LMFDB - Embedded newform 946.2.f.d.861.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(345,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("946.345");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.f (of order $5$, degree $4$, 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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 19 x^{13} + 105 x^{12} - 200 x^{11} + 787 x^{10} - 2046 x^{9} + \cdots + 121 $ x^16 - 4x^15 + 10x^14 - 19x^13 + 105x^12 - 200x^11 + 787x^10 - 2046x^9 + 5617x^8 - 11198x^7 + 15283x^6 - 13157x^5 + 7968x^4 - 3535x^3 + 1389x^2 - 341*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			861.2
Root			$-2.31549 - 1.68230i$ of defining polynomial
Character	$\chi$	$=$	946.861
Dual form			946.2.f.d.345.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.278455 + 0.856996i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.74007 + 1.99078i) q^{5} +(0.729004 + 0.529653i) q^{6} +(-0.459142 + 1.41309i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.77015 - 1.28609i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.278455 + 0.856996i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.74007 + 1.99078i) q^{5} +(0.729004 + 0.529653i) q^{6} +(-0.459142 + 1.41309i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.77015 - 1.28609i) q^{9} +3.38691 q^{10} +(0.746733 + 3.23147i) q^{11} +0.901099 q^{12} +(-0.212170 + 0.154150i) q^{13} +(0.459142 + 1.41309i) q^{14} +(-0.943102 + 2.90257i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.82585 - 1.32656i) q^{17} +(0.676136 - 2.08093i) q^{18} +(-0.899434 - 2.76817i) q^{19} +(2.74007 - 1.99078i) q^{20} -1.33886 q^{21} +(2.50353 + 2.17539i) q^{22} +0.213938 q^{23} +(0.729004 - 0.529653i) q^{24} +(1.99970 + 6.15445i) q^{25} +(-0.0810416 + 0.249420i) q^{26} +(3.78209 + 2.74785i) q^{27} +(1.20205 + 0.873339i) q^{28} +(-1.00114 + 3.08118i) q^{29} +(0.943102 + 2.90257i) q^{30} +(-3.25231 + 2.36294i) q^{31} -1.00000 q^{32} +(-2.56142 + 1.53977i) q^{33} -2.25688 q^{34} +(-4.07123 + 2.95792i) q^{35} +(-0.676136 - 2.08093i) q^{36} +(-0.315136 + 0.969889i) q^{37} +(-2.35475 - 1.71083i) q^{38} +(-0.191186 - 0.138905i) q^{39} +(1.04661 - 3.22114i) q^{40} +(-3.15332 - 9.70491i) q^{41} +(-1.08316 + 0.786965i) q^{42} +1.00000 q^{43} +(3.30406 + 0.288393i) q^{44} +7.41063 q^{45} +(0.173079 - 0.125749i) q^{46} +(-0.418800 - 1.28894i) q^{47} +(0.278455 - 0.856996i) q^{48} +(3.87710 + 2.81688i) q^{49} +(5.23529 + 3.80366i) q^{50} +(0.628438 - 1.93413i) q^{51} +(0.0810416 + 0.249420i) q^{52} +(9.51960 - 6.91640i) q^{53} +4.67492 q^{54} +(-4.38703 + 10.3410i) q^{55} +1.48581 q^{56} +(2.12186 - 1.54162i) q^{57} +(1.00114 + 3.08118i) q^{58} +(-0.259483 + 0.798607i) q^{59} +(2.46907 + 1.79389i) q^{60} +(-1.48750 - 1.08073i) q^{61} +(-1.24227 + 3.82332i) q^{62} +(1.00461 + 3.09188i) q^{63} +(-0.809017 + 0.587785i) q^{64} -0.888238 q^{65} +(-1.16718 + 2.75126i) q^{66} -5.26488 q^{67} +(-1.82585 + 1.32656i) q^{68} +(0.0595720 + 0.183344i) q^{69} +(-1.55507 + 4.78602i) q^{70} +(0.0520975 + 0.0378511i) q^{71} +(-1.77015 - 1.28609i) q^{72} +(1.49284 - 4.59448i) q^{73} +(0.315136 + 0.969889i) q^{74} +(-4.71751 + 3.42747i) q^{75} -2.91063 q^{76} +(-4.90922 - 0.428498i) q^{77} -0.236319 q^{78} +(-0.986031 + 0.716394i) q^{79} +(-1.04661 - 3.22114i) q^{80} +(0.726652 - 2.23641i) q^{81} +(-8.25549 - 5.99797i) q^{82} +(4.35492 + 3.16404i) q^{83} +(-0.413732 + 1.27334i) q^{84} +(-2.36208 - 7.26973i) q^{85} +(0.809017 - 0.587785i) q^{86} -2.91933 q^{87} +(2.84256 - 1.70876i) q^{88} -3.98623 q^{89} +(5.99533 - 4.35586i) q^{90} +(-0.120413 - 0.370592i) q^{91} +(0.0661104 - 0.203467i) q^{92} +(-2.93066 - 2.12925i) q^{93} +(-1.09643 - 0.796606i) q^{94} +(3.04630 - 9.37556i) q^{95} +(-0.278455 - 0.856996i) q^{96} +(12.4365 - 9.03566i) q^{97} +4.79236 q^{98} +(5.47777 + 4.75981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 4 * q^8	\( 16 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 6 q^{10} + 7 q^{11} + 4 q^{12} - 6 q^{13} + 6 q^{14} + 14 q^{15} - 4 q^{16} - 12 q^{17} + 10 q^{18} - q^{19} + 9 q^{20} + 46 q^{21} + 3 q^{22} + 26 q^{23} + 6 q^{24} - 19 q^{25} + q^{26} - 14 q^{27} - q^{28} - 6 q^{29} - 14 q^{30} - 6 q^{31} - 16 q^{32} - 59 q^{33} + 2 q^{34} + 4 q^{35} - 10 q^{36} - 33 q^{37} - 9 q^{38} - 21 q^{39} + 6 q^{40} - 5 q^{41} + 19 q^{42} + 16 q^{43} - 8 q^{44} - 60 q^{45} + 24 q^{46} - 2 q^{47} + 4 q^{48} + 12 q^{49} - 16 q^{50} - 9 q^{51} - q^{52} + 34 q^{53} + 14 q^{54} + 19 q^{55} - 14 q^{56} - 43 q^{57} + 6 q^{58} + 29 q^{59} - q^{60} - 8 q^{61} - 24 q^{62} + 73 q^{63} - 4 q^{64} - 18 q^{65} + 29 q^{66} - 48 q^{67} - 12 q^{68} + 29 q^{69} + 31 q^{70} + 9 q^{71} - 39 q^{73} + 33 q^{74} + 33 q^{75} - 16 q^{76} - 3 q^{77} - 64 q^{78} + 11 q^{79} - 6 q^{80} - 74 q^{81} + 28 q^{83} - 4 q^{84} + 9 q^{85} + 4 q^{86} - 20 q^{87} + 8 q^{88} - 52 q^{89} + 20 q^{90} - 10 q^{91} + 11 q^{92} + 3 q^{93} - 18 q^{94} + 17 q^{95} - 4 q^{96} - 3 q^{97} - 2 q^{98} - 59 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 4 * q^8 + 6 * q^10 + 7 * q^11 + 4 * q^12 - 6 * q^13 + 6 * q^14 + 14 * q^15 - 4 * q^16 - 12 * q^17 + 10 * q^18 - q^19 + 9 * q^20 + 46 * q^21 + 3 * q^22 + 26 * q^23 + 6 * q^24 - 19 * q^25 + q^26 - 14 * q^27 - q^28 - 6 * q^29 - 14 * q^30 - 6 * q^31 - 16 * q^32 - 59 * q^33 + 2 * q^34 + 4 * q^35 - 10 * q^36 - 33 * q^37 - 9 * q^38 - 21 * q^39 + 6 * q^40 - 5 * q^41 + 19 * q^42 + 16 * q^43 - 8 * q^44 - 60 * q^45 + 24 * q^46 - 2 * q^47 + 4 * q^48 + 12 * q^49 - 16 * q^50 - 9 * q^51 - q^52 + 34 * q^53 + 14 * q^54 + 19 * q^55 - 14 * q^56 - 43 * q^57 + 6 * q^58 + 29 * q^59 - q^60 - 8 * q^61 - 24 * q^62 + 73 * q^63 - 4 * q^64 - 18 * q^65 + 29 * q^66 - 48 * q^67 - 12 * q^68 + 29 * q^69 + 31 * q^70 + 9 * q^71 - 39 * q^73 + 33 * q^74 + 33 * q^75 - 16 * q^76 - 3 * q^77 - 64 * q^78 + 11 * q^79 - 6 * q^80 - 74 * q^81 + 28 * q^83 - 4 * q^84 + 9 * q^85 + 4 * q^86 - 20 * q^87 + 8 * q^88 - 52 * q^89 + 20 * q^90 - 10 * q^91 + 11 * q^92 + 3 * q^93 - 18 * q^94 + 17 * q^95 - 4 * q^96 - 3 * q^97 - 2 * q^98 - 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.278455	+	0.856996i	0.160766	+	0.494787i	0.998699	−	0.0509856i	$-0.0162363\pi$
$3$	0.278455	+	0.856996i	0.160766	+	0.494787i	−0.837933	+	0.545773i	$0.816236\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.74007	+	1.99078i	1.22540	+	0.890303i	0.996536	−	0.0831568i	$-0.0265002\pi$
$5$	2.74007	+	1.99078i	1.22540	+	0.890303i	0.228860	+	0.973459i	$0.426500\pi$
$6$	0.729004	+	0.529653i	0.297615	+	0.216230i
$7$	−0.459142	+	1.41309i	−0.173539	+	0.534099i	−0.999564	−	0.0295354i	$-0.990597\pi$
$7$	−0.459142	+	1.41309i	−0.173539	+	0.534099i	0.826025	+	0.563634i	$0.190597\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	1.77015	−	1.28609i	0.590049	−	0.428695i
$10$	3.38691			1.07104
$11$	0.746733	+	3.23147i	0.225149	+	0.974324i
$11$	0.746733	+	3.23147i	0.225149	+	0.974324i
$12$	0.901099			0.260125
$13$	−0.212170	+	0.154150i	−0.0588453	+	0.0427536i	−0.616819	−	0.787105i	$-0.711579\pi$
$13$	−0.212170	+	0.154150i	−0.0588453	+	0.0427536i	0.557974	+	0.829859i	$0.311579\pi$
$14$	0.459142	+	1.41309i	0.122711	+	0.377665i
$15$	−0.943102	+	2.90257i	−0.243508	+	0.749440i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.82585	−	1.32656i	−0.442834	−	0.321738i	0.343926	−	0.938997i	$-0.388243\pi$
$17$	−1.82585	−	1.32656i	−0.442834	−	0.321738i	−0.786760	+	0.617259i	$0.788243\pi$
$18$	0.676136	−	2.08093i	0.159367	−	0.490480i
$19$	−0.899434	−	2.76817i	−0.206344	−	0.635063i	−0.999656	−	0.0262462i	$-0.991645\pi$
$19$	−0.899434	−	2.76817i	−0.206344	−	0.635063i	0.793311	−	0.608816i	$-0.208355\pi$
$20$	2.74007	−	1.99078i	0.612698	−	0.445151i
$21$	−1.33886			−0.292164
$22$	2.50353	+	2.17539i	0.533754	+	0.463796i
$23$	0.213938			0.0446091			0.0223046	−	0.999751i	$-0.492900\pi$
$23$	0.213938			0.0446091			0.0223046	+	0.999751i	$0.492900\pi$
$24$	0.729004	−	0.529653i	0.148807	−	0.108115i
$25$	1.99970	+	6.15445i	0.399941	+	1.23089i
$26$	−0.0810416	+	0.249420i	−0.0158936	+	0.0489154i
$27$	3.78209	+	2.74785i	0.727864	+	0.528824i
$28$	1.20205	+	0.873339i	0.227166	+	0.165046i
$29$	−1.00114	+	3.08118i	−0.185906	+	0.572161i	−0.999963	−	0.00862460i	$-0.997255\pi$
$29$	−1.00114	+	3.08118i	−0.185906	+	0.572161i	0.814056	+	0.580786i	$0.197255\pi$
$30$	0.943102	+	2.90257i	0.172186	+	0.529934i
$31$	−3.25231	+	2.36294i	−0.584133	+	0.424397i	−0.840212	−	0.542259i	$-0.817569\pi$
$31$	−3.25231	+	2.36294i	−0.584133	+	0.424397i	0.256079	+	0.966656i	$0.417569\pi$
$32$	−1.00000			−0.176777
$33$	−2.56142	+	1.53977i	−0.445887	+	0.268039i
$34$	−2.25688			−0.387051
$35$	−4.07123	+	2.95792i	−0.688164	+	0.499980i
$36$	−0.676136	−	2.08093i	−0.112689	−	0.346822i
$37$	−0.315136	+	0.969889i	−0.0518080	+	0.159449i	−0.973613	−	0.228205i	$-0.926714\pi$
$37$	−0.315136	+	0.969889i	−0.0518080	+	0.159449i	0.921805	+	0.387654i	$0.126714\pi$
$38$	−2.35475	−	1.71083i	−0.381991	−	0.277532i
$39$	−0.191186	−	0.138905i	−0.0306142	−	0.0222425i
$40$	1.04661	−	3.22114i	0.165484	−	0.509308i
$41$	−3.15332	−	9.70491i	−0.492465	−	1.51565i	−0.820870	−	0.571115i	$-0.806511\pi$
$41$	−3.15332	−	9.70491i	−0.492465	−	1.51565i	0.328404	−	0.944537i	$-0.393489\pi$
$42$	−1.08316	+	0.786965i	−0.167136	+	0.121431i
$43$	1.00000			0.152499
$43$	1.00000			0.152499
$44$	3.30406	+	0.288393i	0.498106	+	0.0434769i
$45$	7.41063			1.10471
$46$	0.173079	−	0.125749i	0.0255191	−	0.0185407i
$47$	−0.418800	−	1.28894i	−0.0610883	−	0.188011i	0.915855	−	0.401509i	$-0.131514\pi$
