LMFDB - Embedded newform 1170.2.bj.d.829.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(199,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.199"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.2
Root			$2.00607 - 1.30680i$ of defining polynomial
Character	$\chi$	$=$	1170.829
Dual form			1170.2.bj.d.199.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.26873 + 1.84128i) q^{5} +(-2.17283 + 3.76344i) q^{7} -1.00000 q^{8} +(-2.22896 - 0.178114i) q^{10} +(2.04055 - 1.17811i) q^{11} +(-3.18419 + 1.69144i) q^{13} -4.34565 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.60564 - 1.50437i) q^{17} +(0.585872 + 0.338254i) q^{19} +(-0.960230 - 2.01940i) q^{20} +(2.04055 + 1.17811i) q^{22} +(5.58405 - 3.22396i) q^{23} +(-1.78064 - 4.67219i) q^{25} +(-3.05692 - 1.91187i) q^{26} +(-2.17283 - 3.76344i) q^{28} +(-4.82620 - 8.35922i) q^{29} +7.11493i q^{31} +(0.500000 - 0.866025i) q^{32} -3.00874i q^{34} +(-4.17283 - 8.77559i) q^{35} +(3.74165 + 6.48073i) q^{37} +0.676507i q^{38} +(1.26873 - 1.84128i) q^{40} +(2.60564 - 1.50437i) q^{41} +(-5.91710 - 3.41624i) q^{43} +2.35623i q^{44} +(5.58405 + 3.22396i) q^{46} -5.61529 q^{47} +(-5.94234 - 10.2924i) q^{49} +(3.15592 - 3.87817i) q^{50} +(0.127265 - 3.60330i) q^{52} +9.43400i q^{53} +(-0.419677 + 5.25194i) q^{55} +(2.17283 - 3.76344i) q^{56} +(4.82620 - 8.35922i) q^{58} +(4.56364 + 2.63482i) q^{59} +(2.15646 - 3.73509i) q^{61} +(-6.16171 + 3.55746i) q^{62} +1.00000 q^{64} +(0.925468 - 8.00896i) q^{65} +(-2.91329 - 5.04596i) q^{67} +(2.60564 - 1.50437i) q^{68} +(5.51347 - 8.00157i) q^{70} +(-2.52520 - 1.45793i) q^{71} -7.67804 q^{73} +(-3.74165 + 6.48073i) q^{74} +(-0.585872 + 0.338254i) q^{76} +10.2393i q^{77} -3.74519 q^{79} +(2.22896 + 0.178114i) q^{80} +(2.60564 + 1.50437i) q^{82} -10.3557 q^{83} +(6.07583 - 2.88908i) q^{85} -6.83247i q^{86} +(-2.04055 + 1.17811i) q^{88} +(-4.15208 + 2.39720i) q^{89} +(0.553049 - 15.6587i) q^{91} +6.44791i q^{92} +(-2.80764 - 4.86298i) q^{94} +(-1.36614 + 0.649603i) q^{95} +(-8.17066 + 14.1520i) q^{97} +(5.94234 - 10.2924i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - 6 q^{16} - 18 q^{17} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 6 q^{23} - 10 q^{25} + 2 q^{26} - 2 q^{28} - 14 q^{29}+ \cdots - 8 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^7 - 12 * q^8 - 2 * q^10 - 6 * q^11 - 8 * q^13 - 4 * q^14 - 6 * q^16 - 18 * q^17 - 6 * q^19 - 4 * q^20 - 6 * q^22 - 6 * q^23 - 10 * q^25 + 2 * q^26 - 2 * q^28 - 14 * q^29 + 6 * q^32 - 26 * q^35 - 12 * q^37 - 2 * q^40 + 18 * q^41 - 36 * q^43 - 6 * q^46 - 16 * q^47 + 8 * q^49 + 10 * q^50 + 10 * q^52 - 28 * q^55 + 2 * q^56 + 14 * q^58 + 36 * q^59 + 10 * q^61 - 6 * q^62 + 12 * q^64 - 6 * q^65 + 4 * q^67 + 18 * q^68 - 4 * q^70 + 12 * q^71 + 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 2 * q^80 + 18 * q^82 - 72 * q^83 + 18 * q^85 + 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 + 42 * q^95 - 48 * q^97 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.26873	+	1.84128i	−0.567394	+	0.823446i
$5$	−1.26873	+	1.84128i	−0.567394	+	0.823446i
$6$		0			0
$7$	−2.17283	+	3.76344i	−0.821251	+	1.42245i	0.0835003	+	0.996508i	$0.473390\pi$
$7$	−2.17283	+	3.76344i	−0.821251	+	1.42245i	−0.904751	+	0.425940i	$0.859943\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.22896	−	0.178114i	−0.704860	−	0.0563246i
$11$	2.04055	−	1.17811i	0.615250	−	0.355215i	−0.159767	−	0.987155i	$-0.551074\pi$
$11$	2.04055	−	1.17811i	0.615250	−	0.355215i	0.775017	+	0.631940i	$0.217741\pi$
$12$		0			0
$13$	−3.18419	+	1.69144i	−0.883134	+	0.469120i
$13$	−3.18419	+	1.69144i	−0.883134	+	0.469120i
$14$	−4.34565			−1.16142
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.60564	−	1.50437i	−0.631962	−	0.364863i	0.149550	−	0.988754i	$-0.452218\pi$
$17$	−2.60564	−	1.50437i	−0.631962	−	0.364863i	−0.781511	+	0.623891i	$0.785551\pi$
$18$		0			0
$19$	0.585872	+	0.338254i	0.134408	+	0.0776007i	0.565696	−	0.824614i	$-0.308607\pi$
$19$	0.585872	+	0.338254i	0.134408	+	0.0776007i	−0.431288	+	0.902214i	$0.641941\pi$
$20$	−0.960230	−	2.01940i	−0.214714	−	0.451551i
$21$		0			0
$22$	2.04055	+	1.17811i	0.435047	+	0.251175i
$23$	5.58405	−	3.22396i	1.16436	−	0.672241i	0.212012	−	0.977267i	$-0.431998\pi$
$23$	5.58405	−	3.22396i	1.16436	−	0.672241i	0.952344	+	0.305026i	$0.0986651\pi$
$24$		0			0
$25$	−1.78064	−	4.67219i	−0.356127	−	0.934438i
$26$	−3.05692	−	1.91187i	−0.599511	−	0.374948i
$27$		0			0
$28$	−2.17283	−	3.76344i	−0.410625	−	0.711224i
$29$	−4.82620	−	8.35922i	−0.896202	−	1.55227i	−0.832310	−	0.554311i	$-0.812982\pi$
$29$	−4.82620	−	8.35922i	−0.896202	−	1.55227i	−0.0638921	−	0.997957i	$-0.520351\pi$
$30$		0			0
$31$			7.11493i			1.27788i	0.769257	+	0.638939i	$0.220626\pi$
$31$			7.11493i			1.27788i	−0.769257	+	0.638939i	$0.779374\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		−	3.00874i		−	0.515995i
$35$	−4.17283	−	8.77559i	−0.705336	−	1.48335i
$36$		0			0
$37$	3.74165	+	6.48073i	0.615123	+	1.06542i	0.990363	+	0.138497i	$0.0442271\pi$
$37$	3.74165	+	6.48073i	0.615123	+	1.06542i	−0.375240	+	0.926928i	$0.622440\pi$
$38$			0.676507i			0.109744i
$39$		0			0
$40$	1.26873	−	1.84128i	0.200604	−	0.291132i
$41$	2.60564	−	1.50437i	0.406933	−	0.234943i	−0.282538	−	0.959256i	$-0.591176\pi$
$41$	2.60564	−	1.50437i	0.406933	−	0.234943i	0.689471	+	0.724313i	$0.257843\pi$
$42$		0			0
$43$	−5.91710	−	3.41624i	−0.902349	−	0.520971i	−0.0243872	−	0.999703i	$-0.507763\pi$
$43$	−5.91710	−	3.41624i	−0.902349	−	0.520971i	−0.877961	+	0.478731i	$0.841097\pi$
$44$			2.35623i			0.355215i
$45$		0			0
$46$	5.58405	+	3.22396i	0.823324	+	0.475346i
$47$	−5.61529			−0.819074			−0.409537	−	0.912294i	$-0.634310\pi$
$47$	−5.61529			−0.819074			−0.409537	+	0.912294i	$0.634310\pi$
$48$		0			0
$49$	−5.94234	−	10.2924i	−0.848906	−	1.47035i
$50$	3.15592	−	3.87817i	0.446314	−	0.548456i
$51$		0			0
$52$	0.127265	−	3.60330i	0.0176485	−	0.499688i
$53$			9.43400i			1.29586i	0.761700	+	0.647930i	$0.224365\pi$
$53$			9.43400i			1.29586i	−0.761700	+	0.647930i	$0.775635\pi$
$54$		0			0
$55$	−0.419677	+	5.25194i	−0.0565892	+	0.708172i
$56$	2.17283	−	3.76344i	0.290356	−	0.502911i
$57$		0			0
$58$	4.82620	−	8.35922i	0.633711	−	1.09762i
$59$	4.56364	+	2.63482i	0.594135	+	0.343024i	0.766731	−	0.641969i	$-0.221882\pi$
$59$	4.56364	+	2.63482i	0.594135	+	0.343024i	−0.172596	+	0.984993i	$0.555215\pi$
$60$		0			0
$61$	2.15646	−	3.73509i	0.276106	−	0.478230i	−0.694307	−	0.719679i	$-0.744289\pi$
$61$	2.15646	−	3.73509i	0.276106	−	0.478230i	0.970414	+	0.241449i	$0.0776225\pi$
$62$	−6.16171	+	3.55746i	−0.782538	+	0.451798i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.925468	−	8.00896i	0.114790	−	0.993390i
$66$		0			0
$67$	−2.91329	−	5.04596i	−0.355915	−	0.616463i	0.631359	−	0.775490i	$-0.282497\pi$
$67$	−2.91329	−	5.04596i	−0.355915	−	0.616463i	−0.987274	+	0.159028i	$0.949164\pi$
$68$	2.60564	−	1.50437i	0.315981	−	0.182432i
$69$		0			0
$70$	5.51347	−	8.00157i	0.658986	−	0.956370i
$71$	−2.52520	−	1.45793i	−0.299686	−	0.173024i	0.342616	−	0.939476i	$-0.388687\pi$
$71$	−2.52520	−	1.45793i	−0.299686	−	0.173024i	−0.642302	+	0.766452i	$0.722020\pi$
$72$		0			0
$73$	−7.67804			−0.898647			−0.449323	−	0.893369i	$-0.648335\pi$
$73$	−7.67804			−0.898647			−0.449323	+	0.893369i	$0.648335\pi$
