LMFDB - Embedded newform 483.2.i.g.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} + \cdots + 6400 $ x^16 - x^15 + 16x^14 - 7x^13 + 161x^12 - 50x^11 + 929x^10 - 47x^9 + 3741x^8 - 158x^7 + 8993x^6 + 265x^5 + 15176x^4 + 383x^3 + 12649x^2 + 2960x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.1
Root			$1.37292 + 2.37797i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.g.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37292 + 2.37797i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.76984 - 4.79751i) q^{4} +(0.957403 - 1.65827i) q^{5} +2.74585 q^{6} +(1.61005 + 2.09946i) q^{7} +9.71944 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.62888 + 4.55336i) q^{10} +(-2.66166 - 4.61013i) q^{11} +(-2.76984 + 4.79751i) q^{12} -4.78352 q^{13} +(-7.20294 + 0.946247i) q^{14} -1.91481 q^{15} +(-7.80437 + 13.5176i) q^{16} +(-1.30891 - 2.26709i) q^{17} +(-1.37292 - 2.37797i) q^{18} +(-2.23012 + 3.86268i) q^{19} -10.6074 q^{20} +(1.01317 - 2.44407i) q^{21} +14.6170 q^{22} +(0.500000 - 0.866025i) q^{23} +(-4.85972 - 8.41728i) q^{24} +(0.666760 + 1.15486i) q^{25} +(6.56741 - 11.3751i) q^{26} +1.00000 q^{27} +(5.61262 - 13.5394i) q^{28} -8.86099 q^{29} +(2.62888 - 4.55336i) q^{30} +(-2.95449 - 5.11732i) q^{31} +(-11.7102 - 20.2826i) q^{32} +(-2.66166 + 4.61013i) q^{33} +7.18812 q^{34} +(5.02294 - 0.659861i) q^{35} +5.53968 q^{36} +(1.45965 - 2.52818i) q^{37} +(-6.12357 - 10.6063i) q^{38} +(2.39176 + 4.14265i) q^{39} +(9.30542 - 16.1175i) q^{40} +4.98968 q^{41} +(4.42095 + 5.76481i) q^{42} -6.45341 q^{43} +(-14.7448 + 25.5387i) q^{44} +(0.957403 + 1.65827i) q^{45} +(1.37292 + 2.37797i) q^{46} +(3.47180 - 6.01333i) q^{47} +15.6087 q^{48} +(-1.81550 + 6.76047i) q^{49} -3.66165 q^{50} +(-1.30891 + 2.26709i) q^{51} +(13.2496 + 22.9490i) q^{52} +(-0.506141 - 0.876662i) q^{53} +(-1.37292 + 2.37797i) q^{54} -10.1931 q^{55} +(15.6488 + 20.4056i) q^{56} +4.46024 q^{57} +(12.1655 - 21.0712i) q^{58} +(-3.07828 - 5.33173i) q^{59} +(5.30371 + 9.18629i) q^{60} +(-1.12186 + 1.94312i) q^{61} +16.2252 q^{62} +(-2.62321 + 0.344610i) q^{63} +33.0913 q^{64} +(-4.57975 + 7.93237i) q^{65} +(-7.30852 - 12.6587i) q^{66} +(-4.69424 - 8.13065i) q^{67} +(-7.25093 + 12.5590i) q^{68} -1.00000 q^{69} +(-5.32698 + 12.8504i) q^{70} -10.2261 q^{71} +(-4.85972 + 8.41728i) q^{72} +(-1.92559 - 3.33522i) q^{73} +(4.00797 + 6.94200i) q^{74} +(0.666760 - 1.15486i) q^{75} +24.7083 q^{76} +(5.39340 - 13.0106i) q^{77} -13.1348 q^{78} +(-1.48890 + 2.57886i) q^{79} +(14.9438 + 25.8835i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.85046 + 11.8653i) q^{82} -2.29460 q^{83} +(-14.5318 + 1.90903i) q^{84} -5.01260 q^{85} +(8.86005 - 15.3461i) q^{86} +(4.43049 + 7.67384i) q^{87} +(-25.8698 - 44.8079i) q^{88} +(5.04082 - 8.73095i) q^{89} -5.25777 q^{90} +(-7.70169 - 10.0428i) q^{91} -5.53968 q^{92} +(-2.95449 + 5.11732i) q^{93} +(9.53303 + 16.5117i) q^{94} +(4.27024 + 7.39627i) q^{95} +(-11.7102 + 20.2826i) q^{96} +13.2317 q^{97} +(-13.5837 - 13.5988i) q^{98} +5.32332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19}+ \cdots + 20 q^{99}+O(q^{100}) $ 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.37292	+	2.37797i	−0.970804	+	1.68148i	−0.277665	+	0.960678i	$0.589561\pi$
$2$	−1.37292	+	2.37797i	−0.970804	+	1.68148i	−0.693139	+	0.720804i	$0.743773\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.76984	−	4.79751i	−1.38492	−	2.39875i
$5$	0.957403	−	1.65827i	0.428163	−	0.741601i	−0.568547	−	0.822651i	$-0.692494\pi$
$5$	0.957403	−	1.65827i	0.428163	−	0.741601i	0.996710	+	0.0810502i	$0.0258274\pi$
$6$	2.74585			1.12099
$7$	1.61005	+	2.09946i	0.608541	+	0.793523i
$7$	1.61005	+	2.09946i	0.608541	+	0.793523i
$8$	9.71944			3.43634
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.62888	+	4.55336i	0.831326	+	1.43990i
$11$	−2.66166	−	4.61013i	−0.802521	−	1.39001i	−0.917952	−	0.396692i	$-0.870158\pi$
$11$	−2.66166	−	4.61013i	−0.802521	−	1.39001i	0.115431	−	0.993315i	$-0.463175\pi$
$12$	−2.76984	+	4.79751i	−0.799585	+	1.38492i
$13$	−4.78352			−1.32671			−0.663355	−	0.748305i	$-0.730868\pi$
$13$	−4.78352			−1.32671			−0.663355	+	0.748305i	$0.730868\pi$
$14$	−7.20294	+	0.946247i	−1.92507	+	0.252895i
$15$	−1.91481			−0.494401
$16$	−7.80437	+	13.5176i	−1.95109	+	3.37939i
$17$	−1.30891	−	2.26709i	−0.317457	−	0.549851i	0.662500	−	0.749062i	$-0.269495\pi$
$17$	−1.30891	−	2.26709i	−0.317457	−	0.549851i	−0.979957	+	0.199211i	$0.936162\pi$
$18$	−1.37292	−	2.37797i	−0.323601	−	0.560494i
$19$	−2.23012	+	3.86268i	−0.511624	+	0.886159i	0.488285	+	0.872684i	$0.337623\pi$
$19$	−2.23012	+	3.86268i	−0.511624	+	0.886159i	−0.999909	+	0.0134748i	$0.995711\pi$
$20$	−10.6074			−2.37189
$21$	1.01317	−	2.44407i	0.221091	−	0.533341i
$22$	14.6170			3.11636
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	−4.85972	−	8.41728i	−0.991986	−	1.71817i
$25$	0.666760	+	1.15486i	0.133352	+	0.230973i
$26$	6.56741	−	11.3751i	1.28798	−	2.23084i
$27$	1.00000			0.192450
$28$	5.61262	−	13.5394i	1.06068	−	2.55871i
$29$	−8.86099			−1.64544			−0.822722	−	0.568444i	$-0.807546\pi$
$29$	−8.86099			−1.64544			−0.822722	+	0.568444i	$0.807546\pi$
$30$	2.62888	−	4.55336i	0.479966	−	0.831326i
$31$	−2.95449	−	5.11732i	−0.530642	−	0.919098i	−0.999361	−	0.0357510i	$-0.988618\pi$
$31$	−2.95449	−	5.11732i	−0.530642	−	0.919098i	0.468719	−	0.883347i	$-0.344716\pi$
$32$	−11.7102	−	20.2826i	−2.07009	−	3.58549i
$33$	−2.66166	+	4.61013i	−0.463336	+	0.802521i
$34$	7.18812			1.23275
$35$	5.02294	−	0.659861i	0.849032	−	0.111537i
$36$	5.53968			0.923281
$37$	1.45965	−	2.52818i	0.239964	−	0.415630i	−0.720739	−	0.693206i	$-0.756198\pi$
$37$	1.45965	−	2.52818i	0.239964	−	0.415630i	0.960704	+	0.277576i	$0.0895309\pi$
$38$	−6.12357	−	10.6063i	−0.993374	−	1.72057i
$39$	2.39176	+	4.14265i	0.382988	+	0.663355i
$40$	9.30542	−	16.1175i	1.47132	−	2.54839i
$41$	4.98968			0.779258			0.389629	−	0.920972i	$-0.372603\pi$
$41$	4.98968			0.779258			0.389629	+	0.920972i	$0.372603\pi$
$42$	4.42095	+	5.76481i	0.682167	+	0.889529i
$43$	−6.45341			−0.984136			−0.492068	−	0.870557i	$-0.663759\pi$
$43$	−6.45341			−0.984136			−0.492068	+	0.870557i	$0.663759\pi$
$44$	−14.7448	+	25.5387i	−2.22286	+	3.85010i
$45$	0.957403	+	1.65827i	0.142721	+	0.247200i
$46$	1.37292	+	2.37797i	0.202427	+	0.350613i
$47$	3.47180	−	6.01333i	0.506414	−	0.877135i	−0.493559	−	0.869713i	$-0.664304\pi$
$47$	3.47180	−	6.01333i	0.506414	−	0.877135i	0.999972	−	0.00742198i	$-0.00236251\pi$
$48$	15.6087			2.25293
$49$	−1.81550	+	6.76047i	−0.259356	+	0.965782i
$50$	−3.66165			−0.517835
$51$	−1.30891	+	2.26709i	−0.183284	+	0.317457i
$52$	13.2496	+	22.9490i	1.83739	+	3.18245i
$53$	−0.506141	−	0.876662i	−0.0695238	−	0.120419i	0.829168	−	0.559000i	$-0.188815\pi$
$53$	−0.506141	−	0.876662i	−0.0695238	−	0.120419i	−0.898692	+	0.438581i	$0.855481\pi$
$54$	−1.37292	+	2.37797i	−0.186831	+	0.323601i
$55$	−10.1931			−1.37444
$56$	15.6488	+	20.4056i	2.09115	+	2.72681i
$57$	4.46024			0.590773
$58$	12.1655	−	21.0712i	1.59740	−	2.76678i
$59$	−3.07828	−	5.33173i	−0.400758	−	0.694133i	0.593060	−	0.805158i	$-0.297920\pi$
$59$	−3.07828	−	5.33173i	−0.400758	−	0.694133i	−0.993818	+	0.111026i	$0.964586\pi$
$60$	5.30371	+	9.18629i	0.684706	+	1.18595i
$61$	−1.12186	+	1.94312i	−0.143639	+	0.248791i	−0.928864	−	0.370420i	$-0.879214\pi$
$61$	−1.12186	+	1.94312i	−0.143639	+	0.248791i	0.785225	+	0.619210i	$0.212547\pi$
$62$	16.2252			2.06060
$63$	−2.62321	+	0.344610i	−0.330494	+	0.0434168i
$64$	33.0913			4.13641
$65$	−4.57975	+	7.93237i	−0.568049	+	0.983889i
$66$	−7.30852	−	12.6587i	−0.899616	−	1.55818i
$67$	−4.69424	−	8.13065i	−0.573492	−	0.993317i	−0.996204	−	0.0870532i	$-0.972255\pi$
$67$	−4.69424	−	8.13065i	−0.573492	−	0.993317i	0.422712	−	0.906264i	$-0.361078\pi$
$68$	−7.25093	+	12.5590i	−0.879305	+	1.52300i
$69$	−1.00000			−0.120386
$70$	−5.32698	+	12.8504i	−0.636696	+	1.53591i
$71$	−10.2261			−1.21362			−0.606810	−	0.794847i	$-0.707551\pi$
$71$	−10.2261			−1.21362			−0.606810	+	0.794847i	$0.707551\pi$
$72$	−4.85972	+	8.41728i	−0.572723	+	0.991986i
$73$	−1.92559	−	3.33522i	−0.225373	−	0.390358i	0.731058	−	0.682315i	$-0.239027\pi$
$73$	−1.92559	−	3.33522i	−0.225373	−	0.390358i	−0.956431	+	0.291957i	$0.905694\pi$
$74$	4.00797	+	6.94200i	0.465917	+	0.806991i
$75$	0.666760	−	1.15486i	0.0769909	−	0.133352i
