LMFDB - Embedded newform 798.2.bu.b.431.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			431.10
Character	$\chi$	$=$	798.431
Dual form			798.2.bu.b.611.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.881939 + 1.49070i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.36601 - 1.62795i) q^{5} +(-1.33860 + 1.09916i) q^{6} +(-0.0385504 - 2.64547i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.44437 - 2.62941i) q^{9} +(-0.726838 - 1.99697i) q^{10} +4.02535i q^{11} +(-1.63381 + 0.575043i) q^{12} +(-2.04188 - 5.61002i) q^{13} +(0.868579 - 2.49911i) q^{14} +(3.63152 - 0.600560i) q^{15} +(0.173648 + 0.984808i) q^{16} +(6.67261 - 1.17656i) q^{17} +(-0.457951 - 2.96484i) q^{18} +(-3.87478 - 1.99651i) q^{19} -2.12513i q^{20} +(3.97760 + 2.27568i) q^{21} +(-1.37675 + 3.78259i) q^{22} +(-1.99655 - 5.48548i) q^{23} +(-1.73195 - 0.0184316i) q^{24} +(0.0840125 - 0.476459i) q^{25} -5.97006i q^{26} +(5.19350 + 0.165859i) q^{27} +(1.67094 - 2.05133i) q^{28} +(-2.43331 - 2.04179i) q^{29} +(3.61791 + 0.677709i) q^{30} +(2.24232 - 1.29460i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-6.00059 - 3.55011i) q^{33} +(6.67261 + 1.17656i) q^{34} +(-4.25402 + 3.67650i) q^{35} +(0.583702 - 2.94267i) q^{36} +(8.07321 - 4.66107i) q^{37} +(-2.95826 - 3.20136i) q^{38} +(10.1637 + 1.90386i) q^{39} +(0.726838 - 1.99697i) q^{40} +(-2.13288 - 0.776304i) q^{41} +(2.95939 + 3.49885i) q^{42} +(2.12461 + 12.0493i) q^{43} +(-2.58745 + 3.08360i) q^{44} +(-2.30752 + 5.94315i) q^{45} -5.83752i q^{46} +(-2.66102 - 0.469209i) q^{47} +(-1.62120 - 0.609683i) q^{48} +(-6.99703 + 0.203968i) q^{49} +(0.241904 - 0.418991i) q^{50} +(-4.13094 + 10.9845i) q^{51} +(2.04188 - 5.61002i) q^{52} +(-0.142441 - 0.119522i) q^{53} +(4.82357 + 1.93214i) q^{54} +(6.55305 - 5.49867i) q^{55} +(2.27177 - 1.35612i) q^{56} +(6.39352 - 4.01534i) q^{57} +(-1.58823 - 2.75090i) q^{58} +(-1.15106 - 6.52801i) q^{59} +(3.16793 + 1.87424i) q^{60} +(-1.22738 + 0.446730i) q^{61} +(2.54987 - 0.449611i) q^{62} +(-6.90035 + 3.92240i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-6.34359 + 10.9874i) q^{65} +(-4.42450 - 5.38834i) q^{66} +(4.04730 + 11.1199i) q^{67} +(5.86780 + 3.38777i) q^{68} +(9.93803 + 1.86160i) q^{69} +(-5.25491 + 1.99981i) q^{70} +(-0.639621 - 3.62747i) q^{71} +(1.55495 - 2.56557i) q^{72} +(10.4745 - 8.78913i) q^{73} +(9.18052 - 1.61877i) q^{74} +(0.636163 + 0.545444i) q^{75} +(-1.68493 - 4.02008i) q^{76} +(10.6489 - 0.155179i) q^{77} +(8.89956 + 5.26523i) q^{78} +(-9.16534 + 1.61610i) q^{79} +(1.36601 - 1.62795i) q^{80} +(-4.82760 + 7.59568i) q^{81} +(-1.73874 - 1.45898i) q^{82} +(-5.32128 - 3.07224i) q^{83} +(1.58424 + 4.30002i) q^{84} +(-11.0302 - 9.25546i) q^{85} +(-2.12461 + 12.0493i) q^{86} +(5.18973 - 1.82660i) q^{87} +(-3.48606 + 2.01268i) q^{88} +(-1.04320 - 0.875346i) q^{89} +(-4.20104 + 4.79552i) q^{90} +(-14.7624 + 5.61800i) q^{91} +(1.99655 - 5.48548i) q^{92} +(-0.0477231 + 4.48438i) q^{93} +(-2.34006 - 1.35103i) q^{94} +(2.04278 + 9.03519i) q^{95} +(-1.31491 - 1.12740i) q^{96} +(-3.17345 - 3.78197i) q^{97} +(-6.64482 - 2.20146i) q^{98} +(10.5843 - 5.81409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.881939	+	1.49070i	−0.509187	+	0.860656i
$3$	−0.881939	+	1.49070i	−0.509187	+	0.860656i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−1.36601	−	1.62795i	−0.610898	−	0.728040i	0.368579	−	0.929596i	$-0.379844\pi$
$5$	−1.36601	−	1.62795i	−0.610898	−	0.728040i	−0.979477	+	0.201557i	$0.935400\pi$
$6$	−1.33860	+	1.09916i	−0.546481	+	0.448730i
$7$	−0.0385504	−	2.64547i	−0.0145707	−	0.999894i
$7$	−0.0385504	−	2.64547i	−0.0145707	−	0.999894i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.44437	−	2.62941i	−0.481456	−	0.876470i
$10$	−0.726838	−	1.99697i	−0.229846	−	0.631498i
$11$			4.02535i			1.21369i	0.794821	+	0.606844i	$0.207565\pi$
$11$			4.02535i			1.21369i	−0.794821	+	0.606844i	$0.792435\pi$
$12$	−1.63381	+	0.575043i	−0.471640	+	0.166001i
$13$	−2.04188	−	5.61002i	−0.566316	−	1.55594i	−0.810211	−	0.586138i	$-0.800648\pi$
$13$	−2.04188	−	5.61002i	−0.566316	−	1.55594i	0.243895	−	0.969802i	$-0.421575\pi$
$14$	0.868579	−	2.49911i	0.232137	−	0.667916i
$15$	3.63152	−	0.600560i	0.937653	−	0.155064i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	6.67261	−	1.17656i	1.61835	−	0.285358i	0.710197	−	0.704003i	$-0.248606\pi$
$17$	6.67261	−	1.17656i	1.61835	−	0.285358i	0.908150	+	0.418645i	$0.137495\pi$
$18$	−0.457951	−	2.96484i	−0.107940	−	0.698820i
$19$	−3.87478	−	1.99651i	−0.888936	−	0.458031i
$19$	−3.87478	−	1.99651i	−0.888936	−	0.458031i
$20$		−	2.12513i		−	0.475194i
$21$	3.97760	+	2.27568i	0.867983	+	0.496593i
$22$	−1.37675	+	3.78259i	−0.293524	+	0.806451i
$23$	−1.99655	−	5.48548i	−0.416309	−	1.14380i	−0.953777	−	0.300516i	$-0.902841\pi$
$23$	−1.99655	−	5.48548i	−0.416309	−	1.14380i	0.537467	−	0.843285i	$-0.319381\pi$
$24$	−1.73195	−	0.0184316i	−0.353533	−	0.00376233i
$25$	0.0840125	−	0.476459i	0.0168025	−	0.0952917i
$26$		−	5.97006i		−	1.17082i
$27$	5.19350	+	0.165859i	0.999490	+	0.0319196i
$28$	1.67094	−	2.05133i	0.315779	−	0.387664i
$29$	−2.43331	−	2.04179i	−0.451855	−	0.379151i	0.388269	−	0.921546i	$-0.373073\pi$
$29$	−2.43331	−	2.04179i	−0.451855	−	0.379151i	−0.840124	+	0.542395i	$0.817518\pi$
$30$	3.61791	+	0.677709i	0.660537	+	0.123732i
$31$	2.24232	−	1.29460i	0.402732	−	0.232518i	−0.284930	−	0.958548i	$-0.591970\pi$
$31$	2.24232	−	1.29460i	0.402732	−	0.232518i	0.687662	+	0.726031i	$0.258637\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−6.00059	−	3.55011i	−1.04457	−	0.617995i
$34$	6.67261	+	1.17656i	1.14434	+	0.201779i
$35$	−4.25402	+	3.67650i	−0.719061	+	0.621441i
$36$	0.583702	−	2.94267i	0.0972836	−	0.490445i
$37$	8.07321	−	4.66107i	1.32723	−	0.766275i	0.342358	−	0.939570i	$-0.388775\pi$
$37$	8.07321	−	4.66107i	1.32723	−	0.766275i	0.984870	+	0.173294i	$0.0554412\pi$
$38$	−2.95826	−	3.20136i	−0.479893	−	0.519329i
$39$	10.1637	+	1.90386i	1.62749	+	0.304862i
$40$	0.726838	−	1.99697i	0.114923	−	0.315749i
$41$	−2.13288	−	0.776304i	−0.333100	−	0.121238i	0.170055	−	0.985435i	$-0.445605\pi$
$41$	−2.13288	−	0.776304i	−0.333100	−	0.121238i	−0.503155	+	0.864196i	$0.667828\pi$
$42$	2.95939	+	3.49885i	0.456644	+	0.539885i
$43$	2.12461	+	12.0493i	0.324001	+	1.83750i	0.516607	+	0.856223i	$0.327195\pi$
$43$	2.12461	+	12.0493i	0.324001	+	1.83750i	−0.192606	+	0.981276i	$0.561694\pi$
$44$	−2.58745	+	3.08360i	−0.390072	+	0.464870i
$45$	−2.30752	+	5.94315i	−0.343985	+	0.885953i
$46$		−	5.83752i		−	0.860696i
$47$	−2.66102	−	0.469209i	−0.388149	−	0.0684411i	−0.0238316	−	0.999716i	$-0.507587\pi$
$47$	−2.66102	−	0.469209i	−0.388149	−	0.0684411i	−0.364317	+	0.931275i	$0.618698\pi$
$48$	−1.62120	−	0.609683i	−0.234000	−	0.0880001i
$49$	−6.99703	+	0.203968i	−0.999575	+	0.0291382i
$50$	0.241904	−	0.418991i	0.0342104	−	0.0592542i
$51$	−4.13094	+	10.9845i	−0.578447	+	1.53814i
$52$	2.04188	−	5.61002i	0.283158	−	0.777970i
$53$	−0.142441	−	0.119522i	−0.0195657	−	0.0164176i	0.632952	−	0.774191i	$-0.281843\pi$
$53$	−0.142441	−	0.119522i	−0.0195657	−	0.0164176i	−0.652518	+	0.757773i	$0.726287\pi$
$54$	4.82357	+	1.93214i	0.656405	+	0.262931i
$55$	6.55305	−	5.49867i	0.883614	−	0.741440i
$56$	2.27177	−	1.35612i	0.303578	−	0.181219i
$57$	6.39352	−	4.01534i	0.846842	−	0.531845i
$58$	−1.58823	−	2.75090i	−0.208545	−	0.361211i
$59$	−1.15106	−	6.52801i	−0.149856	−	0.849874i	−0.963339	−	0.268286i	$-0.913543\pi$
$59$	−1.15106	−	6.52801i	−0.149856	−	0.849874i	0.813483	−	0.581588i	$-0.197568\pi$
$60$	3.16793	+	1.87424i	0.408979	+	0.241963i
$61$	−1.22738	+	0.446730i	−0.157150	+	0.0571979i	−0.419397	−	0.907803i	$-0.637759\pi$
$61$	−1.22738	+	0.446730i	−0.157150	+	0.0571979i	0.262247	+	0.965001i	$0.415536\pi$
$62$	2.54987	−	0.449611i	0.323834	−	0.0571007i
$63$	−6.90035	+	3.92240i	−0.869362	+	0.494176i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−6.34359	+	10.9874i	−0.786825	+	1.36282i
$66$	−4.42450	−	5.38834i	−0.544618	−	0.663258i
$67$	4.04730	+	11.1199i	0.494456	+	1.35851i	0.896564	+	0.442915i	$0.146056\pi$
$67$	4.04730	+	11.1199i	0.494456	+	1.35851i	−0.402108	+	0.915592i	$0.631722\pi$
$68$	5.86780	+	3.38777i	0.711575	+	0.410828i
$69$	9.93803	+	1.86160i	1.19640	+	0.224110i
$70$	−5.25491	+	1.99981i	−0.628082	+	0.239023i
$71$	−0.639621	−	3.62747i	−0.0759090	−	0.430501i	−0.998951	−	0.0458012i	$-0.985416\pi$
$71$	−0.639621	−	3.62747i	−0.0759090	−	0.430501i	0.923042	−	0.384700i	$-0.125695\pi$
$72$	1.55495	−	2.56557i	0.183253	−	0.302355i
$73$	10.4745	−	8.78913i	1.22595	−	1.02869i	0.227454	−	0.973789i	$-0.426960\pi$
$73$	10.4745	−	8.78913i	1.22595	−	1.02869i	0.998492	−	0.0549013i	$-0.0174844\pi$
$74$	9.18052	−	1.61877i	1.06721	−	0.188179i
$75$	0.636163	+	0.545444i	0.0734577	+	0.0629825i
$76$	−1.68493	−	4.02008i	−0.193274	−	0.461135i
$77$	10.6489	−	0.155179i	1.21356	−	0.0176843i
$78$	8.89956	+	5.26523i	1.00768	+	0.596169i
$79$	−9.16534	+	1.61610i	−1.03118	+	0.181825i	−0.663539	−	0.748142i	$-0.730946\pi$
$79$	−9.16534	+	1.61610i	−1.03118	+	0.181825i	−0.367643	+	0.929967i	$0.619835\pi$
$80$	1.36601	−	1.62795i	0.152724	−	0.182010i
$81$	−4.82760	+	7.59568i	−0.536400	+	0.843964i
$82$	−1.73874	−	1.45898i	−0.192012	−	0.161117i