$74$	−3.74165	+	6.48073i	−0.434958	+	0.753369i
$75$		0			0
$76$	−0.585872	+	0.338254i	−0.0672042	+	0.0388004i
$77$			10.2393i			1.16688i
$78$		0			0
$79$	−3.74519			−0.421367			−0.210683	−	0.977554i	$-0.567569\pi$
$79$	−3.74519			−0.421367			−0.210683	+	0.977554i	$0.567569\pi$
$80$	2.22896	+	0.178114i	0.249206	+	0.0199137i
$81$		0			0
$82$	2.60564	+	1.50437i	0.287745	+	0.166130i
$83$	−10.3557			−1.13668			−0.568341	−	0.822793i	$-0.692415\pi$
$83$	−10.3557			−1.13668			−0.568341	+	0.822793i	$0.692415\pi$
$84$		0			0
$85$	6.07583	−	2.88908i	0.659017	−	0.313365i
$86$		−	6.83247i		−	0.736765i
$87$		0			0
$88$	−2.04055	+	1.17811i	−0.217524	+	0.125587i
$89$	−4.15208	+	2.39720i	−0.440119	+	0.254103i	−0.703648	−	0.710549i	$-0.748447\pi$
$89$	−4.15208	+	2.39720i	−0.440119	+	0.254103i	0.263529	+	0.964651i	$0.415114\pi$
$90$		0			0
$91$	0.553049	−	15.6587i	0.0579753	−	1.64148i
$92$			6.44791i			0.672241i
$93$		0			0
$94$	−2.80764	−	4.86298i	−0.289586	−	0.501578i
$95$	−1.36614	+	0.649603i	−0.140163	+	0.0666478i
$96$		0			0
$97$	−8.17066	+	14.1520i	−0.829605	+	1.43692i	0.0687436	+	0.997634i	$0.478101\pi$
$97$	−8.17066	+	14.1520i	−0.829605	+	1.43692i	−0.898349	+	0.439283i	$0.855232\pi$
$98$	5.94234	−	10.2924i	0.600267	−	1.03969i
$99$		0			0
$100$	4.93655	+	0.794019i	0.493655	+	0.0794019i
$101$	6.11911	+	10.5986i	0.608875	+	1.05460i	0.991426	+	0.130668i	$0.0417121\pi$
$101$	6.11911	+	10.5986i	0.608875	+	1.05460i	−0.382552	+	0.923934i	$0.624955\pi$
$102$		0			0
$103$		−	3.75144i		−	0.369640i	−0.982772	−	0.184820i	$-0.940830\pi$
$103$		−	3.75144i		−	0.369640i	0.982772	−	0.184820i	$-0.0591702\pi$
$104$	3.18419	−	1.69144i	0.312235	−	0.165859i
$105$		0			0
$106$	−8.17008	+	4.71700i	−0.793549	+	0.458156i
$107$	−14.3904	+	8.30831i	−1.39117	+	0.803194i	−0.993445	−	0.114309i	$-0.963535\pi$
$107$	−14.3904	+	8.30831i	−1.39117	+	0.803194i	−0.397728	+	0.917503i	$0.630201\pi$
$108$		0			0
$109$			11.1116i			1.06430i	0.846652	+	0.532148i	$0.178615\pi$
$109$			11.1116i			1.06430i	−0.846652	+	0.532148i	$0.821385\pi$
$110$	−4.75816	+	2.26252i	−0.453672	+	0.215723i
$111$		0			0
$112$	4.34565			0.410625
$113$	13.5620	+	7.83002i	1.27581	+	0.736587i	0.976074	−	0.217437i	$-0.0697697\pi$
$113$	13.5620	+	7.83002i	1.27581	+	0.736587i	0.299731	+	0.954024i	$0.403103\pi$
$114$		0			0
$115$	−1.14846	+	14.3722i	−0.107095	+	1.34021i
$116$	9.65239			0.896202
$117$		0			0
$118$			5.26964i			0.485109i
$119$	11.3232	−	6.53747i	1.03800	−	0.599288i
$120$		0			0
$121$	−2.72410	+	4.71827i	−0.247645	+	0.428934i
$122$	4.31292			0.390473
$123$		0			0
$124$	−6.16171	−	3.55746i	−0.553338	−	0.319470i
$125$	10.8620	+	2.64911i	0.971523	+	0.236943i
$126$		0			0
$127$	11.7820	−	6.80236i	1.04549	−	0.603611i	0.124103	−	0.992269i	$-0.460395\pi$
$127$	11.7820	−	6.80236i	1.04549	−	0.603611i	0.921382	+	0.388658i	$0.127061\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	7.39870	−	3.20300i	0.648909	−	0.280922i
$131$	−10.2122			−0.892246			−0.446123	−	0.894972i	$-0.647196\pi$
$131$	−10.2122			−0.892246			−0.446123	+	0.894972i	$0.647196\pi$
$132$		0			0
$133$	−2.54600	+	1.46993i	−0.220766	+	0.127459i
$134$	2.91329	−	5.04596i	0.251670	−	0.435905i
$135$		0			0
$136$	2.60564	+	1.50437i	0.223432	+	0.128999i
$137$	6.20689	−	10.7506i	0.530290	−	0.918489i	−0.469085	−	0.883153i	$-0.655416\pi$
$137$	6.20689	−	10.7506i	0.530290	−	0.918489i	0.999375	−	0.0353365i	$-0.0112503\pi$
$138$		0			0
$139$	−7.80915	+	13.5258i	−0.662363	+	1.14725i	0.317630	+	0.948215i	$0.397113\pi$
$139$	−7.80915	+	13.5258i	−0.662363	+	1.14725i	−0.979993	+	0.199032i	$0.936220\pi$
$140$	9.68629	+	0.774021i	0.818641	+	0.0654167i
$141$		0			0
$142$		−	2.91585i		−	0.244693i
$143$	−4.50479	+	7.20280i	−0.376710	+	0.602329i
$144$		0			0
$145$	21.5148	+	1.71923i	1.78671	+	0.142774i
$146$	−3.83902	−	6.64938i	−0.317720	−	0.550307i
$147$		0			0
$148$	−7.48330			−0.615123
$149$	−16.9104	−	9.76324i	−1.38536	−	0.799836i	−0.392569	−	0.919722i	$-0.628414\pi$
$149$	−16.9104	−	9.76324i	−1.38536	−	0.799836i	−0.992788	+	0.119886i	$0.961747\pi$
$150$		0			0
$151$		−	11.5027i		−	0.936079i	−0.883707	−	0.468040i	$-0.844960\pi$
$151$		−	11.5027i		−	0.936079i	0.883707	−	0.468040i	$-0.155040\pi$
$152$	−0.585872	−	0.338254i	−0.0475205	−	0.0274360i
$153$		0			0
$154$	−8.86753	+	5.11967i	−0.714566	+	0.412555i
$155$	−13.1006	−	9.02694i	−1.05226	−	0.725061i
$156$		0			0
$157$		−	4.47595i		−	0.357220i	−0.983920	−	0.178610i	$-0.942840\pi$
$157$		−	4.47595i		−	0.357220i	0.983920	−	0.178610i	$-0.0571600\pi$
$158$	−1.87260	−	3.24343i	−0.148976	−	0.258033i
$159$		0			0
$160$	0.960230	+	2.01940i	0.0759129	+	0.159647i
$161$			28.0204i			2.20831i
$162$		0			0
$163$	3.87774	−	6.71645i	0.303728	−	0.526073i	−0.673249	−	0.739416i	$-0.735102\pi$
$163$	3.87774	−	6.71645i	0.303728	−	0.526073i	0.976977	+	0.213343i	$0.0684352\pi$
$164$			3.00874i			0.234943i
$165$		0			0
$166$	−5.17783	−	8.96827i	−0.401878	−	0.696073i
$167$	−0.339021	−	0.587202i	−0.0262342	−	0.0454390i	0.852610	−	0.522547i	$-0.175018\pi$
$167$	−0.339021	−	0.587202i	−0.0262342	−	0.0454390i	−0.878844	+	0.477108i	$0.841685\pi$
$168$		0			0
$169$	7.27808	−	10.7717i	0.559852	−	0.828593i
$170$	5.53994	+	3.81729i	0.424894	+	0.292772i
$171$		0			0
$172$	5.91710	−	3.41624i	0.451174	−	0.260486i
$173$	−0.625226	−	0.360974i	−0.0475350	−	0.0274444i	0.476044	−	0.879421i	$-0.342070\pi$
$173$	−0.625226	−	0.360974i	−0.0475350	−	0.0274444i	−0.523579	+	0.851977i	$0.675404\pi$
$174$		0			0
$175$	21.4525	+	3.45053i	1.62166	+	0.260835i
$176$	−2.04055	−	1.17811i	−0.153812	−	0.0888037i
$177$		0			0
$178$	−4.15208	−	2.39720i	−0.311211	−	0.179678i
$179$	−3.18673	−	5.51958i	−0.238187	−	0.412553i	0.722007	−	0.691886i	$-0.243220\pi$
$179$	−3.18673	−	5.51958i	−0.238187	−	0.412553i	−0.960194	+	0.279333i	$0.909887\pi$
$180$		0			0
$181$	22.0214			1.63683			0.818417	−	0.574624i	$-0.194852\pi$
$181$	22.0214			1.63683			0.818417	+	0.574624i	$0.194852\pi$
$182$	13.8374	−	7.35040i	1.02569	−	0.544848i
$183$		0			0
$184$	−5.58405	+	3.22396i	−0.411662	+	0.237673i
$185$	−16.6800	−	1.33288i	−1.22634	−	0.0979953i
$186$		0			0
$187$	−7.08928			−0.518419
$188$	2.80764	−	4.86298i	0.204768	−	0.354669i
$189$		0			0
$190$	−1.24564	−	0.858307i	−0.0903682	−	0.0622681i
$191$	0.293441	−	0.508255i	0.0212326	−	0.0367760i	−0.855214	−	0.518275i	$-0.826574\pi$
$191$	0.293441	−	0.508255i	0.0212326	−	0.0367760i	0.876446	+	0.481499i	$0.159908\pi$
$192$		0			0
$193$	11.3135	+	19.5955i	0.814363	+	1.41052i	0.909784	+	0.415081i	$0.136247\pi$
$193$	11.3135	+	19.5955i	0.814363	+	1.41052i	−0.0954215	+	0.995437i	$0.530420\pi$
$194$	−16.3413			−1.17324
$195$		0			0
$196$	11.8847			0.848906
$197$	0.823770	+	1.42681i	0.0586912	+	0.101656i	0.893878	−	0.448310i	$-0.147974\pi$
$197$	0.823770	+	1.42681i	0.0586912	+	0.101656i	−0.835187	+	0.549966i	$0.814641\pi$
$198$		0			0
$199$	−5.13665	+	8.89694i	−0.364127	+	0.630687i	−0.988636	−	0.150331i	$-0.951966\pi$
$199$	−5.13665	+	8.89694i	−0.364127	+	0.630687i	0.624508	+	0.781018i	$0.285299\pi$
$200$	1.78064	+	4.67219i	0.125910	+	0.330374i
$201$		0			0
$202$	−6.11911	+	10.5986i	−0.430539	+	0.745716i
$203$	41.9459			2.94403
$204$		0			0
$205$	−0.535898	+	6.70637i	−0.0374288	+	0.468393i
$206$	3.24884	−	1.87572i	0.226357	−	0.130688i
$207$		0			0
$208$	3.05692	+	1.91187i	0.211959	+	0.132564i