$76$	24.7083			2.83424
$77$	5.39340	−	13.0106i	0.614635	−	1.48269i
$78$	−13.1348			−1.48723
$79$	−1.48890	+	2.57886i	−0.167515	+	0.290144i	−0.937546	−	0.347863i	$-0.886908\pi$
$79$	−1.48890	+	2.57886i	−0.167515	+	0.290144i	0.770031	+	0.638007i	$0.220241\pi$
$80$	14.9438	+	25.8835i	1.67077	+	2.89386i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.85046	+	11.8653i	−0.756506	+	1.31031i
$83$	−2.29460			−0.251865			−0.125932	−	0.992039i	$-0.540192\pi$
$83$	−2.29460			−0.251865			−0.125932	+	0.992039i	$0.540192\pi$
$84$	−14.5318	+	1.90903i	−1.58555	+	0.208292i
$85$	−5.01260			−0.543693
$86$	8.86005	−	15.3461i	0.955404	−	1.65481i
$87$	4.43049	+	7.67384i	0.474999	+	0.822722i
$88$	−25.8698	−	44.8079i	−2.75774	−	4.77654i
$89$	5.04082	−	8.73095i	0.534325	−	0.925479i	−0.464870	−	0.885379i	$-0.653899\pi$
$89$	5.04082	−	8.73095i	0.534325	−	0.925479i	0.999196	−	0.0400999i	$-0.0127676\pi$
$90$	−5.25777			−0.554217
$91$	−7.70169	−	10.0428i	−0.807357	−	1.05277i
$92$	−5.53968			−0.577552
$93$	−2.95449	+	5.11732i	−0.306366	+	0.530642i
$94$	9.53303	+	16.5117i	0.983257	+	1.70305i
$95$	4.27024	+	7.39627i	0.438118	+	0.758842i
$96$	−11.7102	+	20.2826i	−1.19516	+	2.07009i
$97$	13.2317			1.34347			0.671735	−	0.740791i	$-0.265549\pi$
$97$	13.2317			1.34347			0.671735	+	0.740791i	$0.265549\pi$
$98$	−13.5837	−	13.5988i	−1.37216	−	1.37369i
$99$	5.32332			0.535014
$100$	3.69364	−	6.39758i	0.369364	−	0.639758i
$101$	4.08753	+	7.07982i	0.406725	+	0.704468i	0.994521	−	0.104541i	$-0.0333375\pi$
$101$	4.08753	+	7.07982i	0.406725	+	0.704468i	−0.587796	+	0.809009i	$0.700004\pi$
$102$	−3.59406	−	6.22510i	−0.355865	−	0.616376i
$103$	6.07180	−	10.5167i	0.598273	−	1.03624i	−0.394803	−	0.918766i	$-0.629187\pi$
$103$	6.07180	−	10.5167i	0.598273	−	1.03624i	0.993076	−	0.117473i	$-0.0374794\pi$
$104$	−46.4931			−4.55903
$105$	−3.08293	−	4.02006i	−0.300863	−	0.392318i
$106$	2.77957			0.269976
$107$	−5.83004	+	10.0979i	−0.563611	+	0.976203i	0.433567	+	0.901122i	$0.357255\pi$
$107$	−5.83004	+	10.0979i	−0.563611	+	0.976203i	−0.997177	+	0.0750811i	$0.976078\pi$
$108$	−2.76984	−	4.79751i	−0.266528	−	0.461640i
$109$	−0.442304	−	0.766093i	−0.0423650	−	0.0733784i	0.844065	−	0.536240i	$-0.180156\pi$
$109$	−0.442304	−	0.766093i	−0.0423650	−	0.0733784i	−0.886430	+	0.462862i	$0.846823\pi$
$110$	13.9944	−	24.2390i	1.33431	−	2.31110i
$111$	−2.91929			−0.277087
$112$	−40.9450	+	5.37893i	−3.86894	+	0.508261i
$113$	−1.00924			−0.0949413			−0.0474706	−	0.998873i	$-0.515116\pi$
$113$	−1.00924			−0.0949413			−0.0474706	+	0.998873i	$0.515116\pi$
$114$	−6.12357	+	10.6063i	−0.573524	+	0.993374i
$115$	−0.957403	−	1.65827i	−0.0892783	−	0.154634i
$116$	24.5435	+	42.5107i	2.27881	+	3.94702i
$117$	2.39176	−	4.14265i	0.221118	−	0.382988i
$118$	16.9050			1.55623
$119$	2.65228	−	6.39813i	0.243134	−	0.586516i
$120$	−18.6108			−1.69893
$121$	−8.66888	+	15.0149i	−0.788080	+	1.36499i
$122$	−3.08045	−	5.33550i	−0.278891	−	0.483054i
$123$	−2.49484	−	4.32119i	−0.224952	−	0.389629i
$124$	−16.3669	+	28.3484i	−1.46979	+	2.54576i
$125$	12.1275			1.08471
$126$	2.78200	−	6.71106i	0.247840	−	0.597868i
$127$	−1.94220			−0.172342			−0.0861711	−	0.996280i	$-0.527463\pi$
$127$	−1.94220			−0.172342			−0.0861711	+	0.996280i	$0.527463\pi$
$128$	−22.0115	+	38.1250i	−1.94556	+	3.36980i
$129$	3.22671	+	5.58882i	0.284096	+	0.492068i
$130$	−12.5753	−	21.7811i	−1.10293	−	1.91033i
$131$	3.56193	−	6.16944i	0.311207	−	0.539026i	−0.667417	−	0.744684i	$-0.732600\pi$
$131$	3.56193	−	6.16944i	0.311207	−	0.539026i	0.978624	+	0.205658i	$0.0659334\pi$
$132$	29.4895			2.56673
$133$	−11.7001	+	1.53704i	−1.01453	+	0.133278i
$134$	25.7793			2.22699
$135$	0.957403	−	1.65827i	0.0824001	−	0.142721i
$136$	−12.7218	−	22.0349i	−1.09089	−	1.88947i
$137$	−3.06032	−	5.30063i	−0.261461	−	0.452863i	0.705170	−	0.709039i	$-0.250871\pi$
$137$	−3.06032	−	5.30063i	−0.261461	−	0.452863i	−0.966630	+	0.256175i	$0.917538\pi$
$138$	1.37292	−	2.37797i	0.116871	−	0.202427i
$139$	−13.1313			−1.11378			−0.556892	−	0.830585i	$-0.688006\pi$
$139$	−13.1313			−1.11378			−0.556892	+	0.830585i	$0.688006\pi$
$140$	−17.0784	−	22.2699i	−1.44339	−	1.88215i
$141$	−6.94360			−0.584756
$142$	14.0397	−	24.3175i	1.17819	−	2.04068i
$143$	12.7321	+	22.0527i	1.06471	+	1.84414i
$144$	−7.80437	−	13.5176i	−0.650364	−	1.12646i
$145$	−8.48353	+	14.6939i	−0.704519	+	1.22026i
$146$	10.5748			0.875174
$147$	6.76249	−	1.80797i	0.557761	−	0.149119i
$148$	−16.1720			−1.32933
$149$	−0.981019	+	1.69917i	−0.0803682	+	0.139202i	−0.903408	−	0.428782i	$-0.858943\pi$
$149$	−0.981019	+	1.69917i	−0.0803682	+	0.139202i	0.823040	+	0.567984i	$0.192276\pi$
$150$	1.83082	+	3.17108i	0.149486	+	0.258917i
$151$	7.83183	+	13.5651i	0.637345	+	1.10391i	0.986013	+	0.166668i	$0.0533007\pi$
$151$	7.83183	+	13.5651i	0.637345	+	1.10391i	−0.348668	+	0.937246i	$0.613366\pi$
$152$	−21.6755	+	37.5431i	−1.75811	+	3.04514i
$153$	2.61781			0.211638
$154$	23.5341	+	30.6879i	1.89643	+	2.47290i
$155$	−11.3145			−0.908805
$156$	13.2496	−	22.9490i	1.06082	−	1.83739i
$157$	8.72735	+	15.1162i	0.696518	+	1.20641i	0.969666	+	0.244433i	$0.0786019\pi$
$157$	8.72735	+	15.1162i	0.696518	+	1.20641i	−0.273148	+	0.961972i	$0.588065\pi$
$158$	−4.08831	−	7.08115i	−0.325248	−	0.563346i
$159$	−0.506141	+	0.876662i	−0.0401396	+	0.0695238i
$160$	−44.8454			−3.54534
$161$	2.62321	−	0.344610i	0.206738	−	0.0271591i
$162$	2.74585			0.215734
$163$	5.94933	−	10.3045i	0.465988	−	0.807114i	−0.533258	−	0.845953i	$-0.679032\pi$
$163$	5.94933	−	10.3045i	0.465988	−	0.807114i	0.999246	+	0.0388385i	$0.0123658\pi$
$164$	−13.8206	−	23.9380i	−1.07921	−	1.86925i
$165$	5.09656	+	8.82750i	0.396767	+	0.687220i
$166$	3.15031	−	5.45650i	0.244512	−	0.423506i
$167$	−9.48883			−0.734267			−0.367134	−	0.930168i	$-0.619661\pi$
$167$	−9.48883			−0.734267			−0.367134	+	0.930168i	$0.619661\pi$
$168$	9.84740	−	23.7550i	0.759743	−	1.83274i
$169$	9.88206			0.760158
$170$	6.88193	−	11.9198i	0.527820	−	0.914210i
$171$	−2.23012	−	3.86268i	−0.170541	−	0.295386i
$172$	17.8749	+	30.9603i	1.36295	+	2.36070i
$173$	2.73063	−	4.72959i	0.207606	−	0.359584i	−0.743354	−	0.668898i	$-0.766766\pi$
$173$	2.73063	−	4.72959i	0.207606	−	0.359584i	0.950960	+	0.309314i	$0.100100\pi$
$174$	−24.3309			−1.84452
$175$	−1.35108	+	3.25922i	−0.102132	+	0.246374i
$176$	83.0903			6.26317
$177$	−3.07828	+	5.33173i	−0.231378	+	0.400758i
$178$	13.8413	+	23.9739i	1.03745	+	1.79692i
$179$	0.420079	+	0.727599i	0.0313982	+	0.0543833i	0.881298	−	0.472562i	$-0.156671\pi$
$179$	0.420079	+	0.727599i	0.0313982	+	0.0543833i	−0.849899	+	0.526945i	$0.823337\pi$
$180$	5.30371	−	9.18629i	0.395315	−	0.684706i
$181$	17.2554			1.28258			0.641291	−	0.767298i	$-0.278399\pi$
$181$	17.2554			1.28258			0.641291	+	0.767298i	$0.278399\pi$
$182$	34.4554	−	4.52639i	2.55401	−	0.335518i
$183$	2.24372			0.165860
$184$	4.85972	−	8.41728i	0.358263	−	0.620530i
$185$	−2.79494	−	4.84097i	−0.205488	−	0.355916i
$186$	−8.11258	−	14.0514i	−0.594843	−	1.03030i
$187$	−6.96773	+	12.0685i	−0.509531	+	0.882534i
$188$	−38.4653			−2.80537
$189$	1.61005	+	2.09946i	0.117114	+	0.152714i
$190$	−23.4509			−1.70131
$191$	6.89422	−	11.9411i	0.498849	−	0.864031i	−0.501151	−	0.865360i	$-0.667090\pi$
$191$	6.89422	−	11.9411i	0.498849	−	0.864031i	0.999999	+	0.00132911i	$0.000423069\pi$
$192$	−16.5456	−	28.6579i	−1.19408	−	2.06820i
$193$	9.79078	+	16.9581i	0.704756	+	1.22067i	0.966780	+	0.255611i	$0.0822768\pi$
$193$	9.79078	+	16.9581i	0.704756	+	1.22067i	−0.262024	+	0.965061i	$0.584390\pi$
$194$	−18.1661	+	31.4645i	−1.30425	+	2.25902i
$195$	9.15951			0.655926
$196$	37.4621	−	10.0156i	2.67586	−	0.715399i
$197$	−18.8814			−1.34525			−0.672623	−	0.739986i	$-0.734832\pi$
$197$	−18.8814			−1.34525			−0.672623	+	0.739986i	$0.734832\pi$
$198$	−7.30852	+	12.6587i	−0.519394	+	0.899616i
$199$	3.52040	+	6.09750i	0.249554	+	0.432241i	0.963402	−	0.268060i	$-0.0863826\pi$
$199$	3.52040	+	6.09750i	0.249554	+	0.432241i	−0.713848	+	0.700301i	$0.753049\pi$
$200$	6.48054	+	11.2246i	0.458243	+	0.793700i
$201$	−4.69424	+	8.13065i	−0.331106	+	0.573492i
$202$	−22.4475			−1.57940
$203$	−14.2666	−	18.6033i	−1.00132	−	1.30570i
$204$	14.5019			1.01533
$205$	4.77714	−	8.27424i	0.333650	−	0.577898i
$206$	16.6723	+	28.8772i	1.16161	+	2.01197i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	37.3323	−	64.6615i	2.58853	−	4.48347i
