LMFDB - Embedded newform 462.2.s.a.125.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(125,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 2]))

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

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

chi := DirichletCharacter("462.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.s (of order $10$, degree $4$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			125.2
Character	$\chi$	$=$	462.125
Dual form			462.2.s.a.377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-1.70765 + 0.289739i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.820027 - 0.595785i) q^{5} +(0.769325 - 1.55182i) q^{6} +(-1.08488 - 2.41309i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.83210 - 0.989542i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.70765 + 0.289739i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.820027 - 0.595785i) q^{5} +(0.769325 - 1.55182i) q^{6} +(-1.08488 - 2.41309i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.83210 - 0.989542i) q^{9} +1.01361i q^{10} +(0.0474828 + 3.31628i) q^{11} +(0.803249 + 1.53453i) q^{12} +(-2.98650 + 4.11057i) q^{13} +(2.58991 + 0.540692i) q^{14} +(-1.22769 + 1.25498i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.55268 + 1.12809i) q^{17} +(-0.864112 + 2.87286i) q^{18} +(-7.85640 - 2.55270i) q^{19} +(-0.820027 - 0.595785i) q^{20} +(2.55176 + 3.80638i) q^{21} +(-2.71084 - 1.91085i) q^{22} -5.21231i q^{23} +(-1.71360 - 0.252133i) q^{24} +(-1.22760 + 3.77816i) q^{25} +(-1.57010 - 4.83226i) q^{26} +(-4.54952 + 2.51036i) q^{27} +(-1.95974 + 1.77747i) q^{28} +(0.520932 - 0.169261i) q^{29} +(-0.293682 - 1.73088i) q^{30} +(2.14878 - 2.95754i) q^{31} -1.00000i q^{32} +(-1.04194 - 5.64928i) q^{33} -1.91922i q^{34} +(-2.32732 - 1.33245i) q^{35} +(-1.81628 - 2.38770i) q^{36} +(-1.56326 - 4.81122i) q^{37} +(6.68305 - 4.85552i) q^{38} +(3.90889 - 7.88470i) q^{39} +(0.964000 - 0.313222i) q^{40} +(-1.10320 + 3.39530i) q^{41} +(-4.57931 - 0.172911i) q^{42} -7.12586 q^{43} +(3.13930 - 1.06995i) q^{44} +(1.73285 - 2.49877i) q^{45} +(4.21685 + 3.06372i) q^{46} +(-2.60985 + 8.03230i) q^{47} +(1.21121 - 1.23813i) q^{48} +(-4.64605 + 5.23586i) q^{49} +(-2.33503 - 3.21390i) q^{50} +(2.32458 - 2.37625i) q^{51} +(4.83226 + 1.57010i) q^{52} +(-8.30483 + 11.4306i) q^{53} +(0.643219 - 5.15619i) q^{54} +(2.01473 + 2.69115i) q^{55} +(-0.286099 - 2.63024i) q^{56} +(14.1556 + 2.08280i) q^{57} +(-0.169261 + 0.520932i) q^{58} +(-2.84960 - 8.77015i) q^{59} +(1.57294 + 0.779795i) q^{60} +(-5.06513 - 6.97155i) q^{61} +(1.12968 + 3.47679i) q^{62} +(-5.46036 - 5.76059i) q^{63} +(0.809017 + 0.587785i) q^{64} +5.15009i q^{65} +(5.18280 + 2.47762i) q^{66} -6.40079 q^{67} +(1.55268 + 1.12809i) q^{68} +(1.51021 + 8.90077i) q^{69} +(2.44594 - 1.09965i) q^{70} +(5.17867 + 7.12783i) q^{71} +(2.99928 - 0.0659423i) q^{72} +(2.49755 - 0.811503i) q^{73} +(4.81122 + 1.56326i) q^{74} +(1.00162 - 6.80745i) q^{75} +8.26070i q^{76} +(7.95100 - 3.71237i) q^{77} +(4.08126 + 7.79687i) q^{78} +(-2.10051 - 1.52611i) q^{79} +(-0.313222 + 0.964000i) q^{80} +(7.04161 - 5.60497i) q^{81} +(-2.09841 - 2.88821i) q^{82} +(-10.3171 + 7.49579i) q^{83} +(2.83154 - 3.60311i) q^{84} +(-0.601143 + 1.85013i) q^{85} +(4.18847 - 5.76494i) q^{86} +(-0.840526 + 0.439972i) q^{87} +(-0.979630 + 3.16865i) q^{88} +15.4473 q^{89} +(1.00301 + 2.87065i) q^{90} +(13.1592 + 2.74722i) q^{91} +(-4.95720 + 1.61069i) q^{92} +(-2.81243 + 5.67300i) q^{93} +(-4.96423 - 6.83268i) q^{94} +(-7.96332 + 2.58744i) q^{95} +(0.289739 + 1.70765i) q^{96} +(6.74995 - 9.29051i) q^{97} +(-1.50502 - 6.83629i) q^{98} +(3.41608 + 9.34507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9}+O(q^{10}) $ 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9	$ 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9} + 12 q^{15} - 32 q^{16} - 16 q^{18} - 20 q^{21} - 36 q^{25} - 6 q^{28} + 8 q^{36} - 16 q^{37} + 60 q^{39} + 4 q^{42} - 64 q^{43} - 8 q^{46} - 40 q^{49} - 28 q^{51} + 88 q^{57} + 92 q^{58} + 8 q^{60} - 42 q^{63} + 32 q^{64} - 64 q^{67} - 26 q^{70} - 24 q^{72} - 64 q^{78} + 136 q^{79} - 116 q^{81} - 28 q^{85} - 40 q^{91} - 76 q^{93} - 160 q^{99}+O(q^{100}) $ 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9 + 12 * q^15 - 32 * q^16 - 16 * q^18 - 20 * q^21 - 36 * q^25 - 6 * q^28 + 8 * q^36 - 16 * q^37 + 60 * q^39 + 4 * q^42 - 64 * q^43 - 8 * q^46 - 40 * q^49 - 28 * q^51 + 88 * q^57 + 92 * q^58 + 8 * q^60 - 42 * q^63 + 32 * q^64 - 64 * q^67 - 26 * q^70 - 24 * q^72 - 64 * q^78 + 136 * q^79 - 116 * q^81 - 28 * q^85 - 40 * q^91 - 76 * q^93 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−1.70765	+	0.289739i	−0.985909	+	0.167281i
$3$	−1.70765	+	0.289739i	−0.985909	+	0.167281i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	0.820027	−	0.595785i	0.366727	−	0.266443i	−0.389125	−	0.921185i	$-0.627223\pi$
$5$	0.820027	−	0.595785i	0.366727	−	0.266443i	0.755853	+	0.654742i	$0.227223\pi$
$6$	0.769325	−	1.55182i	0.314076	−	0.633527i
$7$	−1.08488	−	2.41309i	−0.410048	−	0.912064i
$7$	−1.08488	−	2.41309i	−0.410048	−	0.912064i
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	2.83210	−	0.989542i	0.944034	−	0.329847i
$10$			1.01361i			0.320531i
$11$	0.0474828	+	3.31628i	0.0143166	+	0.999898i
$11$	0.0474828	+	3.31628i	0.0143166	+	0.999898i
$12$	0.803249	+	1.53453i	0.231878	+	0.442981i
$13$	−2.98650	+	4.11057i	−0.828307	+	1.14007i	0.159929	+	0.987128i	$0.448873\pi$
$13$	−2.98650	+	4.11057i	−0.828307	+	1.14007i	−0.988236	+	0.152938i	$0.951127\pi$
$14$	2.58991	+	0.540692i	0.692184	+	0.144506i
$15$	−1.22769	+	1.25498i	−0.316989	+	0.324035i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.55268	+	1.12809i	−0.376581	+	0.273602i	−0.759934	−	0.650000i	$-0.774769\pi$
$17$	−1.55268	+	1.12809i	−0.376581	+	0.273602i	0.383354	+	0.923602i	$0.374769\pi$
$18$	−0.864112	+	2.87286i	−0.203673	+	0.677139i
$19$	−7.85640	−	2.55270i	−1.80238	−	0.585629i	−0.802443	−	0.596729i	$-0.796467\pi$
$19$	−7.85640	−	2.55270i	−1.80238	−	0.585629i	−0.999938	+	0.0111001i	$0.996467\pi$
$20$	−0.820027	−	0.595785i	−0.183364	−	0.133221i
$21$	2.55176	+	3.80638i	0.556841	+	0.830619i
$22$	−2.71084	−	1.91085i	−0.577953	−	0.407394i
$23$		−	5.21231i		−	1.08684i	−0.839461	−	0.543421i	$-0.817129\pi$
$23$		−	5.21231i		−	1.08684i	0.839461	−	0.543421i	$-0.182871\pi$
$24$	−1.71360	−	0.252133i	−0.349787	−	0.0514665i
$25$	−1.22760	+	3.77816i	−0.245520	+	0.755633i
$26$	−1.57010	−	4.83226i	−0.307921	−	0.947685i
$27$	−4.54952	+	2.51036i	−0.875555	+	0.483118i
$28$	−1.95974	+	1.77747i	−0.370356	+	0.335911i
$29$	0.520932	−	0.169261i	0.0967347	−	0.0314310i	−0.260250	−	0.965541i	$-0.583805\pi$
$29$	0.520932	−	0.169261i	0.0967347	−	0.0314310i	0.356984	+	0.934110i	$0.383805\pi$
$30$	−0.293682	−	1.73088i	−0.0536187	−	0.316015i
$31$	2.14878	−	2.95754i	0.385931	−	0.531189i	−0.571212	−	0.820802i	$-0.693527\pi$
$31$	2.14878	−	2.95754i	0.385931	−	0.531189i	0.957144	+	0.289613i	$0.0935267\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.04194	−	5.64928i	−0.181378	−	0.983413i
$34$		−	1.91922i		−	0.329144i
$35$	−2.32732	−	1.33245i	−0.393389	−	0.225224i
$36$	−1.81628	−	2.38770i	−0.302713	−	0.397951i
$37$	−1.56326	−	4.81122i	−0.256998	−	0.790959i	−0.993429	−	0.114447i	$-0.963491\pi$
$37$	−1.56326	−	4.81122i	−0.256998	−	0.790959i	0.736431	−	0.676512i	$-0.236509\pi$
$38$	6.68305	−	4.85552i	1.08413	−	0.787669i
$39$	3.90889	−	7.88470i	0.625924	−	1.26256i
$40$	0.964000	−	0.313222i	0.152422	−	0.0495248i
$41$	−1.10320	+	3.39530i	−0.172291	+	0.530256i	−0.999499	−	0.0316386i	$-0.989927\pi$
$41$	−1.10320	+	3.39530i	−0.172291	+	0.530256i	0.827209	+	0.561895i	$0.189927\pi$
$42$	−4.57931	−	0.172911i	−0.706603	−	0.0266808i
$43$	−7.12586			−1.08668			−0.543341	−	0.839512i	$-0.682841\pi$
$43$	−7.12586			−1.08668			−0.543341	+	0.839512i	$0.682841\pi$
$44$	3.13930	−	1.06995i	0.473267	−	0.161301i
$45$	1.73285	−	2.49877i	0.258318	−	0.372495i
$46$	4.21685	+	3.06372i	0.621740	+	0.451721i
$47$	−2.60985	+	8.03230i	−0.380686	+	1.17163i	0.558876	+	0.829252i	$0.311233\pi$
$47$	−2.60985	+	8.03230i	−0.380686	+	1.17163i	−0.939562	+	0.342380i	$0.888767\pi$
$48$	1.21121	−	1.23813i	0.174823	−	0.178709i
$49$	−4.64605	+	5.23586i	−0.663722	+	0.747979i
$50$	−2.33503	−	3.21390i	−0.330224	−	0.454514i
$51$	2.32458	−	2.37625i	0.325506	−	0.332741i
$52$	4.83226	+	1.57010i	0.670114	+	0.217733i
$53$	−8.30483	+	11.4306i	−1.14076	+	1.57012i	−0.374949	+	0.927045i	$0.622340\pi$
$53$	−8.30483	+	11.4306i	−1.14076	+	1.57012i	−0.765807	+	0.643070i	$0.777660\pi$
$54$	0.643219	−	5.15619i	0.0875310	−	0.701668i
$55$	2.01473	+	2.69115i	0.271666	+	0.362875i
$56$	−0.286099	−	2.63024i	−0.0382316	−	0.351480i
$57$	14.1556	+	2.08280i	1.87495	+	0.275874i
$58$	−0.169261	+	0.520932i	−0.0222251	+	0.0684018i
$59$	−2.84960	−	8.77015i	−0.370986	−	1.14178i	−0.946147	−	0.323737i	$-0.895061\pi$
$59$	−2.84960	−	8.77015i	−0.370986	−	1.14178i	0.575162	−	0.818040i	$-0.304939\pi$
$60$	1.57294	+	0.779795i	0.203065	+	0.100671i
$61$	−5.06513	−	6.97155i	−0.648523	−	0.892616i	0.350511	−	0.936559i	$-0.386008\pi$
$61$	−5.06513	−	6.97155i	−0.648523	−	0.892616i	−0.999034	+	0.0439430i	$0.986008\pi$
$62$	1.12968	+	3.47679i	0.143469	+	0.441553i
$63$	−5.46036	−	5.76059i	−0.687941	−	0.725767i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$			5.15009i			0.638790i
$66$	5.18280	+	2.47762i	0.637959	+	0.304973i
