LMFDB - Embedded newform 352.2.bf.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(5,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([0, 5, 16]))

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

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

chi := DirichletCharacter("352.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$352 = 2^{5} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	352.bf (of order $40$ , degree $16$ , 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$736$
Relative dimension:	$46$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	352.5
Dual form			352.2.bf.a.141.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32175 + 0.502961i) q^{2} +(0.0699635 - 0.291419i) q^{3} +(1.49406 - 1.32958i) q^{4} +(-1.39403 + 1.63220i) q^{5} +(0.0540980 + 0.420372i) q^{6} +(-2.54848 - 0.403640i) q^{7} +(-1.30605 + 2.50883i) q^{8} +(2.59299 + 1.32119i) q^{9} +(1.02163 - 2.85850i) q^{10} +(-2.18109 - 2.49857i) q^{11} +(-0.282935 - 0.528419i) q^{12} +(-1.96677 - 2.30279i) q^{13} +(3.57148 - 0.748276i) q^{14} +(0.378122 + 0.520440i) q^{15} +(0.464428 - 3.97295i) q^{16} +(-1.33872 - 0.434977i) q^{17} +(-4.09180 - 0.442118i) q^{18} +(-3.12581 - 0.750441i) q^{19} +(0.0873777 + 4.29207i) q^{20} +(-0.295929 + 0.714435i) q^{21} +(4.13954 + 2.20549i) q^{22} +(-5.25943 + 5.25943i) q^{23} +(0.639745 + 0.556134i) q^{24} +(0.0614196 + 0.387788i) q^{25} +(3.75780 + 2.05451i) q^{26} +(1.15035 - 1.34689i) q^{27} +(-4.34425 + 2.78535i) q^{28} +(-4.03703 - 2.47389i) q^{29} +(-0.761545 - 0.497712i) q^{30} +(-2.83606 - 8.72850i) q^{31} +(1.38438 + 5.48484i) q^{32} +(-0.880727 + 0.460801i) q^{33} +(1.98823 - 0.0983934i) q^{34} +(4.21147 - 3.59694i) q^{35} +(5.63072 - 1.47365i) q^{36} +(-5.79103 + 1.39030i) q^{37} +(4.50899 - 0.580266i) q^{38} +(-0.808679 + 0.412042i) q^{39} +(-2.27424 - 5.62911i) q^{40} +(-1.12234 + 0.177761i) q^{41} +(0.0318112 - 1.09315i) q^{42} +(2.73645 - 6.60637i) q^{43} +(-6.58073 - 0.833082i) q^{44} +(-5.77115 + 2.39049i) q^{45} +(4.30637 - 9.59695i) q^{46} +(-5.66983 + 7.80385i) q^{47} +(-1.12530 - 0.413304i) q^{48} +(-0.325568 - 0.105783i) q^{49} +(-0.276224 - 0.481668i) q^{50} +(-0.220422 + 0.359696i) q^{51} +(-6.00022 - 0.825527i) q^{52} +(9.56996 + 0.753172i) q^{53} +(-0.843048 + 2.35884i) q^{54} +(7.11865 - 0.0768858i) q^{55} +(4.34110 - 5.86654i) q^{56} +(-0.437385 + 0.858417i) q^{57} +(6.58023 + 1.23941i) q^{58} +(-0.781941 + 0.187727i) q^{59} +(1.25690 + 0.274825i) q^{60} +(-0.763355 + 0.0600774i) q^{61} +(8.13867 + 10.1105i) q^{62} +(-6.07490 - 4.41367i) q^{63} +(-4.58847 - 6.55331i) q^{64} +6.50034 q^{65} +(0.932338 - 1.05204i) q^{66} +(0.150571 + 0.363511i) q^{67} +(-2.57847 + 1.13006i) q^{68} +(1.16473 + 1.90066i) q^{69} +(-3.75740 + 6.87247i) q^{70} +(3.73200 - 1.90155i) q^{71} +(-6.70122 + 4.77983i) q^{72} +(-2.05944 + 13.0028i) q^{73} +(6.95504 - 4.75030i) q^{74} +(0.117306 + 0.00923217i) q^{75} +(-5.66792 + 3.03482i) q^{76} +(4.54994 + 7.24793i) q^{77} +(0.861632 - 0.951352i) q^{78} +(10.2072 - 3.31652i) q^{79} +(5.83721 + 6.29643i) q^{80} +(4.81966 + 6.63369i) q^{81} +(1.39405 - 0.799451i) q^{82} +(-0.527481 - 6.70228i) q^{83} +(0.507764 + 1.46087i) q^{84} +(2.57618 - 1.57869i) q^{85} +(-0.294158 + 10.1083i) q^{86} +(-1.00338 + 1.00338i) q^{87} +(9.11710 - 2.20872i) q^{88} +(12.9060 + 12.9060i) q^{89} +(6.42571 - 6.06230i) q^{90} +(4.08278 + 6.66249i) q^{91} +(-0.865062 + 14.8507i) q^{92} +(-2.74207 + 0.215806i) q^{93} +(3.56907 - 13.1665i) q^{94} +(5.58233 - 4.05580i) q^{95} +(1.69524 - 0.0196961i) q^{96} +(-0.340640 - 1.04838i) q^{97} +(0.483525 - 0.0239286i) q^{98} +(-2.35444 - 9.36041i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20}+ \cdots - 68 q^{99}+O(q^{100})$ 736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$ .

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.32175	+	0.502961i	−0.934620	+	0.355647i
$2$	−1.32175	+	0.502961i	−0.934620	+	0.355647i
$3$	0.0699635	−	0.291419i	0.0403934	−	0.168251i	−0.948527	−	0.316695i	$-0.897427\pi$
$3$	0.0699635	−	0.291419i	0.0403934	−	0.168251i	0.988921	+	0.148445i	$0.0474267\pi$
$4$	1.49406	−	1.32958i	0.747030	−	0.664791i
$5$	−1.39403	+	1.63220i	−0.623428	+	0.729940i	−0.978808	−	0.204782i	$-0.934352\pi$
$5$	−1.39403	+	1.63220i	−0.623428	+	0.729940i	0.355380	+	0.934722i	$0.384352\pi$
$6$	0.0540980	+	0.420372i	0.0220854	+	0.171616i
$7$	−2.54848	−	0.403640i	−0.963235	−	0.152561i	−0.345042	−	0.938587i	$-0.612135\pi$
$7$	−2.54848	−	0.403640i	−0.963235	−	0.152561i	−0.618194	+	0.786026i	$0.712135\pi$
$8$	−1.30605	+	2.50883i	−0.461758	+	0.887006i
$9$	2.59299	+	1.32119i	0.864330	+	0.440398i
$10$	1.02163	−	2.85850i	0.323067	−	0.903938i
$11$	−2.18109	−	2.49857i	−0.657623	−	0.753348i
$11$	−2.18109	−	2.49857i	−0.657623	−	0.753348i
$12$	−0.282935	−	0.528419i	−0.0816764	−	0.152541i
$13$	−1.96677	−	2.30279i	−0.545484	−	0.638679i	0.417359	−	0.908742i	$-0.362956\pi$
$13$	−1.96677	−	2.30279i	−0.545484	−	0.638679i	−0.962843	+	0.270062i	$0.912956\pi$
$14$	3.57148	−	0.748276i	0.954517	−	0.199985i
$15$	0.378122	+	0.520440i	0.0976306	+	0.134377i
$16$	0.464428	−	3.97295i	0.116107	−	0.993237i
$17$	−1.33872	−	0.434977i	−0.324688	−	0.105497i	0.142138	−	0.989847i	$-0.454602\pi$
$17$	−1.33872	−	0.434977i	−0.324688	−	0.105497i	−0.466825	+	0.884349i	$0.654602\pi$
$18$	−4.09180	−	0.442118i	−0.964447	−	0.104208i
$19$	−3.12581	−	0.750441i	−0.717110	−	0.172163i	−0.141560	−	0.989930i	$-0.545212\pi$
$19$	−3.12581	−	0.750441i	−0.717110	−	0.172163i	−0.575550	+	0.817767i	$0.695212\pi$
$20$	0.0873777	+	4.29207i	0.0195383	+	0.959736i
$21$	−0.295929	+	0.714435i	−0.0645769	+	0.155903i
$22$	4.13954	+	2.20549i	0.882553	+	0.470212i
$23$	−5.25943	+	5.25943i	−1.09667	+	1.09667i	−0.101869	+	0.994798i	$0.532482\pi$
$23$	−5.25943	+	5.25943i	−1.09667	+	1.09667i	−0.994798	+	0.101869i	$0.967518\pi$
$24$	0.639745	+	0.556134i	0.130587	+	0.113520i
$25$	0.0614196	+	0.387788i	0.0122839	+	0.0775576i
$26$	3.75780	+	2.05451i	0.736965	+	0.402923i
$27$	1.15035	−	1.34689i	0.221386	−	0.259209i
$28$	−4.34425	+	2.78535i	−0.820987	+	0.526382i
$29$	−4.03703	−	2.47389i	−0.749657	−	0.459391i	0.0944739	−	0.995527i	$-0.469883\pi$
$29$	−4.03703	−	2.47389i	−0.749657	−	0.459391i	−0.844131	+	0.536137i	$0.819883\pi$
$30$	−0.761545	−	0.497712i	−0.139038	−	0.0908694i
$31$	−2.83606	−	8.72850i	−0.509372	−	1.56769i	−0.793295	−	0.608838i	$-0.791636\pi$
$31$	−2.83606	−	8.72850i	−0.509372	−	1.56769i	0.283923	−	0.958847i	$-0.408364\pi$
$32$	1.38438	+	5.48484i	0.244726	+	0.969592i
$33$	−0.880727	+	0.460801i	−0.153315	+	0.0802152i
$34$	1.98823	−	0.0983934i	0.340979	−	0.0168743i
$35$	4.21147	−	3.59694i	0.711869	−	0.607993i
$36$	5.63072	−	1.47365i	0.938453	−	0.245608i
$37$	−5.79103	+	1.39030i	−0.952039	+	0.228564i	−0.679579	−	0.733603i	$-0.737837\pi$
$37$	−5.79103	+	1.39030i	−0.952039	+	0.228564i	−0.272460	+	0.962167i	$0.587837\pi$
$38$	4.50899	−	0.580266i	0.731455	−	0.0941315i
$39$	−0.808679	+	0.412042i	−0.129492	+	0.0659796i
$40$	−2.27424	−	5.62911i	−0.359589	−	0.890040i
$41$	−1.12234	+	0.177761i	−0.175280	+	0.0277617i	−0.243458	−	0.969912i	$-0.578282\pi$
$41$	−1.12234	+	0.177761i	−0.175280	+	0.0277617i	0.0681773	+	0.997673i	$0.478282\pi$
$42$	0.0318112	−	1.09315i	0.00490857	−	0.168676i
$43$	2.73645	−	6.60637i	0.417305	−	1.00746i	−0.565820	−	0.824529i	$-0.691440\pi$
$43$	2.73645	−	6.60637i	0.417305	−	1.00746i	0.983125	−	0.182934i	$-0.0585595\pi$
$44$	−6.58073	−	0.833082i	−0.992082	−	0.125592i
$45$	−5.77115	+	2.39049i	−0.860312	+	0.356353i
$46$	4.30637	−	9.59695i	0.634940	−	1.41499i
$47$	−5.66983	+	7.80385i	−0.827029	+	1.13831i	0.161439	+	0.986883i	$0.448386\pi$
$47$	−5.66983	+	7.80385i	−0.827029	+	1.13831i	−0.988469	+	0.151425i	$0.951614\pi$
$48$	−1.12530	−	0.413304i	−0.162423	−	0.0596553i
$49$	−0.325568	−	0.105783i	−0.0465096	−	0.0151119i
$50$	−0.276224	−	0.481668i	−0.0390640	−	0.0681182i
$51$	−0.220422	+	0.359696i	−0.0308653	+	0.0503675i
$52$	−6.00022	−	0.825527i	−0.832081	−	0.114480i
$53$	9.56996	+	0.753172i	1.31453	+	0.103456i	0.716259	−	0.697834i	$-0.245853\pi$
$53$	9.56996	+	0.753172i	1.31453	+	0.103456i	0.598275	+	0.801291i	$0.295853\pi$
$54$	−0.843048	+	2.35884i	−0.114724	+	0.320997i
$55$	7.11865	−	0.0768858i	0.959879	−	0.0103673i
$56$	4.34110	−	5.86654i	0.580104	−	0.783949i
$57$	−0.437385	+	0.858417i	−0.0579331	+	0.113700i
$58$	6.58023	+	1.23941i	0.864026	+	0.162742i
$59$	−0.781941	+	0.187727i	−0.101800	+	0.0244400i	−0.284025	−	0.958817i	$-0.591670\pi$
$59$	−0.781941	+	0.187727i	−0.101800	+	0.0244400i	0.182225	+	0.983257i	$0.441670\pi$
$60$	1.25690	+	0.274825i	0.162266	+	0.0354797i
$61$	−0.763355	+	0.0600774i	−0.0977376	+	0.00769212i	−0.127234	−	0.991873i	$-0.540610\pi$
$61$	−0.763355	+	0.0600774i	−0.0977376	+	0.00769212i	0.0294960	+	0.999565i	$0.490610\pi$
$62$	8.13867	+	10.1105i	1.03361	+	1.28403i
$63$	−6.07490	−	4.41367i	−0.765365	−	0.556070i
$64$	−4.58847	−	6.55331i	−0.573559	−	0.819164i
$65$	6.50034			0.806268
$66$	0.932338	−	1.05204i	0.114763	−	0.129497i
$67$	0.150571	+	0.363511i	0.0183952	+	0.0444099i	0.932810	−	0.360368i	$-0.117349\pi$
