LMFDB - Embedded newform 360.2.d.e.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(109,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.d (of order $2$, degree $1$, 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:	$6$
Coefficient field:	6.0.839056.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 8x^{2} + 1 $ x^6 + 6x^4 + 8x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.6
Root			$-0.373087i$ of defining polynomial
Character	$\chi$	$=$	360.109
Dual form			360.2.d.e.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16170 + 0.806504i) q^{2} +(0.699104 + 1.87383i) q^{4} +(-1.86081 + 1.23992i) q^{5} -0.746175i q^{7} +(-0.699104 + 2.74067i) q^{8} +O(q^{10})$	\(q+(1.16170 + 0.806504i) q^{2} +(0.699104 + 1.87383i) q^{4} +(-1.86081 + 1.23992i) q^{5} -0.746175i q^{7} +(-0.699104 + 2.74067i) q^{8} +(-3.16170 - 0.0603290i) q^{10} +5.36068i q^{11} +2.92520 q^{13} +(0.601793 - 0.866833i) q^{14} +(-3.02251 + 2.62001i) q^{16} +2.13466i q^{17} +1.73367i q^{19} +(-3.62430 - 2.62001i) q^{20} +(-4.32340 + 6.22751i) q^{22} -7.49534i q^{23} +(1.92520 - 4.61450i) q^{25} +(3.39821 + 2.35918i) q^{26} +(1.39821 - 0.521653i) q^{28} -6.74916i q^{29} +2.64681 q^{31} +(-5.62430 + 0.606006i) q^{32} +(-1.72161 + 2.47984i) q^{34} +(0.925197 + 1.38849i) q^{35} +1.07480 q^{37} +(-1.39821 + 2.01400i) q^{38} +(-2.09731 - 5.96668i) q^{40} +11.2936 q^{41} -7.44322 q^{43} +(-10.0450 + 3.74767i) q^{44} +(6.04502 - 8.70735i) q^{46} +1.73367i q^{47} +6.44322 q^{49} +(5.95812 - 3.80800i) q^{50} +(2.04502 + 5.48133i) q^{52} +7.72161 q^{53} +(-6.64681 - 9.97518i) q^{55} +(2.04502 + 0.521653i) q^{56} +(5.44322 - 7.84052i) q^{58} -6.85302i q^{59} +6.45203i q^{61} +(3.07480 + 2.13466i) q^{62} +(-7.02251 - 3.83202i) q^{64} +(-5.44322 + 3.62701i) q^{65} +7.44322 q^{67} +(-4.00000 + 1.49235i) q^{68} +(-0.0450160 + 2.35918i) q^{70} -13.2936 q^{71} -0.690358i q^{73} +(1.24860 + 0.866833i) q^{74} +(-3.24860 + 1.21201i) q^{76} +4.00000 q^{77} -2.64681 q^{79} +(2.37570 - 8.62300i) q^{80} +(13.1198 + 9.10834i) q^{82} -5.85039 q^{83} +(-2.64681 - 3.97219i) q^{85} +(-8.64681 - 6.00299i) q^{86} +(-14.6918 - 3.74767i) q^{88} +7.59283 q^{89} -2.18271i q^{91} +(14.0450 - 5.24002i) q^{92} +(-1.39821 + 2.01400i) q^{94} +(-2.14961 - 3.22601i) q^{95} +14.1887i q^{97} +(7.48511 + 5.19648i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{4} - q^{8}+O(q^{10}) $ 6 * q - q^2 + q^4 - q^8	$ 6 q - q^{2} + q^{4} - q^{8} - 11 q^{10} + 8 q^{13} + 10 q^{14} + q^{16} - 9 q^{20} - 10 q^{22} + 2 q^{25} + 14 q^{26} + 2 q^{28} - 16 q^{31} - 21 q^{32} + 12 q^{34} - 4 q^{35} + 16 q^{37} - 2 q^{38} - 3 q^{40} + 4 q^{41} - 22 q^{44} - 2 q^{46} - 6 q^{49} + 15 q^{50} - 26 q^{52} + 24 q^{53} - 8 q^{55} - 26 q^{56} - 12 q^{58} + 28 q^{62} - 23 q^{64} + 12 q^{65} - 24 q^{68} + 38 q^{70} - 16 q^{71} - 18 q^{74} + 6 q^{76} + 24 q^{77} + 16 q^{79} + 27 q^{80} + 50 q^{82} - 16 q^{83} + 16 q^{85} - 20 q^{86} - 18 q^{88} + 20 q^{89} + 46 q^{92} - 2 q^{94} - 32 q^{95} + 21 q^{98}+O(q^{100}) $ 6 * q - q^2 + q^4 - q^8 - 11 * q^10 + 8 * q^13 + 10 * q^14 + q^16 - 9 * q^20 - 10 * q^22 + 2 * q^25 + 14 * q^26 + 2 * q^28 - 16 * q^31 - 21 * q^32 + 12 * q^34 - 4 * q^35 + 16 * q^37 - 2 * q^38 - 3 * q^40 + 4 * q^41 - 22 * q^44 - 2 * q^46 - 6 * q^49 + 15 * q^50 - 26 * q^52 + 24 * q^53 - 8 * q^55 - 26 * q^56 - 12 * q^58 + 28 * q^62 - 23 * q^64 + 12 * q^65 - 24 * q^68 + 38 * q^70 - 16 * q^71 - 18 * q^74 + 6 * q^76 + 24 * q^77 + 16 * q^79 + 27 * q^80 + 50 * q^82 - 16 * q^83 + 16 * q^85 - 20 * q^86 - 18 * q^88 + 20 * q^89 + 46 * q^92 - 2 * q^94 - 32 * q^95 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	1.16170	+	0.806504i	0.821447	+	0.570284i
$2$	1.16170	+	0.806504i	0.821447	+	0.570284i
$3$		0			0
$3$		0			0
$4$	0.699104	+	1.87383i	0.349552	+	0.936917i
$5$	−1.86081	+	1.23992i	−0.832178	+	0.554509i
$5$	−1.86081	+	1.23992i	−0.832178	+	0.554509i
$6$		0			0
$7$		−	0.746175i		−	0.282028i	−0.990008	−	0.141014i	$-0.954964\pi$
$7$		−	0.746175i		−	0.282028i	0.990008	−	0.141014i	$-0.0450362\pi$
$8$	−0.699104	+	2.74067i	−0.247170	+	0.968972i
$9$		0			0
$10$	−3.16170	−	0.0603290i	−0.999818	−	0.0190777i
$11$			5.36068i			1.61630i	0.588974	+	0.808152i	$0.299532\pi$
$11$			5.36068i			1.61630i	−0.588974	+	0.808152i	$0.700468\pi$
$12$		0			0
$13$	2.92520			0.811304			0.405652	−	0.914028i	$-0.367045\pi$
$13$	2.92520			0.811304			0.405652	+	0.914028i	$0.367045\pi$
$14$	0.601793	−	0.866833i	0.160836	−	0.231671i
$15$		0			0
$16$	−3.02251	+	2.62001i	−0.755627	+	0.655002i
$17$			2.13466i			0.517731i	0.965913	+	0.258866i	$0.0833487\pi$
$17$			2.13466i			0.517731i	−0.965913	+	0.258866i	$0.916651\pi$
$18$		0			0
$19$			1.73367i			0.397730i	0.980027	+	0.198865i	$0.0637255\pi$
$19$			1.73367i			0.397730i	−0.980027	+	0.198865i	$0.936274\pi$
$20$	−3.62430	−	2.62001i	−0.810418	−	0.585852i
$21$		0			0
$22$	−4.32340	+	6.22751i	−0.921753	+	1.32771i
$23$		−	7.49534i		−	1.56289i	−0.623977	−	0.781443i	$-0.714484\pi$
$23$		−	7.49534i		−	1.56289i	0.623977	−	0.781443i	$-0.285516\pi$
$24$		0			0
$25$	1.92520	−	4.61450i	0.385039	−	0.922900i
$26$	3.39821	+	2.35918i	0.666443	+	0.462674i
$27$		0			0
$28$	1.39821	−	0.521653i	0.264236	−	0.0985832i
$29$		−	6.74916i		−	1.25329i	−0.779306	−	0.626644i	$-0.784428\pi$
$29$		−	6.74916i		−	1.25329i	0.779306	−	0.626644i	$-0.215572\pi$
$30$		0			0
$31$	2.64681			0.475381			0.237690	−	0.971341i	$-0.423610\pi$
$31$	2.64681			0.475381			0.237690	+	0.971341i	$0.423610\pi$
$32$	−5.62430	+	0.606006i	−0.994245	+	0.107128i
$33$		0			0
$34$	−1.72161	+	2.47984i	−0.295254	+	0.425289i
$35$	0.925197	+	1.38849i	0.156387	+	0.234697i
$36$		0			0
$37$	1.07480			0.176697			0.0883483	−	0.996090i	$-0.471841\pi$
$37$	1.07480			0.176697			0.0883483	+	0.996090i	$0.471841\pi$
$38$	−1.39821	+	2.01400i	−0.226819	+	0.326714i
$39$		0			0
$40$	−2.09731	−	5.96668i	−0.331614	−	0.943415i
$41$	11.2936			1.76377			0.881883	−	0.471468i	$-0.156276\pi$
$41$	11.2936			1.76377			0.881883	+	0.471468i	$0.156276\pi$
$42$		0			0
$43$	−7.44322			−1.13508			−0.567540	−	0.823346i	$-0.692105\pi$
$43$	−7.44322			−1.13508			−0.567540	+	0.823346i	$0.692105\pi$
$44$	−10.0450	+	3.74767i	−1.51434	+	0.564982i
$45$		0			0
$46$	6.04502	−	8.70735i	0.891289	−	1.28383i
$47$			1.73367i			0.252881i	0.991974	+	0.126441i	$0.0403553\pi$
$47$			1.73367i			0.252881i	−0.991974	+	0.126441i	$0.959645\pi$
$48$		0			0
$49$	6.44322			0.920460
$50$	5.95812	−	3.80800i	0.842605	−	0.538532i
$51$		0			0
$52$	2.04502	+	5.48133i	0.283593	+	0.760124i
$53$	7.72161			1.06064			0.530322	−	0.847796i	$-0.322071\pi$
$53$	7.72161			1.06064			0.530322	+	0.847796i	$0.322071\pi$
$54$		0			0
$55$	−6.64681	−	9.97518i	−0.896255	−	1.34505i
$56$	2.04502	+	0.521653i	0.273277	+	0.0697089i
$57$		0			0
$58$	5.44322	−	7.84052i	0.714730	−	1.02951i
$59$		−	6.85302i		−	0.892188i	−0.894986	−	0.446094i	$-0.852815\pi$
$59$		−	6.85302i		−	0.892188i	0.894986	−	0.446094i	$-0.147185\pi$
$60$		0			0
$61$			6.45203i			0.826098i	0.910709	+	0.413049i	$0.135536\pi$
$61$			6.45203i			0.826098i	−0.910709	+	0.413049i	$0.864464\pi$
$62$	3.07480	+	2.13466i	0.390500	+	0.271102i
$63$		0			0
$64$	−7.02251	−	3.83202i	−0.877813	−	0.479003i
