LMFDB - Embedded newform 546.2.q.i.251.3

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			251.3
Character	$\chi$	$=$	546.251
Dual form			546.2.q.i.335.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.19343 - 1.25528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.68382 - 0.405895i) q^{6} +(2.62938 + 0.293915i) q^{7} +1.00000 q^{8} +(-0.151472 + 2.99617i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.19343 - 1.25528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.68382 - 0.405895i) q^{6} +(2.62938 + 0.293915i) q^{7} +1.00000 q^{8} +(-0.151472 + 2.99617i) 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} +(0.584516 - 0.555713i) 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} +(-1.19343 - 1.25528i) q^{24} +4.78317 q^{25} +(3.44457 + 1.06535i) q^{26} +(3.94182 - 3.38557i) q^{27} +(-1.06015 - 2.42406i) q^{28} +(4.01364 + 2.31727i) q^{29} +(0.189003 + 0.784062i) q^{30} +1.94747 q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.70452 - 1.13405i) q^{33} +1.01671 q^{34} +(-0.136860 + 1.22436i) q^{35} +(2.67050 - 1.36691i) q^{36} +(4.51505 + 2.60676i) q^{37} +1.63525 q^{38} +(-3.45893 + 5.19960i) q^{39} +0.465645i q^{40} +(9.35517 + 5.40121i) q^{41} +(4.54669 - 0.572351i) q^{42} +(-3.24949 - 5.62828i) q^{43} +2.79396 q^{44} +(-1.39515 - 0.0705321i) q^{45} +(-7.14652 + 4.12605i) q^{46} -0.277466i q^{47} +(1.68382 - 0.405895i) q^{48} +(6.82723 + 1.54563i) q^{49} +(-2.39159 + 4.14235i) q^{50} +(-0.498589 + 1.68894i) q^{51} +(-2.64490 + 2.45041i) q^{52} -8.99975i q^{53} +(0.961081 + 5.10650i) q^{54} +(-1.12669 - 0.650496i) q^{55} +(2.62938 + 0.293915i) 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} +(-1.27890 + 7.83354i) 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} +(-3.34948 - 13.8950i) q^{69} +(-0.991893 - 0.730702i) q^{70} +(-5.01505 - 8.68632i) q^{71} +(-0.151472 + 2.99617i) q^{72} +1.46098 q^{73} +(-4.51505 + 2.60676i) q^{74} +(-5.70836 - 6.00424i) q^{75} +(-0.817625 + 1.41617i) q^{76} +(-4.38435 + 5.95154i) q^{77} +(-2.77352 - 5.59532i) q^{78} -4.98126 q^{79} +(-0.403261 - 0.232823i) q^{80} +(-8.95411 - 0.907671i) q^{81} +(-9.35517 + 5.40121i) q^{82} +12.2750i q^{83} +(-1.77768 + 4.22373i) q^{84} +(0.409999 - 0.236713i) q^{85} +6.49897 q^{86} +(-1.88114 - 7.80374i) q^{87} +(-1.39698 + 2.41964i) q^{88} +(-10.1441 - 5.85671i) q^{89} +(0.758659 - 1.17297i) q^{90} +(-1.06929 - 9.47927i) q^{91} -8.25209i q^{92} +(-2.32416 - 2.44463i) 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} +(-4.75217 + 5.13974i) 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} - 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 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 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * 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
$3$	−1.19343	−	1.25528i	−0.689024	−	0.724738i
$3$	−1.19343	−	1.25528i	−0.689024	−	0.724738i
$4$	−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	$0.966797\pi$
$6$	1.68382	−	0.405895i	0.687417	−	0.165706i
$7$	2.62938	+	0.293915i	0.993810	+	0.111089i
$7$	2.62938	+	0.293915i	0.993810	+	0.111089i
$8$	1.00000			0.353553
$9$	−0.151472	+	2.99617i	−0.0504906	+	0.998725i
$10$	−0.403261	−	0.232823i	−0.127522	−	0.0736250i
$11$	−1.39698	+	2.41964i	−0.421205	+	0.729548i	−0.996058	−	0.0887086i	$-0.971726\pi$
$11$	−1.39698	+	2.41964i	−0.421205	+	0.729548i	0.574853	+	0.818257i	$0.305059\pi$
$12$	−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
$15$	0.584516	−	0.555713i	0.150922	−	0.143484i
$16$	−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	0.756865	−	0.653571i	$-0.226730\pi$
$19$	−0.817625	−	1.41617i	−0.187576	−	0.324891i	−0.944442	+	0.328679i	$0.893396\pi$
$20$	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	0.999937	−	0.0112612i	$-0.00358462\pi$
$23$	7.14652	+	4.12605i	1.49015	+	0.860340i	0.490216	+	0.871601i	$0.336918\pi$
$24$	−1.19343	−	1.25528i	−0.243607	−	0.256234i
$25$	4.78317			0.956635
$26$	3.44457	+	1.06535i	0.675535	+	0.208932i
$27$	3.94182	−	3.38557i	0.758603	−	0.651553i
$28$	−1.06015	−	2.42406i	−0.200349	−	0.458105i
$29$	4.01364	+	2.31727i	0.745313	+	0.430307i	0.823998	−	0.566593i	$-0.191739\pi$
$29$	4.01364	+	2.31727i	0.745313	+	0.430307i	−0.0786847	+	0.996900i	$0.525072\pi$
$30$	0.189003	+	0.784062i	0.0345071	+	0.143150i
$31$	1.94747			0.349777			0.174888	−	0.984588i	$-0.444044\pi$
$31$	1.94747			0.349777			0.174888	+	0.984588i	$0.444044\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	4.70452	−	1.13405i	0.818952	−	0.197413i
$34$	1.01671			0.174364
$35$	−0.136860	+	1.22436i	−0.0231336	+	0.206954i
$36$	2.67050	−	1.36691i	0.445083	−	0.227818i
$37$	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
$39$	−3.45893	+	5.19960i	−0.553872	+	0.832602i
$40$			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	$0.347142\pi$
$42$	4.54669	−	0.572351i	0.701570	−	0.0883156i
$43$	−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
$45$	−1.39515	−	0.0705321i	−0.207977	−	0.0105143i
$46$	−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	$-0.00644186\pi$
$48$	1.68382	−	0.405895i	0.243038	−	0.0585859i
$49$	6.82723	+	1.54563i	0.975318	+	0.220804i
$50$	−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	$-0.787901\pi$
$53$		−	8.99975i		−	1.23621i	0.786095	−	0.618105i	$-0.212099\pi$
$54$	0.961081	+	5.10650i	0.130787	+	0.694906i
$55$	−1.12669	−	0.650496i	−0.151923	−	0.0877129i
$56$	2.62938	+	0.293915i	0.351365	+	0.0392760i
$57$	−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	0.441872	−	0.897078i	$-0.354315\pi$
$61$	11.2444	−	6.49197i	1.43970	−	0.831211i	0.997828	+	0.0658671i	$0.0209813\pi$
$62$	−0.973737	+	1.68656i	−0.123665	+	0.214194i
$63$	−1.27890	+	7.83354i	−0.161126	+	0.986934i
$64$	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
$69$	−3.34948	−	13.8950i	−0.403230	−	1.67277i
$70$	−0.991893	−	0.730702i	−0.118554	−	0.0873356i
$71$	−5.01505	−	8.68632i	−0.595177	−	1.03088i	−0.993522	−	0.113640i	$-0.963749\pi$
$71$	−5.01505	−	8.68632i	−0.595177	−	1.03088i	0.398345	−	0.917235i	$-0.369585\pi$
