LMFDB - Embedded newform 1089.2.e.l.727.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 15 x^{18} - 2 x^{17} + 150 x^{16} - 30 x^{15} + 830 x^{14} - 321 x^{13} + 3324 x^{12} + \cdots + 9 $ x^20 + 15x^18 - 2x^17 + 150x^16 - 30x^15 + 830x^14 - 321x^13 + 3324x^12 - 1529x^11 + 8388x^10 - 4959x^9 + 15449x^8 - 9234x^7 + 16749x^6 - 11141x^5 + 12630x^4 - 5604x^3 + 2737x^2 - 165x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.10
Root			$1.35844 + 2.35288i$ of defining polynomial
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.l.364.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35844 - 2.35288i) q^{2} +(-0.755083 - 1.55880i) q^{3} +(-2.69069 - 4.66041i) q^{4} +(-0.835704 - 1.44748i) q^{5} +(-4.69339 - 0.340905i) q^{6} +(1.29605 - 2.24483i) q^{7} -9.18678 q^{8} +(-1.85970 + 2.35404i) q^{9} +O(q^{10})$	\(q+(1.35844 - 2.35288i) q^{2} +(-0.755083 - 1.55880i) q^{3} +(-2.69069 - 4.66041i) q^{4} +(-0.835704 - 1.44748i) q^{5} +(-4.69339 - 0.340905i) q^{6} +(1.29605 - 2.24483i) q^{7} -9.18678 q^{8} +(-1.85970 + 2.35404i) q^{9} -4.54100 q^{10} +(-5.23294 + 7.71324i) q^{12} +(0.0996757 + 0.172643i) q^{13} +(-3.52121 - 6.09891i) q^{14} +(-1.62530 + 2.39566i) q^{15} +(-7.09826 + 12.2945i) q^{16} +7.79195 q^{17} +(3.01250 + 7.57346i) q^{18} -1.13361 q^{19} +(-4.49724 + 7.78945i) q^{20} +(-4.47786 - 0.325250i) q^{21} +(-0.898734 - 1.55665i) q^{23} +(6.93678 + 14.3203i) q^{24} +(1.10320 - 1.91079i) q^{25} +0.541612 q^{26} +(5.07370 + 1.12139i) q^{27} -13.9491 q^{28} +(2.01333 - 3.48718i) q^{29} +(3.42883 + 7.07850i) q^{30} +(-2.21567 - 3.83765i) q^{31} +(10.0983 + 17.4907i) q^{32} +(10.5849 - 18.3335i) q^{34} -4.33247 q^{35} +(15.9747 + 2.33296i) q^{36} +4.55523 q^{37} +(-1.53993 + 2.66724i) q^{38} +(0.193853 - 0.285735i) q^{39} +(7.67743 + 13.2977i) q^{40} +(-2.24775 - 3.89322i) q^{41} +(-6.84816 + 10.0940i) q^{42} +(-1.68314 + 2.91529i) q^{43} +(4.96159 + 0.724595i) q^{45} -4.88349 q^{46} +(-4.17610 + 7.23321i) q^{47} +(24.5245 + 1.78134i) q^{48} +(0.140496 + 0.243346i) q^{49} +(-2.99724 - 5.19138i) q^{50} +(-5.88358 - 12.1461i) q^{51} +(0.536393 - 0.929061i) q^{52} +0.660920 q^{53} +(9.53080 - 10.4145i) q^{54} +(-11.9065 + 20.6227i) q^{56} +(0.855969 + 1.76706i) q^{57} +(-5.46994 - 9.47422i) q^{58} +(-2.26932 - 3.93059i) q^{59} +(15.5380 + 1.12860i) q^{60} +(-0.227860 + 0.394665i) q^{61} -12.0394 q^{62} +(2.87416 + 7.22567i) q^{63} +26.4783 q^{64} +(0.166599 - 0.288558i) q^{65} +(5.77168 + 9.99685i) q^{67} +(-20.9657 - 36.3137i) q^{68} +(-1.74789 + 2.57635i) q^{69} +(-5.88537 + 10.1938i) q^{70} +13.4057 q^{71} +(17.0846 - 21.6261i) q^{72} -10.7548 q^{73} +(6.18799 - 10.7179i) q^{74} +(-3.81155 - 0.276852i) q^{75} +(3.05019 + 5.28308i) q^{76} +(-0.408962 - 0.844263i) q^{78} +(-5.95069 + 10.3069i) q^{79} +23.7282 q^{80} +(-2.08305 - 8.75562i) q^{81} -12.2137 q^{82} +(1.44638 - 2.50520i) q^{83} +(10.5327 + 21.7438i) q^{84} +(-6.51177 - 11.2787i) q^{85} +(4.57288 + 7.92046i) q^{86} +(-6.95604 - 0.505253i) q^{87} +11.6422 q^{89} +(8.44489 - 10.6897i) q^{90} +0.516740 q^{91} +(-4.83643 + 8.37694i) q^{92} +(-4.30911 + 6.35153i) q^{93} +(11.3459 + 19.6517i) q^{94} +(0.947361 + 1.64088i) q^{95} +(19.6394 - 28.9481i) q^{96} +(2.36406 - 4.09467i) q^{97} +0.763417 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{3} - 10 q^{4} - 3 q^{5} - 10 q^{6} + q^{7} + 6 q^{8} + q^{9}+O(q^{10}) $ 20 * q - q^3 - 10 * q^4 - 3 * q^5 - 10 * q^6 + q^7 + 6 * q^8 + q^9	$ 20 q - q^{3} - 10 q^{4} - 3 q^{5} - 10 q^{6} + q^{7} + 6 q^{8} + q^{9} - 5 q^{12} + q^{13} - 15 q^{14} - 7 q^{15} - 10 q^{16} + 6 q^{17} - 17 q^{18} + 4 q^{19} - 15 q^{20} - 4 q^{21} - 18 q^{23} + 27 q^{24} - 7 q^{25} + 12 q^{26} + 23 q^{27} - 8 q^{28} + 12 q^{29} + 26 q^{30} + 7 q^{31} + 24 q^{32} + 6 q^{34} + 36 q^{35} + 20 q^{36} - 2 q^{37} + 12 q^{38} - 4 q^{39} - 12 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 35 q^{45} - 36 q^{46} - 27 q^{47} + 19 q^{48} - 15 q^{49} + 15 q^{50} + 2 q^{51} - 5 q^{52} + 12 q^{53} + 44 q^{54} - 60 q^{56} - 27 q^{57} - 9 q^{58} - 21 q^{59} - 5 q^{60} - 20 q^{61} - 6 q^{62} - 74 q^{63} + 62 q^{64} + 12 q^{65} + 10 q^{67} - 69 q^{68} + 16 q^{69} - 6 q^{70} + 36 q^{71} + 102 q^{72} - 14 q^{73} - 6 q^{74} - 26 q^{75} - 2 q^{76} + 92 q^{78} + q^{79} + 102 q^{80} - 35 q^{81} - 60 q^{82} + 30 q^{83} + 70 q^{84} - 24 q^{85} - 36 q^{86} - 60 q^{87} + 108 q^{89} - 11 q^{90} + 20 q^{91} - 6 q^{92} - 19 q^{93} - 15 q^{94} + 12 q^{95} + 106 q^{96} + 16 q^{97} - 120 q^{98}+O(q^{100}) $ 20 * q - q^3 - 10 * q^4 - 3 * q^5 - 10 * q^6 + q^7 + 6 * q^8 + q^9 - 5 * q^12 + q^13 - 15 * q^14 - 7 * q^15 - 10 * q^16 + 6 * q^17 - 17 * q^18 + 4 * q^19 - 15 * q^20 - 4 * q^21 - 18 * q^23 + 27 * q^24 - 7 * q^25 + 12 * q^26 + 23 * q^27 - 8 * q^28 + 12 * q^29 + 26 * q^30 + 7 * q^31 + 24 * q^32 + 6 * q^34 + 36 * q^35 + 20 * q^36 - 2 * q^37 + 12 * q^38 - 4 * q^39 - 12 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 35 * q^45 - 36 * q^46 - 27 * q^47 + 19 * q^48 - 15 * q^49 + 15 * q^50 + 2 * q^51 - 5 * q^52 + 12 * q^53 + 44 * q^54 - 60 * q^56 - 27 * q^57 - 9 * q^58 - 21 * q^59 - 5 * q^60 - 20 * q^61 - 6 * q^62 - 74 * q^63 + 62 * q^64 + 12 * q^65 + 10 * q^67 - 69 * q^68 + 16 * q^69 - 6 * q^70 + 36 * q^71 + 102 * q^72 - 14 * q^73 - 6 * q^74 - 26 * q^75 - 2 * q^76 + 92 * q^78 + q^79 + 102 * q^80 - 35 * q^81 - 60 * q^82 + 30 * q^83 + 70 * q^84 - 24 * q^85 - 36 * q^86 - 60 * q^87 + 108 * q^89 - 11 * q^90 + 20 * q^91 - 6 * q^92 - 19 * q^93 - 15 * q^94 + 12 * q^95 + 106 * q^96 + 16 * q^97 - 120 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	1.35844	−	2.35288i	0.960559	−	1.66374i	0.239457	−	0.970907i	$-0.423031\pi$
$2$	1.35844	−	2.35288i	0.960559	−	1.66374i	0.721102	−	0.692829i	$-0.243636\pi$
$3$	−0.755083	−	1.55880i	−0.435948	−	0.899972i
$3$	−0.755083	−	1.55880i	−0.435948	−	0.899972i
$4$	−2.69069	−	4.66041i	−1.34535	−	2.33021i
$5$	−0.835704	−	1.44748i	−0.373738	−	0.647334i	0.616399	−	0.787434i	$-0.288591\pi$
$5$	−0.835704	−	1.44748i	−0.373738	−	0.647334i	−0.990137	+	0.140100i	$0.955257\pi$
$6$	−4.69339	−	0.340905i	−1.91607	−	0.139174i
$7$	1.29605	−	2.24483i	0.489862	−	0.848466i	−0.510070	−	0.860133i	$-0.670381\pi$
$7$	1.29605	−	2.24483i	0.489862	−	0.848466i	0.999932	+	0.0116673i	$0.00371389\pi$
$8$	−9.18678			−3.24802
$9$	−1.85970	+	2.35404i	−0.619899	+	0.784681i
$10$	−4.54100			−1.43599
$11$		0			0
$11$		0			0
$12$	−5.23294	+	7.71324i	−1.51062	+	2.22662i
$13$	0.0996757	+	0.172643i	0.0276451	+	0.0478827i	0.879517	−	0.475868i	$-0.157866\pi$
$13$	0.0996757	+	0.172643i	0.0276451	+	0.0478827i	−0.851872	+	0.523750i	$0.824533\pi$
$14$	−3.52121	−	6.09891i	−0.941082	−	1.63000i
$15$	−1.62530	+	2.39566i	−0.419652	+	0.618558i
$16$	−7.09826	+	12.2945i	−1.77456	+	3.07364i
$17$	7.79195			1.88983			0.944913	−	0.327321i	$-0.106146\pi$
$17$	7.79195			1.88983			0.944913	+	0.327321i	$0.106146\pi$
$18$	3.01250	+	7.57346i	0.710053	+	1.78508i
$19$	−1.13361			−0.260067			−0.130034	−	0.991510i	$-0.541509\pi$
$19$	−1.13361			−0.260067			−0.130034	+	0.991510i	$0.541509\pi$
$20$	−4.49724	+	7.78945i	−1.00561	+	1.74178i
$21$	−4.47786	−	0.325250i	−0.977149	−	0.0709754i
$22$		0			0
$23$	−0.898734	−	1.55665i	−0.187399	−	0.324584i	0.756983	−	0.653434i	$-0.226672\pi$
$23$	−0.898734	−	1.55665i	−0.187399	−	0.324584i	−0.944382	+	0.328850i	$0.893339\pi$
$24$	6.93678	+	14.3203i	1.41597	+	2.92312i
$25$	1.10320	−	1.91079i	0.220639	−	0.382159i
$26$	0.541612			0.106219
$27$	5.07370	+	1.12139i	0.976435	+	0.215812i
$28$	−13.9491			−2.63613
$29$	2.01333	−	3.48718i	0.373865	−	0.647553i	−0.616291	−	0.787518i	$-0.711366\pi$
$29$	2.01333	−	3.48718i	0.373865	−	0.647553i	0.990156	+	0.139965i	$0.0446989\pi$
$30$	3.42883	+	7.07850i	0.626016	+	1.29235i
$31$	−2.21567	−	3.83765i	−0.397946	−	0.689263i	0.595526	−	0.803336i	$-0.296944\pi$
$31$	−2.21567	−	3.83765i	−0.397946	−	0.689263i	−0.993472	+	0.114073i	$0.963610\pi$
$32$	10.0983	+	17.4907i	1.78514	+	3.09195i
$33$		0			0
$34$	10.5849	−	18.3335i	1.81529	−	3.14417i
$35$	−4.33247			−0.732320
$36$	15.9747	+	2.33296i	2.66245	+	0.388826i
$37$	4.55523			0.748876			0.374438	−	0.927252i	$-0.377836\pi$
$37$	4.55523			0.748876			0.374438	+	0.927252i	$0.377836\pi$
$38$	−1.53993	+	2.66724i	−0.249810	+	0.432684i
$39$	0.193853	−	0.285735i	0.0310413	−	0.0457541i
$40$	7.67743	+	13.2977i	1.21391	+	2.10255i
$41$	−2.24775	−	3.89322i	−0.351040	−	0.608019i	0.635392	−	0.772190i	$-0.280839\pi$
$41$	−2.24775	−	3.89322i	−0.351040	−	0.608019i	−0.986432	+	0.164171i	$0.947505\pi$
$42$	−6.84816	+	10.0940i	−1.05669	+	1.55754i
$43$	−1.68314	+	2.91529i	−0.256677	+	0.444577i	−0.965350	−	0.260960i	$-0.915961\pi$
$43$	−1.68314	+	2.91529i	−0.256677	+	0.444577i	0.708673	+	0.705537i	$0.249294\pi$
$44$		0			0
$45$	4.96159	+	0.724595i	0.739631	+	0.108016i
$46$	−4.88349			−0.720031
