LMFDB - Embedded newform 429.2.i.c.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.7965937851507.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 $ x^10 - 2x^9 + 8x^8 - 6x^7 + 28x^6 - 23x^5 + 51x^4 - 10x^3 + 25x^2 - 6*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$0.724205 + 1.25436i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.c.133.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.724205 + 1.25436i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.0489465 - 0.0847779i) q^{4} -0.404514 q^{5} +(-0.724205 - 1.25436i) q^{6} +(-1.43979 - 2.49379i) q^{7} -2.75503 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.724205 + 1.25436i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.0489465 - 0.0847779i) q^{4} -0.404514 q^{5} +(-0.724205 - 1.25436i) q^{6} +(-1.43979 - 2.49379i) q^{7} -2.75503 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.292951 - 0.507407i) q^{10} +(0.500000 - 0.866025i) q^{11} +0.0978930 q^{12} +(-2.32079 - 2.75933i) q^{13} +4.17082 q^{14} +(0.202257 - 0.350320i) q^{15} +(2.09310 - 3.62536i) q^{16} +(-0.617693 - 1.06987i) q^{17} +1.44841 q^{18} +(-2.41662 - 4.18571i) q^{19} +(0.0197996 + 0.0342939i) q^{20} +2.87958 q^{21} +(0.724205 + 1.25436i) q^{22} +(-2.99605 + 5.18931i) q^{23} +(1.37752 - 2.38593i) q^{24} -4.83637 q^{25} +(5.14193 - 0.912788i) q^{26} +1.00000 q^{27} +(-0.140946 + 0.244125i) q^{28} +(-2.37487 + 4.11340i) q^{29} +(0.292951 + 0.507407i) q^{30} +6.43354 q^{31} +(0.276639 + 0.479152i) q^{32} +(0.500000 + 0.866025i) q^{33} +1.78934 q^{34} +(0.582416 + 1.00877i) q^{35} +(-0.0489465 + 0.0847779i) q^{36} +(3.04500 - 5.27409i) q^{37} +7.00052 q^{38} +(3.55005 - 0.630200i) q^{39} +1.11445 q^{40} +(1.14802 - 1.98844i) q^{41} +(-2.08541 + 3.61203i) q^{42} +(1.38736 + 2.40297i) q^{43} -0.0978930 q^{44} +(0.202257 + 0.350320i) q^{45} +(-4.33951 - 7.51626i) q^{46} -1.93113 q^{47} +(2.09310 + 3.62536i) q^{48} +(-0.645996 + 1.11890i) q^{49} +(3.50252 - 6.06655i) q^{50} +1.23539 q^{51} +(-0.120336 + 0.331812i) q^{52} -4.21042 q^{53} +(-0.724205 + 1.25436i) q^{54} +(-0.202257 + 0.350320i) q^{55} +(3.96667 + 6.87047i) q^{56} +4.83324 q^{57} +(-3.43979 - 5.95789i) q^{58} +(-3.59823 - 6.23232i) q^{59} -0.0395991 q^{60} +(-5.53971 - 9.59506i) q^{61} +(-4.65920 + 8.06998i) q^{62} +(-1.43979 + 2.49379i) q^{63} +7.57103 q^{64} +(0.938794 + 1.11619i) q^{65} -1.44841 q^{66} +(-7.91979 + 13.7175i) q^{67} +(-0.0604678 + 0.104733i) q^{68} +(-2.99605 - 5.18931i) q^{69} -1.68715 q^{70} +(1.44098 + 2.49584i) q^{71} +(1.37752 + 2.38593i) q^{72} -6.31312 q^{73} +(4.41041 + 7.63905i) q^{74} +(2.41818 - 4.18842i) q^{75} +(-0.236570 + 0.409752i) q^{76} -2.87958 q^{77} +(-1.78047 + 4.90943i) q^{78} -2.73419 q^{79} +(-0.846689 + 1.46651i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.66281 + 2.88007i) q^{82} +3.55488 q^{83} +(-0.140946 - 0.244125i) q^{84} +(0.249865 + 0.432780i) q^{85} -4.01893 q^{86} +(-2.37487 - 4.11340i) q^{87} +(-1.37752 + 2.38593i) q^{88} +(-2.75231 + 4.76713i) q^{89} -0.585903 q^{90} +(-3.53974 + 9.76044i) q^{91} +0.586585 q^{92} +(-3.21677 + 5.57161i) q^{93} +(1.39854 - 2.42234i) q^{94} +(0.977557 + 1.69318i) q^{95} -0.553277 q^{96} +(-1.60965 - 2.78800i) q^{97} +(-0.935667 - 1.62062i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.724205	+	1.25436i	−0.512090	+	0.886967i	0.487811	+	0.872949i	$0.337795\pi$
$2$	−0.724205	+	1.25436i	−0.512090	+	0.886967i	−0.999902	+	0.0140176i	$0.995538\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.0489465	−	0.0847779i	−0.0244733	−	0.0423889i
$5$	−0.404514			−0.180904			−0.0904521	−	0.995901i	$-0.528831\pi$
$5$	−0.404514			−0.180904			−0.0904521	+	0.995901i	$0.528831\pi$
$6$	−0.724205	−	1.25436i	−0.295656	−	0.512090i
$7$	−1.43979	−	2.49379i	−0.544190	−	0.942564i	−0.998657	−	0.0518011i	$-0.983504\pi$
$7$	−1.43979	−	2.49379i	−0.544190	−	0.942564i	0.454468	−	0.890763i	$-0.349830\pi$
$8$	−2.75503			−0.974051
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.292951	−	0.507407i	0.0926394	−	0.160456i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.0978930			0.0282593
$13$	−2.32079	−	2.75933i	−0.643672	−	0.765301i
$13$	−2.32079	−	2.75933i	−0.643672	−	0.765301i
$14$	4.17082			1.11470
$15$	0.202257	−	0.350320i	0.0522226	−	0.0904521i
$16$	2.09310	−	3.62536i	0.523275	−	0.906340i
$17$	−0.617693	−	1.06987i	−0.149812	−	0.259483i	0.781346	−	0.624099i	$-0.214534\pi$
$17$	−0.617693	−	1.06987i	−0.149812	−	0.259483i	−0.931158	+	0.364616i	$0.881200\pi$
$18$	1.44841			0.341394
$19$	−2.41662	−	4.18571i	−0.554411	−	0.960268i	−0.997949	−	0.0640123i	$-0.979610\pi$
$19$	−2.41662	−	4.18571i	−0.554411	−	0.960268i	0.443538	−	0.896255i	$-0.353723\pi$
$20$	0.0197996	+	0.0342939i	0.00442732	+	0.00766834i
$21$	2.87958			0.628376
$22$	0.724205	+	1.25436i	0.154401	+	0.267431i
$23$	−2.99605	+	5.18931i	−0.624720	+	1.08205i	0.363875	+	0.931448i	$0.381454\pi$
$23$	−2.99605	+	5.18931i	−0.624720	+	1.08205i	−0.988595	+	0.150599i	$0.951880\pi$
$24$	1.37752	−	2.38593i	0.281184	−	0.487025i
$25$	−4.83637			−0.967274
$26$	5.14193	−	0.912788i	1.00842	−	0.179012i
$27$	1.00000			0.192450
$28$	−0.140946	+	0.244125i	−0.0266362	+	0.0461352i
$29$	−2.37487	+	4.11340i	−0.441003	+	0.763839i	−0.997764	−	0.0668332i	$-0.978710\pi$
$29$	−2.37487	+	4.11340i	−0.441003	+	0.763839i	0.556761	+	0.830673i	$0.312044\pi$
$30$	0.292951	+	0.507407i	0.0534854	+	0.0926394i
$31$	6.43354			1.15550			0.577749	−	0.816214i	$-0.303931\pi$
$31$	6.43354			1.15550			0.577749	+	0.816214i	$0.303931\pi$
$32$	0.276639	+	0.479152i	0.0489032	+	0.0847029i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	1.78934			0.306870
$35$	0.582416	+	1.00877i	0.0984463	+	0.170514i
$36$	−0.0489465	+	0.0847779i	−0.00815775	+	0.0141296i
$37$	3.04500	−	5.27409i	0.500595	−	0.867055i	−0.499405	−	0.866369i	$-0.666448\pi$
$37$	3.04500	−	5.27409i	0.500595	−	0.867055i	1.00000		0.000686858i	$-0.000218634\pi$
$38$	7.00052			1.13563
$39$	3.55005	−	0.630200i	0.568463	−	0.100913i
$40$	1.11445			0.176210
$41$	1.14802	−	1.98844i	0.179291	−	0.310542i	−0.762347	−	0.647169i	$-0.775953\pi$
$41$	1.14802	−	1.98844i	0.179291	−	0.310542i	0.941638	+	0.336627i	$0.109286\pi$
$42$	−2.08541	+	3.61203i	−0.321785	+	0.557349i
$43$	1.38736	+	2.40297i	0.211570	+	0.366450i	0.952206	−	0.305456i	$-0.0988090\pi$
$43$	1.38736	+	2.40297i	0.211570	+	0.366450i	−0.740636	+	0.671906i	$0.765476\pi$
$44$	−0.0978930			−0.0147579
$45$	0.202257	+	0.350320i	0.0301507	+	0.0522226i
$46$	−4.33951	−	7.51626i	−0.639826	−	1.10821i
$47$	−1.93113			−0.281685			−0.140842	−	0.990032i	$-0.544981\pi$
$47$	−1.93113			−0.281685			−0.140842	+	0.990032i	$0.544981\pi$
$48$	2.09310	+	3.62536i	0.302113	+	0.523275i
$49$	−0.645996	+	1.11890i	−0.0922851	+	0.159842i
$50$	3.50252	−	6.06655i	0.495332	−	0.857939i
$51$	1.23539			0.172989
$52$	−0.120336	+	0.331812i	−0.0166875	+	0.0460140i
$53$	−4.21042			−0.578345			−0.289173	−	0.957277i	$-0.593380\pi$
$53$	−4.21042			−0.578345			−0.289173	+	0.957277i	$0.593380\pi$
$54$	−0.724205	+	1.25436i	−0.0985519	+	0.170697i
$55$	−0.202257	+	0.350320i	−0.0272723	+	0.0472371i
$56$	3.96667	+	6.87047i	0.530069	+	0.918106i
$57$	4.83324			0.640178
$58$	−3.43979	−	5.95789i	−0.451667	−	0.782310i
$59$	−3.59823	−	6.23232i	−0.468450	−	0.811380i	0.530900	−	0.847435i	$-0.321854\pi$
$59$	−3.59823	−	6.23232i	−0.468450	−	0.811380i	−0.999350	+	0.0360552i	$0.988521\pi$
$60$	−0.0395991			−0.00511223
$61$	−5.53971	−	9.59506i	−0.709288	−	1.22852i	−0.965122	−	0.261801i	$-0.915683\pi$
$61$	−5.53971	−	9.59506i	−0.709288	−	1.22852i	0.255834	−	0.966721i	$-0.417650\pi$
$62$	−4.65920	+	8.06998i	−0.591720	+	1.02489i
$63$	−1.43979	+	2.49379i	−0.181397	+	0.314188i
$64$	7.57103			0.946379
$65$	0.938794	+	1.11619i	0.116443	+	0.138446i
$66$	−1.44841			−0.178287
$67$	−7.91979	+	13.7175i	−0.967556	+	1.67586i	−0.264972	+	0.964256i	$0.585363\pi$
$67$	−7.91979	+	13.7175i	−0.967556	+	1.67586i	−0.702584	+	0.711600i	$0.747971\pi$
$68$	−0.0604678	+	0.104733i	−0.00733280	+	0.0127008i
$69$	−2.99605	−	5.18931i	−0.360682	−	0.624720i
$70$	−1.68715			−0.201654
$71$	1.44098	+	2.49584i	0.171012	+	0.296202i	0.938774	−	0.344533i	$-0.111963\pi$
$71$	1.44098	+	2.49584i	0.171012	+	0.296202i	−0.767762	+	0.640736i	$0.778630\pi$
$72$	1.37752	+	2.38593i	0.162342	+	0.281184i
$73$	−6.31312			−0.738895			−0.369448	−	0.929252i	$-0.620453\pi$
$73$	−6.31312			−0.738895			−0.369448	+	0.929252i	$0.620453\pi$
$74$	4.41041	+	7.63905i	0.512700	+	0.888022i