$72$	−0.151472	+	2.99617i	−0.0178511	+	0.353102i
$73$	1.46098			0.170995			0.0854975	−	0.996338i	$-0.472752\pi$
$73$	1.46098			0.170995			0.0854975	+	0.996338i	$0.472752\pi$
$74$	−4.51505	+	2.60676i	−0.524863	+	0.303030i
$75$	−5.70836	−	6.00424i	−0.659145	−	0.693310i
$76$	−0.817625	+	1.41617i	−0.0937881	+	0.162446i
$77$	−4.38435	+	5.95154i	−0.499643	+	0.678241i
$78$	−2.77352	−	5.59532i	−0.314039	−	0.633545i
$79$	−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
$81$	−8.95411	−	0.907671i	−0.994901	−	0.100852i
$82$	−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	$0.764713\pi$
$84$	−1.77768	+	4.22373i	−0.193960	+	0.460846i
$85$	0.409999	−	0.236713i	0.0444706	−	0.0256751i
$86$	6.49897			0.700802
$87$	−1.88114	−	7.80374i	−0.201679	−	0.836649i
$88$	−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
$91$	−1.06929	−	9.47927i	−0.112092	−	0.993698i
$92$		−	8.25209i		−	0.860340i
$93$	−2.32416	−	2.44463i	−0.241005	−	0.253496i
$94$	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	$0.125802\pi$
$97$	7.82871	+	13.5597i	0.794885	+	1.37678i	−0.128027	+	0.991771i	$0.540864\pi$
$98$	−4.75217	+	5.13974i	−0.480041	+	0.519192i
$99$	−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	$0.101878\pi$
$102$	−1.21337	−	1.27626i	−0.120141	−	0.126368i
$103$			3.03761i			0.299305i	0.988739	+	0.149652i	$0.0478154\pi$
$103$			3.03761i			0.299305i	−0.988739	+	0.149652i	$0.952185\pi$
$104$	−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	0.935560	−	0.353168i	$-0.114895\pi$
$107$	11.3525	+	6.55437i	1.09749	+	0.633635i	0.161928	+	0.986803i	$0.448229\pi$
$108$	−4.90290	−	1.72093i	−0.471782	−	0.165596i
$109$			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
$111$	−2.11614	−	8.77864i	−0.200856	−	0.833232i
$112$	−1.56923	+	2.13015i	−0.148278	+	0.201280i
$113$	−0.251978	+	0.145480i	−0.0237041	+	0.0136856i	−0.511805	−	0.859102i	$-0.671023\pi$
$113$	−0.251978	+	0.145480i	−0.0237041	+	0.0136856i	0.488101	+	0.872787i	$0.337690\pi$
$114$	−1.95155	−	2.05270i	−0.182779	−	0.192253i
$115$	−1.92127	+	3.32774i	−0.179160	+	0.310314i
$116$		−	4.63455i		−	0.430307i
$117$	10.6549	−	1.86340i	0.985050	−	0.172271i
$118$		−	10.1723i		−	0.936440i
$119$	−1.07786	−	2.46457i	−0.0988077	−	0.225927i
$120$	0.584516	−	0.555713i	0.0533588	−	0.0507294i
$121$	1.59690	+	2.76591i	0.145173	+	0.251447i
$122$			12.9839i			1.17551i
$123$	−4.38465	−	18.1893i	−0.395350	−	1.64008i
$124$	−0.973737	−	1.68656i	−0.0874441	−	0.151458i
$125$			4.55549i			0.407455i
$126$	−6.14460	−	5.02433i	−0.547405	−	0.447603i
$127$	−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	$0.625692\pi$
$132$	−3.33438	−	3.50721i	−0.290221	−	0.305263i
$133$	−1.73361	−	3.96395i	−0.150323	−	0.343718i
$134$	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	$-0.907392\pi$
$137$	−8.51407	−	14.7468i	−0.727407	−	1.25991i	0.230569	−	0.973056i	$-0.425941\pi$
$138$	13.7082	+	4.04678i	1.16692	+	0.344485i
$139$	−17.3730	+	10.0303i	−1.47356	+	0.850757i	−0.999557	−	0.0297682i	$-0.990523\pi$
$139$	−17.3730	+	10.0303i	−1.47356	+	0.850757i	−0.473998	+	0.880526i	$0.657190\pi$
$140$	1.12875	−	0.493654i	0.0953971	−	0.0417213i
$141$	−0.348299	+	0.331135i	−0.0293321	+	0.0278866i
$142$	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
$147$	−6.20759	−	10.4147i	−0.511993	−	0.858989i
$148$		−	5.21353i		−	0.428549i
$149$	−1.91703	−	3.32040i	−0.157049	−	0.272017i	0.776754	−	0.629804i	$-0.216865\pi$
$149$	−1.91703	−	3.32040i	−0.157049	−	0.272017i	−0.933803	+	0.357787i	$0.883531\pi$
$150$	8.05400	−	1.94147i	0.657607	−	0.158520i
$151$		−	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
$153$	2.71512	−	1.38975i	0.219505	−	0.112355i
$154$	−2.96201	−	6.77273i	−0.238686	−	0.545762i
$155$			0.906832i			0.0728385i
$156$	6.23245	+	0.395721i	0.498995	+	0.0316830i
$157$		−	6.10387i		−	0.487142i	−0.969883	−	0.243571i	$-0.921681\pi$
$157$		−	6.10387i		−	0.487142i	0.969883	−	0.243571i	$-0.0783189\pi$
$158$	2.49063	−	4.31389i	0.198144	−	0.343195i
$159$	−11.2972	+	10.7405i	−0.895929	+	0.851779i
$160$	0.403261	−	0.232823i	0.0318805	−	0.0184062i
$161$	17.5782	+	12.9494i	1.38535	+	1.02055i
$162$	5.26312	−	7.30065i	0.413510	−	0.573594i
$163$	−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
$165$	0.528067	+	2.19064i	0.0411099	+	0.170541i
$166$	−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
$171$	4.36693	−	2.23524i	0.333948	−	0.170933i
$172$	−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
$175$	12.5768	+	1.40585i	0.950714	+	0.106272i
$176$	−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	$-0.934014\pi$
$179$	−22.0237	−	12.7154i	−1.64613	−	0.950393i	−0.667540	−	0.744574i	$-0.732652\pi$
$180$	0.636494	+	1.24350i	0.0474415	+	0.0926854i
$181$			0.270132i			0.0200788i	0.999950	+	0.0100394i	$0.00319569\pi$
$181$			0.270132i			0.0200788i	−0.999950	+	0.0100394i	$0.996804\pi$
$182$	8.74393	+	3.81361i	0.648144	+	0.282683i
$183$	−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
$186$	3.27919	−	0.790470i	0.240442	−	0.0579601i
$187$	2.84064			0.207728
$188$	−0.240293	+	0.138733i	−0.0175252	+	0.0101182i
$189$	11.3596	−	7.74337i	0.826288	−	0.563248i
$190$			0.761446i			0.0552411i
$191$	−5.43711	+	3.13912i	−0.393415	+	0.227138i	−0.683639	−	0.729820i	$-0.739604\pi$
$191$	−5.43711	+	3.13912i	−0.393415	+	0.227138i	0.290224	+	0.956959i	$0.406270\pi$
$192$	−1.19343	−	1.25528i	−0.0861281	−	0.0905923i
$193$	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
$195$	−2.42117	−	1.61063i	−0.173383	−	0.115340i
$196$	−2.07506	−	6.68537i	−0.148219	−	0.477526i
$197$	−5.68452	+	9.84588i	−0.405005	+	0.701490i	−0.994322	−	0.106412i	$-0.966064\pi$
$197$	−5.68452	+	9.84588i	−0.405005	+	0.701490i	0.589317	+	0.807902i	$0.299397\pi$
$198$	7.46126	−	3.81908i	0.530249	−	0.271410i
$199$	3.95997	−	2.28629i	0.280715	−	0.162071i	−0.353032	−	0.935611i	$-0.614849\pi$
$199$	3.95997	−	2.28629i	0.280715	−	0.162071i	0.633747	+	0.773540i	$0.281516\pi$
$200$	4.78317			0.338222
$201$	0.144513	+	0.599498i	0.0101931	+	0.0422853i
