LMFDB - Embedded newform 186.2.f.c.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 = [8,-2,2] 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.9240015625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 6x^{6} + 6x^{5} + 69x^{4} + 98x^{3} + 664x^{2} + 704x + 1936 $ x^8 - 3x^7 + 6x^6 + 6x^5 + 69x^4 + 98x^3 + 664x^2 + 704*x + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			109.1
Root			$-0.585709 - 1.80263i$ of defining polynomial
Character	$\chi$	$=$	186.109
Dual form			186.2.f.c.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} -2.51343 q^{5} -1.00000 q^{6} +(-1.13868 + 3.50450i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(2.03341 - 1.47736i) q^{10} +(-1.39473 + 4.29252i) q^{11} +(0.809017 - 0.587785i) q^{12} +(3.15144 + 2.28965i) q^{13} +(-1.13868 - 3.50450i) q^{14} +(-2.03341 - 1.47736i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.17142 - 3.60525i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(2.53341 - 1.84063i) q^{19} +(-0.776692 + 2.39041i) q^{20} +(-2.98110 + 2.16590i) q^{21} +(-1.39473 - 4.29252i) q^{22} +(0.618034 + 1.90211i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.31732 q^{25} -3.89539 q^{26} +(-0.309017 + 0.951057i) q^{27} +(2.98110 + 2.16590i) q^{28} +(0.256714 - 0.186513i) q^{29} +2.51343 q^{30} +(-5.11978 - 2.18811i) q^{31} +1.00000 q^{32} +(-3.65144 + 2.65293i) q^{33} +(3.06681 + 2.22817i) q^{34} +(2.86199 - 8.80829i) q^{35} +1.00000 q^{36} +4.49007 q^{37} +(-0.967675 + 2.97820i) q^{38} +(1.20374 + 3.70474i) q^{39} +(-0.776692 - 2.39041i) q^{40} +(4.96220 - 3.60525i) q^{41} +(1.13868 - 3.50450i) q^{42} +(6.18376 - 4.49277i) q^{43} +(3.65144 + 2.65293i) q^{44} +(-0.776692 - 2.39041i) q^{45} +(-1.61803 - 1.17557i) q^{46} +(10.0290 + 7.28650i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-5.32178 - 3.86650i) q^{49} +(-1.06573 + 0.774299i) q^{50} +(1.17142 - 3.60525i) q^{51} +(3.15144 - 2.28965i) q^{52} +(-0.926639 - 2.85190i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(3.50554 - 10.7889i) q^{55} -3.68484 q^{56} +3.13146 q^{57} +(-0.0980558 + 0.301785i) q^{58} +(-2.36132 - 1.71560i) q^{59} +(-2.03341 + 1.47736i) q^{60} -12.3718 q^{61} +(5.42813 - 1.23911i) q^{62} -3.68484 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.92091 - 5.75488i) q^{65} +(1.39473 - 4.29252i) q^{66} +11.2651 q^{67} -3.79079 q^{68} +(-0.618034 + 1.90211i) q^{69} +(2.86199 + 8.80829i) q^{70} +(4.98556 + 15.3440i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-4.73607 + 14.5761i) q^{73} +(-3.63254 + 2.63920i) q^{74} +(1.06573 + 0.774299i) q^{75} +(-0.967675 - 2.97820i) q^{76} +(-13.4550 - 9.77562i) q^{77} +(-3.15144 - 2.28965i) q^{78} +(2.17034 + 6.67961i) q^{79} +(2.03341 + 1.47736i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.89539 + 5.83342i) q^{82} +(11.7082 - 8.50651i) q^{83} +(1.13868 + 3.50450i) q^{84} +(2.94427 + 9.06154i) q^{85} +(-2.36199 + 7.26945i) q^{86} +0.317315 q^{87} -4.51343 q^{88} +(1.74949 - 5.38439i) q^{89} +(2.03341 + 1.47736i) q^{90} +(-11.6126 + 8.43702i) q^{91} +2.00000 q^{92} +(-2.85585 - 4.77955i) q^{93} -12.3965 q^{94} +(-6.36753 + 4.62628i) q^{95} +(0.809017 + 0.587785i) q^{96} +(1.69032 - 5.20226i) q^{97} +6.57808 q^{98} -4.51343 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 7 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 7 q^{14} - 2 q^{15} - 2 q^{16} + 6 q^{17} - 2 q^{18} + 6 q^{19} - 3 q^{20}+ \cdots - 14 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 7 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 7 * q^14 - 2 * q^15 - 2 * q^16 + 6 * q^17 - 2 * q^18 + 6 * q^19 - 3 * q^20 - 3 * q^21 + q^22 - 4 * q^23 + 2 * q^24 + 22 * q^25 - 18 * q^26 + 2 * q^27 + 3 * q^28 - 9 * q^29 - 2 * q^30 - 18 * q^31 + 8 * q^32 - 6 * q^33 - 4 * q^34 + 24 * q^35 + 8 * q^36 + 30 * q^37 - 9 * q^38 - 7 * q^39 - 3 * q^40 - 2 * q^41 + 7 * q^42 + 25 * q^43 + 6 * q^44 - 3 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 - 17 * q^49 + 7 * q^50 - 6 * q^51 + 2 * q^52 - 6 * q^53 + 2 * q^54 - 22 * q^55 + 8 * q^56 - 6 * q^57 + 16 * q^58 - 21 * q^59 - 2 * q^60 + 2 * q^61 + 17 * q^62 + 8 * q^63 - 2 * q^64 - 8 * q^65 - q^66 + 2 * q^67 - 4 * q^68 + 4 * q^69 + 24 * q^70 - 18 * q^71 - 2 * q^72 - 20 * q^73 + 15 * q^74 - 7 * q^75 - 9 * q^76 - 37 * q^77 - 2 * q^78 + 15 * q^79 + 2 * q^80 - 2 * q^81 - 2 * q^82 + 40 * q^83 + 7 * q^84 - 48 * q^85 - 20 * q^86 + 14 * q^87 - 14 * q^88 - 26 * q^89 + 2 * q^90 - 41 * q^91 + 16 * q^92 + 18 * q^93 + 20 * q^94 - 2 * q^95 + 2 * q^96 + 19 * q^97 + 28 * q^98 - 14 * 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
$5$	−2.51343			−1.12404			−0.562019	−	0.827124i	$-0.689975\pi$
$5$	−2.51343			−1.12404			−0.562019	+	0.827124i	$0.689975\pi$
$6$	−1.00000			−0.408248
$7$	−1.13868	+	3.50450i	−0.430380	+	1.32457i	0.467367	+	0.884064i	$0.345203\pi$
$7$	−1.13868	+	3.50450i	−0.430380	+	1.32457i	−0.897747	+	0.440511i	$0.854797\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	2.03341	−	1.47736i	0.643019	−	0.467181i
$11$	−1.39473	+	4.29252i	−0.420526	+	1.29424i	0.486689	+	0.873576i	$0.338205\pi$
$11$	−1.39473	+	4.29252i	−0.420526	+	1.29424i	−0.907214	+	0.420669i	$0.861795\pi$
$12$	0.809017	−	0.587785i	0.233543	−	0.169679i
$13$	3.15144	+	2.28965i	0.874052	+	0.635036i	0.931671	−	0.363303i	$-0.118351\pi$
$13$	3.15144	+	2.28965i	0.874052	+	0.635036i	−0.0576192	+	0.998339i	$0.518351\pi$
$14$	−1.13868	−	3.50450i	−0.304325	−	0.936616i
$15$	−2.03341	−	1.47736i	−0.525023	−	0.381452i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.17142	−	3.60525i	−0.284110	−	0.874402i	−0.986664	−	0.162771i	$-0.947957\pi$
$17$	−1.17142	−	3.60525i	−0.284110	−	0.874402i	0.702553	−	0.711631i	$-0.252043\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	2.53341	−	1.84063i	0.581203	−	0.422269i	−0.257955	−	0.966157i	$-0.583048\pi$
$19$	2.53341	−	1.84063i	0.581203	−	0.422269i	0.839158	+	0.543888i	$0.183048\pi$
$20$	−0.776692	+	2.39041i	−0.173674	+	0.534512i
$21$	−2.98110	+	2.16590i	−0.650530	+	0.472638i
$22$	−1.39473	−	4.29252i	−0.297357	−	0.915169i
$23$	0.618034	+	1.90211i	0.128869	+	0.396618i	0.994586	−	0.103916i	$-0.0331372\pi$
$23$	0.618034	+	1.90211i	0.128869	+	0.396618i	−0.865717	+	0.500534i	$0.833137\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	1.31732			0.263463
$26$	−3.89539			−0.763949
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	2.98110	+	2.16590i	0.563375	+	0.409316i
$29$	0.256714	−	0.186513i	0.0476705	−	0.0346346i	−0.563695	−	0.825983i	$-0.690621\pi$
$29$	0.256714	−	0.186513i	0.0476705	−	0.0346346i	0.611365	+	0.791348i	$0.290621\pi$
$30$	2.51343			0.458887
$31$	−5.11978	−	2.18811i	−0.919540	−	0.392997i
$31$	−5.11978	−	2.18811i	−0.919540	−	0.392997i
$32$	1.00000			0.176777
$33$	−3.65144	+	2.65293i	−0.635634	+	0.461815i
$34$	3.06681	+	2.22817i	0.525954	+	0.382128i
$35$	2.86199	−	8.80829i	0.483764	−	1.48887i
$36$	1.00000			0.166667
$37$	4.49007			0.738163			0.369081	−	0.929397i	$-0.379672\pi$
$37$	4.49007			0.738163			0.369081	+	0.929397i	$0.379672\pi$
$38$	−0.967675	+	2.97820i	−0.156978	+	0.483127i
$39$	1.20374	+	3.70474i	0.192753	+	0.593233i
$40$	−0.776692	−	2.39041i	−0.122806	−	0.377957i
$41$	4.96220	−	3.60525i	0.774966	−	0.563046i	−0.128498	−	0.991710i	$-0.541016\pi$
$41$	4.96220	−	3.60525i	0.774966	−	0.563046i	0.903464	+	0.428664i	$0.141016\pi$
$42$	1.13868	−	3.50450i	0.175702	−	0.540755i
$43$	6.18376	−	4.49277i	0.943015	−	0.685141i	−0.00612934	−	0.999981i	$-0.501951\pi$
$43$	6.18376	−	4.49277i	0.943015	−	0.685141i	0.949145	+	0.314841i	$0.101951\pi$
$44$	3.65144	+	2.65293i	0.550475	+	0.399944i
$45$	−0.776692	−	2.39041i	−0.115782	−	0.356341i
$46$	−1.61803	−	1.17557i	−0.238566	−	0.173328i
$47$	10.0290	+	7.28650i	1.46288	+	1.06285i	0.982601	+	0.185732i	$0.0594655\pi$
$47$	10.0290	+	7.28650i	1.46288	+	1.06285i	0.480281	+	0.877114i	$0.340535\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−5.32178	−	3.86650i	−0.760254	−	0.552357i
$50$	−1.06573	+	0.774299i	−0.150717	+	0.109502i
$51$	1.17142	−	3.60525i	0.164031	−	0.504836i
$52$	3.15144	−	2.28965i	0.437026	−	0.317518i
$53$	−0.926639	−	2.85190i	−0.127284	−	0.391739i	0.867027	−	0.498262i	$-0.166028\pi$
$53$	−0.926639	−	2.85190i	−0.127284	−	0.391739i	−0.994310	+	0.106523i	$0.966028\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	3.50554	−	10.7889i	0.472687	−	1.45478i
$56$	−3.68484			−0.492408
$57$	3.13146			0.414772
$58$	−0.0980558	+	0.301785i	−0.0128754	+	0.0396263i
$59$	−2.36132	−	1.71560i	−0.307418	−	0.223352i	0.423370	−	0.905957i	$-0.360847\pi$
$59$	−2.36132	−	1.71560i	−0.307418	−	0.223352i	−0.730788	+	0.682605i	$0.760847\pi$
$60$	−2.03341	+	1.47736i	−0.262511	+	0.190726i
$61$	−12.3718			−1.58405			−0.792026	−	0.610487i	$-0.790974\pi$
$61$	−12.3718			−1.58405			−0.792026	+	0.610487i	$0.790974\pi$
$62$	5.42813	−	1.23911i	0.689373	−	0.157367i
$63$	−3.68484			−0.464247
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−7.92091	−	5.75488i	−0.982468	−	0.713805i
$66$	1.39473	−	4.29252i	0.171679	−	0.528373i
