LMFDB - Embedded newform 770.2.o.b.549.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.20
Character	$\chi$	$=$	770.549
Dual form			770.2.o.b.439.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.987813 - 1.71094i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.23241 + 0.127806i) q^{5} +1.97563 q^{6} +(-1.58012 - 2.12208i) q^{7} -1.00000 q^{8} +(-0.451550 - 0.782108i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.987813 - 1.71094i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.23241 + 0.127806i) q^{5} +1.97563 q^{6} +(-1.58012 - 2.12208i) q^{7} -1.00000 q^{8} +(-0.451550 - 0.782108i) q^{9} +(1.00552 + 1.99723i) q^{10} +(1.14408 - 3.11305i) q^{11} +(0.987813 + 1.71094i) q^{12} -4.36408i q^{13} +(1.04772 - 2.42946i) q^{14} +(2.42388 - 3.69328i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.154692 + 0.0893117i) q^{17} +(0.451550 - 0.782108i) q^{18} +(-1.57718 - 2.73176i) q^{19} +(-1.22689 + 1.86942i) q^{20} +(-5.19162 + 0.607271i) q^{21} +(3.26802 - 0.565719i) q^{22} +(-6.01796 + 3.47447i) q^{23} +(-0.987813 + 1.71094i) q^{24} +(4.96733 + 0.570633i) q^{25} +(3.77940 - 2.18204i) q^{26} +4.14269 q^{27} +(2.62783 - 0.307382i) q^{28} +7.86643i q^{29} +(4.41041 + 0.252497i) q^{30} +(6.35873 + 3.67121i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.19611 - 5.03257i) q^{33} +0.178623i q^{34} +(-3.25626 - 4.93931i) q^{35} +0.903100 q^{36} +(1.87189 - 1.08073i) q^{37} +(1.57718 - 2.73176i) q^{38} +(-7.46669 - 4.31089i) q^{39} +(-2.23241 - 0.127806i) q^{40} +7.35367 q^{41} +(-3.12172 - 4.19244i) q^{42} +1.81767 q^{43} +(2.12394 + 2.54733i) q^{44} +(-0.908088 - 1.80370i) q^{45} +(-6.01796 - 3.47447i) q^{46} +(-1.99798 - 3.46061i) q^{47} -1.97563 q^{48} +(-2.00646 + 6.70628i) q^{49} +(1.98948 + 4.58715i) q^{50} +(0.305614 - 0.176446i) q^{51} +(3.77940 + 2.18204i) q^{52} +(-10.2416 - 5.91299i) q^{53} +(2.07135 + 3.58768i) q^{54} +(2.95193 - 6.80339i) q^{55} +(1.58012 + 2.12208i) q^{56} -6.23184 q^{57} +(-6.81253 + 3.93322i) q^{58} +(-6.30410 - 3.63967i) q^{59} +(1.98654 + 3.94578i) q^{60} +(7.80138 + 13.5124i) q^{61} +7.34243i q^{62} +(-0.946193 + 2.19405i) q^{63} +1.00000 q^{64} +(0.557757 - 9.74242i) q^{65} +(2.26028 - 6.15022i) q^{66} +(-5.07171 - 2.92815i) q^{67} +(-0.154692 + 0.0893117i) q^{68} +13.7285i q^{69} +(2.64944 - 5.28966i) q^{70} +7.02825 q^{71} +(0.451550 + 0.782108i) q^{72} +(4.65502 + 2.68758i) q^{73} +(1.87189 + 1.08073i) q^{74} +(5.88312 - 7.93514i) q^{75} +3.15436 q^{76} +(-8.41393 + 2.49115i) q^{77} -8.62179i q^{78} +(5.13159 - 2.96273i) q^{79} +(-1.00552 - 1.99723i) q^{80} +(5.44686 - 9.43423i) q^{81} +(3.67683 + 6.36846i) q^{82} -2.33535i q^{83} +(2.06990 - 4.79971i) q^{84} +(0.333922 + 0.219151i) q^{85} +(0.908835 + 1.57415i) q^{86} +(13.4590 + 7.77057i) q^{87} +(-1.14408 + 3.11305i) q^{88} +(-5.10571 + 2.94778i) q^{89} +(1.10800 - 1.68828i) q^{90} +(-9.26093 + 6.89576i) q^{91} -6.94895i q^{92} +(12.5625 - 7.25295i) q^{93} +(1.99798 - 3.46061i) q^{94} +(-3.17178 - 6.29998i) q^{95} +(-0.987813 - 1.71094i) q^{96} -2.52195 q^{97} +(-6.81103 + 1.61550i) q^{98} +(-2.95135 + 0.510901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.987813	−	1.71094i	0.570314	−	0.987813i	−0.426219	−	0.904620i	$-0.640155\pi$
$3$	0.987813	−	1.71094i	0.570314	−	0.987813i	0.996533	−	0.0831933i	$-0.0265119\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.23241	+	0.127806i	0.998365	+	0.0571567i
$5$	2.23241	+	0.127806i	0.998365	+	0.0571567i
$6$	1.97563			0.806546
$7$	−1.58012	−	2.12208i	−0.597228	−	0.802071i
$7$	−1.58012	−	2.12208i	−0.597228	−	0.802071i
$8$	−1.00000			−0.353553
$9$	−0.451550	−	0.782108i	−0.150517	−	0.260703i
$10$	1.00552	+	1.99723i	0.317974	+	0.631579i
$11$	1.14408	−	3.11305i	0.344954	−	0.938620i
$11$	1.14408	−	3.11305i	0.344954	−	0.938620i
$12$	0.987813	+	1.71094i	0.285157	+	0.493907i
$13$		−	4.36408i		−	1.21038i	−0.796082	−	0.605189i	$-0.793098\pi$
$13$		−	4.36408i		−	1.21038i	0.796082	−	0.605189i	$-0.206902\pi$
$14$	1.04772	−	2.42946i	0.280014	−	0.649301i
$15$	2.42388	−	3.69328i	0.625842	−	0.953601i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.154692	+	0.0893117i	0.0375184	+	0.0216613i	0.518642	−	0.854992i	$-0.326438\pi$
$17$	0.154692	+	0.0893117i	0.0375184	+	0.0216613i	−0.481123	+	0.876653i	$0.659771\pi$
$18$	0.451550	−	0.782108i	0.106431	−	0.184345i
$19$	−1.57718	−	2.73176i	−0.361830	−	0.626708i	0.626432	−	0.779476i	$-0.284515\pi$
$19$	−1.57718	−	2.73176i	−0.361830	−	0.626708i	−0.988262	+	0.152768i	$0.951181\pi$
$20$	−1.22689	+	1.86942i	−0.274341	+	0.418016i
$21$	−5.19162	+	0.607271i	−1.13290	+	0.132517i
$22$	3.26802	−	0.565719i	0.696744	−	0.120612i
$23$	−6.01796	+	3.47447i	−1.25483	+	0.724478i	−0.972065	−	0.234711i	$-0.924586\pi$
$23$	−6.01796	+	3.47447i	−1.25483	+	0.724478i	−0.282767	+	0.959189i	$0.591252\pi$
$24$	−0.987813	+	1.71094i	−0.201637	+	0.349245i
$25$	4.96733	+	0.570633i	0.993466	+	0.114127i
$26$	3.77940	−	2.18204i	0.741202	−	0.427933i
$27$	4.14269			0.797261
$28$	2.62783	−	0.307382i	0.496614	−	0.0580897i
$29$			7.86643i			1.46076i	0.683041	+	0.730380i	$0.260657\pi$
$29$			7.86643i			1.46076i	−0.683041	+	0.730380i	$0.739343\pi$
$30$	4.41041	+	0.252497i	0.805228	+	0.0460995i
$31$	6.35873	+	3.67121i	1.14206	+	0.659369i	0.946940	−	0.321410i	$-0.104157\pi$
$31$	6.35873	+	3.67121i	1.14206	+	0.659369i	0.195121	+	0.980779i	$0.437490\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−4.19611	−	5.03257i	−0.730449	−	0.876058i
$34$			0.178623i			0.0306336i
$35$	−3.25626	−	4.93931i	−0.550408	−	0.834896i
$36$	0.903100			0.150517
$37$	1.87189	−	1.08073i	0.307736	−	0.177672i	−0.338177	−	0.941083i	$-0.609810\pi$
$37$	1.87189	−	1.08073i	0.307736	−	0.177672i	0.645913	+	0.763411i	$0.276477\pi$
$38$	1.57718	−	2.73176i	0.255852	−	0.443149i
$39$	−7.46669	−	4.31089i	−1.19563	−	0.690296i
$40$	−2.23241	−	0.127806i	−0.352975	−	0.0202079i
$41$	7.35367			1.14845			0.574225	−	0.818697i	$-0.305303\pi$
$41$	7.35367			1.14845			0.574225	+	0.818697i	$0.305303\pi$
$42$	−3.12172	−	4.19244i	−0.481692	−	0.646907i
$43$	1.81767			0.277192			0.138596	−	0.990349i	$-0.455741\pi$
$43$	1.81767			0.277192			0.138596	+	0.990349i	$0.455741\pi$
$44$	2.12394	+	2.54733i	0.320196	+	0.384024i
$45$	−0.908088	−	1.80370i	−0.135370	−	0.268879i
$46$	−6.01796	−	3.47447i	−0.887300	−	0.512283i
$47$	−1.99798	−	3.46061i	−0.291436	−	0.504781i	0.682714	−	0.730686i	$-0.260800\pi$
$47$	−1.99798	−	3.46061i	−0.291436	−	0.504781i	−0.974149	+	0.225905i	$0.927466\pi$
$48$	−1.97563			−0.285157
$49$	−2.00646	+	6.70628i	−0.286637	+	0.958039i
$50$	1.98948	+	4.58715i	0.281355	+	0.648721i
$51$	0.305614	−	0.176446i	0.0427946	−	0.0247074i
$52$	3.77940	+	2.18204i	0.524109	+	0.302594i
$53$	−10.2416	−	5.91299i	−1.40679	−	0.812212i	−0.411714	−	0.911313i	$-0.635070\pi$
$53$	−10.2416	−	5.91299i	−1.40679	−	0.812212i	−0.995077	+	0.0991014i	$0.968403\pi$
$54$	2.07135	+	3.58768i	0.281874	+	0.488221i
$55$	2.95193	−	6.80339i	0.398039	−	0.917369i
$56$	1.58012	+	2.12208i	0.211152	+	0.283575i
$57$	−6.23184			−0.825427
$58$	−6.81253	+	3.93322i	−0.894529	+	0.516457i
$59$	−6.30410	−	3.63967i	−0.820724	−	0.473845i	0.0299422	−	0.999552i	$-0.490468\pi$
$59$	−6.30410	−	3.63967i	−0.820724	−	0.473845i	−0.850666	+	0.525707i	$0.823801\pi$
$60$	1.98654	+	3.94578i	0.256461	+	0.509398i
$61$	7.80138	+	13.5124i	0.998865	+	1.73008i	0.540683	+	0.841226i	$0.318166\pi$
$61$	7.80138	+	13.5124i	0.998865	+	1.73008i	0.458182	+	0.888859i	$0.348501\pi$
$62$			7.34243i			0.932489i
$63$	−0.946193	+	2.19405i	−0.119209	+	0.276424i
$64$	1.00000			0.125000
$65$	0.557757	−	9.74242i	0.0691812	−	1.20840i
$66$	2.26028	−	6.15022i	0.278221	−	0.757040i
$67$	−5.07171	−	2.92815i	−0.619608	−	0.357731i	0.157109	−	0.987581i	$-0.449783\pi$
$67$	−5.07171	−	2.92815i	−0.619608	−	0.357731i	−0.776716	+	0.629851i	$0.783116\pi$
$68$	−0.154692	+	0.0893117i	−0.0187592	+	0.0108306i
$69$			13.7285i			1.65272i
$70$	2.64944	−	5.28966i	0.316668	−	0.632235i
$71$	7.02825			0.834100			0.417050	−	0.908884i	$-0.363064\pi$
$71$	7.02825			0.834100			0.417050	+	0.908884i	$0.363064\pi$
$72$	0.451550	+	0.782108i	0.0532157	+	0.0921723i
$73$	4.65502	+	2.68758i	0.544829	+	0.314557i	0.747034	−	0.664786i	$-0.231477\pi$
$73$	4.65502	+	2.68758i	0.544829	+	0.314557i	−0.202205	+	0.979343i	$0.564811\pi$
$74$	1.87189	+	1.08073i	0.217602	+	0.125633i
$75$	5.88312	−	7.93514i	0.679324	−	0.916271i
$76$	3.15436			0.361830
$77$	−8.41393	+	2.49115i	−0.958856	+	0.283893i
$78$		−	8.62179i		−	0.976225i
$79$	5.13159	−	2.96273i	0.577349	−	0.333333i	−0.182730	−	0.983163i	$-0.558493\pi$
$79$	5.13159	−	2.96273i	0.577349	−	0.333333i	0.760079	+	0.649830i	$0.225160\pi$
$80$	−1.00552	−	1.99723i	−0.112421	−	0.223297i
$81$	5.44686	−	9.43423i	0.605206	−	1.04825i