$202$	2.03145	+	3.51858i	0.142932	+	0.247566i
$203$	9.87227	+	7.27265i	0.692898	+	0.510440i
$204$	1.71196	−	0.412677i	0.119861	−	0.0288932i
$205$	−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
$210$	0.266512	+	2.11715i	0.0183911	+	0.146097i
$211$	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
$217$	5.12064	+	0.572392i	0.347612	+	0.0388565i
$218$	−9.36799	−	5.40861i	−0.634481	−	0.366318i
$219$	−1.74357	−	1.83395i	−0.117820	−	0.123927i
$220$			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	$0.351776\pi$
$223$	−8.20296	+	14.2079i	−0.549311	+	0.951434i	−0.998322	+	0.0579082i	$0.981557\pi$
$224$	−1.06015	−	2.42406i	−0.0708342	−	0.161965i
$225$	−0.724516	+	14.3312i	−0.0483010	+	0.955415i
$226$		−	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	$-0.0248537\pi$
$228$	2.75347	−	0.663740i	0.182353	−	0.0439573i
$229$	5.93616			0.392272			0.196136	−	0.980577i	$-0.437161\pi$
$229$	5.93616			0.392272			0.196136	+	0.980577i	$0.437161\pi$
$230$	−1.92127	−	3.32774i	−0.126685	−	0.219425i
$231$	12.7033	−	1.59912i	0.835814	−	0.105215i
$232$	4.01364	+	2.31727i	0.263508	+	0.152136i
$233$			19.9017i			1.30380i	0.758303	+	0.651902i	$0.226029\pi$
$233$			19.9017i			1.30380i	−0.758303	+	0.651902i	$0.773971\pi$
$234$	−3.71372	+	10.1591i	−0.242774	+	0.664124i
$235$	0.129201			0.00842814
$236$	8.80951	+	5.08617i	0.573450	+	0.331082i
$237$	5.94476	+	6.25289i	0.386154	+	0.406169i
$238$	2.67331	+	0.298826i	0.173285	+	0.0193700i
$239$	5.37098			0.347420			0.173710	−	0.984797i	$-0.444424\pi$
$239$	5.37098			0.347420			0.173710	+	0.984797i	$0.444424\pi$
$240$	0.189003	+	0.784062i	0.0122001	+	0.0506110i
$241$	−4.43996	−	7.69024i	−0.286003	−	0.495372i	0.686849	−	0.726800i	$-0.258993\pi$
$241$	−4.43996	−	7.69024i	−0.286003	−	0.495372i	−0.972852	+	0.231428i	$0.925660\pi$
$242$	−3.19380			−0.205305
$243$	9.54668	+	12.3232i	0.612420	+	0.790533i
$244$	−11.2444	−	6.49197i	−0.719850	−	0.415606i
$245$	−0.719713	+	3.17907i	−0.0459808	+	0.203103i
$246$	17.9447	+	5.29745i	1.14411	+	0.337753i
$247$	−4.32508	+	4.00703i	−0.275198	+	0.254961i
$248$	1.94747			0.123665
$249$	15.4086	−	14.6493i	0.976481	−	0.928362i
$250$	−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	$-0.0833435\pi$
$258$	−7.75604	−	8.15805i	−0.482870	−	0.507898i
$259$	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	0.444147	−	0.895954i	$-0.353507\pi$
$263$	−1.77900	−	1.02711i	−0.109698	−	0.0633341i	−0.553845	+	0.832620i	$0.686840\pi$
$264$	4.70452	−	1.13405i	0.289543	−	0.0697962i
$265$	4.19069			0.257432
$266$	4.29969	+	0.480625i	0.263631	+	0.0294690i
$267$	4.75442	+	19.7233i	0.290966	+	1.20705i
$268$			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	$-0.337806\pi$
$270$	−2.37782	+	0.447523i	−0.144709	+	0.0272354i
$271$	−15.4047	+	26.6817i	−0.935767	+	1.62080i	−0.162507	+	0.986707i	$0.551958\pi$
$271$	−15.4047	+	26.6817i	−0.935767	+	1.62080i	−0.773260	+	0.634089i	$0.781375\pi$
$272$	1.01671			0.0616471
$273$	−10.6231	+	12.6551i	−0.642937	+	0.765919i
$274$	17.0281			1.02871
$275$	−6.68199	+	11.5736i	−0.402939	+	0.697911i
$276$	−10.3587	+	9.84825i	−0.623521	+	0.592795i
$277$	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
$279$	−0.294987	+	5.83497i	−0.0176604	+	0.349330i
$280$	−0.136860	+	1.22436i	−0.00817896	+	0.0731693i
$281$	−5.68985			−0.339428			−0.169714	−	0.985493i	$-0.554284\pi$
$281$	−5.68985			−0.339428			−0.169714	+	0.985493i	$0.554284\pi$
$282$	−0.112622	−	0.467203i	−0.00670656	−	0.0278216i
$283$	12.9779	+	7.49278i	0.771455	+	0.445400i	0.833393	−	0.552680i	$-0.186395\pi$
$283$	12.9779	+	7.49278i	0.771455	+	0.445400i	−0.0619386	+	0.998080i	$0.519728\pi$
$284$	−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
$288$	2.67050	−	1.36691i	0.157361	−	0.0805459i
$289$	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
$297$	2.68522	+	14.2673i	0.155812	+	0.827875i
$298$	3.83406			0.222101
$299$	8.79134	−	28.4249i	0.508417	−	1.64385i
$300$	−2.34564	+	7.94571i	−0.135426	+	0.458746i
$301$	−6.88989	−	15.7539i	−0.397126	−	0.908041i
$302$	17.9655	+	10.3724i	1.03380	+	0.596864i
$303$	−6.84120	+	1.64911i	−0.393017	+	0.0947391i
$304$	1.63525			0.0937881
$305$	3.02295	+	5.23591i	0.173094	+	0.299807i
$306$	−0.154003	+	3.04624i	−0.00880375	+	0.174142i
$307$	−11.0362			−0.629869			−0.314935	−	0.949113i	$-0.601983\pi$
$307$	−11.0362			−0.629869			−0.314935	+	0.949113i	$0.601983\pi$
$308$	7.34636	+	0.821186i	0.418598	+	0.0467914i
$309$	3.81306	−	3.62516i	0.216918	−	0.206228i
$310$	−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	$0.709820\pi$
$312$	−3.45893	+	5.19960i	−0.195823	+	0.294369i
$313$			3.56747i			0.201645i	0.994904	+	0.100823i	$0.0321474\pi$
$313$			3.56747i			0.201645i	−0.994904	+	0.100823i	$0.967853\pi$
$314$	5.28611	+	3.05194i	0.298312	+	0.172231i
$315$	−3.64765	−	0.595512i	−0.205522	−	0.0335533i
$316$	2.49063	+	4.31389i	0.140109	+	0.242676i
$317$	21.5505			1.21040			0.605199	−	0.796074i	$-0.293093\pi$
$317$	21.5505			1.21040			0.605199	+	0.796074i	$0.293093\pi$
$318$	−3.65295	−	15.1540i	−0.204848	−	0.849792i
$319$	−11.2139	+	6.47436i	−0.627859	+	0.362495i
$320$			0.465645i			0.0260304i
$321$	−5.32077	−	22.0728i	−0.296977	−	1.23198i
$322$	−20.0036	+	8.74845i	−1.11476	+	0.487532i
$323$	−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
$327$	13.5787	−	12.9096i	0.750903	−	0.713900i
$328$	9.35517	+	5.40121i	0.516553	+	0.298232i
$329$	0.0815515	−	0.729563i	0.00449608	−	0.0402221i
$330$	−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
$336$	4.54669	−	0.572351i	0.248042	−	0.0312243i
$337$	−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
$342$	−0.247694	+	4.89949i	−0.0133938	+	0.264934i
$343$	17.4971	+	6.07065i	0.944753	+	0.327785i
$344$	−3.24949	−	5.62828i	−0.175201	−	0.303456i
$345$	6.47015	−	1.55967i	0.348341	−	0.0839698i
$346$	7.68155			0.412963
$347$	−13.6612	+	7.88727i	−0.733369	+	0.423411i	−0.819654	−	0.572860i	$-0.805834\pi$
$347$	−13.6612	+	7.88727i	−0.733369	+	0.423411i	0.0862842	+	0.996271i	$0.472501\pi$