$67$	−6.40079			−0.781980			−0.390990	−	0.920395i	$-0.627867\pi$
$67$	−6.40079			−0.781980			−0.390990	+	0.920395i	$0.627867\pi$
$68$	1.55268	+	1.12809i	0.188290	+	0.136801i
$69$	1.51021	+	8.90077i	0.181808	+	1.07153i
$70$	2.44594	−	1.09965i	0.292345	−	0.131433i
$71$	5.17867	+	7.12783i	0.614595	+	0.845918i	0.996946	−	0.0780994i	$-0.0248852\pi$
$71$	5.17867	+	7.12783i	0.614595	+	0.845918i	−0.382350	+	0.924018i	$0.624885\pi$
$72$	2.99928	−	0.0659423i	0.353468	−	0.00777138i
$73$	2.49755	−	0.811503i	0.292316	−	0.0949792i	−0.159188	−	0.987248i	$-0.550888\pi$
$73$	2.49755	−	0.811503i	0.292316	−	0.0949792i	0.451504	+	0.892269i	$0.350888\pi$
$74$	4.81122	+	1.56326i	0.559292	+	0.181725i
$75$	1.00162	−	6.80745i	0.115658	−	0.786056i
$76$			8.26070i			0.947568i
$77$	7.95100	−	3.71237i	0.906100	−	0.423063i
$78$	4.08126	+	7.79687i	0.462112	+	0.882822i
$79$	−2.10051	−	1.52611i	−0.236326	−	0.171701i	0.463319	−	0.886192i	$-0.346658\pi$
$79$	−2.10051	−	1.52611i	−0.236326	−	0.171701i	−0.699645	+	0.714491i	$0.746658\pi$
$80$	−0.313222	+	0.964000i	−0.0350193	+	0.107778i
$81$	7.04161	−	5.60497i	0.782402	−	0.622774i
$82$	−2.09841	−	2.88821i	−0.231730	−	0.318950i
$83$	−10.3171	+	7.49579i	−1.13245	+	0.822770i	−0.986049	−	0.166456i	$-0.946768\pi$
$83$	−10.3171	+	7.49579i	−1.13245	+	0.822770i	−0.146396	+	0.989226i	$0.546768\pi$
$84$	2.83154	−	3.60311i	0.308946	−	0.393131i
$85$	−0.601143	+	1.85013i	−0.0652031	+	0.200675i
$86$	4.18847	−	5.76494i	0.451655	−	0.621649i
$87$	−0.840526	+	0.439972i	−0.0901138	+	0.0471700i
$88$	−0.979630	+	3.16865i	−0.104429	+	0.337779i
$89$	15.4473			1.63741			0.818704	−	0.574215i	$-0.194693\pi$
$89$	15.4473			1.63741			0.818704	+	0.574215i	$0.194693\pi$
$90$	1.00301	+	2.87065i	0.105726	+	0.302593i
$91$	13.1592	+	2.74722i	1.37946	+	0.287987i
$92$	−4.95720	+	1.61069i	−0.516824	+	0.167926i
$93$	−2.81243	+	5.67300i	−0.291636	+	0.588263i
$94$	−4.96423	−	6.83268i	−0.512022	−	0.704737i
$95$	−7.96332	+	2.58744i	−0.817019	+	0.265466i
$96$	0.289739	+	1.70765i	0.0295713	+	0.174286i
$97$	6.74995	−	9.29051i	0.685354	−	0.943308i	−0.314629	−	0.949215i	$-0.601880\pi$
$97$	6.74995	−	9.29051i	0.685354	−	0.943308i	0.999983	+	0.00590636i	$0.00188006\pi$
$98$	−1.50502	−	6.83629i	−0.152030	−	0.690570i
$99$	3.41608	+	9.34507i	0.343329	+	0.939215i
$100$	3.97260			0.397260
$101$	7.40043	+	5.37673i	0.736371	+	0.535005i	0.891572	−	0.452878i	$-0.149603\pi$
$101$	7.40043	+	5.37673i	0.736371	+	0.535005i	−0.155202	+	0.987883i	$0.549603\pi$
$102$	0.556073	+	3.27735i	0.0550594	+	0.324506i
$103$	8.10663	−	2.63400i	0.798770	−	0.259536i	0.118936	−	0.992902i	$-0.462052\pi$
$103$	8.10663	−	2.63400i	0.798770	−	0.259536i	0.679834	+	0.733366i	$0.262052\pi$
$104$	−4.11057	+	2.98650i	−0.403074	+	0.292851i
$105$	4.36030	+	1.60103i	0.425521	+	0.156245i
$106$	−4.36611	−	13.4375i	−0.424074	−	1.30516i
$107$	−1.69523	−	0.550812i	−0.163884	−	0.0532490i	0.225926	−	0.974144i	$-0.427459\pi$
$107$	−1.69523	−	0.550812i	−0.163884	−	0.0532490i	−0.389810	+	0.920895i	$0.627459\pi$
$108$	3.79337	+	3.55111i	0.365017	+	0.341705i
$109$	10.1884			0.975876			0.487938	−	0.872878i	$-0.337749\pi$
$109$	10.1884			0.975876			0.487938	+	0.872878i	$0.337749\pi$
$110$	−3.36142	+	0.0481290i	−0.320499	+	0.00458892i
$111$	4.06349	+	7.76291i	0.385689	+	0.736823i
$112$	2.29607	+	1.31456i	0.216958	+	0.124214i
$113$	−7.61373	−	2.47385i	−0.716240	−	0.232720i	−0.0718476	−	0.997416i	$-0.522890\pi$
$113$	−7.61373	−	2.47385i	−0.716240	−	0.232720i	−0.644392	+	0.764695i	$0.722890\pi$
$114$	−10.0054	+	10.2278i	−0.937096	+	0.957925i
$115$	−3.10541	−	4.27423i	−0.289581	−	0.398574i
$116$	−0.321954	−	0.443131i	−0.0298927	−	0.0411437i
$117$	−4.39050	+	14.5968i	−0.405902	+	1.34948i
$118$	8.77015	+	2.84960i	0.807358	+	0.262327i
$119$	4.40667	+	2.52292i	0.403959	+	0.231276i
$120$	−1.55542	+	0.814181i	−0.141989	+	0.0743242i
$121$	−10.9955	+	0.314933i	−0.999590	+	0.0286303i
$122$	8.61731			0.780175
$123$	0.900123	−	6.11760i	0.0811613	−	0.551606i
$124$	−3.47679	−	1.12968i	−0.312225	−	0.101448i
$125$	2.81042	+	8.64958i	0.251372	+	0.773642i
$126$	7.86994	−	1.03153i	0.701110	−	0.0918963i
$127$	0.806567	−	0.586005i	0.0715712	−	0.0519996i	−0.551424	−	0.834225i	$-0.685915\pi$
$127$	0.806567	−	0.586005i	0.0715712	−	0.0519996i	0.622996	+	0.782225i	$0.285915\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	12.1684	−	2.06464i	1.07137	−	0.181781i
$130$	−4.16651	−	3.02715i	−0.365427	−	0.265498i
$131$	8.06675			0.704795			0.352398	−	0.935850i	$-0.385366\pi$
$131$	8.06675			0.704795			0.352398	+	0.935850i	$0.385366\pi$
$132$	−5.05081	+	2.73667i	−0.439616	+	0.238196i
$133$	2.36338	+	21.7276i	0.204931	+	1.88402i
$134$	3.76229	−	5.17834i	0.325012	−	0.447341i
$135$	−2.23510	+	4.76909i	−0.192366	+	0.410458i
$136$	−1.82529	+	0.593072i	−0.156517	+	0.0508555i
$137$	−10.2262	−	14.0751i	−0.873679	−	1.20252i	−0.978132	−	0.207986i	$-0.933309\pi$
$137$	−10.2262	−	14.0751i	−0.873679	−	1.20252i	0.104453	−	0.994530i	$-0.466691\pi$
$138$	−8.08855	−	4.00996i	−0.688543	−	0.341350i
$139$	−0.461104	+	0.149822i	−0.0391103	+	0.0127077i	−0.328507	−	0.944502i	$-0.606545\pi$
$139$	−0.461104	+	0.149822i	−0.0391103	+	0.0127077i	0.289396	+	0.957209i	$0.406545\pi$
$140$	−0.548050	+	2.62516i	−0.0463187	+	0.221867i
$141$	2.12943	−	14.4725i	0.179331	−	1.21880i
$142$	−8.81049			−0.739360
$143$	−13.7736	−	9.70891i	−1.15181	−	0.811900i
$144$	−1.70958	+	2.46522i	−0.142465	+	0.205435i
$145$	0.326335	−	0.449162i	0.0271007	−	0.0373009i
$146$	−0.811503	+	2.49755i	−0.0671604	+	0.206699i
$147$	6.41678	−	10.2871i	0.529247	−	0.848468i
$148$	−4.09266	+	2.97349i	−0.336415	+	0.244420i
$149$	−3.35397	−	4.61635i	−0.274768	−	0.378186i	0.649224	−	0.760597i	$-0.275094\pi$
$149$	−3.35397	−	4.61635i	−0.274768	−	0.378186i	−0.923992	+	0.382411i	$0.875094\pi$
$150$	4.91860	+	4.81165i	0.401602	+	0.392869i
$151$	−1.86872	+	5.75134i	−0.152075	+	0.468037i	−0.997853	−	0.0654974i	$-0.979137\pi$
$151$	−1.86872	+	5.75134i	−0.152075	+	0.468037i	0.845778	+	0.533535i	$0.179137\pi$
$152$	−6.68305	−	4.85552i	−0.542067	−	0.393835i
$153$	−3.28106	+	4.73131i	−0.265258	+	0.382504i
$154$	−1.67011	+	8.61456i	−0.134581	+	0.694181i
$155$		−	3.70547i		−	0.297630i
$156$	−8.70671	−	1.28107i	−0.697094	−	0.102568i
$157$	−5.65240	−	1.83658i	−0.451111	−	0.146575i	0.0746453	−	0.997210i	$-0.476218\pi$
$157$	−5.65240	−	1.83658i	−0.451111	−	0.146575i	−0.525756	+	0.850635i	$0.676218\pi$
$158$	2.46930	−	0.802325i	0.196447	−	0.0638295i
$159$	10.8698	−	21.9257i	0.862032	−	1.73882i
$160$	−0.595785	−	0.820027i	−0.0471009	−	0.0648288i
$161$	−12.5778	+	5.65475i	−0.991269	+	0.445657i
$162$	0.395558	+	8.99130i	0.0310780	+	0.706423i
$163$	13.8289	+	10.0473i	1.08316	+	0.786964i	0.978232	−	0.207516i	$-0.0665379\pi$
$163$	13.8289	+	10.0473i	1.08316	+	0.786964i	0.104931	+	0.994480i	$0.466538\pi$
$164$	3.57003			0.278772
$165$	−4.22017	−	4.01179i	−0.328540	−	0.312317i
$166$		−	12.7526i		−	0.989793i
$167$	−7.95802	−	5.78184i	−0.615810	−	0.447412i	0.235645	−	0.971839i	$-0.424280\pi$
$167$	−7.95802	−	5.78184i	−0.615810	−	0.447412i	−0.851455	+	0.524427i	$0.824280\pi$
$168$	1.25064	+	4.40862i	0.0964887	+	0.340132i
$169$	−3.96035	−	12.1887i	−0.304642	−	0.937592i
$170$	−1.14344	−	1.57381i	−0.0876980	−	0.120706i
$171$	−24.7761	+	0.544730i	−1.89468	+	0.0416565i
$172$	2.20201	+	6.77709i	0.167902	+	0.516748i
$173$	6.64471	−	20.4503i	0.505188	−	1.55481i	−0.295267	−	0.955415i	$-0.595409\pi$
$173$	6.64471	−	20.4503i	0.505188	−	1.55481i	0.800455	−	0.599393i	$-0.204591\pi$
$174$	0.138104	−	0.938609i	0.0104696	−	0.0711558i
$175$	10.4489	−	1.13656i	0.789860	−	0.0859155i
$176$	−1.98768	−	2.65502i	−0.149827	−	0.200130i
$177$	7.40715	+	14.1507i	0.556755	+	1.06363i
$178$	−9.07969	+	12.4971i	−0.680551	+	0.936698i
$179$	16.9761	+	5.51588i	1.26886	+	0.412276i	0.864642	−	0.502389i	$-0.167545\pi$
$179$	16.9761	+	5.51588i	1.26886	+	0.412276i	0.404213	+	0.914665i	$0.367545\pi$
$180$	−2.91196	−	0.875872i	−0.217044	−	0.0652837i
$181$	4.72552	+	6.50411i	0.351245	+	0.483447i	0.947683	−	0.319212i	$-0.103418\pi$
$181$	4.72552	+	6.50411i	0.351245	+	0.483447i	−0.596439	+	0.802659i	$0.703418\pi$
$182$	−9.95733	+	9.03124i	−0.738087	+	0.669440i
$183$	10.6694	+	10.4374i	0.788703	+	0.771553i
$184$	1.61069	−	4.95720i	0.118742	−	0.365450i
$185$	−4.14836	−	3.01396i	−0.304994	−	0.221591i
$186$	−2.93645	−	5.60981i	−0.215311	−	0.411332i
$187$	−3.81479	−	5.09557i	−0.278965	−	0.372625i
$188$	8.44566			0.615963
$189$	10.9934	+	8.25497i	0.799654	+	0.600461i
$190$	2.58744	−	7.96332i	0.187713	−	0.577720i
$191$	9.23017	−	2.99906i	0.667872	−	0.217005i	0.0445940	−	0.999005i	$-0.485801\pi$
$191$	9.23017	−	2.99906i	0.667872	−	0.217005i	0.623278	+	0.782000i	$0.285801\pi$
$192$	−1.55182	−	0.769325i	−0.111993	−	0.0555212i
$193$	2.82361	−	2.05147i	0.203248	−	0.147668i	−0.481505	−	0.876443i	$-0.659910\pi$
$193$	2.82361	−	2.05147i	0.203248	−	0.147668i	0.684754	+	0.728775i	$0.259910\pi$
$194$	3.54866	+	10.9216i	0.254779	+	0.784129i
$195$	−1.49218	−	8.79452i	−0.106857	−	0.629789i
$196$	6.41530	+	2.80069i	0.458236	+	0.200049i
$197$			9.98859i			0.711658i	0.934551	+	0.355829i	$0.115801\pi$
$197$			9.98859i			0.711658i	−0.934551	+	0.355829i	$0.884199\pi$
$198$	−9.56824	−	2.72923i	−0.679986	−	0.193958i
$199$		−	8.94584i		−	0.634154i	−0.948400	−	0.317077i	$-0.897299\pi$
$199$		−	8.94584i		−	0.634154i	0.948400	−	0.317077i	$-0.102701\pi$
