LMFDB - Embedded newform 1089.2.e.o.727.17

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			727.17
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.o.364.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10759 - 1.91839i) q^{2} +(-1.72523 + 0.153513i) q^{3} +(-1.45349 - 2.51752i) q^{4} +(0.311236 + 0.539077i) q^{5} +(-1.61634 + 3.47971i) q^{6} +(1.28962 - 2.23368i) q^{7} -2.00911 q^{8} +(2.95287 - 0.529693i) q^{9} +1.37888 q^{10} +(2.89408 + 4.12018i) q^{12} +(0.0564158 + 0.0977150i) q^{13} +(-2.85672 - 4.94798i) q^{14} +(-0.619711 - 0.882255i) q^{15} +(0.681716 - 1.18077i) q^{16} +2.37133 q^{17} +(2.25439 - 6.25144i) q^{18} +5.87259 q^{19} +(0.904757 - 1.56709i) q^{20} +(-1.88199 + 4.05159i) q^{21} +(0.964846 + 1.67116i) q^{23} +(3.46619 - 0.308426i) q^{24} +(2.30626 - 3.99457i) q^{25} +0.249941 q^{26} +(-5.01307 + 1.36715i) q^{27} -7.49777 q^{28} +(-3.45830 + 5.98996i) q^{29} +(-2.37890 + 0.211677i) q^{30} +(-5.01162 - 8.68037i) q^{31} +(-3.51923 - 6.09548i) q^{32} +(2.62645 - 4.54915i) q^{34} +1.60550 q^{35} +(-5.62547 - 6.66399i) q^{36} -10.0160 q^{37} +(6.50439 - 11.2659i) q^{38} +(-0.112331 - 0.159921i) q^{39} +(-0.625309 - 1.08307i) q^{40} +(-4.19484 - 7.26568i) q^{41} +(5.68809 + 8.09788i) q^{42} +(-1.07224 + 1.85718i) q^{43} +(1.20458 + 1.42696i) q^{45} +4.27460 q^{46} +(3.16594 - 5.48357i) q^{47} +(-0.994856 + 2.14175i) q^{48} +(0.173783 + 0.301001i) q^{49} +(-5.10877 - 8.84864i) q^{50} +(-4.09110 + 0.364031i) q^{51} +(0.163999 - 0.284055i) q^{52} +10.8566 q^{53} +(-2.92968 + 11.1313i) q^{54} +(-2.59098 + 4.48771i) q^{56} +(-10.1316 + 0.901521i) q^{57} +(7.66073 + 13.2688i) q^{58} +(-1.26146 - 2.18491i) q^{59} +(-1.32035 + 2.84248i) q^{60} +(-0.851634 + 1.47507i) q^{61} -22.2032 q^{62} +(2.62490 - 7.27886i) q^{63} -12.8645 q^{64} +(-0.0351173 + 0.0608249i) q^{65} +(1.66588 + 2.88539i) q^{67} +(-3.44671 - 5.96987i) q^{68} +(-1.92113 - 2.73503i) q^{69} +(1.77823 - 3.07998i) q^{70} +5.77804 q^{71} +(-5.93264 + 1.06421i) q^{72} -5.87253 q^{73} +(-11.0935 + 19.2145i) q^{74} +(-3.36563 + 7.24561i) q^{75} +(-8.53575 - 14.7843i) q^{76} +(-0.431207 + 0.0383693i) q^{78} +(-0.487061 + 0.843614i) q^{79} +0.848699 q^{80} +(8.43885 - 3.12823i) q^{81} -18.5846 q^{82} +(3.09960 - 5.36867i) q^{83} +(12.9354 - 1.15101i) q^{84} +(0.738045 + 1.27833i) q^{85} +(2.37520 + 4.11397i) q^{86} +(5.04685 - 10.8650i) q^{87} -3.94867 q^{89} +(4.07166 - 0.730384i) q^{90} +0.291019 q^{91} +(2.80479 - 4.85804i) q^{92} +(9.97877 + 14.2063i) q^{93} +(-7.01310 - 12.1470i) q^{94} +(1.82776 + 3.16578i) q^{95} +(7.00723 + 9.97589i) q^{96} +(-0.164416 + 0.284776i) q^{97} +0.769917 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 $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.10759	−	1.91839i	0.783181	−	1.35651i	−0.146899	−	0.989152i	$-0.546929\pi$
$2$	1.10759	−	1.91839i	0.783181	−	1.35651i	0.930080	−	0.367358i	$-0.119737\pi$
$3$	−1.72523	+	0.153513i	−0.996065	+	0.0886310i
$3$	−1.72523	+	0.153513i	−0.996065	+	0.0886310i
$4$	−1.45349	−	2.51752i	−0.726745	−	1.25876i
$5$	0.311236	+	0.539077i	0.139189	+	0.241083i	0.927190	−	0.374592i	$-0.122217\pi$
$5$	0.311236	+	0.539077i	0.139189	+	0.241083i	−0.788001	+	0.615674i	$0.788884\pi$
$6$	−1.61634	+	3.47971i	−0.659870	+	1.42058i
$7$	1.28962	−	2.23368i	0.487429	−	0.844252i	−0.512467	−	0.858707i	$-0.671268\pi$
$7$	1.28962	−	2.23368i	0.487429	−	0.844252i	0.999896	+	0.0144555i	$0.00460150\pi$
$8$	−2.00911			−0.710329
$9$	2.95287	−	0.529693i	0.984289	−	0.176564i
$10$	1.37888			0.436041
$11$		0			0
$11$		0			0
$12$	2.89408	+	4.12018i	0.835450	+	1.18939i
$13$	0.0564158	+	0.0977150i	0.0156469	+	0.0271013i	0.873743	−	0.486388i	$-0.161686\pi$
$13$	0.0564158	+	0.0977150i	0.0156469	+	0.0271013i	−0.858096	+	0.513489i	$0.828353\pi$
$14$	−2.85672	−	4.94798i	−0.763490	−	1.32240i
$15$	−0.619711	−	0.882255i	−0.160009	−	0.227797i
$16$	0.681716	−	1.18077i	0.170429	−	0.295192i
$17$	2.37133			0.575133			0.287566	−	0.957761i	$-0.407154\pi$
$17$	2.37133			0.575133			0.287566	+	0.957761i	$0.407154\pi$
$18$	2.25439	−	6.25144i	0.531365	−	1.47348i
$19$	5.87259			1.34726			0.673632	−	0.739067i	$-0.264733\pi$
$19$	5.87259			1.34726			0.673632	+	0.739067i	$0.264733\pi$
$20$	0.904757	−	1.56709i	0.202310	−	0.350411i
$21$	−1.88199	+	4.05159i	−0.410684	+	0.884130i
$22$		0			0
$23$	0.964846	+	1.67116i	0.201184	+	0.348462i	0.948910	−	0.315546i	$-0.102188\pi$
$23$	0.964846	+	1.67116i	0.201184	+	0.348462i	−0.747726	+	0.664007i	$0.768854\pi$
$24$	3.46619	−	0.308426i	0.707533	−	0.0629571i
$25$	2.30626	−	3.99457i	0.461253	−	0.798913i
$26$	0.249941			0.0490175
$27$	−5.01307	+	1.36715i	−0.964766	+	0.263108i
$28$	−7.49777			−1.41695
$29$	−3.45830	+	5.98996i	−0.642191	+	1.11231i	0.342752	+	0.939426i	$0.388641\pi$
$29$	−3.45830	+	5.98996i	−0.642191	+	1.11231i	−0.984943	+	0.172882i	$0.944692\pi$
$30$	−2.37890	+	0.211677i	−0.434325	+	0.0386467i
$31$	−5.01162	−	8.68037i	−0.900113	−	1.55904i	−0.827346	−	0.561692i	$-0.810150\pi$
$31$	−5.01162	−	8.68037i	−0.900113	−	1.55904i	−0.0727668	−	0.997349i	$-0.523183\pi$
$32$	−3.51923	−	6.09548i	−0.622118	−	1.07754i
$33$		0			0
$34$	2.62645	−	4.54915i	0.450433	−	0.780173i
$35$	1.60550			0.271379
$36$	−5.62547	−	6.66399i	−0.937579	−	1.11067i
$37$	−10.0160			−1.64661			−0.823307	−	0.567597i	$-0.807873\pi$
$37$	−10.0160			−1.64661			−0.823307	+	0.567597i	$0.807873\pi$
$38$	6.50439	−	11.2659i	1.05515	−	1.82758i
$39$	−0.112331	−	0.159921i	−0.0179874	−	0.0256078i
$40$	−0.625309	−	1.08307i	−0.0988700	−	0.171248i
$41$	−4.19484	−	7.26568i	−0.655124	−	1.13471i	−0.981863	−	0.189593i	$-0.939283\pi$
$41$	−4.19484	−	7.26568i	−0.655124	−	1.13471i	0.326739	−	0.945115i	$-0.394050\pi$
$42$	5.68809	+	8.09788i	0.877691	+	1.24953i
$43$	−1.07224	+	1.85718i	−0.163515	+	0.283217i	−0.936127	−	0.351662i	$-0.885617\pi$
$43$	−1.07224	+	1.85718i	−0.163515	+	0.283217i	0.772612	+	0.634879i	$0.218950\pi$
$44$		0			0
$45$	1.20458	+	1.42696i	0.179569	+	0.212719i
$46$	4.27460			0.630255
$47$	3.16594	−	5.48357i	0.461800	−	0.799861i	−0.537251	−	0.843423i	$-0.680537\pi$
$47$	3.16594	−	5.48357i	0.461800	−	0.799861i	0.999051	+	0.0435614i	$0.0138704\pi$
$48$	−0.994856	+	2.14175i	−0.143595	+	0.309135i
$49$	0.173783	+	0.301001i	0.0248261	+	0.0430001i
$50$	−5.10877	−	8.84864i	−0.722489	−	1.25139i
$51$	−4.09110	+	0.364031i	−0.572869	+	0.0509746i
$52$	0.163999	−	0.284055i	0.0227426	−	0.0393914i
$53$	10.8566			1.49127			0.745634	−	0.666355i	$-0.232147\pi$
$53$	10.8566			1.49127			0.745634	+	0.666355i	$0.232147\pi$
$54$	−2.92968	+	11.1313i	−0.398678	+	1.51478i
$55$		0			0
$56$	−2.59098	+	4.48771i	−0.346235	+	0.599696i
$57$	−10.1316	+	0.901521i	−1.34196	+	0.119409i
$58$	7.66073	+	13.2688i	1.00590	+	1.74228i
$59$	−1.26146	−	2.18491i	−0.164228	−	0.284451i	0.772153	−	0.635437i	$-0.219180\pi$
$59$	−1.26146	−	2.18491i	−0.164228	−	0.284451i	−0.936381	+	0.350986i	$0.885847\pi$
$60$	−1.32035	+	2.84248i	−0.170456	+	0.366963i
$61$	−0.851634	+	1.47507i	−0.109041	+	0.188864i	−0.915382	−	0.402587i	$-0.868111\pi$
$61$	−0.851634	+	1.47507i	−0.109041	+	0.188864i	0.806341	+	0.591451i	$0.201445\pi$
$62$	−22.2032			−2.81981
$63$	2.62490	−	7.27886i	0.330706	−	0.917050i
$64$	−12.8645			−1.60806
$65$	−0.0351173	+	0.0608249i	−0.00435576	+	0.00754440i
$66$		0			0
$67$	1.66588	+	2.88539i	0.203520	+	0.352507i	0.949660	−	0.313282i	$-0.101429\pi$
$67$	1.66588	+	2.88539i	0.203520	+	0.352507i	−0.746140	+	0.665789i	$0.768095\pi$
$68$	−3.44671	−	5.96987i	−0.417975	−	0.723953i
$69$	−1.92113	−	2.73503i	−0.231277	−	0.329259i
$70$	1.77823	−	3.07998i	0.212539	−	0.368128i
$71$	5.77804			0.685728			0.342864	−	0.939385i	$-0.388603\pi$
$71$	5.77804			0.685728			0.342864	+	0.939385i	$0.388603\pi$
$72$	−5.93264	+	1.06421i	−0.699169	+	0.125419i
$73$	−5.87253			−0.687327			−0.343664	−	0.939093i	$-0.611668\pi$
$73$	−5.87253			−0.687327			−0.343664	+	0.939093i	$0.611668\pi$
$74$	−11.0935	+	19.2145i	−1.28960	+	2.23365i
$75$	−3.36563	+	7.24561i	−0.388629	+	0.836650i
$76$	−8.53575	−	14.7843i	−0.979117	−	1.69588i
$77$		0			0
$78$	−0.431207	+	0.0383693i	−0.0488246	+	0.00434447i
$79$	−0.487061	+	0.843614i	−0.0547986	+	0.0949140i	−0.892123	−	0.451792i	$-0.850785\pi$
$79$	−0.487061	+	0.843614i	−0.0547986	+	0.0949140i	0.837325	+	0.546706i	$0.184118\pi$
$80$	0.848699			0.0948874
$81$	8.43885	−	3.12823i	0.937650	−	0.347581i
