LMFDB - Embedded newform 798.2.cc.a.725.13

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			725.13
Character	$\chi$	$=$	798.725
Dual form			798.2.cc.a.317.13

$q$-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} +(-0.282599 - 1.70884i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.726838 + 1.99697i) q^{5} +(-1.73195 - 0.0184316i) q^{6} +(2.31032 + 1.28935i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.84028 + 0.965833i) q^{9} +(2.09285 - 0.369026i) q^{10} +(3.48606 - 2.01268i) q^{11} +(-0.318902 + 1.70244i) q^{12} +(-2.04188 + 5.61002i) q^{13} +(1.67094 - 2.05133i) q^{14} +(3.20710 - 1.80639i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.31737 + 6.36693i) q^{17} +(0.457951 + 2.96484i) q^{18} +(0.208365 - 4.35392i) q^{19} -2.12513i q^{20} +(1.55040 - 4.31234i) q^{21} +(-1.37675 - 3.78259i) q^{22} +(3.75229 + 4.47180i) q^{23} +(1.62120 + 0.609683i) q^{24} +(0.370619 - 0.310986i) q^{25} +(5.17022 + 2.98503i) q^{26} +(2.45311 + 4.58064i) 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} +(-4.42450 - 5.38834i) q^{33} +(6.67261 - 1.17656i) q^{34} +(-0.895566 + 5.55079i) q^{35} +(2.99932 + 0.0638452i) q^{36} +(-8.07321 + 4.66107i) q^{37} +(-4.25159 - 0.961249i) q^{38} +(10.1637 + 1.90386i) q^{39} +(-2.09285 - 0.369026i) q^{40} +(2.13288 - 0.776304i) q^{41} +(-3.97760 - 2.27568i) 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} +(0.881939 - 1.49070i) q^{48} +(3.67516 + 5.95762i) q^{49} +(-0.241904 - 0.418991i) q^{50} +(10.2252 - 5.75931i) q^{51} +(3.83748 - 4.57333i) q^{52} +(-0.174729 - 0.0635963i) q^{53} +(4.93703 - 1.62043i) q^{54} +(6.55305 + 5.49867i) q^{55} +(-2.27177 + 1.35612i) q^{56} +(-7.49903 + 0.874349i) q^{57} +(-1.58823 - 2.75090i) q^{58} +(-6.22895 + 2.26715i) q^{59} +(-3.63152 + 0.600560i) q^{60} +(1.00057 - 0.839577i) q^{61} +(-2.54987 - 0.449611i) q^{62} +(-7.80724 - 1.43072i) q^{63} +(-0.500000 - 0.866025i) q^{64} -12.6872 q^{65} +(-6.07478 + 3.42160i) q^{66} +(-11.6537 + 2.05487i) q^{67} -6.77555i q^{68} +(6.58121 - 7.67579i) q^{69} +(5.31095 + 1.84585i) q^{70} +(0.639621 - 3.62747i) q^{71} +(0.583702 - 2.94267i) q^{72} +(2.37437 - 13.4657i) q^{73} +(3.18836 + 8.75995i) q^{74} +(-0.636163 - 0.545444i) q^{75} +(-1.68493 + 4.02008i) q^{76} +(10.6489 - 0.155179i) q^{77} +(3.63984 - 9.67866i) q^{78} +(5.98225 - 7.12937i) q^{79} +(-0.726838 + 1.99697i) q^{80} +(7.13433 - 5.48647i) q^{81} +(-0.394140 - 2.23528i) q^{82} +(5.32128 - 3.07224i) q^{83} +(-2.93181 + 3.52200i) q^{84} +(-11.0302 + 9.25546i) q^{85} +(-11.4973 - 4.18467i) q^{86} +(-4.17675 - 3.58114i) q^{87} +4.02535i q^{88} +(0.236473 + 1.34111i) q^{89} +(-5.58785 + 3.06948i) q^{90} +(-11.9507 + 10.3282i) q^{91} +(-1.99655 - 5.48548i) q^{92} +(-4.42454 + 0.731707i) q^{93} +(2.34006 + 1.35103i) q^{94} +(8.84610 - 2.74849i) q^{95} +(-1.31491 - 1.12740i) q^{96} +(-3.17345 + 3.78197i) q^{97} +(6.50529 - 2.58479i) q^{98} +(-7.95745 + 9.08350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 9 q^{14} + 27 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 - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 9 * q^14 + 27 * 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 - 3 * q^60 - 9 * q^61 + 36 * q^62 + 12 * 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 - 6 * q^78 + 21 * q^79 + 12 * q^81 - 3 * q^84 - 6 * q^85 + 36 * q^86 + 24 * q^87 - 54 * q^89 + 36 * q^90 + 75 * q^91 + 42 * q^93 + 72 * q^94 - 12 * q^97 + 12 * q^98 - 57 * q^99

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$	$-1$

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
$3$	−0.282599	−	1.70884i	−0.163159	−	0.986600i
$3$	−0.282599	−	1.70884i	−0.163159	−	0.986600i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.726838	+	1.99697i	0.325052	+	0.893073i	0.989344	+	0.145600i	$0.0465111\pi$
$5$	0.726838	+	1.99697i	0.325052	+	0.893073i	−0.664292	+	0.747474i	$0.731267\pi$
$6$	−1.73195	−	0.0184316i	−0.707067	−	0.00752465i
$7$	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
$9$	−2.84028	+	0.965833i	−0.946759	+	0.321944i
$10$	2.09285	−	0.369026i	0.661817	−	0.116696i
$11$	3.48606	−	2.01268i	1.05109	−	0.606844i	0.128132	−	0.991757i	$-0.459102\pi$
$11$	3.48606	−	2.01268i	1.05109	−	0.606844i	0.922953	+	0.384913i	$0.125768\pi$
$12$	−0.318902	+	1.70244i	−0.0920591	+	0.491452i
$13$	−2.04188	+	5.61002i	−0.566316	+	1.55594i	0.243895	+	0.969802i	$0.421575\pi$
$13$	−2.04188	+	5.61002i	−0.566316	+	1.55594i	−0.810211	+	0.586138i	$0.800648\pi$
$14$	1.67094	−	2.05133i	0.446579	−	0.548240i
$15$	3.20710	−	1.80639i	0.828071	−	0.466409i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	2.31737	+	6.36693i	0.562046	+	1.54421i	0.816632	+	0.577158i	$0.195838\pi$
$17$	2.31737	+	6.36693i	0.562046	+	1.54421i	−0.254586	+	0.967050i	$0.581939\pi$
$18$	0.457951	+	2.96484i	0.107940	+	0.698820i
$19$	0.208365	−	4.35392i	0.0478022	−	0.998857i
$19$	0.208365	−	4.35392i	0.0478022	−	0.998857i
$20$		−	2.12513i		−	0.475194i
$21$	1.55040	−	4.31234i	0.338325	−	0.941029i
$22$	−1.37675	−	3.78259i	−0.293524	−	0.806451i
$23$	3.75229	+	4.47180i	0.782406	+	0.932435i	0.999040	−	0.0438179i	$-0.0139521\pi$
$23$	3.75229	+	4.47180i	0.782406	+	0.932435i	−0.216634	+	0.976253i	$0.569508\pi$
$24$	1.62120	+	0.609683i	0.330926	+	0.124451i
$25$	0.370619	−	0.310986i	0.0741238	−	0.0621972i
$26$	5.17022	+	2.98503i	1.01396	+	0.585412i
$27$	2.45311	+	4.58064i	0.472102	+	0.881544i
$28$	−1.73001	−	2.00177i	−0.326941	−	0.378299i
$29$	2.43331	−	2.04179i	0.451855	−	0.379151i	−0.388269	−	0.921546i	$-0.626927\pi$
$29$	2.43331	−	2.04179i	0.451855	−	0.379151i	0.840124	+	0.542395i	$0.182482\pi$
$30$	−1.22204	−	3.47206i	−0.223113	−	0.633908i
$31$		−	2.58921i		−	0.465035i	−0.972592	−	0.232518i	$-0.925304\pi$
$31$		−	2.58921i		−	0.465035i	0.972592	−	0.232518i	$-0.0746964\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−4.42450	−	5.38834i	−0.770206	−	0.937989i
$34$	6.67261	−	1.17656i	1.14434	−	0.201779i
$35$	−0.895566	+	5.55079i	−0.151378	+	0.938255i
$36$	2.99932	+	0.0638452i	0.499887	+	0.0106409i
$37$	−8.07321	+	4.66107i	−1.32723	+	0.766275i	−0.984870	−	0.173294i	$-0.944559\pi$
$37$	−8.07321	+	4.66107i	−1.32723	+	0.766275i	−0.342358	+	0.939570i	$0.611225\pi$
$38$	−4.25159	−	0.961249i	−0.689699	−	0.155935i
$39$	10.1637	+	1.90386i	1.62749	+	0.304862i
$40$	−2.09285	−	0.369026i	−0.330908	−	0.0583481i
$41$	2.13288	−	0.776304i	0.333100	−	0.121238i	−0.170055	−	0.985435i	$-0.554395\pi$
$41$	2.13288	−	0.776304i	0.333100	−	0.121238i	0.503155	+	0.864196i	$0.332172\pi$
$42$	−3.97760	−	2.27568i	−0.613757	−	0.351144i
$43$	2.12461	−	12.0493i	0.324001	−	1.83750i	−0.192606	−	0.981276i	$-0.561694\pi$
$43$	2.12461	−	12.0493i	0.324001	−	1.83750i	0.516607	−	0.856223i	$-0.327195\pi$
$44$	−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	$-0.952031\pi$
$47$	−0.924161	+	2.53911i	−0.134803	+	0.370367i	0.853864	+	0.520497i	$0.174253\pi$
$48$	0.881939	−	1.49070i	0.127297	−	0.215164i
$49$	3.67516	+	5.95762i	0.525022	+	0.851089i
$50$	−0.241904	−	0.418991i	−0.0342104	−	0.0592542i
$51$	10.2252	−	5.75931i	1.43181	−	0.806465i
$52$	3.83748	−	4.57333i	0.532163	−	0.634207i
$53$	−0.174729	−	0.0635963i	−0.0240009	−	0.00873563i	0.329992	−	0.943984i	$-0.392954\pi$
$53$	−0.174729	−	0.0635963i	−0.0240009	−	0.00873563i	−0.353993	+	0.935248i	$0.615176\pi$
$54$	4.93703	−	1.62043i	0.671844	−	0.220512i
$55$	6.55305	+	5.49867i	0.883614	+	0.741440i
$56$	−2.27177	+	1.35612i	−0.303578	+	0.181219i
$57$	−7.49903	+	0.874349i	−0.993271	+	0.115810i
$58$	−1.58823	−	2.75090i	−0.208545	−	0.361211i
$59$	−6.22895	+	2.26715i	−0.810941	+	0.295158i	−0.714012	−	0.700133i	$-0.753124\pi$
$59$	−6.22895	+	2.26715i	−0.810941	+	0.295158i	−0.0969283	+	0.995291i	$0.530902\pi$
$60$	−3.63152	+	0.600560i	−0.468827	+	0.0775320i
$61$	1.00057	−	0.839577i	0.128110	−	0.107497i	−0.576482	−	0.817110i	$-0.695575\pi$
$61$	1.00057	−	0.839577i	0.128110	−	0.107497i	0.704591	+	0.709613i	$0.251130\pi$
$62$	−2.54987	−	0.449611i	−0.323834	−	0.0571007i
$63$	−7.80724	−	1.43072i	−0.983620	−	0.180254i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−12.6872			−1.57365
$66$	−6.07478	+	3.42160i	−0.747754	+	0.421170i
$67$	−11.6537	+	2.05487i	−1.42373	+	0.251042i	−0.831857	−	0.554990i	$-0.812722\pi$
$67$	−11.6537	+	2.05487i	−1.42373	+	0.251042i	−0.591873	+	0.806032i	$0.701611\pi$
$68$		−	6.77555i		−	0.821656i
$69$	6.58121	−	7.67579i	0.792284	−	0.924056i
$70$	5.31095	+	1.84585i	0.634780	+	0.220621i
$71$	0.639621	−	3.62747i	0.0759090	−	0.430501i	−0.923042	−	0.384700i	$-0.874305\pi$
$71$	0.639621	−	3.62747i	0.0759090	−	0.430501i	0.998951	−	0.0458012i	$-0.0145841\pi$
