LMFDB - Embedded newform 399.2.j.d.172.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(58,399)] 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("399.58"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.3
Root			$-0.198169 - 0.343239i$ of defining polynomial
Character	$\chi$	$=$	399.172
Dual form			399.2.j.d.58.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.198169 + 0.343239i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.921458 - 1.59601i) q^{4} +(0.421458 + 0.729986i) q^{5} +0.396339 q^{6} +(1.79981 + 1.93925i) q^{7} +1.52310 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.167040 + 0.289322i) q^{10} +(0.0179894 - 0.0311586i) q^{11} +(-0.921458 - 1.59601i) q^{12} +1.96402 q^{13} +(-0.308961 + 1.00206i) q^{14} +0.842916 q^{15} +(-1.54109 - 2.66924i) q^{16} +(-1.62676 + 2.81763i) q^{17} +(0.198169 - 0.343239i) q^{18} +(-0.500000 - 0.866025i) q^{19} +1.55342 q^{20} +(2.57934 - 0.589053i) q^{21} +0.0142598 q^{22} +(-0.641921 - 1.11184i) q^{23} +(0.761548 - 1.31904i) q^{24} +(2.14475 - 3.71481i) q^{25} +(0.389209 + 0.674129i) q^{26} -1.00000 q^{27} +(4.75351 - 1.08558i) q^{28} -7.06045 q^{29} +(0.167040 + 0.289322i) q^{30} +(1.80976 - 3.13460i) q^{31} +(2.13389 - 3.69600i) q^{32} +(-0.0179894 - 0.0311586i) q^{33} -1.28949 q^{34} +(-0.657084 + 2.13115i) q^{35} -1.84292 q^{36} +(1.08137 + 1.87298i) q^{37} +(0.198169 - 0.343239i) q^{38} +(0.982011 - 1.70089i) q^{39} +(0.641921 + 1.11184i) q^{40} +0.130805 q^{41} +(0.713333 + 0.768600i) q^{42} -4.50884 q^{43} +(-0.0331530 - 0.0574227i) q^{44} +(0.421458 - 0.729986i) q^{45} +(0.254418 - 0.440665i) q^{46} +(3.99277 + 6.91568i) q^{47} -3.08217 q^{48} +(-0.521390 + 6.98056i) q^{49} +1.70009 q^{50} +(1.62676 + 2.81763i) q^{51} +(1.80976 - 3.13460i) q^{52} +(-1.49085 + 2.58222i) q^{53} +(-0.198169 - 0.343239i) q^{54} +0.0303272 q^{55} +(2.74128 + 2.95366i) q^{56} -1.00000 q^{57} +(-1.39916 - 2.42342i) q^{58} +(-6.48994 + 11.2409i) q^{59} +(0.776711 - 1.34530i) q^{60} +(-1.29380 - 2.24092i) q^{61} +1.43456 q^{62} +(0.779537 - 2.52830i) q^{63} -4.47286 q^{64} +(0.827752 + 1.43371i) q^{65} +(0.00712991 - 0.0123494i) q^{66} +(-2.25952 + 3.91361i) q^{67} +(2.99798 + 5.19265i) q^{68} -1.28384 q^{69} +(-0.861707 + 0.196791i) q^{70} -2.64985 q^{71} +(-0.761548 - 1.31904i) q^{72} +(-3.10649 + 5.38059i) q^{73} +(-0.428588 + 0.742336i) q^{74} +(-2.14475 - 3.71481i) q^{75} -1.84292 q^{76} +(0.0928019 - 0.0211935i) q^{77} +0.778417 q^{78} +(-5.18641 - 8.98312i) q^{79} +(1.29900 - 2.24994i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0259214 + 0.0448973i) q^{82} +10.2752 q^{83} +(1.43662 - 4.65945i) q^{84} -2.74244 q^{85} +(-0.893513 - 1.54761i) q^{86} +(-3.53023 + 6.11453i) q^{87} +(0.0273996 - 0.0474576i) q^{88} +(-4.18641 - 7.25107i) q^{89} +0.334080 q^{90} +(3.53486 + 3.80873i) q^{91} -2.36601 q^{92} +(-1.80976 - 3.13460i) q^{93} +(-1.58249 + 2.74095i) q^{94} +(0.421458 - 0.729986i) q^{95} +(-2.13389 - 3.69600i) q^{96} -2.55162 q^{97} +(-2.49932 + 1.20437i) q^{98} -0.0359789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{5} + 2 q^{7} - 6 q^{8} - 4 q^{9} + 3 q^{10} + 2 q^{11} + 12 q^{13} + 2 q^{14} - 8 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{19} + 24 q^{20} + q^{21} - 12 q^{22} - 5 q^{23} - 3 q^{24} + 4 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 - 6 * q^8 - 4 * q^9 + 3 * q^10 + 2 * q^11 + 12 * q^13 + 2 * q^14 - 8 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^19 + 24 * q^20 + q^21 - 12 * q^22 - 5 * q^23 - 3 * q^24 + 4 * q^25 + 6 * q^26 - 8 * q^27 + 8 * q^28 - 8 * q^29 - 3 * q^30 - 17 * q^31 - 4 * q^32 - 2 * q^33 + 16 * q^34 - 20 * q^35 + 3 * q^37 + 6 * q^39 + 5 * q^40 + 14 * q^41 + 19 * q^42 - 30 * q^43 - 17 * q^44 - 4 * q^45 - q^46 - 16 * q^47 + 8 * q^48 + 14 * q^49 - 28 * q^50 - 2 * q^51 - 17 * q^52 - 4 * q^53 + 30 * q^55 + 18 * q^56 - 8 * q^57 + 5 * q^58 - 17 * q^59 + 12 * q^60 + 9 * q^61 - 14 * q^62 - q^63 - 26 * q^64 - 23 * q^65 - 6 * q^66 + 5 * q^67 + 10 * q^68 - 10 * q^69 + 33 * q^70 + 12 * q^71 + 3 * q^72 - 15 * q^73 + 10 * q^74 - 4 * q^75 - 4 * q^77 + 12 * q^78 - 5 * q^79 + 25 * q^80 - 4 * q^81 - 31 * q^82 + 68 * q^83 + 19 * q^84 - 24 * q^85 - 17 * q^86 - 4 * q^87 - 11 * q^88 + 3 * q^89 - 6 * q^90 + 45 * q^91 + 14 * q^92 + 17 * q^93 + 6 * q^94 - 4 * q^95 + 4 * q^96 + 22 * q^97 + 27 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.198169	+	0.343239i	0.140127	+	0.242707i	0.927544	−	0.373713i	$-0.121916\pi$
$2$	0.198169	+	0.343239i	0.140127	+	0.242707i	−0.787417	+	0.616420i	$0.788582\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.921458	−	1.59601i	0.460729	−	0.798006i
$5$	0.421458	+	0.729986i	0.188482	+	0.326460i	0.944744	−	0.327808i	$-0.106310\pi$
$5$	0.421458	+	0.729986i	0.188482	+	0.326460i	−0.756263	+	0.654268i	$0.772977\pi$
$6$	0.396339			0.161805
$7$	1.79981	+	1.93925i	0.680263	+	0.732968i
$7$	1.79981	+	1.93925i	0.680263	+	0.732968i
$8$	1.52310			0.538496
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.167040	+	0.289322i	−0.0528227	+	0.0914916i
$11$	0.0179894	−	0.0311586i	0.00542402	−	0.00939468i	−0.863301	−	0.504690i	$-0.831607\pi$
$11$	0.0179894	−	0.0311586i	0.00542402	−	0.00939468i	0.868725	+	0.495295i	$0.164940\pi$
$12$	−0.921458	−	1.59601i	−0.266002	−	0.460729i
$13$	1.96402			0.544721			0.272361	−	0.962195i	$-0.412196\pi$
$13$	1.96402			0.544721			0.272361	+	0.962195i	$0.412196\pi$
$14$	−0.308961	+	1.00206i	−0.0825732	+	0.267813i
$15$	0.842916			0.217640
$16$	−1.54109	−	2.66924i	−0.385271	−	0.667309i
$17$	−1.62676	+	2.81763i	−0.394547	+	0.683375i	−0.993043	−	0.117751i	$-0.962432\pi$
$17$	−1.62676	+	2.81763i	−0.394547	+	0.683375i	0.598497	+	0.801125i	$0.295765\pi$
$18$	0.198169	−	0.343239i	0.0467089	−	0.0809023i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	1.55342			0.347356
$21$	2.57934	−	0.589053i	0.562859	−	0.128542i
$22$	0.0142598			0.00304020
$23$	−0.641921	−	1.11184i	−0.133850	−	0.231834i	0.791308	−	0.611418i	$-0.209401\pi$
$23$	−0.641921	−	1.11184i	−0.133850	−	0.231834i	−0.925157	+	0.379584i	$0.876067\pi$
$24$	0.761548	−	1.31904i	0.155450	−	0.269248i
$25$	2.14475	−	3.71481i	0.428949	−	0.742962i
$26$	0.389209	+	0.674129i	0.0763301	+	0.132208i
$27$	−1.00000			−0.192450
$28$	4.75351	−	1.08558i	0.898330	−	0.205154i
$29$	−7.06045			−1.31109			−0.655546	−	0.755155i	$-0.727562\pi$
$29$	−7.06045			−1.31109			−0.655546	+	0.755155i	$0.727562\pi$
$30$	0.167040	+	0.289322i	0.0304972	+	0.0528227i
$31$	1.80976	−	3.13460i	0.325043	−	0.562991i	−0.656478	−	0.754345i	$-0.727955\pi$
$31$	1.80976	−	3.13460i	0.325043	−	0.562991i	0.981521	+	0.191354i	$0.0612879\pi$
$32$	2.13389	−	3.69600i	0.377221	−	0.653367i
$33$	−0.0179894	−	0.0311586i	−0.00313156	−	0.00542402i
$34$	−1.28949			−0.221146
$35$	−0.657084	+	2.13115i	−0.111068	+	0.360230i
$36$	−1.84292			−0.307153
$37$	1.08137	+	1.87298i	0.177776	+	0.307917i	0.941118	−	0.338077i	$-0.109776\pi$
$37$	1.08137	+	1.87298i	0.177776	+	0.307917i	−0.763343	+	0.645994i	$0.776443\pi$
$38$	0.198169	−	0.343239i	0.0321473	−	0.0556808i
$39$	0.982011	−	1.70089i	0.157248	−	0.272361i
$40$	0.641921	+	1.11184i	0.101497	+	0.175797i
$41$	0.130805			0.0204282			0.0102141	−	0.999948i	$-0.496749\pi$
$41$	0.130805			0.0204282			0.0102141	+	0.999948i	$0.496749\pi$
$42$	0.713333	+	0.768600i	0.110070	+	0.118598i
$43$	−4.50884			−0.687591			−0.343796	−	0.939045i	$-0.611713\pi$
$43$	−4.50884			−0.687591			−0.343796	+	0.939045i	$0.611713\pi$
$44$	−0.0331530	−	0.0574227i	−0.00499801	−	0.00865680i
$45$	0.421458	−	0.729986i	0.0628272	−	0.108820i
$46$	0.254418	−	0.440665i	0.0375119	−	0.0649725i
$47$	3.99277	+	6.91568i	0.582405	+	1.00876i	0.995193	+	0.0979283i	$0.0312216\pi$
$47$	3.99277	+	6.91568i	0.582405	+	1.00876i	−0.412788	+	0.910827i	$0.635445\pi$
$48$	−3.08217			−0.444873
$49$	−0.521390	+	6.98056i	−0.0744842	+	0.997222i
$50$	1.70009			0.240429
$51$	1.62676	+	2.81763i	0.227792	+	0.394547i
$52$	1.80976	−	3.13460i	0.250969	−	0.434691i
$53$	−1.49085	+	2.58222i	−0.204783	+	0.354695i	−0.950064	−	0.312056i	$-0.898982\pi$
$53$	−1.49085	+	2.58222i	−0.204783	+	0.354695i	0.745280	+	0.666751i	$0.232316\pi$
$54$	−0.198169	−	0.343239i	−0.0269674	−	0.0467089i
$55$	0.0303272			0.00408931
$56$	2.74128	+	2.95366i	0.366319	+	0.394700i
$57$	−1.00000			−0.132453
$58$	−1.39916	−	2.42342i	−0.183719	−	0.318211i
$59$	−6.48994	+	11.2409i	−0.844919	+	1.46344i	0.0407734	+	0.999168i	$0.487018\pi$
$59$	−6.48994	+	11.2409i	−0.844919	+	1.46344i	−0.885692	+	0.464273i	$0.846315\pi$
$60$	0.776711	−	1.34530i	0.100273	−	0.173678i
$61$	−1.29380	−	2.24092i	−0.165654	−	0.286921i	0.771234	−	0.636552i	$-0.219640\pi$
$61$	−1.29380	−	2.24092i	−0.165654	−	0.286921i	−0.936887	+	0.349632i	$0.886307\pi$
$62$	1.43456			0.182189
$63$	0.779537	−	2.52830i	0.0982125	−	0.318536i
$64$	−4.47286			−0.559107
$65$	0.827752	+	1.43371i	0.102670	+	0.177830i
