1.18710	+	2.05612i
$122$	−1.11879	+	1.93780i	−0.101290	+	0.175440i
$123$	−9.63690			−0.868930
$124$	0.256619	−	0.444477i	0.0230451	−	0.0399152i
$125$	10.8167			0.967471
$126$	−0.151388	−	2.64142i	−0.0134867	−	0.235316i
$127$	−5.95554	+	10.3153i	−0.528469	+	0.915335i	0.470980	+	0.882144i	$0.343900\pi$
$127$	−5.95554	+	10.3153i	−0.528469	+	0.915335i	−0.999449	+	0.0331911i	$0.989433\pi$
$128$	−1.00000			−0.0883883
$129$	−6.00032	+	10.3929i	−0.528299	+	0.915040i
$130$	1.08831	−	4.56941i	0.0954507	−	0.400764i
$131$	4.63340	+	8.02529i	0.404822	+	0.701173i	0.994301	−	0.106611i	$-0.0340000\pi$
$131$	4.63340	+	8.02529i	0.404822	+	0.701173i	−0.589478	+	0.807784i	$0.700667\pi$
$132$	−3.04616	+	5.27610i	−0.265134	+	0.459225i
$133$	0.252931	+	4.41314i	0.0219319	+	0.382668i
$134$	−1.07770	−	1.86663i	−0.0930989	−	0.161252i
$135$	0.651388	+	1.12824i	0.0560625	+	0.0971032i
$136$	−3.48676			−0.298987
$137$	10.3055			0.880461			0.440230	−	0.897885i	$-0.354897\pi$
$137$	10.3055			0.880461			0.440230	+	0.897885i	$0.354897\pi$
$138$	−0.408007	−	0.706688i	−0.0347318	−	0.0601573i
$139$	−0.106609	−	0.184652i	−0.00904245	−	0.0156620i	0.861469	−	0.507811i	$-0.169545\pi$
$139$	−0.106609	−	0.184652i	−0.00904245	−	0.0156620i	−0.870511	+	0.492149i	$0.836212\pi$
$140$	3.07876	+	1.54979i	0.260202	+	0.130981i
$141$	−6.57401	+	11.3865i	−0.553632	+	0.958918i
$142$	−5.44093	−	9.42396i	−0.456592	−	0.790841i
$143$	5.08936	−	21.3684i	0.425594	−	1.78692i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.634142			−0.0526626
$146$	−2.44198	+	4.22964i	−0.202100	+	0.350047i
$147$	−6.95416	+	0.799757i	−0.573570	+	0.0659628i
$148$	10.7631			0.884718
$149$	−6.01673	+	10.4213i	−0.492910	+	0.853745i	−0.999967	−	0.00816779i	$-0.997400\pi$
$149$	−6.01673	+	10.4213i	−0.492910	+	0.853745i	0.507057	+	0.861913i	$0.330733\pi$
$150$	3.30278			0.269671
$151$	2.23969	−	3.87926i	0.182264	−	0.315690i	−0.760387	−	0.649470i	$-0.774991\pi$
$151$	2.23969	−	3.87926i	0.182264	−	0.315690i	0.942651	+	0.333780i	$0.108324\pi$
$152$	0.835374	−	1.44691i	0.0677578	−	0.117360i
$153$	−1.74338	+	3.01962i	−0.140944	+	0.244122i
$154$	14.3975	+	7.24743i	1.16019	+	0.584015i
$155$	0.668634			0.0537059
$156$	0.835374	−	3.50744i	0.0668835	−	0.280820i
$157$	−10.2859	+	17.8156i	−0.820900	+	1.42184i	0.0841125	+	0.996456i	$0.473194\pi$
$157$	−10.2859	+	17.8156i	−0.820900	+	1.42184i	−0.905013	+	0.425385i	$0.860139\pi$
$158$	−5.95628	−	10.3166i	−0.473856	−	0.820743i
$159$	12.4895			0.990483
$160$	−0.651388	−	1.12824i	−0.0514967	−	0.0891950i
$161$	−1.80489	+	1.18470i	−0.142245	+	0.0933674i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−5.25800	+	9.10712i	−0.411838	+	0.713324i	−0.995091	−	0.0989663i	$-0.968446\pi$
$163$	−5.25800	+	9.10712i	−0.411838	+	0.713324i	0.583253	+	0.812291i	$0.301780\pi$
$164$	4.81845	−	8.34580i	0.376258	−	0.651697i
$165$	−7.93692			−0.617888
$166$	0.486762			0.0377801
$167$	−3.45416	+	5.98279i	−0.267291	+	0.462962i	−0.968161	−	0.250327i	$-0.919462\pi$
$167$	−3.45416	+	5.98279i	−0.267291	+	0.462962i	0.700870	+	0.713289i	$0.252795\pi$
$168$	2.36323	+	1.18960i	0.182327	+	0.0917798i
$169$	0.727193	+	12.9796i	0.0559379	+	0.998434i
$170$	−2.27123	−	3.93389i	−0.174196	−	0.301716i
$171$	−0.835374	−	1.44691i	−0.0638827	−	0.110648i
$172$	−6.00032	−	10.3929i	−0.457520	−	0.792448i
$173$	−2.69828	+	4.67356i	−0.205147	+	0.355324i	−0.950179	−	0.311703i	$-0.899100\pi$
$173$	−2.69828	+	4.67356i	−0.205147	+	0.355324i	0.745033	+	0.667028i	$0.232434\pi$
$174$	−0.486762			−0.0369014
$175$	−0.500000	−	8.72401i	−0.0377964	−	0.659473i
$176$	−3.04616	−	5.27610i	−0.229613	−	0.397701i
$177$	−4.57507	−	7.92425i	−0.343883	−	0.595623i
$178$	7.69998			0.577138
$179$	1.56151	+	2.70461i	0.116713	+	0.202152i	0.918463	−	0.395507i	$-0.129431\pi$
$179$	1.56151	+	2.70461i	0.116713	+	0.202152i	−0.801750	+	0.597659i	$0.796098\pi$
$180$	−1.30278			−0.0971032
$181$	−21.0972			−1.56814			−0.784071	−	0.620672i	$-0.786860\pi$
$181$	−21.0972			−1.56814			−0.784071	+	0.620672i	$0.786860\pi$
$182$	−9.39108	−	1.67559i	−0.696113	−	0.124203i
$183$	−2.23758			−0.165407
$184$	0.816013			0.0601573
$185$	7.01093	+	12.1433i	0.515454	+	0.892792i
$186$	0.513238			0.0376324
$187$	−10.6212	−	18.3965i	−0.776701	−	1.34529i
$188$	−6.57401	−	11.3865i	−0.479459	−	0.830447i
$189$	2.21184	−	1.45181i	0.160888	−	0.105604i
$190$	2.17661			0.157908
$191$	−2.80415	+	4.85694i	−0.202901	+	0.351436i	−0.949462	−	0.313882i	$-0.898370\pi$
$191$	−2.80415	+	4.85694i	−0.202901	+	0.351436i	0.746561	+	0.665317i	$0.231704\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−3.83537	−	6.64306i	−0.276076	−	0.478178i	0.694330	−	0.719657i	$-0.255701\pi$
$193$	−3.83537	−	6.64306i	−0.276076	−	0.478178i	−0.970406	+	0.241479i	$0.922368\pi$
$194$	7.84999	+	13.5966i	0.563596	+	0.976178i
$195$	4.50138	−	1.34220i	0.322350	−	0.0961173i
$196$	2.78447	−	6.42236i	0.198891	−	0.458740i
$197$	7.08968	−	12.2797i	0.505119	−	0.874892i	−0.494863	−	0.868971i	$-0.664782\pi$
$197$	7.08968	−	12.2797i	0.505119	−	0.874892i	0.999982	−	0.00592106i	$-0.00188474\pi$
$198$	−6.09231			−0.432962
$199$	3.49202			0.247543			0.123771	−	0.992311i	$-0.460501\pi$
$199$	3.49202			0.247543			0.123771	+	0.992311i	$0.460501\pi$
$200$	−1.65139	+	2.86029i	−0.116771	+	0.202253i
$201$	1.07770	−	1.86663i	0.0760150	−	0.131662i
$202$	−8.19386	−	14.1922i	−0.576518	−	0.998558i
$203$	0.0736899	+	1.28574i	0.00517202	+	0.0902414i
$204$	−1.74338	−	3.01962i	−0.122061	−	0.211416i
$205$	12.5547			0.876859
$206$	−2.45785	−	4.25712i	−0.171247	−	0.296608i
$207$	0.408007	−	0.706688i	0.0283584	−	0.0491182i
$208$	2.61985	+	2.47718i	0.181654	+	0.171761i
$209$	10.1787			0.704077
$210$	0.197224	+	3.44117i	0.0136098	+	0.237464i
$211$	6.56109	−	11.3641i	0.451684	−	0.782340i	−0.546807	−	0.837259i	$-0.684157\pi$
$211$	6.56109	−	11.3641i	0.451684	−	0.782340i	0.998491	+	0.0549189i	$0.0174900\pi$
$212$	−6.24476	+	10.8162i	−0.428892	+	0.742862i
$213$	5.44093	−	9.42396i	0.372806	−	0.645719i
$214$	4.87910			0.333528
$215$	7.81707	−	13.5396i	0.533120	−	0.923391i
$216$	−1.00000			−0.0680414
$217$	−0.0776979	−	1.35567i	−0.00527448	−	0.0920292i
$218$	5.50000	−	9.52628i	0.372507	−	0.645201i
$219$	−4.88397			−0.330028
$220$	3.96846	−	6.87357i	0.267553	−	0.463416i
$221$	9.13478	+	8.63733i	0.614472	+	0.581009i
$222$	5.38153	+	9.32109i	0.361185	+	0.625590i
$223$	−4.92875	+	8.53684i	−0.330053	+	0.571669i	−0.982522	−	0.186147i	$-0.940400\pi$
$223$	−4.92875	+	8.53684i	−0.330053	+	0.571669i	0.652469	+	0.757816i	$0.273733\pi$
$224$	−2.21184	+	1.45181i	−0.147785	+	0.0970034i
$225$	1.65139	+	2.86029i	0.110093	+	0.190686i
$226$	6.36829	+	11.0302i	0.423613	+	0.733719i
$227$	−6.35912			−0.422070			−0.211035	−	0.977479i	$-0.567683\pi$
$227$	−6.35912			−0.422070			−0.211035	+	0.977479i	$0.567683\pi$
$228$	1.67075			0.110648
$229$	−5.60767	−	9.71276i	−0.370565	−	0.641837i	0.619088	−	0.785322i	$-0.287503\pi$
$229$	−5.60767	−	9.71276i	−0.370565	−	0.641837i	−0.989653	+	0.143485i	$0.954169\pi$
$230$	0.531541	+	0.920656i	0.0350488	+	0.0607063i
$231$	0.922302	+	16.0923i	0.0606830	+	1.05880i
$232$	0.243381	−	0.421549i	0.0159788	−	0.0276760i
$233$	4.74845	+	8.22455i	0.311081	+	0.538808i	0.978597	−	0.205788i	$-0.0659756\pi$
$233$	4.74845	+	8.22455i	0.311081	+	0.538808i	−0.667516	+	0.744596i	$0.732642\pi$