$72$	0.583702	−	2.94267i	0.0687899	−	0.346797i
$73$	2.37437	−	13.4657i	0.277899	−	1.57604i	−0.451700	−	0.892170i	$-0.649182\pi$
$73$	2.37437	−	13.4657i	0.277899	−	1.57604i	0.729599	−	0.683875i	$-0.239707\pi$
$74$	3.18836	+	8.75995i	0.370639	+	1.01832i
$75$	−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
$78$	3.63984	−	9.67866i	0.412131	−	1.09589i
$79$	5.98225	−	7.12937i	0.673056	−	0.802116i	−0.316141	−	0.948712i	$-0.602387\pi$
$79$	5.98225	−	7.12937i	0.673056	−	0.802116i	0.989196	+	0.146596i	$0.0468317\pi$
$80$	−0.726838	+	1.99697i	−0.0812630	+	0.223268i
$81$	7.13433	−	5.48647i	0.792704	−	0.609607i
$82$	−0.394140	−	2.23528i	−0.0435255	−	0.246845i
$83$	5.32128	−	3.07224i	0.584087	−	0.337223i	−0.178669	−	0.983909i	$-0.557179\pi$
$83$	5.32128	−	3.07224i	0.584087	−	0.337223i	0.762756	+	0.646687i	$0.223846\pi$
$84$	−2.93181	+	3.52200i	−0.319886	+	0.384282i
$85$	−11.0302	+	9.25546i	−1.19640	+	1.00390i
$86$	−11.4973	−	4.18467i	−1.23979	−	0.451245i
$87$	−4.17675	−	3.58114i	−0.447795	−	0.383938i
$88$			4.02535i			0.429104i
$89$	0.236473	+	1.34111i	0.0250661	+	0.142157i	0.994772	−	0.102117i	$-0.0325615\pi$
$89$	0.236473	+	1.34111i	0.0250661	+	0.142157i	−0.969706	+	0.244274i	$0.921450\pi$
$90$	−5.58785	+	3.06948i	−0.589011	+	0.323551i
$91$	−11.9507	+	10.3282i	−1.25277	+	1.08269i
$92$	−1.99655	−	5.48548i	−0.208155	−	0.571900i
$93$	−4.42454	+	0.731707i	−0.458804	+	0.0758745i
$94$	2.34006	+	1.35103i	0.241359	+	0.139348i
$95$	8.84610	−	2.74849i	0.907590	−	0.281990i
$96$	−1.31491	−	1.12740i	−0.134202	−	0.115064i
$97$	−3.17345	+	3.78197i	−0.322215	+	0.384001i	−0.902700	−	0.430270i	$-0.858418\pi$
$97$	−3.17345	+	3.78197i	−0.322215	+	0.384001i	0.580485	+	0.814271i	$0.302863\pi$
$98$	6.50529	−	2.58479i	0.657134	−	0.261103i
$99$	−7.95745	+	9.08350i	−0.799754	+	0.912926i
$100$	−0.454631	+	0.165472i	−0.0454631	+	0.0165472i
$101$	−0.882767	−	1.05204i	−0.0878386	−	0.104682i	0.720335	−	0.693626i	$-0.243988\pi$
$101$	−0.882767	−	1.05204i	−0.0878386	−	0.104682i	−0.808174	+	0.588944i	$0.799544\pi$
$102$	−3.89623	−	11.0699i	−0.385784	−	1.09609i
$103$			1.97723i			0.194822i	0.995244	+	0.0974110i	$0.0310561\pi$
$103$			1.97723i			0.194822i	−0.995244	+	0.0974110i	$0.968944\pi$
$104$	−3.83748	−	4.57333i	−0.376296	−	0.448452i
$105$	9.73851	−	0.0382679i	0.950381	−	0.00373456i
$106$	−0.0929716	+	0.161032i	−0.00903020	+	0.0156408i
$107$	−1.45698	+	2.52356i	−0.140851	+	0.243961i	−0.927817	−	0.373035i	$-0.878317\pi$
$107$	−1.45698	+	2.52356i	−0.140851	+	0.243961i	0.786966	+	0.616996i	$0.211651\pi$
$108$	−0.738503	−	5.14340i	−0.0710625	−	0.494924i
$109$	−4.36851	+	5.20619i	−0.418428	+	0.498663i	−0.933547	−	0.358456i	$-0.883303\pi$
$109$	−4.36851	+	5.20619i	−0.418428	+	0.498663i	0.515119	+	0.857119i	$0.327748\pi$
$110$	6.55305	−	5.49867i	0.624809	−	0.524277i
$111$	10.2465	+	12.4786i	0.972556	+	1.18442i
$112$	0.941030	+	2.47274i	0.0889189	+	0.233652i
$113$	15.8970			1.49547			0.747734	−	0.663998i	$-0.231142\pi$
$113$	15.8970			1.49547			0.747734	+	0.663998i	$0.231142\pi$
$114$	−0.441127	+	7.53694i	−0.0413154	+	0.705899i
$115$	−6.20276	+	10.7435i	−0.578410	+	1.00184i
$116$	−2.98490	+	1.08641i	−0.277141	+	0.100871i
$117$	0.381159	−	17.9061i	0.0352382	−	1.65542i
$118$	1.15106	+	6.52801i	0.105964	+	0.600952i
$119$	−2.85533	+	17.6976i	−0.261747	+	1.62233i
$120$	−0.0391695	+	3.68063i	−0.00357567	+	0.335994i
$121$	2.60172	−	4.50631i	0.236520	−	0.409665i
$122$	−0.653075	−	1.13116i	−0.0591266	−	0.102410i
$123$	−1.92933	−	3.42537i	−0.173962	−	0.308855i
$124$	−0.885561	+	2.43306i	−0.0795257	+	0.218495i
$125$	10.0925	+	5.82691i	0.902701	+	0.521175i
$126$	−2.76470	+	7.44019i	−0.246299	+	0.662825i
$127$	−5.40357	+	14.8462i	−0.479489	+	1.31739i	0.430439	+	0.902620i	$0.358359\pi$
$127$	−5.40357	+	14.8462i	−0.479489	+	1.31739i	−0.909928	+	0.414766i	$0.863863\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−21.1907	−	0.225513i	−1.86574	−	0.0198553i
$130$	−2.20310	+	12.4944i	−0.193225	+	1.09583i
$131$	2.08008	+	0.366774i	0.181737	+	0.0320452i	0.263776	−	0.964584i	$-0.415032\pi$
$131$	2.08008	+	0.366774i	0.181737	+	0.0320452i	−0.0820387	+	0.996629i	$0.526143\pi$
$132$	2.31475	+	6.57665i	0.201473	+	0.572424i
$133$	6.09511	−	9.79028i	0.528513	−	0.848925i
$134$			11.8335i			1.02226i
$135$	−7.36439	+	8.22818i	−0.633825	+	0.708169i
$136$	−6.67261	−	1.17656i	−0.572172	−	0.100889i
$137$	0.0761117	−	0.209115i	0.00650266	−	0.0178659i	−0.936399	−	0.350938i	$-0.885863\pi$
$137$	0.0761117	−	0.209115i	0.00650266	−	0.0178659i	0.942901	+	0.333072i	$0.108085\pi$
$138$	−6.41636	−	7.81411i	−0.546197	−	0.665181i
$139$	11.4179	+	4.15576i	0.968450	+	0.352487i	0.777339	−	0.629081i	$-0.216569\pi$
$139$	11.4179	+	4.15576i	0.968450	+	0.352487i	0.191111	+	0.981568i	$0.438791\pi$
$140$	2.74004	−	4.90974i	0.231576	−	0.414949i
$141$	4.60010	+	0.861694i	0.387399	+	0.0725677i
$142$	−3.46129	−	1.25981i	−0.290465	−	0.105721i
$143$	4.17304	+	23.6665i	0.348967	+	1.97909i
$144$	−2.79660	−	1.08582i	−0.233050	−	0.0904852i
$145$	5.84603	+	3.37521i	0.485486	+	0.280296i
$146$	−12.8489	−	4.67660i	−1.06338	−	0.387038i
$147$	9.14203	−	7.96387i	0.754022	−	0.656849i
$148$	9.18052	−	1.61877i	0.754634	−	0.133062i
$149$	8.97671	−	10.6980i	0.735401	−	0.876417i	−0.260629	−	0.965439i	$-0.583930\pi$
$149$	8.97671	−	10.6980i	0.735401	−	0.876417i	0.996030	+	0.0890225i	$0.0283743\pi$
$150$	−0.647626	+	0.531782i	−0.0528785	+	0.0434198i
$151$	−12.8483	−	7.41799i	−1.04558	−	0.603667i	−0.124173	−	0.992261i	$-0.539628\pi$
$151$	−12.8483	−	7.41799i	−1.04558	−	0.603667i	−0.921409	+	0.388593i	$0.872961\pi$
$152$	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
$156$	−8.89956	−	5.26523i	−0.712535	−	0.421555i
$157$	6.05410	+	5.08000i	0.483170	+	0.405428i	0.851571	−	0.524239i	$-0.175650\pi$
$157$	6.05410	+	5.08000i	0.483170	+	0.405428i	−0.368401	+	0.929667i	$0.620095\pi$
$158$	−5.98225	−	7.12937i	−0.475922	−	0.567182i
$159$	−0.0592977	+	0.316557i	−0.00470261	+	0.0251046i
$160$	1.84042	+	1.06257i	0.145498	+	0.0840033i
$161$	2.90327	+	15.1693i	0.228810	+	1.19551i
$162$	−4.16425	−	7.97866i	−0.327174	−	0.626863i
$163$	−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
$165$	7.54446	−	12.7520i	0.587335	−	0.992745i
$166$	−2.10154	−	5.77393i	−0.163111	−	0.448144i
$167$	3.15045	+	17.8671i	0.243789	+	1.38260i	0.823288	+	0.567624i	$0.192137\pi$
$167$	3.15045	+	17.8671i	0.243789	+	1.38260i	−0.579499	+	0.814973i	$0.696752\pi$
$168$	2.95939	+	3.49885i	0.228322	+	0.269942i
$169$	−17.3445	−	14.5537i	−1.33419	−	1.11952i
$170$	7.19947	+	12.4699i	0.552174	+	0.956394i
$171$	3.61334	+	12.5676i	0.276319	+	0.961066i
$172$	−6.11758	+	10.5960i	−0.466461	+	0.807935i
$173$	−0.631369	+	3.58067i	−0.0480021	+	0.272234i	−0.999357	−	0.0358647i	$-0.988581\pi$
$173$	−0.631369	+	3.58067i	−0.0480021	+	0.272234i	0.951355	+	0.308098i	$0.0996926\pi$
$174$	−4.25202	+	3.49144i	−0.322345	+	0.264685i
$175$	1.25722	−	0.240620i	0.0950368	−	0.0181892i
$176$	3.96420	+	0.698995i	0.298813	+	0.0526887i
$177$	5.63450	+	10.0036i	0.423515	+	0.751916i
$178$	1.36180			0.102071
$179$	−3.69233	−	6.39530i	−0.275978	−	0.478007i	0.694404	−	0.719586i	$-0.255668\pi$
$179$	−3.69233	−	6.39530i	−0.275978	−	0.478007i	−0.970381	+	0.241578i	$0.922335\pi$
$180$	2.05252	+	6.03596i	0.152986	+	0.449894i
$181$	−0.453714	−	0.540715i	−0.0337243	−	0.0401910i	0.748919	−	0.662662i	$-0.230573\pi$
$181$	−0.453714	−	0.540715i	−0.0337243	−	0.0401910i	−0.782643	+	0.622471i	$0.786129\pi$
$182$	8.09612	+	13.5626i	0.600124	+	1.00533i
$183$	−1.71746	−	1.47255i	−0.126959	−	0.108854i
$184$	−5.74884	+	1.01368i	−0.423810	+	0.0747291i
$185$	−15.1759	−	12.7341i	−1.11576	−	0.936232i
$186$	−0.0477231	+	4.48438i	−0.00349923	+	0.328811i
$187$	20.8931	+	17.5314i	1.52785	+	1.28202i
$188$	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	$-0.0107457\pi$
$192$	−1.33860	+	1.09916i	−0.0966052	+	0.0793249i
$193$	−17.4978	−	3.08533i	−1.25952	−	0.222087i	−0.496257	−	0.868176i	$-0.665293\pi$
$193$	−17.4978	−	3.08533i	−1.25952	−	0.222087i	−0.763263	+	0.646088i	$0.776404\pi$
$194$	3.17345	+	3.78197i	0.227840	+	0.271529i
$195$	3.58538	+	21.6804i	0.256754	+	1.55256i
$196$	−1.41589	−	6.85531i	−0.101135	−	0.489665i
$197$	−9.04201	+	5.22041i	−0.644217	+	0.371939i	−0.786237	−	0.617925i	$-0.787973\pi$
$197$	−9.04201	+	5.22041i	−0.644217	+	0.371939i	0.142020	+	0.989864i	$0.454640\pi$
$198$	7.56370	+	9.41389i	0.537529	+	0.669016i
$199$	0.583635	+	3.30996i	0.0413728	+	0.234637i	0.998481	−	0.0550932i	$-0.0175456\pi$
$199$	0.583635	+	3.30996i	0.0413728	+	0.234637i	−0.957108	+	0.289730i	$0.906434\pi$