$83$	−5.32128	−	3.07224i	−0.584087	−	0.337223i	0.178669	−	0.983909i	$-0.442821\pi$
$83$	−5.32128	−	3.07224i	−0.584087	−	0.337223i	−0.762756	+	0.646687i	$0.776154\pi$
$84$	1.58424	+	4.30002i	0.172855	+	0.469171i
$85$	−11.0302	−	9.25546i	−1.19640	−	1.00390i
$86$	−2.12461	+	12.0493i	−0.229103	+	1.29931i
$87$	5.18973	−	1.82660i	0.556397	−	0.195832i
$88$	−3.48606	+	2.01268i	−0.371615	+	0.214552i
$89$	−1.04320	−	0.875346i	−0.110579	−	0.0927865i	0.585822	−	0.810440i	$-0.300772\pi$
$89$	−1.04320	−	0.875346i	−0.110579	−	0.0927865i	−0.696401	+	0.717653i	$0.745216\pi$
$90$	−4.20104	+	4.79552i	−0.442828	+	0.505492i
$91$	−14.7624	+	5.61800i	−1.54752	+	0.588927i
$92$	1.99655	−	5.48548i	0.208155	−	0.571900i
$93$	−0.0477231	+	4.48438i	−0.00494866	+	0.465009i
$94$	−2.34006	−	1.35103i	−0.241359	−	0.139348i
$95$	2.04278	+	9.03519i	0.209585	+	0.926991i
$96$	−1.31491	−	1.12740i	−0.134202	−	0.115064i
$97$	−3.17345	−	3.78197i	−0.322215	−	0.384001i	0.580485	−	0.814271i	$-0.302863\pi$
$97$	−3.17345	−	3.78197i	−0.322215	−	0.384001i	−0.902700	+	0.430270i	$0.858418\pi$
$98$	−6.64482	−	2.20146i	−0.671228	−	0.222381i
$99$	10.5843	−	5.81409i	1.06376	−	0.584338i
$100$	0.370619	−	0.310986i	0.0370619	−	0.0310986i
$101$	−1.35248	−	0.238478i	−0.134576	−	0.0237295i	0.105954	−	0.994371i	$-0.466210\pi$
$101$	−1.35248	−	0.238478i	−0.134576	−	0.0237295i	−0.240531	+	0.970642i	$0.577321\pi$
$102$	−7.63874	+	8.90921i	−0.756348	+	0.882143i
$103$	1.71233	+	0.988614i	0.168721	+	0.0974110i	0.581983	−	0.813201i	$-0.302277\pi$
$103$	1.71233	+	0.988614i	0.168721	+	0.0974110i	−0.413262	+	0.910612i	$0.635611\pi$
$104$	3.83748	−	4.57333i	0.376296	−	0.448452i
$105$	−1.72876	−	9.58391i	−0.168710	−	0.935294i
$106$	−0.0929716	−	0.161032i	−0.00903020	−	0.0156408i
$107$	−2.91395			−0.281702			−0.140851	−	0.990031i	$-0.544984\pi$
$107$	−2.91395			−0.281702			−0.140851	+	0.990031i	$0.544984\pi$
$108$	3.87184	+	3.46538i	0.372568	+	0.333456i
$109$	−2.32444	+	6.38634i	−0.222641	+	0.611700i	−0.999846	−	0.0175468i	$-0.994414\pi$
$109$	−2.32444	+	6.38634i	−0.222641	+	0.611700i	0.777205	+	0.629247i	$0.216637\pi$
$110$	8.03851	−	2.92578i	0.766442	−	0.278962i
$111$	−0.171822	+	16.1455i	−0.0163086	+	1.53246i
$112$	2.59859	−	0.497346i	0.245543	−	0.0469948i
$113$	−15.8970			−1.49547			−0.747734	−	0.663998i	$-0.768858\pi$
$113$	−15.8970			−1.49547			−0.747734	+	0.663998i	$0.768858\pi$
$114$	7.38127	−	1.58647i	0.691319	−	0.148587i
$115$	−6.20276	+	10.7435i	−0.578410	+	1.00184i
$116$	−0.551587	−	3.12821i	−0.0512136	−	0.290447i
$117$	−11.8018	+	13.4719i	−1.09108	+	1.24548i
$118$	1.15106	−	6.52801i	0.105964	−	0.600952i
$119$	−3.36979	−	17.6068i	−0.308908	−	1.61402i
$120$	2.33586	+	2.84470i	0.213234	+	0.259685i
$121$	−5.20344			−0.473040
$122$	−1.30615			−0.118253
$123$	3.03830	−	2.49483i	0.273955	−	0.224951i
$124$	2.54987	+	0.449611i	0.228985	+	0.0403763i
$125$	−10.0925	+	5.82691i	−0.902701	+	0.521175i
$126$	−7.82574	+	1.32579i	−0.697173	+	0.118111i
$127$	−5.40357	−	14.8462i	−0.479489	−	1.31739i	−0.909928	−	0.414766i	$-0.863863\pi$
$127$	−5.40357	−	14.8462i	−0.479489	−	1.31739i	0.430439	−	0.902620i	$-0.358359\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−19.8356	−	7.45957i	−1.74643	−	0.656778i
$130$	−9.71894	+	8.15516i	−0.852407	+	0.715255i
$131$	0.722404	−	1.98479i	0.0631167	−	0.173412i	−0.904126	−	0.427267i	$-0.859476\pi$
$131$	0.722404	−	1.98479i	0.0631167	−	0.173412i	0.967242	+	0.253855i	$0.0816987\pi$
$132$	−2.31475	−	6.57665i	−0.201473	−	0.572424i
$133$	−5.13233	+	10.3276i	−0.445029	+	0.895516i
$134$			11.8335i			1.02226i
$135$	−6.82437	−	8.68131i	−0.587348	−	0.747168i
$136$	4.35524	+	5.19037i	0.373459	+	0.445071i
$137$	−0.143043	+	0.170472i	−0.0122210	+	0.0145644i	−0.772120	−	0.635476i	$-0.780804\pi$
$137$	−0.143043	+	0.170472i	−0.0122210	+	0.0145644i	0.759899	+	0.650041i	$0.225248\pi$
$138$	8.70199	+	5.14834i	0.740763	+	0.438255i
$139$	11.4179	−	4.15576i	0.968450	−	0.352487i	0.191111	−	0.981568i	$-0.438791\pi$
$139$	11.4179	−	4.15576i	0.968450	−	0.352487i	0.777339	+	0.629081i	$0.216569\pi$
$140$	−5.62198	+	0.0819247i	−0.475144	+	0.00692390i
$141$	3.04630	−	3.55296i	0.256545	−	0.299213i
$142$	0.639621	−	3.62747i	0.0536758	−	0.304410i
$143$	22.5823	−	8.21928i	1.88843	−	0.687331i
$144$	2.33865	−	1.87902i	0.194888	−	0.156585i
$145$			6.75041i			0.560591i
$146$	12.8489	−	4.67660i	1.06338	−	0.387038i
$147$	5.86689	−	10.6104i	0.483893	−	0.875127i
$148$	9.18052	+	1.61877i	0.754634	+	0.133062i
$149$	13.7531	−	2.42505i	1.12670	−	0.198668i	0.420919	−	0.907098i	$-0.361708\pi$
$149$	13.7531	−	2.42505i	1.12670	−	0.198668i	0.705780	+	0.708431i	$0.250597\pi$
$150$	0.411244	+	0.730131i	0.0335779	+	0.0596149i
$151$	12.8483	+	7.41799i	1.04558	+	0.603667i	0.921409	−	0.388593i	$-0.127039\pi$
$151$	12.8483	+	7.41799i	1.04558	+	0.603667i	0.124173	+	0.992261i	$0.460372\pi$
$152$	−0.208365	−	4.35392i	−0.0169006	−	0.353149i
$153$	−12.7314	−	15.8457i	−1.02927	−	1.28104i
$154$	10.0598	+	3.49633i	0.810643	+	0.281743i
$155$	−5.17057	−	1.88194i	−0.415311	−	0.151161i
$156$	6.56204	+	7.99152i	0.525384	+	0.639834i
$157$	−7.42646	−	2.70301i	−0.592696	−	0.215724i	0.0282188	−	0.999602i	$-0.491016\pi$
$157$	−7.42646	−	2.70301i	−0.592696	−	0.215724i	−0.620915	+	0.783878i	$0.713239\pi$
$158$	−9.16534	−	1.61610i	−0.729155	−	0.128570i
$159$	0.303795	−	0.106925i	0.0240925	−	0.00847973i
$160$	1.84042	−	1.06257i	0.145498	−	0.0840033i
$161$	−14.4347	+	5.49328i	−1.13761	+	0.432931i
$162$	−7.13433	+	5.48647i	−0.560526	+	0.431057i
$163$	7.99260	−	13.8436i	0.626029	−	1.08431i	−0.362312	−	0.932057i	$-0.618013\pi$
$163$	7.99260	−	13.8436i	0.626029	−	1.08431i	0.988341	−	0.152257i	$-0.0486542\pi$
$164$	−1.13488	−	1.96567i	−0.0886193	−	0.153493i
$165$	2.41747	+	14.6181i	0.188199	+	1.13802i
$166$	−3.94960	−	4.70695i	−0.306548	−	0.365330i
$167$	−3.15045	+	17.8671i	−0.243789	+	1.38260i	0.579499	+	0.814973i	$0.303248\pi$
$167$	−3.15045	+	17.8671i	−0.243789	+	1.38260i	−0.823288	+	0.567624i	$0.807863\pi$
$168$	0.0180073	+	4.58254i	0.00138929	+	0.353551i
$169$	−17.3445	+	14.5537i	−1.33419	+	1.11952i
$170$	−7.19947	−	12.4699i	−0.552174	−	0.956394i
$171$	0.346976	+	13.0721i	0.0265340	+	0.999648i
$172$	−6.11758	+	10.5960i	−0.466461	+	0.807935i
$173$	−3.41664	−	1.24356i	−0.259762	−	0.0945457i	0.208856	−	0.977946i	$-0.433026\pi$
$173$	−3.41664	−	1.24356i	−0.259762	−	0.0945457i	−0.468619	+	0.883401i	$0.655248\pi$
$174$	5.50149	+	0.0585472i	0.417067	+	0.00443845i
$175$	−1.26370	−	0.203885i	−0.0955264	−	0.0154123i
$176$	−3.96420	+	0.698995i	−0.298813	+	0.0526887i
$177$	10.7465	+	4.04141i	0.807754	+	0.303771i
$178$	−0.680898	−	1.17935i	−0.0510355	−	0.0883960i
$179$	−7.38466			−0.551955			−0.275978	−	0.961164i	$-0.589002\pi$
$179$	−7.38466			−0.551955			−0.275978	+	0.961164i	$0.589002\pi$
$180$	−5.58785	+	3.06948i	−0.416494	+	0.228785i
$181$	−0.453714	+	0.540715i	−0.0337243	+	0.0401910i	−0.782643	−	0.622471i	$-0.786129\pi$
$181$	−0.453714	+	0.540715i	−0.0337243	+	0.0401910i	0.748919	+	0.662662i	$0.230573\pi$
$182$	−15.7936	+	0.230148i	−1.17070	+	0.0170597i
$183$	0.416534	−	2.22364i	0.0307911	−	0.164376i
$184$	3.75229	−	4.47180i	0.276622	−	0.329666i
$185$	−18.6161	−	6.77569i	−1.36868	−	0.498159i
$186$	−1.57860	+	4.19762i	−0.115748	+	0.307785i
$187$	4.73607	+	26.8596i	0.346336	+	1.96417i
$188$	−1.73685	−	2.06990i	−0.126673	−	0.150963i
$189$	0.238563	−	13.7457i	0.0173529	−	0.999849i
$190$	−1.17063	+	9.18897i	−0.0849264	+	0.666638i
$191$	21.1226	−	12.1951i	1.52838	−	0.882408i	0.528945	−	0.848656i	$-0.322588\pi$
$191$	21.1226	−	12.1951i	1.52838	−	0.882408i	0.999430	−	0.0337522i	$-0.0107457\pi$
$192$	−0.850014	−	1.50913i	−0.0613445	−	0.108912i
$193$	11.4209	+	13.6109i	0.822093	+	0.979732i	0.999991	−	0.00431673i	$-0.00137406\pi$
$193$	11.4209	+	13.6109i	0.822093	+	0.979732i	−0.177898	+	0.984049i	$0.556930\pi$
$194$	−1.68856	−	4.63927i	−0.121231	−	0.333080i
$195$	−10.7843	−	19.1466i	−0.772278	−	1.37112i
$196$	−5.49114	−	4.34135i	−0.392224	−	0.310097i
$197$	9.04201	+	5.22041i	0.644217	+	0.371939i	0.786237	−	0.617925i	$-0.212027\pi$
$197$	9.04201	+	5.22041i	0.644217	+	0.371939i	−0.142020	+	0.989864i	$0.545360\pi$
$198$	11.9345	−	1.84341i	0.848150	−	0.131006i
$199$	−3.15833	+	1.14954i	−0.223888	+	0.0814885i	−0.451528	−	0.892257i	$-0.649121\pi$
$199$	−3.15833	+	1.14954i	−0.223888	+	0.0814885i	0.227641	+	0.973745i	$0.426899\pi$
$200$	0.454631	−	0.165472i	0.0321473	−	0.0117007i
$201$	−20.1458	−	3.77373i	−1.42098	−	0.266178i
$202$	−1.18935	−	0.686671i	−0.0836823	−	0.0483140i
$203$	−5.30770	+	6.51597i	−0.372527	+	0.457331i
$204$	−10.2252	+	5.75931i	−0.715907	+	0.403233i
$205$	1.64975	+	4.53265i	0.115224	+	0.316574i
$206$	1.27094	+	1.51464i	0.0885504	+	0.105530i
$207$	−11.5398	+	13.1728i	−0.802073	+	0.915573i
$208$	5.17022	−	2.98503i	0.358490	−	0.206975i
$209$	8.03665	−	15.5974i	0.555906	−	1.07889i
$210$	1.65339	−	9.59720i	0.114095	−	0.662270i
$211$	14.2096	+	16.9344i	0.978233	+	1.16581i	0.986152	+	0.165844i	$0.0530347\pi$
$211$	14.2096	+	16.9344i	0.978233	+	1.16581i	−0.00791948	+	0.999969i	$0.502521\pi$
$212$	−0.0322887	−	0.183118i	−0.00221760	−	0.0125766i
$213$	5.97157	+	2.24572i	0.409165	+	0.153874i
