LMFDB - Embedded newform 186.2.f.a.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [186,2,Mod(97,186)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("186.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(186, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			109.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	186.109
Dual form			186.2.f.a.157.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -0.618034 q^{5} -1.00000 q^{6} +(1.19098 - 3.66547i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.500000 + 0.363271i) q^{10} +(0.427051 - 1.31433i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-0.618034 - 0.449028i) q^{13} +(-1.19098 - 3.66547i) q^{14} +(0.500000 + 0.363271i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.23607 + 3.80423i) q^{17} +(0.809017 + 0.587785i) q^{18} +(2.00000 - 1.45309i) q^{19} +(-0.190983 + 0.587785i) q^{20} +(-3.11803 + 2.26538i) q^{21} +(-0.427051 - 1.31433i) q^{22} +(2.61803 + 8.05748i) q^{23} +(-0.309017 + 0.951057i) q^{24} -4.61803 q^{25} -0.763932 q^{26} +(0.309017 - 0.951057i) q^{27} +(-3.11803 - 2.26538i) q^{28} +(1.30902 - 0.951057i) q^{29} +0.618034 q^{30} +(3.30902 + 4.47777i) q^{31} -1.00000 q^{32} +(-1.11803 + 0.812299i) q^{33} +(3.23607 + 2.35114i) q^{34} +(-0.736068 + 2.26538i) q^{35} +1.00000 q^{36} +6.76393 q^{37} +(0.763932 - 2.35114i) q^{38} +(0.236068 + 0.726543i) q^{39} +(0.190983 + 0.587785i) q^{40} +(-6.47214 + 4.70228i) q^{41} +(-1.19098 + 3.66547i) q^{42} +(5.85410 - 4.25325i) q^{43} +(-1.11803 - 0.812299i) q^{44} +(-0.190983 - 0.587785i) q^{45} +(6.85410 + 4.97980i) q^{46} +(1.23607 + 0.898056i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-6.35410 - 4.61653i) q^{49} +(-3.73607 + 2.71441i) q^{50} +(1.23607 - 3.80423i) q^{51} +(-0.618034 + 0.449028i) q^{52} +(0.736068 + 2.26538i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.263932 + 0.812299i) q^{55} -3.85410 q^{56} -2.47214 q^{57} +(0.500000 - 1.53884i) q^{58} +(-6.54508 - 4.75528i) q^{59} +(0.500000 - 0.363271i) q^{60} -11.2361 q^{61} +(5.30902 + 1.67760i) q^{62} +3.85410 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.381966 + 0.277515i) q^{65} +(-0.427051 + 1.31433i) q^{66} +10.9443 q^{67} +4.00000 q^{68} +(2.61803 - 8.05748i) q^{69} +(0.736068 + 2.26538i) q^{70} +(-0.618034 - 1.90211i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-0.736068 + 2.26538i) q^{73} +(5.47214 - 3.97574i) q^{74} +(3.73607 + 2.71441i) q^{75} +(-0.763932 - 2.35114i) q^{76} +(-4.30902 - 3.13068i) q^{77} +(0.618034 + 0.449028i) q^{78} +(-3.50000 - 10.7719i) q^{79} +(0.500000 + 0.363271i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.47214 + 7.60845i) q^{82} +(-5.23607 + 3.80423i) q^{83} +(1.19098 + 3.66547i) q^{84} +(-0.763932 - 2.35114i) q^{85} +(2.23607 - 6.88191i) q^{86} -1.61803 q^{87} -1.38197 q^{88} +(0.909830 - 2.80017i) q^{89} +(-0.500000 - 0.363271i) q^{90} +(-2.38197 + 1.73060i) q^{91} +8.47214 q^{92} +(-0.0450850 - 5.56758i) q^{93} +1.52786 q^{94} +(-1.23607 + 0.898056i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-2.14590 + 6.60440i) q^{97} -7.85410 q^{98} +1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + 2 q^{5} - 4 q^{6} + 7 q^{7} + q^{8} - q^{9} - 2 q^{10} - 5 q^{11} - q^{12} + 2 q^{13} - 7 q^{14} + 2 q^{15} - q^{16} - 4 q^{17} + q^{18} + 8 q^{19} - 3 q^{20} - 8 q^{21}+ \cdots + 10 q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + 2 * q^5 - 4 * q^6 + 7 * q^7 + q^8 - q^9 - 2 * q^10 - 5 * q^11 - q^12 + 2 * q^13 - 7 * q^14 + 2 * q^15 - q^16 - 4 * q^17 + q^18 + 8 * q^19 - 3 * q^20 - 8 * q^21 + 5 * q^22 + 6 * q^23 + q^24 - 14 * q^25 - 12 * q^26 - q^27 - 8 * q^28 + 3 * q^29 - 2 * q^30 + 11 * q^31 - 4 * q^32 + 4 * q^34 + 6 * q^35 + 4 * q^36 + 36 * q^37 + 12 * q^38 - 8 * q^39 + 3 * q^40 - 8 * q^41 - 7 * q^42 + 10 * q^43 - 3 * q^45 + 14 * q^46 - 4 * q^47 - q^48 - 12 * q^49 - 6 * q^50 - 4 * q^51 + 2 * q^52 - 6 * q^53 + q^54 - 10 * q^55 - 2 * q^56 + 8 * q^57 + 2 * q^58 - 15 * q^59 + 2 * q^60 - 36 * q^61 + 19 * q^62 + 2 * q^63 - q^64 + 6 * q^65 + 5 * q^66 + 8 * q^67 + 16 * q^68 + 6 * q^69 - 6 * q^70 + 2 * q^71 + q^72 + 6 * q^73 + 4 * q^74 + 6 * q^75 - 12 * q^76 - 15 * q^77 - 2 * q^78 - 14 * q^79 + 2 * q^80 - q^81 + 8 * q^82 - 12 * q^83 + 7 * q^84 - 12 * q^85 - 2 * q^87 - 10 * q^88 + 26 * q^89 - 2 * q^90 - 14 * q^91 + 16 * q^92 + 11 * q^93 + 24 * q^94 + 4 * q^95 + q^96 - 22 * q^97 - 18 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.618034			−0.276393			−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034			−0.276393			−0.138197	+	0.990405i	$0.544131\pi$
$6$	−1.00000			−0.408248
$7$	1.19098	−	3.66547i	0.450149	−	1.38542i	−0.426587	−	0.904446i	$-0.640284\pi$
$7$	1.19098	−	3.66547i	0.450149	−	1.38542i	0.876737	−	0.480971i	$-0.159716\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−0.500000	+	0.363271i	−0.158114	+	0.114876i
$11$	0.427051	−	1.31433i	0.128761	−	0.396285i	−0.865807	−	0.500378i	$-0.833194\pi$
$11$	0.427051	−	1.31433i	0.128761	−	0.396285i	0.994567	+	0.104094i	$0.0331942\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	−0.618034	−	0.449028i	−0.171412	−	0.124538i	0.498772	−	0.866733i	$-0.333785\pi$
$13$	−0.618034	−	0.449028i	−0.171412	−	0.124538i	−0.670184	+	0.742195i	$0.733785\pi$
$14$	−1.19098	−	3.66547i	−0.318304	−	0.979638i
$15$	0.500000	+	0.363271i	0.129099	+	0.0937962i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.23607	+	3.80423i	0.299791	+	0.922660i	0.981570	+	0.191103i	$0.0612063\pi$
$17$	1.23607	+	3.80423i	0.299791	+	0.922660i	−0.681780	+	0.731558i	$0.738794\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	2.00000	−	1.45309i	0.458831	−	0.333361i	−0.334241	−	0.942488i	$-0.608480\pi$
$19$	2.00000	−	1.45309i	0.458831	−	0.333361i	0.793073	+	0.609127i	$0.208480\pi$
$20$	−0.190983	+	0.587785i	−0.0427051	+	0.131433i
$21$	−3.11803	+	2.26538i	−0.680411	+	0.494347i
$22$	−0.427051	−	1.31433i	−0.0910476	−	0.280216i
$23$	2.61803	+	8.05748i	0.545898	+	1.68010i	0.718846	+	0.695170i	$0.244671\pi$
$23$	2.61803	+	8.05748i	0.545898	+	1.68010i	−0.172948	+	0.984931i	$0.555329\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−4.61803			−0.923607
$26$	−0.763932			−0.149819
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−3.11803	−	2.26538i	−0.589253	−	0.428117i
$29$	1.30902	−	0.951057i	0.243078	−	0.176607i	−0.459575	−	0.888139i	$-0.651998\pi$
$29$	1.30902	−	0.951057i	0.243078	−	0.176607i	0.702654	+	0.711532i	$0.251998\pi$
$30$	0.618034			0.112837
$31$	3.30902	+	4.47777i	0.594317	+	0.804231i
$31$	3.30902	+	4.47777i	0.594317	+	0.804231i
$32$	−1.00000			−0.176777
$33$	−1.11803	+	0.812299i	−0.194625	+	0.141403i
$34$	3.23607	+	2.35114i	0.554981	+	0.403217i
$35$	−0.736068	+	2.26538i	−0.124418	+	0.382920i
$36$	1.00000			0.166667
$37$	6.76393			1.11198			0.555992	−	0.831188i	$-0.312339\pi$
$37$	6.76393			1.11198			0.555992	+	0.831188i	$0.312339\pi$
$38$	0.763932	−	2.35114i	0.123926	−	0.381405i
$39$	0.236068	+	0.726543i	0.0378011	+	0.116340i
$40$	0.190983	+	0.587785i	0.0301971	+	0.0929370i
$41$	−6.47214	+	4.70228i	−1.01078	+	0.734373i	−0.964372	−	0.264550i	$-0.914777\pi$
$41$	−6.47214	+	4.70228i	−1.01078	+	0.734373i	−0.0464057	+	0.998923i	$0.514777\pi$
$42$	−1.19098	+	3.66547i	−0.183773	+	0.565594i
$43$	5.85410	−	4.25325i	0.892742	−	0.648615i	−0.0438494	−	0.999038i	$-0.513962\pi$
$43$	5.85410	−	4.25325i	0.892742	−	0.648615i	0.936592	+	0.350423i	$0.113962\pi$
$44$	−1.11803	−	0.812299i	−0.168550	−	0.122459i
$45$	−0.190983	−	0.587785i	−0.0284701	−	0.0876219i
$46$	6.85410	+	4.97980i	1.01058	+	0.734231i
$47$	1.23607	+	0.898056i	0.180299	+	0.130995i	0.674274	−	0.738481i	$-0.264457\pi$
$47$	1.23607	+	0.898056i	0.180299	+	0.130995i	−0.493975	+	0.869476i	$0.664457\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−6.35410	−	4.61653i	−0.907729	−	0.659504i
$50$	−3.73607	+	2.71441i	−0.528360	+	0.383876i
$51$	1.23607	−	3.80423i	0.173084	−	0.532698i
$52$	−0.618034	+	0.449028i	−0.0857059	+	0.0622690i
$53$	0.736068	+	2.26538i	0.101107	+	0.311174i	0.988797	−	0.149267i	$-0.0476913\pi$
$53$	0.736068	+	2.26538i	0.101107	+	0.311174i	−0.887690	+	0.460441i	$0.847691\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−0.263932	+	0.812299i	−0.0355886	+	0.109530i
$56$	−3.85410			−0.515026
$57$	−2.47214			−0.327442
$58$	0.500000	−	1.53884i	0.0656532	−	0.202060i
$59$	−6.54508	−	4.75528i	−0.852097	−	0.619085i	0.0736261	−	0.997286i	$-0.476543\pi$
$59$	−6.54508	−	4.75528i	−0.852097	−	0.619085i	−0.925724	+	0.378201i	$0.876543\pi$
$60$	0.500000	−	0.363271i	0.0645497	−	0.0468981i
$61$	−11.2361			−1.43863			−0.719316	−	0.694683i	$-0.755544\pi$
$61$	−11.2361			−1.43863			−0.719316	+	0.694683i	$0.755544\pi$
$62$	5.30902	+	1.67760i	0.674246	+	0.213055i
$63$	3.85410			0.485571
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.381966	+	0.277515i	0.0473771	+	0.0344214i
$66$	−0.427051	+	1.31433i	−0.0525663	+	0.161783i
$67$	10.9443			1.33706			0.668528	−	0.743687i	$-0.266925\pi$
$67$	10.9443			1.33706			0.668528	+	0.743687i	$0.266925\pi$
$68$	4.00000			0.485071