$75$	2.41818	−	4.18842i	0.279228	−	0.483637i
$76$	−0.236570	+	0.409752i	−0.0271365	+	0.0470018i
$77$	−2.87958			−0.328159
$78$	−1.78047	+	4.90943i	−0.201598	+	0.555884i
$79$	−2.73419			−0.307621			−0.153810	−	0.988100i	$-0.549155\pi$
$79$	−2.73419			−0.307621			−0.153810	+	0.988100i	$0.549155\pi$
$80$	−0.846689	+	1.46651i	−0.0946628	+	0.163961i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.66281	+	2.88007i	0.183627	+	0.318051i
$83$	3.55488			0.390199			0.195099	−	0.980783i	$-0.437497\pi$
$83$	3.55488			0.390199			0.195099	+	0.980783i	$0.437497\pi$
$84$	−0.140946	−	0.244125i	−0.0153784	−	0.0266362i
$85$	0.249865	+	0.432780i	0.0271017	+	0.0469415i
$86$	−4.01893			−0.433372
$87$	−2.37487	−	4.11340i	−0.254613	−	0.441003i
$88$	−1.37752	+	2.38593i	−0.146844	+	0.254341i
$89$	−2.75231	+	4.76713i	−0.291744	+	0.505315i	−0.974222	−	0.225591i	$-0.927569\pi$
$89$	−2.75231	+	4.76713i	−0.291744	+	0.505315i	0.682478	+	0.730906i	$0.260902\pi$
$90$	−0.585903			−0.0617596
$91$	−3.53974	+	9.76044i	−0.371066	+	1.02317i
$92$	0.586585			0.0611558
$93$	−3.21677	+	5.57161i	−0.333564	+	0.577749i
$94$	1.39854	−	2.42234i	0.144248	−	0.249845i
$95$	0.977557	+	1.69318i	0.100295	+	0.173717i
$96$	−0.553277			−0.0564686
$97$	−1.60965	−	2.78800i	−0.163435	−	0.283078i	0.772663	−	0.634816i	$-0.218924\pi$
$97$	−1.60965	−	2.78800i	−0.163435	−	0.283078i	−0.936098	+	0.351738i	$0.885591\pi$
$98$	−0.935667	−	1.62062i	−0.0945166	−	0.163708i
$99$	−1.00000			−0.100504
$100$	0.236723	+	0.410017i	0.0236723	+	0.0410017i
$101$	−7.00275	+	12.1291i	−0.696800	+	1.20689i	0.272771	+	0.962079i	$0.412060\pi$
$101$	−7.00275	+	12.1291i	−0.696800	+	1.20689i	−0.969570	+	0.244813i	$0.921273\pi$
$102$	−0.894672	+	1.54962i	−0.0885858	+	0.153435i
$103$	−13.4197			−1.32228			−0.661140	−	0.750263i	$-0.729927\pi$
$103$	−13.4197			−1.32228			−0.661140	+	0.750263i	$0.729927\pi$
$104$	6.39386	+	7.60205i	0.626970	+	0.745442i
$105$	−1.16483			−0.113676
$106$	3.04921	−	5.28138i	0.296165	−	0.512973i
$107$	0.879315	−	1.52302i	0.0850066	−	0.147236i	−0.820387	−	0.571808i	$-0.806242\pi$
$107$	0.879315	−	1.52302i	0.0850066	−	0.147236i	0.905394	+	0.424572i	$0.139576\pi$
$108$	−0.0489465	−	0.0847779i	−0.00470988	−	0.00815775i
$109$	9.54438			0.914185			0.457093	−	0.889419i	$-0.348891\pi$
$109$	9.54438			0.914185			0.457093	+	0.889419i	$0.348891\pi$
$110$	−0.292951	−	0.507407i	−0.0279318	−	0.0483793i
$111$	3.04500	+	5.27409i	0.289018	+	0.500595i
$112$	−12.0545			−1.13904
$113$	−9.49848	−	16.4519i	−0.893542	−	1.54766i	−0.835599	−	0.549340i	$-0.814879\pi$
$113$	−9.49848	−	16.4519i	−0.893542	−	1.54766i	−0.0579434	−	0.998320i	$-0.518454\pi$
$114$	−3.50026	+	6.06263i	−0.327829	+	0.567817i
$115$	1.21195	−	2.09915i	0.113015	−	0.195747i
$116$	0.464967			0.0431711
$117$	−1.22926	+	3.38953i	−0.113645	+	0.313362i
$118$	10.4234			0.959556
$119$	−1.77870	+	3.08079i	−0.163053	+	0.282416i
$120$	−0.557225	+	0.965142i	−0.0508674	+	0.0881050i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	16.0476			1.45288
$123$	1.14802	+	1.98844i	0.103514	+	0.179291i
$124$	−0.314899	−	0.545422i	−0.0282788	−	0.0489803i
$125$	3.97895			0.355888
$126$	−2.08541	−	3.61203i	−0.185783	−	0.321785i
$127$	−0.0650006	+	0.112584i	−0.00576787	+	0.00999025i	−0.868895	−	0.494997i	$-0.835169\pi$
$127$	−0.0650006	+	0.112584i	−0.00576787	+	0.00999025i	0.863127	+	0.504987i	$0.168503\pi$
$128$	−6.03626	+	10.4551i	−0.533535	+	0.924110i
$129$	−2.77472			−0.244300
$130$	−2.07998	+	0.369236i	−0.182427	+	0.0323841i
$131$	8.28393			0.723770			0.361885	−	0.932223i	$-0.382133\pi$
$131$	8.28393			0.723770			0.361885	+	0.932223i	$0.382133\pi$
$132$	0.0489465	−	0.0847779i	0.00426025	−	0.00737897i
$133$	−6.95886	+	12.0531i	−0.603409	+	1.04514i
$134$	−11.4711	−	19.8685i	−0.990953	−	1.71638i
$135$	−0.404514			−0.0348150
$136$	1.70176	+	2.94754i	0.145925	+	0.252749i
$137$	−10.3614	−	17.9465i	−0.885236	−	1.53327i	−0.845443	−	0.534066i	$-0.820663\pi$
$137$	−10.3614	−	17.9465i	−0.885236	−	1.53327i	−0.0397936	−	0.999208i	$-0.512670\pi$
$138$	8.67903			0.738808
$139$	3.49018	+	6.04517i	0.296033	+	0.512745i	0.975225	−	0.221216i	$-0.0710027\pi$
$139$	3.49018	+	6.04517i	0.296033	+	0.512745i	−0.679191	+	0.733961i	$0.737669\pi$
$140$	0.0570145	−	0.0987520i	0.00481860	−	0.00834606i
$141$	0.965567	−	1.67241i	0.0813154	−	0.140842i
$142$	−4.17425			−0.350295
$143$	−3.55005	+	0.630200i	−0.296870	+	0.0527000i
$144$	−4.18620			−0.348850
$145$	0.960670	−	1.66393i	0.0797793	−	0.138182i
$146$	4.57200	−	7.91893i	0.378381	−	0.655375i
$147$	−0.645996	−	1.11890i	−0.0532808	−	0.0922851i
$148$	−0.596168			−0.0490047
$149$	−9.92783	−	17.1955i	−0.813320	−	1.40871i	−0.910528	−	0.413447i	$-0.864325\pi$
$149$	−9.92783	−	17.1955i	−0.813320	−	1.40871i	0.0972085	−	0.995264i	$-0.469009\pi$
$150$	3.50252	+	6.06655i	0.285980	+	0.495332i
$151$	−13.3172			−1.08374			−0.541868	−	0.840463i	$-0.682283\pi$
$151$	−13.3172			−1.08374			−0.541868	+	0.840463i	$0.682283\pi$
$152$	6.65787	+	11.5318i	0.540024	+	0.935349i
$153$	−0.617693	+	1.06987i	−0.0499375	+	0.0864943i
$154$	2.08541	−	3.61203i	0.168047	−	0.291066i
$155$	−2.60246			−0.209035
$156$	−0.227190	−	0.270119i	−0.0181897	−	0.0216269i
$157$	21.3752			1.70592			0.852962	−	0.521973i	$-0.174804\pi$
$157$	21.3752			1.70592			0.852962	+	0.521973i	$0.174804\pi$
$158$	1.98012	−	3.42966i	0.157530	−	0.272849i
$159$	2.10521	−	3.64633i	0.166954	−	0.289173i
$160$	−0.111904	−	0.193824i	−0.00884681	−	0.0153231i
$161$	17.2548			1.35987
$162$	−0.724205	−	1.25436i	−0.0568989	−	0.0985519i
$163$	6.05115	+	10.4809i	0.473963	+	0.820928i	0.999556	−	0.0298086i	$-0.00948979\pi$
$163$	6.05115	+	10.4809i	0.473963	+	0.820928i	−0.525593	+	0.850736i	$0.676156\pi$
$164$	−0.224767			−0.0175514
$165$	−0.202257	−	0.350320i	−0.0157457	−	0.0272723i
$166$	−2.57446	+	4.45910i	−0.199817	+	0.346093i
$167$	1.55446	−	2.69241i	0.120288	−	0.208345i	−0.799593	−	0.600542i	$-0.794952\pi$
$167$	1.55446	−	2.69241i	0.120288	−	0.208345i	0.919881	+	0.392197i	$0.128285\pi$
$168$	−7.93334			−0.612070
$169$	−2.22783	+	12.8077i	−0.171372	+	0.985206i
$170$	−0.723816			−0.0555141
$171$	−2.41662	+	4.18571i	−0.184804	+	0.320089i
$172$	0.135813	−	0.235234i	0.0103556	−	0.0179365i
$173$	2.12152	+	3.67458i	0.161296	+	0.279373i	0.935334	−	0.353766i	$-0.115099\pi$
$173$	2.12152	+	3.67458i	0.161296	+	0.279373i	−0.774038	+	0.633140i	$0.781766\pi$
$174$	6.87958			0.521540
$175$	6.96336	+	12.0609i	0.526380	+	0.911718i
$176$	−2.09310	−	3.62536i	−0.157773	−	0.273272i
$177$	7.19647			0.540920
$178$	−3.98647	−	6.90477i	−0.298799	−	0.517534i
$179$	1.46166	−	2.53166i	0.109249	−	0.189225i	−0.806217	−	0.591620i	$-0.798489\pi$
$179$	1.46166	−	2.53166i	0.109249	−	0.189225i	0.915466	+	0.402394i	$0.131822\pi$
$180$	0.0197996	−	0.0342939i	0.00147577	−	0.00255611i
$181$	−2.77704			−0.206416			−0.103208	−	0.994660i	$-0.532911\pi$
$181$	−2.77704			−0.206416			−0.103208	+	0.994660i	$0.532911\pi$
$182$	−9.67960	−	11.5087i	−0.717500	−	0.853079i
$183$	11.0794			0.819015
$184$	8.25422	−	14.2967i	0.608509	−	1.05397i
$185$	−1.23175	+	2.13345i	−0.0905597	+	0.156854i
$186$	−4.65920	−	8.06998i	−0.341629	−	0.591720i
$187$	−1.23539			−0.0903403
$188$	0.0945223	+	0.163717i	0.00689375	+	0.0119403i
$189$	−1.43979	−	2.49379i	−0.104729	−	0.181397i
$190$	−2.83181			−0.205441
$191$	11.4344	+	19.8049i	0.827363	+	1.43303i	0.900100	+	0.435684i	$0.143493\pi$
$191$	11.4344	+	19.8049i	0.827363	+	1.43303i	−0.0727367	+	0.997351i	$0.523173\pi$
$192$	−3.78552	+	6.55671i	−0.273196	+	0.473190i
$193$	4.04125	−	6.99966i	0.290896	−	0.503846i	−0.683126	−	0.730301i	$-0.739380\pi$
$193$	4.04125	−	6.99966i	0.290896	−	0.503846i	0.974022	+	0.226454i	$0.0727134\pi$
$194$	4.66287			0.334774
$195$	−1.43605	+	0.254925i	−0.102837	+	0.0182555i
$196$	0.126477			0.00903407
$197$	11.1283	−	19.2747i	0.792857	−	1.37327i	−0.131334	−	0.991338i	$-0.541926\pi$
$197$	11.1283	−	19.2747i	0.792857	−	1.37327i	0.924191	−	0.381931i	$-0.124741\pi$
$198$	0.724205	−	1.25436i	0.0514670	−	0.0891435i
$199$	11.2834	+	19.5434i	0.799859	+	1.38540i	0.919708	+	0.392604i	$0.128426\pi$
$199$	11.2834	+	19.5434i	0.799859	+	1.38540i	−0.119849	+	0.992792i	$0.538241\pi$
$200$	13.3243			0.942174
$201$	−7.91979	−	13.7175i	−0.558619	−	0.967556i
$202$	−10.1429	−	17.5679i	−0.713649	−	1.23608i
$203$	13.6773			0.959957
$204$	−0.0604678	−	0.104733i	−0.00423359	−	0.00733280i
$205$	−0.464392	+	0.804351i	−0.0324346	+	0.0561783i
$206$	9.71860	−	16.8331i	0.677127	−	1.17282i