$82$	−18.5846			−2.05232
$83$	3.09960	−	5.36867i	0.340225	−	0.589288i	−0.644249	−	0.764816i	$-0.722830\pi$
$83$	3.09960	−	5.36867i	0.340225	−	0.589288i	0.984474	+	0.175528i	$0.0561633\pi$
$84$	12.9354	−	1.15101i	1.41137	−	0.125585i
$85$	0.738045	+	1.27833i	0.0800522	+	0.138654i
$86$	2.37520	+	4.11397i	0.256124	+	0.443621i
$87$	5.04685	−	10.8650i	0.541079	−	1.16485i
$88$		0			0
$89$	−3.94867			−0.418558			−0.209279	−	0.977856i	$-0.567112\pi$
$89$	−3.94867			−0.418558			−0.209279	+	0.977856i	$0.567112\pi$
$90$	4.07166	−	0.730384i	0.429190	−	0.0769893i
$91$	0.291019			0.0305070
$92$	2.80479	−	4.85804i	0.292419	−	0.506485i
$93$	9.97877	+	14.2063i	1.03475	+	1.47313i
$94$	−7.01310	−	12.1470i	−0.723346	−	1.25287i
$95$	1.82776	+	3.16578i	0.187524	+	0.324802i
$96$	7.00723	+	9.97589i	0.715173	+	1.01816i
$97$	−0.164416	+	0.284776i	−0.0166939	+	0.0289146i	−0.874252	−	0.485473i	$-0.838647\pi$
$97$	−0.164416	+	0.284776i	−0.0166939	+	0.0289146i	0.857558	+	0.514388i	$0.171981\pi$
$98$	0.769917			0.0777734
$99$		0			0
$100$	−13.4085			−1.34085
$101$	−6.60359	+	11.4378i	−0.657082	+	1.13810i	0.324286	+	0.945959i	$0.394876\pi$
$101$	−6.60359	+	11.4378i	−0.657082	+	1.13810i	−0.981368	+	0.192140i	$0.938457\pi$
$102$	−3.83289	+	8.25154i	−0.379513	+	0.817025i
$103$	−0.723835	−	1.25372i	−0.0713215	−	0.123533i	0.828159	−	0.560493i	$-0.189388\pi$
$103$	−0.723835	−	1.25372i	−0.0713215	−	0.123533i	−0.899481	+	0.436960i	$0.856055\pi$
$104$	−0.113346	−	0.196320i	−0.0111145	−	0.0192508i
$105$	−2.76986	+	0.246466i	−0.270311	+	0.0240526i
$106$	12.0246	−	20.8272i	1.16793	−	2.02292i
$107$	10.1921			0.985311			0.492656	−	0.870224i	$-0.336026\pi$
$107$	10.1921			0.985311			0.492656	+	0.870224i	$0.336026\pi$
$108$	10.7283	+	10.6334i	1.03233	+	1.02320i
$109$	−1.77230			−0.169755			−0.0848775	−	0.996391i	$-0.527050\pi$
$109$	−1.77230			−0.169755			−0.0848775	+	0.996391i	$0.527050\pi$
$110$		0			0
$111$	17.2799	−	1.53758i	1.64013	−	0.145941i
$112$	−1.75830	−	3.04547i	−0.166144	−	0.287770i
$113$	8.47405	+	14.6775i	0.797171	+	1.38074i	0.921451	+	0.388494i	$0.127004\pi$
$113$	8.47405	+	14.6775i	0.797171	+	1.38074i	−0.124280	+	0.992247i	$0.539662\pi$
$114$	−9.49213	+	20.4349i	−0.889019	+	1.91390i
$115$	−0.600590	+	1.04025i	−0.0560053	+	0.0970041i
$116$	20.1064			1.86684
$117$	0.218347	+	0.258656i	0.0201862	+	0.0239128i
$118$	−5.58869			−0.514480
$119$	3.05811	−	5.29680i	0.280336	−	0.485557i
$120$	1.24507	+	1.77255i	0.113659	+	0.161811i
$121$		0			0
$122$	1.88651	+	3.26754i	0.170797	+	0.295829i
$123$	8.35246	+	11.8910i	0.753116	+	1.07218i
$124$	−14.5687	+	25.2337i	−1.30830	+	2.26605i
$125$	5.98353			0.535184
$126$	−11.0564	−	13.0975i	−0.984984	−	1.16682i
$127$	−10.0230			−0.889398			−0.444699	−	0.895680i	$-0.646689\pi$
$127$	−10.0230			−0.889398			−0.444699	+	0.895680i	$0.646689\pi$
$128$	−7.21009	+	12.4882i	−0.637288	+	1.10382i
$129$	1.56477	−	3.36867i	0.137770	−	0.296595i
$130$	0.0777907	+	0.134737i	0.00682270	+	0.0118173i
$131$	2.28104	+	3.95088i	0.199295	+	0.345190i	0.948300	−	0.317375i	$-0.102801\pi$
$131$	2.28104	+	3.95088i	0.199295	+	0.345190i	−0.749005	+	0.662565i	$0.769468\pi$
$132$		0			0
$133$	7.57338	−	13.1175i	0.656696	−	1.13743i
$134$	7.38042			0.637572
$135$	−2.29725	−	2.27693i	−0.197716	−	0.195967i
$136$	−4.76427			−0.408533
$137$	0.497970	−	0.862509i	0.0425445	−	0.0736891i	−0.843969	−	0.536392i	$-0.819787\pi$
$137$	0.497970	−	0.862509i	0.0425445	−	0.0736891i	0.886514	+	0.462703i	$0.153120\pi$
$138$	−7.37468	+	0.656208i	−0.627775	+	0.0558601i
$139$	6.34670	+	10.9928i	0.538320	+	0.932398i	0.998995	+	0.0448287i	$0.0142742\pi$
$139$	6.34670	+	10.9928i	0.538320	+	0.932398i	−0.460675	+	0.887569i	$0.652392\pi$
$140$	−2.33358	−	4.04188i	−0.197223	−	0.341601i
$141$	−4.62019	+	9.94646i	−0.389090	+	0.837643i
$142$	6.39968	−	11.0846i	0.537049	−	0.930196i
$143$		0			0
$144$	1.38757	−	3.84775i	0.115631	−	0.320646i
$145$	−4.30540			−0.357544
$146$	−6.50432	+	11.2658i	−0.538302	+	0.932366i
$147$	−0.346024	−	0.492619i	−0.0285396	−	0.0406305i
$148$	14.5581	+	25.2153i	1.19667	+	2.07269i
$149$	−0.708953	−	1.22794i	−0.0580797	−	0.100597i	0.835524	−	0.549454i	$-0.185164\pi$
$149$	−0.708953	−	1.22794i	−0.0580797	−	0.100597i	−0.893603	+	0.448858i	$0.851831\pi$
$150$	10.1722	+	14.4817i	0.830557	+	1.18243i
$151$	9.17319	−	15.8884i	0.746504	−	1.29298i	−0.202985	−	0.979182i	$-0.565064\pi$
$151$	9.17319	−	15.8884i	0.746504	−	1.29298i	0.949489	−	0.313800i	$-0.101602\pi$
$152$	−11.7987			−0.957000
$153$	7.00223	−	1.25608i	0.566097	−	0.101548i
$154$		0			0
$155$	3.11959	−	5.40329i	0.250572	−	0.434003i
$156$	−0.239331	+	0.515238i	−0.0191618	+	0.0412521i
$157$	−6.70950	−	11.6212i	−0.535476	−	0.927472i	−0.999140	−	0.0414610i	$-0.986799\pi$
$157$	−6.70950	−	11.6212i	−0.535476	−	0.927472i	0.463664	−	0.886011i	$-0.346535\pi$
$158$	1.07892	+	1.86875i	0.0858345	+	0.148670i
$159$	−18.7302	+	1.66663i	−1.48540	+	0.132173i
$160$	2.19062	−	3.79427i	0.173184	−	0.299963i
$161$	4.97712			0.392252
$162$	3.34558	−	19.6538i	0.262853	−	1.54415i
$163$	15.6465			1.22553			0.612763	−	0.790267i	$-0.290058\pi$
$163$	15.6465			1.22553			0.612763	+	0.790267i	$0.290058\pi$
$164$	−12.1943	+	21.1212i	−0.952216	+	1.64929i
$165$		0			0
$166$	−6.86614	−	11.8925i	−0.532916	−	0.923038i
$167$	4.64904	+	8.05238i	0.359754	+	0.623112i	0.987920	−	0.154968i	$-0.0495274\pi$
$167$	4.64904	+	8.05238i	0.359754	+	0.623112i	−0.628166	+	0.778079i	$0.716194\pi$
$168$	3.78113	−	8.14011i	0.291720	−	0.628023i
$169$	6.49363	−	11.2473i	0.499510	−	0.865177i
$170$	3.26979			0.250781
$171$	17.3410	−	3.11067i	1.32610	−	0.237879i
$172$	6.23397			0.475336
$173$	−6.73874	+	11.6718i	−0.512337	+	0.887394i	0.487560	+	0.873089i	$0.337887\pi$
$173$	−6.73874	+	11.6718i	−0.512337	+	0.887394i	−0.999898	+	0.0143049i	$0.995446\pi$
$174$	−15.2535	−	21.7157i	−1.15636	−	1.64627i
$175$	−5.94839	−	10.3029i	−0.449656	−	0.778827i
$176$		0			0
$177$	2.51172	+	3.57583i	0.188793	+	0.268776i
$178$	−4.37349	+	7.57511i	−0.327807	+	0.567778i
$179$	20.3030			1.51752			0.758759	−	0.651371i	$-0.225806\pi$
$179$	20.3030			1.51752			0.758759	+	0.651371i	$0.225806\pi$
$180$	1.84155	−	5.10664i	0.137261	−	0.380626i
$181$	−5.82634			−0.433068			−0.216534	−	0.976275i	$-0.569475\pi$
$181$	−5.82634			−0.433068			−0.216534	+	0.976275i	$0.569475\pi$
$182$	0.322328	−	0.558288i	0.0238925	−	0.0413831i
$183$	1.24283	−	2.67559i	0.0918723	−	0.197785i
$184$	−1.93849	−	3.35755i	−0.142907	−	0.247522i
$185$	−3.11733	−	5.39937i	−0.229191	−	0.396970i
$186$	38.3057	−	3.40848i	2.80871	−	0.249922i
$187$		0			0
$188$	−18.4067			−1.34244
$189$	−3.41116	+	12.9607i	−0.248126	+	0.942752i
$190$	8.09761			0.587462
$191$	2.15874	−	3.73906i	0.156201	−	0.270549i	−0.777295	−	0.629137i	$-0.783408\pi$
$191$	2.15874	−	3.73906i	0.156201	−	0.270549i	0.933496	+	0.358588i	$0.116742\pi$
$192$	22.1943	−	1.97488i	1.60174	−	0.142524i
$193$	12.6000	+	21.8238i	0.906968	+	1.57092i	0.818253	+	0.574858i	$0.194943\pi$
$193$	12.6000	+	21.8238i	0.906968	+	1.57092i	0.0887150	+	0.996057i	$0.471724\pi$
$194$	0.364208	+	0.630827i	0.0261486	+	0.0452908i
$195$	0.0512481	−	0.110328i	0.00366995	−	0.00790076i
$196$	0.505183	−	0.875003i	0.0360845	−	0.0625002i
$197$	−1.17388			−0.0836352			−0.0418176	−	0.999125i	$-0.513315\pi$
$197$	−1.17388			−0.0836352			−0.0418176	+	0.999125i	$0.513315\pi$
$198$		0			0
$199$	−1.84404			−0.130721			−0.0653604	−	0.997862i	$-0.520820\pi$
$199$	−1.84404			−0.130721			−0.0653604	+	0.997862i	$0.520820\pi$
$200$	−4.63354	+	8.02553i	−0.327641	+	0.567491i
$201$	−3.31698	−	4.72224i	−0.233962	−	0.333081i
$202$	14.6281	+	25.3366i	1.02923	+	1.78267i
$203$	8.91977	+	15.4495i	0.626045	+	1.08434i
$204$	6.86283	+	9.77031i	0.480494	+	0.684059i
$205$	2.61117	−	4.52268i	0.182372	−	0.315878i
$206$	−3.20683			−0.223431
$207$	3.73427	+	4.42365i	0.259549	+	0.307465i
$208$	0.153838			0.0106668
$209$		0			0
$210$	−2.59504	+	5.58667i	−0.179075	+	0.385517i
$211$	−7.21938	−	12.5043i	−0.497002	−	0.860833i	0.502992	−	0.864291i	$-0.332233\pi$
$211$	−7.21938	−	12.5043i	−0.497002	−	0.860833i	−0.999994	+	0.00345786i	$0.998899\pi$
$212$	−15.7800	−	27.3317i	−1.08377	−	1.87715i
$213$	−9.96848	+	0.887007i	−0.683029	+	0.0607767i
$214$	11.2887	−	19.5525i	0.771677	−	1.33658i
$215$	−1.33488			−0.0910383
$216$	10.0718	−	2.74676i	0.685301	−	0.186893i