$67$	11.2651			1.37625			0.688124	−	0.725593i	$-0.258434\pi$
$67$	11.2651			1.37625			0.688124	+	0.725593i	$0.258434\pi$
$68$	−3.79079			−0.459700
$69$	−0.618034	+	1.90211i	−0.0744025	+	0.228988i
$70$	2.86199	+	8.80829i	0.342073	+	1.05279i
$71$	4.98556	+	15.3440i	0.591677	+	1.82100i	0.570615	+	0.821218i	$0.306705\pi$
$71$	4.98556	+	15.3440i	0.591677	+	1.82100i	0.0210627	+	0.999778i	$0.493295\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	−4.73607	+	14.5761i	−0.554315	+	1.70601i	0.143431	+	0.989660i	$0.454186\pi$
$73$	−4.73607	+	14.5761i	−0.554315	+	1.70601i	−0.697746	+	0.716345i	$0.745814\pi$
$74$	−3.63254	+	2.63920i	−0.422274	+	0.306800i
$75$	1.06573	+	0.774299i	0.123060	+	0.0894083i
$76$	−0.967675	−	2.97820i	−0.111000	−	0.341623i
$77$	−13.4550	−	9.77562i	−1.53334	−	1.11404i
$78$	−3.15144	−	2.28965i	−0.356830	−	0.259252i
$79$	2.17034	+	6.67961i	0.244182	+	0.751515i	0.995770	+	0.0918821i	$0.0292883\pi$
$79$	2.17034	+	6.67961i	0.244182	+	0.751515i	−0.751588	+	0.659633i	$0.770712\pi$
$80$	2.03341	+	1.47736i	0.227342	+	0.165173i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−1.89539	+	5.83342i	−0.209311	+	0.644193i
$83$	11.7082	−	8.50651i	1.28514	−	0.933711i	0.285447	−	0.958394i	$-0.407858\pi$
$83$	11.7082	−	8.50651i	1.28514	−	0.933711i	0.999695	+	0.0246839i	$0.00785793\pi$
$84$	1.13868	+	3.50450i	0.124240	+	0.382372i
$85$	2.94427	+	9.06154i	0.319351	+	0.982862i
$86$	−2.36199	+	7.26945i	−0.254700	+	0.783885i
$87$	0.317315			0.0340198
$88$	−4.51343			−0.481133
$89$	1.74949	−	5.38439i	0.185446	−	0.570744i	−0.814510	−	0.580150i	$-0.802994\pi$
$89$	1.74949	−	5.38439i	0.185446	−	0.570744i	0.999956	+	0.00940558i	$0.00299393\pi$
$90$	2.03341	+	1.47736i	0.214340	+	0.155727i
$91$	−11.6126	+	8.43702i	−1.21733	+	0.884440i
$92$	2.00000			0.208514
$93$	−2.85585	−	4.77955i	−0.296138	−	0.495617i
$94$	−12.3965			−1.27861
$95$	−6.36753	+	4.62628i	−0.653295	+	0.474646i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	1.69032	−	5.20226i	0.171626	−	0.528209i	−0.827838	−	0.560968i	$-0.810429\pi$
$97$	1.69032	−	5.20226i	0.171626	−	0.528209i	0.999463	+	0.0327585i	$0.0104292\pi$
$98$	6.57808			0.664486
$99$	−4.51343			−0.453616
$100$	0.407073	−	1.25284i	0.0407073	−	0.125284i
$101$	2.36921	+	7.29167i	0.235745	+	0.725548i	0.997022	+	0.0771211i	$0.0245728\pi$
$101$	2.36921	+	7.29167i	0.235745	+	0.725548i	−0.761277	+	0.648427i	$0.775427\pi$
$102$	1.17142	+	3.60525i	0.115988	+	0.356973i
$103$	−9.76400	+	7.09396i	−0.962076	+	0.698989i	−0.953632	−	0.300975i	$-0.902688\pi$
$103$	−9.76400	+	7.09396i	−0.962076	+	0.698989i	−0.00844380	+	0.999964i	$0.502688\pi$
$104$	−1.20374	+	3.70474i	−0.118037	+	0.363280i
$105$	7.49278	−	5.44382i	0.731221	−	0.531263i
$106$	2.42597	+	1.76257i	0.235631	+	0.171196i
$107$	−2.26326	−	6.96561i	−0.218798	−	0.673391i	−0.998862	−	0.0476915i	$-0.984814\pi$
$107$	−2.26326	−	6.96561i	−0.218798	−	0.673391i	0.780064	−	0.625700i	$-0.215186\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	−13.5947	−	9.87716i	−1.30214	−	0.946060i	−0.302166	−	0.953255i	$-0.597710\pi$
$109$	−13.5947	−	9.87716i	−1.30214	−	0.946060i	−0.999974	+	0.00719492i	$0.997710\pi$
$110$	3.50554	+	10.7889i	0.334240	+	1.02869i
$111$	3.63254	+	2.63920i	0.344786	+	0.250501i
$112$	2.98110	−	2.16590i	0.281688	−	0.204658i
$113$	−1.76393	+	5.42882i	−0.165937	+	0.510701i	−0.999104	−	0.0423201i	$-0.986525\pi$
$113$	−1.76393	+	5.42882i	−0.165937	+	0.510701i	0.833167	+	0.553021i	$0.186525\pi$
$114$	−2.53341	+	1.84063i	−0.237275	+	0.172390i
$115$	−1.55338	−	4.78082i	−0.144854	−	0.445814i
$116$	−0.0980558	−	0.301785i	−0.00910426	−	0.0280200i
$117$	−1.20374	+	3.70474i	−0.111286	+	0.342503i
$118$	2.91875			0.268693
$119$	13.9685			1.28049
$120$	0.776692	−	2.39041i	0.0709019	−	0.218214i
$121$	−7.58132	−	5.50815i	−0.689211	−	0.500741i
$122$	10.0090	−	7.27199i	0.906175	−	0.658375i
$123$	6.13362			0.553050
$124$	−3.66312	+	4.19304i	−0.328958	+	0.376546i
$125$	9.25616			0.827896
$126$	2.98110	−	2.16590i	0.265578	−	0.192953i
$127$	−11.9849	−	8.70754i	−1.06349	−	0.772669i	−0.0887571	−	0.996053i	$-0.528289\pi$
$127$	−11.9849	−	8.70754i	−1.06349	−	0.772669i	−0.974730	+	0.223384i	$0.928289\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	7.64355			0.672977
$130$	9.79079			0.858709
$131$	5.39201	−	16.5949i	0.471102	−	1.44990i	−0.380041	−	0.924970i	$-0.624090\pi$
$131$	5.39201	−	16.5949i	0.471102	−	1.44990i	0.851143	−	0.524934i	$-0.175910\pi$
$132$	1.39473	+	4.29252i	0.121395	+	0.373616i
$133$	3.56573	+	10.9742i	0.309188	+	0.951583i
$134$	−9.11364	+	6.62145i	−0.787299	+	0.572006i
$135$	0.776692	−	2.39041i	0.0668470	−	0.205734i
$136$	3.06681	−	2.22817i	0.262977	−	0.191064i
$137$	−3.23607	−	2.35114i	−0.276476	−	0.200872i	0.440903	−	0.897555i	$-0.354658\pi$
$137$	−3.23607	−	2.35114i	−0.276476	−	0.200872i	−0.717379	+	0.696683i	$0.754658\pi$
$138$	−0.618034	−	1.90211i	−0.0526105	−	0.161919i
$139$	6.97671	+	5.06888i	0.591757	+	0.429937i	0.842943	−	0.538002i	$-0.180821\pi$
$139$	6.97671	+	5.06888i	0.591757	+	0.429937i	−0.251187	+	0.967939i	$0.580821\pi$
$140$	−7.49278	−	5.44382i	−0.633256	−	0.460087i
$141$	3.83074	+	11.7898i	0.322607	+	0.992881i
$142$	−13.0524	−	9.48310i	−1.09533	−	0.795804i
$143$	−14.2238	+	10.3342i	−1.18945	+	0.864188i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−0.645231	+	0.468788i	−0.0535835	+	0.0389307i
$146$	−4.73607	−	14.5761i	−0.391960	−	1.20633i
$147$	−2.03274	−	6.25612i	−0.167657	−	0.515996i
$148$	1.38751	−	4.27031i	0.114052	−	0.351017i
$149$	−12.4977			−1.02385			−0.511924	−	0.859031i	$-0.671067\pi$
$149$	−12.4977			−1.02385			−0.511924	+	0.859031i	$0.671067\pi$
$150$	−1.31732			−0.107558
$151$	−3.13868	+	9.65986i	−0.255422	+	0.786108i	0.738324	+	0.674446i	$0.235618\pi$
$151$	−3.13868	+	9.65986i	−0.255422	+	0.786108i	−0.993746	+	0.111662i	$0.964382\pi$
$152$	2.53341	+	1.84063i	0.205486	+	0.149295i
$153$	3.06681	−	2.22817i	0.247937	−	0.180137i
$154$	16.6313			1.34019
$155$	12.8682	+	5.49966i	1.03360	+	0.441744i
$156$	3.89539			0.311881
$157$	18.4812	−	13.4274i	1.47496	−	1.07162i	0.495820	−	0.868426i	$-0.334868\pi$
$157$	18.4812	−	13.4274i	1.47496	−	1.07162i	0.979138	−	0.203194i	$-0.0651323\pi$
$158$	−5.68202	−	4.12823i	−0.452037	−	0.328424i
$159$	0.926639	−	2.85190i	0.0734872	−	0.226170i
$160$	−2.51343			−0.198704
$161$	−7.36969			−0.580813
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	−1.15144	−	3.54377i	−0.0901877	−	0.277569i	0.895782	−	0.444494i	$-0.146616\pi$
$163$	−1.15144	−	3.54377i	−0.0901877	−	0.277569i	−0.985970	+	0.166925i	$0.946616\pi$
$164$	−1.89539	−	5.83342i	−0.148005	−	0.455514i
$165$	9.17763	−	6.66794i	0.714477	−	0.519098i
$166$	−4.47214	+	13.7638i	−0.347105	+	1.06828i
$167$	12.3029	−	8.93856i	0.952025	−	0.691687i	0.000740289	−	1.00000i	$-0.499764\pi$
$167$	12.3029	−	8.93856i	0.952025	−	0.691687i	0.951285	+	0.308313i	$0.0997644\pi$
$168$	−2.98110	−	2.16590i	−0.229997	−	0.167103i
$169$	0.671830	+	2.06768i	0.0516792	+	0.159052i
$170$	−7.70820	−	5.60034i	−0.591192	−	0.429526i
$171$	2.53341	+	1.84063i	0.193734	+	0.140756i
$172$	−2.36199	−	7.26945i	−0.180100	−	0.554290i
$173$	7.94156	+	5.76988i	0.603785	+	0.438676i	0.847221	−	0.531241i	$-0.178274\pi$
$173$	7.94156	+	5.76988i	0.603785	+	0.438676i	−0.243435	+	0.969917i	$0.578274\pi$
$174$	−0.256714	+	0.186513i	−0.0194614	+	0.0141395i
$175$	−1.50000	+	4.61653i	−0.113389	+	0.348977i
$176$	3.65144	−	2.65293i	0.275238	−	0.199972i
$177$	−0.901944	−	2.77590i	−0.0677943	−	0.208649i
$178$	1.74949	+	5.38439i	0.131130	+	0.403577i
$179$	−4.20482	+	12.9411i	−0.314283	+	0.967264i	0.661765	+	0.749711i	$0.269808\pi$
$179$	−4.20482	+	12.9411i	−0.314283	+	0.967264i	−0.976048	+	0.217553i	$0.930192\pi$
$180$	−2.51343			−0.187340
$181$	18.4569			1.37189			0.685944	−	0.727654i	$-0.259389\pi$
$181$	18.4569			1.37189			0.685944	+	0.727654i	$0.259389\pi$
$182$	4.43560	−	13.6514i	0.328789	−	1.01191i
$183$	−10.0090	−	7.27199i	−0.739889	−	0.537561i
$184$	−1.61803	+	1.17557i	−0.119283	+	0.0866642i
$185$	−11.2855			−0.829723
$186$	5.11978	+	2.18811i	0.375401	+	0.160440i
$187$	17.1094			1.25117
$188$	10.0290	−	7.28650i	0.731441	−	0.531423i
$189$	−2.98110	−	2.16590i	−0.216843	−	0.157546i
$190$	2.43218	−	7.48548i	0.176449	−	0.543054i
$191$	−0.768251			−0.0555887			−0.0277944	−	0.999614i	$-0.508848\pi$
$191$	−0.768251			−0.0555887			−0.0277944	+	0.999614i	$0.508848\pi$
$192$	−1.00000			−0.0721688
$193$	−2.96112	+	9.11340i	−0.213146	+	0.655997i	0.786134	+	0.618057i	$0.212080\pi$
$193$	−2.96112	+	9.11340i	−0.213146	+	0.655997i	−0.999280	+	0.0379405i	$0.987920\pi$
$194$	1.69032	+	5.20226i	0.121358	+	0.373500i
$195$	−3.02552	−	9.31159i	−0.216662	−	0.666817i
$196$	−5.32178	+	3.86650i	−0.380127	+	0.276178i
$197$	−2.86686	+	8.82329i	−0.204255	+	0.628634i	0.795488	+	0.605970i	$0.207215\pi$
$197$	−2.86686	+	8.82329i	−0.204255	+	0.628634i	−0.999743	+	0.0226639i	$0.992785\pi$
$198$	3.65144	−	2.65293i	0.259496	−	0.188535i
$199$	−10.6154	−	7.71253i	−0.752505	−	0.546727i	0.144097	−	0.989564i	$-0.453972\pi$
