LMFDB - Embedded newform 798.2.cc.b.317.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (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			317.9
Character	$\chi$	$=$	798.317
Dual form			798.2.cc.b.725.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.850014 - 1.50913i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.726838 + 1.99697i) q^{5} +(-1.33860 + 1.09916i) q^{6} +(2.31032 - 1.28935i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.55495 + 2.56557i) q^{9} +(2.09285 + 0.369026i) q^{10} +(-3.48606 - 2.01268i) q^{11} +(1.31491 + 1.12740i) q^{12} +(-2.04188 - 5.61002i) q^{13} +(-1.67094 - 2.05133i) q^{14} +(3.63152 - 0.600560i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.31737 + 6.36693i) q^{17} +(2.79660 + 1.08582i) q^{18} +(0.208365 + 4.35392i) q^{19} -2.12513i q^{20} +(-3.90960 - 2.39061i) q^{21} +(-1.37675 + 3.78259i) q^{22} +(-3.75229 + 4.47180i) q^{23} +(0.881939 - 1.49070i) q^{24} +(0.370619 + 0.310986i) q^{25} +(-5.17022 + 2.98503i) q^{26} +(5.19350 + 0.165859i) q^{27} +(-1.73001 + 2.00177i) q^{28} +(-2.43331 - 2.04179i) q^{29} +(-1.22204 - 3.47206i) q^{30} +2.58921i q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.0741935 + 6.97172i) q^{33} +(6.67261 + 1.17656i) q^{34} +(0.895566 + 5.55079i) q^{35} +(0.583702 - 2.94267i) q^{36} +(-8.07321 - 4.66107i) q^{37} +(4.25159 - 0.961249i) q^{38} +(-6.73063 + 7.85006i) q^{39} +(-2.09285 + 0.369026i) q^{40} +(-2.13288 - 0.776304i) q^{41} +(-1.67540 + 4.26533i) q^{42} +(2.12461 + 12.0493i) q^{43} +(3.96420 + 0.698995i) q^{44} +(-3.99316 - 4.96995i) q^{45} +(5.05544 + 2.91876i) q^{46} +(0.924161 + 2.53911i) q^{47} +(-1.62120 - 0.609683i) q^{48} +(3.67516 - 5.95762i) q^{49} +(0.241904 - 0.418991i) q^{50} +(11.5783 - 1.91476i) q^{51} +(3.83748 + 4.57333i) q^{52} +(0.174729 - 0.0635963i) q^{53} +(-0.738503 - 5.14340i) 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} +(6.22895 + 2.26715i) q^{59} +(-3.20710 + 1.80639i) q^{60} +(1.00057 + 0.839577i) q^{61} +(2.54987 - 0.449611i) q^{62} +(-0.284525 + 7.93215i) q^{63} +(-0.500000 + 0.866025i) q^{64} +12.6872 q^{65} +(6.87868 - 1.13756i) q^{66} +(-11.6537 - 2.05487i) q^{67} -6.77555i q^{68} +(9.93803 + 1.86160i) q^{69} +(5.31095 - 1.84585i) q^{70} +(-0.639621 - 3.62747i) q^{71} +(-2.99932 - 0.0638452i) q^{72} +(2.37437 + 13.4657i) q^{73} +(-3.18836 + 8.75995i) q^{74} +(0.154288 - 0.823655i) q^{75} +(-1.68493 - 4.02008i) q^{76} +(-10.6489 - 0.155179i) q^{77} +(8.89956 + 5.26523i) q^{78} +(5.98225 + 7.12937i) q^{79} +(0.726838 + 1.99697i) q^{80} +(-4.16425 - 7.97866i) q^{81} +(-0.394140 + 2.23528i) q^{82} +(-5.32128 - 3.07224i) q^{83} +(4.49146 + 0.909275i) q^{84} +(-11.0302 - 9.25546i) q^{85} +(11.4973 - 4.18467i) q^{86} +(-1.01298 + 5.40774i) q^{87} -4.02535i q^{88} +(-0.236473 + 1.34111i) q^{89} +(-4.20104 + 4.79552i) q^{90} +(-11.9507 - 10.3282i) q^{91} +(1.99655 - 5.48548i) q^{92} +(3.90745 - 2.20086i) q^{93} +(2.34006 - 1.35103i) q^{94} +(-8.84610 - 2.74849i) q^{95} +(-0.318902 + 1.70244i) q^{96} +(-3.17345 - 3.78197i) q^{97} +(-6.50529 - 2.58479i) q^{98} +(10.5843 - 5.81409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Character values

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

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

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−0.850014	−	1.50913i	−0.490756	−	0.871297i
$3$	−0.850014	−	1.50913i	−0.490756	−	0.871297i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.726838	+	1.99697i	−0.325052	+	0.893073i	0.664292	+	0.747474i	$0.268733\pi$
$5$	−0.726838	+	1.99697i	−0.325052	+	0.893073i	−0.989344	+	0.145600i	$0.953489\pi$
$6$	−1.33860	+	1.09916i	−0.546481	+	0.448730i
$7$	2.31032	−	1.28935i	0.873219	−	0.487328i
$7$	2.31032	−	1.28935i	0.873219	−	0.487328i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.55495	+	2.56557i	−0.518317	+	0.855188i
$10$	2.09285	+	0.369026i	0.661817	+	0.116696i
$11$	−3.48606	−	2.01268i	−1.05109	−	0.606844i	−0.128132	−	0.991757i	$-0.540898\pi$
$11$	−3.48606	−	2.01268i	−1.05109	−	0.606844i	−0.922953	+	0.384913i	$0.874232\pi$
$12$	1.31491	+	1.12740i	0.379580	+	0.325452i
$13$	−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	$-0.421575\pi$
$14$	−1.67094	−	2.05133i	−0.446579	−	0.548240i
$15$	3.63152	−	0.600560i	0.937653	−	0.155064i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−2.31737	+	6.36693i	−0.562046	+	1.54421i	0.254586	+	0.967050i	$0.418061\pi$
$17$	−2.31737	+	6.36693i	−0.562046	+	1.54421i	−0.816632	+	0.577158i	$0.804162\pi$
$18$	2.79660	+	1.08582i	0.659166	+	0.255931i
$19$	0.208365	+	4.35392i	0.0478022	+	0.998857i
$19$	0.208365	+	4.35392i	0.0478022	+	0.998857i
$20$		−	2.12513i		−	0.475194i
$21$	−3.90960	−	2.39061i	−0.853145	−	0.521674i
$22$	−1.37675	+	3.78259i	−0.293524	+	0.806451i
$23$	−3.75229	+	4.47180i	−0.782406	+	0.932435i	−0.999040	−	0.0438179i	$-0.986048\pi$
$23$	−3.75229	+	4.47180i	−0.782406	+	0.932435i	0.216634	+	0.976253i	$0.430492\pi$
$24$	0.881939	−	1.49070i	0.180025	−	0.304288i
$25$	0.370619	+	0.310986i	0.0741238	+	0.0621972i
$26$	−5.17022	+	2.98503i	−1.01396	+	0.585412i
$27$	5.19350	+	0.165859i	0.999490	+	0.0319196i
$28$	−1.73001	+	2.00177i	−0.326941	+	0.378299i
$29$	−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	$0.817518\pi$
$30$	−1.22204	−	3.47206i	−0.223113	−	0.633908i
$31$			2.58921i			0.465035i	0.972592	+	0.232518i	$0.0746964\pi$
$31$			2.58921i			0.465035i	−0.972592	+	0.232518i	$0.925304\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−0.0741935	+	6.97172i	−0.0129154	+	1.21362i
$34$	6.67261	+	1.17656i	1.14434	+	0.201779i
$35$	0.895566	+	5.55079i	0.151378	+	0.938255i
$36$	0.583702	−	2.94267i	0.0972836	−	0.490445i
$37$	−8.07321	−	4.66107i	−1.32723	−	0.766275i	−0.342358	−	0.939570i	$-0.611225\pi$
$37$	−8.07321	−	4.66107i	−1.32723	−	0.766275i	−0.984870	+	0.173294i	$0.944559\pi$
$38$	4.25159	−	0.961249i	0.689699	−	0.155935i
$39$	−6.73063	+	7.85006i	−1.07776	+	1.25702i
$40$	−2.09285	+	0.369026i	−0.330908	+	0.0583481i
$41$	−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	$0.667828\pi$
$42$	−1.67540	+	4.26533i	−0.258519	+	0.658155i
$43$	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	$0.561694\pi$
$44$	3.96420	+	0.698995i	0.597625	+	0.105377i
$45$	−3.99316	−	4.96995i	−0.595266	−	0.740876i
$46$	5.05544	+	2.91876i	0.745384	+	0.430348i
$47$	0.924161	+	2.53911i	0.134803	+	0.370367i	0.988666	−	0.150129i	$-0.0479690\pi$
$47$	0.924161	+	2.53911i	0.134803	+	0.370367i	−0.853864	+	0.520497i	$0.825747\pi$
$48$	−1.62120	−	0.609683i	−0.234000	−	0.0880001i
$49$	3.67516	−	5.95762i	0.525022	−	0.851089i
$50$	0.241904	−	0.418991i	0.0342104	−	0.0592542i
$51$	11.5783	−	1.91476i	1.62129	−	0.268120i
$52$	3.83748	+	4.57333i	0.532163	+	0.634207i
$53$	0.174729	−	0.0635963i	0.0240009	−	0.00873563i	−0.329992	−	0.943984i	$-0.607046\pi$
$53$	0.174729	−	0.0635963i	0.0240009	−	0.00873563i	0.353993	+	0.935248i	$0.384824\pi$
$54$	−0.738503	−	5.14340i	−0.100498	−	0.699929i
$55$	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
$59$	6.22895	+	2.26715i	0.810941	+	0.295158i	0.714012	−	0.700133i	$-0.246876\pi$
$59$	6.22895	+	2.26715i	0.810941	+	0.295158i	0.0969283	+	0.995291i	$0.469098\pi$
$60$	−3.20710	+	1.80639i	−0.414035	+	0.233204i
$61$	1.00057	+	0.839577i	0.128110	+	0.107497i	0.704591	−	0.709613i	$-0.251130\pi$
$61$	1.00057	+	0.839577i	0.128110	+	0.107497i	−0.576482	+	0.817110i	$0.695575\pi$
$62$	2.54987	−	0.449611i	0.323834	−	0.0571007i
$63$	−0.284525	+	7.93215i	−0.0358468	+	0.999357i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	12.6872			1.57365
$66$	6.87868	−	1.13756i	0.846707	−	0.140024i
$67$	−11.6537	−	2.05487i	−1.42373	−	0.251042i	−0.591873	−	0.806032i	$-0.701611\pi$
$67$	−11.6537	−	2.05487i	−1.42373	−	0.251042i	−0.831857	+	0.554990i	$0.812722\pi$
$68$		−	6.77555i		−	0.821656i
$69$	9.93803	+	1.86160i	1.19640	+	0.224110i
$70$	5.31095	−	1.84585i	0.634780	−	0.220621i
$71$	−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	$-0.125695\pi$
$72$	−2.99932	−	0.0638452i	−0.353473	−	0.00752422i
$73$	2.37437	+	13.4657i	0.277899	+	1.57604i	0.729599	+	0.683875i	$0.239707\pi$
$73$	2.37437	+	13.4657i	0.277899	+	1.57604i	−0.451700	+	0.892170i	$0.649182\pi$
$74$	−3.18836	+	8.75995i	−0.370639	+	1.01832i
$75$	0.154288	−	0.823655i	0.0178156	−	0.0951075i
$76$	−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
$79$	5.98225	+	7.12937i	0.673056	+	0.802116i	0.989196	−	0.146596i	$-0.0468317\pi$