$69$	2.61803	−	8.05748i	0.315174	−	0.970007i
$70$	0.736068	+	2.26538i	0.0879770	+	0.270765i
$71$	−0.618034	−	1.90211i	−0.0733471	−	0.225739i	0.907662	−	0.419703i	$-0.137866\pi$
$71$	−0.618034	−	1.90211i	−0.0733471	−	0.225739i	−0.981009	+	0.193963i	$0.937866\pi$
$72$	0.809017	−	0.587785i	0.0953436	−	0.0692712i
$73$	−0.736068	+	2.26538i	−0.0861502	+	0.265143i	−0.984846	−	0.173428i	$-0.944515\pi$
$73$	−0.736068	+	2.26538i	−0.0861502	+	0.265143i	0.898696	+	0.438572i	$0.144515\pi$
$74$	5.47214	−	3.97574i	0.636123	−	0.462170i
$75$	3.73607	+	2.71441i	0.431404	+	0.313433i
$76$	−0.763932	−	2.35114i	−0.0876290	−	0.269694i
$77$	−4.30902	−	3.13068i	−0.491058	−	0.356775i
$78$	0.618034	+	0.449028i	0.0699786	+	0.0508424i
$79$	−3.50000	−	10.7719i	−0.393781	−	1.21193i	−0.929907	−	0.367795i	$-0.880113\pi$
$79$	−3.50000	−	10.7719i	−0.393781	−	1.21193i	0.536126	−	0.844138i	$-0.319887\pi$
$80$	0.500000	+	0.363271i	0.0559017	+	0.0406150i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.47214	+	7.60845i	−0.273002	+	0.840213i
$83$	−5.23607	+	3.80423i	−0.574733	+	0.417568i	−0.836822	−	0.547476i	$-0.815589\pi$
$83$	−5.23607	+	3.80423i	−0.574733	+	0.417568i	0.262088	+	0.965044i	$0.415589\pi$
$84$	1.19098	+	3.66547i	0.129947	+	0.399935i
$85$	−0.763932	−	2.35114i	−0.0828601	−	0.255017i
$86$	2.23607	−	6.88191i	0.241121	−	0.742095i
$87$	−1.61803			−0.173471
$88$	−1.38197			−0.147318
$89$	0.909830	−	2.80017i	0.0964418	−	0.296817i	−0.891185	−	0.453640i	$-0.850125\pi$
$89$	0.909830	−	2.80017i	0.0964418	−	0.296817i	0.987627	+	0.156823i	$0.0501252\pi$
$90$	−0.500000	−	0.363271i	−0.0527046	−	0.0382922i
$91$	−2.38197	+	1.73060i	−0.249698	+	0.181416i
$92$	8.47214			0.883281
$93$	−0.0450850	−	5.56758i	−0.00467509	−	0.577331i
$94$	1.52786			0.157587
$95$	−1.23607	+	0.898056i	−0.126818	+	0.0921386i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−2.14590	+	6.60440i	−0.217883	+	0.670575i	0.781053	+	0.624464i	$0.214683\pi$
$97$	−2.14590	+	6.60440i	−0.217883	+	0.670575i	−0.998936	+	0.0461105i	$0.985317\pi$
$98$	−7.85410			−0.793384
$99$	1.38197			0.138893
$100$	−1.42705	+	4.39201i	−0.142705	+	0.439201i
$101$	3.13525	+	9.64932i	0.311970	+	0.960143i	0.976984	+	0.213313i	$0.0684254\pi$
$101$	3.13525	+	9.64932i	0.311970	+	0.960143i	−0.665014	+	0.746831i	$0.731575\pi$
$102$	−1.23607	−	3.80423i	−0.122389	−	0.376675i
$103$	−7.23607	+	5.25731i	−0.712991	+	0.518018i	−0.884137	−	0.467227i	$-0.845253\pi$
$103$	−7.23607	+	5.25731i	−0.712991	+	0.518018i	0.171146	+	0.985246i	$0.445253\pi$
$104$	−0.236068	+	0.726543i	−0.0231484	+	0.0712434i
$105$	1.92705	−	1.40008i	0.188061	−	0.136634i
$106$	1.92705	+	1.40008i	0.187172	+	0.135988i
$107$	−6.04508	−	18.6049i	−0.584400	−	1.79860i	−0.601665	−	0.798749i	$-0.705496\pi$
$107$	−6.04508	−	18.6049i	−0.584400	−	1.79860i	0.0172645	−	0.999851i	$-0.494504\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−3.23607	−	2.35114i	−0.309959	−	0.225198i	0.421920	−	0.906633i	$-0.361356\pi$
$109$	−3.23607	−	2.35114i	−0.309959	−	0.225198i	−0.731879	+	0.681435i	$0.761356\pi$
$110$	0.263932	+	0.812299i	0.0251649	+	0.0774497i
$111$	−5.47214	−	3.97574i	−0.519392	−	0.377360i
$112$	−3.11803	+	2.26538i	−0.294627	+	0.214059i
$113$	3.76393	−	11.5842i	0.354081	−	1.08975i	−0.602460	−	0.798149i	$-0.705813\pi$
$113$	3.76393	−	11.5842i	0.354081	−	1.08975i	0.956540	−	0.291600i	$-0.0941875\pi$
$114$	−2.00000	+	1.45309i	−0.187317	+	0.136094i
$115$	−1.61803	−	4.97980i	−0.150882	−	0.464368i
$116$	−0.500000	−	1.53884i	−0.0464238	−	0.142878i
$117$	0.236068	−	0.726543i	0.0218245	−	0.0671689i
$118$	−8.09017			−0.744761
$119$	15.4164			1.41322
$120$	0.190983	−	0.587785i	0.0174343	−	0.0536572i
$121$	7.35410	+	5.34307i	0.668555	+	0.485733i
$122$	−9.09017	+	6.60440i	−0.822985	+	0.597934i
$123$	8.00000			0.721336
$124$	5.28115	−	1.76336i	0.474262	−	0.158354i
$125$	5.94427			0.531672
$126$	3.11803	−	2.26538i	0.277777	−	0.201816i
$127$	6.39919	+	4.64928i	0.567836	+	0.412557i	0.834318	−	0.551283i	$-0.185861\pi$
$127$	6.39919	+	4.64928i	0.567836	+	0.412557i	−0.266482	+	0.963840i	$0.585861\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−7.23607			−0.637100
$130$	0.472136			0.0414091
$131$	5.26393	−	16.2007i	0.459912	−	1.41546i	−0.405359	−	0.914158i	$-0.632853\pi$
$131$	5.26393	−	16.2007i	0.459912	−	1.41546i	0.865270	−	0.501305i	$-0.167147\pi$
$132$	0.427051	+	1.31433i	0.0371700	+	0.114398i
$133$	−2.94427	−	9.06154i	−0.255301	−	0.785735i
$134$	8.85410	−	6.43288i	0.764878	−	0.555716i
$135$	−0.190983	+	0.587785i	−0.0164372	+	0.0505885i
$136$	3.23607	−	2.35114i	0.277491	−	0.201609i
$137$	13.7082	+	9.95959i	1.17117	+	0.850905i	0.991149	−	0.132757i	$-0.0423830\pi$
$137$	13.7082	+	9.95959i	1.17117	+	0.850905i	0.180022	+	0.983663i	$0.442383\pi$
$138$	−2.61803	−	8.05748i	−0.222862	−	0.685898i
$139$	−3.85410	−	2.80017i	−0.326901	−	0.237507i	0.412214	−	0.911087i	$-0.364756\pi$
$139$	−3.85410	−	2.80017i	−0.326901	−	0.237507i	−0.739114	+	0.673580i	$0.764756\pi$
$140$	1.92705	+	1.40008i	0.162866	+	0.118329i
$141$	−0.472136	−	1.45309i	−0.0397610	−	0.122372i
$142$	−1.61803	−	1.17557i	−0.135782	−	0.0986517i
$143$	−0.854102	+	0.620541i	−0.0714236	+	0.0518923i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−0.809017	+	0.587785i	−0.0671852	+	0.0488129i
$146$	0.736068	+	2.26538i	0.0609174	+	0.187485i
$147$	2.42705	+	7.46969i	0.200180	+	0.616090i
$148$	2.09017	−	6.43288i	0.171811	−	0.528780i
$149$	−15.3262			−1.25557			−0.627787	−	0.778385i	$-0.716039\pi$
$149$	−15.3262			−1.25557			−0.627787	+	0.778385i	$0.716039\pi$
$150$	4.61803			0.377061
$151$	−7.28115	+	22.4091i	−0.592532	+	1.82363i	−0.0258846	+	0.999665i	$0.508240\pi$
$151$	−7.28115	+	22.4091i	−0.592532	+	1.82363i	−0.566647	+	0.823961i	$0.691760\pi$
$152$	−2.00000	−	1.45309i	−0.162221	−	0.117861i
$153$	−3.23607	+	2.35114i	−0.261621	+	0.190078i
$154$	−5.32624			−0.429200
$155$	−2.04508	−	2.76741i	−0.164265	−	0.222284i
$156$	0.763932			0.0611635
$157$	−18.7984	+	13.6578i	−1.50027	+	1.09001i	−0.530001	+	0.847997i	$0.677809\pi$
$157$	−18.7984	+	13.6578i	−1.50027	+	1.09001i	−0.970272	+	0.242016i	$0.922191\pi$
$158$	−9.16312	−	6.65740i	−0.728979	−	0.529634i
$159$	0.736068	−	2.26538i	0.0583740	−	0.179657i
$160$	0.618034			0.0488599
$161$	32.6525			2.57338
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	3.56231	+	10.9637i	0.279021	+	0.858739i	0.988127	+	0.153637i	$0.0490988\pi$
$163$	3.56231	+	10.9637i	0.279021	+	0.858739i	−0.709106	+	0.705102i	$0.750901\pi$
$164$	2.47214	+	7.60845i	0.193041	+	0.594120i
$165$	0.690983	−	0.502029i	0.0537930	−	0.0390829i
$166$	−2.00000	+	6.15537i	−0.155230	+	0.477749i
$167$	−16.1803	+	11.7557i	−1.25207	+	0.909684i	−0.998340	−	0.0575908i	$-0.981658\pi$
$167$	−16.1803	+	11.7557i	−1.25207	+	0.909684i	−0.253732	+	0.967275i	$0.581658\pi$
$168$	3.11803	+	2.26538i	0.240562	+	0.174778i
$169$	−3.83688	−	11.8087i	−0.295145	−	0.908362i
$170$	−2.00000	−	1.45309i	−0.153393	−	0.111447i
$171$	2.00000	+	1.45309i	0.152944	+	0.111120i
$172$	−2.23607	−	6.88191i	−0.170499	−	0.524741i
$173$	6.69098	+	4.86128i	0.508706	+	0.369597i	0.812332	−	0.583195i	$-0.198197\pi$
$173$	6.69098	+	4.86128i	0.508706	+	0.369597i	−0.303626	+	0.952791i	$0.598197\pi$
$174$	−1.30902	+	0.951057i	−0.0992363	+	0.0720994i
$175$	−5.50000	+	16.9273i	−0.415761	+	1.27958i
$176$	−1.11803	+	0.812299i	−0.0842750	+	0.0612294i
$177$	2.50000	+	7.69421i	0.187912	+	0.578332i
$178$	−0.909830	−	2.80017i	−0.0681946	−	0.209882i
$179$	−1.79180	+	5.51458i	−0.133925	+	0.412179i	−0.995421	−	0.0955849i	$-0.969528\pi$
$179$	−1.79180	+	5.51458i	−0.133925	+	0.412179i	0.861496	+	0.507764i	$0.169528\pi$
$180$	−0.618034			−0.0460655
$181$	6.94427			0.516164			0.258082	−	0.966123i	$-0.416910\pi$
$181$	6.94427			0.516164			0.258082	+	0.966123i	$0.416910\pi$
$182$	−0.909830	+	2.80017i	−0.0674411	+	0.207562i
$183$	9.09017	+	6.60440i	0.671965	+	0.488211i
$184$	6.85410	−	4.97980i	0.505291	−	0.367115i
$185$	−4.18034			−0.307345
$186$	−3.30902	−	4.47777i	−0.242629	−	0.328326i
$187$	5.52786			0.404237
$188$	1.23607	−	0.898056i	0.0901495	−	0.0654975i
$189$	−3.11803	−	2.26538i	−0.226804	−	0.164782i
$190$	−0.472136	+	1.45309i	−0.0342523	+	0.105418i
$191$	8.29180			0.599973			0.299987	−	0.953943i	$-0.403018\pi$
$191$	8.29180			0.599973			0.299987	+	0.953943i	$0.403018\pi$
$192$	1.00000			0.0721688
$193$	−2.44427	+	7.52270i	−0.175943	+	0.541495i	−0.999675	−	0.0254829i	$-0.991888\pi$
$193$	−2.44427	+	7.52270i	−0.175943	+	0.541495i	0.823733	+	0.566978i	$0.191888\pi$
$194$	2.14590	+	6.60440i	0.154067	+	0.474168i
$195$	−0.145898	−	0.449028i	−0.0104480	−	0.0321556i
$196$	−6.35410	+	4.61653i	−0.453864	+	0.329752i
$197$	−5.51722	+	16.9803i	−0.393086	+	1.20979i	0.537357	+	0.843355i	$0.319423\pi$
$197$	−5.51722	+	16.9803i	−0.393086	+	1.20979i	−0.930442	+	0.366438i	$0.880577\pi$
$198$	1.11803	−	0.812299i	0.0794552	−	0.0577276i
$199$	3.30902	+	2.40414i	0.234570	+	0.170425i	0.698861	−	0.715258i	$-0.253691\pi$
$199$	3.30902	+	2.40414i	0.234570	+	0.170425i	−0.464291	+	0.885683i	$0.653691\pi$