$199$	−10.6154	−	7.71253i	−0.752505	−	0.546727i	−0.896602	+	0.442837i	$0.853972\pi$
$200$	0.407073	+	1.25284i	0.0287844	+	0.0885893i
$201$	9.11364	+	6.62145i	0.642827	+	0.467041i
$202$	−6.20266	−	4.50650i	−0.436418	−	0.317076i
$203$	0.361320	+	1.11203i	0.0253597	+	0.0780492i
$204$	−3.06681	−	2.22817i	−0.214720	−	0.156003i
$205$	−12.4721	+	9.06154i	−0.871092	+	0.632885i
$206$	3.72952	−	11.4783i	0.259848	−	0.799729i
$207$	−1.61803	+	1.17557i	−0.112461	+	0.0817078i
$208$	−1.20374	−	3.70474i	−0.0834645	−	0.256877i
$209$	4.36753	+	13.4419i	0.302108	+	0.929794i
$210$	−2.86199	+	8.80829i	−0.197496	+	0.607830i
$211$	4.49007			0.309109			0.154554	−	0.987984i	$-0.450606\pi$
$211$	4.49007			0.309109			0.154554	+	0.987984i	$0.450606\pi$
$212$	−2.99867			−0.205949
$213$	−4.98556	+	15.3440i	−0.341605	+	1.05135i
$214$	5.92530	+	4.30499i	0.405045	+	0.294283i
$215$	−15.5424	+	11.2922i	−1.05999	+	0.770125i
$216$	−1.00000			−0.0680414
$217$	13.4980	−	15.4507i	0.916306	−	1.04886i
$218$	16.8040			1.13811
$219$	−12.3992	+	9.00854i	−0.837859	+	0.608740i
$220$	−9.17763	−	6.66794i	−0.618755	−	0.449552i
$221$	4.56313	−	14.0439i	0.306949	−	0.944693i
$222$	−4.49007			−0.301354
$223$	7.11904			0.476726			0.238363	−	0.971176i	$-0.423389\pi$
$223$	7.11904			0.476726			0.238363	+	0.971176i	$0.423389\pi$
$224$	−1.13868	+	3.50450i	−0.0760812	+	0.234154i
$225$	0.407073	+	1.25284i	0.0271382	+	0.0835228i
$226$	−1.76393	−	5.42882i	−0.117335	−	0.361120i
$227$	−18.6805	+	13.5721i	−1.23987	+	0.900815i	−0.997589	−	0.0693926i	$-0.977894\pi$
$227$	−18.6805	+	13.5721i	−1.23987	+	0.900815i	−0.242276	+	0.970207i	$0.577894\pi$
$228$	0.967675	−	2.97820i	0.0640858	−	0.197236i
$229$	11.1101	−	8.07200i	0.734179	−	0.533412i	−0.156704	−	0.987646i	$-0.550087\pi$
$229$	11.1101	−	8.07200i	0.734179	−	0.533412i	0.890883	+	0.454233i	$0.150087\pi$
$230$	4.06681	+	2.95471i	0.268158	+	0.194828i
$231$	−5.13935	−	15.8173i	−0.338144	−	1.04070i
$232$	0.256714	+	0.186513i	0.0168541	+	0.0122452i
$233$	−7.00565	−	5.08991i	−0.458956	−	0.333451i	0.334166	−	0.942514i	$-0.391545\pi$
$233$	−7.00565	−	5.08991i	−0.458956	−	0.333451i	−0.793121	+	0.609064i	$0.791545\pi$
$234$	−1.20374	−	3.70474i	−0.0786911	−	0.242186i
$235$	−25.2072	−	18.3141i	−1.64434	−	1.19468i
$236$	−2.36132	+	1.71560i	−0.153709	+	0.111676i
$237$	−2.17034	+	6.67961i	−0.140979	+	0.433887i
$238$	−11.3007	+	8.21045i	−0.732517	+	0.532205i
$239$	−4.21271	−	12.9654i	−0.272497	−	0.838661i	−0.989871	−	0.141972i	$-0.954656\pi$
$239$	−4.21271	−	12.9654i	−0.272497	−	0.838661i	0.717373	−	0.696689i	$-0.245344\pi$
$240$	0.776692	+	2.39041i	0.0501352	+	0.154300i
$241$	−0.899230	+	2.76755i	−0.0579245	+	0.178273i	−0.975832	−	0.218520i	$-0.929877\pi$
$241$	−0.899230	+	2.76755i	−0.0579245	+	0.178273i	0.917908	+	0.396793i	$0.129877\pi$
$242$	9.37102			0.602392
$243$	−1.00000			−0.0641500
$244$	−3.82311	+	11.7663i	−0.244750	+	0.753262i
$245$	13.3759	+	9.71816i	0.854555	+	0.620870i
$246$	−4.96220	+	3.60525i	−0.316379	+	0.229862i
$247$	12.1983			0.776157
$248$	0.498920	−	5.54537i	0.0316815	−	0.352131i
$249$	14.4721			0.917134
$250$	−7.48839	+	5.44063i	−0.473607	+	0.344096i
$251$	6.54899	+	4.75812i	0.413369	+	0.300330i	0.774964	−	0.632005i	$-0.217768\pi$
$251$	6.54899	+	4.75812i	0.413369	+	0.300330i	−0.361595	+	0.932335i	$0.617768\pi$
$252$	−1.13868	+	3.50450i	−0.0717301	+	0.220762i
$253$	−9.02685			−0.567513
$254$	14.8141			0.929522
$255$	−2.94427	+	9.06154i	−0.184377	+	0.567455i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.06815	−	18.6758i	−0.378520	−	1.16497i	−0.941073	−	0.338204i	$-0.890180\pi$
$257$	−6.06815	−	18.6758i	−0.378520	−	1.16497i	0.562552	−	0.826762i	$-0.309820\pi$
$258$	−6.18376	+	4.49277i	−0.384984	+	0.279708i
$259$	−5.11275	+	15.7354i	−0.317691	+	0.977751i
$260$	−7.92091	+	5.75488i	−0.491234	+	0.356902i
$261$	0.256714	+	0.186513i	0.0158902	+	0.0115449i
$262$	5.39201	+	16.5949i	0.333120	+	1.02524i
$263$	10.6036	+	7.70396i	0.653846	+	0.475047i	0.864579	−	0.502497i	$-0.167585\pi$
$263$	10.6036	+	7.70396i	0.653846	+	0.475047i	−0.210733	+	0.977544i	$0.567585\pi$
$264$	−3.65144	−	2.65293i	−0.224731	−	0.163276i
$265$	2.32904	+	7.16804i	0.143072	+	0.440329i
$266$	−9.33520	−	6.78242i	−0.572378	−	0.415857i
$267$	4.58024	−	3.32774i	0.280306	−	0.203654i
$268$	3.48110	−	10.7137i	0.212642	−	0.654445i
$269$	6.47869	−	4.70704i	0.395013	−	0.286993i	−0.372494	−	0.928035i	$-0.621497\pi$
$269$	6.47869	−	4.70704i	0.395013	−	0.286993i	0.767506	+	0.641041i	$0.221497\pi$
$270$	0.776692	+	2.39041i	0.0472679	+	0.145476i
$271$	1.09605	+	3.37331i	0.0665805	+	0.204914i	0.978812	−	0.204762i	$-0.0656419\pi$
$271$	1.09605	+	3.37331i	0.0665805	+	0.204914i	−0.912231	+	0.409675i	$0.865642\pi$
$272$	−1.17142	+	3.60525i	−0.0710276	+	0.218600i
$273$	−14.3539			−0.868739
$274$	4.00000			0.241649
$275$	−1.83729	+	5.65461i	−0.110793	+	0.340986i
$276$	1.61803	+	1.17557i	0.0973942	+	0.0707610i
$277$	24.5280	−	17.8206i	1.47374	−	1.07074i	0.494238	−	0.869326i	$-0.335447\pi$
$277$	24.5280	−	17.8206i	1.47374	−	1.07074i	0.979507	−	0.201412i	$-0.0645530\pi$
$278$	−8.62369			−0.517214
$279$	0.498920	−	5.54537i	0.0298696	−	0.331992i
$280$	9.26159			0.553486
$281$	−16.1227	+	11.7138i	−0.961798	+	0.698787i	−0.953568	−	0.301179i	$-0.902620\pi$
$281$	−16.1227	+	11.7138i	−0.961798	+	0.698787i	−0.00823063	+	0.999966i	$0.502620\pi$
$282$	−10.0290	−	7.28650i	−0.597219	−	0.433905i
$283$	5.19273	−	15.9816i	0.308676	−	0.950006i	−0.669604	−	0.742718i	$-0.733536\pi$
$283$	5.19273	−	15.9816i	0.308676	−	0.950006i	0.978280	−	0.207288i	$-0.0664638\pi$
$284$	16.1336			0.957354
$285$	−7.87070			−0.466220
$286$	5.43300	−	16.7211i	0.321260	−	0.988738i
$287$	6.98423	+	21.4952i	0.412266	+	1.26882i
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	2.12767	−	1.54584i	0.125157	−	0.0909318i
$290$	0.246456	−	0.758514i	0.0144724	−	0.0445415i
$291$	4.42530	−	3.21517i	0.259416	−	0.188477i
$292$	12.3992	+	9.00854i	0.725608	+	0.527185i
$293$	1.62019	+	4.98644i	0.0946527	+	0.291311i	0.987163	−	0.159716i	$-0.0510578\pi$
$293$	1.62019	+	4.98644i	0.0946527	+	0.291311i	−0.892510	+	0.451027i	$0.851058\pi$
$294$	5.32178	+	3.86650i	0.310372	+	0.225499i
$295$	5.93501	+	4.31203i	0.345549	+	0.251056i
$296$	1.38751	+	4.27031i	0.0806472	+	0.248207i
$297$	−3.65144	−	2.65293i	−0.211878	−	0.153938i
$298$	10.1108	−	7.34594i	0.585704	−	0.425539i
$299$	−2.40749	+	7.40948i	−0.139228	+	0.428501i
$300$	1.06573	−	0.774299i	0.0615300	−	0.0447041i
$301$	8.70356	+	26.7868i	0.501665	+	1.54397i
$302$	−3.13868	−	9.65986i	−0.180611	−	0.555863i
$303$	−2.36921	+	7.29167i	−0.136107	+	0.418895i
$304$	−3.13146			−0.179602
$305$	31.0957			1.78054
$306$	−1.17142	+	3.60525i	−0.0669655	+	0.206099i
$307$	−3.31854	−	2.41106i	−0.189399	−	0.137606i	0.489045	−	0.872259i	$-0.337345\pi$
$307$	−3.31854	−	2.41106i	−0.189399	−	0.137606i	−0.678444	+	0.734652i	$0.737345\pi$
$308$	−13.4550	+	9.77562i	−0.766669	+	0.557018i
$309$	−12.0690			−0.686580
$310$	−13.6432	+	3.11441i	−0.774882	+	0.176887i
$311$	−23.0490			−1.30699			−0.653495	−	0.756931i	$-0.726698\pi$
$311$	−23.0490			−1.30699			−0.653495	+	0.756931i	$0.726698\pi$
$312$	−3.15144	+	2.28965i	−0.178415	+	0.129626i
$313$	−18.7874	−	13.6498i	−1.06192	−	0.771533i	−0.0874810	−	0.996166i	$-0.527882\pi$
$313$	−18.7874	−	13.6498i	−1.06192	−	0.771533i	−0.974443	+	0.224633i	$0.927882\pi$
$314$	−7.05918	+	21.7259i	−0.398373	+	1.22606i
$315$	9.26159			0.521831
$316$	7.02336			0.395095
$317$	−0.301544	+	0.928056i	−0.0169364	+	0.0521248i	−0.959168	−	0.282839i	$-0.908724\pi$
$317$	−0.301544	+	0.928056i	−0.0169364	+	0.0521248i	0.942231	+	0.334963i	$0.108724\pi$
$318$	0.926639	+	2.85190i	0.0519633	+	0.159927i
$319$	0.442568	+	1.36208i	0.0247790	+	0.0762621i
$320$	2.03341	−	1.47736i	0.113671	−	0.0825867i
$321$	2.26326	−	6.96561i	0.126323	−	0.388783i
$322$	5.96220	−	4.33179i	0.332261	−	0.241401i
$323$	−9.60360	−	6.97742i	−0.534358	−	0.388234i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	4.15144	+	3.01620i	0.230280	+	0.167309i
$326$	3.01451	+	2.19017i	0.166958	+	0.121302i
$327$	−5.19273	−	15.9816i	−0.287159	−	0.883783i
$328$	4.96220	+	3.60525i	0.273992	+	0.199067i
$329$	−36.9554	+	26.8496i	−2.03741	+	1.48027i
$330$	−3.50554	+	10.7889i	−0.192974	+	0.593912i
$331$	−9.23607	+	6.71040i	−0.507660	+	0.368837i	−0.811935	−	0.583747i	$-0.801586\pi$
$331$	−9.23607	+	6.71040i	−0.507660	+	0.368837i	0.304275	+	0.952584i	$0.401586\pi$
$332$	−4.47214	−	13.7638i	−0.245440	−	0.755388i
$333$	1.38751	+	4.27031i	0.0760349	+	0.234011i
$334$	−4.69928	+	14.4629i	−0.257133	+	0.791375i
$335$	−28.3140			−1.54696
$336$	3.68484			0.201025
$337$	−0.389597	+	1.19906i	−0.0212227	+	0.0653168i	−0.961107	−	0.276176i	$-0.910933\pi$
$337$	−0.389597	+	1.19906i	−0.0212227	+	0.0653168i	0.939884	+	0.341493i	$0.110933\pi$
$338$	−1.75887	−	1.27790i	−0.0956701	−	0.0695084i
$339$	−4.61803	+	3.35520i	−0.250817	+	0.182229i
$340$	9.52786			0.516721
$341$	16.5332	−	18.9250i	0.895324	−	1.02484i
$342$	−3.13146			−0.169330
$343$	−1.25779	+	0.913840i	−0.0679145	+	0.0493427i