$217$	−25.8522			−1.75496
$218$	−1.96297	+	3.39996i	−0.132949	+	0.230274i
$219$	10.1315	−	0.901511i	0.684622	−	0.0609185i
$220$		0			0
$221$	0.133781	+	0.231715i	0.00899905	+	0.0155868i
$222$	16.1892	−	34.8526i	1.08655	−	2.33915i
$223$	7.54189	−	13.0629i	0.505042	−	0.874758i	−0.494941	−	0.868927i	$-0.664810\pi$
$223$	7.54189	−	13.0629i	0.505042	−	0.874758i	0.999983	−	0.00583187i	$-0.00185635\pi$
$224$	−18.1538			−1.21295
$225$	4.69420	−	13.0170i	0.312947	−	0.867802i
$226$	37.5429			2.49732
$227$	−2.18894	+	3.79136i	−0.145285	+	0.251641i	−0.929479	−	0.368874i	$-0.879743\pi$
$227$	−2.18894	+	3.79136i	−0.145285	+	0.251641i	0.784194	+	0.620516i	$0.213077\pi$
$228$	16.9958	+	24.1961i	1.12557	+	1.60243i
$229$	−6.52384	−	11.2996i	−0.431107	−	0.746700i	0.565862	−	0.824500i	$-0.308544\pi$
$229$	−6.52384	−	11.2996i	−0.431107	−	0.746700i	−0.996969	+	0.0778005i	$0.975210\pi$
$230$	1.33041	+	2.30434i	0.0877246	+	0.151944i
$231$		0			0
$232$	6.94812	−	12.0345i	0.456167	−	0.790104i
$233$	15.0351			0.984982			0.492491	−	0.870317i	$-0.336086\pi$
$233$	15.0351			0.984982			0.492491	+	0.870317i	$0.336086\pi$
$234$	0.738043	−	0.132392i	0.0482474	−	0.00865474i
$235$	3.94142			0.257110
$236$	−3.66703	+	6.35148i	−0.238703	+	0.413446i
$237$	0.710788	−	1.53020i	0.0461706	−	0.0993973i
$238$	−6.77423	−	11.7333i	−0.439108	−	0.760557i
$239$	4.33017	+	7.50007i	0.280095	+	0.485140i	0.971408	−	0.237416i	$-0.0763006\pi$
$239$	4.33017	+	7.50007i	0.280095	+	0.485140i	−0.691313	+	0.722556i	$0.742967\pi$
$240$	−1.46420	+	0.130287i	−0.0945140	+	0.00840996i
$241$	−14.9277	+	25.8556i	−0.961580	+	1.66551i	−0.243046	+	0.970015i	$0.578146\pi$
$241$	−14.9277	+	25.8556i	−0.961580	+	1.66551i	−0.718535	+	0.695491i	$0.755187\pi$
$242$		0			0
$243$	−14.0788	+	6.69240i	−0.903154	+	0.429318i
$244$	4.95137			0.316979
$245$	−0.108175	+	0.187365i	−0.00691105	+	0.0119703i
$246$	32.0627	−	2.85298i	2.04425	−	0.181899i
$247$	0.331307	+	0.573840i	0.0210805	+	0.0365126i
$248$	10.0689	+	17.4399i	0.639376	+	1.10743i
$249$	−4.52338	+	9.73804i	−0.286657	+	0.617123i
$250$	6.62727	−	11.4788i	0.419146	−	0.725981i
$251$	−17.3230			−1.09342			−0.546710	−	0.837322i	$-0.684120\pi$
$251$	−17.3230			−1.09342			−0.546710	+	0.837322i	$0.684120\pi$
$252$	−22.1399	+	3.97152i	−1.39468	+	0.250182i
$253$		0			0
$254$	−11.1013	+	19.2281i	−0.696559	+	1.20648i
$255$	−1.46954	−	2.09212i	−0.0920262	−	0.131014i
$256$	3.10706	+	5.38159i	0.194191	+	0.336349i
$257$	5.91966	+	10.2532i	0.369258	+	0.639574i	0.989450	−	0.144876i	$-0.0462784\pi$
$257$	5.91966	+	10.2532i	0.369258	+	0.639574i	−0.620191	+	0.784451i	$0.712945\pi$
$258$	−4.72933	−	6.73293i	−0.294435	−	0.419174i
$259$	−12.9167	+	22.3724i	−0.802607	+	1.39016i
$260$	0.204170			0.0126621
$261$	−7.03908	+	19.5194i	−0.435708	+	1.20822i
$262$	10.1058			0.624338
$263$	−7.90974	+	13.7001i	−0.487736	+	0.844783i	−0.999901	−	0.0141042i	$-0.995510\pi$
$263$	−7.90974	+	13.7001i	−0.487736	+	0.844783i	0.512165	+	0.858887i	$0.328844\pi$
$264$		0			0
$265$	3.37897	+	5.85254i	0.207568	+	0.359519i
$266$	−16.7763	−	29.0575i	−1.02862	−	1.78163i
$267$	6.81238	−	0.606174i	0.416911	−	0.0370972i
$268$	4.84268	−	8.38777i	0.295814	−	0.512365i
$269$	0.960150			0.0585414			0.0292707	−	0.999572i	$-0.490682\pi$
$269$	0.960150			0.0585414			0.0292707	+	0.999572i	$0.490682\pi$
$270$	−6.91244	+	1.88514i	−0.420678	+	0.114726i
$271$	−28.1202			−1.70818			−0.854091	−	0.520123i	$-0.825886\pi$
$271$	−28.1202			−1.70818			−0.854091	+	0.520123i	$0.825886\pi$
$272$	1.61657	−	2.79999i	0.0980192	−	0.169774i
$273$	−0.502075	+	0.0446752i	−0.0303870	+	0.00270387i
$274$	−1.10309	−	1.91061i	−0.0666400	−	0.115424i
$275$		0			0
$276$	−4.09314	+	8.81182i	−0.246378	+	0.530409i
$277$	−0.529780	+	0.917606i	−0.0318314	+	0.0551336i	−0.881502	−	0.472180i	$-0.843467\pi$
$277$	−0.529780	+	0.917606i	−0.0318314	+	0.0551336i	0.849671	+	0.527313i	$0.176801\pi$
$278$	28.1180			1.68641
$279$	−19.3966	−	22.9774i	−1.16124	−	1.37562i
$280$	−3.22563			−0.192768
$281$	−11.8467	+	20.5191i	−0.706715	+	1.22407i	0.259353	+	0.965782i	$0.416491\pi$
$281$	−11.8467	+	20.5191i	−0.706715	+	1.22407i	−0.966069	+	0.258285i	$0.916843\pi$
$282$	13.9640	+	19.8799i	0.831543	+	1.18383i
$283$	4.01611	+	6.95611i	0.238733	+	0.413498i	0.960351	−	0.278794i	$-0.0899346\pi$
$283$	4.01611	+	6.95611i	0.238733	+	0.413498i	−0.721618	+	0.692291i	$0.756601\pi$
$284$	−8.39833	−	14.5463i	−0.498349	−	0.863166i
$285$	−3.63931	−	5.18112i	−0.215574	−	0.306903i
$286$		0			0
$287$	−21.6389			−1.27731
$288$	−13.6206	−	16.1350i	−0.802599	−	0.950766i
$289$	−11.3768			−0.669222
$290$	−4.76860	+	8.25945i	−0.280022	+	0.485012i
$291$	0.239938	−	0.516545i	0.0140654	−	0.0302804i
$292$	8.53566	+	14.7842i	0.499512	+	0.865179i
$293$	2.23171	+	3.86544i	0.130378	+	0.225821i	0.923822	−	0.382822i	$-0.125048\pi$
$293$	2.23171	+	3.86544i	0.130378	+	0.225821i	−0.793444	+	0.608643i	$0.791714\pi$
$294$	−1.32829	+	0.118193i	−0.0774673	+	0.00689313i
$295$	0.785223	−	1.36005i	0.0457174	−	0.0791849i
$296$	20.1232			1.16964
$297$		0			0
$298$	−3.14090			−0.181948
$299$	−0.108865	+	0.188560i	−0.00629583	+	0.0109047i
$300$	23.1328	−	2.05839i	1.33558	−	0.118841i
$301$	2.76556	+	4.79009i	0.159404	+	0.276096i
$302$	−20.3202	−	35.1956i	−1.16929	−	2.02528i
$303$	9.63689	−	20.7465i	0.553625	−	1.19186i
$304$	4.00344	−	6.93416i	0.229613	−	0.397701i
$305$	−1.06024			−0.0607090
$306$	5.34591	−	14.8242i	0.305606	−	0.847446i
$307$	29.8960			1.70625			0.853126	−	0.521704i	$-0.174704\pi$
$307$	29.8960			1.70625			0.853126	+	0.521704i	$0.174704\pi$
$308$		0			0
$309$	1.44125	+	2.05184i	0.0819897	+	0.116725i
$310$	−6.91043	−	11.9692i	−0.392486	−	0.679806i
$311$	−5.06521	−	8.77319i	−0.287221	−	0.497482i	0.685924	−	0.727673i	$-0.259398\pi$
$311$	−5.06521	−	8.77319i	−0.287221	−	0.497482i	−0.973145	+	0.230191i	$0.926065\pi$
$312$	0.225686	+	0.321299i	0.0127769	+	0.0181900i
$313$	5.80162	−	10.0487i	0.327927	−	0.567986i	−0.654174	−	0.756344i	$-0.726983\pi$
$313$	5.80162	−	10.0487i	0.327927	−	0.567986i	0.982100	+	0.188359i	$0.0603167\pi$
$314$	−29.7254			−1.67750
$315$	4.74083	−	0.850422i	0.267116	−	0.0479159i
$316$	2.83175			0.159298
$317$	−7.83872	+	13.5771i	−0.440267	+	0.762564i	−0.997709	−	0.0676515i	$-0.978449\pi$
$317$	−7.83872	+	13.5771i	−0.440267	+	0.762564i	0.557442	+	0.830216i	$0.311783\pi$
$318$	−17.5480	+	37.7778i	−0.984043	+	2.11847i
$319$		0			0
$320$	−4.00390	−	6.93497i	−0.223825	−	0.387676i
$321$	−17.5838	+	1.56463i	−0.981433	+	0.0873291i
$322$	5.51259	−	9.54808i	0.307205	−	0.532094i
$323$	13.9259			0.774856
$324$	−20.1411	−	16.6981i	−1.11895	−	0.927673i
$325$	0.520439			0.0288687
$326$	17.3298	−	30.0161i	0.959808	−	1.66244i
$327$	3.05762	−	0.272071i	0.169087	−	0.0150456i
$328$	8.42791	+	14.5976i	0.465353	+	0.806015i
$329$	−8.16570	−	14.1434i	−0.450189	−	0.779751i
$330$		0			0
$331$	−9.89830	+	17.1444i	−0.544060	+	0.942339i	0.454606	+	0.890693i	$0.349780\pi$
$331$	−9.89830	+	17.1444i	−0.544060	+	0.942339i	−0.998665	+	0.0516463i	$0.983553\pi$
$332$	−18.0209			−0.989028
$333$	−29.5758	+	5.30538i	−1.62074	+	0.290733i
$334$	20.5968			1.12701
$335$	−1.03697	+	1.79608i	−0.0566555	+	0.0981302i
$336$	3.50100	+	4.98423i	0.190995	+	0.271912i
$337$	−4.49565	−	7.78669i	−0.244894	−	0.424168i	0.717208	−	0.696859i	$-0.245420\pi$
$337$	−4.49565	−	7.78669i	−0.244894	−	0.424168i	−0.962102	+	0.272691i	$0.912086\pi$
$338$	−14.3845	−	24.9147i	−0.782414	−	1.35518i
$339$	−16.8729	−	24.0212i	−0.916410	−	1.30465i
$340$	2.14548	−	3.71608i	0.116355	−	0.201533i
$341$		0			0
$342$	13.2391	−	36.7122i	0.715890	−	1.98517i
$343$	18.9511			1.02326
$344$	2.15426	−	3.73128i	0.116150	−	0.201177i
$345$	0.876466	−	1.88688i	0.0471874	−	0.101586i
$346$	14.9275	+	25.8551i	0.802506	+	1.38998i
$347$	8.95095	+	15.5035i	0.480512	+	0.832272i	0.999750	−	0.0223582i	$-0.00711744\pi$
$347$	8.95095	+	15.5035i	0.480512	+	0.832272i	−0.519238	+	0.854630i	$0.673784\pi$
$348$	−34.6883	+	3.08661i	−1.85949	+	0.165459i
$349$	−2.29691	+	3.97836i	−0.122951	+	0.212957i	−0.920930	−	0.389728i	$-0.872569\pi$
$349$	−2.29691	+	3.97836i	−0.122951	+	0.212957i	0.797979	+	0.602685i	$0.205902\pi$
$350$	−26.3534			−1.40865
$351$	−0.416407	−	0.412724i	−0.0222262	−	0.0220296i
$352$		0			0
$353$	−3.76892	+	6.52796i	−0.200599	+	0.347448i	−0.948722	−	0.316112i	$-0.897622\pi$
