LMFDB - Embedded newform 693.2.w.a.428.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(428,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("693.428");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.w (of order $6$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			428.2
Character	$\chi$	$=$	693.428
Dual form			693.2.w.a.659.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36423 - 2.36292i) q^{2} +(-0.653554 + 1.60402i) q^{3} +(-2.72227 + 4.71511i) q^{4} +(3.54289 + 2.04549i) q^{5} +(4.68177 - 0.643954i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.39831 q^{8} +(-2.14573 - 2.09662i) q^{9} +O(q^{10})$	\(q+(-1.36423 - 2.36292i) q^{2} +(-0.653554 + 1.60402i) q^{3} +(-2.72227 + 4.71511i) q^{4} +(3.54289 + 2.04549i) q^{5} +(4.68177 - 0.643954i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.39831 q^{8} +(-2.14573 - 2.09662i) q^{9} -11.1621i q^{10} +(3.21768 - 0.804069i) q^{11} +(-5.78396 - 7.44814i) q^{12} +(3.37529 + 1.94872i) q^{13} +(2.36292 + 1.36423i) q^{14} +(-5.59647 + 4.34602i) q^{15} +(-7.37695 - 12.7773i) q^{16} -2.95665 q^{17} +(-2.02688 + 7.93049i) q^{18} -3.18480i q^{19} +(-19.2894 + 11.1367i) q^{20} +(-0.236013 - 1.71590i) q^{21} +(-6.28962 - 6.50619i) q^{22} +(2.74084 + 1.58242i) q^{23} +(-6.14231 + 15.0750i) q^{24} +(5.86805 + 10.1638i) q^{25} -10.6341i q^{26} +(4.76537 - 2.07153i) q^{27} -5.44454i q^{28} +(1.95812 + 3.39156i) q^{29} +(17.9042 + 7.29504i) q^{30} +(0.471156 - 0.816067i) q^{31} +(-10.7295 + 18.5840i) q^{32} +(-0.813191 + 5.68671i) q^{33} +(4.03356 + 6.98633i) q^{34} -4.09098 q^{35} +(15.7271 - 4.40979i) q^{36} +1.25619 q^{37} +(-7.52544 + 4.34482i) q^{38} +(-5.33172 + 4.14042i) q^{39} +(33.2972 + 19.2241i) q^{40} +(-3.94106 + 6.82612i) q^{41} +(-3.73255 + 2.89856i) q^{42} +(4.80129 - 2.77203i) q^{43} +(-4.96812 + 17.3606i) q^{44} +(-3.31348 - 11.8172i) q^{45} -8.63518i q^{46} +(-1.29618 + 0.748351i) q^{47} +(25.3162 - 3.48212i) q^{48} +(0.500000 - 0.866025i) q^{49} +(16.0108 - 27.7315i) q^{50} +(1.93233 - 4.74251i) q^{51} +(-18.3769 + 10.6099i) q^{52} +1.78594i q^{53} +(-11.3960 - 8.43415i) q^{54} +(13.0446 + 3.73300i) q^{55} +(-8.13917 + 4.69915i) q^{56} +(5.10847 + 2.08144i) q^{57} +(5.34266 - 9.25375i) q^{58} +(-6.63117 - 3.82851i) q^{59} +(-5.25683 - 38.2190i) q^{60} +(-10.4766 + 6.04867i) q^{61} -2.57107 q^{62} +(2.90657 + 0.742862i) q^{63} +29.0422 q^{64} +(7.97219 + 13.8082i) q^{65} +(14.5466 - 5.83650i) q^{66} +(-1.30389 + 2.25841i) q^{67} +(8.04878 - 13.9409i) q^{68} +(-4.32952 + 3.36215i) q^{69} +(5.58105 + 9.66667i) q^{70} +1.01440i q^{71} +(-20.1663 - 19.7047i) q^{72} +5.74751i q^{73} +(-1.71373 - 2.96828i) q^{74} +(-20.1379 + 2.76988i) q^{75} +(15.0167 + 8.66989i) q^{76} +(-2.38456 + 2.30518i) q^{77} +(17.0572 + 6.94994i) q^{78} +(5.95916 - 3.44052i) q^{79} -60.3579i q^{80} +(0.208342 + 8.99759i) q^{81} +21.5061 q^{82} +(-3.13378 - 5.42787i) q^{83} +(8.73312 + 3.55830i) q^{84} +(-10.4751 - 6.04779i) q^{85} +(-13.1002 - 7.56339i) q^{86} +(-6.71984 + 0.924282i) q^{87} +(30.2408 - 7.55689i) q^{88} +10.8283i q^{89} +(-23.4027 + 23.9509i) q^{90} -3.89745 q^{91} +(-14.9226 + 8.61556i) q^{92} +(1.00106 + 1.28909i) q^{93} +(3.53659 + 2.04185i) q^{94} +(6.51448 - 11.2834i) q^{95} +(-22.7967 - 29.3559i) q^{96} +(-8.67456 - 15.0248i) q^{97} -2.72847 q^{98} +(-8.59012 - 5.02095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{3} - 72 q^{4} + 6 q^{5} - 22 q^{9}+O(q^{10}) $ 144 * q + 6 * q^3 - 72 * q^4 + 6 * q^5 - 22 * q^9	$ 144 q + 6 q^{3} - 72 q^{4} + 6 q^{5} - 22 q^{9} + 12 q^{11} - 16 q^{12} + 16 q^{15} - 72 q^{16} - 24 q^{20} - 6 q^{22} + 78 q^{25} - 6 q^{31} + 28 q^{33} - 12 q^{34} + 36 q^{36} + 12 q^{37} - 60 q^{38} + 66 q^{45} - 24 q^{47} - 12 q^{48} + 72 q^{49} - 90 q^{59} - 32 q^{60} + 144 q^{64} - 150 q^{66} + 6 q^{67} - 54 q^{69} - 38 q^{75} + 152 q^{78} - 86 q^{81} - 24 q^{82} + 108 q^{86} + 6 q^{88} - 24 q^{91} - 228 q^{92} + 94 q^{93} - 30 q^{97} - 42 q^{99}+O(q^{100}) $ 144 * q + 6 * q^3 - 72 * q^4 + 6 * q^5 - 22 * q^9 + 12 * q^11 - 16 * q^12 + 16 * q^15 - 72 * q^16 - 24 * q^20 - 6 * q^22 + 78 * q^25 - 6 * q^31 + 28 * q^33 - 12 * q^34 + 36 * q^36 + 12 * q^37 - 60 * q^38 + 66 * q^45 - 24 * q^47 - 12 * q^48 + 72 * q^49 - 90 * q^59 - 32 * q^60 + 144 * q^64 - 150 * q^66 + 6 * q^67 - 54 * q^69 - 38 * q^75 + 152 * q^78 - 86 * q^81 - 24 * q^82 + 108 * q^86 + 6 * q^88 - 24 * q^91 - 228 * q^92 + 94 * q^93 - 30 * q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.36423	−	2.36292i	−0.964659	−	1.67084i	−0.710528	−	0.703669i	$-0.751544\pi$
$2$	−1.36423	−	2.36292i	−0.964659	−	1.67084i	−0.254131	−	0.967170i	$-0.581789\pi$
$3$	−0.653554	+	1.60402i	−0.377330	+	0.926079i
$3$	−0.653554	+	1.60402i	−0.377330	+	0.926079i
$4$	−2.72227	+	4.71511i	−1.36113	+	2.35755i
$5$	3.54289	+	2.04549i	1.58443	+	0.914771i	0.994201	+	0.107534i	$0.0342954\pi$
$5$	3.54289	+	2.04549i	1.58443	+	0.914771i	0.590228	+	0.807237i	$0.299038\pi$
$6$	4.68177	−	0.643954i	1.91132	−	0.262893i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$	9.39831			3.32280
$9$	−2.14573	−	2.09662i	−0.715244	−	0.698874i
$10$		−	11.1621i		−	3.52977i
$11$	3.21768	−	0.804069i	0.970167	−	0.242436i
$11$	3.21768	−	0.804069i	0.970167	−	0.242436i
$12$	−5.78396	−	7.44814i	−1.66968	−	2.15009i
$13$	3.37529	+	1.94872i	0.936137	+	0.540479i	0.888747	−	0.458398i	$-0.151576\pi$
$13$	3.37529	+	1.94872i	0.936137	+	0.540479i	0.0473894	+	0.998876i	$0.484910\pi$
$14$	2.36292	+	1.36423i	0.631518	+	0.364607i
$15$	−5.59647	+	4.34602i	−1.44500	+	1.12214i
$16$	−7.37695	−	12.7773i	−1.84424	−	3.19431i
$17$	−2.95665			−0.717092			−0.358546	−	0.933512i	$-0.616727\pi$
$17$	−2.95665			−0.717092			−0.358546	+	0.933512i	$0.616727\pi$
$18$	−2.02688	+	7.93049i	−0.477739	+	1.86923i
$19$		−	3.18480i		−	0.730644i	−0.930881	−	0.365322i	$-0.880959\pi$
$19$		−	3.18480i		−	0.730644i	0.930881	−	0.365322i	$-0.119041\pi$
$20$	−19.2894	+	11.1367i	−4.31324	+	2.49025i
$21$	−0.236013	−	1.71590i	−0.0515023	−	0.374439i
$22$	−6.28962	−	6.50619i	−1.34095	−	1.38713i
$23$	2.74084	+	1.58242i	0.571504	+	0.329958i	0.757750	−	0.652545i	$-0.226299\pi$
$23$	2.74084	+	1.58242i	0.571504	+	0.329958i	−0.186246	+	0.982503i	$0.559632\pi$
$24$	−6.14231	+	15.0750i	−1.25379	+	3.07718i
$25$	5.86805	+	10.1638i	1.17361	+	2.03275i
$26$		−	10.6341i		−	2.08551i
$27$	4.76537	−	2.07153i	0.917096	−	0.398667i
$28$		−	5.44454i		−	1.02892i
$29$	1.95812	+	3.39156i	0.363613	+	0.629796i	0.988553	−	0.150877i	$-0.0482097\pi$
$29$	1.95812	+	3.39156i	0.363613	+	0.629796i	−0.624940	+	0.780673i	$0.714876\pi$
$30$	17.9042	+	7.29504i	3.26884	+	1.33189i
$31$	0.471156	−	0.816067i	0.0846222	−	0.146570i	−0.820608	−	0.571492i	$-0.806365\pi$
$31$	0.471156	−	0.816067i	0.0846222	−	0.146570i	0.905230	+	0.424922i	$0.139698\pi$
$32$	−10.7295	+	18.5840i	−1.89672	+	3.28522i
$33$	−0.813191	+	5.68671i	−0.141558	+	0.989930i
$34$	4.03356	+	6.98633i	0.691749	+	1.19815i
$35$	−4.09098			−0.691502
$36$	15.7271	−	4.40979i	2.62118	−	0.734965i
$37$	1.25619			0.206516			0.103258	−	0.994655i	$-0.467073\pi$
$37$	1.25619			0.206516			0.103258	+	0.994655i	$0.467073\pi$
$38$	−7.52544	+	4.34482i	−1.22079	+	0.704822i
$39$	−5.33172	+	4.14042i	−0.853758	+	0.662998i
$40$	33.2972	+	19.2241i	5.26475	+	3.03960i
$41$	−3.94106	+	6.82612i	−0.615491	+	1.06606i	0.374807	+	0.927103i	$0.377709\pi$
$41$	−3.94106	+	6.82612i	−0.615491	+	1.06606i	−0.990298	+	0.138959i	$0.955625\pi$
$42$	−3.73255	+	2.89856i	−0.575945	+	0.447258i
$43$	4.80129	−	2.77203i	0.732190	−	0.422730i	−0.0870325	−	0.996205i	$-0.527738\pi$
$43$	4.80129	−	2.77203i	0.732190	−	0.422730i	0.819223	+	0.573475i	$0.194405\pi$
$44$	−4.96812	+	17.3606i	−0.748973	+	2.61721i
$45$	−3.31348	−	11.8172i	−0.493944	−	1.76160i
$46$		−	8.63518i		−	1.27319i
$47$	−1.29618	+	0.748351i	−0.189068	+	0.109158i	−0.591546	−	0.806271i	$-0.701482\pi$
$47$	−1.29618	+	0.748351i	−0.189068	+	0.109158i	0.402478	+	0.915429i	$0.368149\pi$
$48$	25.3162	−	3.48212i	3.65407	−	0.502600i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	16.0108	−	27.7315i	2.26427	−	3.92183i
$51$	1.93233	−	4.74251i	0.270580	−	0.664084i
$52$	−18.3769	+	10.6099i	−2.54841	+	1.47133i
$53$			1.78594i			0.245318i	0.992449	+	0.122659i	$0.0391421\pi$
$53$			1.78594i			0.245318i	−0.992449	+	0.122659i	$0.960858\pi$
$54$	−11.3960	−	8.43415i	−1.55079	−	1.14774i
$55$	13.0446	+	3.73300i	1.75893	+	0.503358i
$56$	−8.13917	+	4.69915i	−1.08764	+	0.627951i
$57$	5.10847	+	2.08144i	0.676634	+	0.275694i
$58$	5.34266	−	9.25375i	0.701525	−	1.21508i
$59$	−6.63117	−	3.82851i	−0.863305	−	0.498429i	0.00181283	−	0.999998i	$-0.499423\pi$
$59$	−6.63117	−	3.82851i	−0.863305	−	0.498429i	−0.865118	+	0.501569i	$0.832756\pi$
$60$	−5.25683	−	38.2190i	−0.678654	−	4.93405i
$61$	−10.4766	+	6.04867i	−1.34139	+	0.774453i	−0.987012	−	0.160649i	$-0.948641\pi$
$61$	−10.4766	+	6.04867i	−1.34139	+	0.774453i	−0.354380	+	0.935102i	$0.615308\pi$
$62$	−2.57107			−0.326526