$207$	5.99210			0.416480
$208$	−14.8612	+	2.63814i	−1.03044	+	0.182922i
$209$	−4.83324			−0.334322
$210$	0.843577	−	1.46112i	0.0582124	−	0.100827i
$211$	14.2890	−	24.7493i	0.983695	−	1.70381i	0.336098	−	0.941827i	$-0.390893\pi$
$211$	14.2890	−	24.7493i	0.983695	−	1.70381i	0.647597	−	0.761983i	$-0.275774\pi$
$212$	0.206085	+	0.356950i	0.0141540	+	0.0245154i
$213$	−2.88195			−0.197468
$214$	1.27361	+	2.20596i	0.0870621	+	0.150796i
$215$	−0.561206	−	0.972037i	−0.0382739	−	0.0662924i
$216$	−2.75503			−0.187456
$217$	−9.26295	−	16.0439i	−0.628810	−	1.08913i
$218$	−6.91209	+	11.9721i	−0.468146	+	0.810852i
$219$	3.15656	−	5.46733i	0.213301	−	0.369448i
$220$	0.0395991			0.00266977
$221$	−1.51860	+	4.18738i	−0.102152	+	0.281674i
$222$	−8.82082			−0.592014
$223$	−7.73996	+	13.4060i	−0.518306	+	0.897733i	0.481467	+	0.876464i	$0.340104\pi$
$223$	−7.73996	+	13.4060i	−0.518306	+	0.897733i	−0.999774	+	0.0212689i	$0.993229\pi$
$224$	0.796603	−	1.37976i	0.0532253	−	0.0921889i
$225$	2.41818	+	4.18842i	0.161212	+	0.279228i
$226$	27.5154			1.83030
$227$	−6.63768	−	11.4968i	−0.440558	−	0.763069i	0.557173	−	0.830397i	$-0.311886\pi$
$227$	−6.63768	−	11.4968i	−0.440558	−	0.763069i	−0.997731	+	0.0673273i	$0.978553\pi$
$228$	−0.236570	−	0.409752i	−0.0156673	−	0.0271365i
$229$	27.9909			1.84969			0.924846	−	0.380342i	$-0.124194\pi$
$229$	27.9909			1.84969			0.924846	+	0.380342i	$0.124194\pi$
$230$	1.75540	+	3.04043i	0.115747	+	0.200480i
$231$	1.43979	−	2.49379i	0.0947313	−	0.164079i
$232$	6.54285	−	11.3325i	0.429559	−	0.744018i
$233$	−18.2051			−1.19266			−0.596329	−	0.802740i	$-0.703375\pi$
$233$	−18.2051			−1.19266			−0.596329	+	0.802740i	$0.703375\pi$
$234$	−3.36146	−	3.99665i	−0.219746	−	0.261269i
$235$	0.781171			0.0509580
$236$	−0.352242	+	0.610101i	−0.0229290	+	0.0397142i
$237$	1.36710	−	2.36788i	0.0888025	−	0.153810i
$238$	−2.57628	−	4.46225i	−0.166996	−	0.289245i
$239$	16.3923			1.06033			0.530166	−	0.847894i	$-0.322130\pi$
$239$	16.3923			1.06033			0.530166	+	0.847894i	$0.322130\pi$
$240$	−0.846689	−	1.46651i	−0.0546536	−	0.0946628i
$241$	5.07453	+	8.78934i	0.326879	+	0.566171i	0.981891	−	0.189447i	$-0.0606697\pi$
$241$	5.07453	+	8.78934i	0.326879	+	0.566171i	−0.655012	+	0.755619i	$0.727336\pi$
$242$	1.44841			0.0931074
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.542299	+	0.939290i	−0.0347172	+	0.0601319i
$245$	0.261314	−	0.452610i	0.0166948	−	0.0289162i
$246$	−3.32562			−0.212034
$247$	−5.94129	+	16.3824i	−0.378035	+	1.04239i
$248$	−17.7246			−1.12551
$249$	−1.77744	+	3.07862i	−0.112641	+	0.195099i
$250$	−2.88158	+	4.99104i	−0.182247	+	0.315661i
$251$	−9.38566	−	16.2564i	−0.592418	−	1.02610i	−0.993906	−	0.110233i	$-0.964840\pi$
$251$	−9.38566	−	16.2564i	−0.592418	−	1.02610i	0.401488	−	0.915864i	$-0.368493\pi$
$252$	0.281891			0.0177575
$253$	2.99605	+	5.18931i	0.188360	+	0.326249i
$254$	−0.0941476	−	0.163068i	−0.00590734	−	0.0102318i
$255$	−0.499731			−0.0312944
$256$	−1.17195	−	2.02987i	−0.0732468	−	0.126867i
$257$	9.05547	−	15.6845i	0.564865	−	0.978375i	−0.432197	−	0.901779i	$-0.642262\pi$
$257$	9.05547	−	15.6845i	0.564865	−	0.978375i	0.997062	−	0.0765955i	$-0.0244050\pi$
$258$	2.00946	−	3.48049i	0.125104	−	0.216686i
$259$	−17.5366			−1.08967
$260$	0.0486775	−	0.134223i	0.00301885	−	0.00832413i
$261$	4.74975			0.294002
$262$	−5.99927	+	10.3910i	−0.370636	+	0.641960i
$263$	−12.9584	+	22.4446i	−0.799049	+	1.38399i	0.121187	+	0.992630i	$0.461330\pi$
$263$	−12.9584	+	22.4446i	−0.799049	+	1.38399i	−0.920236	+	0.391364i	$0.872003\pi$
$264$	−1.37752	−	2.38593i	−0.0847802	−	0.146844i
$265$	1.70317			0.104625
$266$	−10.0793	−	17.4578i	−0.618000	−	1.07041i
$267$	−2.75231	−	4.76713i	−0.168438	−	0.291744i
$268$	1.55058			0.0947170
$269$	10.9664	+	18.9944i	0.668634	+	1.15811i	0.978286	+	0.207258i	$0.0664540\pi$
$269$	10.9664	+	18.9944i	0.668634	+	1.15811i	−0.309652	+	0.950850i	$0.600213\pi$
$270$	0.292951	−	0.507407i	0.0178285	−	0.0308798i
$271$	2.82212	−	4.88806i	0.171432	−	0.296928i	−0.767489	−	0.641062i	$-0.778494\pi$
$271$	2.82212	−	4.88806i	0.171432	−	0.296928i	0.938921	+	0.344134i	$0.111827\pi$
$272$	−5.17157			−0.313573
$273$	−6.68291	−	7.94572i	−0.404468	−	0.480897i
$274$	30.0152			1.81328
$275$	−2.41818	+	4.18842i	−0.145822	+	0.252571i
$276$	−0.293293	+	0.507998i	−0.0176541	+	0.0305779i
$277$	2.71494	+	4.70241i	0.163125	+	0.282541i	0.935988	−	0.352032i	$-0.114509\pi$
$277$	2.71494	+	4.70241i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$278$	−10.1104			−0.606383
$279$	−3.21677	−	5.57161i	−0.192583	−	0.333564i
$280$	−1.60457	−	2.77920i	−0.0958917	−	0.166089i
$281$	−21.3960			−1.27638			−0.638188	−	0.769881i	$-0.720316\pi$
$281$	−21.3960			−1.27638			−0.638188	+	0.769881i	$0.720316\pi$
$282$	1.39854	+	2.42234i	0.0832817	+	0.144248i
$283$	−4.57498	+	7.92410i	−0.271954	+	0.471039i	−0.969362	−	0.245636i	$-0.921003\pi$
$283$	−4.57498	+	7.92410i	−0.271954	+	0.471039i	0.697408	+	0.716675i	$0.254337\pi$
$284$	0.141062	−	0.244326i	0.00837046	−	0.0144981i
$285$	−1.95511			−0.115811
$286$	1.78047	−	4.90943i	0.105281	−	0.290301i
$287$	−6.61166			−0.390274
$288$	0.276639	−	0.479152i	0.0163011	−	0.0282343i
$289$	7.73691	−	13.4007i	0.455112	−	0.788278i
$290$	1.39144	+	2.41005i	0.0817084	+	0.141523i
$291$	3.21930			0.188719
$292$	0.309005	+	0.535213i	0.0180832	+	0.0313210i
$293$	−1.18603	−	2.05426i	−0.0692884	−	0.120011i	0.829300	−	0.558804i	$-0.188740\pi$
$293$	−1.18603	−	2.05426i	−0.0692884	−	0.120011i	−0.898588	+	0.438793i	$0.855406\pi$
$294$	1.87133			0.109138
$295$	1.45554	+	2.52106i	0.0847446	+	0.146782i
$296$	−8.38907	+	14.5303i	−0.487605	+	0.844556i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	28.7592			1.66597
$299$	21.2723	−	3.77622i	1.23021	−	0.218385i
$300$	−0.473447			−0.0273345
$301$	3.99501	−	6.91956i	0.230269	−	0.398837i
$302$	9.64437	−	16.7045i	0.554971	−	0.961238i
$303$	−7.00275	−	12.1291i	−0.402297	−	0.696800i
$304$	−20.2329			−1.16044
$305$	2.24089	+	3.88134i	0.128313	+	0.222245i
$306$	−0.894672	−	1.54962i	−0.0511450	−	0.0885858i
$307$	11.6946			0.667448			0.333724	−	0.942671i	$-0.391695\pi$
$307$	11.6946			0.667448			0.333724	+	0.942671i	$0.391695\pi$
$308$	0.140946	+	0.244125i	0.00803112	+	0.0139103i
$309$	6.70984	−	11.6218i	0.381709	−	0.661140i
$310$	1.88471	−	3.26442i	0.107045	−	0.185407i
$311$	3.94022			0.223429			0.111715	−	0.993740i	$-0.464366\pi$
$311$	3.94022			0.223429			0.111715	+	0.993740i	$0.464366\pi$
$312$	−9.78050	+	1.73622i	−0.553712	+	0.0982941i
$313$	−4.96530			−0.280655			−0.140328	−	0.990105i	$-0.544816\pi$
$313$	−4.96530			−0.280655			−0.140328	+	0.990105i	$0.544816\pi$
$314$	−15.4800	+	26.8122i	−0.873588	+	1.51310i
$315$	0.582416	−	1.00877i	0.0328154	−	0.0568380i
$316$	0.133829	+	0.231799i	0.00752849	+	0.0130397i
$317$	2.24582			0.126138			0.0630688	−	0.998009i	$-0.479911\pi$
$317$	2.24582			0.126138			0.0630688	+	0.998009i	$0.479911\pi$
$318$	3.04921	+	5.28138i	0.170991	+	0.296165i
$319$	2.37487	+	4.11340i	0.132967	+	0.230306i
$320$	−3.06259			−0.171204
$321$	0.879315	+	1.52302i	0.0490786	+	0.0850066i
$322$	−12.4960	+	21.6437i	−0.696374	+	1.20616i
$323$	−2.98546	+	5.17096i	−0.166115	+	0.287720i
$324$	0.0978930			0.00543850
$325$	11.2242	+	13.3451i	0.622607	+	0.740256i
$326$	−17.5291			−0.970847
$327$	−4.77219	+	8.26567i	−0.263903	+	0.457093i
$328$	−3.16284	+	5.47821i	−0.174639	+	0.302483i
$329$	2.78043	+	4.81585i	0.153290	+	0.265506i
$330$	0.585903			0.0322529
$331$	2.02129	+	3.50097i	0.111100	+	0.192431i	0.916214	−	0.400689i	$-0.131229\pi$
$331$	2.02129	+	3.50097i	0.111100	+	0.192431i	−0.805114	+	0.593120i	$0.797896\pi$
$332$	−0.173999	−	0.301375i	−0.00954944	−	0.0165401i
$333$	−6.09000			−0.333730
$334$	2.25150	+	3.89971i	0.123197	+	0.213383i
$335$	3.20367	−	5.54891i	0.175035	−	0.303170i
$336$	6.02726	−	10.4395i	0.328814	−	0.569522i
$337$	−10.1170			−0.551106			−0.275553	−	0.961286i	$-0.588861\pi$
$337$	−10.1170			−0.551106			−0.275553	+	0.961286i	$0.588861\pi$
$338$	−14.4520	−	12.0699i	−0.786087	−	0.656516i
$339$	18.9970			1.03177
$340$	0.0244601	−	0.0423661i	0.00132653	−	0.00229763i
$341$	3.21677	−	5.57161i	0.174198	−	0.301720i
$342$	−3.50026	−	6.06263i	−0.189272	−	0.327829i
$343$	−16.4367			−0.887497
$344$	−3.82221	−	6.62027i	−0.206080	−	0.356941i
$345$	1.21195	+	2.09915i	0.0652490	+	0.113015i
$346$	−6.14567			−0.330393
$347$	6.10946	+	10.5819i	0.327973	+	0.568066i	0.982110	−	0.188311i	$-0.0603012\pi$