$79$	5.98225	+	7.12937i	0.673056	+	0.802116i	−0.316141	+	0.948712i	$0.602387\pi$
$80$	0.726838	+	1.99697i	0.0812630	+	0.223268i
$81$	−4.16425	−	7.97866i	−0.462694	−	0.886518i
$82$	−0.394140	+	2.23528i	−0.0435255	+	0.246845i
$83$	−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	$0.776154\pi$
$84$	4.49146	+	0.909275i	0.490059	+	0.0992101i
$85$	−11.0302	−	9.25546i	−1.19640	−	1.00390i
$86$	11.4973	−	4.18467i	1.23979	−	0.451245i
$87$	−1.01298	+	5.40774i	−0.108603	+	0.579771i
$88$		−	4.02535i		−	0.429104i
$89$	−0.236473	+	1.34111i	−0.0250661	+	0.142157i	−0.994772	−	0.102117i	$-0.967438\pi$
$89$	−0.236473	+	1.34111i	−0.0250661	+	0.142157i	0.969706	+	0.244274i	$0.0785496\pi$
$90$	−4.20104	+	4.79552i	−0.442828	+	0.505492i
$91$	−11.9507	−	10.3282i	−1.25277	−	1.08269i
$92$	1.99655	−	5.48548i	0.208155	−	0.571900i
$93$	3.90745	−	2.20086i	0.405184	−	0.228219i
$94$	2.34006	−	1.35103i	0.241359	−	0.139348i
$95$	−8.84610	−	2.74849i	−0.907590	−	0.281990i
$96$	−0.318902	+	1.70244i	−0.0325478	+	0.173755i
$97$	−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	$0.858418\pi$
$98$	−6.50529	−	2.58479i	−0.657134	−	0.261103i
$99$	10.5843	−	5.81409i	1.06376	−	0.584338i
$100$	−0.454631	−	0.165472i	−0.0454631	−	0.0165472i
$101$	0.882767	−	1.05204i	0.0878386	−	0.104682i	−0.720335	−	0.693626i	$-0.756012\pi$
$101$	0.882767	−	1.05204i	0.0878386	−	0.104682i	0.808174	+	0.588944i	$0.200456\pi$
$102$	−3.89623	−	11.0699i	−0.385784	−	1.09609i
$103$		−	1.97723i		−	0.194822i	−0.995244	−	0.0974110i	$-0.968944\pi$
$103$		−	1.97723i		−	0.194822i	0.995244	−	0.0974110i	$-0.0310561\pi$
$104$	3.83748	−	4.57333i	0.376296	−	0.448452i
$105$	7.61563	−	6.06978i	0.743209	−	0.592350i
$106$	−0.0929716	−	0.161032i	−0.00903020	−	0.0156408i
$107$	1.45698	+	2.52356i	0.140851	+	0.243961i	0.927817	−	0.373035i	$-0.121683\pi$
$107$	1.45698	+	2.52356i	0.140851	+	0.243961i	−0.786966	+	0.616996i	$0.788349\pi$
$108$	−4.93703	+	1.62043i	−0.475065	+	0.155926i
$109$	−4.36851	−	5.20619i	−0.418428	−	0.498663i	0.515119	−	0.857119i	$-0.327748\pi$
$109$	−4.36851	−	5.20619i	−0.418428	−	0.498663i	−0.933547	+	0.358456i	$0.883303\pi$
$110$	−6.55305	−	5.49867i	−0.624809	−	0.524277i
$111$	−0.171822	+	16.1455i	−0.0163086	+	1.53246i
$112$	0.941030	−	2.47274i	0.0889189	−	0.233652i
$113$	−15.8970			−1.49547			−0.747734	−	0.663998i	$-0.768858\pi$
$113$	−15.8970			−1.49547			−0.747734	+	0.663998i	$0.768858\pi$
$114$	−5.06456	−	5.59913i	−0.474340	−	0.524406i
$115$	−6.20276	−	10.7435i	−0.578410	−	1.00184i
$116$	2.98490	+	1.08641i	0.277141	+	0.100871i
$117$	17.5679	+	3.48473i	1.62415	+	0.322164i
$118$	1.15106	−	6.52801i	0.105964	−	0.600952i
$119$	2.85533	+	17.6976i	0.261747	+	1.62233i
$120$	2.33586	+	2.84470i	0.213234	+	0.259685i
$121$	2.60172	+	4.50631i	0.236520	+	0.409665i
$122$	0.653075	−	1.13116i	0.0591266	−	0.102410i
$123$	0.641432	+	3.87866i	0.0578360	+	0.349727i
$124$	−0.885561	−	2.43306i	−0.0795257	−	0.218495i
$125$	−10.0925	+	5.82691i	−0.902701	+	0.521175i
$126$	7.86105	−	1.09720i	0.700318	−	0.0977464i
$127$	−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	$-0.358359\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	16.3780	−	13.4484i	1.44200	−	1.18406i
$130$	−2.20310	−	12.4944i	−0.193225	−	1.09583i
$131$	−2.08008	+	0.366774i	−0.181737	+	0.0320452i	−0.263776	−	0.964584i	$-0.584968\pi$
$131$	−2.08008	+	0.366774i	−0.181737	+	0.0320452i	0.0820387	+	0.996629i	$0.473857\pi$
$132$	−2.31475	−	6.57665i	−0.201473	−	0.572424i
$133$	6.09511	+	9.79028i	0.528513	+	0.848925i
$134$			11.8335i			1.02226i
$135$	−4.10605	+	10.2507i	−0.353393	+	0.882242i
$136$	−6.67261	+	1.17656i	−0.572172	+	0.100889i
$137$	−0.0761117	−	0.209115i	−0.00650266	−	0.0178659i	0.936399	−	0.350938i	$-0.114137\pi$
$137$	−0.0761117	−	0.209115i	−0.00650266	−	0.0178659i	−0.942901	+	0.333072i	$0.891915\pi$
$138$	0.107595	−	10.1103i	0.00915906	−	0.860647i
$139$	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	$0.216569\pi$
$140$	−2.74004	−	4.90974i	−0.231576	−	0.414949i
$141$	3.04630	−	3.55296i	0.256545	−	0.299213i
$142$	−3.46129	+	1.25981i	−0.290465	+	0.105721i
$143$	−4.17304	+	23.6665i	−0.348967	+	1.97909i
$144$	0.457951	+	2.96484i	0.0381626	+	0.247070i
$145$	5.84603	−	3.37521i	0.485486	−	0.280296i
$146$	12.8489	−	4.67660i	1.06338	−	0.387038i
$147$	−12.1148	−	0.482229i	−0.999209	−	0.0397735i
$148$	9.18052	+	1.61877i	0.754634	+	0.133062i
$149$	−8.97671	−	10.6980i	−0.735401	−	0.876417i	0.260629	−	0.965439i	$-0.416070\pi$
$149$	−8.97671	−	10.6980i	−0.735401	−	0.876417i	−0.996030	+	0.0890225i	$0.971626\pi$
$150$	−0.837934	−	0.00891735i	−0.0684170	−	0.000728098i
$151$	−12.8483	+	7.41799i	−1.04558	+	0.603667i	−0.921409	−	0.388593i	$-0.872961\pi$
$151$	−12.8483	+	7.41799i	−1.04558	+	0.603667i	−0.124173	+	0.992261i	$0.539628\pi$
$152$	−3.66642	+	2.35741i	−0.297386	+	0.191211i
$153$	−12.7314	−	15.8457i	−1.02927	−	1.28104i
$154$	1.69635	+	10.5141i	0.136696	+	0.847251i
$155$	−5.17057	−	1.88194i	−0.415311	−	0.151161i
$156$	3.63984	−	9.67866i	0.291421	−	0.774913i
$157$	6.05410	−	5.08000i	0.483170	−	0.405428i	−0.368401	−	0.929667i	$-0.620095\pi$
$157$	6.05410	−	5.08000i	0.483170	−	0.405428i	0.851571	+	0.524239i	$0.175650\pi$
$158$	5.98225	−	7.12937i	0.475922	−	0.567182i
$159$	−0.244498	−	0.209632i	−0.0193899	−	0.0166249i
$160$	1.84042	−	1.06257i	0.145498	−	0.0840033i
$161$	−2.90327	+	15.1693i	−0.228810	+	1.19551i
$162$	−7.13433	+	5.48647i	−0.560526	+	0.431057i
$163$	−15.9852			−1.25206			−0.626029	−	0.779800i	$-0.715321\pi$
$163$	−15.9852			−1.25206			−0.626029	+	0.779800i	$0.715321\pi$
$164$	2.26976			0.177239
$165$	−13.8684	−	5.21547i	−1.07965	−	0.406024i
$166$	−2.10154	+	5.77393i	−0.163111	+	0.448144i
$167$	−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	$0.807863\pi$
$168$	0.115528	−	4.58112i	0.00891314	−	0.353441i
$169$	−17.3445	+	14.5537i	−1.33419	+	1.11952i
$170$	−7.19947	+	12.4699i	−0.552174	+	0.956394i
$171$	−11.4943	−	6.23556i	−0.878987	−	0.476845i
$172$	−6.11758	−	10.5960i	−0.466461	−	0.807935i
$173$	0.631369	+	3.58067i	0.0480021	+	0.272234i	0.999357	−	0.0358647i	$-0.0114185\pi$
$173$	0.631369	+	3.58067i	0.0480021	+	0.272234i	−0.951355	+	0.308098i	$0.900307\pi$
$174$	5.50149	+	0.0585472i	0.417067	+	0.00443845i
$175$	1.25722	+	0.240620i	0.0950368	+	0.0181892i
$176$	−3.96420	+	0.698995i	−0.298813	+	0.0526887i
$177$	−1.87327	−	11.3274i	−0.140803	−	0.851421i
$178$	1.36180			0.102071
$179$	3.69233	−	6.39530i	0.275978	−	0.478007i	−0.694404	−	0.719586i	$-0.744332\pi$
$179$	3.69233	−	6.39530i	0.275978	−	0.478007i	0.970381	+	0.241578i	$0.0776651\pi$
$180$	5.45217	+	3.30448i	0.406381	+	0.246301i
$181$	−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	$0.230573\pi$
$182$	−8.09612	+	13.5626i	−0.600124	+	1.00533i
$183$	0.416534	−	2.22364i	0.0307911	−	0.164376i
$184$	−5.74884	−	1.01368i	−0.423810	−	0.0747291i
$185$	15.1759	−	12.7341i	1.11576	−	0.936232i
$186$	−2.84595	−	3.46591i	−0.208675	−	0.254133i
$187$	20.8931	−	17.5314i	1.52785	−	1.28202i
$188$	−1.73685	−	2.06990i	−0.126673	−	0.150963i
$189$	12.2125	−	6.31306i	0.888329	−	0.459207i
$190$	−1.17063	+	9.18897i	−0.0849264	+	0.666638i
$191$	−21.1226	−	12.1951i	−1.52838	−	0.882408i	−0.999430	−	0.0337522i	$-0.989254\pi$
$191$	−21.1226	−	12.1951i	−1.52838	−	0.882408i	−0.528945	−	0.848656i	$-0.677412\pi$
$192$	1.73195	+	0.0184316i	0.124993	+	0.00133018i
$193$	−17.4978	+	3.08533i	−1.25952	+	0.222087i	−0.763263	−	0.646088i	$-0.776404\pi$
$193$	−17.4978	+	3.08533i	−1.25952	+	0.222087i	−0.496257	+	0.868176i	$0.665293\pi$
$194$	−3.17345	+	3.78197i	−0.227840	+	0.271529i
$195$	−10.7843	−	19.1466i	−0.772278	−	1.37112i
$196$	−1.41589	+	6.85531i	−0.101135	+	0.489665i
$197$	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	$0.545360\pi$
$198$	−7.56370	−	9.41389i	−0.537529	−	0.669016i
$199$	0.583635	−	3.30996i	0.0413728	−	0.234637i	−0.957108	−	0.289730i	$-0.906434\pi$
$199$	0.583635	−	3.30996i	0.0413728	−	0.234637i	0.998481	+	0.0550932i	$0.0175456\pi$
$200$	−0.0840125	+	0.476459i	−0.00594058	+	0.0336907i
$201$	6.80477	+	19.3337i	0.479972	+	1.36369i
$202$	−1.18935	−	0.686671i	−0.0836823	−	0.0483140i
$203$	−8.25431	−	1.57980i	−0.579339	−	0.110880i
$204$	−10.2252	+	5.75931i	−0.715907	+	0.403233i
$205$	3.10052	−	3.69505i	0.216549	−	0.258074i
$206$	−1.94719	+	0.343342i	−0.135667	+	0.0239218i
$207$	−5.63807	−	16.5802i	−0.391873	−	1.15240i
$208$	−5.17022	−	2.98503i	−0.358490	−	0.206975i
