LMFDB - Embedded newform 546.2.u.a.425.10

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			425.10
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.0864870 + 1.72989i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.886718 + 1.53584i) q^{5} +(-0.790045 - 1.54137i) q^{6} +(2.61154 - 0.424103i) q^{7} +1.00000i q^{8} +(-2.98504 - 0.299226i) q^{9} +O(q^{10})$	\(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} +(-0.790045 - 1.54137i) 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} +(1.45489 + 0.939845i) q^{12} +(1.84344 + 3.09866i) q^{13} +(-2.04961 + 1.67305i) q^{14} +(-2.58014 - 1.66675i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.74970 + 6.49467i) q^{17} +(2.73473 - 1.23338i) q^{18} -0.805715i q^{19} +(0.886718 + 1.53584i) q^{20} +(0.507788 + 4.55436i) 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} +(-1.75166 + 2.43551i) q^{36} +(-1.84733 - 3.19966i) q^{37} +(0.402858 + 0.697770i) q^{38} +(-5.51978 + 2.92096i) q^{39} +(-1.53584 - 0.886718i) q^{40} +(3.47099 - 6.01193i) q^{41} +(-2.71693 - 3.69029i) q^{42} +(1.93884 + 3.35816i) q^{43} +(0.773984 + 0.446860i) q^{44} +(3.10645 - 4.31921i) q^{45} +(-2.72647 + 4.72239i) q^{46} +(-4.19126 + 7.25948i) q^{47} +(1.54137 - 0.790045i) q^{48} +(6.64027 - 2.21512i) q^{49} +(-1.60641 - 0.927464i) q^{50} +(-10.9108 - 7.04827i) q^{51} +(3.60524 - 0.0471388i) q^{52} +(2.72420 - 1.57281i) q^{53} +(1.89710 + 4.83746i) 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} +(-2.73352 + 1.40109i) q^{60} -8.21094i q^{61} +(4.73713 - 8.20495i) q^{62} +(-7.92245 + 0.484525i) q^{63} -1.00000 q^{64} +(-6.39366 + 0.0835977i) q^{65} +(1.37756 - 0.706079i) q^{66} -7.98740 q^{67} +(3.74970 + 6.49467i) q^{68} +(4.30807 + 8.40502i) 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} +(-2.85914 + 1.46548i) q^{75} +(-0.697770 - 0.402858i) q^{76} +(0.379030 + 2.33398i) q^{77} +(3.31979 - 5.28952i) 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} +(4.19808 + 1.83742i) q^{84} +(-6.64985 - 11.5179i) q^{85} +(-3.35816 - 1.93884i) q^{86} +(8.27845 - 12.8151i) 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} +(-7.48509 - 14.6034i) q^{93} -8.38252i q^{94} +(1.23745 + 0.714442i) q^{95} +(-0.939845 + 1.45489i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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	$-0.963127\pi$
$5$	−0.886718	+	1.53584i	−0.396552	+	0.686848i	0.596746	+	0.802430i	$0.296460\pi$
$6$	−0.790045	−	1.54137i	−0.322535	−	0.629263i
$7$	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	$0.956982\pi$
$12$	1.45489	+	0.939845i	0.419989	+	0.271310i
$13$	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
$15$	−2.58014	−	1.66675i	−0.666190	−	0.430354i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.74970	+	6.49467i	−0.909436	+	1.57519i	−0.0945862	+	0.995517i	$0.530153\pi$
$17$	−3.74970	+	6.49467i	−0.909436	+	1.57519i	−0.814850	+	0.579672i	$0.803181\pi$
$18$	2.73473	−	1.23338i	0.644583	−	0.290711i
$19$		−	0.805715i		−	0.184844i	−0.995720	−	0.0924219i	$-0.970539\pi$
$19$		−	0.805715i		−	0.184844i	0.995720	−	0.0924219i	$-0.0294608\pi$
$20$	0.886718	+	1.53584i	0.198276	+	0.343424i
$21$	0.507788	+	4.55436i	0.110808	+	0.993842i
$22$	−0.446860	−	0.773984i	−0.0952709	−	0.165014i
$23$	4.72239	−	2.72647i	0.984686	−	0.568509i	0.0810046	−	0.996714i	$-0.474187\pi$
$23$	4.72239	−	2.72647i	0.984686	−	0.568509i	0.903682	+	0.428205i	$0.140854\pi$
$24$	−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	$-0.638157\pi$
$29$	−7.62822	−	4.40416i	−1.41653	−	0.817832i	−0.995992	+	0.0894452i	$0.971491\pi$
$30$	3.06785	+	0.153379i	0.560110	+	0.0280031i
$31$	−8.20495	+	4.73713i	−1.47365	+	0.850813i	−0.999560	−	0.0296621i	$-0.990557\pi$
$31$	−8.20495	+	4.73713i	−1.47365	+	0.850813i	−0.474092	+	0.880475i	$0.657224\pi$
$32$	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
$36$	−1.75166	+	2.43551i	−0.291943	+	0.405918i
$37$	−1.84733	−	3.19966i	−0.303699	−	0.526022i	0.673272	−	0.739395i	$-0.264888\pi$
$37$	−1.84733	−	3.19966i	−0.303699	−	0.526022i	−0.976971	+	0.213373i	$0.931555\pi$
$38$	0.402858	+	0.697770i	0.0653521	+	0.113193i
$39$	−5.51978	+	2.92096i	−0.883872	+	0.467728i
$40$	−1.53584	−	0.886718i	−0.242838	−	0.140202i
$41$	3.47099	−	6.01193i	0.542078	−	0.938906i	−0.456707	−	0.889617i	$-0.650971\pi$
$41$	3.47099	−	6.01193i	0.542078	−	0.938906i	0.998785	−	0.0492887i	$-0.0156954\pi$
$42$	−2.71693	−	3.69029i	−0.419232	−	0.569425i
$43$	1.93884	+	3.35816i	0.295670	+	0.512115i	0.975140	−	0.221588i	$-0.0711239\pi$
$43$	1.93884	+	3.35816i	0.295670	+	0.512115i	−0.679471	+	0.733703i	$0.737791\pi$
$44$	0.773984	+	0.446860i	0.116682	+	0.0673667i
$45$	3.10645	−	4.31921i	0.463082	−	0.643870i
$46$	−2.72647	+	4.72239i	−0.401996	+	0.696278i
$47$	−4.19126	+	7.25948i	−0.611358	+	1.05890i	0.379653	+	0.925129i	$0.376043\pi$
$47$	−4.19126	+	7.25948i	−0.611358	+	1.05890i	−0.991012	+	0.133775i	$0.957290\pi$
$48$	1.54137	−	0.790045i	0.222478	−	0.114033i
$49$	6.64027	−	2.21512i	0.948610	−	0.316446i
$50$	−1.60641	−	0.927464i	−0.227181	−	0.131163i
$51$	−10.9108	−	7.04827i	−1.52781	−	0.986956i
$52$	3.60524	−	0.0471388i	0.499957	−	0.00653698i
$53$	2.72420	−	1.57281i	0.374197	−	0.216043i	−0.301093	−	0.953595i	$-0.597352\pi$
$53$	2.72420	−	1.57281i	0.374197	−	0.216043i	0.675290	+	0.737552i	$0.264018\pi$
$54$	1.89710	+	4.83746i	0.258162	+	0.658295i
$55$	−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	$-0.903287\pi$
$59$	−1.67450	+	2.90031i	−0.218001	+	0.377589i	0.736196	+	0.676769i	$0.236620\pi$
$60$	−2.73352	+	1.40109i	−0.352896	+	0.180880i
$61$		−	8.21094i		−	1.05130i	−0.850700	−	0.525652i	$-0.823822\pi$
$61$		−	8.21094i		−	1.05130i	0.850700	−	0.525652i	$-0.176178\pi$
$62$	4.73713	−	8.20495i	0.601616	−	1.04203i
$63$	−7.92245	+	0.484525i	−0.998135	+	0.0610444i
$64$	−1.00000			−0.125000
$65$	−6.39366	+	0.0835977i	−0.793036	+	0.0103690i
$66$	1.37756	−	0.706079i	0.169565	−	0.0869123i
$67$	−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
$69$	4.30807	+	8.40502i	0.518631	+	1.01185i
$70$	−0.752120	−	4.63139i	−0.0898955	−	0.553558i
$71$	1.97967	−	1.14296i	0.234943	−	0.135645i	−0.377907	−	0.925843i	$-0.623356\pi$
$71$	1.97967	−	1.14296i	0.234943	−	0.135645i	0.612850	+	0.790199i	$0.290023\pi$
$72$	0.299226	−	2.98504i	0.0352641	−	0.351790i
$73$	−7.54968	+	4.35881i	−0.883624	+	0.510160i	−0.871851	−	0.489770i	$-0.837081\pi$
$73$	−7.54968	+	4.35881i	−0.883624	+	0.510160i	−0.0117722	+	0.999931i	$0.503747\pi$
$74$	3.19966	+	1.84733i	0.371953	+	0.214747i
$75$	−2.85914	+	1.46548i	−0.330144	+	0.169219i
$76$	−0.697770	−	0.402858i	−0.0800397	−	0.0462109i
$77$	0.379030	+	2.33398i	0.0431944	+	0.265982i
$78$	3.31979	−	5.28952i	0.375892	−	0.598920i
$79$	−6.40376	+	11.0916i	−0.720479	+	1.24791i	0.240329	+	0.970692i	$0.422745\pi$
$79$	−6.40376	+	11.0916i	−0.720479	+	1.24791i	−0.960808	+	0.277215i	$0.910589\pi$