$347$	6.10946	+	10.5819i	0.327973	+	0.568066i	−0.654137	+	0.756376i	$0.726968\pi$
$348$	−0.232484	+	0.402673i	−0.0124624	+	0.0215856i
$349$	−0.729499	+	1.26353i	−0.0390492	+	0.0676352i	−0.884889	−	0.465801i	$-0.845766\pi$
$349$	−0.729499	+	1.26353i	−0.0390492	+	0.0676352i	0.845840	+	0.533436i	$0.179100\pi$
$350$	−20.1716			−1.07822
$351$	−2.32079	−	2.75933i	−0.123875	−	0.147282i
$352$	0.553277			0.0294898
$353$	−0.366324	+	0.634491i	−0.0194974	+	0.0337706i	−0.875610	−	0.483020i	$-0.839540\pi$
$353$	−0.366324	+	0.634491i	−0.0194974	+	0.0337706i	0.856112	+	0.516790i	$0.172873\pi$
$354$	−5.21172	+	9.02696i	−0.277000	+	0.479778i
$355$	−0.582895	−	1.00960i	−0.0309369	−	0.0535842i
$356$	0.538863			0.0285597
$357$	−1.77870	−	3.08079i	−0.0941386	−	0.163053i
$358$	2.11708	+	3.66689i	0.111891	+	0.193801i
$359$	−4.82640			−0.254728			−0.127364	−	0.991856i	$-0.540652\pi$
$359$	−4.82640			−0.254728			−0.127364	+	0.991856i	$0.540652\pi$
$360$	−0.557225	−	0.965142i	−0.0293683	−	0.0508674i
$361$	−2.18011	+	3.77606i	−0.114743	+	0.198740i
$362$	2.01115	−	3.48341i	0.105704	−	0.183084i
$363$	1.00000			0.0524864
$364$	1.00073	−	0.177648i	0.0524523	−	0.00931127i
$365$	2.55375			0.133669
$366$	−8.02378	+	13.8976i	−0.419410	+	0.726439i
$367$	4.27675	−	7.40755i	0.223245	−	0.386671i	−0.732547	−	0.680717i	$-0.761668\pi$
$367$	4.27675	−	7.40755i	0.223245	−	0.386671i	0.955791	+	0.294046i	$0.0950018\pi$
$368$	12.5421	+	21.7235i	0.653801	+	1.13242i
$369$	−2.29605			−0.119528
$370$	−1.78407	−	3.09011i	−0.0927495	−	0.160647i
$371$	6.06212	+	10.4999i	0.314730	+	0.545127i
$372$	0.629799			0.0326536
$373$	14.6875	+	25.4394i	0.760487	+	1.31720i	0.942600	+	0.333925i	$0.108373\pi$
$373$	14.6875	+	25.4394i	0.760487	+	1.31720i	−0.182112	+	0.983278i	$0.558293\pi$
$374$	0.894672	−	1.54962i	0.0462624	−	0.0801288i
$375$	−1.98948	+	3.44587i	−0.102736	+	0.177944i
$376$	5.32034			0.274375
$377$	16.8618	−	2.99329i	0.868428	−	0.154162i
$378$	4.17082			0.214524
$379$	7.21290	−	12.4931i	0.370502	−	0.641728i	−0.619141	−	0.785280i	$-0.712519\pi$
$379$	7.21290	−	12.4931i	0.370502	−	0.641728i	0.989643	+	0.143552i	$0.0458524\pi$
$380$	0.0956961	−	0.165750i	0.00490911	−	0.00850282i
$381$	−0.0650006	−	0.112584i	−0.00333008	−	0.00576787i
$382$	−33.1234			−1.69474
$383$	0.771413	+	1.33613i	0.0394173	+	0.0682729i	0.885061	−	0.465475i	$-0.154116\pi$
$383$	0.771413	+	1.33613i	0.0394173	+	0.0682729i	−0.845644	+	0.533748i	$0.820783\pi$
$384$	−6.03626	−	10.4551i	−0.308037	−	0.533535i
$385$	1.16483			0.0593653
$386$	5.85339	+	10.1384i	0.297930	+	0.516030i
$387$	1.38736	−	2.40297i	0.0705234	−	0.122150i
$388$	−0.157574	+	0.272925i	−0.00799958	+	0.0138557i
$389$	−29.5984			−1.50070			−0.750349	−	0.661042i	$-0.770114\pi$
$389$	−29.5984			−1.50070			−0.750349	+	0.661042i	$0.770114\pi$
$390$	0.720224	−	1.98594i	0.0364700	−	0.100562i
$391$	7.40256			0.374363
$392$	1.77974	−	3.08260i	0.0898904	−	0.155695i
$393$	−4.14197	+	7.17409i	−0.208935	+	0.361885i
$394$	16.1183	+	27.9177i	0.812029	+	1.40648i
$395$	1.10602			0.0556499
$396$	0.0489465	+	0.0847779i	0.00245966	+	0.00426025i
$397$	−11.6942	−	20.2550i	−0.586916	−	1.01657i	−0.994634	−	0.103460i	$-0.967009\pi$
$397$	−11.6942	−	20.2550i	−0.586916	−	1.01657i	0.407718	−	0.913108i	$-0.366325\pi$
$398$	−32.6860			−1.63840
$399$	−6.95886	−	12.0531i	−0.348379	−	0.603409i
$400$	−10.1230	+	17.5336i	−0.506150	+	0.876678i
$401$	−14.7911	+	25.6190i	−0.738634	+	1.27935i	0.214476	+	0.976729i	$0.431196\pi$
$401$	−14.7911	+	25.6190i	−0.738634	+	1.27935i	−0.953110	+	0.302623i	$0.902138\pi$
$402$	22.9422			1.14425
$403$	−14.9309	−	17.7523i	−0.743762	−	0.884304i
$404$	1.37104			0.0682118
$405$	0.202257	−	0.350320i	0.0100502	−	0.0174075i
$406$	−9.90516	+	17.1562i	−0.491585	+	0.851450i
$407$	−3.04500	−	5.27409i	−0.150935	−	0.261427i
$408$	−3.40353			−0.168500
$409$	−10.0276	−	17.3683i	−0.495831	−	0.858805i	0.504157	−	0.863612i	$-0.331803\pi$
$409$	−10.0276	−	17.3683i	−0.495831	−	0.858805i	−0.999988	+	0.00480681i	$0.998470\pi$
$410$	−0.672631	−	1.16503i	−0.0332189	−	0.0575368i
$411$	20.7228			1.02218
$412$	0.656847	+	1.13769i	0.0323605	+	0.0560500i
$413$	−10.3614	+	17.9465i	−0.509852	+	0.883089i
$414$	−4.33951	+	7.51626i	−0.213275	+	0.369404i
$415$	−1.43800			−0.0705887
$416$	0.680119	−	1.87535i	0.0333456	−	0.0919466i
$417$	−6.98036			−0.341830
$418$	3.50026	−	6.06263i	0.171203	−	0.296533i
$419$	1.18168	−	2.04673i	0.0577288	−	0.0999892i	−0.835717	−	0.549161i	$-0.814947\pi$
$419$	1.18168	−	2.04673i	0.0577288	−	0.0999892i	0.893446	+	0.449172i	$0.148281\pi$
$420$	0.0570145	+	0.0987520i	0.00278202	+	0.00481860i
$421$	−33.6475			−1.63988			−0.819938	−	0.572452i	$-0.805992\pi$
$421$	−33.6475			−1.63988			−0.819938	+	0.572452i	$0.805992\pi$
$422$	20.6963	+	35.8471i	1.00748	+	1.74501i
$423$	0.965567	+	1.67241i	0.0469475	+	0.0813154i
$424$	11.5998			0.563337
$425$	2.98739	+	5.17431i	0.144910	+	0.250991i
$426$	2.08712	−	3.61501i	0.101122	−	0.175148i
$427$	−15.9521	+	27.6298i	−0.771974	+	1.33710i
$428$	−0.172158			−0.00832155
$429$	1.22926	−	3.38953i	0.0593490	−	0.163648i
$430$	1.62571			0.0783989
$431$	8.50343	−	14.7284i	0.409596	−	0.709441i	−0.585249	−	0.810854i	$-0.699003\pi$
$431$	8.50343	−	14.7284i	0.409596	−	0.709441i	0.994844	+	0.101413i	$0.0323364\pi$
$432$	2.09310	−	3.62536i	0.100704	−	0.174425i
$433$	−11.1458	−	19.3051i	−0.535632	−	0.927742i	−0.999132	−	0.0416456i	$-0.986740\pi$
$433$	−11.1458	−	19.3051i	−0.535632	−	0.927742i	0.463500	−	0.886097i	$-0.346593\pi$
$434$	26.8331			1.28803
$435$	0.960670	+	1.66393i	0.0460606	+	0.0797793i
$436$	−0.467164	−	0.809152i	−0.0223731	−	0.0387513i
$437$	28.9613			1.38541
$438$	4.57200	+	7.91893i	0.218458	+	0.378381i
$439$	1.86488	−	3.23006i	0.0890058	−	0.154163i	−0.818085	−	0.575097i	$-0.804964\pi$
$439$	1.86488	−	3.23006i	0.0890058	−	0.154163i	0.907091	+	0.420934i	$0.138298\pi$
$440$	0.557225	−	0.965142i	0.0265647	−	0.0460113i
$441$	1.29199			0.0615234
$442$	−4.15270	−	4.93740i	−0.197524	−	0.234848i
$443$	17.4170			0.827506			0.413753	−	0.910389i	$-0.364218\pi$
$443$	17.4170			0.827506			0.413753	+	0.910389i	$0.364218\pi$
$444$	0.298084	−	0.516297i	0.0141465	−	0.0245024i
$445$	1.11335	−	1.92837i	0.0527777	−	0.0914137i
$446$	−11.2106	−	19.4174i	−0.530839	−	0.919441i
$447$	19.8557			0.939141
$448$	−10.9007	−	18.8806i	−0.515010	−	0.892023i
$449$	−6.08463	−	10.5389i	−0.287151	−	0.497361i	0.685977	−	0.727623i	$-0.259375\pi$
$449$	−6.08463	−	10.5389i	−0.287151	−	0.497361i	−0.973129	+	0.230262i	$0.926042\pi$
$450$	−7.00505			−0.330221
$451$	−1.14802	−	1.98844i	−0.0540584	−	0.0936318i
$452$	−0.929835	+	1.61052i	−0.0437358	+	0.0757526i
$453$	6.65859	−	11.5330i	0.312848	−	0.541868i
$454$	19.2282			0.902423
$455$	1.43188	−	3.94824i	0.0671274	−	0.185096i
$456$	−13.3157			−0.623566
$457$	−4.97322	+	8.61388i	−0.232638	+	0.402940i	−0.958583	−	0.284812i	$-0.908069\pi$
$457$	−4.97322	+	8.61388i	−0.232638	+	0.402940i	0.725946	+	0.687752i	$0.241402\pi$
$458$	−20.2712	+	35.1107i	−0.947210	+	1.64062i
$459$	−0.617693	−	1.06987i	−0.0288314	−	0.0499375i
$460$	−0.237282			−0.0110633
$461$	−15.4780	−	26.8087i	−0.720883	−	1.24861i	−0.960646	−	0.277775i	$-0.910403\pi$
$461$	−15.4780	−	26.8087i	−0.720883	−	1.24861i	0.239763	−	0.970831i	$-0.422930\pi$
$462$	2.08541	+	3.61203i	0.0970220	+	0.168047i
$463$	16.1357			0.749891			0.374945	−	0.927047i	$-0.377661\pi$
$463$	16.1357			0.749891			0.374945	+	0.927047i	$0.377661\pi$
$464$	9.94170	+	17.2195i	0.461532	+	0.799397i
$465$	1.30123	−	2.25380i	0.0603431	−	0.104517i
$466$	13.1843	−	22.8358i	0.610749	−	1.05785i
$467$	16.4891			0.763027			0.381513	−	0.924363i	$-0.375403\pi$
$467$	16.4891			0.763027			0.381513	+	0.924363i	$0.375403\pi$
$468$	0.347525	−	0.0616922i	0.0160644	−	0.00285172i
$469$	45.6114			2.10614
$470$	−0.565728	+	0.979870i	−0.0260951	+	0.0451980i
$471$	−10.6876	+	18.5114i	−0.492458	+	0.852962i
$472$	9.91325	+	17.1703i	0.456294	+	0.790325i
$473$	2.77472			0.127582
$474$	1.98012	+	3.42966i	0.0909498	+	0.157530i
$475$	11.6877	+	20.2436i	0.536267	+	0.928842i
$476$	0.348244			0.0159617
$477$	2.10521	+	3.64633i	0.0963908	+	0.166954i
$478$	−11.8714	+	20.5619i	−0.542986	+	0.940479i
$479$	−17.5645	+	30.4225i	−0.802541	+	1.39004i	0.115398	+	0.993319i	$0.463186\pi$
$479$	−17.5645	+	30.4225i	−0.802541	+	1.39004i	−0.917939	+	0.396722i	$0.870148\pi$
$480$	0.223808			0.0102154
$481$	−21.6198	+	3.83792i	−0.985778	+	0.174994i
$482$	−14.7000			−0.669567
$483$	−8.62738	+	14.9431i	−0.392559	+	0.679933i