$209$	8.03665	−	15.5974i	0.555906	−	1.07889i
$210$	−7.30001	−	6.44592i	−0.503748	−	0.444811i
$211$	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	$0.502521\pi$
$212$	−0.142441	+	0.119522i	−0.00978287	+	0.00820880i
$213$	−4.93064	+	4.04867i	−0.337842	+	0.277410i
$214$	2.23222	−	1.87305i	0.152591	−	0.128039i
$215$	−25.6063	−	4.51509i	−1.74634	−	0.307926i
$216$	2.45311	+	4.58064i	0.166913	+	0.311673i
$217$	3.33839	+	5.98190i	0.226625	+	0.406078i
$218$	−4.36851	+	5.20619i	−0.295873	+	0.352608i
$219$	18.3033	−	15.0293i	1.23682	−	1.01559i
$220$	−4.27720	+	7.40833i	−0.288369	+	0.499470i
$221$	40.4504			2.72099
$222$	15.9301	−	2.63443i	1.06916	−	0.176811i
$223$	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	$0.338967\pi$
$224$	−2.59859	−	0.497346i	−0.173625	−	0.0332303i
$225$	−1.37415	+	0.467278i	−0.0916100	+	0.0311519i
$226$	2.76049	+	15.6555i	0.183625	+	1.04139i
$227$	−6.90589	−	11.9613i	−0.458360	−	0.793902i	0.540515	−	0.841335i	$-0.318230\pi$
$227$	−6.90589	−	11.9613i	−0.458360	−	0.793902i	−0.998874	+	0.0474323i	$0.984896\pi$
$228$	−4.63461	+	5.95990i	−0.306935	+	0.394704i
$229$	3.25244	−	5.63339i	0.214927	−	0.372265i	−0.738323	−	0.674447i	$-0.764382\pi$
$229$	3.25244	−	5.63339i	0.214927	−	0.372265i	0.953250	+	0.302183i	$0.0977153\pi$
$230$	−9.50317	+	7.97411i	−0.626621	+	0.525797i
$231$	8.81757	+	16.2026i	0.580153	+	1.06605i
$232$	0.551587	−	3.12821i	0.0362135	−	0.205377i
$233$	7.71621	−	21.2001i	0.505505	−	1.38886i	−0.380324	−	0.924853i	$-0.624187\pi$
$233$	7.71621	−	21.2001i	0.505505	−	1.38886i	0.885829	−	0.464011i	$-0.153590\pi$
$234$	0.381159	−	17.9061i	0.0249172	−	1.17056i
$235$	−5.74225			−0.374583
$236$	−6.62871			−0.431493
$237$	5.67415	−	15.0881i	0.368576	−	0.980075i
$238$	16.9329	−	5.88510i	1.09760	−	0.381474i
$239$	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	$0.0421339\pi$
$240$	2.39587	−	2.79435i	0.154653	−	0.180374i
$241$	−0.659930	+	0.786475i	−0.0425099	+	0.0506613i	−0.786880	−	0.617105i	$-0.788305\pi$
$241$	−0.659930	+	0.786475i	−0.0425099	+	0.0506613i	0.744371	+	0.667767i	$0.232750\pi$
$242$	3.98607	−	3.34471i	0.256234	−	0.215006i
$243$	−8.50117	+	13.0664i	−0.545350	+	0.838208i
$244$	−1.22738	−	0.446730i	−0.0785749	−	0.0285989i
$245$	9.22596	+	11.6694i	0.589425	+	0.745531i
$246$	3.70835	−	1.30521i	0.236436	−	0.0832172i
$247$	24.0001	−	10.0591i	1.52709	−	0.640046i
$248$	−2.24232	+	1.29460i	−0.142387	+	0.0822074i
$249$	−0.113252	+	10.6420i	−0.00717708	+	0.674407i
$250$	7.49093	+	8.92735i	0.473768	+	0.564615i
$251$	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	$0.187142\pi$
$252$	−2.44559	−	7.55110i	−0.154058	−	0.475675i
$253$	22.0810	−	8.03681i	1.38822	−	0.505270i
$254$	−13.6823	+	7.89949i	−0.858505	+	0.495658i
$255$	−4.59185	+	24.5133i	−0.287553	+	1.53508i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	7.63428	−	2.77865i	0.476213	−	0.173327i	−0.0927517	−	0.995689i	$-0.529566\pi$
$257$	7.63428	−	2.77865i	0.476213	−	0.173327i	0.568965	+	0.822362i	$0.307344\pi$
$258$	−16.0881	−	13.7939i	−1.00160	−	0.858770i
$259$	−24.6614	−	0.359372i	−1.53239	−	0.0223303i
$260$	−11.9220	+	4.33927i	−0.739374	+	0.269110i
$261$	9.02203	−	3.06793i	0.558450	−	0.189900i
$262$	0.722404	+	1.98479i	0.0446303	+	0.122621i
$263$	−1.63952	+	0.289091i	−0.101097	+	0.0178261i	−0.223968	−	0.974597i	$-0.571901\pi$
$263$	−1.63952	+	0.289091i	−0.101097	+	0.0178261i	0.122871	+	0.992423i	$0.460790\pi$
$264$	−6.07478	+	3.42160i	−0.373877	+	0.210585i
$265$			0.395154i			0.0242741i
$266$	8.58314	−	7.70258i	0.526266	−	0.472275i
$267$	2.22491	−	0.783091i	0.136162	−	0.0479244i
$268$	11.6537	−	2.05487i	0.711865	−	0.125521i
$269$	−2.61483	−	14.8295i	−0.159429	−	0.904168i	−0.954624	−	0.297814i	$-0.903742\pi$
$269$	−2.61483	−	14.8295i	−0.159429	−	0.904168i	0.795195	−	0.606354i	$-0.207369\pi$
$270$	10.8080	+	2.26365i	0.657754	+	0.137762i
$271$	−3.13443	−	1.14084i	−0.190403	−	0.0693011i	0.245059	−	0.969508i	$-0.421193\pi$
$271$	−3.13443	−	1.14084i	−0.190403	−	0.0693011i	−0.435462	+	0.900207i	$0.643415\pi$
$272$	2.31737	+	6.36693i	0.140511	+	0.386052i
$273$	−5.42843	+	26.8143i	−0.328543	+	1.62287i
$274$	−0.192722	+	0.111268i	−0.0116427	+	0.00672194i
$275$	−0.666084	−	1.83005i	−0.0401664	−	0.110356i
$276$	−9.97540	+	1.64968i	−0.600448	+	0.0992989i
$277$	4.72473	−	8.18347i	0.283881	−	0.491697i	−0.688456	−	0.725278i	$-0.741711\pi$
$277$	4.72473	−	8.18347i	0.283881	−	0.491697i	0.972337	+	0.233581i	$0.0750445\pi$
$278$	−6.07532	−	10.5228i	−0.364373	−	0.631113i
$279$	−6.64278	−	4.02609i	−0.397693	−	0.241036i
$280$	−4.35934	+	3.55098i	−0.260521	+	0.212212i
$281$	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	$-0.200095\pi$
$282$	−4.02797	−	2.38306i	−0.239862	−	0.141909i
$283$	−28.6832	−	10.4398i	−1.70504	−	0.620583i	−0.708655	−	0.705555i	$-0.750698\pi$
$283$	−28.6832	−	10.4398i	−1.70504	−	0.620583i	−0.996383	+	0.0849718i	$0.972920\pi$
$284$	1.84171	+	3.18994i	0.109286	+	0.189288i
$285$	3.37147	+	15.6862i	0.199709	+	0.929169i
$286$	24.0316			1.42102
$287$	−5.92856	+	0.956515i	−0.349952	+	0.0564613i
$288$	2.84028	−	0.965833i	0.167365	−	0.0569123i
$289$	−22.1449	−	18.5818i	−1.30264	−	1.09304i
$290$	−4.33908	−	5.17111i	−0.254800	−	0.303658i
$291$	−3.01001	+	8.00387i	−0.176450	+	0.469195i
$292$	−6.83673	−	11.8416i	−0.400089	−	0.692975i
$293$	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	$0.812495\pi$
$294$	1.62880	+	12.0144i	0.0949938	+	0.700697i
$295$	−9.05488	+	10.7912i	−0.527196	+	0.628287i
$296$		−	9.32214i		−	0.541838i
$297$	−17.7710	−	11.0310i	−1.03118	−	0.640085i
$298$	−8.97671	+	10.6980i	−0.520007	+	0.619720i
$299$	32.7486	+	11.9195i	1.89390	+	0.689324i
$300$	0.136724	+	0.826752i	0.00789375	+	0.0477326i
$301$	20.4443	+	25.0983i	1.17839	+	1.44664i
$302$	9.53638	+	11.3650i	0.548757	+	0.653983i
$303$	−2.33803	−	0.437961i	−0.134316	−	0.0251602i
$304$	2.95826	+	3.20136i	0.169668	+	0.183611i
$305$	−2.40386	+	1.38787i	−0.137645	+	0.0794693i
$306$	−13.3941	+	15.2895i	−0.765692	+	0.874044i
$307$	−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	$0.995864\pi$
$308$	10.0598	−	3.49633i	0.573211	−	0.199222i
$309$	−2.98389	+	1.68067i	−0.169748	+	0.0956100i
$310$	−0.955484	+	5.41882i	−0.0542678	+	0.307768i
$311$			6.72464i			0.381320i	0.981656	+	0.190660i	$0.0610627\pi$
$311$			6.72464i			0.381320i	−0.981656	+	0.190660i	$0.938937\pi$
$312$	−10.1637	−	1.90386i	−0.575404	−	0.107785i
$313$	−8.95310	+	3.25866i	−0.506059	+	0.184191i	−0.582417	−	0.812890i	$-0.697893\pi$
$313$	−8.95310	+	3.25866i	−0.506059	+	0.184191i	0.0763581	+	0.997080i	$0.475671\pi$
$314$	−6.05410	−	5.08000i	−0.341653	−	0.286681i
$315$	−15.6335	−	6.33358i	−0.880847	−	0.356857i
$316$	−8.05986	−	4.65336i	−0.453403	−	0.261772i
$317$	1.50568	−	8.53916i	0.0845676	−	0.479607i	−0.912881	−	0.408225i	$-0.866148\pi$
$317$	1.50568	−	8.53916i	0.0845676	−	0.479607i	0.997449	−	0.0713820i	$-0.0227409\pi$
$318$	−0.163990	+	0.277185i	−0.00919613	+	0.0155438i
$319$	4.37320	+	12.0153i	0.244852	+	0.672726i
$320$	−1.36601	−	1.62795i	−0.0763622	−	0.0910050i
$321$	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
$324$	6.64198	+	6.07323i	0.368999	+	0.337402i
$325$	0.987879	−	2.71418i	0.0547977	−	0.150555i
$326$	2.77580	+	15.7424i	0.153737	+	0.871888i
$327$	−4.14353	+	11.0180i	−0.229137	+	0.609296i
$328$	−0.394140	−	2.23528i	−0.0217627	−	0.123423i
$329$	5.40891	+	4.67459i	0.298203	+	0.257719i
$330$	−2.72802	+	14.5634i	−0.150172	+	0.801687i
$331$			23.2724i			1.27916i	0.768723	+	0.639582i	$0.220893\pi$
$331$			23.2724i			1.27916i	−0.768723	+	0.639582i	$0.779107\pi$
$332$	6.05114	+	1.06698i	0.332099	+	0.0585581i
$333$	24.5117	−	13.4646i	1.34323	−	0.737856i
$334$	18.1427			0.992725
$335$	12.5739	−	21.7786i	0.686985	−	1.18989i
$336$	−4.53158	+	0.681731i	−0.247218	+	0.0371915i
$337$	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	$0.377463\pi$
$338$	17.3445	+	14.5537i	0.943415	+	0.791619i
$339$	13.5127	+	23.9907i	0.733910	+	1.30300i
$340$	13.5306	+	4.92473i	0.733799	+	0.267081i
$341$	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
$345$	−10.9409	+	18.4929i	−0.589038	+	0.995624i
$346$	3.41664	−	1.24356i	0.183680	−	0.0668539i
$347$	8.36504	+	9.96907i	0.449059	+	0.535168i	0.942320	−	0.334714i	$-0.108640\pi$
$347$	8.36504	+	9.96907i	0.449059	+	0.535168i	−0.493261	+	0.869881i	$0.664195\pi$
$348$	−0.897665	−	5.42807i	−0.0481199	−	0.290975i
$349$	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	$0.162373\pi$
