LMFDB - Embedded newform 425.2.k.b.86.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] 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("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.6
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23201 + 0.895109i) q^{2} +(-0.658347 + 2.02618i) q^{3} +(0.0985994 - 0.303458i) q^{4} +(1.71600 + 1.43365i) q^{5} +(-1.00256 - 3.08558i) q^{6} -1.63215 q^{7} +(-0.791021 - 2.43451i) q^{8} +(-1.24495 - 0.904509i) q^{9} +(-3.39740 - 0.230264i) q^{10} +(-2.50425 + 1.81944i) q^{11} +(0.549949 + 0.399561i) q^{12} +(-3.78312 - 2.74860i) q^{13} +(2.01082 - 1.46095i) q^{14} +(-4.03456 + 2.53309i) q^{15} +(3.66998 + 2.66639i) q^{16} +(0.309017 + 0.951057i) q^{17} +2.34343 q^{18} +(0.290347 + 0.893595i) q^{19} +(0.604248 - 0.379377i) q^{20} +(1.07452 - 3.30703i) q^{21} +(1.45666 - 4.48315i) q^{22} +(-3.53943 + 2.57154i) q^{23} +5.45354 q^{24} +(0.889309 + 4.92028i) q^{25} +7.12114 q^{26} +(-2.51841 + 1.82973i) q^{27} +(-0.160929 + 0.495288i) q^{28} +(2.46844 - 7.59708i) q^{29} +(2.70323 - 6.73217i) q^{30} +(-1.33397 - 4.10554i) q^{31} -1.78857 q^{32} +(-2.03786 - 6.27189i) q^{33} +(-1.23201 - 0.895109i) q^{34} +(-2.80076 - 2.33992i) q^{35} +(-0.397232 + 0.288606i) q^{36} +(3.87963 + 2.81871i) q^{37} +(-1.15758 - 0.841028i) q^{38} +(8.05976 - 5.85576i) q^{39} +(2.13284 - 5.31167i) q^{40} +(8.62327 + 6.26517i) q^{41} +(1.63633 + 5.03611i) q^{42} -10.6885 q^{43} +(0.305207 + 0.939329i) q^{44} +(-0.839587 - 3.33696i) q^{45} +(2.05880 - 6.33635i) q^{46} +(2.70092 - 8.31259i) q^{47} +(-7.81872 + 5.68064i) q^{48} -4.33610 q^{49} +(-5.49983 - 5.26581i) q^{50} -2.13046 q^{51} +(-1.20710 + 0.877006i) q^{52} +(-0.570769 + 1.75665i) q^{53} +(1.46490 - 4.50851i) q^{54} +(-6.90573 - 0.468046i) q^{55} +(1.29106 + 3.97348i) q^{56} -2.00174 q^{57} +(3.75907 + 11.5692i) q^{58} +(3.75867 + 2.73083i) q^{59} +(0.370882 + 1.47408i) q^{60} +(0.146978 - 0.106786i) q^{61} +(5.31838 + 3.86403i) q^{62} +(2.03194 + 1.47629i) q^{63} +(-5.13641 + 3.73182i) q^{64} +(-2.55131 - 10.1402i) q^{65} +(8.12470 + 5.90294i) q^{66} +(4.39886 + 13.5383i) q^{67} +0.319074 q^{68} +(-2.88025 - 8.86450i) q^{69} +(5.54506 + 0.375825i) q^{70} +(-0.327871 + 1.00908i) q^{71} +(-1.21726 + 3.74633i) q^{72} +(0.130725 - 0.0949771i) q^{73} -7.30281 q^{74} +(-10.5549 - 1.43735i) q^{75} +0.299796 q^{76} +(4.08730 - 2.96960i) q^{77} +(-4.68818 + 14.4287i) q^{78} +(-3.76514 + 11.5879i) q^{79} +(2.47501 + 9.83698i) q^{80} +(-3.47597 - 10.6980i) q^{81} -16.2320 q^{82} +(-2.92215 - 8.99346i) q^{83} +(-0.897597 - 0.652142i) q^{84} +(-0.833207 + 2.07503i) q^{85} +(13.1683 - 9.56733i) q^{86} +(13.7680 + 10.0030i) q^{87} +(6.41037 + 4.65741i) q^{88} +(-10.5336 + 7.65312i) q^{89} +(4.02132 + 3.35965i) q^{90} +(6.17460 + 4.48611i) q^{91} +(0.431370 + 1.32762i) q^{92} +9.19680 q^{93} +(4.11310 + 12.6588i) q^{94} +(-0.782866 + 1.94966i) q^{95} +(1.17750 - 3.62397i) q^{96} +(-4.99180 + 15.3632i) q^{97} +(5.34212 - 3.88128i) q^{98} +4.76337 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.23201	+	0.895109i	−0.871164	+	0.632938i	−0.930899	−	0.365276i	$-0.880974\pi$
$2$	−1.23201	+	0.895109i	−0.871164	+	0.632938i	0.0597350	+	0.998214i	$0.480974\pi$
$3$	−0.658347	+	2.02618i	−0.380097	+	1.16982i	0.559878	+	0.828575i	$0.310848\pi$
$3$	−0.658347	+	2.02618i	−0.380097	+	1.16982i	−0.939975	+	0.341243i	$0.889152\pi$
$4$	0.0985994	−	0.303458i	0.0492997	−	0.151729i
$5$	1.71600	+	1.43365i	0.767418	+	0.641147i
$5$	1.71600	+	1.43365i	0.767418	+	0.641147i
$6$	−1.00256	−	3.08558i	−0.409295	−	1.25968i
$7$	−1.63215			−0.616894			−0.308447	−	0.951242i	$-0.599809\pi$
$7$	−1.63215			−0.616894			−0.308447	+	0.951242i	$0.599809\pi$
$8$	−0.791021	−	2.43451i	−0.279668	−	0.860730i
$9$	−1.24495	−	0.904509i	−0.414983	−	0.301503i
$10$	−3.39740	−	0.230264i	−1.07435	−	0.0728159i
$11$	−2.50425	+	1.81944i	−0.755059	+	0.548582i	−0.897391	−	0.441237i	$-0.854540\pi$
$11$	−2.50425	+	1.81944i	−0.755059	+	0.548582i	0.142332	+	0.989819i	$0.454540\pi$
$12$	0.549949	+	0.399561i	0.158756	+	0.115343i
$13$	−3.78312	−	2.74860i	−1.04925	−	0.762323i	−0.0771785	−	0.997017i	$-0.524591\pi$
$13$	−3.78312	−	2.74860i	−1.04925	−	0.762323i	−0.972069	+	0.234694i	$0.924591\pi$
$14$	2.01082	−	1.46095i	0.537416	−	0.390455i
$15$	−4.03456	+	2.53309i	−1.04172	+	0.654042i
$16$	3.66998	+	2.66639i	0.917494	+	0.666598i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	2.34343			0.552351
$19$	0.290347	+	0.893595i	0.0666101	+	0.205005i	0.978822	−	0.204715i	$-0.0656266\pi$
$19$	0.290347	+	0.893595i	0.0666101	+	0.205005i	−0.912212	+	0.409719i	$0.865627\pi$
$20$	0.604248	−	0.379377i	0.135114	−	0.0848312i
$21$	1.07452	−	3.30703i	0.234479	−	0.721653i
$22$	1.45666	−	4.48315i	0.310562	−	0.955811i
$23$	−3.53943	+	2.57154i	−0.738021	+	0.536204i	−0.892091	−	0.451856i	$-0.850762\pi$
$23$	−3.53943	+	2.57154i	−0.738021	+	0.536204i	0.154069	+	0.988060i	$0.450762\pi$
$24$	5.45354			1.11320
$25$	0.889309	+	4.92028i	0.177862	+	0.984055i
$26$	7.12114			1.39657
$27$	−2.51841	+	1.82973i	−0.484669	+	0.352133i
$28$	−0.160929	+	0.495288i	−0.0304127	+	0.0936006i
$29$	2.46844	−	7.59708i	0.458378	−	1.41074i	−0.408745	−	0.912649i	$-0.634033\pi$
$29$	2.46844	−	7.59708i	0.458378	−	1.41074i	0.867123	−	0.498094i	$-0.165967\pi$
$30$	2.70323	−	6.73217i	0.493540	−	1.22912i
$31$	−1.33397	−	4.10554i	−0.239588	−	0.737377i	−0.996480	−	0.0838364i	$-0.973283\pi$
$31$	−1.33397	−	4.10554i	−0.239588	−	0.737377i	0.756891	−	0.653541i	$-0.226717\pi$
$32$	−1.78857			−0.316178
$33$	−2.03786	−	6.27189i	−0.354746	−	1.09180i
$34$	−1.23201	−	0.895109i	−0.211288	−	0.153510i
$35$	−2.80076	−	2.33992i	−0.473415	−	0.395519i
$36$	−0.397232	+	0.288606i	−0.0662053	+	0.0481010i
$37$	3.87963	+	2.81871i	0.637807	+	0.463394i	0.859096	−	0.511814i	$-0.171026\pi$
$37$	3.87963	+	2.81871i	0.637807	+	0.463394i	−0.221289	+	0.975208i	$0.571026\pi$
$38$	−1.15758	−	0.841028i	−0.187784	−	0.136433i
$39$	8.05976	−	5.85576i	1.29060	−	0.937672i
$40$	2.13284	−	5.31167i	0.337232	−	0.839849i
$41$	8.62327	+	6.26517i	1.34673	+	0.978456i	0.999167	+	0.0407982i	$0.0129901\pi$
$41$	8.62327	+	6.26517i	1.34673	+	0.978456i	0.347561	+	0.937657i	$0.387010\pi$
$42$	1.63633	+	5.03611i	0.252492	+	0.777089i
$43$	−10.6885			−1.62997			−0.814987	−	0.579479i	$-0.803256\pi$
$43$	−10.6885			−1.62997			−0.814987	+	0.579479i	$0.803256\pi$
$44$	0.305207	+	0.939329i	0.0460116	+	0.141609i
$45$	−0.839587	−	3.33696i	−0.125158	−	0.497444i
$46$	2.05880	−	6.33635i	0.303554	−	0.934243i
$47$	2.70092	−	8.31259i	0.393970	−	1.21252i	−0.535791	−	0.844351i	$-0.679986\pi$
$47$	2.70092	−	8.31259i	0.393970	−	1.21252i	0.929761	−	0.368165i	$-0.120014\pi$
$48$	−7.81872	+	5.68064i	−1.12854	+	0.819929i
$49$	−4.33610			−0.619442
$50$	−5.49983	−	5.26581i	−0.777793	−	0.744698i
$51$	−2.13046			−0.298324
$52$	−1.20710	+	0.877006i	−0.167394	+	0.121619i
$53$	−0.570769	+	1.75665i	−0.0784012	+	0.241294i	−0.982574	−	0.185873i	$-0.940489\pi$
$53$	−0.570769	+	1.75665i	−0.0784012	+	0.241294i	0.904172	+	0.427168i	$0.140489\pi$
$54$	1.46490	−	4.50851i	0.199348	−	0.613531i
$55$	−6.90573	−	0.468046i	−0.931168	−	0.0631113i
$56$	1.29106	+	3.97348i	0.172526	+	0.530979i
$57$	−2.00174			−0.265136
$58$	3.75907	+	11.5692i	0.493590	+	1.51911i
$59$	3.75867	+	2.73083i	0.489337	+	0.355524i	0.804929	−	0.593371i	$-0.202203\pi$
$59$	3.75867	+	2.73083i	0.489337	+	0.355524i	−0.315592	+	0.948895i	$0.602203\pi$
$60$	0.370882	+	1.47408i	0.0478806	+	0.190303i
$61$	0.146978	−	0.106786i	0.0188186	−	0.0136725i	−0.578336	−	0.815799i	$-0.696298\pi$
$61$	0.146978	−	0.106786i	0.0188186	−	0.0136725i	0.597155	+	0.802126i	$0.296298\pi$
$62$	5.31838	+	3.86403i	0.675435	+	0.490732i
$63$	2.03194	+	1.47629i	0.256001	+	0.185995i
$64$	−5.13641	+	3.73182i	−0.642051	+	0.466478i
$65$	−2.55131	−	10.1402i	−0.316451	−	1.25774i
$66$	8.12470	+	5.90294i	1.00008	+	0.726601i
$67$	4.39886	+	13.5383i	0.537406	+	1.65396i	0.738393	+	0.674371i	$0.235585\pi$
$67$	4.39886	+	13.5383i	0.537406	+	1.65396i	−0.200987	+	0.979594i	$0.564415\pi$
$68$	0.319074			0.0386934
$69$	−2.88025	−	8.86450i	−0.346741	−	1.06716i
$70$	5.54506	+	0.375825i	0.662762	+	0.0449197i
$71$	−0.327871	+	1.00908i	−0.0389111	+	0.119756i	−0.968625	−	0.248526i	$-0.920054\pi$
$71$	−0.327871	+	1.00908i	−0.0389111	+	0.119756i	0.929714	+	0.368282i	$0.120054\pi$
$72$	−1.21726	+	3.74633i	−0.143455	+	0.441510i
$73$	0.130725	−	0.0949771i	0.0153002	−	0.0111162i	−0.580109	−	0.814539i	$-0.696990\pi$
$73$	0.130725	−	0.0949771i	0.0153002	−	0.0111162i	0.595409	+	0.803423i	$0.296990\pi$
$74$	−7.30281			−0.848934
$75$	−10.5549	−	1.43735i	−1.21877	−	0.165970i
$76$	0.299796			0.0343890
$77$	4.08730	−	2.96960i	0.465791	−	0.338417i
$78$	−4.68818	+	14.4287i	−0.530832	+	1.63373i
$79$	−3.76514	+	11.5879i	−0.423611	+	1.30374i	0.480707	+	0.876881i	$0.340380\pi$
