LMFDB - Embedded newform 132.2.j.a.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,2,Mod(7,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("132.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.j (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:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	132.19
Dual form			132.2.j.a.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.960602 + 1.03790i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.154488 + 1.99402i) q^{4} +(0.725620 + 0.527194i) q^{5} +(-1.23432 - 0.690263i) q^{6} +(-0.489790 + 1.50742i) q^{7} +(-2.21801 + 1.75512i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.960602 + 1.03790i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.154488 + 1.99402i) q^{4} +(0.725620 + 0.527194i) q^{5} +(-1.23432 - 0.690263i) q^{6} +(-0.489790 + 1.50742i) q^{7} +(-2.21801 + 1.75512i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.149856 + 1.25955i) q^{10} +(2.62111 - 2.03219i) q^{11} +(-0.469260 - 1.94417i) q^{12} +(-0.605536 - 0.833449i) q^{13} +(-2.03505 + 0.939673i) q^{14} +(-0.853017 - 0.277162i) q^{15} +(-3.95227 - 0.616106i) q^{16} +(2.49130 - 3.42898i) q^{17} +(1.38721 + 0.275054i) q^{18} +(1.32556 + 4.07966i) q^{19} +(-1.16334 + 1.36546i) q^{20} -1.58499i q^{21} +(4.62706 + 0.768337i) q^{22} -8.34003i q^{23} +(1.56709 - 2.35462i) q^{24} +(-1.29649 - 3.99020i) q^{25} +(0.283361 - 1.42910i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-2.93016 - 1.20953i) q^{28} +(0.588090 + 0.191082i) q^{29} +(-0.531742 - 1.15159i) q^{30} +(3.11863 + 4.29243i) q^{31} +(-3.15710 - 4.69391i) q^{32} +(-1.86484 + 2.74269i) q^{33} +(5.95210 - 0.708155i) q^{34} +(-1.15010 + 0.835598i) q^{35} +(1.04707 + 1.70401i) q^{36} +(-0.924210 + 2.84443i) q^{37} +(-2.96096 + 5.29474i) q^{38} +(0.833449 + 0.605536i) q^{39} +(-2.53472 + 0.104230i) q^{40} +(-0.0662322 + 0.0215201i) q^{41} +(1.64507 - 1.52255i) q^{42} -6.67734 q^{43} +(3.64730 + 5.54051i) q^{44} +0.896916 q^{45} +(8.65614 - 8.01144i) q^{46} +(1.49099 - 0.484451i) q^{47} +(3.94922 - 0.635366i) q^{48} +(3.63071 + 2.63786i) q^{49} +(2.89603 - 5.17863i) q^{50} +(-1.30975 + 4.03101i) q^{51} +(1.75547 - 1.07870i) q^{52} +(-9.74373 + 7.07923i) q^{53} +(-1.40431 + 0.167079i) q^{54} +(2.97329 - 0.0927624i) q^{55} +(-1.55934 - 4.20310i) q^{56} +(-2.52137 - 3.47037i) q^{57} +(0.366596 + 0.793935i) q^{58} +(-7.81130 - 2.53804i) q^{59} +(0.684449 - 1.65812i) q^{60} +(-7.51474 + 10.3431i) q^{61} +(-1.45936 + 7.36016i) q^{62} +(0.489790 + 1.50742i) q^{63} +(1.83911 - 7.78574i) q^{64} -0.924002i q^{65} +(-4.63802 + 0.699107i) q^{66} -13.8430i q^{67} +(6.45259 + 5.49745i) q^{68} +(2.57721 + 7.93184i) q^{69} +(-1.97206 - 0.391018i) q^{70} +(3.76717 - 5.18506i) q^{71} +(-0.762772 + 2.72363i) q^{72} +(-4.25213 - 1.38160i) q^{73} +(-3.84004 + 1.77312i) q^{74} +(2.46608 + 3.39427i) q^{75} +(-8.33973 + 2.01294i) q^{76} +(1.77956 + 4.94645i) q^{77} +(0.172124 + 1.44672i) q^{78} +(-6.25795 + 4.54667i) q^{79} +(-2.54304 - 2.53067i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.0859586 - 0.0480703i) q^{82} +(12.5105 + 9.08942i) q^{83} +(3.16051 + 0.244863i) q^{84} +(3.61547 - 1.17474i) q^{85} +(-6.41427 - 6.93044i) q^{86} -0.618355 q^{87} +(-2.24691 + 9.10777i) q^{88} +3.00882 q^{89} +(0.861579 + 0.930912i) q^{90} +(1.55294 - 0.504581i) q^{91} +(16.6302 + 1.28844i) q^{92} +(-4.29243 - 3.11863i) q^{93} +(1.93506 + 1.08214i) q^{94} +(-1.18892 + 3.65911i) q^{95} +(4.45307 + 3.48857i) q^{96} +(11.6217 - 8.44368i) q^{97} +(0.749816 + 6.30226i) q^{98} +(0.926033 - 3.18472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) $ 48 * q - 4 * q^4 + 12 * q^9	$ 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.960602	+	1.03790i	0.679248	+	0.733909i
$2$	0.960602	+	1.03790i	0.679248	+	0.733909i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	−0.154488	+	1.99402i	−0.0772441	+	0.997012i
$5$	0.725620	+	0.527194i	0.324507	+	0.235768i	0.738096	−	0.674695i	$-0.235725\pi$
$5$	0.725620	+	0.527194i	0.324507	+	0.235768i	−0.413589	+	0.910464i	$0.635725\pi$
$6$	−1.23432	−	0.690263i	−0.503908	−	0.281799i
$7$	−0.489790	+	1.50742i	−0.185123	+	0.569750i	−0.999950	−	0.00995348i	$-0.996832\pi$
$7$	−0.489790	+	1.50742i	−0.185123	+	0.569750i	0.814827	+	0.579704i	$0.196832\pi$
$8$	−2.21801	+	1.75512i	−0.784184	+	0.620529i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	0.149856	+	1.25955i	0.0473885	+	0.398304i
$11$	2.62111	−	2.03219i	0.790294	−	0.612727i
$11$	2.62111	−	2.03219i	0.790294	−	0.612727i
$12$	−0.469260	−	1.94417i	−0.135464	−	0.561233i
$13$	−0.605536	−	0.833449i	−0.167945	−	0.231157i	0.716746	−	0.697335i	$-0.245631\pi$
$13$	−0.605536	−	0.833449i	−0.167945	−	0.231157i	−0.884691	+	0.466177i	$0.845631\pi$
$14$	−2.03505	+	0.939673i	−0.543889	+	0.251138i
$15$	−0.853017	−	0.277162i	−0.220248	−	0.0715630i
$16$	−3.95227	−	0.616106i	−0.988067	−	0.154027i
$17$	2.49130	−	3.42898i	0.604229	−	0.831650i	−0.391858	−	0.920026i	$-0.628168\pi$
$17$	2.49130	−	3.42898i	0.604229	−	0.831650i	0.996087	+	0.0883758i	$0.0281676\pi$
$18$	1.38721	+	0.275054i	0.326968	+	0.0648309i
$19$	1.32556	+	4.07966i	0.304105	+	0.935938i	0.980010	+	0.198950i	$0.0637530\pi$
$19$	1.32556	+	4.07966i	0.304105	+	0.935938i	−0.675905	+	0.736989i	$0.736247\pi$
$20$	−1.16334	+	1.36546i	−0.260130	+	0.305326i
$21$		−	1.58499i		−	0.345874i
$22$	4.62706	+	0.768337i	0.986492	+	0.163810i
$23$		−	8.34003i		−	1.73902i	−0.493919	−	0.869508i	$-0.664436\pi$
$23$		−	8.34003i		−	1.73902i	0.493919	−	0.869508i	$-0.335564\pi$
$24$	1.56709	−	2.35462i	0.319881	−	0.480635i
$25$	−1.29649	−	3.99020i	−0.259299	−	0.798040i
$26$	0.283361	−	1.42910i	0.0555716	−	0.280270i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−2.93016	−	1.20953i	−0.553748	−	0.228580i
$29$	0.588090	+	0.191082i	0.109206	+	0.0354831i	0.363110	−	0.931746i	$-0.381715\pi$
$29$	0.588090	+	0.191082i	0.109206	+	0.0354831i	−0.253904	+	0.967229i	$0.581715\pi$
$30$	−0.531742	−	1.15159i	−0.0970825	−	0.210251i
$31$	3.11863	+	4.29243i	0.560123	+	0.770943i	0.991342	−	0.131304i	$-0.0419164\pi$
$31$	3.11863	+	4.29243i	0.560123	+	0.770943i	−0.431219	+	0.902247i	$0.641916\pi$
$32$	−3.15710	−	4.69391i	−0.558101	−	0.829773i
$33$	−1.86484	+	2.74269i	−0.324628	+	0.477441i
$34$	5.95210	−	0.708155i	1.02078	−	0.121448i
$35$	−1.15010	+	0.835598i	−0.194403	+	0.141242i
$36$	1.04707	+	1.70401i	0.174512	+	0.284001i
$37$	−0.924210	+	2.84443i	−0.151939	+	0.467621i	−0.997838	−	0.0657227i	$-0.979065\pi$
$37$	−0.924210	+	2.84443i	−0.151939	+	0.467621i	0.845899	+	0.533344i	$0.179065\pi$
$38$	−2.96096	+	5.29474i	−0.480331	+	0.858920i
$39$	0.833449	+	0.605536i	0.133459	+	0.0969634i
$40$	−2.53472	+	0.104230i	−0.400774	+	0.0164803i
$41$	−0.0662322	+	0.0215201i	−0.0103437	+	0.00336088i	−0.314184	−	0.949362i	$-0.601731\pi$
$41$	−0.0662322	+	0.0215201i	−0.0103437	+	0.00336088i	0.303841	+	0.952723i	$0.401731\pi$
$42$	1.64507	−	1.52255i	0.253840	−	0.234934i
$43$	−6.67734			−1.01829			−0.509143	−	0.860682i	$-0.670037\pi$
$43$	−6.67734			−1.01829			−0.509143	+	0.860682i	$0.670037\pi$
$44$	3.64730	+	5.54051i	0.549851	+	0.835263i
$45$	0.896916			0.133704
$46$	8.65614	−	8.01144i	1.27628	−	1.18122i
$47$	1.49099	−	0.484451i	0.217483	−	0.0706644i	−0.198249	−	0.980152i	$-0.563525\pi$
$47$	1.49099	−	0.484451i	0.217483	−	0.0706644i	0.415732	+	0.909487i	$0.363525\pi$
$48$	3.94922	−	0.635366i	0.570020	−	0.0917071i
$49$	3.63071	+	2.63786i	0.518672	+	0.376838i
$50$	2.89603	−	5.17863i	0.409560	−	0.732369i
$51$	−1.30975	+	4.03101i	−0.183402	+	0.564454i
$52$	1.75547	−	1.07870i	0.243439	−	0.149588i
$53$	−9.74373	+	7.07923i	−1.33840	+	0.972407i	−0.338903	+	0.940821i	$0.610056\pi$
$53$	−9.74373	+	7.07923i	−1.33840	+	0.972407i	−0.999501	+	0.0315858i	$0.989944\pi$
$54$	−1.40431	+	0.167079i	−0.191102	+	0.0227365i
$55$	2.97329	−	0.0927624i	0.400918	−	0.0125081i
$56$	−1.55934	−	4.20310i	−0.208376	−	0.561663i
$57$	−2.52137	−	3.47037i	−0.333964	−	0.459661i
$58$	0.366596	+	0.793935i	0.0481364	+	0.104249i
$59$	−7.81130	−	2.53804i	−1.01694	−	0.330425i	−0.247328	−	0.968932i	$-0.579553\pi$
$59$	−7.81130	−	2.53804i	−1.01694	−	0.330425i	−0.769616	+	0.638507i	$0.779553\pi$
$60$	0.684449	−	1.65812i	0.0883620	−	0.214062i
$61$	−7.51474	+	10.3431i	−0.962163	+	1.32430i	−0.0162558	+	0.999868i	$0.505175\pi$
$61$	−7.51474	+	10.3431i	−0.962163	+	1.32430i	−0.945908	+	0.324436i	$0.894825\pi$
$62$	−1.45936	+	7.36016i	−0.185340	+	0.934741i
$63$	0.489790	+	1.50742i	0.0617077	+	0.189917i
$64$	1.83911	−	7.78574i	0.229889	−	0.973217i
$65$		−	0.924002i		−	0.114608i
$66$	−4.63802	+	0.699107i	−0.570901	+	0.0860541i
$67$		−	13.8430i		−	1.69120i	−0.533820	−	0.845598i	$-0.679244\pi$
$67$		−	13.8430i		−	1.69120i	0.533820	−	0.845598i	$-0.320756\pi$
$68$	6.45259	+	5.49745i	0.782492	+	0.666664i
$69$	2.57721	+	7.93184i	0.310260	+	0.954881i
$70$	−1.97206	−	0.391018i	−0.235706	−	0.0467356i
$71$	3.76717	−	5.18506i	0.447081	−	0.615354i	−0.524687	−	0.851296i	$-0.675817\pi$
$71$	3.76717	−	5.18506i	0.447081	−	0.615354i	0.971767	+	0.235942i	$0.0758175\pi$
$72$	−0.762772	+	2.72363i	−0.0898935	+	0.320983i
$73$	−4.25213	−	1.38160i	−0.497674	−	0.161704i	0.0494151	−	0.998778i	$-0.484264\pi$
$73$	−4.25213	−	1.38160i	−0.497674	−	0.161704i	−0.547090	+	0.837074i	$0.684264\pi$
$74$	−3.84004	+	1.77312i	−0.446396	+	0.206121i
$75$	2.46608	+	3.39427i	0.284758	+	0.391936i
$76$	−8.33973	+	2.01294i	−0.956632	+	0.230901i