$209$	23.7433			1.64236
$210$	13.7922	−	1.81188i	0.951755	−	0.125032i
$211$	−16.1639			−1.11277			−0.556386	−	0.830924i	$-0.687812\pi$
$211$	−16.1639			−1.11277			−0.556386	+	0.830924i	$0.687812\pi$
$212$	−2.80386	+	4.85643i	−0.192570	+	0.333541i
$213$	5.11307	+	8.85610i	0.350342	+	0.606810i
$214$	−16.0084	−	27.7274i	−1.09431	−	1.89540i
$215$	−6.17851	+	10.7015i	−0.421371	+	0.729836i
$216$	9.71944			0.661324
$217$	5.98677	−	14.4420i	0.406408	−	0.980385i
$218$	2.42900			0.164513
$219$	−1.92559	+	3.33522i	−0.130119	+	0.225373i
$220$	28.2333	+	48.9016i	1.90349	+	3.29694i
$221$	6.26118	+	10.8447i	0.421173	+	0.729492i
$222$	4.00797	−	6.94200i	0.268997	−	0.465917i
$223$	1.72721			0.115662			0.0578312	−	0.998326i	$-0.481581\pi$
$223$	1.72721			0.115662			0.0578312	+	0.998326i	$0.481581\pi$
$224$	23.7287	−	57.2411i	1.58544	−	3.82458i
$225$	−1.33352			−0.0889014
$226$	1.38561	−	2.39995i	0.0921694	−	0.159642i
$227$	−1.53444	−	2.65772i	−0.101844	−	0.176399i	0.810600	−	0.585600i	$-0.199141\pi$
$227$	−1.53444	−	2.65772i	−0.101844	−	0.176399i	−0.912444	+	0.409201i	$0.865808\pi$
$228$	−12.3541	−	21.3980i	−0.818174	−	1.41712i
$229$	−1.43742	+	2.48968i	−0.0949872	+	0.164523i	−0.909603	−	0.415478i	$-0.863614\pi$
$229$	−1.43742	+	2.48968i	−0.0949872	+	0.164523i	0.814616	+	0.580001i	$0.196948\pi$
$230$	5.25777			0.346687
$231$	−13.9642	+	1.83447i	−0.918777	+	0.120699i
$232$	−86.1238			−5.65431
$233$	4.53137	−	7.84857i	0.296860	−	0.514177i	−0.678556	−	0.734549i	$-0.737394\pi$
$233$	4.53137	−	7.84857i	0.296860	−	0.514177i	0.975416	+	0.220372i	$0.0707272\pi$
$234$	6.56741	+	11.3751i	0.429325	+	0.743613i
$235$	−6.64782	−	11.5144i	−0.433656	−	0.751114i
$236$	−17.0527	+	29.5361i	−1.11004	+	1.92264i
$237$	2.97781			0.193429
$238$	11.5732	+	15.0912i	0.750180	+	0.978217i
$239$	28.5432			1.84630			0.923152	−	0.384436i	$-0.125604\pi$
$239$	28.5432			1.84630			0.923152	+	0.384436i	$0.125604\pi$
$240$	14.9438	−	25.8835i	0.964621	−	1.67077i
$241$	5.18116	+	8.97403i	0.333748	+	0.578068i	0.983244	−	0.182297i	$-0.0583532\pi$
$241$	5.18116	+	8.97403i	0.333748	+	0.578068i	−0.649496	+	0.760365i	$0.725020\pi$
$242$	−23.8034	−	41.2287i	−1.53014	−	2.65028i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	12.4295			0.795716
$245$	9.47253	+	9.48307i	0.605178	+	0.605851i
$246$	13.7009			0.873538
$247$	10.6678	−	18.4772i	0.678777	−	1.17568i
$248$	−28.7160	−	49.7375i	−1.82347	−	3.15833i
$249$	1.14730	+	1.98718i	0.0727072	+	0.125932i
$250$	−16.6501	+	28.8388i	−1.05304	+	1.82393i
$251$	−13.6387			−0.860865			−0.430433	−	0.902623i	$-0.641639\pi$
$251$	−13.6387			−0.860865			−0.430433	+	0.902623i	$0.641639\pi$
$252$	8.91915	+	11.6304i	0.561854	+	0.732644i
$253$	−5.32332			−0.334674
$254$	2.66649	−	4.61850i	0.167311	−	0.289790i
$255$	2.50630	+	4.34104i	0.156951	+	0.271847i
$256$	−27.3489	−	47.3696i	−1.70930	−	2.96060i
$257$	−5.49840	+	9.52351i	−0.342981	+	0.594060i	−0.984985	−	0.172641i	$-0.944770\pi$
$257$	−5.49840	+	9.52351i	−0.342981	+	0.594060i	0.642004	+	0.766701i	$0.278103\pi$
$258$	−17.7201			−1.10320
$259$	7.65792	−	1.00602i	0.475840	−	0.0625109i
$260$	50.7408			3.14681
$261$	4.43049	−	7.67384i	0.274241	−	0.474999i
$262$	9.78051	+	16.9403i	0.604242	+	1.04658i
$263$	−4.14585	−	7.18083i	−0.255644	−	0.442789i	0.709426	−	0.704780i	$-0.248954\pi$
$263$	−4.14585	−	7.18083i	−0.255644	−	0.442789i	−0.965070	+	0.261991i	$0.915621\pi$
$264$	−25.8698	+	44.8079i	−1.59218	+	2.75774i
$265$	−1.93832			−0.119070
$266$	12.4084	−	29.9329i	0.760806	−	1.83530i
$267$	−10.0816			−0.616986
$268$	−26.0046	+	45.0413i	−1.58848	+	2.75133i
$269$	0.530280	+	0.918472i	0.0323318	+	0.0560002i	0.881739	−	0.471738i	$-0.156373\pi$
$269$	0.530280	+	0.918472i	0.0323318	+	0.0560002i	−0.849407	+	0.527739i	$0.823040\pi$
$270$	2.62888	+	4.55336i	0.159989	+	0.277109i
$271$	11.1576	−	19.3256i	0.677779	−	1.17395i	−0.297869	−	0.954607i	$-0.596276\pi$
$271$	11.1576	−	19.3256i	0.677779	−	1.17395i	0.975648	−	0.219341i	$-0.0703907\pi$
$272$	40.8608			2.47755
$273$	−4.84650	+	11.6913i	−0.293323	+	0.707588i
$274$	16.8063			1.01531
$275$	3.54938	−	6.14771i	0.214036	−	0.370721i
$276$	2.76984	+	4.79751i	0.166725	+	0.288776i
$277$	−12.2065	−	21.1424i	−0.733420	−	1.27032i	−0.955413	−	0.295273i	$-0.904590\pi$
$277$	−12.2065	−	21.1424i	−0.733420	−	1.27032i	0.221993	−	0.975048i	$-0.428744\pi$
$278$	18.0283	−	31.2260i	1.08127	−	1.87281i
$279$	5.90898			0.353761
$280$	48.8202	−	6.41348i	2.91756	−	0.383279i
$281$	−0.764668			−0.0456163			−0.0228081	−	0.999740i	$-0.507261\pi$
$281$	−0.764668			−0.0456163			−0.0228081	+	0.999740i	$0.507261\pi$
$282$	9.53303	−	16.5117i	0.567684	−	0.983257i
$283$	−1.41016	−	2.44246i	−0.0838252	−	0.145189i	0.821065	−	0.570835i	$-0.193380\pi$
$283$	−1.41016	−	2.44246i	−0.0838252	−	0.145189i	−0.904890	+	0.425646i	$0.860047\pi$
$284$	28.3248	+	49.0600i	1.68077	+	2.91117i
$285$	4.27024	−	7.39627i	0.252947	−	0.438118i
$286$	−69.9209			−4.13451
$287$	8.03363	+	10.4757i	0.474210	+	0.618359i
$288$	23.4204			1.38006
$289$	5.07353	−	8.78760i	0.298443	−	0.516918i
$290$	−23.2945	−	40.3473i	−1.36790	−	2.36927i
$291$	−6.61583	−	11.4589i	−0.387827	−	0.671735i
$292$	−10.6672	+	18.4761i	−0.624249	+	1.08123i
$293$	32.2644			1.88490			0.942452	−	0.334342i	$-0.108514\pi$
$293$	32.2644			1.88490			0.942452	+	0.334342i	$0.108514\pi$
$294$	−4.98507	+	18.5632i	−0.290735	+	1.08263i
$295$	−11.7886			−0.686359
$296$	14.1869	−	24.5725i	0.824599	−	1.42825i
$297$	−2.66166	−	4.61013i	−0.154445	−	0.267507i
$298$	−2.69373	−	4.66568i	−0.156044	−	0.270275i
$299$	−2.39176	+	4.14265i	−0.138319	+	0.239576i
$300$	−7.38728			−0.426505
$301$	−10.3903	−	13.5487i	−0.598887	−	0.780934i
$302$	−43.0100			−2.47495
$303$	4.08753	−	7.07982i	0.234823	−	0.406725i
$304$	−34.8093	−	60.2915i	−1.99645	−	3.45796i
$305$	2.14814	+	3.72069i	0.123002	+	0.213046i
$306$	−3.59406	+	6.22510i	−0.205459	+	0.355865i
$307$	−12.2320			−0.698118			−0.349059	−	0.937101i	$-0.613499\pi$
$307$	−12.2320			−0.698118			−0.349059	+	0.937101i	$0.613499\pi$
$308$	−77.3573	+	10.1624i	−4.40784	+	0.579056i
$309$	−12.1436			−0.690826
$310$	15.5340	−	26.9057i	0.882272	−	1.52814i
$311$	−3.22198	−	5.58064i	−0.182702	−	0.316449i	0.760098	−	0.649809i	$-0.225151\pi$
$311$	−3.22198	−	5.58064i	−0.182702	−	0.316449i	−0.942800	+	0.333360i	$0.891818\pi$
$312$	23.2466	+	40.2642i	1.31608	+	2.27951i
$313$	15.9876	−	27.6913i	0.903673	−	1.56521i	0.0809843	−	0.996715i	$-0.474194\pi$
$313$	15.9876	−	27.6913i	0.903673	−	1.56521i	0.822689	−	0.568492i	$-0.192473\pi$
$314$	−47.9280			−2.70473
$315$	−1.94001	+	4.67993i	−0.109307	+	0.263684i
$316$	16.4961			0.927979
$317$	−7.13572	+	12.3594i	−0.400782	+	0.694175i	−0.993821	−	0.110999i	$-0.964595\pi$
$317$	−7.13572	+	12.3594i	−0.400782	+	0.694175i	0.593038	+	0.805174i	$0.297928\pi$
$318$	−1.38979	−	2.40718i	−0.0779354	−	0.134988i
$319$	23.5849	+	40.8503i	1.32050	+	2.28718i
$320$	31.6817	−	54.8743i	1.77106	−	3.06756i
$321$	11.6601			0.650802
$322$	−2.78200	+	6.71106i	−0.155035	+	0.373993i
$323$	11.6761			0.649674
$324$	−2.76984	+	4.79751i	−0.153880	+	0.266528i
$325$	−3.18946	−	5.52431i	−0.176919	−	0.306434i
$326$	16.3360	+	28.2947i	0.904765	+	1.56710i
$327$	−0.442304	+	0.766093i	−0.0244595	+	0.0423650i
$328$	48.4969			2.67779
$329$	18.2145	−	2.39283i	1.00420	−	0.131921i
$330$	−27.9888			−1.54073
$331$	−2.59635	+	4.49701i	−0.142708	+	0.247178i	−0.928516	−	0.371293i	$-0.878914\pi$
$331$	−2.59635	+	4.49701i	−0.142708	+	0.247178i	0.785807	+	0.618471i	$0.212248\pi$
$332$	6.35568	+	11.0084i	0.348813	+	0.604162i
$333$	1.45965	+	2.52818i	0.0799881	+	0.138543i
$334$	13.0274	−	22.5642i	0.712830	−	1.23466i
$335$	−17.9771			−0.982193
$336$	25.1308	+	32.7700i	1.37100	+	1.78775i
$337$	27.3455			1.48961			0.744803	−	0.667284i	$-0.232543\pi$
$337$	27.3455			1.48961			0.744803	+	0.667284i	$0.232543\pi$
$338$	−13.5673	+	23.4993i	−0.737965	+	1.27819i
$339$	0.504620	+	0.874027i	0.0274072	+	0.0474706i
$340$	13.8841	+	24.0480i	0.752972	+	1.30419i
$341$	−15.7277	+	27.2412i	−0.851702	+	1.47519i
$342$	12.2471			0.662249
$343$	−17.1164	+	7.07311i	−0.924199	+	0.381912i
$344$	−62.7236			−3.38183
$345$	−0.957403	+	1.65827i	−0.0515448	+	0.0892783i
$346$	7.49790	+	12.9867i	0.403089	+	0.698171i
$347$	−2.57954	−	4.46789i	−0.138477	−	0.239849i	0.788443	−	0.615107i	$-0.210887\pi$
