LMFDB - Embedded newform 1014.2.e.m.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$0.222521 - 0.385418i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.m.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.356896 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.02446 - 3.50647i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.356896 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.02446 - 3.50647i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.178448 - 0.309081i) q^{10} +(-0.455927 - 0.789689i) q^{11} +1.00000 q^{12} +4.04892 q^{14} +(0.178448 + 0.309081i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.04892 - 1.81678i) q^{17} -1.00000 q^{18} +(-2.49396 + 4.31966i) q^{19} +(0.178448 - 0.309081i) q^{20} -4.04892 q^{21} +(0.455927 - 0.789689i) q^{22} +(-4.24698 - 7.35598i) q^{23} +(0.500000 + 0.866025i) q^{24} -4.87263 q^{25} +1.00000 q^{27} +(2.02446 + 3.50647i) q^{28} +(-4.25786 - 7.37484i) q^{29} +(-0.178448 + 0.309081i) q^{30} +10.7899 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.455927 + 0.789689i) q^{33} +2.09783 q^{34} +(-0.722521 + 1.25144i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.307979 - 0.533434i) q^{37} -4.98792 q^{38} +0.356896 q^{40} +(-3.80194 - 6.58515i) q^{41} +(-2.02446 - 3.50647i) q^{42} +(3.13706 - 5.43355i) q^{43} +0.911854 q^{44} +(0.178448 - 0.309081i) q^{45} +(4.24698 - 7.35598i) q^{46} -1.78017 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.69687 - 8.13521i) q^{49} +(-2.43631 - 4.21982i) q^{50} -2.09783 q^{51} +10.4112 q^{53} +(0.500000 + 0.866025i) q^{54} +(0.162718 + 0.281837i) q^{55} +(-2.02446 + 3.50647i) q^{56} +4.98792 q^{57} +(4.25786 - 7.37484i) q^{58} +(-3.02446 + 5.23852i) q^{59} -0.356896 q^{60} +(1.55496 - 2.69327i) q^{61} +(5.39493 + 9.34429i) q^{62} +(2.02446 + 3.50647i) q^{63} +1.00000 q^{64} -0.911854 q^{66} +(6.78986 + 11.7604i) q^{67} +(1.04892 + 1.81678i) q^{68} +(-4.24698 + 7.35598i) q^{69} -1.44504 q^{70} +(5.74094 - 9.94360i) q^{71} +(0.500000 - 0.866025i) q^{72} -0.533188 q^{73} +(0.307979 - 0.533434i) q^{74} +(2.43631 + 4.21982i) q^{75} +(-2.49396 - 4.31966i) q^{76} -3.69202 q^{77} -11.7071 q^{79} +(0.178448 + 0.309081i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.80194 - 6.58515i) q^{82} +6.49934 q^{83} +(2.02446 - 3.50647i) q^{84} +(-0.374354 + 0.648401i) q^{85} +6.27413 q^{86} +(-4.25786 + 7.37484i) q^{87} +(0.455927 + 0.789689i) q^{88} +(-3.24698 - 5.62393i) q^{89} +0.356896 q^{90} +8.49396 q^{92} +(-5.39493 - 9.34429i) q^{93} +(-0.890084 - 1.54167i) q^{94} +(0.890084 - 1.54167i) q^{95} -1.00000 q^{96} +(-0.980386 + 1.69808i) q^{97} +(4.69687 - 8.13521i) q^{98} +0.911854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} - 3 q^{16} - 12 q^{17} - 6 q^{18} + 4 q^{19} - 3 q^{20} - 6 q^{21} - q^{22} - 16 q^{23} + 3 q^{24} + 4 q^{25} + 6 q^{27} + 3 q^{28} - 13 q^{29} + 3 q^{30} + 18 q^{31} + 3 q^{32} + q^{33} - 24 q^{34} - 4 q^{35} - 3 q^{36} - 12 q^{37} + 8 q^{38} - 6 q^{40} - 14 q^{41} - 3 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 16 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{49} + 2 q^{50} + 24 q^{51} + 30 q^{53} + 3 q^{54} + 22 q^{55} - 3 q^{56} - 8 q^{57} + 13 q^{58} - 9 q^{59} + 6 q^{60} + 10 q^{61} + 9 q^{62} + 3 q^{63} + 6 q^{64} + 2 q^{66} - 6 q^{67} - 12 q^{68} - 16 q^{69} - 8 q^{70} + 6 q^{71} + 3 q^{72} - 10 q^{73} + 12 q^{74} - 2 q^{75} + 4 q^{76} - 12 q^{77} - 10 q^{79} - 3 q^{80} - 3 q^{81} + 14 q^{82} + 14 q^{83} + 3 q^{84} - 26 q^{85} + 16 q^{86} - 13 q^{87} - q^{88} - 10 q^{89} - 6 q^{90} + 32 q^{92} - 9 q^{93} - 4 q^{94} + 4 q^{95} - 6 q^{96} + 7 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 - 3 * q^16 - 12 * q^17 - 6 * q^18 + 4 * q^19 - 3 * q^20 - 6 * q^21 - q^22 - 16 * q^23 + 3 * q^24 + 4 * q^25 + 6 * q^27 + 3 * q^28 - 13 * q^29 + 3 * q^30 + 18 * q^31 + 3 * q^32 + q^33 - 24 * q^34 - 4 * q^35 - 3 * q^36 - 12 * q^37 + 8 * q^38 - 6 * q^40 - 14 * q^41 - 3 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 16 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^49 + 2 * q^50 + 24 * q^51 + 30 * q^53 + 3 * q^54 + 22 * q^55 - 3 * q^56 - 8 * q^57 + 13 * q^58 - 9 * q^59 + 6 * q^60 + 10 * q^61 + 9 * q^62 + 3 * q^63 + 6 * q^64 + 2 * q^66 - 6 * q^67 - 12 * q^68 - 16 * q^69 - 8 * q^70 + 6 * q^71 + 3 * q^72 - 10 * q^73 + 12 * q^74 - 2 * q^75 + 4 * q^76 - 12 * q^77 - 10 * q^79 - 3 * q^80 - 3 * q^81 + 14 * q^82 + 14 * q^83 + 3 * q^84 - 26 * q^85 + 16 * q^86 - 13 * q^87 - q^88 - 10 * q^89 - 6 * q^90 + 32 * q^92 - 9 * q^93 - 4 * q^94 + 4 * q^95 - 6 * q^96 + 7 * q^97 - 4 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	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
$5$	−0.356896			−0.159609			−0.0798043	−	0.996811i	$-0.525430\pi$
$5$	−0.356896			−0.159609			−0.0798043	+	0.996811i	$0.525430\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	2.02446	−	3.50647i	0.765173	−	1.32532i	−0.174981	−	0.984572i	$-0.555987\pi$
$7$	2.02446	−	3.50647i	0.765173	−	1.32532i	0.940155	−	0.340748i	$-0.110680\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.178448	−	0.309081i	−0.0564302	−	0.0977400i
$11$	−0.455927	−	0.789689i	−0.137467	−	0.238100i	0.789070	−	0.614303i	$-0.210563\pi$
$11$	−0.455927	−	0.789689i	−0.137467	−	0.238100i	−0.926537	+	0.376203i	$0.877229\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	4.04892			1.08212
$15$	0.178448	+	0.309081i	0.0460751	+	0.0798043i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.04892	−	1.81678i	0.254400	−	0.440633i	−0.710333	−	0.703866i	$-0.751455\pi$
$17$	1.04892	−	1.81678i	0.254400	−	0.440633i	0.964732	+	0.263233i	$0.0847888\pi$
$18$	−1.00000			−0.235702
$19$	−2.49396	+	4.31966i	−0.572153	+	0.990999i	0.424191	+	0.905573i	$0.360559\pi$
$19$	−2.49396	+	4.31966i	−0.572153	+	0.990999i	−0.996345	+	0.0854262i	$0.972775\pi$
$20$	0.178448	−	0.309081i	0.0399022	−	0.0691126i
$21$	−4.04892			−0.883546
$22$	0.455927	−	0.789689i	0.0972040	−	0.168362i
$23$	−4.24698	−	7.35598i	−0.885556	−	1.53383i	−0.845075	−	0.534649i	$-0.820444\pi$
$23$	−4.24698	−	7.35598i	−0.885556	−	1.53383i	−0.0404819	−	0.999180i	$-0.512889\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.87263			−0.974525
$26$		0			0
$27$	1.00000			0.192450
$28$	2.02446	+	3.50647i	0.382587	+	0.662660i
$29$	−4.25786	−	7.37484i	−0.790666	−	1.36947i	−0.925555	−	0.378612i	$-0.876401\pi$
$29$	−4.25786	−	7.37484i	−0.790666	−	1.36947i	0.134890	−	0.990861i	$-0.456932\pi$
$30$	−0.178448	+	0.309081i	−0.0325800	+	0.0564302i
$31$	10.7899			1.93792			0.968958	−	0.247227i	$-0.0795192\pi$
$31$	10.7899			1.93792			0.968958	+	0.247227i	$0.0795192\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.455927	+	0.789689i	−0.0793667	+	0.137467i
$34$	2.09783			0.359776
$35$	−0.722521	+	1.25144i	−0.122128	+	0.211532i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.307979	−	0.533434i	−0.0506314	−	0.0876961i	0.839599	−	0.543207i	$-0.182790\pi$
$37$	−0.307979	−	0.533434i	−0.0506314	−	0.0876961i	−0.890230	+	0.455511i	$0.849457\pi$
$38$	−4.98792			−0.809147
$39$		0			0
$40$	0.356896			0.0564302
$41$	−3.80194	−	6.58515i	−0.593763	−	1.02843i	−0.993720	−	0.111894i	$-0.964308\pi$
$41$	−3.80194	−	6.58515i	−0.593763	−	1.02843i	0.399957	−	0.916534i	$-0.369025\pi$
$42$	−2.02446	−	3.50647i	−0.312381	−	0.541059i
$43$	3.13706	−	5.43355i	0.478398	−	0.828609i	−0.521296	−	0.853376i	$-0.674551\pi$
$43$	3.13706	−	5.43355i	0.478398	−	0.828609i	0.999693	+	0.0247671i	$0.00788442\pi$
$44$	0.911854			0.137467
$45$	0.178448	−	0.309081i	0.0266014	−	0.0460751i
$46$	4.24698	−	7.35598i	0.626183	−	1.08458i
$47$	−1.78017			−0.259664			−0.129832	−	0.991536i	$-0.541444\pi$
$47$	−1.78017			−0.259664			−0.129832	+	0.991536i	$0.541444\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−4.69687	−	8.13521i	−0.670981	−	1.16217i
$50$	−2.43631	−	4.21982i	−0.344547	−	0.596772i
$51$	−2.09783			−0.293756
$52$		0			0
$53$	10.4112			1.43009			0.715043	−	0.699080i	$-0.246407\pi$
$53$	10.4112			1.43009			0.715043	+	0.699080i	$0.246407\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	0.162718	+	0.281837i	0.0219410	+	0.0380028i
$56$	−2.02446	+	3.50647i	−0.270530	+	0.468571i
$57$	4.98792			0.660666
$58$	4.25786	−	7.37484i	0.559085	−	0.968364i
$59$	−3.02446	+	5.23852i	−0.393751	+	0.681997i	−0.992941	−	0.118610i	$-0.962156\pi$
$59$	−3.02446	+	5.23852i	−0.393751	+	0.681997i	0.599190	+	0.800607i	$0.295489\pi$
$60$	−0.356896			−0.0460751
$61$	1.55496	−	2.69327i	0.199092	−	0.344837i	−0.749142	−	0.662409i	$-0.769534\pi$
