LMFDB - Embedded newform 360.2.bm.a.11.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.24
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.a.131.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39113 - 0.254469i) q^{2} +(-1.73205 + 0.00397907i) q^{3} +(1.87049 - 0.708000i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40849 + 0.446288i) q^{6} +(2.40441 + 1.38819i) q^{7} +(2.42193 - 1.46090i) q^{8} +(2.99997 - 0.0137839i) q^{9} +O(q^{10})$	\(q+(1.39113 - 0.254469i) q^{2} +(-1.73205 + 0.00397907i) q^{3} +(1.87049 - 0.708000i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40849 + 0.446288i) q^{6} +(2.40441 + 1.38819i) q^{7} +(2.42193 - 1.46090i) q^{8} +(2.99997 - 0.0137839i) q^{9} +(-0.915942 - 1.07752i) q^{10} +(-2.70422 - 1.56128i) q^{11} +(-3.23696 + 1.23373i) q^{12} +(3.30414 - 1.90765i) q^{13} +(3.69810 + 1.31930i) q^{14} +(0.869469 + 1.49801i) q^{15} +(2.99747 - 2.64862i) q^{16} -3.43533i q^{17} +(4.16984 - 0.782575i) q^{18} +1.31386 q^{19} +(-1.54839 - 1.26589i) q^{20} +(-4.17007 - 2.39484i) q^{21} +(-4.15922 - 1.48381i) q^{22} +(2.13186 + 3.69249i) q^{23} +(-4.18909 + 2.53999i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.11106 - 3.49459i) q^{26} +(-5.19603 + 0.0358114i) q^{27} +(5.48026 + 0.894268i) q^{28} +(0.266702 - 0.461941i) q^{29} +(1.59074 + 1.86267i) q^{30} +(-0.413107 + 0.238507i) q^{31} +(3.49588 - 4.44734i) q^{32} +(4.69004 + 2.69345i) q^{33} +(-0.874185 - 4.77899i) q^{34} -2.77637i q^{35} +(5.60165 - 2.14976i) q^{36} +2.26255i q^{37} +(1.82775 - 0.334338i) q^{38} +(-5.71534 + 3.31728i) q^{39} +(-2.47615 - 1.36700i) q^{40} +(-9.97758 + 5.76056i) q^{41} +(-6.41053 - 2.27038i) q^{42} +(-6.25878 + 10.8405i) q^{43} +(-6.16360 - 1.00577i) q^{44} +(-1.51192 - 2.59116i) q^{45} +(3.90532 + 4.59424i) q^{46} +(-1.52710 + 2.64501i) q^{47} +(-5.18122 + 4.59945i) q^{48} +(0.354125 + 0.613362i) q^{49} +(-0.475189 + 1.33199i) q^{50} +(0.0136694 + 5.95014i) q^{51} +(4.82976 - 5.90757i) q^{52} +14.2847 q^{53} +(-7.21924 + 1.37205i) q^{54} +3.12256i q^{55} +(7.85133 - 0.150515i) q^{56} +(-2.27567 + 0.00522795i) q^{57} +(0.253467 - 0.710488i) q^{58} +(-8.89170 + 5.13363i) q^{59} +(2.68692 + 2.18642i) q^{60} +(-10.7109 - 6.18395i) q^{61} +(-0.513993 + 0.436918i) q^{62} +(7.23229 + 4.13137i) q^{63} +(3.73152 - 7.07642i) q^{64} +(-3.30414 - 1.90765i) q^{65} +(7.20986 + 2.55347i) q^{66} +(3.47947 + 6.02663i) q^{67} +(-2.43221 - 6.42575i) q^{68} +(-3.70717 - 6.38708i) q^{69} +(-0.706502 - 3.86230i) q^{70} -7.88557 q^{71} +(7.24559 - 4.41605i) q^{72} +7.92558 q^{73} +(0.575748 + 3.14750i) q^{74} +(0.862577 - 1.50199i) q^{75} +(2.45757 - 0.930215i) q^{76} +(-4.33470 - 7.50792i) q^{77} +(-7.10664 + 6.06915i) q^{78} +(-0.187206 - 0.108084i) q^{79} +(-3.79250 - 1.27158i) q^{80} +(8.99962 - 0.0827023i) q^{81} +(-12.4142 + 10.5527i) q^{82} +(-7.86428 - 4.54044i) q^{83} +(-9.49563 - 1.52711i) q^{84} +(-2.97508 + 1.71766i) q^{85} +(-5.94820 + 16.6732i) q^{86} +(-0.460102 + 0.801164i) q^{87} +(-8.83031 + 0.169283i) q^{88} -4.82215i q^{89} +(-2.76265 - 3.21990i) q^{90} +10.5927 q^{91} +(6.60191 + 5.39741i) q^{92} +(0.714571 - 0.414750i) q^{93} +(-1.45132 + 4.06815i) q^{94} +(-0.656931 - 1.13784i) q^{95} +(-6.03734 + 7.71690i) q^{96} +(-4.20125 + 7.27679i) q^{97} +(0.648716 + 0.763153i) q^{98} +(-8.13409 - 4.64652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.39113	−	0.254469i	0.983678	−	0.179937i
$2$	1.39113	−	0.254469i	0.983678	−	0.179937i
$3$	−1.73205	+	0.00397907i	−0.999997	+	0.00229732i
$3$	−1.73205	+	0.00397907i	−0.999997	+	0.00229732i
$4$	1.87049	−	0.708000i	0.935245	−	0.354000i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−2.40849	+	0.446288i	−0.983262	+	0.182196i
$7$	2.40441	+	1.38819i	0.908782	+	0.524685i	0.880039	−	0.474902i	$-0.157516\pi$
$7$	2.40441	+	1.38819i	0.908782	+	0.524685i	0.0287426	+	0.999587i	$0.490850\pi$
$8$	2.42193	−	1.46090i	0.856283	−	0.516507i
$9$	2.99997	−	0.0137839i	0.999989	−	0.00459462i
$10$	−0.915942	−	1.07752i	−0.289646	−	0.340742i
$11$	−2.70422	−	1.56128i	−0.815352	−	0.470744i	0.0334589	−	0.999440i	$-0.489348\pi$
$11$	−2.70422	−	1.56128i	−0.815352	−	0.470744i	−0.848811	+	0.528696i	$0.822681\pi$
$12$	−3.23696	+	1.23373i	−0.934430	+	0.356148i
$13$	3.30414	−	1.90765i	0.916405	−	0.529086i	0.0339183	−	0.999425i	$-0.489201\pi$
$13$	3.30414	−	1.90765i	0.916405	−	0.529086i	0.882486	+	0.470338i	$0.155868\pi$
$14$	3.69810	+	1.31930i	0.988359	+	0.352598i
$15$	0.869469	+	1.49801i	0.224496	+	0.386784i
$16$	2.99747	−	2.64862i	0.749368	−	0.662154i
$17$		−	3.43533i		−	0.833189i	−0.909092	−	0.416594i	$-0.863224\pi$
$17$		−	3.43533i		−	0.833189i	0.909092	−	0.416594i	$-0.136776\pi$
$18$	4.16984	−	0.782575i	0.982841	−	0.184455i
$19$	1.31386			0.301421			0.150710	−	0.988578i	$-0.451844\pi$
$19$	1.31386			0.301421			0.150710	+	0.988578i	$0.451844\pi$
$20$	−1.54839	−	1.26589i	−0.346231	−	0.283062i
$21$	−4.17007	−	2.39484i	−0.909984	−	0.522596i
$22$	−4.15922	−	1.48381i	−0.886748	−	0.316348i
$23$	2.13186	+	3.69249i	0.444524	+	0.769937i	0.998019	−	0.0629149i	$-0.0200397\pi$
$23$	2.13186	+	3.69249i	0.444524	+	0.769937i	−0.553495	+	0.832852i	$0.686706\pi$
$24$	−4.18909	+	2.53999i	−0.855094	+	0.518473i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.11106	−	3.49459i	0.806245	−	0.685346i
$27$	−5.19603	+	0.0358114i	−0.999976	+	0.00689190i
$28$	5.48026	+	0.894268i	1.03567	+	0.169001i
$29$	0.266702	−	0.461941i	0.0495253	−	0.0857803i	−0.840200	−	0.542277i	$-0.817563\pi$
$29$	0.266702	−	0.461941i	0.0495253	−	0.0857803i	0.889725	+	0.456496i	$0.150896\pi$
$30$	1.59074	+	1.86267i	0.290428	+	0.340075i
$31$	−0.413107	+	0.238507i	−0.0741962	+	0.0428372i	−0.536639	−	0.843812i	$-0.680306\pi$
$31$	−0.413107	+	0.238507i	−0.0741962	+	0.0428372i	0.462443	+	0.886649i	$0.346973\pi$
$32$	3.49588	−	4.44734i	0.617991	−	0.786185i
$33$	4.69004	+	2.69345i	0.816431	+	0.468869i
$34$	−0.874185	−	4.77899i	−0.149921	−	0.819590i
$35$		−	2.77637i		−	0.469293i
$36$	5.60165	−	2.14976i	0.933609	−	0.358293i
$37$			2.26255i			0.371960i	0.982554	+	0.185980i	$0.0595460\pi$
$37$			2.26255i			0.371960i	−0.982554	+	0.185980i	$0.940454\pi$
$38$	1.82775	−	0.334338i	0.296501	−	0.0542367i
$39$	−5.71534	+	3.31728i	−0.915187	+	0.531190i
$40$	−2.47615	−	1.36700i	−0.391513	−	0.216142i
$41$	−9.97758	+	5.76056i	−1.55824	+	0.899648i	−0.560809	+	0.827945i	$0.689510\pi$
$41$	−9.97758	+	5.76056i	−1.55824	+	0.899648i	−0.997426	+	0.0717028i	$0.977157\pi$
$42$	−6.41053	−	2.27038i	−0.989166	−	0.350327i
$43$	−6.25878	+	10.8405i	−0.954454	+	1.65316i	−0.218842	+	0.975760i	$0.570228\pi$
$43$	−6.25878	+	10.8405i	−0.954454	+	1.65316i	−0.735612	+	0.677403i	$0.763105\pi$
$44$	−6.16360	−	1.00577i	−0.929198	−	0.151626i
$45$	−1.51192	−	2.59116i	−0.225384	−	0.386267i
$46$	3.90532	+	4.59424i	0.575808	+	0.677384i
$47$	−1.52710	+	2.64501i	−0.222750	+	0.385814i	−0.955642	−	0.294531i	$-0.904837\pi$
$47$	−1.52710	+	2.64501i	−0.222750	+	0.385814i	0.732892	+	0.680345i	$0.238170\pi$
$48$	−5.18122	+	4.59945i	−0.747845	+	0.663874i
$49$	0.354125	+	0.613362i	0.0505892	+	0.0876231i
$50$	−0.475189	+	1.33199i	−0.0672018	+	0.188372i
$51$	0.0136694	+	5.95014i	0.00191410	+	0.833187i
$52$	4.82976	−	5.90757i	0.669767	−	0.819233i
$53$	14.2847			1.96215			0.981075	−	0.193629i	$-0.0620257\pi$
$53$	14.2847			1.96215			0.981075	+	0.193629i	$0.0620257\pi$
$54$	−7.21924	+	1.37205i	−0.982415	+	0.186712i
$55$			3.12256i			0.421046i
$56$	7.85133	−	0.150515i	1.04918	−	0.0201134i
$57$	−2.27567	+	0.00522795i	−0.301420	+	0.000692459i
$58$	0.253467	−	0.710488i	0.0332819	−	0.0932916i
$59$	−8.89170	+	5.13363i	−1.15760	+	0.668341i	−0.950728	−	0.310026i	$-0.899662\pi$
$59$	−8.89170	+	5.13363i	−1.15760	+	0.668341i	−0.206873	+	0.978368i	$0.566329\pi$
$60$	2.68692	+	2.18642i	0.346880	+	0.282266i
$61$	−10.7109	−	6.18395i	−1.37139	−	0.791774i	−0.380289	−	0.924868i	$-0.624175\pi$
$61$	−10.7109	−	6.18395i	−1.37139	−	0.791774i	−0.991103	+	0.133094i	$0.957509\pi$
$62$	−0.513993	+	0.436918i	−0.0652772	+	0.0554886i
$63$	7.23229	+	4.13137i	0.911183	+	0.520504i
$64$	3.73152	−	7.07642i	0.466440	−	0.884553i
$65$	−3.30414	−	1.90765i	−0.409829	−	0.236615i
$66$	7.20986	+	2.55347i	0.887473	+	0.314310i
$67$	3.47947	+	6.02663i	0.425086	+	0.736270i	0.996428	−	0.0844417i	$-0.0269107\pi$
$67$	3.47947	+	6.02663i	0.425086	+	0.736270i	−0.571343	+	0.820711i	$0.693577\pi$
$68$	−2.43221	−	6.42575i	−0.294949	−	0.779236i
$69$	−3.70717	−	6.38708i	−0.446291	−	0.768914i
$70$	−0.706502	−	3.86230i	−0.0844431	−	0.461633i
$71$	−7.88557			−0.935845			−0.467922	−	0.883770i	$-0.654997\pi$
$71$	−7.88557			−0.935845			−0.467922	+	0.883770i	$0.654997\pi$
$72$	7.24559	−	4.41605i	0.853901	−	0.520436i
$73$	7.92558			0.927620			0.463810	−	0.885935i	$-0.346482\pi$
$73$	7.92558			0.927620			0.463810	+	0.885935i	$0.346482\pi$
$74$	0.575748	+	3.14750i	0.0669294	+	0.365889i
$75$	0.862577	−	1.50199i	0.0996018	−	0.173434i
$76$	2.45757	−	0.930215i	0.281902	−	0.106703i
$77$	−4.33470	−	7.50792i	−0.493985	−	0.855606i
$78$	−7.10664	+	6.06915i	−0.804668	+	0.687196i
$79$	−0.187206	−	0.108084i	−0.0210624	−	0.0121604i	0.489432	−	0.872042i	$-0.337204\pi$