$47$	−4.17610	+	7.23321i	−0.609146	+	1.05507i	0.382235	+	0.924065i	$0.375154\pi$
$47$	−4.17610	+	7.23321i	−0.609146	+	1.05507i	−0.991381	+	0.131007i	$0.958179\pi$
$48$	24.5245	+	1.78134i	3.53980	+	0.257114i
$49$	0.140496	+	0.243346i	0.0200708	+	0.0347637i
$50$	−2.99724	−	5.19138i	−0.423874	−	0.734172i
$51$	−5.88358	−	12.1461i	−0.823866	−	1.70079i
$52$	0.536393	−	0.929061i	0.0743844	−	0.128838i
$53$	0.660920			0.0907844			0.0453922	−	0.998969i	$-0.485546\pi$
$53$	0.660920			0.0907844			0.0453922	+	0.998969i	$0.485546\pi$
$54$	9.53080	−	10.4145i	1.29698	−	1.41723i
$55$		0			0
$56$	−11.9065	+	20.6227i	−1.59108	+	2.75583i
$57$	0.855969	+	1.76706i	0.113376	+	0.234053i
$58$	−5.46994	−	9.47422i	−0.718239	−	1.24403i
$59$	−2.26932	−	3.93059i	−0.295441	−	0.511719i	0.679646	−	0.733540i	$-0.262133\pi$
$59$	−2.26932	−	3.93059i	−0.295441	−	0.511719i	−0.975087	+	0.221821i	$0.928800\pi$
$60$	15.5380	+	1.12860i	2.00594	+	0.145702i
$61$	−0.227860	+	0.394665i	−0.0291745	+	0.0505316i	−0.880244	−	0.474521i	$-0.842621\pi$
$61$	−0.227860	+	0.394665i	−0.0291745	+	0.0505316i	0.851070	+	0.525053i	$0.175955\pi$
$62$	−12.0394			−1.52900
$63$	2.87416	+	7.22567i	0.362110	+	0.910349i
$64$	26.4783			3.30979
$65$	0.166599	−	0.288558i	0.0206640	−	0.0357912i
$66$		0			0
$67$	5.77168	+	9.99685i	0.705123	+	1.22131i	0.966647	+	0.256112i	$0.0824416\pi$
$67$	5.77168	+	9.99685i	0.705123	+	1.22131i	−0.261524	+	0.965197i	$0.584225\pi$
$68$	−20.9657	−	36.3137i	−2.54247	−	4.40369i
$69$	−1.74789	+	2.57635i	−0.210421	+	0.310156i
$70$	−5.88537	+	10.1938i	−0.703437	+	1.21839i
$71$	13.4057			1.59096			0.795481	−	0.605979i	$-0.207218\pi$
$71$	13.4057			1.59096			0.795481	+	0.605979i	$0.207218\pi$
$72$	17.0846	−	21.6261i	2.01344	−	2.54866i
$73$	−10.7548			−1.25875			−0.629375	−	0.777101i	$-0.716689\pi$
$73$	−10.7548			−1.25875			−0.629375	+	0.777101i	$0.716689\pi$
$74$	6.18799	−	10.7179i	0.719339	−	1.24593i
$75$	−3.81155	−	0.276852i	−0.440119	−	0.0319681i
$76$	3.05019	+	5.28308i	0.349881	+	0.606011i
$77$		0			0
$78$	−0.408962	−	0.844263i	−0.0463059	−	0.0955940i
$79$	−5.95069	+	10.3069i	−0.669505	+	1.15962i	0.308538	+	0.951212i	$0.400160\pi$
$79$	−5.95069	+	10.3069i	−0.669505	+	1.15962i	−0.978043	+	0.208404i	$0.933173\pi$
$80$	23.7282			2.65289
$81$	−2.08305	−	8.75562i	−0.231450	−	0.972847i
$82$	−12.2137			−1.34878
$83$	1.44638	−	2.50520i	0.158760	−	0.274981i	−0.775662	−	0.631149i	$-0.782584\pi$
$83$	1.44638	−	2.50520i	0.158760	−	0.274981i	0.934422	+	0.356168i	$0.115917\pi$
$84$	10.5327	+	21.7438i	1.14922	+	2.37245i
$85$	−6.51177	−	11.2787i	−0.706300	−	1.22335i
$86$	4.57288	+	7.92046i	0.493106	+	0.854085i
$87$	−6.95604	−	0.505253i	−0.745766	−	0.0541688i
$88$		0			0
$89$	11.6422			1.23408			0.617038	−	0.786933i	$-0.288333\pi$
$89$	11.6422			1.23408			0.617038	+	0.786933i	$0.288333\pi$
$90$	8.44489	−	10.6897i	0.890169	−	1.12679i
$91$	0.516740			0.0541691
$92$	−4.83643	+	8.37694i	−0.504233	+	0.873357i
$93$	−4.30911	+	6.35153i	−0.446834	+	0.658623i
$94$	11.3459	+	19.6517i	1.17024	+	2.02692i
$95$	0.947361	+	1.64088i	0.0971972	+	0.168350i
$96$	19.6394	−	28.9481i	2.00444	−	2.95450i
$97$	2.36406	−	4.09467i	0.240034	−	0.415751i	−0.720690	−	0.693258i	$-0.756175\pi$
$97$	2.36406	−	4.09467i	0.240034	−	0.415751i	0.960724	+	0.277507i	$0.0895081\pi$
$98$	0.763417			0.0771168
$99$		0			0
$100$	−11.8735			−1.18735
$101$	0.310256	−	0.537378i	0.0308716	−	0.0534712i	−0.850177	−	0.526497i	$-0.823505\pi$
$101$	0.310256	−	0.537378i	0.0308716	−	0.0534712i	0.881048	+	0.473026i	$0.156838\pi$
$102$	−36.5707	−	2.65632i	−3.62104	−	0.263015i
$103$	6.57101	+	11.3813i	0.647461	+	1.12143i	0.983727	+	0.179668i	$0.0575024\pi$
$103$	6.57101	+	11.3813i	0.647461	+	1.12143i	−0.336267	+	0.941767i	$0.609164\pi$
$104$	−0.915699	−	1.58604i	−0.0897917	−	0.155524i
$105$	3.27137	+	6.75344i	0.319253	+	0.659068i
$106$	0.897817	−	1.55507i	0.0872037	−	0.151041i
$107$	0.141493			0.0136787			0.00683933	−	0.999977i	$-0.497823\pi$
$107$	0.141493			0.0136787			0.00683933	+	0.999977i	$0.497823\pi$
$108$	−8.42562	−	26.6629i	−0.810756	−	2.56564i
$109$	−16.0135			−1.53381			−0.766906	−	0.641759i	$-0.778205\pi$
$109$	−16.0135			−1.53381			−0.766906	+	0.641759i	$0.778205\pi$
$110$		0			0
$111$	−3.43958	−	7.10069i	−0.326471	−	0.673967i
$112$	18.3994	+	31.8687i	1.73858	+	3.01131i
$113$	−3.11817	−	5.40083i	−0.293333	−	0.508068i	0.681263	−	0.732039i	$-0.261431\pi$
$113$	−3.11817	−	5.40083i	−0.293333	−	0.508068i	−0.974596	+	0.223971i	$0.928098\pi$
$114$	5.32047	+	0.386453i	0.498307	+	0.0361946i
$115$	−1.50215	+	2.60180i	−0.140076	+	0.242619i
$116$	−21.6690			−2.01191
$117$	−0.591777	−	0.0864236i	−0.0547098	−	0.00798986i
$118$	−12.3309			−1.13515
$119$	10.0988	−	17.4916i	0.925754	−	1.60345i
$120$	14.9313	−	22.0084i	1.36304	−	2.00909i
$121$		0			0
$122$	0.619065	+	1.07225i	0.0560475	+	0.0970772i
$123$	−4.37150	+	6.44350i	−0.394165	+	0.580991i
$124$	−11.9234	+	20.6519i	−1.07075	+	1.85459i
$125$	−12.0448			−1.07732
$126$	20.9055	+	3.05305i	1.86241	+	0.271987i
$127$	3.73490			0.331419			0.165709	−	0.986175i	$-0.447009\pi$
$127$	3.73490			0.331419			0.165709	+	0.986175i	$0.447009\pi$
$128$	15.7726	−	27.3189i	1.39411	−	2.41467i
$129$	5.81526	+	0.422392i	0.512005	+	0.0371895i
$130$	−0.452627	−	0.783974i	−0.0396981	−	0.0687590i
$131$	−6.51821	−	11.2899i	−0.569498	−	0.986400i	−0.996616	−	0.0822040i	$-0.973804\pi$
$131$	−6.51821	−	11.2899i	−0.569498	−	0.986400i	0.427117	−	0.904196i	$-0.359529\pi$
$132$		0			0
$133$	−1.46922	+	2.54476i	−0.127397	+	0.220658i
$134$	31.3618			2.70925
$135$	−2.61692	−	8.28125i	−0.225229	−	0.712736i
$136$	−71.5830			−6.13819
$137$	5.45125	−	9.44185i	0.465732	−	0.806672i	−0.533502	−	0.845799i	$-0.679124\pi$
$137$	5.45125	−	9.44185i	0.465732	−	0.806672i	0.999234	+	0.0391271i	$0.0124577\pi$
$138$	3.68744	+	7.61236i	0.313896	+	0.648007i
$139$	6.86858	+	11.8967i	0.582585	+	1.00907i	0.995172	+	0.0981489i	$0.0312922\pi$
$139$	6.86858	+	11.8967i	0.582585	+	1.00907i	−0.412586	+	0.910918i	$0.635375\pi$
$140$	11.6573	+	20.1911i	0.985224	+	1.70646i
$141$	14.4284	+	1.04801i	1.21509	+	0.0882583i
$142$	18.2107	−	31.5419i	1.52821	−	2.64694i
$143$		0			0
$144$	−15.7413	−	39.5737i	−1.31177	−	3.29781i
$145$	−6.73018			−0.558911
$146$	−14.6097	+	25.3047i	−1.20910	+	2.09423i
$147$	0.273241	−	0.402751i	0.0225365	−	0.0332183i
$148$	−12.2567	−	21.2293i	−1.00750	−	1.74504i
$149$	−2.50144	−	4.33261i	−0.204926	−	0.354942i	0.745183	−	0.666860i	$-0.232362\pi$
$149$	−2.50144	−	4.33261i	−0.204926	−	0.354942i	−0.950109	+	0.311918i	$0.899029\pi$
$150$	−5.82914	+	8.59202i	−0.475947	+	0.701535i
$151$	−9.12419	+	15.8036i	−0.742516	+	1.28608i	0.208830	+	0.977952i	$0.433034\pi$
$151$	−9.12419	+	15.8036i	−0.742516	+	1.28608i	−0.951346	+	0.308124i	$0.900299\pi$
$152$	10.4142			0.844703
$153$	−14.4907	+	18.3426i	−1.17150	+	1.48291i
$154$		0			0
$155$	−3.70329	+	6.41429i	−0.297455	+	0.515208i
$156$	−1.85324	−	0.134610i	−0.148378	−	0.0107774i
$157$	1.58950	+	2.75309i	0.126856	+	0.219720i	0.922457	−	0.386100i	$-0.126178\pi$
$157$	1.58950	+	2.75309i	0.126856	+	0.219720i	−0.795601	+	0.605821i	$0.792845\pi$
$158$	16.1672	+	28.0025i	1.28620	+	2.22776i
$159$	−0.499050	−	1.03024i	−0.0395772	−	0.0817034i
$160$	16.8783	−	29.2341i	1.33435	−	2.31116i
$161$	−4.65922			−0.367198
$162$	−23.4306	−	6.99279i	−1.84088	−	0.549405i
$163$	−15.0397			−1.17800			−0.588999	−	0.808134i	$-0.700478\pi$
$163$	−15.0397			−1.17800			−0.588999	+	0.808134i	$0.700478\pi$
$164$	−12.0960	+	20.9509i	−0.944540	+	1.63599i
$165$		0			0
$166$	−3.92961	−	6.80629i	−0.304997	−	0.528271i
$167$	1.15172	+	1.99484i	0.0891229	+	0.154365i	0.907141	−	0.420828i	$-0.138260\pi$
$167$	1.15172	+	1.99484i	0.0891229	+	0.154365i	−0.818018	+	0.575193i	$0.804927\pi$
$168$	41.1371	+	2.98800i	3.17380	+	0.230529i
$169$	6.48013	−	11.2239i	0.498471	−	0.863378i
$170$	−35.3833			−2.71377
$171$	2.10817	−	2.66856i	0.161216	−	0.204070i
$172$	18.1153			1.38128
$173$	9.84903	−	17.0590i	0.748808	−	1.29697i	−0.199587	−	0.979880i	$-0.563960\pi$
$173$	9.84903	−	17.0590i	0.748808	−	1.29697i	0.948395	−	0.317093i	$-0.102707\pi$
$174$	−10.6381	+	15.6804i	−0.806474	+	1.18873i
$175$	−2.85960	−	4.95298i	−0.216166	−	0.374410i
$176$		0			0
$177$	−4.41346	+	6.50534i	−0.331736	+	0.488971i
$178$	15.8152	−	27.3928i	1.18540	−	2.05318i
$179$	−14.2894			−1.06804			−0.534022	−	0.845471i	$-0.679320\pi$
$179$	−14.2894			−1.06804			−0.534022	+	0.845471i	$0.679320\pi$
$180$	−9.97321	−	25.0727i	−0.743359	−	1.86881i
$181$	14.3355			1.06555			0.532776	−	0.846256i	$-0.321149\pi$
$181$	14.3355			1.06555			0.532776	+	0.846256i	$0.321149\pi$
$182$	0.701958	−	1.21583i	0.0520326	−	0.0901231i
$183$	0.787255	+	0.0571824i	0.0581956	+	0.00422704i
$184$	8.25647	+	14.3006i	0.608675	+	1.05426i
$185$	−3.80683	−	6.59362i	−0.279884	−	0.484773i
$186$	9.09074	+	18.7670i	0.666565	+	1.37606i
$187$		0			0