$77$	1.77956	+	4.94645i	0.202800	+	0.563700i
$78$	0.172124	+	1.44672i	0.0194893	+	0.163809i
$79$	−6.25795	+	4.54667i	−0.704075	+	0.511540i	−0.881257	−	0.472638i	$-0.843302\pi$
$79$	−6.25795	+	4.54667i	−0.704075	+	0.511540i	0.177182	+	0.984178i	$0.443302\pi$
$80$	−2.54304	−	2.53067i	−0.284320	−	0.282937i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.0859586	−	0.0480703i	−0.00949254	−	0.00530848i
$83$	12.5105	+	9.08942i	1.37321	+	0.997694i	0.997479	+	0.0709643i	$0.0226076\pi$
$83$	12.5105	+	9.08942i	1.37321	+	0.997694i	0.375729	+	0.926730i	$0.377392\pi$
$84$	3.16051	+	0.244863i	0.344840	+	0.0267167i
$85$	3.61547	−	1.17474i	0.392153	−	0.127418i
$86$	−6.41427	−	6.93044i	−0.691668	−	0.747329i
$87$	−0.618355			−0.0662946
$88$	−2.24691	+	9.10777i	−0.239521	+	0.970891i
$89$	3.00882			0.318935			0.159467	−	0.987203i	$-0.449022\pi$
$89$	3.00882			0.318935			0.159467	+	0.987203i	$0.449022\pi$
$90$	0.861579	+	0.930912i	0.0908184	+	0.0981267i
$91$	1.55294	−	0.504581i	0.162792	−	0.0528944i
$92$	16.6302	+	1.28844i	1.73382	+	0.134329i
$93$	−4.29243	−	3.11863i	−0.445104	−	0.323387i
$94$	1.93506	+	1.08214i	0.199586	+	0.111614i
$95$	−1.18892	+	3.65911i	−0.121980	+	0.375417i
$96$	4.45307	+	3.48857i	0.454490	+	0.356051i
$97$	11.6217	−	8.44368i	1.18001	−	0.857326i	0.187836	−	0.982200i	$-0.439853\pi$
$97$	11.6217	−	8.44368i	1.18001	−	0.857326i	0.992173	+	0.124874i	$0.0398528\pi$
$98$	0.749816	+	6.30226i	0.0757428	+	0.636624i
$99$	0.926033	−	3.18472i	0.0930698	−	0.320077i
$100$	8.15685	−	1.96880i	0.815685	−	0.196880i
$101$	4.90138	+	6.74617i	0.487706	+	0.671269i	0.979963	−	0.199180i	$-0.0638280\pi$
$101$	4.90138	+	6.74617i	0.487706	+	0.671269i	−0.492257	+	0.870450i	$0.663828\pi$
$102$	−5.44195	+	2.51280i	−0.538833	+	0.248804i
$103$	−14.9233	−	4.84888i	−1.47044	−	0.477775i	−0.539198	−	0.842179i	$-0.681273\pi$
$103$	−14.9233	−	4.84888i	−1.47044	−	0.477775i	−0.931241	+	0.364404i	$0.881273\pi$
$104$	2.80589	+	0.785807i	0.275140	+	0.0770547i
$105$	0.835598	−	1.15010i	0.0815460	−	0.112238i
$106$	−16.7074	−	3.31273i	−1.62277	−	0.321760i
$107$	2.22580	+	6.85031i	0.215176	+	0.662244i	0.999141	+	0.0414391i	$0.0131942\pi$
$107$	2.22580	+	6.85031i	0.215176	+	0.662244i	−0.783965	+	0.620805i	$0.786806\pi$
$108$	−1.52239	−	1.29704i	−0.146492	−	0.124808i
$109$		−	1.57116i		−	0.150490i	−0.997165	−	0.0752449i	$-0.976026\pi$
$109$		−	1.57116i		−	0.150490i	0.997165	−	0.0752449i	$-0.0239738\pi$
$110$	2.95242	+	2.99688i	0.281502	+	0.285741i
$111$		−	2.99081i		−	0.283875i
$112$	2.86451	−	5.65595i	0.270671	−	0.534437i
$113$	−3.51144	−	10.8071i	−0.330328	−	1.01665i	−0.968978	−	0.247148i	$-0.920506\pi$
$113$	−3.51144	−	10.8071i	−0.330328	−	1.01665i	0.638649	−	0.769498i	$-0.279494\pi$
$114$	1.17987	−	5.95058i	0.110505	−	0.557323i
$115$	4.39681	−	6.05169i	0.410005	−	0.564323i
$116$	−0.471875	+	1.14315i	−0.0438125	+	0.106139i
$117$	−0.979778	−	0.318349i	−0.0905805	−	0.0294314i
$118$	−4.86930	−	10.5454i	−0.448256	−	0.970785i
$119$	3.94869	+	5.43491i	0.361976	+	0.498217i
$120$	2.37845	−	0.882400i	0.217122	−	0.0805517i
$121$	2.74043	−	10.6532i	0.249130	−	0.968470i
$122$	−17.9539	+	2.13607i	−1.62547	+	0.193391i
$123$	0.0563405	−	0.0409337i	0.00508005	−	0.00369087i
$124$	−9.04101	+	5.55550i	−0.811906	+	0.498899i
$125$	2.54866	−	7.84396i	0.227959	−	0.701585i
$126$	−1.09406	+	1.95638i	−0.0974667	+	0.174288i
$127$	7.90865	+	5.74597i	0.701780	+	0.509873i	0.880511	−	0.474025i	$-0.157199\pi$
$127$	7.90865	+	5.74597i	0.701780	+	0.509873i	−0.178732	+	0.983898i	$0.557199\pi$
$128$	9.84750	−	5.57017i	0.870404	−	0.492338i
$129$	6.35053	−	2.06341i	0.559133	−	0.181673i
$130$	0.959025	−	0.887598i	0.0841121	−	0.0778475i
$131$	−10.1612			−0.887790			−0.443895	−	0.896079i	$-0.646404\pi$
$131$	−10.1612			−0.887790			−0.443895	+	0.896079i	$0.646404\pi$
$132$	−5.18090	−	4.14226i	−0.450939	−	0.360537i
$133$	−6.79900			−0.589548
$134$	14.3677	−	13.2976i	1.24118	−	1.14874i
$135$	−0.853017	+	0.277162i	−0.0734161	+	0.0238543i
$136$	0.492550	+	11.9780i	0.0422358	+	1.02711i
$137$	−8.09097	−	5.87844i	−0.691258	−	0.502229i	0.185815	−	0.982585i	$-0.440507\pi$
$137$	−8.09097	−	5.87844i	−0.691258	−	0.502229i	−0.877074	+	0.480356i	$0.840507\pi$
$138$	−5.75681	+	10.2942i	−0.490052	+	0.876303i
$139$	4.63670	−	14.2703i	0.393280	−	1.21039i	−0.537013	−	0.843574i	$-0.680447\pi$
$139$	4.63670	−	14.2703i	0.393280	−	1.21039i	0.930293	−	0.366817i	$-0.119553\pi$
$140$	−1.48853	−	2.42242i	−0.125803	−	0.204732i
$141$	−1.26831	+	0.921481i	−0.106811	+	0.0776027i
$142$	9.00034	−	1.07082i	0.755292	−	0.0898614i
$143$	−3.28090	−	0.953999i	−0.274363	−	0.0797774i
$144$	−3.55959	+	1.82464i	−0.296632	+	0.152054i
$145$	0.325993	+	0.448691i	0.0270722	+	0.0372617i
$146$	−2.65064	−	5.74047i	−0.219368	−	0.475085i
$147$	−4.26815	−	1.38681i	−0.352031	−	0.114382i
$148$	−5.52908	−	2.28233i	−0.454487	−	0.187606i
$149$	10.1802	−	14.0119i	0.833996	−	1.14790i	−0.153170	−	0.988200i	$-0.548948\pi$
$149$	10.1802	−	14.0119i	0.833996	−	1.14790i	0.987166	−	0.159697i	$-0.0510517\pi$
$150$	−1.15400	+	5.82009i	−0.0942238	+	0.475208i
$151$	2.57768	+	7.93327i	0.209768	+	0.645600i	0.999484	+	0.0321272i	$0.0102282\pi$
$151$	2.57768	+	7.93327i	0.209768	+	0.645600i	−0.789715	+	0.613473i	$0.789772\pi$
$152$	−10.1004	−	6.72220i	−0.819251	−	0.545242i
$153$		−	4.23845i		−	0.342659i
$154$	−3.42449	+	6.59858i	−0.275953	+	0.531729i
$155$			4.75880i			0.382236i
$156$	−1.33621	+	1.56837i	−0.106983	+	0.125570i
$157$	0.00331991	+	0.0102176i	0.000264958	+	0.000815457i	0.951189	−	0.308609i	$-0.0998635\pi$
$157$	0.00331991	+	0.0102176i	0.000264958	+	0.000815457i	−0.950924	+	0.309425i	$0.899864\pi$
$158$	−10.7304	−	2.12761i	−0.853665	−	0.169264i
$159$	7.07923	−	9.74373i	0.561420	−	0.772728i
$160$	0.183746	−	5.07039i	0.0145264	−	0.400850i
$161$	12.5719	+	4.08486i	0.990804	+	0.321932i
$162$	1.28395	−	0.592857i	0.100876	−	0.0465792i
$163$	7.50140	+	10.3248i	0.587555	+	0.808700i	0.994498	−	0.104754i	$-0.0334054\pi$
$163$	7.50140	+	10.3248i	0.587555	+	0.808700i	−0.406943	+	0.913453i	$0.633405\pi$
$164$	−0.0326796	−	0.135393i	−0.00255185	−	0.0105724i
$165$	−2.79910	+	1.00702i	−0.217909	+	0.0783963i
$166$	2.58368	+	21.7160i	0.200533	+	1.68549i
$167$	−14.6932	+	10.6752i	−1.13699	+	0.826072i	−0.986697	−	0.162569i	$-0.948022\pi$
$167$	−14.6932	+	10.6752i	−1.13699	+	0.826072i	−0.150294	+	0.988641i	$0.548022\pi$
$168$	2.78185	+	3.51552i	0.214624	+	0.271229i
$169$	3.68926	−	11.3544i	0.283789	−	0.873413i
$170$	4.69230	+	2.62406i	0.359883	+	0.201256i
$171$	3.47037	+	2.52137i	0.265386	+	0.192814i
$172$	1.03157	−	13.3148i	0.0786565	−	1.01524i
$173$	−18.1923	+	5.91103i	−1.38313	+	0.449407i	−0.903698	−	0.428171i	$-0.859158\pi$
$173$	−18.1923	+	5.91103i	−1.38313	+	0.449407i	−0.479435	+	0.877578i	$0.659158\pi$
$174$	−0.593993	−	0.641793i	−0.0450305	−	0.0486542i
$175$	6.64990			0.502685
$176$	−11.6114	+	6.41686i	−0.875240	+	0.483689i
$177$	8.21328			0.617348
$178$	2.89028	+	3.12287i	0.216636	+	0.234069i
$179$	−2.24104	+	0.728158i	−0.167503	+	0.0544251i	−0.391568	−	0.920149i	$-0.628067\pi$
$179$	−2.24104	+	0.728158i	−0.167503	+	0.0544251i	0.224065	+	0.974574i	$0.428067\pi$
$180$	−0.138563	+	1.78847i	−0.0103279	+	0.133305i
$181$	19.0177	+	13.8171i	1.41357	+	1.02702i	0.992791	+	0.119857i	$0.0382436\pi$
$181$	19.0177	+	13.8171i	1.41357	+	1.02702i	0.420780	+	0.907163i	$0.361756\pi$
$182$	2.01546	+	1.12710i	0.149396	+	0.0835463i
$183$	3.95073	−	12.1591i	0.292046	−	0.898826i
$184$	14.6377	+	18.4982i	1.07911	+	1.36371i
$185$	−2.17019	+	1.57674i	−0.159556	+	0.115924i
$186$	−0.886476	−	7.45090i	−0.0649996	−	0.546326i
$187$	−0.438357	−	14.0505i	−0.0320558	−	1.02748i
$188$	0.735667	+	3.04791i	0.0536541	+	0.222291i
$189$	−0.931635	−	1.28229i	−0.0677665	−	0.0932726i
$190$	−4.93988	+	2.28097i	−0.358377	+	0.165479i
$191$	−7.43763	−	2.41663i	−0.538168	−	0.174861i	0.0273067	−	0.999627i	$-0.491307\pi$
$191$	−7.43763	−	2.41663i	−0.538168	−	0.174861i	−0.565474	+	0.824766i	$0.691307\pi$
$192$	0.656828	+	7.97299i	0.0474024	+	0.575401i
$193$	−15.0239	+	20.6786i	−1.08144	+	1.48848i	−0.223517	+	0.974700i	$0.571754\pi$
$193$	−15.0239	+	20.6786i	−1.08144	+	1.48848i	−0.857924	+	0.513776i	$0.828246\pi$
$194$	19.9276	+	3.95122i	1.43072	+	0.283681i
$195$	0.285532	+	0.878778i	0.0204474	+	0.0629306i
$196$	−5.82086	+	6.83220i	−0.415776	+	0.488014i
$197$			11.3865i			0.811251i	0.914039	+	0.405626i	$0.132946\pi$
$197$			11.3865i			0.811251i	−0.914039	+	0.405626i	$0.867054\pi$
$198$	4.19499	−	2.09812i	0.298125	−	0.149107i
$199$			16.7427i			1.18686i	0.804887	+	0.593428i	$0.202226\pi$
$199$			16.7427i			1.18686i	−0.804887	+	0.593428i	$0.797774\pi$
$200$	9.87891	+	6.57478i	0.698544	+	0.464907i
$201$	4.27773	+	13.1655i	0.301728	+	0.928623i
$202$	−2.29360	+	11.5675i	−0.161377	+	0.813890i
$203$	−0.576081	+	0.792907i	−0.0404330	+	0.0556512i
$204$	−7.83559	−	3.23442i	−0.548601	−	0.226455i
$205$	−0.0594047	−	0.0193018i	−0.00414900	−	0.00134809i
$206$	−9.30270	−	20.1468i	−0.648150	−	1.40370i
$207$	−4.90214	−	6.74722i	−0.340723	−	0.468964i
$208$	1.87975	+	3.66709i	0.130337	+	0.254267i
$209$	11.7651	+	7.99945i	0.813807	+	0.553334i
$210$	1.99637	−	0.237520i	0.137763	−	0.0163904i
$211$	−1.82420	+	1.32536i	−0.125583	+	0.0912412i	−0.648804	−	0.760956i	$-0.724730\pi$
$211$	−1.82420	+	1.32536i	−0.125583	+	0.0912412i	0.523221	+	0.852197i	$0.324730\pi$