$66$	0.00712991	−	0.0123494i	0.000877631	−	0.00152010i
$67$	−2.25952	+	3.91361i	−0.276045	+	0.478124i	−0.970398	−	0.241511i	$-0.922357\pi$
$67$	−2.25952	+	3.91361i	−0.276045	+	0.478124i	0.694353	+	0.719634i	$0.255690\pi$
$68$	2.99798	+	5.19265i	0.363558	+	0.629701i
$69$	−1.28384			−0.154556
$70$	−0.861707	+	0.196791i	−0.102994	+	0.0235210i
$71$	−2.64985			−0.314480			−0.157240	−	0.987560i	$-0.550260\pi$
$71$	−2.64985			−0.314480			−0.157240	+	0.987560i	$0.550260\pi$
$72$	−0.761548	−	1.31904i	−0.0897493	−	0.155450i
$73$	−3.10649	+	5.38059i	−0.363587	+	0.629751i	−0.988548	−	0.150905i	$-0.951781\pi$
$73$	−3.10649	+	5.38059i	−0.363587	+	0.629751i	0.624961	+	0.780656i	$0.285115\pi$
$74$	−0.428588	+	0.742336i	−0.0498223	+	0.0862948i
$75$	−2.14475	−	3.71481i	−0.247654	−	0.428949i
$76$	−1.84292			−0.211397
$77$	0.0928019	−	0.0211935i	0.0105758	−	0.00241522i
$78$	0.778417			0.0881384
$79$	−5.18641	−	8.98312i	−0.583516	−	1.01068i	−0.995059	−	0.0992892i	$-0.968343\pi$
$79$	−5.18641	−	8.98312i	−0.583516	−	1.01068i	0.411542	−	0.911391i	$-0.364990\pi$
$80$	1.29900	−	2.24994i	0.145233	−	0.251551i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.0259214	+	0.0448973i	0.00286255	+	0.00495807i
$83$	10.2752			1.12785			0.563927	−	0.825825i	$-0.309290\pi$
$83$	10.2752			1.12785			0.563927	+	0.825825i	$0.309290\pi$
$84$	1.43662	−	4.65945i	0.156748	−	0.508388i
$85$	−2.74244			−0.297459
$86$	−0.893513	−	1.54761i	−0.0963499	−	0.166883i
$87$	−3.53023	+	6.11453i	−0.378480	+	0.655546i
$88$	0.0273996	−	0.0474576i	0.00292081	−	0.00505899i
$89$	−4.18641	−	7.25107i	−0.443758	−	0.768612i	0.554207	−	0.832379i	$-0.313022\pi$
$89$	−4.18641	−	7.25107i	−0.443758	−	0.768612i	−0.997965	+	0.0637675i	$0.979688\pi$
$90$	0.334080			0.0352151
$91$	3.53486	+	3.80873i	0.370554	+	0.399263i
$92$	−2.36601			−0.246674
$93$	−1.80976	−	3.13460i	−0.187664	−	0.325043i
$94$	−1.58249	+	2.74095i	−0.163221	+	0.282707i
$95$	0.421458	−	0.729986i	0.0432407	−	0.0748950i
$96$	−2.13389	−	3.69600i	−0.217789	−	0.377221i
$97$	−2.55162			−0.259077			−0.129539	−	0.991574i	$-0.541350\pi$
$97$	−2.55162			−0.259077			−0.129539	+	0.991574i	$0.541350\pi$
$98$	−2.49932	+	1.20437i	−0.252470	+	0.121660i
$99$	−0.0359789			−0.00361601
$100$	−3.95259	−	6.84608i	−0.395259	−	0.684608i
$101$	−3.56508	+	6.17491i	−0.354739	+	0.614426i	−0.987073	−	0.160270i	$-0.948764\pi$
$101$	−3.56508	+	6.17491i	−0.354739	+	0.614426i	0.632334	+	0.774696i	$0.282097\pi$
$102$	−0.644747	+	1.11673i	−0.0638394	+	0.110573i
$103$	−1.45461	−	2.51946i	−0.143327	−	0.248250i	0.785420	−	0.618963i	$-0.212447\pi$
$103$	−1.45461	−	2.51946i	−0.143327	−	0.248250i	−0.928748	+	0.370713i	$0.879113\pi$
$104$	2.99139			0.293330
$105$	1.51709	+	1.63463i	0.148052	+	0.159523i
$106$	−1.18176			−0.114783
$107$	−4.30466	−	7.45588i	−0.416147	−	0.720788i	0.579401	−	0.815042i	$-0.303286\pi$
$107$	−4.30466	−	7.45588i	−0.416147	−	0.720788i	−0.995548	+	0.0942550i	$0.969953\pi$
$108$	−0.921458	+	1.59601i	−0.0886673	+	0.153576i
$109$	−0.287469	+	0.497911i	−0.0275346	+	0.0476913i	−0.879464	−	0.475965i	$-0.842099\pi$
$109$	−0.287469	+	0.497911i	−0.0275346	+	0.0476913i	0.851930	+	0.523656i	$0.175432\pi$
$110$	0.00600991	+	0.0104095i	0.000573023	+	0.000992505i
$111$	2.16274			0.205278
$112$	2.40267	−	7.79266i	0.227031	−	0.736337i
$113$	−15.2784			−1.43727			−0.718637	−	0.695385i	$-0.755234\pi$
$113$	−15.2784			−1.43727			−0.718637	+	0.695385i	$0.755234\pi$
$114$	−0.198169	−	0.343239i	−0.0185603	−	0.0321473i
$115$	0.541085	−	0.937187i	0.0504564	−	0.0873931i
$116$	−6.50591	+	11.2686i	−0.604058	+	1.04626i
$117$	−0.982011	−	1.70089i	−0.0907869	−	0.157248i
$118$	−5.14443			−0.473583
$119$	−8.39193	+	1.91649i	−0.769287	+	0.175685i
$120$	1.28384			0.117198
$121$	5.49935	+	9.52516i	0.499941	+	0.865923i
$122$	0.512782	−	0.888164i	0.0464251	−	0.0804106i
$123$	0.0654023	−	0.113280i	0.00589713	−	0.0102141i
$124$	−3.33524	−	5.77681i	−0.299513	−	0.518772i
$125$	7.83026			0.700360
$126$	1.02229	−	0.233464i	0.0910731	−	0.0207987i
$127$	1.02235			0.0907193			0.0453597	−	0.998971i	$-0.485557\pi$
$127$	1.02235			0.0907193			0.0453597	+	0.998971i	$0.485557\pi$
$128$	−5.15416	−	8.92726i	−0.455567	−	0.789066i
$129$	−2.25442	+	3.90477i	−0.198490	+	0.343796i
$130$	−0.328070	+	0.568234i	−0.0287736	+	0.0498374i
$131$	8.49106	+	14.7070i	0.741868	+	1.28495i	0.951644	+	0.307203i	$0.0993930\pi$
$131$	8.49106	+	14.7070i	0.741868	+	1.28495i	−0.209776	+	0.977749i	$0.567274\pi$
$132$	−0.0663061			−0.00577120
$133$	0.779537	−	2.52830i	0.0675945	−	0.219232i
$134$	−1.79107			−0.154725
$135$	−0.421458	−	0.729986i	−0.0362733	−	0.0628272i
$136$	−2.47771	+	4.29151i	−0.212462	+	0.367994i
$137$	1.12111	−	1.94181i	0.0957825	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$137$	1.12111	−	1.94181i	0.0957825	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$138$	−0.254418	−	0.440665i	−0.0216575	−	0.0375119i
$139$	16.8301			1.42751			0.713753	−	0.700397i	$-0.246994\pi$
$139$	16.8301			1.42751			0.713753	+	0.700397i	$0.246994\pi$
$140$	2.79586	+	3.01248i	0.236293	+	0.254601i
$141$	7.98554			0.672504
$142$	−0.525119	−	0.909533i	−0.0440670	−	0.0763263i
$143$	0.0353316	−	0.0611962i	0.00295458	−	0.00511748i
$144$	−1.54109	+	2.66924i	−0.128424	+	0.222436i
$145$	−2.97568	−	5.15403i	−0.247117	−	0.428019i
$146$	−2.46244			−0.203793
$147$	5.78464	+	3.94181i	0.477109	+	0.325115i
$148$	3.98574			0.327626
$149$	−6.36601	−	11.0263i	−0.521524	−	0.903306i	−0.999687	−	0.0250347i	$-0.992030\pi$
$149$	−6.36601	−	11.0263i	−0.521524	−	0.903306i	0.478163	−	0.878271i	$-0.341303\pi$
$150$	0.850046	−	1.47232i	0.0694059	−	0.120215i
$151$	5.91342	−	10.2424i	0.481228	−	0.833511i	−0.518540	−	0.855053i	$-0.673524\pi$
$151$	5.91342	−	10.2424i	0.481228	−	0.833511i	0.999768	+	0.0215425i	$0.00685771\pi$
$152$	−0.761548	−	1.31904i	−0.0617697	−	0.106988i
$153$	3.25351			0.263031
$154$	0.0256649	+	0.0276534i	0.00206814	+	0.00222837i
$155$	3.05096			0.245059
$156$	−1.80976	−	3.13460i	−0.144897	−	0.250969i
$157$	−3.68843	+	6.38855i	−0.294369	+	0.509862i	−0.974838	−	0.222915i	$-0.928443\pi$
$157$	−3.68843	+	6.38855i	−0.294369	+	0.509862i	0.680469	+	0.732777i	$0.261776\pi$
$158$	2.05557	−	3.56036i	0.163533	−	0.283247i
$159$	1.49085	+	2.58222i	0.118232	+	0.204783i
$160$	3.59737			0.284397
$161$	1.00080	−	3.24594i	0.0788743	−	0.255816i
$162$	−0.396339			−0.0311393
$163$	9.02470	+	15.6312i	0.706869	+	1.22433i	0.966013	+	0.258494i	$0.0832263\pi$
$163$	9.02470	+	15.6312i	0.706869	+	1.22433i	−0.259144	+	0.965839i	$0.583440\pi$
$164$	0.120531	−	0.208766i	0.00941188	−	0.0163019i
$165$	0.0151636	−	0.0262641i	0.00118048	−	0.00204466i
$166$	2.03624	+	3.52686i	0.158043	+	0.273738i
$167$	22.6354			1.75158			0.875790	−	0.482693i	$-0.160341\pi$
$167$	22.6354			1.75158			0.875790	+	0.482693i	$0.160341\pi$
$168$	3.92859	−	0.897184i	0.303097	−	0.0692193i
$169$	−9.14262			−0.703279
$170$	−0.543467	−	0.941312i	−0.0416820	−	0.0721954i
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	−4.15470	+	7.19616i	−0.316793	+	0.548702i
$173$	−3.44141	−	5.96070i	−0.261646	−	0.453183i	0.705034	−	0.709174i	$-0.250932\pi$
$173$	−3.44141	−	5.96070i	−0.261646	−	0.453183i	−0.966679	+	0.255990i	$0.917598\pi$
$174$	−2.79833			−0.212141
$175$	11.0641	−	2.52674i	0.836366	−	0.191003i
$176$	−0.110893			−0.00835888
$177$	6.48994	+	11.2409i	0.487814	+	0.844919i
$178$	1.65923	−	2.87388i	0.124365	−	0.215406i
$179$	−0.310439	+	0.537696i	−0.0232033	+	0.0401893i	−0.877394	−	0.479771i	$-0.840720\pi$
$179$	−0.310439	+	0.537696i	−0.0232033	+	0.0401893i	0.854191	+	0.519960i	$0.174053\pi$
$180$	−0.776711	−	1.34530i	−0.0578926	−	0.100273i
$181$	−9.31058			−0.692050			−0.346025	−	0.938225i	$-0.612469\pi$
$181$	−9.31058			−0.692050			−0.346025	+	0.938225i	$0.612469\pi$
$182$	−0.606805	+	1.96808i	−0.0449794	+	0.145883i
$183$	−2.58759			−0.191280
$184$	−0.977707	−	1.69344i	−0.0720775	−	0.124842i
$185$	−0.911502	+	1.57877i	−0.0670150	+	0.116073i
$186$	0.717279	−	1.24236i	0.0525934	−	0.0910945i
$187$	0.0585289	+	0.101375i	0.00428006	+	0.00741328i
$188$	14.7167			1.07332
$189$	−1.79981	−	1.93925i	−0.130917	−	0.141060i
$190$	0.334080			0.0242367
$191$	−9.16919	−	15.8815i	−0.663459	−	1.14915i	−0.979701	−	0.200466i	$-0.935754\pi$
$191$	−9.16919	−	15.8815i	−0.663459	−	1.14915i	0.316241	−	0.948679i	$-0.397579\pi$
$192$	−2.23643	+	3.87361i	−0.161400	+	0.279554i
$193$	7.60019	−	13.1639i	0.547074	−	0.947559i	−0.451400	−	0.892322i	$-0.649075\pi$
$193$	7.60019	−	13.1639i	0.547074	−	0.947559i	0.998473	−	0.0552373i	$-0.0175915\pi$
$194$	−0.505652	−	0.875814i	−0.0363037	−	0.0628798i
$195$	1.65550			0.118553
$196$	10.6606	+	7.26443i	0.761472	+	0.518888i
$197$	7.77205			0.553736			0.276868	−	0.960908i	$-0.410704\pi$
$197$	7.77205			0.553736			0.276868	+	0.960908i	$0.410704\pi$
$198$	−0.00712991	−	0.0123494i	−0.000506701	−	0.000877631i