$67$	0.150571	+	0.363511i	0.0183952	+	0.0444099i	−0.914415	+	0.404778i	$0.867349\pi$
$68$	−2.57847	+	1.13006i	−0.312685	+	0.137040i
$69$	1.16473	+	1.90066i	0.140217	+	0.228813i
$70$	−3.75740	+	6.87247i	−0.449095	+	0.821417i
$71$	3.73200	−	1.90155i	0.442908	−	0.225673i	−0.218291	−	0.975884i	$-0.570048\pi$
$71$	3.73200	−	1.90155i	0.442908	−	0.225673i	0.661198	+	0.750211i	$0.270048\pi$
$72$	−6.70122	+	4.77983i	−0.789747	+	0.563308i
$73$	−2.05944	+	13.0028i	−0.241039	+	1.52186i	0.509174	+	0.860663i	$0.329951\pi$
$73$	−2.05944	+	13.0028i	−0.241039	+	1.52186i	−0.750213	+	0.661196i	$0.770049\pi$
$74$	6.95504	−	4.75030i	0.808507	−	0.552211i
$75$	0.117306	+	0.00923217i	0.0135453	+	0.00106604i
$76$	−5.66792	+	3.03482i	−0.650155	+	0.348117i
$77$	4.54994	+	7.24793i	0.518513	+	0.825979i
$78$	0.861632	−	0.951352i	0.0975606	−	0.107719i
$79$	10.2072	−	3.31652i	1.14840	−	0.373138i	0.327859	−	0.944727i	$-0.393673\pi$
$79$	10.2072	−	3.31652i	1.14840	−	0.373138i	0.820540	+	0.571589i	$0.193673\pi$
$80$	5.83721	+	6.29643i	0.652619	+	0.703963i
$81$	4.81966	+	6.63369i	0.535517	+	0.737076i
$82$	1.39405	−	0.799451i	0.153947	−	0.0882846i
$83$	−0.527481	−	6.70228i	−0.0578985	−	0.735671i	−0.955524	−	0.294912i	$-0.904710\pi$
$83$	−0.527481	−	6.70228i	−0.0578985	−	0.735671i	0.897626	−	0.440758i	$-0.145290\pi$
$84$	0.507764	+	1.46087i	0.0554016	+	0.159394i
$85$	2.57618	−	1.57869i	0.279426	−	0.171233i
$86$	−0.294158	+	10.1083i	−0.0317198	+	1.09001i
$87$	−1.00338	+	1.00338i	−0.107574	+	0.107574i
$88$	9.11710	−	2.20872i	0.971886	−	0.235451i
$89$	12.9060	+	12.9060i	1.36804	+	1.36804i	0.863235	+	0.504802i	$0.168434\pi$
$89$	12.9060	+	12.9060i	1.36804	+	1.36804i	0.504802	+	0.863235i	$0.331566\pi$
$90$	6.42571	−	6.06230i	0.677329	−	0.639022i
$91$	4.08278	+	6.66249i	0.427991	+	0.698418i
$92$	−0.865062	+	14.8507i	−0.0901889	+	1.54830i
$93$	−2.74207	+	0.215806i	−0.284339	+	0.0223780i
$94$	3.56907	−	13.1665i	0.368122	−	1.35802i
$95$	5.58233	−	4.05580i	0.572735	−	0.416117i
$96$	1.69524	−	0.0196961i	0.173020	−	0.00201022i
$97$	−0.340640	−	1.04838i	−0.0345867	−	0.106447i	0.932273	−	0.361756i	$-0.117823\pi$
$97$	−0.340640	−	1.04838i	−0.0345867	−	0.106447i	−0.966859	+	0.255309i	$0.917823\pi$
$98$	0.483525	−	0.0239286i	0.0488434	−	0.00241715i
$99$	−2.35444	−	9.36041i	−0.236630	−	0.940756i
$100$	0.607360	+	0.497716i	0.0607360	+	0.0497716i
$101$	−0.754103	+	9.58179i	−0.0750361	+	0.953424i	0.838033	+	0.545619i	$0.183705\pi$
$101$	−0.754103	+	9.58179i	−0.0750361	+	0.953424i	−0.913069	+	0.407804i	$0.866295\pi$
$102$	0.110430	−	0.586293i	0.0109342	−	0.0580516i
$103$	2.81930	+	0.446533i	0.277794	+	0.0439982i	0.293777	−	0.955874i	$-0.405088\pi$
$103$	2.81930	+	0.446533i	0.277794	+	0.0439982i	−0.0159831	+	0.999872i	$0.505088\pi$
$104$	8.34601	−	1.92674i	0.818394	−	0.188932i
$105$	−0.753566	−	1.47896i	−0.0735405	−	0.144331i
$106$	−13.0279	+	3.81781i	−1.26538	+	0.370819i
$107$	−11.6912	+	7.16436i	−1.13023	+	0.692605i	−0.956368	−	0.292165i	$-0.905624\pi$
$107$	−11.6912	+	7.16436i	−1.13023	+	0.692605i	−0.173861	+	0.984770i	$0.555624\pi$
$108$	−0.0721042	−	3.54182i	−0.00693823	−	0.340812i
$109$	−3.85528	+	1.59691i	−0.369269	+	0.152956i	−0.559598	−	0.828764i	$-0.689044\pi$
$109$	−3.85528	+	1.59691i	−0.369269	+	0.152956i	0.190329	+	0.981720i	$0.439044\pi$
$110$	−9.37043	+	3.68203i	−0.893435	+	0.351068i
$111$			1.78488i			0.169414i
$112$	−2.78722	+	9.93752i	−0.263368	+	0.939007i
$113$	9.49294	−	13.0659i	0.893021	−	1.22914i	−0.0796200	−	0.996825i	$-0.525371\pi$
$113$	9.49294	−	13.0659i	0.893021	−	1.22914i	0.972641	−	0.232313i	$-0.0746293\pi$
$114$	0.146364	−	1.35460i	0.0137083	−	0.126870i
$115$	−1.25263	−	15.9162i	−0.116809	−	1.48419i
$116$	−9.32080	+	1.67141i	−0.865415	+	0.155187i
$117$	−2.05738	−	8.56960i	−0.190205	−	0.792260i
$118$	0.939113	−	0.641415i	0.0864523	−	0.0590471i
$119$	3.23613	+	1.64889i	0.296656	+	0.151154i
$120$	−1.79954	+	0.268924i	−0.164275	+	0.0245493i
$121$	−1.48572	+	10.8992i	−0.135065	+	0.990837i
$122$	0.978750	−	0.463346i	0.0886119	−	0.0419494i
$123$	−0.0267199	+	0.339508i	−0.00240925	+	0.0306124i
$124$	−15.8425	−	9.27013i	−1.42270	−	0.832482i
$125$	−9.86944	−	6.04800i	−0.882750	−	0.540950i
$126$	10.2494	+	2.77834i	0.913091	+	0.247514i
$127$	−5.75259	+	17.7046i	−0.510460	+	1.57103i	0.280935	+	0.959727i	$0.409356\pi$
$127$	−5.75259	+	17.7046i	−0.510460	+	1.57103i	−0.791394	+	0.611306i	$0.790644\pi$
$128$	9.36089	+	6.35403i	0.827394	+	0.561623i
$129$	−1.73377	−	1.25966i	−0.152650	−	0.110907i
$130$	−8.59184	+	3.26942i	−0.753554	+	0.286747i
$131$	−2.35843	−	5.69376i	−0.206057	−	0.497466i	0.786738	−	0.617287i	$-0.211768\pi$
$131$	−2.35843	−	5.69376i	−0.206057	−	0.497466i	−0.992796	+	0.119820i	$0.961768\pi$
$132$	−0.703186	+	1.85946i	−0.0612045	+	0.161845i
$133$	7.66316	+	3.17419i	0.664481	+	0.275237i
$134$	−0.381850	−	0.404740i	−0.0329868	−	0.0349642i
$135$	0.594766	+	3.75520i	0.0511893	+	0.323197i
$136$	2.83972	−	2.79052i	0.243504	−	0.239286i
$137$	−8.48797	−	16.6586i	−0.725176	−	1.42324i	−0.898770	−	0.438421i	$-0.855538\pi$
$137$	−8.48797	−	16.6586i	−0.725176	−	1.42324i	0.173594	−	0.984817i	$-0.444462\pi$
$138$	−2.49544	−	1.92639i	−0.212426	−	0.163986i
$139$	−0.972490	−	4.05071i	−0.0824855	−	0.343577i	0.915832	−	0.401562i	$-0.131532\pi$
$139$	−0.972490	−	4.05071i	−0.0824855	−	0.343577i	−0.998317	+	0.0579849i	$0.981532\pi$
$140$	1.50977	−	10.9735i	0.127599	−	0.927433i
$141$	1.87751	+	2.19828i	0.158115	+	0.185128i
$142$	−3.97638	+	4.39044i	−0.333690	+	0.368437i
$143$	−1.46399	+	9.93670i	−0.122425	+	0.830949i
$144$	6.45329	−	9.68821i	0.537774	−	0.807351i
$145$	9.66561	−	3.14055i	0.802685	−	0.260808i
$146$	−3.81783	−	18.2223i	−0.315966	−	1.50809i
$147$	−0.0536051	+	0.0874755i	−0.00442127	+	0.00721486i
$148$	−6.80362	+	9.77684i	−0.559254	+	0.803651i
$149$	−3.71726	−	3.17484i	−0.304530	−	0.260093i	0.484029	−	0.875052i	$-0.339173\pi$
$149$	−3.71726	−	3.17484i	−0.304530	−	0.260093i	−0.788560	+	0.614958i	$0.789173\pi$
$150$	−0.159693	+	0.0467977i	−0.0130389	+	0.00382102i
$151$	13.0352	−	2.06458i	1.06079	−	0.168013i	0.398432	−	0.917198i	$-0.369554\pi$
$151$	13.0352	−	2.06458i	1.06079	−	0.168013i	0.662361	+	0.749185i	$0.269554\pi$
$152$	5.96519	−	6.86202i	0.483841	−	0.556584i
$153$	−2.89660	−	2.89660i	−0.234176	−	0.234176i
$154$	−9.65932	−	7.29153i	−0.778370	−	0.587568i
$155$	18.2002	+	7.53876i	1.46187	+	0.605528i
$156$	−0.660370	+	1.69082i	−0.0528719	+	0.135374i
$157$	1.31721	−	5.48657i	0.105125	−	0.437876i	−0.894839	−	0.446389i	$-0.852710\pi$
$157$	1.31721	−	5.48657i	0.105125	−	0.437876i	0.999964	+	0.00851285i	$0.00270976\pi$
$158$	−11.8233	+	9.51745i	−0.940612	+	0.757167i
$159$	0.889036	−	2.73617i	0.0705051	−	0.216992i
$160$	−10.8822	−	5.38644i	−0.860314	−	0.425835i
$161$	15.5265	−	11.2806i	1.22366	−	0.889039i
$162$	−9.70688	−	6.34399i	−0.762645	−	0.498431i
$163$	1.94915	−	1.66473i	0.152669	−	0.130392i	−0.569833	−	0.821761i	$-0.692992\pi$
$163$	1.94915	−	1.66473i	0.152669	−	0.130392i	0.722502	+	0.691369i	$0.242992\pi$
$164$	−1.44050	+	1.75783i	−0.112484	+	0.137263i
$165$	0.475640	−	2.07989i	0.0370285	−	0.161919i
$166$	4.06819	+	8.59345i	0.315752	+	0.666981i
$167$	3.73283	−	7.32609i	0.288855	−	0.566910i	−0.700289	−	0.713859i	$-0.746946\pi$
$167$	3.73283	−	7.32609i	0.288855	−	0.566910i	0.989144	+	0.146950i	$0.0469455\pi$
$168$	−1.40590	−	1.67552i	−0.108468	−	0.129269i
$169$	0.598983	−	3.78183i	0.0460756	−	0.290910i
$170$	−2.61106	+	3.38235i	−0.200259	+	0.259415i
$171$	−7.11372	−	6.07569i	−0.544000	−	0.464620i
$172$	−4.69529	−	13.5086i	−0.358013	−	1.03002i
$173$	−18.3750	−	4.41146i	−1.39703	−	0.335397i	−0.536114	−	0.844146i	$-0.680108\pi$
$173$	−18.3750	−	4.41146i	−1.39703	−	0.335397i	−0.860915	+	0.508749i	$0.830108\pi$
$174$	0.821562	−	1.83089i	0.0622824	−	0.138799i
$175$		−	1.01306i		−	0.0765803i
$176$	−10.9396	+	7.50494i	−0.824607	+	0.565706i
$177$			0.241006i			0.0181151i
$178$	−23.5498	−	10.5673i	−1.76513	−	0.792056i
$179$	−1.97909	−	0.475137i	−0.147924	−	0.0355134i	0.158807	−	0.987310i	$-0.449235\pi$
$179$	−1.97909	−	0.475137i	−0.147924	−	0.0355134i	−0.306731	+	0.951796i	$0.599235\pi$
$180$	−5.44409	+	11.2447i	−0.405779	+	0.838133i
$181$	−2.04754	−	1.74876i	−0.152192	−	0.129984i	0.570092	−	0.821581i	$-0.306908\pi$
$181$	−2.04754	−	1.74876i	−0.152192	−	0.129984i	−0.722284	+	0.691597i	$0.756908\pi$
$182$	−8.74739	−	6.75268i	−0.648400	−	0.500542i
$183$	−0.0358993	+	0.226659i	−0.00265375	+	0.0167551i
$184$	−6.32595	−	20.0641i	−0.466355	−	1.47914i
$185$	5.80360	−	11.3902i	0.426689	−	0.837425i
$186$	3.51580	−	1.66440i	0.257791	−	0.122040i
$187$	1.83305	+	4.29361i	0.134046	+	0.313980i
$188$	1.90479	+	19.1979i	0.138921	+	1.40015i
$189$	−3.47531	+	2.96820i	−0.252792	+	0.215904i
$190$	−5.33855	+	8.16847i	−0.387299	+	0.592603i
$191$	−13.3351	+	9.68850i	−0.964892	+	0.701035i	−0.954282	−	0.298908i	$-0.903378\pi$
$191$	−13.3351	+	9.68850i	−0.964892	+	0.701035i	−0.0106106	+	0.999944i	$0.503378\pi$
$192$	−2.23078	+	0.878675i	−0.160993	+	0.0634129i
$193$	−2.28623	+	7.03628i	−0.164566	+	0.506483i	−0.999004	−	0.0446193i	$-0.985793\pi$
