LMFDB - Embedded newform 546.2.q.j.251.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.12
Character	$\chi$	$=$	546.251
Dual form			546.2.q.j.335.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.68382 + 0.405895i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.19343 - 1.25528i) q^{6} +(1.06015 - 2.42406i) q^{7} -1.00000 q^{8} +(2.67050 + 1.36691i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.68382 + 0.405895i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.19343 - 1.25528i) q^{6} +(1.06015 - 2.42406i) q^{7} -1.00000 q^{8} +(2.67050 + 1.36691i) q^{9} +(0.403261 + 0.232823i) q^{10} +(1.39698 - 2.41964i) q^{11} +(-0.490394 - 1.66118i) q^{12} +(0.799665 + 3.51576i) q^{13} +(-1.56923 - 2.13015i) q^{14} +(-0.189003 + 0.784062i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.508355 - 0.880496i) q^{17} +(2.51903 - 1.62927i) q^{18} +(0.817625 + 1.41617i) q^{19} +(0.403261 - 0.232823i) q^{20} +(2.76902 - 3.65138i) q^{21} +(-1.39698 - 2.41964i) q^{22} +(-7.14652 - 4.12605i) q^{23} +(-1.68382 - 0.405895i) q^{24} +4.78317 q^{25} +(3.44457 + 1.06535i) q^{26} +(3.94182 + 3.38557i) q^{27} +(-2.62938 + 0.293915i) q^{28} +(-4.01364 - 2.31727i) q^{29} +(0.584516 + 0.555713i) q^{30} -1.94747 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.33438 - 3.50721i) q^{33} -1.01671 q^{34} +(1.12875 + 0.493654i) q^{35} +(-0.151472 - 2.99617i) q^{36} +(4.51505 + 2.60676i) q^{37} +1.63525 q^{38} +(-0.0805363 + 6.24448i) q^{39} -0.465645i q^{40} +(9.35517 + 5.40121i) q^{41} +(-1.77768 - 4.22373i) q^{42} +(-3.24949 - 5.62828i) q^{43} -2.79396 q^{44} +(-0.636494 + 1.24350i) q^{45} +(-7.14652 + 4.12605i) q^{46} -0.277466i q^{47} +(-1.19343 + 1.25528i) q^{48} +(-4.75217 - 5.13974i) q^{49} +(2.39159 - 4.14235i) q^{50} +(-0.498589 - 1.68894i) q^{51} +(2.64490 - 2.45041i) q^{52} +8.99975i q^{53} +(4.90290 - 1.72093i) q^{54} +(1.12669 + 0.650496i) q^{55} +(-1.06015 + 2.42406i) q^{56} +(0.801918 + 2.71644i) q^{57} +(-4.01364 + 2.31727i) q^{58} +(-8.80951 + 5.08617i) q^{59} +(0.773520 - 0.228350i) q^{60} +(-11.2444 + 6.49197i) q^{61} +(-0.973737 + 1.68656i) q^{62} +(6.14460 - 5.02433i) q^{63} +1.00000 q^{64} +(-1.63709 + 0.372360i) q^{65} +(-1.37014 - 4.64126i) q^{66} +(-0.308335 - 0.178017i) q^{67} +(-0.508355 + 0.880496i) q^{68} +(-10.3587 - 9.84825i) q^{69} +(0.991893 - 0.730702i) q^{70} +(5.01505 + 8.68632i) q^{71} +(-2.67050 - 1.36691i) q^{72} -1.46098 q^{73} +(4.51505 - 2.60676i) q^{74} +(8.05400 + 1.94147i) q^{75} +(0.817625 - 1.41617i) q^{76} +(-4.38435 - 5.95154i) q^{77} +(5.36761 + 3.19199i) q^{78} -4.98126 q^{79} +(-0.403261 - 0.232823i) q^{80} +(5.26312 + 7.30065i) q^{81} +(9.35517 - 5.40121i) q^{82} +12.2750i q^{83} +(-4.54669 - 0.572351i) q^{84} +(0.409999 - 0.236713i) q^{85} -6.49897 q^{86} +(-5.81767 - 5.53099i) q^{87} +(-1.39698 + 2.41964i) q^{88} +(-10.1441 - 5.85671i) q^{89} +(0.758659 + 1.17297i) q^{90} +(9.37018 + 1.78879i) q^{91} +8.25209i q^{92} +(-3.27919 - 0.790470i) q^{93} +(-0.240293 - 0.138733i) q^{94} +(-0.659432 + 0.380723i) q^{95} +(0.490394 + 1.66118i) q^{96} +(-7.82871 - 13.5597i) q^{97} +(-6.82723 + 1.54563i) q^{98} +(7.03805 - 4.55210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.68382	+	0.405895i	0.972154	+	0.234344i
$3$	1.68382	+	0.405895i	0.972154	+	0.234344i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$			0.465645i			0.208243i	0.994565	+	0.104121i	$0.0332031\pi$
$5$			0.465645i			0.208243i	−0.994565	+	0.104121i	$0.966797\pi$
$6$	1.19343	−	1.25528i	0.487214	−	0.512467i
$7$	1.06015	−	2.42406i	0.400699	−	0.916210i
$7$	1.06015	−	2.42406i	0.400699	−	0.916210i
$8$	−1.00000			−0.353553
$9$	2.67050	+	1.36691i	0.890166	+	0.455636i
$10$	0.403261	+	0.232823i	0.127522	+	0.0736250i
$11$	1.39698	−	2.41964i	0.421205	−	0.729548i	−0.574853	−	0.818257i	$-0.694941\pi$
$11$	1.39698	−	2.41964i	0.421205	−	0.729548i	0.996058	+	0.0887086i	$0.0282740\pi$
$12$	−0.490394	−	1.66118i	−0.141565	−	0.479541i
$13$	0.799665	+	3.51576i	0.221787	+	0.975095i
$13$	0.799665	+	3.51576i	0.221787	+	0.975095i
$14$	−1.56923	−	2.13015i	−0.419393	−	0.569306i
$15$	−0.189003	+	0.784062i	−0.0488004	+	0.202444i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.508355	−	0.880496i	−0.123294	−	0.213552i	0.797771	−	0.602961i	$-0.206013\pi$
$17$	−0.508355	−	0.880496i	−0.123294	−	0.213552i	−0.921065	+	0.389409i	$0.872679\pi$
$18$	2.51903	−	1.62927i	0.593740	−	0.384021i
$19$	0.817625	+	1.41617i	0.187576	+	0.324891i	0.944442	−	0.328679i	$-0.106604\pi$
$19$	0.817625	+	1.41617i	0.187576	+	0.324891i	−0.756865	+	0.653571i	$0.773270\pi$
$20$	0.403261	−	0.232823i	0.0901718	−	0.0520607i
$21$	2.76902	−	3.65138i	0.604249	−	0.796796i
$22$	−1.39698	−	2.41964i	−0.297837	−	0.515869i
$23$	−7.14652	−	4.12605i	−1.49015	−	0.860340i	−0.490216	−	0.871601i	$-0.663082\pi$
$23$	−7.14652	−	4.12605i	−1.49015	−	0.860340i	−0.999937	+	0.0112612i	$0.996415\pi$
$24$	−1.68382	−	0.405895i	−0.343708	−	0.0828530i
$25$	4.78317			0.956635
$26$	3.44457	+	1.06535i	0.675535	+	0.208932i
$27$	3.94182	+	3.38557i	0.758603	+	0.651553i
$28$	−2.62938	+	0.293915i	−0.496905	+	0.0555447i
$29$	−4.01364	−	2.31727i	−0.745313	−	0.430307i	0.0786847	−	0.996900i	$-0.474928\pi$
$29$	−4.01364	−	2.31727i	−0.745313	−	0.430307i	−0.823998	+	0.566593i	$0.808261\pi$
$30$	0.584516	+	0.555713i	0.106718	+	0.101459i
$31$	−1.94747			−0.349777			−0.174888	−	0.984588i	$-0.555956\pi$
$31$	−1.94747			−0.349777			−0.174888	+	0.984588i	$0.555956\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.33438	−	3.50721i	0.580441	−	0.610527i
$34$	−1.01671			−0.174364
$35$	1.12875	+	0.493654i	0.190794	+	0.0834427i
$36$	−0.151472	−	2.99617i	−0.0252453	−	0.499362i
$37$	4.51505	+	2.60676i	0.742269	+	0.428549i	0.822894	−	0.568195i	$-0.192358\pi$
$37$	4.51505	+	2.60676i	0.742269	+	0.428549i	−0.0806247	+	0.996745i	$0.525692\pi$
$38$	1.63525			0.265273
$39$	−0.0805363	+	6.24448i	−0.0128961	+	0.999917i
$40$		−	0.465645i		−	0.0736250i
$41$	9.35517	+	5.40121i	1.46103	+	0.843527i	0.999059	−	0.0433672i	$-0.0138085\pi$
$41$	9.35517	+	5.40121i	1.46103	+	0.843527i	0.461973	+	0.886894i	$0.347142\pi$
$42$	−1.77768	−	4.22373i	−0.274301	−	0.651735i
$43$	−3.24949	−	5.62828i	−0.495542	−	0.858304i	0.504445	−	0.863444i	$-0.331697\pi$
$43$	−3.24949	−	5.62828i	−0.495542	−	0.858304i	−0.999987	+	0.00513985i	$0.998364\pi$
$44$	−2.79396			−0.421205
$45$	−0.636494	+	1.24350i	−0.0948830	+	0.185371i
$46$	−7.14652	+	4.12605i	−1.05370	+	0.608352i
$47$		−	0.277466i		−	0.0404726i	−0.999795	−	0.0202363i	$-0.993558\pi$
$47$		−	0.277466i		−	0.0404726i	0.999795	−	0.0202363i	$-0.00644186\pi$
$48$	−1.19343	+	1.25528i	−0.172256	+	0.181185i
$49$	−4.75217	−	5.13974i	−0.678881	−	0.734249i
$50$	2.39159	−	4.14235i	0.338222	−	0.585817i
$51$	−0.498589	−	1.68894i	−0.0698164	−	0.236498i
$52$	2.64490	−	2.45041i	0.366782	−	0.339810i
$53$			8.99975i			1.23621i	0.786095	+	0.618105i	$0.212099\pi$
$53$			8.99975i			1.23621i	−0.786095	+	0.618105i	$0.787901\pi$
$54$	4.90290	−	1.72093i	0.667200	−	0.234189i
$55$	1.12669	+	0.650496i	0.151923	+	0.0877129i
$56$	−1.06015	+	2.42406i	−0.141668	+	0.323929i
$57$	0.801918	+	2.71644i	0.106217	+	0.359802i
$58$	−4.01364	+	2.31727i	−0.527016	+	0.304273i
$59$	−8.80951	+	5.08617i	−1.14690	+	0.662163i	−0.948130	−	0.317883i	$-0.897028\pi$
$59$	−8.80951	+	5.08617i	−1.14690	+	0.662163i	−0.198770	+	0.980046i	$0.563695\pi$
$60$	0.773520	−	0.228350i	0.0998609	−	0.0294798i
$61$	−11.2444	+	6.49197i	−1.43970	+	0.831211i	−0.997828	−	0.0658671i	$-0.979019\pi$
$61$	−11.2444	+	6.49197i	−1.43970	+	0.831211i	−0.441872	+	0.897078i	$0.645685\pi$
$62$	−0.973737	+	1.68656i	−0.123665	+	0.214194i
$63$	6.14460	−	5.02433i	0.774147	−	0.633006i
$64$	1.00000			0.125000
$65$	−1.63709	+	0.372360i	−0.203057	+	0.0461856i
$66$	−1.37014	−	4.64126i	−0.168653	−	0.571300i
$67$	−0.308335	−	0.178017i	−0.0376691	−	0.0217483i	0.481047	−	0.876695i	$-0.340257\pi$
$67$	−0.308335	−	0.178017i	−0.0376691	−	0.0217483i	−0.518716	+	0.854946i	$0.673590\pi$
$68$	−0.508355	+	0.880496i	−0.0616471	+	0.106776i
$69$	−10.3587	−	9.84825i	−1.24704	−	1.18559i
$70$	0.991893	−	0.730702i	0.118554	−	0.0873356i
$71$	5.01505	+	8.68632i	0.595177	+	1.03088i	0.993522	+	0.113640i	$0.0362512\pi$
$71$	5.01505	+	8.68632i	0.595177	+	1.03088i	−0.398345	+	0.917235i	$0.630415\pi$
$72$	−2.67050	−	1.36691i	−0.314721	−	0.161092i
$73$	−1.46098			−0.170995			−0.0854975	−	0.996338i	$-0.527248\pi$
$73$	−1.46098			−0.170995			−0.0854975	+	0.996338i	$0.527248\pi$
$74$	4.51505	−	2.60676i	0.524863	−	0.303030i
$75$	8.05400	+	1.94147i	0.929996	+	0.224181i
$76$	0.817625	−	1.41617i	0.0937881	−	0.162446i
$77$	−4.38435	−	5.95154i	−0.499643	−	0.678241i
$78$	5.36761	+	3.19199i	0.607762	+	0.361421i
$79$	−4.98126			−0.560435			−0.280218	−	0.959937i	$-0.590407\pi$
$79$	−4.98126			−0.560435			−0.280218	+	0.959937i	$0.590407\pi$
$80$	−0.403261	−	0.232823i	−0.0450859	−	0.0260304i