$80$	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	$-0.225572\pi$
$83$	13.8340			1.51847			0.759237	+	0.650814i	$0.225572\pi$
$84$	4.19808	+	1.83742i	0.458048	+	0.200479i
$85$	−6.64985	−	11.5179i	−0.721277	−	1.24929i
$86$	−3.35816	−	1.93884i	−0.362120	−	0.209070i
$87$	8.27845	−	12.8151i	0.887543	−	1.37392i
$88$	−0.893720			−0.0952709
$89$	7.75816	+	13.4375i	0.822363	+	1.42437i	0.903918	+	0.427706i	$0.140678\pi$
$89$	7.75816	+	13.4375i	0.822363	+	1.42437i	−0.0815547	+	0.996669i	$0.525989\pi$
$90$	−0.530658	+	5.29377i	−0.0559363	+	0.558013i
$91$	6.12838	+	7.31047i	0.642429	+	0.766345i
$92$		−	5.45295i		−	0.568509i
$93$	−7.48509	−	14.6034i	−0.776168	−	1.51430i
$94$		−	8.38252i		−	0.864591i
$95$	1.23745	+	0.714442i	0.126960	+	0.0733002i
$96$	−0.939845	+	1.45489i	−0.0959225	+	0.148489i
$97$	−4.24795	+	2.45256i	−0.431314	+	0.249019i	−0.699906	−	0.714235i	$-0.746775\pi$
$97$	−4.24795	+	2.45256i	−0.431314	+	0.249019i	0.268592	+	0.963254i	$0.413442\pi$
$98$	−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	$-0.189636\pi$
$101$	16.6370			1.65545			0.827724	+	0.561136i	$0.189636\pi$
$102$	12.9731	+	0.648601i	1.28453	+	0.0642210i
$103$	7.46308	+	4.30881i	0.735359	+	0.424560i	0.820379	−	0.571820i	$-0.193762\pi$
$103$	7.46308	+	4.30881i	0.735359	+	0.424560i	−0.0850206	+	0.996379i	$0.527096\pi$
$104$	−3.09866	+	1.84344i	−0.303849	+	0.180765i
$105$	−7.44502	−	3.25855i	−0.726560	−	0.318001i
$106$	−1.57281	+	2.72420i	−0.152765	+	0.264597i
$107$	14.1412	−	8.16443i	1.36708	−	0.789285i	0.376527	−	0.926406i	$-0.377118\pi$
$107$	14.1412	−	8.16443i	1.36708	−	0.789285i	0.990554	+	0.137121i	$0.0437848\pi$
$108$	−4.06166	−	3.24081i	−0.390834	−	0.311848i
$109$	−0.641659	−	1.11139i	−0.0614598	−	0.106452i	0.833658	−	0.552281i	$-0.186242\pi$
$109$	−0.641659	−	1.11139i	−0.0614598	−	0.106452i	−0.895118	+	0.445829i	$0.852909\pi$
$110$	1.58495			0.151119
$111$	5.69484	−	2.91894i	0.540530	−	0.277054i
$112$	−1.67305	−	2.04961i	−0.158089	−	0.193670i
$113$	0.274369	−	0.158407i	0.0258105	−	0.0149017i	−0.487039	−	0.873380i	$-0.661923\pi$
$113$	0.274369	−	0.158407i	0.0258105	−	0.0149017i	0.512850	+	0.858478i	$0.328590\pi$
$114$	−1.24191	+	0.636552i	−0.116315	+	0.0596185i
$115$			9.67044i			0.901774i
$116$	−7.62822	+	4.40416i	−0.708263	+	0.408916i
$117$	−4.57556	−	9.80124i	−0.423010	−	0.906125i
$118$		−	3.34899i		−	0.308300i
$119$	−7.03808	+	18.5513i	−0.645179	+	1.70060i
$120$	1.66675	−	2.58014i	0.152153	−	0.235534i
$121$	10.2013			0.927388
$122$	4.10547	+	7.11088i	0.371692	+	0.643789i
$123$	10.0998	+	6.52439i	0.910667	+	0.588284i
$124$			9.47426i			0.850813i
$125$	−12.1568			−1.08733
$126$	6.61878	−	4.38084i	0.589648	−	0.390276i
$127$	2.45373	−	4.24999i	0.217733	−	0.377125i	−0.736381	−	0.676567i	$-0.763467\pi$
$127$	2.45373	−	4.24999i	0.217733	−	0.377125i	0.954115	+	0.299442i	$0.0968003\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−5.97694	+	3.06354i	−0.526240	+	0.269729i
$130$	5.49528	−	3.26923i	0.481968	−	0.286730i
$131$	−2.64301	+	4.57783i	−0.230921	+	0.399967i	−0.958079	−	0.286503i	$-0.907507\pi$
$131$	−2.64301	+	4.57783i	−0.230921	+	0.399967i	0.727158	+	0.686470i	$0.240841\pi$
$132$	−0.839958	+	1.30026i	−0.0731090	+	0.113173i
$133$	−0.341707	−	2.10416i	−0.0296297	−	0.182454i
$134$	6.91729	−	3.99370i	0.597563	−	0.345003i
$135$	7.20310	+	5.74737i	0.619944	+	0.494655i
$136$	−6.49467	−	3.74970i	−0.556913	−	0.321534i
$137$	−0.350205	−	0.202191i	−0.0299200	−	0.0172743i	0.484965	−	0.874533i	$-0.338832\pi$
$137$	−0.350205	−	0.202191i	−0.0299200	−	0.0172743i	−0.514885	+	0.857259i	$0.672166\pi$
$138$	−7.93341	−	5.12492i	−0.675337	−	0.436262i
$139$	3.91193	−	2.25855i	0.331806	−	0.191568i	−0.324837	−	0.945770i	$-0.605309\pi$
$139$	3.91193	−	2.25855i	0.331806	−	0.191568i	0.656642	+	0.754202i	$0.271976\pi$
$140$	2.96705	+	3.63485i	0.250762	+	0.307201i
$141$	−12.1956	−	7.87827i	−1.02706	−	0.663470i
$142$	−1.14296	+	1.97967i	−0.0959152	+	0.166130i
$143$	−2.76934	+	1.64752i	−0.231584	+	0.137773i
$144$	1.23338	+	2.73473i	0.102782	+	0.227894i
$145$	13.5282	−	7.81049i	1.12345	−	0.648626i
$146$	4.35881	−	7.54968i	0.360738	−	0.624816i
$147$	3.25762	+	11.6785i	0.268684	+	0.963228i
$148$	−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	$0.964114\pi$
$150$	1.74335	−	2.69871i	0.142344	−	0.220349i
$151$	7.11941	+	12.3312i	0.579369	+	1.00350i	0.995552	+	0.0942159i	$0.0300344\pi$
$151$	7.11941	+	12.3312i	0.579369	+	1.00350i	−0.416183	+	0.909281i	$0.636632\pi$
$152$	0.805715			0.0653521
$153$	13.1364	−	18.2648i	1.06201	−	1.47663i
$154$	−1.49524	−	1.83178i	−0.120490	−	0.147609i
$155$		−	16.8020i		−	1.34957i
$156$	−0.230262	+	6.24075i	−0.0184357	+	0.499660i
$157$	19.0276	−	10.9856i	1.51857	−	0.876747i	0.518810	−	0.854889i	$-0.326375\pi$
$157$	19.0276	−	10.9856i	1.51857	−	0.876747i	0.999761	−	0.0218580i	$-0.00695817\pi$
$158$		−	12.8075i		−	1.01891i
$159$	2.48519	+	4.84859i	0.197088	+	0.384518i
$160$	−1.53584	+	0.886718i	−0.121419	+	0.0701012i
$161$	11.1764	−	9.12307i	0.880824	−	0.718999i
$162$	−8.53235	+	2.86339i	−0.670365	+	0.224969i
$163$	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
$165$	1.48961	−	2.30593i	0.115966	−	0.179516i
$166$	−11.9806	+	6.91698i	−0.929872	+	0.536862i
$167$	2.92252	−	5.06195i	0.226151	−	0.391706i	−0.730513	−	0.682899i	$-0.760719\pi$
$167$	2.92252	−	5.06195i	0.226151	−	0.391706i	0.956664	+	0.291193i	$0.0940522\pi$
$168$	−4.55436	+	0.507788i	−0.351376	+	0.0391767i
$169$	−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	$-0.312901\pi$
$173$	14.5872			1.10905			0.554523	+	0.832168i	$0.312901\pi$
$174$	−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
$177$	−4.87240	−	3.14753i	−0.366232	−	0.236583i
$178$	−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	$-0.117850\pi$
$180$	−2.18732	−	4.84987i	−0.163034	−	0.361488i
$181$		−	16.1898i		−	1.20338i	−0.798731	−	0.601688i	$-0.794495\pi$
$181$		−	16.1898i		−	1.20338i	0.798731	−	0.601688i	$-0.205505\pi$
$182$	−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
$186$	13.7840	+	8.90433i	1.01069	+	0.652897i
$187$	−5.80442	−	3.35118i	−0.424461	−	0.245063i
$188$	4.19126	+	7.25948i	0.305679	+	0.529452i
$189$	−0.152985	−	13.7469i	−0.0111281	−	0.999938i
$190$	−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
$195$	0.408354	−	11.0676i	0.0292428	−	0.792565i
$196$	1.40178	−	6.85821i	0.100127	−	0.489872i
$197$	−3.83872	−	2.21629i	−0.273498	−	0.157904i	0.356978	−	0.934113i	$-0.383807\pi$
$197$	−3.83872	−	2.21629i	−0.273498	−	0.157904i	−0.630476	+	0.776209i	$0.717140\pi$
$198$	1.10230	+	2.44409i	0.0783369	+	0.173694i
$199$	10.7128	+	6.18504i	0.759410	+	0.438446i	0.829084	−	0.559124i	$-0.188863\pi$
$199$	10.7128	+	6.18504i	0.759410	+	0.438446i	−0.0696738	+	0.997570i	$0.522196\pi$
$200$	−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
$204$	−11.5594	+	5.92486i	−0.809318	+	0.414823i
$205$	6.15558	+	10.6618i	0.429924	+	0.744650i
$206$	−8.61762			−0.600418