$348$	−5.81767	+	5.53099i	−0.311860	+	0.296492i
$349$	2.93182	−	5.07806i	0.156937	−	0.271822i	−0.776826	−	0.629715i	$-0.783172\pi$
$349$	2.93182	−	5.07806i	0.156937	−	0.271822i	0.933762	+	0.357893i	$0.116505\pi$
$350$	−7.50588	+	10.1889i	−0.401206	+	0.544618i
$351$	−15.0550	−	11.1511i	−0.803575	−	0.595204i
$352$	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	$0.351754\pi$
$354$	−12.7692	+	12.1399i	−0.678674	+	0.645230i
$355$	4.04474	−	2.33523i	0.214673	−	0.123941i
$356$			11.7134i			0.620810i
$357$	−1.80738	+	4.29430i	−0.0956567	+	0.227279i
$358$	22.0237	−	12.7154i	1.16399	−	0.672030i
$359$	−8.80708			−0.464820			−0.232410	−	0.972618i	$-0.574661\pi$
$359$	−8.80708			−0.464820			−0.232410	+	0.972618i	$0.574661\pi$
$360$	−1.39515	−	0.0705321i	−0.0735311	−	0.00371737i
$361$	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
$364$	−7.67465	+	5.66567i	−0.402261	+	0.296962i
$365$			0.680300i			0.0356085i
$366$	16.2985	−	15.4954i	0.851937	−	0.809955i
$367$	3.96802	+	2.29094i	0.207129	+	0.119586i	0.599977	−	0.800018i	$-0.295177\pi$
$367$	3.96802	+	2.29094i	0.207129	+	0.119586i	−0.392847	+	0.919604i	$0.628510\pi$
$368$	−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
$371$	2.64516	−	23.6637i	0.137330	−	1.22856i
$372$	−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
$375$	5.71843	−	5.43663i	0.295298	−	0.280747i
$376$		−	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
$381$	6.38852	−	1.53999i	0.327294	−	0.0788962i
$382$		−	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	$0.245867\pi$
$384$	1.68382	−	0.405895i	0.0859271	−	0.0207132i
$385$	−2.77131	−	2.04155i	−0.141239	−	0.104047i
$386$	−6.96974	+	4.02398i	−0.354751	+	0.204815i
$387$	17.3555	−	8.88350i	0.882230	−	0.451574i
$388$	7.82871	−	13.5597i	0.397443	−	0.688391i
$389$		−	9.76203i		−	0.494955i	−0.968894	−	0.247477i	$-0.920398\pi$
$389$		−	9.76203i		−	0.494955i	0.968894	−	0.247477i	$-0.0796016\pi$
$390$	2.60543	−	1.29148i	0.131931	−	0.0653964i
$391$		−	8.38998i		−	0.424300i
$392$	6.82723	+	1.54563i	0.344827	+	0.0780659i
$393$	10.5093	+	11.0540i	0.530125	+	0.557602i
$394$	−5.68452	−	9.84588i	−0.286382	−	0.496028i
$395$		−	2.31950i		−	0.116707i
$396$	−0.423205	+	8.37118i	−0.0212669	+	0.420668i
$397$	−0.0876790	−	0.151865i	−0.00440048	−	0.00762186i	0.863817	−	0.503806i	$-0.168067\pi$
$397$	−0.0876790	−	0.151865i	−0.00440048	−	0.00762186i	−0.868217	+	0.496184i	$0.834734\pi$
$398$			4.57258i			0.229203i
$399$	−2.90695	+	6.90685i	−0.145529	+	0.345775i
$400$	−2.39159	+	4.14235i	−0.119579	+	0.207118i
$401$	1.96794	−	3.40858i	0.0982743	−	0.170216i	−0.812696	−	0.582688i	$-0.802001\pi$
$401$	1.96794	−	3.40858i	0.0982743	−	0.170216i	0.910970	+	0.412472i	$0.135334\pi$
$402$	−0.591437	−	0.174597i	−0.0294982	−	0.00870812i
$403$	−1.55733	−	6.84684i	−0.0775759	−	0.341065i
$404$	−4.06290			−0.202137
$405$	0.422653	−	4.16944i	0.0210018	−	0.207181i
$406$	−11.2344	+	4.91331i	−0.557556	+	0.243844i
$407$	−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	$-0.973885\pi$
$409$	−11.5132	−	19.9414i	−0.569290	−	0.986038i	0.427347	−	0.904088i	$-0.359448\pi$
$410$	−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
$413$	−24.6584	+	10.7842i	−1.21336	+	0.530656i
$414$	−11.2799	−	22.0372i	−0.554375	−	1.08307i
$415$	−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	$0.956516\pi$
$420$	−1.96676	−	0.827766i	−0.0959680	−	0.0403909i
$421$			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
$423$	0.831338	+	0.0420283i	0.0404210	+	0.00204349i
$424$		−	8.99975i		−	0.437066i
$425$	−2.43155	−	4.21157i	−0.117947	−	0.204291i
$426$	−11.9702	−	12.5906i	−0.579957	−	0.610017i
$427$	31.4739	−	13.7649i	1.52313	−	0.666131i
$428$		−	13.1087i		−	0.633635i
$429$	−7.74910	−	15.6331i	−0.374130	−	0.754772i
$430$			3.02622i			0.145937i
$431$	10.8170	−	18.7355i	0.521035	−	0.902459i	−0.478666	−	0.877997i	$-0.658879\pi$
$431$	10.8170	−	18.7355i	0.521035	−	0.902459i	0.999701	−	0.0244617i	$-0.00778718\pi$
$432$	0.961081	+	5.10650i	0.0462400	+	0.245687i
$433$	9.15166	−	5.28372i	0.439801	−	0.253919i	−0.263712	−	0.964601i	$-0.584947\pi$
$433$	9.15166	−	5.28372i	0.439801	−	0.253919i	0.703513	+	0.710682i	$0.251614\pi$
$434$	−3.05603	+	4.14841i	−0.146694	+	0.199130i
$435$	3.63377	−	0.875944i	0.174226	−	0.0419983i
$436$	9.36799	−	5.40861i	0.448646	−	0.259026i
$437$		−	13.4942i		−	0.645517i
$438$	2.46003	−	0.593006i	0.117545	−	0.0283349i
$439$	28.4269	+	16.4123i	1.35674	+	0.783316i	0.989183	−	0.146684i	$-0.0468600\pi$
$439$	28.4269	+	16.4123i	1.35674	+	0.783316i	0.367560	+	0.930000i	$0.380193\pi$
$440$	−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	$-0.714830\pi$
$443$		−	32.8664i		−	1.56153i	0.624826	−	0.780764i	$-0.285170\pi$
$444$	−6.54445	+	6.22195i	−0.310586	+	0.295281i
$445$	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
$448$	2.62938	+	0.293915i	0.124226	+	0.0138862i
$449$	−2.61300	−	4.52584i	−0.123315	−	0.213588i	0.797758	−	0.602978i	$-0.206019\pi$
$449$	−2.61300	−	4.52584i	−0.123315	−	0.213588i	−0.921073	+	0.389390i	$0.872686\pi$
$450$	−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
$453$	−26.0406	+	24.7573i	−1.22349	+	1.16320i
$454$			27.1917i			1.27617i
$455$	4.41398	−	0.497908i	0.206930	−	0.0233423i
$456$	−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
$459$	−4.98482	−	1.74968i	−0.232672	−	0.0816683i
$460$	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	$0.158707\pi$
$462$	−4.96675	+	11.8009i	−0.231074	+	0.549028i
$463$			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
$465$	1.13833	−	1.08224i	0.0527888	−	0.0501875i
$466$	−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	$0.766942\pi$
$468$	−6.94122	−	8.29575i	−0.320858	−	0.383471i
$469$	−0.758406	−	0.558698i	−0.0350199	−	0.0257983i
$470$	−0.0646004	+	0.111891i	−0.00297980	+	0.00516116i
$471$	−7.66209	+	7.28452i	−0.353050	+	0.335653i
$472$	−8.80951	+	5.08617i	−0.405490	+	0.234110i
$473$	18.1579			0.834899
$474$	−8.38754	+	2.02187i	−0.385252	+	0.0928675i
$475$	−3.91084	−	6.77378i	−0.179442	−	0.310802i