$63$	2.90657	+	0.742862i	0.366194	+	0.0935919i
$64$	29.0422			3.63028
$65$	7.97219	+	13.8082i	0.988828	+	1.71270i
$66$	14.5466	−	5.83650i	1.79057	−	0.718424i
$67$	−1.30389	+	2.25841i	−0.159296	+	0.275909i	−0.934615	−	0.355661i	$-0.884256\pi$
$67$	−1.30389	+	2.25841i	−0.159296	+	0.275909i	0.775319	+	0.631570i	$0.217589\pi$
$68$	8.04878	−	13.9409i	0.976059	−	1.69058i
$69$	−4.32952	+	3.36215i	−0.521213	+	0.404755i
$70$	5.58105	+	9.66667i	0.667063	+	1.15539i
$71$			1.01440i			0.120387i	0.998187	+	0.0601935i	$0.0191718\pi$
$71$			1.01440i			0.120387i	−0.998187	+	0.0601935i	$0.980828\pi$
$72$	−20.1663	−	19.7047i	−2.37662	−	2.32222i
$73$			5.74751i			0.672696i	0.941738	+	0.336348i	$0.109192\pi$
$73$			5.74751i			0.672696i	−0.941738	+	0.336348i	$0.890808\pi$
$74$	−1.71373	−	2.96828i	−0.199218	−	0.345055i
$75$	−20.1379	+	2.76988i	−2.32533	+	0.319838i
$76$	15.0167	+	8.66989i	1.72253	+	0.994505i
$77$	−2.38456	+	2.30518i	−0.271746	+	0.262700i
$78$	17.0572	+	6.94994i	1.93135	+	0.786925i
$79$	5.95916	−	3.44052i	0.670458	−	0.387089i	−0.125792	−	0.992057i	$-0.540147\pi$
$79$	5.95916	−	3.44052i	0.670458	−	0.387089i	0.796250	+	0.604968i	$0.206814\pi$
$80$		−	60.3579i		−	6.74822i
$81$	0.208342	+	8.99759i	0.0231491	+	0.999732i
$82$	21.5061			2.37495
$83$	−3.13378	−	5.42787i	−0.343978	−	0.595787i	0.641190	−	0.767382i	$-0.278441\pi$
$83$	−3.13378	−	5.42787i	−0.343978	−	0.595787i	−0.985167	+	0.171596i	$0.945108\pi$
$84$	8.73312	+	3.55830i	0.952862	+	0.388242i
$85$	−10.4751	−	6.04779i	−1.13618	−	0.655975i
$86$	−13.1002	−	7.56339i	−1.41263	−	0.815581i
$87$	−6.71984	+	0.924282i	−0.720443	+	0.0990934i
$88$	30.2408	−	7.55689i	3.22368	−	0.805567i
$89$			10.8283i			1.14779i	0.818927	+	0.573897i	$0.194569\pi$
$89$			10.8283i			1.14779i	−0.818927	+	0.573897i	$0.805431\pi$
$90$	−23.4027	+	23.9509i	−2.46686	+	2.52465i
$91$	−3.89745			−0.408563
$92$	−14.9226	+	8.61556i	−1.55579	+	0.898234i
$93$	1.00106	+	1.28909i	0.103805	+	0.133672i
$94$	3.53659	+	2.04185i	0.364772	+	0.210601i
$95$	6.51448	−	11.2834i	0.668372	−	1.15765i
$96$	−22.7967	−	29.3559i	−2.32668	−	2.99612i
$97$	−8.67456	−	15.0248i	−0.880768	−	1.52553i	−0.850489	−	0.525993i	$-0.823694\pi$
$97$	−8.67456	−	15.0248i	−0.880768	−	1.52553i	−0.0302786	−	0.999541i	$-0.509639\pi$
$98$	−2.72847			−0.275617
$99$	−8.59012	−	5.02095i	−0.863339	−	0.504624i
$100$	−63.8977			−6.38977
$101$	0.290373	+	0.502941i	0.0288932	+	0.0500445i	0.880110	−	0.474769i	$-0.157468\pi$
$101$	0.290373	+	0.502941i	0.0288932	+	0.0500445i	−0.851217	+	0.524814i	$0.824135\pi$
$102$	−13.8423	+	1.90395i	−1.37059	+	0.188519i
$103$	0.170235	−	0.294856i	0.0167738	−	0.0290530i	−0.857517	−	0.514456i	$-0.827994\pi$
$103$	0.170235	−	0.294856i	0.0167738	−	0.0290530i	0.874290	+	0.485403i	$0.161327\pi$
$104$	31.7220	+	18.3147i	3.11060	+	1.79590i
$105$	2.67368	−	6.56199i	0.260924	−	0.640385i
$106$	4.22004	−	2.43644i	0.409887	−	0.236648i
$107$	18.0166			1.74173			0.870864	−	0.491524i	$-0.163560\pi$
$107$	18.0166			1.74173			0.870864	+	0.491524i	$0.163560\pi$
$108$	−3.20512	+	28.1085i	−0.308413	+	2.70474i
$109$		−	7.15113i		−	0.684954i	−0.939526	−	0.342477i	$-0.888734\pi$
$109$		−	7.15113i		−	0.684954i	0.939526	−	0.342477i	$-0.111266\pi$
$110$	−8.97510	−	35.9161i	−0.855742	−	3.42447i
$111$	−0.820987	+	2.01495i	−0.0779247	+	0.191250i
$112$	12.7773	+	7.37695i	1.20734	+	0.697057i
$113$	8.64742	+	4.99259i	0.813481	+	0.469663i	0.848163	−	0.529735i	$-0.177709\pi$
$113$	8.64742	+	4.99259i	0.813481	+	0.469663i	−0.0346825	+	0.999398i	$0.511042\pi$
$114$	−2.05087	−	14.9105i	−0.192081	−	1.39650i
$115$	6.47366	+	11.2127i	0.603672	+	1.04559i
$116$	−21.3221			−1.97970
$117$	−3.15673	−	11.2581i	−0.291840	−	1.04082i
$118$			20.8919i			1.92326i
$119$	2.56053	−	1.47832i	0.234723	−	0.135518i
$120$	−52.5973	+	40.8452i	−4.80146	+	3.72864i
$121$	9.70695	−	5.17447i	0.882450	−	0.470407i
$122$	28.5851	+	16.5036i	2.58797	+	1.49417i
$123$	−8.37351	−	10.7828i	−0.755014	−	0.972250i
$124$	2.56523	+	4.44311i	0.230364	+	0.399003i
$125$			27.5573i			2.46480i
$126$	−2.20992	−	7.88144i	−0.196875	−	0.702135i
$127$		−	9.71440i		−	0.862014i	−0.902349	−	0.431007i	$-0.858158\pi$
$127$		−	9.71440i		−	0.862014i	0.902349	−	0.431007i	$-0.141842\pi$
$128$	−18.1615	−	31.4566i	−1.60526	−	2.78039i
$129$	1.30847	+	9.51302i	0.115204	+	0.837575i
$130$	21.7519	−	37.6753i	1.90776	−	3.30434i
$131$	−9.55086	+	16.5426i	−0.834462	+	1.44533i	0.0600050	+	0.998198i	$0.480888\pi$
$131$	−9.55086	+	16.5426i	−0.834462	+	1.44533i	−0.894467	+	0.447133i	$0.852445\pi$
$132$	−24.5997	−	19.3150i	−2.14113	−	1.68116i
$133$	1.59240	+	2.75812i	0.138079	+	0.239159i
$134$	7.11526			0.614665
$135$	21.1205	+	2.40830i	1.81776	+	0.207273i
$136$	−27.7875			−2.38276
$137$	−4.17757	+	2.41192i	−0.356914	+	0.206064i	−0.667726	−	0.744407i	$-0.732732\pi$
$137$	−4.17757	+	2.41192i	−0.356914	+	0.206064i	0.310812	+	0.950471i	$0.399399\pi$
$138$	13.8510	+	5.64356i	1.17907	+	0.480412i
$139$	−2.11373	−	1.22036i	−0.179285	−	0.103510i	0.407672	−	0.913128i	$-0.366341\pi$
$139$	−2.11373	−	1.22036i	−0.179285	−	0.103510i	−0.586956	+	0.809618i	$0.699674\pi$
$140$	11.1367	−	19.2894i	0.941226	−	1.63025i
$141$	−0.353241	−	2.56818i	−0.0297483	−	0.216280i
$142$	2.39694	−	1.38388i	0.201147	−	0.116132i
$143$	12.4275	+	3.55641i	1.03924	+	0.297402i
$144$	−10.9601	+	42.8833i	−0.913344	+	3.57361i
$145$			16.0212i			1.33049i
$146$	13.5809	−	7.84095i	1.12397	−	0.648922i
$147$	1.06234	+	1.36800i	0.0876204	+	0.112831i
$148$	−3.41968	+	5.92306i	−0.281096	+	0.486873i
$149$	−7.33738	+	12.7087i	−0.601101	+	1.04114i	0.391553	+	0.920155i	$0.371938\pi$
$149$	−7.33738	+	12.7087i	−0.601101	+	1.04114i	−0.992655	+	0.120983i	$0.961395\pi$
$150$	34.0179	+	43.8056i	2.77755	+	3.57671i
$151$	1.04898	−	0.605627i	0.0853645	−	0.0492852i	−0.456710	−	0.889616i	$-0.650972\pi$
$151$	1.04898	−	0.605627i	0.0853645	−	0.0492852i	0.542075	+	0.840330i	$0.317639\pi$
$152$		−	29.9318i		−	2.42779i
$153$	6.34417	+	6.19897i	0.512896	+	0.501157i
$154$	8.70007	+	2.48972i	0.701072	+	0.200627i
$155$	3.33851	−	1.92749i	0.268156	−	0.154820i
$156$	−5.00815	−	36.4110i	−0.400973	−	2.91521i
$157$	9.52231	−	16.4931i	0.759963	−	1.31630i	−0.182905	−	0.983131i	$-0.558550\pi$
$157$	9.52231	−	16.4931i	0.759963	−	1.31630i	0.942869	−	0.333165i	$-0.108116\pi$
$158$	−16.2594	−	9.38735i	−1.29353	−	0.746818i
$159$	−2.86468	−	1.16721i	−0.227184	−	0.0925658i
$160$	−76.0267	+	43.8940i	−6.01044	+	3.47013i
$161$	−3.16485			−0.249425
$162$	20.9764	−	12.7671i	1.64806	−	1.00308i
$163$	−1.41694			−0.110983			−0.0554915	−	0.998459i	$-0.517673\pi$
$163$	−1.41694			−0.110983			−0.0554915	+	0.998459i	$0.517673\pi$
$164$	−21.4573	−	37.1651i	−1.67553	−	2.90210i
$165$	−14.5132	+	18.4840i	−1.12985	+	1.43898i
$166$	−8.55043	+	14.8098i	−0.663642	+	1.14946i
$167$	6.94560	−	12.0301i	0.537467	−	0.930920i	−0.461573	−	0.887102i	$-0.652715\pi$
$167$	6.94560	−	12.0301i	0.537467	−	0.930920i	0.999040	−	0.0438177i	$-0.0139521\pi$
$168$	−2.21812	−	16.1265i	−0.171132	−	1.24419i
$169$	1.09505	+	1.89668i	0.0842344	+	0.145898i
$170$			33.0024i			2.53117i
$171$	−6.67733	+	6.83374i	−0.510628	+	0.522589i
$172$			30.1848i			2.30157i
$173$	0.852896	+	1.47726i	0.0648445	+	0.112314i	0.896625	−	0.442791i	$-0.146012\pi$
$173$	0.852896	+	1.47726i	0.0648445	+	0.112314i	−0.831781	+	0.555105i	$0.812678\pi$
$174$	11.3514	+	14.6175i	0.860551	+	1.10815i
$175$	−10.1638	−	5.86805i	−0.768308	−	0.443583i
$176$	−34.0105	−	35.1816i	−2.56364	−	2.65191i
$177$	10.4748	−	8.13436i	0.787335	−	0.611416i
$178$	25.5864	−	14.7723i	1.91778	−	1.10723i
$179$			12.8814i			0.962805i	0.876500	+	0.481402i	$0.159872\pi$
$179$			12.8814i			0.962805i	−0.876500	+	0.481402i	$0.840128\pi$
$180$	64.7395	+	16.5461i	4.82539	+	1.23328i
$181$	−9.23303			−0.686286			−0.343143	−	0.939283i	$-0.611492\pi$
$181$	−9.23303			−0.686286			−0.343143	+	0.939283i	$0.611492\pi$
$182$	5.31703	+	9.20937i	0.394124	+	0.682644i
$183$	−2.85513	−	20.7578i	−0.211057	−	1.53446i
$184$	25.7592	+	14.8721i	1.89900	+	1.09639i
$185$	4.45054	+	2.56952i	0.327210	+	0.188915i
$186$	1.68033	−	4.12404i	0.123208	−	0.302389i
$187$	−9.51355	+	2.37735i	−0.695699	+	0.173849i
$188$		−	8.14885i		−	0.594316i
$189$	−3.09117	+	4.17668i	−0.224849	+	0.303809i
$190$	−35.5491			−2.57900
$191$	−4.27657	+	2.46908i	−0.309442	+	0.178656i	−0.646677	−	0.762764i	$-0.723842\pi$
$191$	−4.27657	+	2.46908i	−0.309442	+	0.178656i	0.337235	+	0.941421i	$0.390508\pi$
$192$	−18.9807	+	46.5842i	−1.36981	+	3.36193i
$193$	18.1193	+	10.4612i	1.30426	+	0.753013i	0.981131	−	0.193343i	$-0.0619330\pi$
$193$	18.1193	+	10.4612i	1.30426	+	0.753013i	0.323126	+	0.946356i	$0.395266\pi$
$194$	−23.6682	+	40.9946i	−1.69928	+	2.94324i
$195$	−27.3589	+	3.76308i	−1.95921	+	0.269480i
$196$	2.72227	+	4.71511i	0.194448	+	0.336793i
$197$	22.5531			1.60684			0.803422	−	0.595410i	$-0.203010\pi$
$197$	22.5531			1.60684			0.803422	+	0.595410i	$0.203010\pi$
$198$	−0.145185	+	27.1475i	−0.0103179	+	1.92929i