$214$	−2.73822	−	0.996630i	−0.187181	−	0.0681283i
$215$	16.7133	−	19.9182i	1.13984	−	1.35841i
$216$	2.45311	+	4.58064i	0.166913	+	0.311673i
$217$	−3.51128	−	5.88208i	−0.238361	−	0.399302i
$218$	−4.36851	+	5.20619i	−0.295873	+	0.352608i
$219$	3.86411	+	23.3658i	0.261112	+	1.57891i
$220$	8.55441			0.576738
$221$	−20.2252	−	35.0311i	−1.36050	−	2.35645i
$222$	−5.68355	+	15.1130i	−0.381455	+	1.01432i
$223$	9.56900	−	1.68727i	0.640787	−	0.112988i	0.156192	−	0.987727i	$-0.450078\pi$
$223$	9.56900	−	1.68727i	0.640787	−	0.112988i	0.484595	+	0.874739i	$0.338967\pi$
$224$	2.61197	+	0.421416i	0.174520	+	0.0281571i
$225$	−1.37415	+	0.467278i	−0.0916100	+	0.0311519i
$226$	−14.9383	−	5.43711i	−0.993683	−	0.361671i
$227$	−6.90589	+	11.9613i	−0.458360	+	0.793902i	−0.998874	−	0.0474323i	$-0.984896\pi$
$227$	−6.90589	+	11.9613i	−0.458360	+	0.793902i	0.540515	+	0.841335i	$0.318230\pi$
$228$	7.47873	+	1.03374i	0.495291	+	0.0684614i
$229$	3.25244	+	5.63339i	0.214927	+	0.372265i	0.953250	−	0.302183i	$-0.0977153\pi$
$229$	3.25244	+	5.63339i	0.214927	+	0.372265i	−0.738323	+	0.674447i	$0.764382\pi$
$230$	−9.50317	+	7.97411i	−0.626621	+	0.525797i
$231$	−9.16039	+	16.0112i	−0.602709	+	1.05346i
$232$	0.551587	−	3.12821i	0.0362135	−	0.205377i
$233$	14.5017	+	17.2825i	0.950040	+	1.13221i	0.991108	+	0.133057i	$0.0424792\pi$
$233$	14.5017	+	17.2825i	0.950040	+	1.13221i	−0.0410689	+	0.999156i	$0.513076\pi$
$234$	−15.6977	+	8.62297i	−1.02619	+	0.563701i
$235$	2.87113	+	4.97293i	0.187292	+	0.324398i
$236$	3.31436	−	5.74063i	0.215746	−	0.373683i
$237$	5.67415	−	15.0881i	0.368576	−	0.980075i
$238$	2.85533	−	17.6976i	0.185083	−	1.14716i
$239$	21.2196	−	12.2511i	1.37258	−	0.792459i	0.381327	−	0.924440i	$-0.375467\pi$
$239$	21.2196	−	12.2511i	1.37258	−	0.792459i	0.991252	+	0.131981i	$0.0421339\pi$
$240$	1.22204	+	3.47206i	0.0788825	+	0.224120i
$241$	1.01107	+	0.178279i	0.0651289	+	0.0114840i	0.206118	−	0.978527i	$-0.433917\pi$
$241$	1.01107	+	0.178279i	0.0651289	+	0.0114840i	−0.140989	+	0.990011i	$0.545028\pi$
$242$	−4.88964	−	1.77968i	−0.314318	−	0.114402i
$243$	−7.06522	−	13.8954i	−0.453234	−	0.891391i
$244$	−1.22738	−	0.446730i	−0.0785749	−	0.0285989i
$245$	9.89005	+	11.1122i	0.631852	+	0.709930i
$246$	3.70835	−	1.30521i	0.236436	−	0.0832172i
$247$	−3.28861	+	25.8143i	−0.209249	+	1.64252i
$248$	2.24232	+	1.29460i	0.142387	+	0.0822074i
$249$	9.27283	−	5.22290i	0.587642	−	0.330988i
$250$	−11.4768	+	2.02367i	−0.725855	+	0.127988i
$251$	28.5760	+	5.03872i	1.80370	+	0.318041i	0.971609	−	0.236593i	$-0.0760308\pi$
$251$	28.5760	+	5.03872i	1.80370	+	0.318041i	0.832094	+	0.554635i	$0.187142\pi$
$252$	−7.80724	−	1.43072i	−0.491810	−	0.0901272i
$253$	22.0810	−	8.03681i	1.38822	−	0.505270i
$254$		−	15.7990i		−	0.991316i
$255$	23.5251	−	8.28001i	1.47320	−	0.518514i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−1.41076	+	8.00080i	−0.0880006	+	0.499076i	0.908668	+	0.417519i	$0.137100\pi$
$257$	−1.41076	+	8.00080i	−0.0880006	+	0.499076i	−0.996669	+	0.0815570i	$0.974011\pi$
$258$	−16.0881	−	13.7939i	−1.00160	−	0.858770i
$259$	−12.6419	−	21.1778i	−0.785533	−	1.31592i
$260$	−11.9220	+	4.33927i	−0.739374	+	0.269110i
$261$	−1.85411	+	9.34728i	−0.114766	+	0.578582i
$262$	1.35768	−	1.61801i	0.0838775	−	0.0999613i
$263$	1.07012	+	1.27532i	0.0659863	+	0.0786394i	0.798028	−	0.602621i	$-0.205877\pi$
$263$	1.07012	+	1.27532i	0.0659863	+	0.0786394i	−0.732042	+	0.681260i	$0.761432\pi$
$264$	0.0741935	−	6.97172i	0.00456629	−	0.429079i
$265$			0.395154i			0.0242741i
$266$	−8.35506	+	7.94940i	−0.512281	+	0.487409i
$267$	2.22491	−	0.783091i	0.136162	−	0.0479244i
$268$	−4.04730	+	11.1199i	−0.247228	+	0.679254i
$269$	−11.5353	+	9.67925i	−0.703318	+	0.590154i	−0.922716	−	0.385482i	$-0.874035\pi$
$269$	−11.5353	+	9.67925i	−0.703318	+	0.590154i	0.219397	+	0.975636i	$0.429591\pi$
$270$	−3.44362	−	10.4918i	−0.209572	−	0.638513i
$271$	2.55521	−	2.14408i	0.155218	−	0.130244i	−0.561871	−	0.827225i	$-0.689918\pi$
$271$	2.55521	−	2.14408i	0.155218	−	0.130244i	0.717089	+	0.696981i	$0.245474\pi$
$272$	2.31737	+	6.36693i	0.140511	+	0.386052i
$273$	4.64480	−	26.9611i	0.281116	−	1.63176i
$274$	−0.192722	+	0.111268i	−0.0116427	+	0.00672194i
$275$	1.91791	+	0.338180i	0.115654	+	0.0203930i
$276$	6.41636	+	7.81411i	0.386220	+	0.470354i
$277$	−9.44946			−0.567763			−0.283881	−	0.958859i	$-0.591622\pi$
$277$	−9.44946			−0.567763			−0.283881	+	0.958859i	$0.591622\pi$
$278$	12.1506			0.728747
$279$	−6.64278	−	4.02609i	−0.397693	−	0.241036i
$280$	−5.31095	−	1.84585i	−0.317390	−	0.110310i
$281$	4.18902	−	23.7571i	0.249896	−	1.41723i	−0.558946	−	0.829204i	$-0.688794\pi$
$281$	4.18902	−	23.7571i	0.249896	−	1.41723i	0.808842	−	0.588027i	$-0.200095\pi$
$282$	4.07777	−	2.29679i	0.242828	−	0.136772i
$283$	5.30044	+	30.0603i	0.315078	+	1.78690i	0.571779	+	0.820407i	$0.306253\pi$
$283$	5.30044	+	30.0603i	0.315078	+	1.78690i	−0.256701	+	0.966491i	$0.582636\pi$
$284$	1.84171	−	3.18994i	0.109286	−	0.189288i
$285$	−15.2704	−	4.92331i	−0.904538	−	0.291632i
$286$	24.0316			1.42102
$287$	−1.97147	+	5.67239i	−0.116372	+	0.334831i
$288$	2.84028	−	0.965833i	0.167365	−	0.0569123i
$289$	27.1647	−	9.88714i	1.59792	−	0.581597i
$290$	−2.30878	+	6.34331i	−0.135576	+	0.372492i
$291$	8.43656	−	1.39519i	0.494560	−	0.0817877i
$292$	13.6735			0.800179
$293$	1.11981	+	1.93957i	0.0654199	+	0.113311i	0.896880	−	0.442274i	$-0.145828\pi$
$293$	1.11981	+	1.93957i	0.0654199	+	0.113311i	−0.831460	+	0.555584i	$0.812495\pi$
$294$	9.14203	−	7.96387i	0.533174	−	0.464462i
$295$	−9.05488	+	10.7912i	−0.527196	+	0.628287i
$296$	8.07321	+	4.66107i	0.469246	+	0.270919i
$297$	−0.667640	+	20.9057i	−0.0387404	+	1.21307i
$298$	13.7531	+	2.42505i	0.796697	+	0.140479i
$299$	−26.6969	+	22.4014i	−1.54392	+	1.29550i
$300$	0.136724	+	0.826752i	0.00789375	+	0.0477326i
$301$	31.7941	−	6.08511i	1.83258	−	0.350740i
$302$	9.53638	+	11.3650i	0.548757	+	0.653983i
$303$	1.54830	−	1.80581i	0.0889476	−	0.103741i
$304$	1.29333	−	4.16261i	0.0741775	−	0.238742i
$305$	2.40386	+	1.38787i	0.137645	+	0.0794693i
$306$	−6.54405	−	19.2444i	−0.374098	−	1.10013i
$307$	−4.24523	+	11.6637i	−0.242288	+	0.665681i	0.757627	+	0.652687i	$0.226358\pi$
$307$	−4.24523	+	11.6637i	−0.242288	+	0.665681i	−0.999916	+	0.0129941i	$0.995864\pi$
$308$	8.25731	+	6.72614i	0.470504	+	0.383257i
$309$	−2.98389	+	1.68067i	−0.169748	+	0.0956100i
$310$	−4.21509	−	3.53688i	−0.239401	−	0.200881i
$311$	5.82371	−	3.36232i	0.330232	−	0.190660i	−0.325712	−	0.945469i	$-0.605604\pi$
$311$	5.82371	−	3.36232i	0.330232	−	0.190660i	0.655944	+	0.754809i	$0.272271\pi$
$312$	3.43304	+	9.75393i	0.194358	+	0.552207i
$313$	1.65447	−	9.38295i	0.0935160	−	0.530355i	−0.901676	−	0.432412i	$-0.857663\pi$
$313$	1.65447	−	9.38295i	0.0935160	−	0.530355i	0.995192	−	0.0979432i	$-0.0312264\pi$
$314$	−6.05410	−	5.08000i	−0.341653	−	0.286681i
$315$	15.8114	+	5.87536i	0.890871	+	0.331039i
$316$	−8.05986	−	4.65336i	−0.453403	−	0.261772i
$317$	6.64229	+	5.57354i	0.373068	+	0.313041i	0.809974	−	0.586466i	$-0.199481\pi$
$317$	6.64229	+	5.57354i	0.373068	+	0.313041i	−0.436906	+	0.899507i	$0.643926\pi$
$318$	0.322045	+	0.00342722i	0.0180594	+	0.000192189i
$319$	8.21893	−	9.79494i	0.460172	−	0.548411i
$320$	2.09285	−	0.369026i	0.116994	−	0.0206292i
$321$	2.56993	−	4.34383i	0.143439	−	0.242449i
$322$	−15.4430	+	0.225039i	−0.860604	+	0.0125409i
$323$	−28.2040	−	8.76301i	−1.56931	−	0.487587i
$324$	−8.58056	+	2.71551i	−0.476698	+	0.150861i
$325$	−2.84449	+	0.501560i	−0.157784	+	0.0278215i
$326$	12.2454	−	10.2751i	0.678209	−	0.569085i
$327$	−7.47010	−	9.09739i	−0.413097	−	0.503087i
$328$	−0.394140	−	2.23528i	−0.0217627	−	0.123423i
$329$	−1.13870	+	7.05773i	−0.0627783	+	0.389105i
$330$	−2.72802	+	14.5634i	−0.150172	+	0.801687i
$331$	−20.1545	−	11.6362i	−1.10779	−	0.639582i	−0.169533	−	0.985524i	$-0.554226\pi$
$331$	−20.1545	−	11.6362i	−1.10779	−	0.639582i	−0.938256	+	0.345942i	$0.887559\pi$
$332$	−2.10154	−	5.77393i	−0.115337	−	0.316886i
$333$	−23.9166	−	14.4955i	−1.31062	−	0.794347i
$334$	−9.07136	+	15.7121i	−0.496363	+	0.859725i
$335$	12.5739	−	21.7786i	0.686985	−	1.18989i
$336$	−1.55040	+	4.31234i	−0.0845812	+	0.235257i
$337$	7.55254	−	1.33172i	0.411413	−	0.0725432i	0.0358888	−	0.999356i	$-0.488574\pi$
$337$	7.55254	−	1.33172i	0.411413	−	0.0725432i	0.375524	+	0.926813i	$0.377463\pi$
$338$	−21.2762	+	7.74389i	−1.15727	+	0.421212i
$339$	14.0202	−	23.6977i	0.761474	−	1.28708i
$340$	−2.50035	−	14.1802i	−0.135601	−	0.769029i
$341$	5.21123	+	9.02612i	0.282204	+	0.488792i
$342$	−4.14487	+	12.4024i	−0.224129	+	0.670646i
$343$	0.809329	+	18.5026i	0.0436996	+	0.999045i
$344$	−9.37268	+	7.86461i	−0.505341	+	0.424031i
$345$	−10.5449	−	18.7215i	−0.567716	−	1.00793i
$346$	−2.78527	−	2.33712i	−0.149737	−	0.125644i
$347$	4.45095	−	12.2289i	0.238939	−	0.656480i	−0.761031	−	0.648716i	$-0.775306\pi$
$347$	4.45095	−	12.2289i	0.238939	−	0.656480i	0.999970	−	0.00776437i	$-0.00247150\pi$
$348$	5.14968	+	1.93664i	0.276052	+	0.103815i
$349$	0.251987	−	0.436453i	0.0134885	−	0.0233628i	−0.859202	−	0.511636i	$-0.829040\pi$
$349$	0.251987	−	0.436453i	0.0134885	−	0.0233628i	0.872691	+	0.488273i	$0.162373\pi$
$350$	−1.11775	−	0.623799i	−0.0597464	−	0.0333434i
