LMFDB - Embedded newform 1089.2.e.p.364.11

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)

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")

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);

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			364.11
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.p.727.11

$q$-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	0.959236	−	0.282607i	$-0.0911993\pi$
$2$	0.332160	+	0.575318i	0.234873	+	0.406812i	−0.724363	+	0.689419i	$0.757866\pi$
$3$	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	$0.0975106\pi$
$7$	1.95227	+	3.38143i	0.737889	+	1.27806i	−0.215555	+	0.976492i	$0.569156\pi$
$8$	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	−0.989777	−	0.142624i	$-0.954446\pi$
$13$	−1.33900	+	2.31922i	−0.371372	+	0.643236i	0.618405	+	0.785860i	$0.287779\pi$
$14$	−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	$-0.265169\pi$
$17$	5.54657			1.34524			0.672620	+	0.739988i	$0.265169\pi$
$18$	1.90668	+	0.580070i	0.449408	+	0.136724i
$19$	−5.13234			−1.17744			−0.588720	−	0.808337i	$-0.700368\pi$
$19$	−5.13234			−1.17744			−0.588720	+	0.808337i	$0.700368\pi$
$20$	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	0.811357	−	0.584551i	$-0.198729\pi$
$29$	−0.541520	−	0.937941i	−0.100558	−	0.174171i	−0.911915	+	0.410380i	$0.865396\pi$
$30$	−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	−0.729256	−	0.684241i	$-0.760134\pi$
$41$	1.45954	−	2.52799i	0.227942	−	0.394806i	0.957198	+	0.289434i	$0.0934672\pi$
$42$	−0.661016	+	4.44382i	−0.101997	+	0.685696i
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	0.938501	−	0.345277i	$-0.112215\pi$
$43$	1.11628	+	1.93346i	0.170232	+	0.294850i	−0.768269	+	0.640127i	$0.778882\pi$
$44$		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	0.966636	−	0.256156i	$-0.0824560\pi$
$61$	2.04223	+	3.53724i	0.261480	+	0.452897i	−0.705155	+	0.709053i	$0.749123\pi$
$62$	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	$-0.739365\pi$
$73$	−11.6727			−1.36618			−0.683091	+	0.730333i	$0.739365\pi$
$74$	−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	0.710644	−	0.703552i	$-0.248404\pi$
$79$	−2.25735	−	3.90985i	−0.253972	−	0.439893i	−0.964616	+	0.263659i	$0.915071\pi$
$80$	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	0.852496	−	0.522734i	$-0.175088\pi$
$83$	−0.241002	−	0.417427i	−0.0264534	−	0.0458186i	−0.878949	+	0.476916i	$0.841755\pi$
$84$	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	0.818880	−	0.573965i	$-0.194596\pi$
$101$	−0.880657	−	1.52534i	−0.0876287	−	0.151777i	−0.906508	+	0.422188i	$0.861262\pi$
$102$	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	$-0.665465\pi$
$107$	−10.2764			−0.993456			−0.496728	+	0.867906i	$0.665465\pi$
$108$	−4.60113	−	6.66525i	−0.442744	−	0.641364i
$109$	2.36284			0.226319			0.113160	−	0.993577i	$-0.463903\pi$
$109$	2.36284			0.226319			0.113160	+	0.993577i	$0.463903\pi$
$110$		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	$-0.610249\pi$
$127$	−7.65133			−0.678946			−0.339473	+	0.940616i	$0.610249\pi$
$128$	−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	−0.724901	−	0.688853i	$-0.758114\pi$
$131$	2.67956	−	4.64113i	0.234114	−	0.405498i	0.959015	+	0.283356i	$0.0914477\pi$
$132$		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	$0.364675\pi$
$139$	−6.87006	+	11.8993i	−0.582711	+	1.00928i	−0.995157	+	0.0983023i	$0.968659\pi$
$140$	−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	−0.957136	−	0.289640i	$-0.906464\pi$
$149$	−2.77983	+	4.81480i	−0.227732	+	0.394444i	0.729403	+	0.684084i	$0.239798\pi$
$150$	−0.635387	+	4.27152i	−0.0518791	+	0.348768i
$151$	0.0819538	+	0.141948i	0.00666930	+	0.0115516i	0.869341	−	0.494213i	$-0.164544\pi$
$151$	0.0819538	+	0.141948i	0.00666930	+	0.0115516i	−0.862671	+	0.505765i	$0.831210\pi$
$152$	−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	$0.376657\pi$
$167$	−7.92020	+	13.7182i	−0.612883	+	1.06155i	−0.990752	+	0.135686i	$0.956676\pi$
