LMFDB - Embedded newform 546.2.u.a.185.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (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:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.29
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.0864870 - 1.72989i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.886718 + 1.53584i) q^{5} +(0.939845 - 1.45489i) q^{6} +(2.61154 + 0.424103i) q^{7} +1.00000i q^{8} +(-2.98504 - 0.299226i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.0864870 - 1.72989i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.886718 + 1.53584i) q^{5} +(0.939845 - 1.45489i) q^{6} +(2.61154 + 0.424103i) q^{7} +1.00000i q^{8} +(-2.98504 - 0.299226i) q^{9} +1.77344i q^{10} +0.893720i q^{11} +(1.54137 - 0.790045i) q^{12} +(1.84344 - 3.09866i) q^{13} +(2.04961 + 1.67305i) q^{14} +(2.73352 - 1.40109i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.74970 + 6.49467i) q^{17} +(-2.43551 - 1.75166i) q^{18} +0.805715i q^{19} +(-0.886718 + 1.53584i) q^{20} +(0.959516 - 4.48100i) q^{21} +(-0.446860 + 0.773984i) q^{22} +(-4.72239 - 2.72647i) q^{23} +(1.72989 + 0.0864870i) q^{24} +(0.927464 - 1.60641i) q^{25} +(3.14580 - 1.76180i) q^{26} +(-0.775795 + 5.13791i) q^{27} +(0.938485 + 2.47371i) q^{28} +(7.62822 - 4.40416i) q^{29} +(3.06785 + 0.153379i) q^{30} +(-8.20495 - 4.73713i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.54604 + 0.0772952i) q^{33} +7.49940i q^{34} +(1.66434 + 4.38697i) q^{35} +(-1.23338 - 2.73473i) q^{36} +(-1.84733 + 3.19966i) q^{37} +(-0.402858 + 0.697770i) q^{38} +(-5.20091 - 3.45695i) q^{39} +(-1.53584 + 0.886718i) q^{40} +(-3.47099 - 6.01193i) q^{41} +(3.07146 - 3.40090i) q^{42} +(1.93884 - 3.35816i) q^{43} +(-0.773984 + 0.446860i) q^{44} +(-2.18732 - 4.84987i) q^{45} +(-2.72647 - 4.72239i) q^{46} +(4.19126 + 7.25948i) q^{47} +(1.45489 + 0.939845i) q^{48} +(6.64027 + 2.21512i) q^{49} +(1.60641 - 0.927464i) q^{50} +(11.5594 - 5.92486i) q^{51} +(3.60524 + 0.0471388i) q^{52} +(-2.72420 - 1.57281i) q^{53} +(-3.24081 + 4.06166i) q^{54} +(-1.37261 + 0.792477i) q^{55} +(-0.424103 + 2.61154i) q^{56} +(1.39380 + 0.0696839i) q^{57} +8.80832 q^{58} +(1.67450 + 2.90031i) q^{59} +(2.58014 + 1.66675i) q^{60} +8.21094i q^{61} +(-4.73713 - 8.20495i) q^{62} +(-7.66865 - 2.04741i) q^{63} -1.00000 q^{64} +(6.39366 + 0.0835977i) q^{65} +(1.30026 + 0.839958i) q^{66} -7.98740 q^{67} +(-3.74970 + 6.49467i) q^{68} +(-5.12492 + 7.93341i) q^{69} +(-0.752120 + 4.63139i) q^{70} +(-1.97967 - 1.14296i) q^{71} +(0.299226 - 2.98504i) q^{72} +(-7.54968 - 4.35881i) q^{73} +(-3.19966 + 1.84733i) q^{74} +(-2.69871 - 1.74335i) q^{75} +(-0.697770 + 0.402858i) q^{76} +(-0.379030 + 2.33398i) q^{77} +(-2.77565 - 5.59426i) q^{78} +(-6.40376 - 11.0916i) q^{79} -1.77344 q^{80} +(8.82093 + 1.78640i) q^{81} -6.94198i q^{82} -13.8340 q^{83} +(4.36041 - 1.40953i) q^{84} +(-6.64985 + 11.5179i) q^{85} +(3.35816 - 1.93884i) q^{86} +(-6.95897 - 13.5769i) q^{87} -0.893720 q^{88} +(-7.75816 + 13.4375i) q^{89} +(0.530658 - 5.29377i) q^{90} +(6.12838 - 7.31047i) q^{91} -5.45295i q^{92} +(-8.90433 + 13.7840i) q^{93} +8.38252i q^{94} +(-1.23745 + 0.714442i) q^{95} +(0.790045 + 1.54137i) q^{96} +(-4.24795 - 2.45256i) q^{97} +(4.64308 + 5.23849i) q^{98} +(0.267424 - 2.66779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.0864870	−	1.72989i	0.0499333	−	0.998753i
$3$	0.0864870	−	1.72989i	0.0499333	−	0.998753i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.886718	+	1.53584i	0.396552	+	0.686848i	0.993298	−	0.115582i	$-0.0368733\pi$
$5$	0.886718	+	1.53584i	0.396552	+	0.686848i	−0.596746	+	0.802430i	$0.703540\pi$
$6$	0.939845	−	1.45489i	0.383690	−	0.593954i
$7$	2.61154	+	0.424103i	0.987069	+	0.160296i
$7$	2.61154	+	0.424103i	0.987069	+	0.160296i
$8$			1.00000i			0.353553i
$9$	−2.98504	−	0.299226i	−0.995013	−	0.0997420i
$10$			1.77344i			0.560809i
$11$			0.893720i			0.269467i	0.990882	+	0.134733i	$0.0430178\pi$
$11$			0.893720i			0.269467i	−0.990882	+	0.134733i	$0.956982\pi$
$12$	1.54137	−	0.790045i	0.444956	−	0.228066i
$13$	1.84344	−	3.09866i	0.511280	−	0.859414i
$13$	1.84344	−	3.09866i	0.511280	−	0.859414i
$14$	2.04961	+	1.67305i	0.547781	+	0.447142i
$15$	2.73352	−	1.40109i	0.705793	−	0.361761i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.74970	+	6.49467i	0.909436	+	1.57519i	0.814850	+	0.579672i	$0.196819\pi$
$17$	3.74970	+	6.49467i	0.909436	+	1.57519i	0.0945862	+	0.995517i	$0.469847\pi$
$18$	−2.43551	−	1.75166i	−0.574055	−	0.412870i
$19$			0.805715i			0.184844i	0.995720	+	0.0924219i	$0.0294608\pi$
$19$			0.805715i			0.184844i	−0.995720	+	0.0924219i	$0.970539\pi$
$20$	−0.886718	+	1.53584i	−0.198276	+	0.343424i
$21$	0.959516	−	4.48100i	0.209384	−	0.977834i
$22$	−0.446860	+	0.773984i	−0.0952709	+	0.165014i
$23$	−4.72239	−	2.72647i	−0.984686	−	0.568509i	−0.0810046	−	0.996714i	$-0.525813\pi$
$23$	−4.72239	−	2.72647i	−0.984686	−	0.568509i	−0.903682	+	0.428205i	$0.859146\pi$
$24$	1.72989	+	0.0864870i	0.353112	+	0.0176541i
$25$	0.927464	−	1.60641i	0.185493	−	0.321283i
$26$	3.14580	−	1.76180i	0.616942	−	0.345517i
$27$	−0.775795	+	5.13791i	−0.149302	+	0.988792i
$28$	0.938485	+	2.47371i	0.177357	+	0.467487i
$29$	7.62822	−	4.40416i	1.41653	−	0.817832i	0.420534	−	0.907277i	$-0.361843\pi$
$29$	7.62822	−	4.40416i	1.41653	−	0.817832i	0.995992	+	0.0894452i	$0.0285094\pi$
$30$	3.06785	+	0.153379i	0.560110	+	0.0280031i
$31$	−8.20495	−	4.73713i	−1.47365	−	0.850813i	−0.474092	−	0.880475i	$-0.657224\pi$
$31$	−8.20495	−	4.73713i	−1.47365	−	0.850813i	−0.999560	+	0.0296621i	$0.990557\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.54604	+	0.0772952i	0.269131	+	0.0134554i
$34$			7.49940i			1.28614i
$35$	1.66434	+	4.38697i	0.281325	+	0.741533i
$36$	−1.23338	−	2.73473i	−0.205564	−	0.455789i
$37$	−1.84733	+	3.19966i	−0.303699	+	0.526022i	−0.976971	−	0.213373i	$-0.931555\pi$
$37$	−1.84733	+	3.19966i	−0.303699	+	0.526022i	0.673272	+	0.739395i	$0.264888\pi$
$38$	−0.402858	+	0.697770i	−0.0653521	+	0.113193i
$39$	−5.20091	−	3.45695i	−0.832812	−	0.553555i
$40$	−1.53584	+	0.886718i	−0.242838	+	0.140202i
$41$	−3.47099	−	6.01193i	−0.542078	−	0.938906i	−0.998785	−	0.0492887i	$-0.984305\pi$
$41$	−3.47099	−	6.01193i	−0.542078	−	0.938906i	0.456707	−	0.889617i	$-0.349029\pi$
$42$	3.07146	−	3.40090i	0.473937	−	0.524770i
$43$	1.93884	−	3.35816i	0.295670	−	0.512115i	−0.679471	−	0.733703i	$-0.737791\pi$
$43$	1.93884	−	3.35816i	0.295670	−	0.512115i	0.975140	+	0.221588i	$0.0711239\pi$
$44$	−0.773984	+	0.446860i	−0.116682	+	0.0673667i
$45$	−2.18732	−	4.84987i	−0.326067	−	0.722976i
$46$	−2.72647	−	4.72239i	−0.401996	−	0.696278i
$47$	4.19126	+	7.25948i	0.611358	+	1.05890i	0.991012	+	0.133775i	$0.0427099\pi$
$47$	4.19126	+	7.25948i	0.611358	+	1.05890i	−0.379653	+	0.925129i	$0.623957\pi$
$48$	1.45489	+	0.939845i	0.209995	+	0.135655i
$49$	6.64027	+	2.21512i	0.948610	+	0.316446i
$50$	1.60641	−	0.927464i	0.227181	−	0.131163i
$51$	11.5594	−	5.92486i	1.61864	−	0.829647i
$52$	3.60524	+	0.0471388i	0.499957	+	0.00653698i
$53$	−2.72420	−	1.57281i	−0.374197	−	0.216043i	0.301093	−	0.953595i	$-0.402648\pi$
$53$	−2.72420	−	1.57281i	−0.374197	−	0.216043i	−0.675290	+	0.737552i	$0.735982\pi$
$54$	−3.24081	+	4.06166i	−0.441019	+	0.552723i
$55$	−1.37261	+	0.792477i	−0.185083	+	0.106858i
$56$	−0.424103	+	2.61154i	−0.0566732	+	0.348982i
$57$	1.39380	+	0.0696839i	0.184613	+	0.00922986i
$58$	8.80832			1.15659
$59$	1.67450	+	2.90031i	0.218001	+	0.377589i	0.954197	−	0.299180i	$-0.0967131\pi$
$59$	1.67450	+	2.90031i	0.218001	+	0.377589i	−0.736196	+	0.676769i	$0.763380\pi$
$60$	2.58014	+	1.66675i	0.333095	+	0.215177i
$61$			8.21094i			1.05130i	0.850700	+	0.525652i	$0.176178\pi$
$61$			8.21094i			1.05130i	−0.850700	+	0.525652i	$0.823822\pi$
$62$	−4.73713	−	8.20495i	−0.601616	−	1.04203i
$63$	−7.66865	−	2.04741i	−0.966159	−	0.257949i
$64$	−1.00000			−0.125000
$65$	6.39366	+	0.0835977i	0.793036	+	0.0103690i
$66$	1.30026	+	0.839958i	0.160051	+	0.103392i
$67$	−7.98740			−0.975816			−0.487908	−	0.872895i	$-0.662240\pi$
$67$	−7.98740			−0.975816			−0.487908	+	0.872895i	$0.662240\pi$
$68$	−3.74970	+	6.49467i	−0.454718	+	0.787595i
$69$	−5.12492	+	7.93341i	−0.616968	+	0.955070i
$70$	−0.752120	+	4.63139i	−0.0898955	+	0.553558i
$71$	−1.97967	−	1.14296i	−0.234943	−	0.135645i	0.377907	−	0.925843i	$-0.376644\pi$
$71$	−1.97967	−	1.14296i	−0.234943	−	0.135645i	−0.612850	+	0.790199i	$0.709977\pi$
$72$	0.299226	−	2.98504i	0.0352641	−	0.351790i
$73$	−7.54968	−	4.35881i	−0.883624	−	0.510160i	−0.0117722	−	0.999931i	$-0.503747\pi$
$73$	−7.54968	−	4.35881i	−0.883624	−	0.510160i	−0.871851	+	0.489770i	$0.837081\pi$
$74$	−3.19966	+	1.84733i	−0.371953	+	0.214747i
$75$	−2.69871	−	1.74335i	−0.311620	−	0.201304i
$76$	−0.697770	+	0.402858i	−0.0800397	+	0.0462109i
$77$	−0.379030	+	2.33398i	−0.0431944	+	0.265982i