$212$	−12.6109	−	20.5229i	−0.866118	−	1.40952i
$213$	−1.98052	+	6.09541i	−0.135703	+	0.417650i
$214$	−4.97185	+	8.89059i	−0.339869	+	0.607748i
$215$	−4.84521	−	3.52025i	−0.330441	−	0.240079i
$216$	−0.116210	−	2.82604i	−0.00790708	−	0.192288i
$217$	−7.99796	+	2.59869i	−0.542937	+	0.176411i
$218$	1.63071	−	1.50926i	0.110446	−	0.102220i
$219$	4.47096			0.302119
$220$	−0.274367	+	5.94314i	−0.0184978	+	0.400686i
$221$	−4.36645			−0.293719
$222$	3.10417	−	2.87298i	0.208338	−	0.192821i
$223$	4.97253	−	1.61567i	0.332985	−	0.108193i	−0.137752	−	0.990467i	$-0.543988\pi$
$223$	4.97253	−	1.61567i	0.332985	−	0.108193i	0.470738	+	0.882273i	$0.343988\pi$
$224$	8.62199	−	2.46003i	0.576081	−	0.164368i
$225$	−3.39427	−	2.46608i	−0.226284	−	0.164405i
$226$	7.84363	−	14.0259i	0.521751	−	0.932986i
$227$	−1.26953	+	3.90721i	−0.0842616	+	0.259330i	−0.984307	−	0.176466i	$-0.943533\pi$
$227$	−1.26953	+	3.90721i	−0.0842616	+	0.259330i	0.900045	+	0.435797i	$0.143533\pi$
$228$	7.30952	−	4.49154i	0.484085	−	0.297460i
$229$	−1.29997	+	0.944481i	−0.0859042	+	0.0624131i	−0.629908	−	0.776669i	$-0.716908\pi$
$229$	−1.29997	+	0.944481i	−0.0859042	+	0.0624131i	0.544004	+	0.839083i	$0.316908\pi$
$230$	10.5047	−	1.24980i	0.692656	−	0.0824093i
$231$	−3.22100	−	4.15444i	−0.211926	−	0.273342i
$232$	−1.63976	+	0.608348i	−0.107656	+	0.0399400i
$233$	−6.61953	−	9.11100i	−0.433660	−	0.596882i	0.535129	−	0.844771i	$-0.320263\pi$
$233$	−6.61953	−	9.11100i	−0.433660	−	0.596882i	−0.968788	+	0.247889i	$0.920263\pi$
$234$	−0.610761	−	1.32272i	−0.0399267	−	0.0864690i
$235$	1.33729	+	0.434512i	0.0872351	+	0.0283444i
$236$	6.26768	−	15.1838i	0.407991	−	0.988383i
$237$	4.54667	−	6.25795i	0.295338	−	0.406498i
$238$	−1.84779	+	9.31914i	−0.119774	+	0.604070i
$239$	−1.23014	−	3.78599i	−0.0795713	−	0.244895i	0.903355	−	0.428893i	$-0.141096\pi$
$239$	−1.23014	−	3.78599i	−0.0795713	−	0.244895i	−0.982927	+	0.183997i	$0.941096\pi$
$240$	3.20059	+	1.62097i	0.206597	+	0.104633i
$241$			10.6165i			0.683870i	0.939724	+	0.341935i	$0.111082\pi$
$241$			10.6165i			0.683870i	−0.939724	+	0.341935i	$0.888918\pi$
$242$	13.6894	−	7.38915i	0.879990	−	0.474992i
$243$			1.00000i			0.0641500i
$244$	−19.4635	−	16.5825i	−1.24603	−	1.06158i
$245$	1.24385	+	3.82817i	0.0794666	+	0.244573i
$246$	0.0966060	+	0.0191549i	0.00615938	+	0.00122127i
$247$	2.59751	−	3.57517i	0.165276	−	0.227483i
$248$	−14.4509	−	4.04707i	−0.917632	−	0.256989i
$249$	−14.7070	−	4.77859i	−0.932018	−	0.302831i
$250$	10.5895	−	4.88966i	0.669740	−	0.309249i
$251$	5.28407	+	7.27290i	0.333528	+	0.459061i	0.942537	−	0.334102i	$-0.108433\pi$
$251$	5.28407	+	7.27290i	0.333528	+	0.459061i	−0.609010	+	0.793163i	$0.708433\pi$
$252$	−3.08149	+	0.743774i	−0.194116	+	0.0468534i
$253$	−16.9485	−	21.8601i	−1.06554	−	1.37433i
$254$	1.63330	+	13.7280i	0.102482	+	0.861372i
$255$	−3.07551	+	2.23449i	−0.192596	+	0.139929i
$256$	15.2408	+	4.87003i	0.952552	+	0.304377i
$257$	−5.82270	+	17.9204i	−0.363210	+	1.11784i	0.587885	+	0.808945i	$0.299961\pi$
$257$	−5.82270	+	17.9204i	−0.363210	+	1.11784i	−0.951094	+	0.308900i	$0.900039\pi$
$258$	8.24196	+	4.60912i	0.513122	+	0.286951i
$259$	−3.83507	−	2.78634i	−0.238300	−	0.173135i
$260$	1.84248	+	0.142747i	0.114266	+	0.00885281i
$261$	0.588090	−	0.191082i	0.0364019	−	0.0118277i
$262$	−9.76089	−	10.5464i	−0.603030	−	0.651557i
$263$	17.5390			1.08150			0.540750	−	0.841183i	$-0.318140\pi$
$263$	17.5390			1.08150			0.540750	+	0.841183i	$0.318140\pi$
$264$	−0.677517	−	9.35633i	−0.0416983	−	0.575843i
$265$	−10.8024			−0.663584
$266$	−6.53113	−	7.05670i	−0.400449	−	0.432674i
$267$	−2.86156	+	0.929777i	−0.175125	+	0.0569014i
$268$	27.6033	+	2.13858i	1.68614	+	0.130635i
$269$	−10.2497	−	7.44686i	−0.624936	−	0.454043i	0.229706	−	0.973260i	$-0.426224\pi$
$269$	−10.2497	−	7.44686i	−0.624936	−	0.454043i	−0.854642	+	0.519217i	$0.826224\pi$
$270$	−1.10708	−	0.619107i	−0.0673746	−	0.0376777i
$271$	−7.47193	+	22.9962i	−0.453888	+	1.39692i	0.418549	+	0.908194i	$0.362539\pi$
$271$	−7.47193	+	22.9962i	−0.453888	+	1.39692i	−0.872436	+	0.488728i	$0.837461\pi$
$272$	−11.9589	+	12.0173i	−0.725115	+	0.728658i
$273$	−1.32101	+	0.959770i	−0.0799511	+	0.0580879i
$274$	−1.67095	−	14.0445i	−0.100946	−	0.848459i
$275$	−11.5071	−	7.82403i	−0.693903	−	0.471807i
$276$	−16.2144	+	3.91364i	−0.975994	+	0.235574i
$277$	6.66973	+	9.18010i	0.400745	+	0.551579i	0.960931	−	0.276789i	$-0.0892701\pi$
$277$	6.66973	+	9.18010i	0.400745	+	0.551579i	−0.560185	+	0.828367i	$0.689270\pi$
$278$	19.2652	−	8.89563i	1.15545	−	0.533524i
$279$	5.04606	+	1.63956i	0.302099	+	0.0981581i
$280$	1.08436	−	3.87193i	0.0648029	−	0.231392i
$281$	7.96394	−	10.9614i	0.475089	−	0.653903i	−0.502463	−	0.864599i	$-0.667573\pi$
$281$	7.96394	−	10.9614i	0.475089	−	0.653903i	0.977552	+	0.210695i	$0.0675727\pi$
$282$	−2.17475	−	0.431207i	−0.129504	−	0.0256780i
$283$	−7.59280	−	23.3682i	−0.451345	−	1.38910i	−0.875373	−	0.483449i	$-0.839384\pi$
$283$	−7.59280	−	23.3682i	−0.451345	−	1.38910i	0.424028	−	0.905649i	$-0.360616\pi$
$284$	9.75716	+	8.31286i	0.578981	+	0.493277i
$285$		−	3.84742i		−	0.227901i
$286$	−2.16148	−	4.32167i	−0.127811	−	0.255546i
$287$		−	0.110380i		−	0.00651552i
$288$	−5.31315	−	1.94175i	−0.313081	−	0.114419i
$289$	−0.298041	−	0.917276i	−0.0175318	−	0.0539574i
$290$	−0.152548	+	0.769362i	−0.00895795	+	0.0451785i
$291$	−8.44368	+	11.6217i	−0.494977	+	0.681278i
$292$	3.41185	−	8.26542i	0.199664	−	0.483697i
$293$	−5.43709	−	1.76662i	−0.317638	−	0.103207i	0.145859	−	0.989305i	$-0.453405\pi$
$293$	−5.43709	−	1.76662i	−0.317638	−	0.103207i	−0.463497	+	0.886099i	$0.653405\pi$
$294$	−2.66062	−	5.76210i	−0.155171	−	0.336052i
$295$	−4.32999	−	5.95972i	−0.252102	−	0.346989i
$296$	−2.94240	−	7.93106i	−0.171024	−	0.460983i
$297$	0.103424	+	3.31501i	0.00600126	+	0.192356i
$298$	24.3221	−	2.89374i	1.40894	−	0.167630i
$299$	−6.95098	+	5.05019i	−0.401986	+	0.292060i
$300$	−7.14923	+	4.39305i	−0.412761	+	0.253633i
$301$	3.27049	−	10.0655i	0.188508	−	0.580168i
$302$	−5.75785	+	10.2961i	−0.331327	+	0.592474i
$303$	−6.74617	−	4.90138i	−0.387558	−	0.281577i
$304$	−2.72547	−	16.9406i	−0.156316	−	0.971610i
$305$	−10.9057	+	3.54347i	−0.624458	+	0.202899i
$306$	4.39911	−	4.07147i	0.251480	−	0.232750i
$307$	7.63441			0.435719			0.217859	−	0.975980i	$-0.430093\pi$
$307$	7.63441			0.435719			0.217859	+	0.975980i	$0.430093\pi$
$308$	−10.1383	+	2.78432i	−0.577681	+	0.158651i
$309$	15.6913			0.892648
$310$	−4.93917	+	4.57131i	−0.280526	+	0.259633i
$311$	20.1706	−	6.55383i	1.14377	−	0.371634i	0.324978	−	0.945722i	$-0.394643\pi$
$311$	20.1706	−	6.55383i	1.14377	−	0.371634i	0.818794	+	0.574088i	$0.194643\pi$
$312$	−2.91138	+	0.119719i	−0.164825	+	0.00677778i
$313$	−3.49829	−	2.54166i	−0.197735	−	0.143663i	0.484512	−	0.874785i	$-0.338997\pi$
$313$	−3.49829	−	2.54166i	−0.197735	−	0.143663i	−0.682247	+	0.731122i	$0.738997\pi$
$314$	−0.00741581	+	0.0132608i	−0.000418499	+	0.000748352i
$315$	−0.439300	+	1.35203i	−0.0247517	+	0.0761780i
$316$	−8.09939	−	13.1809i	−0.455626	−	0.741484i
$317$	5.71480	−	4.15205i	0.320975	−	0.233202i	−0.415616	−	0.909540i	$-0.636434\pi$
$317$	5.71480	−	4.15205i	0.320975	−	0.233202i	0.736592	+	0.676338i	$0.236434\pi$
$318$	16.9134	−	2.01228i	0.948455	−	0.112843i
$319$	1.92976	−	0.694262i	0.108046	−	0.0388712i
$320$	5.43909	−	4.67992i	0.304054	−	0.261615i
$321$	−4.23372	−	5.82722i	−0.236303	−	0.325244i
$322$	7.83690	+	16.9723i	0.436733	+	0.945832i
$323$	17.2915	+	5.61833i	0.962122	+	0.312612i
$324$	1.84869	+	0.763114i	0.102705	+	0.0423952i
$325$	−2.54055	+	3.49677i	−0.140924	+	0.193966i
$326$	−3.51028	+	17.7037i	−0.194416	+	0.980519i
$327$	0.485515	+	1.49426i	0.0268490	+	0.0826328i
$328$	0.109133	−	0.163977i	0.00602586	−	0.00905413i
$329$			2.48482i			0.136992i
$330$	−3.73401	−	1.93785i	−0.205550	−	0.106675i
$331$		−	7.22121i		−	0.396914i	−0.980110	−	0.198457i	$-0.936407\pi$
$331$		−	7.22121i		−	0.396914i	0.980110	−	0.198457i	$-0.0635929\pi$
$332$	−20.0573	+	23.5421i	−1.10079	+	1.29204i
$333$	0.924210	+	2.84443i	0.0506464	+	0.155874i
$334$	−25.1941	−	4.99546i	−1.37856	−	0.273340i
$335$	7.29796	−	10.0448i	0.398730	−	0.548805i
$336$	−0.976524	+	6.26431i	−0.0532737	+	0.341746i
$337$	27.9259	+	9.07368i	1.52122	+	0.494275i	0.946123	−	0.323808i	$-0.104963\pi$
$337$	27.9259	+	9.07368i	1.52122	+	0.494275i	0.575100	+	0.818083i	$0.304963\pi$
$338$	15.3286	−	7.07793i	0.833769	−	0.384989i
$339$	6.67916	+	9.19307i	0.362762	+	0.499299i
$340$	1.78391	+	7.39083i	0.0967461	+	0.400824i
$341$	16.8973	+	4.91329i	0.915040	+	0.266069i
$342$	0.716703	+	6.02394i	0.0387548	+	0.325737i
$343$	−14.7306	+	10.7024i	−0.795380	+	0.577877i
$344$	14.8104	−	11.7195i	0.798523	−	0.631875i
$345$	−2.31154	+	7.11419i	−0.124449	+	0.383015i
$346$	−23.6106	−	13.2037i	−1.26931	−	0.709834i
$347$	3.88937	+	2.82580i	0.208793	+	0.151697i	0.687267	−	0.726405i	$-0.258810\pi$
$347$	3.88937	+	2.82580i	0.208793	+	0.151697i	−0.478475	+	0.878101i	$0.658810\pi$
$348$	0.0955285	−	1.23301i	0.00512087	−	0.0660965i
$349$	19.9638	−	6.48663i	1.06864	−	0.347221i	0.278681	−	0.960384i	$-0.410103\pi$
$349$	19.9638	−	6.48663i	1.06864	−	0.347221i	0.789957	+	0.613163i	$0.210103\pi$
$350$	6.38791	+	6.90196i	0.341448	+	0.368925i
$351$	1.03020			0.0549880
$352$	−17.8140	−	5.88743i	−0.949489	−	0.313801i
$353$	7.06506			0.376035			0.188018	−	0.982166i	$-0.439794\pi$
$353$	7.06506			0.376035			0.188018	+	0.982166i	$0.439794\pi$