$188$	44.9464			3.27805
$189$	9.09312	−	9.93622i	0.661427	−	0.722753i
$190$	5.14771			0.373454
$191$	3.35069	−	5.80357i	0.242448	−	0.419931i	−0.718963	−	0.695048i	$-0.755383\pi$
$191$	3.35069	−	5.80357i	0.242448	−	0.419931i	0.961411	+	0.275117i	$0.0887164\pi$
$192$	−19.9933	−	41.2743i	−1.44290	−	2.97872i
$193$	−12.3581	−	21.4048i	−0.889555	−	1.54075i	−0.840402	−	0.541963i	$-0.817681\pi$
$193$	−12.3581	−	21.4048i	−0.889555	−	1.54075i	−0.0491528	−	0.998791i	$-0.515652\pi$
$194$	−6.42285	−	11.1247i	−0.461133	−	0.798707i
$195$	−0.575599	−	0.0418087i	−0.0412195	−	0.00299398i
$196$	0.756061	−	1.30954i	0.0540044	−	0.0935383i
$197$	3.16677			0.225623			0.112811	−	0.993616i	$-0.464014\pi$
$197$	3.16677			0.225623			0.112811	+	0.993616i	$0.464014\pi$
$198$		0			0
$199$	−8.30214			−0.588523			−0.294261	−	0.955725i	$-0.595074\pi$
$199$	−8.30214			−0.588523			−0.294261	+	0.955725i	$0.595074\pi$
$200$	−10.1348	+	17.5540i	−0.716641	+	1.24126i
$201$	11.2250	−	16.5453i	0.791747	−	1.16702i
$202$	−0.842924	−	1.45999i	−0.0593079	−	0.102724i
$203$	−5.21875	−	9.03914i	−0.366285	−	0.634423i
$204$	−40.7749	+	60.1013i	−2.85481	+	4.20793i
$205$	−3.75691	+	6.50716i	−0.262394	+	0.454480i
$206$	35.7052			2.48770
$207$	5.33580	+	0.779244i	0.370864	+	0.0541612i
$208$	−2.83010			−0.196232
$209$		0			0
$210$	20.3340	+	1.47696i	1.40318	+	0.101920i
$211$	−11.2467	−	19.4798i	−0.774254	−	1.34105i	−0.935213	−	0.354086i	$-0.884792\pi$
$211$	−11.2467	−	19.4798i	−0.774254	−	1.34105i	0.160959	−	0.986961i	$-0.448541\pi$
$212$	−1.77833	−	3.08016i	−0.122136	−	0.211546i
$213$	−10.1224	−	20.8967i	−0.693576	−	1.43182i
$214$	0.192209	−	0.332916i	0.0131392	−	0.0227577i
$215$	5.62644			0.383720
$216$	−46.6110	−	10.3020i	−3.17148	−	0.700961i
$217$	−11.4865			−0.779755
$218$	−21.7533	+	37.6778i	−1.47332	+	2.55186i
$219$	8.12075	+	16.7645i	0.548749	+	1.13284i
$220$		0			0
$221$	0.776669	+	1.34523i	0.0522444	+	0.0904900i
$222$	−21.3795	−	1.55290i	−1.43490	−	0.104224i
$223$	−6.33470	+	10.9720i	−0.424203	+	0.734741i	−0.996346	−	0.0854133i	$-0.972779\pi$
$223$	−6.33470	+	10.9720i	−0.424203	+	0.734741i	0.572143	+	0.820154i	$0.306112\pi$
$224$	52.3515			3.49788
$225$	2.44648	+	6.15047i	0.163099	+	0.410032i
$226$	−16.9433			−1.12705
$227$	−2.84810	+	4.93306i	−0.189035	+	0.327419i	−0.944929	−	0.327276i	$-0.893869\pi$
$227$	−2.84810	+	4.93306i	−0.189035	+	0.327419i	0.755894	+	0.654694i	$0.227203\pi$
$228$	5.93211	−	8.74379i	0.392863	−	0.579072i
$229$	3.36424	+	5.82703i	0.222315	+	0.385061i	0.955511	−	0.294957i	$-0.0953053\pi$
$229$	3.36424	+	5.82703i	0.222315	+	0.385061i	−0.733195	+	0.680018i	$0.761972\pi$
$230$	4.08115	+	7.06876i	0.269103	+	0.466100i
$231$		0			0
$232$	−18.4960	+	32.0360i	−1.21432	+	2.10326i
$233$	6.62352			0.433921			0.216961	−	0.976180i	$-0.430386\pi$
$233$	6.62352			0.433921			0.216961	+	0.976180i	$0.430386\pi$
$234$	−1.00723	+	1.27498i	−0.0658450	+	0.0833480i
$235$	13.9599			0.910645
$236$	−12.2121	+	21.1520i	−0.794940	+	1.37688i
$237$	20.5596	+	1.49335i	1.33549	+	0.0970035i
$238$	−27.4371	−	47.5224i	−1.77848	−	3.08042i
$239$	2.34001	+	4.05301i	0.151362	+	0.262167i	0.931729	−	0.363155i	$-0.118301\pi$
$239$	2.34001	+	4.05301i	0.151362	+	0.262167i	−0.780366	+	0.625323i	$0.784967\pi$
$240$	−17.9168	−	36.9874i	−1.15652	−	2.38753i
$241$	−1.89833	+	3.28800i	−0.122282	+	0.211799i	−0.920667	−	0.390348i	$-0.872355\pi$
$241$	−1.89833	+	3.28800i	−0.122282	+	0.211799i	0.798385	+	0.602147i	$0.205688\pi$
$242$		0			0
$243$	−12.0754	+	9.85827i	−0.774635	+	0.632409i
$244$	2.45240			0.156999
$245$	0.234826	−	0.406730i	0.0150025	−	0.0259850i
$246$	9.22236	+	19.0387i	0.587996	+	1.21386i
$247$	−0.112993	−	0.195710i	−0.00718959	−	0.0124527i
$248$	20.3549	+	35.2557i	1.29254	+	2.23874i
$249$	−4.99723	−	0.362974i	−0.316686	−	0.0230026i
$250$	−16.3621	+	28.3400i	−1.03483	+	1.79238i
$251$	11.5694			0.730253			0.365126	−	0.930958i	$-0.381026\pi$
$251$	11.5694			0.730253			0.365126	+	0.930958i	$0.381026\pi$
$252$	25.9411	−	32.8368i	1.63414	−	2.06853i
$253$		0			0
$254$	5.07362	−	8.78777i	0.318347	−	0.551394i
$255$	−12.6643	+	18.6669i	−0.793069	+	1.16897i
$256$	−16.3736	−	28.3600i	−1.02335	−	1.77250i
$257$	6.63973	+	11.5003i	0.414175	+	0.717372i	0.995341	−	0.0964128i	$-0.0307369\pi$
$257$	6.63973	+	11.5003i	0.414175	+	0.717372i	−0.581167	+	0.813785i	$0.697404\pi$
$258$	8.89349	−	13.1088i	0.553684	−	0.816118i
$259$	5.90382	−	10.2257i	0.366846	−	0.635395i
$260$	−1.79306			−0.111201
$261$	4.46480	+	11.2246i	0.276364	+	0.694783i
$262$	−35.4182			−2.18815
$263$	8.23855	−	14.2696i	0.508011	−	0.879901i	−0.491946	−	0.870626i	$-0.663714\pi$
$263$	8.23855	−	14.2696i	0.508011	−	0.879901i	0.999957	−	0.00927492i	$-0.00295234\pi$
$264$		0			0
$265$	−0.552334	−	0.956670i	−0.0339296	−	0.0587678i
$266$	3.99167	+	6.91377i	0.244745	+	0.423910i
$267$	−8.79087	−	18.1479i	−0.537992	−	1.11063i
$268$	31.0596	−	53.7969i	1.89727	−	3.28617i
$269$	16.8816			1.02929			0.514643	−	0.857404i	$-0.327924\pi$
$269$	16.8816			1.02929			0.514643	+	0.857404i	$0.327924\pi$
$270$	−23.0397	−	5.09224i	−1.40215	−	0.309904i
$271$	28.0885			1.70625			0.853126	−	0.521704i	$-0.174704\pi$
$271$	28.0885			1.70625			0.853126	+	0.521704i	$0.174704\pi$
$272$	−55.3093	+	95.7985i	−3.35362	+	5.80864i
$273$	−0.390182	−	0.805493i	−0.0236149	−	0.0487507i
$274$	−14.8103	−	25.6523i	−0.894726	−	1.54971i
$275$		0			0
$276$	16.7099	+	1.21372i	1.00582	+	0.0730575i
$277$	−5.73251	+	9.92900i	−0.344433	+	0.596576i	−0.985251	−	0.171117i	$-0.945262\pi$
$277$	−5.73251	+	9.92900i	−0.344433	+	0.596576i	0.640817	+	0.767693i	$0.278596\pi$
$278$	37.3221			2.23843
$279$	13.1545	+	1.92109i	0.787538	+	0.115013i
$280$	39.8014			2.37859
$281$	−6.45621	+	11.1825i	−0.385145	+	0.667091i	−0.991789	−	0.127883i	$-0.959182\pi$
$281$	−6.45621	+	11.1825i	−0.385145	+	0.667091i	0.606644	+	0.794973i	$0.292515\pi$
$282$	22.0659	−	32.5246i	1.31401	−	1.93681i
$283$	−12.6335	−	21.8818i	−0.750981	−	1.30074i	−0.947348	−	0.320207i	$-0.896248\pi$
$283$	−12.6335	−	21.8818i	−0.750981	−	1.30074i	0.196366	−	0.980531i	$-0.437086\pi$
$284$	−36.0705	−	62.4760i	−2.14039	−	3.70727i
$285$	1.84246	−	2.71574i	0.109138	−	0.160867i
$286$		0			0
$287$	−11.6528			−0.687844
$288$	−59.9536	−	8.75567i	−3.53280	−	0.515933i
$289$	43.7146			2.57144
$290$	−9.14251	+	15.8353i	−0.536867	+	0.929880i
$291$	−8.16783	−	0.593271i	−0.478807	−	0.0347782i
$292$	28.9378	+	50.1217i	1.69346	+	2.93315i
$293$	−1.14253	−	1.97891i	−0.0667471	−	0.115609i	0.830721	−	0.556690i	$-0.187929\pi$
$293$	−1.14253	−	1.97891i	−0.0667471	−	0.115609i	−0.897468	+	0.441080i	$0.854595\pi$
$294$	−0.576444	−	1.19001i	−0.0336189	−	0.0694029i
$295$	−3.79297	+	6.56961i	−0.220835	+	0.382498i
$296$	−41.8479			−2.43236
$297$		0			0
$298$	−13.5922			−0.787372
$299$	0.179164	−	0.310321i	0.0103613	−	0.0179463i
$300$	8.96545	+	18.5083i	0.517620	+	1.06858i
$301$	4.36288	+	7.55674i	0.251472	+	0.435563i
$302$	24.7892	+	42.9362i	1.42646	+	2.47070i
$303$	−1.07193	−	0.0778600i	−0.0615809	−	0.00447294i
$304$	8.04664	−	13.9372i	0.461507	−	0.799353i
$305$	0.761693			0.0436144
$306$	23.4733	+	59.0121i	1.34188	+	3.37349i
$307$	2.56109			0.146169			0.0730847	−	0.997326i	$-0.476716\pi$
$307$	2.56109			0.146169			0.0730847	+	0.997326i	$0.476716\pi$
$308$		0			0
$309$	12.7795	−	18.8367i	0.727001	−	1.07158i
$310$	10.0614	+	17.4268i	0.571447	+	0.989775i
$311$	1.70546	+	2.95394i	0.0967075	+	0.167502i	0.910320	−	0.413905i	$-0.135836\pi$
$311$	1.70546	+	2.95394i	0.0967075	+	0.167502i	−0.813612	+	0.581408i	$0.802502\pi$
$312$	−1.78088	+	2.62498i	−0.100823	+	0.148610i
$313$	−13.9881	+	24.2282i	−0.790657	+	1.36946i	0.134904	+	0.990859i	$0.456927\pi$
$313$	−13.9881	+	24.2282i	−0.790657	+	1.36946i	−0.925561	+	0.378599i	$0.876406\pi$
$314$	8.63690			0.487409
$315$	8.05708	−	10.1988i	0.453965	−	0.574638i
$316$	64.0458			3.60286
$317$	15.3664	−	26.6154i	0.863064	−	1.49487i	−0.00589349	−	0.999983i	$-0.501876\pi$
$317$	15.3664	−	26.6154i	0.863064	−	1.49487i	0.868957	−	0.494887i	$-0.164791\pi$
$318$	−3.10196	−	0.225311i	−0.173949	−	0.0126348i
$319$		0			0
$320$	−22.1280	−	38.3269i	−1.23700	−	2.14254i
$321$	−0.106839	−	0.220559i	−0.00596318	−	0.0123104i
$322$	−6.32925	+	10.9626i	−0.352716	+	0.610921i
$323$	−8.83302			−0.491482
$324$	−35.2000	+	33.2665i	−1.95555	+	1.84814i
$325$	0.439848			0.0243984
$326$	−20.4304	+	35.3865i	−1.13154	+	1.95988i
$327$	12.0915	+	24.9618i	0.668662	+	1.38039i
$328$	20.6496	+	35.7662i	1.14018	+	1.97486i
$329$	10.8249	+	18.7492i	0.596795	+	1.03368i
$330$		0			0
$331$	2.98877	−	5.17671i	0.164278	−	0.284538i	−0.772121	−	0.635476i	$-0.780804\pi$
$331$	2.98877	−	5.17671i	0.164278	−	0.284538i	0.936399	+	0.350938i	$0.114137\pi$
$332$	−15.5670			−0.854350
$333$	−8.47136	+	10.7232i	−0.464228	+	0.587629i
$334$	6.25816			0.342431
$335$	9.64684	−	16.7088i	0.527063	−	0.912900i