$209$	1.59401			0.110260
$210$		0			0
$211$	12.1905	+	21.1145i	0.839226	+	1.45358i	0.890543	+	0.454900i	$0.150325\pi$
$211$	12.1905	+	21.1145i	0.839226	+	1.45358i	−0.0513166	+	0.998682i	$0.516342\pi$
$212$	−8.17008	−	4.71700i	−0.561124	−	0.323965i
$213$		0			0
$214$	−14.3904	−	8.30831i	−0.983708	−	0.567944i
$215$	13.7975	−	6.56075i	0.940979	−	0.447439i
$216$		0			0
$217$	−26.7766	−	15.4595i	−1.81772	−	1.04946i
$218$	−9.62290	+	5.55578i	−0.651745	+	0.376285i
$219$		0			0
$220$	−4.33848	−	2.98942i	−0.292500	−	0.201547i
$221$	10.8414	+	0.382907i	0.729272	+	0.0257571i
$222$		0			0
$223$	2.31792	+	4.01476i	0.155220	+	0.268848i	0.933139	−	0.359516i	$-0.117058\pi$
$223$	2.31792	+	4.01476i	0.155220	+	0.268848i	−0.777919	+	0.628364i	$0.783725\pi$
$224$	2.17283	+	3.76344i	0.145178	+	0.251456i
$225$		0			0
$226$			15.6600i			1.04169i
$227$	8.89213	−	15.4016i	0.590192	−	1.02224i	−0.404015	−	0.914753i	$-0.632385\pi$
$227$	8.89213	−	15.4016i	0.590192	−	1.02224i	0.994206	−	0.107489i	$-0.0342812\pi$
$228$		0			0
$229$			15.3361i			1.01344i	0.862111	+	0.506720i	$0.169142\pi$
$229$			15.3361i			1.01344i	−0.862111	+	0.506720i	$0.830858\pi$
$230$	−13.0209	+	6.19148i	−0.858572	+	0.408254i
$231$		0			0
$232$	4.82620	+	8.35922i	0.316855	+	0.548809i
$233$		−	7.75548i		−	0.508079i	−0.967194	−	0.254039i	$-0.918241\pi$
$233$		−	7.75548i		−	0.508079i	0.967194	−	0.254039i	$-0.0817593\pi$
$234$		0			0
$235$	7.12430	−	10.3393i	0.464738	−	0.674463i
$236$	−4.56364	+	2.63482i	−0.297068	+	0.171512i
$237$		0			0
$238$	11.3232	+	6.53747i	0.733975	+	0.423761i
$239$			18.6409i			1.20578i	0.797824	+	0.602890i	$0.205984\pi$
$239$			18.6409i			1.20578i	−0.797824	+	0.602890i	$0.794016\pi$
$240$		0			0
$241$	−2.65884	−	1.53508i	−0.171271	−	0.0988833i	0.411914	−	0.911223i	$-0.364860\pi$
$241$	−2.65884	−	1.53508i	−0.171271	−	0.0988833i	−0.583185	+	0.812339i	$0.698194\pi$
$242$	−5.44819			−0.350223
$243$		0			0
$244$	2.15646	+	3.73509i	0.138053	+	0.239115i
$245$	26.4905	+	2.11683i	1.69242	+	0.135239i
$246$		0			0
$247$	−2.43766	−	0.0860957i	−0.155105	−	0.00547814i
$248$		−	7.11493i		−	0.451798i
$249$		0			0
$250$	3.13679	+	10.7313i	0.198388	+	0.678706i
$251$	3.56404	−	6.17309i	0.224960	−	0.389642i	−0.731347	−	0.682005i	$-0.761108\pi$
$251$	3.56404	−	6.17309i	0.224960	−	0.389642i	0.956307	+	0.292363i	$0.0944415\pi$
$252$		0			0
$253$	7.59637	−	13.1573i	0.477580	−	0.827193i
$254$	11.7820	+	6.80236i	0.739270	+	0.426818i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.3353	+	7.12178i	−0.769454	+	0.444244i	−0.832680	−	0.553755i	$-0.813194\pi$
$257$	−12.3353	+	7.12178i	−0.769454	+	0.444244i	0.0632261	+	0.997999i	$0.479861\pi$
$258$		0			0
$259$	−32.5198			−2.02068
$260$	6.47323	+	4.80596i	0.401453	+	0.298053i
$261$		0			0
$262$	−5.10611	−	8.84404i	−0.315457	−	0.546387i
$263$	−13.3385	+	7.70101i	−0.822490	+	0.474865i	−0.851274	−	0.524721i	$-0.824170\pi$
$263$	−13.3385	+	7.70101i	−0.822490	+	0.474865i	0.0287845	+	0.999586i	$0.490836\pi$
$264$		0			0
$265$	−17.3707	−	11.9692i	−1.06707	−	0.735264i
$266$	−2.54600	−	1.46993i	−0.156105	−	0.0901273i
$267$		0			0
$268$	5.82658			0.355915
$269$	−13.3134	+	23.0595i	−0.811732	+	1.40596i	0.0999185	+	0.994996i	$0.468142\pi$
$269$	−13.3134	+	23.0595i	−0.811732	+	1.40596i	−0.911651	+	0.410966i	$0.865192\pi$
$270$		0			0
$271$	−6.66899	+	3.85034i	−0.405112	+	0.233892i	−0.688687	−	0.725058i	$-0.741813\pi$
$271$	−6.66899	+	3.85034i	−0.405112	+	0.233892i	0.283575	+	0.958950i	$0.408479\pi$
$272$			3.00874i			0.182432i
$273$		0			0
$274$	12.4138			0.749943
$275$	−9.13785	−	7.43606i	−0.551033	−	0.448411i
$276$		0			0
$277$	12.3861	+	7.15114i	0.744211	+	0.429671i	0.823599	−	0.567173i	$-0.191963\pi$
$277$	12.3861	+	7.15114i	0.744211	+	0.429671i	−0.0793871	+	0.996844i	$0.525296\pi$
$278$	−15.6183			−0.936723
$279$		0			0
$280$	4.17283	+	8.77559i	0.249374	+	0.524442i
$281$			7.96746i			0.475299i	0.971351	+	0.237649i	$0.0763769\pi$
$281$			7.96746i			0.475299i	−0.971351	+	0.237649i	$0.923623\pi$
$282$		0			0
$283$	−12.7095	+	7.33785i	−0.755503	+	0.436190i	−0.827679	−	0.561202i	$-0.810339\pi$
$283$	−12.7095	+	7.33785i	−0.755503	+	0.436190i	0.0721756	+	0.997392i	$0.477006\pi$
$284$	2.52520	−	1.45793i	0.149843	−	0.0865120i
$285$		0			0
$286$	−8.49021	−	0.299865i	−0.502036	−	0.0177314i
$287$			13.0749i			0.771789i
$288$		0			0
$289$	−3.97374	−	6.88273i	−0.233750	−	0.404866i
$290$	9.26852	+	19.4920i	0.544266	+	1.14461i
$291$		0			0
$292$	3.83902	−	6.64938i	0.224662	−	0.389125i
$293$	3.43198	−	5.94436i	0.200498	−	0.347273i	−0.748191	−	0.663484i	$-0.769077\pi$
$293$	3.43198	−	5.94436i	0.200498	−	0.347273i	0.948689	+	0.316210i	$0.102411\pi$
$294$		0			0
$295$	−10.6415	+	5.06006i	−0.619571	+	0.294608i
$296$	−3.74165	−	6.48073i	−0.217479	−	0.376685i
$297$		0			0
$298$		−	19.5265i		−	1.13114i
$299$	−12.3275	+	19.7108i	−0.712921	+	1.13990i
$300$		0			0
$301$	25.7136	−	14.8458i	1.48211	−	0.855696i
$302$	9.96166	−	5.75137i	0.573229	−	0.330954i
$303$		0			0
$304$		−	0.676507i		−	0.0388004i
$305$	4.14139	+	8.70948i	0.237135	+	0.498704i
$306$		0			0
$307$	10.9917			0.627328			0.313664	−	0.949534i	$-0.398443\pi$
$307$	10.9917			0.627328			0.313664	+	0.949534i	$0.398443\pi$
$308$	−8.86753	−	5.11967i	−0.505275	−	0.291720i
$309$		0			0
$310$	1.26727	−	15.8589i	0.0719760	−	0.900725i
$311$	13.9044			0.788446			0.394223	−	0.919015i	$-0.371014\pi$
$311$	13.9044			0.788446			0.394223	+	0.919015i	$0.371014\pi$
$312$		0			0
$313$			14.1734i			0.801130i	0.916268	+	0.400565i	$0.131186\pi$
$313$			14.1734i			0.801130i	−0.916268	+	0.400565i	$0.868814\pi$
$314$	3.87629	−	2.23798i	0.218752	−	0.126296i
$315$		0			0
$316$	1.87260	−	3.24343i	0.105342	−	0.182457i
$317$	3.20808			0.180184			0.0900920	−	0.995933i	$-0.471284\pi$
$317$	3.20808			0.180184			0.0900920	+	0.995933i	$0.471284\pi$
$318$		0			0
$319$	−19.6962	−	11.3716i	−1.10278	−	0.636688i
$320$	−1.26873	+	1.84128i	−0.0709243	+	0.102931i
$321$		0			0
$322$	−24.2664	+	14.0102i	−1.35231	+	0.780757i
$323$	−1.01772	−	1.76274i	−0.0566273	−	0.0980813i
$324$		0			0
$325$	13.5726	+	11.8653i	0.752872	+	0.658167i
$326$	7.75548			0.429537
$327$		0			0
$328$	−2.60564	+	1.50437i	−0.143873	+	0.0830649i
$329$	12.2010	−	21.1328i	0.672665	−	1.16509i
$330$		0			0
$331$	−22.3066	−	12.8787i	−1.22608	−	0.707878i	−0.259873	−	0.965643i	$-0.583681\pi$
$331$	−22.3066	−	12.8787i	−1.22608	−	0.707878i	−0.966208	+	0.257765i	$0.917014\pi$
$332$	5.17783	−	8.96827i	0.284170	−	0.492198i
$333$		0			0
$334$	0.339021	−	0.587202i	0.0185504	−	0.0321302i
$335$	12.9872	+	1.03779i	0.709568	+	0.0567008i
$336$		0			0
$337$			0.772078i			0.0420578i	0.999779	+	0.0210289i	$0.00669420\pi$
$337$			0.772078i			0.0420578i	−0.999779	+	0.0210289i	$0.993306\pi$
$338$	12.9676	+	0.917149i	0.705345	+	0.0498863i
$339$		0			0
$340$	−0.535898	+	6.70637i	−0.0290632	+	0.363704i
$341$	8.38219	+	14.5184i	0.453921	+	0.786215i
$342$		0			0
$343$	21.2271			1.14616
$344$	5.91710	+	3.41624i	0.319028	+	0.184191i
$345$		0			0
$346$		−	0.721948i		−	0.0388122i
$347$	−21.7856	−	12.5779i	−1.16951	−	0.675218i	−0.215946	−	0.976405i	$-0.569284\pi$
$347$	−21.7856	−	12.5779i	−1.16951	−	0.675218i	−0.953565	+	0.301188i	$0.902617\pi$
$348$		0			0
$349$	−23.6602	+	13.6602i	−1.26650	+	0.731214i	−0.974324	−	0.225151i	$-0.927713\pi$