$200$	1.42705	+	4.39201i	0.100908	+	0.310562i
$201$	−8.85410	−	6.43288i	−0.624520	−	0.453740i
$202$	8.20820	+	5.96361i	0.577527	+	0.419598i
$203$	−1.92705	−	5.93085i	−0.135252	−	0.416264i
$204$	−3.23607	−	2.35114i	−0.226570	−	0.164613i
$205$	4.00000	−	2.90617i	0.279372	−	0.202976i
$206$	−2.76393	+	8.50651i	−0.192572	+	0.592677i
$207$	−6.85410	+	4.97980i	−0.476393	+	0.346120i
$208$	0.236068	+	0.726543i	0.0163684	+	0.0503767i
$209$	−1.05573	−	3.24920i	−0.0730262	−	0.224752i
$210$	0.736068	−	2.26538i	0.0507935	−	0.156326i
$211$	−11.7082			−0.806026			−0.403013	−	0.915194i	$-0.632037\pi$
$211$	−11.7082			−0.806026			−0.403013	+	0.915194i	$0.632037\pi$
$212$	2.38197			0.163594
$213$	−0.618034	+	1.90211i	−0.0423470	+	0.130331i
$214$	−15.8262	−	11.4984i	−1.08186	−	0.786017i
$215$	−3.61803	+	2.62866i	−0.246748	+	0.179273i
$216$	−1.00000			−0.0680414
$217$	20.3541	−	6.79615i	1.38173	−	0.461353i
$218$	−4.00000			−0.270914
$219$	1.92705	−	1.40008i	0.130218	−	0.0946089i
$220$	0.690983	+	0.502029i	0.0465861	+	0.0338468i
$221$	0.944272	−	2.90617i	0.0635186	−	0.195490i
$222$	−6.76393			−0.453965
$223$	28.2148			1.88940			0.944701	−	0.327934i	$-0.106352\pi$
$223$	28.2148			1.88940			0.944701	+	0.327934i	$0.106352\pi$
$224$	−1.19098	+	3.66547i	−0.0795759	+	0.244909i
$225$	−1.42705	−	4.39201i	−0.0951367	−	0.292801i
$226$	−3.76393	−	11.5842i	−0.250373	−	0.770569i
$227$	−9.11803	+	6.62464i	−0.605185	+	0.439693i	−0.847716	−	0.530451i	$-0.822023\pi$
$227$	−9.11803	+	6.62464i	−0.605185	+	0.439693i	0.242530	+	0.970144i	$0.422023\pi$
$228$	−0.763932	+	2.35114i	−0.0505926	+	0.155708i
$229$	12.4721	−	9.06154i	0.824182	−	0.598803i	−0.0937254	−	0.995598i	$-0.529878\pi$
$229$	12.4721	−	9.06154i	0.824182	−	0.598803i	0.917907	+	0.396795i	$0.129878\pi$
$230$	−4.23607	−	3.07768i	−0.279318	−	0.202936i
$231$	1.64590	+	5.06555i	0.108292	+	0.333289i
$232$	−1.30902	−	0.951057i	−0.0859412	−	0.0624399i
$233$	−18.0902	−	13.1433i	−1.18513	−	0.861045i	−0.192386	−	0.981319i	$-0.561622\pi$
$233$	−18.0902	−	13.1433i	−1.18513	−	0.861045i	−0.992741	+	0.120275i	$0.961622\pi$
$234$	−0.236068	−	0.726543i	−0.0154322	−	0.0474956i
$235$	−0.763932	−	0.555029i	−0.0498334	−	0.0362061i
$236$	−6.54508	+	4.75528i	−0.426049	+	0.309543i
$237$	−3.50000	+	10.7719i	−0.227349	+	0.699710i
$238$	12.4721	−	9.06154i	0.808448	−	0.587372i
$239$	−7.61803	−	23.4459i	−0.492770	−	1.51659i	−0.820404	−	0.571784i	$-0.806251\pi$
$239$	−7.61803	−	23.4459i	−0.492770	−	1.51659i	0.327634	−	0.944805i	$-0.393749\pi$
$240$	−0.190983	−	0.587785i	−0.0123279	−	0.0379414i
$241$	−5.80902	+	17.8783i	−0.374192	+	1.15164i	0.569831	+	0.821762i	$0.307009\pi$
$241$	−5.80902	+	17.8783i	−0.374192	+	1.15164i	−0.944022	+	0.329881i	$0.892991\pi$
$242$	9.09017			0.584338
$243$	1.00000			0.0641500
$244$	−3.47214	+	10.6861i	−0.222281	+	0.684110i
$245$	3.92705	+	2.85317i	0.250890	+	0.182282i
$246$	6.47214	−	4.70228i	0.412648	−	0.299807i
$247$	−1.88854			−0.120165
$248$	3.23607	−	4.53077i	0.205491	−	0.287704i
$249$	6.47214			0.410155
$250$	4.80902	−	3.49396i	0.304149	−	0.220977i
$251$	−17.2984	−	12.5680i	−1.09186	−	0.793285i	−0.112151	−	0.993691i	$-0.535774\pi$
$251$	−17.2984	−	12.5680i	−1.09186	−	0.793285i	−0.979713	+	0.200406i	$0.935774\pi$
$252$	1.19098	−	3.66547i	0.0750249	−	0.230903i
$253$	11.7082			0.736088
$254$	7.90983			0.496307
$255$	−0.763932	+	2.35114i	−0.0478393	+	0.147234i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	0.562306	+	1.73060i	0.0350757	+	0.107952i	0.967061	−	0.254543i	$-0.0819250\pi$
$257$	0.562306	+	1.73060i	0.0350757	+	0.107952i	−0.931986	+	0.362495i	$0.881925\pi$
$258$	−5.85410	+	4.25325i	−0.364460	+	0.264796i
$259$	8.05573	−	24.7930i	0.500559	−	1.54056i
$260$	0.381966	−	0.277515i	0.0236885	−	0.0172107i
$261$	1.30902	+	0.951057i	0.0810261	+	0.0588689i
$262$	−5.26393	−	16.2007i	−0.325207	−	1.00088i
$263$	−4.70820	−	3.42071i	−0.290320	−	0.210930i	0.433086	−	0.901353i	$-0.357425\pi$
$263$	−4.70820	−	3.42071i	−0.290320	−	0.210930i	−0.723406	+	0.690423i	$0.757425\pi$
$264$	1.11803	+	0.812299i	0.0688102	+	0.0499936i
$265$	−0.454915	−	1.40008i	−0.0279452	−	0.0860065i
$266$	−7.70820	−	5.60034i	−0.472620	−	0.343379i
$267$	−2.38197	+	1.73060i	−0.145774	+	0.105911i
$268$	3.38197	−	10.4086i	0.206586	−	0.635808i
$269$	5.20820	−	3.78398i	0.317550	−	0.230713i	−0.417579	−	0.908640i	$-0.637121\pi$
$269$	5.20820	−	3.78398i	0.317550	−	0.230713i	0.735129	+	0.677927i	$0.237121\pi$
$270$	0.190983	+	0.587785i	0.0116229	+	0.0357715i
$271$	−6.13525	−	18.8824i	−0.372690	−	1.14702i	−0.945024	−	0.327002i	$-0.893962\pi$
$271$	−6.13525	−	18.8824i	−0.372690	−	1.14702i	0.572334	−	0.820021i	$-0.306038\pi$
$272$	1.23607	−	3.80423i	0.0749476	−	0.230665i
$273$	2.94427			0.178195
$274$	16.9443			1.02364
$275$	−1.97214	+	6.06961i	−0.118924	+	0.366011i
$276$	−6.85410	−	4.97980i	−0.412568	−	0.299749i
$277$	−11.4721	+	8.33499i	−0.689294	+	0.500801i	−0.876428	−	0.481533i	$-0.840080\pi$
$277$	−11.4721	+	8.33499i	−0.689294	+	0.500801i	0.187134	+	0.982334i	$0.440080\pi$
$278$	−4.76393			−0.285722
$279$	−3.23607	+	4.53077i	−0.193738	+	0.271250i
$280$	2.38197			0.142350
$281$	14.4721	−	10.5146i	0.863335	−	0.627250i	−0.0654550	−	0.997856i	$-0.520850\pi$
$281$	14.4721	−	10.5146i	0.863335	−	0.627250i	0.928790	+	0.370606i	$0.120850\pi$
$282$	−1.23607	−	0.898056i	−0.0736068	−	0.0534785i
$283$	10.0000	−	30.7768i	0.594438	−	1.82949i	0.0369359	−	0.999318i	$-0.488240\pi$
$283$	10.0000	−	30.7768i	0.594438	−	1.82949i	0.557502	−	0.830175i	$-0.311760\pi$
$284$	−2.00000			−0.118678
$285$	1.52786			0.0905029
$286$	−0.326238	+	1.00406i	−0.0192909	+	0.0593711i
$287$	9.52786	+	29.3238i	0.562412	+	1.73093i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$	−0.309017	+	0.951057i	−0.0181461	+	0.0558480i
$291$	5.61803	−	4.08174i	0.329335	−	0.239276i
$292$	1.92705	+	1.40008i	0.112772	+	0.0819337i
$293$	−0.145898	−	0.449028i	−0.00852345	−	0.0262325i	0.946704	−	0.322104i	$-0.104390\pi$
$293$	−0.145898	−	0.449028i	−0.00852345	−	0.0262325i	−0.955228	+	0.295871i	$0.904390\pi$
$294$	6.35410	+	4.61653i	0.370579	+	0.269241i
$295$	4.04508	+	2.93893i	0.235514	+	0.171111i
$296$	−2.09017	−	6.43288i	−0.121489	−	0.373904i
$297$	−1.11803	−	0.812299i	−0.0648749	−	0.0471344i
$298$	−12.3992	+	9.00854i	−0.718266	+	0.521851i
$299$	2.00000	−	6.15537i	0.115663	−	0.355974i
$300$	3.73607	−	2.71441i	0.215702	−	0.156717i
$301$	−8.61803	−	26.5236i	−0.496735	−	1.52879i
$302$	7.28115	+	22.4091i	0.418983	+	1.28950i
$303$	3.13525	−	9.64932i	0.180116	−	0.554339i
$304$	−2.47214			−0.141787
$305$	6.94427			0.397628
$306$	−1.23607	+	3.80423i	−0.0706613	+	0.217473i
$307$	−0.381966	−	0.277515i	−0.0218000	−	0.0158386i	0.576832	−	0.816863i	$-0.304289\pi$
$307$	−0.381966	−	0.277515i	−0.0218000	−	0.0158386i	−0.598632	+	0.801024i	$0.704289\pi$
$308$	−4.30902	+	3.13068i	−0.245529	+	0.178387i
$309$	8.94427			0.508822
$310$	−3.28115	−	1.03681i	−0.186357	−	0.0588870i
$311$	−29.1246			−1.65151			−0.825753	−	0.564032i	$-0.809249\pi$
$311$	−29.1246			−1.65151			−0.825753	+	0.564032i	$0.809249\pi$
$312$	0.618034	−	0.449028i	0.0349893	−	0.0254212i
$313$	−4.38197	−	3.18368i	−0.247683	−	0.179952i	0.457016	−	0.889458i	$-0.348918\pi$
$313$	−4.38197	−	3.18368i	−0.247683	−	0.179952i	−0.704699	+	0.709506i	$0.748918\pi$
$314$	−7.18034	+	22.0988i	−0.405210	+	1.24711i
$315$	−2.38197			−0.134209
$316$	−11.3262			−0.637151
$317$	7.56231	−	23.2744i	0.424741	−	1.30722i	−0.478500	−	0.878087i	$-0.658819\pi$
$317$	7.56231	−	23.2744i	0.424741	−	1.30722i	0.903242	−	0.429132i	$-0.141181\pi$
$318$	−0.736068	−	2.26538i	−0.0412766	−	0.127036i
$319$	−0.690983	−	2.12663i	−0.0386876	−	0.119068i
$320$	0.500000	−	0.363271i	0.0279508	−	0.0203075i
$321$	−6.04508	+	18.6049i	−0.337404	+	1.03842i
$322$	26.4164	−	19.1926i	1.47213	−	1.06956i
$323$	8.00000	+	5.81234i	0.445132	+	0.323407i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	2.85410	+	2.07363i	0.158317	+	0.115024i
$326$	9.32624	+	6.77591i	0.516533	+	0.375283i
$327$	1.23607	+	3.80423i	0.0683547	+	0.210374i
$328$	6.47214	+	4.70228i	0.357364	+	0.259640i
$329$	4.76393	−	3.46120i	0.262644	−	0.190822i
$330$	0.263932	−	0.812299i	0.0145290	−	0.0447156i
$331$	−21.7082	+	15.7719i	−1.19319	+	0.866904i	−0.993598	−	0.112975i	$-0.963962\pi$
$331$	−21.7082	+	15.7719i	−1.19319	+	0.866904i	−0.199593	+	0.979879i	$0.563962\pi$
$332$	2.00000	+	6.15537i	0.109764	+	0.337820i
$333$	2.09017	+	6.43288i	0.114541	+	0.352520i
$334$	−6.18034	+	19.0211i	−0.338173	+	1.04079i
$335$	−6.76393			−0.369553
$336$	3.85410			0.210258
$337$	7.85410	−	24.1724i	0.427840	−	1.31676i	−0.472408	−	0.881380i	$-0.656615\pi$
$337$	7.85410	−	24.1724i	0.427840	−	1.31676i	0.900248	−	0.435377i	$-0.143385\pi$
$338$	−10.0451	−	7.29818i	−0.546381	−	0.396969i
$339$	−9.85410	+	7.15942i	−0.535201	+	0.388847i
$340$	−2.47214			−0.134070
$341$	7.29837	−	2.43690i	0.395229	−	0.131965i
$342$	2.47214			0.133678
$343$	−2.66312	+	1.93487i	−0.143795	+	0.104473i
$344$	−5.85410	−	4.25325i	−0.315632	−	0.229320i
$345$	−1.61803	+	4.97980i	−0.0871120	+	0.268103i