$61$	1.55496	−	2.69327i	0.199092	−	0.344837i	0.948234	+	0.317572i	$0.102867\pi$
$62$	5.39493	+	9.34429i	0.685157	+	1.18673i
$63$	2.02446	+	3.50647i	0.255058	+	0.441773i
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.911854			−0.112241
$67$	6.78986	+	11.7604i	0.829513	+	1.43676i	0.898421	+	0.439136i	$0.144715\pi$
$67$	6.78986	+	11.7604i	0.829513	+	1.43676i	−0.0689079	+	0.997623i	$0.521951\pi$
$68$	1.04892	+	1.81678i	0.127200	+	0.220317i
$69$	−4.24698	+	7.35598i	−0.511276	+	0.885556i
$70$	−1.44504			−0.172716
$71$	5.74094	−	9.94360i	0.681324	−	1.18009i	−0.293253	−	0.956035i	$-0.594738\pi$
$71$	5.74094	−	9.94360i	0.681324	−	1.18009i	0.974577	−	0.224053i	$-0.0719289\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−0.533188			−0.0624049			−0.0312025	−	0.999513i	$-0.509934\pi$
$73$	−0.533188			−0.0624049			−0.0312025	+	0.999513i	$0.509934\pi$
$74$	0.307979	−	0.533434i	0.0358018	−	0.0620105i
$75$	2.43631	+	4.21982i	0.281321	+	0.487263i
$76$	−2.49396	−	4.31966i	−0.286077	−	0.495499i
$77$	−3.69202			−0.420745
$78$		0			0
$79$	−11.7071			−1.31715			−0.658575	−	0.752515i	$-0.728841\pi$
$79$	−11.7071			−1.31715			−0.658575	+	0.752515i	$0.728841\pi$
$80$	0.178448	+	0.309081i	0.0199511	+	0.0345563i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.80194	−	6.58515i	0.419854	−	0.727208i
$83$	6.49934			0.713395			0.356697	−	0.934220i	$-0.383903\pi$
$83$	6.49934			0.713395			0.356697	+	0.934220i	$0.383903\pi$
$84$	2.02446	−	3.50647i	0.220887	−	0.382587i
$85$	−0.374354	+	0.648401i	−0.0406044	+	0.0703289i
$86$	6.27413			0.676556
$87$	−4.25786	+	7.37484i	−0.456491	+	0.790666i
$88$	0.455927	+	0.789689i	0.0486020	+	0.0841811i
$89$	−3.24698	−	5.62393i	−0.344179	−	0.596136i	0.641025	−	0.767520i	$-0.278509\pi$
$89$	−3.24698	−	5.62393i	−0.344179	−	0.596136i	−0.985204	+	0.171384i	$0.945176\pi$
$90$	0.356896			0.0376201
$91$		0			0
$92$	8.49396			0.885556
$93$	−5.39493	−	9.34429i	−0.559428	−	0.968958i
$94$	−0.890084	−	1.54167i	−0.0918051	−	0.159011i
$95$	0.890084	−	1.54167i	0.0913207	−	0.158172i
$96$	−1.00000			−0.102062
$97$	−0.980386	+	1.69808i	−0.0995431	+	0.172414i	−0.911496	−	0.411310i	$-0.865071\pi$
$97$	−0.980386	+	1.69808i	−0.0995431	+	0.172414i	0.811953	+	0.583723i	$0.198405\pi$
$98$	4.69687	−	8.13521i	0.474455	−	0.821780i
$99$	0.911854			0.0916448
$100$	2.43631	−	4.21982i	0.243631	−	0.421982i
$101$	−3.49127	−	6.04706i	−0.347394	−	0.601705i	0.638391	−	0.769712i	$-0.279600\pi$
$101$	−3.49127	−	6.04706i	−0.347394	−	0.601705i	−0.985786	+	0.168007i	$0.946267\pi$
$102$	−1.04892	−	1.81678i	−0.103858	−	0.179888i
$103$	4.94869			0.487609			0.243804	−	0.969824i	$-0.421604\pi$
$103$	4.94869			0.487609			0.243804	+	0.969824i	$0.421604\pi$
$104$		0			0
$105$	1.44504			0.141022
$106$	5.20560	+	9.01636i	0.505612	+	0.875746i
$107$	2.13437	+	3.69685i	0.206338	+	0.357388i	0.950558	−	0.310547i	$-0.100512\pi$
$107$	2.13437	+	3.69685i	0.206338	+	0.357388i	−0.744220	+	0.667934i	$0.767179\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	6.21983			0.595752			0.297876	−	0.954605i	$-0.403722\pi$
$109$	6.21983			0.595752			0.297876	+	0.954605i	$0.403722\pi$
$110$	−0.162718	+	0.281837i	−0.0155146	+	0.0268721i
$111$	−0.307979	+	0.533434i	−0.0292320	+	0.0506314i
$112$	−4.04892			−0.382587
$113$	−6.49396	+	11.2479i	−0.610900	+	1.05811i	0.380189	+	0.924909i	$0.375859\pi$
$113$	−6.49396	+	11.2479i	−0.610900	+	1.05811i	−0.991089	+	0.133201i	$0.957474\pi$
$114$	2.49396	+	4.31966i	0.233581	+	0.404574i
$115$	1.51573	+	2.62532i	0.141343	+	0.244812i
$116$	8.51573			0.790666
$117$		0			0
$118$	−6.04892			−0.556848
$119$	−4.24698	−	7.35598i	−0.389320	−	0.674322i
$120$	−0.178448	−	0.309081i	−0.0162900	−	0.0282151i
$121$	5.08426	−	8.80620i	0.462206	−	0.800564i
$122$	3.10992			0.281559
$123$	−3.80194	+	6.58515i	−0.342809	+	0.593763i
$124$	−5.39493	+	9.34429i	−0.484479	+	0.839142i
$125$	3.52350			0.315151
$126$	−2.02446	+	3.50647i	−0.180353	+	0.312381i
$127$	−4.61141	−	7.98719i	−0.409196	−	0.708749i	0.585604	−	0.810598i	$-0.300858\pi$
$127$	−4.61141	−	7.98719i	−0.409196	−	0.708749i	−0.994800	+	0.101849i	$0.967524\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.27413			−0.552406
$130$		0			0
$131$	−14.5526			−1.27146			−0.635732	−	0.771910i	$-0.719302\pi$
$131$	−14.5526			−1.27146			−0.635732	+	0.771910i	$0.719302\pi$
$132$	−0.455927	−	0.789689i	−0.0396834	−	0.0687336i
$133$	10.0978	+	17.4900i	0.875593	+	1.51657i
$134$	−6.78986	+	11.7604i	−0.586554	+	1.01594i
$135$	−0.356896			−0.0307167
$136$	−1.04892	+	1.81678i	−0.0899439	+	0.155787i
$137$	−7.70171	+	13.3398i	−0.658002	+	1.13969i	0.323131	+	0.946354i	$0.395265\pi$
$137$	−7.70171	+	13.3398i	−0.658002	+	1.13969i	−0.981132	+	0.193338i	$0.938069\pi$
$138$	−8.49396			−0.723054
$139$	−1.35690	+	2.35021i	−0.115090	+	0.199342i	−0.917816	−	0.397006i	$-0.870049\pi$
$139$	−1.35690	+	2.35021i	−0.115090	+	0.199342i	0.802725	+	0.596349i	$0.203382\pi$
$140$	−0.722521	−	1.25144i	−0.0610642	−	0.105766i
$141$	0.890084	+	1.54167i	0.0749586	+	0.129832i
$142$	11.4819			0.963538
$143$		0			0
$144$	1.00000			0.0833333
$145$	1.51961	+	2.63205i	0.126197	+	0.218580i
$146$	−0.266594	−	0.461754i	−0.0220635	−	0.0382151i
$147$	−4.69687	+	8.13521i	−0.387391	+	0.670981i
$148$	0.615957			0.0506314
$149$	−7.36778	+	12.7614i	−0.603592	+	1.04545i	0.388680	+	0.921373i	$0.372931\pi$
$149$	−7.36778	+	12.7614i	−0.603592	+	1.04545i	−0.992272	+	0.124079i	$0.960402\pi$
$150$	−2.43631	+	4.21982i	−0.198924	+	0.344547i
$151$	15.8213			1.28752			0.643760	−	0.765227i	$-0.277373\pi$
$151$	15.8213			1.28752			0.643760	+	0.765227i	$0.277373\pi$
$152$	2.49396	−	4.31966i	0.202287	−	0.350371i
$153$	1.04892	+	1.81678i	0.0847999	+	0.146878i
$154$	−1.84601	−	3.19738i	−0.148756	−	0.257653i
$155$	−3.85086			−0.309308
$156$		0			0
$157$	−4.27413			−0.341112			−0.170556	−	0.985348i	$-0.554556\pi$
$157$	−4.27413			−0.341112			−0.170556	+	0.985348i	$0.554556\pi$
$158$	−5.85354	−	10.1386i	−0.465683	−	0.806586i
$159$	−5.20560	−	9.01636i	−0.412831	−	0.715043i
$160$	−0.178448	+	0.309081i	−0.0141075	+	0.0244350i
$161$	−34.3913			−2.71042
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−0.158834	+	0.275108i	−0.0124408	+	0.0215481i	−0.872179	−	0.489187i	$-0.837293\pi$
$163$	−0.158834	+	0.275108i	−0.0124408	+	0.0215481i	0.859738	+	0.510735i	$0.170627\pi$
$164$	7.60388			0.593763
$165$	0.162718	−	0.281837i	0.0126676	−	0.0219410i
$166$	3.24967	+	5.62859i	0.252223	+	0.436863i
$167$	6.18060	+	10.7051i	0.478269	+	0.828387i	0.999690	−	0.0249130i	$-0.00793089\pi$
$167$	6.18060	+	10.7051i	0.478269	+	0.828387i	−0.521420	+	0.853300i	$0.674598\pi$
$168$	4.04892			0.312381
$169$		0			0
$170$	−0.748709			−0.0574233
$171$	−2.49396	−	4.31966i	−0.190718	−	0.330333i
$172$	3.13706	+	5.43355i	0.239199	+	0.414305i
$173$	8.53199	−	14.7778i	0.648675	−	1.12354i	−0.334764	−	0.942302i	$-0.608657\pi$
$173$	8.53199	−	14.7778i	0.648675	−	1.12354i	0.983440	−	0.181237i	$-0.0580100\pi$
$174$	−8.51573			−0.645576
$175$	−9.86443	+	17.0857i	−0.745681	+	1.29156i
$176$	−0.455927	+	0.789689i	−0.0343668	+	0.0595250i
$177$	6.04892			0.454664
$178$	3.24698	−	5.62393i	0.243371	−	0.421532i
$179$	12.4840	+	21.6230i	0.933100	+	1.61618i	0.777987	+	0.628281i	$0.216241\pi$
$179$	12.4840	+	21.6230i	0.933100	+	1.61618i	0.155114	+	0.987897i	$0.450426\pi$
$180$	0.178448	+	0.309081i	0.0133007	+	0.0230375i
$181$	5.26205			0.391125			0.195562	−	0.980691i	$-0.437347\pi$
$181$	5.26205			0.391125			0.195562	+	0.980691i	$0.437347\pi$
$182$		0			0
$183$	−3.10992			−0.229892
$184$	4.24698	+	7.35598i	0.313091	+	0.542290i
$185$	0.109916	+	0.190381i	0.00808120	+	0.0139971i
$186$	5.39493	−	9.34429i	0.395575	−	0.685157i
$187$	−1.91292			−0.139886
$188$	0.890084	−	1.54167i	0.0649160	−	0.112438i
$189$	2.02446	−	3.50647i	0.147258	−	0.255058i
$190$	1.78017			0.129147
$191$	−5.26875	+	9.12574i	−0.381233	+	0.660316i	−0.991239	−	0.132082i	$-0.957834\pi$
$191$	−5.26875	+	9.12574i	−0.381233	+	0.660316i	0.610005	+	0.792397i	$0.291167\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	1.71379	+	2.96837i	0.123361	+	0.213668i	0.921091	−	0.389347i	$-0.127299\pi$
$193$	1.71379	+	2.96837i	0.123361	+	0.213668i	−0.797730	+	0.603015i	$0.793966\pi$
$194$	−1.96077			−0.140775
$195$		0			0
$196$	9.39373			0.670981
$197$	1.88740	+	3.26906i	0.134471	+	0.232911i	0.925395	−	0.379003i	$-0.123733\pi$
$197$	1.88740	+	3.26906i	0.134471	+	0.232911i	−0.790924	+	0.611914i	$0.790400\pi$
$198$	0.455927	+	0.789689i	0.0324013	+	0.0561207i
$199$	−8.97703	+	15.5487i	−0.636365	+	1.10222i	0.349859	+	0.936802i	$0.386229\pi$
