LMFDB - Embedded newform 483.2.n.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(47,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("483.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.n (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	483.47
Dual form			483.2.n.a.185.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.01952 - 1.16597i) q^{2} +(0.890949 + 1.48533i) q^{3} +(1.71897 + 2.97735i) q^{4} +(1.28353 - 2.22314i) q^{5} +(-0.0674375 - 4.03848i) q^{6} +(-0.527114 + 2.59271i) q^{7} -3.35320i q^{8} +(-1.41242 + 2.64671i) q^{9} +(-5.18423 + 2.99312i) q^{10} +(-4.14629 + 2.39386i) q^{11} +(-2.89083 + 5.20591i) q^{12} +5.43360i q^{13} +(4.08754 - 4.62143i) q^{14} +(4.44566 - 0.0742370i) q^{15} +(-0.471791 + 0.817165i) q^{16} +(-1.74375 - 3.02026i) q^{17} +(5.93839 - 3.69824i) q^{18} +(-6.42934 - 3.71198i) q^{19} +8.82542 q^{20} +(-4.32067 + 1.52703i) q^{21} +11.1647 q^{22} +(-0.866025 - 0.500000i) q^{23} +(4.98062 - 2.98754i) q^{24} +(-0.794906 - 1.37682i) q^{25} +(6.33542 - 10.9733i) q^{26} +(-5.18963 + 0.260175i) q^{27} +(-8.62550 + 2.88740i) q^{28} +4.21293i q^{29} +(-9.06466 - 5.03359i) q^{30} +(2.98453 - 1.72312i) q^{31} +(-3.90234 + 2.25302i) q^{32} +(-7.24981 - 4.02580i) q^{33} +8.13262i q^{34} +(5.08740 + 4.49968i) q^{35} +(-10.3081 + 0.344360i) q^{36} +(-0.0154961 + 0.0268401i) q^{37} +(8.65613 + 14.9928i) q^{38} +(-8.07070 + 4.84106i) q^{39} +(-7.45465 - 4.30394i) q^{40} -5.98000 q^{41} +(10.5061 + 1.95389i) q^{42} +2.44923 q^{43} +(-14.2547 - 8.22997i) q^{44} +(4.07113 + 6.53714i) q^{45} +(1.16597 + 2.01952i) q^{46} +(-3.44476 + 5.96650i) q^{47} +(-1.63410 + 0.0272875i) q^{48} +(-6.44430 - 2.73331i) q^{49} +3.70735i q^{50} +(2.93249 - 5.28094i) q^{51} +(-16.1777 + 9.34021i) q^{52} +(8.25130 - 4.76389i) q^{53} +(10.7839 + 5.52553i) q^{54} +12.2904i q^{55} +(8.69389 + 1.76752i) q^{56} +(-0.214694 - 12.8569i) q^{57} +(4.91215 - 8.50810i) q^{58} +(7.14409 + 12.3739i) q^{59} +(7.86301 + 13.1087i) q^{60} +(3.45906 + 1.99709i) q^{61} -8.03642 q^{62} +(-6.11765 - 5.05711i) q^{63} +12.3950 q^{64} +(12.0797 + 6.97420i) q^{65} +(9.94717 + 16.5833i) q^{66} +(0.991845 + 1.71793i) q^{67} +(5.99490 - 10.3835i) q^{68} +(-0.0289190 - 1.73181i) q^{69} +(-5.02761 - 15.0189i) q^{70} +7.28959i q^{71} +(8.87496 + 4.73613i) q^{72} +(7.27473 - 4.20007i) q^{73} +(0.0625895 - 0.0361361i) q^{74} +(1.33681 - 2.40737i) q^{75} -25.5232i q^{76} +(-4.02102 - 12.0120i) q^{77} +(21.9435 - 0.366428i) q^{78} +(-4.03398 + 6.98707i) q^{79} +(1.21112 + 2.09772i) q^{80} +(-5.01015 - 7.47653i) q^{81} +(12.0767 + 6.97250i) q^{82} -4.68166 q^{83} +(-11.9736 - 10.2392i) q^{84} -8.95261 q^{85} +(-4.94628 - 2.85573i) q^{86} +(-6.25760 + 3.75351i) q^{87} +(8.02711 + 13.9034i) q^{88} +(-4.81051 + 8.33205i) q^{89} +(-0.599609 - 17.9487i) q^{90} +(-14.0878 - 2.86413i) q^{91} -3.43795i q^{92} +(5.21846 + 2.89780i) q^{93} +(13.9135 - 8.03297i) q^{94} +(-16.5045 + 9.52890i) q^{95} +(-6.82326 - 3.78894i) q^{96} +1.08553i q^{97} +(9.82744 + 13.0338i) q^{98} +(-0.479560 - 14.3552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 20 q^{15} - 52 q^{16} - 10 q^{18} + 6 q^{19} - 6 q^{21} - 16 q^{22} - 66 q^{25} + 16 q^{28} - 32 q^{30} - 42 q^{31} - 30 q^{33} + 8 q^{36}+ \cdots + 24 q^{99}+O(q^{100}) $ 116 * q + 56 * q^4 - 10 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 20 * q^15 - 52 * q^16 - 10 * q^18 + 6 * q^19 - 6 * q^21 - 16 * q^22 - 66 * q^25 + 16 * q^28 - 32 * q^30 - 42 * q^31 - 30 * q^33 + 8 * q^36 - 2 * q^37 - 22 * q^39 - 36 * q^40 + 46 * q^42 + 20 * q^43 + 30 * q^45 - 22 * q^49 + 12 * q^51 + 48 * q^52 - 54 * q^54 - 44 * q^57 + 52 * q^58 + 32 * q^60 + 36 * q^61 - 38 * q^63 - 160 * q^64 + 10 * q^67 - 20 * q^70 + 62 * q^72 + 18 * q^73 + 78 * q^75 + 12 * q^78 + 10 * q^79 - 28 * q^81 + 32 * q^84 - 32 * q^85 - 30 * q^87 - 36 * q^88 + 50 * q^91 + 60 * q^94 + 84 * q^96 + 24 * q^99

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.01952	−	1.16597i	−1.42802	−	0.824465i	−0.431052	−	0.902327i	$-0.641857\pi$
$2$	−2.01952	−	1.16597i	−1.42802	−	0.824465i	−0.996964	+	0.0778617i	$0.975191\pi$
$3$	0.890949	+	1.48533i	0.514390	+	0.857556i
$3$	0.890949	+	1.48533i	0.514390	+	0.857556i
$4$	1.71897	+	2.97735i	0.859487	+	1.48867i
$5$	1.28353	−	2.22314i	0.574013	−	0.994219i	−0.422135	−	0.906533i	$-0.638719\pi$
$5$	1.28353	−	2.22314i	0.574013	−	0.994219i	0.996148	−	0.0876864i	$-0.0279473\pi$
$6$	−0.0674375	−	4.03848i	−0.0275312	−	1.64870i
$7$	−0.527114	+	2.59271i	−0.199230	+	0.979953i
$7$	−0.527114	+	2.59271i	−0.199230	+	0.979953i
$8$		−	3.35320i		−	1.18554i
$9$	−1.41242	+	2.64671i	−0.470806	+	0.882237i
$10$	−5.18423	+	2.99312i	−1.63940	+	0.946507i
$11$	−4.14629	+	2.39386i	−1.25015	+	0.721776i	−0.971140	−	0.238511i	$-0.923341\pi$
$11$	−4.14629	+	2.39386i	−1.25015	+	0.721776i	−0.279013	+	0.960287i	$0.590007\pi$
$12$	−2.89083	+	5.20591i	−0.834511	+	1.50282i
$13$			5.43360i			1.50701i	0.657442	+	0.753505i	$0.271638\pi$
$13$			5.43360i			1.50701i	−0.657442	+	0.753505i	$0.728362\pi$
$14$	4.08754	−	4.62143i	1.09244	−	1.23513i
$15$	4.44566	−	0.0742370i	1.14787	−	0.0191679i
$16$	−0.471791	+	0.817165i	−0.117948	+	0.204291i
$17$	−1.74375	−	3.02026i	−0.422921	−	0.732520i	0.573303	−	0.819343i	$-0.305662\pi$
$17$	−1.74375	−	3.02026i	−0.422921	−	0.732520i	−0.996224	+	0.0868235i	$0.972328\pi$
$18$	5.93839	−	3.69824i	1.39969	−	0.871685i
$19$	−6.42934	−	3.71198i	−1.47499	−	0.851588i	−0.475390	−	0.879775i	$-0.657693\pi$
$19$	−6.42934	−	3.71198i	−1.47499	−	0.851588i	−0.999603	+	0.0281876i	$0.991026\pi$
$20$	8.82542			1.97342
$21$	−4.32067	+	1.52703i	−0.942847	+	0.333226i
$22$	11.1647			2.38032
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	4.98062	−	2.98754i	1.01666	−	0.609828i
$25$	−0.794906	−	1.37682i	−0.158981	−	0.275364i
$26$	6.33542	−	10.9733i	1.24248	−	2.15203i
$27$	−5.18963	+	0.260175i	−0.998746	+	0.0500706i
$28$	−8.62550	+	2.88740i	−1.63007	+	0.545667i
$29$			4.21293i			0.782322i	0.920322	+	0.391161i	$0.127926\pi$
$29$			4.21293i			0.782322i	−0.920322	+	0.391161i	$0.872074\pi$
$30$	−9.06466	−	5.03359i	−1.65497	−	0.919003i
$31$	2.98453	−	1.72312i	0.536037	−	0.309481i	−0.207434	−	0.978249i	$-0.566511\pi$
$31$	2.98453	−	1.72312i	0.536037	−	0.309481i	0.743471	+	0.668768i	$0.233178\pi$
$32$	−3.90234	+	2.25302i	−0.689843	+	0.398281i
$33$	−7.24981	−	4.02580i	−1.26203	−	0.700803i
$34$			8.13262i			1.39473i
$35$	5.08740	+	4.49968i	0.859927	+	0.760584i
$36$	−10.3081	+	0.344360i	−1.71801	+	0.0573934i
$37$	−0.0154961	+	0.0268401i	−0.00254755	+	0.00441249i	−0.867296	−	0.497792i	$-0.834144\pi$
$37$	−0.0154961	+	0.0268401i	−0.00254755	+	0.00441249i	0.864749	+	0.502205i	$0.167478\pi$
$38$	8.65613	+	14.9928i	1.40421	+	2.43216i
$39$	−8.07070	+	4.84106i	−1.29235	+	0.775191i
$40$	−7.45465	−	4.30394i	−1.17868	−	0.680513i
$41$	−5.98000			−0.933919			−0.466959	−	0.884279i	$-0.654651\pi$
$41$	−5.98000			−0.933919			−0.466959	+	0.884279i	$0.654651\pi$
$42$	10.5061	+	1.95389i	1.62113	+	0.301492i
$43$	2.44923			0.373505			0.186752	−	0.982407i	$-0.440204\pi$
$43$	2.44923			0.373505			0.186752	+	0.982407i	$0.440204\pi$
$44$	−14.2547	−	8.22997i	−2.14898	−	1.24071i
$45$	4.07113	+	6.53714i	0.606888	+	0.974500i
$46$	1.16597	+	2.01952i	0.171913	+	0.297762i
$47$	−3.44476	+	5.96650i	−0.502470	+	0.870303i	0.497526	+	0.867449i	$0.334242\pi$
$47$	−3.44476	+	5.96650i	−0.502470	+	0.870303i	−0.999996	+	0.00285418i	$0.999091\pi$
$48$	−1.63410	+	0.0272875i	−0.235862	+	0.00393861i
$49$	−6.44430	−	2.73331i	−0.920614	−	0.390473i
$50$			3.70735i			0.524298i
$51$	2.93249	−	5.28094i	0.410631	−	0.739479i
$52$	−16.1777	+	9.34021i	−2.24345	+	1.29525i
$53$	8.25130	−	4.76389i	1.13340	−	0.654370i	0.188614	−	0.982051i	$-0.439600\pi$
$53$	8.25130	−	4.76389i	1.13340	−	0.654370i	0.944788	+	0.327681i	$0.106267\pi$
$54$	10.7839	+	5.52553i	1.46751	+	0.751930i
$55$			12.2904i			1.65724i
$56$	8.69389	+	1.76752i	1.16177	+	0.236195i
$57$	−0.214694	−	12.8569i	−0.0284369	−	1.70294i
$58$	4.91215	−	8.50810i	0.644997	−	1.11717i
$59$	7.14409	+	12.3739i	0.930081	+	1.61095i	0.783179	+	0.621797i	$0.213597\pi$
$59$	7.14409	+	12.3739i	0.930081	+	1.61095i	0.146902	+	0.989151i	$0.453070\pi$
$60$	7.86301	+	13.1087i	1.01511	+	1.69232i
$61$	3.45906	+	1.99709i	0.442888	+	0.255701i	0.704822	−	0.709384i	$-0.251027\pi$
$61$	3.45906	+	1.99709i	0.442888	+	0.255701i	−0.261934	+	0.965086i	$0.584360\pi$
$62$	−8.03642			−1.02063
$63$	−6.11765	−	5.05711i	−0.770751	−	0.637136i
$64$	12.3950			1.54937
$65$	12.0797	+	6.97420i	1.49830	+	0.865043i
$66$	9.94717	+	16.5833i	1.22441	+	2.04126i
$67$	0.991845	+	1.71793i	0.121173	+	0.209878i	0.920231	−	0.391377i	$-0.128001\pi$
$67$	0.991845	+	1.71793i	0.121173	+	0.209878i	−0.799057	+	0.601255i	$0.794668\pi$
$68$	5.99490	−	10.3835i	0.726989	−	1.25918i
$69$	−0.0289190	−	1.73181i	−0.00348144	−	0.208485i
$70$	−5.02761	−	15.0189i	−0.600914	−	1.79511i