$65$	−5.44322	+	3.62701i	−0.675149	+	0.449875i
$66$		0			0
$67$	7.44322			0.909334			0.454667	−	0.890661i	$-0.349758\pi$
$67$	7.44322			0.909334			0.454667	+	0.890661i	$0.349758\pi$
$68$	−4.00000	+	1.49235i	−0.485071	+	0.180974i
$69$		0			0
$70$	−0.0450160	+	2.35918i	−0.00538044	+	0.281976i
$71$	−13.2936			−1.57766			−0.788831	−	0.614610i	$-0.789313\pi$
$71$	−13.2936			−1.57766			−0.788831	+	0.614610i	$0.789313\pi$
$72$		0			0
$73$		−	0.690358i		−	0.0808003i	−0.999184	−	0.0404002i	$-0.987137\pi$
$73$		−	0.690358i		−	0.0808003i	0.999184	−	0.0404002i	$-0.0128633\pi$
$74$	1.24860	+	0.866833i	0.145147	+	0.100767i
$75$		0			0
$76$	−3.24860	+	1.21201i	−0.372640	+	0.139027i
$77$	4.00000			0.455842
$78$		0			0
$79$	−2.64681			−0.297789			−0.148895	−	0.988853i	$-0.547572\pi$
$79$	−2.64681			−0.297789			−0.148895	+	0.988853i	$0.547572\pi$
$80$	2.37570	−	8.62300i	0.265611	−	0.964080i
$81$		0			0
$82$	13.1198	+	9.10834i	1.44884	+	1.00585i
$83$	−5.85039			−0.642164			−0.321082	−	0.947051i	$-0.604047\pi$
$83$	−5.85039			−0.642164			−0.321082	+	0.947051i	$0.604047\pi$
$84$		0			0
$85$	−2.64681	−	3.97219i	−0.287087	−	0.430844i
$86$	−8.64681	−	6.00299i	−0.932409	−	0.647319i
$87$		0			0
$88$	−14.6918	−	3.74767i	−1.56615	−	0.399503i
$89$	7.59283			0.804838			0.402419	−	0.915456i	$-0.368169\pi$
$89$	7.59283			0.804838			0.402419	+	0.915456i	$0.368169\pi$
$90$		0			0
$91$		−	2.18271i		−	0.228810i
$92$	14.0450	−	5.24002i	1.46429	−	0.546310i
$93$		0			0
$94$	−1.39821	+	2.01400i	−0.144214	+	0.207729i
$95$	−2.14961	−	3.22601i	−0.220545	−	0.330982i
$96$		0			0
$97$			14.1887i			1.44064i	0.693641	+	0.720321i	$0.256006\pi$
$97$			14.1887i			1.44064i	−0.693641	+	0.720321i	$0.743994\pi$
$98$	7.48511	+	5.19648i	0.756110	+	0.524924i
$99$		0			0
$100$	9.99272	+	0.381485i	0.999272	+	0.0381485i
$101$		−	7.43952i		−	0.740260i	−0.928980	−	0.370130i	$-0.879313\pi$
$101$		−	7.43952i		−	0.740260i	0.928980	−	0.370130i	$-0.120687\pi$
$102$		0			0
$103$			7.19820i			0.709260i	0.935007	+	0.354630i	$0.115393\pi$
$103$			7.19820i			0.709260i	−0.935007	+	0.354630i	$0.884607\pi$
$104$	−2.04502	+	8.01699i	−0.200530	+	0.786131i
$105$		0			0
$106$	8.97021	+	6.22751i	0.871264	+	0.604869i
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$		0			0
$109$		−	19.9504i		−	1.91090i	−0.295158	−	0.955449i	$-0.595372\pi$
$109$		−	19.9504i		−	1.91090i	0.295158	−	0.955449i	$-0.404628\pi$
$110$	0.323404	−	16.9489i	0.0308354	−	1.61601i
$111$		0			0
$112$	1.95498	+	2.25532i	0.184729	+	0.213108i
$113$		−	12.0540i		−	1.13395i	−0.823736	−	0.566973i	$-0.808114\pi$
$113$		−	12.0540i		−	1.13395i	0.823736	−	0.566973i	$-0.191886\pi$
$114$		0			0
$115$	9.29362	+	13.9474i	0.866634	+	1.30060i
$116$	12.6468	−	4.71836i	1.17423	−	0.438089i
$117$		0			0
$118$	5.52699	−	7.96117i	0.508801	−	0.732885i
$119$	1.59283			0.146014
$120$		0			0
$121$	−17.7368			−1.61244
$122$	−5.20359	+	7.49534i	−0.471110	+	0.678596i
$123$		0			0
$124$	1.85039	+	4.95968i	0.166170	+	0.445392i
$125$	2.13919	+	10.9738i	0.191335	+	0.981525i
$126$		0			0
$127$			4.21351i			0.373888i	0.982371	+	0.186944i	$0.0598583\pi$
$127$			4.21351i			0.373888i	−0.982371	+	0.186944i	$0.940142\pi$
$128$	−5.06752	−	10.1153i	−0.447910	−	0.894079i
$129$		0			0
$130$	−9.24860	−	0.176474i	−0.811156	−	0.0154778i
$131$			10.3204i			0.901694i	0.892601	+	0.450847i	$0.148878\pi$
$131$			10.3204i			0.901694i	−0.892601	+	0.450847i	$0.851122\pi$
$132$		0			0
$133$	1.29362			0.112171
$134$	8.64681	+	6.00299i	0.746970	+	0.518579i
$135$		0			0
$136$	−5.85039	−	1.49235i	−0.501667	−	0.127968i
$137$			15.0387i			1.28484i	0.766351	+	0.642422i	$0.222070\pi$
$137$			15.0387i			1.28484i	−0.766351	+	0.642422i	$0.777930\pi$
$138$		0			0
$139$		−	9.47032i		−	0.803262i	−0.915802	−	0.401631i	$-0.868443\pi$
$139$		−	9.47032i		−	0.803262i	0.915802	−	0.401631i	$-0.131557\pi$
$140$	−1.95498	+	2.70436i	−0.165226	+	0.228560i
$141$		0			0
$142$	−15.4432	−	10.7214i	−1.29597	−	0.899716i
$143$			15.6810i			1.31131i
$144$		0			0
$145$	8.36842	+	12.5589i	0.694959	+	1.04296i
$146$	0.556777	−	0.801991i	0.0460792	−	0.0663732i
$147$		0			0
$148$	0.751399	+	2.01400i	0.0617646	+	0.165550i
$149$		−	1.78948i		−	0.146600i	−0.997310	−	0.0733000i	$-0.976647\pi$
$149$		−	1.78948i		−	0.146600i	0.997310	−	0.0733000i	$-0.0233531\pi$
$150$		0			0
$151$	10.6468			0.866425			0.433212	−	0.901292i	$-0.357380\pi$
$151$	10.6468			0.866425			0.433212	+	0.901292i	$0.357380\pi$
$152$	−4.75140	−	1.21201i	−0.385389	−	0.0983071i
$153$		0			0
$154$	4.64681	+	3.22601i	0.374451	+	0.259960i
$155$	−4.92520	+	3.28183i	−0.395601	+	0.263603i
$156$		0			0
$157$	−6.92520			−0.552691			−0.276345	−	0.961058i	$-0.589123\pi$
$157$	−6.92520			−0.552691			−0.276345	+	0.961058i	$0.589123\pi$
$158$	−3.07480	−	2.13466i	−0.244618	−	0.169824i
$159$		0			0
$160$	9.71433	−	8.10134i	0.767985	−	0.640467i
$161$	−5.59283			−0.440777
$162$		0			0
$163$	−7.70079			−0.603172			−0.301586	−	0.953439i	$-0.597516\pi$
$163$	−7.70079			−0.603172			−0.301586	+	0.953439i	$0.597516\pi$
$164$	7.89541	+	21.1624i	0.616528	+	1.65250i
$165$		0			0
$166$	−6.79641	−	4.71836i	−0.527504	−	0.366216i
$167$		−	3.22601i		−	0.249637i	−0.992180	−	0.124818i	$-0.960165\pi$
$167$		−	3.22601i		−	0.249637i	0.992180	−	0.124818i	$-0.0398348\pi$
$168$		0			0
$169$	−4.44322			−0.341786
$170$	0.128782	−	6.74916i	0.00987713	−	0.517637i
$171$		0			0
$172$	−5.20359	−	13.9474i	−0.396770	−	1.06348i
$173$	−6.42799			−0.488711			−0.244356	−	0.969686i	$-0.578576\pi$
$173$	−6.42799			−0.488711			−0.244356	+	0.969686i	$0.578576\pi$
$174$		0			0
$175$	−3.44322	−	1.43653i	−0.260283	−	0.108592i
$176$	−14.0450	−	16.2027i	−1.05868	−	1.22132i
$177$		0			0
$178$	8.82061	+	6.12364i	0.661132	+	0.458987i
$179$		−	8.13765i		−	0.608236i	−0.952634	−	0.304118i	$-0.901638\pi$
$179$		−	8.13765i		−	0.608236i	0.952634	−	0.304118i	$-0.0983618\pi$
$180$		0			0
$181$			1.49235i			0.110925i	0.998461	+	0.0554627i	$0.0176634\pi$
$181$			1.49235i			0.110925i	−0.998461	+	0.0554627i	$0.982337\pi$
$182$	1.76036	−	2.53566i	0.130487	−	0.187955i
$183$		0			0
$184$	20.5422	+	5.24002i	1.51439	+	0.386299i
$185$	−2.00000	+	1.33267i	−0.147043	+	0.0979798i
$186$		0			0
$187$	−11.4432			−0.836811
$188$	−3.24860	+	1.21201i	−0.236929	+	0.0883951i
$189$		0			0
$190$	0.104590	−	5.48133i	0.00758778	−	0.397658i
$191$	−6.88645			−0.498286			−0.249143	−	0.968467i	$-0.580149\pi$
$191$	−6.88645			−0.498286			−0.249143	+	0.968467i	$0.580149\pi$
$192$		0			0
$193$		−	16.4830i		−	1.18647i	−0.805028	−	0.593237i	$-0.797850\pi$
$193$		−	16.4830i		−	1.18647i	0.805028	−	0.593237i	$-0.202150\pi$
$194$	−11.4432	+	16.4830i	−0.821576	+	1.18341i
$195$		0			0
$196$	4.50448	+	12.0735i	0.321749	+	0.862395i
$197$	−13.5720			−0.966965			−0.483483	−	0.875354i	$-0.660628\pi$
$197$	−13.5720			−0.966965			−0.483483	+	0.875354i	$0.660628\pi$
$198$		0			0
$199$	−9.05398			−0.641820			−0.320910	−	0.947110i	$-0.603989\pi$
$199$	−9.05398			−0.641820			−0.320910	+	0.947110i	$0.603989\pi$
$200$	11.3009	+	8.50234i	0.799094	+	0.601206i
$201$		0			0
$202$	6.00000	−	8.64251i	0.422159	−	0.608085i
$203$	−5.03605			−0.353462
$204$		0			0
$205$	−21.0152	+	14.0032i	−1.46777	+	0.978025i
$206$	−5.80538	+	8.36217i	−0.404480	+	0.582620i