$207$	−14.9124	+	6.72557i	−1.03648	+	0.467459i
$208$	1.76180	−	3.14580i	0.122159	−	0.218122i
$209$	0.720084			0.0498092
$210$	8.07685	−	0.900529i	0.557356	−	0.0621424i
$211$	−9.95733	+	17.2466i	−0.685491	+	1.18731i	0.287791	+	0.957693i	$0.407079\pi$
$211$	−9.95733	+	17.2466i	−0.685491	+	1.18731i	−0.973282	+	0.229612i	$0.926254\pi$
$212$		−	3.14563i		−	0.216043i
$213$	1.80598	+	3.52346i	0.123744	+	0.241423i
$214$	−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
$219$	−6.88732	−	13.4371i	−0.465402	−	0.907995i
$220$	−1.37261	+	0.792477i	−0.0925414	+	0.0534288i
$221$	−27.0372	+	0.353513i	−1.81872	+	0.0237799i
$222$	−3.47240	+	5.37530i	−0.233052	+	0.360766i
$223$	6.77255	+	3.91013i	0.453523	+	0.261842i	0.709317	−	0.704890i	$-0.249003\pi$
$223$	6.77255	+	3.91013i	0.453523	+	0.261842i	−0.255794	+	0.966731i	$0.582337\pi$
$224$	2.47371	+	0.938485i	0.165282	+	0.0627052i
$225$	−2.28784	−	5.07273i	−0.152522	−	0.338182i
$226$	−0.158407	+	0.274369i	−0.0105371	+	0.0182508i
$227$	−11.3466	+	19.6528i	−0.753098	+	1.30440i	0.193217	+	0.981156i	$0.438108\pi$
$227$	−11.3466	+	19.6528i	−0.753098	+	1.30440i	−0.946315	+	0.323247i	$0.895225\pi$
$228$	0.757248	−	1.17222i	0.0501499	−	0.0776324i
$229$	2.94903	+	1.70262i	0.194877	+	0.112513i	0.594264	−	0.804270i	$-0.297443\pi$
$229$	2.94903	+	1.70262i	0.194877	+	0.112513i	−0.399386	+	0.916783i	$0.630777\pi$
$230$	−4.83522	−	8.37485i	−0.318825	−	0.552221i
$231$	−4.07032	+	0.453820i	−0.267807	+	0.0298592i
$232$	4.40416	−	7.62822i	0.289147	−	0.500817i
$233$	−5.66985	−	3.27349i	−0.371444	−	0.214453i	0.302645	−	0.953103i	$-0.402130\pi$
$233$	−5.66985	−	3.27349i	−0.371444	−	0.214453i	−0.674089	+	0.738650i	$0.735464\pi$
$234$	8.86317	+	6.20034i	0.579403	+	0.405329i
$235$	−7.43293	−	12.8742i	−0.484871	−	0.839821i
$236$	1.67450	+	2.90031i	0.109000	+	0.188794i
$237$	−18.6335	−	12.0371i	−1.21037	−	0.781892i
$238$	−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	0.661131	−	0.750270i	$-0.270077\pi$
$241$	5.30840	+	3.06480i	0.341944	+	0.197421i	−0.319187	+	0.947692i	$0.603410\pi$
$242$	−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	$-0.296917\pi$
$251$	−6.30342	−	10.9178i	−0.397868	−	0.689128i	−0.993463	+	0.114157i	$0.963583\pi$
$252$	−3.54161	+	7.10331i	−0.223101	+	0.447466i
$253$	2.43670	+	4.22049i	0.153194	+	0.265340i
$254$			4.90746i			0.307921i
$255$	20.4998	−	10.5074i	1.28375	−	0.657997i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.6331	−	23.6133i	−0.850411	−	1.47295i	−0.880838	−	0.473417i	$-0.843020\pi$
$257$	−13.6331	−	23.6133i	−0.850411	−	1.47295i	0.0304278	−	0.999537i	$-0.490313\pi$
$258$	3.64441	−	5.64157i	0.226891	−	0.351229i
$259$	−6.18135	−	7.57259i	−0.384091	−	0.470538i
$260$	−3.12443	+	5.57887i	−0.193769	+	0.345987i
$261$	21.4527	+	15.4291i	1.32789	+	0.955040i
$262$		−	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
$267$	−23.9164	+	12.2586i	−1.46366	+	0.750214i
$268$	−3.99370	+	6.91729i	−0.243954	+	0.422541i
$269$	1.96598	−	3.40518i	0.119868	−	0.207617i	−0.799847	−	0.600204i	$-0.795086\pi$
$269$	1.96598	−	3.40518i	0.119868	−	0.207617i	0.919715	+	0.392586i	$0.128420\pi$
$270$	−9.11175	−	1.37582i	−0.554524	−	0.0837299i
$271$	0.759673	−	0.438598i	0.0461469	−	0.0266429i	−0.476749	−	0.879039i	$-0.658185\pi$
$271$	0.759673	−	0.438598i	0.0461469	−	0.0266429i	0.522896	+	0.852397i	$0.324852\pi$
$272$	7.49940			0.454718
$273$	−13.1763	+	9.96917i	−0.797468	+	0.603361i
$274$	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	−0.612138	−	0.790751i	$-0.709690\pi$
$277$	6.30351	−	10.9180i	0.378741	−	0.655999i	0.990879	+	0.134752i	$0.0430237\pi$
$278$	−2.25855	+	3.91193i	−0.135459	+	0.234622i
$279$	25.9096	−	11.6854i	1.55117	−	0.699586i
$280$	−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	$-0.992801\pi$
$283$		−	0.760814i		−	0.0452257i	0.999744	−	0.0226129i	$-0.00719851\pi$
$284$		−	2.28592i		−	0.135645i
$285$	−1.34293	+	2.07886i	−0.0795483	+	0.123141i
$286$	1.57455	−	2.81147i	0.0931053	−	0.166245i
$287$	6.51495	−	17.1725i	0.384565	−	1.01366i
$288$	−2.43551	−	1.75166i	−0.143514	−	0.103217i
$289$	−19.6205	−	33.9837i	−1.15415	−	1.99904i
$290$	−7.81049	+	13.5282i	−0.458648	+	0.794401i
$291$	−3.87526	−	7.56061i	−0.227172	−	0.443211i
$292$			8.71762i			0.510160i
$293$	−6.35235	−	11.0026i	−0.371108	−	0.642778i	0.618628	−	0.785684i	$-0.287689\pi$
$293$	−6.35235	−	11.0026i	−0.371108	−	0.642778i	−0.989736	+	0.142906i	$0.954355\pi$
$294$	−8.66045	−	8.48508i	−0.505088	−	0.494860i
$295$	−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	$-0.973590\pi$
$307$		−	2.90418i		−	0.165750i	0.996560	−	0.0828751i	$-0.0264102\pi$
$308$	2.21080	+	0.838743i	0.125972	+	0.0477918i
$309$	−8.09923	+	12.5376i	−0.460749	+	0.713242i
$310$	8.40099	+	14.5509i	0.477144	+	0.826438i
$311$	9.08284	+	15.7319i	0.515040	+	0.892076i	0.999848	+	0.0174552i	$0.00555643\pi$
$311$	9.08284	+	15.7319i	0.515040	+	0.892076i	−0.484807	+	0.874621i	$0.661110\pi$
$312$	−2.92096	−	5.51978i	−0.165367	−	0.312496i
$313$	2.78744	+	1.60933i	0.157556	+	0.0909648i	0.576705	−	0.816953i	$-0.304338\pi$
$313$	2.78744	+	1.60933i	0.157556	+	0.0909648i	−0.419149	+	0.907917i	$0.637672\pi$
$314$	−10.9856	+	19.0276i	−0.619954	+	1.07379i
$315$	6.28082	−	12.5973i	0.353884	−	0.709775i
$316$	6.40376	+	11.0916i	0.360240	+	0.623953i
$317$	0.947773	+	0.547197i	0.0532322	+	0.0307336i	0.526380	−	0.850249i	$-0.323549\pi$
$317$	0.947773	+	0.547197i	0.0532322	+	0.0307336i	−0.473148	+	0.880983i	$0.656882\pi$
$318$	−4.57653	−	2.95640i	−0.256639	−	0.165787i
$319$	3.93608	−	6.81750i	0.220378	−	0.381706i
$320$	0.886718	−	1.53584i	0.0495690	−	0.0858561i
$321$	12.9005	+	25.1688i	0.720037	+	1.40479i
$322$	−5.11751	+	13.4890i	−0.285188	+	0.751713i
$323$	5.23286	+	3.02119i	0.291164	+	0.168104i
$324$	5.95753	−	6.74595i	0.330974	−	0.374775i
$325$	−3.26801	+	5.83524i	−0.181277	+	0.323681i
$326$	−4.75722	+	2.74658i	−0.263478	+	0.152119i
$327$	1.97807	−	1.01388i	0.109388	−	0.0560677i
$328$	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
$333$	4.55692	+	10.1039i	0.249718	+	0.553690i
$334$			5.84504i			0.319826i
$335$	7.08257	−	12.2674i	0.386962	−	0.670238i
$336$	3.69029	−	2.71693i	0.201322	−	0.148221i
$337$	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
$339$	0.250298	+	0.488329i	0.0135943	+	0.0265224i
$340$	−13.2997			−0.721277
$341$	−4.23367	−	7.33292i	−0.229266	−	0.397100i
$342$	−0.993755	−	2.20342i	−0.0537361	−	0.119147i
$343$	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	$-0.536309\pi$
$347$	−19.2078	−	11.0897i	−1.03113	−	0.595324i	−0.917308	+	0.398177i	$0.869643\pi$
$348$	−6.95897	−	13.5769i	−0.373040	−	0.727798i
$349$	9.10947	+	5.25936i	0.487619	+	0.281527i	0.723586	−	0.690234i	$-0.242492\pi$
$349$	9.10947	+	5.25936i	0.487619	+	0.281527i	−0.235967	+	0.971761i	$0.575826\pi$
$350$	−4.58856	−	1.74082i	−0.245269	−	0.0930509i
$351$	17.3508	−	7.06753i	0.926117	−	0.377237i