$200$	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
$204$	−11.5783	+	1.91476i	−0.810646	+	0.134060i
$205$	3.10052	+	3.69505i	0.216549	+	0.258074i
$206$	1.94719	+	0.343342i	0.135667	+	0.0239218i
$207$	−14.9765	−	9.07707i	−1.04094	−	0.630900i
$208$	−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	−0.00791948	−	0.999969i	$-0.502521\pi$
$211$	14.2096	−	16.9344i	0.978233	−	1.16581i	0.986152	−	0.165844i	$-0.0530347\pi$
$212$	0.142441	+	0.119522i	0.00978287	+	0.00820880i
$213$	−6.37952	−	0.0678913i	−0.437118	−	0.00465184i
$214$	2.23222	+	1.87305i	0.152591	+	0.128039i
$215$	25.6063	−	4.51509i	1.74634	−	0.307926i
$216$	−5.19350	−	0.165859i	−0.353373	−	0.0112853i
$217$	3.33839	−	5.98190i	0.226625	−	0.406078i
$218$	4.36851	+	5.20619i	0.295873	+	0.352608i
$219$	−23.6818	−	0.252023i	−1.60027	−	0.0170301i
$220$	−4.27720	−	7.40833i	−0.288369	−	0.499470i
$221$	−40.4504			−2.72099
$222$	14.0683	−	7.92395i	0.944205	−	0.531821i
$223$	9.56900	+	1.68727i	0.640787	+	0.112988i	0.484595	−	0.874739i	$-0.338967\pi$
$223$	9.56900	+	1.68727i	0.640787	+	0.112988i	0.156192	+	0.987727i	$0.450078\pi$
$224$	2.59859	−	0.497346i	0.173625	−	0.0332303i
$225$	−0.752299	+	1.24124i	−0.0501533	+	0.0827495i
$226$	2.76049	−	15.6555i	0.183625	−	1.04139i
$227$	6.90589	−	11.9613i	0.458360	−	0.793902i	−0.540515	−	0.841335i	$-0.681770\pi$
$227$	6.90589	−	11.9613i	0.458360	−	0.793902i	0.998874	+	0.0474323i	$0.0151038\pi$
$228$	7.34583	+	1.74320i	0.486490	+	0.115446i
$229$	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
$231$	−3.27456	−	18.1535i	−0.215450	−	1.19441i
$232$	0.551587	+	3.12821i	0.0362135	+	0.205377i
$233$	−7.71621	−	21.2001i	−0.505505	−	1.38886i	−0.885829	−	0.464011i	$-0.846410\pi$
$233$	−7.71621	−	21.2001i	−0.505505	−	1.38886i	0.380324	−	0.924853i	$-0.375813\pi$
$234$	−17.5679	−	3.48473i	−1.14845	−	0.227804i
$235$	−5.74225			−0.374583
$236$	6.62871			0.431493
$237$	−13.8735	−	8.20796i	−0.901183	−	0.533164i
$238$	16.9329	+	5.88510i	1.09760	+	0.381474i
$239$	−21.2196	−	12.2511i	−1.37258	−	0.792459i	−0.381327	−	0.924440i	$-0.624533\pi$
$239$	−21.2196	−	12.2511i	−1.37258	−	0.792459i	−0.991252	+	0.131981i	$0.957866\pi$
$240$	3.61791	+	0.677709i	0.233535	+	0.0437459i
$241$	−0.659930	−	0.786475i	−0.0425099	−	0.0506613i	0.744371	−	0.667767i	$-0.232750\pi$
$241$	−0.659930	−	0.786475i	−0.0425099	−	0.0506613i	−0.786880	+	0.617105i	$0.788305\pi$
$242$	−3.98607	−	3.34471i	−0.256234	−	0.215006i
$243$	−11.3917	−	10.6410i	−0.730775	−	0.682619i
$244$	−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
$249$	−6.75376	−	8.22501i	−0.428002	−	0.521239i
$250$	7.49093	−	8.92735i	0.473768	−	0.564615i
$251$	−28.5760	+	5.03872i	−1.80370	+	0.318041i	−0.971609	−	0.236593i	$-0.923969\pi$
$251$	−28.5760	+	5.03872i	−1.80370	+	0.318041i	−0.832094	+	0.554635i	$0.812858\pi$
$252$	6.84707	+	4.01468i	0.431325	+	0.252901i
$253$	22.0810	+	8.03681i	1.38822	+	0.505270i
$254$	13.6823	+	7.89949i	0.858505	+	0.495658i
$255$	18.9332	+	16.2333i	1.18565	+	1.01657i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−7.63428	−	2.77865i	−0.476213	−	0.173327i	0.0927517	−	0.995689i	$-0.470434\pi$
$257$	−7.63428	−	2.77865i	−0.476213	−	0.173327i	−0.568965	+	0.822362i	$0.692656\pi$
$258$	−3.90182	+	20.8296i	−0.242917	+	1.29680i
$259$	−24.6614	+	0.359372i	−1.53239	+	0.0223303i
$260$	11.9220	+	4.33927i	0.739374	+	0.269110i
$261$	−4.93925	+	8.14943i	−0.305732	+	0.504437i
$262$	0.722404	−	1.98479i	0.0446303	−	0.122621i
$263$	1.63952	+	0.289091i	0.101097	+	0.0178261i	0.223968	−	0.974597i	$-0.428099\pi$
$263$	1.63952	+	0.289091i	0.101097	+	0.0178261i	−0.122871	+	0.992423i	$0.539210\pi$
$264$	6.87868	−	1.13756i	0.423354	−	0.0700119i
$265$		−	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	−0.795195	−	0.606354i	$-0.792631\pi$
$269$	2.61483	−	14.8295i	0.159429	−	0.904168i	0.954624	−	0.297814i	$-0.0962576\pi$
$270$	6.82437	+	8.68131i	0.415318	+	0.528328i
$271$	−3.13443	+	1.14084i	−0.190403	+	0.0693011i	−0.435462	−	0.900207i	$-0.643415\pi$
$271$	−3.13443	+	1.14084i	−0.190403	+	0.0693011i	0.245059	+	0.969508i	$0.421193\pi$
$272$	−2.31737	+	6.36693i	−0.140511	+	0.386052i
$273$	21.0266	+	17.5031i	1.27259	+	1.05933i
$274$	−0.192722	−	0.111268i	−0.0116427	−	0.00672194i
$275$	0.666084	−	1.83005i	0.0401664	−	0.110356i
$276$	−8.80958	+	4.96198i	−0.530275	+	0.298676i
$277$	4.72473	+	8.18347i	0.283881	+	0.491697i	0.972337	−	0.233581i	$-0.0750445\pi$
$277$	4.72473	+	8.18347i	0.283881	+	0.491697i	−0.688456	+	0.725278i	$0.741711\pi$
$278$	6.07532	−	10.5228i	0.364373	−	0.631113i
$279$	2.50074	+	7.35406i	0.149716	+	0.440276i
$280$	−4.35934	−	3.55098i	−0.260521	−	0.212212i
$281$	−4.18902	−	23.7571i	−0.249896	−	1.41723i	−0.808842	−	0.588027i	$-0.799905\pi$
$281$	−4.18902	−	23.7571i	−0.249896	−	1.41723i	0.558946	−	0.829204i	$-0.311206\pi$
$282$	1.64740	−	4.38059i	0.0981014	−	0.260860i
$283$	−28.6832	+	10.4398i	−1.70504	+	0.620583i	−0.996383	−	0.0849718i	$-0.972920\pi$
$283$	−28.6832	+	10.4398i	−1.70504	+	0.620583i	−0.708655	+	0.705555i	$0.750698\pi$
$284$	−1.84171	+	3.18994i	−0.109286	+	0.189288i
$285$	−7.19664	−	14.3399i	−0.426292	−	0.849419i
$286$	24.0316			1.42102
$287$	5.92856	+	0.956515i	0.349952	+	0.0564613i
$288$	−1.55495	+	2.56557i	−0.0916264	+	0.151177i
$289$	−22.1449	+	18.5818i	−1.30264	+	1.09304i
$290$	4.33908	−	5.17111i	0.254800	−	0.303658i
$291$	7.35960	+	4.35414i	0.431427	+	0.255244i
$292$	−6.83673	+	11.8416i	−0.400089	+	0.692975i
$293$	−1.11981	+	1.93957i	−0.0654199	+	0.113311i	−0.896880	−	0.442274i	$-0.854172\pi$
$293$	−1.11981	+	1.93957i	−0.0654199	+	0.113311i	0.831460	+	0.555584i	$0.187505\pi$
$294$	−6.25539	−	10.3861i	−0.364822	−	0.605727i
$295$	−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
$300$	0.411244	+	0.730131i	0.0237432	+	0.0421541i
$301$	20.4443	−	25.0983i	1.17839	−	1.44664i
$302$	−9.53638	+	11.3650i	−0.548757	+	0.653983i
$303$	−1.54830	+	1.80581i	−0.0889476	+	0.103741i
$304$	2.95826	−	3.20136i	0.169668	−	0.183611i
$305$	2.40386	+	1.38787i	0.137645	+	0.0794693i
$306$	−17.8157	+	9.78639i	−1.01846	+	0.559451i
$307$	−4.24523	−	11.6637i	−0.242288	−	0.665681i	−0.999916	−	0.0129941i	$-0.995864\pi$
$307$	−4.24523	−	11.6637i	−0.242288	−	0.665681i	0.757627	−	0.652687i	$-0.226358\pi$
$308$	−10.0598	−	3.49633i	−0.573211	−	0.199222i
$309$	3.37877	−	0.558762i	0.192211	−	0.0317869i
$310$	−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	$0.938937\pi$
$312$	−6.73063	+	7.85006i	−0.381047	+	0.444422i
$313$	−8.95310	−	3.25866i	−0.506059	−	0.184191i	0.0763581	−	0.997080i	$-0.475671\pi$
$313$	−8.95310	−	3.25866i	−0.506059	−	0.184191i	−0.582417	+	0.812890i	$0.697893\pi$
$314$	6.05410	−	5.08000i	0.341653	−	0.286681i
$315$	−2.81749	−	16.6307i	−0.158747	−	0.937037i
$316$	−8.05986	+	4.65336i	−0.453403	+	0.261772i
$317$	−1.50568	−	8.53916i	−0.0845676	−	0.479607i	−0.997449	−	0.0713820i	$-0.977259\pi$
$317$	−1.50568	−	8.53916i	−0.0845676	−	0.479607i	0.912881	−	0.408225i	$-0.133852\pi$
$318$	0.301451	+	0.113366i	0.0169045	+	0.00635727i
$319$	4.37320	−	12.0153i	0.244852	−	0.672726i
$320$	1.36601	−	1.62795i	0.0763622	−	0.0910050i
$321$	4.72410	+	1.77659i	0.263673	+	0.0991594i
$322$	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
$325$	0.987879	+	2.71418i	0.0547977	+	0.150555i
$326$	−2.77580	+	15.7424i	−0.153737	+	0.871888i
$327$	10.1311	+	5.99383i	0.560251	+	0.331460i
$328$	−0.394140	+	2.23528i	−0.0217627	+	0.123423i
$329$	−5.40891	+	4.67459i	−0.298203	+	0.257719i
$330$	−11.2482	−	9.64421i	−0.619195	−	0.530896i
$331$		−	23.2724i		−	1.27916i	−0.768723	−	0.639582i	$-0.779107\pi$
$331$		−	23.2724i		−	1.27916i	0.768723	−	0.639582i	$-0.220893\pi$
$332$	−6.05114	+	1.06698i	−0.332099	+	0.0585581i
$333$	18.4283	−	21.0361i	1.00987	−	1.15277i
$334$	18.1427			0.992725
$335$	−12.5739	−	21.7786i	−0.686985	−	1.18989i
$336$	3.95959	−	2.30686i	0.216013	−	0.125850i
$337$	7.55254	+	1.33172i	0.411413	+	0.0725432i	0.375524	−	0.926813i	$-0.377463\pi$
$337$	7.55254	+	1.33172i	0.411413	+	0.0725432i	0.0358888	+	0.999356i	$0.488574\pi$
$338$	−17.3445	+	14.5537i	−0.943415	+	0.791619i
$339$	−4.49249	−	27.1655i	−0.243998	−	1.47543i
$340$	13.5306	−	4.92473i	0.733799	−	0.267081i
$341$	−5.21123	−	9.02612i	−0.282204	−	0.488792i
$342$	13.0041	−	1.37611i	0.703181	−	0.0744117i
$343$	0.809329	+	18.5026i	0.0436996	+	0.999045i
$344$	9.37268	+	7.86461i	0.505341	+	0.424031i
$345$	20.1118	+	7.56343i	1.08278	+	0.407201i
$346$	3.41664	+	1.24356i	0.183680	+	0.0668539i
$347$	−8.36504	+	9.96907i	−0.449059	+	0.535168i	−0.942320	−	0.334714i	$-0.891360\pi$