$354$	7.88970	+	8.52460i	0.419333	+	0.453077i
$355$	5.46707	−	1.77636i	0.290162	−	0.0942793i
$356$	−0.464827	+	5.99967i	−0.0246358	+	0.317982i
$357$	−5.43491	−	3.94869i	−0.287646	−	0.208987i
$358$	−2.90850	−	1.62651i	−0.153719	−	0.0859639i
$359$	4.34491	−	13.3723i	0.229316	−	0.705761i	−0.768509	−	0.639839i	$-0.779001\pi$
$359$	4.34491	−	13.3723i	0.229316	−	0.705761i	0.997825	−	0.0659221i	$-0.0209989\pi$
$360$	−1.98937	+	1.57419i	−0.104849	+	0.0829673i
$361$	0.484803	−	0.352230i	0.0255159	−	0.0185384i
$362$	3.92754	+	33.0113i	0.206427	+	1.73503i
$363$	0.685702	+	10.9786i	0.0359900	+	0.576227i
$364$	0.766236	+	3.17455i	0.0401617	+	0.166392i
$365$	−2.35706	−	3.24422i	−0.123374	−	0.169810i
$366$	16.4151	−	7.57957i	0.858029	−	0.396191i
$367$	17.0875	+	5.55207i	0.891961	+	0.289816i	0.718915	−	0.695098i	$-0.244639\pi$
$367$	17.0875	+	5.55207i	0.891961	+	0.289816i	0.173046	+	0.984914i	$0.444639\pi$
$368$	−5.13834	+	32.9620i	−0.267855	+	1.71826i
$369$	−0.0409337	+	0.0563405i	−0.00213093	+	0.00293297i
$370$	−3.72119	−	0.737833i	−0.193455	−	0.0383581i
$371$	−5.89898	−	18.1552i	−0.306260	−	0.942571i
$372$	6.88176	−	8.07742i	0.356803	−	0.418795i
$373$		−	23.1319i		−	1.19773i	−0.800851	−	0.598863i	$-0.795619\pi$
$373$		−	23.1319i		−	1.19773i	0.800851	−	0.598863i	$-0.204381\pi$
$374$	14.1620	−	13.9519i	0.732300	−	0.721437i
$375$			8.24763i			0.425906i
$376$	−2.45675	+	3.69138i	−0.126697	+	0.190368i
$377$	−0.196853	−	0.605850i	−0.0101384	−	0.0312029i
$378$	0.435959	−	2.19871i	0.0224233	−	0.113090i
$379$	−20.1247	+	27.6993i	−1.03374	+	1.42281i	−0.131630	+	0.991299i	$0.542021\pi$
$379$	−20.1247	+	27.6993i	−1.03374	+	1.42281i	−0.902105	+	0.431516i	$0.857979\pi$
$380$	−7.11268	−	2.93602i	−0.364873	−	0.150615i
$381$	−9.29718	−	3.02084i	−0.476309	−	0.154762i
$382$	−4.63637	−	10.0410i	−0.237217	−	0.513740i
$383$	−9.21636	−	12.6852i	−0.470934	−	0.648185i	0.505797	−	0.862653i	$-0.331198\pi$
$383$	−9.21636	−	12.6852i	−0.470934	−	0.648185i	−0.976731	+	0.214467i	$0.931198\pi$
$384$	−7.64425	+	8.34059i	−0.390094	+	0.425629i
$385$	−1.31645	+	4.52742i	−0.0670926	+	0.230738i
$386$	−35.8943	+	4.27055i	−1.82697	+	0.217365i
$387$	−5.40208	+	3.92484i	−0.274603	+	0.199511i
$388$	15.0415	+	24.4785i	0.763616	+	1.24271i
$389$	−0.579547	+	1.78366i	−0.0293842	+	0.0904353i	−0.964673	−	0.263450i	$-0.915140\pi$
$389$	−0.579547	+	1.78366i	−0.0293842	+	0.0904353i	0.935289	+	0.353885i	$0.115140\pi$
$390$	−0.637804	+	1.14051i	−0.0322965	+	0.0577520i
$391$	−28.5978	−	20.7775i	−1.44625	−	1.05076i
$392$	−12.6827	+	0.521527i	−0.640573	+	0.0263411i
$393$	9.66390	−	3.13999i	0.487479	−	0.158392i
$394$	−11.8180	+	10.9379i	−0.595385	+	0.551041i
$395$	−6.93787			−0.349082
$396$	6.20735	+	2.33853i	0.311931	+	0.117516i
$397$	−19.8246			−0.994971			−0.497485	−	0.867472i	$-0.665743\pi$
$397$	−19.8246			−0.994971			−0.497485	+	0.867472i	$0.665743\pi$
$398$	−17.3773	+	16.0830i	−0.871043	+	0.806169i
$399$	6.46623	−	2.10101i	0.323716	−	0.105182i
$400$	2.66570	+	16.5691i	0.133285	+	0.828455i
$401$	8.74238	+	6.35171i	0.436574	+	0.317189i	0.784272	−	0.620417i	$-0.213037\pi$
$401$	8.74238	+	6.35171i	0.436574	+	0.317189i	−0.347698	+	0.937606i	$0.613037\pi$
$402$	−9.55533	+	17.0867i	−0.476577	+	0.852206i
$403$	1.68908	−	5.19844i	0.0841389	−	0.258953i
$404$	−14.2092	+	8.73127i	−0.706936	+	0.434397i
$405$	0.725620	−	0.527194i	0.0360563	−	0.0261965i
$406$	−1.37635	+	0.163752i	−0.0683069	+	0.00812687i
$407$	3.35795	+	9.33372i	0.166447	+	0.462656i
$408$	−4.16986	−	11.2396i	−0.206439	−	0.556442i
$409$	2.42257	+	3.33439i	0.119789	+	0.164875i	0.864700	−	0.502288i	$-0.167508\pi$
$409$	2.42257	+	3.33439i	0.119789	+	0.164875i	−0.744912	+	0.667163i	$0.767508\pi$
$410$	−0.0370309	−	0.0801976i	−0.00182883	−	0.00396068i
$411$	9.51151	+	3.09048i	0.469168	+	0.152442i
$412$	11.9743	−	29.0084i	0.589930	−	1.42914i
$413$	7.65178	−	10.5318i	0.376520	−	0.518235i
$414$	2.29396	−	11.5693i	0.112742	−	0.568602i
$415$	4.28599	+	13.1909i	0.210391	+	0.647518i
$416$	−2.00039	+	5.47361i	−0.0980774	+	0.268366i
$417$			15.0047i			0.734782i
$418$	2.99890	+	19.8953i	0.146681	+	0.973111i
$419$			7.40916i			0.361961i	0.983487	+	0.180981i	$0.0579271\pi$
$419$			7.40916i			0.361961i	−0.983487	+	0.180981i	$0.942073\pi$
$420$	2.16424	+	1.84388i	0.105604	+	0.0899721i
$421$	−0.377897	−	1.16305i	−0.0184176	−	0.0566834i	0.941425	−	0.337221i	$-0.109487\pi$
$421$	−0.377897	−	1.16305i	−0.0184176	−	0.0566834i	−0.959843	+	0.280538i	$0.909487\pi$
$422$	−3.12792	−	0.620200i	−0.152265	−	0.0301909i
$423$	0.921481	−	1.26831i	0.0448039	−	0.0616673i
$424$	9.18675	−	32.8032i	0.446148	−	1.59306i
$425$	−16.9123	−	5.49513i	−0.820365	−	0.266553i
$426$	−8.22893	+	3.79967i	−0.398693	+	0.184095i
$427$	−11.9108	−	16.3938i	−0.576404	−	0.793352i
$428$	−14.0035	+	3.38001i	−0.676887	+	0.163379i
$429$	3.41512	−	0.106547i	0.164884	−	0.00514414i
$430$	−1.00064	−	8.41043i	−0.0482550	−	0.405587i
$431$	15.7477	−	11.4413i	0.758538	−	0.551110i	−0.139923	−	0.990162i	$-0.544686\pi$
$431$	15.7477	−	11.4413i	0.758538	−	0.551110i	0.898462	+	0.439052i	$0.144686\pi$
$432$	2.82152	−	2.83531i	0.135751	−	0.136414i
$433$	5.05505	−	15.5578i	0.242930	−	0.747662i	−0.753040	−	0.657975i	$-0.771413\pi$
$433$	5.05505	−	15.5578i	0.242930	−	0.747662i	0.995970	−	0.0896872i	$-0.0285867\pi$
$434$	−10.3800	−	5.80480i	−0.498258	−	0.278639i
$435$	−0.448691	−	0.325993i	−0.0215131	−	0.0156302i
$436$	3.13293	+	0.242726i	0.150040	+	0.0116244i
$437$	34.0245	−	11.0552i	1.62761	−	0.528843i
$438$	4.29481	+	4.64042i	0.205214	+	0.221728i
$439$	14.7044			0.701804			0.350902	−	0.936412i	$-0.385875\pi$
$439$	14.7044			0.701804			0.350902	+	0.936412i	$0.385875\pi$
$440$	−6.43196	+	5.42422i	−0.306632	+	0.258590i
$441$	4.48780			0.213705
$442$	−4.19442	−	4.53196i	−0.199508	−	0.215563i
$443$	7.00255	−	2.27527i	0.332701	−	0.108101i	−0.137903	−	0.990446i	$-0.544036\pi$
$443$	7.00255	−	2.27527i	0.332701	−	0.108101i	0.470604	+	0.882345i	$0.344036\pi$
$444$	5.96374	+	0.462044i	0.283027	+	0.0219277i
$445$	2.18326	+	1.58623i	0.103497	+	0.0751946i
$446$	6.45353	+	3.60899i	0.305584	+	0.170891i
$447$	−5.35206	+	16.4719i	−0.253144	+	0.779096i
$448$	10.8356	+	6.58568i	0.511933	+	0.311144i
$449$	−4.51170	+	3.27794i	−0.212920	+	0.154696i	−0.689134	−	0.724634i	$-0.742009\pi$
$449$	−4.51170	+	3.27794i	−0.212920	+	0.154696i	0.476214	+	0.879330i	$0.342009\pi$
$450$	−0.700986	−	5.89184i	−0.0330448	−	0.277744i
$451$	−0.129869	+	0.191003i	−0.00611529	+	0.00899397i
$452$	22.0921	−	5.33233i	1.03912	−	0.250812i
$453$	−4.90303	−	6.74844i	−0.230365	−	0.317070i
$454$	−5.27482	+	2.43562i	−0.247559	+	0.114309i
$455$	1.39286	+	0.452566i	0.0652981	+	0.0212166i
$456$	11.6833	+	3.27199i	0.547122	+	0.153225i
$457$	−10.8622	+	14.9505i	−0.508113	+	0.699357i	−0.983600	−	0.180366i	$-0.942272\pi$
$457$	−10.8622	+	14.9505i	−0.508113	+	0.699357i	0.475487	+	0.879723i	$0.342272\pi$
$458$	−2.22903	−	0.441970i	−0.104156	−	0.0206519i
$459$	1.30975	+	4.03101i	0.0611341	+	0.188151i
$460$	11.3880	+	9.70226i	0.530966	+	0.452370i
$461$		−	17.6315i		−	0.821182i	−0.911820	−	0.410591i	$-0.865322\pi$
$461$		−	17.6315i		−	0.821182i	0.911820	−	0.410591i	$-0.134678\pi$
$462$	1.21781	−	7.33385i	0.0566576	−	0.341202i
$463$			13.2658i			0.616515i	0.951303	+	0.308257i	$0.0997458\pi$
$463$			13.2658i			0.616515i	−0.951303	+	0.308257i	$0.900254\pi$
$464$	−2.20656	−	1.11753i	−0.102437	−	0.0518802i
$465$	−1.47055	−	4.52589i	−0.0681951	−	0.209883i
$466$	3.09761	−	15.6225i	0.143494	−	0.723697i
$467$	−12.8463	+	17.6814i	−0.594456	+	0.818198i	−0.995187	−	0.0979976i	$-0.968756\pi$
$467$	−12.8463	+	17.6814i	−0.594456	+	0.818198i	0.400731	+	0.916196i	$0.368756\pi$
$468$	0.786160	−	1.90452i	0.0363403	−	0.0880365i
$469$	20.8672	+	6.78017i	0.963559	+	0.313079i
$470$	0.833621	+	1.80537i	0.0384521	+	0.0832755i
$471$	−0.00631485	−	0.00869165i	−0.000290973	−	0.000400490i
$472$	21.7801	−	8.08036i	1.00251	−	0.371929i
$473$	−17.5021	+	13.5696i	−0.804745	+	0.623931i
$474$	10.8627	−	1.29240i	0.498940	−	0.0593617i
$475$	14.5601	−	10.5785i	0.668062	−	0.485375i
$476$	−11.4474	+	7.03416i	−0.524689	+	0.322410i
$477$	−3.72177	+	11.4544i	−0.170408	+	0.524463i
$478$	2.74781	−	4.91360i	0.125682	−	0.224743i
$479$	−28.7819	−	20.9113i	−1.31508	−	0.955462i	−0.999979	−	0.00640328i	$-0.997962\pi$
$479$	−28.7819	−	20.9113i	−1.31508	−	0.955462i	−0.315101	−	0.949058i	$-0.602038\pi$
$480$	1.39208	+	4.87901i	0.0635397	+	0.222695i
$481$	2.93033	−	0.952121i	0.133611	−	0.0434130i
$482$	−11.0189	+	10.1982i	−0.501898	+	0.464517i
$483$	−13.2189			−0.601480
$484$	20.8193	+	7.11028i	0.946333	+	0.323195i
$485$	12.8844			0.585051
$486$	−1.03790	+	0.960602i	−0.0470803	+	0.0435738i
$487$	−13.0159	+	4.22912i	−0.589806	+	0.191640i	−0.588689	−	0.808360i	$-0.700356\pi$
$487$	−13.0159	+	4.22912i	−0.589806	+	0.191640i	−0.00111710	+	0.999999i	$0.500356\pi$
$488$	−1.48572	−	36.1304i	−0.0672556	−	1.63555i
$489$	−10.3248	−	7.50140i	−0.466903	−	0.339225i
$490$	−2.77843	+	4.96834i	−0.125517	+	0.224447i
$491$	3.07565	−	9.46588i	0.138802	−	0.427189i	−0.857360	−	0.514717i	$-0.827897\pi$
$491$	3.07565	−	9.46588i	0.138802	−	0.427189i	0.996162	+	0.0875283i	$0.0278968\pi$
$492$	0.0729190	+	0.118668i	0.00328744	+	0.00534997i
$493$	2.12033	−	1.54051i	0.0954947	−	0.0693810i
$494$	6.20586	−	0.738347i	0.279215	−	0.0332198i
$495$	2.35091	−	1.82270i	0.105666	−	0.0819243i
$496$	−9.68108	−	18.8862i	−0.434693	−	0.848017i