$353$	−3.76892	+	6.52796i	−0.200599	+	0.347448i	0.748122	+	0.663561i	$0.230956\pi$
$354$	9.64179	−	0.857938i	0.512456	−	0.0455989i
$355$	1.79834	+	3.11481i	0.0954458	+	0.165317i
$356$	5.73935	+	9.94085i	0.304185	+	0.526864i
$357$	−4.46282	+	9.60768i	−0.236198	+	0.508492i
$358$	22.4873	−	38.9492i	1.18849	−	2.05853i
$359$	26.2499			1.38542			0.692709	−	0.721217i	$-0.256417\pi$
$359$	26.2499			1.38542			0.692709	+	0.721217i	$0.256417\pi$
$360$	−2.42015	−	2.86693i	−0.127553	−	0.151100i
$361$	15.4873			0.815121
$362$	−6.45317	+	11.1772i	−0.339171	+	0.587461i
$363$		0			0
$364$	−0.422993	−	0.732645i	−0.0221708	−	0.0384010i
$365$	−1.82774	−	3.16574i	−0.0956685	−	0.165703i
$366$	−3.75629	−	5.34767i	−0.196344	−	0.279527i
$367$	−13.8392	+	23.9703i	−0.722403	+	1.25124i	0.237631	+	0.971355i	$0.423629\pi$
$367$	−13.8392	+	23.9703i	−0.722403	+	1.25124i	−0.960034	+	0.279883i	$0.909704\pi$
$368$	2.63100			0.137151
$369$	−16.2354	−	19.2326i	−0.845180	−	1.00121i
$370$	−13.8108			−0.717991
$371$	14.0008	−	24.2502i	0.726887	−	1.25901i
$372$	21.2607	−	45.7705i	1.10231	−	2.37309i
$373$	4.55954	+	7.89736i	0.236084	+	0.408910i	0.959587	−	0.281412i	$-0.0908026\pi$
$373$	4.55954	+	7.89736i	0.236084	+	0.408910i	−0.723503	+	0.690321i	$0.757469\pi$
$374$		0			0
$375$	−10.3230	+	0.918552i	−0.533077	+	0.0474338i
$376$	−6.36073	+	11.0171i	−0.328030	+	0.568164i
$377$	−0.780412			−0.0401933
$378$	21.0856	+	20.8990i	1.08452	+	1.07493i
$379$	1.21955			0.0626441			0.0313220	−	0.999509i	$-0.490028\pi$
$379$	1.21955			0.0626441			0.0313220	+	0.999509i	$0.490028\pi$
$380$	5.31327	−	9.20285i	0.272565	−	0.472096i
$381$	17.2920	−	1.53867i	0.885898	−	0.0788282i
$382$	−4.78199	−	8.28264i	−0.244668	−	0.423777i
$383$	19.3866	+	33.5786i	0.990609	+	1.71579i	0.613711	+	0.789531i	$0.289676\pi$
$383$	19.3866	+	33.5786i	0.990609	+	1.71579i	0.376898	+	0.926255i	$0.376991\pi$
$384$	10.5220	−	22.6520i	0.536948	−	1.15595i
$385$		0			0
$386$	55.8223			2.84128
$387$	−2.18246	+	6.05196i	−0.110940	+	0.307639i
$388$	0.955905			0.0485287
$389$	−1.92901	+	3.34115i	−0.0978048	+	0.169403i	−0.910776	−	0.412901i	$-0.864515\pi$
$389$	−1.92901	+	3.34115i	−0.0978048	+	0.169403i	0.812971	+	0.582304i	$0.197849\pi$
$390$	−0.154891	−	0.220512i	−0.00784322	−	0.0111661i
$391$	2.28797	+	3.96288i	0.115708	+	0.200412i
$392$	−0.349149	−	0.604745i	−0.0176347	−	0.0305442i
$393$	−4.54184	−	6.46602i	−0.229106	−	0.326168i
$394$	−1.30017	+	2.25196i	−0.0655015	+	0.113452i
$395$	−0.606364			−0.0305095
$396$		0			0
$397$	9.83791			0.493751			0.246875	−	0.969047i	$-0.420596\pi$
$397$	9.83791			0.493751			0.246875	+	0.969047i	$0.420596\pi$
$398$	−2.04244	+	3.53760i	−0.102378	+	0.177324i
$399$	−11.0522	+	23.7934i	−0.553300	+	1.19116i
$400$	−3.14443	−	5.44632i	−0.157222	−	0.272316i
$401$	0.769631	+	1.33304i	0.0384335	+	0.0665688i	0.884602	−	0.466346i	$-0.154430\pi$
$401$	0.769631	+	1.33304i	0.0384335	+	0.0665688i	−0.846169	+	0.532915i	$0.821097\pi$
$402$	−12.7330	+	1.13299i	−0.635062	+	0.0565086i
$403$	0.565468	−	0.979420i	0.0281680	−	0.0487884i
$404$	38.3930			1.91012
$405$	4.31283	+	3.57557i	0.214306	+	0.177672i
$406$	39.5176			1.96123
$407$		0			0
$408$	8.21949	−	0.731380i	0.406925	−	0.0362087i
$409$	6.39119	+	11.0699i	0.316024	+	0.547369i	0.979655	−	0.200691i	$-0.0643187\pi$
$409$	6.39119	+	11.0699i	0.316024	+	0.547369i	−0.663631	+	0.748060i	$0.730985\pi$
$410$	−5.78419	−	10.0185i	−0.285661	−	0.494779i
$411$	−0.726708	+	1.56448i	−0.0358459	+	0.0771699i
$412$	−2.10417	+	3.64453i	−0.103665	+	0.179553i
$413$	−6.50718			−0.320197
$414$	12.6223	−	2.26422i	0.620353	−	0.111281i
$415$	3.85883			0.189423
$416$	0.397080	−	0.687763i	0.0194685	−	0.0337203i
$417$	−12.6371	−	17.9909i	−0.618841	−	0.881017i
$418$		0			0
$419$	−13.5524	−	23.4734i	−0.662076	−	1.14675i	−0.980069	−	0.198657i	$-0.936342\pi$
$419$	−13.5524	−	23.4734i	−0.662076	−	1.14675i	0.317993	−	0.948093i	$-0.396991\pi$
$420$	4.64645	+	6.61495i	0.226724	+	0.322776i
$421$	−1.57916	+	2.73518i	−0.0769633	+	0.133304i	−0.901938	−	0.431865i	$-0.857856\pi$
$421$	−1.57916	+	2.73518i	−0.0769633	+	0.133304i	0.824975	+	0.565169i	$0.191189\pi$
$422$	−31.9843			−1.55697
$423$	6.44400	−	17.8692i	0.313318	−	0.868832i
$424$	−21.8121			−1.05929
$425$	5.46892	−	9.47245i	0.265282	−	0.459481i
$426$	−9.33931	+	20.1059i	−0.452491	+	0.974134i
$427$	2.19656	+	3.80456i	0.106299	+	0.184115i
$428$	−14.8142	−	25.6589i	−0.716070	−	1.24027i
$429$		0			0
$430$	−1.47850	+	2.56083i	−0.0712994	+	0.123494i
$431$	7.96865			0.383836			0.191918	−	0.981411i	$-0.438529\pi$
$431$	7.96865			0.383836			0.191918	+	0.981411i	$0.438529\pi$
$432$	−1.80321	+	6.85127i	−0.0867568	+	0.329632i
$433$	−12.2368			−0.588064			−0.294032	−	0.955796i	$-0.594997\pi$
$433$	−12.2368			−0.588064			−0.294032	+	0.955796i	$0.594997\pi$
$434$	−28.6336	+	49.5948i	−1.37445	+	2.38063i
$435$	7.42782	−	0.660936i	0.356137	−	0.0316895i
$436$	2.57601	+	4.46178i	0.123369	+	0.213681i
$437$	5.66615	+	9.81405i	0.271049	+	0.469470i
$438$	9.49203	−	20.4347i	0.453547	−	0.976407i
$439$	−4.00984	+	6.94524i	−0.191379	+	0.331478i	−0.945707	−	0.325019i	$-0.894629\pi$
$439$	−4.00984	+	6.94524i	−0.191379	+	0.331478i	0.754328	+	0.656497i	$0.227963\pi$
$440$		0			0
$441$	0.672596	+	0.796764i	0.0320284	+	0.0379411i
$442$	0.592693			0.0281915
$443$	3.86761	−	6.69889i	0.183755	−	0.318274i	−0.759401	−	0.650623i	$-0.774508\pi$
$443$	3.86761	−	6.69889i	0.183755	−	0.318274i	0.943156	+	0.332349i	$0.107841\pi$
$444$	−28.9870	−	41.2675i	−1.37566	−	1.95847i
$445$	−1.22897	−	2.12864i	−0.0582587	−	0.100907i
$446$	−16.7066	−	28.9366i	−0.791079	−	1.37019i
$447$	1.41162	+	2.00965i	0.0667671	+	0.0950534i
$448$	−16.5903	+	28.7352i	−0.783817	+	1.35761i
$449$	−19.6646			−0.928031			−0.464016	−	0.885827i	$-0.653592\pi$
$449$	−19.6646			−0.928031			−0.464016	+	0.885827i	$0.653592\pi$
$450$	−19.7726	−	23.4228i	−0.932088	−	1.10416i
$451$		0			0
$452$	24.6339	−	42.6671i	1.15868	−	2.00689i
$453$	−13.3868	+	28.8195i	−0.628968	+	1.35406i
$454$	4.84888	+	8.39850i	0.227569	+	0.394161i
$455$	0.0905756	+	0.156881i	0.00424625	+	0.00735472i
$456$	20.3555	−	1.81126i	0.953234	−	0.0848199i
$457$	−17.7448	+	30.7350i	−0.830068	+	1.43772i	0.0679152	+	0.997691i	$0.478365\pi$
$457$	−17.7448	+	30.7350i	−0.830068	+	1.43772i	−0.897983	+	0.440029i	$0.854968\pi$
$458$	−28.9028			−1.35054
$459$	−11.8877	+	3.24197i	−0.554869	+	0.151322i
$460$	3.49181			0.162806
$461$	9.45037	−	16.3685i	0.440147	−	0.762358i	−0.557553	−	0.830142i	$-0.688260\pi$
$461$	9.45037	−	16.3685i	0.440147	−	0.762358i	0.997700	+	0.0677839i	$0.0215928\pi$
$462$		0			0
$463$	0.525465	+	0.910131i	0.0244204	+	0.0422974i	0.877977	−	0.478702i	$-0.158893\pi$
$463$	0.525465	+	0.910131i	0.0244204	+	0.0422974i	−0.853557	+	0.521000i	$0.825559\pi$
$464$	4.71516	+	8.16690i	0.218896	+	0.379139i
$465$	−4.55255	+	9.80085i	−0.211120	+	0.454503i
$466$	16.6527	−	28.8432i	0.771419	−	1.33614i
$467$	−7.91208			−0.366127			−0.183064	−	0.983101i	$-0.558601\pi$
$467$	−7.91208			−0.366127			−0.183064	+	0.983101i	$0.558601\pi$
$468$	0.333806	−	0.925647i	0.0154302	−	0.0427881i
$469$	8.59339			0.396806
$470$	4.36546	−	7.56120i	0.201364	−	0.348772i
$471$	13.3595	+	19.0193i	0.615572	+	0.876362i
$472$	2.53441	+	4.38973i	0.116656	+	0.202054i
$473$		0			0
$474$	−2.14827	−	3.05840i	−0.0986734	−	0.140477i
$475$	13.5437	−	23.4584i	0.621429	−	1.07635i
$476$	−17.7797			−0.814932
$477$	32.0581	−	5.75066i	1.46784	−	0.263305i
$478$	19.1841			0.877462
$479$	4.18420	−	7.24725i	0.191181	−	0.331135i	−0.754461	−	0.656345i	$-0.772102\pi$
$479$	4.18420	−	7.24725i	0.191181	−	0.331135i	0.945642	+	0.325210i	$0.105435\pi$
$480$	−3.19687	+	6.88230i	−0.145916	+	0.314132i
$481$	−0.565058	−	0.978709i	−0.0257644	−	0.0446253i
$482$	33.0675	+	57.2746i	1.50618	+	2.60878i
$483$	−8.58671	+	0.764055i	−0.390709	+	0.0347657i
$484$		0			0
$485$	−0.204688			−0.00929442
$486$	−2.75478	+	34.4210i	−0.124959	+	1.56137i
$487$	−19.1709			−0.868717			−0.434359	−	0.900740i	$-0.643025\pi$
$487$	−19.1709			−0.868717			−0.434359	+	0.900740i	$0.643025\pi$
$488$	1.71103	−	2.96359i	0.0774546	−	0.134155i
$489$	−26.9938	+	2.40194i	−1.22070	+	0.108619i
$490$	0.239626	+	0.415045i	0.0108252	+	0.0187498i
$491$	3.82689	+	6.62837i	0.172705	+	0.299134i	0.939365	−	0.342920i	$-0.111416\pi$