$347$	−2.57954	−	4.46789i	−0.138477	−	0.239849i	−0.926920	+	0.375258i	$0.877554\pi$
$348$	24.5435	−	42.5107i	1.31567	−	2.27881i
$349$	15.1720			0.812140			0.406070	−	0.913842i	$-0.366899\pi$
$349$	15.1720			0.812140			0.406070	+	0.913842i	$0.366899\pi$
$350$	−5.89542	−	7.68749i	−0.315124	−	0.410914i
$351$	−4.78352			−0.255325
$352$	−62.3370	+	107.971i	−3.32258	+	5.75487i
$353$	−2.48689	−	4.30742i	−0.132364	−	0.229261i	0.792224	−	0.610231i	$-0.208923\pi$
$353$	−2.48689	−	4.30742i	−0.132364	−	0.229261i	−0.924587	+	0.380970i	$0.875590\pi$
$354$	−8.45249	−	14.6401i	−0.449245	−	0.778114i
$355$	−9.79053	+	16.9577i	−0.519627	+	0.900021i
$356$	−55.8491			−2.95999
$357$	−6.86708	+	0.902125i	−0.363445	+	0.0477455i
$358$	−2.30695			−0.121926
$359$	−9.77868	+	16.9372i	−0.516099	+	0.893910i	0.483726	+	0.875219i	$0.339283\pi$
$359$	−9.77868	+	16.9372i	−0.516099	+	0.893910i	−0.999825	+	0.0186906i	$0.994050\pi$
$360$	9.30542	+	16.1175i	0.490438	+	0.849464i
$361$	−0.446850	−	0.773967i	−0.0235184	−	0.0407351i
$362$	−23.6903	+	41.0329i	−1.24514	+	2.15664i
$363$	17.3378			0.909996
$364$	−26.8481	+	64.7660i	−1.40722	+	3.39466i
$365$	−7.37427			−0.385987
$366$	−3.08045	+	5.33550i	−0.161018	+	0.278891i
$367$	5.82625	+	10.0914i	0.304128	+	0.526765i	0.977067	−	0.212933i	$-0.0683016\pi$
$367$	5.82625	+	10.0914i	0.304128	+	0.526765i	−0.672939	+	0.739698i	$0.734968\pi$
$368$	7.80437	+	13.5176i	0.406831	+	0.704652i
$369$	−2.49484	+	4.32119i	−0.129876	+	0.224952i
$370$	15.3490			0.797954
$371$	1.02561	−	2.47409i	0.0532470	−	0.128448i
$372$	32.7339			1.69717
$373$	6.62942	−	11.4825i	0.343258	−	0.594541i	−0.641777	−	0.766891i	$-0.721803\pi$
$373$	6.62942	−	11.4825i	0.343258	−	0.594541i	0.985036	+	0.172350i	$0.0551361\pi$
$374$	−19.1323	−	33.1382i	−0.989310	−	1.71353i
$375$	−6.06373	−	10.5027i	−0.313130	−	0.542356i
$376$	33.7439	−	58.4462i	1.74021	−	3.01413i
$377$	42.3867			2.18303
$378$	−7.20294	+	0.946247i	−0.370479	+	0.0486697i
$379$	−5.81701			−0.298800			−0.149400	−	0.988777i	$-0.547734\pi$
$379$	−5.81701			−0.298800			−0.149400	+	0.988777i	$0.547734\pi$
$380$	23.6558	−	40.9730i	1.21352	−	2.10187i
$381$	0.971099	+	1.68199i	0.0497509	+	0.0861711i
$382$	18.9305	+	32.7886i	0.968568	+	1.67761i
$383$	−8.39284	+	14.5368i	−0.428854	+	0.742797i	−0.996772	−	0.0802884i	$-0.974416\pi$
$383$	−8.39284	+	14.5368i	−0.428854	+	0.742797i	0.567918	+	0.823085i	$0.307749\pi$
$384$	44.0229			2.24653
$385$	−16.4114	−	21.4001i	−0.836403	−	1.09065i
$386$	−53.7680			−2.73672
$387$	3.22671	−	5.58882i	0.164023	−	0.284096i
$388$	−36.6496	−	63.4790i	−1.86060	−	3.22266i
$389$	−1.54205	−	2.67091i	−0.0781852	−	0.135421i	0.824282	−	0.566180i	$-0.191579\pi$
$389$	−1.54205	−	2.67091i	−0.0781852	−	0.135421i	−0.902467	+	0.430759i	$0.858246\pi$
$390$	−12.5753	+	21.7811i	−0.636776	+	1.10293i
$391$	−2.61781			−0.132389
$392$	−17.6456	+	65.7080i	−0.891237	+	3.31875i
$393$	−7.12385			−0.359351
$394$	25.9228	−	44.8995i	1.30597	−	2.26201i
$395$	2.85096	+	4.93801i	0.143447	+	0.248458i
$396$	−14.7448	−	25.5387i	−0.740952	−	1.28337i
$397$	10.3343	−	17.8995i	0.518663	−	0.898350i	−0.481102	−	0.876665i	$-0.659763\pi$
$397$	10.3343	−	17.8995i	0.518663	−	0.898350i	0.999765	−	0.0216858i	$-0.00690333\pi$
$398$	−19.3329			−0.969073
$399$	7.18119	+	9.36410i	0.359509	+	0.468791i
$400$	−20.8146			−1.04073
$401$	−13.6592	+	23.6585i	−0.682109	+	1.18145i	0.292228	+	0.956349i	$0.405604\pi$
$401$	−13.6592	+	23.6585i	−0.682109	+	1.18145i	−0.974336	+	0.225098i	$0.927730\pi$
$402$	−12.8897	−	22.3255i	−0.642878	−	1.11350i
$403$	14.1328	+	24.4788i	0.704007	+	1.21938i
$404$	22.6436	−	39.2199i	1.12656	−	1.95127i
$405$	−1.91481			−0.0951474
$406$	63.8252	−	8.38468i	3.16759	−	0.416125i
$407$	−15.5403			−0.770306
$408$	−12.7218	+	22.0349i	−0.629825	+	1.09089i
$409$	−5.03043	−	8.71295i	−0.248739	−	0.430828i	0.714438	−	0.699699i	$-0.246683\pi$
$409$	−5.03043	−	8.71295i	−0.248739	−	0.430828i	−0.963176	+	0.268871i	$0.913349\pi$
$410$	13.1173	+	22.7198i	0.647817	+	1.12205i
$411$	−3.06032	+	5.30063i	−0.150954	+	0.261461i
$412$	−67.2718			−3.31424
$413$	6.23761	−	15.0471i	0.306933	−	0.740418i
$414$	−2.74585			−0.134951
$415$	−2.19686	+	3.80506i	−0.107839	+	0.186783i
$416$	56.0159	+	97.0223i	2.74640	+	4.75691i
$417$	6.56566	+	11.3721i	0.321522	+	0.556892i
$418$	−32.5977	+	56.4609i	−1.59441	+	2.76159i
$419$	−17.1206			−0.836396			−0.418198	−	0.908356i	$-0.637338\pi$
$419$	−17.1206			−0.836396			−0.418198	+	0.908356i	$0.637338\pi$
$420$	−10.7471	+	25.9253i	−0.524403	+	1.26503i
$421$	−20.4594			−0.997129			−0.498565	−	0.866853i	$-0.666139\pi$
$421$	−20.4594			−0.997129			−0.498565	+	0.866853i	$0.666139\pi$
$422$	22.1919	−	38.4374i	1.08028	−	1.87111i
$423$	3.47180	+	6.01333i	0.168805	+	0.292378i
$424$	−4.91941	−	8.52066i	−0.238907	−	0.413800i
$425$	1.74545	−	3.02322i	0.0846670	−	0.146648i
$426$	−28.0794			−1.36045
$427$	−5.88575	+	0.773207i	−0.284831	+	0.0374181i
$428$	64.5931			3.12223
$429$	12.7321	−	22.0527i	0.614712	−	1.06471i
$430$	−16.9653	−	29.3847i	−0.818138	−	1.41706i
$431$	−9.03285	−	15.6454i	−0.435097	−	0.753610i	0.562206	−	0.826997i	$-0.309953\pi$
$431$	−9.03285	−	15.6454i	−0.435097	−	0.753610i	−0.997304	+	0.0733865i	$0.976619\pi$
$432$	−7.80437	+	13.5176i	−0.375488	+	0.650364i
$433$	−14.9439			−0.718157			−0.359079	−	0.933307i	$-0.616909\pi$
$433$	−14.9439			−0.718157			−0.359079	+	0.933307i	$0.616909\pi$
$434$	26.1233	+	34.0641i	1.25396	+	1.63513i
$435$	16.9671			0.813509
$436$	−2.45022	+	4.24391i	−0.117344	+	0.203247i
$437$	2.23012	+	3.86268i	0.106681	+	0.184777i
$438$	−5.28738	−	9.15802i	−0.252641	−	0.437587i
$439$	11.4874	−	19.8968i	0.548265	−	0.949623i	−0.450128	−	0.892964i	$-0.648622\pi$
$439$	11.4874	−	19.8968i	0.548265	−	0.949623i	0.998394	−	0.0566592i	$-0.0180448\pi$
$440$	−99.0714			−4.72305
$441$	−4.94699	−	4.95250i	−0.235571	−	0.235833i
$442$	−34.3845			−1.63550
$443$	6.84243	−	11.8514i	0.325094	−	0.563079i	−0.656438	−	0.754380i	$-0.727938\pi$
$443$	6.84243	−	11.8514i	0.325094	−	0.563079i	0.981531	+	0.191302i	$0.0612709\pi$
$444$	8.08598	+	14.0053i	0.383744	+	0.664663i
$445$	−9.65218	−	16.7181i	−0.457557	−	0.792512i
$446$	−2.37133	+	4.10726i	−0.112286	+	0.194484i
$447$	1.96204			0.0928012
$448$	53.2785	+	69.4739i	2.51717	+	3.28233i
$449$	−19.1186			−0.902261			−0.451130	−	0.892458i	$-0.648979\pi$
$449$	−19.1186			−0.902261			−0.451130	+	0.892458i	$0.648979\pi$
$450$	1.83082	−	3.17108i	0.0863058	−	0.149486i
$451$	−13.2808	−	23.0031i	−0.625371	−	1.08317i
$452$	2.79544	+	4.84184i	0.131486	+	0.227741i
$453$	7.83183	−	13.5651i	0.367971	−	0.637345i
$454$	8.42667			0.395483
$455$	−24.0273	+	3.15646i	−1.12642	+	0.147977i
$456$	43.3510			2.03010
$457$	9.03283	−	15.6453i	0.422538	−	0.731857i	−0.573649	−	0.819101i	$-0.694473\pi$
$457$	9.03283	−	15.6453i	0.422538	−	0.731857i	0.996187	+	0.0872441i	$0.0278060\pi$
$458$	−3.94693	−	6.83628i	−0.184428	−	0.319439i
$459$	−1.30891	−	2.26709i	−0.0610945	−	0.105819i
$460$	−5.30371	+	9.18629i	−0.247287	+	0.428313i
$461$	32.2584			1.50242			0.751211	−	0.660062i	$-0.229470\pi$
$461$	32.2584			1.50242			0.751211	+	0.660062i	$0.229470\pi$
$462$	14.8095	−	35.7251i	0.688999	−	1.66208i
$463$	24.3695			1.13255			0.566274	−	0.824217i	$-0.308385\pi$
$463$	24.3695			1.13255			0.566274	+	0.824217i	$0.308385\pi$
$464$	69.1544	−	119.779i	3.21041	−	5.56060i
$465$	5.65727	+	9.79868i	0.262350	+	0.454403i
$466$	12.4425	+	21.5510i	0.576386	+	0.998329i
$467$	16.8322	−	29.1543i	0.778903	−	1.34910i	−0.153671	−	0.988122i	$-0.549110\pi$
$467$	16.8322	−	29.1543i	0.778903	−	1.34910i	0.932574	−	0.360978i	$-0.117557\pi$
$468$	−26.4992			−1.22493
$469$	9.51207	−	22.9461i	0.439227	−	1.05955i
$470$	36.5078			1.68398
$471$	8.72735	−	15.1162i	0.402135	−	0.696518i
$472$	−29.9191	−	51.8215i	−1.37714	−	2.38528i
$473$	17.1768	+	29.7511i	0.789790	+	1.36796i
$474$	−4.08831	+	7.08115i	−0.187782	+	0.325248i
$475$	−5.94782			−0.272905
$476$	−38.0415	+	4.99749i	−1.74363	+	0.229060i
$477$	1.01228			0.0463492
$478$	−39.1876	+	67.8749i	−1.79240	+	3.10453i
$479$	−16.3837	−	28.3775i	−0.748592	−	1.29660i	−0.948497	−	0.316785i	$-0.897397\pi$
$479$	−16.3837	−	28.3775i	−0.748592	−	1.29660i	0.199905	−	0.979815i	$-0.435937\pi$
$480$	22.4227	+	38.8373i	1.02345	+	1.77267i
$481$	−6.98224	+	12.0936i	−0.318363	+	0.551421i
$482$	−28.4534			−1.29602