$79$	−0.187206	−	0.108084i	−0.0210624	−	0.0121604i	−0.510494	+	0.859881i	$0.670538\pi$
$80$	−3.79250	−	1.27158i	−0.424015	−	0.142167i
$81$	8.99962	−	0.0827023i	0.999958	−	0.00918915i
$82$	−12.4142	+	10.5527i	−1.37092	+	1.16535i
$83$	−7.86428	−	4.54044i	−0.863217	−	0.498378i	0.00187155	−	0.999998i	$-0.499404\pi$
$83$	−7.86428	−	4.54044i	−0.863217	−	0.498378i	−0.865088	+	0.501620i	$0.832738\pi$
$84$	−9.49563	−	1.52711i	−1.03606	−	0.166621i
$85$	−2.97508	+	1.71766i	−0.322693	+	0.186307i
$86$	−5.94820	+	16.6732i	−0.641411	+	1.79792i
$87$	−0.460102	+	0.801164i	−0.0493281	+	0.0858938i
$88$	−8.83031	+	0.169283i	−0.941315	+	0.0180456i
$89$		−	4.82215i		−	0.511147i	−0.966790	−	0.255573i	$-0.917736\pi$
$89$		−	4.82215i		−	0.511147i	0.966790	−	0.255573i	$-0.0822642\pi$
$90$	−2.76265	−	3.21990i	−0.291209	−	0.339407i
$91$	10.5927			1.11042
$92$	6.60191	+	5.39741i	0.688296	+	0.562719i
$93$	0.714571	−	0.414750i	0.0740976	−	0.0430075i
$94$	−1.45132	+	4.06815i	−0.149692	+	0.419598i
$95$	−0.656931	−	1.13784i	−0.0673997	−	0.116740i
$96$	−6.03734	+	7.71690i	−0.616183	+	0.787603i
$97$	−4.20125	+	7.27679i	−0.426573	+	0.738846i	−0.996566	−	0.0828038i	$-0.973613\pi$
$97$	−4.20125	+	7.27679i	−0.426573	+	0.738846i	0.569993	+	0.821649i	$0.306946\pi$
$98$	0.648716	+	0.763153i	0.0655302	+	0.0770901i
$99$	−8.13409	−	4.64652i	−0.817506	−	0.466993i
$100$	−0.322099	+	1.97389i	−0.0322099	+	0.197389i
$101$	−1.11068	+	1.92376i	−0.110517	+	0.191421i	−0.915979	−	0.401227i	$-0.868584\pi$
$101$	−1.11068	+	1.92376i	−0.110517	+	0.191421i	0.805462	+	0.592648i	$0.201917\pi$
$102$	1.53314	+	8.27395i	0.151804	+	0.819243i
$103$	12.7933	−	7.38623i	1.26056	−	0.727786i	0.287380	−	0.957817i	$-0.407216\pi$
$103$	12.7933	−	7.38623i	1.26056	−	0.727786i	0.973183	+	0.230030i	$0.0738825\pi$
$104$	5.21553	−	9.44723i	0.511424	−	0.926377i
$105$	0.0110474	+	4.80881i	0.00107811	+	0.469292i
$106$	19.8718	−	3.63501i	1.93012	−	0.353063i
$107$		−	14.0755i		−	1.36073i	−0.732872	−	0.680367i	$-0.761820\pi$
$107$		−	14.0755i		−	1.36073i	0.732872	−	0.680367i	$-0.238180\pi$
$108$	−9.69377	+	3.74577i	−0.932783	+	0.360437i
$109$			16.5073i			1.58111i	0.612389	+	0.790557i	$0.290209\pi$
$109$			16.5073i			1.58111i	−0.612389	+	0.790557i	$0.709791\pi$
$110$	0.794596	+	4.34389i	0.0757617	+	0.414174i
$111$	−0.00900283	−	3.91883i	−0.000854511	−	0.371959i
$112$	10.8839	−	2.20731i	1.02843	−	0.208571i
$113$	0.459459	−	0.265268i	0.0432222	−	0.0249544i	−0.478233	−	0.878233i	$-0.658723\pi$
$113$	0.459459	−	0.265268i	0.0432222	−	0.0249544i	0.521455	+	0.853279i	$0.325389\pi$
$114$	−3.16443	+	0.586361i	−0.296376	+	0.0549177i
$115$	2.13186	−	3.69249i	0.198797	−	0.344326i
$116$	0.171809	−	1.05288i	0.0159521	−	0.0977576i
$117$	9.88603	−	5.76843i	0.913964	−	0.533291i
$118$	−11.0632	+	9.40421i	−1.01845	+	0.865728i
$119$	4.76887	−	8.25993i	0.437162	−	0.757187i
$120$	4.29424	+	2.35786i	0.392009	+	0.215242i
$121$	−0.624807	−	1.08220i	−0.0568006	−	0.0983816i
$122$	−16.4739	−	5.87708i	−1.49148	−	0.532086i
$123$	17.2587	−	10.0173i	1.55616	−	0.903225i
$124$	−0.603849	+	0.738606i	−0.0542273	+	0.0663287i
$125$	1.00000			0.0894427
$126$	11.1124	+	3.90689i	0.989968	+	0.348053i
$127$			0.554852i			0.0492352i	0.999697	+	0.0246176i	$0.00783681\pi$
$127$			0.554852i			0.0492352i	−0.999697	+	0.0246176i	$0.992163\pi$
$128$	3.39031	−	10.7938i	0.299663	−	0.954045i
$129$	10.7974	−	18.8012i	0.950654	−	1.65535i
$130$	−5.08193	−	1.81299i	−0.445715	−	0.159009i
$131$	5.21744	−	3.01229i	0.455850	−	0.263185i	−0.254448	−	0.967087i	$-0.581894\pi$
$131$	5.21744	−	3.01229i	0.455850	−	0.263185i	0.710298	+	0.703901i	$0.248560\pi$
$132$	10.6796	+	1.71752i	0.929544	+	0.149491i
$133$	3.15906	+	1.82389i	0.273926	+	0.158151i
$134$	6.37400	+	7.49841i	0.550629	+	0.647764i
$135$	2.62903	+	4.48199i	0.226271	+	0.385748i
$136$	−5.01868	−	8.32013i	−0.430348	−	0.713445i
$137$	7.48963	+	4.32414i	0.639883	+	0.369436i	0.784569	−	0.620041i	$-0.212884\pi$
$137$	7.48963	+	4.32414i	0.639883	+	0.369436i	−0.144687	+	0.989478i	$0.546217\pi$
$138$	−6.78248	−	7.94190i	−0.577363	−	0.676060i
$139$	4.72886	+	8.19062i	0.401096	+	0.694719i	0.993859	−	0.110658i	$-0.0352959\pi$
$139$	4.72886	+	8.19062i	0.401096	+	0.694719i	−0.592762	+	0.805378i	$0.701963\pi$
$140$	−1.96567	−	5.19318i	−0.166130	−	0.438904i
$141$	2.63448	−	4.58735i	0.221863	−	0.386325i
$142$	−10.9699	+	2.00663i	−0.920570	+	0.168393i
$143$	−11.9135			−0.996257
$144$	8.95581	−	7.98708i	0.746318	−	0.665590i
$145$	−0.533403			−0.0442967
$146$	11.0255	−	2.01682i	0.912479	−	0.166913i
$147$	−0.615801	−	1.06096i	−0.0507904	−	0.0875067i
$148$	1.60188	+	4.23207i	0.131674	+	0.347874i
$149$	5.42917	+	9.40360i	0.444775	+	0.770373i	0.998037	−	0.0626346i	$-0.0199503\pi$
$149$	5.42917	+	9.40360i	0.444775	+	0.770373i	−0.553261	+	0.833008i	$0.686617\pi$
$150$	0.817749	−	2.30896i	0.0667689	−	0.188526i
$151$	9.37631	+	5.41342i	0.763033	+	0.440538i	0.830384	−	0.557192i	$-0.188121\pi$
$151$	9.37631	+	5.41342i	0.763033	+	0.440538i	−0.0673504	+	0.997729i	$0.521455\pi$
$152$	3.18209	−	1.91943i	0.258101	−	0.155686i
$153$	−0.0473521	−	10.3059i	−0.00382819	−	0.833180i
$154$	−7.94067	−	9.34145i	−0.639877	−	0.752755i
$155$	0.413107	+	0.238507i	0.0331815	+	0.0191574i
$156$	−8.34185	+	10.2514i	−0.667883	+	0.820769i
$157$	−14.2718	+	8.23981i	−1.13901	+	0.657608i	−0.946186	−	0.323625i	$-0.895098\pi$
$157$	−14.2718	+	8.23981i	−1.13901	+	0.657608i	−0.192826	+	0.981233i	$0.561765\pi$
$158$	−0.287932	−	0.102720i	−0.0229067	−	0.00817198i
$159$	−24.7417	+	0.0568397i	−1.96214	+	0.00450768i
$160$	−5.59945	−	0.803857i	−0.442675	−	0.0635505i
$161$			11.8377i			0.932940i
$162$	12.4986	−	2.40518i	0.981983	−	0.188969i
$163$	7.55915			0.592078			0.296039	−	0.955176i	$-0.404334\pi$
$163$	7.55915			0.592078			0.296039	+	0.955176i	$0.404334\pi$
$164$	−14.5845	+	17.8392i	−1.13886	+	1.39301i
$165$	−0.0124249	−	5.40842i	−0.000967276	−	0.421045i
$166$	−12.0956	−	4.31513i	−0.938804	−	0.334919i
$167$	−10.6372	−	18.4242i	−0.823131	−	1.42570i	−0.903340	−	0.428926i	$-0.858892\pi$
$167$	−10.6372	−	18.4242i	−0.823131	−	1.42570i	0.0802091	−	0.996778i	$-0.474441\pi$
$168$	−13.5983	+	0.291939i	−1.04913	+	0.0225236i
$169$	0.778243	−	1.34796i	0.0598649	−	0.103689i
$170$	−3.70163	+	3.14656i	−0.283902	+	0.241330i
$171$	3.94155	−	0.0181101i	0.301418	−	0.00138491i
$172$	−4.03189	+	24.7083i	−0.307429	+	1.88399i
$173$	−10.3166	+	17.8689i	−0.784356	+	1.35854i	0.145027	+	0.989428i	$0.453673\pi$
$173$	−10.3166	+	17.8689i	−0.784356	+	1.35854i	−0.929383	+	0.369116i	$0.879660\pi$
$174$	−0.436190	+	1.23161i	−0.0330675	+	0.0933678i
$175$	−2.40441	+	1.38819i	−0.181756	+	0.104937i
$176$	−12.2410	+	2.48254i	−0.922703	+	0.187128i
$177$	15.3804	−	8.92706i	1.15606	−	0.670999i
$178$	−1.22709	−	6.70824i	−0.0919742	−	0.502804i
$179$		−	7.50778i		−	0.561158i	−0.959831	−	0.280579i	$-0.909474\pi$
$179$		−	7.50778i		−	0.561158i	0.959831	−	0.280579i	$-0.0905264\pi$
$180$	−4.66257	−	3.77629i	−0.347528	−	0.281468i
$181$		−	15.2146i		−	1.13089i	−0.824785	−	0.565447i	$-0.808704\pi$
$181$		−	15.2146i		−	1.13089i	0.824785	−	0.565447i	$-0.191296\pi$
$182$	14.7358	−	2.69551i	1.09229	−	0.199805i
$183$	18.5764	+	10.6683i	1.37321	+	0.788621i
$184$	10.5576	+	5.82852i	0.778316	+	0.429684i
$185$	1.95942	−	1.13127i	0.144060	−	0.0831728i
$186$	0.888521	−	0.758807i	0.0651495	−	0.0556385i
$187$	−5.36351	+	9.28987i	−0.392219	+	0.679342i
$188$	−0.983753	+	6.02865i	−0.0717476	+	0.439684i
$189$	−12.5431	−	7.12695i	−0.912376	−	0.518410i
$190$	−1.20342	−	1.41571i	−0.0873054	−	0.102707i
$191$	−6.80108	+	11.7798i	−0.492109	+	0.852358i	−0.999959	−	0.00908769i	$-0.997107\pi$
$191$	−6.80108	+	11.7798i	−0.492109	+	0.852358i	0.507850	+	0.861446i	$0.330441\pi$
$192$	−6.43501	+	12.2715i	−0.464407	+	0.885622i
$193$	−11.0958	−	19.2185i	−0.798696	−	1.38338i	−0.920466	−	0.390823i	$-0.872190\pi$
$193$	−11.0958	−	19.2185i	−0.798696	−	1.38338i	0.121770	−	0.992558i	$-0.461143\pi$
$194$	−3.99278	+	11.1921i	−0.286665	+	0.803542i
$195$	5.73052	+	3.29099i	0.410371	+	0.235673i
$196$	1.09665	+	0.896567i	0.0783319	+	0.0640405i
$197$	5.87131			0.418314			0.209157	−	0.977882i	$-0.432928\pi$
$197$	5.87131			0.418314			0.209157	+	0.977882i	$0.432928\pi$
$198$	−12.4980	−	4.39404i	−0.888192	−	0.312271i
$199$		−	17.4689i		−	1.23834i	−0.785259	−	0.619168i	$-0.787470\pi$
$199$		−	17.4689i		−	1.23834i	0.785259	−	0.619168i	$-0.212530\pi$
$200$	0.0542127	+	2.82791i	0.00383342	+	0.199963i
$201$	−6.05059	−	10.4246i	−0.426776	−	0.735291i
$202$	−1.05557	+	2.95884i	−0.0742695	+	0.208183i
$203$	1.28252	−	0.740464i	0.0900153	−	0.0519704i
$204$	4.23827	+	11.1200i	0.296738	+	0.778556i
$205$	9.97758	+	5.76056i	0.696864	+	0.402335i
$206$	15.9176	−	13.5307i	1.10903	−	0.942729i
$207$	6.44641	+	11.0480i	0.448056	+	0.767887i
$208$	4.85145	−	14.4695i	0.336388	−	1.00328i
$209$	−3.55297	−	2.05131i	−0.245764	−	0.141892i
$210$	1.23906	+	6.68687i	0.0855034	+	0.461438i
$211$	−8.80440	−	15.2497i	−0.606120	−	1.04983i	−0.991873	−	0.127228i	$-0.959392\pi$
$211$	−8.80440	−	15.2497i	−0.606120	−	1.04983i	0.385754	−	0.922602i	$-0.373941\pi$
$212$	26.7193	−	10.1135i	1.83509	−	0.694601i