$352$	−0.446860	+	0.773984i	−0.0238177	+	0.0412535i
$353$	−25.1674			−1.33952			−0.669762	−	0.742576i	$-0.733604\pi$
$353$	−25.1674			−1.33952			−0.669762	+	0.742576i	$0.733604\pi$
$354$	5.79339	+	0.289644i	0.307915	+	0.0153944i
$355$			4.05394i			0.215161i
$356$	15.5163			0.822363
$357$	−31.4831	−	13.7796i	−1.66626	−	0.729291i
$358$	4.84102	+	8.38489i	0.255856	+	0.443155i
$359$	−20.7408	−	11.9747i	−1.09466	−	0.632002i	−0.159846	−	0.987142i	$-0.551100\pi$
$359$	−20.7408	−	11.9747i	−1.09466	−	0.632002i	−0.934813	+	0.355140i	$0.884433\pi$
$360$	4.31921	+	3.10645i	0.227643	+	0.163724i
$361$	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
$366$	−12.6561	+	6.48701i	−0.661546	+	0.339082i
$367$			14.2995i			0.746425i	0.927746	+	0.373213i	$0.121744\pi$
$367$			14.2995i			0.746425i	−0.927746	+	0.373213i	$0.878256\pi$
$368$	−4.72239	−	2.72647i	−0.246172	−	0.142127i
$369$	−12.1600	+	16.9072i	−0.633023	+	0.880156i
$370$	−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
$378$	7.00593	+	11.8287i	0.360346	+	0.608400i
$379$	9.34507	−	16.1861i	0.480024	−	0.831426i	−0.519714	−	0.854341i	$-0.673961\pi$
$379$	9.34507	−	16.1861i	0.480024	−	0.831426i	0.999737	+	0.0229149i	$0.00729466\pi$
$380$	1.23745	−	0.714442i	0.0634798	−	0.0366501i
$381$	7.13979	+	4.61225i	0.365783	+	0.236293i
$382$	−7.89736	−	13.6786i	−0.404064	−	0.699859i
$383$	32.8148			1.67676			0.838379	−	0.545088i	$-0.183504\pi$
$383$	32.8148			1.67676			0.838379	+	0.545088i	$0.183504\pi$
$384$	0.790045	+	1.54137i	0.0403168	+	0.0786578i
$385$	−3.92072	−	1.48746i	−0.199818	−	0.0758078i
$386$	1.38510	−	0.799689i	0.0704998	−	0.0407031i
$387$	−4.78265	−	10.6044i	−0.243116	−	0.539052i
$388$			4.90511i			0.249019i
$389$	7.54767	−	4.35765i	0.382682	−	0.220941i	−0.296303	−	0.955094i	$-0.595754\pi$
$389$	7.54767	−	4.35765i	0.382682	−	0.220941i	0.678984	+	0.734153i	$0.262420\pi$
$390$	5.18014	+	9.78897i	0.262307	+	0.495684i
$391$			40.8938i			2.06809i
$392$	2.21512	+	6.64027i	0.111881	+	0.335384i
$393$	−7.69056	−	4.96805i	−0.387938	−	0.250605i
$394$	4.43257			0.223310
$395$	−11.3566	−	19.6703i	−0.571415	−	0.989720i
$396$	−2.17666	−	1.56549i	−0.109381	−	0.0786689i
$397$		−	39.0196i		−	1.95834i	−0.203043	−	0.979170i	$-0.565083\pi$
$397$		−	39.0196i		−	1.95834i	0.203043	−	0.979170i	$-0.434917\pi$
$398$	−12.3701			−0.620056
$399$	3.66951	−	0.409133i	0.183705	−	0.0204822i
$400$	0.927464	−	1.60641i	0.0463732	−	0.0803207i
$401$	6.18619	−	3.57160i	0.308923	−	0.178357i	−0.337521	−	0.941318i	$-0.609588\pi$
$401$	6.18619	−	3.57160i	0.308923	−	0.178357i	0.646445	+	0.762961i	$0.276255\pi$
$402$	6.31041	+	12.3116i	0.314734	+	0.614045i
$403$	−29.8041	−	16.6917i	−1.48465	−	0.831474i
$404$	8.31852	−	14.4081i	0.413862	−	0.716830i
$405$	−10.5653	+	11.9635i	−0.524994	+	0.594471i
$406$	23.0033	−	3.73564i	1.14163	−	0.185396i
$407$	2.85960	−	1.65099i	0.141745	−	0.0818367i
$408$	7.04827	−	10.9108i	0.348942	−	0.540163i
$409$	−12.9097	−	7.45341i	−0.638343	−	0.368548i	0.145633	−	0.989339i	$-0.453478\pi$
$409$	−12.9097	−	7.45341i	−0.638343	−	0.368548i	−0.783976	+	0.620791i	$0.786812\pi$
$410$	−10.6618	−	6.15558i	−0.526547	−	0.304002i
$411$	0.380056	−	0.588329i	0.0187468	−	0.0290201i
$412$	7.46308	−	4.30881i	0.367679	−	0.212280i
$413$	−3.14298	+	8.28444i	−0.154656	+	0.407651i
$414$	9.55169	−	13.2807i	0.469440	−	0.652710i
$415$	−12.2668	+	21.2468i	−0.602154	+	1.04296i
$416$	0.0471388	+	3.60524i	0.00231117	+	0.176762i
$417$	3.56872	+	6.96255i	0.174761	+	0.340957i
$418$	−0.623611	+	0.360042i	−0.0305018	+	0.0176102i
$419$	−10.6067	+	18.3714i	−0.518172	+	0.897500i	0.481605	+	0.876388i	$0.340054\pi$
$419$	−10.6067	+	18.3714i	−0.518172	+	0.897500i	−0.999777	+	0.0211116i	$0.993279\pi$
$420$	−6.54450	+	4.81831i	−0.319339	+	0.235109i
$421$	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
$423$	14.6833	−	20.4157i	0.713927	−	0.992645i
$424$	1.57281	+	2.72420i	0.0763826	+	0.132299i
$425$	−13.9108			−0.674775
$426$	−3.32576	−	2.14841i	−0.161133	−	0.104091i
$427$	−3.48229	−	21.4432i	−0.168520	−	1.03771i
$428$		−	16.3289i		−	0.789285i
$429$	−2.61052	−	4.93314i	−0.126037	−	0.238174i
$430$	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	$-0.113850\pi$
$432$	−4.83746	+	1.89710i	−0.232742	+	0.0912742i
$433$	1.17784	−	0.680025i	0.0566033	−	0.0326799i	−0.471431	−	0.881903i	$-0.656262\pi$
$433$	1.17784	−	0.680025i	0.0566033	−	0.0326799i	0.528035	+	0.849223i	$0.322929\pi$
$434$	8.89145	−	23.4366i	0.426803	−	1.12499i
$435$	12.3413	+	24.0777i	0.591719	+	1.15444i
$436$	−1.28332			−0.0614598
$437$	−2.19676	−	3.80490i	−0.105085	−	0.182013i
$438$	12.6831	+	8.19322i	0.606024	+	0.391487i
$439$	25.8566	−	14.9283i	1.23407	−	0.712488i	0.266191	−	0.963920i	$-0.414235\pi$
$439$	25.8566	−	14.9283i	1.23407	−	0.712488i	0.967875	+	0.251432i	$0.0809014\pi$
$440$	0.792477	−	1.37261i	0.0377799	−	0.0654366i
$441$	−20.4843	+	4.62529i	−0.975443	+	0.220252i
$442$	23.2381	−	13.8247i	1.10532	−	0.657575i
$443$	31.3793	+	18.1168i	1.49087	+	0.860757i	0.999945	−	0.0104432i	$-0.00332424\pi$
$443$	31.3793	+	18.1168i	1.49087	+	0.860757i	0.490929	+	0.871200i	$0.336658\pi$
$444$	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	$-0.385256\pi$
$449$	28.3824	−	16.3866i	1.33945	−	0.773331i	0.986726	+	0.162397i	$0.0519225\pi$
$450$	4.51769	+	3.24920i	0.212966	+	0.153169i
$451$	5.37298	+	3.10209i	0.253004	+	0.146072i
$452$		−	0.316814i		−	0.0149017i
$453$	−21.9473	+	11.2493i	−1.03117	+	0.528539i
$454$		−	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	0.964857	−	0.262775i	$-0.0846377\pi$
$457$	5.44826	+	9.43666i	0.254859	+	0.441428i	−0.709998	+	0.704203i	$0.751304\pi$
$458$	−3.40525			−0.159117
$459$	30.4600	+	24.3042i	1.42175	+	1.13442i
$460$	8.37485	+	4.83522i	0.390479	+	0.225443i
$461$	16.4579	+	28.5059i	0.766520	+	1.32765i	0.939439	+	0.342715i	$0.111347\pi$
$461$	16.4579	+	28.5059i	0.766520	+	1.32765i	−0.172919	+	0.984936i	$0.555320\pi$
$462$	3.29809	−	2.42818i	0.153441	−	0.112969i
$463$	−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	$-0.672802\pi$
$467$	10.4424	−	18.0868i	0.483217	−	0.836956i	0.999814	+	0.0192723i	$0.00613493\pi$
$468$	−10.7759	−	0.938071i	−0.498116	−	0.0433624i
$469$	−20.8594	+	3.38748i	−0.963198	+	0.156419i
$470$	12.8742	+	7.43293i	0.593843	+	0.342855i
$471$	17.3583	+	33.8658i	0.799827	+	1.56046i
$472$	−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
$477$	−8.60246	+	3.87976i	−0.393880	+	0.177642i
$478$	1.37549	+	2.38241i	0.0629133	+	0.108969i
$479$	−11.8605			−0.541919			−0.270960	−	0.962591i	$-0.587341\pi$
$479$	−11.8605			−0.541919			−0.270960	+	0.962591i	$0.587341\pi$
$480$	−1.40109	−	2.73352i	−0.0639509	−	0.124768i
$481$	6.50923	−	11.6226i	0.296796	−	0.529947i
$482$	−6.12961			−0.279196
$483$	14.8153	+	20.1230i	0.674119	+	0.915627i
$484$	5.10063	−	8.83455i	0.231847	−	0.401571i
$485$		−	8.69890i		−	0.394997i
$486$	−4.21542	−	15.0077i	−0.191215	−	0.680762i