$483$	−1.61005	−	2.09946i	−0.0732597	−	0.0955289i
$484$	96.0457			4.36571
$485$	12.6680	−	21.9417i	0.575225	−	0.996319i
$486$	−1.37292	−	2.37797i	−0.0622771	−	0.107867i
$487$	−10.8791	−	18.8431i	−0.492977	−	0.853861i	0.506990	−	0.861952i	$-0.330758\pi$
$487$	−10.8791	−	18.8431i	−0.492977	−	0.853861i	−0.999967	+	0.00809040i	$0.997425\pi$
$488$	−10.9038	+	18.8860i	−0.493593	+	0.854929i
$489$	−11.8987			−0.538076
$490$	−35.5556	+	9.50589i	−1.60624	+	0.429432i
$491$	37.4957			1.69216			0.846078	−	0.533059i	$-0.178958\pi$
$491$	37.4957			1.69216			0.846078	+	0.533059i	$0.178958\pi$
$492$	−13.8206	+	23.9380i	−0.623082	+	1.07921i
$493$	11.5982	+	20.0887i	0.522357	+	0.904749i
$494$	29.2922	+	50.7356i	1.31792	+	2.28270i
$495$	5.09656	−	8.82750i	0.229073	−	0.396767i
$496$	92.2316			4.14132
$497$	−16.4646	−	21.4694i	−0.738537	−	0.963034i
$498$	−6.30062			−0.282338
$499$	−3.81146	+	6.60165i	−0.170625	+	0.295530i	−0.938638	−	0.344903i	$-0.887912\pi$
$499$	−3.81146	+	6.60165i	−0.170625	+	0.295530i	0.768014	+	0.640433i	$0.221245\pi$
$500$	−33.5911	−	58.1816i	−1.50224	−	2.60196i
$501$	4.74441	+	8.21757i	0.211965	+	0.367134i
$502$	18.7249	−	32.4324i	0.835731	−	1.44753i
$503$	−18.3255			−0.817092			−0.408546	−	0.912738i	$-0.633964\pi$
$503$	−18.3255			−0.817092			−0.408546	+	0.912738i	$0.633964\pi$
$504$	−25.4962	+	3.34942i	−1.13569	+	0.149195i
$505$	15.6537			0.696579
$506$	7.30852	−	12.6587i	0.324903	−	0.562749i
$507$	−4.94103	−	8.55811i	−0.219439	−	0.380079i
$508$	5.37958	+	9.31771i	0.238680	+	0.413407i
$509$	−18.6741	+	32.3444i	−0.827713	+	1.43364i	0.0721153	+	0.997396i	$0.477025\pi$
$509$	−18.6741	+	32.3444i	−0.827713	+	1.43364i	−0.899828	+	0.436244i	$0.856308\pi$
$510$	−13.7639			−0.609474
$511$	3.90188	−	9.41258i	0.172609	−	0.416388i
$512$	62.1458			2.74648
$513$	−2.23012	+	3.86268i	−0.0984621	+	0.170541i
$514$	−15.0978	−	26.1501i	−0.665935	−	1.15343i
$515$	−11.6263	−	20.1374i	−0.512317	−	0.887359i
$516$	17.8749	−	30.9603i	0.786900	−	1.36295i
$517$	−36.9630			−1.62563
$518$	−8.12147	+	19.5915i	−0.356837	+	0.860803i
$519$	−5.46126			−0.239723
$520$	−44.5126	+	77.0981i	−1.95201	+	3.38098i
$521$	13.3119	+	23.0568i	0.583204	+	1.01014i	0.995097	+	0.0989064i	$0.0315344\pi$
$521$	13.3119	+	23.0568i	0.583204	+	1.01014i	−0.411893	+	0.911232i	$0.635132\pi$
$522$	12.1655	+	21.0712i	0.532468	+	0.922262i
$523$	−20.4400	+	35.4031i	−0.893780	+	1.54807i	−0.0584718	+	0.998289i	$0.518623\pi$
$523$	−20.4400	+	35.4031i	−0.893780	+	1.54807i	−0.835308	+	0.549783i	$0.814711\pi$
$524$	−39.4639			−1.72399
$525$	3.49811	−	0.459545i	0.152670	−	0.0200562i
$526$	22.7678			0.992722
$527$	−7.73430	+	13.3962i	−0.336911	+	0.583548i
$528$	−41.5452	−	71.9583i	−1.80802	−	3.13158i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	2.66117	−	4.60928i	0.115594	−	0.200214i
$531$	6.15656			0.267172
$532$	39.7815	+	51.8742i	1.72475	+	2.24903i
$533$	−23.8682			−1.03385
$534$	13.8413	−	23.9739i	0.598972	−	1.03745i
$535$	11.1634	+	19.3355i	0.482635	+	0.835949i
$536$	−45.6253	−	79.0254i	−1.97071	−	3.41338i
$537$	0.420079	−	0.727599i	0.0181278	−	0.0313982i
$538$	−2.91214			−0.125551
$539$	35.9989	−	9.62441i	1.55058	−	0.414553i
$540$	−10.6074			−0.456471
$541$	−11.0688	+	19.1717i	−0.475884	+	0.824255i	−0.999618	−	0.0276266i	$-0.991205\pi$
$541$	−11.0688	+	19.1717i	−0.475884	+	0.824255i	0.523735	+	0.851882i	$0.324538\pi$
$542$	30.6372	+	53.0652i	1.31598	+	2.27935i
$543$	−8.62769	−	14.9436i	−0.370250	−	0.641291i
$544$	−30.6551	+	53.0961i	−1.31433	+	2.27648i
$545$	−1.69385			−0.0725566
$546$	−21.1477	−	27.5761i	−0.905037	−	1.18015i
$547$	−24.7940			−1.06012			−0.530058	−	0.847962i	$-0.677830\pi$
$547$	−24.7940			−1.06012			−0.530058	+	0.847962i	$0.677830\pi$
$548$	−16.9532	+	29.3638i	−0.724205	+	1.25436i
$549$	−1.12186	−	1.94312i	−0.0478798	−	0.0829302i
$550$	9.74606	+	16.8807i	0.415573	+	0.719794i
$551$	19.7610	−	34.2271i	0.841849	−	1.45813i
$552$	−9.71944			−0.413687
$553$	−7.81143	+	1.02618i	−0.332176	+	0.0436377i
$554$	67.0346			2.84803
$555$	−2.79494	+	4.84097i	−0.118639	+	0.205488i
$556$	36.3717	+	62.9976i	1.54250	+	2.67169i
$557$	−5.26824	−	9.12486i	−0.223223	−	0.386633i	0.732562	−	0.680700i	$-0.238324\pi$
$557$	−5.26824	−	9.12486i	−0.223223	−	0.386633i	−0.955785	+	0.294067i	$0.904991\pi$
$558$	−8.11258	+	14.0514i	−0.343433	+	0.594843i
$559$	30.8700			1.30566
$560$	−30.2812	+	73.0477i	−1.27961	+	3.08683i
$561$	13.9355			0.588356
$562$	1.04983	−	1.81836i	0.0442844	−	0.0767029i
$563$	2.06160	+	3.57079i	0.0868859	+	0.150491i	0.906193	−	0.422864i	$-0.138975\pi$
$563$	2.06160	+	3.57079i	0.0868859	+	0.150491i	−0.819307	+	0.573355i	$0.805642\pi$
$564$	19.2327	+	33.3120i	0.809841	+	1.40269i
$565$	−0.966249	+	1.67359i	−0.0406504	+	0.0704085i
$566$	7.74416			0.325511
$567$	1.01317	−	2.44407i	0.0425489	−	0.102641i
$568$	−99.3923			−4.17041
$569$	−10.0429	+	17.3948i	−0.421019	+	0.729226i	−0.996039	−	0.0889127i	$-0.971661\pi$
$569$	−10.0429	+	17.3948i	−0.421019	+	0.729226i	0.575020	+	0.818139i	$0.304994\pi$
$570$	11.7254	+	20.3091i	0.491124	+	0.850653i
$571$	−19.6437	−	34.0239i	−0.822064	−	1.42386i	−0.904143	−	0.427230i	$-0.859489\pi$
$571$	−19.6437	−	34.0239i	−0.822064	−	1.42386i	0.0820795	−	0.996626i	$-0.473844\pi$
$572$	70.5319	−	122.165i	2.94908	−	5.10797i
$573$	−13.7884			−0.576021
$574$	−35.9404	+	4.72147i	−1.50012	+	0.197070i
$575$	1.33352			0.0556117
$576$	−16.5456	+	28.6579i	−0.689401	+	1.19408i
$577$	−3.27016	−	5.66409i	−0.136139	−	0.235799i	0.789893	−	0.613244i	$-0.210136\pi$
$577$	−3.27016	−	5.66409i	−0.136139	−	0.235799i	−0.926032	+	0.377445i	$0.876803\pi$
$578$	13.9311	+	24.1294i	0.579459	+	1.00365i
$579$	9.79078	−	16.9581i	0.406891	−	0.704756i
$580$	93.9922			3.90281
$581$	−3.69441	−	4.81743i	−0.153270	−	0.199861i
$582$	36.3321			1.50601
$583$	−2.69435	+	4.66675i	−0.111589	+	0.193277i
$584$	−18.7157	−	32.4165i	−0.774460	−	1.34140i
$585$	−4.57975	−	7.93237i	−0.189350	−	0.327963i
$586$	−44.2965	+	76.7238i	−1.82987	+	3.16943i
$587$	45.0583			1.85976			0.929878	−	0.367868i	$-0.119912\pi$
$587$	45.0583			1.85976			0.929878	+	0.367868i	$0.119912\pi$
$588$	−27.4048	−	27.4353i	−1.13015	−	1.13141i
$589$	26.3554			1.08596
$590$	16.1849	−	28.0330i	0.666320	−	1.15410i
$591$	9.44071	+	16.3518i	0.388339	+	0.672623i
$592$	22.7832	+	39.4617i	0.936385	+	1.62187i
$593$	−2.53671	+	4.39370i	−0.104170	+	0.180428i	−0.913399	−	0.407066i	$-0.866552\pi$
$593$	−2.53671	+	4.39370i	−0.104170	+	0.180428i	0.809229	+	0.587494i	$0.199885\pi$
$594$	14.6170			0.599744
$595$	−8.07053	−	10.5238i	−0.330859	−	0.431433i
$596$	10.8691			0.445214
$597$	3.52040	−	6.09750i	0.144080	−	0.249554i
$598$	−6.56741	−	11.3751i	−0.268561	−	0.465162i
$599$	−22.6765	−	39.2768i	−0.926536	−	1.60481i	−0.789072	−	0.614301i	$-0.789438\pi$
$599$	−22.6765	−	39.2768i	−0.926536	−	1.60481i	−0.137464	−	0.990507i	$-0.543895\pi$
$600$	6.48054	−	11.2246i	0.264567	−	0.458243i
$601$	−4.71581			−0.192362			−0.0961810	−	0.995364i	$-0.530663\pi$
$601$	−4.71581			−0.192362			−0.0961810	+	0.995364i	$0.530663\pi$
$602$	46.4836	−	6.10652i	1.89453	−	0.248883i
$603$	9.38847			0.382328
$604$	43.3859	−	75.1465i	1.76535	−	3.05767i
$605$	16.5992	+	28.7507i	0.674854	+	1.16888i
$606$	11.2237	+	19.4401i	0.455934	+	0.789700i
$607$	15.9840	−	27.6850i	0.648769	−	1.12370i	−0.334648	−	0.942343i	$-0.608617\pi$
$607$	15.9840	−	27.6850i	0.648769	−	1.12370i	0.983417	−	0.181358i	$-0.0580493\pi$
$608$	104.460			4.23642
$609$	−8.97764	+	21.6569i	−0.363793	+	0.877582i
$610$	−11.7969			−0.477644
$611$	−16.6074	+	28.7649i	−0.671864	+	1.16370i
$612$	−7.25093	−	12.5590i	−0.293102	−	0.507667i
$613$	−8.72001	−	15.1035i	−0.352198	−	0.610025i	0.634436	−	0.772975i	$-0.281232\pi$
$613$	−8.72001	−	15.1035i	−0.352198	−	0.610025i	−0.986634	+	0.162950i	$0.947899\pi$
$614$	16.7936	−	29.0874i	0.677736	−	1.17387i
$615$	−9.55427			−0.385265
$616$	52.4209	−	126.456i	2.11210	−	5.09504i
$617$	−2.50110			−0.100691			−0.0503453	−	0.998732i	$-0.516032\pi$
$617$	−2.50110			−0.100691			−0.0503453	+	0.998732i	$0.516032\pi$
$618$	16.6723	−	28.8772i	0.670656	−	1.16161i
$619$	−8.09658	−	14.0237i	−0.325429	−	0.563660i	0.656170	−	0.754613i	$-0.272175\pi$
$619$	−8.09658	−	14.0237i	−0.325429	−	0.563660i	−0.981599	+	0.190953i	$0.938842\pi$
$620$	31.3395	+	54.2816i	1.25862	+	2.18000i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	17.6942			0.709471