$79$	−3.76514	+	11.5879i	−0.423611	+	1.30374i	−0.904318	+	0.426860i	$0.859620\pi$
$80$	2.47501	+	9.83698i	0.276714	+	1.09981i
$81$	−3.47597	−	10.6980i	−0.386219	−	1.18866i
$82$	−16.2320			−1.79252
$83$	−2.92215	−	8.99346i	−0.320748	−	0.987161i	−0.973324	−	0.229437i	$-0.926312\pi$
$83$	−2.92215	−	8.99346i	−0.320748	−	0.987161i	0.652576	−	0.757724i	$-0.273688\pi$
$84$	−0.897597	−	0.652142i	−0.0979359	−	0.0711546i
$85$	−0.833207	+	2.07503i	−0.0903740	+	0.225069i
$86$	13.1683	−	9.56733i	1.41997	−	1.03167i
$87$	13.7680	+	10.0030i	1.47608	+	1.07244i
$88$	6.41037	+	4.65741i	0.683348	+	0.496481i
$89$	−10.5336	+	7.65312i	−1.11656	+	0.811229i	−0.983684	−	0.179904i	$-0.942421\pi$
$89$	−10.5336	+	7.65312i	−1.11656	+	0.811229i	−0.132877	+	0.991133i	$0.542421\pi$
$90$	4.02132	+	3.35965i	0.423885	+	0.354138i
$91$	6.17460	+	4.48611i	0.647274	+	0.470272i
$92$	0.431370	+	1.32762i	0.0449734	+	0.138414i
$93$	9.19680			0.953664
$94$	4.11310	+	12.6588i	0.424234	+	1.30566i
$95$	−0.782866	+	1.94966i	−0.0803203	+	0.200031i
$96$	1.17750	−	3.62397i	0.120178	−	0.369870i
$97$	−4.99180	+	15.3632i	−0.506840	+	1.55989i	0.290814	+	0.956780i	$0.406074\pi$
$97$	−4.99180	+	15.3632i	−0.506840	+	1.55989i	−0.797654	+	0.603115i	$0.793926\pi$
$98$	5.34212	−	3.88128i	0.539636	−	0.392068i
$99$	4.76337			0.478736
$100$	1.58078	+	0.215269i	0.158078	+	0.0215269i
$101$	−2.66287			−0.264965			−0.132483	−	0.991185i	$-0.542295\pi$
$101$	−2.66287			−0.264965			−0.132483	+	0.991185i	$0.542295\pi$
$102$	2.62475	−	1.90699i	0.259889	−	0.188820i
$103$	−0.00446771	+	0.0137502i	−0.000440217	+	0.00135485i	−0.951276	−	0.308339i	$-0.900227\pi$
$103$	−0.00446771	+	0.0137502i	−0.000440217	+	0.00135485i	0.950836	+	0.309694i	$0.100227\pi$
$104$	−3.69897	+	11.3842i	−0.362713	+	1.11632i
$105$	6.58499	−	4.13438i	0.642629	−	0.403474i
$106$	−0.869197	−	2.67511i	−0.0844238	−	0.259830i
$107$	18.1546			1.75508			0.877538	−	0.479507i	$-0.159185\pi$
$107$	18.1546			1.75508			0.877538	+	0.479507i	$0.159185\pi$
$108$	0.306933	+	0.944643i	0.0295346	+	0.0908983i
$109$	−6.52611	−	4.74150i	−0.625088	−	0.454153i	0.229607	−	0.973283i	$-0.426256\pi$
$109$	−6.52611	−	4.74150i	−0.625088	−	0.454153i	−0.854695	+	0.519130i	$0.826256\pi$
$110$	8.92689	−	5.60474i	0.851146	−	0.534391i
$111$	−8.26538	+	6.00515i	−0.784515	+	0.569983i
$112$	−5.98994	−	4.35195i	−0.565996	−	0.411220i
$113$	−7.86499	−	5.71425i	−0.739876	−	0.537552i	0.152796	−	0.988258i	$-0.451172\pi$
$113$	−7.86499	−	5.71425i	−0.739876	−	0.537552i	−0.892672	+	0.450706i	$0.851172\pi$
$114$	2.46616	−	1.79177i	0.230977	−	0.167815i
$115$	−9.76034	−	0.661522i	−0.910157	−	0.0616873i
$116$	−2.06201	−	1.49814i	−0.191452	−	0.139098i
$117$	2.22366	+	6.84373i	0.205578	+	0.632703i
$118$	−7.07512			−0.651317
$119$	−0.504361	−	1.55226i	−0.0462347	−	0.142296i
$120$	9.35827	+	7.81845i	0.854289	+	0.713724i
$121$	−0.438302	+	1.34896i	−0.0398456	+	0.122632i
$122$	−0.0854937	+	0.263123i	−0.00774024	+	0.0238220i
$123$	−18.3715	+	13.3477i	−1.65650	+	1.20352i
$124$	−1.37739			−0.123693
$125$	−5.52789	+	9.71815i	−0.494430	+	0.869218i
$126$	−3.82482			−0.340742
$127$	−10.1696	+	7.38865i	−0.902406	+	0.655636i	−0.939083	−	0.343691i	$-0.888323\pi$
$127$	−10.1696	+	7.38865i	−0.902406	+	0.655636i	0.0366768	+	0.999327i	$0.488323\pi$
$128$	4.09313	−	12.5974i	0.361785	−	1.11346i
$129$	7.03671	−	21.6568i	0.619548	−	1.90677i
$130$	12.2199	+	10.2092i	1.07175	+	0.895406i
$131$	0.433017	+	1.33269i	0.0378329	+	0.116438i	0.968189	−	0.250219i	$-0.0805025\pi$
$131$	0.433017	+	1.33269i	0.0378329	+	0.116438i	−0.930356	+	0.366656i	$0.880502\pi$
$132$	−2.10419			−0.183146
$133$	−0.473888	−	1.45848i	−0.0410913	−	0.126466i
$134$	−17.5377	−	12.7419i	−1.51503	−	1.10073i
$135$	−6.94479	−	0.470694i	−0.597712	−	0.0405109i
$136$	2.07092	−	1.50461i	0.177580	−	0.129019i
$137$	−1.21929	−	0.885867i	−0.104171	−	0.0756848i	0.534480	−	0.845181i	$-0.320507\pi$
$137$	−1.21929	−	0.885867i	−0.104171	−	0.0756848i	−0.638651	+	0.769496i	$0.720507\pi$
$138$	11.4832	+	8.34303i	0.977515	+	0.710206i
$139$	−6.33252	+	4.60084i	−0.537117	+	0.390239i	−0.823013	−	0.568022i	$-0.807709\pi$
$139$	−6.33252	+	4.60084i	−0.537117	+	0.390239i	0.285896	+	0.958261i	$0.407709\pi$
$140$	−0.986221	+	0.619198i	−0.0833509	+	0.0523318i
$141$	15.0647	+	10.9451i	1.26868	+	0.921747i
$142$	−0.499299	−	1.53668i	−0.0419002	−	0.128956i
$143$	14.4748			1.21044
$144$	−2.15716	−	6.63906i	−0.179763	−	0.553255i
$145$	15.1274	−	9.49771i	1.25626	−	0.788742i
$146$	−0.0760396	+	0.234026i	−0.00629308	+	0.0193681i
$147$	2.85466	−	8.78573i	0.235448	−	0.724635i
$148$	1.23789	−	0.899379i	0.101754	−	0.0739285i
$149$	8.69564			0.712375			0.356187	−	0.934415i	$-0.384076\pi$
$149$	8.69564			0.712375			0.356187	+	0.934415i	$0.384076\pi$
$150$	14.2903	−	7.67693i	1.16680	−	0.626818i
$151$	−23.1447			−1.88349			−0.941746	−	0.336326i	$-0.890816\pi$
$151$	−23.1447			−1.88349			−0.941746	+	0.336326i	$0.890816\pi$
$152$	1.94580	−	1.41371i	0.157825	−	0.114667i
$153$	0.475529	−	1.46353i	0.0384442	−	0.118319i
$154$	−2.37749	+	7.31716i	−0.191584	+	0.589633i
$155$	3.59681	−	8.95756i	0.288903	−	0.719488i
$156$	−0.982288	−	3.02317i	−0.0786460	−	0.242047i
$157$	1.37572			0.109794			0.0548972	−	0.998492i	$-0.482517\pi$
$157$	1.37572			0.109794			0.0548972	+	0.998492i	$0.482517\pi$
$158$	−5.73374	−	17.6466i	−0.456152	−	1.40389i
$159$	−3.18353	−	2.31297i	−0.252470	−	0.183430i
$160$	−3.06919	−	2.56418i	−0.242641	−	0.202716i
$161$	5.77686	−	4.19714i	0.455281	−	0.330781i
$162$	13.8583	+	10.0686i	1.08881	+	0.791066i
$163$	−5.29311	−	3.84567i	−0.414588	−	0.301216i	0.360869	−	0.932617i	$-0.382480\pi$
$163$	−5.29311	−	3.84567i	−0.414588	−	0.301216i	−0.775457	+	0.631401i	$0.782480\pi$
$164$	2.75146	−	1.99906i	0.214853	−	0.156100i
$165$	5.49471	−	13.6841i	0.427763	−	1.06531i
$166$	11.6503	+	8.46441i	0.904235	+	0.656965i
$167$	3.87799	+	11.9352i	0.300088	+	0.923575i	0.981465	+	0.191642i	$0.0613814\pi$
$167$	3.87799	+	11.9352i	0.300088	+	0.923575i	−0.681377	+	0.731933i	$0.738619\pi$
$168$	−8.90098			−0.686725
$169$	2.73998	+	8.43278i	0.210767	+	0.648675i
$170$	−0.830861	−	3.30228i	−0.0637241	−	0.253273i
$171$	0.446798	−	1.37510i	0.0341675	−	0.105157i
$172$	−1.05388	+	3.24349i	−0.0803572	+	0.247314i
$173$	0.444819	−	0.323180i	0.0338189	−	0.0245709i	−0.570747	−	0.821126i	$-0.693346\pi$
$173$	0.444819	−	0.323180i	0.0338189	−	0.0245709i	0.604566	+	0.796555i	$0.293346\pi$
$174$	−25.9161			−1.96470
$175$	−1.45148	−	8.03062i	−0.109722	−	0.607057i
$176$	−14.0419			−1.05845
$177$	−8.00768	+	5.81792i	−0.601894	+	0.437301i
$178$	6.12716	−	18.8575i	0.459250	−	1.41343i
$179$	0.316718	−	0.974757i	0.0236726	−	0.0728568i	−0.938522	−	0.345219i	$-0.887805\pi$
$179$	0.316718	−	0.974757i	0.0236726	−	0.0728568i	0.962195	+	0.272362i	$0.0878048\pi$
$180$	−1.09541	−	0.0742430i	−0.0816469	−	0.00553374i
$181$	−0.819517	−	2.52221i	−0.0609142	−	0.187475i	0.915969	−	0.401250i	$-0.131424\pi$
$181$	−0.819517	−	2.52221i	−0.0609142	−	0.187475i	−0.976883	+	0.213775i	$0.931424\pi$
$182$	−11.6227			−0.861535
$183$	0.119605	+	0.368106i	0.00884146	+	0.0272112i
$184$	9.06022	+	6.58263i	0.667928	+	0.485278i
$185$	2.61640	+	10.3989i	0.192361	+	0.764545i
$186$	−11.3306	+	8.23214i	−0.830798	+	0.603610i
$187$	−2.50425	−	1.81944i	−0.183129	−	0.133051i
$188$	−2.25621	−	1.63923i	−0.164551	−	0.119553i
$189$	4.11042	−	2.98640i	0.298989	−	0.217228i
$190$	−0.780662	−	3.10276i	−0.0566351	−	0.225098i
$191$	4.16182	+	3.02374i	0.301138	+	0.218790i	0.728085	−	0.685487i	$-0.240411\pi$
$191$	4.16182	+	3.02374i	0.301138	+	0.218790i	−0.426946	+	0.904277i	$0.640411\pi$
$192$	−4.17982	−	12.8641i	−0.301652	−	0.928390i
$193$	7.63389			0.549500			0.274750	−	0.961516i	$-0.411405\pi$
$193$	7.63389			0.549500			0.274750	+	0.961516i	$0.411405\pi$
$194$	−7.60177	−	23.3958i	−0.545775	−	1.67972i
$195$	22.2257	+	1.50638i	1.59161	+	0.107874i
$196$	−0.427536	+	1.31582i	−0.0305383	+	0.0939873i
$197$	4.97916	−	15.3243i	0.354750	−	1.09181i	−0.601404	−	0.798945i	$-0.705392\pi$
$197$	4.97916	−	15.3243i	0.354750	−	1.09181i	0.956154	−	0.292864i	$-0.0946084\pi$
$198$	−5.86852	+	4.26373i	−0.417058	+	0.303010i
$199$	16.0306			1.13638			0.568188	−	0.822899i	$-0.307645\pi$
$199$	16.0306			1.13638			0.568188	+	0.822899i	$0.307645\pi$
$200$	11.2750	−	6.05708i	0.797264	−	0.428300i
$201$	−30.3270			−2.13910
$202$	3.28069	−	2.38356i	0.230828	−	0.167707i
$203$	−4.02886	+	12.3996i	−0.282770	+	0.870278i
$204$	−0.210062	+	0.646503i	−0.0147073	+	0.0452643i
$205$	5.81548	+	23.1138i	0.406171	+	1.61434i
$206$	−0.00680365	−	0.0209395i	−0.000474033	−	0.00145892i
$207$	6.73240			0.467934
$208$	−6.55511	−	20.1746i	−0.454515	−	1.39885i
$209$	−2.35294	−	1.70951i	−0.162757	−	0.118250i
$210$	−4.41207	+	10.9879i	−0.304461	+	0.758237i