$199$	−4.16933			−0.295556			−0.147778	−	0.989021i	$-0.547212\pi$
$199$	−4.16933			−0.295556			−0.147778	+	0.989021i	$0.547212\pi$
$200$	55.1498	+	95.5222i	3.89968	+	6.75444i
$201$	−2.77036	−	3.56746i	−0.195406	−	0.251629i
$202$	0.792274	−	1.37226i	0.0557442	−	0.0965518i
$203$	−3.39156	−	1.95812i	−0.238041	−	0.137433i
$204$	17.1011	+	22.0215i	1.19732	+	1.54181i
$205$	−27.9255	+	16.1228i	−1.95040	+	1.12607i
$206$	−0.928963			−0.0647239
$207$	−2.56336	−	9.14196i	−0.178166	−	0.635410i
$208$		−	57.5026i		−	3.98709i
$209$	−2.56080	−	10.2477i	−0.177134	−	0.708847i
$210$	−19.1530	+	2.63440i	−1.32168	+	0.181791i
$211$	−24.1672	−	13.9529i	−1.66374	−	0.960560i	−0.970906	−	0.239462i	$-0.923029\pi$
$211$	−24.1672	−	13.9529i	−1.66374	−	0.960560i	−0.692833	−	0.721098i	$-0.743638\pi$
$212$	−8.42090	−	4.86181i	−0.578350	−	0.333911i
$213$	−1.62711	−	0.662964i	−0.111488	−	0.0454256i
$214$	−24.5788	−	42.5718i	−1.68017	−	2.91015i
$215$	22.6806			1.54681
$216$	44.7864	−	19.4689i	3.04733	−	1.32469i
$217$			0.942313i			0.0639683i
$218$	−16.8976	+	9.75581i	−1.14445	+	0.660747i
$219$	−9.21910	−	3.75631i	−0.622969	−	0.253828i
$220$	−53.1124	+	51.3445i	−3.58084	+	3.46165i
$221$	−9.97953	−	5.76169i	−0.671296	−	0.387573i
$222$	5.88118	−	0.808928i	0.394719	−	0.0542917i
$223$	−4.93751	−	8.55202i	−0.330640	−	0.572686i	0.651997	−	0.758221i	$-0.273931\pi$
$223$	−4.93751	−	8.55202i	−0.330640	−	0.572686i	−0.982638	+	0.185536i	$0.940598\pi$
$224$		−	21.4589i		−	1.43379i
$225$	8.71831	−	34.1118i	0.581221	−	2.27412i
$226$		−	27.2442i		−	1.81226i
$227$	−2.25865	−	3.91210i	−0.149912	−	0.259655i	0.781283	−	0.624177i	$-0.214566\pi$
$227$	−2.25865	−	3.91210i	−0.149912	−	0.259655i	−0.931195	+	0.364522i	$0.881232\pi$
$228$	−23.7209	+	18.4208i	−1.57095	+	1.21994i
$229$	14.4148	−	24.9672i	0.952560	−	1.64988i	0.212704	−	0.977117i	$-0.431773\pi$
$229$	14.4148	−	24.9672i	0.952560	−	1.64988i	0.739856	−	0.672766i	$-0.234894\pi$
$230$	17.6632	−	30.5935i	1.16468	−	2.01728i
$231$	−2.13911	−	5.33143i	−0.140743	−	0.350783i
$232$	18.4030	+	31.8749i	1.20821	+	2.09269i
$233$	−11.8685			−0.777533			−0.388767	−	0.921336i	$-0.627099\pi$
$233$	−11.8685			−0.777533			−0.388767	+	0.921336i	$0.627099\pi$
$234$	−22.2956	+	22.8179i	−1.45751	+	1.49165i
$235$	−6.12298			−0.399419
$236$	36.1036	−	20.8445i	2.35015	−	1.35686i
$237$	1.62402	+	11.8072i	0.105491	+	0.766957i
$238$	−6.98633	−	4.03356i	−0.452856	−	0.261457i
$239$	−5.05114	+	8.74883i	−0.326731	+	0.565915i	−0.981861	−	0.189601i	$-0.939280\pi$
$239$	−5.05114	+	8.74883i	−0.326731	+	0.565915i	0.655130	+	0.755516i	$0.272614\pi$
$240$	96.8151	+	39.4472i	6.24939	+	2.54631i
$241$	2.42996	−	1.40294i	0.156527	−	0.0903711i	−0.419690	−	0.907667i	$-0.637861\pi$
$241$	2.42996	−	1.40294i	0.156527	−	0.0903711i	0.576218	+	0.817296i	$0.304528\pi$
$242$	−25.4694	−	15.8776i	−1.63724	−	1.02065i
$243$	−14.5684	−	5.54623i	−0.934566	−	0.355791i
$244$		−	65.8644i		−	4.21654i
$245$	3.54289	−	2.04549i	0.226347	−	0.130682i
$246$	−14.0554	+	34.4962i	−0.896141	+	2.19940i
$247$	6.20630	−	10.7496i	0.394897	−	0.683983i
$248$	4.42807	−	7.66965i	0.281183	−	0.487023i
$249$	10.7545	−	1.47923i	0.681538	−	0.0937423i
$250$	65.1157	−	37.5946i	4.11828	−	2.37769i
$251$		−	20.7317i		−	1.30858i	−0.756245	−	0.654288i	$-0.772968\pi$
$251$		−	20.7317i		−	1.30858i	0.756245	−	0.654288i	$-0.227032\pi$
$252$	−11.4151	+	11.6825i	−0.719086	+	0.735930i
$253$	10.0915	+	2.88791i	0.634448	+	0.181561i
$254$	−22.9544	+	13.2527i	−1.44029	+	0.831549i
$255$	16.5468	−	12.8496i	1.03620	−	0.804675i
$256$	−20.5107	+	35.5256i	−1.28192	+	2.22035i
$257$	2.73306	+	1.57793i	0.170483	+	0.0984287i	0.582814	−	0.812606i	$-0.301952\pi$
$257$	2.73306	+	1.57793i	0.170483	+	0.0984287i	−0.412330	+	0.911034i	$0.635285\pi$
$258$	20.6935	−	16.0698i	1.28832	−	1.00046i
$259$	−1.08789	+	0.628094i	−0.0675982	+	0.0390279i
$260$	−86.8097			−5.38371
$261$	2.90922	−	11.3828i	0.180076	−	0.704578i
$262$	52.1184			3.21989
$263$	−7.74608	−	13.4166i	−0.477644	−	0.827303i	0.522028	−	0.852928i	$-0.325176\pi$
$263$	−7.74608	−	13.4166i	−0.477644	−	0.827303i	−0.999672	+	0.0256252i	$0.991842\pi$
$264$	−7.64262	+	53.4455i	−0.470371	+	3.28934i
$265$	−3.65312	+	6.32740i	−0.224410	+	0.388689i
$266$	4.34482	−	7.52544i	0.266398	−	0.461415i
$267$	−17.3687	−	7.07687i	−1.06295	−	0.433097i
$268$	−7.09909	−	12.2960i	−0.433646	−	0.751097i
$269$		−	13.2413i		−	0.807334i	−0.914906	−	0.403667i	$-0.867735\pi$
$269$		−	13.2413i		−	0.807334i	0.914906	−	0.403667i	$-0.132265\pi$
$270$	−23.1227	−	53.1916i	−1.40720	−	3.23714i
$271$		−	12.1461i		−	0.737822i	−0.929465	−	0.368911i	$-0.879731\pi$
$271$		−	12.1461i		−	0.737822i	0.929465	−	0.368911i	$-0.120269\pi$
$272$	21.8110	+	37.7778i	1.32249	+	2.29062i
$273$	2.54719	−	6.25157i	0.154163	−	0.378362i
$274$	11.3984	+	6.58085i	0.688601	+	0.397564i
$275$	27.0539	+	27.9854i	1.63141	+	1.68759i
$276$	−4.06677	−	29.5668i	−0.244791	−	1.77971i
$277$	−15.4570	+	8.92411i	−0.928722	+	0.536198i	−0.886407	−	0.462907i	$-0.846807\pi$
$277$	−15.4570	+	8.92411i	−0.928722	+	0.536198i	−0.0423147	+	0.999104i	$0.513473\pi$
$278$			6.65945i			0.399407i
$279$	−2.72196	+	0.763224i	−0.162959	+	0.0456930i
$280$	−38.4483			−2.29772
$281$	−4.46862	−	7.73988i	−0.266575	−	0.461722i	0.701400	−	0.712768i	$-0.252559\pi$
$281$	−4.46862	−	7.73988i	−0.266575	−	0.461722i	−0.967975	+	0.251046i	$0.919225\pi$
$282$	−5.58652	+	4.33829i	−0.332672	+	0.258341i
$283$	−4.86596	−	2.80937i	−0.289252	−	0.166999i	0.348353	−	0.937364i	$-0.386741\pi$
$283$	−4.86596	−	2.80937i	−0.289252	−	0.166999i	−0.637604	+	0.770364i	$0.720074\pi$
$284$	−4.78300	−	2.76146i	−0.283819	−	0.163863i
$285$	13.8412	+	17.8237i	0.819882	+	1.05578i
$286$	−8.55052	−	34.2170i	−0.505603	−	2.02329i
$287$		−	7.88213i		−	0.465267i
$288$	61.9862	−	17.3806i	3.65257	−	1.02416i
$289$	−8.25824			−0.485779
$290$	37.8569	−	21.8567i	2.22303	−	1.28347i
$291$	29.7693	−	4.09462i	1.74511	−	0.240031i
$292$	−27.1001	−	15.6463i	−1.58592	−	0.915629i
$293$	9.84487	−	17.0518i	0.575143	−	0.996177i	−0.420883	−	0.907115i	$-0.638280\pi$
$293$	9.84487	−	17.0518i	0.575143	−	0.996177i	0.996026	−	0.0890623i	$-0.0283870\pi$
$294$	1.78320	−	4.37651i	0.103998	−	0.255243i
$295$	−15.6623	−	27.1280i	−0.911897	−	1.57945i
$296$	11.8060			0.686212
$297$	13.6678	−	10.4972i	0.793086	−	0.609110i
$298$	40.0396			2.31943
$299$	6.16741	+	10.6823i	0.356671	+	0.617772i
$300$	41.7606	−	102.493i	2.41105	−	5.91743i
$301$	−2.77203	+	4.80129i	−0.159777	+	0.276742i
$302$	−2.86210	−	1.65243i	−0.164695	−	0.0950869i
$303$	−0.996500	+	0.137064i	−0.0572474	+	0.00787411i
$304$	−40.6931	+	23.4941i	−2.33391	+	1.34748i
$305$	−49.4899			−2.83379
$306$	5.99276	−	23.4476i	0.342583	−	1.34041i
$307$		−	3.39255i		−	0.193623i	−0.995303	−	0.0968116i	$-0.969136\pi$
$307$		−	3.39255i		−	0.193623i	0.995303	−	0.0968116i	$-0.0308644\pi$
$308$	−4.37778	−	17.5188i	−0.249447	−	0.998225i
$309$	0.361696	+	0.465765i	0.0205762	+	0.0264964i
$310$	−9.10902	−	5.25910i	−0.517358	−	0.298697i
$311$	−11.9574	−	6.90363i	−0.678044	−	0.391469i	0.121074	−	0.992643i	$-0.461366\pi$
$311$	−11.9574	−	6.90363i	−0.678044	−	0.391469i	−0.799118	+	0.601175i	$0.794700\pi$
$312$	−50.1091	+	38.9129i	−2.83687	+	2.20301i
$313$	6.11482	+	10.5912i	0.345630	+	0.598649i	0.985468	−	0.169861i	$-0.0543319\pi$
$313$	6.11482	+	10.5912i	0.345630	+	0.598649i	−0.639838	+	0.768510i	$0.720999\pi$
$314$	−51.9627			−2.93242
$315$	8.77815	+	8.57724i	0.494593	+	0.483273i
$316$			37.4641i			2.10752i
$317$	10.5245	−	6.07632i	0.591114	−	0.341280i	−0.174424	−	0.984671i	$-0.555806\pi$
$317$	10.5245	−	6.07632i	0.591114	−	0.341280i	0.765538	+	0.643391i	$0.222473\pi$
$318$	1.15006	+	8.36136i	0.0644924	+	0.468882i
$319$	9.02764	+	9.33849i	0.505451	+	0.522855i
$320$	102.893	+	59.4056i	5.75192	+	3.32087i
$321$	−11.7748	+	28.8989i	−0.657206	+	1.61298i
$322$	4.31759	+	7.47829i	0.240610	+	0.416749i
$323$			9.41634i			0.523939i
$324$	−42.9918	−	23.5115i	−2.38843	−	1.30619i
$325$			45.7409i			2.53725i
$326$	1.93303	+	3.34811i	0.107061	+	0.185435i
$327$	11.4705	+	4.67365i	0.634321	+	0.258454i
$328$	−37.0393	+	64.1540i	−2.04515	+	3.54231i
$329$	0.748351	−	1.29618i	0.0412579	−	0.0714608i
$330$	63.4757	+	9.07692i	3.49422	+	0.499668i
$331$	11.5117	+	19.9388i	0.632739	+	1.09594i	0.986989	+	0.160786i	$0.0514029\pi$
$331$	11.5117	+	19.9388i	0.632739	+	1.09594i	−0.354250	+	0.935151i	$0.615264\pi$
$332$	34.1240			1.87280
$333$	−2.69544	−	2.63375i	−0.147709	−	0.144329i
$334$	−37.9017			−2.07389
$335$	−9.23910	+	5.33420i	−0.504786	+	0.291438i
$336$	−20.1834	+	15.6737i	−1.10109	+	0.855070i
$337$	−16.2041	−	9.35543i	−0.882693	−	0.509623i	−0.0111473	−	0.999938i	$-0.503548\pi$
$337$	−16.2041	−	9.35543i	−0.882693	−	0.509623i	−0.871545	+	0.490315i	$0.836882\pi$
$338$	2.98780	−	5.17502i	0.162515	−	0.281484i
$339$	−13.6598	+	10.6077i	−0.741896	+	0.576129i
$340$	57.0319	−	32.9274i	3.09299	−	1.78574i