$82$	3.67683	+	6.36846i	0.406038	+	0.703279i
$83$		−	2.33535i		−	0.256338i	−0.991752	−	0.128169i	$-0.959090\pi$
$83$		−	2.33535i		−	0.256338i	0.991752	−	0.128169i	$-0.0409099\pi$
$84$	2.06990	−	4.79971i	0.225844	−	0.523691i
$85$	0.333922	+	0.219151i	0.0362190	+	0.0237703i
$86$	0.908835	+	1.57415i	0.0980022	+	0.169745i
$87$	13.4590	+	7.77057i	1.44296	+	0.833092i
$88$	−1.14408	+	3.11305i	−0.121960	+	0.331852i
$89$	−5.10571	+	2.94778i	−0.541205	+	0.312465i	−0.745567	−	0.666431i	$-0.767821\pi$
$89$	−5.10571	+	2.94778i	−0.541205	+	0.312465i	0.204362	+	0.978895i	$0.434488\pi$
$90$	1.10800	−	1.68828i	0.116794	−	0.177960i
$91$	−9.26093	+	6.89576i	−0.970809	+	0.722872i
$92$		−	6.94895i		−	0.724478i
$93$	12.5625	−	7.25295i	1.30267	−	0.752095i
$94$	1.99798	−	3.46061i	0.206076	−	0.356934i
$95$	−3.17178	−	6.29998i	−0.325418	−	0.646364i
$96$	−0.987813	−	1.71094i	−0.100818	−	0.174622i
$97$	−2.52195			−0.256065			−0.128033	−	0.991770i	$-0.540866\pi$
$97$	−2.52195			−0.256065			−0.128033	+	0.991770i	$0.540866\pi$
$98$	−6.81103	+	1.61550i	−0.688018	+	0.163190i
$99$	−2.95135	+	0.510901i	−0.296622	+	0.0513475i
$100$	−2.97785	+	4.01652i	−0.297785	+	0.401652i
$101$	−8.06901	+	13.9759i	−0.802896	+	1.39066i	0.114806	+	0.993388i	$0.463376\pi$
$101$	−8.06901	+	13.9759i	−0.802896	+	1.39066i	−0.917702	+	0.397269i	$0.869958\pi$
$102$	0.305614	+	0.176446i	0.0302603	+	0.0174708i
$103$	2.64162	+	4.57542i	0.260287	+	0.450830i	0.966318	−	0.257351i	$-0.0828496\pi$
$103$	2.64162	+	4.57542i	0.260287	+	0.450830i	−0.706031	+	0.708181i	$0.749516\pi$
$104$			4.36408i			0.427933i
$105$	−11.6675	+	0.692159i	−1.13863	+	0.0675478i
$106$		−	11.8260i		−	1.14864i
$107$	9.35777	+	16.2081i	0.904650	+	1.56690i	0.821387	+	0.570372i	$0.193201\pi$
$107$	9.35777	+	16.2081i	0.904650	+	1.56690i	0.0832632	+	0.996528i	$0.473466\pi$
$108$	−2.07135	+	3.58768i	−0.199315	+	0.345224i
$109$	−2.01734	−	1.16471i	−0.193226	−	0.111559i	0.400266	−	0.916399i	$-0.368918\pi$
$109$	−2.01734	−	1.16471i	−0.193226	−	0.111559i	−0.593492	+	0.804840i	$0.702251\pi$
$110$	7.36787	−	0.845246i	0.702499	−	0.0805910i
$111$		−	4.27025i		−	0.405314i
$112$	−1.04772	+	2.42946i	−0.0990000	+	0.229563i
$113$			14.0499i			1.32171i	0.750515	+	0.660853i	$0.229805\pi$
$113$			14.0499i			1.32171i	−0.750515	+	0.660853i	$0.770195\pi$
$114$	−3.11592	−	5.39693i	−0.291833	−	0.505469i
$115$	−13.8786	+	6.98732i	−1.29419	+	0.651571i
$116$	−6.81253	−	3.93322i	−0.632528	−	0.365190i
$117$	−3.41318	+	1.97060i	−0.315548	+	0.182182i
$118$		−	7.27935i		−	0.670118i
$119$	−0.0549055	−	0.469393i	−0.00503318	−	0.0430291i
$120$	−2.42388	+	3.69328i	−0.221269	+	0.337149i
$121$	−8.38215	−	7.12317i	−0.762013	−	0.647561i
$122$	−7.80138	+	13.5124i	−0.706304	+	1.22335i
$123$	7.26405	−	12.5817i	0.654978	−	1.13445i
$124$	−6.35873	+	3.67121i	−0.571031	+	0.329685i
$125$	11.0162	+	1.90874i	0.985319	+	0.170723i
$126$	−2.37320	+	0.277596i	−0.211421	+	0.0247303i
$127$	−9.83136			−0.872392			−0.436196	−	0.899852i	$-0.643675\pi$
$127$	−9.83136			−0.872392			−0.436196	+	0.899852i	$0.643675\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.79552	−	3.10993i	0.158087	−	0.273814i
$130$	8.71606	−	4.38818i	0.764449	−	0.384869i
$131$	−2.41046	−	4.17503i	−0.210603	−	0.364774i	0.741301	−	0.671173i	$-0.234209\pi$
$131$	−2.41046	−	4.17503i	−0.210603	−	0.364774i	−0.951903	+	0.306399i	$0.900876\pi$
$132$	6.45639	−	1.11765i	0.561957	−	0.0972790i
$133$	−3.30488	+	7.66340i	−0.286569	+	0.664501i
$134$		−	5.85630i		−	0.505907i
$135$	9.24820	+	0.529462i	0.795958	+	0.0455688i
$136$	−0.154692	−	0.0893117i	−0.0132648	−	0.00765841i
$137$	9.45131	+	5.45672i	0.807480	+	0.466199i	0.846080	−	0.533056i	$-0.178956\pi$
$137$	9.45131	+	5.45672i	0.807480	+	0.466199i	−0.0385998	+	0.999255i	$0.512290\pi$
$138$	−11.8892	+	6.86426i	−1.01208	+	0.584325i
$139$	2.07680			0.176152			0.0880758	−	0.996114i	$-0.471928\pi$
$139$	2.07680			0.176152			0.0880758	+	0.996114i	$0.471928\pi$
$140$	5.90570	−	0.350349i	0.499122	−	0.0296099i
$141$	−7.89453			−0.664840
$142$	3.51412	+	6.08664i	0.294899	+	0.510780i
$143$	−13.5856	−	4.99287i	−1.13608	−	0.417525i
$144$	−0.451550	+	0.782108i	−0.0376292	+	0.0651756i
$145$	−1.00538	+	17.5611i	−0.0834922	+	1.45837i
$146$			5.37516i			0.444851i
$147$	9.49205	+	10.0575i	0.782891	+	0.829527i
$148$			2.16147i			0.177672i
$149$	−1.87921	+	1.08496i	−0.153951	+	0.0888834i	−0.574996	−	0.818156i	$-0.694997\pi$
$149$	−1.87921	+	1.08496i	−0.153951	+	0.0888834i	0.421046	+	0.907039i	$0.361663\pi$
$150$	9.81359	+	1.12736i	0.801276	+	0.0920483i
$151$	−11.2778	−	6.51125i	−0.917776	−	0.529878i	−0.0348512	−	0.999393i	$-0.511096\pi$
$151$	−11.2778	−	6.51125i	−0.917776	−	0.529878i	−0.882925	+	0.469514i	$0.844429\pi$
$152$	1.57718	+	2.73176i	0.127926	+	0.221575i
$153$		−	0.161315i		−	0.0130415i
$154$	−6.36436	−	6.04110i	−0.512855	−	0.486806i
$155$	13.7261	+	9.00835i	1.10251	+	0.723568i
$156$	7.46669	−	4.31089i	0.597813	−	0.345148i
$157$	0.993687	−	1.72112i	0.0793048	−	0.137360i	−0.823645	−	0.567105i	$-0.808063\pi$
$157$	0.993687	−	1.72112i	0.0793048	−	0.137360i	0.902950	+	0.429745i	$0.141397\pi$
$158$	5.13159	+	2.96273i	0.408248	+	0.235702i
$159$	−20.2336	+	11.6819i	−1.60463	+	0.926432i
$160$	1.22689	−	1.86942i	0.0969941	−	0.147791i
$161$	16.8822	+	7.28053i	1.33050	+	0.573786i
$162$	10.8937			0.855891
$163$	−10.0095	+	5.77901i	−0.784008	+	0.452647i	−0.837849	−	0.545902i	$-0.816187\pi$
$163$	−10.0095	+	5.77901i	−0.784008	+	0.452647i	0.0538407	+	0.998550i	$0.482854\pi$
$164$	−3.67683	+	6.36846i	−0.287113	+	0.497294i
$165$	−8.72425	−	11.7711i	−0.679182	−	0.916376i
$166$	2.02247	−	1.16767i	0.156974	−	0.0906290i
$167$			0.276322i			0.0213825i	0.999943	+	0.0106912i	$0.00340319\pi$
$167$			0.276322i			0.0213825i	−0.999943	+	0.0106912i	$0.996597\pi$
$168$	5.19162	−	0.607271i	0.400542	−	0.0468520i
$169$	−6.04518			−0.465014
$170$	−0.0228292	+	0.398761i	−0.00175092	+	0.0305836i
$171$	−1.42435	+	2.46705i	−0.108923	+	0.188660i
$172$	−0.908835	+	1.57415i	−0.0692980	+	0.120028i
$173$	−19.7516	+	11.4036i	−1.50168	+	0.866998i	−0.501686	+	0.865050i	$0.667287\pi$
$173$	−19.7516	+	11.4036i	−1.50168	+	0.866998i	−0.999998	+	0.00194834i	$0.999380\pi$
$174$			15.5411i			1.17817i
$175$	−6.63804	−	11.4427i	−0.501789	−	0.864990i
$176$	−3.26802	+	0.565719i	−0.246336	+	0.0426427i
$177$	−12.4545	+	7.19064i	−0.936141	+	0.540481i
$178$	−5.10571	−	2.94778i	−0.382689	−	0.220946i
$179$	−8.74527	+	15.1473i	−0.653652	+	1.13216i	0.328578	+	0.944477i	$0.393431\pi$
$179$	−8.74527	+	15.1473i	−0.653652	+	1.13216i	−0.982230	+	0.187682i	$0.939903\pi$
$180$	2.01609	+	0.115422i	0.150271	+	0.00860304i
$181$		−	8.43456i		−	0.626936i	−0.949599	−	0.313468i	$-0.898509\pi$
$181$		−	8.43456i		−	0.626936i	0.949599	−	0.313468i	$-0.101491\pi$
$182$	−10.6024	−	4.57232i	−0.785900	−	0.338923i
$183$	30.8252			2.27867
$184$	6.01796	−	3.47447i	0.443650	−	0.256142i
$185$	4.31695	−	2.17340i	0.317388	−	0.159792i
$186$	12.5625	+	7.25295i	0.921125	+	0.531812i
$187$	0.455012	−	0.379385i	0.0332738	−	0.0277434i
$188$	3.99596			0.291436
$189$	−6.54594	−	8.79113i	−0.476147	−	0.639460i
$190$	3.87005	−	5.89683i	0.280763	−	0.427801i
$191$	−3.18911	−	5.52371i	−0.230756	−	0.399681i	0.727275	−	0.686346i	$-0.240787\pi$
$191$	−3.18911	−	5.52371i	−0.230756	−	0.399681i	−0.958031	+	0.286665i	$0.907453\pi$
$192$	0.987813	−	1.71094i	0.0712893	−	0.123477i
$193$	10.6511	−	18.4483i	0.766683	−	1.32793i	−0.172669	−	0.984980i	$-0.555239\pi$
$193$	10.6511	−	18.4483i	0.766683	−	1.32793i	0.939352	−	0.342954i	$-0.111428\pi$
$194$	−1.26098	−	2.18407i	−0.0905328	−	0.156807i
$195$	−16.1178	−	10.5780i	−1.15422	−	0.757505i
$196$	−4.80458	−	5.09078i	−0.343184	−	0.363627i
$197$	9.64819			0.687405			0.343703	−	0.939079i	$-0.388319\pi$
$197$	9.64819			0.687405			0.343703	+	0.939079i	$0.388319\pi$
$198$	−1.91813	−	2.30049i	−0.136315	−	0.163489i
$199$	−0.513139	−	0.296261i	−0.0363754	−	0.0210014i	0.481702	−	0.876335i	$-0.340019\pi$
$199$	−0.513139	−	0.296261i	−0.0363754	−	0.0210014i	−0.518077	+	0.855334i	$0.673352\pi$
$200$	−4.96733	−	0.570633i	−0.351243	−	0.0403498i
$201$	−10.0198	+	5.78493i	−0.706742	+	0.408038i
$202$	−16.1380			−1.13547
$203$	16.6932	−	12.4299i	1.17163	−	0.872407i
$204$			0.352893i			0.0247074i
$205$	16.4164	+	0.939845i	1.14657	+	0.0656416i
$206$	−2.64162	+	4.57542i	−0.184051	+	0.318785i
$207$	5.43482	+	3.13780i	0.377746	+	0.218092i
$208$	−3.77940	+	2.18204i	−0.262054	+	0.151297i
$209$	−10.3085	+	1.78448i	−0.713055	+	0.123435i
$210$	−6.43315	−	9.75823i	−0.443930	−	0.673382i
$211$		−	5.63839i		−	0.388163i	−0.980985	−	0.194081i	$-0.937827\pi$
$211$		−	5.63839i		−	0.388163i	0.980985	−	0.194081i	$-0.0621726\pi$
$212$	10.2416	−	5.91299i	0.703396	−	0.406106i