$347$	−8.36504	+	9.96907i	−0.449059	+	0.535168i	0.493261	+	0.869881i	$0.335805\pi$
$348$	2.70004	+	4.79370i	0.144737	+	0.256969i
$349$	0.251987	+	0.436453i	0.0134885	+	0.0233628i	0.872691	−	0.488273i	$-0.162373\pi$
$349$	0.251987	+	0.436453i	0.0134885	+	0.0233628i	−0.859202	+	0.511636i	$0.829040\pi$
$350$	−0.0186510	−	1.27990i	−0.000996938	−	0.0684136i
$351$	−30.7064	+	4.40891i	−1.63899	+	0.235330i
$352$	1.37675	−	3.78259i	0.0733811	−	0.201613i
$353$	−0.839628	+	0.484760i	−0.0446889	+	0.0258012i	−0.522178	−	0.852837i	$-0.674880\pi$
$353$	−0.839628	+	0.484760i	−0.0446889	+	0.0258012i	0.477489	+	0.878638i	$0.341547\pi$
$354$	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
$357$	31.0492	−	0.122009i	1.64330	−	0.00645741i
$358$	−6.93931	+	2.52570i	−0.366754	+	0.133487i
$359$	10.9624	+	1.93297i	0.578573	+	0.102018i	0.455274	−	0.890351i	$-0.349541\pi$
$359$	10.9624	+	1.93297i	0.578573	+	0.102018i	0.123299	+	0.992370i	$0.460652\pi$
$360$	6.30068	−	0.973208i	0.332075	−	0.0512925i
$361$	−18.9132	−	1.81441i	−0.995430	−	0.0954951i
$362$	−0.611287	+	0.352927i	−0.0321285	+	0.0185494i
$363$	−8.43582	−	3.17245i	−0.442766	−	0.166510i
$364$	14.7624	−	5.61800i	0.773761	−	0.294463i
$365$	28.6165	−	5.04586i	1.49785	−	0.264112i
$366$	−1.74841	+	1.43567i	−0.0913910	+	0.0750435i
$367$	14.2448	−	11.9528i	0.743574	−	0.623933i	−0.190221	−	0.981741i	$-0.560920\pi$
$367$	14.2448	−	11.9528i	0.743574	−	0.623933i	0.933795	+	0.357809i	$0.116476\pi$
$368$			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
$372$	4.40797	+	0.825703i	0.228543	+	0.0428107i
$373$	−15.5650	−	8.98646i	−0.805925	−	0.465301i	0.0396135	−	0.999215i	$-0.487387\pi$
$373$	−15.5650	−	8.98646i	−0.805925	−	0.465301i	−0.845539	+	0.533914i	$0.820721\pi$
$374$	20.8931	−	17.5314i	1.08035	−	0.906525i
$375$	7.10514	−	18.8932i	0.366908	−	0.975639i
$376$	−1.73685	−	2.06990i	−0.0895714	−	0.106747i
$377$	6.48596	+	17.8200i	0.334044	+	0.917778i
$378$	13.4954	+	2.62185i	0.694129	+	0.134853i
$379$		−	10.5738i		−	0.543138i	−0.962419	−	0.271569i	$-0.912457\pi$
$379$		−	10.5738i		−	0.543138i	0.962419	−	0.271569i	$-0.0875426\pi$
$380$	−9.25265	−	0.442803i	−0.474651	−	0.0227153i
$381$	26.8968	+	5.03833i	1.37797	+	0.258121i
$382$	−8.34195	−	22.9193i	−0.426812	−	1.17266i
$383$	−12.7887	−	10.7310i	−0.653473	−	0.548329i	0.254649	−	0.967033i	$-0.418040\pi$
$383$	−12.7887	−	10.7310i	−0.653473	−	0.548329i	−0.908123	+	0.418704i	$0.862484\pi$
$384$	0.850014	+	1.50913i	0.0433771	+	0.0770125i
$385$	8.04995	+	21.1529i	0.410263	+	1.07805i
$386$	−6.07692	+	16.6962i	−0.309307	+	0.849815i
$387$	5.60311	+	36.2753i	0.284822	+	1.84398i
$388$	4.27557	−	2.46850i	0.217059	−	0.125319i
$389$	3.21757	−	0.567344i	0.163137	−	0.0287655i	−0.0914829	−	0.995807i	$-0.529161\pi$
$389$	3.21757	−	0.567344i	0.163137	−	0.0287655i	0.254620	+	0.967041i	$0.418050\pi$
$390$	21.9736	+	0.233844i	1.11268	+	0.0118412i
$391$	−19.7762	+	34.2534i	−1.00013	+	1.73227i
$392$	−6.99703	+	0.203968i	−0.353403	+	0.0103019i
$393$	0.0389305	−	3.65818i	0.00196379	−	0.184531i
$394$	3.57097	+	9.81116i	0.179903	+	0.494279i
$395$	18.5853	+	6.76449i	0.935127	+	0.340358i
$396$	10.5843	−	5.81409i	0.531881	−	0.292169i
$397$	5.65472	−	32.0695i	0.283802	−	1.60952i	−0.425732	−	0.904850i	$-0.639983\pi$
$397$	5.65472	−	32.0695i	0.283802	−	1.60952i	0.709534	−	0.704672i	$-0.248906\pi$
$398$	3.36102			0.168473
$399$	−18.4525	−	7.64885i	−0.923781	−	0.382921i
$400$	0.483809			0.0241904
$401$	−4.02183	+	22.8089i	−0.200841	+	1.13902i	0.703012	+	0.711178i	$0.251838\pi$
$401$	−4.02183	+	22.8089i	−0.200841	+	1.13902i	−0.903852	+	0.427845i	$0.859273\pi$
$402$	20.2216	−	3.34414i	1.00856	−	0.166790i
$403$	14.5255	+	5.28685i	0.723567	+	0.263357i
$404$	0.469710	+	1.29052i	0.0233690	+	0.0642057i
$405$	16.1418	+	10.2593i	0.802094	+	0.509788i
$406$	−0.122454	−	8.40324i	−0.00607728	−	0.417046i
$407$	−18.7624	+	32.4975i	−0.930020	+	1.61084i
$408$	−0.124884	+	11.7349i	−0.00618268	+	0.580966i
$409$	3.59248	−	0.633451i	0.177637	−	0.0313221i	−0.0841222	−	0.996455i	$-0.526809\pi$
$409$	3.59248	−	0.633451i	0.177637	−	0.0313221i	0.261759	+	0.965133i	$0.415698\pi$
$410$	4.17731	−	2.41177i	0.206303	−	0.119109i
$411$	−0.378854	−	0.0709671i	−0.0186875	−	0.00350055i
$412$	0.676251	−	1.85799i	0.0333165	−	0.0915364i
$413$	−17.3140	−	2.79345i	−0.851968	−	0.137457i
$414$	−11.5398	+	13.1728i	−0.567151	+	0.647408i
$415$	10.0029	+	8.39343i	0.491023	+	0.412017i
$416$	2.04188	+	5.61002i	0.100111	+	0.275054i
$417$	3.87486	−	20.6857i	0.189753	−	1.01298i
$418$	−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	$0.938166\pi$
$420$	−9.16429	−	3.29481i	−0.447172	−	0.160770i
$421$	−0.813545	−	2.23520i	−0.0396498	−	0.108937i	0.918288	−	0.395914i	$-0.129572\pi$
$421$	−0.813545	−	2.23520i	−0.0396498	−	0.108937i	−0.957938	+	0.286977i	$0.907350\pi$
$422$	−14.2096	−	16.9344i	−0.691715	−	0.824354i
$423$	0.172514	−	8.10436i	0.00838791	−	0.394048i
$424$	0.142441	−	0.119522i	0.00691754	−	0.00580450i
$425$	2.83889	+	1.63903i	0.137706	+	0.0795049i
$426$	−1.17465	+	6.27082i	−0.0569121	+	0.303822i
$427$	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	$-0.875746\pi$
$431$	−14.7529	+	12.3792i	−0.710622	+	0.596283i	0.214151	+	0.976800i	$0.431301\pi$
$432$	−1.06518	+	5.08580i	−0.0512486	+	0.244691i
$433$	27.6771	−	4.88022i	1.33008	−	0.234528i	0.536964	−	0.843605i	$-0.319571\pi$
$433$	27.6771	−	4.88022i	1.33008	−	0.234528i	0.793111	+	0.609077i	$0.208460\pi$
$434$	−5.31131	−	4.32642i	−0.254951	−	0.207675i
$435$	4.11561	−	10.9438i	0.197328	−	0.524713i
$436$	5.88568	−	3.39810i	0.281873	−	0.162739i
$437$	20.2517	−	15.4054i	0.968770	−	0.736939i
$438$	−4.36049	+	23.2783i	−0.208352	+	1.11228i
$439$	12.1116	+	2.13561i	0.578056	+	0.101927i	0.455029	−	0.890476i	$-0.349629\pi$
$439$	12.1116	+	2.13561i	0.578056	+	0.101927i	0.123027	+	0.992403i	$0.460740\pi$
$440$	−8.03851	+	2.92578i	−0.383221	+	0.139481i
$441$	−16.1925	−	13.3717i	−0.771072	−	0.636747i
$442$	−7.02414	+	39.8359i	−0.334104	+	1.89480i
$443$	22.6177	−	3.98811i	1.07460	−	0.189481i	0.391773	−	0.920062i	$-0.371862\pi$
$443$	22.6177	−	3.98811i	1.07460	−	0.189481i	0.682826	+	0.730581i	$0.260751\pi$
$444$	−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
$447$	−20.8180	−	12.3165i	−0.984659	−	0.582552i
$448$	−0.0385504	−	2.64547i	−0.00182133	−	0.124987i
$449$	6.95776	+	12.0512i	0.328357	+	0.568731i	0.982186	−	0.187911i	$-0.0601718\pi$
$449$	6.95776	+	12.0512i	0.328357	+	0.568731i	−0.653829	+	0.756642i	$0.726838\pi$
$450$	1.09175	+	0.956410i	0.0514656	+	0.0450856i
$451$	5.87289	−	6.99903i	0.276543	−	0.329572i
$452$	−14.9383	−	5.43711i	−0.702640	−	0.255740i
$453$	−9.04524	+	24.0521i	−0.424982	+	1.13007i
$454$	−10.5804	−	8.87803i	−0.496564	−	0.416667i
$455$	−29.3114	−	16.3582i	−1.37414	−	0.766884i
$456$	2.99231	−	6.93153i	0.140128	−	0.324599i
$457$	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	$0.777173\pi$
$458$	6.11258	−	2.22480i	0.285622	−	0.103958i
$459$	−23.4798	+	26.2339i	−1.09594	+	1.22449i
$460$	9.50317	−	7.97411i	0.443088	−	0.371795i
$461$	−19.5269	−	3.44312i	−0.909460	−	0.160362i	−0.300702	−	0.953718i	$-0.597221\pi$
$461$	−19.5269	−	3.44312i	−0.909460	−	0.160362i	−0.608758	+	0.793356i	$0.708332\pi$
$462$	−18.4463	+	0.0724856i	−0.858201	+	0.00337234i
$463$	−6.24074	−	10.8093i	−0.290032	−	0.502350i	0.683785	−	0.729683i	$-0.260333\pi$
$463$	−6.24074	−	10.8093i	−0.290032	−	0.502350i	−0.973817	+	0.227334i	$0.926999\pi$
$464$	3.17646			0.147464
$465$	−4.67713	−	8.30386i	−0.216897	−	0.385082i
$466$	−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	$-0.419697\pi$
$468$	−6.48243	+	16.6959i	−0.299650	+	0.771768i
$469$	−29.5733	−	10.2783i	−1.36557	−	0.474609i
$470$	−0.997131	+	5.65501i	−0.0459942	+	0.260846i
$471$	6.97002	−	11.7811i	0.321162	−	0.542845i
$472$	1.15106	−	6.52801i	0.0529820	−	0.300476i
$473$	−16.8448	−	46.2806i	−0.774523	−	2.12799i
$474$	−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
$477$	0.557703	+	0.0118716i	0.0255355	+	0.000543562i
$478$	−15.7497	+	18.7698i	−0.720376	+	0.858511i
$479$	−8.05372	+	22.1274i	−0.367984	+	1.01103i	0.608144	+	0.793827i	$0.291914\pi$
$479$	−8.05372	+	22.1274i	−0.367984	+	1.01103i	−0.976127	+	0.217200i	$0.930308\pi$
$480$	1.29566	−	3.44526i	0.0591384	−	0.157254i
$481$	−9.66417	−	54.8082i	−0.440648	−	2.49904i
$482$	−0.889122	+	0.513335i	−0.0404984	+	0.0233818i
$483$	25.1015	−	9.24805i	1.14216	−	0.420801i
$484$	−3.98607	+	3.34471i	−0.181185	+	0.152032i
$485$	−9.85907	−	3.58841i	−0.447677	−	0.162941i
$486$	−12.4575	+	9.37080i	−0.565081	+	0.425068i
$487$			0.0122637i			0.000555720i	1.00000		0.000277860i	$8.84456e-5\pi$