$341$	0.859857	−	3.00468i	0.0465639	−	0.162713i
$342$	25.2570	+	6.45520i	1.36574	+	0.349057i
$343$			1.00000i			0.0539949i
$344$	45.1240	−	26.0524i	2.43293	−	1.40465i
$345$	−22.2162	+	3.05574i	−1.19608	+	0.164515i
$346$	2.32710	−	4.03065i	0.125106	−	0.216689i
$347$	2.79049	−	4.83326i	0.149801	−	0.259463i	−0.781353	−	0.624090i	$-0.785470\pi$
$347$	2.79049	−	4.83326i	0.149801	−	0.259463i	0.931154	+	0.364627i	$0.118803\pi$
$348$	13.9351	−	34.2009i	0.747001	−	1.83336i
$349$	−8.49043	+	4.90195i	−0.454483	+	0.262396i	−0.709721	−	0.704482i	$-0.751179\pi$
$349$	−8.49043	+	4.90195i	−0.454483	+	0.262396i	0.255239	+	0.966878i	$0.417846\pi$
$350$			32.0216i			1.71163i
$351$	20.1213	+	2.29437i	1.07400	+	0.122464i
$352$	−19.5812	+	68.4246i	−1.04368	+	3.64704i
$353$	−8.79190	+	5.07601i	−0.467946	+	0.270169i	−0.715379	−	0.698736i	$-0.753746\pi$
$353$	−8.79190	+	5.07601i	−0.467946	+	0.270169i	0.247434	+	0.968905i	$0.420413\pi$
$354$	−33.5110	−	13.6540i	−1.78109	−	0.725702i
$355$	−2.07494	+	3.59390i	−0.110126	+	0.190745i
$356$	−51.0565	−	29.4775i	−2.70599	−	1.56230i
$357$	0.697807	+	5.07330i	0.0369319	+	0.268507i
$358$	30.4379	−	17.5733i	1.60869	−	0.928778i
$359$	35.9919			1.89958			0.949790	−	0.312888i	$-0.101296\pi$
$359$	35.9919			1.89958			0.949790	+	0.312888i	$0.101296\pi$
$360$	−31.1411	−	111.062i	−1.64128	−	5.85346i
$361$	8.85703			0.466159
$362$	12.5960	+	21.8169i	0.662032	+	1.14667i
$363$	1.95592	+	18.9519i	0.102659	+	0.994717i
$364$	10.6099	−	18.3769i	0.556110	−	0.963210i
$365$	−11.7565	+	20.3628i	−0.615362	+	1.06584i
$366$	−45.1539	+	35.0649i	−2.36023	+	1.83287i
$367$	10.0411	+	17.3916i	0.524139	+	0.907835i	0.999605	+	0.0281012i	$0.00894606\pi$
$367$	10.0411	+	17.3916i	0.524139	+	0.907835i	−0.475466	+	0.879734i	$0.657721\pi$
$368$		−	46.6939i		−	2.43409i
$369$	22.7683	−	6.38411i	1.18527	−	0.332344i
$370$		−	14.0217i		−	0.728954i
$371$	−0.892971	−	1.54667i	−0.0463607	−	0.0802991i
$372$	−8.80333	+	1.21085i	−0.456431	+	0.0627799i
$373$	−25.1559	−	14.5237i	−1.30252	−	0.752011i	−0.321686	−	0.946847i	$-0.604249\pi$
$373$	−25.1559	−	14.5237i	−1.30252	−	0.752011i	−0.980836	+	0.194835i	$0.937583\pi$
$374$	18.5962	+	19.2365i	0.961586	+	0.994696i
$375$	−44.2023	−	18.0102i	−2.28260	−	0.930041i
$376$	−12.1819	+	7.03323i	−0.628234	+	0.362711i
$377$			15.2633i			0.786100i
$378$	14.0863	+	1.60621i	0.724519	+	0.0826145i
$379$	9.64108			0.495229			0.247614	−	0.968859i	$-0.420353\pi$
$379$	9.64108			0.495229			0.247614	+	0.968859i	$0.420353\pi$
$380$	35.4683	+	61.4330i	1.81949	+	3.15144i
$381$	15.5821	+	6.34889i	0.798293	+	0.325263i
$382$	11.6685	+	6.73681i	0.597012	+	0.344685i
$383$	11.0233	+	6.36433i	0.563266	+	0.325202i	0.754455	−	0.656351i	$-0.227901\pi$
$383$	11.0233	+	6.36433i	0.563266	+	0.325202i	−0.191189	+	0.981553i	$0.561234\pi$
$384$	62.3263	−	8.57268i	3.18058	−	0.437473i
$385$	−13.1635	+	3.28943i	−0.670872	+	0.167645i
$386$		−	57.0861i		−	2.90560i
$387$	−16.1142	−	4.11847i	−0.819131	−	0.209354i
$388$	94.4579			4.79537
$389$	17.4072	−	10.0501i	0.882580	−	0.509558i	0.0110719	−	0.999939i	$-0.496476\pi$
$389$	17.4072	−	10.0501i	0.882580	−	0.509558i	0.871508	+	0.490381i	$0.163142\pi$
$390$	46.2158	+	59.5132i	2.34023	+	3.01357i
$391$	−8.10369	−	4.67867i	−0.409821	−	0.236610i
$392$	4.69915	−	8.13917i	0.237343	−	0.411090i
$393$	−20.2925	−	26.1312i	−1.02362	−	1.31814i
$394$	−30.7678	−	53.2913i	−1.55006	−	2.68478i
$395$	28.1502			1.41639
$396$	47.0589	−	26.8349i	2.36480	−	1.34851i
$397$	33.5415			1.68340			0.841700	−	0.539945i	$-0.181555\pi$
$397$	33.5415			1.68340			0.841700	+	0.539945i	$0.181555\pi$
$398$	5.68794	+	9.85181i	0.285111	+	0.493827i
$399$	−5.46479	+	0.751655i	−0.273582	+	0.0376298i
$400$	86.5767	−	149.955i	4.32884	−	7.49776i
$401$	−21.6614	−	12.5062i	−1.08172	−	0.624531i	−0.150360	−	0.988631i	$-0.548043\pi$
$401$	−21.6614	−	12.5062i	−1.08172	−	0.624531i	−0.931360	+	0.364100i	$0.881376\pi$
$402$	−4.65021	+	11.4130i	−0.231931	+	0.569228i
$403$	3.18058	−	1.83631i	0.158436	−	0.0914730i
$404$	−3.16189			−0.157310
$405$	−17.6663	+	32.3036i	−0.877847	+	1.60518i
$406$			10.6853i			0.530303i
$407$	4.04201	−	1.01006i	0.200355	−	0.0500669i
$408$	18.1606	−	44.5715i	0.899085	−	2.20662i
$409$	10.9612	+	6.32842i	0.541994	+	0.312920i	0.745887	−	0.666073i	$-0.232026\pi$
$409$	10.9612	+	6.32842i	0.541994	+	0.312920i	−0.203893	+	0.978993i	$0.565359\pi$
$410$	76.1939	+	43.9906i	3.76295	+	2.17254i
$411$	−1.13849	−	8.27722i	−0.0561576	−	0.408285i
$412$	0.926853	+	1.60536i	0.0456627	+	0.0790902i
$413$	7.65702			0.376777
$414$	−18.1047	+	18.5288i	−0.889799	+	0.910641i
$415$		−	25.6405i		−	1.25864i
$416$	−72.4301	+	41.8176i	−3.55118	+	2.05027i
$417$	3.33892	−	2.59289i	0.163508	−	0.126974i
$418$	−20.7209	+	20.0312i	−1.01349	+	0.979759i
$419$	−33.8807	−	19.5610i	−1.65518	−	0.955620i	−0.974892	−	0.222676i	$-0.928521\pi$
$419$	−33.8807	−	19.5610i	−1.65518	−	0.955620i	−0.680290	−	0.732943i	$-0.738146\pi$
$420$	23.6620	+	30.4702i	1.15459	+	1.48679i
$421$	0.0930595	+	0.161184i	0.00453544	+	0.00785561i	0.868284	−	0.496067i	$-0.165223\pi$
$421$	0.0930595	+	0.161184i	0.00453544	+	0.00785561i	−0.863749	+	0.503923i	$0.831890\pi$
$422$			76.1403i			3.70645i
$423$	4.35027	+	1.11184i	0.211517	+	0.0540597i
$424$			16.7848i			0.815143i
$425$	−17.3498	−	30.0507i	−0.841587	−	1.45767i
$426$	0.653226	+	4.74918i	0.0316489	+	0.230098i
$427$	6.04867	−	10.4766i	0.292716	−	0.506998i
$428$	−49.0459	+	84.9501i	−2.37073	+	4.10622i
$429$	−13.8266	+	17.6096i	−0.667554	+	0.850200i
$430$	−30.9417	−	53.5925i	−1.49214	−	2.58446i
$431$	27.7226			1.33535			0.667675	−	0.744453i	$-0.267290\pi$
$431$	27.7226			1.33535			0.667675	+	0.744453i	$0.267290\pi$
$432$	−61.6224	−	45.6068i	−2.96481	−	2.19426i
$433$	32.9705			1.58446			0.792231	−	0.610222i	$-0.208920\pi$
$433$	32.9705			1.58446			0.792231	+	0.610222i	$0.208920\pi$
$434$	2.22661	−	1.28553i	0.106881	−	0.0617076i
$435$	−25.6983	−	10.4707i	−1.23214	−	0.502033i
$436$	33.7183	+	19.4673i	1.61482	+	0.932314i
$437$	5.03971	−	8.72903i	0.241082	−	0.417566i
$438$	3.70114	+	26.9085i	0.176847	+	1.28574i
$439$	−8.56111	+	4.94276i	−0.408599	+	0.235905i	−0.690188	−	0.723630i	$-0.742472\pi$
$439$	−8.56111	+	4.94276i	−0.408599	+	0.235905i	0.281588	+	0.959535i	$0.409139\pi$
$440$	122.597	+	35.0839i	5.84460	+	1.67256i
$441$	−2.88860	+	0.809948i	−0.137552	+	0.0385689i
$442$			31.4412i			1.49550i
$443$	31.3341	−	18.0907i	1.48873	−	0.859517i	0.488810	−	0.872390i	$-0.337431\pi$
$443$	31.3341	−	18.0907i	1.48873	−	0.859517i	0.999917	+	0.0128735i	$0.00409788\pi$
$444$	−7.26574	−	9.35627i	−0.344817	−	0.444029i
$445$	−22.1491	+	38.3634i	−1.04997	+	1.81860i
$446$	−13.4718	+	23.3339i	−0.637910	+	1.10489i
$447$	−15.5896	−	20.0751i	−0.737363	−	0.949520i
$448$	−25.1513	+	14.5211i	−1.18829	+	0.686058i
$449$			17.5997i			0.830581i	0.909689	+	0.415290i	$0.136320\pi$
$449$			17.5997i			0.830581i	−0.909689	+	0.415290i	$0.863680\pi$
$450$	−92.4974	+	25.9358i	−4.36037	+	1.22263i
$451$	−7.19241	+	25.1332i	−0.338678	+	1.18347i
$452$	−47.0812	+	27.1823i	−2.21451	+	1.27855i
$453$	0.285872	+	2.07838i	0.0134314	+	0.0976510i
$454$	−6.16266	+	10.6740i	−0.289228	+	0.500957i
$455$	−13.8082	−	7.97219i	−0.647340	−	0.373742i
$456$	48.0110	+	19.5620i	2.24832	+	0.916076i
$457$	29.0259	−	16.7581i	1.35777	−	0.783910i	0.368449	−	0.929648i	$-0.379889\pi$
$457$	29.0259	−	16.7581i	1.35777	−	0.783910i	0.989323	+	0.145738i	$0.0465555\pi$
$458$	−78.6609			−3.67558
$459$	−14.0895	+	6.12479i	−0.657642	+	0.285881i
$460$	−70.4922			−3.28671
$461$	1.57490	+	2.72781i	0.0733504	+	0.127047i	0.900368	−	0.435130i	$-0.143298\pi$
$461$	1.57490	+	2.72781i	0.0733504	+	0.127047i	−0.827017	+	0.562176i	$0.809964\pi$
$462$	−9.67952	+	12.3279i	−0.450332	+	0.573545i
$463$	1.08358	−	1.87681i	0.0503580	−	0.0872226i	−0.839748	−	0.542977i	$-0.817297\pi$
$463$	1.08358	−	1.87681i	0.0503580	−	0.0872226i	0.890106	+	0.455754i	$0.150630\pi$
$464$	28.8899	−	50.0387i	1.34118	−	2.32299i
$465$	0.909826	+	6.61474i	0.0421922	+	0.306751i
$466$	16.1915	+	28.0444i	0.750054	+	1.29913i
$467$		−	1.80493i		−	0.0835223i	−0.999128	−	0.0417612i	$-0.986703\pi$
$467$		−	1.80493i		−	0.0835223i	0.999128	−	0.0417612i	$-0.0132969\pi$
$468$	61.6768	+	15.7634i	2.85101	+	0.728663i
$469$		−	2.60779i		−	0.120416i
$470$	8.35317	+	14.4681i	0.385303	+	0.667365i
$471$	20.2319	+	26.0531i	0.932236	+	1.20046i
$472$	−62.3218	−	35.9815i	−2.86859	−	1.65618i
$473$	13.2201	−	12.7801i	0.607862	−	0.587628i
$474$	25.6838	−	19.9451i	1.17970	−	0.916111i
$475$	32.3696	−	18.6886i	1.48522	−	0.857491i
$476$			16.0976i			0.737831i
$477$	3.74445	−	3.83215i	0.171446	−	0.175462i
$478$	27.5637			1.26074
$479$	−7.71761	−	13.3673i	−0.352627	−	0.610767i	0.634082	−	0.773266i	$-0.281378\pi$
$479$	−7.71761	−	13.3673i	−0.352627	−	0.610767i	−0.986709	+	0.162498i	$0.948045\pi$
$480$	−20.7191	−	150.635i	−0.945695	−	6.87553i
$481$	4.24000	+	2.44796i	0.193327	+	0.111618i
$482$	−6.63006	−	3.82787i	−0.301991	−	0.174355i