$78$	−2.77565	−	5.59426i	−0.314280	−	0.633426i
$79$	−6.40376	−	11.0916i	−0.720479	−	1.24791i	−0.960808	−	0.277215i	$-0.910589\pi$
$79$	−6.40376	−	11.0916i	−0.720479	−	1.24791i	0.240329	−	0.970692i	$-0.422745\pi$
$80$	−1.77344			−0.198276
$81$	8.82093	+	1.78640i	0.980103	+	0.198489i
$82$		−	6.94198i		−	0.766613i
$83$	−13.8340			−1.51847			−0.759237	−	0.650814i	$-0.774428\pi$
$83$	−13.8340			−1.51847			−0.759237	+	0.650814i	$0.774428\pi$
$84$	4.36041	−	1.40953i	0.475760	−	0.153793i
$85$	−6.64985	+	11.5179i	−0.721277	+	1.24929i
$86$	3.35816	−	1.93884i	0.362120	−	0.209070i
$87$	−6.95897	−	13.5769i	−0.746080	−	1.45560i
$88$	−0.893720			−0.0952709
$89$	−7.75816	+	13.4375i	−0.822363	+	1.42437i	0.0815547	+	0.996669i	$0.474011\pi$
$89$	−7.75816	+	13.4375i	−0.822363	+	1.42437i	−0.903918	+	0.427706i	$0.859322\pi$
$90$	0.530658	−	5.29377i	0.0559363	−	0.558013i
$91$	6.12838	−	7.31047i	0.642429	−	0.766345i
$92$		−	5.45295i		−	0.568509i
$93$	−8.90433	+	13.7840i	−0.923336	+	1.42933i
$94$			8.38252i			0.864591i
$95$	−1.23745	+	0.714442i	−0.126960	+	0.0733002i
$96$	0.790045	+	1.54137i	0.0806336	+	0.157316i
$97$	−4.24795	−	2.45256i	−0.431314	−	0.249019i	0.268592	−	0.963254i	$-0.413442\pi$
$97$	−4.24795	−	2.45256i	−0.431314	−	0.249019i	−0.699906	+	0.714235i	$0.746775\pi$
$98$	4.64308	+	5.23849i	0.469022	+	0.529167i
$99$	0.267424	−	2.66779i	0.0268771	−	0.268123i
$100$	1.85493			0.185493
$101$	−16.6370			−1.65545			−0.827724	−	0.561136i	$-0.810364\pi$
$101$	−16.6370			−1.65545			−0.827724	+	0.561136i	$0.810364\pi$
$102$	12.9731	+	0.648601i	1.28453	+	0.0642210i
$103$	7.46308	−	4.30881i	0.735359	−	0.424560i	−0.0850206	−	0.996379i	$-0.527096\pi$
$103$	7.46308	−	4.30881i	0.735359	−	0.424560i	0.820379	+	0.571820i	$0.193762\pi$
$104$	3.09866	+	1.84344i	0.303849	+	0.180765i
$105$	7.73291	−	2.49971i	0.754655	−	0.243947i
$106$	−1.57281	−	2.72420i	−0.152765	−	0.264597i
$107$	−14.1412	−	8.16443i	−1.36708	−	0.789285i	−0.376527	−	0.926406i	$-0.622882\pi$
$107$	−14.1412	−	8.16443i	−1.36708	−	0.789285i	−0.990554	+	0.137121i	$0.956215\pi$
$108$	−4.83746	+	1.89710i	−0.465485	+	0.182548i
$109$	−0.641659	+	1.11139i	−0.0614598	+	0.106452i	−0.895118	−	0.445829i	$-0.852909\pi$
$109$	−0.641659	+	1.11139i	−0.0614598	+	0.106452i	0.833658	+	0.552281i	$0.186242\pi$
$110$	−1.58495			−0.151119
$111$	5.37530	+	3.47240i	0.510201	+	0.329586i
$112$	−1.67305	+	2.04961i	−0.158089	+	0.193670i
$113$	−0.274369	−	0.158407i	−0.0258105	−	0.0149017i	0.487039	−	0.873380i	$-0.338077\pi$
$113$	−0.274369	−	0.158407i	−0.0258105	−	0.0149017i	−0.512850	+	0.858478i	$0.671410\pi$
$114$	1.17222	+	0.757248i	0.109789	+	0.0709227i
$115$		−	9.67044i		−	0.901774i
$116$	7.62822	+	4.40416i	0.708263	+	0.408916i
$117$	−6.42996	+	8.69803i	−0.594450	+	0.804133i
$118$			3.34899i			0.308300i
$119$	7.03808	+	18.5513i	0.645179	+	1.70060i
$120$	1.40109	+	2.73352i	0.127902	+	0.249535i
$121$	10.2013			0.927388
$122$	−4.10547	+	7.11088i	−0.371692	+	0.643789i
$123$	−10.7002	+	5.48448i	−0.964802	+	0.494519i
$124$		−	9.47426i		−	0.850813i
$125$	12.1568			1.08733
$126$	−5.61754	−	5.60743i	−0.500450	−	0.499549i
$127$	2.45373	+	4.24999i	0.217733	+	0.377125i	0.954115	−	0.299442i	$-0.0968003\pi$
$127$	2.45373	+	4.24999i	0.217733	+	0.377125i	−0.736381	+	0.676567i	$0.763467\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−5.64157	−	3.64441i	−0.496712	−	0.320873i
$130$	5.49528	+	3.26923i	0.481968	+	0.286730i
$131$	2.64301	+	4.57783i	0.230921	+	0.399967i	0.958079	−	0.286503i	$-0.0924927\pi$
$131$	2.64301	+	4.57783i	0.230921	+	0.399967i	−0.727158	+	0.686470i	$0.759159\pi$
$132$	0.706079	+	1.37756i	0.0614563	+	0.119901i
$133$	−0.341707	+	2.10416i	−0.0296297	+	0.182454i
$134$	−6.91729	−	3.99370i	−0.597563	−	0.345003i
$135$	−8.57892	+	3.36438i	−0.738356	+	0.289560i
$136$	−6.49467	+	3.74970i	−0.556913	+	0.321534i
$137$	0.350205	−	0.202191i	0.0299200	−	0.0172743i	−0.484965	−	0.874533i	$-0.661168\pi$
$137$	0.350205	−	0.202191i	0.0299200	−	0.0172743i	0.514885	+	0.857259i	$0.327834\pi$
$138$	−8.40502	+	4.30807i	−0.715483	+	0.366728i
$139$	3.91193	+	2.25855i	0.331806	+	0.191568i	0.656642	−	0.754202i	$-0.271976\pi$
$139$	3.91193	+	2.25855i	0.331806	+	0.191568i	−0.324837	+	0.945770i	$0.605309\pi$
$140$	−2.96705	+	3.63485i	−0.250762	+	0.307201i
$141$	12.9206	−	6.62257i	1.08811	−	0.557721i
$142$	−1.14296	−	1.97967i	−0.0959152	−	0.166130i
$143$	2.76934	+	1.64752i	0.231584	+	0.137773i
$144$	1.75166	−	2.43551i	0.145971	−	0.202959i
$145$	13.5282	+	7.81049i	1.12345	+	0.648626i
$146$	−4.35881	−	7.54968i	−0.360738	−	0.624816i
$147$	4.40622	−	11.2954i	0.363419	−	0.931626i
$148$	−3.69465			−0.303699
$149$			2.74649i			0.225001i	0.993652	+	0.112500i	$0.0358860\pi$
$149$			2.74649i			0.225001i	−0.993652	+	0.112500i	$0.964114\pi$
$150$	−1.46548	−	2.85914i	−0.119656	−	0.233447i
$151$	7.11941	−	12.3312i	0.579369	−	1.00350i	−0.416183	−	0.909281i	$-0.636632\pi$
$151$	7.11941	−	12.3312i	0.579369	−	1.00350i	0.995552	−	0.0942159i	$-0.0300344\pi$
$152$	−0.805715			−0.0653521
$153$	−9.24963	−	20.5089i	−0.747788	−	1.65804i
$154$	−1.49524	+	1.83178i	−0.120490	+	0.147609i
$155$		−	16.8020i		−	1.34957i
$156$	0.393352	−	6.23260i	0.0314933	−	0.499007i
$157$	19.0276	+	10.9856i	1.51857	+	0.876747i	0.999761	+	0.0218580i	$0.00695817\pi$
$157$	19.0276	+	10.9856i	1.51857	+	0.876747i	0.518810	+	0.854889i	$0.326375\pi$
$158$		−	12.8075i		−	1.01891i
$159$	−2.95640	+	4.57653i	−0.234458	+	0.362942i
$160$	−1.53584	−	0.886718i	−0.121419	−	0.0701012i
$161$	−11.1764	−	9.12307i	−0.880824	−	0.718999i
$162$	6.74595	+	5.95753i	0.530012	+	0.468068i
$163$	5.49317			0.430258			0.215129	−	0.976586i	$-0.430983\pi$
$163$	5.49317			0.430258			0.215129	+	0.976586i	$0.430983\pi$
$164$	3.47099	−	6.01193i	0.271039	−	0.469453i
$165$	1.25219	+	2.44300i	0.0974825	+	0.190188i
$166$	−11.9806	−	6.91698i	−0.929872	−	0.536862i
$167$	−2.92252	−	5.06195i	−0.226151	−	0.391706i	0.730513	−	0.682899i	$-0.239281\pi$
$167$	−2.92252	−	5.06195i	−0.226151	−	0.391706i	−0.956664	+	0.291193i	$0.905948\pi$
$168$	4.48100	+	0.959516i	0.345716	+	0.0740283i
$169$	−6.20342	−	11.4244i	−0.477186	−	0.878802i
$170$	−11.5179	+	6.64985i	−0.883381	+	0.510020i
$171$	0.241091	−	2.40509i	0.0184367	−	0.183922i
$172$	3.87767			0.295670
$173$	−14.5872			−1.10905			−0.554523	−	0.832168i	$-0.687099\pi$
$173$	−14.5872			−1.10905			−0.554523	+	0.832168i	$0.687099\pi$
$174$	0.761805	−	15.2374i	0.0577523	−	1.15515i
$175$	3.10339	−	3.80187i	0.234595	−	0.287395i
$176$	−0.773984	−	0.446860i	−0.0583412	−	0.0336833i
$177$	5.16204	−	2.64586i	0.388003	−	0.198875i
$178$	−13.4375	+	7.75816i	−1.00719	+	0.581499i
$179$		−	9.68204i		−	0.723670i	−0.932242	−	0.361835i	$-0.882150\pi$
$179$		−	9.68204i		−	0.723670i	0.932242	−	0.361835i	$-0.117850\pi$
$180$	3.10645	−	4.31921i	0.231541	−	0.321935i
$181$			16.1898i			1.20338i	0.798731	+	0.601688i	$0.205505\pi$
$181$			16.1898i			1.20338i	−0.798731	+	0.601688i	$0.794495\pi$
$182$	8.96257	−	3.26686i	0.664350	−	0.242156i
$183$	14.2040	+	0.710140i	1.04999	+	0.0524950i
$184$	2.72647	−	4.72239i	0.200998	−	0.348139i
$185$	−6.55223			−0.481729
$186$	−14.6034	+	7.48509i	−1.07077	+	0.548833i
$187$	−5.80442	+	3.35118i	−0.424461	+	0.245063i
$188$	−4.19126	+	7.25948i	−0.305679	+	0.529452i
$189$	−4.20503	+	13.0888i	−0.305871	+	0.952073i
$190$	−1.42888			−0.103662
$191$			15.7947i			1.14287i	0.820649	+	0.571433i	$0.193612\pi$
$191$			15.7947i			1.14287i	−0.820649	+	0.571433i	$0.806388\pi$
$192$	−0.0864870	+	1.72989i	−0.00624166	+	0.124844i
$193$	−1.59938			−0.115126			−0.0575629	−	0.998342i	$-0.518333\pi$
$193$	−1.59938			−0.115126			−0.0575629	+	0.998342i	$0.518333\pi$
$194$	−2.45256	−	4.24795i	−0.176083	−	0.304985i
$195$	0.697584	−	11.0531i	0.0499550	−	0.791529i
$196$	1.40178	+	6.85821i	0.100127	+	0.489872i
$197$	3.83872	−	2.21629i	0.273498	−	0.157904i	−0.356978	−	0.934113i	$-0.616193\pi$
$197$	3.83872	−	2.21629i	0.273498	−	0.157904i	0.630476	+	0.776209i	$0.282860\pi$
$198$	1.56549	−	2.17666i	0.111255	−	0.154689i
$199$	10.7128	−	6.18504i	0.759410	−	0.438446i	−0.0696738	−	0.997570i	$-0.522196\pi$
$199$	10.7128	−	6.18504i	0.759410	−	0.438446i	0.829084	+	0.559124i	$0.188863\pi$
$200$	1.60641	+	0.927464i	0.113591	+	0.0655816i
$201$	−0.690806	+	13.8173i	−0.0487257	+	0.974599i
$202$	−14.4081	−	8.31852i	−1.01375	−	0.585289i
$203$	21.7892	−	8.26647i	1.52930	−	0.580193i
$204$	10.9108	+	7.04827i	0.763906	+	0.493478i
$205$	6.15558	−	10.6618i	0.429924	−	0.744650i
$206$	8.61762			0.600418
$207$	13.2807	+	9.55169i	0.923072	+	0.663889i
$208$	1.76180	+	3.14580i	0.122159	+	0.218122i
$209$	−0.720084			−0.0498092
$210$	7.94676	+	1.70164i	0.548378	+	0.117424i
$211$	−9.95733	−	17.2466i	−0.685491	−	1.18731i	−0.973282	−	0.229612i	$-0.926254\pi$
$211$	−9.95733	−	17.2466i	−0.685491	−	1.18731i	0.287791	−	0.957693i	$-0.407079\pi$
$212$		−	3.14563i		−	0.216043i
$213$	−2.14841	+	3.32576i	−0.147207	+	0.227877i