$213$	13.6582	−	0.0313772i	0.935842	−	0.00214993i
$214$	−3.58179	−	19.5809i	−0.244846	−	1.33852i
$215$	12.5176			0.853690
$216$	−12.5321	+	7.67763i	−0.852703	+	0.522396i
$217$	−1.32437			−0.0899042
$218$	4.20060	+	22.9638i	0.284501	+	1.55531i
$219$	−13.7275	+	0.0315365i	−0.927617	+	0.00213104i
$220$	2.21077	+	5.84072i	0.149050	+	0.393781i
$221$	−6.55339	−	11.3508i	−0.440829	−	0.763538i
$222$	−1.00975	−	5.44932i	−0.0677698	−	0.365734i
$223$	−7.41753	−	4.28251i	−0.496714	−	0.286778i	0.230641	−	0.973039i	$-0.425918\pi$
$223$	−7.41753	−	4.28251i	−0.496714	−	0.286778i	−0.727356	+	0.686261i	$0.759251\pi$
$224$	14.5793	−	5.84028i	0.974119	−	0.390220i
$225$	−1.48805	+	2.60494i	−0.0992031	+	0.173663i
$226$	0.571664	−	0.485941i	0.0380265	−	0.0323243i
$227$	20.0247	+	11.5612i	1.32908	+	0.767347i	0.985158	−	0.171651i	$-0.0549100\pi$
$227$	20.0247	+	11.5612i	1.32908	+	0.767347i	0.343925	+	0.938997i	$0.388243\pi$
$228$	−4.25292	+	1.62095i	−0.281656	+	0.107350i
$229$	6.36677	−	3.67586i	0.420728	−	0.242907i	−0.274661	−	0.961541i	$-0.588566\pi$
$229$	6.36677	−	3.67586i	0.420728	−	0.242907i	0.695389	+	0.718634i	$0.255232\pi$
$230$	2.02607	−	5.67923i	0.133595	−	0.374477i
$231$	7.53777	+	12.9868i	0.495949	+	0.854469i
$232$	−0.0289172	−	1.50842i	−0.00189851	−	0.0990323i
$233$			20.6717i			1.35425i	0.735868	+	0.677125i	$0.236774\pi$
$233$			20.6717i			1.35425i	−0.735868	+	0.677125i	$0.763226\pi$
$234$	12.2849	−	10.5403i	0.803088	−	0.689043i
$235$	3.05419			0.199233
$236$	−12.9972	+	15.8977i	−0.846048	+	1.03485i
$237$	0.324680	+	0.186461i	0.0210902	+	0.0121119i
$238$	4.53223	−	12.7042i	0.293781	−	0.823490i
$239$	2.31092	+	4.00263i	0.149481	+	0.258908i	0.931036	−	0.364928i	$-0.118906\pi$
$239$	2.31092	+	4.00263i	0.149481	+	0.258908i	−0.781555	+	0.623837i	$0.785573\pi$
$240$	6.57385	+	2.18734i	0.424340	+	0.141192i
$241$	−10.0859	+	17.4693i	−0.649690	+	1.12530i	0.333507	+	0.942748i	$0.391768\pi$
$241$	−10.0859	+	17.4693i	−0.649690	+	1.12530i	−0.983197	+	0.182548i	$0.941565\pi$
$242$	−1.14457	−	1.34648i	−0.0735760	−	0.0865553i
$243$	−15.5874	+	0.179054i	−0.999934	+	0.0114863i
$244$	−24.4129	−	3.98369i	−1.56288	−	0.255030i
$245$	0.354125	−	0.613362i	0.0226242	−	0.0391863i
$246$	21.4600	−	18.3271i	1.36824	−	1.16849i
$247$	4.34119	−	2.50639i	0.276223	−	0.159478i
$248$	−0.652081	+	1.18116i	−0.0414072	+	0.0750036i
$249$	13.6394	+	7.83296i	0.864359	+	0.496394i
$250$	1.39113	−	0.254469i	0.0879828	−	0.0160940i
$251$		−	15.2472i		−	0.962397i	−0.876612	−	0.481199i	$-0.840202\pi$
$251$		−	15.2472i		−	0.962397i	0.876612	−	0.481199i	$-0.159798\pi$
$252$	16.4529	+	2.60724i	1.03644	+	0.164240i
$253$		−	13.3137i		−	0.837027i
$254$	0.141193	+	0.771872i	0.00885923	+	0.0484316i
$255$	5.14614	−	2.98691i	0.322264	−	0.187048i
$256$	1.96967	−	15.8783i	0.123104	−	0.992394i
$257$	1.24545	−	0.719060i	0.0776889	−	0.0448537i	−0.460652	−	0.887581i	$-0.652384\pi$
$257$	1.24545	−	0.719060i	0.0776889	−	0.0448537i	0.538341	+	0.842727i	$0.319051\pi$
$258$	10.2362	−	28.9025i	0.637279	−	1.79939i
$259$	−3.14084	+	5.44009i	−0.195162	+	0.338031i
$260$	−7.53099	−	1.22890i	−0.467052	−	0.0762134i
$261$	0.793729	−	1.38948i	0.0491306	−	0.0860069i
$262$	6.49161	−	5.51817i	0.401053	−	0.340914i
$263$	2.20868	−	3.82555i	0.136193	−	0.235893i	−0.789860	−	0.613288i	$-0.789847\pi$
$263$	2.20868	−	3.82555i	0.136193	−	0.235893i	0.926053	+	0.377395i	$0.123180\pi$
$264$	15.2938	−	0.328342i	0.941271	−	0.0202080i
$265$	−7.14233	−	12.3709i	−0.438750	−	0.759937i
$266$	4.85880	+	1.73338i	0.297912	+	0.106280i
$267$	0.0191877	+	8.35219i	0.00117427	+	0.511145i
$268$	10.7752	+	8.80928i	0.658199	+	0.538113i
$269$	24.9314			1.52010			0.760048	−	0.649867i	$-0.225175\pi$
$269$	24.9314			1.52010			0.760048	+	0.649867i	$0.225175\pi$
$270$	4.79785	+	5.56602i	0.291988	+	0.338737i
$271$		−	21.5066i		−	1.30643i	−0.757172	−	0.653215i	$-0.773420\pi$
$271$		−	21.5066i		−	1.30643i	0.757172	−	0.653215i	$-0.226580\pi$
$272$	−9.09886	−	10.2973i	−0.551699	−	0.624365i
$273$	−18.3470	+	0.0421491i	−1.11041	+	0.00255098i
$274$	11.5194	+	4.10957i	0.695914	+	0.248268i
$275$	2.70422	−	1.56128i	0.163070	−	0.0941488i
$276$	−11.4563	−	9.32230i	−0.689587	−	0.561136i
$277$	0.693110	+	0.400167i	0.0416449	+	0.0240437i	0.520678	−	0.853753i	$-0.325679\pi$
$277$	0.693110	+	0.400167i	0.0416449	+	0.0240437i	−0.479033	+	0.877797i	$0.659013\pi$
$278$	8.66272	+	10.1909i	0.519556	+	0.611208i
$279$	−1.23602	+	0.721209i	−0.0739986	+	0.0431776i
$280$	−4.05601	−	6.72419i	−0.242393	−	0.401847i
$281$	−17.8052	−	10.2798i	−1.06217	−	0.613244i	−0.136139	−	0.990690i	$-0.543469\pi$
$281$	−17.8052	−	10.2798i	−1.06217	−	0.613244i	−0.926032	+	0.377445i	$0.876803\pi$
$282$	2.49756	−	7.05200i	0.148728	−	0.419940i
$283$	7.32132	+	12.6809i	0.435207	+	0.753801i	0.997313	−	0.0732645i	$-0.0233417\pi$
$283$	7.32132	+	12.6809i	0.435207	+	0.753801i	−0.562105	+	0.827066i	$0.690008\pi$
$284$	−14.7499	+	5.58298i	−0.875245	+	0.331289i
$285$	1.14236	+	1.96817i	0.0676677	+	0.116585i
$286$	−16.5732	+	3.03162i	−0.979996	+	0.179263i
$287$	−31.9869			−1.88813
$288$	10.4262	−	13.3901i	0.614372	−	0.789016i
$289$	5.19853			0.305796
$290$	−0.742034	+	0.135735i	−0.0435737	+	0.00797062i
$291$	7.24781	−	12.6204i	0.424874	−	0.739824i
$292$	14.8247	−	5.61132i	0.867552	−	0.328377i
$293$	13.4417	+	23.2817i	0.785273	+	1.36013i	0.928836	+	0.370491i	$0.120811\pi$
$293$	13.4417	+	23.2817i	0.785273	+	1.36013i	−0.143563	+	0.989641i	$0.545856\pi$
$294$	−1.12664	−	1.31923i	−0.0657071	−	0.0769393i
$295$	8.89170	+	5.13363i	0.517695	+	0.298891i
$296$	3.30536	+	5.47974i	0.192120	+	0.318503i
$297$	14.1071	+	8.01562i	0.818577	+	0.465113i
$298$	9.94562	+	11.7001i	0.576134	+	0.677768i
$299$	14.0879	+	8.13368i	0.814727	+	0.470383i
$300$	0.550037	−	3.42015i	0.0317564	−	0.197463i
$301$	−30.0973	+	17.3767i	−1.73478	+	1.00158i
$302$	14.4212	+	5.14479i	0.829848	+	0.296049i
$303$	1.91610	−	3.33646i	0.110077	−	0.191675i
$304$	3.93827	−	3.47992i	0.225875	−	0.199587i
$305$			12.3679i			0.708184i
$306$	−2.68840	−	14.3248i	−0.153686	−	0.818892i
$307$	−21.3839			−1.22044			−0.610221	−	0.792231i	$-0.708920\pi$
$307$	−21.3839			−1.22044			−0.610221	+	0.792231i	$0.708920\pi$
$308$	−13.4236	−	10.9745i	−0.764882	−	0.625331i
$309$	−22.1292	+	12.8442i	−1.25889	+	0.730680i
$310$	0.635379	+	0.226672i	0.0360871	+	0.0128741i
$311$	10.7043	+	18.5404i	0.606985	+	1.05133i	0.991734	+	0.128308i	$0.0409547\pi$
$311$	10.7043	+	18.5404i	0.606985	+	1.05133i	−0.384749	+	0.923021i	$0.625712\pi$
$312$	−8.99594	+	16.3838i	−0.509295	+	0.927550i
$313$	2.91819	−	5.05445i	0.164946	−	0.285694i	−0.771690	−	0.635998i	$-0.780588\pi$
$313$	2.91819	−	5.05445i	0.164946	−	0.285694i	0.936636	+	0.350304i	$0.113922\pi$
$314$	−17.7571	+	15.0944i	−1.00209	+	0.851825i
$315$	−0.0382692	−	8.32903i	−0.00215622	−	0.469288i
$316$	−0.426691	−	0.0696273i	−0.0240032	−	0.00391684i
$317$	−4.19064	+	7.25841i	−0.235370	+	0.407673i	−0.959380	−	0.282117i	$-0.908964\pi$
$317$	−4.19064	+	7.25841i	−0.235370	+	0.407673i	0.724010	+	0.689789i	$0.242297\pi$
$318$	−34.4045	+	6.37507i	−1.92931	+	0.357496i
$319$	−1.44244	+	0.832792i	−0.0807611	+	0.0466274i
$320$	−7.99412	+	0.306617i	−0.446885	+	0.0171404i
$321$	0.0560076	+	24.3795i	0.00312604	+	1.36073i
$322$	3.01233	+	16.4678i	0.167870	+	0.917712i
$323$		−	4.51355i		−	0.251140i
$324$	16.7752	−	6.52643i	0.931953	−	0.362579i
$325$			3.81530i			0.211635i
$326$	10.5158	−	1.92357i	0.582414	−	0.106537i
$327$	−0.0656837	−	28.5914i	−0.00363232	−	1.58111i
$328$	−15.7494	+	28.5280i	−0.869616	+	1.57519i
$329$	−7.34353	+	4.23979i	−0.404862	+	0.233747i
$330$	−1.39356	−	7.52066i	−0.0767130	−	0.413999i
$331$	−0.901119	+	1.56078i	−0.0495300	+	0.0857884i	−0.889727	−	0.456492i	$-0.849106\pi$
$331$	−0.901119	+	1.56078i	−0.0495300	+	0.0857884i	0.840197	+	0.542281i	$0.182439\pi$
$332$	−17.9247	−	2.92495i	−0.983745	−	0.160527i
$333$	0.0311866	+	6.78757i	0.00170902	+	0.371956i
$334$	−19.4861	−	22.9236i	−1.06623	−	1.25432i
$335$	3.47947	−	6.02663i	0.190104	−	0.329270i
$336$	−18.8427	+	3.86647i	−1.02795	+	0.210933i
$337$	−11.9797	−	20.7495i	−0.652577	−	1.13030i	−0.982495	−	0.186287i	$-0.940355\pi$
$337$	−11.9797	−	20.7495i	−0.652577	−	1.13030i	0.329918	−	0.944009i	$-0.392979\pi$
$338$	0.739625	−	2.07322i	0.0402303	−	0.112769i
$339$	−0.794748	+	0.461286i	−0.0431648	+	0.0250536i
$340$	−4.34875	+	5.31923i	−0.235844	+	0.288476i
$341$	1.48951			0.0806614
$342$	5.47860	−	1.02820i	0.296249	−	0.0555985i
$343$		−	17.4682i		−	0.943197i
$344$	0.678610	+	35.3985i	0.0365882	+	1.90856i
$345$	−3.67779	+	6.40405i	−0.198005	+	0.344782i
$346$	−9.80465	+	27.4832i	−0.527101	+	1.47750i
$347$	−15.0256	+	8.67502i	−0.806615	+	0.465699i	−0.845779	−	0.533533i	$-0.820864\pi$
$347$	−15.0256	+	8.67502i	−0.806615	+	0.465699i	0.0391641	+	0.999233i	$0.487530\pi$
$348$	−0.293391	+	1.82432i	−0.0157274	+	0.0977939i
$349$	7.29528	+	4.21193i	0.390507	+	0.225460i	0.682380	−	0.730998i	$-0.260945\pi$
$349$	7.29528	+	4.21193i	0.390507	+	0.225460i	−0.291873	+	0.956457i	$0.594278\pi$
$350$	−2.99160	+	2.54300i	−0.159908	+	0.135929i
$351$	−17.1001	+	10.0305i	−0.912736	+	0.535390i
$352$	−16.3972	+	6.56850i	−0.873972	+	0.350102i