$483$	2.06840	−	5.07646i	0.0941154	−	0.230987i
$484$	−2.02671	+	59.8556i	−0.0921233	+	2.72071i
$485$		−	70.9748i		−	3.22280i
$486$	6.76944	+	41.9904i	0.307068	+	1.90473i
$487$	−29.4669			−1.33527			−0.667637	−	0.744487i	$-0.732694\pi$
$487$	−29.4669			−1.33527			−0.667637	+	0.744487i	$0.732694\pi$
$488$	−98.4623	+	56.8472i	−4.45718	+	2.57335i
$489$	0.926045	−	2.27279i	0.0418772	−	0.102779i
$490$	−9.66667	−	5.58105i	−0.436695	−	0.252126i
$491$	16.4954	−	28.5709i	0.744428	−	1.28939i	−0.206034	−	0.978545i	$-0.566056\pi$
$491$	16.4954	−	28.5709i	0.744428	−	1.28939i	0.950462	−	0.310842i	$-0.100611\pi$
$492$	73.6369	−	10.1284i	3.31981	−	0.456623i
$493$	−5.78946	−	10.0276i	−0.260744	−	0.451622i
$494$	−33.8674			−1.52377
$495$	−20.1635	−	35.3597i	−0.906284	−	1.58930i
$496$	−13.9028			−0.624254
$497$	−0.507199	−	0.878495i	−0.0227510	−	0.0394059i
$498$	−18.1670	−	23.3940i	−0.814081	−	1.04831i
$499$	2.41029	−	4.17475i	0.107900	−	0.186887i	−0.807020	−	0.590525i	$-0.798921\pi$
$499$	2.41029	−	4.17475i	0.107900	−	0.186887i	0.914919	+	0.403637i	$0.132254\pi$
$500$	−129.935	−	75.0183i	−5.81089	−	3.35492i
$501$	14.7572	+	19.0032i	0.659303	+	0.849001i
$502$	−48.9875	+	28.2829i	−2.18642	+	1.26233i
$503$	18.9727			0.845951			0.422975	−	0.906141i	$-0.360986\pi$
$503$	18.9727			0.845951			0.422975	+	0.906141i	$0.360986\pi$
$504$	27.3169	+	6.98165i	1.21679	+	0.310987i
$505$			2.37582i			0.105723i
$506$	−6.94328	−	27.7853i	−0.308666	−	1.23521i
$507$	−3.75797	+	0.516891i	−0.166897	+	0.0229559i
$508$	45.8044	+	26.4452i	2.03224	+	1.17332i
$509$	−17.8400	−	10.2999i	−0.790743	−	0.456536i	0.0494812	−	0.998775i	$-0.484243\pi$
$509$	−17.8400	−	10.2999i	−0.790743	−	0.456536i	−0.840224	+	0.542240i	$0.817577\pi$
$510$	−52.9364	−	21.5689i	−2.34406	−	0.955085i
$511$	−2.87376	−	4.97749i	−0.127128	−	0.220191i
$512$	39.2798			1.73594
$513$	−6.59742	−	15.1768i	−0.291283	−	0.670071i
$514$		−	8.61067i		−	0.379801i
$515$	1.20625	−	0.696429i	0.0531538	−	0.0306883i
$516$	−48.4169	−	19.7274i	−2.13144	−	0.868451i
$517$	−3.56898	+	3.45017i	−0.156963	+	0.151739i
$518$	2.96828	+	1.71373i	0.130419	+	0.0752972i
$519$	−2.92696	+	0.402589i	−0.128479	+	0.0176717i
$520$	74.9251	+	129.774i	3.28568	+	5.69097i
$521$			27.1096i			1.18769i	0.804579	+	0.593846i	$0.202391\pi$
$521$			27.1096i			1.18769i	−0.804579	+	0.593846i	$0.797609\pi$
$522$	−30.8655	+	8.65455i	−1.35095	+	0.378799i
$523$			6.35707i			0.277975i	0.990294	+	0.138988i	$0.0443848\pi$
$523$			6.35707i			0.277975i	−0.990294	+	0.138988i	$0.955615\pi$
$524$	−52.0000	−	90.0666i	−2.27163	−	3.93458i
$525$	16.0550	−	12.4677i	0.700699	−	0.544137i
$526$	−21.1349	+	36.6068i	−0.921527	+	1.59613i
$527$	−1.39304	+	2.41282i	−0.0606819	+	0.105104i
$528$	78.6595	−	31.5603i	3.42322	−	1.37348i
$529$	−6.49187	−	11.2443i	−0.282255	−	0.488881i
$530$	19.9349			0.865915
$531$	6.20178	+	22.1180i	0.269134	+	0.959840i
$532$	−17.3398			−0.751775
$533$	−26.6045	+	15.3601i	−1.15237	+	0.665319i
$534$	6.97291	+	50.6954i	0.301747	+	2.19381i
$535$	63.8308	+	36.8527i	2.75964	+	1.59328i
$536$	−12.2544	+	21.2252i	−0.529309	+	0.916790i
$537$	−20.6620	−	8.41873i	−0.891633	−	0.363295i
$538$	−31.2881	+	18.0642i	−1.34892	+	0.778802i
$539$	0.912497	−	3.18863i	0.0393040	−	0.137344i
$540$	−68.8510	+	93.0293i	−2.96288	+	4.00334i
$541$		−	16.5026i		−	0.709504i	−0.934960	−	0.354752i	$-0.884565\pi$
$541$		−	16.5026i		−	0.709504i	0.934960	−	0.354752i	$-0.115435\pi$
$542$	−28.7003	+	16.5701i	−1.23278	+	0.711747i
$543$	6.03429	−	14.8099i	0.258956	−	0.635555i
$544$	31.7233	−	54.9463i	1.36012	−	2.35580i
$545$	14.6276	−	25.3357i	0.626576	−	1.08526i
$546$	−18.2469	+	2.50978i	−0.780897	+	0.107409i
$547$	−21.1150	+	12.1907i	−0.902812	+	0.521239i	−0.878111	−	0.478456i	$-0.841196\pi$
$547$	−21.1150	+	12.1907i	−0.902812	+	0.521239i	−0.0247003	+	0.999695i	$0.507863\pi$
$548$		−	26.2636i		−	1.12193i
$549$	35.1618	+	8.98666i	1.50067	+	0.383541i
$550$	29.2196	−	102.105i	1.24593	−	4.35377i
$551$	10.8014	−	6.23621i	0.460157	−	0.265672i
$552$	−40.6902	+	31.5985i	−1.73189	+	1.34492i
$553$	−3.44052	+	5.95916i	−0.146306	+	0.253409i
$554$	42.1740	+	24.3491i	1.79180	+	1.03450i
$555$	−7.03022	+	5.45941i	−0.298416	+	0.231739i
$556$	11.5083	−	6.64432i	0.488061	−	0.281782i
$557$	26.4611			1.12119			0.560597	−	0.828088i	$-0.310572\pi$
$557$	26.4611			1.12119			0.560597	+	0.828088i	$0.310572\pi$
$558$	5.51683	+	5.39056i	0.233546	+	0.228201i
$559$	21.6077			0.913907
$560$	30.1790	+	52.2715i	1.27529	+	2.20887i
$561$	2.40432	−	16.8136i	0.101510	−	0.709871i
$562$	−12.1925	+	21.1180i	−0.514309	+	0.890809i
$563$	−14.5805	+	25.2541i	−0.614493	+	1.06433i	0.375980	+	0.926628i	$0.377306\pi$
$563$	−14.5805	+	25.2541i	−0.614493	+	1.06433i	−0.990473	+	0.137705i	$0.956027\pi$
$564$	13.0709	+	5.32572i	0.550384	+	0.224253i
$565$	20.4246	+	35.3764i	0.859268	+	1.48830i
$566$			15.3305i			0.644390i
$567$	−4.67922	−	7.68797i	−0.196509	−	0.322864i
$568$			9.53363i			0.400022i
$569$	19.0244	+	32.9512i	0.797544	+	1.38139i	0.921211	+	0.389064i	$0.127201\pi$
$569$	19.0244	+	32.9512i	0.797544	+	1.38139i	−0.123666	+	0.992324i	$0.539465\pi$
$570$	23.2333	−	57.0213i	0.973135	−	2.38836i
$571$	31.6456	+	18.2706i	1.32433	+	0.764600i	0.984416	−	0.175858i	$-0.0562699\pi$
$571$	31.6456	+	18.2706i	1.32433	+	0.764600i	0.339910	+	0.940458i	$0.389603\pi$
$572$	−50.5999	+	48.9155i	−2.11569	+	2.04526i
$573$	−1.16547	−	8.47337i	−0.0486883	−	0.353980i
$574$	−18.6249	+	10.7531i	−0.777386	+	0.448824i
$575$			37.1430i			1.54897i
$576$	−62.3169	−	60.8906i	−2.59654	−	2.53711i
$577$	9.65991			0.402147			0.201074	−	0.979576i	$-0.435557\pi$
$577$	9.65991			0.402147			0.201074	+	0.979576i	$0.435557\pi$
$578$	11.2662	+	19.5136i	0.468611	+	0.811658i
$579$	−28.6219	+	22.2267i	−1.18948	+	0.923711i
$580$	−75.5418	−	43.6141i	−3.13670	−	1.81098i
$581$	5.42787	+	3.13378i	0.225186	+	0.130011i
$582$	−50.2875	−	64.7564i	−2.08448	−	2.68424i
$583$	1.43602	+	5.74659i	0.0594739	+	0.237999i
$584$			54.0169i			2.23524i
$585$	11.8445	−	46.3435i	0.489709	−	1.91607i
$586$	−53.7228			−2.21927
$587$	0.478094	−	0.276027i	0.0197330	−	0.0113929i	−0.490101	−	0.871666i	$-0.663040\pi$
$587$	0.478094	−	0.276027i	0.0197330	−	0.0113929i	0.509834	+	0.860273i	$0.329707\pi$
$588$	−9.34226	+	1.28498i	−0.385268	+	0.0529918i
$589$	−2.59901	−	1.50054i	−0.107090	−	0.0618287i
$590$	−42.7342	+	74.0178i	−1.75934	+	3.04726i
$591$	−14.7397	+	36.1756i	−0.606310	+	1.48806i
$592$	−9.26684	−	16.0506i	−0.380865	−	0.659677i
$593$	−17.5723			−0.721606			−0.360803	−	0.932642i	$-0.617497\pi$
$593$	−17.5723			−0.721606			−0.360803	+	0.932642i	$0.617497\pi$
$594$	−43.4502	−	17.9753i	−1.78278	−	0.737534i
$595$	12.0956			0.495870
$596$	−39.9486	−	69.1930i	−1.63636	−	2.83426i
$597$	2.72489	−	6.68767i	0.111522	−	0.273708i
$598$	16.8276	−	29.1462i	0.688131	−	1.19188i
$599$	−10.0818	−	5.82071i	−0.411930	−	0.237828i	0.279689	−	0.960091i	$-0.409769\pi$
$599$	−10.0818	−	5.82071i	−0.411930	−	0.237828i	−0.691619	+	0.722263i	$0.743102\pi$
$600$	−189.262	+	26.0321i	−7.72661	+	1.06276i
$601$	25.9823	−	15.0009i	1.05984	−	0.611900i	0.134453	−	0.990920i	$-0.457072\pi$
$601$	25.9823	−	15.0009i	1.05984	−	0.611900i	0.925389	+	0.379020i	$0.123739\pi$
$602$	15.1268			0.616522
$603$	7.53284	−	2.11217i	0.306761	−	0.0860142i
$604$			6.59472i			0.268335i
$605$	44.9750	+	1.52285i	1.82849	+	0.0619128i
$606$	1.68333	+	2.16767i	0.0683806	+	0.0880554i
$607$	7.17521	+	4.14261i	0.291233	+	0.168143i	0.638498	−	0.769624i	$-0.279556\pi$
$607$	7.17521	+	4.14261i	0.291233	+	0.168143i	−0.347265	+	0.937767i	$0.612890\pi$
$608$	59.1864	+	34.1713i	2.40032	+	1.38583i
$609$	5.35741	−	4.16037i	0.217093	−	0.168587i
$610$	67.5159	+	116.941i	2.73364	+	4.73480i
$611$	−5.83332			−0.235991
$612$	−46.4994	+	13.0382i	−1.87963	+	0.527038i
$613$		−	37.2710i		−	1.50536i	−0.658385	−	0.752681i	$-0.728760\pi$
$613$		−	37.2710i		−	1.50536i	0.658385	−	0.752681i	$-0.271240\pi$
$614$	−8.01634	+	4.62823i	−0.323513	+	0.186780i
$615$	−7.61039	−	55.3301i	−0.306880	−	2.23113i
$616$	−22.4108	+	21.6648i	−0.902958	+	0.872901i
$617$	−30.3988	−	17.5508i	−1.22381	−	0.706567i	−0.258082	−	0.966123i	$-0.583091\pi$
$617$	−30.3988	−	17.5508i	−1.22381	−	0.706567i	−0.965728	+	0.259556i	$0.916424\pi$
$618$	0.607128	−	1.49007i	0.0244223	−	0.0599395i
$619$	−18.3103	−	31.7144i	−0.735953	−	1.27471i	−0.954304	−	0.298837i	$-0.903401\pi$
$619$	−18.3103	−	31.7144i	−0.735953	−	1.27471i	0.218351	−	0.975870i	$-0.429932\pi$
$620$			20.9886i			0.842922i
$621$	16.3391	+	1.86310i	0.655667	+	0.0747636i
$622$			37.6726i			1.51054i
$623$	−5.41414	−	9.37756i	−0.216913	−	0.375704i
$624$	92.2350	+	37.5811i	3.69236	+	1.50445i
$625$	−27.0278	+	46.8136i	−1.08111	+	1.87254i
$626$	16.6841	−	28.8977i	0.666830	−	1.15498i
$627$	18.1111	+	2.58985i	0.723286	+	0.103429i
$628$	51.8446	+	89.7975i	2.06882	+	3.58331i
$629$	−3.71410			−0.148091
$630$	8.29191	−	32.4434i	0.330357	−	1.29258i