$81$	5.26312	+	7.30065i	0.584791	+	0.811184i
$82$	9.35517	−	5.40121i	1.03311	−	0.596464i
$83$			12.2750i			1.34736i	0.739024	+	0.673679i	$0.235287\pi$
$83$			12.2750i			1.34736i	−0.739024	+	0.673679i	$0.764713\pi$
$84$	−4.54669	−	0.572351i	−0.496085	−	0.0624486i
$85$	0.409999	−	0.236713i	0.0444706	−	0.0256751i
$86$	−6.49897			−0.700802
$87$	−5.81767	−	5.53099i	−0.623720	−	0.592984i
$88$	−1.39698	+	2.41964i	−0.148918	+	0.257934i
$89$	−10.1441	−	5.85671i	−1.07527	−	0.620810i	−0.145657	−	0.989335i	$-0.546530\pi$
$89$	−10.1441	−	5.85671i	−1.07527	−	0.620810i	−0.929618	+	0.368525i	$0.879863\pi$
$90$	0.758659	+	1.17297i	0.0799697	+	0.123642i
$91$	9.37018	+	1.78879i	0.982262	+	0.187516i
$92$			8.25209i			0.860340i
$93$	−3.27919	−	0.790470i	−0.340037	−	0.0819679i
$94$	−0.240293	−	0.138733i	−0.0247843	−	0.0143092i
$95$	−0.659432	+	0.380723i	−0.0676563	+	0.0390614i
$96$	0.490394	+	1.66118i	0.0500507	+	0.169543i
$97$	−7.82871	−	13.5597i	−0.794885	−	1.37678i	−0.922912	−	0.385011i	$-0.874198\pi$
$97$	−7.82871	−	13.5597i	−0.794885	−	1.37678i	0.128027	−	0.991771i	$-0.459136\pi$
$98$	−6.82723	+	1.54563i	−0.689654	+	0.156132i
$99$	7.03805	−	4.55210i	0.707351	−	0.457503i
$100$	−2.39159	−	4.14235i	−0.239159	−	0.414235i
$101$	2.03145	−	3.51858i	0.202137	−	0.350112i	−0.747080	−	0.664734i	$-0.768545\pi$
$101$	2.03145	−	3.51858i	0.202137	−	0.350112i	0.949217	+	0.314623i	$0.101878\pi$
$102$	−1.71196	−	0.412677i	−0.169509	−	0.0408612i
$103$		−	3.03761i		−	0.299305i	−0.988739	−	0.149652i	$-0.952185\pi$
$103$		−	3.03761i		−	0.299305i	0.988739	−	0.149652i	$-0.0478154\pi$
$104$	−0.799665	−	3.51576i	−0.0784136	−	0.344748i
$105$	1.70025	+	1.28938i	0.165927	+	0.125831i
$106$	7.79401	+	4.49987i	0.757021	+	0.437066i
$107$	−11.3525	−	6.55437i	−1.09749	−	0.633635i	−0.161928	−	0.986803i	$-0.551771\pi$
$107$	−11.3525	−	6.55437i	−1.09749	−	0.633635i	−0.935560	+	0.353168i	$0.885105\pi$
$108$	0.961081	−	5.10650i	0.0924801	−	0.491373i
$109$			10.8172i			1.03610i	0.855350	+	0.518051i	$0.173342\pi$
$109$			10.8172i			1.03610i	−0.855350	+	0.518051i	$0.826658\pi$
$110$	1.12669	−	0.650496i	0.107426	−	0.0620224i
$111$	6.54445	+	6.22195i	0.621172	+	0.590562i
$112$	1.56923	+	2.13015i	0.148278	+	0.201280i
$113$	0.251978	−	0.145480i	0.0237041	−	0.0136856i	−0.488101	−	0.872787i	$-0.662310\pi$
$113$	0.251978	−	0.145480i	0.0237041	−	0.0136856i	0.511805	+	0.859102i	$0.328977\pi$
$114$	2.75347	+	0.663740i	0.257886	+	0.0621650i
$115$	1.92127	−	3.32774i	0.179160	−	0.310314i
$116$			4.63455i			0.430307i
$117$	−2.67021	+	10.4819i	−0.246861	+	0.969051i
$118$			10.1723i			0.936440i
$119$	−2.67331	+	0.298826i	−0.245062	+	0.0273934i
$120$	0.189003	−	0.784062i	0.0172535	−	0.0715748i
$121$	1.59690	+	2.76591i	0.145173	+	0.251447i
$122$			12.9839i			1.17551i
$123$	13.5601	+	12.8919i	1.22267	+	1.16242i
$124$	0.973737	+	1.68656i	0.0874441	+	0.151458i
$125$			4.55549i			0.407455i
$126$	−1.27890	−	7.83354i	−0.113933	−	0.697868i
$127$	−1.89703	+	3.28576i	−0.168334	+	0.291564i	−0.937834	−	0.347083i	$-0.887172\pi$
$127$	−1.89703	+	3.28576i	−0.168334	+	0.291564i	0.769500	+	0.638647i	$0.220506\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.18706	−	10.7960i	−0.280605	−	0.950531i
$130$	−0.496074	+	1.60395i	−0.0435086	+	0.140675i
$131$	−8.80601			−0.769384			−0.384692	−	0.923045i	$-0.625692\pi$
$131$	−8.80601			−0.769384			−0.384692	+	0.923045i	$0.625692\pi$
$132$	−4.70452	−	1.13405i	−0.409476	−	0.0987067i
$133$	4.29969	−	0.480625i	0.372830	−	0.0416754i
$134$	−0.308335	+	0.178017i	−0.0266361	+	0.0153783i
$135$	−1.57647	+	1.83549i	−0.135681	+	0.157974i
$136$	0.508355	+	0.880496i	0.0435911	+	0.0755019i
$137$	8.51407	+	14.7468i	0.727407	+	1.25991i	0.957976	+	0.286849i	$0.0926078\pi$
$137$	8.51407	+	14.7468i	0.727407	+	1.25991i	−0.230569	+	0.973056i	$0.574059\pi$
$138$	−13.7082	+	4.04678i	−1.16692	+	0.344485i
$139$	17.3730	−	10.0303i	1.47356	−	0.850757i	0.473998	−	0.880526i	$-0.342810\pi$
$139$	17.3730	−	10.0303i	1.47356	−	0.850757i	0.999557	+	0.0297682i	$0.00947692\pi$
$140$	−0.136860	−	1.22436i	−0.0115668	−	0.103477i
$141$	0.112622	−	0.467203i	0.00948451	−	0.0393456i
$142$	10.0301			0.841707
$143$	9.62397	+	2.97654i	0.804797	+	0.248910i
$144$	−2.51903	+	1.62927i	−0.209919	+	0.135772i
$145$	1.07903	−	1.86893i	0.0896083	−	0.155206i
$146$	−0.730491	+	1.26525i	−0.0604559	+	0.104713i
$147$	−5.91559	−	10.5833i	−0.487910	−	0.872894i
$148$		−	5.21353i		−	0.428549i
$149$	1.91703	+	3.32040i	0.157049	+	0.272017i	0.933803	−	0.357787i	$-0.116469\pi$
$149$	1.91703	+	3.32040i	0.157049	+	0.272017i	−0.776754	+	0.629804i	$0.783135\pi$
$150$	5.70836	−	6.00424i	0.466086	−	0.490244i
$151$		−	20.7448i		−	1.68819i	−0.536197	−	0.844093i	$-0.680140\pi$
$151$		−	20.7448i		−	1.68819i	0.536197	−	0.844093i	$-0.319860\pi$
$152$	−0.817625	−	1.41617i	−0.0663182	−	0.114866i
$153$	−0.154003	−	3.04624i	−0.0124504	−	0.246274i
$154$	−7.34636	+	0.821186i	−0.591987	+	0.0661731i
$155$		−	0.906832i		−	0.0728385i
$156$	5.44815	−	3.05249i	0.436201	−	0.244395i
$157$			6.10387i			0.487142i	0.969883	+	0.243571i	$0.0783189\pi$
$157$			6.10387i			0.487142i	−0.969883	+	0.243571i	$0.921681\pi$
$158$	−2.49063	+	4.31389i	−0.198144	+	0.343195i
$159$	−3.65295	+	15.1540i	−0.289698	+	1.20179i
$160$	−0.403261	+	0.232823i	−0.0318805	+	0.0184062i
$161$	−17.5782	+	12.9494i	−1.38535	+	1.02055i
$162$	8.95411	−	0.907671i	0.703502	−	0.0713134i
$163$	−4.36215	+	2.51849i	−0.341670	+	0.197263i	−0.661010	−	0.750377i	$-0.729872\pi$
$163$	−4.36215	+	2.51849i	−0.341670	+	0.197263i	0.319340	+	0.947640i	$0.396539\pi$
$164$		−	10.8024i		−	0.843527i
$165$	1.63311	+	1.55264i	0.127138	+	0.120873i
$166$	10.6305	+	6.13751i	0.825085	+	0.476363i
$167$	−0.975840	−	0.563401i	−0.0755128	−	0.0435973i	0.461768	−	0.887001i	$-0.347215\pi$
$167$	−0.975840	−	0.563401i	−0.0755128	−	0.0435973i	−0.537281	+	0.843403i	$0.680549\pi$
$168$	−2.76902	+	3.65138i	−0.213634	+	0.281710i
$169$	−11.7211	+	5.62285i	−0.901621	+	0.432527i
$170$		−	0.473426i		−	0.0363101i
$171$	0.247694	+	4.89949i	0.0189416	+	0.374674i
$172$	−3.24949	+	5.62828i	−0.247771	+	0.429152i
$173$	−3.84077	−	6.65242i	−0.292009	−	0.505774i	0.682276	−	0.731095i	$-0.260990\pi$
$173$	−3.84077	−	6.65242i	−0.292009	−	0.505774i	−0.974285	+	0.225321i	$0.927657\pi$
$174$	−7.69881	+	2.27276i	−0.583645	+	0.172297i
$175$	5.07088	−	11.5947i	0.383323	−	0.876478i
$176$	1.39698	+	2.41964i	0.105301	+	0.182387i
$177$	−16.8981	+	4.98846i	−1.27014	+	0.374956i
$178$	−10.1441	+	5.85671i	−0.760334	+	0.438979i
$179$	22.0237	+	12.7154i	1.64613	+	0.950393i	0.978590	+	0.205819i	$0.0659858\pi$
$179$	22.0237	+	12.7154i	1.64613	+	0.950393i	0.667540	+	0.744574i	$0.267348\pi$
$180$	1.39515	−	0.0705321i	0.103989	−	0.00525715i
$181$		−	0.270132i		−	0.0200788i	−0.999950	−	0.0100394i	$-0.996804\pi$
$181$		−	0.270132i		−	0.0200788i	0.999950	−	0.0100394i	$-0.00319569\pi$
$182$	6.23423	−	7.22042i	0.462112	−	0.535213i
$183$	−21.5686	+	6.36725i	−1.59440	+	0.470681i
$184$	7.14652	+	4.12605i	0.526848	+	0.304176i
$185$	−1.21383	+	2.10241i	−0.0892423	+	0.154572i
$186$	−2.32416	+	2.44463i	−0.170416	+	0.179249i
$187$	−2.84064			−0.207728
$188$	−0.240293	+	0.138733i	−0.0175252	+	0.0101182i
$189$	12.3858	−	5.96600i	0.900931	−	0.433963i
$190$			0.761446i			0.0552411i
$191$	5.43711	−	3.13912i	0.393415	−	0.227138i	−0.290224	−	0.956959i	$-0.593730\pi$
$191$	5.43711	−	3.13912i	0.393415	−	0.227138i	0.683639	+	0.729820i	$0.260396\pi$
$192$	1.68382	+	0.405895i	0.121519	+	0.0292930i
$193$	6.96974	+	4.02398i	0.501693	+	0.289653i	0.729413	−	0.684074i	$-0.239794\pi$
$193$	6.96974	+	4.02398i	0.501693	+	0.289653i	−0.227719	+	0.973727i	$0.573127\pi$
$194$	−15.6574			−1.12414
$195$	−2.90771	−	0.0375014i	−0.208226	−	0.00268553i
$196$	−2.07506	+	6.68537i	−0.148219	+	0.477526i
$197$	5.68452	−	9.84588i	0.405005	−	0.701490i	−0.589317	−	0.807902i	$-0.700603\pi$
$197$	5.68452	−	9.84588i	0.405005	−	0.701490i	0.994322	+	0.106412i	$0.0339364\pi$
$198$	−0.423205	−	8.37118i	−0.0300759	−	0.594914i
$199$	−3.95997	+	2.28629i	−0.280715	+	0.162071i	−0.633747	−	0.773540i	$-0.718484\pi$
$199$	−3.95997	+	2.28629i	−0.280715	+	0.162071i	0.353032	+	0.935611i	$0.385151\pi$
$200$	−4.78317			−0.338222
$201$	−0.446924	−	0.424900i	−0.0315236	−	0.0299702i
$202$	−2.03145	−	3.51858i	−0.142932	−	0.247566i
$203$	−9.87227	+	7.27265i	−0.692898	+	0.510440i
$204$	−1.21337	+	1.27626i	−0.0849527	+	0.0893560i
$205$	−2.51505	+	4.35619i	−0.175658	+	0.304249i
$206$	−2.63065	−	1.51881i	−0.183286	−	0.105820i
$207$	−13.4448	−	20.7872i	−0.934481	−	1.44481i
$208$	−3.44457	−	1.06535i	−0.238838	−	0.0738686i
$209$	4.56882			0.316032
$210$	1.96676	−	0.827766i	0.135719	−	0.0571213i
$211$	5.13457	−	8.89333i	0.353478	−	0.612242i	−0.633378	−	0.773843i	$-0.718332\pi$
$211$	5.13457	−	8.89333i	0.353478	−	0.612242i	0.986856	+	0.161600i	$0.0516655\pi$
$212$	7.79401	−	4.49987i	0.535295	−	0.309053i