$336$	35.7838	−	52.7445i	1.95217	−	2.87745i
$337$	−0.657458	−	1.13875i	−0.0358140	−	0.0620317i	0.847563	−	0.530695i	$-0.178069\pi$
$337$	−0.657458	−	1.13875i	−0.0358140	−	0.0620317i	−0.883377	+	0.468663i	$0.844736\pi$
$338$	−17.6057	−	30.4939i	−0.957622	−	1.65865i
$339$	−6.06432	+	8.93868i	−0.329369	+	0.485482i
$340$	−35.0423	+	60.6951i	−1.90044	+	3.29165i
$341$		0			0
$342$	−3.41500	−	8.58533i	−0.184662	−	0.464242i
$343$	18.8731			1.01905
$344$	15.4627	−	26.7821i	0.833691	−	1.44399i
$345$	5.18993	+	0.376971i	0.279416	+	0.0202954i
$346$	−26.7585	−	46.3471i	−1.43855	−	2.49164i
$347$	−8.96788	−	15.5328i	−0.481421	−	0.833846i	0.518351	−	0.855168i	$-0.326546\pi$
$347$	−8.96788	−	15.5328i	−0.481421	−	0.833846i	−0.999773	+	0.0213217i	$0.993213\pi$
$348$	16.3619	+	33.7775i	0.877088	+	1.81066i
$349$	12.8616	−	22.2769i	0.688466	−	1.19246i	−0.283868	−	0.958863i	$-0.591618\pi$
$349$	12.8616	−	22.2769i	0.688466	−	1.19246i	0.972334	−	0.233594i	$-0.0750488\pi$
$350$	−15.5383			−0.830559
$351$	0.312124	+	0.987718i	0.0166600	+	0.0527205i
$352$		0			0
$353$	9.95335	−	17.2397i	0.529763	−	0.917577i	−0.469634	−	0.882861i	$-0.655614\pi$
$353$	9.95335	−	17.2397i	0.529763	−	0.917577i	0.999397	−	0.0347159i	$-0.0110526\pi$
$354$	9.31087	+	19.2214i	0.494867	+	1.02161i
$355$	−11.2032	−	19.4045i	−0.594603	−	1.02988i
$356$	−31.3257	−	54.2577i	−1.66026	−	2.87565i
$357$	−34.8913	−	2.53433i	−1.84664	−	0.134131i
$358$	−19.4113	+	33.6213i	−1.02592	+	1.77694i
$359$	29.2180			1.54207			0.771033	−	0.636796i	$-0.219740\pi$
$359$	29.2180			1.54207			0.771033	+	0.636796i	$0.219740\pi$
$360$	−45.5811	−	6.65669i	−2.40233	−	0.350838i
$361$	−17.7149			−0.932365
$362$	19.4739	−	33.7298i	1.02353	−	1.77280i
$363$		0			0
$364$	−1.39039	−	2.40822i	−0.0728761	−	0.126225i
$365$	8.98781	+	15.5673i	0.470443	+	0.814832i
$366$	1.20398	−	1.77464i	0.0629330	−	0.0927618i
$367$	−8.57383	+	14.8503i	−0.447550	+	0.775180i	−0.998226	−	0.0595394i	$-0.981037\pi$
$367$	−8.57383	+	14.8503i	−0.447550	+	0.775180i	0.550676	+	0.834719i	$0.314370\pi$
$368$	25.5178			1.33021
$369$	13.3450	+	1.94891i	0.694711	+	0.101456i
$370$	−20.6853			−1.07538
$371$	0.856588	−	1.48365i	0.0444718	−	0.0770274i
$372$	41.1952	+	2.99222i	2.13587	+	0.155139i
$373$	10.1208	+	17.5297i	0.524034	+	0.907654i	0.999609	+	0.0279786i	$0.00890703\pi$
$373$	10.1208	+	17.5297i	0.524034	+	0.907654i	−0.475574	+	0.879676i	$0.657760\pi$
$374$		0			0
$375$	9.09485	+	18.7754i	0.469656	+	0.969560i
$376$	38.3649	−	66.4499i	1.97852	−	3.42689i
$377$	0.802719			0.0413421
$378$	−11.0263	−	34.8927i	−0.567131	−	1.79469i
$379$	−20.1090			−1.03293			−0.516465	−	0.856308i	$-0.672752\pi$
$379$	−20.1090			−1.03293			−0.516465	+	0.856308i	$0.672752\pi$
$380$	5.09811	−	8.83019i	0.261528	−	0.452979i
$381$	−2.82016	−	5.82195i	−0.144481	−	0.298268i
$382$	−9.10339	−	15.7675i	−0.465770	−	0.806737i
$383$	10.6542	+	18.4536i	0.544402	+	0.942932i	0.998644	+	0.0520541i	$0.0165768\pi$
$383$	10.6542	+	18.4536i	0.544402	+	0.942932i	−0.454242	+	0.890878i	$0.650090\pi$
$384$	−54.4942	−	3.95819i	−2.78089	−	0.201991i
$385$		0			0
$386$	−67.1507			−3.41788
$387$	−3.73258	−	9.38375i	−0.189738	−	0.477003i
$388$	−25.4438			−1.29171
$389$	−17.2712	+	29.9146i	−0.875685	+	1.51673i	−0.0196533	+	0.999807i	$0.506256\pi$
$389$	−17.2712	+	29.9146i	−0.875685	+	1.51673i	−0.856031	+	0.516924i	$0.827077\pi$
$390$	−0.880285	+	1.29752i	−0.0445749	+	0.0657025i
$391$	−7.00289	−	12.1294i	−0.354152	−	0.613408i
$392$	−1.29070	−	2.23556i	−0.0651903	−	0.112913i
$393$	−12.6768	+	18.6854i	−0.639461	+	0.942552i
$394$	4.30184	−	7.45101i	0.216724	−	0.375377i
$395$	19.8921			1.00088
$396$		0			0
$397$	−2.61262			−0.131124			−0.0655619	−	0.997849i	$-0.520884\pi$
$397$	−2.61262			−0.131124			−0.0655619	+	0.997849i	$0.520884\pi$
$398$	−11.2779	+	19.5339i	−0.565311	+	0.979147i
$399$	5.07614	+	0.368706i	0.254125	+	0.0184584i
$400$	15.6616	+	27.1266i	0.783078	+	1.35633i
$401$	−5.12601	−	8.87852i	−0.255981	−	0.443372i	0.709181	−	0.705027i	$-0.249065\pi$
$401$	−5.12601	−	8.87852i	−0.255981	−	0.443372i	−0.965161	+	0.261655i	$0.915732\pi$
$402$	−23.6808	−	48.8867i	−1.18109	−	2.43825i
$403$	0.441697	−	0.765042i	0.0220025	−	0.0381095i
$404$	−3.33921			−0.166132
$405$	−10.9328	+	10.3323i	−0.543255	+	0.513415i
$406$	−28.3573			−1.40735
$407$		0			0
$408$	54.0511	+	111.583i	2.67593	+	5.52420i
$409$	−1.98229	−	3.43343i	−0.0980181	−	0.169772i	0.812846	−	0.582478i	$-0.197917\pi$
$409$	−1.98229	−	3.43343i	−0.0980181	−	0.169772i	−0.910864	+	0.412706i	$0.864584\pi$
$410$	10.2070	+	17.6791i	0.504090	+	0.873109i
$411$	−18.8341	−	1.36802i	−0.929017	−	0.0674792i
$412$	35.3611	−	61.2473i	1.74212	−	3.01744i
$413$	−11.7647			−0.578901
$414$	9.08181	−	11.4959i	0.446346	−	0.564995i
$415$	−4.83497			−0.237339
$416$	−2.01310	+	3.48680i	−0.0987006	+	0.170954i
$417$	13.3582	−	19.6897i	0.654156	−	0.964211i
$418$		0			0
$419$	−16.3884	−	28.3856i	−0.800628	−	1.38673i	−0.919203	−	0.393783i	$-0.871166\pi$
$419$	−16.3884	−	28.3856i	−0.800628	−	1.38673i	0.118575	−	0.992945i	$-0.462167\pi$
$420$	22.6716	−	33.4174i	1.10626	−	1.63060i
$421$	18.7961	−	32.5558i	0.916066	−	1.58667i	0.110732	−	0.993850i	$-0.464681\pi$
$421$	18.7961	−	32.5558i	0.916066	−	1.58667i	0.805334	−	0.592822i	$-0.201986\pi$
$422$	−61.1116			−2.97487
$423$	−9.26102	−	23.2823i	−0.450286	−	1.13202i
$424$	−6.07173			−0.294869
$425$	8.59606	−	14.8888i	0.416970	−	0.722214i
$426$	−62.9181	−	4.57007i	−3.04839	−	0.221420i
$427$	0.590636	+	1.02301i	0.0285829	+	0.0495070i
$428$	−0.380715	−	0.659417i	−0.0184025	−	0.0318741i
$429$		0			0
$430$	7.64315	−	13.2383i	0.368585	−	0.638409i
$431$	−30.0260			−1.44630			−0.723152	−	0.690689i	$-0.757307\pi$
$431$	−30.0260			−1.44630			−0.723152	+	0.690689i	$0.757307\pi$
$432$	−49.8015	+	54.4190i	−2.39607	+	2.61823i
$433$	17.8078			0.855788			0.427894	−	0.903829i	$-0.359256\pi$
$433$	17.8078			0.855788			0.427894	+	0.903829i	$0.359256\pi$
$434$	−15.6037	+	27.0263i	−0.749000	+	1.29731i
$435$	5.08185	+	10.4910i	0.243656	+	0.503004i
$436$	43.0873	+	74.6294i	2.06351	+	3.57410i
$437$	1.01881	+	1.76463i	0.0487364	+	0.0844139i
$438$	50.4764	+	3.66636i	2.41185	+	0.175185i
$439$	1.17026	−	2.02694i	0.0558533	−	0.0967407i	−0.836747	−	0.547590i	$-0.815545\pi$
$439$	1.17026	−	2.02694i	0.0558533	−	0.0967407i	0.892600	+	0.450849i	$0.148879\pi$
$440$		0			0
$441$	−0.834126	−	0.121816i	−0.0397203	−	0.00580078i
$442$	4.22022			0.200735
$443$	−3.20338	+	5.54842i	−0.152197	+	0.263613i	−0.932035	−	0.362368i	$-0.881968\pi$
$443$	−3.20338	+	5.54842i	−0.152197	+	0.263613i	0.779838	+	0.625982i	$0.215302\pi$
$444$	−23.8373	+	35.1356i	−1.13127	+	1.66746i
$445$	−9.72947	−	16.8519i	−0.461221	−	0.798859i
$446$	17.2105	+	29.8095i	0.814943	+	1.41152i
$447$	−4.86487	+	7.17072i	−0.230101	+	0.339163i
$448$	34.3173	−	59.4393i	1.62134	−	2.80824i
$449$	21.7677			1.02728			0.513640	−	0.858006i	$-0.328297\pi$
$449$	21.7677			1.02728			0.513640	+	0.858006i	$0.328297\pi$
$450$	17.7947	+	2.59875i	0.838850	+	0.122506i
$451$		0			0
$452$	−16.7801	+	29.0640i	−0.789269	+	1.36705i
$453$	31.5241	+	2.28975i	1.48113	+	0.107582i
$454$	7.73793	+	13.4025i	0.363159	+	0.629010i
$455$	−0.431842	−	0.747972i	−0.0202451	−	0.0350655i
$456$	−7.86359	−	16.2336i	−0.368247	−	0.760210i
$457$	3.57114	−	6.18539i	0.167051	−	0.289340i	−0.770331	−	0.637644i	$-0.779909\pi$
$457$	3.57114	−	6.18539i	0.167051	−	0.289340i	0.937382	+	0.348304i	$0.113242\pi$
$458$	18.2804			0.854187
$459$	39.5341	+	8.73784i	1.84529	+	0.407847i
$460$	16.1673			0.753804
$461$	−1.44390	+	2.50091i	−0.0672491	+	0.116479i	−0.897689	−	0.440629i	$-0.854756\pi$
$461$	−1.44390	+	2.50091i	−0.0672491	+	0.116479i	0.830440	+	0.557108i	$0.188089\pi$
$462$		0			0
$463$	−0.726039	−	1.25754i	−0.0337419	−	0.0584426i	0.848661	−	0.528937i	$-0.177409\pi$
$463$	−0.726039	−	1.25754i	−0.0337419	−	0.0584426i	−0.882403	+	0.470494i	$0.844076\pi$
$464$	28.5822	+	49.5058i	1.32690	+	2.29825i
$465$	12.7949	+	0.929357i	0.593348	+	0.0430979i
$466$	8.99763	−	15.5843i	0.416807	−	0.721931i
$467$	5.50281			0.254640			0.127320	−	0.991862i	$-0.459363\pi$
$467$	5.50281			0.254640			0.127320	+	0.991862i	$0.459363\pi$
$468$	1.18952	+	2.99047i	0.0549856	+	0.138234i
$469$	29.9216			1.38165
$470$	18.9637	−	32.8460i	0.874728	−	1.51507i
$471$	3.09130	−	4.55651i	0.142440	−	0.209953i
$472$	20.8478	+	36.1094i	0.959597	+	1.66207i
$473$		0			0
$474$	31.4426	−	46.3457i	1.44421	−	2.12873i
$475$	−1.25059	+	2.16609i	−0.0573812	+	0.0993871i
$476$	−108.691			−4.98184
$477$	−1.22911	+	1.55584i	−0.0562772	+	0.0712368i
$478$	12.7150			0.581570
$479$	5.22744	−	9.05419i	0.238848	−	0.413696i	−0.721536	−	0.692377i	$-0.756564\pi$
$479$	5.22744	−	9.05419i	0.238848	−	0.413696i	0.960384	+	0.278680i	$0.0898970\pi$
$480$	−58.3146	−	4.23569i	−2.66169	−	0.193332i
$481$	0.454046	+	0.786431i	0.0207027	+	0.0358582i