$350$	0.0186510	−	1.27990i	0.000996938	−	0.0684136i
$351$	−9.67404	−	29.4743i	−0.516362	−	1.57322i
$352$	1.37675	+	3.78259i	0.0733811	+	0.201613i
$353$	0.839628	+	0.484760i	0.0446889	+	0.0258012i	0.522178	−	0.852837i	$-0.325120\pi$
$353$	0.839628	+	0.484760i	0.0446889	+	0.0258012i	−0.477489	+	0.878638i	$0.658453\pi$
$354$	−10.8300	+	3.81179i	−0.575610	+	0.202595i
$355$	7.70886	+	1.35928i	0.409144	+	0.0721430i
$356$	−0.236473	−	1.34111i	−0.0125331	−	0.0710786i
$357$	24.2809	−	19.3522i	1.28508	−	1.02423i
$358$	−6.93931	−	2.52570i	−0.366754	−	0.133487i
$359$	−10.9624	+	1.93297i	−0.578573	+	0.102018i	−0.455274	−	0.890351i	$-0.650459\pi$
$359$	−10.9624	+	1.93297i	−0.578573	+	0.102018i	−0.123299	+	0.992370i	$0.539348\pi$
$360$	2.30752	−	5.94315i	0.121617	−	0.313232i
$361$	−18.9132	+	1.81441i	−0.995430	+	0.0954951i
$362$	0.611287	+	0.352927i	0.0321285	+	0.0185494i
$363$	4.58912	−	7.75677i	0.240866	−	0.407125i
$364$	14.7624	+	5.61800i	0.773761	+	0.294463i
$365$	−28.6165	−	5.04586i	−1.49785	−	0.264112i
$366$	−2.26219	−	0.0240744i	−0.118247	−	0.00125839i
$367$	14.2448	+	11.9528i	0.743574	+	0.623933i	0.933795	−	0.357809i	$-0.116476\pi$
$367$	14.2448	+	11.9528i	0.743574	+	0.623933i	−0.190221	+	0.981741i	$0.560920\pi$
$368$			5.83752i			0.304302i
$369$	5.30818	−	4.26492i	0.276333	−	0.222023i
$370$	−15.1759	−	12.7341i	−0.788960	−	0.662016i
$371$	0.321683	−	0.372215i	0.0167010	−	0.0193245i
$372$	−2.91907	+	3.40456i	−0.151346	+	0.176518i
$373$	−15.5650	+	8.98646i	−0.805925	+	0.465301i	−0.845539	−	0.533914i	$-0.820721\pi$
$373$	−15.5650	+	8.98646i	−0.805925	+	0.465301i	0.0396135	+	0.999215i	$0.487387\pi$
$374$	−20.8931	−	17.5314i	−1.08035	−	0.906525i
$375$	17.3723	+	10.2780i	0.897104	+	0.530751i
$376$	−1.73685	+	2.06990i	−0.0895714	+	0.106747i
$377$	−6.48596	+	17.8200i	−0.334044	+	0.917778i
$378$	−8.33783	−	10.9307i	−0.428852	−	0.562216i
$379$			10.5738i			0.543138i	0.962419	+	0.271569i	$0.0875426\pi$
$379$			10.5738i			0.543138i	−0.962419	+	0.271569i	$0.912457\pi$
$380$	9.25265	−	0.442803i	0.474651	−	0.0227153i
$381$	−17.8117	+	20.7742i	−0.912522	+	1.06429i
$382$	−8.34195	+	22.9193i	−0.426812	+	1.17266i
$383$	12.7887	−	10.7310i	0.653473	−	0.548329i	−0.254649	−	0.967033i	$-0.581960\pi$
$383$	12.7887	−	10.7310i	0.653473	−	0.548329i	0.908123	+	0.418704i	$0.137516\pi$
$384$	−0.282599	−	1.70884i	−0.0144213	−	0.0872039i
$385$	8.04995	−	21.1529i	0.410263	−	1.07805i
$386$	6.07692	+	16.6962i	0.309307	+	0.849815i
$387$	−34.2169	−	13.2852i	−1.73934	−	0.675326i
$388$	4.27557	+	2.46850i	0.217059	+	0.125319i
$389$	−3.21757	−	0.567344i	−0.163137	−	0.0287655i	0.0914829	−	0.995807i	$-0.470839\pi$
$389$	−3.21757	−	0.567344i	−0.163137	−	0.0287655i	−0.254620	+	0.967041i	$0.581950\pi$
$390$	−16.9831	+	13.9452i	−0.859970	+	0.706143i
$391$	−19.7762	−	34.2534i	−1.00013	−	1.73227i
$392$	6.99703	+	0.203968i	0.353403	+	0.0103019i
$393$	2.32161	+	2.82735i	0.117110	+	0.142621i
$394$	3.57097	−	9.81116i	0.179903	−	0.494279i
$395$	−18.5853	+	6.76449i	−0.935127	+	0.340358i
$396$	−7.95745	+	9.08350i	−0.399877	+	0.456463i
$397$	5.65472	+	32.0695i	0.283802	+	1.60952i	0.709534	+	0.704672i	$0.248906\pi$
$397$	5.65472	+	32.0695i	0.283802	+	1.60952i	−0.425732	+	0.904850i	$0.639983\pi$
$398$	−3.36102			−0.168473
$399$	9.59389	−	17.5202i	0.480295	−	0.877107i
$400$	0.483809			0.0241904
$401$	4.02183	+	22.8089i	0.200841	+	1.13902i	0.903852	+	0.427845i	$0.140727\pi$
$401$	4.02183	+	22.8089i	0.200841	+	1.13902i	−0.703012	+	0.711178i	$0.748162\pi$
$402$	17.8583	−	10.0587i	0.890692	−	0.501680i
$403$	14.5255	−	5.28685i	0.723567	−	0.263357i
$404$	−0.469710	+	1.29052i	−0.0233690	+	0.0642057i
$405$	18.9599	−	2.51669i	0.942125	−	0.125056i
$406$	−0.122454	+	8.40324i	−0.00607728	+	0.417046i
$407$	18.7624	+	32.4975i	0.930020	+	1.61084i
$408$	7.44740	+	9.06975i	0.368701	+	0.449020i
$409$	3.59248	+	0.633451i	0.177637	+	0.0313221i	0.261759	−	0.965133i	$-0.415698\pi$
$409$	3.59248	+	0.633451i	0.177637	+	0.0313221i	−0.0841222	+	0.996455i	$0.526809\pi$
$410$	−4.17731	−	2.41177i	−0.206303	−	0.119109i
$411$	−0.250886	+	0.292613i	−0.0123753	+	0.0144336i
$412$	0.676251	+	1.85799i	0.0333165	+	0.0915364i
$413$	17.3140	−	2.79345i	0.851968	−	0.137457i
$414$	−15.3492	+	8.43153i	−0.754374	+	0.414387i
$415$	10.0029	−	8.39343i	0.491023	−	0.412017i
$416$	−2.04188	+	5.61002i	−0.100111	+	0.275054i
$417$	−15.9769	−	13.6986i	−0.782394	−	0.670823i
$418$	−16.7560	−	5.20610i	−0.819560	−	0.254639i
$419$			7.90283i			0.386078i	0.981191	+	0.193039i	$0.0618344\pi$
$419$			7.90283i			0.386078i	−0.981191	+	0.193039i	$0.938166\pi$
$420$	−5.08036	+	8.30842i	−0.247896	+	0.405410i
$421$	−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	$0.129572\pi$
$422$	14.2096	−	16.9344i	0.691715	−	0.824354i
$423$	−7.95128	−	1.57720i	−0.386605	−	0.0766861i
$424$	0.142441	+	0.119522i	0.00691754	+	0.00580450i
$425$	−2.83889	+	1.63903i	−0.137706	+	0.0795049i
$426$	4.84336	+	4.15269i	0.234662	+	0.201198i
$427$	3.39414	+	0.649608i	0.164254	+	0.0314368i
$428$	−2.23222	−	1.87305i	−0.107898	−	0.0905374i
$429$	39.2630	−	13.8192i	1.89563	−	0.667197i
$430$			26.0014i			1.25390i
$431$	14.7529	+	12.3792i	0.710622	+	0.596283i	0.924774	−	0.380518i	$-0.124254\pi$
$431$	14.7529	+	12.3792i	0.710622	+	0.596283i	−0.214151	+	0.976800i	$0.568699\pi$
$432$	4.08507	−	3.21127i	0.196543	−	0.154502i
$433$	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	$0.319571\pi$
$434$	5.31131	−	4.32642i	0.254951	−	0.207675i
$435$	−10.0628	−	5.95345i	−0.482476	−	0.285446i
$436$	5.88568	+	3.39810i	0.281873	+	0.162739i
$437$	−20.2517	−	15.4054i	−0.968770	−	0.736939i
$438$	−17.9793	−	15.4154i	−0.859085	−	0.736577i
$439$	12.1116	−	2.13561i	0.578056	−	0.101927i	0.123027	−	0.992403i	$-0.460740\pi$
$439$	12.1116	−	2.13561i	0.578056	−	0.101927i	0.455029	+	0.890476i	$0.349629\pi$
$440$	8.03851	+	2.92578i	0.383221	+	0.139481i
$441$	9.56997	+	18.6927i	0.455713	+	0.890127i
$442$	−7.02414	−	39.8359i	−0.334104	−	1.89480i
$443$	−22.6177	−	3.98811i	−1.07460	−	0.189481i	−0.391773	−	0.920062i	$-0.628138\pi$
$443$	−22.6177	−	3.98811i	−1.07460	−	0.189481i	−0.682826	+	0.730581i	$0.739249\pi$
$444$	−5.36063	−	15.2306i	−0.254404	−	0.722811i
$445$	−2.50628	−	1.44700i	−0.118809	−	0.0685944i
$446$	−3.32328	−	9.13063i	−0.157362	−	0.432348i
$447$	−8.51439	+	22.6405i	−0.402717	+	1.07086i
$448$	−0.0385504	+	2.64547i	−0.00182133	+	0.124987i
$449$	−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	$0.273162\pi$
$450$	0.698798	+	1.27213i	0.0329417	+	0.0599689i
$451$	5.87289	+	6.99903i	0.276543	+	0.329572i
$452$	14.9383	−	5.43711i	0.702640	−	0.255740i
$453$	22.1160	+	13.0844i	1.03910	+	0.614760i
$454$	−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	−0.764821	−	0.644243i	$-0.777173\pi$
$457$	3.75219	−	6.49899i	0.175520	−	0.304010i	0.940341	+	0.340233i	$0.110506\pi$
$458$	−6.11258	−	2.22480i	−0.285622	−	0.103958i
$459$	−13.0913	+	32.6823i	−0.611050	+	1.52548i
$460$	9.50317	+	7.97411i	0.443088	+	0.371795i
$461$	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	$0.291668\pi$
$462$	14.4252	−	11.4972i	0.671123	−	0.534896i
$463$	−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	$0.260333\pi$
$464$	−3.17646			−0.147464
$465$	1.55498	+	9.40275i	0.0721103	+	0.436042i
$466$	−22.2179	−	3.91762i	−1.02923	−	0.181480i
$467$		−	41.8523i		−	1.93669i	−0.249610	−	0.968346i	$-0.580303\pi$
$467$		−	41.8523i		−	1.93669i	0.249610	−	0.968346i	$-0.419697\pi$
$468$	−17.7003	+	2.73400i	−0.818195	+	0.126379i
$469$	−29.5733	+	10.2783i	−1.36557	+	0.474609i
$470$	0.997131	+	5.65501i	0.0459942	+	0.260846i
$471$	−12.8125	−	4.81837i	−0.590367	−	0.222019i
$472$	1.15106	+	6.52801i	0.0529820	+	0.300476i
$473$	16.8448	−	46.2806i	0.774523	−	2.12799i
$474$	−15.8441	−	2.96793i	−0.727746	−	0.136322i
$475$	−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
$478$	−15.7497	−	18.7698i	−0.720376	−	0.858511i
$479$	8.05372	+	22.1274i	0.367984	+	1.01103i	0.976127	+	0.217200i	$0.0696923\pi$
$479$	8.05372	+	22.1274i	0.367984	+	1.01103i	−0.608144	+	0.793827i	$0.708086\pi$
$480$	−3.16793	−	1.87424i	−0.144596	−	0.0855468i
$481$	−9.66417	+	54.8082i	−0.440648	+	2.49904i
$482$	0.889122	+	0.513335i	0.0404984	+	0.0233818i
$483$	25.3603	−	8.51271i	1.15393	−	0.387342i
$484$	−3.98607	−	3.34471i	−0.181185	−	0.152032i
$485$	9.85907	−	3.58841i	0.447677	−	0.162941i
$486$	14.3441	+	6.10307i	0.650661	+	0.276841i
$487$		−	0.0122637i		−	0.000555720i	−1.00000		0.000277860i	$-0.999912\pi$