$71$			7.28959i			0.865115i	0.901606	+	0.432558i	$0.142389\pi$
$71$			7.28959i			0.865115i	−0.901606	+	0.432558i	$0.857611\pi$
$72$	8.87496	+	4.73613i	1.04592	+	0.558158i
$73$	7.27473	−	4.20007i	0.851443	−	0.491581i	−0.00969441	−	0.999953i	$-0.503086\pi$
$73$	7.27473	−	4.20007i	0.851443	−	0.491581i	0.861138	+	0.508372i	$0.169753\pi$
$74$	0.0625895	−	0.0361361i	0.00727589	−	0.00420074i
$75$	1.33681	−	2.40737i	0.154361	−	0.277980i
$76$		−	25.5232i		−	2.92771i
$77$	−4.02102	−	12.0120i	−0.458238	−	1.36889i
$78$	21.9435	−	0.366428i	2.48461	−	0.0414898i
$79$	−4.03398	+	6.98707i	−0.453859	+	0.786106i	−0.998622	−	0.0524836i	$-0.983286\pi$
$79$	−4.03398	+	6.98707i	−0.453859	+	0.786106i	0.544763	+	0.838590i	$0.316620\pi$
$80$	1.21112	+	2.09772i	0.135407	+	0.234532i
$81$	−5.01015	−	7.47653i	−0.556683	−	0.830725i
$82$	12.0767	+	6.97250i	1.33365	+	0.769984i
$83$	−4.68166			−0.513879			−0.256940	−	0.966427i	$-0.582714\pi$
$83$	−4.68166			−0.513879			−0.256940	+	0.966427i	$0.582714\pi$
$84$	−11.9736	−	10.2392i	−1.30643	−	1.11719i
$85$	−8.95261			−0.971047
$86$	−4.94628	−	2.85573i	−0.533371	−	0.307942i
$87$	−6.25760	+	3.75351i	−0.670885	+	0.402418i
$88$	8.02711	+	13.9034i	0.855692	+	1.48210i
$89$	−4.81051	+	8.33205i	−0.509913	+	0.883195i	0.490021	+	0.871711i	$0.336989\pi$
$89$	−4.81051	+	8.33205i	−0.509913	+	0.883195i	−0.999934	+	0.0114845i	$0.996344\pi$
$90$	−0.599609	−	17.9487i	−0.0632043	−	1.89196i
$91$	−14.0878	−	2.86413i	−1.47680	−	0.300242i
$92$		−	3.43795i		−	0.358431i
$93$	5.21846	+	2.89780i	0.541130	+	0.300488i
$94$	13.9135	−	8.03297i	1.43507	−	0.828538i
$95$	−16.5045	+	9.52890i	−1.69333	+	0.977644i
$96$	−6.82326	−	3.78894i	−0.696396	−	0.386707i
$97$			1.08553i			0.110219i	0.998480	+	0.0551094i	$0.0175508\pi$
$97$			1.08553i			0.110219i	−0.998480	+	0.0551094i	$0.982449\pi$
$98$	9.82744	+	13.0338i	0.992721	+	1.31662i
$99$	−0.479560	−	14.3552i	−0.0481976	−	1.44275i
$100$	2.73284	−	4.73343i	0.273284	−	0.473343i
$101$	−0.973042	−	1.68536i	−0.0968213	−	0.167699i	0.813546	−	0.581501i	$-0.197534\pi$
$101$	−0.973042	−	1.68536i	−0.0968213	−	0.167699i	−0.910367	+	0.413801i	$0.864201\pi$
$102$	−12.0796	+	7.24576i	−1.19606	+	0.717437i
$103$	5.86487	+	3.38608i	0.577883	+	0.333641i	0.760292	−	0.649582i	$-0.225056\pi$
$103$	5.86487	+	3.38608i	0.577883	+	0.333641i	−0.182409	+	0.983223i	$0.558389\pi$
$104$	18.2200			1.78662
$105$	−2.15090	+	11.5655i	−0.209906	+	1.12867i
$106$	−22.2182			−2.15802
$107$	8.70610	+	5.02647i	0.841651	+	0.485927i	0.857825	−	0.513942i	$-0.171815\pi$
$107$	8.70610	+	5.02647i	0.841651	+	0.485927i	−0.0161744	+	0.999869i	$0.505149\pi$
$108$	−9.69547	−	15.0041i	−0.932947	−	1.44377i
$109$	1.99054	+	3.44771i	0.190659	+	0.330231i	0.945469	−	0.325713i	$-0.105604\pi$
$109$	1.99054	+	3.44771i	0.190659	+	0.330231i	−0.754810	+	0.655943i	$0.772271\pi$
$110$	14.3302	−	24.8207i	1.36633	−	2.36656i
$111$	−0.0536727		0.000896267i	−0.00509439		8.50699e-5i
$112$	−1.86999	−	1.65396i	−0.176697	−	0.156284i
$113$		−	12.6329i		−	1.18840i	−0.804318	−	0.594199i	$-0.797469\pi$
$113$		−	12.6329i		−	1.18840i	0.804318	−	0.594199i	$-0.202531\pi$
$114$	−14.5572	+	26.2151i	−1.36340	+	2.45527i
$115$	−2.22314	+	1.28353i	−0.207309	+	0.119690i
$116$	−12.5434	+	7.24191i	−1.16462	+	0.672395i
$117$	−14.3812	−	7.67452i	−1.32954	−	0.709510i
$118$		−	33.3192i		−	3.06728i
$119$	8.74981	−	2.92901i	0.802093	−	0.268502i
$120$	−0.248932	−	14.9072i	−0.0227243	−	1.36084i
$121$	5.96114	−	10.3250i	0.541922	−	0.938637i
$122$	−4.65710	−	8.06633i	−0.421634	−	0.730291i
$123$	−5.32787	−	8.88228i	−0.480398	−	0.800888i
$124$	10.2606	+	5.92399i	0.921433	+	0.531990i
$125$	8.75417			0.782996
$126$	6.45827	+	17.3459i	0.575348	+	1.54530i
$127$	7.38884			0.655654			0.327827	−	0.944738i	$-0.393684\pi$
$127$	7.38884			0.655654			0.327827	+	0.944738i	$0.393684\pi$
$128$	−17.2272	−	9.94613i	−1.52268	−	0.879122i
$129$	2.18214	+	3.63792i	0.192127	+	0.320301i
$130$	−16.2634	−	28.1691i	−1.42640	−	2.47059i
$131$	6.61603	−	11.4593i	0.578045	−	1.00120i	−0.417658	−	0.908604i	$-0.637149\pi$
$131$	6.61603	−	11.4593i	0.578045	−	1.00120i	0.995703	−	0.0925994i	$-0.0295176\pi$
$132$	−0.476005	−	28.5055i	−0.0414309	−	2.48108i
$133$	13.0131	−	14.7128i	1.12838	−	1.27576i
$134$		−	4.62585i		−	0.399612i
$135$	−6.08265	+	11.8712i	−0.523512	+	1.02171i
$136$	−10.1275	+	5.84714i	−0.868429	+	0.501388i
$137$	8.05914	−	4.65294i	0.688538	−	0.397528i	−0.114526	−	0.993420i	$-0.536535\pi$
$137$	8.05914	−	4.65294i	0.688538	−	0.397528i	0.803064	+	0.595892i	$0.203202\pi$
$138$	−1.96084	+	3.53114i	−0.166917	+	0.300591i
$139$			4.02844i			0.341688i	0.985298	+	0.170844i	$0.0546494\pi$
$139$			4.02844i			0.341688i	−0.985298	+	0.170844i	$0.945351\pi$
$140$	−4.65201	+	22.8818i	−0.393166	+	1.93386i
$141$	−11.9313	+	0.199238i	−1.00480	+	0.0167789i
$142$	8.49944	−	14.7215i	0.713257	−	1.23540i
$143$	−13.0073	−	22.5293i	−1.08772	−	1.88399i
$144$	−1.49643	−	2.40287i	−0.124703	−	0.200239i
$145$	9.36594	+	5.40743i	0.777799	+	0.449063i
$146$	−19.5886			−1.62117
$147$	−1.68168	−	12.0072i	−0.138702	−	0.990334i
$148$	−0.106550			−0.00875834
$149$	−12.5381	−	7.23888i	−1.02716	−	0.593032i	−0.110991	−	0.993821i	$-0.535403\pi$
$149$	−12.5381	−	7.23888i	−1.02716	−	0.593032i	−0.916170	+	0.400790i	$0.868736\pi$
$150$	−5.50664	+	3.30306i	−0.449615	+	0.269694i
$151$	11.7778	+	20.3998i	0.958466	+	1.66011i	0.726228	+	0.687453i	$0.241271\pi$
$151$	11.7778	+	20.3998i	0.958466	+	1.66011i	0.232238	+	0.972659i	$0.425395\pi$
$152$	−12.4470	+	21.5589i	−1.00959	+	1.74866i
$153$	10.4566	−	0.349323i	0.845369	−	0.0282411i
$154$	−5.88506	+	28.9468i	−0.474232	+	2.33260i
$155$		−	8.84671i		−	0.710584i
$156$	−28.2868	−	15.7076i	−2.26476	−	1.25762i
$157$	14.8426	−	8.56938i	1.18457	−	0.683911i	0.227501	−	0.973778i	$-0.426944\pi$
$157$	14.8426	−	8.56938i	1.18457	−	0.683911i	0.957067	+	0.289867i	$0.0936111\pi$
$158$	16.2934	−	9.40701i	1.29624	−	0.748382i
$159$	14.4274	+	8.01153i	1.14417	+	0.635355i
$160$			11.5673i			0.914473i
$161$	1.75285	−	1.98180i	0.138144	−	0.156187i
$162$	1.40068	+	20.9407i	0.110048	+	1.64525i
$163$	−3.57693	+	6.19542i	−0.280166	+	0.485263i	−0.971426	−	0.237344i	$-0.923723\pi$
$163$	−3.57693	+	6.19542i	−0.280166	+	0.485263i	0.691259	+	0.722607i	$0.257056\pi$
$164$	−10.2795	−	17.8045i	−0.802691	−	1.39030i
$165$	−18.2553	+	10.9501i	−1.42117	+	0.852465i
$166$	9.45471	+	5.45868i	0.733828	+	0.423676i
$167$	−8.69175			−0.672588			−0.336294	−	0.941757i	$-0.609174\pi$
$167$	−8.69175			−0.672588			−0.336294	+	0.941757i	$0.609174\pi$
$168$	5.12046	+	14.4881i	0.395052	+	1.11778i
$169$	−16.5240			−1.27108
$170$	18.0800	+	10.4385i	1.38667	+	0.800595i
$171$	18.9055	−	11.7737i	1.44574	−	0.900360i
$172$	4.21017	+	7.29222i	0.321022	+	0.556027i
$173$	4.99157	−	8.64565i	0.379502	−	0.657317i	−0.611488	−	0.791254i	$-0.709429\pi$
$173$	4.99157	−	8.64565i	0.379502	−	0.657317i	0.990990	+	0.133937i	$0.0427620\pi$
$174$	17.0138	−	0.284109i	1.28981	−	0.0215383i
$175$	3.98870	−	1.33522i	0.301517	−	0.100933i
$176$		−	4.51761i		−	0.340527i
$177$	−12.0144	+	21.6359i	−0.903054	+	1.62625i
$178$	19.4298	−	11.2178i	1.45633	−	0.840811i
$179$	−7.21082	+	4.16317i	−0.538962	+	0.311170i	−0.744658	−	0.667446i	$-0.767388\pi$
$179$	−7.21082	+	4.16317i	−0.538962	+	0.311170i	0.205696	+	0.978616i	$0.434054\pi$
$180$	−12.4652	+	23.3583i	−0.929101	+	1.74103i
$181$		−	20.7438i		−	1.54187i	−0.636913	−	0.770936i	$-0.719789\pi$
$181$		−	20.7438i		−	1.54187i	0.636913	−	0.770936i	$-0.280211\pi$
$182$	25.1110	+	22.2101i	1.86135	+	1.64632i
$183$	0.115508	+	6.91716i	0.00853859	+	0.511332i
$184$	−1.67660	+	2.90396i	−0.123601	+	0.214083i
$185$	0.0397796	+	0.0689003i	0.00292465	+	0.00506565i
$186$	−7.16004	−	11.9367i	−0.525000	−	0.875244i
$187$	14.4602	+	8.34857i	1.05743	+	0.610508i
$188$	−23.6858			−1.72746
$189$	2.06097	−	13.5924i	0.149914	−	0.988699i
$190$	44.4416			3.22414
$191$	−0.404373	−	0.233465i	−0.0292594	−	0.0168929i	0.485299	−	0.874348i	$-0.338711\pi$
$191$	−0.404373	−	0.233465i	−0.0292594	−	0.0168929i	−0.514558	+	0.857455i	$0.672044\pi$
$192$	11.0433	+	18.4106i	0.796980	+	1.32867i
$193$	−3.65407	−	6.32903i	−0.263025	−	0.455573i	0.704019	−	0.710181i	$-0.251387\pi$
$193$	−3.65407	−	6.32903i	−0.263025	−	0.455573i	−0.967044	+	0.254608i	$0.918054\pi$
$194$	1.26570	−	2.19225i	0.0908716	−	0.157394i
$195$	0.403374	+	24.1560i	0.0288862	+	1.72984i
$196$	−2.93957	−	23.8854i	−0.209969	−	1.70610i
$197$			15.7710i			1.12364i	0.827261	+	0.561818i	$0.189898\pi$
$197$			15.7710i			1.12364i	−0.827261	+	0.561818i	$0.810102\pi$
$198$	−15.7692	+	29.5497i	−1.12067	+	2.10000i
$199$	−14.7167	+	8.49667i	−1.04324	+	0.602313i	−0.920748	−	0.390157i	$-0.872421\pi$
$199$	−14.7167	+	8.49667i	−1.04324	+	0.602313i	−0.122489	+	0.992470i	$0.539087\pi$
$200$	−4.61675	+	2.66548i	−0.326454	+	0.188478i
$201$	−1.66801	+	3.00380i	−0.117652	+	0.211872i
$202$			4.53815i			0.319303i