$482$	5.15751	+	8.93307i	0.234918	+	0.406890i
$483$	3.51810	+	7.26279i	0.160079	+	0.330468i
$484$		0			0
$485$	−7.90262			−0.358840
$486$	6.79172	+	41.8037i	0.308079	+	1.89625i
$487$	5.69868			0.258232			0.129116	−	0.991630i	$-0.458786\pi$
$487$	5.69868			0.258232			0.129116	+	0.991630i	$0.458786\pi$
$488$	2.09330	−	3.62570i	0.0947591	−	0.164128i
$489$	11.3562	+	23.4438i	0.513546	+	1.06017i
$490$	−0.637991	−	1.10503i	−0.0288215	−	0.0499203i
$491$	4.15018	+	7.18832i	0.187295	+	0.324404i	0.944347	−	0.328950i	$-0.106695\pi$
$491$	4.15018	+	7.18832i	0.187295	+	0.324404i	−0.757053	+	0.653354i	$0.773361\pi$
$492$	41.7917	+	3.03555i	1.88412	+	0.136853i
$493$	15.6877	−	27.1720i	0.706540	−	1.22376i
$494$	−0.613976			−0.0276241
$495$		0			0
$496$	62.9096			2.82472
$497$	17.3745	−	30.0935i	0.779351	−	1.34988i
$498$	−7.64244	+	11.2648i	−0.342466	+	0.504787i
$499$	−6.95262	−	12.0423i	−0.311242	−	0.539087i	0.667389	−	0.744709i	$-0.267412\pi$
$499$	−6.95262	−	12.0423i	−0.311242	−	0.539087i	−0.978632	+	0.205622i	$0.934078\pi$
$500$	32.4089	+	56.1339i	1.44937	+	2.51038i
$501$	2.23991	−	3.30157i	0.100072	−	0.147503i
$502$	15.7162	−	27.2213i	0.701451	−	1.21495i
$503$	29.2592			1.30460			0.652302	−	0.757959i	$-0.273803\pi$
$503$	29.2592			1.30460			0.652302	+	0.757959i	$0.273803\pi$
$504$	−26.4043	−	66.3806i	−1.17614	−	2.95683i
$505$	−1.03713			−0.0461516
$506$		0			0
$507$	−22.3888	−	1.62622i	−0.994323	−	0.0722228i
$508$	−10.0495	−	17.4062i	−0.445873	−	0.772275i
$509$	18.3346	+	31.7565i	0.812669	+	1.40758i	0.910990	+	0.412429i	$0.135319\pi$
$509$	18.3346	+	31.7565i	0.812669	+	1.40758i	−0.0983212	+	0.995155i	$0.531347\pi$
$510$	26.7173	+	55.1553i	1.18306	+	2.44232i
$511$	−13.9387	+	24.1426i	−0.616614	+	1.06801i
$512$	−25.8799			−1.14374
$513$	−5.75159	−	1.27122i	−0.253939	−	0.0561257i
$514$	36.0785			1.59136
$515$	10.9828	−	19.0228i	0.483962	−	0.838246i
$516$	−13.6785	−	28.2380i	−0.602164	−	1.24311i
$517$		0			0
$518$	−16.0399	−	27.7820i	−0.704754	−	1.22067i
$519$	−34.0284	−	2.47166i	−1.49368	−	0.108494i
$520$	−1.53051	+	2.65092i	−0.0671172	+	0.116250i
$521$	42.0462			1.84208			0.921039	−	0.389469i	$-0.127342\pi$
$521$	42.0462			1.84208			0.921039	+	0.389469i	$0.127342\pi$
$522$	32.4752	+	4.74270i	1.42140	+	0.207582i
$523$	−36.3284			−1.58853			−0.794264	−	0.607573i	$-0.792143\pi$
$523$	−36.3284			−1.58853			−0.794264	+	0.607573i	$0.792143\pi$
$524$	−35.0770	+	60.7551i	−1.53234	+	2.65410i
$525$	−5.56145	+	8.19745i	−0.242722	+	0.357766i
$526$	−22.3831	−	38.7686i	−0.975948	−	1.69039i
$527$	−17.2644	−	29.9028i	−0.752049	−	1.30259i
$528$		0			0
$529$	9.88456	−	17.1206i	0.429763	−	0.744372i
$530$	−3.00124			−0.130365
$531$	13.4730	+	1.96761i	0.584680	+	0.0853871i
$532$	15.8128			0.685573
$533$	0.448093	−	0.776119i	0.0194091	−	0.0336175i
$534$	−54.6416	−	3.96890i	−2.36457	−	0.171751i
$535$	−0.118246	−	0.204809i	−0.00511224	−	0.00885466i
$536$	−53.0232	−	91.8388i	−2.29025	−	3.96683i
$537$	10.7897	+	22.2744i	0.465611	+	0.961209i
$538$	22.9325	−	39.7203i	0.988690	−	1.71246i
$539$		0			0
$540$	−31.5527	+	34.4782i	−1.35781	+	1.48371i
$541$	16.4772			0.708409			0.354205	−	0.935168i	$-0.384752\pi$
$541$	16.4772			0.708409			0.354205	+	0.935168i	$0.384752\pi$
$542$	38.1564	−	66.0887i	1.63896	−	2.83875i
$543$	−10.8245	−	22.3462i	−0.464525	−	0.958968i
$544$	78.6852	+	136.287i	3.37360	+	5.84325i
$545$	13.3825	+	23.1792i	0.573244	+	0.992888i
$546$	−2.42526	−	0.176159i	−0.103792	−	0.00753892i
$547$	6.74141	−	11.6765i	0.288242	−	0.499250i	−0.685148	−	0.728404i	$-0.740263\pi$
$547$	6.74141	−	11.6765i	0.288242	−	0.499250i	0.973390	+	0.229154i	$0.0735960\pi$
$548$	−58.6706			−2.50628
$549$	−0.505308	−	1.27035i	−0.0215660	−	0.0542172i
$550$		0			0
$551$	−2.28232	+	3.95310i	−0.0972302	+	0.168408i
$552$	16.0574	−	23.6683i	0.683450	−	1.00739i
$553$	15.4248	+	26.7165i	0.655929	+	1.13610i
$554$	15.5745	+	26.9758i	0.661697	+	1.14609i
$555$	−7.40364	+	10.9128i	−0.314267	+	0.463223i
$556$	36.9625	−	64.0209i	1.56756	−	2.71509i
$557$	−41.2760			−1.74892			−0.874460	−	0.485098i	$-0.838784\pi$
$557$	−41.2760			−1.74892			−0.874460	+	0.485098i	$0.838784\pi$
$558$	22.3896	−	28.3412i	0.947828	−	1.19978i
$559$	−0.671074			−0.0283834
$560$	30.7530	−	53.2657i	1.29955	−	2.25089i
$561$		0			0
$562$	17.5407	+	30.3813i	0.739909	+	1.28156i
$563$	−0.715826	−	1.23985i	−0.0301685	−	0.0522533i	0.850547	−	0.525899i	$-0.176271\pi$
$563$	−0.715826	−	1.23985i	−0.0301685	−	0.0522533i	−0.880715	+	0.473646i	$0.842938\pi$
$564$	−33.9382	−	70.0623i	−1.42906	−	2.95015i
$565$	−5.21174	+	9.02700i	−0.219260	+	0.379769i
$566$	−68.6469			−2.88545
$567$	−22.3546	−	6.67166i	−0.938805	−	0.280183i
$568$	−123.155			−5.16747
$569$	−14.6876	+	25.4396i	−0.615734	+	1.06648i	0.374521	+	0.927218i	$0.377807\pi$
$569$	−14.6876	+	25.4396i	−0.615734	+	1.06648i	−0.990255	+	0.139265i	$0.955526\pi$
$570$	−3.88695	−	8.02424i	−0.162807	−	0.336098i
$571$	11.9853	+	20.7591i	0.501569	+	0.868743i	0.999998	+	0.00181287i	$0.000577056\pi$
$571$	11.9853	+	20.7591i	0.501569	+	0.868743i	−0.498429	+	0.866930i	$0.666090\pi$
$572$		0			0
$573$	−11.5766	−	0.840870i	−0.483621	−	0.0351279i
$574$	−15.8296	+	27.4177i	−0.660715	+	1.14439i
$575$	−3.96592			−0.165390
$576$	−49.2417	+	62.3311i	−2.05174	+	2.59713i
$577$	41.8351			1.74162			0.870810	−	0.491620i	$-0.163595\pi$
$577$	41.8351			1.74162			0.870810	+	0.491620i	$0.163595\pi$
$578$	59.3834	−	102.855i	2.47002	−	4.27821i
$579$	−24.0344	+	35.4262i	−0.998836	+	1.47226i
$580$	18.1088	+	31.3654i	0.751928	+	1.30238i
$581$	−3.74916	−	6.49373i	−0.155541	−	0.269405i
$582$	−12.4914	+	18.4120i	−0.517784	+	0.763202i
$583$		0			0
$584$	98.8017			4.08844
$585$	0.369454	+	0.928811i	0.0152750	+	0.0384016i
$586$	−6.20819			−0.256458
$587$	−1.57929	+	2.73540i	−0.0651841	+	0.112902i	−0.896776	−	0.442486i	$-0.854097\pi$
$587$	−1.57929	+	2.73540i	−0.0651841	+	0.112902i	0.831592	+	0.555388i	$0.187430\pi$
$588$	−2.61219	−	0.189737i	−0.107725	−	0.00782461i
$589$	2.51170	+	4.35040i	0.103493	+	0.179255i
$590$	10.3050	+	17.8488i	0.424250	+	0.734823i
$591$	−2.39117	−	4.93635i	−0.0983597	−	0.203054i
$592$	−32.3342	+	56.0045i	−1.32893	+	2.30177i
$593$	42.1283			1.73000			0.865001	−	0.501770i	$-0.167318\pi$
$593$	42.1283			1.73000			0.865001	+	0.501770i	$0.167318\pi$
$594$		0			0
$595$	−33.7584			−1.38396
$596$	−13.4612	+	23.3155i	−0.551392	+	0.955038i
$597$	6.26881	+	12.9413i	0.256565	+	0.529654i
$598$	−0.486765	−	0.843102i	−0.0199053	−	0.0344770i
$599$	−11.4511	−	19.8340i	−0.467881	−	0.810393i	0.531445	−	0.847093i	$-0.321649\pi$
$599$	−11.4511	−	19.8340i	−0.467881	−	0.810393i	−0.999326	+	0.0366990i	$0.988316\pi$
$600$	35.0158	+	2.54338i	1.42952	+	0.103833i
$601$	−1.47861	+	2.56102i	−0.0603136	+	0.104466i	−0.894606	−	0.446857i	$-0.852543\pi$
$601$	−1.47861	+	2.56102i	−0.0603136	+	0.104466i	0.834292	+	0.551323i	$0.185877\pi$
$602$	23.7068			0.966216
$603$	−34.2666	−	5.00432i	−1.39544	−	0.203792i
$604$	98.2015			3.99576
$605$		0			0
$606$	−1.63935	+	2.41636i	−0.0665939	+	0.0981579i
$607$	−8.38100	−	14.5163i	−0.340174	−	0.589199i	0.644291	−	0.764781i	$-0.277153\pi$
$607$	−8.38100	−	14.5163i	−0.340174	−	0.589199i	−0.984465	+	0.175582i	$0.943819\pi$
$608$	−11.4475	−	19.8276i	−0.464256	−	0.804116i
$609$	−10.1496	+	14.9603i	−0.411282	+	0.606221i
$610$	1.03471	−	1.79217i	0.0418942	−	0.0725629i
$611$	−1.66502			−0.0673596
$612$	124.474	+	18.1783i	5.03157	+	0.734814i
$613$	−27.4806			−1.10993			−0.554965	−	0.831874i	$-0.687268\pi$
$613$	−27.4806			−1.10993			−0.554965	+	0.831874i	$0.687268\pi$
$614$	3.47908	−	6.02594i	0.140404	−	0.243187i
$615$	12.9801	+	0.942813i	0.523409	+	0.0380179i
$616$		0			0
$617$	17.9737	+	31.1313i	0.723592	+	1.25330i	0.959551	+	0.281535i	$0.0908436\pi$
$617$	17.9737	+	31.1313i	0.723592	+	1.25330i	−0.235959	+	0.971763i	$0.575823\pi$
$618$	−26.9604	−	55.6571i	−1.08451	−	2.23886i
$619$	−15.4945	+	26.8373i	−0.622778	+	1.07868i	0.366188	+	0.930541i	$0.380663\pi$
$619$	−15.4945	+	26.8373i	−0.622778	+	1.07868i	−0.988966	+	0.148143i	$0.952671\pi$
$620$	39.8576			1.60072
$621$	−2.81429	−	8.90583i	−0.112934	−	0.357379i
$622$	9.26700			0.371573
$623$	15.0890	−	26.1349i	0.604527	−	1.04707i
$624$	2.13696	+	4.41155i	0.0855468	+	0.176603i
$625$	4.54992	+	7.88070i	0.181997	+	0.315228i
$626$	38.0040	+	65.8248i	1.51894	+	2.63089i
$627$		0			0
$628$	8.55368	−	14.8154i	0.341329	−	0.591199i
$629$	35.4942			1.41525
$630$	−13.0516	−	32.8118i	−0.519987	−	1.30725i
$631$	17.8066			0.708868			0.354434	−	0.935081i	$-0.384674\pi$
$631$	17.8066			0.708868			0.354434	+	0.935081i	$0.384674\pi$
$632$	54.6676	−	94.6871i	2.17456	−	3.76645i
$633$	−21.8729	+	32.2402i	−0.869371	+	1.28143i
$634$	−41.7485	−	72.3106i	−1.65805	−	2.87182i
$635$	−3.12127	−	5.40620i	−0.123864	−	0.214539i
$636$	−3.45856	+	5.09784i	−0.137141	+	0.202143i