$484$	−0.0489465	+	0.0847779i	−0.00222484	+	0.00385354i
$485$	0.651126	+	1.12778i	0.0295661	+	0.0512100i
$486$	1.44841			0.0657012
$487$	7.95054	+	13.7707i	0.360273	+	0.624012i	0.988006	−	0.154418i	$-0.0493501\pi$
$487$	7.95054	+	13.7707i	0.360273	+	0.624012i	−0.627732	+	0.778429i	$0.716017\pi$
$488$	15.2621	+	26.4347i	0.690882	+	1.19664i
$489$	−12.1023			−0.547285
$490$	0.378491	+	0.655565i	0.0170985	+	0.0296154i
$491$	20.0569	−	34.7395i	0.905153	−	1.56777i	0.0844414	−	0.996428i	$-0.473089\pi$
$491$	20.0569	−	34.7395i	0.905153	−	1.56777i	0.820712	−	0.571343i	$-0.193577\pi$
$492$	0.112384	−	0.194654i	0.00506665	−	0.00877569i
$493$	5.86777			0.264271
$494$	−16.2468	−	19.3168i	−0.730976	−	0.869102i
$495$	0.404514			0.0181816
$496$	13.4661	−	23.3239i	0.604644	−	1.04727i
$497$	4.14941	−	7.18699i	0.186126	−	0.322380i
$498$	−2.57446	−	4.45910i	−0.115364	−	0.199817i
$499$	−7.56383			−0.338604			−0.169302	−	0.985564i	$-0.554151\pi$
$499$	−7.56383			−0.338604			−0.169302	+	0.985564i	$0.554151\pi$
$500$	−0.194756	−	0.337327i	−0.00870975	−	0.0150857i
$501$	1.55446	+	2.69241i	0.0694482	+	0.120288i
$502$	27.1886			1.21349
$503$	8.06631	+	13.9713i	0.359659	+	0.622948i	0.987904	−	0.155068i	$-0.0495597\pi$
$503$	8.06631	+	13.9713i	0.359659	+	0.622948i	−0.628245	+	0.778016i	$0.716226\pi$
$504$	3.96667	−	6.87047i	0.176690	−	0.306035i
$505$	2.83271	−	4.90640i	0.126054	−	0.218332i
$506$	−8.67903			−0.385830
$507$	−9.97786	−	8.33320i	−0.443132	−	0.370091i
$508$	0.0127262			0.000564634
$509$	18.1695	−	31.4705i	0.805350	−	1.39491i	−0.110705	−	0.993853i	$-0.535311\pi$
$509$	18.1695	−	31.4705i	0.805350	−	1.39491i	0.916055	−	0.401054i	$-0.131356\pi$
$510$	0.361908	−	0.626843i	0.0160255	−	0.0277571i
$511$	9.08958	+	15.7436i	0.402099	+	0.696456i
$512$	−20.7501			−0.917034
$513$	−2.41662	−	4.18571i	−0.106696	−	0.184804i
$514$	13.1160	+	22.7176i	0.578524	+	1.00203i
$515$	5.42845			0.239206
$516$	0.135813	+	0.235234i	0.00597882	+	0.0103556i
$517$	−0.965567	+	1.67241i	−0.0424656	+	0.0735526i
$518$	12.7001	−	21.9973i	0.558012	−	0.966505i
$519$	−4.24304			−0.186249
$520$	−2.58641	−	3.07514i	−0.113421	−	0.134854i
$521$	7.15961			0.313668			0.156834	−	0.987625i	$-0.449871\pi$
$521$	7.15961			0.313668			0.156834	+	0.987625i	$0.449871\pi$
$522$	−3.43979	+	5.95789i	−0.150556	+	0.260770i
$523$	8.38919	−	14.5305i	0.366834	−	0.635375i	−0.622235	−	0.782831i	$-0.713775\pi$
$523$	8.38919	−	14.5305i	0.366834	−	0.635375i	0.989069	+	0.147456i	$0.0471085\pi$
$524$	−0.405470	−	0.702294i	−0.0177130	−	0.0306799i
$525$	−13.9267			−0.607812
$526$	−18.7691	−	32.5090i	−0.818371	−	1.41746i
$527$	−3.97395	−	6.88309i	−0.173108	−	0.299832i
$528$	4.18620			0.182181
$529$	−6.45266	−	11.1763i	−0.280550	−	0.485927i
$530$	−1.23345	+	2.13639i	−0.0535775	+	0.0927990i
$531$	−3.59823	+	6.23232i	−0.156150	+	0.270460i
$532$	1.36245			0.0590696
$533$	−8.15109	+	1.44697i	−0.353063	+	0.0626752i
$534$	7.97294			0.345023
$535$	−0.355695	+	0.616083i	−0.0153781	+	0.0266356i
$536$	21.8193	−	37.7921i	0.942449	−	1.63237i
$537$	1.46166	+	2.53166i	0.0630751	+	0.109249i
$538$	−31.7677			−1.36960
$539$	0.645996	+	1.11890i	0.0278250	+	0.0481943i
$540$	0.0197996	+	0.0342939i	0.000852038	+	0.00147577i
$541$	−21.7571			−0.935410			−0.467705	−	0.883885i	$-0.654919\pi$
$541$	−21.7571			−0.935410			−0.467705	+	0.883885i	$0.654919\pi$
$542$	4.08759	+	7.07991i	0.175577	+	0.304108i
$543$	1.38852	−	2.40499i	0.0595871	−	0.103208i
$544$	0.341755	−	0.591937i	0.0146526	−	0.0253791i
$545$	−3.86084			−0.165380
$546$	14.8066	−	2.62845i	0.633664	−	0.112487i
$547$	6.24061			0.266829			0.133415	−	0.991060i	$-0.457406\pi$
$547$	6.24061			0.266829			0.133415	+	0.991060i	$0.457406\pi$
$548$	−1.01431	+	1.75684i	−0.0433292	+	0.0750484i
$549$	−5.53971	+	9.59506i	−0.236429	+	0.409507i
$550$	−3.50252	−	6.06655i	−0.149348	−	0.258678i
$551$	22.9567			0.977987
$552$	8.25422	+	14.2967i	0.351323	+	0.608509i
$553$	3.93667	+	6.81851i	0.167404	+	0.289952i
$554$	−7.86470			−0.334139
$555$	−1.23175	−	2.13345i	−0.0522847	−	0.0905597i
$556$	0.341664	−	0.591780i	0.0144898	−	0.0250971i
$557$	4.00105	−	6.93002i	0.169530	−	0.293635i	−0.768725	−	0.639580i	$-0.779108\pi$
$557$	4.00105	−	6.93002i	0.169530	−	0.293635i	0.938255	+	0.345945i	$0.112442\pi$
$558$	9.31841			0.394480
$559$	3.41083	−	9.40499i	0.144263	−	0.397789i
$560$	4.87622			0.206058
$561$	0.617693	−	1.06987i	0.0260790	−	0.0451702i
$562$	15.4951	−	26.8382i	0.653620	−	1.13210i
$563$	9.47769	+	16.4158i	0.399437	+	0.691845i	0.993657	−	0.112458i	$-0.0358723\pi$
$563$	9.47769	+	16.4158i	0.399437	+	0.691845i	−0.594219	+	0.804303i	$0.702539\pi$
$564$	−0.189045			−0.00796021
$565$	3.84227	+	6.65501i	0.161646	+	0.279978i
$566$	−6.62645	−	11.4774i	−0.278531	−	0.482429i
$567$	2.87958			0.120931
$568$	−3.96993	−	6.87613i	−0.166575	−	0.288516i
$569$	−22.2615	+	38.5580i	−0.933250	+	1.61644i	−0.155524	+	0.987832i	$0.549707\pi$
$569$	−22.2615	+	38.5580i	−0.933250	+	1.61644i	−0.777726	+	0.628604i	$0.783627\pi$
$570$	1.41590	−	2.45242i	0.0593057	−	0.102721i
$571$	−17.1753			−0.718763			−0.359382	−	0.933191i	$-0.617012\pi$
$571$	−17.1753			−0.718763			−0.359382	+	0.933191i	$0.617012\pi$
$572$	0.227190	+	0.270119i	0.00949927	+	0.0112943i
$573$	−22.8688			−0.955357
$574$	4.78820	−	8.29341i	0.199856	−	0.346160i
$575$	14.4900	−	25.0974i	0.604275	−	1.04664i
$576$	−3.78552	−	6.55671i	−0.157730	−	0.273196i
$577$	−5.66586			−0.235873			−0.117936	−	0.993021i	$-0.537628\pi$
$577$	−5.66586			−0.235873			−0.117936	+	0.993021i	$0.537628\pi$
$578$	11.2062	+	19.4097i	0.466117	+	0.807339i
$579$	4.04125	+	6.99966i	0.167949	+	0.290896i
$580$	−0.188086			−0.00780984
$581$	−5.11829	−	8.86513i	−0.212342	−	0.367788i
$582$	−2.33143	+	4.03816i	−0.0966410	+	0.167387i
$583$	−2.10521	+	3.64633i	−0.0871888	+	0.151015i
$584$	17.3929			0.719721
$585$	0.497251	−	1.37111i	0.0205588	−	0.0566886i
$586$	3.43571			0.141928
$587$	9.04923	−	15.6737i	0.373502	−	0.646924i	−0.616600	−	0.787277i	$-0.711490\pi$
$587$	9.04923	−	15.6737i	0.373502	−	0.646924i	0.990102	+	0.140353i	$0.0448236\pi$
$588$	−0.0632385	+	0.109532i	−0.00260791	+	0.00451704i
$589$	−15.5474	−	26.9289i	−0.640621	−	1.10959i
$590$	−4.21643			−0.173588
$591$	11.1283	+	19.2747i	0.457756	+	0.792857i
$592$	−12.7470	−	22.0784i	−0.523898	−	0.907418i
$593$	23.3821			0.960190			0.480095	−	0.877217i	$-0.340602\pi$
$593$	23.3821			0.960190			0.480095	+	0.877217i	$0.340602\pi$
$594$	0.724205	+	1.25436i	0.0297145	+	0.0514670i
$595$	0.719508	−	1.24622i	0.0294970	−	0.0510902i
$596$	−0.971866	+	1.68332i	−0.0398092	+	0.0689515i
$597$	−22.5668			−0.923598
$598$	−10.6687	+	29.4178i	−0.436277	+	1.20299i
$599$	−34.5355			−1.41108			−0.705540	−	0.708670i	$-0.749296\pi$
$599$	−34.5355			−1.41108			−0.705540	+	0.708670i	$0.749296\pi$
$600$	−6.66217	+	11.5392i	−0.271982	+	0.471087i
$601$	10.4494	−	18.0989i	0.426240	−	0.738269i	−0.570295	−	0.821440i	$-0.693171\pi$
$601$	10.4494	−	18.0989i	0.426240	−	0.738269i	0.996535	+	0.0831704i	$0.0265046\pi$
$602$	5.78641	+	10.0224i	0.235837	+	0.408481i
$603$	15.8396			0.645037
$604$	0.651830	+	1.12900i	0.0265226	+	0.0459384i
$605$	0.202257	+	0.350320i	0.00822292	+	0.0142425i
$606$	20.2857			0.824051
$607$	2.57892	+	4.46683i	0.104675	+	0.181303i	0.913605	−	0.406602i	$-0.133286\pi$
$607$	2.57892	+	4.46683i	0.104675	+	0.181303i	−0.808930	+	0.587905i	$0.799953\pi$
$608$	1.33706	−	2.31586i	0.0542250	−	0.0939204i
$609$	−6.83864	+	11.8449i	−0.277116	+	0.479978i
$610$	−6.49147			−0.262832
$611$	4.48176	+	5.32864i	0.181313	+	0.215574i
$612$	0.120936			0.00488853
$613$	−2.94669	+	5.10381i	−0.119016	+	0.206141i	−0.919378	−	0.393376i	$-0.871307\pi$
$613$	−2.94669	+	5.10381i	−0.119016	+	0.206141i	0.800362	+	0.599517i	$0.204640\pi$
$614$	−8.46932	+	14.6693i	−0.341794	+	0.592005i
$615$	−0.464392	−	0.804351i	−0.0187261	−	0.0324346i
$616$	7.93334			0.319643
$617$	−21.1451	−	36.6244i	−0.851271	−	1.47444i	−0.880062	−	0.474859i	$-0.842499\pi$
$617$	−21.1451	−	36.6244i	−0.851271	−	1.47444i	0.0287915	−	0.999585i	$-0.490834\pi$
$618$	9.71860	+	16.8331i	0.390939	+	0.677127i
$619$	−25.9026			−1.04111			−0.520556	−	0.853828i	$-0.674275\pi$
$619$	−25.9026			−1.04111			−0.520556	+	0.853828i	$0.674275\pi$
$620$	0.127381	+	0.220631i	0.00511576	+	0.00886075i
$621$	−2.99605	+	5.18931i	−0.120227	+	0.208240i
$622$	−2.85353	+	4.94246i	−0.114416	+	0.198174i
$623$	15.8510			0.635056
$624$	5.14591	−	14.1893i	0.206001	−	0.568025i
$625$	22.5723			0.902892