$207$		0			0
$208$	−8.84143	+	7.66404i	−0.613043	+	0.531406i
$209$	−9.29362			−0.642853
$210$		0			0
$211$		−	2.53566i		−	0.174562i	−0.996184	−	0.0872809i	$-0.972182\pi$
$211$		−	2.53566i		−	0.174562i	0.996184	−	0.0872809i	$-0.0278178\pi$
$212$	5.39821	+	14.4690i	0.370750	+	0.993736i
$213$		0			0
$214$	−4.64681	−	3.22601i	−0.317649	−	0.220526i
$215$	13.8504	−	9.22900i	0.944589	−	0.629413i
$216$		0			0
$217$		−	1.97498i		−	0.134070i
$218$	16.0900	−	23.1764i	1.08975	−	1.56970i
$219$		0			0
$220$	14.0450	−	19.4287i	0.946915	−	1.30988i
$221$			6.24430i			0.420037i
$222$		0			0
$223$			12.1579i			0.814152i	0.913394	+	0.407076i	$0.133452\pi$
$223$			12.1579i			0.814152i	−0.913394	+	0.407076i	$0.866548\pi$
$224$	0.452186	+	4.19671i	0.0302130	+	0.280405i
$225$		0			0
$226$	9.72161	−	14.0032i	0.646672	−	0.931478i
$227$	20.7368			1.37635			0.688176	−	0.725544i	$-0.258412\pi$
$227$	20.7368			1.37635			0.688176	+	0.725544i	$0.258412\pi$
$228$		0			0
$229$			19.9504i			1.31836i	0.751987	+	0.659178i	$0.229096\pi$
$229$			19.9504i			1.31836i	−0.751987	+	0.659178i	$0.770904\pi$
$230$	−0.452186	+	23.6980i	−0.0298163	+	1.56260i
$231$		0			0
$232$	18.4972	+	4.71836i	1.21440	+	0.309776i
$233$			13.3386i			0.873844i	0.899499	+	0.436922i	$0.143931\pi$
$233$			13.3386i			0.873844i	−0.899499	+	0.436922i	$0.856069\pi$
$234$		0			0
$235$	−2.14961	−	3.22601i	−0.140225	−	0.210442i
$236$	12.8414	−	4.79097i	0.835906	−	0.311866i
$237$		0			0
$238$	1.85039	+	1.28462i	0.119943	+	0.0832697i
$239$	22.8864			1.48040			0.740201	−	0.672386i	$-0.234731\pi$
$239$	22.8864			1.48040			0.740201	+	0.672386i	$0.234731\pi$
$240$		0			0
$241$	3.59283			0.231435			0.115717	−	0.993282i	$-0.463083\pi$
$241$	3.59283			0.231435			0.115717	+	0.993282i	$0.463083\pi$
$242$	−20.6049	−	14.3048i	−1.32453	−	0.919549i
$243$		0			0
$244$	−12.0900	+	4.51064i	−0.773985	+	0.288764i
$245$	−11.9896	+	7.98908i	−0.765987	+	0.510404i
$246$		0			0
$247$			5.07131i			0.322680i
$248$	−1.85039	+	7.25402i	−0.117500	+	0.460631i
$249$		0			0
$250$	−6.36529	+	14.4735i	−0.402576	+	0.915387i
$251$		−	8.82801i		−	0.557219i	−0.960404	−	0.278609i	$-0.910127\pi$
$251$		−	8.82801i		−	0.557219i	0.960404	−	0.278609i	$-0.0898735\pi$
$252$		0			0
$253$	40.1801			2.52610
$254$	−3.39821	+	4.89484i	−0.213222	+	0.307129i
$255$		0			0
$256$	2.27111	−	15.8380i	0.141944	−	0.989875i
$257$		−	22.2927i		−	1.39058i	−0.718728	−	0.695291i	$-0.755275\pi$
$257$		−	22.2927i		−	1.39058i	0.718728	−	0.695291i	$-0.244725\pi$
$258$		0			0
$259$		−	0.801991i		−	0.0498333i
$260$	−10.6018	−	7.66404i	−0.657495	−	0.475304i
$261$		0			0
$262$	−8.32340	+	11.9892i	−0.514222	+	0.740694i
$263$			21.2014i			1.30733i	0.756783	+	0.653667i	$0.226770\pi$
$263$			21.2014i			1.30733i	−0.756783	+	0.653667i	$0.773230\pi$
$264$		0			0
$265$	−14.3684	+	9.57418i	−0.882645	+	0.588137i
$266$	1.50280	+	1.04331i	0.0921424	+	0.0639693i
$267$		0			0
$268$	5.20359	+	13.9474i	0.317860	+	0.851971i
$269$		−	14.6935i		−	0.895881i	−0.894063	−	0.447940i	$-0.852158\pi$
$269$		−	14.6935i		−	0.895881i	0.894063	−	0.447940i	$-0.147842\pi$
$270$		0			0
$271$	−20.2396			−1.22947			−0.614735	−	0.788734i	$-0.710737\pi$
$271$	−20.2396			−1.22947			−0.614735	+	0.788734i	$0.710737\pi$
$272$	−5.59283	−	6.45203i	−0.339115	−	0.391212i
$273$		0			0
$274$	−12.1288	+	17.4705i	−0.732727	+	1.05543i
$275$	24.7368	+	10.3204i	1.49169	+	0.622341i
$276$		0			0
$277$	−0.518027			−0.0311252			−0.0155626	−	0.999879i	$-0.504954\pi$
$277$	−0.518027			−0.0311252			−0.0155626	+	0.999879i	$0.504954\pi$
$278$	7.63785	−	11.0017i	0.458088	−	0.659837i
$279$		0			0
$280$	−4.45219	+	1.56496i	−0.266069	+	0.0935243i
$281$	−13.7008			−0.817320			−0.408660	−	0.912687i	$-0.634004\pi$
$281$	−13.7008			−0.817320			−0.408660	+	0.912687i	$0.634004\pi$
$282$		0			0
$283$	−18.0305			−1.07180			−0.535900	−	0.844282i	$-0.680027\pi$
$283$	−18.0305			−1.07180			−0.535900	+	0.844282i	$0.680027\pi$
$284$	−9.29362	−	24.9100i	−0.551475	−	1.47814i
$285$		0			0
$286$	−12.6468	+	18.2167i	−0.747821	+	1.07718i
$287$		−	8.42701i		−	0.497431i
$288$		0			0
$289$	12.4432			0.731954
$290$	−0.407170	+	21.3388i	−0.0239099	+	1.25306i
$291$		0			0
$292$	1.29362	−	0.482632i	0.0757032	−	0.0282439i
$293$	15.9792			0.933513			0.466757	−	0.884386i	$-0.345422\pi$
$293$	15.9792			0.933513			0.466757	+	0.884386i	$0.345422\pi$
$294$		0			0
$295$	8.49720	+	12.7521i	0.494726	+	0.742459i
$296$	−0.751399	+	2.94568i	−0.0436742	+	0.171214i
$297$		0			0
$298$	1.44322	−	2.07884i	0.0836037	−	0.120424i
$299$		−	21.9253i		−	1.26797i
$300$		0			0
$301$			5.55394i			0.320124i
$302$	12.3684	+	8.58669i	0.711723	+	0.494108i
$303$		0			0
$304$	−4.54222	−	5.24002i	−0.260514	−	0.300536i
$305$	−8.00000	−	12.0060i	−0.458079	−	0.687460i
$306$		0			0
$307$	22.5872			1.28912			0.644561	−	0.764553i	$-0.277040\pi$
$307$	22.5872			1.28912			0.644561	+	0.764553i	$0.277040\pi$
$308$	2.79641	+	7.49534i	0.159341	+	0.427086i
$309$		0			0
$310$	−8.36842	−	0.159679i	−0.475294	−	0.00906918i
$311$	18.5872			1.05399			0.526993	−	0.849870i	$-0.323320\pi$
$311$	18.5872			1.05399			0.526993	+	0.849870i	$0.323320\pi$
$312$		0			0
$313$		−	29.3871i		−	1.66106i	−0.556977	−	0.830528i	$-0.688039\pi$
$313$		−	29.3871i		−	1.66106i	0.556977	−	0.830528i	$-0.311961\pi$
$314$	−8.04502	−	5.58520i	−0.454007	−	0.315191i
$315$		0			0
$316$	−1.85039	−	4.95968i	−0.104093	−	0.279004i
$317$	−5.57201			−0.312955			−0.156478	−	0.987682i	$-0.550014\pi$
$317$	−5.57201			−0.312955			−0.156478	+	0.987682i	$0.550014\pi$
$318$		0			0
$319$	36.1801			2.02569
$320$	17.8189	−	1.57670i	0.996108	−	0.0881403i
$321$		0			0
$322$	−6.49720	−	4.51064i	−0.362075	−	0.251368i
$323$	−3.70079			−0.205917
$324$		0			0
$325$	5.63158	−	13.4983i	0.312384	−	0.748752i
$326$	−8.94602	−	6.21071i	−0.495474	−	0.343980i
$327$		0			0
$328$	−7.89541	+	30.9520i	−0.435951	+	1.70904i
$329$	1.29362			0.0713194
$330$		0			0
$331$		−	13.7396i		−	0.755199i	−0.925969	−	0.377599i	$-0.876750\pi$
$331$		−	13.7396i		−	0.755199i	0.925969	−	0.377599i	$-0.123250\pi$
$332$	−4.09003	−	10.9627i	−0.224470	−	0.601655i
$333$		0			0
$334$	2.60179	−	3.74767i	0.142364	−	0.205063i
$335$	−13.8504	+	9.22900i	−0.756728	+	0.504234i
$336$		0			0
$337$		−	20.7523i		−	1.13045i	−0.824936	−	0.565226i	$-0.808789\pi$
$337$		−	20.7523i		−	1.13045i	0.824936	−	0.565226i	$-0.191211\pi$
$338$	−5.16170	−	3.58348i	−0.280760	−	0.194915i
$339$		0			0
$340$	5.59283	−	7.73665i	0.303314	−	0.419579i
$341$			14.1887i			0.768360i
$342$		0			0
$343$		−	10.0310i		−	0.541623i
$344$	5.20359	−	20.3994i	0.280559	−	1.09986i
$345$		0			0
$346$	−7.46742	−	5.18420i	−0.401451	−	0.278704i
$347$	−4.73684			−0.254287			−0.127143	−	0.991884i	$-0.540581\pi$
$347$	−4.73684			−0.254287			−0.127143	+	0.991884i	$0.540581\pi$
$348$		0			0
$349$			0.482632i			0.0258347i	0.999917	+	0.0129174i	$0.00411184\pi$
$349$			0.482632i			0.0258347i	−0.999917	+	0.0129174i	$0.995888\pi$
$350$	−2.84143	−	4.44580i	−0.151881	−	0.237638i
$351$		0			0
$352$	−3.24860	−	30.1500i	−0.173151	−	1.60700i
$353$			2.13466i			0.113617i	0.998385	+	0.0568083i	$0.0180924\pi$
$353$			2.13466i			0.113617i	−0.998385	+	0.0568083i	$0.981908\pi$
$354$		0			0