$344$	6.18376	+	4.49277i	0.333406	+	0.242234i
$345$	1.55338	−	4.78082i	0.0836313	−	0.257391i
$346$	−9.81631			−0.527728
$347$	5.74949			0.308649			0.154325	−	0.988020i	$-0.450680\pi$
$347$	5.74949			0.308649			0.154325	+	0.988020i	$0.450680\pi$
$348$	0.0980558	−	0.301785i	0.00525634	−	0.0161774i
$349$	−5.57254	−	17.1505i	−0.298291	−	0.918045i	−0.982096	−	0.188381i	$-0.939676\pi$
$349$	−5.57254	−	17.1505i	−0.298291	−	0.918045i	0.683805	−	0.729665i	$-0.260324\pi$
$350$	−1.50000	−	4.61653i	−0.0801784	−	0.246764i
$351$	−3.15144	+	2.28965i	−0.168211	+	0.122213i
$352$	−1.39473	+	4.29252i	−0.0743391	+	0.228792i
$353$	7.70820	−	5.60034i	0.410266	−	0.298076i	−0.363443	−	0.931616i	$-0.618399\pi$
$353$	7.70820	−	5.60034i	0.410266	−	0.298076i	0.773710	+	0.633540i	$0.218399\pi$
$354$	2.36132	+	1.71560i	0.125503	+	0.0911831i
$355$	−12.5308	−	38.5660i	−0.665068	−	2.04687i
$356$	−4.58024	−	3.32774i	−0.242752	−	0.176370i
$357$	11.3007	+	8.21045i	0.598097	+	0.434543i
$358$	−4.20482	−	12.9411i	−0.222232	−	0.683959i
$359$	2.20705	+	1.60352i	0.116484	+	0.0846305i	0.644502	−	0.764603i	$-0.277065\pi$
$359$	2.20705	+	1.60352i	0.116484	+	0.0846305i	−0.528018	+	0.849233i	$0.677065\pi$
$360$	2.03341	−	1.47736i	0.107170	−	0.0778635i
$361$	−2.84109	+	8.74397i	−0.149531	+	0.460209i
$362$	−14.9319	+	10.8487i	−0.784805	+	0.570194i
$363$	−2.89581	−	8.91237i	−0.151990	−	0.467778i
$364$	4.43560	+	13.6514i	0.232489	+	0.715527i
$365$	11.9038	−	36.6360i	0.623071	−	1.91762i
$366$	12.3718			0.646687
$367$	33.1903			1.73252			0.866260	−	0.499593i	$-0.166517\pi$
$367$	33.1903			1.73252			0.866260	+	0.499593i	$0.166517\pi$
$368$	0.618034	−	1.90211i	0.0322172	−	0.0991545i
$369$	4.96220	+	3.60525i	0.258322	+	0.187682i
$370$	9.13013	−	6.63343i	0.474653	−	0.344855i
$371$	11.0496			0.573667
$372$	−5.42813	+	1.23911i	−0.281435	+	0.0642449i
$373$	−7.51016			−0.388861			−0.194431	−	0.980916i	$-0.562286\pi$
$373$	−7.51016			−0.388861			−0.194431	+	0.980916i	$0.562286\pi$
$374$	−13.8418	+	10.0567i	−0.715744	+	0.520018i
$375$	7.48839	+	5.44063i	0.386699	+	0.280953i
$376$	−3.83074	+	11.7898i	−0.197555	+	0.608013i
$377$	1.23607			0.0636607
$378$	3.68484			0.189528
$379$	3.52023	−	10.8342i	0.180822	−	0.556514i	−0.819029	−	0.573752i	$-0.805487\pi$
$379$	3.52023	−	10.8342i	0.180822	−	0.556514i	0.999851	+	0.0172383i	$0.00548738\pi$
$380$	2.43218	+	7.48548i	0.124768	+	0.383997i
$381$	−4.57782	−	14.0891i	−0.234529	−	0.721806i
$382$	0.621528	−	0.451567i	0.0318002	−	0.0231042i
$383$	2.47214	−	7.60845i	0.126320	−	0.388774i	−0.867819	−	0.496880i	$-0.834479\pi$
$383$	2.47214	−	7.60845i	0.126320	−	0.388774i	0.994139	+	0.108107i	$0.0344788\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	33.8181	+	24.5703i	1.72353	+	1.25222i
$386$	−2.96112	−	9.11340i	−0.150717	−	0.463860i
$387$	6.18376	+	4.49277i	0.314338	+	0.228380i
$388$	−4.42530	−	3.21517i	−0.224661	−	0.163226i
$389$	−8.74161	−	26.9039i	−0.443217	−	1.36408i	−0.884427	−	0.466678i	$-0.845451\pi$
$389$	−8.74161	−	26.9039i	−0.443217	−	1.36408i	0.441210	−	0.897404i	$-0.354549\pi$
$390$	7.92091	+	5.75488i	0.401091	+	0.291410i
$391$	6.13362	−	4.45634i	0.310191	−	0.225367i
$392$	2.03274	−	6.25612i	0.102669	−	0.315982i
$393$	14.1165	−	10.2562i	0.712082	−	0.517358i
$394$	−2.86686	−	8.82329i	−0.144430	−	0.444511i
$395$	−5.45498	−	16.7887i	−0.274470	−	0.844732i
$396$	−1.39473	+	4.29252i	−0.0700876	+	0.215707i
$397$	−19.1026			−0.958731			−0.479366	−	0.877615i	$-0.659133\pi$
$397$	−19.1026			−0.958731			−0.479366	+	0.877615i	$0.659133\pi$
$398$	13.1213			0.657714
$399$	−3.56573	+	10.9742i	−0.178510	+	0.549397i
$400$	−1.06573	−	0.774299i	−0.0532865	−	0.0387149i
$401$	5.92091	−	4.30179i	0.295676	−	0.214821i	−0.430050	−	0.902805i	$-0.641504\pi$
$401$	5.92091	−	4.30179i	0.295676	−	0.214821i	0.725726	+	0.687984i	$0.241504\pi$
$402$	−11.2651			−0.561851
$403$	−11.1247	−	18.6182i	−0.554159	−	0.927440i
$404$	7.66691			0.381443
$405$	2.03341	−	1.47736i	0.101041	−	0.0734104i
$406$	−0.945949	−	0.687272i	−0.0469467	−	0.0341088i
$407$	−6.26241	+	19.2737i	−0.310416	+	0.955363i
$408$	3.79079			0.187672
$409$	36.0010			1.78013			0.890067	−	0.455831i	$-0.150658\pi$
$409$	36.0010			1.78013			0.890067	+	0.455831i	$0.150658\pi$
$410$	4.76393	−	14.6619i	0.235274	−	0.724098i
$411$	−1.23607	−	3.80423i	−0.0609707	−	0.187649i
$412$	3.72952	+	11.4783i	0.183740	+	0.565494i
$413$	8.70110	−	6.32172i	0.428153	−	0.311071i
$414$	0.618034	−	1.90211i	0.0303747	−	0.0934838i
$415$	−29.4277	+	21.3805i	−1.44455	+	1.04953i
$416$	3.15144	+	2.28965i	0.154512	+	0.112260i
$417$	2.66487	+	8.20161i	0.130499	+	0.401635i
$418$	−11.4343	−	8.30753i	−0.559272	−	0.406335i
$419$	−2.64928	−	1.92481i	−0.129426	−	0.0940333i	0.521189	−	0.853441i	$-0.325489\pi$
$419$	−2.64928	−	1.92481i	−0.129426	−	0.0940333i	−0.650615	+	0.759408i	$0.725489\pi$
$420$	−2.86199	−	8.80829i	−0.139651	−	0.429801i
$421$	−15.8507	−	11.5162i	−0.772515	−	0.561265i	0.130208	−	0.991487i	$-0.458435\pi$
$421$	−15.8507	−	11.5162i	−0.772515	−	0.561265i	−0.902723	+	0.430222i	$0.858435\pi$
$422$	−3.63254	+	2.63920i	−0.176829	+	0.128474i
$423$	−3.83074	+	11.7898i	−0.186257	+	0.573240i
$424$	2.42597	−	1.76257i	0.117816	−	0.0855980i
$425$	−1.54313	−	4.74925i	−0.0748526	−	0.230373i
$426$	−4.98556	−	15.3440i	−0.241551	−	0.743419i
$427$	14.0876	−	43.3571i	0.681745	−	2.09820i
$428$	−7.32408			−0.354023
$429$	−17.5816			−0.848846
$430$	5.93668	−	18.2712i	0.286292	−	0.881117i
$431$	−11.5746	−	8.40943i	−0.557528	−	0.405068i	0.273025	−	0.962007i	$-0.411976\pi$
$431$	−11.5746	−	8.40943i	−0.557528	−	0.405068i	−0.830553	+	0.556939i	$0.811976\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	36.7160			1.76446			0.882230	−	0.470819i	$-0.156042\pi$
$433$	36.7160			1.76446			0.882230	+	0.470819i	$0.156042\pi$
$434$	−1.83844	+	20.4338i	−0.0882481	+	0.980854i
$435$	−0.797549			−0.0382395
$436$	−13.5947	+	9.87716i	−0.651070	+	0.473030i
$437$	5.06681	+	3.68125i	0.242378	+	0.176098i
$438$	4.73607	−	14.5761i	0.226298	−	0.696474i
$439$	−31.1187			−1.48521			−0.742607	−	0.669728i	$-0.766411\pi$
$439$	−31.1187			−1.48521			−0.742607	+	0.669728i	$0.766411\pi$
$440$	11.3442			0.540812
$441$	2.03274	−	6.25612i	0.0967970	−	0.297911i
$442$	4.56313	+	14.0439i	0.217046	+	0.667999i
$443$	10.5077	+	32.3394i	0.499236	+	1.53649i	0.810250	+	0.586085i	$0.199331\pi$
$443$	10.5077	+	32.3394i	0.499236	+	1.53649i	−0.311014	+	0.950405i	$0.600669\pi$
$444$	3.63254	−	2.63920i	0.172393	−	0.125251i
$445$	−4.39723	+	13.5333i	−0.208449	+	0.641539i
$446$	−5.75943	+	4.18447i	−0.272717	+	0.198140i
$447$	−10.1108	−	7.34594i	−0.478225	−	0.347451i
$448$	−1.13868	−	3.50450i	−0.0537976	−	0.165572i
$449$	7.23607	+	5.25731i	0.341491	+	0.248108i	0.745291	−	0.666740i	$-0.232311\pi$
$449$	7.23607	+	5.25731i	0.341491	+	0.248108i	−0.403800	+	0.914847i	$0.632311\pi$
$450$	−1.06573	−	0.774299i	−0.0502390	−	0.0365008i
$451$	8.55472	+	26.3287i	0.402826	+	1.23977i
$452$	4.61803	+	3.35520i	0.217214	+	0.157815i
$453$	−8.21717	+	5.97012i	−0.386076	+	0.280501i
$454$	7.13530	−	21.9602i	0.334876	−	1.03064i
$455$	29.1873	−	21.2058i	1.36832	−	0.994145i
$456$	0.967675	+	2.97820i	0.0453155	+	0.139467i
$457$	1.10077	+	3.38782i	0.0514918	+	0.158476i	0.973496	−	0.228705i	$-0.0734491\pi$
$457$	1.10077	+	3.38782i	0.0514918	+	0.158476i	−0.922004	+	0.387180i	$0.873449\pi$
$458$	−4.24370	+	13.0608i	−0.198295	+	0.610289i
$459$	3.79079			0.176939
$460$	−5.02685			−0.234378
$461$	3.79683	−	11.6854i	0.176836	−	0.544245i	−0.822877	−	0.568220i	$-0.807632\pi$
$461$	3.79683	−	11.6854i	0.176836	−	0.544245i	0.999713	+	0.0239751i	$0.00763225\pi$
$462$	13.4550	+	9.77562i	0.625983	+	0.454803i
$463$	−15.0745	+	10.9523i	−0.700572	+	0.508995i	−0.880118	−	0.474754i	$-0.842537\pi$
$463$	−15.0745	+	10.9523i	−0.700572	+	0.508995i	0.179546	+	0.983749i	$0.442537\pi$
$464$	−0.317315			−0.0147310
$465$	7.17797	+	12.0131i	0.332870	+	0.557092i
$466$	8.65946			0.401142
$467$	23.2769	−	16.9117i	1.07713	−	0.782580i	0.0999485	−	0.994993i	$-0.468132\pi$
$467$	23.2769	−	16.9117i	1.07713	−	0.782580i	0.977180	+	0.212413i	$0.0681322\pi$
$468$	3.15144	+	2.28965i	0.145675	+	0.105839i
$469$	−12.8273	+	39.4784i	−0.592311	+	1.82294i
$470$	31.1578			1.43720
$471$	22.8440			1.05260
$472$	0.901944	−	2.77590i	0.0415153	−	0.127771i
$473$	10.6607	+	32.8101i	0.490178	+	1.50861i
$474$	−2.17034	−	6.67961i	−0.0996869	−	0.306805i
$475$	3.33729	−	2.42469i	0.153126	−	0.111252i
$476$	4.31649	−	13.2848i	0.197846	−	0.608907i
$477$	2.42597	−	1.76257i	0.111078	−	0.0807026i
$478$	11.0290	+	8.01305i	0.504455	+	0.366508i
$479$	−10.8307	−	33.3336i	−0.494869	−	1.52305i	−0.817160	−	0.576410i	$-0.804453\pi$
$479$	−10.8307	−	33.3336i	−0.494869	−	1.52305i	0.322291	−	0.946641i	$-0.395547\pi$
$480$	−2.03341	−	1.47736i	−0.0928118	−	0.0674317i
$481$	14.1502	+	10.2807i	0.645192	+	0.468760i
$482$	−0.899230	−	2.76755i	−0.0409588	−	0.126058i
$483$	−5.96220	−	4.33179i	−0.271290	−	0.197103i
$484$	−7.58132	+	5.50815i	−0.344605	+	0.250370i