$213$	4.91870	+	16.6618i	0.337024	+	1.14165i
$214$	−11.3525	+	6.55437i	−0.776041	+	0.448048i
$215$	2.62078	−	1.51311i	0.178736	−	0.103193i
$216$	−3.94182	−	3.38557i	−0.268207	−	0.230359i
$217$	−2.06461	+	4.72080i	−0.140155	+	0.320469i
$218$	9.36799	+	5.40861i	0.634481	+	0.366318i
$219$	−2.46003	−	0.593006i	−0.166234	−	0.0400716i
$220$		−	1.30099i		−	0.0877129i
$221$	2.68910	−	2.49135i	0.180888	−	0.167587i
$222$	8.66060	−	2.55668i	0.581261	−	0.171593i
$223$	8.20296	−	14.2079i	0.549311	−	0.951434i	−0.449011	−	0.893526i	$-0.648224\pi$
$223$	8.20296	−	14.2079i	0.549311	−	0.951434i	0.998322	−	0.0579082i	$-0.0184431\pi$
$224$	2.62938	−	0.293915i	0.175683	−	0.0196380i
$225$	12.7735	+	6.53816i	0.851564	+	0.435877i
$226$		−	0.290959i		−	0.0193543i
$227$	23.5487	−	13.5958i	1.56298	−	0.902387i	0.566027	−	0.824386i	$-0.308480\pi$
$227$	23.5487	−	13.5958i	1.56298	−	0.902387i	0.996953	−	0.0780009i	$-0.0248537\pi$
$228$	1.95155	−	2.05270i	0.129245	−	0.135944i
$229$	−5.93616			−0.392272			−0.196136	−	0.980577i	$-0.562839\pi$
$229$	−5.93616			−0.392272			−0.196136	+	0.980577i	$0.562839\pi$
$230$	−1.92127	−	3.32774i	−0.126685	−	0.219425i
$231$	−4.96675	−	11.8009i	−0.326788	−	0.776443i
$232$	4.01364	+	2.31727i	0.263508	+	0.152136i
$233$		−	19.9017i		−	1.30380i	−0.758303	−	0.651902i	$-0.773971\pi$
$233$		−	19.9017i		−	1.30380i	0.758303	−	0.651902i	$-0.226029\pi$
$234$	7.74247	+	7.55342i	0.506141	+	0.493782i
$235$	0.129201			0.00842814
$236$	8.80951	+	5.08617i	0.573450	+	0.331082i
$237$	−8.38754	−	2.02187i	−0.544829	−	0.131334i
$238$	−1.07786	+	2.46457i	−0.0698676	+	0.159754i
$239$	−5.37098			−0.347420			−0.173710	−	0.984797i	$-0.555576\pi$
$239$	−5.37098			−0.347420			−0.173710	+	0.984797i	$0.555576\pi$
$240$	−0.584516	−	0.555713i	−0.0377304	−	0.0358711i
$241$	4.43996	+	7.69024i	0.286003	+	0.495372i	0.972852	−	0.231428i	$-0.0743399\pi$
$241$	4.43996	+	7.69024i	0.286003	+	0.495372i	−0.686849	+	0.726800i	$0.741007\pi$
$242$	3.19380			0.205305
$243$	5.89885	+	14.4293i	0.378411	+	0.925638i
$244$	11.2444	+	6.49197i	0.719850	+	0.415606i
$245$	2.39329	−	2.21282i	0.152902	−	0.141372i
$246$	17.9447	−	5.29745i	1.14411	−	0.337753i
$247$	−4.32508	+	4.00703i	−0.275198	+	0.254961i
$248$	1.94747			0.123665
$249$	−4.98237	+	20.6689i	−0.315745	+	1.30984i
$250$	3.94517	+	2.27774i	0.249514	+	0.144057i
$251$	−4.21323	−	7.29753i	−0.265937	−	0.460616i	0.701872	−	0.712303i	$-0.252348\pi$
$251$	−4.21323	−	7.29753i	−0.265937	−	0.460616i	−0.967809	+	0.251687i	$0.919015\pi$
$252$	−7.42350	−	2.80922i	−0.467636	−	0.176964i
$253$	−19.9671	+	11.5280i	−1.25532	+	0.724759i
$254$	1.89703	+	3.28576i	0.119030	+	0.206167i
$255$	0.786445	−	0.232165i	0.0492491	−	0.0145388i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.3361	−	19.6348i	0.707129	−	1.22478i	−0.258788	−	0.965934i	$-0.583323\pi$
$257$	11.3361	−	19.6348i	0.707129	−	1.22478i	0.965918	−	0.258850i	$-0.0833435\pi$
$258$	−10.9431	−	2.63790i	−0.681288	−	0.164229i
$259$	11.1056	−	8.18120i	0.690067	−	0.508355i
$260$	1.14102	+	1.23159i	0.0707631	+	0.0763797i
$261$	−7.55091	−	11.6745i	−0.467389	−	0.722636i
$262$	−4.40300	+	7.62623i	−0.272018	+	0.471150i
$263$	1.77900	+	1.02711i	0.109698	+	0.0633341i	0.553845	−	0.832620i	$-0.313160\pi$
$263$	1.77900	+	1.02711i	0.109698	+	0.0633341i	−0.444147	+	0.895954i	$0.646493\pi$
$264$	−3.33438	+	3.50721i	−0.205217	+	0.215854i
$265$	−4.19069			−0.257432
$266$	1.73361	−	3.96395i	0.106294	−	0.243045i
$267$	−14.7037	−	13.9791i	−0.899850	−	0.855507i
$268$			0.356034i			0.0217483i
$269$	−8.39939	−	14.5482i	−0.512120	−	0.887018i	−0.999901	−	0.0140519i	$-0.995527\pi$
$269$	−8.39939	−	14.5482i	−0.512120	−	0.887018i	0.487781	−	0.872966i	$-0.337806\pi$
$270$	0.801342	+	2.28301i	0.0487681	+	0.138940i
$271$	15.4047	−	26.6817i	0.935767	−	1.62080i	0.162507	−	0.986707i	$-0.448042\pi$
$271$	15.4047	−	26.6817i	0.935767	−	1.62080i	0.773260	−	0.634089i	$-0.218625\pi$
$272$	1.01671			0.0616471
$273$	15.0516	+	6.81531i	0.910966	+	0.412481i
$274$	17.0281			1.02871
$275$	6.68199	−	11.5736i	0.402939	−	0.697911i
$276$	−3.34948	+	13.8950i	−0.201615	+	0.836383i
$277$	5.58729	+	9.67746i	0.335708	+	0.581462i	0.983620	−	0.180252i	$-0.0576913\pi$
$277$	5.58729	+	9.67746i	0.335708	+	0.581462i	−0.647913	+	0.761714i	$0.724358\pi$
$278$		−	20.0606i		−	1.20315i
$279$	−5.20072	−	2.66202i	−0.311359	−	0.159371i
$280$	−1.12875	−	0.493654i	−0.0674559	−	0.0295014i
$281$	5.68985			0.339428			0.169714	−	0.985493i	$-0.445716\pi$
$281$	5.68985			0.339428			0.169714	+	0.985493i	$0.445716\pi$
$282$	−0.348299	−	0.331135i	−0.0207409	−	0.0197188i
$283$	−12.9779	−	7.49278i	−0.771455	−	0.445400i	0.0619386	−	0.998080i	$-0.480272\pi$
$283$	−12.9779	−	7.49278i	−0.771455	−	0.445400i	−0.833393	+	0.552680i	$0.813605\pi$
$284$	5.01505	−	8.68632i	0.297588	−	0.515438i
$285$	−1.26490	+	0.373409i	−0.0749261	+	0.0221188i
$286$	7.38974	−	6.84634i	0.436965	−	0.404832i
$287$	23.0107	−	16.9514i	1.35828	−	1.00061i
$288$	0.151472	+	2.99617i	0.00892555	+	0.176551i
$289$	7.98315	−	13.8272i	0.469597	−	0.813366i
$290$	−1.07903	−	1.86893i	−0.0633626	−	0.109747i
$291$	−7.67831	−	26.0098i	−0.450111	−	1.52472i
$292$	0.730491	+	1.26525i	0.0427488	+	0.0740431i
$293$	−17.5737	+	10.1462i	−1.02667	+	0.592747i	−0.916028	−	0.401113i	$-0.868623\pi$
$293$	−17.5737	+	10.1462i	−1.02667	+	0.592747i	−0.110640	+	0.993861i	$0.535290\pi$
$294$	−12.1232	−	0.168583i	−0.707038	−	0.00983197i
$295$	−2.36835	−	4.10210i	−0.137891	−	0.238834i
$296$	−4.51505	−	2.60676i	−0.262432	−	0.151515i
$297$	13.6985	−	4.80820i	0.794867	−	0.279000i
$298$	3.83406			0.222101
$299$	8.79134	−	28.4249i	0.508417	−	1.64385i
$300$	−2.34564	−	7.94571i	−0.135426	−	0.458746i
$301$	−17.0882	+	1.91015i	−0.984950	+	0.110099i
$302$	−17.9655	−	10.3724i	−1.03380	−	0.596864i
$303$	4.84877	−	5.10009i	0.278555	−	0.292993i
$304$	−1.63525			−0.0937881
$305$	−3.02295	−	5.23591i	−0.173094	−	0.299807i
$306$	−2.71512	−	1.38975i	−0.155213	−	0.0794467i
$307$	11.0362			0.629869			0.314935	−	0.949113i	$-0.398017\pi$
$307$	11.0362			0.629869			0.314935	+	0.949113i	$0.398017\pi$
$308$	−2.96201	+	6.77273i	−0.168776	+	0.385912i
$309$	1.23295	−	5.11479i	0.0701402	−	0.290970i
$310$	−0.785339	−	0.453416i	−0.0446043	−	0.0257523i
$311$	−21.6017			−1.22492			−0.612460	−	0.790502i	$-0.709820\pi$
$311$	−21.6017			−1.22492			−0.612460	+	0.790502i	$0.709820\pi$
$312$	0.0805363	−	6.24448i	0.00455947	−	0.353524i
$313$		−	3.56747i		−	0.201645i	−0.994904	−	0.100823i	$-0.967853\pi$
$313$		−	3.56747i		−	0.201645i	0.994904	−	0.100823i	$-0.0321474\pi$
$314$	5.28611	+	3.05194i	0.298312	+	0.172231i
$315$	2.33955	+	2.86120i	0.131819	+	0.161211i
$316$	2.49063	+	4.31389i	0.140109	+	0.242676i
$317$	−21.5505			−1.21040			−0.605199	−	0.796074i	$-0.706907\pi$
$317$	−21.5505			−1.21040			−0.605199	+	0.796074i	$0.706907\pi$
$318$	11.2972	+	10.7405i	0.633517	+	0.602299i
$319$	−11.2139	+	6.47436i	−0.627859	+	0.362495i
$320$			0.465645i			0.0260304i
$321$	−16.4552	−	15.6443i	−0.918439	−	0.873180i
$322$	2.42541	+	21.6978i	0.135163	+	1.20917i
$323$	0.831288	−	1.43983i	0.0462541	−	0.0801144i
$324$	3.69099	−	8.20832i	0.205055	−	0.456018i
$325$	3.82494	+	16.8165i	0.212169	+	0.932810i
$326$			5.03698i			0.278973i
$327$	−4.39066	+	18.2143i	−0.242804	+	1.00725i
$328$	−9.35517	−	5.40121i	−0.516553	−	0.298232i
$329$	−0.672596	−	0.294156i	−0.0370814	−	0.0162173i
$330$	2.16118	−	0.638000i	0.118969	−	0.0351207i
$331$	26.3507	−	15.2136i	1.44836	−	0.836214i	0.449980	−	0.893039i	$-0.351431\pi$
$331$	26.3507	−	15.2136i	1.44836	−	0.836214i	0.998384	+	0.0568249i	$0.0180977\pi$
$332$	10.6305	−	6.13751i	0.583423	−	0.336839i
$333$	8.49422	+	13.1330i	0.465480	+	0.719685i
$334$	−0.975840	+	0.563401i	−0.0533956	+	0.0308280i
$335$	0.0828928	−	0.143575i	0.00452892	−	0.00784432i
$336$	1.77768	+	4.22373i	0.0969802	+	0.230423i
$337$	−19.4209			−1.05793			−0.528963	−	0.848645i	$-0.677419\pi$
$337$	−19.4209			−1.05793			−0.528963	+	0.848645i	$0.677419\pi$
$338$	−0.991003	+	12.9622i	−0.0539035	+	0.705049i
$339$	0.483335	−	0.142685i	0.0262512	−	0.00774957i
$340$	−0.409999	−	0.236713i	−0.0222353	−	0.0128376i
$341$	−2.72058	+	4.71218i	−0.147328	+	0.255179i
$342$	4.36693	+	2.23524i	0.236137	+	0.120868i
$343$	−17.4971	+	6.07065i	−0.944753	+	0.327785i
$344$	3.24949	+	5.62828i	0.175201	+	0.303456i
$345$	4.58579	−	4.82348i	0.246891	−	0.259688i
$346$	−7.68155			−0.412963
$347$	13.6612	−	7.88727i	0.733369	−	0.423411i	−0.0862842	−	0.996271i	$-0.527499\pi$
$347$	13.6612	−	7.88727i	0.733369	−	0.423411i	0.819654	+	0.572860i	$0.194166\pi$
$348$	−1.88114	+	7.80374i	−0.100840	+	0.418324i
$349$	−2.93182	+	5.07806i	−0.156937	+	0.271822i	−0.933762	−	0.357893i	$-0.883495\pi$
$349$	−2.93182	+	5.07806i	−0.156937	+	0.271822i	0.776826	+	0.629715i	$0.216828\pi$
$350$	−7.50588	−	10.1889i	−0.401206	−	0.544618i
$351$	−8.75070	+	16.5658i	−0.467078	+	0.884216i