$47$	−0.418800	−	1.28894i	−0.0610883	−	0.188011i	−0.976943	+	0.213498i	$0.931514\pi$
$48$	0.278455	−	0.856996i	0.0401915	−	0.123697i
$49$	3.87710	+	2.81688i	0.553871	+	0.402411i
$50$	5.23529	+	3.80366i	0.740382	+	0.537919i
$51$	0.628438	−	1.93413i	0.0879990	−	0.270833i
$52$	0.0810416	+	0.249420i	0.0112384	+	0.0345884i
$53$	9.51960	−	6.91640i	1.30762	−	0.950040i	0.307619	−	0.951510i	$-0.400468\pi$
$53$	9.51960	−	6.91640i	1.30762	−	0.950040i	0.999999	+	0.00146924i	$0.000467674\pi$
$54$	4.67492			0.636176
$55$	−4.38703	+	10.3410i	−0.591547	+	1.39438i
$56$	1.48581			0.198550
$57$	2.12186	−	1.54162i	0.281047	−	0.204193i
$58$	1.00114	+	3.08118i	0.131456	+	0.404579i
$59$	−0.259483	+	0.798607i	−0.0337818	+	0.103970i	−0.966526	−	0.256570i	$-0.917408\pi$
$59$	−0.259483	+	0.798607i	−0.0337818	+	0.103970i	0.932744	+	0.360540i	$0.117408\pi$
$60$	2.46907	+	1.79389i	0.318756	+	0.231590i
$61$	−1.48750	−	1.08073i	−0.190455	−	0.138374i	0.488472	−	0.872580i	$-0.337555\pi$
$61$	−1.48750	−	1.08073i	−0.190455	−	0.138374i	−0.678927	+	0.734206i	$0.737555\pi$
$62$	−1.24227	+	3.82332i	−0.157769	+	0.485563i
$63$	1.00461	+	3.09188i	0.126569	+	0.389540i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.888238			−0.110172
$66$	−1.16718	+	2.75126i	−0.143670	+	0.338657i
$67$	−5.26488			−0.643207			−0.321604	−	0.946874i	$-0.604222\pi$
$67$	−5.26488			−0.643207			−0.321604	+	0.946874i	$0.604222\pi$
$68$	−1.82585	+	1.32656i	−0.221417	+	0.160869i
$69$	0.0595720	+	0.183344i	0.00717163	+	0.0220720i
$70$	−1.55507	+	4.78602i	−0.185867	+	0.572039i
$71$	0.0520975	+	0.0378511i	0.00618284	+	0.00449210i	0.590872	−	0.806765i	$-0.298784\pi$
$71$	0.0520975	+	0.0378511i	0.00618284	+	0.00449210i	−0.584690	+	0.811257i	$0.698784\pi$
$72$	−1.77015	−	1.28609i	−0.208614	−	0.151567i
$73$	1.49284	−	4.59448i	0.174723	−	0.537743i	−0.824897	−	0.565282i	$-0.808767\pi$
$73$	1.49284	−	4.59448i	0.174723	−	0.537743i	0.999621	+	0.0275394i	$0.00876716\pi$
$74$	0.315136	+	0.969889i	0.0366338	+	0.112747i
$75$	−4.71751	+	3.42747i	−0.544732	+	0.395771i
$76$	−2.91063			−0.333872
$77$	−4.90922	−	0.428498i	−0.559458	−	0.0488319i
$78$	−0.236319			−0.0267578
$79$	−0.986031	+	0.716394i	−0.110937	+	0.0806006i	−0.641871	−	0.766813i	$-0.721841\pi$
$79$	−0.986031	+	0.716394i	−0.110937	+	0.0806006i	0.530933	+	0.847414i	$0.321841\pi$
$80$	−1.04661	−	3.22114i	−0.117015	−	0.360135i
$81$	0.726652	−	2.23641i	0.0807391	−	0.248489i
$82$	−8.25549	−	5.99797i	−0.911667	−	0.662365i
$83$	4.35492	+	3.16404i	0.478015	+	0.347298i	0.800557	−	0.599257i	$-0.204537\pi$
$83$	4.35492	+	3.16404i	0.478015	+	0.347298i	−0.322542	+	0.946555i	$0.604537\pi$
$84$	−0.413732	+	1.27334i	−0.0451419	+	0.138932i
$85$	−2.36208	−	7.26973i	−0.256203	−	0.788513i
$86$	0.809017	−	0.587785i	0.0872385	−	0.0633825i
$87$	−2.91933			−0.312985
$88$	2.84256	−	1.70876i	0.303017	−	0.182155i
$89$	−3.98623			−0.422539			−0.211270	−	0.977428i	$-0.567760\pi$
$89$	−3.98623			−0.422539			−0.211270	+	0.977428i	$0.567760\pi$
$90$	5.99533	−	4.35586i	0.631963	−	0.459148i
$91$	−0.120413	−	0.370592i	−0.0126227	−	0.0388486i
$92$	0.0661104	−	0.203467i	0.00689249	−	0.0212129i
$93$	−2.93066	−	2.12925i	−0.303895	−	0.220793i
$94$	−1.09643	−	0.796606i	−0.113089	−	0.0821636i
$95$	3.04630	−	9.37556i	0.312544	−	0.961912i
$96$	−0.278455	−	0.856996i	−0.0284197	−	0.0874668i
$97$	12.4365	−	9.03566i	1.26274	−	0.917432i	0.263849	−	0.964564i	$-0.415008\pi$
$97$	12.4365	−	9.03566i	1.26274	−	0.917432i	0.998889	+	0.0471316i	$0.0150080\pi$
$98$	4.79236			0.484101
$99$	5.47777	+	4.75981i	0.550537	+	0.478379i
$100$	6.47117			0.647117
$101$	1.32227	−	0.960686i	0.131571	−	0.0955918i	−0.520053	−	0.854134i	$-0.674088\pi$
$101$	1.32227	−	0.960686i	0.131571	−	0.0955918i	0.651624	+	0.758542i	$0.274088\pi$
$102$	−0.628438	−	1.93413i	−0.0622247	−	0.191508i
$103$	−3.38471	+	10.4171i	−0.333505	+	1.02642i	0.633949	+	0.773375i	$0.281433\pi$
$103$	−3.38471	+	10.4171i	−0.333505	+	1.02642i	−0.967454	+	0.253048i	$0.918567\pi$
$104$	0.212170	+	0.154150i	0.0208049	+	0.0151157i
$105$	−3.66858	−	2.66538i	−0.358017	−	0.260115i
$106$	3.63617	−	11.1910i	0.353176	−	1.08696i
$107$	−1.44821	−	4.45713i	−0.140004	−	0.430887i	0.856331	−	0.516428i	$-0.172738\pi$
$107$	−1.44821	−	4.45713i	−0.140004	−	0.430887i	−0.996335	+	0.0855401i	$0.972738\pi$
$108$	3.78209	−	2.74785i	0.363932	−	0.264412i
$109$	1.10768			0.106096			0.0530482	−	0.998592i	$-0.483106\pi$
$109$	1.10768			0.106096			0.0530482	+	0.998592i	$0.483106\pi$
$110$	2.52912	+	10.9447i	0.241142	+	1.04354i
$111$	−0.918942			−0.0872221
$112$	1.20205	−	0.873339i	0.113583	−	0.0825228i
$113$	−2.59809	−	7.99611i	−0.244408	−	0.752211i	−0.995733	−	0.0922788i	$-0.970585\pi$
$113$	−2.59809	−	7.99611i	−0.244408	−	0.752211i	0.751325	−	0.659932i	$-0.229415\pi$
$114$	0.810479	−	2.49440i	0.0759083	−	0.233622i
$115$	0.586204	+	0.425902i	0.0546638	+	0.0397156i
$116$	2.62101	+	1.90428i	0.243355	+	0.176808i
$117$	−0.177321	+	0.545737i	−0.0163933	+	0.0504534i
$118$	0.259483	+	0.798607i	0.0238874	+	0.0735177i
$119$	2.71287	−	1.97102i	0.248689	−	0.180683i
$120$	3.05194			0.278603
$121$	−9.88478	+	4.82609i	−0.898616	+	0.438735i
$122$	−1.83865			−0.166464
$123$	7.43902	−	5.40476i	0.670753	−	0.487331i
$124$	1.24227	+	3.82332i	0.111559	+	0.343345i
$125$	−1.53975	+	4.73887i	−0.137719	+	0.423857i
$126$	2.63011	+	1.91088i	0.234308	+	0.170235i
$127$	−9.52687	−	6.92168i	−0.845373	−	0.614199i	0.0784934	−	0.996915i	$-0.474989\pi$
$127$	−9.52687	−	6.92168i	−0.845373	−	0.614199i	−0.923866	+	0.382715i	$0.874989\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	0.278455	+	0.856996i	0.0245166	+	0.0754543i
$130$	−0.718600	+	0.522093i	−0.0630254	+	0.0457906i
$131$	−1.69235			−0.147862			−0.0739308	−	0.997263i	$-0.523554\pi$
$131$	−1.69235			−0.147862			−0.0739308	+	0.997263i	$0.523554\pi$
$132$	0.672881	+	2.91187i	0.0585667	+	0.253446i
$133$	4.32465			0.374995
$134$	−4.25938	+	3.09462i	−0.367954	+	0.267334i
$135$	4.89283	+	15.0586i	0.421108	+	1.29604i
$136$	−0.697413	+	2.14642i	−0.0598027	+	0.184054i
$137$	−11.2814	−	8.19640i	−0.963832	−	0.700265i	−0.00979482	−	0.999952i	$-0.503118\pi$
$137$	−11.2814	−	8.19640i	−0.963832	−	0.700265i	−0.954038	+	0.299687i	$0.903118\pi$
$138$	0.155962	+	0.113313i	0.0132763	+	0.00964582i
$139$	4.56524	−	14.0504i	0.387218	−	1.19174i	−0.547640	−	0.836714i	$-0.684474\pi$
$139$	4.56524	−	14.0504i	0.387218	−	1.19174i	0.934858	−	0.355021i	$-0.115526\pi$
$140$	1.55507	+	4.78602i	0.131428	+	0.404492i
$141$	0.987995	−	0.717821i	0.0832042	−	0.0604514i
$142$	0.0643961			0.00540400
$143$	−0.656566	−	0.570510i	−0.0549048	−	0.0477085i
$144$	−2.18802			−0.182335
$145$	−8.87713	+	6.44962i	−0.737206	+	0.535611i
$146$	−1.49284	−	4.59448i	−0.123548	−	0.380242i
$147$	−1.33446	+	4.10703i	−0.110064	+	0.338742i
$148$	0.825037	+	0.599424i	0.0678176	+	0.0492724i
$149$	−3.02403	−	2.19709i	−0.247738	−	0.179993i	0.456985	−	0.889474i	$-0.348929\pi$
$149$	−3.02403	−	2.19709i	−0.247738	−	0.179993i	−0.704724	+	0.709482i	$0.748929\pi$
$150$	−1.80193	+	5.54577i	−0.147127	+	0.452810i
$151$	2.17799	+	6.70317i	0.177243	+	0.545496i	0.999729	−	0.0232885i	$-0.00741364\pi$
$151$	2.17799	+	6.70317i	0.177243	+	0.545496i	−0.822486	+	0.568785i	$0.807414\pi$
$152$	−2.35475	+	1.71083i	−0.190995	+	0.138766i
$153$	−4.93809			−0.399221
$154$	−4.22351	+	2.53890i	−0.340340	+	0.204591i
$155$	−13.6157			−1.09364
$156$	−0.191186	+	0.138905i	−0.0153071	+	0.0111213i
$157$	−4.09546	−	12.6045i	−0.326853	−	1.00595i	−0.970597	−	0.240710i	$-0.922620\pi$
$157$	−4.09546	−	12.6045i	−0.326853	−	1.00595i	0.643744	−	0.765241i	$-0.277380\pi$
$158$	−0.376631	+	1.15915i	−0.0299631	+	0.0922170i
$159$	8.57811	+	6.23236i	0.680288	+	0.494258i
$160$	−2.74007	−	1.99078i	−0.216622	−	0.157385i
$161$	−0.0982277	+	0.302314i	−0.00774143	+	0.0238257i
$162$	−0.726652	−	2.23641i	−0.0570912	−	0.175709i
$163$	4.86182	−	3.53232i	0.380807	−	0.276672i	−0.380871	−	0.924628i	$-0.624376\pi$
$163$	4.86182	−	3.53232i	0.380807	−	0.276672i	0.761678	+	0.647956i	$0.224376\pi$
$164$	−10.2043			−0.796826
$165$	−10.0838	−	0.880160i	−0.785024	−	0.0685203i
$166$	5.38298			0.417800
$167$	4.10667	−	2.98367i	0.317783	−	0.230883i	−0.417446	−	0.908702i	$-0.637075\pi$
$167$	4.10667	−	2.98367i	0.317783	−	0.230883i	0.735229	+	0.677819i	$0.237075\pi$
$168$	0.413732	+	1.27334i	0.0319201	+	0.0982400i
$169$	−3.99597	+	12.2983i	−0.307382	+	0.946025i
$170$	−6.18400	−	4.49294i	−0.474291	−	0.344593i
$171$	−5.15224	−	3.74332i	−0.394002	−	0.286259i
$172$	0.309017	−	0.951057i	0.0235623	−	0.0725174i
$173$	1.52928	+	4.70665i	0.116269	+	0.357840i	0.992210	−	0.124579i	$-0.0397581\pi$
$173$	1.52928	+	4.70665i	0.116269	+	0.357840i	−0.875940	+	0.482419i	$0.839758\pi$
$174$	−2.36179	+	1.71594i	−0.179047	+	0.130085i
$175$	−9.61496			−0.726822
$176$	1.29529	−	3.05323i	0.0976361	−	0.230146i
$177$	−0.756657			−0.0568738
$178$	−3.22492	+	2.34304i	−0.241718	+	0.175619i
$179$	−0.300653	−	0.925314i	−0.0224718	−	0.0691612i	0.939192	−	0.343393i	$-0.111576\pi$
$179$	−0.300653	−	0.925314i	−0.0224718	−	0.0691612i	−0.961664	+	0.274232i	$0.911576\pi$
$180$	2.29001	−	7.04793i	0.170687	−	0.525322i
$181$	−0.672405	−	0.488531i	−0.0499795	−	0.0363122i	0.562515	−	0.826787i	$-0.309834\pi$
$181$	−0.672405	−	0.488531i	−0.0499795	−	0.0363122i	−0.612495	+	0.790475i	$0.709834\pi$
$182$	−0.315244	−	0.229039i	−0.0233675	−	0.0169775i
$183$	0.511982	−	1.57572i	0.0378468	−	0.116480i
$184$	−0.0661104	−	0.203467i	−0.00487372	−	0.0149998i
$185$	−2.79433	+	2.03020i	−0.205443	+	0.149263i