$214$	−8.16443	−	14.1412i	−0.558109	−	0.966673i
$215$	6.87680			0.468994
$216$	−5.13791	−	0.775795i	−0.349591	−	0.0527862i
$217$	−19.4185	−	15.8509i	−1.31821	−	1.07603i
$218$	−1.11139	+	0.641659i	−0.0752726	+	0.0434587i
$219$	−8.19322	+	12.6831i	−0.553646	+	0.857047i
$220$	−1.37261	−	0.792477i	−0.0925414	−	0.0534288i
$221$	27.0372	+	0.353513i	1.81872	+	0.0237799i
$222$	2.91894	+	5.69484i	0.195907	+	0.382212i
$223$	6.77255	−	3.91013i	0.453523	−	0.261842i	−0.255794	−	0.966731i	$-0.582337\pi$
$223$	6.77255	−	3.91013i	0.453523	−	0.261842i	0.709317	+	0.704890i	$0.249003\pi$
$224$	−2.47371	+	0.938485i	−0.165282	+	0.0627052i
$225$	−3.24920	+	4.51769i	−0.216613	+	0.301179i
$226$	−0.158407	−	0.274369i	−0.0105371	−	0.0182508i
$227$	11.3466	+	19.6528i	0.753098	+	1.30440i	0.946315	+	0.323247i	$0.104775\pi$
$227$	11.3466	+	19.6528i	0.753098	+	1.30440i	−0.193217	+	0.981156i	$0.561892\pi$
$228$	0.636552	+	1.24191i	0.0421567	+	0.0822473i
$229$	2.94903	−	1.70262i	0.194877	−	0.112513i	−0.399386	−	0.916783i	$-0.630777\pi$
$229$	2.94903	−	1.70262i	0.194877	−	0.112513i	0.594264	+	0.804270i	$0.297443\pi$
$230$	4.83522	−	8.37485i	0.318825	−	0.552221i
$231$	4.00476	+	0.857539i	0.263494	+	0.0564219i
$232$	4.40416	+	7.62822i	0.289147	+	0.500817i
$233$	5.66985	−	3.27349i	0.371444	−	0.214453i	−0.302645	−	0.953103i	$-0.597870\pi$
$233$	5.66985	−	3.27349i	0.371444	−	0.214453i	0.674089	+	0.738650i	$0.264536\pi$
$234$	−9.91752	+	4.31773i	−0.648329	+	0.282259i
$235$	−7.43293	+	12.8742i	−0.484871	+	0.839821i
$236$	−1.67450	+	2.90031i	−0.109000	+	0.188794i
$237$	−19.7412	+	10.1185i	−1.28233	+	0.657268i
$238$	−3.18052	+	19.5850i	−0.206163	+	1.26951i
$239$		−	2.75097i		−	0.177946i	−0.996034	−	0.0889729i	$-0.971642\pi$
$239$		−	2.75097i		−	0.177946i	0.996034	−	0.0889729i	$-0.0283584\pi$
$240$	−0.153379	+	3.06785i	−0.00990058	+	0.198029i
$241$	5.30840	−	3.06480i	0.341944	−	0.197421i	−0.319187	−	0.947692i	$-0.603410\pi$
$241$	5.30840	−	3.06480i	0.341944	−	0.197421i	0.661131	+	0.750270i	$0.270077\pi$
$242$	8.83455	+	5.10063i	0.567907	+	0.327881i
$243$	3.85318	−	15.1047i	0.247181	−	0.968969i
$244$	−7.11088	+	4.10547i	−0.455228	+	0.262826i
$245$	2.48597	+	12.1626i	0.158823	+	0.777039i
$246$	−12.0089	−	0.600391i	−0.765657	−	0.0382795i
$247$	2.49664	+	1.48529i	0.158857	+	0.0945069i
$248$	4.73713	−	8.20495i	0.300808	−	0.521015i
$249$	−1.19646	+	23.9312i	−0.0758224	+	1.51658i
$250$	10.5281	+	6.07838i	0.665854	+	0.384431i
$251$	6.30342	−	10.9178i	0.397868	−	0.689128i	−0.595594	−	0.803285i	$-0.703083\pi$
$251$	6.30342	−	10.9178i	0.397868	−	0.689128i	0.993463	+	0.114157i	$0.0364167\pi$
$252$	−2.06122	−	7.66495i	−0.129845	−	0.482846i
$253$	2.43670	−	4.22049i	0.153194	−	0.265340i
$254$			4.90746i			0.307921i
$255$	19.3495	+	12.4997i	1.21171	+	0.782759i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.6331	−	23.6133i	0.850411	−	1.47295i	−0.0304278	−	0.999537i	$-0.509687\pi$
$257$	13.6331	−	23.6133i	0.850411	−	1.47295i	0.880838	−	0.473417i	$-0.156980\pi$
$258$	−3.06354	−	5.97694i	−0.190727	−	0.372108i
$259$	−6.18135	+	7.57259i	−0.384091	+	0.470538i
$260$	3.12443	+	5.57887i	0.193769	+	0.345987i
$261$	−24.0884	+	10.8640i	−1.49103	+	0.672466i
$262$			5.28603i			0.326572i
$263$			0.562483i			0.0346842i	0.999850	+	0.0173421i	$0.00552043\pi$
$263$			0.562483i			0.0346842i	−0.999850	+	0.0173421i	$0.994480\pi$
$264$	−0.0772952	+	1.54604i	−0.00475719	+	0.0951520i
$265$		−	5.57857i		−	0.342689i
$266$	−1.34801	+	1.65140i	−0.0826515	+	0.101254i
$267$	22.5745	+	14.5829i	1.38153	+	0.892461i
$268$	−3.99370	−	6.91729i	−0.243954	−	0.422541i
$269$	−1.96598	−	3.40518i	−0.119868	−	0.207617i	0.799847	−	0.600204i	$-0.204914\pi$
$269$	−1.96598	−	3.40518i	−0.119868	−	0.207617i	−0.919715	+	0.392586i	$0.871580\pi$
$270$	−9.11175	−	1.37582i	−0.554524	−	0.0837299i
$271$	0.759673	+	0.438598i	0.0461469	+	0.0266429i	0.522896	−	0.852397i	$-0.324852\pi$
$271$	0.759673	+	0.438598i	0.0461469	+	0.0266429i	−0.476749	+	0.879039i	$0.658185\pi$
$272$	−7.49940			−0.454718
$273$	−12.1163	−	11.2337i	−0.733311	−	0.679894i
$274$	0.404382			0.0244296
$275$	1.43568	+	0.828893i	0.0865751	+	0.0499841i
$276$	−9.43300	−	0.471609i	−0.567800	−	0.0283875i
$277$	6.30351	+	10.9180i	0.378741	+	0.655999i	0.990879	−	0.134752i	$-0.0430237\pi$
$277$	6.30351	+	10.9180i	0.378741	+	0.655999i	−0.612138	+	0.790751i	$0.709690\pi$
$278$	2.25855	+	3.91193i	0.135459	+	0.234622i
$279$	23.0746	+	16.5956i	1.38144	+	0.993556i
$280$	−4.38697	+	1.66434i	−0.262171	+	0.0994635i
$281$			6.37716i			0.380429i	0.981743	+	0.190215i	$0.0609184\pi$
$281$			6.37716i			0.380429i	−0.981743	+	0.190215i	$0.939082\pi$
$282$	14.5008	+	0.724979i	0.863513	+	0.0431719i
$283$			0.760814i			0.0452257i	0.999744	+	0.0226129i	$0.00719851\pi$
$283$			0.760814i			0.0452257i	−0.999744	+	0.0226129i	$0.992801\pi$
$284$		−	2.28592i		−	0.135645i
$285$	1.12888	+	2.20244i	0.0668692	+	0.130461i
$286$	1.57455	+	2.81147i	0.0931053	+	0.166245i
$287$	−6.51495	−	17.1725i	−0.384565	−	1.01366i
$288$	2.73473	−	1.23338i	0.161146	−	0.0726778i
$289$	−19.6205	+	33.9837i	−1.15415	+	1.99904i
$290$	7.81049	+	13.5282i	0.458648	+	0.794401i
$291$	−4.61005	+	7.13638i	−0.270246	+	0.418342i
$292$		−	8.71762i		−	0.510160i
$293$	6.35235	−	11.0026i	0.371108	−	0.642778i	−0.618628	−	0.785684i	$-0.712311\pi$
$293$	6.35235	−	11.0026i	0.371108	−	0.642778i	0.989736	+	0.142906i	$0.0456446\pi$
$294$	9.46358	−	7.57896i	0.551927	−	0.442014i
$295$	−2.96961	+	5.14352i	−0.172897	+	0.299467i
$296$	−3.19966	−	1.84733i	−0.185977	−	0.107374i
$297$	−4.59185	−	0.693344i	−0.266446	−	0.0402319i
$298$	−1.37324	+	2.37853i	−0.0795499	+	0.137784i
$299$	−17.1539	+	9.60699i	−0.992035	+	0.555587i
$300$	0.160427	−	3.20882i	0.00926227	−	0.185261i
$301$	6.48756	−	7.94771i	0.373936	−	0.458098i
$302$	12.3312	−	7.11941i	0.709579	−	0.409676i
$303$	−1.43889	+	28.7802i	−0.0826619	+	1.65338i
$304$	−0.697770	−	0.402858i	−0.0400199	−	0.0231055i
$305$	−12.6107	+	7.28078i	−0.722086	+	0.416897i
$306$	2.24402	−	22.3860i	0.128282	−	1.27972i
$307$			2.90418i			0.165750i	0.996560	+	0.0828751i	$0.0264102\pi$
$307$			2.90418i			0.165750i	−0.996560	+	0.0828751i	$0.973590\pi$
$308$	−2.21080	+	0.838743i	−0.125972	+	0.0477918i
$309$	−6.80831	−	13.2830i	−0.387311	−	0.755641i
$310$	8.40099	−	14.5509i	0.477144	−	0.826438i
$311$	−9.08284	+	15.7319i	−0.515040	+	0.892076i	0.484807	+	0.874621i	$0.338890\pi$
$311$	−9.08284	+	15.7319i	−0.515040	+	0.892076i	−0.999848	+	0.0174552i	$0.994444\pi$
$312$	3.45695	−	5.20091i	0.195711	−	0.294444i
$313$	2.78744	−	1.60933i	0.157556	−	0.0909648i	−0.419149	−	0.907917i	$-0.637672\pi$
$313$	2.78744	−	1.60933i	0.157556	−	0.0909648i	0.576705	+	0.816953i	$0.304338\pi$
$314$	10.9856	+	19.0276i	0.619954	+	1.07379i
$315$	−3.65544	−	13.5933i	−0.205960	−	0.765895i
$316$	6.40376	−	11.0916i	0.360240	−	0.623953i
$317$	−0.947773	+	0.547197i	−0.0532322	+	0.0307336i	−0.526380	−	0.850249i	$-0.676451\pi$
$317$	−0.947773	+	0.547197i	−0.0532322	+	0.0307336i	0.473148	+	0.880983i	$0.343118\pi$
$318$	−4.84859	+	2.48519i	−0.271895	+	0.139362i
$319$	3.93608	+	6.81750i	0.220378	+	0.381706i
$320$	−0.886718	−	1.53584i	−0.0495690	−	0.0858561i
$321$	−15.3466	+	23.7566i	−0.856563	+	1.32596i
$322$	−5.11751	−	13.4890i	−0.285188	−	0.751713i
$323$	−5.23286	+	3.02119i	−0.291164	+	0.168104i
$324$	2.86339	+	8.53235i	0.159077	+	0.474019i
$325$	−3.26801	−	5.83524i	−0.181277	−	0.323681i
$326$	4.75722	+	2.74658i	0.263478	+	0.152119i
$327$	1.86708	+	1.20612i	0.103250	+	0.0666986i
$328$	6.01193	−	3.47099i	0.331953	−	0.191653i
$329$	7.86687	+	20.7359i	0.433715	+	1.14321i
$330$	−0.137078	+	2.74180i	−0.00754589	+	0.150931i
$331$	−21.6269			−1.18872			−0.594360	−	0.804199i	$-0.702595\pi$
$331$	−21.6269			−1.18872			−0.594360	+	0.804199i	$0.702595\pi$
$332$	−6.91698	−	11.9806i	−0.379619	−	0.657519i
$333$	6.47177	−	8.99836i	0.354651	−	0.493107i
$334$		−	5.84504i		−	0.319826i
$335$	−7.08257	−	12.2674i	−0.386962	−	0.670238i
$336$	3.40090	+	3.07146i	0.185534	+	0.167562i
$337$	16.9544			0.923564			0.461782	−	0.886993i	$-0.347210\pi$
$337$	16.9544			0.923564			0.461782	+	0.886993i	$0.347210\pi$
$338$	0.339894	−	12.9956i	0.0184878	−	0.706865i
$339$	−0.297756	+	0.460929i	−0.0161719	+	0.0250342i
$340$	−13.2997			−0.721277
$341$	4.23367	−	7.33292i	0.229266	−	0.397100i
$342$	1.41134	−	1.96233i	0.0763164	−	0.106110i
$343$	16.4019	+	8.60105i	0.885619	+	0.464413i
$344$	3.35816	+	1.93884i	0.181060	+	0.104535i
$345$	−16.7288	−	0.836368i	−0.900649	−	0.0450285i
$346$	−12.6329	−	7.29361i	−0.679149	−	0.392107i
$347$	19.2078	−	11.0897i	1.03113	−	0.595324i	0.113822	−	0.993501i	$-0.463691\pi$
$347$	19.2078	−	11.0897i	1.03113	−	0.595324i	0.917308	+	0.398177i	$0.130357\pi$
$348$	8.27845	−	12.8151i	0.443772	−	0.686961i
$349$	9.10947	−	5.25936i	0.487619	−	0.281527i	−0.235967	−	0.971761i	$-0.575826\pi$