$351$	−9.67404	−	29.4743i	−0.516362	−	1.57322i
$352$	−3.96420	−	0.698995i	−0.211292	−	0.0372565i
$353$		−	0.969519i		−	0.0516023i	−0.999667	−	0.0258012i	$-0.991786\pi$
$353$		−	0.969519i		−	0.0516023i	0.999667	−	0.0258012i	$-0.00821367\pi$
$354$	8.71613	+	7.47319i	0.463257	+	0.397196i
$355$	−5.03160	+	5.99643i	−0.267049	+	0.318257i
$356$	−0.236473	−	1.34111i	−0.0125331	−	0.0710786i
$357$	29.2185	+	10.5048i	1.54640	+	0.555974i
$358$	−6.93931	−	2.52570i	−0.366754	−	0.133487i
$359$	3.80720	−	10.4602i	0.200936	−	0.552068i	−0.797767	−	0.602965i	$-0.793986\pi$
$359$	3.80720	−	10.4602i	0.200936	−	0.552068i	0.998704	+	0.0508969i	$0.0162080\pi$
$360$	−6.30068	+	0.973208i	−0.332075	+	0.0512925i
$361$	11.0279	+	15.4721i	0.580416	+	0.814320i
$362$	−0.611287	+	0.352927i	−0.0321285	+	0.0185494i
$363$	4.58912	−	7.75677i	0.240866	−	0.407125i
$364$	−14.9199	−	5.18547i	−0.782013	−	0.271792i
$365$	−28.6165	−	5.04586i	−1.49785	−	0.264112i
$366$	1.15194	−	1.94708i	0.0602131	−	0.101775i
$367$	3.22904	−	18.3128i	0.168555	−	0.955921i	−0.776769	−	0.629786i	$-0.783143\pi$
$367$	3.22904	−	18.3128i	0.168555	−	0.955921i	0.945323	−	0.326135i	$-0.105746\pi$
$368$	5.05544	−	2.91876i	0.263533	−	0.152151i
$369$	1.03944	+	6.72948i	0.0541111	+	0.350323i
$370$	−15.1759	−	12.7341i	−0.788960	−	0.662016i
$371$	−0.310701	+	0.381430i	−0.0161308	+	0.0198029i
$372$	−2.91907	+	3.40456i	−0.151346	+	0.176518i
$373$		−	17.9729i		−	0.930602i	−0.885152	−	0.465301i	$-0.845946\pi$
$373$		−	17.9729i		−	0.930602i	0.885152	−	0.465301i	$-0.154054\pi$
$374$	−4.73607	+	26.8596i	−0.244897	+	1.38888i
$375$	0.214798	−	20.1839i	0.0110921	−	1.04229i
$376$	−0.924161	−	2.53911i	−0.0476600	−	0.130945i
$377$	−6.48596	+	17.8200i	−0.334044	+	0.917778i
$378$	4.92547	−	12.8351i	0.253339	−	0.660166i
$379$			10.5738i			0.543138i	0.962419	+	0.271569i	$0.0875426\pi$
$379$			10.5738i			0.543138i	−0.962419	+	0.271569i	$0.912457\pi$
$380$	−4.24285	+	8.23443i	−0.217653	+	0.422417i
$381$	26.8968	+	5.03833i	1.37797	+	0.258121i
$382$	24.0197	−	4.23532i	1.22895	−	0.216698i
$383$	2.89897	+	16.4409i	0.148130	+	0.840089i	0.964800	+	0.262984i	$0.0847066\pi$
$383$	2.89897	+	16.4409i	0.148130	+	0.840089i	−0.816670	+	0.577105i	$0.804182\pi$
$384$	−0.282599	−	1.70884i	−0.0144213	−	0.0872039i
$385$	−14.7992	−	17.1239i	−0.754236	−	0.872717i
$386$	6.07692	+	16.6962i	0.309307	+	0.849815i
$387$	28.6138	−	22.9901i	1.45452	−	1.16865i
$388$		−	4.93701i		−	0.250639i
$389$	1.11745	+	3.07017i	0.0566570	+	0.155664i	0.964792	−	0.263013i	$-0.0847162\pi$
$389$	1.11745	+	3.07017i	0.0566570	+	0.155664i	−0.908135	+	0.418677i	$0.862494\pi$
$390$	−3.58538	−	21.6804i	−0.181553	−	1.09783i
$391$	−19.7762	−	34.2534i	−1.00013	−	1.73227i
$392$	−3.67516	−	5.95762i	−0.185623	−	0.300905i
$393$	2.32161	+	2.82735i	0.117110	+	0.142621i
$394$	6.71123	+	7.99813i	0.338107	+	0.402940i
$395$	15.1509	+	12.7131i	0.762322	+	0.639664i
$396$	11.8453	+	2.34960i	0.595247	+	0.118072i
$397$	−30.6003	−	11.1376i	−1.53579	−	0.558981i	−0.570757	−	0.821119i	$-0.693350\pi$
$397$	−30.6003	−	11.1376i	−1.53579	−	0.558981i	−0.965030	+	0.262138i	$0.915572\pi$
$398$	−3.36102			−0.168473
$399$	−10.8689	−	16.7591i	−0.544127	−	0.839003i
$400$	0.483809			0.0241904
$401$	−21.7640	−	7.92146i	−1.08684	−	0.395579i	−0.264393	−	0.964415i	$-0.585171\pi$
$401$	−21.7640	−	7.92146i	−1.08684	−	0.395579i	−0.822451	+	0.568836i	$0.807394\pi$
$402$	−17.6402	−	10.4364i	−0.879813	−	0.520522i
$403$	−11.8413	−	9.93603i	−0.589857	−	0.494949i
$404$	−0.882767	−	1.05204i	−0.0439193	−	0.0523410i
$405$	18.9599	−	2.51669i	0.942125	−	0.125056i
$406$	−7.21619	+	4.30767i	−0.358134	+	0.213786i
$407$	18.7624	+	32.4975i	0.930020	+	1.61084i
$408$	−11.5783	+	1.91476i	−0.573213	+	0.0947949i
$409$	−1.24765	−	3.42790i	−0.0616925	−	0.169499i	0.905017	−	0.425376i	$-0.139858\pi$
$409$	−1.24765	−	3.42790i	−0.0616925	−	0.169499i	−0.966709	+	0.255877i	$0.917636\pi$
$410$			4.82355i			0.238218i
$411$	−0.127968	−	0.363580i	−0.00631217	−	0.0179341i
$412$	0.676251	+	1.85799i	0.0333165	+	0.0915364i
$413$	−17.2253	+	3.29676i	−0.847601	+	0.162223i
$414$	−15.3492	+	8.43153i	−0.754374	+	0.414387i
$415$	2.26747	+	12.8595i	0.111306	+	0.631247i
$416$	5.87936	−	1.03669i	0.288259	−	0.0508279i
$417$	−3.87486	+	20.6857i	−0.189753	+	1.01298i
$418$	12.8866	−	11.9080i	0.630304	−	0.582441i
$419$			7.90283i			0.386078i	0.981191	+	0.193039i	$0.0618344\pi$
$419$			7.90283i			0.386078i	−0.981191	+	0.193039i	$0.938166\pi$
$420$	4.83611	−	8.45293i	0.235978	−	0.412461i
$421$	−0.813545	+	2.23520i	−0.0396498	+	0.108937i	−0.957938	−	0.286977i	$-0.907350\pi$
$421$	−0.813545	+	2.23520i	−0.0396498	+	0.108937i	0.918288	+	0.395914i	$0.129572\pi$
$422$	7.56080	+	20.7731i	0.368054	+	1.01122i
$423$	2.60975	+	7.67461i	0.126890	+	0.373152i
$424$	0.0322887	−	0.183118i	0.00156808	−	0.00889301i
$425$		−	3.27807i		−	0.159010i
$426$	4.84336	+	4.15269i	0.234662	+	0.201198i
$427$	1.22913	+	3.22978i	0.0594816	+	0.156300i
$428$	−2.23222	−	1.87305i	−0.107898	−	0.0905374i
$429$	−7.66372	+	40.9123i	−0.370008	+	1.97527i
$430$	22.5178	−	13.0007i	1.08591	−	0.626948i
$431$	3.34421	−	18.9660i	0.161085	−	0.913558i	−0.791925	−	0.610619i	$-0.790921\pi$
$431$	3.34421	−	18.9660i	0.161085	−	0.913558i	0.953010	−	0.302940i	$-0.0979681\pi$
$432$	0.738503	+	5.14340i	0.0355313	+	0.247462i
$433$	27.6771	+	4.88022i	1.33008	+	0.234528i	0.793111	−	0.609077i	$-0.208460\pi$
$433$	27.6771	+	4.88022i	1.33008	+	0.234528i	0.536964	+	0.843605i	$0.319571\pi$
$434$	−1.28773	−	6.72828i	−0.0618131	−	0.322968i
$435$	−10.0628	−	5.95345i	−0.482476	−	0.285446i
$436$	−5.88568	+	3.39810i	−0.281873	+	0.162739i
$437$	−3.21560	+	25.2412i	−0.153823	+	1.20745i
$438$	−4.36049	+	23.2783i	−0.208352	+	1.11228i
$439$	−4.20632	+	11.5568i	−0.200757	+	0.551575i	−0.998690	−	0.0511712i	$-0.983705\pi$
$439$	−4.20632	+	11.5568i	−0.200757	+	0.551575i	0.797933	+	0.602746i	$0.205927\pi$
$440$	8.03851	+	2.92578i	0.383221	+	0.139481i
$441$	10.6426	+	18.1035i	0.506791	+	0.862069i
$442$	−7.02414	−	39.8359i	−0.334104	−	1.89480i
$443$	14.7626	−	17.5934i	0.701394	−	0.835889i	−0.291289	−	0.956635i	$-0.594084\pi$
$443$	14.7626	−	17.5934i	0.701394	−	0.835889i	0.992683	+	0.120746i	$0.0385286\pi$
$444$	−10.5098	+	12.2577i	−0.498771	+	0.581726i
$445$			2.89400i			0.137189i
$446$	9.56900	+	1.68727i	0.453105	+	0.0798947i
$447$	−8.51439	+	22.6405i	−0.402717	+	1.07086i
$448$	2.31032	+	1.28935i	0.109152	+	0.0609160i
$449$	−6.95776	+	12.0512i	−0.328357	+	0.568731i	−0.982186	−	0.187911i	$-0.939828\pi$
$449$	−6.95776	+	12.0512i	−0.328357	+	0.568731i	0.653829	+	0.756642i	$0.273162\pi$
$450$	−1.45110	−	0.0308888i	−0.0684054	−	0.00145611i
$451$	3.12490	−	8.58558i	0.147146	−	0.404279i
$452$	−12.1778	−	10.2184i	−0.572798	−	0.480634i
$453$	−22.3894	+	12.6108i	−1.05195	+	0.592507i
$454$	−10.5804	+	8.87803i	−0.496564	+	0.416667i
$455$	29.3114	+	16.3582i	1.37414	+	0.766884i
$456$	6.67414	+	3.52928i	0.312545	+	0.165274i
$457$	3.75219	+	6.49899i	0.175520	+	0.304010i	0.940341	−	0.340233i	$-0.110506\pi$
$457$	3.75219	+	6.49899i	0.175520	+	0.304010i	−0.764821	+	0.644243i	$0.777173\pi$
$458$	1.12956	+	6.40605i	0.0527808	+	0.299335i
$459$	34.8494	−	5.00377i	1.62663	−	0.233556i
$460$	−11.6574	+	4.24294i	−0.543528	+	0.197828i
$461$	19.5269	−	3.44312i	0.909460	−	0.160362i	0.300702	−	0.953718i	$-0.402779\pi$
$461$	19.5269	−	3.44312i	0.909460	−	0.160362i	0.608758	+	0.793356i	$0.291668\pi$
$462$	−14.0841	+	11.9126i	−0.655252	+	0.554224i
$463$	−6.24074	+	10.8093i	−0.290032	+	0.502350i	−0.973817	−	0.227334i	$-0.926999\pi$
$463$	−6.24074	+	10.8093i	−0.290032	+	0.502350i	0.683785	+	0.729683i	$0.260333\pi$
$464$	1.58823	−	2.75090i	0.0737318	−	0.127707i
$465$	7.36553	−	6.04802i	0.341568	−	0.280470i
$466$	7.71621	+	21.2001i	0.357446	+	0.982076i
$467$	36.2451	+	20.9261i	1.67723	+	0.968346i	0.963418	+	0.268004i	$0.0863641\pi$
$467$	36.2451	+	20.9261i	1.67723	+	0.968346i	0.713807	+	0.700342i	$0.246969\pi$
$468$	−17.7003	+	2.73400i	−0.818195	+	0.126379i
$469$	29.2612	−	11.1357i	1.35116	−	0.514198i
$470$	0.997131	+	5.65501i	0.0459942	+	0.260846i
$471$	10.5791	−	8.68673i	0.487457	−	0.400263i
$472$	5.07789	−	4.26085i	0.233729	−	0.196122i
$473$	−48.5026	+	8.55232i	−2.23015	+	0.393236i
$474$	10.4924	−	12.2375i	0.481931	−	0.562085i
$475$	−1.27678	+	1.67844i	−0.0585829	+	0.0770122i
$476$	8.73605	−	15.6537i	0.400416	−	0.717486i
$477$	−0.108535	+	0.547169i	−0.00496949	+	0.0250532i
$478$	24.1300	−	4.25477i	1.10368	−	0.194609i
$479$	15.1360	−	18.0384i	0.691583	−	0.824197i	−0.299963	−	0.953951i	$-0.596974\pi$
$479$	15.1360	−	18.0384i	0.691583	−	0.824197i	0.991546	+	0.129754i	$0.0414188\pi$
$480$	−0.0391695	+	3.68063i	−0.00178784	+	0.167997i
$481$	−42.6332	−	35.7735i	−1.94391	−	1.63113i
$482$	0.889122	+	0.513335i	0.0404984	+	0.0233818i
$483$	4.54169	−	26.3625i	0.206654	−	1.19954i
$484$	−3.98607	−	3.34471i	−0.181185	−	0.152032i
$485$	−1.82188	+	10.3324i	−0.0827274	+	0.469170i
$486$	−1.88663	−	15.4739i	−0.0855791	−	0.701909i
$487$	−0.0106207	+	0.00613184i	−0.000481268	+	0.000277860i	−0.500241	−	0.865886i	$-0.666755\pi$
$487$	−0.0106207	+	0.00613184i	−0.000481268	+	0.000277860i	0.499759	+	0.866164i	$0.333422\pi$
$488$	−1.00057	−	0.839577i	−0.0452936	−	0.0380059i