$186$	−3.62249			−0.265614
$187$	2.92331	−	6.89077i	0.213774	−	0.503903i
$188$	−1.35527			−0.0988430
$189$	−5.61948	+	4.08279i	−0.408757	+	0.296979i
$190$	−3.04630	−	9.37556i	−0.221002	−	0.680175i
$191$	−3.95041	+	12.1581i	−0.285842	+	0.879730i	0.700304	+	0.713845i	$0.253048\pi$
$191$	−3.95041	+	12.1581i	−0.285842	+	0.879730i	−0.986145	+	0.165885i	$0.946952\pi$
$192$	−0.729004	−	0.529653i	−0.0526114	−	0.0382244i
$193$	−9.19944	−	6.68379i	−0.662190	−	0.481109i	0.205212	−	0.978718i	$-0.434212\pi$
$193$	−9.19944	−	6.68379i	−0.662190	−	0.481109i	−0.867402	+	0.497608i	$0.834212\pi$
$194$	4.75033	−	14.6200i	0.341054	−	1.04966i
$195$	−0.247334	−	0.761217i	−0.0177120	−	0.0545119i
$196$	3.87710	−	2.81688i	0.276936	−	0.201206i
$197$	−11.4883			−0.818510			−0.409255	−	0.912420i	$-0.634211\pi$
$197$	−11.4883			−0.818510			−0.409255	+	0.912420i	$0.634211\pi$
$198$	7.22936	+	0.631010i	0.513768	+	0.0448439i
$199$	−14.1463			−1.00280			−0.501402	−	0.865215i	$-0.667182\pi$
$199$	−14.1463			−1.00280			−0.501402	+	0.865215i	$0.667182\pi$
$200$	5.23529	−	3.80366i	0.370191	−	0.268959i
$201$	−1.46603	−	4.51198i	−0.103406	−	0.318251i
$202$	0.505062	−	1.55442i	0.0355361	−	0.109369i
$203$	−3.89433	−	2.82940i	−0.273329	−	0.198585i
$204$	−1.64527	−	1.19536i	−0.115192	−	0.0836920i
$205$	10.6800	−	32.8697i	0.745924	−	2.29572i
$206$	3.38471	+	10.4171i	0.235824	+	0.725791i
$207$	0.378701	−	0.275142i	0.0263215	−	0.0191237i
$208$	0.262256			0.0181842
$209$	8.27363	−	4.97358i	0.572299	−	0.344030i
$210$	−4.53462			−0.312918
$211$	−18.0482	+	13.1128i	−1.24249	+	0.902722i	−0.997762	−	0.0668699i	$-0.978699\pi$
$211$	−18.0482	+	13.1128i	−1.24249	+	0.902722i	−0.244728	+	0.969592i	$0.578699\pi$
$212$	−3.63617	−	11.1910i	−0.249733	−	0.768599i
$213$	−0.0179314	+	0.0551872i	−0.00122864	+	0.00378137i
$214$	−3.79147	−	2.75466i	−0.259179	−	0.188305i
$215$	2.74007	+	1.99078i	0.186871	+	0.135770i
$216$	1.44463	−	4.44611i	0.0982946	−	0.302520i
$217$	−1.84579	−	5.68075i	−0.125300	−	0.385634i
$218$	0.896131	−	0.651078i	0.0606937	−	0.0440965i
$219$	4.35314			0.294158
$220$	8.47923	+	7.36787i	0.571670	+	0.496742i
$221$	0.591880			0.0398141
$222$	−0.743440	+	0.540140i	−0.0498964	+	0.0362519i
$223$	1.89945	+	5.84591i	0.127197	+	0.391471i	0.994295	−	0.106666i	$-0.0340176\pi$
$223$	1.89945	+	5.84591i	0.127197	+	0.391471i	−0.867098	+	0.498137i	$0.834018\pi$
$224$	0.459142	−	1.41309i	0.0306777	−	0.0944162i
$225$	11.4549	+	8.32249i	0.763661	+	0.554833i
$226$	−6.80190	−	4.94187i	−0.452456	−	0.328728i
$227$	1.13218	−	3.48448i	0.0751452	−	0.231273i	−0.906428	−	0.422361i	$-0.861202\pi$
$227$	1.13218	−	3.48448i	0.0751452	−	0.231273i	0.981573	+	0.191088i	$0.0612015\pi$
$228$	−0.810479	−	2.49440i	−0.0536753	−	0.165196i
$229$	−8.49983	+	6.17549i	−0.561684	+	0.408088i	−0.832075	−	0.554663i	$-0.812847\pi$
$229$	−8.49983	+	6.17549i	−0.561684	+	0.408088i	0.270391	+	0.962751i	$0.412847\pi$
$230$	0.724588			0.0477779
$231$	−0.999775	−	4.32650i	−0.0657804	−	0.284663i
$232$	3.23975			0.212700
$233$	−11.8580	+	8.61533i	−0.776842	+	0.564409i	−0.904030	−	0.427470i	$-0.859405\pi$
$233$	−11.8580	+	8.61533i	−0.776842	+	0.564409i	0.127187	+	0.991879i	$0.459405\pi$
$234$	0.177321	+	0.545737i	0.0115918	+	0.0356759i
$235$	1.41844	−	4.36551i	0.0925289	−	0.284775i
$236$	0.679336	+	0.493566i	0.0442210	+	0.0321284i
$237$	−0.888512	−	0.645542i	−0.0577151	−	0.0419324i
$238$	1.03623	−	3.18918i	0.0671685	−	0.206724i
$239$	−0.483730	−	1.48877i	−0.0312899	−	0.0963004i	0.934192	−	0.356771i	$-0.116122\pi$
$239$	−0.483730	−	1.48877i	−0.0312899	−	0.0963004i	−0.965482	+	0.260471i	$0.916122\pi$
$240$	2.46907	−	1.79389i	0.159378	−	0.115795i
$241$	2.18191			0.140549			0.0702747	−	0.997528i	$-0.477612\pi$
$241$	2.18191			0.140549			0.0702747	+	0.997528i	$0.477612\pi$
$242$	−5.16025	+	9.71452i	−0.331713	+	0.624473i
$243$	16.1437			1.03562
$244$	−1.48750	+	1.08073i	−0.0952276	+	0.0691869i
$245$	5.01575	+	15.4369i	0.320444	+	0.986226i
$246$	2.84145	−	8.74509i	0.181164	−	0.557566i
$247$	0.617547	+	0.448674i	0.0392936	+	0.0285485i
$248$	3.25231	+	2.36294i	0.206522	+	0.150047i
$249$	−1.49892	+	4.61319i	−0.0949900	+	0.292349i
$250$	1.53975	+	4.73887i	0.0973824	+	0.299712i
$251$	−7.94542	+	5.77269i	−0.501510	+	0.364369i	−0.809594	−	0.586991i	$-0.800312\pi$
$251$	−7.94542	+	5.77269i	−0.501510	+	0.364369i	0.308083	+	0.951359i	$0.400312\pi$
$252$	3.25099			0.204793
$253$	0.159754	+	0.691333i	0.0100437	+	0.0434637i
$254$	−11.7759			−0.738883
$255$	5.57240	−	4.04858i	0.348957	−	0.253532i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.52936	−	7.78458i	0.157777	−	0.485589i	−0.840654	−	0.541572i	$-0.817829\pi$
$257$	2.52936	−	7.78458i	0.157777	−	0.485589i	0.998432	+	0.0559833i	$0.0178294\pi$
$258$	0.729004	+	0.529653i	0.0453858	+	0.0329747i
$259$	−1.22585	−	0.890632i	−0.0761706	−	0.0553412i
$260$	−0.274481	+	0.844765i	−0.0170226	+	0.0523901i
$261$	2.19051	+	6.74169i	0.135589	+	0.417300i
$262$	−1.36914	+	0.994740i	−0.0845859	+	0.0614553i
$263$	−16.8392			−1.03835			−0.519175	−	0.854668i	$-0.673761\pi$
$263$	−16.8392			−1.03835			−0.519175	+	0.854668i	$0.673761\pi$
$264$	2.25593	+	1.96025i	0.138843	+	0.120645i
$265$	39.8534			2.44817
$266$	3.49872	−	2.54197i	0.214520	−	0.155858i
$267$	−1.10998	−	3.41618i	−0.0679299	−	0.209067i
$268$	−1.62694	+	5.00720i	−0.0993810	+	0.305863i
$269$	21.6180	+	15.7064i	1.31808	+	0.957638i	0.999954	+	0.00958791i	$0.00305197\pi$
$269$	21.6180	+	15.7064i	1.31808	+	0.957638i	0.318121	+	0.948050i	$0.396948\pi$
$270$	12.8096	+	9.30672i	0.779568	+	0.566389i
$271$	0.485775	−	1.49506i	0.0295088	−	0.0908186i	−0.935217	−	0.354074i	$-0.884796\pi$
$271$	0.485775	−	1.49506i	0.0295088	−	0.0908186i	0.964726	+	0.263255i	$0.0847961\pi$
$272$	0.697413	+	2.14642i	0.0422869	+	0.130146i
$273$	0.284066	−	0.206386i	0.0171925	−	0.0124911i
$274$	−13.9445			−0.842420
$275$	−18.3947	+	11.0577i	−1.10924	+	0.666805i
$276$	0.192779			0.0116039
$277$	8.46156	−	6.14768i	0.508406	−	0.369378i	−0.303813	−	0.952732i	$-0.598260\pi$
$277$	8.46156	−	6.14768i	0.508406	−	0.369378i	0.812218	+	0.583353i	$0.198260\pi$
$278$	−4.56524	−	14.0504i	−0.273805	−	0.842684i
$279$	−2.71812	+	8.36551i	−0.162730	+	0.500830i
$280$	4.07123	+	2.95792i	0.243303	+	0.176770i
$281$	−7.85127	−	5.70428i	−0.468368	−	0.340289i	0.328437	−	0.944526i	$-0.393478\pi$
$281$	−7.85127	−	5.70428i	−0.468368	−	0.340289i	−0.796805	+	0.604237i	$0.793478\pi$
$282$	0.377381	−	1.16146i	0.0224727	−	0.0691638i
$283$	−5.22468	−	16.0799i	−0.310575	−	0.955851i	−0.977538	−	0.210760i	$-0.932406\pi$
$283$	−5.22468	−	16.0799i	−0.310575	−	0.955851i	0.666963	−	0.745091i	$-0.267594\pi$
$284$	0.0520975	−	0.0378511i	0.00309142	−	0.00224605i
$285$	8.88308			0.526188
$286$	−0.866511	−	0.0756329i	−0.0512378	−	0.00447227i
$287$	15.1618			0.894970
$288$	−1.77015	+	1.28609i	−0.104307	+	0.0757834i
$289$	−3.67931	−	11.3238i	−0.216430	−	0.666104i
$290$	−3.39076	+	10.4357i	−0.199112	+	0.612805i
$291$	11.2065	+	8.14203i	0.656939	+	0.477294i
$292$	−3.90830	−	2.83954i	−0.228716	−	0.166172i
$293$	7.72656	−	23.7799i	0.451391	−	1.38924i	−0.423930	−	0.905695i	$-0.639350\pi$
$293$	7.72656	−	23.7799i	0.451391	−	1.38924i	0.875321	−	0.483542i	$-0.160650\pi$
$294$	1.33446	+	4.10703i	0.0778271	+	0.239527i
$295$	−2.30085	+	1.67167i	−0.133961	+	0.0973281i
$296$	1.01980			0.0592747
$297$	−6.05538	+	14.2736i	−0.351369	+	0.828239i
$298$	−3.73791			−0.216531
$299$	−0.0453911	+	0.0329786i	−0.00262503	+	0.00190720i
$300$	1.80193	+	5.54577i	0.104034	+	0.320185i
$301$	−0.459142	+	1.41309i	−0.0264645	+	0.0814493i
$302$	5.70206	+	4.14279i	0.328117	+	0.238391i
$303$	1.19150	+	0.865673i	0.0684497	+	0.0497316i
$304$	−0.899434	+	2.76817i	−0.0515861	+	0.158766i
$305$	−1.92436	−	5.92257i	−0.110189	−	0.339125i
$306$	−3.99500	+	2.90254i	−0.228379	+	0.165927i
$307$	31.4171			1.79307			0.896533	−	0.442977i	$-0.146078\pi$
$307$	31.4171			1.79307			0.896533	+	0.442977i	$0.146078\pi$
$308$	−1.92456	+	4.53653i	−0.109662	+	0.258493i
$309$	−9.86986			−0.561477
$310$	−11.0153	+	8.00308i	−0.625627	+	0.454545i
$311$	−5.56097	−	17.1149i	−0.315334	−	0.970498i	−0.975617	−	0.219481i	$-0.929564\pi$
$311$	−5.56097	−	17.1149i	−0.315334	−	0.970498i	0.660283	−	0.751017i	$-0.270436\pi$
$312$	−0.0730265	+	0.224752i	−0.00413431	+	0.0127241i
$313$	24.2703	+	17.6334i	1.37184	+	0.996698i	0.997591	+	0.0693682i	$0.0220983\pi$
$313$	24.2703	+	17.6334i	1.37184	+	0.996698i	0.374246	+	0.927330i	$0.377902\pi$
$314$	−10.7221	−	7.79003i	−0.605081	−	0.439617i
$315$	−3.40253	+	10.4719i	−0.191711	+	0.590025i
$316$	0.376631	+	1.15915i	0.0211871	+	0.0652073i
$317$	−19.8508	+	14.4224i	−1.11493	+	0.810044i	−0.983433	−	0.181273i	$-0.941978\pi$
$317$	−19.8508	+	14.4224i	−1.11493	+	0.810044i	−0.131497	+	0.991317i	$0.541978\pi$
$318$	10.6031			0.594594
$319$	−10.7043	−	0.934321i	−0.599327	−	0.0523119i
$320$	−3.38691			−0.189334
$321$	3.41649	−	2.48222i	0.190690	−	0.138544i
$322$	0.0982277	+	0.302314i	0.00547402	+	0.0168473i
$323$	−2.02991	+	6.24743i	−0.112947	+	0.347616i
$324$	−1.90240	−	1.38217i	−0.105689	−	0.0767875i
$325$	−1.37299	−	0.997533i	−0.0761596	−	0.0553332i
$326$	1.85705	−	5.71541i	0.102852	−	0.316547i
$327$	0.308439	+	0.949277i	0.0170567	+	0.0524951i
$328$	−8.25549	+	5.99797i	−0.455833	+	0.331182i
$329$	2.01367			0.111017
$330$	−8.67532	+	5.21505i	−0.477561	+	0.287079i
$331$	30.7892			1.69233			0.846165	−	0.532921i	$-0.178906\pi$
$331$	30.7892			1.69233			0.846165	+	0.532921i	$0.178906\pi$