$487$			0.0122637i			0.000555720i	−1.00000		0.000277860i	$0.999912\pi$
$488$	0.226811	+	1.28631i	0.0102672	+	0.0582284i
$489$	4.51740	+	27.3162i	0.204284	+	1.23528i
$490$	9.89005	+	11.1122i	0.446787	+	0.501996i
$491$	−7.23268	−	19.8716i	−0.326406	−	0.896793i	−0.989013	−	0.147826i	$-0.952772\pi$
$491$	−7.23268	−	19.8716i	−0.326406	−	0.896793i	0.662607	−	0.748967i	$-0.269450\pi$
$492$	0.641432	+	3.87866i	0.0289180	+	0.174864i
$493$	18.6389	+	10.7611i	0.839452	+	0.484658i
$494$	14.0739	−	21.8887i	0.633213	−	0.984821i
$495$	−23.9233	−	9.28857i	−1.07527	−	0.417490i
$496$	1.66431	−	1.98345i	0.0747297	−	0.0890594i
$497$	6.15480	−	7.55592i	0.276081	−	0.338929i
$498$	−9.27283	+	5.22290i	−0.415526	+	0.234044i
$499$	−16.2720	+	5.92254i	−0.728437	+	0.265129i	−0.679503	−	0.733673i	$-0.737805\pi$
$499$	−16.2720	+	5.92254i	−0.728437	+	0.265129i	−0.0489338	+	0.998802i	$0.515582\pi$
$500$	−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	$-0.0449555\pi$
$503$	15.2396	+	18.1618i	0.679500	+	0.809796i	−0.310543	+	0.950559i	$0.600511\pi$
$504$	5.14267	−	6.04591i	0.229073	−	0.269306i
$505$	1.45927	−	2.52752i	0.0649365	−	0.112473i
$506$	11.7490	−	20.3499i	0.522308	−	0.904665i
$507$	−19.9685	+	33.7518i	−0.886833	+	1.49897i
$508$	10.1554	−	12.1027i	0.450572	−	0.536971i
$509$	19.5597	−	16.4126i	0.866970	−	0.727474i	−0.0964881	−	0.995334i	$-0.530761\pi$
$509$	19.5597	−	16.4126i	0.866970	−	0.727474i	0.963458	+	0.267860i	$0.0863165\pi$
$510$	19.2744	−	15.8267i	0.853486	−	0.700819i
$511$	22.8476	−	28.0488i	1.01072	−	1.24080i
$512$	1.00000			0.0441942
$513$	20.4548	−	9.72621i	0.903104	−	0.429423i
$514$	−4.06211	+	7.03579i	−0.179172	+	0.310335i
$515$	−3.94847	+	1.43712i	−0.173990	+	0.0633273i
$516$	19.8356	+	7.45957i	0.873215	+	0.328389i
$517$	1.88873	+	10.7115i	0.0830662	+	0.471092i
$518$	−3.92850	+	24.3492i	−0.172609	+	1.06984i
$519$	6.29723	+	0.0670155i	0.276418	+	0.00294165i
$520$	6.34359	−	10.9874i	0.278185	−	0.481830i
$521$	15.3192	+	26.5336i	0.671145	+	1.16246i	0.977580	+	0.210566i	$0.0675306\pi$
$521$	15.3192	+	26.5336i	0.671145	+	1.16246i	−0.306435	+	0.951892i	$0.599136\pi$
$522$	7.16793	+	6.27934i	0.313732	+	0.274839i
$523$	11.6011	−	31.8739i	0.507283	−	1.39375i	−0.376747	−	0.926316i	$-0.622957\pi$
$523$	11.6011	−	31.8739i	0.507283	−	1.39375i	0.884029	−	0.467431i	$-0.154821\pi$
$524$	−1.82919	−	1.05608i	−0.0799086	−	0.0461353i
$525$	−0.766470	−	2.08039i	−0.0334515	−	0.0907955i
$526$	0.569398	−	1.56441i	0.0248269	−	0.0682114i
$527$	16.4853	−	6.00016i	0.718112	−	0.261371i
$528$	0.0741935	−	6.97172i	0.00322886	−	0.303405i
$529$	−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
$534$	−0.384842	−	2.32709i	−0.0166537	−	0.100703i
$535$	−6.09846	−	1.07532i	−0.263659	−	0.0464903i
$536$	4.04730	−	11.1199i	0.174817	−	0.480305i
$537$	−9.88510	+	8.11691i	−0.426574	+	0.350270i
$538$	−14.1501	−	5.15022i	−0.610055	−	0.222042i
$539$	24.8025	+	13.3717i	1.06832	+	0.575960i
$540$	9.73446	−	5.21319i	0.418905	−	0.224340i
$541$	−33.6781	−	12.2578i	−1.44794	−	0.527006i	−0.505922	−	0.862579i	$-0.668848\pi$
$541$	−33.6781	−	12.2578i	−1.44794	−	0.527006i	−0.942014	+	0.335574i	$0.891070\pi$
$542$	0.579220	+	3.28492i	0.0248796	+	0.141099i
$543$	−0.795777	+	0.928130i	−0.0341501	+	0.0398299i
$544$	5.86780	+	3.38777i	0.251580	+	0.145250i
$545$	−13.5718	−	4.93974i	−0.581353	−	0.211595i
$546$	20.8884	−	17.6678i	0.893940	−	0.756110i
$547$	19.2012	−	3.38568i	0.820982	−	0.144761i	0.252647	−	0.967558i	$-0.418699\pi$
$547$	19.2012	−	3.38568i	0.820982	−	0.144761i	0.568335	+	0.822797i	$0.307588\pi$
$548$	−0.143043	+	0.170472i	−0.00611050	+	0.00728221i
$549$	−2.03100	+	3.35101i	−0.0866810	+	0.143018i
$550$	−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
$555$	−17.4719	+	29.5319i	−0.741641	+	1.25356i
$556$	−9.30792	−	7.81028i	−0.394744	−	0.331229i
$557$	4.90018	+	5.83981i	0.207627	+	0.247441i	0.859801	−	0.510629i	$-0.170587\pi$
$557$	4.90018	+	5.83981i	0.207627	+	0.247441i	−0.652174	+	0.758069i	$0.726143\pi$
$558$	7.67659	−	1.18573i	0.324976	−	0.0501960i
$559$	63.2585	+	36.5223i	2.67555	+	1.54473i
$560$	−4.25402	+	3.67650i	−0.179765	+	0.155360i
$561$	24.0540	−	40.6573i	1.01556	−	1.71655i
$562$	−24.1236			−1.01759
$563$	−9.41398			−0.396752			−0.198376	−	0.980126i	$-0.563567\pi$
$563$	−9.41398			−0.396752			−0.198376	+	0.980126i	$0.563567\pi$
$564$	−4.02797	−	2.38306i	−0.169608	−	0.100345i
$565$	11.5546	+	31.7460i	0.486105	+	1.33556i
$566$	5.30044	+	30.0603i	0.222794	+	1.26353i
$567$	23.5566	−	3.47684i	0.989283	−	0.146014i
$568$	2.82167	+	2.36766i	0.118395	+	0.0993449i
$569$	9.09323	+	15.7499i	0.381208	+	0.660272i	0.991235	−	0.132109i	$-0.0421748\pi$
$569$	9.09323	+	15.7499i	0.381208	+	0.660272i	−0.610027	+	0.792381i	$0.708841\pi$
$570$	−15.3717	+	4.59722i	−0.643849	+	0.192556i
$571$	−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	$0.192663\pi$
$572$	4.17304	−	23.6665i	0.174484	−	0.989545i
$573$	−26.8087	−	32.6488i	−1.11995	−	1.36392i
$574$	1.97147	−	5.67239i	0.0822874	−	0.236761i
$575$	2.78134	+	0.490425i	0.115990	+	0.0204521i
$576$	2.25657	+	1.97683i	0.0940239	+	0.0823681i
$577$	−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
$579$	−0.327487	+	30.7729i	−0.0136099	+	1.27888i
$580$	−4.33908	−	5.17111i	−0.180170	−	0.214719i
$581$	16.2551	−	0.236872i	0.674373	−	0.00982712i
$582$	5.56597	−	6.49170i	0.230717	−	0.269090i
$583$	−0.737115	+	0.129973i	−0.0305282	+	0.00538295i
$584$	10.4745	+	8.78913i	0.433437	+	0.363697i
$585$	36.0351	−	12.2537i	1.48987	−	0.506628i
$586$	1.71565	+	1.43960i	0.0708727	+	0.0594693i
$587$	4.92940	−	5.87463i	0.203458	−	0.242472i	−0.654661	−	0.755923i	$-0.727189\pi$
$587$	4.92940	−	5.87463i	0.203458	−	0.242472i	0.858119	+	0.513451i	$0.171633\pi$
$588$	−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
$591$	11.4761	+	13.9761i	0.472064	+	0.574899i
$592$	−9.18052	−	1.61877i	−0.377317	−	0.0665312i
$593$	28.4677	+	33.9265i	1.16903	+	1.39319i	0.903226	+	0.429165i	$0.141192\pi$
$593$	28.4677	+	33.9265i	1.16903	+	1.39319i	0.265801	+	0.964028i	$0.414364\pi$
$594$	13.9494	−	15.5855i	0.572349	−	0.639482i
$595$	−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	−0.988645	−	0.150268i	$-0.951986\pi$
$599$	−2.71709	−	15.4094i	−0.111017	−	0.629611i	0.877628	−	0.479342i	$-0.159125\pi$
$600$	0.790450	−	0.278211i	0.0322700	−	0.0113579i
$601$	−32.0421	+	18.4995i	−1.30703	+	0.754612i	−0.981599	−	0.190955i	$-0.938842\pi$
$601$	−32.0421	+	18.4995i	−1.30703	+	0.754612i	−0.325428	+	0.945567i	$0.605508\pi$
$602$	−21.1669	−	24.4920i	−0.862699	−	0.998218i
$603$	31.1152	−	17.0920i	1.26711	−	0.696038i
$604$	9.53638	+	11.3650i	0.388030	+	0.462436i
$605$	10.8900	+	1.92020i	0.442742	+	0.0780674i
$606$	1.50952	+	1.83835i	0.0613200	+	0.0746781i
$607$	−4.85391	+	2.80241i	−0.197014	+	0.113746i	−0.595262	−	0.803532i	$-0.702952\pi$
$607$	−4.85391	+	2.80241i	−0.197014	+	0.113746i	0.398248	+	0.917278i	$0.369618\pi$
$608$	−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
$611$	−12.3574	−	10.3691i	−0.499929	−	0.419490i
$612$	6.54405	+	19.2444i	0.264528	+	0.777910i
$613$	6.89916	+	5.78908i	0.278654	+	0.233819i	0.771394	−	0.636358i	$-0.219560\pi$
$613$	6.89916	+	5.78908i	0.278654	+	0.233819i	−0.492739	+	0.870177i	$0.664004\pi$
$614$	−12.2237	+	2.15536i	−0.493307	+	0.0869833i
$615$	5.43805	−	6.34251i	0.219283	−	0.255755i
$616$	−5.19008	+	9.29985i	−0.209114	+	0.374701i
$617$	−15.4083	−	18.3629i	−0.620317	−	0.739265i	0.360808	−	0.932640i	$-0.382501\pi$
$617$	−15.4083	−	18.3629i	−0.620317	−	0.739265i	−0.981125	+	0.193376i	$0.938056\pi$
$618$	0.0364434	−	3.42446i	0.00146597	−	0.137752i
$619$	9.18185	+	15.9034i	0.369050	+	0.639213i	0.989417	−	0.145099i	$-0.0463499\pi$
$619$	9.18185	+	15.9034i	0.369050	+	0.639213i	−0.620368	+	0.784311i	$0.713017\pi$
$620$	−5.50241			−0.220982
$621$	−11.2789	+	28.1577i	−0.452607	+	1.12993i
$622$	6.62248	+	1.16772i	0.265537	+	0.0468214i
$623$	−1.18283	+	3.40328i	−0.0473890	+	0.136350i
$624$	6.56204	+	7.99152i	0.262692	+	0.319917i
$625$	−3.88050	+	22.0074i	−0.155220	+	0.880295i
$626$	−4.76385	+	8.25122i	−0.190402	+	0.329785i
$627$	−24.3823	+	18.1411i	−0.973734	+	0.724488i
$628$	−3.95154	−	6.84426i	−0.157683	−	0.273116i
$629$	−48.3854	−	40.6002i	−1.92925	−	1.61883i
$630$	−16.8673	−	0.113218i	−0.672011	−	0.00451070i
$631$	−5.26155	−	29.8398i	−0.209459	−	1.18790i	−0.890267	−	0.455440i	$-0.849482\pi$
$631$	−5.26155	−	29.8398i	−0.209459	−	1.18790i	0.680808	−	0.732462i	$-0.261629\pi$
$632$	3.18309	+	8.74546i	0.126616	+	0.347876i
$633$	−32.9538	−	19.4964i	−1.30980	−	0.774912i
$634$	−8.67089			−0.344365