$487$		−	0.0122637i		−	0.000555720i	1.00000		0.000277860i	$-8.84456e-5\pi$
$488$	−0.226811	+	1.28631i	−0.0102672	+	0.0582284i
$489$	13.5877	+	24.1238i	0.614455	+	1.09091i
$490$	9.89005	−	11.1122i	0.446787	−	0.501996i
$491$	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	$-0.0472277\pi$
$492$	−1.92933	−	3.42537i	−0.0869809	−	0.154428i
$493$	18.6389	−	10.7611i	0.839452	−	0.484658i
$494$	−14.0739	−	21.8887i	−0.633213	−	0.984821i
$495$	3.91750	+	25.3624i	0.176079	+	1.13996i
$496$	1.66431	+	1.98345i	0.0747297	+	0.0890594i
$497$	−6.15480	−	7.55592i	−0.276081	−	0.338929i
$498$	10.5000	−	1.73643i	0.470514	−	0.0778111i
$499$	−16.2720	−	5.92254i	−0.728437	−	0.265129i	−0.0489338	−	0.998802i	$-0.515582\pi$
$499$	−16.2720	−	5.92254i	−0.728437	−	0.265129i	−0.679503	+	0.733673i	$0.737805\pi$
$500$	7.49093	−	8.92735i	0.335005	−	0.399243i
$501$	29.6417	−	10.4328i	1.32429	−	0.466105i
$502$		−	29.0169i		−	1.29509i
$503$	−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	$0.399489\pi$
$504$	−7.01171	+	3.71967i	−0.312326	+	0.165687i
$505$	1.45927	+	2.52752i	0.0649365	+	0.112473i
$506$	−11.7490	−	20.3499i	−0.522308	−	0.904665i
$507$	36.7066	+	13.8042i	1.63020	+	0.613066i
$508$	10.1554	+	12.1027i	0.450572	+	0.536971i
$509$	−19.5597	−	16.4126i	−0.866970	−	0.727474i	0.0964881	−	0.995334i	$-0.469239\pi$
$509$	−19.5597	−	16.4126i	−0.866970	−	0.727474i	−0.963458	+	0.267860i	$0.913683\pi$
$510$	24.9383	+	0.265395i	1.10429	+	0.0117519i
$511$	22.8476	+	28.0488i	1.01072	+	1.24080i
$512$	−1.00000			−0.0441942
$513$	0.360008	+	22.6466i	0.0158947	+	0.999874i
$514$	−4.06211	−	7.03579i	−0.179172	−	0.310335i
$515$	3.94847	+	1.43712i	0.173990	+	0.0633273i
$516$	−10.7907	+	18.2390i	−0.475032	+	0.802925i
$517$	1.88873	−	10.7115i	0.0830662	−	0.471092i
$518$	3.92850	+	24.3492i	0.172609	+	1.06984i
$519$	4.86703	−	3.99644i	0.213639	−	0.175424i
$520$	6.34359	+	10.9874i	0.278185	+	0.481830i
$521$	−15.3192	+	26.5336i	−0.671145	+	1.16246i	0.306435	+	0.951892i	$0.400864\pi$
$521$	−15.3192	+	26.5336i	−0.671145	+	1.16246i	−0.977580	+	0.210566i	$0.932469\pi$
$522$	−4.58799	−	8.35223i	−0.200811	−	0.365567i
$523$	11.6011	+	31.8739i	0.507283	+	1.39375i	0.884029	+	0.467431i	$0.154821\pi$
$523$	11.6011	+	31.8739i	0.507283	+	1.39375i	−0.376747	+	0.926316i	$0.622957\pi$
$524$	1.82919	−	1.05608i	0.0799086	−	0.0461353i
$525$	−0.705526	−	2.10184i	−0.0307917	−	0.0917317i
$526$	0.569398	+	1.56441i	0.0248269	+	0.0682114i
$527$	−16.4853	−	6.00016i	−0.718112	−	0.261371i
$528$	4.42450	+	5.38834i	0.192552	+	0.234497i
$529$	−1.92344	−	10.9084i	−0.0836279	−	0.474278i
$530$	0.389151	−	0.0686178i	0.0169036	−	0.00298057i
$531$	−15.5023	+	12.4555i	−0.672740	+	0.540521i
$532$	−9.07600	−	7.11521i	−0.393495	−	0.308483i
$533$			13.5506i			0.586942i
$534$	−1.15755	−	2.05513i	−0.0500919	−	0.0889341i
$535$	−6.09846	+	1.07532i	−0.263659	+	0.0464903i
$536$	−4.04730	−	11.1199i	−0.174817	−	0.480305i
$537$	−12.7899	−	0.136111i	−0.551924	−	0.00587361i
$538$	−14.1501	+	5.15022i	−0.610055	+	0.222042i
$539$	−24.8025	+	13.3717i	−1.06832	+	0.575960i
$540$	0.352472	−	11.0369i	0.0151680	−	0.474952i
$541$	−33.6781	+	12.2578i	−1.44794	+	0.527006i	−0.942014	−	0.335574i	$-0.891070\pi$
$541$	−33.6781	+	12.2578i	−1.44794	+	0.527006i	−0.505922	+	0.862579i	$0.668848\pi$
$542$	−0.579220	+	3.28492i	−0.0248796	+	0.141099i
$543$	1.20167	+	0.225098i	0.0515687	+	0.00965988i
$544$	5.86780	−	3.38777i	0.251580	−	0.145250i
$545$	13.5718	−	4.93974i	0.581353	−	0.211595i
$546$	27.3496	+	0.689706i	1.17045	+	0.0295167i
$547$	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	$0.418699\pi$
$548$	0.143043	+	0.170472i	0.00611050	+	0.00728221i
$549$	−3.70983	+	1.26152i	−0.158332	+	0.0538405i
$550$	−1.68658	+	0.973750i	−0.0719162	+	0.0415208i
$551$	8.38277	−	11.0199i	0.357118	−	0.469463i
$552$	3.35682	+	9.53739i	0.142876	+	0.405938i
$553$	23.0132	+	8.75791i	0.978619	+	0.372424i
$554$	−8.87958	−	3.23190i	−0.377257	−	0.137310i
$555$	−32.1172	−	12.0783i	−1.36330	−	0.512695i
$556$	−9.30792	+	7.81028i	−0.394744	+	0.331229i
$557$	−4.90018	+	5.83981i	−0.207627	+	0.247441i	−0.859801	−	0.510629i	$-0.829413\pi$
$557$	−4.90018	+	5.83981i	−0.207627	+	0.247441i	0.652174	+	0.758069i	$0.273857\pi$
$558$	−2.81142	+	7.24099i	−0.119017	+	0.306535i
$559$	63.2585	−	36.5223i	2.67555	−	1.54473i
$560$	4.25402	+	3.67650i	0.179765	+	0.155360i
$561$	−44.2165	−	16.6285i	−1.86682	−	0.702054i
$562$	−24.1236			−1.01759
$563$	9.41398			0.396752			0.198376	−	0.980126i	$-0.436433\pi$
$563$	9.41398			0.396752			0.198376	+	0.980126i	$0.436433\pi$
$564$	−1.64740	+	4.38059i	−0.0693682	+	0.184456i
$565$	11.5546	−	31.7460i	0.486105	−	1.33556i
$566$	−5.30044	+	30.0603i	−0.222794	+	1.26353i
$567$	−19.9080	−	13.0641i	−0.836059	−	0.548640i
$568$	2.82167	−	2.36766i	0.118395	−	0.0993449i
$569$	−9.09323	+	15.7499i	−0.381208	+	0.660272i	−0.991235	−	0.132109i	$-0.957825\pi$
$569$	−9.09323	+	15.7499i	−0.381208	+	0.660272i	0.610027	+	0.792381i	$0.291159\pi$
$570$	14.8624	−	6.04412i	0.622518	−	0.253161i
$571$	−1.94938	−	3.37643i	−0.0815791	−	0.141299i	0.822349	−	0.568983i	$-0.192663\pi$
$571$	−1.94938	−	3.37643i	−0.0815791	−	0.141299i	−0.903928	+	0.427684i	$0.859330\pi$
$572$	−4.17304	−	23.6665i	−0.174484	−	0.989545i
$573$	−0.449550	+	42.2428i	−0.0187802	+	1.76472i
$574$	1.97147	+	5.67239i	0.0822874	+	0.236761i
$575$	−2.78134	+	0.490425i	−0.115990	+	0.0204521i
$576$	−1.44437	−	2.62941i	−0.0601820	−	0.109559i
$577$	−26.9468			−1.12181			−0.560905	−	0.827880i	$-0.689547\pi$
$577$	−26.9468			−1.12181			−0.560905	+	0.827880i	$0.689547\pi$
$578$	−14.4540	+	25.0351i	−0.601209	+	1.04132i
$579$	19.5296	+	23.7839i	0.811621	+	0.988425i
$580$	−4.33908	+	5.17111i	−0.180170	+	0.214719i
$581$	−16.2551	−	0.236872i	−0.674373	−	0.00982712i
$582$	8.40496	+	1.57442i	0.348397	+	0.0652619i
$583$	−0.737115	−	0.129973i	−0.0305282	−	0.00538295i
$584$	−10.4745	+	8.78913i	−0.433437	+	0.363697i
$585$	−19.7279	+	32.5498i	−0.815650	+	1.34577i
$586$	1.71565	−	1.43960i	0.0708727	−	0.0594693i
$587$	−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	$0.828367\pi$
$588$	11.5491	−	3.69035i	0.476276	−	0.152187i
$589$	−11.2732	+	0.539500i	−0.464504	+	0.0222297i
$590$	12.1996	+	7.04345i	0.502250	+	0.289974i
$591$	0.192440	−	18.0830i	0.00791594	−	0.743835i
$592$	−9.18052	+	1.61877i	−0.377317	+	0.0665312i
$593$	−28.4677	+	33.9265i	−1.16903	+	1.39319i	−0.265801	+	0.964028i	$0.585636\pi$
$593$	−28.4677	+	33.9265i	−1.16903	+	1.39319i	−0.903226	+	0.429165i	$0.858808\pi$
$594$	−7.77754	+	19.4166i	−0.319116	+	0.796671i
$595$	−37.4169	−	7.16126i	−1.53394	−	0.293583i
$596$	12.0943	+	6.98264i	0.495401	+	0.286020i
$597$	−5.49126	+	1.93273i	−0.224742	+	0.0791014i
$598$	6.05170	−	34.3209i	0.247472	−	1.40349i
$599$	2.71709	−	15.4094i	0.111017	−	0.629611i	−0.877628	−	0.479342i	$-0.840875\pi$
$599$	2.71709	−	15.4094i	0.111017	−	0.629611i	0.988645	−	0.150268i	$-0.0480137\pi$
$600$	0.790450	−	0.278211i	0.0322700	−	0.0113579i
$601$	−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	$0.938842\pi$
$602$	21.1669	−	24.4920i	0.862699	−	0.998218i
$603$	23.3929	−	26.7032i	0.952632	−	1.08744i
$604$	9.53638	−	11.3650i	0.388030	−	0.462436i
$605$	−10.8900	+	1.92020i	−0.442742	+	0.0780674i
$606$	−0.0253128	+	2.37856i	−0.00102826	+	0.0966225i
$607$	−4.85391	−	2.80241i	−0.197014	−	0.113746i	0.398248	−	0.917278i	$-0.369618\pi$
$607$	−4.85391	−	2.80241i	−0.197014	−	0.113746i	−0.595262	+	0.803532i	$0.702952\pi$
$608$	2.63903	−	3.46923i	0.107027	−	0.140696i
$609$	4.63216	+	13.7997i	0.187704	+	0.559192i
$610$	1.78421	+	2.12634i	0.0722407	+	0.0860931i
$611$	12.3574	−	10.3691i	0.499929	−	0.419490i
$612$	17.3831	+	10.5357i	0.702671	+	0.425879i
$613$	6.89916	−	5.78908i	0.278654	−	0.233819i	−0.492739	−	0.870177i	$-0.664004\pi$
$613$	6.89916	−	5.78908i	0.278654	−	0.233819i	0.771394	+	0.636358i	$0.219560\pi$
$614$	12.2237	+	2.15536i	0.493307	+	0.0869833i
$615$	−8.21180	−	1.53824i	−0.331132	−	0.0620278i
$616$	−5.19008	−	9.29985i	−0.209114	−	0.374701i
$617$	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	$0.0619436\pi$
$618$	2.17329	+	2.64672i	0.0874224	+	0.106467i
$619$	9.18185	−	15.9034i	0.369050	−	0.639213i	−0.620368	−	0.784311i	$-0.713017\pi$
$619$	9.18185	−	15.9034i	0.369050	−	0.639213i	0.989417	+	0.145099i	$0.0463499\pi$
$620$	5.50241			0.220982
$621$	−20.2292	+	22.6020i	−0.811770	+	0.906986i
$622$	6.62248	−	1.16772i	0.265537	−	0.0468214i