$199$	−8.97703	+	15.5487i	−0.636365	+	1.10222i	−0.986224	+	0.165414i	$0.947104\pi$
$200$	4.87263			0.344547
$201$	6.78986	−	11.7604i	0.478920	−	0.829513i
$202$	3.49127	−	6.04706i	0.245645	−	0.425470i
$203$	−34.4795			−2.41999
$204$	1.04892	−	1.81678i	0.0734389	−	0.127200i
$205$	1.35690	+	2.35021i	0.0947697	+	0.164146i
$206$	2.47434	+	4.28569i	0.172396	+	0.298598i
$207$	8.49396			0.590371
$208$		0			0
$209$	4.54825			0.314609
$210$	0.722521	+	1.25144i	0.0498587	+	0.0863578i
$211$	6.26875	+	10.8578i	0.431559	+	0.747481i	0.997008	−	0.0773018i	$-0.0246305\pi$
$211$	6.26875	+	10.8578i	0.431559	+	0.747481i	−0.565449	+	0.824783i	$0.691297\pi$
$212$	−5.20560	+	9.01636i	−0.357522	+	0.619246i
$213$	−11.4819			−0.786725
$214$	−2.13437	+	3.69685i	−0.145903	+	0.252711i
$215$	−1.11960	+	1.93921i	−0.0763564	+	0.132253i
$216$	−1.00000			−0.0680414
$217$	21.8436	−	37.8343i	1.48284	−	2.56836i
$218$	3.10992	+	5.38653i	0.210630	+	0.364822i
$219$	0.266594	+	0.461754i	0.0180147	+	0.0312025i
$220$	−0.325437			−0.0219410
$221$		0			0
$222$	−0.615957			−0.0413403
$223$	2.71379	+	4.70043i	0.181729	+	0.314764i	0.942469	−	0.334292i	$-0.108497\pi$
$223$	2.71379	+	4.70043i	0.181729	+	0.314764i	−0.760740	+	0.649056i	$0.775164\pi$
$224$	−2.02446	−	3.50647i	−0.135265	−	0.234286i
$225$	2.43631	−	4.21982i	0.162421	−	0.281321i
$226$	−12.9879			−0.863943
$227$	8.28836	−	14.3559i	0.550118	−	0.952832i	−0.448147	−	0.893960i	$-0.647916\pi$
$227$	8.28836	−	14.3559i	0.550118	−	0.952832i	0.998265	−	0.0588728i	$-0.0187506\pi$
$228$	−2.49396	+	4.31966i	−0.165166	+	0.286077i
$229$	23.8780			1.57790			0.788951	−	0.614456i	$-0.210624\pi$
$229$	23.8780			1.57790			0.788951	+	0.614456i	$0.210624\pi$
$230$	−1.51573	+	2.62532i	−0.0999442	+	0.173109i
$231$	1.84601	+	3.19738i	0.121459	+	0.210372i
$232$	4.25786	+	7.37484i	0.279543	+	0.484182i
$233$	13.9952			0.916857			0.458428	−	0.888731i	$-0.348413\pi$
$233$	13.9952			0.916857			0.458428	+	0.888731i	$0.348413\pi$
$234$		0			0
$235$	0.635334			0.0414446
$236$	−3.02446	−	5.23852i	−0.196875	−	0.340998i
$237$	5.85354	+	10.1386i	0.380229	+	0.658575i
$238$	4.24698	−	7.35598i	0.275291	−	0.476818i
$239$	−13.2862			−0.859413			−0.429707	−	0.902969i	$-0.641383\pi$
$239$	−13.2862			−0.859413			−0.429707	+	0.902969i	$0.641383\pi$
$240$	0.178448	−	0.309081i	0.0115188	−	0.0199511i
$241$	5.23945	−	9.07499i	0.337502	−	0.584571i	−0.646460	−	0.762948i	$-0.723751\pi$
$241$	5.23945	−	9.07499i	0.337502	−	0.584571i	0.983962	+	0.178377i	$0.0570845\pi$
$242$	10.1685			0.653657
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.55496	+	2.69327i	0.0995460	+	0.172419i
$245$	1.67629	+	2.90342i	0.107094	+	0.185493i
$246$	−7.60388			−0.484805
$247$		0			0
$248$	−10.7899			−0.685157
$249$	−3.24967	−	5.62859i	−0.205939	−	0.356697i
$250$	1.76175	+	3.05144i	0.111423	+	0.192990i
$251$	−1.74363	+	3.02005i	−0.110057	+	0.190624i	−0.915793	−	0.401651i	$-0.868437\pi$
$251$	−1.74363	+	3.02005i	−0.110057	+	0.190624i	0.805736	+	0.592275i	$0.201770\pi$
$252$	−4.04892			−0.255058
$253$	−3.87263	+	6.70758i	−0.243470	+	0.421702i
$254$	4.61141	−	7.98719i	0.289345	−	0.501161i
$255$	0.748709			0.0468859
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.26875	−	5.66164i	−0.203899	−	0.353163i	0.745882	−	0.666078i	$-0.232028\pi$
$257$	−3.26875	−	5.66164i	−0.203899	−	0.353163i	−0.949781	+	0.312914i	$0.898695\pi$
$258$	−3.13706	−	5.43355i	−0.195305	−	0.338278i
$259$	−2.49396			−0.154967
$260$		0			0
$261$	8.51573			0.527110
$262$	−7.27628	−	12.6029i	−0.449530	−	0.778609i
$263$	−4.00969	−	6.94498i	−0.247248	−	0.428246i	0.715513	−	0.698599i	$-0.246193\pi$
$263$	−4.00969	−	6.94498i	−0.247248	−	0.428246i	−0.962761	+	0.270353i	$0.912860\pi$
$264$	0.455927	−	0.789689i	0.0280604	−	0.0486020i
$265$	−3.71571			−0.228254
$266$	−10.0978	+	17.4900i	−0.619138	+	1.07238i
$267$	−3.24698	+	5.62393i	−0.198712	+	0.344179i
$268$	−13.5797			−0.829513
$269$	13.8366	−	23.9657i	0.843633	−	1.46122i	−0.0431692	−	0.999068i	$-0.513745\pi$
$269$	13.8366	−	23.9657i	0.843633	−	1.46122i	0.886803	−	0.462148i	$-0.152921\pi$
$270$	−0.178448	−	0.309081i	−0.0108600	−	0.0188101i
$271$	7.36443	+	12.7556i	0.447357	+	0.774845i	0.998213	−	0.0597550i	$-0.0190319\pi$
$271$	7.36443	+	12.7556i	0.447357	+	0.774845i	−0.550856	+	0.834600i	$0.685699\pi$
$272$	−2.09783			−0.127200
$273$		0			0
$274$	−15.4034			−0.930555
$275$	2.22156	+	3.84786i	0.133965	+	0.232035i
$276$	−4.24698	−	7.35598i	−0.255638	−	0.442778i
$277$	−1.63102	+	2.82501i	−0.0979986	+	0.169739i	−0.910856	−	0.412724i	$-0.864577\pi$
$277$	−1.63102	+	2.82501i	−0.0979986	+	0.169739i	0.812858	+	0.582463i	$0.197911\pi$
$278$	−2.71379			−0.162762
$279$	−5.39493	+	9.34429i	−0.322986	+	0.559428i
$280$	0.722521	−	1.25144i	0.0431789	−	0.0747880i
$281$	−7.72587			−0.460887			−0.230443	−	0.973086i	$-0.574018\pi$
$281$	−7.72587			−0.460887			−0.230443	+	0.973086i	$0.574018\pi$
$282$	−0.890084	+	1.54167i	−0.0530037	+	0.0918051i
$283$	9.89008	+	17.1301i	0.587904	+	1.01828i	0.994506	+	0.104675i	$0.0333802\pi$
$283$	9.89008	+	17.1301i	0.587904	+	1.01828i	−0.406602	+	0.913605i	$0.633286\pi$
$284$	5.74094	+	9.94360i	0.340662	+	0.590044i
$285$	−1.78017			−0.105448
$286$		0			0
$287$	−30.7875			−1.81733
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	6.29954	+	10.9111i	0.370561	+	0.641831i
$290$	−1.51961	+	2.63205i	−0.0892348	+	0.154559i
$291$	1.96077			0.114942
$292$	0.266594	−	0.461754i	0.0156012	−	0.0270221i
$293$	−6.45593	+	11.1820i	−0.377159	+	0.653259i	−0.990648	−	0.136445i	$-0.956432\pi$
$293$	−6.45593	+	11.1820i	−0.377159	+	0.653259i	0.613488	+	0.789704i	$0.289766\pi$
$294$	−9.39373			−0.547854
$295$	1.07942	−	1.86960i	0.0628461	−	0.108853i
$296$	0.307979	+	0.533434i	0.0179009	+	0.0310052i
$297$	−0.455927	−	0.789689i	−0.0264556	−	0.0458224i
$298$	−14.7356			−0.853608
$299$		0			0
$300$	−4.87263			−0.281321
$301$	−12.7017	−	22.0000i	−0.732114	−	1.26806i
$302$	7.91066	+	13.7017i	0.455207	+	0.788442i
$303$	−3.49127	+	6.04706i	−0.200568	+	0.347394i
$304$	4.98792			0.286077
$305$	−0.554958	+	0.961216i	−0.0317768	+	0.0550390i
$306$	−1.04892	+	1.81678i	−0.0599626	+	0.103858i
$307$	−19.9651			−1.13947			−0.569734	−	0.821829i	$-0.692954\pi$
$307$	−19.9651			−1.13947			−0.569734	+	0.821829i	$0.692954\pi$
$308$	1.84601	−	3.19738i	0.105186	−	0.182188i
$309$	−2.47434	−	4.28569i	−0.140761	−	0.243804i
$310$	−1.92543	−	3.33494i	−0.109357	−	0.189412i
$311$	13.4819			0.764487			0.382244	−	0.924062i	$-0.375152\pi$
$311$	13.4819			0.764487			0.382244	+	0.924062i	$0.375152\pi$
$312$		0			0
$313$	12.9245			0.730537			0.365269	−	0.930902i	$-0.380977\pi$
$313$	12.9245			0.730537			0.365269	+	0.930902i	$0.380977\pi$
$314$	−2.13706	−	3.70150i	−0.120601	−	0.208888i
$315$	−0.722521	−	1.25144i	−0.0407094	−	0.0705108i
$316$	5.85354	−	10.1386i	0.329288	−	0.570343i
$317$	11.8726			0.666833			0.333417	−	0.942780i	$-0.391798\pi$
$317$	11.8726			0.666833			0.333417	+	0.942780i	$0.391798\pi$
$318$	5.20560	−	9.01636i	0.291915	−	0.505612i
$319$	−3.88255	+	6.72478i	−0.217381	+	0.376515i
$320$	−0.356896			−0.0199511
$321$	2.13437	−	3.69685i	0.119129	−	0.206338i
$322$	−17.1957	−	29.7838i	−0.958277	−	1.65978i
$323$	5.23191	+	9.06194i	0.291111	+	0.504220i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−0.317667			−0.0175940
$327$	−3.10992	−	5.38653i	−0.171979	−	0.297876i
$328$	3.80194	+	6.58515i	0.209927	+	0.363604i
$329$	−3.60388	+	6.24210i	−0.198688	+	0.344138i
$330$	0.325437			0.0179147
$331$	5.11960	−	8.86742i	0.281399	−	0.487397i	−0.690331	−	0.723494i	$-0.742535\pi$
$331$	5.11960	−	8.86742i	0.281399	−	0.487397i	0.971730	+	0.236097i	$0.0758682\pi$
$332$	−3.24967	+	5.62859i	−0.178349	+	0.308909i
$333$	0.615957			0.0337542
$334$	−6.18060	+	10.7051i	−0.338188	+	0.585758i
$335$	−2.42327	−	4.19723i	−0.132397	−	0.229319i
$336$	2.02446	+	3.50647i	0.110443	+	0.191293i
$337$	1.44935			0.0789513			0.0394757	−	0.999221i	$-0.487431\pi$
$337$	1.44935			0.0789513			0.0394757	+	0.999221i	$0.487431\pi$
$338$		0			0
$339$	12.9879			0.705407
$340$	−0.374354	−	0.648401i	−0.0203022	−	0.0351645i
$341$	−4.91939	−	8.52063i	−0.266400	−	0.461418i
$342$	2.49396	−	4.31966i	0.134858	−	0.233581i
$343$	−9.69202			−0.523320
$344$	−3.13706	+	5.43355i	−0.169139	+	0.292958i
$345$	1.51573	−	2.62532i	0.0816041	−	0.141343i
$346$	17.0640			0.917365
$347$	−3.42058	+	5.92462i	−0.183627	+	0.318050i	−0.943113	−	0.332473i	$-0.892117\pi$
$347$	−3.42058	+	5.92462i	−0.183627	+	0.318050i	0.759486	+	0.650523i	$0.225450\pi$
$348$	−4.25786	−	7.37484i	−0.228246	−	0.395333i