$635$	−33.5749			−1.33238
$636$	0.163990	−	0.277185i	0.00650265	−	0.0109911i
$637$	−40.9266	+	8.45295i	−1.62157	+	0.334918i
$638$	−11.0733	−	6.39319i	−0.438397	−	0.253109i
$639$	1.68683	+	10.9208i	0.0667300	+	0.432019i
$640$	−1.36601	−	1.62795i	−0.0539963	−	0.0643502i
$641$	19.5385	+	16.3948i	0.771725	+	0.647554i	0.941150	−	0.337989i	$-0.109747\pi$
$641$	19.5385	+	16.3948i	0.771725	+	0.647554i	−0.169425	+	0.985543i	$0.554191\pi$
$642$	2.56993	−	4.34383i	0.101427	−	0.171437i
$643$	−1.00942	+	0.367400i	−0.0398077	+	0.0144888i	−0.361847	−	0.932237i	$-0.617854\pi$
$643$	−1.00942	+	0.367400i	−0.0398077	+	0.0144888i	0.322040	+	0.946726i	$0.395632\pi$
$644$	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	$-0.663563\pi$
$647$	−37.9377	−	21.9033i	−1.49148	−	0.861108i	−0.999952	+	0.00975161i	$0.996896\pi$
$648$	1.18425	+	8.92175i	0.0465218	+	0.350479i
$649$	−17.1514	+	20.4403i	−0.673253	+	0.802351i
$650$	2.84449	−	0.501560i	0.111570	−	0.0196728i
$651$	−11.1655	−	4.01431i	−0.437612	−	0.157333i
$652$	15.0212	+	5.46726i	0.588275	+	0.214115i
$653$	−37.3994	−	21.5926i	−1.46355	−	0.844983i	−0.464380	−	0.885636i	$-0.653723\pi$
$653$	−37.3994	−	21.5926i	−1.46355	−	0.844983i	−0.999173	+	0.0406536i	$0.987056\pi$
$654$	7.66202	−	8.93636i	0.299609	−	0.349439i
$655$	0.779444	+	4.42045i	0.0304554	+	0.172721i
$656$	2.13288	+	0.776304i	0.0832749	+	0.0303096i
$657$	6.26178	+	40.5396i	0.244295	+	1.58160i
$658$	3.66433	+	6.13847i	0.142850	+	0.239303i
$659$	35.4707	+	12.9103i	1.38174	+	0.502913i	0.922706	−	0.385504i	$-0.125973\pi$
$659$	35.4707	+	12.9103i	1.38174	+	0.502913i	0.459036	+	0.888417i	$0.348195\pi$
$660$	−11.4509	+	9.40265i	−0.445727	+	0.365998i
$661$	−3.44607	+	9.46799i	−0.134036	+	0.368262i	−0.988494	−	0.151259i	$-0.951667\pi$
$661$	−3.44607	+	9.46799i	−0.134036	+	0.368262i	0.854458	+	0.519521i	$0.173890\pi$
$662$	−22.9188	−	4.04120i	−0.890764	−	0.157066i
$663$	11.4312	+	69.1234i	0.443953	+	2.68453i
$664$			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
$669$	0.179092	−	16.8287i	0.00692411	−	0.650636i
$670$	−23.6312	+	8.60105i	−0.912952	+	0.332287i
$671$	1.79824	−	4.94063i	0.0694204	−	0.190731i
$672$	−1.58424	−	4.30002i	−0.0611135	−	0.165877i
$673$	33.5453	+	19.3674i	1.29308	+	0.746559i	0.979199	−	0.202904i	$-0.0650379\pi$
$673$	33.5453	+	19.3674i	1.29308	+	0.746559i	0.313879	+	0.949463i	$0.398371\pi$
$674$	2.62297	−	7.20655i	0.101033	−	0.277586i
$675$	2.33369	+	0.934786i	0.0898236	+	0.0359799i
$676$	11.3208	+	19.6082i	0.435416	+	0.754162i
$677$	0.104769	−	0.181466i	0.00402662	−	0.00697431i	−0.864005	−	0.503483i	$-0.832052\pi$
$677$	0.104769	−	0.181466i	0.00402662	−	0.00697431i	0.868032	+	0.496509i	$0.165385\pi$
$678$	−27.5329	−	0.293007i	−1.05740	−	0.0112529i
$679$	−12.2080	+	4.64587i	−0.468498	+	0.178292i
$680$	−2.50035	−	14.1802i	−0.0958841	−	0.543786i
$681$	−22.3916	−	8.42080i	−0.858049	−	0.322686i
$682$	−9.79392	+	3.56469i	−0.375028	+	0.136499i
$683$	−22.7187	+	39.3499i	−0.869306	+	1.50568i	−0.00659954	+	0.999978i	$0.502101\pi$
$683$	−22.7187	+	39.3499i	−0.869306	+	1.50568i	−0.862707	+	0.505704i	$0.831233\pi$
$684$	0.902929	−	13.0455i	0.0345244	−	0.498807i
$685$	0.472918			0.0180693
$686$	18.3620	+	2.41590i	0.701065	+	0.0922396i
$687$	8.70743	−	7.14989i	0.332209	−	0.272785i
$688$	9.37268	−	7.86461i	0.357330	−	0.299836i
$689$	0.713553	−	0.850380i	0.0271842	−	0.0323969i
$690$	10.9409	−	18.4929i	0.416513	−	0.704012i
$691$	15.1218	−	26.1918i	0.575262	−	0.996382i	−0.420752	−	0.907176i	$-0.638234\pi$
$691$	15.1218	−	26.1918i	0.575262	−	0.996382i	0.996013	−	0.0892065i	$-0.0284331\pi$
$692$	1.81796	−	3.14879i	0.0691083	−	0.119699i
$693$	−30.0961	+	10.7259i	−1.14325	+	0.407442i
$694$	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
$699$	−34.0470	+	19.1769i	−1.28778	+	0.725337i
$700$	−1.26370	−	0.203885i	−0.0477632	−	0.00770613i
$701$	−4.39883	+	5.24232i	−0.166142	+	0.198000i	−0.842691	−	0.538397i	$-0.819030\pi$
$701$	−4.39883	+	5.24232i	−0.166142	+	0.198000i	0.676550	+	0.736397i	$0.263474\pi$
$702$	−0.990188	+	31.0055i	−0.0373722	+	1.17023i
$703$	18.6117	+	36.1213i	0.701955	+	1.36234i
$704$	−3.48606	−	2.01268i	−0.131386	−	0.0758555i
$705$	1.62275	+	9.81259i	0.0611164	+	0.369564i
$706$	0.331595	+	0.911050i	0.0124797	+	0.0342878i
$707$	−0.683025	−	3.56874i	−0.0256878	−	0.134216i
$708$	−1.87327	−	11.3274i	−0.0704017	−	0.425710i
$709$	3.76539	+	21.3546i	0.141412	+	0.801989i	0.970178	+	0.242393i	$0.0779324\pi$
$709$	3.76539	+	21.3546i	0.141412	+	0.801989i	−0.828766	+	0.559596i	$0.810956\pi$
$710$		−	7.82778i		−	0.293771i
$711$	−10.1055	+	26.0272i	−0.378984	+	0.976097i
$712$	−1.27967	−	0.465762i	−0.0479577	−	0.0174552i
$713$	11.5784	−	9.71545i	0.433615	−	0.363846i
$714$	5.27149	−	30.5987i	0.197280	−	1.14513i
$715$	−44.2282	+	25.5352i	−1.65404	+	0.954961i
$716$	1.28233	+	7.27247i	0.0479230	+	0.271785i
$717$	−14.9386	+	39.7230i	−0.557892	+	1.48348i
$718$	3.80720	−	10.4602i	0.142084	−	0.390371i
$719$	−31.0052	+	36.9506i	−1.15630	+	1.37803i	−0.243359	+	0.969936i	$0.578249\pi$
$719$	−31.0052	+	36.9506i	−1.15630	+	1.37803i	−0.912942	+	0.408089i	$0.866195\pi$
$720$	0.135679	−	6.37396i	0.00505648	−	0.237543i
$721$	−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
$724$	0.241416	+	0.663285i	0.00897216	+	0.0246508i
$725$	0.266863	−	1.51345i	0.00991103	−	0.0562083i
$726$	−4.58912	+	7.75677i	−0.170318	+	0.287881i
$727$	−0.103017	+	0.584238i	−0.00382069	+	0.0216682i	−0.986658	−	0.162804i	$-0.947946\pi$
$727$	−0.103017	+	0.584238i	−0.00382069	+	0.0216682i	0.982838	+	0.184472i	$0.0590574\pi$
$728$	−2.96918	−	15.5137i	−0.110045	−	0.574976i
$729$	−14.9645	+	22.4736i	−0.554239	+	0.832357i
$730$		−	29.0579i		−	1.07548i
$731$	81.6405	−	14.3954i	3.01958	−	0.532434i
$732$	1.11025	+	1.97115i	0.0410359	+	0.0728559i
$733$	−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
$735$	22.5484	+	12.4679i	0.831711	+	0.459887i
$736$	5.74884	+	1.01368i	0.211905	+	0.0373646i
$737$	−36.4898	+	30.6186i	−1.34412	+	1.12785i
$738$	3.27837	+	5.96814i	0.120679	+	0.219690i
$739$	25.0764	−	9.12707i	0.922451	−	0.335745i	0.163238	−	0.986587i	$-0.447806\pi$
$739$	25.0764	−	9.12707i	0.922451	−	0.335745i	0.759213	+	0.650842i	$0.225584\pi$
$740$	9.90540	+	17.1566i	0.364130	+	0.630691i
$741$	10.4070	−	43.8551i	0.382311	−	1.61106i
$742$	−0.422420	+	0.252161i	−0.0155075	+	0.00925714i
$743$	35.8701	+	30.0986i	1.31595	+	1.10421i	0.987148	+	0.159809i	$0.0510879\pi$
$743$	35.8701	+	30.0986i	1.31595	+	1.10421i	0.328798	+	0.944400i	$0.393357\pi$
$744$	1.57860	−	4.19762i	0.0578741	−	0.153892i
$745$	27.8883	+	10.1505i	1.02175	+	0.371886i
$746$	−11.5528	+	13.7681i	−0.422977	+	0.504084i
$747$	−12.1466	+	13.8655i	−0.444422	+	0.507312i
$748$	−13.6370	−	23.6199i	−0.498617	−	0.863631i
$749$	−6.61983	+	3.95167i	−0.241883	+	0.144391i
$750$	−17.3723	−	10.2780i	−0.634348	−	0.375298i
$751$	8.53630	−	23.4533i	0.311494	−	0.855823i	−0.680862	−	0.732412i	$-0.738395\pi$
$751$	8.53630	−	23.4533i	0.311494	−	0.855823i	0.992356	−	0.123411i	$-0.0393832\pi$
$752$	−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
$756$	4.92547	−	12.8351i	0.179138	−	0.466808i
$757$	42.4170	−	15.4385i	1.54167	−	0.561123i	0.575227	−	0.817994i	$-0.304914\pi$
$757$	42.4170	−	15.4385i	1.54167	−	0.561123i	0.966446	+	0.256870i	$0.0826914\pi$
$758$	−10.4131	−	1.83612i	−0.378222	−	0.0666908i
$759$	7.49358	−	40.0041i	0.272000	−	1.45206i
$760$	−2.04278	+	9.03519i	−0.0740995	+	0.327741i
$761$	−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	$0.408398\pi$
$762$	9.63236	−	25.6133i	0.348944	−	0.927872i
$763$	−16.8053	+	6.39543i	−0.608391	+	0.231530i
$764$	−24.0197	+	4.23532i	−0.869002	+	0.153229i
$765$	22.3897	−	36.9414i	0.809500	−	1.33562i
$766$	−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	−0.262081	−	0.965046i	$-0.584409\pi$
$769$	17.8252	−	14.9571i	0.642794	−	0.539368i	0.904875	+	0.425677i	$0.139964\pi$
$770$	22.2294	−	4.25450i	0.801090	−	0.153321i
$771$	−2.59083	+	13.8310i	−0.0933065	+	0.498112i
$772$	15.3873	+	8.88387i	0.553801	+	0.319737i
$773$	−4.32432	+	3.62854i	−0.155535	+	0.130509i	−0.717234	−	0.696832i	$-0.754592\pi$
$773$	−4.32432	+	3.62854i	−0.155535	+	0.130509i	0.561699	+	0.827342i	$0.310148\pi$
$774$	36.6972	+	0.781156i	1.31905	+	0.0280781i
$775$	−0.805208	−	0.959609i	−0.0289239	−	0.0344702i
$776$	−1.68856	−	4.63927i	−0.0606156	−	0.166540i
$777$	7.58341	+	42.0409i	0.272053	+	1.50821i
$778$		−	3.26721i		−	0.117135i
$779$	−2.93555	−	9.44813i	−0.105177	−	0.338514i
$780$	4.04596	−	21.5991i	0.144869	−	0.773374i
$781$	−5.07116	−	13.9329i	−0.181461	−	0.498559i