$349$	9.10947	−	5.25936i	0.487619	−	0.281527i	0.723586	+	0.690234i	$0.242492\pi$
$350$	4.58856	−	1.74082i	0.245269	−	0.0930509i
$351$	14.4905	+	11.8754i	0.773447	+	0.633861i
$352$	−0.446860	−	0.773984i	−0.0238177	−	0.0412535i
$353$	25.1674			1.33952			0.669762	−	0.742576i	$-0.266396\pi$
$353$	25.1674			1.33952			0.669762	+	0.742576i	$0.266396\pi$
$354$	5.79339	+	0.289644i	0.307915	+	0.0153944i
$355$		−	4.05394i		−	0.215161i
$356$	−15.5163			−0.822363
$357$	32.7005	−	10.5706i	1.73069	−	0.559458i
$358$	4.84102	−	8.38489i	0.255856	−	0.443155i
$359$	20.7408	−	11.9747i	1.09466	−	0.632002i	0.159846	−	0.987142i	$-0.448900\pi$
$359$	20.7408	−	11.9747i	1.09466	−	0.632002i	0.934813	+	0.355140i	$0.115567\pi$
$360$	4.84987	−	2.18732i	0.255611	−	0.115282i
$361$	18.3508			0.965833
$362$	−8.09488	+	14.0207i	−0.425458	+	0.736914i
$363$	0.882277	−	17.6471i	0.0463075	−	0.926231i
$364$	9.39524	+	1.65210i	0.492444	+	0.0865936i
$365$		−	15.4601i		−	0.809221i
$366$	11.9460	+	7.71701i	0.624426	+	0.403375i
$367$		−	14.2995i		−	0.746425i	−0.927746	−	0.373213i	$-0.878256\pi$
$367$		−	14.2995i		−	0.746425i	0.927746	−	0.373213i	$-0.121744\pi$
$368$	4.72239	−	2.72647i	0.246172	−	0.142127i
$369$	8.56212	+	18.9845i	0.445726	+	0.988292i
$370$	−5.67440	−	3.27611i	−0.294998	−	0.170317i
$371$	−6.44731	−	5.26281i	−0.334727	−	0.273231i
$372$	−16.3894	−	0.819400i	−0.849752	−	0.0424839i
$373$	5.37410			0.278260			0.139130	−	0.990274i	$-0.455569\pi$
$373$	5.37410			0.278260			0.139130	+	0.990274i	$0.455569\pi$
$374$	−6.70236			−0.346571
$375$	1.05140	−	21.0299i	0.0542942	−	1.08598i
$376$	−7.25948	+	4.19126i	−0.374379	+	0.216148i
$377$	0.415214	−	31.7561i	0.0213846	−	1.63552i
$378$	−10.1861	+	9.23276i	−0.523915	+	0.474882i
$379$	9.34507	+	16.1861i	0.480024	+	0.831426i	0.999737	−	0.0229149i	$-0.00729466\pi$
$379$	9.34507	+	16.1861i	0.480024	+	0.831426i	−0.519714	+	0.854341i	$0.673961\pi$
$380$	−1.23745	−	0.714442i	−0.0634798	−	0.0366501i
$381$	7.56422	−	3.87712i	0.387527	−	0.198631i
$382$	−7.89736	+	13.6786i	−0.404064	+	0.699859i
$383$	−32.8148			−1.67676			−0.838379	−	0.545088i	$-0.816496\pi$
$383$	−32.8148			−1.67676			−0.838379	+	0.545088i	$0.816496\pi$
$384$	−0.939845	+	1.45489i	−0.0479613	+	0.0742443i
$385$	−3.92072	+	1.48746i	−0.199818	+	0.0758078i
$386$	−1.38510	−	0.799689i	−0.0704998	−	0.0407031i
$387$	−6.79235	+	9.44410i	−0.345275	+	0.480071i
$388$		−	4.90511i		−	0.249019i
$389$	−7.54767	−	4.35765i	−0.382682	−	0.220941i	0.296303	−	0.955094i	$-0.404246\pi$
$389$	−7.54767	−	4.35765i	−0.382682	−	0.220941i	−0.678984	+	0.734153i	$0.737580\pi$
$390$	6.13068	−	9.22348i	0.310439	−	0.467049i
$391$		−	40.8938i		−	2.06809i
$392$	−2.21512	+	6.64027i	−0.111881	+	0.335384i
$393$	8.14774	−	4.17620i	0.410999	−	0.210661i
$394$	4.43257			0.223310
$395$	11.3566	−	19.6703i	0.571415	−	0.989720i
$396$	2.44409	−	1.10230i	0.122820	−	0.0553926i
$397$			39.0196i			1.95834i	0.203043	+	0.979170i	$0.434917\pi$
$397$			39.0196i			1.95834i	−0.203043	+	0.979170i	$0.565083\pi$
$398$	12.3701			0.620056
$399$	3.61041	+	0.773097i	0.180746	+	0.0387033i
$400$	0.927464	+	1.60641i	0.0463732	+	0.0803207i
$401$	−6.18619	−	3.57160i	−0.308923	−	0.178357i	0.337521	−	0.941318i	$-0.390412\pi$
$401$	−6.18619	−	3.57160i	−0.308923	−	0.178357i	−0.646445	+	0.762961i	$0.723745\pi$
$402$	−7.50692	+	11.6208i	−0.374411	+	0.579590i
$403$	−29.8041	+	16.6917i	−1.48465	+	0.831474i
$404$	−8.31852	−	14.4081i	−0.413862	−	0.716830i
$405$	5.07804	+	15.1316i	0.252330	+	0.751894i
$406$	23.0033	+	3.73564i	1.14163	+	0.185396i
$407$	−2.85960	−	1.65099i	−0.141745	−	0.0818367i
$408$	5.92486	+	11.5594i	0.293325	+	0.572274i
$409$	−12.9097	+	7.45341i	−0.638343	+	0.368548i	−0.783976	−	0.620791i	$-0.786812\pi$
$409$	−12.9097	+	7.45341i	−0.638343	+	0.368548i	0.145633	+	0.989339i	$0.453478\pi$
$410$	10.6618	−	6.15558i	0.526547	−	0.304002i
$411$	−0.319480	−	0.623303i	−0.0157588	−	0.0307453i
$412$	7.46308	+	4.30881i	0.367679	+	0.212280i
$413$	3.14298	+	8.28444i	0.154656	+	0.407651i
$414$	6.72557	+	14.9124i	0.330544	+	0.732902i
$415$	−12.2668	−	21.2468i	−0.602154	−	1.04296i
$416$	−0.0471388	+	3.60524i	−0.00231117	+	0.176762i
$417$	4.24538	−	6.57187i	0.207897	−	0.321826i
$418$	−0.623611	−	0.360042i	−0.0305018	−	0.0176102i
$419$	10.6067	+	18.3714i	0.518172	+	0.897500i	0.999777	+	0.0211116i	$0.00672052\pi$
$419$	10.6067	+	18.3714i	0.518172	+	0.897500i	−0.481605	+	0.876388i	$0.659946\pi$
$420$	6.03127	+	5.44704i	0.294296	+	0.265788i
$421$	1.98956			0.0969651			0.0484825	−	0.998824i	$-0.484561\pi$
$421$	1.98956			0.0969651			0.0484825	+	0.998824i	$0.484561\pi$
$422$		−	19.9147i		−	0.969430i
$423$	−10.3389	−	22.9240i	−0.502692	−	1.11460i
$424$	1.57281	−	2.72420i	0.0763826	−	0.132299i
$425$	13.9108			0.674775
$426$	−3.52346	+	1.80598i	−0.170712	+	0.0875001i
$427$	−3.48229	+	21.4432i	−0.168520	+	1.03771i
$428$		−	16.3289i		−	0.789285i
$429$	3.08955	−	4.64816i	0.149165	−	0.224415i
$430$	5.95548	+	3.43840i	0.287199	+	0.165814i
$431$		−	14.5363i		−	0.700189i	−0.936714	−	0.350094i	$-0.886150\pi$
$431$		−	14.5363i		−	0.700189i	0.936714	−	0.350094i	$-0.113850\pi$
$432$	−4.06166	−	3.24081i	−0.195417	−	0.155924i
$433$	1.17784	+	0.680025i	0.0566033	+	0.0326799i	0.528035	−	0.849223i	$-0.322929\pi$
$433$	1.17784	+	0.680025i	0.0566033	+	0.0326799i	−0.471431	+	0.881903i	$0.656262\pi$
$434$	−8.89145	−	23.4366i	−0.426803	−	1.12499i
$435$	14.6813	−	22.7267i	0.703914	−	1.08966i
$436$	−1.28332			−0.0614598
$437$	2.19676	−	3.80490i	0.105085	−	0.182013i
$438$	−13.4371	+	6.88732i	−0.642050	+	0.329089i
$439$	25.8566	+	14.9283i	1.23407	+	0.712488i	0.967875	−	0.251432i	$-0.0809014\pi$
$439$	25.8566	+	14.9283i	1.23407	+	0.712488i	0.266191	+	0.963920i	$0.414235\pi$
$440$	−0.792477	−	1.37261i	−0.0377799	−	0.0654366i
$441$	−19.1587	−	8.59918i	−0.912317	−	0.409485i
$442$	23.2381	+	13.8247i	1.10532	+	0.657575i
$443$	−31.3793	+	18.1168i	−1.49087	+	0.860757i	−0.999945	−	0.0104432i	$-0.996676\pi$
$443$	−31.3793	+	18.1168i	−1.49087	+	0.860757i	−0.490929	+	0.871200i	$0.663342\pi$
$444$	−0.319540	+	6.39135i	−0.0151647	+	0.303320i
$445$	−27.5172			−1.30444
$446$	7.82027			0.370300
$447$	4.75112	+	0.237535i	0.224720	+	0.0112350i
$448$	−2.61154	−	0.424103i	−0.123384	−	0.0200370i
$449$	−28.3824	−	16.3866i	−1.33945	−	0.773331i	−0.352723	−	0.935728i	$-0.614744\pi$
$449$	−28.3824	−	16.3866i	−1.33945	−	0.773331i	−0.986726	+	0.162397i	$0.948078\pi$
$450$	−5.07273	+	2.28784i	−0.239131	+	0.107850i
$451$	5.37298	−	3.10209i	0.253004	−	0.146072i
$452$		−	0.316814i		−	0.0149017i
$453$	−20.7158	−	13.3823i	−0.973315	−	0.628754i
$454$			22.6931i			1.06504i
$455$	16.6619	+	2.92989i	0.781120	+	0.137355i
$456$	−0.0696839	+	1.39380i	−0.00326325	+	0.0652706i
$457$	5.44826	−	9.43666i	0.254859	−	0.441428i	−0.709998	−	0.704203i	$-0.751304\pi$
$457$	5.44826	−	9.43666i	0.254859	−	0.441428i	0.964857	+	0.262775i	$0.0846377\pi$
$458$	3.40525			0.159117
$459$	−36.2780	+	14.2271i	−1.69331	+	0.664064i
$460$	8.37485	−	4.83522i	0.390479	−	0.225443i
$461$	−16.4579	+	28.5059i	−0.766520	+	1.32765i	0.172919	+	0.984936i	$0.444680\pi$
$461$	−16.4579	+	28.5059i	−0.766520	+	1.32765i	−0.939439	+	0.342715i	$0.888653\pi$
$462$	3.03945	+	2.74503i	0.141408	+	0.127710i
$463$	−9.98781			−0.464173			−0.232086	−	0.972695i	$-0.574555\pi$
$463$	−9.98781			−0.464173			−0.232086	+	0.972695i	$0.574555\pi$
$464$			8.80832i			0.408916i
$465$	−29.0656	−	1.45315i	−1.34788	−	0.0673883i
$466$	6.54698			0.303283
$467$	−10.4424	−	18.0868i	−0.483217	−	0.836956i	0.516597	−	0.856228i	$-0.327198\pi$
$467$	−10.4424	−	18.0868i	−0.483217	−	0.836956i	−0.999814	+	0.0192723i	$0.993865\pi$
$468$	−10.7477	−	1.21949i	−0.496812	−	0.0563711i
$469$	−20.8594	−	3.38748i	−0.963198	−	0.156419i
$470$	−12.8742	+	7.43293i	−0.593843	+	0.342855i
$471$	20.6496	−	31.9656i	0.951481	−	1.47290i
$472$	−2.90031	+	1.67450i	−0.133498	+	0.0770749i
$473$	3.00126	+	1.73278i	0.137998	+	0.0796732i
$474$	−22.1556	−	1.10768i	−1.01764	−	0.0508776i
$475$	1.29431	+	0.747272i	0.0593872	+	0.0342872i
$476$	−12.5469	+	15.3708i	−0.575086	+	0.704521i
$477$	7.66120	+	5.51006i	0.350782	+	0.252289i
$478$	1.37549	−	2.38241i	0.0629133	−	0.108969i
$479$	11.8605			0.541919			0.270960	−	0.962591i	$-0.412659\pi$
$479$	11.8605			0.541919			0.270960	+	0.962591i	$0.412659\pi$
$480$	−1.66675	+	2.58014i	−0.0760766	+	0.117767i
$481$	6.50923	+	11.6226i	0.296796	+	0.529947i
$482$	6.12961			0.279196
$483$	−16.7485	+	18.5449i	−0.762084	+	0.843823i
$484$	5.10063	+	8.83455i	0.231847	+	0.401571i
$485$		−	8.69890i		−	0.394997i
$486$	10.8893	−	11.1545i	0.493949	−	0.505978i
$487$	9.49393	+	16.4440i	0.430211	+	0.745148i	0.996891	−	0.0787903i	$-0.0251058\pi$
$487$	9.49393	+	16.4440i	0.430211	+	0.745148i	−0.566680	+	0.823938i	$0.691772\pi$
$488$	−8.21094			−0.371692
$489$	0.475088	−	9.50257i	0.0214842	−	0.429721i
$490$	−3.92838	+	11.7761i	−0.177466	+	0.531990i