$623$	26.4463	−	3.47423i	1.05955	−	0.139192i
$624$	−74.6647			−2.98898
$625$	8.27706	−	14.3363i	0.331082	−	0.573451i
$626$	43.8995	+	76.0362i	1.75458	+	3.03902i
$627$	−11.8716	−	20.5623i	−0.474107	−	0.821178i
$628$	48.3468	−	83.7391i	1.92925	−	3.34155i
$629$	−7.64216			−0.304713
$630$	−8.46525	−	11.0385i	−0.337264	−	0.439784i
$631$	−25.3726			−1.01007			−0.505033	−	0.863100i	$-0.668520\pi$
$631$	−25.3726			−1.01007			−0.505033	+	0.863100i	$0.668520\pi$
$632$	−14.4713	+	25.0651i	−0.575638	+	0.997034i
$633$	8.08197	+	13.9984i	0.321229	+	0.556386i
$634$	−19.5936	−	33.9371i	−0.778162	−	1.34782i
$635$	−1.85947	+	3.22069i	−0.0737907	+	0.127809i
$636$	5.60772			0.222361
$637$	8.68446	−	32.3388i	0.344091	−	1.28131i
$638$	−129.521			−5.12780
$639$	5.11307	−	8.85610i	0.202270	−	0.350342i
$640$	42.1477	+	73.0019i	1.66603	+	2.88565i
$641$	−1.28441	−	2.22466i	−0.0507310	−	0.0878687i	0.839545	−	0.543291i	$-0.182822\pi$
$641$	−1.28441	−	2.22466i	−0.0507310	−	0.0878687i	−0.890276	+	0.455422i	$0.849488\pi$
$642$	−16.0084	+	27.7274i	−0.631801	+	1.09431i
$643$	32.1446			1.26766			0.633829	−	0.773473i	$-0.281482\pi$
$643$	32.1446			1.26766			0.633829	+	0.773473i	$0.281482\pi$
$644$	−8.91915	−	11.6304i	−0.351464	−	0.458301i
$645$	12.3570			0.486558
$646$	−16.0304	+	27.7654i	−0.630706	+	1.09241i
$647$	−17.2559	−	29.8881i	−0.678400	−	1.17502i	−0.975462	−	0.220166i	$-0.929340\pi$
$647$	−17.2559	−	29.8881i	−0.678400	−	1.17502i	0.297062	−	0.954858i	$-0.403993\pi$
$648$	−4.85972	−	8.41728i	−0.190908	−	0.330662i
$649$	−16.3867	+	28.3825i	−0.643233	+	1.11411i
$650$	17.5156			0.687017
$651$	−15.5005	+	2.03629i	−0.607512	+	0.0798086i
$652$	−65.9148			−2.58142
$653$	−10.3383	+	17.9064i	−0.404569	+	0.700733i	−0.994271	−	0.106887i	$-0.965912\pi$
$653$	−10.3383	+	17.9064i	−0.404569	+	0.700733i	0.589703	+	0.807621i	$0.299245\pi$
$654$	−1.21450	−	2.10358i	−0.0474907	−	0.0822563i
$655$	−6.82040	−	11.8133i	−0.266495	−	0.461583i
$656$	−38.9413	+	67.4484i	−1.52040	+	2.63342i
$657$	3.85118			0.150249
$658$	−19.3171	+	46.5989i	−0.753058	+	1.81661i
$659$	−10.2297			−0.398491			−0.199246	−	0.979950i	$-0.563849\pi$
$659$	−10.2297			−0.398491			−0.199246	+	0.979950i	$0.563849\pi$
$660$	28.2333	−	48.9016i	1.09898	−	1.90349i
$661$	−2.33387	−	4.04239i	−0.0907771	−	0.157231i	0.817061	−	0.576551i	$-0.195602\pi$
$661$	−2.33387	−	4.04239i	−0.0907771	−	0.157231i	−0.907838	+	0.419320i	$0.862268\pi$
$662$	−7.12918	−	12.3481i	−0.277083	−	0.479923i
$663$	6.26118	−	10.8447i	0.243164	−	0.421173i
$664$	−22.3022			−0.865494
$665$	−8.65292	+	20.8736i	−0.335546	+	0.809442i
$666$	−8.01593			−0.310611
$667$	−4.43049	+	7.67384i	−0.171549	+	0.297132i
$668$	26.2826	+	45.5227i	1.01690	+	1.76133i
$669$	−0.863604	−	1.49581i	−0.0333889	−	0.0578312i
$670$	24.6812	−	42.7491i	0.953517	−	1.65154i
$671$	11.9440			0.461094
$672$	−61.4366	+	8.07089i	−2.36997	+	0.311341i
$673$	−36.2826			−1.39859			−0.699296	−	0.714832i	$-0.746503\pi$
$673$	−36.2826			−1.39859			−0.699296	+	0.714832i	$0.746503\pi$
$674$	−37.5434	+	65.0270i	−1.44612	+	2.50475i
$675$	0.666760	+	1.15486i	0.0256636	+	0.0444507i
$676$	−27.3717	−	47.4092i	−1.05276	−	1.82343i
$677$	−19.8217	+	34.3323i	−0.761811	+	1.31950i	0.180105	+	0.983647i	$0.442356\pi$
$677$	−19.8217	+	34.3323i	−0.761811	+	1.31950i	−0.941916	+	0.335849i	$0.890977\pi$
$678$	−2.77122			−0.106428
$679$	21.3036	+	27.7794i	0.817557	+	1.06607i
$680$	−48.7197			−1.86832
$681$	−1.53444	+	2.65772i	−0.0587998	+	0.101844i
$682$	−43.1859	−	74.8001i	−1.65367	−	2.86424i
$683$	6.93890	+	12.0185i	0.265510	+	0.459876i	0.967697	−	0.252116i	$-0.0811265\pi$
$683$	6.93890	+	12.0185i	0.265510	+	0.459876i	−0.702187	+	0.711992i	$0.747793\pi$
$684$	−12.3541	+	21.3980i	−0.472373	+	0.818174i
$685$	−11.7198			−0.447792
$686$	6.67983	−	50.4132i	0.255037	−	1.92479i
$687$	2.87483			0.109682
$688$	50.3648	−	87.2344i	1.92014	−	3.32578i
$689$	2.42114	+	4.19353i	0.0922379	+	0.159761i
$690$	−2.62888	−	4.55336i	−0.100080	−	0.173343i
$691$	−18.6652	+	32.3291i	−0.710059	+	1.22986i	0.254776	+	0.967000i	$0.417998\pi$
$691$	−18.6652	+	32.3291i	−0.710059	+	1.22986i	−0.964835	+	0.262858i	$0.915335\pi$
$692$	−30.2537			−1.15007
$693$	8.57080	+	11.1761i	0.325578	+	0.424546i
$694$	14.1660			0.537735
$695$	−12.5720	+	21.7753i	−0.476882	+	0.825984i
$696$	43.0619	+	74.5854i	1.63226	+	2.82715i
$697$	−6.53103	−	11.3121i	−0.247380	−	0.428476i
$698$	−20.8301	+	36.0787i	−0.788429	+	1.36560i
$699$	−9.06274			−0.342784
$700$	19.3784	−	2.54573i	0.732435	−	0.0962197i
$701$	7.48359			0.282651			0.141326	−	0.989963i	$-0.454864\pi$
$701$	7.48359			0.282651			0.141326	+	0.989963i	$0.454864\pi$
$702$	6.56741	−	11.3751i	0.247871	−	0.429325i
$703$	6.51036	+	11.2763i	0.245543	+	0.425293i
$704$	−88.0777	−	152.555i	−3.31955	−	5.74964i
$705$	−6.64782	+	11.5144i	−0.250371	+	0.433656i
$706$	13.6572			0.513997
$707$	−8.28269	+	19.9805i	−0.311503	+	0.751443i
$708$	34.1054			1.28176
$709$	−24.2450	+	41.9937i	−0.910542	+	1.57710i	−0.0972414	+	0.995261i	$0.531002\pi$
$709$	−24.2450	+	41.9937i	−0.910542	+	1.57710i	−0.813300	+	0.581844i	$0.802331\pi$
$710$	−26.8833	−	46.5633i	−1.00891	−	1.74749i
$711$	−1.48890	−	2.57886i	−0.0558383	−	0.0967147i
$712$	48.9939	−	84.8599i	1.83612	−	3.18026i
$713$	−5.90898			−0.221293
$714$	7.28275	−	17.5683i	0.272550	−	0.657477i
$715$	48.7590			1.82348
$716$	2.32711	−	4.03067i	0.0869681	−	0.150633i
$717$	−14.2716	−	24.7191i	−0.532982	−	0.923152i
$718$	−26.8508	−	46.5069i	−1.00206	−	1.73562i
$719$	8.05689	−	13.9550i	0.300471	−	0.520432i	−0.675771	−	0.737111i	$-0.736189\pi$
$719$	8.05689	−	13.9550i	0.300471	−	0.520432i	0.976243	+	0.216679i	$0.0695226\pi$
$720$	−29.8877			−1.11385
$721$	31.8553	−	4.18481i	1.18635	−	0.155850i
$722$	2.45397			0.0913272
$723$	5.18116	−	8.97403i	0.192689	−	0.333748i
$724$	−47.7947	−	82.7828i	−1.77628	−	3.07660i
$725$	−5.90816	−	10.2332i	−0.219423	−	0.380052i
$726$	−23.8034	+	41.2287i	−0.883428	+	1.53014i
$727$	16.2362			0.602167			0.301084	−	0.953598i	$-0.402652\pi$
$727$	16.2362			0.602167			0.301084	+	0.953598i	$0.402652\pi$
$728$	−74.8561	−	97.6106i	−2.77435	−	3.61769i
$729$	1.00000			0.0370370
$730$	10.1243	−	17.5358i	0.374717	−	0.649030i
$731$	8.44692	+	14.6305i	0.312421	+	0.541128i
$732$	−6.21474	−	10.7642i	−0.229703	−	0.397858i
$733$	−0.697020	+	1.20727i	−0.0257450	+	0.0445917i	−0.878611	−	0.477538i	$-0.841529\pi$
$733$	−0.697020	+	1.20727i	−0.0257450	+	0.0445917i	0.852866	+	0.522130i	$0.174862\pi$
$734$	−31.9960			−1.18099
$735$	3.47632	−	12.9450i	0.128226	−	0.477483i
$736$	−23.4204			−0.863286
$737$	−24.9889	+	43.2821i	−0.920479	+	1.59432i
$738$	−6.85046	−	11.8653i	−0.252169	−	0.436769i
$739$	4.09940	+	7.10037i	0.150799	+	0.261191i	0.931521	−	0.363687i	$-0.118482\pi$
$739$	4.09940	+	7.10037i	0.150799	+	0.261191i	−0.780723	+	0.624878i	$0.785149\pi$
$740$	−15.4831	+	26.8175i	−0.569169	+	0.985830i
$741$	−21.3356			−0.783784
$742$	4.47524	+	5.83561i	0.164291	+	0.214232i
$743$	−40.6236			−1.49034			−0.745168	−	0.666877i	$-0.767631\pi$
$743$	−40.6236			−1.49034			−0.745168	+	0.666877i	$0.767631\pi$
$744$	−28.7160	+	49.7375i	−1.05278	+	1.82347i
$745$	1.87846	+	3.25359i	0.0688214	+	0.119202i
$746$	18.2034	+	31.5292i	0.666473	+	1.15437i
$747$	1.14730	−	1.98718i	0.0419775	−	0.0727072i
$748$	77.1981			2.82264
$749$	−30.5868	+	4.01818i	−1.11762	+	0.146821i
$750$	33.3002			1.21595
$751$	−15.8834	+	27.5109i	−0.579594	+	1.00389i	0.415932	+	0.909396i	$0.363456\pi$
$751$	−15.8834	+	27.5109i	−0.579594	+	1.00389i	−0.995526	+	0.0944905i	$0.969878\pi$
$752$	54.1904	+	93.8605i	1.97612	+	3.42274i
$753$	6.81933	+	11.8114i	0.248510	+	0.430433i
$754$	−58.1937	+	100.795i	−2.11929	+	3.67072i
$755$	29.9928			1.09155
$756$	5.61262	−	13.5394i	0.204129	−	0.492423i
$757$	14.9385			0.542950			0.271475	−	0.962445i	$-0.412489\pi$
$757$	14.9385			0.542950			0.271475	+	0.962445i	$0.412489\pi$
$758$	7.98631	−	13.8327i	0.290076	−	0.502426i
$759$	2.66166	+	4.61013i	0.0966122	+	0.167337i
$760$	41.5043	+	71.8876i	1.50552	+	2.60764i
$761$	−23.3100	+	40.3740i	−0.844985	+	1.46356i	0.0406489	+	0.999173i	$0.487057\pi$
$761$	−23.3100	+	40.3740i	−0.844985	+	1.46356i	−0.885634	+	0.464384i	$0.846276\pi$
$762$	−5.33298			−0.193194
$763$	0.896254	−	2.16205i	0.0324466	−	0.0782714i
$764$	−76.3837			−2.76346