$782$	30.2989	+	25.4238i	1.08349	+	0.909153i
$783$	15.3219	+	6.13737i	0.547560	+	0.219332i
$784$	−1.01415	+	6.92615i	−0.0362197	+	0.247362i
$785$	−5.74426	+	15.7822i	−0.205021	+	0.563291i
$786$	−3.59584	−	0.673575i	−0.128259	−	0.0240256i
$787$	−26.2042	+	15.1290i	−0.934078	+	0.539290i	−0.888099	−	0.459652i	$-0.847974\pi$
$787$	−26.2042	+	15.1290i	−0.934078	+	0.539290i	−0.0459789	+	0.998942i	$0.514641\pi$
$788$	10.2822	−	1.81303i	0.366288	−	0.0645865i
$789$	0.0306850	−	2.88337i	0.00109241	−	0.102651i
$790$	9.88902	−	17.1283i	0.351835	−	0.609397i
$791$	36.7273	+	20.4969i	1.30587	+	0.728784i
$792$	−3.88782	−	11.4331i	−0.138148	−	0.406258i
$793$	2.66700	+	7.32753i	0.0947080	+	0.260208i
$794$	−30.6003	−	11.1376i	−1.08597	−	0.395259i
$795$	−0.675256	+	0.111670i	−0.0239488	+	0.00396053i
$796$	0.583635	−	3.30996i	0.0206864	−	0.117318i
$797$	25.2933			0.895934			0.447967	−	0.894050i	$-0.352148\pi$
$797$	25.2933			0.895934			0.447967	+	0.894050i	$0.352148\pi$
$798$	−10.7369	+	16.8440i	−0.380082	+	0.596270i
$799$	−18.3080			−0.647690
$800$	0.0840125	−	0.476459i	0.00297029	−	0.0168454i
$801$	−1.96694	−	3.58072i	−0.0694983	−	0.126519i
$802$	21.7640	+	7.92146i	0.768514	+	0.279716i
$803$	−18.8250	−	51.7211i	−0.664318	−	1.82520i
$804$	0.218110	−	20.4951i	0.00769215	−	0.722806i
$805$	−28.1825	+	16.8234i	−0.993301	+	0.592946i
$806$	7.72886	−	13.3868i	0.272238	−	0.471529i
$807$	−26.0802	−	0.277547i	−0.918065	−	0.00977011i
$808$	1.35248	−	0.238478i	0.0475800	−	0.00838963i
$809$	−31.4548	+	18.1604i	−1.10589	+	0.638487i	−0.937762	−	0.347278i	$-0.887106\pi$
$809$	−31.4548	+	18.1604i	−1.10589	+	0.638487i	−0.168129	+	0.985765i	$0.553773\pi$
$810$	12.9064	−	14.1151i	0.453486	−	0.495954i
$811$	11.7876	−	32.3862i	0.413920	−	1.13723i	−0.541169	−	0.840914i	$-0.682018\pi$
$811$	11.7876	−	32.3862i	0.413920	−	1.13723i	0.955088	−	0.296321i	$-0.0957598\pi$
$812$	−8.29684	−	1.33861i	−0.291162	−	0.0469762i
$813$	2.83530	+	5.03385i	0.0994384	+	0.176545i
$814$	28.7457	+	24.1205i	1.00754	+	0.845424i
$815$	−11.6187	−	31.9220i	−0.406984	−	1.11818i
$816$	11.5350	+	2.16074i	0.403805	+	0.0756409i
$817$	−52.0189	−	11.7610i	−1.81991	−	0.411467i
$818$		−	3.64790i		−	0.127546i
$819$	23.9679	−	40.8774i	0.837504	−	1.42837i
$820$	−1.64975	−	4.53265i	−0.0576118	−	0.158287i
$821$	−16.1131	−	19.2028i	−0.562350	−	0.670183i	0.407692	−	0.913120i	$-0.366334\pi$
$821$	−16.1131	−	19.2028i	−0.562350	−	0.670183i	−0.970042	+	0.242937i	$0.921889\pi$
$822$	−0.135676	+	0.360775i	−0.00473225	+	0.0125835i
$823$	−13.5371	+	11.3590i	−0.471874	+	0.395949i	−0.847478	−	0.530831i	$-0.821880\pi$
$823$	−13.5371	+	11.3590i	−0.471874	+	0.395949i	0.375604	+	0.926780i	$0.377435\pi$
$824$	−1.71233	−	0.988614i	−0.0596518	−	0.0344400i
$825$	−3.31550	−	0.621061i	−0.115431	−	0.0216226i
$826$	−5.75756	+	16.5659i	−0.200331	+	0.576402i
$827$	−28.0856	+	23.5666i	−0.976631	+	0.819490i	−0.983578	−	0.180485i	$-0.942233\pi$
$827$	−28.0856	+	23.5666i	−0.976631	+	0.819490i	0.00694693	+	0.999976i	$0.497789\pi$
$828$	10.9688	+	13.6519i	0.381192	+	0.474437i
$829$		−	21.3696i		−	0.742198i	−0.928593	−	0.371099i	$-0.878981\pi$
$829$		−	21.3696i		−	0.742198i	0.928593	−	0.371099i	$-0.121019\pi$
$830$	10.0029	−	8.39343i	0.347206	−	0.291340i
$831$	12.6490	−	10.3864i	0.438791	−	0.360302i
$832$	5.87936	−	1.03669i	0.203830	−	0.0359408i
$833$	−29.4151	+	37.2055i	−1.01917	+	1.28909i
$834$	−19.6986	−	7.40803i	−0.682107	−	0.256519i
$835$	−33.3902	+	19.2778i	−1.15552	+	0.667137i
$836$	2.21737	+	17.4054i	0.0766892	+	0.601979i
$837$	11.8602	−	6.35162i	0.409949	−	0.219544i
$838$	7.78276	+	1.37231i	0.268851	+	0.0474057i
$839$	11.5879	−	4.21765i	0.400058	−	0.145609i	−0.134152	−	0.990961i	$-0.542831\pi$
$839$	11.5879	−	4.21765i	0.400058	−	0.145609i	0.534211	+	0.845351i	$0.320609\pi$
$840$	−4.83611	+	8.45293i	−0.166862	+	0.291654i
$841$	−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
$846$	−7.95128	−	1.57720i	−0.273371	−	0.0542253i
$847$	11.8210	−	7.05650i	0.406175	−	0.242464i
$848$	−0.0929716	−	0.161032i	−0.00319266	−	0.00552985i
$849$	25.9458	+	46.0647i	0.890459	+	1.58094i
$850$	2.10710	−	2.51115i	0.0722730	−	0.0861316i
$851$	−51.1364	−	18.6121i	−1.75293	−	0.638015i
$852$	5.97157	+	2.24572i	0.204583	+	0.0769372i
$853$	−40.7170	−	34.1656i	−1.39412	−	1.16981i	−0.963639	−	0.267209i	$-0.913899\pi$
$853$	−40.7170	−	34.1656i	−1.39412	−	1.16981i	−0.430484	−	0.902598i	$-0.641657\pi$
$854$	−0.0503526	−	3.45538i	−0.00172303	−	0.118241i
$855$	−22.4708	+	16.3503i	−0.768484	+	0.559170i
$856$	−1.45698	−	2.52356i	−0.0497984	−	0.0862534i
$857$	46.1822	−	16.8090i	1.57756	−	0.574183i	0.602885	−	0.797828i	$-0.294018\pi$
$857$	46.1822	−	16.8090i	1.57756	−	0.574183i	0.974671	+	0.223645i	$0.0717956\pi$
$858$	−6.79130	−	41.0661i	−0.231851	−	1.40198i
$859$	−8.10805	+	6.80346i	−0.276643	+	0.232131i	−0.770544	−	0.637387i	$-0.780015\pi$
$859$	−8.10805	+	6.80346i	−0.276643	+	0.232131i	0.493901	+	0.869518i	$0.335571\pi$
$860$	−25.6063	−	4.51509i	−0.873169	−	0.153963i
$861$	−0.0408723	−	10.4013i	−0.00139292	−	0.354475i
$862$	9.62927	+	16.6784i	0.327974	+	0.568068i
$863$	23.9721			0.816021			0.408011	−	0.912977i	$-0.366223\pi$
$863$	23.9721			0.816021			0.408011	+	0.912977i	$0.366223\pi$
$864$	4.82357	+	1.93214i	0.164101	+	0.0657327i
$865$	−7.60941	+	1.34174i	−0.258728	+	0.0456207i
$866$		−	28.1040i		−	0.955014i
$867$	38.0114	+	32.5909i	1.29093	+	1.10684i
$868$	−5.18299	+	4.47935i	−0.175922	+	0.152039i
$869$	6.50535	−	36.8937i	0.220679	−	1.25153i
$870$	−10.0628	−	5.95345i	−0.341162	−	0.201841i
$871$	12.2677	−	69.5735i	0.415674	−	2.35741i
$872$	−2.32444	−	6.38634i	−0.0787154	−	0.216269i
$873$	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
$876$	22.1674	+	8.33647i	0.748967	+	0.281663i
$877$	−16.4133	+	19.5606i	−0.554238	+	0.660516i	−0.968317	−	0.249726i	$-0.919660\pi$
$877$	−16.4133	+	19.5606i	−0.554238	+	0.660516i	0.414078	+	0.910241i	$0.364104\pi$
$878$	4.20632	−	11.5568i	0.141957	−	0.390022i
$879$	3.63087	+	1.36546i	0.122466	+	0.0460557i
$880$	1.48546	+	8.42444i	0.0500747	+	0.283988i
$881$	−26.1261	+	15.0839i	−0.880212	+	0.508190i	−0.870728	−	0.491765i	$-0.836352\pi$
$881$	−26.1261	+	15.0839i	−0.880212	+	0.508190i	−0.00948336	+	0.999955i	$0.503019\pi$
$882$	−15.9804	+	13.6245i	−0.538086	+	0.458762i
$883$	−5.87608	+	4.93062i	−0.197746	+	0.165929i	−0.736284	−	0.676673i	$-0.763421\pi$
$883$	−5.87608	+	4.93062i	−0.197746	+	0.165929i	0.538538	+	0.842601i	$0.318977\pi$
$884$	38.0110	+	13.8349i	1.27845	+	0.465317i
$885$	−15.8815	+	18.5229i	−0.533852	+	0.622642i
$886$		−	22.9666i		−	0.771578i
$887$	−2.37597	−	13.4748i	−0.0797773	−	0.452439i	−0.998362	−	0.0572150i	$-0.981778\pi$
$887$	−2.37597	−	13.4748i	−0.0797773	−	0.452439i	0.918585	−	0.395224i	$-0.129333\pi$
$888$	−15.9301	+	2.63443i	−0.534578	+	0.0884056i
$889$	−31.6259	+	27.3323i	−1.06070	+	0.916697i
$890$	0.989806	+	2.71947i	0.0331784	+	0.0911568i
$891$	13.8282	−	33.4852i	0.463262	−	1.12180i
$892$	−8.41483	−	4.85831i	−0.281749	−	0.162668i
$893$	10.8625	+	4.55278i	0.363500	+	0.152353i
$894$	−15.7444	+	18.3630i	−0.526572	+	0.614151i
$895$	10.0875	−	12.0218i	0.337188	−	0.401845i
$896$	−2.61197	−	0.421416i	−0.0872599	−	0.0140785i
$897$	29.6233	+	52.5937i	0.989093	+	1.75605i
$898$	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
$903$	−48.6666	−	27.8433i	−1.61952	−	0.926566i
$904$	−7.94852	+	13.7672i	−0.264364	+	0.457892i
$905$	0.750016	−	1.29907i	0.0249314	−	0.0431824i
$906$	22.1160	+	13.0844i	0.734754	+	0.434701i
$907$	−2.25977	+	2.69309i	−0.0750344	+	0.0894226i	−0.802256	−	0.596981i	$-0.796367\pi$
$907$	−2.25977	+	2.69309i	−0.0750344	+	0.0894226i	0.727221	+	0.686403i	$0.240811\pi$
$908$	−10.5804	+	8.87803i	−0.351124	+	0.294628i
$909$	3.52340	+	2.13548i	0.116864	+	0.0708294i
$910$	−21.1996	+	26.0255i	−0.702758	+	0.862738i
$911$	−32.1835			−1.06629			−0.533143	−	0.846025i	$-0.678989\pi$
$911$	−32.1835			−1.06629			−0.533143	+	0.846025i	$0.678989\pi$
$912$	−6.30661	−	4.15050i	−0.208833	−	0.137437i
$913$	12.3669	−	21.4200i	0.409283	−	0.708899i
$914$	7.05182	−	2.56665i	0.233253	−	0.0848973i
$915$	1.69232	−	4.50003i	0.0559465	−	0.148766i
$916$	−1.12956	−	6.40605i	−0.0373217	−	0.211662i
$917$	4.33275	+	3.52932i	0.143080	+	0.116548i
$918$	21.7581	+	27.6786i	0.718124	+	0.913529i
$919$	27.9345	−	48.3840i	0.921476	−	1.59604i	0.124342	−	0.992239i	$-0.460318\pi$
$919$	27.9345	−	48.3840i	0.921476	−	1.59604i	0.797134	−	0.603803i	$-0.206349\pi$
$920$	−6.20276	−	10.7435i	−0.204499	−	0.354202i
$921$	−18.7317	+	10.5506i	−0.617230	+	0.347653i
$922$	−6.78163	+	18.6324i	−0.223341	+	0.613625i