$485$	−4.24848	+	13.0755i	−0.192914	+	0.593728i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	5.03442	+	15.4943i	0.228131	+	0.702115i	0.997959	+	0.0638634i	$0.0203422\pi$
$487$	5.03442	+	15.4943i	0.228131	+	0.702115i	−0.769828	+	0.638252i	$0.779658\pi$
$488$	−3.82311	−	11.7663i	−0.173064	−	0.532637i
$489$	1.15144	−	3.54377i	0.0520699	−	0.160255i
$490$	−16.5335			−0.746908
$491$	−22.1916			−1.00150			−0.500748	−	0.865593i	$-0.666941\pi$
$491$	−22.1916			−1.00150			−0.500748	+	0.865593i	$0.666941\pi$
$492$	1.89539	−	5.83342i	0.0854509	−	0.262991i
$493$	−0.973146	−	0.707032i	−0.0438283	−	0.0318431i
$494$	−9.86861	+	7.16996i	−0.444010	+	0.322592i
$495$	11.3442			0.509882
$496$	2.85585	+	4.77955i	0.128231	+	0.214608i
$497$	−59.4499			−2.66669
$498$	−11.7082	+	8.50651i	−0.524657	+	0.381186i
$499$	−1.15360	−	0.838139i	−0.0516422	−	0.0375202i	0.561665	−	0.827365i	$-0.310161\pi$
$499$	−1.15360	−	0.838139i	−0.0516422	−	0.0375202i	−0.613307	+	0.789845i	$0.710161\pi$
$500$	2.86031	−	8.80313i	0.127917	−	0.393688i
$501$	15.2072			0.679407
$502$	−8.09500			−0.361297
$503$	−4.60627	+	14.1766i	−0.205383	+	0.632105i	0.794314	+	0.607507i	$0.207830\pi$
$503$	−4.60627	+	14.1766i	−0.205383	+	0.632105i	−0.999697	+	0.0245975i	$0.992170\pi$
$504$	−1.13868	−	3.50450i	−0.0507208	−	0.156103i
$505$	−5.95483	−	18.3271i	−0.264986	−	0.815544i
$506$	7.30288	−	5.30585i	0.324653	−	0.235874i
$507$	−0.671830	+	2.06768i	−0.0298370	+	0.0918289i
$508$	−11.9849	+	8.70754i	−0.531744	+	0.386334i
$509$	−6.95871	−	5.05580i	−0.308439	−	0.224094i	0.422787	−	0.906229i	$-0.361052\pi$
$509$	−6.95871	−	5.05580i	−0.308439	−	0.224094i	−0.731227	+	0.682135i	$0.761052\pi$
$510$	−2.94427	−	9.06154i	−0.130375	−	0.401252i
$511$	−45.6891	−	33.1951i	−2.02117	−	1.46846i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	0.967675	+	2.97820i	0.0427239	+	0.131491i
$514$	15.8866	+	11.5423i	0.700728	+	0.509109i
$515$	24.5411	−	17.8302i	1.08141	−	0.785691i
$516$	2.36199	−	7.26945i	0.103981	−	0.320020i
$517$	−45.2652	+	32.8871i	−1.99076	+	1.44637i
$518$	−5.11275	−	15.7354i	−0.224641	−	0.691375i
$519$	3.03341	+	9.33586i	0.133152	+	0.409799i
$520$	3.02552	−	9.31159i	0.132678	−	0.408340i
$521$	−4.93728			−0.216306			−0.108153	−	0.994134i	$-0.534494\pi$
$521$	−4.93728			−0.216306			−0.108153	+	0.994134i	$0.534494\pi$
$522$	−0.317315			−0.0138885
$523$	−3.30493	+	10.1715i	−0.144514	+	0.444769i	−0.996948	−	0.0780657i	$-0.975126\pi$
$523$	−3.30493	+	10.1715i	−0.144514	+	0.444769i	0.852434	+	0.522835i	$0.175126\pi$
$524$	−14.1165	−	10.2562i	−0.616681	−	0.448045i
$525$	−3.92705	+	2.85317i	−0.171391	+	0.124523i
$526$	−13.1068			−0.571482
$527$	−1.89130	+	21.0213i	−0.0823863	+	0.915702i
$528$	4.51343			0.196422
$529$	15.3713	−	11.1679i	0.668318	−	0.485562i
$530$	−6.09750	−	4.43009i	−0.264859	−	0.192431i
$531$	0.901944	−	2.77590i	0.0391410	−	0.120464i
$532$	11.5389			0.500277
$533$	23.8929			1.03491
$534$	−1.74949	+	5.38439i	−0.0757081	+	0.233005i
$535$	5.68855	+	17.5076i	0.245937	+	0.756918i
$536$	3.48110	+	10.7137i	0.150361	+	0.462763i
$537$	−11.0084	+	7.99805i	−0.475046	+	0.345141i
$538$	−2.47464	+	7.61615i	−0.106689	+	0.328356i
$539$	24.0195	−	17.4512i	1.03459	−	0.751674i
$540$	−2.03341	−	1.47736i	−0.0875038	−	0.0635753i
$541$	−3.82527	−	11.7730i	−0.164461	−	0.506160i	0.834535	−	0.550955i	$-0.185736\pi$
$541$	−3.82527	−	11.7730i	−0.164461	−	0.506160i	−0.998996	+	0.0447954i	$0.985736\pi$
$542$	−2.86951	−	2.08482i	−0.123256	−	0.0895506i
$543$	14.9319	+	10.8487i	0.640790	+	0.465561i
$544$	−1.17142	−	3.60525i	−0.0502241	−	0.154574i
$545$	34.1694	+	24.8255i	1.46366	+	1.06341i
$546$	11.6126	−	8.43702i	0.496972	−	0.361071i
$547$	−8.77423	+	27.0043i	−0.375159	+	1.15462i	0.568212	+	0.822882i	$0.307635\pi$
$547$	−8.77423	+	27.0043i	−0.375159	+	1.15462i	−0.943371	+	0.331739i	$0.892365\pi$
$548$	−3.23607	+	2.35114i	−0.138238	+	0.100436i
$549$	−3.82311	−	11.7663i	−0.163166	−	0.502175i
$550$	−1.83729	−	5.65461i	−0.0783425	−	0.241113i
$551$	0.307058	−	0.945027i	0.0130811	−	0.0402595i
$552$	−2.00000			−0.0851257
$553$	−25.8800			−1.10053
$554$	−9.36886	+	28.8344i	−0.398045	+	1.22506i
$555$	−9.13013	−	6.63343i	−0.387552	−	0.281573i
$556$	6.97671	−	5.06888i	0.295878	−	0.214968i
$557$	−43.1772			−1.82948			−0.914739	−	0.404046i	$-0.867603\pi$
$557$	−43.1772			−1.82948			−0.914739	+	0.404046i	$0.867603\pi$
$558$	2.85585	+	4.77955i	0.120898	+	0.202335i
$559$	29.7746			1.25933
$560$	−7.49278	+	5.44382i	−0.316628	+	0.230044i
$561$	13.8418	+	10.0567i	0.584402	+	0.424593i
$562$	6.15832	−	18.9533i	0.259773	−	0.799499i
$563$	−15.3241			−0.645833			−0.322916	−	0.946427i	$-0.604663\pi$
$563$	−15.3241			−0.645833			−0.322916	+	0.946427i	$0.604663\pi$
$564$	12.3965			0.521989
$565$	4.43351	−	13.6450i	0.186519	−	0.574048i
$566$	5.19273	+	15.9816i	0.218267	+	0.671756i
$567$	−1.13868	−	3.50450i	−0.0478200	−	0.147175i
$568$	−13.0524	+	9.48310i	−0.547665	+	0.397902i
$569$	2.34283	−	7.21050i	0.0982167	−	0.302280i	−0.889862	−	0.456230i	$-0.849199\pi$
$569$	2.34283	−	7.21050i	0.0982167	−	0.302280i	0.988079	+	0.153950i	$0.0491994\pi$
$570$	6.36753	−	4.62628i	0.266706	−	0.193774i
$571$	3.27037	+	2.37606i	0.136861	+	0.0994351i	0.654109	−	0.756400i	$-0.273044\pi$
$571$	3.27037	+	2.37606i	0.136861	+	0.0994351i	−0.517248	+	0.855835i	$0.673044\pi$
$572$	5.43300	+	16.7211i	0.227165	+	0.699143i
$573$	−0.621528	−	0.451567i	−0.0259647	−	0.0188645i
$574$	−18.2849	−	13.2848i	−0.763199	−	0.554496i
$575$	0.814146	+	2.50568i	0.0339522	+	0.104494i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−30.9600	+	22.4938i	−1.28888	+	0.936429i	−0.999782	−	0.0208700i	$-0.993356\pi$
$577$	−30.9600	+	22.4938i	−1.28888	+	0.936429i	−0.289101	+	0.957299i	$0.593356\pi$
$578$	−0.812697	+	2.50122i	−0.0338037	+	0.104037i
$579$	−7.75232	+	5.63239i	−0.322176	+	0.234074i
$580$	0.246456	+	0.758514i	0.0102335	+	0.0314956i
$581$	16.4791	+	50.7175i	0.683669	+	2.10412i
$582$	−1.69032	+	5.20226i	−0.0700658	+	0.215640i
$583$	13.5343			0.560532
$584$	−15.3262			−0.634204
$585$	3.02552	−	9.31159i	0.125090	−	0.384987i
$586$	−4.24172	−	3.08179i	−0.175224	−	0.127308i
$587$	23.4712	−	17.0529i	0.968762	−	0.703847i	0.0135927	−	0.999908i	$-0.495673\pi$
$587$	23.4712	−	17.0529i	0.968762	−	0.703847i	0.955169	+	0.296061i	$0.0956732\pi$
$588$	−6.57808			−0.271275
$589$	−16.9980	+	3.88023i	−0.700390	+	0.159882i
$590$	−7.33607			−0.302021
$591$	−7.50554	+	5.45309i	−0.308737	+	0.224310i
$592$	−3.63254	−	2.63920i	−0.149297	−	0.108470i
$593$	−1.77368	+	5.45882i	−0.0728363	+	0.224167i	−0.980847	−	0.194780i	$-0.937601\pi$
$593$	−1.77368	+	5.45882i	−0.0728363	+	0.224167i	0.908011	+	0.418947i	$0.137601\pi$
$594$	4.51343			0.185188
$595$	−35.1087			−1.43932
$596$	−3.86199	+	11.8860i	−0.158193	+	0.486869i
$597$	−4.05472	−	12.4791i	−0.165949	−	0.510737i
$598$	−2.40749	−	7.40948i	−0.0984494	−	0.302996i
$599$	6.30504	−	4.58088i	0.257617	−	0.187170i	−0.451479	−	0.892282i	$-0.649103\pi$
$599$	6.30504	−	4.58088i	0.257617	−	0.187170i	0.709096	+	0.705112i	$0.249103\pi$
$600$	−0.407073	+	1.25284i	−0.0166187	+	0.0511470i
$601$	8.39208	−	6.09720i	0.342320	−	0.248710i	−0.403320	−	0.915059i	$-0.632144\pi$
$601$	8.39208	−	6.09720i	0.342320	−	0.248710i	0.745640	+	0.666349i	$0.232144\pi$
$602$	−22.7862	−	16.5552i	−0.928697	−	0.674738i
$603$	3.48110	+	10.7137i	0.141761	+	0.436297i
$604$	8.21717	+	5.97012i	0.334352	+	0.242921i
$605$	19.0551	+	13.8443i	0.774699	+	0.562852i
$606$	−2.36921	−	7.29167i	−0.0962424	−	0.296204i
$607$	4.28368	+	3.11228i	0.173869	+	0.126323i	0.671316	−	0.741171i	$-0.265729\pi$
$607$	4.28368	+	3.11228i	0.173869	+	0.126323i	−0.497447	+	0.867494i	$0.665729\pi$
$608$	2.53341	−	1.84063i	0.102743	−	0.0746473i
$609$	−0.361320	+	1.11203i	−0.0146414	+	0.0450617i
$610$	−25.1570	+	18.2776i	−1.01858	+	0.740039i
$611$	14.9222	+	45.9260i	0.603689	+	1.85797i
$612$	−1.17142	−	3.60525i	−0.0473517	−	0.145734i
$613$	−0.872815	+	2.68625i	−0.0352527	+	0.108497i	−0.967134	−	0.254266i	$-0.918166\pi$
$613$	−0.872815	+	2.68625i	−0.0352527	+	0.108497i	0.931882	+	0.362762i	$0.118166\pi$
$614$	4.10194			0.165541
$615$	−15.4164			−0.621650
$616$	5.13935	−	15.8173i	0.207070	−	0.637297i
$617$	−24.4256	−	17.7462i	−0.983336	−	0.714435i	−0.0248842	−	0.999690i	$-0.507922\pi$
$617$	−24.4256	−	17.7462i	−0.983336	−	0.714435i	−0.958452	+	0.285255i	$0.907922\pi$
$618$	9.76400	−	7.09396i	0.392766	−	0.285361i
$619$	−5.45912			−0.219421			−0.109710	−	0.993964i	$-0.534992\pi$
$619$	−5.45912			−0.219421			−0.109710	+	0.993964i	$0.534992\pi$
$620$	9.20698	−	10.5389i	0.369761	−	0.423252i
$621$	−2.00000			−0.0802572
$622$	18.6470	−	13.5479i	0.747678	−	0.543220i
$623$	16.8775	+	12.2622i	0.676181	+	0.491274i
$624$	1.20374	−	3.70474i	0.0481883	−	0.148308i
$625$	−29.8513			−1.19405
$626$	23.2225			0.928156
$627$	−4.36753	+	13.4419i	−0.174422	+	0.536817i
$628$	−7.05918	−	21.7259i	−0.281692	−	0.866959i
$629$	−5.25974	−	16.1878i	−0.209720	−	0.645451i
$630$	−7.49278	+	5.44382i	−0.298520	+	0.216887i