$200$	−2.33503	+	3.21390i	−0.165112	+	0.227257i
$201$	10.9303	−	1.85456i	0.770962	−	0.130810i
$202$	−8.69973	+	2.82671i	−0.612111	+	0.198887i
$203$	−0.973594	−	1.07343i	−0.0683329	−	0.0753400i
$204$	−2.97828	−	1.47650i	−0.208521	−	0.103376i
$205$	1.11821	+	3.44150i	0.0780994	+	0.240365i
$206$	−2.63400	+	8.10663i	−0.183520	+	0.564816i
$207$	−5.15780	−	14.7618i	−0.358492	−	1.02602i
$208$		−	5.08094i		−	0.352300i
$209$	8.09243	−	26.1753i	0.559765	−	1.81058i
$210$	−3.85818	+	2.58649i	−0.266240	+	0.178485i
$211$	−7.99046	−	5.80541i	−0.550086	−	0.399661i	0.277731	−	0.960659i	$-0.410417\pi$
$211$	−7.99046	−	5.80541i	−0.550086	−	0.399661i	−0.827817	+	0.560998i	$0.810417\pi$
$212$	13.4375	+	4.36611i	0.922891	+	0.299865i
$213$	−10.9085	−	10.6713i	−0.747441	−	0.731189i
$214$	1.44204	−	1.04771i	0.0985761	−	0.0716198i
$215$	−5.84339	+	4.24547i	−0.398516	+	0.289539i
$216$	−5.10259	+	0.981612i	−0.347187	+	0.0667903i
$217$	−9.46799	−	1.97662i	−0.642729	−	0.134181i
$218$	−5.98861	+	8.24262i	−0.405600	+	0.558261i
$219$	−4.02980	+	2.10940i	−0.272309	+	0.142540i
$220$	1.93685	−	2.74773i	0.130583	−	0.185252i
$221$		−	9.75145i		−	0.655953i
$222$	−8.66878	−	1.27550i	−0.581811	−	0.0856056i
$223$	−1.49979	−	0.487311i	−0.100433	−	0.0326327i	0.258369	−	0.966046i	$-0.416815\pi$
$223$	−1.49979	−	0.487311i	−0.100433	−	0.0326327i	−0.358803	+	0.933413i	$0.616815\pi$
$224$	−2.41309	+	1.08488i	−0.161232	+	0.0724869i
$225$	0.261962	+	11.9149i	0.0174641	+	0.794327i
$226$	6.47663	−	4.70555i	0.430819	−	0.313008i
$227$	0.469709	+	1.44562i	0.0311757	+	0.0959489i	0.965434	−	0.260649i	$-0.0839366\pi$
$227$	0.469709	+	1.44562i	0.0311757	+	0.0959489i	−0.934258	+	0.356598i	$0.883937\pi$
$228$	−2.39345	−	14.1064i	−0.158510	−	0.934216i
$229$	6.47472	−	8.91168i	0.427861	−	0.588901i	−0.539599	−	0.841922i	$-0.681424\pi$
$229$	6.47472	−	8.91168i	0.427861	−	0.588901i	0.967461	+	0.253021i	$0.0814243\pi$
$230$	5.28324			0.348367
$231$	−12.5019	+	8.64311i	−0.822562	+	0.568675i
$232$	0.547741			0.0359609
$233$	−5.60505	+	7.71469i	−0.367199	+	0.505406i	−0.952137	−	0.305672i	$-0.901119\pi$
$233$	−5.60505	+	7.71469i	−0.367199	+	0.505406i	0.584938	+	0.811078i	$0.301119\pi$
$234$	−9.22840	−	12.1318i	−0.603280	−	0.793080i
$235$	2.64537	+	8.14161i	0.172565	+	0.531100i
$236$	−7.46034	+	5.42025i	−0.485627	+	0.352828i
$237$	4.02910	+	1.99746i	0.261718	+	0.129749i
$238$	−4.63126	+	2.08213i	−0.300200	+	0.134965i
$239$	−2.65620	−	0.863052i	−0.171815	−	0.0558262i	0.221846	−	0.975082i	$-0.428792\pi$
$239$	−2.65620	−	0.863052i	−0.171815	−	0.0558262i	−0.393661	+	0.919256i	$0.628792\pi$
$240$	0.255565	−	1.73692i	0.0164966	−	0.112118i
$241$			21.5649i			1.38912i	0.719437	+	0.694558i	$0.244400\pi$
$241$			21.5649i			1.38912i	−0.719437	+	0.694558i	$0.755600\pi$
$242$	6.20820	−	9.08065i	0.399078	−	0.583726i
$243$	−10.4006	+	11.6115i	−0.667199	+	0.744880i
$244$	−5.06513	+	6.97155i	−0.324262	+	0.446308i
$245$	−0.690447	+	7.06159i	−0.0441110	+	0.451149i
$246$	4.42016	+	4.32405i	0.281819	+	0.275691i
$247$	33.9562	−	24.6706i	2.16058	−	1.56975i
$248$	2.95754	−	2.14878i	0.187804	−	0.136447i
$249$	15.4461	−	15.7894i	0.978855	−	1.00061i
$250$	−8.64958	−	2.81042i	−0.547047	−	0.177747i
$251$	−18.9003	−	13.7319i	−1.19298	−	0.866748i	−0.199401	−	0.979918i	$-0.563900\pi$
$251$	−18.9003	−	13.7319i	−1.19298	−	0.866748i	−0.993576	+	0.113170i	$0.963900\pi$
$252$	−3.79131	+	6.97323i	−0.238830	+	0.439272i
$253$	17.2855	−	0.247495i	1.08673	−	0.0155599i
$254$			0.996972i			0.0625556i
$255$	0.490485	−	3.33354i	0.0307154	−	0.208754i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−8.10825	−	24.9546i	−0.505779	−	1.55663i	−0.799457	−	0.600723i	$-0.794880\pi$
$257$	−8.10825	−	24.9546i	−0.505779	−	1.55663i	0.293679	−	0.955904i	$-0.405120\pi$
$258$	−5.48210	+	11.0580i	−0.341301	+	0.688443i
$259$	−9.91396	+	8.99190i	−0.616024	+	0.558730i
$260$	4.89803	−	1.59146i	0.303763	−	0.0986985i
$261$	1.30784	−	0.994849i	0.0809534	−	0.0615796i
$262$	−4.74152	+	6.52614i	−0.292932	+	0.403186i
$263$			12.0306i			0.741836i	0.928666	+	0.370918i	$0.120957\pi$
$263$			12.0306i			0.741836i	−0.928666	+	0.370918i	$0.879043\pi$
$264$	0.754780	−	5.69476i	0.0464535	−	0.350488i
$265$			14.3213i			0.879751i
$266$	−18.9672	−	10.8592i	−1.16295	−	0.665818i
$267$	−26.3785	+	4.47568i	−1.61434	+	0.273907i
$268$	1.97795	+	6.08751i	0.120823	+	0.371854i
$269$	4.61604	−	3.35375i	0.281445	−	0.204482i	−0.438102	−	0.898925i	$-0.644349\pi$
$269$	4.61604	−	3.35375i	0.281445	−	0.204482i	0.719547	+	0.694443i	$0.244349\pi$
$270$	−2.54452	−	4.61143i	−0.154855	−	0.280643i
$271$	−28.8487	+	9.37351i	−1.75243	+	0.569400i	−0.996372	−	0.0850998i	$-0.972879\pi$
$271$	−28.8487	+	9.37351i	−1.75243	+	0.569400i	−0.756062	+	0.654500i	$0.772879\pi$
$272$	0.593072	−	1.82529i	0.0359603	−	0.110674i
$273$	−23.2672	−	0.878553i	−1.40820	−	0.0531724i
$274$	17.3978			1.05104
$275$	−12.5878	−	3.89167i	−0.759070	−	0.234677i
$276$	7.99846	−	4.18678i	0.481451	−	0.252015i
$277$	−16.9969	−	12.3489i	−1.02124	−	0.741976i	−0.0547053	−	0.998503i	$-0.517422\pi$
$277$	−16.9969	−	12.3489i	−1.02124	−	0.741976i	−0.966537	+	0.256526i	$0.917422\pi$
$278$	0.149822	−	0.461104i	0.00898572	−	0.0276552i
$279$	3.15895	−	10.5023i	0.189121	−	0.628759i
$280$	−1.80166	−	1.98641i	−0.107670	−	0.118711i
$281$	7.30532	+	10.0549i	0.435799	+	0.599826i	0.969272	−	0.245991i	$-0.0791134\pi$
$281$	7.30532	+	10.0549i	0.435799	+	0.599826i	−0.533473	+	0.845817i	$0.679113\pi$
$282$	10.4568	+	10.2295i	0.622696	+	0.609156i
$283$	−5.32172	−	1.72913i	−0.316343	−	0.102786i	0.146542	−	0.989204i	$-0.453186\pi$
$283$	−5.32172	−	1.72913i	−0.316343	−	0.102786i	−0.462885	+	0.886418i	$0.653186\pi$
$284$	5.17867	−	7.12783i	0.307298	−	0.422959i
$285$	12.8488	−	6.72571i	0.761099	−	0.398397i
$286$	15.9506	−	5.43634i	0.943179	−	0.321457i
$287$	9.39002	−	1.02138i	0.554275	−	0.0602902i
$288$	−0.989542	−	2.83210i	−0.0583093	−	0.166883i
$289$	−4.11505	+	12.6648i	−0.242062	+	0.744990i
$290$	0.171565	+	0.528022i	0.0100746	+	0.0310065i
$291$	−8.83470	+	17.8206i	−0.517899	+	1.04466i
$292$	−1.54357	−	2.12454i	−0.0903306	−	0.124329i
$293$	9.09019	+	27.9767i	0.531055	+	1.63442i	0.752023	+	0.659137i	$0.229078\pi$
$293$	9.09019	+	27.9767i	0.531055	+	1.63442i	−0.220968	+	0.975281i	$0.570922\pi$
$294$	4.55077	+	11.2379i	0.265406	+	0.655408i
$295$	−7.56187	−	5.49402i	−0.440269	−	0.319874i
$296$		−	5.05881i		−	0.294037i
$297$	−8.54108	−	14.9683i	−0.495604	−	0.868549i
$298$	5.70612			0.330547
$299$	21.4255	+	15.5666i	1.23907	+	0.900238i
$300$	−6.78378	+	1.15102i	−0.391662	+	0.0664539i
$301$	7.73073	+	17.1954i	0.445592	+	0.991124i
$302$	−3.55452	−	4.89238i	−0.204540	−	0.281525i
$303$	−14.1952	−	7.03735i	−0.815491	−	0.404285i
$304$	7.85640	−	2.55270i	0.450595	−	0.146407i
$305$	−8.30709	−	2.69914i	−0.475662	−	0.154552i
$306$	−1.89915	−	5.43543i	−0.108567	−	0.310723i
$307$			4.31632i			0.246345i	0.992385	+	0.123173i	$0.0393069\pi$
$307$			4.31632i			0.246345i	−0.992385	+	0.123173i	$0.960693\pi$
$308$	−5.98766	−	6.41466i	−0.341179	−	0.365509i
$309$	−13.0801	+	6.84675i	−0.744099	+	0.389498i
$310$	2.99779	+	2.17802i	0.170263	+	0.123703i
$311$	−2.76039	+	8.49561i	−0.156527	+	0.481742i	−0.998312	−	0.0580710i	$-0.981505\pi$
$311$	−2.76039	+	8.49561i	−0.156527	+	0.481742i	0.841785	+	0.539813i	$0.181505\pi$
$312$	6.15408	−	6.29088i	0.348406	−	0.356151i
$313$	−0.302800	−	0.416768i	−0.0171153	−	0.0235571i	0.800374	−	0.599502i	$-0.204634\pi$
$313$	−0.302800	−	0.416768i	−0.0171153	−	0.0235571i	−0.817489	+	0.575944i	$0.804634\pi$
$314$	4.80822	−	3.49338i	0.271344	−	0.197143i
$315$	−7.90972	−	1.47064i	−0.445662	−	0.0828614i
$316$	−0.802325	+	2.46930i	−0.0451343	+	0.138909i
$317$	2.45186	−	3.37469i	0.137710	−	0.189542i	−0.734592	−	0.678509i	$-0.762626\pi$
$317$	2.45186	−	3.37469i	0.137710	−	0.189542i	0.872302	+	0.488967i	$0.162626\pi$
$318$	11.3491	+	21.6814i	0.636427	+	1.21583i
$319$	0.586054	+	1.71952i	0.0328127	+	0.0962748i
$320$	1.01361			0.0566625
$321$	3.05443	+	0.449419i	0.170482	+	0.0250841i
$322$	2.81825	−	13.4994i	0.157055	−	0.752294i
$323$	15.0782	−	4.89919i	0.838971	−	0.272598i
$324$	−7.50662	−	4.96494i	−0.417034	−	0.275830i
$325$	−11.8642	−	16.3296i	−0.658106	−	0.905805i
$326$	−16.2568	+	5.28217i	−0.900383	+	0.292552i
$327$	−17.3982	+	2.95199i	−0.962125	+	0.163245i
$328$	−2.09841	+	2.88821i	−0.115865	+	0.159475i
$329$	22.2141	−	2.41629i	1.22470	−	0.133215i
$330$	5.72616	−	1.05612i	0.315215	−	0.0581375i
$331$	−6.45848			−0.354990			−0.177495	−	0.984122i	$-0.556799\pi$
$331$	−6.45848			−0.354990			−0.177495	+	0.984122i	$0.556799\pi$
$332$	10.3171	+	7.49579i	0.566223	+	0.411385i
$333$	−9.18821	−	12.0789i	−0.503511	−	0.661922i
$334$	9.35521	−	3.03969i	0.511895	−	0.166325i
$335$	−5.24882	+	3.81349i	−0.286774	+	0.208353i
$336$	−4.30175	−	1.57953i	−0.234680	−	0.0861706i
$337$	−8.87266	−	27.3072i	−0.483324	−	1.48752i	−0.834393	−	0.551170i	$-0.814182\pi$
$337$	−8.87266	−	27.3072i	−0.483324	−	1.48752i	0.351069	−	0.936350i	$-0.385818\pi$
$338$	12.1887	+	3.96035i	0.662978	+	0.215415i
$339$	13.7183	+	2.01847i	0.745077	+	0.109628i
$340$	1.94534			0.105501
$341$	9.91006	+	6.98552i	0.536660	+	0.378287i
$342$	14.1223	−	20.3645i	0.763649	−	1.10119i
$343$	17.6750	+	5.53107i	0.954363	+	0.298650i
$344$	−6.77709	−	2.20201i	−0.365396	−	0.118724i
$345$	6.54135	+	6.39912i	0.352175	+	0.344517i
$346$	12.6390	+	17.3961i	0.679476	+	0.935219i