$352$	2.79396			0.148918
$353$	27.1942	+	15.7006i	1.44740	+	0.835657i	0.998326	−	0.0578380i	$-0.0184207\pi$
$353$	27.1942	+	15.7006i	1.44740	+	0.835657i	0.449074	+	0.893495i	$0.351754\pi$
$354$	−4.12890	+	17.1284i	−0.219449	+	0.910364i
$355$	−4.04474	+	2.33523i	−0.214673	+	0.123941i
$356$			11.7134i			0.620810i
$357$	−4.62267	−	0.581914i	−0.244657	−	0.0307982i
$358$	22.0237	−	12.7154i	1.16399	−	0.672030i
$359$	8.80708			0.464820			0.232410	−	0.972618i	$-0.425339\pi$
$359$	8.80708			0.464820			0.232410	+	0.972618i	$0.425339\pi$
$360$	0.636494	−	1.24350i	0.0335462	−	0.0655384i
$361$	8.16298	−	14.1387i	0.429630	−	0.744142i
$362$	−0.233942	−	0.135066i	−0.0122957	−	0.00709892i
$363$	1.56622	+	5.30547i	0.0822054	+	0.278465i
$364$	−3.13595	−	9.00921i	−0.164369	−	0.472211i
$365$		−	0.680300i		−	0.0356085i
$366$	−5.27012	+	21.8626i	−0.275473	+	1.14278i
$367$	−3.96802	−	2.29094i	−0.207129	−	0.119586i	0.392847	−	0.919604i	$-0.371490\pi$
$367$	−3.96802	−	2.29094i	−0.207129	−	0.119586i	−0.599977	+	0.800018i	$0.704823\pi$
$368$	7.14652	−	4.12605i	0.372538	−	0.215085i
$369$	17.6000	+	27.2116i	0.916219	+	1.41658i
$370$	1.21383	+	2.10241i	0.0631038	+	0.109299i
$371$	21.8160	+	9.54108i	1.13263	+	0.495348i
$372$	0.955030	+	3.23510i	0.0495160	+	0.167732i
$373$	−13.5242	−	23.4245i	−0.700254	−	1.21288i	−0.968377	−	0.249491i	$-0.919737\pi$
$373$	−13.5242	−	23.4245i	−0.700254	−	1.21288i	0.268123	−	0.963385i	$-0.413597\pi$
$374$	−1.42032	+	2.46007i	−0.0734431	+	0.127207i
$375$	−1.84905	+	7.67062i	−0.0954845	+	0.396109i
$376$			0.277466i			0.0143092i
$377$	4.93740	−	15.9640i	0.254289	−	0.822188i
$378$	1.02617	−	13.7094i	0.0527803	−	0.705134i
$379$	5.46704	+	3.15640i	0.280823	+	0.162133i	0.633796	−	0.773500i	$-0.281496\pi$
$379$	5.46704	+	3.15640i	0.280823	+	0.162133i	−0.352973	+	0.935634i	$0.614829\pi$
$380$	0.659432	+	0.380723i	0.0338281	+	0.0195307i
$381$	−4.52793	+	4.76263i	−0.231973	+	0.243997i
$382$		−	6.27823i		−	0.321222i
$383$	9.19749	−	5.31017i	0.469970	−	0.271337i	−0.246257	−	0.969205i	$-0.579201\pi$
$383$	9.19749	−	5.31017i	0.469970	−	0.271337i	0.716227	+	0.697867i	$0.245867\pi$
$384$	1.19343	−	1.25528i	0.0609017	−	0.0640584i
$385$	2.77131	−	2.04155i	0.141239	−	0.104047i
$386$	6.96974	−	4.02398i	0.354751	−	0.204815i
$387$	−0.984411	−	19.4721i	−0.0500404	−	0.989820i
$388$	−7.82871	+	13.5597i	−0.397443	+	0.688391i
$389$			9.76203i			0.494955i	0.968894	+	0.247477i	$0.0796016\pi$
$389$			9.76203i			0.494955i	−0.968894	+	0.247477i	$0.920398\pi$
$390$	−1.48633	+	2.49940i	−0.0752634	+	0.126562i
$391$			8.38998i			0.424300i
$392$	4.75217	+	5.13974i	0.240021	+	0.259596i
$393$	−14.8277	−	3.57432i	−0.747960	−	0.180300i
$394$	−5.68452	−	9.84588i	−0.286382	−	0.496028i
$395$		−	2.31950i		−	0.116707i
$396$	−7.46126	−	3.81908i	−0.374942	−	0.191916i
$397$	0.0876790	+	0.151865i	0.00440048	+	0.00762186i	0.868217	−	0.496184i	$-0.165266\pi$
$397$	0.0876790	+	0.151865i	0.00440048	+	0.00762186i	−0.863817	+	0.503806i	$0.831933\pi$
$398$			4.57258i			0.229203i
$399$	7.43498	+	0.935937i	0.372215	+	0.0468554i
$400$	−2.39159	+	4.14235i	−0.119579	+	0.207118i
$401$	−1.96794	+	3.40858i	−0.0982743	+	0.170216i	−0.910970	−	0.412472i	$-0.864666\pi$
$401$	−1.96794	+	3.40858i	−0.0982743	+	0.170216i	0.812696	+	0.582688i	$0.197999\pi$
$402$	−0.591437	+	0.174597i	−0.0294982	+	0.00870812i
$403$	−1.55733	−	6.84684i	−0.0775759	−	0.341065i
$404$	−4.06290			−0.202137
$405$	−3.39951	+	2.45075i	−0.168923	+	0.121779i
$406$	1.36216	+	12.1860i	0.0676030	+	0.604779i
$407$	12.6148	−	7.28319i	0.625295	−	0.361014i
$408$	0.498589	+	1.68894i	0.0246838	+	0.0836148i
$409$	11.5132	+	19.9414i	0.569290	+	0.986038i	0.996636	+	0.0819507i	$0.0261150\pi$
$409$	11.5132	+	19.9414i	0.569290	+	0.986038i	−0.427347	+	0.904088i	$0.640552\pi$
$410$	2.51505	+	4.35619i	0.124209	+	0.215137i
$411$	8.35051	+	28.2868i	0.411900	+	1.39528i
$412$	−2.63065	+	1.51881i	−0.129603	+	0.0748262i
$413$	2.98980	+	26.7469i	0.147119	+	1.31613i
$414$	−24.7247	+	1.24996i	−1.21515	+	0.0614321i
$415$	−5.71580			−0.280578
$416$	−2.64490	+	2.45041i	−0.129677	+	0.120141i
$417$	33.3242	−	9.83759i	1.63189	−	0.481749i
$418$	2.28441	−	3.95671i	0.111734	−	0.193529i
$419$	−12.5535	+	21.7434i	−0.613280	+	1.06223i	0.377403	+	0.926049i	$0.376817\pi$
$419$	−12.5535	+	21.7434i	−0.613280	+	1.06223i	−0.990684	+	0.136184i	$0.956516\pi$
$420$	0.266512	−	2.11715i	0.0130045	−	0.103306i
$421$			22.3849i			1.09097i	0.838120	+	0.545486i	$0.183655\pi$
$421$			22.3849i			1.09097i	−0.838120	+	0.545486i	$0.816345\pi$
$422$	−5.13457	−	8.89333i	−0.249947	−	0.432921i
$423$	0.379271	−	0.740974i	0.0184408	−	0.0360274i
$424$		−	8.99975i		−	0.437066i
$425$	−2.43155	−	4.21157i	−0.117947	−	0.204291i
$426$	16.8889	+	4.07117i	0.818268	+	0.197249i
$427$	3.81617	+	34.1396i	0.184678	+	1.65213i
$428$			13.1087i			0.633635i
$429$	14.9969	+	8.91827i	0.724056	+	0.430578i
$430$		−	3.02622i		−	0.145937i
$431$	−10.8170	+	18.7355i	−0.521035	+	0.902459i	0.478666	+	0.877997i	$0.341121\pi$
$431$	−10.8170	+	18.7355i	−0.521035	+	0.902459i	−0.999701	+	0.0244617i	$0.992213\pi$
$432$	−4.90290	+	1.72093i	−0.235891	+	0.0827982i
$433$	−9.15166	+	5.28372i	−0.439801	+	0.253919i	−0.703513	−	0.710682i	$-0.748386\pi$
$433$	−9.15166	+	5.28372i	−0.439801	+	0.253919i	0.263712	+	0.964601i	$0.415053\pi$
$434$	3.05603	+	4.14841i	0.146694	+	0.199130i
$435$	2.57548	−	2.70897i	0.123485	−	0.129885i
$436$	9.36799	−	5.40861i	0.448646	−	0.259026i
$437$		−	13.4942i		−	0.645517i
$438$	−1.74357	+	1.83395i	−0.0833112	+	0.0876294i
$439$	−28.4269	−	16.4123i	−1.35674	−	0.783316i	−0.367560	−	0.930000i	$-0.619807\pi$
$439$	−28.4269	−	16.4123i	−1.35674	−	0.783316i	−0.989183	+	0.146684i	$0.953140\pi$
$440$	−1.12669	−	0.650496i	−0.0537130	−	0.0310112i
$441$	−5.66509	−	20.2214i	−0.269766	−	0.962926i
$442$	−0.813027	−	3.57450i	−0.0386718	−	0.170022i
$443$			32.8664i			1.56153i	0.624826	+	0.780764i	$0.285170\pi$
$443$			32.8664i			1.56153i	−0.624826	+	0.780764i	$0.714830\pi$
$444$	2.11614	−	8.77864i	0.100428	−	0.416616i
$445$	2.72715	−	4.72356i	0.129279	−	0.223918i
$446$	−8.20296	−	14.2079i	−0.388421	−	0.672766i
$447$	1.88020	+	6.36906i	0.0889305	+	0.301246i
$448$	1.06015	−	2.42406i	0.0500874	−	0.114526i
$449$	2.61300	+	4.52584i	0.123315	+	0.213588i	0.921073	−	0.389390i	$-0.127314\pi$
$449$	2.61300	+	4.52584i	0.123315	+	0.213588i	−0.797758	+	0.602978i	$0.793981\pi$
$450$	12.0489	−	7.79306i	0.567993	−	0.367368i
$451$	26.1379	−	15.0907i	1.23079	−	0.710596i
$452$	−0.251978	−	0.145480i	−0.0118521	−	0.00684279i
$453$	8.42020	−	34.9305i	0.395616	−	1.64118i
$454$		−	27.1917i		−	1.27617i
$455$	−0.832941	+	4.36318i	−0.0390489	+	0.204549i
$456$	−0.801918	−	2.71644i	−0.0375532	−	0.127209i
$457$	−30.3072	−	17.4979i	−1.41771	−	0.818517i	−0.421615	−	0.906775i	$-0.638537\pi$
$457$	−30.3072	−	17.4979i	−1.41771	−	0.818517i	−0.996098	+	0.0882584i	$0.971870\pi$
$458$	−2.96808	+	5.14086i	−0.138689	+	0.240217i
$459$	0.977141	−	5.19183i	0.0456090	−	0.242334i
$460$	−3.84255			−0.179160
$461$	19.3938	−	11.1970i	0.903260	−	0.521498i	0.0250037	−	0.999687i	$-0.492040\pi$
$461$	19.3938	−	11.1970i	0.903260	−	0.521498i	0.878256	+	0.478190i	$0.158707\pi$
$462$	−12.7033	−	1.59912i	−0.591009	−	0.0743979i
$463$			16.1024i			0.748340i	0.927360	+	0.374170i	$0.122072\pi$
$463$			16.1024i			0.748340i	−0.927360	+	0.374170i	$0.877928\pi$
$464$	4.01364	−	2.31727i	0.186328	−	0.107577i
$465$	0.368078	−	1.52694i	0.0170692	−	0.0708102i
$466$	−17.2354	−	9.95086i	−0.798414	−	0.460965i
$467$	−32.1440			−1.48745			−0.743723	−	0.668488i	$-0.766942\pi$
$467$	−32.1440			−1.48745			−0.743723	+	0.668488i	$0.766942\pi$
$468$	10.4127	−	2.92847i	0.481327	−	0.135369i
$469$	−0.758406	+	0.558698i	−0.0350199	+	0.0257983i
$470$	0.0646004	−	0.111891i	0.00297980	−	0.00516116i
$471$	−2.47753	+	10.2778i	−0.114159	+	0.473577i
$472$	8.80951	−	5.08617i	0.405490	−	0.234110i
$473$	−18.1579			−0.834899
$474$	−5.94476	+	6.25289i	−0.273052	+	0.287205i
$475$	3.91084	+	6.77378i	0.179442	+	0.310802i
$476$	1.59545	+	2.16574i	0.0731272	+	0.0992666i
$477$	−12.3018	+	24.0338i	−0.563262	+	1.10043i
$478$	−2.68549	+	4.65141i	−0.122831	+	0.212750i
$479$	0.698448	+	0.403249i	0.0319129	+	0.0184249i	0.515872	−	0.856666i	$-0.327468\pi$
$479$	0.698448	+	0.403249i	0.0319129	+	0.0184249i	−0.483959	+	0.875091i	$0.660802\pi$
$480$	−0.773520	+	0.228350i	−0.0353062	+	0.0104227i
$481$	−5.55422	+	17.9583i	−0.253251	+	0.818830i
$482$	8.87993			0.404470
$483$	−34.8546	+	14.6695i	−1.58594	+	0.667487i
$484$	1.59690	−	2.76591i	0.0725864	−	0.125723i
$485$	6.31402	−	3.64540i	0.286705	−	0.165529i
$486$	15.4455	+	2.10608i	0.700624	+	0.0955336i
$487$	7.32472	−	4.22893i	0.331915	−	0.191631i	−0.324776	−	0.945791i	$-0.605289\pi$
$487$	7.32472	−	4.22893i	0.331915	−	0.191631i	0.656691	+	0.754160i	$0.271956\pi$
$488$	11.2444	−	6.49197i	0.509011	−	0.293878i
$489$	−8.36732	+	2.47011i	−0.378383	+	0.111702i