$491$	3.82689	+	6.62837i	0.172705	+	0.299134i	−0.766660	+	0.642054i	$0.778083\pi$
$492$	17.7957	−	38.3110i	0.802290	−	1.72719i
$493$	−8.20079	+	14.2042i	−0.369345	+	0.639724i
$494$	1.46780			0.0660395
$495$		0			0
$496$	−13.6660			−0.613621
$497$	7.45146	−	12.9063i	0.334243	−	0.578927i
$498$	13.6714	+	19.4633i	0.612628	+	0.872172i
$499$	−3.43286	−	5.94588i	−0.153676	−	0.266174i	0.778900	−	0.627148i	$-0.215778\pi$
$499$	−3.43286	−	5.94588i	−0.153676	−	0.266174i	−0.932576	+	0.360974i	$0.882444\pi$
$500$	−8.69700	−	15.0637i	−0.388942	−	0.673667i
$501$	−9.25683	−	13.1785i	−0.413565	−	0.588774i
$502$	−19.1867	+	33.2324i	−0.856346	+	1.48323i
$503$	−14.4126			−0.642628			−0.321314	−	0.946973i	$-0.604125\pi$
$503$	−14.4126			−0.642628			−0.321314	+	0.946973i	$0.604125\pi$
$504$	−5.27372	+	14.6241i	−0.234910	+	0.651407i
$505$	−8.22111			−0.365834
$506$		0			0
$507$	−9.47643	+	20.4011i	−0.420863	+	0.906045i
$508$	14.5683	+	25.2331i	0.646365	+	1.11954i
$509$	10.4145	+	18.0385i	0.461616	+	0.799542i	0.999042	−	0.0437689i	$-0.0139365\pi$
$509$	10.4145	+	18.0385i	0.461616	+	0.799542i	−0.537426	+	0.843311i	$0.680603\pi$
$510$	−5.64115	+	0.501956i	−0.249794	+	0.0222270i
$511$	−7.57330	+	13.1173i	−0.335023	+	0.580277i
$512$	−15.0750			−0.666228
$513$	−29.4397	+	8.02871i	−1.29980	+	0.354476i
$514$	26.2261			1.15678
$515$	0.450567	−	0.780405i	0.0198544	−	0.0343888i
$516$	−10.7551	+	0.956998i	−0.473465	+	0.0421295i
$517$		0			0
$518$	28.6128	+	49.5588i	1.25717	+	2.17749i
$519$	9.83413	−	21.1712i	0.431670	−	0.929311i
$520$	0.0705545	−	0.122204i	0.00309402	−	0.00535900i
$521$	−28.5317			−1.25000			−0.624998	−	0.780626i	$-0.714900\pi$
$521$	−28.5317			−1.25000			−0.624998	+	0.780626i	$0.714900\pi$
$522$	29.6495	+	35.1231i	1.29772	+	1.53730i
$523$	17.5399			0.766965			0.383483	−	0.923548i	$-0.374725\pi$
$523$	17.5399			0.766965			0.383483	+	0.923548i	$0.374725\pi$
$524$	6.63094	−	11.4851i	0.289674	−	0.501730i
$525$	11.8440	+	16.8618i	0.516914	+	0.735908i
$526$	17.5214	+	30.3480i	0.763971	+	1.32324i
$527$	−11.8842	−	20.5841i	−0.517684	−	0.896656i
$528$		0			0
$529$	9.63814	−	16.6938i	0.419050	−	0.725815i
$530$	14.9700			0.650254
$531$	−4.88225	−	5.78356i	−0.211871	−	0.250985i
$532$	−44.0313			−1.90900
$533$	0.473310	−	0.819797i	0.0205013	−	0.0355094i
$534$	6.38241	−	13.7402i	0.276194	−	0.594598i
$535$	3.17216	+	5.49435i	0.137145	+	0.237541i
$536$	−3.34694	−	5.79708i	−0.144566	−	0.250396i
$537$	−35.0274	+	3.11678i	−1.51155	+	0.134499i
$538$	1.06345	−	1.84195i	0.0458485	−	0.0794119i
$539$		0			0
$540$	−2.39317	+	9.09285i	−0.102986	+	0.391294i
$541$	17.5466			0.754385			0.377193	−	0.926135i	$-0.376889\pi$
$541$	17.5466			0.754385			0.377193	+	0.926135i	$0.376889\pi$
$542$	−31.1456	+	53.9457i	−1.33782	+	2.31717i
$543$	10.0518	−	0.894421i	0.431364	−	0.0383833i
$544$	−8.34526	−	14.4544i	−0.357800	−	0.619728i
$545$	−0.551602	−	0.955404i	−0.0236281	−	0.0409250i
$546$	−0.470387	+	1.01266i	−0.0201307	+	0.0433378i
$547$	−7.52162	+	13.0278i	−0.321601	+	0.557029i	−0.980819	−	0.194923i	$-0.937554\pi$
$547$	−7.52162	+	13.0278i	−0.321601	+	0.557029i	0.659217	+	0.751952i	$0.270888\pi$
$548$	−2.89518			−0.123676
$549$	−1.73343	+	4.80680i	−0.0739808	+	0.205149i
$550$		0			0
$551$	−20.3092	+	35.1766i	−0.865201	+	1.49857i
$552$	3.85977	+	5.49499i	0.164283	+	0.233882i
$553$	1.25624	+	2.17588i	0.0534209	+	0.0925276i
$554$	1.17355	+	2.03265i	0.0498595	+	0.0863592i
$555$	6.20700	+	8.83663i	0.263472	+	0.375094i
$556$	18.4497	−	31.9559i	0.782443	−	1.35523i
$557$	27.1343			1.14972			0.574859	−	0.818252i	$-0.305057\pi$
$557$	27.1343			1.14972			0.574859	+	0.818252i	$0.305057\pi$
$558$	−65.5630	+	11.7609i	−2.77550	+	0.497877i
$559$	−0.241966			−0.0102341
$560$	1.09449	−	1.89572i	0.0462509	−	0.0801088i
$561$		0			0
$562$	26.2425	+	45.4533i	1.10697	+	1.91733i
$563$	7.62529	+	13.2074i	0.321368	+	0.556625i	0.980771	−	0.195165i	$-0.0625241\pi$
$563$	7.62529	+	13.2074i	0.321368	+	0.556625i	−0.659403	+	0.751790i	$0.729191\pi$
$564$	31.7558	−	2.82567i	1.33716	−	0.118982i
$565$	−5.27486	+	9.13633i	−0.221915	+	0.384368i
$566$	17.7927			0.747884
$567$	3.89542	−	22.8839i	0.163592	−	0.961033i
$568$	−11.6087			−0.487092
$569$	−8.35738	+	14.4754i	−0.350360	+	0.606841i	−0.986312	−	0.164887i	$-0.947274\pi$
$569$	−8.35738	+	14.4754i	−0.350360	+	0.606841i	0.635953	+	0.771728i	$0.280607\pi$
$570$	−13.9703	+	1.24309i	−0.585150	+	0.0520674i
$571$	10.4277	+	18.0614i	0.436388	+	0.755845i	0.997408	−	0.0719567i	$-0.0229243\pi$
$571$	10.4277	+	18.0614i	0.436388	+	0.755845i	−0.561020	+	0.827802i	$0.689591\pi$
$572$		0			0
$573$	−3.15035	+	6.78214i	−0.131608	+	0.283328i
$574$	−23.9670	+	41.5120i	−1.00036	+	1.73268i
$575$	8.90076			0.371187
$576$	−37.9872	+	6.81425i	−1.58280	+	0.283927i
$577$	38.0357			1.58345			0.791723	−	0.610880i	$-0.209184\pi$
$577$	38.0357			1.58345			0.791723	+	0.610880i	$0.209184\pi$
$578$	−12.6008	+	21.8251i	−0.524122	+	0.907806i
$579$	−25.0882	−	35.7170i	−1.04263	−	1.48435i
$580$	6.25785	+	10.8389i	0.259843	+	0.450062i
$581$	−7.99459	−	13.8470i	−0.331671	−	0.574472i
$582$	−0.725185	−	1.03241i	−0.0300599	−	0.0427950i
$583$		0			0
$584$	11.7986			0.488228
$585$	−0.0714781	+	0.198209i	−0.00295526	+	0.00819494i
$586$	9.88724			0.408438
$587$	10.5666	−	18.3019i	0.436130	−	0.755399i	−0.561257	−	0.827642i	$-0.689682\pi$
$587$	10.5666	−	18.3019i	0.436130	−	0.755399i	0.997387	+	0.0722421i	$0.0230154\pi$
$588$	−0.737235	+	1.58714i	−0.0304031	+	0.0654525i
$589$	−29.4312	−	50.9763i	−1.21269	−	2.10044i
$590$	−1.73940	−	3.01273i	−0.0716100	−	0.124032i
$591$	2.02521	−	0.180206i	0.0833060	−	0.00741267i
$592$	−6.82804	+	11.8265i	−0.280631	+	0.486066i
$593$	24.5617			1.00863			0.504314	−	0.863521i	$-0.331746\pi$
$593$	24.5617			1.00863			0.504314	+	0.863521i	$0.331746\pi$
$594$		0			0
$595$	3.80718			0.156079
$596$	−2.06091	+	3.56960i	−0.0844182	+	0.146217i
$597$	3.18141	−	0.283085i	0.130206	−	0.0115859i
$598$	0.241155	+	0.417692i	0.00986155	+	0.0170807i
$599$	7.25413	+	12.5645i	0.296396	+	0.513372i	0.975309	−	0.220846i	$-0.0708819\pi$
$599$	7.25413	+	12.5645i	0.296396	+	0.513372i	−0.678913	+	0.734219i	$0.737549\pi$
$600$	6.76192	−	14.5572i	0.276054	−	0.594297i
$601$	3.47346	−	6.01621i	0.141685	−	0.245406i	−0.786446	−	0.617659i	$-0.788081\pi$
$601$	3.47346	−	6.01621i	0.141685	−	0.245406i	0.928131	+	0.372253i	$0.121415\pi$
$602$	12.2524			0.499370
$603$	6.44750	+	7.63777i	0.262563	+	0.311034i
$604$	−53.3325			−2.17007
$605$		0			0
$606$	−29.1264	−	41.4659i	−1.18318	−	1.68444i
$607$	−10.3062	−	17.8509i	−0.418316	−	0.724544i	0.577454	−	0.816423i	$-0.304046\pi$
$607$	−10.3062	−	17.8509i	−0.418316	−	0.724544i	−0.995770	+	0.0918787i	$0.970713\pi$
$608$	−20.6670	−	35.7963i	−0.838157	−	1.45173i
$609$	−17.7604	−	25.2847i	−0.719687	−	1.02459i
$610$	−1.17430	+	2.03395i	−0.0475462	+	0.0823524i
$611$	0.714436			0.0289030
$612$	−13.3399	−	15.8025i	−0.539232	−	0.638780i
$613$	−27.4397			−1.10828			−0.554140	−	0.832423i	$-0.686953\pi$
$613$	−27.4397			−1.10828			−0.554140	+	0.832423i	$0.686953\pi$
$614$	33.1123	−	57.3522i	1.33630	−	2.31455i
$615$	−3.81059	+	8.20354i	−0.153658	+	0.330799i
$616$		0			0
$617$	−13.7091	−	23.7449i	−0.551908	−	0.955932i	−0.998137	−	0.0610136i	$-0.980567\pi$
$617$	−13.7091	−	23.7449i	−0.551908	−	0.955932i	0.446229	−	0.894919i	$-0.352767\pi$
$618$	5.53254	−	0.492292i	0.222551	−	0.0198029i
$619$	0.291414	−	0.504743i	0.0117129	−	0.0202873i	−0.860110	−	0.510109i	$-0.829605\pi$
$619$	0.291414	−	0.504743i	0.0117129	−	0.0202873i	0.871822	+	0.489822i	$0.162938\pi$
$620$	−18.1372			−0.728407
$621$	−7.12157	−	7.05857i	−0.285779	−	0.283251i
$622$	−22.4406			−0.899785
$623$	−5.09227	+	8.82007i	−0.204017	+	0.353369i
$624$	−0.265407	+	0.0236162i	−0.0106248	+	0.000945404i
$625$	−9.66903	−	16.7472i	−0.386761	−	0.669890i
$626$	−12.8516	−	22.2596i	−0.513652	−	0.889671i
$627$		0			0
$628$	−19.5044	+	33.7826i	−0.778309	+	1.34807i
$629$	−23.7512			−0.947021
$630$	3.61943	−	10.0367i	0.144201	−	0.399871i
$631$	41.8952			1.66782			0.833911	−	0.551899i	$-0.186097\pi$
$631$	41.8952			1.66782			0.833911	+	0.551899i	$0.186097\pi$
$632$	0.978560	−	1.69492i	0.0389250	−	0.0674201i
$633$	14.3747	+	20.4646i	0.571343	+	0.813396i
$634$	17.3641	+	30.0755i	0.689617	+	1.19445i
$635$	−3.11952	−	5.40317i	−0.123794	−	0.214418i
$636$	31.4199	+	44.7311i	1.24588	+	1.77370i