$203$	−10.9229	−	2.22070i	−0.766638	−	0.155862i
$204$	20.7641	−	0.346734i	1.45378	−	0.0242762i
$205$	−7.67552	+	13.2944i	−0.536081	+	0.928520i
$206$	−7.89615	−	13.6765i	−0.550151	−	0.952889i
$207$	2.54655	−	1.58591i	0.176997	−	0.110228i
$208$	−4.44015	−	2.56352i	−0.307869	−	0.177748i
$209$	35.5439			2.45862
$210$	17.8288	−	20.8488i	1.23030	−	1.43870i
$211$	−6.12494			−0.421658			−0.210829	−	0.977523i	$-0.567616\pi$
$211$	−6.12494			−0.421658			−0.210829	+	0.977523i	$0.567616\pi$
$212$	28.3675	+	16.3780i	1.94829	+	1.12485i
$213$	−10.8275	+	6.49465i	−0.741885	+	0.445006i
$214$	−11.7214	−	20.3021i	−0.801260	−	1.38782i
$215$	3.14367	−	5.44500i	0.214396	−	0.371346i
$216$	0.872419	+	17.4019i	0.0593606	+	1.18405i
$217$	2.89436	+	8.64630i	0.196482	+	0.586949i
$218$		−	9.28362i		−	0.628766i
$219$	12.7199	+	7.06334i	0.859532	+	0.477296i
$220$	−36.5928	+	21.1268i	−2.46708	+	1.42437i
$221$	16.4109	−	9.47482i	1.10391	−	0.637345i
$222$	0.109438	+	0.0607708i	0.00734501	+	0.00407867i
$223$		−	22.4386i		−	1.50260i	−0.659962	−	0.751299i	$-0.729428\pi$
$223$		−	22.4386i		−	1.50260i	0.659962	−	0.751299i	$-0.270572\pi$
$224$	−3.78444	−	11.3052i	−0.252859	−	0.755363i
$225$	4.76678	−	0.159243i	0.317785	−	0.0106162i
$226$	−14.7295	+	25.5123i	−0.979794	+	1.69705i
$227$	4.60261	+	7.97195i	0.305486	+	0.529117i	0.977369	−	0.211540i	$-0.0678478\pi$
$227$	4.60261	+	7.97195i	0.305486	+	0.529117i	−0.671884	+	0.740657i	$0.734514\pi$
$228$	37.9104	−	22.7399i	2.51068	−	1.50599i
$229$	−7.85200	−	4.53335i	−0.518875	−	0.299572i	0.217600	−	0.976038i	$-0.430177\pi$
$229$	−7.85200	−	4.53335i	−0.518875	−	0.299572i	−0.736474	+	0.676466i	$0.763511\pi$
$230$	5.98624			0.394721
$231$	14.2592	−	16.6746i	0.938188	−	1.09711i
$232$	14.1268			0.927471
$233$	19.9924	+	11.5426i	1.30974	+	0.756182i	0.982053	−	0.188603i	$-0.0603960\pi$
$233$	19.9924	+	11.5426i	1.30974	+	0.756182i	0.327692	+	0.944785i	$0.393729\pi$
$234$	20.0948	+	32.2669i	1.31364	+	2.10935i
$235$	8.84291	+	15.3164i	0.576848	+	0.999130i
$236$	−24.5610	+	42.5409i	−1.59878	+	2.76918i
$237$	−13.9722	+	0.233318i	−0.907591	+	0.0151556i
$238$	−21.0855	−	4.28682i	−1.36677	−	0.277873i
$239$			8.10574i			0.524317i	0.965025	+	0.262158i	$0.0844343\pi$
$239$			8.10574i			0.524317i	−0.965025	+	0.262158i	$0.915566\pi$
$240$	−2.03676	+	3.66787i	−0.131472	+	0.236760i
$241$	−18.1021	+	10.4513i	−1.16606	+	0.673225i	−0.952749	−	0.303760i	$-0.901758\pi$
$241$	−18.1021	+	10.4513i	−1.16606	+	0.673225i	−0.213311	+	0.976984i	$0.568425\pi$
$242$	−24.0773	+	13.9010i	−1.54775	+	0.893592i
$243$	6.64133	−	14.1029i	0.426042	−	0.904704i
$244$			13.7318i			0.879088i
$245$	−14.3480	+	10.8183i	−0.916660	+	0.691156i
$246$	0.403276	+	24.1501i	0.0257119	+	1.53975i
$247$	20.1694	−	34.9345i	1.28335	−	2.22283i
$248$	−5.77797	−	10.0077i	−0.366901	−	0.635492i
$249$	−4.17112	−	6.95382i	−0.264334	−	0.440681i
$250$	−17.6792	−	10.2071i	−1.11813	−	0.645554i
$251$	17.4339			1.10042			0.550208	−	0.835028i	$-0.314549\pi$
$251$	17.4339			1.10042			0.550208	+	0.835028i	$0.314549\pi$
$252$	4.54071	−	26.9074i	0.286038	−	1.69501i
$253$	4.78772			0.301002
$254$	−14.9219	−	8.61517i	−0.936284	−	0.540564i
$255$	−7.97632	−	13.2976i	−0.499497	−	0.832728i
$256$	10.7988	+	18.7041i	0.674926	+	1.16901i
$257$	−0.959641	+	1.66215i	−0.0598607	+	0.103682i	−0.894403	−	0.447262i	$-0.852399\pi$
$257$	−0.959641	+	1.66215i	−0.0598607	+	0.103682i	0.834542	+	0.550944i	$0.185732\pi$
$258$	−0.165170	−	9.89117i	−0.0102830	−	0.615798i
$259$	−0.0614204	−	0.0543248i	−0.00381648	−	0.00337558i
$260$			47.9538i			2.97397i
$261$	−11.1504	−	5.95042i	−0.690193	−	0.368322i
$262$	−26.7224	+	15.4282i	−1.65092	+	0.953157i
$263$	−9.86015	+	5.69276i	−0.608003	+	0.351031i	−0.772183	−	0.635400i	$-0.780835\pi$
$263$	−9.86015	+	5.69276i	−0.608003	+	0.351031i	0.164181	+	0.986430i	$0.447502\pi$
$264$	−13.4993	+	24.3101i	−0.830827	+	1.49618i
$265$		−	24.4584i		−	1.50247i
$266$	−43.4349	+	14.5399i	−2.66316	+	0.891498i
$267$	−16.6618	+	0.278231i	−1.01968	+	0.0170274i
$268$	−3.40991	+	5.90613i	−0.208293	+	0.360775i
$269$	2.79103	+	4.83421i	0.170172	+	0.294747i	0.938480	−	0.345334i	$-0.112234\pi$
$269$	2.79103	+	4.83421i	0.170172	+	0.294747i	−0.768308	+	0.640081i	$0.778901\pi$
$270$	26.1255	−	16.8820i	1.58995	−	1.02741i
$271$	−1.42578	−	0.823177i	−0.0866102	−	0.0500044i	0.456069	−	0.889944i	$-0.349257\pi$
$271$	−1.42578	−	0.823177i	−0.0866102	−	0.0500044i	−0.542680	+	0.839940i	$0.682590\pi$
$272$	3.29073			0.199530
$273$	−8.29730	−	23.4768i	−0.502175	−	1.42088i
$274$	−21.7008			−1.31099
$275$	6.59182	+	3.80579i	0.397502	+	0.229498i
$276$	5.10649	−	3.06304i	0.307375	−	0.184373i
$277$	−5.85700	−	10.1446i	−0.351913	−	0.609531i	0.634672	−	0.772782i	$-0.281135\pi$
$277$	−5.85700	−	10.1446i	−0.351913	−	0.609531i	−0.986585	+	0.163251i	$0.947802\pi$
$278$	4.69704	−	8.13551i	0.281710	−	0.487936i
$279$	0.345191	+	10.3329i	0.0206660	+	0.618617i
$280$	15.0883	−	17.0591i	0.901700	−	1.01948i
$281$			18.2427i			1.08827i	0.838998	+	0.544134i	$0.183142\pi$
$281$			18.2427i			1.08827i	−0.838998	+	0.544134i	$0.816858\pi$
$282$	24.3279	+	13.5092i	1.44870	+	0.804462i
$283$	−16.0308	+	9.25536i	−0.952929	+	0.550174i	−0.893990	−	0.448088i	$-0.852105\pi$
$283$	−16.0308	+	9.25536i	−0.952929	+	0.550174i	−0.0589396	+	0.998262i	$0.518772\pi$
$284$	−21.7036	+	12.5306i	−1.28787	+	0.743555i
$285$	−28.8583	−	16.0249i	−1.70942	−	0.949235i
$286$			60.6644i			3.58716i
$287$	3.15214	−	15.5044i	0.186065	−	0.915196i
$288$	−0.451345	−	13.5106i	−0.0265957	−	0.796118i
$289$	2.41870	−	4.18931i	0.142276	−	0.246430i
$290$	−12.6098	−	21.8408i	−0.740473	−	1.28254i
$291$	−1.61237	+	0.967152i	−0.0945189	+	0.0566954i
$292$	25.0101	+	14.4396i	1.46361	+	0.845014i
$293$	−11.2951			−0.659869			−0.329935	−	0.944004i	$-0.607027\pi$
$293$	−11.2951			−0.659869			−0.329935	+	0.944004i	$0.607027\pi$
$294$	−10.6038	+	26.2095i	−0.618427	+	1.52857i
$295$	36.6786			2.13551
$296$	0.0900004	+	0.0519618i	0.00523117	+	0.00302022i
$297$	20.8949	−	13.5020i	1.21245	−	0.783467i
$298$	16.8806	+	29.2381i	0.977869	+	1.69372i
$299$	2.71680	−	4.70564i	0.157117	−	0.272134i
$300$	9.46553	−	0.158062i	0.546493	−	0.00912574i
$301$	−1.29103	+	6.35016i	−0.0744135	+	0.366017i
$302$		−	54.9304i		−	3.16089i
$303$	1.63638	−	2.94686i	0.0940078	−	0.169293i
$304$	6.06661	−	3.50256i	0.347944	−	0.200886i
$305$	8.87964	−	5.12666i	0.508447	−	0.293552i
$306$	−21.5247	−	11.4867i	−1.23048	−	0.656649i
$307$		−	29.6114i		−	1.69001i	−0.534759	−	0.845005i	$-0.679598\pi$
$307$		−	29.6114i		−	1.69001i	0.534759	−	0.845005i	$-0.320402\pi$
$308$	28.8518	−	32.6202i	1.64398	−	1.85871i
$309$	0.195845	+	11.7281i	0.0111412	+	0.667189i
$310$	−10.3150	+	17.8661i	−0.585852	+	1.01473i
$311$	−1.53039	−	2.65072i	−0.0867805	−	0.150308i	0.819368	−	0.573268i	$-0.194325\pi$
$311$	−1.53039	−	2.65072i	−0.0867805	−	0.150308i	−0.906149	+	0.422960i	$0.860991\pi$
$312$	16.2331	+	27.0627i	0.919017	+	1.53212i
$313$	21.0325	+	12.1431i	1.18883	+	0.686369i	0.958040	−	0.286636i	$-0.0925369\pi$
$313$	21.0325	+	12.1431i	1.18883	+	0.686369i	0.230786	+	0.973004i	$0.425870\pi$
$314$	−39.9666			−2.25544
$315$	−19.0949	+	7.10944i	−1.07587	+	0.400571i
$316$	−27.7372			−1.56034
$317$	20.3626	+	11.7563i	1.14368	+	0.660301i	0.947338	−	0.320235i	$-0.103762\pi$
$317$	20.3626	+	11.7563i	1.14368	+	0.660301i	0.196337	+	0.980536i	$0.437095\pi$
$318$	−19.7953	−	33.0014i	−1.11007	−	1.85063i
$319$	−10.0852	−	17.4680i	−0.564661	−	0.978022i
$320$	15.9093	−	27.5558i	0.889358	−	1.54041i
$321$	0.290721	+	17.4098i	0.0162265	+	0.971719i
$322$	−5.85063	+	1.95851i	−0.326043	+	0.109143i
$323$			25.8910i			1.44062i
$324$	13.6479	−	27.7689i	0.758217	−	1.54272i
$325$	7.48108	−	4.31920i	0.414976	−	0.239586i
$326$	14.4473	−	8.34118i	0.800164	−	0.461975i
$327$	−3.34752	+	6.02834i	−0.185118	+	0.333368i
$328$			20.0522i			1.10720i
$329$	−13.6536	−	12.0763i	−0.752749	−	0.665787i
$330$	49.6344	−	0.828832i	2.73229	−	0.0456257i
$331$	−9.44890	+	16.3660i	−0.519358	+	0.899555i	0.480389	+	0.877056i	$0.340496\pi$
$331$	−9.44890	+	16.3660i	−0.519358	+	0.899555i	−0.999747	+	0.0224991i	$0.992838\pi$
$332$	−8.04765	−	13.9389i	−0.441672	−	0.764999i
$333$	−0.0491509	−	0.0789233i	−0.00269346	−	0.00432497i
$334$	17.5532	+	10.1343i	0.960466	+	0.554525i
$335$	5.09226			0.278220
$336$	0.790610	−	4.25114i	0.0431313	−	0.231919i
$337$	−33.6275			−1.83180			−0.915902	−	0.401402i	$-0.868523\pi$
$337$	−33.6275			−1.83180			−0.915902	+	0.401402i	$0.868523\pi$
$338$	33.3706	+	19.2665i	1.81512	+	1.04796i
$339$	18.7640	−	11.2552i	1.01912	−	0.611300i
$340$	−15.3893	−	26.6550i	−0.834602	−	1.44557i
$341$	−8.24981	+	14.2891i	−0.446752	+	0.773798i
$342$	−51.9078	+	1.73407i	−2.80685	+	0.0937679i
$343$	10.4836	−	15.2674i	0.566059	−	0.824365i
$344$		−	8.21278i		−	0.442804i
$345$	−3.88718	−	2.15854i	−0.209279	−	0.116212i
$346$	−20.1612	+	11.6400i	−1.08387	+	0.625773i