$497$	5.97093	+	8.21828i	0.267833	+	0.368640i
$498$	−9.16785	−	19.8548i	−0.410821	−	0.889714i
$499$	16.9602	+	5.51072i	0.759245	+	0.246694i	0.662954	−	0.748660i	$-0.269302\pi$
$499$	16.9602	+	5.51072i	0.759245	+	0.246694i	0.0962903	+	0.995353i	$0.469302\pi$
$500$	15.2473	+	6.29388i	0.681880	+	0.281471i
$501$	10.6752	−	14.6932i	0.476933	−	0.656442i
$502$	−2.47268	+	12.4707i	−0.110361	+	0.556595i
$503$	−0.0583996	−	0.179735i	−0.00260391	−	0.00801401i	0.949746	−	0.313021i	$-0.101341\pi$
$503$	−0.0583996	−	0.179735i	−0.00260391	−	0.00801401i	−0.952350	+	0.305007i	$0.901341\pi$
$504$	−3.73205	−	2.48382i	−0.166239	−	0.110638i
$505$			7.47914i			0.332817i
$506$	6.40795	−	38.5898i	0.284868	−	1.71552i
$507$			11.9387i			0.530216i
$508$	−12.6794	+	14.8824i	−0.562558	+	0.660298i
$509$	−4.30669	−	13.2546i	−0.190891	−	0.587501i	0.809109	−	0.587658i	$-0.199950\pi$
$509$	−4.30669	−	13.2546i	−0.190891	−	0.587501i	−1.00000		0.000157233i	$0.999950\pi$
$510$	−5.27352	−	1.04563i	−0.233515	−	0.0463012i
$511$	4.16530	−	5.73304i	0.184262	−	0.253615i
$512$	9.58574	+	20.4967i	0.423634	+	0.905834i
$513$	−4.07966	−	1.32556i	−0.180121	−	0.0585250i
$514$	−24.1930	+	11.1710i	−1.06711	+	0.492731i
$515$	−8.27236	−	11.3859i	−0.364524	−	0.501724i
$516$	3.13341	+	12.9819i	0.137941	+	0.571496i
$517$	2.92355	−	4.29976i	0.128577	−	0.189103i
$518$	−0.792021	−	6.65700i	−0.0347994	−	0.292492i
$519$	15.4753	−	11.2434i	0.679289	−	0.493532i
$520$	1.62173	+	2.04944i	0.0711177	+	0.0898740i
$521$	−5.64640	+	17.3778i	−0.247373	+	0.761337i	0.747864	+	0.663852i	$0.231080\pi$
$521$	−5.64640	+	17.3778i	−0.247373	+	0.761337i	−0.995237	+	0.0974844i	$0.968920\pi$
$522$	0.763246	+	0.426827i	0.0334064	+	0.0186817i
$523$	15.0953	+	10.9674i	0.660070	+	0.479569i	0.866687	−	0.498853i	$-0.166245\pi$
$523$	15.0953	+	10.9674i	0.660070	+	0.479569i	−0.206617	+	0.978422i	$0.566245\pi$
$524$	1.56979	−	20.2617i	0.0685765	−	0.885138i
$525$	−6.32443	+	2.05493i	−0.276021	+	0.0896846i
$526$	16.8480	+	18.2038i	0.734607	+	0.793722i
$527$	22.4881			0.979598
$528$	9.06015	−	9.69091i	0.394292	−	0.421743i
$529$	−46.5560			−2.02417
$530$	−10.3768	−	11.2118i	−0.450738	−	0.487010i
$531$	−7.81130	+	2.53804i	−0.338981	+	0.110142i
$532$	1.05036	−	13.5574i	0.0455391	−	0.587786i
$533$	0.0580419	+	0.0421699i	0.00251407	+	0.00182658i
$534$	−3.71384	−	2.07688i	−0.160714	−	0.0898753i
$535$	−1.99635	+	6.14415i	−0.0863100	+	0.265635i
$536$	24.2962	+	30.7039i	1.04944	+	1.32621i
$537$	1.90634	−	1.38504i	0.0822647	−	0.0597688i
$538$	−2.11678	−	17.7917i	−0.0912608	−	0.767054i
$539$	14.8771	−	0.464145i	0.640802	−	0.0199922i
$540$	−0.420887	−	1.74376i	−0.0181121	−	0.0750393i
$541$	−6.76205	−	9.30716i	−0.290723	−	0.400146i	0.638526	−	0.769600i	$-0.279545\pi$
$541$	−6.76205	−	9.30716i	−0.290723	−	0.400146i	−0.929249	+	0.369454i	$0.879545\pi$
$542$	−31.0454	+	14.3351i	−1.33352	+	0.615745i
$543$	−22.3566	−	7.26410i	−0.959413	−	0.311732i
$544$	−23.9606	−	0.868307i	−1.02730	−	0.0372283i
$545$	0.828305	−	1.14006i	0.0354807	−	0.0488350i
$546$	−2.26511	−	0.449124i	−0.0969379	−	0.0192207i
$547$	−3.33782	−	10.2727i	−0.142715	−	0.439231i	0.853995	−	0.520281i	$-0.174173\pi$
$547$	−3.33782	−	10.2727i	−0.142715	−	0.439231i	−0.996710	+	0.0810500i	$0.974173\pi$
$548$	12.9717	−	15.2254i	0.554124	−	0.650399i
$549$			12.7848i			0.545643i
$550$	−2.93313	−	19.4590i	−0.125069	−	0.829735i
$551$			2.65250i			0.113000i
$552$	−19.6376	−	13.0696i	−0.835831	−	0.556277i
$553$	−3.78865	−	11.6603i	−0.161110	−	0.495844i
$554$	−3.12110	+	15.7410i	−0.132603	+	0.668769i
$555$	1.57674	−	2.17019i	0.0669287	−	0.0921194i
$556$	27.7390	+	11.4503i	1.17640	+	0.485600i
$557$	−32.1819	−	10.4565i	−1.36359	−	0.443057i	−0.466350	−	0.884600i	$-0.654431\pi$
$557$	−32.1819	−	10.4565i	−1.36359	−	0.443057i	−0.897240	+	0.441543i	$0.854431\pi$
$558$	3.14554	+	6.81229i	0.133161	+	0.288387i
$559$	4.04337	+	5.56522i	0.171016	+	0.235384i
$560$	5.06033	−	2.59392i	0.213838	−	0.109613i
$561$	4.75875	+	13.2274i	0.200915	+	0.558460i
$562$	19.0271	−	2.26376i	0.802609	−	0.0954909i
$563$	31.7142	−	23.0417i	1.33659	−	0.971092i	0.337032	−	0.941493i	$-0.390577\pi$
$563$	31.7142	−	23.0417i	1.33659	−	0.971092i	0.999562	−	0.0295994i	$-0.00942314\pi$
$564$	−1.64152	−	2.67140i	−0.0691203	−	0.112486i
$565$	3.14946	−	9.69306i	0.132499	−	0.407790i
$566$	16.9603	−	30.3282i	0.712896	−	1.27479i
$567$	1.28229	+	0.931635i	0.0538509	+	0.0391250i
$568$	0.744800	+	18.1123i	0.0312511	+	0.759977i
$569$	−21.6670	+	7.04003i	−0.908328	+	0.295134i	−0.725670	−	0.688043i	$-0.758470\pi$
$569$	−21.6670	+	7.04003i	−0.908328	+	0.295134i	−0.182658	+	0.983177i	$0.558470\pi$
$570$	3.99325	−	3.69584i	0.167259	−	0.154802i
$571$	−19.5463			−0.817989			−0.408994	−	0.912537i	$-0.634120\pi$
$571$	−19.5463			−0.817989			−0.408994	+	0.912537i	$0.634120\pi$
$572$	2.40916	−	6.39481i	0.100732	−	0.267381i
$573$	7.82038			0.326701
$574$	0.114564	−	0.106031i	0.00478180	−	0.00442565i
$575$	−33.2784	+	10.8128i	−1.38780	+	0.450925i
$576$	−3.08847	−	7.37979i	−0.128686	−	0.307491i
$577$	26.3692	+	19.1583i	1.09776	+	0.797572i	0.980693	−	0.195551i	$-0.0626496\pi$
$577$	26.3692	+	19.1583i	1.09776	+	0.797572i	0.117071	+	0.993124i	$0.462650\pi$
$578$	0.665745	−	1.19047i	0.0276914	−	0.0495172i
$579$	7.89851	−	24.3091i	0.328251	−	1.01025i
$580$	−0.945062	+	0.580720i	−0.0392416	+	0.0241131i
$581$	−19.8291	+	14.4067i	−0.822649	+	0.597689i
$582$	−20.1733	+	2.40013i	−0.836208	+	0.0994885i
$583$	−11.1531	+	38.3565i	−0.461912	+	1.58856i
$584$	11.8561	−	4.39860i	0.490610	−	0.182015i
$585$	−0.543115	−	0.747533i	−0.0224550	−	0.0309067i
$586$	−3.38930	−	7.34019i	−0.140011	−	0.303220i
$587$	22.7419	+	7.38928i	0.938658	+	0.304988i	0.738098	−	0.674693i	$-0.235724\pi$
$587$	22.7419	+	7.38928i	0.938658	+	0.304988i	0.200559	+	0.979682i	$0.435724\pi$
$588$	3.42470	−	8.29655i	0.141232	−	0.342144i
$589$	−13.3777	+	18.4129i	−0.551219	+	0.758688i
$590$	2.02622	−	10.2190i	0.0834182	−	0.420711i
$591$	−3.51861	−	10.8292i	−0.144736	−	0.445452i
$592$	5.40520	−	10.6725i	0.222152	−	0.438638i
$593$			10.8950i			0.447405i	0.974658	+	0.223702i	$0.0718143\pi$
$593$			10.8950i			0.447405i	−0.974658	+	0.223702i	$0.928186\pi$
$594$	−3.34131	+	3.29175i	−0.137096	+	0.135062i
$595$			6.02540i			0.247017i
$596$	26.3673	+	22.4643i	1.08005	+	0.920172i
$597$	−5.17376	−	15.9232i	−0.211748	−	0.651694i
$598$	−11.9187	−	2.36323i	−0.487393	−	0.0966398i
$599$	−4.33733	+	5.96983i	−0.177219	+	0.243921i	−0.888381	−	0.459108i	$-0.848169\pi$
$599$	−4.33733	+	5.96983i	−0.177219	+	0.243921i	0.711162	+	0.703028i	$0.248169\pi$
$600$	−11.4271	−	3.20024i	−0.466510	−	0.130649i
$601$	16.2181	+	5.26959i	0.661552	+	0.214951i	0.620501	−	0.784206i	$-0.286929\pi$
$601$	16.2181	+	5.26959i	0.661552	+	0.214951i	0.0410510	+	0.999157i	$0.486929\pi$
$602$	13.5887	−	6.27452i	0.553834	−	0.255730i
$603$	−8.13673	−	11.1993i	−0.331353	−	0.456069i
$604$	−16.2174	+	3.91435i	−0.659875	+	0.159273i
$605$	7.60480	−	6.28541i	0.309179	−	0.255538i
$606$	−1.39322	−	11.7102i	−0.0565959	−	0.475693i
$607$	26.3836	−	19.1688i	1.07088	−	0.778039i	0.0948089	−	0.995495i	$-0.469776\pi$
$607$	26.3836	−	19.1688i	1.07088	−	0.778039i	0.976070	+	0.217456i	$0.0697760\pi$
$608$	14.9646	−	19.1019i	0.606895	−	0.774686i
$609$	0.302864	−	0.932119i	0.0122727	−	0.0377714i
$610$	−14.1538	−	7.91519i	−0.573071	−	0.320476i
$611$	−1.30661	−	0.949309i	−0.0528598	−	0.0384049i
$612$	8.45158	+	0.654791i	0.341635	+	0.0264683i
$613$	−33.4699	+	10.8750i	−1.35183	+	0.439238i	−0.893309	−	0.449443i	$-0.851622\pi$
$613$	−33.4699	+	10.8750i	−1.35183	+	0.439238i	−0.458526	+	0.888681i	$0.651622\pi$
$614$	7.33362	+	7.92378i	0.295961	+	0.319778i
$615$	0.0624618			0.00251870
$616$	−12.6287	−	7.84792i	−0.508824	−	0.316202i
$617$	12.4123			0.499701			0.249850	−	0.968284i	$-0.419619\pi$
$617$	12.4123			0.499701			0.249850	+	0.968284i	$0.419619\pi$
$618$	15.0731	+	16.2861i	0.606329	+	0.655122i
$619$	−20.1287	+	6.54020i	−0.809039	+	0.262873i	−0.684191	−	0.729303i	$-0.739844\pi$
$619$	−20.1287	+	6.54020i	−0.809039	+	0.262873i	−0.124848	+	0.992176i	$0.539844\pi$
$620$	−9.48916	−	0.735178i	−0.381094	−	0.0295255i
$621$	6.74722	+	4.90214i	0.270757	+	0.196716i
$622$	26.1782	+	14.6395i	1.04965	+	0.586992i
$623$	−1.47369	+	4.53555i	−0.0590421	+	0.181713i
$624$	−2.92094	−	2.90673i	−0.116931	−	0.116362i
$625$	−10.9867	+	7.98229i	−0.439467	+	0.319292i
$626$	−0.722469	−	6.07241i	−0.0288757	−	0.242702i
$627$	−13.6612	−	3.97232i	−0.545577	−	0.158639i
$628$	−0.0208871	+	0.00504148i	−0.000833487	+	0.000201177i
$629$	7.45100	+	10.2554i	0.297091	+	0.408910i
$630$	−1.82526	+	0.842808i	−0.0727203	+	0.0335783i
$631$	12.1486	+	3.94731i	0.483627	+	0.157140i	0.540675	−	0.841231i	$-0.318169\pi$
$631$	12.1486	+	3.94731i	0.483627	+	0.157140i	−0.0570479	+	0.998371i	$0.518169\pi$
$632$	5.90023	−	21.0680i	0.234699	−	0.838040i
$633$	1.32536	−	1.82420i	0.0526781	−	0.0725053i
$634$	9.79908	+	1.94295i	0.389171	+	0.0771644i
$635$	2.70944	+	8.33879i	0.107521	+	0.330915i
$636$	18.3356	+	15.6215i	0.727053	+	0.619431i
$637$		−	4.62333i		−	0.183183i
$638$	2.57431	+	1.33600i	0.101918	+	0.0528927i
$639$		−	6.40909i		−	0.253540i
$640$	10.0821	+	1.14971i	0.398530	+	0.0454462i
$641$	12.4717	+	38.3840i	0.492604	+	1.51608i	0.820658	+	0.571419i	$0.193607\pi$
$641$	12.4717	+	38.3840i	0.492604	+	1.51608i	−0.328055	+	0.944659i	$0.606393\pi$