$349$	−23.6602	+	13.6602i	−1.26650	+	0.731214i	−0.292176	+	0.956365i	$0.594379\pi$
$350$	7.73802	+	20.3037i	0.413614	+	1.08528i
$351$		0			0
$352$		−	2.35623i		−	0.125587i
$353$	−3.75948	−	6.51161i	−0.200097	−	0.346578i	0.748462	−	0.663177i	$-0.230792\pi$
$353$	−3.75948	−	6.51161i	−0.200097	−	0.346578i	−0.948559	+	0.316599i	$0.897459\pi$
$354$		0			0
$355$	5.88826	−	2.79989i	0.312516	−	0.148603i
$356$		−	4.79440i		−	0.254103i
$357$		0			0
$358$	3.18673	−	5.51958i	0.168424	−	0.291719i
$359$		−	10.8402i		−	0.572124i	−0.958211	−	0.286062i	$-0.907654\pi$
$359$		−	10.8402i		−	0.572124i	0.958211	−	0.286062i	$-0.0923463\pi$
$360$		0			0
$361$	−9.27117	−	16.0581i	−0.487956	−	0.845165i
$362$	11.0107	+	19.0711i	0.578708	+	1.00235i
$363$		0			0
$364$	13.2843	+	8.30831i	0.696287	+	0.435474i
$365$	9.74138	−	14.1374i	0.509887	−	0.739987i
$366$		0			0
$367$	6.50838	−	3.75761i	0.339735	−	0.196146i	−0.320420	−	0.947276i	$-0.603824\pi$
$367$	6.50838	−	3.75761i	0.339735	−	0.196146i	0.660155	+	0.751130i	$0.270491\pi$
$368$	−5.58405	−	3.22396i	−0.291089	−	0.168060i
$369$		0			0
$370$	−7.18569	−	15.1117i	−0.373566	−	0.785622i
$371$	−35.5043	−	20.4984i	−1.84329	−	1.06423i
$372$		0			0
$373$	19.8135	+	11.4393i	1.02590	+	0.592305i	0.915808	−	0.401616i	$-0.131551\pi$
$373$	19.8135	+	11.4393i	1.02590	+	0.592305i	0.110095	+	0.993921i	$0.464885\pi$
$374$	−3.54464	−	6.13949i	−0.183289	−	0.317466i
$375$		0			0
$376$	5.61529			0.289586
$377$	29.5066	+	18.4541i	1.51967	+	0.950434i
$378$		0			0
$379$	−22.6152	+	13.0569i	−1.16166	+	0.670687i	−0.951702	−	0.307022i	$-0.900667\pi$
$379$	−22.6152	+	13.0569i	−1.16166	+	0.670687i	−0.209962	+	0.977710i	$0.567334\pi$
$380$	0.120495	−	1.50791i	0.00618128	−	0.0773541i
$381$		0			0
$382$	0.586882			0.0300275
$383$	−6.84652	+	11.8585i	−0.349841	+	0.605942i	−0.986221	−	0.165434i	$-0.947098\pi$
$383$	−6.84652	+	11.8585i	−0.349841	+	0.605942i	0.636380	+	0.771376i	$0.280431\pi$
$384$		0			0
$385$	−18.8535	−	12.9910i	−0.960864	−	0.662082i
$386$	−11.3135	+	19.5955i	−0.575842	+	0.997387i
$387$		0			0
$388$	−8.17066	−	14.1520i	−0.414802	−	0.718459i
$389$	−24.9403			−1.26452			−0.632261	−	0.774755i	$-0.717873\pi$
$389$	−24.9403			−1.26452			−0.632261	+	0.774755i	$0.717873\pi$
$390$		0			0
$391$	−19.4001			−0.981104
$392$	5.94234	+	10.2924i	0.300134	+	0.519847i
$393$		0			0
$394$	−0.823770	+	1.42681i	−0.0415009	+	0.0718817i
$395$	4.75165	−	6.89595i	0.239081	−	0.346973i
$396$		0			0
$397$	14.5517	−	25.2043i	0.730328	−	1.26497i	−0.226415	−	0.974031i	$-0.572700\pi$
$397$	14.5517	−	25.2043i	0.730328	−	1.26497i	0.956743	−	0.290934i	$-0.0939662\pi$
$398$	−10.2733			−0.514954
$399$		0			0
$400$	−3.15592	+	3.87817i	−0.157796	+	0.193908i
$401$	14.4596	−	8.34823i	0.722076	−	0.416891i	−0.0934404	−	0.995625i	$-0.529786\pi$
$401$	14.4596	−	8.34823i	0.722076	−	0.416891i	0.815516	+	0.578734i	$0.196453\pi$
$402$		0			0
$403$	−12.0345	−	22.6552i	−0.599479	−	1.12854i
$404$	−12.2382			−0.608875
$405$		0			0
$406$	20.9730	+	36.3262i	1.04087	+	1.80284i
$407$	15.2701	+	8.81618i	0.756909	+	0.437002i
$408$		0			0
$409$	21.3140	+	12.3056i	1.05391	+	0.608475i	0.923741	−	0.383017i	$-0.125115\pi$
$409$	21.3140	+	12.3056i	1.05391	+	0.608475i	0.130168	+	0.991492i	$0.458448\pi$
$410$	−6.07583	+	2.88908i	−0.300064	+	0.142682i
$411$		0			0
$412$	3.24884	+	1.87572i	0.160059	+	0.0924100i
$413$	−19.8320	+	11.4500i	−0.975868	+	0.563418i
$414$		0			0
$415$	13.1386	−	19.0677i	0.644947	−	0.935996i
$416$	−0.127265	+	3.60330i	−0.00623968	+	0.176667i
$417$		0			0
$418$	0.797003	+	1.38045i	0.0389827	+	0.0675200i
$419$	13.5527	+	23.4739i	0.662091	+	1.14678i	0.980065	+	0.198676i	$0.0636643\pi$
$419$	13.5527	+	23.4739i	0.662091	+	1.14678i	−0.317974	+	0.948099i	$0.603002\pi$
$420$		0			0
$421$			32.9996i			1.60830i	0.594425	+	0.804151i	$0.297380\pi$
$421$			32.9996i			1.60830i	−0.594425	+	0.804151i	$0.702620\pi$
$422$	−12.1905	+	21.1145i	−0.593422	+	1.02784i
$423$		0			0
$424$		−	9.43400i		−	0.458156i
$425$	−2.38900	+	14.8528i	−0.115883	+	0.720466i
$426$		0			0
$427$	9.37121	+	16.2314i	0.453505	+	0.785493i
$428$		−	16.6166i		−	0.803194i
$429$		0			0
$430$	12.5805	+	8.66858i	0.606686	+	0.418036i
$431$	−7.45678	+	4.30517i	−0.359180	+	0.207373i	−0.668721	−	0.743513i	$-0.733158\pi$
$431$	−7.45678	+	4.30517i	−0.359180	+	0.207373i	0.309541	+	0.950886i	$0.399825\pi$
$432$		0			0
$433$	−2.99201	−	1.72744i	−0.143787	−	0.0830155i	0.426381	−	0.904544i	$-0.359788\pi$
$433$	−2.99201	−	1.72744i	−0.143787	−	0.0830155i	−0.570168	+	0.821528i	$0.693122\pi$
$434$		−	30.9190i		−	1.48416i
$435$		0			0
$436$	−9.62290	−	5.55578i	−0.460853	−	0.266074i
$437$	4.36206			0.208666
$438$		0			0
$439$	−12.1229	−	20.9974i	−0.578593	−	1.00215i	−0.995641	−	0.0932675i	$-0.970269\pi$
$439$	−12.1229	−	20.9974i	−0.578593	−	1.00215i	0.417049	−	0.908884i	$-0.363064\pi$
$440$	0.419677	−	5.25194i	0.0200073	−	0.250377i
$441$		0			0
$442$	5.08909	+	9.58038i	0.242064	+	0.455692i
$443$		−	13.1629i		−	0.625390i	−0.949854	−	0.312695i	$-0.898768\pi$
$443$		−	13.1629i		−	0.625390i	0.949854	−	0.312695i	$-0.101232\pi$
$444$		0			0
$445$	0.853950	−	10.6865i	0.0404811	−	0.506591i
$446$	−2.31792	+	4.01476i	−0.109757	+	0.190104i
$447$		0			0
$448$	−2.17283	+	3.76344i	−0.102656	+	0.177806i
$449$	−2.17774	−	1.25732i	−0.102774	−	0.0593365i	0.447732	−	0.894168i	$-0.352232\pi$
$449$	−2.17774	−	1.25732i	−0.102774	−	0.0593365i	−0.550506	+	0.834831i	$0.685565\pi$
$450$		0			0
$451$	3.54464	−	6.13949i	0.166910	−	0.289097i
$452$	−13.5620	+	7.83002i	−0.637903	+	0.368293i
$453$		0			0
$454$	17.7843			0.834657
$455$	28.1304	+	20.8850i	1.31877	+	0.979105i
$456$		0			0
$457$	5.38493	+	9.32698i	0.251897	+	0.436298i	0.964048	−	0.265728i	$-0.0856124\pi$
$457$	5.38493	+	9.32698i	0.251897	+	0.436298i	−0.712151	+	0.702026i	$0.752279\pi$
$458$	−13.2815	+	7.66806i	−0.620602	+	0.358305i
$459$		0			0
$460$	−11.8724	−	8.18068i	−0.553554	−	0.381426i
$461$	−10.2984	−	5.94576i	−0.479642	−	0.276922i	0.240625	−	0.970618i	$-0.422648\pi$
$461$	−10.2984	−	5.94576i	−0.479642	−	0.276922i	−0.720267	+	0.693697i	$0.755981\pi$
$462$		0			0
$463$	29.9462			1.39172			0.695860	−	0.718178i	$-0.255024\pi$
$463$	29.9462			1.39172			0.695860	+	0.718178i	$0.255024\pi$
$464$	−4.82620	+	8.35922i	−0.224051	+	0.388067i
$465$		0			0
$466$	6.71645	−	3.87774i	0.311133	−	0.179633i
$467$		−	21.8940i		−	1.01313i	−0.862201	−	0.506566i	$-0.830915\pi$
$467$		−	21.8940i		−	1.01313i	0.862201	−	0.506566i	$-0.169085\pi$
$468$		0			0
$469$	25.3203			1.16918
$470$	12.5163	+	1.00016i	0.577332	+	0.0461340i
$471$		0			0
$472$	−4.56364	−	2.63482i	−0.210059	−	0.121277i
$473$	−16.0989			−0.740227
$474$		0			0
$475$	0.537159	−	3.33961i	0.0246466	−	0.153232i
$476$			13.0749i			0.599288i
$477$		0			0
$478$	−16.1435	+	9.32045i	−0.738386	+	0.426307i
$479$	7.90106	−	4.56168i	0.361009	−	0.208429i	−0.308514	−	0.951220i	$-0.599832\pi$
$479$	7.90106	−	4.56168i	0.361009	−	0.208429i	0.669523	+	0.742791i	$0.266498\pi$
$480$		0			0
$481$	−22.8758	−	14.3071i	−1.04305	−	0.652346i
$482$		−	3.07016i		−	0.139842i
$483$		0			0
$484$	−2.72410	−	4.71827i	−0.123823	−	0.214467i
$485$	−15.6914	−	32.9996i	−0.712511	−	1.49843i
$486$		0			0
$487$	−10.8587	+	18.8079i	−0.492056	+	0.852265i	−0.999958	−	0.00914916i	$-0.997088\pi$
$487$	−10.8587	+	18.8079i	−0.492056	+	0.852265i	0.507902	+	0.861415i	$0.330421\pi$