$491$	−22.5331	+	13.0095i	−1.01691	+	0.587111i	−0.913206	−	0.407498i	$-0.866401\pi$
$491$	−22.5331	+	13.0095i	−1.01691	+	0.587111i	−0.103699	+	0.994609i	$0.533068\pi$
$492$	−10.0998	−	6.52439i	−0.455333	−	0.294142i
$493$	57.2071	+	33.0285i	2.57648	+	1.48753i
$494$	1.41951	+	2.53462i	0.0638667	+	0.114038i
$495$	4.33443	−	1.95485i	0.194818	−	0.0878642i
$496$	8.20495	−	4.73713i	0.368413	−	0.212703i
$497$	−4.68524	−	3.82447i	−0.210162	−	0.171551i
$498$	−13.0018	+	20.1268i	−0.582624	+	0.901905i
$499$	−5.42439	−	9.39532i	−0.242829	−	0.420592i	0.718690	−	0.695331i	$-0.244742\pi$
$499$	−5.42439	−	9.39532i	−0.242829	−	0.420592i	−0.961519	+	0.274738i	$0.911409\pi$
$500$	6.07838	+	10.5281i	0.271834	+	0.470830i
$501$	−9.00939	+	4.61785i	−0.402510	+	0.206310i
$502$	10.9178	−	6.30342i	0.487287	−	0.281335i
$503$	4.86978	−	8.43471i	0.217133	−	0.376085i	−0.736797	−	0.676114i	$-0.763663\pi$
$503$	4.86978	−	8.43471i	0.217133	−	0.376085i	0.953930	+	0.300029i	$0.0969962\pi$
$504$	2.04741	−	7.66865i	0.0911987	−	0.341589i
$505$	−14.7524	−	25.5518i	−0.656471	−	1.13704i
$506$	4.22049	−	2.43670i	0.187624	−	0.108325i
$507$	−20.2995	+	9.74317i	−0.901533	+	0.432709i
$508$	−2.45373	+	4.24999i	−0.108867	+	0.188563i
$509$	−5.74843	+	9.95658i	−0.254795	+	0.441318i	−0.964840	−	0.262839i	$-0.915341\pi$
$509$	−5.74843	+	9.95658i	−0.254795	+	0.441318i	0.710045	+	0.704156i	$0.248675\pi$
$510$	10.5074	+	20.4998i	0.465274	+	0.907746i
$511$	−17.8677	−	14.5851i	−0.790421	−	0.645205i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.13969	−	0.625070i	−0.182772	−	0.0275975i
$514$	23.6133	−	13.6331i	1.04154	−	0.601331i
$515$	13.2353	+	7.64139i	0.583216	+	0.336720i
$516$	0.335368	−	6.70795i	0.0147638	−	0.295301i
$517$	−6.48794	+	3.74581i	−0.285339	+	0.164741i
$518$	−9.13950	+	3.46738i	−0.401567	+	0.152348i
$519$	−1.26161	+	25.2343i	−0.0553783	+	1.10766i
$520$	−0.0835977	+	6.39366i	−0.00366600	+	0.280381i
$521$	−1.77397	+	3.07261i	−0.0777191	+	0.134613i	−0.902265	−	0.431181i	$-0.858097\pi$
$521$	−1.77397	+	3.07261i	−0.0777191	+	0.134613i	0.824546	+	0.565794i	$0.191430\pi$
$522$	−26.2932	−	2.63568i	−1.15082	−	0.115360i
$523$	−10.3157	−	5.95576i	−0.451073	−	0.260427i	0.257210	−	0.966355i	$-0.417197\pi$
$523$	−10.3157	−	5.95576i	−0.451073	−	0.260427i	−0.708283	+	0.705928i	$0.750530\pi$
$524$	−2.64301	+	4.57783i	−0.115461	+	0.199984i
$525$	−6.30842	−	5.69734i	−0.275322	−	0.248653i
$526$	−0.281241	+	0.487124i	−0.0122627	+	0.0212396i
$527$		−	71.0512i		−	3.09504i
$528$	−0.839958	+	1.30026i	−0.0365545	+	0.0565866i
$529$	3.36731	+	5.83235i	0.146405	+	0.253580i
$530$	2.78928	−	4.83118i	0.121159	−	0.209853i
$531$	−4.13059	−	9.15860i	−0.179252	−	0.397449i
$532$	−1.99311	+	0.756152i	−0.0864121	+	0.0327833i
$533$	−25.0275	−	0.327237i	−1.08406	−	0.0141742i
$534$	12.2586	+	23.9164i	0.530481	+	1.03496i
$535$		−	28.9582i		−	1.25197i
$536$		−	7.98740i		−	0.345003i
$537$	−16.7489	−	0.837371i	−0.722767	−	0.0361352i
$538$		−	3.93196i		−	0.169519i
$539$	−1.97970	+	5.93454i	−0.0852718	+	0.255619i
$540$	−7.20310	−	5.74737i	−0.309972	−	0.247328i
$541$	8.93957	+	15.4838i	0.384342	+	0.665700i	0.991678	−	0.128745i	$-0.0410950\pi$
$541$	8.93957	+	15.4838i	0.384342	+	0.665700i	−0.607336	+	0.794445i	$0.707762\pi$
$542$	0.438598	+	0.759673i	0.0188394	+	0.0326308i
$543$	28.0065	+	1.40020i	1.20187	+	0.0600885i
$544$	−6.49467	−	3.74970i	−0.278457	−	0.160767i
$545$	−2.27588			−0.0974881
$546$	−4.87616	−	15.7868i	−0.208681	−	0.675613i
$547$	−37.3187			−1.59563			−0.797817	−	0.602899i	$-0.794012\pi$
$547$	−37.3187			−1.59563			−0.797817	+	0.602899i	$0.794012\pi$
$548$	0.350205	+	0.202191i	0.0149600	+	0.00863717i
$549$	2.45693	−	24.5100i	0.104859	−	1.04606i
$550$	0.828893	+	1.43568i	0.0353441	+	0.0612178i
$551$	3.54850	+	6.14618i	0.151171	+	0.261836i
$552$	−7.93341	−	5.12492i	−0.337668	−	0.218131i
$553$	−12.0197	−	31.6821i	−0.511128	−	1.34726i
$554$			12.6070i			0.535621i
$555$	−0.566683	+	11.3346i	−0.0240543	+	0.481128i
$556$			4.51711i			0.191568i
$557$			2.55190i			0.108127i	0.998537	+	0.0540637i	$0.0172174\pi$
$557$			2.55190i			0.108127i	−0.998537	+	0.0540637i	$0.982783\pi$
$558$	11.6854	+	25.9096i	0.494682	+	1.09684i
$559$	−6.83168	−	12.1984i	−0.288949	−	0.515937i
$560$	−4.63139	−	0.752120i	−0.195712	−	0.0317829i
$561$	5.29517	+	10.3308i	0.223562	+	0.436168i
$562$	−3.18858	+	5.52278i	−0.134502	+	0.232964i
$563$	2.09878	+	3.63519i	0.0884529	+	0.153205i	0.906857	−	0.421438i	$-0.138474\pi$
$563$	2.09878	+	3.63519i	0.0884529	+	0.153205i	−0.818404	+	0.574643i	$0.805141\pi$
$564$	12.1956	+	7.87827i	0.513528	+	0.331735i
$565$		−	0.561850i		−	0.0236372i
$566$	−0.380407	+	0.658885i	−0.0159897	+	0.0276950i
$567$	22.2786	+	8.40625i	0.935612	+	0.353029i
$568$	1.14296	−	1.97967i	0.0479576	−	0.0830650i
$569$	32.1347	+	18.5530i	1.34716	+	0.777782i	0.987846	−	0.155435i	$-0.0496781\pi$
$569$	32.1347	+	18.5530i	1.34716	+	0.777782i	0.359312	+	0.933218i	$0.383011\pi$
$570$	−0.123580	+	2.47181i	−0.00517619	+	0.103533i
$571$	2.55983	−	4.43376i	0.107126	−	0.185547i	−0.807479	−	0.589896i	$-0.799169\pi$
$571$	2.55983	−	4.43376i	0.107126	−	0.185547i	0.914605	+	0.404349i	$0.132502\pi$
$572$	−0.0421289	+	3.22208i	−0.00176150	+	0.134722i
$573$	27.3231	+	1.36604i	1.14144	+	0.0570670i
$574$	2.94412	−	18.1293i	0.122885	−	0.756700i
$575$	−8.75969	+	5.05741i	−0.365304	+	0.210909i
$576$	2.98504	+	0.299226i	0.124377	+	0.0124678i
$577$	−4.55577	−	2.63028i	−0.189659	−	0.109500i	0.402164	−	0.915568i	$-0.368258\pi$
$577$	−4.55577	−	2.63028i	−0.189659	−	0.109500i	−0.591823	+	0.806068i	$0.701592\pi$
$578$	−33.9837	+	19.6205i	−1.41354	+	0.816105i
$579$	−0.138325	+	2.76675i	−0.00574861	+	0.114982i
$580$			15.6210i			0.648626i
$581$	−36.1279	−	5.86703i	−1.49884	−	0.243405i
$582$	−7.56061	+	3.87526i	−0.313397	+	0.160635i
$583$	1.40566	−	2.43467i	0.0582163	−	0.100834i
$584$	4.35881	−	7.54968i	0.180369	−	0.312408i
$585$	−19.0603	−	2.16269i	−0.788048	−	0.0894164i
$586$	11.0026	−	6.35235i	0.454513	−	0.262413i
$587$	13.2127	+	22.8850i	0.545346	+	0.944567i	0.998585	+	0.0531780i	$0.0169351\pi$
$587$	13.2127	+	22.8850i	0.545346	+	0.944567i	−0.453239	+	0.891389i	$0.649732\pi$
$588$	11.9852	−	1.83178i	0.494261	−	0.0755415i
$589$	3.81678	−	6.61085i	0.157268	−	0.272395i
$590$	−5.14352	+	2.96961i	−0.211755	+	0.122257i
$591$	−3.50193	−	6.83225i	−0.144050	−	0.281041i
$592$	−1.84733	−	3.19966i	−0.0759247	−	0.131505i
$593$	11.1153	+	19.2523i	0.456451	+	0.790596i	0.998770	−	0.0495766i	$-0.0157872\pi$
$593$	11.1153	+	19.2523i	0.456451	+	0.790596i	−0.542320	+	0.840172i	$0.682454\pi$
$594$	−3.62999	−	2.89638i	−0.148940	−	0.118840i
$595$	−22.2511	+	27.2592i	−0.912207	+	1.11752i
$596$	−2.37853	+	1.37324i	−0.0974283	+	0.0562502i
$597$	−9.77292	−	19.0669i	−0.399979	−	0.780356i
$598$	−19.6592	−	0.257046i	−0.803924	−	0.0105114i
$599$	−15.9688	−	9.21958i	−0.652467	−	0.376702i	0.136934	−	0.990580i	$-0.456275\pi$
$599$	−15.9688	−	9.21958i	−0.652467	−	0.376702i	−0.789401	+	0.613878i	$0.789609\pi$
$600$	1.74335	−	2.69871i	0.0711718	−	0.110174i
$601$	−16.9272	+	9.77294i	−0.690476	+	0.398646i	−0.803790	−	0.594913i	$-0.797187\pi$
$601$	−16.9272	+	9.77294i	−0.690476	+	0.398646i	0.113314	+	0.993559i	$0.463853\pi$
$602$	9.59224	−	3.63914i	0.390951	−	0.148320i
$603$	23.8427	+	2.39004i	0.970950	+	0.0973299i
$604$	14.2388			0.579369
$605$	9.04564	+	15.6675i	0.367758	+	0.636975i
$606$	−15.6362	+	24.2050i	−0.635179	+	0.983260i
$607$		−	7.87162i		−	0.319499i	−0.987158	−	0.159750i	$-0.948931\pi$
$607$		−	7.87162i		−	0.319499i	0.987158	−	0.159750i	$-0.0510687\pi$
$608$	−0.402858	−	0.697770i	−0.0163380	−	0.0282983i
$609$	−12.4156	−	38.4079i	−0.503106	−	1.55637i
$610$	−14.5616			−0.589581
$611$	30.2210	+	0.395142i	1.22261	+	0.0159858i
$612$	13.1364	−	18.2648i	0.531007	−	0.738313i
$613$	24.3919			0.985181			0.492591	−	0.870261i	$-0.336050\pi$
$613$	24.3919			0.985181			0.492591	+	0.870261i	$0.336050\pi$
$614$	−1.45209	+	2.51509i	−0.0586015	+	0.101501i
$615$	−17.9113	−	11.5706i	−0.722254	−	0.466571i
$616$	−2.33398	−	0.379030i	−0.0940389	−	0.0152715i
$617$	3.90089	+	2.25218i	0.157044	+	0.0906694i	0.576462	−	0.817124i	$-0.304433\pi$
$617$	3.90089	+	2.25218i	0.157044	+	0.0906694i	−0.419419	+	0.907793i	$0.637766\pi$
$618$	0.745312	−	14.9075i	0.0299808	−	0.599669i
$619$	4.81682	+	2.78099i	0.193604	+	0.111777i	0.593669	−	0.804710i	$-0.297679\pi$
$619$	4.81682	+	2.78099i	0.193604	+	0.111777i	−0.400065	+	0.916487i	$0.631012\pi$
$620$	14.5509	−	8.40099i	0.584380	−	0.337392i
$621$	17.6720	−	22.1480i	0.709152	−	0.888770i
$622$	−15.7319	+	9.08284i	−0.630793	+	0.364189i
$623$	−25.9596	+	31.8024i	−1.04005	+	1.27413i
$624$	5.59426	−	2.77565i	0.223950	−	0.111115i
$625$	6.14230	+	10.6388i	0.245692	+	0.425551i
$626$	3.21866			0.128644
$627$	−0.0622779	+	1.24567i	−0.00248714	+	0.0497471i
$628$			21.9712i			0.876747i