$347$	−4.29047	+	2.47710i	−0.230324	+	0.132978i	−0.610722	−	0.791845i	$-0.709121\pi$
$347$	−4.29047	+	2.47710i	−0.230324	+	0.132978i	0.380397	+	0.924823i	$0.375787\pi$
$348$	−21.9321	−	12.1789i	−1.17569	−	0.652856i
$349$			12.3607i			0.661655i	0.943691	+	0.330827i	$0.107328\pi$
$349$			12.3607i			0.661655i	−0.943691	+	0.330827i	$0.892672\pi$
$350$	−9.61208	−	1.95420i	−0.513787	−	0.104456i
$351$	−1.41368	−	28.1984i	−0.0754569	−	1.50512i
$352$	10.7868	−	18.6833i	0.574939	−	0.995824i
$353$	5.94195	+	10.2918i	0.316258	+	0.547775i	0.979704	−	0.200449i	$-0.0642401\pi$
$353$	5.94195	+	10.2918i	0.316258	+	0.547775i	−0.663446	+	0.748224i	$0.730907\pi$
$354$	49.4900	−	29.6857i	2.63036	−	1.57778i
$355$	16.2058	+	9.35642i	0.860114	+	0.496587i
$356$	−33.0765			−1.75305
$357$	12.1462	+	10.3868i	0.642844	+	0.549726i
$358$	19.4165			1.02620
$359$	−6.57491	−	3.79602i	−0.347010	−	0.200347i	0.316357	−	0.948640i	$-0.397540\pi$
$359$	−6.57491	−	3.79602i	−0.347010	−	0.200347i	−0.663368	+	0.748294i	$0.730873\pi$
$360$	21.9204	−	13.6513i	1.15531	−	0.719488i
$361$	18.0576	+	31.2768i	0.950403	+	1.64615i
$362$	−24.1866	+	41.8924i	−1.27122	+	2.20182i
$363$	20.6471	−	0.344781i	1.08369	−	0.0180963i
$364$	−15.6890	−	46.8675i	−0.822325	−	2.45653i
$365$		−	21.5637i		−	1.12869i
$366$	7.83194	−	14.1040i	0.409382	−	0.737229i
$367$	−0.158187	+	0.0913291i	−0.00825727	+	0.00476734i	−0.504123	−	0.863632i	$-0.668184\pi$
$367$	−0.158187	+	0.0913291i	−0.00825727	+	0.00476734i	0.495866	+	0.868399i	$0.334851\pi$
$368$	0.817165	−	0.471791i	0.0425977	−	0.0245938i
$369$	8.44626	−	15.8273i	0.439695	−	0.823937i
$370$		−	0.185527i		−	0.00964510i
$371$	8.00201	+	23.9043i	0.415444	+	1.24105i
$372$	0.342632	+	20.5184i	0.0177646	+	1.06383i
$373$	7.32060	−	12.6797i	0.379047	−	0.656528i	−0.611877	−	0.790953i	$-0.709585\pi$
$373$	7.32060	−	12.6797i	0.379047	−	0.656528i	0.990924	+	0.134425i	$0.0429187\pi$
$374$	−19.4684	−	33.7202i	−1.00669	−	1.74363i
$375$	7.79952	+	13.0028i	0.402765	+	0.671464i
$376$	20.0069	+	11.5510i	1.03178	+	0.595696i
$377$	−22.8914			−1.17897
$378$	−20.0105	+	25.0470i	−1.02923	+	1.28828i
$379$	0.809023			0.0415567			0.0207784	−	0.999784i	$-0.493386\pi$
$379$	0.809023			0.0415567			0.0207784	+	0.999784i	$0.493386\pi$
$380$	−56.7417	−	32.7598i	−2.91079	−	1.68054i
$381$	6.58309	+	10.9749i	0.337262	+	0.562260i
$382$	0.544426	+	0.942973i	0.0278552	+	0.0482467i
$383$	8.66212	−	15.0032i	0.442614	−	0.766630i	−0.555269	−	0.831671i	$-0.687385\pi$
$383$	8.66212	−	15.0032i	0.442614	−	0.766630i	0.997883	+	0.0650413i	$0.0207179\pi$
$384$	−0.575265	−	34.4496i	−0.0293564	−	1.75800i
$385$	−31.8654	−	6.47844i	−1.62401	−	0.330172i
$386$			17.0421i			0.867422i
$387$	−3.45934	+	6.48241i	−0.175848	+	0.329520i
$388$	−3.23200	+	1.86600i	−0.164080	+	0.0947316i
$389$	−4.72144	+	2.72592i	−0.239386	+	0.138210i	−0.614895	−	0.788609i	$-0.710801\pi$
$389$	−4.72144	+	2.72592i	−0.239386	+	0.138210i	0.375508	+	0.926819i	$0.377468\pi$
$390$	27.3505	−	49.2538i	1.38495	−	2.49406i
$391$			3.48749i			0.176370i
$392$	−9.16535	+	21.6091i	−0.462920	+	1.09142i
$393$	22.9154	−	0.382658i	1.15593	−	0.0193026i
$394$	18.3885	−	31.8498i	0.926400	−	1.60457i
$395$	10.3555	+	17.9362i	0.521041	+	0.902470i
$396$	41.9160	−	26.1039i	2.10636	−	1.31177i
$397$	−12.8771	−	7.43460i	−0.646283	−	0.373132i	0.140747	−	0.990046i	$-0.455049\pi$
$397$	−12.8771	−	7.43460i	−0.646283	−	0.373132i	−0.787031	+	0.616914i	$0.788383\pi$
$398$	39.6275			1.98635
$399$	33.4474	+	6.22041i	1.67446	+	0.311410i
$400$	1.50012			0.0750059
$401$	−2.53714	−	1.46482i	−0.126699	−	0.0731496i	0.435311	−	0.900280i	$-0.356638\pi$
$401$	−2.53714	−	1.46482i	−0.126699	−	0.0731496i	−0.562010	+	0.827131i	$0.689972\pi$
$402$	6.87091	−	4.12139i	0.342690	−	0.205556i
$403$	9.36274	+	16.2167i	0.466391	+	0.807813i
$404$	3.34527	−	5.79417i	0.166433	−	0.288271i
$405$	−23.0521	+	1.54191i	−1.14547	+	0.0766182i
$406$	19.4698	+	17.2205i	0.966269	+	0.854640i
$407$		−	0.148382i		−	0.00735505i
$408$	−17.7081	−	9.83325i	−0.876680	−	0.486818i
$409$	17.0830	−	9.86288i	0.844701	−	0.487688i	−0.0141587	−	0.999900i	$-0.504507\pi$
$409$	17.0830	−	9.86288i	0.844701	−	0.487688i	0.858859	+	0.512212i	$0.171174\pi$
$410$	31.0017	−	17.8988i	1.53107	−	0.883961i
$411$	14.0914	+	7.82495i	0.695080	+	0.385976i
$412$			23.2823i			1.14704i
$413$	−35.8478	+	12.0001i	−1.76395	+	0.590486i
$414$	−6.99192	+	0.233578i	−0.343634	+	0.0114797i
$415$	−6.00906	+	10.4080i	−0.294973	+	0.510909i
$416$	−12.2420	−	21.2038i	−0.600213	−	1.03960i
$417$	−5.98357	+	3.58914i	−0.293017	+	0.175761i
$418$	−71.7816	−	41.4431i	−3.51095	−	2.02705i
$419$	−4.26143			−0.208184			−0.104092	−	0.994568i	$-0.533194\pi$
$419$	−4.26143			−0.208184			−0.104092	+	0.994568i	$0.533194\pi$
$420$	−38.1317	+	13.4767i	−1.86064	+	0.657597i
$421$	−22.8762			−1.11492			−0.557458	−	0.830205i	$-0.688223\pi$
$421$	−22.8762			−1.11492			−0.557458	+	0.830205i	$0.688223\pi$
$422$	12.3694	+	7.14150i	0.602135	+	0.347643i
$423$	−10.9261	−	17.5445i	−0.531247	−	0.853041i
$424$	−15.9743	−	27.6683i	−0.775780	−	1.34369i
$425$	−2.77223	+	4.80164i	−0.134473	+	0.232914i
$426$	29.4388	−	0.491591i	1.42632	−	0.0238177i
$427$	−7.00120	+	7.91566i	−0.338812	+	0.383066i
$428$			34.5615i			1.67059i
$429$	21.8746	−	39.3926i	1.05612	−	1.90189i
$430$	−12.6974	+	7.33085i	−0.612323	+	0.353525i
$431$	3.87607	−	2.23785i	0.186704	−	0.107793i	−0.403735	−	0.914876i	$-0.632288\pi$
$431$	3.87607	−	2.23785i	0.186704	−	0.107793i	0.590439	+	0.807083i	$0.298955\pi$
$432$	2.23582	−	4.36354i	0.107571	−	0.209941i
$433$			6.52242i			0.313447i	0.987642	+	0.156724i	$0.0500932\pi$
$433$			6.52242i			0.313447i	−0.987642	+	0.156724i	$0.949907\pi$
$434$	4.23611	−	20.8361i	0.203340	−	1.00017i
$435$	0.312755	+	18.7293i	0.0149955	+	0.898000i
$436$	−6.84335	+	11.8530i	−0.327737	+	0.567657i
$437$	3.71198	+	6.42934i	0.177568	+	0.307557i
$438$	−17.4525	−	29.0956i	−0.833911	−	1.39024i
$439$	−6.24215	−	3.60391i	−0.297921	−	0.172005i	0.343587	−	0.939121i	$-0.388358\pi$
$439$	−6.24215	−	3.60391i	−0.297921	−	0.172005i	−0.641509	+	0.767116i	$0.721691\pi$
$440$	41.2122			1.96471
$441$	16.3363	−	13.1956i	0.777920	−	0.628363i
$442$	−44.1894			−2.10188
$443$	−5.08767	−	2.93737i	−0.241722	−	0.139559i	0.374246	−	0.927330i	$-0.377902\pi$
$443$	−5.08767	−	2.93737i	−0.241722	−	0.139559i	−0.615968	+	0.787771i	$0.711235\pi$
$444$	−0.0949305	−	0.158262i	−0.00450520	−	0.00751077i
$445$	12.3489	+	21.3889i	0.585393	+	1.01393i
$446$	−26.1627	+	45.3151i	−1.23884	+	2.14573i
$447$	−0.418683	−	25.0727i	−0.0198030	−	1.18590i
$448$	−6.53356	+	32.1366i	−0.308682	+	1.51831i
$449$		−	23.6431i		−	1.11579i	−0.829913	−	0.557893i	$-0.811610\pi$
$449$		−	23.6431i		−	1.11579i	0.829913	−	0.557893i	$-0.188390\pi$
$450$	−9.81227	−	5.23633i	−0.462555	−	0.246843i
$451$	24.7948	−	14.3153i	1.16754	−	0.674080i
$452$	37.6124	−	21.7155i	1.76914	−	1.02141i
$453$	−19.8070	+	35.6692i	−0.930615	+	1.67588i
$454$		−	21.4660i		−	1.00745i
$455$	−24.4494	+	27.6429i	−1.14621	+	1.29592i
$456$	−43.1118	+	0.719913i	−2.01890	+	0.0337130i
$457$	−9.37623	+	16.2401i	−0.438602	+	0.759680i	−0.997582	−	0.0695007i	$-0.977859\pi$
$457$	−9.37623	+	16.2401i	−0.438602	+	0.759680i	0.558980	+	0.829181i	$0.311193\pi$
$458$	10.5715	+	18.3104i	0.493974	+	0.855588i
$459$	9.83520	+	15.2204i	0.459068	+	0.710425i
$460$	−7.64304	−	4.41271i	−0.356359	−	0.205744i
$461$	−0.874577			−0.0407331			−0.0203666	−	0.999793i	$-0.506483\pi$
$461$	−0.874577			−0.0407331			−0.0203666	+	0.999793i	$0.506483\pi$
$462$	−48.2389	+	17.0489i	−2.24428	+	0.793185i
$463$	−5.38348			−0.250192			−0.125096	−	0.992145i	$-0.539924\pi$
$463$	−5.38348			−0.250192			−0.125096	+	0.992145i	$0.539924\pi$
$464$	−3.44266	−	1.98762i	−0.159822	−	0.0922730i
$465$	13.1403	−	7.88197i	0.609366	−	0.365517i
$466$	−26.9167	−	46.6211i	−1.24689	−	2.15968i
$467$	1.17600	−	2.03689i	0.0544187	−	0.0942559i	−0.837533	−	0.546387i	$-0.816003\pi$
$467$	1.17600	−	2.03689i	0.0544187	−	0.0942559i	0.891951	+	0.452131i	$0.149336\pi$
$468$	−1.87112	−	56.0100i	−0.0864924	−	2.58907i
$469$	−4.97690	+	1.66602i	−0.229812	+	0.0769298i
$470$		−	41.2423i		−	1.90237i
$471$	25.9524	+	14.4113i	1.19582	+	0.664037i
$472$	41.4923	−	23.9556i	1.90984	−	1.10265i
$473$	−10.1552	+	5.86313i	−0.466938	+	0.269587i
$474$	28.4891	+	15.8200i	1.30855	+	0.726635i
$475$			11.8027i			0.541546i
$476$	23.7614	+	21.0163i	1.08910	+	0.963282i
$477$	0.954345	+	28.5674i	0.0436965	+	1.30801i
$478$	9.45105	−	16.3697i	0.432281	−	0.748733i
$479$	−9.78877	−	16.9546i	−0.447260	−	0.774677i	0.550946	−	0.834541i	$-0.314267\pi$
$479$	−9.78877	−	16.9546i	−0.447260	−	0.774677i	−0.998207	+	0.0598633i	$0.980934\pi$
$480$	−17.1812	+	10.3059i	−0.784212	+	0.470396i
$481$	−0.145838	−	0.0841999i	−0.00664966	−	0.00383918i
$482$	48.7434			2.22020
$483$	4.50532	+	0.837882i	0.204999	+	0.0381250i
$484$	40.9882			1.86310