$347$	12.7665	+	17.5716i	0.685342	+	0.943292i	0.999982	−	0.00591868i	$-0.00188399\pi$
$347$	12.7665	+	17.5716i	0.685342	+	0.943292i	−0.314641	+	0.949211i	$0.601884\pi$
$348$	0.678175	+	0.663429i	0.0363540	+	0.0355635i
$349$	0.0907931	+	0.0295005i	0.00486004	+	0.00157912i	0.311446	−	0.950264i	$-0.399187\pi$
$349$	0.0907931	+	0.0295005i	0.00486004	+	0.00157912i	−0.306586	+	0.951843i	$0.599187\pi$
$350$	−5.22220	+	9.12136i	−0.279138	+	0.487557i
$351$	3.26816	−	26.1983i	0.174441	−	1.39836i
$352$	3.31628	−	0.0474828i	0.176759	−	0.00253084i
$353$	−24.0019			−1.27749			−0.638747	−	0.769416i	$-0.720547\pi$
$353$	−24.0019			−1.27749			−0.638747	+	0.769416i	$0.720547\pi$
$354$	−15.8019	−	2.32504i	−0.839864	−	0.123575i
$355$	8.49331	+	2.75964i	0.450778	+	0.146467i
$356$	−4.77347	−	14.6912i	−0.252994	−	0.778634i
$357$	−8.25601	−	3.03147i	−0.436954	−	0.160443i
$358$	−14.4408	+	10.4918i	−0.763218	+	0.554510i
$359$	−12.8065	+	4.16110i	−0.675903	+	0.219614i	−0.626801	−	0.779179i	$-0.715636\pi$
$359$	−12.8065	+	4.16110i	−0.675903	+	0.219614i	−0.0491025	+	0.998794i	$0.515636\pi$
$360$	2.42020	−	1.84100i	0.127556	−	0.0970290i
$361$	39.8354	+	28.9421i	2.09660	+	1.52327i
$362$	−8.03953			−0.422548
$363$	18.6851	−	3.72361i	0.980716	−	0.195439i
$364$	−1.45365	−	13.3641i	−0.0761920	−	0.700468i
$365$	1.56458	−	2.15346i	0.0818937	−	0.112717i
$366$	−14.7153	+	2.49677i	−0.769181	+	0.130508i
$367$	20.0916	−	6.52817i	1.04878	−	0.340768i	0.266588	−	0.963811i	$-0.414104\pi$
$367$	20.0916	−	6.52817i	1.04878	−	0.340768i	0.782188	+	0.623043i	$0.214104\pi$
$368$	3.06372	+	4.21685i	0.159707	+	0.219818i
$369$	0.235416	+	10.7075i	0.0122553	+	0.557410i
$370$	4.87669	−	1.58453i	0.253527	−	0.0823760i
$371$	36.5929	+	7.63945i	1.89981	+	0.396620i
$372$	6.26444	+	0.921728i	0.324796	+	0.0477894i
$373$	−13.1476			−0.680755			−0.340377	−	0.940289i	$-0.610555\pi$
$373$	−13.1476			−0.680755			−0.340377	+	0.940289i	$0.610555\pi$
$374$	6.36468	−	0.0911299i	0.329110	−	0.00471222i
$375$	−7.30532	−	13.9561i	−0.377245	−	0.720691i
$376$	−4.96423	+	6.83268i	−0.256011	+	0.352369i
$377$	−0.860006	+	2.64683i	−0.0442926	+	0.136318i
$378$	−13.1402	+	4.04172i	−0.675858	+	0.207884i
$379$	3.99386	−	2.90171i	0.205151	−	0.149051i	−0.480466	−	0.877013i	$-0.659533\pi$
$379$	3.99386	−	2.90171i	0.205151	−	0.149051i	0.685617	+	0.727963i	$0.259533\pi$
$380$	4.92160	+	6.77400i	0.252473	+	0.347499i
$381$	−1.20754	+	1.23438i	−0.0618642	+	0.0632393i
$382$	−2.99906	+	9.23017i	−0.153445	+	0.472257i
$383$	−2.30820	−	1.67701i	−0.117944	−	0.0856912i	0.527250	−	0.849710i	$-0.323223\pi$
$383$	−2.30820	−	1.67701i	−0.117944	−	0.0856912i	−0.645193	+	0.764019i	$0.723223\pi$
$384$	1.53453	−	0.803249i	0.0783088	−	0.0409906i
$385$	4.30826	−	7.78132i	0.219569	−	0.396573i
$386$			3.49018i			0.177645i
$387$	−20.1812	+	7.05133i	−1.02587	+	0.358439i
$388$	−10.9216	−	3.54866i	−0.554463	−	0.180156i
$389$	−13.9784	+	4.54185i	−0.708732	+	0.230281i	−0.641131	−	0.767432i	$-0.721534\pi$
$389$	−13.9784	+	4.54185i	−0.708732	+	0.230281i	−0.0676008	+	0.997712i	$0.521534\pi$
$390$	7.99200	+	3.96209i	0.404691	+	0.200628i
$391$	5.87995	+	8.09306i	0.297362	+	0.409284i
$392$	−6.03663	+	3.54389i	−0.304896	+	0.178993i
$393$	−13.7751	+	2.33725i	−0.694864	+	0.117899i
$394$	−8.08094	−	5.87115i	−0.407112	−	0.295784i
$395$	−2.63171			−0.132416
$396$	7.83207	−	6.13667i	0.393576	−	0.308379i
$397$			19.0866i			0.957930i	0.877834	+	0.478965i	$0.158988\pi$
$397$			19.0866i			0.957930i	−0.877834	+	0.478965i	$0.841012\pi$
$398$	7.23734	+	5.25823i	0.362775	+	0.263571i
$399$	−10.3311	−	36.4183i	−0.517204	−	1.82319i
$400$	−1.22760	−	3.77816i	−0.0613800	−	0.188908i
$401$	−14.0631	−	19.3562i	−0.702278	−	0.966603i	−0.999929	−	0.0119284i	$-0.996203\pi$
$401$	−14.0631	−	19.3562i	−0.702278	−	0.966603i	0.297650	−	0.954675i	$-0.403797\pi$
$402$	−4.92428	+	9.93285i	−0.245601	+	0.495406i
$403$	5.73983	+	17.6654i	0.285921	+	0.879975i
$404$	2.82671	−	8.69973i	0.140634	−	0.432828i
$405$	2.43496	−	8.79151i	0.120994	−	0.436854i
$406$	1.44069	−	0.156708i	0.0715001	−	0.00777728i
$407$	15.8811	−	5.41266i	0.787199	−	0.268296i
$408$	2.94511	−	1.54161i	0.145805	−	0.0763212i
$409$	18.4055	−	25.3331i	0.910095	−	1.25264i	−0.0570387	−	0.998372i	$-0.518166\pi$
$409$	18.4055	−	25.3331i	0.910095	−	1.25264i	0.967134	−	0.254267i	$-0.0818342\pi$
$410$	−3.44150	−	1.11821i	−0.169964	−	0.0552246i
$411$	21.5407	+	21.0723i	1.06253	+	1.03942i
$412$	−5.01017	−	6.89591i	−0.246834	−	0.339737i
$413$	−18.0717	+	16.3909i	−0.889252	+	0.806546i
$414$	14.9742	+	4.50402i	0.735943	+	0.221360i
$415$	−3.99440	+	12.2935i	−0.196077	+	0.603464i
$416$	4.11057	+	2.98650i	0.201537	+	0.146425i
$417$	0.743993	−	0.389442i	0.0364335	−	0.0190711i
$418$	16.4196	+	21.9323i	0.803110	+	1.07275i
$419$	3.54560			0.173214			0.0866070	−	0.996243i	$-0.472398\pi$
$419$	3.54560			0.173214			0.0866070	+	0.996243i	$0.472398\pi$
$420$	0.175265	−	4.64163i	0.00855204	−	0.226489i
$421$	11.2677	−	34.6785i	0.549155	−	1.69013i	−0.161745	−	0.986833i	$-0.551712\pi$
$421$	11.2677	−	34.6785i	0.549155	−	1.69013i	0.710900	−	0.703293i	$-0.248288\pi$
$422$	9.39334	−	3.05208i	0.457261	−	0.148573i
$423$	0.556926	+	25.3309i	0.0270787	+	1.23163i
$424$	−11.4306	+	8.30483i	−0.555120	+	0.403318i
$425$	−2.35603	−	7.25113i	−0.114284	−	0.351731i
$426$	15.0452	−	2.55274i	0.728941	−	0.123681i
$427$	−11.3279	+	19.7860i	−0.548197	+	0.957510i
$428$			1.78247i			0.0861587i
$429$	26.3335	+	12.5886i	1.27139	+	0.607784i
$430$		−	7.22283i		−	0.348316i
$431$	−7.26804	+	10.0036i	−0.350089	+	0.481856i	−0.947354	−	0.320188i	$-0.896254\pi$
$431$	−7.26804	+	10.0036i	−0.350089	+	0.481856i	0.597265	+	0.802044i	$0.296254\pi$
$432$	2.20509	−	4.70506i	0.106092	−	0.226372i
$433$	−1.43561	+	0.466458i	−0.0689910	+	0.0224165i	−0.343309	−	0.939222i	$-0.611548\pi$
$433$	−1.43561	+	0.466458i	−0.0689910	+	0.0224165i	0.274318	+	0.961639i	$0.411548\pi$
$434$	7.16426	−	6.49794i	0.343895	−	0.311911i
$435$	−0.427125	+	0.861562i	−0.0204791	+	0.0413087i
$436$	−3.14840	−	9.68978i	−0.150781	−	0.464056i
$437$	−13.3054	+	40.9500i	−0.636486	+	1.95890i
$438$	0.662122	−	4.50005i	0.0316374	−	0.215021i
$439$		−	12.8099i		−	0.611383i	−0.952131	−	0.305691i	$-0.901112\pi$
$439$		−	12.8099i		−	0.611383i	0.952131	−	0.305691i	$-0.0988876\pi$
$440$	1.08451	+	3.18203i	0.0517019	+	0.151697i
$441$	−7.97700	+	19.4259i	−0.379857	+	0.925045i
$442$	7.88909	+	5.73176i	0.375246	+	0.272632i
$443$	19.5796	+	6.36181i	0.930257	+	0.302259i	0.734668	−	0.678427i	$-0.237338\pi$
$443$	19.5796	+	6.36181i	0.930257	+	0.302259i	0.195589	+	0.980686i	$0.437338\pi$
$444$	6.12728	−	6.26348i	0.290788	−	0.297251i
$445$	12.6672	−	9.20325i	0.600483	−	0.436276i
$446$	1.27580	−	0.926920i	0.0604107	−	0.0438909i
$447$	7.06493	+	6.91131i	0.334160	+	0.326894i
$448$	0.540692	−	2.58991i	0.0255453	−	0.122362i
$449$	−7.09042	+	9.75912i	−0.334617	+	0.460561i	−0.942860	−	0.333190i	$-0.891875\pi$
$449$	−7.09042	+	9.75912i	−0.334617	+	0.460561i	0.608242	+	0.793751i	$0.291875\pi$
$450$	−9.79334	−	6.79148i	−0.461663	−	0.320153i
$451$	−11.3122	−	3.49730i	−0.532669	−	0.164682i
$452$			8.00555i			0.376549i
$453$	1.52473	−	10.3627i	0.0716381	−	0.486881i
$454$	−1.44562	−	0.469709i	−0.0678461	−	0.0220445i
$455$	12.4277	−	5.58725i	0.582617	−	0.261934i
$456$	12.8191	+	6.35517i	0.600310	+	0.297608i
$457$	6.52749	−	4.74250i	0.305343	−	0.221845i	−0.424553	−	0.905403i	$-0.639569\pi$
$457$	6.52749	−	4.74250i	0.305343	−	0.221845i	0.729896	+	0.683558i	$0.239569\pi$
$458$	3.40396	+	10.4763i	0.159057	+	0.489526i
$459$	4.23205	−	9.03005i	0.197535	−	0.421487i
$460$	−3.10541	+	4.27423i	−0.144791	+	0.199287i
$461$	10.6013			0.493750			0.246875	−	0.969047i	$-0.420596\pi$
$461$	10.6013			0.493750			0.246875	+	0.969047i	$0.420596\pi$
$462$	0.355985	−	15.1945i	0.0165619	−	0.706913i
$463$	−3.94527			−0.183352			−0.0916762	−	0.995789i	$-0.529222\pi$
$463$	−3.94527			−0.183352			−0.0916762	+	0.995789i	$0.529222\pi$
$464$	−0.321954	+	0.443131i	−0.0149463	+	0.0205719i
$465$	1.07362	+	6.32762i	0.0497878	+	0.293436i
$466$	−2.94675	−	9.06917i	−0.136506	−	0.420121i
$467$	0.847134	−	0.615479i	0.0392007	−	0.0284810i	−0.568012	−	0.823020i	$-0.692287\pi$
$467$	0.847134	−	0.615479i	0.0392007	−	0.0284810i	0.607213	+	0.794539i	$0.292287\pi$
$468$	15.2391	−	0.335049i	0.704429	−	0.0154876i
$469$	6.94411	+	15.4457i	0.320649	+	0.713216i
$470$	−8.14161	−	2.64537i	−0.375545	−	0.122022i
$471$	10.1844	+	1.49850i	0.469273	+	0.0690473i
$472$		−	9.22148i		−	0.424453i
$473$	−0.338355	−	23.6314i	−0.0155576	−	1.08657i
$474$	−3.98422	+	2.08554i	−0.183002	+	0.0957919i
$475$	19.2890	−	26.5491i	0.885041	−	1.21815i
$476$	1.03771	−	4.97062i	0.0475632	−	0.227828i
$477$	−12.2091	+	40.5907i	−0.559014	+	1.85852i
$478$	2.25950	−	1.64162i	0.103347	−	0.0750860i
$479$	−19.8267	+	14.4050i	−0.905907	+	0.658180i	−0.939976	−	0.341240i	$-0.889153\pi$
$479$	−19.8267	+	14.4050i	−0.905907	+	0.658180i	0.0340695	+	0.999419i	$0.489153\pi$
$480$	1.25498	+	1.22769i	0.0572818	+	0.0560363i
$481$	24.4455	+	7.94282i	1.11462	+	0.362162i
$482$	−17.4463	−	12.6755i	−0.794659	−	0.577354i
$483$	19.8400	−	13.3006i	0.902752	−	0.605197i
$484$	3.69731	+	10.3600i	0.168060	+	0.470910i
$485$		−	11.6400i		−	0.528545i
$486$	−3.28060	−	15.2393i	−0.148811	−	0.691271i
$487$	−5.62488	+	17.3116i	−0.254888	+	0.784463i	0.738964	+	0.673745i	$0.235315\pi$