$489$	13.5877	+	24.1238i	0.614455	+	1.09091i
$490$	5.49303	+	13.8246i	0.248150	+	0.624533i
$491$	7.23268	−	19.8716i	0.326406	−	0.896793i	−0.662607	−	0.748967i	$-0.730550\pi$
$491$	7.23268	−	19.8716i	0.326406	−	0.896793i	0.989013	−	0.147826i	$-0.0472277\pi$
$492$	3.93112	+	0.0418352i	0.177229	+	0.00188608i
$493$	−18.6389	−	10.7611i	−0.839452	−	0.484658i
$494$	−11.9193	+	23.1327i	−0.536274	+	1.04079i
$495$	−23.9233	−	9.28857i	−1.07527	−	0.417490i
$496$	1.66431	+	1.98345i	0.0747297	+	0.0890594i
$497$	−9.57170	+	1.83194i	−0.429350	+	0.0821736i
$498$	10.5000	−	1.73643i	0.470514	−	0.0778111i
$499$	13.2651	−	11.1307i	0.593827	−	0.498280i	−0.295628	−	0.955303i	$-0.595529\pi$
$499$	13.2651	−	11.1307i	0.593827	−	0.498280i	0.889455	+	0.457023i	$0.151084\pi$
$500$	−11.4768	−	2.02367i	−0.513257	−	0.0905011i
$501$	−23.8560	−	20.4541i	−1.06581	−	0.913820i
$502$	25.1293	+	14.5084i	1.12158	+	0.647543i
$503$	−15.2396	+	18.1618i	−0.679500	+	0.809796i	−0.990043	−	0.140763i	$-0.955045\pi$
$503$	−15.2396	+	18.1618i	−0.679500	+	0.809796i	0.310543	+	0.950559i	$0.399489\pi$
$504$	−6.84707	−	4.01468i	−0.304993	−	0.178828i
$505$	1.45927	+	2.52752i	0.0649365	+	0.112473i
$506$	23.4981			1.04462
$507$	−6.39849	−	38.6909i	−0.284167	−	1.71832i
$508$	5.40357	−	14.8462i	0.239745	−	0.658693i
$509$	23.9936	−	8.73294i	1.06350	−	0.387081i	0.249755	−	0.968309i	$-0.419650\pi$
$509$	23.9936	−	8.73294i	1.06350	−	0.387081i	0.813741	+	0.581228i	$0.197428\pi$
$510$	24.9383	+	0.265395i	1.10429	+	0.0117519i
$511$	−23.6552	−	27.3711i	−1.04644	−	1.21083i
$512$	−1.00000			−0.0441942
$513$	−19.7926	−	11.0115i	−0.873863	−	0.486172i
$514$	−4.06211	+	7.03579i	−0.179172	+	0.310335i
$515$	−0.729647	−	4.13804i	−0.0321521	−	0.182344i
$516$	−10.4001	−	18.4645i	−0.457837	−	0.812853i
$517$	1.88873	−	10.7115i	0.0830662	−	0.471092i
$518$	−4.63633	−	24.2244i	−0.203709	−	1.06436i
$519$	4.86703	−	3.99644i	0.213639	−	0.175424i
$520$	−12.6872			−0.556369
$521$	30.6383			1.34229			0.671145	−	0.741326i	$-0.265803\pi$
$521$	30.6383			1.34229			0.671145	+	0.741326i	$0.265803\pi$
$522$	−4.93925	+	8.14943i	−0.216185	+	0.356691i
$523$	−33.4042	−	5.89006i	−1.46066	−	0.257554i	−0.613840	−	0.789430i	$-0.710376\pi$
$523$	−33.4042	−	5.89006i	−1.46066	−	0.257554i	−0.846822	+	0.531876i	$0.821487\pi$
$524$	1.82919	−	1.05608i	0.0799086	−	0.0461353i
$525$	1.41843	−	1.70398i	0.0619055	−	0.0743676i
$526$	0.569398	+	1.56441i	0.0248269	+	0.0682114i
$527$	13.4390	−	11.2766i	0.585410	−	0.491217i
$528$	2.45419	−	6.52589i	0.106805	−	0.284003i
$529$	−8.48522	+	7.11994i	−0.368923	+	0.309563i
$530$	−0.135151	+	0.371323i	−0.00587057	+	0.0161293i
$531$	−15.5023	+	12.4555i	−0.672740	+	0.540521i
$532$	−10.5700	+	4.61240i	−0.458269	+	0.199973i
$533$			13.5506i			0.586942i
$534$	2.35857	+	0.0251000i	0.102065	+	0.00108618i
$535$	3.98049	+	4.74376i	0.172091	+	0.205091i
$536$	−7.60643	+	9.06499i	−0.328548	+	0.391548i
$537$	6.51281	−	11.0083i	0.281049	−	0.475043i
$538$	−14.1501	+	5.15022i	−0.610055	+	0.222042i
$539$	−0.821041	−	28.1655i	−0.0353648	−	1.21317i
$540$	0.352472	−	11.0369i	0.0151680	−	0.474952i
$541$	6.22347	−	35.2950i	0.267568	−	1.51745i	−0.494055	−	0.869431i	$-0.664486\pi$
$541$	6.22347	−	35.2950i	0.267568	−	1.51745i	0.761622	−	0.648021i	$-0.224403\pi$
$542$	3.13443	−	1.14084i	0.134635	−	0.0490033i
$543$	−0.405896	−	1.15323i	−0.0174187	−	0.0494898i
$544$			6.77555i			0.290499i
$545$	13.5718	−	4.93974i	0.581353	−	0.211595i
$546$	13.5859	−	23.7465i	0.581424	−	1.01626i
$547$	19.2012	+	3.38568i	0.820982	+	0.144761i	0.568335	−	0.822797i	$-0.307588\pi$
$547$	19.2012	+	3.38568i	0.820982	+	0.144761i	0.252647	+	0.967558i	$0.418699\pi$
$548$	−0.219155	+	0.0386429i	−0.00936183	+	0.00165074i
$549$	2.94742	+	2.58204i	0.125793	+	0.110199i
$550$	1.68658	+	0.973750i	0.0719162	+	0.0415208i
$551$	5.35211	+	12.7696i	0.228007	+	0.544005i
$552$	3.35682	+	9.53739i	0.142876	+	0.405938i
$553$	4.62866	+	24.1843i	0.196831	+	1.02842i
$554$	−8.87958	−	3.23190i	−0.377257	−	0.137310i
$555$	26.5187	−	21.7752i	1.12566	−	0.924306i
$556$	11.4179	+	4.15576i	0.484225	+	0.176244i
$557$	7.50752	+	1.32378i	0.318104	+	0.0560903i	0.330420	−	0.943834i	$-0.392809\pi$
$557$	7.50752	+	1.32378i	0.318104	+	0.0560903i	−0.0123166	+	0.999924i	$0.503921\pi$
$558$	−4.86517	−	6.05525i	−0.205959	−	0.256339i
$559$	63.2585	−	36.5223i	2.67555	−	1.54473i
$560$	−4.35934	−	3.55098i	−0.184216	−	0.150056i
$561$	−44.2165	−	16.6285i	−1.86682	−	0.702054i
$562$	12.0618	−	20.8917i	0.508797	−	0.881262i
$563$	−4.70699	−	8.15274i	−0.198376	−	0.343597i	0.749626	−	0.661862i	$-0.230233\pi$
$563$	−4.70699	−	8.15274i	−0.198376	−	0.343597i	−0.948002	+	0.318264i	$0.896900\pi$
$564$	4.61740	−	0.763601i	0.194428	−	0.0321534i
$565$	21.7155	+	25.8795i	0.913579	+	1.08876i
$566$	−5.30044	+	30.0603i	−0.222794	+	1.26353i
$567$	20.2802	+	12.4785i	0.851690	+	0.524046i
$568$	2.82167	−	2.36766i	0.118395	−	0.0993449i
$569$	−9.09323	−	15.7499i	−0.381208	−	0.660272i	0.610027	−	0.792381i	$-0.291159\pi$
$569$	−9.09323	−	15.7499i	−0.381208	−	0.660272i	−0.991235	+	0.132109i	$0.957825\pi$
$570$	−12.6656	−	9.84917i	−0.530503	−	0.412536i
$571$	−1.94938	+	3.37643i	−0.0815791	+	0.141299i	−0.903928	−	0.427684i	$-0.859330\pi$
$571$	−1.94938	+	3.37643i	−0.0815791	+	0.141299i	0.822349	+	0.568983i	$0.192663\pi$
$572$	22.5823	+	8.21928i	0.944213	+	0.343666i
$573$	−0.449550	+	42.2428i	−0.0187802	+	1.76472i
$574$	−3.79265	+	4.65603i	−0.158302	+	0.194339i
$575$	−2.78134	+	0.490425i	−0.115990	+	0.0204521i
$576$	2.99932	+	0.0638452i	0.124972	+	0.00266022i
$577$	13.4734	+	23.3366i	0.560905	+	0.971516i	0.997418	+	0.0718176i	$0.0228800\pi$
$577$	13.4734	+	23.3366i	0.560905	+	0.971516i	−0.436513	+	0.899698i	$0.643787\pi$
$578$	28.9081			1.20242
$579$	−30.3622	+	5.02114i	−1.26181	+	0.208672i
$580$	−4.33908	+	5.17111i	−0.180170	+	0.214719i
$581$	−7.92239	+	14.1957i	−0.328676	+	0.588938i
$582$	8.40496	+	1.57442i	0.348397	+	0.0652619i
$583$	0.481118	−	0.573374i	0.0199259	−	0.0237467i
$584$	12.8489	+	4.67660i	0.531689	+	0.193519i
$585$	38.0529	+	0.810015i	1.57329	+	0.0334900i
$586$	0.388906	+	2.20559i	0.0160655	+	0.0911122i
$587$	−4.92940	−	5.87463i	−0.203458	−	0.242472i	0.654661	−	0.755923i	$-0.272811\pi$
$587$	−4.92940	−	5.87463i	−0.203458	−	0.242472i	−0.858119	+	0.513451i	$0.828367\pi$
$588$	11.3145	−	4.35683i	0.466602	−	0.179673i
$589$	−11.2732	+	0.539500i	−0.464504	+	0.0222297i
$590$	−12.1996	+	7.04345i	−0.502250	+	0.289974i
$591$	−15.7566	+	8.87484i	−0.648138	+	0.365062i
$592$	5.99216	+	7.14117i	0.246276	+	0.293500i
$593$	−15.1473	−	41.6170i	−0.622026	−	1.70900i	−0.701972	−	0.712205i	$-0.747697\pi$
$593$	−15.1473	−	41.6170i	−0.622026	−	1.70900i	0.0799455	−	0.996799i	$-0.474525\pi$
$594$	−7.77754	+	19.4166i	−0.319116	+	0.796671i
$595$	−24.0598	+	29.5370i	−0.986357	+	1.21090i
$596$	12.0943	+	6.98264i	0.495401	+	0.286020i
$597$	1.07184	−	5.72194i	0.0438673	−	0.234183i
$598$	−32.7486	+	11.9195i	−1.33919	+	0.487426i
$599$	−14.7035	+	5.35162i	−0.600767	+	0.218661i	−0.624459	−	0.781058i	$-0.714680\pi$
$599$	−14.7035	+	5.35162i	−0.600767	+	0.218661i	0.0236912	+	0.999719i	$0.492458\pi$
$600$	−0.154288	+	0.823655i	−0.00629876	+	0.0336256i
$601$	−32.0421	−	18.4995i	−1.30703	−	0.754612i	−0.325428	−	0.945567i	$-0.605508\pi$
$601$	−32.0421	−	18.4995i	−1.30703	−	0.754612i	−0.981599	+	0.190955i	$0.938842\pi$
$602$	31.9579	+	5.15610i	1.30251	+	0.210147i
$603$	23.3929	−	26.7032i	0.952632	−	1.08744i
$604$	5.07420	+	13.9413i	0.206466	+	0.567262i
$605$	7.10795	+	8.47093i	0.288979	+	0.344392i
$606$	2.07255	−	1.16736i	0.0841916	−	0.0474207i
$607$	4.85391	−	2.80241i	0.197014	−	0.113746i	−0.398248	−	0.917278i	$-0.630382\pi$
$607$	4.85391	−	2.80241i	0.197014	−	0.113746i	0.595262	+	0.803532i	$0.297048\pi$
$608$	2.63903	−	3.46923i	0.107027	−	0.140696i
$609$	−5.03229	−	13.6589i	−0.203919	−	0.553485i
$610$	1.78421	+	2.12634i	0.0722407	+	0.0860931i
$611$	2.80120	+	15.8864i	0.113325	+	0.642696i
$612$	0.432586	−	20.3220i	0.0174863	−	0.821470i
$613$	−8.46307	−	3.08031i	−0.341820	−	0.124412i	0.165405	−	0.986226i	$-0.447107\pi$
$613$	−8.46307	−	3.08031i	−0.341820	−	0.124412i	−0.507226	+	0.861813i	$0.669329\pi$
$614$	−7.97843	+	9.50832i	−0.321983	+	0.383725i
$615$	−8.21180	−	1.53824i	−0.331132	−	0.0620278i
$616$	5.45886	+	9.14467i	0.219944	+	0.368449i
$617$	15.4083	−	18.3629i	0.620317	−	0.739265i	−0.360808	−	0.932640i	$-0.617499\pi$
$617$	15.4083	−	18.3629i	0.620317	−	0.739265i	0.981125	+	0.193376i	$0.0619436\pi$
$618$	−3.37877	+	0.558762i	−0.135914	+	0.0224767i
$619$	−18.3637			−0.738099			−0.369050	−	0.929410i	$-0.620317\pi$
$619$	−18.3637			−0.738099			−0.369050	+	0.929410i	$0.620317\pi$
$620$	−2.75121	−	4.76523i	−0.110491	−	0.191376i
$621$	−9.45928	−	28.8200i	−0.379588	−	1.15651i
$622$	6.62248	−	1.16772i	0.265537	−	0.0468214i
$623$	−2.27549	+	2.79349i	−0.0911654	+	0.111919i
$624$	−0.110037	+	10.3399i	−0.00440502	+	0.413926i
$625$	20.9992	+	7.64309i	0.839968	+	0.305723i
$626$	4.76385	−	8.25122i	0.190402	−	0.329785i
$627$	16.1631	+	25.7361i	0.645494	+	1.02780i
$628$	−3.95154	−	6.84426i	−0.157683	−	0.273116i
$629$	48.3854	−	40.6002i	1.92925	−	1.61883i
$630$	12.8484	+	10.9288i	0.511891	+	0.435416i
