LMFDB - Embedded newform 1089.2.e.o.364.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1089,2,Mod(364,1089)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1089.364"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1089, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,-2,9,-12,1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.8
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.o.727.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.332160 - 0.575318i) q^{2} +(1.61109 - 0.635904i) q^{3} +(0.779339 - 1.34985i) q^{4} +(-0.558312 + 0.967024i) q^{5} +(-0.900989 - 0.715670i) q^{6} +(-1.95227 - 3.38143i) q^{7} -2.36410 q^{8} +(2.19125 - 2.04900i) q^{9} +0.741796 q^{10} +(0.397211 - 2.67033i) q^{12} +(1.33900 - 2.31922i) q^{13} +(-1.29693 + 2.24635i) q^{14} +(-0.284558 + 1.91300i) q^{15} +(-0.773417 - 1.33960i) q^{16} -5.54657 q^{17} +(-1.90668 - 0.580070i) q^{18} +5.13234 q^{19} +(0.870228 + 1.50728i) q^{20} +(-5.29556 - 4.20635i) q^{21} +(-1.05719 + 1.83110i) q^{23} +(-3.80879 + 1.50334i) q^{24} +(1.87658 + 3.25033i) q^{25} -1.77905 q^{26} +(2.22734 - 4.69457i) q^{27} -6.08592 q^{28} +(0.541520 + 0.937941i) q^{29} +(1.19510 - 0.471711i) q^{30} +(0.215081 - 0.372532i) q^{31} +(-2.87790 + 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} +4.35990 q^{35} +(-1.05813 - 4.55474i) q^{36} -8.70580 q^{37} +(-1.70476 - 2.95273i) q^{38} +(0.682457 - 4.58796i) q^{39} +(1.31991 - 2.28614i) q^{40} +(-1.45954 + 2.52799i) q^{41} +(-0.661016 + 4.44382i) q^{42} +(-1.11628 - 1.93346i) q^{43} +(0.758035 + 3.26298i) q^{45} +1.40462 q^{46} +(-6.41773 - 11.1158i) q^{47} +(-2.09790 - 1.66640i) q^{48} +(-4.12272 + 7.14077i) q^{49} +(1.24665 - 2.15926i) q^{50} +(-8.93605 + 3.52709i) q^{51} +(-2.08707 - 3.61492i) q^{52} +5.64118 q^{53} +(-3.44070 + 0.277916i) q^{54} +(4.61537 + 7.99405i) q^{56} +(8.26869 - 3.26368i) q^{57} +(0.359743 - 0.623093i) q^{58} +(1.18769 - 2.05713i) q^{59} +(2.36051 + 1.87499i) q^{60} +(-2.04223 - 3.53724i) q^{61} -0.285766 q^{62} +(-11.2065 - 3.40936i) q^{63} +0.730027 q^{64} +(1.49516 + 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(-4.32266 + 7.48706i) q^{68} +(-0.538824 + 3.62235i) q^{69} +(-1.44819 - 2.50833i) q^{70} +6.31707 q^{71} +(-5.18034 + 4.84406i) q^{72} +11.6727 q^{73} +(2.89172 + 5.00861i) q^{74} +(5.09024 + 4.04326i) q^{75} +(3.99983 - 6.92792i) q^{76} +(-2.86622 + 1.13131i) q^{78} +(2.25735 + 3.90985i) q^{79} +1.72723 q^{80} +(0.603167 - 8.97977i) q^{81} +1.93920 q^{82} +(0.241002 + 0.417427i) q^{83} +(-9.80500 + 3.87007i) q^{84} +(3.09671 - 5.36367i) q^{85} +(-0.741570 + 1.28444i) q^{86} +(1.46888 + 1.16676i) q^{87} +16.0830 q^{89} +(1.62546 - 1.51994i) q^{90} -10.4564 q^{91} +(1.64782 + 2.85410i) q^{92} +(0.109622 - 0.736955i) q^{93} +(-4.26343 + 7.38448i) q^{94} +(-2.86545 + 4.96310i) q^{95} +(-1.46680 + 9.86084i) q^{96} +(-4.00783 - 6.94176i) q^{97} +5.47762 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.332160	−	0.575318i	−0.234873	−	0.406812i	0.724363	−	0.689419i	$-0.242134\pi$
$2$	−0.332160	−	0.575318i	−0.234873	−	0.406812i	−0.959236	+	0.282607i	$0.908801\pi$
$3$	1.61109	−	0.635904i	0.930166	−	0.367139i
$3$	1.61109	−	0.635904i	0.930166	−	0.367139i
$4$	0.779339	−	1.34985i	0.389670	−	0.674927i
$5$	−0.558312	+	0.967024i	−0.249685	+	0.432466i	−0.963438	−	0.267930i	$-0.913660\pi$
$5$	−0.558312	+	0.967024i	−0.249685	+	0.432466i	0.713754	+	0.700397i	$0.246994\pi$
$6$	−0.900989	−	0.715670i	−0.367827	−	0.292171i
$7$	−1.95227	−	3.38143i	−0.737889	−	1.27806i	−0.953444	−	0.301570i	$-0.902489\pi$
$7$	−1.95227	−	3.38143i	−0.737889	−	1.27806i	0.215555	−	0.976492i	$-0.430844\pi$
$8$	−2.36410			−0.835837
$9$	2.19125	−	2.04900i	0.730417	−	0.683001i
$10$	0.741796			0.234576
$11$		0			0
$11$		0			0
$12$	0.397211	−	2.67033i	0.114665	−	0.770858i
$13$	1.33900	−	2.31922i	0.371372	−	0.643236i	−0.618405	−	0.785860i	$-0.712221\pi$
$13$	1.33900	−	2.31922i	0.371372	−	0.643236i	0.989777	+	0.142624i	$0.0455540\pi$
$14$	−1.29693	+	2.24635i	−0.346620	+	0.600364i
$15$	−0.284558	+	1.91300i	−0.0734726	+	0.493934i
$16$	−0.773417	−	1.33960i	−0.193354	−	0.334900i
$17$	−5.54657			−1.34524			−0.672620	−	0.739988i	$-0.734831\pi$
$17$	−5.54657			−1.34524			−0.672620	+	0.739988i	$0.734831\pi$
$18$	−1.90668	−	0.580070i	−0.449408	−	0.136724i
$19$	5.13234			1.17744			0.588720	−	0.808337i	$-0.299632\pi$
$19$	5.13234			1.17744			0.588720	+	0.808337i	$0.299632\pi$
$20$	0.870228	+	1.50728i	0.194589	+	0.337038i
$21$	−5.29556	−	4.20635i	−1.15559	−	0.917901i
$22$		0			0
$23$	−1.05719	+	1.83110i	−0.220439	+	0.381812i	−0.954941	−	0.296795i	$-0.904082\pi$
$23$	−1.05719	+	1.83110i	−0.220439	+	0.381812i	0.734502	+	0.678606i	$0.237416\pi$
$24$	−3.80879	+	1.50334i	−0.777467	+	0.306869i
$25$	1.87658	+	3.25033i	0.375315	+	0.650065i
$26$	−1.77905			−0.348901
$27$	2.22734	−	4.69457i	0.428652	−	0.903469i
$28$	−6.08592			−1.15013
$29$	0.541520	+	0.937941i	0.100558	+	0.174171i	0.911915	−	0.410380i	$-0.134604\pi$
$29$	0.541520	+	0.937941i	0.100558	+	0.174171i	−0.811357	+	0.584551i	$0.801271\pi$
$30$	1.19510	−	0.471711i	0.218195	−	0.0861223i
$31$	0.215081	−	0.372532i	0.0386297	−	0.0669087i	−0.846064	−	0.533081i	$-0.821034\pi$
$31$	0.215081	−	0.372532i	0.0386297	−	0.0669087i	0.884694	+	0.466172i	$0.154367\pi$
$32$	−2.87790	+	4.98467i	−0.508746	+	0.881173i
$33$		0			0
$34$	1.84235	+	3.19104i	0.315960	+	0.547259i
$35$	4.35990			0.736958
$36$	−1.05813	−	4.55474i	−0.176355	−	0.759123i
$37$	−8.70580			−1.43122			−0.715612	−	0.698498i	$-0.753852\pi$
$37$	−8.70580			−1.43122			−0.715612	+	0.698498i	$0.753852\pi$
$38$	−1.70476	−	2.95273i	−0.276549	−	0.478996i
$39$	0.682457	−	4.58796i	0.109281	−	0.734661i
$40$	1.31991	−	2.28614i	0.208695	−	0.361471i
$41$	−1.45954	+	2.52799i	−0.227942	+	0.394806i	−0.957198	−	0.289434i	$-0.906533\pi$
$41$	−1.45954	+	2.52799i	−0.227942	+	0.394806i	0.729256	+	0.684241i	$0.239866\pi$
$42$	−0.661016	+	4.44382i	−0.101997	+	0.685696i
$43$	−1.11628	−	1.93346i	−0.170232	−	0.294850i	0.768269	−	0.640127i	$-0.221118\pi$
$43$	−1.11628	−	1.93346i	−0.170232	−	0.294850i	−0.938501	+	0.345277i	$0.887785\pi$
$44$		0			0
$45$	0.758035	+	3.26298i	0.113001	+	0.486416i
$46$	1.40462			0.207101
$47$	−6.41773	−	11.1158i	−0.936123	−	1.62141i	−0.772619	−	0.634870i	$-0.781054\pi$
$47$	−6.41773	−	11.1158i	−0.936123	−	1.62141i	−0.163503	−	0.986543i	$-0.552279\pi$
$48$	−2.09790	−	1.66640i	−0.302806	−	0.240524i
$49$	−4.12272	+	7.14077i	−0.588961	+	1.02011i
$50$	1.24665	−	2.15926i	0.176303	−	0.305365i
$51$	−8.93605	+	3.52709i	−1.25130	+	0.493891i
$52$	−2.08707	−	3.61492i	−0.289425	−	0.501299i
$53$	5.64118			0.774876			0.387438	−	0.921896i	$-0.373360\pi$
$53$	5.64118			0.774876			0.387438	+	0.921896i	$0.373360\pi$
$54$	−3.44070	+	0.277916i	−0.468221	+	0.0378196i
$55$		0			0
$56$	4.61537	+	7.99405i	0.616755	+	1.06825i
$57$	8.26869	−	3.26368i	1.09521	−	0.432285i
$58$	0.359743	−	0.623093i	0.0472366	−	0.0818162i
$59$	1.18769	−	2.05713i	0.154623	−	0.267816i	−0.778298	−	0.627895i	$-0.783917\pi$
$59$	1.18769	−	2.05713i	0.154623	−	0.267816i	0.932922	+	0.360079i	$0.117250\pi$
$60$	2.36051	+	1.87499i	0.304740	+	0.242060i
$61$	−2.04223	−	3.53724i	−0.261480	−	0.452897i	0.705155	−	0.709053i	$-0.250877\pi$
$61$	−2.04223	−	3.53724i	−0.261480	−	0.452897i	−0.966636	+	0.256156i	$0.917544\pi$
$62$	−0.285766			−0.0362923
$63$	−11.2065	−	3.40936i	−1.41188	−	0.429539i
$64$	0.730027			0.0912533
$65$	1.49516	+	2.58969i	0.185452	+	0.321212i
$66$		0			0
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	−0.397772	−	0.917484i	$-0.630216\pi$
$67$	4.87584	−	8.44521i	0.595679	−	1.03175i	0.993451	−	0.114262i	$-0.0364503\pi$
$68$	−4.32266	+	7.48706i	−0.524199	+	0.907940i
$69$	−0.538824	+	3.62235i	−0.0648668	+	0.436080i
$70$	−1.44819	−	2.50833i	−0.173091	−	0.299803i
$71$	6.31707			0.749699			0.374849	−	0.927086i	$-0.377694\pi$
$71$	6.31707			0.749699			0.374849	+	0.927086i	$0.377694\pi$
$72$	−5.18034	+	4.84406i	−0.610509	+	0.570877i
$73$	11.6727			1.36618			0.683091	−	0.730333i	$-0.260635\pi$
$73$	11.6727			1.36618			0.683091	+	0.730333i	$0.260635\pi$
$74$	2.89172	+	5.00861i	0.336156	+	0.582239i
$75$	5.09024	+	4.04326i	0.587770	+	0.466875i
$76$	3.99983	−	6.92792i	0.458812	−	0.794686i
$77$		0			0
$78$	−2.86622	+	1.13131i	−0.324536	+	0.128095i
$79$	2.25735	+	3.90985i	0.253972	+	0.439893i	0.964616	−	0.263659i	$-0.0849295\pi$