$211$	11.4637	−	8.32887i	0.789195	−	0.573383i	−0.118530	−	0.992950i	$-0.537818\pi$
$211$	11.4637	−	8.32887i	0.789195	−	0.573383i	0.907724	+	0.419567i	$0.137818\pi$
$212$	0.476791	+	0.346409i	0.0327461	+	0.0237915i
$213$	−1.82874	−	1.32865i	−0.125303	−	0.0910379i
$214$	−22.3667	+	16.2504i	−1.52896	+	1.11085i
$215$	−18.3414	−	15.3235i	−1.25087	−	1.04505i
$216$	6.44663	+	4.68375i	0.438638	+	0.318689i
$217$	2.17724	+	6.70085i	0.147801	+	0.454883i
$218$	12.2844			0.832005
$219$	0.106379	+	0.327400i	0.00718841	+	0.0221237i
$220$	−0.822933	+	2.04945i	−0.0554821	+	0.138174i
$221$	1.44502	−	4.44732i	0.0972027	−	0.299159i
$222$	4.80778	−	14.7968i	0.322677	−	0.993098i
$223$	−7.15090	+	5.19543i	−0.478859	+	0.347912i	−0.800884	−	0.598820i	$-0.795637\pi$
$223$	−7.15090	+	5.19543i	−0.478859	+	0.347912i	0.322025	+	0.946731i	$0.395637\pi$
$224$	2.91921			0.195048
$225$	3.34329	−	6.92989i	0.222886	−	0.461993i
$226$	14.8046			0.984790
$227$	−16.6317	+	12.0836i	−1.10388	+	0.802018i	−0.981689	−	0.190489i	$-0.938993\pi$
$227$	−16.6317	+	12.0836i	−1.10388	+	0.802018i	−0.122193	+	0.992506i	$0.538993\pi$
$228$	−0.197370	+	0.607442i	−0.0130711	+	0.0402289i
$229$	5.01792	−	15.4436i	0.331593	−	1.02054i	−0.636782	−	0.771044i	$-0.719735\pi$
$229$	5.01792	−	15.4436i	0.331593	−	1.02054i	0.968376	−	0.249496i	$-0.0802649\pi$
$230$	12.6170	−	7.92157i	0.831940	−	0.522333i
$231$	3.32609	+	10.2366i	0.218841	+	0.673522i
$232$	−20.4478			−1.34246
$233$	2.73941	+	8.43104i	0.179465	+	0.552336i	0.999809	−	0.0195340i	$-0.00621828\pi$
$233$	2.73941	+	8.43104i	0.179465	+	0.552336i	−0.820344	+	0.571870i	$0.806218\pi$
$234$	−8.86546	−	6.44114i	−0.579554	−	0.421070i
$235$	16.5521	−	10.3922i	1.07974	−	0.677914i
$236$	1.19929	−	0.871338i	0.0780674	−	0.0567193i
$237$	−21.0005	−	15.2577i	−1.36413	−	0.991096i
$238$	2.01082	+	1.46095i	0.130342	+	0.0946993i
$239$	−12.1783	+	8.84804i	−0.787747	+	0.572332i	−0.907294	−	0.420497i	$-0.861856\pi$
$239$	−12.1783	+	8.84804i	−0.787747	+	0.572332i	0.119547	+	0.992829i	$0.461856\pi$
$240$	−21.5610	−	1.46133i	−1.39175	−	0.0943282i
$241$	−10.6093	−	7.70808i	−0.683403	−	0.496521i	0.191082	−	0.981574i	$-0.438800\pi$
$241$	−10.6093	−	7.70808i	−0.683403	−	0.496521i	−0.874485	+	0.485053i	$0.838800\pi$
$242$	−0.667469	−	2.05426i	−0.0429065	−	0.132053i
$243$	14.6256			0.938234
$244$	−0.0179130	−	0.0551306i	−0.00114676	−	0.00352937i
$245$	−7.44074	−	6.21643i	−0.475371	−	0.397153i
$246$	10.6863	−	32.8890i	0.681332	−	2.09693i
$247$	1.35772	−	4.17862i	0.0863894	−	0.265879i
$248$	−8.93980	+	6.49515i	−0.567678	+	0.412442i
$249$	20.1462			1.27671
$250$	−1.88838	−	16.9209i	−0.119432	−	1.07017i
$251$	−2.60320			−0.164312			−0.0821562	−	0.996619i	$-0.526181\pi$
$251$	−2.60320			−0.164312			−0.0821562	+	0.996619i	$0.526181\pi$
$252$	0.648340	−	0.471047i	0.0408416	−	0.0296732i
$253$	4.18482	−	12.8796i	0.263098	−	0.809731i
$254$	5.91542	−	18.2058i	0.371167	−	1.14233i
$255$	−3.65586	−	3.05432i	−0.228939	−	0.191269i
$256$	2.30936	+	7.10748i	0.144335	+	0.444217i
$257$	13.6691			0.852653			0.426327	−	0.904569i	$-0.359807\pi$
$257$	13.6691			0.852653			0.426327	+	0.904569i	$0.359807\pi$
$258$	10.7159	+	32.9800i	0.667141	+	2.05325i
$259$	−6.33212	−	4.60056i	−0.393459	−	0.285865i
$260$	−3.32869	−	0.225607i	−0.206437	−	0.0139916i
$261$	−9.94472	+	7.22526i	−0.615563	+	0.447232i
$262$	−1.72639	−	1.25429i	−0.106656	−	0.0774905i
$263$	8.39312	+	6.09796i	0.517542	+	0.376016i	0.815677	−	0.578507i	$-0.196365\pi$
$263$	8.39312	+	6.09796i	0.517542	+	0.376016i	−0.298135	+	0.954524i	$0.596365\pi$
$264$	−13.6570	+	9.92240i	−0.840531	+	0.610681i
$265$	−3.49785	+	2.19612i	−0.214871	+	0.134907i
$266$	1.88933	+	1.37268i	0.115842	+	0.0841645i
$267$	−8.57185	−	26.3815i	−0.524589	−	1.61452i
$268$	4.54202			0.277448
$269$	0.510805	+	1.57210i	0.0311443	+	0.0958524i	0.965420	−	0.260698i	$-0.0839527\pi$
$269$	0.510805	+	1.57210i	0.0311443	+	0.0958524i	−0.934276	+	0.356551i	$0.883953\pi$
$270$	8.97739	−	5.63645i	0.546347	−	0.343023i
$271$	−6.15404	+	18.9402i	−0.373832	+	1.15054i	0.570432	+	0.821345i	$0.306776\pi$
$271$	−6.15404	+	18.9402i	−0.373832	+	1.15054i	−0.944264	+	0.329190i	$0.893224\pi$
$272$	−1.40181	+	4.31432i	−0.0849970	+	0.261594i
$273$	−13.1547	+	9.55746i	−0.796160	+	0.578444i
$274$	2.29513			0.138654
$275$	−11.1792	−	10.7035i	−0.674132	−	0.645448i
$276$	−2.97399			−0.179013
$277$	16.4183	−	11.9286i	0.986481	−	0.716721i	0.0273337	−	0.999626i	$-0.491298\pi$
$277$	16.4183	−	11.9286i	0.986481	−	0.716721i	0.959148	+	0.282906i	$0.0912983\pi$
$278$	3.68348	−	11.3366i	0.220921	−	0.679924i
$279$	−2.05277	+	6.31779i	−0.122896	+	0.378236i
$280$	−3.48111	+	8.66943i	−0.208036	+	0.518097i
$281$	5.87839	+	18.0918i	0.350675	+	1.07927i	0.958475	+	0.285177i	$0.0920523\pi$
$281$	5.87839	+	18.0918i	0.350675	+	1.07927i	−0.607800	+	0.794090i	$0.707948\pi$
$282$	−28.3570			−1.68863
$283$	3.27599	+	10.0825i	0.194737	+	0.599340i	0.999980	+	0.00639372i	$0.00203520\pi$
$283$	3.27599	+	10.0825i	0.194737	+	0.599340i	−0.805242	+	0.592946i	$0.797965\pi$
$284$	0.273886	+	0.198990i	0.0162522	+	0.0118079i
$285$	−3.43498	−	2.86978i	−0.203471	−	0.169991i
$286$	−17.8331	+	12.9565i	−1.05449	+	0.766134i
$287$	−14.0744	−	10.2257i	−0.830788	−	0.603603i
$288$	2.22668	+	1.61778i	0.131209	+	0.0953286i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−10.1356	+	25.2420i	−0.595185	+	1.48226i
$291$	−27.8423	−	20.2286i	−1.63214	−	1.18582i
$292$	−0.0159321	−	0.0490341i	−0.000932358	−	0.00286950i
$293$	23.4992			1.37284			0.686419	−	0.727206i	$-0.259182\pi$
$293$	23.4992			1.37284			0.686419	+	0.727206i	$0.259182\pi$
$294$	4.34722	+	13.3794i	0.253535	+	0.780300i
$295$	2.53482	+	10.0747i	0.147583	+	0.586572i
$296$	3.79333	−	11.6747i	0.220483	−	0.678576i
$297$	2.97763	−	9.16422i	0.172780	−	0.531762i
$298$	−10.7131	+	7.78355i	−0.620595	+	0.450889i
$299$	20.4582			1.18313
$300$	−1.47688	+	3.06123i	−0.0852675	+	0.176740i
$301$	17.4451			1.00552
$302$	28.5146	−	20.7171i	1.64083	−	1.19213i
$303$	1.75309	−	5.39546i	0.100713	−	0.309961i
$304$	−1.31711	+	4.05365i	−0.0755415	+	0.232493i
$305$	0.405307	+	0.0274703i	0.0232078	+	0.00157295i
$306$	0.724159	+	2.22873i	0.0413974	+	0.127408i
$307$	21.1552			1.20739			0.603695	−	0.797215i	$-0.293694\pi$
$307$	21.1552			1.20739			0.603695	+	0.797215i	$0.293694\pi$
$308$	−0.498142	−	1.53312i	−0.0283843	−	0.0873578i
$309$	−0.0249191	−	0.0181048i	−0.00141760	−	0.00102995i
$310$	3.58668	+	14.2554i	0.203710	+	0.809650i
$311$	−10.5617	+	7.67354i	−0.598901	+	0.435127i	−0.845488	−	0.533994i	$-0.820691\pi$
$311$	−10.5617	+	7.67354i	−0.598901	+	0.435127i	0.246588	+	0.969120i	$0.420691\pi$
$312$	−20.6314	−	14.9896i	−1.16802	−	0.848617i
$313$	19.6503	+	14.2768i	1.11070	+	0.806972i	0.982774	−	0.184811i	$-0.0591674\pi$
$313$	19.6503	+	14.2768i	1.11070	+	0.806972i	0.127928	+	0.991783i	$0.459167\pi$
$314$	−1.69490	+	1.23142i	−0.0956490	+	0.0694931i
$315$	1.37033	+	5.44641i	0.0772093	+	0.306870i
$316$	3.14520	+	2.28512i	0.176931	+	0.128548i
$317$	0.915938	+	2.81897i	0.0514442	+	0.158329i	0.973478	−	0.228780i	$-0.0734737\pi$
$317$	0.915938	+	2.81897i	0.0514442	+	0.158329i	−0.922034	+	0.387109i	$0.873474\pi$
$318$	5.99250			0.336043
$319$	7.64086	+	23.5162i	0.427806	+	1.31665i
$320$	−14.1642	−	0.960000i	−0.791803	−	0.0536656i
$321$	−11.9521	+	36.7847i	−0.667099	+	2.05312i
$322$	−3.36027	+	10.3418i	−0.187261	+	0.576329i
$323$	−0.760137	+	0.552272i	−0.0422952	+	0.0307292i
$324$	−3.58910			−0.199395
$325$	10.1595	−	21.0583i	0.563547	−	1.16811i
$326$	9.96346			0.551825
$327$	13.9036	−	10.1016i	0.768870	−	0.558617i
$328$	8.43146	−	25.9494i	0.465549	−	1.43281i
$329$	−4.40830	+	13.5674i	−0.243038	+	0.747993i
$330$	5.47924	+	21.7774i	0.301622	+	1.19881i
$331$	4.54541	+	13.9893i	0.249838	+	0.768923i	0.994803	+	0.101819i	$0.0324664\pi$
$331$	4.54541	+	13.9893i	0.249838	+	0.768923i	−0.744965	+	0.667104i	$0.767534\pi$
$332$	−3.01726			−0.165594
$333$	−2.28039	−	7.01832i	−0.124965	−	0.384602i
$334$	−15.4611	−	11.2331i	−0.845991	−	0.614649i
$335$	−11.8607	+	29.5381i	−0.648019	+	1.61384i
$336$	12.7613	−	9.27163i	0.696186	−	0.505809i
$337$	29.0076	+	21.0752i	1.58014	+	1.14804i	0.916532	+	0.399962i	$0.130977\pi$
$337$	29.0076	+	21.0752i	1.58014	+	1.14804i	0.663610	+	0.748078i	$0.269023\pi$
$338$	−10.9239	−	7.93671i	−0.594184	−	0.431700i
$339$	16.7560	−	12.1740i	0.910062	−	0.661199i
$340$	0.547531	+	0.457440i	0.0296941	+	0.0248082i
$341$	10.8104	+	7.85421i	0.585416	+	0.425329i
$342$	0.680406	+	2.09408i	0.0367922	+	0.113235i
$343$	18.5022			0.999024
$344$	8.45480	+	26.0212i	0.455852	+	1.40297i
$345$	7.76606	−	19.3407i	0.418111	−	1.04127i
$346$	−0.258741	+	0.796323i	−0.0139100	+	0.0428106i
$347$	9.85667	−	30.3357i	0.529134	−	1.62851i	−0.226860	−	0.973927i	$-0.572846\pi$
$347$	9.85667	−	30.3357i	0.529134	−	1.62851i	0.755993	−	0.654579i	$-0.227154\pi$