$353$	14.9442	+	8.62801i	0.795397	+	0.459223i	0.841859	−	0.539697i	$-0.181461\pi$
$353$	14.9442	+	8.62801i	0.795397	+	0.459223i	−0.0464619	+	0.998920i	$0.514795\pi$
$354$	19.1245	−	16.3326i	1.01646	−	0.868065i
$355$	3.94278	+	6.82910i	0.209261	+	0.362451i
$356$	−3.41408	−	9.01979i	−0.180946	−	0.478048i
$357$	−8.22704	+	14.3256i	−0.435421	+	0.758189i
$358$	−1.91050	−	10.4443i	−0.100973	−	0.551998i
$359$	7.13071			0.376344			0.188172	−	0.982136i	$-0.439744\pi$
$359$	7.13071			0.376344			0.188172	+	0.982136i	$0.439744\pi$
$360$	−7.44720	−	4.06684i	−0.392502	−	0.214341i
$361$	−17.2738			−0.909146
$362$	−3.87165	−	21.1655i	−0.203490	−	1.11244i
$363$	1.08650	+	1.87193i	0.0570265	+	0.0982508i
$364$	19.8135	−	7.49962i	1.03851	−	0.393087i
$365$	−3.96279	−	6.86376i	−0.207422	−	0.359266i
$366$	28.5570	+	10.1138i	1.49270	+	0.528658i
$367$	−29.3780	−	16.9614i	−1.53352	−	0.885379i	−0.999196	−	0.0401004i	$-0.987232\pi$
$367$	−29.3780	−	16.9614i	−1.53352	−	0.885379i	−0.534326	−	0.845279i	$-0.679434\pi$
$368$	16.1702	+	5.42166i	0.842929	+	0.282623i
$369$	−29.8530	+	17.4190i	−1.55409	+	0.906798i
$370$	2.43794	−	2.07236i	0.126742	−	0.107737i
$371$	34.3462	+	19.8298i	1.78317	+	1.02951i
$372$	1.04296	−	1.28170i	0.0540748	−	0.0664531i
$373$	8.48032	−	4.89612i	0.439095	−	0.253511i	−0.264119	−	0.964490i	$-0.585081\pi$
$373$	8.48032	−	4.89612i	0.439095	−	0.253511i	0.703213	+	0.710979i	$0.251748\pi$
$374$	−5.09736	+	14.2883i	−0.263578	+	0.738829i
$375$	−1.73205	+	0.00397907i	−0.0894425	+	0.000205478i
$376$	0.165576	+	8.63697i	0.00853893	+	0.445418i
$377$		−	2.03509i		−	0.104813i
$378$	−19.2627	−	6.72269i	−0.990765	−	0.345778i
$379$	15.9453			0.819054			0.409527	−	0.912298i	$-0.365694\pi$
$379$	15.9453			0.819054			0.409527	+	0.912298i	$0.365694\pi$
$380$	−2.03437	−	1.66321i	−0.104361	−	0.0853208i
$381$	−0.00220780	−	0.961030i	−0.000113109	−	0.0492350i
$382$	−6.46360	+	18.1179i	−0.330706	+	0.926995i
$383$	−3.70162	−	6.41139i	−0.189144	−	0.327607i	0.755821	−	0.654778i	$-0.227238\pi$
$383$	−3.70162	−	6.41139i	−0.189144	−	0.327607i	−0.944965	+	0.327171i	$0.893905\pi$
$384$	−5.82922	+	18.7088i	−0.297471	+	0.954731i
$385$	−4.33470	+	7.50792i	−0.220917	+	0.382639i
$386$	−20.3263	−	23.9120i	−1.03458	−	1.21709i
$387$	−18.6267	+	32.6075i	−0.946849	+	1.65753i
$388$	−2.70644	+	16.5856i	−0.137399	+	0.842009i
$389$	13.0021	−	22.5203i	0.659233	−	1.14182i	−0.321582	−	0.946882i	$-0.604214\pi$
$389$	13.0021	−	22.5203i	0.659233	−	1.14182i	0.980815	−	0.194943i	$-0.0624522\pi$
$390$	8.80936	+	3.11995i	0.446079	+	0.157985i
$391$	12.6849	−	7.32363i	0.641503	−	0.370372i
$392$	1.75373	+	0.968180i	0.0885767	+	0.0489005i
$393$	−9.02487	+	5.23819i	−0.455244	+	0.264232i
$394$	8.16777	−	1.49407i	0.411486	−	0.0752701i
$395$			0.216167i			0.0108766i
$396$	−18.5045	−	2.93233i	−0.929884	−	0.147355i
$397$			26.9039i			1.35027i	0.737694	+	0.675135i	$0.235915\pi$
$397$			26.9039i			1.35027i	−0.737694	+	0.675135i	$0.764085\pi$
$398$	−4.44529	−	24.3015i	−0.222822	−	1.21812i
$399$	−5.47890	−	3.14649i	−0.274288	−	0.157521i
$400$	0.795033	+	3.92019i	0.0397516	+	0.196010i
$401$	−9.03940	+	5.21890i	−0.451406	+	0.260619i	−0.708424	−	0.705787i	$-0.750593\pi$
$401$	−9.03940	+	5.21890i	−0.451406	+	0.260619i	0.257018	+	0.966407i	$0.417260\pi$
$402$	−11.0699	−	12.9622i	−0.552116	−	0.646497i
$403$	−0.909976	+	1.57613i	−0.0453291	+	0.0785124i
$404$	−0.715500	+	4.38474i	−0.0355975	+	0.218149i
$405$	−4.57143	−	7.75255i	−0.227156	−	0.385227i
$406$	1.59573	−	1.35644i	0.0791947	−	0.0673192i
$407$	3.53247	−	6.11842i	0.175098	−	0.303279i
$408$	8.72569	+	14.3909i	0.431986	+	0.712455i
$409$	2.09390	+	3.62675i	0.103537	+	0.179331i	0.913140	−	0.407647i	$-0.133651\pi$
$409$	2.09390	+	3.62675i	0.103537	+	0.179331i	−0.809603	+	0.586978i	$0.800317\pi$
$410$	15.3460	+	5.47470i	0.757885	+	0.270376i
$411$	−12.9896	−	7.45981i	−0.640730	−	0.367965i
$412$	18.7003	−	22.8735i	0.921299	−	1.12690i
$413$	−28.5057			−1.40268
$414$	11.7792	+	13.7288i	0.578914	+	0.674732i
$415$			9.08089i			0.445763i
$416$	3.06695	−	21.3636i	0.150370	−	1.04743i
$417$	−8.22319	−	14.1677i	−0.402691	−	0.693796i
$418$	−5.46464	−	1.94952i	−0.267284	−	0.0953540i
$419$	2.80884	−	1.62169i	0.137221	−	0.0792245i	−0.429818	−	0.902916i	$-0.641422\pi$
$419$	2.80884	−	1.62169i	0.137221	−	0.0792245i	0.567039	+	0.823691i	$0.308089\pi$
$420$	3.42530	+	8.98701i	0.167138	+	0.438521i
$421$	−5.45534	−	3.14964i	−0.265877	−	0.153504i	0.361135	−	0.932513i	$-0.382389\pi$
$421$	−5.45534	−	3.14964i	−0.265877	−	0.153504i	−0.627013	+	0.779009i	$0.715723\pi$
$422$	−16.1286	−	18.9738i	−0.785130	−	0.923632i
$423$	−4.54478	+	7.95599i	−0.220975	+	0.386833i
$424$	34.5965	−	20.8685i	1.68016	−	1.01346i
$425$	2.97508	+	1.71766i	0.144313	+	0.0833189i
$426$	18.9923	−	3.51923i	0.920181	−	0.170507i
$427$	−17.1690	−	29.7375i	−0.830864	−	1.43910i
$428$	−9.96549	−	26.3282i	−0.481700	−	1.27262i
$429$	20.6347	−	0.0474046i	0.996254	−	0.00228872i
$430$	17.4136	−	3.18533i	0.839756	−	0.153610i
$431$	−16.9856			−0.818167			−0.409084	−	0.912497i	$-0.634152\pi$
$431$	−16.9856			−0.818167			−0.409084	+	0.912497i	$0.634152\pi$
$432$	−15.4801	+	13.8696i	−0.744787	+	0.667303i
$433$	−17.6526			−0.848331			−0.424166	−	0.905585i	$-0.639433\pi$
$433$	−17.6526			−0.848331			−0.424166	+	0.905585i	$0.639433\pi$
$434$	−1.84237	+	0.337012i	−0.0884368	+	0.0161771i
$435$	0.923879	−	0.00212245i	0.0442966	−	0.000101764i
$436$	11.6872	+	30.8768i	0.559714	+	1.47873i
$437$	2.80097	+	4.85142i	0.133989	+	0.232075i
$438$	−19.0887	+	3.53709i	−0.912093	+	0.169009i
$439$	33.1600	+	19.1449i	1.58264	+	0.913738i	0.994472	+	0.105000i	$0.0334841\pi$
$439$	33.1600	+	19.1449i	1.58264	+	0.913738i	0.588168	+	0.808738i	$0.299849\pi$
$440$	4.56176	+	7.56263i	0.217473	+	0.360534i
$441$	1.07082	+	1.83519i	0.0509913	+	0.0873898i
$442$	−12.0051	−	14.1228i	−0.571023	−	0.671754i
$443$	−11.3515	−	6.55380i	−0.539327	−	0.311381i	0.205479	−	0.978661i	$-0.434125\pi$
$443$	−11.3515	−	6.55380i	−0.539327	−	0.311381i	−0.744806	+	0.667281i	$0.767458\pi$
$444$	−2.79137	−	7.32377i	−0.132473	−	0.347571i
$445$	−4.17610	+	2.41107i	−0.197966	+	0.114296i
$446$	−11.4085	−	4.07000i	−0.540209	−	0.192720i
$447$	−9.44099	−	16.2659i	−0.446544	−	0.769349i
$448$	18.7955	−	11.8346i	0.888004	−	0.559131i
$449$			24.9459i			1.17727i	0.808400	+	0.588634i	$0.200334\pi$
$449$			24.9459i			1.17727i	−0.808400	+	0.588634i	$0.799666\pi$
$450$	−1.40719	+	4.00248i	−0.0663356	+	0.188679i
$451$	35.9754			1.69401
$452$	0.671603	−	0.821479i	0.0315895	−	0.0386391i
$453$	−16.2617	−	9.33898i	−0.764043	−	0.438783i
$454$	30.7989	+	10.9875i	1.44546	+	0.515671i
$455$	−5.29634	−	9.17354i	−0.248296	−	0.430062i
$456$	−5.50389	+	3.33720i	−0.257743	+	0.156279i
$457$	13.2777	−	22.9976i	0.621103	−	1.07578i	−0.368178	−	0.929755i	$-0.620018\pi$
$457$	13.2777	−	22.9976i	0.621103	−	1.07578i	0.989281	−	0.146026i	$-0.0466483\pi$
$458$	7.92162	−	6.73375i	0.370153	−	0.314647i
$459$	0.123024	+	17.8501i	0.00574226	+	0.833169i
$460$	1.37334	−	8.41612i	0.0640324	−	0.392404i
$461$	5.99710	−	10.3873i	0.279313	−	0.483784i	−0.691901	−	0.721992i	$-0.743227\pi$
$461$	5.99710	−	10.3873i	0.279313	−	0.483784i	0.971214	+	0.238208i	$0.0765601\pi$
$462$	13.7908	+	16.1482i	0.641605	+	0.751283i
$463$	−21.9062	+	12.6476i	−1.01807	+	0.587782i	−0.913544	−	0.406740i	$-0.866666\pi$
$463$	−21.9062	+	12.6476i	−1.01807	+	0.587782i	−0.104525	+	0.994522i	$0.533332\pi$
$464$	−0.424073	−	2.09105i	−0.0196871	−	0.0970743i
$465$	−0.716469	−	0.411462i	−0.0332255	−	0.0190811i
$466$	5.26032	+	28.7571i	0.243680	+	1.33215i
$467$			7.44030i			0.344296i	0.985071	+	0.172148i	$0.0550707\pi$
$467$			7.44030i			0.344296i	−0.985071	+	0.172148i	$0.944929\pi$
$468$	14.4077	−	17.7891i	0.665995	−	0.822302i
$469$			19.3206i			0.892144i
$470$	4.24878	−	0.777198i	0.195982	−	0.0358495i
$471$	24.6866	−	14.3285i	1.13750	−	0.660223i
$472$	−14.0354	+	25.4232i	−0.646031	+	1.17020i
$473$	33.8502	−	19.5434i	1.55643	−	0.898607i
$474$	0.499121	+	0.176770i	0.0229254	+	0.00811934i
$475$	−0.656931	+	1.13784i	−0.0301421	+	0.0522076i
$476$	3.07210	−	18.8265i	0.140810	−	0.862911i
$477$	42.8535	−	0.196898i	1.96213	−	0.00901534i
$478$	4.23333	+	4.98012i	0.193628	+	0.227785i
$479$	19.5734	−	33.9022i	0.894333	−	1.54903i	0.0597054	−	0.998216i	$-0.480984\pi$
$479$	19.5734	−	33.9022i	0.894333	−	1.54903i	0.834628	−	0.550814i	$-0.185683\pi$
$480$	9.70170	+	1.37004i	0.442820	+	0.0625333i
$481$	4.31614	+	7.47578i	0.196799	+	0.340866i
$482$	−9.58541	+	26.8686i	−0.436603	+	1.22383i
$483$	−0.0471030	−	20.5034i	−0.00214326	−	0.932937i
$484$	−1.93489	−	1.58188i	−0.0879496	−	0.0719035i
$485$	8.40251			0.381538
$486$	−21.6386	+	4.21561i	−0.981546	+	0.191224i
$487$			20.0755i			0.909707i	0.890566	+	0.454854i	$0.150308\pi$
$487$			20.0755i			0.909707i	−0.890566	+	0.454854i	$0.849692\pi$
$488$	−34.9753	+	0.670497i	−1.58326	+	0.0303520i
$489$	−13.0928	+	0.0300784i	−0.592077	+	0.00136019i
$490$	0.336552	−	0.943381i	0.0152039	−	0.0426176i
$491$	18.3558	−	10.5977i	0.828385	−	0.478268i	−0.0249145	−	0.999690i	$-0.507931\pi$
$491$	18.3558	−	10.5977i	0.828385	−	0.478268i	0.853299	+	0.521421i	$0.174598\pi$