$631$	16.2697			0.647685			0.323842	−	0.946111i	$-0.395025\pi$
$631$	16.2697			0.647685			0.323842	+	0.946111i	$0.395025\pi$
$632$	56.0060	−	32.3351i	2.22780	−	1.28622i
$633$	38.1753	−	29.6456i	1.51733	−	1.17831i
$634$	−28.7157	−	16.5790i	−1.14045	−	0.658437i
$635$	19.8707	−	34.4171i	0.788545	−	1.36580i
$636$	13.3019	−	10.3298i	0.527456	−	0.409603i
$637$	3.37529	−	1.94872i	0.133734	−	0.0772112i
$638$	9.75031	−	34.0715i	0.386019	−	1.34890i
$639$	2.12681	−	2.17663i	0.0841353	−	0.0861061i
$640$		−	148.596i		−	5.87378i
$641$	7.25531	−	4.18886i	0.286568	−	0.165450i	−0.349825	−	0.936815i	$-0.613759\pi$
$641$	7.25531	−	4.18886i	0.286568	−	0.165450i	0.636393	+	0.771365i	$0.280426\pi$
$642$	84.3494	−	11.6018i	3.32900	−	0.457888i
$643$	−4.88192	+	8.45573i	−0.192524	+	0.333462i	−0.946086	−	0.323915i	$-0.895001\pi$
$643$	−4.88192	+	8.45573i	−0.192524	+	0.333462i	0.753562	+	0.657377i	$0.228334\pi$
$644$	8.61556	−	14.9226i	0.339501	−	0.588032i
$645$	−14.8230	+	36.3801i	−0.583656	+	1.43246i
$646$	22.2501	−	12.8461i	0.875417	−	0.505422i
$647$		−	6.45586i		−	0.253806i	−0.991915	−	0.126903i	$-0.959496\pi$
$647$		−	6.45586i		−	0.253806i	0.991915	−	0.126903i	$-0.0405037\pi$
$648$	1.95806	+	84.5621i	0.0769199	+	3.32191i
$649$	−24.4154	−	6.98700i	−0.958387	−	0.274264i
$650$	108.082	−	62.4012i	4.23933	−	2.44758i
$651$	−1.51148	−	0.615853i	−0.0592397	−	0.0241372i
$652$	3.85728	−	6.68101i	0.151063	−	0.261648i
$653$	−18.0106	−	10.3984i	−0.704809	−	0.406921i	0.104327	−	0.994543i	$-0.466731\pi$
$653$	−18.0106	−	10.3984i	−0.704809	−	0.406921i	−0.809136	+	0.587622i	$0.800064\pi$
$654$	−4.60500	−	33.4799i	−0.180070	−	1.30917i
$655$	−67.6753	+	39.0724i	−2.64429	+	1.52668i
$656$	116.292			4.54045
$657$	12.0504	−	12.3326i	0.470130	−	0.481142i
$658$	−4.08370			−0.159199
$659$	0.857570	+	1.48535i	0.0334062	+	0.0578612i	0.882245	−	0.470790i	$-0.156031\pi$
$659$	0.857570	+	1.48535i	0.0334062	+	0.0578612i	−0.848839	+	0.528652i	$0.822698\pi$
$660$	−47.6455	−	118.750i	−1.85460	−	4.62232i
$661$	−10.4877	+	18.1652i	−0.407923	+	0.706543i	−0.994657	−	0.103237i	$-0.967080\pi$
$661$	−10.4877	+	18.1652i	−0.407923	+	0.706543i	0.586734	+	0.809780i	$0.300413\pi$
$662$	31.4093	−	54.4024i	1.22076	−	2.11441i
$663$	15.7640	−	12.2418i	0.612223	−	0.475430i
$664$	−29.4523	−	51.0128i	−1.14297	−	1.97968i
$665$			13.0290i			0.505241i
$666$	−2.54614	+	9.96218i	−0.0986608	+	0.386027i
$667$			12.3943i			0.479908i
$668$	37.8156	+	65.4985i	1.46313	+	2.53421i
$669$	16.9445	−	2.33063i	0.655112	−	0.0901075i
$670$	25.2086	+	14.5542i	0.973893	+	0.562277i
$671$	−28.8468	+	27.8866i	−1.11362	+	1.07655i
$672$	34.4205	+	14.0246i	1.32780	+	0.541010i
$673$	14.5571	−	8.40454i	0.561135	−	0.323971i	−0.192466	−	0.981304i	$-0.561649\pi$
$673$	14.5571	−	8.40454i	0.561135	−	0.323971i	0.753601	+	0.657332i	$0.228315\pi$
$674$			51.0520i			1.96645i
$675$	49.0180	+	36.2782i	1.88670	+	1.39635i
$676$	−11.9241			−0.458617
$677$	12.2216	+	21.1684i	0.469713	+	0.813567i	0.999400	−	0.0346262i	$-0.0110241\pi$
$677$	12.2216	+	21.1684i	0.469713	+	0.813567i	−0.529687	+	0.848193i	$0.677691\pi$
$678$	43.7002	+	17.8056i	1.67830	+	0.683820i
$679$	15.0248	+	8.67456i	0.576598	+	0.332899i
$680$	−98.4480	−	56.8390i	−3.77531	−	2.17968i
$681$	7.75122	−	1.06614i	0.297027	−	0.0408547i
$682$	−8.27288	+	2.06732i	−0.316785	+	0.0791617i
$683$			9.72687i			0.372189i	0.982532	+	0.186094i	$0.0595830\pi$
$683$			9.72687i			0.372189i	−0.982532	+	0.186094i	$0.940417\pi$
$684$	−14.0443	−	50.0876i	−0.536998	−	1.91515i
$685$	−19.7343			−0.754007
$686$	2.36292	−	1.36423i	0.0902168	−	0.0520867i
$687$	30.6270	+	39.4391i	1.16849	+	1.50470i
$688$	−70.8379	−	40.8983i	−2.70067	−	1.55923i
$689$	−3.48031	+	6.02807i	−0.132589	+	0.229651i
$690$	37.5286	+	48.3265i	1.42869	+	1.83976i
$691$	−22.1177	−	38.3090i	−0.841397	−	1.45734i	−0.888714	−	0.458462i	$-0.848401\pi$
$691$	−22.1177	−	38.3090i	−0.841397	−	1.45734i	0.0473175	−	0.998880i	$-0.484933\pi$
$692$	−9.28725			−0.353048
$693$	9.94973	+	0.0532113i	0.377959	+	0.00202133i
$694$	−15.2275			−0.578028
$695$	−4.99249	−	8.64724i	−0.189376	−	0.328008i
$696$	−63.1552	+	8.68669i	−2.39389	+	0.329268i
$697$	11.6523	−	20.1824i	0.441364	−	0.764464i
$698$	23.1659	+	13.3748i	0.876841	+	0.506245i
$699$	7.75673	−	19.0373i	0.293386	−	0.720057i
$700$	55.3370	−	31.9488i	2.09154	−	1.20755i
$701$	−40.9874			−1.54807			−0.774036	−	0.633142i	$-0.781765\pi$
$701$	−40.9874			−1.54807			−0.774036	+	0.633142i	$0.781765\pi$
$702$	−22.0288	−	50.6752i	−0.831423	−	1.91261i
$703$		−	4.00071i		−	0.150890i
$704$	93.4487	−	23.3520i	3.52198	−	0.880110i
$705$	4.00170	−	9.82135i	0.150713	−	0.369893i
$706$	23.9884	+	13.8497i	0.902816	+	0.521241i
$707$	−0.502941	−	0.290373i	−0.0189150	−	0.0109206i
$708$	9.83913	+	71.5338i	0.369777	+	2.68840i
$709$	−9.97132	−	17.2708i	−0.374481	−	0.648620i	0.615768	−	0.787927i	$-0.288846\pi$
$709$	−9.97132	−	17.2708i	−0.374481	−	0.648620i	−0.990249	+	0.139307i	$0.955512\pi$
$710$	11.3228			0.424938
$711$	−20.0002	−	5.11167i	−0.750068	−	0.191703i
$712$			101.767i			3.81390i
$713$	2.58273	−	1.49114i	0.0967238	−	0.0558435i
$714$	11.0358	−	8.57003i	0.413006	−	0.320725i
$715$	36.7547	+	38.0203i	1.37455	+	1.42188i
$716$	−60.7374	−	35.0668i	−2.26986	−	1.31051i
$717$	−10.7321	−	13.8199i	−0.400796	−	0.516115i
$718$	−49.1014	−	85.0461i	−1.83245	−	3.17389i
$719$			13.6662i			0.509665i	0.966985	+	0.254832i	$0.0820203\pi$
$719$			13.6662i			0.509665i	−0.966985	+	0.254832i	$0.917980\pi$
$720$	−126.548	+	129.512i	−4.71616	+	4.82663i
$721$			0.340471i			0.0126798i
$722$	−12.0831	−	20.9285i	−0.449685	−	0.778877i
$723$	0.662223	+	4.81459i	0.0246283	+	0.179056i
$724$	25.1348	−	43.5347i	0.934127	−	1.61796i
$725$	−22.9807	+	39.8037i	−0.853480	+	1.47827i
$726$	42.1135	−	30.4765i	1.56298	−	1.13109i
$727$	11.1527	+	19.3171i	0.413632	+	0.716432i	0.995284	−	0.0970059i	$-0.0309266\pi$
$727$	11.1527	+	19.3171i	0.413632	+	0.716432i	−0.581651	+	0.813438i	$0.697593\pi$
$728$	−36.6294			−1.35758
$729$	18.4175	−	19.7432i	0.682130	−	0.731231i
$730$	64.1543			2.37446
$731$	−14.1957	+	8.19591i	−0.525048	+	0.303137i
$732$	105.648	+	43.0460i	3.90485	+	1.59102i
$733$	−18.0801	−	10.4385i	−0.667803	−	0.385556i	0.127441	−	0.991846i	$-0.459324\pi$
$733$	−18.0801	−	10.4385i	−0.667803	−	0.385556i	−0.795244	+	0.606290i	$0.792657\pi$
$734$	27.3967	−	47.4525i	1.01123	−	1.75150i
$735$	0.965525	+	7.01969i	0.0356139	+	0.258925i
$736$	−58.8155	+	33.9571i	−2.16797	+	1.25168i
$737$	−2.37960	+	8.31526i	−0.0876535	+	0.306297i
$738$	−46.1464	−	45.0903i	−1.69867	−	1.65980i
$739$		−	45.4339i		−	1.67131i	−0.549251	−	0.835657i	$-0.685087\pi$
$739$		−	45.4339i		−	1.67131i	0.549251	−	0.835657i	$-0.314913\pi$
$740$	−24.2311	+	13.9898i	−0.890754	+	0.514277i
$741$	13.1864	+	16.9805i	0.484415	+	0.623793i
$742$	−2.43644	+	4.22004i	−0.0894446	+	0.154923i
$743$	−9.93402	+	17.2062i	−0.364444	+	0.631235i	−0.988687	−	0.149995i	$-0.952074\pi$
$743$	−9.93402	+	17.2062i	−0.364444	+	0.631235i	0.624243	+	0.781230i	$0.285408\pi$
$744$	9.40825	+	12.1152i	0.344923	+	0.444166i
$745$	−51.9911	+	30.0171i	−1.90481	+	1.09974i
$746$			79.2552i			2.90174i
$747$	−4.65594	+	18.2171i	−0.170352	+	0.666530i
$748$	14.6890	−	51.3292i	0.537082	−	1.87678i
$749$	−15.6028	+	9.00829i	−0.570114	+	0.329156i
$750$	17.7456	+	129.017i	0.647978	+	4.71102i
$751$	13.2768	−	22.9960i	0.484475	−	0.839136i	−0.515365	−	0.856971i	$-0.672344\pi$
$751$	13.2768	−	22.9960i	0.484475	−	0.839136i	0.999841	+	0.0178343i	$0.00567714\pi$
$752$	19.1238	+	11.0411i	0.697371	+	0.402628i
$753$	33.2540	+	13.5493i	1.21184	+	0.493765i
$754$	36.0660	−	20.8227i	1.31345	−	0.758319i
$755$	4.95521			0.180339
$756$	−11.2785	−	25.9452i	−0.410196	−	0.943619i
$757$	−10.3275			−0.375359			−0.187680	−	0.982230i	$-0.560097\pi$
$757$	−10.3275			−0.375359			−0.187680	+	0.982230i	$0.560097\pi$
$758$	−13.1527	−	22.7811i	−0.477727	−	0.827447i
$759$	−11.2276	+	14.2995i	−0.407537	+	0.519041i
$760$	61.2251	−	106.045i	2.22087	−	3.84666i
$761$	4.37667	−	7.58061i	0.158654	−	0.274797i	−0.775730	−	0.631066i	$-0.782618\pi$
$761$	4.37667	−	7.58061i	0.158654	−	0.274797i	0.934384	+	0.356269i	$0.115951\pi$
$762$	−6.25563	−	45.4806i	−0.226618	−	1.64759i
$763$	3.57556	+	6.19306i	0.129444	+	0.224204i
$764$		−	26.8860i		−	0.972702i
$765$	9.79679	+	34.9392i	0.354204	+	1.26323i
$766$		−	34.7297i		−	1.25484i
$767$	−14.9214	−	25.8446i	−0.538781	−	0.933196i
$768$	−43.5787	−	56.1174i	−1.57251	−	2.02496i
$769$	−13.6671	−	7.89068i	−0.492847	−	0.284545i	0.232908	−	0.972499i	$-0.425176\pi$
$769$	−13.6671	−	7.89068i	−0.492847	−	0.284545i	−0.725755	+	0.687953i	$0.758509\pi$
$770$	25.7307	+	26.6167i	0.927270	+	0.959199i
$771$	−4.31723	+	3.35260i	−0.155481	+	0.120741i
$772$	−98.6513	+	56.9563i	−3.55054	+	2.04990i
$773$			30.3640i			1.09212i	0.837747	+	0.546058i	$0.183872\pi$
$773$			30.3640i			1.09212i	−0.837747	+	0.546058i	$0.816128\pi$
$774$	12.2519	+	43.6952i	0.440386	+	1.57059i