$213$	6.94260	−	12.0249i	0.475699	−	0.823935i
$214$	−9.35777	+	16.2081i	−0.639684	+	1.10797i
$215$	4.05779	+	0.232310i	0.276739	+	0.0158434i
$216$	−4.14269			−0.281874
$217$	−2.25693	−	19.2947i	−0.153210	−	1.30981i
$218$		−	2.32943i		−	0.157769i
$219$	9.19659	−	5.30965i	0.621448	−	0.358793i
$220$	4.41594	+	5.95814i	0.297723	+	0.401698i
$221$	0.389763	−	0.675089i	0.0262183	−	0.0454114i
$222$	3.69815	−	2.13513i	0.248203	−	0.143300i
$223$	19.3814			1.29788			0.648938	−	0.760841i	$-0.275213\pi$
$223$	19.3814			1.29788			0.648938	+	0.760841i	$0.275213\pi$
$224$	−2.62783	+	0.307382i	−0.175580	+	0.0205378i
$225$	−1.79670	−	4.14266i	−0.119780	−	0.276177i
$226$	−12.1676	+	7.02497i	−0.809376	+	0.467294i
$227$	−13.0070	−	7.50957i	−0.863302	−	0.498428i	0.00181443	−	0.999998i	$-0.499422\pi$
$227$	−13.0070	−	7.50957i	−0.863302	−	0.498428i	−0.865117	+	0.501571i	$0.832756\pi$
$228$	3.11592	−	5.39693i	0.206357	−	0.357420i
$229$	−10.9482	+	6.32093i	−0.723476	+	0.417699i	−0.816031	−	0.578009i	$-0.803830\pi$
$229$	−10.9482	+	6.32093i	−0.723476	+	0.417699i	0.0925547	+	0.995708i	$0.470497\pi$
$230$	−12.9905	−	8.52559i	−0.856569	−	0.562161i
$231$	−4.04918	+	16.8565i	−0.266416	+	1.10908i
$232$		−	7.86643i		−	0.516457i
$233$	9.23373	+	15.9933i	0.604922	+	1.04775i	0.992064	+	0.125735i	$0.0401289\pi$
$233$	9.23373	+	15.9933i	0.604922	+	1.04775i	−0.387142	+	0.922020i	$0.626538\pi$
$234$	−3.41318	−	1.97060i	−0.223126	−	0.128822i
$235$	−4.01803	−	7.98086i	−0.262108	−	0.520614i
$236$	6.30410	−	3.63967i	0.410362	−	0.236923i
$237$		−	11.7065i		−	0.760418i
$238$	0.379053	−	0.282246i	0.0245704	−	0.0182953i
$239$		−	20.8538i		−	1.34892i	−0.738313	−	0.674459i	$-0.764377\pi$
$239$		−	20.8538i		−	1.34892i	0.738313	−	0.674459i	$-0.235623\pi$
$240$	−4.41041	−	0.252497i	−0.284691	−	0.0162986i
$241$	5.40162	−	9.35589i	0.347949	−	0.602666i	−0.637936	−	0.770089i	$-0.720212\pi$
$241$	5.40162	−	9.35589i	0.347949	−	0.602666i	0.985885	+	0.167424i	$0.0535449\pi$
$242$	1.97778	−	10.8207i	0.127136	−	0.695583i
$243$	−4.54691	−	7.87549i	−0.291685	−	0.505213i
$244$	−15.6028			−0.998865
$245$	−5.33634	+	14.7147i	−0.340926	+	0.940090i
$246$	14.5281			0.926278
$247$	−11.9216	+	6.88294i	−0.758553	+	0.437951i
$248$	−6.35873	−	3.67121i	−0.403780	−	0.233122i
$249$	−3.99564	−	2.30689i	−0.253214	−	0.146193i
$250$	3.85508	+	10.4947i	0.243817	+	0.663742i
$251$			20.1617i			1.27259i	0.771444	+	0.636297i	$0.219535\pi$
$251$			20.1617i			1.27259i	−0.771444	+	0.636297i	$0.780465\pi$
$252$	−1.42700	−	1.91645i	−0.0898928	−	0.120725i
$253$	3.93115	+	22.7093i	0.247150	+	1.42772i
$254$	−4.91568	−	8.51420i	−0.308437	−	0.534229i
$255$	0.704808	−	0.354842i	0.0441368	−	0.0222211i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.8817	−	25.7759i	−0.928297	−	1.60786i	−0.786171	−	0.618010i	$-0.787939\pi$
$257$	−14.8817	−	25.7759i	−0.928297	−	1.60786i	−0.142127	−	0.989848i	$-0.545394\pi$
$258$	3.59104			0.223568
$259$	−5.25120	−	2.26461i	−0.326294	−	0.140716i
$260$	8.15831	+	5.35424i	0.505957	+	0.332056i
$261$	6.15240	−	3.55209i	0.380824	−	0.219869i
$262$	2.41046	−	4.17503i	0.148918	−	0.257934i
$263$	−1.96141	+	3.39725i	−0.120945	+	0.209484i	−0.920141	−	0.391588i	$-0.871926\pi$
$263$	−1.96141	+	3.39725i	−0.120945	+	0.209484i	0.799195	+	0.601071i	$0.205259\pi$
$264$	4.19611	+	5.03257i	0.258253	+	0.309733i
$265$	−22.1078	−	14.5092i	−1.35807	−	0.891291i
$266$	−8.28914	+	0.969592i	−0.508240	+	0.0594495i
$267$			11.6474i			0.712812i
$268$	5.07171	−	2.92815i	0.309804	−	0.178865i
$269$	14.6282	+	8.44561i	0.891899	+	0.514938i	0.874563	−	0.484912i	$-0.161148\pi$
$269$	14.6282	+	8.44561i	0.891899	+	0.514938i	0.0173358	+	0.999850i	$0.494482\pi$
$270$	4.16557	+	8.27390i	0.253509	+	0.503534i
$271$	−2.87507	−	4.97977i	−0.174648	−	0.302499i	0.765391	−	0.643565i	$-0.222545\pi$
$271$	−2.87507	−	4.97977i	−0.174648	−	0.302499i	−0.940039	+	0.341066i	$0.889212\pi$
$272$		−	0.178623i		−	0.0108306i
$273$	2.65018	+	22.6566i	0.160396	+	1.37124i
$274$			10.9134i			0.659305i
$275$	7.45945	−	14.8107i	0.449822	−	0.893118i
$276$	−11.8892	−	6.86426i	−0.715649	−	0.413180i
$277$	−3.68820	+	6.38815i	−0.221602	+	0.383827i	−0.955295	−	0.295655i	$-0.904462\pi$
$277$	−3.68820	+	6.38815i	−0.221602	+	0.383827i	0.733692	+	0.679482i	$0.237795\pi$
$278$	1.03840	+	1.79856i	0.0622790	+	0.107870i
$279$		−	6.63095i		−	0.396984i
$280$	3.25626	+	4.93931i	0.194599	+	0.295180i
$281$		−	30.0400i		−	1.79203i	−0.444019	−	0.896017i	$-0.646448\pi$
$281$		−	30.0400i		−	1.79203i	0.444019	−	0.896017i	$-0.353552\pi$
$282$	−3.94727	−	6.83687i	−0.235056	−	0.407129i
$283$	13.2401	+	7.64415i	0.787040	+	0.454397i	0.838919	−	0.544256i	$-0.183188\pi$
$283$	13.2401	+	7.64415i	0.787040	+	0.454397i	−0.0518798	+	0.998653i	$0.516521\pi$
$284$	−3.51412	+	6.08664i	−0.208525	+	0.361176i
$285$	−13.9120	−	0.796468i	−0.824078	−	0.0471787i
$286$	−2.46884	−	14.2619i	−0.145986	−	0.843324i
$287$	−11.6197	−	15.6051i	−0.685887	−	0.921139i
$288$	−0.903100			−0.0532157
$289$	−8.48405	−	14.6948i	−0.499062	−	0.864400i
$290$	−15.7111	+	7.90988i	−0.922586	+	0.464484i
$291$	−2.49122	+	4.31491i	−0.146038	+	0.252945i
$292$	−4.65502	+	2.68758i	−0.272415	+	0.157279i
$293$			29.9497i			1.74968i	0.484410	+	0.874841i	$0.339034\pi$
$293$			29.9497i			1.74968i	−0.484410	+	0.874841i	$0.660966\pi$
$294$	−3.96401	+	13.2491i	−0.231186	+	0.772703i
$295$	−13.6082	−	8.93096i	−0.792299	−	0.519980i
$296$	−1.87189	+	1.08073i	−0.108801	+	0.0628164i
$297$	4.73958	−	12.8964i	0.275018	−	0.748325i
$298$	−1.87921	−	1.08496i	−0.108860	−	0.0628501i
$299$	15.1629	+	26.2629i	0.876891	+	1.51882i
$300$	3.93048	+	9.06250i	0.226926	+	0.523224i
$301$	−2.87213	−	3.85724i	−0.165547	−	0.222328i
$302$		−	13.0225i		−	0.749361i
$303$	15.9413	+	27.6112i	0.915807	+	1.58622i
$304$	−1.57718	+	2.73176i	−0.0904575	+	0.156677i
$305$	15.6889	+	31.1623i	0.898346	+	1.78435i
$306$	0.139703	−	0.0806574i	0.00798627	−	0.00461087i
$307$		−	3.93017i		−	0.224307i	−0.993691	−	0.112153i	$-0.964225\pi$
$307$		−	3.93017i		−	0.224307i	0.993691	−	0.112153i	$-0.0357748\pi$
$308$	2.04957	−	8.53225i	0.116785	−	0.486170i
$309$	10.4377			0.593781
$310$	−0.938408	+	16.3913i	−0.0532980	+	0.930965i
$311$	12.6022	+	7.27587i	0.714603	+	0.412576i	0.812763	−	0.582594i	$-0.197962\pi$
$311$	12.6022	+	7.27587i	0.714603	+	0.412576i	−0.0981598	+	0.995171i	$0.531296\pi$
$312$	7.46669	+	4.31089i	0.422718	+	0.244056i
$313$	1.20860	+	2.09335i	0.0683139	+	0.118323i	0.898159	−	0.439670i	$-0.144905\pi$
$313$	1.20860	+	2.09335i	0.0683139	+	0.118323i	−0.829845	+	0.557993i	$0.811571\pi$
$314$	1.98737			0.112154
$315$	−2.39271	+	4.77709i	−0.134814	+	0.269159i
$316$			5.92545i			0.333333i
$317$	−1.53637	+	0.887026i	−0.0862914	+	0.0498203i	−0.542525	−	0.840040i	$-0.682532\pi$
$317$	−1.53637	+	0.887026i	−0.0862914	+	0.0498203i	0.456233	+	0.889860i	$0.349198\pi$
$318$	−20.2336	−	11.6819i	−1.13464	−	0.655086i
$319$	24.4886	+	8.99985i	1.37110	+	0.503895i
$320$	2.23241	+	0.127806i	0.124796	+	0.00714459i
$321$	36.9749			2.06374
$322$	2.13598	+	18.2607i	0.119033	+	1.01763i
$323$		−	0.563442i		−	0.0313508i
$324$	5.44686	+	9.43423i	0.302603	+	0.524124i
$325$	2.49029	−	21.6778i	0.138136	−	1.20247i
$326$	−10.0095	−	5.77901i	−0.554378	−	0.320070i
$327$	−3.98552	+	2.30104i	−0.220400	+	0.127248i
$328$	−7.35367			−0.406038
$329$	−4.18664	+	9.70805i	−0.230817	+	0.535222i
$330$	5.83192	−	13.4410i	0.321036	−	0.739900i
$331$	−8.25467	−	14.2975i	−0.453718	−	0.785862i	0.544896	−	0.838504i	$-0.316569\pi$
$331$	−8.25467	−	14.2975i	−0.453718	−	0.785862i	−0.998613	+	0.0526416i	$0.983236\pi$
$332$	2.02247	+	1.16767i	0.110997	+	0.0640844i
$333$	−1.69050	−	0.976011i	−0.0926388	−	0.0534851i
$334$	−0.239302	+	0.138161i	−0.0130940	+	0.00755985i
$335$	−10.9479	−	7.18504i	−0.598148	−	0.392561i
$336$	3.12172	+	4.19244i	0.170304	+	0.228716i
$337$	−14.7633			−0.804210			−0.402105	−	0.915594i	$-0.631721\pi$
$337$	−14.7633			−0.804210			−0.402105	+	0.915594i	$0.631721\pi$
$338$	−3.02259	−	5.23528i	−0.164407	−	0.284762i
$339$	24.0386	+	13.8787i	1.30560	+	0.753788i
$340$	−0.356752	+	0.179610i	−0.0193476	+	0.00974071i
$341$	18.7036	−	15.5949i	1.01286	−	0.844509i
$342$	−2.84870			−0.154040
$343$	17.4017	−	6.33884i	0.939603	−	0.342265i
$344$	−1.81767			−0.0980022
$345$	−1.75459	+	30.6477i	−0.0944640	+	1.65002i
$346$	−19.7516	−	11.4036i	−1.06185	−	0.613060i
$347$	8.38785	−	14.5282i	0.450284	−	0.779914i	−0.548120	−	0.836400i	$-0.684656\pi$
$347$	8.38785	−	14.5282i	0.450284	−	0.779914i	0.998403	+	0.0564858i	$0.0179896\pi$
$348$	−13.4590	+	7.77057i	−0.721479	+	0.416546i
$349$	−30.4718			−1.63112			−0.815558	−	0.578676i	$-0.803570\pi$
$349$	−30.4718			−1.63112			−0.815558	+	0.578676i	$0.803570\pi$
$350$	6.59069	−	11.4701i	0.352287	−	0.613102i