$492$	25.1900	−	30.9563i	1.13565	−	1.39562i
$493$	−1.58692	−	0.916207i	−0.0714712	−	0.0412639i
$494$	5.40137	−	4.59141i	0.243019	−	0.206577i
$495$	0.0430410	+	9.36758i	0.00193455	+	0.421042i
$496$	−0.606562	+	1.80908i	−0.0272354	+	0.0812301i
$497$	−18.9601	−	10.9466i	−0.850479	−	0.491024i
$498$	20.9674	+	7.42588i	0.939571	+	0.332762i
$499$	−4.07075	−	7.05075i	−0.182232	−	0.315635i	0.760408	−	0.649445i	$-0.224999\pi$
$499$	−4.07075	−	7.05075i	−0.182232	−	0.315635i	−0.942640	+	0.333810i	$0.891665\pi$
$500$	1.87049	−	0.708000i	0.0836509	−	0.0316627i
$501$	18.4974	+	31.8692i	0.826404	+	1.42381i
$502$	−3.87995	−	21.2109i	−0.173171	−	0.946689i
$503$	−9.59614			−0.427871			−0.213935	−	0.976848i	$-0.568628\pi$
$503$	−9.59614			−0.427871			−0.213935	+	0.976848i	$0.568628\pi$
$504$	23.5517	−	0.559761i	1.04907	−	0.0249337i
$505$	2.22137			0.0988495
$506$	−3.38793	−	18.5211i	−0.150612	−	0.823365i
$507$	−1.34259	+	2.33782i	−0.0596265	+	0.103826i
$508$	0.392835	+	1.03785i	0.0174293	+	0.0460470i
$509$	0.164517	+	0.284953i	0.00729211	+	0.0126303i	0.869648	−	0.493672i	$-0.164345\pi$
$509$	0.164517	+	0.284953i	0.00729211	+	0.0126303i	−0.862356	+	0.506302i	$0.831012\pi$
$510$	6.39888	−	5.46472i	0.283347	−	0.241982i
$511$	19.0564	+	11.0022i	0.843004	+	0.486708i
$512$	−1.30047	−	22.5900i	−0.0574731	−	0.998347i
$513$	−6.82687	+	0.0470512i	−0.301414	+	0.00207736i
$514$	1.54960	−	1.31723i	0.0683500	−	0.0581007i
$515$	−12.7933	−	7.38623i	−0.563741	−	0.325476i
$516$	6.88511	−	42.8120i	0.303100	−	1.88469i
$517$	8.25920	−	4.76845i	0.363239	−	0.209716i
$518$	−2.98498	+	8.36712i	−0.131152	+	0.367630i
$519$	17.7977	−	30.9907i	0.781233	−	1.36034i
$520$	−10.7893	+	0.206838i	−0.473142	+	0.00907043i
$521$		−	14.4490i		−	0.633021i	−0.948589	−	0.316510i	$-0.897489\pi$
$521$		−	14.4490i		−	0.633021i	0.948589	−	0.316510i	$-0.102511\pi$
$522$	0.750600	−	2.13493i	0.0328529	−	0.0934435i
$523$	18.1246			0.792534			0.396267	−	0.918135i	$-0.370305\pi$
$523$	18.1246			0.792534			0.396267	+	0.918135i	$0.370305\pi$
$524$	7.62648	−	9.32842i	0.333164	−	0.407514i
$525$	4.15903	−	2.41397i	0.181515	−	0.105354i
$526$	2.09908	−	5.88388i	0.0915242	−	0.256549i
$527$	0.819351	+	1.41916i	0.0356915	+	0.0618194i
$528$	21.1922	−	4.34858i	0.922271	−	0.189248i
$529$	2.41035	−	4.17484i	0.104798	−	0.181515i
$530$	−13.0839	−	15.3920i	−0.568330	−	0.668586i
$531$	−26.6041	+	15.5233i	−1.15452	+	0.673653i
$532$	7.20031	+	1.17495i	0.312173	+	0.0509403i
$533$	−21.9782	+	38.0674i	−0.951983	+	1.64888i
$534$	2.15207	+	11.6141i	0.0931290	+	0.502591i
$535$	−12.1898	+	7.03777i	−0.527010	+	0.304269i
$536$	17.2314	+	9.51291i	0.744282	+	0.410895i
$537$	0.0298740	+	13.0038i	0.00128916	+	0.561156i
$538$	34.6829	−	6.34428i	1.49529	−	0.273521i
$539$		−	2.21155i		−	0.0952583i
$540$	8.09082	+	6.52216i	0.348173	+	0.280669i
$541$		−	3.63353i		−	0.156218i	−0.996945	−	0.0781089i	$-0.975112\pi$
$541$		−	3.63353i		−	0.156218i	0.996945	−	0.0781089i	$-0.0248882\pi$
$542$	−5.47276	−	29.9184i	−0.235075	−	1.28511i
$543$	0.0605401	+	26.3524i	0.00259802	+	1.13089i
$544$	−15.2780	−	12.0095i	−0.655041	−	0.514903i
$545$	14.2957	−	8.25365i	0.612363	−	0.353548i
$546$	−25.5124	+	4.72739i	−1.09183	+	0.202314i
$547$	11.7873	−	20.4162i	0.503987	−	0.872932i	−0.496002	−	0.868321i	$-0.665199\pi$
$547$	11.7873	−	20.4162i	0.503987	−	0.872932i	0.999989	−	0.00461043i	$-0.00146755\pi$
$548$	17.0708	+	2.78561i	0.729228	+	0.118995i
$549$	−32.2176	−	18.4040i	−1.37502	−	0.785464i
$550$	3.36462	−	2.86009i	0.143468	−	0.121954i
$551$	0.350409	−	0.606927i	0.0149279	−	0.0258560i
$552$	−18.3094	−	10.0533i	−0.779301	−	0.427895i
$553$	−0.300081	−	0.519755i	−0.0127607	−	0.0221022i
$554$	1.06604	+	0.380310i	0.0452916	+	0.0161578i
$555$	−3.38931	+	1.96721i	−0.143868	+	0.0835036i
$556$	14.6442	+	11.9724i	0.621054	+	0.507745i
$557$	32.3117			1.36909			0.684544	−	0.728971i	$-0.260001\pi$
$557$	32.3117			1.36909			0.684544	+	0.728971i	$0.260001\pi$
$558$	−1.53594	+	1.31782i	−0.0650215	+	0.0557880i
$559$			47.7582i			2.01996i
$560$	−7.35355	−	8.32210i	−0.310744	−	0.351673i
$561$	9.25288	−	16.1118i	0.390657	−	0.680242i
$562$	−27.3853	−	9.76974i	−1.15518	−	0.412111i
$563$	−13.2429	+	7.64582i	−0.558124	+	0.322233i	−0.752392	−	0.658716i	$-0.771100\pi$
$563$	−13.2429	+	7.64582i	−0.558124	+	0.322233i	0.194268	+	0.980948i	$0.437767\pi$
$564$	1.67992	−	10.4458i	0.0707373	−	0.439848i
$565$	−0.459459	−	0.265268i	−0.0193296	−	0.0111599i
$566$	13.4118	+	15.7777i	0.563741	+	0.663188i
$567$	21.7536	+	12.2943i	0.913565	+	0.516312i
$568$	−19.0983	+	11.5201i	−0.801348	+	0.483371i
$569$	−18.3848	−	10.6145i	−0.770730	−	0.444981i	0.0624050	−	0.998051i	$-0.480123\pi$
$569$	−18.3848	−	10.6145i	−0.770730	−	0.444981i	−0.833135	+	0.553070i	$0.813456\pi$
$570$	2.09002	+	2.44729i	0.0875412	+	0.102506i
$571$	−20.3971	−	35.3288i	−0.853591	−	1.47846i	−0.877946	−	0.478760i	$-0.841086\pi$
$571$	−20.3971	−	35.3288i	−0.853591	−	1.47846i	0.0243545	−	0.999703i	$-0.492247\pi$
$572$	−22.2841	+	8.43476i	−0.931744	+	0.352675i
$573$	11.7329	−	20.4303i	0.490150	−	0.853486i
$574$	−44.4980	+	8.13968i	−1.85731	+	0.339744i
$575$	−4.26372			−0.177809
$576$	11.0969	−	21.2805i	0.462371	−	0.886686i
$577$	29.2113			1.21608			0.608040	−	0.793906i	$-0.291956\pi$
$577$	29.2113			1.21608			0.608040	+	0.793906i	$0.291956\pi$
$578$	7.23184	−	1.32287i	0.300805	−	0.0550240i
$579$	19.2950	+	33.2433i	0.801872	+	1.38154i
$580$	−0.997726	+	0.377650i	−0.0414283	+	0.0156811i
$581$	−12.6060	−	21.8342i	−0.522984	−	0.905834i
$582$	6.87114	−	19.4010i	0.284818	−	0.804199i
$583$	−38.6288	−	22.3024i	−1.59984	−	0.923670i
$584$	19.1952	−	11.5785i	0.794305	−	0.479122i
$585$	−9.93862	−	5.67734i	−0.410911	−	0.234729i
$586$	24.6237	+	28.9674i	1.01719	+	1.19663i
$587$	−2.09726	−	1.21086i	−0.0865634	−	0.0499774i	0.456093	−	0.889932i	$-0.349248\pi$
$587$	−2.09726	−	1.21086i	−0.0865634	−	0.0499774i	−0.542657	+	0.839954i	$0.682582\pi$
$588$	−1.90301	−	1.54853i	−0.0784789	−	0.0638604i
$589$	−0.542766	+	0.313366i	−0.0223643	+	0.0129120i
$590$	13.6759	+	4.87888i	0.563027	+	0.200860i
$591$	−10.1694	+	0.0233624i	−0.418313	+	0.000961000i
$592$	5.99261	+	6.78192i	0.246295	+	0.278735i
$593$			7.77622i			0.319331i	0.987171	+	0.159666i	$0.0510416\pi$
$593$			7.77622i			0.319331i	−0.987171	+	0.159666i	$0.948958\pi$
$594$	21.6646	+	7.56095i	0.888907	+	0.310229i
$595$	−9.53775			−0.391010
$596$	16.8130	+	13.7455i	0.688686	+	0.563037i
$597$	0.0695099	+	30.2569i	0.00284485	+	1.23833i
$598$	21.6679	+	7.73006i	0.886068	+	0.316106i
$599$	9.47635	+	16.4135i	0.387193	+	0.670638i	0.992071	−	0.125680i	$-0.0401113\pi$
$599$	9.47635	+	16.4135i	0.387193	+	0.670638i	−0.604878	+	0.796318i	$0.706778\pi$
$600$	−0.105151	−	4.89785i	−0.00429279	−	0.199954i
$601$	−11.5216	+	19.9560i	−0.469976	+	0.814023i	−0.999411	−	0.0343283i	$-0.989071\pi$
$601$	−11.5216	+	19.9560i	−0.469976	+	0.814023i	0.529434	+	0.848351i	$0.322404\pi$
$602$	−37.4475	+	31.8321i	−1.52625	+	1.29738i
$603$	10.5214	+	18.0317i	0.428464	+	0.734309i
$604$	21.3710	+	3.48731i	0.869574	+	0.141897i
$605$	−0.624807	+	1.08220i	−0.0254020	+	0.0439976i
$606$	1.81652	−	5.12904i	0.0737910	−	0.208353i
$607$	26.8628	−	15.5092i	1.09033	−	0.629500i	0.156662	−	0.987652i	$-0.449927\pi$
$607$	26.8628	−	15.5092i	1.09033	−	0.629500i	0.933663	+	0.358153i	$0.116593\pi$
$608$	4.59311	−	5.84319i	0.186275	−	0.236973i
$609$	−2.21844	+	1.28762i	−0.0898957	+	0.0521770i
$610$	3.14725	+	17.2054i	0.127428	+	0.696625i
$611$			11.6526i			0.471416i
$612$	−7.38513	−	19.2435i	−0.298526	−	0.777873i
$613$		−	43.8644i		−	1.77167i	−0.464002	−	0.885834i	$-0.653587\pi$
$613$		−	43.8644i		−	1.77167i	0.464002	−	0.885834i	$-0.346413\pi$
$614$	−29.7478	+	5.44154i	−1.20052	+	0.219603i
$615$	−17.3045	−	9.93785i	−0.697787	−	0.400733i
$616$	−21.4667	−	11.8511i	−0.864918	−	0.477494i
$617$	20.2819	−	11.7098i	0.816520	−	0.471418i	−0.0326947	−	0.999465i	$-0.510409\pi$
$617$	20.2819	−	11.7098i	0.816520	−	0.471418i	0.849215	+	0.528047i	$0.177076\pi$
$618$	−27.5162	+	23.4992i	−1.10686	+	0.945275i
$619$	13.1137	−	22.7136i	0.527084	−	0.912935i	−0.472418	−	0.881374i	$-0.656619\pi$
$619$	13.1137	−	22.7136i	0.527084	−	0.912935i	0.999502	−	0.0315610i	$-0.0100479\pi$
$620$	0.941576	+	0.153646i	0.0378146	+	0.00617058i
$621$	−11.2094	−	19.1099i	−0.449819	−	0.766855i
$622$	19.6091	+	23.0682i	0.786251	+	0.924951i
$623$	6.69404	−	11.5944i	0.268191	−	0.464521i
$624$	−8.34536	+	25.0812i	−0.334082	+	1.00405i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.77338	−	7.77398i	0.110846	−	0.310711i
$627$	6.16207	+	3.53882i	0.246089	+	0.141327i
$628$	−20.8614	+	25.5169i	−0.832461	+	1.01824i
$629$	7.77258			0.309913
$630$	−2.17272	−	11.5770i	−0.0865632	−	0.461240i
$631$		−	7.35292i		−	0.292715i	−0.989232	−	0.146358i	$-0.953245\pi$
$631$		−	7.35292i		−	0.292715i	0.989232	−	0.146358i	$-0.0467550\pi$
$632$	−0.611301	+	0.0117190i	−0.0243162	+	0.000466157i
$633$	15.3103	+	26.3781i	0.608530	+	1.04843i
$634$	−3.98269	+	11.1638i	−0.158173	+	0.443370i
$635$	0.480516	−	0.277426i	0.0190687	−	0.0110093i
$636$	−46.2389	+	17.6234i	−1.83349	+	0.698815i