$637$	−0.0280080	+	0.0485113i	−0.00110972	+	0.00192209i
$638$		0			0
$639$	−24.9305	+	31.5576i	−0.986236	+	1.24840i
$640$	−52.7247			−2.08413
$641$	−6.42074	+	11.1210i	−0.253604	+	0.439255i	−0.964515	−	0.264027i	$-0.914949\pi$
$641$	−6.42074	+	11.1210i	−0.253604	+	0.439255i	0.710911	+	0.703282i	$0.248283\pi$
$642$	−0.664083	−	0.0482358i	−0.0262093	−	0.00190371i
$643$	−8.08421	−	14.0023i	−0.318810	−	0.552195i	0.661430	−	0.750007i	$-0.269950\pi$
$643$	−8.08421	−	14.0023i	−0.318810	−	0.552195i	−0.980240	+	0.197812i	$0.936617\pi$
$644$	12.5365	+	21.7139i	0.494009	+	0.855648i
$645$	−4.24843	−	8.77048i	−0.167282	−	0.345337i
$646$	−11.9991	+	20.7830i	−0.472098	+	0.817697i
$647$	0.875926			0.0344362			0.0172181	−	0.999852i	$-0.494519\pi$
$647$	0.875926			0.0344362			0.0172181	+	0.999852i	$0.494519\pi$
$648$	19.1365	+	80.4360i	0.751753	+	3.15982i
$649$		0			0
$650$	0.597505	−	1.03491i	0.0234361	−	0.0405925i
$651$	8.67327	+	17.9051i	0.339932	+	0.701757i
$652$	40.4671	+	70.0911i	1.58482	+	2.74498i
$653$	−15.8631	−	27.4757i	−0.620771	−	1.07521i	−0.989342	−	0.145607i	$-0.953486\pi$
$653$	−15.8631	−	27.4757i	−0.620771	−	1.07521i	0.368572	−	0.929599i	$-0.379847\pi$
$654$	75.1575	+	5.45907i	2.93889	+	0.213467i
$655$	−10.8946	+	18.8700i	−0.425687	+	0.737311i
$656$	63.8205			2.49177
$657$	20.0006	−	25.3172i	0.780299	−	0.987718i
$658$	58.8196			2.29303
$659$	−5.99686	+	10.3869i	−0.233605	+	0.404615i	−0.958866	−	0.283858i	$-0.908385\pi$
$659$	−5.99686	+	10.3869i	−0.233605	+	0.404615i	0.725262	+	0.688473i	$0.241719\pi$
$660$		0			0
$661$	11.9234	+	20.6520i	0.463768	+	0.803270i	0.999145	−	0.0413433i	$-0.0131637\pi$
$661$	11.9234	+	20.6520i	0.463768	+	0.803270i	−0.535377	+	0.844613i	$0.679830\pi$
$662$	−8.12011	−	14.0644i	−0.315597	−	0.546630i
$663$	1.51049	−	2.22643i	0.0586626	−	0.0864674i
$664$	−13.2875	+	23.0147i	−0.515656	+	0.893143i
$665$	4.91132			0.190453
$666$	13.7226	+	34.4989i	0.531742	+	1.33680i
$667$	−7.23777			−0.280248
$668$	6.19786	−	10.7350i	0.239802	−	0.415350i
$669$	21.8864	+	1.58972i	0.846176	+	0.0614621i
$670$	−26.2092	−	45.3957i	−1.01255	−	1.75379i
$671$		0			0
$672$	−39.5298	−	81.6054i	−1.52489	−	3.14800i
$673$	−16.4861	+	28.5547i	−0.635491	+	1.10070i	0.350920	+	0.936406i	$0.385869\pi$
$673$	−16.4861	+	28.5547i	−0.635491	+	1.10070i	−0.986411	+	0.164297i	$0.947464\pi$
$674$	−3.57245			−0.137606
$675$	7.74005	−	8.45769i	0.297915	−	0.325537i
$676$	−69.7441			−2.68247
$677$	−13.2643	+	22.9745i	−0.509789	+	0.882980i	0.490147	+	0.871640i	$0.336943\pi$
$677$	−13.2643	+	22.9745i	−0.509789	+	0.882980i	−0.999936	+	0.0113405i	$0.996390\pi$
$678$	12.7936	+	26.4112i	0.491337	+	1.01432i
$679$	−6.12789	−	10.6138i	−0.235167	−	0.407321i
$680$	59.8222	+	103.615i	2.29408	+	3.97346i
$681$	9.84020	+	0.714744i	0.377077	+	0.0273890i
$682$		0			0
$683$	17.4229			0.666669			0.333334	−	0.942809i	$-0.391826\pi$
$683$	17.4229			0.666669			0.333334	+	0.942809i	$0.391826\pi$
$684$	−18.1090	−	2.64466i	−0.692416	−	0.101121i
$685$	−18.2225			−0.696247
$686$	25.6379	−	44.4061i	0.978859	−	1.69543i
$687$	6.54288	−	9.64406i	0.249626	−	0.367944i
$688$	−23.8948	−	41.3869i	−0.910979	−	1.57786i
$689$	0.0658777	+	0.114104i	0.00250974	+	0.00434700i
$690$	7.93715	−	11.6992i	0.302162	−	0.445380i
$691$	−21.7319	+	37.6408i	−0.826721	+	1.43192i	0.0738765	+	0.997267i	$0.476463\pi$
$691$	−21.7319	+	37.6408i	−0.826721	+	1.43192i	−0.900597	+	0.434655i	$0.856870\pi$
$692$	−106.003			−4.02962
$693$		0			0
$694$	−48.7292			−1.84973
$695$	11.4802	−	19.8843i	0.435469	−	0.754254i
$696$	63.9036	+	4.64164i	2.42226	+	0.175941i
$697$	−17.5144	−	30.3358i	−0.663405	−	1.14905i
$698$	−34.9433	−	60.5236i	−1.32262	−	2.29085i
$699$	−5.00131	−	10.3247i	−0.189167	−	0.390517i
$700$	−15.3886	+	26.6539i	−0.581635	+	1.00742i
$701$	−16.2104			−0.612258			−0.306129	−	0.951990i	$-0.599034\pi$
$701$	−16.2104			−0.612258			−0.306129	+	0.951990i	$0.599034\pi$
$702$	2.74798	+	0.607360i	0.103716	+	0.0229233i
$703$	−5.16385			−0.194758
$704$		0			0
$705$	−10.5409	−	21.7607i	−0.396994	−	0.819555i
$706$	−27.0420	−	46.8381i	−1.01774	−	1.76277i
$707$	−0.804215	−	1.39294i	−0.0302456	−	0.0523870i
$708$	42.1928	+	3.06468i	1.58570	+	0.115178i
$709$	−4.56049	+	7.89900i	−0.171273	+	0.296653i	−0.938865	−	0.344285i	$-0.888121\pi$
$709$	−4.56049	+	7.89900i	−0.171273	+	0.296653i	0.767592	+	0.640938i	$0.221455\pi$
$710$	−60.8752			−2.28460
$711$	−13.1964	−	33.1759i	−0.494904	−	1.24419i
$712$	−106.955			−4.00830
$713$	−3.98260	+	6.89806i	−0.149149	+	0.258334i
$714$	−53.3605	+	78.6522i	−1.99697	+	2.94349i
$715$		0			0
$716$	38.4485	+	66.5947i	1.43689	+	2.48876i
$717$	4.55092	−	6.70796i	0.169957	−	0.250513i
$718$	39.6907	−	68.7463i	1.48124	−	2.56559i
$719$	30.5511			1.13936			0.569682	−	0.821865i	$-0.307066\pi$
$719$	30.5511			1.13936			0.569682	+	0.821865i	$0.307066\pi$
$720$	−44.1272	+	55.8572i	−1.64452	+	2.08167i
$721$	34.0655			1.26867
$722$	−24.0646	+	41.6811i	−0.895591	+	1.55121i
$723$	6.55873	+	0.476394i	0.243922	+	0.0177173i
$724$	−38.5725	−	66.8096i	−1.43354	−	2.48296i
$725$	−4.44219	−	7.69410i	−0.164979	−	0.285752i
$726$		0			0
$727$	−8.34868	+	14.4603i	−0.309635	+	0.536304i	−0.978283	−	0.207276i	$-0.933540\pi$
$727$	−8.34868	+	14.4603i	−0.309635	+	0.536304i	0.668647	+	0.743580i	$0.266874\pi$
$728$	−4.74718			−0.175942
$729$	24.4850	+	11.3792i	0.906850	+	0.421453i
$730$	48.8374			1.80755
$731$	−13.1150	+	22.7158i	−0.485075	+	0.840174i
$732$	−1.85177	−	3.82280i	−0.0684433	−	0.141295i
$733$	16.1822	+	28.0283i	0.597702	+	1.03525i	0.993159	+	0.116766i	$0.0372528\pi$
$733$	16.1822	+	28.0283i	0.597702	+	1.03525i	−0.395457	+	0.918484i	$0.629414\pi$
$734$	23.2940	+	40.3464i	0.859797	+	1.48921i
$735$	−0.811322	−	0.0589305i	−0.0299261	−	0.00217368i
$736$	18.1513	−	31.4390i	0.669066	−	1.15886i
$737$		0			0
$738$	22.7138	−	28.7516i	0.836106	−	1.05836i
$739$	27.6489			1.01708			0.508541	−	0.861038i	$-0.330185\pi$
$739$	27.6489			1.01708			0.508541	+	0.861038i	$0.330185\pi$
$740$	−20.4860	+	35.4828i	−0.753080	+	1.30437i
$741$	−0.219753	+	0.323911i	−0.00807282	+	0.0118992i
$742$	−2.32724	−	4.03089i	−0.0854356	−	0.147979i
$743$	−3.42693	−	5.93562i	−0.125722	−	0.217757i	0.796293	−	0.604911i	$-0.206791\pi$
$743$	−3.42693	−	5.93562i	−0.125722	−	0.217757i	−0.922015	+	0.387154i	$0.873458\pi$
$744$	39.5868	−	58.3501i	1.45132	−	2.13922i
$745$	−4.18092	+	7.24157i	−0.153177	+	0.265310i
$746$	54.9937			2.01346
$747$	3.20752	+	8.06374i	0.117357	+	0.295037i
$748$		0			0
$749$	0.183383	−	0.317628i	0.00670066	−	0.0116059i
$750$	56.5311	+	4.10614i	2.06422	+	0.149935i
$751$	−11.4092	−	19.7613i	−0.416327	−	0.721099i	0.579240	−	0.815157i	$-0.303349\pi$
$751$	−11.4092	−	19.7613i	−0.416327	−	0.721099i	−0.995567	+	0.0940582i	$0.970016\pi$
$752$	−59.2860	−	102.686i	−2.16194	−	3.74459i
$753$	−8.73585	−	18.0343i	−0.318352	−	0.657207i
$754$	1.09044	−	1.88870i	0.0397115	−	0.0687824i
$755$	30.5005			1.11003
$756$	−70.7737	−	15.6424i	−2.57401	−	0.568909i
$757$	−2.07971			−0.0755884			−0.0377942	−	0.999286i	$-0.512033\pi$
$757$	−2.07971			−0.0755884			−0.0377942	+	0.999286i	$0.512033\pi$
$758$	−27.3168	+	47.3140i	−0.992190	+	1.71852i
$759$		0			0
$760$	−8.70319	−	15.0744i	−0.315698	−	0.546805i
$761$	10.9223	+	18.9179i	0.395931	+	0.685773i	0.993220	−	0.116253i	$-0.0370884\pi$
$761$	10.9223	+	18.9179i	0.395931	+	0.685773i	−0.597288	+	0.802027i	$0.703755\pi$
$762$	−17.5294	−	1.27325i	−0.635022	−	0.0461249i
$763$	−20.7543	+	35.9475i	−0.751356	+	1.30139i
$764$	−36.0627			−1.30470
$765$	38.6605	+	5.64601i	1.39777	+	0.204132i
$766$	57.8920			2.09172
$767$	0.452393	−	0.783568i	0.0163350	−	0.0282930i
$768$	−31.8440	+	46.9374i	−1.14907	+	1.69371i
$769$	−1.78408	−	3.09013i	−0.0643357	−	0.111433i	0.832063	−	0.554681i	$-0.187160\pi$
$769$	−1.78408	−	3.09013i	−0.0643357	−	0.111433i	−0.896399	+	0.443248i	$0.853826\pi$
$770$		0			0
$771$	12.9132	−	19.0337i	0.465056	−	0.685482i
$772$	−66.5036	+	115.188i	−2.39352	+	4.14569i
$773$	−9.24340			−0.332462			−0.166231	−	0.986087i	$-0.553160\pi$
$773$	−9.24340			−0.332462			−0.166231	+	0.986087i	$0.553160\pi$
$774$	−27.1493	−	3.96490i	−0.975861	−	0.142515i
$775$	−9.77729			−0.351211
$776$	−21.7181	+	37.6169i	−0.779634	+	1.35037i
$777$	−20.3977	−	1.48159i	−0.731764	−	0.0531517i
$778$	46.9236	+	81.2741i	1.68229	+	2.91382i
$779$	2.54807	+	4.41339i	0.0912941	+	0.158126i
$780$	1.35391	+	2.79502i	0.0484779	+	0.100078i
$781$		0			0
$782$	−38.0519			−1.36073
$783$	14.1255	−	15.4352i	0.504805	−	0.551609i
$784$	−3.98910			−0.142468
$785$	2.65670	−	4.60153i	0.0948215	−	0.164236i
$786$	26.7437	+	55.2099i	0.953917	+	1.96927i
$787$	7.35288	+	12.7356i	0.262102	+	0.453974i	0.966800	−	0.255533i	$-0.0822510\pi$
$787$	7.35288	+	12.7356i	0.262102	+	0.453974i	−0.704698	+	0.709507i	$0.748918\pi$
$788$	−8.52079	−	14.7584i	−0.303541	−	0.525748i