$355$	24.7368	−	16.4830i	1.31290	−	0.874828i
$356$	5.30818	+	14.2277i	0.281333	+	0.754067i
$357$		0			0
$358$	6.56304	−	9.45352i	0.346868	−	0.499634i
$359$	−9.59283			−0.506290			−0.253145	−	0.967428i	$-0.581465\pi$
$359$	−9.59283			−0.506290			−0.253145	+	0.967428i	$0.581465\pi$
$360$		0			0
$361$	15.9944			0.841811
$362$	−1.20359	+	1.73367i	−0.0632590	+	0.0911194i
$363$		0			0
$364$	4.09003	−	1.52594i	0.214376	−	0.0799809i
$365$	0.855989	+	1.28462i	0.0448045	+	0.0672402i
$366$		0			0
$367$		−	34.0832i		−	1.77913i	−0.456809	−	0.889565i	$-0.651008\pi$
$367$		−	34.0832i		−	1.77913i	0.456809	−	0.889565i	$-0.348992\pi$
$368$	19.6378	+	22.6547i	1.02369	+	1.18096i
$369$		0			0
$370$	−3.39821	−	0.0648418i	−0.176664	−	0.00337097i
$371$		−	5.76167i		−	0.299131i
$372$		0			0
$373$	−4.33796			−0.224611			−0.112306	−	0.993674i	$-0.535824\pi$
$373$	−4.33796			−0.224611			−0.112306	+	0.993674i	$0.535824\pi$
$374$	−13.2936	−	9.22900i	−0.687397	−	0.477220i
$375$		0			0
$376$	−4.75140	−	1.21201i	−0.245035	−	0.0625047i
$377$		−	19.7426i		−	1.01680i
$378$		0			0
$379$		−	6.90107i		−	0.354484i	−0.984167	−	0.177242i	$-0.943282\pi$
$379$		−	6.90107i		−	0.354484i	0.984167	−	0.177242i	$-0.0567176\pi$
$380$	4.54222	−	6.28332i	0.233011	−	0.322328i
$381$		0			0
$382$	−8.00000	−	5.55394i	−0.409316	−	0.284165i
$383$		−	22.3744i		−	1.14328i	−0.820506	−	0.571639i	$-0.806308\pi$
$383$		−	22.3744i		−	1.14328i	0.820506	−	0.571639i	$-0.193692\pi$
$384$		0			0
$385$	−7.44322	+	4.95968i	−0.379342	+	0.252769i
$386$	13.2936	−	19.1484i	0.676627	−	0.974626i
$387$		0			0
$388$	−26.5872	+	9.91936i	−1.34976	+	0.503579i
$389$			11.0185i			0.558659i	0.960195	+	0.279330i	$0.0901122\pi$
$389$			11.0185i			0.558659i	−0.960195	+	0.279330i	$0.909888\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	−4.50448	+	17.6587i	−0.227511	+	0.891900i
$393$		0			0
$394$	−15.7666	−	10.9459i	−0.794311	−	0.551445i
$395$	4.92520	−	3.28183i	0.247814	−	0.165127i
$396$		0			0
$397$	−25.2549			−1.26751			−0.633753	−	0.773536i	$-0.718486\pi$
$397$	−25.2549			−1.26751			−0.633753	+	0.773536i	$0.718486\pi$
$398$	−10.5180	−	7.30207i	−0.527221	−	0.366020i
$399$		0			0
$400$	6.27111	+	18.9914i	0.313555	+	0.949570i
$401$	−7.29362			−0.364226			−0.182113	−	0.983278i	$-0.558294\pi$
$401$	−7.29362			−0.364226			−0.182113	+	0.983278i	$0.558294\pi$
$402$		0			0
$403$	7.74244			0.385678
$404$	13.9404	−	5.20100i	0.693562	−	0.258759i
$405$		0			0
$406$	−5.85039	−	4.06160i	−0.290350	−	0.201574i
$407$			5.76167i			0.285595i
$408$		0			0
$409$	−15.8504			−0.783752			−0.391876	−	0.920018i	$-0.628174\pi$
$409$	−15.8504			−0.783752			−0.391876	+	0.920018i	$0.628174\pi$
$410$	−35.7071	−	0.681333i	−1.76345	−	0.0336486i
$411$		0			0
$412$	−13.4882	+	5.03229i	−0.664518	+	0.247923i
$413$	−5.11355			−0.251622
$414$		0			0
$415$	10.8864	−	7.25402i	0.534395	−	0.356086i
$416$	−16.4522	+	1.77269i	−0.806635	+	0.0869131i
$417$		0			0
$418$	−10.7964	−	7.49534i	−0.528070	−	0.366609i
$419$			8.02602i			0.392097i	0.980594	+	0.196048i	$0.0628109\pi$
$419$			8.02602i			0.392097i	−0.980594	+	0.196048i	$0.937189\pi$
$420$		0			0
$421$		−	22.9351i		−	1.11779i	−0.829240	−	0.558893i	$-0.811226\pi$
$421$		−	22.9351i		−	1.11779i	0.829240	−	0.558893i	$-0.188774\pi$
$422$	2.04502	−	2.94568i	0.0995498	−	0.143393i
$423$		0			0
$424$	−5.39821	+	21.1624i	−0.262160	+	1.02774i
$425$	9.85039	+	4.10964i	0.477814	+	0.199347i
$426$		0			0
$427$	4.81434			0.232982
$428$	−2.79641	−	7.49534i	−0.135170	−	0.362301i
$429$		0			0
$430$	23.5333	+	0.449042i	1.13487	+	0.0216547i
$431$	35.0665			1.68909			0.844547	−	0.535481i	$-0.179870\pi$
$431$	35.0665			1.68909			0.844547	+	0.535481i	$0.179870\pi$
$432$		0			0
$433$			17.0773i			0.820682i	0.911932	+	0.410341i	$0.134590\pi$
$433$			17.0773i			0.820682i	−0.911932	+	0.410341i	$0.865410\pi$
$434$	1.59283	−	2.29434i	0.0764583	−	0.110132i
$435$		0			0
$436$	37.3836	−	13.9474i	1.79035	−	0.667958i
$437$	12.9944			0.621607
$438$		0			0
$439$	−8.53885			−0.407537			−0.203769	−	0.979019i	$-0.565319\pi$
$439$	−8.53885			−0.407537			−0.203769	+	0.979019i	$0.565319\pi$
$440$	31.9854	−	11.2430i	1.52485	−	0.535989i
$441$		0			0
$442$	−5.03605	+	7.25402i	−0.239541	+	0.345039i
$443$	−20.7368			−0.985237			−0.492619	−	0.870245i	$-0.663960\pi$
$443$	−20.7368			−0.985237			−0.492619	+	0.870245i	$0.663960\pi$
$444$		0			0
$445$	−14.1288	+	9.41450i	−0.669769	+	0.446290i
$446$	−9.80538	+	14.1238i	−0.464298	+	0.668783i
$447$		0			0
$448$	−2.85936	+	5.24002i	−0.135092	+	0.247568i
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$		0			0
$451$			60.5414i			2.85078i
$452$	22.5872	−	8.42701i	1.06241	−	0.396373i
$453$		0			0
$454$	24.0900	+	16.7243i	1.13060	+	0.784912i
$455$	2.70638	+	4.06160i	0.126877	+	0.190411i
$456$		0			0
$457$		−	1.28462i		−	0.0600921i	−0.999549	−	0.0300461i	$-0.990435\pi$
$457$		−	1.28462i		−	0.0600921i	0.999549	−	0.0300461i	$-0.00956540\pi$
$458$	−16.0900	+	23.1764i	−0.751838	+	1.08296i
$459$		0			0
$460$	−19.6378	+	27.1654i	−0.915619	+	1.26659i
$461$			15.7033i			0.731374i	0.930738	+	0.365687i	$0.119166\pi$
$461$			15.7033i			0.731374i	−0.930738	+	0.365687i	$0.880834\pi$
$462$		0			0
$463$			18.7215i			0.870064i	0.900415	+	0.435032i	$0.143263\pi$
$463$			18.7215i			0.870064i	−0.900415	+	0.435032i	$0.856737\pi$
$464$	17.6829	+	20.3994i	0.820906	+	0.947018i
$465$		0			0
$466$	−10.7577	+	15.4955i	−0.498339	+	0.717817i
$467$	−2.14961			−0.0994719			−0.0497360	−	0.998762i	$-0.515838\pi$
$467$	−2.14961			−0.0994719			−0.0497360	+	0.998762i	$0.515838\pi$
$468$		0			0
$469$		−	5.55394i		−	0.256457i
$470$	0.104590	−	5.48133i	0.00482439	−	0.252835i
$471$		0			0
$472$	18.7819	+	4.79097i	0.864505	+	0.220522i
$473$		−	39.9007i		−	1.83464i
$474$		0			0
$475$	8.00000	+	3.33765i	0.367065	+	0.153142i
$476$	1.11355	+	2.98470i	0.0510396	+	0.136803i
$477$		0			0
$478$	26.5872	+	18.4580i	1.21607	+	0.844249i
$479$	−12.1801			−0.556521			−0.278261	−	0.960506i	$-0.589758\pi$
$479$	−12.1801			−0.556521			−0.278261	+	0.960506i	$0.589758\pi$
$480$		0			0
$481$	3.14401			0.143355
$482$	4.17380	+	2.89763i	0.190111	+	0.131983i
$483$		0			0
$484$	−12.3999	−	33.2359i	−0.563631	−	1.51072i
$485$	−17.5928	−	26.4024i	−0.798849	−	1.19887i
$486$		0			0
$487$		−	25.7678i		−	1.16765i	−0.811879	−	0.583826i	$-0.801555\pi$
$487$		−	25.7678i		−	1.16765i	0.811879	−	0.583826i	$-0.198445\pi$
$488$	−17.6829	−	4.51064i	−0.800466	−	0.204187i
$489$		0			0
$490$	−20.3716	−	0.388713i	−0.920293	−	0.0175603i
$491$		−	16.7724i		−	0.756927i	−0.925616	−	0.378464i	$-0.876453\pi$
$491$		−	16.7724i		−	0.756927i	0.925616	−	0.378464i	$-0.123547\pi$
$492$		0			0
$493$	14.4072			0.648866
$494$	−4.09003	+	5.89135i	−0.184019	+	0.265065i
$495$		0			0
$496$	−8.00000	+	6.93466i	−0.359211	+	0.311375i
$497$			9.91936i			0.444944i
$498$		0			0
$499$			17.6224i			0.788888i	0.918920	+	0.394444i	$0.129063\pi$
$499$			17.6224i			0.788888i	−0.918920	+	0.394444i	$0.870937\pi$
$500$	−19.0675	+	11.6803i	−0.852726	+	0.522359i
$501$		0			0
$502$	7.11982	−	10.2555i	0.317773	−	0.457726i
$503$			27.1263i			1.20950i	0.796414	+	0.604752i	$0.206728\pi$
$503$			27.1263i			1.20950i	−0.796414	+	0.604752i	$0.793272\pi$
$504$		0			0