$623$	1.18283	+	3.40328i	0.0473890	+	0.136350i
$624$	−0.110037	+	10.3399i	−0.00440502	+	0.413926i
$625$	−3.88050	−	22.0074i	−0.155220	−	0.880295i
$626$	4.76385	+	8.25122i	0.190402	+	0.329785i
$627$	−30.3697	+	1.12963i	−1.21285	+	0.0451130i
$628$	−3.95154	+	6.84426i	−0.157683	+	0.273116i
$629$	48.3854	−	40.6002i	1.92925	−	1.61883i
$630$	−3.52264	+	16.4958i	−0.140345	+	0.657208i
$631$	−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	$0.849482\pi$
$632$	−3.18309	+	8.74546i	−0.126616	+	0.347876i
$633$	13.4778	−	35.8387i	0.535695	−	1.42446i
$634$	−8.67089			−0.344365
$635$	33.5749			1.33238
$636$	0.301451	+	0.113366i	0.0119533	+	0.00449527i
$637$	−40.9266	−	8.45295i	−1.62157	−	0.334918i
$638$	11.0733	−	6.39319i	0.438397	−	0.253109i
$639$	10.3011	+	3.99955i	0.407505	+	0.158220i
$640$	−1.36601	+	1.62795i	−0.0539963	+	0.0643502i
$641$	−19.5385	+	16.3948i	−0.771725	+	0.647554i	−0.941150	−	0.337989i	$-0.890253\pi$
$641$	−19.5385	+	16.3948i	−0.771725	+	0.647554i	0.169425	+	0.985543i	$0.445809\pi$
$642$	−4.72410	−	1.77659i	−0.186445	−	0.0701163i
$643$	−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	$0.617854\pi$
$644$	−2.46003	−	15.2475i	−0.0969387	−	0.600834i
$645$	14.9519	+	42.4812i	0.588730	+	1.67270i
$646$	−3.73231	+	29.2972i	−0.146846	+	1.15268i
$647$	37.9377	−	21.9033i	1.49148	−	0.861108i	0.491531	−	0.870860i	$-0.336437\pi$
$647$	37.9377	−	21.9033i	1.49148	−	0.861108i	0.999952	+	0.00975161i	$0.00310408\pi$
$648$	4.82760	−	7.59568i	0.189646	−	0.298386i
$649$	−17.1514	−	20.4403i	−0.673253	−	0.802351i
$650$	−2.84449	−	0.501560i	−0.111570	−	0.0196728i
$651$	6.18978	−	10.1228i	0.242597	−	0.396743i
$652$	15.0212	−	5.46726i	0.588275	−	0.214115i
$653$	37.3994	−	21.5926i	1.46355	−	0.844983i	0.464380	−	0.885636i	$-0.346277\pi$
$653$	37.3994	−	21.5926i	1.46355	−	0.844983i	0.999173	+	0.0406536i	$0.0129440\pi$
$654$	11.5701	+	2.16732i	0.452428	+	0.0847490i
$655$	0.779444	−	4.42045i	0.0304554	−	0.172721i
$656$	−2.13288	+	0.776304i	−0.0832749	+	0.0303096i
$657$	−38.2393	−	14.8470i	−1.49186	−	0.579235i
$658$	3.66433	−	6.13847i	0.142850	−	0.239303i
$659$	−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	$0.651805\pi$
$660$	14.8158	+	0.157671i	0.576705	+	0.00613734i
$661$	−3.44607	−	9.46799i	−0.134036	−	0.368262i	0.854458	−	0.519521i	$-0.173890\pi$
$661$	−3.44607	−	9.46799i	−0.134036	−	0.368262i	−0.988494	+	0.151259i	$0.951667\pi$
$662$	22.9188	−	4.04120i	0.890764	−	0.157066i
$663$	−34.3834	−	61.0450i	−1.33534	−	2.37079i
$664$		−	6.14449i		−	0.238452i
$665$	−23.9811	+	5.05581i	−0.929946	+	0.196056i
$666$	−17.5165	−	21.8012i	−0.678749	−	0.844781i
$667$	18.2610	−	3.21990i	0.707068	−	0.124675i
$668$	−3.15045	−	17.8671i	−0.121895	−	0.691298i
$669$	−10.6801	−	13.0067i	−0.412916	−	0.502867i
$670$	−23.6312	−	8.60105i	−0.912952	−	0.332287i
$671$	−1.79824	−	4.94063i	−0.0694204	−	0.190731i
$672$	1.45827	+	4.34436i	0.0562542	+	0.167587i
$673$	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	$0.0650379\pi$
$674$	−2.62297	−	7.20655i	−0.101033	−	0.277586i
$675$	1.87323	+	1.67658i	0.0721007	+	0.0645315i
$676$	11.3208	−	19.6082i	0.435416	−	0.754162i
$677$	−0.104769	−	0.181466i	−0.00402662	−	0.00697431i	0.864005	−	0.503483i	$-0.167948\pi$
$677$	−0.104769	−	0.181466i	−0.00402662	−	0.00697431i	−0.868032	+	0.496509i	$0.834615\pi$
$678$	21.2798	−	17.4734i	0.817246	−	0.671061i
$679$	−12.2080	−	4.64587i	−0.468498	−	0.178292i
$680$	2.50035	−	14.1802i	0.0958841	−	0.543786i
$681$	−12.1811	+	20.5892i	−0.466782	+	0.788980i
$682$	−9.79392	−	3.56469i	−0.375028	−	0.136499i
$683$	22.7187	+	39.3499i	0.869306	+	1.50568i	0.862707	+	0.505704i	$0.168767\pi$
$683$	22.7187	+	39.3499i	0.869306	+	1.50568i	0.00659954	+	0.999978i	$0.497899\pi$
$684$	12.9338	+	1.92824i	0.494534	+	0.0737281i
$685$	0.472918			0.0180693
$686$	−18.3620	+	2.41590i	−0.701065	+	0.0922396i
$687$	−11.2661	−	0.119895i	−0.429830	−	0.00457428i
$688$	9.37268	+	7.86461i	0.357330	+	0.299836i
$689$	−0.713553	−	0.850380i	−0.0271842	−	0.0323969i
$690$	20.1118	+	7.56343i	0.765643	+	0.287935i
$691$	15.1218	+	26.1918i	0.575262	+	0.996382i	0.996013	+	0.0892065i	$0.0284331\pi$
$691$	15.1218	+	26.1918i	0.575262	+	0.996382i	−0.420752	+	0.907176i	$0.638234\pi$
$692$	−1.81796	−	3.14879i	−0.0691083	−	0.119699i
$693$	16.9567	−	27.0793i	0.644132	−	1.02866i
$694$	8.36504	−	9.96907i	0.317533	−	0.378421i
$695$			25.8217i			0.979473i
$696$	−5.18973	+	1.82660i	−0.196716	+	0.0692372i
$697$	9.88536	−	11.7809i	0.374435	−	0.446234i
$698$	−0.473580	−	0.172369i	−0.0179253	−	0.00652426i
$699$	−38.5526	+	6.37562i	−1.45819	+	0.241148i
$700$	−1.26370	+	0.203885i	−0.0477632	+	0.00770613i
$701$	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	$0.736526\pi$
$702$	−27.3467	+	14.6452i	−1.03213	+	0.552749i
$703$	18.6117	−	36.1213i	0.701955	−	1.36234i
$704$	3.48606	−	2.01268i	0.131386	−	0.0758555i
$705$	4.88099	+	8.66581i	0.183829	+	0.326373i
$706$	0.331595	−	0.911050i	0.0124797	−	0.0342878i
$707$	0.683025	−	3.56874i	0.0256878	−	0.134216i
$708$	5.63450	+	10.0036i	0.211757	+	0.375958i
$709$	3.76539	−	21.3546i	0.141412	−	0.801989i	−0.828766	−	0.559596i	$-0.810956\pi$
$709$	3.76539	−	21.3546i	0.141412	−	0.801989i	0.970178	−	0.242393i	$-0.0779324\pi$
$710$		−	7.82778i		−	0.293771i
$711$	−27.5930	+	4.26203i	−1.03482	+	0.159839i
$712$	−1.27967	+	0.465762i	−0.0479577	+	0.0174552i
$713$	−11.5784	−	9.71545i	−0.433615	−	0.363846i
$714$	−23.2746	−	20.5515i	−0.871029	−	0.769121i
$715$	−44.2282	−	25.5352i	−1.65404	−	0.954961i
$716$	−1.28233	+	7.27247i	−0.0479230	+	0.271785i
$717$	−36.5255	−	21.6095i	−1.36407	−	0.807020i
$718$	3.80720	+	10.4602i	0.142084	+	0.390371i
$719$	31.0052	+	36.9506i	1.15630	+	1.37803i	0.912942	+	0.408089i	$0.133805\pi$
$719$	31.0052	+	36.9506i	1.15630	+	1.37803i	0.243359	+	0.969936i	$0.421751\pi$
$720$	−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
$723$	1.74784	+	0.327407i	0.0650030	+	0.0121764i
$724$	0.241416	−	0.663285i	0.00897216	−	0.0246508i
$725$	−0.266863	−	1.51345i	−0.00991103	−	0.0562083i
$726$	−8.43582	−	3.17245i	−0.313083	−	0.117741i
$727$	−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	$0.947946\pi$
$728$	2.96918	−	15.5137i	0.110045	−	0.574976i
$729$	26.9450	+	1.72278i	0.997962	+	0.0638066i
$730$			29.0579i			1.07548i
$731$	−81.6405	−	14.3954i	−3.01958	−	0.532434i
$732$	0.369117	+	2.23200i	0.0136429	+	0.0824972i
$733$	−24.6716			−0.911268			−0.455634	−	0.890167i	$-0.650587\pi$
$733$	−24.6716			−0.911268			−0.455634	+	0.890167i	$0.650587\pi$
$734$	9.29765	−	16.1040i	0.343183	−	0.594410i
$735$	9.76847	−	23.8423i	0.360315	−	0.879438i
$736$	5.74884	−	1.01368i	0.211905	−	0.0373646i
$737$	36.4898	+	30.6186i	1.34412	+	1.12785i
$738$	−5.12189	−	4.48694i	−0.188539	−	0.165167i
$739$	25.0764	+	9.12707i	0.922451	+	0.335745i	0.759213	−	0.650842i	$-0.225584\pi$
$739$	25.0764	+	9.12707i	0.922451	+	0.335745i	0.163238	+	0.986587i	$0.447806\pi$
$740$	−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	$0.948912\pi$
$744$	3.85973	+	2.28352i	0.141505	+	0.0837180i
$745$	27.8883	−	10.1505i	1.02175	−	0.371886i
$746$	11.5528	+	13.7681i	0.422977	+	0.504084i
$747$	16.1564	−	8.87490i	0.591131	−	0.324716i
$748$	−13.6370	+	23.6199i	−0.498617	+	0.863631i
$749$	6.61983	+	3.95167i	0.241883	+	0.144391i
$750$	7.10514	−	18.8932i	0.259443	−	0.689881i
$751$	8.53630	+	23.4533i	0.311494	+	0.855823i	0.992356	+	0.123411i	$0.0393832\pi$
$751$	8.53630	+	23.4533i	0.311494	+	0.855823i	−0.680862	+	0.732412i	$0.738395\pi$
$752$	2.34006	+	1.35103i	0.0853331	+	0.0492671i
$753$	−16.6859	−	47.4080i	−0.608069	−	1.72764i
$754$	18.6756	+	3.29301i	0.680124	+	0.119924i
$755$	−5.47486	−	31.0494i	−0.199250	−	1.13001i
$756$	−9.31681	+	10.1093i	−0.338849	+	0.367670i
$757$	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	$0.304914\pi$
$758$	10.4131	−	1.83612i	0.378222	−	0.0666908i
$759$	−30.8977	−	26.4917i	−1.12152	−	0.961586i
$760$	−2.04278	−	9.03519i	−0.0740995	−	0.327741i
$761$	11.1636	+	6.44533i	0.404682	+	0.233643i	0.688502	−	0.725234i	$-0.258269\pi$
$761$	11.1636	+	6.44533i	0.404682	+	0.233643i	−0.283820	+	0.958877i	$0.591602\pi$
$762$	23.5515	+	13.9337i	0.853182	+	0.504766i
$763$	−16.8053	−	6.39543i	−0.608391	−	0.231530i
$764$	24.0197	+	4.23532i	0.869002	+	0.153229i
$765$	40.8970	−	13.9070i	1.47863	−	0.502808i
$766$	−12.7887	−	10.7310i	−0.462075	−	0.387727i
$767$		−	39.5738i		−	1.42893i
$768$	−1.63381	+	0.575043i	−0.0589549	+	0.0207501i