$193$	−2.28623	+	7.03628i	−0.164566	+	0.506483i	0.834438	+	0.551102i	$0.185793\pi$
$194$	0.977537	+	1.21437i	0.0701830	+	0.0871868i
$195$	0.454786	−	1.89432i	0.0325679	−	0.135655i
$196$	−0.627065	+	0.274822i	−0.0447903	+	0.0196301i
$197$	5.14203	+	2.12990i	0.366354	+	0.151749i	0.558263	−	0.829664i	$-0.311468\pi$
$197$	5.14203	+	2.12990i	0.366354	+	0.151749i	−0.191909	+	0.981413i	$0.561468\pi$
$198$	7.81991	+	11.1880i	0.555737	+	0.795093i
$199$	−5.12192	−	5.12192i	−0.363084	−	0.363084i	0.501863	−	0.864947i	$-0.332648\pi$
$199$	−5.12192	−	5.12192i	−0.363084	−	0.363084i	−0.864947	+	0.501863i	$0.832648\pi$
$200$	−1.05311	−	0.352379i	−0.0744663	−	0.0249169i
$201$	0.116468	−	0.0184468i	0.00821505	−	0.00130114i
$202$	−3.82253	−	13.0440i	−0.268952	−	0.917775i
$203$	9.28973	+	7.93418i	0.652011	+	0.556870i
$204$	0.148921	+	0.830476i	0.0104266	+	0.0581450i
$205$	1.27443	−	2.07969i	0.0890103	−	0.145252i
$206$	−3.95100	+	0.827792i	−0.275279	+	0.0576750i
$207$	−20.5864	+	6.68892i	−1.43085	+	0.464912i
$208$	−10.0623	+	6.74439i	−0.697694	+	0.467639i
$209$	4.94264	+	9.44684i	0.341889	+	0.653452i
$210$	1.73989	+	1.57580i	0.120063	+	0.108740i
$211$	12.8418	+	15.0358i	0.884067	+	1.03511i	0.999128	+	0.0417514i	$0.0132937\pi$
$211$	12.8418	+	15.0358i	0.884067	+	1.03511i	−0.115061	+	0.993358i	$0.536706\pi$
$212$	15.2995	−	11.5987i	1.05077	−	0.796605i
$213$	−0.293044	−	1.22062i	−0.0200790	−	0.0836352i
$214$	11.8494	−	15.3497i	0.810011	−	1.04929i
$215$	6.96822	+	13.6759i	0.475228	+	0.932688i
$216$	1.87670	+	4.64515i	0.127694	+	0.316062i
$217$	3.70448	+	23.3892i	0.251476	+	1.58776i
$218$	4.29254	−	4.04978i	0.290728	−	0.274285i
$219$	3.64517	+	1.50988i	0.246318	+	0.102028i
$220$	10.5335	−	9.57970i	0.710166	−	0.645863i
$221$	1.63129	+	3.93829i	0.109733	+	0.264918i
$222$	−0.897728	−	2.35918i	−0.0602516	−	0.158338i
$223$	−6.79568	−	4.93735i	−0.455072	−	0.330630i	0.336523	−	0.941675i	$-0.390749\pi$
$223$	−6.79568	−	4.93735i	−0.455072	−	0.330630i	−0.791595	+	0.611046i	$0.790749\pi$
$224$	−1.31417	−	14.5368i	−0.0878065	−	0.971281i
$225$	−0.353083	+	1.08668i	−0.0235389	+	0.0724452i
$226$	−5.97567	+	22.0445i	−0.397496	+	1.46638i
$227$	−17.7850	−	10.8987i	−1.18043	−	0.723369i	−0.213136	−	0.977023i	$-0.568368\pi$
$227$	−17.7850	−	10.8987i	−1.18043	−	0.723369i	−0.967295	+	0.253653i	$0.918368\pi$
$228$	0.487855	+	1.86407i	0.0323090	+	0.123451i
$229$	−1.17662	+	14.9503i	−0.0777530	+	0.987946i	0.827054	+	0.562123i	$0.190015\pi$
$229$	−1.17662	+	14.9503i	−0.0777530	+	0.987946i	−0.904807	+	0.425823i	$0.859985\pi$
$230$	9.66091	+	20.4073i	0.637021	+	1.34561i
$231$	2.43051	−	0.818846i	0.159916	−	0.0538761i
$232$	11.4791	−	6.89720i	0.753642	−	0.452823i
$233$	−11.6474	−	5.93464i	−0.763046	−	0.388791i	0.0287425	−	0.999587i	$-0.490850\pi$
$233$	−11.6474	−	5.93464i	−0.763046	−	0.388791i	−0.791788	+	0.610796i	$0.790850\pi$
$234$	7.02952	+	10.2921i	0.459534	+	0.672816i
$235$	−4.83352	−	20.1330i	−0.315304	−	1.31334i
$236$	−0.918667	+	1.32013i	−0.0598002	+	0.0859331i
$237$	−0.252365	−	3.20660i	−0.0163929	−	0.208291i
$238$	−5.10669	−	0.551777i	−0.331018	−	0.0357664i
$239$	−10.1981	+	14.0365i	−0.659659	+	0.907943i	−0.999470	−	0.0325509i	$-0.989637\pi$
$239$	−10.1981	+	14.0365i	−0.659659	+	0.907943i	0.339811	+	0.940494i	$0.389637\pi$
$240$	2.24329	−	1.26055i	0.144804	−	0.0813682i
$241$		−	26.8713i		−	1.73093i	−0.500966	−	0.865467i	$-0.667022\pi$
$241$		−	26.8713i		−	1.73093i	0.500966	−	0.865467i	$-0.332978\pi$
$242$	−3.51813	−	15.1533i	−0.226154	−	0.974092i
$243$	7.17972	−	2.97394i	0.460580	−	0.190778i
$244$	−1.06062	+	1.10470i	−0.0678993	+	0.0707213i
$245$	0.626509	−	0.383925i	0.0400262	−	0.0245281i
$246$	−0.135442	−	0.462185i	−0.00863550	−	0.0294678i
$247$	4.41964	+	8.67404i	0.281215	+	0.551916i
$248$	25.6024	+	4.28465i	1.62575	+	0.272075i
$249$	−1.99007	−	0.315197i	−0.126116	−	0.0199748i
$250$	16.0869	+	3.03001i	1.01742	+	0.191635i
$251$	−1.76629	+	22.4428i	−0.111487	+	1.41658i	0.645806	+	0.763501i	$0.276521\pi$
$251$	−1.76629	+	22.4428i	−0.111487	+	1.41658i	−0.757293	+	0.653075i	$0.773479\pi$
$252$	−14.9446	+	1.48278i	−0.941421	+	0.0934065i
$253$	24.6123	+	1.66978i	1.54736	+	0.104978i
$254$	−1.30126	−	26.2945i	−0.0816481	−	1.64986i
$255$	−0.279820	−	0.861198i	−0.0175230	−	0.0539303i
$256$	−15.5686	−	3.69029i	−0.973038	−	0.230643i
$257$	−1.86677	+	1.35629i	−0.116446	+	0.0846028i	−0.644484	−	0.764618i	$-0.722928\pi$
$257$	−1.86677	+	1.35629i	−0.116446	+	0.0846028i	0.528038	+	0.849221i	$0.322928\pi$
$258$	2.92517	+	0.792936i	0.182113	+	0.0493661i
$259$	15.3195	−	1.20567i	0.951907	−	0.0749167i
$260$	9.71189	−	8.64273i	0.602306	−	0.535999i
$261$	−7.19948	−	11.7485i	−0.445636	−	0.727213i
$262$	5.98101	+	6.33955i	0.369508	+	0.391658i
$263$	6.45925	+	6.45925i	0.398294	+	0.398294i	0.877631	−	0.479337i	$-0.159123\pi$
$263$	6.45925	+	6.45925i	0.398294	+	0.398294i	−0.479337	+	0.877631i	$0.659123\pi$
$264$	−0.00579990	−	2.81142i	−0.000356959	−	0.173031i
$265$	−14.5701	+	14.5701i	−0.895034	+	0.895034i
$266$	−11.7253	−	0.341213i	−0.718924	−	0.0209211i
$267$	4.66401	−	2.85811i	0.285433	−	0.174914i
$268$	0.708280	+	0.342911i	0.0432651	+	0.0209466i
$269$	−2.28725	−	29.0622i	−0.139456	−	1.77196i	−0.526770	−	0.850008i	$-0.676597\pi$
$269$	−2.28725	−	29.0622i	−0.139456	−	1.77196i	0.387314	−	0.921948i	$-0.373403\pi$
$270$	−2.67486	−	4.66431i	−0.162787	−	0.283861i
$271$	4.70134	+	6.47084i	0.285586	+	0.393076i	0.927574	−	0.373639i	$-0.121890\pi$
$271$	4.70134	+	6.47084i	0.285586	+	0.393076i	−0.641988	+	0.766715i	$0.721890\pi$
$272$	−2.34988	+	5.11665i	−0.142482	+	0.310243i
$273$	2.22722	−	0.723667i	0.134797	−	0.0437983i
$274$	19.5976	+	17.7494i	1.18394	+	1.07228i
$275$	0.834955	−	0.999261i	0.0503497	−	0.0602577i
$276$	4.26726	+	1.29110i	0.256859	+	0.0777153i
$277$	16.5936	+	1.30595i	0.997015	+	0.0784668i	0.566453	−	0.824094i	$-0.308315\pi$
$277$	16.5936	+	1.30595i	0.997015	+	0.0784668i	0.430562	+	0.902561i	$0.358315\pi$
$278$	3.32274	+	4.86491i	0.199285	+	0.291778i
$279$	4.17817	−	26.3799i	0.250140	−	1.57932i
$280$	3.52372	+	15.2636i	0.210583	+	0.912177i
$281$	−11.4144	+	5.81592i	−0.680925	+	0.346948i	−0.760003	−	0.649920i	$-0.774802\pi$
$281$	−11.4144	+	5.81592i	−0.680925	+	0.346948i	0.0790779	+	0.996868i	$0.474802\pi$
$282$	−3.58725	−	1.96127i	−0.213618	−	0.116792i
$283$	−7.47826	−	12.2034i	−0.444536	−	0.725417i	0.549378	−	0.835574i	$-0.314865\pi$
$283$	−7.47826	−	12.2034i	−0.444536	−	0.725417i	−0.993914	+	0.110157i	$0.964865\pi$
$284$	3.04757	−	7.80303i	0.180840	−	0.463025i
$285$	−0.791378	−	1.91056i	−0.0468772	−	0.113172i
$286$	−3.06274	−	13.8702i	−0.181104	−	0.820162i
$287$	2.93202			0.173072
$288$	−3.65686	+	16.0512i	−0.215482	+	0.945824i
$289$	−12.1503	−	8.82772i	−0.714725	−	0.519278i
$290$	−11.1960	+	9.01245i	−0.657450	+	0.529230i
$291$	−0.329350	+	0.0259204i	−0.0193069	+	0.00151948i
$292$	14.2113	+	22.1651i	0.831655	+	1.29711i
$293$	−27.2992	+	6.55395i	−1.59483	+	0.382886i	−0.931008	−	0.365000i	$-0.881069\pi$
$293$	−27.2992	+	6.55395i	−1.59483	+	0.382886i	−0.663827	+	0.747886i	$0.731069\pi$
$294$	0.0268558	−	0.142582i	0.00156626	−	0.00831557i
$295$	0.783639	−	1.53798i	0.0456252	−	0.0895446i
$296$	4.07533	−	16.3445i	0.236874	−	0.950006i
$297$	−5.87432	+	0.0634462i	−0.340863	+	0.00368152i
$298$	6.51013	+	2.32672i	0.377122	+	0.134783i
$299$	22.4554	+	1.76728i	1.29863	+	0.102205i
$300$	0.187537	−	0.142174i	0.0108274	−	0.00820844i
$301$	−9.64038	+	15.7317i	−0.555663	+	0.906759i
$302$	−16.1910	+	9.28509i	−0.931686	+	0.534297i
$303$	2.73955	+	0.890135i	0.157383	+	0.0511369i
$304$	−4.43318	+	12.0702i	−0.254260	+	0.692271i
$305$	0.966080	−	1.32970i	0.0553176	−	0.0761381i
$306$	5.28547	+	2.37171i	0.302150	+	0.135582i
$307$	−9.33497	+	3.86667i	−0.532775	+	0.220683i	−0.632818	−	0.774300i	$-0.718102\pi$
$307$	−9.33497	+	3.86667i	−0.532775	+	0.220683i	0.100043	+	0.994983i	$0.468102\pi$
$308$	16.4346	+	4.77934i	0.936448	+	0.272328i
$309$	0.327376	−	0.790355i	0.0186238	−	0.0449617i
$310$	−27.8478	−	0.810387i	−1.58165	−	0.0460269i
$311$	−10.1635	+	1.60974i	−0.576319	+	0.0912800i	−0.437788	−	0.899078i	$-0.644238\pi$
$311$	−10.1635	+	1.60974i	−0.576319	+	0.0912800i	−0.138531	+	0.990358i	$0.544238\pi$
$312$	0.0224289	−	2.56699i	0.00126979	−	0.145327i
$313$	21.6678	−	11.0403i	1.22474	−	0.624036i	0.282593	−	0.959240i	$-0.408805\pi$
$313$	21.6678	−	11.0403i	1.22474	−	0.624036i	0.942146	+	0.335204i	$0.108805\pi$
$314$	1.01851	+	7.91440i	0.0574778	+	0.446635i
$315$	15.6726	−	3.76265i	0.883048	−	0.212001i
$316$	10.8406	−	18.5264i	0.609830	−	1.04219i
$317$	13.2550	−	11.3209i	0.744477	−	0.635843i	−0.194073	−	0.980987i	$-0.562170\pi$
$317$	13.2550	−	11.3209i	0.744477	−	0.635843i	0.938550	+	0.345144i	$0.112170\pi$
$318$	0.201103	+	4.06369i	0.0112773	+	0.227880i
$319$	2.62391	+	15.4826i	0.146911	+	0.866858i
$320$	17.0928	+	1.64621i	0.955514	+	0.0920259i
$321$	1.26987	+	3.90827i	0.0708775	+	0.218139i
$322$	−14.8484	+	22.7194i	−0.827470	+	1.26610i
$323$	3.85817	+	2.36429i	0.214674	+	0.131552i
$324$	16.0209	+	3.50300i	0.890049	+	0.194611i
$325$	0.772197	−	0.904127i	0.0428338	−	0.0501519i