$490$	−0.719713	−	3.17907i	−0.0325133	−	0.143616i
$491$	4.29055	+	2.47715i	0.193630	+	0.111792i	0.593681	−	0.804701i	$-0.297674\pi$
$491$	4.29055	+	2.47715i	0.193630	+	0.111792i	−0.400051	+	0.916493i	$0.631008\pi$
$492$	4.38465	−	18.1893i	0.197675	−	0.820038i
$493$			4.71199i			0.212217i
$494$	1.30765	+	5.74914i	0.0588341	+	0.258666i
$495$	2.11966	+	3.27724i	0.0952717	+	0.147301i
$496$	0.973737	−	1.68656i	0.0437221	−	0.0757288i
$497$	26.3729	−	2.94799i	1.18299	−	0.132236i
$498$	15.4086	+	14.6493i	0.690477	+	0.656451i
$499$		−	10.4075i		−	0.465906i	−0.972488	−	0.232953i	$-0.925161\pi$
$499$		−	10.4075i		−	0.465906i	0.972488	−	0.232953i	$-0.0748388\pi$
$500$	3.94517	−	2.27774i	0.176433	−	0.101864i
$501$	−1.41446	−	1.34476i	−0.0631933	−	0.0600792i
$502$	−8.42646			−0.376091
$503$	−2.19872	−	3.80829i	−0.0980359	−	0.169803i	0.812836	−	0.582493i	$-0.197923\pi$
$503$	−2.19872	−	3.80829i	−0.0980359	−	0.169803i	−0.910872	+	0.412690i	$0.864589\pi$
$504$	−6.14460	+	5.02433i	−0.273702	+	0.223801i
$505$	1.63841	+	0.945936i	0.0729082	+	0.0420936i
$506$			23.0560i			1.02496i
$507$	−22.0185	+	4.71034i	−0.977874	+	0.209194i
$508$	3.79407			0.168334
$509$	−14.7836	−	8.53531i	−0.655271	−	0.378321i	0.135202	−	0.990818i	$-0.456832\pi$
$509$	−14.7836	−	8.53531i	−0.655271	−	0.378321i	−0.790473	+	0.612497i	$0.790165\pi$
$510$	0.192161	−	0.797164i	0.00850904	−	0.0352990i
$511$	−1.54886	+	3.54151i	−0.0685176	+	0.156667i
$512$	−1.00000			−0.0441942
$513$	−1.57161	+	8.35040i	−0.0693882	+	0.368679i
$514$	−11.3361	−	19.6348i	−0.500016	−	0.866053i
$515$	1.41445			0.0623281
$516$	−7.75604	+	8.15805i	−0.341441	+	0.359138i
$517$	−0.671368	−	0.387615i	−0.0295267	−	0.0170473i
$518$	−1.53233	−	13.7083i	−0.0673269	−	0.602309i
$519$	−3.76699	−	12.7604i	−0.165352	−	0.560120i
$520$	1.63709	−	0.372360i	0.0717913	−	0.0163291i
$521$	−36.0935			−1.58128			−0.790642	−	0.612279i	$-0.790253\pi$
$521$	−36.0935			−1.58128			−0.790642	+	0.612279i	$0.790253\pi$
$522$	−13.8859	+	0.702003i	−0.607770	+	0.0307258i
$523$	17.5784	+	10.1489i	0.768648	+	0.443779i	0.832392	−	0.554187i	$-0.186971\pi$
$523$	17.5784	+	10.1489i	0.768648	+	0.443779i	−0.0637443	+	0.997966i	$0.520304\pi$
$524$	4.40300	+	7.62623i	0.192346	+	0.333153i
$525$	13.2447	−	17.4652i	0.578046	−	0.762242i
$526$	1.77900	−	1.02711i	0.0775681	−	0.0447840i
$527$	0.990008	+	1.71474i	0.0431254	+	0.0746954i
$528$	1.37014	+	4.64126i	0.0596277	+	0.201985i
$529$	22.5485	+	39.0551i	0.980370	+	1.69805i
$530$	−2.09534	+	3.62924i	−0.0910160	+	0.157644i
$531$	−30.4781	+	1.54082i	−1.32264	+	0.0668660i
$532$	−2.56608	−	3.48333i	−0.111254	−	0.151021i
$533$	−11.5083	+	37.2096i	−0.498481	+	1.61173i
$534$	−19.4581	+	5.74420i	−0.842034	+	0.248576i
$535$	3.05201	−	5.28624i	0.131950	−	0.228544i
$536$	0.308335	+	0.178017i	0.0133180	+	0.00768917i
$537$	31.9228	+	30.3498i	1.37757	+	1.30969i
$538$	−16.7988			−0.724247
$539$	−19.0750	+	4.31841i	−0.821618	+	0.186007i
$540$	2.37782	+	0.447523i	0.102325	+	0.0192583i
$541$			27.0224i			1.16178i	0.813981	+	0.580892i	$0.197296\pi$
$541$			27.0224i			1.16178i	−0.813981	+	0.580892i	$0.802704\pi$
$542$	−15.4047	−	26.6817i	−0.661687	−	1.14608i
$543$	0.109645	−	0.454854i	0.00470534	−	0.0195197i
$544$	0.508355	−	0.880496i	0.0217955	−	0.0377510i
$545$	−5.03699			−0.215761
$546$	13.4280	−	9.62744i	0.574667	−	0.412016i
$547$	−9.23401			−0.394818			−0.197409	−	0.980321i	$-0.563253\pi$
$547$	−9.23401			−0.394818			−0.197409	+	0.980321i	$0.563253\pi$
$548$	8.51407	−	14.7468i	0.363703	−	0.629953i
$549$	−38.9021	+	1.96670i	−1.66030	+	0.0839366i
$550$	−6.68199	−	11.5736i	−0.284921	−	0.493498i
$551$		−	7.57865i		−	0.322861i
$552$	10.3587	+	9.84825i	0.440896	+	0.419170i
$553$	−5.28088	+	12.0749i	−0.224566	+	0.513476i
$554$	11.1746			0.474762
$555$	−2.89722	+	3.04739i	−0.122980	+	0.129355i
$556$	−17.3730	−	10.0303i	−0.736778	−	0.425379i
$557$	18.5481	−	32.1263i	0.785910	−	1.36124i	−0.142544	−	0.989788i	$-0.545528\pi$
$557$	18.5481	−	32.1263i	0.785910	−	1.36124i	0.928454	−	0.371447i	$-0.121138\pi$
$558$	−4.90574	+	3.17295i	−0.207676	+	0.134322i
$559$	17.1891	−	15.9251i	0.727023	−	0.673562i
$560$	−0.991893	+	0.730702i	−0.0419151	+	0.0308778i
$561$	−4.78313	−	1.15300i	−0.201944	−	0.0486798i
$562$	2.84492	−	4.92755i	0.120006	−	0.207856i
$563$	−10.9911	−	19.0372i	−0.463220	−	0.802321i	0.535899	−	0.844282i	$-0.319973\pi$
$563$	−10.9911	−	19.0372i	−0.463220	−	0.802321i	−0.999119	+	0.0419612i	$0.986639\pi$
$564$	−0.460921	+	0.136068i	−0.0194083	+	0.00572950i
$565$	0.0677419	+	0.117332i	0.00284992	+	0.00493621i
$566$	−12.9779	+	7.49278i	−0.545501	+	0.314945i
$567$	23.2769	−	5.01836i	0.977540	−	0.210751i
$568$	−5.01505	−	8.68632i	−0.210427	−	0.364470i
$569$	38.0392	+	21.9620i	1.59469	+	0.920693i	0.992487	+	0.122348i	$0.0390425\pi$
$569$	38.0392	+	21.9620i	1.59469	+	0.920693i	0.602200	+	0.798345i	$0.294291\pi$
$570$	−0.309067	+	1.28214i	−0.0129454	+	0.0537029i
$571$	7.22333			0.302287			0.151143	−	0.988512i	$-0.451704\pi$
$571$	7.22333			0.302287			0.151143	+	0.988512i	$0.451704\pi$
$572$	−2.23423	−	9.82287i	−0.0934178	−	0.410715i
$573$	10.4293	−	3.07881i	0.435689	−	0.128619i
$574$	−3.17499	−	28.4036i	−0.132522	−	1.18554i
$575$	−34.1831	−	19.7356i	−1.42553	−	0.823031i
$576$	2.67050	+	1.36691i	0.111271	+	0.0569545i
$577$	−4.24210			−0.176601			−0.0883004	−	0.996094i	$-0.528144\pi$
$577$	−4.24210			−0.176601			−0.0883004	+	0.996094i	$0.528144\pi$
$578$	−7.98315	−	13.8272i	−0.332055	−	0.575137i
$579$	10.1025	+	9.60465i	0.419845	+	0.399156i
$580$	−2.15805			−0.0896083
$581$	29.7554	+	13.0134i	1.23446	+	0.539885i
$582$	−26.3643	−	6.35527i	−1.09283	−	0.263435i
$583$	21.7761	+	12.5725i	0.901875	+	0.520698i
$584$	1.46098			0.0604559
$585$	−4.88084	−	1.24337i	−0.201798	−	0.0514071i
$586$			20.2924i			0.838271i
$587$	34.2636	+	19.7821i	1.41421	+	0.816494i	0.995782	−	0.0917557i	$-0.0292479\pi$
$587$	34.2636	+	19.7821i	1.41421	+	0.816494i	0.418428	+	0.908250i	$0.362581\pi$
$588$	−6.20759	+	10.4147i	−0.255997	+	0.429495i
$589$	−1.59230	−	2.75795i	−0.0656097	−	0.113639i
$590$	−4.73670			−0.195007
$591$	13.5681	−	14.2714i	0.558117	−	0.587045i
$592$	−4.51505	+	2.60676i	−0.185567	+	0.107137i
$593$		−	0.231641i		−	0.00951238i	−0.999989	−	0.00475619i	$-0.998486\pi$
$593$		−	0.231641i		−	0.00951238i	0.999989	−	0.00475619i	$-0.00151395\pi$
$594$	2.68522	−	14.2673i	0.110176	−	0.585396i
$595$	−0.139147	−	1.24481i	−0.00570447	−	0.0510324i
$596$	1.91703	−	3.32040i	0.0785246	−	0.136009i
$597$	−7.59588	+	2.24237i	−0.310878	+	0.0917741i
$598$	−20.2210	−	21.8260i	−0.826898	−	0.892530i
$599$		−	1.45949i		−	0.0596333i	−0.999555	−	0.0298167i	$-0.990508\pi$
$599$		−	1.45949i		−	0.0596333i	0.999555	−	0.0298167i	$-0.00949235\pi$
$600$	−8.05400	−	1.94147i	−0.328803	−	0.0792601i
$601$	−14.1862	−	8.19043i	−0.578669	−	0.334095i	0.181935	−	0.983311i	$-0.441764\pi$
$601$	−14.1862	−	8.19043i	−0.578669	−	0.334095i	−0.760604	+	0.649216i	$0.775097\pi$
$602$	−6.88989	+	15.7539i	−0.280811	+	0.642082i
$603$	−0.580074	−	0.896860i	−0.0236225	−	0.0365230i
$604$	−17.9655	+	10.3724i	−0.731006	+	0.422046i
$605$	−1.28793	+	0.743589i	−0.0523620	+	0.0302312i
$606$	−1.99243	−	6.74921i	−0.0809367	−	0.274168i
$607$	15.9865	−	9.22984i	0.648874	−	0.374627i	−0.139151	−	0.990271i	$-0.544437\pi$
$607$	15.9865	−	9.22984i	0.648874	−	0.374627i	0.788025	+	0.615644i	$0.211104\pi$
$608$	−0.817625	+	1.41617i	−0.0331591	+	0.0574332i
$609$	−19.5751	+	8.23872i	−0.793221	+	0.333850i
$610$	−6.04591			−0.244792
$611$	0.975504	−	0.221880i	0.0394647	−	0.00897631i
$612$	−2.56112	+	1.65649i	−0.103527	+	0.0669596i
$613$	−19.8455	−	11.4578i	−0.801554	−	0.462777i	0.0424606	−	0.999098i	$-0.486480\pi$
$613$	−19.8455	−	11.4578i	−0.801554	−	0.462777i	−0.844014	+	0.536321i	$0.819814\pi$
$614$	5.51810	−	9.55763i	0.222692	−	0.385715i
$615$	−6.00304	+	6.31419i	−0.242066	+	0.254613i
$616$	4.38435	+	5.95154i	0.176650	+	0.239795i
$617$	−11.9139	−	20.6355i	−0.479636	−	0.830754i	0.520091	−	0.854111i	$-0.325898\pi$
$617$	−11.9139	−	20.6355i	−0.479636	−	0.830754i	−0.999727	+	0.0233564i	$0.992565\pi$
$618$	−3.81306	−	3.62516i	−0.153384	−	0.145825i
$619$	24.6008			0.988789			0.494394	−	0.869238i	$-0.335390\pi$
$619$	24.6008			0.988789			0.494394	+	0.869238i	$0.335390\pi$
$620$	−0.785339	+	0.453416i	−0.0315400	+	0.0182096i
$621$	−14.2013	−	40.4592i	−0.569877	−	1.62357i
$622$	−10.8008	+	18.7076i	−0.433074	+	0.750107i
$623$	−24.9513	+	18.3810i	−0.999654	+	0.736419i
$624$	−5.36761	−	3.19199i	−0.214876	−	0.127782i
$625$	21.7946			0.871785
$626$	−3.08952	−	1.78373i	−0.123482	−	0.0712923i
$627$	7.69307	+	1.85446i	0.307232	+	0.0740601i
$628$	5.28611	−	3.05194i	0.210939	−	0.121786i
$629$		−	5.30064i		−	0.211350i
$630$	3.64765	−	0.595512i	0.145326	−	0.0237258i
$631$	−18.8984	+	10.9110i	−0.752332	+	0.434359i	−0.826536	−	0.562884i	$-0.809692\pi$