$199$	−12.8631	+	22.2795i	−0.911840	+	1.57935i	−0.100377	+	0.994950i	$0.532005\pi$
$199$	−12.8631	+	22.2795i	−0.911840	+	1.57935i	−0.811463	+	0.584403i	$0.801329\pi$
$200$	3.26665	−	5.65801i	0.230987	−	0.400082i
$201$	2.25952	+	3.91361i	0.159375	+	0.276045i
$202$	−2.82596			−0.198834
$203$	−12.7074	−	13.6920i	−0.891888	−	0.960989i
$204$	5.99595			0.419801
$205$	0.0551286	+	0.0954856i	0.00385035	+	0.00666900i
$206$	0.576518	−	0.998559i	0.0401679	−	0.0695729i
$207$	−0.641921	+	1.11184i	−0.0446166	+	0.0772782i
$208$	−3.02672	−	5.24244i	−0.209866	−	0.363498i
$209$	−0.0359789			−0.00248871
$210$	−0.260428	+	0.844656i	−0.0179712	+	0.0582868i
$211$	17.2470			1.18733			0.593667	−	0.804711i	$-0.297680\pi$
$211$	17.2470			1.18733			0.593667	+	0.804711i	$0.297680\pi$
$212$	2.74750	+	4.75882i	0.188699	+	0.326837i
$213$	−1.32493	+	2.29484i	−0.0907825	+	0.157240i
$214$	1.70610	−	2.95505i	0.116627	−	0.202003i
$215$	−1.90028	−	3.29139i	−0.129598	−	0.224471i
$216$	−1.52310			−0.103634
$217$	9.33600	−	2.13209i	0.633769	−	0.144736i
$218$	−0.227870			−0.0154333
$219$	3.10649	+	5.38059i	0.209917	+	0.363587i
$220$	0.0279452	−	0.0484025i	0.00188407	−	0.00326330i
$221$	−3.19499	+	5.53388i	−0.214918	+	0.372249i
$222$	0.428588	+	0.742336i	0.0287649	+	0.0498223i
$223$	15.7257			1.05307			0.526537	−	0.850152i	$-0.323490\pi$
$223$	15.7257			1.05307			0.526537	+	0.850152i	$0.323490\pi$
$224$	11.0081	−	2.51395i	0.735507	−	0.167970i
$225$	−4.28949			−0.285966
$226$	−3.02772	−	5.24416i	−0.201401	−	0.348836i
$227$	3.25181	−	5.63230i	0.215830	−	0.373829i	−0.737699	−	0.675130i	$-0.764088\pi$
$227$	3.25181	−	5.63230i	0.215830	−	0.373829i	0.953529	+	0.301301i	$0.0974209\pi$
$228$	−0.921458	+	1.59601i	−0.0610250	+	0.105698i
$229$	−3.93630	−	6.81788i	−0.260118	−	0.450538i	0.706155	−	0.708057i	$-0.250428\pi$
$229$	−3.93630	−	6.81788i	−0.260118	−	0.450538i	−0.966273	+	0.257519i	$0.917095\pi$
$230$	0.428906			0.0282812
$231$	0.0280469	−	0.0909656i	0.00184535	−	0.00598510i
$232$	−10.7537			−0.706018
$233$	−11.1395	−	19.2941i	−0.729771	−	1.26400i	−0.956980	−	0.290155i	$-0.906293\pi$
$233$	−11.1395	−	19.2941i	−0.729771	−	1.26400i	0.227208	−	0.973846i	$-0.427040\pi$
$234$	0.389209	−	0.674129i	0.0254434	−	0.0440692i
$235$	−3.36557	+	5.82933i	−0.219545	+	0.380264i
$236$	11.9604	+	20.7161i	0.778557	+	1.34850i
$237$	−10.3728			−0.673787
$238$	−2.32084	−	2.50065i	−0.150438	−	0.162093i
$239$	26.5221			1.71557			0.857784	−	0.514009i	$-0.171840\pi$
$239$	26.5221			1.71557			0.857784	+	0.514009i	$0.171840\pi$
$240$	−1.29900	−	2.24994i	−0.0838504	−	0.145233i
$241$	−5.54028	+	9.59605i	−0.356881	+	0.618136i	−0.987438	−	0.158007i	$-0.949493\pi$
$241$	−5.54028	+	9.59605i	−0.356881	+	0.618136i	0.630557	+	0.776143i	$0.282827\pi$
$242$	−2.17961	+	3.77519i	−0.140110	+	0.242678i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.76872			−0.305286
$245$	−5.31545	+	2.56140i	−0.339592	+	0.163642i
$246$	0.0518429			0.00330538
$247$	−0.982011	−	1.70089i	−0.0624838	−	0.108225i
$248$	2.75644	−	4.77430i	0.175034	−	0.303168i
$249$	5.13762	−	8.89861i	0.325583	−	0.563927i
$250$	1.55172	+	2.68765i	0.0981392	+	0.169982i
$251$	3.32163			0.209659			0.104830	−	0.994490i	$-0.466570\pi$
$251$	3.32163			0.209659			0.104830	+	0.994490i	$0.466570\pi$
$252$	−3.31689	−	3.57388i	−0.208945	−	0.225133i
$253$	−0.0461912			−0.00290401
$254$	0.202599	+	0.350912i	0.0127122	+	0.0220182i
$255$	−1.37122	+	2.37502i	−0.0858691	+	0.148730i
$256$	−2.43007	+	4.20900i	−0.151879	+	0.263062i
$257$	−15.0595	−	26.0837i	−0.939383	−	1.62706i	−0.766625	−	0.642095i	$-0.778065\pi$
$257$	−15.0595	−	26.0837i	−0.939383	−	1.62706i	−0.172758	−	0.984964i	$-0.555268\pi$
$258$	−1.78703			−0.111255
$259$	−1.68593	+	5.46805i	−0.104759	+	0.339768i
$260$	3.05096			0.189212
$261$	3.53023	+	6.11453i	0.218515	+	0.378480i
$262$	−3.36534	+	5.82893i	−0.207911	+	0.360113i
$263$	12.7833	−	22.1414i	0.788253	−	1.36529i	−0.138783	−	0.990323i	$-0.544319\pi$
$263$	12.7833	−	22.1414i	0.788253	−	1.36529i	0.927036	−	0.374972i	$-0.122348\pi$
$264$	−0.0273996	−	0.0474576i	−0.00168633	−	0.00292081i
$265$	−2.51332			−0.154392
$266$	1.02229	−	0.233464i	0.0626808	−	0.0143146i
$267$	−8.37281			−0.512408
$268$	4.16411	+	7.21245i	0.254364	+	0.440571i
$269$	3.17565	−	5.50038i	0.193623	−	0.335364i	−0.752825	−	0.658220i	$-0.771310\pi$
$269$	3.17565	−	5.50038i	0.193623	−	0.335364i	0.946448	+	0.322856i	$0.104643\pi$
$270$	0.167040	−	0.289322i	0.0101657	−	0.0176076i
$271$	−3.93087	−	6.80846i	−0.238783	−	0.413585i	0.721582	−	0.692329i	$-0.243415\pi$
$271$	−3.93087	−	6.80846i	−0.238783	−	0.413585i	−0.960365	+	0.278744i	$0.910082\pi$
$272$	10.0279			0.608030
$273$	5.06589	−	1.15691i	0.306601	−	0.0700195i
$274$	0.888674			0.0536868
$275$	−0.0771656	−	0.133655i	−0.00465326	−	0.00805968i
$276$	−1.18301	+	2.04903i	−0.0712086	+	0.123337i
$277$	2.93784	−	5.08849i	0.176518	−	0.305738i	−0.764168	−	0.645018i	$-0.776850\pi$
$277$	2.93784	−	5.08849i	0.176518	−	0.305738i	0.940686	+	0.339280i	$0.110183\pi$
$278$	3.33520	+	5.77674i	0.200032	+	0.346466i
$279$	−3.61953			−0.216695
$280$	−1.00080	+	3.24594i	−0.0598094	+	0.193982i
$281$	16.7309			0.998084			0.499042	−	0.866578i	$-0.333685\pi$
$281$	16.7309			0.998084			0.499042	+	0.866578i	$0.333685\pi$
$282$	1.58249	+	2.74095i	0.0942358	+	0.163221i
$283$	10.4479	−	18.0962i	0.621060	−	1.07571i	−0.368228	−	0.929735i	$-0.620036\pi$
$283$	10.4479	−	18.0962i	0.621060	−	1.07571i	0.989289	−	0.145973i	$-0.0466312\pi$
$284$	−2.44173	+	4.22920i	−0.144890	+	0.250957i
$285$	−0.421458	−	0.729986i	−0.0249650	−	0.0432407i
$286$	0.0280066			0.00165606
$287$	0.235423	+	0.253663i	0.0138966	+	0.0149732i
$288$	−4.26777			−0.251481
$289$	3.20732	+	5.55525i	0.188666	+	0.326779i
$290$	1.17938	−	2.04274i	0.0692554	−	0.119954i
$291$	−1.27581	+	2.20976i	−0.0747892	+	0.129539i
$292$	5.72499	+	9.91598i	0.335030	+	0.580289i
$293$	−12.1831			−0.711744			−0.355872	−	0.934535i	$-0.615816\pi$
$293$	−12.1831			−0.711744			−0.355872	+	0.934535i	$0.615816\pi$
$294$	−0.206647	+	2.76666i	−0.0120519	+	0.161355i
$295$	−10.9409			−0.637007
$296$	1.64703	+	2.85273i	0.0957315	+	0.165812i
$297$	−0.0179894	+	0.0311586i	−0.00104385	+	0.00180801i
$298$	2.52310	−	4.37013i	0.146159	−	0.253155i
$299$	−1.26075	−	2.18368i	−0.0729108	−	0.126285i
$300$	−7.90517			−0.456405
$301$	−8.11503	−	8.74376i	−0.467743	−	0.503982i
$302$	4.68744			0.269732
$303$	3.56508	+	6.17491i	0.204809	+	0.354739i
$304$	−1.54109	+	2.66924i	−0.0883873	+	0.153091i
$305$	1.09056	−	1.88891i	0.0624454	−	0.108159i
$306$	0.644747	+	1.11673i	0.0368577	+	0.0638394i
$307$	−25.2971			−1.44378			−0.721890	−	0.692008i	$-0.756726\pi$
$307$	−25.2971			−1.44378			−0.721890	+	0.692008i	$0.756726\pi$
$308$	0.0516880	−	0.167642i	0.00294520	−	0.00955228i
$309$	−2.90922			−0.165500
$310$	0.604606	+	1.04721i	0.0343393	+	0.0594774i
$311$	−4.94365	+	8.56265i	−0.280329	+	0.485543i	−0.971466	−	0.237180i	$-0.923777\pi$
$311$	−4.94365	+	8.56265i	−0.280329	+	0.485543i	0.691137	+	0.722724i	$0.257110\pi$
$312$	1.49570	−	2.59062i	0.0846771	−	0.146665i
$313$	0.687371	+	1.19056i	0.0388525	+	0.0672945i	0.884798	−	0.465975i	$-0.154296\pi$
$313$	0.687371	+	1.19056i	0.0388525	+	0.0672945i	−0.845945	+	0.533270i	$0.820963\pi$
$314$	−2.92373			−0.164996
$315$	2.17417	−	0.496522i	0.122501	−	0.0279758i
$316$	−19.1162			−1.07537
$317$	−13.3451	−	23.1144i	−0.749535	−	1.29823i	−0.948046	−	0.318134i	$-0.896944\pi$
$317$	−13.3451	−	23.1144i	−0.749535	−	1.29823i	0.198511	−	0.980099i	$-0.436390\pi$
$318$	−0.590880	+	1.02343i	−0.0331349	+	0.0573913i
$319$	−0.127014	+	0.219994i	−0.00711140	+	0.0123173i
$320$	−1.88512	−	3.26513i	−0.105381	−	0.182526i
$321$	−8.60931			−0.480525
$322$	1.31246	−	0.299731i	0.0731407	−	0.0167034i
$323$	3.25351			0.181030
$324$	0.921458	+	1.59601i	0.0511921	+	0.0886673i
$325$	4.21233	−	7.29597i	0.233658	−	0.404707i
$326$	−3.57684	+	6.19526i	−0.198103	+	0.343124i
$327$	0.287469	+	0.497911i	0.0158971	+	0.0275346i
$328$	0.199228			0.0110005
$329$	−6.22502	+	20.1899i	−0.343197	+	1.11310i
$330$	0.0120198			0.000661670
$331$	18.1868	+	31.5004i	0.999635	+	1.73142i	0.523223	+	0.852196i	$0.324729\pi$
$331$	18.1868	+	31.5004i	0.999635	+	1.73142i	0.476412	+	0.879222i	$0.341937\pi$
$332$	9.46819	−	16.3994i	0.519635	−	0.900034i
$333$	1.08137	−	1.87298i	0.0592586	−	0.102639i
$334$	4.48564	+	7.76935i	0.245443	+	0.425120i
$335$	−3.80918			−0.208118
$336$	−5.54731	−	5.97710i	−0.302631	−	0.326078i
$337$	30.0191			1.63524			0.817622	−	0.575756i	$-0.195292\pi$
$337$	30.0191			1.63524			0.817622	+	0.575756i	$0.195292\pi$
$338$	−1.81179	−	3.13811i	−0.0985482	−	0.170690i
$339$	−7.63922	+	13.2315i	−0.414906	+	0.718637i
$340$	−2.52704	+	4.37696i	−0.137048	+	0.237374i
$341$	−0.0651132	−	0.112779i	−0.00352608	−	0.00610735i
$342$	−0.396339			−0.0214315
$343$	−14.4755	+	11.5525i	−0.781601	+	0.623779i
$344$	−6.86739			−0.370265
$345$	−0.541085	−	0.937187i	−0.0291310	−	0.0504564i