$631$	−7.10081	+	21.8541i	−0.282679	+	0.869996i	0.704406	+	0.709797i	$0.251214\pi$
$631$	−7.10081	+	21.8541i	−0.282679	+	0.869996i	−0.987085	+	0.160199i	$0.948786\pi$
$632$	−5.68202	+	4.12823i	−0.226019	+	0.164212i
$633$	3.63254	+	2.63920i	0.144381	+	0.104899i
$634$	−0.301544	−	0.928056i	−0.0119758	−	0.0368578i
$635$	30.1232	+	21.8858i	1.19540	+	0.868510i
$636$	−2.42597	−	1.76257i	−0.0961960	−	0.0698905i
$637$	−7.91831	−	24.3701i	−0.313735	−	0.965577i
$638$	−1.15866	−	0.841814i	−0.0458717	−	0.0333277i
$639$	−13.0524	+	9.48310i	−0.516344	+	0.375146i
$640$	−0.776692	+	2.39041i	−0.0307014	+	0.0944893i
$641$	17.3930	−	12.6368i	0.686984	−	0.499123i	−0.188683	−	0.982038i	$-0.560422\pi$
$641$	17.3930	−	12.6368i	0.686984	−	0.499123i	0.875667	+	0.482915i	$0.160422\pi$
$642$	2.26326	+	6.96561i	0.0893239	+	0.274911i
$643$	12.8763	+	39.6292i	0.507792	+	1.56282i	0.796025	+	0.605263i	$0.206932\pi$
$643$	12.8763	+	39.6292i	0.507792	+	1.56282i	−0.288233	+	0.957560i	$0.593068\pi$
$644$	−2.27736	+	7.00899i	−0.0897405	+	0.276193i
$645$	−19.2115			−0.756453
$646$	11.8707			0.467046
$647$	−1.25317	+	3.85687i	−0.0492674	+	0.151629i	−0.972664	−	0.232219i	$-0.925401\pi$
$647$	−1.25317	+	3.85687i	−0.0492674	+	0.151629i	0.923396	+	0.383848i	$0.125401\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	10.6576	−	7.74323i	0.418349	−	0.303949i
$650$	−5.13146			−0.201272
$651$	20.0018	−	4.56593i	0.783933	−	0.178953i
$652$	−3.72614			−0.145927
$653$	15.5808	−	11.3201i	0.609723	−	0.442990i	−0.239593	−	0.970873i	$-0.577014\pi$
$653$	15.5808	−	11.3201i	0.609723	−	0.442990i	0.849317	+	0.527883i	$0.177014\pi$
$654$	13.5947	+	9.87716i	0.531597	+	0.386228i
$655$	−13.5524	+	41.7101i	−0.529537	+	1.62975i
$656$	−6.13362			−0.239478
$657$	−15.3262			−0.597933
$658$	14.1157	−	43.4436i	0.550287	−	1.69361i
$659$	−9.49929	−	29.2358i	−0.370040	−	1.13887i	−0.946765	−	0.321927i	$-0.895670\pi$
$659$	−9.49929	−	29.2358i	−0.370040	−	1.13887i	0.576725	−	0.816938i	$-0.304330\pi$
$660$	−3.50554	−	10.7889i	−0.136453	−	0.419959i
$661$	25.5122	−	18.5357i	0.992308	−	0.720954i	0.0318828	−	0.999492i	$-0.489850\pi$
$661$	25.5122	−	18.5357i	0.992308	−	0.720954i	0.960425	+	0.278538i	$0.0898497\pi$
$662$	3.52786	−	10.8576i	0.137114	−	0.421995i
$663$	11.9464	−	8.67959i	0.463961	−	0.337087i
$664$	11.7082	+	8.50651i	0.454366	+	0.330117i
$665$	−8.96220	−	27.5828i	−0.347539	−	1.06962i
$666$	−3.63254	−	2.63920i	−0.140758	−	0.102267i
$667$	0.513427	+	0.373027i	0.0198800	+	0.0144436i
$668$	−4.69928	−	14.4629i	−0.181821	−	0.559586i
$669$	5.75943	+	4.18447i	0.222672	+	0.161781i
$670$	22.9065	−	16.6425i	0.884954	−	0.642957i
$671$	17.2553	−	53.1065i	0.666135	−	2.05015i
$672$	−2.98110	+	2.16590i	−0.114998	+	0.0835513i
$673$	−1.99227	−	6.13158i	−0.0767964	−	0.236355i	0.905287	−	0.424800i	$-0.139655\pi$
$673$	−1.99227	−	6.13158i	−0.0767964	−	0.236355i	−0.982084	+	0.188444i	$0.939655\pi$
$674$	−0.389597	−	1.19906i	−0.0150067	−	0.0461859i
$675$	−0.407073	+	1.25284i	−0.0156682	+	0.0482219i
$676$	2.17409			0.0836187
$677$	−9.40399			−0.361425			−0.180712	−	0.983536i	$-0.557840\pi$
$677$	−9.40399			−0.361425			−0.180712	+	0.983536i	$0.557840\pi$
$678$	1.76393	−	5.42882i	0.0677434	−	0.208493i
$679$	16.3066	+	11.8474i	0.625788	+	0.454662i
$680$	−7.70820	+	5.60034i	−0.295596	+	0.214763i
$681$	−23.0903			−0.884823
$682$	−2.25184	+	25.0286i	−0.0862274	+	0.958395i
$683$	21.1675			0.809950			0.404975	−	0.914328i	$-0.367280\pi$
$683$	21.1675			0.809950			0.404975	+	0.914328i	$0.367280\pi$
$684$	2.53341	−	1.84063i	0.0968672	−	0.0703781i
$685$	8.13362	+	5.90942i	0.310770	+	0.225787i
$686$	0.480434	−	1.47862i	0.0183431	−	0.0564542i
$687$	13.7329			0.523943
$688$	−7.64355			−0.291408
$689$	3.60962	−	11.1093i	0.137516	−	0.423230i
$690$	1.55338	+	4.78082i	0.0591363	+	0.182003i
$691$	11.7445	+	36.1460i	0.446783	+	1.37506i	0.880516	+	0.474016i	$0.157196\pi$
$691$	11.7445	+	36.1460i	0.446783	+	1.37506i	−0.433733	+	0.901041i	$0.642804\pi$
$692$	7.94156	−	5.76988i	0.301893	−	0.219338i
$693$	5.13935	−	15.8173i	0.195228	−	0.600849i
$694$	−4.65144	+	3.37947i	−0.176566	+	0.128283i
$695$	−17.5355	−	12.7403i	−0.665158	−	0.483265i
$696$	0.0980558	+	0.301785i	0.00371680	+	0.0114391i
$697$	−18.8107	−	13.6667i	−0.712504	−	0.517665i
$698$	14.5891	+	10.5996i	0.552205	+	0.401201i
$699$	−2.67592	−	8.23564i	−0.101213	−	0.311501i
$700$	3.92705	+	2.85317i	0.148429	+	0.107840i
$701$	32.6026	−	23.6872i	1.23138	−	0.894653i	0.234391	−	0.972142i	$-0.424690\pi$
$701$	32.6026	−	23.6872i	1.23138	−	0.894653i	0.996993	+	0.0774894i	$0.0246904\pi$
$702$	1.20374	−	3.70474i	0.0454323	−	0.139826i
$703$	11.3752	−	8.26454i	0.429022	−	0.311703i
$704$	−1.39473	−	4.29252i	−0.0525657	−	0.161781i
$705$	−9.62829	−	29.6328i	−0.362622	−	1.11604i
$706$	−2.94427	+	9.06154i	−0.110809	+	0.341035i
$707$	−28.2514			−1.06250
$708$	−2.91875			−0.109693
$709$	2.23823	−	6.88856i	0.0840584	−	0.258705i	−0.900190	−	0.435498i	$-0.856572\pi$
$709$	2.23823	−	6.88856i	0.0840584	−	0.258705i	0.984248	+	0.176793i	$0.0565723\pi$
$710$	32.8062	+	23.8351i	1.23119	+	0.894515i
$711$	−5.68202	+	4.12823i	−0.213092	+	0.154821i
$712$	5.66148			0.212173
$713$	0.997840	−	11.0907i	0.0373694	−	0.415351i
$714$	−13.9685			−0.522756
$715$	35.7505	−	25.9742i	1.33699	−	0.971381i
$716$	11.0084	+	7.99805i	0.411402	+	0.298901i
$717$	4.21271	−	12.9654i	0.157326	−	0.484201i
$718$	−2.72807			−0.101811
$719$	12.4035			0.462574			0.231287	−	0.972886i	$-0.425706\pi$
$719$	12.4035			0.462574			0.231287	+	0.972886i	$0.425706\pi$
$720$	−0.776692	+	2.39041i	−0.0289456	+	0.0890854i
$721$	−13.7427	−	42.2956i	−0.511804	−	1.57517i
$722$	−2.84109	−	8.74397i	−0.105734	−	0.325417i
$723$	−2.35421	+	1.71044i	−0.0875542	+	0.0636118i
$724$	5.70349	−	17.5535i	0.211968	−	0.652372i
$725$	0.338173	−	0.245697i	0.0125594	−	0.00912495i
$726$	7.58132	+	5.50815i	0.281369	+	0.204427i
$727$	−2.01060	−	6.18799i	−0.0745690	−	0.229500i	0.906824	−	0.421509i	$-0.138500\pi$
$727$	−2.01060	−	6.18799i	−0.0745690	−	0.229500i	−0.981393	+	0.192010i	$0.938500\pi$
$728$	−11.6126	−	8.43702i	−0.430390	−	0.312697i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	11.9038	+	36.6360i	0.440578	+	1.35596i
$731$	−23.4413	−	17.0311i	−0.867009	−	0.629919i
$732$	−10.0090	+	7.27199i	−0.369945	+	0.268780i
$733$	1.63679	−	5.03752i	0.0604562	−	0.186065i	−0.916267	−	0.400568i	$-0.868813\pi$
$733$	1.63679	−	5.03752i	0.0604562	−	0.186065i	0.976723	+	0.214502i	$0.0688130\pi$
$734$	−26.8515	+	19.5088i	−0.991108	+	0.720082i
$735$	5.10914	+	15.7243i	0.188453	+	0.580000i
$736$	0.618034	+	1.90211i	0.0227810	+	0.0701128i
$737$	−15.7117	+	48.3556i	−0.578748	+	1.78120i
$738$	−6.13362			−0.225782
$739$	17.5927			0.647159			0.323580	−	0.946201i	$-0.395114\pi$
$739$	17.5927			0.647159			0.323580	+	0.946201i	$0.395114\pi$
$740$	−3.48740	+	10.7331i	−0.128199	+	0.394557i
$741$	9.86861	+	7.16996i	0.362532	+	0.263395i
$742$	−8.93933	+	6.49480i	−0.328173	+	0.238432i
$743$	−18.4738			−0.677737			−0.338869	−	0.940834i	$-0.610044\pi$
$743$	−18.4738			−0.677737			−0.338869	+	0.940834i	$0.610044\pi$
$744$	3.66312	−	4.19304i	0.134296	−	0.153724i
$745$	31.4119			1.15084
$746$	6.07585	−	4.41436i	0.222453	−	0.161621i
$747$	11.7082	+	8.50651i	0.428381	+	0.311237i
$748$	5.28711	−	16.2720i	0.193316	−	0.594965i
$749$	26.9881			0.986123
$750$	−9.25616			−0.337987
$751$	5.02685	−	15.4711i	0.183433	−	0.564547i	−0.816485	−	0.577366i	$-0.804081\pi$
$751$	5.02685	−	15.4711i	0.183433	−	0.564547i	0.999918	+	0.0128190i	$0.00408052\pi$
$752$	−3.83074	−	11.7898i	−0.139693	−	0.429930i
$753$	2.50149	+	7.69880i	0.0911594	+	0.280560i
$754$	−1.00000	+	0.726543i	−0.0364179	+	0.0264591i
$755$	7.88884	−	24.2794i	0.287104	−	0.883616i
$756$	−2.98110	+	2.16590i	−0.108422	+	0.0787729i
$757$	30.3374	+	22.0414i	1.10263	+	0.801110i	0.981488	−	0.191525i	$-0.0613434\pi$
$757$	30.3374	+	22.0414i	1.10263	+	0.801110i	0.121145	+	0.992635i	$0.461343\pi$
$758$	3.52023	+	10.8342i	0.127861	+	0.393515i
$759$	−7.30288	−	5.30585i	−0.265078	−	0.192590i
$760$	−6.36753	−	4.62628i	−0.230975	−	0.167813i
$761$	3.00298	+	9.24224i	0.108858	+	0.335031i	0.990617	−	0.136670i	$-0.0436401\pi$
$761$	3.00298	+	9.24224i	0.108858	+	0.335031i	−0.881758	+	0.471701i	$0.843640\pi$
$762$	11.9849	+	8.70754i	0.434167	+	0.315441i
$763$	50.0945	−	36.3958i	1.81354	−	1.31762i
$764$	−0.237403	+	0.730650i	−0.00858893	+	0.0264340i
$765$	−7.70820	+	5.60034i	−0.278691	+	0.202481i
$766$	2.47214	+	7.60845i	0.0893219	+	0.274905i
$767$	−3.51343	−	10.8132i	−0.126862	−	0.390443i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	35.5885			1.28335			0.641677	−	0.766975i	$-0.278239\pi$
$769$	35.5885			1.28335			0.641677	+	0.766975i	$0.278239\pi$
$770$	−41.8015			−1.50642
$771$	6.06815	−	18.6758i	0.218539	−	0.672594i
$772$	7.75232	+	5.63239i	0.279012	+	0.202714i
$773$	1.54550	−	1.12287i	0.0555877	−	0.0403868i	−0.559644	−	0.828733i	$-0.689062\pi$
$773$	1.54550	−	1.12287i	0.0555877	−	0.0403868i	0.615232	+	0.788346i	$0.289062\pi$
$774$	−7.64355			−0.274742
$775$	−6.74437	−	2.88244i	−0.242265	−	0.103540i