$332$	4.35492	−	3.16404i	0.239007	−	0.173649i
$333$	0.689524	+	2.12214i	0.0377857	+	0.116292i
$334$	1.56861	−	4.82767i	0.0858303	−	0.264159i
$335$	−14.4261	−	10.4812i	−0.788184	−	0.572649i
$336$	1.08316	+	0.786965i	0.0590915	+	0.0429325i
$337$	−5.10880	+	15.7233i	−0.278294	+	0.856502i	0.710035	+	0.704167i	$0.248679\pi$
$337$	−5.10880	+	15.7233i	−0.278294	+	0.856502i	−0.988329	+	0.152335i	$0.951321\pi$
$338$	3.99597	+	12.2983i	0.217352	+	0.668941i
$339$	6.12919	−	4.45311i	0.332892	−	0.241860i
$340$	−7.64384			−0.414546
$341$	−10.0644	−	8.74526i	−0.545017	−	0.473582i
$342$	−6.36852			−0.344370
$343$	−14.1750	+	10.2987i	−0.765377	+	0.556079i
$344$	−0.309017	−	0.951057i	−0.0166611	−	0.0512775i
$345$	−0.201765	+	0.620969i	−0.0108627	+	0.0334319i
$346$	4.00372	+	2.90887i	0.215241	+	0.156382i
$347$	−21.1850	−	15.3918i	−1.13727	−	0.826275i	−0.150533	−	0.988605i	$-0.548099\pi$
$347$	−21.1850	−	15.3918i	−1.13727	−	0.826275i	−0.986736	+	0.162330i	$0.948099\pi$
$348$	−0.902124	+	2.77645i	−0.0483589	+	0.148833i
$349$	4.24628	+	13.0687i	0.227298	+	0.699552i	0.998050	+	0.0624168i	$0.0198808\pi$
$349$	4.24628	+	13.0687i	0.227298	+	0.699552i	−0.770752	+	0.637135i	$0.780119\pi$
$350$	−7.77866	+	5.65153i	−0.415787	+	0.302087i
$351$	−1.22603			−0.0654404
$352$	−0.746733	−	3.23147i	−0.0398010	−	0.172238i
$353$	28.8134			1.53358			0.766792	−	0.641896i	$-0.221852\pi$
$353$	28.8134			1.53358			0.766792	+	0.641896i	$0.221852\pi$
$354$	−0.612149	+	0.444752i	−0.0325353	+	0.0236383i
$355$	0.0673978	+	0.207429i	0.00357711	+	0.0110092i
$356$	−1.23181	+	3.79113i	−0.0652859	+	0.200929i
$357$	2.44457	+	1.77608i	0.129380	+	0.0940003i
$358$	−0.787119	−	0.571876i	−0.0416005	−	0.0302246i
$359$	−11.1268	+	34.2447i	−0.587248	+	1.80736i	0.00279931	+	0.999996i	$0.499109\pi$
$359$	−11.1268	+	34.2447i	−0.587248	+	1.80736i	−0.590048	+	0.807368i	$0.700891\pi$
$360$	−2.29001	−	7.04793i	−0.120694	−	0.371459i
$361$	8.51752	−	6.18834i	0.448291	−	0.325702i
$362$	−0.831138			−0.0436837
$363$	−6.88841	−	7.12737i	−0.361548	−	0.374090i
$364$	−0.389664			−0.0204239
$365$	13.2371	−	9.61729i	0.692859	−	0.503392i
$366$	−0.511982	−	1.57572i	−0.0267617	−	0.0823641i
$367$	7.17995	−	22.0976i	0.374790	−	1.15349i	−0.568830	−	0.822455i	$-0.692604\pi$
$367$	7.17995	−	22.0976i	0.374790	−	1.15349i	0.943620	−	0.331031i	$-0.107396\pi$
$368$	−0.173079	−	0.125749i	−0.00902238	−	0.00655514i
$369$	−18.0632	−	13.1237i	−0.940332	−	0.683191i
$370$	−1.06734	+	3.28493i	−0.0554882	+	0.170775i
$371$	5.40266	+	16.6277i	0.280492	+	0.863266i
$372$	−2.93066	+	2.12925i	−0.151947	+	0.110396i
$373$	28.5251			1.47697			0.738486	−	0.674269i	$-0.235541\pi$
$373$	28.5251			1.47697			0.738486	+	0.674269i	$0.235541\pi$
$374$	−1.68529	−	7.29303i	−0.0871440	−	0.377113i
$375$	−4.48994			−0.231860
$376$	−1.09643	+	0.796606i	−0.0565443	+	0.0410818i
$377$	−0.262554	−	0.808059i	−0.0135222	−	0.0416172i
$378$	−2.14645	+	6.60609i	−0.110401	+	0.339781i
$379$	2.87947	+	2.09206i	0.147908	+	0.107462i	0.659279	−	0.751899i	$-0.270862\pi$
$379$	2.87947	+	2.09206i	0.147908	+	0.107462i	−0.511370	+	0.859361i	$0.670862\pi$
$380$	−7.97533	−	5.79441i	−0.409126	−	0.297247i
$381$	3.27905	−	10.0919i	0.167991	−	0.517022i
$382$	3.95041	+	12.1581i	0.202121	+	0.622063i
$383$	−27.8897	+	20.2631i	−1.42510	+	1.03539i	−0.434194	+	0.900819i	$0.642967\pi$
$383$	−27.8897	+	20.2631i	−1.42510	+	1.03539i	−0.990903	+	0.134575i	$0.957033\pi$
$384$	−0.901099			−0.0459840
$385$	−12.5986	−	10.9473i	−0.642082	−	0.557925i
$386$	−11.3711			−0.578776
$387$	1.77015	−	1.28609i	0.0899816	−	0.0653754i
$388$	−4.75033	−	14.6200i	−0.241161	−	0.742218i
$389$	−4.87919	+	15.0166i	−0.247385	+	0.761372i	0.747850	+	0.663867i	$0.231086\pi$
$389$	−4.87919	+	15.0166i	−0.247385	+	0.761372i	−0.995235	+	0.0975045i	$0.968914\pi$
$390$	−0.647530	−	0.470458i	−0.0327889	−	0.0238226i
$391$	−0.390619	−	0.283801i	−0.0197544	−	0.0143524i
$392$	1.48092	−	4.55780i	0.0747978	−	0.230204i
$393$	−0.471244	−	1.45034i	−0.0237711	−	0.0731600i
$394$	−9.29425	+	6.75267i	−0.468238	+	0.340195i
$395$	−4.12798			−0.207701
$396$	6.21957	−	3.73881i	0.312545	−	0.187882i
$397$	35.7808			1.79579			0.897893	−	0.440213i	$-0.145097\pi$
$397$	35.7808			1.79579			0.897893	+	0.440213i	$0.145097\pi$
$398$	−11.4446	+	8.31498i	−0.573665	+	0.416792i
$399$	1.20422	+	3.70621i	0.0602864	+	0.185543i
$400$	1.99970	−	6.15445i	0.0999851	−	0.307723i
$401$	−5.68062	−	4.12721i	−0.283677	−	0.206103i	0.436843	−	0.899538i	$-0.356097\pi$
$401$	−5.68062	−	4.12721i	−0.283677	−	0.206103i	−0.720519	+	0.693435i	$0.756097\pi$
$402$	−3.83812	−	2.78856i	−0.191428	−	0.139081i
$403$	0.325794	−	1.00269i	0.0162289	−	0.0499476i
$404$	−0.505062	−	1.55442i	−0.0251278	−	0.0773354i
$405$	6.44326	−	4.68130i	0.320168	−	0.232616i
$406$	−4.81366			−0.238898
$407$	−3.36949	−	0.294104i	−0.167019	−	0.0145782i
$408$	−2.03367			−0.100682
$409$	−25.4946	+	18.5229i	−1.26062	+	0.915897i	−0.998788	−	0.0492147i	$-0.984328\pi$
$409$	−25.4946	+	18.5229i	−1.26062	+	0.915897i	−0.261837	+	0.965112i	$0.584328\pi$
$410$	−10.6800	−	32.8697i	−0.527448	−	1.62332i
$411$	3.88293	−	11.9504i	0.191531	−	0.589471i
$412$	8.86128	+	6.43809i	0.436564	+	0.317182i
$413$	−1.00937	−	0.733347i	−0.0496676	−	0.0360857i
$414$	0.144651	−	0.445190i	0.00710920	−	0.0218799i
$415$	5.63390	+	17.3394i	0.276557	+	0.851156i
$416$	0.212170	−	0.154150i	0.0104025	−	0.00755784i
$417$	13.3123			0.651907
$418$	3.77011	−	8.88683i	0.184402	−	0.434669i
$419$	12.5611			0.613649			0.306825	−	0.951766i	$-0.400733\pi$
$419$	12.5611			0.613649			0.306825	+	0.951766i	$0.400733\pi$
$420$	−3.66858	+	2.66538i	−0.179009	+	0.130057i
$421$	−9.81977	−	30.2221i	−0.478586	−	1.47294i	−0.841059	−	0.540943i	$-0.818068\pi$
$421$	−9.81977	−	30.2221i	−0.478586	−	1.47294i	0.362473	−	0.931994i	$-0.381932\pi$
$422$	−6.89380	+	21.2169i	−0.335585	+	1.03282i
$423$	−2.39902	−	1.74299i	−0.116644	−	0.0847471i
$424$	−9.51960	−	6.91640i	−0.462313	−	0.335890i
$425$	4.51308	−	13.8898i	0.218917	−	0.673756i
$426$	0.0179314	+	0.0551872i	0.000868780	+	0.00267383i
$427$	2.21015	−	1.60577i	0.106957	−	0.0777086i
$428$	−4.68651			−0.226531
$429$	0.306101	−	0.721536i	0.0147787	−	0.0348361i
$430$	3.38691			0.163331
$431$	19.3592	−	14.0653i	0.932499	−	0.677500i	−0.0141046	−	0.999901i	$-0.504490\pi$
$431$	19.3592	−	14.0653i	0.932499	−	0.677500i	0.946603	+	0.322401i	$0.104490\pi$
$432$	−1.44463	−	4.44611i	−0.0695048	−	0.213914i
$433$	1.40320	−	4.31862i	0.0674337	−	0.207540i	−0.911662	−	0.410942i	$-0.865200\pi$
$433$	1.40320	−	4.31862i	0.0674337	−	0.207540i	0.979095	+	0.203402i	$0.0651999\pi$
$434$	−4.83233	−	3.51089i	−0.231959	−	0.168528i
$435$	−7.99918	−	5.81174i	−0.383531	−	0.278652i
$436$	0.342292	−	1.05347i	0.0163928	−	0.0504519i
$437$	−0.192423	−	0.592217i	−0.00920484	−	0.0283296i
$438$	3.52176	−	2.55871i	0.168276	−	0.122260i
$439$	34.6864			1.65549			0.827745	−	0.561104i	$-0.189623\pi$
$439$	34.6864			1.65549			0.827745	+	0.561104i	$0.189623\pi$
$440$	11.1906	+	0.976762i	0.533489	+	0.0465653i
$441$	10.4858			0.499323
$442$	0.478841	−	0.347898i	0.0227761	−	0.0165478i
$443$	9.93474	+	30.5760i	0.472014	+	1.45271i	0.849943	+	0.526875i	$0.176636\pi$
$443$	9.93474	+	30.5760i	0.472014	+	1.45271i	−0.377929	+	0.925835i	$0.623364\pi$
$444$	−0.283969	+	0.873966i	−0.0134766	+	0.0414766i
$445$	−10.9225	−	7.93569i	−0.517778	−	0.376188i
$446$	4.97283	+	3.61297i	0.235470	+	0.171079i
$447$	1.04084	−	3.20337i	0.0492300	−	0.151514i
$448$	−0.459142	−	1.41309i	−0.0216924	−	0.0667623i
$449$	−9.88743	+	7.18364i	−0.466617	+	0.339017i	−0.796121	−	0.605137i	$-0.793118\pi$
$449$	−9.88743	+	7.18364i	−0.466617	+	0.339017i	0.329505	+	0.944154i	$0.393118\pi$
$450$	14.1591			0.667465
$451$	29.0064	−	17.4368i	1.36586	−	0.821068i
$452$	−8.40761			−0.395461
$453$	−5.13812	+	3.73306i	−0.241410	+	0.175395i
$454$	−1.13218	−	3.48448i	−0.0531357	−	0.163535i
$455$	0.407827	−	1.25516i	0.0191192	−	0.0588429i
$456$	−2.12186	−	1.54162i	−0.0993653	−	0.0721931i
$457$	7.40305	+	5.37863i	0.346300	+	0.251602i	0.747315	−	0.664470i	$-0.231343\pi$
$457$	7.40305	+	5.37863i	0.346300	+	0.251602i	−0.401015	+	0.916071i	$0.631343\pi$
$458$	−3.24664	+	9.99215i	−0.151706	+	0.466902i
$459$	−3.26035	−	10.0343i	−0.152180	−	0.468362i
$460$	0.586204	−	0.425902i	0.0273319	−	0.0198578i
$461$	5.36735			0.249982			0.124991	−	0.992158i	$-0.460110\pi$
$461$	5.36735			0.249982			0.124991	+	0.992158i	$0.460110\pi$
$462$	−3.35189	−	2.91256i	−0.155944	−	0.135504i
$463$	23.3357			1.08450			0.542252	−	0.840216i	$-0.317572\pi$
$463$	23.3357			1.08450			0.542252	+	0.840216i	$0.317572\pi$
$464$	2.62101	−	1.90428i	0.121677	−	0.0884038i
$465$	−3.79135	−	11.6686i	−0.175820	−	0.541117i
$466$	−4.52935	+	13.9399i	−0.209818	+	0.645753i
$467$	−19.1386	−	13.9050i	−0.885629	−	0.643447i	0.0491059	−	0.998794i	$-0.484363\pi$
$467$	−19.1386	−	13.9050i	−0.885629	−	0.643447i	−0.934735	+	0.355347i	$0.884363\pi$
$468$	0.464232	+	0.337284i	0.0214591	+	0.0155910i
$469$	2.41733	−	7.43976i	0.111622	−	0.343536i
$470$	−1.41844	−	4.36551i	−0.0654278	−	0.201366i
$471$	9.66163	−	7.01959i	0.445185	−	0.323445i
$472$	0.839705			0.0386506
$473$	0.746733	+	3.23147i	0.0343348	+	0.148583i
$474$	−1.09826			−0.0504448
$475$	15.2380	−	11.0710i	0.699167	−	0.507975i
$476$	−1.03623	−	3.18918i	−0.0474953	−	0.146176i
$477$	7.95600	−	24.4861i	0.364280	−	1.12114i
$478$	−1.26642	−	0.920109i	−0.0579248	−	0.0420848i
$479$	10.2097	+	7.41782i	0.466495	+	0.338929i	0.796074	−	0.605199i	$-0.206907\pi$
$479$	10.2097	+	7.41782i	0.466495	+	0.338929i	−0.329579	+	0.944128i	$0.606907\pi$