$351$		−	18.0790i		−	0.964987i
$352$	−2.12394	−	2.54733i	−0.113206	−	0.135773i
$353$	17.4485	−	30.2217i	0.928690	−	1.60854i	0.143174	−	0.989698i	$-0.454269\pi$
$353$	17.4485	−	30.2217i	0.928690	−	1.60854i	0.785516	−	0.618841i	$-0.212398\pi$
$354$	−12.4545	−	7.19064i	−0.661952	−	0.382178i
$355$	15.6899	+	0.898254i	0.832736	+	0.0476744i
$356$		−	5.89557i		−	0.312465i
$357$	−0.857340	−	0.369732i	−0.0453753	−	0.0195683i
$358$	−17.4905			−0.924404
$359$	23.2099	−	13.4003i	1.22497	−	0.707238i	0.258999	−	0.965878i	$-0.416607\pi$
$359$	23.2099	−	13.4003i	1.22497	−	0.707238i	0.965974	+	0.258639i	$0.0832741\pi$
$360$	0.908088	+	1.80370i	0.0478604	+	0.0950632i
$361$	4.52501	−	7.83754i	0.238158	−	0.412502i
$362$	7.30454	−	4.21728i	0.383918	−	0.221655i
$363$	−20.4673	+	7.30501i	−1.07426	+	0.383414i
$364$	−1.34144	−	11.4681i	−0.0703104	−	0.601091i
$365$	10.0484	+	6.59473i	0.525960	+	0.345184i
$366$	15.4126	+	26.6954i	0.805631	+	1.39539i
$367$	−10.3971	+	18.0084i	−0.542726	+	0.940030i	0.456020	+	0.889970i	$0.349275\pi$
$367$	−10.3971	+	18.0084i	−0.542726	+	0.940030i	−0.998746	+	0.0500602i	$0.984059\pi$
$368$	6.01796	+	3.47447i	0.313708	+	0.181119i
$369$	−3.32055	−	5.75136i	−0.172861	−	0.299404i
$370$	4.04070	+	2.65188i	0.210066	+	0.137865i
$371$	3.63509	+	31.0767i	0.188724	+	1.61342i
$372$			14.5059i			0.752095i
$373$	7.56342	+	13.1002i	0.391619	+	0.678304i	0.992663	−	0.120912i	$-0.0385819\pi$
$373$	7.56342	+	13.1002i	0.391619	+	0.678304i	−0.601044	+	0.799216i	$0.705249\pi$
$374$	0.556063	+	0.204360i	0.0287533	+	0.0105672i
$375$	14.1477	−	16.9626i	0.730584	−	0.875945i
$376$	1.99798	+	3.46061i	0.103038	+	0.178467i
$377$	34.3297			1.76807
$378$	4.34037	−	10.0645i	0.223244	−	0.517663i
$379$	10.7917			0.554331			0.277165	−	0.960822i	$-0.410605\pi$
$379$	10.7917			0.554331			0.277165	+	0.960822i	$0.410605\pi$
$380$	7.04183	+	0.403147i	0.361238	+	0.0206810i
$381$	−9.71154	+	16.8209i	−0.497537	+	0.861760i
$382$	3.18911	−	5.52371i	0.163169	−	0.282617i
$383$	16.4139	+	28.4297i	0.838710	+	1.45269i	0.890973	+	0.454056i	$0.150023\pi$
$383$	16.4139	+	28.4297i	0.838710	+	1.45269i	−0.0522629	+	0.998633i	$0.516643\pi$
$384$	1.97563			0.100818
$385$	−19.1017	+	4.48592i	−0.973515	+	0.228623i
$386$	21.3022			1.08425
$387$	−0.820769	−	1.42161i	−0.0417220	−	0.0722646i
$388$	1.26098	−	2.18407i	0.0640163	−	0.110880i
$389$	11.5381	−	19.9845i	0.585004	−	1.01326i	−0.409871	−	0.912143i	$-0.634426\pi$
$389$	11.5381	−	19.9845i	0.585004	−	1.01326i	0.994875	−	0.101113i	$-0.0322404\pi$
$390$	1.10192	−	19.2474i	0.0557978	−	0.974629i
$391$	−1.24124			−0.0627724
$392$	2.00646	−	6.70628i	0.101341	−	0.338718i
$393$	−9.52432			−0.480439
$394$	4.82410	+	8.35558i	0.243034	+	0.420948i
$395$	11.8345	−	5.95818i	0.595458	−	0.299789i
$396$	1.03322	−	2.81139i	0.0519213	−	0.141278i
$397$	−3.51225	−	6.08339i	−0.176275	−	0.305316i	0.764327	−	0.644829i	$-0.223071\pi$
$397$	−3.51225	−	6.08339i	−0.176275	−	0.305316i	−0.940602	+	0.339512i	$0.889738\pi$
$398$		−	0.592521i		−	0.0297004i
$399$	9.84704	+	13.2245i	0.492968	+	0.662051i
$400$	−1.98948	−	4.58715i	−0.0994742	−	0.229358i
$401$	19.3734	+	33.5556i	0.967460	+	1.67569i	0.702856	+	0.711332i	$0.251908\pi$
$401$	19.3734	+	33.5556i	0.967460	+	1.67569i	0.264603	+	0.964357i	$0.414759\pi$
$402$	−10.0198	−	5.78493i	−0.499742	−	0.288526i
$403$	16.0215	−	27.7500i	0.798086	−	1.38233i
$404$	−8.06901	−	13.9759i	−0.401448	−	0.695329i
$405$	13.3654	−	20.3650i	0.664131	−	1.01194i
$406$	19.1112	+	8.24180i	0.948473	+	0.409034i
$407$	−1.22278	−	7.06372i	−0.0606112	−	0.350136i
$408$	−0.305614	+	0.176446i	−0.0151302	+	0.00873540i
$409$	3.50302	−	6.06741i	0.173213	−	0.300014i	−0.766328	−	0.642449i	$-0.777918\pi$
$409$	3.50302	−	6.06741i	0.173213	−	0.300014i	0.939541	+	0.342435i	$0.111252\pi$
$410$	7.39428	+	14.6870i	0.365178	+	0.725337i
$411$	18.6723	−	10.7804i	0.921035	−	0.531760i
$412$	−5.28324			−0.260287
$413$	2.23754	+	19.1289i	0.110102	+	0.941273i
$414$			6.27559i			0.308429i
$415$	0.298472	−	5.21346i	0.0146514	−	0.255918i
$416$	−3.77940	−	2.18204i	−0.185300	−	0.106983i
$417$	2.05149	−	3.55328i	0.100462	−	0.174005i
$418$	−6.69967	−	8.03520i	−0.327691	−	0.393014i
$419$		−	19.9310i		−	0.973692i	−0.873488	−	0.486846i	$-0.838147\pi$
$419$		−	19.9310i		−	0.973692i	0.873488	−	0.486846i	$-0.161853\pi$
$420$	5.23430	−	10.4504i	0.255408	−	0.509927i
$421$	−7.61783			−0.371270			−0.185635	−	0.982619i	$-0.559434\pi$
$421$	−7.61783			−0.371270			−0.185635	+	0.982619i	$0.559434\pi$
$422$	4.88299	−	2.81919i	0.237700	−	0.137236i
$423$	−1.80438	+	3.12527i	−0.0877319	+	0.151956i
$424$	10.2416	+	5.91299i	0.497376	+	0.287160i
$425$	0.717444	+	0.531913i	0.0348011	+	0.0258016i
$426$	13.8852			0.672740
$427$	16.3473	−	37.9063i	0.791101	−	1.83442i
$428$	−18.7155			−0.904650
$429$	−21.9625	+	18.3121i	−1.06036	+	0.884119i
$430$	1.82771	+	3.63030i	0.0881399	+	0.175069i
$431$	0.553219	+	0.319401i	0.0266476	+	0.0153850i	0.513265	−	0.858230i	$-0.328436\pi$
$431$	0.553219	+	0.319401i	0.0266476	+	0.0153850i	−0.486617	+	0.873615i	$0.661769\pi$
$432$	−2.07135	−	3.58768i	−0.0996577	−	0.172612i
$433$	−14.4902			−0.696355			−0.348178	−	0.937429i	$-0.613199\pi$
$433$	−14.4902			−0.696355			−0.348178	+	0.937429i	$0.613199\pi$
$434$	15.5812	−	11.6019i	0.747923	−	0.556909i
$435$	29.0529	+	19.0673i	1.39298	+	0.914205i
$436$	2.01734	−	1.16471i	0.0966132	−	0.0557797i
$437$	18.9828	+	10.9597i	0.908072	+	0.524275i
$438$	9.19659	+	5.30965i	0.439430	+	0.253705i
$439$	4.74897	+	8.22545i	0.226656	+	0.392579i	0.956815	−	0.290698i	$-0.0938874\pi$
$439$	4.74897	+	8.22545i	0.226656	+	0.392579i	−0.730159	+	0.683277i	$0.760554\pi$
$440$	−2.95193	+	6.80339i	−0.140728	+	0.324339i
$441$	6.15104	−	1.45895i	0.292907	−	0.0694740i
$442$	0.779526			0.0370783
$443$	1.45039	−	0.837383i	0.0689101	−	0.0397852i	−0.465149	−	0.885232i	$-0.653999\pi$
$443$	1.45039	−	0.837383i	0.0689101	−	0.0397852i	0.534059	+	0.845447i	$0.320666\pi$
$444$	3.69815	+	2.13513i	0.175506	+	0.101329i
$445$	−11.7748	+	5.92813i	−0.558179	+	0.281020i
$446$	9.69072	+	16.7848i	0.458869	+	0.794784i
$447$			4.28695i			0.202766i
$448$	−1.58012	−	2.12208i	−0.0746535	−	0.100259i
$449$	−32.3888			−1.52852			−0.764260	−	0.644908i	$-0.776896\pi$
$449$	−32.3888			−1.52852			−0.764260	+	0.644908i	$0.776896\pi$
$450$	2.68929	−	3.62732i	0.126775	−	0.170993i
$451$	8.41321	−	22.8923i	0.396163	−	1.07796i
$452$	−12.1676	−	7.02497i	−0.572316	−	0.330427i
$453$	−22.2808	+	12.8638i	−1.04684	+	0.604394i
$454$		−	15.0191i		−	0.704883i
$455$	−21.5555	+	14.2106i	−1.01054	+	0.666202i
$456$	6.23184			0.291833
$457$	1.19633	+	2.07211i	0.0559620	+	0.0969291i	0.892649	−	0.450752i	$-0.148844\pi$
$457$	1.19633	+	2.07211i	0.0559620	+	0.0969291i	−0.836687	+	0.547681i	$0.815511\pi$
$458$	−10.9482	−	6.32093i	−0.511575	−	0.295358i
$459$	0.640842	+	0.369991i	0.0299120	+	0.0172697i
$460$	0.888119	−	15.5129i	0.0414087	−	0.723293i
$461$	−38.8993			−1.81172			−0.905861	−	0.423575i	$-0.860775\pi$
$461$	−38.8993			−1.81172			−0.905861	+	0.423575i	$0.860775\pi$
$462$	−16.6228	+	4.92158i	−0.773362	+	0.228972i
$463$		−	15.9410i		−	0.740840i	−0.928864	−	0.370420i	$-0.879214\pi$
$463$		−	15.9410i		−	0.740840i	0.928864	−	0.370420i	$-0.120786\pi$
$464$	6.81253	−	3.93322i	0.316264	−	0.182595i
$465$	28.9716	−	14.5860i	1.34353	−	0.676410i
$466$	−9.23373	+	15.9933i	−0.427744	+	0.740875i
$467$	2.48834	+	4.30994i	0.115147	+	0.199440i	0.917838	−	0.396954i	$-0.129933\pi$
$467$	2.48834	+	4.30994i	0.115147	+	0.199440i	−0.802692	+	0.596394i	$0.796599\pi$
$468$		−	3.94120i		−	0.182182i
$469$	1.80012	+	15.3894i	0.0831218	+	0.710616i
$470$	4.90261	−	7.47015i	0.226140	−	0.344572i
$471$	−1.96315	−	3.40028i	−0.0904573	−	0.156677i
$472$	6.30410	+	3.63967i	0.290170	+	0.167530i
$473$	2.07956	−	5.65849i	0.0956185	−	0.260178i
$474$	10.1381	−	5.85324i	0.465659	−	0.268848i
$475$	−6.27555	−	14.4695i	−0.287942	−	0.663907i
$476$	0.433959	+	0.187147i	0.0198905	+	0.00857786i
$477$			10.6800i			0.489006i
$478$	18.0599	−	10.4269i	0.826040	−	0.476914i
$479$	4.29500	−	7.43916i	0.196244	−	0.339904i	−0.751064	−	0.660230i	$-0.770459\pi$
$479$	4.29500	−	7.43916i	0.196244	−	0.339904i	0.947308	+	0.320326i	$0.103792\pi$
$480$	−1.98654	−	3.94578i	−0.0906726	−	0.180099i
$481$	−4.71641	−	8.16906i	−0.215050	−	0.372477i
$482$	10.8032			0.492074
$483$	29.1330	−	21.6927i	1.32560	−	0.987051i
$484$	10.3599	−	3.69757i	0.470906	−	0.168071i
$485$	−5.63003	−	0.322321i	−0.255647	−	0.0146358i
$486$	4.54691	−	7.87549i	0.206252	−	0.357239i
$487$	−10.3406	−	5.97015i	−0.468578	−	0.270533i	0.247066	−	0.968999i	$-0.420533\pi$
$487$	−10.3406	−	5.97015i	−0.468578	−	0.270533i	−0.715644	+	0.698465i	$0.753867\pi$
$488$	−7.80138	−	13.5124i	−0.353152	−	0.611677i