$637$	2.34016	+	1.35109i	0.0927204	+	0.0535322i
$638$	−1.79470	+	1.52558i	−0.0710529	+	0.0603983i
$639$	−23.6565	+	0.108694i	−0.935835	+	0.00429985i
$640$	−11.0428	+	2.46080i	−0.436507	+	0.0972718i
$641$	4.75502	+	2.74531i	0.187812	+	0.108433i	0.590958	−	0.806702i	$-0.298750\pi$
$641$	4.75502	+	2.74531i	0.187812	+	0.108433i	−0.403146	+	0.915136i	$0.632083\pi$
$642$	6.28175	+	33.9008i	0.247921	+	1.33796i
$643$	−10.2614	−	17.7733i	−0.404670	−	0.700909i	0.589613	−	0.807686i	$-0.299280\pi$
$643$	−10.2614	−	17.7733i	−0.404670	−	0.700909i	−0.994283	+	0.106777i	$0.965947\pi$
$644$	8.38108	+	22.1423i	0.330261	+	0.872528i
$645$	−21.6810	+	0.0498082i	−0.853688	+	0.00196120i
$646$	−1.14856	−	6.27893i	−0.0451894	−	0.247041i
$647$	39.5969			1.55672			0.778358	−	0.627820i	$-0.216053\pi$
$647$	39.5969			1.55672			0.778358	+	0.627820i	$0.216053\pi$
$648$	21.6757	−	13.3479i	0.851500	−	0.524354i
$649$	32.0601			1.25847
$650$	0.970876	+	5.30758i	0.0380809	+	0.208180i
$651$	2.29387	−	0.00526977i	0.0899039	−	0.000206538i
$652$	14.1393	−	5.35188i	0.553738	−	0.209596i
$653$	−22.5179	−	39.0021i	−0.881193	−	1.52627i	−0.850016	−	0.526757i	$-0.823408\pi$
$653$	−22.5179	−	39.0021i	−0.881193	−	1.52627i	−0.0311765	−	0.999514i	$-0.509925\pi$
$654$	−7.36701	−	39.7577i	−0.288073	−	1.55465i
$655$	−5.21744	−	3.01229i	−0.203862	−	0.117700i
$656$	−14.6500	+	43.6939i	−0.571986	+	1.70596i
$657$	23.7765	−	0.109245i	0.927610	−	0.00426206i
$658$	−9.13691	+	7.76680i	−0.356194	+	0.302781i
$659$	−22.1927	−	12.8129i	−0.864504	−	0.499121i	0.00101427	−	0.999999i	$-0.499677\pi$
$659$	−22.1927	−	12.8129i	−0.864504	−	0.499121i	−0.865518	+	0.500878i	$0.833010\pi$
$660$	−3.85240	−	10.1076i	−0.149955	−	0.393438i
$661$	9.96758	−	5.75478i	0.387694	−	0.223835i	−0.293467	−	0.955969i	$-0.594809\pi$
$661$	9.96758	−	5.75478i	0.387694	−	0.223835i	0.681160	+	0.732134i	$0.261476\pi$
$662$	−0.856403	+	2.40056i	−0.0332851	+	0.0933005i
$663$	11.3959	+	19.6341i	0.442582	+	0.762523i
$664$	−25.6799	+	0.492299i	−0.996574	+	0.0191049i
$665$		−	3.64777i		−	0.141455i
$666$	1.77061	+	9.43446i	0.0686098	+	0.365578i
$667$	2.27428			0.0880606
$668$	−32.9411	−	26.9311i	−1.27453	−	1.04199i
$669$	12.8645	+	7.38799i	0.497372	+	0.285636i
$670$	3.30681	−	9.26925i	0.127753	−	0.358102i
$671$	19.3098	+	33.4455i	0.745445	+	1.29115i
$672$	−25.2287	+	10.1736i	−0.973219	+	0.392457i
$673$	23.4948	−	40.6943i	0.905660	−	1.56865i	0.0856300	−	0.996327i	$-0.472710\pi$
$673$	23.4948	−	40.6943i	0.905660	−	1.56865i	0.820029	−	0.572321i	$-0.193957\pi$
$674$	−21.9455	−	25.8168i	−0.845308	−	0.994425i
$675$	2.56700	−	4.51780i	0.0988039	−	0.173890i
$676$	0.501343	−	3.07234i	0.0192824	−	0.118167i
$677$	−8.46874	+	14.6683i	−0.325480	+	0.563748i	−0.981609	−	0.190900i	$-0.938859\pi$
$677$	−8.46874	+	14.6683i	−0.325480	+	0.563748i	0.656129	+	0.754649i	$0.272193\pi$
$678$	−0.988215	+	0.843947i	−0.0379522	+	0.0324116i
$679$	−20.2031	+	11.6642i	−0.775323	+	0.447633i
$680$	−4.69611	+	8.50637i	−0.180087	+	0.326204i
$681$	−34.7296	−	19.9449i	−1.33084	−	0.764291i
$682$	2.07210	−	0.379034i	0.0793448	−	0.0145140i
$683$			2.98462i			0.114203i	0.998368	+	0.0571017i	$0.0181859\pi$
$683$			2.98462i			0.114203i	−0.998368	+	0.0571017i	$0.981814\pi$
$684$	7.35980	−	2.82449i	0.281409	−	0.107997i
$685$		−	8.64828i		−	0.330434i
$686$	−4.44513	−	24.3006i	−0.169716	−	0.927802i
$687$	−11.0129	+	6.39209i	−0.420169	+	0.243873i
$688$	9.95186	+	49.0712i	0.379411	+	1.87082i
$689$	47.1986	−	27.2501i	1.79812	−	1.03815i
$690$	−3.48665	+	9.84475i	−0.132735	+	0.374783i
$691$	4.17425	−	7.23001i	0.158796	−	0.275043i	−0.775639	−	0.631177i	$-0.782572\pi$
$691$	4.17425	−	7.23001i	0.158796	−	0.275043i	0.934435	+	0.356134i	$0.115905\pi$
$692$	−6.64593	+	40.7277i	−0.252640	+	1.54823i
$693$	−13.1074	−	22.4638i	−0.497911	−	0.853328i
$694$	−18.6950	+	15.8916i	−0.709653	+	0.603238i
$695$	4.72886	−	8.19062i	0.179376	−	0.310688i
$696$	0.0560881	+	2.61253i	0.00212601	+	0.0990277i
$697$	19.7894	+	34.2762i	0.749577	+	1.29830i
$698$	11.2205	+	4.00292i	0.424702	+	0.151513i
$699$	−0.0822543	−	35.8044i	−0.00311114	−	1.35425i
$700$	−3.51459	+	4.29891i	−0.132839	+	0.162484i
$701$	−9.37518			−0.354096			−0.177048	−	0.984202i	$-0.556655\pi$
$701$	−9.37518			−0.354096			−0.177048	+	0.984202i	$0.556655\pi$
$702$	−21.2360	+	18.3052i	−0.801502	+	0.690886i
$703$			2.97267i			0.112117i
$704$	−21.1391	+	13.3102i	−0.796711	+	0.501648i
$705$	−5.29000	+	0.0121528i	−0.199233	+	0.000457703i
$706$	22.9848	+	8.19987i	0.865046	+	0.308606i
$707$	−5.34107	+	3.08367i	−0.200872	+	0.115973i
$708$	22.4486	−	27.5873i	0.843669	−	1.03679i
$709$	−33.2487	−	19.1962i	−1.24868	−	0.720927i	−0.277836	−	0.960629i	$-0.589617\pi$
$709$	−33.2487	−	19.1962i	−1.24868	−	0.720927i	−0.970847	+	0.239702i	$0.922950\pi$
$710$	7.22273	+	8.49686i	0.271064	+	0.318881i
$711$	−0.563103	−	0.321667i	−0.0211180	−	0.0120635i
$712$	−7.04469	−	11.6789i	−0.264011	−	0.437686i
$713$	−1.76137	−	1.01693i	−0.0659639	−	0.0380843i
$714$	−7.79948	+	22.0223i	−0.291888	+	0.824162i
$715$	5.95675	+	10.3174i	0.222770	+	0.385848i
$716$	−5.31551	−	14.0432i	−0.198650	−	0.524820i
$717$	−4.01854	−	6.92354i	−0.150075	−	0.258564i
$718$	9.91975	−	1.81455i	0.370202	−	0.0677182i
$719$	−12.8804			−0.480356			−0.240178	−	0.970729i	$-0.577206\pi$
$719$	−12.8804			−0.480356			−0.240178	+	0.970729i	$0.577206\pi$
$720$	−11.3949	−	3.76242i	−0.424664	−	0.140217i
$721$	41.0138			1.52744
$722$	−24.0301	+	4.39564i	−0.894307	+	0.163589i
$723$	17.3997	−	30.2977i	0.647103	−	1.12679i
$724$	−10.7720	−	28.4588i	−0.400337	−	1.05766i
$725$	0.266702	+	0.461941i	0.00990505	+	0.0171561i
$726$	1.98781	+	2.32762i	0.0737747	+	0.0863860i
$727$	3.75846	+	2.16995i	0.139393	+	0.0804788i	0.568075	−	0.822977i	$-0.307688\pi$
$727$	3.75846	+	2.16995i	0.139393	+	0.0804788i	−0.428681	+	0.903456i	$0.641022\pi$
$728$	25.6548	−	15.4749i	0.950830	−	0.573538i
$729$	26.9974	−	0.372154i	0.999905	−	0.0137835i
$730$	−7.25938	−	8.53998i	−0.268682	−	0.316079i
$731$	37.2407	+	21.5009i	1.37740	+	0.795241i
$732$	42.3001	+	6.80280i	1.56346	+	0.251439i
$733$	18.8815	−	10.9012i	0.697404	−	0.402646i	−0.108976	−	0.994044i	$-0.534757\pi$
$733$	18.8815	−	10.9012i	0.697404	−	0.402646i	0.806380	+	0.591398i	$0.201424\pi$
$734$	−45.1849	−	16.1197i	−1.66780	−	0.594991i
$735$	−0.610920	+	1.06378i	−0.0225341	+	0.0392381i
$736$	23.8745	+	3.42742i	0.880025	+	0.126336i
$737$		−	21.7297i		−	0.800425i
$738$	−37.0968	+	31.8288i	−1.36555	+	1.17163i
$739$	−31.8843			−1.17288			−0.586441	−	0.809992i	$-0.699471\pi$
$739$	−31.8843			−1.17288			−0.586441	+	0.809992i	$0.699471\pi$
$740$	2.86414	−	3.50331i	0.105288	−	0.128784i
$741$	−7.50917	+	4.35845i	−0.275856	+	0.160112i
$742$	52.8261	+	18.8458i	1.93931	+	0.691850i
$743$	12.2533	+	21.2234i	0.449532	+	0.778612i	0.998355	−	0.0573263i	$-0.0182575\pi$
$743$	12.2533	+	21.2234i	0.449532	+	0.778612i	−0.548824	+	0.835938i	$0.684924\pi$
$744$	1.12473	−	2.04842i	0.0412348	−	0.0750985i
$745$	5.42917	−	9.40360i	0.198909	−	0.344521i
$746$	10.5513	−	8.96912i	0.386312	−	0.328383i
$747$	−23.6552	−	13.5128i	−0.865497	−	0.494407i
$748$	−3.45516	+	21.1740i	−0.126333	+	0.774197i
$749$	19.5395	−	33.8434i	0.713957	−	1.23661i
$750$	−2.40849	+	0.446288i	−0.0879456	+	0.0162961i
$751$	−5.51362	+	3.18329i	−0.201195	+	0.116160i	−0.597213	−	0.802083i	$-0.703725\pi$
$751$	−5.51362	+	3.18329i	−0.201195	+	0.116160i	0.396018	+	0.918243i	$0.370392\pi$
$752$	2.42818	+	11.9730i	0.0885467	+	0.436611i
$753$	0.0606699	+	26.4089i	0.00221093	+	0.962395i
$754$	−0.517868	−	2.83108i	−0.0188597	−	0.103102i
$755$		−	10.8268i		−	0.394029i
$756$	−28.5076	−	4.45039i	−1.03681	−	0.161859i
$757$		−	25.0713i		−	0.911232i	−0.890176	−	0.455616i	$-0.849419\pi$
$757$		−	25.0713i		−	0.911232i	0.890176	−	0.455616i	$-0.150581\pi$
$758$	22.1820	−	4.05759i	0.805686	−	0.147378i
$759$	0.0529763	+	23.0600i	0.00192292	+	0.837024i
$760$	−3.25332	−	1.79606i	−0.118010	−	0.0651498i
$761$	11.3876	−	6.57465i	0.412801	−	0.238331i	−0.279191	−	0.960235i	$-0.590066\pi$
$761$	11.3876	−	6.57465i	0.412801	−	0.238331i	0.691993	+	0.721905i	$0.256733\pi$
$762$	−0.247624	−	1.33636i	−0.00897047	−	0.0484111i
$763$	−22.9152	+	39.6903i	−0.829587	+	1.43689i
$764$	−4.38125	+	26.8492i	−0.158508	+	0.971371i
$765$	−8.90147	+	5.19394i	−0.321833	+	0.187787i
$766$	−6.78093	−	7.97713i	−0.245005	−	0.288225i
$767$	−19.5863	+	33.9245i	−0.707221	+	1.22494i
$768$	−3.34838	+	27.5098i	−0.120824	+	0.992674i
$769$	−11.6041	−	20.0990i	−0.418456	−	0.724787i	0.577329	−	0.816512i	$-0.304095\pi$
$769$	−11.6041	−	20.0990i	−0.418456	−	0.724787i	−0.995784	+	0.0917252i	$0.970762\pi$
$770$	−4.11960	+	11.5475i	−0.148460	+	0.416145i
$771$	−2.15431	+	1.25040i	−0.0775856	+	0.0450321i
$772$	−34.3614	−	28.0923i	−1.23669	−	1.01106i
$773$	−32.0701			−1.15348			−0.576740	−	0.816928i	$-0.695675\pi$
$773$	−32.0701			−1.15348			−0.576740	+	0.816928i	$0.695675\pi$
$774$	−17.6146	+	50.1012i	−0.633143	+	1.80085i
$775$		−	0.477015i		−	0.0171349i
$776$	0.455523	+	23.7615i	0.0163523	+	0.852989i
$777$	5.41843	−	9.43498i	0.194385	−	0.338478i
$778$	12.3569	−	34.6373i	0.443017	−	1.24181i
$779$	−13.1092	+	7.56858i	−0.469685	+	0.271172i