$488$	−2.15646	+	3.73509i	−0.0976183	+	0.169080i
$489$		0			0
$490$	11.4120	+	23.9999i	0.515543	+	1.08420i
$491$	−16.5438	−	28.6548i	−0.746613	−	1.29317i	−0.949437	−	0.313957i	$-0.898345\pi$
$491$	−16.5438	−	28.6548i	−0.746613	−	1.29317i	0.202824	−	0.979215i	$-0.434988\pi$
$492$		0			0
$493$			29.0415i			1.30796i
$494$	−1.14427	−	2.15412i	−0.0514831	−	0.0969187i
$495$		0			0
$496$	6.16171	−	3.55746i	0.276669	−	0.159735i
$497$	10.9736	−	6.33564i	0.492235	−	0.284192i
$498$		0			0
$499$		−	10.4889i		−	0.469546i	−0.972050	−	0.234773i	$-0.924565\pi$
$499$		−	10.4889i		−	0.469546i	0.972050	−	0.234773i	$-0.0754347\pi$
$500$	−7.72518	+	8.08218i	−0.345480	+	0.361446i
$501$		0			0
$502$	7.12807			0.318142
$503$	−7.14818	−	4.12700i	−0.318722	−	0.184014i	0.332101	−	0.943244i	$-0.392243\pi$
$503$	−7.14818	−	4.12700i	−0.318722	−	0.184014i	−0.650823	+	0.759230i	$0.725576\pi$
$504$		0			0
$505$	−27.2786	−	2.17980i	−1.21388	−	0.0969998i
$506$	15.1927			0.675400
$507$		0			0
$508$			13.6047i			0.603611i
$509$	−5.84526	+	3.37476i	−0.259087	+	0.149584i	−0.623918	−	0.781490i	$-0.714460\pi$
$509$	−5.84526	+	3.37476i	−0.259087	+	0.149584i	0.364831	+	0.931074i	$0.381127\pi$
$510$		0			0
$511$	16.6830	−	28.8959i	0.738014	−	1.27828i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−12.3353	−	7.12178i	−0.544086	−	0.314128i
$515$	6.90745	+	4.75957i	0.304379	+	0.209732i
$516$		0			0
$517$	−11.4583	+	6.61545i	−0.503935	+	0.290947i
$518$	−16.2599	−	28.1630i	−0.714419	−	1.23741i
$519$		0			0
$520$	−0.925468	+	8.00896i	−0.0405844	+	0.351216i
$521$	30.4048			1.33206			0.666029	−	0.745926i	$-0.267993\pi$
$521$	30.4048			1.33206			0.666029	+	0.745926i	$0.267993\pi$
$522$		0			0
$523$	2.72235	−	1.57175i	0.119040	−	0.0687279i	−0.439298	−	0.898342i	$-0.644773\pi$
$523$	2.72235	−	1.57175i	0.119040	−	0.0687279i	0.558338	+	0.829614i	$0.311439\pi$
$524$	5.10611	−	8.84404i	0.223062	−	0.386354i
$525$		0			0
$526$	−13.3385	−	7.70101i	−0.581588	−	0.335780i
$527$	10.7035	−	18.5390i	0.466251	−	0.807570i
$528$		0			0
$529$	9.28778	−	16.0869i	0.403816	−	0.699431i
$530$	1.68033	−	21.0280i	0.0729887	−	0.913400i
$531$		0			0
$532$		−	2.93986i		−	0.127459i
$533$	−5.75231	+	9.19748i	−0.249160	+	0.398387i
$534$		0			0
$535$	2.95965	−	37.0378i	0.127957	−	1.60128i
$536$	2.91329	+	5.04596i	0.125835	+	0.217952i
$537$		0			0
$538$	−26.6268			−1.14796
$539$	−24.2513	−	14.0015i	−1.04458	−	0.603088i
$540$		0			0
$541$			17.6144i			0.757301i	0.925540	+	0.378650i	$0.123612\pi$
$541$			17.6144i			0.757301i	−0.925540	+	0.378650i	$0.876388\pi$
$542$	−6.66899	−	3.85034i	−0.286458	−	0.165386i
$543$		0			0
$544$	−2.60564	+	1.50437i	−0.111716	+	0.0644993i
$545$	−20.4595	−	14.0976i	−0.876390	−	0.603875i
$546$		0			0
$547$		−	40.8067i		−	1.74477i	−0.488820	−	0.872385i	$-0.662572\pi$
$547$		−	40.8067i		−	1.74477i	0.488820	−	0.872385i	$-0.337428\pi$
$548$	6.20689	+	10.7506i	0.265145	+	0.459245i
$549$		0			0
$550$	1.87089	−	11.6316i	0.0797750	−	0.495975i
$551$		−	6.52991i		−	0.278184i
$552$		0			0
$553$	8.13765	−	14.0948i	0.346048	−	0.599373i
$554$			14.3023i			0.607646i
$555$		0			0
$556$	−7.80915	−	13.5258i	−0.331182	−	0.573623i
$557$	−12.6109	−	21.8427i	−0.534340	−	0.925504i	−0.999195	−	0.0401170i	$-0.987227\pi$
$557$	−12.6109	−	21.8427i	−0.534340	−	0.925504i	0.464855	−	0.885387i	$-0.346106\pi$
$558$		0			0
$559$	24.6195	+	0.869535i	1.04129	+	0.0367774i
$560$	−5.51347	+	8.00157i	−0.232987	+	0.338128i
$561$		0			0
$562$	−6.90002	+	3.98373i	−0.291060	+	0.168043i
$563$	31.5356	+	18.2071i	1.32907	+	0.767337i	0.985155	−	0.171664i	$-0.0549145\pi$
$563$	31.5356	+	18.2071i	1.32907	+	0.767337i	0.343912	+	0.939002i	$0.388248\pi$
$564$		0			0
$565$	−31.6238	+	15.0372i	−1.33042	+	0.632622i
$566$	−12.7095	−	7.33785i	−0.534222	−	0.308433i
$567$		0			0
$568$	2.52520	+	1.45793i	0.105955	+	0.0611732i
$569$	13.6768	+	23.6888i	0.573360	+	0.993088i	0.996218	+	0.0868922i	$0.0276936\pi$
$569$	13.6768	+	23.6888i	0.573360	+	0.993088i	−0.422858	+	0.906196i	$0.638973\pi$
$570$		0			0
$571$	45.7020			1.91257			0.956285	−	0.292438i	$-0.0944664\pi$
$571$	45.7020			1.91257			0.956285	+	0.292438i	$0.0944664\pi$
$572$	−3.98541	−	7.50267i	−0.166638	−	0.313702i
$573$		0			0
$574$	−11.3232	+	6.53747i	−0.472622	+	0.272869i
$575$	−25.0061	−	20.3491i	−1.04283	−	0.848615i
$576$		0			0
$577$	31.1697			1.29761			0.648806	−	0.760954i	$-0.275269\pi$
$577$	31.1697			1.29761			0.648806	+	0.760954i	$0.275269\pi$
$578$	3.97374	−	6.88273i	0.165286	−	0.286284i
$579$		0			0
$580$	−12.2463	+	17.7728i	−0.508500	+	0.737974i
$581$	22.5011	−	38.9730i	0.933501	−	1.61687i
$582$		0			0
$583$	11.1143	+	19.2506i	0.460308	+	0.797278i
$584$	7.67804			0.317720
$585$		0			0
$586$	6.86396			0.283547
$587$	−7.61411	−	13.1880i	−0.314268	−	0.544328i	0.665014	−	0.746831i	$-0.268426\pi$
$587$	−7.61411	−	13.1880i	−0.314268	−	0.544328i	−0.979282	+	0.202503i	$0.935092\pi$
$588$		0			0
$589$	−2.40665	+	4.16844i	−0.0991643	+	0.171758i
$590$	−9.70288	−	6.68576i	−0.399461	−	0.275248i
$591$		0			0
$592$	3.74165	−	6.48073i	0.153781	−	0.266356i
$593$	15.1921			0.623865			0.311933	−	0.950104i	$-0.399024\pi$
$593$	15.1921			0.623865			0.311933	+	0.950104i	$0.399024\pi$
$594$		0			0
$595$	−2.32883	+	29.1435i	−0.0954726	+	1.19477i
$596$	16.9104	−	9.76324i	0.692678	−	0.399918i
$597$		0			0
$598$	−23.2338	−	0.820594i	−0.950100	−	0.0335566i
$599$	−4.34655			−0.177595			−0.0887975	−	0.996050i	$-0.528302\pi$
$599$	−4.34655			−0.177595			−0.0887975	+	0.996050i	$0.528302\pi$
$600$		0			0
$601$	−5.14622	−	8.91351i	−0.209918	−	0.363590i	0.741770	−	0.670654i	$-0.233987\pi$
$601$	−5.14622	−	8.91351i	−0.209918	−	0.363590i	−0.951689	+	0.307065i	$0.900653\pi$
$602$	25.7136	+	14.8458i	1.04801	+	0.605069i
$603$		0			0
$604$	9.96166	+	5.75137i	0.405334	+	0.234020i
$605$	−5.23152	−	11.0021i	−0.212691	−	0.447297i
$606$		0			0
$607$	−37.6094	−	21.7138i	−1.52652	−	0.881335i	−0.999504	−	0.0314772i	$-0.989979\pi$
$607$	−37.6094	−	21.7138i	−1.52652	−	0.881335i	−0.527012	−	0.849858i	$-0.676688\pi$
$608$	0.585872	−	0.338254i	0.0237603	−	0.0137180i
$609$		0			0
$610$	−5.47194	+	7.94129i	−0.221552	+	0.321534i
$611$	17.8801	−	9.49791i	0.723352	−	0.384244i
$612$		0			0
$613$	16.3258	+	28.2771i	0.659392	+	1.14210i	0.980773	+	0.195150i	$0.0625194\pi$
$613$	16.3258	+	28.2771i	0.659392	+	1.14210i	−0.321382	+	0.946950i	$0.604147\pi$
$614$	5.49584	+	9.51907i	0.221794	+	0.384159i
$615$		0			0
$616$		−	10.2393i		−	0.412555i
$617$	4.83488	−	8.37426i	0.194645	−	0.337135i	−0.752139	−	0.659004i	$-0.770978\pi$
$617$	4.83488	−	8.37426i	0.194645	−	0.337135i	0.946784	+	0.321869i	$0.104311\pi$
$618$		0			0
$619$		−	5.20064i		−	0.209031i	−0.994523	−	0.104516i	$-0.966671\pi$
$619$		−	5.20064i		−	0.209031i	0.994523	−	0.104516i	$-0.0333292\pi$
$620$	14.3678	−	6.83197i	0.577027	−	0.274378i
$621$		0			0
$622$	6.95220	+	12.0416i	0.278758	+	0.482823i
$623$		−	20.8348i		−	0.834729i
$624$		0			0
$625$	−18.6587	+	16.6389i	−0.746347	+	0.665557i
$626$	−12.2746	+	7.08672i	−0.490590	+	0.283242i
$627$		0			0
$628$	3.87629	+	2.23798i	0.154681	+	0.0893050i
$629$		−	22.5153i		−	0.897743i
$630$		0			0
$631$	−6.86811	−	3.96531i	−0.273415	−	0.157856i	0.357023	−	0.934095i	$-0.383792\pi$
$631$	−6.86811	−	3.96531i	−0.273415	−	0.157856i	−0.630439	+	0.776239i	$0.717125\pi$