$485$	2.41329	+	1.39331i	0.109582	+	0.0632670i
$486$	−29.8559	+	20.7376i	−1.35429	+	0.940675i
$487$	14.4335	+	24.9995i	0.654044	+	1.13284i	0.982133	+	0.188191i	$0.0602623\pi$
$487$	14.4335	+	24.9995i	0.654044	+	1.13284i	−0.328088	+	0.944647i	$0.606404\pi$
$488$	6.69666	−	11.5990i	0.303143	−	0.525060i
$489$	−12.3891	+	0.206882i	−0.560255	+	0.00935555i
$490$	41.5899	−	5.11845i	1.87884	−	0.231228i
$491$			20.2654i			0.914565i	0.889321	+	0.457283i	$0.151177\pi$
$491$			20.2654i			0.914565i	−0.889321	+	0.457283i	$0.848823\pi$
$492$	17.2872	−	31.1313i	0.779366	−	1.40351i
$493$	12.7241	−	7.34628i	0.573066	−	0.330860i
$494$	−81.4652	+	47.0339i	−3.66529	+	2.11616i
$495$	−32.5291	−	17.3592i	−1.46207	−	0.780237i
$496$			3.25180i			0.146010i
$497$	−18.8998	−	3.84245i	−0.847772	−	0.172357i
$498$	0.315720	+	18.9068i	0.0141477	+	0.847233i
$499$	−7.85672	+	13.6082i	−0.351715	+	0.609188i	−0.986550	−	0.163460i	$-0.947735\pi$
$499$	−7.85672	+	13.6082i	−0.351715	+	0.609188i	0.634835	+	0.772648i	$0.281068\pi$
$500$	15.0482	+	26.0642i	0.672975	+	1.16563i
$501$	−7.74391	−	12.9101i	−0.345972	−	0.576782i
$502$	−35.2080	−	20.3274i	−1.57141	−	0.907254i
$503$	23.4495			1.04556			0.522780	−	0.852467i	$-0.324895\pi$
$503$	23.4495			1.04556			0.522780	+	0.852467i	$0.324895\pi$
$504$	−16.9575	+	20.5137i	−0.755348	+	0.913754i
$505$	−4.99572			−0.222307
$506$	−9.66890	−	5.58234i	−0.429835	−	0.248165i
$507$	−14.7221	−	24.5437i	−0.653830	−	1.09002i
$508$	12.7012	+	21.9992i	0.563526	+	0.976055i
$509$	3.73037	−	6.46120i	0.165346	−	0.286388i	−0.771432	−	0.636312i	$-0.780459\pi$
$509$	3.73037	−	6.46120i	0.165346	−	0.286388i	0.936778	+	0.349924i	$0.113793\pi$
$510$	0.603741	+	36.1549i	0.0267341	+	1.60097i
$511$	7.05495	+	21.0752i	0.312093	+	0.932312i
$512$		−	10.5799i		−	0.467568i
$513$	34.3317	+	17.5911i	1.51578	+	0.776666i
$514$	3.87603	−	2.23782i	0.170964	−	0.0987062i
$515$	15.0555	−	8.69229i	0.663424	−	0.383028i
$516$	−7.08032	+	12.7505i	−0.311694	+	0.561309i
$517$		−	32.9851i		−	1.45068i
$518$	0.0606986	+	0.181324i	0.00266694	+	0.00796694i
$519$	17.2889	−	0.288703i	0.758898	−	0.0126726i
$520$	23.3859	−	40.5056i	1.02554	−	1.77629i
$521$	4.46725	+	7.73750i	0.195714	+	0.338986i	0.947134	−	0.320838i	$-0.103964\pi$
$521$	4.46725	+	7.73750i	0.195714	+	0.338986i	−0.751421	+	0.659824i	$0.770631\pi$
$522$	15.5804	+	25.0180i	0.681938	+	1.09501i
$523$	10.8087	+	6.24042i	0.472633	+	0.272875i	0.717341	−	0.696722i	$-0.245359\pi$
$523$	10.8087	+	6.24042i	0.472633	+	0.272875i	−0.244709	+	0.969597i	$0.578692\pi$
$524$	45.4911			1.98729
$525$	5.53697	+	4.73492i	0.241653	+	0.206649i
$526$	26.5504			1.15765
$527$	−10.4085	−	6.00936i	−0.453402	−	0.261772i
$528$	6.71014	−	4.02496i	0.292021	−	0.175164i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−28.5178	+	49.3942i	−1.23873	+	2.14555i
$531$	−42.8406	+	1.43117i	−1.85912	+	0.0621074i
$532$	66.1743	+	13.4536i	2.86902	+	0.583289i
$533$		−	32.4929i		−	1.40742i
$534$	33.9732	+	18.8652i	1.47016	+	0.816379i
$535$	22.3491	−	12.9033i	0.966236	−	0.557857i
$536$	5.76056	−	3.32586i	0.248818	−	0.143655i
$537$	−12.6082	−	7.00129i	−0.544083	−	0.302128i
$538$		−	13.0170i		−	0.561205i
$539$	33.2631	−	4.09367i	1.43274	−	0.176327i
$540$	−45.8007	+	2.29615i	−1.97095	+	0.0988106i
$541$	13.2106	−	22.8814i	0.567967	−	0.983747i	−0.428800	−	0.903399i	$-0.641064\pi$
$541$	13.2106	−	22.8814i	0.567967	−	0.983747i	0.996767	−	0.0803477i	$-0.0256031\pi$
$542$	1.91960	+	3.32484i	0.0824539	+	0.142814i
$543$	30.8114	−	18.4816i	1.32224	−	0.793123i
$544$	13.6094	+	7.85738i	0.583497	+	0.336882i
$545$	10.2197			0.437762
$546$	−10.6167	+	57.0862i	−0.454352	+	2.44307i
$547$	−8.01629			−0.342752			−0.171376	−	0.985206i	$-0.554821\pi$
$547$	−8.01629			−0.342752			−0.171376	+	0.985206i	$0.554821\pi$
$548$	27.7069	+	15.9966i	1.18358	+	0.683340i
$549$	−10.1714	+	6.33441i	−0.434104	+	0.270346i
$550$	−8.87488	−	15.3717i	−0.378426	−	0.655453i
$551$	15.6383	−	27.0864i	0.666215	−	1.15392i
$552$	−5.80711	+	0.0969714i	−0.247167	+	0.00412738i
$553$	−15.9891	−	14.1419i	−0.679925	−	0.601376i
$554$			27.3163i			1.16056i
$555$	−0.0668981	+	0.120473i	−0.00283967	+	0.00511377i
$556$	−11.9941	+	6.92478i	−0.508662	+	0.293676i
$557$	−10.5756	+	6.10584i	−0.448104	+	0.258713i	−0.707029	−	0.707184i	$-0.749965\pi$
$557$	−10.5756	+	6.10584i	−0.448104	+	0.258713i	0.258925	+	0.965897i	$0.416632\pi$
$558$	11.3508	−	21.2701i	0.480517	−	0.900434i
$559$			13.3082i			0.562875i
$560$	−6.07717	+	2.03434i	−0.256807	+	0.0859665i
$561$	0.482865	+	28.9163i	0.0203866	+	1.22085i
$562$	21.2704	−	36.8415i	0.897239	−	1.55406i
$563$	23.0751	+	39.9673i	0.972501	+	1.68442i	0.687946	+	0.725762i	$0.258513\pi$
$563$	23.0751	+	39.9673i	0.972501	+	1.68442i	0.284556	+	0.958659i	$0.408154\pi$
$564$	−21.1028	−	35.1813i	−0.888590	−	1.48140i
$565$	−28.0846	−	16.2147i	−1.18153	−	0.682156i
$566$	43.1659			1.81440
$567$	22.0254	−	9.04888i	0.924979	−	0.380017i
$568$	24.4435			1.02563
$569$	23.5279	+	13.5839i	0.986342	+	0.569465i	0.904179	−	0.427154i	$-0.140484\pi$
$569$	23.5279	+	13.5839i	0.986342	+	0.569465i	0.0821630	+	0.996619i	$0.473817\pi$
$570$	39.5952	+	66.0106i	1.65846	+	2.76488i
$571$	−3.57320	−	6.18896i	−0.149534	−	0.259000i	0.781521	−	0.623878i	$-0.214444\pi$
$571$	−3.57320	−	6.18896i	−0.149534	−	0.259000i	−0.931055	+	0.364878i	$0.881111\pi$
$572$	44.7184	−	77.4545i	1.86977	−	3.23853i
$573$	−0.0135031	−	0.808633i	−0.000564102	−	0.0337811i
$574$	−24.4435	+	27.6361i	−1.02025	+	1.15351i
$575$			1.58981i			0.0662998i
$576$	−17.5069	+	32.8059i	−0.729453	+	1.36691i
$577$	−18.9143	+	10.9202i	−0.787412	+	0.454613i	−0.839051	−	0.544053i	$-0.816889\pi$
$577$	−18.9143	+	10.9202i	−0.787412	+	0.454613i	0.0516386	+	0.998666i	$0.483556\pi$
$578$	−9.76922	+	5.64026i	−0.406346	+	0.234604i
$579$	6.14512	−	11.0663i	0.255382	−	0.459902i
$580$			37.1809i			1.54385i
$581$	2.46777	−	12.1382i	0.102380	−	0.503577i
$582$	4.38389	−	0.0732054i	0.181718	−	0.00303446i
$583$	−22.8082	+	39.5049i	−0.944618	+	1.63613i
$584$	−14.0837	−	24.3937i	−0.582787	−	1.00942i
$585$	−35.5202	+	22.1209i	−1.46858	+	0.914586i
$586$	22.8108	+	13.1698i	0.942304	+	0.544039i
$587$	−16.7438			−0.691089			−0.345544	−	0.938402i	$-0.612306\pi$
$587$	−16.7438			−0.691089			−0.345544	+	0.938402i	$0.612306\pi$
$588$	32.8588	−	25.6469i	1.35507	−	1.05766i
$589$	−25.5847			−1.05420
$590$	−74.0733	−	42.7662i	−3.04955	−	1.76066i
$591$	−23.4251	+	14.0512i	−0.963582	+	0.577987i
$592$	−0.0146219	−	0.0253258i	−0.000600955	−	0.00104089i
$593$	6.19398	−	10.7283i	0.254356	−	0.440558i	−0.710364	−	0.703834i	$-0.751470\pi$
$593$	6.19398	−	10.7283i	0.254356	−	0.440558i	0.964721	+	0.263276i	$0.0848030\pi$
$594$	−57.9406	+	2.90477i	−2.37733	+	0.119184i
$595$	4.71905	−	23.2115i	0.193462	−	0.951580i
$596$		−	49.7737i		−	2.03881i
$597$	−25.7322	−	14.2890i	−1.05315	−	0.584811i
$598$	−10.9733	+	6.33542i	−0.448730	+	0.259074i
$599$	−32.6010	+	18.8222i	−1.33204	+	0.769055i	−0.985612	−	0.169021i	$-0.945939\pi$
$599$	−32.6010	+	18.8222i	−1.33204	+	0.769055i	−0.346430	+	0.938076i	$0.612606\pi$
$600$	−8.07242	−	4.48260i	−0.329555	−	0.183001i
$601$			40.9286i			1.66951i	0.550619	+	0.834757i	$0.314392\pi$
$601$			40.9286i			1.66951i	−0.550619	+	0.834757i	$0.685608\pi$
$602$	10.0113	−	11.3190i	0.408032	−	0.461327i
$603$	−5.94775	+	0.198695i	−0.242211	+	0.00809150i
$604$	−40.4916	+	70.1334i	−1.64758	+	2.85369i
$605$	−15.3026	−	26.5049i	−0.622140	−	1.07758i
$606$	−6.74066	+	4.04326i	−0.273821	+	0.164246i
$607$	13.3516	+	7.70852i	0.541923	+	0.312879i	0.745858	−	0.666105i	$-0.232040\pi$
$607$	13.3516	+	7.70852i	0.541923	+	0.312879i	−0.203935	+	0.978984i	$0.565373\pi$
$608$	33.4527			1.35668
$609$	−6.43329	−	18.2027i	−0.260690	−	0.737609i
$610$	−23.9101			−0.968093
$611$	−32.4196	−	18.7174i	−1.31156	−	0.757227i
$612$	19.0147	+	30.5326i	0.768625	+	1.23421i
$613$	5.99516	+	10.3839i	0.242142	+	0.419402i	0.961324	−	0.275419i	$-0.0888167\pi$
$613$	5.99516	+	10.3839i	0.242142	+	0.419402i	−0.719182	+	0.694822i	$0.755483\pi$
$614$	−34.5260	+	59.8007i	−1.39335	+	2.41336i
$615$	−26.5851	+	0.443937i	−1.07201	+	0.0179013i
$616$	−40.2786	+	13.4833i	−1.62287	+	0.543258i
$617$			36.9710i			1.48840i	0.667959	+	0.744198i	$0.267168\pi$
$617$			36.9710i			1.48840i	−0.667959	+	0.744198i	$0.732832\pi$
$618$	13.2791	−	23.9135i	0.534164	−	0.961941i
$619$	19.7805	−	11.4203i	0.795046	−	0.459020i	−0.0466898	−	0.998909i	$-0.514867\pi$
$619$	19.7805	−	11.4203i	0.795046	−	0.459020i	0.841736	+	0.539889i	$0.181534\pi$
$620$	26.3397	−	15.2072i	1.05783	−	0.610738i
$621$	4.62444	+	2.36950i	0.185572	+	0.0950847i
$622$			7.13756i			0.286190i
$623$	−19.0669	−	16.8642i	−0.763899	−	0.675650i
$624$	−0.148269	−	8.87907i	−0.00593552	−	0.355447i
$625$	15.2108	−	26.3458i	0.608431	−	1.05383i
$626$	−28.3170	−	49.0465i	−1.13178	−	1.96029i
$627$	31.6678	+	52.7945i	1.26469	+	2.10841i