$769$	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	$0.584409\pi$
$770$	−22.2294	−	4.25450i	−0.801090	−	0.153321i
$771$	−10.6826	−	9.15923i	−0.384724	−	0.329862i
$772$	15.3873	−	8.88387i	0.553801	−	0.319737i
$773$	4.32432	+	3.62854i	0.155535	+	0.130509i	0.717234	−	0.696832i	$-0.245408\pi$
$773$	4.32432	+	3.62854i	0.155535	+	0.130509i	−0.561699	+	0.827342i	$0.689852\pi$
$774$	−7.14169	+	36.0040i	−0.256703	+	1.29414i
$775$	−0.805208	+	0.959609i	−0.0289239	+	0.0344702i
$776$	1.68856	−	4.63927i	0.0606156	−	0.166540i
$777$	20.4202	+	37.5228i	0.732572	+	1.34612i
$778$			3.26721i			0.117135i
$779$	2.93555	−	9.44813i	0.105177	−	0.338514i
$780$	16.6824	+	14.3035i	0.597327	+	0.512147i
$781$	−5.07116	+	13.9329i	−0.181461	+	0.498559i
$782$	−30.2989	+	25.4238i	−1.08349	+	0.909153i
$783$	−12.2988	−	11.0076i	−0.439522	−	0.393381i
$784$	−1.01415	−	6.92615i	−0.0362197	−	0.247362i
$785$	5.74426	+	15.7822i	0.205021	+	0.563291i
$786$	2.38125	−	2.77730i	0.0849365	−	0.0990631i
$787$	−26.2042	−	15.1290i	−0.934078	−	0.539290i	−0.0459789	−	0.998942i	$-0.514641\pi$
$787$	−26.2042	−	15.1290i	−0.934078	−	0.539290i	−0.888099	+	0.459652i	$0.847974\pi$
$788$	−10.2822	−	1.81303i	−0.366288	−	0.0645865i
$789$	1.82989	+	2.22851i	0.0651457	+	0.0793371i
$790$	9.88902	+	17.1283i	0.351835	+	0.609397i
$791$	−36.7273	+	20.4969i	−1.30587	+	0.728784i
$792$	10.3273	+	6.25923i	0.366965	+	0.222412i
$793$	2.66700	−	7.32753i	0.0947080	−	0.260208i
$794$	30.6003	−	11.1376i	1.08597	−	0.395259i
$795$	0.596339	−	0.335887i	0.0211500	−	0.0119127i
$796$	0.583635	+	3.30996i	0.0206864	+	0.117318i
$797$	−25.2933			−0.895934			−0.447967	−	0.894050i	$-0.647852\pi$
$797$	−25.2933			−0.895934			−0.447967	+	0.894050i	$0.647852\pi$
$798$	−18.9200	−	6.40579i	−0.669760	−	0.226762i
$799$	−18.3080			−0.647690
$800$	−0.0840125	−	0.476459i	−0.00297029	−	0.0168454i
$801$	−3.07299	−	2.69205i	−0.108579	−	0.0951188i
$802$	21.7640	−	7.92146i	0.768514	−	0.279716i
$803$	18.8250	−	51.7211i	0.664318	−	1.82520i
$804$	−13.0069	−	15.8403i	−0.458718	−	0.558646i
$805$	−28.1825	−	16.8234i	−0.993301	−	0.592946i
$806$	−7.72886	−	13.3868i	−0.272238	−	0.471529i
$807$	−20.1570	+	16.5514i	−0.709559	+	0.582636i
$808$	1.35248	+	0.238478i	0.0475800	+	0.00838963i
$809$	31.4548	+	18.1604i	1.10589	+	0.638487i	0.937762	−	0.347278i	$-0.112894\pi$
$809$	31.4548	+	18.1604i	1.10589	+	0.638487i	0.168129	+	0.985765i	$0.446227\pi$
$810$	−5.77081	−	18.2348i	−0.202766	−	0.640707i
$811$	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	$0.682018\pi$
$812$	8.29684	−	1.33861i	0.291162	−	0.0469762i
$813$	0.942635	+	5.70000i	0.0330597	+	0.199908i
$814$	28.7457	−	24.1205i	1.00754	−	0.845424i
$815$	11.6187	−	31.9220i	0.406984	−	1.11818i
$816$	7.63874	−	8.90921i	0.267409	−	0.311885i
$817$	−52.0189	+	11.7610i	−1.81991	+	0.411467i
$818$		−	3.64790i		−	0.127546i
$819$	45.0805	−	14.6003i	1.57524	−	0.510176i
$820$	−1.64975	+	4.53265i	−0.0576118	+	0.158287i
$821$	16.1131	−	19.2028i	0.562350	−	0.670183i	−0.407692	−	0.913120i	$-0.633666\pi$
$821$	16.1131	−	19.2028i	0.562350	−	0.670183i	0.970042	+	0.242937i	$0.0781107\pi$
$822$	0.331734	+	0.196263i	0.0115705	+	0.00684545i
$823$	−13.5371	−	11.3590i	−0.471874	−	0.395949i	0.375604	−	0.926780i	$-0.377435\pi$
$823$	−13.5371	−	11.3590i	−0.471874	−	0.395949i	−0.847478	+	0.530831i	$0.821880\pi$
$824$	1.71233	−	0.988614i	0.0596518	−	0.0344400i
$825$	−2.19561	+	2.56078i	−0.0764412	+	0.0891548i
$826$	−5.75756	−	16.5659i	−0.200331	−	0.576402i
$827$	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	$0.502211\pi$
$828$	10.9688	+	13.6519i	0.381192	+	0.474437i
$829$			21.3696i			0.742198i	0.928593	+	0.371099i	$0.121019\pi$
$829$			21.3696i			0.742198i	−0.928593	+	0.371099i	$0.878981\pi$
$830$	−10.0029	−	8.39343i	−0.347206	−	0.291340i
$831$	−16.3660	−	0.174168i	−0.567731	−	0.00604183i
$832$	5.87936	+	1.03669i	0.203830	+	0.0359408i
$833$	29.4151	+	37.2055i	1.01917	+	1.28909i
$834$	−10.7161	+	18.1129i	−0.371069	+	0.627200i
$835$	−33.3902	−	19.2778i	−1.15552	−	0.667137i
$836$	−2.21737	+	17.4054i	−0.0766892	+	0.601979i
$837$	−0.429443	+	13.4471i	−0.0148437	+	0.464798i
$838$	7.78276	−	1.37231i	0.268851	−	0.0474057i
$839$	−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	$0.679391\pi$
$840$	9.06440	+	3.56044i	0.312751	+	0.122847i
$841$	−3.28370	−	18.6228i	−0.113231	−	0.642165i
$842$	2.34251	+	0.413048i	0.0807283	+	0.0142346i
$843$	−39.4133	+	13.8721i	−1.35747	+	0.477781i
$844$	−19.1446	−	11.0531i	−0.658985	−	0.380465i
$845$	−16.4568	−	45.2147i	−0.566131	−	1.55543i
$846$	−0.172514	+	8.10436i	−0.00593115	+	0.278634i
$847$	11.8210	+	7.05650i	0.406175	+	0.242464i
$848$	0.0929716	−	0.161032i	0.00319266	−	0.00552985i
$849$	8.62605	+	52.1607i	0.296045	+	1.79015i
$850$	2.10710	+	2.51115i	0.0722730	+	0.0861316i
$851$	51.1364	−	18.6121i	1.75293	−	0.638015i
$852$	3.24856	−	5.49088i	0.111294	−	0.188115i
$853$	−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
$857$	−46.1822	−	16.8090i	−1.57756	−	0.574183i	−0.602885	−	0.797828i	$-0.705982\pi$
$857$	−46.1822	−	16.8090i	−1.57756	−	0.574183i	−0.974671	+	0.223645i	$0.928204\pi$
$858$	−20.4272	−	36.2668i	−0.697373	−	1.23813i
$859$	−8.10805	−	6.80346i	−0.276643	−	0.232131i	0.493901	−	0.869518i	$-0.335571\pi$
$859$	−8.10805	−	6.80346i	−0.276643	−	0.232131i	−0.770544	+	0.637387i	$0.780015\pi$
$860$	25.6063	−	4.51509i	0.873169	−	0.153963i
$861$	6.48287	+	8.13392i	0.220936	+	0.277203i
$862$	9.62927	−	16.6784i	0.327974	−	0.568068i
$863$	−23.9721			−0.816021			−0.408011	−	0.912977i	$-0.633777\pi$
$863$	−23.9721			−0.816021			−0.408011	+	0.912977i	$0.633777\pi$
$864$	−3.87184	−	3.46538i	−0.131723	−	0.117894i
$865$	−7.60941	−	1.34174i	−0.258728	−	0.0456207i
$866$		−	28.1040i		−	0.955014i
$867$	−9.21884	+	49.2143i	−0.313088	+	1.67140i
$868$	−5.18299	−	4.47935i	−0.175922	−	0.152039i
$869$	−6.50535	−	36.8937i	−0.220679	−	1.25153i
$870$	−4.11561	+	10.9438i	−0.139532	+	0.371028i
$871$	12.2677	+	69.5735i	0.415674	+	2.35741i
$872$	2.32444	−	6.38634i	0.0787154	−	0.216269i
$873$	14.6374	−	2.26091i	0.495402	−	0.0765202i
$874$	−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
$877$	−16.4133	−	19.5606i	−0.554238	−	0.660516i	0.414078	−	0.910241i	$-0.364104\pi$
$877$	−16.4133	−	19.5606i	−0.554238	−	0.660516i	−0.968317	+	0.249726i	$0.919660\pi$
$878$	−4.20632	−	11.5568i	−0.141957	−	0.390022i
$879$	1.97521	−	3.33860i	0.0666220	−	0.112608i
$880$	1.48546	−	8.42444i	0.0500747	−	0.283988i
$881$	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	$0.496981\pi$
$882$	16.7469	−	12.6705i	0.563896	−	0.426639i
$883$	−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	$0.763421\pi$
$884$	−38.0110	+	13.8349i	−1.27845	+	0.465317i
$885$	23.9821	+	4.49234i	0.806149	+	0.151008i
$886$			22.9666i			0.771578i
$887$	2.37597	−	13.4748i	0.0797773	−	0.452439i	−0.918585	−	0.395224i	$-0.870667\pi$
$887$	2.37597	−	13.4748i	0.0797773	−	0.452439i	0.998362	−	0.0572150i	$-0.0182220\pi$
$888$	−14.0683	+	7.92395i	−0.472102	+	0.265910i
$889$	−31.6259	−	27.3323i	−1.06070	−	0.916697i
$890$	−0.989806	+	2.71947i	−0.0331784	+	0.0911568i
$891$	−1.54165	+	36.1953i	−0.0516471	+	1.21259i
$892$	−8.41483	+	4.85831i	−0.281749	+	0.162668i
$893$	−10.8625	+	4.55278i	−0.363500	+	0.152353i
$894$	23.7751	+	4.45356i	0.795157	+	0.148949i
$895$	10.0875	+	12.0218i	0.337188	+	0.401845i
$896$	2.61197	−	0.421416i	0.0872599	−	0.0140785i
$897$	−9.84867	−	59.5537i	−0.328838	−	1.98844i
$898$	13.0763	+	4.75939i	0.436362	+	0.158823i
$899$	5.28662	−	6.30035i	0.176319	−	0.210129i
$900$	1.13146	−	0.909085i	0.0377153	−	0.0303028i
$901$			1.25987i			0.0419723i
$902$	5.87289	−	6.99903i	0.195546	−	0.233042i
$903$	20.4987	−	52.1870i	0.682155	−	1.73668i
$904$	−7.94852	−	13.7672i	−0.264364	−	0.457892i
$905$	−0.750016	−	1.29907i	−0.0249314	−	0.0431824i
$906$	9.04524	−	24.0521i	0.300508	−	0.799077i
$907$	−2.25977	−	2.69309i	−0.0750344	−	0.0894226i	0.727221	−	0.686403i	$-0.240811\pi$
$907$	−2.25977	−	2.69309i	−0.0750344	−	0.0894226i	−0.802256	+	0.596981i	$0.796367\pi$
$908$	10.5804	+	8.87803i	0.351124	+	0.294628i
$909$	1.32642	+	3.90067i	0.0439945	+	0.129377i
$910$	−21.1996	−	26.0255i	−0.702758	−	0.862738i
$911$	32.1835			1.06629			0.533143	−	0.846025i	$-0.321011\pi$
$911$	32.1835			1.06629			0.533143	+	0.846025i	$0.321011\pi$
$912$	2.31671	−	7.18560i	0.0767138	−	0.237939i
$913$	12.3669	+	21.4200i	0.409283	+	0.708899i
$914$	−7.05182	−	2.56665i	−0.233253	−	0.0848973i
$915$	4.13780	+	2.44804i	0.136791	+	0.0809295i