$775$	11.0591			0.397254
$776$	−81.5261	−	141.207i	−2.92662	−	5.06905i
$777$	−0.296477	−	2.15549i	−0.0106360	−	0.0773277i
$778$	−47.4950	−	27.4212i	−1.70278	−	0.983099i
$779$	21.7399	+	12.5515i	0.778911	+	0.449705i
$780$	56.7349	−	139.244i	2.03143	−	4.98574i
$781$	0.815646	+	3.26401i	0.0291861	+	0.116795i
$782$			25.5312i			0.912993i
$783$	16.3569	+	12.1057i	0.584547	+	0.432623i
$784$	−14.7539			−0.526925
$785$	67.4730	−	38.9556i	2.40822	−	1.39038i
$786$	−34.0622	+	83.5988i	−1.21496	+	2.98187i
$787$	−43.6277	−	25.1885i	−1.55516	−	0.897871i	−0.997708	−	0.0676614i	$-0.978446\pi$
$787$	−43.6277	−	25.1885i	−1.55516	−	0.897871i	−0.557451	−	0.830210i	$-0.688220\pi$
$788$	−61.3957	+	106.340i	−2.18713	+	3.78822i
$789$	26.5829	−	3.65635i	0.946377	−	0.130170i
$790$	−38.4035	−	66.5167i	−1.36633	−	2.36656i
$791$	−9.98518			−0.355032
$792$	−80.7326	−	47.1884i	−2.86871	−	1.67677i
$793$	−47.1487			−1.67430
$794$	−45.7585	−	79.2560i	−1.62391	−	2.81269i
$795$	−7.76173	−	9.99497i	−0.275280	−	0.354485i
$796$	11.3500	−	19.6588i	0.402292	−	0.696789i
$797$	42.7073	+	24.6571i	1.51277	+	0.873399i	0.999888	+	0.0149405i	$0.00475590\pi$
$797$	42.7073	+	24.6571i	1.51277	+	0.873399i	0.512883	+	0.858458i	$0.328577\pi$
$798$	9.23136	+	11.8874i	0.326786	+	0.420811i
$799$	3.83235	−	2.21261i	0.135579	−	0.0782765i
$800$	−251.844			−8.90405
$801$	22.7028	−	23.2346i	0.802164	−	0.820954i
$802$			68.2456i			2.40984i
$803$	4.62140	+	18.4937i	0.163086	+	0.652627i
$804$	24.3626	−	3.35096i	0.859203	−	0.118179i
$805$	−11.2127	−	6.47366i	−0.395196	−	0.228167i
$806$	−8.67810	−	5.01030i	−0.305673	−	0.176480i
$807$	21.2392	+	8.65389i	0.747655	+	0.304631i
$808$	2.72902	+	4.72680i	0.0960065	+	0.166288i
$809$	−8.69516			−0.305706			−0.152853	−	0.988249i	$-0.548846\pi$
$809$	−8.69516			−0.305706			−0.152853	+	0.988249i	$0.548846\pi$
$810$	100.432	−	2.32553i	3.52882	−	0.0817109i
$811$			11.3135i			0.397271i	0.980073	+	0.198635i	$0.0636510\pi$
$811$			11.3135i			0.397271i	−0.980073	+	0.198635i	$0.936349\pi$
$812$	18.4655	−	10.6610i	0.648010	−	0.374129i
$813$	19.4825	+	7.93813i	0.683281	+	0.278402i
$814$	−7.90095	−	8.17300i	−0.276928	−	0.286464i
$815$	−5.02005	−	2.89833i	−0.175845	−	0.101524i
$816$	−74.8510	+	10.2954i	−2.62031	+	0.360411i
$817$	−8.82837	−	15.2912i	−0.308865	−	0.534971i
$818$		−	34.5338i		−	1.20745i
$819$	8.36288	+	8.17148i	0.292223	+	0.285535i
$820$		−	175.562i		−	6.13091i
$821$	21.1240	+	36.5878i	0.737232	+	1.27692i	0.953737	+	0.300642i	$0.0972010\pi$
$821$	21.1240	+	36.5878i	0.737232	+	1.27692i	−0.216505	+	0.976282i	$0.569466\pi$
$822$	−18.0053	+	13.9822i	−0.628005	+	0.487686i
$823$	−13.0264	+	22.5625i	−0.454073	+	0.786478i	−0.998634	−	0.0522433i	$-0.983363\pi$
$823$	−13.0264	+	22.5625i	−0.454073	+	0.786478i	0.544561	+	0.838721i	$0.316696\pi$
$824$	1.59992	−	2.77115i	0.0557360	−	0.0965376i
$825$	−62.5703	+	25.1049i	−2.17842	+	0.874039i
$826$	−10.4460	−	18.0929i	−0.363461	−	0.629534i
$827$	37.7595			1.31302			0.656512	−	0.754315i	$-0.272031\pi$
$827$	37.7595			1.31302			0.656512	+	0.754315i	$0.272031\pi$
$828$	50.0835	+	12.8004i	1.74052	+	0.444843i
$829$	−20.7188			−0.719593			−0.359796	−	0.933031i	$-0.617154\pi$
$829$	−20.7188			−0.719593			−0.359796	+	0.933031i	$0.617154\pi$
$830$	−60.5865	+	34.9796i	−2.10299	+	1.21416i
$831$	−4.21241	−	30.6257i	−0.146127	−	1.06239i
$832$	98.0259	+	56.5953i	3.39844	+	1.96209i
$833$	−1.47832	+	2.56053i	−0.0512209	+	0.0887171i
$834$	−10.6819	−	4.35231i	−0.369883	−	0.150708i
$835$	49.2150	−	28.4143i	1.70316	−	0.983318i
$836$	55.2901	+	15.8225i	1.91225	+	0.547232i
$837$	0.554726	−	4.86488i	0.0191741	−	0.168155i
$838$			106.743i			3.68739i
$839$	−37.0081	+	21.3666i	−1.27766	+	0.737658i	−0.976418	−	0.215890i	$-0.930735\pi$
$839$	−37.0081	+	21.3666i	−1.27766	+	0.737658i	−0.301243	+	0.953547i	$0.597401\pi$
$840$	25.1280	−	61.6716i	0.867000	−	2.12787i
$841$	6.83157	−	11.8326i	0.235571	−	0.408021i
$842$	0.253910	−	0.439785i	0.00875031	−	0.0151560i
$843$	15.3354	−	2.10931i	0.528178	−	0.0726483i
$844$	131.579	−	75.9673i	4.52914	−	2.61490i
$845$			8.95963i			0.308221i
$846$	−3.30759	−	11.7962i	−0.113717	−	0.405561i
$847$	−5.81923	+	9.33470i	−0.199951	+	0.320744i
$848$	22.8194	−	13.1748i	0.783623	−	0.452425i
$849$	7.68644	−	5.96901i	0.263798	−	0.204856i
$850$	−47.3383	+	81.9923i	−1.62369	+	2.81231i
$851$	3.44301	+	1.98782i	0.118025	+	0.0681416i
$852$	7.55538	−	5.86723i	0.258843	−	0.201008i
$853$	20.3981	−	11.7769i	0.698419	−	0.403232i	−0.108340	−	0.994114i	$-0.534553\pi$
$853$	20.3981	−	11.7769i	0.698419	−	0.403232i	0.806758	+	0.590882i	$0.201220\pi$
$854$	−33.0072			−1.12948
$855$	−37.6354	+	10.5528i	−1.28710	+	0.360897i
$856$	169.325			5.78742
$857$	0.817501	+	1.41595i	0.0279253	+	0.0483681i	0.879650	−	0.475621i	$-0.157777\pi$
$857$	0.817501	+	1.41595i	0.0279253	+	0.0483681i	−0.851725	+	0.523989i	$0.824443\pi$
$858$	60.4729	+	8.64752i	2.06451	+	0.295221i
$859$	18.8589	−	32.6646i	0.643457	−	1.11450i	−0.341198	−	0.939991i	$-0.610833\pi$
$859$	18.8589	−	32.6646i	0.643457	−	1.11450i	0.984655	−	0.174510i	$-0.0558340\pi$
$860$	−61.7427	+	106.942i	−2.10541	+	3.64668i
$861$	12.6431	+	5.15140i	0.430874	+	0.175559i
$862$	−37.8201	−	65.5063i	−1.28816	−	2.23115i
$863$		−	25.8731i		−	0.880731i	−0.897819	−	0.440365i	$-0.854849\pi$
$863$		−	25.8731i		−	0.880731i	0.897819	−	0.440365i	$-0.145151\pi$
$864$	−12.6326	+	110.786i	−0.429769	+	3.76902i
$865$			6.97836i			0.237271i
$866$	−44.9795	−	77.9067i	−1.52847	−	2.64738i
$867$	5.39721	−	13.2464i	0.183299	−	0.449870i
$868$	−4.44311	−	2.56523i	−0.150809	−	0.0870695i
$869$	16.4083	−	15.8621i	0.556612	−	0.538084i
$870$	10.3169	+	75.0076i	0.349777	+	2.54300i
$871$	−8.80203	+	5.08185i	−0.298245	+	0.172192i
$872$		−	67.2085i		−	2.27597i
$873$	−12.8880	+	50.4264i	−0.436193	+	1.70668i
$874$	−27.5014			−0.930247
$875$	−13.7786	−	23.8653i	−0.465803	−	0.806794i
$876$	42.8083	−	33.2434i	1.44636	−	1.12319i
$877$	25.2531	+	14.5799i	0.852738	+	0.492328i	0.861574	−	0.507633i	$-0.169479\pi$
$877$	25.2531	+	14.5799i	0.852738	+	0.492328i	−0.00883585	+	0.999961i	$0.502813\pi$
$878$	23.3587	+	13.4862i	0.788318	+	0.455136i
$879$	20.9172	+	26.9356i	0.705520	+	0.908515i
$880$	−48.5319	−	194.213i	−1.63601	−	6.54690i
$881$			12.8604i			0.433278i	0.976252	+	0.216639i	$0.0695095\pi$
$881$			12.8604i			0.433278i	−0.976252	+	0.216639i	$0.930490\pi$
$882$	5.85456	+	5.72057i	0.197133	+	0.192622i
$883$	−37.7818			−1.27146			−0.635729	−	0.771912i	$-0.719301\pi$
$883$	−37.7818			−1.27146			−0.635729	+	0.771912i	$0.719301\pi$
$884$	54.3339	−	31.3697i	1.82745	−	1.05508i
$885$	53.7499	−	7.39304i	1.80678	−	0.248514i
$886$	−85.4940	−	49.3600i	−2.87223	−	1.65828i
$887$	−2.92855	+	5.07239i	−0.0983310	+	0.170314i	−0.910994	−	0.412420i	$-0.864684\pi$
$887$	−2.92855	+	5.07239i	−0.0983310	+	0.170314i	0.812663	+	0.582734i	$0.198017\pi$
$888$	−7.71589	+	18.9371i	−0.258928	+	0.635487i
$889$	4.85720	+	8.41292i	0.162905	+	0.282160i
$890$	120.866			4.05145
$891$	7.90506	+	28.7839i	0.264829	+	0.964295i
$892$	53.7649			1.80018
$893$	2.38335	+	4.12808i	0.0797558	+	0.138141i
$894$	−26.1681	+	64.2241i	−0.875191	+	2.14798i
$895$	−26.3489	+	45.6376i	−0.880745	+	1.52550i
$896$	31.4566	+	18.1615i	1.05089	+	0.606732i
$897$	−21.1653	+	2.91118i	−0.706688	+	0.0972015i
$898$	41.5867	−	24.0101i	1.38777	−	0.801227i
$899$	3.69031			0.123079
$900$	137.107	+	133.969i	4.57024	+	4.46564i
$901$		−	5.28040i		−	0.175916i
$902$	69.1999	−	17.2924i	2.30410	−	0.575774i
$903$	−5.88968	−	7.58428i	−0.195996	−	0.252389i
$904$	81.2711	+	46.9219i	2.70304	+	1.56060i
$905$	−32.7116	−	18.8861i	−1.08737	−	0.627794i
$906$	4.52107	−	3.51090i	0.150202	−	0.116642i
$907$	21.9558	+	38.0285i	0.729029	+	1.26272i	0.957294	+	0.289116i	$0.0933614\pi$
$907$	21.9558	+	38.0285i	0.729029	+	1.26272i	−0.228265	+	0.973599i	$0.573305\pi$
$908$	24.5946			0.816201
$909$	0.431415	−	1.68798i	0.0143091	−	0.0559868i
$910$			43.5037i			1.44213i
$911$	8.19814	−	4.73320i	0.271617	−	0.156818i	−0.358005	−	0.933720i	$-0.616543\pi$
$911$	8.19814	−	4.73320i	0.271617	−	0.156818i	0.629622	+	0.776902i	$0.283210\pi$
$912$	−11.0899	−	80.6270i	−0.367222	−	2.66983i
$913$	−14.4479	−	14.9454i	−0.478156	−	0.494620i
$914$	−79.1961	−	45.7239i	−2.61958	−	1.51241i
$915$	32.3444	−	79.3827i	1.06927	−	2.62431i
$916$	78.4822	+	135.935i	2.59312	+	4.49142i
$917$		−	19.1017i		−	0.630794i
$918$	33.6938	+	24.9368i	1.11206	+	0.823037i
$919$		−	24.3500i		−	0.803232i	−0.915808	−	0.401616i	$-0.868449\pi$
$919$		−	24.3500i		−	0.803232i	0.915808	−	0.401616i	$-0.131551\pi$
$920$	60.8415	+	105.380i	2.00588	+	3.47429i
$921$	5.44171	+	2.21722i	0.179310	+	0.0730598i
$922$	4.29707	−	7.44274i	0.141516	−	0.245113i
$923$	−1.97678	+	3.42389i	−0.0650666	+	0.112699i
$924$	30.9615	+	4.42745i	1.01856	+	0.145652i
$925$	7.37138	+	12.7676i	0.242369	+	0.419796i
$926$	−5.91300			−0.194313
$927$	−0.983482	+	0.275763i	−0.0323018	+	0.00905726i
$928$	−84.0382			−2.75869