$628$	51.0281	+	29.4611i	2.03624	+	1.17562i
$629$	0.108085			0.00430965
$630$	46.8519	+	7.90640i	1.86662	+	0.314999i
$631$	−29.0520			−1.15654			−0.578270	−	0.815845i	$-0.696272\pi$
$631$	−29.0520			−1.15654			−0.578270	+	0.815845i	$0.696272\pi$
$632$	23.4291	+	13.5268i	0.931958	+	0.538066i
$633$	−5.45701	−	9.09756i	−0.216897	−	0.361596i
$634$	−27.4151	−	47.4843i	−1.08879	−	1.88584i
$635$	9.48381	−	16.4264i	0.376354	−	0.651864i
$636$	0.947271	+	56.7271i	0.0375618	+	2.24938i
$637$	14.8517	−	35.0158i	0.588446	−	1.38738i
$638$			47.0360i			1.86217i
$639$	−19.2934	−	10.2960i	−0.763236	−	0.407302i
$640$	−44.2233	+	25.5323i	−1.74808	+	1.00925i
$641$	13.3767	−	7.72303i	0.528347	−	0.305041i	−0.211996	−	0.977271i	$-0.567996\pi$
$641$	13.3767	−	7.72303i	0.528347	−	0.305041i	0.740343	+	0.672229i	$0.234663\pi$
$642$	19.7122	−	35.4984i	0.777977	−	1.40101i
$643$		−	33.6099i		−	1.32544i	−0.748865	−	0.662722i	$-0.769401\pi$
$643$		−	33.6099i		−	1.32544i	0.748865	−	0.662722i	$-0.230599\pi$
$644$	8.91360	+	1.81219i	0.351245	+	0.0714103i
$645$	10.8885	−	0.181824i	0.428733	−	0.00715930i
$646$	30.1882	−	52.2874i	1.18774	−	2.05722i
$647$	1.01349	+	1.75541i	0.0398443	+	0.0690124i	0.885260	−	0.465097i	$-0.153980\pi$
$647$	1.01349	+	1.75541i	0.0398443	+	0.0690124i	−0.845416	+	0.534109i	$0.820647\pi$
$648$	−25.0703	+	16.8000i	−0.984855	+	0.659968i
$649$	−59.2429	−	34.2039i	−2.32549	−	1.34262i
$650$	−20.1442			−0.790122
$651$	−10.2639	+	12.0025i	−0.402274	+	0.470415i
$652$	−24.5946			−0.963197
$653$	−19.9332	−	11.5084i	−0.780046	−	0.450360i	0.0564009	−	0.998408i	$-0.482038\pi$
$653$	−19.9332	−	11.5084i	−0.780046	−	0.450360i	−0.836446	+	0.548049i	$0.815371\pi$
$654$	13.7892	−	8.27123i	0.539202	−	0.323431i
$655$	−16.9838	−	29.4167i	−0.663611	−	1.14941i
$656$	2.82131	−	4.88665i	0.110154	−	0.190792i
$657$	0.841396	+	25.1864i	0.0328260	+	0.982614i
$658$	13.4932	+	40.3080i	0.526018	+	1.57137i
$659$			12.3551i			0.481287i	0.970614	+	0.240643i	$0.0773584\pi$
$659$			12.3551i			0.481287i	−0.970614	+	0.240643i	$0.922642\pi$
$660$	−63.9827	−	35.5294i	−2.49052	−	1.38298i
$661$	12.7437	−	7.35755i	0.495671	−	0.286176i	−0.231253	−	0.972894i	$-0.574283\pi$
$661$	12.7437	−	7.35755i	0.495671	−	0.286176i	0.726924	+	0.686718i	$0.240949\pi$
$662$	38.1645	−	22.0343i	1.48330	−	0.856386i
$663$	28.6945	+	15.9340i	1.11440	+	0.618825i
$664$			15.6986i			0.609223i
$665$	−16.0059	−	47.8143i	−0.620682	−	1.85416i
$666$	0.00723911	+	0.216696i	0.000280510	+	0.00839679i
$667$	2.10647	−	3.64851i	0.0815627	−	0.141271i
$668$	−14.9409	−	25.8784i	−0.578080	−	1.00126i
$669$	33.3287	−	19.9916i	1.28856	−	0.772921i
$670$	−10.2839	−	5.93742i	−0.397302	−	0.229382i
$671$	−19.1230			−0.738237
$672$	13.4203	−	15.6935i	0.517698	−	0.605392i
$673$	45.7248			1.76256			0.881280	−	0.472594i	$-0.156682\pi$
$673$	45.7248			1.76256			0.881280	+	0.472594i	$0.156682\pi$
$674$	67.9113	+	39.2086i	2.61585	+	1.51026i
$675$	4.48349	+	6.93837i	0.172569	+	0.267058i
$676$	−28.4044	−	49.1978i	−1.09248	−	1.89222i
$677$	12.8588	−	22.2722i	0.494205	−	0.855989i	−0.505772	−	0.862667i	$-0.668792\pi$
$677$	12.8588	−	22.2722i	0.494205	−	0.855989i	0.999978	+	0.00667815i	$0.00212574\pi$
$678$	−51.0175	+	0.851928i	−1.95931	+	0.0327181i
$679$	−2.81446	−	0.572198i	−0.108009	−	0.0219589i
$680$			30.0199i			1.15121i
$681$	−7.74030	+	13.9390i	−0.296609	+	0.534144i
$682$	33.3213	−	19.2381i	1.27594	−	0.736664i
$683$	7.09154	−	4.09430i	0.271350	−	0.156664i	−0.358151	−	0.933664i	$-0.616593\pi$
$683$	7.09154	−	4.09430i	0.271350	−	0.156664i	0.629501	+	0.777000i	$0.283259\pi$
$684$	67.5525	+	36.0494i	2.58293	+	1.37839i
$685$		−	23.8888i		−	0.912744i
$686$	−38.9731	+	18.6094i	−1.48800	+	0.710510i
$687$	−0.262200	−	15.7018i	−0.0100036	−	0.599061i
$688$	−1.15553	+	2.00143i	−0.0440540	+	0.0763038i
$689$	25.8851	+	44.8343i	0.986143	+	1.70805i
$690$	5.33343	+	8.89155i	0.203040	+	0.338495i
$691$	24.9066	+	14.3798i	0.947491	+	0.547034i	0.892301	−	0.451441i	$-0.149090\pi$
$691$	24.9066	+	14.3798i	0.947491	+	0.547034i	0.0551907	+	0.998476i	$0.482423\pi$
$692$	34.3215			1.30471
$693$	37.4716	+	6.32345i	1.42343	+	0.240208i
$694$	11.5529			0.438543
$695$	8.95579	+	5.17063i	0.339713	+	0.196133i
$696$	12.5863	+	20.9830i	0.477082	+	0.795359i
$697$	10.4276	+	18.0611i	0.394973	+	0.684114i
$698$	14.4122	−	24.9627i	0.545511	−	0.944853i
$699$	0.667602	+	39.9792i	0.0252510	+	1.51215i
$700$	10.8319	+	9.58053i	0.409407	+	0.362110i
$701$		−	19.7772i		−	0.746974i	−0.927635	−	0.373487i	$-0.878162\pi$
$701$		−	19.7772i		−	0.746974i	0.927635	−	0.373487i	$-0.121838\pi$
$702$	−30.0235	+	58.5956i	−1.13317	+	2.21155i
$703$	0.199260	−	0.115043i	0.00751524	−	0.00433892i
$704$	−51.3931	+	29.6718i	−1.93695	+	1.11830i
$705$	−14.8713	+	26.7808i	−0.560086	+	1.00862i
$706$		−	27.7125i		−	1.04298i
$707$	4.88255	−	1.63444i	0.183627	−	0.0614695i
$708$	−85.0699	+	1.42056i	−3.19712	+	0.0533879i
$709$	24.3590	−	42.1911i	0.914822	−	1.58452i	0.107661	−	0.994188i	$-0.465664\pi$
$709$	24.3590	−	42.1911i	0.914822	−	1.58452i	0.807161	−	0.590331i	$-0.201003\pi$
$710$	−21.8186	−	37.7909i	−0.818838	−	1.41827i
$711$	−12.7951	−	20.5455i	−0.479852	−	0.770515i
$712$	27.9391	+	16.1306i	1.04706	+	0.604521i
$713$	−3.44624			−0.129063
$714$	−12.4188	−	35.1384i	−0.464762	−	1.31502i
$715$	−66.7811			−2.49747
$716$	−24.7904	−	14.3128i	−0.926462	−	0.534893i
$717$	−12.0397	+	7.22180i	−0.449631	+	0.269703i
$718$	8.85210	+	15.3323i	0.330358	+	0.572196i
$719$	11.7981	−	20.4350i	0.439996	−	0.762096i	−0.557692	−	0.830048i	$-0.688313\pi$
$719$	11.7981	−	20.4350i	0.439996	−	0.762096i	0.997689	+	0.0679518i	$0.0216464\pi$
$720$	−7.26265	+	0.242622i	−0.270663	+	0.00904198i
$721$	−11.8706	+	13.4211i	−0.442084	+	0.499826i
$722$		−	84.2187i		−	3.13430i
$723$	−31.6516	−	17.5761i	−1.17714	−	0.653662i
$724$	61.7614	−	35.6580i	2.29535	−	1.32522i
$725$	5.80044	−	3.34888i	0.215423	−	0.124374i
$726$	−42.0993	−	23.3776i	−1.56245	−	0.867626i
$727$			14.5036i			0.537908i	0.963153	+	0.268954i	$0.0866780\pi$
$727$			14.5036i			0.537908i	−0.963153	+	0.268954i	$0.913322\pi$
$728$	−9.60401	+	47.2391i	−0.355948	+	1.75080i
$729$	26.8646	−	2.70042i	0.994986	−	0.100016i
$730$	−25.1426	+	43.5483i	−0.930570	+	1.61179i
$731$	−4.27084	−	7.39732i	−0.157963	−	0.273600i
$732$	−20.3963	+	12.2343i	−0.753867	+	0.452194i
$733$	44.0932	+	25.4572i	1.62862	+	0.940285i	0.984505	+	0.175357i	$0.0561081\pi$
$733$	44.0932	+	25.4572i	1.62862	+	0.940285i	0.644116	+	0.764927i	$0.277225\pi$
$734$	0.425948			0.0157220
$735$	−28.8521	−	11.6730i	−1.06423	−	0.430564i
$736$	4.50603			0.166095
$737$	−8.22495	−	4.74868i	−0.302970	−	0.174920i
$738$	−35.5116	+	22.1155i	−1.30720	+	0.814083i
$739$	−21.6728	−	37.5383i	−0.797246	−	1.38087i	−0.921403	−	0.388607i	$-0.872956\pi$
$739$	−21.6728	−	37.5383i	−0.797246	−	1.38087i	0.124158	−	0.992262i	$-0.460377\pi$
$740$	−0.136760	+	0.236875i	−0.00502740	+	0.00870771i
$741$	69.8593	−	1.16656i	2.56634	−	0.0428547i
$742$	11.7115	−	57.6054i	0.429944	−	2.11476i
$743$			23.6885i			0.869048i	0.900660	+	0.434524i	$0.143083\pi$
$743$			23.6885i			0.869048i	−0.900660	+	0.434524i	$0.856917\pi$
$744$	9.71692	−	17.4986i	0.356240	−	0.641529i
$745$	−32.1861	+	18.5827i	−1.17921	+	0.680816i
$746$	−29.5682	+	17.0712i	−1.08257	+	0.625022i
$747$	6.61247	−	12.3910i	0.241938	−	0.453363i
$748$			57.4039i			2.09889i
$749$	−17.6213	+	19.9229i	−0.643868	+	0.727966i
$750$	−0.590359	−	35.3535i	−0.0215569	−	1.29093i
$751$	−17.0576	+	29.5446i	−0.622440	+	1.07810i	0.366589	+	0.930383i	$0.380525\pi$
$751$	−17.0576	+	29.5446i	−0.622440	+	1.07810i	−0.989030	+	0.147716i	$0.952808\pi$
$752$	−3.25041	−	5.62988i	−0.118530	−	0.205300i
$753$	15.5327	+	25.8950i	0.566042	+	0.943668i
$754$	46.2296	+	26.6907i	1.68358	+	0.972017i
$755$	60.4689			2.20069
$756$	44.0120	−	17.2287i	1.60070	−	0.626601i
$757$	14.9501			0.543369			0.271685	−	0.962386i	$-0.412419\pi$
$757$	14.9501			0.543369			0.271685	+	0.962386i	$0.412419\pi$
$758$	−1.63384	−	0.943297i	−0.0593437	−	0.0342621i
$759$	4.26562	+	7.11135i	0.154832	+	0.258126i
$760$	31.9523	+	55.3431i	1.15903	+	2.00750i
$761$	13.5232	−	23.4228i	0.490215	−	0.849077i	−0.509722	−	0.860339i	$-0.670252\pi$
$761$	13.5232	−	23.4228i	0.490215	−	0.849077i	0.999937	+	0.0112621i	$0.00358492\pi$
$762$	−0.498285	−	29.8397i	−0.0180510	−	1.08098i
$763$	−9.98815	+	3.34355i	−0.361595	+	0.121045i
$764$		−	1.60528i		−	0.0580769i
$765$	12.6448	−	23.6950i	0.457175	−	0.856693i
$766$	−34.9867	+	20.1996i	−1.26412	+	0.729840i
$767$	−67.2350	+	38.8181i	−2.42771	+	1.40164i
$768$	−18.1606	+	32.7042i	−0.655313	+	1.18011i
$769$			39.6991i			1.43159i	0.698312	+	0.715793i	$0.253935\pi$
$769$			39.6991i			1.43159i	−0.698312	+	0.715793i	$0.746065\pi$
$770$	56.7992	+	50.2375i	2.04690	+	1.81043i
$771$	−3.32383	+	0.0555038i	−0.119705	+	0.00199892i
$772$	12.5625	−	21.7589i	0.452134	−	0.783118i