$480$	0.943102	−	2.90257i	0.0430465	−	0.132484i
$481$	−0.0826463	−	0.254359i	−0.00376835	−	0.0115978i
$482$	1.76521	−	1.28250i	0.0804029	−	0.0584161i
$483$	−0.286434			−0.0130332
$484$	1.53532	+	10.8923i	0.0697873	+	0.495106i
$485$	52.0649			2.36415
$486$	13.0605	−	9.48902i	0.592437	−	0.430431i
$487$	0.00532932	+	0.0164020i	0.000241495	+	0.000743244i	0.951177	−	0.308645i	$-0.0998756\pi$
$487$	0.00532932	+	0.0164020i	0.000241495	+	0.000743244i	−0.950936	+	0.309389i	$0.899876\pi$
$488$	−0.568175	+	1.74866i	−0.0257201	+	0.0791583i
$489$	4.38098	+	3.18297i	0.198115	+	0.143939i
$490$	13.1314	+	9.54052i	0.593216	+	0.430997i
$491$	−9.05323	+	27.8630i	−0.408567	+	1.25744i	0.509314	+	0.860581i	$0.329899\pi$
$491$	−9.05323	+	27.8630i	−0.408567	+	1.25744i	−0.917880	+	0.396858i	$0.870101\pi$
$492$	−2.84145	−	8.74509i	−0.128103	−	0.394259i
$493$	5.91530	−	4.29772i	0.266412	−	0.193559i
$494$	0.763330			0.0343439
$495$	5.53377	+	23.9472i	0.248724	+	1.07635i
$496$	4.02008			0.180507
$497$	−0.0774072	+	0.0562396i	−0.00347219	+	0.00252269i
$498$	1.49892	+	4.61319i	0.0671681	+	0.206722i
$499$	2.07197	−	6.37686i	0.0927540	−	0.285467i	−0.893908	−	0.448251i	$-0.852047\pi$
$499$	2.07197	−	6.37686i	0.0927540	−	0.285467i	0.986662	+	0.162783i	$0.0520472\pi$
$500$	4.03112	+	2.92878i	0.180277	+	0.130979i
$501$	3.70051	+	2.68858i	0.165327	+	0.120117i
$502$	−3.03488	+	9.34040i	−0.135453	+	0.416883i
$503$	9.51611	+	29.2876i	0.424303	+	1.30587i	0.903661	+	0.428250i	$0.140870\pi$
$503$	9.51611	+	29.2876i	0.424303	+	1.30587i	−0.479358	+	0.877619i	$0.659130\pi$
$504$	2.63011	−	1.91088i	0.117154	−	0.0851175i
$505$	5.53562			0.246332
$506$	0.535599	+	0.465399i	0.0238103	+	0.0206895i
$507$	−11.6523			−0.517497
$508$	−9.52687	+	6.92168i	−0.422686	+	0.307100i
$509$	−2.64182	−	8.13069i	−0.117097	−	0.360386i	0.875282	−	0.483613i	$-0.160676\pi$
$509$	−2.64182	−	8.13069i	−0.117097	−	0.360386i	−0.992379	+	0.123227i	$0.960676\pi$
$510$	2.12847	−	6.55074i	0.0942501	−	0.290072i
$511$	5.80700	+	4.21903i	0.256887	+	0.186639i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	4.20478	−	12.9410i	0.185646	−	0.571359i
$514$	−2.52936	−	7.78458i	−0.111565	−	0.343363i
$515$	−30.0124	+	21.8053i	−1.32250	+	0.960855i
$516$	0.901099			0.0396687
$517$	3.85242	−	2.31583i	0.169429	−	0.101850i
$518$	−1.51523			−0.0665756
$519$	−3.60774	+	2.62118i	−0.158362	+	0.115057i
$520$	0.274481	+	0.844765i	0.0120368	+	0.0370454i
$521$	−8.03926	+	24.7423i	−0.352207	+	1.08398i	0.605405	+	0.795918i	$0.293011\pi$
$521$	−8.03926	+	24.7423i	−0.352207	+	1.08398i	−0.957612	+	0.288063i	$0.906989\pi$
$522$	5.73483	+	4.16659i	0.251007	+	0.182367i
$523$	18.8464	+	13.6927i	0.824097	+	0.598742i	0.917883	−	0.396851i	$-0.129897\pi$
$523$	18.8464	+	13.6927i	0.824097	+	0.598742i	−0.0937858	+	0.995592i	$0.529897\pi$
$524$	−0.522966	+	1.60952i	−0.0228459	+	0.0703124i
$525$	−2.67733	−	8.23998i	−0.116848	−	0.359622i
$526$	−13.6232	+	9.89784i	−0.594000	+	0.431566i
$527$	9.07283			0.395219
$528$	2.97729	+	0.259871i	0.129570	+	0.0113094i
$529$	−22.9542			−0.998010
$530$	32.2421	−	23.4252i	1.40051	−	1.01753i
$531$	0.567754	+	1.74737i	0.0246384	+	0.0758293i
$532$	1.33639	−	4.11299i	0.0579399	−	0.178321i
$533$	2.16505	+	1.57300i	0.0937789	+	0.0681343i
$534$	−2.90598	−	2.11132i	−0.125754	−	0.0913655i
$535$	4.90496	−	15.0959i	0.212060	−	0.652654i
$536$	1.62694	+	5.00720i	0.0702730	+	0.216278i
$537$	0.709272	−	0.515317i	0.0306074	−	0.0222376i
$538$	26.7214			1.15204
$539$	−6.20749	+	14.6322i	−0.267376	+	0.630253i
$540$	15.8335			0.681367
$541$	−25.4602	+	18.4979i	−1.09462	+	0.795288i	−0.980173	−	0.198142i	$-0.936509\pi$
$541$	−25.4602	+	18.4979i	−1.09462	+	0.795288i	−0.114446	+	0.993429i	$0.536509\pi$
$542$	−0.485775	−	1.49506i	−0.0208658	−	0.0642185i
$543$	0.231435	−	0.712282i	0.00993181	−	0.0305670i
$544$	1.82585	+	1.32656i	0.0782827	+	0.0568757i
$545$	3.03512	+	2.20514i	0.130010	+	0.0944579i
$546$	0.108504	−	0.333940i	0.00464353	−	0.0142913i
$547$	−10.3452	−	31.8393i	−0.442329	−	1.36135i	−0.885386	−	0.464856i	$-0.846106\pi$
$547$	−10.3452	−	31.8393i	−0.442329	−	1.36135i	0.443057	−	0.896493i	$-0.353894\pi$
$548$	−11.2814	+	8.19640i	−0.481916	+	0.350133i
$549$	−4.02301			−0.171698
$550$	−8.38205	+	19.7580i	−0.357412	+	0.842484i
$551$	9.42971			0.401719
$552$	0.155962	−	0.113313i	0.00663816	−	0.00482291i
$553$	−0.559603	−	1.72228i	−0.0237967	−	0.0732388i
$554$	3.23203	−	9.94716i	0.137316	−	0.422614i
$555$	−2.51796	−	1.82941i	−0.106882	−	0.0776541i
$556$	−11.9519	−	8.68360i	−0.506875	−	0.368267i
$557$	−2.36422	+	7.27633i	−0.100175	+	0.308308i	−0.988568	−	0.150777i	$-0.951823\pi$
$557$	−2.36422	+	7.27633i	−0.100175	+	0.308308i	0.888392	+	0.459085i	$0.151823\pi$
$558$	2.71812	+	8.36551i	0.115067	+	0.354140i
$559$	−0.212170	+	0.154150i	−0.00897382	+	0.00651986i
$560$	5.03232			0.212654
$561$	6.71937	+	0.586496i	0.283692	+	0.0247619i
$562$	−9.70470			−0.409368
$563$	4.04190	−	2.93662i	0.170346	−	0.123764i	−0.499346	−	0.866403i	$-0.666426\pi$
$563$	4.04190	−	2.93662i	0.170346	−	0.123764i	0.669692	+	0.742639i	$0.266426\pi$
$564$	−0.377381	−	1.16146i	−0.0158906	−	0.0489062i
$565$	8.79952	−	27.0821i	0.370199	−	1.13935i
$566$	−13.6784	−	9.93793i	−0.574945	−	0.417722i
$567$	2.82661	+	2.05365i	0.118707	+	0.0862453i
$568$	0.0198995	−	0.0612443i	0.000834964	−	0.00256976i
$569$	9.40772	+	28.9540i	0.394392	+	1.21381i	0.929434	+	0.368989i	$0.120296\pi$
$569$	9.40772	+	28.9540i	0.394392	+	1.21381i	−0.535042	+	0.844826i	$0.679704\pi$
$570$	7.18656	−	5.22134i	0.301012	−	0.218698i
$571$	10.2321			0.428200			0.214100	−	0.976812i	$-0.431318\pi$
$571$	10.2321			0.428200			0.214100	+	0.976812i	$0.431318\pi$
$572$	−0.745478	+	0.448134i	−0.0311700	+	0.0187374i
$573$	−11.5195			−0.481232
$574$	12.2661	−	8.91186i	0.511978	−	0.371974i
$575$	0.427812	+	1.31667i	0.0178410	+	0.0549089i
$576$	−0.676136	+	2.08093i	−0.0281723	+	0.0867055i
$577$	30.4692	+	22.1371i	1.26845	+	0.921581i	0.999140	−	0.0414726i	$-0.0132049\pi$
$577$	30.4692	+	22.1371i	1.26845	+	0.921581i	0.269308	+	0.963054i	$0.413205\pi$
$578$	−9.63257	−	6.99847i	−0.400662	−	0.291098i
$579$	3.16635	−	9.74502i	0.131589	−	0.404989i
$580$	3.39076	+	10.4357i	0.140794	+	0.433319i
$581$	−6.47060	+	4.70117i	−0.268446	+	0.195037i
$582$	13.8520			0.574186
$583$	29.4587	+	25.5976i	1.22006	+	1.06014i
$584$	−4.83092			−0.199905
$585$	−1.57231	+	1.14235i	−0.0650071	+	0.0472304i
$586$	−7.72656	−	23.7799i	−0.319181	−	0.982339i
$587$	−12.9850	+	39.9637i	−0.535949	+	1.64948i	0.205642	+	0.978627i	$0.434072\pi$
$587$	−12.9850	+	39.9637i	−0.535949	+	1.64948i	−0.741591	+	0.670853i	$0.765928\pi$
$588$	3.49365	+	2.53829i	0.144076	+	0.104677i
$589$	9.46628	+	6.87766i	0.390051	+	0.283389i
$590$	−0.878847	+	2.70481i	−0.0361815	+	0.111355i
$591$	−3.19898	−	9.84545i	−0.131589	−	0.404988i
$592$	0.825037	−	0.599424i	0.0339088	−	0.0246362i
$593$	−7.77775			−0.319394			−0.159697	−	0.987166i	$-0.551052\pi$
$593$	−7.77775			−0.319394			−0.159697	+	0.987166i	$0.551052\pi$
$594$	3.49092	+	15.1069i	0.143234	+	0.619842i
$595$	11.3573			0.465605
$596$	−3.02403	+	2.19709i	−0.123869	+	0.0899963i
$597$	−3.93910	−	12.1233i	−0.161217	−	0.496174i
$598$	−0.0173379	+	0.0533604i	−0.000708998	+	0.00218207i
$599$	−13.0038	−	9.44784i	−0.531322	−	0.386028i	0.289530	−	0.957169i	$-0.406501\pi$
$599$	−13.0038	−	9.44784i	−0.531322	−	0.386028i	−0.820852	+	0.571141i	$0.806501\pi$
$600$	4.71751	+	3.42747i	0.192592	+	0.139926i
$601$	11.7217	−	36.0756i	0.478138	−	1.47156i	−0.363542	−	0.931578i	$-0.618433\pi$
$601$	11.7217	−	36.0756i	0.478138	−	1.47156i	0.841679	−	0.539978i	$-0.181567\pi$
$602$	0.459142	+	1.41309i	0.0187132	+	0.0575933i
$603$	−9.31961	+	6.77109i	−0.379524	+	0.275740i
$604$	7.04813			0.286784
$605$	−36.6927	−	6.45457i	−1.49177	−	0.262415i
$606$	1.47277			0.0598272
$607$	−17.1631	+	12.4698i	−0.696630	+	0.506132i	−0.878833	−	0.477129i	$-0.841677\pi$
$607$	−17.1631	+	12.4698i	−0.696630	+	0.506132i	0.182203	+	0.983261i	$0.441677\pi$
$608$	0.899434	+	2.76817i	0.0364769	+	0.112264i
$609$	1.34039	−	4.12529i	0.0543152	−	0.167165i
$610$	−5.03804	−	3.66035i	−0.203984	−	0.148203i
$611$	0.287546	+	0.208915i	0.0116329	+	0.00845179i
$612$	−1.52595	+	4.69641i	−0.0616831	+	0.189841i
$613$	−4.04047	−	12.4353i	−0.163193	−	0.502257i	0.835705	−	0.549178i	$-0.185059\pi$
$613$	−4.04047	−	12.4353i	−0.163193	−	0.502257i	−0.998899	+	0.0469211i	$0.985059\pi$
$614$	25.4169	−	18.4665i	1.02574	−	0.745247i
$615$	31.1431			1.25581
$616$	1.10951	+	4.80136i	0.0447033	+	0.193452i
$617$	−27.5521			−1.10921			−0.554603	−	0.832115i	$-0.687130\pi$
$617$	−27.5521			−1.10921			−0.554603	+	0.832115i	$0.687130\pi$
$618$	−7.98489	+	5.80136i	−0.321199	+	0.233365i
$619$	5.68448	+	17.4950i	0.228479	+	0.703185i	0.997920	+	0.0644672i	$0.0205348\pi$
$619$	5.68448	+	17.4950i	0.228479	+	0.703185i	−0.769441	+	0.638718i	$0.779465\pi$
$620$	−4.20747	+	12.9493i	−0.168976	+	0.520055i
$621$	0.809132	+	0.587869i	0.0324693	+	0.0235904i
$622$	−14.5588	−	10.5776i	−0.583755	−	0.424123i
$623$	1.83024	−	5.63291i	0.0733271	−	0.225678i
$624$	0.0730265	+	0.224752i	0.00292340	+	0.00899730i
$625$	12.5234	−	9.09878i	0.500936	−	0.363951i
$626$	29.9997			1.19903
$627$	6.56617	+	5.70555i	0.262228	+	0.227858i
$628$	−13.2532			−0.528860
$629$	1.86201	−	1.35283i	0.0742430	−	0.0539407i
$630$	3.40253	+	10.4719i	0.135560	+	0.417211i
$631$	−1.18979	+	3.66180i	−0.0473649	+	0.145774i	−0.971942	−	0.235221i	$-0.924419\pi$