$626$	3.59590	−	6.22827i	0.143721	−	0.248932i
$627$	2.41662	−	4.18571i	0.0965105	−	0.167161i
$628$	−1.04624	−	1.81214i	−0.0417495	−	0.0723123i
$629$	−7.52349			−0.299981
$630$	0.843577	+	1.46112i	0.0336089	+	0.0582124i
$631$	−17.7601	−	30.7615i	−0.707020	−	1.22460i	−0.965957	−	0.258701i	$-0.916706\pi$
$631$	−17.7601	−	30.7615i	−0.707020	−	1.22460i	0.258937	−	0.965894i	$-0.416628\pi$
$632$	7.53279			0.299638
$633$	14.2890	+	24.7493i	0.567937	+	0.983695i
$634$	−1.62643	+	2.81706i	−0.0645939	+	0.111880i
$635$	0.0262937	−	0.0455420i	0.00104343	−	0.00180728i
$636$	−0.412170			−0.0163436
$637$	4.58663	−	0.814213i	0.181729	−	0.0322603i
$638$	−6.87958			−0.272365
$639$	1.44098	−	2.49584i	0.0570041	−	0.0987341i
$640$	2.44175	−	4.22924i	0.0965188	−	0.167175i
$641$	1.08897	+	1.88614i	0.0430116	+	0.0744982i	0.886730	−	0.462288i	$-0.152971\pi$
$641$	1.08897	+	1.88614i	0.0430116	+	0.0744982i	−0.843718	+	0.536786i	$0.819638\pi$
$642$	−2.54722			−0.100531
$643$	−18.5917	−	32.2018i	−0.733187	−	1.26992i	−0.955514	−	0.294945i	$-0.904699\pi$
$643$	−18.5917	−	32.2018i	−0.733187	−	1.26992i	0.222328	−	0.974972i	$-0.428635\pi$
$644$	−0.844560	−	1.46282i	−0.0332803	−	0.0576432i
$645$	1.12241			0.0441949
$646$	−4.32417	−	7.48968i	−0.170132	−	0.294677i
$647$	23.0883	−	39.9902i	0.907696	−	1.57218i	0.0904389	−	0.995902i	$-0.471173\pi$
$647$	23.0883	−	39.9902i	0.907696	−	1.57218i	0.817257	−	0.576273i	$-0.195494\pi$
$648$	1.37752	−	2.38593i	0.0541139	−	0.0937281i
$649$	−7.19647			−0.282486
$650$	−24.8683	+	4.41458i	−0.975413	+	0.173154i
$651$	18.5259			0.726088
$652$	0.592366	−	1.02601i	0.0231988	−	0.0401816i
$653$	13.6238	−	23.5971i	0.533141	−	0.923427i	−0.466110	−	0.884727i	$-0.654345\pi$
$653$	13.6238	−	23.5971i	0.533141	−	0.923427i	0.999251	−	0.0387002i	$-0.0123217\pi$
$654$	−6.91209	−	11.9721i	−0.270284	−	0.468146i
$655$	−3.35097			−0.130933
$656$	−4.80586	−	8.32400i	−0.187637	−	0.324998i
$657$	3.15656	+	5.46733i	0.123149	+	0.213301i
$658$	−8.05441			−0.313993
$659$	0.453557	+	0.785584i	0.0176681	+	0.0306020i	0.874724	−	0.484621i	$-0.161042\pi$
$659$	0.453557	+	0.785584i	0.0176681	+	0.0306020i	−0.857056	+	0.515223i	$0.827709\pi$
$660$	−0.0197996	+	0.0342939i	−0.000770697	+	0.00133489i
$661$	−10.8251	+	18.7497i	−0.421049	+	0.729278i	−0.996042	−	0.0888801i	$-0.971671\pi$
$661$	−10.8251	+	18.7497i	−0.421049	+	0.729278i	0.574994	+	0.818158i	$0.305005\pi$
$662$	−5.85531			−0.227573
$663$	−2.86707	−	3.40884i	−0.111348	−	0.132388i
$664$	−9.79381			−0.380074
$665$	2.81496	−	4.87565i	0.109159	−	0.189070i
$666$	4.41041	−	7.63905i	0.170900	−	0.296007i
$667$	−14.2305	−	24.6479i	−0.551007	−	0.954372i
$668$	−0.304342			−0.0117753
$669$	−7.73996	−	13.4060i	−0.299244	−	0.518306i
$670$	4.64023	+	8.03711i	0.179268	+	0.310501i
$671$	−11.0794			−0.427716
$672$	0.796603	+	1.37976i	0.0307296	+	0.0532253i
$673$	−1.88496	+	3.26485i	−0.0726600	+	0.125851i	−0.900066	−	0.435753i	$-0.856482\pi$
$673$	−1.88496	+	3.26485i	−0.0726600	+	0.125851i	0.827406	+	0.561604i	$0.189815\pi$
$674$	7.32676	−	12.6903i	0.282216	−	0.488813i
$675$	−4.83637			−0.186152
$676$	1.19485	−	0.438020i	0.0459559	−	0.0168469i
$677$	−32.8356			−1.26197			−0.630986	−	0.775794i	$-0.717350\pi$
$677$	−32.8356			−1.26197			−0.630986	+	0.775794i	$0.717350\pi$
$678$	−13.7577	+	23.8290i	−0.528361	+	0.915149i
$679$	−4.63512	+	8.02826i	−0.177880	+	0.308096i
$680$	−0.688387	−	1.19232i	−0.0263984	−	0.0457235i
$681$	13.2754			0.508713
$682$	4.65920	+	8.06998i	0.178410	+	0.309015i
$683$	−11.3861	−	19.7213i	−0.435676	−	0.754613i	0.561674	−	0.827358i	$-0.310157\pi$
$683$	−11.3861	−	19.7213i	−0.435676	−	0.754613i	−0.997351	+	0.0727452i	$0.976824\pi$
$684$	0.473141			0.0180910
$685$	4.19134	+	7.25962i	0.160143	+	0.277376i
$686$	11.9035	−	20.6175i	0.454479	−	0.787180i
$687$	−13.9955	+	24.2409i	−0.533960	+	0.924846i
$688$	11.6155			0.442838
$689$	9.77151	+	11.6179i	0.372265	+	0.442608i
$690$	−3.51079			−0.133653
$691$	12.8285	−	22.2197i	0.488020	−	0.845275i	−0.511885	−	0.859054i	$-0.671053\pi$
$691$	12.8285	−	22.2197i	0.488020	−	0.845275i	0.999905	+	0.0137785i	$0.00438598\pi$
$692$	0.207682	−	0.359716i	0.00789489	−	0.0136743i
$693$	1.43979	+	2.49379i	0.0546931	+	0.0947313i
$694$	−17.6980			−0.671807
$695$	−1.41183	−	2.44536i	−0.0535537	−	0.0927577i
$696$	6.54285	+	11.3325i	0.248006	+	0.429559i
$697$	−2.83651			−0.107440
$698$	−1.05661	−	1.83011i	−0.0399934	−	0.0692707i
$699$	9.10256	−	15.7661i	0.344291	−	0.596329i
$700$	0.681664	−	1.18068i	0.0257645	−	0.0446254i
$701$	11.7804			0.444939			0.222469	−	0.974940i	$-0.428588\pi$
$701$	11.7804			0.444939			0.222469	+	0.974940i	$0.428588\pi$
$702$	5.14193	−	0.912788i	0.194070	−	0.0344510i
$703$	−29.4344			−1.11014
$704$	3.78552	−	6.55671i	0.142672	−	0.247115i
$705$	−0.390586	+	0.676514i	−0.0147103	+	0.0254790i
$706$	−0.530587	−	0.919004i	−0.0199689	−	0.0345872i
$707$	40.3300			1.51676
$708$	−0.352242	−	0.610101i	−0.0132381	−	0.0229290i
$709$	5.56072	+	9.63145i	0.208837	+	0.361717i	0.951349	−	0.308117i	$-0.0996988\pi$
$709$	5.56072	+	9.63145i	0.208837	+	0.361717i	−0.742511	+	0.669834i	$0.766365\pi$
$710$	1.68854			0.0633699
$711$	1.36710	+	2.36788i	0.0512701	+	0.0888025i
$712$	7.58269	−	13.1336i	0.284173	−	0.492203i
$713$	−19.2752	+	33.3857i	−0.721863	+	1.25030i
$714$	5.15257			0.192830
$715$	1.43605	−	0.254925i	0.0537051	−	0.00953365i
$716$	−0.286172			−0.0106947
$717$	−8.19617	+	14.1962i	−0.306092	+	0.530166i
$718$	3.49531	−	6.05405i	0.130444	−	0.225935i
$719$	−7.43722	−	12.8816i	−0.277362	−	0.480404i	0.693367	−	0.720585i	$-0.256127\pi$
$719$	−7.43722	−	12.8816i	−0.277362	−	0.480404i	−0.970728	+	0.240181i	$0.922793\pi$
$720$	1.69338			0.0631085
$721$	19.3215	+	33.4659i	0.719571	+	1.24633i
$722$	−3.15769	−	5.46929i	−0.117517	−	0.203546i
$723$	−10.1491			−0.377447
$724$	0.135926	+	0.235431i	0.00505167	+	0.00874974i
$725$	11.4858	−	19.8939i	0.426570	−	0.738842i
$726$	−0.724205	+	1.25436i	−0.0268778	+	0.0465537i
$727$	9.26833			0.343743			0.171872	−	0.985119i	$-0.445019\pi$
$727$	9.26833			0.343743			0.171872	+	0.985119i	$0.445019\pi$
$728$	9.75210	−	26.8903i	0.361437	−	0.996621i
$729$	1.00000			0.0370370
$730$	−1.84944	+	3.20332i	−0.0684508	+	0.118560i
$731$	1.71392	−	2.96860i	0.0633917	−	0.109798i
$732$	−0.542299	−	0.939290i	−0.0200440	−	0.0347172i
$733$	−21.4862			−0.793611			−0.396805	−	0.917903i	$-0.629881\pi$
$733$	−21.4862			−0.793611			−0.396805	+	0.917903i	$0.629881\pi$
$734$	6.19449	+	10.7292i	0.228643	+	0.396021i
$735$	0.261314	+	0.452610i	0.00963873	+	0.0166948i
$736$	−3.31529			−0.122203
$737$	7.91979	+	13.7175i	0.291729	+	0.505290i
$738$	1.66281	−	2.88007i	0.0612089	−	0.106017i
$739$	−17.8400	+	30.8999i	−0.656256	+	1.13667i	0.325321	+	0.945604i	$0.394528\pi$
$739$	−17.8400	+	30.8999i	−0.656256	+	1.13667i	−0.981577	+	0.191066i	$0.938806\pi$
$740$	0.241159			0.00886517
$741$	−11.2170	−	13.3365i	−0.412065	−	0.489929i
$742$	−17.5609			−0.644680
$743$	−6.74294	+	11.6791i	−0.247374	+	0.428465i	−0.962796	−	0.270228i	$-0.912901\pi$
$743$	−6.74294	+	11.6791i	−0.247374	+	0.428465i	0.715422	+	0.698692i	$0.246234\pi$
$744$	8.86231	−	15.3500i	0.324908	−	0.562757i
$745$	4.01595	+	6.95583i	0.147133	+	0.254842i
$746$	−42.5469			−1.55775
$747$	−1.77744	−	3.07862i	−0.0650332	−	0.112641i
$748$	0.0604678	+	0.104733i	0.00221092	+	0.00382943i
$749$	−5.06412			−0.185039
$750$	−2.88158	−	4.99104i	−0.105220	−	0.182247i
$751$	8.97312	−	15.5419i	0.327434	−	0.567132i	−0.654568	−	0.756003i	$-0.727149\pi$
$751$	8.97312	−	15.5419i	0.327434	−	0.567132i	0.982002	+	0.188871i	$0.0604828\pi$
$752$	−4.04206	+	7.00105i	−0.147399	+	0.255302i
$753$	18.7713			0.684065
$754$	−8.45676	+	23.3186i	−0.307977	+	0.849212i
$755$	5.38699			0.196053
$756$	−0.140946	+	0.244125i	−0.00512614	+	0.00887873i
$757$	19.4507	−	33.6896i	0.706948	−	1.22447i	−0.259035	−	0.965868i	$-0.583405\pi$
$757$	19.4507	−	33.6896i	0.706948	−	1.22447i	0.965984	−	0.258603i	$-0.0832620\pi$
$758$	10.4472	+	18.0951i	0.379461	+	0.657245i
$759$	−5.99210			−0.217500
$760$	−2.69320	−	4.66476i	−0.0976927	−	0.169209i
$761$	26.9123	+	46.6135i	0.975571	+	1.68974i	0.678036	+	0.735028i	$0.262831\pi$
$761$	26.9123	+	46.6135i	0.975571	+	1.68974i	0.297535	+	0.954711i	$0.403836\pi$
$762$	0.188295			0.00682121
$763$	−13.7419	−	23.8017i	−0.497490	−	0.861679i
$764$	1.11935	−	1.93877i	0.0404965	−	0.0701421i
$765$	0.249865	−	0.432780i	0.00903390	−	0.0156472i
$766$	−2.23464			−0.0807410
$767$	−8.84630	+	24.3927i	−0.319421	+	0.880768i