$79$	2.25735	+	3.90985i	0.253972	+	0.439893i	−0.710644	+	0.703552i	$0.751596\pi$
$80$	1.72723			0.193110
$81$	0.603167	−	8.97977i	0.0670185	−	0.997752i
$82$	1.93920			0.214149
$83$	0.241002	+	0.417427i	0.0264534	+	0.0458186i	0.878949	−	0.476916i	$-0.158245\pi$
$83$	0.241002	+	0.417427i	0.0264534	+	0.0458186i	−0.852496	+	0.522734i	$0.824912\pi$
$84$	−9.80500	+	3.87007i	−1.06981	+	0.422259i
$85$	3.09671	−	5.36367i	0.335886	−	0.581771i
$86$	−0.741570	+	1.28444i	−0.0799656	+	0.138504i
$87$	1.46888	+	1.16676i	0.157481	+	0.125089i
$88$		0			0
$89$	16.0830			1.70480			0.852399	−	0.522891i	$-0.175147\pi$
$89$	16.0830			1.70480			0.852399	+	0.522891i	$0.175147\pi$
$90$	1.62546	−	1.51994i	0.171339	−	0.160216i
$91$	−10.4564			−1.09613
$92$	1.64782	+	2.85410i	0.171797	+	0.297561i
$93$	0.109622	−	0.736955i	0.0113672	−	0.0764187i
$94$	−4.26343	+	7.38448i	−0.439739	+	0.761651i
$95$	−2.86545	+	4.96310i	−0.293989	+	0.509203i
$96$	−1.46680	+	9.86084i	−0.149704	+	1.00642i
$97$	−4.00783	−	6.94176i	−0.406933	−	0.704829i	0.587611	−	0.809143i	$-0.300068\pi$
$97$	−4.00783	−	6.94176i	−0.406933	−	0.704829i	−0.994544	+	0.104315i	$0.966735\pi$
$98$	5.47762			0.553323
$99$		0			0
$100$	5.84996			0.584996
$101$	0.880657	+	1.52534i	0.0876287	+	0.151777i	0.906508	−	0.422188i	$-0.138738\pi$
$101$	0.880657	+	1.52534i	0.0876287	+	0.151777i	−0.818880	+	0.573965i	$0.805404\pi$
$102$	4.99740	+	3.96951i	0.494816	+	0.393040i
$103$	−1.34383	+	2.32759i	−0.132412	+	0.229344i	−0.924606	−	0.380925i	$-0.875605\pi$
$103$	−1.34383	+	2.32759i	−0.132412	+	0.229344i	0.792194	+	0.610269i	$0.208939\pi$
$104$	−3.16554	+	5.48287i	−0.310407	+	0.537640i
$105$	7.02422	−	2.77248i	0.685493	−	0.270566i
$106$	−1.87378	−	3.24548i	−0.181997	−	0.315229i
$107$	10.2764			0.993456			0.496728	−	0.867906i	$-0.334535\pi$
$107$	10.2764			0.993456			0.496728	+	0.867906i	$0.334535\pi$
$108$	−4.60113	−	6.66525i	−0.442744	−	0.641364i
$109$	−2.36284			−0.226319			−0.113160	−	0.993577i	$-0.536097\pi$
$109$	−2.36284			−0.226319			−0.113160	+	0.993577i	$0.536097\pi$
$110$		0			0
$111$	−14.0259	+	5.53605i	−1.33128	+	0.525459i
$112$	−3.01984	+	5.23052i	−0.285348	+	0.494237i
$113$	−0.766216	+	1.32713i	−0.0720796	+	0.124845i	−0.899813	−	0.436277i	$-0.856297\pi$
$113$	−0.766216	+	1.32713i	−0.0720796	+	0.124845i	0.827733	+	0.561122i	$0.189630\pi$
$114$	−4.62418	−	3.67306i	−0.433094	−	0.344014i
$115$	−1.18048	−	2.04465i	−0.110080	−	0.190665i
$116$	1.68811			0.156737
$117$	−1.81800	−	7.82561i	−0.168074	−	0.723478i
$118$	−1.57801			−0.145267
$119$	10.8284	+	18.7553i	0.992638	+	1.71930i
$120$	0.672725	−	4.52253i	0.0614111	−	0.412849i
$121$		0			0
$122$	−1.35669	+	2.34986i	−0.122829	+	0.212746i
$123$	−0.743892	+	5.00096i	−0.0670745	+	0.450922i
$124$	−0.335242	−	0.580657i	−0.0301057	−	0.0521445i
$125$	−9.77397			−0.874211
$126$	1.76088	+	7.57975i	0.156872	+	0.675258i
$127$	7.65133			0.678946			0.339473	−	0.940616i	$-0.389751\pi$
$127$	7.65133			0.678946			0.339473	+	0.940616i	$0.389751\pi$
$128$	5.51331	+	9.54934i	0.487313	+	0.844050i
$129$	−3.02793	−	2.40514i	−0.266595	−	0.211761i
$130$	0.993266	−	1.72039i	0.0871152	−	0.150888i
$131$	−2.67956	+	4.64113i	−0.234114	+	0.405498i	−0.959015	−	0.283356i	$-0.908552\pi$
$131$	−2.67956	+	4.64113i	−0.234114	+	0.405498i	0.724901	+	0.688853i	$0.241886\pi$
$132$		0			0
$133$	−10.0197	−	17.3547i	−0.868820	−	1.50484i
$134$	−6.47825			−0.559635
$135$	3.29621	+	4.77493i	0.283692	+	0.410960i
$136$	13.1127			1.12440
$137$	−8.36560	−	14.4896i	−0.714721	−	1.23793i	−0.963067	−	0.269262i	$-0.913220\pi$
$137$	−8.36560	−	14.4896i	−0.714721	−	1.23793i	0.248346	−	0.968672i	$-0.420113\pi$
$138$	2.26298	−	0.893207i	0.192638	−	0.0760348i
$139$	6.87006	−	11.8993i	0.582711	−	1.00928i	−0.412446	−	0.910982i	$-0.635325\pi$
$139$	6.87006	−	11.8993i	0.582711	−	1.00928i	0.995157	−	0.0983023i	$-0.0313412\pi$
$140$	3.39784	−	5.88524i	0.287170	−	0.497393i
$141$	−17.4082	−	13.8276i	−1.46603	−	1.16449i
$142$	−2.09828	−	3.63433i	−0.176084	−	0.304986i
$143$		0			0
$144$	−4.43959	−	1.35066i	−0.369966	−	0.112555i
$145$	−1.20935			−0.100431
$146$	−3.87720	−	6.71550i	−0.320879	−	0.555779i
$147$	−2.10125	+	14.1261i	−0.173309	+	1.16510i
$148$	−6.78477	+	11.7516i	−0.557704	+	0.965973i
$149$	2.77983	−	4.81480i	0.227732	−	0.394444i	−0.729403	−	0.684084i	$-0.760202\pi$
$149$	2.77983	−	4.81480i	0.227732	−	0.394444i	0.957136	+	0.289640i	$0.0935355\pi$
$150$	0.635387	−	4.27152i	0.0518791	−	0.348768i
$151$	−0.0819538	−	0.141948i	−0.00666930	−	0.0115516i	0.862671	−	0.505765i	$-0.168790\pi$
$151$	−0.0819538	−	0.141948i	−0.00666930	−	0.0115516i	−0.869341	+	0.494213i	$0.835456\pi$
$152$	−12.1334			−0.984147
$153$	−12.1539	+	11.3649i	−0.982587	+	0.918801i
$154$		0			0
$155$	0.240165	+	0.415978i	0.0192905	+	0.0334121i
$156$	−5.66121	−	4.49679i	−0.453260	−	0.360032i
$157$	−11.9265	+	20.6573i	−0.951839	+	1.64863i	−0.210397	+	0.977616i	$0.567476\pi$
$157$	−11.9265	+	20.6573i	−0.951839	+	1.64863i	−0.741442	+	0.671018i	$0.765858\pi$
$158$	1.49961	−	2.59739i	0.119302	−	0.206638i
$159$	9.08848	−	3.58725i	0.720763	−	0.284488i
$160$	−3.21353	−	5.56600i	−0.254052	−	0.440031i
$161$	8.25568			0.650638
$162$	−5.36657	+	2.63571i	−0.421638	+	0.207081i
$163$	−4.19602			−0.328658			−0.164329	−	0.986406i	$-0.552546\pi$
$163$	−4.19602			−0.328658			−0.164329	+	0.986406i	$0.552546\pi$
$164$	2.27495	+	3.94033i	0.177644	+	0.307688i
$165$		0			0
$166$	0.160102	−	0.277306i	0.0124264	−	0.0215231i
$167$	7.92020	−	13.7182i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$167$	7.92020	−	13.7182i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$168$	12.5193	+	9.94425i	0.965881	+	0.767215i
$169$	2.91415	+	5.04745i	0.224165	+	0.388265i
$170$	−4.11442			−0.315562
$171$	11.2462	−	10.5162i	0.860022	−	0.804193i
$172$	−3.47985			−0.265336
$173$	−1.30144	−	2.25417i	−0.0989470	−	0.171381i	0.812302	−	0.583237i	$-0.198214\pi$
$173$	−1.30144	−	2.25417i	−0.0989470	−	0.171381i	−0.911249	+	0.411856i	$0.864881\pi$
$174$	0.183352	−	1.23262i	0.0138999	−	0.0934450i
$175$	7.32717	−	12.6910i	0.553882	−	0.959352i
$176$		0			0
$177$	0.605335	−	4.06949i	0.0454997	−	0.305881i
$178$	−5.34215	−	9.25287i	−0.400411	−	0.693532i
$179$	7.58802			0.567155			0.283578	−	0.958949i	$-0.408479\pi$
$179$	7.58802			0.567155			0.283578	+	0.958949i	$0.408479\pi$
$180$	4.99531	+	1.51973i	0.372328	+	0.113274i
$181$	−2.40019			−0.178405			−0.0892023	−	0.996014i	$-0.528432\pi$
$181$	−2.40019			−0.178405			−0.0892023	+	0.996014i	$0.528432\pi$
$182$	3.47319	+	6.01575i	0.257450	+	0.445917i
$183$	−5.53957	−	4.40017i	−0.409497	−	0.325270i
$184$	2.49930	−	4.32892i	0.184251	−	0.319132i
$185$	4.86055	−	8.41872i	0.357355	−	0.618956i
$186$	−0.460396	+	0.181720i	−0.0337579	+	0.0133243i
$187$		0			0
$188$	−20.0064			−1.45911
$189$	−20.2227	+	1.63345i	−1.47099	+	0.118816i
$190$	3.80715			0.276200
$191$	8.25912	+	14.3052i	0.597609	+	1.03509i	0.993173	+	0.116650i	$0.0372157\pi$
$191$	8.25912	+	14.3052i	0.597609	+	1.03509i	−0.395564	+	0.918438i	$0.629451\pi$
$192$	1.17614	−	0.464227i	0.0848807	−	0.0335027i
$193$	−4.06748	+	7.04508i	−0.292784	+	0.507116i	−0.974467	−	0.224531i	$-0.927915\pi$
$193$	−4.06748	+	7.04508i	−0.292784	+	0.507116i	0.681683	+	0.731647i	$0.261248\pi$
$194$	−2.66248	+	4.61155i	−0.191155	+	0.331090i
$195$	4.05564	+	3.22146i	0.290431	+	0.230694i
$196$	6.42600	+	11.1302i	0.459000	+	0.795011i
$197$	22.9072			1.63207			0.816035	−	0.578003i	$-0.196168\pi$
$197$	22.9072			1.63207			0.816035	+	0.578003i	$0.196168\pi$
$198$		0			0
$199$	9.27177			0.657259			0.328629	−	0.944459i	$-0.393413\pi$
$199$	9.27177			0.657259			0.328629	+	0.944459i	$0.393413\pi$
$200$	−4.43642	−	7.68410i	−0.313702	−	0.543348i
$201$	2.48510	−	16.7066i	0.175286	−	1.17839i
$202$	0.585039	−	1.01332i	0.0411632	−	0.0712967i
$203$	2.11439	−	3.66223i	0.148401	−	0.257038i
$204$	−2.20316	+	14.8112i	−0.154252	+	1.03699i
$205$	−1.62975	−	2.82282i	−0.113827	−	0.197154i
$206$	1.78547			0.124400
$207$	1.43537	+	6.17860i	0.0997654	+	0.429442i
$208$	−4.14243			−0.287226
$209$		0			0
$210$	−3.92822	−	3.12025i	−0.271073	−	0.215318i
$211$	2.10529	−	3.64647i	0.144934	−	0.251033i	−0.784414	−	0.620237i	$-0.787036\pi$
$211$	2.10529	−	3.64647i	0.144934	−	0.251033i	0.929348	+	0.369204i	$0.120370\pi$
$212$	4.39640	−	7.61478i	0.301946	−	0.522985i
$213$	10.1774	−	4.01705i	0.697344	−	0.275244i