$631$	−1.18979	+	3.66180i	−0.0473649	+	0.145774i	0.924577	+	0.380995i	$0.124419\pi$
$632$	0.986031	+	0.716394i	0.0392222	+	0.0284966i
$633$	−16.2632	−	11.8159i	−0.646405	−	0.469641i
$634$	−7.58232	+	23.3360i	−0.301132	+	0.926790i
$635$	−12.3248	−	37.9317i	−0.489094	−	1.50528i
$636$	8.57811	−	6.23236i	0.340144	−	0.247129i
$637$	−1.25683			−0.0497972
$638$	−9.20916	+	5.53597i	−0.364594	+	0.219171i
$639$	0.140900			0.00557392
$640$	−2.74007	+	1.99078i	−0.108311	+	0.0786924i
$641$	−5.93102	−	18.2538i	−0.234261	−	0.720982i	−0.997219	−	0.0745334i	$-0.976253\pi$
$641$	−5.93102	−	18.2538i	−0.234261	−	0.720982i	0.762957	−	0.646449i	$-0.223747\pi$
$642$	1.30498	−	4.01632i	0.0515035	−	0.158511i
$643$	−6.01854	−	4.37272i	−0.237348	−	0.172443i	0.462753	−	0.886487i	$-0.346862\pi$
$643$	−6.01854	−	4.37272i	−0.237348	−	0.172443i	−0.700101	+	0.714044i	$0.746862\pi$
$644$	0.257163	+	0.186840i	0.0101337	+	0.00736253i
$645$	−0.943102	+	2.90257i	−0.0371346	+	0.114289i
$646$	2.02991	+	6.24743i	0.0798658	+	0.245802i
$647$	−0.642208	+	0.466592i	−0.0252478	+	0.0183436i	−0.600338	−	0.799747i	$-0.704967\pi$
$647$	−0.642208	+	0.466592i	−0.0252478	+	0.0183436i	0.575090	+	0.818090i	$0.304967\pi$
$648$	−2.35150			−0.0923755
$649$	−2.77444	−	0.242165i	−0.108906	−	0.00950582i
$650$	−1.69710			−0.0665659
$651$	4.35441	−	3.16366i	0.170663	−	0.123994i
$652$	−1.85705	−	5.71541i	−0.0727276	−	0.223833i
$653$	−5.14160	+	15.8242i	−0.201206	+	0.619250i	0.798641	+	0.601807i	$0.205552\pi$
$653$	−5.14160	+	15.8242i	−0.201206	+	0.619250i	−0.999848	+	0.0174425i	$0.994448\pi$
$654$	0.807503	+	0.586685i	0.0315759	+	0.0229412i
$655$	−4.63716	−	3.36910i	−0.181189	−	0.131642i
$656$	−3.15332	+	9.70491i	−0.123116	+	0.378913i
$657$	−3.26636	−	10.0528i	−0.127433	−	0.392198i
$658$	1.62910	−	1.18361i	0.0635088	−	0.0461418i
$659$	−22.7100			−0.884658			−0.442329	−	0.896853i	$-0.645848\pi$
$659$	−22.7100			−0.884658			−0.442329	+	0.896853i	$0.645848\pi$
$660$	−3.95315	+	9.31829i	−0.153876	+	0.362714i
$661$	42.7224			1.66171			0.830855	−	0.556489i	$-0.187852\pi$
$661$	42.7224			1.66171			0.830855	+	0.556489i	$0.187852\pi$
$662$	24.9090	−	18.0975i	0.968117	−	0.703378i
$663$	0.164812	+	0.507239i	0.00640076	+	0.0196995i
$664$	1.66343	−	5.11952i	0.0645537	−	0.198676i
$665$	11.8498	+	8.60942i	0.459517	+	0.333859i
$666$	1.80520	+	1.31155i	0.0699500	+	0.0508216i
$667$	−0.214181	+	0.659181i	−0.00829312	+	0.0255236i
$668$	−1.56861	−	4.82767i	−0.0606912	−	0.186788i
$669$	−4.48101	+	3.25564i	−0.173246	+	0.125870i
$670$	−17.8317			−0.688898
$671$	2.38159	−	5.61384i	0.0919402	−	0.216720i
$672$	1.33886			0.0516478
$673$	11.0218	−	8.00778i	0.424858	−	0.308677i	−0.354732	−	0.934968i	$-0.615428\pi$
$673$	11.0218	−	8.00778i	0.424858	−	0.308677i	0.779589	+	0.626291i	$0.215428\pi$
$674$	5.10880	+	15.7233i	0.196784	+	0.605638i
$675$	−9.34845	+	28.7716i	−0.359822	+	1.10742i
$676$	10.4616	+	7.60078i	0.402368	+	0.292338i
$677$	11.5838	+	8.41614i	0.445203	+	0.323459i	0.787699	−	0.616061i	$-0.211272\pi$
$677$	11.5838	+	8.41614i	0.445203	+	0.323459i	−0.342496	+	0.939519i	$0.611272\pi$
$678$	2.34114	−	7.20529i	0.0899110	−	0.276718i
$679$	7.05810	+	21.7226i	0.270865	+	0.833637i
$680$	−6.18400	+	4.49294i	−0.237146	+	0.172296i
$681$	3.30145			0.126512
$682$	−13.2826	−	1.15936i	−0.508617	−	0.0443943i
$683$	−18.7271			−0.716574			−0.358287	−	0.933611i	$-0.616639\pi$
$683$	−18.7271			−0.716574			−0.358287	+	0.933611i	$0.616639\pi$
$684$	−5.15224	+	3.74332i	−0.197001	+	0.143129i
$685$	−14.5945	−	44.9174i	−0.557629	−	1.71621i
$686$	−5.41436	+	16.6637i	−0.206721	+	0.636223i
$687$	−7.65919	−	5.56472i	−0.292216	−	0.212307i
$688$	−0.809017	−	0.587785i	−0.0308435	−	0.0224091i
$689$	−0.953607	+	2.93490i	−0.0363295	+	0.111811i
$690$	0.201765	+	0.620969i	0.00768107	+	0.0236399i
$691$	−17.7293	+	12.8811i	−0.674455	+	0.490020i	−0.871513	−	0.490372i	$-0.836861\pi$
$691$	−17.7293	+	12.8811i	−0.674455	+	0.490020i	0.197059	+	0.980392i	$0.436861\pi$
$692$	4.94886			0.188128
$693$	−9.24112	+	5.55518i	−0.351041	+	0.211024i
$694$	−26.1861			−0.994010
$695$	40.4802	−	29.4106i	1.53550	−	1.11561i
$696$	0.902124	+	2.77645i	0.0341949	+	0.105241i
$697$	−7.11665	+	21.9028i	−0.269562	+	0.829627i
$698$	11.1169	+	8.07691i	0.420781	+	0.305716i
$699$	−10.6852	−	7.76326i	−0.404152	−	0.293634i
$700$	−2.97118	+	9.14437i	−0.112300	+	0.345625i
$701$	10.7618	+	33.1214i	0.406467	+	1.25098i	0.919664	+	0.392707i	$0.128461\pi$
$701$	10.7618	+	33.1214i	0.406467	+	1.25098i	−0.513197	+	0.858271i	$0.671539\pi$
$702$	−0.991876	+	0.720640i	−0.0374360	+	0.0271988i
$703$	2.96826			0.111950
$704$	−2.50353	−	2.17539i	−0.0943553	−	0.0819883i
$705$	4.13620			0.155778
$706$	23.3106	−	16.9361i	0.877304	−	0.637399i
$707$	0.750428	+	2.30958i	0.0282228	+	0.0868607i
$708$	−0.233820	+	0.719624i	−0.00878749	+	0.0270451i
$709$	−18.5851	−	13.5029i	−0.697979	−	0.507111i	0.181295	−	0.983429i	$-0.441971\pi$
$709$	−18.5851	−	13.5029i	−0.697979	−	0.507111i	−0.879273	+	0.476318i	$0.841971\pi$
$710$	0.176450	+	0.128198i	0.00662204	+	0.00481120i
$711$	−0.824075	+	2.53624i	−0.0309052	+	0.0951165i
$712$	1.23181	+	3.79113i	0.0461641	+	0.142078i
$713$	−0.695793	+	0.505523i	−0.0260576	+	0.0189320i
$714$	3.02165			0.113083
$715$	−0.663277	−	2.87031i	−0.0248052	−	0.107344i
$716$	−0.972933			−0.0363602
$717$	1.14117	−	0.829110i	0.0426178	−	0.0309637i
$718$	11.1268	+	34.2447i	0.415247	+	1.27800i
$719$	−7.27380	+	22.3865i	−0.271267	+	0.834874i	0.718916	+	0.695097i	$0.244639\pi$
$719$	−7.27380	+	22.3865i	−0.271267	+	0.834874i	−0.990183	+	0.139777i	$0.955361\pi$
$720$	−5.99533	−	4.35586i	−0.223433	−	0.162333i
$721$	−13.1662	−	9.56581i	−0.490335	−	0.356249i
$722$	3.25340	−	10.0129i	0.121079	−	0.372643i
$723$	0.607565	+	1.86989i	0.0225956	+	0.0695420i
$724$	−0.672405	+	0.488531i	−0.0249897	+	0.0181561i
$725$	−20.9650			−0.778620
$726$	−9.76220	−	1.71726i	−0.362309	−	0.0637334i
$727$	38.6005			1.43162			0.715808	−	0.698298i	$-0.246059\pi$
$727$	38.6005			1.43162			0.715808	+	0.698298i	$0.246059\pi$
$728$	−0.315244	+	0.229039i	−0.0116837	+	0.00848873i
$729$	2.31533	+	7.12586i	0.0857531	+	0.263921i
$730$	5.05611	−	15.5611i	0.187135	−	0.575942i
$731$	−1.82585	−	1.32656i	−0.0675316	−	0.0490646i
$732$	−1.34039	−	0.973848i	−0.0495421	−	0.0359945i
$733$	−9.83489	+	30.2687i	−0.363260	+	1.11800i	0.587803	+	0.809004i	$0.299993\pi$
$733$	−9.83489	+	30.2687i	−0.363260	+	1.11800i	−0.951063	+	0.308996i	$0.900007\pi$
$734$	−7.17995	−	22.0976i	−0.265017	−	0.815638i
$735$	−11.8327	+	8.59695i	−0.436455	+	0.317103i
$736$	−0.213938			−0.00788585
$737$	−3.93146	−	17.0133i	−0.144817	−	0.626693i
$738$	−22.3273			−0.821880
$739$	−37.6290	+	27.3391i	−1.38421	+	1.00568i	−0.387733	+	0.921772i	$0.626742\pi$
$739$	−37.6290	+	27.3391i	−1.38421	+	1.00568i	−0.996473	+	0.0839131i	$0.973258\pi$
$740$	1.06734	+	3.28493i	0.0392361	+	0.120756i
$741$	−0.212553	+	0.654171i	−0.00780833	+	0.0240316i
$742$	14.1444	+	10.2765i	0.519256	+	0.377261i
$743$	−16.3137	−	11.8526i	−0.598490	−	0.434829i	0.246853	−	0.969053i	$-0.420604\pi$
$743$	−16.3137	−	11.8526i	−0.598490	−	0.434829i	−0.845343	+	0.534225i	$0.820604\pi$
$744$	−1.11941	+	3.44519i	−0.0410396	+	0.126307i
$745$	−3.91215	−	12.0404i	−0.143330	−	0.441124i
$746$	23.0773	−	16.7666i	0.844919	−	0.613869i
$747$	11.7781			0.430937
$748$	−5.65016	−	4.90960i	−0.206590	−	0.179513i
$749$	6.96328			0.254433
$750$	−3.63244	+	2.63912i	−0.132638	+	0.0963671i
$751$	11.0604	+	34.0405i	0.403601	+	1.24215i	0.922058	+	0.387051i	$0.126506\pi$
$751$	11.0604	+	34.0405i	0.403601	+	1.24215i	−0.518458	+	0.855103i	$0.673494\pi$
$752$	−0.418800	+	1.28894i	−0.0152721	+	0.0470026i
$753$	−7.15961	−	5.20176i	−0.260911	−	0.189563i
$754$	−0.687376	−	0.499408i	−0.0250328	−	0.0181874i
$755$	−7.37667	+	22.7031i	−0.268465	+	0.826249i
$756$	2.14645	+	6.60609i	0.0780656	+	0.240261i
$757$	−19.2442	+	13.9817i	−0.699441	+	0.508173i	−0.879750	−	0.475437i	$-0.842290\pi$
$757$	−19.2442	+	13.9817i	−0.699441	+	0.508173i	0.180309	+	0.983610i	$0.442290\pi$
$758$	3.55922			0.129277
$759$	−0.547985	+	0.329414i	−0.0198906	+	0.0119570i
$760$	−9.85805			−0.357589
$761$	−12.0177	+	8.73140i	−0.435643	+	0.316513i	−0.783901	−	0.620886i	$-0.786773\pi$
$761$	−12.0177	+	8.73140i	−0.435643	+	0.316513i	0.348258	+	0.937399i	$0.386773\pi$
$762$	−3.27905	−	10.0919i	−0.118787	−	0.365590i
$763$	−0.508582	+	1.56525i	−0.0184119	+	0.0566660i
$764$	10.3423	+	7.51412i	0.374171	+	0.271851i
$765$	−13.5307	−	9.83064i	−0.489204	−	0.355428i
$766$	−10.6529	+	32.7863i	−0.384906	+	1.18462i
$767$	−0.0680510	−	0.209440i	−0.00245718	−	0.00756242i
$768$	−0.729004	+	0.529653i	−0.0263057	+	0.0191122i
$769$	−38.5350			−1.38961			−0.694804	−	0.719199i	$-0.744509\pi$
$769$	−38.5350			−1.38961			−0.694804	+	0.719199i	$0.744509\pi$
$770$	−16.6271	−	1.45129i	−0.599199	−	0.0523007i
$771$	7.37567			0.265628
$772$	−9.19944	+	6.68379i	−0.331095	+	0.240555i
$773$	−0.766594	−	2.35933i	−0.0275725	−	0.0848593i	0.936323	−	0.351139i	$-0.114206\pi$
$773$	−0.766594	−	2.35933i	−0.0275725	−	0.0848593i	−0.963896	+	0.266280i	$0.914206\pi$
$774$	0.676136	−	2.08093i	0.0243032	−	0.0747975i
$775$	−21.0463	−	15.2910i	−0.756005	−	0.549270i
$776$	−12.4365	−	9.03566i	−0.446445	−	0.324361i
$777$	0.421924	−	1.29855i	0.0151365	−	0.0465852i
$778$	4.87919	+	15.0166i	0.174927	+	0.538371i
$779$	−24.0287	+	17.4579i	−0.860917	+	0.625493i
$780$	−0.800391			−0.0286586
$781$	−0.0834116	+	0.196616i	−0.00298470	+	0.00703548i
$782$	−0.482831			−0.0172660
$783$	−12.2530	+	8.90234i	−0.437887	+	0.318144i