$631$	−5.26155	+	29.8398i	−0.209459	+	1.18790i	0.680808	+	0.732462i	$0.261629\pi$
$631$	−5.26155	+	29.8398i	−0.209459	+	1.18790i	−0.890267	+	0.455440i	$0.849482\pi$
$632$	−5.98225	−	7.12937i	−0.237961	−	0.283591i
$633$	−37.7761	+	6.24721i	−1.50147	+	0.248304i
$634$	4.33544	+	7.50921i	0.172182	+	0.298229i
$635$	−16.7875	+	29.0767i	−0.666190	+	1.15388i
$636$	0.301451	+	0.113366i	0.0119533	+	0.00449527i
$637$	15.4314	+	38.8370i	0.611413	+	1.53878i
$638$	11.0733	−	6.39319i	0.438397	−	0.253109i
$639$	−8.61426	+	6.92123i	−0.340775	+	0.273800i
$640$	2.09285	+	0.369026i	0.0827271	+	0.0145870i
$641$	23.9675	+	8.72347i	0.946660	+	0.344556i	0.768793	−	0.639498i	$-0.220858\pi$
$641$	23.9675	+	8.72347i	0.946660	+	0.344556i	0.177868	+	0.984054i	$0.443080\pi$
$642$	3.90062	−	3.20290i	0.153945	−	0.126408i
$643$	−1.00942	−	0.367400i	−0.0398077	−	0.0144888i	0.322040	−	0.946726i	$-0.395632\pi$
$643$	−1.00942	−	0.367400i	−0.0398077	−	0.0144888i	−0.361847	+	0.932237i	$0.617854\pi$
$644$	−14.5886	−	5.07035i	−0.574873	−	0.199800i
$645$	14.9519	+	42.4812i	0.588730	+	1.67270i
$646$	−23.5059	−	17.8809i	−0.924828	−	0.703513i
$647$	−37.9377	−	21.9033i	−1.49148	−	0.861108i	−0.491531	−	0.870860i	$-0.663563\pi$
$647$	−37.9377	−	21.9033i	−1.49148	−	0.861108i	−0.999952	+	0.00975161i	$0.996896\pi$
$648$	−8.99185	−	0.382984i	−0.353233	−	0.0150450i
$649$	26.2775	−	4.63344i	1.03148	−	0.181878i
$650$	−2.84449	−	0.501560i	−0.111570	−	0.0196728i
$651$	11.8651	−	0.0466246i	0.465032	−	0.00182736i
$652$	15.0212	−	5.46726i	0.588275	−	0.214115i
$653$			43.1851i			1.68997i	0.534794	+	0.844983i	$0.320389\pi$
$653$			43.1851i			1.68997i	−0.534794	+	0.844983i	$0.679611\pi$
$654$	−3.90811	−	11.1037i	−0.152819	−	0.434188i
$655$	−4.21794	+	1.53521i	−0.164809	+	0.0599854i
$656$	0.394140	−	2.23528i	0.0153886	−	0.0872730i
$657$	−38.2393	−	14.8470i	−1.49186	−	0.579235i
$658$	−3.48391	+	6.24264i	−0.135817	+	0.243363i
$659$	−35.4707	+	12.9103i	−1.38174	+	0.502913i	−0.922706	−	0.385504i	$-0.874027\pi$
$659$	−35.4707	+	12.9103i	−1.38174	+	0.502913i	−0.459036	+	0.888417i	$0.651805\pi$
$660$	−7.54446	+	12.7520i	−0.293668	+	0.496373i
$661$	−6.47649	+	7.71838i	−0.251906	+	0.300210i	−0.877147	−	0.480222i	$-0.840556\pi$
$661$	−6.47649	+	7.71838i	−0.251906	+	0.300210i	0.625241	+	0.780432i	$0.285001\pi$
$662$	−14.9592	−	17.8277i	−0.581405	−	0.692892i
$663$	70.0582	+	0.745564i	2.72084	+	0.0289553i
$664$		−	6.14449i		−	0.238452i
$665$	23.8236	−	5.75243i	0.923839	−	0.223070i
$666$	−17.5165	−	21.8012i	−0.678749	−	0.844781i
$667$	−6.34197	+	17.4244i	−0.245562	+	0.674676i
$668$	−13.8981	+	11.6619i	−0.537735	+	0.451213i
$669$	−5.92405	+	15.7526i	−0.229037	+	0.609029i
$670$	19.2643	−	16.1647i	0.744246	−	0.624496i
$671$	−1.79824	−	4.94063i	−0.0694204	−	0.190731i
$672$	−2.93181	+	3.52200i	−0.113097	+	0.135864i
$673$	33.5453	−	19.3674i	1.29308	−	0.746559i	0.313879	−	0.949463i	$-0.398371\pi$
$673$	33.5453	−	19.3674i	1.29308	−	0.746559i	0.979199	+	0.202904i	$0.0650379\pi$
$674$	7.55254	+	1.33172i	0.290913	+	0.0512958i
$675$	0.515344	−	2.46056i	0.0198356	−	0.0947068i
$676$	−22.6416			−0.870831
$677$	0.209539			0.00805324			0.00402662	−	0.999992i	$-0.498718\pi$
$677$	0.209539			0.00805324			0.00402662	+	0.999992i	$0.498718\pi$
$678$	21.2798	−	17.4734i	0.817246	−	0.671061i
$679$	−9.88275	+	8.54106i	−0.379265	+	0.327776i
$680$	2.50035	−	14.1802i	0.0958841	−	0.543786i
$681$	−11.7402	−	20.8438i	−0.449885	−	0.798735i
$682$	1.80984	+	10.2641i	0.0693024	+	0.393034i
$683$	22.7187	−	39.3499i	0.869306	−	1.50568i	0.00659954	−	0.999978i	$-0.497899\pi$
$683$	22.7187	−	39.3499i	0.869306	−	1.50568i	0.862707	−	0.505704i	$-0.168767\pi$
$684$	−8.13678	+	10.2368i	−0.311118	+	0.391415i
$685$	0.472918			0.0180693
$686$	−5.56773	+	17.6635i	−0.212577	+	0.674397i
$687$	−11.2661	−	0.119895i	−0.429830	−	0.00457428i
$688$	−11.4973	+	4.18467i	−0.438330	+	0.159539i
$689$	−0.379674	+	1.04315i	−0.0144644	+	0.0397407i
$690$	−3.50578	−	21.1990i	−0.133463	−	0.807034i
$691$	−30.2437			−1.15052			−0.575262	−	0.817969i	$-0.695100\pi$
$691$	−30.2437			−1.15052			−0.575262	+	0.817969i	$0.695100\pi$
$692$	−1.81796	−	3.14879i	−0.0691083	−	0.119699i
$693$	−15.7890	−	27.7763i	−0.599776	−	1.05513i
$694$	8.36504	−	9.96907i	0.317533	−	0.378421i
$695$	−22.3623	−	12.9109i	−0.848249	−	0.489737i
$696$	4.17675	+	3.58114i	0.158319	+	0.135743i
$697$	−15.1452	−	2.67052i	−0.573667	−	0.101153i
$698$	0.386066	−	0.323948i	0.0146128	−	0.0122616i
$699$	−38.5526	+	6.37562i	−1.45819	+	0.241148i
$700$	−0.836992	−	0.968473i	−0.0316353	−	0.0366048i
$701$	4.39883	+	5.24232i	0.166142	+	0.198000i	0.842691	−	0.538397i	$-0.180970\pi$
$701$	4.39883	+	5.24232i	0.166142	+	0.198000i	−0.676550	+	0.736397i	$0.736526\pi$
$702$	0.990188	−	31.0055i	0.0373722	−	1.17023i
$703$	−40.5878	+	1.94241i	−1.53080	+	0.0732592i
$704$	−3.48606	−	2.01268i	−0.131386	−	0.0758555i
$705$	−9.94531	−	0.105839i	−0.374562	−	0.00398611i
$706$	0.331595	−	0.911050i	0.0124797	−	0.0342878i
$707$	−0.578749	+	3.58713i	−0.0217661	+	0.134908i
$708$	5.63450	+	10.0036i	0.211757	+	0.375958i
$709$	16.6109	+	13.9382i	0.623836	+	0.523461i	0.899007	−	0.437935i	$-0.144290\pi$
$709$	16.6109	+	13.9382i	0.623836	+	0.523461i	−0.275170	+	0.961395i	$0.588734\pi$
$710$	−6.77905	+	3.91389i	−0.254413	+	0.146886i
$711$	17.4875	+	21.7652i	0.655833	+	0.816259i
$712$	0.236473	−	1.34111i	0.00886222	−	0.0502601i
$713$	−11.5784	−	9.71545i	−0.433615	−	0.363846i
$714$	23.8635	+	19.8646i	0.893070	+	0.743414i
$715$	−44.2282	−	25.5352i	−1.65404	−	0.954961i
$716$	−5.65697	−	4.74677i	−0.211411	−	0.177395i
$717$	−0.451614	+	42.4367i	−0.0168658	+	1.58483i
$718$	7.15520	−	8.52723i	0.267030	−	0.318234i
$719$	−47.5028	+	8.37602i	−1.77156	+	0.312373i	−0.961669	−	0.274213i	$-0.911583\pi$
$719$	−47.5028	+	8.37602i	−1.77156	+	0.312373i	−0.809887	+	0.586586i	$0.800471\pi$
$720$	−6.25356	−	1.24044i	−0.233056	−	0.0462286i
$721$	2.54934	−	4.56803i	0.0949423	−	0.170122i
$722$	5.07108	+	18.3108i	0.188726	+	0.681456i
$723$	−1.15746	+	1.34997i	−0.0430466	+	0.0502060i
$724$	−0.695130	+	0.122570i	−0.0258343	+	0.00455528i
$725$	−1.17726	+	0.987837i	−0.0437223	+	0.0366873i
$726$	6.96533	−	5.71941i	0.258508	−	0.212267i
$727$	−0.103017	−	0.584238i	−0.00382069	−	0.0216682i	0.982838	−	0.184472i	$-0.0590574\pi$
$727$	−0.103017	−	0.584238i	−0.00382069	−	0.0216682i	−0.986658	+	0.162804i	$0.947946\pi$
$728$	−12.2465	−	9.97564i	−0.453887	−	0.369722i
$729$	26.9450	+	1.72278i	0.997962	+	0.0638066i
$730$	−25.1649	−	14.5290i	−0.931395	−	0.537741i
$731$	28.3535	+	77.9005i	1.04869	+	2.88125i
$732$	1.74841	−	1.43567i	0.0646232	−	0.0530637i
$733$	12.3358	−	21.3663i	0.455634	−	0.789181i	−0.543091	−	0.839674i	$-0.682746\pi$
$733$	12.3358	−	21.3663i	0.455634	−	0.789181i	0.998724	+	0.0504932i	$0.0160793\pi$
$734$	9.29765	−	16.1040i	0.343183	−	0.594410i
$735$	−25.2873	+	4.94285i	−0.932737	+	0.182320i
$736$	5.74884	−	1.01368i	0.211905	−	0.0373646i
$737$	−44.7613	+	16.2918i	−1.64880	+	0.600116i
$738$	−1.32486	+	6.67916i	−0.0487689	+	0.245863i
$739$	−4.63393	−	26.2803i	−0.170462	−	0.966738i	−0.943252	−	0.332077i	$-0.892251\pi$
$739$	−4.63393	−	26.2803i	−0.170462	−	0.966738i	0.772790	−	0.634661i	$-0.218860\pi$
$740$	−9.90540	−	17.1566i	−0.364130	−	0.630691i
$741$	−35.5809	−	27.6689i	−1.30710	−	1.01644i
$742$	−0.422420	+	0.252161i	−0.0155075	+	0.00925714i
$743$	−35.8701	+	30.0986i	−1.31595	+	1.10421i	−0.328798	+	0.944400i	$0.606643\pi$
$743$	−35.8701	+	30.0986i	−1.31595	+	1.10421i	−0.987148	+	0.159809i	$0.948912\pi$
$744$	−3.90745	+	2.20086i	−0.143254	+	0.0806876i
$745$	−22.7347	−	19.0767i	−0.832936	−	0.698917i
$746$	6.14710	−	16.8890i	0.225061	−	0.618351i
$747$	−0.392296	+	18.4293i	−0.0143534	+	0.674292i
$748$	−13.6370	+	23.6199i	−0.498617	+	0.863631i
$749$	0.112334	+	7.70878i	0.00410459	+	0.281673i
$750$	7.10514	−	18.8932i	0.259443	−	0.689881i
$751$	−24.5793	−	4.33399i	−0.896911	−	0.158150i	−0.293856	−	0.955850i	$-0.594939\pi$
$751$	−24.5793	−	4.33399i	−0.896911	−	0.158150i	−0.603055	+	0.797700i	$0.706050\pi$
$752$		−	2.70207i		−	0.0985342i
$753$	−32.7135	+	38.1544i	−1.19215	+	1.39042i
$754$	−12.1896	+	14.5270i	−0.443920	+	0.529043i
$755$	−5.47486	−	31.0494i	−0.199250	−	1.13001i
$756$	9.01829	−	10.3764i	0.327992	−	0.377387i
$757$	42.4170	+	15.4385i	1.54167	+	0.561123i	0.966446	−	0.256870i	$-0.0826914\pi$
$757$	42.4170	+	15.4385i	1.54167	+	0.561123i	0.575227	+	0.817994i	$0.304914\pi$
$758$	−3.61644	+	9.93610i	−0.131355	+	0.360895i
$759$	−7.49358	+	40.0041i	−0.272000	+	1.45206i
$760$	−6.80331	+	6.28670i	−0.246782	+	0.228042i
$761$	−11.1636	+	6.44533i	−0.404682	+	0.233643i	−0.688502	−	0.725234i	$-0.741731\pi$
$761$	−11.1636	+	6.44533i	−0.404682	+	0.233643i	0.283820	+	0.958877i	$0.408398\pi$
$762$	23.5515	+	13.9337i	0.853182	+	0.504766i
$763$	16.9845	+	5.90303i	0.614879	+	0.213704i
$764$	24.0197	+	4.23532i	0.869002	+	0.153229i
$765$	−8.40469	+	42.3713i	−0.303872	+	1.53194i
$766$	−2.89897	+	16.4409i	−0.104744	+	0.594033i
$767$	−34.2719	+	19.7869i	−1.23749	+	0.714464i
$768$	0.318902	−	1.70244i	0.0115074	−	0.0614315i
$769$	17.8252	+	14.9571i	0.642794	+	0.539368i	0.904875	−	0.425677i	$-0.139964\pi$
$769$	17.8252	+	14.9571i	0.642794	+	0.539368i	−0.262081	+	0.965046i	$0.584409\pi$