$168$	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	0.911249	−	0.411856i	$-0.135119\pi$
$173$	1.30144	+	2.25417i	0.0989470	+	0.171381i	−0.812302	+	0.583237i	$0.801786\pi$
$174$	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	−0.681683	−	0.731647i	$-0.738752\pi$
$193$	4.06748	−	7.04508i	0.292784	−	0.507116i	0.974467	+	0.224531i	$0.0720851\pi$
$194$	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	$-0.803832\pi$
$197$	−22.9072			−1.63207			−0.816035	+	0.578003i	$0.803832\pi$
$198$		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	−0.929348	−	0.369204i	$-0.879630\pi$
$211$	−2.10529	+	3.64647i	−0.144934	+	0.251033i	0.784414	+	0.620237i	$0.212964\pi$
$212$	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	$-0.783383\pi$
$227$	−14.0650	−	24.3612i	−0.933524	−	1.61691i	−0.156279	−	0.987713i	$-0.549950\pi$
$228$	−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	$-0.657653\pi$
$233$	−14.5096			−0.950557			−0.475278	+	0.879835i	$0.657653\pi$
$234$	−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	$-0.530976\pi$
$239$	12.5741	−	21.7789i	0.813349	−	1.40876i	0.910508	−	0.413492i	$-0.135691\pi$
$240$	2.78273	−	1.09835i	0.179625	−	0.0708984i
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	−0.996419	−	0.0845570i	$-0.973053\pi$
$241$	−8.87110	−	15.3652i	−0.571438	−	0.989759i	0.424981	−	0.905202i	$-0.360281\pi$
$242$		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	$0.162954\pi$
$263$	13.9491	+	24.1605i	0.860135	+	1.48980i	−0.0116625	+	0.999932i	$0.503712\pi$
$264$		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	$-0.780096\pi$
$271$	−25.3748			−1.54141			−0.770705	+	0.637192i	$0.780096\pi$
$272$	−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	0.979940	−	0.199294i	$-0.0638649\pi$
$277$	5.28219	+	9.14903i	0.317376	+	0.549712i	−0.662564	+	0.749006i	$0.730532\pi$
$278$	−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	$0.0684235\pi$
$281$	11.2853	+	19.5466i	0.673222	+	1.16605i	−0.303763	+	0.952748i	$0.598243\pi$
$282$	2.17297	−	14.6082i	0.129398	−	0.869908i
$283$	2.93862	−	5.08983i	0.174683	−	0.302559i	−0.765369	−	0.643592i	$-0.777443\pi$
$283$	2.93862	−	5.08983i	0.174683	−	0.302559i	0.940051	+	0.341033i	$0.110777\pi$
$284$	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	−0.950838	−	0.309688i	$-0.899775\pi$
$293$	−3.54705	+	6.14368i	−0.207221	+	0.358918i	0.743617	+	0.668606i	$0.233109\pi$
$294$	−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	$-0.677426\pi$
$307$	−18.5370			−1.05796			−0.528981	+	0.848633i	$0.677426\pi$
$308$		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	$-0.492947\pi$
$337$	16.0976	−	27.8818i	0.876891	−	1.51882i	0.854735	−	0.519065i	$-0.173720\pi$
$338$	−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	$-0.637286\pi$
$347$	10.7612	−	18.6390i	0.577694	−	1.00060i	0.995743	−	0.0921708i	$-0.0293806\pi$
$348$	−2.71971	+	1.07348i	−0.145792	+	0.0575444i
$349$	8.40998	+	14.5665i	0.450176	+	0.779727i	0.998397	−	0.0566062i	$-0.0180280\pi$
$349$	8.40998	+	14.5665i	0.450176	+	0.779727i	−0.548221	+	0.836334i	$0.684695\pi$
$350$	−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	$-0.428086\pi$
$359$	8.48869			0.448016			0.224008	+	0.974587i	$0.428086\pi$
$360$	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	−0.972599	−	0.232491i	$-0.925312\pi$
$373$	−5.50342	+	9.53220i	−0.284956	+	0.493558i	0.687642	+	0.726050i	$0.258646\pi$
$374$		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	−0.994462	−	0.105094i	$-0.966486\pi$
$409$	−8.21523	+	14.2292i	−0.406217	+	0.703588i	0.588245	+	0.808682i	$0.299819\pi$
$410$	−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	$-0.402784\pi$
$431$	12.4848			0.601372			0.300686	+	0.953723i	$0.402784\pi$
$432$	−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	0.910871	−	0.412692i	$-0.135411\pi$
$439$	2.05404	+	3.55769i	0.0980338	+	0.169799i	−0.812837	+	0.582491i	$0.802078\pi$
$440$		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	0.960999	−	0.276553i	$-0.0891923\pi$