$348$	4.39301	−	3.19171i	0.235490	−	0.171094i
$349$	−18.5999			−0.995629			−0.497815	−	0.867283i	$-0.665864\pi$
$349$	−18.5999			−0.995629			−0.497815	+	0.867283i	$0.665864\pi$
$350$	8.97652	+	8.59458i	0.479815	+	0.459400i
$351$	14.5567			0.776977
$352$	4.47902	−	3.25420i	0.238733	−	0.173450i
$353$	−10.2010	+	31.3955i	−0.542945	+	1.67101i	0.182882	+	0.983135i	$0.441458\pi$
$353$	−10.2010	+	31.3955i	−0.542945	+	1.67101i	−0.725827	+	0.687878i	$0.758542\pi$
$354$	4.65788	−	14.3355i	0.247564	−	0.761923i
$355$	−2.00930	+	1.26153i	−0.106642	+	0.0669553i
$356$	1.28379	+	3.95110i	0.0680407	+	0.209408i
$357$	3.47722			0.184034
$358$	0.482314	+	1.48441i	0.0254911	+	0.0784535i
$359$	19.0226	+	13.8207i	1.00398	+	0.729431i	0.962937	−	0.269727i	$-0.0869334\pi$
$359$	19.0226	+	13.8207i	1.00398	+	0.729431i	0.0410385	+	0.999158i	$0.486933\pi$
$360$	−7.45974	+	4.68359i	−0.393163	+	0.246847i
$361$	14.6571	−	10.6490i	0.771427	−	0.560474i
$362$	3.26731	+	2.37384i	0.171726	+	0.124766i
$363$	−2.44468	−	1.77616i	−0.128312	−	0.0932243i
$364$	1.97016	−	1.43140i	0.103264	−	0.0750259i
$365$	0.360487	+	0.0244326i	0.0188688	+	0.00127886i
$366$	−0.476850	−	0.346452i	−0.0249254	−	0.0181093i
$367$	−2.15592	−	6.63524i	−0.112538	−	0.346357i	0.878887	−	0.477029i	$-0.158286\pi$
$367$	−2.15592	−	6.63524i	−0.112538	−	0.346357i	−0.991426	+	0.130672i	$0.958286\pi$
$368$	−19.8464			−1.03456
$369$	−5.06864	−	15.5997i	−0.263863	−	0.812086i
$370$	−12.5316	−	10.4696i	−0.651487	−	0.544291i
$371$	0.931580	−	2.86711i	0.0483652	−	0.148853i
$372$	0.906799	−	2.79084i	0.0470154	−	0.144698i
$373$	−2.58238	+	1.87621i	−0.133711	+	0.0971465i	−0.652630	−	0.757677i	$-0.726334\pi$
$373$	−2.58238	+	1.87621i	−0.133711	+	0.0971465i	0.518920	+	0.854823i	$0.326334\pi$
$374$	4.71386			0.243748
$375$	−16.0515	−	17.5984i	−0.828895	−	0.908779i
$376$	−22.3736			−1.15383
$377$	−30.2197	+	21.9559i	−1.55639	+	1.13079i
$378$	−2.39094	+	7.35855i	−0.122977	+	0.378483i
$379$	−2.82386	+	8.69096i	−0.145052	+	0.446424i	−0.997018	−	0.0771733i	$-0.975411\pi$
$379$	−2.82386	+	8.69096i	−0.145052	+	0.446424i	0.851966	+	0.523598i	$0.175411\pi$
$380$	0.514450	+	0.429802i	0.0263907	+	0.0220484i
$381$	−8.27563	−	25.4698i	−0.423973	−	1.30486i
$382$	−7.83398			−0.400821
$383$	−0.582476	−	1.79268i	−0.0297631	−	0.0916015i	0.935071	−	0.354459i	$-0.115335\pi$
$383$	−0.582476	−	1.79268i	−0.0297631	−	0.0916015i	−0.964835	+	0.262858i	$0.915335\pi$
$384$	22.8299	+	16.5869i	1.16503	+	0.846445i
$385$	11.2712	+	0.763920i	0.574432	+	0.0389330i
$386$	−9.40505	+	6.83317i	−0.478704	+	0.347799i
$387$	13.3066	+	9.66781i	0.676412	+	0.491442i
$388$	4.16989	+	3.02960i	0.211694	+	0.153805i
$389$	9.39049	−	6.82259i	0.476117	−	0.345919i	−0.323703	−	0.946159i	$-0.604928\pi$
$389$	9.39049	−	6.82259i	0.476117	−	0.345919i	0.799820	+	0.600239i	$0.204928\pi$
$390$	−28.7306	+	18.0385i	−1.45483	+	0.913415i
$391$	−3.53943	−	2.57154i	−0.178996	−	0.130049i
$392$	3.42994	+	10.5563i	0.173238	+	0.533173i
$393$	−2.98535			−0.150591
$394$	7.58252	+	23.3366i	0.382002	+	1.17568i
$395$	−23.0739	+	14.4870i	−1.16098	+	0.728918i
$396$	0.469665	−	1.44548i	0.0236016	−	0.0726381i
$397$	−8.28193	+	25.4892i	−0.415658	+	1.27926i	0.496003	+	0.868321i	$0.334801\pi$
$397$	−8.28193	+	25.4892i	−0.415658	+	1.27926i	−0.911661	+	0.410943i	$0.865199\pi$
$398$	−19.7498	+	14.3491i	−0.989970	+	0.719255i
$399$	3.26713			0.163561
$400$	−9.85565	+	20.4285i	−0.492783	+	1.02143i
$401$	20.0436			1.00093			0.500465	−	0.865757i	$-0.333162\pi$
$401$	20.0436			1.00093			0.500465	+	0.865757i	$0.333162\pi$
$402$	37.3633	−	27.1460i	1.86351	−	1.35392i
$403$	−6.23791	+	19.1983i	−0.310732	+	0.956336i
$404$	−0.262557	+	0.808068i	−0.0130627	+	0.0402029i
$405$	9.37232	−	23.3410i	0.465714	−	1.15982i
$406$	−6.13535	−	18.8827i	−0.304492	−	0.937131i
$407$	−14.8440			−0.735792
$408$	1.68524	+	5.18662i	0.0834316	+	0.256776i
$409$	−13.6761	−	9.93624i	−0.676238	−	0.491316i	0.195870	−	0.980630i	$-0.437247\pi$
$409$	−13.6761	−	9.93624i	−0.676238	−	0.491316i	−0.872107	+	0.489314i	$0.837247\pi$
$410$	−27.8541	−	23.2709i	−1.37562	−	1.14927i
$411$	2.59765	−	1.88730i	0.128133	−	0.0930937i
$412$	0.00373209	+	0.00271152i	0.000183867	+	0.000133587i
$413$	−6.13470	−	4.45712i	−0.301869	−	0.219320i
$414$	−8.29439	+	6.02623i	−0.407647	+	0.296173i
$415$	7.87904	−	19.6221i	0.386767	−	0.963212i
$416$	6.76637	+	4.91606i	0.331749	+	0.241030i
$417$	−5.15316	−	15.8598i	−0.252351	−	0.776658i
$418$	4.42906			0.216632
$419$	3.41195	+	10.5009i	0.166685	+	0.513003i	0.999157	−	0.0410644i	$-0.0130749\pi$
$419$	3.41195	+	10.5009i	0.166685	+	0.513003i	−0.832472	+	0.554068i	$0.813075\pi$
$420$	−0.605334	−	2.40591i	−0.0295373	−	0.117397i
$421$	7.42367	−	22.8477i	0.361808	−	1.11353i	−0.590149	−	0.807295i	$-0.700931\pi$
$421$	7.42367	−	22.8477i	0.361808	−	1.11353i	0.951956	−	0.306234i	$-0.0990691\pi$
$422$	−6.66818	+	20.5225i	−0.324602	+	0.999022i
$423$	−10.8813	+	7.90575i	−0.529068	+	0.384391i
$424$	4.72807			0.229616
$425$	−4.40465	+	2.36623i	−0.213657	+	0.114779i
$426$	3.44232			0.166781
$427$	−0.239890	+	0.174290i	−0.0116091	+	0.00843448i
$428$	1.79004	−	5.50917i	0.0865247	−	0.266296i
$429$	−9.52942	+	29.3286i	−0.460085	+	1.41600i
$430$	36.3130	+	2.46117i	1.75117	+	0.118688i
$431$	3.71327	+	11.4283i	0.178862	+	0.550480i	0.999789	−	0.0205531i	$-0.00654271\pi$
$431$	3.71327	+	11.4283i	0.178862	+	0.550480i	−0.820927	+	0.571033i	$0.806543\pi$
$432$	−14.1213			−0.679412
$433$	−1.60947	−	4.95345i	−0.0773463	−	0.238047i	0.904906	−	0.425611i	$-0.139941\pi$
$433$	−1.60947	−	4.95345i	−0.0773463	−	0.238047i	−0.982252	+	0.187564i	$0.939941\pi$
$434$	−8.68038	−	6.30666i	−0.416671	−	0.302730i
$435$	9.28505	+	36.9037i	0.445184	+	1.76939i
$436$	−2.08231	+	1.51289i	−0.0997248	+	0.0724543i
$437$	−3.32558	−	2.41617i	−0.159084	−	0.115581i
$438$	−0.424119	−	0.308140i	−0.0202652	−	0.0147235i
$439$	17.5835	−	12.7752i	0.839216	−	0.609726i	−0.0829355	−	0.996555i	$-0.526430\pi$
$439$	17.5835	−	12.7752i	0.839216	−	0.609726i	0.922152	+	0.386829i	$0.126430\pi$
$440$	4.32311	+	17.1823i	0.206096	+	0.819135i
$441$	5.39822	+	3.92204i	0.257058	+	0.186764i
$442$	2.20055	+	6.77261i	0.104670	+	0.322140i
$443$	6.94352			0.329897			0.164948	−	0.986302i	$-0.447254\pi$
$443$	6.94352			0.329897			0.164948	+	0.986302i	$0.447254\pi$
$444$	1.00735	+	3.10030i	0.0478066	+	0.147134i
$445$	−29.0476	−	1.96874i	−1.37699	−	0.0933273i
$446$	4.15951	−	12.8017i	0.196959	−	0.606176i
$447$	−5.72475	+	17.6190i	−0.270771	+	0.833349i
$448$	8.38338	−	6.09088i	0.396077	−	0.287767i
$449$	−19.0811			−0.900492			−0.450246	−	0.892905i	$-0.648664\pi$
$449$	−19.0811			−0.900492			−0.450246	+	0.892905i	$0.648664\pi$
$450$	2.08403	+	11.5303i	0.0982422	+	0.543544i
$451$	−32.9939			−1.55362
$452$	−2.50952	+	1.82327i	−0.118038	+	0.0857595i
$453$	15.2373	−	46.8955i	0.715909	−	2.20334i
$454$	9.67426	−	29.7743i	0.454036	−	1.39738i
$455$	4.16411	+	16.5504i	0.195217	+	0.775893i
$456$	1.58342	+	4.87325i	0.0741503	+	0.228211i
$457$	−28.1840			−1.31839			−0.659197	−	0.751971i	$-0.729103\pi$
$457$	−28.1840			−1.31839			−0.659197	+	0.751971i	$0.729103\pi$
$458$	7.64154	+	23.5182i	0.357066	+	1.09894i
$459$	−2.51841	−	1.82973i	−0.117549	−	0.0854047i
$460$	−1.16311	+	2.89663i	−0.0542302	+	0.135056i
$461$	−30.9481	+	22.4851i	−1.44140	+	1.04724i	−0.453650	+	0.891180i	$0.649878\pi$
$461$	−30.9481	+	22.4851i	−1.44140	+	1.04724i	−0.987748	+	0.156057i	$0.950122\pi$
$462$	−13.2607	−	9.63446i	−0.616944	−	0.448236i
$463$	−8.68292	−	6.30851i	−0.403530	−	0.293181i	0.367448	−	0.930044i	$-0.380232\pi$
$463$	−8.68292	−	6.30851i	−0.403530	−	0.293181i	−0.770977	+	0.636863i	$0.780232\pi$
$464$	29.3159	−	21.2993i	1.36096	−	0.988794i
$465$	15.7817	+	13.1850i	0.731859	+	0.611439i
$466$	−10.9217	−	7.93507i	−0.505937	−	0.367585i
$467$	−3.24253	−	9.97948i	−0.150046	−	0.461795i	0.847579	−	0.530669i	$-0.178059\pi$
$467$	−3.24253	−	9.97948i	−0.150046	−	0.461795i	−0.997625	+	0.0688740i	$0.978059\pi$
$468$	2.29603			0.106134
$469$	−7.17958	−	22.0965i	−0.331522	−	1.02032i
$470$	−11.0902	+	27.6193i	−0.511554	+	1.27398i
$471$	−0.905702	+	2.78746i	−0.0417325	+	0.128440i
$472$	3.67506	−	11.3107i	0.169158	−	0.520616i
$473$	26.7665	−	19.4470i	1.23073	−	0.894175i
$474$	39.5302			1.81568
$475$	−4.13853	+	2.22327i	−0.189889	+	0.102011i
$476$	−0.520776			−0.0238697
$477$	2.29948	−	1.67067i	0.105286	−	0.0764949i
$478$	7.08383	−	21.8018i	0.324007	−	0.997190i
$479$	11.6647	−	35.9002i	0.532973	−	1.64032i	−0.215017	−	0.976610i	$-0.568981\pi$
$479$	11.6647	−	35.9002i	0.532973	−	1.64032i	0.747989	−	0.663711i	$-0.231019\pi$
$480$	7.21609	−	4.53062i	0.329368	−	0.206793i
$481$	−6.92958	−	21.3271i	−0.315962	−	0.972430i
$482$	19.9703			0.909623
$483$	4.70099	+	14.4682i	0.213903	+	0.658324i