$505$	9.22441	+	13.8435i	0.410481	+	0.616028i
$506$	46.6773	+	32.4054i	2.07506	+	1.44059i
$507$		0			0
$508$	−7.89541	+	2.94568i	−0.350302	+	0.130693i
$509$			15.9782i			0.708220i	0.935204	+	0.354110i	$0.115216\pi$
$509$			15.9782i			0.708220i	−0.935204	+	0.354110i	$0.884784\pi$
$510$		0			0
$511$	−0.515128			−0.0227879
$512$	15.4118	−	16.5674i	0.681110	−	0.732181i
$513$		0			0
$514$	17.9792	−	25.8975i	0.793027	−	1.14229i
$515$	−8.92520	−	13.3945i	−0.393291	−	0.590230i
$516$		0			0
$517$	−9.29362			−0.408733
$518$	0.646809	−	0.931674i	0.0284191	−	0.0409354i
$519$		0			0
$520$	−6.13505	−	17.4537i	−0.269040	−	0.765396i
$521$	−0.886447			−0.0388359			−0.0194180	−	0.999811i	$-0.506181\pi$
$521$	−0.886447			−0.0388359			−0.0194180	+	0.999811i	$0.506181\pi$
$522$		0			0
$523$	−41.7729			−1.82660			−0.913301	−	0.407286i	$-0.866475\pi$
$523$	−41.7729			−1.82660			−0.913301	+	0.407286i	$0.866475\pi$
$524$	−19.3386	+	7.21500i	−0.844812	+	0.315189i
$525$		0			0
$526$	−17.0990	+	24.6297i	−0.745552	+	1.07391i
$527$			5.65004i			0.246120i
$528$		0			0
$529$	−33.1801			−1.44261
$530$	−24.4134	−	0.465837i	−1.06045	−	0.0202347i
$531$		0			0
$532$	0.904373	+	2.42402i	0.0392095	+	0.105095i
$533$	33.0361			1.43095
$534$		0			0
$535$	7.44322	−	4.95968i	0.321799	−	0.214426i
$536$	−5.20359	+	20.3994i	−0.224761	+	0.881120i
$537$		0			0
$538$	11.8504	−	17.0695i	0.510907	−	0.735919i
$539$			34.5400i			1.48774i
$540$		0			0
$541$			4.47705i			0.192483i	0.995358	+	0.0962417i	$0.0306822\pi$
$541$			4.47705i			0.192483i	−0.995358	+	0.0962417i	$0.969318\pi$
$542$	−23.5124	−	16.3233i	−1.00995	−	0.701148i
$543$		0			0
$544$	−1.29362	−	12.0060i	−0.0554634	−	0.514752i
$545$	24.7368	+	37.1237i	1.05961	+	1.59021i
$546$		0			0
$547$	14.3297			0.612692			0.306346	−	0.951920i	$-0.400893\pi$
$547$	14.3297			0.612692			0.306346	+	0.951920i	$0.400893\pi$
$548$	−28.1801	+	10.5136i	−1.20379	+	0.449120i
$549$		0			0
$550$	20.4134	+	31.9395i	0.870432	+	1.36191i
$551$	11.7008			0.498470
$552$		0			0
$553$			1.97498i			0.0839848i
$554$	−0.601793	−	0.417790i	−0.0255677	−	0.0177502i
$555$		0			0
$556$	17.7458	−	6.62073i	0.752590	−	0.280782i
$557$	2.68556			0.113791			0.0568954	−	0.998380i	$-0.481880\pi$
$557$	2.68556			0.113791			0.0568954	+	0.998380i	$0.481880\pi$
$558$		0			0
$559$	−21.7729			−0.920895
$560$	−6.43426	−	1.77269i	−0.271897	−	0.0749097i
$561$		0			0
$562$	−15.9162	−	11.0497i	−0.671386	−	0.466105i
$563$	20.7368			0.873954			0.436977	−	0.899473i	$-0.356049\pi$
$563$	20.7368			0.873954			0.436977	+	0.899473i	$0.356049\pi$
$564$		0			0
$565$	14.9460	+	22.4302i	0.628784	+	0.943645i
$566$	−20.9460	−	14.5416i	−0.880427	−	0.611230i
$567$		0			0
$568$	9.29362	−	36.4334i	0.389952	−	1.52871i
$569$	4.40717			0.184758			0.0923791	−	0.995724i	$-0.470553\pi$
$569$	4.40717			0.184758			0.0923791	+	0.995724i	$0.470553\pi$
$570$		0			0
$571$		−	23.6590i		−	0.990098i	−0.868865	−	0.495049i	$-0.835150\pi$
$571$		−	23.6590i		−	0.990098i	0.868865	−	0.495049i	$-0.164850\pi$
$572$	−29.3836	+	10.9627i	−1.22859	+	0.458372i
$573$		0			0
$574$	6.79641	−	9.78968i	0.283677	−	0.408613i
$575$	−34.5872	−	14.4300i	−1.44239	−	0.601772i
$576$		0			0
$577$			6.56366i			0.273249i	0.990623	+	0.136624i	$0.0436253\pi$
$577$			6.56366i			0.273249i	−0.990623	+	0.136624i	$0.956375\pi$
$578$	14.4553	+	10.0355i	0.601262	+	0.417422i
$579$		0			0
$580$	−17.6829	+	24.4610i	−0.734241	+	1.01569i
$581$			4.36542i			0.181108i
$582$		0			0
$583$			41.3931i			1.71433i
$584$	1.89204	+	0.482632i	0.0782933	+	0.0199715i
$585$		0			0
$586$	18.5630	+	12.8873i	0.766832	+	0.532368i
$587$	−16.2992			−0.672741			−0.336370	−	0.941730i	$-0.609199\pi$
$587$	−16.2992			−0.672741			−0.336370	+	0.941730i	$0.609199\pi$
$588$		0			0
$589$			4.58868i			0.189073i
$590$	−0.413436	+	21.6672i	−0.0170209	+	0.892025i
$591$		0			0
$592$	−3.24860	+	2.81599i	−0.133517	+	0.115737i
$593$			16.3233i			0.670319i	0.942161	+	0.335160i	$0.108790\pi$
$593$			16.3233i			0.670319i	−0.942161	+	0.335160i	$0.891210\pi$
$594$		0			0
$595$	−2.96395	+	1.97498i	−0.121510	+	0.0809663i
$596$	3.35319	−	1.25103i	0.137352	−	0.0512443i
$597$		0			0
$598$	17.6829	−	25.4707i	0.723106	−	1.04157i
$599$	−25.5928			−1.04569			−0.522847	−	0.852426i	$-0.675130\pi$
$599$	−25.5928			−1.04569			−0.522847	+	0.852426i	$0.675130\pi$
$600$		0			0
$601$	29.9225			1.22056			0.610282	−	0.792184i	$-0.291056\pi$
$601$	29.9225			1.22056			0.610282	+	0.792184i	$0.291056\pi$
$602$	−4.47928	+	6.45203i	−0.182562	+	0.262965i
$603$		0			0
$604$	7.44322	+	19.9504i	0.302860	+	0.811768i
$605$	33.0048	−	21.9923i	1.34184	−	0.894113i
$606$		0			0
$607$			20.6965i			0.840046i	0.907513	+	0.420023i	$0.137978\pi$
$607$			20.6965i			0.840046i	−0.907513	+	0.420023i	$0.862022\pi$
$608$	−1.05061	−	9.75065i	−0.0426079	−	0.395441i
$609$		0			0
$610$	0.389245	−	20.3994i	0.0157601	−	0.825947i
$611$			5.07131i			0.205163i
$612$		0			0
$613$	−22.6676			−0.915537			−0.457769	−	0.889071i	$-0.651351\pi$
$613$	−22.6676			−0.915537			−0.457769	+	0.889071i	$0.651351\pi$
$614$	26.2396	+	18.2167i	1.05895	+	0.735166i
$615$		0			0
$616$	−2.79641	+	10.9627i	−0.112671	+	0.441698i
$617$			22.1966i			0.893603i	0.894633	+	0.446802i	$0.147437\pi$
$617$			22.1966i			0.893603i	−0.894633	+	0.446802i	$0.852563\pi$
$618$		0			0
$619$		−	16.8204i		−	0.676070i	−0.941133	−	0.338035i	$-0.890238\pi$
$619$		−	16.8204i		−	0.676070i	0.941133	−	0.338035i	$-0.109762\pi$
$620$	−9.59283	−	6.93466i	−0.385257	−	0.278503i
$621$		0			0
$622$	21.5928	+	14.9907i	0.865794	+	0.601071i
$623$		−	5.66558i		−	0.226987i
$624$		0			0
$625$	−17.5872	−	17.7676i	−0.703489	−	0.710706i
$626$	23.7008	−	34.1390i	0.947274	−	1.36447i
$627$		0			0
$628$	−4.84143	−	12.9767i	−0.193194	−	0.517825i
$629$			2.29434i			0.0914813i
$630$		0			0
$631$	−44.1205			−1.75641			−0.878204	−	0.478285i	$-0.841258\pi$
$631$	−44.1205			−1.75641			−0.878204	+	0.478285i	$0.841258\pi$
$632$	1.85039	−	7.25402i	0.0736047	−	0.288549i
$633$		0			0
$634$	−6.47301	−	4.49384i	−0.257076	−	0.178473i
$635$	−5.22441	−	7.84052i	−0.207324	−	0.311141i
$636$		0			0
$637$	18.8477			0.746773
$638$	42.0305	+	29.1794i	1.66400	+	1.15522i
$639$		0			0
$640$	21.9719	+	12.5394i	0.868515	+	0.495662i
$641$	1.18566			0.0468307			0.0234154	−	0.999726i	$-0.492546\pi$
$641$	1.18566			0.0468307			0.0234154	+	0.999726i	$0.492546\pi$
$642$		0			0
$643$	22.5872			0.890754			0.445377	−	0.895343i	$-0.353070\pi$
$643$	22.5872			0.890754			0.445377	+	0.895343i	$0.353070\pi$
$644$	−3.90997	−	10.4800i	−0.154074	−	0.412971i
$645$		0			0
$646$	−4.29921	−	2.98470i	−0.169150	−	0.117431i
$647$		−	19.7090i		−	0.774842i	−0.921903	−	0.387421i	$-0.873366\pi$
$647$		−	19.7090i		−	0.774842i	0.921903	−	0.387421i	$-0.126634\pi$
$648$		0			0
$649$	36.7368			1.44205
$650$	17.4287	−	11.1391i	0.683608	−	0.436913i
$651$		0			0
$652$	−5.38365	−	14.4300i	−0.210840	−	0.565122i
$653$	−44.4585			−1.73979			−0.869897	−	0.493234i	$-0.835815\pi$
$653$	−44.4585			−1.73979			−0.869897	+	0.493234i	$0.835815\pi$
$654$		0			0
$655$	−12.7964	−	19.2042i	−0.499997	−	0.750369i
$656$	−34.1350	+	29.5894i	−1.33275	+	1.15527i
$657$		0			0
$658$	1.50280	+	1.04331i	0.0585852	+	0.0406723i