$346$	1.36396	−	2.36245i	0.0733271	−	0.127006i
$347$	−14.1044	+	24.4295i	−0.757162	+	1.31144i	0.187131	+	0.982335i	$0.440081\pi$
$347$	−14.1044	+	24.4295i	−0.757162	+	1.31144i	−0.944292	+	0.329108i	$0.893252\pi$
$348$	6.50591	+	11.2686i	0.348753	+	0.604058i
$349$	−4.32568			−0.231548			−0.115774	−	0.993276i	$-0.536935\pi$
$349$	−4.32568			−0.231548			−0.115774	+	0.993276i	$0.536935\pi$
$350$	3.05984	+	3.29690i	0.163555	+	0.176227i
$351$	−1.96402			−0.104832
$352$	−0.0767749	−	0.132978i	−0.00409211	−	0.00708775i
$353$	10.1227	−	17.5330i	0.538776	−	0.933187i	−0.460194	−	0.887818i	$-0.652220\pi$
$353$	10.1227	−	17.5330i	0.538776	−	0.933187i	0.998970	−	0.0453691i	$-0.0144464\pi$
$354$	−2.57221	+	4.45521i	−0.136712	+	0.236792i
$355$	−1.11680	−	1.93436i	−0.0592737	−	0.102665i
$356$	−15.4304			−0.817809
$357$	−2.53624	+	8.22587i	−0.134232	+	0.435359i
$358$	−0.246078			−0.0130056
$359$	−6.57989	−	11.3967i	−0.347273	−	0.601495i	0.638491	−	0.769629i	$-0.279559\pi$
$359$	−6.57989	−	11.3967i	−0.347273	−	0.601495i	−0.985764	+	0.168134i	$0.946226\pi$
$360$	0.641921	−	1.11184i	0.0338322	−	0.0585991i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	−1.84507	−	3.19576i	−0.0969747	−	0.167965i
$363$	10.9987			0.577282
$364$	9.33600	−	2.13209i	0.489339	−	0.111752i
$365$	−5.23701			−0.274118
$366$	−0.512782	−	0.888164i	−0.0268035	−	0.0464251i
$367$	−12.2002	+	21.1314i	−0.636848	+	1.10305i	0.349273	+	0.937021i	$0.386429\pi$
$367$	−12.2002	+	21.1314i	−0.636848	+	1.10305i	−0.986120	+	0.166031i	$0.946905\pi$
$368$	−1.97851	+	3.42688i	−0.103137	+	0.178638i
$369$	−0.0654023	−	0.113280i	−0.00340471	−	0.00589713i
$370$	−0.722527			−0.0375624
$371$	−7.69081	+	1.75638i	−0.399287	+	0.0911864i
$372$	−6.67048			−0.345848
$373$	−1.23438	−	2.13800i	−0.0639136	−	0.110702i	0.832298	−	0.554328i	$-0.187025\pi$
$373$	−1.23438	−	2.13800i	−0.0639136	−	0.110702i	−0.896212	+	0.443627i	$0.853692\pi$
$374$	−0.0231973	+	0.0401788i	−0.00119950	+	0.00207760i
$375$	3.91513	−	6.78120i	0.202176	−	0.350180i
$376$	6.08137	+	10.5332i	0.313623	+	0.543210i
$377$	−13.8669			−0.714180
$378$	0.308961	−	1.00206i	0.0158912	−	0.0515406i
$379$	−18.7800			−0.964665			−0.482332	−	0.875988i	$-0.660210\pi$
$379$	−18.7800			−0.964665			−0.482332	+	0.875988i	$0.660210\pi$
$380$	−0.776711	−	1.34530i	−0.0398445	−	0.0690126i
$381$	0.511177	−	0.885385i	0.0261884	−	0.0453597i
$382$	3.63410	−	6.29445i	0.185937	−	0.322052i
$383$	−15.8144	−	27.3914i	−0.808081	−	1.39964i	−0.914192	−	0.405282i	$-0.867173\pi$
$383$	−15.8144	−	27.3914i	−0.808081	−	1.39964i	0.106111	−	0.994354i	$-0.466160\pi$
$384$	−10.3083			−0.526044
$385$	0.0545831	+	0.0588120i	0.00278181	+	0.00299734i
$386$	6.02449			0.306639
$387$	2.25442	+	3.90477i	0.114599	+	0.198490i
$388$	−2.35121	+	4.07241i	−0.119364	+	0.206745i
$389$	2.16873	−	3.75636i	0.109959	−	0.190455i	−0.805794	−	0.592196i	$-0.798261\pi$
$389$	2.16873	−	3.75636i	0.109959	−	0.190455i	0.915754	+	0.401741i	$0.131595\pi$
$390$	0.328070	+	0.568234i	0.0166125	+	0.0287736i
$391$	4.17700			0.211240
$392$	−0.794126	+	10.6321i	−0.0401094	+	0.537000i
$393$	16.9821			0.856635
$394$	1.54018	+	2.66767i	0.0775932	+	0.134395i
$395$	4.37170	−	7.57201i	0.219964	−	0.380989i
$396$	−0.0331530	+	0.0574227i	−0.00166600	+	0.00288560i
$397$	−0.682778	−	1.18261i	−0.0342676	−	0.0593533i	0.848383	−	0.529383i	$-0.177577\pi$
$397$	−0.682778	−	1.18261i	−0.0342676	−	0.0593533i	−0.882651	+	0.470030i	$0.844243\pi$
$398$	−10.1963			−0.511093
$399$	−1.79981	−	1.93925i	−0.0901030	−	0.0970840i
$400$	−13.2209			−0.661047
$401$	−11.3302	−	19.6246i	−0.565806	−	0.980004i	−0.996974	−	0.0777327i	$-0.975232\pi$
$401$	−11.3302	−	19.6246i	−0.565806	−	0.980004i	0.431169	−	0.902271i	$-0.358101\pi$
$402$	−0.895536	+	1.55111i	−0.0446653	+	0.0773626i
$403$	3.55441	−	6.15642i	0.177058	−	0.306673i
$404$	6.57015	+	11.3798i	0.326877	+	0.566168i
$405$	−0.842916			−0.0418848
$406$	2.18140	−	7.07503i	0.108261	−	0.351128i
$407$	0.0778128			0.00385704
$408$	2.47771	+	4.29151i	0.122665	+	0.212462i
$409$	13.3916	−	23.1950i	0.662174	−	1.14692i	−0.317869	−	0.948135i	$-0.602967\pi$
$409$	13.3916	−	23.1950i	0.662174	−	1.14692i	0.980043	−	0.198785i	$-0.0636994\pi$
$410$	−0.0218496	+	0.0378446i	−0.00107907	+	0.00186901i
$411$	−1.12111	−	1.94181i	−0.0553000	−	0.0957825i
$412$	−5.36145			−0.264140
$413$	−33.4796	+	7.64584i	−1.64742	+	0.376227i
$414$	−0.508836			−0.0250079
$415$	4.33058	+	7.50078i	0.212580	+	0.368199i
$416$	4.19100	−	7.25902i	0.205481	−	0.355903i
$417$	8.41503	−	14.5753i	0.412086	−	0.713753i
$418$	−0.00712991	−	0.0123494i	−0.000348735	−	0.000604027i
$419$	29.9706			1.46416			0.732081	−	0.681218i	$-0.238549\pi$
$419$	29.9706			1.46416			0.732081	+	0.681218i	$0.238549\pi$
$420$	4.00681	−	0.915048i	0.195512	−	0.0446498i
$421$	−28.9616			−1.41150			−0.705750	−	0.708460i	$-0.749390\pi$
$421$	−28.9616			−1.41150			−0.705750	+	0.708460i	$0.749390\pi$
$422$	3.41783	+	5.91986i	0.166377	+	0.288174i
$423$	3.99277	−	6.91568i	0.194135	−	0.336252i
$424$	−2.27070	+	3.93297i	−0.110275	+	0.191002i
$425$	6.97796	+	12.0862i	0.338481	+	0.586266i
$426$	−1.05024			−0.0508842
$427$	2.01713	−	6.54222i	0.0976156	−	0.316600i
$428$	−15.8662			−0.766924
$429$	−0.0353316	−	0.0611962i	−0.00170583	−	0.00295458i
$430$	0.753156	−	1.30450i	0.0363204	−	0.0629088i
$431$	−10.4379	+	18.0789i	−0.502774	+	0.870831i	0.497220	+	0.867624i	$0.334354\pi$
$431$	−10.4379	+	18.0789i	−0.502774	+	0.870831i	−0.999995	+	0.00320655i	$0.998979\pi$
$432$	1.54109	+	2.66924i	0.0741455	+	0.128424i
$433$	−7.01266			−0.337007			−0.168503	−	0.985701i	$-0.553893\pi$
$433$	−7.01266			−0.337007			−0.168503	+	0.985701i	$0.553893\pi$
$434$	2.58193	+	2.78197i	0.123936	+	0.133539i
$435$	−5.95137			−0.285346
$436$	0.529782	+	0.917609i	0.0253719	+	0.0439455i
$437$	−0.641921	+	1.11184i	−0.0307072	+	0.0531865i
$438$	−1.23122	+	2.13254i	−0.0588300	+	0.101897i
$439$	0.874034	+	1.51387i	0.0417153	+	0.0722531i	0.886129	−	0.463438i	$-0.153384\pi$
$439$	0.874034	+	1.51387i	0.0417153	+	0.0722531i	−0.844414	+	0.535691i	$0.820051\pi$
$440$	0.0461912			0.00220208
$441$	6.30603	−	3.03874i	0.300287	−	0.144702i
$442$	−2.53259			−0.120463
$443$	9.44051	+	16.3514i	0.448532	+	0.776880i	0.998291	−	0.0584433i	$-0.0186137\pi$
$443$	9.44051	+	16.3514i	0.448532	+	0.776880i	−0.549759	+	0.835323i	$0.685280\pi$
$444$	1.99287	−	3.45175i	0.0945774	−	0.163813i
$445$	3.52879	−	6.11204i	0.167281	−	0.289738i
$446$	3.11636	+	5.39769i	0.147564	+	0.255588i
$447$	−12.7320			−0.602204
$448$	−8.05028	−	8.67399i	−0.380340	−	0.409808i
$449$	19.9572			0.941839			0.470920	−	0.882176i	$-0.343922\pi$
$449$	19.9572			0.941839			0.470920	+	0.882176i	$0.343922\pi$
$450$	−0.850046	−	1.47232i	−0.0400715	−	0.0694059i
$451$	0.00235310	−	0.00407569i	0.000110803	−	0.000191917i
$452$	−14.0784	+	24.3846i	−0.662194	+	1.14695i
$453$	−5.91342	−	10.2424i	−0.277837	−	0.481228i
$454$	2.57763			0.120974
$455$	−1.29053	+	4.18562i	−0.0605009	+	0.196225i
$456$	−1.52310			−0.0713255
$457$	10.7787	+	18.6693i	0.504208	+	0.873314i	0.999988	+	0.00486577i	$0.00154883\pi$
$457$	10.7787	+	18.6693i	0.504208	+	0.873314i	−0.495780	+	0.868448i	$0.665118\pi$
$458$	1.56011	−	2.70219i	0.0728991	−	0.126265i
$459$	1.62676	−	2.81763i	0.0759305	−	0.131516i
$460$	−0.997174	−	1.72716i	−0.0464935	−	0.0805291i
$461$	−27.9766			−1.30300			−0.651500	−	0.758649i	$-0.725860\pi$
$461$	−27.9766			−1.30300			−0.651500	+	0.758649i	$0.725860\pi$
$462$	0.0367810	−	0.00839979i	0.00171121	−	0.000390794i
$463$	38.8491			1.80547			0.902736	−	0.430195i	$-0.141555\pi$
$463$	38.8491			1.80547			0.902736	+	0.430195i	$0.141555\pi$
$464$	10.8808	+	18.8460i	0.505126	+	0.874905i
$465$	1.52548	−	2.64220i	0.0707423	−	0.122529i
$466$	4.41500	−	7.64701i	0.204521	−	0.354241i
$467$	4.31966	+	7.48187i	0.199890	+	0.346219i	0.948493	−	0.316799i	$-0.102608\pi$
$467$	4.31966	+	7.48187i	0.199890	+	0.346219i	−0.748603	+	0.663019i	$0.769275\pi$
$468$	−3.61953			−0.167313
$469$	−11.6562	+	2.66196i	−0.538232	+	0.122918i
$470$	−2.66781			−0.123057
$471$	3.68843	+	6.38855i	0.169954	+	0.294369i
$472$	−9.88480	+	17.1210i	−0.454985	+	0.788057i
$473$	−0.0811114	+	0.140489i	−0.00372951	+	0.00645970i
$474$	−2.05557	−	3.56036i	−0.0944156	−	0.163533i
$475$	−4.28949			−0.196815
$476$	−4.67407	+	15.1596i	−0.214236	+	0.694839i
$477$	2.98169			0.136522
$478$	5.25586	+	9.10341i	0.240397	+	0.416380i
$479$	−7.42013	+	12.8521i	−0.339035	+	0.587225i	−0.984251	−	0.176774i	$-0.943434\pi$
$479$	−7.42013	+	12.8521i	−0.339035	+	0.587225i	0.645217	+	0.764000i	$0.276767\pi$
$480$	1.79869	−	3.11542i	0.0820985	−	0.142199i
$481$	2.12383	+	3.67858i	0.0968383	+	0.167729i
$482$	−4.39166			−0.200034
$483$	−2.31067	−	2.48969i	−0.105139	−	0.113285i
$484$	20.2697			0.921349
$485$	−1.07540	−	1.86264i	−0.0488313	−	0.0845783i
$486$	−0.198169	+	0.343239i	−0.00898914	+	0.0155696i