$642$	1.98117	−	9.99184i	0.0781906	−	0.394346i
$643$	3.43492	−	4.72776i	0.135460	−	0.186444i	−0.735898	−	0.677092i	$-0.763240\pi$
$643$	3.43492	−	4.72776i	0.135460	−	0.186444i	0.871358	+	0.490648i	$0.163240\pi$
$644$	−10.0875	+	24.4376i	−0.397504	+	0.962977i
$645$	5.69589	+	1.85071i	0.224275	+	0.0728715i
$646$	10.7789	+	23.3438i	0.424091	+	0.918451i
$647$	−13.8164	−	19.0166i	−0.543179	−	0.747621i	0.445888	−	0.895089i	$-0.352888\pi$
$647$	−13.8164	−	19.0166i	−0.543179	−	0.747621i	−0.989067	+	0.147467i	$0.952888\pi$
$648$	0.983816	+	2.65181i	0.0386480	+	0.104173i
$649$	−25.6321	+	9.22152i	−1.00615	+	0.361976i
$650$	−6.06977	+	0.722155i	−0.238076	+	0.0283253i
$651$	6.80347	−	4.94301i	0.266649	−	0.193732i
$652$	−21.7468	+	13.3629i	−0.851669	+	0.523332i
$653$	0.182276	−	0.560987i	0.00713300	−	0.0219531i	−0.947427	−	0.319973i	$-0.896326\pi$
$653$	0.182276	−	0.560987i	0.00713300	−	0.0219531i	0.954560	+	0.298020i	$0.0963262\pi$
$654$	−1.08451	+	1.93931i	−0.0424078	+	0.0758329i
$655$	−7.37319	−	5.35693i	−0.288094	−	0.209313i
$656$	0.275026	−	0.0442473i	0.0107380	−	0.00172757i
$657$	−4.25213	+	1.38160i	−0.165891	+	0.0539014i
$658$	−2.57900	+	2.38692i	−0.100540	+	0.0930519i
$659$	−45.0533			−1.75503			−0.877514	−	0.479550i	$-0.840800\pi$
$659$	−45.0533			−1.75503			−0.877514	+	0.479550i	$0.840800\pi$
$660$	−1.57559	−	5.73704i	−0.0613298	−	0.223314i
$661$	14.0486			0.546425			0.273213	−	0.961954i	$-0.411914\pi$
$661$	14.0486			0.546425			0.273213	+	0.961954i	$0.411914\pi$
$662$	7.49492	−	6.93671i	0.291298	−	0.269603i
$663$	4.15274	−	1.34931i	0.161279	−	0.0524028i
$664$	−43.7014	+	1.79705i	−1.69594	+	0.0697392i
$665$	−4.93349	−	3.58439i	−0.191312	−	0.138997i
$666$	−2.06444	+	3.69160i	−0.0799955	+	0.143047i
$667$	1.59363	−	4.90469i	0.0617056	−	0.189910i
$668$	−19.0167	−	30.9477i	−0.735778	−	1.19740i
$669$	−4.22989	+	3.07319i	−0.163537	+	0.118816i
$670$	17.4360	−	2.07446i	0.673610	−	0.0801432i
$671$	1.32226	+	42.3819i	0.0510451	+	1.63613i
$672$	−7.43980	+	5.00397i	−0.286997	+	0.193032i
$673$	18.5003	+	25.4634i	0.713133	+	0.981544i	0.999724	+	0.0234905i	$0.00747794\pi$
$673$	18.5003	+	25.4634i	0.713133	+	0.981544i	−0.286591	+	0.958053i	$0.592522\pi$
$674$	17.4081	+	37.7006i	0.670535	+	1.45217i
$675$	3.99020	+	1.29649i	0.153583	+	0.0499021i
$676$	22.0709	+	9.11059i	0.848882	+	0.350407i
$677$	−5.17890	+	7.12815i	−0.199041	+	0.273957i	−0.896857	−	0.442320i	$-0.854155\pi$
$677$	−5.17890	+	7.12815i	−0.199041	+	0.273957i	0.697816	+	0.716277i	$0.254155\pi$
$678$	−3.12551	+	15.7632i	−0.120035	+	0.605382i
$679$	7.03595	+	21.6544i	0.270015	+	0.831021i
$680$	−5.95734	+	8.95117i	−0.228454	+	0.343262i
$681$		−	4.10828i		−	0.157430i
$682$	11.1321	+	22.2575i	0.426269	+	0.852283i
$683$			24.3800i			0.932875i	0.884554	+	0.466438i	$0.154463\pi$
$683$			24.3800i			0.932875i	−0.884554	+	0.466438i	$0.845537\pi$
$684$	−5.56380	+	6.53048i	−0.212737	+	0.249699i
$685$	−2.77190	−	8.53102i	−0.105909	−	0.325954i
$686$	−25.2584	−	5.00821i	−0.964369	−	0.191214i
$687$	0.944481	−	1.29997i	0.0360342	−	0.0495968i
$688$	26.3906	+	4.11395i	1.00613	+	0.156843i
$689$	11.8004	+	3.83417i	0.449558	+	0.146070i
$690$	−9.60431	+	4.43475i	−0.365630	+	0.168828i
$691$	1.04830	+	1.44287i	0.0398794	+	0.0548893i	0.828491	−	0.560002i	$-0.189200\pi$
$691$	1.04830	+	1.44287i	0.0398794	+	0.0548893i	−0.788612	+	0.614892i	$0.789200\pi$
$692$	−8.97624	−	37.1890i	−0.341225	−	1.41371i
$693$	4.34715	+	2.95576i	0.165134	+	0.112280i
$694$	0.803236	+	6.75126i	0.0304904	+	0.256274i
$695$	10.8877	−	7.91038i	0.412994	−	0.300058i
$696$	1.37152	−	1.08529i	0.0519872	−	0.0411377i
$697$	−0.0912121	+	0.280722i	−0.00345491	+	0.0106331i
$698$	25.9098	+	14.4894i	0.980699	+	0.548433i
$699$	9.11100	+	6.61953i	0.344610	+	0.250374i
$700$	−1.02733	+	13.2601i	−0.0388295	+	0.501183i
$701$	32.1497	−	10.4461i	1.21428	−	0.394542i	0.369282	−	0.929317i	$-0.379604\pi$
$701$	32.1497	−	10.4461i	1.21428	−	0.394542i	0.844995	+	0.534775i	$0.179604\pi$
$702$	0.989611	+	1.06925i	0.0373505	+	0.0403562i
$703$	−12.8294			−0.483870
$704$	−11.0016	−	24.1447i	−0.414637	−	0.909987i
$705$	−1.40611			−0.0529571
$706$	6.78671	+	7.33286i	0.255421	+	0.275976i
$707$	−12.5699	+	4.08422i	−0.472741	+	0.153603i
$708$	−1.26886	+	16.3775i	−0.0476865	+	0.615504i
$709$	2.04093	+	1.48282i	0.0766487	+	0.0556886i	0.625450	−	0.780264i	$-0.284916\pi$
$709$	2.04093	+	1.48282i	0.0766487	+	0.0556886i	−0.548801	+	0.835953i	$0.684916\pi$
$710$	7.09536	+	3.96792i	0.266284	+	0.148913i
$711$	−2.39033	+	7.35666i	−0.0896442	+	0.275896i
$712$	−6.67359	+	5.28084i	−0.250103	+	0.197908i
$713$	35.7990	−	26.0095i	1.34068	−	0.974063i
$714$	−1.12242	−	9.43403i	−0.0420055	−	0.353060i
$715$	−1.87774	−	2.42191i	−0.0702237	−	0.0905743i
$716$	−1.10575	−	4.58118i	−0.0413238	−	0.171207i
$717$	2.33987	+	3.22055i	0.0873840	+	0.120274i
$718$	18.0528	−	8.33582i	0.673726	−	0.311090i
$719$	−35.8763	−	11.6569i	−1.33796	−	0.434730i	−0.449335	−	0.893363i	$-0.648339\pi$
$719$	−35.8763	−	11.6569i	−1.33796	−	0.434730i	−0.888626	+	0.458633i	$0.848339\pi$
$720$	−3.54485	−	0.552595i	−0.132109	−	0.0205940i
$721$	14.6186	−	20.1207i	0.544424	−	0.749336i
$722$	0.831283	+	0.164826i	0.0309372	+	0.00613419i
$723$	−3.28068	−	10.0969i	−0.122010	−	0.375508i
$724$	−30.4897	+	35.7871i	−1.13314	+	1.33002i
$725$		−	2.59433i		−	0.0963511i
$726$	−10.7360	+	11.2578i	−0.398452	+	0.417815i
$727$		−	36.4726i		−	1.35269i	−0.736584	−	0.676347i	$-0.763562\pi$
$727$		−	36.4726i		−	1.35269i	0.736584	−	0.676347i	$-0.236438\pi$
$728$	−2.55883	+	3.84476i	−0.0948366	+	0.142496i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	1.10299	−	5.56280i	0.0408234	−	0.205889i
$731$	−16.6353	+	22.8965i	−0.615278	+	0.846857i
$732$	23.6352	+	9.75629i	0.873582	+	0.360603i
$733$	10.7638	+	3.49738i	0.397571	+	0.129179i	0.500977	−	0.865461i	$-0.332974\pi$
$733$	10.7638	+	3.49738i	0.397571	+	0.129179i	−0.103406	+	0.994639i	$0.532974\pi$
$734$	10.6518	+	23.0685i	0.393165	+	0.851475i
$735$	−2.36594	−	3.25644i	−0.0872690	−	0.120115i
$736$	−39.1473	+	26.3303i	−1.44299	+	0.970546i
$737$	−28.1316	−	36.2841i	−1.03624	−	1.33654i
$738$	−0.0977970	+	0.0116355i	−0.00359996	+	0.000428308i
$739$	40.1538	−	29.1734i	1.47708	−	1.07316i	0.498598	−	0.866833i	$-0.333848\pi$
$739$	40.1538	−	29.1734i	1.47708	−	1.07316i	0.978483	−	0.206329i	$-0.0661516\pi$
$740$	−2.80878	−	4.57100i	−0.103253	−	0.168033i
$741$	−1.36559	+	4.20286i	−0.0501663	+	0.154396i
$742$	13.1768	−	23.5625i	0.483734	−	0.865006i
$743$	33.8825	+	24.6171i	1.24303	+	0.903113i	0.997796	−	0.0663513i	$-0.0211358\pi$
$743$	33.8825	+	24.6171i	1.24303	+	0.903113i	0.245232	+	0.969464i	$0.421136\pi$
$744$	14.9942	−	0.616579i	0.549715	−	0.0226049i
$745$	14.7739	−	4.80034i	0.541275	−	0.175871i
$746$	24.0087	−	22.2206i	0.879022	−	0.813553i
$747$	15.4639			0.565793
$748$	28.0848	+	1.29654i	1.02688	+	0.0474064i
$749$	−11.4164			−0.417148
$750$	−8.56024	+	7.92268i	−0.312576	+	0.289296i
$751$	7.26705	−	2.36121i	0.265178	−	0.0861616i	−0.173410	−	0.984850i	$-0.555479\pi$
$751$	7.26705	−	2.36121i	0.265178	−	0.0861616i	0.438588	+	0.898688i	$0.355479\pi$
$752$	−6.19125	+	0.996073i	−0.225772	+	0.0363231i
$753$	−7.27290	−	5.28407i	−0.265039	−	0.192562i
$754$	0.439717	−	0.786295i	0.0160136	−	0.0286352i
$755$	−2.31196	+	7.11547i	−0.0841408	+	0.258959i
$756$	2.70084	−	1.65961i	0.0982284	−	0.0603593i
$757$	28.7250	−	20.8699i	1.04403	−	0.758531i	0.0729604	−	0.997335i	$-0.476755\pi$
$757$	28.7250	−	20.8699i	1.04403	−	0.758531i	0.971068	+	0.238804i	$0.0767553\pi$
$758$	−48.0810	+	5.72047i	−1.74638	+	0.207777i
$759$	22.8741	+	15.5528i	0.830278	+	0.564532i
$760$	−3.78515	−	10.2026i	−0.137302	−	0.370088i
$761$	−27.8808	−	38.3747i	−1.01068	−	1.39108i	−0.918537	−	0.395335i	$-0.870629\pi$
$761$	−27.8808	−	38.3747i	−1.01068	−	1.39108i	−0.0921424	−	0.995746i	$-0.529371\pi$
$762$	−5.79555	−	12.5514i	−0.209951	−	0.454689i
$763$	2.36839	+	0.769537i	0.0857416	+	0.0278591i
$764$	5.96785	−	14.4575i	0.215909	−	0.523053i
$765$	2.23449	−	3.07551i	0.0807880	−	0.111195i
$766$	4.31280	−	21.7512i	0.155828	−	0.785901i
$767$	2.61469	+	8.04719i	0.0944111	+	0.290567i
$768$	−15.9998	+	0.0779975i	−0.577343	+	0.00281449i
$769$		−	18.3147i		−	0.660444i	−0.943903	−	0.330222i	$-0.892876\pi$
$769$		−	18.3147i		−	0.660444i	0.943903	−	0.330222i	$-0.107124\pi$
$770$	−5.96361	+	2.98269i	−0.214914	+	0.107489i
$771$		−	18.8426i		−	0.678601i
$772$	−38.9126	−	33.1525i	−1.40049	−	1.19319i
$773$	0.791057	+	2.43462i	0.0284524	+	0.0875674i	0.964274	−	0.264906i	$-0.0853408\pi$
$773$	0.791057	+	2.43462i	0.0284524	+	0.0875674i	−0.935822	+	0.352473i	$0.885341\pi$
$774$	−9.26286	−	1.83663i	−0.332947	−	0.0660163i
$775$	13.0844	−	18.0091i	0.470004	−	0.646905i
$776$	−10.9574	+	39.1257i	−0.393348	+	1.40453i
$777$	4.50839	+	1.46487i	0.161738	+	0.0525518i
$778$	−2.40798	+	1.11188i	−0.0863304	+	0.0398627i
$779$	−0.175590	−	0.241679i	−0.00629116	−	0.00865904i
$780$	−1.79642	+	0.433598i	−0.0643220	+	0.0155253i
$781$	−0.662852	−	21.2462i	−0.0237187	−	0.760249i
$782$	−5.90603	−	49.6407i	−0.211199	−	1.77515i
$783$	−0.500260	+	0.363460i	−0.0178778	+	0.0129890i
$784$	−12.7243	−	12.6624i	−0.454440	−	0.452230i
$785$	−0.00297768	+	0.00916436i	−0.000106278	+	0.000327090i
$786$	12.5422	+	7.01391i	0.447364	+	0.250178i
$787$	17.2890	+	12.5612i	0.616285	+	0.447757i	0.851622	−	0.524157i	$-0.175619\pi$
$787$	17.2890	+	12.5612i	0.616285	+	0.447757i	−0.235337	+	0.971914i	$0.575619\pi$
