LMFDB - Embedded newform 547.2.c.a.40.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.8
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.981507 - 1.70002i) q^{2} +0.337082 q^{3} +(-0.926713 + 1.60511i) q^{4} +(-0.170480 + 0.295281i) q^{5} +(-0.330849 - 0.573047i) q^{6} +(2.30708 + 3.99598i) q^{7} -0.287726 q^{8} -2.88638 q^{9} +O(q^{10})$	\(q+(-0.981507 - 1.70002i) q^{2} +0.337082 q^{3} +(-0.926713 + 1.60511i) q^{4} +(-0.170480 + 0.295281i) q^{5} +(-0.330849 - 0.573047i) q^{6} +(2.30708 + 3.99598i) q^{7} -0.287726 q^{8} -2.88638 q^{9} +0.669311 q^{10} +(-0.611778 - 1.05963i) q^{11} +(-0.312379 + 0.541056i) q^{12} +(-2.10596 - 3.64764i) q^{13} +(4.52883 - 7.84416i) q^{14} +(-0.0574659 + 0.0995338i) q^{15} +(2.13583 + 3.69937i) q^{16} +(3.38452 + 5.86216i) q^{17} +(2.83300 + 4.90690i) q^{18} +(-4.12484 + 7.14444i) q^{19} +(-0.315973 - 0.547281i) q^{20} +(0.777675 + 1.34697i) q^{21} +(-1.20093 + 2.08007i) q^{22} +(-1.14627 + 1.98540i) q^{23} -0.0969874 q^{24} +(2.44187 + 4.22945i) q^{25} +(-4.13404 + 7.16036i) q^{26} -1.98419 q^{27} -8.55200 q^{28} +8.69498 q^{29} +0.225613 q^{30} -7.91100 q^{31} +(3.90494 - 6.76356i) q^{32} +(-0.206220 - 0.357183i) q^{33} +(6.64387 - 11.5075i) q^{34} -1.57325 q^{35} +(2.67484 - 4.63296i) q^{36} +(-1.42532 - 2.46872i) q^{37} +16.1943 q^{38} +(-0.709883 - 1.22955i) q^{39} +(0.0490516 - 0.0849599i) q^{40} +(-1.32347 - 2.29231i) q^{41} +(1.52659 - 2.64413i) q^{42} +(2.86667 + 4.96521i) q^{43} +2.26777 q^{44} +(0.492070 - 0.852291i) q^{45} +4.50030 q^{46} +(4.48602 - 7.77002i) q^{47} +(0.719951 + 1.24699i) q^{48} +(-7.14523 + 12.3759i) q^{49} +(4.79343 - 8.30247i) q^{50} +(1.14086 + 1.97603i) q^{51} +7.80650 q^{52} +(1.61765 + 2.80185i) q^{53} +(1.94750 + 3.37317i) q^{54} +0.417185 q^{55} +(-0.663807 - 1.14975i) q^{56} +(-1.39041 + 2.40826i) q^{57} +(-8.53419 - 14.7816i) q^{58} +(1.23696 + 2.14248i) q^{59} +(-0.106509 - 0.184479i) q^{60} +(-0.198336 - 0.343529i) q^{61} +(7.76470 + 13.4489i) q^{62} +(-6.65910 - 11.5339i) q^{63} -6.78759 q^{64} +1.43610 q^{65} +(-0.404812 + 0.701155i) q^{66} +(0.759416 + 1.31535i) q^{67} -12.5459 q^{68} +(-0.386388 + 0.669244i) q^{69} +(1.54415 + 2.67455i) q^{70} +(-1.19574 - 2.07109i) q^{71} +0.830486 q^{72} +(3.98336 + 6.89938i) q^{73} +(-2.79791 + 4.84613i) q^{74} +(0.823112 + 1.42567i) q^{75} +(-7.64509 - 13.2417i) q^{76} +(2.82284 - 4.88930i) q^{77} +(-1.39351 + 2.41363i) q^{78} +0.983152 q^{79} -1.45647 q^{80} +7.99029 q^{81} +(-2.59798 + 4.49984i) q^{82} +(-7.06842 - 12.2429i) q^{83} -2.88273 q^{84} -2.30798 q^{85} +(5.62731 - 9.74679i) q^{86} +2.93092 q^{87} +(0.176025 + 0.304883i) q^{88} -10.4059 q^{89} -1.93188 q^{90} +(9.71725 - 16.8308i) q^{91} +(-2.12453 - 3.67980i) q^{92} -2.66666 q^{93} -17.6123 q^{94} +(-1.40641 - 2.43597i) q^{95} +(1.31629 - 2.27988i) q^{96} +(-1.06778 + 1.84944i) q^{97} +28.0524 q^{98} +(1.76582 + 3.05849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.981507	−	1.70002i	−0.694030	−	1.20210i	−0.970506	−	0.241075i	$-0.922500\pi$
$2$	−0.981507	−	1.70002i	−0.694030	−	1.20210i	0.276476	−	0.961021i	$-0.410833\pi$
$3$	0.337082			0.194615			0.0973073	−	0.995254i	$-0.468977\pi$
$3$	0.337082			0.194615			0.0973073	+	0.995254i	$0.468977\pi$
$4$	−0.926713	+	1.60511i	−0.463357	+	0.802557i
$5$	−0.170480	+	0.295281i	−0.0762411	+	0.132053i	−0.901625	−	0.432518i	$-0.857625\pi$
$5$	−0.170480	+	0.295281i	−0.0762411	+	0.132053i	0.825384	+	0.564571i	$0.190959\pi$
$6$	−0.330849	−	0.573047i	−0.135068	−	0.233945i
$7$	2.30708	+	3.99598i	0.871994	+	1.51034i	0.859931	+	0.510410i	$0.170507\pi$
$7$	2.30708	+	3.99598i	0.871994	+	1.51034i	0.0120630	+	0.999927i	$0.496160\pi$
$8$	−0.287726			−0.101727
$9$	−2.88638			−0.962125
$10$	0.669311			0.211655
$11$	−0.611778	−	1.05963i	−0.184458	−	0.319491i	0.758936	−	0.651166i	$-0.225720\pi$
$11$	−0.611778	−	1.05963i	−0.184458	−	0.319491i	−0.943394	+	0.331675i	$0.892386\pi$
$12$	−0.312379	+	0.541056i	−0.0901759	+	0.156189i
$13$	−2.10596	−	3.64764i	−0.584089	−	1.01167i	−0.994988	−	0.0999916i	$-0.968118\pi$
$13$	−2.10596	−	3.64764i	−0.584089	−	1.01167i	0.410899	−	0.911681i	$-0.365215\pi$
$14$	4.52883	−	7.84416i	1.21038	−	2.09644i
$15$	−0.0574659	+	0.0995338i	−0.0148376	+	0.0256995i
$16$	2.13583	+	3.69937i	0.533958	+	0.924842i
$17$	3.38452	+	5.86216i	0.820867	+	1.42178i	0.905037	+	0.425332i	$0.139843\pi$
$17$	3.38452	+	5.86216i	0.820867	+	1.42178i	−0.0841702	+	0.996451i	$0.526824\pi$
$18$	2.83300	+	4.90690i	0.667744	+	1.15657i
$19$	−4.12484	+	7.14444i	−0.946304	+	1.63905i	−0.193184	+	0.981163i	$0.561881\pi$
$19$	−4.12484	+	7.14444i	−0.946304	+	1.63905i	−0.753120	+	0.657884i	$0.771452\pi$
$20$	−0.315973	−	0.547281i	−0.0706537	−	0.122376i
$21$	0.777675	+	1.34697i	0.169703	+	0.293934i
$22$	−1.20093	+	2.08007i	−0.256039	+	0.443473i
$23$	−1.14627	+	1.98540i	−0.239014	+	0.413985i	−0.960432	−	0.278516i	$-0.910158\pi$
$23$	−1.14627	+	1.98540i	−0.239014	+	0.413985i	0.721417	+	0.692500i	$0.243491\pi$
$24$	−0.0969874			−0.0197975
$25$	2.44187	+	4.22945i	0.488375	+	0.845890i
$26$	−4.13404	+	7.16036i	−0.810752	+	1.40426i
$27$	−1.98419			−0.381858
$28$	−8.55200			−1.61618
$29$	8.69498			1.61462			0.807309	−	0.590130i	$-0.200923\pi$
$29$	8.69498			1.61462			0.807309	+	0.590130i	$0.200923\pi$
$30$	0.225613			0.0411911
$31$	−7.91100			−1.42086			−0.710429	−	0.703769i	$-0.751499\pi$
$31$	−7.91100			−1.42086			−0.710429	+	0.703769i	$0.751499\pi$
$32$	3.90494	−	6.76356i	0.690303	−	1.19564i
$33$	−0.206220	−	0.357183i	−0.0358982	−	0.0621775i
$34$	6.64387	−	11.5075i	1.13941	−	1.97352i
$35$	−1.57325			−0.265927
$36$	2.67484	−	4.63296i	0.445807	−	0.772160i
$37$	−1.42532	−	2.46872i	−0.234320	−	0.405855i	0.724755	−	0.689007i	$-0.241953\pi$
$37$	−1.42532	−	2.46872i	−0.234320	−	0.405855i	−0.959075	+	0.283152i	$0.908620\pi$
$38$	16.1943			2.62705
$39$	−0.709883	−	1.22955i	−0.113672	−	0.196886i
$40$	0.0490516	−	0.0849599i	0.00775575	−	0.0134333i
$41$	−1.32347	−	2.29231i	−0.206691	−	0.357999i	0.743979	−	0.668203i	$-0.232936\pi$
$41$	−1.32347	−	2.29231i	−0.206691	−	0.357999i	−0.950670	+	0.310204i	$0.899603\pi$
$42$	1.52659	−	2.64413i	0.235558	−	0.407998i
$43$	2.86667	+	4.96521i	0.437163	+	0.757188i	0.997469	−	0.0710972i	$-0.0226500\pi$
$43$	2.86667	+	4.96521i	0.437163	+	0.757188i	−0.560307	+	0.828285i	$0.689317\pi$
$44$	2.26777			0.341879
$45$	0.492070	−	0.852291i	0.0733535	−	0.127052i
$46$	4.50030			0.663533
$47$	4.48602	−	7.77002i	0.654354	−	1.13337i	−0.327702	−	0.944781i	$-0.606274\pi$
$47$	4.48602	−	7.77002i	0.654354	−	1.13337i	0.982055	−	0.188593i	$-0.0603926\pi$
$48$	0.719951	+	1.24699i	0.103916	+	0.179988i
$49$	−7.14523	+	12.3759i	−1.02075	+	1.76799i
$50$	4.79343	−	8.30247i	0.677894	−	1.17415i
$51$	1.14086	+	1.97603i	0.159753	+	0.276700i
$52$	7.80650			1.08257
$53$	1.61765	+	2.80185i	0.222201	+	0.384864i	0.955476	−	0.295069i	$-0.0953425\pi$
$53$	1.61765	+	2.80185i	0.222201	+	0.384864i	−0.733275	+	0.679932i	$0.762009\pi$
$54$	1.94750	+	3.37317i	0.265021	+	0.459030i
$55$	0.417185			0.0562531
$56$	−0.663807	−	1.14975i	−0.0887049	−	0.153641i
$57$	−1.39041	+	2.40826i	−0.184164	+	0.318982i
$58$	−8.53419	−	14.7816i	−1.12059	−	1.94092i
$59$	1.23696	+	2.14248i	0.161039	+	0.278927i	0.935241	−	0.354011i	$-0.115182\pi$
$59$	1.23696	+	2.14248i	0.161039	+	0.278927i	−0.774203	+	0.632938i	$0.781849\pi$
$60$	−0.106509	−	0.184479i	−0.0137502	−	0.0238161i
$61$	−0.198336	−	0.343529i	−0.0253944	−	0.0439843i	0.853049	−	0.521831i	$-0.174751\pi$
$61$	−0.198336	−	0.343529i	−0.0253944	−	0.0439843i	−0.878443	+	0.477847i	$0.841417\pi$
$62$	7.76470	+	13.4489i	0.986118	+	1.70801i
$63$	−6.65910	−	11.5339i	−0.838967	−	1.45313i
$64$	−6.78759			−0.848449
$65$	1.43610			0.178127
$66$	−0.404812	+	0.701155i	−0.0498289	+	0.0863062i
$67$	0.759416	+	1.31535i	0.0927775	+	0.160695i	0.908679	−	0.417496i	$-0.137092\pi$
$67$	0.759416	+	1.31535i	0.0927775	+	0.160695i	−0.815901	+	0.578191i	$0.803759\pi$
$68$	−12.5459			−1.52142
$69$	−0.386388	+	0.669244i	−0.0465156	+	0.0805675i
$70$	1.54415	+	2.67455i	0.184562	+	0.319670i
$71$	−1.19574	−	2.07109i	−0.141908	−	0.245793i	0.786307	−	0.617836i	$-0.211991\pi$
$71$	−1.19574	−	2.07109i	−0.141908	−	0.245793i	−0.928215	+	0.372044i	$0.878657\pi$
$72$	0.830486			0.0978737
$73$	3.98336	+	6.89938i	0.466217	+	0.807512i	0.999256	−	0.0385793i	$-0.0122832\pi$