$487$	−8.95213	+	15.5055i	−0.405660	+	0.702623i	−0.994398	−	0.105701i	$-0.966291\pi$
$487$	−8.95213	+	15.5055i	−0.405660	+	0.702623i	0.588738	+	0.808324i	$0.299625\pi$
$488$	−1.97058	−	3.41314i	−0.0892038	−	0.154506i
$489$	18.0494			0.816222
$490$	−1.93253	−	1.31688i	−0.0873030	−	0.0594906i
$491$	19.1867			0.865883			0.432942	−	0.901422i	$-0.357476\pi$
$491$	19.1867			0.865883			0.432942	+	0.901422i	$0.357476\pi$
$492$	−0.120531	−	0.208766i	−0.00543395	−	0.00941188i
$493$	11.4856	−	19.8937i	0.517287	−	0.895968i
$494$	0.389209	−	0.674129i	0.0175113	−	0.0303305i
$495$	−0.0151636	−	0.0262641i	−0.000681552	−	0.00118048i
$496$	−11.1560			−0.500919
$497$	−4.76922	−	5.13873i	−0.213929	−	0.230504i
$498$	4.07247			0.182492
$499$	−12.2922	−	21.2906i	−0.550272	−	0.953100i	−0.998255	−	0.0590574i	$-0.981191\pi$
$499$	−12.2922	−	21.2906i	−0.550272	−	0.953100i	0.447982	−	0.894043i	$-0.352143\pi$
$500$	7.21525	−	12.4972i	0.322676	−	0.558891i
$501$	11.3177	−	19.6028i	0.505637	−	0.875790i
$502$	0.658245	+	1.14011i	0.0293789	+	0.0508857i
$503$	16.7355			0.746199			0.373099	−	0.927791i	$-0.378295\pi$
$503$	16.7355			0.746199			0.373099	+	0.927791i	$0.378295\pi$
$504$	1.18731	−	3.85085i	0.0528870	−	0.171530i
$505$	−6.01013			−0.267447
$506$	−0.00915367	−	0.0158546i	−0.000406930	−	0.000704824i
$507$	−4.57131	+	7.91774i	−0.203019	+	0.351639i
$508$	0.942057	−	1.63169i	0.0417970	−	0.0723946i
$509$	11.7592	+	20.3675i	0.521217	+	0.902775i	0.999696	+	0.0246752i	$0.00785517\pi$
$509$	11.7592	+	20.3675i	0.521217	+	0.902775i	−0.478478	+	0.878099i	$0.658811\pi$
$510$	−1.08693			−0.0481302
$511$	−16.0254	+	3.65977i	−0.708922	+	0.161899i
$512$	−22.5429			−0.996264
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	5.96864	−	10.3380i	0.263266	−	0.455989i
$515$	1.22611	−	2.12369i	0.0540291	−	0.0935811i
$516$	4.15470	+	7.19616i	0.182901	+	0.316793i
$517$	0.287311			0.0126359
$518$	−2.21095	+	0.504922i	−0.0971436	+	0.0221850i
$519$	−6.88282			−0.302122
$520$	1.26075	+	2.18368i	0.0552874	+	0.0957605i
$521$	−3.02740	+	5.24361i	−0.132633	+	0.229727i	−0.924691	−	0.380719i	$-0.875676\pi$
$521$	−3.02740	+	5.24361i	−0.132633	+	0.229727i	0.792058	+	0.610446i	$0.209010\pi$
$522$	−1.39916	+	2.42342i	−0.0612398	+	0.106070i
$523$	−18.6378	−	32.2816i	−0.814973	−	1.41157i	−0.909347	−	0.416038i	$-0.863418\pi$
$523$	−18.6378	−	32.2816i	−0.814973	−	1.41157i	0.0943746	−	0.995537i	$-0.469915\pi$
$524$	31.2966			1.36720
$525$	3.34382	−	10.8451i	0.145936	−	0.473321i
$526$	10.1330			0.441822
$527$	5.88809	+	10.1985i	0.256489	+	0.444252i
$528$	−0.0554465	+	0.0960362i	−0.00241300	+	0.00417944i
$529$	10.6759	−	18.4912i	0.464169	−	0.803963i
$530$	−0.498062	−	0.862669i	−0.0216344	−	0.0374719i
$531$	12.9799			0.563279
$532$	−3.31689	−	3.57388i	−0.143806	−	0.154947i
$533$	0.256903			0.0111277
$534$	−1.65923	−	2.87388i	−0.0718021	−	0.124365i
$535$	3.62846	−	6.28468i	0.156872	−	0.271711i
$536$	−3.44147	+	5.96080i	−0.148649	+	0.257467i
$537$	0.310439	+	0.537696i	0.0133964	+	0.0232033i
$538$	2.51726			0.108527
$539$	0.208125	+	0.141822i	0.00896458	+	0.00610871i
$540$	−1.55342			−0.0668487
$541$	2.26300	+	3.91963i	0.0972938	+	0.168518i	0.910564	−	0.413369i	$-0.135648\pi$
$541$	2.26300	+	3.91963i	0.0972938	+	0.168518i	−0.813270	+	0.581887i	$0.802315\pi$
$542$	1.55795	−	2.69846i	0.0669199	−	0.115909i
$543$	−4.65529	+	8.06320i	−0.199778	+	0.346025i
$544$	6.94263	+	12.0250i	0.297663	+	0.515567i
$545$	−0.484625			−0.0207590
$546$	1.40100	+	1.50955i	0.0599573	+	0.0646026i
$547$	11.7047			0.500456			0.250228	−	0.968187i	$-0.419494\pi$
$547$	11.7047			0.500456			0.250228	+	0.968187i	$0.419494\pi$
$548$	−2.06610	−	3.57859i	−0.0882595	−	0.152870i
$549$	−1.29380	+	2.24092i	−0.0552179	+	0.0956402i
$550$	0.0305837	−	0.0529725i	0.00130409	−	0.00225876i
$551$	3.53023	+	6.11453i	0.150393	+	0.260488i
$552$	−1.95541			−0.0832279
$553$	8.08599	−	26.2256i	0.343851	−	1.11523i
$554$	2.32876			0.0989396
$555$	0.911502	+	1.57877i	0.0386911	+	0.0670150i
$556$	15.5082	−	26.8610i	0.657694	−	1.13916i
$557$	−7.63463	+	13.2236i	−0.323490	+	0.560300i	−0.981206	−	0.192966i	$-0.938189\pi$
$557$	−7.63463	+	13.2236i	−0.323490	+	0.560300i	0.657716	+	0.753266i	$0.271523\pi$
$558$	−0.717279	−	1.24236i	−0.0303648	−	0.0525934i
$559$	−8.85545			−0.374546
$560$	6.70116	−	1.53037i	0.283176	−	0.0646697i
$561$	0.117058			0.00494218
$562$	3.31556	+	5.74271i	0.139858	+	0.242242i
$563$	15.2869	−	26.4777i	0.644267	−	1.11590i	−0.340203	−	0.940352i	$-0.610496\pi$
$563$	15.2869	−	26.4777i	0.644267	−	1.11590i	0.984470	−	0.175551i	$-0.0561708\pi$
$564$	7.35834	−	12.7450i	0.309842	−	0.536662i
$565$	−6.43922	−	11.1531i	−0.270900	−	0.469213i
$566$	8.28177			0.348109
$567$	−2.57934	+	0.589053i	−0.108322	+	0.0247379i
$568$	−4.03598			−0.169346
$569$	4.32265	+	7.48704i	0.181215	+	0.313873i	0.942294	−	0.334785i	$-0.108664\pi$
$569$	4.32265	+	7.48704i	0.181215	+	0.313873i	−0.761080	+	0.648658i	$0.775330\pi$
$570$	0.167040	−	0.289322i	0.00699654	−	0.0121184i
$571$	−0.587899	+	1.01827i	−0.0246028	+	0.0426133i	−0.878065	−	0.478542i	$-0.841165\pi$
$571$	−0.587899	+	1.01827i	−0.0246028	+	0.0426133i	0.853462	+	0.521155i	$0.174499\pi$
$572$	−0.0651132	−	0.112779i	−0.00272252	−	0.00471555i
$573$	−18.3384			−0.766097
$574$	−0.0404135	+	0.131075i	−0.00168683	+	0.00547095i
$575$	−5.50703			−0.229659
$576$	2.23643	+	3.87361i	0.0931845	+	0.161400i
$577$	6.17057	−	10.6877i	0.256884	−	0.444936i	−0.708522	−	0.705689i	$-0.750637\pi$
$577$	6.17057	−	10.6877i	0.256884	−	0.444936i	0.965406	+	0.260753i	$0.0839708\pi$
$578$	−1.27119	+	2.20176i	−0.0528744	+	0.0915811i
$579$	−7.60019	−	13.1639i	−0.315853	−	0.547074i
$580$	−10.9679			−0.455416
$581$	18.4934	+	19.9263i	0.767237	+	0.826680i
$582$	−1.01130			−0.0419199
$583$	0.0536390	+	0.0929055i	0.00222150	+	0.00384775i
$584$	−4.73148	+	8.19516i	−0.195790	+	0.339118i
$585$	0.827752	−	1.43371i	0.0342233	−	0.0592766i
$586$	−2.41432	−	4.18172i	−0.0997345	−	0.172745i
$587$	19.9966			0.825350			0.412675	−	0.910878i	$-0.364595\pi$
$587$	19.9966			0.825350			0.412675	+	0.910878i	$0.364595\pi$
$588$	11.6215	−	5.60014i	0.479262	−	0.230946i
$589$	−3.61953			−0.149140
$590$	−2.16816	−	3.75536i	−0.0892617	−	0.154606i
$591$	3.88602	−	6.73079i	0.159850	−	0.276868i
$592$	3.33296	−	5.77286i	0.136984	−	0.237263i
$593$	−5.58702	−	9.67700i	−0.229431	−	0.397387i	0.728208	−	0.685356i	$-0.240353\pi$
$593$	−5.58702	−	9.67700i	−0.229431	−	0.397387i	−0.957640	+	0.287969i	$0.907020\pi$
$594$	−0.0142598			−0.000585087
$595$	−4.93586	−	5.31828i	−0.202351	−	0.218028i
$596$	−23.4640			−0.961125
$597$	12.8631	+	22.2795i	0.526451	+	0.911840i
$598$	0.499682	−	0.865475i	0.0204335	−	0.0353919i
$599$	12.0269	−	20.8313i	0.491407	−	0.851143i	−0.508544	−	0.861036i	$-0.669816\pi$
$599$	12.0269	−	20.8313i	0.491407	−	0.851143i	0.999951	+	0.00989358i	$0.00314928\pi$
$600$	−3.26665	−	5.65801i	−0.133361	−	0.230987i
$601$	32.2158			1.31411			0.657054	−	0.753843i	$-0.271802\pi$
$601$	32.2158			1.31411			0.657054	+	0.753843i	$0.271802\pi$
$602$	1.39305	−	4.51814i	0.0567766	−	0.184146i
$603$	4.51905			0.184030
$604$	−10.8979	−	18.8758i	−0.443431	−	0.768045i
$605$	−4.63549	+	8.02891i	−0.188460	+	0.326421i
$606$	−1.41298	+	2.44735i	−0.0573984	+	0.0994169i
$607$	1.12862	+	1.95482i	0.0458092	+	0.0793438i	0.888021	−	0.459803i	$-0.152080\pi$
$607$	1.12862	+	1.95482i	0.0458092	+	0.0793438i	−0.842212	+	0.539147i	$0.818747\pi$
$608$	−4.26777			−0.173081
$609$	−18.2113	+	4.15898i	−0.737960	+	0.168530i
$610$	0.864463			0.0350011
$611$	7.84188	+	13.5825i	0.317249	+	0.549491i
$612$	2.99798	−	5.19265i	0.121186	−	0.209900i
$613$	−6.44356	+	11.1606i	−0.260253	+	0.450771i	−0.966309	−	0.257385i	$-0.917139\pi$
$613$	−6.44356	+	11.1606i	−0.260253	+	0.450771i	0.706056	+	0.708156i	$0.250473\pi$
$614$	−5.01310	−	8.68294i	−0.202312	−	0.350415i
$615$	0.110257			0.00444600
$616$	0.141346	−	0.0322797i	0.00569500	−	0.00130059i
$617$	25.0627			1.00899			0.504493	−	0.863416i	$-0.331679\pi$
$617$	25.0627			1.00899			0.504493	+	0.863416i	$0.331679\pi$
$618$	−0.576518	−	0.998559i	−0.0231910	−	0.0401679i
$619$	8.41827	−	14.5809i	0.338359	−	0.586055i	−0.645765	−	0.763536i	$-0.723462\pi$
$619$	8.41827	−	14.5809i	0.338359	−	0.586055i	0.984124	+	0.177481i	$0.0567949\pi$
$620$	2.81133	−	4.86936i	0.112906	−	0.195558i
$621$	0.641921	+	1.11184i	0.0257594	+	0.0446166i
$622$	−3.91872			−0.157126
$623$	6.52692	−	21.1690i	0.261495	−	0.848119i
$624$	−6.05345			−0.242332
$625$	−7.42361	−	12.8581i	−0.296944	−	0.514323i
$626$	−0.272432	+	0.471865i	−0.0108886	+	0.0188595i
$627$	−0.0179894	+	0.0311586i	−0.000718429	+	0.00124436i
$628$	6.79747	+	11.7736i	0.271248	+	0.469816i
$629$	−7.03649			−0.280563
$630$	0.601280	+	0.647865i	0.0239555	+	0.0258116i
$631$	−25.8497			−1.02906			−0.514530	−	0.857472i	$-0.672034\pi$
$631$	−25.8497			−1.02906			−0.514530	+	0.857472i	$0.672034\pi$