$326$	−1.73900	+	3.18071i	−0.0963141	+	0.176163i
$327$	0.195641	+	1.23523i	0.0108189	+	0.0683082i
$328$	1.01986	−	3.04793i	0.0563123	−	0.168294i
$329$	17.5994	−	17.5994i	0.970286	−	0.970286i
$330$	0.417426	+	2.98833i	0.0229785	+	0.164502i
$331$	−7.59642	+	18.3394i	−0.417537	+	1.00802i	0.565522	+	0.824733i	$0.308675\pi$
$331$	−7.59642	+	18.3394i	−0.417537	+	1.00802i	−0.983059	+	0.183290i	$0.941325\pi$
$332$	−9.69931	−	9.31227i	−0.532319	−	0.511077i
$333$	−16.8529	−	4.04603i	−0.923535	−	0.221721i
$334$	−1.24914	+	11.5607i	−0.0683497	+	0.632576i
$335$	−0.803222	−	0.260983i	−0.0438847	−	0.0142590i
$336$	2.70098	+	1.50751i	0.147350	+	0.0822415i
$337$	18.0410	+	24.8313i	0.982754	+	1.35264i	0.935333	+	0.353770i	$0.115100\pi$
$337$	18.0410	+	24.8313i	0.982754	+	1.35264i	0.0474212	+	0.998875i	$0.484900\pi$
$338$	1.11041	+	5.29991i	0.0603982	+	0.288277i
$339$	−3.14349	−	3.68056i	−0.170731	−	0.199901i
$340$	1.74998	−	5.78389i	0.0949058	−	0.313676i
$341$	−15.6231	+	26.1237i	−0.846037	+	1.41468i
$342$	12.4584	+	4.45263i	0.673674	+	0.240771i
$343$	16.8801	+	8.60085i	0.911441	+	0.464402i
$344$	13.0003	+	15.4935i	0.700932	+	0.835356i
$345$	−4.72592	−	0.748512i	−0.254435	−	0.0402985i
$346$	26.5061	−	3.41108i	1.42497	−	0.183381i
$347$	−14.5369	+	17.0206i	−0.780384	+	0.913712i	−0.998057	−	0.0623099i	$-0.980153\pi$
$347$	−14.5369	+	17.0206i	−0.780384	+	0.913712i	0.217673	+	0.976022i	$0.430153\pi$
$348$	−0.165035	+	2.83319i	−0.00884680	+	0.151875i
$349$	5.63371	−	23.4661i	0.301566	−	1.25611i	−0.591544	−	0.806273i	$-0.701481\pi$
$349$	5.63371	−	23.4661i	0.301566	−	1.25611i	0.893110	−	0.449839i	$-0.148519\pi$
$350$	0.509531	+	1.33902i	0.0272356	+	0.0715735i
$351$	−5.36409			−0.286314
$352$	10.6848	−	15.4219i	0.569502	−	0.821990i
$353$	−12.5006			−0.665342			−0.332671	−	0.943043i	$-0.607950\pi$
$353$	−12.5006			−0.665342			−0.332671	+	0.943043i	$0.607950\pi$
$354$	−0.121217	−	0.318551i	−0.00644261	−	0.0169308i
$355$	−2.09881	+	8.74218i	−0.111393	+	0.463987i
$356$	36.4420	+	2.12276i	1.93142	+	0.112506i
$357$	0.706929	−	0.827707i	0.0374146	−	0.0438069i
$358$	2.85484	−	0.367391i	0.150883	−	0.0194172i
$359$	−6.06311	−	0.960303i	−0.319999	−	0.0506828i	−0.00563116	−	0.999984i	$-0.501792\pi$
$359$	−6.06311	−	0.960303i	−0.319999	−	0.0506828i	−0.314368	+	0.949301i	$0.601792\pi$
$360$	1.54007	−	17.6009i	0.0811688	−	0.927650i
$361$	−7.72159	−	3.93434i	−0.406399	−	0.207071i
$362$	3.58590	+	1.28160i	0.188471	+	0.0673593i
$363$	3.07229	+	1.19551i	0.161253	+	0.0627481i
$364$	14.9582	+	4.52577i	0.784024	+	0.237215i
$365$	−18.3522	−	21.4876i	−0.960596	−	1.12471i
$366$	−0.0665509	−	0.317643i	−0.00347867	−	0.0166035i
$367$	−10.2013	−	14.0409i	−0.532505	−	0.732930i	0.455005	−	0.890489i	$-0.349638\pi$
$367$	−10.2013	−	14.0409i	−0.532505	−	0.732930i	−0.987510	+	0.157559i	$0.949638\pi$
$368$	18.4528	+	23.3381i	0.961919	+	1.21658i
$369$	−3.14508	−	1.02190i	−0.163726	−	0.0531979i
$370$	−1.94209	+	17.9740i	−0.100964	+	0.934425i
$371$	−24.0848	−	5.78226i	−1.25042	−	0.300200i
$372$	−3.80988	+	3.96823i	−0.197533	+	0.205743i
$373$	10.7128	−	25.8629i	0.554686	−	1.33913i	−0.359239	−	0.933246i	$-0.616964\pi$
$373$	10.7128	−	25.8629i	0.554686	−	1.33913i	0.913924	−	0.405884i	$-0.133036\pi$
$374$	−4.58236	−	4.75314i	−0.236948	−	0.245779i
$375$	−2.45300	+	2.45300i	−0.126672	+	0.126672i
$376$	−12.1735	−	24.4168i	−0.627799	−	1.25920i
$377$	2.24304	+	14.1620i	0.115523	+	0.729381i
$378$	3.10061	−	5.67117i	0.159478	−	0.291693i
$379$	−16.2610	+	19.0391i	−0.835269	+	0.977975i	−0.999965	−	0.00836981i	$-0.997336\pi$
$379$	−16.2610	+	19.0391i	−0.835269	+	0.977975i	0.164696	+	0.986344i	$0.447336\pi$
$380$	2.94782	−	13.4818i	0.151220	−	0.691601i
$381$	4.75700	+	2.91509i	0.243708	+	0.149345i
$382$	12.7527	−	19.5128i	0.652487	−	0.998363i
$383$	−8.15761	−	25.1065i	−0.416834	−	1.28288i	−0.910600	−	0.413289i	$-0.864380\pi$
$383$	−8.15761	−	25.1065i	−0.416834	−	1.28288i	0.493766	−	0.869595i	$-0.335620\pi$
$384$	2.50661	−	2.28339i	0.127915	−	0.116524i
$385$	−18.1728	−	2.67743i	−0.926171	−	0.136454i
$386$	−0.517153	−	10.4501i	−0.0263224	−	0.531897i
$387$	15.8239	−	13.5149i	0.804374	−	0.687000i
$388$	−1.90284	−	1.11344i	−0.0966023	−	0.0565261i
$389$	29.2009	−	7.01052i	1.48054	−	0.355447i	0.588909	−	0.808200i	$-0.299558\pi$
$389$	29.2009	−	7.01052i	1.48054	−	0.355447i	0.891636	+	0.452752i	$0.149558\pi$
$390$	0.351656	+	2.73256i	0.0178068	+	0.138369i
$391$	9.32864	−	4.75318i	0.471769	−	0.240379i
$392$	0.690600	−	0.678636i	0.0348805	−	0.0342763i
$393$	−1.82427	+	0.288937i	−0.0920225	+	0.0145749i
$394$	−7.86774	−	0.228956i	−0.396371	−	0.0115346i
$395$	−8.81590	+	21.2835i	−0.443576	+	1.07089i
$396$	−15.9631	−	10.8546i	−0.802176	−	0.545464i
$397$	−13.9773	+	5.78960i	−0.701502	+	0.290572i	−0.704783	−	0.709423i	$-0.748956\pi$
$397$	−13.9773	+	5.78960i	−0.701502	+	0.290572i	0.00328111	+	0.999995i	$0.498956\pi$
$398$	9.34605	+	4.19379i	0.468475	+	0.210215i
$399$	1.46116	−	2.01111i	0.0731494	−	0.100682i
$400$	1.56919	−	0.0639173i	0.0784593	−	0.00319587i
$401$	−13.4151	−	4.35883i	−0.669918	−	0.217670i	−0.0457419	−	0.998953i	$-0.514565\pi$
$401$	−13.4151	−	4.35883i	−0.669918	−	0.217670i	−0.624176	+	0.781284i	$0.714565\pi$
$402$	−0.144664	+	0.0829612i	−0.00721521	+	0.00413773i
$403$	−14.5220	+	23.6978i	−0.723394	+	1.18047i
$404$	11.6131	+	15.3184i	0.577773	+	0.762119i
$405$	−17.5462	−	1.38092i	−0.871878	−	0.0686183i
$406$	−16.2693	−	5.81464i	−0.807432	−	0.288576i
$407$	16.1045	+	11.4369i	0.798271	+	0.566907i
$408$	−0.614535	−	1.02278i	−0.0304240	−	0.0506353i
$409$	6.29015	−	12.3451i	0.311028	−	0.610427i	−0.681587	−	0.731737i	$-0.738710\pi$
$409$	6.29015	−	12.3451i	0.311028	−	0.610427i	0.992615	+	0.121311i	$0.0387098\pi$
$410$	−0.638483	+	3.38982i	−0.0315325	+	0.167411i
$411$	−5.44847	+	1.30806i	−0.268753	+	0.0645219i
$412$	4.80590	−	3.08134i	0.236770	−	0.151807i
$413$	2.06854	−	0.162797i	0.101786	−	0.00801073i
$414$	23.8458	−	19.1952i	1.17196	−	0.943395i
$415$	11.6748	+	8.48221i	0.573091	+	0.416375i
$416$	9.90769	−	13.9754i	0.485764	−	0.685198i
$417$	−1.24849			−0.0611389
$418$	−11.2843	−	10.0004i	−0.551935	−	0.489137i
$419$	−6.37130	−	15.3817i	−0.311259	−	0.751445i	−0.999659	−	0.0261138i	$-0.991687\pi$
$419$	−6.37130	−	15.3817i	−0.311259	−	0.751445i	0.688400	−	0.725331i	$-0.258313\pi$
$420$	−3.09226	−	1.20772i	−0.150887	−	0.0589308i
$421$	8.83035	+	14.4098i	0.430365	+	0.702291i	0.992159	−	0.124986i	$-0.0398885\pi$
$421$	8.83035	+	14.4098i	0.430365	+	0.702291i	−0.561794	+	0.827277i	$0.689889\pi$
$422$	−24.5362	−	13.4147i	−1.19440	−	0.653018i
$423$	−25.0122	+	12.7444i	−1.21613	+	0.619652i
$424$	−14.3884	+	23.0257i	−0.698763	+	1.11823i
$425$	0.0864552	−	0.545856i	0.00419369	−	0.0264779i
$426$	1.00125	+	1.46596i	0.0485109	+	0.0710261i
$427$	1.96965	+	0.155014i	0.0953178	+	0.00750168i
$428$	−7.94171	+	26.2484i	−0.383877	+	1.26876i
$429$	2.79332	+	1.12184i	0.134863	+	0.0541630i
$430$	−16.0887	−	14.5714i	−0.775866	−	0.702695i
$431$	6.84002	−	2.22246i	0.329472	−	0.107052i	−0.139610	−	0.990207i	$-0.544585\pi$
$431$	6.84002	−	2.22246i	0.329472	−	0.107052i	0.469082	+	0.883155i	$0.344585\pi$
$432$	−4.81687	−	5.19583i	−0.231752	−	0.249984i
$433$	−6.15393	−	8.47016i	−0.295739	−	0.407050i	0.635129	−	0.772406i	$-0.280947\pi$
$433$	−6.15393	−	8.47016i	−0.295739	−	0.407050i	−0.930868	+	0.365356i	$0.880947\pi$
$434$	−16.6603	−	29.0515i	−0.799718	−	1.39452i
$435$	−0.238975	−	3.03646i	−0.0114580	−	0.145587i
$436$	−3.63680	+	7.51178i	−0.174171	+	0.359749i
$437$	20.3869	−	12.4931i	0.975236	−	0.597626i
$438$	−5.57742	−	0.162306i	−0.266499	−	0.00775528i
$439$	1.24742	−	1.24742i	0.0595359	−	0.0595359i	−0.676712	−	0.736248i	$-0.736596\pi$
$439$	1.24742	−	1.24742i	0.0595359	−	0.0595359i	0.736248	+	0.676712i	$0.236596\pi$
$440$	−9.10442	+	17.9599i	−0.434036	+	0.856206i
$441$	−0.704433	−	0.704433i	−0.0335444	−	0.0335444i
$442$	−4.13698	−	4.38497i	−0.196776	−	0.208572i
$443$	−6.13253	−	10.0074i	−0.291366	−	0.475465i	0.673145	−	0.739511i	$-0.264943\pi$
$443$	−6.13253	−	10.0074i	−0.291366	−	0.475465i	−0.964510	+	0.264045i	$0.914943\pi$
$444$	2.37315	+	2.66672i	0.112625	+	0.126557i
$445$	−39.0566	+	3.07382i	−1.85146	+	0.145713i
$446$	11.4655	+	3.10799i	0.542907	+	0.147168i
$447$	−1.18528	+	0.861158i	−0.0560619	+	0.0407314i
$448$	9.04846	+	18.5531i	0.427499	+	0.876551i
$449$	−4.93104	−	15.1762i	−0.232710	−	0.716209i	−0.997417	−	0.0718300i	$-0.977116\pi$
$449$	−4.93104	−	15.1762i	−0.232710	−	0.716209i	0.764707	−	0.644379i	$-0.222884\pi$
$450$	−0.0798687	−	1.61391i	−0.00376505	−	0.0760803i
$451$	2.89207	+	2.41654i	0.136182	+	0.113790i
$452$	−3.18917	−	32.1429i	−0.150006	−	1.51187i
$453$	0.310334	−	3.94316i	0.0145807	−	0.185266i
$454$	28.9890	+	5.46016i	1.36052	+	0.256258i
$455$	−16.5660	−	2.62379i	−0.776625	−	0.123005i
$456$	−1.58238	−	2.21846i	−0.0741016	−	0.103889i
$457$	4.01119	+	7.87240i	0.187636	+	0.368255i	0.965592	−	0.260063i	$-0.0837434\pi$
$457$	4.01119	+	7.87240i	0.187636	+	0.368255i	−0.777956	+	0.628319i	$0.783743\pi$
$458$	−5.96424	−	20.3524i	−0.278691	−	0.951007i
$459$	−2.12587	+	1.30273i	−0.0992270	+	0.0608064i