$487$	9.49393	−	16.4440i	0.430211	−	0.745148i	−0.566680	−	0.823938i	$-0.691772\pi$
$487$	9.49393	−	16.4440i	0.430211	−	0.745148i	0.996891	+	0.0787903i	$0.0251058\pi$
$488$	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	$-0.133599\pi$
$491$	22.5331	+	13.0095i	1.01691	+	0.587111i	0.103699	+	0.994609i	$0.466932\pi$
$492$	10.7002	−	5.48448i	0.482401	−	0.247259i
$493$	57.2071	−	33.0285i	2.57648	−	1.48753i
$494$	−1.41951	+	2.53462i	−0.0638667	+	0.114038i
$495$	3.86017	+	2.77630i	0.173502	+	0.124785i
$496$	8.20495	+	4.73713i	0.368413	+	0.212703i
$497$	4.68524	−	3.82447i	0.210162	−	0.171551i
$498$	−10.9295	−	21.3233i	−0.489761	−	0.955519i
$499$	−5.42439	+	9.39532i	−0.242829	+	0.420592i	−0.961519	−	0.274738i	$-0.911409\pi$
$499$	−5.42439	+	9.39532i	−0.242829	+	0.420592i	0.718690	+	0.695331i	$0.244742\pi$
$500$	−6.07838	+	10.5281i	−0.271834	+	0.470830i
$501$	8.50387	+	5.49343i	0.379925	+	0.245428i
$502$	10.9178	+	6.30342i	0.487287	+	0.281335i
$503$	−4.86978	−	8.43471i	−0.217133	−	0.376085i	0.736797	−	0.676114i	$-0.236337\pi$
$503$	−4.86978	−	8.43471i	−0.217133	−	0.376085i	−0.953930	+	0.300029i	$0.903004\pi$
$504$	−0.484525	−	7.92245i	−0.0215824	−	0.352894i
$505$	−14.7524	+	25.5518i	−0.656471	+	1.13704i
$506$	−4.22049	−	2.43670i	−0.187624	−	0.108325i
$507$	−19.2265	−	11.7193i	−0.853878	−	0.520472i
$508$	−2.45373	−	4.24999i	−0.108867	−	0.188563i
$509$	5.74843	+	9.95658i	0.254795	+	0.441318i	0.964840	−	0.262839i	$-0.0846587\pi$
$509$	5.74843	+	9.95658i	0.254795	+	0.441318i	−0.710045	+	0.704156i	$0.751325\pi$
$510$	−12.4997	+	19.3495i	−0.553494	+	0.856812i
$511$	−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	$-0.141903\pi$
$521$	1.77397	+	3.07261i	0.0777191	+	0.134613i	−0.824546	+	0.565794i	$0.808570\pi$
$522$	−26.2932	−	2.63568i	−1.15082	−	0.115360i
$523$	−10.3157	+	5.95576i	−0.451073	+	0.260427i	−0.708283	−	0.705928i	$-0.750530\pi$
$523$	−10.3157	+	5.95576i	−0.451073	+	0.260427i	0.257210	+	0.966355i	$0.417197\pi$
$524$	2.64301	+	4.57783i	0.115461	+	0.199984i
$525$	−6.84523	+	5.03972i	−0.298750	+	0.219951i
$526$	−0.281241	−	0.487124i	−0.0122627	−	0.0212396i
$527$		−	71.0512i		−	3.09504i
$528$	0.706079	+	1.37756i	0.0307281	+	0.0599504i
$529$	3.36731	−	5.83235i	0.146405	−	0.253580i
$530$	−2.78928	−	4.83118i	−0.121159	−	0.209853i
$531$	5.86629	−	8.15650i	0.254575	−	0.353962i
$532$	−1.99311	−	0.756152i	−0.0864121	−	0.0327833i
$533$	25.0275	−	0.327237i	1.08406	−	0.0141742i
$534$	14.5829	−	22.5745i	0.631065	−	0.976893i
$535$			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
$540$	8.57892	−	3.36438i	0.369178	−	0.144780i
$541$	8.93957	−	15.4838i	0.384342	−	0.665700i	−0.607336	−	0.794445i	$-0.707762\pi$
$541$	8.93957	−	15.4838i	0.384342	−	0.665700i	0.991678	+	0.128745i	$0.0410950\pi$
$542$	−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
$546$	6.42645	−	15.2217i	0.275027	−	0.651429i
$547$	−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
$552$	−8.40502	+	4.30807i	−0.357741	+	0.183364i
$553$	−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	$0.982783\pi$
$558$	−16.5956	+	23.0746i	−0.702550	+	0.976827i
$559$	−6.83168	+	12.1984i	−0.288949	+	0.515937i
$560$	4.63139	−	0.752120i	0.195712	−	0.0317829i
$561$	6.29918	−	9.75117i	0.265952	−	0.411695i
$562$	−3.18858	−	5.52278i	−0.134502	−	0.232964i
$563$	−2.09878	+	3.63519i	−0.0884529	+	0.153205i	−0.906857	−	0.421438i	$-0.861526\pi$
$563$	−2.09878	+	3.63519i	−0.0884529	+	0.153205i	0.818404	+	0.574643i	$0.194859\pi$
$564$	−12.9206	+	6.62257i	−0.544055	+	0.278861i
$565$			0.561850i			0.0236372i
$566$	0.380407	+	0.658885i	0.0159897	+	0.0276950i
$567$	23.7938	+	0.924278i	0.999246	+	0.0388160i
$568$	1.14296	+	1.97967i	0.0479576	+	0.0830650i
$569$	−32.1347	+	18.5530i	−1.34716	+	0.777782i	−0.987846	−	0.155435i	$-0.950322\pi$
$569$	−32.1347	+	18.5530i	−1.34716	+	0.777782i	−0.359312	+	0.933218i	$0.616989\pi$
$570$	0.123580	−	2.47181i	0.00517619	−	0.103533i
$571$	2.55983	+	4.43376i	0.107126	+	0.185547i	0.914605	−	0.404349i	$-0.132502\pi$
$571$	2.55983	+	4.43376i	0.107126	+	0.185547i	−0.807479	+	0.589896i	$0.799169\pi$
$572$	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	−0.591823	−	0.806068i	$-0.701592\pi$
$577$	−4.55577	+	2.63028i	−0.189659	+	0.109500i	0.402164	+	0.915568i	$0.368258\pi$
$578$	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
$582$	7.13638	+	4.61005i	0.295812	+	0.191093i
$583$	1.40566	+	2.43467i	0.0582163	+	0.100834i
$584$	−4.35881	−	7.54968i	−0.180369	−	0.312408i
$585$	19.1104	+	1.66361i	0.790116	+	0.0687817i
$586$	11.0026	+	6.35235i	0.454513	+	0.262413i
$587$	−13.2127	+	22.8850i	−0.545346	+	0.944567i	0.453239	+	0.891389i	$0.350268\pi$
$587$	−13.2127	+	22.8850i	−0.545346	+	0.944567i	−0.998585	+	0.0531780i	$0.983065\pi$
$588$	11.7427	+	3.01808i	0.484261	+	0.124463i
$589$	3.81678	+	6.61085i	0.157268	+	0.272395i
$590$	5.14352	+	2.96961i	0.211755	+	0.122257i
$591$	4.16593	−	6.44889i	0.171364	−	0.265272i
$592$	−1.84733	+	3.19966i	−0.0759247	+	0.131505i
$593$	−11.1153	+	19.2523i	−0.456451	+	0.790596i	−0.998770	−	0.0495766i	$-0.984213\pi$
$593$	−11.1153	+	19.2523i	−0.456451	+	0.790596i	0.542320	+	0.840172i	$0.317546\pi$
$594$	−4.32333	+	1.69547i	−0.177389	+	0.0695661i
$595$	−22.2511	−	27.2592i	−0.912207	−	1.11752i
$596$	2.37853	+	1.37324i	0.0974283	+	0.0562502i
$597$	−11.6260	+	17.9970i	−0.475819	+	0.736570i
$598$	−19.6592	+	0.257046i	−0.803924	+	0.0105114i
$599$	15.9688	−	9.21958i	0.652467	−	0.376702i	−0.136934	−	0.990580i	$-0.543725\pi$
$599$	15.9688	−	9.21958i	0.652467	−	0.376702i	0.789401	+	0.613878i	$0.210391\pi$
$600$	−1.46548	−	2.85914i	−0.0598278	−	0.116724i
$601$	−16.9272	−	9.77294i	−0.690476	−	0.398646i	0.113314	−	0.993559i	$-0.463853\pi$
$601$	−16.9272	−	9.77294i	−0.690476	−	0.398646i	−0.803790	+	0.594913i	$0.797187\pi$
$602$	−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
$606$	−13.1440	−	25.6439i	−0.533939	−	1.04171i
$607$			7.87162i			0.319499i	0.987158	+	0.159750i	$0.0510687\pi$
$607$			7.87162i			0.319499i	−0.987158	+	0.159750i	$0.948931\pi$
$608$	0.402858	−	0.697770i	0.0163380	−	0.0282983i
$609$	16.1846	−	36.9780i	0.655832	−	1.49843i
$610$	−14.5616			−0.589581
$611$	−30.2210	+	0.395142i	−1.22261	+	0.0159858i
$612$	−9.24963	−	20.5089i	−0.373894	−	0.829022i
$613$	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
$615$	−18.9761	+	9.72636i	−0.765189	+	0.392205i
$616$	−2.33398	+	0.379030i	−0.0940389	+	0.0152715i
$617$	−3.90089	+	2.25218i	−0.157044	+	0.0906694i	−0.576462	−	0.817124i	$-0.695567\pi$
$617$	−3.90089	+	2.25218i	−0.157044	+	0.0906694i	0.419419	+	0.907793i	$0.362234\pi$
$618$	0.745312	−	14.9075i	0.0299808	−	0.599669i
$619$	4.81682	−	2.78099i	0.193604	−	0.111777i	−0.400065	−	0.916487i	$-0.631012\pi$
$619$	4.81682	−	2.78099i	0.193604	−	0.111777i	0.593669	+	0.804710i	$0.297679\pi$
$620$	−14.5509	−	8.40099i	−0.584380	−	0.337392i
$621$	−10.3448	−	26.3784i	−0.415121	−	1.05853i