$776$	5.46998			0.196361
$777$	−13.3853	+	9.72502i	−0.480197	+	0.348883i
$778$	22.8858	+	16.6275i	0.820497	+	0.596126i
$779$	5.93535	−	18.2671i	0.212656	−	0.654488i
$780$	−9.79079			−0.350566
$781$	−72.8179			−2.60563
$782$	−2.34283	+	7.21050i	−0.0837796	+	0.257847i
$783$	0.0980558	+	0.301785i	0.00350423	+	0.0107849i
$784$	2.03274	+	6.25612i	0.0725978	+	0.223433i
$785$	−46.4511	+	33.7487i	−1.65791	+	1.20454i
$786$	−5.39201	+	16.5949i	−0.192327	+	0.591921i
$787$	26.0167	−	18.9023i	0.927396	−	0.673793i	−0.0179575	−	0.999839i	$-0.505716\pi$
$787$	26.0167	−	18.9023i	0.927396	−	0.673793i	0.945354	+	0.326046i	$0.105716\pi$
$788$	7.50554	+	5.45309i	0.267374	+	0.194258i
$789$	4.05021	+	12.4653i	0.144191	+	0.443776i
$790$	14.2813	+	10.3760i	0.508107	+	0.369161i
$791$	−17.0167	−	12.3634i	−0.605045	−	0.439591i
$792$	−1.39473	−	4.29252i	−0.0495594	−	0.152528i
$793$	−38.9891	−	28.3273i	−1.38454	−	1.00593i
$794$	15.4543	−	11.2282i	0.548453	−	0.398475i
$795$	−2.32904	+	7.16804i	−0.0826025	+	0.254224i
$796$	−10.6154	+	7.71253i	−0.376253	+	0.273363i
$797$	5.33145	+	16.4085i	0.188850	+	0.581220i	0.999993	−	0.00362709i	$-0.00115454\pi$
$797$	5.33145	+	16.4085i	0.188850	+	0.581220i	−0.811144	+	0.584847i	$0.801155\pi$
$798$	−3.56573	−	10.9742i	−0.126225	−	0.388482i
$799$	14.5215	−	44.6927i	0.513735	−	1.58111i
$800$	1.31732			0.0465741
$801$	5.66148			0.200039
$802$	−2.26159	+	6.96045i	−0.0798594	+	0.245782i
$803$	−55.9628	−	40.6594i	−1.97489	−	1.43484i
$804$	9.11364	−	6.62145i	0.321413	−	0.233520i
$805$	18.5232			0.652856
$806$	19.9436	+	8.52356i	0.702482	+	0.300230i
$807$	8.00810			0.281898
$808$	−6.20266	+	4.50650i	−0.218209	+	0.158538i
$809$	−33.2419	−	24.1516i	−1.16872	−	0.849126i	−0.177866	−	0.984055i	$-0.556919\pi$
$809$	−33.2419	−	24.1516i	−1.16872	−	0.849126i	−0.990855	+	0.134929i	$0.956919\pi$
$810$	−0.776692	+	2.39041i	−0.0272902	+	0.0839905i
$811$	−41.9711			−1.47381			−0.736903	−	0.675999i	$-0.763712\pi$
$811$	−41.9711			−1.47381			−0.736903	+	0.675999i	$0.763712\pi$
$812$	1.16926			0.0410329
$813$	−1.09605	+	3.37331i	−0.0384403	+	0.118307i
$814$	−6.26241	−	19.2737i	−0.219497	−	0.675544i
$815$	2.89406	+	8.90700i	0.101374	+	0.311998i
$816$	−3.06681	+	2.22817i	−0.107360	+	0.0780015i
$817$	7.39647	−	22.7640i	0.258770	−	0.796412i
$818$	−29.1254	+	21.1608i	−1.01835	+	0.739871i
$819$	−11.6126	−	8.43702i	−0.405776	−	0.294813i
$820$	4.76393	+	14.6619i	0.166364	+	0.512015i
$821$	21.3702	+	15.5264i	0.745827	+	0.541875i	0.894530	−	0.447007i	$-0.147510\pi$
$821$	21.3702	+	15.5264i	0.745827	+	0.541875i	−0.148704	+	0.988882i	$0.547510\pi$
$822$	3.23607	+	2.35114i	0.112871	+	0.0820055i
$823$	0.764942	+	2.35425i	0.0266642	+	0.0820640i	0.963503	−	0.267697i	$-0.0862627\pi$
$823$	0.764942	+	2.35425i	0.0266642	+	0.0820640i	−0.936839	+	0.349761i	$0.886263\pi$
$824$	−9.76400	−	7.09396i	−0.340145	−	0.247130i
$825$	−4.81010	+	3.49474i	−0.167466	+	0.121671i
$826$	−3.32352	+	10.2288i	−0.115640	+	0.355904i
$827$	−38.0661	+	27.6566i	−1.32369	+	0.961714i	−0.323808	+	0.946123i	$0.604963\pi$
$827$	−38.0661	+	27.6566i	−1.32369	+	0.961714i	−0.999878	+	0.0155916i	$0.995037\pi$
$828$	0.618034	+	1.90211i	0.0214782	+	0.0661030i
$829$	−12.7414	−	39.2139i	−0.442526	−	1.36195i	−0.885175	−	0.465259i	$-0.845961\pi$
$829$	−12.7414	−	39.2139i	−0.442526	−	1.36195i	0.442649	−	0.896695i	$-0.354039\pi$
$830$	11.2404	−	34.5944i	0.390160	−	1.20079i
$831$	30.3183			1.05173
$832$	−3.89539			−0.135048
$833$	−7.70567	+	23.7156i	−0.266986	+	0.821698i
$834$	−6.97671	−	5.06888i	−0.241584	−	0.175521i
$835$	−30.9224	+	22.4664i	−1.07011	+	0.777483i
$836$	14.1336			0.488821
$837$	3.66312	−	4.19304i	0.126616	−	0.144933i
$838$	3.27469			0.113122
$839$	−8.98423	+	6.52742i	−0.310170	+	0.225352i	−0.731969	−	0.681337i	$-0.761399\pi$
$839$	−8.98423	+	6.52742i	−0.310170	+	0.225352i	0.421799	+	0.906689i	$0.361399\pi$
$840$	7.49278	+	5.44382i	0.258526	+	0.187830i
$841$	−8.93038	+	27.4849i	−0.307944	+	0.947754i
$842$	19.5925			0.675203
$843$	−19.9287			−0.686382
$844$	1.38751	−	4.27031i	0.0477600	−	0.146990i
$845$	−1.68860	−	5.19696i	−0.0580894	−	0.178781i
$846$	−3.83074	−	11.7898i	−0.131704	−	0.405342i
$847$	27.9360	−	20.2967i	0.959891	−	0.697402i
$848$	−0.926639	+	2.85190i	−0.0318209	+	0.0979347i
$849$	13.5947	−	9.87716i	0.466570	−	0.338983i
$850$	4.03996	+	2.93520i	0.138569	+	0.100677i
$851$	2.77501	+	8.54062i	0.0951263	+	0.292769i
$852$	13.0524	+	9.48310i	0.447167	+	0.324886i
$853$	−3.23391	−	2.34957i	−0.110727	−	0.0804478i	0.531044	−	0.847344i	$-0.321800\pi$
$853$	−3.23391	−	2.34957i	−0.110727	−	0.0804478i	−0.641771	+	0.766897i	$0.721800\pi$
$854$	14.0876	+	43.3571i	0.482067	+	1.48365i
$855$	−6.36753	−	4.62628i	−0.217765	−	0.158215i
$856$	5.92530	−	4.30499i	0.202523	−	0.147141i
$857$	−11.4466	+	35.2291i	−0.391009	+	1.20340i	0.541017	+	0.841011i	$0.318039\pi$
$857$	−11.4466	+	35.2291i	−0.391009	+	1.20340i	−0.932026	+	0.362390i	$0.881961\pi$
$858$	14.2238	−	10.3342i	0.485592	−	0.352803i
$859$	10.8418	+	33.3676i	0.369917	+	1.13849i	0.946844	+	0.321693i	$0.104252\pi$
$859$	10.8418	+	33.3676i	0.369917	+	1.13849i	−0.576927	+	0.816796i	$0.695748\pi$
$860$	5.93668	+	18.2712i	0.202439	+	0.623044i
$861$	−6.98423	+	21.4952i	−0.238022	+	0.732556i
$862$	14.3070			0.487297
$863$	−9.81267			−0.334027			−0.167014	−	0.985955i	$-0.553412\pi$
$863$	−9.81267			−0.334027			−0.167014	+	0.985955i	$0.553412\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−19.9605	−	14.5022i	−0.678678	−	0.493089i
$866$	−29.7039	+	21.5811i	−1.00938	+	0.733357i
$867$	2.62994			0.0893175
$868$	−10.5234	−	17.6119i	−0.357186	−	0.597787i
$869$	−31.6994			−1.07533
$870$	0.645231	−	0.468788i	0.0218754	−	0.0158934i
$871$	35.5012	+	25.7931i	1.20291	+	0.873967i
$872$	5.19273	−	15.9816i	0.175848	−	0.541205i
$873$	5.46998			0.185131
$874$	−6.26292			−0.211846
$875$	−10.5398	+	32.4382i	−0.356310	+	1.09661i
$876$	4.73607	+	14.5761i	0.160017	+	0.492481i
$877$	9.52869	+	29.3263i	0.321761	+	0.990278i	0.972882	+	0.231304i	$0.0742992\pi$
$877$	9.52869	+	29.3263i	0.321761	+	0.990278i	−0.651121	+	0.758974i	$0.725701\pi$
$878$	25.1755	−	18.2911i	0.849633	−	0.617295i
$879$	−1.62019	+	4.98644i	−0.0546478	+	0.168189i
$880$	−9.17763	+	6.66794i	−0.309378	+	0.224776i
$881$	−5.30853	−	3.85687i	−0.178849	−	0.129941i	0.494759	−	0.869030i	$-0.335256\pi$
$881$	−5.30853	−	3.85687i	−0.178849	−	0.129941i	−0.673608	+	0.739089i	$0.735256\pi$
$882$	2.03274	+	6.25612i	0.0684458	+	0.210655i
$883$	34.0836	+	24.7632i	1.14701	+	0.833348i	0.988080	−	0.153943i	$-0.0491971\pi$
$883$	34.0836	+	24.7632i	1.14701	+	0.833348i	0.158925	+	0.987291i	$0.449197\pi$
$884$	−11.9464	−	8.67959i	−0.401802	−	0.291926i
$885$	2.26697	+	6.97702i	0.0762034	+	0.234530i
$886$	−27.5095	−	19.9868i	−0.924200	−	0.671471i
$887$	15.0089	−	10.9046i	0.503950	−	0.366141i	−0.306574	−	0.951847i	$-0.599183\pi$
$887$	15.0089	−	10.9046i	0.503950	−	0.366141i	0.810524	+	0.585706i	$0.199183\pi$
$888$	−1.38751	+	4.27031i	−0.0465617	+	0.143302i
$889$	44.1625	−	32.0859i	1.48116	−	1.07613i
$890$	−4.39723	−	13.5333i	−0.147395	−	0.453636i
$891$	−1.39473	−	4.29252i	−0.0467251	−	0.143805i
$892$	2.19991	−	6.77061i	0.0736583	−	0.226697i
$893$	38.8193			1.29904
$894$	12.4977			0.417984
$895$	10.5685	−	32.5265i	0.353266	−	1.08724i
$896$	2.98110	+	2.16590i	0.0995916	+	0.0723575i
$897$	−6.30288	+	4.57931i	−0.210447	+	0.152899i
$898$	−8.94427			−0.298474
$899$	−1.72243	+	0.393189i	−0.0574462	+	0.0131136i
$900$	1.31732			0.0439105
$901$	−9.19634	+	6.68153i	−0.306374	+	0.222594i
$902$	−22.3965	−	16.2720i	−0.745723	−	0.541800i
$903$	−8.70356	+	26.7868i	−0.289636	+	0.891409i
$904$	−5.70820			−0.189852
$905$	−46.3900			−1.54206
$906$	3.13868	−	9.65986i	0.104276	−	0.320927i
$907$	−7.15068	−	22.0075i	−0.237435	−	0.730748i	−0.996789	−	0.0800714i	$-0.974485\pi$
$907$	−7.15068	−	22.0075i	−0.237435	−	0.730748i	0.759355	−	0.650677i	$-0.225515\pi$
$908$	7.13530	+	21.9602i	0.236793	+	0.728774i
$909$	−6.20266	+	4.50650i	−0.205729	+	0.149471i
$910$	−11.1486	+	34.3118i	−0.369571	+	1.13742i
$911$	−7.70820	+	5.60034i	−0.255384	+	0.185547i	−0.708110	−	0.706102i	$-0.750452\pi$
$911$	−7.70820	+	5.60034i	−0.255384	+	0.185547i	0.452725	+	0.891650i	$0.350452\pi$
$912$	−2.53341	−	1.84063i	−0.0838894	−	0.0609492i
$913$	20.1847	+	62.1220i	0.668015	+	2.05594i
$914$	−2.88185	−	2.09379i	−0.0953232	−	0.0692564i
$915$	25.1570	+	18.2776i	0.831664	+	0.604239i
$916$	−4.24370	−	13.0608i	−0.140216	−	0.431540i
$917$	52.0170	+	37.7926i	1.71775	+	1.24802i
$918$	−3.06681	+	2.22817i	−0.101220	+	0.0735405i
$919$	8.70057	−	26.7776i	0.287005	−	0.883312i	−0.698785	−	0.715332i	$-0.746276\pi$
$919$	8.70057	−	26.7776i	0.287005	−	0.883312i	0.985790	−	0.167980i	$-0.0537244\pi$
$920$	4.06681	−	2.95471i	0.134079	−	0.0974139i
$921$	−1.26757	−	3.90117i	−0.0417678	−	0.128548i
$922$	3.79683	+	11.6854i	0.125042	+	0.384839i
$923$	−19.4207	+	59.7709i	−0.639241	+	1.96738i
$924$	−16.6313			−0.547129
$925$	5.91483			0.194479
$926$	5.75795	−	17.7212i	0.189218	−	0.582353i