$346$	8.27051			0.444625
$347$	−15.5623			−0.835428			−0.417714	−	0.908578i	$-0.637169\pi$
$347$	−15.5623			−0.835428			−0.417714	+	0.908578i	$0.637169\pi$
$348$	−0.500000	+	1.53884i	−0.0268028	+	0.0824906i
$349$	5.38197	+	16.5640i	0.288090	+	0.886650i	0.985455	+	0.169934i	$0.0543555\pi$
$349$	5.38197	+	16.5640i	0.288090	+	0.886650i	−0.697365	+	0.716716i	$0.745644\pi$
$350$	5.50000	+	16.9273i	0.293987	+	0.904800i
$351$	−0.618034	+	0.449028i	−0.0329882	+	0.0239673i
$352$	−0.427051	+	1.31433i	−0.0227619	+	0.0700539i
$353$	1.23607	−	0.898056i	0.0657893	−	0.0477987i	−0.554405	−	0.832247i	$-0.687054\pi$
$353$	1.23607	−	0.898056i	0.0657893	−	0.0477987i	0.620194	+	0.784449i	$0.287054\pi$
$354$	6.54508	+	4.75528i	0.347867	+	0.252740i
$355$	0.381966	+	1.17557i	0.0202727	+	0.0623928i
$356$	−2.38197	−	1.73060i	−0.126244	−	0.0917216i
$357$	−12.4721	−	9.06154i	−0.660095	−	0.479587i
$358$	1.79180	+	5.51458i	0.0946994	+	0.291455i
$359$	−11.4721	−	8.33499i	−0.605476	−	0.439904i	0.242342	−	0.970191i	$-0.422084\pi$
$359$	−11.4721	−	8.33499i	−0.605476	−	0.439904i	−0.847818	+	0.530287i	$0.822084\pi$
$360$	−0.500000	+	0.363271i	−0.0263523	+	0.0191461i
$361$	−3.98278	+	12.2577i	−0.209620	+	0.645144i
$362$	5.61803	−	4.08174i	0.295277	−	0.214532i
$363$	−2.80902	−	8.64527i	−0.147435	−	0.453759i
$364$	0.909830	+	2.80017i	0.0476881	+	0.146769i
$365$	0.454915	−	1.40008i	0.0238113	−	0.0732838i
$366$	11.2361			0.587319
$367$	−6.20163			−0.323722			−0.161861	−	0.986814i	$-0.551750\pi$
$367$	−6.20163			−0.323722			−0.161861	+	0.986814i	$0.551750\pi$
$368$	2.61803	−	8.05748i	0.136474	−	0.420025i
$369$	−6.47214	−	4.70228i	−0.336926	−	0.244791i
$370$	−3.38197	+	2.45714i	−0.175820	+	0.127741i
$371$	9.18034			0.476619
$372$	−5.30902	−	1.67760i	−0.275260	−	0.0869795i
$373$	26.9443			1.39512			0.697561	−	0.716526i	$-0.254269\pi$
$373$	26.9443			1.39512			0.697561	+	0.716526i	$0.254269\pi$
$374$	4.47214	−	3.24920i	0.231249	−	0.168012i
$375$	−4.80902	−	3.49396i	−0.248337	−	0.180427i
$376$	0.472136	−	1.45309i	0.0243486	−	0.0749371i
$377$	−1.23607			−0.0636607
$378$	−3.85410			−0.198234
$379$	5.47214	−	16.8415i	0.281085	−	0.865090i	−0.706460	−	0.707753i	$-0.749709\pi$
$379$	5.47214	−	16.8415i	0.281085	−	0.865090i	0.987545	−	0.157337i	$-0.0502909\pi$
$380$	0.472136	+	1.45309i	0.0242201	+	0.0745417i
$381$	−2.44427	−	7.52270i	−0.125224	−	0.385399i
$382$	6.70820	−	4.87380i	0.343222	−	0.249365i
$383$	−7.23607	+	22.2703i	−0.369746	+	1.13796i	0.577210	+	0.816596i	$0.304142\pi$
$383$	−7.23607	+	22.2703i	−0.369746	+	1.13796i	−0.946956	+	0.321365i	$0.895858\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	2.66312	+	1.93487i	0.135725	+	0.0986101i
$386$	2.44427	+	7.52270i	0.124410	+	0.382895i
$387$	5.85410	+	4.25325i	0.297581	+	0.216205i
$388$	5.61803	+	4.08174i	0.285212	+	0.207219i
$389$	10.2082	+	31.4176i	0.517576	+	1.59294i	0.778545	+	0.627589i	$0.215958\pi$
$389$	10.2082	+	31.4176i	0.517576	+	1.59294i	−0.260968	+	0.965347i	$0.584042\pi$
$390$	−0.381966	−	0.277515i	−0.0193416	−	0.0140525i
$391$	−27.4164	+	19.9192i	−1.38651	+	1.00736i
$392$	−2.42705	+	7.46969i	−0.122585	+	0.377277i
$393$	−13.7812	+	10.0126i	−0.695167	+	0.505069i
$394$	5.51722	+	16.9803i	0.277954	+	0.855453i
$395$	2.16312	+	6.65740i	0.108838	+	0.334970i
$396$	0.427051	−	1.31433i	0.0214601	−	0.0660475i
$397$	−11.5967			−0.582024			−0.291012	−	0.956719i	$-0.593992\pi$
$397$	−11.5967			−0.582024			−0.291012	+	0.956719i	$0.593992\pi$
$398$	4.09017			0.205022
$399$	−2.94427	+	9.06154i	−0.147398	+	0.453644i
$400$	3.73607	+	2.71441i	0.186803	+	0.135721i
$401$	20.0902	−	14.5964i	1.00326	−	0.728908i	0.0404715	−	0.999181i	$-0.487114\pi$
$401$	20.0902	−	14.5964i	1.00326	−	0.728908i	0.962784	+	0.270273i	$0.0871140\pi$
$402$	−10.9443			−0.545851
$403$	−0.0344419	−	4.25325i	−0.00171567	−	0.211870i
$404$	10.1459			0.504777
$405$	0.500000	−	0.363271i	0.0248452	−	0.0180511i
$406$	−5.04508	−	3.66547i	−0.250383	−	0.181914i
$407$	2.88854	−	8.89002i	0.143180	−	0.440662i
$408$	−4.00000			−0.198030
$409$	−37.0344			−1.83124			−0.915618	−	0.402050i	$-0.868298\pi$
$409$	−37.0344			−1.83124			−0.915618	+	0.402050i	$0.868298\pi$
$410$	1.52786	−	4.70228i	0.0754558	−	0.232229i
$411$	−5.23607	−	16.1150i	−0.258276	−	0.794892i
$412$	2.76393	+	8.50651i	0.136169	+	0.419086i
$413$	−25.2254	+	18.3273i	−1.24126	+	0.901830i
$414$	−2.61803	+	8.05748i	−0.128669	+	0.396004i
$415$	3.23607	−	2.35114i	0.158852	−	0.115413i
$416$	0.618034	+	0.449028i	0.0303016	+	0.0220154i
$417$	1.47214	+	4.53077i	0.0720908	+	0.221873i
$418$	−2.76393	−	2.00811i	−0.135188	−	0.0982201i
$419$	−21.8262	−	15.8577i	−1.06628	−	0.774699i	−0.0910413	−	0.995847i	$-0.529020\pi$
$419$	−21.8262	−	15.8577i	−1.06628	−	0.774699i	−0.975240	+	0.221148i	$0.929020\pi$
$420$	−0.736068	−	2.26538i	−0.0359164	−	0.110539i
$421$	13.7082	+	9.95959i	0.668097	+	0.485401i	0.869388	−	0.494131i	$-0.164514\pi$
$421$	13.7082	+	9.95959i	0.668097	+	0.485401i	−0.201291	+	0.979532i	$0.564514\pi$
$422$	−9.47214	+	6.88191i	−0.461096	+	0.335006i
$423$	−0.472136	+	1.45309i	−0.0229560	+	0.0706514i
$424$	1.92705	−	1.40008i	0.0935859	−	0.0679941i
$425$	−5.70820	−	17.5680i	−0.276889	−	0.852175i
$426$	0.618034	+	1.90211i	0.0299438	+	0.0921577i
$427$	−13.3820	+	41.1855i	−0.647599	+	1.99310i
$428$	−19.5623			−0.945580
$429$	1.05573			0.0509710
$430$	−1.38197	+	4.25325i	−0.0666443	+	0.205110i
$431$	12.9443	+	9.40456i	0.623504	+	0.453002i	0.854144	−	0.520037i	$-0.174082\pi$
$431$	12.9443	+	9.40456i	0.623504	+	0.453002i	−0.230640	+	0.973039i	$0.574082\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	20.6869			0.994150			0.497075	−	0.867708i	$-0.334407\pi$
$433$	20.6869			0.994150			0.497075	+	0.867708i	$0.334407\pi$
$434$	12.4721	−	17.4620i	0.598682	−	0.838205i
$435$	1.00000			0.0479463
$436$	−3.23607	+	2.35114i	−0.154980	+	0.112599i
$437$	16.9443	+	12.3107i	0.810554	+	0.588902i
$438$	0.736068	−	2.26538i	0.0351707	−	0.108244i
$439$	27.3262			1.30421			0.652105	−	0.758129i	$-0.273886\pi$
$439$	27.3262			1.30421			0.652105	+	0.758129i	$0.273886\pi$
$440$	0.854102			0.0407177
$441$	2.42705	−	7.46969i	0.115574	−	0.355700i
$442$	−0.944272	−	2.90617i	−0.0449144	−	0.138232i
$443$	4.55573	+	14.0211i	0.216449	+	0.666162i	0.999048	+	0.0436351i	$0.0138939\pi$
$443$	4.55573	+	14.0211i	0.216449	+	0.666162i	−0.782598	+	0.622527i	$0.786106\pi$
$444$	−5.47214	+	3.97574i	−0.259696	+	0.188680i
$445$	−0.562306	+	1.73060i	−0.0266559	+	0.0820383i
$446$	22.8262	−	16.5842i	1.08085	−	0.785286i
$447$	12.3992	+	9.00854i	0.586461	+	0.426089i
$448$	1.19098	+	3.66547i	0.0562687	+	0.173177i
$449$	−3.23607	−	2.35114i	−0.152719	−	0.110957i	0.508801	−	0.860884i	$-0.330089\pi$
$449$	−3.23607	−	2.35114i	−0.152719	−	0.110957i	−0.661521	+	0.749927i	$0.730089\pi$
$450$	−3.73607	−	2.71441i	−0.176120	−	0.127959i
$451$	3.41641	+	10.5146i	0.160872	+	0.495114i
$452$	−9.85410	−	7.15942i	−0.463498	−	0.336751i
$453$	19.0623	−	13.8496i	0.895625	−	0.650710i
$454$	−3.48278	+	10.7189i	−0.163455	+	0.503063i
$455$	1.47214	−	1.06957i	0.0690148	−	0.0501422i
$456$	0.763932	+	2.35114i	0.0357744	+	0.110102i
$457$	1.71885	+	5.29007i	0.0804043	+	0.247459i	0.983176	−	0.182661i	$-0.0584712\pi$
$457$	1.71885	+	5.29007i	0.0804043	+	0.247459i	−0.902772	+	0.430120i	$0.858471\pi$
$458$	4.76393	−	14.6619i	0.222604	−	0.685104i
$459$	4.00000			0.186704
$460$	−5.23607			−0.244133
$461$	2.97214	−	9.14729i	0.138426	−	0.426032i	−0.857681	−	0.514182i	$-0.828096\pi$
$461$	2.97214	−	9.14729i	0.138426	−	0.426032i	0.996107	+	0.0881502i	$0.0280955\pi$
$462$	4.30902	+	3.13068i	0.200474	+	0.145653i
$463$	−13.7082	+	9.95959i	−0.637074	+	0.462862i	−0.858844	−	0.512238i	$-0.828817\pi$
$463$	−13.7082	+	9.95959i	−0.637074	+	0.462862i	0.221770	+	0.975099i	$0.428817\pi$
$464$	−1.61803			−0.0751153
$465$	0.0278640	+	3.44095i	0.00129216	+	0.159570i
$466$	−22.3607			−1.03584
$467$	33.9615	−	24.6745i	1.57155	−	1.14180i	0.645898	−	0.763424i	$-0.276483\pi$
$467$	33.9615	−	24.6745i	1.57155	−	1.14180i	0.925653	−	0.378374i	$-0.123517\pi$
$468$	−0.618034	−	0.449028i	−0.0285686	−	0.0207563i
$469$	13.0344	−	40.1159i	0.601875	−	1.85238i
$470$	−0.944272			−0.0435560
$471$	23.2361			1.07066
$472$	−2.50000	+	7.69421i	−0.115072	+	0.354155i
$473$	−3.09017	−	9.51057i	−0.142086	−	0.437296i
$474$	3.50000	+	10.7719i	0.160760	+	0.494769i
$475$	−9.23607	+	6.71040i	−0.423780	+	0.307894i
$476$	4.76393	−	14.6619i	0.218354	−	0.672026i
$477$	−1.92705	+	1.40008i	−0.0882336	+	0.0641055i
$478$	−19.9443	−	14.4904i	−0.912230	−	0.662774i
$479$	1.76393	+	5.42882i	0.0805961	+	0.248049i	0.983233	−	0.182353i	$-0.0583715\pi$
$479$	1.76393	+	5.42882i	0.0805961	+	0.248049i	−0.902637	+	0.430403i	$0.858372\pi$
$480$	−0.500000	−	0.363271i	−0.0228218	−	0.0165810i
$481$	−4.18034	−	3.03719i	−0.190607	−	0.138484i
$482$	5.80902	+	17.8783i	0.264593	+	0.814335i
$483$	−26.4164	−	19.1926i	−1.20199	−	0.873296i
$484$	7.35410	−	5.34307i	0.334277	−	0.242867i
$485$	1.32624	−	4.08174i	0.0602214	−	0.185342i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−2.00000	−	6.15537i	−0.0906287	−	0.278926i	0.895461	−	0.445140i	$-0.146846\pi$