$632$	3.74519			0.148976
$633$		0			0
$634$	1.60404	+	2.77828i	0.0637046	+	0.110340i
$635$	−2.42319	+	30.3244i	−0.0961613	+	1.20339i
$636$		0			0
$637$	36.3305	+	22.7219i	1.43947	+	0.900276i
$638$		−	22.7432i		−	0.900413i
$639$		0			0
$640$	−2.22896	−	0.178114i	−0.0881075	−	0.00704057i
$641$	1.69937	−	2.94340i	0.0671212	−	0.116257i	−0.830512	−	0.557001i	$-0.811952\pi$
$641$	1.69937	−	2.94340i	0.0671212	−	0.116257i	0.897633	+	0.440744i	$0.145285\pi$
$642$		0			0
$643$	4.69916	−	8.13918i	0.185317	−	0.320978i	−0.758367	−	0.651828i	$-0.774002\pi$
$643$	4.69916	−	8.13918i	0.185317	−	0.320978i	0.943683	+	0.330851i	$0.107336\pi$
$644$	−24.2664	−	14.0102i	−0.956228	−	0.552079i
$645$		0			0
$646$	1.01772	−	1.76274i	0.0400415	−	0.0693540i
$647$	34.6972	−	20.0324i	1.36409	−	0.787555i	0.373921	−	0.927461i	$-0.378013\pi$
$647$	34.6972	−	20.0324i	1.36409	−	0.787555i	0.990165	+	0.139905i	$0.0446798\pi$
$648$		0			0
$649$	12.4165			0.487389
$650$	−3.48934	+	17.6868i	−0.136863	+	0.693735i
$651$		0			0
$652$	3.87774	+	6.71645i	0.151864	+	0.263036i
$653$	−27.1900	+	15.6981i	−1.06403	+	0.614316i	−0.926543	−	0.376189i	$-0.877234\pi$
$653$	−27.1900	+	15.6981i	−1.06403	+	0.614316i	−0.137483	+	0.990504i	$0.543901\pi$
$654$		0			0
$655$	12.9566	−	18.8036i	0.506255	−	0.734717i
$656$	−2.60564	−	1.50437i	−0.101733	−	0.0587358i
$657$		0			0
$658$	24.4021			0.951292
$659$	−9.48950	+	16.4363i	−0.369659	+	0.640268i	−0.989512	−	0.144450i	$-0.953859\pi$
$659$	−9.48950	+	16.4363i	−0.369659	+	0.640268i	0.619853	+	0.784718i	$0.287192\pi$
$660$		0			0
$661$	11.4484	−	6.60972i	0.445290	−	0.257088i	−0.260549	−	0.965461i	$-0.583904\pi$
$661$	11.4484	−	6.60972i	0.445290	−	0.257088i	0.705839	+	0.708372i	$0.250570\pi$
$662$		−	25.7574i		−	1.00109i
$663$		0			0
$664$	10.3557			0.401878
$665$	0.523631	−	6.55285i	0.0203055	−	0.254109i
$666$		0			0
$667$	−53.8995	−	31.1189i	−2.08700	−	1.20493i
$668$	0.678042			0.0262342
$669$		0			0
$670$	5.59485	+	11.7662i	0.216148	+	0.454566i
$671$		−	10.1622i		−	0.392308i
$672$		0			0
$673$	7.44817	−	4.30020i	0.287106	−	0.165761i	−0.349530	−	0.936925i	$-0.613659\pi$
$673$	7.44817	−	4.30020i	0.287106	−	0.165761i	0.636636	+	0.771164i	$0.280325\pi$
$674$	−0.668639	+	0.386039i	−0.0257550	+	0.0148697i
$675$		0			0
$676$	5.68953	+	11.6889i	0.218828	+	0.449571i
$677$			25.8539i			0.993646i	0.867852	+	0.496823i	$0.165500\pi$
$677$			25.8539i			0.993646i	−0.867852	+	0.496823i	$0.834500\pi$
$678$		0			0
$679$	−35.5068	−	61.4997i	−1.36263	−	2.36014i
$680$	−6.07583	+	2.88908i	−0.232998	+	0.110791i
$681$		0			0
$682$	−8.38219	+	14.5184i	−0.320971	+	0.555938i
$683$	−10.4524	+	18.1041i	−0.399950	+	0.692734i	−0.993719	−	0.111901i	$-0.964306\pi$
$683$	−10.4524	+	18.1041i	−0.399950	+	0.692734i	0.593769	+	0.804636i	$0.297639\pi$
$684$		0			0
$685$	11.9201	+	25.0683i	0.455443	+	0.957811i
$686$	10.6136	+	18.3832i	0.405228	+	0.701875i
$687$		0			0
$688$			6.83247i			0.260486i
$689$	−15.9570	−	30.0396i	−0.607914	−	1.14442i
$690$		0			0
$691$	−42.3440	+	24.4473i	−1.61084	+	0.930019i	−0.621665	+	0.783283i	$0.713543\pi$
$691$	−42.3440	+	24.4473i	−1.61084	+	0.930019i	−0.989176	+	0.146736i	$0.953123\pi$
$692$	0.625226	−	0.360974i	0.0237675	−	0.0137222i
$693$		0			0
$694$		−	25.1558i		−	0.954902i
$695$	−14.9972	−	31.5395i	−0.568875	−	1.19636i
$696$		0			0
$697$	−9.05251			−0.342888
$698$	−23.6602	−	13.6602i	−0.895551	−	0.517046i
$699$		0			0
$700$	−13.7145	+	16.8532i	−0.518360	+	0.636990i
$701$	−31.9805			−1.20789			−0.603944	−	0.797027i	$-0.706405\pi$
$701$	−31.9805			−1.20789			−0.603944	+	0.797027i	$0.706405\pi$
$702$		0			0
$703$			5.06250i			0.190936i
$704$	2.04055	−	1.17811i	0.0769062	−	0.0444018i
$705$		0			0
$706$	3.75948	−	6.51161i	0.141490	−	0.245068i
$707$	−53.1831			−2.00016
$708$		0			0
$709$	−5.42026	−	3.12939i	−0.203562	−	0.117527i	0.394754	−	0.918787i	$-0.370830\pi$
$709$	−5.42026	−	3.12939i	−0.203562	−	0.117527i	−0.598316	+	0.801260i	$0.704163\pi$
$710$	5.36890	+	3.69944i	0.201491	+	0.138837i
$711$		0			0
$712$	4.15208	−	2.39720i	0.155606	−	0.0898389i
$713$	22.9382	+	39.7301i	0.859043	+	1.48791i
$714$		0			0
$715$	−7.54701	−	17.4330i	−0.282242	−	0.651958i
$716$	6.37346			0.238187
$717$		0			0
$718$	9.38789	−	5.42010i	0.350353	−	0.202276i
$719$	9.52308	−	16.4945i	0.355151	−	0.615140i	−0.631993	−	0.774974i	$-0.717763\pi$
$719$	9.52308	−	16.4945i	0.355151	−	0.615140i	0.987144	+	0.159835i	$0.0510961\pi$
$720$		0			0
$721$	14.1183	+	8.15122i	0.525794	+	0.303567i
$722$	9.27117	−	16.0581i	0.345037	−	0.597622i
$723$		0			0
$724$	−11.0107	+	19.0711i	−0.409209	+	0.708770i
$725$	−30.4621	+	37.4336i	−1.13134	+	1.39025i
$726$		0			0
$727$			28.2602i			1.04811i	0.851684	+	0.524056i	$0.175582\pi$
$727$			28.2602i			1.04811i	−0.851684	+	0.524056i	$0.824418\pi$
$728$	−0.553049	+	15.6587i	−0.0204974	+	0.580350i
$729$		0			0
$730$	17.1141	+	1.36757i	0.633420	+	0.0506159i
$731$	10.2786	+	17.8030i	0.380166	+	0.658468i
$732$		0			0
$733$	−5.28165			−0.195082			−0.0975410	−	0.995232i	$-0.531098\pi$
$733$	−5.28165			−0.195082			−0.0975410	+	0.995232i	$0.531098\pi$
$734$	6.50838	+	3.75761i	0.240229	+	0.138696i
$735$		0			0
$736$		−	6.44791i		−	0.237673i
$737$	−11.8894	−	6.86437i	−0.437953	−	0.252852i
$738$		0			0
$739$	34.5736	−	19.9611i	1.27181	−	0.734280i	0.296482	−	0.955038i	$-0.404187\pi$
$739$	34.5736	−	19.9611i	1.27181	−	0.734280i	0.975329	+	0.220758i	$0.0708533\pi$
$740$	9.49430	−	13.7789i	0.349018	−	0.506521i
$741$		0			0
$742$		−	40.9969i		−	1.50504i
$743$	9.28543	+	16.0828i	0.340650	+	0.590022i	0.984553	−	0.175084i	$-0.0560197\pi$
$743$	9.28543	+	16.0828i	0.340650	+	0.590022i	−0.643904	+	0.765106i	$0.722686\pi$
$744$		0			0
$745$	39.4317	−	18.7499i	1.44467	−	0.686944i
$746$			22.8786i			0.837646i
$747$		0			0
$748$	3.54464	−	6.13949i	0.129605	−	0.224482i
$749$		−	72.2100i		−	2.63850i
$750$		0			0
$751$	15.1001	+	26.1541i	0.551010	+	0.954377i	0.998202	+	0.0599394i	$0.0190907\pi$
$751$	15.1001	+	26.1541i	0.551010	+	0.954377i	−0.447192	+	0.894438i	$0.647576\pi$
$752$	2.80764	+	4.86298i	0.102384	+	0.177335i
$753$		0			0
$754$	−1.22841	+	34.7805i	−0.0447361	+	1.26663i
$755$	21.1798	+	14.5939i	0.770811	+	0.531126i
$756$		0			0
$757$	−4.85341	+	2.80211i	−0.176400	+	0.101845i	−0.585600	−	0.810600i	$-0.699141\pi$
$757$	−4.85341	+	2.80211i	−0.176400	+	0.101845i	0.409200	+	0.912445i	$0.365808\pi$
$758$	−22.6152	−	13.0569i	−0.821421	−	0.474247i
$759$		0			0
$760$	1.36614	−	0.649603i	0.0495549	−	0.0235636i
$761$	5.77640	+	3.33501i	0.209394	+	0.120894i	0.601030	−	0.799227i	$-0.294757\pi$
$761$	5.77640	+	3.33501i	0.209394	+	0.120894i	−0.391635	+	0.920120i	$0.628091\pi$
$762$		0			0
$763$	−41.8178	−	24.1435i	−1.51391	−	0.874053i
$764$	0.293441	+	0.508255i	0.0106163	+	0.0183880i
$765$		0			0
$766$	−13.6930			−0.494750
$767$	−18.9881	−	0.670640i	−0.685621	−	0.0242154i
$768$		0			0
$769$	6.03234	−	3.48277i	0.217532	−	0.125592i	−0.387275	−	0.921964i	$-0.626584\pi$
$769$	6.03234	−	3.48277i	0.217532	−	0.125592i	0.604807	+	0.796372i	$0.293250\pi$
$770$	1.82377	−	22.8231i	0.0657241	−	0.822488i
$771$		0			0
$772$	−22.6270			−0.814363
$773$	10.6748	−	18.4893i	0.383945	−	0.665013i	−0.607677	−	0.794184i	$-0.707898\pi$
$773$	10.6748	−	18.4893i	0.383945	−	0.665013i	0.991622	+	0.129172i	$0.0412318\pi$
$774$		0			0