$234$	3.45522	−	1.03027i	0.225875	−	0.0673506i
$235$	8.56446	−	14.8341i	0.558684	−	0.967669i
$236$	9.15014			0.595623
$237$	5.95628	−	10.3166i	0.386902	−	0.670134i
$238$	−7.71216	+	5.06213i	−0.499905	+	0.328129i
$239$	4.32714			0.279899			0.139950	−	0.990159i	$-0.455306\pi$
$239$	4.32714			0.279899			0.139950	+	0.990159i	$0.455306\pi$
$240$	0.651388	−	1.12824i	0.0420469	−	0.0728274i
$241$	17.1603			1.10539			0.552695	−	0.833384i	$-0.313599\pi$
$241$	17.1603			1.10539			0.552695	+	0.833384i	$0.313599\pi$
$242$	13.0581	−	22.6174i	0.839409	−	1.45390i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.11879	−	1.93780i	0.0716231	−	0.124055i
$245$	9.05971	−	1.04190i	0.578804	−	0.0665648i
$246$	9.63690			0.614426
$247$	−5.77281	+	1.72131i	−0.367315	+	0.109525i
$248$	−0.256619	+	0.444477i	−0.0162953	+	0.0282243i
$249$	0.243381	+	0.421549i	0.0154237	+	0.0267146i
$250$	−10.8167			−0.684105
$251$	5.56308	+	9.63554i	0.351139	+	0.608190i	0.986449	−	0.164067i	$-0.0524612\pi$
$251$	5.56308	+	9.63554i	0.351139	+	0.608190i	−0.635311	+	0.772257i	$0.719128\pi$
$252$	0.151388	+	2.64142i	0.00953654	+	0.166394i
$253$	2.48570	+	4.30537i	0.156275	+	0.270676i
$254$	5.95554	−	10.3153i	0.373684	−	0.647240i
$255$	2.27123	−	3.93389i	0.142230	−	0.246350i
$256$	1.00000			0.0625000
$257$	2.30425			0.143735			0.0718676	−	0.997414i	$-0.477104\pi$
$257$	2.30425			0.143735			0.0718676	+	0.997414i	$0.477104\pi$
$258$	6.00032	−	10.3929i	0.373564	−	0.647031i
$259$	23.8062	−	15.6260i	1.47924	−	0.970950i
$260$	−1.08831	+	4.56941i	−0.0674938	+	0.283383i
$261$	−0.243381	−	0.421549i	−0.0150649	−	0.0260932i
$262$	−4.63340	−	8.02529i	−0.286253	−	0.495804i
$263$	9.39720	+	16.2764i	0.579456	+	1.00365i	0.995542	+	0.0943224i	$0.0300685\pi$
$263$	9.39720	+	16.2764i	0.579456	+	1.00365i	−0.416085	+	0.909326i	$0.636598\pi$
$264$	3.04616	−	5.27610i	0.187478	−	0.324721i
$265$	−16.2710			−0.999522
$266$	−0.252931	−	4.41314i	−0.0155082	−	0.270587i
$267$	3.84999	+	6.66838i	0.235616	+	0.408098i
$268$	1.07770	+	1.86663i	0.0658309	+	0.114022i
$269$	27.6397			1.68522			0.842610	−	0.538525i	$-0.181018\pi$
$269$	27.6397			1.68522			0.842610	+	0.538525i	$0.181018\pi$
$270$	−0.651388	−	1.12824i	−0.0396422	−	0.0686623i
$271$	−11.7588			−0.714298			−0.357149	−	0.934047i	$-0.616251\pi$
$271$	−11.7588			−0.714298			−0.357149	+	0.934047i	$0.616251\pi$
$272$	3.48676			0.211416
$273$	−3.24444	−	8.97071i	−0.196362	−	0.542932i
$274$	−10.3055			−0.622580
$275$	−20.1215			−1.21337
$276$	0.408007	+	0.706688i	0.0245591	+	0.0425376i
$277$	−29.0640			−1.74628			−0.873142	−	0.487465i	$-0.837922\pi$
$277$	−29.0640			−1.74628			−0.873142	+	0.487465i	$0.837922\pi$
$278$	0.106609	+	0.184652i	0.00639398	+	0.0110747i
$279$	0.256619	+	0.444477i	0.0153634	+	0.0266101i
$280$	−3.07876	−	1.54979i	−0.183991	−	0.0926174i
$281$	−5.76306			−0.343795			−0.171898	−	0.985115i	$-0.554990\pi$
$281$	−5.76306			−0.343795			−0.171898	+	0.985115i	$0.554990\pi$
$282$	6.57401	−	11.3865i	0.391477	−	0.678057i
$283$	3.36060	+	5.82073i	0.199767	+	0.346006i	0.948453	−	0.316919i	$-0.102648\pi$
$283$	3.36060	+	5.82073i	0.199767	+	0.346006i	−0.748686	+	0.662925i	$0.769315\pi$
$284$	5.44093	+	9.42396i	0.322860	+	0.559209i
$285$	1.08831	+	1.88500i	0.0644657	+	0.111658i
$286$	−5.08936	+	21.3684i	−0.300940	+	1.26354i
$287$	−1.45891	−	25.4551i	−0.0861167	−	1.50256i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−4.84249			−0.284852
$290$	0.634142			0.0372381
$291$	−7.84999	+	13.5966i	−0.460175	+	0.797046i
$292$	2.44198	−	4.22964i	0.142906	−	0.247521i
$293$	2.99769	+	5.19215i	0.175127	+	0.303329i	0.940205	−	0.340609i	$-0.110633\pi$
$293$	2.99769	+	5.19215i	0.175127	+	0.303329i	−0.765078	+	0.643937i	$0.777300\pi$
$294$	6.95416	−	0.799757i	0.405575	−	0.0466428i
$295$	5.96029	+	10.3235i	0.347021	+	0.601059i
$296$	−10.7631			−0.625590
$297$	−3.04616	−	5.27610i	−0.176756	−	0.306150i
$298$	6.01673	−	10.4213i	0.348540	−	0.603689i
$299$	−2.13783	−	2.02141i	−0.123634	−	0.116901i
$300$	−3.30278			−0.190686
$301$	−28.3602	−	14.2760i	−1.63466	−	0.822855i
$302$	−2.23969	+	3.87926i	−0.128880	+	0.223226i
$303$	8.19386	−	14.1922i	0.470725	−	0.815319i
$304$	−0.835374	+	1.44691i	−0.0479120	+	0.0829860i
$305$	2.91506			0.166916
$306$	1.74338	−	3.01962i	0.0996625	−	0.172620i
$307$	9.00340			0.513851			0.256925	−	0.966431i	$-0.417291\pi$
$307$	9.00340			0.513851			0.256925	+	0.966431i	$0.417291\pi$
$308$	−14.3975	−	7.24743i	−0.820375	−	0.412961i
$309$	2.45785	−	4.25712i	0.139822	−	0.242179i
$310$	−0.668634			−0.0379758
$311$	7.31771	−	12.6746i	0.414949	−	0.718713i	−0.580474	−	0.814279i	$-0.697133\pi$
$311$	7.31771	−	12.6746i	0.414949	−	0.718713i	0.995423	+	0.0955656i	$0.0304660\pi$
$312$	−0.835374	+	3.50744i	−0.0472938	+	0.198570i
$313$	1.72540	+	2.98848i	0.0975253	+	0.168919i	0.910660	−	0.413157i	$-0.135574\pi$
$313$	1.72540	+	2.98848i	0.0975253	+	0.168919i	−0.813134	+	0.582076i	$0.802241\pi$
$314$	10.2859	−	17.8156i	0.580464	−	1.00539i
$315$	−2.88153	+	1.89139i	−0.162356	+	0.106568i
$316$	5.95628	+	10.3166i	0.335067	+	0.580353i
$317$	−6.67850	−	11.5675i	−0.375102	−	0.649696i	0.615240	−	0.788340i	$-0.289059\pi$
$317$	−6.67850	−	11.5675i	−0.375102	−	0.649696i	−0.990342	+	0.138644i	$0.955726\pi$
$318$	−12.4895			−0.700377
$319$	2.96551			0.166037
$320$	0.651388	+	1.12824i	0.0364137	+	0.0630704i
$321$	2.43955	+	4.22542i	0.136162	+	0.235840i
$322$	1.80489	−	1.18470i	0.100583	−	0.0660207i
$323$	−2.91275	+	5.04503i	−0.162070	+	0.280713i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	11.4118	−	3.40274i	0.633014	−	0.188750i
$326$	5.25800	−	9.10712i	0.291214	−	0.504397i
$327$	11.0000			0.608301
$328$	−4.81845	+	8.34580i	−0.266054	+	0.460820i
$329$	−31.0718	−	15.6409i	−1.71304	−	0.862312i
$330$	7.93692			0.436913
$331$	1.71691	−	2.97377i	0.0943697	−	0.163453i	−0.814976	−	0.579495i	$-0.803250\pi$
$331$	1.71691	−	2.97377i	0.0943697	−	0.163453i	0.909345	+	0.416042i	$0.136583\pi$
$332$	−0.486762			−0.0267146
$333$	−5.38153	+	9.32109i	−0.294906	+	0.510792i
$334$	3.45416	−	5.98279i	0.189003	−	0.327364i
$335$	−1.40400	+	2.43180i	−0.0767086	+	0.132863i
$336$	−2.36323	−	1.18960i	−0.128925	−	0.0648981i
$337$	−6.17386			−0.336311			−0.168156	−	0.985760i	$-0.553781\pi$
$337$	−6.17386			−0.336311			−0.168156	+	0.985760i	$0.553781\pi$
$338$	−0.727193	−	12.9796i	−0.0395541	−	0.706000i
$339$	−6.36829	+	11.0302i	−0.345878	+	0.599079i
$340$	2.27123	+	3.93389i	0.123175	+	0.213345i
$341$	−3.12681			−0.169326
$342$	0.835374	+	1.44691i	0.0451719	+	0.0782400i
$343$	−3.16527	−	18.2478i	−0.170908	−	0.985287i
$344$	6.00032	+	10.3929i	0.323516	+	0.560345i
$345$	−0.531541	+	0.920656i	−0.0286172	+	0.0495665i
$346$	2.69828	−	4.67356i	0.145061	−	0.251252i
$347$	−0.144624			−0.00776382			−0.00388191	−	0.999992i	$-0.501236\pi$
$347$	−0.144624			−0.00776382			−0.00388191	+	0.999992i	$0.501236\pi$
$348$	0.486762			0.0260932
$349$	13.8792	−	24.0395i	0.742938	−	1.28681i	−0.208214	−	0.978083i	$-0.566765\pi$
$349$	13.8792	−	24.0395i	0.742938	−	1.28681i	0.951152	−	0.308723i	$-0.0999015\pi$
$350$	0.500000	+	8.72401i	0.0267261	+	0.466318i
$351$	2.61985	+	2.47718i	0.139837	+	0.132222i
$352$	3.04616	+	5.27610i	0.162361	+	0.281217i
$353$	0.483589	+	0.837601i	0.0257389	+	0.0445810i	0.878608	−	0.477544i	$-0.158473\pi$