$784$	−1.48092	−	4.55780i	−0.0528900	−	0.162779i
$785$	13.8710	−	42.6904i	0.495076	−	1.52369i
$786$	−1.23373	−	0.896359i	−0.0440058	−	0.0319721i
$787$	−2.33501	−	1.69649i	−0.0832343	−	0.0604732i	0.545390	−	0.838182i	$-0.316382\pi$
$787$	−2.33501	−	1.69649i	−0.0832343	−	0.0604732i	−0.628624	+	0.777709i	$0.716382\pi$
$788$	−3.55009	+	10.9260i	−0.126467	+	0.389224i
$789$	−4.68896	−	14.4311i	−0.166931	−	0.513762i
$790$	−3.33960	+	2.42636i	−0.118818	+	0.0863261i
$791$	12.4921			0.444169
$792$	2.83412	−	6.68053i	0.100706	−	0.237382i
$793$	0.482198			0.0171234
$794$	28.9473	−	21.0314i	1.02730	−	0.746377i
$795$	11.0974	+	34.1542i	0.393583	+	1.21132i
$796$	−4.37144	+	13.4539i	−0.154942	+	0.476861i
$797$	10.0522	+	7.30336i	0.356068	+	0.258698i	0.751410	−	0.659836i	$-0.229374\pi$
$797$	10.0522	+	7.30336i	0.356068	+	0.258698i	−0.395342	+	0.918534i	$0.629374\pi$
$798$	3.15269	+	2.29056i	0.111604	+	0.0810851i
$799$	−0.945181	+	2.90897i	−0.0334381	+	0.102912i
$800$	−1.99970	−	6.15445i	−0.0707002	−	0.217593i
$801$	−7.05620	+	5.12663i	−0.249319	+	0.181141i
$802$	−7.02163			−0.247942
$803$	15.9617	+	1.39320i	0.563275	+	0.0491651i
$804$	−4.74418			−0.167314
$805$	−0.870990	+	0.632811i	−0.0306984	+	0.0223037i
$806$	−0.325794	−	1.00269i	−0.0114756	−	0.0353183i
$807$	−7.44070	+	22.9001i	−0.261925	+	0.806122i
$808$	−1.32227	−	0.960686i	−0.0465173	−	0.0337968i
$809$	19.9407	+	14.4878i	0.701078	+	0.509363i	0.880283	−	0.474449i	$-0.157353\pi$
$809$	19.9407	+	14.4878i	0.701078	+	0.509363i	−0.179205	+	0.983812i	$0.557353\pi$
$810$	2.46111	−	7.57451i	0.0864745	−	0.266141i
$811$	−8.83140	−	27.1803i	−0.310112	−	0.954428i	−0.977720	−	0.209914i	$-0.932681\pi$
$811$	−8.83140	−	27.1803i	−0.310112	−	0.954428i	0.667607	−	0.744514i	$-0.267319\pi$
$812$	−3.89433	+	2.82940i	−0.136664	+	0.0992924i
$813$	1.41653			0.0496799
$814$	−2.89884	+	1.74260i	−0.101604	+	0.0610781i
$815$	20.3538			0.712961
$816$	−1.64527	+	1.19536i	−0.0575961	+	0.0418460i
$817$	−0.899434	−	2.76817i	−0.0314672	−	0.0968461i
$818$	−9.73805	+	29.9707i	−0.340483	+	1.04790i
$819$	−0.689761	−	0.501141i	−0.0241022	−	0.0175113i
$820$	−27.9606	−	20.3146i	−0.976427	−	0.709416i
$821$	15.1520	−	46.6329i	0.528807	−	1.62750i	−0.227856	−	0.973695i	$-0.573171\pi$
$821$	15.1520	−	46.6329i	0.528807	−	1.62750i	0.756663	−	0.653806i	$-0.226829\pi$
$822$	−3.88293	−	11.9504i	−0.135433	−	0.416819i
$823$	3.06573	−	2.22739i	0.106865	−	0.0776418i	−0.533069	−	0.846071i	$-0.678962\pi$
$823$	3.06573	−	2.22739i	0.106865	−	0.0776418i	0.639934	+	0.768430i	$0.278962\pi$
$824$	10.9531			0.381571
$825$	−14.5985	−	12.6851i	−0.508255	−	0.441638i
$826$	−1.24764			−0.0434111
$827$	18.9612	−	13.7761i	0.659345	−	0.479042i	−0.207097	−	0.978320i	$-0.566401\pi$
$827$	18.9612	−	13.7761i	0.659345	−	0.479042i	0.866442	+	0.499278i	$0.166401\pi$
$828$	−0.144651	−	0.445190i	−0.00502697	−	0.0154714i
$829$	−13.6907	+	42.1357i	−0.475498	+	1.46343i	0.369786	+	0.929117i	$0.379431\pi$
$829$	−13.6907	+	42.1357i	−0.475498	+	1.46343i	−0.845285	+	0.534316i	$0.820569\pi$
$830$	14.7497	+	10.7163i	0.511971	+	0.371969i
$831$	7.62470	+	5.53967i	0.264498	+	0.192169i
$832$	0.0810416	−	0.249420i	0.00280961	−	0.00864710i
$833$	−3.34226	−	10.2864i	−0.115802	−	0.356403i
$834$	10.7699	−	7.82478i	0.372931	−	0.270950i
$835$	17.1924			0.594966
$836$	−2.17346	−	9.40561i	−0.0751708	−	0.325300i
$837$	−18.7936			−0.649600
$838$	10.1621	−	7.38322i	0.351045	−	0.255049i
$839$	−7.90894	−	24.3412i	−0.273047	−	0.840352i	−0.989730	−	0.142952i	$-0.954340\pi$
$839$	−7.90894	−	24.3412i	−0.273047	−	0.840352i	0.716683	−	0.697399i	$-0.245660\pi$
$840$	−1.40127	+	4.31268i	−0.0483485	+	0.148802i
$841$	14.9701	+	10.8764i	0.516210	+	0.375048i
$842$	−25.7085	−	18.6783i	−0.885973	−	0.643697i
$843$	2.70232	−	8.31689i	0.0930729	−	0.286449i
$844$	6.89380	+	21.2169i	0.237294	+	0.730317i
$845$	−35.4324	+	25.7432i	−1.21891	+	0.885592i
$846$	−2.96535			−0.101951
$847$	−2.28120	−	16.1840i	−0.0783829	−	0.556088i
$848$	−11.7669			−0.404076
$849$	12.3256	−	8.95505i	0.423013	−	0.307337i
$850$	−4.51308	−	13.8898i	−0.154797	−	0.476418i
$851$	−0.0674195	+	0.207496i	−0.00231111	+	0.00711286i
$852$	0.0469450	+	0.0341076i	0.00160831	+	0.00116851i
$853$	−3.09658	−	2.24980i	−0.106025	−	0.0770316i	0.533510	−	0.845794i	$-0.320873\pi$
$853$	−3.09658	−	2.24980i	−0.106025	−	0.0770316i	−0.639534	+	0.768762i	$0.720873\pi$
$854$	0.844202	−	2.59819i	0.0288880	−	0.0889081i
$855$	−6.66538	−	20.5139i	−0.227951	−	0.701561i
$856$	−3.79147	+	2.75466i	−0.129590	+	0.0941524i
$857$	−23.2861			−0.795440			−0.397720	−	0.917507i	$-0.630198\pi$
$857$	−23.2861			−0.795440			−0.397720	+	0.917507i	$0.630198\pi$
$858$	−0.176467	−	0.763657i	−0.00602449	−	0.0260708i
$859$	9.03160			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$859$	9.03160			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$860$	2.74007	−	1.99078i	0.0934356	−	0.0678849i
$861$	4.22187	+	12.9936i	0.143881	+	0.442820i
$862$	7.39455	−	22.7581i	0.251859	−	0.775143i
$863$	−20.4033	−	14.8239i	−0.694536	−	0.504610i	0.183612	−	0.982999i	$-0.441221\pi$
$863$	−20.4033	−	14.8239i	−0.694536	−	0.504610i	−0.878148	+	0.478389i	$0.841221\pi$
$864$	−3.78209	−	2.74785i	−0.128669	−	0.0934837i
$865$	−5.17955	+	15.9410i	−0.176110	+	0.542011i
$866$	−1.40320	−	4.31862i	−0.0476828	−	0.146753i
$867$	8.67990	−	6.30631i	0.294785	−	0.214174i
$868$	−5.97309			−0.202740
$869$	−3.05131	−	2.65137i	−0.103508	−	0.0899417i
$870$	−9.88753			−0.335219
$871$	1.11705	−	0.811583i	0.0378497	−	0.0274994i
$872$	−0.342292	−	1.05347i	−0.0115915	−	0.0356749i
$873$	10.3938	−	31.9889i	0.351777	−	1.08266i
$874$	−0.503770	−	0.366010i	−0.0170403	−	0.0123805i
$875$	−5.98949	−	4.35162i	−0.202482	−	0.147112i
$876$	1.34519	−	4.14008i	0.0454499	−	0.139880i
$877$	−2.11470	−	6.50838i	−0.0714083	−	0.219772i	0.908983	−	0.416834i	$-0.136860\pi$
$877$	−2.11470	−	6.50838i	−0.0714083	−	0.219772i	−0.980391	+	0.197061i	$0.936860\pi$
$878$	28.0619	−	20.3881i	0.947042	−	0.688066i
$879$	22.5308			0.759945
$880$	9.62749	−	5.78743i	0.324543	−	0.195094i
$881$	−21.5402			−0.725707			−0.362853	−	0.931846i	$-0.618197\pi$
$881$	−21.5402			−0.725707			−0.362853	+	0.931846i	$0.618197\pi$
$882$	8.48317	−	6.16339i	0.285643	−	0.207532i
$883$	−12.8003	−	39.3951i	−0.430763	−	1.32575i	−0.897367	−	0.441285i	$-0.854523\pi$
$883$	−12.8003	−	39.3951i	−0.430763	−	1.32575i	0.466604	−	0.884466i	$-0.345477\pi$
$884$	0.182901	−	0.562911i	0.00615162	−	0.0189327i
$885$	−2.07329	−	1.50634i	−0.0696930	−	0.0506349i
$886$	26.0095	+	18.8970i	0.873806	+	0.634857i
$887$	3.40511	−	10.4799i	0.114333	−	0.351879i	−0.877475	−	0.479623i	$-0.840773\pi$
$887$	3.40511	−	10.4799i	0.114333	−	0.351879i	0.991807	+	0.127744i	$0.0407735\pi$
$888$	0.283969	+	0.873966i	0.00952936	+	0.0293284i
$889$	14.1551	−	10.2843i	0.474748	−	0.344925i
$890$	−13.5010			−0.452554
$891$	7.76949	+	0.678155i	0.260288	+	0.0227191i
$892$	6.14675			0.205808
$893$	−3.19131	+	2.31862i	−0.106793	+	0.0775898i
$894$	−1.04084	−	3.20337i	−0.0348109	−	0.107137i
$895$	1.01828	−	3.13396i	0.0340375	−	0.104757i
$896$	−1.20205	−	0.873339i	−0.0401576	−	0.0291762i
$897$	−0.0409019	−	0.0297169i	−0.00136567	−	0.000992220i
$898$	−3.77666	+	11.6234i	−0.126029	+	0.387877i
$899$	−4.02465	−	12.3866i	−0.134230	−	0.413116i
$900$	11.4549	−	8.32249i	0.381831	−	0.277416i
$901$	−26.5564			−0.884722
$902$	13.2176	−	31.1562i	0.440098	−	1.03739i
$903$	−1.33886			−0.0445546
$904$	−6.80190	+	4.94187i	−0.226228	+	0.164364i
$905$	−0.869881	−	2.67722i	−0.0289158	−	0.0889937i
$906$	−1.96259	+	6.04022i	−0.0652026	+	0.200673i
$907$	−42.8127	−	31.1053i	−1.42157	−	1.03283i	−0.991509	−	0.130035i	$-0.958491\pi$
$907$	−42.8127	−	31.1053i	−1.42157	−	1.03283i	−0.430064	−	0.902798i	$-0.641509\pi$
$908$	−2.96408	−	2.15353i	−0.0983663	−	0.0714673i
$909$	1.10509	−	3.40111i	0.0366534	−	0.112808i
$910$	−0.407827	−	1.25516i	−0.0135193	−	0.0416082i
$911$	12.5212	−	9.09719i	0.414846	−	0.301404i	−0.360715	−	0.932676i	$-0.617467\pi$
$911$	12.5212	−	9.09719i	0.414846	−	0.301404i	0.775561	+	0.631273i	$0.217467\pi$
$912$	−2.62277			−0.0868484
$913$	−6.97252	+	16.4355i	−0.230757	+	0.543935i
$914$	9.15067			0.302677
$915$	4.53977	−	3.29834i	0.150080	−	0.109040i
$916$	3.24664	+	9.99215i	0.107272	+	0.330150i
$917$	0.777030	−	2.39145i	0.0256598	−	0.0789727i
$918$	−8.53571	−	6.20156i	−0.281720	−	0.204682i
$919$	36.8423	+	26.7675i	1.21532	+	0.882979i	0.995703	−	0.0926077i	$-0.0295202\pi$
$919$	36.8423	+	26.7675i	1.21532	+	0.882979i	0.219614	+	0.975587i	$0.429520\pi$
$920$	0.223910	−	0.689124i	0.00738210	−	0.0227198i
$921$	8.74823	+	26.9243i	0.288264	+	0.887186i
$922$	4.34228	−	3.15485i	0.143005	−	0.103899i
$923$	−0.0168883			−0.000555884
$924$	−4.42369	−	0.386119i	−0.145529	−	0.0127024i
$925$	−6.59931			−0.216984
$926$	18.8790	−	13.7164i	0.620403	−	0.450749i
$927$	7.40581	+	22.7927i	0.243239	+	0.748612i
$928$	1.00114	−	3.08118i	0.0328639	−	0.101145i
$929$	−13.3723	−	9.71556i	−0.438731	−	0.318757i	0.346399	−	0.938087i	$-0.387404\pi$
$929$	−13.3723	−	9.71556i	−0.438731	−	0.318757i	−0.785131	+	0.619330i	$0.787404\pi$
$930$	−9.92588	−	7.21157i	−0.325482	−	0.236477i
$931$	4.31041	−	13.2661i	0.141268	−	0.434778i
$932$	4.52935	+	13.9399i	0.148364	+	0.456616i
$933$	13.1189	−	9.53147i	0.429495	−	0.312046i
$934$	−23.6566			−0.774068
$935$	21.7281	−	13.0615i	0.710583	−	0.427158i
$936$	0.573822			0.0187560
$937$	24.7086	−	17.9518i	0.807194	−	0.586460i	−0.105822	−	0.994385i	$-0.533747\pi$