$484$	0.366135	+	0.266012i	0.0166425	+	0.0120915i
$485$	−30.5913	+	19.2067i	−1.38908	+	0.872133i
$486$	−18.0189	+	13.0915i	−0.817356	+	0.593844i
$487$	−23.4984	−	17.0726i	−1.06481	−	0.773633i	−0.0898416	−	0.995956i	$-0.528636\pi$
$487$	−23.4984	−	17.0726i	−1.06481	−	0.773633i	−0.974973	+	0.222323i	$0.928636\pi$
$488$	−0.376234	−	0.273350i	−0.0170313	−	0.0123740i
$489$	11.2767	−	8.19302i	0.509951	−	0.370501i
$490$	14.7315	+	0.998448i	0.665500	+	0.0451053i
$491$	27.0761	+	19.6720i	1.22193	+	0.887783i	0.996259	−	0.0864205i	$-0.0275429\pi$
$491$	27.0761	+	19.6720i	1.22193	+	0.887783i	0.225670	+	0.974204i	$0.427543\pi$
$492$	2.23904	+	6.89105i	0.100944	+	0.310672i
$493$	7.98804			0.359763
$494$	2.06760	+	6.36341i	0.0930256	+	0.286303i
$495$	8.17393	+	6.82899i	0.367391	+	0.306940i
$496$	6.05135	−	18.6241i	0.271714	−	0.836249i
$497$	0.535134	−	1.64697i	0.0240040	−	0.0738768i
$498$	−24.8204	+	18.0330i	−1.11223	+	0.808080i
$499$	25.1237			1.12469			0.562346	−	0.826902i	$-0.309899\pi$
$499$	25.1237			1.12469			0.562346	+	0.826902i	$0.309899\pi$
$500$	2.40400	+	2.63568i	0.107510	+	0.117871i
$501$	−26.7360			−1.19448
$502$	3.20717	−	2.33015i	0.143143	−	0.104000i
$503$	6.64545	−	20.4526i	0.296306	−	0.911937i	−0.686473	−	0.727155i	$-0.740842\pi$
$503$	6.64545	−	20.4526i	0.296306	−	0.911937i	0.982780	−	0.184782i	$-0.0591578\pi$
$504$	1.98674	−	6.11457i	0.0884966	−	0.272365i
$505$	−4.56948	−	3.81762i	−0.203339	−	0.169882i
$506$	6.37286	+	19.6137i	0.283308	+	0.871933i
$507$	−18.8902			−0.838944
$508$	1.23943	+	3.81456i	0.0549906	+	0.169244i
$509$	17.0019	+	12.3526i	0.753597	+	0.547521i	0.896940	−	0.442153i	$-0.145785\pi$
$509$	17.0019	+	12.3526i	0.753597	+	0.547521i	−0.143342	+	0.989673i	$0.545785\pi$
$510$	7.23802	+	0.490568i	0.320505	+	0.0217227i
$511$	−0.213362	+	0.155017i	−0.00943858	+	0.00685753i
$512$	12.2248	+	8.88183i	0.540264	+	0.392525i
$513$	−2.36625	−	1.71918i	−0.104473	−	0.0759038i
$514$	−16.8405	+	12.2353i	−0.742801	+	0.539677i
$515$	−0.0273795	+	0.0171902i	−0.00120649	+	0.000757491i
$516$	−5.87810	−	4.27069i	−0.258769	−	0.188007i
$517$	8.36049	+	25.7309i	0.367694	+	1.13165i
$518$	11.9193			0.523702
$519$	0.361977	+	1.11405i	0.0158890	+	0.0489013i
$520$	−22.6684	+	14.2323i	−0.994076	+	0.624130i
$521$	1.39376	−	4.28955i	0.0610617	−	0.187929i	−0.915872	−	0.401469i	$-0.868500\pi$
$521$	1.39376	−	4.28955i	0.0610617	−	0.187929i	0.976934	+	0.213541i	$0.0684996\pi$
$522$	5.78462	−	17.8032i	0.253186	−	0.779226i
$523$	10.8796	−	7.90450i	0.475732	−	0.345640i	−0.323939	−	0.946078i	$-0.605007\pi$
$523$	10.8796	−	7.90450i	0.475732	−	0.345640i	0.799671	+	0.600438i	$0.205007\pi$
$524$	0.447110			0.0195321
$525$	17.2271	+	2.34596i	0.751852	+	0.102386i
$526$	−15.7988			−0.688859
$527$	3.49238	−	2.53737i	0.152131	−	0.110529i
$528$	9.24443	−	28.4514i	0.402312	−	1.23819i
$529$	−1.19269	+	3.67072i	−0.0518561	+	0.159597i
$530$	2.34363	−	5.83661i	0.101801	−	0.253526i
$531$	−2.20929	−	6.79950i	−0.0958751	−	0.295073i
$532$	−0.489312			−0.0212143
$533$	−15.4024	−	47.4038i	−0.667153	−	2.05328i
$534$	34.1749	+	24.8295i	1.47889	+	1.07448i
$535$	31.1534	+	26.0274i	1.34688	+	1.12526i
$536$	29.4795	−	21.4181i	1.27332	−	0.925123i
$537$	1.76653	+	1.28346i	0.0762313	+	0.0553853i
$538$	−2.03652	−	1.47962i	−0.0878004	−	0.0637907i
$539$	10.8587	−	7.88928i	0.467716	−	0.339815i
$540$	−0.827588	+	2.06104i	−0.0356137	+	0.0886931i
$541$	−13.7502	−	9.99008i	−0.591166	−	0.429507i	0.251567	−	0.967840i	$-0.419054\pi$
$541$	−13.7502	−	9.99008i	−0.591166	−	0.429507i	−0.842732	+	0.538333i	$0.819054\pi$
$542$	−9.37169	−	28.8431i	−0.402549	−	1.23892i
$543$	5.65000			0.242465
$544$	−0.552699	−	1.70103i	−0.0236968	−	0.0729312i
$545$	−4.40117	−	17.4925i	−0.188525	−	0.749298i
$546$	7.65180	−	23.5498i	0.327467	−	1.00784i
$547$	7.49078	−	23.0542i	0.320283	−	0.985729i	−0.653243	−	0.757149i	$-0.726592\pi$
$547$	7.49078	−	23.0542i	0.320283	−	0.985729i	0.973525	−	0.228580i	$-0.0734082\pi$
$548$	−0.389045	+	0.282658i	−0.0166192	+	0.0120745i
$549$	−0.279569			−0.0119317
$550$	23.3538	+	3.18028i	0.995808	+	0.135608i
$551$	7.50542			0.319741
$552$	−19.3024	+	14.0240i	−0.821565	+	0.596902i
$553$	6.14526	−	18.9132i	0.261323	−	0.804270i
$554$	−9.55016	+	29.3924i	−0.405748	+	1.24876i
$555$	−22.7926	−	1.54481i	−0.967494	−	0.0655734i
$556$	0.771779	+	2.37529i	0.0327307	+	0.100735i
$557$	41.8652			1.77389			0.886943	−	0.461880i	$-0.152825\pi$
$557$	41.8652			1.77389			0.886943	+	0.461880i	$0.152825\pi$
$558$	−3.12607	−	9.62105i	−0.132337	−	0.407291i
$559$	40.4357	+	29.3782i	1.71025	+	1.24257i
$560$	−4.03958	−	16.0554i	−0.170703	−	0.678465i
$561$	5.33519	−	3.87624i	0.225252	−	0.163655i
$562$	−23.4364	−	17.0275i	−0.988605	−	0.718263i
$563$	−12.9020	−	9.37384i	−0.543754	−	0.395060i	0.281723	−	0.959496i	$-0.409094\pi$
$563$	−12.9020	−	9.37384i	−0.543754	−	0.395060i	−0.825477	+	0.564435i	$0.809094\pi$
$564$	4.80676	−	3.49231i	0.202401	−	0.147053i
$565$	−5.30410	−	21.0813i	−0.223145	−	0.886896i
$566$	−13.0610	−	9.48934i	−0.548993	−	0.398867i
$567$	5.67330	+	17.4606i	0.238256	+	0.733277i
$568$	2.71598			0.113960
$569$	−5.26812	−	16.2136i	−0.220851	−	0.679710i	−0.998686	−	0.0512415i	$-0.983682\pi$
$569$	−5.26812	−	16.2136i	−0.220851	−	0.679710i	0.777835	−	0.628468i	$-0.216318\pi$
$570$	6.80071	+	0.460928i	0.284850	+	0.0193062i
$571$	9.30128	−	28.6264i	0.389246	−	1.19798i	−0.544106	−	0.839016i	$-0.683131\pi$
$571$	9.30128	−	28.6264i	0.389246	−	1.19798i	0.933353	−	0.358961i	$-0.116869\pi$
$572$	1.42720	−	4.39248i	0.0596744	−	0.183659i
$573$	−8.86657	+	6.44194i	−0.370406	+	0.269116i
$574$	26.4930			1.10580
$575$	−15.8004	−	15.1281i	−0.658920	−	0.630884i
$576$	9.77004			0.407085
$577$	−26.4063	+	19.1853i	−1.09931	+	0.798696i	−0.980947	−	0.194275i	$-0.937765\pi$
$577$	−26.4063	+	19.1853i	−1.09931	+	0.798696i	−0.118363	+	0.992970i	$0.537765\pi$
$578$	0.470587	−	1.44832i	0.0195738	−	0.0602420i
$579$	−5.02575	+	15.4677i	−0.208863	+	0.642815i
$580$	−1.39060	−	5.52699i	−0.0577417	−	0.229496i
$581$	4.76938	+	14.6786i	0.197867	+	0.608973i
$582$	52.4089			2.17242
$583$	−1.76677	−	5.43756i	−0.0731722	−	0.225201i
$584$	−0.334629	−	0.243122i	−0.0138470	−	0.0100605i
$585$	−5.99569	+	14.9318i	−0.247891	+	0.617353i
$586$	−28.9513	+	21.0344i	−1.19597	+	0.868921i
$587$	−0.939665	−	0.682707i	−0.0387841	−	0.0281783i	0.568224	−	0.822874i	$-0.307631\pi$
$587$	−0.939665	−	0.682707i	−0.0387841	−	0.0281783i	−0.607008	+	0.794695i	$0.707631\pi$
$588$	−2.38463	−	1.73254i	−0.0983405	−	0.0714485i
$589$	3.28138	−	2.38406i	0.135207	−	0.0982335i
$590$	−12.1409	−	10.1432i	−0.499833	−	0.417590i
$591$	27.7718	+	20.1774i	1.14238	+	0.829987i
$592$	6.72234	+	20.6892i	0.276286	+	0.850322i
$593$	13.9190			0.571583			0.285792	−	0.958292i	$-0.407743\pi$
$593$	13.9190			0.571583			0.285792	+	0.958292i	$0.407743\pi$
$594$	4.53449	+	13.9557i	0.186052	+	0.572611i
$595$	1.35992	−	3.38676i	0.0557511	−	0.138844i
$596$	0.857385	−	2.63876i	0.0351199	−	0.108088i
$597$	−10.5537	+	32.4808i	−0.431933	+	1.32935i
$598$	−25.2047	+	18.3123i	−1.03070	+	0.748846i
$599$	−34.1703			−1.39616			−0.698080	−	0.716020i	$-0.745962\pi$
$599$	−34.1703			−1.39616			−0.698080	+	0.716020i	$0.745962\pi$
$600$	4.84988	+	26.8329i	0.197996	+	1.09545i
$601$	−36.5372			−1.49038			−0.745192	−	0.666850i	$-0.767642\pi$
$601$	−36.5372			−1.49038			−0.745192	+	0.666850i	$0.767642\pi$
$602$	−21.4926	+	15.6153i	−0.875973	+	0.636432i
$603$	6.76915	−	20.8333i	0.275661	−	0.848398i
$604$	−2.28206	+	7.02345i	−0.0928556	+	0.285780i
$605$	−2.68605	+	1.68644i	−0.109204	+	0.0685634i
$606$	2.66970	+	8.21649i	0.108449	+	0.333772i
$607$	14.8506			0.602766			0.301383	−	0.953503i	$-0.402552\pi$
$607$	14.8506			0.602766			0.301383	+	0.953503i	$0.402552\pi$
$608$	−0.519306	−	1.59826i	−0.0210606	−	0.0648179i
$609$	−22.4714	−	16.3264i	−0.910587	−	0.661580i
$610$	−0.523932	+	0.328950i	−0.0212134	+	0.0133188i
$611$	−33.0658	+	24.0237i	−1.33770	+	0.971897i
$612$	−0.397232	−	0.288606i	−0.0160571	−	0.0116662i
$613$	−35.2365	−	25.6008i	−1.42319	−	1.03401i	−0.991235	−	0.132110i	$-0.957825\pi$
$613$	−35.2365	−	25.6008i	−1.42319	−	1.03401i	−0.431952	−	0.901896i	$-0.642175\pi$
$614$	−26.0634	+	18.9362i	−1.05184	+	0.764203i
$615$	−50.6613	−	3.43365i	−2.04286	−	0.138458i
$616$	−10.4627	−	7.60157i	−0.421553	−	0.306276i
$617$	−10.4052	−	32.0239i	−0.418898	−	1.28924i	−0.908717	−	0.417412i	$-0.862937\pi$
$617$	−10.4052	−	32.0239i	−0.418898	−	1.28924i	0.489819	−	0.871824i	$-0.337063\pi$
$618$	0.0469064			0.00188685
$619$	−2.26021	−	6.95621i	−0.0908455	−	0.279594i	0.895303	−	0.445457i	$-0.146959\pi$
$619$	−2.26021	−	6.95621i	−0.0908455	−	0.279594i	−0.986149	+	0.165863i	$0.946959\pi$
$620$	−2.36360	−	1.97469i	−0.0949243	−	0.0793054i
$621$	4.20850	−	12.9524i	0.168881	−	0.519763i
$622$	6.14352	−	18.9078i	0.246333	−	0.758134i