$632$	−7.89939	−	13.6821i	−0.314221	−	0.544247i
$633$	8.62351	−	14.9364i	0.342754	−	0.593667i
$634$	5.28918	−	9.16112i	0.210060	−	0.363835i
$635$	0.430880	+	0.746305i	0.0170989	+	0.0296162i
$636$	5.49501			0.217891
$637$	−1.02402	+	13.7100i	−0.0405732	+	0.543208i
$638$	−0.100681			−0.00398599
$639$	1.32493	+	2.29484i	0.0524133	+	0.0907825i
$640$	4.34452	−	7.52493i	0.171732	−	0.297449i
$641$	−24.6670	+	42.7244i	−0.974286	+	1.68751i	−0.292016	+	0.956413i	$0.594326\pi$
$641$	−24.6670	+	42.7244i	−0.974286	+	1.68751i	−0.682270	+	0.731100i	$0.739007\pi$
$642$	−1.70610	−	2.95505i	−0.0673344	−	0.116627i
$643$	−2.55951			−0.100937			−0.0504686	−	0.998726i	$-0.516071\pi$
$643$	−2.55951			−0.100937			−0.0504686	+	0.998726i	$0.516071\pi$
$644$	−4.25836	−	4.58829i	−0.167803	−	0.180804i
$645$	−3.80057			−0.149647
$646$	0.644747	+	1.11673i	0.0253672	+	0.0439373i
$647$	17.5916	−	30.4696i	0.691597	−	1.19788i	−0.279717	−	0.960082i	$-0.590241\pi$
$647$	17.5916	−	30.4696i	0.691597	−	1.19788i	0.971314	−	0.237799i	$-0.0764260\pi$
$648$	−0.761548	+	1.31904i	−0.0299164	+	0.0518168i
$649$	0.233501	+	0.404435i	0.00916571	+	0.0158755i
$650$	3.33902			0.130967
$651$	2.82155	−	9.15126i	0.110585	−	0.358666i
$652$	33.2635			1.30270
$653$	14.0120	+	24.2695i	0.548332	+	0.949739i	0.998389	+	0.0567392i	$0.0180703\pi$
$653$	14.0120	+	24.2695i	0.548332	+	0.949739i	−0.450057	+	0.893000i	$0.648596\pi$
$654$	−0.113935	+	0.197341i	−0.00445522	+	0.00771666i
$655$	−7.15725	+	12.3967i	−0.279657	+	0.484380i
$656$	−0.201581	−	0.349149i	−0.00787042	−	0.0136320i
$657$	6.21297			0.242391
$658$	−8.16356	+	1.86434i	−0.318249	+	0.0726795i
$659$	30.0543			1.17075			0.585374	−	0.810763i	$-0.300948\pi$
$659$	30.0543			1.17075			0.585374	+	0.810763i	$0.300948\pi$
$660$	−0.0279452	−	0.0484025i	−0.00108777	−	0.00188407i
$661$	−4.19955	+	7.27383i	−0.163343	+	0.282919i	−0.936066	−	0.351825i	$-0.885561\pi$
$661$	−4.19955	+	7.27383i	−0.163343	+	0.282919i	0.772722	+	0.634744i	$0.218895\pi$
$662$	−7.20811	+	12.4848i	−0.280151	+	0.485236i
$663$	3.19499	+	5.53388i	0.124083	+	0.214918i
$664$	15.6502			0.607344
$665$	2.17417	−	0.496522i	0.0843107	−	0.0192543i
$666$	0.857176			0.0332149
$667$	4.53225	+	7.85009i	0.175489	+	0.303957i
$668$	20.8576	−	36.1264i	0.807003	−	1.39777i
$669$	7.86287	−	13.6189i	0.303996	−	0.526537i
$670$	−0.754862	−	1.30746i	−0.0291629	−	0.0505115i
$671$	−0.0930988			−0.00359404
$672$	3.32689	−	10.7902i	0.128338	−	0.416242i
$673$	12.5476			0.483673			0.241837	−	0.970317i	$-0.422250\pi$
$673$	12.5476			0.483673			0.241837	+	0.970317i	$0.422250\pi$
$674$	5.94886	+	10.3037i	0.229141	+	0.396885i
$675$	−2.14475	+	3.71481i	−0.0825513	+	0.142983i
$676$	−8.42454	+	14.5917i	−0.324021	+	0.561220i
$677$	7.58276	+	13.1337i	0.291429	+	0.504770i	0.974148	−	0.225911i	$-0.0725360\pi$
$677$	7.58276	+	13.1337i	0.291429	+	0.504770i	−0.682719	+	0.730681i	$0.739203\pi$
$678$	−6.05544			−0.232558
$679$	−4.59241	−	4.94822i	−0.176241	−	0.189895i
$680$	−4.17700			−0.160180
$681$	−3.25181	−	5.63230i	−0.124610	−	0.215830i
$682$	0.0258069	−	0.0446988i	0.000988197	−	0.00171161i
$683$	−14.8908	+	25.7916i	−0.569781	+	0.986890i	0.426806	+	0.904343i	$0.359639\pi$
$683$	−14.8908	+	25.7916i	−0.569781	+	0.986890i	−0.996587	+	0.0825467i	$0.973695\pi$
$684$	0.921458	+	1.59601i	0.0352328	+	0.0610250i
$685$	1.88999			0.0722130
$686$	−6.83388	−	2.67918i	−0.260919	−	0.102292i
$687$	−7.87261			−0.300359
$688$	6.94850	+	12.0352i	0.264909	+	0.458836i
$689$	−2.92805	+	5.07154i	−0.111550	+	0.193210i
$690$	0.214453	−	0.371443i	0.00816408	−	0.0141406i
$691$	13.9759	+	24.2070i	0.531668	+	0.920876i	0.999317	+	0.0369619i	$0.0117680\pi$
$691$	13.9759	+	24.2070i	0.531668	+	0.920876i	−0.467648	+	0.883915i	$0.654899\pi$
$692$	−12.6845			−0.482191
$693$	−0.0647551	−	0.0697721i	−0.00245984	−	0.00265042i
$694$	−11.1802			−0.424395
$695$	7.09316	+	12.2857i	0.269059	+	0.466024i
$696$	−5.37687	+	9.31301i	−0.203810	+	0.353009i
$697$	−0.212787	+	0.368558i	−0.00805989	+	0.0139601i
$698$	−0.857216	−	1.48474i	−0.0324461	−	0.0561983i
$699$	−22.2790			−0.842667
$700$	6.16238	−	19.9867i	0.232916	−	0.755426i
$701$	−3.66534			−0.138438			−0.0692190	−	0.997601i	$-0.522051\pi$
$701$	−3.66534			−0.138438			−0.0692190	+	0.997601i	$0.522051\pi$
$702$	−0.389209	−	0.674129i	−0.0146897	−	0.0254434i
$703$	1.08137	−	1.87298i	0.0407846	−	0.0706409i
$704$	−0.0804642	+	0.139368i	−0.00303261	+	0.00525263i
$705$	3.36557	+	5.82933i	0.126755	+	0.219545i
$706$	8.02402			0.301988
$707$	−18.3912	+	4.20005i	−0.691671	+	0.157959i
$708$	23.9208			0.899000
$709$	8.48085	+	14.6893i	0.318505	+	0.551667i	0.980176	−	0.198127i	$-0.0634859\pi$
$709$	8.48085	+	14.6893i	0.318505	+	0.551667i	−0.661671	+	0.749794i	$0.730153\pi$
$710$	0.442631	−	0.766660i	0.0166117	−	0.0287722i
$711$	−5.18641	+	8.98312i	−0.194505	+	0.336893i
$712$	−6.37630	−	11.0441i	−0.238962	−	0.413894i
$713$	−4.64690			−0.174028
$714$	−3.32605	+	0.759580i	−0.124474	+	0.0284266i
$715$	0.0595632			0.00222754
$716$	0.572113	+	0.990928i	0.0213809	+	0.0370327i
$717$	13.2610	−	22.9688i	0.495242	−	0.857784i
$718$	2.60786	−	4.51695i	0.0973246	−	0.168571i
$719$	18.9783	+	32.8715i	0.707773	+	1.22590i	0.965681	+	0.259729i	$0.0836333\pi$
$719$	18.9783	+	32.8715i	0.707773	+	1.22590i	−0.257909	+	0.966169i	$0.583033\pi$
$720$	−2.59801			−0.0968221
$721$	2.26785	−	7.35540i	0.0844590	−	0.273929i
$722$	−0.396339			−0.0147502
$723$	5.54028	+	9.59605i	0.206045	+	0.356881i
$724$	−8.57930	+	14.8598i	−0.318847	+	0.552260i
$725$	−15.1429	+	26.2282i	−0.562392	+	0.974092i
$726$	2.17961	+	3.77519i	0.0808927	+	0.140110i
$727$	32.1265			1.19150			0.595752	−	0.803168i	$-0.296854\pi$
$727$	32.1265			1.19150			0.595752	+	0.803168i	$0.296854\pi$
$728$	5.38393	+	5.80106i	0.199542	+	0.215002i
$729$	1.00000			0.0370370
$730$	−1.03782	−	1.79755i	−0.0384113	−	0.0665303i
$731$	7.33478	−	12.7042i	0.271287	−	0.469882i
$732$	−2.38436	+	4.12983i	−0.0881284	+	0.152643i
$733$	−7.31092	−	12.6629i	−0.270035	−	0.467715i	0.698835	−	0.715282i	$-0.253702\pi$
$733$	−7.31092	−	12.6629i	−0.270035	−	0.467715i	−0.968871	+	0.247568i	$0.920369\pi$
$734$	−9.67086			−0.356958
$735$	−0.439488	+	5.88402i	−0.0162107	+	0.217035i
$736$	−5.47914			−0.201964
$737$	0.0812952	+	0.140807i	0.00299455	+	0.00518671i
$738$	0.0259214	−	0.0448973i	0.000954182	−	0.00165269i
$739$	−14.4596	+	25.0447i	−0.531904	+	0.921286i	0.467402	+	0.884045i	$0.345190\pi$
$739$	−14.4596	+	25.0447i	−0.531904	+	0.921286i	−0.999306	+	0.0372406i	$0.988143\pi$
$740$	1.67982	+	2.90954i	0.0617515	+	0.106957i
$741$	−1.96402			−0.0721501
$742$	−2.12694	−	2.29173i	−0.0780824	−	0.0841320i
$743$	20.8522			0.764992			0.382496	−	0.923957i	$-0.375065\pi$
$743$	20.8522			0.764992			0.382496	+	0.923957i	$0.375065\pi$
$744$	−2.75644	−	4.77430i	−0.101056	−	0.175034i
$745$	5.36601	−	9.29420i	0.196595	−	0.340513i
$746$	0.489231	−	0.847372i	0.0179120	−	0.0310245i
$747$	−5.13762	−	8.89861i	−0.187976	−	0.325583i
$748$	0.215728			0.00788779
$749$	6.71128	−	21.7670i	0.245225	−	0.795347i
$750$	3.10343			0.113321
$751$	16.4962	+	28.5722i	0.601954	+	1.04261i	0.992525	+	0.122042i	$0.0389442\pi$
$751$	16.4962	+	28.5722i	0.601954	+	1.04261i	−0.390571	+	0.920573i	$0.627722\pi$
$752$	12.3064	−	21.3153i	0.448768	−	0.777289i
$753$	1.66081	−	2.87661i	0.0605234	−	0.104830i
$754$	−2.74799	−	4.75966i	−0.100076	−	0.173336i
$755$	9.96904			0.362810
$756$	−4.75351	+	1.08558i	−0.172884	+	0.0394820i
$757$	14.8974			0.541455			0.270728	−	0.962656i	$-0.412736\pi$
$757$	14.8974			0.541455			0.270728	+	0.962656i	$0.412736\pi$
$758$	−3.72162	−	6.44604i	−0.135175	−	0.234131i
$759$	−0.0230956	+	0.0400027i	−0.000838317	+	0.00145201i
$760$	0.641921	−	1.11184i	0.0232849	−	0.0403306i
$761$	5.78718	+	10.0237i	0.209785	+	0.363358i	0.951647	−	0.307195i	$-0.0993902\pi$
$761$	5.78718	+	10.0237i	0.209785	+	0.363358i	−0.741862	+	0.670553i	$0.766057\pi$
$762$	0.405199			0.0146788
$763$	−1.48296	+	0.338669i	−0.0536869	+	0.0122606i
$764$	−33.7961			−1.22270
$765$	1.37122	+	2.37502i	0.0495765	+	0.0858691i
$766$	6.26788	−	10.8563i	0.226468	−	0.392253i
$767$	−12.7464	+	22.0774i	−0.460245	+	0.797168i
$768$	2.43007	+	4.20900i	0.0876875	+	0.151879i
$769$	−52.4315			−1.89073			−0.945365	−	0.326015i	$-0.894294\pi$
$769$	−52.4315			−1.89073			−0.945365	+	0.326015i	$0.894294\pi$
$770$	−0.00936990	+	0.0303898i	−0.000337668	+	0.00109517i
$771$	−30.1189			−1.08471
$772$	−14.0065	−	24.2600i	−0.504105	−	0.873136i
$773$	−21.6869	+	37.5628i	−0.780023	+	1.35104i	0.151904	+	0.988395i	$0.451459\pi$
$773$	−21.6869	+	37.5628i	−0.780023	+	1.35104i	−0.931927	+	0.362645i	$0.881874\pi$
$774$	−0.893513	+	1.54761i	−0.0321166	+	0.0556277i
$775$	−7.76296	−	13.4458i	−0.278854	−	0.482989i
$776$	−3.88635			−0.139512
$777$	3.89251	+	4.19409i	0.139643	+	0.150462i
$778$	1.71911			0.0616329
$779$	−0.0654023	−	0.113280i	−0.00234328	−	0.00405868i