$780$	13.0489	+	2.09855i	0.467226	+	0.0751402i
$781$	21.3243	+	12.3116i	0.763043	+	0.440543i
$782$	15.7827	−	13.4161i	0.564389	−	0.479757i
$783$	−1.36925	+	2.40981i	−0.0489329	+	0.0861196i
$784$	2.68604	+	0.900595i	0.0959299	+	0.0321641i
$785$	14.2718	+	8.23981i	0.509381	+	0.294091i
$786$	−11.2218	+	9.58356i	−0.400269	+	0.341834i
$787$	20.0375	+	34.7059i	0.714258	+	1.23713i	0.963245	+	0.268624i	$0.0865690\pi$
$787$	20.0375	+	34.7059i	0.714258	+	1.23713i	−0.248987	+	0.968507i	$0.580098\pi$
$788$	10.9822	−	4.15689i	0.391226	−	0.148083i
$789$	−3.81031	+	6.63481i	−0.135651	+	0.236205i
$790$	0.0550079	+	0.300717i	0.00195709	+	0.0106990i
$791$	1.47297			0.0523727
$792$	−26.4883	+	0.629558i	−0.941222	+	0.0223704i
$793$	−47.1872			−1.67567
$794$	6.84622	+	37.4269i	0.242963	+	1.32823i
$795$	12.4201	+	21.3985i	0.440495	+	0.758927i
$796$	−12.3680	−	32.6754i	−0.438371	−	1.15815i
$797$	−28.1638	−	48.7811i	−0.997612	−	1.72791i	−0.558622	−	0.829423i	$-0.688670\pi$
$797$	−28.1638	−	48.7811i	−0.997612	−	1.72791i	−0.438990	−	0.898492i	$-0.644664\pi$
$798$	−8.42256	−	2.98296i	−0.298155	−	0.105596i
$799$	9.08646	+	5.24607i	0.321456	+	0.185593i
$800$	2.10356	+	5.25119i	0.0743722	+	0.185658i
$801$	−0.0664679	−	14.4663i	−0.00234853	−	0.511141i
$802$	−11.2469	+	9.56042i	−0.397143	+	0.337590i
$803$	−21.4325	−	12.3741i	−0.756337	−	0.436671i
$804$	−18.6982	−	15.2152i	−0.659433	−	0.536599i
$805$	10.2517	−	5.91884i	0.361326	−	0.208612i
$806$	−0.864821	+	2.42416i	−0.0304620	+	0.0853873i
$807$	−43.1824	+	0.0992039i	−1.52009	+	0.00349214i
$808$	0.120426	+	6.28182i	0.00423658	+	0.220994i
$809$			17.2021i			0.604793i	0.953182	+	0.302397i	$0.0977867\pi$
$809$			17.2021i			0.604793i	−0.953182	+	0.302397i	$0.902213\pi$
$810$	−8.33225	−	9.62152i	−0.292765	−	0.338066i
$811$	−56.3100			−1.97731			−0.988656	−	0.150196i	$-0.952010\pi$
$811$	−56.3100			−1.97731			−0.988656	+	0.150196i	$0.952010\pi$
$812$	1.87469	−	2.29305i	0.0657889	−	0.0804705i
$813$	0.0855761	+	37.2503i	0.00300128	+	1.30643i
$814$	3.35718	−	9.41042i	0.117669	−	0.329835i
$815$	−3.77957	−	6.54641i	−0.132393	−	0.229311i
$816$	15.8006	+	17.7992i	0.553132	+	0.623096i
$817$	−8.22317	+	14.2430i	−0.287692	+	0.498298i
$818$	3.83579	+	4.51245i	0.134115	+	0.157774i
$819$	31.7777	−	0.146008i	1.11040	−	0.00510194i
$820$	22.7414	+	3.71094i	0.794165	+	0.129592i
$821$	−1.37477	+	2.38117i	−0.0479797	+	0.0831033i	−0.889018	−	0.457873i	$-0.848612\pi$
$821$	−1.37477	+	2.38117i	−0.0479797	+	0.0831033i	0.841038	+	0.540976i	$0.181945\pi$
$822$	−19.9685	−	7.07212i	−0.696482	−	0.246669i
$823$	−23.4482	+	13.5378i	−0.817353	+	0.471899i	−0.849503	−	0.527584i	$-0.823098\pi$
$823$	−23.4482	+	13.5378i	−0.817353	+	0.471899i	0.0321498	+	0.999483i	$0.489765\pi$
$824$	20.1940	−	36.5787i	0.703491	−	1.27428i
$825$	−4.67762	+	2.71497i	−0.162854	+	0.0945231i
$826$	−39.6552	+	7.25383i	−1.37978	+	0.252393i
$827$			29.3670i			1.02119i	0.859821	+	0.510596i	$0.170575\pi$
$827$			29.3670i			1.02119i	−0.859821	+	0.510596i	$0.829425\pi$
$828$	19.8799	+	16.1011i	0.690875	+	0.559551i
$829$			30.1503i			1.04716i	0.851975	+	0.523582i	$0.175405\pi$
$829$			30.1503i			1.04716i	−0.851975	+	0.523582i	$0.824595\pi$
$830$	2.31081	+	12.6327i	0.0802093	+	0.438487i
$831$	−1.20209	−	0.690350i	−0.0417001	−	0.0239480i
$832$	−1.16984	−	30.4999i	−0.0405567	−	1.05740i
$833$	2.10710	−	1.21653i	0.0730066	−	0.0421504i
$834$	−15.0448	−	17.6166i	−0.520958	−	0.610013i
$835$	−10.6372	+	18.4242i	−0.368115	+	0.637594i
$836$	−8.09812	−	1.32145i	−0.280079	−	0.0457033i
$837$	2.13797	−	1.25409i	0.0738992	−	0.0433475i
$838$	3.49480	−	2.97074i	0.120726	−	0.102623i
$839$	−3.81222	+	6.60296i	−0.131612	+	0.227959i	−0.924298	−	0.381671i	$-0.875349\pi$
$839$	−3.81222	+	6.60296i	−0.131612	+	0.227959i	0.792686	+	0.609630i	$0.208682\pi$
$840$	7.05196	+	11.6305i	0.243316	+	0.401289i
$841$	14.3577	+	24.8683i	0.495094	+	0.857529i
$842$	−8.39058	−	2.99335i	−0.289159	−	0.103158i
$843$	30.8804	+	17.7343i	1.06358	+	0.610803i
$844$	−27.2653	−	22.2908i	−0.938511	−	0.767282i
$845$	−1.55649			−0.0535448
$846$	−4.29783	+	12.2243i	−0.147762	+	0.420281i
$847$		−	3.46939i		−	0.119210i
$848$	42.8179	−	37.8346i	1.47037	−	1.29925i
$849$	−12.7313	−	21.9348i	−0.436938	−	0.752799i
$850$	4.57582	+	1.63243i	0.156949	+	0.0559918i
$851$	−8.35443	+	4.82343i	−0.286386	+	0.165345i
$852$	25.5253	−	9.72868i	0.874481	−	0.333299i
$853$	19.9923	+	11.5426i	0.684525	+	0.395211i	0.801558	−	0.597917i	$-0.204005\pi$
$853$	19.9923	+	11.5426i	0.684525	+	0.395211i	−0.117033	+	0.993128i	$0.537338\pi$
$854$	−31.4515	−	36.9998i	−1.07625	−	1.26611i
$855$	−1.98646	−	3.40442i	−0.0679354	−	0.116429i
$856$	−20.5630	−	34.0900i	−0.702829	−	1.16517i
$857$	0.537623	+	0.310397i	0.0183649	+	0.0106030i	0.509154	−	0.860675i	$-0.329958\pi$
$857$	0.537623	+	0.310397i	0.0183649	+	0.0106030i	−0.490789	+	0.871278i	$0.663292\pi$
$858$	28.6935	−	5.31685i	0.979581	−	0.181514i
$859$	−12.4175	−	21.5077i	−0.423678	−	0.733833i	0.572618	−	0.819823i	$-0.305928\pi$
$859$	−12.4175	−	21.5077i	−0.423678	−	0.733833i	−0.996296	+	0.0859901i	$0.972595\pi$
$860$	23.4140	−	8.86243i	0.798410	−	0.302206i
$861$	55.4028	−	0.127278i	1.88812	−	0.00433763i
$862$	−23.6292	+	4.32231i	−0.804813	+	0.147219i
$863$	2.55660			0.0870275			0.0435138	−	0.999053i	$-0.486145\pi$
$863$	2.55660			0.0870275			0.0435138	+	0.999053i	$0.486145\pi$
$864$	−18.0055	+	23.2337i	−0.612558	+	0.790426i
$865$	20.6332			0.701549
$866$	−24.5571	+	4.49205i	−0.834485	+	0.152646i
$867$	−9.00410	+	0.0206853i	−0.305795	+	0.000702511i
$868$	−2.47722	+	0.937655i	−0.0840825	+	0.0318261i
$869$	0.337498	+	0.584563i	0.0114488	+	0.0198299i
$870$	1.28470	−	0.238052i	0.0435553	−	0.00807070i
$871$	22.9934	+	13.2752i	0.779101	+	0.449814i
$872$	24.1156	+	39.9796i	0.816657	+	1.35388i
$873$	−12.5033	+	21.8880i	−0.423173	+	0.740798i
$874$	5.13106	+	6.03621i	0.173561	+	0.204178i
$875$	2.40441	+	1.38819i	0.0812839	+	0.0469293i
$876$	−25.6548	+	9.77805i	−0.866795	+	0.330370i
$877$	14.8560	−	8.57713i	0.501653	−	0.289629i	−0.227743	−	0.973721i	$-0.573135\pi$
$877$	14.8560	−	8.57713i	0.501653	−	0.289629i	0.729396	+	0.684092i	$0.239801\pi$
$878$	51.0017	+	18.1949i	1.72122	+	0.614049i
$879$	−23.3743	−	40.2715i	−0.788396	−	1.35832i
$880$	8.27046	+	9.35979i	0.278797	+	0.315518i
$881$			0.662030i			0.0223043i	0.999938	+	0.0111522i	$0.00354992\pi$
$881$			0.662030i			0.0223043i	−0.999938	+	0.0111522i	$0.996450\pi$
$882$	1.95665	+	2.28049i	0.0658837	+	0.0767882i
$883$	−11.4683			−0.385939			−0.192969	−	0.981205i	$-0.561812\pi$
$883$	−11.4683			−0.385939			−0.192969	+	0.981205i	$0.561812\pi$
$884$	−20.2944	−	16.5918i	−0.682576	−	0.558042i
$885$	−15.4213	−	8.85630i	−0.518380	−	0.297701i
$886$	−17.4592	−	6.22858i	−0.586553	−	0.209253i
$887$	23.5408	+	40.7738i	0.790422	+	1.36905i	0.925706	+	0.378245i	$0.123472\pi$
$887$	23.5408	+	40.7738i	0.790422	+	1.36905i	−0.135283	+	0.990807i	$0.543194\pi$
$888$	−5.74684	−	9.47800i	−0.192851	−	0.318061i
$889$	−0.770239	+	1.33409i	−0.0258330	+	0.0447440i
$890$	−5.19596	+	4.41681i	−0.174169	+	0.148052i
$891$	−24.4660	−	13.8273i	−0.819643	−	0.463231i
$892$	−16.9064	−	2.75879i	−0.566069	−	0.0923710i
$893$	−2.00639	+	3.47518i	−0.0671414	+	0.116292i
$894$	−17.2728	−	20.2255i	−0.577690	−	0.676442i
$895$	−6.50193	+	3.75389i	−0.217335	+	0.125479i
$896$	23.1355	−	21.2463i	0.772902	−	0.709789i
$897$	−24.4333	−	14.0318i	−0.815805	−	0.468510i
$898$	6.34796	+	34.7030i	0.211834	+	1.15805i
$899$			0.254441i			0.00848609i
$900$	−0.939080	+	5.92606i	−0.0313027	+	0.197535i
$901$		−	49.0725i		−	1.63484i
$902$	50.0465	−	9.15463i	1.66636	−	0.304816i
$903$	52.0608	−	30.2170i	1.73248	−	1.00556i
$904$	0.725246	−	1.31369i	0.0241213	−	0.0436926i
$905$	−13.1762	+	7.60731i	−0.437993	+	0.252876i
$906$	−24.9987	−	8.85363i	−0.830526	−	0.294142i
$907$	5.68246	−	9.84232i	0.188683	−	0.326809i	−0.756128	−	0.654423i	$-0.772911\pi$
$907$	5.68246	−	9.84232i	0.188683	−	0.326809i	0.944811	+	0.327615i	$0.106245\pi$
$908$	45.6413	+	7.44773i	1.51466	+	0.247162i
$909$	−3.30550	+	5.78653i	−0.109636	+	0.191927i
$910$	−9.70229	−	11.4138i	−0.321628	−	0.378365i
$911$	0.698984	−	1.21068i	0.0231584	−	0.0401115i	−0.854214	−	0.519922i	$-0.825961\pi$
$911$	0.698984	−	1.21068i	0.0231584	−	0.0401115i	0.877372	+	0.479810i	$0.159294\pi$
$912$	−6.80741	+	6.04305i	−0.225416	+	0.200105i
$913$	14.1778	+	24.5567i	0.469217	+	0.812708i
$914$	12.6188	−	35.3714i	0.417392	−	1.16998i
$915$	−0.0492127	−	21.4218i	−0.00162692	−	0.708182i
$916$	9.30648	−	11.3833i	0.307495	−	0.376116i
$917$	16.7265			0.552358
$918$	4.71343	+	24.8005i	0.155566	+	0.818537i
$919$		−	7.89210i		−	0.260336i	−0.991492	−	0.130168i	$-0.958448\pi$
$919$		−	7.89210i		−	0.260336i	0.991492	−	0.130168i	$-0.0415517\pi$
$920$	−0.231148	−	12.0574i	−0.00762072	−	0.397521i
$921$	37.0379	−	0.0850880i	1.22044	−	0.00280374i
$922$	5.69950	−	15.9761i	0.187703	−	0.526146i
$923$	−26.0551	+	15.0429i	−0.857612	+	0.495143i
$924$	23.2940	+	18.9550i	0.766316	+	0.623573i
$925$	−1.95942	−	1.13127i	−0.0644254	−	0.0371960i
$926$	−27.2560	+	23.1689i	−0.895688	+	0.761377i
$927$	38.2777	−	22.3348i	1.25721	−	0.733571i