$768$	2.34390			0.0845781
$769$	24.2900	−	42.0715i	0.875919	−	1.51714i	0.0201395	−	0.999797i	$-0.493589\pi$
$769$	24.2900	−	42.0715i	0.875919	−	1.51714i	0.855780	−	0.517340i	$-0.173078\pi$
$770$	−0.843577	+	1.46112i	−0.0304004	+	0.0526551i
$771$	9.05547	+	15.6845i	0.326125	+	0.564865i
$772$	−0.791221			−0.0284767
$773$	20.6253	+	35.7241i	0.741842	+	1.28491i	0.951656	+	0.307166i	$0.0993807\pi$
$773$	20.6253	+	35.7241i	0.741842	+	1.28491i	−0.209814	+	0.977741i	$0.567286\pi$
$774$	2.00946	+	3.48049i	0.0722287	+	0.125104i
$775$	−31.1150			−1.11768
$776$	4.43464	+	7.68102i	0.159194	+	0.275732i
$777$	8.76832	−	15.1872i	0.314562	−	0.544837i
$778$	21.4353	−	37.1270i	0.768493	−	1.33107i
$779$	−11.0974			−0.397604
$780$	0.0919014	+	0.109267i	0.00329060	+	0.00391239i
$781$	2.88195			0.103124
$782$	−5.36097	+	9.28547i	−0.191708	+	0.332048i
$783$	−2.37487	+	4.11340i	−0.0848710	+	0.147001i
$784$	2.70427	+	4.68393i	0.0965811	+	0.167283i
$785$	−8.64656			−0.308609
$786$	−5.99927	−	10.3910i	−0.213987	−	0.370636i
$787$	−0.281033	−	0.486764i	−0.0100178	−	0.0173513i	0.860973	−	0.508651i	$-0.169855\pi$
$787$	−0.281033	−	0.486764i	−0.0100178	−	0.0173513i	−0.870991	+	0.491299i	$0.836522\pi$
$788$	−2.17876			−0.0776152
$789$	−12.9584	−	22.4446i	−0.461331	−	0.799049i
$790$	−0.800986	+	1.38735i	−0.0284978	+	0.0493596i
$791$	−27.3517	+	47.3745i	−0.972513	+	1.68444i
$792$	2.75503			0.0978958
$793$	−13.6194	+	37.5541i	−0.483641	+	1.33358i
$794$	33.8760			1.20222
$795$	−0.851587	+	1.47499i	−0.0302027	+	0.0523125i
$796$	1.10457	−	1.91316i	0.0391503	−	0.0678103i
$797$	5.64114	+	9.77075i	0.199820	+	0.346098i	0.948470	−	0.316868i	$-0.102631\pi$
$797$	5.64114	+	9.77075i	0.199820	+	0.346098i	−0.748650	+	0.662965i	$0.769298\pi$
$798$	20.1586			0.713605
$799$	1.19285	+	2.06607i	0.0421999	+	0.0730924i
$800$	−1.33793	−	2.31736i	−0.0473028	−	0.0819309i
$801$	5.50461			0.194496
$802$	−21.4236	−	37.1068i	−0.756495	−	1.31029i
$803$	−3.15656	+	5.46733i	−0.111393	+	0.192938i
$804$	−0.775292	+	1.34285i	−0.0273425	+	0.0473585i
$805$	−6.97979			−0.246005
$806$	33.0808	−	5.87246i	1.16522	−	0.206849i
$807$	−21.9328			−0.772072
$808$	19.2928	−	33.4161i	0.678718	−	1.17557i
$809$	10.0515	−	17.4097i	0.353392	−	0.612092i	−0.633450	−	0.773784i	$-0.718362\pi$
$809$	10.0515	−	17.4097i	0.353392	−	0.612092i	0.986841	+	0.161692i	$0.0516950\pi$
$810$	0.292951	+	0.507407i	0.0102933	+	0.0178285i
$811$	−5.46027			−0.191736			−0.0958681	−	0.995394i	$-0.530563\pi$
$811$	−5.46027			−0.191736			−0.0958681	+	0.995394i	$0.530563\pi$
$812$	−0.669455	−	1.15953i	−0.0234933	−	0.0406916i
$813$	2.82212	+	4.88806i	0.0989761	+	0.171432i
$814$	8.82082			0.309169
$815$	−2.44778	−	4.23967i	−0.0857419	−	0.148509i
$816$	2.58579	−	4.47871i	0.0905206	−	0.156786i
$817$	6.70543	−	11.6142i	0.234593	−	0.406328i
$818$	29.0481			1.01564
$819$	10.2227	−	1.81471i	0.357209	−	0.0634112i
$820$	0.0909216			0.00317512
$821$	−8.48504	+	14.6965i	−0.296130	+	0.512912i	−0.975247	−	0.221118i	$-0.929029\pi$
$821$	−8.48504	+	14.6965i	−0.296130	+	0.512912i	0.679117	+	0.734030i	$0.262363\pi$
$822$	−15.0076	+	25.9939i	−0.523450	+	0.906642i
$823$	22.8699	+	39.6118i	0.797194	+	1.38078i	0.921437	+	0.388528i	$0.127016\pi$
$823$	22.8699	+	39.6118i	0.797194	+	1.38078i	−0.124243	+	0.992252i	$0.539650\pi$
$824$	36.9716			1.28797
$825$	−2.41818	−	4.18842i	−0.0841904	−	0.145822i
$826$	−15.0076	−	25.9939i	−0.522180	−	0.904443i
$827$	−25.8174			−0.897760			−0.448880	−	0.893592i	$-0.648177\pi$
$827$	−25.8174			−0.897760			−0.448880	+	0.893592i	$0.648177\pi$
$828$	−0.293293	−	0.507998i	−0.0101926	−	0.0176541i
$829$	2.23405	−	3.86948i	0.0775917	−	0.134393i	−0.824619	−	0.565689i	$-0.808610\pi$
$829$	2.23405	−	3.86948i	0.0775917	−	0.134393i	0.902210	+	0.431296i	$0.141944\pi$
$830$	1.04141	−	1.80377i	0.0361478	−	0.0626098i
$831$	−5.42988			−0.188360
$832$	−17.5708	−	20.8910i	−0.609158	−	0.724265i
$833$	1.59611			0.0553018
$834$	5.05522	−	8.75589i	0.175048	−	0.303192i
$835$	−0.628802	+	1.08912i	−0.0217606	+	0.0376905i
$836$	0.236570	+	0.409752i	0.00818196	+	0.0141716i
$837$	6.43354			0.222376
$838$	1.71156	+	2.96450i	0.0591247	+	0.102407i
$839$	20.3407	+	35.2311i	0.702239	+	1.21631i	0.967679	+	0.252186i	$0.0811494\pi$
$839$	20.3407	+	35.2311i	0.702239	+	1.21631i	−0.265440	+	0.964127i	$0.585517\pi$
$840$	3.20915			0.110726
$841$	3.21996	+	5.57713i	0.111033	+	0.192315i
$842$	24.3677	−	42.2060i	0.839765	−	1.45452i
$843$	10.6980	−	18.5294i	0.368458	−	0.638188i
$844$	−2.79759			−0.0962969
$845$	0.901191	−	5.18089i	0.0310019	−	0.178228i
$846$	−2.79708			−0.0961654
$847$	−1.43979	+	2.49379i	−0.0494718	+	0.0856877i
$848$	−8.81283	+	15.2643i	−0.302634	+	0.524177i
$849$	−4.57498	−	7.92410i	−0.157013	−	0.271954i
$850$	−8.65393			−0.296827
$851$	18.2460	+	31.6029i	0.625463	+	1.08333i
$852$	0.141062	+	0.244326i	0.00483269	+	0.00837046i
$853$	51.5651			1.76556			0.882778	−	0.469790i	$-0.155670\pi$
$853$	51.5651			1.76556			0.882778	+	0.469790i	$0.155670\pi$
$854$	−23.1051	−	40.0193i	−0.790641	−	1.36943i
$855$	0.977557	−	1.69318i	0.0334318	−	0.0579055i
$856$	−2.42254	+	4.19596i	−0.0828007	+	0.143415i
$857$	10.5103			0.359024			0.179512	−	0.983756i	$-0.442548\pi$
$857$	10.5103			0.359024			0.179512	+	0.983756i	$0.442548\pi$
$858$	3.36146	+	3.99665i	0.114758	+	0.136443i
$859$	−44.7522			−1.52692			−0.763462	−	0.645853i	$-0.776502\pi$
$859$	−44.7522			−1.52692			−0.763462	+	0.645853i	$0.776502\pi$
$860$	−0.0549382	+	0.0951557i	−0.00187338	+	0.00324478i
$861$	3.30583	−	5.72587i	0.112662	−	0.195137i
$862$	12.3165	+	21.3327i	0.419500	+	0.726596i
$863$	−8.14973			−0.277420			−0.138710	−	0.990333i	$-0.544296\pi$
$863$	−8.14973			−0.277420			−0.138710	+	0.990333i	$0.544296\pi$
$864$	0.276639	+	0.479152i	0.00941143	+	0.0163011i
$865$	−0.858185	−	1.48642i	−0.0291792	−	0.0505398i
$866$	32.2874			1.09717
$867$	7.73691	+	13.4007i	0.262759	+	0.455112i
$868$	−0.906779	+	1.57059i	−0.0307781	+	0.0533092i
$869$	−1.36710	+	2.36788i	−0.0463756	+	0.0803249i
$870$	−2.78289			−0.0943488
$871$	56.2313	−	9.98210i	1.90532	−	0.338231i
$872$	−26.2951			−0.890463
$873$	−1.60965	+	2.78800i	−0.0544784	+	0.0943594i
$874$	−20.9739	+	36.3279i	−0.709453	+	1.22881i
$875$	−5.72886	−	9.92267i	−0.193671	−	0.335448i
$876$	−0.618011			−0.0208807
$877$	26.9784	+	46.7280i	0.910996	+	1.57789i	0.812660	+	0.582738i	$0.198019\pi$
$877$	26.9784	+	46.7280i	0.910996	+	1.57789i	0.0983361	+	0.995153i	$0.468648\pi$
$878$	2.70111	+	4.67846i	0.0911580	+	0.157890i
$879$	2.37205			0.0800074
$880$	0.846689	+	1.46651i	0.0285419	+	0.0494360i
$881$	−4.27748	+	7.40882i	−0.144112	+	0.249609i	−0.929041	−	0.369976i	$-0.879366\pi$
$881$	−4.27748	+	7.40882i	−0.144112	+	0.249609i	0.784929	+	0.619585i	$0.212699\pi$
$882$	−0.935667	+	1.62062i	−0.0315055	+	0.0545692i
$883$	−18.3554			−0.617709			−0.308855	−	0.951109i	$-0.599946\pi$
$883$	−18.3554			−0.617709			−0.308855	+	0.951109i	$0.599946\pi$
$884$	0.429327	−	0.0762136i	0.0144398	−	0.00256334i
$885$	−2.91107			−0.0978547
$886$	−12.6135	+	21.8472i	−0.423758	+	0.733970i
$887$	−15.9843	+	27.6856i	−0.536699	+	0.929590i	0.462380	+	0.886682i	$0.346996\pi$
$887$	−15.9843	+	27.6856i	−0.536699	+	0.929590i	−0.999079	+	0.0429082i	$0.986338\pi$
$888$	−8.38907	−	14.5303i	−0.281519	−	0.487605i
$889$	0.374349			0.0125553
$890$	1.61258	+	2.79308i	0.0540539	+	0.0936241i
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	1.51538			0.0507386
$893$	4.66682	+	8.08317i	0.156169	+	0.270493i
$894$	−14.3796	+	24.9062i	−0.480925	+	0.832986i
$895$	−0.591261	+	1.02409i	−0.0197637	+	0.0342317i
$896$	34.7638			1.16138
$897$	−7.36583	+	20.3104i	−0.245938	+	0.678146i
$898$	17.6261			0.588190
$899$	−15.2788	+	26.4637i	−0.509578	+	0.882615i
$900$	0.236723	−	0.410017i	0.00789078	−	0.0136672i
$901$	2.60074	+	4.50462i	0.0866433	+	0.150071i
$902$	3.32562			0.110731
$903$	3.99501	+	6.91956i	0.132946	+	0.230269i
$904$	26.1686	+	45.3254i	0.870355	+	1.50750i
$905$	1.12335			0.0373415
$906$	9.64437	+	16.7045i	0.320413	+	0.554971i
$907$	26.6981	−	46.2425i	0.886496	−	1.53546i	0.0425064	−	0.999096i	$-0.486466\pi$
$907$	26.6981	−	46.2425i	0.886496	−	1.53546i	0.843989	−	0.536360i	$-0.180201\pi$
$908$	−0.649783	+	1.12546i	−0.0215638	+	0.0373496i
$909$	14.0055			0.464533
$910$	3.91554	+	4.65542i	0.129799	+	0.154326i
$911$	−31.2277			−1.03462			−0.517309	−	0.855798i	$-0.673066\pi$
$911$	−31.2277			−1.03462			−0.517309	+	0.855798i	$0.673066\pi$