$73$	3.98336	+	6.89938i	0.466217	+	0.807512i	−0.533038	+	0.846091i	$0.678950\pi$
$74$	−2.79791	+	4.84613i	−0.325251	+	0.563351i
$75$	0.823112	+	1.42567i	0.0950448	+	0.164622i
$76$	−7.64509	−	13.2417i	−0.876952	−	1.51893i
$77$	2.82284	−	4.88930i	0.321693	−	0.557188i
$78$	−1.39351	+	2.41363i	−0.157784	+	0.273290i
$79$	0.983152			0.110613			0.0553066	−	0.998469i	$-0.482386\pi$
$79$	0.983152			0.110613			0.0553066	+	0.998469i	$0.482386\pi$
$80$	−1.45647			−0.162838
$81$	7.99029			0.887810
$82$	−2.59798	+	4.49984i	−0.286899	+	0.496924i
$83$	−7.06842	−	12.2429i	−0.775860	−	1.34383i	−0.934310	−	0.356462i	$-0.883983\pi$
$83$	−7.06842	−	12.2429i	−0.775860	−	1.34383i	0.158450	−	0.987367i	$-0.449350\pi$
$84$	−2.88273			−0.314531
$85$	−2.30798			−0.250335
$86$	5.62731	−	9.74679i	0.606809	−	1.05102i
$87$	2.93092			0.314228
$88$	0.176025	+	0.304883i	0.0187643	+	0.0325007i
$89$	−10.4059			−1.10302			−0.551511	−	0.834168i	$-0.685949\pi$
$89$	−10.4059			−1.10302			−0.551511	+	0.834168i	$0.685949\pi$
$90$	−1.93188			−0.203638
$91$	9.71725	−	16.8308i	1.01864	−	1.76434i
$92$	−2.12453	−	3.67980i	−0.221498	−	0.383645i
$93$	−2.66666			−0.276519
$94$	−17.6123			−1.81657
$95$	−1.40641	−	2.43597i	−0.144295	−	0.249925i
$96$	1.31629	−	2.27988i	0.134343	−	0.232689i
$97$	−1.06778	+	1.84944i	−0.108416	+	0.187783i	−0.915129	−	0.403161i	$-0.867911\pi$
$97$	−1.06778	+	1.84944i	−0.108416	+	0.187783i	0.806713	+	0.590944i	$0.201245\pi$
$98$	28.0524			2.83372
$99$	1.76582	+	3.05849i	0.177472	+	0.307390i
$100$	−9.05166			−0.905166
$101$	10.9377			1.08834			0.544169	−	0.838975i	$-0.316845\pi$
$101$	10.9377			1.08834			0.544169	+	0.838975i	$0.316845\pi$
$102$	2.23953	−	3.87898i	0.221746	−	0.384076i
$103$	0.674934			0.0665032			0.0332516	−	0.999447i	$-0.489414\pi$
$103$	0.674934			0.0665032			0.0332516	+	0.999447i	$0.489414\pi$
$104$	0.605941	+	1.04952i	0.0594174	+	0.102914i
$105$	−0.530313			−0.0517533
$106$	3.17547	−	5.50007i	0.308429	−	0.534214i
$107$	−14.4667			−1.39855			−0.699277	−	0.714851i	$-0.746494\pi$
$107$	−14.4667			−1.39855			−0.699277	+	0.714851i	$0.746494\pi$
$108$	1.83878	−	3.18486i	0.176936	−	0.306463i
$109$	−0.344221	+	0.596209i	−0.0329704	+	0.0571065i	−0.882040	−	0.471175i	$-0.843830\pi$
$109$	−0.344221	+	0.596209i	−0.0329704	+	0.0571065i	0.849069	+	0.528281i	$0.177163\pi$
$110$	−0.409470	−	0.709222i	−0.0390414	−	0.0676217i
$111$	−0.480448	−	0.832161i	−0.0456021	−	0.0789852i
$112$	−9.85506	+	17.0695i	−0.931216	+	1.61291i
$113$	−4.67370	+	8.09509i	−0.439665	+	0.761522i	−0.997663	−	0.0683198i	$-0.978236\pi$
$113$	−4.67370	+	8.09509i	−0.439665	+	0.761522i	0.557998	+	0.829842i	$0.311570\pi$
$114$	5.45879			0.511263
$115$	−0.390834	−	0.676944i	−0.0364454	−	0.0631253i
$116$	−8.05775	+	13.9564i	−0.748143	+	1.29582i
$117$	6.07860	+	10.5285i	0.561967	+	0.973356i
$118$	2.42817	−	4.20572i	0.223531	−	0.387168i
$119$	−15.6167	+	27.0490i	−1.43158	+	2.47957i
$120$	0.0165344	−	0.0286385i	0.00150938	−	0.00261432i
$121$	4.75146	−	8.22976i	0.431950	−	0.748160i
$122$	−0.389337	+	0.674352i	−0.0352489	+	0.0610529i
$123$	−0.446117	−	0.772697i	−0.0402250	−	0.0696718i
$124$	7.33123	−	12.6981i	0.658363	−	1.14032i
$125$	−3.36997			−0.301419
$126$	−13.0719	+	22.6412i	−1.16454	+	2.01704i
$127$	−9.54522	+	16.5328i	−0.847001	+	1.46705i	0.0368712	+	0.999320i	$0.488261\pi$
$127$	−9.54522	+	16.5328i	−0.847001	+	1.46705i	−0.883872	+	0.467729i	$0.845072\pi$
$128$	−1.14781	−	1.98807i	−0.101453	−	0.175722i
$129$	0.966303	+	1.67369i	0.0850782	+	0.147360i
$130$	−1.40954	−	2.44140i	−0.123625	−	0.214125i
$131$	4.45560			0.389287			0.194644	−	0.980874i	$-0.437645\pi$
$131$	4.45560			0.389287			0.194644	+	0.980874i	$0.437645\pi$
$132$	0.764425			0.0665347
$133$	−38.0653			−3.30068
$134$	1.49075	−	2.58205i	0.128781	−	0.223055i
$135$	0.338266	−	0.585894i	0.0291133	−	0.0504257i
$136$	−0.973815	−	1.68670i	−0.0835040	−	0.144633i
$137$	−10.5970	−	18.3545i	−0.905360	−	1.56813i	−0.820434	−	0.571742i	$-0.806268\pi$
$137$	−10.5970	−	18.3545i	−0.905360	−	1.56813i	−0.0849258	−	0.996387i	$-0.527065\pi$
$138$	1.51697			0.129133
$139$	5.33413	+	9.23899i	0.452435	+	0.783641i	0.998537	−	0.0540784i	$-0.0172221\pi$
$139$	5.33413	+	9.23899i	0.452435	+	0.783641i	−0.546102	+	0.837719i	$0.683889\pi$
$140$	1.45795	−	2.52524i	0.123219	−	0.213422i
$141$	1.51216	−	2.61914i	0.127347	−	0.220571i
$142$	−2.34726	+	4.06557i	−0.196978	+	0.341175i
$143$	−2.57677	+	4.46309i	−0.215480	+	0.373222i
$144$	−6.16481	−	10.6778i	−0.513734	−	0.889814i
$145$	−1.48232	+	2.56746i	−0.123100	+	0.213216i
$146$	7.81940	−	13.5436i	0.647138	−	1.12088i
$147$	−2.40853	+	4.17169i	−0.198652	+	0.344076i
$148$	5.28343			0.434296
$149$	18.4104			1.50824			0.754118	−	0.656739i	$-0.228065\pi$
$149$	18.4104			1.50824			0.754118	+	0.656739i	$0.228065\pi$
$150$	1.61578	−	2.79861i	0.131928	−	0.228506i
$151$	3.33987			0.271794			0.135897	−	0.990723i	$-0.456608\pi$
$151$	3.33987			0.271794			0.135897	+	0.990723i	$0.456608\pi$
$152$	1.18682	−	2.05564i	0.0962642	−	0.166734i
$153$	−9.76900	−	16.9204i	−0.789777	−	1.36793i
$154$	−11.0826			−0.893058
$155$	1.34867	−	2.33596i	0.108328	−	0.187629i
$156$	2.63143			0.210683
$157$	−3.44372	−	5.96469i	−0.274838	−	0.476034i	0.695256	−	0.718762i	$-0.255291\pi$
$157$	−3.44372	−	5.96469i	−0.274838	−	0.476034i	−0.970094	+	0.242728i	$0.921958\pi$
$158$	−0.964971	−	1.67138i	−0.0767690	−	0.132968i
$159$	0.545281	+	0.944454i	0.0432436	+	0.0749001i
$160$	1.33143	+	2.30611i	0.105259	+	0.182314i
$161$	−10.5782			−0.833676
$162$	−7.84253	−	13.5837i	−0.616167	−	1.06723i
$163$	9.46810	+	16.3992i	0.741599	+	1.28449i	0.951767	+	0.306822i	$0.0992657\pi$
$163$	9.46810	+	16.3992i	0.741599	+	1.28449i	−0.210168	+	0.977665i	$0.567401\pi$
$164$	4.90589			0.383086
$165$	0.140625			0.0109477
$166$	−13.8754	+	24.0329i	−1.07694	+	1.86532i
$167$	−5.79053			−0.448085			−0.224042	−	0.974579i	$-0.571925\pi$
$167$	−5.79053			−0.448085			−0.224042	+	0.974579i	$0.571925\pi$
$168$	−0.223758	−	0.387559i	−0.0172633	−	0.0299009i
$169$	−2.37017	+	4.10526i	−0.182321	+	0.315789i
$170$	2.26530	+	3.92361i	0.173740	+	0.300927i
$171$	11.9058	−	20.6215i	0.910463	−	1.57697i
$172$	−10.6263			−0.810249
$173$	5.51650			0.419411			0.209706	−	0.977765i	$-0.432749\pi$
$173$	5.51650			0.419411			0.209706	+	0.977765i	$0.432749\pi$
$174$	−2.87672	−	4.98263i	−0.218084	−	0.377732i
$175$	−11.2672	+	19.5153i	−0.851719	+	1.47522i
$176$	2.61331	−	4.52639i	0.196986	−	0.341189i
$177$	0.416957	+	0.722192i	0.0313404	+	0.0542832i
$178$	10.2135	+	17.6902i	0.765531	+	1.32594i
$179$	5.67591			0.424238			0.212119	−	0.977244i	$-0.431964\pi$
$179$	5.67591			0.424238			0.212119	+	0.977244i	$0.431964\pi$
$180$	0.912016	+	1.57966i	0.0679777	+	0.117741i
$181$	7.36447	−	12.7556i	0.547396	−	0.948118i	−0.451055	−	0.892496i	$-0.648952\pi$
$181$	7.36447	−	12.7556i	0.547396	−	0.948118i	0.998452	−	0.0556225i	$-0.0177143\pi$
$182$	−38.1502			−2.82788
$183$	−0.0668557	−	0.115797i	−0.00494211	−	0.00855999i
$184$	0.329812	−	0.571252i	0.0243141	−	0.0421132i
$185$	0.971953			0.0714594
$186$	2.61734	+	4.53337i	0.191913	+	0.332403i
$187$	4.14115	−	7.17269i	0.302831	−	0.524519i
$188$	8.31451	+	14.4012i	0.606398	+	1.05031i
$189$	−4.57769	−	7.92879i	−0.332978	−	0.576735i
$190$	−2.76080	+	4.78185i	−0.200290	+	0.346912i
$191$	−11.6267	+	20.1380i	−0.841275	+	1.45713i	0.0475421	+	0.998869i	$0.484861\pi$
$191$	−11.6267	+	20.1380i	−0.841275	+	1.45713i	−0.888817	+	0.458262i	$0.848472\pi$
$192$	−2.28798			−0.165121
$193$	3.29099	−	5.70016i	0.236891	−	0.410307i	−0.722930	−	0.690921i	$-0.757205\pi$
$193$	3.29099	−	5.70016i	0.236891	−	0.410307i	0.959820	+	0.280615i	$0.0905384\pi$
$194$	4.19212			0.300977
$195$	0.484084			0.0346660
$196$	−13.2432	−	22.9378i	−0.945939	−	1.63842i
$197$	7.24868			0.516447			0.258223	−	0.966085i	$-0.416863\pi$
$197$	7.24868			0.516447			0.258223	+	0.966085i	$0.416863\pi$
$198$	3.46633	−	6.00387i	0.246342	−	0.426676i
$199$	−10.5106	+	18.2049i	−0.745077	+	1.29051i	0.205082	+	0.978745i	$0.434254\pi$
$199$	−10.5106	+	18.2049i	−0.745077	+	1.29051i	−0.950159	+	0.311766i	$0.899080\pi$
$200$	−0.702591	−	1.21692i	−0.0496807	−	0.0860494i
$201$	0.255986	+	0.443380i	0.0180558	+	0.0312736i
$202$	−10.7354	−	18.5943i	−0.755340	−	1.30829i
$203$	20.0600	+	34.7449i	1.40794	+	2.43862i