$773$	−6.26626	−	10.8535i	−0.225382	−	0.390373i	0.731052	−	0.682322i	$-0.239030\pi$
$773$	−6.26626	−	10.8535i	−0.225382	−	0.390373i	−0.956434	+	0.291949i	$0.905696\pi$
$774$	14.5445	−	9.05787i	0.522792	−	0.325578i
$775$	−4.74484	−	2.73943i	−0.170440	−	0.0984034i
$776$	3.64000			0.130668
$777$	0.0259679	−	0.139630i	0.000931593	−	0.00500921i
$778$	12.7134			0.455797
$779$	38.4475	+	22.1977i	1.37752	+	0.795314i
$780$	−71.2273	+	42.7244i	−2.55035	+	1.52978i
$781$	−17.4503	−	30.2247i	−0.624420	−	1.08153i
$782$	4.06631	−	7.04306i	0.145411	−	0.251859i
$783$	−1.09610	−	21.8636i	−0.0391713	−	0.781340i
$784$	5.27393	−	3.97651i	0.188355	−	0.142018i
$785$		−	43.9963i		−	1.57029i
$786$	−46.7243	−	25.9459i	−1.66660	−	0.925459i
$787$	38.3209	−	22.1246i	1.36599	−	0.788656i	0.375579	−	0.926790i	$-0.377444\pi$
$787$	38.3209	−	22.1246i	1.36599	−	0.788656i	0.990414	+	0.138134i	$0.0441105\pi$
$788$	−46.9557	+	27.1099i	−1.67273	+	0.965751i
$789$	−17.2405	−	9.57363i	−0.613779	−	0.340830i
$790$		−	48.2968i		−	1.71832i
$791$	32.7533	+	6.65896i	1.16457	+	0.236765i
$792$	−48.1358	+	1.60806i	−1.71043	+	0.0571400i
$793$	−10.8514	+	18.7952i	−0.385345	+	0.667436i
$794$	17.3370	+	30.0286i	0.615269	+	1.06568i
$795$	36.3288	−	21.7912i	1.28845	−	0.772854i
$796$	−50.5951	−	29.2111i	−1.79330	−	1.03536i
$797$	9.70003			0.343593			0.171796	−	0.985132i	$-0.445043\pi$
$797$	9.70003			0.343593			0.171796	+	0.985132i	$0.445043\pi$
$798$	−60.2948	−	51.5609i	−2.13441	−	1.82524i
$799$	24.0271			0.850019
$800$	6.20399	+	3.58187i	0.219344	+	0.126638i
$801$	−15.2581	−	24.5004i	−0.539117	−	0.865678i
$802$	3.41587	+	5.91646i	0.120619	+	0.208918i
$803$	−20.1088	+	34.8294i	−0.709623	+	1.22910i
$804$	−11.8106	+	0.197223i	−0.416529	+	0.00695550i
$805$	−2.15598	−	6.44053i	−0.0759882	−	0.226999i
$806$		−	43.6667i		−	1.53809i
$807$	−4.69374	+	8.45265i	−0.165227	+	0.297547i
$808$	−5.65135	+	3.26281i	−0.198814	+	0.114785i
$809$	−46.4908	+	26.8415i	−1.63453	+	0.943697i	−0.651859	+	0.758340i	$0.726011\pi$
$809$	−46.4908	+	26.8415i	−1.63453	+	0.943697i	−0.982671	+	0.185356i	$0.940656\pi$
$810$	48.3519	+	23.7641i	1.69891	+	0.834985i
$811$		−	40.1751i		−	1.41074i	−0.708841	−	0.705369i	$-0.750781\pi$
$811$		−	40.1751i		−	1.41074i	0.708841	−	0.705369i	$-0.249219\pi$
$812$	−12.1644	−	36.3386i	−0.426887	−	1.27524i
$813$	−0.0476110	−	2.85117i	−0.00166979	−	0.0999949i
$814$	−0.173010	+	0.299661i	−0.00606398	+	0.0105031i
$815$	9.18219	+	15.9040i	0.321638	+	0.557094i
$816$	2.93188	+	4.88783i	0.102636	+	0.171108i
$817$	−15.7470	−	9.09152i	−0.550917	−	0.318072i
$818$	−45.9993			−1.60833
$819$	27.4783	−	33.2409i	0.960171	−	1.16153i
$820$	−52.7760			−1.84302
$821$	−25.8248	−	14.9100i	−0.901292	−	0.520361i	−0.0236726	−	0.999720i	$-0.507536\pi$
$821$	−25.8248	−	14.9100i	−0.901292	−	0.520361i	−0.877619	+	0.479359i	$0.840869\pi$
$822$	−19.3343	−	32.2328i	−0.674361	−	1.12425i
$823$	1.80805	+	3.13164i	0.0630248	+	0.109162i	0.895816	−	0.444425i	$-0.146592\pi$
$823$	1.80805	+	3.13164i	0.0630248	+	0.109162i	−0.832791	+	0.553587i	$0.813259\pi$
$824$	11.3542	−	19.6661i	0.395543	−	0.685101i
$825$	0.220120	+	13.1818i	0.00766358	+	0.458932i
$826$	86.3870	+	17.5630i	3.00579	+	0.611095i
$827$		−	30.9107i		−	1.07487i	−0.843305	−	0.537436i	$-0.819393\pi$
$827$		−	30.9107i		−	1.07487i	0.843305	−	0.537436i	$-0.180607\pi$
$828$	9.09925	+	4.85582i	0.316221	+	0.168751i
$829$	−13.9435	+	8.05028i	−0.484278	+	0.279598i	−0.722197	−	0.691687i	$-0.756868\pi$
$829$	−13.9435	+	8.05028i	−0.484278	+	0.279598i	0.237920	+	0.971285i	$0.423534\pi$
$830$	24.2708	−	14.0128i	0.842453	−	0.486391i
$831$	9.84983	−	17.7379i	0.341687	−	0.615322i
$832$			67.3493i			2.33492i
$833$	2.98193	+	24.2296i	0.103318	+	0.839507i
$834$	16.2688	−	0.271668i	0.563341	−	0.00940709i
$835$	−11.1561	+	19.3230i	−0.386074	+	0.668699i
$836$	61.0990	+	105.827i	2.11315	+	3.66009i
$837$	−15.0403	+	9.71885i	−0.519869	+	0.335933i
$838$	8.60603	+	4.96870i	0.297291	+	0.171641i
$839$	35.5171			1.22619			0.613093	−	0.790011i	$-0.289925\pi$
$839$	35.5171			1.22619			0.613093	+	0.790011i	$0.289925\pi$
$840$	38.7813	+	7.21240i	1.33808	+	0.248851i
$841$	11.2512			0.387973
$842$	46.1989	+	26.6729i	1.59212	+	0.919210i
$843$	−27.0964	+	16.2533i	−0.933251	+	0.559794i
$844$	−10.5286	−	18.2361i	−0.362410	−	0.627712i
$845$	−21.2091	+	36.7352i	−0.729615	+	1.26373i
$846$	1.60924	+	48.1710i	0.0553267	+	1.65615i
$847$	23.6275	+	20.8980i	0.811852	+	0.718063i
$848$			8.99023i			0.308726i
$849$	−28.0299	−	15.5649i	−0.961982	−	0.534187i
$850$	11.1971	−	6.46467i	0.384059	−	0.221736i
$851$	0.0268401	−	0.0154961i	0.000920067	−	0.000531201i
$852$	−37.9490	−	21.0730i	−1.30011	−	0.721948i
$853$			40.0808i			1.37234i	0.727442	+	0.686169i	$0.240709\pi$
$853$			40.0808i			1.37234i	−0.727442	+	0.686169i	$0.759291\pi$
$854$	23.3685	−	7.82264i	0.799653	−	0.267685i
$855$	−1.90891	−	57.1415i	−0.0652835	−	1.95420i
$856$	16.8548	−	29.1933i	0.576085	−	0.997808i
$857$	−2.13974	−	3.70614i	−0.0730922	−	0.126599i	0.827163	−	0.561962i	$-0.189953\pi$
$857$	−2.13974	−	3.70614i	−0.0730922	−	0.126599i	−0.900255	+	0.435363i	$0.856620\pi$
$858$	−90.1068	+	54.0489i	−3.07620	+	1.84520i
$859$	−1.48598	−	0.857929i	−0.0507009	−	0.0292722i	0.474435	−	0.880290i	$-0.342652\pi$
$859$	−1.48598	−	0.857929i	−0.0507009	−	0.0292722i	−0.525136	+	0.851018i	$0.675986\pi$
$860$	21.6155			0.737084
$861$	25.8376	−	9.13167i	0.880542	−	0.311206i
$862$	−10.4371			−0.355488
$863$	24.2618	+	14.0076i	0.825882	+	0.476823i	0.852440	−	0.522824i	$-0.175122\pi$
$863$	24.2618	+	14.0076i	0.825882	+	0.476823i	−0.0265589	+	0.999647i	$0.508455\pi$
$864$	19.6655	−	12.7076i	0.669035	−	0.432322i
$865$	−12.8137	−	22.1939i	−0.435678	−	0.754617i
$866$	7.60494	−	13.1722i	0.258427	−	0.447608i
$867$	8.37745	−	0.139893i	0.284513	−	0.00475101i
$868$	−20.7677	+	23.4803i	−0.704902	+	0.796972i
$869$		−	38.6272i		−	1.31034i
$870$	21.2062	−	38.1888i	0.718956	−	1.29472i
$871$	−9.33452	+	5.38929i	−0.316288	+	0.182609i
$872$	11.5609	−	6.67467i	0.391500	−	0.226033i
$873$	−2.87308	−	1.53322i	−0.0972391	−	0.0518917i
$874$		−	17.3123i		−	0.585596i
$875$	−4.61444	+	22.6970i	−0.155997	+	0.767299i
$876$	0.835159	+	50.0133i	0.0282174	+	1.68979i
$877$	−28.4095	+	49.2066i	−0.959319	+	1.66159i	−0.235160	+	0.971957i	$0.575561\pi$
$877$	−28.4095	+	49.2066i	−0.959319	+	1.66159i	−0.724159	+	0.689633i	$0.757772\pi$
$878$	8.40409	+	14.5563i	0.283624	+	0.491252i
$879$	−10.0634	−	16.7770i	−0.339430	−	0.565875i
$880$	−10.0433	−	5.79849i	−0.338559	−	0.195467i
$881$	−15.3346			−0.516637			−0.258319	−	0.966060i	$-0.583168\pi$
$881$	−15.3346			−0.516637			−0.258319	+	0.966060i	$0.583168\pi$
$882$	−48.3772	+	7.60114i	−1.62895	+	0.255944i
$883$	−41.5291			−1.39757			−0.698783	−	0.715334i	$-0.746275\pi$
$883$	−41.5291			−1.39757			−0.698783	+	0.715334i	$0.746275\pi$
$884$	56.4197	+	32.5739i	1.89760	+	1.09558i
$885$	32.6788	+	54.4799i	1.09849	+	1.83132i
$886$	6.84977	+	11.8641i	0.230122	+	0.398584i
$887$	25.8476	−	44.7693i	0.867876	−	1.50321i	0.00371341	−	0.999993i	$-0.498818\pi$
$887$	25.8476	−	44.7693i	0.867876	−	1.50321i	0.864163	−	0.503212i	$-0.167849\pi$
$888$	0.00300537	+	0.179976i	0.000100854	+	0.00603959i
$889$	−3.89476	+	19.1571i	−0.130626	+	0.642510i
$890$		−	57.5937i		−	1.93055i
$891$	38.6713	+	19.0062i	1.29554	+	0.636733i
$892$	66.8074	−	38.5713i	2.23688	−	1.29146i
$893$	44.2951	−	25.5738i	1.48228	−	0.855794i
$894$	−28.3885	+	51.1230i	−0.949453	+	1.70981i
$895$			21.3742i			0.714462i
$896$	34.8681	−	39.4224i	1.16486	−	1.31701i
$897$	9.40996	−	0.157135i	0.314189	−	0.00524657i
$898$	−27.5671	+	47.7477i	−0.919927	+	1.59336i
$899$	7.25938	+	12.5736i	0.242114	+	0.419353i
$900$	8.66808	+	13.9186i	0.288936	+	0.463954i
$901$	−28.7763	−	16.6140i	−0.958679	−	0.553493i
$902$	−66.7648			−2.22302
$903$	−10.5823	+	3.74007i	−0.352158	+	0.124462i
$904$	−42.3605			−1.40889
$905$	−46.1163	−	26.6253i	−1.53296	−	0.885054i
$906$	81.5899	−	48.9402i	2.71064	−	1.62593i
$907$	−10.6540	−	18.4532i	−0.353759	−	0.612728i	0.633146	−	0.774032i	$-0.281763\pi$
$907$	−10.6540	−	18.4532i	−0.353759	−	0.612728i	−0.986905	+	0.161304i	$0.948430\pi$
$908$	−15.8235	+	27.4071i	−0.525122	+	0.909538i
$909$	5.83500	−	0.194929i	0.193535	−	0.00646537i
$910$	81.6069	−	27.3180i	2.70524	−	0.905584i
$911$			58.6272i			1.94241i	0.238251	+	0.971204i	$0.423426\pi$
$911$			58.6272i			1.94241i	−0.238251	+	0.971204i	$0.576574\pi$
$912$	10.6075	+	5.89032i	0.351250	+	0.195048i
$913$	19.4115	−	11.2073i	0.642428	−	0.370906i
$914$	37.8710	−	21.8648i	1.25266	−	0.723224i
$915$	15.5261	+	8.62161i	0.513277	+	0.285022i
$916$		−	31.1708i		−	1.02991i
$917$	26.2232	+	23.1938i	0.865968	+	0.765927i
$918$	−2.11590	−	42.2053i	−0.0698352	−	1.39298i
$919$	−2.38220	+	4.12609i	−0.0785815	+	0.136107i	−0.902638	−	0.430400i	$-0.858372\pi$
$919$	−2.38220	+	4.12609i	−0.0785815	+	0.136107i	0.824057	+	0.566507i	$0.191706\pi$