$214$	−3.41341	−	5.91219i	−0.233336	−	0.404149i
$215$	2.49294			0.170017
$216$	−5.26567	+	11.0984i	−0.358283	+	0.755153i
$217$	−1.67959			−0.114018
$218$	0.784842	+	1.35939i	0.0531562	+	0.0920693i
$219$	18.8058	−	7.42270i	1.27078	−	0.501580i
$220$		0			0
$221$	−7.42687	+	12.8637i	−0.499585	+	0.865307i
$222$	7.84383	+	6.23048i	0.526443	+	0.418162i
$223$	3.42953	+	5.94012i	0.229658	+	0.397780i	0.957707	−	0.287746i	$-0.0929058\pi$
$223$	3.42953	+	5.94012i	0.229658	+	0.397780i	−0.728049	+	0.685526i	$0.759572\pi$
$224$	22.4738			1.50159
$225$	10.7720	+	3.27717i	0.718132	+	0.218478i
$226$	1.01803			0.0677181
$227$	14.0650	+	24.3612i	0.933524	+	1.61691i	0.777245	+	0.629198i	$0.216617\pi$
$227$	14.0650	+	24.3612i	0.933524	+	1.61691i	0.156279	+	0.987713i	$0.450050\pi$
$228$	2.03862	−	13.7050i	0.135011	−	0.907638i
$229$	7.01735	−	12.1544i	0.463719	−	0.803186i	−0.535423	−	0.844584i	$-0.679848\pi$
$229$	7.01735	−	12.1544i	0.463719	−	0.803186i	0.999143	+	0.0413982i	$0.0131812\pi$
$230$	−0.784218	+	1.35831i	−0.0517098	+	0.0895640i
$231$		0			0
$232$	−1.28021	−	2.21739i	−0.0840499	−	0.145579i
$233$	14.5096			0.950557			0.475278	−	0.879835i	$-0.342347\pi$
$233$	14.5096			0.950557			0.475278	+	0.879835i	$0.342347\pi$
$234$	−3.89835	+	3.64529i	−0.254843	+	0.238300i
$235$	14.3324			0.934942
$236$	−1.85122	−	3.20641i	−0.120504	−	0.208719i
$237$	6.12310	+	4.86368i	0.397738	+	0.315930i
$238$	7.19353	−	12.4596i	0.466287	−	0.807633i
$239$	−12.5741	+	21.7789i	−0.813349	+	1.40876i	0.0971591	+	0.995269i	$0.469024\pi$
$239$	−12.5741	+	21.7789i	−0.813349	+	1.40876i	−0.910508	+	0.413492i	$0.864309\pi$
$240$	2.78273	−	1.09835i	0.179625	−	0.0708984i
$241$	8.87110	+	15.3652i	0.571438	+	0.989759i	0.996419	+	0.0845570i	$0.0269475\pi$
$241$	8.87110	+	15.3652i	0.571438	+	0.989759i	−0.424981	+	0.905202i	$0.639719\pi$
$242$		0			0
$243$	−4.73851	−	14.8508i	−0.303976	−	0.952680i
$244$	−6.36635			−0.407564
$245$	−4.60353	−	7.97355i	−0.294109	−	0.509411i
$246$	3.12424	−	1.23315i	0.199194	−	0.0786226i
$247$	6.87222	−	11.9030i	0.437269	−	0.757371i
$248$	−0.508474	+	0.880703i	−0.0322881	+	0.0559247i
$249$	0.653721	+	0.519261i	0.0414279	+	0.0329068i
$250$	3.24653	+	5.62315i	0.205328	+	0.355639i
$251$	−21.8775			−1.38090			−0.690448	−	0.723382i	$-0.742586\pi$
$251$	−21.8775			−1.38090			−0.690448	+	0.723382i	$0.742586\pi$
$252$	−13.3358	+	12.4701i	−0.840076	+	0.785541i
$253$		0			0
$254$	−2.54147	−	4.40195i	−0.159466	−	0.276203i
$255$	1.57832	−	10.6106i	0.0988383	−	0.664461i
$256$	4.39263	−	7.60827i	0.274540	−	0.475517i
$257$	−2.58186	+	4.47191i	−0.161052	+	0.278950i	−0.935246	−	0.353998i	$-0.884822\pi$
$257$	−2.58186	+	4.47191i	−0.161052	+	0.278950i	0.774194	+	0.632948i	$0.218155\pi$
$258$	−0.377961	+	2.54092i	−0.0235308	+	0.158191i
$259$	16.9961	+	29.4381i	1.05608	+	1.82919i
$260$	4.66095			0.289060
$261$	3.10845	+	0.945687i	0.192408	+	0.0585366i
$262$	3.56017			0.219948
$263$	−13.9491	−	24.1605i	−0.860135	−	1.48980i	−0.871798	−	0.489866i	$-0.837046\pi$
$263$	−13.9491	−	24.1605i	−0.860135	−	1.48980i	0.0116625	−	0.999932i	$-0.496288\pi$
$264$		0			0
$265$	−3.14954	+	5.45516i	−0.193475	+	0.335108i
$266$	−6.65631	+	11.5291i	−0.408124	+	0.706892i
$267$	25.9113	−	10.2273i	1.58575	−	0.625899i
$268$	−7.59987	−	13.1634i	−0.464236	−	0.804080i
$269$	3.01959			0.184108			0.0920538	−	0.995754i	$-0.470657\pi$
$269$	3.01959			0.184108			0.0920538	+	0.995754i	$0.470657\pi$
$270$	1.65223	−	3.48241i	0.100552	−	0.211933i
$271$	25.3748			1.54141			0.770705	−	0.637192i	$-0.219904\pi$
$271$	25.3748			1.54141			0.770705	+	0.637192i	$0.219904\pi$
$272$	4.28981	+	7.43017i	0.260108	+	0.450520i
$273$	−16.8462	+	6.64926i	−1.01958	+	0.402431i
$274$	−5.55744	+	9.62577i	−0.335737	+	0.581514i
$275$		0			0
$276$	4.46973	+	3.55038i	0.269046	+	0.213708i
$277$	−5.28219	−	9.14903i	−0.317376	−	0.549712i	0.662564	−	0.749006i	$-0.269468\pi$
$277$	−5.28219	−	9.14903i	−0.317376	−	0.549712i	−0.979940	+	0.199294i	$0.936135\pi$
$278$	−9.12784			−0.547451
$279$	−0.292022	−	1.25701i	−0.0174829	−	0.0752554i
$280$	−10.3073			−0.615976
$281$	−11.2853	−	19.5466i	−0.673222	−	1.16605i	−0.976985	−	0.213307i	$-0.931576\pi$
$281$	−11.2853	−	19.5466i	−0.673222	−	1.16605i	0.303763	−	0.952748i	$-0.401757\pi$
$282$	−2.17297	+	14.6082i	−0.129398	+	0.869908i
$283$	−2.93862	+	5.08983i	−0.174683	+	0.302559i	−0.940051	−	0.341033i	$-0.889223\pi$
$283$	−2.93862	+	5.08983i	−0.174683	+	0.302559i	0.765369	+	0.643592i	$0.222557\pi$
$284$	4.92314	−	8.52713i	0.292135	−	0.505992i
$285$	−1.46045	+	9.81817i	−0.0865095	+	0.581578i
$286$		0			0
$287$	11.3977			0.672782
$288$	3.90740	+	16.8195i	0.230246	+	0.991098i
$289$	13.7644			0.809672
$290$	0.401698	+	0.695761i	0.0235885	+	0.0408565i
$291$	−10.8713	−	8.63524i	−0.637286	−	0.506207i
$292$	9.09697	−	15.7564i	0.532360	−	0.922074i
$293$	3.54705	−	6.14368i	0.207221	−	0.358918i	−0.743617	−	0.668606i	$-0.766891\pi$
$293$	3.54705	−	6.14368i	0.207221	−	0.358918i	0.950838	+	0.309688i	$0.100225\pi$
$294$	8.82496	−	3.48324i	0.514682	−	0.203147i
$295$	1.32620	+	2.29704i	0.0772142	+	0.133739i
$296$	20.5814			1.19627
$297$		0			0
$298$	−3.69339			−0.213953
$299$	2.83116	+	4.90371i	0.163730	+	0.283589i
$300$	9.42483	−	3.72001i	0.544143	−	0.214775i
$301$	−4.35858	+	7.54928i	−0.251224	+	0.435133i
$302$	−0.0544436	+	0.0942990i	−0.00313287	+	0.00542630i
$303$	2.38879	+	1.89746i	0.137233	+	0.109006i
$304$	−3.96944	−	6.87527i	−0.227663	−	0.394324i
$305$	4.56080			0.261150
$306$	10.5755	+	3.21740i	0.604562	+	0.183926i
$307$	18.5370			1.05796			0.528981	−	0.848633i	$-0.322574\pi$
$307$	18.5370			1.05796			0.528981	+	0.848633i	$0.322574\pi$
$308$		0			0
$309$	−0.684919	+	4.60451i	−0.0389637	+	0.261941i
$310$	0.159546	−	0.276342i	0.00906162	−	0.0156952i
$311$	−3.43812	+	5.95500i	−0.194958	+	0.337677i	−0.946887	−	0.321567i	$-0.895790\pi$
$311$	−3.43812	+	5.95500i	−0.194958	+	0.337677i	0.751929	+	0.659244i	$0.229124\pi$
$312$	−1.61340	+	10.8464i	−0.0913408	+	0.614057i
$313$	12.6629	+	21.9328i	0.715749	+	1.23971i	0.962670	+	0.270679i	$0.0872480\pi$
$313$	12.6629	+	21.9328i	0.715749	+	1.23971i	−0.246920	+	0.969036i	$0.579419\pi$
$314$	15.8460			0.894244
$315$	9.55364	−	8.93346i	0.538287	−	0.503343i
$316$	7.03698			0.395861
$317$	−5.48963	−	9.50832i	−0.308328	−	0.534041i	0.669668	−	0.742660i	$-0.266436\pi$
$317$	−5.48963	−	9.50832i	−0.308328	−	0.534041i	−0.977997	+	0.208620i	$0.933103\pi$
$318$	−5.08265	−	4.03723i	−0.285021	−	0.226397i
$319$		0			0
$320$	−0.407582	+	0.705953i	−0.0227845	+	0.0394640i
$321$	16.5562	−	6.53480i	0.924079	−	0.364737i
$322$	−2.74221	−	4.74964i	−0.152817	−	0.264687i
$323$	−28.4669			−1.58394
$324$	−11.6513	−	7.81247i	−0.647295	−	0.434026i
$325$	10.0510			0.557527
$326$	1.39375	+	2.41405i	0.0771928	+	0.133702i
$327$	−3.80676	+	1.50254i	−0.210514	+	0.0830907i
$328$	3.45050	−	5.97644i	0.190522	−	0.329994i
$329$	−25.0583	+	43.4023i	−1.38151	+	2.39284i
$330$		0			0
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	0.912495	−	0.409088i	$-0.134153\pi$
$331$	1.85513	+	3.21317i	0.101967	+	0.176612i	−0.810528	+	0.585700i	$0.800820\pi$
$332$	0.751289			0.0412323
$333$	−19.0766	+	17.8382i	−1.04539	+	0.977528i
$334$	−10.5231			−0.575798
$335$	5.44448	+	9.43012i	0.297464	+	0.515222i
$336$	−1.53914	+	10.3472i	−0.0839670	+	0.564485i
$337$	−16.0976	+	27.8818i	−0.876891	+	1.51882i	−0.0221561	+	0.999755i	$0.507053\pi$
$337$	−16.0976	+	27.8818i	−0.876891	+	1.51882i	−0.854735	+	0.519065i	$0.826280\pi$
$338$	1.93593	−	3.35312i	0.105301	−	0.182386i
$339$	−0.390522	+	2.62536i	−0.0212102	+	0.142590i
$340$	−4.82678	−	8.36023i	−0.261769	−	0.453397i
$341$		0			0
$342$	−9.78571	−	2.97712i	−0.529151	−	0.160984i
$343$	4.86291			0.262572
$344$	2.63901	+	4.57090i	0.142286	+	0.246446i
$345$	−3.20207	−	2.54346i	−0.172394	−	0.136935i
$346$	−0.864576	+	1.49749i	−0.0464799	+	0.0805055i
$347$	−10.7612	+	18.6390i	−0.577694	+	1.00060i	0.418049	+	0.908424i	$0.362714\pi$
$347$	−10.7612	+	18.6390i	−0.577694	+	1.00060i	−0.995743	+	0.0921708i	$0.970619\pi$
$348$	2.71971	−	1.07348i	0.145792	−	0.0575444i
$349$	−8.40998	−	14.5665i	−0.450176	−	0.779727i	0.548221	−	0.836334i	$-0.315305\pi$
$349$	−8.40998	−	14.5665i	−0.450176	−	0.779727i	−0.998397	+	0.0566062i	$0.981972\pi$
$350$	−9.73518			−0.520367
$351$	−7.90531	−	11.4517i	−0.421954	−	0.611248i
$352$		0			0