$489$			22.8344i			1.03261i
$490$	−15.4115	+	2.73596i	−0.696221	+	0.123598i
$491$		−	17.9683i		−	0.810897i	−0.914118	−	0.405448i	$-0.867115\pi$
$491$		−	17.9683i		−	0.810897i	0.914118	−	0.405448i	$-0.132885\pi$
$492$	7.26405	+	12.5817i	0.327489	+	0.567227i
$493$	−0.702564	+	1.21688i	−0.0316419	+	0.0548054i
$494$	−11.9216	−	6.88294i	−0.536378	−	0.309678i
$495$	−6.65393	+	0.763341i	−0.299072	+	0.0343096i
$496$		−	7.34243i		−	0.329685i
$497$	−11.1055	−	14.9145i	−0.498148	−	0.669007i
$498$		−	4.61377i		−	0.206748i
$499$	−16.1760	−	28.0177i	−0.724138	−	1.25424i	−0.959328	−	0.282295i	$-0.908904\pi$
$499$	−16.1760	−	28.0177i	−0.724138	−	1.25424i	0.235189	−	0.971950i	$-0.424429\pi$
$500$	−7.16112	+	8.58594i	−0.320255	+	0.383975i
$501$	0.472772	+	0.272955i	0.0211219	+	0.0121947i
$502$	−17.4605	+	10.0808i	−0.779301	+	0.449930i
$503$			24.9326i			1.11169i	0.831287	+	0.555844i	$0.187605\pi$
$503$			24.9326i			1.11169i	−0.831287	+	0.555844i	$0.812395\pi$
$504$	0.946193	−	2.19405i	0.0421468	−	0.0977307i
$505$	−19.7996	+	30.1688i	−0.881069	+	1.34249i
$506$	−17.7013	+	14.7591i	−0.786917	+	0.656123i
$507$	−5.97151	+	10.3430i	−0.265204	+	0.459347i
$508$	4.91568	−	8.51420i	0.218098	−	0.377757i
$509$	−18.1708	+	10.4909i	−0.805407	+	0.465002i	−0.845359	−	0.534199i	$-0.820613\pi$
$509$	−18.1708	+	10.4909i	−0.805407	+	0.465002i	0.0399510	+	0.999202i	$0.487280\pi$
$510$	0.659706	+	0.432961i	0.0292123	+	0.0191718i
$511$	−1.65223	−	14.1250i	−0.0730901	−	0.624855i
$512$	−1.00000			−0.0441942
$513$	−6.53377	−	11.3168i	−0.288473	−	0.499650i
$514$	14.8817	−	25.7759i	0.656405	−	1.13693i
$515$	5.31242	+	10.5518i	0.234093	+	0.464970i
$516$	1.79552	+	3.10993i	0.0790433	+	0.136907i
$517$	−13.0589	+	2.26059i	−0.574330	+	0.0994209i
$518$	−0.664395	−	5.67998i	−0.0291919	−	0.249564i
$519$			45.0584i			1.97785i
$520$	−0.557757	+	9.74242i	−0.0244592	+	0.427233i
$521$	14.2612	+	8.23369i	0.624794	+	0.360725i	0.778733	−	0.627356i	$-0.215863\pi$
$521$	14.2612	+	8.23369i	0.624794	+	0.360725i	−0.153939	+	0.988080i	$0.549196\pi$
$522$	6.15240	+	3.55209i	0.269283	+	0.155471i
$523$	12.6939	−	7.32883i	0.555065	−	0.320467i	−0.196097	−	0.980584i	$-0.562827\pi$
$523$	12.6939	−	7.32883i	0.555065	−	0.320467i	0.751163	+	0.660117i	$0.229493\pi$
$524$	4.82091			0.210603
$525$	−26.1350	+	0.0540100i	−1.14063	+	0.00235719i
$526$	−3.92281			−0.171043
$527$	0.655764	+	1.13582i	0.0285655	+	0.0494770i
$528$	−2.26028	+	6.15022i	−0.0983661	+	0.267654i
$529$	12.6439	−	21.8999i	0.549736	−	0.952170i
$530$	1.51143	−	26.4005i	0.0656525	−	1.14676i
$531$			6.57398i			0.285286i
$532$	−4.98426	−	6.69381i	−0.216095	−	0.290213i
$533$		−	32.0920i		−	1.39006i
$534$	−10.0870	+	5.82372i	−0.436506	+	0.252017i
$535$	18.8189	+	37.3792i	0.813612	+	1.61604i
$536$	5.07171	+	2.92815i	0.219064	+	0.126477i
$537$	17.2774	+	29.9253i	0.745574	+	1.29137i
$538$			16.8912i			0.728232i
$539$	18.5814	+	13.9187i	0.800358	+	0.599522i
$540$	−5.08263	+	7.74444i	−0.218721	+	0.333268i
$541$	−25.0216	+	14.4462i	−1.07576	+	0.621093i	−0.929751	−	0.368190i	$-0.879978\pi$
$541$	−25.0216	+	14.4462i	−1.07576	+	0.621093i	−0.146013	+	0.989283i	$0.546644\pi$
$542$	2.87507	−	4.97977i	0.123495	−	0.213899i
$543$	−14.4311	−	8.33177i	−0.619296	−	0.357551i
$544$	0.154692	−	0.0893117i	0.00663238	−	0.00382921i
$545$	−4.35468	−	2.85795i	−0.186534	−	0.122421i
$546$	−18.2961	+	13.6234i	−0.783002	+	0.583029i
$547$	11.8738			0.507685			0.253843	−	0.967246i	$-0.418305\pi$
$547$	11.8738			0.507685			0.253843	+	0.967246i	$0.418305\pi$
$548$	−9.45131	+	5.45672i	−0.403740	+	0.233099i
$549$	7.04543	−	12.2030i	0.300692	−	0.520813i
$550$	16.5562	−	0.945277i	0.705957	−	0.0403067i
$551$	21.4892	−	12.4068i	0.915470	−	0.528547i
$552$		−	13.7285i		−	0.584325i
$553$	−14.3957	−	6.20820i	−0.612166	−	0.263999i
$554$	−7.37640			−0.313393
$555$	0.545765	−	9.53297i	0.0231664	−	0.404652i
$556$	−1.03840	+	1.79856i	−0.0440379	+	0.0762759i
$557$	4.16354	−	7.21146i	0.176415	−	0.305559i	−0.764235	−	0.644938i	$-0.776883\pi$
$557$	4.16354	−	7.21146i	0.176415	−	0.305559i	0.940650	+	0.339378i	$0.110217\pi$
$558$	5.74257	−	3.31547i	0.243102	−	0.140355i
$559$		−	7.93245i		−	0.335507i
$560$	−2.64944	+	5.28966i	−0.111959	+	0.223529i
$561$	−0.199638	−	1.15326i	−0.00842874	−	0.0486907i
$562$	26.0154	−	15.0200i	1.09739	−	0.633580i
$563$	−15.2000	−	8.77570i	−0.640602	−	0.369852i	0.144245	−	0.989542i	$-0.453925\pi$
$563$	−15.2000	−	8.77570i	−0.640602	−	0.369852i	−0.784846	+	0.619691i	$0.787258\pi$
$564$	3.94727	−	6.83687i	0.166210	−	0.287884i
$565$	−1.79567	+	31.3652i	−0.0755444	+	1.31955i
$566$			15.2883i			0.642615i
$567$	−28.6269	+	3.34853i	−1.20222	+	0.140625i
$568$	−7.02825			−0.294899
$569$	33.2610	−	19.2033i	1.39437	−	0.805042i	0.400578	−	0.916263i	$-0.368809\pi$
$569$	33.2610	−	19.2033i	1.39437	−	0.805042i	0.993796	+	0.111220i	$0.0354760\pi$
$570$	−6.26625	−	12.4464i	−0.262465	−	0.521323i
$571$	−13.3246	−	7.69297i	−0.557618	−	0.321941i	0.194571	−	0.980888i	$-0.437669\pi$
$571$	−13.3246	−	7.69297i	−0.557618	−	0.321941i	−0.752189	+	0.658948i	$0.771002\pi$
$572$	11.1167	−	9.26903i	0.464814	−	0.387558i
$573$	−12.6010			−0.526414
$574$	7.70457	−	17.8655i	0.321582	−	0.745690i
$575$	−31.8759	+	13.8248i	−1.32932	+	0.576534i
$576$	−0.451550	−	0.782108i	−0.0188146	−	0.0325878i
$577$	0.289829	−	0.501999i	0.0120657	−	0.0208985i	−0.859929	−	0.510413i	$-0.829493\pi$
$577$	0.289829	−	0.501999i	0.0120657	−	0.0208985i	0.871995	+	0.489514i	$0.162826\pi$
$578$	8.48405	−	14.6948i	0.352890	−	0.611223i
$579$	−21.0426	−	36.4469i	−0.874501	−	1.51468i
$580$	−14.7057	−	9.65125i	−0.610621	−	0.400746i
$581$	−4.95579	+	3.69012i	−0.205601	+	0.153092i
$582$	−4.98243			−0.206528
$583$	−30.1247	+	25.1176i	−1.24764	+	1.04027i
$584$	−4.65502	−	2.68758i	−0.192626	−	0.111213i
$585$	−7.87148	+	3.96297i	−0.325446	+	0.163848i
$586$	−25.9372	+	14.9749i	−1.07146	+	0.618606i
$587$	−27.7068			−1.14358			−0.571791	−	0.820399i	$-0.693751\pi$
$587$	−27.7068			−1.14358			−0.571791	+	0.820399i	$0.693751\pi$
$588$	−13.4561	+	3.19162i	−0.554918	+	0.131620i
$589$		−	23.1607i		−	0.954318i
$590$	0.930346	−	16.2505i	0.0383017	−	0.669023i
$591$	9.53061	−	16.5075i	0.392037	−	0.679028i
$592$	−1.87189	−	1.08073i	−0.0769340	−	0.0444179i
$593$	17.1649	−	9.91015i	0.704877	−	0.406961i	−0.104284	−	0.994548i	$-0.533255\pi$
$593$	17.1649	−	9.91015i	0.704877	−	0.406961i	0.809161	+	0.587586i	$0.199922\pi$
$594$	13.5384	−	2.34360i	0.555487	−	0.0961591i
$595$	−0.0625805	−	1.05490i	−0.00256555	−	0.0432465i
$596$		−	2.16992i		−	0.0888834i
$597$	−1.01377	+	0.585301i	−0.0414909	+	0.0239548i
$598$	−15.1629	+	26.2629i	−0.620056	+	1.07397i
$599$	−23.1312	+	40.0644i	−0.945114	+	1.63699i	−0.189591	+	0.981863i	$0.560716\pi$
$599$	−23.1312	+	40.0644i	−0.945114	+	1.63699i	−0.755523	+	0.655122i	$0.772617\pi$
$600$	−5.88312	+	7.93514i	−0.240177	+	0.323951i
$601$	35.4217			1.44488			0.722440	−	0.691434i	$-0.243021\pi$
$601$	35.4217			1.44488			0.722440	+	0.691434i	$0.243021\pi$
$602$	1.90440	−	4.41596i	0.0776177	−	0.179981i
$603$			5.28883i			0.215378i
$604$	11.2778	−	6.51125i	0.458888	−	0.264939i
$605$	−17.8020	−	16.9732i	−0.723755	−	0.690057i
$606$	−15.9413	+	27.6112i	−0.647573	+	1.12163i
$607$	−16.4801	+	9.51482i	−0.668909	+	0.386195i	−0.795663	−	0.605740i	$-0.792877\pi$
$607$	−16.4801	+	9.51482i	−0.668909	+	0.386195i	0.126754	+	0.991934i	$0.459544\pi$
$608$	−3.15436			−0.127926
$609$	−4.77706	−	40.8395i	−0.193576	−	1.65490i
$610$	−19.1429	+	29.1682i	−0.775072	+	1.18098i
$611$	−15.1024	+	8.71935i	−0.610976	+	0.352747i
$612$	0.139703	+	0.0806574i	0.00564714	+	0.00326038i
$613$	19.6507	−	34.0360i	0.793684	−	1.37470i	−0.129987	−	0.991516i	$-0.541494\pi$
$613$	19.6507	−	34.0360i	0.793684	−	1.37470i	0.923671	−	0.383186i	$-0.125173\pi$
$614$	3.40363	−	1.96509i	0.137359	−	0.0793044i
$615$	17.8244	−	27.1592i	0.718748	−	1.09516i
$616$	8.41393	−	2.49115i	0.339007	−	0.100371i
$617$			12.7809i			0.514538i	0.966340	+	0.257269i	$0.0828226\pi$
$617$			12.7809i			0.514538i	−0.966340	+	0.257269i	$0.917177\pi$
$618$	5.21886	+	9.03933i	0.209933	+	0.363615i
$619$	13.0008	+	7.50601i	0.522546	+	0.301692i	0.737976	−	0.674827i	$-0.235782\pi$
$619$	13.0008	+	7.50601i	0.522546	+	0.301692i	−0.215430	+	0.976519i	$0.569115\pi$
$620$	−14.6645	+	7.38298i	−0.588941	+	0.296507i
$621$	−24.9306	+	14.3937i	−1.00043	+	0.577598i
$622$			14.5517i			0.583471i
$623$	14.3231	+	6.17689i	0.573842	+	0.247472i
$624$			8.62179i			0.345148i
$625$	24.3488	+	5.66904i	0.973950	+	0.226762i
$626$	−1.20860	+	2.09335i	−0.0483052	+	0.0836671i
$627$	−7.12974	+	19.4000i	−0.284734	+	0.774762i
$628$	0.993687	+	1.72112i	0.0396524	+	0.0686800i
$629$	0.386088			0.0153944
$630$	−5.33344	+	0.316400i	−0.212489	+	0.0126057i