$920$	4.30394	+	7.45465i	0.141897	+	0.245773i
$921$	43.9827	−	26.3822i	1.44928	−	0.869324i
$922$	1.76623	+	1.01973i	0.0581675	+	0.0335830i
$923$	−39.6087			−1.30374
$924$	74.1573	+	13.7915i	2.43960	+	0.453707i
$925$	0.0492719			0.00162005
$926$	10.8720	+	6.27698i	0.357278	+	0.206274i
$927$	−17.2456	+	10.7400i	−0.566421	+	0.352749i
$928$	−9.49180	−	16.4403i	−0.311584	−	0.539679i
$929$	5.43603	−	9.41549i	0.178350	−	0.308912i	−0.762965	−	0.646440i	$-0.776257\pi$
$929$	5.43603	−	9.41549i	0.178350	−	0.308912i	0.941316	+	0.337527i	$0.109591\pi$
$930$	−35.7272	+	0.596599i	−1.17154	+	0.0195633i
$931$	31.2866	+	41.4945i	1.02538	+	1.35993i
$932$			79.3658i			2.59971i
$933$	2.57369	−	4.63479i	0.0842588	−	0.151736i
$934$	−4.74990	+	2.74236i	−0.155421	+	0.0897326i
$935$	37.1201	−	21.4313i	1.21396	−	0.700879i
$936$	−25.7342	+	48.2230i	−0.841150	+	1.57622i
$937$			18.7609i			0.612893i	0.951888	+	0.306447i	$0.0991401\pi$
$937$			18.7609i			0.612893i	−0.951888	+	0.306447i	$0.900860\pi$
$938$	11.9935	+	2.43835i	0.391601	+	0.0796149i
$939$	0.702334	+	42.0591i	0.0229198	+	1.37255i
$940$	−30.4015	+	52.6569i	−0.991586	+	1.71748i
$941$	6.65812	+	11.5322i	0.217048	+	0.375939i	0.953904	−	0.300111i	$-0.0970237\pi$
$941$	6.65812	+	11.5322i	0.217048	+	0.375939i	−0.736856	+	0.676050i	$0.763690\pi$
$942$	−35.6082	−	59.3636i	−1.16018	−	1.93417i
$943$	5.17883	+	2.99000i	0.168646	+	0.0973678i
$944$	−13.4821			−0.438804
$945$	−27.5724	−	22.0281i	−0.896931	−	0.716573i
$946$	27.3449			0.889060
$947$	−14.0430	−	8.10773i	−0.456336	−	0.263466i	0.254166	−	0.967161i	$-0.418199\pi$
$947$	−14.0430	−	8.10773i	−0.456336	−	0.263466i	−0.710503	+	0.703695i	$0.751532\pi$
$948$	−24.7125	−	41.1990i	−0.802624	−	1.33808i
$949$	22.8215	+	39.5280i	0.740817	+	1.28313i
$950$	13.7616	−	23.8358i	0.446486	−	0.773336i
$951$	0.679963	+	40.7194i	0.0220493	+	1.32042i
$952$	−9.82157	−	29.3399i	−0.318319	−	0.950911i
$953$			3.22083i			0.104333i	0.998638	+	0.0521665i	$0.0166127\pi$
$953$			3.22083i			0.104333i	−0.998638	+	0.0521665i	$0.983387\pi$
$954$	31.3814	−	58.8052i	1.01601	−	1.90389i
$955$	−1.03805	+	0.599319i	−0.0335905	+	0.0193935i
$956$	−24.1336	+	13.9335i	−0.780537	+	0.450643i
$957$	16.9604	−	30.5430i	0.548253	−	0.987313i
$958$			45.6536i			1.47500i
$959$	7.81566	+	23.3476i	0.252381	+	0.753935i
$960$	55.1038	−	0.920165i	1.77847	−	0.0296982i
$961$	−9.56173	+	16.5614i	−0.308443	+	0.534239i
$962$	0.196349	+	0.340087i	0.00633055	+	0.0109648i
$963$	−25.6003	+	15.9430i	−0.824957	+	0.513757i
$964$	−62.2341	−	35.9309i	−2.00442	−	1.15726i
$965$	−18.7604			−0.603920
$966$	−8.12165	−	6.94519i	−0.261310	−	0.223458i
$967$	30.5062			0.981012			0.490506	−	0.871438i	$-0.336812\pi$
$967$	30.5062			0.981012			0.490506	+	0.871438i	$0.336812\pi$
$968$	−34.6218	−	19.9889i	−1.11279	−	0.642469i
$969$	−38.4568	+	23.0676i	−1.23541	+	0.741038i
$970$	−3.24912	−	5.62764i	−0.104323	−	0.180693i
$971$	−27.5870	+	47.7821i	−0.885310	+	1.53340i	−0.0399516	+	0.999202i	$0.512720\pi$
$971$	−27.5870	+	47.7821i	−0.885310	+	1.53340i	−0.845358	+	0.534200i	$0.820613\pi$
$972$	53.4056	−	4.46901i	1.71299	−	0.143343i
$973$	−10.4446	−	2.12345i	−0.334838	−	0.0680746i
$974$		−	67.3161i		−	2.15695i
$975$	13.0807	+	7.26369i	0.418918	+	0.232624i
$976$	−3.26391	+	1.88442i	−0.104475	+	0.0603188i
$977$	−4.03649	+	2.33047i	−0.129139	+	0.0745584i	−0.563178	−	0.826336i	$-0.690421\pi$
$977$	−4.03649	+	2.33047i	−0.129139	+	0.0745584i	0.434039	+	0.900894i	$0.357088\pi$
$978$	25.2613	+	14.0275i	0.807766	+	0.448551i
$979$		−	46.0628i		−	1.47217i
$980$	−56.8737	−	24.1226i	−1.81676	−	0.770569i
$981$	−11.9366	+	0.398762i	−0.381105	+	0.0127315i
$982$	23.6289	−	40.9264i	0.754027	−	1.30601i
$983$	−7.23382	−	12.5293i	−0.230723	−	0.399624i	0.727298	−	0.686322i	$-0.240776\pi$
$983$	−7.23382	−	12.5293i	−0.230723	−	0.399624i	−0.958021	+	0.286698i	$0.907442\pi$
$984$	−29.7841	+	17.8655i	−0.949482	+	0.569530i
$985$	35.0611	+	20.2426i	1.11714	+	0.644982i
$986$	−34.2622			−1.09113
$987$	5.77261	−	31.0395i	0.183744	−	0.987999i
$988$	138.683			4.41209
$989$	−2.12110	−	1.22462i	−0.0674470	−	0.0389406i
$990$	45.4528	+	72.9851i	1.44459	+	2.31962i
$991$	−14.1237	−	24.4629i	−0.448653	−	0.777090i	0.549645	−	0.835398i	$-0.314763\pi$
$991$	−14.1237	−	24.4629i	−0.448653	−	0.777090i	−0.998299	+	0.0583079i	$0.981430\pi$
$992$	−7.76443	+	13.4484i	−0.246521	+	0.426987i
$993$	−32.7274	+	0.546506i	−1.03857	+	0.0173428i
$994$	33.6883	+	29.7965i	1.06853	+	0.945087i
$995$			43.6230i			1.38294i
$996$	13.5339	−	24.3723i	0.428838	−	0.772267i
$997$	−20.9215	+	12.0790i	−0.662591	+	0.382547i	−0.793263	−	0.608879i	$-0.791620\pi$
$997$	−20.9215	+	12.0790i	−0.662591	+	0.382547i	0.130673	+	0.991426i	$0.458286\pi$
$998$	31.7336	−	18.3214i	1.00451	−	0.579954i
$999$	0.0734362	−	0.143322i	0.00232342	−	0.00453451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.n.a.47.6	✓	116
3.2	odd	2	inner	483.2.n.a.47.53	yes	116
7.3	odd	6	inner	483.2.n.a.185.53	yes	116
21.17	even	6	inner	483.2.n.a.185.6	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.n.a.47.6	✓	116	1.1	even	1	trivial
483.2.n.a.47.53	yes	116	3.2	odd	2	inner
483.2.n.a.185.6	yes	116	21.17	even	6	inner
483.2.n.a.185.53	yes	116	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.01952 - 1.16597i) q^{2} +(0.890949 + 1.48533i) q^{3} +(1.71897 + 2.97735i) q^{4} +(1.28353 - 2.22314i) q^{5} +(-0.0674375 - 4.03848i) q^{6} +(-0.527114 + 2.59271i) q^{7} -3.35320i q^{8} +(-1.41242 + 2.64671i) q^{9} +(-5.18423 + 2.99312i) q^{10} +(-4.14629 + 2.39386i) q^{11} +(-2.89083 + 5.20591i) q^{12} +5.43360i q^{13} +(4.08754 - 4.62143i) q^{14} +(4.44566 - 0.0742370i) q^{15} +(-0.471791 + 0.817165i) q^{16} +(-1.74375 - 3.02026i) q^{17} +(5.93839 - 3.69824i) q^{18} +(-6.42934 - 3.71198i) q^{19} +8.82542 q^{20} +(-4.32067 + 1.52703i) q^{21} +11.1647 q^{22} +(-0.866025 - 0.500000i) q^{23} +(4.98062 - 2.98754i) q^{24} +(-0.794906 - 1.37682i) q^{25} +(6.33542 - 10.9733i) q^{26} +(-5.18963 + 0.260175i) q^{27} +(-8.62550 + 2.88740i) q^{28} +4.21293i q^{29} +(-9.06466 - 5.03359i) q^{30} +(2.98453 - 1.72312i) q^{31} +(-3.90234 + 2.25302i) q^{32} +(-7.24981 - 4.02580i) q^{33} +8.13262i q^{34} +(5.08740 + 4.49968i) q^{35} +(-10.3081 + 0.344360i) q^{36} +(-0.0154961 + 0.0268401i) q^{37} +(8.65613 + 14.9928i) q^{38} +(-8.07070 + 4.84106i) q^{39} +(-7.45465 - 4.30394i) q^{40} -5.98000 q^{41} +(10.5061 + 1.95389i) q^{42} +2.44923 q^{43} +(-14.2547 - 8.22997i) q^{44} +(4.07113 + 6.53714i) q^{45} +(1.16597 + 2.01952i) q^{46} +(-3.44476 + 5.96650i) q^{47} +(-1.63410 + 0.0272875i) q^{48} +(-6.44430 - 2.73331i) q^{49} +3.70735i q^{50} +(2.93249 - 5.28094i) q^{51} +(-16.1777 + 9.34021i) q^{52} +(8.25130 - 4.76389i) q^{53} +(10.7839 + 5.52553i) q^{54} +12.2904i q^{55} +(8.69389 + 1.76752i) q^{56} +(-0.214694 - 12.8569i) q^{57} +(4.91215 - 8.50810i) q^{58} +(7.14409 + 12.3739i) q^{59} +(7.86301 + 13.1087i) q^{60} +(3.45906 + 1.99709i) q^{61} -8.03642 q^{62} +(-6.11765 - 5.05711i) q^{63} +12.3950 q^{64} +(12.0797 + 6.97420i) q^{65} +(9.94717 + 16.5833i) q^{66} +(0.991845 + 1.71793i) q^{67} +(5.99490 - 10.3835i) q^{68} +(-0.0289190 - 1.73181i) q^{69} +(-5.02761 - 15.0189i) q^{70} +7.28959i q^{71} +(8.87496 + 4.73613i) q^{72} +(7.27473 - 4.20007i) q^{73} +(0.0625895 - 0.0361361i) q^{74} +(1.33681 - 2.40737i) q^{75} -25.5232i q^{76} +(-4.02102 - 12.0120i) q^{77} +(21.9435 - 0.366428i) q^{78} +(-4.03398 + 6.98707i) q^{79} +(1.21112 + 2.09772i) q^{80} +(-5.01015 - 7.47653i) q^{81} +(12.0767 + 6.97250i) q^{82} -4.68166 q^{83} +(-11.9736 - 10.2392i) q^{84} -8.95261 q^{85} +(-4.94628 - 2.85573i) q^{86} +(-6.25760 + 3.75351i) q^{87} +(8.02711 + 13.9034i) q^{88} +(-4.81051 + 8.33205i) q^{89} +(-0.599609 - 17.9487i) q^{90} +(-14.0878 - 2.86413i) q^{91} -3.43795i q^{92} +(5.21846 + 2.89780i) q^{93} +(13.9135 - 8.03297i) q^{94} +(-16.5045 + 9.52890i) q^{95} +(-6.82326 - 3.78894i) q^{96} +1.08553i q^{97} +(9.82744 + 13.0338i) q^{98} +(-0.479560 - 14.3552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 20 q^{15} - 52 q^{16} - 10 q^{18} + 6 q^{19} - 6 q^{21} - 16 q^{22} - 66 q^{25} + 16 q^{28} - 32 q^{30} - 42 q^{31} - 30 q^{33} + 8 q^{36}+ \cdots + 24 q^{99}+O(q^{100}) \) 116 * q + 56 * q^4 - 10 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 20 * q^15 - 52 * q^16 - 10 * q^18 + 6 * q^19 - 6 * q^21 - 16 * q^22 - 66 * q^25 + 16 * q^28 - 32 * q^30 - 42 * q^31 - 30 * q^33 + 8 * q^36 - 2 * q^37 - 22 * q^39 - 36 * q^40 + 46 * q^42 + 20 * q^43 + 30 * q^45 - 22 * q^49 + 12 * q^51 + 48 * q^52 - 54 * q^54 - 44 * q^57 + 52 * q^58 + 32 * q^60 + 36 * q^61 - 38 * q^63 - 160 * q^64 + 10 * q^67 - 20 * q^70 + 62 * q^72 + 18 * q^73 + 78 * q^75 + 12 * q^78 + 10 * q^79 - 28 * q^81 + 32 * q^84 - 32 * q^85 - 30 * q^87 - 36 * q^88 + 50 * q^91 + 60 * q^94 + 84 * q^96 + 24 * q^99

Introduction

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