$629$	−27.7077			−1.10478
$630$	3.63094	−	13.5998i	0.144660	−	0.541831i
$631$	−17.4066	+	30.1491i	−0.692944	+	1.20021i	0.277924	+	0.960603i	$0.410354\pi$
$631$	−17.4066	+	30.1491i	−0.692944	+	1.20021i	−0.970869	+	0.239612i	$0.922980\pi$
$632$	11.0916	−	6.40376i	0.441202	−	0.254728i
$633$	−30.6959	+	15.7335i	−1.22005	+	0.625350i
$634$	−1.09439			−0.0434639
$635$	−4.35153	+	7.53707i	−0.172685	+	0.299100i
$636$	−5.44159	−	0.272056i	−0.215773	−	0.0107877i
$637$	19.1049	−	16.4925i	0.756964	−	0.653457i
$638$			7.87217i			0.311662i
$639$	5.56738	+	4.00415i	0.220242	+	0.158402i
$640$		−	1.77344i		−	0.0701012i
$641$	13.1123	−	7.57036i	0.517903	−	0.299011i	−0.218173	−	0.975910i	$-0.570010\pi$
$641$	13.1123	−	7.57036i	0.517903	−	0.299011i	0.736076	+	0.676899i	$0.236676\pi$
$642$	−25.1688	+	12.9005i	−0.993335	+	0.509143i
$643$	17.4033	+	10.0478i	0.686317	+	0.396246i	0.802231	−	0.597014i	$-0.203646\pi$
$643$	17.4033	+	10.0478i	0.686317	+	0.396246i	−0.115914	+	0.993259i	$0.536980\pi$
$644$	2.31261	−	14.2406i	0.0911297	−	0.561157i
$645$	0.594754	−	11.8961i	0.0234184	−	0.468409i
$646$	−6.04238			−0.237734
$647$	22.0525			0.866973			0.433486	−	0.901160i	$-0.357283\pi$
$647$	22.0525			0.866973			0.433486	+	0.901160i	$0.357283\pi$
$648$	−1.78640	+	8.82093i	−0.0701766	+	0.346519i
$649$	−2.59207	+	1.49653i	−0.101748	+	0.0587440i
$650$	0.0874392	−	6.68747i	0.00342965	−	0.262304i
$651$	−29.0998	+	32.2210i	−1.14051	+	1.26284i
$652$	2.74658	+	4.75722i	0.107564	+	0.186307i
$653$	−30.3575	−	17.5269i	−1.18798	−	0.685882i	−0.230134	−	0.973159i	$-0.573917\pi$
$653$	−30.3575	−	17.5269i	−1.18798	−	0.685882i	−0.957847	+	0.287277i	$0.907250\pi$
$654$	1.01388	+	1.97807i	0.0396458	+	0.0773487i
$655$	−4.68721	+	8.11849i	−0.183145	+	0.317216i
$656$	6.94198			0.271039
$657$	21.2318	+	15.2703i	0.828333	+	0.595751i
$658$	−3.55506	+	21.8913i	−0.138590	+	0.853411i
$659$	−6.09325	−	3.51794i	−0.237359	−	0.137039i	0.376603	−	0.926375i	$-0.377092\pi$
$659$	−6.09325	−	3.51794i	−0.237359	−	0.137039i	−0.613962	+	0.789335i	$0.710425\pi$
$660$	−1.48961	+	2.30593i	−0.0579830	+	0.0897581i
$661$			32.6925i			1.27159i	0.771858	+	0.635795i	$0.219328\pi$
$661$			32.6925i			1.27159i	−0.771858	+	0.635795i	$0.780672\pi$
$662$	−18.7294	−	10.8134i	−0.727940	−	0.420276i
$663$	2.94990	−	46.7407i	0.114565	−	1.81526i
$664$		−	13.8340i		−	0.536862i
$665$	−3.53465	+	1.34099i	−0.137068	+	0.0520012i
$666$	10.1039	−	4.55692i	0.391518	−	0.176577i
$667$	−48.0313			−1.85978
$668$	2.92252	−	5.06195i	0.113076	−	0.195853i
$669$	−6.17836	−	12.0539i	−0.238869	−	0.466032i
$670$		−	14.1651i		−	0.547247i
$671$	−7.33828			−0.283291
$672$	1.40953	+	4.36041i	0.0543739	+	0.168207i
$673$	−11.4876	−	19.8971i	−0.442814	−	0.766976i	0.555083	−	0.831795i	$-0.312686\pi$
$673$	−11.4876	−	19.8971i	−0.442814	−	0.766976i	−0.997897	+	0.0648191i	$0.979353\pi$
$674$	14.6829	+	8.47719i	0.565565	+	0.326529i
$675$	7.53410	+	6.01148i	0.289988	+	0.231382i
$676$	6.79213	−	11.0845i	0.261236	−	0.426328i
$677$	0.619754	+	1.07345i	0.0238191	+	0.0412559i	0.877689	−	0.479230i	$-0.159084\pi$
$677$	0.619754	+	1.07345i	0.0238191	+	0.0412559i	−0.853870	+	0.520486i	$0.825751\pi$
$678$	−0.488329	+	0.250298i	−0.0187542	+	0.00961262i
$679$	−10.0536	−	8.20652i	−0.385820	−	0.314937i
$680$	−11.5179	−	6.64985i	−0.441690	−	0.255010i
$681$	34.9785	−	17.9286i	1.34038	−	0.687025i
$682$	7.33292	−	4.23367i	0.280792	−	0.162115i
$683$	1.95788	−	1.13038i	0.0749160	−	0.0432528i	−0.462074	−	0.886841i	$-0.652895\pi$
$683$	1.95788	−	1.13038i	0.0749160	−	0.0432528i	0.536990	+	0.843589i	$0.319561\pi$
$684$	2.20342	−	0.993755i	0.0842497	−	0.0379972i
$685$	0.621066	+	0.358572i	0.0237297	+	0.0137003i
$686$	9.90393	+	15.6497i	0.378134	+	0.597507i
$687$	−2.69030	−	5.24875i	−0.102641	−	0.200252i
$688$	1.93884	+	3.35816i	0.0739174	+	0.128029i
$689$	−9.89553	+	5.54196i	−0.376990	+	0.211132i
$690$	−14.0694	−	9.08872i	−0.535612	−	0.346002i
$691$	−40.1735	−	23.1942i	−1.52827	−	0.882349i	−0.999434	−	0.0336272i	$-0.989294\pi$
$691$	−40.1735	−	23.1942i	−1.52827	−	0.882349i	−0.528839	−	0.848722i	$-0.677373\pi$
$692$	−7.29361	−	12.6329i	−0.277262	−	0.480231i
$693$	1.82981	−	6.85362i	0.0695086	−	0.260348i
$694$	22.1793			0.841915
$695$			8.01080i			0.303867i
$696$	13.5769	−	6.95897i	0.514631	−	0.263779i
$697$	26.0303	−	45.0859i	0.985970	−	1.70775i
$698$	10.5187			0.398139
$699$	−5.17241	−	10.0913i	−0.195638	−	0.381689i
$700$	4.84422	+	0.786681i	0.183094	+	0.0297338i
$701$			41.1479i			1.55413i	0.629418	+	0.777067i	$0.283293\pi$
$701$			41.1479i			1.55413i	−0.629418	+	0.777067i	$0.716707\pi$
$702$	6.61147	+	17.5296i	0.249534	+	0.661614i
$703$	−2.57802	−	1.48842i	−0.0972318	−	0.0561368i
$704$		−	0.893720i		−	0.0336833i
$705$	21.6281	+	13.9716i	0.814562	+	0.526201i
$706$	21.7956	+	12.5837i	0.820288	+	0.473593i
$707$	−43.4483	−	7.05582i	−1.63404	−	0.265362i
$708$	4.87240	+	3.14753i	0.183116	+	0.118292i
$709$	3.23191			0.121377			0.0606885	−	0.998157i	$-0.480670\pi$
$709$	3.23191			0.121377			0.0606885	+	0.998157i	$0.480670\pi$
$710$	2.02697	−	3.51081i	0.0760707	−	0.131758i
$711$	15.7966	+	35.0251i	0.592418	+	1.31355i
$712$	−13.4375	−	7.75816i	−0.503593	−	0.290749i
$713$	25.8313	+	44.7411i	0.967390	+	1.67557i
$714$	33.6048	+	7.19580i	1.25763	+	0.269296i
$715$	−0.0747129	+	5.71415i	−0.00279410	+	0.213697i
$716$	8.38489	−	4.84102i	0.313358	−	0.180917i
$717$	−4.75888	−	0.237924i	−0.177724	−	0.00888542i
$718$	23.9494			0.893785
$719$	23.3708			0.871583			0.435791	−	0.900048i	$-0.356469\pi$
$719$	23.3708			0.871583			0.435791	+	0.900048i	$0.356469\pi$
$720$	5.29377	+	0.530658i	0.197287	+	0.0197765i
$721$	21.3175	−	8.08751i	0.793905	−	0.301195i
$722$	15.8923	+	9.17541i	0.591449	+	0.341473i
$723$	−4.84267	−	9.44801i	−0.180101	−	0.351375i
$724$	−14.0207	+	8.09488i	−0.521077	+	0.300844i
$725$		−	16.3388i		−	0.606808i
$726$	9.58761	−	14.8417i	0.355830	−	0.550826i
$727$		−	34.2889i		−	1.27171i	−0.771810	−	0.635853i	$-0.780649\pi$
$727$		−	34.2889i		−	1.27171i	0.771810	−	0.635853i	$-0.219351\pi$
$728$	7.31047	+	6.12838i	0.270944	+	0.227133i
$729$	−25.7963	−	7.97194i	−0.955418	−	0.295257i
$730$	7.73007	−	13.3889i	0.286103	−	0.495544i
$731$	29.0802			1.07557
$732$	6.48701	+	12.6561i	0.239767	+	0.467784i
$733$	19.4049	−	11.2034i	0.716736	−	0.413808i	−0.0968139	−	0.995303i	$-0.530865\pi$
$733$	19.4049	−	11.2034i	0.716736	−	0.413808i	0.813550	+	0.581495i	$0.197532\pi$
$734$	7.14973	−	12.3837i	0.263901	−	0.457090i
$735$	21.2549	−	3.24855i	0.784000	−	0.119825i
$736$	5.45295			0.200998
$737$		−	7.13850i		−	0.262950i
$738$	−2.07722	+	20.7221i	−0.0764636	+	0.762791i
$739$	−4.78891			−0.176163			−0.0880814	−	0.996113i	$-0.528074\pi$
$739$	−4.78891			−0.176163			−0.0880814	+	0.996113i	$0.528074\pi$
$740$	−3.27611	−	5.67440i	−0.120432	−	0.208595i
$741$	2.78532	−	4.19045i	0.102321	−	0.153940i
$742$	−2.95213	−	7.78138i	−0.108376	−	0.285663i
$743$	37.6419	−	21.7325i	1.38095	−	0.797289i	0.388674	−	0.921375i	$-0.372933\pi$
$743$	37.6419	−	21.7325i	1.38095	−	0.797289i	0.992272	+	0.124086i	$0.0395998\pi$
$744$	−13.7840	−	8.90433i	−0.505344	−	0.326449i
$745$	−4.21816	+	2.43536i	−0.154542	+	0.0892246i
$746$	4.65411	+	2.68705i	0.170399	+	0.0983799i
$747$	41.2949	+	4.13948i	1.51090	+	0.151456i
$748$	−5.80442	−	3.35118i	−0.212230	−	0.122531i
$749$	−33.4677	−	27.3191i	−1.22288	−	0.998216i
$750$	11.4255	−	17.6867i	0.417200	−	0.645827i
$751$	−13.8241	+	23.9440i	−0.504447	+	0.873728i	0.495539	+	0.868585i	$0.334970\pi$
$751$	−13.8241	+	23.9440i	−0.504447	+	0.873728i	−0.999987	+	0.00514292i	$0.998363\pi$
$752$	−8.38252			−0.305679
$753$	−18.3415	−	11.8485i	−0.668402	−	0.431783i
$754$	16.2376	−	27.2940i	0.591340	−	0.993989i
$755$	25.2516			0.919000
$756$	−13.4378	+	2.90276i	−0.488727	+	0.105572i
$757$	−12.4453	−	21.5558i	−0.452330	−	0.783459i	0.546200	−	0.837655i	$-0.316074\pi$
$757$	−12.4453	−	21.5558i	−0.452330	−	0.783459i	−0.998530	+	0.0541956i	$0.982741\pi$
$758$			18.6901i			0.678856i
$759$	−7.09025	−	4.58025i	−0.257360	−	0.166252i
$760$	−0.714442	−	1.23745i	−0.0259155	−	0.0448870i
$761$	35.1534			1.27431			0.637156	−	0.770735i	$-0.280111\pi$
$761$	35.1534			1.27431			0.637156	+	0.770735i	$0.280111\pi$
$762$	8.48937	+	0.424432i	0.307537	+	0.0153755i
$763$	−2.14706	+	2.63030i	−0.0777288	+	0.0952233i
$764$	−13.6786	+	7.89736i	−0.494875	+	0.285716i
$765$	23.2965	−	32.3915i	0.842287	−	1.17112i
$766$	−28.4184	−	16.4074i	−1.02680	−	0.592823i
$767$	12.0739	+	0.157868i	0.435964	+	0.00570027i
$768$	−1.54137	+	0.790045i	−0.0556195	+	0.0285083i
$769$	−21.8138	+	12.5942i	−0.786626	+	0.454159i	−0.838773	−	0.544481i	$-0.816727\pi$
$769$	−21.8138	+	12.5942i	−0.786626	+	0.454159i	0.0521474	+	0.998639i	$0.483393\pi$
$770$	−4.13917	−	0.672184i	−0.149165	−	0.0242238i
$771$	−39.6692	−	25.6260i	−1.42865	−	0.922899i
$772$	−0.799689	−	1.38510i	−0.0287814	−	0.0498509i