$487$	−2.00000	−	6.15537i	−0.0906287	−	0.278926i	−0.986090	+	0.166213i	$0.946846\pi$
$488$	3.47214	+	10.6861i	0.157176	+	0.483739i
$489$	3.56231	−	10.9637i	0.161093	−	0.495793i
$490$	4.85410			0.219286
$491$	25.5279			1.15206			0.576028	−	0.817430i	$-0.304602\pi$
$491$	25.5279			1.15206			0.576028	+	0.817430i	$0.304602\pi$
$492$	2.47214	−	7.60845i	0.111452	−	0.343016i
$493$	5.23607	+	3.80423i	0.235821	+	0.171334i
$494$	−1.52786	+	1.11006i	−0.0687419	+	0.0499439i
$495$	−0.854102			−0.0383890
$496$	−0.0450850	−	5.56758i	−0.00202437	−	0.249992i
$497$	−7.70820			−0.345760
$498$	5.23607	−	3.80423i	0.234634	−	0.170471i
$499$	−7.61803	−	5.53483i	−0.341030	−	0.247773i	0.404066	−	0.914730i	$-0.367597\pi$
$499$	−7.61803	−	5.53483i	−0.341030	−	0.247773i	−0.745096	+	0.666957i	$0.767597\pi$
$500$	1.83688	−	5.65334i	0.0821478	−	0.252825i
$501$	20.0000			0.893534
$502$	−21.3820			−0.954324
$503$	−8.52786	+	26.2461i	−0.380239	+	1.17025i	0.559637	+	0.828738i	$0.310941\pi$
$503$	−8.52786	+	26.2461i	−0.380239	+	1.17025i	−0.939876	+	0.341517i	$0.889059\pi$
$504$	−1.19098	−	3.66547i	−0.0530506	−	0.163273i
$505$	−1.93769	−	5.96361i	−0.0862263	−	0.265377i
$506$	9.47214	−	6.88191i	0.421088	−	0.305938i
$507$	−3.83688	+	11.8087i	−0.170402	+	0.524443i
$508$	6.39919	−	4.64928i	0.283918	−	0.206279i
$509$	3.61803	+	2.62866i	0.160367	+	0.116513i	0.665074	−	0.746777i	$-0.268400\pi$
$509$	3.61803	+	2.62866i	0.160367	+	0.116513i	−0.504708	+	0.863290i	$0.668400\pi$
$510$	0.763932	+	2.35114i	0.0338275	+	0.104110i
$511$	7.42705	+	5.39607i	0.328553	+	0.238708i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.763932	−	2.35114i	−0.0337284	−	0.103805i
$514$	1.47214	+	1.06957i	0.0649331	+	0.0471767i
$515$	4.47214	−	3.24920i	0.197066	−	0.143177i
$516$	−2.23607	+	6.88191i	−0.0984374	+	0.302959i
$517$	1.70820	−	1.24108i	0.0751267	−	0.0545828i
$518$	−8.05573	−	24.7930i	−0.353948	−	1.08934i
$519$	−2.55573	−	7.86572i	−0.112184	−	0.345267i
$520$	0.145898	−	0.449028i	0.00639805	−	0.0196912i
$521$	10.2918			0.450892			0.225446	−	0.974256i	$-0.427616\pi$
$521$	10.2918			0.450892			0.225446	+	0.974256i	$0.427616\pi$
$522$	1.61803			0.0708194
$523$	−2.56231	+	7.88597i	−0.112042	+	0.344829i	−0.991319	−	0.131482i	$-0.958026\pi$
$523$	−2.56231	+	7.88597i	−0.112042	+	0.344829i	0.879277	+	0.476311i	$0.158026\pi$
$524$	−13.7812	−	10.0126i	−0.602032	−	0.437402i
$525$	14.3992	−	10.4616i	0.628432	−	0.456583i
$526$	−5.81966			−0.253749
$527$	−12.9443	+	18.1231i	−0.563861	+	0.789454i
$528$	1.38197			0.0601424
$529$	−39.4615	+	28.6705i	−1.71572	+	1.24654i
$530$	−1.19098	−	0.865300i	−0.0517330	−	0.0375862i
$531$	2.50000	−	7.69421i	0.108491	−	0.333900i
$532$	−9.52786			−0.413085
$533$	6.11146			0.264717
$534$	−0.909830	+	2.80017i	−0.0393722	+	0.121175i
$535$	3.73607	+	11.4984i	0.161524	+	0.497121i
$536$	−3.38197	−	10.4086i	−0.146079	−	0.449584i
$537$	4.69098	−	3.40820i	0.202431	−	0.147075i
$538$	1.98936	−	6.12261i	0.0857673	−	0.263965i
$539$	−8.78115	+	6.37988i	−0.378231	+	0.274801i
$540$	0.500000	+	0.363271i	0.0215166	+	0.0156327i
$541$	−0.472136	−	1.45309i	−0.0202987	−	0.0624730i	0.940394	−	0.340087i	$-0.110456\pi$
$541$	−0.472136	−	1.45309i	−0.0202987	−	0.0624730i	−0.960693	+	0.277614i	$0.910456\pi$
$542$	−16.0623	−	11.6699i	−0.689935	−	0.501267i
$543$	−5.61803	−	4.08174i	−0.241093	−	0.175164i
$544$	−1.23607	−	3.80423i	−0.0529960	−	0.163105i
$545$	2.00000	+	1.45309i	0.0856706	+	0.0622433i
$546$	2.38197	−	1.73060i	0.101939	−	0.0740628i
$547$	11.4721	−	35.3076i	0.490513	−	1.50964i	−0.333321	−	0.942813i	$-0.608169\pi$
$547$	11.4721	−	35.3076i	0.490513	−	1.50964i	0.823834	−	0.566831i	$-0.191831\pi$
$548$	13.7082	−	9.95959i	0.585585	−	0.425453i
$549$	−3.47214	−	10.6861i	−0.148187	−	0.456073i
$550$	1.97214	+	6.06961i	0.0840922	+	0.258809i
$551$	1.23607	−	3.80423i	0.0526583	−	0.162065i
$552$	−8.47214			−0.360598
$553$	−43.6525			−1.85629
$554$	−4.38197	+	13.4863i	−0.186172	+	0.572978i
$555$	3.38197	+	2.45714i	0.143556	+	0.104300i
$556$	−3.85410	+	2.80017i	−0.163450	+	0.118754i
$557$	−30.5066			−1.29261			−0.646303	−	0.763081i	$-0.723686\pi$
$557$	−30.5066			−1.29261			−0.646303	+	0.763081i	$0.723686\pi$
$558$	0.0450850	+	5.56758i	0.00190860	+	0.235695i
$559$	−5.52786			−0.233804
$560$	1.92705	−	1.40008i	0.0814328	−	0.0591644i
$561$	−4.47214	−	3.24920i	−0.188814	−	0.137181i
$562$	5.52786	−	17.0130i	0.233179	−	0.717651i
$563$	6.32624			0.266619			0.133310	−	0.991074i	$-0.457440\pi$
$563$	6.32624			0.266619			0.133310	+	0.991074i	$0.457440\pi$
$564$	−1.52786			−0.0643347
$565$	−2.32624	+	7.15942i	−0.0978656	+	0.301199i
$566$	−10.0000	−	30.7768i	−0.420331	−	1.29365i
$567$	1.19098	+	3.66547i	0.0500166	+	0.153935i
$568$	−1.61803	+	1.17557i	−0.0678912	+	0.0493258i
$569$	−11.2361	+	34.5811i	−0.471040	+	1.44971i	0.380184	+	0.924911i	$0.375861\pi$
$569$	−11.2361	+	34.5811i	−0.471040	+	1.44971i	−0.851224	+	0.524802i	$0.824139\pi$
$570$	1.23607	−	0.898056i	0.0517732	−	0.0376154i
$571$	−2.14590	−	1.55909i	−0.0898030	−	0.0652457i	0.541978	−	0.840393i	$-0.317676\pi$
$571$	−2.14590	−	1.55909i	−0.0898030	−	0.0652457i	−0.631781	+	0.775147i	$0.717676\pi$
$572$	0.326238	+	1.00406i	0.0136407	+	0.0419817i
$573$	−6.70820	−	4.87380i	−0.280239	−	0.203606i
$574$	24.9443	+	18.1231i	1.04115	+	0.756443i
$575$	−12.0902	−	37.2097i	−0.504195	−	1.55175i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	21.2082	−	15.4087i	0.882909	−	0.641471i	−0.0511104	−	0.998693i	$-0.516276\pi$
$577$	21.2082	−	15.4087i	0.882909	−	0.641471i	0.934020	+	0.357222i	$0.116276\pi$
$578$	0.309017	−	0.951057i	0.0128534	−	0.0395587i
$579$	6.39919	−	4.64928i	0.265941	−	0.193218i
$580$	0.309017	+	0.951057i	0.0128312	+	0.0394905i
$581$	7.70820	+	23.7234i	0.319790	+	0.984213i
$582$	2.14590	−	6.60440i	0.0889503	−	0.273761i
$583$	3.29180			0.136332
$584$	2.38197			0.0985665
$585$	−0.145898	+	0.449028i	−0.00603214	+	0.0185650i
$586$	−0.381966	−	0.277515i	−0.0157789	−	0.0114640i
$587$	−1.40983	+	1.02430i	−0.0581899	+	0.0422774i	−0.616500	−	0.787355i	$-0.711450\pi$
$587$	−1.40983	+	1.02430i	−0.0581899	+	0.0422774i	0.558310	+	0.829632i	$0.311450\pi$
$588$	7.85410			0.323898
$589$	13.1246	+	4.14725i	0.540790	+	0.170885i
$590$	5.00000			0.205847
$591$	14.4443	−	10.4944i	0.594158	−	0.431681i
$592$	−5.47214	−	3.97574i	−0.224903	−	0.163402i
$593$	4.67376	−	14.3844i	0.191928	−	0.590695i	−0.808070	−	0.589086i	$-0.799488\pi$
$593$	4.67376	−	14.3844i	0.191928	−	0.590695i	0.999999	−	0.00160883i	$-0.000512107\pi$
$594$	−1.38197			−0.0567028
$595$	−9.52786			−0.390604
$596$	−4.73607	+	14.5761i	−0.193997	+	0.597061i
$597$	−1.26393	−	3.88998i	−0.0517293	−	0.159206i
$598$	−2.00000	−	6.15537i	−0.0817861	−	0.251712i
$599$	15.4721	−	11.2412i	0.632174	−	0.459302i	−0.224978	−	0.974364i	$-0.572231\pi$
$599$	15.4721	−	11.2412i	0.632174	−	0.459302i	0.857153	+	0.515062i	$0.172231\pi$
$600$	1.42705	−	4.39201i	0.0582591	−	0.179303i
$601$	1.02786	−	0.746787i	0.0419274	−	0.0304621i	−0.566624	−	0.823976i	$-0.691751\pi$
$601$	1.02786	−	0.746787i	0.0419274	−	0.0304621i	0.608552	+	0.793514i	$0.291751\pi$
$602$	−22.5623	−	16.3925i	−0.919571	−	0.668107i
$603$	3.38197	+	10.4086i	0.137724	+	0.423872i
$604$	19.0623	+	13.8496i	0.775634	+	0.563531i
$605$	−4.54508	−	3.30220i	−0.184784	−	0.134253i
$606$	−3.13525	−	9.64932i	−0.127361	−	0.391977i
$607$	16.5451	+	12.0207i	0.671544	+	0.487905i	0.870542	−	0.492095i	$-0.163769\pi$
$607$	16.5451	+	12.0207i	0.671544	+	0.487905i	−0.198997	+	0.980000i	$0.563769\pi$
$608$	−2.00000	+	1.45309i	−0.0811107	+	0.0589304i
$609$	−1.92705	+	5.93085i	−0.0780880	+	0.240330i
$610$	5.61803	−	4.08174i	0.227468	−	0.165265i
$611$	−0.360680	−	1.11006i	−0.0145915	−	0.0449081i
$612$	1.23607	+	3.80423i	0.0499651	+	0.153777i
$613$	−8.61803	+	26.5236i	−0.348079	+	1.07128i	0.611836	+	0.790985i	$0.290431\pi$
$613$	−8.61803	+	26.5236i	−0.348079	+	1.07128i	−0.959915	+	0.280292i	$0.909569\pi$
$614$	−0.472136			−0.0190539
$615$	−4.94427			−0.199372
$616$	−1.64590	+	5.06555i	−0.0663151	+	0.204097i
$617$	−2.94427	−	2.13914i	−0.118532	−	0.0861185i	0.526940	−	0.849902i	$-0.323339\pi$
$617$	−2.94427	−	2.13914i	−0.118532	−	0.0861185i	−0.645472	+	0.763784i	$0.723339\pi$
$618$	7.23607	−	5.25731i	0.291077	−	0.211480i
$619$	8.18034			0.328796			0.164398	−	0.986394i	$-0.447432\pi$
$619$	8.18034			0.328796			0.164398	+	0.986394i	$0.447432\pi$
$620$	−3.26393	+	1.08981i	−0.131083	+	0.0437680i
$621$	8.47214			0.339975
$622$	−23.5623	+	17.1190i	−0.944762	+	0.686410i
$623$	−9.18034	−	6.66991i	−0.367803	−	0.267224i
$624$	0.236068	−	0.726543i	0.00945028	−	0.0290850i
$625$	19.4164			0.776656
$626$	−5.41641			−0.216483
$627$	−1.05573	+	3.24920i	−0.0421617	+	0.129760i
$628$	7.18034	+	22.0988i	0.286527	+	0.881839i
$629$	8.36068	+	25.7315i	0.333362	+	1.02598i
$630$	−1.92705	+	1.40008i	−0.0767755	+	0.0557807i
$631$	8.89919	−	27.3889i	0.354271	−	1.09033i	−0.602160	−	0.798376i	$-0.705693\pi$