$622$	−15.7319	−	9.08284i	−0.630793	−	0.364189i
$623$	25.9596	+	31.8024i	1.04005	+	1.27413i
$624$	5.28952	+	3.31979i	0.211750	+	0.132898i
$625$	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
$630$	0.859273	+	14.0500i	0.0342343	+	0.559764i
$631$	−17.4066	−	30.1491i	−0.692944	−	1.20021i	−0.970869	−	0.239612i	$-0.922980\pi$
$631$	−17.4066	−	30.1491i	−0.692944	−	1.20021i	0.277924	−	0.960603i	$-0.410354\pi$
$632$	−11.0916	−	6.40376i	−0.441202	−	0.254728i
$633$	−28.9735	−	18.7167i	−1.15160	−	0.743922i
$634$	−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
$639$	−6.25139	+	2.81942i	−0.247301	+	0.111534i
$640$			1.77344i			0.0701012i
$641$	−13.1123	−	7.57036i	−0.517903	−	0.299011i	0.218173	−	0.975910i	$-0.429990\pi$
$641$	−13.1123	−	7.57036i	−0.517903	−	0.299011i	−0.736076	+	0.676899i	$0.763324\pi$
$642$	−23.7566	−	15.3466i	−0.937599	−	0.605682i
$643$	17.4033	−	10.0478i	0.686317	−	0.396246i	−0.115914	−	0.993259i	$-0.536980\pi$
$643$	17.4033	−	10.0478i	0.686317	−	0.396246i	0.802231	+	0.597014i	$0.203646\pi$
$644$	−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	$-0.642717\pi$
$647$	−22.0525			−0.866973			−0.433486	+	0.901160i	$0.642717\pi$
$648$	−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
$651$	−25.7409	−	34.9628i	−1.00887	−	1.37030i
$652$	2.74658	−	4.75722i	0.107564	−	0.186307i
$653$	30.3575	−	17.5269i	1.18798	−	0.685882i	0.230134	−	0.973159i	$-0.426083\pi$
$653$	30.3575	−	17.5269i	1.18798	−	0.685882i	0.957847	+	0.287277i	$0.0927501\pi$
$654$	−1.20612	+	1.86708i	−0.0471631	+	0.0730087i
$655$	−4.68721	−	8.11849i	−0.183145	−	0.317216i
$656$	−6.94198			−0.271039
$657$	23.8404	−	10.7522i	0.930102	−	0.419482i
$658$	−3.55506	−	21.8913i	−0.138590	−	0.853411i
$659$	6.09325	−	3.51794i	0.237359	−	0.137039i	−0.376603	−	0.926375i	$-0.622908\pi$
$659$	6.09325	−	3.51794i	0.237359	−	0.137039i	0.613962	+	0.789335i	$0.289575\pi$
$660$	−1.25219	−	2.44300i	−0.0487412	−	0.0950938i
$661$		−	32.6925i		−	1.27159i	−0.771858	−	0.635795i	$-0.780672\pi$
$661$		−	32.6925i		−	1.27159i	0.771858	−	0.635795i	$-0.219328\pi$
$662$	18.7294	−	10.8134i	0.727940	−	0.420276i
$663$	1.72682	−	46.8019i	0.0670643	−	1.81763i
$664$			13.8340i			0.536862i
$665$	3.53465	+	1.34099i	0.137068	+	0.0520012i
$666$	−8.99836	−	6.47177i	−0.348679	−	0.250776i
$667$	−48.0313			−1.85978
$668$	−2.92252	−	5.06195i	−0.113076	−	0.195853i
$669$	−7.34984	+	11.3776i	−0.284161	+	0.439883i
$670$			14.1651i			0.547247i
$671$	7.33828			0.283291
$672$	−1.83742	+	4.19808i	−0.0708800	+	0.161945i
$673$	−11.4876	+	19.8971i	−0.442814	+	0.766976i	−0.997897	−	0.0648191i	$-0.979353\pi$
$673$	−11.4876	+	19.8971i	−0.442814	+	0.766976i	0.555083	+	0.831795i	$0.312686\pi$
$674$	−14.6829	+	8.47719i	−0.565565	+	0.326529i
$675$	8.97314	−	3.51898i	0.345376	−	0.135446i
$676$	6.79213	+	11.0845i	0.261236	+	0.426328i
$677$	−0.619754	+	1.07345i	−0.0238191	+	0.0412559i	−0.877689	−	0.479230i	$-0.840916\pi$
$677$	−0.619754	+	1.07345i	−0.0238191	+	0.0412559i	0.853870	+	0.520486i	$0.174249\pi$
$678$	−0.460929	−	0.297756i	−0.0177019	−	0.0114353i
$679$	−10.0536	+	8.20652i	−0.385820	+	0.314937i
$680$	11.5179	−	6.64985i	0.441690	−	0.255010i
$681$	−33.0159	−	21.3280i	−1.26517	−	0.817291i
$682$	7.33292	+	4.23367i	0.280792	+	0.162115i
$683$	−1.95788	−	1.13038i	−0.0749160	−	0.0432528i	0.462074	−	0.886841i	$-0.347105\pi$
$683$	−1.95788	−	1.13038i	−0.0749160	−	0.0432528i	−0.536990	+	0.843589i	$0.680439\pi$
$684$	1.96233	+	1.41134i	0.0750314	+	0.0539638i
$685$	0.621066	−	0.358572i	0.0237297	−	0.0137003i
$686$	−9.90393	+	15.6497i	−0.378134	+	0.597507i
$687$	−3.20040	+	4.95424i	−0.122103	+	0.189016i
$688$	1.93884	−	3.35816i	0.0739174	−	0.128029i
$689$	9.89553	+	5.54196i	0.376990	+	0.211132i
$690$	14.9058	−	7.64009i	0.567452	−	0.290853i
$691$	−40.1735	+	23.1942i	−1.52827	+	0.882349i	−0.528839	+	0.848722i	$0.677373\pi$
$691$	−40.1735	+	23.1942i	−1.52827	+	0.882349i	−0.999434	+	0.0336272i	$0.989294\pi$
$692$	7.29361	−	12.6329i	0.277262	−	0.480231i
$693$	−0.433029	−	7.08045i	−0.0164494	−	0.268964i
$694$	22.1793			0.841915
$695$			8.01080i			0.303867i
$696$	12.8151	+	8.27845i	0.485755	+	0.313794i
$697$	26.0303	+	45.0859i	0.985970	+	1.70775i
$698$	−10.5187			−0.398139
$699$	6.15314	−	9.52510i	0.232733	−	0.360272i
$700$	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	$0.716707\pi$
$702$	−11.4925	+	14.7961i	−0.433755	+	0.558441i
$703$	−2.57802	+	1.48842i	−0.0972318	+	0.0561368i
$704$		−	0.893720i		−	0.0336833i
$705$	22.9138	−	11.7447i	0.862985	−	0.442331i
$706$	21.7956	−	12.5837i	0.820288	−	0.473593i
$707$	43.4483	−	7.05582i	1.63404	−	0.265362i
$708$	−5.16204	+	2.64586i	−0.194001	+	0.0994373i
$709$	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
$711$	22.4344	−	31.1928i	0.841355	−	1.16982i
$712$	−13.4375	+	7.75816i	−0.503593	+	0.290749i
$713$	−25.8313	+	44.7411i	−0.967390	+	1.67557i
$714$	34.1549	−	3.80810i	1.27822	−	0.142515i
$715$	−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	$-0.643531\pi$
$719$	−23.3708			−0.871583			−0.435791	+	0.900048i	$0.643531\pi$
$720$	−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
$723$	−5.76088	+	8.91788i	−0.214250	+	0.331659i
$724$	−14.0207	−	8.09488i	−0.521077	−	0.300844i
$725$		−	16.3388i		−	0.606808i
$726$	−8.05946	−	15.7239i	−0.299115	−	0.583570i
$727$			34.2889i			1.27171i	0.771810	+	0.635853i	$0.219351\pi$
$727$			34.2889i			1.27171i	−0.771810	+	0.635853i	$0.780649\pi$
$728$	−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
$732$	7.71701	−	11.9460i	0.285229	−	0.441536i
$733$	19.4049	+	11.2034i	0.716736	+	0.413808i	0.813550	−	0.581495i	$-0.197532\pi$
$733$	19.4049	+	11.2034i	0.716736	+	0.413808i	−0.0968139	+	0.995303i	$0.530865\pi$
$734$	−7.14973	−	12.3837i	−0.263901	−	0.457090i
$735$	−20.8249	−	5.35236i	−0.768139	−	0.197425i
$736$	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
$741$	2.35347	+	4.44737i	0.0864567	+	0.163378i
$742$	−2.95213	+	7.78138i	−0.108376	+	0.285663i
$743$	−37.6419	−	21.7325i	−1.38095	−	0.797289i	−0.388674	−	0.921375i	$-0.627067\pi$
$743$	−37.6419	−	21.7325i	−1.38095	−	0.797289i	−0.992272	+	0.124086i	$0.960400\pi$
$744$	14.6034	−	7.48509i	0.535385	−	0.274417i
$745$	−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
$750$	9.60440	+	18.7381i	0.350703	+	0.684219i
$751$	−13.8241	−	23.9440i	−0.504447	−	0.873728i	−0.999987	−	0.00514292i	$-0.998363\pi$
$751$	−13.8241	−	23.9440i	−0.504447	−	0.873728i	0.495539	−	0.868585i	$-0.334970\pi$
$752$	8.38252			0.305679
$753$	19.4318	−	9.95997i	0.708136	−	0.362962i
$754$	16.2376	+	27.2940i	0.591340	+	0.993989i
$755$	−25.2516			−0.919000
$756$	−11.9816	−	6.74095i	−0.435768	−	0.245166i
$757$	−12.4453	+	21.5558i	−0.452330	+	0.783459i	−0.998530	−	0.0541956i	$-0.982741\pi$
$757$	−12.4453	+	21.5558i	−0.452330	+	0.783459i	0.546200	+	0.837655i	$0.316074\pi$
$758$			18.6901i			0.678856i
$759$	−7.51173	+	3.85021i	−0.272659	+	0.139754i