$916$	−1.12956	+	6.40605i	−0.0373217	+	0.211662i
$917$	−4.33275	+	3.52932i	−0.143080	+	0.116548i
$918$	34.4591	+	7.21719i	1.13732	+	0.238203i
$919$	27.9345	+	48.3840i	0.921476	+	1.59604i	0.797134	+	0.603803i	$0.206349\pi$
$919$	27.9345	+	48.3840i	0.921476	+	1.59604i	0.124342	+	0.992239i	$0.460318\pi$
$920$	6.20276	−	10.7435i	0.204499	−	0.354202i
$921$	21.2105	−	3.50768i	0.698911	−	0.115582i
$922$	−6.78163	−	18.6324i	−0.223341	−	0.613625i
$923$	−19.0441	+	10.9951i	−0.626846	+	0.361910i
$924$	−13.8274	−	12.2096i	−0.454888	−	0.401668i
$925$	−1.54256	−	4.23814i	−0.0507189	−	0.139349i
$926$	11.7288	+	4.26892i	0.385431	+	0.140285i
$927$	5.07270	+	3.07449i	0.166609	+	0.100980i
$928$	0.551587	+	3.12821i	0.0181067	+	0.102688i
$929$	17.2150	−	3.03547i	0.564805	−	0.0995904i	0.116047	−	0.993244i	$-0.462978\pi$
$929$	17.2150	−	3.03547i	0.564805	−	0.0995904i	0.448758	+	0.893653i	$0.351866\pi$
$930$	8.98988	−	3.16412i	0.294790	−	0.103756i
$931$	26.7047	+	14.7600i	0.875213	+	0.483738i
$932$			22.5607i			0.739000i
$933$	10.1484	−	5.71604i	0.332243	−	0.187135i
$934$	−41.2165	+	7.26757i	−1.34864	+	0.237802i
$935$	19.8238	+	54.4653i	0.648306	+	1.78121i
$936$	5.76608	+	16.9566i	0.188470	+	0.554244i
$937$	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	$0.352239\pi$
$938$	15.2575	+	27.3392i	0.498176	+	0.892656i
$939$	12.5280	+	10.7415i	0.408836	+	0.350535i
$940$	5.39595	−	1.96397i	0.175996	−	0.0640575i
$941$	3.73287	−	21.1701i	0.121688	−	0.690127i	−0.861532	−	0.507703i	$-0.830495\pi$
$941$	3.73287	−	21.1701i	0.121688	−	0.690127i	0.983220	−	0.182423i	$-0.0583942\pi$
$942$	−2.52031	+	13.4545i	−0.0821160	+	0.438371i
$943$	11.4747	−	6.62489i	0.373666	−	0.215736i
$944$	6.22895	−	2.26715i	0.202735	−	0.0737896i
$945$	3.73048	+	28.9766i	0.121352	+	0.942609i
$946$	−48.5026	−	8.55232i	−1.57696	−	0.278060i
$947$	19.9189	+	23.7384i	0.647277	+	0.771395i	0.985501	−	0.169671i	$-0.0542705\pi$
$947$	19.9189	+	23.7384i	0.647277	+	0.771395i	−0.338224	+	0.941066i	$0.609826\pi$
$948$	−0.171537	+	16.1188i	−0.00557128	+	0.523515i
$949$	70.6949	−	40.8157i	2.29485	−	1.32493i
$950$	1.87465	+	0.965928i	0.0608218	+	0.0313388i
$951$	−14.1666	+	4.98613i	−0.459382	+	0.161686i
$952$	−13.8989	+	11.3216i	−0.450465	+	0.366934i
$953$	−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	$0.877311\pi$
$954$	0.557703	+	0.0118716i	0.0180563	+	0.000384356i
$955$	39.7060	−	33.3173i	1.28486	−	1.07812i
$956$	−15.7497	+	18.7698i	−0.509383	+	0.607059i
$957$	14.4153	−	16.8129i	0.465981	−	0.543483i
$958$	20.3927	−	11.7737i	0.658859	−	0.380392i
$959$	−0.445465	−	0.384988i	−0.0143848	−	0.0124319i
$960$	−1.29566	+	3.44526i	−0.0418172	+	0.111195i
$961$	24.2960			0.783742
$962$	55.6537			1.79435
$963$	−8.73988	−	0.186042i	−0.281639	−	0.00599511i
$964$	0.351142	−	0.964754i	0.0113095	−	0.0310726i
$965$	6.55675	−	37.1852i	0.211069	−	1.19703i
$966$	−12.7871	−	23.4968i	−0.411420	−	0.755997i
$967$	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
$969$	10.7492	+	50.0121i	0.345315	+	1.60662i
$970$	−5.24590	−	9.08617i	−0.168436	−	0.291739i
$971$	1.71325	+	9.71635i	0.0549809	+	0.311812i	0.999879	−	0.0155521i	$-0.00495060\pi$
$971$	1.71325	+	9.71635i	0.0549809	+	0.311812i	−0.944898	+	0.327365i	$0.893839\pi$
$972$	3.51953	−	15.1859i	0.112889	−	0.487089i
$973$	21.0207	−	24.3228i	0.673892	−	0.779752i
$974$	−0.0120774	+	0.00212956i	−0.000386984	+	6.82357e-5i
$975$	−4.93576	+	0.816249i	−0.158071	+	0.0261409i
$976$	1.30615			0.0418088
$977$	1.95106	−	3.37934i	0.0624200	−	0.108115i	−0.833127	−	0.553082i	$-0.813452\pi$
$977$	1.95106	−	3.37934i	0.0624200	−	0.108115i	0.895547	+	0.444968i	$0.146785\pi$
$978$	21.3978	−	17.5703i	0.684226	−	0.561835i
$979$	3.52357	−	4.19923i	0.112614	−	0.134208i
$980$	−12.6607	−	7.81019i	−0.404432	−	0.249488i
$981$	20.1496	−	3.11233i	0.643329	−	0.0993690i
$982$	−20.8257	−	3.67213i	−0.664574	−	0.117182i
$983$	−20.2666	+	17.0057i	−0.646405	+	0.542398i	−0.905978	−	0.423326i	$-0.860863\pi$
$983$	−20.2666	+	17.0057i	−0.646405	+	0.542398i	0.259573	+	0.965724i	$0.416418\pi$
$984$	−3.03830	+	2.49483i	−0.0968576	+	0.0795322i
$985$	−16.9971	+	14.2623i	−0.541572	+	0.454433i
$986$	−13.8343	−	16.4870i	−0.440573	−	0.525054i
$987$	2.45692	−	12.1362i	0.0782047	−	0.386300i
$988$	−19.1123	+	17.6610i	−0.608043	+	0.561871i
$989$	−61.8542	−	35.7115i	−1.96685	−	1.13556i
$990$	24.2969	−	8.26213i	0.772205	−	0.262588i
$991$	41.8613	−	7.38128i	1.32977	−	0.234474i	0.536786	−	0.843719i	$-0.319638\pi$
$991$	41.8613	−	7.38128i	1.32977	−	0.234474i	0.792982	+	0.609245i	$0.208527\pi$
$992$	1.66431	−	1.98345i	0.0528419	−	0.0629745i
$993$	35.1210	−	19.7818i	1.11453	−	0.627758i
$994$	−6.37236	+	7.37337i	−0.202119	+	0.233869i
$995$	6.18569	+	3.57131i	0.196099	+	0.113218i
$996$	−3.53334	−	10.0389i	−0.111958	−	0.318095i
$997$	5.45441	−	30.9335i	0.172743	−	0.979674i	−0.767974	−	0.640481i	$-0.778735\pi$
$997$	5.45441	−	30.9335i	0.172743	−	0.979674i	0.940717	−	0.339193i	$-0.110154\pi$
$998$	−3.00695	+	17.0533i	−0.0951834	+	0.539812i
$999$	−41.1552	−	25.5463i	−1.30209	−	0.808249i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.24	✓	162	21.11	odd	6
798.2.bu.a.611.24	yes	162	19.3	odd	18
798.2.bu.b.431.10	yes	162	7.4	even	3
798.2.bu.b.611.10	yes	162	57.41	even	18
798.2.cc.a.317.13	yes	162	3.2	odd	2
798.2.cc.a.725.13	yes	162	133.60	odd	18
798.2.cc.b.317.9	yes	162	1.1	even	1	trivial
798.2.cc.b.725.9	yes	162	399.326	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.850014 - 1.50913i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.726838 + 1.99697i) q^{5} +(-1.33860 + 1.09916i) q^{6} +(2.31032 - 1.28935i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.55495 + 2.56557i) q^{9} +(2.09285 + 0.369026i) q^{10} +(-3.48606 - 2.01268i) q^{11} +(1.31491 + 1.12740i) q^{12} +(-2.04188 - 5.61002i) q^{13} +(-1.67094 - 2.05133i) q^{14} +(3.63152 - 0.600560i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.31737 + 6.36693i) q^{17} +(2.79660 + 1.08582i) q^{18} +(0.208365 + 4.35392i) q^{19} -2.12513i q^{20} +(-3.90960 - 2.39061i) q^{21} +(-1.37675 + 3.78259i) q^{22} +(-3.75229 + 4.47180i) q^{23} +(0.881939 - 1.49070i) q^{24} +(0.370619 + 0.310986i) q^{25} +(-5.17022 + 2.98503i) q^{26} +(5.19350 + 0.165859i) q^{27} +(-1.73001 + 2.00177i) q^{28} +(-2.43331 - 2.04179i) q^{29} +(-1.22204 - 3.47206i) q^{30} +2.58921i q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.0741935 + 6.97172i) q^{33} +(6.67261 + 1.17656i) q^{34} +(0.895566 + 5.55079i) q^{35} +(0.583702 - 2.94267i) q^{36} +(-8.07321 - 4.66107i) q^{37} +(4.25159 - 0.961249i) q^{38} +(-6.73063 + 7.85006i) q^{39} +(-2.09285 + 0.369026i) q^{40} +(-2.13288 - 0.776304i) q^{41} +(-1.67540 + 4.26533i) q^{42} +(2.12461 + 12.0493i) q^{43} +(3.96420 + 0.698995i) q^{44} +(-3.99316 - 4.96995i) q^{45} +(5.05544 + 2.91876i) q^{46} +(0.924161 + 2.53911i) q^{47} +(-1.62120 - 0.609683i) q^{48} +(3.67516 - 5.95762i) q^{49} +(0.241904 - 0.418991i) q^{50} +(11.5783 - 1.91476i) q^{51} +(3.83748 + 4.57333i) q^{52} +(0.174729 - 0.0635963i) q^{53} +(-0.738503 - 5.14340i) 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} +(6.22895 + 2.26715i) q^{59} +(-3.20710 + 1.80639i) q^{60} +(1.00057 + 0.839577i) q^{61} +(2.54987 - 0.449611i) q^{62} +(-0.284525 + 7.93215i) q^{63} +(-0.500000 + 0.866025i) q^{64} +12.6872 q^{65} +(6.87868 - 1.13756i) q^{66} +(-11.6537 - 2.05487i) q^{67} -6.77555i q^{68} +(9.93803 + 1.86160i) q^{69} +(5.31095 - 1.84585i) q^{70} +(-0.639621 - 3.62747i) q^{71} +(-2.99932 - 0.0638452i) q^{72} +(2.37437 + 13.4657i) q^{73} +(-3.18836 + 8.75995i) q^{74} +(0.154288 - 0.823655i) q^{75} +(-1.68493 - 4.02008i) q^{76} +(-10.6489 - 0.155179i) q^{77} +(8.89956 + 5.26523i) q^{78} +(5.98225 + 7.12937i) q^{79} +(0.726838 + 1.99697i) q^{80} +(-4.16425 - 7.97866i) q^{81} +(-0.394140 + 2.23528i) q^{82} +(-5.32128 - 3.07224i) q^{83} +(4.49146 + 0.909275i) q^{84} +(-11.0302 - 9.25546i) q^{85} +(11.4973 - 4.18467i) q^{86} +(-1.01298 + 5.40774i) q^{87} -4.02535i q^{88} +(-0.236473 + 1.34111i) q^{89} +(-4.20104 + 4.79552i) q^{90} +(-11.9507 - 10.3282i) q^{91} +(1.99655 - 5.48548i) q^{92} +(3.90745 - 2.20086i) q^{93} +(2.34006 - 1.35103i) q^{94} +(-8.84610 - 2.74849i) q^{95} +(-0.318902 + 1.70244i) q^{96} +(-3.17345 - 3.78197i) q^{97} +(-6.50529 - 2.58479i) q^{98} +(10.5843 - 5.81409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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