$631$	8.89919	−	27.3889i	0.354271	−	1.09033i	0.956431	−	0.291959i	$-0.0943070\pi$
$632$	−9.16312	+	6.65740i	−0.364489	+	0.264817i
$633$	9.47214	+	6.88191i	0.376484	+	0.273531i
$634$	−7.56231	−	23.2744i	−0.300338	−	0.924344i
$635$	−3.95492	−	2.87341i	−0.156946	−	0.114028i
$636$	−1.92705	−	1.40008i	−0.0764125	−	0.0555170i
$637$	1.85410	+	5.70634i	0.0734622	+	0.226093i
$638$	−1.80902	−	1.31433i	−0.0716197	−	0.0520347i
$639$	1.61803	−	1.17557i	0.0640084	−	0.0465049i
$640$	0.190983	−	0.587785i	0.00754927	−	0.0232343i
$641$	21.0902	−	15.3229i	0.833012	−	0.605218i	−0.0873981	−	0.996173i	$-0.527855\pi$
$641$	21.0902	−	15.3229i	0.833012	−	0.605218i	0.920410	+	0.390955i	$0.127855\pi$
$642$	6.04508	+	18.6049i	0.238580	+	0.734275i
$643$	−3.18034	−	9.78808i	−0.125420	−	0.386004i	0.868557	−	0.495589i	$-0.165048\pi$
$643$	−3.18034	−	9.78808i	−0.125420	−	0.386004i	−0.993977	+	0.109585i	$0.965048\pi$
$644$	10.0902	−	31.0543i	0.397608	−	1.22371i
$645$	4.47214			0.176090
$646$	9.88854			0.389060
$647$	5.50658	−	16.9475i	0.216486	−	0.666275i	−0.782559	−	0.622577i	$-0.786086\pi$
$647$	5.50658	−	16.9475i	0.216486	−	0.666275i	0.999045	−	0.0436985i	$-0.0139141\pi$
$648$	0.809017	+	0.587785i	0.0317812	+	0.0230904i
$649$	−9.04508	+	6.57164i	−0.355051	+	0.257959i
$650$	3.52786			0.138374
$651$	−20.4615	−	6.46564i	−0.801949	−	0.253408i
$652$	11.5279			0.451466
$653$	−32.4336	+	23.5644i	−1.26923	+	0.922147i	−0.999171	−	0.0406984i	$-0.987042\pi$
$653$	−32.4336	+	23.5644i	−1.26923	+	0.922147i	−0.270054	+	0.962845i	$0.587042\pi$
$654$	3.23607	+	2.35114i	0.126540	+	0.0919369i
$655$	−3.25329	+	10.0126i	−0.127117	+	0.391224i
$656$	8.00000			0.312348
$657$	−2.38197			−0.0929293
$658$	1.81966	−	5.60034i	0.0709377	−	0.218324i
$659$	5.31966	+	16.3722i	0.207225	+	0.637772i	0.999615	+	0.0277569i	$0.00883644\pi$
$659$	5.31966	+	16.3722i	0.207225	+	0.637772i	−0.792390	+	0.610015i	$0.791164\pi$
$660$	−0.263932	−	0.812299i	−0.0102735	−	0.0316187i
$661$	10.1803	−	7.39645i	0.395969	−	0.287689i	−0.371928	−	0.928262i	$-0.621303\pi$
$661$	10.1803	−	7.39645i	0.395969	−	0.287689i	0.767897	+	0.640573i	$0.221303\pi$
$662$	−8.29180	+	25.5195i	−0.322270	+	0.991844i
$663$	−2.47214	+	1.79611i	−0.0960098	+	0.0697552i
$664$	5.23607	+	3.80423i	0.203199	+	0.147633i
$665$	1.81966	+	5.60034i	0.0705634	+	0.217172i
$666$	5.47214	+	3.97574i	0.212041	+	0.154057i
$667$	11.0902	+	8.05748i	0.429413	+	0.311987i
$668$	6.18034	+	19.0211i	0.239125	+	0.735950i
$669$	−22.8262	−	16.5842i	−0.882513	−	0.641183i
$670$	−5.47214	+	3.97574i	−0.211407	+	0.153596i
$671$	−4.79837	+	14.7679i	−0.185239	+	0.570108i
$672$	3.11803	−	2.26538i	0.120281	−	0.0873891i
$673$	3.62868	+	11.1679i	0.139875	+	0.430492i	0.996316	−	0.0857529i	$-0.0273296\pi$
$673$	3.62868	+	11.1679i	0.139875	+	0.430492i	−0.856441	+	0.516245i	$0.827330\pi$
$674$	−7.85410	−	24.1724i	−0.302529	−	0.931088i
$675$	−1.42705	+	4.39201i	−0.0549272	+	0.169049i
$676$	−12.4164			−0.477554
$677$	−18.1459			−0.697404			−0.348702	−	0.937234i	$-0.613377\pi$
$677$	−18.1459			−0.697404			−0.348702	+	0.937234i	$0.613377\pi$
$678$	−3.76393	+	11.5842i	−0.144553	+	0.444888i
$679$	21.6525	+	15.7314i	0.830946	+	0.603717i
$680$	−2.00000	+	1.45309i	−0.0766965	+	0.0557233i
$681$	11.2705			0.431887
$682$	4.47214	−	6.26137i	0.171247	−	0.239760i
$683$	22.8328			0.873673			0.436837	−	0.899541i	$-0.356099\pi$
$683$	22.8328			0.873673			0.436837	+	0.899541i	$0.356099\pi$
$684$	2.00000	−	1.45309i	0.0764719	−	0.0555601i
$685$	−8.47214	−	6.15537i	−0.323704	−	0.235184i
$686$	−1.01722	+	3.13068i	−0.0388377	+	0.119530i
$687$	−15.4164			−0.588173
$688$	−7.23607			−0.275873
$689$	0.562306	−	1.73060i	0.0214221	−	0.0659306i
$690$	1.61803	+	4.97980i	0.0615975	+	0.189578i
$691$	−6.67376	−	20.5397i	−0.253882	−	0.781368i	−0.994048	−	0.108944i	$-0.965253\pi$
$691$	−6.67376	−	20.5397i	−0.253882	−	0.781368i	0.740166	−	0.672424i	$-0.234747\pi$
$692$	6.69098	−	4.86128i	0.254353	−	0.184798i
$693$	1.64590	−	5.06555i	0.0625225	−	0.192424i
$694$	−12.5902	+	9.14729i	−0.477916	+	0.347227i
$695$	2.38197	+	1.73060i	0.0903531	+	0.0656454i
$696$	0.500000	+	1.53884i	0.0189525	+	0.0583296i
$697$	−25.8885	−	18.8091i	−0.980599	−	0.712447i
$698$	14.0902	+	10.2371i	0.533321	+	0.387480i
$699$	6.90983	+	21.2663i	0.261354	+	0.804364i
$700$	14.3992	+	10.4616i	0.544238	+	0.395412i
$701$	−12.5623	+	9.12705i	−0.474472	+	0.344724i	−0.799181	−	0.601090i	$-0.794733\pi$
$701$	−12.5623	+	9.12705i	−0.474472	+	0.344724i	0.324710	+	0.945814i	$0.394733\pi$
$702$	−0.236068	+	0.726543i	−0.00890981	+	0.0274216i
$703$	13.5279	−	9.82857i	0.510213	−	0.370691i
$704$	0.427051	+	1.31433i	0.0160951	+	0.0495356i
$705$	0.291796	+	0.898056i	0.0109897	+	0.0338227i
$706$	0.472136	−	1.45309i	0.0177691	−	0.0546876i
$707$	39.1033			1.47063
$708$	8.09017			0.304047
$709$	3.34752	−	10.3026i	0.125719	−	0.386923i	−0.868312	−	0.496018i	$-0.834795\pi$
$709$	3.34752	−	10.3026i	0.125719	−	0.386923i	0.994031	+	0.109095i	$0.0347951\pi$
$710$	1.00000	+	0.726543i	0.0375293	+	0.0272667i
$711$	9.16312	−	6.65740i	0.343644	−	0.249672i
$712$	−2.94427			−0.110341
$713$	−27.4164	+	38.3853i	−1.02675	+	1.43754i
$714$	−15.4164			−0.576945
$715$	0.527864	−	0.383516i	0.0197410	−	0.0143427i
$716$	4.69098	+	3.40820i	0.175310	+	0.127370i
$717$	−7.61803	+	23.4459i	−0.284501	+	0.875603i
$718$	−14.1803			−0.529206
$719$	18.6525			0.695620			0.347810	−	0.937565i	$-0.386925\pi$
$719$	18.6525			0.695620			0.347810	+	0.937565i	$0.386925\pi$
$720$	−0.190983	+	0.587785i	−0.00711752	+	0.0219055i
$721$	10.6525	+	32.7849i	0.396719	+	1.22098i
$722$	3.98278	+	12.2577i	0.148224	+	0.456186i
$723$	15.2082	−	11.0494i	0.565599	−	0.410932i
$724$	2.14590	−	6.60440i	0.0797517	−	0.245450i
$725$	−6.04508	+	4.39201i	−0.224509	+	0.163115i
$726$	−7.35410	−	5.34307i	−0.272936	−	0.198300i
$727$	−10.0451	−	30.9156i	−0.372552	−	1.14660i	−0.945116	−	0.326736i	$-0.894051\pi$
$727$	−10.0451	−	30.9156i	−0.372552	−	1.14660i	0.572564	−	0.819860i	$-0.305949\pi$
$728$	2.38197	+	1.73060i	0.0882815	+	0.0641403i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−0.454915	−	1.40008i	−0.0168372	−	0.0518195i
$731$	23.4164	+	17.0130i	0.866087	+	0.629249i
$732$	9.09017	−	6.60440i	0.335982	−	0.244105i
$733$	7.23607	−	22.2703i	0.267270	−	0.822573i	−0.723891	−	0.689914i	$-0.757648\pi$
$733$	7.23607	−	22.2703i	0.267270	−	0.822573i	0.991162	−	0.132659i	$-0.0423516\pi$
$734$	−5.01722	+	3.64522i	−0.185189	+	0.134548i
$735$	−1.50000	−	4.61653i	−0.0553283	−	0.170283i
$736$	−2.61803	−	8.05748i	−0.0965020	−	0.297003i
$737$	4.67376	−	14.3844i	0.172160	−	0.529855i
$738$	−8.00000			−0.294484
$739$	−31.1246			−1.14494			−0.572469	−	0.819927i	$-0.694014\pi$
$739$	−31.1246			−1.14494			−0.572469	+	0.819927i	$0.694014\pi$
$740$	−1.29180	+	3.97574i	−0.0474874	+	0.146151i
$741$	1.52786	+	1.11006i	0.0561275	+	0.0407790i
$742$	7.42705	−	5.39607i	0.272656	−	0.198096i
$743$	34.6525			1.27128			0.635638	−	0.771987i	$-0.280737\pi$
$743$	34.6525			1.27128			0.635638	+	0.771987i	$0.280737\pi$
$744$	−5.28115	+	1.76336i	−0.193616	+	0.0646478i
$745$	9.47214			0.347032
$746$	21.7984	−	15.8374i	0.798095	−	0.579850i
$747$	−5.23607	−	3.80423i	−0.191578	−	0.139189i
$748$	1.70820	−	5.25731i	0.0624581	−	0.192226i
$749$	−75.3951			−2.75488
$750$	−5.94427			−0.217054
$751$	−10.7639	+	33.1280i	−0.392781	+	1.20886i	0.537894	+	0.843012i	$0.319220\pi$
$751$	−10.7639	+	33.1280i	−0.392781	+	1.20886i	−0.930676	+	0.365845i	$0.880780\pi$
$752$	−0.472136	−	1.45309i	−0.0172170	−	0.0529886i
$753$	6.60739	+	20.3355i	0.240787	+	0.741065i
$754$	−1.00000	+	0.726543i	−0.0364179	+	0.0264591i
$755$	4.50000	−	13.8496i	0.163772	−	0.504038i
$756$	−3.11803	+	2.26538i	−0.113402	+	0.0823912i
$757$	−9.76393	−	7.09391i	−0.354876	−	0.257833i	0.396036	−	0.918235i	$-0.370386\pi$
$757$	−9.76393	−	7.09391i	−0.354876	−	0.257833i	−0.750912	+	0.660403i	$0.770386\pi$
$758$	−5.47214	−	16.8415i	−0.198757	−	0.611711i
$759$	−9.47214	−	6.88191i	−0.343817	−	0.249797i
$760$	1.23607	+	0.898056i	0.0448369	+	0.0325759i
$761$	−6.96556	−	21.4378i	−0.252501	−	0.777119i	−0.994312	−	0.106509i	$-0.966033\pi$
$761$	−6.96556	−	21.4378i	−0.252501	−	0.777119i	0.741810	−	0.670610i	$-0.233967\pi$
$762$	−6.39919	−	4.64928i	−0.231818	−	0.168426i
$763$	−12.4721	+	9.06154i	−0.451522	+	0.328050i
$764$	2.56231	−	7.88597i	0.0927010	−	0.285304i
$765$	2.00000	−	1.45309i	0.0723102	−	0.0525364i
$766$	7.23607	+	22.2703i	0.261450	+	0.804660i
$767$	1.90983	+	5.87785i	0.0689600	+	0.212237i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	24.4721			0.882488			0.441244	−	0.897387i	$-0.354537\pi$
$769$	24.4721			0.882488			0.441244	+	0.897387i	$0.354537\pi$
$770$	3.29180			0.118628
$771$	0.562306	−	1.73060i	0.0202510	−	0.0623260i
$772$	6.39919	+	4.64928i	0.230312	+	0.167331i
$773$	−14.6803	+	10.6659i	−0.528015	+	0.383625i	−0.819615	−	0.572915i	$-0.805813\pi$
$773$	−14.6803	+	10.6659i	−0.528015	+	0.383625i	0.291600	+	0.956540i	$0.405813\pi$
$774$	7.23607			0.260095
$775$	−15.2812	−	20.6785i	−0.548915	−	0.742793i
$776$	6.94427			0.249285
$777$	−21.0902	+	15.3229i	−0.756606	+	0.549706i