$460$	−23.0334	−	22.1143i	−1.07394	−	1.03108i
$461$	21.3806	−	8.85613i	0.995793	−	0.412471i	0.175540	−	0.984472i	$-0.443833\pi$
$461$	21.3806	−	8.85613i	0.995793	−	0.412471i	0.820253	+	0.572001i	$0.193833\pi$
$462$	−2.80069	+	2.30477i	−0.130300	+	0.107227i
$463$		−	14.9858i		−	0.696447i	−0.937411	−	0.348224i	$-0.886785\pi$
$463$		−	14.9858i		−	0.696447i	0.937411	−	0.348224i	$-0.113215\pi$
$464$	−11.7036	+	14.8900i	−0.543324	+	0.691249i
$465$	3.47028	−	4.77644i	0.160931	−	0.221502i
$466$	18.3799	+	1.98594i	0.851431	+	0.0919969i
$467$	0.468668	+	5.95499i	0.0216874	+	0.275564i	0.998194	+	0.0600760i	$0.0191343\pi$
$467$	0.468668	+	5.95499i	0.0216874	+	0.275564i	−0.976506	+	0.215488i	$0.930866\pi$
$468$	−14.4678	−	10.0680i	−0.668775	−	0.465395i
$469$	−0.237000	−	0.987177i	−0.0109437	−	0.0455836i
$470$	16.5149	+	24.1798i	0.761774	+	1.11533i
$471$	−1.50673	−	0.767719i	−0.0694266	−	0.0353746i
$472$	0.550276	−	2.20694i	0.0253285	−	0.101583i
$473$	−22.4749	+	7.57186i	−1.03340	+	0.348155i
$474$	1.94636	+	4.11141i	0.0893994	+	0.188843i
$475$	0.0990260	−	1.25824i	0.00454363	−	0.0577322i
$476$	7.02731	−	1.83916i	0.322096	−	0.0842976i
$477$	23.8197	+	14.5967i	1.09063	+	0.668339i
$478$	6.41954	−	23.6820i	0.293623	−	1.08319i
$479$	3.48711	−	10.7322i	0.159330	−	0.490368i	−0.839244	−	0.543756i	$-0.817002\pi$
$479$	3.48711	−	10.7322i	0.159330	−	0.490368i	0.998574	+	0.0533874i	$0.0170018\pi$
$480$	−2.33107	+	2.79443i	−0.106398	+	0.127547i
$481$	14.5912	+	10.6011i	0.665301	+	0.483370i
$482$	13.5152	+	35.5172i	0.615602	+	1.61777i
$483$	−2.20110	−	5.31394i	−0.100154	−	0.241792i
$484$	12.2716	+	18.2594i	0.557801	+	0.829975i
$485$	2.18603	+	0.905481i	0.0992623	+	0.0411158i
$486$	−7.99404	+	7.54194i	−0.362617	+	0.342109i
$487$	1.48087	+	9.34985i	0.0671047	+	0.423682i	0.998255	+	0.0590472i	$0.0188063\pi$
$487$	1.48087	+	9.34985i	0.0671047	+	0.423682i	−0.931151	+	0.364635i	$0.881194\pi$
$488$	0.846255	−	1.99359i	0.0383082	−	0.0902458i
$489$	−0.348764	−	0.684489i	−0.0157717	−	0.0309537i
$490$	−0.634990	+	0.822564i	−0.0286859	+	0.0371597i
$491$	6.01087	+	25.0371i	0.271267	+	1.12991i	0.927044	+	0.374953i	$0.122341\pi$
$491$	6.01087	+	25.0371i	0.271267	+	1.12991i	−0.655777	+	0.754954i	$0.727659\pi$
$492$	0.411483	+	0.542772i	0.0185511	+	0.0244700i
$493$	4.32837	+	5.06787i	0.194940	+	0.228245i
$494$	−10.2044	−	9.24202i	−0.459117	−	0.415818i
$495$	18.5602	+	9.20576i	0.834218	+	0.413768i
$496$	−35.9950	+	7.21377i	−1.61622	+	0.323908i
$497$	−10.2785	+	3.33968i	−0.461053	+	0.149805i
$498$	2.78892	−	0.584318i	0.124974	−	0.0261839i
$499$	11.4826	−	18.7379i	0.514031	−	0.838823i	−0.485338	−	0.874327i	$-0.661303\pi$
$499$	11.4826	−	18.7379i	0.514031	−	0.838823i	0.999370	+	0.0355035i	$0.0113035\pi$
$500$	−22.7868	+	4.08615i	−1.01906	+	0.182738i
$501$	−1.87380	−	1.60038i	−0.0837151	−	0.0714995i
$502$	−8.95326	−	30.5522i	−0.399604	−	1.36361i
$503$	25.4915	−	4.03746i	1.13661	−	0.180021i	0.440361	−	0.897821i	$-0.354851\pi$
$503$	25.4915	−	4.03746i	1.13661	−	0.180021i	0.696250	+	0.717800i	$0.254851\pi$
$504$	19.0073	−	9.47642i	0.846651	−	0.422113i
$505$	−14.5881	−	14.5881i	−0.649163	−	0.649163i
$506$	−33.3712	+	10.1720i	−1.48353	+	0.452201i
$507$	−1.06019	−	0.439145i	−0.0470846	−	0.0195031i
$508$	14.9451	+	34.1003i	0.663080	+	1.51296i
$509$	−7.05602	+	29.3904i	−0.312753	+	1.30271i	0.565594	+	0.824684i	$0.308647\pi$
$509$	−7.05602	+	29.3904i	−0.312753	+	1.30271i	−0.878346	+	0.478025i	$0.841353\pi$
$510$	0.803003	+	0.997552i	0.0355575	+	0.0441723i
$511$	10.4969	−	32.3060i	0.464354	−	1.42914i
$512$	22.4339	−	2.95276i	0.991449	−	0.130495i
$513$	−4.60655	+	3.34685i	−0.203384	+	0.147767i
$514$	1.78524	−	2.73159i	0.0787438	−	0.120485i
$515$	−4.65901	+	3.97917i	−0.205300	+	0.175343i
$516$	−4.26517	+	0.423185i	−0.187764	+	0.0186297i
$517$	31.8649	−	2.85440i	1.40141	−	0.125537i
$518$	−19.6422	+	9.29872i	−0.863028	+	0.408562i
$519$	−2.57116	+	5.04619i	−0.112862	+	0.221503i
$520$	−8.48976	+	16.3083i	−0.372301	+	0.715164i
$521$	−2.66904	+	16.8516i	−0.116933	+	0.738284i	0.857646	+	0.514240i	$0.171926\pi$
$521$	−2.66904	+	16.8516i	−0.116933	+	0.738284i	−0.974579	+	0.224044i	$0.928074\pi$
$522$	15.4250	+	11.9075i	0.675132	+	0.521178i
$523$	1.08953	+	0.930549i	0.0476420	+	0.0406901i	0.672950	−	0.739688i	$-0.265027\pi$
$523$	1.08953	+	0.930549i	0.0476420	+	0.0406901i	−0.625308	+	0.780378i	$0.715027\pi$
$524$	−11.0940	−	5.37109i	−0.484642	−	0.234637i
$525$	−0.295225	−	0.0708773i	−0.0128847	−	0.00309334i
$526$	−11.7863	−	5.28878i	−0.513907	−	0.230602i
$527$			12.9186i			0.562745i
$528$	1.42170	+	3.71309i	0.0618717	+	0.161592i
$529$		−	32.3232i		−	1.40535i
$530$	11.9299	−	26.5863i	0.518201	−	1.15483i
$531$	−2.27559	−	0.546321i	−0.0987521	−	0.0237083i
$532$	15.6696	−	5.44637i	0.679362	−	0.236130i
$533$	2.61673	+	2.23490i	0.113343	+	0.0968044i
$534$	−4.72715	+	6.12353i	−0.204564	+	0.264991i
$535$	4.60418	−	29.0696i	0.199056	−	1.25679i
$536$	−1.10864	−	0.0970054i	−0.0478860	−	0.00418999i
$537$	−0.276928	+	0.543501i	−0.0119503	+	0.0234538i
$538$	17.6404	+	37.2627i	0.760530	+	1.60651i
$539$	0.445784	+	1.04418i	0.0192013	+	0.0449759i
$540$	5.88147	+	4.81971i	0.253098	+	0.207407i
$541$	−11.7840	+	10.0645i	−0.506635	+	0.432707i	−0.865669	−	0.500618i	$-0.833106\pi$
$541$	−11.7840	+	10.0645i	−0.506635	+	0.432707i	0.359034	+	0.933325i	$0.383106\pi$
$542$	−9.46859	−	6.18826i	−0.406711	−	0.265808i
$543$	−0.652875	+	0.474342i	−0.0280176	+	0.0203559i
$544$	0.532479	−	7.94485i	0.0228299	−	0.340632i
$545$	2.76790	−	8.51871i	0.118564	−	0.364901i
$546$	−2.57986	+	2.07671i	−0.110408	+	0.0888752i
$547$	−10.5815	+	44.0753i	−0.452434	+	1.88452i	0.0138793	+	0.999904i	$0.495582\pi$
$547$	−10.5815	+	44.0753i	−0.452434	+	1.88452i	−0.466313	+	0.884620i	$0.654418\pi$
$548$	−34.8305	−	13.6035i	−1.48788	−	0.581111i
$549$	−2.05875	−	0.852761i	−0.0878651	−	0.0363949i
$550$	−0.601014	+	1.74073i	−0.0256273	+	0.0742248i
$551$	10.7625	+	10.7625i	0.458497	+	0.458497i
$552$	−6.28964	+	0.439748i	−0.267705	+	0.0187169i
$553$	−27.3515	+	4.33206i	−1.16311	+	0.184218i
$554$	−22.5895	+	6.61982i	−0.959737	+	0.281249i
$555$	−2.91328	−	2.48818i	−0.123662	−	0.105617i
$556$	−6.83871	−	4.75900i	−0.290026	−	0.201826i
$557$	8.16395	−	13.3224i	0.345918	−	0.564486i	−0.631612	−	0.775285i	$-0.717606\pi$
$557$	8.16395	−	13.3224i	0.345918	−	0.564486i	0.977530	+	0.210798i	$0.0676064\pi$
$558$	7.74557	+	36.9692i	0.327896	+	1.56503i
$559$	−20.5951	+	6.69174i	−0.871079	+	0.283031i
$560$	−12.3345	−	18.4025i	−0.521228	−	0.777646i
$561$	1.37949	−	0.233788i	0.0582419	−	0.00987055i
$562$	12.1618	−	13.4282i	0.513015	−	0.566434i
$563$	1.41850	+	1.66085i	0.0597826	+	0.0699965i	0.789491	−	0.613762i	$-0.210344\pi$
$563$	1.41850	+	1.66085i	0.0597826	+	0.0699965i	−0.729709	+	0.683758i	$0.760344\pi$
$564$	5.72790	+	0.788061i	0.241188	+	0.0331833i
$565$	8.09272	+	33.7086i	0.340463	+	1.41813i
$566$	16.0222	+	12.3686i	0.673465	+	0.519891i
$567$	−9.60518	−	18.8512i	−0.403380	−	0.791677i
$568$	−0.103508	+	11.8465i	−0.00434310	+	0.497068i
$569$	−2.06696	−	13.0502i	−0.0866513	−	0.547095i	−0.992378	−	0.123232i	$-0.960674\pi$
$569$	−2.06696	−	13.0502i	−0.0866513	−	0.547095i	0.905727	−	0.423863i	$-0.139326\pi$
$570$	2.00694	+	2.12725i	0.0840615	+	0.0891006i
$571$	28.8610	+	11.9546i	1.20780	+	0.500286i	0.893510	−	0.449043i	$-0.148235\pi$
$571$	28.8610	+	11.9546i	1.20780	+	0.500286i	0.314286	+	0.949328i	$0.398235\pi$
$572$	11.0244	+	16.7925i	0.460952	+	0.702131i
$573$	1.89044	+	4.56393i	0.0789744	+	0.190661i
$574$	−3.87540	+	1.47469i	−0.161756	+	0.0615524i
$575$	−2.36258	−	1.71651i	−0.0985262	−	0.0715835i
$576$	−3.23966	−	23.0549i	−0.134986	−	0.960622i
$577$	−5.40589	+	16.6376i	−0.225050	+	0.692633i	0.773237	+	0.634118i	$0.218637\pi$
$577$	−5.40589	+	16.6376i	−0.225050	+	0.692633i	−0.998287	+	0.0585149i	$0.981363\pi$
$578$	20.4997	+	5.55692i	0.852676	+	0.231138i
$579$	1.89055	+	1.15853i	0.0785687	+	0.0481470i
$580$	10.2654	−	17.5434i	0.426247	−	0.728449i
$581$	−1.36103	+	17.2935i	−0.0564651	+	0.717457i
$582$	0.422283	−	0.199911i	0.0175042	−	0.00828657i
$583$	−18.9911	−	25.5539i	−0.786529	−	1.05834i
$584$	−29.9320	−	22.1490i	−1.23860	−	0.916534i
$585$	16.8553	+	8.58821i	0.696881	+	0.355079i
$586$	32.7864	−	22.3931i	1.35439	−	0.925052i
$587$	−9.32679	−	38.8489i	−0.384958	−	1.60347i	−0.742686	−	0.669640i	$-0.766449\pi$
$587$	−9.32679	−	38.8489i	−0.384958	−	1.60347i	0.357728	−	0.933826i	$-0.383551\pi$
$588$	0.0362167	+	0.201966i	0.00149355	+	0.00832894i
$589$	2.31477	+	29.4119i	0.0953785	+	1.21190i
$590$	−0.262233	+	2.42697i	−0.0107960	+	0.0999166i
$591$	0.980446	−	1.34947i	0.0403302	−	0.0555097i
$592$	2.83409	+	23.6531i	0.116480	+	0.972138i
$593$		−	17.1695i		−	0.705066i	−0.935799	−	0.352533i	$-0.885320\pi$
$593$		−	17.1695i		−	0.705066i	0.935799	−	0.352533i	$-0.114680\pi$
$594$	7.73249	−	3.03842i	0.317268	−	0.124668i
$595$	−7.20257	+	2.98340i	−0.295277	+	0.122308i
$596$	−9.77503	+	0.198999i	−0.400401	+	0.00815133i
$597$	−1.85097	+	1.13428i	−0.0757553	+	0.0464229i
$598$	−30.5694	+	8.95832i	−1.25008	+	0.366333i