$349$	−17.1685	−	29.7368i	−0.919010	−	1.59177i	−0.800922	−	0.598769i	$-0.795657\pi$
$349$	−17.1685	−	29.7368i	−0.919010	−	1.59177i	−0.118088	−	0.993003i	$-0.537676\pi$
$350$	−19.7289			−1.05455
$351$		0			0
$352$	−0.911854			−0.0486020
$353$	13.0248	+	22.5595i	0.693238	+	1.20072i	0.970771	+	0.240007i	$0.0771497\pi$
$353$	13.0248	+	22.5595i	0.693238	+	1.20072i	−0.277533	+	0.960716i	$0.589517\pi$
$354$	3.02446	+	5.23852i	0.160748	+	0.278424i
$355$	−2.04892	+	3.54883i	−0.108745	+	0.188352i
$356$	6.49396			0.344179
$357$	−4.24698	+	7.35598i	−0.224774	+	0.389320i
$358$	−12.4840	+	21.6230i	−0.659802	+	1.14281i
$359$	−8.49396			−0.448294			−0.224147	−	0.974555i	$-0.571960\pi$
$359$	−8.49396			−0.448294			−0.224147	+	0.974555i	$0.571960\pi$
$360$	−0.178448	+	0.309081i	−0.00940503	+	0.0162900i
$361$	−2.93967	−	5.09165i	−0.154719	−	0.267982i
$362$	2.63102	+	4.55706i	0.138283	+	0.239514i
$363$	−10.1685			−0.533709
$364$		0			0
$365$	0.190293			0.00996037
$366$	−1.55496	−	2.69327i	−0.0812790	−	0.140779i
$367$	−13.7262	−	23.7744i	−0.716500	−	1.24101i	−0.962378	−	0.271714i	$-0.912410\pi$
$367$	−13.7262	−	23.7744i	−0.716500	−	1.24101i	0.245878	−	0.969301i	$-0.420924\pi$
$368$	−4.24698	+	7.35598i	−0.221389	+	0.383457i
$369$	7.60388			0.395842
$370$	−0.109916	+	0.190381i	−0.00571427	+	0.00989741i
$371$	21.0770	−	36.5065i	1.09426	−	1.89532i
$372$	10.7899			0.559428
$373$	−13.3110	+	23.0553i	−0.689216	+	1.19376i	0.282876	+	0.959156i	$0.408711\pi$
$373$	−13.3110	+	23.0553i	−0.689216	+	1.19376i	−0.972092	+	0.234600i	$0.924622\pi$
$374$	−0.956459	−	1.65664i	−0.0494573	−	0.0856626i
$375$	−1.76175	−	3.05144i	−0.0909764	−	0.157576i
$376$	1.78017			0.0918051
$377$		0			0
$378$	4.04892			0.208254
$379$	5.82371	+	10.0870i	0.299144	+	0.518132i	0.975940	−	0.218038i	$-0.0699656\pi$
$379$	5.82371	+	10.0870i	0.299144	+	0.518132i	−0.676797	+	0.736170i	$0.736632\pi$
$380$	0.890084	+	1.54167i	0.0456603	+	0.0790860i
$381$	−4.61141	+	7.98719i	−0.236250	+	0.409196i
$382$	−10.5375			−0.539145
$383$	5.25906	−	9.10896i	0.268725	−	0.465446i	−0.699807	−	0.714331i	$-0.746731\pi$
$383$	5.25906	−	9.10896i	0.268725	−	0.465446i	0.968533	+	0.248885i	$0.0800642\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	1.31767			0.0671545
$386$	−1.71379	+	2.96837i	−0.0872297	+	0.151086i
$387$	3.13706	+	5.43355i	0.159466	+	0.276203i
$388$	−0.980386	−	1.69808i	−0.0497715	−	0.0862068i
$389$	−9.25965			−0.469483			−0.234742	−	0.972058i	$-0.575424\pi$
$389$	−9.25965			−0.469483			−0.234742	+	0.972058i	$0.575424\pi$
$390$		0			0
$391$	−17.8189			−0.901142
$392$	4.69687	+	8.13521i	0.237228	+	0.410890i
$393$	7.27628	+	12.6029i	0.367040	+	0.635732i
$394$	−1.88740	+	3.26906i	−0.0950856	+	0.164693i
$395$	4.17821			0.210229
$396$	−0.455927	+	0.789689i	−0.0229112	+	0.0396834i
$397$	7.25667	−	12.5689i	0.364202	−	0.630816i	−0.624446	−	0.781068i	$-0.714675\pi$
$397$	7.25667	−	12.5689i	0.364202	−	0.630816i	0.988648	+	0.150252i	$0.0480085\pi$
$398$	−17.9541			−0.899956
$399$	10.0978	−	17.4900i	0.505524	−	0.875593i
$400$	2.43631	+	4.21982i	0.121816	+	0.210991i
$401$	−19.4209	−	33.6379i	−0.969832	−	1.67980i	−0.696030	−	0.718013i	$-0.745052\pi$
$401$	−19.4209	−	33.6379i	−0.969832	−	1.67980i	−0.273803	−	0.961786i	$-0.588282\pi$
$402$	13.5797			0.677294
$403$		0			0
$404$	6.98254			0.347394
$405$	0.178448	+	0.309081i	0.00886715	+	0.0153584i
$406$	−17.2397	−	29.8601i	−0.855594	−	1.48193i
$407$	−0.280831	+	0.486414i	−0.0139203	+	0.0241107i
$408$	2.09783			0.103858
$409$	16.9611	−	29.3774i	0.838671	−	1.45262i	−0.0523356	−	0.998630i	$-0.516667\pi$
$409$	16.9611	−	29.3774i	0.838671	−	1.45262i	0.891006	−	0.453991i	$-0.150000\pi$
$410$	−1.35690	+	2.35021i	−0.0670123	+	0.116069i
$411$	15.4034			0.759795
$412$	−2.47434	+	4.28569i	−0.121902	+	0.211141i
$413$	12.2458	+	21.2103i	0.602576	+	1.04369i
$414$	4.24698	+	7.35598i	0.208728	+	0.361527i
$415$	−2.31959			−0.113864
$416$		0			0
$417$	2.71379			0.132895
$418$	2.27413	+	3.93890i	0.111231	+	0.192658i
$419$	−0.477697	−	0.827396i	−0.0233370	−	0.0404209i	0.854121	−	0.520074i	$-0.174096\pi$
$419$	−0.477697	−	0.827396i	−0.0233370	−	0.0404209i	−0.877458	+	0.479653i	$0.840762\pi$
$420$	−0.722521	+	1.25144i	−0.0352554	+	0.0610642i
$421$	−5.68233			−0.276940			−0.138470	−	0.990367i	$-0.544218\pi$
$421$	−5.68233			−0.276940			−0.138470	+	0.990367i	$0.544218\pi$
$422$	−6.26875	+	10.8578i	−0.305158	+	0.528549i
$423$	0.890084	−	1.54167i	0.0432774	−	0.0749586i
$424$	−10.4112			−0.505612
$425$	−5.11098	+	8.85248i	−0.247919	+	0.429408i
$426$	−5.74094	−	9.94360i	−0.278149	−	0.481769i
$427$	−6.29590	−	10.9048i	−0.304680	−	0.527721i
$428$	−4.26875			−0.206338
$429$		0			0
$430$	−2.23921			−0.107984
$431$	7.42327	+	12.8575i	0.357566	+	0.619323i	0.987554	−	0.157282i	$-0.0502732\pi$
$431$	7.42327	+	12.8575i	0.357566	+	0.619323i	−0.629987	+	0.776605i	$0.716940\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	13.0749	−	22.6463i	0.628338	−	1.08831i	−0.359547	−	0.933127i	$-0.617069\pi$
$433$	13.0749	−	22.6463i	0.628338	−	1.08831i	0.987885	−	0.155187i	$-0.0495979\pi$
$434$	43.6872			2.09705
$435$	1.51961	−	2.63205i	0.0728599	−	0.126197i
$436$	−3.10992	+	5.38653i	−0.148938	+	0.257968i
$437$	42.3672			2.02670
$438$	−0.266594	+	0.461754i	−0.0127384	+	0.0220635i
$439$	11.7751	+	20.3950i	0.561994	+	0.973403i	0.997322	+	0.0731307i	$0.0232990\pi$
$439$	11.7751	+	20.3950i	0.561994	+	0.973403i	−0.435328	+	0.900272i	$0.643368\pi$
$440$	−0.162718	−	0.281837i	−0.00775730	−	0.0134360i
$441$	9.39373			0.447321
$442$		0			0
$443$	21.9433			1.04256			0.521279	−	0.853386i	$-0.325455\pi$
$443$	21.9433			1.04256			0.521279	+	0.853386i	$0.325455\pi$
$444$	−0.307979	−	0.533434i	−0.0146160	−	0.0253157i
$445$	1.15883	+	2.00716i	0.0549340	+	0.0951484i
$446$	−2.71379	+	4.70043i	−0.128502	+	0.222572i
$447$	14.7356			0.696968
$448$	2.02446	−	3.50647i	0.0956467	−	0.165665i
$449$	−5.70171	+	9.87565i	−0.269080	+	0.466061i	−0.968625	−	0.248528i	$-0.920053\pi$
$449$	−5.70171	+	9.87565i	−0.269080	+	0.466061i	0.699544	+	0.714589i	$0.253386\pi$
$450$	4.87263			0.229698
$451$	−3.46681	+	6.00469i	−0.163246	+	0.282750i
$452$	−6.49396	−	11.2479i	−0.305450	−	0.529055i
$453$	−7.91066	−	13.7017i	−0.371675	−	0.643760i
$454$	16.5767			0.777984
$455$		0			0
$456$	−4.98792			−0.233581
$457$	−3.83459	−	6.64171i	−0.179375	−	0.310686i	0.762292	−	0.647233i	$-0.224074\pi$
$457$	−3.83459	−	6.64171i	−0.179375	−	0.310686i	−0.941667	+	0.336547i	$0.890741\pi$
$458$	11.9390	+	20.6790i	0.557873	+	0.966264i
$459$	1.04892	−	1.81678i	0.0489593	−	0.0847999i
$460$	−3.03146			−0.141343
$461$	14.2540	−	24.6886i	0.663874	−	1.14986i	−0.315715	−	0.948854i	$-0.602244\pi$
$461$	14.2540	−	24.6886i	0.663874	−	1.14986i	0.979589	−	0.201010i	$-0.0644222\pi$
$462$	−1.84601	+	3.19738i	−0.0858842	+	0.148756i
$463$	−14.3284			−0.665898			−0.332949	−	0.942945i	$-0.608044\pi$
$463$	−14.3284			−0.665898			−0.332949	+	0.942945i	$0.608044\pi$
$464$	−4.25786	+	7.37484i	−0.197666	+	0.342368i
$465$	1.92543	+	3.33494i	0.0892896	+	0.154654i
$466$	6.99761	+	12.1202i	0.324158	+	0.561458i
$467$	33.3207			1.54190			0.770948	−	0.636898i	$-0.219783\pi$
$467$	33.3207			1.54190			0.770948	+	0.636898i	$0.219783\pi$
$468$		0			0
$469$	54.9831			2.53889
$470$	0.317667	+	0.550216i	0.0146529	+	0.0253796i
$471$	2.13706	+	3.70150i	0.0984707	+	0.170556i
$472$	3.02446	−	5.23852i	0.139212	−	0.241122i
$473$	−5.72109			−0.263056
$474$	−5.85354	+	10.1386i	−0.268862	+	0.465683i
$475$	12.1521	−	21.0481i	0.557578	−	0.965753i
$476$	8.49396			0.389320
$477$	−5.20560	+	9.01636i	−0.238348	+	0.412831i
$478$	−6.64310	−	11.5062i	−0.303849	−	0.526281i
$479$	11.0640	+	19.1634i	0.505526	+	0.875597i	0.999980	+	0.00639300i	$0.00203497\pi$
$479$	11.0640	+	19.1634i	0.505526	+	0.875597i	−0.494453	+	0.869204i	$0.664632\pi$
$480$	0.356896			0.0162900
$481$		0			0
$482$	10.4789			0.477301
$483$	17.1957	+	29.7838i	0.782430	+	1.35521i
$484$	5.08426	+	8.80620i	0.231103	+	0.400282i
$485$	0.349896	−	0.606037i	0.0158879	−	0.0275187i
$486$	−1.00000			−0.0453609
$487$	0.0631549	−	0.109387i	0.00286182	−	0.00495682i	−0.864591	−	0.502476i	$-0.832422\pi$
$487$	0.0631549	−	0.109387i	0.00286182	−	0.00495682i	0.867453	+	0.497520i	$0.165756\pi$
$488$	−1.55496	+	2.69327i	−0.0703896	+	0.121918i
$489$	0.317667			0.0143654
$490$	−1.67629	+	2.90342i	−0.0757272	+	0.131163i
$491$	−6.97166	−	12.0753i	−0.314626	−	0.544949i	0.664732	−	0.747082i	$-0.268546\pi$
$491$	−6.97166	−	12.0753i	−0.314626	−	0.544949i	−0.979358	+	0.202133i	$0.935213\pi$
$492$	−3.80194	−	6.58515i	−0.171405	−	0.296881i