$912$	10.1165	−	17.5222i	0.334990	−	0.580219i
$913$	1.77744	−	3.07862i	0.0588247	−	0.101887i
$914$	−7.20327	−	12.4764i	−0.238263	−	0.412684i
$915$	−4.48179			−0.148163
$916$	−1.37006	−	2.37301i	−0.0452680	−	0.0784065i
$917$	−11.9271	−	20.6584i	−0.393868	−	0.682200i
$918$	1.78934			0.0590572
$919$	−24.9724	−	43.2535i	−0.823765	−	1.42680i	−0.902860	−	0.429935i	$-0.858536\pi$
$919$	−24.9724	−	43.2535i	−0.823765	−	1.42680i	0.0790948	−	0.996867i	$-0.474797\pi$
$920$	−3.33895	+	5.78323i	−0.110082	+	0.190667i
$921$	−5.84732	+	10.1279i	−0.192676	+	0.333724i
$922$	44.8370			1.47663
$923$	3.54266	−	9.76847i	0.116608	−	0.321533i
$924$	−0.281891			−0.00927353
$925$	−14.7267	+	25.5075i	−0.484212	+	0.838680i
$926$	−11.6856	+	20.2400i	−0.384012	+	0.665128i
$927$	6.70984	+	11.6218i	0.220380	+	0.381709i
$928$	−2.62793			−0.0862659
$929$	−18.5874	−	32.1943i	−0.609832	−	1.05626i	−0.991268	−	0.131865i	$-0.957903\pi$
$929$	−18.5874	−	32.1943i	−0.609832	−	1.05626i	0.381435	−	0.924396i	$-0.375430\pi$
$930$	1.88471	+	3.26442i	0.0618022	+	0.107045i
$931$	6.24451			0.204655
$932$	0.891078	+	1.54339i	0.0291882	+	0.0505555i
$933$	−1.97011	+	3.41233i	−0.0644985	+	0.111715i
$934$	−11.9415	+	20.6833i	−0.390739	+	0.676779i
$935$	0.499731			0.0163429
$936$	3.38664	−	9.33827i	0.110696	−	0.305231i
$937$	44.1132			1.44112			0.720558	−	0.693394i	$-0.243886\pi$
$937$	44.1132			1.44112			0.720558	+	0.693394i	$0.243886\pi$
$938$	−33.0320	+	57.2131i	−1.07853	+	1.86807i
$939$	2.48265	−	4.30007i	0.0810182	−	0.140328i
$940$	−0.0382356	−	0.0662260i	−0.00124711	−	0.00216006i
$941$	−58.9062			−1.92029			−0.960144	−	0.279504i	$-0.909830\pi$
$941$	−58.9062			−1.92029			−0.960144	+	0.279504i	$0.909830\pi$
$942$	−15.4800	−	26.8122i	−0.504366	−	0.873588i
$943$	6.87908	+	11.9149i	0.224014	+	0.388003i
$944$	−30.1259			−0.980514
$945$	0.582416	+	1.00877i	0.0189460	+	0.0328154i
$946$	−2.00946	+	3.48049i	−0.0653333	+	0.113161i
$947$	5.68080	−	9.83943i	0.184601	−	0.319739i	−0.758841	−	0.651276i	$-0.774234\pi$
$947$	5.68080	−	9.83943i	0.184601	−	0.319739i	0.943442	+	0.331538i	$0.107567\pi$
$948$	−0.267659			−0.00869315
$949$	14.6515	+	17.4200i	0.475606	+	0.565477i
$950$	−33.8571			−1.09847
$951$	−1.12291	+	1.94493i	−0.0364128	+	0.0630688i
$952$	4.90037	−	8.48768i	0.158822	−	0.275087i
$953$	−7.94132	−	13.7548i	−0.257245	−	0.445561i	0.708258	−	0.705954i	$-0.249481\pi$
$953$	−7.94132	−	13.7548i	−0.257245	−	0.445561i	−0.965503	+	0.260393i	$0.916148\pi$
$954$	−6.09841			−0.197443
$955$	−4.62537	−	8.01138i	−0.149674	−	0.259242i
$956$	−0.802348	−	1.38971i	−0.0259498	−	0.0449463i
$957$	−4.74975			−0.153537
$958$	−25.4406	−	44.0643i	−0.821947	−	1.42365i
$959$	−29.8366	+	51.6785i	−0.963473	+	1.66878i
$960$	1.53130	−	2.65228i	0.0494224	−	0.0856020i
$961$	10.3905			0.335176
$962$	10.8430	−	29.8984i	0.349594	−	0.963965i
$963$	−1.75863			−0.0566711
$964$	0.496761	−	0.860415i	0.0159996	−	0.0277121i
$965$	−1.63474	+	2.83146i	−0.0526243	+	0.0911479i
$966$	−12.4960	−	21.6437i	−0.402052	−	0.696374i
$967$	−27.1682			−0.873669			−0.436834	−	0.899542i	$-0.643900\pi$
$967$	−27.1682			−0.873669			−0.436834	+	0.899542i	$0.643900\pi$
$968$	1.37752	+	2.38593i	0.0442750	+	0.0766866i
$969$	−2.98546	−	5.17096i	−0.0959067	−	0.166115i
$970$	−1.88620			−0.0605621
$971$	6.50726	+	11.2709i	0.208828	+	0.361701i	0.951346	−	0.308126i	$-0.0997018\pi$
$971$	6.50726	+	11.2709i	0.208828	+	0.361701i	−0.742518	+	0.669826i	$0.766368\pi$
$972$	−0.0489465	+	0.0847779i	−0.00156996	+	0.00271925i
$973$	10.0503	−	17.4076i	0.322197	−	0.558061i
$974$	−23.0313			−0.737970
$975$	−17.1693	+	3.04788i	−0.549859	+	0.0976102i
$976$	−46.3807			−1.48461
$977$	8.23434	−	14.2623i	0.263440	−	0.456291i	−0.703714	−	0.710484i	$-0.748476\pi$
$977$	8.23434	−	14.2623i	0.263440	−	0.456291i	0.967154	+	0.254192i	$0.0818096\pi$
$978$	8.76455	−	15.1806i	0.280259	−	0.485424i
$979$	2.75231	+	4.76713i	0.0879641	+	0.152358i
$980$	−0.0511617			−0.00163430
$981$	−4.77219	−	8.26567i	−0.152364	−	0.263903i
$982$	29.0506	+	50.3170i	0.927040	+	1.60568i
$983$	55.0035			1.75434			0.877169	−	0.480181i	$-0.159429\pi$
$983$	55.0035			1.75434			0.877169	+	0.480181i	$0.159429\pi$
$984$	−3.16284	−	5.47821i	−0.100828	−	0.174639i
$985$	−4.50155	+	7.79691i	−0.143431	+	0.248430i
$986$	−4.24947	+	7.36029i	−0.135331	+	0.234399i
$987$	−5.56086			−0.177004
$988$	1.67967	−	0.298173i	0.0534375	−	0.00948615i
$989$	−16.6264			−0.528688
$990$	−0.292951	+	0.507407i	−0.00931061	+	0.0161264i
$991$	−11.8413	+	20.5098i	−0.376153	+	0.651516i	−0.990499	−	0.137521i	$-0.956087\pi$
$991$	−11.8413	+	20.5098i	−0.376153	+	0.651516i	0.614346	+	0.789037i	$0.289420\pi$
$992$	1.77977	+	3.08264i	0.0565076	+	0.0978741i
$993$	−4.04258			−0.128287
$994$	6.01005	+	10.4097i	0.190627	+	0.330176i
$995$	−4.56430	−	7.90559i	−0.144698	−	0.250624i
$996$	0.347998			0.0110267
$997$	20.3594	+	35.2635i	0.644789	+	1.11681i	0.984350	+	0.176223i	$0.0563880\pi$
$997$	20.3594	+	35.2635i	0.644789	+	1.11681i	−0.339561	+	0.940584i	$0.610279\pi$
$998$	5.47777	−	9.48777i	0.173396	−	0.300330i
$999$	3.04500	−	5.27409i	0.0963395	−	0.166865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.c.100.2	✓	10
13.3	even	3	inner	429.2.i.c.133.2	yes	10
13.4	even	6		5577.2.a.p.1.2		5
13.9	even	3		5577.2.a.v.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.c.100.2	✓	10	1.1	even	1	trivial
429.2.i.c.133.2	yes	10	13.3	even	3	inner
5577.2.a.p.1.2		5	13.4	even	6
5577.2.a.v.1.4		5	13.9	even	3

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.724205 + 1.25436i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.0489465 - 0.0847779i) q^{4} -0.404514 q^{5} +(-0.724205 - 1.25436i) q^{6} +(-1.43979 - 2.49379i) q^{7} -2.75503 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.724205 + 1.25436i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.0489465 - 0.0847779i) q^{4} -0.404514 q^{5} +(-0.724205 - 1.25436i) q^{6} +(-1.43979 - 2.49379i) q^{7} -2.75503 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.292951 - 0.507407i) q^{10} +(0.500000 - 0.866025i) q^{11} +0.0978930 q^{12} +(-2.32079 - 2.75933i) q^{13} +4.17082 q^{14} +(0.202257 - 0.350320i) q^{15} +(2.09310 - 3.62536i) q^{16} +(-0.617693 - 1.06987i) q^{17} +1.44841 q^{18} +(-2.41662 - 4.18571i) q^{19} +(0.0197996 + 0.0342939i) q^{20} +2.87958 q^{21} +(0.724205 + 1.25436i) q^{22} +(-2.99605 + 5.18931i) q^{23} +(1.37752 - 2.38593i) q^{24} -4.83637 q^{25} +(5.14193 - 0.912788i) q^{26} +1.00000 q^{27} +(-0.140946 + 0.244125i) q^{28} +(-2.37487 + 4.11340i) q^{29} +(0.292951 + 0.507407i) q^{30} +6.43354 q^{31} +(0.276639 + 0.479152i) q^{32} +(0.500000 + 0.866025i) q^{33} +1.78934 q^{34} +(0.582416 + 1.00877i) q^{35} +(-0.0489465 + 0.0847779i) q^{36} +(3.04500 - 5.27409i) q^{37} +7.00052 q^{38} +(3.55005 - 0.630200i) q^{39} +1.11445 q^{40} +(1.14802 - 1.98844i) q^{41} +(-2.08541 + 3.61203i) q^{42} +(1.38736 + 2.40297i) q^{43} -0.0978930 q^{44} +(0.202257 + 0.350320i) q^{45} +(-4.33951 - 7.51626i) q^{46} -1.93113 q^{47} +(2.09310 + 3.62536i) q^{48} +(-0.645996 + 1.11890i) q^{49} +(3.50252 - 6.06655i) q^{50} +1.23539 q^{51} +(-0.120336 + 0.331812i) q^{52} -4.21042 q^{53} +(-0.724205 + 1.25436i) q^{54} +(-0.202257 + 0.350320i) q^{55} +(3.96667 + 6.87047i) q^{56} +4.83324 q^{57} +(-3.43979 - 5.95789i) q^{58} +(-3.59823 - 6.23232i) q^{59} -0.0395991 q^{60} +(-5.53971 - 9.59506i) q^{61} +(-4.65920 + 8.06998i) q^{62} +(-1.43979 + 2.49379i) q^{63} +7.57103 q^{64} +(0.938794 + 1.11619i) q^{65} -1.44841 q^{66} +(-7.91979 + 13.7175i) q^{67} +(-0.0604678 + 0.104733i) q^{68} +(-2.99605 - 5.18931i) q^{69} -1.68715 q^{70} +(1.44098 + 2.49584i) q^{71} +(1.37752 + 2.38593i) q^{72} -6.31312 q^{73} +(4.41041 + 7.63905i) q^{74} +(2.41818 - 4.18842i) q^{75} +(-0.236570 + 0.409752i) q^{76} -2.87958 q^{77} +(-1.78047 + 4.90943i) q^{78} -2.73419 q^{79} +(-0.846689 + 1.46651i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.66281 + 2.88007i) q^{82} +3.55488 q^{83} +(-0.140946 - 0.244125i) q^{84} +(0.249865 + 0.432780i) q^{85} -4.01893 q^{86} +(-2.37487 - 4.11340i) q^{87} +(-1.37752 + 2.38593i) q^{88} +(-2.75231 + 4.76713i) q^{89} -0.585903 q^{90} +(-3.53974 + 9.76044i) q^{91} +0.586585 q^{92} +(-3.21677 + 5.57161i) q^{93} +(1.39854 - 2.42234i) q^{94} +(0.977557 + 1.69318i) q^{95} -0.553277 q^{96} +(-1.60965 - 2.78800i) q^{97} +(-0.935667 - 1.62062i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

Introduction

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