$929$	−14.7509	+	8.51644i	−0.483962	+	0.279415i	−0.722066	−	0.691824i	$-0.756807\pi$
$929$	−14.7509	+	8.51644i	−0.483962	+	0.279415i	0.238104	+	0.971240i	$0.423474\pi$
$930$	14.3889	−	11.1739i	0.471831	−	0.366407i
$931$	−2.75812	−	1.59240i	−0.0903937	−	0.0521889i
$932$	32.3093	−	55.9614i	1.05833	−	1.83308i
$933$	18.8884	−	14.6680i	0.618377	−	0.480209i
$934$	−4.26492	+	2.46235i	−0.139552	+	0.0805706i
$935$	−38.5683	−	11.0372i	−1.26132	−	0.360954i
$936$	−29.6679	−	105.808i	−0.969726	−	3.45843i
$937$		−	54.0665i		−	1.76628i	−0.469112	−	0.883138i	$-0.655426\pi$
$937$		−	54.0665i		−	1.76628i	0.469112	−	0.883138i	$-0.344574\pi$
$938$	−6.16200	+	3.55763i	−0.201196	+	0.116161i
$939$	−20.9848	+	2.88635i	−0.684812	+	0.0941926i
$940$	16.6684	−	28.8705i	0.543663	−	0.941652i
$941$	10.3893	−	17.9949i	0.338683	−	0.586615i	−0.645503	−	0.763758i	$-0.723352\pi$
$941$	10.3893	−	17.9949i	0.338683	−	0.586615i	0.984185	+	0.177143i	$0.0566854\pi$
$942$	33.9604	−	83.3489i	1.10649	−	2.71565i
$943$	−21.6036	+	12.4729i	−0.703511	+	0.406172i
$944$			112.971i			3.67689i
$945$	−19.4950	+	8.47459i	−0.634173	+	0.275679i
$946$	−48.2337	−	13.8031i	−1.56821	−	0.448779i
$947$	24.0767	−	13.9007i	0.782388	−	0.451712i	−0.0548881	−	0.998493i	$-0.517480\pi$
$947$	24.0767	−	13.9007i	0.782388	−	0.451712i	0.837276	+	0.546781i	$0.184147\pi$
$948$	−60.0930	−	24.4848i	−1.95173	−	0.795230i
$949$	−11.2003	+	19.3995i	−0.363578	+	0.629735i
$950$	−88.3194	−	50.9912i	−2.86546	−	1.65437i
$951$	2.86818	+	20.8526i	0.0930071	+	0.676193i
$952$	24.0647	−	13.8937i	0.779940	−	0.450299i
$953$	39.1391			1.26784			0.633920	−	0.773399i	$-0.281445\pi$
$953$	39.1391			1.26784			0.633920	+	0.773399i	$0.281445\pi$
$954$	−14.1634	−	3.61988i	−0.458556	−	0.117198i
$955$	−20.2019			−0.653719
$956$	−27.5011	−	47.6333i	−0.889449	−	1.54057i
$957$	−20.8791	+	8.37726i	−0.674926	+	0.270798i
$958$	−21.0573	+	36.4722i	−0.680329	+	1.17836i
$959$	2.41192	−	4.17757i	0.0778851	−	0.134901i
$960$	−162.534	+	126.218i	−5.24576	+	4.07367i
$961$	15.0560	+	26.0778i	0.485678	+	0.841219i
$962$		−	13.3584i		−	0.430691i
$963$	−38.6588	−	37.7740i	−1.24576	−	1.21725i
$964$			15.2767i			0.492029i
$965$	42.7965	+	74.1257i	1.37767	+	2.38619i
$966$	−14.8171	+	2.03802i	−0.476731	+	0.0655721i
$967$	−16.5361	−	9.54712i	−0.531765	−	0.307015i	0.209970	−	0.977708i	$-0.432663\pi$
$967$	−16.5361	−	9.54712i	−0.531765	−	0.307015i	−0.741735	+	0.670693i	$0.765997\pi$
$968$	91.2289	−	48.6313i	2.93221	−	1.56307i
$969$	−15.1040	−	6.15409i	−0.485209	−	0.197698i
$970$	−167.708	+	96.8263i	−5.38478	+	3.10890i
$971$			0.109970i			0.00352911i	0.999998	+	0.00176455i	$0.000561675\pi$
$971$			0.109970i			0.00352911i	−0.999998	+	0.00176455i	$0.999438\pi$
$972$	65.8103	−	53.5934i	2.11087	−	1.71901i
$973$	2.44073			0.0782462
$974$	40.1998	+	69.6281i	1.28808	+	2.23103i
$975$	−73.3690	−	29.8941i	−2.34969	−	0.957379i
$976$	154.571	+	89.2415i	4.94769	+	2.85655i
$977$	−11.9160	−	6.87972i	−0.381228	−	0.220102i	0.297125	−	0.954839i	$-0.403972\pi$
$977$	−11.9160	−	6.87972i	−0.381228	−	0.220102i	−0.678352	+	0.734737i	$0.737306\pi$
$978$	−6.63376	+	0.912442i	−0.212124	+	0.0291767i
$979$	8.70668	+	34.8419i	0.278267	+	1.11355i
$980$			22.2735i			0.711500i
$981$	−14.9932	+	15.3444i	−0.478697	+	0.489909i
$982$	−90.0144			−2.87248
$983$	−6.19171	+	3.57479i	−0.197485	+	0.114018i	−0.595482	−	0.803369i	$-0.703039\pi$
$983$	−6.19171	+	3.57479i	−0.197485	+	0.114018i	0.397997	+	0.917387i	$0.369705\pi$
$984$	−78.6968	−	101.340i	−2.50876	−	3.23059i
$985$	79.9033	+	46.1322i	2.54593	+	1.46989i
$986$	−15.7963	+	27.3601i	−0.503058	+	0.871322i
$987$	1.59001	+	2.04749i	0.0506105	+	0.0651724i
$988$	33.7904	+	58.5268i	1.07502	+	1.86198i
$989$	17.5461			0.557933
$990$	−56.0443	+	95.8838i	−1.78121	+	3.04739i
$991$	−58.5632			−1.86032			−0.930160	−	0.367154i	$-0.880332\pi$
$991$	−58.5632			−1.86032			−0.930160	+	0.367154i	$0.880332\pi$
$992$	10.1105	+	17.5119i	0.321009	+	0.556004i
$993$	−39.5057	+	5.43382i	−1.25368	+	0.172437i
$994$	−1.38388	+	2.39694i	−0.0438939	+	0.0760265i
$995$	−14.7715	−	8.52832i	−0.468288	−	0.270366i
$996$	−22.3019	+	54.7355i	−0.706663	+	1.73436i
$997$	27.8486	−	16.0784i	0.881973	−	0.509207i	0.0106647	−	0.999943i	$-0.496605\pi$
$997$	27.8486	−	16.0784i	0.881973	−	0.509207i	0.871309	+	0.490736i	$0.163272\pi$
$998$	−13.1528			−0.416345
$999$	5.98620	−	2.60223i	0.189395	−	0.0823311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.w.a.428.2	✓	144
9.2	odd	6	inner	693.2.w.a.659.71	yes	144
11.10	odd	2	inner	693.2.w.a.428.71	yes	144
99.65	even	6	inner	693.2.w.a.659.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.w.a.428.2	✓	144	1.1	even	1	trivial
693.2.w.a.428.71	yes	144	11.10	odd	2	inner
693.2.w.a.659.2	yes	144	99.65	even	6	inner
693.2.w.a.659.71	yes	144	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36423 - 2.36292i) q^{2} +(-0.653554 + 1.60402i) q^{3} +(-2.72227 + 4.71511i) q^{4} +(3.54289 + 2.04549i) q^{5} +(4.68177 - 0.643954i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.39831 q^{8} +(-2.14573 - 2.09662i) q^{9} +O(q^{10})\)	\(q+(-1.36423 - 2.36292i) q^{2} +(-0.653554 + 1.60402i) q^{3} +(-2.72227 + 4.71511i) q^{4} +(3.54289 + 2.04549i) q^{5} +(4.68177 - 0.643954i) q^{6} +(-0.866025 + 0.500000i) q^{7} +9.39831 q^{8} +(-2.14573 - 2.09662i) q^{9} -11.1621i q^{10} +(3.21768 - 0.804069i) q^{11} +(-5.78396 - 7.44814i) q^{12} +(3.37529 + 1.94872i) q^{13} +(2.36292 + 1.36423i) q^{14} +(-5.59647 + 4.34602i) q^{15} +(-7.37695 - 12.7773i) q^{16} -2.95665 q^{17} +(-2.02688 + 7.93049i) q^{18} -3.18480i q^{19} +(-19.2894 + 11.1367i) q^{20} +(-0.236013 - 1.71590i) q^{21} +(-6.28962 - 6.50619i) q^{22} +(2.74084 + 1.58242i) q^{23} +(-6.14231 + 15.0750i) q^{24} +(5.86805 + 10.1638i) q^{25} -10.6341i q^{26} +(4.76537 - 2.07153i) q^{27} -5.44454i q^{28} +(1.95812 + 3.39156i) q^{29} +(17.9042 + 7.29504i) q^{30} +(0.471156 - 0.816067i) q^{31} +(-10.7295 + 18.5840i) q^{32} +(-0.813191 + 5.68671i) q^{33} +(4.03356 + 6.98633i) q^{34} -4.09098 q^{35} +(15.7271 - 4.40979i) q^{36} +1.25619 q^{37} +(-7.52544 + 4.34482i) q^{38} +(-5.33172 + 4.14042i) q^{39} +(33.2972 + 19.2241i) q^{40} +(-3.94106 + 6.82612i) q^{41} +(-3.73255 + 2.89856i) q^{42} +(4.80129 - 2.77203i) q^{43} +(-4.96812 + 17.3606i) q^{44} +(-3.31348 - 11.8172i) q^{45} -8.63518i q^{46} +(-1.29618 + 0.748351i) q^{47} +(25.3162 - 3.48212i) q^{48} +(0.500000 - 0.866025i) q^{49} +(16.0108 - 27.7315i) q^{50} +(1.93233 - 4.74251i) q^{51} +(-18.3769 + 10.6099i) q^{52} +1.78594i q^{53} +(-11.3960 - 8.43415i) q^{54} +(13.0446 + 3.73300i) q^{55} +(-8.13917 + 4.69915i) q^{56} +(5.10847 + 2.08144i) q^{57} +(5.34266 - 9.25375i) q^{58} +(-6.63117 - 3.82851i) q^{59} +(-5.25683 - 38.2190i) q^{60} +(-10.4766 + 6.04867i) q^{61} -2.57107 q^{62} +(2.90657 + 0.742862i) q^{63} +29.0422 q^{64} +(7.97219 + 13.8082i) q^{65} +(14.5466 - 5.83650i) q^{66} +(-1.30389 + 2.25841i) q^{67} +(8.04878 - 13.9409i) q^{68} +(-4.32952 + 3.36215i) q^{69} +(5.58105 + 9.66667i) q^{70} +1.01440i q^{71} +(-20.1663 - 19.7047i) q^{72} +5.74751i q^{73} +(-1.71373 - 2.96828i) q^{74} +(-20.1379 + 2.76988i) q^{75} +(15.0167 + 8.66989i) q^{76} +(-2.38456 + 2.30518i) q^{77} +(17.0572 + 6.94994i) q^{78} +(5.95916 - 3.44052i) q^{79} -60.3579i q^{80} +(0.208342 + 8.99759i) q^{81} +21.5061 q^{82} +(-3.13378 - 5.42787i) q^{83} +(8.73312 + 3.55830i) q^{84} +(-10.4751 - 6.04779i) q^{85} +(-13.1002 - 7.56339i) q^{86} +(-6.71984 + 0.924282i) q^{87} +(30.2408 - 7.55689i) q^{88} +10.8283i q^{89} +(-23.4027 + 23.9509i) q^{90} -3.89745 q^{91} +(-14.9226 + 8.61556i) q^{92} +(1.00106 + 1.28909i) q^{93} +(3.53659 + 2.04185i) q^{94} +(6.51448 - 11.2834i) q^{95} +(-22.7967 - 29.3559i) q^{96} +(-8.67456 - 15.0248i) q^{97} -2.72847 q^{98} +(-8.59012 - 5.02095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{3} - 72 q^{4} + 6 q^{5} - 22 q^{9}+O(q^{10}) \) 144 * q + 6 * q^3 - 72 * q^4 + 6 * q^5 - 22 * q^9	\( 144 q + 6 q^{3} - 72 q^{4} + 6 q^{5} - 22 q^{9} + 12 q^{11} - 16 q^{12} + 16 q^{15} - 72 q^{16} - 24 q^{20} - 6 q^{22} + 78 q^{25} - 6 q^{31} + 28 q^{33} - 12 q^{34} + 36 q^{36} + 12 q^{37} - 60 q^{38} + 66 q^{45} - 24 q^{47} - 12 q^{48} + 72 q^{49} - 90 q^{59} - 32 q^{60} + 144 q^{64} - 150 q^{66} + 6 q^{67} - 54 q^{69} - 38 q^{75} + 152 q^{78} - 86 q^{81} - 24 q^{82} + 108 q^{86} + 6 q^{88} - 24 q^{91} - 228 q^{92} + 94 q^{93} - 30 q^{97} - 42 q^{99}+O(q^{100}) \) 144 * q + 6 * q^3 - 72 * q^4 + 6 * q^5 - 22 * q^9 + 12 * q^11 - 16 * q^12 + 16 * q^15 - 72 * q^16 - 24 * q^20 - 6 * q^22 + 78 * q^25 - 6 * q^31 + 28 * q^33 - 12 * q^34 + 36 * q^36 + 12 * q^37 - 60 * q^38 + 66 * q^45 - 24 * q^47 - 12 * q^48 + 72 * q^49 - 90 * q^59 - 32 * q^60 + 144 * q^64 - 150 * q^66 + 6 * q^67 - 54 * q^69 - 38 * q^75 + 152 * q^78 - 86 * q^81 - 24 * q^82 + 108 * q^86 + 6 * q^88 - 24 * q^91 - 228 * q^92 + 94 * q^93 - 30 * q^97 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more