$487$	−5.62488	+	17.3116i	−0.254888	+	0.784463i	−0.993852	+	0.110719i	$0.964685\pi$
$488$	−2.66290	−	8.19555i	−0.120544	−	0.370995i
$489$	−26.5259	−	13.1504i	−1.19954	−	0.594682i
$490$	−5.30711	−	4.70928i	−0.239751	−	0.212744i
$491$	−20.1057	+	6.53274i	−0.907358	+	0.294819i	−0.725271	−	0.688464i	$-0.758285\pi$
$491$	−20.1057	+	6.53274i	−0.907358	+	0.294819i	−0.182088	+	0.983282i	$0.558285\pi$
$492$	−6.09634	+	1.03437i	−0.274844	+	0.0466332i
$493$	−0.617901	+	0.850467i	−0.0278288	+	0.0383031i
$494$			41.9722i			1.88842i
$495$	8.36893	+	5.62797i	0.376155	+	0.252958i
$496$			3.65572i			0.164146i
$497$	11.5819	−	20.2295i	0.519518	−	0.907417i
$498$	3.69492	+	21.7769i	0.165573	+	0.975847i
$499$	−3.79351	−	11.6752i	−0.169821	−	0.522654i	0.829538	−	0.558450i	$-0.188604\pi$
$499$	−3.79351	−	11.6752i	−0.169821	−	0.522654i	−0.999359	+	0.0357953i	$0.988604\pi$
$500$	7.35777	−	5.34573i	0.329050	−	0.239069i
$501$	15.2647	+	7.56758i	0.681976	+	0.338095i
$502$	22.2186	−	7.21927i	0.991667	−	0.322212i
$503$	8.31118	−	25.5792i	0.370577	−	1.14052i	−0.575837	−	0.817564i	$-0.695324\pi$
$503$	8.31118	−	25.5792i	0.370577	−	1.14052i	0.946414	−	0.322955i	$-0.104676\pi$
$504$	−3.41299	−	7.16600i	−0.152027	−	0.319199i
$505$	9.27193			0.412595
$506$	−9.95993	+	14.1297i	−0.442773	+	0.628143i
$507$	10.2944	+	19.6665i	0.457191	+	0.873420i
$508$	−0.806567	−	0.586005i	−0.0357856	−	0.0259998i
$509$	−5.15149	+	15.8547i	−0.228336	+	0.702746i	0.769600	+	0.638526i	$0.220456\pi$
$509$	−5.15149	+	15.8547i	−0.228336	+	0.702746i	−0.997936	+	0.0642192i	$0.979544\pi$
$510$	2.40859	+	2.35621i	0.106654	+	0.104335i
$511$	−4.66778	−	5.14644i	−0.206491	−	0.227665i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	42.1510	−	8.10881i	1.86101	−	0.358013i
$514$	24.9546	+	8.10825i	1.10070	+	0.357640i
$515$	5.07836	−	6.98976i	0.223779	−	0.308006i
$516$	−5.72384	−	10.9349i	−0.251978	−	0.481380i
$517$	−26.7613	−	8.27362i	−1.17696	−	0.363873i
$518$	−1.44732	−	13.3059i	−0.0635916	−	0.584627i
$519$	−5.42156	+	36.8471i	−0.237980	+	1.61741i
$520$	−1.59146	+	4.89803i	−0.0697904	+	0.214793i
$521$	−3.78190	−	11.6395i	−0.165688	−	0.509935i	0.833398	−	0.552673i	$-0.186392\pi$
$521$	−3.78190	−	11.6395i	−0.165688	−	0.509935i	−0.999086	+	0.0427377i	$0.986392\pi$
$522$	0.0361193	+	1.64282i	0.00158090	+	0.0719045i
$523$	16.7754	+	23.0894i	0.733538	+	1.00963i	0.998964	+	0.0454977i	$0.0144874\pi$
$523$	16.7754	+	23.0894i	0.733538	+	1.00963i	−0.265426	+	0.964131i	$0.585513\pi$
$524$	−2.49276	−	7.67194i	−0.108897	−	0.335150i
$525$	−17.5137	+	4.96828i	−0.764359	+	0.216833i
$526$	−9.73293	−	7.07139i	−0.424376	−	0.308327i
$527$			7.01612i			0.305627i
$528$	4.16351	+	3.95793i	0.181194	+	0.172247i
$529$	−4.16816			−0.181224
$530$	−11.5862	−	8.41785i	−0.503271	−	0.365648i
$531$	−16.7488	−	22.0182i	−0.726835	−	0.955508i
$532$	19.9339	−	8.96191i	0.864243	−	0.388548i
$533$	−10.6619	−	14.6748i	−0.461818	−	0.635638i
$534$	11.8840	−	23.9714i	0.514270	−	1.03734i
$535$	−1.71830	+	0.558308i	−0.0742884	+	0.0241378i
$536$	−6.08751	−	1.97795i	−0.262940	−	0.0854345i
$537$	−30.5874	−	4.50052i	−1.31994	−	0.194212i
$538$			5.70574i			0.245992i
$539$	−17.5842	−	15.1590i	−0.757405	−	0.652945i
$540$	5.22636	+	0.651972i	0.224907	+	0.0280564i
$541$	−17.7621	−	12.9049i	−0.763654	−	0.554827i	0.136375	−	0.990657i	$-0.456455\pi$
$541$	−17.7621	−	12.9049i	−0.763654	−	0.554827i	−0.900029	+	0.435830i	$0.856455\pi$
$542$	9.37351	−	28.8487i	0.402627	−	1.23916i
$543$	−9.95400	−	9.73755i	−0.427167	−	0.417878i
$544$	1.12809	+	1.55268i	0.0483664	+	0.0665707i
$545$	8.35480	−	6.07012i	0.357880	−	0.260015i
$546$	14.3869	−	18.3072i	0.615702	−	0.783475i
$547$	9.94519	−	30.6081i	0.425226	−	1.30871i	−0.477552	−	0.878603i	$-0.658476\pi$
$547$	9.94519	−	30.6081i	0.425226	−	1.30871i	0.902778	−	0.430107i	$-0.141524\pi$
$548$	−10.2262	+	14.0751i	−0.436840	+	0.601258i
$549$	−21.2436	−	14.7320i	−0.906655	−	0.628746i
$550$	10.5473	−	7.89624i	0.449740	−	0.336697i
$551$	−4.52472			−0.192760
$552$	−1.31420	+	8.93182i	−0.0559359	+	0.380163i
$553$	−1.40384	+	6.72439i	−0.0596973	+	0.285950i
$554$	19.9810	−	6.49222i	0.848912	−	0.275828i
$555$	7.95719	+	3.94484i	0.337764	+	0.167449i
$556$	0.284978	+	0.392239i	0.0120858	+	0.0166346i
$557$	−2.55036	+	0.828662i	−0.108062	+	0.0351115i	−0.362549	−	0.931965i	$-0.618093\pi$
$557$	−2.55036	+	0.828662i	−0.108062	+	0.0351115i	0.254487	+	0.967076i	$0.418093\pi$
$558$	6.63980	+	8.72877i	0.281085	+	0.369518i
$559$	21.2814	−	29.2913i	0.900107	−	1.23889i
$560$	2.66603	−	0.289992i	0.112660	−	0.0122544i
$561$	7.99070	+	7.59613i	0.337367	+	0.320709i
$562$	−12.4286			−0.524267
$563$	12.2852	+	8.92575i	0.517761	+	0.376176i	0.815760	−	0.578391i	$-0.196319\pi$
$563$	12.2852	+	8.92575i	0.517761	+	0.376176i	−0.297999	+	0.954566i	$0.596319\pi$
$564$	−14.4222	+	2.44704i	−0.607284	+	0.103039i
$565$	−7.71735	+	2.50752i	−0.324671	+	0.105492i
$566$	4.52692	−	3.28900i	0.190281	−	0.138247i
$567$	−21.1647	−	10.9113i	−0.888832	−	0.458233i
$568$	2.72259	+	8.37927i	0.114237	+	0.351586i
$569$	7.34653	+	2.38703i	0.307983	+	0.100070i	0.458931	−	0.888472i	$-0.348233\pi$
$569$	7.34653	+	2.38703i	0.307983	+	0.100070i	−0.150948	+	0.988542i	$0.548233\pi$
$570$	−2.11114	+	14.3482i	−0.0884261	+	0.600980i
$571$	−18.4345			−0.771458			−0.385729	−	0.922612i	$-0.626050\pi$
$571$	−18.4345			−0.771458			−0.385729	+	0.922612i	$0.626050\pi$
$572$	−4.97744	+	16.0997i	−0.208117	+	0.673163i
$573$	−14.8929	+	7.79568i	−0.622160	+	0.325669i
$574$	−4.69300	+	8.19703i	−0.195882	+	0.342138i
$575$	19.6930	+	6.39863i	0.821253	+	0.266841i
$576$	2.87286	+	0.864112i	0.119702	+	0.0360047i
$577$	8.44416	+	11.6224i	0.351535	+	0.483847i	0.947766	−	0.318966i	$-0.103336\pi$
$577$	8.44416	+	11.6224i	0.351535	+	0.483847i	−0.596231	+	0.802813i	$0.703336\pi$
$578$	−7.82730	−	10.7733i	−0.325573	−	0.448112i
$579$	−4.22733	+	4.32130i	−0.175682	+	0.179587i
$580$	−0.528022	−	0.171565i	−0.0219249	−	0.00712384i
$581$	29.2809	+	16.7640i	1.21478	+	0.695488i
$582$	−9.22428	−	17.6221i	−0.382359	−	0.730460i
$583$	−38.3015	−	26.9984i	−1.58629	−	1.11816i
$584$	2.62608			0.108668
$585$	5.09623	+	14.5856i	0.210703	+	0.603040i
$586$	−27.9767	−	9.09019i	−1.15571	−	0.375512i
$587$	8.32919	+	25.6346i	0.343782	+	1.05805i	0.962232	+	0.272229i	$0.0877608\pi$
$587$	8.32919	+	25.6346i	0.343782	+	1.05805i	−0.618450	+	0.785824i	$0.712239\pi$
$588$	−11.7665	−	2.92382i	−0.485244	−	0.120576i
$589$	−24.4313	+	17.7504i	−1.00668	+	0.731392i
$590$	8.88951	−	2.88838i	0.365975	−	0.118913i
$591$	−2.89408	−	17.0570i	−0.119047	−	0.701630i
$592$	4.09266	+	2.97349i	0.168207	+	0.122210i
$593$	−20.9730			−0.861258			−0.430629	−	0.902529i	$-0.641708\pi$
$593$	−20.9730			−0.861258			−0.430629	+	0.902529i	$0.641708\pi$
$594$	17.1299	+	1.88827i	0.702849	+	0.0774765i
$595$	5.11671	−	0.556559i	0.209764	−	0.0228167i
$596$	−3.35397	+	4.61635i	−0.137384	+	0.189093i
$597$	2.59196	+	15.2763i	0.106082	+	0.625218i
$598$	−25.1872	+	8.18383i	−1.02998	+	0.334662i
$599$	−8.93324	−	12.2955i	−0.365002	−	0.502382i	0.586532	−	0.809926i	$-0.300493\pi$
$599$	−8.93324	−	12.2955i	−0.365002	−	0.502382i	−0.951534	+	0.307544i	$0.900493\pi$
$600$	3.05622	−	6.16475i	0.124770	−	0.251675i
$601$	−32.2651	+	10.4836i	−1.31612	+	0.427633i	−0.881161	−	0.472817i	$-0.843237\pi$
$601$	−32.2651	+	10.4836i	−1.31612	+	0.427633i	−0.434959	+	0.900450i	$0.643237\pi$
$602$	−18.4553	−	3.85289i	−0.752184	−	0.157032i
$603$	−18.1277	+	6.33385i	−0.738216	+	0.257934i
$604$	6.04732			0.246062
$605$	−8.82897	+	6.80920i	−0.358949	+	0.276833i
$606$	14.0370	−	7.34767i	0.570216	−	0.298479i
$607$	−13.2814	+	18.2803i	−0.539076	+	0.741974i	−0.988479	−	0.151355i	$-0.951636\pi$
$607$	−13.2814	+	18.2803i	−0.539076	+	0.741974i	0.449404	+	0.893329i	$0.351636\pi$
$608$	−2.55270	+	7.85640i	−0.103526	+	0.318619i
$609$	1.97357	+	1.55095i	0.0799730	+	0.0628477i
$610$	7.06643	−	5.13406i	0.286111	−	0.207872i
$611$	−25.2230	−	34.7165i	−1.02041	−	1.40448i
$612$	5.51365	+	1.65842i	0.222876	+	0.0670377i
$613$	−7.72272	+	23.7681i	−0.311918	+	0.959984i	0.665087	+	0.746766i	$0.268394\pi$
$613$	−7.72272	+	23.7681i	−0.311918	+	0.959984i	−0.977005	+	0.213218i	$0.931606\pi$
$614$	−3.49198	−	2.53707i	−0.140925	−	0.102388i
$615$	−2.90665	−	5.55288i	−0.117207	−	0.223914i
$616$	8.70903	−	1.07368i	0.350897	−	0.0432596i
$617$		−	5.82704i		−	0.234588i	−0.993097	−	0.117294i	$-0.962578\pi$
$617$		−	5.82704i		−	0.234588i	0.993097	−	0.117294i	$-0.0374219\pi$
$618$	2.14914	−	14.6064i	0.0864510	−	0.587556i
$619$	−21.3983	−	6.95272i	−0.860070	−	0.279454i	−0.154412	−	0.988007i	$-0.549348\pi$
$619$	−21.3983	−	6.95272i	−0.860070	−	0.279454i	−0.705658	+	0.708553i	$0.749348\pi$
$620$	−3.52411	+	1.14505i	−0.141532	+	0.0459864i
$621$	13.0848	+	23.7135i	0.525073	+	0.951590i
$622$	−5.25058	−	7.22680i	−0.210529	−	0.289768i
$623$	−16.7585	−	37.2758i	−0.671416	−	1.49342i
$624$	1.47215	+	8.67644i	0.0589330	+	0.347336i
$625$	−8.61158	−	6.25668i	−0.344463	−	0.250267i
$626$	0.515154			0.0205897
$627$	−6.23501	+	47.0427i	−0.249002	+	1.87871i
$628$			5.94329i			0.237163i
$629$	7.85473	+	5.70679i	0.313188	+	0.227545i
$630$	5.83899	−	5.53467i	0.232631	−	0.220507i
$631$	−1.98371	−	6.10522i	−0.0789701	−	0.243045i	0.903776	−	0.428006i	$-0.140784\pi$
$631$	−1.98371	−	6.10522i	−0.0789701	−	0.243045i	−0.982746	+	0.184962i	$0.940784\pi$
$632$	−1.52611	−	2.10051i	−0.0607055	−	0.0835539i