$778$	26.7254	+	19.4172i	0.958153	+	0.696139i
$779$	−6.11146	+	18.8091i	−0.218966	+	0.673907i
$780$	−0.472136			−0.0169052
$781$	−2.76393			−0.0989013
$782$	−10.4721	+	32.2299i	−0.374483	+	1.15254i
$783$	−0.500000	−	1.53884i	−0.0178685	−	0.0549937i
$784$	2.42705	+	7.46969i	0.0866804	+	0.266775i
$785$	11.6180	−	8.44100i	0.414665	−	0.301272i
$786$	−5.26393	+	16.2007i	−0.187758	+	0.577860i
$787$	8.61803	−	6.26137i	0.307200	−	0.223194i	−0.423494	−	0.905899i	$-0.639197\pi$
$787$	8.61803	−	6.26137i	0.307200	−	0.223194i	0.730694	+	0.682705i	$0.239197\pi$
$788$	14.4443	+	10.4944i	0.514556	+	0.373847i
$789$	1.79837	+	5.53483i	0.0640238	+	0.197045i
$790$	5.66312	+	4.11450i	0.201485	+	0.146387i
$791$	−37.9787	−	27.5932i	−1.35037	−	0.981099i
$792$	−0.427051	−	1.31433i	−0.0151746	−	0.0467026i
$793$	6.94427	+	5.04531i	0.246598	+	0.179164i
$794$	−9.38197	+	6.81640i	−0.332954	+	0.241905i
$795$	−0.454915	+	1.40008i	−0.0161342	+	0.0496559i
$796$	3.30902	−	2.40414i	0.117285	−	0.0852125i
$797$	6.97214	+	21.4580i	0.246966	+	0.760082i	0.995307	+	0.0967684i	$0.0308506\pi$
$797$	6.97214	+	21.4580i	0.246966	+	0.760082i	−0.748341	+	0.663314i	$0.769149\pi$
$798$	2.94427	+	9.06154i	0.104226	+	0.320775i
$799$	−1.88854	+	5.81234i	−0.0668119	+	0.205626i
$800$	4.61803			0.163272
$801$	2.94427			0.104031
$802$	7.67376	−	23.6174i	0.270970	−	0.833960i
$803$	2.66312	+	1.93487i	0.0939794	+	0.0682801i
$804$	−8.85410	+	6.43288i	−0.312260	+	0.226870i
$805$	−20.1803			−0.711264
$806$	−2.52786	−	3.42071i	−0.0890402	−	0.120489i
$807$	−6.43769			−0.226618
$808$	8.20820	−	5.96361i	0.288764	−	0.209799i
$809$	−2.61803	−	1.90211i	−0.0920452	−	0.0668747i	0.540811	−	0.841144i	$-0.318117\pi$
$809$	−2.61803	−	1.90211i	−0.0920452	−	0.0668747i	−0.632856	+	0.774270i	$0.718117\pi$
$810$	0.190983	−	0.587785i	0.00671046	−	0.0206527i
$811$	44.0689			1.54747			0.773734	−	0.633511i	$-0.218387\pi$
$811$	44.0689			1.54747			0.773734	+	0.633511i	$0.218387\pi$
$812$	−6.23607			−0.218843
$813$	−6.13525	+	18.8824i	−0.215173	+	0.662234i
$814$	−2.88854	−	8.89002i	−0.101243	−	0.311595i
$815$	−2.20163	−	6.77591i	−0.0771196	−	0.237350i
$816$	−3.23607	+	2.35114i	−0.113285	+	0.0823064i
$817$	5.52786	−	17.0130i	0.193395	−	0.595210i
$818$	−29.9615	+	21.7683i	−1.04758	+	0.761111i
$819$	−2.38197	−	1.73060i	−0.0832326	−	0.0604720i
$820$	−1.52786	−	4.70228i	−0.0533553	−	0.164211i
$821$	−22.3992	−	16.2740i	−0.781737	−	0.567965i	0.123763	−	0.992312i	$-0.460504\pi$
$821$	−22.3992	−	16.2740i	−0.781737	−	0.567965i	−0.905500	+	0.424347i	$0.860504\pi$
$822$	−13.7082	−	9.95959i	−0.478129	−	0.347381i
$823$	−0.0278640	−	0.0857567i	−0.000971280	−	0.00298929i	0.950570	−	0.310511i	$-0.100500\pi$
$823$	−0.0278640	−	0.0857567i	−0.000971280	−	0.00298929i	−0.951541	+	0.307522i	$0.900500\pi$
$824$	7.23607	+	5.25731i	0.252080	+	0.183147i
$825$	5.16312	−	3.75123i	0.179757	−	0.130601i
$826$	−9.63525	+	29.6543i	−0.335253	+	1.03180i
$827$	−14.1180	+	10.2574i	−0.490932	+	0.356683i	−0.805543	−	0.592538i	$-0.798126\pi$
$827$	−14.1180	+	10.2574i	−0.490932	+	0.356683i	0.314611	+	0.949221i	$0.398126\pi$
$828$	2.61803	+	8.05748i	0.0909830	+	0.280017i
$829$	−13.7984	−	42.4670i	−0.479237	−	1.47494i	−0.840157	−	0.542344i	$-0.817537\pi$
$829$	−13.7984	−	42.4670i	−0.479237	−	1.47494i	0.360919	−	0.932597i	$-0.382463\pi$
$830$	1.23607	−	3.80423i	0.0429045	−	0.132047i
$831$	14.1803			0.491911
$832$	0.763932			0.0264846
$833$	9.70820	−	29.8788i	0.336369	−	1.03524i
$834$	3.85410	+	2.80017i	0.133457	+	0.0969619i
$835$	10.0000	−	7.26543i	0.346064	−	0.251430i
$836$	−3.41641			−0.118159
$837$	5.28115	−	1.76336i	0.182543	−	0.0609505i
$838$	−26.9787			−0.931964
$839$	−25.8885	+	18.8091i	−0.893772	+	0.649363i	−0.936859	−	0.349708i	$-0.886281\pi$
$839$	−25.8885	+	18.8091i	−0.893772	+	0.649363i	0.0430869	+	0.999071i	$0.486281\pi$
$840$	−1.92705	−	1.40008i	−0.0664896	−	0.0483075i
$841$	−8.15248	+	25.0907i	−0.281120	+	0.865198i
$842$	16.9443			0.583938
$843$	−17.8885			−0.616114
$844$	−3.61803	+	11.1352i	−0.124538	+	0.383288i
$845$	2.37132	+	7.29818i	0.0815760	+	0.251065i
$846$	0.472136	+	1.45309i	0.0162324	+	0.0499581i
$847$	28.3435	−	20.5927i	0.973893	−	0.707575i
$848$	0.736068	−	2.26538i	0.0252767	−	0.0777936i
$849$	−26.1803	+	19.0211i	−0.898507	+	0.652804i
$850$	−14.9443	−	10.8576i	−0.512584	−	0.372414i
$851$	17.7082	+	54.5002i	0.607029	+	1.86824i
$852$	1.61803	+	1.17557i	0.0554329	+	0.0402744i
$853$	23.4721	+	17.0535i	0.803671	+	0.583901i	0.911989	−	0.410215i	$-0.134546\pi$
$853$	23.4721	+	17.0535i	0.803671	+	0.583901i	−0.108318	+	0.994116i	$0.534546\pi$
$854$	13.3820	+	41.1855i	0.457921	+	1.40934i
$855$	−1.23607	−	0.898056i	−0.0422726	−	0.0307129i
$856$	−15.8262	+	11.4984i	−0.540930	+	0.393008i
$857$	14.4377	−	44.4347i	0.493182	−	1.51786i	−0.326588	−	0.945167i	$-0.605899\pi$
$857$	14.4377	−	44.4347i	0.493182	−	1.51786i	0.819771	−	0.572692i	$-0.194101\pi$
$858$	0.854102	−	0.620541i	0.0291586	−	0.0211849i
$859$	−2.25735	−	6.94742i	−0.0770199	−	0.237043i	0.905133	−	0.425130i	$-0.139771\pi$
$859$	−2.25735	−	6.94742i	−0.0770199	−	0.237043i	−0.982152	+	0.188087i	$0.939771\pi$
$860$	1.38197	+	4.25325i	0.0471246	+	0.145035i
$861$	9.52786	−	29.3238i	0.324709	−	0.999351i
$862$	16.0000			0.544962
$863$	45.7771			1.55827			0.779135	−	0.626856i	$-0.215659\pi$
$863$	45.7771			1.55827			0.779135	+	0.626856i	$0.215659\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−4.13525	−	3.00444i	−0.140603	−	0.102154i
$866$	16.7361	−	12.1595i	0.568715	−	0.413195i
$867$	−1.00000			−0.0339618
$868$	−0.173762	−	21.4580i	−0.00589787	−	0.728333i
$869$	−15.6525			−0.530974
$870$	0.809017	−	0.587785i	0.0274282	−	0.0199278i
$871$	−6.76393	−	4.91428i	−0.229187	−	0.166514i
$872$	−1.23607	+	3.80423i	−0.0418585	+	0.128827i
$873$	−6.94427			−0.235028
$874$	20.9443			0.708451
$875$	7.07953	−	21.7885i	0.239332	−	0.736587i
$876$	−0.736068	−	2.26538i	−0.0248694	−	0.0765402i
$877$	−6.27051	−	19.2986i	−0.211740	−	0.651669i	−0.999369	−	0.0355191i	$-0.988692\pi$
$877$	−6.27051	−	19.2986i	−0.211740	−	0.651669i	0.787629	−	0.616150i	$-0.211308\pi$
$878$	22.1074	−	16.0620i	0.746088	−	0.542065i
$879$	−0.145898	+	0.449028i	−0.00492102	+	0.0151453i
$880$	0.690983	−	0.502029i	0.0232930	−	0.0169234i
$881$	−9.32624	−	6.77591i	−0.314209	−	0.228286i	0.419491	−	0.907759i	$-0.362208\pi$
$881$	−9.32624	−	6.77591i	−0.314209	−	0.228286i	−0.733700	+	0.679473i	$0.762208\pi$
$882$	−2.42705	−	7.46969i	−0.0817231	−	0.251518i
$883$	27.0902	+	19.6822i	0.911657	+	0.662357i	0.941433	−	0.337199i	$-0.109480\pi$
$883$	27.0902	+	19.6822i	0.911657	+	0.662357i	−0.0297765	+	0.999557i	$0.509480\pi$
$884$	−2.47214	−	1.79611i	−0.0831469	−	0.0604098i
$885$	−1.54508	−	4.75528i	−0.0519375	−	0.159847i
$886$	11.9271	+	8.66551i	0.400697	+	0.291123i
$887$	40.0689	−	29.1117i	1.34538	−	0.977477i	0.346154	−	0.938178i	$-0.387487\pi$
$887$	40.0689	−	29.1117i	1.34538	−	0.977477i	0.999227	−	0.0392991i	$-0.0125125\pi$
$888$	−2.09017	+	6.43288i	−0.0701415	+	0.215873i
$889$	24.6631	−	17.9188i	0.827174	−	0.600977i
$890$	0.562306	+	1.73060i	0.0188485	+	0.0580098i
$891$	0.427051	+	1.31433i	0.0143067	+	0.0440316i
$892$	8.71885	−	26.8339i	0.291929	−	0.898464i
$893$	3.77709			0.126395
$894$	15.3262			0.512586
$895$	1.10739	−	3.40820i	0.0370160	−	0.113924i
$896$	3.11803	+	2.26538i	0.104166	+	0.0756812i
$897$	−5.23607	+	3.80423i	−0.174827	+	0.127019i
$898$	−4.00000			−0.133482
$899$	8.59017	+	2.71441i	0.286498	+	0.0905307i
$900$	−4.61803			−0.153934
$901$	−7.70820	+	5.60034i	−0.256798	+	0.186574i
$902$	8.94427	+	6.49839i	0.297812	+	0.216373i
$903$	−8.61803	+	26.5236i	−0.286790	+	0.882650i
$904$	−12.1803			−0.405112
$905$	−4.29180			−0.142664
$906$	7.28115	−	22.4091i	0.241900	−	0.744492i
$907$	−9.41641	−	28.9807i	−0.312667	−	0.962289i	−0.976704	−	0.214590i	$-0.931159\pi$
$907$	−9.41641	−	28.9807i	−0.312667	−	0.962289i	0.664038	−	0.747699i	$-0.268841\pi$
$908$	3.48278	+	10.7189i	0.115580	+	0.355719i
$909$	−8.20820	+	5.96361i	−0.272249	+	0.197800i
$910$	0.562306	−	1.73060i	0.0186403	−	0.0573688i
$911$	−18.4721	+	13.4208i	−0.612009	+	0.444651i	−0.850121	−	0.526587i	$-0.823471\pi$
$911$	−18.4721	+	13.4208i	−0.612009	+	0.444651i	0.238112	+	0.971238i	$0.423471\pi$
$912$	2.00000	+	1.45309i	0.0662266	+	0.0481165i
$913$	2.76393	+	8.50651i	0.0914728	+	0.281524i
$914$	4.50000	+	3.26944i	0.148847	+	0.108144i
$915$	−5.61803	−	4.08174i	−0.185726	−	0.134938i
$916$	−4.76393	−	14.6619i	−0.157405	−	0.484442i
$917$	−53.1140	−	38.5896i	−1.75398	−	1.27434i
$918$	3.23607	−	2.35114i	0.106806	−	0.0775992i
$919$	8.00000	−	24.6215i	0.263896	−	0.812187i	−0.728050	−	0.685524i	$-0.759573\pi$
$919$	8.00000	−	24.6215i	0.263896	−	0.812187i	0.991946	−	0.126663i	$-0.0404268\pi$
$920$	−4.23607	+	3.07768i	−0.139659	+	0.101468i
$921$	0.145898	+	0.449028i	0.00480750	+	0.0147960i
$922$	−2.97214	−	9.14729i	−0.0978821	−	0.301250i
$923$	−0.472136	+	1.45309i	−0.0155405	+	0.0478289i
$924$	5.32624			0.175220
$925$	−31.2361			−1.02704
$926$	−5.23607	+	16.1150i	−0.172068	+	0.529570i