$353$	0.483589	+	0.837601i	0.0257389	+	0.0445810i	−0.852869	+	0.522125i	$0.825139\pi$
$354$	4.57507	+	7.92425i	0.243162	+	0.421169i
$355$	−7.08831	+	12.2773i	−0.376208	+	0.651612i
$356$	−7.69998			−0.408098
$357$	−8.24001	−	4.14786i	−0.436108	−	0.219528i
$358$	−1.56151	−	2.70461i	−0.0825284	−	0.142943i
$359$	−7.57507	−	13.1204i	−0.399797	−	0.692468i	0.593904	−	0.804536i	$-0.297586\pi$
$359$	−7.57507	−	13.1204i	−0.399797	−	0.692468i	−0.993701	+	0.112068i	$0.964253\pi$
$360$	1.30278			0.0686623
$361$	8.10430	+	14.0371i	0.426542	+	0.738793i
$362$	21.0972			1.10884
$363$	26.1163			1.37075
$364$	9.39108	+	1.67559i	0.492226	+	0.0878247i
$365$	6.36271			0.333040
$366$	2.23758			0.116960
$367$	2.41676	+	4.18595i	0.126154	+	0.218505i	0.922183	−	0.386753i	$-0.126403\pi$
$367$	2.41676	+	4.18595i	0.126154	+	0.218505i	−0.796030	+	0.605258i	$0.793070\pi$
$368$	−0.816013			−0.0425376
$369$	4.81845	+	8.34580i	0.250838	+	0.434465i
$370$	−7.01093	−	12.1433i	−0.364481	−	0.631299i
$371$	1.89076	+	32.9900i	0.0981634	+	1.71276i
$372$	−0.513238			−0.0266101
$373$	−4.28078	+	7.41454i	−0.221651	+	0.383910i	−0.955309	−	0.295608i	$-0.904478\pi$
$373$	−4.28078	+	7.41454i	−0.221651	+	0.383910i	0.733659	+	0.679518i	$0.237811\pi$
$374$	10.6212	+	18.3965i	0.549210	+	0.951260i
$375$	−5.40833	−	9.36750i	−0.279285	−	0.483735i
$376$	6.57401	+	11.3865i	0.339029	+	0.587215i
$377$	−1.68187	+	0.501494i	−0.0866208	+	0.0258283i
$378$	−2.21184	+	1.45181i	−0.113765	+	0.0746733i
$379$	−16.3161	+	28.2604i	−0.838104	+	1.45164i	0.0533744	+	0.998575i	$0.483002\pi$
$379$	−16.3161	+	28.2604i	−0.838104	+	1.45164i	−0.891478	+	0.453064i	$0.850331\pi$
$380$	−2.17661			−0.111658
$381$	11.9111			0.610223
$382$	2.80415	−	4.85694i	0.143473	−	0.248502i
$383$	−9.62196	+	16.6657i	−0.491659	+	0.851579i	−0.999954	−	0.00960439i	$-0.996943\pi$
$383$	−9.62196	+	16.6657i	−0.491659	+	0.851579i	0.508295	+	0.861183i	$0.330276\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−1.20155	−	20.9647i	−0.0612368	−	1.06846i
$386$	3.83537	+	6.64306i	0.195215	+	0.338123i
$387$	12.0006			0.610027
$388$	−7.84999	−	13.5966i	−0.398523	−	0.690262i
$389$	−6.40570	+	11.0950i	−0.324782	+	0.562538i	−0.981468	−	0.191625i	$-0.938624\pi$
$389$	−6.40570	+	11.0950i	−0.324782	+	0.562538i	0.656686	+	0.754164i	$0.271958\pi$
$390$	−4.50138	+	1.34220i	−0.227936	+	0.0679652i
$391$	−2.84524			−0.143890
$392$	−2.78447	+	6.42236i	−0.140637	+	0.324378i
$393$	4.63340	−	8.02529i	0.233724	−	0.404822i
$394$	−7.08968	+	12.2797i	−0.357173	+	0.618642i
$395$	−7.75969	+	13.4402i	−0.390433	+	0.676249i
$396$	6.09231			0.306150
$397$	2.21764	−	3.84107i	0.111300	−	0.192778i	−0.804994	−	0.593282i	$-0.797832\pi$
$397$	2.21764	−	3.84107i	0.111300	−	0.192778i	0.916295	+	0.400505i	$0.131165\pi$
$398$	−3.49202			−0.175039
$399$	3.69543	−	2.42562i	0.185003	−	0.121433i
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	23.0982			1.15347			0.576735	−	0.816931i	$-0.304327\pi$
$401$	23.0982			1.15347			0.576735	+	0.816931i	$0.304327\pi$
$402$	−1.07770	+	1.86663i	−0.0537507	+	0.0930989i
$403$	1.77335	−	0.528771i	0.0883368	−	0.0263400i
$404$	8.19386	+	14.1922i	0.407660	+	0.706087i
$405$	0.651388	−	1.12824i	0.0323677	−	0.0560625i
$406$	−0.0736899	−	1.28574i	−0.00365717	−	0.0638103i
$407$	−32.7860	−	56.7870i	−1.62514	−	2.81483i
$408$	1.74338	+	3.01962i	0.0863102	+	0.149494i
$409$	−19.9354			−0.985744			−0.492872	−	0.870102i	$-0.664053\pi$
$409$	−19.9354			−0.985744			−0.492872	+	0.870102i	$0.664053\pi$
$410$	−12.5547			−0.620033
$411$	−5.15277	−	8.92485i	−0.254167	−	0.440230i
$412$	2.45785	+	4.25712i	0.121090	+	0.209733i
$413$	20.2386	−	13.2843i	0.995878	−	0.653677i
$414$	−0.408007	+	0.706688i	−0.0200524	+	0.0347318i
$415$	−0.317071	−	0.549183i	−0.0155644	−	0.0269583i
$416$	−2.61985	−	2.47718i	−0.128449	−	0.121454i
$417$	−0.106609	+	0.184652i	−0.00522066	+	0.00904245i
$418$	−10.1787			−0.497858
$419$	3.23489	−	5.60299i	0.158035	−	0.273724i	−0.776125	−	0.630579i	$-0.782818\pi$
$419$	3.23489	−	5.60299i	0.158035	−	0.273724i	0.934160	+	0.356855i	$0.116151\pi$
$420$	−0.197224	−	3.44117i	−0.00962356	−	0.167912i
$421$	−6.65600			−0.324393			−0.162197	−	0.986758i	$-0.551858\pi$
$421$	−6.65600			−0.324393			−0.162197	+	0.986758i	$0.551858\pi$
$422$	−6.56109	+	11.3641i	−0.319389	+	0.553198i
$423$	13.1480			0.639279
$424$	6.24476	−	10.8162i	0.303272	−	0.525283i
$425$	5.75800	−	9.97314i	0.279304	−	0.483768i
$426$	−5.44093	+	9.42396i	−0.263614	+	0.456592i
$427$	−0.338742	−	5.91038i	−0.0163929	−	0.286023i
$428$	−4.87910			−0.235840
$429$	−21.0503	+	6.27670i	−1.01632	+	0.303042i
$430$	−7.81707	+	13.5396i	−0.376973	+	0.652936i
$431$	−6.66495	−	11.5440i	−0.321039	−	0.556056i	0.659664	−	0.751561i	$-0.270699\pi$
$431$	−6.66495	−	11.5440i	−0.321039	−	0.556056i	−0.980703	+	0.195505i	$0.937365\pi$
$432$	1.00000			0.0481125
$433$	3.01693	+	5.22547i	0.144984	+	0.251120i	0.929367	−	0.369157i	$-0.120354\pi$
$433$	3.01693	+	5.22547i	0.144984	+	0.251120i	−0.784383	+	0.620277i	$0.787020\pi$
$434$	0.0776979	+	1.35567i	0.00372962	+	0.0650745i
$435$	0.317071	+	0.549183i	0.0152024	+	0.0263313i
$436$	−5.50000	+	9.52628i	−0.263402	+	0.456226i
$437$	0.681677	−	1.18070i	0.0326090	−	0.0564805i
$438$	4.88397			0.233365
$439$	7.65324			0.365269			0.182635	−	0.983181i	$-0.441537\pi$
$439$	7.65324			0.365269			0.182635	+	0.983181i	$0.441537\pi$
$440$	−3.96846	+	6.87357i	−0.189189	+	0.327685i
$441$	4.16969	+	5.62260i	0.198557	+	0.267743i
$442$	−9.13478	−	8.63733i	−0.434497	−	0.410836i
$443$	13.2991	+	23.0347i	0.631859	+	1.09441i	0.987171	+	0.159664i	$0.0510411\pi$
$443$	13.2991	+	23.0347i	0.631859	+	1.09441i	−0.355313	+	0.934747i	$0.615626\pi$
$444$	−5.38153	−	9.32109i	−0.255396	−	0.442359i
$445$	−5.01567	−	8.68740i	−0.237766	−	0.411822i
$446$	4.92875	−	8.53684i	0.233383	−	0.404231i
$447$	12.0335			0.569163
$448$	2.21184	−	1.45181i	0.104500	−	0.0685918i
$449$	−0.721905	−	1.25038i	−0.0340688	−	0.0590089i	0.848488	−	0.529214i	$-0.177513\pi$
$449$	−0.721905	−	1.25038i	−0.0340688	−	0.0590089i	−0.882557	+	0.470205i	$0.844180\pi$
$450$	−1.65139	−	2.86029i	−0.0778472	−	0.134835i
$451$	−58.7110			−2.76459
$452$	−6.36829	−	11.0302i	−0.299539	−	0.518817i
$453$	−4.47939			−0.210460
$454$	6.35912			0.298448
$455$	4.22678	+	11.6868i	0.198154	+	0.547887i
$456$	−1.67075			−0.0782400
$457$	−23.3803			−1.09369			−0.546843	−	0.837235i	$-0.684171\pi$
$457$	−23.3803			−1.09369			−0.546843	+	0.837235i	$0.684171\pi$
$458$	5.60767	+	9.71276i	0.262029	+	0.453848i
$459$	3.48676			0.162748
$460$	−0.531541	−	0.920656i	−0.0247832	−	0.0429258i
$461$	4.69123	+	8.12544i	0.218492	+	0.378440i	0.954347	−	0.298700i	$-0.0965528\pi$
$461$	4.69123	+	8.12544i	0.218492	+	0.378440i	−0.735855	+	0.677139i	$0.763220\pi$
$462$	−0.922302	−	16.0923i	−0.0429094	−	0.748683i
$463$	16.0637			0.746545			0.373272	−	0.927722i	$-0.378236\pi$
$463$	16.0637			0.746545			0.373272	+	0.927722i	$0.378236\pi$
$464$	−0.243381	+	0.421549i	−0.0112987	+	0.0195699i
$465$	−0.334317	−	0.579054i	−0.0155036	−	0.0268530i
$466$	−4.74845	−	8.22455i	−0.219968	−	0.380995i
$467$	−13.3195	−	23.0701i	−0.616353	−	1.06756i	−0.990145	−	0.140043i	$-0.955276\pi$
$467$	−13.3195	−	23.0701i	−0.616353	−	1.06756i	0.373792	−	0.927512i	$-0.378057\pi$
$468$	−3.45522	+	1.03027i	−0.159718	+	0.0476240i
$469$	5.09369	+	2.56406i	0.235205	+	0.118398i