$633$	15.3269	+	7.59843i	0.609190	+	0.302010i
$634$	1.28902	+	3.96719i	0.0511935	+	0.157557i
$635$	0.312274	−	0.961080i	0.0123922	−	0.0381393i
$636$	−24.2115	−	3.56240i	−0.960048	−	0.141258i
$637$	−7.64689	−	34.7348i	−0.302981	−	1.37624i
$638$	−1.73560	−	0.536583i	−0.0687129	−	0.0212435i
$639$	21.7198	+	15.0622i	0.859223	+	0.595853i
$640$	−0.595785	+	0.820027i	−0.0235505	+	0.0324144i
$641$	12.0721	+	3.92246i	0.476819	+	0.154928i	0.537560	−	0.843226i	$-0.319346\pi$
$641$	12.0721	+	3.92246i	0.476819	+	0.154928i	−0.0607408	+	0.998154i	$0.519346\pi$
$642$	−2.15894	+	2.20693i	−0.0852065	+	0.0871005i
$643$	−9.65314	−	13.2864i	−0.380683	−	0.523965i	0.575082	−	0.818095i	$-0.304970\pi$
$643$	−9.65314	−	13.2864i	−0.380683	−	0.523965i	−0.955765	+	0.294130i	$0.904970\pi$
$644$	9.26474	+	10.2148i	0.365082	+	0.402519i
$645$	8.74837	−	8.94282i	0.344467	−	0.352123i
$646$	−4.89919	+	15.0782i	−0.192756	+	0.593242i
$647$	28.3351	+	20.5867i	1.11397	+	0.809345i	0.983284	−	0.182079i	$-0.0582825\pi$
$647$	28.3351	+	20.5867i	1.11397	+	0.809345i	0.130684	+	0.991424i	$0.458283\pi$
$648$	8.42900	−	3.15466i	0.331123	−	0.123927i
$649$	28.9490	−	9.86650i	1.13635	−	0.387294i
$650$	20.1845			0.791702
$651$	16.7407	+	0.632115i	0.656118	+	0.0247745i
$652$	5.28217	−	16.2568i	0.206866	−	0.636667i
$653$	−16.9538	+	5.50862i	−0.663453	+	0.215569i	−0.621337	−	0.783544i	$-0.713410\pi$
$653$	−16.9538	+	5.50862i	−0.663453	+	0.215569i	−0.0421165	+	0.999113i	$0.513410\pi$
$654$	7.83822	−	15.8106i	0.306499	−	0.618244i
$655$	6.61495	−	4.80605i	0.258468	−	0.187788i
$656$	−1.10320	−	3.39530i	−0.0430727	−	0.132564i
$657$	6.27030	−	4.76969i	0.244628	−	0.186083i
$658$	−11.1023	+	19.3918i	−0.432812	+	0.755973i
$659$		−	19.0631i		−	0.742592i	−0.928514	−	0.371296i	$-0.878913\pi$
$659$		−	19.0631i		−	0.742592i	0.928514	−	0.371296i	$-0.121087\pi$
$660$	−2.51133	+	5.25333i	−0.0977536	+	0.204486i
$661$			25.6299i			0.996889i	0.866922	+	0.498445i	$0.166095\pi$
$661$			25.6299i			0.996889i	−0.866922	+	0.498445i	$0.833905\pi$
$662$	3.79620	−	5.22502i	0.147543	−	0.203076i
$663$	2.82537	+	16.6520i	0.109728	+	0.646710i
$664$	−12.1284	+	3.94077i	−0.470675	+	0.152931i
$665$	14.8830	+	16.4092i	0.577138	+	0.636320i
$666$	15.1728	−	0.333590i	0.587933	−	0.0129263i
$667$	−0.882241	−	2.71526i	−0.0341605	−	0.105135i
$668$	−3.03969	+	9.35521i	−0.117609	+	0.361964i
$669$	2.70230	+	0.397607i	0.104477	+	0.0153724i
$670$		−	6.48790i		−	0.250649i
$671$	22.8791	−	17.1284i	0.883240	−	0.661236i
$672$	3.80638	−	2.55176i	0.146834	−	0.0984364i
$673$	−8.65306	−	6.28682i	−0.333551	−	0.242339i	0.408385	−	0.912810i	$-0.366092\pi$
$673$	−8.65306	−	6.28682i	−0.333551	−	0.242339i	−0.741936	+	0.670471i	$0.766092\pi$
$674$	27.3072	+	8.87266i	1.05184	+	0.341762i
$675$	−3.89955	−	20.2705i	−0.150094	−	0.780213i
$676$	−10.3683	+	7.53303i	−0.398782	+	0.289732i
$677$	−0.560407	+	0.407160i	−0.0215382	+	0.0156484i	−0.598502	−	0.801121i	$-0.704237\pi$
$677$	−0.560407	+	0.407160i	−0.0215382	+	0.0156484i	0.576964	+	0.816770i	$0.304237\pi$
$678$	−9.69640	+	9.91193i	−0.372388	+	0.380665i
$679$	−29.7418	−	6.20914i	−1.14139	−	0.238285i
$680$	−1.14344	+	1.57381i	−0.0438490	+	0.0603530i
$681$	−1.22095	−	2.33251i	−0.0467868	−	0.0893818i
$682$	−11.4764	+	3.91142i	−0.439454	+	0.149776i
$683$		−	9.64920i		−	0.369216i	−0.982812	−	0.184608i	$-0.940898\pi$
$683$		−	9.64920i		−	0.369216i	0.982812	−	0.184608i	$-0.0591016\pi$
$684$	8.17431	+	23.3952i	0.312553	+	0.894537i
$685$	−16.7714	−	5.44937i	−0.640804	−	0.208210i
$686$	−14.8639	+	11.0483i	−0.567505	+	0.421827i
$687$	−8.47446	+	17.0940i	−0.323321	+	0.652175i
$688$	5.76494	−	4.18847i	0.219786	−	0.159684i
$689$	−22.1839	−	68.2751i	−0.845140	−	2.60107i
$690$	−9.02191	+	1.53076i	−0.343458	+	0.0582751i
$691$	−28.3605	+	39.0349i	−1.07889	+	1.48496i	−0.218145	+	0.975916i	$0.570001\pi$
$691$	−28.3605	+	39.0349i	−1.07889	+	1.48496i	−0.860741	+	0.509043i	$0.829999\pi$
$692$	−21.5027			−0.817411
$693$	18.8445	−	18.3816i	0.715843	−	0.698261i
$694$	−21.7197			−0.824468
$695$	−0.288856	+	0.397577i	−0.0109569	+	0.0150809i
$696$	−0.935347	+	0.158702i	−0.0354542	+	0.00601557i
$697$	−2.11728	−	6.51632i	−0.0801978	−	0.246823i
$698$	−0.0772332	+	0.0561132i	−0.00292332	+	0.00212392i
$699$	7.33619	−	14.7980i	0.277480	−	0.559710i
$700$	−4.30981	−	9.58625i	−0.162895	−	0.362326i
$701$	−0.932054	−	0.302843i	−0.0352032	−	0.0114382i	0.291362	−	0.956613i	$-0.405891\pi$
$701$	−0.932054	−	0.302843i	−0.0352032	−	0.0114382i	−0.326566	+	0.945175i	$0.605891\pi$
$702$	19.2739	+	18.0430i	0.727446	+	0.680988i
$703$			41.7893i			1.57612i
$704$	−1.91085	+	2.71084i	−0.0720178	+	0.102169i
$705$	−6.87630	−	13.1365i	−0.258976	−	0.494750i
$706$	14.1080	−	19.4180i	0.530961	−	0.730805i
$707$	4.94595	−	23.6911i	0.186011	−	0.890995i
$708$	11.1692	−	11.4174i	0.419762	−	0.429093i
$709$	−21.4031	+	15.5503i	−0.803811	+	0.584003i	−0.912030	−	0.410124i	$-0.865485\pi$
$709$	−21.4031	+	15.5503i	−0.803811	+	0.584003i	0.108218	+	0.994127i	$0.465485\pi$
$710$	−7.22484	+	5.24915i	−0.271143	+	0.196997i
$711$	−7.45902	−	2.24356i	−0.279735	−	0.0841401i
$712$	14.6912	+	4.77347i	0.550578	+	0.178893i
$713$	−15.4156	−	11.2001i	−0.577318	−	0.419446i
$714$	7.30528	−	4.89740i	0.273393	−	0.183281i
$715$	−17.0792	+	0.244541i	−0.638724	+	0.00914530i
$716$		−	17.8498i		−	0.667077i
$717$	4.78591	+	0.704182i	0.178733	+	0.0262982i
$718$	4.16110	−	12.8065i	0.155291	−	0.477936i
$719$	15.5196	+	47.7643i	0.578782	+	1.78131i	0.622923	+	0.782283i	$0.285945\pi$
$719$	15.5196	+	47.7643i	0.578782	+	1.78131i	−0.0441414	+	0.999025i	$0.514055\pi$
$720$	0.0668397	+	3.04009i	0.00249097	+	0.113298i
$721$	−15.1509	−	16.7045i	−0.564247	−	0.622107i
$722$	−46.8293	+	15.2158i	−1.74281	+	0.566272i
$723$	−6.24818	−	36.8251i	−0.232372	−	1.36954i
$724$	4.72552	−	6.50411i	0.175622	−	0.241723i
$725$			2.17595i			0.0808128i
$726$	−7.97039	+	17.3053i	−0.295809	+	0.642259i
$727$			14.2750i			0.529430i	0.964327	+	0.264715i	$0.0852779\pi$
$727$			14.2750i			0.529430i	−0.964327	+	0.264715i	$0.914722\pi$
$728$	11.6662	+	6.67918i	0.432378	+	0.247547i
$729$	14.3962	−	22.8418i	0.533193	−	0.845993i
$730$	0.822547	+	2.53154i	0.0304438	+	0.0936964i
$731$	11.0642	−	8.03860i	0.409224	−	0.297318i
$732$	6.62951	−	13.3725i	0.245034	−	0.494262i
$733$	−3.36003	+	1.09174i	−0.124106	+	0.0403244i	−0.370411	−	0.928868i	$-0.620783\pi$
$733$	−3.36003	+	1.09174i	−0.124106	+	0.0403244i	0.246306	+	0.969192i	$0.420783\pi$
$734$	−6.52817	+	20.0916i	−0.240959	+	0.741596i
$735$	−0.866978	−	12.2587i	−0.0319790	−	0.452170i
$736$	−5.21231			−0.192128
$737$	−0.303927	−	21.2268i	−0.0111953	−	0.781900i
$738$	−8.80092	−	6.10325i	−0.323966	−	0.224664i
$739$	24.1844	+	17.5710i	0.889637	+	0.646359i	0.935783	−	0.352575i	$-0.114694\pi$
$739$	24.1844	+	17.5710i	0.889637	+	0.646359i	−0.0461461	+	0.998935i	$0.514694\pi$
$740$	−1.58453	+	4.87669i	−0.0582486	+	0.179271i
$741$	−50.8371	+	51.9671i	−1.86755	+	1.90906i
$742$	−27.6892	+	25.1140i	−1.01650	+	0.921962i
$743$	26.6778	+	36.7189i	0.978714	+	1.34708i	0.937519	+	0.347933i	$0.113116\pi$
$743$	26.6778	+	36.7189i	0.978714	+	1.34708i	0.0411944	+	0.999151i	$0.486884\pi$
$744$	−4.42784	+	4.52626i	−0.162332	+	0.165941i
$745$	−5.50070	−	1.78729i	−0.201530	−	0.0654811i
$746$	7.72794	−	10.6366i	0.282940	−	0.389434i
$747$	−21.8016	+	31.4380i	−0.797679	+	1.15026i
$748$	−3.66734	+	5.20270i	−0.134091	+	0.190230i
$749$	0.509961	+	4.68831i	0.0186336	+	0.171307i
$750$	15.5847	+	2.29308i	0.569073	+	0.0837314i
$751$	−10.4682	+	32.2177i	−0.381988	+	1.17564i	0.556653	+	0.830745i	$0.312085\pi$
$751$	−10.4682	+	32.2177i	−0.381988	+	1.17564i	−0.938642	+	0.344894i	$0.887915\pi$
$752$	−2.60985	−	8.03230i	−0.0951715	−	0.292908i
$753$	36.2537	+	17.9730i	1.32116	+	0.654973i
$754$	−1.63583	−	2.25152i	−0.0595734	−	0.0819957i
$755$	1.89416	+	5.82961i	0.0689354	+	0.212161i
$756$	4.45379	−	13.0063i	0.161983	−	0.473034i
$757$	6.29849	+	4.57612i	0.228923	+	0.166322i	0.696334	−	0.717718i	$-0.254813\pi$
$757$	6.29849	+	4.57612i	0.228923	+	0.166322i	−0.467411	+	0.884040i	$0.654813\pi$
$758$			4.93668i			0.179308i
$759$	−29.4458	+	5.43091i	−1.06881	+	0.197130i
$760$	−8.37313			−0.303725
$761$	−25.6965	−	18.6696i	−0.931498	−	0.676773i	0.0148614	−	0.999890i	$-0.495269\pi$
$761$	−25.6965	−	18.6696i	−0.931498	−	0.676773i	−0.946359	+	0.323117i	$0.895269\pi$
$762$	−0.288861	−	1.70247i	−0.0104643	−	0.0616741i
$763$	−11.0533	−	24.5857i	−0.400155	−	0.890061i
$764$	−5.70456	−	7.85165i	−0.206384	−	0.284063i
$765$	0.128280	+	5.83461i	0.00463798	+	0.210951i
$766$	2.71346	−	0.881656i	0.0980412	−	0.0318555i
$767$	44.5606	+	14.4786i	1.60899	+	0.522793i
$768$	−0.252133	+	1.71360i	−0.00909808	+	0.0618343i
$769$		−	46.6841i		−	1.68347i	−0.539889	−	0.841736i	$-0.681534\pi$
$769$		−	46.6841i		−	1.68347i	0.539889	−	0.841736i	$-0.318466\pi$
$770$	3.76289	+	8.05920i	0.135605	+	0.290434i
$771$	21.0763	+	40.2644i	0.759046	+	1.45009i
$772$	−2.82361	−	2.05147i	−0.101624	−	0.0738342i
$773$	10.8127	−	33.2781i	0.388906	−	1.19693i	−0.544701	−	0.838630i	$-0.683357\pi$
$773$	10.8127	−	33.2781i	0.388906	−	1.19693i	0.933607	−	0.358299i	$-0.116643\pi$
$774$	6.15754	−	20.4716i	0.221328	−	0.735835i
$775$	8.53622	+	11.7491i	0.306630	+	0.422040i
$776$	9.29051	−	6.74995i	0.333510	−	0.242309i
$777$	14.3242	−	18.2274i	0.513879	−	0.653906i
$778$	4.54185	−	13.9784i	0.162833	−	0.501149i
$779$	17.3343	−	23.8587i	0.621067	−	0.854825i