$659$			41.5863i			1.61997i	0.586448	+	0.809987i	$0.300526\pi$
$659$			41.5863i			1.61997i	−0.586448	+	0.809987i	$0.699474\pi$
$660$		0			0
$661$			12.0060i			0.466978i	0.972359	+	0.233489i	$0.0750143\pi$
$661$			12.0060i			0.466978i	−0.972359	+	0.233489i	$0.924986\pi$
$662$	11.0811	−	15.9614i	0.430678	−	0.620356i
$663$		0			0
$664$	4.09003	−	16.0340i	0.158724	−	0.622239i
$665$	−2.40717	+	1.60398i	−0.0933461	+	0.0621997i
$666$		0			0
$667$	−50.5872			−1.95875
$668$	6.04502	−	2.25532i	0.233889	−	0.0872609i
$669$		0			0
$670$	−23.5333	−	0.449042i	−0.909169	−	0.0173480i
$671$	−34.5872			−1.33523
$672$		0			0
$673$			14.5080i			0.559244i	0.960110	+	0.279622i	$0.0902091\pi$
$673$			14.5080i			0.559244i	−0.960110	+	0.279622i	$0.909791\pi$
$674$	16.7368	−	24.1080i	0.644679	−	0.928607i
$675$		0			0
$676$	−3.10627	−	8.32586i	−0.119472	−	0.320226i
$677$	−43.8600			−1.68568			−0.842839	−	0.538166i	$-0.819117\pi$
$677$	−43.8600			−1.68568			−0.842839	+	0.538166i	$0.819117\pi$
$678$		0			0
$679$	10.5872			0.406301
$680$	12.7368	−	4.47705i	0.488436	−	0.171687i
$681$		0			0
$682$	−11.4432	+	16.4830i	−0.438184	+	0.631168i
$683$	5.33527			0.204148			0.102074	−	0.994777i	$-0.467452\pi$
$683$	5.33527			0.204148			0.102074	+	0.994777i	$0.467452\pi$
$684$		0			0
$685$	−18.6468	−	27.9841i	−0.712458	−	1.06922i
$686$	8.09003	−	11.6530i	0.308879	−	0.444915i
$687$		0			0
$688$	22.4972	−	19.5013i	0.857698	−	0.743480i
$689$	22.5872			0.860505
$690$		0			0
$691$		−	39.7710i		−	1.51296i	−0.654016	−	0.756480i	$-0.726917\pi$
$691$		−	39.7710i		−	1.51296i	0.654016	−	0.756480i	$-0.273083\pi$
$692$	−4.49383	−	12.0450i	−0.170830	−	0.457882i
$693$		0			0
$694$	−5.50280	−	3.82028i	−0.208883	−	0.145016i
$695$	11.7424	+	17.6224i	0.445416	+	0.668457i
$696$		0			0
$697$			24.1080i			0.913157i
$698$	−0.389245	+	0.560675i	−0.0147331	+	0.0212219i
$699$		0			0
$700$	0.284654	−	7.45631i	0.0107589	−	0.281822i
$701$		−	27.5015i		−	1.03872i	−0.854556	−	0.519359i	$-0.826171\pi$
$701$		−	27.5015i		−	1.03872i	0.854556	−	0.519359i	$-0.173829\pi$
$702$		0			0
$703$			1.86335i			0.0702775i
$704$	20.5422	−	37.6454i	0.774214	−	1.41881i
$705$		0			0
$706$	−1.72161	+	2.47984i	−0.0647937	+	0.0933300i
$707$	−5.55118			−0.208774
$708$		0			0
$709$			0.111632i			0.00419244i	0.999998	+	0.00209622i	$0.000667249\pi$
$709$			0.111632i			0.00419244i	−0.999998	+	0.00209622i	$0.999333\pi$
$710$	42.0305	+	0.801991i	1.57737	+	0.0300982i
$711$		0			0
$712$	−5.30818	+	20.8094i	−0.198932	+	0.779866i
$713$		−	19.8387i		−	0.742966i
$714$		0			0
$715$	−19.4432	−	29.1794i	−0.727135	−	1.09125i
$716$	15.2486	−	5.68906i	0.569867	−	0.212610i
$717$		0			0
$718$	−11.1440	−	7.73665i	−0.415891	−	0.288729i
$719$	10.7064			0.399281			0.199640	−	0.979869i	$-0.436023\pi$
$719$	10.7064			0.399281			0.199640	+	0.979869i	$0.436023\pi$
$720$		0			0
$721$	5.37112			0.200031
$722$	18.5807	+	12.8995i	0.691503	+	0.480071i
$723$		0			0
$724$	−2.79641	+	1.04331i	−0.103928	+	0.0387742i
$725$	−31.1440	−	12.9935i	−1.15666	−	0.482565i
$726$		0			0
$727$			25.6562i			0.951536i	0.879571	+	0.475768i	$0.157830\pi$
$727$			25.6562i			0.951536i	−0.879571	+	0.475768i	$0.842170\pi$
$728$	5.98207	+	1.52594i	0.221710	+	0.0565551i
$729$		0			0
$730$	−0.0416486	+	2.18271i	−0.00154149	+	0.0807856i
$731$		−	15.8888i		−	0.587667i
$732$		0			0
$733$	30.3684			1.12168			0.560842	−	0.827923i	$-0.310478\pi$
$733$	30.3684			1.12168			0.560842	+	0.827923i	$0.310478\pi$
$734$	27.4882	−	39.5945i	1.01461	−	1.46146i
$735$		0			0
$736$	4.54222	+	42.1560i	0.167428	+	1.55389i
$737$			39.9007i			1.46976i
$738$		0			0
$739$			20.1917i			0.742763i	0.928480	+	0.371381i	$0.121116\pi$
$739$			20.1917i			0.742763i	−0.928480	+	0.371381i	$0.878884\pi$
$740$	−3.89541	−	2.81599i	−0.143198	−	0.103518i
$741$		0			0
$742$	4.64681	−	6.69335i	0.170590	−	0.245720i
$743$		−	46.3863i		−	1.70175i	−0.525369	−	0.850875i	$-0.676073\pi$
$743$		−	46.3863i		−	1.70175i	0.525369	−	0.850875i	$-0.323927\pi$
$744$		0			0
$745$	2.21881	+	3.32988i	0.0812911	+	0.121997i
$746$	−5.03942	−	3.49858i	−0.184506	−	0.128092i
$747$		0			0
$748$	−8.00000	−	21.4427i	−0.292509	−	0.784023i
$749$			2.98470i			0.109059i
$750$		0			0
$751$	−27.1261			−0.989845			−0.494922	−	0.868937i	$-0.664804\pi$
$751$	−27.1261			−0.989845			−0.494922	+	0.868937i	$0.664804\pi$
$752$	−4.54222	−	5.24002i	−0.165638	−	0.191084i
$753$		0			0
$754$	15.9225	−	22.9351i	0.579863	−	0.835245i
$755$	−19.8116	+	13.2012i	−0.721020	+	0.480441i
$756$		0			0
$757$	45.2549			1.64482			0.822408	−	0.568898i	$-0.192630\pi$
$757$	45.2549			1.64482			0.822408	+	0.568898i	$0.192630\pi$
$758$	5.56574	−	8.01699i	0.202157	−	0.291190i
$759$		0			0
$760$	10.3442	−	3.63604i	0.375225	−	0.131893i
$761$	−16.8864			−0.612133			−0.306067	−	0.952010i	$-0.599013\pi$
$761$	−16.8864			−0.612133			−0.306067	+	0.952010i	$0.599013\pi$
$762$		0			0
$763$	−14.8864			−0.538926
$764$	−4.81434	−	12.9041i	−0.174177	−	0.466852i
$765$		0			0
$766$	18.0450	−	25.9924i	0.651993	−	0.939142i
$767$		−	20.0464i		−	0.723835i
$768$		0			0
$769$	−16.3297			−0.588863			−0.294431	−	0.955673i	$-0.595130\pi$
$769$	−16.3297			−0.588863			−0.294431	+	0.955673i	$0.595130\pi$
$770$	−12.6468	−	0.241316i	−0.455759	−	0.00869643i
$771$		0			0
$772$	30.8864	−	11.5233i	1.11163	−	0.414734i
$773$	41.3144			1.48598			0.742989	−	0.669304i	$-0.233408\pi$
$773$	41.3144			1.48598			0.742989	+	0.669304i	$0.233408\pi$
$774$		0			0
$775$	5.09563	−	12.2137i	0.183040	−	0.438729i
$776$	−38.8864	−	9.91936i	−1.39594	−	0.356084i
$777$		0			0
$778$	−8.88645	+	12.8002i	−0.318595	+	0.458909i
$779$			19.5794i			0.701503i
$780$		0			0
$781$		−	71.2628i		−	2.54998i
$782$	18.5872	+	12.9041i	0.664678	+	0.461448i
$783$		0			0
$784$	−19.4747	+	16.8813i	−0.695525	+	0.602904i
$785$	12.8864	−	8.58669i	0.459937	−	0.306472i
$786$		0			0
$787$	11.4849			0.409391			0.204696	−	0.978826i	$-0.434380\pi$
$787$	11.4849			0.409391			0.204696	+	0.978826i	$0.434380\pi$
$788$	−9.48824	−	25.4317i	−0.338005	−	0.905966i
$789$		0			0
$790$	8.36842	+	0.159679i	0.297735	+	0.00568114i
$791$	−8.99440			−0.319804
$792$		0			0
$793$			18.8735i			0.670216i
$794$	−29.3386	−	20.3681i	−1.04119	−	0.722838i
$795$		0			0
$796$	−6.32967	−	16.9657i	−0.224349	−	0.601332i
$797$	45.4945			1.61150			0.805749	−	0.592257i	$-0.201763\pi$
$797$	45.4945			1.61150			0.805749	+	0.592257i	$0.201763\pi$
$798$		0			0
$799$	−3.70079			−0.130924
$800$	−8.03147	+	27.1200i	−0.283955	+	0.958837i
$801$		0			0
$802$	−8.47301	−	5.88233i	−0.299192	−	0.207712i
$803$	3.70079			0.130598
$804$		0			0
$805$	10.4072	−	6.93466i	0.366805	−	0.244415i
$806$	8.99440	+	6.24430i	0.316814	+	0.219946i
$807$		0			0
$808$	20.3892	+	5.20100i	0.717291	+	0.182970i
$809$	−36.0721			−1.26823			−0.634114	−	0.773240i	$-0.718635\pi$
$809$	−36.0721			−1.26823			−0.634114	+	0.773240i	$0.718635\pi$
$810$		0			0
$811$			44.5230i			1.56341i	0.623646	+	0.781707i	$0.285651\pi$
$811$			44.5230i			1.56341i	−0.623646	+	0.781707i	$0.714349\pi$
$812$	−3.52072	−	9.43673i	−0.123553	−	0.331164i
$813$		0			0
$814$	−4.64681	+	6.69335i	−0.162871	+	0.234602i
$815$	14.3297	−	9.54836i	0.501946	−	0.334464i
$816$		0			0
$817$		−	12.9041i		−	0.451456i