$789$	−28.4642	−	2.06750i	−1.01335	−	0.0736049i
$790$	27.0221	−	46.8036i	0.961402	−	1.66520i
$791$	−16.1653			−0.574771
$792$		0			0
$793$	−0.0908484			−0.00322612
$794$	−3.54908	+	6.14718i	−0.125952	+	0.218155i
$795$	−1.07420	+	1.58334i	−0.0380978	+	0.0561554i
$796$	22.3385	+	38.6914i	0.791767	+	1.37138i
$797$	10.5634	+	18.2964i	0.374176	+	0.648092i	0.990203	−	0.139633i	$-0.0445923\pi$
$797$	10.5634	+	18.2964i	0.374176	+	0.648092i	−0.616027	+	0.787725i	$0.711259\pi$
$798$	7.76312	−	11.4427i	0.274812	−	0.405066i
$799$	−32.5400	+	56.3609i	−1.15118	+	1.99390i
$800$	44.5615			1.57549
$801$	−21.6511	+	27.4064i	−0.765003	+	0.968356i
$802$	−27.8534			−0.983539
$803$		0			0
$804$	−107.311	−	7.79455i	−3.78457	−	0.274893i
$805$	3.89373	+	6.74414i	0.137236	+	0.237700i
$806$	−1.20003	−	2.07852i	−0.0422694	−	0.0732127i
$807$	−12.7470	−	26.3149i	−0.448715	−	0.926329i
$808$	−2.85025	+	4.93678i	−0.100271	+	0.173675i
$809$	−29.6574			−1.04270			−0.521349	−	0.853344i	$-0.674571\pi$
$809$	−29.6574			−1.04270			−0.521349	+	0.853344i	$0.674571\pi$
$810$	9.45912	+	39.7593i	0.332360	+	1.39700i
$811$	6.19031			0.217371			0.108686	−	0.994076i	$-0.465336\pi$
$811$	6.19031			0.217371			0.108686	+	0.994076i	$0.465336\pi$
$812$	−28.0841	+	48.6431i	−0.985559	+	1.70704i
$813$	−21.2091	−	43.7842i	−0.743837	−	1.53558i
$814$		0			0
$815$	12.5687	+	21.7697i	0.440263	+	0.762558i
$816$	191.094	+	13.8801i	6.68962	+	0.485901i
$817$	1.90802	−	3.30479i	0.0667533	−	0.115620i
$818$	−10.7713			−0.376608
$819$	−0.960980	+	1.21643i	−0.0335794	+	0.0425055i
$820$	40.4348			1.41204
$821$	10.6296	−	18.4109i	0.370974	−	0.642546i	−0.618742	−	0.785595i	$-0.712357\pi$
$821$	10.6296	−	18.4109i	0.370974	−	0.642546i	0.989716	+	0.143049i	$0.0456906\pi$
$822$	−28.8036	+	42.4559i	−1.00464	+	1.48082i
$823$	20.0091	+	34.6568i	0.697474	+	1.20806i	0.969340	+	0.245725i	$0.0790259\pi$
$823$	20.0091	+	34.6568i	0.697474	+	1.20806i	−0.271866	+	0.962335i	$0.587641\pi$
$824$	−60.3664	−	104.558i	−2.10296	−	3.64244i
$825$		0			0
$826$	−15.9815	+	27.6808i	−0.556068	+	0.963138i
$827$	−22.0260			−0.765919			−0.382960	−	0.923765i	$-0.625095\pi$
$827$	−22.0260			−0.765919			−0.382960	+	0.923765i	$0.625095\pi$
$828$	−10.7254	−	26.9638i	−0.372733	−	0.937055i
$829$	−30.6206			−1.06350			−0.531749	−	0.846902i	$-0.678465\pi$
$829$	−30.6206			−1.06350			−0.531749	+	0.846902i	$0.678465\pi$
$830$	−6.56799	+	11.3761i	−0.227978	+	0.394870i
$831$	19.8058	+	1.43860i	0.687057	+	0.0499044i
$832$	2.63925	+	4.57131i	0.0914994	+	0.158482i
$833$	1.09474	+	1.89614i	0.0379304	+	0.0656973i
$834$	−28.1813	−	58.1776i	−0.975838	−	2.01452i
$835$	1.92500	−	3.33419i	0.0666173	−	0.115385i
$836$		0			0
$837$	−6.93814	−	21.9558i	−0.239817	−	0.758902i
$838$	−89.0506			−3.07620
$839$	−4.32169	+	7.48538i	−0.149201	+	0.258424i	−0.930932	−	0.365191i	$-0.881004\pi$
$839$	−4.32169	+	7.48538i	−0.149201	+	0.258424i	0.781731	+	0.623615i	$0.214337\pi$
$840$	−30.0534	−	62.0423i	−1.03694	−	2.14066i
$841$	6.39304	+	11.0731i	0.220450	+	0.381830i
$842$	−51.0665	−	88.4498i	−1.75987	−	3.04818i
$843$	22.3062	+	1.62021i	0.768266	+	0.0558031i
$844$	−60.5227	+	104.828i	−2.08328	+	3.60834i
$845$	−21.6619			−0.745191
$846$	−67.3609	−	9.83744i	−2.31592	−	0.338218i
$847$		0			0
$848$	−4.69138	+	8.12572i	−0.161103	+	0.279038i
$849$	−24.5700	+	36.2156i	−0.843239	+	1.24292i
$850$	−23.3544	−	40.4510i	−0.801049	−	1.38746i
$851$	−4.09394	−	7.09092i	−0.140339	−	0.243073i
$852$	−70.1512	+	103.401i	−2.40334	+	3.54247i
$853$	−2.62208	+	4.54158i	−0.0897784	+	0.155501i	−0.907417	−	0.420231i	$-0.861949\pi$
$853$	−2.62208	+	4.54158i	−0.0897784	+	0.155501i	0.817639	+	0.575731i	$0.195283\pi$
$854$	3.20936			0.109822
$855$	−5.62450	−	0.821406i	−0.192354	−	0.0280915i
$856$	−1.29987			−0.0444285
$857$	11.2020	−	19.4024i	0.382653	−	0.662774i	−0.608788	−	0.793333i	$-0.708344\pi$
$857$	11.2020	−	19.4024i	0.382653	−	0.662774i	0.991441	+	0.130559i	$0.0416772\pi$
$858$		0			0
$859$	−0.190301	−	0.329611i	−0.00649299	−	0.0112462i	0.862761	−	0.505613i	$-0.168733\pi$
$859$	−0.190301	−	0.329611i	−0.00649299	−	0.0112462i	−0.869254	+	0.494366i	$0.835400\pi$
$860$	−15.1390	−	26.2215i	−0.516236	−	0.894147i
$861$	8.79885	+	18.1644i	0.299864	+	0.619041i
$862$	−40.7884	+	70.6476i	−1.38926	+	2.40627i
$863$	14.6703			0.499382			0.249691	−	0.968326i	$-0.419671\pi$
$863$	14.6703			0.499382			0.249691	+	0.968326i	$0.419671\pi$
$864$	31.6217	+	100.067i	1.07579	+	3.40434i
$865$	−32.9235			−1.11943
$866$	24.1907	−	41.8996i	0.822034	−	1.42380i
$867$	−33.0081	−	68.1421i	−1.12102	−	2.31423i
$868$	30.9066	+	53.5319i	1.04904	+	1.81699i
$869$		0			0
$870$	31.5874	+	2.29435i	1.07091	+	0.0777858i
$871$	−1.15059	+	1.99289i	−0.0389864	+	0.0675264i
$872$	147.112			4.98185
$873$	5.24260	+	13.1800i	0.177435	+	0.446074i
$874$	5.53596			0.187257
$875$	−15.6107	+	27.0386i	−0.527739	+	0.914071i
$876$	56.2791	−	82.9542i	1.90150	−	2.80276i
$877$	−13.8909	−	24.0597i	−0.469061	−	0.812438i	0.530313	−	0.847802i	$-0.322074\pi$
$877$	−13.8909	−	24.0597i	−0.469061	−	0.812438i	−0.999375	+	0.0353638i	$0.988741\pi$
$878$	−3.17943	−	5.50694i	−0.107301	−	0.185850i
$879$	−2.22202	+	3.27521i	−0.0749469	+	0.110470i
$880$		0			0
$881$	12.5329			0.422243			0.211122	−	0.977460i	$-0.432288\pi$
$881$	12.5329			0.422243			0.211122	+	0.977460i	$0.432288\pi$
$882$	−1.41972	+	1.79712i	−0.0478046	+	0.0605121i
$883$	−51.2943			−1.72619			−0.863095	−	0.505042i	$-0.831477\pi$
$883$	−51.2943			−1.72619			−0.863095	+	0.505042i	$0.831477\pi$
$884$	4.17955	−	7.23920i	0.140574	−	0.243481i
$885$	13.1047	+	0.951862i	0.440510	+	0.0319965i
$886$	8.70317	+	15.0743i	0.292389	+	0.506432i
$887$	1.28108	+	2.21890i	0.0430146	+	0.0745034i	0.886731	−	0.462286i	$-0.152970\pi$
$887$	1.28108	+	2.21890i	0.0430146	+	0.0745034i	−0.843717	+	0.536789i	$0.819637\pi$
$888$	31.5987	+	65.2324i	1.06038	+	2.18906i
$889$	4.84063	−	8.38421i	0.162349	−	0.281197i
$890$	−52.8674			−1.77212
$891$		0			0
$892$	68.1789			2.28280
$893$	4.73406	−	8.19963i	0.158419	−	0.274390i
$894$	10.2632	+	21.1874i	0.343253	+	0.708613i
$895$	11.9417	+	20.6837i	0.399169	+	0.691380i
$896$	−40.8841	−	70.8134i	−1.36584	−	2.36571i
$897$	−0.619011	−	0.0449620i	−0.0206682	−	0.00150124i
$898$	29.5700	−	51.2167i	0.986763	−	1.70912i
$899$	−17.8435			−0.595113
$900$	22.0810	−	27.9506i	0.736035	−	0.931688i
$901$	5.14986			0.171567
$902$		0			0
$903$	8.48508	−	12.5068i	0.282366	−	0.416201i
$904$	28.6460	+	49.6163i	0.952751	+	1.65021i
$905$	−11.9803	−	20.7504i	−0.398238	−	0.689768i
$906$	48.2109	−	71.0618i	1.60170	−	2.36087i
$907$	−23.9715	+	41.5198i	−0.795960	+	1.37864i	0.126268	+	0.991996i	$0.459700\pi$
$907$	−23.9715	+	41.5198i	−0.795960	+	1.37864i	−0.922228	+	0.386647i	$0.873633\pi$
$908$	30.6535			1.01727
$909$	0.688031	+	1.72972i	0.0228205	+	0.0573711i
$910$	−2.34652			−0.0777862
$911$	−27.2103	+	47.1296i	−0.901517	+	1.56147i	−0.0759919	+	0.997108i	$0.524212\pi$
$911$	−27.2103	+	47.1296i	−0.901517	+	1.56147i	−0.825525	+	0.564365i	$0.809121\pi$
$912$	−27.8011	−	2.01934i	−0.920588	−	0.0668670i
$913$		0			0
$914$	−9.70232	−	16.8049i	−0.320924	−	0.555857i
$915$	−0.575142	−	1.18733i	−0.0190136	−	0.0392518i
$916$	18.1043	−	31.3575i	0.598181	−	1.03608i
$917$	−33.7918			−1.11590
$918$	74.2635	−	81.1491i	2.45106	−	2.67832i
$919$	−3.69832			−0.121996			−0.0609982	−	0.998138i	$-0.519428\pi$
$919$	−3.69832			−0.121996			−0.0609982	+	0.998138i	$0.519428\pi$
$920$	13.7999	−	23.9022i	0.454970	−	0.788031i
$921$	−1.93384	−	3.99223i	−0.0637222	−	0.131548i
$922$	3.92288	+	6.79464i	0.129193	+	0.223769i
$923$	1.33622	+	2.31440i	0.0439823	+	0.0761795i
$924$		0			0
$925$	5.02532	−	8.70411i	0.165232	−	0.286189i
$926$	−3.94511			−0.129644
$927$	−39.0122	−	5.69737i	−1.28133	−	0.187126i
$928$	81.3244			2.66960
$929$	12.9204	−	22.3787i	0.423903	−	0.734222i	−0.572414	−	0.819965i	$-0.693993\pi$
$929$	12.9204	−	22.3787i	0.423903	−	0.734222i	0.996317	+	0.0857426i	$0.0273263\pi$
$930$	19.5677	−	28.8423i	0.641649	−	0.945776i
$931$	−0.159267	−	0.275859i	−0.00521977	−	0.00904090i
$932$	−17.8219	−	30.8684i	−0.583774	−	1.01113i
$933$	3.31682	−	4.88893i	0.108588	−	0.160056i
$934$	7.47521	−	12.9474i	0.244596	−	0.423653i
$935$		0			0
$936$	5.43652	+	0.793954i	0.177698	+	0.0259512i
$937$	28.1689			0.920239			0.460120	−	0.887857i	$-0.347806\pi$
$937$	28.1689			0.920239			0.460120	+	0.887857i	$0.347806\pi$
$938$	40.6466	−	70.4019i	1.32716	−	2.29870i
$939$	48.3290	+	3.51039i	1.57716	+	0.114557i
$940$	−37.5619	−	65.0590i	−1.22513	−	2.12199i
$941$	−15.2435	−	26.4026i	−0.496925	−	0.860700i	0.503068	−	0.864247i	$-0.332204\pi$
$941$	−15.2435	−	26.4026i	−0.496925	−	0.860700i	−0.999994	+	0.00354657i	$0.998871\pi$
$942$	−6.52158	−	13.4632i	−0.212485	−	0.438654i
$943$	−4.04026	+	6.99794i	−0.131569	+	0.227884i
$944$	64.4330			2.09712
$945$	−21.9817	−	4.85839i	−0.715063	−	0.158044i