$353$	−1.56543	−	2.71140i	−0.0833193	−	0.144313i	0.821355	−	0.570418i	$-0.193219\pi$
$353$	−1.56543	−	2.71140i	−0.0833193	−	0.144313i	−0.904674	+	0.426105i	$0.859885\pi$
$354$	−2.54232	+	1.00346i	−0.135123	+	0.0533334i
$355$	−3.52690	+	6.10876i	−0.187188	+	0.324219i
$356$	12.5341	−	21.7098i	0.664308	−	1.15062i
$357$	29.3722	+	23.3308i	1.55454	+	1.23480i
$358$	−2.52044	−	4.36553i	−0.133209	−	0.230725i
$359$	−8.48869			−0.448016			−0.224008	−	0.974587i	$-0.571914\pi$
$359$	−8.48869			−0.448016			−0.224008	+	0.974587i	$0.571914\pi$
$360$	−1.79207	−	7.71401i	−0.0944505	−	0.406564i
$361$	7.34092			0.386364
$362$	0.797247	+	1.38087i	0.0419024	+	0.0725770i
$363$		0			0
$364$	−8.14907	+	14.1146i	−0.427127	+	0.739806i
$365$	−6.51699	+	11.2878i	−0.341115	+	0.590828i
$366$	−0.691474	+	4.64858i	−0.0361439	+	0.242985i
$367$	5.50548	+	9.53578i	0.287384	+	0.497763i	0.973184	−	0.230026i	$-0.0738811\pi$
$367$	5.50548	+	9.53578i	0.287384	+	0.497763i	−0.685801	+	0.727789i	$0.740548\pi$
$368$	3.27059			0.170491
$369$	1.98165	+	8.53007i	0.103161	+	0.444058i
$370$	−6.45792			−0.335731
$371$	−11.0131	−	19.0753i	−0.571773	−	0.990339i
$372$	−0.909350	−	0.722311i	−0.0471476	−	0.0374501i
$373$	5.50342	−	9.53220i	0.284956	−	0.493558i	−0.687642	−	0.726050i	$-0.741354\pi$
$373$	5.50342	−	9.53220i	0.284956	−	0.493558i	0.972599	+	0.232491i	$0.0746876\pi$
$374$		0			0
$375$	−15.7468	+	6.21531i	−0.813161	+	0.320957i
$376$	15.1722	+	26.2790i	0.782446	+	1.35524i
$377$	2.90039			0.149378
$378$	7.65694	+	11.0919i	0.393831	+	0.570508i
$379$	25.3868			1.30403			0.652017	−	0.758204i	$-0.273923\pi$
$379$	25.3868			1.30403			0.652017	+	0.758204i	$0.273923\pi$
$380$	4.46631	+	7.73587i	0.229117	+	0.396842i
$381$	12.3270	−	4.86551i	0.631532	−	0.249268i
$382$	5.48670	−	9.50324i	0.280724	−	0.486228i
$383$	6.05737	−	10.4917i	0.309517	−	0.536099i	−0.668740	−	0.743497i	$-0.733166\pi$
$383$	6.05737	−	10.4917i	0.309517	−	0.536099i	0.978257	+	0.207397i	$0.0664993\pi$
$384$	14.9549	+	11.8789i	0.763166	+	0.606195i
$385$		0			0
$386$	5.40422			0.275068
$387$	−6.40773	−	1.94943i	−0.325723	−	0.0990950i
$388$	−12.4938			−0.634278
$389$	−7.17554	−	12.4284i	−0.363814	−	0.630145i	0.624771	−	0.780808i	$-0.285192\pi$
$389$	−7.17554	−	12.4284i	−0.363814	−	0.630145i	−0.988585	+	0.150663i	$0.951859\pi$
$390$	0.506244	−	3.40333i	0.0256347	−	0.172334i
$391$	5.86377	−	10.1563i	0.296544	−	0.513629i
$392$	9.74654	−	16.8815i	0.492275	−	0.852645i
$393$	−1.36571	+	9.18125i	−0.0688908	+	0.463133i
$394$	−7.60886	−	13.1789i	−0.383329	−	0.663945i
$395$	−5.04123			−0.253652
$396$		0			0
$397$	−5.03882			−0.252891			−0.126446	−	0.991974i	$-0.540357\pi$
$397$	−5.03882			−0.252891			−0.126446	+	0.991974i	$0.540357\pi$
$398$	−3.07971	−	5.33422i	−0.154372	−	0.267380i
$399$	−27.1786	−	21.5884i	−1.36063	−	1.08077i
$400$	2.90275	−	5.02772i	0.145138	−	0.251386i
$401$	9.10009	−	15.7618i	0.454437	−	0.787108i	−0.544219	−	0.838943i	$-0.683174\pi$
$401$	9.10009	−	15.7618i	0.454437	−	0.787108i	0.998656	+	0.0518357i	$0.0165072\pi$
$402$	−10.4371	+	4.11954i	−0.520554	+	0.205464i
$403$	−0.575989	−	0.997641i	−0.0286920	−	0.0496961i
$404$	2.74532			0.136585
$405$	8.34689	+	5.59678i	0.414761	+	0.278106i
$406$	−2.80926			−0.139421
$407$		0			0
$408$	21.1257	−	8.33840i	1.04588	−	0.412812i
$409$	8.21523	−	14.2292i	0.406217	−	0.703588i	−0.588245	−	0.808682i	$-0.700181\pi$
$409$	8.21523	−	14.2292i	0.406217	−	0.703588i	0.994462	+	0.105094i	$0.0335144\pi$
$410$	−1.08268	+	1.87526i	−0.0534697	+	0.0926123i
$411$	−22.6918	−	18.0245i	−1.11930	−	0.889081i
$412$	2.09460	+	3.62796i	0.103194	+	0.178737i
$413$	−9.27473			−0.456380
$414$	3.07789	−	2.87808i	0.151270	−	0.141450i
$415$	−0.538216			−0.0264200
$416$	7.70703	+	13.3490i	0.377868	+	0.654487i
$417$	3.50150	−	23.5396i	0.171469	−	1.15274i
$418$		0			0
$419$	8.70324	−	15.0745i	0.425181	−	0.736435i	−0.571256	−	0.820772i	$-0.693544\pi$
$419$	8.70324	−	15.0745i	0.425181	−	0.736435i	0.996437	+	0.0843365i	$0.0268771\pi$
$420$	1.73180	−	11.6424i	0.0845032	−	0.568090i
$421$	−2.27432	−	3.93924i	−0.110844	−	0.191987i	0.805267	−	0.592912i	$-0.202022\pi$
$421$	−2.27432	−	3.93924i	−0.110844	−	0.191987i	−0.916111	+	0.400925i	$0.868689\pi$
$422$	−2.79717			−0.136164
$423$	−36.8393	−	11.2076i	−1.79119	−	0.544934i
$424$	−13.3363			−0.647670
$425$	−10.4086	−	18.0282i	−0.504889	−	0.874494i
$426$	−5.69161	−	4.52094i	−0.275760	−	0.219040i
$427$	−7.97396	+	13.8113i	−0.385887	+	0.668376i
$428$	8.00879	−	13.8716i	0.387120	−	0.670511i
$429$		0			0
$430$	−0.828055	−	1.43423i	−0.0399323	−	0.0691648i
$431$	−12.4848			−0.601372			−0.300686	−	0.953723i	$-0.597216\pi$
$431$	−12.4848			−0.601372			−0.300686	+	0.953723i	$0.597216\pi$
$432$	−8.01150	+	0.647113i	−0.385453	+	0.0311342i
$433$	28.6862			1.37857			0.689284	−	0.724491i	$-0.257925\pi$
$433$	28.6862			1.37857			0.689284	+	0.724491i	$0.257925\pi$
$434$	0.557892	+	0.966298i	0.0267797	+	0.0463838i
$435$	−1.94837	+	0.769030i	−0.0934174	+	0.0368722i
$436$	−1.84146	+	3.18949i	−0.0881897	+	0.152749i
$437$	−5.42585	+	9.39785i	−0.259554	+	0.449560i
$438$	−10.5169	−	8.35378i	−0.502519	−	0.399159i
$439$	−2.05404	−	3.55769i	−0.0980338	−	0.169799i	0.812837	−	0.582491i	$-0.197922\pi$
$439$	−2.05404	−	3.55769i	−0.0980338	−	0.169799i	−0.910871	+	0.412692i	$0.864589\pi$
$440$		0			0
$441$	5.59753	+	24.0947i	0.266549	+	1.14737i
$442$	9.86764			0.469356
$443$	10.6149	+	18.3855i	0.504327	+	0.873520i	0.999987	+	0.00500337i	$0.00159263\pi$
$443$	10.6149	+	18.3855i	0.504327	+	0.873520i	−0.495661	+	0.868516i	$0.665074\pi$
$444$	−3.45803	+	23.2473i	−0.164111	+	1.10327i
$445$	−8.97935	+	15.5527i	−0.425662	+	0.737268i
$446$	2.27831	−	3.94614i	0.107881	−	0.186855i
$447$	1.41681	−	9.52481i	0.0670129	−	0.450508i
$448$	−1.42521	−	2.46854i	−0.0673348	−	0.116627i
$449$	25.8949			1.22205			0.611027	−	0.791610i	$-0.290757\pi$
$449$	25.8949			1.22205			0.611027	+	0.791610i	$0.290757\pi$
$450$	−1.69261	−	7.28586i	−0.0797903	−	0.343459i
$451$		0			0
$452$	1.19428	+	2.06856i	0.0561744	+	0.0972970i
$453$	−0.222301	−	0.176577i	−0.0104446	−	0.00829631i
$454$	9.34364	−	16.1837i	0.438519	−	0.759537i
$455$	5.83792	−	10.1116i	0.273686	−	0.474038i
$456$	−19.5480	+	7.71567i	−0.915420	+	0.361319i
$457$	−5.15193	−	8.92340i	−0.240997	−	0.417419i	0.720002	−	0.693972i	$-0.244141\pi$
$457$	−5.15193	−	8.92340i	−0.240997	−	0.417419i	−0.960999	+	0.276553i	$0.910808\pi$
$458$	−9.32354			−0.435660
$459$	−12.3541	+	26.0387i	−0.576641	+	1.21538i
$460$	−3.67998			−0.171580
$461$	−12.7266	−	22.0432i	−0.592738	−	1.02665i	−0.993862	−	0.110628i	$-0.964714\pi$
$461$	−12.7266	−	22.0432i	−0.592738	−	1.02665i	0.401124	−	0.916024i	$-0.368620\pi$
$462$		0			0
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.136368	−	0.990658i	$-0.456457\pi$
$463$	19.9277	−	34.5158i	0.926119	−	1.60409i	0.789751	−	0.613427i	$-0.210210\pi$
$464$	0.837642	−	1.45084i	0.0388866	−	0.0673535i
$465$	0.651450	+	0.517457i	0.0302103	+	0.0239965i
$466$	−4.81952	−	8.34765i	−0.223260	−	0.386697i
$467$	−17.3769			−0.804108			−0.402054	−	0.915616i	$-0.631704\pi$
$467$	−17.3769			−0.804108			−0.402054	+	0.915616i	$0.631704\pi$
$468$	−11.9803	−	3.64477i	−0.553789	−	0.168480i
$469$	−38.0759			−1.75818
$470$	−4.76065	−	8.24568i	−0.219592	−	0.380345i
$471$	−6.07866	+	40.8650i	−0.280090	+	1.88296i
$472$	−2.80781	+	4.86327i	−0.129240	+	0.223850i
$473$		0			0
$474$	0.764314	−	5.13826i	0.0351061	−	0.236008i
$475$	9.63123	+	16.6818i	0.441911	+	0.765412i
$476$	33.7560			1.54720
$477$	12.3613	−	11.5588i	0.565983	−	0.529241i
$478$	16.7064			0.764134
$479$	−10.9480	−	18.9625i	−0.500226	−	0.866417i	−1.00000		0.000261184i	$-0.999917\pi$
$479$	−10.9480	−	18.9625i	−0.500226	−	0.866417i	0.499774	−	0.866156i	$-0.333416\pi$
$480$	−8.71674	−	6.92385i	−0.397863	−	0.316029i
$481$	−11.6571	+	20.1907i	−0.531517	+	0.920615i
$482$	5.89325	−	10.2074i	0.268430	−	0.464935i
$483$	13.3007	−	5.24982i	0.605202	−	0.238875i
$484$		0			0
$485$	8.95046			0.406420
$486$	−6.97000	+	7.65900i	−0.316166	+	0.347419i
$487$	3.27116			0.148230			0.0741152	−	0.997250i	$-0.476387\pi$
$487$	3.27116			0.148230			0.0741152	+	0.997250i	$0.476387\pi$
$488$	4.82803	+	8.36240i	0.218555	+	0.378548i
$489$	−6.76019	+	2.66827i	−0.305706	+	0.120663i
$490$	−3.05822	+	5.29699i	−0.138156	+	0.239294i
$491$	−3.61195	+	6.25608i	−0.163005	+	0.282333i	−0.935945	−	0.352146i	$-0.885452\pi$