$780$	−7.90298	+	4.13681i	−0.282972	+	0.148121i
$781$	−23.3920	+	17.5124i	−0.837032	+	0.626643i
$782$	−10.0036			−0.357727
$783$	−1.94508	+	2.07778i	−0.0695117	+	0.0742539i
$784$	0.681177	−	6.96678i	0.0243277	−	0.248814i
$785$	−5.72933	+	1.86157i	−0.204488	+	0.0664423i
$786$	6.20595	−	12.5181i	0.221359	−	0.446507i
$787$	25.4599	+	35.0425i	0.907546	+	1.24913i	0.967998	+	0.250959i	$0.0807458\pi$
$787$	25.4599	+	35.0425i	0.907546	+	1.24913i	−0.0604520	+	0.998171i	$0.519254\pi$
$788$	9.49972	−	3.08665i	0.338413	−	0.109957i
$789$	−3.48572	−	20.5439i	−0.124095	−	0.731383i
$790$	1.54688	−	2.12910i	0.0550356	−	0.0757500i
$791$	2.29038	+	21.0565i	0.0814365	+	0.748683i
$792$	0.361097	+	9.94332i	0.0128310	+	0.353320i
$793$	43.7840			1.55482
$794$	−15.4414	−	11.2188i	−0.547995	−	0.398142i
$795$	−4.14944	−	24.4557i	−0.147165	−	0.867354i
$796$	−8.50800	+	2.76442i	−0.301558	+	0.0979821i
$797$	−30.9608	+	22.4943i	−1.09669	+	0.796791i	−0.980516	−	0.196438i	$-0.937062\pi$
$797$	−30.9608	+	22.4943i	−1.09669	+	0.796791i	−0.116172	+	0.993229i	$0.537062\pi$
$798$	35.5355	+	13.0481i	1.25794	+	0.461896i
$799$	−5.00888	−	15.4158i	−0.177202	−	0.545370i
$800$	3.77816	+	1.22760i	0.133578	+	0.0434022i
$801$	43.7483	−	15.2857i	1.54577	−	0.540095i
$802$	23.9256			0.844842
$803$	2.80976	+	8.24405i	0.0991545	+	0.290926i
$804$	−5.14143	−	9.82222i	−0.181324	−	0.346403i
$805$	−6.94512	+	12.1307i	−0.244783	+	0.427551i
$806$	−17.6654	−	5.73983i	−0.622236	−	0.202177i
$807$	−6.91085	+	7.06446i	−0.243273	+	0.248681i
$808$	5.37673	+	7.40043i	0.189153	+	0.260346i
$809$	−13.8544	−	19.0689i	−0.487094	−	0.670427i	0.492755	−	0.870168i	$-0.335990\pi$
$809$	−13.8544	−	19.0689i	−0.487094	−	0.670427i	−0.979849	+	0.199741i	$0.935990\pi$
$810$	5.68125	+	7.13745i	0.199619	+	0.250784i
$811$	−28.0236	−	9.10542i	−0.984042	−	0.319735i	−0.227571	−	0.973762i	$-0.573078\pi$
$811$	−28.0236	−	9.10542i	−0.984042	−	0.319735i	−0.756471	+	0.654027i	$0.773078\pi$
$812$	−0.720036	+	1.25765i	−0.0252683	+	0.0441349i
$813$	46.5475	−	24.3652i	1.63249	−	0.854526i
$814$	−4.95576	+	16.0296i	−0.173699	+	0.561837i
$815$	17.3261			0.606906
$816$	−0.483900	+	3.28878i	−0.0169399	+	0.115130i
$817$	55.9835	+	18.1902i	1.95862	+	0.636393i
$818$	9.67637	+	29.7808i	0.338326	+	1.04126i
$819$	39.9867	−	5.24116i	1.39725	−	0.183141i
$820$	2.92752	−	2.12697i	0.102233	−	0.0742769i
$821$	−52.4193	+	17.0321i	−1.82945	+	0.594423i	−0.830126	+	0.557576i	$0.811732\pi$
$821$	−52.4193	+	17.0321i	−1.82945	+	0.594423i	−0.999321	+	0.0368475i	$0.988268\pi$
$822$	−29.7092	+	5.04081i	−1.03623	+	0.175818i
$823$	−26.2208	−	19.0505i	−0.914000	−	0.664060i	0.0280236	−	0.999607i	$-0.491079\pi$
$823$	−26.2208	−	19.0505i	−0.914000	−	0.664060i	−0.942023	+	0.335548i	$0.891079\pi$
$824$	8.52382			0.296941
$825$	22.6230	+	2.99843i	0.787631	+	0.104392i
$826$	−2.63826	−	24.2547i	−0.0917966	−	0.843929i
$827$	21.0028	−	28.9079i	0.730340	−	1.00523i	−0.268777	−	0.963203i	$-0.586619\pi$
$827$	21.0028	−	28.9079i	0.730340	−	1.00523i	0.999117	−	0.0420242i	$-0.0133807\pi$
$828$	−12.4455	+	9.46700i	−0.432509	+	0.329001i
$829$	−16.6075	+	5.39611i	−0.576803	+	0.187415i	−0.582868	−	0.812567i	$-0.698070\pi$
$829$	−16.6075	+	5.39611i	−0.576803	+	0.187415i	0.00606465	+	0.999982i	$0.498070\pi$
$830$	−7.59780	−	10.4575i	−0.263723	−	0.362984i
$831$	32.6026	+	16.1630i	1.13097	+	0.560687i
$832$	−4.83226	+	1.57010i	−0.167529	+	0.0544333i
$833$	1.30733	−	13.3708i	0.0452962	−	0.463270i
$834$	−0.122243	+	0.830811i	−0.00423292	+	0.0287686i
$835$	−9.97052			−0.345044
$836$	−27.3948	+	0.392241i	−0.947471	+	0.0135659i
$837$	−2.35142	+	18.8496i	−0.0812771	+	0.651536i
$838$	−2.08405	+	2.86845i	−0.0719924	+	0.0990890i
$839$	−0.0414202	+	0.127478i	−0.00142998	+	0.00440104i	−0.951769	−	0.306816i	$-0.900736\pi$
$839$	−0.0414202	+	0.127478i	−0.00142998	+	0.00440104i	0.950339	+	0.311217i	$0.100736\pi$
$840$	3.65214	+	2.87008i	0.126011	+	0.0990270i
$841$	−23.2188	+	16.8694i	−0.800647	+	0.581704i
$842$	21.4325	+	29.4993i	0.738612	+	1.01661i
$843$	−15.3882	−	15.0536i	−0.529998	−	0.518473i
$844$	−3.05208	+	9.39334i	−0.105057	+	0.323332i
$845$	−10.5094	−	7.63555i	−0.361536	−	0.262671i
$846$	−20.8204	−	14.4385i	−0.715822	−	0.496407i
$847$	12.6888	+	26.1915i	0.435992	+	0.899950i
$848$		−	14.1290i		−	0.485192i
$849$	9.58860	+	1.41083i	0.329080	+	0.0484197i
$850$	7.25113	+	2.35603i	0.248712	+	0.0808113i
$851$	−25.0775	+	8.14819i	−0.859647	+	0.279316i
$852$	−6.77813	+	13.6723i	−0.232215	+	0.468404i
$853$	16.8800	+	23.2333i	0.577960	+	0.795493i	0.993470	−	0.114095i	$-0.0363970\pi$
$853$	16.8800	+	23.2333i	0.577960	+	0.795493i	−0.415510	+	0.909589i	$0.636397\pi$
$854$	−9.34878	−	20.7944i	−0.319909	−	0.711569i
$855$	−19.9926	+	15.2079i	−0.683731	+	0.520100i
$856$	−1.44204	−	1.04771i	−0.0492881	−	0.0358099i
$857$	−3.42384			−0.116956			−0.0584781	−	0.998289i	$-0.518625\pi$
$857$	−3.42384			−0.116956			−0.0584781	+	0.998289i	$0.518625\pi$
$858$	−25.6629	+	13.9048i	−0.876115	+	0.474704i
$859$		−	34.7965i		−	1.18724i	−0.804745	−	0.593621i	$-0.797698\pi$
$859$		−	34.7965i		−	1.18724i	0.804745	−	0.593621i	$-0.202302\pi$
$860$	5.84339	+	4.24547i	0.199258	+	0.144769i
$861$	−15.7389	+	4.46481i	−0.536380	+	0.152160i
$862$	−3.82103	−	11.7599i	−0.130145	−	0.400545i
$863$	23.7530	+	32.6933i	0.808563	+	1.11289i	0.991543	+	0.129775i	$0.0414255\pi$
$863$	23.7530	+	32.6933i	0.808563	+	1.11289i	−0.182980	+	0.983117i	$0.558574\pi$
$864$	2.51036	+	4.54952i	0.0854041	+	0.154778i
$865$	−6.73514	−	20.7286i	−0.229002	−	0.704794i
$866$	0.466458	−	1.43561i	0.0158509	−	0.0487840i
$867$	3.35756	−	22.8193i	0.114029	−	0.774985i
$868$	1.04590	+	9.61540i	0.0355000	+	0.326368i
$869$	4.96128	−	7.03836i	0.168300	−	0.238760i
$870$	−0.445960	−	0.851965i	−0.0151195	−	0.0288843i
$871$	19.1160	−	26.3109i	0.647720	−	0.891510i
$872$	9.68978	+	3.14840i	0.328137	+	0.106618i
$873$	9.92321	−	32.9910i	0.335850	−	1.11658i
$874$	−25.3085	−	34.8341i	−0.856072	−	1.17828i
$875$	17.8233	−	16.1656i	0.602537	−	0.546497i
$876$	3.25143	+	3.18073i	0.109856	+	0.107467i
$877$	8.31993	−	25.6061i	0.280944	−	0.864657i	−0.706641	−	0.707572i	$-0.749790\pi$
$877$	8.31993	−	25.6061i	0.280944	−	0.864657i	0.987585	−	0.157085i	$-0.0502096\pi$
$878$	10.3634	+	7.52947i	0.349749	+	0.254107i
$879$	−23.6288	−	45.1406i	−0.796979	−	1.52255i
$880$	−3.21177	−	0.992962i	−0.108269	−	0.0334727i
$881$	−23.1397			−0.779596			−0.389798	−	0.920900i	$-0.627455\pi$
$881$	−23.1397			−0.779596			−0.389798	+	0.920900i	$0.627455\pi$
$882$	−11.0272	−	17.8718i	−0.371304	−	0.601775i
$883$	−10.5821	+	32.5683i	−0.356115	+	1.09601i	0.599245	+	0.800566i	$0.295468\pi$
$883$	−10.5821	+	32.5683i	−0.356115	+	1.09601i	−0.955360	+	0.295444i	$0.904532\pi$
$884$	−9.27418	+	3.01336i	−0.311924	+	0.101350i
$885$	14.5048	+	7.19087i	0.487574	+	0.241718i
$886$	−16.6554	+	12.1009i	−0.559550	+	0.406537i
$887$	8.12304	+	25.0002i	0.272745	+	0.839423i	0.989807	+	0.142414i	$0.0454864\pi$
$887$	8.12304	+	25.0002i	0.272745	+	0.839423i	−0.717062	+	0.697009i	$0.754514\pi$
$888$	1.46573	+	8.63865i	0.0491868	+	0.289894i
$889$	−2.28912	−	1.31057i	−0.0767745	−	0.0439553i
$890$			15.6575i			0.524841i
$891$	18.9220	+	23.0859i	0.633912	+	0.773405i
$892$			1.57697i			0.0528009i
$893$	41.0081	−	56.4428i	1.37228	−	1.88879i
$894$	−9.74403	+	1.65328i	−0.325889	+	0.0552941i
$895$	17.2072	−	5.59094i	0.575172	−	0.186885i
$896$	1.77747	+	1.95974i	0.0593812	+	0.0654704i
$897$	−41.0975	−	20.3744i	−1.37220	−	0.680280i
$898$	−3.72765	−	11.4725i	−0.124393	−	0.382843i
$899$	0.618771	−	1.90438i	0.0206372	−	0.0635146i
$900$	11.2508	−	3.93105i	0.375027	−	0.131035i
$901$		−	27.1167i		−	0.903388i
$902$	9.47850	−	7.09606i	0.315599	−	0.236273i
$903$	−18.1835	−	27.1237i	−0.605109	−	0.902620i
$904$	−6.47663	−	4.70555i	−0.215409	−	0.156504i
$905$	7.75010	+	2.51816i	0.257622	+	0.0837065i
$906$	7.48738	+	7.32457i	0.248751	+	0.243342i
$907$	10.4744	−	7.61012i	0.347798	−	0.252690i	−0.400147	−	0.916451i	$-0.631041\pi$
$907$	10.4744	−	7.61012i	0.347798	−	0.252690i	0.747945	+	0.663761i	$0.231041\pi$
$908$	1.22971	−	0.893440i	0.0408095	−	0.0296498i
$909$	26.2793	+	7.90441i	0.871629	+	0.262173i
$910$	−2.78461	+	13.3383i	−0.0923090	+	0.442160i
$911$	−11.9218	+	16.4090i	−0.394988	+	0.543655i	−0.959477	−	0.281786i	$-0.909073\pi$
$911$	−11.9218	+	16.4090i	−0.394988	+	0.543655i	0.564489	+	0.825441i	$0.309073\pi$
$912$	−12.6763	+	6.63540i	−0.419755	+	0.219720i
$913$	−25.3481	−	33.8584i	−0.838898	−	1.12055i
$914$			8.06842i			0.266880i
$915$	14.9676	+	2.20228i	0.494814	+	0.0728052i
$916$	−10.4763	−	3.40396i	−0.346147	−	0.112470i
$917$	−8.75149	−	19.4658i	−0.289000	−	0.642818i
$918$	4.81793	+	8.73153i	0.159015	+	0.288183i
$919$	34.7816	−	25.2703i	1.14734	−	0.833591i	0.159215	−	0.987244i	$-0.449104\pi$
$919$	34.7816	−	25.2703i	1.14734	−	0.833591i	0.988125	+	0.153653i	$0.0491037\pi$
$920$	−1.63261	−	5.02466i	−0.0538256	−	0.165658i
$921$	−1.25060	−	7.37074i	−0.0412088	−	0.242874i
$922$	−6.23127	+	8.57660i	−0.205216	+	0.282455i
$923$	−44.7656			−1.47348
$924$	12.0834	+	9.21911i	0.397514	+	0.303286i
$925$	20.0966			0.660773
$926$	2.31897	−	3.19179i	0.0762062	−	0.104889i
$927$	20.3524	−	15.4816i	0.668459	−	0.508483i
$928$	−0.169261	−	0.520932i	−0.00555627	−	0.0171004i
$929$	7.71023	−	5.60181i	0.252965	−	0.183790i	−0.454075	−	0.890963i	$-0.650030\pi$
$929$	7.71023	−	5.60181i	0.252965	−	0.183790i	0.707040	+	0.707174i	$0.250030\pi$