$818$	−18.4134	−	12.7834i	−0.643811	−	0.446961i
$819$		0			0
$820$	−40.9315	−	29.5894i	−1.42939	−	1.03331i
$821$		−	34.1613i		−	1.19224i	−0.802897	−	0.596118i	$-0.796709\pi$
$821$		−	34.1613i		−	1.19224i	0.802897	−	0.596118i	$-0.203291\pi$
$822$		0			0
$823$		−	2.12689i		−	0.0741388i	−0.999313	−	0.0370694i	$-0.988198\pi$
$823$		−	2.12689i		−	0.0741388i	0.999313	−	0.0370694i	$-0.0118023\pi$
$824$	−19.7279	−	5.03229i	−0.687253	−	0.175308i
$825$		0			0
$826$	−5.94043	−	4.12410i	−0.206694	−	0.143496i
$827$	38.5872			1.34181			0.670905	−	0.741543i	$-0.265906\pi$
$827$	38.5872			1.34181			0.670905	+	0.741543i	$0.265906\pi$
$828$		0			0
$829$			34.2351i			1.18904i	0.804083	+	0.594518i	$0.202657\pi$
$829$			34.2351i			1.18904i	−0.804083	+	0.594518i	$0.797343\pi$
$830$	18.4972	+	0.352949i	0.642047	+	0.0122510i
$831$		0			0
$832$	−20.5422	−	11.2094i	−0.712173	−	0.388617i
$833$			13.7541i			0.476551i
$834$		0			0
$835$	4.00000	+	6.00299i	0.138426	+	0.207742i
$836$	−6.49720	−	17.4147i	−0.224710	−	0.602300i
$837$		0			0
$838$	−6.47301	+	9.32384i	−0.223606	+	0.322087i
$839$	−41.5928			−1.43594			−0.717972	−	0.696072i	$-0.754929\pi$
$839$	−41.5928			−1.43594			−0.717972	+	0.696072i	$0.754929\pi$
$840$		0			0
$841$	−16.5512			−0.570730
$842$	18.4972	−	26.6437i	0.637456	−	0.918202i
$843$		0			0
$844$	4.75140	−	1.77269i	0.163550	−	0.0610184i
$845$	8.26798	−	5.50924i	0.284427	−	0.189524i
$846$		0			0
$847$			13.2348i			0.454752i
$848$	−23.3386	+	20.2307i	−0.801452	+	0.694725i
$849$		0			0
$850$	8.12878	+	12.7186i	0.278815	+	0.436243i
$851$		−	8.05601i		−	0.276156i
$852$		0			0
$853$	−23.1828			−0.793763			−0.396881	−	0.917870i	$-0.629908\pi$
$853$	−23.1828			−0.793763			−0.396881	+	0.917870i	$0.629908\pi$
$854$	5.59283	+	3.88278i	0.191383	+	0.132866i
$855$		0			0
$856$	2.79641	−	10.9627i	0.0955795	−	0.374696i
$857$			9.38868i			0.320711i	0.987059	+	0.160356i	$0.0512641\pi$
$857$			9.38868i			0.320711i	−0.987059	+	0.160356i	$0.948736\pi$
$858$		0			0
$859$			8.98769i			0.306656i	0.988175	+	0.153328i	$0.0489991\pi$
$859$			8.98769i			0.306656i	−0.988175	+	0.153328i	$0.951001\pi$
$860$	26.9765	+	19.5013i	0.919890	+	0.664989i
$861$		0			0
$862$	40.7368	+	28.2813i	1.38750	+	0.963264i
$863$			12.2473i			0.416903i	0.978033	+	0.208451i	$0.0668423\pi$
$863$			12.2473i			0.416903i	−0.978033	+	0.208451i	$0.933158\pi$
$864$		0			0
$865$	11.9612	−	7.97020i	0.406695	−	0.270995i
$866$	−13.7729	+	19.8387i	−0.468022	+	0.674147i
$867$		0			0
$868$	3.70079	−	1.38072i	0.125613	−	0.0468646i
$869$		−	14.1887i		−	0.481318i
$870$		0			0
$871$	21.7729			0.737746
$872$	54.6773	+	13.9474i	1.85161	+	0.472317i
$873$		0			0
$874$	15.0956	+	10.4800i	0.510617	+	0.354492i
$875$	8.18836	−	1.59621i	0.276817	−	0.0539618i
$876$		0			0
$877$	−26.1109			−0.881701			−0.440850	−	0.897581i	$-0.645323\pi$
$877$	−26.1109			−0.881701			−0.440850	+	0.897581i	$0.645323\pi$
$878$	−9.91960	−	6.88661i	−0.334770	−	0.232412i
$879$		0			0
$880$	46.2251	+	12.7354i	1.55825	+	0.429309i
$881$	38.4793			1.29640			0.648200	−	0.761470i	$-0.275522\pi$
$881$	38.4793			1.29640			0.648200	+	0.761470i	$0.275522\pi$
$882$		0			0
$883$	6.58723			0.221678			0.110839	−	0.993838i	$-0.464646\pi$
$883$	6.58723			0.221678			0.110839	+	0.993838i	$0.464646\pi$
$884$	−11.7008	+	4.36542i	−0.393540	+	0.146825i
$885$		0			0
$886$	−24.0900	−	16.7243i	−0.809320	−	0.561865i
$887$			50.9595i			1.71105i	0.517760	+	0.855526i	$0.326766\pi$
$887$			50.9595i			1.71105i	−0.517760	+	0.855526i	$0.673234\pi$
$888$		0			0
$889$	3.14401			0.105447
$890$	−24.0063	−	0.458068i	−0.804692	−	0.0153545i
$891$		0			0
$892$	−22.7819	+	8.49962i	−0.762793	+	0.284588i
$893$	−3.00560			−0.100578
$894$		0			0
$895$	10.0900	+	15.1426i	0.337273	+	0.506161i
$896$	−7.54781	+	3.78126i	−0.252155	+	0.126323i
$897$		0			0
$898$	−2.32340	−	1.61301i	−0.0775330	−	0.0538268i
$899$		−	17.8637i		−	0.595789i
$900$		0			0
$901$			16.4830i			0.549129i
$902$	−48.8269	+	70.3311i	−1.62576	+	2.34177i
$903$		0			0
$904$	33.0361	+	8.42701i	1.09876	+	0.280278i
$905$	−1.85039	−	2.77697i	−0.0615092	−	0.0923097i
$906$		0			0
$907$	24.5568			0.815394			0.407697	−	0.913117i	$-0.366332\pi$
$907$	24.5568			0.815394			0.407697	+	0.913117i	$0.366332\pi$
$908$	14.4972	+	38.8574i	0.481107	+	1.28953i
$909$		0			0
$910$	−0.131681	+	6.90107i	−0.00436517	+	0.228768i
$911$	−16.0000			−0.530104			−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000			−0.530104			−0.265052	+	0.964234i	$0.585389\pi$
$912$		0			0
$913$		−	31.3621i		−	1.03793i
$914$	1.03605	−	1.49235i	0.0342696	−	0.0493625i
$915$		0			0
$916$	−37.3836	+	13.9474i	−1.23519	+	0.460834i
$917$	7.70079			0.254302
$918$		0			0
$919$	−28.7548			−0.948532			−0.474266	−	0.880382i	$-0.657287\pi$
$919$	−28.7548			−0.948532			−0.474266	+	0.880382i	$0.657287\pi$
$920$	−44.7223	+	15.7201i	−1.47445	+	0.518275i
$921$		0			0
$922$	−12.6647	+	18.2425i	−0.417091	+	0.600785i
$923$	−38.8864			−1.27996
$924$		0			0
$925$	2.06921	−	4.95968i	0.0680351	−	0.163073i
$926$	−15.0990	+	21.7489i	−0.496184	+	0.714712i
$927$		0			0
$928$	4.09003	+	37.9593i	0.134262	+	1.24608i
$929$	28.2880			0.928100			0.464050	−	0.885809i	$-0.346396\pi$
$929$	28.2880			0.928100			0.464050	+	0.885809i	$0.346396\pi$
$930$		0			0
$931$			11.1704i			0.366095i
$932$	−24.9944	+	9.32510i	−0.818719	+	0.305454i
$933$		0			0
$934$	−2.49720	−	1.73367i	−0.0817110	−	0.0567273i
$935$	21.2936	−	14.1887i	0.696376	−	0.464020i
$936$		0			0
$937$			33.9313i			1.10849i	0.832354	+	0.554244i	$0.186992\pi$
$937$			33.9313i			1.10849i	−0.832354	+	0.554244i	$0.813008\pi$
$938$	4.47928	−	6.45203i	0.146254	−	0.210666i
$939$		0			0
$940$	4.54222	−	6.28332i	0.148151	−	0.204939i
$941$		−	38.8016i		−	1.26490i	−0.774603	−	0.632448i	$-0.782050\pi$
$941$		−	38.8016i		−	1.26490i	0.774603	−	0.632448i	$-0.217950\pi$
$942$		0			0
$943$		−	84.6495i		−	2.75657i
$944$	17.9550	+	20.7133i	0.584385	+	0.674161i
$945$		0			0
$946$	32.1801	−	46.3527i	1.04626	−	1.50706i
$947$	17.7729			0.577541			0.288771	−	0.957398i	$-0.406753\pi$
$947$	17.7729			0.577541			0.288771	+	0.957398i	$0.406753\pi$
$948$		0			0
$949$		−	2.01943i		−	0.0655536i
$950$	6.60179	+	10.3294i	0.214190	+	0.335129i
$951$		0			0
$952$	−1.11355	+	4.36542i	−0.0360905	+	0.141484i
$953$			46.3047i			1.49996i	0.661463	+	0.749978i	$0.269936\pi$
$953$			46.3047i			1.49996i	−0.661463	+	0.749978i	$0.730064\pi$
$954$		0			0
$955$	12.8143	−	8.53864i	0.414662	−	0.276304i
$956$	16.0000	+	42.8854i	0.517477	+	1.38701i
$957$		0			0
$958$	−14.1496	−	9.82327i	−0.457153	−	0.317375i
$959$	11.2215			0.362361
$960$		0			0
$961$	−23.9944			−0.774013
$962$	3.65240	+	2.53566i	0.117758	+	0.0817528i
$963$		0			0
$964$	2.51176	+	6.73237i	0.0808984	+	0.216835i
$965$	20.4376	+	30.6717i	0.657911	+	0.987357i
$966$		0			0
$967$		−	9.28482i		−	0.298580i	−0.988793	−	0.149290i	$-0.952301\pi$
$967$		−	9.28482i		−	0.298580i	0.988793	−	0.149290i	$-0.0476987\pi$
$968$	12.3999	−	48.6108i	0.398548	−	1.56241i
$969$		0			0
$970$	0.855989	−	44.8604i	0.0274842	−	1.44038i
$971$			20.9301i			0.671678i	0.941919	+	0.335839i	$0.109020\pi$
$971$			20.9301i			0.671678i	−0.941919	+	0.335839i	$0.890980\pi$
$972$		0			0
$973$	−7.06651			−0.226542