$491$	−3.61195	+	6.25608i	−0.163005	+	0.282333i	0.772940	+	0.634479i	$0.218785\pi$
$492$	6.17083	+	4.90159i	0.278203	+	0.220981i
$493$	−3.00358	−	5.20235i	−0.135274	−	0.234302i
$494$	−9.13071			−0.410810
$495$		0			0
$496$	−0.665390			−0.0298769
$497$	−12.3326	−	21.3608i	−0.553194	−	0.958161i
$498$	0.0816004	−	0.548575i	0.00365660	−	0.0245822i
$499$	−7.41726	+	12.8471i	−0.332042	+	0.575114i	−0.982912	−	0.184076i	$-0.941071\pi$
$499$	−7.41726	+	12.8471i	−0.332042	+	0.575114i	0.650870	+	0.759189i	$0.274404\pi$
$500$	−7.61724	+	13.1934i	−0.340653	+	0.590029i
$501$	4.03674	−	27.1378i	0.180348	−	1.21243i
$502$	7.26683	+	12.5865i	0.324335	+	0.561764i
$503$	32.9813			1.47057			0.735283	−	0.677760i	$-0.237049\pi$
$503$	32.9813			1.47057			0.735283	+	0.677760i	$0.237049\pi$
$504$	26.4933	+	8.06007i	1.18010	+	0.359024i
$505$	−1.96673			−0.0875181
$506$		0			0
$507$	7.90466	+	6.27880i	0.351058	+	0.278851i
$508$	5.96298	−	10.3282i	0.264565	−	0.458239i
$509$	−19.3347	+	33.4887i	−0.856995	+	1.48436i	0.0177866	+	0.999842i	$0.494338\pi$
$509$	−19.3347	+	33.4887i	−0.856995	+	1.48436i	−0.874782	+	0.484517i	$0.838995\pi$
$510$	−6.62872	+	2.61638i	−0.293525	+	0.115855i
$511$	−22.7882	−	39.4704i	−1.00809	−	1.74607i
$512$	16.2170			0.716698
$513$	11.4315	−	24.0941i	0.504712	−	1.06378i
$514$	3.43036			0.151307
$515$	−1.50055	−	2.59904i	−0.0661223	−	0.114527i
$516$	−5.60638	+	2.21285i	−0.246807	+	0.0974155i
$517$		0			0
$518$	11.2908	−	19.5563i	0.496091	−	0.859255i
$519$	−3.53018	−	2.80408i	−0.154958	−	0.123086i
$520$	−3.53471	−	6.12230i	−0.155007	−	0.268481i
$521$	−17.4844			−0.766005			−0.383002	−	0.923747i	$-0.625110\pi$
$521$	−17.4844			−0.766005			−0.383002	+	0.923747i	$0.625110\pi$
$522$	−0.488433	−	2.10247i	−0.0213781	−	0.0920226i
$523$	−14.4881			−0.633522			−0.316761	−	0.948505i	$-0.602595\pi$
$523$	−14.4881			−0.633522			−0.316761	+	0.948505i	$0.602595\pi$
$524$	4.17657	+	7.23404i	0.182454	+	0.316020i
$525$	3.73448	−	25.1058i	0.162986	−	1.09571i
$526$	−9.26664	+	16.0503i	−0.404045	+	0.699826i
$527$	−1.19296	+	2.06627i	−0.0519663	+	0.0900082i
$528$		0			0
$529$	9.26470	+	16.0469i	0.402813	+	0.697693i
$530$	4.18461			0.181768
$531$	−1.61255	−	6.94126i	−0.0699788	−	0.301225i
$532$	−31.2350			−1.35421
$533$	3.90865	+	6.76998i	0.169302	+	0.293240i
$534$	−14.4906	−	11.5102i	−0.627071	−	0.498093i
$535$	−5.73743	+	9.93751i	−0.248051	+	0.429636i
$536$	−11.5270	+	19.9653i	−0.497890	+	0.862371i
$537$	12.2250	−	4.82525i	0.527548	−	0.208225i
$538$	−1.00299	−	1.73722i	−0.0432418	−	0.0748971i
$539$		0			0
$540$	9.01432	−	0.728114i	0.387915	−	0.0313330i
$541$	−33.0983			−1.42301			−0.711503	−	0.702683i	$-0.751985\pi$
$541$	−33.0983			−1.42301			−0.711503	+	0.702683i	$0.751985\pi$
$542$	−8.42851	−	14.5986i	−0.362035	−	0.627064i
$543$	−3.86693	+	1.52629i	−0.165946	+	0.0654994i
$544$	15.9625	−	27.6478i	0.684385	−	1.18539i
$545$	1.31920	−	2.28493i	0.0565084	−	0.0978754i
$546$	9.42108	+	7.48332i	0.403185	+	0.320257i
$547$	4.60707	+	7.97968i	0.196984	+	0.341186i	0.947549	−	0.319610i	$-0.103552\pi$
$547$	4.60707	+	7.97968i	0.196984	+	0.341186i	−0.750565	+	0.660796i	$0.770219\pi$
$548$	−26.0786			−1.11402
$549$	−11.7229	−	3.56645i	−0.500319	−	0.152213i
$550$		0			0
$551$	2.77927	+	4.81383i	0.118401	+	0.205076i
$552$	1.27384	−	8.56362i	0.0542180	−	0.364492i
$553$	8.81393	−	15.2662i	0.374807	−	0.649184i
$554$	−3.50907	+	6.07788i	−0.149086	+	0.258225i
$555$	2.47730	−	16.6542i	0.105156	−	0.706931i
$556$	−10.7082	−	18.5472i	−0.454129	−	0.786575i
$557$	−37.0518			−1.56994			−0.784968	−	0.619536i	$-0.787321\pi$
$557$	−37.0518			−1.56994			−0.784968	+	0.619536i	$0.787321\pi$
$558$	−0.626185	+	0.585535i	−0.0265085	+	0.0247877i
$559$	−5.97883			−0.252877
$560$	−3.37202	−	5.84052i	−0.142494	−	0.246807i
$561$		0			0
$562$	−7.49703	+	12.9852i	−0.316243	+	0.547749i
$563$	−13.4970	+	23.3775i	−0.568832	+	0.985246i	0.427850	+	0.903850i	$0.359271\pi$
$563$	−13.4970	+	23.3775i	−0.568832	+	0.985246i	−0.996682	+	0.0813962i	$0.974062\pi$
$564$	−32.2322	+	12.7221i	−1.35722	+	0.535698i
$565$	−0.855575	−	1.48190i	−0.0359943	−	0.0623440i
$566$	3.90436			0.164113
$567$	−31.5420	+	15.4914i	−1.32464	+	0.650576i
$568$	−14.9342			−0.626625
$569$	−13.7379	−	23.7947i	−0.575921	−	0.997524i	−0.995941	−	0.0900095i	$-0.971310\pi$
$569$	−13.7379	−	23.7947i	−0.575921	−	0.997524i	0.420020	−	0.907515i	$-0.362023\pi$
$570$	6.13368	−	2.42098i	0.256911	−	0.101404i
$571$	−19.5052	+	33.7840i	−0.816266	+	1.41381i	0.0921492	+	0.995745i	$0.470626\pi$
$571$	−19.5052	+	33.7840i	−0.816266	+	1.41381i	−0.908415	+	0.418069i	$0.862707\pi$
$572$		0			0
$573$	22.4030	+	17.7950i	0.935897	+	0.743398i
$574$	−3.78585	−	6.55728i	−0.158018	−	0.273696i
$575$	−7.93558			−0.330937
$576$	1.59967	−	1.49583i	0.0666530	−	0.0623261i
$577$	−29.1659			−1.21419			−0.607096	−	0.794629i	$-0.707666\pi$
$577$	−29.1659			−1.21419			−0.607096	+	0.794629i	$0.707666\pi$
$578$	−4.57199	−	7.91893i	−0.190170	−	0.329384i
$579$	−2.07310	+	13.9368i	−0.0861550	+	0.579195i
$580$	−0.942493	+	1.63245i	−0.0391349	+	0.0677836i
$581$	0.941002	−	1.62986i	0.0390393	−	0.0676181i
$582$	−1.35700	+	9.12273i	−0.0562496	+	0.378149i
$583$		0			0
$584$	−27.5954			−1.14191
$585$	8.58257	+	2.61108i	0.354846	+	0.107955i
$586$	−4.71276			−0.194682
$587$	2.54397	+	4.40628i	0.105001	+	0.181867i	0.913739	−	0.406303i	$-0.133182\pi$
$587$	2.54397	+	4.40628i	0.105001	+	0.181867i	−0.808738	+	0.588169i	$0.799849\pi$
$588$	17.4306	+	13.8454i	0.718826	+	0.570975i
$589$	1.10387	−	1.91196i	0.0454842	−	0.0787809i
$590$	0.881020	−	1.52597i	0.0362710	−	0.0628232i
$591$	36.9057	−	14.5668i	1.51810	−	0.599197i
$592$	6.73321	+	11.6623i	0.276733	+	0.479316i
$593$	−3.46422			−0.142258			−0.0711292	−	0.997467i	$-0.522660\pi$
$593$	−3.46422			−0.142258			−0.0711292	+	0.997467i	$0.522660\pi$
$594$		0			0
$595$	−24.1825			−0.991386
$596$	−4.33286	−	7.50473i	−0.177481	−	0.307406i
$597$	14.9377	−	5.89596i	0.611360	−	0.241306i
$598$	1.88080	−	3.25763i	0.0769114	−	0.133215i
$599$	−12.4374	+	21.5422i	−0.508179	+	0.880192i	0.491776	+	0.870722i	$0.336348\pi$
$599$	−12.4374	+	21.5422i	−0.508179	+	0.880192i	−0.999955	+	0.00947029i	$0.996985\pi$
$600$	−12.0338	−	9.55868i	−0.491280	−	0.390231i
$601$	5.53406	+	9.58527i	0.225739	+	0.390991i	0.956541	−	0.291598i	$-0.0941870\pi$
$601$	5.53406	+	9.58527i	0.225739	+	0.390991i	−0.730802	+	0.682590i	$0.760854\pi$
$602$	5.79098			0.236023
$603$	−6.62007	−	28.4962i	−0.269590	−	1.16045i
$604$	−0.255479			−0.0103953
$605$		0			0
$606$	0.298180	−	2.00458i	0.0121127	−	0.0814304i
$607$	−13.9805	+	24.2149i	−0.567451	+	0.982854i	0.429366	+	0.903131i	$0.358737\pi$
$607$	−13.9805	+	24.2149i	−0.567451	+	0.982854i	−0.996817	+	0.0797235i	$0.974596\pi$
$608$	−14.7704	+	25.5830i	−0.599017	+	1.03753i
$609$	1.07765	−	7.24475i	0.0436687	−	0.293572i
$610$	−1.51492	−	2.62391i	−0.0613371	−	0.106239i
$611$	−34.3734			−1.39060
$612$	5.86899	+	25.2632i	0.237240	+	1.02120i
$613$	−10.9923			−0.443974			−0.221987	−	0.975050i	$-0.571254\pi$
$613$	−10.9923			−0.443974			−0.221987	+	0.975050i	$0.571254\pi$
$614$	−6.15726	−	10.6647i	−0.248487	−	0.430391i
$615$	−4.42073	−	3.51146i	−0.178261	−	0.141596i
$616$		0			0
$617$	−9.31311	+	16.1308i	−0.374932	+	0.649401i	−0.990317	−	0.138826i	$-0.955667\pi$
$617$	−9.31311	+	16.1308i	−0.374932	+	0.649401i	0.615385	+	0.788227i	$0.289001\pi$
$618$	2.87656	−	1.13539i	0.115712	−	0.0456720i
$619$	−1.34424	−	2.32829i	−0.0540296	−	0.0935820i	0.837746	−	0.546061i	$-0.183873\pi$
$619$	−1.34424	−	2.32829i	−0.0540296	−	0.0935820i	−0.891775	+	0.452479i	$0.850540\pi$
$620$	0.748679			0.0300677
$621$	6.24152	+	9.04154i	0.250463	+	0.362825i
$622$	4.56803			0.183161
$623$	−31.3985	−	54.3837i	−1.25795	−	2.17884i
$624$	−6.67385	+	2.63419i	−0.267168	+	0.105452i
$625$	−3.92596	+	6.79996i	−0.157038	+	0.271998i
$626$	8.41222	−	14.5704i	0.336220	−	0.582350i
$627$		0			0
$628$	18.5896	+	32.1981i	0.741805	+	1.28484i
$629$	48.2873			1.92534
$630$	−8.31292	−	2.52905i	−0.331195	−	0.100760i
$631$	−39.2289			−1.56168			−0.780839	−	0.624732i	$-0.785208\pi$
$631$	−39.2289			−1.56168			−0.780839	+	0.624732i	$0.785208\pi$
$632$	−5.33662	−	9.24329i	−0.212279	−	0.367678i
$633$	1.07302	−	7.21356i	0.0426485	−	0.286713i
$634$	−3.64688	+	6.31657i	−0.144836	+	0.250863i
$635$	−4.27183	+	7.39902i	−0.169522	+	0.293621i