$457$	5.15193	+	8.92340i	0.240997	+	0.417419i	−0.720002	+	0.693972i	$0.755859\pi$
$458$	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	$0.0352863\pi$
$461$	12.7266	+	22.0432i	0.592738	+	1.02665i	−0.401124	+	0.916024i	$0.631380\pi$
$462$		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	$8.31374e-5\pi$
$479$	10.9480	+	18.9625i	0.500226	+	0.866417i	−0.499774	+	0.866156i	$0.666584\pi$
$480$	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	−0.772940	−	0.634479i	$-0.781215\pi$
$491$	3.61195	−	6.25608i	0.163005	−	0.282333i	0.935945	+	0.352146i	$0.114548\pi$
$492$	−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	$-0.762951\pi$
$503$	−32.9813			−1.47057			−0.735283	+	0.677760i	$0.762951\pi$
$504$	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	$-0.397405\pi$
$523$	14.4881			0.633522			0.316761	+	0.948505i	$0.397405\pi$
$524$	−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	$-0.248015\pi$
$541$	33.0983			1.42301			0.711503	+	0.702683i	$0.248015\pi$
$542$	−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	0.750565	−	0.660796i	$-0.229781\pi$
$547$	−4.60707	−	7.97968i	−0.196984	−	0.341186i	−0.947549	+	0.319610i	$0.896448\pi$
$548$	−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	$-0.212679\pi$
$557$	37.0518			1.56994			0.784968	+	0.619536i	$0.212679\pi$
$558$	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	$-0.640729\pi$
$563$	13.4970	−	23.3775i	0.568832	−	0.985246i	0.996682	−	0.0813962i	$-0.0259379\pi$
$564$	−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	$0.0286898\pi$
$569$	13.7379	+	23.7947i	0.575921	+	0.997524i	−0.420020	+	0.907515i	$0.637977\pi$
$570$	6.13368	−	2.42098i	0.256911	−	0.101404i
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	−0.0921492	−	0.995745i	$-0.529374\pi$
$571$	19.5052	−	33.7840i	0.816266	−	1.41381i	0.908415	−	0.418069i	$-0.137293\pi$
$572$		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	$-0.477340\pi$
$593$	3.46422			0.142258			0.0711292	+	0.997467i	$0.477340\pi$
$594$		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	0.730802	−	0.682590i	$-0.239146\pi$
$601$	−5.53406	−	9.58527i	−0.225739	−	0.390991i	−0.956541	+	0.291598i	$0.905813\pi$
$602$	−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	$-0.641263\pi$
$607$	13.9805	−	24.2149i	0.567451	−	0.982854i	0.996817	−	0.0797235i	$-0.0254037\pi$
$608$	−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	$-0.428746\pi$
$613$	10.9923			0.443974			0.221987	+	0.975050i	$0.428746\pi$
$614$	−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	$0.0114442\pi$
$659$	13.6263	+	23.6015i	0.530806	+	0.919383i	−0.468547	+	0.883438i	$0.655223\pi$
$660$		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	$0.00529938\pi$
$673$	13.3433	+	23.1113i	0.514348	+	0.890877i	−0.485513	+	0.874229i	$0.661367\pi$
$674$	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	$-0.992433\pi$
$677$	−13.5415	−	23.4546i	−0.520443	−	0.901434i	0.479274	−	0.877665i	$-0.340900\pi$
$678$	−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	$-0.438296\pi$
$701$	10.2007			0.385275			0.192637	+	0.981270i	$0.438296\pi$
$702$	−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	−0.848184	−	0.529702i	$-0.822304\pi$
$733$	0.937944	−	1.62457i	0.0346438	−	0.0600048i	0.882827	+	0.469697i	$0.155637\pi$
$734$	−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	$-0.918174\pi$
$739$	−52.5826			−1.93428			−0.967140	+	0.254243i	$0.918174\pi$
$740$	−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	$-0.623928\pi$
$743$	16.6664	−	28.8671i	0.611431	−	1.05903i	0.990999	−	0.133866i	$-0.0427392\pi$
$744$	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	−0.988700	−	0.149906i	$-0.952103\pi$
$761$	−10.0560	+	17.4174i	−0.364528	+	0.631381i	0.624172	+	0.781287i	$0.285436\pi$
$762$	−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	−0.871623	−	0.490178i	$-0.836932\pi$
$769$	−0.313500	+	0.542997i	−0.0113051	+	0.0195810i	0.860318	+	0.509759i	$0.170265\pi$