$780$	1.52548	−	2.64220i	0.0546209	−	0.0946061i
$781$	−0.0476694	+	0.0825658i	−0.00170574	+	0.00295444i
$782$	0.827752	+	1.43371i	0.0296004	+	0.0512693i
$783$	7.06045			0.252320
$784$	19.4363	−	9.36592i	0.694152	−	0.334497i
$785$	−6.21807			−0.221932
$786$	3.36534	+	5.82893i	0.120038	+	0.207911i
$787$	−10.6928	+	18.5204i	−0.381156	+	0.660182i	−0.991228	−	0.132165i	$-0.957807\pi$
$787$	−10.6928	+	18.5204i	−0.381156	+	0.660182i	0.610072	+	0.792346i	$0.291141\pi$
$788$	7.16162	−	12.4043i	0.255122	−	0.441884i
$789$	−12.7833	−	22.1414i	−0.455098	−	0.788253i
$790$	3.46535			0.123292
$791$	−27.4982	−	29.6287i	−0.977725	−	1.05348i
$792$	−0.0547993			−0.00194721
$793$	−2.54104	−	4.40122i	−0.0902351	−	0.156292i
$794$	0.270611	−	0.468712i	0.00960363	−	0.0166340i
$795$	−1.25666	+	2.17660i	−0.0445691	+	0.0771959i
$796$	23.7056	+	41.0593i	0.840222	+	1.45531i
$797$	−44.1477			−1.56379			−0.781897	−	0.623408i	$-0.785748\pi$
$797$	−44.1477			−1.56379			−0.781897	+	0.623408i	$0.785748\pi$
$798$	0.308961	−	1.00206i	0.0109371	−	0.0354727i
$799$	−25.9811			−0.919144
$800$	−9.15329	−	15.8540i	−0.323618	−	0.560522i
$801$	−4.18641	+	7.25107i	−0.147919	+	0.256204i
$802$	4.49061	−	7.77797i	0.158569	−	0.274650i
$803$	0.111768	+	0.193588i	0.00394421	+	0.00683156i
$804$	8.32822			0.293714
$805$	2.79129	−	0.637456i	0.0983800	−	0.0224674i
$806$	2.81750			0.0992422
$807$	−3.17565	−	5.50038i	−0.111788	−	0.193623i
$808$	−5.42996	+	9.40497i	−0.191025	+	0.330866i
$809$	11.9496	−	20.6974i	0.420127	−	0.727681i	−0.575825	−	0.817573i	$-0.695319\pi$
$809$	11.9496	−	20.6974i	0.420127	−	0.727681i	0.995951	+	0.0898924i	$0.0286523\pi$
$810$	−0.167040	−	0.289322i	−0.00586919	−	0.0101657i
$811$	−45.1710			−1.58617			−0.793083	−	0.609113i	$-0.791526\pi$
$811$	−45.1710			−1.58617			−0.793083	+	0.609113i	$0.791526\pi$
$812$	−33.5620	+	7.66465i	−1.17779	+	0.268976i
$813$	−7.86174			−0.275723
$814$	0.0154201	+	0.0267084i	0.000540475	+	0.000936130i
$815$	−7.60706	+	13.1758i	−0.266464	+	0.461529i
$816$	5.01394	−	8.68440i	0.175523	−	0.304015i
$817$	2.25442	+	3.90477i	0.0788721	+	0.136610i
$818$	10.6152			0.371153
$819$	1.53103	−	4.96564i	0.0534984	−	0.173514i
$820$	0.203195			0.00709587
$821$	10.8031	+	18.7115i	0.377030	+	0.653035i	0.990629	−	0.136583i	$-0.0436120\pi$
$821$	10.8031	+	18.7115i	0.377030	+	0.653035i	−0.613599	+	0.789618i	$0.710279\pi$
$822$	0.444337	−	0.769615i	0.0154980	−	0.0268434i
$823$	3.65882	−	6.33726i	0.127538	−	0.220903i	−0.795184	−	0.606368i	$-0.792626\pi$
$823$	3.65882	−	6.33726i	0.127538	−	0.220903i	0.922722	+	0.385465i	$0.125959\pi$
$824$	−2.21551	−	3.83738i	−0.0771810	−	0.133681i
$825$	−0.154331			−0.00537312
$826$	−9.25898	−	9.97634i	−0.322161	−	0.347121i
$827$	46.0507			1.60134			0.800669	−	0.599106i	$-0.204477\pi$
$827$	46.0507			1.60134			0.800669	+	0.599106i	$0.204477\pi$
$828$	1.18301	+	2.04903i	0.0411123	+	0.0712086i
$829$	−16.0223	+	27.7515i	−0.556478	+	0.963848i	0.441309	+	0.897355i	$0.354514\pi$
$829$	−16.0223	+	27.7515i	−0.556478	+	0.963848i	−0.997787	+	0.0664930i	$0.978819\pi$
$830$	−1.71637	+	2.97285i	−0.0595762	+	0.103189i
$831$	−2.93784	−	5.08849i	−0.101913	−	0.176518i
$832$	−8.78479			−0.304558
$833$	−18.8204	−	12.8247i	−0.652089	−	0.444351i
$834$	6.67040			0.230977
$835$	9.53986	+	16.5235i	0.330141	+	0.571820i
$836$	−0.0331530	+	0.0574227i	−0.00114662	+	0.00198601i
$837$	−1.80976	+	3.13460i	−0.0625546	+	0.108348i
$838$	5.93926	+	10.2871i	0.205168	+	0.355362i
$839$	12.5994			0.434980			0.217490	−	0.976063i	$-0.430213\pi$
$839$	12.5994			0.434980			0.217490	+	0.976063i	$0.430213\pi$
$840$	2.31067	+	2.48969i	0.0797256	+	0.0859025i
$841$	20.8500			0.718964
$842$	−5.73929	−	9.94075i	−0.197789	−	0.342581i
$843$	8.36547	−	14.4894i	0.288122	−	0.499042i
$844$	15.8924	−	27.5265i	0.547039	−	0.947500i
$845$	−3.85323	−	6.67399i	−0.132555	−	0.229592i
$846$	3.16498			0.108814
$847$	−8.57390	+	27.8081i	−0.294603	+	0.955497i
$848$	9.19008			0.315589
$849$	−10.4479	−	18.0962i	−0.358569	−	0.621060i
$850$	−2.76564	+	4.79022i	−0.0948605	+	0.164303i
$851$	1.38830	−	2.40461i	0.0475905	−	0.0824291i
$852$	2.44173	+	4.22920i	0.0836522	+	0.144890i
$853$	−37.1154			−1.27081			−0.635403	−	0.772181i	$-0.719166\pi$
$853$	−37.1154			−1.27081			−0.635403	+	0.772181i	$0.719166\pi$
$854$	2.64528	−	0.604111i	0.0905196	−	0.0206723i
$855$	−0.842916			−0.0288271
$856$	−6.55640	−	11.3560i	−0.224093	−	0.388141i
$857$	−25.2112	+	43.6670i	−0.861197	+	1.49164i	0.00957724	+	0.999954i	$0.496951\pi$
$857$	−25.2112	+	43.6670i	−0.861197	+	1.49164i	−0.870774	+	0.491683i	$0.836382\pi$
$858$	0.0140033	−	0.0242544i	0.000478065	−	0.000828032i
$859$	−4.92248	−	8.52598i	−0.167953	−	0.290903i	0.769747	−	0.638349i	$-0.220382\pi$
$859$	−4.92248	−	8.52598i	−0.167953	−	0.290903i	−0.937700	+	0.347446i	$0.887049\pi$
$860$	−7.00413			−0.238839
$861$	0.337390	−	0.0770508i	0.0114982	−	0.00262589i
$862$	−8.27386			−0.281809
$863$	−16.3611	−	28.3382i	−0.556937	−	0.964643i	−0.997750	−	0.0670442i	$-0.978643\pi$
$863$	−16.3611	−	28.3382i	−0.556937	−	0.964643i	0.440813	−	0.897599i	$-0.354690\pi$
$864$	−2.13389	+	3.69600i	−0.0725963	+	0.125740i
$865$	2.90082	−	5.02437i	0.0986308	−	0.170834i
$866$	−1.38969	−	2.40702i	−0.0472237	−	0.0817938i
$867$	6.41465			0.217853
$868$	5.19989	−	16.8650i	0.176496	−	0.572436i
$869$	−0.373202			−0.0126600
$870$	−1.17938	−	2.04274i	−0.0399846	−	0.0692554i
$871$	−4.43775	+	7.68641i	−0.150368	+	0.260444i
$872$	−0.437843	+	0.758367i	−0.0148272	+	0.0256815i
$873$	1.27581	+	2.20976i	0.0431795	+	0.0747892i
$874$	−0.508836			−0.0172116
$875$	14.0930	+	15.1848i	0.476429	+	0.513341i
$876$	11.4500			0.386859
$877$	−3.43836	−	5.95541i	−0.116105	−	0.201100i	0.802116	−	0.597168i	$-0.203708\pi$
$877$	−3.43836	−	5.95541i	−0.116105	−	0.201100i	−0.918221	+	0.396069i	$0.870374\pi$
$878$	−0.346413	+	0.600005i	−0.0116909	+	0.0202492i
$879$	−6.09155	+	10.5509i	−0.205463	+	0.355872i
$880$	−0.0467368	−	0.0809504i	−0.00157550	−	0.00272884i
$881$	−40.9688			−1.38027			−0.690137	−	0.723679i	$-0.742450\pi$
$881$	−40.9688			−1.38027			−0.690137	+	0.723679i	$0.742450\pi$
$882$	2.29268	+	1.56229i	0.0771985	+	0.0526051i
$883$	3.64432			0.122641			0.0613206	−	0.998118i	$-0.480469\pi$
$883$	3.64432			0.122641			0.0613206	+	0.998118i	$0.480469\pi$
$884$	5.88809	+	10.1985i	0.198038	+	0.343012i
$885$	−5.47047	+	9.47514i	−0.183888	+	0.318503i
$886$	−3.74164	+	6.48070i	−0.125703	+	0.217724i
$887$	−3.14427	−	5.44604i	−0.105574	−	0.182860i	0.808398	−	0.588636i	$-0.200335\pi$
$887$	−3.14427	−	5.44604i	−0.105574	−	0.182860i	−0.913973	+	0.405776i	$0.867001\pi$
$888$	3.29405			0.110541
$889$	1.84004	+	1.98260i	0.0617130	+	0.0664944i
$890$	2.79719			0.0937620
$891$	0.0179894	+	0.0311586i	0.000602669	+	0.00104385i
$892$	14.4906	−	25.0985i	0.485181	−	0.840359i
$893$	3.99277	−	6.91568i	0.133613	−	0.231424i
$894$	−2.52310	−	4.37013i	−0.0843849	−	0.146159i
$895$	−0.523348			−0.0174936
$896$	8.03571	−	26.0626i	0.268454	−	0.870689i
$897$	−2.52149			−0.0841901
$898$	3.95491	+	6.85010i	0.131977	+	0.228591i
$899$	−12.7777	+	22.1317i	−0.426162	+	0.738133i
$900$	−3.95259	+	6.84608i	−0.131753	+	0.228203i
$901$	−4.85049	−	8.40129i	−0.161593	−	0.279888i
$902$	0.00186525			6.21060e−5
$903$	−11.6298	+	2.65594i	−0.387017	+	0.0883843i
$904$	−23.2705			−0.773966
$905$	−3.92402	−	6.79659i	−0.130439	−	0.225926i
$906$	2.34372	−	4.05944i	0.0778648	−	0.134866i
$907$	25.8334	−	44.7447i	0.857782	−	1.48572i	−0.0162569	−	0.999868i	$-0.505175\pi$
$907$	25.8334	−	44.7447i	0.857782	−	1.48572i	0.874039	−	0.485855i	$-0.161492\pi$
$908$	−5.99281	−	10.3798i	−0.198878	−	0.344467i
$909$	7.13017			0.236493
$910$	−1.69241	+	0.386501i	−0.0561029	+	0.0128124i
$911$	−48.0342			−1.59144			−0.795722	−	0.605662i	$-0.792909\pi$
$911$	−48.0342			−1.59144			−0.795722	+	0.605662i	$0.792909\pi$
$912$	1.54109	+	2.66924i	0.0510304	+	0.0883873i
$913$	0.184846	−	0.320162i	0.00611750	−	0.0105958i
$914$	−4.27203	+	7.39937i	−0.141306	+	0.244749i
$915$	−1.09056	−	1.88891i	−0.0360529	−	0.0624454i
$916$	−14.5086			−0.479376
$917$	−13.2382	+	42.9360i	−0.437164	+	1.41787i
$918$	1.28949			0.0425596
$919$	−11.8773	−	20.5720i	−0.391794	−	0.678608i	0.600892	−	0.799330i	$-0.294812\pi$
$919$	−11.8773	−	20.5720i	−0.391794	−	0.678608i	−0.992686	+	0.120722i	$0.961479\pi$
$920$	0.824124	−	1.42743i	0.0271706	−	0.0470608i
$921$	−12.6485	+	21.9079i	−0.416783	+	0.721890i
$922$	−5.54410	−	9.60267i	−0.182585	−	0.316247i
$923$	−5.20437			−0.171304
$924$	−0.119338	−	0.128584i	−0.00392594	−	0.00423011i
$925$	9.27704			0.305027
$926$	7.69870	+	13.3345i	0.252995	+	0.438200i
$927$	−1.45461	+	2.51946i	−0.0477757	+	0.0827499i
$928$	−15.0662	+	26.0954i	−0.494572	+	0.856625i
$929$	2.86320	+	4.95920i	0.0939384	+	0.162706i	0.909165	−	0.416436i	$-0.136721\pi$
$929$	2.86320	+	4.95920i	0.0939384	+	0.162706i	−0.815227	+	0.579142i	$0.803388\pi$