$631$	−16.7682			−0.667532			−0.333766	−	0.942656i	$-0.608319\pi$
$631$	−16.7682			−0.667532			−0.333766	+	0.942656i	$0.608319\pi$
$632$	−5.13159	+	2.96273i	−0.204124	+	0.117851i
$633$	−9.64696	−	5.56967i	−0.383432	−	0.221375i
$634$	−1.53637	−	0.887026i	−0.0610172	−	0.0352283i
$635$	−21.9476	−	1.25651i	−0.870966	−	0.0498630i
$636$		−	23.3637i		−	0.926432i
$637$	29.2667	+	8.75633i	1.15959	+	0.346938i
$638$	4.45019	+	25.7077i	0.176185	+	1.01778i
$639$	−3.17361	−	5.49685i	−0.125546	−	0.217452i
$640$	1.00552	+	1.99723i	0.0397468	+	0.0789474i
$641$	3.55679	−	6.16054i	0.140485	−	0.243327i	−0.787194	−	0.616705i	$-0.788467\pi$
$641$	3.55679	−	6.16054i	0.140485	−	0.243327i	0.927679	+	0.373378i	$0.121801\pi$
$642$	18.4875	+	32.0212i	0.729642	+	1.26378i
$643$	24.4130			0.962754			0.481377	−	0.876514i	$-0.340137\pi$
$643$	24.4130			0.962754			0.481377	+	0.876514i	$0.340137\pi$
$644$	−14.7462	+	10.9802i	−0.581083	+	0.432679i
$645$	4.40580	−	6.71316i	0.173478	−	0.264331i
$646$	0.487955	−	0.281721i	0.0191983	−	0.0110842i
$647$	12.9611	−	22.4494i	0.509555	−	0.882575i	−0.490384	−	0.871507i	$-0.663143\pi$
$647$	12.9611	−	22.4494i	0.509555	−	0.882575i	0.999939	−	0.0110687i	$-0.00352335\pi$
$648$	−5.44686	+	9.43423i	−0.213973	+	0.370612i
$649$	−18.5429	+	15.4609i	−0.727872	+	0.606893i
$650$	20.0187	−	8.68226i	0.785197	−	0.340546i
$651$	−35.2415	−	15.1981i	−1.38122	−	0.595659i
$652$		−	11.5580i		−	0.452647i
$653$	−21.1492	+	12.2105i	−0.827634	+	0.477835i	−0.853042	−	0.521842i	$-0.825245\pi$
$653$	−21.1492	+	12.2105i	−0.827634	+	0.477835i	0.0254079	+	0.999677i	$0.491912\pi$
$654$	−3.98552	−	2.30104i	−0.155846	−	0.0899777i
$655$	−4.84754	−	9.62847i	−0.189409	−	0.376215i
$656$	−3.67683	−	6.36846i	−0.143556	−	0.248647i
$657$		−	4.85431i		−	0.189385i
$658$	−10.5007	+	1.22829i	−0.409361	+	0.0478836i
$659$			10.2409i			0.398930i	0.979905	+	0.199465i	$0.0639204\pi$
$659$			10.2409i			0.398930i	−0.979905	+	0.199465i	$0.936080\pi$
$660$	14.5562	−	1.66989i	0.566598	−	0.0650004i
$661$	−20.5160	−	11.8449i	−0.797978	−	0.460713i	0.0447856	−	0.998997i	$-0.485740\pi$
$661$	−20.5160	−	11.8449i	−0.797978	−	0.460713i	−0.842764	+	0.538284i	$0.819073\pi$
$662$	8.25467	−	14.2975i	0.320827	−	0.555689i
$663$	−0.770026	−	1.33372i	−0.0299053	−	0.0517976i
$664$			2.33535i			0.0906290i
$665$	−8.35728	+	16.6855i	−0.324081	+	0.647035i
$666$		−	1.95202i		−	0.0756393i
$667$	−27.3317	−	47.3399i	−1.05829	−	1.83301i
$668$	−0.239302	−	0.138161i	−0.00925888	−	0.00534562i
$669$	19.1452	−	33.1605i	0.740198	−	1.28206i
$670$	0.748472	−	13.0737i	0.0289160	−	0.505080i
$671$	50.9902	−	8.82679i	1.96845	−	0.340754i
$672$	−2.06990	+	4.79971i	−0.0798480	+	0.185153i
$673$	−41.4261			−1.59686			−0.798430	−	0.602088i	$-0.794336\pi$
$673$	−41.4261			−1.59686			−0.798430	+	0.602088i	$0.794336\pi$
$674$	−7.38166	−	12.7854i	−0.284331	−	0.492476i
$675$	20.5781	+	2.36395i	0.792052	+	0.0909887i
$676$	3.02259	−	5.23528i	0.116253	−	0.201357i
$677$	27.4620	−	15.8552i	1.05545	−	0.609364i	0.131280	−	0.991345i	$-0.458091\pi$
$677$	27.4620	−	15.8552i	1.05545	−	0.609364i	0.924170	+	0.381981i	$0.124758\pi$
$678$			27.7574i			1.06602i
$679$	3.98498	+	5.35178i	0.152929	+	0.205383i
$680$	−0.333922	−	0.219151i	−0.0128053	−	0.00840406i
$681$	−25.6969	+	14.8361i	−0.984707	+	0.568521i
$682$	22.8573	+	8.40035i	0.875253	+	0.321666i
$683$	16.0918	+	9.29059i	0.615734	+	0.355494i	0.775206	−	0.631708i	$-0.217646\pi$
$683$	16.0918	+	9.29059i	0.615734	+	0.355494i	−0.159472	+	0.987202i	$0.550979\pi$
$684$	−1.42435	−	2.46705i	−0.0544614	−	0.0943300i
$685$	20.4018	+	13.3896i	0.779514	+	0.511590i
$686$	14.1904	+	11.9009i	0.541794	+	0.454378i
$687$			24.9756i			0.952879i
$688$	−0.908835	−	1.57415i	−0.0346490	−	0.0600138i
$689$	−25.8047	+	44.6951i	−0.983083	+	1.70275i
$690$	−27.4190	+	13.8043i	−1.04382	+	0.525522i
$691$	−14.2486	+	8.22644i	−0.542043	+	0.312948i	−0.745906	−	0.666051i	$-0.767983\pi$
$691$	−14.2486	+	8.22644i	−0.542043	+	0.312948i	0.203864	+	0.978999i	$0.434650\pi$
$692$		−	22.8072i		−	0.866998i
$693$	5.74765	+	5.45572i	0.218335	+	0.207246i
$694$	16.7757			0.636797
$695$	4.63627	+	0.265428i	0.175864	+	0.0100682i
$696$	−13.4590	−	7.77057i	−0.510163	−	0.294543i
$697$	1.13756	+	0.656768i	0.0430880	+	0.0248769i
$698$	−15.2359	−	26.3893i	−0.576686	−	0.998850i
$699$	36.4848			1.37998
$700$	13.2287	−	0.0273382i	0.499999	−	0.00103329i
$701$			14.9935i			0.566298i	0.959076	+	0.283149i	$0.0913791\pi$
$701$			14.9935i			0.566298i	−0.959076	+	0.283149i	$0.908621\pi$
$702$	15.6569	−	9.03951i	0.590932	−	0.341174i
$703$	−5.90460	−	3.40902i	−0.222696	−	0.128574i
$704$	1.14408	−	3.11305i	0.0431193	−	0.117327i
$705$	−17.6239	−	1.00897i	−0.663753	−	0.0380000i
$706$	34.8970			1.31337
$707$	42.4081	−	4.96053i	1.59492	−	0.186560i
$708$		−	14.3813i		−	0.540481i
$709$	10.0817	+	17.4620i	0.378626	+	0.655800i	0.990863	−	0.134875i	$-0.0430633\pi$
$709$	10.0817	+	17.4620i	0.378626	+	0.655800i	−0.612237	+	0.790675i	$0.709730\pi$
$710$	7.06706	+	14.0370i	0.265222	+	0.526800i
$711$	−4.63434	−	2.67564i	−0.173801	−	0.100344i
$712$	5.10571	−	2.94778i	0.191345	−	0.110473i
$713$	−51.0221			−1.91079
$714$	−0.108473	−	0.927344i	−0.00405949	−	0.0347050i
$715$	−29.6905	−	12.8825i	−1.11036	−	0.481777i
$716$	−8.74527	−	15.1473i	−0.326826	−	0.566079i
$717$	−35.6796	−	20.5996i	−1.33248	−	0.769307i
$718$	23.2099	+	13.4003i	0.866187	+	0.500093i
$719$	9.27051	−	5.35233i	0.345732	−	0.199608i	−0.317072	−	0.948401i	$-0.602700\pi$
$719$	9.27051	−	5.35233i	0.345732	−	0.199608i	0.662804	+	0.748793i	$0.269366\pi$
$720$	−1.10800	+	1.68828i	−0.0412929	+	0.0629183i
$721$	5.53534	−	12.8354i	0.206147	−	0.478017i
$722$	9.05001			0.336807
$723$	−10.6716	−	18.4837i	−0.396881	−	0.687417i
$724$	7.30454	+	4.21728i	0.271471	+	0.156734i
$725$	−4.48884	+	39.0752i	−0.166711	+	1.45122i
$726$	−16.5600	−	14.0727i	−0.614599	−	0.522288i
$727$	38.1856			1.41622			0.708112	−	0.706100i	$-0.249547\pi$
$727$	38.1856			1.41622			0.708112	+	0.706100i	$0.249547\pi$
$728$	9.26093	−	6.89576i	0.343233	−	0.255574i
$729$	14.7151			0.545004
$730$	−0.686979	+	11.9996i	−0.0254262	+	0.444124i
$731$	0.281179	+	0.162339i	0.0103998	+	0.00600433i
$732$	−15.4126	+	26.6954i	−0.569667	+	0.986692i
$733$	3.60697	−	2.08248i	0.133226	−	0.0769183i	−0.431905	−	0.901919i	$-0.642159\pi$
$733$	3.60697	−	2.08248i	0.133226	−	0.0769183i	0.565132	+	0.825001i	$0.308825\pi$
$734$	−20.7943			−0.767531
$735$	19.9048	+	23.6656i	0.734198	+	0.872918i
$736$			6.94895i			0.256142i
$737$	−14.9179	+	12.4384i	−0.549509	+	0.458175i
$738$	3.32055	−	5.75136i	0.122231	−	0.211711i
$739$	−18.9725	−	10.9538i	−0.697915	−	0.402941i	0.108655	−	0.994079i	$-0.465345\pi$
$739$	−18.9725	−	10.9538i	−0.697915	−	0.402941i	−0.806570	+	0.591138i	$0.798679\pi$
$740$	−0.276249	+	4.82529i	−0.0101551	+	0.177381i
$741$			27.1962i			0.999078i
$742$	−25.0957	+	18.6864i	−0.921292	+	0.686001i
$743$	7.34089			0.269311			0.134656	−	0.990892i	$-0.457007\pi$
$743$	7.34089			0.269311			0.134656	+	0.990892i	$0.457007\pi$
$744$	−12.5625	+	7.25295i	−0.460563	+	0.265906i
$745$	−4.33383	+	2.18190i	−0.158779	+	0.0799388i
$746$	−7.56342	+	13.1002i	−0.276916	+	0.479633i
$747$	−1.82649	+	1.05453i	−0.0668278	+	0.0385831i
$748$	0.101051	+	0.583745i	0.00369478	+	0.0213438i
$749$	19.6086	−	45.4687i	0.716482	−	1.66139i
$750$	21.7639	+	3.77096i	0.794705	+	0.137696i
$751$	19.7890	+	34.2756i	0.722112	+	1.25074i	0.960152	+	0.279480i	$0.0901620\pi$
$751$	19.7890	+	34.2756i	0.722112	+	1.25074i	−0.238039	+	0.971256i	$0.576505\pi$
$752$	−1.99798	+	3.46061i	−0.0728589	+	0.126195i
$753$	34.4955	+	19.9160i	1.25708	+	0.725778i
$754$	17.1649	+	29.7304i	0.625107	+	1.08272i
$755$	−24.3446	−	15.9772i	−0.885990	−	0.581469i
$756$	10.8863	−	1.27339i	0.395931	−	0.0463126i
$757$		−	12.7613i		−	0.463818i	−0.972737	−	0.231909i	$-0.925503\pi$
$757$		−	12.7613i		−	0.463818i	0.972737	−	0.231909i	$-0.0744972\pi$
$758$	5.39583	+	9.34586i	0.195986	+	0.339457i
$759$	42.7376	+	15.7066i	1.55127	+	0.570112i
$760$	3.17178	+	6.29998i	0.115053	+	0.228524i
$761$	−4.45466	−	7.71570i	−0.161481	−	0.279694i	0.773919	−	0.633285i	$-0.218294\pi$
$761$	−4.45466	−	7.71570i	−0.161481	−	0.279694i	−0.935400	+	0.353591i	$0.884960\pi$
$762$	−19.4231			−0.703624
$763$	0.716023	+	6.12135i	0.0259218	+	0.221608i
$764$	6.37823			0.230756
$765$	0.0206170	−	0.360121i	0.000745410	−	0.0130202i
$766$	−16.4139	+	28.4297i	−0.593058	+	1.02721i
$767$	−15.8838	+	27.5116i	−0.573531	+	0.993386i
$768$	0.987813	+	1.71094i	0.0356446	+	0.0617383i
$769$	−20.9501			−0.755479			−0.377740	−	0.925912i	$-0.623299\pi$
$769$	−20.9501			−0.755479			−0.377740	+	0.925912i	$0.623299\pi$
$770$	−13.4358	−	14.2996i	−0.484192	−	0.515323i