$770$		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	−0.712542	−	0.701629i	$-0.752456\pi$
$787$	7.05147	−	12.2135i	0.251358	−	0.435364i	0.963900	+	0.266265i	$0.0857896\pi$
$788$	−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	$-0.410101\pi$
$809$	15.8533			0.557374			0.278687	+	0.960382i	$0.410101\pi$
$810$	−0.447427	+	6.66115i	−0.0157210	+	0.234049i
$811$	−36.3264			−1.27559			−0.637796	−	0.770206i	$-0.720154\pi$
$811$	−36.3264			−1.27559			−0.637796	+	0.770206i	$0.720154\pi$
$812$	−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	0.972713	−	0.232013i	$-0.0745313\pi$
$821$	8.17837	+	14.1653i	0.285427	+	0.494374i	−0.687286	+	0.726387i	$0.741198\pi$
$822$	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	$-0.469296\pi$
$827$	5.53930			0.192620			0.0963101	+	0.995351i	$0.469296\pi$
$828$	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	0.521815	−	0.853059i	$-0.325255\pi$
$853$	−13.9565	−	24.1734i	−0.477863	−	0.827683i	−0.999678	+	0.0253757i	$0.991922\pi$
$854$	−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	0.929437	−	0.368981i	$-0.120293\pi$
$857$	4.24983	+	7.36093i	0.145172	+	0.251445i	−0.784265	+	0.620426i	$0.786960\pi$
$858$		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	$0.375827\pi$
$877$	−18.0890	+	31.3310i	−0.610822	+	1.05797i	−0.991102	+	0.133103i	$0.957506\pi$
$878$	−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	$-0.652798\pi$
$887$	16.0006	−	27.7138i	0.537247	−	0.930539i	0.999051	−	0.0435570i	$-0.0138690\pi$
$888$	−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	$-0.540002\pi$
$919$	−7.59931			−0.250678			−0.125339	+	0.992114i	$0.540002\pi$
$920$	−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	$-0.405969\pi$
$937$	17.8231			0.582257			0.291128	+	0.956684i	$0.405969\pi$
$938$	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	$0.411406\pi$
$941$	−21.3296	+	36.9439i	−0.695324	+	1.20434i	−0.970071	+	0.242820i	$0.921928\pi$
$942$	−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	$-0.625296\pi$
$953$	−23.6805			−0.767085			−0.383543	+	0.923523i	$0.625296\pi$
$954$	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	$-0.666411\pi$
$967$	15.5700	−	26.9680i	0.500696	−	0.867231i	1.00000		0.000804082i	$-0.000255947\pi$
$968$		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	0.890564	−	0.454857i	$-0.150310\pi$
$997$	1.62184	+	2.80910i	0.0513641	+	0.0889652i	−0.839200	+	0.543823i	$0.816976\pi$
$998$	−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.p.364.11		36
9.4	even	3		9801.2.a.cm.1.8		18
9.5	odd	6		9801.2.a.cp.1.11		18
9.7	even	3	inner	1089.2.e.p.727.11		36
11.5	even	5		99.2.m.b.58.4	yes	72
11.9	even	5		99.2.m.b.4.6	✓	72
11.10	odd	2		1089.2.e.o.364.8		36
33.5	odd	10		297.2.n.b.91.6		72
33.20	odd	10		297.2.n.b.37.4		72
99.5	odd	30		891.2.f.e.487.4		36
99.16	even	15		99.2.m.b.25.6	yes	72
99.20	odd	30		297.2.n.b.235.6		72
99.31	even	15		891.2.f.f.730.6		36
99.32	even	6		9801.2.a.cn.1.8		18
99.38	odd	30		297.2.n.b.289.4		72
99.43	odd	6		1089.2.e.o.727.8		36
99.49	even	15		891.2.f.f.487.6		36
99.76	odd	6		9801.2.a.co.1.11		18
99.86	odd	30		891.2.f.e.730.4		36
99.97	even	15		99.2.m.b.70.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.6	✓	72	11.9	even	5
99.2.m.b.25.6	yes	72	99.16	even	15
99.2.m.b.58.4	yes	72	11.5	even	5
99.2.m.b.70.4	yes	72	99.97	even	15
297.2.n.b.37.4		72	33.20	odd	10
297.2.n.b.91.6		72	33.5	odd	10
297.2.n.b.235.6		72	99.20	odd	30
297.2.n.b.289.4		72	99.38	odd	30
891.2.f.e.487.4		36	99.5	odd	30
891.2.f.e.730.4		36	99.86	odd	30
891.2.f.f.487.6		36	99.49	even	15
891.2.f.f.730.6		36	99.31	even	15
1089.2.e.o.364.8		36	11.10	odd	2
1089.2.e.o.727.8		36	99.43	odd	6
1089.2.e.p.364.11		36	1.1	even	1	trivial
1089.2.e.p.727.11		36	9.7	even	3	inner
9801.2.a.cm.1.8		18	9.4	even	3
9801.2.a.cn.1.8		18	99.32	even	6
9801.2.a.co.1.11		18	99.76	odd	6
9801.2.a.cp.1.11		18	9.5	odd	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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