$204$	−4.22901			−0.296090
$205$	0.902500			0.0630333
$206$	−0.662453	−	1.14740i	−0.0461553	−	0.0799433i
$207$	3.30857	−	5.73061i	0.229962	−	0.398305i
$208$	8.99597	−	15.5815i	0.623758	−	1.08038i
$209$	10.0940			0.698213
$210$	0.520506	+	0.901544i	0.0359184	+	0.0622124i
$211$	5.12442	−	8.87575i	0.352780	−	0.611032i	−0.633956	−	0.773369i	$-0.718570\pi$
$211$	5.12442	−	8.87575i	0.352780	−	0.611032i	0.986735	+	0.162337i	$0.0519032\pi$
$212$	−5.99639			−0.411833
$213$	−0.403063	−	0.698126i	−0.0276174	−	0.0478348i
$214$	14.1992	+	24.5938i	0.970638	+	1.68120i
$215$	−1.95484			−0.133319
$216$	0.570904			0.0388451
$217$	−18.2513	−	31.6122i	−1.23898	−	2.14597i
$218$	1.35142			0.0915299
$219$	1.34272	+	2.32566i	0.0907326	+	0.157154i
$220$	−0.386610	+	0.669629i	−0.0260653	+	0.0451464i
$221$	14.2554	−	24.6910i	0.958920	−	1.66090i
$222$	−0.943127	+	1.63354i	−0.0632986	+	0.109636i
$223$	12.0423	−	20.8578i	0.806411	−	1.39674i	−0.108923	−	0.994050i	$-0.534740\pi$
$223$	12.0423	−	20.8578i	0.806411	−	1.39674i	0.915334	−	0.402695i	$-0.131926\pi$
$224$	36.0360			2.40776
$225$	−7.04816	−	12.2078i	−0.469877	−	0.813852i
$226$	18.3491			1.22056
$227$	−0.511431	+	0.885825i	−0.0339449	+	0.0587943i	−0.882499	−	0.470315i	$-0.844140\pi$
$227$	−0.511431	+	0.885825i	−0.0339449	+	0.0587943i	0.848554	+	0.529109i	$0.177474\pi$
$228$	−2.57702	−	4.46354i	−0.170668	−	0.295605i
$229$	−6.52428	+	11.3004i	−0.431136	+	0.746750i	−0.996971	−	0.0777684i	$-0.975221\pi$
$229$	−6.52428	+	11.3004i	−0.431136	+	0.746750i	0.565835	+	0.824518i	$0.308554\pi$
$230$	−0.767212	+	1.32885i	−0.0505885	+	0.0876218i
$231$	0.951530	−	1.64810i	0.0626060	−	0.108437i
$232$	−2.50177			−0.164249
$233$	−9.89123	+	17.1321i	−0.647996	+	1.12236i	0.335605	+	0.942003i	$0.391059\pi$
$233$	−9.89123	+	17.1321i	−0.647996	+	1.12236i	−0.983601	+	0.180359i	$0.942274\pi$
$234$	11.9324	−	20.6675i	0.780045	−	1.35108i
$235$	1.52956	+	2.64927i	0.0997773	+	0.172819i
$236$	−4.58523			−0.298473
$237$	0.331403			0.0215270
$238$	61.3117			3.97425
$239$	0.866500	+	1.50082i	0.0560492	+	0.0970801i	0.892689	−	0.450674i	$-0.148816\pi$
$239$	0.866500	+	1.50082i	0.0560492	+	0.0970801i	−0.836639	+	0.547754i	$0.815483\pi$
$240$	−0.490950			−0.0316907
$241$	12.4397	−	21.5462i	0.801313	−	1.38792i	−0.117439	−	0.993080i	$-0.537468\pi$
$241$	12.4397	−	21.5462i	0.801313	−	1.38792i	0.918752	−	0.394835i	$-0.129198\pi$
$242$	−18.6544			−1.19915
$243$	8.64596			0.554639
$244$	0.735204			0.0470666
$245$	−2.43624	−	4.21969i	−0.155646	−	0.269586i
$246$	−0.875734	+	1.51682i	−0.0558348	+	0.0967087i
$247$	34.7471			2.21090
$248$	2.27620			0.144539
$249$	−2.38264	−	4.12685i	−0.150994	−	0.261529i
$250$	3.30765	+	5.72902i	0.209194	+	0.362335i
$251$	−4.18777	−	7.25343i	−0.264330	−	0.457833i	0.703058	−	0.711132i	$-0.251817\pi$
$251$	−4.18777	−	7.25343i	−0.264330	−	0.457833i	−0.967388	+	0.253300i	$0.918484\pi$
$252$	24.6843			1.55496
$253$	2.80506			0.176352
$254$	37.4748			2.35138
$255$	−0.777978			−0.0487189
$256$	−9.04077	+	15.6591i	−0.565048	+	0.978692i
$257$	−1.52959			−0.0954131			−0.0477065	−	0.998861i	$-0.515191\pi$
$257$	−1.52959			−0.0954131			−0.0477065	+	0.998861i	$0.515191\pi$
$258$	1.89687	−	3.28547i	0.118094	−	0.204544i
$259$	6.57663	−	11.3911i	0.408652	−	0.707806i
$260$	−1.33085	+	2.30511i	−0.0825361	+	0.142957i
$261$	−25.0970			−1.55346
$262$	−4.37320	−	7.57461i	−0.270177	−	0.467961i
$263$	−30.1940			−1.86184			−0.930920	−	0.365224i	$-0.880992\pi$
$263$	−30.1940			−1.86184			−0.930920	+	0.365224i	$0.880992\pi$
$264$	0.0593347	+	0.102771i	0.00365180	+	0.00632511i
$265$	−1.10311			−0.0677635
$266$	37.3614	+	64.7119i	2.29078	+	3.96774i
$267$	−3.50764			−0.214664
$268$	−2.81504			−0.171956
$269$	9.71700	−	16.8303i	0.592456	−	1.02616i	−0.401445	−	0.915883i	$-0.631492\pi$
$269$	9.71700	−	16.8303i	0.592456	−	1.02616i	0.993901	−	0.110280i	$-0.0351749\pi$
$270$	−1.32804			−0.0808220
$271$	1.75982	+	3.04810i	0.106902	+	0.185159i	0.914514	−	0.404555i	$-0.132574\pi$
$271$	1.75982	+	3.04810i	0.106902	+	0.185159i	−0.807612	+	0.589714i	$0.799240\pi$
$272$	−14.4575	+	25.0412i	−0.876617	+	1.51835i
$273$	3.27551	−	5.67336i	0.198243	−	0.343367i
$274$	−20.8020	+	36.0301i	−1.25669	+	2.17666i
$275$	2.98777	−	5.17497i	0.180169	−	0.312062i
$276$	−0.716142	−	1.24039i	−0.0431067	−	0.0746629i
$277$	−7.71160			−0.463345			−0.231673	−	0.972794i	$-0.574420\pi$
$277$	−7.71160			−0.463345			−0.231673	+	0.972794i	$0.574420\pi$
$278$	10.4710	−	18.1363i	0.628008	−	1.08774i
$279$	22.8341			1.36704
$280$	0.452664			0.0270519
$281$	8.65595	+	14.9925i	0.516371	+	0.894380i	0.999819	+	0.0190074i	$0.00605062\pi$
$281$	8.65595	+	14.9925i	0.516371	+	0.894380i	−0.483449	+	0.875373i	$0.660616\pi$
$282$	−5.93678			−0.353530
$283$	−7.75930	−	13.4395i	−0.461242	−	0.798895i	0.537781	−	0.843085i	$-0.319263\pi$
$283$	−7.75930	−	13.4395i	−0.461242	−	0.798895i	−0.999023	+	0.0441895i	$0.985929\pi$
$284$	4.43244			0.263017
$285$	−0.474075	−	0.821123i	−0.0280818	−	0.0486391i
$286$	10.1165			0.598199
$287$	6.10668	−	10.5771i	0.360466	−	0.624346i
$288$	−11.2711	+	19.5222i	−0.664158	+	1.15036i
$289$	−14.4100	+	24.9588i	−0.847646	+	1.46817i
$290$	5.81964			0.341741
$291$	−0.359929	+	0.623415i	−0.0210994	+	0.0365452i
$292$	−14.7657			−0.864099
$293$	18.3517			1.07212			0.536059	−	0.844180i	$-0.319912\pi$
$293$	18.3517			1.07212			0.536059	+	0.844180i	$0.319912\pi$
$294$	9.45596			0.551483
$295$	−0.843510			−0.0491110
$296$	0.410100	+	0.710315i	0.0238366	+	0.0412862i
$297$	1.21389	+	2.10251i	0.0704368	+	0.122000i
$298$	−18.0699	−	31.2980i	−1.04676	−	1.81304i
$299$	9.65603			0.558423
$300$	−3.05116			−0.176159
$301$	−13.2273	+	22.9103i	−0.762406	+	1.32053i
$302$	−3.27810	−	5.67784i	−0.188634	−	0.326723i
$303$	3.68689			0.211806
$304$	−35.2399			−2.02115
$305$	0.135250			0.00774438
$306$	−19.1767	+	33.2150i	−1.09626	+	1.89878i
$307$	−1.01148			−0.0577280			−0.0288640	−	0.999583i	$-0.509189\pi$
$307$	−1.01148			−0.0577280			−0.0288640	+	0.999583i	$0.509189\pi$
$308$	5.23193	+	9.06196i	0.298117	+	0.516353i
$309$	0.227508			0.0129425
$310$	−5.29492			−0.300731
$311$	29.1559			1.65328			0.826640	−	0.562731i	$-0.190249\pi$
$311$	29.1559			1.65328			0.826640	+	0.562731i	$0.190249\pi$
$312$	0.204252	+	0.353775i	0.0115635	+	0.0200285i
$313$	11.7973	−	20.4336i	0.666825	−	1.15497i	−0.311963	−	0.950094i	$-0.600986\pi$
$313$	11.7973	−	20.4336i	0.666825	−	1.15497i	0.978787	−	0.204880i	$-0.0656803\pi$
$314$	−6.76007	+	11.7088i	−0.381493	+	0.660765i
$315$	4.54098			0.255855
$316$	−0.911100	+	1.57807i	−0.0512534	+	0.0887735i
$317$	1.13423	−	1.96454i	0.0637046	−	0.110340i	−0.832414	−	0.554154i	$-0.813042\pi$
$317$	1.13423	−	1.96454i	0.0637046	−	0.110340i	0.896119	+	0.443815i	$0.146375\pi$
$318$	1.07039	−	1.85398i	0.0600247	−	0.103966i
$319$	−5.31940	−	9.21347i	−0.297829	−	0.515855i
$320$	1.15715	−	2.00424i	0.0646867	−	0.112041i
$321$	−4.87648			−0.272179
$322$	10.3825	+	17.9831i	0.578596	+	1.00216i
$323$	−55.8425			−3.10716
$324$	−7.40471	+	12.8253i	−0.411373	+	0.712518i
$325$	10.2850	−	17.8141i	0.570509	−	0.988150i
$326$	18.5860	−	32.1919i	1.02938	−	1.78295i
$327$	−0.116031	+	0.200971i	−0.00641653	+	0.0111137i
$328$	0.380796	+	0.659558i	0.0210259	+	0.0364180i
$329$	41.3984			2.28237
$330$	−0.138025	−	0.239066i	−0.00759802	−	0.0131602i
$331$	32.5743			1.79045			0.895223	−	0.445619i	$-0.147016\pi$
$331$	32.5743			1.79045			0.895223	+	0.445619i	$0.147016\pi$
$332$	26.2016			1.43800
$333$	4.11399	+	7.12565i	0.225446	+	0.390483i
$334$	5.68345	+	9.84402i	0.310984	+	0.538641i
$335$	−0.517862			−0.0282938
$336$	−3.32197	+	5.75382i	−0.181228	+	0.313896i
$337$	−1.85311	−	3.20968i	−0.100945	−	0.174842i	0.811129	−	0.584867i	$-0.198853\pi$
$337$	−1.85311	−	3.20968i	−0.100945	−	0.174842i	−0.912074	+	0.410025i	$0.865520\pi$
$338$	9.30536			0.506145
$339$	−1.57542	+	2.72871i	−0.0855652	+	0.148203i
$340$	2.13883	−	3.70457i	0.115995	−	0.200908i
$341$	4.83977	+	8.38274i	0.262089	+	0.453951i
$342$	−46.7427			−2.52756
$343$	−33.6393			−1.81635
$344$	−0.824815	−	1.42862i	−0.0444711	−	0.0770261i
$345$	−0.131743	−	0.228186i	−0.00709281	−	0.0122851i
$346$	−5.41448	−	9.37816i	−0.291084	−	0.504173i
$347$	−0.233537	−	0.404498i	−0.0125369	−	0.0217146i	0.859689	−	0.510818i	$-0.170657\pi$