$773$	23.6135	+	40.8998i	0.849318	+	1.47106i	0.881817	+	0.471591i	$0.156320\pi$
$773$	23.6135	+	40.8998i	0.849318	+	1.47106i	−0.0324991	+	0.999472i	$0.510347\pi$
$774$	−10.6044	+	4.78265i	−0.381167	+	0.171909i
$775$	−15.2196	+	8.78703i	−0.546704	+	0.315640i
$776$	2.45256	−	4.24795i	0.0880417	−	0.152493i
$777$	12.5651	+	11.3480i	0.450772	+	0.407107i
$778$	−4.35765	−	7.54767i	−0.156229	−	0.270597i
$779$	4.84391	−	2.79663i	0.173551	−	0.100200i
$780$	9.92106	−	4.92243i	0.355231	−	0.176251i
$781$	1.02149	−	1.76927i	0.0365517	−	0.0633094i
$782$	20.4469	−	35.4151i	0.731180	−	1.26644i
$783$	16.7102	+	42.6099i	0.597175	+	1.52275i
$784$	−5.23849	+	4.64308i	−0.187089	+	0.165824i
$785$			38.9645i			1.39070i
$786$	9.14425	+	0.457173i	0.326164	+	0.0163068i
$787$	23.5031	−	13.5695i	0.837796	−	0.483701i	−0.0187187	−	0.999825i	$-0.505959\pi$
$787$	23.5031	−	13.5695i	0.837796	−	0.483701i	0.856514	+	0.516123i	$0.172625\pi$
$788$	3.83872	+	2.21629i	0.136749	+	0.0789520i
$789$	0.973033	+	0.0486474i	0.0346409	+	0.00173189i
$790$	19.6703	−	11.3566i	0.699838	−	0.404051i
$791$	−0.649345	−	0.530048i	−0.0230881	−	0.0188463i
$792$	2.66779	+	0.267424i	0.0947958	+	0.00950251i
$793$	25.4429	+	15.1364i	0.903505	+	0.537510i
$794$	−19.5098	+	33.7920i	−0.692378	+	1.19923i
$795$	−9.65031	−	0.482474i	−0.342261	−	0.0171116i
$796$	10.7128	+	6.18504i	0.379705	+	0.219223i
$797$	16.0179	−	27.7438i	0.567382	−	0.982735i	−0.429441	−	0.903095i	$-0.641289\pi$
$797$	16.0179	−	27.7438i	0.567382	−	0.982735i	0.996824	−	0.0796404i	$-0.0253772\pi$
$798$	2.74016	+	2.47473i	0.0970005	+	0.0876043i
$799$	−31.4319	+	54.4417i	−1.11198	+	1.92601i
$800$			1.85493i			0.0655816i
$801$	27.1793	−	37.7901i	0.960332	−	1.33525i
$802$	−3.57160	−	6.18619i	−0.126117	−	0.218442i
$803$	3.89556	−	6.74730i	0.137471	−	0.238107i
$804$	−12.3116	+	6.31041i	−0.434195	+	0.222551i
$805$	4.10127	−	25.2547i	0.144551	−	0.890113i
$806$	−34.1570	−	0.446605i	−1.20313	−	0.0157310i
$807$	−6.06062	+	3.10643i	−0.213344	+	0.109351i
$808$		−	16.6370i		−	0.585289i
$809$		−	33.8311i		−	1.18944i	−0.803934	−	0.594719i	$-0.797263\pi$
$809$		−	33.8311i		−	1.18944i	0.803934	−	0.594719i	$-0.202737\pi$
$810$	−3.16807	+	15.6433i	−0.111315	+	0.549651i
$811$			23.0154i			0.808181i	0.914719	+	0.404090i	$0.132412\pi$
$811$			23.0154i			0.808181i	−0.914719	+	0.404090i	$0.867588\pi$
$812$	18.0536	+	14.7368i	0.633557	+	0.517160i
$813$	0.824428	−	1.27622i	0.0289139	−	0.0447589i
$814$	−1.65099	−	2.85960i	−0.0578673	−	0.100229i
$815$	4.87089	+	8.43662i	0.170620	+	0.295522i
$816$	−0.648601	+	12.9731i	−0.0227056	+	0.454151i
$817$	2.70572	+	1.56215i	0.0946613	+	0.0546527i
$818$	−14.9068			−0.521205
$819$	−20.4809	+	19.9883i	−0.715662	+	0.698447i
$820$	12.3112			0.429924
$821$	3.37615	+	1.94922i	0.117828	+	0.0680282i	0.557756	−	0.830005i	$-0.311663\pi$
$821$	3.37615	+	1.94922i	0.117828	+	0.0680282i	−0.439928	+	0.898033i	$0.644996\pi$
$822$	0.0349738	−	0.699536i	0.00121985	−	0.0243991i
$823$	2.19747	+	3.80613i	0.0765989	+	0.132673i	0.901780	−	0.432194i	$-0.142261\pi$
$823$	2.19747	+	3.80613i	0.0765989	+	0.132673i	−0.825182	+	0.564868i	$0.808927\pi$
$824$	4.30881	+	7.46308i	0.150104	+	0.259989i
$825$	1.55806	−	2.41189i	0.0542448	−	0.0839712i
$826$	−1.42032	+	8.74602i	−0.0494192	+	0.304313i
$827$			48.0745i			1.67171i	0.548948	+	0.835856i	$0.315028\pi$
$827$			48.0745i			1.67171i	−0.548948	+	0.835856i	$0.684972\pi$
$828$	−1.63166	+	16.2773i	−0.0567042	+	0.565674i
$829$			6.19286i			0.215087i	0.994200	+	0.107543i	$0.0342985\pi$
$829$			6.19286i			0.215087i	−0.994200	+	0.107543i	$0.965702\pi$
$830$		−	24.5336i		−	0.851575i
$831$	19.4321	−	9.96012i	0.674093	−	0.345513i
$832$	−1.84344	+	3.09866i	−0.0639100	+	0.107427i
$833$	10.5125	+	51.4324i	0.364237	+	1.78203i
$834$	6.96255	−	3.56872i	0.241093	−	0.123575i
$835$	5.18290	−	8.97705i	0.179362	−	0.310664i
$836$	−0.360042	−	0.623611i	−0.0124523	−	0.0215680i
$837$	30.7043	−	38.4813i	1.06130	−	1.33011i
$838$			21.2134i			0.732805i
$839$	−27.1029	+	46.9435i	−0.935695	+	1.62067i	−0.162305	+	0.986741i	$0.551893\pi$
$839$	−27.1029	+	46.9435i	−0.935695	+	1.62067i	−0.773390	+	0.633930i	$0.781441\pi$
$840$	2.49971	+	7.73291i	0.0862484	+	0.266811i
$841$	24.2932	−	42.0771i	0.837697	−	1.45093i
$842$	1.72301	+	0.994778i	0.0593787	+	0.0342823i
$843$	11.0318	+	0.551541i	0.379955	+	0.0189961i
$844$	9.95733	−	17.2466i	0.342745	−	0.593653i
$845$	12.0454	−	19.6577i	0.414375	−	0.676246i
$846$	2.50827	−	25.0222i	0.0862361	−	0.860280i
$847$	26.6410	+	4.32639i	0.915396	+	0.148657i
$848$	2.72420	−	1.57281i	0.0935492	−	0.0540107i
$849$	1.31613	+	0.0658006i	0.0451693	+	0.00225827i
$850$	12.0471	+	6.95542i	0.413214	+	0.238569i
$851$	17.4476	−	10.0734i	0.598096	−	0.345311i
$852$	−3.95440	−	0.197703i	−0.135475	−	0.00677318i
$853$		−	15.5780i		−	0.533381i	−0.963782	−	0.266690i	$-0.914070\pi$
$853$		−	15.5780i		−	0.533381i	0.963782	−	0.266690i	$-0.0859301\pi$
$854$	−13.7373	+	16.8292i	−0.470082	+	0.575884i
$855$	3.90762	−	1.76236i	0.133638	−	0.0602715i
$856$	8.16443	−	14.1412i	0.279054	−	0.483336i
$857$	14.2172	−	24.6250i	0.485652	−	0.841173i	−0.514213	−	0.857663i	$-0.671916\pi$
$857$	14.2172	−	24.6250i	0.485652	−	0.841173i	0.999864	+	0.0164897i	$0.00524907\pi$
$858$	4.99970	−	2.48065i	0.170687	−	0.0846880i
$859$	−23.4649	+	13.5474i	−0.800610	+	0.462233i	−0.843685	−	0.536839i	$-0.819618\pi$
$859$	−23.4649	+	13.5474i	−0.800610	+	0.462233i	0.0430741	+	0.999072i	$0.486285\pi$
$860$	3.43840	+	5.95548i	0.117248	+	0.203080i
$861$	−30.2699	+	9.78495i	−1.03160	+	0.333470i
$862$	7.26815	−	12.5888i	0.247554	−	0.428776i
$863$	−11.4245	+	6.59595i	−0.388895	+	0.224529i	−0.681681	−	0.731649i	$-0.738751\pi$
$863$	−11.4245	+	6.59595i	−0.388895	+	0.224529i	0.292786	+	0.956178i	$0.405418\pi$
$864$	−1.89710	−	4.83746i	−0.0645406	−	0.164574i
$865$	−12.9347	−	22.4036i	−0.439795	−	0.761747i
$866$	0.680025	+	1.17784i	0.0231082	+	0.0400246i
$867$	57.0912	+	36.8805i	1.93892	+	1.25253i
$868$	4.01806	−	24.7424i	0.136382	−	0.839811i
$869$	9.91281	−	5.72317i	0.336269	−	0.194145i
$870$	24.0777	−	12.3413i	0.816312	−	0.418408i
$871$	−14.7243	+	24.7503i	−0.498915	+	0.838630i
$872$	−1.11139	−	0.641659i	−0.0376363	−	0.0217293i
$873$	11.9464	+	8.59208i	0.404326	+	0.290798i
$874$	3.80490	−	2.19676i	0.128703	−	0.0743066i
$875$	31.7479	+	5.15573i	1.07327	+	0.174295i
$876$	−15.0805	−	0.753961i	−0.509524	−	0.0254740i
$877$	−3.59790			−0.121492			−0.0607462	−	0.998153i	$-0.519348\pi$
$877$	−3.59790			−0.121492			−0.0607462	+	0.998153i	$0.519348\pi$
$878$	14.9283	+	25.8566i	0.503805	+	0.872617i
$879$	−18.4839	−	11.9404i	−0.623446	−	0.402741i
$880$		−	1.58495i		−	0.0534288i
$881$	10.4378	+	18.0787i	0.351657	+	0.609088i	0.986540	−	0.163520i	$-0.0522849\pi$
$881$	10.4378	+	18.0787i	0.351657	+	0.609088i	−0.634883	+	0.772609i	$0.718952\pi$
$882$	−12.2923	−	17.0264i	−0.413903	−	0.573310i
$883$	29.7344			1.00064			0.500321	−	0.865840i	$-0.333215\pi$
$883$	29.7344			1.00064			0.500321	+	0.865840i	$0.333215\pi$
$884$	13.2124	+	23.5916i	0.444382	+	0.793472i
$885$	8.64088	+	5.58195i	0.290460	+	0.187635i
$886$	−36.2337			−1.21729
$887$	−1.38815	+	2.40435i	−0.0466095	+	0.0807300i	−0.888389	−	0.459092i	$-0.848175\pi$
$887$	−1.38815	+	2.40435i	−0.0466095	+	0.0807300i	0.841779	+	0.539822i	$0.181508\pi$
$888$	−3.47240	+	5.37530i	−0.116526	+	0.180383i
$889$	4.60558	+	12.1396i	0.154466	+	0.407150i
$890$	−23.8306	−	13.7586i	−0.798803	−	0.461189i
$891$	−1.59654	+	7.88344i	−0.0534862	+	0.264105i
$892$	6.77255	+	3.91013i	0.226762	+	0.130921i
$893$	−5.84907	+	3.37696i	−0.195732	+	0.113006i
$894$	3.99582	+	2.58127i	0.133640	+	0.0863306i
$895$	14.8701	−	8.58523i	0.497051	−	0.286973i
$896$	−2.04961	−	1.67305i	−0.0684726	−	0.0558928i
$897$	15.1354	+	30.5052i	0.505358	+	1.01854i
$898$	−16.3866	−	28.3824i	−0.546828	−	0.947133i
$899$	−83.4522			−2.78329
$900$	−5.53703	−	0.555043i	−0.184568	−	0.0185014i
$901$		−	23.5903i		−	0.785908i
$902$	6.20419			0.206577
$903$	−13.1876	−	11.9101i	−0.438855	−	0.396344i
$904$	0.158407	−	0.274369i	0.00526855	−	0.00912539i
$905$	−24.8649	+	14.3557i	−0.826537	+	0.477201i
$906$	−11.2493	−	21.9473i	−0.373733	−	0.729151i
$907$	−28.2882			−0.939294			−0.469647	−	0.882854i	$-0.655619\pi$
$907$	−28.2882			−0.939294			−0.469647	+	0.882854i	$0.655619\pi$
$908$	−11.3466	+	19.6528i	−0.376549	+	0.652202i
$909$	49.6622	+	4.97824i	1.64719	+	0.165118i
$910$	12.9646	+	10.8683i	0.429774	+	0.360280i
$911$		−	12.5281i		−	0.415076i	−0.978227	−	0.207538i	$-0.933455\pi$
$911$		−	12.5281i		−	0.415076i	0.978227	−	0.207538i	$-0.0665451\pi$
$912$	−0.757248	+	1.17222i	−0.0250750	+	0.0388162i
$913$		−	12.3637i		−	0.409178i
$914$	9.43666	−	5.44826i	0.312137	−	0.180212i
$915$	11.5043	+	22.4448i	0.380320	+	0.742002i
$916$	2.94903	+	1.70262i	0.0974387	+	0.0562563i
$917$	4.96086	+	13.0761i	0.163822	+	0.431811i