$599$	−12.6570	−	24.8408i	−0.517152	−	1.01497i	−0.990937	−	0.134328i	$-0.957113\pi$
$599$	−12.6570	−	24.8408i	−0.517152	−	1.01497i	0.473785	−	0.880641i	$-0.342887\pi$
$600$	−0.176369	+	0.282243i	−0.00720024	+	0.0115225i
$601$	−21.5265	−	3.40946i	−0.878083	−	0.139075i	−0.298912	−	0.954281i	$-0.596624\pi$
$601$	−21.5265	−	3.40946i	−0.878083	−	0.139075i	−0.579171	+	0.815206i	$0.696624\pi$
$602$	4.82977	−	25.6421i	0.196847	−	1.04510i
$603$	−0.0898391	+	1.14151i	−0.00365853	+	0.0464861i
$604$	16.7304	−	20.4160i	0.680751	−	0.830716i
$605$	−15.7185	−	17.6188i	−0.639048	−	0.716305i
$606$	−4.06872	+	0.201352i	−0.165280	+	0.00817936i
$607$	−2.02301	−	6.22618i	−0.0821114	−	0.252713i	0.901570	−	0.432634i	$-0.142416\pi$
$607$	−2.02301	−	6.22618i	−0.0821114	−	0.252713i	−0.983681	+	0.179921i	$0.942416\pi$
$608$	−0.211264	−	18.1835i	−0.00856787	−	0.737437i
$609$	2.96211	−	2.15210i	0.120031	−	0.0872074i
$610$	−0.608133	+	2.24343i	−0.0246226	+	0.0908338i
$611$	29.1219	−	2.29194i	1.17814	−	0.0927220i
$612$	−8.17896	−	0.476428i	−0.330615	−	0.0192585i
$613$	17.9729	+	29.3292i	0.725921	+	1.18459i	0.976295	+	0.216446i	$0.0694464\pi$
$613$	17.9729	+	29.3292i	0.725921	+	1.18459i	−0.250374	+	0.968149i	$0.580554\pi$
$614$	10.3937	−	9.80591i	0.419457	−	0.395734i
$615$	−0.516896	−	0.516896i	−0.0208433	−	0.0208433i
$616$	−24.1263	+	1.94887i	−0.972076	+	0.0785221i
$617$	4.41197	−	4.41197i	0.177619	−	0.177619i	−0.612698	−	0.790317i	$-0.709916\pi$
$617$	4.41197	−	4.41197i	0.177619	−	0.177619i	0.790317	+	0.612698i	$0.209916\pi$
$618$	−0.0351916	+	1.20931i	−0.00141561	+	0.0486456i
$619$	−10.7119	+	6.56424i	−0.430546	+	0.263839i	−0.720844	−	0.693097i	$-0.756246\pi$
$619$	−10.7119	+	6.56424i	−0.430546	+	0.263839i	0.290298	+	0.956936i	$0.406246\pi$
$620$	37.2155	−	12.9353i	1.49461	−	0.519492i
$621$	1.03367	+	13.1341i	0.0414799	+	0.527052i
$622$	12.6240	−	7.23953i	0.506176	−	0.290279i
$623$	−27.6814	−	38.1002i	−1.10903	−	1.52645i
$624$	1.26145	+	3.40420i	0.0504984	+	0.136277i
$625$	21.7628	−	7.07115i	0.870511	−	0.282846i
$626$	−23.0867	+	25.4907i	−0.922729	+	1.01881i
$627$	3.09879	−	0.779444i	0.123754	−	0.0311280i
$628$	−5.32685	−	9.94860i	−0.212565	−	0.396993i
$629$	8.35732	+	0.657735i	0.333228	+	0.0262256i
$630$	−18.8228	+	12.8560i	−0.749917	+	0.512194i
$631$	2.52015	−	15.9116i	0.100326	−	0.633430i	−0.885369	−	0.464889i	$-0.846094\pi$
$631$	2.52015	−	15.9116i	0.100326	−	0.633430i	0.985695	−	0.168541i	$-0.0539057\pi$
$632$	−5.01051	+	29.9397i	−0.199307	+	1.19094i
$633$	5.28018	−	2.69039i	0.209868	−	0.106933i
$634$	−11.8259	+	21.6302i	−0.469667	+	0.859043i
$635$	−20.8782	−	34.0701i	−0.828526	−	1.35203i
$636$	−2.30969	−	5.27005i	−0.0915851	−	0.208971i
$637$	0.396719	+	0.957765i	0.0157186	+	0.0379480i
$638$	−11.2553	−	19.1444i	−0.445602	−	0.757935i
$639$	12.1894			0.482204
$640$	−23.4204	+	6.42111i	−0.925771	+	0.253817i
$641$	12.4774	+	9.06537i	0.492828	+	0.358060i	0.806271	−	0.591547i	$-0.201482\pi$
$641$	12.4774	+	9.06537i	0.492828	+	0.358060i	−0.313443	+	0.949607i	$0.601482\pi$
$642$	−3.64417	−	4.52707i	−0.143824	−	0.178669i
$643$	10.6289	−	0.836511i	0.419162	−	0.0329888i	0.132875	−	0.991133i	$-0.457579\pi$
$643$	10.6289	−	0.836511i	0.419162	−	0.0329888i	0.286287	+	0.958144i	$0.407579\pi$
$644$	8.19894	−	37.4976i	0.323083	−	1.47761i
$645$	4.47293	−	1.07386i	0.176122	−	0.0422830i
$646$	−6.28869	−	1.18449i	−0.247425	−	0.0466033i
$647$	5.86292	−	11.5066i	0.230495	−	0.452372i	−0.746572	−	0.665305i	$-0.768302\pi$
$647$	5.86292	−	11.5066i	0.230495	−	0.452372i	0.977067	+	0.212933i	$0.0683016\pi$
$648$	−22.9375	+	3.42779i	−0.901071	+	0.134656i
$649$	2.17453	+	1.54429i	0.0853578	+	0.0606185i
$650$	−0.565913	+	1.58342i	−0.0221969	+	0.0621067i
$651$	7.07522	+	0.556832i	0.277300	+	0.0218240i
$652$	0.698750	−	5.07876i	0.0273652	−	0.198899i
$653$	2.42574	−	3.95845i	0.0949266	−	0.154906i	−0.801652	−	0.597791i	$-0.796045\pi$
$653$	2.42574	−	3.95845i	0.0949266	−	0.154906i	0.896578	+	0.442885i	$0.146045\pi$
$654$	−0.879860	−	1.53426i	−0.0344052	−	0.0599944i
$655$	12.5811	+	4.08784i	0.491583	+	0.159725i
$656$	0.184990	+	4.54156i	0.00722266	+	0.177318i
$657$	−22.5193	+	30.9951i	−0.878561	+	1.20924i
$658$	−14.4102	+	32.1138i	−0.561769	+	1.25193i
$659$	−4.15909	+	1.72275i	−0.162015	+	0.0671089i	−0.462217	−	0.886767i	$-0.652946\pi$
$659$	−4.15909	+	1.72275i	−0.162015	+	0.0671089i	0.300202	+	0.953876i	$0.402946\pi$
$660$	−2.05475	−	3.73988i	−0.0799809	−	0.145575i
$661$	−6.91080	+	16.6842i	−0.268799	+	0.648938i	−0.999427	−	0.0338371i	$-0.989227\pi$
$661$	−6.91080	+	16.6842i	−0.268799	+	0.648938i	0.730628	+	0.682775i	$0.239227\pi$
$662$	0.816586	−	28.0608i	0.0317375	−	1.09062i
$663$	1.26182	−	0.199853i	0.0490052	−	0.00776166i
$664$	17.5038	+	7.43014i	0.679279	+	0.288345i
$665$	−15.8636	+	8.08289i	−0.615162	+	0.313441i
$666$	24.3104	−	3.12852i	0.942009	−	0.121228i
$667$	34.2437	−	8.22119i	1.32592	−	0.318326i
$668$	−4.16356	−	15.9087i	−0.161093	−	0.615527i
$669$	−1.91429	+	1.63496i	−0.0740106	+	0.0632110i
$670$	1.19292	−	0.0590352i	0.0460867	−	0.00228073i
$671$	1.81505	+	1.77626i	0.0700693	+	0.0685719i
$672$	−4.32824	−	0.634072i	−0.166966	−	0.0244599i
$673$	−3.53022	−	10.8649i	−0.136080	−	0.418811i	0.859677	−	0.510839i	$-0.170665\pi$
$673$	−3.53022	−	10.8649i	−0.136080	−	0.418811i	−0.995756	+	0.0920280i	$0.970665\pi$
$674$	−36.3349	−	23.7469i	−1.39957	−	0.914695i
$675$	0.592963	+	0.363368i	0.0228231	+	0.0139860i
$676$	−4.13333	−	6.44667i	−0.158974	−	0.247949i
$677$	20.1321	−	23.5717i	0.773740	−	0.905934i	−0.223898	−	0.974612i	$-0.571878\pi$
$677$	20.1321	−	23.5717i	0.773740	−	0.905934i	0.997639	+	0.0686789i	$0.0218784\pi$
$678$	6.00610	+	3.28373i	0.230663	+	0.126111i
$679$	0.444945	+	2.80927i	0.0170754	+	0.107810i
$680$	0.596039	+	8.52505i	0.0228570	+	0.326921i
$681$	−4.42037	+	4.42037i	−0.169389	+	0.169389i
$682$	7.51062	−	42.3869i	0.287597	−	1.62308i
$683$	−13.9736	+	33.7353i	−0.534686	+	1.29085i	0.393704	+	0.919237i	$0.371194\pi$
$683$	−13.9736	+	33.7353i	−0.534686	+	1.29085i	−0.928390	+	0.371608i	$0.878806\pi$
$684$	−18.7064	+	0.380825i	−0.715259	+	0.0145612i
$685$	39.0225	+	9.36848i	1.49097	+	0.357951i
$686$	−26.6372	−	2.87815i	−1.01701	−	0.109888i
$687$	4.27449	+	1.38887i	0.163082	+	0.0529885i
$688$	−24.9759	−	13.9400i	−0.952197	−	0.531456i
$689$	−17.0875	−	23.5189i	−0.650982	−	0.896000i
$690$	6.62297	−	1.38761i	0.252132	−	0.0528253i
$691$	12.3335	+	14.4407i	0.469190	+	0.549351i	0.943658	−	0.330922i	$-0.107360\pi$
$691$	12.3335	+	14.4407i	0.469190	+	0.549351i	−0.474468	+	0.880273i	$0.657360\pi$
$692$	−33.3188	+	17.8401i	−1.26659	+	0.678180i
$693$	2.22201	+	24.8052i	0.0844071	+	0.942270i
$694$	10.6535	−	29.8085i	0.404403	−	1.13151i
$695$	7.96723	+	4.05951i	0.302214	+	0.153986i
$696$	−1.20685	−	3.82779i	−0.0457456	−	0.145092i
$697$	1.57982	+	0.250220i	0.0598401	+	0.00947774i
$698$	4.35617	+	33.8499i	0.164884	+	1.28124i
$699$	−2.54436	+	2.97906i	−0.0962364	+	0.112678i
$700$	−1.34695	−	1.51358i	−0.0509099	−	0.0572078i
$701$	4.74081	−	19.7469i	0.179058	−	0.745829i	−0.808490	−	0.588510i	$-0.799715\pi$
$701$	4.74081	−	19.7469i	0.179058	−	0.745829i	0.987548	−	0.157319i	$-0.0502852\pi$
$702$	7.09000	−	2.69793i	0.267595	−	0.101827i
$703$	19.1450			0.722067
$704$	−6.36606	+	25.7580i	−0.239930	+	0.970790i
$705$	−6.20532			−0.233706
$706$	16.5228	−	6.28734i	0.621842	−	0.236627i
$707$	5.78941	−	24.1146i	0.217733	−	0.906923i
$708$	0.320437	+	0.360078i	0.0120428	+	0.0135326i
$709$	20.7991	−	24.3526i	0.781126	−	0.914581i	−0.216975	−	0.976177i	$-0.569619\pi$
$709$	20.7991	−	24.3526i	0.781126	−	0.914581i	0.998101	+	0.0615963i	$0.0196191\pi$
$710$	−1.62287	−	12.6106i	−0.0609052	−	0.473268i
$711$	30.8489	+	4.88599i	1.15692	+	0.183239i
$712$	−49.2350	+	15.5232i	−1.84516	+	0.581755i
$713$	60.8230	+	30.9909i	2.27784	+	1.16062i
$714$	−0.518080	+	1.44958i	−0.0193887	+	0.0542492i
$715$	−14.1778	−	16.2416i	−0.530220	−	0.607400i
$716$	−3.58861	+	1.92148i	−0.134113	+	0.0718089i
$717$	3.37699	+	3.95395i	0.126116	+	0.147663i
$718$	8.49693	−	1.78023i	0.317103	−	0.0664376i
$719$	0.667887	+	0.919267i	0.0249080	+	0.0342829i	0.821289	−	0.570512i	$-0.193255\pi$
$719$	0.667887	+	0.919267i	0.0249080	+	0.0342829i	−0.796381	+	0.604795i	$0.793255\pi$
$720$	6.81700	+	24.0387i	0.254055	+	0.895868i
$721$	−7.00468	−	2.27596i	−0.260868	−	0.0847612i
$722$	12.1848	+	1.31657i	0.453473	+	0.0489976i
$723$	−7.83081	−	1.88001i	−0.291231	−	0.0699184i
$724$	−5.38427	+	0.109613i	−0.200105	+	0.00407372i
$725$	0.711394	−	1.71746i	0.0264205	−	0.0637848i
$726$	−4.66210	−	0.0349290i	−0.173027	−	0.00129634i
$727$	−24.8103	+	24.8103i	−0.920164	+	0.920164i	−0.997041	−	0.0768768i	$-0.975505\pi$
$727$	−24.8103	+	24.8103i	−0.920164	+	0.920164i	0.0768768	+	0.997041i	$0.475505\pi$
$728$	−22.0474	+	1.54147i	−0.817129	+	0.0571306i
$729$	3.48380	+	21.9958i	0.129030	+	0.814661i
$730$	35.0645	+	19.1709i	1.29779	+	0.709547i
$731$	−6.53696	+	7.65380i	−0.241778	+	0.283086i
$732$	0.247726	+	0.386374i	0.00915623	+	0.0142808i
$733$	26.7132	+	16.3699i	0.986674	+	0.604635i	0.919493	−	0.393106i	$-0.128599\pi$
$733$	26.7132	+	16.3699i	0.986674	+	0.604635i	0.0671812	+	0.997741i	$0.478599\pi$