$928$	−1.12205	−	2.80100i	−0.0368330	−	0.0919475i
$929$	−15.9015	−	9.18072i	−0.521710	−	0.301210i	0.215924	−	0.976410i	$-0.430724\pi$
$929$	−15.9015	−	9.18072i	−0.521710	−	0.301210i	−0.737634	+	0.675201i	$0.764057\pi$
$930$	−1.10141	−	0.390078i	−0.0361166	−	0.0127912i
$931$	0.465271	+	0.805873i	0.0152486	+	0.0264114i
$932$	14.6356	+	38.6663i	0.479405	+	1.26656i
$933$	−18.6141	−	32.0702i	−0.609399	−	1.04993i
$934$	1.89333	+	10.3504i	0.0619515	+	0.338676i
$935$	10.7270			0.350811
$936$	15.5162	−	28.4133i	0.507163	−	0.928717i
$937$	−11.5833			−0.378411			−0.189205	−	0.981938i	$-0.560591\pi$
$937$	−11.5833			−0.378411			−0.189205	+	0.981938i	$0.560591\pi$
$938$	4.91651	+	26.8775i	0.160530	+	0.877583i
$939$	−5.03432	+	8.76614i	−0.164289	+	0.286072i
$940$	5.71284	−	2.16237i	0.186332	−	0.0705287i
$941$	2.75857	+	4.77799i	0.0899270	+	0.155758i	0.907480	−	0.420095i	$-0.138003\pi$
$941$	2.75857	+	4.77799i	0.0899270	+	0.155758i	−0.817553	+	0.575853i	$0.804670\pi$
$942$	30.6961	−	26.2148i	1.00013	−	0.854125i
$943$	−42.5416	−	24.5614i	−1.38534	−	0.799829i
$944$	−13.0556	+	38.9386i	−0.424924	+	1.26734i
$945$	0.0994258	+	14.4261i	0.00323432	+	0.469282i
$946$	42.1168	−	35.8013i	1.36934	−	1.16400i
$947$	−14.0517	−	8.11276i	−0.456620	−	0.263629i	0.254002	−	0.967204i	$-0.418253\pi$
$947$	−14.0517	−	8.11276i	−0.456620	−	0.263629i	−0.710622	+	0.703574i	$0.751586\pi$
$948$	0.739326	+	0.118900i	0.0240122	+	0.00386169i
$949$	26.1873	−	15.1192i	0.850075	−	0.490791i
$950$	−0.624333	+	1.75005i	−0.0202560	+	0.0567792i
$951$	7.22951	−	12.5886i	0.234433	−	0.408212i
$952$	−0.517067	−	26.9719i	−0.0167582	−	0.874163i
$953$		−	0.197221i		−	0.00638861i	−0.999995	−	0.00319431i	$-0.998983\pi$
$953$		−	0.197221i		−	0.00638861i	0.999995	−	0.00319431i	$-0.00101678\pi$
$954$	59.5648	−	11.1788i	1.92848	−	0.361928i
$955$	13.6022			0.440156
$956$	7.15641	+	5.85075i	0.231455	+	0.189227i
$957$	2.49506	−	1.44817i	0.0806537	−	0.0468128i
$958$	18.6021	−	52.1432i	0.601008	−	1.68467i
$959$	12.0054	+	20.7940i	0.387676	+	0.671474i
$960$	13.8450	−	0.562884i	0.446844	−	0.0181670i
$961$	−15.3862	+	26.6497i	−0.496330	+	0.859669i
$962$	7.90667	+	9.30146i	0.254921	+	0.299891i
$963$	−0.194015	−	42.2262i	−0.00625206	−	1.36072i
$964$	−6.49732	+	39.8170i	−0.209265	+	1.28242i
$965$	−11.0958	+	19.2185i	−0.357188	+	0.618667i
$966$	−5.28301	−	28.5109i	−0.169978	−	0.917324i
$967$	21.8675	−	12.6252i	0.703213	−	0.406000i	−0.105330	−	0.994437i	$-0.533590\pi$
$967$	21.8675	−	12.6252i	0.703213	−	0.406000i	0.808543	+	0.588437i	$0.200257\pi$
$968$	−3.09423	−	1.70823i	−0.0994522	−	0.0549045i
$969$	0.0179597	+	7.81767i	0.000576949	+	0.251140i
$970$	11.6890	−	2.13818i	0.375311	−	0.0686528i
$971$		−	10.6137i		−	0.340610i	−0.985391	−	0.170305i	$-0.945525\pi$
$971$		−	10.6137i		−	0.340610i	0.985391	−	0.170305i	$-0.0544753\pi$
$972$	−29.0294	+	11.3708i	−0.931118	+	0.364719i
$973$			26.2581i			0.841798i
$974$	5.10860	+	27.9276i	0.163690	+	0.894859i
$975$	−0.0151813	−	6.60827i	−0.000486192	−	0.211634i
$976$	−48.4846	+	9.83288i	−1.55195	+	0.314743i
$977$	−24.4452	+	14.1134i	−0.782071	+	0.451529i	−0.837164	−	0.546952i	$-0.815788\pi$
$977$	−24.4452	+	14.1134i	−0.782071	+	0.451529i	0.0550925	+	0.998481i	$0.482455\pi$
$978$	−18.2061	+	3.37356i	−0.582168	+	0.107874i
$979$	−7.52873	+	13.0401i	−0.240619	+	0.416765i
$980$	0.228127	−	1.39801i	0.00728724	−	0.0446577i
$981$	0.227535	+	49.5214i	0.00726462	+	1.58110i
$982$	22.8385	−	19.4138i	0.728806	−	0.619519i
$983$	22.5114	−	38.9908i	0.718001	−	1.24361i	−0.243790	−	0.969828i	$-0.578391\pi$
$983$	22.5114	−	38.9908i	0.718001	−	1.24361i	0.961791	−	0.273786i	$-0.0882760\pi$
$984$	27.1652	−	49.4744i	0.865995	−	1.57719i
$985$	−2.93566	−	5.08471i	−0.0935378	−	0.162012i
$986$	−2.44076	−	0.870743i	−0.0777295	−	0.0277301i
$987$	12.7025	−	7.37273i	0.404324	−	0.234677i
$988$	6.34563	−	7.76174i	0.201882	−	0.246934i
$989$	−53.3713			−1.69711
$990$	2.44364	+	13.0206i	0.0776639	+	0.413821i
$991$			45.4039i			1.44230i	0.692778	+	0.721151i	$0.256387\pi$
$991$			45.4039i			1.44230i	−0.692778	+	0.721151i	$0.743613\pi$
$992$	−0.383452	+	2.67102i	−0.0121746	+	0.0848049i
$993$	1.55457	−	2.70694i	0.0493328	−	0.0859020i
$994$	−29.1616	−	10.4034i	−0.924950	−	0.329977i
$995$	−15.1285	+	8.73444i	−0.479605	+	0.276900i
$996$	31.0580	+	4.99482i	0.984111	+	0.158267i
$997$	−15.3295	−	8.85052i	−0.485492	−	0.280299i	0.237211	−	0.971458i	$-0.423767\pi$
$997$	−15.3295	−	8.85052i	−0.485492	−	0.280299i	−0.722702	+	0.691160i	$0.757100\pi$
$998$	−7.45715	−	8.77263i	−0.236052	−	0.277693i
$999$	−0.0810249	−	11.7563i	−0.00256351	−	0.371951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.a.11.24	✓	48
3.2	odd	2		1080.2.bm.b.251.1		48
4.3	odd	2		1440.2.cc.a.911.24		48
8.3	odd	2		360.2.bm.b.11.15	yes	48
8.5	even	2		1440.2.cc.b.911.24		48
9.4	even	3		1080.2.bm.a.611.10		48
9.5	odd	6		360.2.bm.b.131.15	yes	48
12.11	even	2		4320.2.cc.b.1871.6		48
24.5	odd	2		4320.2.cc.a.1871.19		48
24.11	even	2		1080.2.bm.a.251.10		48
36.23	even	6		1440.2.cc.b.1391.24		48
36.31	odd	6		4320.2.cc.a.3311.19		48
72.5	odd	6		1440.2.cc.a.1391.24		48
72.13	even	6		4320.2.cc.b.3311.6		48
72.59	even	6	inner	360.2.bm.a.131.24	yes	48
72.67	odd	6		1080.2.bm.b.611.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.24	✓	48	1.1	even	1	trivial
360.2.bm.a.131.24	yes	48	72.59	even	6	inner
360.2.bm.b.11.15	yes	48	8.3	odd	2
360.2.bm.b.131.15	yes	48	9.5	odd	6
1080.2.bm.a.251.10		48	24.11	even	2
1080.2.bm.a.611.10		48	9.4	even	3
1080.2.bm.b.251.1		48	3.2	odd	2
1080.2.bm.b.611.1		48	72.67	odd	6
1440.2.cc.a.911.24		48	4.3	odd	2
1440.2.cc.a.1391.24		48	72.5	odd	6
1440.2.cc.b.911.24		48	8.5	even	2
1440.2.cc.b.1391.24		48	36.23	even	6
4320.2.cc.a.1871.19		48	24.5	odd	2
4320.2.cc.a.3311.19		48	36.31	odd	6
4320.2.cc.b.1871.6		48	12.11	even	2
4320.2.cc.b.3311.6		48	72.13	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39113 - 0.254469i) q^{2} +(-1.73205 + 0.00397907i) q^{3} +(1.87049 - 0.708000i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40849 + 0.446288i) q^{6} +(2.40441 + 1.38819i) q^{7} +(2.42193 - 1.46090i) q^{8} +(2.99997 - 0.0137839i) q^{9} +O(q^{10})\)	\(q+(1.39113 - 0.254469i) q^{2} +(-1.73205 + 0.00397907i) q^{3} +(1.87049 - 0.708000i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.40849 + 0.446288i) q^{6} +(2.40441 + 1.38819i) q^{7} +(2.42193 - 1.46090i) q^{8} +(2.99997 - 0.0137839i) q^{9} +(-0.915942 - 1.07752i) q^{10} +(-2.70422 - 1.56128i) q^{11} +(-3.23696 + 1.23373i) q^{12} +(3.30414 - 1.90765i) q^{13} +(3.69810 + 1.31930i) q^{14} +(0.869469 + 1.49801i) q^{15} +(2.99747 - 2.64862i) q^{16} -3.43533i q^{17} +(4.16984 - 0.782575i) q^{18} +1.31386 q^{19} +(-1.54839 - 1.26589i) q^{20} +(-4.17007 - 2.39484i) q^{21} +(-4.15922 - 1.48381i) q^{22} +(2.13186 + 3.69249i) q^{23} +(-4.18909 + 2.53999i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.11106 - 3.49459i) q^{26} +(-5.19603 + 0.0358114i) q^{27} +(5.48026 + 0.894268i) q^{28} +(0.266702 - 0.461941i) q^{29} +(1.59074 + 1.86267i) q^{30} +(-0.413107 + 0.238507i) q^{31} +(3.49588 - 4.44734i) q^{32} +(4.69004 + 2.69345i) q^{33} +(-0.874185 - 4.77899i) q^{34} -2.77637i q^{35} +(5.60165 - 2.14976i) q^{36} +2.26255i q^{37} +(1.82775 - 0.334338i) q^{38} +(-5.71534 + 3.31728i) q^{39} +(-2.47615 - 1.36700i) q^{40} +(-9.97758 + 5.76056i) q^{41} +(-6.41053 - 2.27038i) q^{42} +(-6.25878 + 10.8405i) q^{43} +(-6.16360 - 1.00577i) q^{44} +(-1.51192 - 2.59116i) q^{45} +(3.90532 + 4.59424i) q^{46} +(-1.52710 + 2.64501i) q^{47} +(-5.18122 + 4.59945i) q^{48} +(0.354125 + 0.613362i) q^{49} +(-0.475189 + 1.33199i) q^{50} +(0.0136694 + 5.95014i) q^{51} +(4.82976 - 5.90757i) q^{52} +14.2847 q^{53} +(-7.21924 + 1.37205i) q^{54} +3.12256i q^{55} +(7.85133 - 0.150515i) q^{56} +(-2.27567 + 0.00522795i) q^{57} +(0.253467 - 0.710488i) q^{58} +(-8.89170 + 5.13363i) q^{59} +(2.68692 + 2.18642i) q^{60} +(-10.7109 - 6.18395i) q^{61} +(-0.513993 + 0.436918i) q^{62} +(7.23229 + 4.13137i) q^{63} +(3.73152 - 7.07642i) q^{64} +(-3.30414 - 1.90765i) q^{65} +(7.20986 + 2.55347i) q^{66} +(3.47947 + 6.02663i) q^{67} +(-2.43221 - 6.42575i) q^{68} +(-3.70717 - 6.38708i) q^{69} +(-0.706502 - 3.86230i) q^{70} -7.88557 q^{71} +(7.24559 - 4.41605i) q^{72} +7.92558 q^{73} +(0.575748 + 3.14750i) q^{74} +(0.862577 - 1.50199i) q^{75} +(2.45757 - 0.930215i) q^{76} +(-4.33470 - 7.50792i) q^{77} +(-7.10664 + 6.06915i) q^{78} +(-0.187206 - 0.108084i) q^{79} +(-3.79250 - 1.27158i) q^{80} +(8.99962 - 0.0827023i) q^{81} +(-12.4142 + 10.5527i) q^{82} +(-7.86428 - 4.54044i) q^{83} +(-9.49563 - 1.52711i) q^{84} +(-2.97508 + 1.71766i) q^{85} +(-5.94820 + 16.6732i) q^{86} +(-0.460102 + 0.801164i) q^{87} +(-8.83031 + 0.169283i) q^{88} -4.82215i q^{89} +(-2.76265 - 3.21990i) q^{90} +10.5927 q^{91} +(6.60191 + 5.39741i) q^{92} +(0.714571 - 0.414750i) q^{93} +(-1.45132 + 4.06815i) q^{94} +(-0.656931 - 1.13784i) q^{95} +(-6.03734 + 7.71690i) q^{96} +(-4.20125 + 7.27679i) q^{97} +(0.648716 + 0.763153i) q^{98} +(-8.13409 - 4.64652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

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