$636$	2.24074	−	15.0638i	0.0888510	−	0.597319i
$637$	11.0407	+	19.1230i	0.437447	+	0.757681i
$638$		0			0
$639$	13.8423	−	12.9437i	0.547593	−	0.512045i
$640$	−12.3126			−0.486698
$641$	−12.8745	−	22.2993i	−0.508511	−	0.880768i	−0.999951	−	0.00985628i	$-0.996863\pi$
$641$	−12.8745	−	22.2993i	−0.508511	−	0.880768i	0.491440	−	0.870911i	$-0.336471\pi$
$642$	−9.25891	−	7.35450i	−0.365420	−	0.290259i
$643$	6.66603	−	11.5459i	0.262883	−	0.455326i	−0.704124	−	0.710077i	$-0.748660\pi$
$643$	6.66603	−	11.5459i	0.262883	−	0.455326i	0.967007	+	0.254751i	$0.0819935\pi$
$644$	6.43397	−	11.1440i	0.253534	−	0.439134i
$645$	4.01636	−	1.58527i	0.158144	−	0.0624199i
$646$	9.45557	+	16.3775i	0.372024	+	0.644365i
$647$	23.8506			0.937663			0.468832	−	0.883288i	$-0.344675\pi$
$647$	23.8506			0.937663			0.468832	+	0.883288i	$0.344675\pi$
$648$	−1.42595	+	21.2291i	−0.0560165	+	0.833957i
$649$		0			0
$650$	−3.33853	−	5.78250i	−0.130948	−	0.226808i
$651$	−2.70597	+	1.06806i	−0.106056	+	0.0418605i
$652$	−3.27013	+	5.66402i	−0.128068	+	0.221820i
$653$	−6.36247	+	11.0201i	−0.248983	+	0.431251i	−0.963244	−	0.268629i	$-0.913430\pi$
$653$	−6.36247	+	11.0201i	−0.248983	+	0.431251i	0.714261	+	0.699879i	$0.246763\pi$
$654$	2.12889	+	1.69102i	0.0832464	+	0.0661239i
$655$	−2.99206	−	5.18240i	−0.116909	−	0.202493i
$656$	4.51533			0.176294
$657$	25.5778	−	23.9173i	0.997883	−	0.933105i
$658$	33.2935			1.29792
$659$	−13.6263	−	23.6015i	−0.530806	−	0.919383i	−0.999354	−	0.0359452i	$-0.988556\pi$
$659$	−13.6263	−	23.6015i	−0.530806	−	0.919383i	0.468547	−	0.883438i	$-0.344777\pi$
$660$		0			0
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	0.0335234	+	0.999438i	$0.489327\pi$
$661$	−21.8220	+	37.7968i	−0.848777	+	1.47012i	−0.882300	+	0.470687i	$0.844006\pi$
$662$	1.23240	−	2.13458i	0.0478985	−	0.0829627i
$663$	−3.78530	+	25.4474i	−0.147009	+	0.988296i
$664$	−0.569753	−	0.986841i	−0.0221107	−	0.0382969i
$665$	22.3765			0.867724
$666$	16.5991	+	5.04997i	0.643203	+	0.195682i
$667$	−2.28996			−0.0886675
$668$	−12.3450	−	21.3822i	−0.477644	−	0.827304i
$669$	9.30265	+	7.38924i	0.359661	+	0.285685i
$670$	3.61688	−	6.26462i	0.139732	−	0.242023i
$671$		0			0
$672$	36.2074	−	14.2912i	1.39673	−	0.551294i
$673$	−13.3433	−	23.1113i	−0.514348	−	0.890877i	−0.999861	−	0.0166477i	$-0.994701\pi$
$673$	−13.3433	−	23.1113i	−0.514348	−	0.890877i	0.485513	−	0.874229i	$-0.338633\pi$
$674$	21.3879			0.823831
$675$	19.4386	−	1.57012i	0.748194	−	0.0604339i
$676$	9.08443			0.349401
$677$	13.5415	+	23.4546i	0.520443	+	0.901434i	0.999717	+	0.0237689i	$0.00756659\pi$
$677$	13.5415	+	23.4546i	0.520443	+	0.901434i	−0.479274	+	0.877665i	$0.659100\pi$
$678$	1.64014	−	0.647367i	0.0629891	−	0.0248620i
$679$	−15.6487	+	27.1044i	−0.600543	+	1.04017i
$680$	−7.32095	+	12.6803i	−0.280746	+	0.486266i
$681$	38.1514	+	30.3043i	1.46196	+	1.16126i
$682$		0			0
$683$	−16.7343			−0.640322			−0.320161	−	0.947363i	$-0.603737\pi$
$683$	−16.7343			−0.640322			−0.320161	+	0.947363i	$0.603737\pi$
$684$	−5.43068	−	23.3765i	−0.207647	−	0.893822i
$685$	18.6824			0.713820
$686$	−1.61526	−	2.79772i	−0.0616711	−	0.106817i
$687$	3.57657	−	24.0443i	0.136455	−	0.917346i
$688$	−1.72671	+	2.99074i	−0.0658301	+	0.114021i
$689$	7.55356	−	13.0831i	0.287768	−	0.498428i
$690$	−0.399697	+	2.68705i	−0.0152162	+	0.102294i
$691$	18.7598	+	32.4929i	0.713656	+	1.23609i	0.963476	+	0.267796i	$0.0862953\pi$
$691$	18.7598	+	32.4929i	0.713656	+	1.23609i	−0.249820	+	0.968292i	$0.580371\pi$
$692$	−4.05707			−0.154226
$693$		0			0
$694$	14.2978			0.542738
$695$	7.67127	+	13.2870i	0.290988	+	0.504005i
$696$	−3.47259	−	2.75833i	−0.131628	−	0.104554i
$697$	8.09543	−	14.0217i	0.306636	−	0.531109i
$698$	−5.58692	+	9.67683i	−0.211468	+	0.366273i
$699$	23.3764	−	9.22673i	0.884175	−	0.348987i
$700$	−11.4207	−	19.7812i	−0.431662	−	0.747660i
$701$	−10.2007			−0.385275			−0.192637	−	0.981270i	$-0.561704\pi$
$701$	−10.2007			−0.385275			−0.192637	+	0.981270i	$0.561704\pi$
$702$	−3.96256	+	8.35188i	−0.149557	+	0.315221i
$703$	−44.6811			−1.68518
$704$		0			0
$705$	23.0908	−	9.11402i	0.869651	−	0.343254i
$706$	−1.03995	+	1.80124i	−0.0391388	+	0.0677905i
$707$	3.43856	−	5.95577i	0.129321	−	0.223990i
$708$	−5.02146	−	3.98862i	−0.188718	−	0.149902i
$709$	7.24884	+	12.5554i	0.272236	+	0.471526i	0.969434	−	0.245352i	$-0.0789036\pi$
$709$	7.24884	+	12.5554i	0.272236	+	0.471526i	−0.697198	+	0.716878i	$0.745570\pi$
$710$	4.68598			0.175862
$711$	12.9577	+	3.94214i	0.485953	+	0.147842i
$712$	−38.0220			−1.42493
$713$	0.454763	+	0.787673i	0.0170310	+	0.0294986i
$714$	3.66637	−	24.6479i	0.137210	−	0.922426i
$715$		0			0
$716$	5.91364	−	10.2427i	0.221003	−	0.382789i
$717$	−6.40870	+	43.0838i	−0.239337	+	1.60899i
$718$	2.81961	+	4.88370i	0.105227	+	0.182258i
$719$	19.2266			0.717032			0.358516	−	0.933524i	$-0.383283\pi$
$719$	19.2266			0.717032			0.358516	+	0.933524i	$0.383283\pi$
$720$	3.78480	−	3.53910i	0.141051	−	0.131895i
$721$	10.4941			0.390821
$722$	−2.43836	−	4.22337i	−0.0907464	−	0.157177i
$723$	24.0630	+	19.1136i	0.894912	+	0.710843i
$724$	−1.87056	+	3.23991i	−0.0695188	+	0.120410i
$725$	−2.03241	+	3.52023i	−0.0754818	+	0.130738i
$726$		0			0
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	0.859208	−	0.511627i	$-0.170957\pi$
$727$	−0.363414	−	0.629451i	−0.0134783	−	0.0233450i	−0.872686	+	0.488282i	$0.837624\pi$
$728$	24.7200			0.916183
$729$	−17.0779	−	20.9128i	−0.632514	−	0.774549i
$730$	8.65874			0.320474
$731$	6.19154	+	10.7241i	0.229003	+	0.396644i
$732$	−10.2568	+	4.04839i	−0.379102	+	0.149633i
$733$	−0.937944	+	1.62457i	−0.0346438	+	0.0600048i	−0.882827	−	0.469697i	$-0.844363\pi$
$733$	−0.937944	+	1.62457i	−0.0346438	+	0.0600048i	0.848184	+	0.529702i	$0.177696\pi$
$734$	3.65740	−	6.33481i	0.134997	−	0.233822i
$735$	−12.4871	−	9.91874i	−0.460595	−	0.365858i
$736$	−6.08497	−	10.5395i	−0.224295	−	0.388490i
$737$		0			0
$738$	4.24928	−	3.97343i	0.156418	−	0.146264i
$739$	52.5826			1.93428			0.967140	−	0.254243i	$-0.0818262\pi$
$739$	52.5826			1.93428			0.967140	+	0.254243i	$0.0818262\pi$
$740$	−7.57603	−	13.1221i	−0.278500	−	0.482377i
$741$	3.50260	−	23.5470i	0.128671	−	0.865020i
$742$	−7.31624	+	12.6721i	−0.268588	+	0.465208i
$743$	−16.6664	+	28.8671i	−0.611431	+	1.05903i	0.379568	+	0.925164i	$0.376072\pi$
$743$	−16.6664	+	28.8671i	−0.611431	+	1.05903i	−0.990999	+	0.133866i	$0.957261\pi$
$744$	−0.259157	+	1.74224i	−0.00950116	+	0.0638735i
$745$	3.10402	+	5.37632i	0.113723	+	0.196973i
$746$	−7.31206			−0.267714
$747$	1.38341	+	0.420875i	0.0506162	+	0.0153990i
$748$		0			0
$749$	−20.0623	−	34.7489i	−0.733060	−	1.26970i
$750$	8.80624	+	6.99494i	0.321559	+	0.255419i
$751$	11.6820	−	20.2339i	0.426284	−	0.738345i	−0.570256	−	0.821467i	$-0.693156\pi$
$751$	11.6820	−	20.2339i	0.426284	−	0.738345i	0.996539	+	0.0831223i	$0.0264892\pi$
$752$	−9.92717	+	17.1944i	−0.362007	+	0.627014i
$753$	−35.2467	+	13.9120i	−1.28446	+	0.506981i
$754$	−0.963394	−	1.66865i	−0.0350847	−	0.0607685i
$755$	0.183023			0.00666089
$756$	−13.5554	+	28.5708i	−0.493007	+	1.03911i
$757$	−33.8030			−1.22859			−0.614296	−	0.789076i	$-0.710560\pi$
$757$	−33.8030			−1.22859			−0.614296	+	0.789076i	$0.710560\pi$
$758$	−8.43250	−	14.6055i	−0.306282	−	0.530496i
$759$		0			0
$760$	6.77421	−	11.7333i	0.245726	−	0.425611i
$761$	10.0560	−	17.4174i	0.364528	−	0.631381i	−0.624172	−	0.781287i	$-0.714564\pi$
$761$	10.0560	−	17.4174i	0.364528	−	0.631381i	0.988700	+	0.149906i	$0.0478970\pi$
$762$	−6.89376	−	5.47583i	−0.249735	−	0.198368i
$763$	4.61291	+	7.98979i	0.166998	+	0.289250i
$764$	25.7466			0.931480
$765$	−4.20449	−	18.0983i	−0.152014	−	0.654346i
$766$	−8.04807			−0.290788
$767$	−3.18063	−	5.50901i	−0.114846	−	0.198919i
$768$	2.23882	−	15.0509i	0.0807865	−	0.543104i
$769$	0.313500	−	0.542997i	0.0113051	−	0.0195810i	−0.860318	−	0.509759i	$-0.829735\pi$
$769$	0.313500	−	0.542997i	0.0113051	−	0.0195810i	0.871623	+	0.490178i	$0.163068\pi$
$770$		0			0
$771$	−1.31591	+	8.84649i	−0.0473914	+	0.318598i
$772$	6.33989	+	10.9810i	0.228178	+	0.395215i
$773$	28.7378			1.03363			0.516813	−	0.856098i	$-0.327118\pi$
$773$	28.7378			1.03363			0.516813	+	0.856098i	$0.327118\pi$
$774$	1.00685	+	4.33401i	0.0361905	+	0.155783i
$775$	1.61447			0.0579933
$776$	9.47491	+	16.4110i	0.340130	+	0.589122i
$777$	46.1021	+	36.6196i	1.65390	+	1.31372i