$631$	−18.8984	+	10.9110i	−0.752332	+	0.434359i	0.0742037	+	0.997243i	$0.476358\pi$
$632$	4.98126			0.198144
$633$	12.2554	−	12.8907i	0.487110	−	0.512358i
$634$	−10.7753	+	18.6633i	−0.427941	+	0.741215i
$635$	−1.53000	−	0.883344i	−0.0607161	−	0.0350544i
$636$	14.9502	−	4.41343i	0.592814	−	0.175004i
$637$	14.2699	−	20.8175i	0.565395	−	0.824820i
$638$			12.9487i			0.512645i
$639$	1.51928	+	30.0519i	0.0601016	+	1.18883i
$640$	0.403261	+	0.232823i	0.0159403	+	0.00920312i
$641$	−26.9800	+	15.5769i	−1.06565	+	0.615251i	−0.926989	−	0.375089i	$-0.877612\pi$
$641$	−26.9800	+	15.5769i	−1.06565	+	0.615251i	−0.138658	+	0.990340i	$0.544279\pi$
$642$	−21.7760	+	6.42845i	−0.859428	+	0.253711i
$643$	7.10597	+	12.3079i	0.280232	+	0.485376i	0.971442	−	0.237278i	$-0.0762552\pi$
$643$	7.10597	+	12.3079i	0.280232	+	0.485376i	−0.691210	+	0.722654i	$0.742922\pi$
$644$	20.0036	+	8.74845i	0.788252	+	0.344737i
$645$	5.02708	−	1.48404i	0.197941	−	0.0584340i
$646$	−0.831288	−	1.43983i	−0.0327066	−	0.0566494i
$647$	−12.4757	+	21.6085i	−0.490468	+	0.849516i	−0.999940	−	0.0109713i	$-0.996508\pi$
$647$	−12.4757	+	21.6085i	−0.490468	+	0.849516i	0.509471	+	0.860488i	$0.329841\pi$
$648$	−5.26312	−	7.30065i	−0.206755	−	0.286797i
$649$			28.4211i			1.11563i
$650$	16.4760	+	5.09574i	0.646240	+	0.199872i
$651$	−5.39259	+	7.11096i	−0.211352	+	0.278700i
$652$	4.36215	+	2.51849i	0.170835	+	0.0986317i
$653$	−3.86444	−	2.23114i	−0.151227	−	0.0873111i	0.422477	−	0.906374i	$-0.361161\pi$
$653$	−3.86444	−	2.23114i	−0.151227	−	0.0873111i	−0.573704	+	0.819063i	$0.694494\pi$
$654$	13.5787	+	12.9096i	0.530969	+	0.504804i
$655$		−	4.10047i		−	0.160219i
$656$	−9.35517	+	5.40121i	−0.365258	+	0.210882i
$657$	−3.90155	−	1.99703i	−0.152214	−	0.0779116i
$658$	−0.591045	+	0.435407i	−0.0230413	+	0.0169739i
$659$	−11.7305	+	6.77262i	−0.456956	+	0.263824i	−0.710763	−	0.703431i	$-0.751650\pi$
$659$	−11.7305	+	6.77262i	−0.456956	+	0.263824i	0.253807	+	0.967255i	$0.418317\pi$
$660$	0.528067	−	2.19064i	0.0205550	−	0.0852704i
$661$	14.7691	−	25.5809i	0.574452	−	0.994980i	−0.421649	−	0.906759i	$-0.638548\pi$
$661$	14.7691	−	25.5809i	0.574452	−	0.994980i	0.996101	−	0.0882210i	$-0.0281182\pi$
$662$		−	30.4271i		−	1.18258i
$663$	5.53918	−	3.10350i	0.215124	−	0.120530i
$664$		−	12.2750i		−	0.476363i
$665$	0.223801	+	2.00213i	0.00867861	+	0.0776392i
$666$	15.6206	−	0.789702i	0.605287	−	0.0306003i
$667$	19.1223	+	33.1209i	0.740420	+	1.28245i
$668$			1.12680i			0.0435973i
$669$	19.5792	−	20.5941i	0.756977	−	0.796213i
$670$	−0.0828928	−	0.143575i	−0.00320243	−	0.00554677i
$671$			36.2766i			1.40044i
$672$	4.54669	+	0.572351i	0.175392	+	0.0220789i
$673$	10.7301	−	18.5850i	0.413614	−	0.716400i	−0.581668	−	0.813426i	$-0.697600\pi$
$673$	10.7301	−	18.5850i	0.413614	−	0.716400i	0.995282	+	0.0970262i	$0.0309331\pi$
$674$	−9.71046	+	16.8190i	−0.374033	+	0.647844i
$675$	18.8544	+	16.1938i	0.725706	+	0.623299i
$676$	10.7301	+	7.33932i	0.412695	+	0.282282i
$677$	43.1118			1.65692			0.828461	−	0.560046i	$-0.189217\pi$
$677$	43.1118			1.65692			0.828461	+	0.560046i	$0.189217\pi$
$678$	0.118099	−	0.489923i	0.00453556	−	0.0188154i
$679$	−41.1692	+	4.60195i	−1.57993	+	0.176607i
$680$	−0.409999	+	0.236713i	−0.0157227	+	0.00907753i
$681$	45.1702	−	13.3346i	1.73093	−	0.510985i
$682$	2.72058	+	4.71218i	0.104176	+	0.180439i
$683$	−10.3942	−	18.0033i	−0.397724	−	0.688878i	0.595721	−	0.803192i	$-0.296866\pi$
$683$	−10.3942	−	18.0033i	−0.397724	−	0.688878i	−0.993445	+	0.114314i	$0.963533\pi$
$684$	4.11924	−	2.66426i	0.157503	−	0.101870i
$685$	−6.86678	+	3.96454i	−0.262366	+	0.151477i
$686$	−3.49119	+	18.1882i	−0.133294	+	0.694430i
$687$	−9.99542	−	2.40946i	−0.381349	−	0.0919266i
$688$	6.49897			0.247771
$689$	−31.6409	+	7.19678i	−1.20542	+	0.274176i
$690$	−1.88436	−	6.38315i	−0.0717365	−	0.243003i
$691$	−1.39220	+	2.41136i	−0.0529617	+	0.0917323i	−0.891291	−	0.453432i	$-0.850199\pi$
$691$	−1.39220	+	2.41136i	−0.0529617	+	0.0917323i	0.838329	+	0.545164i	$0.183533\pi$
$692$	−3.84077	+	6.65242i	−0.146004	+	0.252887i
$693$	−3.57318	−	21.8866i	−0.135734	−	0.831403i
$694$		−	15.7745i		−	0.598794i
$695$	4.67055	+	8.08963i	0.177164	+	0.306857i
$696$	5.81767	+	5.53099i	0.220518	+	0.209651i
$697$		−	10.9829i		−	0.416008i
$698$	2.93182	+	5.07806i	0.110971	+	0.192207i
$699$	8.07801	−	33.5109i	0.305538	−	1.26750i
$700$	−12.5768	+	1.40585i	−0.475357	+	0.0531360i
$701$		−	1.61057i		−	0.0608302i	−0.999537	−	0.0304151i	$-0.990317\pi$
$701$		−	1.61057i		−	0.0608302i	0.999537	−	0.0304151i	$-0.00968292\pi$
$702$	9.97104	+	15.8612i	0.376333	+	0.598643i
$703$			8.52542i			0.321542i
$704$	1.39698	−	2.41964i	0.0526506	−	0.0911935i
$705$	0.217551	+	0.0524420i	0.00819344	+	0.00197508i
$706$	27.1942	−	15.7006i	1.02347	−	0.590899i
$707$	−6.37561	−	8.65459i	−0.239780	−	0.325489i
$708$	12.7692	+	12.1399i	0.479895	+	0.456247i
$709$	−15.0171	+	8.67010i	−0.563978	+	0.325613i	−0.754740	−	0.656024i	$-0.772237\pi$
$709$	−15.0171	+	8.67010i	−0.563978	+	0.325613i	0.190763	+	0.981636i	$0.438904\pi$
$710$			4.67046i			0.175279i
$711$	−13.3024	−	6.80892i	−0.498880	−	0.255355i
$712$	10.1441	+	5.85671i	0.380167	+	0.219490i
$713$	13.9177	+	8.03536i	0.521220	+	0.300927i
$714$	−2.81529	+	3.71239i	−0.105359	+	0.138933i
$715$	−1.38601	+	4.48136i	−0.0518338	+	0.167593i
$716$		−	25.4308i		−	0.950393i
$717$	−9.04376	−	2.18006i	−0.337746	−	0.0814157i
$718$	4.40354	−	7.62715i	0.164339	−	0.284643i
$719$	1.33248	+	2.30792i	0.0496931	+	0.0860710i	0.889802	−	0.456347i	$-0.150842\pi$
$719$	1.33248	+	2.30792i	0.0496931	+	0.0860710i	−0.840109	+	0.542418i	$0.817509\pi$
$720$	−0.758659	−	1.17297i	−0.0282736	−	0.0437141i
$721$	−7.36336	−	3.22032i	−0.274226	−	0.119931i
$722$	−8.16298	−	14.1387i	−0.303795	−	0.526188i
$723$	4.35467	+	14.7511i	0.161952	+	0.548601i
$724$	−0.233942	+	0.135066i	−0.00869437	+	0.00501970i
$725$	−19.1979	−	11.0839i	−0.712993	−	0.411647i
$726$	5.37779	+	1.29635i	0.199588	+	0.0481120i
$727$			42.0015i			1.55775i	0.627180	+	0.778874i	$0.284209\pi$
$727$			42.0015i			1.55775i	−0.627180	+	0.778874i	$0.715791\pi$
$728$	−9.37018	−	1.78879i	−0.347282	−	0.0662969i
$729$	4.07583	+	26.6906i	0.150957	+	0.988540i
$730$	−0.589157	−	0.340150i	−0.0218057	−	0.0125895i
$731$	−3.30378	+	5.72232i	−0.122195	+	0.211648i
$732$	16.2985	+	15.4954i	0.602410	+	0.572725i
$733$	−0.682575			−0.0252115			−0.0126057	−	0.999921i	$-0.504013\pi$
$733$	−0.682575			−0.0252115			−0.0126057	+	0.999921i	$0.504013\pi$
$734$	−3.96802	+	2.29094i	−0.146462	+	0.0845601i
$735$	4.92805	−	2.75457i	0.181774	−	0.101604i
$736$		−	8.25209i		−	0.304176i
$737$	−0.861474	+	0.497372i	−0.0317328	+	0.0183209i
$738$	32.3659	−	1.63626i	1.19141	−	0.0602316i
$739$	4.21534	+	2.43373i	0.155064	+	0.0895262i	0.575524	−	0.817785i	$-0.304798\pi$
$739$	4.21534	+	2.43373i	0.155064	+	0.0895262i	−0.420460	+	0.907311i	$0.638131\pi$
$740$	2.42765			0.0892423
$741$	−8.90908	+	4.99159i	−0.327283	+	0.183371i
$742$	19.1708	−	14.1226i	0.703782	−	0.518458i
$743$	22.2628	−	38.5603i	0.816743	−	1.41464i	−0.0913265	−	0.995821i	$-0.529111\pi$
$743$	22.2628	−	38.5603i	0.816743	−	1.41464i	0.908070	−	0.418819i	$-0.137556\pi$
$744$	3.27919	+	0.790470i	0.120221	+	0.0289800i
$745$	−1.54613	+	0.892656i	−0.0566457	+	0.0327044i
$746$	−27.0483			−0.990309
$747$	−16.7788	+	32.7804i	−0.613905	+	1.19937i
$748$	1.42032	+	2.46007i	0.0519321	+	0.0899490i
$749$	−27.9236	+	20.5706i	−1.02030	+	0.751632i
$750$	5.71843	+	5.43663i	0.208807	+	0.198518i
$751$	−15.0480	+	26.0639i	−0.549108	+	0.951084i	0.449228	+	0.893417i	$0.351699\pi$
$751$	−15.0480	+	26.0639i	−0.549108	+	0.951084i	−0.998336	+	0.0576662i	$0.981634\pi$
$752$	0.240293	+	0.138733i	0.00876258	+	0.00505908i
$753$	−4.13229	−	13.9979i	−0.150589	−	0.510110i
$754$	−11.3565	−	12.2579i	−0.413580	−	0.446407i
$755$	9.65970			0.351553
$756$	−11.3596	−	7.74337i	−0.413144	−	0.281624i
$757$	20.1948	−	34.9785i	0.733994	−	1.27132i	−0.221169	−	0.975235i	$-0.570987\pi$
$757$	20.1948	−	34.9785i	0.733994	−	1.27132i	0.955163	−	0.296080i	$-0.0956794\pi$
$758$	5.46704	−	3.15640i	0.198572	−	0.114645i
$759$	−38.3001	+	11.3065i	−1.39021	+	0.410401i
$760$	0.659432	−	0.380723i	0.0239201	−	0.0138103i
$761$	8.22094	−	4.74636i	0.298009	−	0.172056i	−0.343539	−	0.939138i	$-0.611626\pi$
$761$	8.22094	−	4.74636i	0.298009	−	0.172056i	0.641548	+	0.767083i	$0.278292\pi$
$762$	1.86059	+	6.30262i	0.0674020	+	0.228320i
$763$	26.2216	+	11.4679i	0.949287	+	0.415165i
$764$	−5.43711	−	3.13912i	−0.196708	−	0.113569i
$765$	1.41847	−	0.0717106i	0.0512848	−	0.00259270i
$766$		−	10.6203i		−	0.383729i
$767$	−24.9264	−	26.9048i	−0.900040	−	0.971478i
$768$	−0.490394	−	1.66118i	−0.0176956	−	0.0599426i
$769$	−23.9804	+	41.5353i	−0.864757	+	1.49780i	0.00253209	+	0.999997i	$0.499194\pi$
$769$	−23.9804	+	41.5353i	−0.864757	+	1.49780i	−0.867289	+	0.497806i	$0.834139\pi$
$770$	−0.382381	−	3.42080i	−0.0137801	−	0.123277i