$476$	−1.59545	+	2.16574i	−0.0731272	+	0.0992666i
$477$	26.9648	+	1.36321i	1.23463	+	0.0624170i
$478$	−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
$483$	−4.72309	−	37.5197i	−0.214908	−	1.70721i
$484$	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
$490$	−2.39329	−	2.21282i	−0.108118	−	0.0999651i
$491$	−4.29055	−	2.47715i	−0.193630	−	0.111792i	0.400051	−	0.916493i	$-0.368992\pi$
$491$	−4.29055	−	2.47715i	−0.193630	−	0.111792i	−0.593681	+	0.804701i	$0.702326\pi$
$492$	−13.5601	+	12.8919i	−0.611336	+	0.581211i
$493$		−	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
$497$	−10.6334	−	24.3136i	−0.476973	−	1.09061i
$498$	4.98237	+	20.6689i	0.223265	+	0.926196i
$499$		−	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
$501$	0.457364	+	1.89733i	0.0204335	+	0.0847666i
$502$	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	$0.864589\pi$
$504$	−1.27890	+	7.83354i	−0.0569666	+	0.348934i
$505$	1.63841	+	0.945936i	0.0729082	+	0.0420936i
$506$		−	23.0560i		−	1.02496i
$507$	21.0465	+	8.00281i	0.934708	+	0.355417i
$508$	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	$0.790165\pi$
$510$	0.594284	−	0.564998i	0.0263153	−	0.0250186i
$511$	3.84147	+	0.429405i	0.169937	+	0.0189957i
$512$	1.00000			0.0441942
$513$	−8.01747	−	2.81415i	−0.353980	−	0.124248i
$514$	11.3361	+	19.6348i	0.500016	+	0.866053i
$515$	−1.41445			−0.0623281
$516$	10.9431	−	2.63790i	0.481743	−	0.116127i
$517$	0.671368	+	0.387615i	0.0295267	+	0.0170473i
$518$	−12.6379	+	5.52712i	−0.555278	+	0.242848i
$519$	−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	$0.790253\pi$
$522$	−6.33500	−	12.3765i	−0.277275	−	0.541707i
$523$	−17.5784	−	10.1489i	−0.768648	−	0.443779i	0.0637443	−	0.997966i	$-0.479696\pi$
$523$	−17.5784	−	10.1489i	−0.768648	−	0.443779i	−0.832392	+	0.554187i	$0.813029\pi$
$524$	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
$531$	−13.9047	−	27.1652i	−0.603411	−	1.17887i
$532$	−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
$537$	10.3222	+	42.8209i	0.445437	+	1.84786i
$538$	16.7988			0.724247
$539$	−13.2773	+	14.3602i	−0.571896	+	0.618538i
$540$	0.801342	−	2.28301i	0.0344843	−	0.0982451i
$541$			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
$543$	0.339093	−	0.322383i	0.0145519	−	0.0138348i
$544$	−0.508355	+	0.880496i	−0.0217955	+	0.0377510i
$545$	−5.03699			−0.215761
$546$	−5.64808	−	15.5274i	−0.241715	−	0.664510i
$547$	−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
$549$	17.7478	+	34.6736i	0.757460	+	1.47983i
$550$	−6.68199	−	11.5736i	−0.284921	−	0.493498i
$551$		−	7.57865i		−	0.322861i
$552$	−3.34948	−	13.8950i	−0.142563	−	0.591412i
$553$	−13.0976	−	1.46407i	−0.556966	−	0.0622584i
$554$	−11.1746			−0.474762
$555$	4.08773	−	0.985373i	0.173515	−	0.0418267i
$556$	17.3730	+	10.0303i	0.736778	+	0.425379i
$557$	−18.5481	+	32.1263i	−0.785910	+	1.36124i	0.142544	+	0.989788i	$0.454472\pi$
$557$	−18.5481	+	32.1263i	−0.785910	+	1.36124i	−0.928454	+	0.371447i	$0.878862\pi$
$558$	−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
$561$	−3.39010	−	3.56581i	−0.143130	−	0.150549i
$562$	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	$-0.960957\pi$
$569$	−38.0392	−	21.9620i	−1.59469	−	0.920693i	−0.602200	−	0.798345i	$-0.705709\pi$
$570$	0.955831	−	0.908730i	0.0400354	−	0.0380625i
$571$	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
$574$	−26.1857	+	11.4522i	−1.09297	+	0.478005i
$575$	34.1831	+	19.7356i	1.42553	+	0.823031i
$576$	−0.151472	+	2.99617i	−0.00631132	+	0.124841i
$577$	4.24210			0.176601			0.0883004	−	0.996094i	$-0.471856\pi$
$577$	4.24210			0.176601			0.0883004	+	0.996094i	$0.471856\pi$
$578$	7.98315	+	13.8272i	0.332055	+	0.575137i
$579$	−3.26663	−	13.5513i	−0.135757	−	0.563174i
$580$	2.15805			0.0896083
$581$	−3.60781	+	32.2756i	−0.149677	+	1.33902i
$582$	18.6860	+	19.6545i	0.774558	+	0.814705i
$583$	21.7761	+	12.5725i	0.901875	+	0.520698i
$584$	1.46098			0.0604559
$585$	0.867682	+	4.96142i	0.0358742	+	0.205130i
$586$		−	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	$0.362581\pi$
$588$	−5.91559	+	10.5833i	−0.243955	+	0.436447i
$589$	−1.59230	−	2.75795i	−0.0656097	−	0.113639i
$590$	4.73670			0.195007
$591$	19.1434	−	4.61464i	0.787455	−	0.189821i
$592$	−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	$-0.00151395\pi$
$594$	−13.6985	−	4.80820i	−0.562056	−	0.197283i
$595$	1.14761	−	0.501902i	0.0470476	−	0.0205760i
$596$	−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	$0.00949235\pi$
$599$			1.45949i			0.0596333i	−0.999555	+	0.0298167i	$0.990508\pi$
$600$	−5.70836	−	6.00424i	−0.233043	−	0.245122i
$601$	14.1862	+	8.19043i	0.578669	+	0.334095i	0.760604	−	0.649216i	$-0.224903\pi$
$601$	14.1862	+	8.19043i	0.578669	+	0.334095i	−0.181935	+	0.983311i	$0.558236\pi$
$602$	17.0882	+	1.91015i	0.696465	+	0.0778517i
$603$	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	−0.788025	−	0.615644i	$-0.788896\pi$
$607$	−15.9865	+	9.22984i	−0.648874	+	0.374627i	0.139151	+	0.990271i	$0.455563\pi$
$608$	−0.817625	+	1.41617i	−0.0331591	+	0.0574332i
$609$	−2.65259	−	21.0719i	−0.107488	−	0.853875i
$610$	−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
$615$	8.46977	−	2.04169i	0.341534	−	0.0823289i
$616$	−4.38435	+	5.95154i	−0.176650	+	0.239795i
$617$	11.9139	+	20.6355i	0.479636	+	0.830754i	0.999727	−	0.0233564i	$-0.00743526\pi$
$617$	11.9139	+	20.6355i	0.479636	+	0.830754i	−0.520091	+	0.854111i	$0.674102\pi$
$618$	1.23295	+	5.11479i	0.0495966	+	0.205747i
$619$	−24.6008			−0.988789			−0.494394	−	0.869238i	$-0.664610\pi$
$619$	−24.6008			−0.988789			−0.494394	+	0.869238i	$0.664610\pi$
$620$	0.785339	−	0.453416i	0.0315400	−	0.0182096i
$621$	42.1393	−	7.93093i	1.69099	−	0.318257i
$622$	10.8008	−	18.7076i	0.433074	−	0.750107i
$623$	−24.9513	−	18.3810i	−0.999654	−	0.736419i
$624$	−2.77352	−	5.59532i	−0.111030	−	0.223992i
$625$	21.7946			0.871785
$626$	−3.08952	−	1.78373i	−0.123482	−	0.0712923i
$627$	−5.45255	−	5.73516i	−0.217754	−	0.229040i
$628$	−5.28611	+	3.05194i	−0.210939	+	0.121786i
$629$		−	5.30064i		−	0.211350i