$923$	19.0441	+	10.9951i	0.626846	+	0.361910i
$924$	−3.13179	+	18.1787i	−0.103028	+	0.598035i
$925$	−1.54256	+	4.23814i	−0.0507189	+	0.139349i
$926$	−11.7288	+	4.26892i	−0.385431	+	0.140285i
$927$	−1.90967	−	5.61587i	−0.0627218	−	0.184449i
$928$	0.551587	−	3.12821i	0.0181067	−	0.102688i
$929$	−17.2150	−	3.03547i	−0.564805	−	0.0995904i	−0.116047	−	0.993244i	$-0.537022\pi$
$929$	−17.2150	−	3.03547i	−0.564805	−	0.0995904i	−0.448758	+	0.893653i	$0.648134\pi$
$930$	−8.98988	+	3.16412i	−0.294790	+	0.103756i
$931$	26.7047	−	14.7600i	0.875213	−	0.483738i
$932$			22.5607i			0.739000i
$933$	11.4913	−	1.90038i	0.376210	−	0.0622156i
$934$	−41.2165	−	7.26757i	−1.34864	−	0.237802i
$935$	−19.8238	+	54.4653i	−0.648306	+	1.78121i
$936$	15.3166	+	9.28315i	0.500638	+	0.303429i
$937$	6.60919	+	2.40555i	0.215913	+	0.0785859i	0.447712	−	0.894178i	$-0.352239\pi$
$937$	6.60919	+	2.40555i	0.215913	+	0.0785859i	−0.231799	+	0.972764i	$0.574461\pi$
$938$	−15.2575	+	27.3392i	−0.498176	+	0.892656i
$939$	−3.03840	+	16.2203i	−0.0991544	+	0.529330i
$940$	5.39595	+	1.96397i	0.175996	+	0.0640575i
$941$	−3.73287	−	21.1701i	−0.121688	−	0.690127i	−0.983220	−	0.182423i	$-0.941606\pi$
$941$	−3.73287	−	21.1701i	−0.121688	−	0.690127i	0.861532	−	0.507703i	$-0.169505\pi$
$942$	−10.3918	−	8.90990i	−0.338583	−	0.290300i
$943$	11.4747	+	6.62489i	0.373666	+	0.215736i
$944$	−6.22895	−	2.26715i	−0.202735	−	0.0737896i
$945$	−27.6231	+	9.51447i	−0.898579	+	0.309506i
$946$	−48.5026	+	8.55232i	−1.57696	+	0.278060i
$947$	−19.9189	+	23.7384i	−0.647277	+	0.771395i	−0.985501	−	0.169671i	$-0.945730\pi$
$947$	−19.9189	+	23.7384i	−0.647277	+	0.771395i	0.338224	+	0.941066i	$0.390174\pi$
$948$	10.2296	+	12.4580i	0.332241	+	0.404617i
$949$	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	$-0.344911\pi$
$953$	43.0588	−	15.6721i	1.39481	−	0.507670i	0.926634	+	0.375965i	$0.122689\pi$
$954$	0.108535	−	0.547169i	0.00351396	−	0.0177153i
$955$	39.7060	+	33.3173i	1.28486	+	1.07812i
$956$	15.7497	+	18.7698i	0.509383	+	0.607059i
$957$	−21.7680	−	4.07760i	−0.703661	−	0.131810i
$958$	20.3927	+	11.7737i	0.658859	+	0.380392i
$959$	0.445465	−	0.384988i	0.0143848	−	0.0124319i
$960$	−3.16793	−	1.87424i	−0.102245	−	0.0604907i
$961$	24.2960			0.783742
$962$	−55.6537			−1.79435
$963$	1.70088	−	8.57479i	0.0548101	−	0.276319i
$964$	0.351142	+	0.964754i	0.0113095	+	0.0310726i
$965$	−6.55675	−	37.1852i	−0.211069	−	1.19703i
$966$	−4.74873	−	26.3260i	−0.152788	−	0.847026i
$967$	0.810496	+	0.680087i	0.0260638	+	0.0218701i	0.655726	−	0.754999i	$-0.272362\pi$
$967$	0.810496	+	0.680087i	0.0260638	+	0.0218701i	−0.629663	+	0.776869i	$0.716807\pi$
$968$	2.60172	+	4.50631i	0.0836225	+	0.144838i
$969$	−22.9450	−	45.7197i	−0.737099	−	1.46873i
$970$	−5.24590	+	9.08617i	−0.168436	+	0.291739i
$971$	−1.71325	+	9.71635i	−0.0549809	+	0.311812i	−0.999879	−	0.0155521i	$-0.995049\pi$
$971$	−1.71325	+	9.71635i	−0.0549809	+	0.311812i	0.944898	+	0.327365i	$0.106161\pi$
$972$	7.06522	+	13.8954i	0.226617	+	0.445696i
$973$	21.0207	+	24.3228i	0.673892	+	0.779752i
$974$	0.0120774	+	0.00212956i	0.000386984	+	6.82357e-5i
$975$	4.35892	−	2.45515i	0.139597	−	0.0786278i
$976$	1.30615			0.0418088
$977$	−1.95106	−	3.37934i	−0.0624200	−	0.108115i	0.833127	−	0.553082i	$-0.186548\pi$
$977$	−1.95106	−	3.37934i	−0.0624200	−	0.108115i	−0.895547	+	0.444968i	$0.853215\pi$
$978$	27.6856	+	0.294632i	0.885289	+	0.00942130i
$979$	3.52357	+	4.19923i	0.112614	+	0.134208i
$980$	12.6607	−	7.81019i	0.404432	−	0.249488i
$981$	7.37947	−	19.0063i	0.235608	−	0.606824i
$982$	−20.8257	+	3.67213i	−0.664574	+	0.117182i
$983$	20.2666	+	17.0057i	0.646405	+	0.542398i	0.905978	−	0.423326i	$-0.139137\pi$
$983$	20.2666	+	17.0057i	0.646405	+	0.542398i	−0.259573	+	0.965724i	$0.583582\pi$
$984$	3.93112	+	0.0418352i	0.125320	+	0.00133366i
$985$	−16.9971	−	14.2623i	−0.541572	−	0.454433i
$986$	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
$990$	−13.3017	+	21.9469i	−0.422755	+	0.697518i
$991$	41.8613	+	7.38128i	1.32977	+	0.234474i	0.792982	−	0.609245i	$-0.208527\pi$
$991$	41.8613	+	7.38128i	1.32977	+	0.234474i	0.536786	+	0.843719i	$0.319638\pi$
$992$	−1.66431	−	1.98345i	−0.0528419	−	0.0629745i
$993$	−39.7688	+	6.57674i	−1.26202	+	0.208707i
$994$	−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	0.940717	+	0.339193i	$0.110154\pi$
$997$	5.45441	+	30.9335i	0.172743	+	0.979674i	−0.767974	+	0.640481i	$0.778735\pi$
$998$	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.a.725.13	yes	162
3.2	odd	2		798.2.cc.b.725.9	yes	162
7.2	even	3		798.2.bu.a.611.24	yes	162
19.13	odd	18		798.2.bu.b.431.10	yes	162
21.2	odd	6		798.2.bu.b.611.10	yes	162
57.32	even	18		798.2.bu.a.431.24	✓	162
133.51	odd	18		798.2.cc.b.317.9	yes	162
399.317	even	18	inner	798.2.cc.a.317.13	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.24	✓	162	57.32	even	18
798.2.bu.a.611.24	yes	162	7.2	even	3
798.2.bu.b.431.10	yes	162	19.13	odd	18
798.2.bu.b.611.10	yes	162	21.2	odd	6
798.2.cc.a.317.13	yes	162	399.317	even	18	inner
798.2.cc.a.725.13	yes	162	1.1	even	1	trivial
798.2.cc.b.317.9	yes	162	133.51	odd	18
798.2.cc.b.725.9	yes	162	3.2	odd	2

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} +(-0.282599 - 1.70884i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.726838 + 1.99697i) q^{5} +(-1.73195 - 0.0184316i) q^{6} +(2.31032 + 1.28935i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.84028 + 0.965833i) q^{9} +(2.09285 - 0.369026i) q^{10} +(3.48606 - 2.01268i) q^{11} +(-0.318902 + 1.70244i) q^{12} +(-2.04188 + 5.61002i) q^{13} +(1.67094 - 2.05133i) q^{14} +(3.20710 - 1.80639i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.31737 + 6.36693i) q^{17} +(0.457951 + 2.96484i) q^{18} +(0.208365 - 4.35392i) q^{19} -2.12513i q^{20} +(1.55040 - 4.31234i) q^{21} +(-1.37675 - 3.78259i) q^{22} +(3.75229 + 4.47180i) q^{23} +(1.62120 + 0.609683i) q^{24} +(0.370619 - 0.310986i) q^{25} +(5.17022 + 2.98503i) q^{26} +(2.45311 + 4.58064i) 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} +(-4.42450 - 5.38834i) q^{33} +(6.67261 - 1.17656i) q^{34} +(-0.895566 + 5.55079i) q^{35} +(2.99932 + 0.0638452i) q^{36} +(-8.07321 + 4.66107i) q^{37} +(-4.25159 - 0.961249i) q^{38} +(10.1637 + 1.90386i) q^{39} +(-2.09285 - 0.369026i) q^{40} +(2.13288 - 0.776304i) q^{41} +(-3.97760 - 2.27568i) 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} +(0.881939 - 1.49070i) q^{48} +(3.67516 + 5.95762i) q^{49} +(-0.241904 - 0.418991i) q^{50} +(10.2252 - 5.75931i) q^{51} +(3.83748 - 4.57333i) q^{52} +(-0.174729 - 0.0635963i) q^{53} +(4.93703 - 1.62043i) q^{54} +(6.55305 + 5.49867i) q^{55} +(-2.27177 + 1.35612i) q^{56} +(-7.49903 + 0.874349i) q^{57} +(-1.58823 - 2.75090i) q^{58} +(-6.22895 + 2.26715i) q^{59} +(-3.63152 + 0.600560i) q^{60} +(1.00057 - 0.839577i) q^{61} +(-2.54987 - 0.449611i) q^{62} +(-7.80724 - 1.43072i) q^{63} +(-0.500000 - 0.866025i) q^{64} -12.6872 q^{65} +(-6.07478 + 3.42160i) q^{66} +(-11.6537 + 2.05487i) q^{67} -6.77555i q^{68} +(6.58121 - 7.67579i) q^{69} +(5.31095 + 1.84585i) q^{70} +(0.639621 - 3.62747i) q^{71} +(0.583702 - 2.94267i) q^{72} +(2.37437 - 13.4657i) q^{73} +(3.18836 + 8.75995i) q^{74} +(-0.636163 - 0.545444i) q^{75} +(-1.68493 + 4.02008i) q^{76} +(10.6489 - 0.155179i) q^{77} +(3.63984 - 9.67866i) q^{78} +(5.98225 - 7.12937i) q^{79} +(-0.726838 + 1.99697i) q^{80} +(7.13433 - 5.48647i) q^{81} +(-0.394140 - 2.23528i) q^{82} +(5.32128 - 3.07224i) q^{83} +(-2.93181 + 3.52200i) q^{84} +(-11.0302 + 9.25546i) q^{85} +(-11.4973 - 4.18467i) q^{86} +(-4.17675 - 3.58114i) q^{87} +4.02535i q^{88} +(0.236473 + 1.34111i) q^{89} +(-5.58785 + 3.06948i) q^{90} +(-11.9507 + 10.3282i) q^{91} +(-1.99655 - 5.48548i) q^{92} +(-4.42454 + 0.731707i) q^{93} +(2.34006 + 1.35103i) q^{94} +(8.84610 - 2.74849i) q^{95} +(-1.31491 - 1.12740i) q^{96} +(-3.17345 + 3.78197i) q^{97} +(6.50529 - 2.58479i) q^{98} +(-7.95745 + 9.08350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 9 q^{14} + 27 q^{15} + 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} - 9 q^{27} - 12 q^{28} + 6 q^{29} + 12 q^{33} + 6 q^{34} - 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 9 * q^14 + 27 * 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 - 3 * q^60 - 9 * q^61 + 36 * q^62 + 12 * 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 - 6 * q^78 + 21 * q^79 + 12 * q^81 - 3 * q^84 - 6 * q^85 + 36 * q^86 + 24 * q^87 - 54 * q^89 + 36 * q^90 + 75 * q^91 + 42 * q^93 + 72 * q^94 - 12 * q^97 + 12 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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