$946$		0			0
$947$	27.4071	−	47.4705i	0.890611	−	1.54258i	0.0514664	−	0.998675i	$-0.483610\pi$
$947$	27.4071	−	47.4705i	0.890611	−	1.54258i	0.839144	−	0.543909i	$-0.183056\pi$
$948$	−48.3600	−	99.8345i	−1.57066	−	3.24247i
$949$	−1.07199	−	1.85674i	−0.0347983	−	0.0602724i
$950$	3.39770	+	5.88499i	0.110236	+	0.190934i
$951$	−53.0909	−	3.85627i	−1.72159	−	0.125048i
$952$	−92.7753	+	160.691i	−3.00686	+	5.20804i
$953$	−38.8502			−1.25848			−0.629240	−	0.777211i	$-0.716634\pi$
$953$	−38.8502			−1.25848			−0.629240	+	0.777211i	$0.716634\pi$
$954$	1.99102	+	5.00545i	0.0644618	+	0.162058i
$955$	−11.2007			−0.362448
$956$	12.5925	−	21.8108i	0.407270	−	0.705412i
$957$		0			0
$958$	−14.2023	−	24.5991i	−0.458855	−	0.794759i
$959$	−14.1302	−	24.4743i	−0.456289	−	0.790315i
$960$	−43.0353	+	63.4331i	−1.38896	+	2.04730i
$961$	5.68161	−	9.84083i	0.183278	−	0.317446i
$962$	2.46717			0.0795448
$963$	−0.263135	+	0.333081i	−0.00847940	+	0.0107334i
$964$	20.4313			0.658047
$965$	−20.6554	+	35.7762i	−0.664921	+	1.15168i
$966$	21.8676	+	1.58835i	0.703577	+	0.0511044i
$967$	−12.9249	−	22.3865i	−0.415636	−	0.719903i	0.579859	−	0.814717i	$-0.303108\pi$
$967$	−12.9249	−	22.3865i	−0.415636	−	0.719903i	−0.995495	+	0.0948141i	$0.969774\pi$
$968$		0			0
$969$	6.66967	+	13.7689i	0.214261	+	0.442320i
$970$	−10.7352	+	18.5939i	−0.344686	+	0.597014i
$971$	14.7459			0.473219			0.236609	−	0.971605i	$-0.423964\pi$
$971$	14.7459			0.473219			0.236609	+	0.971605i	$0.423964\pi$
$972$	78.4347	+	29.7506i	2.51579	+	0.954252i
$973$	35.6082			1.14155
$974$	7.74129	−	13.4083i	0.248047	−	0.429630i
$975$	−0.332122	−	0.685634i	−0.0106364	−	0.0219579i
$976$	−3.23481	−	5.60286i	−0.103544	−	0.179343i
$977$	−18.8198	−	32.5968i	−0.602099	−	1.04287i	−0.992503	−	0.122222i	$-0.960998\pi$
$977$	−18.8198	−	32.5968i	−0.602099	−	1.04287i	0.390404	−	0.920644i	$-0.372335\pi$
$978$	70.5871	+	5.12710i	2.25713	+	0.163947i
$979$		0			0
$980$	−2.52737			−0.0807340
$981$	29.7802	−	37.6964i	0.950809	−	1.20355i
$982$	22.5510			0.719631
$983$	−3.21486	+	5.56830i	−0.102538	+	0.177601i	−0.912730	−	0.408564i	$-0.866030\pi$
$983$	−3.21486	+	5.56830i	−0.102538	+	0.177601i	0.810192	+	0.586165i	$0.199363\pi$
$984$	40.1600	−	59.1950i	1.28025	−	1.88707i
$985$	−2.64648	−	4.58384i	−0.0843238	−	0.146053i
$986$	−42.6216	−	73.8227i	−1.35735	−	2.35099i
$987$	21.0526	−	31.0310i	0.670111	−	0.987729i
$988$	−0.608060	+	1.05319i	−0.0193450	+	0.0335064i
$989$	6.05079			0.192404
$990$		0			0
$991$	35.1704			1.11722			0.558612	−	0.829429i	$-0.311334\pi$
$991$	35.1704			1.11722			0.558612	+	0.829429i	$0.311334\pi$
$992$	44.7489	−	77.5073i	1.42078	−	2.46086i
$993$	−10.3262	−	0.750045i	−0.327692	−	0.0238020i
$994$	−47.2042	−	81.7600i	−1.49723	−	2.59327i
$995$	6.93813	+	12.0172i	0.219954	+	0.380971i
$996$	11.7544	+	24.2658i	0.372452	+	0.768891i
$997$	0.0643563	−	0.111468i	0.00203818	−	0.00353024i	−0.865005	−	0.501764i	$-0.832685\pi$
$997$	0.0643563	−	0.111468i	0.00203818	−	0.00353024i	0.867043	+	0.498234i	$0.166018\pi$
$998$	−37.7787			−1.19587
$999$	23.1119	+	5.10820i	0.731229	+	0.161616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.l.727.10	yes	20
9.2	odd	6		9801.2.a.cb.1.10		10
9.4	even	3	inner	1089.2.e.l.364.10	✓	20
9.7	even	3		9801.2.a.cd.1.1		10
11.10	odd	2		1089.2.e.m.727.1	yes	20
99.43	odd	6		9801.2.a.ce.1.10		10
99.65	even	6		9801.2.a.cc.1.1		10
99.76	odd	6		1089.2.e.m.364.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1089.2.e.l.364.10	✓	20	9.4	even	3	inner
1089.2.e.l.727.10	yes	20	1.1	even	1	trivial
1089.2.e.m.364.1	yes	20	99.76	odd	6
1089.2.e.m.727.1	yes	20	11.10	odd	2
9801.2.a.cb.1.10		10	9.2	odd	6
9801.2.a.cc.1.1		10	99.65	even	6
9801.2.a.cd.1.1		10	9.7	even	3
9801.2.a.ce.1.10		10	99.43	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.35844 - 2.35288i) q^{2} +(-0.755083 - 1.55880i) q^{3} +(-2.69069 - 4.66041i) q^{4} +(-0.835704 - 1.44748i) q^{5} +(-4.69339 - 0.340905i) q^{6} +(1.29605 - 2.24483i) q^{7} -9.18678 q^{8} +(-1.85970 + 2.35404i) q^{9} +O(q^{10})\)	\(q+(1.35844 - 2.35288i) q^{2} +(-0.755083 - 1.55880i) q^{3} +(-2.69069 - 4.66041i) q^{4} +(-0.835704 - 1.44748i) q^{5} +(-4.69339 - 0.340905i) q^{6} +(1.29605 - 2.24483i) q^{7} -9.18678 q^{8} +(-1.85970 + 2.35404i) q^{9} -4.54100 q^{10} +(-5.23294 + 7.71324i) q^{12} +(0.0996757 + 0.172643i) q^{13} +(-3.52121 - 6.09891i) q^{14} +(-1.62530 + 2.39566i) q^{15} +(-7.09826 + 12.2945i) q^{16} +7.79195 q^{17} +(3.01250 + 7.57346i) q^{18} -1.13361 q^{19} +(-4.49724 + 7.78945i) q^{20} +(-4.47786 - 0.325250i) q^{21} +(-0.898734 - 1.55665i) q^{23} +(6.93678 + 14.3203i) q^{24} +(1.10320 - 1.91079i) q^{25} +0.541612 q^{26} +(5.07370 + 1.12139i) q^{27} -13.9491 q^{28} +(2.01333 - 3.48718i) q^{29} +(3.42883 + 7.07850i) q^{30} +(-2.21567 - 3.83765i) q^{31} +(10.0983 + 17.4907i) q^{32} +(10.5849 - 18.3335i) q^{34} -4.33247 q^{35} +(15.9747 + 2.33296i) q^{36} +4.55523 q^{37} +(-1.53993 + 2.66724i) q^{38} +(0.193853 - 0.285735i) q^{39} +(7.67743 + 13.2977i) q^{40} +(-2.24775 - 3.89322i) q^{41} +(-6.84816 + 10.0940i) q^{42} +(-1.68314 + 2.91529i) q^{43} +(4.96159 + 0.724595i) q^{45} -4.88349 q^{46} +(-4.17610 + 7.23321i) q^{47} +(24.5245 + 1.78134i) q^{48} +(0.140496 + 0.243346i) q^{49} +(-2.99724 - 5.19138i) q^{50} +(-5.88358 - 12.1461i) q^{51} +(0.536393 - 0.929061i) q^{52} +0.660920 q^{53} +(9.53080 - 10.4145i) q^{54} +(-11.9065 + 20.6227i) q^{56} +(0.855969 + 1.76706i) q^{57} +(-5.46994 - 9.47422i) q^{58} +(-2.26932 - 3.93059i) q^{59} +(15.5380 + 1.12860i) q^{60} +(-0.227860 + 0.394665i) q^{61} -12.0394 q^{62} +(2.87416 + 7.22567i) q^{63} +26.4783 q^{64} +(0.166599 - 0.288558i) q^{65} +(5.77168 + 9.99685i) q^{67} +(-20.9657 - 36.3137i) q^{68} +(-1.74789 + 2.57635i) q^{69} +(-5.88537 + 10.1938i) q^{70} +13.4057 q^{71} +(17.0846 - 21.6261i) q^{72} -10.7548 q^{73} +(6.18799 - 10.7179i) q^{74} +(-3.81155 - 0.276852i) q^{75} +(3.05019 + 5.28308i) q^{76} +(-0.408962 - 0.844263i) q^{78} +(-5.95069 + 10.3069i) q^{79} +23.7282 q^{80} +(-2.08305 - 8.75562i) q^{81} -12.2137 q^{82} +(1.44638 - 2.50520i) q^{83} +(10.5327 + 21.7438i) q^{84} +(-6.51177 - 11.2787i) q^{85} +(4.57288 + 7.92046i) q^{86} +(-6.95604 - 0.505253i) q^{87} +11.6422 q^{89} +(8.44489 - 10.6897i) q^{90} +0.516740 q^{91} +(-4.83643 + 8.37694i) q^{92} +(-4.30911 + 6.35153i) q^{93} +(11.3459 + 19.6517i) q^{94} +(0.947361 + 1.64088i) q^{95} +(19.6394 - 28.9481i) q^{96} +(2.36406 - 4.09467i) q^{97} +0.763417 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{3} - 10 q^{4} - 3 q^{5} - 10 q^{6} + q^{7} + 6 q^{8} + q^{9}+O(q^{10}) \) 20 * q - q^3 - 10 * q^4 - 3 * q^5 - 10 * q^6 + q^7 + 6 * q^8 + q^9	\( 20 q - q^{3} - 10 q^{4} - 3 q^{5} - 10 q^{6} + q^{7} + 6 q^{8} + q^{9} - 5 q^{12} + q^{13} - 15 q^{14} - 7 q^{15} - 10 q^{16} + 6 q^{17} - 17 q^{18} + 4 q^{19} - 15 q^{20} - 4 q^{21} - 18 q^{23} + 27 q^{24} - 7 q^{25} + 12 q^{26} + 23 q^{27} - 8 q^{28} + 12 q^{29} + 26 q^{30} + 7 q^{31} + 24 q^{32} + 6 q^{34} + 36 q^{35} + 20 q^{36} - 2 q^{37} + 12 q^{38} - 4 q^{39} - 12 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 35 q^{45} - 36 q^{46} - 27 q^{47} + 19 q^{48} - 15 q^{49} + 15 q^{50} + 2 q^{51} - 5 q^{52} + 12 q^{53} + 44 q^{54} - 60 q^{56} - 27 q^{57} - 9 q^{58} - 21 q^{59} - 5 q^{60} - 20 q^{61} - 6 q^{62} - 74 q^{63} + 62 q^{64} + 12 q^{65} + 10 q^{67} - 69 q^{68} + 16 q^{69} - 6 q^{70} + 36 q^{71} + 102 q^{72} - 14 q^{73} - 6 q^{74} - 26 q^{75} - 2 q^{76} + 92 q^{78} + q^{79} + 102 q^{80} - 35 q^{81} - 60 q^{82} + 30 q^{83} + 70 q^{84} - 24 q^{85} - 36 q^{86} - 60 q^{87} + 108 q^{89} - 11 q^{90} + 20 q^{91} - 6 q^{92} - 19 q^{93} - 15 q^{94} + 12 q^{95} + 106 q^{96} + 16 q^{97} - 120 q^{98}+O(q^{100}) \) 20 * q - q^3 - 10 * q^4 - 3 * q^5 - 10 * q^6 + q^7 + 6 * q^8 + q^9 - 5 * q^12 + q^13 - 15 * q^14 - 7 * q^15 - 10 * q^16 + 6 * q^17 - 17 * q^18 + 4 * q^19 - 15 * q^20 - 4 * q^21 - 18 * q^23 + 27 * q^24 - 7 * q^25 + 12 * q^26 + 23 * q^27 - 8 * q^28 + 12 * q^29 + 26 * q^30 + 7 * q^31 + 24 * q^32 + 6 * q^34 + 36 * q^35 + 20 * q^36 - 2 * q^37 + 12 * q^38 - 4 * q^39 - 12 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 35 * q^45 - 36 * q^46 - 27 * q^47 + 19 * q^48 - 15 * q^49 + 15 * q^50 + 2 * q^51 - 5 * q^52 + 12 * q^53 + 44 * q^54 - 60 * q^56 - 27 * q^57 - 9 * q^58 - 21 * q^59 - 5 * q^60 - 20 * q^61 - 6 * q^62 - 74 * q^63 + 62 * q^64 + 12 * q^65 + 10 * q^67 - 69 * q^68 + 16 * q^69 - 6 * q^70 + 36 * q^71 + 102 * q^72 - 14 * q^73 - 6 * q^74 - 26 * q^75 - 2 * q^76 + 92 * q^78 + q^79 + 102 * q^80 - 35 * q^81 - 60 * q^82 + 30 * q^83 + 70 * q^84 - 24 * q^85 - 36 * q^86 - 60 * q^87 + 108 * q^89 - 11 * q^90 + 20 * q^91 - 6 * q^92 - 19 * q^93 - 15 * q^94 + 12 * q^95 + 106 * q^96 + 16 * q^97 - 120 * q^98

Introduction

L-functions

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