$760$	−0.714442	+	1.23745i	−0.0259155	+	0.0448870i
$761$	−35.1534			−1.27431			−0.637156	−	0.770735i	$-0.719889\pi$
$761$	−35.1534			−1.27431			−0.637156	+	0.770735i	$0.719889\pi$
$762$	−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
$765$	16.4036	+	36.3711i	0.593074	+	1.31500i
$766$	−28.4184	+	16.4074i	−1.02680	+	0.592823i
$767$	−12.0739	+	0.157868i	−0.435964	+	0.00570027i
$768$	−1.45489	−	0.939845i	−0.0524987	−	0.0339137i
$769$	−21.8138	−	12.5942i	−0.786626	−	0.454159i	0.0521474	−	0.998639i	$-0.483393\pi$
$769$	−21.8138	−	12.5942i	−0.786626	−	0.454159i	−0.838773	+	0.544481i	$0.816727\pi$
$770$	4.13917	−	0.672184i	0.149165	−	0.0242238i
$771$	42.0274	−	21.5416i	1.51358	−	0.775800i
$772$	−0.799689	+	1.38510i	−0.0287814	+	0.0498509i
$773$	−23.6135	+	40.8998i	−0.849318	+	1.47106i	0.0324991	+	0.999472i	$0.489653\pi$
$773$	−23.6135	+	40.8998i	−0.849318	+	1.47106i	−0.881817	+	0.471591i	$0.843680\pi$
$774$	9.44410	+	6.79235i	0.339461	+	0.244146i
$775$	−15.2196	−	8.78703i	−0.546704	−	0.315640i
$776$	−2.45256	−	4.24795i	−0.0880417	−	0.152493i
$777$	13.6344	−	10.0381i	0.489130	−	0.360116i
$778$	−4.35765	+	7.54767i	−0.156229	+	0.270597i
$779$	−4.84391	−	2.79663i	−0.173551	−	0.100200i
$780$	−9.38062	−	5.88743i	−0.335880	−	0.210804i
$781$	1.02149	+	1.76927i	0.0365517	+	0.0633094i
$782$	−20.4469	−	35.4151i	−0.731180	−	1.26644i
$783$	−28.5461	+	35.7764i	−1.02015	+	1.27855i
$784$	−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	0.856514	−	0.516123i	$-0.172625\pi$
$787$	23.5031	+	13.5695i	0.837796	+	0.483701i	−0.0187187	+	0.999825i	$0.505959\pi$
$788$	−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	−0.996824	−	0.0796404i	$-0.974623\pi$
$797$	−16.0179	−	27.7438i	−0.567382	−	0.982735i	0.429441	−	0.903095i	$-0.358711\pi$
$798$	−2.97333	+	2.18908i	−0.105255	+	0.0774925i
$799$	−31.4319	−	54.4417i	−1.11198	−	1.92601i
$800$			1.85493i			0.0655816i
$801$	−19.1376	−	42.4330i	−0.676192	−	1.49930i
$802$	−3.57160	+	6.18619i	−0.126117	+	0.218442i
$803$	−3.89556	−	6.74730i	−0.137471	−	0.238107i
$804$	−11.6208	−	7.50692i	−0.409832	−	0.264749i
$805$	4.10127	+	25.2547i	0.144551	+	0.890113i
$806$	34.1570	−	0.446605i	1.20313	−	0.0157310i
$807$	5.72055	+	3.69543i	0.201373	+	0.130085i
$808$			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	$-0.867588\pi$
$811$		−	23.0154i		−	0.808181i	0.914719	−	0.404090i	$-0.132412\pi$
$812$	−18.0536	+	14.7368i	−0.633557	+	0.517160i
$813$	0.693024	+	1.35208i	0.0243054	+	0.0474197i
$814$	−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
$819$	−16.1060	−	23.6558i	−0.562789	−	0.826601i
$820$	12.3112			0.429924
$821$	−3.37615	+	1.94922i	−0.117828	+	0.0680282i	−0.557756	−	0.830005i	$-0.688337\pi$
$821$	−3.37615	+	1.94922i	−0.117828	+	0.0680282i	0.439928	+	0.898033i	$0.355004\pi$
$822$	−0.0349738	+	0.699536i	−0.00121985	+	0.0243991i
$823$	2.19747	−	3.80613i	0.0765989	−	0.132673i	−0.825182	−	0.564868i	$-0.808927\pi$
$823$	2.19747	−	3.80613i	0.0765989	−	0.132673i	0.901780	+	0.432194i	$0.142261\pi$
$824$	−4.30881	+	7.46308i	−0.150104	+	0.259989i
$825$	−1.30973	−	2.55527i	−0.0455988	−	0.0889629i
$826$	−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	$-0.965702\pi$
$829$		−	6.19286i		−	0.215087i	0.994200	−	0.107543i	$-0.0342985\pi$
$830$		−	24.5336i		−	0.851575i
$831$	18.3418	+	11.8486i	0.636269	+	0.411025i
$832$	−1.84344	−	3.09866i	−0.0639100	−	0.107427i
$833$	−10.5125	+	51.4324i	−0.364237	+	1.78203i
$834$	−6.57187	−	4.24538i	−0.227565	−	0.147006i
$835$	5.18290	+	8.97705i	0.179362	+	0.310664i
$836$	0.360042	−	0.623611i	0.0124523	−	0.0215680i
$837$	17.9736	+	45.8313i	0.621258	+	1.58416i
$838$		−	21.2134i		−	0.732805i
$839$	27.1029	+	46.9435i	0.935695	+	1.62067i	0.773390	+	0.633930i	$0.218559\pi$
$839$	27.1029	+	46.9435i	0.935695	+	1.62067i	0.162305	+	0.986741i	$0.448107\pi$
$840$	3.25855	−	7.44502i	0.112431	−	0.256878i
$841$	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	$0.0859301\pi$
$853$			15.5780i			0.533381i	−0.963782	+	0.266690i	$0.914070\pi$
$854$	13.7373	+	16.8292i	0.470082	+	0.575884i
$855$	−3.48006	−	2.50291i	−0.119015	−	0.0855979i
$856$	8.16443	+	14.1412i	0.279054	+	0.483336i
$857$	−14.2172	−	24.6250i	−0.485652	−	0.841173i	0.514213	−	0.857663i	$-0.328084\pi$
$857$	−14.2172	−	24.6250i	−0.485652	−	0.841173i	−0.999864	+	0.0164897i	$0.994751\pi$
$858$	4.72735	+	2.96696i	0.161389	+	0.101290i
$859$	−23.4649	−	13.5474i	−0.800610	−	0.462233i	0.0430741	−	0.999072i	$-0.486285\pi$
$859$	−23.4649	−	13.5474i	−0.800610	−	0.462233i	−0.843685	+	0.536839i	$0.819618\pi$
$860$	−3.43840	+	5.95548i	−0.117248	+	0.203080i
$861$	29.1430	+	12.7553i	0.993191	+	0.434701i
$862$	7.26815	+	12.5888i	0.247554	+	0.428776i
$863$	11.4245	+	6.59595i	0.388895	+	0.224529i	0.681681	−	0.731649i	$-0.261249\pi$
$863$	11.4245	+	6.59595i	0.388895	+	0.224529i	−0.292786	+	0.956178i	$0.594582\pi$
$864$	3.24081	−	4.06166i	0.110255	−	0.138181i
$865$	−12.9347	+	22.4036i	−0.439795	+	0.761747i
$866$	−0.680025	+	1.17784i	−0.0231082	+	0.0400246i
$867$	60.4850	−	31.0022i	2.05418	−	1.05289i
$868$	4.01806	+	24.7424i	0.136382	+	0.839811i
$869$	−9.91281	−	5.72317i	−0.336269	−	0.194145i
$870$	−22.7267	−	14.6813i	−0.770508	−	0.497743i
$871$	−14.7243	−	24.7503i	−0.498915	−	0.838630i
$872$	1.11139	−	0.641659i	0.0376363	−	0.0217293i
$873$	13.4142	−	6.04988i	0.454001	−	0.204758i
$874$	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
$879$	19.5827	−	10.0373i	0.660507	−	0.338549i
$880$			1.58495i			0.0534288i
$881$	−10.4378	+	18.0787i	−0.351657	+	0.609088i	−0.986540	−	0.163520i	$-0.947715\pi$
$881$	−10.4378	+	18.0787i	−0.351657	+	0.609088i	0.634883	+	0.772609i	$0.281048\pi$
$882$	15.4273	−	14.2478i	0.519464	−	0.479747i
$883$	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
$885$	9.15455	−	4.69225i	0.307727	−	0.157728i
$886$	−36.2337			−1.21729
$887$	1.38815	+	2.40435i	0.0466095	+	0.0807300i	0.888389	−	0.459092i	$-0.151825\pi$
$887$	1.38815	+	2.40435i	0.0466095	+	0.0807300i	−0.841779	+	0.539822i	$0.818492\pi$
$888$	2.91894	+	5.69484i	0.0979533	+	0.191106i
$889$	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
$894$	4.23336	−	2.16985i	0.141585	−	0.0725706i
$895$	14.8701	+	8.58523i	0.497051	+	0.286973i
$896$	2.04961	−	1.67305i	0.0684726	−	0.0558928i
$897$	−18.1026	+	28.8435i	−0.604429	+	0.963055i
$898$	−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
$903$	−14.3098	+	10.5354i	−0.476199	+	0.350596i
$904$	0.158407	+	0.274369i	0.00526855	+	0.00912539i
$905$	24.8649	+	14.3557i	0.826537	+	0.477201i
$906$	13.3823	−	20.7158i	0.444597	−	0.688238i
$907$	−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	$-0.0665451\pi$
$912$	−0.636552	−	1.24191i	−0.0210783	−	0.0411237i
$913$			12.3637i			0.409178i
$914$	−9.43666	−	5.44826i	−0.312137	−	0.180212i
$915$	−13.6856	+	21.1854i	−0.452433	+	0.700368i
$916$	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
$924$	−1.64214	+	3.75191i	−0.0540224	+	0.123429i