$770$	−8.04995	−	21.1529i	−0.290100	−	0.762296i
$771$	−10.6826	−	9.15923i	−0.384724	−	0.329862i
$772$			17.7677i			0.639475i
$773$	0.980244	−	5.55924i	0.0352569	−	0.199952i	−0.962091	−	0.272727i	$-0.912074\pi$
$773$	0.980244	−	5.55924i	0.0352569	−	0.199952i	0.997348	+	0.0727751i	$0.0231855\pi$
$774$	34.7512	−	11.8171i	1.24911	−	0.424758i
$775$	−0.428442	−	1.17714i	−0.0153901	−	0.0422839i
$776$	1.68856	−	4.63927i	0.0606156	−	0.166540i
$777$	42.7191	−	0.167866i	1.53254	−	0.00602217i
$778$			3.26721i			0.117135i
$779$	6.71455	+	7.26632i	0.240574	+	0.260343i
$780$	4.04596	−	21.5991i	0.144869	−	0.773374i
$781$	14.6018	−	2.57470i	0.522495	−	0.0921299i
$782$	−6.86821	−	38.9515i	−0.245607	−	1.39290i
$783$	−12.2988	−	11.0076i	−0.439522	−	0.393381i
$784$	−1.41589	−	6.85531i	−0.0505675	−	0.244832i
$785$	5.74426	+	15.7822i	0.205021	+	0.563291i
$786$	1.21459	+	3.45088i	0.0433229	+	0.123089i
$787$			30.2580i			1.07858i	0.842120	+	0.539290i	$0.181307\pi$
$787$			30.2580i			1.07858i	−0.842120	+	0.539290i	$0.818693\pi$
$788$	3.57097	+	9.81116i	0.127211	+	0.349508i
$789$	−2.84489	+	0.470473i	−0.101281	+	0.0167493i
$790$	9.88902	+	17.1283i	0.351835	+	0.609397i
$791$	0.612837	+	42.0552i	0.0217900	+	1.49531i
$792$	10.3273	+	6.25923i	0.366965	+	0.222412i
$793$	5.01233	+	5.97346i	0.177993	+	0.212124i
$794$	−24.9456	−	20.9319i	−0.885287	−	0.742844i
$795$	−0.589056	−	0.348502i	−0.0208917	−	0.0123601i
$796$	−3.15833	−	1.14954i	−0.111944	−	0.0407442i
$797$	−25.2933			−0.895934			−0.447967	−	0.894050i	$-0.647852\pi$
$797$	−25.2933			−0.895934			−0.447967	+	0.894050i	$0.647852\pi$
$798$	−4.48152	−	19.4658i	−0.158644	−	0.689081i
$799$	−18.3080			−0.647690
$800$	0.454631	+	0.165472i	0.0160736	+	0.00585033i
$801$	−0.794883	+	4.00731i	−0.0280858	+	0.141591i
$802$	−17.7422	−	14.8875i	−0.626499	−	0.525695i
$803$	35.3793	+	42.1635i	1.24851	+	1.48792i
$804$	−13.0069	−	15.8403i	−0.458718	−	0.558646i
$805$	28.6607	+	15.9950i	1.01016	+	0.563751i
$806$	−7.72886	−	13.3868i	−0.272238	−	0.471529i
$807$	−4.25544	−	25.7321i	−0.149799	−	0.905814i
$808$	−0.469710	−	1.29052i	−0.0165244	−	0.0454003i
$809$		−	36.3209i		−	1.27697i	−0.769633	−	0.638487i	$-0.779561\pi$
$809$		−	36.3209i		−	1.27697i	0.769633	−	0.638487i	$-0.220439\pi$
$810$	18.6772	+	4.11975i	0.656251	+	0.144753i
$811$	11.7876	+	32.3862i	0.413920	+	1.13723i	0.955088	+	0.296321i	$0.0957598\pi$
$811$	11.7876	+	32.3862i	0.413920	+	1.13723i	−0.541169	+	0.840914i	$0.682018\pi$
$812$	−8.25431	+	1.57980i	−0.289670	+	0.0554402i
$813$	0.942635	+	5.70000i	0.0330597	+	0.199908i
$814$	6.51613	+	36.9548i	0.228390	+	1.29526i
$815$	−33.4546	+	5.89895i	−1.17186	+	0.206631i
$816$	−11.5350	−	2.16074i	−0.403805	−	0.0756409i
$817$	15.8241	−	50.9302i	0.553615	−	1.78182i
$818$		−	3.64790i		−	0.127546i
$819$	36.0944	+	30.7020i	1.26124	+	1.07282i
$820$	−1.64975	+	4.53265i	−0.0576118	+	0.158287i
$821$	8.57359	+	23.5557i	0.299220	+	0.822101i	0.994631	+	0.103488i	$0.0330004\pi$
$821$	8.57359	+	23.5557i	0.299220	+	0.822101i	−0.695410	+	0.718613i	$0.744777\pi$
$822$	0.00410168	−	0.385421i	0.000143062	−	0.0134431i
$823$	−3.06861	+	17.4030i	−0.106965	+	0.606629i	0.883452	+	0.468522i	$0.155213\pi$
$823$	−3.06861	+	17.4030i	−0.106965	+	0.606629i	−0.990417	+	0.138108i	$0.955898\pi$
$824$			1.97723i			0.0688800i
$825$	−2.19561	+	2.56078i	−0.0764412	+	0.0891548i
$826$	−17.3140	−	2.79345i	−0.602432	−	0.0971965i
$827$	28.0856	+	23.5666i	0.976631	+	0.819490i	0.983578	−	0.180485i	$-0.0577669\pi$
$827$	28.0856	+	23.5666i	0.976631	+	0.819490i	−0.00694693	+	0.999976i	$0.502211\pi$
$828$	−17.3073	+	2.67330i	−0.601471	+	0.0929036i
$829$	18.5066	−	10.6848i	0.642762	−	0.371099i	−0.142915	−	0.989735i	$-0.545648\pi$
$829$	18.5066	−	10.6848i	0.642762	−	0.371099i	0.785678	+	0.618636i	$0.212314\pi$
$830$	−2.26747	+	12.8595i	−0.0787051	+	0.446359i
$831$	8.33384	−	14.0863i	0.289098	−	0.488648i
$832$	5.87936	+	1.03669i	0.203830	+	0.0359408i
$833$	−46.4485	+	9.59343i	−1.60934	+	0.332393i
$834$	−10.7161	+	18.1129i	−0.371069	+	0.627200i
$835$	33.3902	−	19.2778i	1.15552	−	0.667137i
$836$	16.1822	−	6.78242i	0.559674	−	0.234575i
$837$	11.8602	−	6.35162i	0.409949	−	0.219544i
$838$	−2.70293	+	7.42623i	−0.0933710	+	0.256535i
$839$	−11.5879	−	4.21765i	−0.400058	−	0.145609i	0.134152	−	0.990961i	$-0.457169\pi$
$839$	−11.5879	−	4.21765i	−0.400058	−	0.145609i	−0.534211	+	0.845351i	$0.679391\pi$
$840$	7.43553	−	6.28911i	0.256550	−	0.216995i
$841$	−3.28370	−	18.6228i	−0.113231	−	0.642165i
$842$	−1.52897	+	1.82215i	−0.0526916	+	0.0627954i
$843$	31.7203	+	27.1969i	1.09250	+	0.936711i
$844$			22.1063i			0.760930i
$845$	47.3854	+	8.35533i	1.63011	+	0.287432i
$846$	−0.172514	+	8.10436i	−0.00593115	+	0.278634i
$847$	0.200595	+	13.7656i	0.00689251	+	0.472990i
$848$	0.0929716	−	0.161032i	0.00319266	−	0.00552985i
$849$	−49.4855	−	18.6100i	−1.69834	−	0.638692i
$850$	1.12117	−	3.08038i	0.0384557	−	0.105656i
$851$	−41.6868	−	34.9793i	−1.42900	−	1.19908i
$852$	3.13097	+	5.55878i	0.107265	+	0.190441i
$853$	−40.7170	+	34.1656i	−1.39412	+	1.16981i	−0.430484	+	0.902598i	$0.641657\pi$
$853$	−40.7170	+	34.1656i	−1.39412	+	1.16981i	−0.963639	+	0.267209i	$0.913899\pi$
$854$	0.0503526	+	3.45538i	0.00172303	+	0.118241i
$855$	20.8067	−	18.4215i	0.711574	−	0.630001i
$856$	−1.45698	−	2.52356i	−0.0497984	−	0.0862534i
$857$	8.53413	+	48.3995i	0.291520	+	1.65329i	0.681018	+	0.732267i	$0.261538\pi$
$857$	8.53413	+	48.3995i	0.291520	+	1.65329i	−0.389497	+	0.921028i	$0.627351\pi$
$858$	−21.1944	+	35.8239i	−0.723564	+	1.22301i
$859$	9.94599	−	3.62005i	0.339353	−	0.123514i	−0.166722	−	0.986004i	$-0.553318\pi$
$859$	9.94599	−	3.62005i	0.339353	−	0.123514i	0.506075	+	0.862490i	$0.331096\pi$
$860$	25.6063	−	4.51509i	0.873169	−	0.153963i
$861$	−6.71712	−	7.94157i	−0.228919	−	0.270648i
$862$	9.62927	−	16.6784i	0.327974	−	0.568068i
$863$	11.9861	−	20.7605i	0.408011	−	0.706695i	−0.586656	−	0.809836i	$-0.699556\pi$
$863$	11.9861	−	20.7605i	0.408011	−	0.706695i	0.994667	+	0.103141i	$0.0328893\pi$
$864$	−1.06518	+	5.08580i	−0.0362382	+	0.173023i
$865$	2.64272	+	7.26081i	0.0898552	+	0.246875i
$866$	24.3388	+	14.0520i	0.827067	+	0.477507i
$867$	−9.21884	+	49.2143i	−0.313088	+	1.67140i
$868$	1.09113	−	6.76294i	0.0370355	−	0.229549i
$869$	−6.50535	−	36.8937i	−0.220679	−	1.25153i
$870$	−7.41977	−	9.03610i	−0.251554	−	0.306353i
$871$	54.1185	−	45.4109i	1.83374	−	1.53869i
$872$	−6.69295	+	1.18015i	−0.226652	+	0.0399648i
$873$	−5.36072	+	13.8069i	−0.181433	+	0.467291i
$874$	−11.6547	+	22.6191i	−0.394225	+	0.765104i
$875$	15.8040	+	26.4748i	0.534272	+	0.895012i
$876$	−12.0592	+	20.3830i	−0.407441	+	0.688679i
$877$	25.1467	−	4.43404i	0.849142	−	0.149727i	0.267889	−	0.963450i	$-0.413674\pi$
$877$	25.1467	−	4.43404i	0.849142	−	0.149727i	0.581253	+	0.813723i	$0.302563\pi$
$878$	−7.90530	+	9.42117i	−0.266791	+	0.317949i
$879$	−3.87891	−	0.0412796i	−0.130832	−	0.00139233i
$880$	6.55305	+	5.49867i	0.220903	+	0.185360i
$881$	26.1261	+	15.0839i	0.880212	+	0.508190i	0.870728	−	0.491765i	$-0.163648\pi$
$881$	26.1261	+	15.0839i	0.880212	+	0.508190i	0.00948336	+	0.999955i	$0.496981\pi$
$882$	3.80903	+	20.6517i	0.128257	+	0.695378i
$883$	−5.87608	−	4.93062i	−0.197746	−	0.165929i	0.538538	−	0.842601i	$-0.318977\pi$
$883$	−5.87608	−	4.93062i	−0.197746	−	0.165929i	−0.736284	+	0.676673i	$0.763421\pi$
$884$	7.02414	−	39.8359i	0.236248	−	1.33983i
$885$	−8.10057	−	23.0153i	−0.272298	−	0.773650i
$886$	19.8897	−	11.4833i	0.668206	−	0.385789i
$887$	10.4815	+	8.79505i	0.351935	+	0.295309i	0.801567	−	0.597905i	$-0.204000\pi$
$887$	10.4815	+	8.79505i	0.351935	+	0.295309i	−0.449631	+	0.893214i	$0.648445\pi$
$888$	−14.0683	+	7.92395i	−0.472102	+	0.265910i
$889$	−39.0668	+	14.8673i	−1.31026	+	0.498634i
$890$	−0.989806	+	2.71947i	−0.0331784	+	0.0911568i
$891$	−30.5753	−	19.4328i	−1.02431	−	0.651022i
$892$	8.41483	+	4.85831i	0.281749	+	0.162668i
$893$	9.37408	+	7.13082i	0.313692	+	0.238624i
$894$	−15.7444	+	18.3630i	−0.526572	+	0.614151i
$895$	10.0875	+	12.0218i	0.337188	+	0.401845i
$896$	1.73001	+	2.00177i	0.0577955	+	0.0668744i
$897$	−9.84867	−	59.5537i	−0.328838	−	1.98844i
$898$	−10.6599	+	8.94472i	−0.355726	+	0.298489i
$899$	−8.09958	−	1.42817i	−0.270136	−	0.0476323i
$900$	−1.35302	−	0.525330i	−0.0451007	−	0.0175110i
$901$	−1.09108	−	0.629934i	−0.0363491	−	0.0209861i
$902$	5.87289	−	6.99903i	0.195546	−	0.233042i
$903$	−18.9694	+	52.7622i	−0.631262	+	1.75581i
$904$	−7.94852	−	13.7672i	−0.264364	−	0.457892i
$905$	1.50003			0.0498628
$906$	−25.3523	+	4.19263i	−0.842275	+	0.139291i
$907$	−1.20240	+	3.30356i	−0.0399250	+	0.109693i	−0.958053	−	0.286591i	$-0.907478\pi$
$907$	−1.20240	+	3.30356i	−0.0399250	+	0.109693i	0.918128	+	0.396284i	$0.129700\pi$
$908$	−12.9788	+	4.72390i	−0.430717	+	0.156768i
$909$	1.32642	+	3.90067i	0.0439945	+	0.129377i
$910$	21.9489	+	25.3968i	0.727599	+	0.841895i
$911$	32.1835			1.06629			0.533143	−	0.846025i	$-0.321011\pi$
$911$	32.1835			1.06629			0.533143	+	0.846025i	$0.321011\pi$
$912$	5.06456	+	5.59913i	0.167704	+	0.185406i
$913$	12.3669	−	21.4200i	0.409283	−	0.708899i
$914$	1.30312	+	7.39038i	0.0431035	+	0.244452i
$915$	−4.18896	+	2.35942i	−0.138483	+	0.0780001i