$623$	17.1924	−	12.4910i	0.688799	−	0.500442i
$624$	45.1929			1.80916
$625$	−23.4183	+	8.75129i	−0.936730	+	0.350052i
$626$	−36.9887			−1.47837
$627$	5.01284	−	3.64204i	0.200194	−	0.145449i
$628$	0.135645	−	0.417473i	0.00541283	−	0.0166590i
$629$	−1.48189	+	4.56078i	−0.0590867	+	0.181850i
$630$	−6.56339	−	5.48344i	−0.261492	−	0.218466i
$631$	−1.98434	−	6.10717i	−0.0789953	−	0.243122i	0.903758	−	0.428044i	$-0.140797\pi$
$631$	−1.98434	−	6.10717i	−0.0789953	−	0.243122i	−0.982753	+	0.184921i	$0.940797\pi$
$632$	31.1892			1.24064
$633$	9.32873	+	28.7109i	0.370784	+	1.14116i
$634$	−3.65173	−	2.65314i	−0.145029	−	0.105370i
$635$	−28.0437	−	1.90071i	−1.11288	−	0.0754273i
$636$	−1.01578	+	0.738009i	−0.0402784	+	0.0292640i
$637$	16.4040	+	11.9182i	0.649949	+	0.472215i
$638$	−30.4632	−	22.1328i	−1.20605	−	0.876245i
$639$	1.32091	−	0.959696i	0.0522543	−	0.0379650i
$640$	25.0840	−	15.7490i	0.991532	−	0.622532i
$641$	−5.18929	−	3.77024i	−0.204965	−	0.148916i	0.480568	−	0.876958i	$-0.340431\pi$
$641$	−5.18929	−	3.77024i	−0.204965	−	0.148916i	−0.685533	+	0.728042i	$0.740431\pi$
$642$	−18.2012	−	56.0175i	−0.718344	−	2.21084i
$643$	46.9666			1.85218			0.926091	−	0.377299i	$-0.123147\pi$
$643$	46.9666			1.85218			0.926091	+	0.377299i	$0.123147\pi$
$644$	−0.704058	−	2.16687i	−0.0277438	−	0.0853866i
$645$	43.1232	−	27.0749i	1.69797	−	1.06607i
$646$	0.442154	−	1.36081i	0.0173963	−	0.0535404i
$647$	−8.67765	+	26.7071i	−0.341154	+	1.04996i	0.622457	+	0.782654i	$0.286135\pi$
$647$	−8.67765	+	26.7071i	−0.341154	+	1.04996i	−0.963611	+	0.267309i	$0.913865\pi$
$648$	−23.2947	+	16.9246i	−0.915104	+	0.664862i
$649$	−14.3812			−0.564512
$650$	6.33289	+	35.0380i	0.248397	+	1.37430i
$651$	−15.0105			−0.588309
$652$	−1.68889	+	1.22705i	−0.0661422	+	0.0480551i
$653$	−5.62126	+	17.3005i	−0.219977	+	0.677019i	0.778786	+	0.627290i	$0.215836\pi$
$653$	−5.62126	+	17.3005i	−0.219977	+	0.677019i	−0.998763	+	0.0497292i	$0.984164\pi$
$654$	−8.08740	+	24.8905i	−0.316242	+	0.973294i
$655$	−1.16755	+	2.90769i	−0.0456200	+	0.113613i
$656$	14.9418	+	45.9861i	0.583378	+	1.79545i
$657$	−0.248653			−0.00970089
$658$	−6.71319	−	20.6611i	−0.261707	−	0.805452i
$659$	−30.3504	−	22.0508i	−1.18228	−	0.858979i	−0.189855	−	0.981812i	$-0.560802\pi$
$659$	−30.3504	−	22.0508i	−1.18228	−	0.858979i	−0.992427	+	0.122833i	$0.960802\pi$
$660$	−3.61078	−	3.01666i	−0.140549	−	0.117423i
$661$	30.4590	−	22.1297i	1.18472	−	0.860747i	0.192020	−	0.981391i	$-0.438496\pi$
$661$	30.4590	−	22.1297i	1.18472	−	0.860747i	0.992696	+	0.120644i	$0.0384960\pi$
$662$	−18.1220	−	13.1664i	−0.704331	−	0.511726i
$663$	8.05976	+	5.85576i	0.313015	+	0.227419i
$664$	−19.5832	+	14.2280i	−0.759976	+	0.552155i
$665$	1.27775	−	3.18214i	0.0495491	−	0.123398i
$666$	9.09163	+	6.60546i	0.352294	+	0.255956i
$667$	10.7994	+	33.2370i	0.418153	+	1.28694i
$668$	4.00420			0.154927
$669$	−5.81913	−	17.9094i	−0.224980	−	0.692419i
$670$	−11.8273	−	47.0079i	−0.456929	−	1.81607i
$671$	−0.173779	+	0.534836i	−0.00670865	+	0.0206471i
$672$	−1.92185	+	5.91486i	−0.0741371	+	0.228171i
$673$	1.32635	−	0.963652i	0.0511272	−	0.0371461i	−0.561928	−	0.827186i	$-0.689940\pi$
$673$	1.32635	−	0.963652i	0.0511272	−	0.0371461i	0.613055	+	0.790040i	$0.289940\pi$
$674$	−54.6023			−2.10320
$675$	−11.2424	−	10.7641i	−0.432722	−	0.414310i
$676$	2.82915			0.108814
$677$	−16.6581	+	12.1028i	−0.640223	+	0.465149i	−0.859927	−	0.510417i	$-0.829491\pi$
$677$	−16.6581	+	12.1028i	−0.640223	+	0.465149i	0.219704	+	0.975567i	$0.429491\pi$
$678$	−9.74660	+	29.9969i	−0.374316	+	1.15203i
$679$	8.14735	−	25.0750i	0.312667	−	0.962289i
$680$	5.71078	+	0.387057i	0.218999	+	0.0148430i
$681$	−13.5342	−	41.6540i	−0.518632	−	1.59619i
$682$	−20.3489			−0.779200
$683$	3.29590	+	10.1437i	0.126114	+	0.388140i	0.994102	−	0.108445i	$-0.0345872\pi$
$683$	3.29590	+	10.1437i	0.126114	+	0.388140i	−0.867988	+	0.496585i	$0.834587\pi$
$684$	−0.373231	−	0.271169i	−0.0142709	−	0.0103684i
$685$	−0.822283	−	3.26818i	−0.0314178	−	0.124871i
$686$	−22.7949	+	16.5615i	−0.870313	+	0.632320i
$687$	27.9880	+	20.3345i	1.06781	+	0.775808i
$688$	−39.2264	−	28.4996i	−1.49549	−	1.08654i
$689$	6.98760	−	5.07679i	0.266206	−	0.193410i
$690$	7.74419	+	30.7795i	0.294816	+	1.17176i
$691$	5.17618	+	3.76071i	0.196911	+	0.143064i	0.681872	−	0.731472i	$-0.261166\pi$
$691$	5.17618	+	3.76071i	0.196911	+	0.143064i	−0.484961	+	0.874536i	$0.661166\pi$
$692$	−0.0542125	−	0.166849i	−0.00206085	−	0.00634265i
$693$	−7.77451			−0.295329
$694$	15.0102	+	46.1968i	0.569781	+	1.75361i
$695$	−17.4626	−	1.18355i	−0.662394	−	0.0448948i
$696$	13.4617	−	41.4310i	0.510266	−	1.57044i
$697$	−3.29380	+	10.1373i	−0.124761	+	0.383976i
$698$	22.9153	−	16.6489i	0.867356	−	0.630171i
$699$	−18.8863			−0.714346
$700$	−2.58007	−	0.351350i	−0.0975174	−	0.0132798i
$701$	11.6481			0.439942			0.219971	−	0.975506i	$-0.429404\pi$
$701$	11.6481			0.439942			0.219971	+	0.975506i	$0.429404\pi$
$702$	−17.9340	+	13.0298i	−0.676874	+	0.491778i
$703$	−1.39235	+	4.28522i	−0.0525136	+	0.161620i
$704$	6.07301	−	18.6908i	0.228885	−	0.704436i
$705$	10.1595	+	40.3793i	0.382630	+	1.52077i
$706$	−15.5346	−	47.8106i	−0.584653	−	1.79938i
$707$	4.34619			0.163455
$708$	0.975940	+	3.00363i	0.0366781	+	0.112883i
$709$	14.9734	+	10.8788i	0.562337	+	0.408561i	0.832313	−	0.554305i	$-0.187016\pi$
$709$	14.9734	+	10.8788i	0.562337	+	0.408561i	−0.269977	+	0.962867i	$0.587016\pi$
$710$	1.34627	−	3.35277i	0.0505245	−	0.125827i
$711$	15.1688	−	11.0208i	0.568874	−	0.413311i
$712$	26.9639	+	19.5904i	1.01052	+	0.734183i
$713$	15.2791	+	11.1009i	0.572206	+	0.415732i
$714$	−4.28397	+	3.11249i	−0.160324	+	0.116482i
$715$	24.8387	+	20.7517i	0.928915	+	0.776070i
$716$	−0.264569	−	0.192221i	−0.00988742	−	0.00718363i
$717$	−9.91022	−	30.5005i	−0.370104	−	1.13906i
$718$	−35.8072			−1.33631
$719$	8.24732	+	25.3826i	0.307573	+	0.946613i	0.978704	+	0.205274i	$0.0658087\pi$
$719$	8.24732	+	25.3826i	0.307573	+	0.946613i	−0.671131	+	0.741338i	$0.734191\pi$
$720$	5.81638	−	14.4852i	0.216764	−	0.539832i
$721$	0.00729196	−	0.0224423i	0.000271567	−	0.000835796i
$722$	−8.52571	+	26.2394i	−0.317294	+	0.976531i
$723$	22.6026	−	16.4217i	0.840599	−	0.610731i
$724$	−0.846189			−0.0314484
$725$	39.5750	+	5.38926i	1.46978	+	0.200152i
$726$	4.60173			0.170786
$727$	−0.0987245	+	0.0717276i	−0.00366149	+	0.00266023i	−0.589614	−	0.807685i	$-0.700720\pi$
$727$	−0.0987245	+	0.0717276i	−0.00366149	+	0.00266023i	0.585953	+	0.810345i	$0.300720\pi$
$728$	6.03726	−	18.5808i	0.223756	−	0.688649i
$729$	0.799186	−	2.45964i	0.0295995	−	0.0910978i
$730$	−0.465994	+	0.292574i	−0.0172472	+	0.0108287i
$731$	−3.30291	−	10.1653i	−0.122163	−	0.375978i
$732$	0.123498			0.00456461
$733$	16.6338	+	51.1936i	0.614384	+	1.89088i	0.410406	+	0.911903i	$0.365387\pi$
$733$	16.6338	+	51.1936i	0.614384	+	1.89088i	0.203978	+	0.978975i	$0.434613\pi$
$734$	8.59538	+	6.24491i	0.317261	+	0.230504i
$735$	17.4942	−	10.9837i	0.645284	−	0.405141i
$736$	6.33052	−	4.59939i	0.233346	−	0.169536i
$737$	−35.6480	−	25.8998i	−1.31311	−	0.954030i
$738$	20.2080	+	14.6820i	0.743867	+	0.540451i
$739$	−30.8699	+	22.4283i	−1.13557	+	0.825037i	−0.986495	−	0.163789i	$-0.947628\pi$
$739$	−30.8699	+	22.4283i	−1.13557	+	0.825037i	−0.149071	+	0.988827i	$0.547628\pi$
$740$	3.41361	+	0.231363i	0.125487	+	0.00850506i
$741$	7.57280	+	5.50196i	0.278194	+	0.202120i
$742$	1.41866	+	4.36618i	0.0520805	+	0.160287i
$743$	3.61274			0.132539			0.0662694	−	0.997802i	$-0.478890\pi$
$743$	3.61274			0.132539			0.0662694	+	0.997802i	$0.478890\pi$
$744$	−7.27487	−	22.3897i	−0.266710	−	0.820848i
$745$	14.9217	+	12.4665i	0.546689	+	0.456737i
$746$	1.50211	−	4.62303i	0.0549962	−	0.169261i
$747$	−4.49673	+	13.8395i	−0.164527	+	0.506362i
$748$	−0.799041	+	0.580537i	−0.0292158	+	0.0212265i
$749$	−29.6311			−1.08270
$750$	35.5282	+	7.31365i	1.29730	+	0.267057i
$751$	6.73028			0.245591			0.122796	−	0.992432i	$-0.460814\pi$
$751$	6.73028			0.245591			0.122796	+	0.992432i	$0.460814\pi$
$752$	32.0770	−	23.3053i	1.16973	−	0.849856i
$753$	1.71381	−	5.27456i	0.0624547	−	0.192216i
$754$	17.5781	−	54.0999i	0.640157	−	1.97020i
$755$	−39.7163	−	33.1814i	−1.44543	−	1.20759i
$756$	−0.500960	−	1.54180i	−0.0182197	−	0.0560746i
$757$	27.3629			0.994522			0.497261	−	0.867601i	$-0.334339\pi$
$757$	27.3629			0.994522			0.497261	+	0.867601i	$0.334339\pi$
$758$	−4.30032	−	13.2350i	−0.156195	−	0.480718i
$759$	23.3413	+	16.9584i	0.847236	+	0.615553i
$760$	5.36574	+	0.363672i	0.194636	+	0.0131918i
$761$	−16.8423	+	12.2367i	−0.610533	+	0.443578i	−0.849602	−	0.527424i	$-0.823158\pi$
$761$	−16.8423	+	12.2367i	−0.610533	+	0.443578i	0.239069	+	0.971003i	$0.423158\pi$
$762$	32.9939	+	23.9715i	1.19524	+	0.868395i
$763$	10.6516	+	7.73882i	0.385613	+	0.280164i