$771$	27.0577	−	28.4602i	0.974459	−	1.02497i
$772$		−	8.04797i		−	0.289653i
$773$	36.4656	−	21.0534i	1.31158	−	0.757239i	0.329219	−	0.944254i	$-0.393215\pi$
$773$	36.4656	−	21.0534i	1.31158	−	0.757239i	0.982357	+	0.187015i	$0.0598813\pi$
$774$	−17.3555	−	8.88350i	−0.623831	−	0.319311i
$775$	−9.31511			−0.334608
$776$	7.82871	+	13.5597i	0.281034	+	0.486766i
$777$	22.0205	−	9.26796i	0.789981	−	0.332486i
$778$	8.45417	+	4.88102i	0.303097	+	0.174993i
$779$			17.6647i			0.632902i
$780$	1.42138	+	2.53690i	0.0508935	+	0.0908357i
$781$	28.0237			1.00277
$782$	7.26594	+	4.19499i	0.259829	+	0.150013i
$783$	−7.97572	−	22.7227i	−0.285029	−	0.812043i
$784$	6.82723	−	1.54563i	0.243830	−	0.0552009i
$785$	−2.84224			−0.101444
$786$	−10.5093	+	11.0540i	−0.374855	+	0.394284i
$787$	−4.69267	−	8.12794i	−0.167276	−	0.289730i	0.770185	−	0.637820i	$-0.220164\pi$
$787$	−4.69267	−	8.12794i	−0.167276	−	0.289730i	−0.937461	+	0.348090i	$0.886830\pi$
$788$	−11.3690			−0.405005
$789$	2.57862	+	2.45155i	0.0918012	+	0.0872775i
$790$	−2.00874	−	1.15975i	−0.0714679	−	0.0412620i
$791$	−0.0855173	−	0.765041i	−0.00304065	−	0.0272017i
$792$	−7.03805	+	4.55210i	−0.250086	+	0.161752i
$793$	−31.8159	−	34.3412i	−1.12982	−	1.21949i
$794$	0.175358			0.00622322
$795$	−7.05637	−	1.70098i	−0.250264	−	0.0603276i
$796$	3.95997	+	2.28629i	0.140358	+	0.0810354i
$797$	−9.91670	−	17.1762i	−0.351267	−	0.608413i	0.635204	−	0.772344i	$-0.280916\pi$
$797$	−9.91670	−	17.1762i	−0.351267	−	0.608413i	−0.986472	+	0.163931i	$0.947583\pi$
$798$	4.52804	−	5.97091i	0.160291	−	0.211368i
$799$	−0.244308	+	0.141051i	−0.00864300	+	0.00499004i
$800$	2.39159	+	4.14235i	0.0845554	+	0.146454i
$801$	−19.0843	−	29.5064i	−0.674310	−	1.04256i
$802$	1.96794	+	3.40858i	0.0694905	+	0.120361i
$803$	−2.04096	+	3.53505i	−0.0720240	+	0.124749i
$804$	−0.144513	+	0.599498i	−0.00509657	+	0.0211427i
$805$	−6.02982	−	8.18519i	−0.212523	−	0.288490i
$806$	−6.70820	−	2.07474i	−0.236286	−	0.0730795i
$807$	−8.23803	−	27.9058i	−0.289992	−	0.982330i
$808$	−2.03145	+	3.51858i	−0.0714662	+	0.123783i
$809$	−4.75939	−	2.74783i	−0.167331	−	0.0966087i	0.413996	−	0.910279i	$-0.364133\pi$
$809$	−4.75939	−	2.74783i	−0.167331	−	0.0966087i	−0.581327	+	0.813670i	$0.697466\pi$
$810$	0.422653	+	4.16944i	0.0148505	+	0.146499i
$811$	24.5564			0.862292			0.431146	−	0.902282i	$-0.358109\pi$
$811$	24.5564			0.862292			0.431146	+	0.902282i	$0.358109\pi$
$812$	11.2344	+	4.91331i	0.394251	+	0.172423i
$813$	36.7686	−	38.6744i	1.28953	−	1.35637i
$814$		−	14.5664i		−	0.510551i
$815$	−1.17272	−	2.03121i	−0.0410787	−	0.0711504i
$816$	1.71196	+	0.412677i	0.0599304	+	0.0144466i
$817$	5.31373	−	9.20364i	0.185904	−	0.321995i
$818$	23.0263			0.805097
$819$	22.5779	+	17.5851i	0.788937	+	0.614474i
$820$	5.03009			0.175658
$821$	21.8976	−	37.9278i	0.764233	−	1.32369i	−0.176419	−	0.984315i	$-0.556451\pi$
$821$	21.8976	−	37.9278i	0.764233	−	1.32369i	0.940651	−	0.339374i	$-0.110215\pi$
$822$	28.6723	+	6.91164i	1.00006	+	0.241071i
$823$	−15.4742	−	26.8020i	−0.539395	−	0.934260i	−0.998937	−	0.0461039i	$-0.985319\pi$
$823$	−15.4742	−	26.8020i	−0.539395	−	0.934260i	0.459541	−	0.888156i	$-0.348014\pi$
$824$			3.03761i			0.105820i
$825$	15.9489	−	16.7756i	0.555270	−	0.584051i
$826$	24.6584	+	10.7842i	0.857976	+	0.375231i
$827$	−1.75319			−0.0609644			−0.0304822	−	0.999535i	$-0.509704\pi$
$827$	−1.75319			−0.0609644			−0.0304822	+	0.999535i	$0.509704\pi$
$828$	−11.2799	+	22.0372i	−0.392002	+	0.765845i
$829$	25.4012	+	14.6654i	0.882219	+	0.509349i	0.871389	−	0.490592i	$-0.163219\pi$
$829$	25.4012	+	14.6654i	0.882219	+	0.509349i	0.0108294	+	0.999941i	$0.496553\pi$
$830$	−2.85790	+	4.95003i	−0.0991992	+	0.171818i
$831$	5.47995	+	18.5630i	0.190097	+	0.643942i
$832$	0.799665	+	3.51576i	0.0277234	+	0.121887i
$833$	−2.10974	+	6.79708i	−0.0730980	+	0.235505i
$834$	8.14249	−	33.7784i	0.281951	−	1.16965i
$835$	0.262345	−	0.454395i	0.00907883	−	0.0157250i
$836$	−2.28441	−	3.95671i	−0.0790080	−	0.136846i
$837$	−7.67658	−	6.59331i	−0.265342	−	0.227898i
$838$	12.5535	+	21.7434i	0.433655	+	0.751112i
$839$	13.7040	−	7.91198i	0.473113	−	0.273152i	−0.244429	−	0.969667i	$-0.578601\pi$
$839$	13.7040	−	7.91198i	0.473113	−	0.273152i	0.717542	+	0.696515i	$0.245267\pi$
$840$	−1.70025	−	1.28938i	−0.0586640	−	0.0444878i
$841$	−3.76049	−	6.51336i	−0.129672	−	0.224599i
$842$	19.3859	+	11.1924i	0.668081	+	0.385717i
$843$	9.58067	+	2.30948i	0.329976	+	0.0795427i
$844$	−10.2691			−0.353478
$845$	−2.61825	−	5.45786i	−0.0900707	−	0.187756i
$846$	−0.452066	−	0.698945i	−0.0155424	−	0.0240302i
$847$	8.39770	−	0.938706i	0.288548	−	0.0322543i
$848$	−7.79401	−	4.49987i	−0.267647	−	0.154526i
$849$	−18.8111	−	17.8841i	−0.645596	−	0.613782i
$850$	−4.86310			−0.166803
$851$	−21.5112	−	37.2586i	−0.737396	−	1.27721i
$852$	11.9702	−	12.5906i	0.410091	−	0.431347i
$853$	42.9298			1.46989			0.734943	−	0.678129i	$-0.237209\pi$
$853$	42.9298			1.46989			0.734943	+	0.678129i	$0.237209\pi$
$854$	31.4739	+	13.7649i	1.07701	+	0.471026i
$855$	−2.28143	+	0.115338i	−0.0780231	+	0.00394446i
$856$	11.3525	+	6.55437i	0.388021	+	0.224024i
$857$	18.4280			0.629489			0.314744	−	0.949176i	$-0.398081\pi$
$857$	18.4280			0.629489			0.314744	+	0.949176i	$0.398081\pi$
$858$	15.2219	−	8.52854i	0.519667	−	0.291159i
$859$			39.0164i			1.33122i	0.746299	+	0.665611i	$0.231829\pi$
$859$			39.0164i			1.33122i	−0.746299	+	0.665611i	$0.768171\pi$
$860$	−2.62078	−	1.51311i	−0.0893678	−	0.0515966i
$861$	45.6265	−	19.2032i	1.55495	−	0.654443i
$862$	10.8170	+	18.7355i	0.368427	+	0.638135i
$863$	−18.8674			−0.642255			−0.321128	−	0.947036i	$-0.604062\pi$
$863$	−18.8674			−0.642255			−0.321128	+	0.947036i	$0.604062\pi$
$864$	−0.961081	+	5.10650i	−0.0326966	+	0.173727i
$865$	3.09767	−	1.78844i	0.105324	−	0.0608087i
$866$			10.5674i			0.359096i
$867$	19.0546	−	20.0422i	0.647128	−	0.680670i
$868$	5.12064	−	0.572392i	0.173806	−	0.0194282i
$869$	−6.95871	+	12.0528i	−0.236058	+	0.408865i
$870$	−1.05830	−	3.58491i	−0.0358797	−	0.121540i
$871$	0.379300	−	1.22638i	0.0128521	−	0.0415544i
$872$		−	10.8172i		−	0.366318i
$873$	−2.37166	−	46.9124i	−0.0802684	−	1.58774i
$874$	−11.6864	−	6.74712i	−0.395297	−	0.228225i
$875$	11.0428	+	4.82950i	0.373314	+	0.163267i
$876$	0.716458	+	2.42695i	0.0242069	+	0.0819991i
$877$	−23.3402	+	13.4755i	−0.788143	+	0.455034i	−0.839308	−	0.543656i	$-0.817040\pi$
$877$	−23.3402	+	13.4755i	−0.788143	+	0.455034i	0.0511656	+	0.998690i	$0.483706\pi$
$878$	−28.4269	+	16.4123i	−0.959362	+	0.553888i
$879$	−33.7093	+	9.95128i	−1.13699	+	0.335648i
$880$	−1.12669	+	0.650496i	−0.0379808	+	0.0219282i
$881$	−18.9761	+	32.8676i	−0.639321	+	1.10734i	0.346261	+	0.938138i	$0.387451\pi$
$881$	−18.9761	+	32.8676i	−0.639321	+	1.10734i	−0.985582	+	0.169199i	$0.945882\pi$
$882$	−20.3448	−	5.20460i	−0.685046	−	0.175248i
$883$	16.0384			0.539736			0.269868	−	0.962897i	$-0.413020\pi$
$883$	16.0384			0.539736			0.269868	+	0.962897i	$0.413020\pi$
$884$	−3.50212	−	1.08315i	−0.117789	−	0.0364302i
$885$	−2.32285	−	7.86851i	−0.0780818	−	0.264497i
$886$	28.4631	+	16.4332i	0.956237	+	0.552084i
$887$	24.2258	−	41.9604i	0.813424	−	1.40889i	−0.0970303	−	0.995281i	$-0.530934\pi$
$887$	24.2258	−	41.9604i	0.813424	−	1.40889i	0.910454	−	0.413610i	$-0.135732\pi$
$888$	−6.54445	−	6.22195i	−0.219617	−	0.208795i
$889$	5.95374	+	8.08192i	0.199682	+	0.271059i
$890$	−2.72715	−	4.72356i	−0.0914143	−	0.158334i
$891$	25.0174	−	2.53599i	0.838115	−	0.0849590i
$892$	−16.4059			−0.549311
$893$	0.392939	−	0.226864i	0.0131492	−	0.00759170i
$894$	6.45587	+	1.55623i	0.215917	+	0.0520480i
$895$	−5.92086	+	10.2552i	−0.197913	+	0.342795i
$896$	−1.56923	−	2.13015i	−0.0524241	−	0.0711633i
$897$	26.3406	−	44.2940i	0.879486	−	1.47893i
$898$	5.22599			0.174394
$899$	7.81645	+	4.51283i	0.260693	+	0.150511i
$900$	−0.724516	−	14.3312i	−0.0241505	−	0.477707i
$901$	7.92425	−	4.57507i	0.263995	−	0.152418i
$902$		−	30.1815i		−	1.00493i
$903$	−29.5488	−	3.71969i	−0.983324	−	0.123784i
$904$	−0.251978	+	0.145480i	−0.00838067	+	0.00483858i
$905$	0.125786			0.00418126
$906$	−26.0406	−	24.7573i	−0.865140	−	0.822507i
$907$	15.7893	−	27.3479i	0.524275	−	0.908070i	−0.475326	−	0.879810i	$-0.657670\pi$
$907$	15.7893	−	27.3479i	0.524275	−	0.908070i	0.999601	−	0.0282607i	$-0.00899685\pi$
$908$	−23.5487	−	13.5958i	−0.781490	−	0.451194i
$909$	10.2346	−	6.61955i	0.339459	−	0.219557i
$910$	3.36215	+	2.90294i	0.111454	+	0.0962314i
$911$		−	9.32478i		−	0.308944i	−0.987997	−	0.154472i	$-0.950632\pi$
$911$		−	9.32478i		−	0.308944i	0.987997	−	0.154472i	$-0.0493676\pi$
$912$	−2.75347	−	0.663740i	−0.0911764	−	0.0219786i
$913$	29.7011	+	17.1479i	0.982963	+	0.567514i
$914$	−30.3072	+	17.4979i	−1.00247	+	0.578779i
$915$	−2.96488	−	10.0433i	−0.0980159	−	0.332022i
$916$	2.96808	+	5.14086i	0.0980681	+	0.169859i
$917$	−9.33569	+	21.3463i	−0.308291	+	0.704917i