$493$	−17.8646			−0.804581
$494$		0			0
$495$	−0.325437			−0.0146273
$496$	−5.39493	−	9.34429i	−0.242239	−	0.419571i
$497$	−23.2446	−	40.2608i	−1.04266	−	1.80594i
$498$	3.24967	−	5.62859i	0.145621	−	0.252223i
$499$	28.3913			1.27097			0.635485	−	0.772113i	$-0.280800\pi$
$499$	28.3913			1.27097			0.635485	+	0.772113i	$0.280800\pi$
$500$	−1.76175	+	3.05144i	−0.0787878	+	0.136465i
$501$	6.18060	−	10.7051i	0.276129	−	0.478269i
$502$	−3.48725			−0.155644
$503$	−6.28382	+	10.8839i	−0.280181	+	0.485289i	−0.971429	−	0.237329i	$-0.923728\pi$
$503$	−6.28382	+	10.8839i	−0.280181	+	0.485289i	0.691248	+	0.722618i	$0.257061\pi$
$504$	−2.02446	−	3.50647i	−0.0901766	−	0.156190i
$505$	1.24602	+	2.15817i	0.0554472	+	0.0960373i
$506$	−7.74525			−0.344318
$507$		0			0
$508$	9.22282			0.409196
$509$	−2.18837	−	3.79037i	−0.0969980	−	0.168005i	0.813443	−	0.581645i	$-0.197591\pi$
$509$	−2.18837	−	3.79037i	−0.0969980	−	0.168005i	−0.910441	+	0.413640i	$0.864257\pi$
$510$	0.374354	+	0.648401i	0.0165767	+	0.0287117i
$511$	−1.07942	+	1.86960i	−0.0477506	+	0.0827064i
$512$	−1.00000			−0.0441942
$513$	−2.49396	+	4.31966i	−0.110111	+	0.190718i
$514$	3.26875	−	5.66164i	0.144178	−	0.249724i
$515$	−1.76617			−0.0778266
$516$	3.13706	−	5.43355i	0.138102	−	0.239199i
$517$	0.811626	+	1.40578i	0.0356953	+	0.0618261i
$518$	−1.24698	−	2.15983i	−0.0547891	−	0.0948976i
$519$	−17.0640			−0.749026
$520$		0			0
$521$	−23.2707			−1.01951			−0.509753	−	0.860321i	$-0.670263\pi$
$521$	−23.2707			−1.01951			−0.509753	+	0.860321i	$0.670263\pi$
$522$	4.25786	+	7.37484i	0.186362	+	0.322788i
$523$	−18.9976	−	32.9048i	−0.830707	−	1.43883i	−0.897478	−	0.441059i	$-0.854603\pi$
$523$	−18.9976	−	32.9048i	−0.830707	−	1.43883i	0.0667707	−	0.997768i	$-0.478730\pi$
$524$	7.27628	−	12.6029i	0.317866	−	0.550560i
$525$	19.7289			0.861038
$526$	4.00969	−	6.94498i	0.174831	−	0.302816i
$527$	11.3177	−	19.6028i	0.493005	−	0.853910i
$528$	0.911854			0.0396834
$529$	−24.5737	+	42.5628i	−1.06842	+	1.85056i
$530$	−1.85786	−	3.21790i	−0.0807001	−	0.139777i
$531$	−3.02446	−	5.23852i	−0.131250	−	0.227332i
$532$	−20.1957			−0.875593
$533$		0			0
$534$	−6.49396			−0.281021
$535$	−0.761750	−	1.31939i	−0.0329333	−	0.0570422i
$536$	−6.78986	−	11.7604i	−0.293277	−	0.507971i
$537$	12.4840	−	21.6230i	0.538726	−	0.933100i
$538$	27.6732			1.19308
$539$	−4.28286	+	7.41812i	−0.184476	+	0.319521i
$540$	0.178448	−	0.309081i	0.00767918	−	0.0133007i
$541$	3.16421			0.136040			0.0680200	−	0.997684i	$-0.478332\pi$
$541$	3.16421			0.136040			0.0680200	+	0.997684i	$0.478332\pi$
$542$	−7.36443	+	12.7556i	−0.316329	+	0.547898i
$543$	−2.63102	−	4.55706i	−0.112908	−	0.195562i
$544$	−1.04892	−	1.81678i	−0.0449720	−	0.0778937i
$545$	−2.21983			−0.0950872
$546$		0			0
$547$	7.56033			0.323257			0.161628	−	0.986852i	$-0.448325\pi$
$547$	7.56033			0.323257			0.161628	+	0.986852i	$0.448325\pi$
$548$	−7.70171	−	13.3398i	−0.329001	−	0.569846i
$549$	1.55496	+	2.69327i	0.0663640	+	0.114946i
$550$	−2.22156	+	3.84786i	−0.0947277	+	0.164073i
$551$	42.4758			1.80953
$552$	4.24698	−	7.35598i	0.180763	−	0.313091i
$553$	−23.7005	+	41.0505i	−1.00785	+	1.74564i
$554$	−3.26205			−0.138591
$555$	0.109916	−	0.190381i	0.00466569	−	0.00808120i
$556$	−1.35690	−	2.35021i	−0.0575452	−	0.0996712i
$557$	0.207751	+	0.359835i	0.00880269	+	0.0152467i	0.870393	−	0.492357i	$-0.163865\pi$
$557$	0.207751	+	0.359835i	0.00880269	+	0.0152467i	−0.861591	+	0.507604i	$0.830531\pi$
$558$	−10.7899			−0.456771
$559$		0			0
$560$	1.44504			0.0610642
$561$	0.956459	+	1.65664i	0.0403818	+	0.0699432i
$562$	−3.86294	−	6.69080i	−0.162948	−	0.282234i
$563$	14.5233	−	25.1550i	0.612083	−	1.06016i	−0.378806	−	0.925476i	$-0.623665\pi$
$563$	14.5233	−	25.1550i	0.612083	−	1.06016i	0.990889	−	0.134682i	$-0.0430013\pi$
$564$	−1.78017			−0.0749586
$565$	2.31767	−	4.01432i	0.0975050	−	0.168884i
$566$	−9.89008	+	17.1301i	−0.415711	+	0.720033i
$567$	−4.04892			−0.170039
$568$	−5.74094	+	9.94360i	−0.240884	+	0.417224i
$569$	−19.8431	−	34.3692i	−0.831865	−	1.44083i	−0.896557	−	0.442928i	$-0.853940\pi$
$569$	−19.8431	−	34.3692i	−0.831865	−	1.44083i	0.0646918	−	0.997905i	$-0.479394\pi$
$570$	−0.890084	−	1.54167i	−0.0372815	−	0.0645735i
$571$	−7.09651			−0.296980			−0.148490	−	0.988914i	$-0.547441\pi$
$571$	−7.09651			−0.296980			−0.148490	+	0.988914i	$0.547441\pi$
$572$		0			0
$573$	10.5375			0.440210
$574$	−15.3937	−	26.6627i	−0.642522	−	1.11288i
$575$	20.6939	+	35.8430i	0.862997	+	1.49475i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.78687			−0.365802			−0.182901	−	0.983131i	$-0.558549\pi$
$577$	−8.78687			−0.365802			−0.182901	+	0.983131i	$0.558549\pi$
$578$	−6.29954	+	10.9111i	−0.262027	+	0.453843i
$579$	1.71379	−	2.96837i	0.0712228	−	0.123361i
$580$	−3.03923			−0.126197
$581$	13.1576	−	22.7897i	0.545871	−	0.945476i
$582$	0.980386	+	1.69808i	0.0406383	+	0.0703876i
$583$	−4.74674	−	8.22160i	−0.196590	−	0.340504i
$584$	0.533188			0.0220635
$585$		0			0
$586$	−12.9119			−0.533384
$587$	18.3533	+	31.7889i	0.757522	+	1.31207i	0.944111	+	0.329629i	$0.106923\pi$
$587$	18.3533	+	31.7889i	0.757522	+	1.31207i	−0.186589	+	0.982438i	$0.559743\pi$
$588$	−4.69687	−	8.13521i	−0.193695	−	0.335490i
$589$	−26.9095	+	46.6086i	−1.10879	+	1.92047i
$590$	2.15883			0.0888778
$591$	1.88740	−	3.26906i	0.0776371	−	0.134471i
$592$	−0.307979	+	0.533434i	−0.0126578	+	0.0219240i
$593$	−10.8310			−0.444776			−0.222388	−	0.974958i	$-0.571385\pi$
$593$	−10.8310			−0.444776			−0.222388	+	0.974958i	$0.571385\pi$
$594$	0.455927	−	0.789689i	0.0187069	−	0.0324013i
$595$	1.51573	+	2.62532i	0.0621389	+	0.107628i
$596$	−7.36778	−	12.7614i	−0.301796	−	0.522726i
$597$	17.9541			0.734811
$598$		0			0
$599$	23.5254			0.961223			0.480611	−	0.876934i	$-0.340415\pi$
$599$	23.5254			0.961223			0.480611	+	0.876934i	$0.340415\pi$
$600$	−2.43631	−	4.21982i	−0.0994620	−	0.172273i
$601$	−13.9107	−	24.0940i	−0.567428	−	0.982813i	−0.996819	−	0.0796950i	$-0.974605\pi$
$601$	−13.9107	−	24.0940i	−0.567428	−	0.982813i	0.429392	−	0.903118i	$-0.358728\pi$
$602$	12.7017	−	22.0000i	0.517683	−	0.896653i
$603$	−13.5797			−0.553009
$604$	−7.91066	+	13.7017i	−0.321880	+	0.557513i
$605$	−1.81455	+	3.14290i	−0.0737720	+	0.127777i
$606$	−6.98254			−0.283646
$607$	−0.0486218	+	0.0842155i	−0.00197350	+	0.00341820i	−0.867010	−	0.498290i	$-0.833962\pi$
$607$	−0.0486218	+	0.0842155i	−0.00197350	+	0.00341820i	0.865037	+	0.501708i	$0.167295\pi$
$608$	2.49396	+	4.31966i	0.101143	+	0.175186i
$609$	17.2397	+	29.8601i	0.698590	+	1.20999i
$610$	−1.10992			−0.0449392
$611$		0			0
$612$	−2.09783			−0.0847999
$613$	−4.03252	−	6.98454i	−0.162872	−	0.282103i	0.773025	−	0.634375i	$-0.218742\pi$
$613$	−4.03252	−	6.98454i	−0.162872	−	0.282103i	−0.935898	+	0.352272i	$0.885409\pi$
$614$	−9.98254	−	17.2903i	−0.402863	−	0.697778i
$615$	1.35690	−	2.35021i	0.0547153	−	0.0947697i
$616$	3.69202			0.148756
$617$	9.60925	−	16.6437i	0.386854	−	0.670051i	−0.605171	−	0.796096i	$-0.706895\pi$
$617$	9.60925	−	16.6437i	0.386854	−	0.670051i	0.992025	+	0.126045i	$0.0402284\pi$
$618$	2.47434	−	4.28569i	0.0995327	−	0.172396i
$619$	12.3827			0.497703			0.248852	−	0.968542i	$-0.419947\pi$
$619$	12.3827			0.497703			0.248852	+	0.968542i	$0.419947\pi$
$620$	1.92543	−	3.33494i	0.0773270	−	0.133934i
$621$	−4.24698	−	7.35598i	−0.170425	−	0.295185i
$622$	6.74094	+	11.6756i	0.270287	+	0.468151i
$623$	−26.2935			−1.05343
$624$		0			0
$625$	23.1056			0.924224
$626$	6.46226	+	11.1930i	0.258284	+	0.447361i
$627$	−2.27413	−	3.93890i	−0.0908199	−	0.157305i
$628$	2.13706	−	3.70150i	0.0852781	−	0.147706i
$629$	−1.29218			−0.0515224
$630$	0.722521	−	1.25144i	0.0287859	−	0.0498587i
$631$	2.37167	−	4.10785i	0.0944145	−	0.163531i	−0.814950	−	0.579532i	$-0.803235\pi$
$631$	2.37167	−	4.10785i	0.0944145	−	0.163531i	0.909364	+	0.416001i	$0.136569\pi$
$632$	11.7071			0.465683
$633$	6.26875	−	10.8578i	0.249160	−	0.431559i
$634$	5.93631	+	10.2820i	0.235761	+	0.408350i
$635$	1.64579	+	2.85060i	0.0653113	+	0.113122i
$636$	10.4112			0.412831
$637$		0			0
$638$	−7.76510			−0.307423
$639$	5.74094	+	9.94360i	0.227108	+	0.393363i
$640$	−0.178448	−	0.309081i	−0.00705377	−	0.0122175i
$641$	8.22282	−	14.2423i	0.324782	−	0.562538i	−0.656686	−	0.754164i	$-0.728042\pi$
$641$	8.22282	−	14.2423i	0.324782	−	0.562538i	0.981468	+	0.191625i	$0.0613758\pi$
$642$	4.26875			0.168474
$643$	−0.872625	+	1.51143i	−0.0344130	+	0.0596050i	−0.882719	−	0.469901i	$-0.844289\pi$
$643$	−0.872625	+	1.51143i	−0.0344130	+	0.0596050i	0.848306	+	0.529506i	$0.177623\pi$