$927$	−7.23607	−	5.25731i	−0.237664	−	0.172673i
$928$	−1.30902	+	0.951057i	−0.0429706	+	0.0312200i
$929$	1.23607			0.0405541			0.0202770	−	0.999794i	$-0.493545\pi$
$929$	1.23607			0.0405541			0.0202770	+	0.999794i	$0.493545\pi$
$930$	2.04508	+	2.76741i	0.0670610	+	0.0907470i
$931$	−19.4164			−0.636347
$932$	−18.0902	+	13.1433i	−0.592563	+	0.430522i
$933$	23.5623	+	17.1190i	0.771395	+	0.560451i
$934$	12.9721	−	39.9241i	0.424461	−	1.30636i
$935$	−3.41641			−0.111728
$936$	−0.763932			−0.0249699
$937$	−4.38854	+	13.5065i	−0.143367	+	0.441240i	−0.996797	−	0.0799678i	$-0.974518\pi$
$937$	−4.38854	+	13.5065i	−0.143367	+	0.441240i	0.853430	+	0.521208i	$0.174518\pi$
$938$	−13.0344	−	40.1159i	−0.425590	−	1.30983i
$939$	1.67376	+	5.15131i	0.0546212	+	0.168107i
$940$	−0.763932	+	0.555029i	−0.0249167	+	0.0181031i
$941$	1.73607	−	5.34307i	0.0565942	−	0.174179i	−0.918764	−	0.394808i	$-0.870811\pi$
$941$	1.73607	−	5.34307i	0.0565942	−	0.174179i	0.975358	+	0.220629i	$0.0708110\pi$
$942$	18.7984	−	13.6578i	0.612484	−	0.444996i
$943$	−54.8328	−	39.8384i	−1.78560	−	1.29732i
$944$	2.50000	+	7.69421i	0.0813681	+	0.250425i
$945$	1.92705	+	1.40008i	0.0626870	+	0.0455448i
$946$	−8.09017	−	5.87785i	−0.263034	−	0.191105i
$947$	−10.3885	−	31.9727i	−0.337582	−	1.03897i	−0.965436	−	0.260640i	$-0.916066\pi$
$947$	−10.3885	−	31.9727i	−0.337582	−	1.03897i	0.627854	−	0.778331i	$-0.283934\pi$
$948$	9.16312	+	6.65740i	0.297604	+	0.216222i
$949$	1.47214	−	1.06957i	0.0477876	−	0.0347197i
$950$	−3.52786	+	10.8576i	−0.114459	+	0.352269i
$951$	−19.7984	+	14.3844i	−0.642006	+	0.466445i
$952$	−4.76393	−	14.6619i	−0.154400	−	0.475194i
$953$	−16.8328	−	51.8061i	−0.545268	−	1.67816i	−0.720351	−	0.693610i	$-0.756019\pi$
$953$	−16.8328	−	51.8061i	−0.545268	−	1.67816i	0.175083	−	0.984554i	$-0.443981\pi$
$954$	−0.736068	+	2.26538i	−0.0238311	+	0.0733445i
$955$	−5.12461			−0.165829
$956$	−24.6525			−0.797318
$957$	−0.690983	+	2.12663i	−0.0223363	+	0.0687441i
$958$	4.61803	+	3.35520i	0.149202	+	0.108402i
$959$	52.8328	−	38.3853i	1.70606	−	1.23953i
$960$	−0.618034			−0.0199470
$961$	−9.10081	+	29.6340i	−0.293575	+	0.955936i
$962$	−5.16718			−0.166597
$963$	15.8262	−	11.4984i	0.509993	−	0.370532i
$964$	15.2082	+	11.0494i	0.489823	+	0.355877i
$965$	1.51064	−	4.64928i	0.0486293	−	0.149666i
$966$	−32.6525			−1.05058
$967$	16.9443			0.544891			0.272446	−	0.962171i	$-0.412168\pi$
$967$	16.9443			0.544891			0.272446	+	0.962171i	$0.412168\pi$
$968$	2.80902	−	8.64527i	0.0902852	−	0.277869i
$969$	−3.05573	−	9.40456i	−0.0981641	−	0.302118i
$970$	−1.32624	−	4.08174i	−0.0425829	−	0.131057i
$971$	−28.7254	+	20.8702i	−0.921843	+	0.669758i	−0.943982	−	0.329997i	$-0.892952\pi$
$971$	−28.7254	+	20.8702i	−0.921843	+	0.669758i	0.0221393	+	0.999755i	$0.492952\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−14.8541	+	10.7921i	−0.476201	+	0.345980i
$974$	−5.23607	−	3.80423i	−0.167774	−	0.121895i
$975$	−1.09017	−	3.35520i	−0.0349134	−	0.107452i
$976$	9.09017	+	6.60440i	0.290969	+	0.211402i
$977$	23.3262	+	16.9475i	0.746272	+	0.542199i	0.894669	−	0.446729i	$-0.147411\pi$
$977$	23.3262	+	16.9475i	0.746272	+	0.542199i	−0.148397	+	0.988928i	$0.547411\pi$
$978$	−3.56231	−	10.9637i	−0.113910	−	0.350579i
$979$	−3.29180	−	2.39163i	−0.105206	−	0.0764368i
$980$	3.92705	−	2.85317i	0.125445	−	0.0911412i
$981$	1.23607	−	3.80423i	0.0394646	−	0.121460i
$982$	20.6525	−	15.0049i	0.659047	−	0.478826i
$983$	6.23607	+	19.1926i	0.198900	+	0.612150i	0.999909	+	0.0134983i	$0.00429676\pi$
$983$	6.23607	+	19.1926i	0.198900	+	0.612150i	−0.801009	+	0.598652i	$0.795703\pi$
$984$	−2.47214	−	7.60845i	−0.0788088	−	0.242549i
$985$	3.40983	−	10.4944i	0.108646	−	0.334379i
$986$	6.47214			0.206115
$987$	−5.88854			−0.187434
$988$	−0.583592	+	1.79611i	−0.0185665	+	0.0571419i
$989$	49.5967	+	36.0341i	1.57708	+	1.14582i
$990$	−0.690983	+	0.502029i	−0.0219609	+	0.0159555i
$991$	−22.5623			−0.716715			−0.358358	−	0.933584i	$-0.616663\pi$
$991$	−22.5623			−0.716715			−0.358358	+	0.933584i	$0.616663\pi$
$992$	−3.30902	−	4.47777i	−0.105061	−	0.142169i
$993$	26.8328			0.851514
$994$	−6.23607	+	4.53077i	−0.197796	+	0.143707i
$995$	−2.04508	−	1.48584i	−0.0648336	−	0.0471043i
$996$	2.00000	−	6.15537i	0.0633724	−	0.195040i
$997$	44.8328			1.41987			0.709935	−	0.704267i	$-0.248724\pi$
$997$	44.8328			1.41987			0.709935	+	0.704267i	$0.248724\pi$
$998$	−9.41641			−0.298071
$999$	2.09017	−	6.43288i	0.0661301	−	0.203527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.f.a.109.1	✓	4
3.2	odd	2		558.2.i.b.109.1		4
31.2	even	5	inner	186.2.f.a.157.1	yes	4
31.8	even	5		5766.2.a.q.1.1		2
31.23	odd	10		5766.2.a.m.1.1		2
93.2	odd	10		558.2.i.b.343.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.f.a.109.1	✓	4	1.1	even	1	trivial
186.2.f.a.157.1	yes	4	31.2	even	5	inner
558.2.i.b.109.1		4	3.2	odd	2
558.2.i.b.343.1		4	93.2	odd	10
5766.2.a.m.1.1		2	31.23	odd	10
5766.2.a.q.1.1		2	31.8	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -0.618034 q^{5} -1.00000 q^{6} +(1.19098 - 3.66547i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.500000 + 0.363271i) q^{10} +(0.427051 - 1.31433i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-0.618034 - 0.449028i) q^{13} +(-1.19098 - 3.66547i) q^{14} +(0.500000 + 0.363271i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.23607 + 3.80423i) q^{17} +(0.809017 + 0.587785i) q^{18} +(2.00000 - 1.45309i) q^{19} +(-0.190983 + 0.587785i) q^{20} +(-3.11803 + 2.26538i) q^{21} +(-0.427051 - 1.31433i) q^{22} +(2.61803 + 8.05748i) q^{23} +(-0.309017 + 0.951057i) q^{24} -4.61803 q^{25} -0.763932 q^{26} +(0.309017 - 0.951057i) q^{27} +(-3.11803 - 2.26538i) q^{28} +(1.30902 - 0.951057i) q^{29} +0.618034 q^{30} +(3.30902 + 4.47777i) q^{31} -1.00000 q^{32} +(-1.11803 + 0.812299i) q^{33} +(3.23607 + 2.35114i) q^{34} +(-0.736068 + 2.26538i) q^{35} +1.00000 q^{36} +6.76393 q^{37} +(0.763932 - 2.35114i) q^{38} +(0.236068 + 0.726543i) q^{39} +(0.190983 + 0.587785i) q^{40} +(-6.47214 + 4.70228i) q^{41} +(-1.19098 + 3.66547i) q^{42} +(5.85410 - 4.25325i) q^{43} +(-1.11803 - 0.812299i) q^{44} +(-0.190983 - 0.587785i) q^{45} +(6.85410 + 4.97980i) q^{46} +(1.23607 + 0.898056i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-6.35410 - 4.61653i) q^{49} +(-3.73607 + 2.71441i) q^{50} +(1.23607 - 3.80423i) q^{51} +(-0.618034 + 0.449028i) q^{52} +(0.736068 + 2.26538i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.263932 + 0.812299i) q^{55} -3.85410 q^{56} -2.47214 q^{57} +(0.500000 - 1.53884i) q^{58} +(-6.54508 - 4.75528i) q^{59} +(0.500000 - 0.363271i) q^{60} -11.2361 q^{61} +(5.30902 + 1.67760i) q^{62} +3.85410 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.381966 + 0.277515i) q^{65} +(-0.427051 + 1.31433i) q^{66} +10.9443 q^{67} +4.00000 q^{68} +(2.61803 - 8.05748i) q^{69} +(0.736068 + 2.26538i) q^{70} +(-0.618034 - 1.90211i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-0.736068 + 2.26538i) q^{73} +(5.47214 - 3.97574i) q^{74} +(3.73607 + 2.71441i) q^{75} +(-0.763932 - 2.35114i) q^{76} +(-4.30902 - 3.13068i) q^{77} +(0.618034 + 0.449028i) q^{78} +(-3.50000 - 10.7719i) q^{79} +(0.500000 + 0.363271i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.47214 + 7.60845i) q^{82} +(-5.23607 + 3.80423i) q^{83} +(1.19098 + 3.66547i) q^{84} +(-0.763932 - 2.35114i) q^{85} +(2.23607 - 6.88191i) q^{86} -1.61803 q^{87} -1.38197 q^{88} +(0.909830 - 2.80017i) q^{89} +(-0.500000 - 0.363271i) q^{90} +(-2.38197 + 1.73060i) q^{91} +8.47214 q^{92} +(-0.0450850 - 5.56758i) q^{93} +1.52786 q^{94} +(-1.23607 + 0.898056i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-2.14590 + 6.60440i) q^{97} -7.85410 q^{98} +1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + 2 q^{5} - 4 q^{6} + 7 q^{7} + q^{8} - q^{9} - 2 q^{10} - 5 q^{11} - q^{12} + 2 q^{13} - 7 q^{14} + 2 q^{15} - q^{16} - 4 q^{17} + q^{18} + 8 q^{19} - 3 q^{20} - 8 q^{21}+ \cdots + 10 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 2 * q^5 - 4 * q^6 + 7 * q^7 + q^8 - q^9 - 2 * q^10 - 5 * q^11 - q^12 + 2 * q^13 - 7 * q^14 + 2 * q^15 - q^16 - 4 * q^17 + q^18 + 8 * q^19 - 3 * q^20 - 8 * q^21 + 5 * q^22 + 6 * q^23 + q^24 - 14 * q^25 - 12 * q^26 - q^27 - 8 * q^28 + 3 * q^29 - 2 * q^30 + 11 * q^31 - 4 * q^32 + 4 * q^34 + 6 * q^35 + 4 * q^36 + 36 * q^37 + 12 * q^38 - 8 * q^39 + 3 * q^40 - 8 * q^41 - 7 * q^42 + 10 * q^43 - 3 * q^45 + 14 * q^46 - 4 * q^47 - q^48 - 12 * q^49 - 6 * q^50 - 4 * q^51 + 2 * q^52 - 6 * q^53 + q^54 - 10 * q^55 - 2 * q^56 + 8 * q^57 + 2 * q^58 - 15 * q^59 + 2 * q^60 - 36 * q^61 + 19 * q^62 + 2 * q^63 - q^64 + 6 * q^65 + 5 * q^66 + 8 * q^67 + 16 * q^68 + 6 * q^69 - 6 * q^70 + 2 * q^71 + q^72 + 6 * q^73 + 4 * q^74 + 6 * q^75 - 12 * q^76 - 15 * q^77 - 2 * q^78 - 14 * q^79 + 2 * q^80 - q^81 + 8 * q^82 - 12 * q^83 + 7 * q^84 - 12 * q^85 - 2 * q^87 - 10 * q^88 + 26 * q^89 - 2 * q^90 - 14 * q^91 + 16 * q^92 + 11 * q^93 + 24 * q^94 + 4 * q^95 + q^96 - 22 * q^97 - 18 * q^98 + 10 * q^99

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