$918$	−4.00768	−	3.44214i	−0.132273	−	0.113608i
$919$	20.1504	+	34.9016i	0.664701	+	1.15130i	0.979366	+	0.202094i	$0.0647745\pi$
$919$	20.1504	+	34.9016i	0.664701	+	1.15130i	−0.314665	+	0.949203i	$0.601892\pi$
$920$	−1.92127	+	3.32774i	−0.0633425	+	0.109712i
$921$	18.5830	+	4.47954i	0.612330	+	0.147606i
$922$		−	22.3941i		−	0.737509i
$923$	−26.5286	+	24.5778i	−0.873200	+	0.808989i
$924$	−7.73651	+	10.2018i	−0.254513	+	0.335614i
$925$	21.5963	+	12.4686i	0.710081	+	0.409965i
$926$	13.9451	+	8.05118i	0.458263	+	0.264578i
$927$	4.15214	−	8.11194i	0.136374	−	0.266431i
$928$		−	4.63455i		−	0.152136i
$929$	−48.3894	+	27.9376i	−1.58760	+	0.916604i	−0.593903	+	0.804536i	$0.702414\pi$
$929$	−48.3894	+	27.9376i	−1.58760	+	0.916604i	−0.993701	+	0.112067i	$0.964253\pi$
$930$	−1.13833	−	1.08224i	−0.0373273	−	0.0354879i
$931$	3.39325	−	10.9322i	0.111209	−	0.358290i
$932$	−17.2354	+	9.95086i	−0.564564	+	0.325951i
$933$	−36.3734	−	8.76802i	−1.19081	−	0.287052i
$934$	−16.0720	+	27.8375i	−0.525892	+	0.910871i
$935$		−	1.32273i		−	0.0432580i
$936$	2.67021	−	10.4819i	0.0872786	−	0.342611i
$937$		−	47.2565i		−	1.54380i	−0.635742	−	0.771902i	$-0.719306\pi$
$937$		−	47.2565i		−	1.54380i	0.635742	−	0.771902i	$-0.280694\pi$
$938$	0.104644	+	0.936148i	0.00341674	+	0.0305663i
$939$	1.44802	−	6.00697i	0.0472543	−	0.196030i
$940$	−0.0646004	−	0.111891i	−0.00210703	−	0.00364949i
$941$			35.6378i			1.16176i	0.813990	+	0.580879i	$0.197291\pi$
$941$			35.6378i			1.16176i	−0.813990	+	0.580879i	$0.802709\pi$
$942$	7.66209	+	7.28452i	0.249644	+	0.237342i
$943$	−44.5713	−	77.1997i	−1.45144	−	2.51397i
$944$		−	10.1723i		−	0.331082i
$945$	2.77804	+	5.76736i	0.0903696	+	0.187612i
$946$	−9.07893	+	15.7252i	−0.295181	+	0.511269i
$947$	−4.77969	+	8.27867i	−0.155319	+	0.269021i	−0.933175	−	0.359422i	$-0.882974\pi$
$947$	−4.77969	+	8.27867i	−0.155319	+	0.269021i	0.777856	+	0.628443i	$0.216307\pi$
$948$	2.44278	+	8.27476i	0.0793378	+	0.268752i
$949$	−1.16830	−	5.13646i	−0.0379245	−	0.166736i
$950$	7.82169			0.253769
$951$	−36.2872	−	8.74726i	−1.17669	−	0.283649i
$952$	2.67331	−	0.298826i	0.0866425	−	0.00968501i
$953$	25.8589	−	14.9297i	0.837653	−	0.483619i	−0.0188130	−	0.999823i	$-0.505989\pi$
$953$	25.8589	−	14.9297i	0.837653	−	0.483619i	0.856466	+	0.516204i	$0.172655\pi$
$954$	14.6630	+	22.6706i	0.474731	+	0.733988i
$955$	1.46171	+	2.53176i	0.0472999	+	0.0819259i
$956$	2.68549	+	4.65141i	0.0868550	+	0.150437i
$957$	−21.5101	+	6.34998i	−0.695324	+	0.205266i
$958$	0.698448	−	0.403249i	0.0225658	−	0.0130284i
$959$	44.7734	−	5.00483i	1.44581	−	0.161614i
$960$	−0.189003	+	0.784062i	−0.00610005	+	0.0253055i
$961$	−27.2073			−0.877656
$962$	12.7753	+	13.7893i	0.411891	+	0.444584i
$963$	−21.3576	−	33.0213i	−0.688240	−	1.06410i
$964$	4.43996	−	7.69024i	0.143002	−	0.247686i
$965$	−1.87375	+	3.24543i	−0.0603181	+	0.104474i
$966$	−4.72309	+	37.5197i	−0.151963	+	1.20718i
$967$			24.3574i			0.783281i	0.920118	+	0.391640i	$0.128092\pi$
$967$			24.3574i			0.783281i	−0.920118	+	0.391640i	$0.871908\pi$
$968$	−1.59690	−	2.76591i	−0.0513263	−	0.0888998i
$969$	1.98416	−	2.08700i	0.0637404	−	0.0670442i
$970$		−	7.29080i		−	0.234094i
$971$	21.4689	+	37.1852i	0.688970	+	1.19333i	0.972171	+	0.234271i	$0.0752702\pi$
$971$	21.4689	+	37.1852i	0.688970	+	1.19333i	−0.283201	+	0.959060i	$0.591396\pi$
$972$	9.54668	−	12.3232i	0.306210	−	0.395266i
$973$	−5.89610	−	52.7468i	−0.189020	−	1.69098i
$974$		−	8.45786i		−	0.271007i
$975$	−0.385219	+	29.8684i	−0.0123369	+	0.956555i
$976$		−	12.9839i		−	0.415606i
$977$	11.3672	−	19.6885i	0.363667	−	0.629890i	−0.624894	−	0.780710i	$-0.714858\pi$
$977$	11.3672	−	19.6885i	0.363667	−	0.629890i	0.988561	+	0.150819i	$0.0481911\pi$
$978$	−2.04449	+	8.48137i	−0.0653754	+	0.271204i
$979$	−28.3422	+	16.3634i	−0.905822	+	0.522977i
$980$	−3.11301	−	0.966243i	−0.0994414	−	0.0308655i
$981$	−14.7862	+	28.8874i	−0.472086	+	0.922303i
$982$	4.29055	−	2.47715i	0.136917	−	0.0790490i
$983$		−	58.8980i		−	1.87855i	−0.343159	−	0.939277i	$-0.611497\pi$
$983$		−	58.8980i		−	1.87855i	0.343159	−	0.939277i	$-0.388503\pi$
$984$	−13.5601	−	12.8919i	−0.432280	−	0.410978i
$985$	4.58468	+	2.64697i	0.146080	+	0.0843394i
$986$	4.08070	+	2.35599i	0.129956	+	0.0750301i
$987$	−1.01313	−	0.768309i	−0.0322484	−	0.0244555i
$988$	5.63273	+	1.74211i	0.179201	+	0.0554239i
$989$			53.6301i			1.70534i
$990$	3.89800	−	0.197064i	0.123887	−	0.00626309i
$991$	−27.7404	+	48.0478i	−0.881204	+	1.52629i	−0.0312004	+	0.999513i	$0.509933\pi$
$991$	−27.7404	+	48.0478i	−0.881204	+	1.52629i	−0.850004	+	0.526777i	$0.823400\pi$
$992$	−0.973737	−	1.68656i	−0.0309162	−	0.0535484i
$993$	50.5449	−	14.9213i	1.60399	−	0.473513i
$994$	10.6334	−	24.3136i	0.337271	−	0.771180i
$995$	−1.06460	−	1.84394i	−0.0337501	−	0.0584569i
$996$	20.3910	−	6.01960i	0.646113	−	0.190738i
$997$	35.9697	−	20.7671i	1.13917	−	0.657702i	0.192947	−	0.981209i	$-0.438195\pi$
$997$	35.9697	−	20.7671i	1.13917	−	0.657702i	0.946226	+	0.323507i	$0.104862\pi$
$998$	−9.01320	−	5.20377i	−0.285308	−	0.164722i
$999$	8.97211	+	25.5614i	0.283865	+	0.808727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.j.251.12	yes	24
3.2	odd	2		546.2.q.i.251.10	yes	24
7.6	odd	2	inner	546.2.q.j.251.1	yes	24
13.10	even	6		546.2.q.i.335.3	yes	24
21.20	even	2		546.2.q.i.251.3	✓	24
39.23	odd	6	inner	546.2.q.j.335.1	yes	24
91.62	odd	6		546.2.q.i.335.10	yes	24
273.62	even	6	inner	546.2.q.j.335.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.3	✓	24	21.20	even	2
546.2.q.i.251.10	yes	24	3.2	odd	2
546.2.q.i.335.3	yes	24	13.10	even	6
546.2.q.i.335.10	yes	24	91.62	odd	6
546.2.q.j.251.1	yes	24	7.6	odd	2	inner
546.2.q.j.251.12	yes	24	1.1	even	1	trivial
546.2.q.j.335.1	yes	24	39.23	odd	6	inner
546.2.q.j.335.12	yes	24	273.62	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.68382 + 0.405895i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.19343 - 1.25528i) q^{6} +(1.06015 - 2.42406i) q^{7} -1.00000 q^{8} +(2.67050 + 1.36691i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.68382 + 0.405895i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.19343 - 1.25528i) q^{6} +(1.06015 - 2.42406i) q^{7} -1.00000 q^{8} +(2.67050 + 1.36691i) q^{9} +(0.403261 + 0.232823i) q^{10} +(1.39698 - 2.41964i) q^{11} +(-0.490394 - 1.66118i) q^{12} +(0.799665 + 3.51576i) q^{13} +(-1.56923 - 2.13015i) q^{14} +(-0.189003 + 0.784062i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.508355 - 0.880496i) q^{17} +(2.51903 - 1.62927i) q^{18} +(0.817625 + 1.41617i) q^{19} +(0.403261 - 0.232823i) q^{20} +(2.76902 - 3.65138i) q^{21} +(-1.39698 - 2.41964i) q^{22} +(-7.14652 - 4.12605i) q^{23} +(-1.68382 - 0.405895i) q^{24} +4.78317 q^{25} +(3.44457 + 1.06535i) q^{26} +(3.94182 + 3.38557i) q^{27} +(-2.62938 + 0.293915i) q^{28} +(-4.01364 - 2.31727i) q^{29} +(0.584516 + 0.555713i) q^{30} -1.94747 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.33438 - 3.50721i) q^{33} -1.01671 q^{34} +(1.12875 + 0.493654i) q^{35} +(-0.151472 - 2.99617i) q^{36} +(4.51505 + 2.60676i) q^{37} +1.63525 q^{38} +(-0.0805363 + 6.24448i) q^{39} -0.465645i q^{40} +(9.35517 + 5.40121i) q^{41} +(-1.77768 - 4.22373i) q^{42} +(-3.24949 - 5.62828i) q^{43} -2.79396 q^{44} +(-0.636494 + 1.24350i) q^{45} +(-7.14652 + 4.12605i) q^{46} -0.277466i q^{47} +(-1.19343 + 1.25528i) q^{48} +(-4.75217 - 5.13974i) q^{49} +(2.39159 - 4.14235i) q^{50} +(-0.498589 - 1.68894i) q^{51} +(2.64490 - 2.45041i) q^{52} +8.99975i q^{53} +(4.90290 - 1.72093i) q^{54} +(1.12669 + 0.650496i) q^{55} +(-1.06015 + 2.42406i) q^{56} +(0.801918 + 2.71644i) q^{57} +(-4.01364 + 2.31727i) q^{58} +(-8.80951 + 5.08617i) q^{59} +(0.773520 - 0.228350i) q^{60} +(-11.2444 + 6.49197i) q^{61} +(-0.973737 + 1.68656i) q^{62} +(6.14460 - 5.02433i) q^{63} +1.00000 q^{64} +(-1.63709 + 0.372360i) q^{65} +(-1.37014 - 4.64126i) q^{66} +(-0.308335 - 0.178017i) q^{67} +(-0.508355 + 0.880496i) q^{68} +(-10.3587 - 9.84825i) q^{69} +(0.991893 - 0.730702i) q^{70} +(5.01505 + 8.68632i) q^{71} +(-2.67050 - 1.36691i) q^{72} -1.46098 q^{73} +(4.51505 - 2.60676i) q^{74} +(8.05400 + 1.94147i) q^{75} +(0.817625 - 1.41617i) q^{76} +(-4.38435 - 5.95154i) q^{77} +(5.36761 + 3.19199i) q^{78} -4.98126 q^{79} +(-0.403261 - 0.232823i) q^{80} +(5.26312 + 7.30065i) q^{81} +(9.35517 - 5.40121i) q^{82} +12.2750i q^{83} +(-4.54669 - 0.572351i) q^{84} +(0.409999 - 0.236713i) q^{85} -6.49897 q^{86} +(-5.81767 - 5.53099i) q^{87} +(-1.39698 + 2.41964i) q^{88} +(-10.1441 - 5.85671i) q^{89} +(0.758659 + 1.17297i) q^{90} +(9.37018 + 1.78879i) q^{91} +8.25209i q^{92} +(-3.27919 - 0.790470i) q^{93} +(-0.240293 - 0.138733i) q^{94} +(-0.659432 + 0.380723i) q^{95} +(0.490394 + 1.66118i) q^{96} +(-7.82871 - 13.5597i) q^{97} +(-6.82723 + 1.54563i) q^{98} +(7.03805 - 4.55210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

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