$644$	17.1957	−	29.7838i	0.677604	−	1.17365i
$645$	2.23921			0.0881688
$646$	−5.23191	+	9.06194i	−0.205847	+	0.356537i
$647$	−14.3817	−	24.9097i	−0.565401	−	0.979303i	−0.997012	−	0.0772436i	$-0.975388\pi$
$647$	−14.3817	−	24.9097i	−0.565401	−	0.979303i	0.431611	−	0.902060i	$-0.357945\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	5.51573			0.216511
$650$		0			0
$651$	−43.6872			−1.71224
$652$	−0.158834	−	0.275108i	−0.00622040	−	0.0107741i
$653$	8.08306	+	14.0003i	0.316315	+	0.547873i	0.979716	−	0.200391i	$-0.0642211\pi$
$653$	8.08306	+	14.0003i	0.316315	+	0.547873i	−0.663401	+	0.748264i	$0.730888\pi$
$654$	3.10992	−	5.38653i	0.121607	−	0.210630i
$655$	5.19375			0.202937
$656$	−3.80194	+	6.58515i	−0.148441	+	0.257107i
$657$	0.266594	−	0.461754i	0.0104008	−	0.0180147i
$658$	−7.20775			−0.280987
$659$	8.17792	−	14.1646i	0.318566	−	0.551773i	−0.661623	−	0.749837i	$-0.730132\pi$
$659$	8.17792	−	14.1646i	0.318566	−	0.551773i	0.980189	+	0.198064i	$0.0634653\pi$
$660$	0.162718	+	0.281837i	0.00633381	+	0.0109705i
$661$	16.5579	+	28.6792i	0.644029	+	1.11549i	0.984525	+	0.175245i	$0.0560719\pi$
$661$	16.5579	+	28.6792i	0.644029	+	1.11549i	−0.340495	+	0.940246i	$0.610595\pi$
$662$	10.2392			0.397958
$663$		0			0
$664$	−6.49934			−0.252223
$665$	−3.60388	−	6.24210i	−0.139752	−	0.242058i
$666$	0.307979	+	0.533434i	0.0119339	+	0.0206702i
$667$	−36.1661	+	62.6416i	−1.40036	+	2.42549i
$668$	−12.3612			−0.478269
$669$	2.71379	−	4.70043i	0.104921	−	0.181729i
$670$	2.42327	−	4.19723i	0.0936191	−	0.162153i
$671$	−2.83579			−0.109474
$672$	−2.02446	+	3.50647i	−0.0780952	+	0.135265i
$673$	17.5770	+	30.4443i	0.677544	+	1.17354i	0.975718	+	0.219030i	$0.0702892\pi$
$673$	17.5770	+	30.4443i	0.677544	+	1.17354i	−0.298174	+	0.954512i	$0.596377\pi$
$674$	0.724677	+	1.25518i	0.0279135	+	0.0483476i
$675$	−4.87263			−0.187547
$676$		0			0
$677$	23.7855			0.914153			0.457076	−	0.889427i	$-0.348897\pi$
$677$	23.7855			0.914153			0.457076	+	0.889427i	$0.348897\pi$
$678$	6.49396	+	11.2479i	0.249399	+	0.431972i
$679$	3.96950	+	6.87538i	0.152335	+	0.263853i
$680$	0.374354	−	0.648401i	0.0143558	−	0.0248650i
$681$	−16.5767			−0.635222
$682$	4.91939	−	8.52063i	0.188373	−	0.326272i
$683$	−1.49612	+	2.59135i	−0.0572473	+	0.0991552i	−0.893229	−	0.449602i	$-0.851566\pi$
$683$	−1.49612	+	2.59135i	−0.0572473	+	0.0991552i	0.835982	+	0.548758i	$0.184899\pi$
$684$	4.98792			0.190718
$685$	2.74871	−	4.76090i	0.105023	−	0.181905i
$686$	−4.84601	−	8.39354i	−0.185022	−	0.320467i
$687$	−11.9390	−	20.6790i	−0.455501	−	0.788951i
$688$	−6.27413			−0.239199
$689$		0			0
$690$	3.03146			0.115406
$691$	−5.81163	−	10.0660i	−0.221085	−	0.382930i	0.734053	−	0.679092i	$-0.237626\pi$
$691$	−5.81163	−	10.0660i	−0.221085	−	0.382930i	−0.955138	+	0.296162i	$0.904293\pi$
$692$	8.53199	+	14.7778i	0.324338	+	0.561769i
$693$	1.84601	−	3.19738i	0.0701241	−	0.121459i
$694$	−6.84117			−0.259687
$695$	0.484271	−	0.838781i	0.0183694	−	0.0318168i
$696$	4.25786	−	7.37484i	0.161394	−	0.279543i
$697$	−15.9517			−0.604213
$698$	17.1685	−	29.7368i	0.649838	−	1.12555i
$699$	−6.99761	−	12.1202i	−0.264674	−	0.458428i
$700$	−9.86443	−	17.0857i	−0.372840	−	0.645778i
$701$	−33.8431			−1.27824			−0.639118	−	0.769109i	$-0.720700\pi$
$701$	−33.8431			−1.27824			−0.639118	+	0.769109i	$0.720700\pi$
$702$		0			0
$703$	3.07234			0.115876
$704$	−0.455927	−	0.789689i	−0.0171834	−	0.0297625i
$705$	−0.317667	−	0.550216i	−0.0119640	−	0.0207223i
$706$	−13.0248	+	22.5595i	−0.490193	+	0.849039i
$707$	−28.2717			−1.06327
$708$	−3.02446	+	5.23852i	−0.113666	+	0.196875i
$709$	13.0954	−	22.6820i	0.491810	−	0.851839i	−0.508146	−	0.861271i	$-0.669669\pi$
$709$	13.0954	−	22.6820i	0.491810	−	0.851839i	0.999956	+	0.00943173i	$0.00300226\pi$
$710$	−4.09783			−0.153789
$711$	5.85354	−	10.1386i	0.219525	−	0.380229i
$712$	3.24698	+	5.62393i	0.121686	+	0.210766i
$713$	−45.8243	−	79.3700i	−1.71613	−	2.97243i
$714$	−8.49396			−0.317878
$715$		0			0
$716$	−24.9681			−0.933100
$717$	6.64310	+	11.5062i	0.248091	+	0.429707i
$718$	−4.24698	−	7.35598i	−0.158496	−	0.274523i
$719$	10.8672	−	18.8226i	0.405280	−	0.701966i	−0.589074	−	0.808079i	$-0.700507\pi$
$719$	10.8672	−	18.8226i	0.405280	−	0.701966i	0.994354	+	0.106114i	$0.0338407\pi$
$720$	−0.356896			−0.0133007
$721$	10.0184	−	17.3524i	0.373105	−	0.646237i
$722$	2.93967	−	5.09165i	0.109403	−	0.189492i
$723$	−10.4789			−0.389714
$724$	−2.63102	+	4.55706i	−0.0977812	+	0.169362i
$725$	20.7470	+	35.9348i	0.770523	+	1.33459i
$726$	−5.08426	−	8.80620i	−0.188695	−	0.326829i
$727$	−2.01400			−0.0746951			−0.0373476	−	0.999302i	$-0.511891\pi$
$727$	−2.01400			−0.0746951			−0.0373476	+	0.999302i	$0.511891\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	0.0951463	+	0.164798i	0.00352152	+	0.00609945i
$731$	−6.58104	−	11.3987i	−0.243409	−	0.421596i
$732$	1.55496	−	2.69327i	0.0574729	−	0.0995460i
$733$	13.5013			0.498680			0.249340	−	0.968416i	$-0.419786\pi$
$733$	13.5013			0.498680			0.249340	+	0.968416i	$0.419786\pi$
$734$	13.7262	−	23.7744i	0.506642	−	0.877530i
$735$	1.67629	−	2.90342i	0.0618310	−	0.107094i
$736$	−8.49396			−0.313091
$737$	6.19136	−	10.7237i	0.228062	−	0.395014i
$738$	3.80194	+	6.58515i	0.139951	+	0.242403i
$739$	8.29590	+	14.3689i	0.305170	+	0.528569i	0.977299	−	0.211864i	$-0.0679535\pi$
$739$	8.29590	+	14.3689i	0.305170	+	0.528569i	−0.672130	+	0.740434i	$0.734620\pi$
$740$	−0.219833			−0.00808120
$741$		0			0
$742$	42.1540			1.54752
$743$	9.92394	+	17.1888i	0.364074	+	0.630594i	0.988627	−	0.150388i	$-0.0480522\pi$
$743$	9.92394	+	17.1888i	0.364074	+	0.630594i	−0.624553	+	0.780982i	$0.714719\pi$
$744$	5.39493	+	9.34429i	0.197788	+	0.342578i
$745$	2.62953	−	4.55448i	0.0963385	−	0.166863i
$746$	−26.6219			−0.974698
$747$	−3.24967	+	5.62859i	−0.118899	+	0.205939i
$748$	0.956459	−	1.65664i	0.0349716	−	0.0605726i
$749$	17.2838			0.631537
$750$	1.76175	−	3.05144i	0.0643300	−	0.111423i
$751$	−13.9673	−	24.1922i	−0.509676	−	0.882784i	−0.999937	−	0.0112087i	$-0.996432\pi$
$751$	−13.9673	−	24.1922i	−0.509676	−	0.882784i	0.490262	−	0.871575i	$-0.336901\pi$
$752$	0.890084	+	1.54167i	0.0324580	+	0.0562189i
$753$	3.48725			0.127083
$754$		0			0
$755$	−5.64656			−0.205499
$756$	2.02446	+	3.50647i	0.0736288	+	0.127529i
$757$	0.274127	+	0.474801i	0.00996330	+	0.0172569i	0.870964	−	0.491347i	$-0.163495\pi$
$757$	0.274127	+	0.474801i	0.00996330	+	0.0172569i	−0.861001	+	0.508604i	$0.830162\pi$
$758$	−5.82371	+	10.0870i	−0.211527	+	0.366375i
$759$	7.74525			0.281135
$760$	−0.890084	+	1.54167i	−0.0322867	+	0.0559223i
$761$	−0.987918	+	1.71112i	−0.0358120	+	0.0620282i	−0.883376	−	0.468665i	$-0.844735\pi$
$761$	−0.987918	+	1.71112i	−0.0358120	+	0.0620282i	0.847564	+	0.530693i	$0.178068\pi$
$762$	−9.22282			−0.334107
$763$	12.5918	−	21.8096i	0.455854	−	0.789562i
$764$	−5.26875	−	9.12574i	−0.190617	−	0.330158i
$765$	−0.374354	−	0.648401i	−0.0135348	−	0.0234430i
$766$	10.5181			0.380035
$767$		0			0
$768$	1.00000			0.0360844
$769$	−14.3056	−	24.7780i	−0.515873	−	0.893518i	−0.999830	−	0.0184261i	$-0.994134\pi$
$769$	−14.3056	−	24.7780i	−0.515873	−	0.893518i	0.483958	−	0.875091i	$-0.339199\pi$
$770$	0.658834	+	1.14113i	0.0237427	+	0.0411236i
$771$	−3.26875	+	5.66164i	−0.117721	+	0.203899i
$772$	−3.42758			−0.123361
$773$	−26.2540	+	45.4732i	−0.944290	+	1.63556i	−0.187123	+	0.982336i	$0.559916\pi$
$773$	−26.2540	+	45.4732i	−0.944290	+	1.63556i	−0.757167	+	0.653222i	$0.773417\pi$
$774$	−3.13706	+	5.43355i	−0.112759	+	0.195305i
$775$	−52.5749			−1.88855
$776$	0.980386	−	1.69808i	0.0351938	−	0.0609574i
$777$	1.24698	+	2.15983i	0.0447351	+	0.0774835i
$778$	−4.62983	−	8.01909i	−0.165987	−	0.287498i
$779$	37.9275			1.35889
$780$		0			0
$781$	−10.4698			−0.374639
$782$	−8.90946	−	15.4316i	−0.318602	−	0.551834i
$783$	−4.25786	−	7.37484i	−0.152164	−	0.263555i
$784$	−4.69687	+	8.13521i	−0.167745	+	0.290543i
$785$	1.52542			0.0544445
$786$	−7.27628	+	12.6029i	−0.259536	+	0.449530i
$787$	−11.8213	+	20.4751i	−0.421384	+	0.729859i	−0.996075	−	0.0885115i	$-0.971789\pi$
$787$	−11.8213	+	20.4751i	−0.421384	+	0.729859i	0.574691	+	0.818371i	$0.305122\pi$
$788$	−3.77479			−0.134471
$789$	−4.00969	+	6.94498i	−0.142749	+	0.247248i
$790$	2.08911	+	3.61844i	0.0743270	+	0.128738i
$791$	26.2935	+	45.5417i	0.934889	+	1.61928i
$792$	−0.911854			−0.0324013
$793$		0			0
$794$	14.5133			0.515059
$795$	1.85786	+	3.21790i	0.0658913	+	0.114127i
$796$	−8.97703	−	15.5487i	−0.318183	−	0.551108i
$797$	−20.8279	+	36.0750i	−0.737762	+	1.27784i	0.215739	+	0.976451i	$0.430784\pi$