$927$	−9.76400	−	7.09396i	−0.320692	−	0.232996i
$928$	0.256714	−	0.186513i	0.00842703	−	0.00612260i
$929$	17.8199			0.584653			0.292327	−	0.956319i	$-0.405571\pi$
$929$	17.8199			0.584653			0.292327	+	0.956319i	$0.405571\pi$
$930$	−12.8682	−	5.49966i	−0.421965	−	0.180341i
$931$	−20.5990			−0.675105
$932$	−7.00565	+	5.08991i	−0.229478	+	0.166725i
$933$	−18.6470	−	13.5479i	−0.610477	−	0.443537i
$934$	−8.89100	+	27.3637i	−0.290922	+	0.895367i
$935$	−43.0033			−1.40636
$936$	−3.89539			−0.127325
$937$	3.33916	−	10.2769i	0.109085	−	0.335730i	−0.881582	−	0.472031i	$-0.843521\pi$
$937$	3.33916	−	10.2769i	0.109085	−	0.335730i	0.990668	+	0.136300i	$0.0435212\pi$
$938$	−12.8273	−	39.4784i	−0.418827	−	1.28902i
$939$	−7.17613	−	22.0859i	−0.234184	−	0.720745i
$940$	−25.2072	+	18.3141i	−0.822168	+	0.597340i
$941$	8.67480	−	26.6983i	0.282790	−	0.870339i	−0.704262	−	0.709940i	$-0.748722\pi$
$941$	8.67480	−	26.6983i	0.282790	−	0.870339i	0.987052	−	0.160399i	$-0.0512781\pi$
$942$	−18.4812	+	13.4274i	−0.602149	+	0.437487i
$943$	9.92441	+	7.21050i	0.323183	+	0.234806i
$944$	0.901944	+	2.77590i	0.0293558	+	0.0903478i
$945$	7.49278	+	5.44382i	0.243740	+	0.177088i
$946$	−27.9100	−	20.2778i	−0.907431	−	0.659287i
$947$	7.58977	+	23.3589i	0.246634	+	0.759063i	0.995363	+	0.0961865i	$0.0306645\pi$
$947$	7.58977	+	23.3589i	0.246634	+	0.759063i	−0.748729	+	0.662876i	$0.769335\pi$
$948$	5.68202	+	4.12823i	0.184543	+	0.134079i
$949$	−48.2997	+	35.0918i	−1.56787	+	1.13913i
$950$	−1.27473	+	3.92322i	−0.0413578	+	0.127286i
$951$	−0.789451	+	0.573570i	−0.0255997	+	0.0185993i
$952$	4.31649	+	13.2848i	0.139898	+	0.430563i
$953$	−17.3561	−	53.4165i	−0.562218	−	1.73033i	−0.676075	−	0.736833i	$-0.736320\pi$
$953$	−17.3561	−	53.4165i	−0.562218	−	1.73033i	0.113856	−	0.993497i	$-0.463680\pi$
$954$	−0.926639	+	2.85190i	−0.0300010	+	0.0923337i
$955$	1.93094			0.0624839
$956$	−13.6326			−0.440910
$957$	−0.442568	+	1.36208i	−0.0143062	+	0.0440299i
$958$	28.3553	+	20.6013i	0.916117	+	0.665598i
$959$	11.9244	−	8.66359i	0.385059	−	0.279762i
$960$	2.51343			0.0811205
$961$	21.4243	+	22.4053i	0.691107	+	0.722752i
$962$	−17.4906			−0.563919
$963$	5.92530	−	4.30499i	0.190940	−	0.138726i
$964$	2.35421	+	1.71044i	0.0758242	+	0.0550895i
$965$	7.44257	−	22.9059i	0.239585	−	0.737366i
$966$	7.36969			0.237116
$967$	50.9516			1.63849			0.819247	−	0.573441i	$-0.194392\pi$
$967$	50.9516			1.63849			0.819247	+	0.573441i	$0.194392\pi$
$968$	2.89581	−	8.91237i	0.0930747	−	0.286455i
$969$	−3.66825	−	11.2897i	−0.117841	−	0.362678i
$970$	−4.24848	−	13.0755i	−0.136411	−	0.419829i
$971$	−2.05182	+	1.49073i	−0.0658460	+	0.0478399i	−0.620221	−	0.784427i	$-0.712957\pi$
$971$	−2.05182	+	1.49073i	−0.0658460	+	0.0478399i	0.554375	+	0.832267i	$0.312957\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−25.7081	+	18.6780i	−0.824164	+	0.598790i
$974$	−13.1803	−	9.57603i	−0.422323	−	0.306836i
$975$	1.58571	+	4.88031i	0.0507833	+	0.156295i
$976$	10.0090	+	7.27199i	0.320381	+	0.232771i
$977$	39.0881	+	28.3992i	1.25054	+	0.908571i	0.998253	−	0.0590813i	$-0.0188171\pi$
$977$	39.0881	+	28.3992i	1.25054	+	0.908571i	0.252288	+	0.967652i	$0.418817\pi$
$978$	1.15144	+	3.54377i	0.0368190	+	0.113317i
$979$	20.6726	+	15.0195i	0.660698	+	0.480025i
$980$	13.3759	−	9.71816i	0.427277	−	0.310435i
$981$	5.19273	−	15.9816i	0.165791	−	0.510253i
$982$	17.9534	−	13.0439i	0.572917	−	0.416248i
$983$	−1.85075	−	5.69601i	−0.0590297	−	0.181675i	0.917194	−	0.398442i	$-0.130449\pi$
$983$	−1.85075	−	5.69601i	−0.0590297	−	0.181675i	−0.976223	+	0.216767i	$0.930449\pi$
$984$	1.89539	+	5.83342i	0.0604229	+	0.185963i
$985$	7.20565	−	22.1767i	0.229591	−	0.706608i
$986$	1.20287			0.0383073
$987$	−45.6793			−1.45399
$988$	3.76947	−	11.6012i	0.119923	−	0.369085i
$989$	12.3675	+	8.98554i	0.393265	+	0.285723i
$990$	−9.17763	+	6.66794i	−0.291684	+	0.211921i
$991$	−28.7607			−0.913614			−0.456807	−	0.889566i	$-0.651007\pi$
$991$	−28.7607			−0.913614			−0.456807	+	0.889566i	$0.651007\pi$
$992$	−5.11978	−	2.18811i	−0.162553	−	0.0694727i
$993$	−11.4164			−0.362289
$994$	48.0960	−	34.9438i	1.52551	−	1.10835i
$995$	26.6810	+	19.3849i	0.845845	+	0.614542i
$996$	4.47214	−	13.7638i	0.141705	−	0.436123i
$997$	9.38330			0.297172			0.148586	−	0.988899i	$-0.452528\pi$
$997$	9.38330			0.297172			0.148586	+	0.988899i	$0.452528\pi$
$998$	1.42593			0.0451369
$999$	−1.38751	+	4.27031i	−0.0438988	+	0.135107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.f.c.109.1	✓	8
3.2	odd	2		558.2.i.h.109.2		8
31.2	even	5	inner	186.2.f.c.157.1	yes	8
31.8	even	5		5766.2.a.be.1.1		4
31.23	odd	10		5766.2.a.bi.1.1		4
93.2	odd	10		558.2.i.h.343.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.f.c.109.1	✓	8	1.1	even	1	trivial
186.2.f.c.157.1	yes	8	31.2	even	5	inner
558.2.i.h.109.2		8	3.2	odd	2
558.2.i.h.343.2		8	93.2	odd	10
5766.2.a.be.1.1		4	31.8	even	5
5766.2.a.bi.1.1		4	31.23	odd	10

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} -2.51343 q^{5} -1.00000 q^{6} +(-1.13868 + 3.50450i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(2.03341 - 1.47736i) q^{10} +(-1.39473 + 4.29252i) q^{11} +(0.809017 - 0.587785i) q^{12} +(3.15144 + 2.28965i) q^{13} +(-1.13868 - 3.50450i) q^{14} +(-2.03341 - 1.47736i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.17142 - 3.60525i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(2.53341 - 1.84063i) q^{19} +(-0.776692 + 2.39041i) q^{20} +(-2.98110 + 2.16590i) q^{21} +(-1.39473 - 4.29252i) q^{22} +(0.618034 + 1.90211i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.31732 q^{25} -3.89539 q^{26} +(-0.309017 + 0.951057i) q^{27} +(2.98110 + 2.16590i) q^{28} +(0.256714 - 0.186513i) q^{29} +2.51343 q^{30} +(-5.11978 - 2.18811i) q^{31} +1.00000 q^{32} +(-3.65144 + 2.65293i) q^{33} +(3.06681 + 2.22817i) q^{34} +(2.86199 - 8.80829i) q^{35} +1.00000 q^{36} +4.49007 q^{37} +(-0.967675 + 2.97820i) q^{38} +(1.20374 + 3.70474i) q^{39} +(-0.776692 - 2.39041i) q^{40} +(4.96220 - 3.60525i) q^{41} +(1.13868 - 3.50450i) q^{42} +(6.18376 - 4.49277i) q^{43} +(3.65144 + 2.65293i) q^{44} +(-0.776692 - 2.39041i) q^{45} +(-1.61803 - 1.17557i) q^{46} +(10.0290 + 7.28650i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-5.32178 - 3.86650i) q^{49} +(-1.06573 + 0.774299i) q^{50} +(1.17142 - 3.60525i) q^{51} +(3.15144 - 2.28965i) q^{52} +(-0.926639 - 2.85190i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(3.50554 - 10.7889i) q^{55} -3.68484 q^{56} +3.13146 q^{57} +(-0.0980558 + 0.301785i) q^{58} +(-2.36132 - 1.71560i) q^{59} +(-2.03341 + 1.47736i) q^{60} -12.3718 q^{61} +(5.42813 - 1.23911i) q^{62} -3.68484 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.92091 - 5.75488i) q^{65} +(1.39473 - 4.29252i) q^{66} +11.2651 q^{67} -3.79079 q^{68} +(-0.618034 + 1.90211i) q^{69} +(2.86199 + 8.80829i) q^{70} +(4.98556 + 15.3440i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(-4.73607 + 14.5761i) q^{73} +(-3.63254 + 2.63920i) q^{74} +(1.06573 + 0.774299i) q^{75} +(-0.967675 - 2.97820i) q^{76} +(-13.4550 - 9.77562i) q^{77} +(-3.15144 - 2.28965i) q^{78} +(2.17034 + 6.67961i) q^{79} +(2.03341 + 1.47736i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.89539 + 5.83342i) q^{82} +(11.7082 - 8.50651i) q^{83} +(1.13868 + 3.50450i) q^{84} +(2.94427 + 9.06154i) q^{85} +(-2.36199 + 7.26945i) q^{86} +0.317315 q^{87} -4.51343 q^{88} +(1.74949 - 5.38439i) q^{89} +(2.03341 + 1.47736i) q^{90} +(-11.6126 + 8.43702i) q^{91} +2.00000 q^{92} +(-2.85585 - 4.77955i) q^{93} -12.3965 q^{94} +(-6.36753 + 4.62628i) q^{95} +(0.809017 + 0.587785i) q^{96} +(1.69032 - 5.20226i) q^{97} +6.57808 q^{98} -4.51343 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 7 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 7 q^{14} - 2 q^{15} - 2 q^{16} + 6 q^{17} - 2 q^{18} + 6 q^{19} - 3 q^{20}+ \cdots - 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 7 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 7 * q^14 - 2 * q^15 - 2 * q^16 + 6 * q^17 - 2 * q^18 + 6 * q^19 - 3 * q^20 - 3 * q^21 + q^22 - 4 * q^23 + 2 * q^24 + 22 * q^25 - 18 * q^26 + 2 * q^27 + 3 * q^28 - 9 * q^29 - 2 * q^30 - 18 * q^31 + 8 * q^32 - 6 * q^33 - 4 * q^34 + 24 * q^35 + 8 * q^36 + 30 * q^37 - 9 * q^38 - 7 * q^39 - 3 * q^40 - 2 * q^41 + 7 * q^42 + 25 * q^43 + 6 * q^44 - 3 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 - 17 * q^49 + 7 * q^50 - 6 * q^51 + 2 * q^52 - 6 * q^53 + 2 * q^54 - 22 * q^55 + 8 * q^56 - 6 * q^57 + 16 * q^58 - 21 * q^59 - 2 * q^60 + 2 * q^61 + 17 * q^62 + 8 * q^63 - 2 * q^64 - 8 * q^65 - q^66 + 2 * q^67 - 4 * q^68 + 4 * q^69 + 24 * q^70 - 18 * q^71 - 2 * q^72 - 20 * q^73 + 15 * q^74 - 7 * q^75 - 9 * q^76 - 37 * q^77 - 2 * q^78 + 15 * q^79 + 2 * q^80 - 2 * q^81 - 2 * q^82 + 40 * q^83 + 7 * q^84 - 48 * q^85 - 20 * q^86 + 14 * q^87 - 14 * q^88 - 26 * q^89 + 2 * q^90 - 41 * q^91 + 16 * q^92 + 18 * q^93 + 20 * q^94 - 2 * q^95 + 2 * q^96 + 19 * q^97 + 28 * q^98 - 14 * q^99

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