$974$	20.7819	−	29.9346i	0.665894	−	0.959165i
$975$		0			0
$976$	−16.9044	−	19.5013i	−0.541096	−	0.624222i
$977$		−	30.8314i		−	0.986383i	−0.869921	−	0.493192i	$-0.835830\pi$
$977$		−	30.8314i		−	0.986383i	0.869921	−	0.493192i	$-0.164170\pi$
$978$		0			0
$979$			40.7027i			1.30086i
$980$	−23.3522	−	16.8813i	−0.745958	−	0.539253i
$981$		0			0
$982$	13.5270	−	19.4845i	0.431664	−	0.621776i
$983$		−	31.3285i		−	0.999223i	−0.866250	−	0.499612i	$-0.833476\pi$
$983$		−	31.3285i		−	0.999223i	0.866250	−	0.499612i	$-0.166524\pi$
$984$		0			0
$985$	25.2549	−	16.8282i	0.804687	−	0.536191i
$986$	16.7368	+	11.6194i	0.533010	+	0.370038i
$987$		0			0
$988$	−9.50280	+	3.54537i	−0.302324	+	0.112793i
$989$			55.7895i			1.77400i
$990$		0			0
$991$	31.3420			0.995611			0.497806	−	0.867289i	$-0.334139\pi$
$991$	31.3420			0.995611			0.497806	+	0.867289i	$0.334139\pi$
$992$	−14.8864	+	1.60398i	−0.472645	+	0.0509265i
$993$		0			0
$994$	−8.00000	+	11.5233i	−0.253745	+	0.365498i
$995$	16.8477	−	11.2262i	0.534108	−	0.355895i
$996$		0			0
$997$	−20.9557			−0.663672			−0.331836	−	0.943337i	$-0.607668\pi$
$997$	−20.9557			−0.663672			−0.331836	+	0.943337i	$0.607668\pi$
$998$	−14.2125	+	20.4720i	−0.449890	+	0.648030i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.d.e.109.6		6
3.2	odd	2		120.2.d.b.109.1	yes	6
4.3	odd	2		1440.2.d.f.1009.2		6
5.2	odd	4		1800.2.k.u.901.4		12
5.3	odd	4		1800.2.k.u.901.9		12
5.4	even	2		360.2.d.f.109.1		6
8.3	odd	2		1440.2.d.e.1009.5		6
8.5	even	2		360.2.d.f.109.2		6
12.11	even	2		480.2.d.b.49.5		6
15.2	even	4		600.2.k.f.301.9		12
15.8	even	4		600.2.k.f.301.4		12
15.14	odd	2		120.2.d.a.109.6	yes	6
20.3	even	4		7200.2.k.u.3601.7		12
20.7	even	4		7200.2.k.u.3601.5		12
20.19	odd	2		1440.2.d.e.1009.6		6
24.5	odd	2		120.2.d.a.109.5	✓	6
24.11	even	2		480.2.d.a.49.2		6
40.3	even	4		7200.2.k.u.3601.8		12
40.13	odd	4		1800.2.k.u.901.10		12
40.19	odd	2		1440.2.d.f.1009.1		6
40.27	even	4		7200.2.k.u.3601.6		12
40.29	even	2	inner	360.2.d.e.109.5		6
40.37	odd	4		1800.2.k.u.901.3		12
48.5	odd	4		3840.2.f.l.769.11		12
48.11	even	4		3840.2.f.m.769.5		12
48.29	odd	4		3840.2.f.l.769.2		12
48.35	even	4		3840.2.f.m.769.8		12
60.23	odd	4		2400.2.k.f.1201.10		12
60.47	odd	4		2400.2.k.f.1201.3		12
60.59	even	2		480.2.d.a.49.1		6
120.29	odd	2		120.2.d.b.109.2	yes	6
120.53	even	4		600.2.k.f.301.3		12
120.59	even	2		480.2.d.b.49.6		6
120.77	even	4		600.2.k.f.301.10		12
120.83	odd	4		2400.2.k.f.1201.4		12
120.107	odd	4		2400.2.k.f.1201.9		12
240.29	odd	4		3840.2.f.l.769.8		12
240.59	even	4		3840.2.f.m.769.11		12
240.149	odd	4		3840.2.f.l.769.5		12
240.179	even	4		3840.2.f.m.769.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.5	✓	6	24.5	odd	2
120.2.d.a.109.6	yes	6	15.14	odd	2
120.2.d.b.109.1	yes	6	3.2	odd	2
120.2.d.b.109.2	yes	6	120.29	odd	2
360.2.d.e.109.5		6	40.29	even	2	inner
360.2.d.e.109.6		6	1.1	even	1	trivial
360.2.d.f.109.1		6	5.4	even	2
360.2.d.f.109.2		6	8.5	even	2
480.2.d.a.49.1		6	60.59	even	2
480.2.d.a.49.2		6	24.11	even	2
480.2.d.b.49.5		6	12.11	even	2
480.2.d.b.49.6		6	120.59	even	2
600.2.k.f.301.3		12	120.53	even	4
600.2.k.f.301.4		12	15.8	even	4
600.2.k.f.301.9		12	15.2	even	4
600.2.k.f.301.10		12	120.77	even	4
1440.2.d.e.1009.5		6	8.3	odd	2
1440.2.d.e.1009.6		6	20.19	odd	2
1440.2.d.f.1009.1		6	40.19	odd	2
1440.2.d.f.1009.2		6	4.3	odd	2
1800.2.k.u.901.3		12	40.37	odd	4
1800.2.k.u.901.4		12	5.2	odd	4
1800.2.k.u.901.9		12	5.3	odd	4
1800.2.k.u.901.10		12	40.13	odd	4
2400.2.k.f.1201.3		12	60.47	odd	4
2400.2.k.f.1201.4		12	120.83	odd	4
2400.2.k.f.1201.9		12	120.107	odd	4
2400.2.k.f.1201.10		12	60.23	odd	4
3840.2.f.l.769.2		12	48.29	odd	4
3840.2.f.l.769.5		12	240.149	odd	4
3840.2.f.l.769.8		12	240.29	odd	4
3840.2.f.l.769.11		12	48.5	odd	4
3840.2.f.m.769.2		12	240.179	even	4
3840.2.f.m.769.5		12	48.11	even	4
3840.2.f.m.769.8		12	48.35	even	4
3840.2.f.m.769.11		12	240.59	even	4
7200.2.k.u.3601.5		12	20.7	even	4
7200.2.k.u.3601.6		12	40.27	even	4
7200.2.k.u.3601.7		12	20.3	even	4
7200.2.k.u.3601.8		12	40.3	even	4

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16170 + 0.806504i) q^{2} +(0.699104 + 1.87383i) q^{4} +(-1.86081 + 1.23992i) q^{5} -0.746175i q^{7} +(-0.699104 + 2.74067i) q^{8} +O(q^{10})\)	\(q+(1.16170 + 0.806504i) q^{2} +(0.699104 + 1.87383i) q^{4} +(-1.86081 + 1.23992i) q^{5} -0.746175i q^{7} +(-0.699104 + 2.74067i) q^{8} +(-3.16170 - 0.0603290i) q^{10} +5.36068i q^{11} +2.92520 q^{13} +(0.601793 - 0.866833i) q^{14} +(-3.02251 + 2.62001i) q^{16} +2.13466i q^{17} +1.73367i q^{19} +(-3.62430 - 2.62001i) q^{20} +(-4.32340 + 6.22751i) q^{22} -7.49534i q^{23} +(1.92520 - 4.61450i) q^{25} +(3.39821 + 2.35918i) q^{26} +(1.39821 - 0.521653i) q^{28} -6.74916i q^{29} +2.64681 q^{31} +(-5.62430 + 0.606006i) q^{32} +(-1.72161 + 2.47984i) q^{34} +(0.925197 + 1.38849i) q^{35} +1.07480 q^{37} +(-1.39821 + 2.01400i) q^{38} +(-2.09731 - 5.96668i) q^{40} +11.2936 q^{41} -7.44322 q^{43} +(-10.0450 + 3.74767i) q^{44} +(6.04502 - 8.70735i) q^{46} +1.73367i q^{47} +6.44322 q^{49} +(5.95812 - 3.80800i) q^{50} +(2.04502 + 5.48133i) q^{52} +7.72161 q^{53} +(-6.64681 - 9.97518i) q^{55} +(2.04502 + 0.521653i) q^{56} +(5.44322 - 7.84052i) q^{58} -6.85302i q^{59} +6.45203i q^{61} +(3.07480 + 2.13466i) q^{62} +(-7.02251 - 3.83202i) q^{64} +(-5.44322 + 3.62701i) q^{65} +7.44322 q^{67} +(-4.00000 + 1.49235i) q^{68} +(-0.0450160 + 2.35918i) q^{70} -13.2936 q^{71} -0.690358i q^{73} +(1.24860 + 0.866833i) q^{74} +(-3.24860 + 1.21201i) q^{76} +4.00000 q^{77} -2.64681 q^{79} +(2.37570 - 8.62300i) q^{80} +(13.1198 + 9.10834i) q^{82} -5.85039 q^{83} +(-2.64681 - 3.97219i) q^{85} +(-8.64681 - 6.00299i) q^{86} +(-14.6918 - 3.74767i) q^{88} +7.59283 q^{89} -2.18271i q^{91} +(14.0450 - 5.24002i) q^{92} +(-1.39821 + 2.01400i) q^{94} +(-2.14961 - 3.22601i) q^{95} +14.1887i q^{97} +(7.48511 + 5.19648i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{4} - q^{8}+O(q^{10}) \) 6 * q - q^2 + q^4 - q^8	\( 6 q - q^{2} + q^{4} - q^{8} - 11 q^{10} + 8 q^{13} + 10 q^{14} + q^{16} - 9 q^{20} - 10 q^{22} + 2 q^{25} + 14 q^{26} + 2 q^{28} - 16 q^{31} - 21 q^{32} + 12 q^{34} - 4 q^{35} + 16 q^{37} - 2 q^{38} - 3 q^{40} + 4 q^{41} - 22 q^{44} - 2 q^{46} - 6 q^{49} + 15 q^{50} - 26 q^{52} + 24 q^{53} - 8 q^{55} - 26 q^{56} - 12 q^{58} + 28 q^{62} - 23 q^{64} + 12 q^{65} - 24 q^{68} + 38 q^{70} - 16 q^{71} - 18 q^{74} + 6 q^{76} + 24 q^{77} + 16 q^{79} + 27 q^{80} + 50 q^{82} - 16 q^{83} + 16 q^{85} - 20 q^{86} - 18 q^{88} + 20 q^{89} + 46 q^{92} - 2 q^{94} - 32 q^{95} + 21 q^{98}+O(q^{100}) \) 6 * q - q^2 + q^4 - q^8 - 11 * q^10 + 8 * q^13 + 10 * q^14 + q^16 - 9 * q^20 - 10 * q^22 + 2 * q^25 + 14 * q^26 + 2 * q^28 - 16 * q^31 - 21 * q^32 + 12 * q^34 - 4 * q^35 + 16 * q^37 - 2 * q^38 - 3 * q^40 + 4 * q^41 - 22 * q^44 - 2 * q^46 - 6 * q^49 + 15 * q^50 - 26 * q^52 + 24 * q^53 - 8 * q^55 - 26 * q^56 - 12 * q^58 + 28 * q^62 - 23 * q^64 + 12 * q^65 - 24 * q^68 + 38 * q^70 - 16 * q^71 - 18 * q^74 + 6 * q^76 + 24 * q^77 + 16 * q^79 + 27 * q^80 + 50 * q^82 - 16 * q^83 + 16 * q^85 - 20 * q^86 - 18 * q^88 + 20 * q^89 + 46 * q^92 - 2 * q^94 - 32 * q^95 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more