$765$	2.50630	−	4.34104i	0.0906155	−	0.156951i
$766$	−23.0455	−	39.9159i	−0.832667	−	1.44222i
$767$	14.7250	+	25.5045i	0.531689	+	0.920913i
$768$	−27.3489	+	47.3696i	−0.986867	+	1.70930i
$769$	−32.7623			−1.18144			−0.590720	−	0.806876i	$-0.701156\pi$
$769$	−32.7623			−1.18144			−0.590720	+	0.806876i	$0.701156\pi$
$770$	73.4205	−	9.64521i	2.64589	−	0.347589i
$771$	10.9968			0.396040
$772$	54.2378	−	93.9427i	1.95206	−	3.38107i
$773$	−19.7400	−	34.1907i	−0.709998	−	1.22975i	−0.964857	−	0.262775i	$-0.915362\pi$
$773$	−19.7400	−	34.1907i	−0.709998	−	1.22975i	0.254859	−	0.966978i	$-0.417971\pi$
$774$	8.86005	+	15.3461i	0.318468	+	0.551602i
$775$	3.93987	−	6.82406i	0.141524	−	0.245127i
$776$	128.604			4.61662
$777$	−4.70020	−	6.12895i	−0.168619	−	0.219875i
$778$	8.46849			0.303610
$779$	−11.1276	+	19.2735i	−0.398687	+	0.690546i
$780$	−25.3704	−	43.9428i	−0.908406	−	1.57341i
$781$	27.2185	+	47.1438i	0.973955	+	1.68694i
$782$	3.59406	−	6.22510i	0.128523	−	0.222609i
$783$	−8.86099			−0.316666
$784$	−77.2163	−	77.3023i	−2.75773	−	2.76080i
$785$	33.4224			1.19289
$786$	9.78051	−	16.9403i	0.348859	−	0.604242i
$787$	10.2577	+	17.7669i	0.365649	+	0.633323i	0.988880	−	0.148715i	$-0.0475137\pi$
$787$	10.2577	+	17.7669i	0.365649	+	0.633323i	−0.623231	+	0.782038i	$0.714180\pi$
$788$	52.2985	+	90.5837i	1.86306	+	3.22691i
$789$	−4.14585	+	7.18083i	−0.147596	+	0.255644i
$790$	−15.6566			−0.557038
$791$	−1.62492	−	2.11886i	−0.0577756	−	0.0753381i
$792$	51.7397			1.83849
$793$	5.36643	−	9.29493i	0.190568	−	0.330073i
$794$	28.3764	+	49.1493i	1.00704	+	1.74424i
$795$	0.969161	+	1.67864i	0.0343726	+	0.0595351i
$796$	19.5019	−	33.7783i	0.691226	−	1.19724i
$797$	11.1887			0.396325			0.198162	−	0.980169i	$-0.436503\pi$
$797$	11.1887			0.396325			0.198162	+	0.980169i	$0.436503\pi$
$798$	−32.1268	+	4.22048i	−1.13728	+	0.149404i
$799$	−18.1770			−0.643058
$800$	15.6158	−	27.0473i	0.552101	−	0.956266i
$801$	5.04082	+	8.73095i	0.178108	+	0.308493i
$802$	−37.5061	−	64.9625i	−1.32439	−	2.29391i
$803$	−10.2505	+	17.7545i	−0.361734	+	0.626541i
$804$	52.0092			1.83422
$805$	1.94001	−	4.67993i	0.0683765	−	0.164946i
$806$	−77.6133			−2.73381
$807$	0.530280	−	0.918472i	0.0186667	−	0.0323318i
$808$	39.7285	+	68.8118i	1.39764	+	2.42079i
$809$	−4.41606	−	7.64884i	−0.155260	−	0.268919i	0.777893	−	0.628396i	$-0.216288\pi$
$809$	−4.41606	−	7.64884i	−0.155260	−	0.268919i	−0.933154	+	0.359477i	$0.882955\pi$
$810$	2.62888	−	4.55336i	0.0923695	−	0.159989i
$811$	40.0206			1.40531			0.702657	−	0.711529i	$-0.251997\pi$
$811$	40.0206			1.40531			0.702657	+	0.711529i	$0.251997\pi$
$812$	−49.7333	+	119.972i	−1.74530	+	4.21021i
$813$	−22.3153			−0.782632
$814$	21.3357	−	36.9545i	0.747816	−	1.29525i
$815$	−11.3918	−	19.7312i	−0.399038	−	0.691154i
$816$	−20.4304	−	35.3865i	−0.715207	−	1.23877i
$817$	14.3919	−	24.9275i	0.503508	−	0.872101i
$818$	27.6256			0.965906
$819$	12.5482	−	1.64845i	0.438469	−	0.0576015i
$820$	−52.9277			−1.84831
$821$	16.8320	−	29.1539i	0.587442	−	1.01748i	−0.407124	−	0.913373i	$-0.633468\pi$
$821$	16.8320	−	29.1539i	0.587442	−	1.01748i	0.994566	−	0.104107i	$-0.0331984\pi$
$822$	−8.40317	−	14.5547i	−0.293094	−	0.507654i
$823$	−6.18690	−	10.7160i	−0.215662	−	0.373537i	0.737815	−	0.675003i	$-0.235858\pi$
$823$	−6.18690	−	10.7160i	−0.215662	−	0.373537i	−0.953477	+	0.301466i	$0.902524\pi$
$824$	59.0145	−	102.216i	2.05587	−	3.56087i
$825$	−7.09876			−0.247147
$826$	27.2178	+	35.4914i	0.947029	+	1.23490i
$827$	8.19126			0.284838			0.142419	−	0.989806i	$-0.454512\pi$
$827$	8.19126			0.284838			0.142419	+	0.989806i	$0.454512\pi$
$828$	2.76984	−	4.79751i	0.0962587	−	0.166725i
$829$	4.00150	+	6.93081i	0.138978	+	0.240717i	0.927110	−	0.374789i	$-0.122285\pi$
$829$	4.00150	+	6.93081i	0.138978	+	0.240717i	−0.788132	+	0.615506i	$0.788952\pi$
$830$	−6.03223	−	10.4481i	−0.209382	−	0.362660i
$831$	−12.2065	+	21.1424i	−0.423440	+	0.733420i
$832$	−158.293			−5.48781
$833$	17.7029	−	4.73293i	0.613370	−	0.163986i
$834$	−36.0566			−1.24854
$835$	−9.08463	+	15.7350i	−0.314387	+	0.544533i
$836$	−65.7651	−	113.909i	−2.27453	−	3.93961i
$837$	−2.95449	−	5.11732i	−0.102122	−	0.176881i
$838$	23.5053	−	40.7124i	0.811977	−	1.40639i
$839$	−30.7825			−1.06273			−0.531365	−	0.847143i	$-0.678321\pi$
$839$	−30.7825			−1.06273			−0.531365	+	0.847143i	$0.678321\pi$
$840$	−29.9643	−	39.0728i	−1.03387	−	1.34814i
$841$	49.5171			1.70749
$842$	28.0892	−	48.6519i	0.968017	−	1.67665i
$843$	0.382334	+	0.662222i	0.0131683	+	0.0228081i
$844$	44.7716	+	77.5466i	1.54110	+	2.66927i
$845$	9.46111	−	16.3871i	0.325472	−	0.563734i
$846$	−19.0661			−0.655505
$847$	−45.4806	+	5.97476i	−1.56273	+	0.205295i
$848$	15.8004			0.542589
$849$	−1.41016	+	2.44246i	−0.0483965	+	0.0838252i
$850$	4.79275	+	8.30129i	0.164390	+	0.284732i
$851$	−1.45965	−	2.52818i	−0.0500360	−	0.0866649i
$852$	28.3248	−	49.0600i	0.970391	−	1.68077i
$853$	37.1025			1.27037			0.635183	−	0.772362i	$-0.280925\pi$
$853$	37.1025			1.27037			0.635183	+	0.772362i	$0.280925\pi$
$854$	6.24202	−	15.0577i	0.213597	−	0.515264i
$855$	−8.54048			−0.292078
$856$	−56.6647	+	98.1461i	−1.93676	+	3.35456i
$857$	−19.6090	−	33.9638i	−0.669832	−	1.16018i	−0.977951	−	0.208835i	$-0.933033\pi$
$857$	−19.6090	−	33.9638i	−0.669832	−	1.16018i	0.308119	−	0.951348i	$-0.400300\pi$
$858$	34.9604	+	60.5533i	1.19353	+	2.06725i
$859$	13.2764	−	22.9955i	0.452986	−	0.784595i	−0.545584	−	0.838056i	$-0.683692\pi$
$859$	13.2764	−	22.9955i	0.452986	−	0.784595i	0.998570	+	0.0534613i	$0.0170254\pi$
$860$	68.4540			2.33426
$861$	5.05537	−	12.1952i	0.172287	−	0.415610i
$862$	49.6057			1.68958
$863$	21.7856	−	37.7338i	0.741591	−	1.28447i	−0.210179	−	0.977663i	$-0.567405\pi$
$863$	21.7856	−	37.7338i	0.741591	−	1.28447i	0.951770	−	0.306811i	$-0.0992619\pi$
$864$	−11.7102	−	20.2826i	−0.398388	−	0.690029i
$865$	−5.22862	−	9.05624i	−0.177779	−	0.307921i
$866$	20.5168	−	35.5362i	0.697190	−	1.20757i
$867$	−10.1471			−0.344612
$868$	−85.8679	+	11.2804i	−2.91455	+	0.382882i
$869$	15.8518			0.537737
$870$	−23.2945	+	40.3473i	−0.789757	+	1.36790i
$871$	22.4550	+	38.8931i	0.760857	+	1.31784i
$872$	−4.29895	−	7.44599i	−0.145581	−	0.252153i
$873$	−6.61583	+	11.4589i	−0.223912	+	0.387827i
$874$	−12.2471			−0.414265
$875$	19.5258	+	25.4612i	0.660092	+	0.860744i
$876$	21.3343			0.720821
$877$	28.3042	−	49.0243i	0.955765	−	1.65543i	0.223156	−	0.974783i	$-0.428364\pi$
$877$	28.3042	−	49.0243i	0.955765	−	1.65543i	0.732609	−	0.680650i	$-0.238303\pi$
$878$	31.5427	+	54.6336i	1.06452	+	1.84380i
$879$	−16.1322	−	27.9417i	−0.544125	−	0.942452i
$880$	79.5509	−	137.786i	2.68166	−	4.64477i
$881$	12.0366			0.405524			0.202762	−	0.979228i	$-0.435008\pi$
$881$	12.0366			0.405524			0.202762	+	0.979228i	$0.435008\pi$
$882$	18.5688	−	4.96441i	0.625243	−	0.167161i
$883$	2.42054			0.0814577			0.0407289	−	0.999170i	$-0.487032\pi$
$883$	2.42054			0.0814577			0.0407289	+	0.999170i	$0.487032\pi$
$884$	34.6850	−	60.0761i	1.16658	−	2.02058i
$885$	5.89430	+	10.2092i	0.198135	+	0.343180i
$886$	18.7883	+	32.5422i	0.631204	+	1.09328i
$887$	−8.61886	+	14.9283i	−0.289393	+	0.501244i	−0.973665	−	0.227983i	$-0.926787\pi$
$887$	−8.61886	+	14.9283i	−0.289393	+	0.501244i	0.684272	+	0.729227i	$0.260120\pi$
$888$	−28.3739			−0.952165
$889$	−3.12703	−	4.07758i	−0.104877	−	0.136757i
$890$	53.0069			1.77679
$891$	−2.66166	+	4.61013i	−0.0891690	+	0.154445i
$892$	−4.78410	−	8.28630i	−0.160183	−	0.277446i
$893$	15.4850	+	26.8209i	0.518187	+	0.897526i
$894$	−2.69373	+	4.66568i	−0.0900918	+	0.156044i
$895$	1.60874			0.0537743
$896$	−115.481	+	15.1707i	−3.85796	+	0.506819i
$897$	4.78352			0.159717
$898$	26.2483	−	45.4635i	0.875919	−	1.51714i
$899$	26.1797	+	45.3445i	0.873141	+	1.51232i
$900$	3.69364	+	6.39758i	0.123121	+	0.213253i
$901$	−1.32498	+	2.29494i	−0.0441416	+	0.0764555i
$902$	72.9344			2.42845
$903$	−6.53837	+	15.7726i	−0.217583	+	0.524880i
$904$	−9.80924			−0.326251
$905$	16.5203	−	28.6141i	0.549155	−	0.951164i
$906$	21.5050	+	37.2478i	0.714456	+	1.23747i
$907$	11.5513	+	20.0075i	0.383555	+	0.664337i	0.991568	−	0.129590i	$-0.0413663\pi$
$907$	11.5513	+	20.0075i	0.383555	+	0.664337i	−0.608012	+	0.793928i	$0.708033\pi$
$908$	−8.50030	+	14.7230i	−0.282092	+	0.488598i
$909$	−8.17507			−0.271150
$910$	25.4817	−	61.4700i	0.844711	−	2.03771i