$778$	−4.76686	+	8.25644i	−0.170900	+	0.296008i
$779$	−7.49085	+	12.9745i	−0.268387	+	0.464861i
$780$	7.50923	−	2.96392i	0.268874	−	0.106125i
$781$		0			0
$782$	−7.79085			−0.278600
$783$	5.60938	−	0.453087i	0.200463	−	0.0161920i
$784$	12.7543			0.455512
$785$	−13.3174	−	23.0664i	−0.475319	−	0.823277i
$786$	5.73578	−	2.26393i	0.204588	−	0.0807517i
$787$	−7.05147	+	12.2135i	−0.251358	+	0.435364i	−0.963900	−	0.266265i	$-0.914210\pi$
$787$	−7.05147	+	12.2135i	−0.251358	+	0.435364i	0.712542	+	0.701629i	$0.247544\pi$
$788$	17.8525	−	30.9214i	0.635968	−	1.10153i
$789$	−37.8370	−	30.0545i	−1.34703	−	1.06997i
$790$	1.67450	+	2.90031i	0.0595759	+	0.103188i
$791$	5.98345			0.212747
$792$		0			0
$793$	−10.9382			−0.388426
$794$	1.67370	+	2.89893i	0.0593973	+	0.102879i
$795$	−1.60524	+	10.7916i	−0.0569322	+	0.382738i
$796$	7.22586	−	12.5156i	0.256114	−	0.443602i
$797$	−13.0773	+	22.6506i	−0.463223	+	0.802326i	−0.999119	−	0.0419576i	$-0.986641\pi$
$797$	−13.0773	+	22.6506i	−0.463223	+	0.802326i	0.535896	+	0.844284i	$0.319974\pi$
$798$	−3.39256	+	22.8072i	−0.120095	+	0.807365i
$799$	35.5964	+	61.6548i	1.25931	+	2.18119i
$800$	−21.6024			−0.763760
$801$	35.2420	−	32.9542i	1.24521	−	1.16438i
$802$	−12.0908			−0.426939
$803$		0			0
$804$	−20.6148	−	16.3746i	−0.727026	−	0.577489i
$805$	−4.60924	+	7.98344i	−0.162454	+	0.281379i
$806$	−0.382641	+	0.662754i	−0.0134780	+	0.0233445i
$807$	4.86484	−	1.92017i	0.171251	−	0.0675932i
$808$	−2.08196	−	3.60607i	−0.0732433	−	0.126861i
$809$	−15.8533			−0.557374			−0.278687	−	0.960382i	$-0.589899\pi$
$809$	−15.8533			−0.557374			−0.278687	+	0.960382i	$0.589899\pi$
$810$	0.447427	−	6.66115i	0.0157210	−	0.234049i
$811$	36.3264			1.27559			0.637796	−	0.770206i	$-0.279846\pi$
$811$	36.3264			1.27559			0.637796	+	0.770206i	$0.279846\pi$
$812$	−3.29565	−	5.70824i	−0.115655	−	0.200320i
$813$	40.8812	−	16.1360i	1.43377	−	0.565913i
$814$		0			0
$815$	2.34269	−	4.05766i	0.0820608	−	0.142134i
$816$	11.6362	+	9.24280i	0.407347	+	0.323563i
$817$	−5.72915	−	9.92318i	−0.200438	−	0.347168i
$818$	−10.9151			−0.381637
$819$	−22.9126	+	21.4252i	−0.800630	+	0.748656i
$820$	−5.08053			−0.177420
$821$	−8.17837	−	14.1653i	−0.285427	−	0.494374i	0.687286	−	0.726387i	$-0.258802\pi$
$821$	−8.17837	−	14.1653i	−0.285427	−	0.494374i	−0.972713	+	0.232013i	$0.925469\pi$
$822$	−2.83249	+	19.0420i	−0.0987946	+	0.664167i
$823$	13.0873	−	22.6678i	0.456193	−	0.790150i	−0.542563	−	0.840015i	$-0.682546\pi$
$823$	13.0873	−	22.6678i	0.456193	−	0.790150i	0.998756	+	0.0498656i	$0.0158793\pi$
$824$	3.17696	−	5.50265i	0.110675	−	0.191694i
$825$		0			0
$826$	3.08070	+	5.33592i	0.107191	+	0.185661i
$827$	−5.53930			−0.192620			−0.0963101	−	0.995351i	$-0.530704\pi$
$827$	−5.53930			−0.192620			−0.0963101	+	0.995351i	$0.530704\pi$
$828$	9.45885	+	2.87767i	0.328718	+	0.100006i
$829$	18.5033			0.642647			0.321324	−	0.946969i	$-0.395872\pi$
$829$	18.5033			0.642647			0.321324	+	0.946969i	$0.395872\pi$
$830$	0.178774	+	0.309646i	0.00620534	+	0.0107480i
$831$	−14.3280	−	11.3810i	−0.497033	−	0.394802i
$832$	0.977507	−	1.69309i	0.0338890	−	0.0586974i
$833$	22.8670	−	39.6068i	0.792294	−	1.37229i
$834$	−14.7058	+	5.80443i	−0.509221	+	0.200991i
$835$	8.84388	+	15.3180i	0.306055	+	0.530103i
$836$		0			0
$837$	−1.26981	−	1.83947i	−0.0438912	−	0.0635813i
$838$	−11.5635			−0.399454
$839$	8.98265	+	15.5584i	0.310115	+	0.537136i	0.978387	−	0.206782i	$-0.0662990\pi$
$839$	8.98265	+	15.5584i	0.310115	+	0.537136i	−0.668272	+	0.743917i	$0.732966\pi$
$840$	−16.6060	+	6.55443i	−0.572960	+	0.226149i
$841$	13.9135	−	24.0989i	0.479776	−	0.830997i
$842$	−1.51088	+	2.61692i	−0.0520683	+	0.0901850i
$843$	−30.6114	−	24.3151i	−1.05431	−	0.837458i
$844$	−3.28147	−	5.68367i	−0.112953	−	0.195640i
$845$	−6.50801			−0.223882
$846$	5.78858	+	24.9170i	0.199015	+	0.856666i
$847$		0			0
$848$	−4.36299	−	7.55692i	−0.149826	−	0.259506i
$849$	−1.49774	+	10.0689i	−0.0514024	+	0.345563i
$850$	−6.91462	+	11.9765i	−0.237169	+	0.410790i
$851$	9.20367	−	15.9412i	0.315498	−	0.546458i
$852$	2.50921	−	16.8687i	0.0859640	−	0.577911i
$853$	13.9565	+	24.1734i	0.477863	+	0.827683i	0.999678	−	0.0253757i	$-0.00807822\pi$
$853$	13.9565	+	24.1734i	0.477863	+	0.827683i	−0.521815	+	0.853059i	$0.674745\pi$
$854$	10.5945			0.362537
$855$	3.89049	+	16.7467i	0.133052	+	0.572725i
$856$	−24.2944			−0.830367
$857$	−4.24983	−	7.36093i	−0.145172	−	0.251445i	0.784265	−	0.620426i	$-0.213040\pi$
$857$	−4.24983	−	7.36093i	−0.145172	−	0.251445i	−0.929437	+	0.368981i	$0.879707\pi$
$858$		0			0
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	−0.999595	−	0.0284667i	$-0.990938\pi$
$859$	−13.9259	+	24.1203i	−0.475145	+	0.822974i	0.524450	+	0.851441i	$0.324271\pi$
$860$	1.94284	−	3.36510i	0.0662504	−	0.114749i
$861$	18.3627	−	7.24782i	0.625799	−	0.247005i
$862$	4.14695	+	7.18273i	0.141246	+	0.244645i
$863$	13.5940			0.462745			0.231372	−	0.972865i	$-0.425678\pi$
$863$	13.5940			0.462745			0.231372	+	0.972865i	$0.425678\pi$
$864$	16.9908	+	24.6131i	0.578038	+	0.837353i
$865$	2.90645			0.0988221
$866$	−9.52840	−	16.5037i	−0.323788	−	0.560818i
$867$	22.1758	−	8.75286i	0.753129	−	0.297263i
$868$	−1.30897	+	2.26720i	−0.0444293	+	0.0769538i
$869$		0			0
$870$	1.08961	+	0.865495i	0.0369412	+	0.0293430i
$871$	−13.0575	−	22.6163i	−0.442438	−	0.766324i
$872$	5.58600			0.189166
$873$	−23.0058	−	6.99909i	−0.778630	−	0.236883i
$874$	7.20901			0.243848
$875$	19.0814	+	33.0500i	0.645071	+	1.11730i
$876$	4.63651	−	31.1699i	0.156653	−	1.05313i
$877$	18.0890	−	31.3310i	0.610822	−	1.05797i	−0.380281	−	0.924871i	$-0.624173\pi$
$877$	18.0890	−	31.3310i	0.610822	−	1.05797i	0.991102	−	0.133103i	$-0.0424941\pi$
$878$	−1.36454	+	2.36345i	−0.0460509	+	0.0797625i
$879$	1.80785	−	12.1536i	0.0609772	−	0.409932i
$880$		0			0
$881$	26.6423			0.897601			0.448800	−	0.893632i	$-0.351851\pi$
$881$	26.6423			0.897601			0.448800	+	0.893632i	$0.351851\pi$
$882$	12.0028	−	11.2237i	0.404157	−	0.377920i
$883$	−20.4764			−0.689087			−0.344544	−	0.938770i	$-0.611966\pi$
$883$	−20.4764			−0.689087			−0.344544	+	0.938770i	$0.611966\pi$
$884$	11.5761	+	20.0504i	0.389346	+	0.674367i
$885$	3.59733	+	2.85741i	0.120923	+	0.0960510i
$886$	7.05166	−	12.2138i	0.236905	−	0.410332i
$887$	−16.0006	+	27.7138i	−0.537247	+	0.930539i	0.461804	+	0.886982i	$0.347202\pi$
$887$	−16.0006	+	27.7138i	−0.537247	+	0.930539i	−0.999051	+	0.0435570i	$0.986131\pi$
$888$	33.1586	−	13.0878i	1.11273	−	0.439198i
$889$	−14.9375	−	25.8725i	−0.500987	−	0.867734i
$890$	11.9303			0.399906
$891$		0			0
$892$	10.6911			0.357963
$893$	−32.9380	−	57.0503i	−1.10223	−	1.90912i
$894$	−5.95041	+	2.34865i	−0.199011	+	0.0785504i
$895$	−4.23648	+	7.33780i	−0.141610	+	0.245275i
$896$	21.5270	−	37.2858i	0.719165	−	1.24563i
$897$	7.67955	+	6.09999i	0.256413	+	0.203673i
$898$	−8.60125	−	14.8978i	−0.287027	−	0.497146i
$899$	0.465884			0.0155381
$900$	12.8187	−	11.9866i	0.427291	−	0.399553i
$901$	−31.2892			−1.04239
$902$		0			0
$903$	−2.22146	+	14.9342i	−0.0739256	+	0.496980i
$904$	1.81141	−	3.13746i	0.0602467	−	0.104350i
$905$	1.34005	−	2.32104i	0.0445449	−	0.0771540i
$906$	−0.0277486	+	0.186546i	−0.000921885	+	0.00619756i
$907$	24.5251	+	42.4788i	0.814344	+	1.41048i	0.909798	+	0.415051i	$0.136236\pi$
$907$	24.5251	+	42.4788i	0.814344	+	1.41048i	−0.0954547	+	0.995434i	$0.530431\pi$
$908$	43.8455			1.45506
$909$	5.05518	+	1.53794i	0.167670	+	0.0510103i
$910$	−7.75650			−0.257125
$911$	11.6906	+	20.2488i	0.387328	+	0.670872i	0.992089	−	0.125535i	$-0.0400647\pi$
$911$	11.6906	+	20.2488i	0.387328	+	0.670872i	−0.604761	+	0.796407i	$0.706731\pi$
$912$	−10.7672	−	8.55253i	−0.356536	−	0.283203i
$913$		0			0
$914$	−3.42253	+	5.92800i	−0.113207	+	0.196081i
$915$	7.34787	−	2.90023i	0.242913	−	0.0958786i
$916$	−10.9378	−	18.9448i	−0.361395	−	0.625954i
$917$	20.9249			0.691001
$918$	19.0841	−	1.54148i	0.629869	−	0.0508765i
$919$	7.59931			0.250678			0.125339	−	0.992114i	$-0.459998\pi$
$919$	7.59931			0.250678			0.125339	+	0.992114i	$0.459998\pi$
$920$	2.79078	+	4.83377i	0.0920093	+	0.159365i
$921$	29.8649	−	11.7878i	0.984081	−	0.388420i
$922$	−8.45456	+	14.6437i	−0.278436	+	0.482265i
$923$	8.45857	−	14.6507i	0.278417	−	0.482233i
$924$		0			0
$925$	−16.3371	−	28.2967i	−0.537160	−	0.930389i
$926$	−26.4768			−0.870081
$927$	1.82456	+	7.85384i	0.0599263	+	0.257954i
$928$	−6.23377			−0.204633