$771$	−58.8015			−2.11768
$772$	10.6511	+	18.4483i	0.383342	+	0.663967i
$773$	−18.0107	+	31.1955i	−0.647800	+	1.12202i	0.335847	+	0.941917i	$0.390978\pi$
$773$	−18.0107	+	31.1955i	−0.647800	+	1.12202i	−0.983647	+	0.180107i	$0.942356\pi$
$774$	0.820769	−	1.42161i	0.0295019	−	0.0510988i
$775$	29.4910	+	21.8646i	1.05935	+	0.785401i
$776$	2.52195			0.0905328
$777$	−9.06182	+	6.74750i	−0.325091	+	0.242065i
$778$	23.0762			0.827320
$779$	−11.5981	−	20.0884i	−0.415544	−	0.719743i
$780$	17.2197	−	8.66940i	0.616564	−	0.310414i
$781$	8.04090	−	21.8793i	0.287726	−	0.782902i
$782$	−0.620622	−	1.07495i	−0.0221934	−	0.0384401i
$783$			32.5882i			1.16461i
$784$	6.81103	−	1.61550i	0.243251	−	0.0576963i
$785$	2.43829	−	3.71524i	0.0870262	−	0.132603i
$786$	−4.76216	−	8.24831i	−0.169861	−	0.294207i
$787$	31.6072	+	18.2484i	1.12667	+	0.650486i	0.943096	−	0.332519i	$-0.107899\pi$
$787$	31.6072	+	18.2484i	1.12667	+	0.650486i	0.183578	+	0.983005i	$0.441232\pi$
$788$	−4.82410	+	8.35558i	−0.171851	+	0.297655i
$789$	3.87501	+	6.71171i	0.137954	+	0.238943i
$790$	11.0772	+	7.26988i	0.394108	+	0.258651i
$791$	29.8151	−	22.2005i	1.06010	−	0.789360i
$792$	2.95135	−	0.510901i	0.104872	−	0.0181541i
$793$	58.9691	−	34.0459i	2.09406	−	1.20900i
$794$	3.51225	−	6.08339i	0.124645	−	0.215891i
$795$	−46.6627	+	23.4927i	−1.65496	+	0.833202i
$796$	0.513139	−	0.296261i	0.0181877	−	0.0105007i
$797$	−23.3800			−0.828163			−0.414082	−	0.910240i	$-0.635897\pi$
$797$	−23.3800			−0.828163			−0.414082	+	0.910240i	$0.635897\pi$
$798$	−6.52920	+	15.1400i	−0.231131	+	0.535951i
$799$		−	0.713772i		−	0.0252515i
$800$	2.97785	−	4.01652i	0.105283	−	0.142005i
$801$	4.61097	+	2.66214i	0.162921	+	0.0940623i
$802$	−19.3734	+	33.5556i	−0.684097	+	1.18489i
$803$	13.6923	−	11.4165i	0.483191	−	0.402880i
$804$		−	11.5699i		−	0.408038i
$805$	36.7575	+	18.4108i	1.29553	+	0.648895i
$806$	32.0429			1.12866
$807$	28.8999	−	16.6854i	1.01733	−	0.587353i
$808$	8.06901	−	13.9759i	0.283867	−	0.491672i
$809$	−8.11068	−	4.68270i	−0.285156	−	0.164635i	0.350599	−	0.936526i	$-0.385978\pi$
$809$	−8.11068	−	4.68270i	−0.285156	−	0.164635i	−0.635755	+	0.771891i	$0.719311\pi$
$810$	24.3193	+	1.39228i	0.854492	+	0.0489199i
$811$	−44.3133			−1.55605			−0.778025	−	0.628234i	$-0.783778\pi$
$811$	−44.3133			−1.55605			−0.778025	+	0.628234i	$0.783778\pi$
$812$	2.41800	+	20.6717i	0.0848551	+	0.725434i
$813$	−11.3601			−0.398417
$814$	5.50597	−	4.59082i	0.192984	−	0.160908i
$815$	−23.0840	+	11.6219i	−0.808598	+	0.407096i
$816$	−0.305614	−	0.176446i	−0.0106986	−	0.00617686i
$817$	−2.86679	−	4.96543i	−0.100296	−	0.173718i
$818$	7.00604			0.244961
$819$	9.57500	+	4.12926i	0.334577	+	0.144288i
$820$	−9.02214	+	13.7471i	−0.315067	+	0.480070i
$821$	22.9664	−	13.2597i	0.801533	−	0.462765i	−0.0424740	−	0.999098i	$-0.513524\pi$
$821$	22.9664	−	13.2597i	0.801533	−	0.462765i	0.844007	+	0.536332i	$0.180191\pi$
$822$	18.6723	+	10.7804i	0.651270	+	0.376011i
$823$	−25.5709	−	14.7634i	−0.891346	−	0.514619i	−0.0169633	−	0.999856i	$-0.505400\pi$
$823$	−25.5709	−	14.7634i	−0.891346	−	0.514619i	−0.874382	+	0.485237i	$0.838733\pi$
$824$	−2.64162	−	4.57542i	−0.0920253	−	0.159392i
$825$	−17.9717	−	27.3929i	−0.625695	−	0.953698i
$826$	−15.4474	+	11.5022i	−0.537483	+	0.400214i
$827$	−37.7138			−1.31144			−0.655719	−	0.755005i	$-0.727634\pi$
$827$	−37.7138			−1.31144			−0.655719	+	0.755005i	$0.727634\pi$
$828$	−5.43482	+	3.13780i	−0.188873	+	0.109046i
$829$	−8.29650	−	4.78999i	−0.288150	−	0.166363i	0.348958	−	0.937139i	$-0.386536\pi$
$829$	−8.29650	−	4.78999i	−0.288150	−	0.166363i	−0.637107	+	0.770775i	$0.719869\pi$
$830$	4.66422	−	2.34824i	0.161897	−	0.0815087i
$831$	7.28650	+	12.6206i	0.252766	+	0.437803i
$832$		−	4.36408i		−	0.151297i
$833$	−0.909332	+	0.858210i	−0.0315065	+	0.0297352i
$834$	4.10298			0.142074
$835$	−0.0353157	+	0.616866i	−0.00122215	+	0.0213475i
$836$	3.60885	−	9.81968i	0.124815	−	0.339621i
$837$	26.3422	+	15.2087i	0.910521	+	0.525690i
$838$	17.2607	−	9.96549i	0.596262	−	0.344252i
$839$		−	52.9963i		−	1.82964i	−0.403866	−	0.914818i	$-0.632334\pi$
$839$		−	52.9963i		−	1.82964i	0.403866	−	0.914818i	$-0.367666\pi$
$840$	11.6675	−	0.692159i	0.402565	−	0.0238817i
$841$	−32.8808			−1.13382
$842$	−3.80891	−	6.59723i	−0.131264	−	0.227356i
$843$	−51.3967	−	29.6739i	−1.77020	−	1.02202i
$844$	4.88299	+	2.81919i	0.168079	+	0.0970406i
$845$	−13.4953	−	0.772612i	−0.464253	−	0.0265786i
$846$	−3.60876			−0.124072
$847$	−1.87117	+	29.0430i	−0.0642942	+	0.997931i
$848$			11.8260i			0.406106i
$849$	26.1574	−	15.1020i	0.897720	−	0.518299i
$850$	−0.101928	+	0.887281i	−0.00349611	+	0.0304335i
$851$	−7.50996	+	13.0076i	−0.257438	+	0.445896i
$852$	6.94260	+	12.0249i	0.237849	+	0.411967i
$853$			7.11598i			0.243647i	0.992552	+	0.121823i	$0.0388741\pi$
$853$			7.11598i			0.243647i	−0.992552	+	0.121823i	$0.961126\pi$
$854$	41.0015	−	4.79600i	1.40304	−	0.164116i
$855$	−3.49504	+	5.32543i	−0.119528	+	0.182126i
$856$	−9.35777	−	16.2081i	−0.319842	−	0.553983i
$857$	26.4437	+	15.2673i	0.903300	+	0.521520i	0.878269	−	0.478166i	$-0.158698\pi$
$857$	26.4437	+	15.2673i	0.903300	+	0.521520i	0.0250306	+	0.999687i	$0.492032\pi$
$858$	−26.8400	−	9.86404i	−0.916304	−	0.336753i
$859$	7.10294	−	4.10089i	0.242349	−	0.139920i	−0.373907	−	0.927466i	$-0.621982\pi$
$859$	7.10294	−	4.10089i	0.242349	−	0.139920i	0.616256	+	0.787546i	$0.288649\pi$
$860$	−2.23008	+	3.39799i	−0.0760451	+	0.115871i
$861$	−38.1775	+	4.46567i	−1.30108	+	0.152190i
$862$			0.638803i			0.0217577i
$863$	9.69382	−	5.59673i	0.329982	−	0.190515i	−0.325851	−	0.945421i	$-0.605651\pi$
$863$	9.69382	−	5.59673i	0.329982	−	0.190515i	0.655833	+	0.754906i	$0.272318\pi$
$864$	2.07135	−	3.58768i	0.0704686	−	0.122055i
$865$	−45.5511	+	22.9331i	−1.54878	+	0.779749i
$866$	−7.24511	−	12.5489i	−0.246199	−	0.426429i
$867$	−33.5226			−1.13849
$868$	17.8382	+	7.69279i	0.605466	+	0.261110i
$869$	−3.35214	−	19.3645i	−0.113714	−	0.656896i
$870$	−1.98625	+	34.6942i	−0.0673403	+	1.17624i
$871$	−12.7787	+	22.1333i	−0.432989	+	0.749959i
$872$	2.01734	+	1.16471i	0.0683158	+	0.0394422i
$873$	1.13879	+	1.97244i	0.0385421	+	0.0667569i
$874$			21.9195i			0.741437i
$875$	−13.3564	−	26.3933i	−0.451528	−	0.892257i
$876$			10.6193i			0.358793i
$877$	−23.0068	−	39.8489i	−0.776884	−	1.34560i	−0.933730	−	0.357979i	$-0.883466\pi$
$877$	−23.0068	−	39.8489i	−0.776884	−	1.34560i	0.156846	−	0.987623i	$-0.449867\pi$
$878$	−4.74897	+	8.22545i	−0.160270	+	0.277596i
$879$	51.2423	+	29.5847i	1.72836	+	0.997869i
$880$	−7.36787	+	0.845246i	−0.248371	+	0.0284932i
$881$			29.4873i			0.993454i	0.867907	+	0.496727i	$0.165465\pi$
$881$			29.4873i			0.993454i	−0.867907	+	0.496727i	$0.834535\pi$
$882$	4.33901	+	4.59748i	0.146102	+	0.154805i
$883$			28.8414i			0.970590i	0.874351	+	0.485295i	$0.161288\pi$
$883$			28.8414i			0.970590i	−0.874351	+	0.485295i	$0.838712\pi$
$884$	0.389763	+	0.675089i	0.0131091	+	0.0227057i
$885$	−28.7227	+	14.4607i	−0.965503	+	0.486091i
$886$	1.45039	+	0.837383i	0.0487268	+	0.0281324i
$887$	−22.2902	+	12.8693i	−0.748432	+	0.432107i	−0.825127	−	0.564947i	$-0.808897\pi$
$887$	−22.2902	+	12.8693i	−0.748432	+	0.432107i	0.0766951	+	0.997055i	$0.475563\pi$
$888$			4.27025i			0.143300i
$889$	15.5347	+	20.8629i	0.521017	+	0.699720i
$890$	−11.0213	−	7.23321i	−0.369435	−	0.242458i
$891$	−23.1376	−	27.7499i	−0.775138	−	0.929656i
$892$	−9.69072	+	16.7848i	−0.324469	+	0.561997i
$893$	−6.30236	+	10.9160i	−0.210900	+	0.365290i
$894$	−3.71261	+	2.14348i	−0.124168	+	0.0716886i
$895$	−21.4590	+	32.6972i	−0.717294	+	1.09295i
$896$	1.04772	−	2.42946i	0.0350018	−	0.0811627i
$897$	59.9123			2.00041
$898$	−16.1944	−	28.0495i	−0.540414	−	0.936024i
$899$	−28.8794	+	50.0205i	−0.963180	+	1.66828i
$900$	4.48600	+	0.515338i	0.149533	+	0.0171779i
$901$	−1.05620	−	1.82939i	−0.0351870	−	0.0609458i
$902$	24.0319	−	4.16011i	0.800176	−	0.138517i
$903$	−9.43665	+	1.10382i	−0.314032	+	0.0367328i
$904$		−	14.0499i		−	0.467294i
$905$	1.07799	−	18.8294i	0.0358336	−	0.625911i
$906$	−22.2808	−	12.8638i	−0.740229	−	0.427371i
$907$	−11.3660	−	6.56215i	−0.377401	−	0.217893i	0.299286	−	0.954164i	$-0.403252\pi$
$907$	−11.3660	−	6.56215i	−0.377401	−	0.217893i	−0.676687	+	0.736271i	$0.736585\pi$
$908$	13.0070	−	7.50957i	0.431651	−	0.249214i
$909$	14.5742			0.483397
$910$	−23.0845	−	11.5624i	−0.765243	−	0.383288i
$911$	−14.9639			−0.495777			−0.247888	−	0.968789i	$-0.579737\pi$
$911$	−14.9639			−0.495777			−0.247888	+	0.968789i	$0.579737\pi$
$912$	3.11592	+	5.39693i	0.103178	+	0.178710i
$913$	−7.27005	−	2.67183i	−0.240603	−	0.0884247i
$914$	−1.19633	+	2.07211i	−0.0395711	+	0.0685392i
$915$	68.8147	+	3.93966i	2.27494	+	0.130241i
$916$		−	12.6419i		−	0.417699i
$917$	−5.05095	+	11.7122i	−0.166797	+	0.386772i