$775$	33.2423	−	12.6691i	1.19410	−	0.455087i
$776$	8.17066	−	14.1520i	0.293310	−	0.508027i
$777$		0			0
$778$	−12.4701	−	21.5989i	−0.447076	−	0.774359i
$779$	2.03543			0.0729270
$780$		0			0
$781$	−6.87041			−0.245843
$782$	−9.70004	−	16.8010i	−0.346873	−	0.600801i
$783$		0			0
$784$	−5.94234	+	10.2924i	−0.212226	+	0.367587i
$785$	8.24149	+	5.67879i	0.294151	+	0.202685i
$786$		0			0
$787$	9.61648	−	16.6562i	0.342791	−	0.593731i	−0.642159	−	0.766571i	$-0.721961\pi$
$787$	9.61648	−	16.6562i	0.342791	−	0.593731i	0.984950	+	0.172841i	$0.0552945\pi$
$788$	−1.64754			−0.0586912
$789$		0			0
$790$	8.34789	+	0.667071i	0.297005	+	0.0237333i
$791$	−58.9357	+	34.0265i	−2.09551	+	1.20984i
$792$		0			0
$793$	−0.548883	+	15.5407i	−0.0194914	+	0.551868i
$794$	29.1034			1.03284
$795$		0			0
$796$	−5.13665	−	8.89694i	−0.182064	−	0.315344i
$797$	19.7080	+	11.3784i	0.698094	+	0.403044i	0.806637	−	0.591047i	$-0.201285\pi$
$797$	19.7080	+	11.3784i	0.698094	+	0.403044i	−0.108543	+	0.994092i	$0.534619\pi$
$798$		0			0
$799$	14.6314	+	8.44747i	0.517623	+	0.298850i
$800$	−4.93655	−	0.794019i	−0.174533	−	0.0280728i
$801$		0			0
$802$	14.4596	+	8.34823i	0.510585	+	0.294786i
$803$	−15.6675	+	9.04561i	−0.552892	+	0.319213i
$804$		0			0
$805$	−51.5934	−	35.5504i	−1.81843	−	1.25299i
$806$	13.6028	−	21.7498i	0.479138	−	0.766103i
$807$		0			0
$808$	−6.11911	−	10.5986i	−0.215270	−	0.372858i
$809$	17.7054	+	30.6667i	0.622490	+	1.07818i	0.989020	+	0.147779i	$0.0472123\pi$
$809$	17.7054	+	30.6667i	0.622490	+	1.07818i	−0.366530	+	0.930406i	$0.619454\pi$
$810$		0			0
$811$			1.41268i			0.0496060i	0.999692	+	0.0248030i	$0.00789586\pi$
$811$			1.41268i			0.0496060i	−0.999692	+	0.0248030i	$0.992104\pi$
$812$	−20.9730	+	36.3262i	−0.736007	+	1.27480i
$813$		0			0
$814$			17.6324i			0.618014i
$815$	7.44705	+	15.6614i	0.260859	+	0.548595i
$816$		0			0
$817$	−2.31111	−	4.00296i	−0.0808555	−	0.140046i
$818$			24.6113i			0.860513i
$819$		0			0
$820$	−5.53994	−	3.81729i	−0.193463	−	0.133305i
$821$	−14.7591	+	8.52118i	−0.515097	+	0.297391i	−0.734926	−	0.678147i	$-0.762783\pi$
$821$	−14.7591	+	8.52118i	−0.515097	+	0.297391i	0.219829	+	0.975538i	$0.429450\pi$
$822$		0			0
$823$	3.83623	+	2.21485i	0.133723	+	0.0772047i	0.565369	−	0.824838i	$-0.308734\pi$
$823$	3.83623	+	2.21485i	0.133723	+	0.0772047i	−0.431646	+	0.902043i	$0.642067\pi$
$824$			3.75144i			0.130688i
$825$		0			0
$826$	−19.8320	−	11.4500i	−0.690043	−	0.398396i
$827$	−41.2574			−1.43466			−0.717330	−	0.696734i	$-0.754636\pi$
$827$	−41.2574			−1.43466			−0.717330	+	0.696734i	$0.754636\pi$
$828$		0			0
$829$	21.3857	+	37.0411i	0.742756	+	1.28649i	0.951236	+	0.308465i	$0.0998153\pi$
$829$	21.3857	+	37.0411i	0.742756	+	1.28649i	−0.208479	+	0.978027i	$0.566851\pi$
$830$	23.0824	+	1.84449i	0.801202	+	0.0640231i
$831$		0			0
$832$	−3.18419	+	1.69144i	−0.110392	+	0.0586400i
$833$			35.7579i			1.23894i
$834$		0			0
$835$	1.51133	+	0.120769i	0.0523017	+	0.00417937i
$836$	−0.797003	+	1.38045i	−0.0275649	+	0.0477438i
$837$		0			0
$838$	−13.5527	+	23.4739i	−0.468169	+	0.810893i
$839$	0.249908	+	0.144284i	0.00862777	+	0.00498124i	0.504308	−	0.863524i	$-0.331748\pi$
$839$	0.249908	+	0.144284i	0.00862777	+	0.00498124i	−0.495680	+	0.868505i	$0.665081\pi$
$840$		0			0
$841$	−32.0843	+	55.5717i	−1.10636	+	1.91626i
$842$	−28.5785	+	16.4998i	−0.984880	+	0.568621i
$843$		0			0
$844$	−24.3809			−0.839226
$845$	10.5998	+	27.0674i	0.364644	+	0.931147i
$846$		0			0
$847$	−11.8380	−	20.5040i	−0.406757	−	0.704524i
$848$	8.17008	−	4.71700i	0.280562	−	0.161982i
$849$		0			0
$850$	−14.0574	+	5.35747i	−0.482165	+	0.183760i
$851$	41.7871	+	24.1258i	1.43244	+	0.827022i
$852$		0			0
$853$	−42.9336			−1.47002			−0.735009	−	0.678058i	$-0.762822\pi$
$853$	−42.9336			−1.47002			−0.735009	+	0.678058i	$0.762822\pi$
$854$	−9.37121	+	16.2314i	−0.320676	+	0.555428i
$855$		0			0
$856$	14.3904	−	8.30831i	0.491854	−	0.283972i
$857$		−	43.6929i		−	1.49252i	−0.665654	−	0.746261i	$-0.731847\pi$
$857$		−	43.6929i		−	1.49252i	0.665654	−	0.746261i	$-0.268153\pi$
$858$		0			0
$859$	−50.5362			−1.72427			−0.862137	−	0.506676i	$-0.830874\pi$
$859$	−50.5362			−1.72427			−0.862137	+	0.506676i	$0.830874\pi$
$860$	−1.21696	+	15.2293i	−0.0414979	+	0.519316i
$861$		0			0
$862$	−7.45678	−	4.30517i	−0.253979	−	0.146635i
$863$	9.24937			0.314852			0.157426	−	0.987531i	$-0.449680\pi$
$863$	9.24937			0.314852			0.157426	+	0.987531i	$0.449680\pi$
$864$		0			0
$865$	1.45790	−	0.693237i	0.0495701	−	0.0235707i
$866$		−	3.45488i		−	0.117402i
$867$		0			0
$868$	26.7766	−	15.4595i	0.908858	−	0.524729i
$869$	−7.64226	+	4.41226i	−0.259246	+	0.149676i
$870$		0			0
$871$	17.8114	+	11.1396i	0.603516	+	0.377452i
$872$		−	11.1116i		−	0.376285i
$873$		0			0
$874$	2.18103	+	3.77765i	0.0737744	+	0.127781i
$875$	−33.5709	+	35.1223i	−1.13490	+	1.18735i
$876$		0			0
$877$	28.4654	−	49.3035i	0.961208	−	1.66486i	0.241731	−	0.970343i	$-0.422285\pi$
$877$	28.4654	−	49.3035i	0.961208	−	1.66486i	0.719476	−	0.694517i	$-0.244382\pi$
$878$	12.1229	−	20.9974i	0.409127	−	0.708628i
$879$		0			0
$880$	4.75816	−	2.26252i	0.160397	−	0.0762696i
$881$	−7.98900	−	13.8374i	−0.269156	−	0.466192i	0.699488	−	0.714644i	$-0.253412\pi$
$881$	−7.98900	−	13.8374i	−0.269156	−	0.466192i	−0.968644	+	0.248452i	$0.920078\pi$
$882$		0			0
$883$			0.189481i			0.00637654i	0.999995	+	0.00318827i	$0.00101486\pi$
$883$			0.189481i			0.00637654i	−0.999995	+	0.00318827i	$0.998985\pi$
$884$	−5.75231	+	9.19748i	−0.193471	+	0.309345i
$885$		0			0
$886$	11.3994	−	6.58147i	0.382972	−	0.221109i
$887$	15.5339	−	8.96852i	0.521578	−	0.301133i	−0.216002	−	0.976393i	$-0.569302\pi$
$887$	15.5339	−	8.96852i	0.521578	−	0.301133i	0.737580	+	0.675260i	$0.235968\pi$
$888$		0			0
$889$			59.1213i			1.98287i
$890$	9.68180	−	4.60373i	0.324535	−	0.154317i
$891$		0			0
$892$	−4.63585			−0.155220
$893$	−3.28984	−	1.89939i	−0.110090	−	0.0635607i
$894$		0			0
$895$	14.2062	+	1.13520i	0.474861	+	0.0379456i
$896$	−4.34565			−0.145178
$897$		0			0
$898$		−	2.51464i		−	0.0839145i
$899$	59.4752	−	34.3380i	1.98361	−	1.14524i
$900$		0			0
$901$	14.1922	−	24.5817i	0.472812	−	0.818934i
$902$	7.08928			0.236047
$903$		0			0
$904$	−13.5620	−	7.83002i	−0.451065	−	0.260423i
$905$	−27.9392	+	40.5475i	−0.928731	+	1.34784i
$906$		0			0
$907$	28.5874	−	16.5050i	0.949230	−	0.548038i	0.0563882	−	0.998409i	$-0.482042\pi$
$907$	28.5874	−	16.5050i	0.949230	−	0.548038i	0.892842	+	0.450371i	$0.148708\pi$
$908$	8.89213	+	15.4016i	0.295096	+	0.511121i
$909$		0			0
$910$	−4.02176	+	34.8042i	−0.133320	+	1.15375i
$911$	−13.9676			−0.462768			−0.231384	−	0.972863i	$-0.574325\pi$
$911$	−13.9676			−0.462768			−0.231384	+	0.972863i	$0.574325\pi$
$912$		0			0
$913$	−21.1313	+	12.2002i	−0.699344	+	0.403766i
$914$	−5.38493	+	9.32698i	−0.178118	+	0.308509i
$915$		0			0
$916$	−13.2815	−	7.66806i	−0.438832	−	0.253360i
$917$	22.1894	−	38.4331i	0.732758	−	1.26917i
$918$		0			0
$919$	9.50273	−	16.4592i	0.313466	−	0.542939i	−0.665644	−	0.746269i	$-0.731843\pi$
$919$	9.50273	−	16.4592i	0.313466	−	0.542939i	0.979110	+	0.203330i	$0.0651764\pi$
$920$	1.14846	−	14.3722i	0.0378637	−	0.473836i
$921$		0			0
$922$		−	11.8915i		−	0.391626i
$923$	10.5067	+	0.371086i	0.345832	+	0.0122144i
$924$		0			0
$925$	23.6167	−	29.0215i	0.776511	−	0.954221i