$347$	−0.233537	−	0.404498i	−0.0125369	−	0.0217146i	−0.872226	+	0.489103i	$0.837324\pi$
$348$	−2.71613	+	4.70447i	−0.145600	+	0.252186i
$349$	16.8274	−	29.1459i	0.900749	−	1.56014i	0.0742249	−	0.997242i	$-0.476352\pi$
$349$	16.8274	−	29.1459i	0.900749	−	1.56014i	0.826524	−	0.562901i	$-0.190315\pi$
$350$	44.2353			2.36448
$351$	4.17864	+	7.23761i	0.223039	+	0.386315i
$352$	−9.55583			−0.509328
$353$	−4.01095			−0.213481			−0.106741	−	0.994287i	$-0.534041\pi$
$353$	−4.01095			−0.213481			−0.106741	+	0.994287i	$0.534041\pi$
$354$	0.818494	−	1.41767i	0.0435024	−	0.0753484i
$355$	0.815402			0.0432770
$356$	9.64328	−	16.7026i	0.511093	−	0.885238i
$357$	−5.26412	+	9.11772i	−0.278607	+	0.482561i
$358$	−5.57095	−	9.64917i	−0.294434	−	0.509974i
$359$	7.16738	+	12.4143i	0.378280	+	0.655200i	0.990812	−	0.135246i	$-0.0431824\pi$
$359$	7.16738	+	12.4143i	0.378280	+	0.655200i	−0.612532	+	0.790445i	$0.709849\pi$
$360$	−0.141581	+	0.245226i	−0.00746200	+	0.0129246i
$361$	−24.5286	−	42.4849i	−1.29098	−	2.23605i
$362$	−28.9131			−1.51964
$363$	1.60163	−	2.77411i	0.0840638	−	0.145603i
$364$	18.0102	+	31.1946i	0.943992	+	1.63504i
$365$	−2.71634			−0.142180
$366$	−0.131239	+	0.227312i	−0.00685995	+	0.0118818i
$367$	3.22612	+	5.58780i	0.168402	+	0.291681i	0.937858	−	0.347019i	$-0.112806\pi$
$367$	3.22612	+	5.58780i	0.168402	+	0.291681i	−0.769456	+	0.638700i	$0.779473\pi$
$368$	−9.79298			−0.510494
$369$	3.82002	+	6.61647i	0.198862	+	0.344440i
$370$	−0.953979	−	1.65234i	−0.0495950	−	0.0859010i
$371$	−7.46409	+	12.9282i	−0.387516	+	0.671198i
$372$	2.47123	−	4.28029i	0.128127	−	0.221923i
$373$	−6.28692	−	10.8893i	−0.325525	−	0.563825i	0.656094	−	0.754679i	$-0.272208\pi$
$373$	−6.28692	−	10.8893i	−0.325525	−	0.563825i	−0.981618	+	0.190854i	$0.938874\pi$
$374$	−16.2583			−0.840696
$375$	−1.13596			−0.0586605
$376$	−1.29075	+	2.23564i	−0.0665651	+	0.115294i
$377$	−18.3113	−	31.7161i	−0.943081	−	1.63346i
$378$	−8.98607	+	15.5643i	−0.462194	+	0.800543i
$379$	14.7781	+	25.5964i	0.759098	+	1.31480i	0.943311	+	0.331910i	$0.107693\pi$
$379$	14.7781	+	25.5964i	0.759098	+	1.31480i	−0.184213	+	0.982886i	$0.558973\pi$
$380$	5.21335			0.267439
$381$	−3.21752	+	5.57291i	−0.164839	+	0.285509i
$382$	45.6466			2.33548
$383$	5.29833			0.270732			0.135366	−	0.990796i	$-0.456779\pi$
$383$	5.29833			0.270732			0.135366	+	0.990796i	$0.456779\pi$
$384$	−0.386908	−	0.670144i	−0.0197443	−	0.0341981i
$385$	0.962478	+	1.66706i	0.0490524	+	0.0849613i
$386$	−12.9205			−0.657637
$387$	−8.27428	−	14.3315i	−0.420605	−	0.728510i
$388$	−1.97905	−	3.42781i	−0.100471	−	0.174021i
$389$	1.87258	+	3.24341i	0.0949437	+	0.164447i	0.909585	−	0.415518i	$-0.136400\pi$
$389$	1.87258	+	3.24341i	0.0949437	+	0.164447i	−0.814641	+	0.579965i	$0.803066\pi$
$390$	−0.475132	−	0.822954i	−0.0240593	−	0.0416719i
$391$	−15.5183			−0.784796
$392$	2.05587	−	3.56087i	0.103837	−	0.179851i
$393$	1.50190			0.0757610
$394$	−7.11463	−	12.3229i	−0.358430	−	0.620819i
$395$	−0.167608	+	0.290306i	−0.00843328	+	0.0146069i
$396$	−6.54564			−0.328931
$397$	−7.60503	+	13.1723i	−0.381686	+	0.661099i	−0.991303	−	0.131597i	$-0.957990\pi$
$397$	−7.60503	+	13.1723i	−0.381686	+	0.661099i	0.609618	+	0.792696i	$0.291323\pi$
$398$	41.2649			2.06842
$399$	−12.8312			−0.642361
$400$	−10.4309	+	18.0668i	−0.521543	+	0.903339i
$401$	2.36094	−	4.08926i	0.117899	−	0.204208i	−0.801036	−	0.598617i	$-0.795717\pi$
$401$	2.36094	−	4.08926i	0.117899	−	0.204208i	0.918935	+	0.394409i	$0.129051\pi$
$402$	0.502504	−	0.870362i	0.0250626	−	0.0434097i
$403$	16.6603	+	28.8564i	0.829908	+	1.43744i
$404$	−10.1361	+	17.5562i	−0.504289	+	0.873454i
$405$	−1.36219	+	2.35938i	−0.0676876	+	0.117238i
$406$	39.3781	−	68.2048i	1.95430	−	3.38495i
$407$	−1.74395	+	3.02062i	−0.0864446	+	0.149726i
$408$	−0.328256	−	0.568556i	−0.0162511	−	0.0281477i
$409$	16.4366			0.812738			0.406369	−	0.913709i	$-0.366795\pi$
$409$	16.4366			0.812738			0.406369	+	0.913709i	$0.366795\pi$
$410$	−0.885810	−	1.53427i	−0.0437470	−	0.0757721i
$411$	−3.57205	−	6.18697i	−0.176196	−	0.305181i
$412$	−0.625470	+	1.08335i	−0.0308147	+	0.0533726i
$413$	−5.70753	+	9.88574i	−0.280849	+	0.486445i
$414$	−12.9896			−0.638402
$415$	4.82011			0.236610
$416$	−32.8947			−1.61279
$417$	1.79804	+	3.11430i	0.0880504	+	0.152508i
$418$	−9.90729	−	17.1599i	−0.484581	−	0.839319i
$419$	6.23941	+	10.8070i	0.304815	+	0.527955i	0.977220	−	0.212228i	$-0.0680720\pi$
$419$	6.23941	+	10.8070i	0.304815	+	0.527955i	−0.672405	+	0.740183i	$0.734739\pi$
$420$	0.491448	−	0.851214i	0.0239802	−	0.0415350i
$421$	−7.66004	+	13.2676i	−0.373327	+	0.646622i	−0.990075	−	0.140539i	$-0.955117\pi$
$421$	−7.66004	+	13.2676i	−0.373327	+	0.646622i	0.616748	+	0.787161i	$0.288450\pi$
$422$	−20.1186			−0.979359
$423$	−12.9483	+	22.4272i	−0.629570	+	1.09045i
$424$	−0.465440	−	0.806165i	−0.0226038	−	0.0391509i
$425$	−16.5291	+	28.6293i	−0.801781	+	1.38873i
$426$	−0.791219	+	1.37043i	−0.0383347	+	0.0663976i
$427$	0.915155	−	1.58510i	0.0442875	−	0.0767081i
$428$	13.4065	−	23.2208i	0.648029	−	1.12242i
$429$	−0.868582	+	1.50443i	−0.0419355	+	0.0726345i
$430$	1.91869	+	3.32327i	0.0925275	+	0.160262i
$431$	3.49914	−	6.06069i	0.168548	−	0.291933i	−0.769362	−	0.638813i	$-0.779426\pi$
$431$	3.49914	−	6.06069i	0.168548	−	0.291933i	0.937909	+	0.346880i	$0.112759\pi$
$432$	−4.23790	−	7.34026i	−0.203896	−	0.353158i
$433$	−7.98369			−0.383672			−0.191836	−	0.981427i	$-0.561444\pi$
$433$	−7.98369			−0.383672			−0.191836	+	0.981427i	$0.561444\pi$
$434$	−35.8276	+	62.0552i	−1.71978	+	2.97874i
$435$	−0.499665	+	0.865445i	−0.0239571	+	0.0414949i
$436$	−0.637989	−	1.10503i	−0.0305541	−	0.0529213i
$437$	−9.45638	−	16.3789i	−0.452360	−	0.783511i
$438$	2.63578	−	4.56530i	0.125942	−	0.218139i
$439$	−2.67075	+	4.62587i	−0.127468	+	0.220781i	−0.922695	−	0.385531i	$-0.874018\pi$
$439$	−2.67075	+	4.62587i	−0.127468	+	0.220781i	0.795227	+	0.606312i	$0.207352\pi$
$440$	−0.120035			−0.00572244
$441$	20.6238	−	35.7215i	0.982086	−	1.70102i
$442$	−55.9670			−2.66208
$443$	−12.0004	−	20.7854i	−0.570158	−	0.987542i	−0.996549	−	0.0830035i	$-0.973549\pi$
$443$	−12.0004	−	20.7854i	−0.570158	−	0.987542i	0.426391	−	0.904539i	$-0.359785\pi$
$444$	1.78095			0.0845202
$445$	1.77400	−	3.07266i	0.0840957	−	0.145658i
$446$	−47.2784			−2.23870
$447$	6.20581			0.293525
$448$	−15.6595	−	27.1231i	−0.739842	−	1.28144i
$449$	21.9186			1.03440			0.517201	−	0.855864i	$-0.326974\pi$
$449$	21.9186			1.03440			0.517201	+	0.855864i	$0.326974\pi$
$450$	−13.8356	+	23.9640i	−0.652219	+	1.12968i
$451$	−1.61934	+	2.80477i	−0.0762515	+	0.132072i
$452$	−8.66237	−	15.0037i	−0.407443	−	0.705713i
$453$	1.12581			0.0528951
$454$	2.00789			0.0942351
$455$	3.31320	+	5.73863i	0.155325	+	0.269031i
$456$	0.400058	−	0.692920i	0.0187344	−	0.0324490i
$457$	−8.79450			−0.411389			−0.205695	−	0.978616i	$-0.565945\pi$
$457$	−8.79450			−0.411389			−0.205695	+	0.978616i	$0.565945\pi$
$458$	25.6145			1.19689
$459$	−6.71554	−	11.6317i	−0.313455	−	0.542920i
$460$	1.44876			0.0675489
$461$	−6.37938	+	11.0494i	−0.297117	+	0.514622i	−0.975475	−	0.220109i	$-0.929359\pi$
$461$	−6.37938	+	11.0494i	−0.297117	+	0.514622i	0.678358	+	0.734732i	$0.262692\pi$
$462$	−3.73573			−0.173802
$463$	32.6400			1.51691			0.758454	−	0.651726i	$-0.225955\pi$
$463$	32.6400			1.51691			0.758454	+	0.651726i	$0.225955\pi$
$464$	18.5710	+	32.1659i	0.862138	+	1.49327i
$465$	0.454613	−	0.787412i	0.0210822	−	0.0365154i
$466$	38.8333			1.79892
$467$	4.90694			0.227066			0.113533	−	0.993534i	$-0.463783\pi$
$467$	4.90694			0.227066			0.113533	+	0.993534i	$0.463783\pi$
$468$	−22.5325			−1.04156
$469$	−3.50407	+	6.06922i	−0.161803	+	0.280251i
$470$	3.00254	−	5.20056i	0.138497	−	0.239884i
$471$	−1.16082	−	2.01059i	−0.0534876	−	0.0926432i
$472$	−0.355906	−	0.616447i	−0.0163819	−	0.0283743i
$473$	3.50753	−	6.07522i	0.161276	−	0.279339i
$474$	−0.325275	−	0.563392i	−0.0149404	−	0.0258775i
$475$	−40.2894			−1.84860
$476$	−28.9444	−	50.1332i	−1.32667	−	2.29785i
$477$	−4.66914	−	8.08719i	−0.213785	−	0.370287i
$478$	1.70095	−	2.94614i	0.0777997	−	0.134753i
$479$	19.9206			0.910193			0.455097	−	0.890442i	$-0.349605\pi$
$479$	19.9206			0.910193			0.455097	+	0.890442i	$0.349605\pi$
$480$	0.448802	+	0.777348i	0.0204849	+	0.0354809i
$481$	−6.00333	+	10.3981i	−0.273728	+	0.474111i