$797$	−20.8279	+	36.0750i	−0.737762	+	1.27784i	−0.953501	+	0.301390i	$0.902549\pi$
$798$	20.1957			0.714919
$799$	−1.86725	+	3.23417i	−0.0660585	+	0.114417i
$800$	−2.43631	+	4.21982i	−0.0861367	+	0.149193i
$801$	6.49396			0.229453
$802$	19.4209	−	33.6379i	0.685775	−	1.18780i
$803$	0.243095	+	0.421052i	0.00857863	+	0.0148586i
$804$	6.78986	+	11.7604i	0.239460	+	0.414756i
$805$	12.2741			0.432606
$806$		0			0
$807$	−27.6732			−0.974144
$808$	3.49127	+	6.04706i	0.122822	+	0.212735i
$809$	22.1196	+	38.3123i	0.777684	+	1.34699i	0.933274	+	0.359166i	$0.116939\pi$
$809$	22.1196	+	38.3123i	0.777684	+	1.34699i	−0.155590	+	0.987822i	$0.549728\pi$
$810$	−0.178448	+	0.309081i	−0.00627002	+	0.0108600i
$811$	−52.3913			−1.83971			−0.919854	−	0.392260i	$-0.871693\pi$
$811$	−52.3913			−1.83971			−0.919854	+	0.392260i	$0.871693\pi$
$812$	17.2397	−	29.8601i	0.604996	−	1.04788i
$813$	7.36443	−	12.7556i	0.258282	−	0.447357i
$814$	−0.561663			−0.0196863
$815$	0.0566871	−	0.0981849i	0.00198566	−	0.00343927i
$816$	1.04892	+	1.81678i	0.0367195	+	0.0636000i
$817$	15.6474	+	27.1021i	0.547434	+	0.948183i
$818$	33.9221			1.18606
$819$		0			0
$820$	−2.71379			−0.0947697
$821$	−12.8138	−	22.1941i	−0.447204	−	0.774580i	0.550999	−	0.834506i	$-0.314247\pi$
$821$	−12.8138	−	22.1941i	−0.447204	−	0.774580i	−0.998203	+	0.0599259i	$0.980914\pi$
$822$	7.70171	+	13.3398i	0.268628	+	0.465277i
$823$	20.1277	−	34.8621i	0.701606	−	1.21522i	−0.266296	−	0.963891i	$-0.585800\pi$
$823$	20.1277	−	34.8621i	0.701606	−	1.21522i	0.967902	−	0.251327i	$-0.0808669\pi$
$824$	−4.94869			−0.172396
$825$	2.22156	−	3.84786i	0.0773448	−	0.133965i
$826$	−12.2458	+	21.2103i	−0.426085	+	0.738001i
$827$	18.0519			0.627726			0.313863	−	0.949468i	$-0.398377\pi$
$827$	18.0519			0.627726			0.313863	+	0.949468i	$0.398377\pi$
$828$	−4.24698	+	7.35598i	−0.147593	+	0.255638i
$829$	−11.3327	−	19.6289i	−0.393602	−	0.681739i	0.599320	−	0.800510i	$-0.295438\pi$
$829$	−11.3327	−	19.6289i	−0.393602	−	0.681739i	−0.992922	+	0.118771i	$0.962105\pi$
$830$	−1.15979	−	2.00882i	−0.0402570	−	0.0697272i
$831$	3.26205			0.113159
$832$		0			0
$833$	−19.7065			−0.682790
$834$	1.35690	+	2.35021i	0.0469855	+	0.0813812i
$835$	−2.20583	−	3.82061i	−0.0763360	−	0.132218i
$836$	−2.27413	+	3.93890i	−0.0786523	+	0.136230i
$837$	10.7899			0.372952
$838$	0.477697	−	0.827396i	0.0165018	−	0.0285819i
$839$	11.0411	−	19.1238i	0.381183	−	0.660228i	−0.610049	−	0.792364i	$-0.708850\pi$
$839$	11.0411	−	19.1238i	0.381183	−	0.660228i	0.991232	+	0.132136i	$0.0421835\pi$
$840$	−1.44504			−0.0498587
$841$	−21.7588	+	37.6874i	−0.750304	+	1.29957i
$842$	−2.84117	−	4.92104i	−0.0979131	−	0.169590i
$843$	3.86294	+	6.69080i	0.133047	+	0.230443i
$844$	−12.5375			−0.431559
$845$		0			0
$846$	1.78017			0.0612034
$847$	−20.5858	−	35.6556i	−0.707335	−	1.22514i
$848$	−5.20560	−	9.01636i	−0.178761	−	0.309623i
$849$	9.89008	−	17.1301i	0.339427	−	0.587904i
$850$	−10.2220			−0.350610
$851$	−2.61596	+	4.53097i	−0.0896739	+	0.155320i
$852$	5.74094	−	9.94360i	0.196681	−	0.340662i
$853$	−28.9831			−0.992364			−0.496182	−	0.868219i	$-0.665265\pi$
$853$	−28.9831			−0.992364			−0.496182	+	0.868219i	$0.665265\pi$
$854$	6.29590	−	10.9048i	0.215441	−	0.373155i
$855$	0.890084	+	1.54167i	0.0304402	+	0.0527240i
$856$	−2.13437	−	3.69685i	−0.0729514	−	0.126356i
$857$	−42.9047			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$857$	−42.9047			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$858$		0			0
$859$	−47.0616			−1.60572			−0.802860	−	0.596167i	$-0.796690\pi$
$859$	−47.0616			−1.60572			−0.802860	+	0.596167i	$0.796690\pi$
$860$	−1.11960	−	1.93921i	−0.0381782	−	0.0661266i
$861$	15.3937	+	26.6627i	0.524617	+	0.908663i
$862$	−7.42327	+	12.8575i	−0.252838	+	0.437928i
$863$	−42.6064			−1.45034			−0.725169	−	0.688571i	$-0.758238\pi$
$863$	−42.6064			−1.45034			−0.725169	+	0.688571i	$0.758238\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−3.04503	+	5.27415i	−0.103534	+	0.179327i
$866$	26.1497			0.888604
$867$	6.29954	−	10.9111i	0.213944	−	0.370561i
$868$	21.8436	+	37.8343i	0.741421	+	1.28418i
$869$	5.33758	+	9.24495i	0.181065	+	0.313614i
$870$	3.03923			0.103040
$871$		0			0
$872$	−6.21983			−0.210630
$873$	−0.980386	−	1.69808i	−0.0331810	−	0.0574712i
$874$	21.1836	+	36.6911i	0.716546	+	1.24109i
$875$	7.13318	−	12.3550i	0.241145	−	0.417676i
$876$	−0.533188			−0.0180147
$877$	−13.7041	+	23.7362i	−0.462755	+	0.801515i	−0.999097	−	0.0424859i	$-0.986472\pi$
$877$	−13.7041	+	23.7362i	−0.462755	+	0.801515i	0.536342	+	0.844000i	$0.319806\pi$
$878$	−11.7751	+	20.3950i	−0.397390	+	0.688300i
$879$	12.9119			0.435506
$880$	0.162718	−	0.281837i	0.00548524	−	0.00950071i
$881$	−12.1588	−	21.0597i	−0.409642	−	0.709520i	0.585208	−	0.810883i	$-0.301013\pi$
$881$	−12.1588	−	21.0597i	−0.409642	−	0.709520i	−0.994849	+	0.101363i	$0.967680\pi$
$882$	4.69687	+	8.13521i	0.158152	+	0.273927i
$883$	−32.2306			−1.08465			−0.542323	−	0.840170i	$-0.682455\pi$
$883$	−32.2306			−1.08465			−0.542323	+	0.840170i	$0.682455\pi$
$884$		0			0
$885$	−2.15883			−0.0725684
$886$	10.9717	+	19.0035i	0.368600	+	0.638434i
$887$	17.5821	+	30.4531i	0.590349	+	1.02252i	0.994185	+	0.107684i	$0.0343433\pi$
$887$	17.5821	+	30.4531i	0.590349	+	1.02252i	−0.403836	+	0.914831i	$0.632323\pi$
$888$	0.307979	−	0.533434i	0.0103351	−	0.0179009i
$889$	−37.3424			−1.25242
$890$	−1.15883	+	2.00716i	−0.0388442	+	0.0672801i
$891$	−0.455927	+	0.789689i	−0.0152741	+	0.0264556i
$892$	−5.42758			−0.181729
$893$	4.43967	−	7.68973i	0.148568	−	0.257327i
$894$	7.36778	+	12.7614i	0.246415	+	0.426804i
$895$	−4.45550	−	7.71715i	−0.148931	−	0.257956i
$896$	4.04892			0.135265
$897$		0			0
$898$	−11.4034			−0.380537
$899$	−45.9417	−	79.5734i	−1.53224	−	2.65392i
$900$	2.43631	+	4.21982i	0.0812104	+	0.140661i
$901$	10.9205	−	18.9148i	0.363814	−	0.630144i
$902$	−6.93362			−0.230864
$903$	−12.7017	+	22.0000i	−0.422686	+	0.732114i
$904$	6.49396	−	11.2479i	0.215986	−	0.374099i
$905$	−1.87800			−0.0624269
$906$	7.91066	−	13.7017i	0.262814	−	0.455207i
$907$	6.56033	+	11.3628i	0.217832	+	0.377297i	0.954145	−	0.299345i	$-0.0967681\pi$
$907$	6.56033	+	11.3628i	0.217832	+	0.377297i	−0.736313	+	0.676641i	$0.763435\pi$
$908$	8.28836	+	14.3559i	0.275059	+	0.476416i
$909$	6.98254			0.231596
$910$		0			0
$911$	45.7453			1.51561			0.757804	−	0.652482i	$-0.226272\pi$
$911$	45.7453			1.51561			0.757804	+	0.652482i	$0.226272\pi$
$912$	−2.49396	−	4.31966i	−0.0825832	−	0.143038i
$913$	−2.96322	−	5.13245i	−0.0980684	−	0.169859i
$914$	3.83459	−	6.64171i	0.126837	−	0.219688i
$915$	1.10992			0.0366927
$916$	−11.9390	+	20.6790i	−0.394476	+	0.683252i
$917$	−29.4611	+	51.0281i	−0.972890	+	1.68510i
$918$	2.09783			0.0692389
$919$	−8.99247	+	15.5754i	−0.296634	+	0.513785i	−0.975364	−	0.220603i	$-0.929198\pi$
$919$	−8.99247	+	15.5754i	−0.296634	+	0.513785i	0.678730	+	0.734388i	$0.262531\pi$
$920$	−1.51573	−	2.62532i	−0.0499721	−	0.0865543i
$921$	9.98254	+	17.2903i	0.328936	+	0.569734i
$922$	28.5080			0.938860
$923$		0			0
$924$	−3.69202			−0.121459
$925$	1.50066	+	2.59923i	0.0493415	+	0.0854620i
$926$	−7.16421	−	12.4088i	−0.235431	−	0.407778i
$927$	−2.47434	+	4.28569i	−0.0812681	+	0.140761i
$928$	−8.51573			−0.279543
$929$	−15.8442	+	27.4429i	−0.519830	+	0.900371i	0.479905	+	0.877321i	$0.340671\pi$
$929$	−15.8442	+	27.4429i	−0.519830	+	0.900371i	−0.999734	+	0.0230508i	$0.992662\pi$
$930$	−1.92543	+	3.33494i	−0.0631373	+	0.109357i
$931$	46.8552			1.53562
$932$	−6.99761	+	12.1202i	−0.229214	+	0.397011i
$933$	−6.74094	−	11.6756i	−0.220688	−	0.382244i
$934$	16.6603	+	28.8565i	0.545143	+	0.944215i
$935$	0.682713			0.0223271
$936$		0			0
$937$	−53.0484			−1.73302			−0.866509	−	0.499162i	$-0.833641\pi$
$937$	−53.0484			−1.73302			−0.866509	+	0.499162i	$0.833641\pi$
$938$	27.4916	+	47.6168i	0.897631	+	1.55474i
$939$	−6.46226	−	11.1930i	−0.210888	−	0.365269i
$940$	−0.317667	+	0.550216i	−0.0103612	+	0.0179461i
$941$	21.9433			0.715332			0.357666	−	0.933850i	$-0.383573\pi$
$941$	21.9433			0.715332			0.357666	+	0.933850i	$0.383573\pi$
$942$	−2.13706	+	3.70150i	−0.0696293	+	0.120601i
$943$	−32.2935	+	55.9340i	−1.05162	+	1.82146i
$944$	6.04892			0.196875
$945$	−0.722521	+	1.25144i	−0.0235036	+	0.0407094i
$946$	−2.86054	−	4.95461i	−0.0930043	−	0.161088i
$947$	−6.11207	−	10.5864i	−0.198616	−	0.344012i	0.749464	−	0.662045i	$-0.230311\pi$
$947$	−6.11207	−	10.5864i	−0.198616	−	0.344012i	−0.948080	+	0.318033i	$0.896978\pi$
$948$	−11.7071			−0.380229
$949$		0			0
$950$	24.3043			0.788534