$916$	−1.12956	+	6.40605i	−0.0373217	+	0.211662i
$917$	−5.27855	−	1.83458i	−0.174313	−	0.0605833i
$918$	34.4591	+	7.21719i	1.13732	+	0.238203i
$919$	−55.8691			−1.84295			−0.921476	−	0.388436i	$-0.873015\pi$
$919$	−55.8691			−1.84295			−0.921476	+	0.388436i	$0.873015\pi$
$920$	−12.4055			−0.408998
$921$	−13.6430	−	16.6150i	−0.449552	−	0.547483i
$922$	19.5269	+	3.44312i	0.643085	+	0.113393i
$923$	−19.0441	+	10.9951i	−0.626846	+	0.361910i
$924$	−17.3091	+	6.37713i	−0.569427	+	0.209792i
$925$	−1.54256	−	4.23814i	−0.0507189	−	0.139349i
$926$	−9.56137	+	8.02294i	−0.314206	+	0.263650i
$927$	0.126236	−	5.93034i	0.00414615	−	0.194778i
$928$	2.43331	−	2.04179i	0.0798774	−	0.0670251i
$929$	−5.97870	+	16.4264i	−0.196155	+	0.538931i	−0.998305	−	0.0581907i	$-0.981467\pi$
$929$	−5.97870	+	16.4264i	−0.196155	+	0.538931i	0.802151	+	0.597122i	$0.203689\pi$
$930$	8.98988	−	3.16412i	0.294790	−	0.103756i
$931$	27.5192	+	13.1793i	0.901905	+	0.431934i
$932$			22.5607i			0.739000i
$933$	−0.123946	+	11.6468i	−0.00405780	+	0.381298i
$934$	26.9021	+	32.0607i	0.880265	+	1.04906i
$935$	37.2565	−	44.4005i	1.21842	−	1.45205i
$936$	−17.5679	−	3.48473i	−0.574225	−	0.113902i
$937$	6.60919	−	2.40555i	0.215913	−	0.0785859i	−0.231799	−	0.972764i	$-0.574461\pi$
$937$	6.60919	−	2.40555i	0.215913	−	0.0785859i	0.447712	+	0.894178i	$0.352239\pi$
$938$	31.3052	−	0.456186i	1.02215	−	0.0148950i
$939$	12.5280	+	10.7415i	0.408836	+	0.350535i
$940$	−0.997131	+	5.65501i	−0.0325228	+	0.184446i
$941$	−20.2003	+	7.35231i	−0.658511	+	0.239678i	−0.649593	−	0.760282i	$-0.725061\pi$
$941$	−20.2003	+	7.35231i	−0.658511	+	0.239678i	−0.00891768	+	0.999960i	$0.502839\pi$
$942$	12.9121	−	4.54460i	0.420699	−	0.148071i
$943$			13.2498i			0.431472i
$944$	6.22895	−	2.26715i	0.202735	−	0.0737896i
$945$	−22.7031	+	18.3883i	−0.738531	+	0.598172i
$946$	−48.5026	−	8.55232i	−1.57696	−	0.278060i
$947$	−30.5175	+	5.38106i	−0.991686	+	0.174861i	−0.645875	−	0.763443i	$-0.723507\pi$
$947$	−30.5175	+	5.38106i	−0.991686	+	0.174861i	−0.345811	+	0.938304i	$0.612396\pi$
$948$	14.0451	−	7.91085i	0.456163	−	0.256932i
$949$	−70.6949	−	40.8157i	−2.29485	−	1.32493i
$950$	−1.77385	+	1.14053i	−0.0575511	+	0.0370038i
$951$	−14.1666	+	4.98613i	−0.459382	+	0.161686i
$952$	13.5631	−	11.7217i	0.439582	−	0.379904i
$953$	−43.0588	−	15.6721i	−1.39481	−	0.507670i	−0.468177	−	0.883635i	$-0.655089\pi$
$953$	−43.0588	−	15.6721i	−1.39481	−	0.507670i	−0.926634	+	0.375965i	$0.877311\pi$
$954$	−0.289133	+	0.477049i	−0.00936102	+	0.0154450i
$955$	−48.7066	−	17.7278i	−1.57611	−	0.573657i
$956$	24.1300	+	4.25477i	0.780420	+	0.137609i
$957$	7.35272	+	20.8905i	0.237680	+	0.675293i
$958$	20.3927	−	11.7737i	0.658859	−	0.380392i
$959$	0.456494	+	0.371845i	0.0147409	+	0.0120075i
$960$	−1.29566	+	3.44526i	−0.0418172	+	0.111195i
$961$	−12.1480	+	21.0410i	−0.391871	+	0.678741i
$962$	−27.8269	−	48.1975i	−0.897174	−	1.55395i
$963$	4.20882	+	7.66198i	0.135627	+	0.246904i
$964$	0.659930	+	0.786475i	0.0212549	+	0.0253306i
$965$	6.55675	−	37.1852i	0.211069	−	1.19703i
$966$	13.2843	−	23.2193i	0.427416	−	0.747070i
$967$	0.810496	−	0.680087i	0.0260638	−	0.0218701i	−0.629663	−	0.776869i	$-0.716807\pi$
$967$	0.810496	−	0.680087i	0.0260638	−	0.0218701i	0.655726	+	0.754999i	$0.272362\pi$
$968$	−2.60172	−	4.50631i	−0.0836225	−	0.144838i
$969$	37.9372	−	34.3152i	1.21872	−	1.10236i
$970$	−5.24590	+	9.08617i	−0.168436	+	0.291739i
$971$	−9.27123	−	3.37445i	−0.297528	−	0.108291i	0.188943	−	0.981988i	$-0.439494\pi$
$971$	−9.27123	−	3.37445i	−0.297528	−	0.108291i	−0.486471	+	0.873697i	$0.661716\pi$
$972$	3.51953	−	15.1859i	0.112889	−	0.487089i
$973$	−11.4341	−	30.0454i	−0.366561	−	0.963211i
$974$	−0.0120774	+	0.00212956i	−0.000386984	+	6.82357e-5i
$975$	1.76099	−	4.68262i	0.0563967	−	0.149964i
$976$	−0.653075	−	1.13116i	−0.0209044	−	0.0362075i
$977$	−3.90212			−0.124840			−0.0624200	−	0.998050i	$-0.519882\pi$
$977$	−3.90212			−0.124840			−0.0624200	+	0.998050i	$0.519882\pi$
$978$	4.51740	+	27.3162i	0.144451	+	0.873475i
$979$	3.52357	−	4.19923i	0.112614	−	0.134208i
$980$	0.433459	+	14.8696i	0.0138463	+	0.474992i
$981$	20.1496	−	3.11233i	0.643329	−	0.0993690i
$982$	13.5930	−	16.1995i	0.433770	−	0.516946i
$983$	24.8607	+	9.04855i	0.792933	+	0.288604i	0.706555	−	0.707658i	$-0.250248\pi$
$983$	24.8607	+	9.04855i	0.792933	+	0.288604i	0.0863782	+	0.996262i	$0.472471\pi$
$984$	3.67974	+	1.38383i	0.117306	+	0.0441150i
$985$	−3.85293	−	21.8510i	−0.122764	−	0.696232i
$986$	−13.8343	−	16.4870i	−0.440573	−	0.525054i
$987$	−9.51669	−	7.92193i	−0.302920	−	0.252158i
$988$	−19.1123	+	17.6610i	−0.608043	+	0.561871i
$989$	61.8542	−	35.7115i	1.96685	−	1.13556i
$990$	−19.3036	−	16.9106i	−0.613510	−	0.537455i
$991$	−27.3230	−	32.5623i	−0.867944	−	1.03438i	−0.999075	−	0.0430106i	$-0.986305\pi$
$991$	−27.3230	−	32.5623i	−0.867944	−	1.03438i	0.131130	−	0.991365i	$-0.458139\pi$
$992$	0.885561	+	2.43306i	0.0281166	+	0.0772497i
$993$	35.1210	−	19.7818i	1.11453	−	0.627758i
$994$	−9.62102	−	1.55226i	−0.305160	−	0.0492346i
$995$	6.18569	+	3.57131i	0.196099	+	0.113218i
$996$	10.4606	+	1.95949i	0.331457	+	0.0620888i
$997$	−29.5164	+	10.7431i	−0.934794	+	0.340237i	−0.764108	−	0.645088i	$-0.776821\pi$
$997$	−29.5164	+	10.7431i	−0.934794	+	0.340237i	−0.170686	+	0.985325i	$0.554598\pi$
$998$	16.2720	−	5.92254i	0.515083	−	0.187475i
$999$	42.7013	−	22.8683i	1.35101	−	0.723520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.b.431.10	yes	162
3.2	odd	2		798.2.bu.a.431.24	✓	162
7.2	even	3		798.2.cc.b.317.9	yes	162
19.3	odd	18		798.2.cc.a.725.13	yes	162
21.2	odd	6		798.2.cc.a.317.13	yes	162
57.41	even	18		798.2.cc.b.725.9	yes	162
133.79	odd	18		798.2.bu.a.611.24	yes	162
399.212	even	18	inner	798.2.bu.b.611.10	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.24	✓	162	3.2	odd	2
798.2.bu.a.611.24	yes	162	133.79	odd	18
798.2.bu.b.431.10	yes	162	1.1	even	1	trivial
798.2.bu.b.611.10	yes	162	399.212	even	18	inner
798.2.cc.a.317.13	yes	162	21.2	odd	6
798.2.cc.a.725.13	yes	162	19.3	odd	18
798.2.cc.b.317.9	yes	162	7.2	even	3
798.2.cc.b.725.9	yes	162	57.41	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.881939 + 1.49070i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.36601 - 1.62795i) q^{5} +(-1.33860 + 1.09916i) q^{6} +(-0.0385504 - 2.64547i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.44437 - 2.62941i) q^{9} +(-0.726838 - 1.99697i) q^{10} +4.02535i q^{11} +(-1.63381 + 0.575043i) q^{12} +(-2.04188 - 5.61002i) q^{13} +(0.868579 - 2.49911i) q^{14} +(3.63152 - 0.600560i) q^{15} +(0.173648 + 0.984808i) q^{16} +(6.67261 - 1.17656i) q^{17} +(-0.457951 - 2.96484i) q^{18} +(-3.87478 - 1.99651i) q^{19} -2.12513i q^{20} +(3.97760 + 2.27568i) q^{21} +(-1.37675 + 3.78259i) q^{22} +(-1.99655 - 5.48548i) q^{23} +(-1.73195 - 0.0184316i) q^{24} +(0.0840125 - 0.476459i) q^{25} -5.97006i q^{26} +(5.19350 + 0.165859i) q^{27} +(1.67094 - 2.05133i) q^{28} +(-2.43331 - 2.04179i) q^{29} +(3.61791 + 0.677709i) q^{30} +(2.24232 - 1.29460i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-6.00059 - 3.55011i) q^{33} +(6.67261 + 1.17656i) q^{34} +(-4.25402 + 3.67650i) q^{35} +(0.583702 - 2.94267i) q^{36} +(8.07321 - 4.66107i) q^{37} +(-2.95826 - 3.20136i) q^{38} +(10.1637 + 1.90386i) q^{39} +(0.726838 - 1.99697i) q^{40} +(-2.13288 - 0.776304i) q^{41} +(2.95939 + 3.49885i) q^{42} +(2.12461 + 12.0493i) q^{43} +(-2.58745 + 3.08360i) q^{44} +(-2.30752 + 5.94315i) q^{45} -5.83752i q^{46} +(-2.66102 - 0.469209i) q^{47} +(-1.62120 - 0.609683i) q^{48} +(-6.99703 + 0.203968i) q^{49} +(0.241904 - 0.418991i) q^{50} +(-4.13094 + 10.9845i) q^{51} +(2.04188 - 5.61002i) q^{52} +(-0.142441 - 0.119522i) q^{53} +(4.82357 + 1.93214i) q^{54} +(6.55305 - 5.49867i) q^{55} +(2.27177 - 1.35612i) q^{56} +(6.39352 - 4.01534i) q^{57} +(-1.58823 - 2.75090i) q^{58} +(-1.15106 - 6.52801i) q^{59} +(3.16793 + 1.87424i) q^{60} +(-1.22738 + 0.446730i) q^{61} +(2.54987 - 0.449611i) q^{62} +(-6.90035 + 3.92240i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-6.34359 + 10.9874i) q^{65} +(-4.42450 - 5.38834i) q^{66} +(4.04730 + 11.1199i) q^{67} +(5.86780 + 3.38777i) q^{68} +(9.93803 + 1.86160i) q^{69} +(-5.25491 + 1.99981i) q^{70} +(-0.639621 - 3.62747i) q^{71} +(1.55495 - 2.56557i) q^{72} +(10.4745 - 8.78913i) q^{73} +(9.18052 - 1.61877i) q^{74} +(0.636163 + 0.545444i) q^{75} +(-1.68493 - 4.02008i) q^{76} +(10.6489 - 0.155179i) q^{77} +(8.89956 + 5.26523i) q^{78} +(-9.16534 + 1.61610i) q^{79} +(1.36601 - 1.62795i) q^{80} +(-4.82760 + 7.59568i) q^{81} +(-1.73874 - 1.45898i) q^{82} +(-5.32128 - 3.07224i) q^{83} +(1.58424 + 4.30002i) q^{84} +(-11.0302 - 9.25546i) q^{85} +(-2.12461 + 12.0493i) q^{86} +(5.18973 - 1.82660i) q^{87} +(-3.48606 + 2.01268i) q^{88} +(-1.04320 - 0.875346i) q^{89} +(-4.20104 + 4.79552i) q^{90} +(-14.7624 + 5.61800i) q^{91} +(1.99655 - 5.48548i) q^{92} +(-0.0477231 + 4.48438i) q^{93} +(-2.34006 - 1.35103i) q^{94} +(2.04278 + 9.03519i) q^{95} +(-1.31491 - 1.12740i) q^{96} +(-3.17345 - 3.78197i) q^{97} +(-6.64482 - 2.20146i) q^{98} +(10.5843 - 5.81409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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