$925$	3.42666	−	5.93515i	0.112668	−	0.195146i
$926$	8.64969	−	4.99390i	0.284247	−	0.164110i
$927$	−20.9883	−	15.0951i	−0.689345	−	0.495789i
$928$	−4.40416	−	7.62822i	−0.144574	−	0.250409i
$929$	43.9601			1.44229			0.721143	−	0.692786i	$-0.243617\pi$
$929$	43.9601			1.44229			0.721143	+	0.692786i	$0.243617\pi$
$930$	−25.8981	+	13.2743i	−0.849232	+	0.435282i
$931$	−1.78476	−	5.35017i	−0.0584931	−	0.175345i
$932$	−5.66985	+	3.27349i	−0.185722	+	0.107227i
$933$	−28.0001	+	14.3517i	−0.916681	+	0.469854i
$934$			20.8848i			0.683372i
$935$	10.2938	−	5.94310i	0.336642	−	0.194360i
$936$	9.80124	−	4.57556i	0.320364	−	0.149557i
$937$		−	32.4932i		−	1.06151i	−0.847527	−	0.530753i	$-0.821909\pi$
$937$		−	32.4932i		−	1.06151i	0.847527	−	0.530753i	$-0.178091\pi$
$938$	16.3710	−	13.3633i	0.534533	−	0.436329i
$939$	−3.02504	+	4.68279i	−0.0987186	+	0.152817i
$940$	−14.8659			−0.484871
$941$	−26.4431	−	45.8008i	−0.862021	−	1.49306i	−0.869975	−	0.493095i	$-0.835865\pi$
$941$	−26.4431	−	45.8008i	−0.862021	−	1.49306i	0.00795494	−	0.999968i	$-0.497468\pi$
$942$	−31.9656	−	20.6496i	−1.04150	−	0.672799i
$943$		−	37.8542i		−	1.23270i
$944$	3.34899			0.109000
$945$	21.2487	+	11.9546i	0.691219	+	0.388884i
$946$	1.73278	−	3.00126i	0.0563374	−	0.0975793i
$947$	−5.56032	+	3.21025i	−0.180686	+	0.104319i	−0.587615	−	0.809141i	$-0.699933\pi$
$947$	−5.56032	+	3.21025i	−0.180686	+	0.104319i	0.406929	+	0.913460i	$0.366600\pi$
$948$	−19.7412	+	10.1185i	−0.641163	+	0.328634i
$949$	−27.4239	−	15.3587i	−0.890218	−	0.498564i
$950$	−0.747272	+	1.29431i	−0.0242447	+	0.0419931i
$951$	−1.02856	+	1.59222i	−0.0333534	+	0.0516312i
$952$	−18.5513	−	7.03808i	−0.601253	−	0.228105i
$953$	30.0111	−	17.3269i	0.972155	−	0.561274i	0.0722625	−	0.997386i	$-0.476978\pi$
$953$	30.0111	−	17.3269i	0.972155	−	0.561274i	0.899893	+	0.436112i	$0.143645\pi$
$954$	5.51006	−	7.66120i	0.178395	−	0.248041i
$955$	−24.2582	−	14.0055i	−0.784975	−	0.453206i
$956$	−2.38241	−	1.37549i	−0.0770528	−	0.0444864i
$957$	11.4531	+	7.39862i	0.370226	+	0.239163i
$958$	10.2715	−	5.93024i	0.331857	−	0.191597i
$959$	−1.00032	−	0.379506i	−0.0323021	−	0.0122549i
$960$	2.58014	+	1.66675i	0.0832738	+	0.0537943i
$961$	29.3808	−	50.8890i	0.947766	−	1.64158i
$962$	0.174162	+	13.3201i	0.00561520	+	0.429458i
$963$	−44.6551	+	20.1397i	−1.43899	+	0.648994i
$964$	5.30840	−	3.06480i	0.170972	−	0.0987107i
$965$	1.41820	−	2.45639i	0.0456534	−	0.0790739i
$966$	−22.8919	−	10.0194i	−0.736535	−	0.322367i
$967$	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
$969$	−5.67890	+	8.79097i	−0.182433	+	0.282407i
$970$	4.34945	+	7.53347i	0.139652	+	0.241885i
$971$	−30.8875			−0.991228			−0.495614	−	0.868543i	$-0.665057\pi$
$971$	−30.8875			−0.991228			−0.495614	+	0.868543i	$0.665057\pi$
$972$	11.1545	+	10.8893i	0.357781	+	0.349275i
$973$	9.25830	−	7.55736i	0.296807	−	0.242278i
$974$			18.9879i			0.608410i
$975$	−9.81168	−	6.15797i	−0.314225	−	0.197213i
$976$	−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	$-0.350801\pi$
$978$	−4.33985	−	8.46701i	−0.138773	−	0.270745i
$979$	−12.0094	+	6.93362i	−0.383822	+	0.221599i
$980$	9.29012	+	8.23421i	0.296762	+	0.263032i
$981$	1.58282	+	3.50954i	0.0505357	+	0.112051i
$982$	−26.0190			−0.830300
$983$	−4.09336	−	7.08990i	−0.130558	−	0.226133i	0.793334	−	0.608787i	$-0.208343\pi$
$983$	−4.09336	−	7.08990i	−0.130558	−	0.226133i	−0.923892	+	0.382654i	$0.875010\pi$
$984$	−6.52439	+	10.0998i	−0.207990	+	0.321969i
$985$	6.80772	−	3.93044i	0.216912	−	0.125234i
$986$	−33.0285	+	57.2071i	−1.05184	+	1.82185i
$987$	−35.1905	−	15.4022i	−1.12013	−	0.490258i
$988$	−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
$996$	20.1268	+	13.0018i	0.637743	+	0.411977i
$997$	−28.4330	−	16.4158i	−0.900483	−	0.519894i	−0.0231262	−	0.999733i	$-0.507362\pi$
$997$	−28.4330	−	16.4158i	−0.900483	−	0.519894i	−0.877357	+	0.479838i	$0.840695\pi$
$998$		−	10.8488i		−	0.343412i
$999$	−17.8727	+	7.00912i	−0.565468	+	0.221759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.425.10	yes	76
3.2	odd	2	inner	546.2.u.a.425.29	yes	76
7.3	odd	6		546.2.bb.a.269.3	yes	76
13.3	even	3		546.2.bb.a.341.4	yes	76
21.17	even	6		546.2.bb.a.269.23	yes	76
39.29	odd	6		546.2.bb.a.341.22	yes	76
91.3	odd	6	inner	546.2.u.a.185.29	yes	76
273.185	even	6	inner	546.2.u.a.185.10	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.10	✓	76	273.185	even	6	inner
546.2.u.a.185.29	yes	76	91.3	odd	6	inner
546.2.u.a.425.10	yes	76	1.1	even	1	trivial
546.2.u.a.425.29	yes	76	3.2	odd	2	inner
546.2.bb.a.269.3	yes	76	7.3	odd	6
546.2.bb.a.269.23	yes	76	21.17	even	6
546.2.bb.a.341.4	yes	76	13.3	even	3
546.2.bb.a.341.22	yes	76	39.29	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.0864870 + 1.72989i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.886718 + 1.53584i) q^{5} +(-0.790045 - 1.54137i) q^{6} +(2.61154 - 0.424103i) q^{7} +1.00000i q^{8} +(-2.98504 - 0.299226i) q^{9} +O(q^{10})\)	\(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} +(-0.790045 - 1.54137i) 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} +(1.45489 + 0.939845i) q^{12} +(1.84344 + 3.09866i) q^{13} +(-2.04961 + 1.67305i) q^{14} +(-2.58014 - 1.66675i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.74970 + 6.49467i) q^{17} +(2.73473 - 1.23338i) q^{18} -0.805715i q^{19} +(0.886718 + 1.53584i) q^{20} +(0.507788 + 4.55436i) 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} +(-1.75166 + 2.43551i) q^{36} +(-1.84733 - 3.19966i) q^{37} +(0.402858 + 0.697770i) q^{38} +(-5.51978 + 2.92096i) q^{39} +(-1.53584 - 0.886718i) q^{40} +(3.47099 - 6.01193i) q^{41} +(-2.71693 - 3.69029i) q^{42} +(1.93884 + 3.35816i) q^{43} +(0.773984 + 0.446860i) q^{44} +(3.10645 - 4.31921i) q^{45} +(-2.72647 + 4.72239i) q^{46} +(-4.19126 + 7.25948i) q^{47} +(1.54137 - 0.790045i) q^{48} +(6.64027 - 2.21512i) q^{49} +(-1.60641 - 0.927464i) q^{50} +(-10.9108 - 7.04827i) q^{51} +(3.60524 - 0.0471388i) q^{52} +(2.72420 - 1.57281i) q^{53} +(1.89710 + 4.83746i) 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} +(-2.73352 + 1.40109i) q^{60} -8.21094i q^{61} +(4.73713 - 8.20495i) q^{62} +(-7.92245 + 0.484525i) q^{63} -1.00000 q^{64} +(-6.39366 + 0.0835977i) q^{65} +(1.37756 - 0.706079i) q^{66} -7.98740 q^{67} +(3.74970 + 6.49467i) q^{68} +(4.30807 + 8.40502i) 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} +(-2.85914 + 1.46548i) q^{75} +(-0.697770 - 0.402858i) q^{76} +(0.379030 + 2.33398i) q^{77} +(3.31979 - 5.28952i) 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} +(4.19808 + 1.83742i) q^{84} +(-6.64985 - 11.5179i) q^{85} +(-3.35816 - 1.93884i) q^{86} +(8.27845 - 12.8151i) 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} +(-7.48509 - 14.6034i) q^{93} -8.38252i q^{94} +(1.23745 + 0.714442i) q^{95} +(-0.939845 + 1.45489i) 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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