$637$	−0.0196082	+	0.0339624i	−0.000776905	+	0.00134564i
$638$		0			0
$639$	17.0618	−	3.06059i	0.674954	−	0.121075i
$640$	−8.97617			−0.354814
$641$	2.09341	−	3.62589i	0.0826847	−	0.143214i	−0.821718	−	0.569895i	$-0.806984\pi$
$641$	2.09341	−	3.62589i	0.0826847	−	0.143214i	0.904402	+	0.426681i	$0.140317\pi$
$642$	−16.4740	+	35.4657i	−0.650177	+	1.39972i
$643$	−13.6847	−	23.7026i	−0.539673	−	0.934741i	−0.998921	−	0.0464328i	$-0.985215\pi$
$643$	−13.6847	−	23.7026i	−0.539673	−	0.934741i	0.459249	−	0.888308i	$-0.348119\pi$
$644$	−7.23420	−	12.5300i	−0.285067	−	0.493751i
$645$	2.30299	−	0.204922i	0.0906800	−	0.00806881i
$646$	15.4241	−	26.7153i	0.606852	−	1.05110i
$647$	24.4553			0.961439			0.480719	−	0.876875i	$-0.340376\pi$
$647$	24.4553			0.961439			0.480719	+	0.876875i	$0.340376\pi$
$648$	−16.9546	+	6.28496i	−0.666040	+	0.246897i
$649$		0			0
$650$	0.576430	−	0.998406i	0.0226094	−	0.0391607i
$651$	44.6012	−	3.96866i	1.74806	−	0.155544i
$652$	−22.7420	−	39.3902i	−0.890644	−	1.54264i
$653$	12.8867	+	22.3204i	0.504294	+	0.873463i	0.999988	+	0.00496583i	$0.00158068\pi$
$653$	12.8867	+	22.3204i	0.504294	+	0.873463i	−0.495693	+	0.868498i	$0.665086\pi$
$654$	2.86464	−	6.16707i	0.112016	−	0.241151i
$655$	−1.41989	+	2.45931i	−0.0554795	+	0.0960933i
$656$	−11.4388			−0.446608
$657$	−17.3408	+	3.11064i	−0.676529	+	0.121357i
$658$	−36.1768			−1.41032
$659$	−10.3211	+	17.8767i	−0.402053	+	0.696375i	−0.993974	−	0.109621i	$-0.965036\pi$
$659$	−10.3211	+	17.8767i	−0.402053	+	0.696375i	0.591921	+	0.805996i	$0.298370\pi$
$660$		0			0
$661$	6.00967	+	10.4091i	0.233749	+	0.404865i	0.958908	−	0.283716i	$-0.0915672\pi$
$661$	6.00967	+	10.4091i	0.233749	+	0.404865i	−0.725159	+	0.688581i	$0.758234\pi$
$662$	21.9264	+	37.9777i	0.852194	+	1.47604i
$663$	−0.266374	−	0.379225i	−0.0103451	−	0.0147279i
$664$	−6.22745	+	10.7863i	−0.241672	+	0.418588i
$665$	9.42845			0.365619
$666$	−22.5799	+	62.6142i	−0.874953	+	2.42625i
$667$	−13.3469			−0.516795
$668$	13.5147	−	23.4081i	0.522898	−	0.905686i
$669$	−11.0062	+	23.6944i	−0.425524	+	0.916078i
$670$	2.29706	+	3.97862i	0.0887430	+	0.153707i
$671$		0			0
$672$	31.3196	−	2.78685i	1.20818	−	0.107505i
$673$	1.28202	−	2.22052i	0.0494182	−	0.0855948i	−0.840258	−	0.542186i	$-0.817597\pi$
$673$	1.28202	−	2.22052i	0.0494182	−	0.0855948i	0.889676	+	0.456592i	$0.150930\pi$
$674$	−19.9173			−0.767184
$675$	−6.10030	+	23.1781i	−0.234801	+	0.892124i
$676$	−37.7537			−1.45207
$677$	10.9565	−	18.9772i	0.421093	−	0.729355i	−0.574954	−	0.818186i	$-0.694980\pi$
$677$	10.9565	−	18.9772i	0.421093	−	0.729355i	0.996047	+	0.0888314i	$0.0283132\pi$
$678$	−64.7703	+	5.76334i	−2.48749	+	0.221340i
$679$	0.424066	+	0.734503i	0.0162741	+	0.0281877i
$680$	−1.48281	−	2.56831i	−0.0568634	−	0.0984902i
$681$	3.19441	−	6.87701i	0.122410	−	0.263528i
$682$		0			0
$683$	25.4426			0.973533			0.486767	−	0.873532i	$-0.338176\pi$
$683$	25.4426			0.973533			0.486767	+	0.873532i	$0.338176\pi$
$684$	−33.0361	−	39.1349i	−1.26317	−	1.49636i
$685$	0.619945			0.0236869
$686$	20.9899	−	36.3556i	0.801399	−	1.38806i
$687$	12.9898	+	18.4930i	0.495591	+	0.705552i
$688$	1.46193	+	2.53214i	0.0557355	+	0.0965368i
$689$	0.612483	+	1.06085i	0.0233338	+	0.0404153i
$690$	−2.64902	−	3.77129i	−0.100846	−	0.143570i
$691$	21.0655	−	36.4865i	0.801369	−	1.38801i	−0.117347	−	0.993091i	$-0.537439\pi$
$691$	21.0655	−	36.4865i	0.801369	−	1.38801i	0.918715	−	0.394920i	$-0.129228\pi$
$692$	39.1788			1.48935
$693$		0			0
$694$	39.6558			1.50531
$695$	−3.95065	+	6.84272i	−0.149857	+	0.259559i
$696$	−10.1397	+	21.8290i	−0.384344	+	0.827425i
$697$	−9.94736	−	17.2293i	−0.376783	−	0.652608i
$698$	5.08805	+	8.81275i	0.192585	+	0.333568i
$699$	−25.9391	+	2.30809i	−0.981106	+	0.0872999i
$700$	−17.2918	+	29.9503i	−0.653570	+	1.13202i
$701$	−29.9679			−1.13187			−0.565937	−	0.824449i	$-0.691485\pi$
$701$	−29.9679			−1.13187			−0.565937	+	0.824449i	$0.691485\pi$
$702$	−1.25297	+	0.341707i	−0.0472904	+	0.0128969i
$703$	−58.8196			−2.21842
$704$		0			0
$705$	−6.79988	+	0.605061i	−0.256098	+	0.0227879i
$706$	8.34880	+	14.4605i	0.314211	+	0.544230i
$707$	17.0322	+	29.5006i	0.640561	+	1.10948i
$708$	5.35145	−	11.5207i	0.201120	−	0.432976i
$709$	2.52050	−	4.36563i	0.0946593	−	0.163955i	−0.814807	−	0.579732i	$-0.803157\pi$
$709$	2.52050	−	4.36563i	0.0946593	−	0.163955i	0.909466	+	0.415778i	$0.136491\pi$
$710$	7.96724			0.299005
$711$	−0.991369	+	2.74907i	−0.0371793	+	0.103098i
$712$	7.93332			0.297314
$713$	9.67088	−	16.7505i	0.362177	−	0.627310i
$714$	13.4884	+	19.2028i	0.504789	+	0.718646i
$715$		0			0
$716$	−29.5102	−	51.1132i	−1.10285	−	1.91019i
$717$	−8.62192	−	12.2746i	−0.321992	−	0.458405i
$718$	29.0740	−	50.3577i	1.08503	−	1.87933i
$719$	36.6597			1.36718			0.683589	−	0.729868i	$-0.260418\pi$
$719$	36.6597			1.36718			0.683589	+	0.729868i	$0.260418\pi$
$720$	2.50609	−	0.449550i	0.0933966	−	0.0167537i
$721$	−3.73387			−0.139057
$722$	17.1535	−	29.7107i	0.638387	−	1.10572i
$723$	21.7847	−	46.8986i	0.810181	−	1.74418i
$724$	8.46852	+	14.6679i	0.314730	+	0.545129i
$725$	15.9515	+	27.6289i	0.592425	+	1.02611i
$726$		0			0
$727$	4.53305	−	7.85147i	0.168121	−	0.291195i	−0.769638	−	0.638481i	$-0.779563\pi$
$727$	4.53305	−	7.85147i	0.168121	−	0.291195i	0.937759	+	0.347286i	$0.112897\pi$
$728$	−0.584689			−0.0216700
$729$	23.2618	−	13.7072i	0.861548	−	0.507675i
$730$	−8.09753			−0.299703
$731$	−2.54264	+	4.40399i	−0.0940431	+	0.162887i
$732$	−8.54227	+	0.760101i	−0.315731	+	0.0280941i
$733$	10.3602	+	17.9444i	0.382664	+	0.662793i	0.991442	−	0.130547i	$-0.0416734\pi$
$733$	10.3602	+	17.9444i	0.382664	+	0.662793i	−0.608778	+	0.793340i	$0.708340\pi$
$734$	30.6563	+	53.0982i	1.13154	+	1.95989i
$735$	0.157864	−	0.339854i	0.00582292	−	0.0125357i
$736$	6.79103	−	11.7624i	0.250321	−	0.433568i
$737$		0			0
$738$	−54.8778	+	9.84412i	−2.02008	+	0.362367i
$739$	−38.9295			−1.43204			−0.716022	−	0.698078i	$-0.754039\pi$
$739$	−38.9295			−1.43204			−0.716022	+	0.698078i	$0.754039\pi$
$740$	−9.06201	+	15.6959i	−0.333126	+	0.576991i
$741$	−0.659674	−	0.939148i	−0.0242337	−	0.0345005i
$742$	−31.0142	−	53.7182i	−1.13857	−	1.97206i
$743$	9.95247	+	17.2382i	0.365121	+	0.632407i	0.988796	−	0.149276i	$-0.0476944\pi$
$743$	9.95247	+	17.2382i	0.365121	+	0.632407i	−0.623675	+	0.781684i	$0.714361\pi$
$744$	−20.0485	−	28.5421i	−0.735012	−	1.04640i
$745$	0.441304	−	0.764360i	0.0161681	−	0.0280040i
$746$	20.2003			0.739586
$747$	6.30896	−	17.4948i	0.230833	−	0.640101i
$748$		0			0
$749$	13.1439	−	22.7660i	0.480269	−	0.831851i
$750$	−9.67145	+	20.8210i	−0.353152	+	0.760274i
$751$	−9.75621	−	16.8982i	−0.356009	−	0.616626i	0.631281	−	0.775554i	$-0.282529\pi$
$751$	−9.75621	−	16.8982i	−0.356009	−	0.616626i	−0.987290	+	0.158928i	$0.949196\pi$
$752$	−4.31654	−	7.47648i	−0.157408	−	0.272639i
$753$	29.8863	−	2.65932i	1.08912	−	0.0969109i
$754$	−0.864372	+	1.49714i	−0.0314786	+	0.0545225i
$755$	11.4201			0.415621
$756$	37.5869	−	10.2506i	1.36702	−	0.372810i
$757$	9.13601			0.332054			0.166027	−	0.986121i	$-0.446906\pi$
$757$	9.13601			0.332054			0.166027	+	0.986121i	$0.446906\pi$
$758$	1.35075	−	2.33958i	0.0490616	−	0.0849772i
$759$		0			0
$760$	−3.67218	−	6.36040i	−0.133204	−	0.230716i
$761$	−24.1139	−	41.7665i	−0.874129	−	1.51404i	−0.857687	−	0.514171i	$-0.828100\pi$
$761$	−24.1139	−	41.7665i	−0.874129	−	1.51404i	−0.0164417	−	0.999865i	$-0.505234\pi$
$762$	16.2006	−	34.8771i	0.586887	−	1.26347i
$763$	−2.28558	+	3.95874i	−0.0827435	+	0.143316i
$764$	−12.5509			−0.454074
$765$	2.85647	+	3.38380i	0.103276	+	0.122342i
$766$	85.8893			3.10330
$767$	0.142332	−	0.246527i	0.00513932	−	0.00890156i
$768$	−6.18655	−	8.80752i	−0.223238	−	0.317814i
$769$	−12.4766	−	21.6102i	−0.449919	−	0.779283i	0.548461	−	0.836176i	$-0.315214\pi$
$769$	−12.4766	−	21.6102i	−0.449919	−	0.779283i	−0.998380	+	0.0568934i	$0.981880\pi$
$770$		0			0
$771$	−11.7868	−	16.7804i	−0.424491	−	0.604330i
$772$	36.6279	−	63.4415i	1.31827	−	2.28331i
$773$	−29.9296			−1.07649			−0.538246	−	0.842788i	$-0.680913\pi$
$773$	−29.9296			−1.07649			−0.538246	+	0.842788i	$0.680913\pi$
$774$	9.19279	+	10.8899i	0.330428	+	0.391428i
$775$	−46.2324			−1.66072
$776$	0.330329	−	0.572147i	0.0118581	−	0.0205389i
$777$	18.8499	−	40.5806i	0.676237	−	1.45582i
$778$	4.27309	+	7.40121i	0.153198	+	0.265346i