$911$	−22.5226			−0.746209			−0.373104	−	0.927789i	$-0.621707\pi$
$911$	−22.5226			−0.746209			−0.373104	+	0.927789i	$0.621707\pi$
$912$	−34.8093	+	60.2915i	−1.15265	+	1.99645i
$913$	6.10744	+	10.5784i	0.202127	+	0.350094i
$914$	24.8028	+	42.9597i	0.820403	+	1.42098i
$915$	2.14814	−	3.72069i	0.0710153	−	0.123002i
$916$	15.9257			0.526199
$917$	18.6874	−	2.45495i	0.617112	−	0.0810696i
$918$	7.18812			0.237243
$919$	7.57950	−	13.1281i	0.250025	−	0.433056i	−0.713508	−	0.700647i	$-0.752895\pi$
$919$	7.57950	−	13.1281i	0.250025	−	0.433056i	0.963532	+	0.267592i	$0.0862279\pi$
$920$	−9.30542	−	16.1175i	−0.306790	−	0.531377i
$921$	6.11601	+	10.5932i	0.201529	+	0.349059i
$922$	−44.2883	+	76.7096i	−1.45856	+	2.52630i
$923$	48.9169			1.61012
$924$	47.4795	+	61.9122i	1.56196	+	2.03676i
$925$	3.89294			0.127999
$926$	−33.4575	+	57.9501i	−1.09948	+	1.90436i
$927$	6.07180	+	10.5167i	0.199424	+	0.345413i
$928$	103.764	+	179.724i	3.40621	+	5.89973i
$929$	−23.8827	+	41.3661i	−0.783567	+	1.35718i	0.146284	+	0.989243i	$0.453269\pi$
$929$	−23.8827	+	41.3661i	−0.783567	+	1.35718i	−0.929851	+	0.367936i	$0.880065\pi$
$930$	−31.0680			−1.01876
$931$	−22.0648	−	22.0893i	−0.723143	−	0.723948i
$932$	−50.2047			−1.64451
$933$	−3.22198	+	5.58064i	−0.105483	+	0.182702i
$934$	46.2188	+	80.0533i	1.51232	+	2.61942i
$935$	13.3419	+	23.1088i	0.436325	+	0.755737i
$936$	23.2466	−	40.2642i	0.759838	−	1.31608i
$937$	−55.2717			−1.80565			−0.902824	−	0.430011i	$-0.858510\pi$
$937$	−55.2717			−1.80565			−0.902824	+	0.430011i	$0.858510\pi$
$938$	41.5059	+	54.1227i	1.35522	+	1.76717i
$939$	−31.9752			−1.04347
$940$	−36.8268	+	63.7859i	−1.20116	+	2.08047i
$941$	−4.80951	−	8.33032i	−0.156786	−	0.271561i	0.776922	−	0.629597i	$-0.216780\pi$
$941$	−4.80951	−	8.33032i	−0.156786	−	0.271561i	−0.933708	+	0.358036i	$0.883447\pi$
$942$	23.9640	+	41.5068i	0.780789	+	1.35237i
$943$	2.49484	−	4.32119i	0.0812432	−	0.140717i
$944$	96.0961			3.12766
$945$	5.02294	−	0.659861i	0.163396	−	0.0214653i
$946$	−94.3298			−3.06693
$947$	20.4703	−	35.4556i	0.665195	−	1.15215i	−0.314037	−	0.949411i	$-0.601682\pi$
$947$	20.4703	−	35.4556i	0.665195	−	1.15215i	0.979232	−	0.202741i	$-0.0649849\pi$
$948$	−8.24806	−	14.2861i	−0.267885	−	0.463990i
$949$	9.21110	+	15.9541i	0.299005	+	0.517892i
$950$	8.16590	−	14.1438i	0.264937	−	0.458884i
$951$	14.2714			0.462783
$952$	25.7787	−	62.1862i	0.835491	−	2.01547i
$953$	−40.0752			−1.29816			−0.649081	−	0.760719i	$-0.724846\pi$
$953$	−40.0752			−1.29816			−0.649081	+	0.760719i	$0.724846\pi$
$954$	−1.38979	+	2.40718i	−0.0449960	+	0.0779354i
$955$	−13.2011	−	22.8650i	−0.427177	−	0.739893i
$956$	−79.0600	−	136.936i	−2.55698	−	4.42883i
$957$	23.5849	−	40.8503i	0.762393	−	1.32050i
$958$	89.9746			2.90695
$959$	6.20122	−	14.9593i	0.200248	−	0.483061i
$960$	−63.3633			−2.04504
$961$	−1.95799	+	3.39135i	−0.0631611	+	0.109398i
$962$	−19.1722	−	33.2072i	−0.618136	−	1.07064i
$963$	−5.83004	−	10.0979i	−0.187870	−	0.325401i
$964$	28.7020	−	49.7133i	0.924429	−	1.60116i
$965$	37.4949			1.20700
$966$	7.20294	−	0.946247i	0.231751	−	0.0304450i
$967$	45.8542			1.47457			0.737285	−	0.675582i	$-0.236107\pi$
$967$	45.8542			1.47457			0.737285	+	0.675582i	$0.236107\pi$
$968$	−84.2566	+	145.937i	−2.70811	+	4.69058i
$969$	−5.83803	−	10.1118i	−0.187545	−	0.324837i
$970$	34.7845	+	60.2485i	1.11686	+	1.93446i
$971$	15.3622	−	26.6081i	0.492996	−	0.853893i	−0.506972	−	0.861963i	$-0.669235\pi$
$971$	15.3622	−	26.6081i	0.492996	−	0.853893i	0.999967	+	0.00806927i	$0.00256856\pi$
$972$	5.53968			0.177685
$973$	−21.1421	−	27.5687i	−0.677783	−	0.883813i
$974$	59.7445			1.91434
$975$	−3.18946	+	5.52431i	−0.102145	+	0.176919i
$976$	−17.5108	−	30.3296i	−0.560507	−	0.970826i
$977$	−0.134468	−	0.232905i	−0.00430201	−	0.00745130i	0.863866	−	0.503721i	$-0.168036\pi$
$977$	−0.134468	−	0.232905i	−0.00430201	−	0.00745130i	−0.868168	+	0.496270i	$0.834703\pi$
$978$	16.3360	−	28.2947i	0.522367	−	0.904765i
$979$	−53.6678			−1.71523
$980$	19.2577	−	71.7111i	0.615165	−	2.29073i
$981$	0.884608			0.0282434
$982$	−51.4787	+	89.1637i	−1.64275	+	2.84533i
$983$	4.29742	+	7.44336i	0.137067	+	0.237406i	0.926385	−	0.376578i	$-0.122899\pi$
$983$	4.29742	+	7.44336i	0.137067	+	0.237406i	−0.789318	+	0.613984i	$0.789566\pi$
$984$	−24.2485	−	41.9996i	−0.773013	−	1.33890i
$985$	−18.0771	+	31.3105i	−0.575985	+	0.997635i
$986$	−63.6939			−2.02843
$987$	−11.1795	−	14.5778i	−0.355848	−	0.464017i
$988$	−118.193			−3.76021
$989$	−3.22671	+	5.58882i	−0.102603	+	0.177714i
$990$	13.9944	+	24.2390i	0.444771	+	0.770366i
$991$	−12.1155	−	20.9846i	−0.384861	−	0.666599i	0.606889	−	0.794787i	$-0.292417\pi$
$991$	−12.1155	−	20.9846i	−0.384861	−	0.666599i	−0.991750	+	0.128188i	$0.959084\pi$
$992$	−69.1951	+	119.850i	−2.19695	+	3.80523i
$993$	5.19270			0.164785
$994$	73.6583	−	9.67645i	2.33630	−	0.306918i
$995$	13.4817			0.427400
$996$	6.35568	−	11.0084i	0.201387	−	0.348813i
$997$	18.9978	+	32.9051i	0.601665	+	1.04211i	0.992569	+	0.121683i	$0.0388291\pi$
$997$	18.9978	+	32.9051i	0.601665	+	1.04211i	−0.390904	+	0.920431i	$0.627838\pi$
$998$	−10.4657	−	18.1271i	−0.331286	−	0.573804i
$999$	1.45965	−	2.52818i	0.0461812	−	0.0799881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.g.415.1	yes	16
7.2	even	3		3381.2.a.bf.1.8		8
7.4	even	3	inner	483.2.i.g.277.1	✓	16
7.5	odd	6		3381.2.a.be.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.1	✓	16	7.4	even	3	inner
483.2.i.g.415.1	yes	16	1.1	even	1	trivial
3381.2.a.be.1.8		8	7.5	odd	6
3381.2.a.bf.1.8		8	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37292 + 2.37797i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.76984 - 4.79751i) q^{4} +(0.957403 - 1.65827i) q^{5} +2.74585 q^{6} +(1.61005 + 2.09946i) q^{7} +9.71944 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.62888 + 4.55336i) q^{10} +(-2.66166 - 4.61013i) q^{11} +(-2.76984 + 4.79751i) q^{12} -4.78352 q^{13} +(-7.20294 + 0.946247i) q^{14} -1.91481 q^{15} +(-7.80437 + 13.5176i) q^{16} +(-1.30891 - 2.26709i) q^{17} +(-1.37292 - 2.37797i) q^{18} +(-2.23012 + 3.86268i) q^{19} -10.6074 q^{20} +(1.01317 - 2.44407i) q^{21} +14.6170 q^{22} +(0.500000 - 0.866025i) q^{23} +(-4.85972 - 8.41728i) q^{24} +(0.666760 + 1.15486i) q^{25} +(6.56741 - 11.3751i) q^{26} +1.00000 q^{27} +(5.61262 - 13.5394i) q^{28} -8.86099 q^{29} +(2.62888 - 4.55336i) q^{30} +(-2.95449 - 5.11732i) q^{31} +(-11.7102 - 20.2826i) q^{32} +(-2.66166 + 4.61013i) q^{33} +7.18812 q^{34} +(5.02294 - 0.659861i) q^{35} +5.53968 q^{36} +(1.45965 - 2.52818i) q^{37} +(-6.12357 - 10.6063i) q^{38} +(2.39176 + 4.14265i) q^{39} +(9.30542 - 16.1175i) q^{40} +4.98968 q^{41} +(4.42095 + 5.76481i) q^{42} -6.45341 q^{43} +(-14.7448 + 25.5387i) q^{44} +(0.957403 + 1.65827i) q^{45} +(1.37292 + 2.37797i) q^{46} +(3.47180 - 6.01333i) q^{47} +15.6087 q^{48} +(-1.81550 + 6.76047i) q^{49} -3.66165 q^{50} +(-1.30891 + 2.26709i) q^{51} +(13.2496 + 22.9490i) q^{52} +(-0.506141 - 0.876662i) q^{53} +(-1.37292 + 2.37797i) q^{54} -10.1931 q^{55} +(15.6488 + 20.4056i) q^{56} +4.46024 q^{57} +(12.1655 - 21.0712i) q^{58} +(-3.07828 - 5.33173i) q^{59} +(5.30371 + 9.18629i) q^{60} +(-1.12186 + 1.94312i) q^{61} +16.2252 q^{62} +(-2.62321 + 0.344610i) q^{63} +33.0913 q^{64} +(-4.57975 + 7.93237i) q^{65} +(-7.30852 - 12.6587i) q^{66} +(-4.69424 - 8.13065i) q^{67} +(-7.25093 + 12.5590i) q^{68} -1.00000 q^{69} +(-5.32698 + 12.8504i) q^{70} -10.2261 q^{71} +(-4.85972 + 8.41728i) q^{72} +(-1.92559 - 3.33522i) q^{73} +(4.00797 + 6.94200i) q^{74} +(0.666760 - 1.15486i) q^{75} +24.7083 q^{76} +(5.39340 - 13.0106i) q^{77} -13.1348 q^{78} +(-1.48890 + 2.57886i) q^{79} +(14.9438 + 25.8835i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.85046 + 11.8653i) q^{82} -2.29460 q^{83} +(-14.5318 + 1.90903i) q^{84} -5.01260 q^{85} +(8.86005 - 15.3461i) q^{86} +(4.43049 + 7.67384i) q^{87} +(-25.8698 - 44.8079i) q^{88} +(5.04082 - 8.73095i) q^{89} -5.25777 q^{90} +(-7.70169 - 10.0428i) q^{91} -5.53968 q^{92} +(-2.95449 + 5.11732i) q^{93} +(9.53303 + 16.5117i) q^{94} +(4.27024 + 7.39627i) q^{95} +(-11.7102 + 20.2826i) q^{96} +13.2317 q^{97} +(-13.5837 - 13.5988i) q^{98} +5.32332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19}+ \cdots + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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