$482$	−48.8387			−2.22454
$483$	−3.56571			−0.162245
$484$	8.80647	+	15.2533i	0.400294	+	0.693330i
$485$	−0.364070	−	0.630588i	−0.0165316	−	0.0286335i
$486$	−8.48608	−	14.6983i	−0.384936	−	0.666729i
$487$	9.09492	+	15.7529i	0.412130	+	0.713831i	0.995122	−	0.0986471i	$-0.0314515\pi$
$487$	9.09492	+	15.7529i	0.412130	+	0.713831i	−0.582992	+	0.812478i	$0.698118\pi$
$488$	0.0570665	+	0.0988422i	0.00258328	+	0.00447437i
$489$	3.19153	+	5.52789i	0.144326	+	0.249980i
$490$	−4.78238	+	8.28332i	−0.216046	+	0.374202i
$491$	−3.29570	−	5.70832i	−0.148733	−	0.257613i	0.782026	−	0.623245i	$-0.214186\pi$
$491$	−3.29570	−	5.70832i	−0.148733	−	0.257613i	−0.930759	+	0.365632i	$0.880853\pi$
$492$	1.65369			0.0745541
$493$	29.4283	+	50.9714i	1.32539	+	2.29564i
$494$	−34.1045	−	59.0707i	−1.53443	−	2.65772i
$495$	−1.20415			−0.0541226
$496$	−16.8966	−	29.2657i	−0.758678	−	1.31407i
$497$	5.51734	−	9.55631i	0.247487	−	0.428659i
$498$	−4.67715	+	8.10107i	−0.209588	+	0.363018i
$499$	3.90663	+	6.76649i	0.174885	+	0.302910i	0.940121	−	0.340840i	$-0.110711\pi$
$499$	3.90663	+	6.76649i	0.174885	+	0.302910i	−0.765236	+	0.643749i	$0.777378\pi$
$500$	3.12299	−	5.40918i	0.139665	−	0.241906i
$501$	−1.95189			−0.0872038
$502$	−8.22066	+	14.2386i	−0.366906	+	0.635499i
$503$	16.1390			0.719602			0.359801	−	0.933029i	$-0.382845\pi$
$503$	16.1390			0.719602			0.359801	+	0.933029i	$0.382845\pi$
$504$	1.91600	+	3.31860i	0.0853452	+	0.147822i
$505$	−1.86466	+	3.22968i	−0.0829761	+	0.143719i
$506$	−2.75318	−	4.76865i	−0.122394	−	0.211993i
$507$	−0.798942	+	1.38381i	−0.0354823	+	0.0614571i
$508$	−17.6914	−	30.6423i	−0.784927	−	1.35953i
$509$	−15.8379			−0.702004			−0.351002	−	0.936375i	$-0.614159\pi$
$509$	−15.8379			−0.702004			−0.351002	+	0.936375i	$0.614159\pi$
$510$	0.763591	+	1.32258i	0.0338124	+	0.0585648i
$511$	−18.3799	+	31.8348i	−0.813077	+	1.40829i
$512$	30.9031			1.36574
$513$	8.18448	−	14.1759i	0.361354	−	0.625883i
$514$	1.50130	+	2.60033i	0.0662196	+	0.114696i
$515$	−0.115063	+	0.199295i	−0.00507028	+	0.00878198i
$516$	−3.58194			−0.157686
$517$	−10.9778			−0.482803
$518$	−25.8200			−1.13447
$519$	1.85951			0.0816236
$520$	−0.413204			−0.0181202
$521$	−9.51791	+	16.4855i	−0.416987	+	0.722243i	−0.995635	−	0.0933348i	$-0.970247\pi$
$521$	−9.51791	+	16.4855i	−0.416987	+	0.722243i	0.578648	+	0.815578i	$0.303581\pi$
$522$	24.6329	+	42.6654i	1.07815	+	1.86741i
$523$	40.7914			1.78368			0.891841	−	0.452348i	$-0.149414\pi$
$523$	40.7914			1.78368			0.891841	+	0.452348i	$0.149414\pi$
$524$	−4.12906	+	7.15175i	−0.180379	+	0.312425i
$525$	−3.79797	+	6.57828i	−0.165757	+	0.287099i
$526$	29.6356	+	51.3304i	1.29217	+	2.23811i
$527$	−26.7749	−	46.3756i	−1.16633	−	2.02015i
$528$	0.880900	−	1.52576i	0.0383363	−	0.0664004i
$529$	8.87212	+	15.3670i	0.385744	+	0.668129i
$530$	1.08271	+	1.87531i	0.0470299	+	0.0814582i
$531$	−3.57033	−	6.18400i	−0.154939	−	0.268363i
$532$	35.2757	−	61.0992i	1.52939	−	2.64899i
$533$	−5.57435	+	9.65505i	−0.241452	+	0.418207i
$534$	3.44278	+	5.96306i	0.148983	+	0.258047i
$535$	2.46630	−	4.27175i	0.106627	−	0.184684i
$536$	−0.218504	−	0.378460i	−0.00943793	−	0.0163470i
$537$	1.91325			0.0825628
$538$	−38.1492			−1.64473
$539$	17.4852			0.753140
$540$	0.626951	+	1.08591i	0.0269797	+	0.0467302i
$541$	12.6371	+	21.8881i	0.543311	+	0.941043i	0.998711	+	0.0507558i	$0.0161630\pi$
$541$	12.6371	+	21.8881i	0.543311	+	0.941043i	−0.455400	+	0.890287i	$0.650504\pi$
$542$	3.45456	−	5.98347i	0.148386	−	0.257012i
$543$	2.48243	−	4.29970i	0.106531	−	0.184518i
$544$	52.8655			2.26659
$545$	−0.117366	−	0.203284i	−0.00502741	−	0.00870772i
$546$	−12.8598			−0.550347
$547$	13.2889	−	19.2459i	0.568193	−	0.822895i
$547$	13.2889	−	19.2459i	0.568193	−	0.822895i
$548$	39.2814			1.67802
$549$	0.572473	+	0.991553i	0.0244326	+	0.0423184i
$550$	−11.7301			−0.500172
$551$	−35.8654	+	62.1207i	−1.52792	+	2.64643i
$552$	0.111174	−	0.192559i	0.00473188	−	0.00819585i
$553$	2.26821	+	3.92866i	0.0964541	+	0.167063i
$554$	7.56899	+	13.1099i	0.321576	+	0.556986i
$555$	0.327628			0.0139070
$556$	−19.7728			−0.838555
$557$	−12.6029			−0.534001			−0.267000	−	0.963696i	$-0.586032\pi$
$557$	−12.6029			−0.534001			−0.267000	+	0.963696i	$0.586032\pi$
$558$	−22.4118	−	38.8185i	−0.948769	−	1.64332i
$559$	12.0742	−	20.9131i	0.510684	−	0.884531i
$560$	−3.36019	−	5.82002i	−0.141994	−	0.245941i
$561$	1.39591	−	2.41779i	0.0589353	−	0.102079i
$562$	16.9918	−	29.4306i	0.716754	−	1.24145i
$563$	3.48791	+	6.04124i	0.146998	+	0.254608i	0.930117	−	0.367264i	$-0.119706\pi$
$563$	3.48791	+	6.04124i	0.146998	+	0.254608i	−0.783119	+	0.621872i	$0.786372\pi$
$564$	2.80268	+	4.85438i	0.118014	+	0.204406i
$565$	−1.59355	−	2.76011i	−0.0670411	−	0.116119i
$566$	−15.2316	+	26.3819i	−0.640233	+	1.10892i
$567$	18.4342	+	31.9290i	0.774165	+	1.34089i
$568$	0.344046	+	0.595905i	0.0144359	+	0.0250036i
$569$	8.22555	−	14.2471i	0.344833	−	0.597268i	−0.640491	−	0.767966i	$-0.721269\pi$
$569$	8.22555	−	14.2471i	0.344833	−	0.597268i	0.985323	+	0.170698i	$0.0546023\pi$
$570$	−0.930617	+	1.61188i	−0.0389793	+	0.0675141i
$571$	4.29643			0.179800			0.0899000	−	0.995951i	$-0.471345\pi$
$571$	4.29643			0.179800			0.0899000	+	0.995951i	$0.471345\pi$
$572$	−4.77585	−	8.27201i	−0.199688	−	0.345870i
$573$	−3.91914	+	6.78815i	−0.163724	+	0.283579i
$574$	−23.9750			−1.00070
$575$	−11.1962			−0.466914
$576$	19.5915			0.816314
$577$	41.5211			1.72855			0.864273	−	0.503022i	$-0.167779\pi$
$577$	41.5211			1.72855			0.864273	+	0.503022i	$0.167779\pi$
$578$	56.5740			2.35317
$579$	1.10933	−	1.92142i	0.0461024	−	0.0798516i
$580$	−2.74738	−	4.75860i	−0.114079	−	0.197590i
$581$	32.6148	−	56.4905i	1.35309	−	2.34362i
$582$	1.41309			0.0585745
$583$	1.97928	−	3.42822i	0.0819736	−	0.141982i
$584$	−1.14612	−	1.98513i	−0.0474267	−	0.0821454i
$585$	−4.14513			−0.171380
$586$	−18.0123	−	31.1983i	−0.744083	−	1.28879i
$587$	4.17096	−	7.22431i	0.172154	−	0.298179i	−0.767019	−	0.641625i	$-0.778261\pi$
$587$	4.17096	−	7.22431i	0.172154	−	0.298179i	0.939173	+	0.343445i	$0.111594\pi$
$588$	−4.46403	−	7.73193i	−0.184094	−	0.318859i
$589$	32.6316	−	56.5196i	1.34456	−	2.32885i
$590$	0.827911	+	1.43398i	0.0340846	+	0.0590362i
$591$	2.44340			0.100508
$592$	6.08847	−	10.5455i	0.250234	−	0.433419i
$593$	−32.2900			−1.32599			−0.662996	−	0.748623i	$-0.730715\pi$
$593$	−32.2900			−1.32599			−0.662996	+	0.748623i	$0.730715\pi$
$594$	2.38288	−	4.12726i	0.0977706	−	0.169344i
$595$	−5.32469	−	9.22263i	−0.218291	−	0.378091i
$596$	−17.0611	+	29.5507i	−0.698851	+	1.21045i
$597$	−3.54294	+	6.13655i	−0.145003	+	0.251152i
$598$	−9.47747	−	16.4155i	−0.387562	−	0.671278i
$599$	−7.94854			−0.324768			−0.162384	−	0.986728i	$-0.551918\pi$
$599$	−7.94854			−0.324768			−0.162384	+	0.986728i	$0.551918\pi$
$600$	−0.236831	−	0.410203i	−0.00966858	−	0.0167465i
$601$	−9.74856	−	16.8850i	−0.397652	−	0.688754i	0.595784	−	0.803145i	$-0.296842\pi$
$601$	−9.74856	−	16.8850i	−0.397652	−	0.688754i	−0.993436	+	0.114391i	$0.963508\pi$
$602$	51.9306			2.11653
$603$	−2.19196	−	3.79659i	−0.0892635	−	0.154609i
$604$	−3.09510	+	5.36087i	−0.125938	+	0.218131i
$605$	1.62006	+	2.80602i	0.0658648	+	0.114081i
$606$	−3.61871	−	6.26779i	−0.147000	−	0.254612i
$607$	6.41182	+	11.1056i	0.260248	+	0.450763i	0.966308	−	0.257390i	$-0.0828624\pi$
$607$	6.41182	+	11.1056i	0.260248	+	0.450763i	−0.706060	+	0.708152i	$0.749529\pi$
$608$	32.2145	+	55.7972i	1.30647	+	2.26288i
$609$	6.76187	+	11.7119i	0.274005	+	0.474590i
$610$	−0.132749	−	0.229927i	−0.00537484	−	0.00930949i
$611$	−37.7896			−1.52880
$612$	36.2122			1.46379
$613$	−3.74451	+	6.48567i	−0.151239	+	0.261954i	−0.931683	−	0.363272i	$-0.881660\pi$
$613$	−3.74451	+	6.48567i	−0.151239	+	0.261954i	0.780444	+	0.625226i	$0.214993\pi$
$614$	0.992772	+	1.71953i	0.0400650	+	0.0693947i
$615$	0.304217			0.0122672
$616$	−0.812205	+	1.40678i	−0.0327247	+	0.0566808i
$617$	−8.72925	−	15.1195i	−0.351426	−	0.608688i	0.635073	−	0.772452i	$-0.280970\pi$
$617$	−8.72925	−	15.1195i	−0.351426	−	0.608688i	−0.986500	+	0.163764i	$0.947637\pi$
$618$	−0.223301	−	0.386769i	−0.00898249	−	0.0155581i
$619$	−28.1485			−1.13139			−0.565693	−	0.824616i	$-0.691391\pi$
$619$	−28.1485			−1.13139			−0.565693	+	0.824616i	$0.691391\pi$
$620$	2.49966	+	4.32954i	0.100389	+	0.173878i