$930$	1.20921			0.0396516
$931$	6.30603	−	3.03874i	0.206672	−	0.0995907i
$932$	−41.0582			−1.34491
$933$	4.94365	+	8.56265i	0.161848	+	0.280329i
$934$	−1.71205	+	2.96535i	−0.0560199	+	0.0970293i
$935$	−0.0493349	+	0.0854506i	−0.00161343	+	0.00279453i
$936$	−1.49570	−	2.59062i	−0.0488884	−	0.0846771i
$937$	−24.1920			−0.790319			−0.395159	−	0.918613i	$-0.629311\pi$
$937$	−24.1920			−0.790319			−0.395159	+	0.918613i	$0.629311\pi$
$938$	−3.22359	−	3.47334i	−0.105254	−	0.113409i
$939$	1.37474			0.0448630
$940$	6.20246	+	10.7430i	0.202302	+	0.350397i
$941$	−3.07866	+	5.33239i	−0.100361	+	0.173831i	−0.911834	−	0.410560i	$-0.865333\pi$
$941$	−3.07866	+	5.33239i	−0.100361	+	0.173831i	0.811472	+	0.584391i	$0.198667\pi$
$942$	−1.46187	+	2.53203i	−0.0476302	+	0.0824979i
$943$	−0.0839662	−	0.145434i	−0.00273431	−	0.00473597i
$944$	40.0062			1.30209
$945$	0.657084	−	2.13115i	0.0213750	−	0.0693262i
$946$	−0.0642952			−0.00209042
$947$	12.7265	+	22.0430i	0.413557	+	0.716301i	0.995276	−	0.0970888i	$-0.0309531\pi$
$947$	12.7265	+	22.0430i	0.413557	+	0.716301i	−0.581719	+	0.813390i	$0.697620\pi$
$948$	−9.55811	+	16.5551i	−0.310433	+	0.537686i
$949$	−6.10121	+	10.5676i	−0.198054	+	0.343039i
$950$	−0.850046	−	1.47232i	−0.0275791	−	0.0477684i
$951$	−26.6902			−0.865489
$952$	−12.7817	+	2.91900i	−0.414258	+	0.0946054i
$953$	11.3961			0.369157			0.184579	−	0.982818i	$-0.440908\pi$
$953$	11.3961			0.369157			0.184579	+	0.982818i	$0.440908\pi$
$954$	0.590880	+	1.02343i	0.0191304	+	0.0331349i
$955$	7.72885	−	13.3868i	0.250100	−	0.433186i
$956$	24.4390	−	42.3295i	0.790412	−	1.36903i
$957$	0.127014	+	0.219994i	0.00410577	+	0.00711140i
$958$	−5.88177			−0.190031
$959$	5.78343	−	1.32078i	0.186757	−	0.0426502i
$960$	−3.77024			−0.121684
$961$	8.94952	+	15.5010i	0.288694	+	0.500033i
$962$	−0.841755	+	1.45796i	−0.0271393	+	0.0470066i
$963$	−4.30466	+	7.45588i	−0.138716	+	0.240263i
$964$	10.2103	+	17.6847i	0.328851	+	0.569586i
$965$	12.8126			0.412453
$966$	0.396656	−	1.28649i	0.0127622	−	0.0413922i
$967$	45.9401			1.47733			0.738667	−	0.674071i	$-0.235456\pi$
$967$	45.9401			1.47733			0.738667	+	0.674071i	$0.235456\pi$
$968$	8.37604	+	14.5077i	0.269216	+	0.466296i
$969$	1.62676	−	2.81763i	0.0522590	−	0.0905152i
$970$	0.426222	−	0.738238i	0.0136852	−	0.0237034i
$971$	0.347191	+	0.601352i	0.0111419	+	0.0192983i	0.871543	−	0.490320i	$-0.163120\pi$
$971$	0.347191	+	0.601352i	0.0111419	+	0.0192983i	−0.860401	+	0.509618i	$0.829787\pi$
$972$	1.84292			0.0591116
$973$	30.2909	+	32.6377i	0.971080	+	1.04632i
$974$	−7.09615			−0.227375
$975$	−4.21233	−	7.29597i	−0.134902	−	0.233658i
$976$	−3.98770	+	6.90690i	−0.127643	+	0.221085i
$977$	18.3718	−	31.8208i	0.587765	−	1.01804i	−0.406760	−	0.913535i	$-0.633341\pi$
$977$	18.3718	−	31.8208i	0.587765	−	1.01804i	0.994525	−	0.104503i	$-0.0333252\pi$
$978$	3.57684	+	6.19526i	0.114375	+	0.198103i
$979$	−0.301244			−0.00962781
$980$	−0.809939	+	10.8438i	−0.0258725	+	0.346391i
$981$	0.574938			0.0183564
$982$	3.80221	+	6.58563i	0.121334	+	0.210156i
$983$	6.67886	−	11.5681i	0.213022	−	0.368966i	−0.739637	−	0.673006i	$-0.765003\pi$
$983$	6.67886	−	11.5681i	0.213022	−	0.368966i	0.952659	+	0.304041i	$0.0983359\pi$
$984$	0.0996139	−	0.172536i	0.00317558	−	0.00550026i
$985$	3.27559	+	5.67349i	0.104369	+	0.180772i
$986$	9.10440			0.289943
$987$	14.3724	+	15.4860i	0.457479	+	0.492924i
$988$	−3.61953			−0.115152
$989$	2.89431	+	5.01310i	0.0920339	+	0.159407i
$990$	0.00600991	−	0.0104095i	0.000191008	−	0.000330835i
$991$	−20.1635	+	34.9241i	−0.640514	+	1.10940i	0.344805	+	0.938674i	$0.387945\pi$
$991$	−20.1635	+	34.9241i	−0.640514	+	1.10940i	−0.985318	+	0.170728i	$0.945388\pi$
$992$	−7.72366	−	13.3778i	−0.245226	−	0.424745i
$993$	36.3735			1.15428
$994$	0.818700	−	2.65532i	0.0259676	−	0.0842217i
$995$	−21.6850			−0.687460
$996$	−9.46819	−	16.3994i	−0.300011	−	0.519635i
$997$	3.94737	−	6.83704i	0.125014	−	0.216531i	−0.796724	−	0.604343i	$-0.793436\pi$
$997$	3.94737	−	6.83704i	0.125014	−	0.216531i	0.921739	+	0.387812i	$0.126769\pi$
$998$	4.87185	−	8.43830i	0.154216	−	0.267110i
$999$	−1.08137	−	1.87298i	−0.0342130	−	0.0592586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.j.d.172.3	yes	8
3.2	odd	2		1197.2.j.k.172.2		8
7.2	even	3	inner	399.2.j.d.58.3	✓	8
7.3	odd	6		2793.2.a.bd.1.2		4
7.4	even	3		2793.2.a.bc.1.2		4
21.2	odd	6		1197.2.j.k.856.2		8
21.11	odd	6		8379.2.a.br.1.3		4
21.17	even	6		8379.2.a.bt.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.d.58.3	✓	8	7.2	even	3	inner
399.2.j.d.172.3	yes	8	1.1	even	1	trivial
1197.2.j.k.172.2		8	3.2	odd	2
1197.2.j.k.856.2		8	21.2	odd	6
2793.2.a.bc.1.2		4	7.4	even	3
2793.2.a.bd.1.2		4	7.3	odd	6
8379.2.a.br.1.3		4	21.11	odd	6
8379.2.a.bt.1.3		4	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.198169 + 0.343239i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.921458 - 1.59601i) q^{4} +(0.421458 + 0.729986i) q^{5} +0.396339 q^{6} +(1.79981 + 1.93925i) q^{7} +1.52310 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.167040 + 0.289322i) q^{10} +(0.0179894 - 0.0311586i) q^{11} +(-0.921458 - 1.59601i) q^{12} +1.96402 q^{13} +(-0.308961 + 1.00206i) q^{14} +0.842916 q^{15} +(-1.54109 - 2.66924i) q^{16} +(-1.62676 + 2.81763i) q^{17} +(0.198169 - 0.343239i) q^{18} +(-0.500000 - 0.866025i) q^{19} +1.55342 q^{20} +(2.57934 - 0.589053i) q^{21} +0.0142598 q^{22} +(-0.641921 - 1.11184i) q^{23} +(0.761548 - 1.31904i) q^{24} +(2.14475 - 3.71481i) q^{25} +(0.389209 + 0.674129i) q^{26} -1.00000 q^{27} +(4.75351 - 1.08558i) q^{28} -7.06045 q^{29} +(0.167040 + 0.289322i) q^{30} +(1.80976 - 3.13460i) q^{31} +(2.13389 - 3.69600i) q^{32} +(-0.0179894 - 0.0311586i) q^{33} -1.28949 q^{34} +(-0.657084 + 2.13115i) q^{35} -1.84292 q^{36} +(1.08137 + 1.87298i) q^{37} +(0.198169 - 0.343239i) q^{38} +(0.982011 - 1.70089i) q^{39} +(0.641921 + 1.11184i) q^{40} +0.130805 q^{41} +(0.713333 + 0.768600i) q^{42} -4.50884 q^{43} +(-0.0331530 - 0.0574227i) q^{44} +(0.421458 - 0.729986i) q^{45} +(0.254418 - 0.440665i) q^{46} +(3.99277 + 6.91568i) q^{47} -3.08217 q^{48} +(-0.521390 + 6.98056i) q^{49} +1.70009 q^{50} +(1.62676 + 2.81763i) q^{51} +(1.80976 - 3.13460i) q^{52} +(-1.49085 + 2.58222i) q^{53} +(-0.198169 - 0.343239i) q^{54} +0.0303272 q^{55} +(2.74128 + 2.95366i) q^{56} -1.00000 q^{57} +(-1.39916 - 2.42342i) q^{58} +(-6.48994 + 11.2409i) q^{59} +(0.776711 - 1.34530i) q^{60} +(-1.29380 - 2.24092i) q^{61} +1.43456 q^{62} +(0.779537 - 2.52830i) q^{63} -4.47286 q^{64} +(0.827752 + 1.43371i) q^{65} +(0.00712991 - 0.0123494i) q^{66} +(-2.25952 + 3.91361i) q^{67} +(2.99798 + 5.19265i) q^{68} -1.28384 q^{69} +(-0.861707 + 0.196791i) q^{70} -2.64985 q^{71} +(-0.761548 - 1.31904i) q^{72} +(-3.10649 + 5.38059i) q^{73} +(-0.428588 + 0.742336i) q^{74} +(-2.14475 - 3.71481i) q^{75} -1.84292 q^{76} +(0.0928019 - 0.0211935i) q^{77} +0.778417 q^{78} +(-5.18641 - 8.98312i) q^{79} +(1.29900 - 2.24994i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0259214 + 0.0448973i) q^{82} +10.2752 q^{83} +(1.43662 - 4.65945i) q^{84} -2.74244 q^{85} +(-0.893513 - 1.54761i) q^{86} +(-3.53023 + 6.11453i) q^{87} +(0.0273996 - 0.0474576i) q^{88} +(-4.18641 - 7.25107i) q^{89} +0.334080 q^{90} +(3.53486 + 3.80873i) q^{91} -2.36601 q^{92} +(-1.80976 - 3.13460i) q^{93} +(-1.58249 + 2.74095i) q^{94} +(0.421458 - 0.729986i) q^{95} +(-2.13389 - 3.69600i) q^{96} -2.55162 q^{97} +(-2.49932 + 1.20437i) q^{98} -0.0359789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{5} + 2 q^{7} - 6 q^{8} - 4 q^{9} + 3 q^{10} + 2 q^{11} + 12 q^{13} + 2 q^{14} - 8 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{19} + 24 q^{20} + q^{21} - 12 q^{22} - 5 q^{23} - 3 q^{24} + 4 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 - 6 * q^8 - 4 * q^9 + 3 * q^10 + 2 * q^11 + 12 * q^13 + 2 * q^14 - 8 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^19 + 24 * q^20 + q^21 - 12 * q^22 - 5 * q^23 - 3 * q^24 + 4 * q^25 + 6 * q^26 - 8 * q^27 + 8 * q^28 - 8 * q^29 - 3 * q^30 - 17 * q^31 - 4 * q^32 - 2 * q^33 + 16 * q^34 - 20 * q^35 + 3 * q^37 + 6 * q^39 + 5 * q^40 + 14 * q^41 + 19 * q^42 - 30 * q^43 - 17 * q^44 - 4 * q^45 - q^46 - 16 * q^47 + 8 * q^48 + 14 * q^49 - 28 * q^50 - 2 * q^51 - 17 * q^52 - 4 * q^53 + 30 * q^55 + 18 * q^56 - 8 * q^57 + 5 * q^58 - 17 * q^59 + 12 * q^60 + 9 * q^61 - 14 * q^62 - q^63 - 26 * q^64 - 23 * q^65 - 6 * q^66 + 5 * q^67 + 10 * q^68 - 10 * q^69 + 33 * q^70 + 12 * q^71 + 3 * q^72 - 15 * q^73 + 10 * q^74 - 4 * q^75 - 4 * q^77 + 12 * q^78 - 5 * q^79 + 25 * q^80 - 4 * q^81 - 31 * q^82 + 68 * q^83 + 19 * q^84 - 24 * q^85 - 17 * q^86 - 4 * q^87 - 11 * q^88 + 3 * q^89 - 6 * q^90 + 45 * q^91 + 14 * q^92 + 17 * q^93 + 6 * q^94 - 4 * q^95 + 4 * q^96 + 22 * q^97 + 27 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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