$470$	−8.56446	+	14.8341i	−0.395049	+	0.684245i
$471$	20.5717			0.947894
$472$	−9.15014			−0.421169
$473$	−36.5558	+	63.3166i	−1.68084	+	2.91130i
$474$	−5.95628	+	10.3166i	−0.273581	+	0.473856i
$475$	2.75905	+	4.77882i	0.126594	+	0.219267i
$476$	7.71216	−	5.06213i	0.353486	−	0.232022i
$477$	−6.24476	−	10.8162i	−0.285928	−	0.495242i
$478$	−4.32714			−0.197919
$479$	−4.78765	−	8.29244i	−0.218753	−	0.378891i	0.735674	−	0.677336i	$-0.236866\pi$
$479$	−4.78765	−	8.29244i	−0.218753	−	0.378891i	−0.954427	+	0.298444i	$0.903532\pi$
$480$	−0.651388	+	1.12824i	−0.0297317	+	0.0514967i
$481$	28.1976	+	26.6620i	1.28570	+	1.21568i
$482$	−17.1603			−0.781629
$483$	1.92843	+	0.970732i	0.0877464	+	0.0441698i
$484$	−13.0581	+	22.6174i	−0.593552	+	1.02806i
$485$	10.2268	−	17.7133i	0.464374	−	0.804319i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	28.3232			1.28344			0.641722	−	0.766937i	$-0.278220\pi$
$487$	28.3232			1.28344			0.641722	+	0.766937i	$0.278220\pi$
$488$	−1.11879	+	1.93780i	−0.0506452	+	0.0877201i
$489$	10.5160			0.475550
$490$	−9.05971	+	1.04190i	−0.409276	+	0.0470684i
$491$	−16.2403	+	28.1291i	−0.732916	+	1.26945i	0.222716	+	0.974883i	$0.428508\pi$
$491$	−16.2403	+	28.1291i	−0.732916	+	1.26945i	−0.955632	+	0.294564i	$0.904825\pi$
$492$	−9.63690			−0.434465
$493$	−0.848612	+	1.46984i	−0.0382196	+	0.0661982i
$494$	5.77281	−	1.72131i	0.259731	−	0.0774456i
$495$	3.96846	+	6.87357i	0.178369	+	0.308944i
$496$	0.256619	−	0.444477i	0.0115225	−	0.0199576i
$497$	25.7163	+	12.9451i	1.15353	+	0.580666i
$498$	−0.243381	−	0.421549i	−0.0109062	−	0.0188900i
$499$	5.41650	+	9.38165i	0.242476	+	0.419980i	0.961419	−	0.275089i	$-0.0887072\pi$
$499$	5.41650	+	9.38165i	0.242476	+	0.419980i	−0.718943	+	0.695069i	$0.755374\pi$
$500$	10.8167			0.483735
$501$	6.90833			0.308641
$502$	−5.56308	−	9.63554i	−0.248293	−	0.430055i
$503$	7.43429	+	12.8766i	0.331478	+	0.574138i	0.982802	−	0.184663i	$-0.0591192\pi$
$503$	7.43429	+	12.8766i	0.331478	+	0.574138i	−0.651323	+	0.758800i	$0.725786\pi$
$504$	−0.151388	−	2.64142i	−0.00674335	−	0.117658i
$505$	−10.6748	+	18.4892i	−0.475020	+	0.822760i
$506$	−2.48570	−	4.30537i	−0.110503	−	0.191397i
$507$	10.8771	−	7.11959i	0.483069	−	0.316192i
$508$	−5.95554	+	10.3153i	−0.264234	+	0.457667i
$509$	19.6936			0.872905			0.436452	−	0.899727i	$-0.356235\pi$
$509$	19.6936			0.872905			0.436452	+	0.899727i	$0.356235\pi$
$510$	−2.27123	+	3.93389i	−0.100572	+	0.174196i
$511$	−0.739373	−	12.9006i	−0.0327079	−	0.570689i
$512$	−1.00000			−0.0441942
$513$	−0.835374	+	1.44691i	−0.0368827	+	0.0638827i
$514$	−2.30425			−0.101636
$515$	−3.20203	+	5.54608i	−0.141098	+	0.244389i
$516$	−6.00032	+	10.3929i	−0.264149	+	0.457520i
$517$	−40.0509	+	69.3702i	−1.76144	+	3.05090i
$518$	−23.8062	+	15.6260i	−1.04598	+	0.686565i
$519$	5.39656			0.236883
$520$	1.08831	−	4.56941i	0.0477254	−	0.200382i
$521$	16.9583	−	29.3726i	0.742956	−	1.28684i	−0.208187	−	0.978089i	$-0.566756\pi$
$521$	16.9583	−	29.3726i	0.742956	−	1.28684i	0.951143	−	0.308749i	$-0.0999104\pi$
$522$	0.243381	+	0.421549i	0.0106525	+	0.0184507i
$523$	11.9327			0.521780			0.260890	−	0.965369i	$-0.415984\pi$
$523$	11.9327			0.521780			0.260890	+	0.965369i	$0.415984\pi$
$524$	4.63340	+	8.02529i	0.202411	+	0.350587i
$525$	−7.30521	+	4.79502i	−0.318826	+	0.209272i
$526$	−9.39720	−	16.2764i	−0.409738	−	0.709686i
$527$	0.894769	−	1.54979i	0.0389767	−	0.0675097i
$528$	−3.04616	+	5.27610i	−0.132567	+	0.229613i
$529$	−22.3341			−0.971049
$530$	16.2710			0.706769
$531$	−4.57507	+	7.92425i	−0.198541	+	0.343883i
$532$	0.252931	+	4.41314i	0.0109660	+	0.191334i
$533$	33.2976	−	9.92856i	1.44228	−	0.430054i
$534$	−3.84999	−	6.66838i	−0.166605	−	0.288569i
$535$	−3.17818	−	5.50478i	−0.137405	−	0.237992i
$536$	−1.07770	−	1.86663i	−0.0465495	−	0.0806260i
$537$	1.56151	−	2.70461i	0.0673841	−	0.116713i
$538$	−27.6397			−1.19163
$539$	−42.3669	+	4.87237i	−1.82487	+	0.209868i
$540$	0.651388	+	1.12824i	0.0280313	+	0.0485516i
$541$	13.3341	+	23.0954i	0.573279	+	0.992948i	0.996226	+	0.0867937i	$0.0276621\pi$
$541$	13.3341	+	23.0954i	0.573279	+	0.992948i	−0.422948	+	0.906154i	$0.639005\pi$
$542$	11.7588			0.505085
$543$	10.5486	+	18.2707i	0.452683	+	0.784071i
$544$	−3.48676			−0.149494
$545$	−14.3305			−0.613853
$546$	3.24444	+	8.97071i	0.138849	+	0.383911i
$547$	−19.9689			−0.853809			−0.426904	−	0.904297i	$-0.640396\pi$
$547$	−19.9689			−0.853809			−0.426904	+	0.904297i	$0.640396\pi$
$548$	10.3055			0.440230
$549$	1.11879	+	1.93780i	0.0477488	+	0.0827033i
$550$	20.1215			0.857986
$551$	−0.406629	−	0.704302i	−0.0173230	−	0.0300043i
$552$	−0.408007	−	0.706688i	−0.0173659	−	0.0300787i
$553$	28.1521	+	14.1712i	1.19715	+	0.602621i
$554$	29.0640			1.23481
$555$	7.01093	−	12.1433i	0.297597	−	0.515454i
$556$	−0.106609	−	0.184652i	−0.00452123	−	0.00783099i
$557$	−14.1698	−	24.5427i	−0.600392	−	1.03991i	−0.992762	−	0.120101i	$-0.961678\pi$
$557$	−14.1698	−	24.5427i	−0.600392	−	1.03991i	0.392370	−	0.919807i	$-0.371655\pi$
$558$	−0.256619	−	0.444477i	−0.0108635	−	0.0188162i
$559$	10.0250	−	42.0916i	0.424014	−	1.78028i
$560$	3.07876	+	1.54979i	0.130101	+	0.0654904i
$561$	−10.6212	+	18.3965i	−0.448428	+	0.776701i
$562$	5.76306			0.243100
$563$	−32.4328			−1.36688			−0.683439	−	0.730007i	$-0.739517\pi$
$563$	−32.4328			−1.36688			−0.683439	+	0.730007i	$0.739517\pi$
$564$	−6.57401	+	11.3865i	−0.276816	+	0.479459i
$565$	8.29646	−	14.3699i	0.349035	−	0.604546i
$566$	−3.36060	−	5.82073i	−0.141256	−	0.244663i
$567$	−2.36323	−	1.18960i	−0.0992462	−	0.0499586i
$568$	−5.44093	−	9.42396i	−0.228296	−	0.395421i
$569$	−24.9763			−1.04706			−0.523530	−	0.852007i	$-0.675385\pi$
$569$	−24.9763			−1.04706			−0.523530	+	0.852007i	$0.675385\pi$
$570$	−1.08831	−	1.88500i	−0.0455841	−	0.0789540i
$571$	0.0710597	−	0.123079i	0.00297376	−	0.00515070i	−0.864535	−	0.502573i	$-0.832387\pi$
$571$	0.0710597	−	0.123079i	0.00297376	−	0.00515070i	0.867508	+	0.497422i	$0.165720\pi$
$572$	5.08936	−	21.3684i	0.212797	−	0.893459i
$573$	5.60831			0.234290
$574$	1.45891	+	25.4551i	0.0608937	+	1.06247i
$575$	−1.34755	+	2.33403i	−0.0561969	+	0.0973359i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	17.0033	−	29.4505i	0.707855	−	1.22604i	−0.257796	−	0.966199i	$-0.582996\pi$
$577$	17.0033	−	29.4505i	0.707855	−	1.22604i	0.965651	−	0.259842i	$-0.0836705\pi$
$578$	4.84249			0.201421
$579$	−3.83537	+	6.64306i	−0.159393	+	0.276076i
$580$	−0.634142			−0.0263313
$581$	−1.07664	+	0.706688i	−0.0446666	+	0.0293184i
$582$	7.84999	−	13.5966i	0.325393	−	0.563596i
$583$	76.0901			3.15133
$584$	−2.44198	+	4.22964i	−0.101050	+	0.175024i
$585$	−3.41307	−	3.22721i	−0.141113	−	0.133429i
$586$	−2.99769	−	5.19215i	−0.123833	−	0.214486i
$587$	10.8444	−	18.7831i	0.447598	−	0.775263i	−0.550631	−	0.834749i	$-0.685613\pi$
$587$	10.8444	−	18.7831i	0.447598	−	0.775263i	0.998229	+	0.0594859i	$0.0189461\pi$
$588$	−6.95416	+	0.799757i	−0.286785	+	0.0329814i
$589$	0.428746	+	0.742609i	0.0176662	+	0.0305987i
$590$	−5.96029	−	10.3235i	−0.245381	−	0.425013i
$591$	−14.1794			−0.583261
$592$	10.7631			0.442359
$593$	−1.39002	−	2.40759i	−0.0570814	−	0.0988679i	0.836073	−	0.548619i	$-0.184846\pi$
$593$	−1.39002	−	2.40759i	−0.0570814	−	0.0988679i	−0.893154	+	0.449751i	$0.851513\pi$
$594$	3.04616	+	5.27610i	0.124985	+	0.216481i