$621$	2.27442	−	3.93942i	0.0912695	−	0.158083i
$622$	−28.6168	−	49.5657i	−1.14743	−	1.98740i
$623$	−24.0072	−	41.5817i	−0.961829	−	1.66594i
$624$	3.03238	−	5.25224i	0.121392	−	0.210258i
$625$	−11.6349	+	20.1522i	−0.465394	+	0.806086i
$626$	−46.3167			−1.85119
$627$	3.40249			0.135882
$628$	12.7653			0.509393
$629$	9.64802	−	16.7109i	0.384692	−	0.666306i
$630$	−4.45700	−	7.71976i	−0.177571	−	0.307563i
$631$	44.7890			1.78302			0.891511	−	0.452999i	$-0.149646\pi$
$631$	44.7890			1.78302			0.891511	+	0.452999i	$0.149646\pi$
$632$	−0.282879			−0.0112523
$633$	1.72735	−	2.99186i	0.0686560	−	0.118916i
$634$	−4.45301			−0.176852
$635$	−3.25454	−	5.63703i	−0.129153	−	0.223699i
$636$	−2.02128			−0.0801488
$637$	60.1904			2.38483
$638$	−10.4421	+	18.0862i	−0.413405	+	0.716038i
$639$	3.45136	+	5.97793i	0.136534	+	0.236483i
$640$	0.782719			0.0309397
$641$	21.0792			0.832578			0.416289	−	0.909232i	$-0.363330\pi$
$641$	21.0792			0.832578			0.416289	+	0.909232i	$0.363330\pi$
$642$	4.78630	+	8.29012i	0.188900	+	0.327185i
$643$	15.6025	−	27.0243i	0.615301	−	1.06573i	−0.375030	−	0.927013i	$-0.622368\pi$
$643$	15.6025	−	27.0243i	0.615301	−	1.06573i	0.990332	−	0.138721i	$-0.0442990\pi$
$644$	9.80292	−	16.9792i	0.386289	−	0.669073i
$645$	−0.658943			−0.0259458
$646$	54.8098	+	94.9334i	2.15646	+	3.73510i
$647$	−21.8494			−0.858987			−0.429494	−	0.903070i	$-0.641308\pi$
$647$	−21.8494			−0.858987			−0.429494	+	0.903070i	$0.641308\pi$
$648$	−2.29902			−0.0903139
$649$	1.51349	−	2.62144i	0.0594097	−	0.102901i
$650$	−40.3792			−1.58380
$651$	−6.15219	−	10.6559i	−0.241123	−	0.417638i
$652$	−35.0969			−1.37450
$653$	−23.4427	+	40.6040i	−0.917385	+	1.58896i	−0.114013	+	0.993479i	$0.536371\pi$
$653$	−23.4427	+	40.6040i	−0.917385	+	1.58896i	−0.803372	+	0.595478i	$0.796963\pi$
$654$	0.455541			0.0178131
$655$	−0.759592	+	1.31565i	−0.0296797	+	0.0514068i
$656$	5.65340	−	9.79198i	0.220728	−	0.382313i
$657$	−11.4975	−	19.9142i	−0.448559	−	0.776927i
$658$	−40.6329	−	70.3782i	−1.58403	−	2.74363i
$659$	−7.76551	+	13.4503i	−0.302501	+	0.523948i	−0.976702	−	0.214601i	$-0.931155\pi$
$659$	−7.76551	+	13.4503i	−0.302501	+	0.523948i	0.674200	+	0.738548i	$0.264488\pi$
$660$	−0.130320	+	0.225720i	−0.00507268	+	0.00878614i
$661$	−25.0345			−0.973728			−0.486864	−	0.873478i	$-0.661859\pi$
$661$	−25.0345			−0.973728			−0.486864	+	0.873478i	$0.661859\pi$
$662$	−31.9719	−	55.3770i	−1.24262	−	2.15229i
$663$	4.80523	−	8.32290i	0.186620	−	0.323235i
$664$	2.03377	+	3.52259i	0.0789255	+	0.136703i
$665$	6.48939	−	11.2400i	0.251648	−	0.435867i
$666$	8.07583	−	13.9878i	0.312932	−	0.542014i
$667$	−9.96681	+	17.2630i	−0.385917	+	0.668427i
$668$	5.36616	−	9.29447i	0.207623	−	0.359614i
$669$	4.05924	−	7.03081i	0.156939	−	0.271827i
$670$	0.508285	+	0.880376i	0.0196368	+	0.0340119i
$671$	−0.242676	+	0.420327i	−0.00936839	+	0.0162265i
$672$	12.1471			0.468585
$673$	−14.3973	+	24.9368i	−0.554974	+	0.961243i	0.442932	+	0.896555i	$0.353938\pi$
$673$	−14.3973	+	24.9368i	−0.554974	+	0.961243i	−0.997906	+	0.0646873i	$0.979395\pi$
$674$	−3.63768	+	6.30065i	−0.140118	+	0.242692i
$675$	−4.84515	−	8.39204i	−0.186490	−	0.323010i
$676$	−4.39294	−	7.60879i	−0.168959	−	0.292646i
$677$	12.6299	+	21.8756i	0.485405	+	0.840747i	0.999859	−	0.0167713i	$-0.00533871\pi$
$677$	12.6299	+	21.8756i	0.485405	+	0.840747i	−0.514454	+	0.857518i	$0.672005\pi$
$678$	6.18516			0.237539
$679$	−9.85379			−0.378154
$680$	0.664065			0.0254657
$681$	−0.172394	+	0.298596i	−0.00660617	+	0.0114422i
$682$	9.50055	−	16.4554i	0.363795	−	0.630111i
$683$	−22.4350	−	38.8586i	−0.858452	−	1.48688i	−0.873406	−	0.486994i	$-0.838094\pi$
$683$	−22.4350	−	38.8586i	−0.858452	−	1.48688i	0.0149540	−	0.999888i	$-0.495240\pi$
$684$	22.0666	+	38.2205i	0.843738	+	1.46140i
$685$	7.22629			0.276103
$686$	33.0172	+	57.1875i	1.26060	+	2.18343i
$687$	−2.19922	+	3.80916i	−0.0839054	+	0.145328i
$688$	−12.2454	+	21.2097i	−0.466853	+	0.808613i
$689$	6.81342	−	11.8012i	0.259571	−	0.449590i
$690$	−0.258614	+	0.447932i	−0.00984525	+	0.0170525i
$691$	7.24390	+	12.5468i	0.275571	+	0.477303i	0.970279	−	0.241989i	$-0.0777998\pi$
$691$	7.24390	+	12.5468i	0.275571	+	0.477303i	−0.694708	+	0.719292i	$0.744466\pi$
$692$	−5.11221	+	8.85461i	−0.194337	+	0.336602i
$693$	−8.14778	+	14.1124i	−0.309509	+	0.536084i
$694$	−0.458437	+	0.794036i	−0.0174020	+	0.0301412i
$695$	−3.63746			−0.137977
$696$	−0.843303			−0.0319653
$697$	8.95860	−	15.5168i	0.339331	−	0.587739i
$698$	−66.0648			−2.50059
$699$	−3.33416	+	5.77493i	−0.126109	+	0.218428i
$700$	−20.8829	−	36.1702i	−0.789300	−	1.36711i
$701$	8.44625			0.319010			0.159505	−	0.987197i	$-0.449010\pi$
$701$	8.44625			0.319010			0.159505	+	0.987197i	$0.449010\pi$
$702$	8.20273	−	14.2075i	0.309592	−	0.536229i
$703$	23.5168			0.886953
$704$	4.15250	+	7.19234i	0.156503	+	0.271072i
$705$	0.515587	+	0.893022i	0.0194181	+	0.0336332i
$706$	3.93678	+	6.81870i	0.148163	+	0.256625i
$707$	25.2341	+	43.7067i	0.949025	+	1.64376i
$708$	−1.54560			−0.0580872
$709$	21.3479	+	36.9756i	0.801736	+	1.38865i	0.918473	+	0.395484i	$0.129423\pi$
$709$	21.3479	+	36.9756i	0.801736	+	1.38865i	−0.116737	+	0.993163i	$0.537243\pi$
$710$	−0.800323	−	1.38620i	−0.0300356	−	0.0520231i
$711$	−2.83775			−0.106424
$712$	2.99405			0.112207
$713$	9.06816	−	15.7065i	0.339605	−	0.588213i
$714$	20.6671			0.773446
$715$	−0.878576	−	1.52174i	−0.0328569	−	0.0569098i
$716$	−5.25994	+	9.11049i	−0.196573	+	0.340475i
$717$	0.292082	+	0.505900i	0.0109080	+	0.0188932i
$718$	14.0697	−	24.3694i	0.525075	−	0.909457i
$719$	42.2199			1.57454			0.787268	−	0.616611i	$-0.211495\pi$
$719$	42.2199			1.57454			0.787268	+	0.616611i	$0.211495\pi$
$720$	4.20392			0.156671
$721$	1.55713	+	2.69702i	0.0579904	+	0.100442i
$722$	−48.1501	+	83.3984i	−1.79196	+	3.10377i
$723$	4.19321	−	7.26286i	0.155947	−	0.270109i
$724$	13.6495	+	23.6416i	0.507280	+	0.878634i
$725$	21.2320	+	36.7750i	0.788538	+	1.36579i
$726$	−6.28805			−0.233371
$727$	3.63105	+	6.28916i	0.134668	+	0.233252i	0.925471	−	0.378819i	$-0.123670\pi$
$727$	3.63105	+	6.28916i	0.134668	+	0.233252i	−0.790802	+	0.612071i	$0.790336\pi$
$728$	−2.79591	+	4.84265i	−0.103623	+	0.179481i
$729$	−21.0565			−0.779869
$730$	2.66611	+	4.61783i	0.0986770	+	0.170914i
$731$	−19.4046	+	33.6098i	−0.717705	+	1.24310i
$732$	0.247824			0.00915984
$733$	−2.44999	−	4.24350i	−0.0904924	−	0.156737i	0.817226	−	0.576317i	$-0.195511\pi$
$733$	−2.44999	−	4.24350i	−0.0904924	−	0.156737i	−0.907718	+	0.419580i	$0.862177\pi$
$734$	6.33292	−	10.9689i	0.233752	−	0.404871i
$735$	−0.821214	−	1.42238i	−0.0302909	−	0.0524654i
$736$	8.95225	+	15.5058i	0.329984	+	0.571550i
$737$	0.929188	−	1.60940i	0.0342271	−	0.0592831i
$738$	7.49876	−	12.9882i	0.276033	−	0.478103i
$739$	−28.5334			−1.04962			−0.524810	−	0.851220i	$-0.675863\pi$
$739$	−28.5334			−1.04962			−0.524810	+	0.851220i	$0.675863\pi$
$740$	−0.900721	+	1.56010i	−0.0331112	+	0.0573502i
$741$	11.7126			0.430274
$742$	29.3042			1.07579
$743$	−10.7002	−	18.5333i	−0.392553	−	0.679921i	0.600233	−	0.799825i	$-0.295075\pi$
$743$	−10.7002	−	18.5333i	−0.392553	−	0.679921i	−0.992785	+	0.119904i	$0.961741\pi$
$744$	0.767267			0.0281294
$745$	−3.13860	+	5.43622i	−0.114990	+	0.199168i
$746$	−12.3413	+	21.3758i	−0.451848	+	0.782624i
$747$	20.4021	+	35.3375i	0.746474	+	1.29293i
$748$	7.67532	+	13.2940i	0.280638	+	0.486079i
$749$	−33.3759	−	57.8088i	−1.21953	−	2.11229i
$750$	1.11495	+	1.93115i	0.0407122	+	0.0705156i
$751$	−6.57806			−0.240037			−0.120018	−	0.992772i	$-0.538295\pi$
$751$	−6.57806			−0.240037			−0.120018	+	0.992772i	$0.538295\pi$
$752$	38.3256			1.39759
$753$	−1.41162	−	2.44500i	−0.0514424	−	0.0891009i
$754$	−35.9454	+	62.2592i	−1.30905	+	2.26735i
$755$	−0.569381	+	0.986197i	−0.0207219	+	0.0358914i
$756$	16.9688			0.617150
$757$	10.4042	+	18.0207i	0.378148	+	0.654972i	0.990793	−	0.135387i	$-0.0432276\pi$
$757$	10.4042	+	18.0207i	0.378148	+	0.654972i	−0.612645	+	0.790358i	$0.709894\pi$
$758$	29.0096	−	50.2460i	1.05367	−	1.82502i
$759$	0.945535			0.0343207
$760$	0.404661	+	0.700893i	0.0146786	+	0.0254240i
$761$	−22.6826	−	39.2874i	−0.822242	−	1.42417i	−0.904009	−	0.427514i	$-0.859389\pi$
$761$	−22.6826	−	39.2874i	−0.822242	−	1.42417i	0.0817662	−	0.996652i	$-0.473944\pi$
$762$	12.6321			0.457612
$763$	−3.17658			−0.115000