$918$			0.739981i			0.0244230i
$919$	−42.3187	+	24.4327i	−1.39596	+	0.805961i	−0.993967	−	0.109680i	$-0.965017\pi$
$919$	−42.3187	+	24.4327i	−1.39596	+	0.805961i	−0.401998	+	0.915641i	$0.631684\pi$
$920$	13.8786	−	6.98732i	0.457565	−	0.230365i
$921$	−6.72430	−	3.88228i	−0.221573	−	0.127925i
$922$	−19.4497	−	33.6878i	−0.640541	−	1.10945i
$923$		−	30.6718i		−	1.00958i
$924$	−12.5736	−	11.9350i	−0.413641	−	0.392631i
$925$	9.91498	−	4.30020i	0.326002	−	0.141390i
$926$	13.8053	−	7.97048i	0.453670	−	0.261926i
$927$	2.38565	−	4.13206i	0.0783550	−	0.135715i
$928$	6.81253	+	3.93322i	0.223632	+	0.129114i
$929$	34.4469	−	19.8879i	1.13017	−	0.652502i	0.186190	−	0.982514i	$-0.440386\pi$
$929$	34.4469	−	19.8879i	1.13017	−	0.652502i	0.943977	+	0.330011i	$0.107053\pi$
$930$	27.1176	+	17.7971i	0.889223	+	0.583591i
$931$	21.4845	−	5.09586i	0.704124	−	0.167010i
$932$	−18.4675			−0.604922
$933$	24.8972	−	14.3744i	0.815097	−	0.470596i
$934$	−2.48834	+	4.30994i	−0.0814211	+	0.141025i
$935$	1.06426	−	0.788790i	0.0348051	−	0.0257962i
$936$	3.41318	−	1.97060i	0.111563	−	0.0644111i
$937$		−	30.1564i		−	0.985166i	−0.870266	−	0.492583i	$-0.836053\pi$
$937$		−	30.1564i		−	0.985166i	0.870266	−	0.492583i	$-0.163947\pi$
$938$	−12.4275	+	9.25365i	−0.405774	+	0.302142i
$939$	4.77547			0.155841
$940$	8.92064	+	0.510709i	0.290959	+	0.0166575i
$941$	2.43328	−	4.21457i	0.0793228	−	0.137391i	−0.823635	−	0.567120i	$-0.808058\pi$
$941$	2.43328	−	4.21457i	0.0793228	−	0.137391i	0.902958	+	0.429729i	$0.141391\pi$
$942$	1.96315	−	3.40028i	0.0639630	−	0.110787i
$943$	−44.2541	+	25.5501i	−1.44111	+	0.832026i
$944$			7.27935i			0.236923i
$945$	−13.4897	−	20.4620i	−0.438819	−	0.665630i
$946$	5.94018	−	1.02829i	0.193132	−	0.0334326i
$947$	−39.7368	+	22.9421i	−1.29127	+	0.745517i	−0.978880	−	0.204435i	$-0.934464\pi$
$947$	−39.7368	+	22.9421i	−1.29127	+	0.745517i	−0.312394	+	0.949953i	$0.601131\pi$
$948$	10.1381	+	5.85324i	0.329271	+	0.190104i
$949$	11.7288	−	20.3149i	0.380733	−	0.659449i
$950$	9.39321	−	12.6695i	0.304756	−	0.411054i
$951$			3.50486i			0.113653i
$952$	0.0549055	+	0.469393i	0.00177950	+	0.0152131i
$953$	3.57061			0.115663			0.0578316	−	0.998326i	$-0.481581\pi$
$953$	3.57061			0.115663			0.0578316	+	0.998326i	$0.481581\pi$
$954$	−9.24919	+	5.34002i	−0.299453	+	0.172890i
$955$	−6.41345	−	12.7388i	−0.207534	−	0.412217i
$956$	18.0599	+	10.4269i	0.584098	+	0.337229i
$957$	39.5884	−	33.0084i	1.27971	−	1.06701i
$958$	8.59001			0.277531
$959$	−3.35459	−	28.6787i	−0.108325	−	0.926084i
$960$	2.42388	−	3.69328i	0.0782303	−	0.119200i
$961$	11.4556	+	19.8417i	0.369536	+	0.640055i
$962$	4.71641	−	8.16906i	0.152063	−	0.263381i
$963$	8.45100	−	14.6376i	0.272330	−	0.471689i
$964$	5.40162	+	9.35589i	0.173975	+	0.301333i
$965$	26.1355	−	39.8228i	0.841330	−	1.28194i
$966$	33.3529	+	14.3836i	1.07311	+	0.462785i
$967$	−49.2916			−1.58511			−0.792556	−	0.609799i	$-0.791250\pi$
$967$	−49.2916			−1.58511			−0.792556	+	0.609799i	$0.791250\pi$
$968$	8.38215	+	7.12317i	0.269412	+	0.228947i
$969$	−0.964017	−	0.556576i	−0.0309687	−	0.0178798i
$970$	−2.53588	−	5.03691i	−0.0814222	−	0.161726i
$971$	19.2797	−	11.1312i	0.618716	−	0.357216i	−0.157653	−	0.987495i	$-0.550393\pi$
$971$	19.2797	−	11.1312i	0.618716	−	0.357216i	0.776369	+	0.630279i	$0.217059\pi$
$972$	9.09383			0.291685
$973$	−3.28158	−	4.40713i	−0.105203	−	0.141286i
$974$		−	11.9403i		−	0.382592i
$975$	−34.6296	−	25.6744i	−1.10903	−	0.822238i
$976$	7.80138	−	13.5124i	0.249716	−	0.432521i
$977$	−3.69332	−	2.13234i	−0.118160	−	0.0682195i	0.439755	−	0.898118i	$-0.355065\pi$
$977$	−3.69332	−	2.13234i	−0.118160	−	0.0682195i	−0.557915	+	0.829898i	$0.688398\pi$
$978$	−19.7751	+	11.4172i	−0.632339	+	0.365081i
$979$	3.33524	+	19.2668i	0.106595	+	0.615771i
$980$	−10.0752	−	11.9788i	−0.321839	−	0.382648i
$981$			2.10371i			0.0671661i
$982$	15.5610	−	8.98414i	0.496571	−	0.286695i
$983$	3.31912	−	5.74888i	0.105863	−	0.183361i	−0.808227	−	0.588871i	$-0.799573\pi$
$983$	3.31912	−	5.74888i	0.105863	−	0.183361i	0.914091	+	0.405510i	$0.132906\pi$
$984$	−7.26405	+	12.5817i	−0.231570	+	0.401090i
$985$	21.5387	+	1.23310i	0.686281	+	0.0392898i
$986$	−1.40513			−0.0447484
$987$	12.4743	+	16.7528i	0.397061	+	0.533249i
$988$		−	13.7659i		−	0.437951i
$989$	−10.9387	+	6.31544i	−0.347829	+	0.200819i
$990$	−3.98804	−	5.38080i	−0.126748	−	0.171013i
$991$	−11.3164	+	19.6005i	−0.359476	+	0.622631i	−0.987873	−	0.155262i	$-0.950378\pi$
$991$	−11.3164	+	19.6005i	−0.359476	+	0.622631i	0.628397	+	0.777893i	$0.283711\pi$
$992$	6.35873	−	3.67121i	0.201890	−	0.116561i
$993$	−32.6163			−1.03505
$994$	7.36362	−	17.0749i	0.233560	−	0.541582i
$995$	−1.10767	−	0.726958i	−0.0351156	−	0.0230461i
$996$	3.99564	−	2.30689i	0.126607	−	0.0730965i
$997$	22.6982	+	13.1048i	0.718858	+	0.415033i	0.814332	−	0.580399i	$-0.197103\pi$
$997$	22.6982	+	13.1048i	0.718858	+	0.415033i	−0.0954742	+	0.995432i	$0.530437\pi$
$998$	16.1760	−	28.0177i	0.512043	−	0.886885i
$999$	7.75465	−	4.47715i	0.245346	−	0.141651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.b.549.20	yes	48
5.4	even	2		770.2.o.a.549.5	yes	48
7.5	odd	6	inner	770.2.o.b.439.5	yes	48
11.10	odd	2		770.2.o.a.549.20	yes	48
35.19	odd	6		770.2.o.a.439.20	yes	48
55.54	odd	2	inner	770.2.o.b.549.5	yes	48
77.54	even	6		770.2.o.a.439.5	✓	48
385.54	even	6	inner	770.2.o.b.439.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.5	✓	48	77.54	even	6
770.2.o.a.439.20	yes	48	35.19	odd	6
770.2.o.a.549.5	yes	48	5.4	even	2
770.2.o.a.549.20	yes	48	11.10	odd	2
770.2.o.b.439.5	yes	48	7.5	odd	6	inner
770.2.o.b.439.20	yes	48	385.54	even	6	inner
770.2.o.b.549.5	yes	48	55.54	odd	2	inner
770.2.o.b.549.20	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.987813 - 1.71094i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.23241 + 0.127806i) q^{5} +1.97563 q^{6} +(-1.58012 - 2.12208i) q^{7} -1.00000 q^{8} +(-0.451550 - 0.782108i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.987813 - 1.71094i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.23241 + 0.127806i) q^{5} +1.97563 q^{6} +(-1.58012 - 2.12208i) q^{7} -1.00000 q^{8} +(-0.451550 - 0.782108i) q^{9} +(1.00552 + 1.99723i) q^{10} +(1.14408 - 3.11305i) q^{11} +(0.987813 + 1.71094i) q^{12} -4.36408i q^{13} +(1.04772 - 2.42946i) q^{14} +(2.42388 - 3.69328i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.154692 + 0.0893117i) q^{17} +(0.451550 - 0.782108i) q^{18} +(-1.57718 - 2.73176i) q^{19} +(-1.22689 + 1.86942i) q^{20} +(-5.19162 + 0.607271i) q^{21} +(3.26802 - 0.565719i) q^{22} +(-6.01796 + 3.47447i) q^{23} +(-0.987813 + 1.71094i) q^{24} +(4.96733 + 0.570633i) q^{25} +(3.77940 - 2.18204i) q^{26} +4.14269 q^{27} +(2.62783 - 0.307382i) q^{28} +7.86643i q^{29} +(4.41041 + 0.252497i) q^{30} +(6.35873 + 3.67121i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.19611 - 5.03257i) q^{33} +0.178623i q^{34} +(-3.25626 - 4.93931i) q^{35} +0.903100 q^{36} +(1.87189 - 1.08073i) q^{37} +(1.57718 - 2.73176i) q^{38} +(-7.46669 - 4.31089i) q^{39} +(-2.23241 - 0.127806i) q^{40} +7.35367 q^{41} +(-3.12172 - 4.19244i) q^{42} +1.81767 q^{43} +(2.12394 + 2.54733i) q^{44} +(-0.908088 - 1.80370i) q^{45} +(-6.01796 - 3.47447i) q^{46} +(-1.99798 - 3.46061i) q^{47} -1.97563 q^{48} +(-2.00646 + 6.70628i) q^{49} +(1.98948 + 4.58715i) q^{50} +(0.305614 - 0.176446i) q^{51} +(3.77940 + 2.18204i) q^{52} +(-10.2416 - 5.91299i) q^{53} +(2.07135 + 3.58768i) q^{54} +(2.95193 - 6.80339i) q^{55} +(1.58012 + 2.12208i) q^{56} -6.23184 q^{57} +(-6.81253 + 3.93322i) q^{58} +(-6.30410 - 3.63967i) q^{59} +(1.98654 + 3.94578i) q^{60} +(7.80138 + 13.5124i) q^{61} +7.34243i q^{62} +(-0.946193 + 2.19405i) q^{63} +1.00000 q^{64} +(0.557757 - 9.74242i) q^{65} +(2.26028 - 6.15022i) q^{66} +(-5.07171 - 2.92815i) q^{67} +(-0.154692 + 0.0893117i) q^{68} +13.7285i q^{69} +(2.64944 - 5.28966i) q^{70} +7.02825 q^{71} +(0.451550 + 0.782108i) q^{72} +(4.65502 + 2.68758i) q^{73} +(1.87189 + 1.08073i) q^{74} +(5.88312 - 7.93514i) q^{75} +3.15436 q^{76} +(-8.41393 + 2.49115i) q^{77} -8.62179i q^{78} +(5.13159 - 2.96273i) q^{79} +(-1.00552 - 1.99723i) q^{80} +(5.44686 - 9.43423i) q^{81} +(3.67683 + 6.36846i) q^{82} -2.33535i q^{83} +(2.06990 - 4.79971i) q^{84} +(0.333922 + 0.219151i) q^{85} +(0.908835 + 1.57415i) q^{86} +(13.4590 + 7.77057i) q^{87} +(-1.14408 + 3.11305i) q^{88} +(-5.10571 + 2.94778i) q^{89} +(1.10800 - 1.68828i) q^{90} +(-9.26093 + 6.89576i) q^{91} -6.94895i q^{92} +(12.5625 - 7.25295i) q^{93} +(1.99798 - 3.46061i) q^{94} +(-3.17178 - 6.29998i) q^{95} +(-0.987813 - 1.71094i) q^{96} -2.52195 q^{97} +(-6.81103 + 1.61550i) q^{98} +(-2.95135 + 0.510901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more