$595$	10.7349	+	5.40373i	0.440088	+	0.221531i
$596$	−6.01673	+	10.4213i	−0.246455	+	0.426872i
$597$	−1.74601	−	3.02418i	−0.0714595	−	0.123771i
$598$	2.13783	+	2.02141i	0.0874224	+	0.0826616i
$599$	−8.54173	+	14.7947i	−0.349006	+	0.604496i	−0.986073	−	0.166313i	$-0.946814\pi$
$599$	−8.54173	+	14.7947i	−0.349006	+	0.604496i	0.637067	+	0.770808i	$0.280147\pi$
$600$	3.30278			0.134835
$601$	17.7386	−	30.7242i	0.723574	−	1.25327i	−0.235984	−	0.971757i	$-0.575831\pi$
$601$	17.7386	−	30.7242i	0.723574	−	1.25327i	0.959558	−	0.281510i	$-0.0908353\pi$
$602$	28.3602	+	14.2760i	1.15588	+	0.581846i
$603$	−2.15540			−0.0877745
$604$	2.23969	−	3.87926i	0.0911318	−	0.157845i
$605$	−34.0237			−1.38326
$606$	−8.19386	+	14.1922i	−0.332853	+	0.576518i
$607$	10.4446	−	18.0906i	0.423934	−	0.734275i	−0.572386	−	0.819984i	$-0.693982\pi$
$607$	10.4446	−	18.0906i	0.423934	−	0.734275i	0.996320	+	0.0857092i	$0.0273156\pi$
$608$	0.835374	−	1.44691i	0.0338789	−	0.0586800i
$609$	1.07664	−	0.706688i	0.0436277	−	0.0286365i
$610$	−2.91506			−0.118027
$611$	10.9835	−	46.1159i	0.444346	−	1.86565i
$612$	−1.74338	+	3.01962i	−0.0704720	+	0.122061i
$613$	−19.5334	−	33.8328i	−0.788945	−	1.36649i	−0.926614	−	0.376015i	$-0.877294\pi$
$613$	−19.5334	−	33.8328i	−0.788945	−	1.36649i	0.137668	−	0.990478i	$-0.456039\pi$
$614$	−9.00340			−0.363348
$615$	−6.27736	−	10.8727i	−0.253128	−	0.438430i
$616$	14.3975	+	7.24743i	0.580093	+	0.292007i
$617$	5.75569	+	9.96914i	0.231715	+	0.401343i	0.958313	−	0.285721i	$-0.0922329\pi$
$617$	5.75569	+	9.96914i	0.231715	+	0.401343i	−0.726598	+	0.687063i	$0.758900\pi$
$618$	−2.45785	+	4.25712i	−0.0988693	+	0.171247i
$619$	−17.6738	+	30.6120i	−0.710371	+	1.23040i	0.254347	+	0.967113i	$0.418139\pi$
$619$	−17.6738	+	30.6120i	−0.710371	+	1.23040i	−0.964718	+	0.263286i	$0.915194\pi$
$620$	0.668634			0.0268530
$621$	−0.816013			−0.0327455
$622$	−7.31771	+	12.6746i	−0.293413	+	0.508207i
$623$	−17.0311	+	11.1789i	−0.682338	+	0.447875i
$624$	0.835374	−	3.50744i	0.0334417	−	0.140410i
$625$	−1.21110	−	2.09769i	−0.0484441	−	0.0839076i
$626$	−1.72540	−	2.98848i	−0.0689608	−	0.119444i
$627$	−5.08936	−	8.81504i	−0.203250	−	0.352039i
$628$	−10.2859	+	17.8156i	−0.410450	+	0.710920i
$629$	37.5282			1.49635
$630$	2.88153	−	1.89139i	0.114803	−	0.0753547i
$631$	−13.8346	−	23.9623i	−0.550748	−	0.953924i	−0.998221	−	0.0596262i	$-0.981009\pi$
$631$	−13.8346	−	23.9623i	−0.550748	−	0.953924i	0.447473	−	0.894298i	$-0.352324\pi$
$632$	−5.95628	−	10.3166i	−0.236928	−	0.410371i
$633$	−13.1222			−0.521560
$634$	6.67850	+	11.5675i	0.265237	+	0.459404i
$635$	−15.5175			−0.615792
$636$	12.4895			0.495242
$637$	23.2042	−	9.92797i	0.919384	−	0.393361i
$638$	−2.96551			−0.117406
$639$	−10.8819			−0.430479
$640$	−0.651388	−	1.12824i	−0.0257484	−	0.0445975i
$641$	30.0129			1.18544			0.592719	−	0.805409i	$-0.298055\pi$
$641$	30.0129			1.18544			0.592719	+	0.805409i	$0.298055\pi$
$642$	−2.43955	−	4.22542i	−0.0962813	−	0.166764i
$643$	17.4779	+	30.2725i	0.689259	+	1.19383i	0.972078	+	0.234659i	$0.0753972\pi$
$643$	17.4779	+	30.2725i	0.689259	+	1.19383i	−0.282819	+	0.959173i	$0.591269\pi$
$644$	−1.80489	+	1.18470i	−0.0711227	+	0.0466837i
$645$	−15.6341			−0.615594
$646$	2.91275	−	5.04503i	0.114601	−	0.198494i
$647$	−12.5327	−	21.7072i	−0.492710	−	0.853398i	0.507255	−	0.861796i	$-0.330660\pi$
$647$	−12.5327	−	21.7072i	−0.492710	−	0.853398i	−0.999965	+	0.00839785i	$0.997327\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−27.8727	−	48.2770i	−1.09410	−	1.89504i
$650$	−11.4118	+	3.40274i	−0.447608	+	0.133466i
$651$	−1.13520	+	0.745126i	−0.0444920	+	0.0292038i
$652$	−5.25800	+	9.10712i	−0.205919	+	0.356662i
$653$	−0.116167			−0.00454595			−0.00227298	−	0.999997i	$-0.500724\pi$
$653$	−0.116167			−0.00454595			−0.00227298	+	0.999997i	$0.500724\pi$
$654$	−11.0000			−0.430134
$655$	−6.03629	+	10.4552i	−0.235857	+	0.408517i
$656$	4.81845	−	8.34580i	0.188129	−	0.325849i
$657$	2.44198	+	4.22964i	0.0952708	+	0.165014i
$658$	31.0718	+	15.6409i	1.21130	+	0.609747i
$659$	6.83643	+	11.8410i	0.266310	+	0.461262i	0.967906	−	0.251313i	$-0.0808623\pi$
$659$	6.83643	+	11.8410i	0.266310	+	0.461262i	−0.701596	+	0.712575i	$0.747529\pi$
$660$	−7.93692			−0.308944
$661$	25.4912	+	44.1521i	0.991493	+	1.71732i	0.608466	+	0.793580i	$0.291785\pi$
$661$	25.4912	+	44.1521i	0.991493	+	1.71732i	0.383027	+	0.923737i	$0.374881\pi$
$662$	−1.71691	+	2.97377i	−0.0667294	+	0.115579i
$663$	2.91275	−	12.2296i	0.113122	−	0.474959i
$664$	0.486762			0.0188900
$665$	−4.81432	+	3.16003i	−0.186691	+	0.122541i
$666$	5.38153	−	9.32109i	0.208530	−	0.361185i
$667$	0.198602	−	0.343989i	0.00768991	−	0.0133193i
$668$	−3.45416	+	5.98279i	−0.133646	+	0.231481i
$669$	9.85749			0.381113
$670$	1.40400	−	2.43180i	0.0542412	−	0.0939485i
$671$	−13.6320			−0.526259
$672$	2.36323	+	1.18960i	0.0911635	+	0.0458899i
$673$	17.2877	−	29.9432i	0.666394	−	1.15423i	−0.312512	−	0.949914i	$-0.601170\pi$
$673$	17.2877	−	29.9432i	0.666394	−	1.15423i	0.978905	−	0.204314i	$-0.0654962\pi$
$674$	6.17386			0.237808
$675$	1.65139	−	2.86029i	0.0635619	−	0.110093i
$676$	0.727193	+	12.9796i	0.0279690	+	0.499217i
$677$	6.93750	+	12.0161i	0.266630	+	0.461816i	0.967989	−	0.250991i	$-0.0807566\pi$
$677$	6.93750	+	12.0161i	0.266630	+	0.461816i	−0.701360	+	0.712808i	$0.747423\pi$
$678$	6.36829	−	11.0302i	0.244573	−	0.423613i
$679$	−37.1026	−	18.6767i	−1.42387	−	0.716747i
$680$	−2.27123	−	3.93389i	−0.0870979	−	0.150858i
$681$	3.17956	+	5.50716i	0.121841	+	0.211035i
$682$	3.12681			0.119732
$683$	10.8575			0.415450			0.207725	−	0.978187i	$-0.433394\pi$
$683$	10.8575			0.415450			0.207725	+	0.978187i	$0.433394\pi$
$684$	−0.835374	−	1.44691i	−0.0319413	−	0.0553240i
$685$	6.71290	+	11.6271i	0.256487	+	0.444248i
$686$	3.16527	+	18.2478i	0.120850	+	0.696703i
$687$	−5.60767	+	9.71276i	−0.213946	+	0.370565i
$688$	−6.00032	−	10.3929i	−0.228760	−	0.396224i
$689$	−43.1540	+	12.8675i	−1.64404	+	0.490213i
$690$	0.531541	−	0.920656i	0.0202354	−	0.0350488i
$691$	6.78403			0.258077			0.129038	−	0.991640i	$-0.458811\pi$
$691$	6.78403			0.258077			0.129038	+	0.991640i	$0.458811\pi$
$692$	−2.69828	+	4.67356i	−0.102573	+	0.177662i
$693$	13.4752	−	8.84491i	0.511881	−	0.335990i
$694$	0.144624			0.00548985
$695$	0.138888	−	0.240560i	0.00526830	−	0.00912497i
$696$	−0.486762			−0.0184507
$697$	16.8008	−	29.0998i	0.636375	−	1.10223i
$698$	−13.8792	+	24.0395i	−0.525336	+	0.909909i
$699$	4.74845	−	8.22455i	0.179603	−	0.311081i
$700$	−0.500000	−	8.72401i	−0.0188982	−	0.329736i
$701$	19.3000			0.728952			0.364476	−	0.931213i	$-0.381248\pi$
$701$	19.3000			0.728952			0.364476	+	0.931213i	$0.381248\pi$
$702$	−2.61985	−	2.47718i	−0.0988797	−	0.0934950i
$703$	−8.99119	+	15.5732i	−0.339109	+	0.587354i
$704$	−3.04616	−	5.27610i	−0.114806	−	0.198850i
$705$	−17.1289			−0.645112
$706$	−0.483589	−	0.837601i	−0.0182001	−	0.0315235i
$707$	38.7279	+	19.4949i	1.45651	+	0.733180i
$708$	−4.57507	−	7.92425i	−0.171942	−	0.297812i
$709$	−2.42262	+	4.19610i	−0.0909835	+	0.157588i	−0.907925	−	0.419132i	$-0.862334\pi$
$709$	−2.42262	+	4.19610i	−0.0909835	+	0.157588i	0.816942	+	0.576720i	$0.195668\pi$
$710$	7.08831	−	12.2773i	0.266019	−	0.460759i
$711$	−11.9126			−0.446756
$712$	7.69998			0.288569
$713$	−0.209404	+	0.362699i	−0.00784226	+	0.0135832i