$764$	−21.5491	−	37.3242i	−0.779621	−	1.35034i
$765$	6.66169			0.240854
$766$	−5.20035	−	9.00728i	−0.187896	−	0.325446i
$767$	5.20999	−	9.02397i	0.188122	−	0.325837i
$768$	−3.04748	+	5.27839i	−0.109967	+	0.190468i
$769$	12.4394	−	21.5457i	0.448577	−	0.776959i	−0.549716	−	0.835351i	$-0.685264\pi$
$769$	12.4394	−	21.5457i	0.448577	−	0.776959i	0.998294	+	0.0583926i	$0.0185975\pi$
$770$	1.88936	−	3.27246i	0.0680877	−	0.117931i
$771$	−0.515597			−0.0185688
$772$	6.09961	+	10.5648i	0.219530	+	0.380237i
$773$	38.9809			1.40205			0.701024	−	0.713138i	$-0.252727\pi$
$773$	38.9809			1.40205			0.701024	+	0.713138i	$0.252727\pi$
$774$	−16.2425	+	28.1329i	−0.583826	+	1.01122i
$775$	−19.3177	−	33.4592i	−0.693910	−	1.20189i
$776$	0.307227	−	0.532133i	0.0110288	−	0.0191025i
$777$	2.21687	−	3.83972i	0.0795296	−	0.137749i
$778$	3.67591	−	6.36686i	0.131788	−	0.228263i
$779$	21.8364			0.782369
$780$	−0.448607	+	0.777011i	−0.0160627	+	0.0278215i
$781$	−1.46306	+	2.53409i	−0.0523523	+	0.0906768i
$782$	15.2314	+	26.3815i	0.544672	+	0.943400i
$783$	−17.2525			−0.616555
$784$	−61.0440			−2.18014
$785$	2.34834			0.0838160
$786$	−1.47413	−	2.55327i	−0.0525804	−	0.0910720i
$787$	−52.5492			−1.87318			−0.936588	−	0.350433i	$-0.886035\pi$
$787$	−52.5492			−1.87318			−0.936588	+	0.350433i	$0.886035\pi$
$788$	−6.71744	+	11.6350i	−0.239299	+	0.414478i
$789$	−10.1778			−0.362341
$790$	0.658035			0.0234118
$791$	−43.1304			−1.53354
$792$	−0.508073	−	0.880008i	−0.0180536	−	0.0312697i
$793$	−0.835378	+	1.44692i	−0.0296652	+	0.0513816i
$794$	29.8576			1.05961
$795$	−0.371839			−0.0131878
$796$	−19.4806	−	33.7414i	−0.690472	−	1.19593i
$797$	−6.93602	−	12.0135i	−0.245686	−	0.425541i	0.716638	−	0.697445i	$-0.245680\pi$
$797$	−6.93602	−	12.0135i	−0.245686	−	0.425541i	−0.962324	+	0.271904i	$0.912347\pi$
$798$	12.5939	+	21.8132i	0.445818	+	0.772180i
$799$	60.7322			2.14855
$800$	38.1415			1.34851
$801$	30.0353			1.06125
$802$	−9.26910			−0.327303
$803$	4.87387	−	8.44178i	0.171995	−	0.297904i
$804$	−0.948901			−0.0334652
$805$	1.80337	−	3.12353i	0.0635604	−	0.110090i
$806$	32.7044	−	56.6456i	1.15196	−	1.99526i
$807$	3.27543	−	5.67321i	0.115301	−	0.199706i
$808$	−3.14705			−0.110713
$809$	−10.8316	−	18.7608i	−0.380817	−	0.659594i	0.610362	−	0.792122i	$-0.291024\pi$
$809$	−10.8316	−	18.7608i	−0.380817	−	0.659594i	−0.991179	+	0.132528i	$0.957691\pi$
$810$	5.34799			0.187909
$811$	17.2373	+	29.8558i	0.605282	+	1.04838i	0.992007	+	0.126184i	$0.0402731\pi$
$811$	17.2373	+	29.8558i	0.605282	+	1.04838i	−0.386725	+	0.922195i	$0.626394\pi$
$812$	−74.3595			−2.60951
$813$	0.593205	+	1.02746i	0.0208046	+	0.0360347i
$814$	6.84681			0.239981
$815$	−6.45650			−0.226161
$816$	−4.87338	+	8.44094i	−0.170602	+	0.295492i
$817$	−47.2982			−1.65475
$818$	−16.1327	−	27.9426i	−0.564065	−	0.976989i
$819$	−28.0476	+	48.5799i	−0.980064	+	1.69752i
$820$	−0.836358	+	1.44862i	−0.0292069	+	0.0505878i
$821$	−5.27538	+	9.13723i	−0.184112	+	0.318891i	−0.943277	−	0.332007i	$-0.892274\pi$
$821$	−5.27538	+	9.13723i	−0.184112	+	0.318891i	0.759165	+	0.650898i	$0.225608\pi$
$822$	−7.01198	+	12.1451i	−0.244571	+	0.423609i
$823$	17.0660	+	29.5593i	0.594885	+	1.03037i	0.993563	+	0.113280i	$0.0361358\pi$
$823$	17.0660	+	29.5593i	0.594885	+	1.03037i	−0.398678	+	0.917091i	$0.630531\pi$
$824$	−0.194196			−0.00676514
$825$	1.00712	−	1.74439i	0.0350636	−	0.0607319i
$826$	22.4079			0.779672
$827$	43.0150			1.49578			0.747890	−	0.663823i	$-0.231067\pi$
$827$	43.0150			1.49578			0.747890	+	0.663823i	$0.231067\pi$
$828$	6.13219	+	10.6213i	0.213108	+	0.369115i
$829$	36.5965			1.27105			0.635524	−	0.772081i	$-0.280784\pi$
$829$	36.5965			1.27105			0.635524	+	0.772081i	$0.280784\pi$
$830$	−4.73097	−	8.19428i	−0.164214	−	0.284428i
$831$	−2.59944			−0.0901737
$832$	14.2944	+	24.7587i	0.495570	+	0.858353i
$833$	−96.7327			−3.35159
$834$	3.52958	−	6.11341i	0.122219	−	0.211690i
$835$	0.987172	−	1.70983i	0.0341625	−	0.0591712i
$836$	−9.35420	+	16.2019i	−0.323522	+	0.560356i
$837$	15.6969			0.542566
$838$	12.2480	−	21.2142i	0.423102	−	0.732834i
$839$	6.64573			0.229436			0.114718	−	0.993398i	$-0.463404\pi$
$839$	6.64573			0.229436			0.114718	+	0.993398i	$0.463404\pi$
$840$	0.152585			0.00526468
$841$	46.6027			1.60699
$842$	30.0735			1.03640
$843$	2.91777	+	5.05372i	0.100493	+	0.174059i
$844$	9.49773	+	16.4506i	0.326925	+	0.566252i
$845$	−0.808135	−	1.39973i	−0.0278007	−	0.0481522i
$846$	50.8356			1.74776
$847$	43.8479			1.50663
$848$	−6.91005	+	11.9686i	−0.237292	+	0.411002i
$849$	−2.61552	−	4.53022i	−0.0897645	−	0.155477i
$850$	64.8939			2.22584
$851$	6.53520			0.224024
$852$	1.49410			0.0511869
$853$	11.1099	−	19.2429i	0.380395	−	0.658863i	−0.610724	−	0.791844i	$-0.709121\pi$
$853$	11.1099	−	19.2429i	0.380395	−	0.658863i	0.991119	+	0.132981i	$0.0424548\pi$
$854$	−3.59293			−0.122947
$855$	4.05942	+	7.03113i	0.138829	+	0.240460i
$856$	4.16246			0.142270
$857$	−33.8635			−1.15675			−0.578377	−	0.815770i	$-0.696314\pi$
$857$	−33.8635			−1.15675			−0.578377	+	0.815770i	$0.696314\pi$
$858$	3.41008			0.116418
$859$	20.8978	+	36.1961i	0.713025	+	1.23500i	0.963716	+	0.266929i	$0.0860088\pi$
$859$	20.8978	+	36.1961i	0.713025	+	1.23500i	−0.250691	+	0.968067i	$0.580658\pi$
$860$	1.81158	−	3.13774i	0.0617743	−	0.106996i
$861$	2.05845	−	3.56535i	0.0701519	−	0.121507i
$862$	−13.7377			−0.467909
$863$	−3.91842	+	6.78691i	−0.133385	+	0.231029i	−0.924979	−	0.380018i	$-0.875918\pi$
$863$	−3.91842	+	6.78691i	−0.133385	+	0.231029i	0.791595	+	0.611047i	$0.209251\pi$
$864$	−7.74816	+	13.4202i	−0.263598	+	0.456565i
$865$	−0.940454	+	1.62891i	−0.0319764	+	0.0553847i
$866$	7.83605	+	13.5724i	0.266280	+	0.461210i
$867$	−4.85735	+	8.41317i	−0.164964	+	0.285726i
$868$	67.6549			2.29636
$869$	−0.601471	−	1.04178i	−0.0204035	−	0.0353399i
$870$	1.96170			0.0665078
$871$	3.19861	−	5.54015i	0.108381	−	0.187721i
$872$	0.0990415	−	0.171545i	0.00335397	−	0.00580924i
$873$	3.08201	−	5.33819i	0.104310	−	0.180670i
$874$	−18.5630	+	32.1521i	−0.627903	+	1.08756i
$875$	−7.77478	−	13.4663i	−0.262836	−	0.455245i
$876$	−4.97727			−0.168166
$877$	−4.89431	−	8.47719i	−0.165269	−	0.286254i	0.771482	−	0.636251i	$-0.219516\pi$
$877$	−4.89431	−	8.47719i	−0.165269	−	0.286254i	−0.936751	+	0.349997i	$0.886183\pi$
$878$	10.4854			0.353866
$879$	6.18604			0.208650
$880$	0.891036	+	1.54332i	0.0300368	+	0.0520253i
$881$	14.9123	+	25.8289i	0.502409	+	0.870197i	0.999996	+	0.00278350i	$0.000886016\pi$
$881$	14.9123	+	25.8289i	0.502409	+	0.870197i	−0.497587	+	0.867414i	$0.665781\pi$
$882$	−80.9697			−2.72639
$883$	−15.0946	+	26.1447i	−0.507974	+	0.879838i	0.491983	+	0.870605i	$0.336272\pi$
$883$	−15.0946	+	26.1447i	−0.507974	+	0.879838i	−0.999957	+	0.00923272i	$0.997061\pi$
$884$	26.4213	+	45.7630i	0.888643	+	1.53918i
$885$	−0.284332			−0.00955772
$886$	−23.5570	+	40.8020i	−0.791414	+	1.37077i
$887$	−11.3420	+	19.6449i	−0.380826	+	0.659610i	−0.991181	−	0.132518i	$-0.957694\pi$
$887$	−11.3420	+	19.6449i	−0.380826	+	0.659610i	0.610355	+	0.792128i	$0.291027\pi$
$888$	0.138238	+	0.239434i	0.00463895	+	0.00803490i
$889$	−88.0863			−2.95432
$890$	−6.96477			−0.233460
$891$	−4.88828	−	8.46676i	−0.163764	−	0.283647i
$892$	22.3195	+	38.6585i	0.747312	+	1.29438i
$893$	37.0083	+	64.1002i	1.23843	+	2.14503i
$894$	−6.09104	−	10.5500i	−0.203715	−	0.352845i
$895$	−0.967632	+	1.67599i	−0.0323444	+	0.0560221i
$896$	5.29619	−	9.17328i	0.176933	−	0.306458i
$897$	3.25488			0.108677
$898$	−21.5133	−	37.2621i	−0.717907	−	1.24345i
$899$	−68.7860			−2.29414
$900$	26.1265			0.870883
$901$	−10.9499	+	18.9658i	−0.364795	+	0.631844i
$902$	6.35756			0.211684
$903$	−4.45867	+	7.72265i	−0.148375	+	0.256994i
$904$	1.34475	−	2.32917i	0.0447256	−	0.0774670i
$905$	2.51099	+	4.34917i	0.0834682	+	0.144571i
$906$	−1.10499	−	1.91390i	−0.0367108	−	0.0635850i
$907$	−15.9037	+	27.5461i	−0.528075	+	0.914653i	0.471389	+	0.881925i	$0.343753\pi$
$907$	−15.9037	+	27.5461i	−0.528075	+	0.914653i	−0.999464	+	0.0327277i	$0.989581\pi$
$908$	−0.947900	−	1.64181i	−0.0314572	−	0.0544854i
$909$	−31.5702			−1.04712
$910$	6.50386	−	11.2650i	0.215601	−	0.373432i
$911$	8.96710	+	15.5315i	0.297093	+	0.514580i	0.975470	−	0.220134i	$-0.0706495\pi$
$911$	8.96710	+	15.5315i	0.297093	+	0.514580i	−0.678376	+	0.734714i	$0.737316\pi$
$912$	−11.8787			−0.393344