$788$	−22.7049	−	1.75907i	−0.808828	−	0.0626644i
$789$	−16.6806	+	5.41984i	−0.593844	+	0.192952i
$790$	−6.66453	−	7.20084i	−0.237113	−	0.256194i
$791$	18.0107			0.640386
$792$	3.53562	+	8.68904i	0.125633	+	0.308751i
$793$	13.1709			0.467713
$794$	−19.0436	−	20.5761i	−0.675832	−	0.730218i
$795$	10.2737	−	3.33812i	0.364369	−	0.118391i
$796$	−33.3853	−	2.58654i	−1.18331	−	0.0916775i
$797$	1.47840	+	1.07412i	0.0523675	+	0.0380472i	0.613661	−	0.789570i	$-0.289696\pi$
$797$	1.47840	+	1.07412i	0.0523675	+	0.0380472i	−0.561294	+	0.827617i	$0.689696\pi$
$798$	8.39212	+	4.69309i	0.297078	+	0.166134i
$799$	2.05332	−	6.31948i	0.0726413	−	0.223567i
$800$	−14.6365	+	18.6831i	−0.517477	+	0.660546i
$801$	2.43419	−	1.76854i	0.0860078	−	0.0624883i
$802$	1.80548	+	15.1752i	0.0637538	+	0.535855i
$803$	−13.9530	+	5.01980i	−0.492390	+	0.177145i
$804$	−26.9132	+	6.49599i	−0.949156	+	0.229096i
$805$	6.96891	+	9.59188i	0.245622	+	0.338069i
$806$	7.01801	−	3.24054i	0.247199	−	0.114143i
$807$	12.0493	+	3.91504i	0.424154	+	0.137816i
$808$	−22.7116	−	6.36055i	−0.798993	−	0.223763i
$809$	−8.16002	+	11.2313i	−0.286891	+	0.394872i	−0.928001	−	0.372577i	$-0.878474\pi$
$809$	−8.16002	+	11.2313i	−0.286891	+	0.394872i	0.641110	+	0.767449i	$0.278474\pi$
$810$	1.24421	+	0.246700i	0.0437170	+	0.00866817i
$811$	−10.5825	−	32.5697i	−0.371603	−	1.14368i	−0.945742	−	0.324919i	$-0.894663\pi$
$811$	−10.5825	−	32.5697i	−0.371603	−	1.14368i	0.574139	−	0.818758i	$-0.305337\pi$
$812$	−1.49208	−	1.27121i	−0.0523617	−	0.0446109i
$813$		−	24.1797i		−	0.848018i
$814$	−6.46185	+	12.4512i	−0.226488	+	0.436415i
$815$			11.4466i			0.400956i
$816$	7.66003	−	15.1247i	0.268155	−	0.529469i
$817$	−8.85124	−	27.2413i	−0.309666	−	0.953052i
$818$	−1.13364	+	5.71742i	−0.0396369	+	0.199905i
$819$	0.959770	−	1.32101i	0.0335371	−	0.0461598i
$820$	0.0476655	−	0.115473i	0.00166455	−	0.00403247i
$821$	−17.2622	−	5.60881i	−0.602453	−	0.195749i	−0.00811908	−	0.999967i	$-0.502584\pi$
$821$	−17.2622	−	5.60881i	−0.602453	−	0.195749i	−0.594334	+	0.804218i	$0.702584\pi$
$822$	5.92916	+	12.8407i	0.206803	+	0.447873i
$823$	−33.1901	−	45.6823i	−1.15693	−	1.59238i	−0.721947	−	0.691948i	$-0.756753\pi$
$823$	−33.1901	−	45.6823i	−1.15693	−	1.59238i	−0.434987	−	0.900436i	$-0.643247\pi$
$824$	41.6104	−	15.4374i	1.44957	−	0.537786i
$825$	13.3616	+	3.88521i	0.465193	+	0.135266i
$826$	18.2813	−	2.17503i	0.636087	−	0.0756790i
$827$	3.49657	−	2.54041i	0.121588	−	0.0883387i	−0.525329	−	0.850899i	$-0.676058\pi$
$827$	3.49657	−	2.54041i	0.121588	−	0.0883387i	0.646917	+	0.762560i	$0.276058\pi$
$828$	14.2114	−	8.73263i	0.493882	−	0.303480i
$829$	0.143533	−	0.441750i	0.00498512	−	0.0153426i	−0.948533	−	0.316678i	$-0.897432\pi$
$829$	0.143533	−	0.441750i	0.00498512	−	0.0153426i	0.953518	+	0.301336i	$0.0974325\pi$
$830$	−9.57379	+	17.1197i	−0.332311	+	0.594233i
$831$	−9.18010	−	6.66973i	−0.318454	−	0.231370i
$832$	−7.60266	+	3.18174i	−0.263575	+	0.110307i
$833$	18.0904	−	5.87791i	0.626794	−	0.203658i
$834$	−15.5734	+	14.4135i	−0.539263	+	0.499100i
$835$	−16.2895			−0.563723
$836$	−17.7687	+	22.2240i	−0.614542	+	0.768634i
$837$	−5.30574			−0.183393
$838$	−7.69000	+	7.11725i	−0.265646	+	0.245861i
$839$	−46.8242	+	15.2141i	−1.61655	+	0.525249i	−0.971125	−	0.238573i	$-0.923320\pi$
$839$	−46.8242	+	15.2141i	−1.61655	+	0.525249i	−0.645427	+	0.763822i	$0.723320\pi$
$840$	0.165205	+	4.01751i	0.00570010	+	0.138617i
$841$	−23.1522	−	16.8210i	−0.798350	−	0.580035i
$842$	0.844122	−	1.50944i	0.0290904	−	0.0520189i
$843$	−4.18689	+	12.8859i	−0.144204	+	0.443815i
$844$	−2.36097	−	3.84224i	−0.0812681	−	0.132255i
$845$	8.66295	−	6.29400i	0.298015	−	0.216520i
$846$	2.20156	−	0.261932i	0.0756912	−	0.00900541i
$847$	14.7165	+	9.34879i	0.505666	+	0.321228i
$848$	42.8714	−	21.9758i	1.47221	−	0.754653i
$849$	14.4424	+	19.8782i	0.495661	+	0.682219i
$850$	−10.5425	−	22.8319i	−0.361606	−	0.783129i
$851$	23.7226	+	7.70794i	0.813200	+	0.264225i
$852$	−11.8484	−	4.89087i	−0.405920	−	0.167558i
$853$	3.74183	−	5.15019i	0.128118	−	0.176339i	−0.740139	−	0.672454i	$-0.765240\pi$
$853$	3.74183	−	5.15019i	0.128118	−	0.176339i	0.868257	+	0.496115i	$0.165240\pi$
$854$	5.57366	−	28.1102i	0.190727	−	0.961911i
$855$	1.18892	+	3.65911i	0.0406601	+	0.125139i
$856$	−16.9600	−	11.2875i	−0.579679	−	0.385798i
$857$		−	36.2659i		−	1.23882i	−0.785067	−	0.619410i	$-0.787372\pi$
$857$		−	36.2659i		−	1.23882i	0.785067	−	0.619410i	$-0.212628\pi$
$858$	3.39116	+	3.44222i	0.115772	+	0.117515i
$859$			7.69096i			0.262412i	0.991355	+	0.131206i	$0.0418850\pi$
$859$			7.69096i			0.262412i	−0.991355	+	0.131206i	$0.958115\pi$
$860$	7.76800	−	9.11764i	0.264887	−	0.310909i
$861$	0.0341093	+	0.104978i	0.00116244	+	0.00357762i
$862$	27.0023	+	5.35398i	0.919700	+	0.182357i
$863$	19.8376	−	27.3041i	0.675280	−	0.929443i	−0.324586	−	0.945856i	$-0.605225\pi$
$863$	19.8376	−	27.3041i	0.675280	−	0.929443i	0.999865	+	0.0164137i	$0.00522487\pi$
$864$	5.65314	+	0.204864i	0.192324	+	0.00696962i
$865$	−16.3169	−	5.30169i	−0.554792	−	0.180263i
$866$	21.0034	−	9.69824i	0.713726	−	0.329559i
$867$	0.566908	+	0.780282i	0.0192532	+	0.0264998i
$868$	−3.94627	−	16.3496i	−0.133945	−	0.554941i
$869$	−7.16310	+	24.6346i	−0.242992	+	0.835673i
$870$	−0.0926639	−	0.778847i	−0.00314160	−	0.0264054i
$871$	−11.5375	+	8.38246i	−0.390932	+	0.284029i
$872$	2.75757	+	3.48484i	0.0933832	+	0.118012i
$873$	4.43911	−	13.6622i	0.150241	−	0.462394i
$874$	44.1582	+	24.6945i	1.49367	+	0.835303i
$875$	10.5758	+	7.68378i	0.357528	+	0.259759i
$876$	−0.690710	+	8.91520i	−0.0233369	+	0.301217i
$877$	−17.3624	+	5.64139i	−0.586287	+	0.190496i	−0.587115	−	0.809503i	$-0.699736\pi$
$877$	−17.3624	+	5.64139i	−0.586287	+	0.190496i	0.000827907		1.00000i	$0.499736\pi$
$878$	14.1251	+	15.2618i	0.476699	+	0.515060i
$879$	5.71689			0.192826
$880$	−11.8084	−	1.46524i	−0.398060	−	0.0493932i
$881$	37.3245			1.25749			0.628747	−	0.777610i	$-0.283568\pi$
$881$	37.3245			1.25749			0.628747	+	0.777610i	$0.283568\pi$
$882$	4.31099	+	4.65790i	0.145159	+	0.156840i
$883$	7.36835	−	2.39412i	0.247965	−	0.0805686i	−0.182398	−	0.983225i	$-0.558386\pi$
$883$	7.36835	−	2.39412i	0.247965	−	0.0805686i	0.430362	+	0.902656i	$0.358386\pi$
$884$	0.674565	−	8.70681i	0.0226881	−	0.292842i
$885$	5.95972	+	4.32999i	0.200334	+	0.145551i
$886$	9.08817	+	5.08235i	0.305323	+	0.170745i
$887$	−12.3998	+	38.1626i	−0.416344	+	1.28138i	0.494699	+	0.869065i	$0.335278\pi$
$887$	−12.3998	+	38.1626i	−0.416344	+	1.28138i	−0.911043	+	0.412311i	$0.864722\pi$
$888$	5.24923	+	6.63363i	0.176152	+	0.222610i
$889$	−12.5352	+	9.10732i	−0.420416	+	0.305450i
$890$	0.450889	+	3.78975i	0.0151138	+	0.127033i
$891$	−1.12276	−	3.12080i	−0.0376138	−	0.104551i
$892$	2.45349	+	10.1649i	0.0821491	+	0.340348i
$893$	3.95279	+	5.44055i	0.132275	+	0.182061i
$894$	−22.2375	+	10.2681i	−0.743732	+	0.343415i
$895$	−2.01002	−	0.653096i	−0.0671877	−	0.0218306i
$896$	3.57337	+	17.5725i	0.119378	+	0.587056i
$897$	5.05019	−	6.95098i	0.168621	−	0.232087i
$898$	−7.73613	−	1.53391i	−0.258158	−	0.0511873i
$899$	1.01383	+	3.12025i	0.0338132	+	0.104066i
$900$	5.44179	−	6.38727i	0.181393	−	0.212909i
$901$			51.0475i			1.70064i
$902$	−0.322995	+	0.0486863i	−0.0107546	+	0.00162108i
$903$			10.5835i			0.352198i
$904$	26.7562	+	17.8072i	0.889896	+	0.592260i
$905$	6.51528	+	20.0520i	0.216575	+	0.666550i
$906$	2.29437	−	11.5714i	0.0762255	−	0.384435i
$907$	−28.1825	+	38.7899i	−0.935784	+	1.28800i	0.0217756	+	0.999763i	$0.493068\pi$
$907$	−28.1825	+	38.7899i	−0.935784	+	1.28800i	−0.957560	+	0.288234i	$0.906932\pi$
$908$	−7.59494	−	3.13509i	−0.252047	−	0.104042i
$909$	7.93060	+	2.57681i	0.263041	+	0.0854674i
$910$	0.868260	+	1.88039i	0.0287825	+	0.0623342i
$911$	12.8537	+	17.6916i	0.425863	+	0.586150i	0.966997	−	0.254786i	$-0.0820051\pi$
$911$	12.8537	+	17.6916i	0.425863	+	0.586150i	−0.541135	+	0.840936i	$0.682005\pi$
$912$	7.82701	+	15.2692i	0.259178	+	0.505615i
$913$	51.2629	−	1.59933i	1.69655	−	0.0529301i
$914$	−25.9515	+	3.08760i	−0.858399	+	0.102129i
$915$	9.27693	−	6.74008i	0.306686	−	0.222820i
$916$	−1.68249	−	2.73808i	−0.0555910	−	0.0904686i
$917$	4.97686	−	15.3172i	0.164350	−	0.505819i
$918$	−2.92565	+	5.23159i	−0.0965607	+	0.172668i
$919$	−26.8892	−	19.5362i	−0.886993	−	0.644438i	0.0480990	−	0.998843i	$-0.484684\pi$
$919$	−26.8892	−	19.5362i	−0.886993	−	0.644438i	−0.935092	+	0.354404i	$0.884684\pi$
$920$	0.869285	+	21.1396i	0.0286595	+	0.696952i
$921$	−7.26075	+	2.35916i	−0.239250	+	0.0777370i
$922$	18.2998	−	16.9369i	0.602673	−	0.557786i
$923$	−6.60264			−0.217329
$924$	8.78166	−	5.78094i	0.288895	−	0.190179i
$925$	12.5481			0.412578
$926$	−13.7686	+	12.7432i	−0.452466	+	0.418766i
$927$	−14.9233	+	4.84888i	−0.490146	+	0.159258i
$928$	−0.959736	−	3.36371i	−0.0315049	−	0.110419i
$929$	−20.7577	−	15.0813i	−0.681038	−	0.494803i	0.192664	−	0.981265i	$-0.438287\pi$
$929$	−20.7577	−	15.0813i	−0.681038	−	0.494803i	−0.873702	+	0.486462i	$0.838287\pi$
$930$	3.28482	−	5.87386i	0.107714	−	0.192612i
$931$	−5.94886	+	18.3087i	−0.194966	+	0.600044i
$932$	19.1902	−	11.7920i	0.628596	−	0.386259i
$933$	−17.1582	+	12.4661i	−0.561733	+	0.408123i
$934$	−30.6918	+	3.65158i	−1.00427	+	0.119483i
$935$	7.08927	−	10.4264i	0.231844	−	0.340981i
$936$	2.73189	−	1.01353i	0.0892948	−	0.0331282i
$937$	0.340605	+	0.468802i	0.0111271	+	0.0153151i	0.814544	−	0.580101i	$-0.196987\pi$