$764$	1.32793	−	0.964797i	0.0480428	−	0.0349051i
$765$	2.91419	−	1.82967i	0.105363	−	0.0661519i
$766$	2.32226	+	1.68722i	0.0839067	+	0.0609618i
$767$	−6.71353	−	20.6621i	−0.242411	−	0.746066i
$768$	−15.9214			−0.574515
$769$	11.1568	+	34.3372i	0.402326	+	1.23823i	0.923108	+	0.384541i	$0.125640\pi$
$769$	11.1568	+	34.3372i	0.402326	+	1.23823i	−0.520782	+	0.853690i	$0.674360\pi$
$770$	−14.5700	+	9.14776i	−0.525066	+	0.329662i
$771$	−8.99900	+	27.6961i	−0.324091	+	0.997449i
$772$	0.752697	−	2.31656i	0.0270902	−	0.0833750i
$773$	18.7624	−	13.6317i	0.674837	−	0.490297i	−0.196804	−	0.980443i	$-0.563056\pi$
$773$	18.7624	−	13.6317i	0.674837	−	0.490297i	0.871641	+	0.490145i	$0.163056\pi$
$774$	−25.0476			−0.900318
$775$	19.0141	−	10.2146i	0.683007	−	0.366920i
$776$	41.3505			1.48440
$777$	13.4903	−	9.80128i	0.483962	−	0.351619i
$778$	−5.46224	+	16.8110i	−0.195831	+	0.602705i
$779$	−3.09479	+	9.52478i	−0.110882	+	0.341261i
$780$	2.64856	−	6.59602i	0.0948336	−	0.236175i
$781$	−1.01490	−	3.12354i	−0.0363159	−	0.111769i
$782$	6.66243			0.238248
$783$	7.68409	+	23.6492i	0.274607	+	0.845153i
$784$	−15.9134	−	11.5617i	−0.568335	−	0.412919i
$785$	2.36074	+	1.97230i	0.0842583	+	0.0703944i
$786$	3.67799	−	2.67222i	0.131190	−	0.0953148i
$787$	−37.9992	−	27.6080i	−1.35452	−	0.984120i	−0.998772	−	0.0495396i	$-0.984225\pi$
$787$	−37.9992	−	27.6080i	−1.35452	−	0.984120i	−0.355753	−	0.934580i	$-0.615775\pi$
$788$	−4.15933	−	3.02193i	−0.148170	−	0.107652i
$789$	−17.8812	+	12.9914i	−0.636587	+	0.462507i
$790$	15.4600	−	38.5018i	0.550041	−	1.36983i
$791$	12.8368	+	9.32650i	0.456425	+	0.331612i
$792$	−3.76792	−	11.5965i	−0.133887	−	0.412063i
$793$	−0.849545			−0.0301682
$794$	−12.6121	−	38.8162i	−0.447588	−	1.37754i
$795$	−2.14695	−	8.53311i	−0.0761445	−	0.302638i
$796$	1.58060	−	4.86459i	0.0560230	−	0.172421i
$797$	−9.59939	+	29.5439i	−0.340028	+	1.04650i	0.624164	+	0.781293i	$0.285440\pi$
$797$	−9.59939	+	29.5439i	−0.340028	+	1.04650i	−0.964192	+	0.265205i	$0.914560\pi$
$798$	−4.02514	+	2.92444i	−0.142488	+	0.103524i
$799$	8.74037			0.309212
$800$	−1.59059	−	8.80027i	−0.0562359	−	0.311136i
$801$	20.0361			0.707942
$802$	−24.6940	+	17.9412i	−0.871974	+	0.633527i
$803$	−0.154562	+	0.475692i	−0.00545436	+	0.0167868i
$804$	−2.99023	+	9.20297i	−0.105457	+	0.324564i
$805$	15.9303	+	1.07970i	0.561470	+	0.0380545i
$806$	−9.49940	−	29.2361i	−0.334602	−	1.02980i
$807$	−3.52164			−0.123968
$808$	2.10639	+	6.48279i	0.0741024	+	0.228064i
$809$	−34.4702	−	25.0441i	−1.21191	−	0.880503i	−0.216505	−	0.976281i	$-0.569466\pi$
$809$	−34.4702	−	25.0441i	−1.21191	−	0.880503i	−0.995403	+	0.0957790i	$0.969466\pi$
$810$	9.34593	+	37.1456i	0.328383	+	1.30517i
$811$	−21.3603	+	15.5191i	−0.750060	+	0.544951i	−0.895846	−	0.444365i	$-0.853429\pi$
$811$	−21.3603	+	15.5191i	−0.750060	+	0.544951i	0.145785	+	0.989316i	$0.453429\pi$
$812$	3.36550	+	2.44518i	0.118106	+	0.0858089i
$813$	−34.3248	−	24.9385i	−1.20382	−	0.874630i
$814$	18.2880	−	13.2870i	0.640995	−	0.465710i
$815$	−3.56964	−	14.1876i	−0.125039	−	0.496970i
$816$	−7.81872	−	5.68064i	−0.273710	−	0.198862i
$817$	−3.10336	−	9.55115i	−0.108573	−	0.334152i
$818$	25.7431			0.900086
$819$	−3.62934	−	11.1700i	−0.126820	−	0.390310i
$820$	7.58745	+	0.514251i	0.264965	+	0.0179584i
$821$	0.218997	−	0.674003i	0.00764305	−	0.0235229i	−0.947162	−	0.320755i	$-0.896063\pi$
$821$	0.218997	−	0.674003i	0.00764305	−	0.0235229i	0.954805	+	0.297232i	$0.0960635\pi$
$822$	−1.51099	+	4.65036i	−0.0527019	+	0.162200i
$823$	36.1912	−	26.2944i	1.26155	−	0.916566i	0.262713	−	0.964874i	$-0.415383\pi$
$823$	36.1912	−	26.2944i	1.26155	−	0.916566i	0.998832	+	0.0483080i	$0.0153829\pi$
$824$	0.0370091			0.00128927
$825$	29.0472	−	15.6045i	1.01129	−	0.543279i
$826$	11.5476			0.401793
$827$	−7.04217	+	5.11643i	−0.244880	+	0.177916i	−0.703455	−	0.710740i	$-0.748360\pi$
$827$	−7.04217	+	5.11643i	−0.244880	+	0.177916i	0.458575	+	0.888656i	$0.348360\pi$
$828$	0.663810	−	2.04300i	0.0230690	−	0.0709991i
$829$	−12.3396	+	37.9775i	−0.428573	+	1.31901i	0.470958	+	0.882156i	$0.343908\pi$
$829$	−12.3396	+	37.9775i	−0.428573	+	1.31901i	−0.899531	+	0.436857i	$0.856092\pi$
$830$	7.85686	+	31.2273i	0.272716	+	1.08391i
$831$	13.3606	+	41.1197i	0.463474	+	1.42643i
$832$	29.6889			1.02928
$833$	−1.33993	−	4.12387i	−0.0464257	−	0.142884i
$834$	20.5450	+	14.9268i	0.711416	+	0.516874i
$835$	−10.4563	+	26.0405i	−0.361854	+	0.901169i
$836$	−0.750764	+	0.545462i	−0.0259657	+	0.0188652i
$837$	10.8715	+	7.89864i	0.375776	+	0.273017i
$838$	−13.6030	−	9.88318i	−0.469909	−	0.341409i
$839$	31.5746	−	22.9403i	1.09008	−	0.791987i	0.110664	−	0.993858i	$-0.464702\pi$
$839$	31.5746	−	22.9403i	1.09008	−	0.791987i	0.979412	+	0.201871i	$0.0647022\pi$
$840$	−15.2741	−	12.7609i	−0.527006	−	0.440292i
$841$	−28.1609	−	20.4601i	−0.971067	−	0.705522i
$842$	11.3051	+	34.7936i	0.389601	+	1.19907i
$843$	−40.5274			−1.39584
$844$	−1.39715	−	4.29997i	−0.0480918	−	0.148011i
$845$	−7.38784	+	18.3988i	−0.254149	+	0.632938i
$846$	6.32942	−	19.4800i	0.217610	−	0.669735i
$847$	0.715373	−	2.20169i	0.0245805	−	0.0756511i
$848$	−6.77863	+	4.92496i	−0.232779	+	0.169124i
$849$	−22.5856			−0.775137
$850$	3.30855	−	6.85787i	0.113482	−	0.235223i
$851$	−20.9801			−0.719189
$852$	−0.583503	+	0.423939i	−0.0199905	+	0.0145239i
$853$	−9.59139	+	29.5193i	−0.328403	+	1.01072i	0.641478	+	0.767141i	$0.278321\pi$
$853$	−9.59139	+	29.5193i	−0.328403	+	1.01072i	−0.969881	+	0.243579i	$0.921679\pi$
$854$	0.139538	−	0.429455i	0.00477490	−	0.0146956i
$855$	2.73812	−	1.71912i	0.0936416	−	0.0587928i
$856$	−14.3607	−	44.1977i	−0.490839	−	1.51065i
$857$	33.7064			1.15139			0.575694	−	0.817665i	$-0.304732\pi$
$857$	33.7064			1.15139			0.575694	+	0.817665i	$0.304732\pi$
$858$	−14.5119	−	44.6630i	−0.495428	−	1.52477i
$859$	−17.6824	−	12.8470i	−0.603316	−	0.438335i	0.243738	−	0.969841i	$-0.421626\pi$
$859$	−17.6824	−	12.8470i	−0.603316	−	0.438335i	−0.847054	+	0.531506i	$0.821626\pi$
$860$	−6.45848	+	4.05495i	−0.220232	+	0.138273i
$861$	29.9850	−	21.7854i	1.02189	−	0.742443i
$862$	−14.8043	−	10.7560i	−0.504238	−	0.366350i
$863$	33.5340	+	24.3639i	1.14151	+	0.829356i	0.987329	−	0.158687i	$-0.0507259\pi$
$863$	33.5340	+	24.3639i	1.14151	+	0.829356i	0.154182	+	0.988043i	$0.450726\pi$
$864$	4.50436	−	3.27261i	0.153242	−	0.111336i
$865$	1.22663	+	0.0831371i	0.0417068	+	0.00282674i
$866$	6.41677	+	4.66205i	0.218051	+	0.158423i
$867$	−0.658347	−	2.02618i	−0.0223586	−	0.0688128i
$868$	2.24810			0.0763055
$869$	−11.6547	−	35.8694i	−0.395358	−	1.21679i
$870$	−44.4721	−	37.1546i	−1.50775	−	1.25966i
$871$	20.5699	−	63.3076i	0.696984	−	2.14510i
$872$	−6.38094	+	19.6385i	−0.216086	+	0.665044i
$873$	20.1107	−	14.6113i	0.680643	−	0.494516i
$874$	6.25989			0.211744
$875$	9.02233	−	15.8614i	0.305010	−	0.536215i
$876$	0.109841			0.00371118
$877$	−38.7658	+	28.1650i	−1.30903	+	0.951065i	−0.309029	+	0.951053i	$0.600004\pi$
$877$	−38.7658	+	28.1650i	−1.30903	+	0.951065i	−1.00000		1.24228e-5i	$0.999996\pi$
$878$	−10.2279	+	31.4784i	−0.345176	+	1.06234i
$879$	−15.4706	+	47.6137i	−0.521811	+	1.60597i
$880$	−24.0959	−	20.1311i	−0.812271	−	0.678619i
$881$	4.90518	+	15.0966i	0.165260	+	0.508617i	0.999055	−	0.0434561i	$-0.0138369\pi$
$881$	4.90518	+	15.0966i	0.165260	+	0.508617i	−0.833796	+	0.552073i	$0.813837\pi$
$882$	−10.1613			−0.342150
$883$	2.48676	+	7.65346i	0.0836861	+	0.257559i	0.984140	−	0.177391i	$-0.0567658\pi$
$883$	2.48676	+	7.65346i	0.0836861	+	0.257559i	−0.900454	+	0.434951i	$0.856766\pi$
$884$	−1.20710	−	0.877006i	−0.0405990	−	0.0294969i
$885$	−22.0820	−	1.49664i	−0.742279	−	0.0503091i
$886$	−8.55451	+	6.21521i	−0.287394	+	0.208804i
$887$	13.8550	+	10.0663i	0.465207	+	0.337992i	0.795570	−	0.605861i	$-0.207171\pi$
$887$	13.8550	+	10.0663i	0.465207	+	0.337992i	−0.330364	+	0.943854i	$0.607171\pi$
$888$	21.1577	+	15.3720i	0.710006	+	0.515850i
$889$	16.5983	−	12.0594i	0.556688	−	0.404458i
$890$	37.5492	−	23.5752i	1.25865	−	0.790243i
$891$	28.1690	+	20.4660i	0.943697	+	0.685636i
$892$	0.871519	+	2.68226i	0.0291806	+	0.0898087i
$893$	8.21229			0.274814
$894$	−8.71794	−	26.8311i	−0.291572	−	0.897365i
$895$	1.94095	−	1.21862i	0.0648787	−	0.0407340i
$896$	−6.68059	+	20.5607i	−0.223183	+	0.686886i
$897$	−13.4686	+	41.4521i	−0.449703	+	1.38404i
$898$	23.5081	−	17.0797i	0.784476	−	0.569955i
$899$	−34.4830			−1.15007
$900$	−1.77328	−	1.69783i	−0.0591094	−	0.0565943i
$901$	−1.84705			−0.0615341
$902$	40.6489	−	29.5332i	1.35346	−	0.983347i
$903$	−11.4850	+	35.3470i	−0.382195	+	1.17628i
$904$	−7.69005	+	23.6675i	−0.255767	+	0.787170i
$905$	2.20968	−	5.50302i	0.0734521	−	0.182926i
$906$	23.2041	+	71.4148i	0.770904	+	2.37260i
$907$	43.2566			1.43631			0.718156	−	0.695882i	$-0.244986\pi$
$907$	43.2566			1.43631			0.718156	+	0.695882i	$0.244986\pi$