$779$	−24.6346	−	42.6683i	−0.882625	−	1.52875i
$780$	−0.352242	+	0.0313429i	−0.0126123	+	0.00112225i
$781$		0			0
$782$	10.1365			0.362480
$783$	9.14757	−	34.7561i	0.326907	−	1.24208i
$784$	0.473882			0.0169244
$785$	4.17648	−	7.23387i	0.149065	−	0.258188i
$786$	−17.4349	+	1.55137i	−0.621881	+	0.0553356i
$787$	−11.0499	−	19.1390i	−0.393887	−	0.682233i	0.599071	−	0.800696i	$-0.295537\pi$
$787$	−11.0499	−	19.1390i	−0.393887	−	0.682233i	−0.992958	+	0.118463i	$0.962203\pi$
$788$	1.70622	+	2.95525i	0.0607814	+	0.105277i
$789$	11.5430	−	24.8501i	0.410942	−	0.884687i
$790$	−0.671599	+	1.16324i	−0.0238944	+	0.0413864i
$791$	43.7130			1.55426
$792$		0			0
$793$	−0.192182			−0.00682460
$794$	10.8963	−	18.8730i	0.386696	−	0.669777i
$795$	−6.72795	−	9.57829i	−0.238616	−	0.339707i
$796$	2.68030	+	4.64241i	0.0950007	+	0.164546i
$797$	−25.1313	−	43.5288i	−0.890198	−	1.54187i	−0.839638	−	0.543147i	$-0.817233\pi$
$797$	−25.1313	−	43.5288i	−0.890198	−	1.54187i	−0.0505598	−	0.998721i	$-0.516101\pi$
$798$	33.4038	+	47.5555i	1.18248	+	1.68345i
$799$	7.50750	−	13.0034i	0.265596	−	0.460026i
$800$	−32.4651			−1.14781
$801$	−11.6599	+	2.09158i	−0.411982	+	0.0739025i
$802$	3.40973			0.120402
$803$		0			0
$804$	−7.06713	+	15.2143i	−0.249238	+	0.536567i
$805$	1.54906	+	2.68305i	0.0545972	+	0.0945652i
$806$	−1.25261	−	2.16958i	−0.0441213	−	0.0764203i
$807$	−1.65648	+	0.147396i	−0.0583110	+	0.00518858i
$808$	13.2674	−	22.9797i	0.466744	−	0.808424i
$809$	9.53522			0.335240			0.167620	−	0.985852i	$-0.446392\pi$
$809$	9.53522			0.335240			0.167620	+	0.985852i	$0.446392\pi$
$810$	11.6362	−	4.31346i	0.408854	−	0.151559i
$811$	28.8840			1.01425			0.507127	−	0.861871i	$-0.330707\pi$
$811$	28.8840			1.01425			0.507127	+	0.861871i	$0.330707\pi$
$812$	25.9296	−	44.9113i	0.909950	−	1.57608i
$813$	48.5140	−	4.31683i	1.70146	−	0.151398i
$814$		0			0
$815$	4.86975	+	8.43465i	0.170580	+	0.295453i
$816$	−2.35913	+	5.07880i	−0.0825862	+	0.177794i
$817$	−6.29684	+	10.9064i	−0.220299	+	0.381568i
$818$	28.3151			0.990016
$819$	0.859339	−	0.154151i	0.0300278	−	0.00538646i
$820$	−15.1812			−0.530152
$821$	7.98575	−	13.8317i	0.278705	−	0.482731i	−0.692358	−	0.721554i	$-0.743428\pi$
$821$	7.98575	−	13.8317i	0.278705	−	0.482731i	0.971063	+	0.238823i	$0.0767616\pi$
$822$	2.19639	+	3.12690i	0.0766079	+	0.109063i
$823$	−11.9137	−	20.6351i	−0.415286	−	0.719296i	0.580173	−	0.814493i	$-0.302985\pi$
$823$	−11.9137	−	20.6351i	−0.415286	−	0.719296i	−0.995458	+	0.0951976i	$0.969652\pi$
$824$	1.45427	+	2.51886i	0.0506617	+	0.0877487i
$825$		0			0
$826$	−7.20726	+	12.4833i	−0.250773	+	0.434351i
$827$	27.1081			0.942639			0.471320	−	0.881962i	$-0.343778\pi$
$827$	27.1081			0.942639			0.471320	+	0.881962i	$0.343778\pi$
$828$	5.70890	−	15.8308i	0.198398	−	0.550159i
$829$	−28.7521			−0.998602			−0.499301	−	0.866429i	$-0.666410\pi$
$829$	−28.7521			−0.998602			−0.499301	+	0.866429i	$0.666410\pi$
$830$	4.27398	−	7.40276i	0.148352	−	0.256954i
$831$	0.773130	−	1.66441i	0.0268196	−	0.0577379i
$832$	−0.725762	−	1.25706i	−0.0251613	−	0.0435806i
$833$	0.412097	+	0.713773i	0.0142783	+	0.0247308i
$834$	−48.5102	+	4.31649i	−1.67977	+	0.149468i
$835$	−2.89390	+	5.01238i	−0.100148	+	0.173461i
$836$		0			0
$837$	36.9910	+	36.6637i	1.27859	+	1.26728i
$838$	−60.0416			−2.07410
$839$	−8.28802	+	14.3553i	−0.286134	+	0.495599i	−0.972884	−	0.231295i	$-0.925704\pi$
$839$	−8.28802	+	14.3553i	−0.286134	+	0.495599i	0.686749	+	0.726894i	$0.259037\pi$
$840$	5.56497	−	0.495177i	0.192010	−	0.0170852i
$841$	−9.41975	−	16.3155i	−0.324819	−	0.562603i
$842$	3.49810	+	6.05888i	0.120552	+	0.208803i
$843$	17.2884	−	37.2189i	0.595444	−	1.28189i
$844$	−20.9866	+	36.3498i	−0.722388	+	1.25121i
$845$	8.08422			0.278106
$846$	−27.1430	−	32.1538i	−0.933194	−	1.10547i
$847$		0			0
$848$	7.40111	−	12.8191i	0.254155	−	0.440210i
$849$	−7.99659	−	11.3844i	−0.274442	−	0.390711i
$850$	−12.1146	−	20.9831i	−0.415527	−	0.719714i
$851$	−9.66386	−	16.7383i	−0.331273	−	0.573781i
$852$	16.7221	+	23.8066i	0.572891	+	0.815600i
$853$	−25.0943	+	43.4646i	−0.859213	+	1.48820i	0.0134684	+	0.999909i	$0.495713\pi$
$853$	−25.0943	+	43.4646i	−0.859213	+	1.48820i	−0.872681	+	0.488291i	$0.837621\pi$
$854$	9.73152			0.333006
$855$	7.07403	+	8.37997i	0.241927	+	0.286589i
$856$	−20.4772			−0.699895
$857$	−15.1504	+	26.2413i	−0.517529	+	0.896387i	0.482264	+	0.876026i	$0.339815\pi$
$857$	−15.1504	+	26.2413i	−0.517529	+	0.896387i	−0.999793	+	0.0203605i	$0.993519\pi$
$858$		0			0
$859$	−15.7661	−	27.3077i	−0.537932	−	0.931725i	−0.999015	−	0.0443684i	$-0.985872\pi$
$859$	−15.7661	−	27.3077i	−0.537932	−	0.931725i	0.461083	−	0.887357i	$-0.347461\pi$
$860$	1.94024	+	3.36059i	0.0661616	+	0.114595i
$861$	37.3322	−	3.32186i	1.27228	−	0.113209i
$862$	8.82596	−	15.2870i	0.300613	−	0.520678i
$863$	−7.96783			−0.271228			−0.135614	−	0.990762i	$-0.543301\pi$
$863$	−7.96783			−0.271228			−0.135614	+	0.990762i	$0.543301\pi$
$864$	25.9756	+	25.7458i	0.883707	+	0.875890i
$865$	−8.38937			−0.285247
$866$	−13.5533	+	23.4750i	−0.460560	+	0.797714i
$867$	19.6276	−	1.74649i	0.666589	−	0.0593138i
$868$	37.5760	+	65.0835i	1.27541	+	2.20908i
$869$		0			0
$870$	6.95901	−	14.9815i	0.235933	−	0.507921i
$871$	−0.187964	+	0.325563i	−0.00636892	+	0.0110313i
$872$	3.56074			0.120582
$873$	−0.334653	+	0.927996i	−0.0113263	+	0.0314079i
$874$	25.1030			0.849120
$875$	7.71646	−	13.3653i	0.260864	−	0.451830i
$876$	−16.9956	−	24.1959i	−0.574227	−	0.817502i
$877$	11.1897	+	19.3812i	0.377851	+	0.654457i	0.990749	−	0.135705i	$-0.0433299\pi$
$877$	11.1897	+	19.3812i	0.377851	+	0.654457i	−0.612898	+	0.790162i	$0.709997\pi$
$878$	8.88247	+	15.3849i	0.299769	+	0.519215i
$879$	−4.44362	−	6.32619i	−0.149880	−	0.213377i
$880$		0			0
$881$	0.173710			0.00585243			0.00292622	−	0.999996i	$-0.499069\pi$
$881$	0.173710			0.00585243			0.00292622	+	0.999996i	$0.499069\pi$
$882$	2.27346	−	0.407820i	0.0765515	−	0.0137320i
$883$	11.0388			0.371486			0.185743	−	0.982598i	$-0.440531\pi$
$883$	11.0388			0.371486			0.185743	+	0.982598i	$0.440531\pi$
$884$	0.388897	−	0.673590i	0.0130800	−	0.0226553i
$885$	−1.14591	+	2.46694i	−0.0385193	+	0.0829253i
$886$	−8.56740	−	14.8392i	−0.287828	−	0.498532i
$887$	−17.9615	−	31.1103i	−0.603089	−	1.04458i	−0.992350	−	0.123453i	$-0.960603\pi$
$887$	−17.9615	−	31.1103i	−0.603089	−	1.04458i	0.389261	−	0.921127i	$-0.372730\pi$
$888$	−34.7172	+	3.08918i	−1.16503	+	0.103666i
$889$	−12.9258	+	22.3882i	−0.433518	+	0.750876i
$890$	−5.44475			−0.182509
$891$		0			0
$892$	−43.8482			−1.46815
$893$	18.5923	−	32.2028i	0.622167	−	1.07762i
$894$	5.41879	−	0.482170i	0.181232	−	0.0161262i
$895$	6.31903	+	10.9449i	0.211222	+	0.365847i
$896$	18.5965	+	32.2101i	0.621265	+	1.07606i
$897$	0.158871	−	0.342022i	0.00530456	−	0.0114198i
$898$	−21.7802	+	37.7245i	−0.726816	+	1.25888i
$899$	69.3268			2.31218
$900$	−39.5936	+	7.10240i	−1.31979	+	0.236747i
$901$	25.7446			0.857677
$902$		0			0
$903$	−5.50659	−	7.83948i	−0.183248	−	0.260882i
$904$	−17.0253	−	29.4887i	−0.566253	−	0.980780i
$905$	−1.81337	−	3.14085i	−0.0602784	−	0.104405i
$906$	40.4601	+	57.6012i	1.34420	+	1.91367i
$907$	−22.2801	+	38.5902i	−0.739798	+	1.28137i	0.212788	+	0.977098i	$0.431746\pi$
$907$	−22.2801	+	38.5902i	−0.739798	+	1.28137i	−0.952586	+	0.304269i	$0.901588\pi$
$908$	12.7264			0.422341
$909$	−13.4410	+	37.2720i	−0.445811	+	1.23624i
$910$	0.401281			0.0133023
$911$	19.6230	−	33.9881i	0.650140	−	1.12608i	−0.332948	−	0.942945i	$-0.608043\pi$
$911$	19.6230	−	33.9881i	0.650140	−	1.12608i	0.983089	−	0.183131i	$-0.0586232\pi$
$912$	−5.84238	+	12.5776i	−0.193461	+	0.416487i
$913$		0			0
$914$	39.3078	+	68.0831i	1.30019	+	2.25199i
$915$	1.82916	−	0.162761i	0.0604701	−	0.00538070i
$916$	−18.9647	+	32.8477i	−0.626610	+	1.08532i
$917$	11.7667			0.388569
$918$	−6.94723	+	26.3960i	−0.229293	+	0.871197i
$919$	−22.4282			−0.739837			−0.369918	−	0.929064i	$-0.620614\pi$
$919$	−22.4282			−0.739837			−0.369918	+	0.929064i	$0.620614\pi$
$920$	1.20665	−	2.08999i	0.0397822	−	0.0689048i
$921$	−51.5775	+	4.58943i	−1.69954	+	0.151227i
$922$	−20.9342	−	36.2590i	−0.689430	−	1.19413i
$923$	0.325973	+	0.564601i	0.0107295	+	0.0185841i
$924$		0			0
$925$	−23.0994	+	40.0094i	−0.759505	+	1.31550i
$926$	2.32799			0.0765024
$927$	−2.80147	−	3.31865i	−0.0920125	−	0.108999i