$714$	8.24001	+	4.14786i	0.308375	+	0.155230i
$715$	27.4238	−	8.17713i	1.02559	−	0.305807i
$716$	1.56151	+	2.70461i	0.0583564	+	0.101076i
$717$	−2.16357	−	3.74741i	−0.0807999	−	0.139950i
$718$	7.57507	+	13.1204i	0.282699	+	0.489649i
$719$	−5.67495	+	9.82930i	−0.211640	+	0.366571i	−0.952228	−	0.305388i	$-0.901214\pi$
$719$	−5.67495	+	9.82930i	−0.211640	+	0.366571i	0.740588	+	0.671959i	$0.234547\pi$
$720$	−1.30278			−0.0485516
$721$	11.6169	+	5.84773i	0.432637	+	0.217781i
$722$	−8.10430	−	14.0371i	−0.301611	−	0.522405i
$723$	−8.58013	−	14.8612i	−0.319099	−	0.552695i
$724$	−21.0972			−0.784071
$725$	0.803833	+	1.39228i	0.0298536	+	0.0517080i
$726$	−26.1163			−0.969266
$727$	−3.52009			−0.130553			−0.0652765	−	0.997867i	$-0.520793\pi$
$727$	−3.52009			−0.130553			−0.0652765	+	0.997867i	$0.520793\pi$
$728$	−9.39108	−	1.67559i	−0.348057	−	0.0621014i
$729$	1.00000			0.0370370
$730$	−6.36271			−0.235495
$731$	−20.9217	−	36.2374i	−0.773817	−	1.34029i
$732$	−2.23758			−0.0827033
$733$	−11.7071	−	20.2773i	−0.432411	−	0.748959i	0.564669	−	0.825317i	$-0.309004\pi$
$733$	−11.7071	−	20.2773i	−0.432411	−	0.748959i	−0.997080	+	0.0763590i	$0.975671\pi$
$734$	−2.41676	−	4.18595i	−0.0892042	−	0.154506i
$735$	−5.43217	−	7.32499i	−0.200369	−	0.270186i
$736$	0.816013			0.0300787
$737$	6.56567	−	11.3721i	0.241850	−	0.418896i
$738$	−4.81845	−	8.34580i	−0.177370	−	0.307213i
$739$	20.9997	+	36.3726i	0.772487	+	1.33799i	0.936196	+	0.351478i	$0.114321\pi$
$739$	20.9997	+	36.3726i	0.772487	+	1.33799i	−0.163709	+	0.986509i	$0.552346\pi$
$740$	7.01093	+	12.1433i	0.257727	+	0.446396i
$741$	4.37711	+	4.13874i	0.160797	+	0.152040i
$742$	−1.89076	−	32.9900i	−0.0694120	−	1.21110i
$743$	−3.47141	+	6.01266i	−0.127354	+	0.220583i	−0.922651	−	0.385637i	$-0.873982\pi$
$743$	−3.47141	+	6.01266i	−0.127354	+	0.220583i	0.795297	+	0.606220i	$0.207315\pi$
$744$	0.513238			0.0188162
$745$	−15.6769			−0.574357
$746$	4.28078	−	7.41454i	0.156731	−	0.271465i
$747$	0.243381	−	0.421549i	0.00890485	−	0.0154237i
$748$	−10.6212	−	18.3965i	−0.388350	−	0.672643i
$749$	−10.7918	+	7.08354i	−0.394323	+	0.258827i
$750$	5.40833	+	9.36750i	0.197484	+	0.342053i
$751$	38.5326			1.40607			0.703037	−	0.711153i	$-0.251827\pi$
$751$	38.5326			1.40607			0.703037	+	0.711153i	$0.251827\pi$
$752$	−6.57401	−	11.3865i	−0.239729	−	0.415224i
$753$	5.56308	−	9.63554i	0.202730	−	0.351139i
$754$	1.68187	−	0.501494i	0.0612501	−	0.0182633i
$755$	5.83564			0.212381
$756$	2.21184	−	1.45181i	0.0804438	−	0.0528020i
$757$	−16.9857	+	29.4201i	−0.617356	+	1.06929i	0.372610	+	0.927988i	$0.378463\pi$
$757$	−16.9857	+	29.4201i	−0.617356	+	1.06929i	−0.989966	+	0.141304i	$0.954871\pi$
$758$	16.3161	−	28.2604i	0.592629	−	1.02646i
$759$	2.48570	−	4.30537i	0.0902254	−	0.156275i
$760$	2.17661			0.0789540
$761$	5.37092	−	9.30271i	0.194696	−	0.337223i	−0.752105	−	0.659043i	$-0.770961\pi$
$761$	5.37092	−	9.30271i	0.194696	−	0.337223i	0.946801	+	0.321820i	$0.104295\pi$
$762$	−11.9111			−0.431493
$763$	1.66527	+	29.0556i	0.0602867	+	1.05188i
$764$	−2.80415	+	4.85694i	−0.101451	+	0.175718i
$765$	−4.54247			−0.164233
$766$	9.62196	−	16.6657i	0.347656	−	0.602157i
$767$	23.9720	+	22.6665i	0.865577	+	0.818440i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	14.3203	−	24.8036i	0.516405	−	0.894439i	−0.483414	−	0.875392i	$-0.660603\pi$
$769$	14.3203	−	24.8036i	0.516405	−	0.894439i	0.999819	−	0.0190473i	$-0.00606331\pi$
$770$	1.20155	+	20.9647i	0.0433010	+	0.755516i
$771$	−1.15213	−	1.99554i	−0.0414928	−	0.0718676i
$772$	−3.83537	−	6.64306i	−0.138038	−	0.239089i
$773$	47.5738			1.71111			0.855556	−	0.517711i	$-0.173216\pi$
$773$	47.5738			1.71111			0.855556	+	0.517711i	$0.173216\pi$
$774$	−12.0006			−0.431354
$775$	−0.847555	−	1.46801i	−0.0304451	−	0.0527324i
$776$	7.84999	+	13.5966i	0.281798	+	0.488089i
$777$	−25.4356	−	12.8038i	−0.912496	−	0.459333i
$778$	6.40570	−	11.0950i	0.229655	−	0.397775i
$779$	8.05042	+	13.9437i	0.288436	+	0.499586i
$780$	4.50138	−	1.34220i	0.161175	−	0.0480586i
$781$	33.1478	−	57.4137i	1.18612	−	2.05442i
$782$	2.84524			0.101746
$783$	−0.243381	+	0.421549i	−0.00869773	+	0.0150649i
$784$	2.78447	−	6.42236i	0.0994454	−	0.229370i
$785$	−26.8003			−0.956544
$786$	−4.63340	+	8.02529i	−0.165268	+	0.286253i
$787$	−17.6003			−0.627383			−0.313691	−	0.949525i	$-0.601566\pi$
$787$	−17.6003			−0.627383			−0.313691	+	0.949525i	$0.601566\pi$
$788$	7.08968	−	12.2797i	0.252560	−	0.437446i
$789$	9.39720	−	16.2764i	0.334549	−	0.579456i
$790$	7.75969	−	13.4402i	0.276078	−	0.478180i
$791$	−30.0995	−	15.1515i	−1.07021	−	0.538725i
$792$	−6.09231			−0.216481
$793$	7.73133	−	2.30530i	0.274547	−	0.0818636i
$794$	−2.21764	+	3.84107i	−0.0787012	+	0.136314i
$795$	8.13552	+	14.0911i	0.288537	+	0.499761i
$796$	3.49202			0.123771
$797$	−6.78755	−	11.7564i	−0.240427	−	0.416432i	0.720409	−	0.693550i	$-0.243954\pi$
$797$	−6.78755	−	11.7564i	−0.240427	−	0.416432i	−0.960836	+	0.277117i	$0.910621\pi$
$798$	−3.69543	+	2.42562i	−0.130817	+	0.0858659i
$799$	−22.9220	−	39.7021i	−0.810922	−	1.40456i
$800$	−1.65139	+	2.86029i	−0.0583854	+	0.101126i
$801$	3.84999	−	6.66838i	0.136033	−	0.235616i
$802$	−23.0982			−0.815626
$803$	−29.7547			−1.05002
$804$	1.07770	−	1.86663i	0.0380075	−	0.0658309i
$805$	−2.51231	−	1.26465i	−0.0885471	−	0.0445729i
$806$	−1.77335	+	0.528771i	−0.0624636	+	0.0186252i
$807$	−13.8198	−	23.9366i	−0.486481	−	0.842610i
$808$	−8.19386	−	14.1922i	−0.288259	−	0.499279i
$809$	−11.2134	−	19.4222i	−0.394243	−	0.682848i	0.598762	−	0.800927i	$-0.295660\pi$
$809$	−11.2134	−	19.4222i	−0.394243	−	0.682848i	−0.993004	+	0.118079i	$0.962326\pi$
$810$	−0.651388	+	1.12824i	−0.0228874	+	0.0396422i
$811$	21.9668			0.771358			0.385679	−	0.922633i	$-0.373967\pi$
$811$	21.9668			0.771358			0.385679	+	0.922633i	$0.373967\pi$
$812$	0.0736899	+	1.28574i	0.00258601	+	0.0451207i
$813$	5.87942	+	10.1834i	0.206200	+	0.357149i
$814$	32.7860	+	56.7870i	1.14915	+	1.99038i
$815$	−13.7000			−0.479889
$816$	−1.74338	−	3.01962i	−0.0610305	−	0.105708i
$817$	20.0501			0.701463
$818$	19.9354			0.697026
$819$	−6.14664	+	7.29512i	−0.214781	+	0.254912i
$820$	12.5547			0.438430
$821$	−29.8628			−1.04222			−0.521109	−	0.853490i	$-0.674481\pi$
$821$	−29.8628			−1.04222			−0.521109	+	0.853490i	$0.674481\pi$
$822$	5.15277	+	8.92485i	0.179723	+	0.311290i
$823$	20.9905			0.731683			0.365842	−	0.930677i	$-0.380781\pi$
$823$	20.9905			0.731683			0.365842	+	0.930677i	$0.380781\pi$
$824$	−2.45785	−	4.25712i	−0.0856233	−	0.148304i
$825$	10.0608	+	17.4258i	0.350271	+	0.606687i
$826$	−20.2386	+	13.2843i	−0.704192	+	0.462220i
$827$	18.3637			0.638570			0.319285	−	0.947659i	$-0.396557\pi$
$827$	18.3637			0.638570			0.319285	+	0.947659i	$0.396557\pi$
$828$	0.408007	−	0.706688i	0.0141792	−	0.0245591i
$829$	5.29092	+	9.16414i	0.183761	+	0.318284i	0.943158	−	0.332344i	$-0.107839\pi$
$829$	5.29092	+	9.16414i	0.183761	+	0.318284i	−0.759397	+	0.650627i	$0.774506\pi$
$830$	0.317071	+	0.549183i	0.0110057	+	0.0190624i
$831$	14.5320	+	25.1701i	0.504109	+	0.873142i
$832$	2.61985	+	2.47718i	0.0908268	+	0.0858806i
$833$	9.70879	−	22.3932i	0.336390	−	0.775880i
$834$	0.106609	−	0.184652i	0.00369157	−	0.00639398i
$835$	−9.00000			−0.311458
$836$	10.1787			0.352039
$837$	0.256619	−	0.444477i	0.00887005	−	0.0153634i