$951$	−5.93631	−	10.2820i	−0.192498	−	0.333417i
$952$	4.24698	+	7.35598i	0.137645	+	0.238409i
$953$	1.92931	−	3.34167i	0.0624966	−	0.108247i	−0.833084	−	0.553146i	$-0.813427\pi$
$953$	1.92931	−	3.34167i	0.0624966	−	0.108247i	0.895581	+	0.444899i	$0.146760\pi$
$954$	−10.4112			−0.337075
$955$	1.88040	−	3.25694i	0.0608482	−	0.105392i
$956$	6.64310	−	11.5062i	0.214853	−	0.372137i
$957$	7.76510			0.251010
$958$	−11.0640	+	19.1634i	−0.357461	+	0.619141i
$959$	31.1836	+	54.0116i	1.00697	+	1.74412i
$960$	0.178448	+	0.309081i	0.00575938	+	0.00997554i
$961$	85.4210			2.75552
$962$		0			0
$963$	−4.26875			−0.137559
$964$	5.23945	+	9.07499i	0.168751	+	0.292286i
$965$	−0.611645	−	1.05940i	−0.0196896	−	0.0341033i
$966$	−17.1957	+	29.7838i	−0.553262	+	0.958277i
$967$	−0.613564			−0.0197309			−0.00986545	−	0.999951i	$-0.503140\pi$
$967$	−0.613564			−0.0197309			−0.00986545	+	0.999951i	$0.503140\pi$
$968$	−5.08426	+	8.80620i	−0.163414	+	0.283042i
$969$	5.23191	−	9.06194i	0.168073	−	0.291111i
$970$	0.699791			0.0224689
$971$	6.48845	−	11.2383i	0.208224	−	0.360655i	−0.742931	−	0.669368i	$-0.766565\pi$
$971$	6.48845	−	11.2383i	0.208224	−	0.360655i	0.951155	+	0.308713i	$0.0998983\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	5.49396	+	9.51582i	0.176128	+	0.305063i
$974$	0.126310			0.00404722
$975$		0			0
$976$	−3.10992			−0.0995460
$977$	18.5308	+	32.0963i	0.592853	+	1.02685i	0.993846	+	0.110770i	$0.0353317\pi$
$977$	18.5308	+	32.0963i	0.592853	+	1.02685i	−0.400993	+	0.916081i	$0.631335\pi$
$978$	0.158834	+	0.275108i	0.00507894	+	0.00879698i
$979$	−2.96077	+	5.12821i	−0.0946267	+	0.163898i
$980$	−3.35258			−0.107094
$981$	−3.10992	+	5.38653i	−0.0992920	+	0.171979i
$982$	6.97166	−	12.0753i	0.222474	−	0.385337i
$983$	−14.1193			−0.450337			−0.225169	−	0.974320i	$-0.572293\pi$
$983$	−14.1193			−0.450337			−0.225169	+	0.974320i	$0.572293\pi$
$984$	3.80194	−	6.58515i	0.121201	−	0.209927i
$985$	−0.673604	−	1.16672i	−0.0214628	−	0.0371747i
$986$	−8.93230	−	15.4712i	−0.284462	−	0.492703i
$987$	7.20775			0.229425
$988$		0			0
$989$	−53.2922			−1.69459
$990$	−0.162718	−	0.281837i	−0.00517153	−	0.00895736i
$991$	−14.2696	−	24.7156i	−0.453288	−	0.785118i	0.545300	−	0.838241i	$-0.316416\pi$
$991$	−14.2696	−	24.7156i	−0.453288	−	0.785118i	−0.998588	+	0.0531230i	$0.983082\pi$
$992$	5.39493	−	9.34429i	0.171289	−	0.296681i
$993$	−10.2392			−0.324932
$994$	23.2446	−	40.2608i	0.737274	−	1.27700i
$995$	3.20387	−	5.54926i	0.101569	−	0.175923i
$996$	6.49934			0.205939
$997$	9.44265	−	16.3551i	0.299052	−	0.517973i	−0.676868	−	0.736105i	$-0.736663\pi$
$997$	9.44265	−	16.3551i	0.299052	−	0.517973i	0.975919	+	0.218132i	$0.0699964\pi$
$998$	14.1957	+	24.5876i	0.449356	+	0.778308i
$999$	−0.307979	−	0.533434i	−0.00974401	−	0.0168771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.m.991.2		6
13.2	odd	12		1014.2.b.g.337.5		6
13.3	even	3		1014.2.a.m.1.2	✓	3
13.4	even	6		1014.2.e.k.529.2		6
13.5	odd	4		1014.2.i.g.361.5		12
13.6	odd	12		1014.2.i.g.823.2		12
13.7	odd	12		1014.2.i.g.823.5		12
13.8	odd	4		1014.2.i.g.361.2		12
13.9	even	3	inner	1014.2.e.m.529.2		6
13.10	even	6		1014.2.a.o.1.2	yes	3
13.11	odd	12		1014.2.b.g.337.2		6
13.12	even	2		1014.2.e.k.991.2		6
39.2	even	12		3042.2.b.r.1351.2		6
39.11	even	12		3042.2.b.r.1351.5		6
39.23	odd	6		3042.2.a.bd.1.2		3
39.29	odd	6		3042.2.a.be.1.2		3
52.3	odd	6		8112.2.a.ce.1.2		3
52.23	odd	6		8112.2.a.bz.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.2	✓	3	13.3	even	3
1014.2.a.o.1.2	yes	3	13.10	even	6
1014.2.b.g.337.2		6	13.11	odd	12
1014.2.b.g.337.5		6	13.2	odd	12
1014.2.e.k.529.2		6	13.4	even	6
1014.2.e.k.991.2		6	13.12	even	2
1014.2.e.m.529.2		6	13.9	even	3	inner
1014.2.e.m.991.2		6	1.1	even	1	trivial
1014.2.i.g.361.2		12	13.8	odd	4
1014.2.i.g.361.5		12	13.5	odd	4
1014.2.i.g.823.2		12	13.6	odd	12
1014.2.i.g.823.5		12	13.7	odd	12
3042.2.a.bd.1.2		3	39.23	odd	6
3042.2.a.be.1.2		3	39.29	odd	6
3042.2.b.r.1351.2		6	39.2	even	12
3042.2.b.r.1351.5		6	39.11	even	12
8112.2.a.bz.1.2		3	52.23	odd	6
8112.2.a.ce.1.2		3	52.3	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.356896 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.02446 - 3.50647i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.356896 q^{5} +(0.500000 - 0.866025i) q^{6} +(2.02446 - 3.50647i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.178448 - 0.309081i) q^{10} +(-0.455927 - 0.789689i) q^{11} +1.00000 q^{12} +4.04892 q^{14} +(0.178448 + 0.309081i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.04892 - 1.81678i) q^{17} -1.00000 q^{18} +(-2.49396 + 4.31966i) q^{19} +(0.178448 - 0.309081i) q^{20} -4.04892 q^{21} +(0.455927 - 0.789689i) q^{22} +(-4.24698 - 7.35598i) q^{23} +(0.500000 + 0.866025i) q^{24} -4.87263 q^{25} +1.00000 q^{27} +(2.02446 + 3.50647i) q^{28} +(-4.25786 - 7.37484i) q^{29} +(-0.178448 + 0.309081i) q^{30} +10.7899 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.455927 + 0.789689i) q^{33} +2.09783 q^{34} +(-0.722521 + 1.25144i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.307979 - 0.533434i) q^{37} -4.98792 q^{38} +0.356896 q^{40} +(-3.80194 - 6.58515i) q^{41} +(-2.02446 - 3.50647i) q^{42} +(3.13706 - 5.43355i) q^{43} +0.911854 q^{44} +(0.178448 - 0.309081i) q^{45} +(4.24698 - 7.35598i) q^{46} -1.78017 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.69687 - 8.13521i) q^{49} +(-2.43631 - 4.21982i) q^{50} -2.09783 q^{51} +10.4112 q^{53} +(0.500000 + 0.866025i) q^{54} +(0.162718 + 0.281837i) q^{55} +(-2.02446 + 3.50647i) q^{56} +4.98792 q^{57} +(4.25786 - 7.37484i) q^{58} +(-3.02446 + 5.23852i) q^{59} -0.356896 q^{60} +(1.55496 - 2.69327i) q^{61} +(5.39493 + 9.34429i) q^{62} +(2.02446 + 3.50647i) q^{63} +1.00000 q^{64} -0.911854 q^{66} +(6.78986 + 11.7604i) q^{67} +(1.04892 + 1.81678i) q^{68} +(-4.24698 + 7.35598i) q^{69} -1.44504 q^{70} +(5.74094 - 9.94360i) q^{71} +(0.500000 - 0.866025i) q^{72} -0.533188 q^{73} +(0.307979 - 0.533434i) q^{74} +(2.43631 + 4.21982i) q^{75} +(-2.49396 - 4.31966i) q^{76} -3.69202 q^{77} -11.7071 q^{79} +(0.178448 + 0.309081i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.80194 - 6.58515i) q^{82} +6.49934 q^{83} +(2.02446 - 3.50647i) q^{84} +(-0.374354 + 0.648401i) q^{85} +6.27413 q^{86} +(-4.25786 + 7.37484i) q^{87} +(0.455927 + 0.789689i) q^{88} +(-3.24698 - 5.62393i) q^{89} +0.356896 q^{90} +8.49396 q^{92} +(-5.39493 - 9.34429i) q^{93} +(-0.890084 - 1.54167i) q^{94} +(0.890084 - 1.54167i) q^{95} -1.00000 q^{96} +(-0.980386 + 1.69808i) q^{97} +(4.69687 - 8.13521i) q^{98} +0.911854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} - 3 q^{16} - 12 q^{17} - 6 q^{18} + 4 q^{19} - 3 q^{20} - 6 q^{21} - q^{22} - 16 q^{23} + 3 q^{24} + 4 q^{25} + 6 q^{27} + 3 q^{28} - 13 q^{29} + 3 q^{30} + 18 q^{31} + 3 q^{32} + q^{33} - 24 q^{34} - 4 q^{35} - 3 q^{36} - 12 q^{37} + 8 q^{38} - 6 q^{40} - 14 q^{41} - 3 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 16 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{49} + 2 q^{50} + 24 q^{51} + 30 q^{53} + 3 q^{54} + 22 q^{55} - 3 q^{56} - 8 q^{57} + 13 q^{58} - 9 q^{59} + 6 q^{60} + 10 q^{61} + 9 q^{62} + 3 q^{63} + 6 q^{64} + 2 q^{66} - 6 q^{67} - 12 q^{68} - 16 q^{69} - 8 q^{70} + 6 q^{71} + 3 q^{72} - 10 q^{73} + 12 q^{74} - 2 q^{75} + 4 q^{76} - 12 q^{77} - 10 q^{79} - 3 q^{80} - 3 q^{81} + 14 q^{82} + 14 q^{83} + 3 q^{84} - 26 q^{85} + 16 q^{86} - 13 q^{87} - q^{88} - 10 q^{89} - 6 q^{90} + 32 q^{92} - 9 q^{93} - 4 q^{94} + 4 q^{95} - 6 q^{96} + 7 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 - 3 * q^16 - 12 * q^17 - 6 * q^18 + 4 * q^19 - 3 * q^20 - 6 * q^21 - q^22 - 16 * q^23 + 3 * q^24 + 4 * q^25 + 6 * q^27 + 3 * q^28 - 13 * q^29 + 3 * q^30 + 18 * q^31 + 3 * q^32 + q^33 - 24 * q^34 - 4 * q^35 - 3 * q^36 - 12 * q^37 + 8 * q^38 - 6 * q^40 - 14 * q^41 - 3 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 16 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^49 + 2 * q^50 + 24 * q^51 + 30 * q^53 + 3 * q^54 + 22 * q^55 - 3 * q^56 - 8 * q^57 + 13 * q^58 - 9 * q^59 + 6 * q^60 + 10 * q^61 + 9 * q^62 + 3 * q^63 + 6 * q^64 + 2 * q^66 - 6 * q^67 - 12 * q^68 - 16 * q^69 - 8 * q^70 + 6 * q^71 + 3 * q^72 - 10 * q^73 + 12 * q^74 - 2 * q^75 + 4 * q^76 - 12 * q^77 - 10 * q^79 - 3 * q^80 - 3 * q^81 + 14 * q^82 + 14 * q^83 + 3 * q^84 - 26 * q^85 + 16 * q^86 - 13 * q^87 - q^88 - 10 * q^89 - 6 * q^90 + 32 * q^92 - 9 * q^93 - 4 * q^94 + 4 * q^95 - 6 * q^96 + 7 * q^97 - 4 * q^98 - 2 * q^99

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