$928$	48.6823			1.59807
$929$	12.7051	−	22.0059i	0.416841	−	0.721990i	−0.578778	−	0.815485i	$-0.696470\pi$
$929$	12.7051	−	22.0059i	0.416841	−	0.721990i	0.995620	+	0.0934944i	$0.0298037\pi$
$930$	13.7595	+	19.5889i	0.451193	+	0.642344i
$931$	1.02056	+	1.76765i	0.0334474	+	0.0579325i
$932$	−21.8534	−	37.8511i	−0.715831	−	1.23986i
$933$	10.0855	+	14.3582i	0.330183	+	0.470068i
$934$	−8.76330	+	15.1785i	−0.286744	+	0.496655i
$935$		0			0
$936$	−0.438684	−	0.519670i	−0.0143388	−	0.0169859i
$937$	2.53489			0.0828114			0.0414057	−	0.999142i	$-0.486816\pi$
$937$	2.53489			0.0828114			0.0414057	+	0.999142i	$0.486816\pi$
$938$	9.51791	−	16.4855i	0.310771	−	0.538271i
$939$	−8.46654	+	18.2270i	−0.276295	+	0.594815i
$940$	−5.72882	−	9.92260i	−0.186853	−	0.323640i
$941$	1.96550	+	3.40435i	0.0640736	+	0.110979i	0.896283	−	0.443483i	$-0.146257\pi$
$941$	1.96550	+	3.40435i	0.0640736	+	0.110979i	−0.832209	+	0.554462i	$0.812924\pi$
$942$	51.2832	−	4.56324i	1.67090	−	0.148678i
$943$	8.09475	−	14.0205i	0.263601	−	0.456571i
$944$	−3.43982			−0.111957
$945$	−8.04849	+	2.19496i	−0.261817	+	0.0714020i
$946$		0			0
$947$	−3.79709	+	6.57676i	−0.123389	+	0.213716i	−0.921102	−	0.389321i	$-0.872710\pi$
$947$	−3.79709	+	6.57676i	−0.123389	+	0.213716i	0.797713	+	0.603037i	$0.206043\pi$
$948$	−4.88543	+	0.434711i	−0.158671	+	0.0141188i
$949$	−0.331303	−	0.573834i	−0.0107546	−	0.0186274i
$950$	−30.0017	−	51.9645i	−0.973383	−	1.68595i
$951$	11.4394	−	24.6270i	0.370947	−	0.798584i
$952$	−6.14408	+	10.6419i	−0.199131	+	0.344905i
$953$	−56.4065			−1.82718			−0.913592	−	0.406632i	$-0.866703\pi$
$953$	−56.4065			−1.82718			−0.913592	+	0.406632i	$0.866703\pi$
$954$	24.4750	−	67.8694i	0.792408	−	2.19735i
$955$	2.68752			0.0869661
$956$	12.5877	−	21.8026i	0.407116	−	0.705145i
$957$		0			0
$958$	−9.26871	−	16.0539i	−0.299459	−	0.518677i
$959$	−1.28438	−	2.22461i	−0.0414748	−	0.0718364i
$960$	7.97228	+	11.3498i	0.257304	+	0.366313i
$961$	−34.7326	+	60.1586i	−1.12041	+	1.94060i
$962$	−2.50340			−0.0807128
$963$	30.0960	−	5.39870i	0.969831	−	0.173971i
$964$	86.7893			2.79529
$965$	−7.84316	+	13.5847i	−0.252480	+	0.437308i
$966$	−8.04475	+	17.3189i	−0.258836	+	0.557228i
$967$	−7.48654	−	12.9671i	−0.240751	−	0.416993i	0.720177	−	0.693790i	$-0.244060\pi$
$967$	−7.48654	−	12.9671i	−0.240751	−	0.416993i	−0.960928	+	0.276797i	$0.910727\pi$
$968$		0			0
$969$	−24.0254	+	2.13781i	−0.771806	+	0.0686762i
$970$	−0.226710	+	0.392673i	−0.00727921	+	0.0126080i
$971$	−17.2702			−0.554227			−0.277114	−	0.960837i	$-0.589378\pi$
$971$	−17.2702			−0.554227			−0.277114	+	0.960837i	$0.589378\pi$
$972$	37.3116	+	25.7162i	1.19677	+	0.824848i
$973$	32.7392			1.04957
$974$	−21.2334	+	36.7774i	−0.680363	+	1.17842i
$975$	−0.897879	+	0.0798943i	−0.0287551	+	0.00255866i
$976$	1.16114	+	2.01116i	0.0371673	+	0.0643757i
$977$	6.99939	+	12.1233i	0.223930	+	0.387858i	0.955998	−	0.293373i	$-0.0947779\pi$
$977$	6.99939	+	12.1233i	0.223930	+	0.387858i	−0.732068	+	0.681232i	$0.761445\pi$
$978$	−25.2901	+	54.4451i	−0.808687	+	1.74096i
$979$		0			0
$980$	0.628925			0.0200903
$981$	−5.23335	+	0.938772i	−0.167088	+	0.0299727i
$982$	16.9544			0.541038
$983$	−20.1991	+	34.9859i	−0.644251	+	1.11588i	0.340223	+	0.940345i	$0.389498\pi$
$983$	−20.1991	+	34.9859i	−0.644251	+	1.11588i	−0.984474	+	0.175531i	$0.943836\pi$
$984$	−16.7810	−	23.8904i	−0.534960	−	0.761599i
$985$	−0.365353	−	0.632809i	−0.0116411	−	0.0201630i
$986$	18.1661	+	31.4647i	0.578528	+	1.00204i
$987$	16.2589	+	23.1471i	0.517528	+	0.736782i
$988$	0.963101	−	1.66814i	0.0306403	−	0.0530706i
$989$	−4.13820			−0.131587
$990$		0			0
$991$	27.9439			0.887667			0.443833	−	0.896109i	$-0.353618\pi$
$991$	27.9439			0.887667			0.443833	+	0.896109i	$0.353618\pi$
$992$	−35.2741	+	61.0965i	−1.11995	+	1.93981i
$993$	14.4450	−	31.0976i	0.458398	−	0.986851i
$994$	−16.5062	−	28.5897i	−0.523546	−	0.906809i
$995$	−0.573933	−	0.994082i	−0.0181949	−	0.0315145i
$996$	31.0904	−	2.76646i	0.985136	−	0.0876585i
$997$	−25.0545	+	43.3956i	−0.793483	+	1.37435i	0.130315	+	0.991473i	$0.458401\pi$
$997$	−25.0545	+	43.3956i	−0.793483	+	1.37435i	−0.923798	+	0.382881i	$0.874932\pi$
$998$	−15.2087			−0.481424
$999$	50.2107	−	13.6933i	1.58860	−	0.433237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.o.727.17		36
9.2	odd	6		9801.2.a.cn.1.17		18
9.4	even	3	inner	1089.2.e.o.364.17		36
9.7	even	3		9801.2.a.co.1.2		18
11.2	odd	10		99.2.m.b.70.9	yes	72
11.6	odd	10		99.2.m.b.25.1	yes	72
11.10	odd	2		1089.2.e.p.727.2		36
33.2	even	10		297.2.n.b.235.1		72
33.17	even	10		297.2.n.b.289.9		72
99.2	even	30		891.2.f.e.730.9		36
99.13	odd	30		99.2.m.b.4.1	✓	72
99.43	odd	6		9801.2.a.cm.1.17		18
99.50	even	30		297.2.n.b.91.1		72
99.61	odd	30		891.2.f.f.487.1		36
99.65	even	6		9801.2.a.cp.1.2		18
99.68	even	30		297.2.n.b.37.9		72
99.76	odd	6		1089.2.e.p.364.2		36
99.79	odd	30		891.2.f.f.730.1		36
99.83	even	30		891.2.f.e.487.9		36
99.94	odd	30		99.2.m.b.58.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.1	✓	72	99.13	odd	30
99.2.m.b.25.1	yes	72	11.6	odd	10
99.2.m.b.58.9	yes	72	99.94	odd	30
99.2.m.b.70.9	yes	72	11.2	odd	10
297.2.n.b.37.9		72	99.68	even	30
297.2.n.b.91.1		72	99.50	even	30
297.2.n.b.235.1		72	33.2	even	10
297.2.n.b.289.9		72	33.17	even	10
891.2.f.e.487.9		36	99.83	even	30
891.2.f.e.730.9		36	99.2	even	30
891.2.f.f.487.1		36	99.61	odd	30
891.2.f.f.730.1		36	99.79	odd	30
1089.2.e.o.364.17		36	9.4	even	3	inner
1089.2.e.o.727.17		36	1.1	even	1	trivial
1089.2.e.p.364.2		36	99.76	odd	6
1089.2.e.p.727.2		36	11.10	odd	2
9801.2.a.cm.1.17		18	99.43	odd	6
9801.2.a.cn.1.17		18	9.2	odd	6
9801.2.a.co.1.2		18	9.7	even	3
9801.2.a.cp.1.2		18	99.65	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+(1.10759 - 1.91839i) q^{2} +(-1.72523 + 0.153513i) q^{3} +(-1.45349 - 2.51752i) q^{4} +(0.311236 + 0.539077i) q^{5} +(-1.61634 + 3.47971i) q^{6} +(1.28962 - 2.23368i) q^{7} -2.00911 q^{8} +(2.95287 - 0.529693i) q^{9} +1.37888 q^{10} +(2.89408 + 4.12018i) q^{12} +(0.0564158 + 0.0977150i) q^{13} +(-2.85672 - 4.94798i) q^{14} +(-0.619711 - 0.882255i) q^{15} +(0.681716 - 1.18077i) q^{16} +2.37133 q^{17} +(2.25439 - 6.25144i) q^{18} +5.87259 q^{19} +(0.904757 - 1.56709i) q^{20} +(-1.88199 + 4.05159i) q^{21} +(0.964846 + 1.67116i) q^{23} +(3.46619 - 0.308426i) q^{24} +(2.30626 - 3.99457i) q^{25} +0.249941 q^{26} +(-5.01307 + 1.36715i) q^{27} -7.49777 q^{28} +(-3.45830 + 5.98996i) q^{29} +(-2.37890 + 0.211677i) q^{30} +(-5.01162 - 8.68037i) q^{31} +(-3.51923 - 6.09548i) q^{32} +(2.62645 - 4.54915i) q^{34} +1.60550 q^{35} +(-5.62547 - 6.66399i) q^{36} -10.0160 q^{37} +(6.50439 - 11.2659i) q^{38} +(-0.112331 - 0.159921i) q^{39} +(-0.625309 - 1.08307i) q^{40} +(-4.19484 - 7.26568i) q^{41} +(5.68809 + 8.09788i) q^{42} +(-1.07224 + 1.85718i) q^{43} +(1.20458 + 1.42696i) q^{45} +4.27460 q^{46} +(3.16594 - 5.48357i) q^{47} +(-0.994856 + 2.14175i) q^{48} +(0.173783 + 0.301001i) q^{49} +(-5.10877 - 8.84864i) q^{50} +(-4.09110 + 0.364031i) q^{51} +(0.163999 - 0.284055i) q^{52} +10.8566 q^{53} +(-2.92968 + 11.1313i) q^{54} +(-2.59098 + 4.48771i) q^{56} +(-10.1316 + 0.901521i) q^{57} +(7.66073 + 13.2688i) q^{58} +(-1.26146 - 2.18491i) q^{59} +(-1.32035 + 2.84248i) q^{60} +(-0.851634 + 1.47507i) q^{61} -22.2032 q^{62} +(2.62490 - 7.27886i) q^{63} -12.8645 q^{64} +(-0.0351173 + 0.0608249i) q^{65} +(1.66588 + 2.88539i) q^{67} +(-3.44671 - 5.96987i) q^{68} +(-1.92113 - 2.73503i) q^{69} +(1.77823 - 3.07998i) q^{70} +5.77804 q^{71} +(-5.93264 + 1.06421i) q^{72} -5.87253 q^{73} +(-11.0935 + 19.2145i) q^{74} +(-3.36563 + 7.24561i) q^{75} +(-8.53575 - 14.7843i) q^{76} +(-0.431207 + 0.0383693i) q^{78} +(-0.487061 + 0.843614i) q^{79} +0.848699 q^{80} +(8.43885 - 3.12823i) q^{81} -18.5846 q^{82} +(3.09960 - 5.36867i) q^{83} +(12.9354 - 1.15101i) q^{84} +(0.738045 + 1.27833i) q^{85} +(2.37520 + 4.11397i) q^{86} +(5.04685 - 10.8650i) q^{87} -3.94867 q^{89} +(4.07166 - 0.730384i) q^{90} +0.291019 q^{91} +(2.80479 - 4.85804i) q^{92} +(9.97877 + 14.2063i) q^{93} +(-7.01310 - 12.1470i) q^{94} +(1.82776 + 3.16578i) q^{95} +(7.00723 + 9.97589i) q^{96} +(-0.164416 + 0.284776i) q^{97} +0.769917 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

Varieties

Fields

Representations

Groups

Database

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