$734$	20.5457	+	13.4278i	0.758355	+	0.495627i
$735$	−0.0680503	−	0.209437i	−0.00251007	−	0.00772521i
$736$	−36.1282	−	21.5661i	−1.33170	−	0.794936i
$737$	0.579849	−	1.16906i	0.0213590	−	0.0430630i
$738$	4.67099	−	0.231157i	0.171941	−	0.00850901i
$739$	−15.0339	+	12.8402i	−0.553031	+	0.472333i	−0.881501	−	0.472181i	$-0.843467\pi$
$739$	−15.0339	+	12.8402i	−0.553031	+	0.472333i	0.328471	+	0.944514i	$0.393467\pi$
$740$	−6.47328	−	24.7340i	−0.237963	−	0.909241i
$741$	2.83699	−	0.681101i	0.104219	−	0.0250209i
$742$	34.7424	−	4.47103i	1.27544	−	0.164137i
$743$	30.5181	−	15.5498i	1.11960	−	0.570466i	0.206602	−	0.978425i	$-0.433759\pi$
$743$	30.5181	−	15.5498i	1.11960	−	0.570466i	0.913000	+	0.407959i	$0.133759\pi$
$744$	3.03986	−	7.16124i	0.111447	−	0.262544i
$745$	10.3639	−	1.64149i	0.379705	−	0.0601394i
$746$	−1.15158	+	39.5725i	−0.0421624	+	1.44885i
$747$	7.48726	−	18.0758i	0.273944	−	0.661360i
$748$	8.44739	+	3.97773i	0.308867	+	0.145440i
$749$	32.6866	−	13.5392i	1.19434	−	0.494712i
$750$	2.00850	−	4.47603i	0.0733399	−	0.163441i
$751$	15.2505	−	20.9906i	0.556500	−	0.765957i	−0.434376	−	0.900732i	$-0.643031\pi$
$751$	15.2505	−	20.9906i	0.556500	−	0.765957i	0.990876	+	0.134775i	$0.0430311\pi$
$752$	28.3710	+	26.1502i	1.03459	+	0.953601i
$753$	6.41667	+	2.08490i	0.233837	+	0.0759781i
$754$	−10.0877	−	17.5905i	−0.367372	−	0.640609i
$755$	−14.8017	+	24.1542i	−0.538689	+	0.879060i
$756$	−1.24586	+	9.05537i	−0.0453116	+	0.329341i
$757$	10.6972	+	0.841884i	0.388795	+	0.0305988i	0.271350	−	0.962481i	$-0.412530\pi$
$757$	10.6972	+	0.841884i	0.388795	+	0.0305988i	0.117444	+	0.993079i	$0.462530\pi$
$758$	11.9170	−	33.3437i	0.432845	−	1.21110i
$759$	2.20857	−	7.05567i	0.0801660	−	0.256105i
$760$	2.88453	+	19.3022i	0.104633	+	0.700165i
$761$	−19.7735	+	38.8077i	−0.716789	+	1.40678i	0.188539	+	0.982066i	$0.439625\pi$
$761$	−19.7735	+	38.8077i	−0.716789	+	1.40678i	−0.905328	+	0.424713i	$0.860375\pi$
$762$	−7.75375	−	1.46044i	−0.280889	−	0.0529063i
$763$	10.4697	−	2.51355i	0.379028	−	0.0909965i
$764$	−7.04175	+	32.2053i	−0.254762	+	1.16515i
$765$	8.76576	−	0.689880i	0.316927	−	0.0249427i
$766$	23.4100	+	29.0817i	0.845836	+	1.05076i
$767$	1.97019	+	1.43143i	0.0711396	+	0.0516859i
$768$	−2.16465	+	4.27880i	−0.0781103	+	0.154398i
$769$	−2.74973			−0.0991579			−0.0495790	−	0.998770i	$-0.515788\pi$
$769$	−2.74973			−0.0991579			−0.0495790	+	0.998770i	$0.515788\pi$
$770$	25.3666	−	5.60131i	0.914148	−	0.201857i
$771$	0.264642	+	0.638902i	0.00953084	+	0.0230095i
$772$	5.93955	+	13.5524i	0.213769	+	0.487760i
$773$	−24.1455	−	39.4019i	−0.868453	−	1.41719i	−0.908453	−	0.417986i	$-0.862736\pi$
$773$	−24.1455	−	39.4019i	−0.868453	−	1.41719i	0.0400005	−	0.999200i	$-0.487264\pi$
$774$	−14.1178	+	25.8221i	−0.507454	+	0.928157i
$775$	3.21062	−	1.63589i	0.115329	−	0.0587630i
$776$	3.07510	+	0.514629i	0.110390	+	0.0184741i
$777$	0.720450	−	4.54874i	0.0258460	−	0.163185i
$778$	−35.0704	+	23.9531i	−1.25733	+	0.858760i
$779$	3.64163	+	0.286602i	0.130475	+	0.0102686i
$780$	−1.83918	−	3.43490i	−0.0658531	−	0.122989i
$781$	−12.8910	−	5.17723i	−0.461276	−	0.185256i
$782$	−9.93948	+	10.9745i	−0.355435	+	0.392446i
$783$	−7.97607	+	2.59158i	−0.285042	+	0.0926156i
$784$	−0.571474	+	1.24433i	−0.0204098	+	0.0444405i
$785$	7.11894	+	9.79838i	0.254086	+	0.349719i
$786$	2.26591	−	1.29944i	0.0808225	−	0.0463496i
$787$	2.77659	+	35.2799i	0.0989747	+	1.25759i	0.823089	+	0.567913i	$0.192249\pi$
$787$	2.77659	+	35.2799i	0.0989747	+	1.25759i	−0.724114	+	0.689680i	$0.757751\pi$
$788$	10.5144	−	3.65455i	0.374559	−	0.130188i
$789$	2.33426	−	1.43044i	0.0831018	−	0.0509249i
$790$	0.947675	−	32.5655i	0.0337168	−	1.15863i
$791$	−29.4665	+	29.4665i	−1.04771	+	1.04771i
$792$	26.5587	+	6.31826i	0.943722	+	0.224510i
$793$	1.63969	+	1.63969i	0.0582271	+	0.0582271i
$794$	15.5626	−	14.6825i	0.552297	−	0.521061i
$795$	3.22663	+	5.26538i	0.114437	+	0.186744i
$796$	−14.4625	−	0.842445i	−0.512609	−	0.0298597i
$797$	−42.3253	+	3.33107i	−1.49924	+	0.117993i	−0.801342	−	0.598207i	$-0.795880\pi$
$797$	−42.3253	+	3.33107i	−1.49924	+	0.117993i	−0.697896	+	0.716199i	$0.745880\pi$
$798$	−0.919778	+	3.39310i	−0.0325598	+	0.120114i
$799$	10.9848	−	7.98093i	0.388615	−	0.282345i
$800$	−2.04193	+	0.873723i	−0.0721931	+	0.0308908i
$801$	16.4138	+	50.5166i	0.579954	+	1.78492i
$802$	19.9238	−	0.985983i	0.703532	−	0.0348163i
$803$	36.9802	−	23.2145i	1.30500	−	0.819223i
$804$	0.149484	−	0.182415i	0.00527190	−	0.00643328i
$805$	−3.23210	+	41.0678i	−0.113917	+	1.44745i
$806$	7.27545	−	38.6267i	0.256267	−	1.36057i
$807$	−8.62930	−	1.36675i	−0.303766	−	0.0481118i
$808$	−23.0542	−	14.4062i	−0.811044	−	0.506808i
$809$	−4.12944	−	8.10448i	−0.145183	−	0.284938i	0.806951	−	0.590618i	$-0.201116\pi$
$809$	−4.12944	−	8.10448i	−0.145183	−	0.284938i	−0.952134	+	0.305680i	$0.901116\pi$
$810$	23.8863	−	6.99984i	0.839279	−	0.245949i
$811$	−22.1815	+	13.5928i	−0.778898	+	0.477309i	−0.854259	−	0.519847i	$-0.825989\pi$
$811$	−22.1815	+	13.5928i	−0.778898	+	0.477309i	0.0753616	+	0.997156i	$0.475989\pi$
$812$	24.4285	−	0.497315i	0.857273	−	0.0174523i
$813$	2.21465	−	0.917337i	0.0776711	−	0.0321724i
$814$	−27.0385	−	7.01684i	−0.947699	−	0.245940i
$815$			5.50207i			0.192729i
$816$	1.32668	+	1.04278i	0.0464432	+	0.0365045i
$817$	−13.5113	+	18.5967i	−0.472701	+	0.650618i
$818$	−2.10490	+	19.4809i	−0.0735963	+	0.681133i
$819$	1.78416	+	22.6699i	0.0623436	+	0.792150i
$820$	−0.861032	−	4.80164i	−0.0300686	−	0.167680i
$821$	−7.69248	−	32.0415i	−0.268469	−	1.11826i	−0.929772	−	0.368136i	$-0.879996\pi$
$821$	−7.69248	−	32.0415i	−0.268469	−	1.11826i	0.661302	−	0.750119i	$-0.270004\pi$
$822$	6.54362	−	4.46930i	0.228235	−	0.155885i
$823$	−28.9178	−	14.7343i	−1.00801	−	0.513607i	−0.129627	−	0.991563i	$-0.541378\pi$
$823$	−28.9178	−	14.7343i	−1.00801	−	0.513607i	−0.878384	+	0.477956i	$0.841378\pi$
$824$	−4.80241	+	6.48995i	−0.167300	+	0.226088i
$825$	−0.232787	−	0.313233i	−0.00810461	−	0.0109054i
$826$	−2.65221	+	1.25557i	−0.0922822	+	0.0436869i
$827$	1.54283	−	19.6035i	0.0536494	−	0.681681i	−0.910017	−	0.414571i	$-0.863932\pi$
$827$	1.54283	−	19.6035i	0.0536494	−	0.681681i	0.963666	−	0.267109i	$-0.0860685\pi$
$828$	−21.8638	+	37.3649i	−0.759820	+	1.29852i
$829$	45.5486	+	27.9122i	1.58197	+	0.969431i	0.986062	+	0.166377i	$0.0532068\pi$
$829$	45.5486	+	27.9122i	1.58197	+	0.969431i	0.595906	+	0.803054i	$0.296793\pi$
$830$	−19.6974	−	5.33943i	−0.683705	−	0.185334i
$831$	1.54153	−	4.74433i	0.0534749	−	0.164579i
$832$	−6.06644	+	23.4552i	−0.210316	+	0.813161i
$833$	0.389831	+	0.283229i	0.0135068	+	0.00981329i
$834$	1.65020	−	0.627943i	0.0571417	−	0.0217439i
$835$	6.75395	+	16.3055i	0.233730	+	0.564274i
$836$	19.9449	+	7.54250i	0.689810	+	0.260863i
$837$	−15.0188	−	6.22099i	−0.519126	−	0.215029i
$838$	16.1577	+	17.1263i	0.558158	+	0.591617i
$839$	0.144095	+	0.909781i	0.00497472	+	0.0314091i	0.990051	−	0.140710i	$-0.0449386\pi$
$839$	0.144095	+	0.909781i	0.00497472	+	0.0314091i	−0.985076	+	0.172119i	$0.944939\pi$
$840$	4.69465	+	0.0410192i	0.161981	+	0.00141530i
$841$	−2.98828	−	5.86483i	−0.103044	−	0.202236i
$842$	−18.9191	−	14.6049i	−0.651996	−	0.503318i
$843$	0.896278	+	3.73327i	0.0308695	+	0.128581i
$844$	39.1778	+	5.39020i	1.34856	+	0.185538i
$845$	5.33769	+	6.24963i	0.183622	+	0.214994i
$846$	26.6500	−	29.4251i	0.916247	−	1.01165i
$847$	8.18567	−	27.1767i	0.281263	−	0.933803i
$848$	7.43686	−	37.6711i	0.255383	−	1.29363i
$849$	−4.07951	+	1.32551i	−0.140008	+	0.0454915i
$850$	0.160272	+	0.764971i	0.00549730	+	0.0262383i
$851$	23.1453	−	37.7697i	0.793410	−	1.29473i
$852$	−2.06073	−	1.43405i	−0.0705995	−	0.0491296i
$853$	−35.7445	−	30.5287i	−1.22387	−	1.04528i	−0.997459	−	0.0712487i	$-0.977302\pi$
$853$	−35.7445	−	30.5287i	−1.22387	−	1.04528i	−0.226408	−	0.974032i	$-0.572698\pi$
$854$	−2.68135	+	0.785765i	−0.0917539	+	0.0268883i
$855$	19.8334	−	3.14131i	0.678289	−	0.107430i
$856$	−2.70493	−	38.6882i	−0.0924527	−	1.32234i
$857$	−19.1511	−	19.1511i	−0.654191	−	0.654191i	0.299809	−	0.953999i	$-0.403077\pi$
$857$	−19.1511	−	19.1511i	−0.654191	−	0.654191i	−0.953999	+	0.299809i	$0.903077\pi$
$858$	−4.25632	−	0.0778659i	−0.145308	−	0.00265830i
$859$	−50.4488	−	20.8966i	−1.72129	−	0.712982i	−0.999788	−	0.0205707i	$-0.993452\pi$
$859$	−50.4488	−	20.8966i	−1.72129	−	0.712982i	−0.721503	−	0.692411i	$-0.756548\pi$
$860$	28.5941	+	11.1678i	0.975052	+	0.380818i
$861$	0.205134	−	0.854445i	0.00699095	−	0.0291194i
$862$	−7.92301	+	6.37781i	−0.269859	+	0.217229i
$863$	−7.83880	+	24.1253i	−0.266836	+	0.821236i	0.724429	+	0.689349i	$0.242104\pi$
$863$	−7.83880	+	24.1253i	−0.266836	+	0.821236i	−0.991265	+	0.131887i	$0.957896\pi$
$864$	8.98001	+	4.44490i	0.305506	+	0.151218i
$865$	32.8157	−	23.8420i	1.11577	−	0.810652i
$866$	12.3941	+	8.10027i	0.421170	+	0.275258i
$867$	−3.42264	+	2.92321i	−0.116239	+	0.0992775i
$868$	36.6325	+	30.0194i	1.24339	+	1.01892i
$869$	−30.5493	−	18.2698i	−1.03632	−	0.619760i
$870$	1.84309	+	3.89326i	0.0624866	+	0.131994i
$871$	0.540951	−	1.06168i	0.0183294	−	0.0359735i