$630$	2.33955	−	2.86120i	0.0932101	−	0.113993i
$631$	−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
$633$	−17.2914	+	4.16819i	−0.687270	+	0.165671i
$634$	−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
$637$	−0.0254525	−	25.2388i	−0.00100847	−	0.999999i
$638$		−	12.9487i		−	0.512645i
$639$	26.7853	−	13.7102i	1.05961	−	0.542368i
$640$	−0.403261	−	0.232823i	−0.0159403	−	0.00920312i
$641$	26.9800	−	15.5769i	1.06565	−	0.615251i	0.138658	−	0.990340i	$-0.455721\pi$
$641$	26.9800	−	15.5769i	1.06565	−	0.615251i	0.926989	+	0.375089i	$0.122388\pi$
$642$	21.7760	+	6.42845i	0.859428	+	0.253711i
$643$	−7.10597	−	12.3079i	−0.280232	−	0.485376i	0.691210	−	0.722654i	$-0.257078\pi$
$643$	−7.10597	−	12.3079i	−0.280232	−	0.485376i	−0.971442	+	0.237278i	$0.923745\pi$
$644$	2.42541	−	21.6978i	0.0955747	−	0.855015i
$645$	−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	$0.329841\pi$
$648$	−8.95411	−	0.907671i	−0.351751	−	0.0356567i
$649$		−	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	0.573704	−	0.819063i	$-0.305506\pi$
$653$	3.86444	+	2.23114i	0.151227	+	0.0873111i	−0.422477	+	0.906374i	$0.638839\pi$
$654$	4.39066	+	18.2143i	0.171688	+	0.712234i
$655$		−	4.10047i		−	0.160219i
$656$	−9.35517	+	5.40121i	−0.365258	+	0.210882i
$657$	−0.221298	+	4.37736i	−0.00863364	+	0.170777i
$658$	0.591045	+	0.435407i	0.0230413	+	0.0169739i
$659$	11.7305	−	6.77262i	0.456956	−	0.263824i	−0.253807	−	0.967255i	$-0.581683\pi$
$659$	11.7305	−	6.77262i	0.456956	−	0.263824i	0.710763	+	0.703431i	$0.248350\pi$
$660$	1.63311	−	1.55264i	0.0635689	−	0.0604363i
$661$	−14.7691	+	25.5809i	−0.574452	+	0.994980i	0.421649	+	0.906759i	$0.361452\pi$
$661$	−14.7691	+	25.5809i	−0.574452	+	0.994980i	−0.996101	+	0.0882210i	$0.971882\pi$
$662$			30.4271i			1.18258i
$663$	6.33659	+	0.402333i	0.246093	+	0.0156253i
$664$			12.2750i			0.476363i
$665$	1.84579	−	0.807247i	0.0715768	−	0.0313037i
$666$	−7.12641	−	13.9227i	−0.276143	−	0.539494i
$667$	19.1223	+	33.1209i	0.740420	+	1.28245i
$668$			1.12680i			0.0435973i
$669$	27.6246	−	6.65908i	1.06803	−	0.257455i
$670$	0.0828928	+	0.143575i	0.00320243	+	0.00554677i
$671$			36.2766i			1.40044i
$672$	−1.77768	+	4.22373i	−0.0685753	+	0.162934i
$673$	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	$0.189217\pi$
$678$	−0.365236	+	0.347238i	−0.0140268	+	0.0133356i
$679$	16.5992	+	37.9546i	0.637019	+	1.45656i
$680$	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	0.993445	−	0.114314i	$-0.0364669\pi$
$683$	10.3942	+	18.0033i	0.397724	+	0.688878i	−0.595721	+	0.803192i	$0.703134\pi$
$684$	−4.11924	−	2.66426i	−0.157503	−	0.101870i
$685$	6.86678	−	3.96454i	0.262366	−	0.151477i
$686$	−14.0059	+	12.1176i	−0.534747	+	0.462651i
$687$	−7.08436	−	7.45156i	−0.270285	−	0.284295i
$688$	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	−0.838329	−	0.545164i	$-0.816467\pi$
$691$	1.39220	−	2.41136i	0.0529617	−	0.0917323i	0.891291	+	0.453432i	$0.149801\pi$
$692$	−3.84077	+	6.65242i	−0.146004	+	0.252887i
$693$	−17.1678	−	14.0378i	−0.652149	−	0.533250i
$694$		−	15.7745i		−	0.598794i
$695$	−4.67055	−	8.08963i	−0.177164	−	0.306857i
$696$	−1.88114	−	7.80374i	−0.0713044	−	0.295800i
$697$		−	10.9829i		−	0.416008i
$698$	2.93182	+	5.07806i	0.110971	+	0.192207i
$699$	24.9823	−	23.7512i	0.944917	−	0.898353i
$700$	−5.07088	−	11.5947i	−0.191661	−	0.438239i
$701$			1.61057i			0.0608302i	0.999537	+	0.0304151i	$0.00968292\pi$
$701$			1.61057i			0.0608302i	−0.999537	+	0.0304151i	$0.990317\pi$
$702$	17.1847	−	7.46241i	0.648593	−	0.281651i
$703$		−	8.52542i		−	0.321542i
$704$	−1.39698	+	2.41964i	−0.0526506	+	0.0911935i
$705$	−0.154192	−	0.162184i	−0.00580719	−	0.00610819i
$706$	−27.1942	+	15.7006i	−1.02347	+	0.590899i
$707$	6.37561	−	8.65459i	0.239780	−	0.325489i
$708$	−4.12890	−	17.1284i	−0.155174	−	0.643724i
$709$	−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
$711$	0.754519	−	14.9247i	0.0282967	−	0.559720i
$712$	−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
$717$	−6.40987	−	6.74210i	−0.239381	−	0.251788i
$718$	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
$721$	−0.892800	+	7.98702i	−0.0332496	+	0.297452i
$722$	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
$726$	3.81156	+	4.00913i	0.141460	+	0.148793i
$727$		−	42.0015i		−	1.55775i	−0.627180	−	0.778874i	$-0.715791\pi$
$727$		−	42.0015i		−	1.55775i	0.627180	−	0.778874i	$-0.284209\pi$
$728$	−1.06929	−	9.47927i	−0.0396304	−	0.351325i
$729$	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
$732$	5.27012	+	21.8626i	0.194789	+	0.808065i
$733$	0.682575			0.0252115			0.0126057	−	0.999921i	$-0.495987\pi$
$733$	0.682575			0.0252115			0.0126057	+	0.999921i	$0.495987\pi$
$734$	−3.96802	+	2.29094i	−0.146462	+	0.0845601i
$735$	4.84955	−	2.89053i	0.178878	−	0.106619i
$736$		−	8.25209i		−	0.304176i
$737$	0.861474	−	0.497372i	0.0317328	−	0.0183209i
$738$	−14.7659	−	28.8478i	−0.543541	−	1.06190i
$739$	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
$741$	10.1916	+	0.647103i	0.374398	+	0.0237719i
$742$	19.1708	+	14.1226i	0.703782	+	0.518458i
$743$	−22.2628	+	38.5603i	−0.816743	+	1.41464i	0.0913265	+	0.995821i	$0.470889\pi$
$743$	−22.2628	+	38.5603i	−0.816743	+	1.41464i	−0.908070	+	0.418819i	$0.862444\pi$
$744$	−2.32416	−	2.44463i	−0.0852080	−	0.0896245i
$745$	1.54613	−	0.892656i	0.0566457	−	0.0327044i
$746$	27.0483			0.990309
$747$	−36.7781	−	1.85932i	−1.34564	−	0.0680288i
$748$	−1.42032	−	2.46007i	−0.0519321	−	0.0899490i
$749$	27.9236	+	20.5706i	1.02030	+	0.751632i
$750$	1.84905	+	7.67062i	0.0675178	+	0.280091i
$751$	−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
$756$	−12.3858	−	5.96600i	−0.450465	−	0.216981i
$757$	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
$763$	−3.17935	+	28.4426i	−0.115100	+	1.02969i
$764$	5.43711	+	3.13912i	0.196708	+	0.113569i
$765$	0.647130	+	1.26428i	0.0233970	+	0.0457102i
$766$			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	$-0.500806\pi$
$769$	23.9804	−	41.5353i	0.864757	−	1.49780i	0.867289	−	0.497806i	$-0.165861\pi$