$838$	−3.23489	+	5.60299i	−0.111747	+	0.193552i
$839$	21.7428	+	37.6596i	0.750644	+	1.30015i	0.947511	+	0.319723i	$0.103590\pi$
$839$	21.7428	+	37.6596i	0.750644	+	1.30015i	−0.196867	+	0.980430i	$0.563077\pi$
$840$	0.197224	+	3.44117i	0.00680489	+	0.118732i
$841$	14.3815	+	24.9095i	0.495915	+	0.858950i
$842$	6.65600			0.229381
$843$	2.88153	+	4.99096i	0.0992452	+	0.171898i
$844$	6.56109	−	11.3641i	0.225842	−	0.391170i
$845$	−14.1704	+	9.27523i	−0.487478	+	0.319078i
$846$	−13.1480			−0.452038
$847$	3.95369	+	68.9840i	0.135850	+	2.37032i
$848$	−6.24476	+	10.8162i	−0.214446	+	0.371431i
$849$	3.36060	−	5.82073i	0.115335	−	0.199767i
$850$	−5.75800	+	9.97314i	−0.197498	+	0.342076i
$851$	−8.78280			−0.301071
$852$	5.44093	−	9.42396i	0.186403	−	0.322860i
$853$	−46.4055			−1.58889			−0.794447	−	0.607334i	$-0.792239\pi$
$853$	−46.4055			−1.58889			−0.794447	+	0.607334i	$0.792239\pi$
$854$	0.338742	+	5.91038i	0.0115915	+	0.202249i
$855$	1.08831	−	1.88500i	0.0372193	−	0.0644657i
$856$	4.87910			0.166764
$857$	9.30499	−	16.1167i	0.317852	−	0.550536i	−0.662187	−	0.749338i	$-0.730372\pi$
$857$	9.30499	−	16.1167i	0.317852	−	0.550536i	0.980040	+	0.198802i	$0.0637050\pi$
$858$	21.0503	−	6.27670i	0.718645	−	0.214283i
$859$	−3.56395	−	6.17293i	−0.121600	−	0.210618i	0.798799	−	0.601598i	$-0.205469\pi$
$859$	−3.56395	−	6.17293i	−0.121600	−	0.210618i	−0.920399	+	0.390981i	$0.872136\pi$
$860$	7.81707	−	13.5396i	0.266560	−	0.461695i
$861$	−21.3153	+	13.9910i	−0.726423	+	0.476811i
$862$	6.66495	+	11.5440i	0.227009	+	0.393191i
$863$	−0.989392	−	1.71368i	−0.0336793	−	0.0583343i	0.848694	−	0.528883i	$-0.177389\pi$
$863$	−0.989392	−	1.71368i	−0.0336793	−	0.0583343i	−0.882374	+	0.470549i	$0.844056\pi$
$864$	−1.00000			−0.0340207
$865$	−7.03051			−0.239045
$866$	−3.01693	−	5.22547i	−0.102519	−	0.177569i
$867$	2.42124	+	4.19372i	0.0822298	+	0.142426i
$868$	−0.0776979	−	1.35567i	−0.00263724	−	0.0460146i
$869$	36.2875	−	62.8518i	1.23097	−	2.13210i
$870$	−0.317071	−	0.549183i	−0.0107497	−	0.0186191i
$871$	−1.80056	+	7.55993i	−0.0610097	+	0.256158i
$872$	5.50000	−	9.52628i	0.186254	−	0.322601i
$873$	15.7000			0.531364
$874$	−0.681677	+	1.18070i	−0.0230581	+	0.0399377i
$875$	23.9247	−	15.7038i	0.808803	−	0.530884i
$876$	−4.88397			−0.165014
$877$	15.1512	−	26.2426i	0.511619	−	0.886151i	−0.488290	−	0.872682i	$-0.662379\pi$
$877$	15.1512	−	26.2426i	0.511619	−	0.886151i	0.999909	−	0.0134694i	$-0.00428756\pi$
$878$	−7.65324			−0.258284
$879$	2.99769	−	5.19215i	0.101110	−	0.175127i
$880$	3.96846	−	6.87357i	0.133777	−	0.231708i
$881$	−4.15581	+	7.19808i	−0.140013	+	0.242509i	−0.927501	−	0.373820i	$-0.878048\pi$
$881$	−4.15581	+	7.19808i	−0.140013	+	0.242509i	0.787488	+	0.616330i	$0.211381\pi$
$882$	−4.16969	−	5.62260i	−0.140401	−	0.189323i
$883$	−48.4829			−1.63158			−0.815790	−	0.578348i	$-0.803698\pi$
$883$	−48.4829			−1.63158			−0.815790	+	0.578348i	$0.803698\pi$
$884$	9.13478	+	8.63733i	0.307236	+	0.290505i
$885$	5.96029	−	10.3235i	0.200353	−	0.347021i
$886$	−13.2991	−	23.0347i	−0.446792	−	0.773866i
$887$	−13.9016			−0.466770			−0.233385	−	0.972384i	$-0.574980\pi$
$887$	−13.9016			−0.466770			−0.233385	+	0.972384i	$0.574980\pi$
$888$	5.38153	+	9.32109i	0.180592	+	0.312795i
$889$	1.80319	+	31.4621i	0.0604771	+	1.05521i
$890$	5.01567	+	8.68740i	0.168126	+	0.291202i
$891$	−3.04616	+	5.27610i	−0.102050	+	0.176756i
$892$	−4.92875	+	8.53684i	−0.165027	+	0.285834i
$893$	21.9670			0.735099
$894$	−12.0335			−0.402459
$895$	−2.03430	+	3.52351i	−0.0679990	+	0.117778i
$896$	−2.21184	+	1.45181i	−0.0738924	+	0.0485017i
$897$	−0.681677	+	2.86212i	−0.0227605	+	0.0955634i
$898$	0.721905	+	1.25038i	0.0240903	+	0.0417256i
$899$	0.124912	+	0.216355i	0.00416606	+	0.00721583i
$900$	1.65139	+	2.86029i	0.0550463	+	0.0953429i
$901$	−21.7740	+	37.7137i	−0.725397	+	1.25642i
$902$	58.7110			1.95486
$903$	1.81675	+	31.6987i	0.0604577	+	1.05487i
$904$	6.36829	+	11.0302i	0.211806	+	0.366859i
$905$	−13.7424	−	23.8026i	−0.456814	−	0.791226i
$906$	4.47939			0.148818
$907$	−17.7078	−	30.6708i	−0.587978	−	1.01841i	−0.994497	−	0.104765i	$-0.966591\pi$
$907$	−17.7078	−	30.6708i	−0.587978	−	1.01841i	0.406519	−	0.913642i	$-0.366742\pi$
$908$	−6.35912			−0.211035
$909$	−16.3877			−0.543546
$910$	−4.22678	−	11.6868i	−0.140116	−	0.387414i
$911$	−19.0938			−0.632605			−0.316303	−	0.948658i	$-0.602442\pi$
$911$	−19.0938			−0.632605			−0.316303	+	0.948658i	$0.602442\pi$
$912$	1.67075			0.0553240
$913$	1.48275	+	2.56821i	0.0490720	+	0.0849952i
$914$	23.3803			0.773353
$915$	−1.45753	−	2.52452i	−0.0481845	−	0.0834580i
$916$	−5.60767	−	9.71276i	−0.185283	−	0.320919i
$917$	21.8996	+	11.0238i	0.723188	+	0.364039i
$918$	−3.48676			−0.115080
$919$	12.5155	−	21.6774i	0.412847	−	0.715071i	−0.582353	−	0.812936i	$-0.697868\pi$
$919$	12.5155	−	21.6774i	0.412847	−	0.715071i	0.995200	+	0.0978646i	$0.0312012\pi$
$920$	0.531541	+	0.920656i	0.0175244	+	0.0303531i
$921$	−4.50170	−	7.79717i	−0.148336	−	0.256925i
$922$	−4.69123	−	8.12544i	−0.154497	−	0.267597i
$923$	−9.09042	+	38.1675i	−0.299215	+	1.25630i
$924$	0.922302	+	16.0923i	0.0303415	+	0.529399i
$925$	17.7740	−	30.7855i	0.584405	−	1.01222i
$926$	−16.0637			−0.527887
$927$	−4.91570			−0.161453
$928$	0.243381	−	0.421549i	0.00798938	−	0.0138380i
$929$	−28.9085	+	50.0709i	−0.948456	+	1.64277i	−0.199776	+	0.979842i	$0.564021\pi$
$929$	−28.9085	+	50.0709i	−0.948456	+	1.64277i	−0.748680	+	0.662932i	$0.769312\pi$
$930$	0.334317	+	0.579054i	0.0109627	+	0.0189879i
$931$	6.96651	+	9.39396i	0.228318	+	0.307875i
$932$	4.74845	+	8.22455i	0.155541	+	0.269404i
$933$	−14.6354			−0.479142
$934$	13.3195	+	23.0701i	0.435828	+	0.754875i
$935$	13.8371	−	23.9665i	0.452521	−	0.783789i
$936$	3.45522	−	1.03027i	0.112937	−	0.0336753i
$937$	−18.2900			−0.597509			−0.298754	−	0.954330i	$-0.596571\pi$
$937$	−18.2900			−0.597509			−0.298754	+	0.954330i	$0.596571\pi$
$938$	−5.09369	−	2.56406i	−0.166315	−	0.0837197i
$939$	1.72540	−	2.98848i	0.0563062	−	0.0975253i
$940$	8.56446	−	14.8341i	0.279342	−	0.483834i
$941$	3.43923	−	5.95692i	0.112116	−	0.194190i	−0.804507	−	0.593943i	$-0.797571\pi$
$941$	3.43923	−	5.95692i	0.112116	−	0.194190i	0.916623	+	0.399753i	$0.130904\pi$
$942$	−20.5717			−0.670262
$943$	−3.93192	+	6.81028i	−0.128041	+	0.221773i
$944$	9.15014			0.297812
$945$	3.07876	+	1.54979i	0.100152	+	0.0504145i
$946$	36.5558	−	63.3166i	1.18853	−	2.05860i
$947$	−51.7068			−1.68024			−0.840122	−	0.542397i	$-0.817517\pi$
$947$	−51.7068			−1.68024			−0.840122	+	0.542397i	$0.817517\pi$
$948$	5.95628	−	10.3166i	0.193451	−	0.335067i
$949$	16.8752	−	5.03178i	0.547792	−	0.163339i
$950$	−2.75905	−	4.77882i	−0.0895155	−	0.155045i
$951$	−6.67850	+	11.5675i	−0.216565	+	0.375102i
$952$	−7.71216	+	5.06213i	−0.249953	+	0.164065i
$953$	−6.62427	−	11.4736i	−0.214581	−	0.371666i	0.738562	−	0.674186i	$-0.235505\pi$
$953$	−6.62427	−	11.4736i	−0.214581	−	0.371666i	−0.953143	+	0.302520i	$0.902172\pi$
$954$	6.24476	+	10.8162i	0.202182	+	0.350189i
$955$	−7.30637			−0.236428
$956$	4.32714			0.139950
$957$	−1.48275	−	2.56821i	−0.0479306	−	0.0830183i
$958$	4.78765	+	8.29244i	0.154682	+	0.267917i
$959$	22.7942	−	14.9617i	0.736063	−	0.483139i
$960$	0.651388	−	1.12824i	0.0210235	−	0.0364137i
$961$	15.3683	+	26.6187i	0.495751	+	0.858667i
$962$	−28.1976	−	26.6620i	−0.909126	−	0.859618i