$872$	1.02881	−	11.7579i	0.0348398	−	0.398172i
$873$	0.501840	−	3.16849i	0.0169847	−	0.107237i
$874$	−20.6629	+	26.7666i	−0.698932	+	0.905393i
$875$	22.7109	+	19.3969i	0.767768	+	0.655735i
$876$	7.45360	−	2.59070i	0.251834	−	0.0875316i
$877$	15.1323	+	3.63295i	0.510983	+	0.122676i	0.480734	−	0.876866i	$-0.340370\pi$
$877$	15.1323	+	3.63295i	0.510983	+	0.122676i	0.0302485	+	0.999542i	$0.490370\pi$
$878$	−1.02137	+	2.27618i	−0.0344697	+	0.0768173i
$879$			8.41403i			0.283798i
$880$	3.00064	−	28.3177i	0.101151	−	0.954591i
$881$			17.2656i			0.581694i	0.956770	+	0.290847i	$0.0939371\pi$
$881$			17.2656i			0.581694i	−0.956770	+	0.290847i	$0.906063\pi$
$882$	1.28539	+	0.576783i	0.0432813	+	0.0194213i
$883$	−18.9685	−	4.55394i	−0.638341	−	0.153252i	−0.0986595	−	0.995121i	$-0.531455\pi$
$883$	−18.9685	−	4.55394i	−0.638341	−	0.153252i	−0.539682	+	0.841869i	$0.681455\pi$
$884$	7.67353	+	3.71511i	0.258089	+	0.124953i
$885$	−0.393370	−	0.335969i	−0.0132230	−	0.0112935i
$886$	13.1390	+	10.1429i	0.441414	+	0.340756i
$887$	−0.804894	+	5.08190i	−0.0270257	+	0.170633i	−0.997509	−	0.0705330i	$-0.977530\pi$
$887$	−0.804894	+	5.08190i	−0.0270257	+	0.170633i	0.970484	+	0.241166i	$0.0775300\pi$
$888$	−4.47797	−	2.33115i	−0.150271	−	0.0782281i
$889$	21.8067	−	42.7980i	0.731372	−	1.43540i
$890$	50.0771	−	23.7068i	1.67859	−	0.794653i
$891$	6.06265	−	26.5109i	0.203106	−	0.888149i
$892$	−16.7178	+	1.65871i	−0.559752	+	0.0555378i
$893$	23.5791	−	20.1385i	0.789046	−	0.673909i
$894$	1.13352	−	1.73439i	0.0379106	−	0.0580066i
$895$	3.53442	−	2.56791i	0.118143	−	0.0858356i
$896$	−21.2913	−	19.9716i	−0.711293	−	0.667203i
$897$	2.08608	−	6.42029i	0.0696522	−	0.214367i
$898$	14.1507	+	17.5790i	0.472214	+	0.586620i
$899$	−10.1441	+	42.2533i	−0.338325	+	1.40923i
$900$	0.917300	+	2.09301i	0.0305767	+	0.0697671i
$901$	−12.4839	−	5.17100i	−0.415899	−	0.172271i
$902$	−5.03803	−	1.73946i	−0.167748	−	0.0579178i
$903$	3.91003	+	3.91003i	0.130118	+	0.130118i
$904$	20.3819	+	40.8809i	0.677893	+	1.35968i
$905$	5.70865	−	0.904161i	0.189762	−	0.0300553i
$906$	1.57307	+	5.36797i	0.0522619	+	0.178339i
$907$	13.1655	+	11.2444i	0.437154	+	0.373365i	0.840616	−	0.541631i	$-0.182193\pi$
$907$	13.1655	+	11.2444i	0.437154	+	0.373365i	−0.403462	+	0.914997i	$0.632193\pi$
$908$	−41.0625	+	7.36335i	−1.36271	+	0.244361i
$909$	−14.6148	+	23.8492i	−0.484742	+	0.791027i
$910$	23.2158	−	4.86405i	0.769596	−	0.161242i
$911$	−36.1009	+	11.7299i	−1.19608	+	0.388629i	−0.838317	−	0.545184i	$-0.816460\pi$
$911$	−36.1009	+	11.7299i	−1.19608	+	0.388629i	−0.357761	+	0.933813i	$0.616460\pi$
$912$	3.20731	+	2.13638i	0.106205	+	0.0707426i
$913$	−15.5956	+	15.9362i	−0.516140	+	0.527411i
$914$	−9.26132	−	8.38789i	−0.306337	−	0.277447i
$915$	−0.319908	−	0.374564i	−0.0105758	−	0.0123827i
$916$	18.1197	+	23.9011i	0.598693	+	0.789714i
$917$	3.71219	+	15.4624i	0.122587	+	0.510614i
$918$	2.15465	−	2.79112i	0.0711139	−	0.0921207i
$919$	−19.3044	−	37.8869i	−0.636792	−	1.24977i	−0.953540	−	0.301265i	$-0.902591\pi$
$919$	−19.3044	−	37.8869i	−0.636792	−	1.24977i	0.316749	−	0.948510i	$-0.397409\pi$
$920$	41.5671	+	17.6447i	1.37043	+	0.581728i
$921$	0.473714	+	2.99091i	0.0156094	+	0.0985539i
$922$	−23.8056	+	22.4592i	−0.783994	+	0.739655i
$923$	−11.7189	−	4.85412i	−0.385731	−	0.159775i
$924$	2.54261	−	4.45497i	0.0836457	−	0.146558i
$925$	−0.894826	−	2.16030i	−0.0294217	−	0.0710302i
$926$	7.53726	+	19.8075i	0.247690	+	0.650914i
$927$	6.72045	+	4.88269i	0.220729	+	0.160369i
$928$	7.98013	−	25.5673i	0.261961	−	0.839287i
$929$	−9.41723	+	28.9833i	−0.308969	+	0.950910i	0.669197	+	0.743085i	$0.266638\pi$
$929$	−9.41723	+	28.9833i	−0.308969	+	0.950910i	−0.978166	+	0.207825i	$0.933362\pi$
$930$	−2.18449	+	8.05869i	−0.0716324	+	0.264255i
$931$	0.938279	+	0.574978i	0.0307508	+	0.0188441i
$932$	−25.2925	+	6.61944i	−0.828483	+	0.216827i
$933$	−0.241965	+	3.07446i	−0.00792158	+	0.100653i
$934$	−3.61460	−	7.63531i	−0.118273	−	0.249835i
$935$	−9.56334	−	2.99352i	−0.312755	−	0.0978986i
$936$	24.1867	+	6.03070i	0.790568	+	0.197120i
$937$	−39.9157	−	20.3381i	−1.30399	−	0.664416i	−0.342568	−	0.939493i	$-0.611297\pi$
$937$	−39.9157	−	20.3381i	−1.30399	−	0.664416i	−0.961422	+	0.275077i	$0.911297\pi$
$938$	0.809768	+	1.18560i	0.0264399	+	0.0387113i
$939$	−1.70140	−	7.08684i	−0.0555230	−	0.231270i
$940$	−33.9901	−	23.6534i	−1.10863	−	0.771489i
$941$	−1.26641	−	16.0913i	−0.0412838	−	0.524560i	−0.982439	−	0.186585i	$-0.940258\pi$
$941$	−1.26641	−	16.0913i	−0.0412838	−	0.524560i	0.941155	−	0.337975i	$-0.109742\pi$
$942$	2.37766	+	0.256906i	0.0774684	+	0.00837044i
$943$	4.96795	−	6.83780i	0.161779	−	0.222669i
$944$	0.382676	+	3.19380i	0.0124550	+	0.103949i
$945$		−	9.81014i		−	0.319124i
$946$	25.8979	−	21.3122i	0.842015	−	0.692918i
$947$	10.2030	−	4.22622i	0.331553	−	0.137334i	−0.210696	−	0.977552i	$-0.567573\pi$
$947$	10.2030	−	4.22622i	0.331553	−	0.137334i	0.542249	+	0.840218i	$0.317573\pi$
$948$	−4.64049	−	4.45532i	−0.150716	−	0.144702i
$949$	33.9931	−	20.8310i	1.10346	−	0.676203i
$950$	0.501961	+	1.71289i	0.0162858	+	0.0555736i
$951$	−2.37175	−	4.65481i	−0.0769091	−	0.150943i
$952$	−8.36333	+	5.96537i	−0.271057	+	0.193339i
$953$	22.1287	+	3.50484i	0.716818	+	0.113533i	0.504180	−	0.863598i	$-0.331795\pi$
$953$	22.1287	+	3.50484i	0.716818	+	0.113533i	0.212638	+	0.977131i	$0.431795\pi$
$954$	−38.8254	−	7.31288i	−1.25702	−	0.236763i
$955$	2.77593	−	35.2715i	0.0898269	−	1.14136i
$956$	3.42607	+	34.5305i	0.110807	+	1.11680i
$957$	4.69549	+	0.318558i	0.151784	+	0.0102975i
$958$	0.788798	+	15.9392i	0.0254849	+	0.514973i
$959$	14.9074	+	45.8801i	0.481384	+	1.48155i
$960$	1.67560	−	4.86597i	0.0540799	−	0.157049i
$961$	−43.0640	+	31.2878i	−1.38916	+	1.00928i
$962$	−24.6179	−	6.67325i	−0.793713	−	0.215154i
$963$	−39.7806	+	3.13080i	−1.28191	+	0.100889i
$964$	−35.7276	−	40.1474i	−1.15071	−	1.29306i
$965$	−8.29753	−	13.5403i	−0.267107	−	0.435879i
$966$	5.58202	+	5.91664i	0.179599	+	0.190365i
$967$	−25.1651	−	25.1651i	−0.809254	−	0.809254i	0.175267	−	0.984521i	$-0.443921\pi$
$967$	−25.1651	−	25.1651i	−0.809254	−	0.809254i	−0.984521	+	0.175267i	$0.943921\pi$
$968$	−25.4038	−	17.9623i	−0.816511	−	0.577330i
$969$	0.958928	−	0.958928i	0.0308052	−	0.0308052i
$970$	−3.34481	−	0.0973357i	−0.107395	−	0.00312526i
$971$	9.16625	−	5.61709i	0.294159	−	0.180261i	−0.367587	−	0.929989i	$-0.619816\pi$
$971$	9.16625	−	5.61709i	0.294159	−	0.180261i	0.661746	+	0.749728i	$0.269816\pi$
$972$	6.77284	−	13.9893i	0.217239	−	0.448706i
$973$	0.843343	+	10.7157i	0.0270363	+	0.343529i
$974$	−6.65996	−	11.6134i	−0.213399	−	0.372116i
$975$	−0.209454	−	0.288289i	−0.00670789	−	0.00923262i
$976$	−0.115839	+	3.06067i	−0.00370792	+	0.0979697i
$977$	39.9365	−	12.9761i	1.27768	−	0.415144i	0.409918	−	0.912122i	$-0.365557\pi$
$977$	39.9365	−	12.9761i	1.27768	−	0.415144i	0.867763	+	0.496979i	$0.165557\pi$
$978$	0.805252	+	0.729310i	0.0257491	+	0.0233208i
$979$	4.09746	−	60.3958i	0.130955	−	1.93026i
$980$	0.425582	−	1.40660i	0.0135947	−	0.0449323i
$981$	−12.1065	−	0.952804i	−0.386532	−	0.0304207i
$982$	−20.5376	−	30.0696i	−0.655380	−	0.959559i
$983$	−6.40051	+	40.4112i	−0.204144	+	1.28892i	0.646394	+	0.763004i	$0.276276\pi$
$983$	−6.40051	+	40.4112i	−0.204144	+	1.28892i	−0.850538	+	0.525913i	$0.823724\pi$
$984$	−0.816872	−	0.510450i	−0.0260409	−	0.0162726i
$985$	−10.6445	+	5.42366i	−0.339163	+	0.172812i
$986$	−8.26997	−	4.52146i	−0.263370	−	0.143993i
$987$	−3.89748	−	6.36011i	−0.124058	−	0.202444i
$988$	18.1360	+	7.08325i	0.576984	+	0.225348i
$989$	20.3536	+	49.1379i	0.647207	+	1.56249i
$990$	−29.1621	−	2.83268i	−0.926833	−	0.0900286i
$991$	8.99309			0.285675			0.142837	−	0.989746i	$-0.454377\pi$
$991$	8.99309			0.285675			0.142837	+	0.989746i	$0.454377\pi$
$992$	43.9483	−	27.6389i	1.39536	−	0.877537i
$993$	4.81297	+	3.49683i	0.152735	+	0.110968i
$994$	11.9059	−	9.58391i	0.377632	−	0.303983i
$995$	15.5001	−	1.21988i	0.491386	−	0.0386729i
$996$	−3.39237	+	2.17504i	−0.107491	+	0.0689189i
$997$	−26.7505	+	6.42222i	−0.847196	+	0.203394i	−0.633727	−	0.773556i	$-0.718476\pi$
$997$	−26.7505	+	6.42222i	−0.847196	+	0.203394i	−0.213468	+	0.976950i	$0.568476\pi$
$998$	−5.75271	+	30.5422i	−0.182099	+	0.966795i
$999$	−4.78914	+	9.39922i	−0.151522	+	0.297378i

Display

a_p

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p

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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

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a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.bf.a.5.7	✓	736
11.9	even	5	inner	352.2.bf.a.229.44	yes	736
32.13	even	8	inner	352.2.bf.a.269.44	yes	736
352.141	even	40	inner	352.2.bf.a.141.7	yes	736

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.bf.a.5.7	✓	736	1.1	even	1	trivial
352.2.bf.a.141.7	yes	736	352.141	even	40	inner
352.2.bf.a.229.44	yes	736	11.9	even	5	inner
352.2.bf.a.269.44	yes	736	32.13	even	8	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	352.2.bf.a.5.7

Level	$352$
Weight	$2$
Character	352.5
Analytic conductor	$2.811$
Analytic rank	$0$
Dimension	$736$
Inner twists	$4$