$770$	3.15369	−	1.37925i	0.113651	−	0.0497046i
$771$	−38.1761	+	9.20257i	−1.37488	+	0.331423i
$772$		−	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	$0.0598813\pi$
$774$	−0.984411	+	19.4721i	−0.0353839	+	0.699909i
$775$	9.31511			0.334608
$776$	7.82871	+	13.5597i	0.281034	+	0.486766i
$777$	−2.98397	−	23.7043i	−0.107049	−	0.850387i
$778$	8.45417	+	4.88102i	0.303097	+	0.174993i
$779$		−	17.6647i		−	0.632902i
$780$	−0.184265	+	2.90211i	−0.00659776	+	0.103912i
$781$	28.0237			1.00277
$782$	7.26594	+	4.19499i	0.259829	+	0.150013i
$783$	23.6663	−	4.45418i	0.845765	−	0.159179i
$784$	−4.75217	+	5.13974i	−0.169720	+	0.183562i
$785$	2.84224			0.101444
$786$	−14.8277	+	3.57432i	−0.528888	+	0.127492i
$787$	4.69267	+	8.12794i	0.167276	+	0.289730i	0.937461	−	0.348090i	$-0.113170\pi$
$787$	4.69267	+	8.12794i	0.167276	+	0.289730i	−0.770185	+	0.637820i	$0.779836\pi$
$788$	11.3690			0.405005
$789$	0.833795	+	3.45892i	0.0296839	+	0.123141i
$790$	2.00874	+	1.15975i	0.0714679	+	0.0412620i
$791$	−0.705304	+	0.308460i	−0.0250777	+	0.0109676i
$792$	−7.03805	−	4.55210i	−0.250086	−	0.161752i
$793$	−31.8159	−	34.3412i	−1.12982	−	1.21949i
$794$	0.175358			0.00622322
$795$	−5.00128	−	5.26050i	−0.177377	−	0.186571i
$796$	−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
$804$	0.446924	−	0.424900i	0.0157618	−	0.0149851i
$805$	−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	0.581327	−	0.813670i	$-0.302534\pi$
$809$	4.75939	+	2.74783i	0.167331	+	0.0966087i	−0.413996	+	0.910279i	$0.635867\pi$
$810$	3.39951	+	2.45075i	0.119447	+	0.0861105i
$811$	−24.5564			−0.862292			−0.431146	−	0.902282i	$-0.641891\pi$
$811$	−24.5564			−0.862292			−0.431146	+	0.902282i	$0.641891\pi$
$812$	1.36216	−	12.1860i	0.0478025	−	0.427643i
$813$	51.8774	−	12.5054i	1.81942	−	0.438582i
$814$		−	14.5664i		−	0.510551i
$815$	−1.17272	−	2.03121i	−0.0410787	−	0.0711504i
$816$	−1.21337	−	1.27626i	−0.0424763	−	0.0446780i
$817$	−5.31373	+	9.20364i	−0.185904	+	0.321995i
$818$	23.0263			0.805097
$819$	28.5635	−	1.76792i	0.998090	−	0.0617763i
$820$	5.03009			0.175658
$821$	−21.8976	+	37.9278i	−0.764233	+	1.32369i	0.176419	+	0.984315i	$0.443549\pi$
$821$	−21.8976	+	37.9278i	−0.764233	+	1.32369i	−0.940651	+	0.339374i	$0.889785\pi$
$822$	−20.3218	−	21.3751i	−0.708805	−	0.745544i
$823$	−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
$825$	22.5025	−	5.42438i	0.783438	−	0.188853i
$826$	2.98980	−	26.7469i	0.104029	−	0.930644i
$827$	1.75319			0.0609644			0.0304822	−	0.999535i	$-0.490296\pi$
$827$	1.75319			0.0609644			0.0304822	+	0.999535i	$0.490296\pi$
$828$	24.7247	+	1.24996i	0.859243	+	0.0434390i
$829$	−25.4012	−	14.6654i	−0.882219	−	0.509349i	−0.0108294	−	0.999941i	$-0.503447\pi$
$829$	−25.4012	−	14.6654i	−0.882219	−	0.509349i	−0.871389	+	0.490592i	$0.836781\pi$
$830$	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
$834$	−25.1817	+	23.9408i	−0.871971	+	0.829002i
$835$	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
$843$	6.79041	+	7.14237i	0.233874	+	0.245996i
$844$	−10.2691			−0.353478
$845$	−2.61825	−	5.45786i	−0.0900707	−	0.187756i
$846$	−0.452066	+	0.698945i	−0.0155424	+	0.0240302i
$847$	3.38591	+	7.74198i	0.116341	+	0.266017i
$848$	7.79401	+	4.49987i	0.267647	+	0.154526i
$849$	−6.08257	−	25.2330i	−0.208753	−	0.865994i
$850$	4.86310			0.166803
$851$	21.5112	+	37.2586i	0.737396	+	1.27721i
$852$	16.8889	−	4.07117i	0.578603	−	0.139476i
$853$	−42.9298			−1.46989			−0.734943	−	0.678129i	$-0.762791\pi$
$853$	−42.9298			−1.46989			−0.734943	+	0.678129i	$0.762791\pi$
$854$	−3.81617	+	34.1396i	−0.130587	+	1.16823i
$855$	1.04083	+	2.03344i	0.0355956	+	0.0695422i
$856$	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	$0.398081\pi$
$858$	17.4132	+	1.10563i	0.594477	+	0.0377455i
$859$		−	39.0164i		−	1.33122i	−0.746299	−	0.665611i	$-0.768171\pi$
$859$		−	39.0164i		−	1.33122i	0.746299	−	0.665611i	$-0.231829\pi$
$860$	−2.62078	−	1.51311i	−0.0893678	−	0.0515966i
$861$	−6.18277	−	49.1153i	−0.210708	−	1.67384i
$862$	10.8170	+	18.7355i	0.368427	+	0.638135i
$863$	18.8674			0.642255			0.321128	−	0.947036i	$-0.395938\pi$
$863$	18.8674			0.642255			0.321128	+	0.947036i	$0.395938\pi$
$864$	−4.90290	−	1.72093i	−0.166800	−	0.0585472i
$865$	3.09767	−	1.78844i	0.105324	−	0.0608087i
$866$			10.5674i			0.359096i
$867$	−26.8844	+	6.48064i	−0.913041	+	0.220094i
$868$	−2.06461	−	4.72080i	−0.0700775	−	0.160234i
$869$	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
$873$	−41.8131	+	21.4023i	−1.41516	+	0.724357i
$874$	11.6864	+	6.74712i	0.395297	+	0.228225i
$875$	−1.33893	+	11.9781i	−0.0452640	+	0.404933i
$876$	−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	$0.945882\pi$
$882$	−14.6797	−	15.0168i	−0.494292	−	0.505643i
$883$	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	$-0.135732\pi$
$888$	−2.11614	−	8.77864i	−0.0710132	−	0.294592i
$889$	−5.95374	+	8.08192i	−0.199682	+	0.271059i
$890$	2.72715	+	4.72356i	0.0914143	+	0.158334i
$891$	14.7049	−	20.3977i	0.492634	−	0.683349i
$892$	16.4059			0.549311
$893$	−0.392939	+	0.226864i	−0.0131492	+	0.00759170i
$894$	−4.57567	−	4.81283i	−0.153033	−	0.160965i
$895$	5.92086	−	10.2552i	0.197913	−	0.342795i
$896$	−1.56923	+	2.13015i	−0.0524241	+	0.0711633i
$897$	−46.1731	+	22.8873i	−1.54167	+	0.764186i
$898$	5.22599			0.174394
$899$	7.81645	+	4.51283i	0.260693	+	0.150511i
$900$	12.7735	−	6.53816i	0.425782	−	0.217939i
$901$	−7.92425	+	4.57507i	−0.263995	+	0.152418i
$902$		−	30.1815i		−	1.00493i
$903$	−11.5531	+	27.4499i	−0.384462	+	0.913475i
$904$	−0.251978	+	0.145480i	−0.00838067	+	0.00483858i
$905$	−0.125786			−0.00418126
$906$	−8.42020	−	34.9305i	−0.279742	−	1.16049i
$907$	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
$910$	−1.77579	+	4.07157i	−0.0588668	+	0.134971i
$911$			9.32478i			0.308944i	0.987997	+	0.154472i	$0.0493676\pi$
$911$			9.32478i			0.308944i	−0.987997	+	0.154472i	$0.950632\pi$
$912$	−1.95155	−	2.05270i	−0.0646223	−	0.0679718i
$913$	−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