$908$	2.02699	+	6.23845i	0.0672682	+	0.207030i
$909$	3.31514	+	2.40859i	0.109956	+	0.0798879i
$910$	−19.9446	−	16.6629i	−0.661158	−	0.552370i
$911$	−18.4692	+	13.4186i	−0.611911	+	0.444580i	−0.850087	−	0.526643i	$-0.823451\pi$
$911$	−18.4692	+	13.4186i	−0.611911	+	0.444580i	0.238176	+	0.971222i	$0.423451\pi$
$912$	−7.34633	−	5.33742i	−0.243261	−	0.176740i
$913$	23.6809	+	17.2052i	0.783723	+	0.569408i
$914$	34.7231	−	25.2278i	1.14854	−	0.834461i
$915$	−0.322493	+	0.803142i	−0.0106613	+	0.0265511i
$916$	−4.19171	−	3.04545i	−0.138498	−	0.100625i
$917$	−0.706748	−	2.17515i	−0.0233389	−	0.0718297i
$918$	4.74053			0.156461
$919$	−10.1707	−	31.3023i	−0.335501	−	1.03257i	−0.966475	−	0.256762i	$-0.917344\pi$
$919$	−10.1707	−	31.3023i	−0.335501	−	1.03257i	0.630974	−	0.775804i	$-0.282656\pi$
$920$	6.11015	+	24.2850i	0.201446	+	0.800651i
$921$	−13.9275	+	42.8643i	−0.458925	+	1.41243i
$922$	18.0018	−	55.4039i	0.592858	−	1.82463i
$923$	4.01394	−	2.91630i	0.132120	−	0.0959910i
$924$	3.43434			0.112981
$925$	−10.4187	+	21.5956i	−0.342564	+	0.710057i
$926$	16.3443			0.537106
$927$	0.0179993	−	0.0130772i	0.000591173	−	0.000429512i
$928$	−4.41498	+	13.5879i	−0.144929	+	0.446045i
$929$	1.83741	−	5.65498i	0.0602836	−	0.185534i	−0.916380	−	0.400310i	$-0.868902\pi$
$929$	1.83741	−	5.65498i	0.0602836	−	0.185534i	0.976663	+	0.214777i	$0.0689023\pi$
$930$	−31.2453	−	2.11770i	−1.02457	−	0.0694420i
$931$	−1.25897	−	3.87471i	−0.0412611	−	0.126989i
$932$	2.82857			0.0926528
$933$	−8.59473	−	26.4519i	−0.281379	−	0.865995i
$934$	12.9276	+	9.39242i	0.423003	+	0.307329i
$935$	−1.68885	−	6.71237i	−0.0552312	−	0.219518i
$936$	14.9022	−	10.8271i	0.487093	−	0.353894i
$937$	21.4879	+	15.6119i	0.701980	+	0.510019i	0.880577	−	0.473904i	$-0.157156\pi$
$937$	21.4879	+	15.6119i	0.701980	+	0.510019i	−0.178596	+	0.983922i	$0.557156\pi$
$938$	28.6241	+	20.7966i	0.934609	+	0.679033i
$939$	−41.8641	+	30.4161i	−1.36618	+	0.992591i
$940$	−1.52157	−	6.04753i	−0.0496282	−	0.197249i
$941$	44.5433	+	32.3626i	1.45207	+	1.05499i	0.985342	+	0.170588i	$0.0545669\pi$
$941$	44.5433	+	32.3626i	1.45207	+	1.05499i	0.466727	+	0.884402i	$0.345433\pi$
$942$	−1.37925	−	4.24489i	−0.0449384	−	0.138306i
$943$	−46.6326			−1.51857
$944$	6.51275	+	20.0442i	0.211972	+	0.652382i
$945$	11.3349	+	0.768242i	0.368725	+	0.0249909i
$946$	−15.5695	+	47.9179i	−0.506208	+	1.55795i
$947$	6.04199	−	18.5953i	0.196338	−	0.604267i	−0.803620	−	0.595143i	$-0.797096\pi$
$947$	6.04199	−	18.5953i	0.196338	−	0.604267i	0.999958	−	0.00912435i	$-0.00290441\pi$
$948$	−6.70071	+	4.86835i	−0.217629	+	0.158117i
$949$	−0.755600			−0.0245278
$950$	3.10865	−	6.44353i	0.100858	−	0.209056i
$951$	−6.31475			−0.204770
$952$	−3.38005	+	2.45575i	−0.109548	+	0.0795912i
$953$	−8.09327	+	24.9085i	−0.262167	+	0.806866i	0.730166	+	0.683270i	$0.239443\pi$
$953$	−8.09327	+	24.9085i	−0.262167	+	0.806866i	−0.992333	+	0.123596i	$0.960557\pi$
$954$	−1.33756	+	4.11658i	−0.0433050	+	0.133279i
$955$	2.80670	+	11.1553i	0.0908227	+	0.360977i
$956$	1.48423	+	4.56800i	0.0480036	+	0.147740i
$957$	−52.6784			−1.70285
$958$	17.7636	+	54.6706i	0.573915	+	1.76633i
$959$	1.99006	+	1.44587i	0.0642625	+	0.0466894i
$960$	11.2701	−	28.0673i	0.363741	−	0.905867i
$961$	10.0035	−	7.26798i	0.322694	−	0.234451i
$962$	27.6274	+	20.0725i	0.890742	+	0.647162i
$963$	−22.6016	−	16.4210i	−0.728327	−	0.529161i
$964$	−3.38514	+	2.45945i	−0.109028	+	0.0792136i
$965$	13.0998	+	10.9443i	0.421696	+	0.352310i
$966$	−18.7423	−	13.6171i	−0.603022	−	0.438121i
$967$	−12.7907	−	39.3657i	−0.411321	−	1.26591i	−0.915501	−	0.402316i	$-0.868205\pi$
$967$	−12.7907	−	39.3657i	−0.411321	−	1.26591i	0.504180	−	0.863599i	$-0.331795\pi$
$968$	3.63076			0.116697
$969$	−0.618571	−	1.90376i	−0.0198714	−	0.0611577i
$970$	20.4967	−	51.0455i	0.658111	−	1.63897i
$971$	15.9583	−	49.1145i	0.512125	−	1.57616i	−0.276329	−	0.961063i	$-0.589118\pi$
$971$	15.9583	−	49.1145i	0.512125	−	1.57616i	0.788453	−	0.615095i	$-0.210882\pi$
$972$	1.44208	−	4.43826i	0.0462547	−	0.142357i
$973$	10.3356	−	7.50925i	0.331344	−	0.240736i
$974$	44.2322			1.41729
$975$	35.9796	+	34.4487i	1.15227	+	1.10324i
$976$	0.824138			0.0263800
$977$	−12.5684	+	9.13146i	−0.402098	+	0.292141i	−0.770395	−	0.637567i	$-0.779941\pi$
$977$	−12.5684	+	9.13146i	−0.402098	+	0.292141i	0.368297	+	0.929708i	$0.379941\pi$
$978$	−6.55942	+	20.1878i	−0.209747	+	0.645535i
$979$	12.4544	−	38.3306i	0.398043	−	1.22505i
$980$	−2.62008	+	1.64501i	−0.0836953	+	0.0525480i
$981$	3.83595	+	11.8059i	0.122473	+	0.376932i
$982$	−50.9667			−1.62641
$983$	15.0804	+	46.4126i	0.480989	+	1.48033i	0.837708	+	0.546119i	$0.183895\pi$
$983$	15.0804	+	46.4126i	0.480989	+	1.48033i	−0.356719	+	0.934212i	$0.616105\pi$
$984$	47.0273	+	34.1674i	1.49918	+	1.08922i
$985$	30.5138	−	19.1581i	0.972252	−	0.610428i
$986$	−9.84137	+	7.15017i	−0.313413	+	0.227708i
$987$	−24.5878	−	17.8641i	−0.782638	−	0.568620i
$988$	−1.13416	−	0.824019i	−0.0360826	−	0.0262155i
$989$	37.8310	−	27.4858i	1.20296	−	0.873999i
$990$	−16.1831	−	1.09683i	−0.514332	−	0.0348596i
$991$	−0.593864	−	0.431468i	−0.0188647	−	0.0137060i	0.578313	−	0.815815i	$-0.303711\pi$
$991$	−0.593864	−	0.431468i	−0.0188647	−	0.0137060i	−0.597178	+	0.802109i	$0.703711\pi$
$992$	2.38590	+	7.34306i	0.0757525	+	0.233142i
$993$	−31.3374			−0.994463
$994$	0.814929	+	2.50809i	0.0258480	+	0.0795519i
$995$	27.5084	+	22.9822i	0.872076	+	0.728583i
$996$	1.98640	−	6.11352i	0.0629416	−	0.193714i
$997$	7.52212	−	23.1507i	0.238228	−	0.733191i	−0.758449	−	0.651733i	$-0.774042\pi$
$997$	7.52212	−	23.1507i	0.238228	−	0.733191i	0.996677	−	0.0814579i	$-0.0259576\pi$
$998$	−30.9527	+	22.4885i	−0.979791	+	0.711860i
$999$	−14.9280			−0.472301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.6	✓	76
25.16	even	5	inner	425.2.k.b.341.6	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.6	✓	76	1.1	even	1	trivial
425.2.k.b.341.6	yes	76	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23201 + 0.895109i) q^{2} +(-0.658347 + 2.02618i) q^{3} +(0.0985994 - 0.303458i) q^{4} +(1.71600 + 1.43365i) q^{5} +(-1.00256 - 3.08558i) q^{6} -1.63215 q^{7} +(-0.791021 - 2.43451i) q^{8} +(-1.24495 - 0.904509i) q^{9} +(-3.39740 - 0.230264i) q^{10} +(-2.50425 + 1.81944i) q^{11} +(0.549949 + 0.399561i) q^{12} +(-3.78312 - 2.74860i) q^{13} +(2.01082 - 1.46095i) q^{14} +(-4.03456 + 2.53309i) q^{15} +(3.66998 + 2.66639i) q^{16} +(0.309017 + 0.951057i) q^{17} +2.34343 q^{18} +(0.290347 + 0.893595i) q^{19} +(0.604248 - 0.379377i) q^{20} +(1.07452 - 3.30703i) q^{21} +(1.45666 - 4.48315i) q^{22} +(-3.53943 + 2.57154i) q^{23} +5.45354 q^{24} +(0.889309 + 4.92028i) q^{25} +7.12114 q^{26} +(-2.51841 + 1.82973i) q^{27} +(-0.160929 + 0.495288i) q^{28} +(2.46844 - 7.59708i) q^{29} +(2.70323 - 6.73217i) q^{30} +(-1.33397 - 4.10554i) q^{31} -1.78857 q^{32} +(-2.03786 - 6.27189i) q^{33} +(-1.23201 - 0.895109i) q^{34} +(-2.80076 - 2.33992i) q^{35} +(-0.397232 + 0.288606i) q^{36} +(3.87963 + 2.81871i) q^{37} +(-1.15758 - 0.841028i) q^{38} +(8.05976 - 5.85576i) q^{39} +(2.13284 - 5.31167i) q^{40} +(8.62327 + 6.26517i) q^{41} +(1.63633 + 5.03611i) q^{42} -10.6885 q^{43} +(0.305207 + 0.939329i) q^{44} +(-0.839587 - 3.33696i) q^{45} +(2.05880 - 6.33635i) q^{46} +(2.70092 - 8.31259i) q^{47} +(-7.81872 + 5.68064i) q^{48} -4.33610 q^{49} +(-5.49983 - 5.26581i) q^{50} -2.13046 q^{51} +(-1.20710 + 0.877006i) q^{52} +(-0.570769 + 1.75665i) q^{53} +(1.46490 - 4.50851i) q^{54} +(-6.90573 - 0.468046i) q^{55} +(1.29106 + 3.97348i) q^{56} -2.00174 q^{57} +(3.75907 + 11.5692i) q^{58} +(3.75867 + 2.73083i) q^{59} +(0.370882 + 1.47408i) q^{60} +(0.146978 - 0.106786i) q^{61} +(5.31838 + 3.86403i) q^{62} +(2.03194 + 1.47629i) q^{63} +(-5.13641 + 3.73182i) q^{64} +(-2.55131 - 10.1402i) q^{65} +(8.12470 + 5.90294i) q^{66} +(4.39886 + 13.5383i) q^{67} +0.319074 q^{68} +(-2.88025 - 8.86450i) q^{69} +(5.54506 + 0.375825i) q^{70} +(-0.327871 + 1.00908i) q^{71} +(-1.21726 + 3.74633i) q^{72} +(0.130725 - 0.0949771i) q^{73} -7.30281 q^{74} +(-10.5549 - 1.43735i) q^{75} +0.299796 q^{76} +(4.08730 - 2.96960i) q^{77} +(-4.68818 + 14.4287i) q^{78} +(-3.76514 + 11.5879i) q^{79} +(2.47501 + 9.83698i) q^{80} +(-3.47597 - 10.6980i) q^{81} -16.2320 q^{82} +(-2.92215 - 8.99346i) q^{83} +(-0.897597 - 0.652142i) q^{84} +(-0.833207 + 2.07503i) q^{85} +(13.1683 - 9.56733i) q^{86} +(13.7680 + 10.0030i) q^{87} +(6.41037 + 4.65741i) q^{88} +(-10.5336 + 7.65312i) q^{89} +(4.02132 + 3.35965i) q^{90} +(6.17460 + 4.48611i) q^{91} +(0.431370 + 1.32762i) q^{92} +9.19680 q^{93} +(4.11310 + 12.6588i) q^{94} +(-0.782866 + 1.94966i) q^{95} +(1.17750 - 3.62397i) q^{96} +(-4.99180 + 15.3632i) q^{97} +(5.34212 - 3.88128i) q^{98} +4.76337 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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