$937$	0.340605	+	0.468802i	0.0111271	+	0.0153151i	−0.803417	+	0.595416i	$0.796987\pi$
$938$	13.0079	+	28.1712i	0.424724	+	0.919823i
$939$	4.11249	+	1.33623i	0.134206	+	0.0436061i
$940$	−1.07302	+	2.59946i	−0.0349981	+	0.0847851i
$941$	−29.1003	+	40.0531i	−0.948643	+	1.30569i	0.00348491	+	0.999994i	$0.498891\pi$
$941$	−29.1003	+	40.0531i	−0.948643	+	1.30569i	−0.952128	+	0.305701i	$0.901109\pi$
$942$	0.00295503	−	0.0149034i	9.62802e−5	−	0.000485580i
$943$	0.179479	+	0.552378i	0.00584463	+	0.0179879i
$944$	29.3086	+	14.8436i	0.953915	+	0.483119i
$945$		−	1.42160i		−	0.0462448i
$946$	−30.8965	−	5.13045i	−1.00453	−	0.166805i
$947$		−	36.6649i		−	1.19145i	−0.803189	−	0.595725i	$-0.796865\pi$
$947$		−	36.6649i		−	1.19145i	0.803189	−	0.595725i	$-0.203135\pi$
$948$	11.7761	+	10.0329i	0.382470	+	0.325855i
$949$	1.42333	+	4.38054i	0.0462031	+	0.142198i
$950$	24.9659	+	4.95021i	0.810001	+	0.160606i
$951$	−4.15205	+	5.71480i	−0.134639	+	0.185315i
$952$	−18.2971	−	5.12424i	−0.593014	−	0.166077i
$953$	29.3372	+	9.53224i	0.950326	+	0.308780i	0.742848	−	0.669460i	$-0.233474\pi$
$953$	29.3372	+	9.53224i	0.950326	+	0.308780i	0.207478	+	0.978240i	$0.433474\pi$
$954$	−15.4637	+	7.14031i	−0.500657	+	0.231176i
$955$	−4.12286	−	5.67463i	−0.133413	−	0.183627i
$956$	7.73940	−	1.86804i	0.250310	−	0.0604168i
$957$	−1.62078	+	1.25661i	−0.0523922	+	0.0406205i
$958$	−5.94406	−	49.9603i	−0.192044	−	1.61414i
$959$	12.8241	−	9.31728i	0.414113	−	0.300871i
$960$	−3.72670	+	6.13164i	−0.120279	+	0.197898i
$961$	0.880437	−	2.70971i	0.0284012	−	0.0874099i
$962$	3.80309	+	2.12679i	0.122616	+	0.0685704i
$963$	5.82722	+	4.23372i	0.187780	+	0.136430i
$964$	−21.1696	−	1.64013i	−0.681827	−	0.0528249i
$965$	−21.8032	+	7.08430i	−0.701871	+	0.228052i
$966$	−12.6981	−	13.7199i	−0.408554	−	0.441431i
$967$	14.2448			0.458082			0.229041	−	0.973417i	$-0.426441\pi$
$967$	14.2448			0.458082			0.229041	+	0.973417i	$0.426441\pi$
$968$	12.6193	+	28.4386i	0.405599	+	0.914051i
$969$	−18.1813			−0.584068
$970$	12.3768	+	13.3728i	0.397395	+	0.429374i
$971$	19.0385	−	6.18597i	0.610973	−	0.198517i	0.0128447	−	0.999918i	$-0.495911\pi$
$971$	19.0385	−	6.18597i	0.610973	−	0.198517i	0.598128	+	0.801400i	$0.295911\pi$
$972$	−1.99402	−	0.154488i	−0.0639584	−	0.00495521i
$973$	19.2403	+	13.9789i	0.616815	+	0.448143i
$974$	−16.8925	−	9.44673i	−0.541270	−	0.302693i
$975$	1.33565	−	4.11070i	0.0427749	−	0.131648i
$976$	36.0727	−	36.2490i	1.15466	−	1.16030i
$977$	−19.9486	+	14.4935i	−0.638211	+	0.463687i	−0.859235	−	0.511581i	$-0.829060\pi$
$977$	−19.9486	+	14.4935i	−0.638211	+	0.463687i	0.221024	+	0.975268i	$0.429060\pi$
$978$	−2.13228	−	17.9220i	−0.0681829	−	0.573082i
$979$	7.88645	−	6.11449i	0.252052	−	0.195420i
$980$	−7.82563	+	1.88886i	−0.249980	+	0.0603373i
$981$	−0.923504	−	1.27109i	−0.0294852	−	0.0405829i
$982$	12.7791	−	5.90071i	0.407799	−	0.188299i
$983$	6.72347	+	2.18459i	0.214445	+	0.0696775i	0.414270	−	0.910154i	$-0.364037\pi$
$983$	6.72347	+	2.18459i	0.214445	+	0.0696775i	−0.199824	+	0.979832i	$0.564037\pi$
$984$	−0.0531199	+	0.189676i	−0.00169340	+	0.00604664i
$985$	−6.00287	+	8.26224i	−0.191267	+	0.263257i
$986$	3.63569	+	0.720880i	0.115784	+	0.0229575i
$987$	−0.767851	−	2.36320i	−0.0244410	−	0.0752216i
$988$	6.72769	+	5.73183i	0.214036	+	0.182354i
$989$			55.6892i			1.77081i
$990$	4.15008	+	0.689134i	0.131898	+	0.0219021i
$991$		−	22.2482i		−	0.706736i	−0.935484	−	0.353368i	$-0.885036\pi$
$991$		−	22.2482i		−	0.706736i	0.935484	−	0.353368i	$-0.114964\pi$
$992$	10.3024	−	28.1902i	0.327103	−	0.895039i
$993$	2.23148	+	6.86778i	0.0708138	+	0.217942i
$994$	−2.79410	+	14.0918i	−0.0886234	+	0.446963i
$995$	−8.82662	+	12.1488i	−0.279823	+	0.385143i
$996$	11.8007	−	28.5879i	0.373919	−	0.905841i
$997$	−34.5506	−	11.2262i	−1.09423	−	0.355536i	−0.294349	−	0.955698i	$-0.595103\pi$
$997$	−34.5506	−	11.2262i	−1.09423	−	0.355536i	−0.799878	+	0.600162i	$0.795103\pi$
$998$	10.5724	+	22.8967i	0.334665	+	0.724783i
$999$	−1.75795	−	2.41961i	−0.0556192	−	0.0765532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.j.a.19.10	yes	48
3.2	odd	2		396.2.r.b.19.3		48
4.3	odd	2	inner	132.2.j.a.19.9	yes	48
11.7	odd	10	inner	132.2.j.a.7.9	✓	48
12.11	even	2		396.2.r.b.19.4		48
33.29	even	10		396.2.r.b.271.4		48
44.7	even	10	inner	132.2.j.a.7.10	yes	48
132.95	odd	10		396.2.r.b.271.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.9	✓	48	11.7	odd	10	inner
132.2.j.a.7.10	yes	48	44.7	even	10	inner
132.2.j.a.19.9	yes	48	4.3	odd	2	inner
132.2.j.a.19.10	yes	48	1.1	even	1	trivial
396.2.r.b.19.3		48	3.2	odd	2
396.2.r.b.19.4		48	12.11	even	2
396.2.r.b.271.3		48	132.95	odd	10
396.2.r.b.271.4		48	33.29	even	10

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.960602 + 1.03790i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.154488 + 1.99402i) q^{4} +(0.725620 + 0.527194i) q^{5} +(-1.23432 - 0.690263i) q^{6} +(-0.489790 + 1.50742i) q^{7} +(-2.21801 + 1.75512i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.960602 + 1.03790i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.154488 + 1.99402i) q^{4} +(0.725620 + 0.527194i) q^{5} +(-1.23432 - 0.690263i) q^{6} +(-0.489790 + 1.50742i) q^{7} +(-2.21801 + 1.75512i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.149856 + 1.25955i) q^{10} +(2.62111 - 2.03219i) q^{11} +(-0.469260 - 1.94417i) q^{12} +(-0.605536 - 0.833449i) q^{13} +(-2.03505 + 0.939673i) q^{14} +(-0.853017 - 0.277162i) q^{15} +(-3.95227 - 0.616106i) q^{16} +(2.49130 - 3.42898i) q^{17} +(1.38721 + 0.275054i) q^{18} +(1.32556 + 4.07966i) q^{19} +(-1.16334 + 1.36546i) q^{20} -1.58499i q^{21} +(4.62706 + 0.768337i) q^{22} -8.34003i q^{23} +(1.56709 - 2.35462i) q^{24} +(-1.29649 - 3.99020i) q^{25} +(0.283361 - 1.42910i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-2.93016 - 1.20953i) q^{28} +(0.588090 + 0.191082i) q^{29} +(-0.531742 - 1.15159i) q^{30} +(3.11863 + 4.29243i) q^{31} +(-3.15710 - 4.69391i) q^{32} +(-1.86484 + 2.74269i) q^{33} +(5.95210 - 0.708155i) q^{34} +(-1.15010 + 0.835598i) q^{35} +(1.04707 + 1.70401i) q^{36} +(-0.924210 + 2.84443i) q^{37} +(-2.96096 + 5.29474i) q^{38} +(0.833449 + 0.605536i) q^{39} +(-2.53472 + 0.104230i) q^{40} +(-0.0662322 + 0.0215201i) q^{41} +(1.64507 - 1.52255i) q^{42} -6.67734 q^{43} +(3.64730 + 5.54051i) q^{44} +0.896916 q^{45} +(8.65614 - 8.01144i) q^{46} +(1.49099 - 0.484451i) q^{47} +(3.94922 - 0.635366i) q^{48} +(3.63071 + 2.63786i) q^{49} +(2.89603 - 5.17863i) q^{50} +(-1.30975 + 4.03101i) q^{51} +(1.75547 - 1.07870i) q^{52} +(-9.74373 + 7.07923i) q^{53} +(-1.40431 + 0.167079i) q^{54} +(2.97329 - 0.0927624i) q^{55} +(-1.55934 - 4.20310i) q^{56} +(-2.52137 - 3.47037i) q^{57} +(0.366596 + 0.793935i) q^{58} +(-7.81130 - 2.53804i) q^{59} +(0.684449 - 1.65812i) q^{60} +(-7.51474 + 10.3431i) q^{61} +(-1.45936 + 7.36016i) q^{62} +(0.489790 + 1.50742i) q^{63} +(1.83911 - 7.78574i) q^{64} -0.924002i q^{65} +(-4.63802 + 0.699107i) q^{66} -13.8430i q^{67} +(6.45259 + 5.49745i) q^{68} +(2.57721 + 7.93184i) q^{69} +(-1.97206 - 0.391018i) q^{70} +(3.76717 - 5.18506i) q^{71} +(-0.762772 + 2.72363i) q^{72} +(-4.25213 - 1.38160i) q^{73} +(-3.84004 + 1.77312i) q^{74} +(2.46608 + 3.39427i) q^{75} +(-8.33973 + 2.01294i) q^{76} +(1.77956 + 4.94645i) q^{77} +(0.172124 + 1.44672i) q^{78} +(-6.25795 + 4.54667i) q^{79} +(-2.54304 - 2.53067i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.0859586 - 0.0480703i) q^{82} +(12.5105 + 9.08942i) q^{83} +(3.16051 + 0.244863i) q^{84} +(3.61547 - 1.17474i) q^{85} +(-6.41427 - 6.93044i) q^{86} -0.618355 q^{87} +(-2.24691 + 9.10777i) q^{88} +3.00882 q^{89} +(0.861579 + 0.930912i) q^{90} +(1.55294 - 0.504581i) q^{91} +(16.6302 + 1.28844i) q^{92} +(-4.29243 - 3.11863i) q^{93} +(1.93506 + 1.08214i) q^{94} +(-1.18892 + 3.65911i) q^{95} +(4.45307 + 3.48857i) q^{96} +(11.6217 - 8.44368i) q^{97} +(0.749816 + 6.30226i) q^{98} +(0.926033 - 3.18472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} + 12 q^{9}+O(q^{10}) \) 48 * q - 4 * q^4 + 12 * q^9	\( 48 q - 4 q^{4} + 12 q^{9} + 8 q^{12} - 14 q^{14} - 24 q^{16} - 10 q^{18} - 22 q^{20} - 26 q^{22} - 30 q^{24} - 20 q^{25} - 38 q^{26} - 10 q^{28} - 20 q^{30} - 4 q^{33} + 4 q^{36} - 48 q^{37} + 58 q^{38} + 70 q^{40} - 40 q^{41} + 12 q^{42} + 34 q^{44} + 70 q^{46} - 16 q^{48} - 28 q^{49} + 70 q^{50} + 30 q^{52} - 64 q^{53} + 60 q^{56} - 54 q^{58} - 12 q^{60} - 40 q^{64} - 8 q^{66} + 4 q^{70} + 10 q^{72} + 20 q^{73} + 50 q^{74} - 8 q^{77} + 40 q^{78} + 58 q^{80} - 12 q^{81} + 62 q^{82} + 60 q^{84} + 40 q^{85} + 8 q^{86} + 8 q^{88} + 48 q^{89} + 20 q^{90} + 42 q^{92} + 24 q^{93} - 10 q^{94} + 50 q^{96} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 12 * q^9 + 8 * q^12 - 14 * q^14 - 24 * q^16 - 10 * q^18 - 22 * q^20 - 26 * q^22 - 30 * q^24 - 20 * q^25 - 38 * q^26 - 10 * q^28 - 20 * q^30 - 4 * q^33 + 4 * q^36 - 48 * q^37 + 58 * q^38 + 70 * q^40 - 40 * q^41 + 12 * q^42 + 34 * q^44 + 70 * q^46 - 16 * q^48 - 28 * q^49 + 70 * q^50 + 30 * q^52 - 64 * q^53 + 60 * q^56 - 54 * q^58 - 12 * q^60 - 40 * q^64 - 8 * q^66 + 4 * q^70 + 10 * q^72 + 20 * q^73 + 50 * q^74 - 8 * q^77 + 40 * q^78 + 58 * q^80 - 12 * q^81 + 62 * q^82 + 60 * q^84 + 40 * q^85 + 8 * q^86 + 8 * q^88 + 48 * q^89 + 20 * q^90 + 42 * q^92 + 24 * q^93 - 10 * q^94 + 50 * q^96 + 48 * q^97

Introduction

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