$937$	24.7086	−	17.9518i	0.807194	−	0.586460i	0.913016	+	0.407925i	$0.133747\pi$
$938$	−2.41733	−	7.43976i	−0.0789285	−	0.242917i
$939$	−8.35357	+	25.7096i	−0.272608	+	0.839002i
$940$	−3.71353	−	2.69803i	−0.121122	−	0.0880002i
$941$	38.4574	+	27.9409i	1.25367	+	0.910848i	0.998429	−	0.0560287i	$-0.0178438\pi$
$941$	38.4574	+	27.9409i	1.25367	+	0.910848i	0.255245	+	0.966876i	$0.417844\pi$
$942$	3.69042	−	11.3579i	0.120240	−	0.370061i
$943$	−0.674614	−	2.07625i	−0.0219684	−	0.0676119i
$944$	0.679336	−	0.493566i	0.0221105	−	0.0160642i
$945$	−23.5257			−0.765291
$946$	2.50353	+	2.17539i	0.0813968	+	0.0707282i
$947$	−46.9552			−1.52584			−0.762920	−	0.646493i	$-0.776235\pi$
$947$	−46.9552			−1.52584			−0.762920	+	0.646493i	$0.776235\pi$
$948$	−0.888512	+	0.645542i	−0.0288575	+	0.0209662i
$949$	0.391506	+	1.20493i	0.0127088	+	0.0391137i
$950$	5.82039	−	17.9133i	0.188839	−	0.581185i
$951$	−17.8875	−	12.9960i	−0.580042	−	0.421425i
$952$	−2.71287	−	1.97102i	−0.0879248	−	0.0638811i
$953$	−1.21511	+	3.73972i	−0.0393612	+	0.121141i	−0.968806	−	0.247819i	$-0.920286\pi$
$953$	−1.21511	+	3.73972i	−0.0393612	+	0.121141i	0.929445	+	0.368960i	$0.120286\pi$
$954$	−7.95600	−	24.4861i	−0.257585	−	0.792766i
$955$	−35.0285	+	25.4497i	−1.13350	+	0.823532i
$956$	−1.56538			−0.0506281
$957$	−2.17996	−	9.43373i	−0.0704682	−	0.304949i
$958$	12.6199			0.407732
$959$	16.7620	−	12.1783i	0.541273	−	0.393258i
$960$	−0.943102	−	2.90257i	−0.0304385	−	0.0936801i
$961$	−4.58549	+	14.1127i	−0.147919	+	0.455248i
$962$	−0.216371	−	0.157203i	−0.00697608	−	0.00506842i
$963$	−8.29580	−	6.02725i	−0.267329	−	0.194226i
$964$	0.674249	−	2.07512i	0.0217161	−	0.0668352i
$965$	−11.9012	−	36.6281i	−0.383113	−	1.17910i
$966$	−0.231730	+	0.168362i	−0.00745578	+	0.00541694i
$967$	38.3331			1.23271			0.616355	−	0.787469i	$-0.288609\pi$
$967$	38.3331			1.23271			0.616355	+	0.787469i	$0.288609\pi$
$968$	7.64445	+	7.90964i	0.245702	+	0.254225i
$969$	−5.91926			−0.190154
$970$	42.1214	−	30.6030i	1.35244	−	0.982603i
$971$	−10.7277	−	33.0166i	−0.344270	−	1.05955i	−0.961974	−	0.273142i	$-0.911937\pi$
$971$	−10.7277	−	33.0166i	−0.344270	−	1.05955i	0.617704	−	0.786411i	$-0.288063\pi$
$972$	4.98867	−	15.3536i	0.160012	−	0.492466i
$973$	17.7584	+	12.9022i	0.569307	+	0.413626i
$974$	0.0139523	+	0.0101370i	0.000447062	+	0.000324809i
$975$	0.472567	−	1.45441i	0.0151343	−	0.0465785i
$976$	0.568175	+	1.74866i	0.0181868	+	0.0559734i
$977$	19.0342	−	13.8291i	0.608957	−	0.442433i	−0.240090	−	0.970751i	$-0.577177\pi$
$977$	19.0342	−	13.8291i	0.608957	−	0.442433i	0.849047	+	0.528318i	$0.177177\pi$
$978$	5.41519			0.173159
$979$	−2.97665	−	12.8814i	−0.0951341	−	0.411690i
$980$	16.2313			0.518490
$981$	1.96075	−	1.42457i	0.0626021	−	0.0454831i
$982$	9.05323	+	27.8630i	0.288900	+	0.889143i
$983$	−4.09780	+	12.6117i	−0.130700	+	0.402252i	−0.994896	−	0.100902i	$-0.967827\pi$
$983$	−4.09780	+	12.6117i	−0.130700	+	0.402252i	0.864197	+	0.503154i	$0.167827\pi$
$984$	−7.43902	−	5.40476i	−0.237147	−	0.172297i
$985$	−31.4788	−	22.8707i	−1.00300	−	0.728721i
$986$	2.25944	−	6.95385i	0.0719553	−	0.221456i
$987$	0.560717	+	1.72571i	0.0178478	+	0.0549300i
$988$	0.617547	−	0.448674i	0.0196468	−	0.0142742i
$989$	0.213938			0.00680282
$990$	18.5527	+	16.1210i	0.589645	+	0.512361i
$991$	17.3908			0.552438			0.276219	−	0.961095i	$-0.410918\pi$
$991$	17.3908			0.552438			0.276219	+	0.961095i	$0.410918\pi$
$992$	3.25231	−	2.36294i	0.103261	−	0.0750236i
$993$	8.57342	+	26.3863i	0.272069	+	0.837343i
$994$	−0.0295669	+	0.0909976i	−0.000937806	+	0.00288627i
$995$	−38.7618	−	28.1621i	−1.22883	−	0.892798i
$996$	3.92422	+	2.85111i	0.124344	+	0.0903409i
$997$	13.7267	−	42.2465i	0.434729	−	1.33796i	−0.458635	−	0.888625i	$-0.651661\pi$
$997$	13.7267	−	42.2465i	0.434729	−	1.33796i	0.893364	−	0.449334i	$-0.148339\pi$
$998$	−2.07197	−	6.37686i	−0.0655870	−	0.201856i
$999$	−3.85698	+	2.80226i	−0.122029	+	0.0886596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.f.d.861.2	yes	16
11.4	even	5	inner	946.2.f.d.345.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.f.d.345.2	✓	16	11.4	even	5	inner
946.2.f.d.861.2	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.278455 + 0.856996i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.74007 + 1.99078i) q^{5} +(0.729004 + 0.529653i) q^{6} +(-0.459142 + 1.41309i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.77015 - 1.28609i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.278455 + 0.856996i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.74007 + 1.99078i) q^{5} +(0.729004 + 0.529653i) q^{6} +(-0.459142 + 1.41309i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.77015 - 1.28609i) q^{9} +3.38691 q^{10} +(0.746733 + 3.23147i) q^{11} +0.901099 q^{12} +(-0.212170 + 0.154150i) q^{13} +(0.459142 + 1.41309i) q^{14} +(-0.943102 + 2.90257i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.82585 - 1.32656i) q^{17} +(0.676136 - 2.08093i) q^{18} +(-0.899434 - 2.76817i) q^{19} +(2.74007 - 1.99078i) q^{20} -1.33886 q^{21} +(2.50353 + 2.17539i) q^{22} +0.213938 q^{23} +(0.729004 - 0.529653i) q^{24} +(1.99970 + 6.15445i) q^{25} +(-0.0810416 + 0.249420i) q^{26} +(3.78209 + 2.74785i) q^{27} +(1.20205 + 0.873339i) q^{28} +(-1.00114 + 3.08118i) q^{29} +(0.943102 + 2.90257i) q^{30} +(-3.25231 + 2.36294i) q^{31} -1.00000 q^{32} +(-2.56142 + 1.53977i) q^{33} -2.25688 q^{34} +(-4.07123 + 2.95792i) q^{35} +(-0.676136 - 2.08093i) q^{36} +(-0.315136 + 0.969889i) q^{37} +(-2.35475 - 1.71083i) q^{38} +(-0.191186 - 0.138905i) q^{39} +(1.04661 - 3.22114i) q^{40} +(-3.15332 - 9.70491i) q^{41} +(-1.08316 + 0.786965i) q^{42} +1.00000 q^{43} +(3.30406 + 0.288393i) q^{44} +7.41063 q^{45} +(0.173079 - 0.125749i) q^{46} +(-0.418800 - 1.28894i) q^{47} +(0.278455 - 0.856996i) q^{48} +(3.87710 + 2.81688i) q^{49} +(5.23529 + 3.80366i) q^{50} +(0.628438 - 1.93413i) q^{51} +(0.0810416 + 0.249420i) q^{52} +(9.51960 - 6.91640i) q^{53} +4.67492 q^{54} +(-4.38703 + 10.3410i) q^{55} +1.48581 q^{56} +(2.12186 - 1.54162i) q^{57} +(1.00114 + 3.08118i) q^{58} +(-0.259483 + 0.798607i) q^{59} +(2.46907 + 1.79389i) q^{60} +(-1.48750 - 1.08073i) q^{61} +(-1.24227 + 3.82332i) q^{62} +(1.00461 + 3.09188i) q^{63} +(-0.809017 + 0.587785i) q^{64} -0.888238 q^{65} +(-1.16718 + 2.75126i) q^{66} -5.26488 q^{67} +(-1.82585 + 1.32656i) q^{68} +(0.0595720 + 0.183344i) q^{69} +(-1.55507 + 4.78602i) q^{70} +(0.0520975 + 0.0378511i) q^{71} +(-1.77015 - 1.28609i) q^{72} +(1.49284 - 4.59448i) q^{73} +(0.315136 + 0.969889i) q^{74} +(-4.71751 + 3.42747i) q^{75} -2.91063 q^{76} +(-4.90922 - 0.428498i) q^{77} -0.236319 q^{78} +(-0.986031 + 0.716394i) q^{79} +(-1.04661 - 3.22114i) q^{80} +(0.726652 - 2.23641i) q^{81} +(-8.25549 - 5.99797i) q^{82} +(4.35492 + 3.16404i) q^{83} +(-0.413732 + 1.27334i) q^{84} +(-2.36208 - 7.26973i) q^{85} +(0.809017 - 0.587785i) q^{86} -2.91933 q^{87} +(2.84256 - 1.70876i) q^{88} -3.98623 q^{89} +(5.99533 - 4.35586i) q^{90} +(-0.120413 - 0.370592i) q^{91} +(0.0661104 - 0.203467i) q^{92} +(-2.93066 - 2.12925i) q^{93} +(-1.09643 - 0.796606i) q^{94} +(3.04630 - 9.37556i) q^{95} +(-0.278455 - 0.856996i) q^{96} +(12.4365 - 9.03566i) q^{97} +4.79236 q^{98} +(5.47777 + 4.75981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 4 * q^8	\( 16 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 4 q^{8} + 6 q^{10} + 7 q^{11} + 4 q^{12} - 6 q^{13} + 6 q^{14} + 14 q^{15} - 4 q^{16} - 12 q^{17} + 10 q^{18} - q^{19} + 9 q^{20} + 46 q^{21} + 3 q^{22} + 26 q^{23} + 6 q^{24} - 19 q^{25} + q^{26} - 14 q^{27} - q^{28} - 6 q^{29} - 14 q^{30} - 6 q^{31} - 16 q^{32} - 59 q^{33} + 2 q^{34} + 4 q^{35} - 10 q^{36} - 33 q^{37} - 9 q^{38} - 21 q^{39} + 6 q^{40} - 5 q^{41} + 19 q^{42} + 16 q^{43} - 8 q^{44} - 60 q^{45} + 24 q^{46} - 2 q^{47} + 4 q^{48} + 12 q^{49} - 16 q^{50} - 9 q^{51} - q^{52} + 34 q^{53} + 14 q^{54} + 19 q^{55} - 14 q^{56} - 43 q^{57} + 6 q^{58} + 29 q^{59} - q^{60} - 8 q^{61} - 24 q^{62} + 73 q^{63} - 4 q^{64} - 18 q^{65} + 29 q^{66} - 48 q^{67} - 12 q^{68} + 29 q^{69} + 31 q^{70} + 9 q^{71} - 39 q^{73} + 33 q^{74} + 33 q^{75} - 16 q^{76} - 3 q^{77} - 64 q^{78} + 11 q^{79} - 6 q^{80} - 74 q^{81} + 28 q^{83} - 4 q^{84} + 9 q^{85} + 4 q^{86} - 20 q^{87} + 8 q^{88} - 52 q^{89} + 20 q^{90} - 10 q^{91} + 11 q^{92} + 3 q^{93} - 18 q^{94} + 17 q^{95} - 4 q^{96} - 3 q^{97} - 2 q^{98} - 59 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 4 * q^8 + 6 * q^10 + 7 * q^11 + 4 * q^12 - 6 * q^13 + 6 * q^14 + 14 * q^15 - 4 * q^16 - 12 * q^17 + 10 * q^18 - q^19 + 9 * q^20 + 46 * q^21 + 3 * q^22 + 26 * q^23 + 6 * q^24 - 19 * q^25 + q^26 - 14 * q^27 - q^28 - 6 * q^29 - 14 * q^30 - 6 * q^31 - 16 * q^32 - 59 * q^33 + 2 * q^34 + 4 * q^35 - 10 * q^36 - 33 * q^37 - 9 * q^38 - 21 * q^39 + 6 * q^40 - 5 * q^41 + 19 * q^42 + 16 * q^43 - 8 * q^44 - 60 * q^45 + 24 * q^46 - 2 * q^47 + 4 * q^48 + 12 * q^49 - 16 * q^50 - 9 * q^51 - q^52 + 34 * q^53 + 14 * q^54 + 19 * q^55 - 14 * q^56 - 43 * q^57 + 6 * q^58 + 29 * q^59 - q^60 - 8 * q^61 - 24 * q^62 + 73 * q^63 - 4 * q^64 - 18 * q^65 + 29 * q^66 - 48 * q^67 - 12 * q^68 + 29 * q^69 + 31 * q^70 + 9 * q^71 - 39 * q^73 + 33 * q^74 + 33 * q^75 - 16 * q^76 - 3 * q^77 - 64 * q^78 + 11 * q^79 - 6 * q^80 - 74 * q^81 + 28 * q^83 - 4 * q^84 + 9 * q^85 + 4 * q^86 - 20 * q^87 + 8 * q^88 - 52 * q^89 + 20 * q^90 - 10 * q^91 + 11 * q^92 + 3 * q^93 - 18 * q^94 + 17 * q^95 - 4 * q^96 - 3 * q^97 - 2 * q^98 - 59 * q^99

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