$926$	14.9731	+	25.9342i	0.492047	+	0.852250i
$927$		0			0
$928$	−9.65239			−0.316855
$929$	50.0606	+	28.9025i	1.64243	+	0.948259i	0.979965	+	0.199169i	$0.0638244\pi$
$929$	50.0606	+	28.9025i	1.64243	+	0.948259i	0.662468	+	0.749090i	$0.269509\pi$
$930$		0			0
$931$		−	8.04007i		−	0.263503i
$932$	6.71645	+	3.87774i	0.220005	+	0.127020i
$933$		0			0
$934$	18.9607	−	10.9470i	0.620414	−	0.358196i
$935$	8.99439	−	13.0534i	0.294148	−	0.426890i
$936$		0			0
$937$			39.7996i			1.30020i	0.759850	+	0.650099i	$0.225273\pi$
$937$			39.7996i			1.30020i	−0.759850	+	0.650099i	$0.774727\pi$
$938$	12.6601	+	21.9280i	0.413368	+	0.715974i
$939$		0			0
$940$	5.39197	+	11.3395i	0.175867	+	0.369853i
$941$			1.26326i			0.0411810i	0.999788	+	0.0205905i	$0.00655462\pi$
$941$			1.26326i			0.0411810i	−0.999788	+	0.0205905i	$0.993445\pi$
$942$		0			0
$943$	9.70004	−	16.8010i	0.315877	−	0.547115i
$944$		−	5.26964i		−	0.171512i
$945$		0			0
$946$	−8.04943	−	13.9420i	−0.261710	−	0.453294i
$947$	4.47761	+	7.75545i	0.145503	+	0.252018i	0.929560	−	0.368670i	$-0.120187\pi$
$947$	4.47761	+	7.75545i	0.145503	+	0.252018i	−0.784058	+	0.620688i	$0.786853\pi$
$948$		0			0
$949$	24.4483	−	12.9869i	0.793626	−	0.421574i
$950$	3.16077	−	1.20461i	0.102549	−	0.0390828i
$951$		0			0
$952$	−11.3232	+	6.53747i	−0.366988	+	0.211880i
$953$	10.7128	+	6.18504i	0.347022	+	0.200353i	0.663373	−	0.748289i	$-0.269124\pi$
$953$	10.7128	+	6.18504i	0.347022	+	0.200353i	−0.316351	+	0.948642i	$0.602458\pi$
$954$		0			0
$955$	0.563542	+	1.18515i	0.0182358	+	0.0383505i
$956$	−16.1435	−	9.32045i	−0.522118	−	0.301445i
$957$		0			0
$958$	7.90106	+	4.56168i	0.255272	+	0.147381i
$959$	26.9730	+	46.7185i	0.871002	+	1.50862i
$960$		0			0
$961$	−19.6222			−0.632973
$962$	0.952362	−	26.9646i	0.0307054	−	0.869374i
$963$		0			0
$964$	2.65884	−	1.53508i	0.0856354	−	0.0494416i
$965$	−50.4347	−	4.03018i	−1.62355	−	0.129736i
$966$		0			0
$967$	6.35606			0.204397			0.102198	−	0.994764i	$-0.467412\pi$
$967$	6.35606			0.204397			0.102198	+	0.994764i	$0.467412\pi$
$968$	2.72410	−	4.71827i	0.0875557	−	0.151651i
$969$		0			0
$970$	20.7328	−	30.0890i	0.665689	−	0.966099i
$971$	−23.6660	+	40.9907i	−0.759477	+	1.31545i	0.183640	+	0.982994i	$0.441212\pi$
$971$	−23.6660	+	40.9907i	−0.759477	+	1.31545i	−0.943117	+	0.332460i	$0.892121\pi$
$972$		0			0
$973$	−33.9358	−	58.7786i	−1.08793	−	1.88435i
$974$	−21.7174			−0.695872
$975$		0			0
$976$	−4.31292			−0.138053
$977$	24.5952	+	42.6002i	0.786871	+	1.36290i	0.927875	+	0.372891i	$0.121633\pi$
$977$	24.5952	+	42.6002i	0.786871	+	1.36290i	−0.141005	+	0.990009i	$0.545033\pi$
$978$		0			0
$979$	−5.64835	+	9.78324i	−0.180522	+	0.312674i
$980$	−15.0785	+	21.8830i	−0.481665	+	0.699028i
$981$		0			0
$982$	16.5438	−	28.6548i	0.527935	−	0.914411i
$983$	22.1542			0.706609			0.353304	−	0.935508i	$-0.385058\pi$
$983$	22.1542			0.706609			0.353304	+	0.935508i	$0.385058\pi$
$984$		0			0
$985$	−3.67231	−	0.293450i	−0.117009	−	0.00935009i
$986$	−25.1507	+	14.5208i	−0.800961	+	0.462435i
$987$		0			0
$988$	1.29339	−	2.06803i	0.0411483	−	0.0657928i
$989$	−44.0552			−1.40087
$990$		0			0
$991$	24.0251	+	41.6127i	0.763182	+	1.32187i	0.941202	+	0.337843i	$0.109697\pi$
$991$	24.0251	+	41.6127i	0.763182	+	1.32187i	−0.178020	+	0.984027i	$0.556969\pi$
$992$	6.16171	+	3.55746i	0.195634	+	0.112950i
$993$		0			0
$994$	10.9736	+	6.33564i	0.348063	+	0.200954i
$995$	−9.86473	−	20.7459i	−0.312733	−	0.657688i
$996$		0			0
$997$	−41.0355	−	23.6919i	−1.29961	−	0.750329i	−0.319271	−	0.947663i	$-0.603438\pi$
$997$	−41.0355	−	23.6919i	−1.29961	−	0.750329i	−0.980336	+	0.197335i	$0.936771\pi$
$998$	9.08363	−	5.24444i	0.287537	−	0.166010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.d.829.2		12
3.2	odd	2		390.2.x.a.49.3	✓	12
5.4	even	2		1170.2.bj.c.829.5		12
13.4	even	6		1170.2.bj.c.199.5		12
15.2	even	4		1950.2.bc.j.751.4		12
15.8	even	4		1950.2.bc.i.751.3		12
15.14	odd	2		390.2.x.b.49.4	yes	12
39.17	odd	6		390.2.x.b.199.4	yes	12
65.4	even	6	inner	1170.2.bj.d.199.2		12
195.17	even	12		1950.2.bc.j.901.4		12
195.134	odd	6		390.2.x.a.199.3	yes	12
195.173	even	12		1950.2.bc.i.901.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.3	✓	12	3.2	odd	2
390.2.x.a.199.3	yes	12	195.134	odd	6
390.2.x.b.49.4	yes	12	15.14	odd	2
390.2.x.b.199.4	yes	12	39.17	odd	6
1170.2.bj.c.199.5		12	13.4	even	6
1170.2.bj.c.829.5		12	5.4	even	2
1170.2.bj.d.199.2		12	65.4	even	6	inner
1170.2.bj.d.829.2		12	1.1	even	1	trivial
1950.2.bc.i.751.3		12	15.8	even	4
1950.2.bc.i.901.3		12	195.173	even	12
1950.2.bc.j.751.4		12	15.2	even	4
1950.2.bc.j.901.4		12	195.17	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.26873 + 1.84128i) q^{5} +(-2.17283 + 3.76344i) q^{7} -1.00000 q^{8} +(-2.22896 - 0.178114i) q^{10} +(2.04055 - 1.17811i) q^{11} +(-3.18419 + 1.69144i) q^{13} -4.34565 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.60564 - 1.50437i) q^{17} +(0.585872 + 0.338254i) q^{19} +(-0.960230 - 2.01940i) q^{20} +(2.04055 + 1.17811i) q^{22} +(5.58405 - 3.22396i) q^{23} +(-1.78064 - 4.67219i) q^{25} +(-3.05692 - 1.91187i) q^{26} +(-2.17283 - 3.76344i) q^{28} +(-4.82620 - 8.35922i) q^{29} +7.11493i q^{31} +(0.500000 - 0.866025i) q^{32} -3.00874i q^{34} +(-4.17283 - 8.77559i) q^{35} +(3.74165 + 6.48073i) q^{37} +0.676507i q^{38} +(1.26873 - 1.84128i) q^{40} +(2.60564 - 1.50437i) q^{41} +(-5.91710 - 3.41624i) q^{43} +2.35623i q^{44} +(5.58405 + 3.22396i) q^{46} -5.61529 q^{47} +(-5.94234 - 10.2924i) q^{49} +(3.15592 - 3.87817i) q^{50} +(0.127265 - 3.60330i) q^{52} +9.43400i q^{53} +(-0.419677 + 5.25194i) q^{55} +(2.17283 - 3.76344i) q^{56} +(4.82620 - 8.35922i) q^{58} +(4.56364 + 2.63482i) q^{59} +(2.15646 - 3.73509i) q^{61} +(-6.16171 + 3.55746i) q^{62} +1.00000 q^{64} +(0.925468 - 8.00896i) q^{65} +(-2.91329 - 5.04596i) q^{67} +(2.60564 - 1.50437i) q^{68} +(5.51347 - 8.00157i) q^{70} +(-2.52520 - 1.45793i) q^{71} -7.67804 q^{73} +(-3.74165 + 6.48073i) q^{74} +(-0.585872 + 0.338254i) q^{76} +10.2393i q^{77} -3.74519 q^{79} +(2.22896 + 0.178114i) q^{80} +(2.60564 + 1.50437i) q^{82} -10.3557 q^{83} +(6.07583 - 2.88908i) q^{85} -6.83247i q^{86} +(-2.04055 + 1.17811i) q^{88} +(-4.15208 + 2.39720i) q^{89} +(0.553049 - 15.6587i) q^{91} +6.44791i q^{92} +(-2.80764 - 4.86298i) q^{94} +(-1.36614 + 0.649603i) q^{95} +(-8.17066 + 14.1520i) q^{97} +(5.94234 - 10.2924i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - 6 q^{16} - 18 q^{17} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 6 q^{23} - 10 q^{25} + 2 q^{26} - 2 q^{28} - 14 q^{29}+ \cdots - 8 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^7 - 12 * q^8 - 2 * q^10 - 6 * q^11 - 8 * q^13 - 4 * q^14 - 6 * q^16 - 18 * q^17 - 6 * q^19 - 4 * q^20 - 6 * q^22 - 6 * q^23 - 10 * q^25 + 2 * q^26 - 2 * q^28 - 14 * q^29 + 6 * q^32 - 26 * q^35 - 12 * q^37 - 2 * q^40 + 18 * q^41 - 36 * q^43 - 6 * q^46 - 16 * q^47 + 8 * q^49 + 10 * q^50 + 10 * q^52 - 28 * q^55 + 2 * q^56 + 14 * q^58 + 36 * q^59 + 10 * q^61 - 6 * q^62 + 12 * q^64 - 6 * q^65 + 4 * q^67 + 18 * q^68 - 4 * q^70 + 12 * q^71 + 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 2 * q^80 + 18 * q^82 - 72 * q^83 + 18 * q^85 + 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 + 42 * q^95 - 48 * q^97 - 8 * q^98

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