$918$	−38.5313	−	5.81800i	−1.27172	−	0.192023i
$919$	44.8198			1.47847			0.739235	−	0.673448i	$-0.235188\pi$
$919$	44.8198			1.47847			0.739235	+	0.673448i	$0.235188\pi$
$920$	9.67044			0.318825
$921$	5.02391	+	0.251174i	0.165543	+	0.00827645i
$922$	−28.5059	+	16.4579i	−0.938791	+	0.542011i
$923$	−7.19106	+	4.02733i	−0.236697	+	0.132561i
$924$	1.25973	+	3.89699i	0.0414420	+	0.128202i
$925$	3.42666	+	5.93515i	0.112668	+	0.195146i
$926$	−8.64969	−	4.99390i	−0.284247	−	0.164110i
$927$	−23.5669	+	10.6288i	−0.774038	+	0.349096i
$928$	−4.40416	+	7.62822i	−0.144574	+	0.250409i
$929$	−43.9601			−1.44229			−0.721143	−	0.692786i	$-0.756383\pi$
$929$	−43.9601			−1.44229			−0.721143	+	0.692786i	$0.756383\pi$
$930$	−24.4449	−	15.7913i	−0.801581	−	0.517816i
$931$	−1.78476	+	5.35017i	−0.0584931	+	0.175345i
$932$	5.66985	+	3.27349i	0.185722	+	0.107227i
$933$	26.4290	+	17.0729i	0.865246	+	0.558942i
$934$		−	20.8848i		−	0.683372i
$935$	−10.2938	−	5.94310i	−0.336642	−	0.194360i
$936$	−8.69803	−	6.42996i	−0.284304	−	0.210170i
$937$			32.4932i			1.06151i	0.847527	+	0.530753i	$0.178091\pi$
$937$			32.4932i			1.06151i	−0.847527	+	0.530753i	$0.821909\pi$
$938$	−16.3710	−	13.3633i	−0.534533	−	0.436329i
$939$	−2.54289	−	4.96116i	−0.0829840	−	0.161901i
$940$	−14.8659			−0.484871
$941$	26.4431	−	45.8008i	0.862021	−	1.49306i	−0.00795494	−	0.999968i	$-0.502532\pi$
$941$	26.4431	−	45.8008i	0.862021	−	1.49306i	0.869975	−	0.493095i	$-0.164135\pi$
$942$	33.8658	−	17.3583i	1.10341	−	0.565563i
$943$			37.8542i			1.23270i
$944$	−3.34899			−0.109000
$945$	−23.8310	+	5.14786i	−0.775224	+	0.167460i
$946$	1.73278	+	3.00126i	0.0563374	+	0.0975793i
$947$	5.56032	+	3.21025i	0.180686	+	0.104319i	0.587615	−	0.809141i	$-0.300067\pi$
$947$	5.56032	+	3.21025i	0.180686	+	0.104319i	−0.406929	+	0.913460i	$0.633400\pi$
$948$	−18.6335	−	12.0371i	−0.605187	−	0.390946i
$949$	−27.4239	+	15.3587i	−0.890218	+	0.498564i
$950$	0.747272	+	1.29431i	0.0242447	+	0.0419931i
$951$	0.864620	+	1.68687i	0.0280372	+	0.0547004i
$952$	−18.5513	+	7.03808i	−0.601253	+	0.228105i
$953$	−30.0111	−	17.3269i	−0.972155	−	0.561274i	−0.0722625	−	0.997386i	$-0.523022\pi$
$953$	−30.0111	−	17.3269i	−0.972155	−	0.561274i	−0.899893	+	0.436112i	$0.856355\pi$
$954$	3.87976	+	8.60246i	0.125612	+	0.278515i
$955$	−24.2582	+	14.0055i	−0.784975	+	0.453206i
$956$	2.38241	−	1.37549i	0.0770528	−	0.0444864i
$957$	12.1339	−	6.21937i	0.392235	−	0.201044i
$958$	10.2715	+	5.93024i	0.331857	+	0.191597i
$959$	1.00032	−	0.379506i	0.0323021	−	0.0122549i
$960$	−2.73352	+	1.40109i	−0.0882241	+	0.0452201i
$961$	29.3808	+	50.8890i	0.947766	+	1.64158i
$962$	−0.174162	+	13.3201i	−0.00561520	+	0.429458i
$963$	39.7690	+	28.6026i	1.28154	+	0.921705i
$964$	5.30840	+	3.06480i	0.170972	+	0.0987107i
$965$	−1.41820	−	2.45639i	−0.0456534	−	0.0790739i
$966$	−23.7771	+	7.68611i	−0.765016	+	0.247296i
$967$	51.5097			1.65644			0.828220	−	0.560404i	$-0.189354\pi$
$967$	51.5097			1.65644			0.828220	+	0.560404i	$0.189354\pi$
$968$			10.2013i			0.327881i
$969$	4.77375	+	9.31356i	0.153355	+	0.299195i
$970$	4.34945	−	7.53347i	0.139652	−	0.241885i
$971$	30.8875			0.991228			0.495614	−	0.868543i	$-0.334943\pi$
$971$	30.8875			0.991228			0.495614	+	0.868543i	$0.334943\pi$
$972$	15.0077	−	4.21542i	0.481371	−	0.135210i
$973$	9.25830	+	7.55736i	0.296807	+	0.242278i
$974$			18.9879i			0.608410i
$975$	−10.3770	+	5.14862i	−0.332329	+	0.164888i
$976$	−7.11088	−	4.10547i	−0.227614	−	0.131413i
$977$		−	55.7716i		−	1.78429i	−0.451747	−	0.892146i	$-0.649199\pi$
$977$		−	55.7716i		−	1.78429i	0.451747	−	0.892146i	$-0.350801\pi$
$978$	5.16273	−	7.99193i	0.165086	−	0.255554i
$979$	−12.0094	−	6.93362i	−0.383822	−	0.221599i
$980$	−9.29012	+	8.23421i	−0.296762	+	0.263032i
$981$	2.24793	−	3.12553i	0.0717710	−	0.0997906i
$982$	−26.0190			−0.830300
$983$	4.09336	−	7.08990i	0.130558	−	0.226133i	−0.793334	−	0.608787i	$-0.791657\pi$
$983$	4.09336	−	7.08990i	0.130558	−	0.226133i	0.923892	+	0.382654i	$0.124990\pi$
$984$	−5.48448	−	10.7002i	−0.174839	−	0.341109i
$985$	6.80772	+	3.93044i	0.216912	+	0.125234i
$986$	33.0285	+	57.2071i	1.05184	+	1.82185i
$987$	36.5513	−	11.8154i	1.16344	−	0.376090i
$988$	−0.0379805	+	2.90480i	−0.00120832	+	0.0924140i
$989$	−18.3119	+	10.5724i	−0.582284	+	0.336182i
$990$	4.73115	+	0.474260i	0.150366	+	0.0150730i
$991$	50.3283			1.59873			0.799366	−	0.600845i	$-0.205169\pi$
$991$	50.3283			1.59873			0.799366	+	0.600845i	$0.205169\pi$
$992$	9.47426			0.300808
$993$	−1.87044	+	37.4121i	−0.0593568	+	1.18724i
$994$	−2.14530	−	5.65471i	−0.0680449	−	0.179357i
$995$	18.9985	+	10.9688i	0.602291	+	0.347733i
$996$	−21.3233	+	10.9295i	−0.675654	+	0.346313i
$997$	−28.4330	+	16.4158i	−0.900483	+	0.519894i	−0.877357	−	0.479838i	$-0.840695\pi$
$997$	−28.4330	+	16.4158i	−0.900483	+	0.519894i	−0.0231262	+	0.999733i	$0.507362\pi$
$998$		−	10.8488i		−	0.343412i
$999$	−15.0064	−	11.9737i	−0.474783	−	0.378831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.185.29	yes	76
3.2	odd	2	inner	546.2.u.a.185.10	✓	76
7.5	odd	6		546.2.bb.a.341.4	yes	76
13.9	even	3		546.2.bb.a.269.3	yes	76
21.5	even	6		546.2.bb.a.341.22	yes	76
39.35	odd	6		546.2.bb.a.269.23	yes	76
91.61	odd	6	inner	546.2.u.a.425.10	yes	76
273.152	even	6	inner	546.2.u.a.425.29	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.10	✓	76	3.2	odd	2	inner
546.2.u.a.185.29	yes	76	1.1	even	1	trivial
546.2.u.a.425.10	yes	76	91.61	odd	6	inner
546.2.u.a.425.29	yes	76	273.152	even	6	inner
546.2.bb.a.269.3	yes	76	13.9	even	3
546.2.bb.a.269.23	yes	76	39.35	odd	6
546.2.bb.a.341.4	yes	76	7.5	odd	6
546.2.bb.a.341.22	yes	76	21.5	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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.0864870 - 1.72989i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.886718 + 1.53584i) q^{5} +(0.939845 - 1.45489i) q^{6} +(2.61154 + 0.424103i) q^{7} +1.00000i q^{8} +(-2.98504 - 0.299226i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.0864870 - 1.72989i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.886718 + 1.53584i) q^{5} +(0.939845 - 1.45489i) q^{6} +(2.61154 + 0.424103i) q^{7} +1.00000i q^{8} +(-2.98504 - 0.299226i) q^{9} +1.77344i q^{10} +0.893720i q^{11} +(1.54137 - 0.790045i) q^{12} +(1.84344 - 3.09866i) q^{13} +(2.04961 + 1.67305i) q^{14} +(2.73352 - 1.40109i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.74970 + 6.49467i) q^{17} +(-2.43551 - 1.75166i) q^{18} +0.805715i q^{19} +(-0.886718 + 1.53584i) q^{20} +(0.959516 - 4.48100i) q^{21} +(-0.446860 + 0.773984i) q^{22} +(-4.72239 - 2.72647i) q^{23} +(1.72989 + 0.0864870i) q^{24} +(0.927464 - 1.60641i) q^{25} +(3.14580 - 1.76180i) q^{26} +(-0.775795 + 5.13791i) q^{27} +(0.938485 + 2.47371i) q^{28} +(7.62822 - 4.40416i) q^{29} +(3.06785 + 0.153379i) q^{30} +(-8.20495 - 4.73713i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.54604 + 0.0772952i) q^{33} +7.49940i q^{34} +(1.66434 + 4.38697i) q^{35} +(-1.23338 - 2.73473i) q^{36} +(-1.84733 + 3.19966i) q^{37} +(-0.402858 + 0.697770i) q^{38} +(-5.20091 - 3.45695i) q^{39} +(-1.53584 + 0.886718i) q^{40} +(-3.47099 - 6.01193i) q^{41} +(3.07146 - 3.40090i) q^{42} +(1.93884 - 3.35816i) q^{43} +(-0.773984 + 0.446860i) q^{44} +(-2.18732 - 4.84987i) q^{45} +(-2.72647 - 4.72239i) q^{46} +(4.19126 + 7.25948i) q^{47} +(1.45489 + 0.939845i) q^{48} +(6.64027 + 2.21512i) q^{49} +(1.60641 - 0.927464i) q^{50} +(11.5594 - 5.92486i) q^{51} +(3.60524 + 0.0471388i) q^{52} +(-2.72420 - 1.57281i) q^{53} +(-3.24081 + 4.06166i) q^{54} +(-1.37261 + 0.792477i) q^{55} +(-0.424103 + 2.61154i) q^{56} +(1.39380 + 0.0696839i) q^{57} +8.80832 q^{58} +(1.67450 + 2.90031i) q^{59} +(2.58014 + 1.66675i) q^{60} +8.21094i q^{61} +(-4.73713 - 8.20495i) q^{62} +(-7.66865 - 2.04741i) q^{63} -1.00000 q^{64} +(6.39366 + 0.0835977i) q^{65} +(1.30026 + 0.839958i) q^{66} -7.98740 q^{67} +(-3.74970 + 6.49467i) q^{68} +(-5.12492 + 7.93341i) q^{69} +(-0.752120 + 4.63139i) q^{70} +(-1.97967 - 1.14296i) q^{71} +(0.299226 - 2.98504i) q^{72} +(-7.54968 - 4.35881i) q^{73} +(-3.19966 + 1.84733i) q^{74} +(-2.69871 - 1.74335i) q^{75} +(-0.697770 + 0.402858i) q^{76} +(-0.379030 + 2.33398i) q^{77} +(-2.77565 - 5.59426i) q^{78} +(-6.40376 - 11.0916i) q^{79} -1.77344 q^{80} +(8.82093 + 1.78640i) q^{81} -6.94198i q^{82} -13.8340 q^{83} +(4.36041 - 1.40953i) q^{84} +(-6.64985 + 11.5179i) q^{85} +(3.35816 - 1.93884i) q^{86} +(-6.95897 - 13.5769i) q^{87} -0.893720 q^{88} +(-7.75816 + 13.4375i) q^{89} +(0.530658 - 5.29377i) q^{90} +(6.12838 - 7.31047i) q^{91} -5.45295i q^{92} +(-8.90433 + 13.7840i) q^{93} +8.38252i q^{94} +(-1.23745 + 0.714442i) q^{95} +(0.790045 + 1.54137i) q^{96} +(-4.24795 - 2.45256i) q^{97} +(4.64308 + 5.23849i) q^{98} +(0.267424 - 2.66779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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