$963$	2.43955	−	4.22542i	0.0786133	−	0.136162i
$964$	17.1603			0.552695
$965$	4.99663	−	8.65442i	0.160847	−	0.278596i
$966$	−1.92843	−	0.970732i	−0.0620461	−	0.0312328i
$967$	−7.83352			−0.251909			−0.125955	−	0.992036i	$-0.540199\pi$
$967$	−7.83352			−0.251909			−0.125955	+	0.992036i	$0.540199\pi$
$968$	13.0581	−	22.6174i	0.419705	−	0.726950i
$969$	5.82550			0.187142
$970$	−10.2268	+	17.7133i	−0.328362	+	0.568740i
$971$	−12.2634	+	21.2408i	−0.393551	+	0.681650i	−0.992915	−	0.118827i	$-0.962087\pi$
$971$	−12.2634	+	21.2408i	−0.393551	+	0.681650i	0.599364	+	0.800476i	$0.295420\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−0.503882	−	0.253645i	−0.0161537	−	0.00813147i
$974$	−28.3232			−0.907532
$975$	−8.65277	−	8.18156i	−0.277110	−	0.262020i
$976$	1.11879	−	1.93780i	0.0358116	−	0.0620274i
$977$	9.74877	+	16.8854i	0.311891	+	0.540211i	0.978772	−	0.204954i	$-0.0657044\pi$
$977$	9.74877	+	16.8854i	0.311891	+	0.540211i	−0.666881	+	0.745164i	$0.732371\pi$
$978$	−10.5160			−0.336264
$979$	23.4553	+	40.6259i	0.749636	+	1.29841i
$980$	9.05971	−	1.04190i	0.289402	−	0.0332824i
$981$	−5.50000	−	9.52628i	−0.175601	−	0.304151i
$982$	16.2403	−	28.1291i	0.518250	−	0.897635i
$983$	−30.1235	+	52.1754i	−0.960789	+	1.66414i	−0.240264	+	0.970708i	$0.577234\pi$
$983$	−30.1235	+	52.1754i	−0.960789	+	1.66414i	−0.720526	+	0.693428i	$0.756099\pi$
$984$	9.63690			0.307213
$985$	18.4725			0.588584
$986$	0.848612	−	1.46984i	0.0270253	−	0.0468092i
$987$	1.99045	+	34.7294i	0.0633567	+	1.10545i
$988$	−5.77281	+	1.72131i	−0.183657	+	0.0547623i
$989$	4.89634	+	8.48071i	0.155695	+	0.269671i
$990$	−3.96846	−	6.87357i	−0.126126	−	0.218456i
$991$	−14.7955	−	25.6265i	−0.469993	−	0.814053i	0.529418	−	0.848361i	$-0.322410\pi$
$991$	−14.7955	−	25.6265i	−0.469993	−	0.814053i	−0.999411	+	0.0343086i	$0.989077\pi$
$992$	−0.256619	+	0.444477i	−0.00814766	+	0.0141122i
$993$	−3.43381			−0.108969
$994$	−25.7163	−	12.9451i	−0.815671	−	0.410593i
$995$	2.27466	+	3.93983i	0.0721116	+	0.124901i
$996$	0.243381	+	0.421549i	0.00771183	+	0.0133573i
$997$	41.3063			1.30818			0.654092	−	0.756415i	$-0.273051\pi$
$997$	41.3063			1.30818			0.654092	+	0.756415i	$0.273051\pi$
$998$	−5.41650	−	9.38165i	−0.171456	−	0.296971i
$999$	10.7631			0.340528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.b.529.4	yes	8
3.2	odd	2		1638.2.m.i.1621.2		8
7.2	even	3		546.2.k.d.373.3	yes	8
13.3	even	3		546.2.k.d.445.3	yes	8
21.2	odd	6		1638.2.p.g.919.1		8
39.29	odd	6		1638.2.p.g.991.1		8
91.16	even	3	inner	546.2.j.b.289.4	✓	8
273.107	odd	6		1638.2.m.i.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.b.289.4	✓	8	91.16	even	3	inner
546.2.j.b.529.4	yes	8	1.1	even	1	trivial
546.2.k.d.373.3	yes	8	7.2	even	3
546.2.k.d.445.3	yes	8	13.3	even	3
1638.2.m.i.289.2		8	273.107	odd	6
1638.2.m.i.1621.2		8	3.2	odd	2
1638.2.p.g.919.1		8	21.2	odd	6
1638.2.p.g.991.1		8	39.29	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 + 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 + 1.12824i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.651388 - 1.12824i) q^{10} +(-3.04616 - 5.27610i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.61985 + 2.47718i) q^{13} +(-2.21184 + 1.45181i) q^{14} +(0.651388 - 1.12824i) q^{15} +1.00000 q^{16} +3.48676 q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.835374 + 1.44691i) q^{19} +(0.651388 + 1.12824i) q^{20} +(-2.36323 - 1.18960i) q^{21} +(3.04616 + 5.27610i) q^{22} -0.816013 q^{23} +(0.500000 + 0.866025i) q^{24} +(1.65139 - 2.86029i) q^{25} +(-2.61985 - 2.47718i) q^{26} +1.00000 q^{27} +(2.21184 - 1.45181i) q^{28} +(-0.243381 + 0.421549i) q^{29} +(-0.651388 + 1.12824i) q^{30} +(0.256619 - 0.444477i) q^{31} -1.00000 q^{32} +(-3.04616 + 5.27610i) q^{33} -3.48676 q^{34} +(3.07876 + 1.54979i) q^{35} +(-0.500000 + 0.866025i) q^{36} +10.7631 q^{37} +(0.835374 - 1.44691i) q^{38} +(0.835374 - 3.50744i) q^{39} +(-0.651388 - 1.12824i) q^{40} +(4.81845 - 8.34580i) q^{41} +(2.36323 + 1.18960i) q^{42} +(-6.00032 - 10.3929i) q^{43} +(-3.04616 - 5.27610i) q^{44} -1.30278 q^{45} +0.816013 q^{46} +(-6.57401 - 11.3865i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(2.78447 - 6.42236i) q^{49} +(-1.65139 + 2.86029i) q^{50} +(-1.74338 - 3.01962i) q^{51} +(2.61985 + 2.47718i) q^{52} +(-6.24476 + 10.8162i) q^{53} -1.00000 q^{54} +(3.96846 - 6.87357i) q^{55} +(-2.21184 + 1.45181i) q^{56} +1.67075 q^{57} +(0.243381 - 0.421549i) q^{58} +9.15014 q^{59} +(0.651388 - 1.12824i) q^{60} +(1.11879 - 1.93780i) q^{61} +(-0.256619 + 0.444477i) q^{62} +(0.151388 + 2.64142i) q^{63} +1.00000 q^{64} +(-1.08831 + 4.56941i) q^{65} +(3.04616 - 5.27610i) q^{66} +(1.07770 + 1.86663i) q^{67} +3.48676 q^{68} +(0.408007 + 0.706688i) q^{69} +(-3.07876 - 1.54979i) q^{70} +(5.44093 + 9.42396i) q^{71} +(0.500000 - 0.866025i) q^{72} +(2.44198 - 4.22964i) q^{73} -10.7631 q^{74} -3.30278 q^{75} +(-0.835374 + 1.44691i) q^{76} +(-14.3975 - 7.24743i) q^{77} +(-0.835374 + 3.50744i) q^{78} +(5.95628 + 10.3166i) q^{79} +(0.651388 + 1.12824i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.81845 + 8.34580i) q^{82} -0.486762 q^{83} +(-2.36323 - 1.18960i) q^{84} +(2.27123 + 3.93389i) q^{85} +(6.00032 + 10.3929i) q^{86} +0.486762 q^{87} +(3.04616 + 5.27610i) q^{88} -7.69998 q^{89} +1.30278 q^{90} +(9.39108 + 1.67559i) q^{91} -0.816013 q^{92} -0.513238 q^{93} +(6.57401 + 11.3865i) q^{94} -2.17661 q^{95} +(0.500000 + 0.866025i) q^{96} +(-7.84999 - 13.5966i) q^{97} +(-2.78447 + 6.42236i) q^{98} +6.09231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} + 12 q^{17} + 4 q^{18} + 2 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} - 7 q^{26} + 8 q^{27} + 3 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} - 8 q^{32} - 2 q^{33} - 12 q^{34} + 8 q^{35} - 4 q^{36} + 24 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} + 4 q^{45} + 8 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} - 8 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} + 12 q^{65} + 2 q^{66} - 7 q^{67} + 12 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 4 q^{72} - 19 q^{73} - 24 q^{74} - 12 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} - 2 q^{80} - 4 q^{81} + 6 q^{82} + 12 q^{83} + 3 q^{84} - 3 q^{85} + 4 q^{86} - 12 q^{87} + 2 q^{88} + 14 q^{89} - 4 q^{90} + 40 q^{91} - 8 q^{92} - 20 q^{93} + 17 q^{94} + 24 q^{95} + 4 q^{96} - 25 q^{97} - 17 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 + 12 * q^17 + 4 * q^18 + 2 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 - 7 * q^26 + 8 * q^27 + 3 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 - 8 * q^32 - 2 * q^33 - 12 * q^34 + 8 * q^35 - 4 * q^36 + 24 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 + 4 * q^45 + 8 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 - 8 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 + 12 * q^65 + 2 * q^66 - 7 * q^67 + 12 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 4 * q^72 - 19 * q^73 - 24 * q^74 - 12 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 - 2 * q^80 - 4 * q^81 + 6 * q^82 + 12 * q^83 + 3 * q^84 - 3 * q^85 + 4 * q^86 - 12 * q^87 + 2 * q^88 + 14 * q^89 - 4 * q^90 + 40 * q^91 - 8 * q^92 - 20 * q^93 + 17 * q^94 + 24 * q^95 + 4 * q^96 - 25 * q^97 - 17 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more