$917$	−23.1543	−	2.58822i	−0.764622	−	0.0854705i
$918$	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
$921$	13.1709	+	13.8536i	0.433995	+	0.456490i
$922$			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
$927$	−9.10121	−	0.460112i	−0.298923	−	0.0151121i
$928$		−	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	$0.964253\pi$
$930$	0.368078	+	1.52694i	0.0120698	+	0.0500704i
$931$	−3.39325	−	10.9322i	−0.111209	−	0.358290i
$932$	17.2354	−	9.95086i	0.564564	−	0.325951i
$933$	25.7800	+	27.1162i	0.843999	+	0.887746i
$934$	16.0720	−	27.8375i	0.525892	−	0.910871i
$935$			1.32273i			0.0432580i
$936$	10.6549	−	1.86340i	0.348268	−	0.0609071i
$937$			47.2565i			1.54380i	0.635742	+	0.771902i	$0.280694\pi$
$937$			47.2565i			1.54380i	−0.635742	+	0.771902i	$0.719306\pi$
$938$	0.863050	−	0.377450i	0.0281796	−	0.0123242i
$939$	4.47818	−	4.25750i	0.146140	−	0.138938i
$940$	−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	$0.802709\pi$
$942$	−2.47753	−	10.2778i	−0.0807224	−	0.334870i
$943$	44.5713	+	77.1997i	1.45144	+	2.51397i
$944$		−	10.1723i		−	0.331082i
$945$	3.60566	+	5.28954i	0.117292	+	0.172069i
$946$	−9.07893	+	15.7252i	−0.295181	+	0.511269i
$947$	4.77969	−	8.27867i	0.155319	−	0.269021i	−0.777856	−	0.628443i	$-0.783693\pi$
$947$	4.77969	−	8.27867i	0.155319	−	0.269021i	0.933175	+	0.359422i	$0.117026\pi$
$948$	2.44278	−	8.27476i	0.0793378	−	0.268752i
$949$	−1.16830	−	5.13646i	−0.0379245	−	0.166736i
$950$	7.82169			0.253769
$951$	−25.7190	−	27.0520i	−0.833994	−	0.877222i
$952$	−1.07786	−	2.46457i	−0.0349338	−	0.0798771i
$953$	−25.8589	+	14.9297i	−0.837653	+	0.483619i	−0.856466	−	0.516204i	$-0.827345\pi$
$953$	−25.8589	+	14.9297i	−0.837653	+	0.483619i	0.0188130	+	0.999823i	$0.494011\pi$
$954$	−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
$959$	−18.0524	−	41.2773i	−0.582942	−	1.33291i
$960$	0.584516	−	0.555713i	0.0188652	−	0.0179356i
$961$	−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
$966$	34.8546	+	14.6695i	1.12143	+	0.471985i
$967$			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
$969$	2.79948	−	0.674831i	0.0899322	−	0.0216787i
$970$		−	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	$0.591396\pi$
$972$	5.89885	−	14.4293i	0.189206	−	0.462819i
$973$	−48.6281	+	21.2672i	−1.55894	+	0.681795i
$974$			8.45786i			0.271007i
$975$	−16.5447	+	24.8706i	−0.529853	+	0.796496i
$976$			12.9839i			0.415606i
$977$	−11.3672	+	19.6885i	−0.363667	+	0.629890i	−0.988561	−	0.150819i	$-0.951809\pi$
$977$	−11.3672	+	19.6885i	−0.363667	+	0.629890i	0.624894	+	0.780710i	$0.285142\pi$
$978$	−6.32284	+	6.01126i	−0.202182	+	0.192219i
$979$	28.3422	−	16.3634i	0.905822	−	0.522977i
$980$	3.11301	−	0.966243i	0.0994414	−	0.0308655i
$981$	−32.4103	−	1.63850i	−1.03478	−	0.0523134i
$982$	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	$-0.388503\pi$
$984$	−4.38465	−	18.1893i	−0.139777	−	0.579854i
$985$	−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
$990$	1.77834	+	3.47430i	0.0565193	+	0.110420i
$991$	−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
$994$	26.3729	+	2.94799i	0.836497	+	0.0935047i
$995$	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	−0.946226	−	0.323507i	$-0.895138\pi$
$997$	−35.9697	+	20.7671i	−1.13917	+	0.657702i	−0.192947	+	0.981209i	$0.561805\pi$
$998$	9.01320	+	5.20377i	0.285308	+	0.164722i
$999$	26.6229	−	5.01062i	0.842310	−	0.158529i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.19343 - 1.25528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.68382 - 0.405895i) q^{6} +(2.62938 + 0.293915i) q^{7} +1.00000 q^{8} +(-0.151472 + 2.99617i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.19343 - 1.25528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.465645i q^{5} +(1.68382 - 0.405895i) q^{6} +(2.62938 + 0.293915i) q^{7} +1.00000 q^{8} +(-0.151472 + 2.99617i) 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} +(0.584516 - 0.555713i) 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} +(-1.19343 - 1.25528i) q^{24} +4.78317 q^{25} +(3.44457 + 1.06535i) q^{26} +(3.94182 - 3.38557i) q^{27} +(-1.06015 - 2.42406i) q^{28} +(4.01364 + 2.31727i) q^{29} +(0.189003 + 0.784062i) q^{30} +1.94747 q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.70452 - 1.13405i) q^{33} +1.01671 q^{34} +(-0.136860 + 1.22436i) q^{35} +(2.67050 - 1.36691i) q^{36} +(4.51505 + 2.60676i) q^{37} +1.63525 q^{38} +(-3.45893 + 5.19960i) q^{39} +0.465645i q^{40} +(9.35517 + 5.40121i) q^{41} +(4.54669 - 0.572351i) q^{42} +(-3.24949 - 5.62828i) q^{43} +2.79396 q^{44} +(-1.39515 - 0.0705321i) q^{45} +(-7.14652 + 4.12605i) q^{46} -0.277466i q^{47} +(1.68382 - 0.405895i) q^{48} +(6.82723 + 1.54563i) q^{49} +(-2.39159 + 4.14235i) q^{50} +(-0.498589 + 1.68894i) q^{51} +(-2.64490 + 2.45041i) q^{52} -8.99975i q^{53} +(0.961081 + 5.10650i) q^{54} +(-1.12669 - 0.650496i) q^{55} +(2.62938 + 0.293915i) 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} +(-1.27890 + 7.83354i) 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} +(-3.34948 - 13.8950i) q^{69} +(-0.991893 - 0.730702i) q^{70} +(-5.01505 - 8.68632i) q^{71} +(-0.151472 + 2.99617i) q^{72} +1.46098 q^{73} +(-4.51505 + 2.60676i) q^{74} +(-5.70836 - 6.00424i) q^{75} +(-0.817625 + 1.41617i) q^{76} +(-4.38435 + 5.95154i) q^{77} +(-2.77352 - 5.59532i) q^{78} -4.98126 q^{79} +(-0.403261 - 0.232823i) q^{80} +(-8.95411 - 0.907671i) q^{81} +(-9.35517 + 5.40121i) q^{82} +12.2750i q^{83} +(-1.77768 + 4.22373i) q^{84} +(0.409999 - 0.236713i) q^{85} +6.49897 q^{86} +(-1.88114 - 7.80374i) q^{87} +(-1.39698 + 2.41964i) q^{88} +(-10.1441 - 5.85671i) q^{89} +(0.758659 - 1.17297i) q^{90} +(-1.06929 - 9.47927i) q^{91} -8.25209i q^{92} +(-2.32416 - 2.44463i) 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} +(-4.75217 + 5.13974i) q^{98} +(-7.03805 - 4.55210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 q^{93} + 36 q^{95} - 36 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * q^93 + 36 * q^95 - 36 * q^99

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