$913$	−8.64861	+	14.9798i	−0.286227	+	0.495760i
$914$	8.63187	+	14.9508i	0.285517	+	0.494530i
$915$	0.0455903			0.00150717
$916$	−12.0923	−	20.9444i	−0.399540	−	0.692023i
$917$	10.2794	+	17.8045i	0.339456	+	0.587956i
$918$	−13.1827	+	22.8331i	−0.435094	+	0.753605i
$919$	6.62645	−	11.4773i	0.218586	−	0.378603i	−0.735790	−	0.677210i	$-0.763189\pi$
$919$	6.62645	−	11.4773i	0.218586	−	0.378603i	0.954376	+	0.298607i	$0.0965221\pi$
$920$	0.112453	+	0.194774i	0.00370747	+	0.00642152i
$921$	−0.340951			−0.0112347
$922$	25.0456			0.824834
$923$	−5.03638	+	8.72326i	−0.165774	+	0.287130i
$924$	1.76359	+	3.05463i	0.0580179	+	0.100490i
$925$	6.96088	−	12.0566i	0.228872	−	0.396418i
$926$	−32.0364	−	55.4886i	−1.05278	−	1.82347i
$927$	−1.94811			−0.0639844
$928$	33.9534	−	58.8090i	1.11457	−	1.93050i
$929$	−41.9598			−1.37666			−0.688328	−	0.725399i	$-0.741655\pi$
$929$	−41.9598			−1.37666			−0.688328	+	0.725399i	$0.741655\pi$
$930$	−1.78482			−0.0585266
$931$	−58.9459	−	102.097i	−1.93187	−	3.34610i
$932$	−18.3327	−	31.7531i	−0.600507	−	1.04011i
$933$	9.82794			0.321752
$934$	−4.81619	−	8.34189i	−0.157591	−	0.272955i
$935$	1.41197	+	2.44560i	0.0461764	+	0.0799798i
$936$	−1.74897	−	3.02931i	−0.0571670	−	0.0990161i
$937$	12.5484	+	21.7344i	0.409937	+	0.710032i	0.994882	−	0.101041i	$-0.0322172\pi$
$937$	12.5484	+	21.7344i	0.409937	+	0.710032i	−0.584945	+	0.811073i	$0.698884\pi$
$938$	13.7571			0.449184
$939$	3.97667	−	6.88780i	0.129774	−	0.224775i
$940$	−5.66984			−0.184930
$941$	−25.9992	−	45.0319i	−0.847548	−	1.46800i	−0.883389	−	0.468640i	$-0.844744\pi$
$941$	−25.9992	−	45.0319i	−0.847548	−	1.46800i	0.0358410	−	0.999358i	$-0.488589\pi$
$942$	−2.27870	+	3.94682i	−0.0742440	+	0.128594i
$943$	6.06821			0.197608
$944$	−5.28388	+	9.15195i	−0.171976	+	0.297871i
$945$	3.12162			0.101546
$946$	−13.7707			−0.447723
$947$	9.73014	−	16.8531i	0.316187	−	0.547652i	−0.663502	−	0.748174i	$-0.730931\pi$
$947$	9.73014	−	16.8531i	0.316187	−	0.547652i	0.979689	+	0.200523i	$0.0642640\pi$
$948$	−0.307116	+	0.531940i	−0.00997466	+	0.0172766i
$949$	16.7776	−	29.0597i	0.544625	−	0.943318i
$950$	39.5443	+	68.4927i	1.28299	+	2.22220i
$951$	0.382328	−	0.662212i	0.0123978	−	0.0214737i
$952$	4.49334	−	7.78269i	0.145630	−	0.252238i
$953$	0.0515030	−	0.0892058i	0.00166834	−	0.00288966i	−0.865190	−	0.501444i	$-0.832802\pi$
$953$	0.0515030	−	0.0892058i	0.00166834	−	0.00288966i	0.866858	+	0.498554i	$0.166136\pi$
$954$	−9.16559	+	15.8753i	−0.296747	+	0.513981i
$955$	−3.96423	−	6.86625i	−0.128280	−	0.222187i
$956$	−3.21199			−0.103883
$957$	−1.79307	−	3.10570i	−0.0579619	−	0.100393i
$958$	−19.5522	−	33.8653i	−0.631702	−	1.09414i
$959$	48.8961	−	84.6905i	1.57894	−	2.73480i
$960$	0.390055	−	0.675595i	0.0125890	−	0.0218047i
$961$	31.5839			1.01883
$962$	23.5692			0.759902
$963$	41.7565			1.34558
$964$	23.0561	+	39.9344i	0.742588	+	1.28620i
$965$	1.12210	+	1.94353i	0.0361216	+	0.0625645i
$966$	3.49977	+	6.06178i	0.112603	+	0.195035i
$967$	−1.56784	+	2.71557i	−0.0504182	+	0.0873269i	−0.890133	−	0.455701i	$-0.849389\pi$
$967$	−1.56784	+	2.71557i	−0.0504182	+	0.0873269i	0.839715	+	0.543028i	$0.182722\pi$
$968$	−1.36712	+	2.36792i	−0.0439408	+	0.0761077i
$969$	−18.8235			−0.604698
$970$	−0.714675	+	1.23785i	−0.0229468	+	0.0397451i
$971$	24.1029	+	41.7475i	0.773500	+	1.33974i	0.935634	+	0.352972i	$0.114829\pi$
$971$	24.1029	+	41.7475i	0.773500	+	1.33974i	−0.162134	+	0.986769i	$0.551838\pi$
$972$	−8.01233	+	13.8778i	−0.256996	+	0.445129i
$973$	−24.6125	+	42.6301i	−0.789041	+	1.36666i
$974$	17.8535	−	30.9231i	0.572062	−	0.990840i
$975$	3.46689	−	6.00483i	0.111029	−	0.192308i
$976$	0.847226	−	1.46744i	0.0271190	−	0.0469716i
$977$	12.7207	+	22.0329i	0.406971	+	0.704894i	0.994549	−	0.104273i	$-0.0332517\pi$
$977$	12.7207	+	22.0329i	0.406971	+	0.704894i	−0.587578	+	0.809168i	$0.699918\pi$
$978$	6.26502	−	10.8513i	0.200333	−	0.346987i
$979$	6.36610	+	11.0264i	0.203461	+	0.352405i
$980$	9.03079			0.288478
$981$	0.993552	−	1.72088i	0.0317217	−	0.0549436i
$982$	−6.46951	+	11.2055i	−0.206450	+	0.357583i
$983$	−7.20599	−	12.4811i	−0.229835	−	0.398086i	0.727924	−	0.685658i	$-0.240485\pi$
$983$	−7.20599	−	12.4811i	−0.229835	−	0.398086i	−0.957759	+	0.287572i	$0.907152\pi$
$984$	0.128360	+	0.222325i	0.00409195	+	0.00708747i
$985$	−1.23576	+	2.14039i	−0.0393745	+	0.0681986i
$986$	57.7683	−	100.058i	1.83972	−	3.18648i
$987$	13.9547			0.444182
$988$	−32.2006	+	55.7730i	−1.02444	+	1.77438i
$989$	−13.1439			−0.417953
$990$	1.18188	+	2.04708i	0.0375627	+	0.0650605i
$991$	9.43238			0.299629			0.149815	−	0.988714i	$-0.452132\pi$
$991$	9.43238			0.299629			0.149815	+	0.988714i	$0.452132\pi$
$992$	−30.8920	+	53.5065i	−0.980822	+	1.69883i
$993$	10.9802			0.348447
$994$	−21.6612			−0.687053
$995$	−3.58370	−	6.20715i	−0.113611	−	0.196780i
$996$	8.83209			0.279856
$997$	21.0019	−	36.3764i	0.665138	−	1.15205i	−0.314110	−	0.949387i	$-0.601706\pi$
$997$	21.0019	−	36.3764i	0.665138	−	1.15205i	0.979248	−	0.202666i	$-0.0649607\pi$
$998$	7.66878	−	13.2827i	0.242751	−	0.420457i
$999$	2.82810	+	4.89841i	0.0894771	+	0.154979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.8	✓	90
547.506	even	3	inner	547.2.c.a.506.8	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.8	✓	90	1.1	even	1	trivial
547.2.c.a.506.8	yes	90	547.506	even	3	inner

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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.981507 - 1.70002i) q^{2} +0.337082 q^{3} +(-0.926713 + 1.60511i) q^{4} +(-0.170480 + 0.295281i) q^{5} +(-0.330849 - 0.573047i) q^{6} +(2.30708 + 3.99598i) q^{7} -0.287726 q^{8} -2.88638 q^{9} +O(q^{10})\)	\(q+(-0.981507 - 1.70002i) q^{2} +0.337082 q^{3} +(-0.926713 + 1.60511i) q^{4} +(-0.170480 + 0.295281i) q^{5} +(-0.330849 - 0.573047i) q^{6} +(2.30708 + 3.99598i) q^{7} -0.287726 q^{8} -2.88638 q^{9} +0.669311 q^{10} +(-0.611778 - 1.05963i) q^{11} +(-0.312379 + 0.541056i) q^{12} +(-2.10596 - 3.64764i) q^{13} +(4.52883 - 7.84416i) q^{14} +(-0.0574659 + 0.0995338i) q^{15} +(2.13583 + 3.69937i) q^{16} +(3.38452 + 5.86216i) q^{17} +(2.83300 + 4.90690i) q^{18} +(-4.12484 + 7.14444i) q^{19} +(-0.315973 - 0.547281i) q^{20} +(0.777675 + 1.34697i) q^{21} +(-1.20093 + 2.08007i) q^{22} +(-1.14627 + 1.98540i) q^{23} -0.0969874 q^{24} +(2.44187 + 4.22945i) q^{25} +(-4.13404 + 7.16036i) q^{26} -1.98419 q^{27} -8.55200 q^{28} +8.69498 q^{29} +0.225613 q^{30} -7.91100 q^{31} +(3.90494 - 6.76356i) q^{32} +(-0.206220 - 0.357183i) q^{33} +(6.64387 - 11.5075i) q^{34} -1.57325 q^{35} +(2.67484 - 4.63296i) q^{36} +(-1.42532 - 2.46872i) q^{37} +16.1943 q^{38} +(-0.709883 - 1.22955i) q^{39} +(0.0490516 - 0.0849599i) q^{40} +(-1.32347 - 2.29231i) q^{41} +(1.52659 - 2.64413i) q^{42} +(2.86667 + 4.96521i) q^{43} +2.26777 q^{44} +(0.492070 - 0.852291i) q^{45} +4.50030 q^{46} +(4.48602 - 7.77002i) q^{47} +(0.719951 + 1.24699i) q^{48} +(-7.14523 + 12.3759i) q^{49} +(4.79343 - 8.30247i) q^{50} +(1.14086 + 1.97603i) q^{51} +7.80650 q^{52} +(1.61765 + 2.80185i) q^{53} +(1.94750 + 3.37317i) q^{54} +0.417185 q^{55} +(-0.663807 - 1.14975i) q^{56} +(-1.39041 + 2.40826i) q^{57} +(-8.53419 - 14.7816i) q^{58} +(1.23696 + 2.14248i) q^{59} +(-0.106509 - 0.184479i) q^{60} +(-0.198336 - 0.343529i) q^{61} +(7.76470 + 13.4489i) q^{62} +(-6.65910 - 11.5339i) q^{63} -6.78759 q^{64} +1.43610 q^{65} +(-0.404812 + 0.701155i) q^{66} +(0.759416 + 1.31535i) q^{67} -12.5459 q^{68} +(-0.386388 + 0.669244i) q^{69} +(1.54415 + 2.67455i) q^{70} +(-1.19574 - 2.07109i) q^{71} +0.830486 q^{72} +(3.98336 + 6.89938i) q^{73} +(-2.79791 + 4.84613i) q^{74} +(0.823112 + 1.42567i) q^{75} +(-7.64509 - 13.2417i) q^{76} +(2.82284 - 4.88930i) q^{77} +(-1.39351 + 2.41363i) q^{78} +0.983152 q^{79} -1.45647 q^{80} +7.99029 q^{81} +(-2.59798 + 4.49984i) q^{82} +(-7.06842 - 12.2429i) q^{83} -2.88273 q^{84} -2.30798 q^{85} +(5.62731 - 9.74679i) q^{86} +2.93092 q^{87} +(0.176025 + 0.304883i) q^{88} -10.4059 q^{89} -1.93188 q^{90} +(9.71725 - 16.8308i) q^{91} +(-2.12453 - 3.67980i) q^{92} -2.66666 q^{93} -17.6123 q^{94} +(-1.40641 - 2.43597i) q^{95} +(1.31629 - 2.27988i) q^{96} +(-1.06778 + 1.84944i) q^{97} +28.0524 q^{98} +(1.76582 + 3.05849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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