$930$	−5.75021	−	2.85071i	−0.188557	−	0.0934784i
$931$	49.8668	−	29.2750i	1.63432	−	0.959449i
$932$	9.06917	+	2.94675i	0.297070	+	0.0965240i
$933$	2.25226	−	15.3073i	0.0737357	−	0.501138i
$934$			1.04712i			0.0342627i
$935$	−6.16410	−	1.90571i	−0.201587	−	0.0623235i
$936$	−8.68628	+	12.5257i	−0.283920	+	0.409414i
$937$	−0.370676	+	0.510192i	−0.0121095	+	0.0166672i	−0.815029	−	0.579420i	$-0.803279\pi$
$937$	−0.370676	+	0.510192i	−0.0121095	+	0.0166672i	0.802919	+	0.596088i	$0.203279\pi$
$938$	−16.5775	−	3.46085i	−0.541274	−	0.113001i
$939$	0.637829	+	0.623959i	0.0208148	+	0.0203621i
$940$	6.92567	−	5.03179i	0.225890	−	0.164119i
$941$	12.0898	−	8.78376i	0.394117	−	0.286342i	−0.373024	−	0.927822i	$-0.621679\pi$
$941$	12.0898	−	8.78376i	0.394117	−	0.286342i	0.767140	+	0.641479i	$0.221679\pi$
$942$	−7.19857	+	7.35857i	−0.234542	+	0.239755i
$943$	17.6973	+	5.75021i	0.576304	+	0.187253i
$944$	7.46034	+	5.42025i	0.242813	+	0.176414i
$945$	13.9331	+	0.219587i	0.453244	+	0.00714316i
$946$	19.3171	+	13.6164i	0.628052	+	0.442708i
$947$		−	21.9105i		−	0.711996i	−0.934487	−	0.355998i	$-0.884141\pi$
$947$		−	21.9105i		−	0.711996i	0.934487	−	0.355998i	$-0.115859\pi$
$948$	0.654633	−	4.44915i	0.0212615	−	0.144502i
$949$	−4.12320	+	12.6899i	−0.133845	+	0.411931i
$950$	10.1408	+	31.2103i	0.329012	+	1.01260i
$951$	−3.20913	+	6.47318i	−0.104063	+	0.209907i
$952$	3.41136	+	3.76118i	0.110563	+	0.121900i
$953$	17.6213	−	5.72551i	0.570810	−	0.185467i	−0.00936930	−	0.999956i	$-0.502982\pi$
$953$	17.6213	−	5.72551i	0.570810	−	0.185467i	0.580180	+	0.814489i	$0.302982\pi$
$954$	−25.6622	−	33.7359i	−0.830845	−	1.09224i
$955$	5.78219	−	7.95851i	0.187107	−	0.257531i
$956$			2.79289i			0.0903287i
$957$	−1.49898	−	2.76653i	−0.0484553	−	0.0894293i
$958$		−	24.5072i		−	0.791792i
$959$	−22.8703	+	39.9465i	−0.738522	+	1.28994i
$960$	−1.73088	+	0.293682i	−0.0558641	+	0.00947854i
$961$	5.44975	+	16.7726i	0.175798	+	0.541051i
$962$	−20.7946	+	15.1082i	−0.670444	+	0.487106i
$963$	−5.34610	+	0.117540i	−0.172276	+	0.00378767i
$964$	20.5094	−	6.66391i	0.660564	−	0.214630i
$965$	1.09320	−	3.36453i	0.0351914	−	0.108308i
$966$	−0.901267	+	23.8688i	−0.0289978	+	0.767966i
$967$	−22.7786			−0.732510			−0.366255	−	0.930515i	$-0.619360\pi$
$967$	−22.7786			−0.732510			−0.366255	+	0.930515i	$0.619360\pi$
$968$	−10.5547	−	3.09827i	−0.339239	−	0.0995823i
$969$	−24.3287	+	12.7348i	−0.781549	+	0.409101i
$970$	9.41695	+	6.84181i	0.302360	+	0.219677i
$971$	−5.68625	+	17.5005i	−0.182480	+	0.561617i	−0.999896	−	0.0144318i	$-0.995406\pi$
$971$	−5.68625	+	17.5005i	−0.182480	+	0.561617i	0.817416	+	0.576048i	$0.195406\pi$
$972$	14.2572	+	6.30340i	0.457299	+	0.202182i
$973$	0.861779	+	0.950149i	0.0276274	+	0.0304604i
$974$	−10.6992	−	14.7261i	−0.342823	−	0.471855i
$975$	24.9911	+	24.4477i	0.800356	+	0.782953i
$976$	8.19555	+	2.66290i	0.262333	+	0.0852372i
$977$	−23.2927	+	32.0596i	−0.745198	+	1.02568i	0.253104	+	0.967439i	$0.418548\pi$
$977$	−23.2927	+	32.0596i	−0.745198	+	1.02568i	−0.998303	+	0.0582385i	$0.981452\pi$
$978$	26.2305	−	13.7303i	0.838758	−	0.439047i
$979$	0.733480	+	51.2276i	0.0234421	+	1.63724i
$980$	6.92933	−	1.52550i	0.221349	−	0.0487302i
$981$	28.8547	−	10.0819i	0.921260	−	0.321890i
$982$	6.53274	−	20.1057i	0.208468	−	0.641599i
$983$	2.54006	+	7.81751i	0.0810155	+	0.249340i	0.983358	−	0.181681i	$-0.0581537\pi$
$983$	2.54006	+	7.81751i	0.0810155	+	0.249340i	−0.902342	+	0.431020i	$0.858154\pi$
$984$	2.74651	−	5.54003i	0.0875556	−	0.176610i
$985$	5.95105	+	8.19092i	0.189616	+	0.260984i
$986$	−0.324850	−	0.999784i	−0.0103453	−	0.0318396i
$987$	−37.2337	+	10.5625i	−1.18516	+	0.336207i
$988$	−33.9562	−	24.6706i	−1.08029	−	0.784877i
$989$			37.1422i			1.18105i
$990$	−9.47225	+	3.46257i	−0.301048	+	0.110048i
$991$	−23.5798			−0.749038			−0.374519	−	0.927219i	$-0.622192\pi$
$991$	−23.5798			−0.749038			−0.374519	+	0.927219i	$0.622192\pi$
$992$	−2.95754	−	2.14878i	−0.0939019	−	0.0682237i
$993$	11.0288	−	1.87127i	0.349988	−	0.0593830i
$994$	9.55836	+	21.2605i	0.303173	+	0.674343i
$995$	−5.32979	−	7.33583i	−0.168966	−	0.232561i
$996$	−19.7897	−	9.81089i	−0.627061	−	0.310870i
$997$	29.8354	−	9.69412i	0.944898	−	0.307016i	0.204257	−	0.978917i	$-0.434522\pi$
$997$	29.8354	−	9.69412i	0.944898	−	0.307016i	0.740641	+	0.671901i	$0.234522\pi$
$998$	11.6752	+	3.79351i	0.369572	+	0.120081i
$999$	19.1899	+	17.9644i	0.607143	+	0.568368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.s.a.125.2	✓	128
3.2	odd	2	inner	462.2.s.a.125.22	yes	128
7.6	odd	2	inner	462.2.s.a.125.15	yes	128
11.3	even	5	inner	462.2.s.a.377.27	yes	128
21.20	even	2	inner	462.2.s.a.125.27	yes	128
33.14	odd	10	inner	462.2.s.a.377.15	yes	128
77.69	odd	10	inner	462.2.s.a.377.22	yes	128
231.146	even	10	inner	462.2.s.a.377.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.s.a.125.2	✓	128	1.1	even	1	trivial
462.2.s.a.125.15	yes	128	7.6	odd	2	inner
462.2.s.a.125.22	yes	128	3.2	odd	2	inner
462.2.s.a.125.27	yes	128	21.20	even	2	inner
462.2.s.a.377.2	yes	128	231.146	even	10	inner
462.2.s.a.377.15	yes	128	33.14	odd	10	inner
462.2.s.a.377.22	yes	128	77.69	odd	10	inner
462.2.s.a.377.27	yes	128	11.3	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.70765 + 0.289739i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.820027 - 0.595785i) q^{5} +(0.769325 - 1.55182i) q^{6} +(-1.08488 - 2.41309i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.83210 - 0.989542i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.70765 + 0.289739i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.820027 - 0.595785i) q^{5} +(0.769325 - 1.55182i) q^{6} +(-1.08488 - 2.41309i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.83210 - 0.989542i) q^{9} +1.01361i q^{10} +(0.0474828 + 3.31628i) q^{11} +(0.803249 + 1.53453i) q^{12} +(-2.98650 + 4.11057i) q^{13} +(2.58991 + 0.540692i) q^{14} +(-1.22769 + 1.25498i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.55268 + 1.12809i) q^{17} +(-0.864112 + 2.87286i) q^{18} +(-7.85640 - 2.55270i) q^{19} +(-0.820027 - 0.595785i) q^{20} +(2.55176 + 3.80638i) q^{21} +(-2.71084 - 1.91085i) q^{22} -5.21231i q^{23} +(-1.71360 - 0.252133i) q^{24} +(-1.22760 + 3.77816i) q^{25} +(-1.57010 - 4.83226i) q^{26} +(-4.54952 + 2.51036i) q^{27} +(-1.95974 + 1.77747i) q^{28} +(0.520932 - 0.169261i) q^{29} +(-0.293682 - 1.73088i) q^{30} +(2.14878 - 2.95754i) q^{31} -1.00000i q^{32} +(-1.04194 - 5.64928i) q^{33} -1.91922i q^{34} +(-2.32732 - 1.33245i) q^{35} +(-1.81628 - 2.38770i) q^{36} +(-1.56326 - 4.81122i) q^{37} +(6.68305 - 4.85552i) q^{38} +(3.90889 - 7.88470i) q^{39} +(0.964000 - 0.313222i) q^{40} +(-1.10320 + 3.39530i) q^{41} +(-4.57931 - 0.172911i) q^{42} -7.12586 q^{43} +(3.13930 - 1.06995i) q^{44} +(1.73285 - 2.49877i) q^{45} +(4.21685 + 3.06372i) q^{46} +(-2.60985 + 8.03230i) q^{47} +(1.21121 - 1.23813i) q^{48} +(-4.64605 + 5.23586i) q^{49} +(-2.33503 - 3.21390i) q^{50} +(2.32458 - 2.37625i) q^{51} +(4.83226 + 1.57010i) q^{52} +(-8.30483 + 11.4306i) q^{53} +(0.643219 - 5.15619i) q^{54} +(2.01473 + 2.69115i) q^{55} +(-0.286099 - 2.63024i) q^{56} +(14.1556 + 2.08280i) q^{57} +(-0.169261 + 0.520932i) q^{58} +(-2.84960 - 8.77015i) q^{59} +(1.57294 + 0.779795i) q^{60} +(-5.06513 - 6.97155i) q^{61} +(1.12968 + 3.47679i) q^{62} +(-5.46036 - 5.76059i) q^{63} +(0.809017 + 0.587785i) q^{64} +5.15009i q^{65} +(5.18280 + 2.47762i) q^{66} -6.40079 q^{67} +(1.55268 + 1.12809i) q^{68} +(1.51021 + 8.90077i) q^{69} +(2.44594 - 1.09965i) q^{70} +(5.17867 + 7.12783i) q^{71} +(2.99928 - 0.0659423i) q^{72} +(2.49755 - 0.811503i) q^{73} +(4.81122 + 1.56326i) q^{74} +(1.00162 - 6.80745i) q^{75} +8.26070i q^{76} +(7.95100 - 3.71237i) q^{77} +(4.08126 + 7.79687i) q^{78} +(-2.10051 - 1.52611i) q^{79} +(-0.313222 + 0.964000i) q^{80} +(7.04161 - 5.60497i) q^{81} +(-2.09841 - 2.88821i) q^{82} +(-10.3171 + 7.49579i) q^{83} +(2.83154 - 3.60311i) q^{84} +(-0.601143 + 1.85013i) q^{85} +(4.18847 - 5.76494i) q^{86} +(-0.840526 + 0.439972i) q^{87} +(-0.979630 + 3.16865i) q^{88} +15.4473 q^{89} +(1.00301 + 2.87065i) q^{90} +(13.1592 + 2.74722i) q^{91} +(-4.95720 + 1.61069i) q^{92} +(-2.81243 + 5.67300i) q^{93} +(-4.96423 - 6.83268i) q^{94} +(-7.96332 + 2.58744i) q^{95} +(0.289739 + 1.70765i) q^{96} +(6.74995 - 9.29051i) q^{97} +(-1.50502 - 6.83629i) q^{98} +(3.41608 + 9.34507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9}+O(q^{10}) \) 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9	\( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9} + 12 q^{15} - 32 q^{16} - 16 q^{18} - 20 q^{21} - 36 q^{25} - 6 q^{28} + 8 q^{36} - 16 q^{37} + 60 q^{39} + 4 q^{42} - 64 q^{43} - 8 q^{46} - 40 q^{49} - 28 q^{51} + 88 q^{57} + 92 q^{58} + 8 q^{60} - 42 q^{63} + 32 q^{64} - 64 q^{67} - 26 q^{70} - 24 q^{72} - 64 q^{78} + 136 q^{79} - 116 q^{81} - 28 q^{85} - 40 q^{91} - 76 q^{93} - 160 q^{99}+O(q^{100}) \) 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9 + 12 * q^15 - 32 * q^16 - 16 * q^18 - 20 * q^21 - 36 * q^25 - 6 * q^28 + 8 * q^36 - 16 * q^37 + 60 * q^39 + 4 * q^42 - 64 * q^43 - 8 * q^46 - 40 * q^49 - 28 * q^51 + 88 * q^57 + 92 * q^58 + 8 * q^60 - 42 * q^63 + 32 * q^64 - 64 * q^67 - 26 * q^70 - 24 * q^72 - 64 * q^78 + 136 * q^79 - 116 * q^81 - 28 * q^85 - 40 * q^91 - 76 * q^93 - 160 * q^99

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