$929$	7.43837	+	12.8836i	0.244045	+	0.422699i	0.961863	−	0.273533i	$-0.0881922\pi$
$929$	7.43837	+	12.8836i	0.244045	+	0.422699i	−0.717818	+	0.696231i	$0.754859\pi$
$930$	0.0813170	−	0.546670i	0.00266649	−	0.0179260i
$931$	−21.1592	+	36.6489i	−0.693466	+	1.20112i
$932$	11.3079	−	19.5859i	0.370403	−	0.641557i
$933$	−1.75233	+	11.7804i	−0.0573686	+	0.385672i
$934$	5.77192	+	9.99727i	0.188863	+	0.327121i
$935$		0			0
$936$	4.29794	+	18.5006i	0.140482	+	0.604710i
$937$	−17.8231			−0.582257			−0.291128	−	0.956684i	$-0.594031\pi$
$937$	−17.8231			−0.582257			−0.291128	+	0.956684i	$0.594031\pi$
$938$	12.6473	+	21.9058i	0.412949	+	0.715248i
$939$	34.3483	+	27.2834i	1.12091	+	0.890360i
$940$	11.1698	−	19.3466i	0.364318	−	0.631018i
$941$	21.3296	−	36.9439i	0.695324	−	1.20434i	−0.274748	−	0.961516i	$-0.588594\pi$
$941$	21.3296	−	36.9439i	0.695324	−	1.20434i	0.970071	−	0.242820i	$-0.0780724\pi$
$942$	25.5295	−	10.0766i	0.831795	−	0.328312i
$943$	−3.08601	−	5.34513i	−0.100494	−	0.174062i
$944$	−3.67430			−0.119588
$945$	9.71100	−	20.4678i	0.315899	−	0.665819i
$946$		0			0
$947$	−3.44670	−	5.96986i	−0.112003	−	0.193994i	0.804575	−	0.593851i	$-0.202393\pi$
$947$	−3.44670	−	5.96986i	−0.112003	−	0.193994i	−0.916578	+	0.399857i	$0.869060\pi$
$948$	11.3372	−	4.47484i	0.368216	−	0.145336i
$949$	15.6297	−	27.0715i	0.507363	−	0.878778i
$950$	6.39822	−	11.0820i	0.207586	−	0.359549i
$951$	−14.8907	−	11.8279i	−0.482864	−	0.383547i
$952$	−25.5995	−	44.3396i	−0.829683	−	1.43705i
$953$	23.6805			0.767085			0.383543	−	0.923523i	$-0.374704\pi$
$953$	23.6805			0.767085			0.383543	+	0.923523i	$0.374704\pi$
$954$	−10.7559	−	3.27228i	−0.348236	−	0.105944i
$955$	−18.4446			−0.596855
$956$	19.5989	+	33.9463i	0.633874	+	1.09790i
$957$		0			0
$958$	−7.27297	+	12.5972i	−0.234979	+	0.406996i
$959$	−32.6638	+	56.5754i	−1.05477	+	1.82692i
$960$	−0.207735	+	1.39654i	−0.00670462	+	0.0450732i
$961$	15.4075	+	26.6865i	0.497015	+	0.860856i
$962$	15.4881			0.499356
$963$	22.5181	−	21.0564i	0.725637	−	0.678532i
$964$	27.6544			0.890688
$965$	−4.54184	−	7.86670i	−0.146207	−	0.253238i
$966$	−7.43827	−	5.90834i	−0.239323	−	0.190098i
$967$	−15.5700	+	26.9680i	−0.500696	+	0.867231i	0.499303	+	0.866427i	$0.333589\pi$
$967$	−15.5700	+	26.9680i	−0.500696	+	0.867231i	−1.00000		0.000804082i	$0.999744\pi$
$968$		0			0
$969$	−45.8628	+	18.1022i	−1.47333	+	0.581527i
$970$	−2.97299	−	5.14937i	−0.0954569	−	0.165336i
$971$	13.3548			0.428577			0.214288	−	0.976770i	$-0.431257\pi$
$971$	13.3548			0.428577			0.214288	+	0.976770i	$0.431257\pi$
$972$	−23.7393	−	5.17751i	−0.761440	−	0.166069i
$973$	−53.6488			−1.71990
$974$	−1.08655	−	1.88196i	−0.0348153	−	0.0603018i
$975$	16.1930	−	6.39145i	0.518592	−	0.204690i
$976$	−3.15899	+	5.47153i	−0.101117	+	0.175139i
$977$	4.45796	−	7.72142i	0.142623	−	0.247030i	−0.785861	−	0.618404i	$-0.787780\pi$
$977$	4.45796	−	7.72142i	0.142623	−	0.247030i	0.928484	+	0.371373i	$0.121113\pi$
$978$	3.78057	+	3.00297i	0.120889	+	0.0960244i
$979$		0			0
$980$	−14.3508			−0.458421
$981$	−5.17758	+	4.84147i	−0.165307	+	0.154576i
$982$	4.79899			0.153142
$983$	8.42927	+	14.5999i	0.268852	+	0.465665i	0.968566	−	0.248758i	$-0.0800224\pi$
$983$	8.42927	+	14.5999i	0.268852	+	0.465665i	−0.699714	+	0.714423i	$0.746689\pi$
$984$	1.75864	−	11.8228i	0.0560633	−	0.376897i
$985$	−12.7894	+	22.1518i	−0.407503	+	0.705815i
$986$	−1.99534	+	3.45603i	−0.0635446	+	0.110062i
$987$	−12.7716	+	85.8599i	−0.406525	+	2.73295i
$988$	−10.7116	−	18.5530i	−0.340781	−	0.590249i
$989$	4.72049			0.150103
$990$		0			0
$991$	−33.5356			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$991$	−33.5356			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$992$	1.23796	+	2.14422i	0.0393054	+	0.0680790i
$993$	5.03205	+	3.99704i	0.159687	+	0.126842i
$994$	−8.19282	+	14.1904i	−0.259861	+	0.450092i
$995$	−5.17654	+	8.96603i	−0.164107	+	0.284242i
$996$	1.21040	−	0.477748i	0.0383529	−	0.0151380i
$997$	−1.62184	−	2.80910i	−0.0513641	−	0.0889652i	0.839200	−	0.543823i	$-0.183024\pi$
$997$	−1.62184	−	2.80910i	−0.0513641	−	0.0889652i	−0.890564	+	0.454857i	$0.849690\pi$
$998$	9.85487			0.311950
$999$	−19.3908	+	40.8699i	−0.613498	+	1.29307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.o.364.8		36
9.4	even	3		9801.2.a.co.1.11		18
9.5	odd	6		9801.2.a.cn.1.8		18
9.7	even	3	inner	1089.2.e.o.727.8		36
11.2	odd	10		99.2.m.b.4.6	✓	72
11.6	odd	10		99.2.m.b.58.4	yes	72
11.10	odd	2		1089.2.e.p.364.11		36
33.2	even	10		297.2.n.b.37.4		72
33.17	even	10		297.2.n.b.91.6		72
99.2	even	30		297.2.n.b.235.6		72
99.13	odd	30		891.2.f.f.730.6		36
99.32	even	6		9801.2.a.cp.1.11		18
99.43	odd	6		1089.2.e.p.727.11		36
99.50	even	30		891.2.f.e.487.4		36
99.61	odd	30		99.2.m.b.25.6	yes	72
99.68	even	30		891.2.f.e.730.4		36
99.76	odd	6		9801.2.a.cm.1.8		18
99.79	odd	30		99.2.m.b.70.4	yes	72
99.83	even	30		297.2.n.b.289.4		72
99.94	odd	30		891.2.f.f.487.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.6	✓	72	11.2	odd	10
99.2.m.b.25.6	yes	72	99.61	odd	30
99.2.m.b.58.4	yes	72	11.6	odd	10
99.2.m.b.70.4	yes	72	99.79	odd	30
297.2.n.b.37.4		72	33.2	even	10
297.2.n.b.91.6		72	33.17	even	10
297.2.n.b.235.6		72	99.2	even	30
297.2.n.b.289.4		72	99.83	even	30
891.2.f.e.487.4		36	99.50	even	30
891.2.f.e.730.4		36	99.68	even	30
891.2.f.f.487.6		36	99.94	odd	30
891.2.f.f.730.6		36	99.13	odd	30
1089.2.e.o.364.8		36	1.1	even	1	trivial
1089.2.e.o.727.8		36	9.7	even	3	inner
1089.2.e.p.364.11		36	11.10	odd	2
1089.2.e.p.727.11		36	99.43	odd	6
9801.2.a.cm.1.8		18	99.76	odd	6
9801.2.a.cn.1.8		18	9.5	odd	6
9801.2.a.co.1.11		18	9.4	even	3
9801.2.a.cp.1.11		18	99.32	even	6

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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.332160 - 0.575318i) q^{2} +(1.61109 - 0.635904i) q^{3} +(0.779339 - 1.34985i) q^{4} +(-0.558312 + 0.967024i) q^{5} +(-0.900989 - 0.715670i) q^{6} +(-1.95227 - 3.38143i) q^{7} -2.36410 q^{8} +(2.19125 - 2.04900i) q^{9} +0.741796 q^{10} +(0.397211 - 2.67033i) q^{12} +(1.33900 - 2.31922i) q^{13} +(-1.29693 + 2.24635i) q^{14} +(-0.284558 + 1.91300i) q^{15} +(-0.773417 - 1.33960i) q^{16} -5.54657 q^{17} +(-1.90668 - 0.580070i) q^{18} +5.13234 q^{19} +(0.870228 + 1.50728i) q^{20} +(-5.29556 - 4.20635i) q^{21} +(-1.05719 + 1.83110i) q^{23} +(-3.80879 + 1.50334i) q^{24} +(1.87658 + 3.25033i) q^{25} -1.77905 q^{26} +(2.22734 - 4.69457i) q^{27} -6.08592 q^{28} +(0.541520 + 0.937941i) q^{29} +(1.19510 - 0.471711i) q^{30} +(0.215081 - 0.372532i) q^{31} +(-2.87790 + 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} +4.35990 q^{35} +(-1.05813 - 4.55474i) q^{36} -8.70580 q^{37} +(-1.70476 - 2.95273i) q^{38} +(0.682457 - 4.58796i) q^{39} +(1.31991 - 2.28614i) q^{40} +(-1.45954 + 2.52799i) q^{41} +(-0.661016 + 4.44382i) q^{42} +(-1.11628 - 1.93346i) q^{43} +(0.758035 + 3.26298i) q^{45} +1.40462 q^{46} +(-6.41773 - 11.1158i) q^{47} +(-2.09790 - 1.66640i) q^{48} +(-4.12272 + 7.14077i) q^{49} +(1.24665 - 2.15926i) q^{50} +(-8.93605 + 3.52709i) q^{51} +(-2.08707 - 3.61492i) q^{52} +5.64118 q^{53} +(-3.44070 + 0.277916i) q^{54} +(4.61537 + 7.99405i) q^{56} +(8.26869 - 3.26368i) q^{57} +(0.359743 - 0.623093i) q^{58} +(1.18769 - 2.05713i) q^{59} +(2.36051 + 1.87499i) q^{60} +(-2.04223 - 3.53724i) q^{61} -0.285766 q^{62} +(-11.2065 - 3.40936i) q^{63} +0.730027 q^{64} +(1.49516 + 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(-4.32266 + 7.48706i) q^{68} +(-0.538824 + 3.62235i) q^{69} +(-1.44819 - 2.50833i) q^{70} +6.31707 q^{71} +(-5.18034 + 4.84406i) q^{72} +11.6727 q^{73} +(2.89172 + 5.00861i) q^{74} +(5.09024 + 4.04326i) q^{75} +(3.99983 - 6.92792i) q^{76} +(-2.86622 + 1.13131i) q^{78} +(2.25735 + 3.90985i) q^{79} +1.72723 q^{80} +(0.603167 - 8.97977i) q^{81} +1.93920 q^{82} +(0.241002 + 0.417427i) q^{83} +(-9.80500 + 3.87007i) q^{84} +(3.09671 - 5.36367i) q^{85} +(-0.741570 + 1.28444i) q^{86} +(1.46888 + 1.16676i) q^{87} +16.0830 q^{89} +(1.62546 - 1.51994i) q^{90} -10.4564 q^{91} +(1.64782 + 2.85410i) q^{92} +(0.109622 - 0.736955i) q^{93} +(-4.26343 + 7.38448i) q^{94} +(-2.86545 + 4.96310i) q^{95} +(-1.46680 + 9.86084i) q^{96} +(-4.00783 - 6.94176i) q^{97} +5.47762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

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Database

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