LMFDB - Embedded newform 1170.2.bj.c.829.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			829.5
Root			$2.00607 - 1.30680i$ of defining polynomial
Character	$\chi$	$=$	1170.829
Dual form			1170.2.bj.c.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.26873 + 1.84128i) q^{5} +(2.17283 - 3.76344i) q^{7} +1.00000 q^{8} +(0.960230 - 2.01940i) q^{10} +(2.04055 - 1.17811i) q^{11} +(3.18419 - 1.69144i) q^{13} -4.34565 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.60564 + 1.50437i) q^{17} +(0.585872 + 0.338254i) q^{19} +(-2.22896 + 0.178114i) q^{20} +(-2.04055 - 1.17811i) q^{22} +(-5.58405 + 3.22396i) q^{23} +(-1.78064 + 4.67219i) q^{25} +(-3.05692 - 1.91187i) q^{26} +(2.17283 + 3.76344i) q^{28} +(-4.82620 - 8.35922i) q^{29} +7.11493i q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00874i q^{34} +(9.68629 - 0.774021i) q^{35} +(-3.74165 - 6.48073i) q^{37} -0.676507i q^{38} +(1.26873 + 1.84128i) q^{40} +(2.60564 - 1.50437i) q^{41} +(5.91710 + 3.41624i) q^{43} +2.35623i q^{44} +(5.58405 + 3.22396i) q^{46} +5.61529 q^{47} +(-5.94234 - 10.2924i) q^{49} +(4.93655 - 0.794019i) q^{50} +(-0.127265 + 3.60330i) q^{52} -9.43400i q^{53} +(4.75816 + 2.26252i) q^{55} +(2.17283 - 3.76344i) q^{56} +(-4.82620 + 8.35922i) q^{58} +(4.56364 + 2.63482i) q^{59} +(2.15646 - 3.73509i) q^{61} +(6.16171 - 3.55746i) q^{62} +1.00000 q^{64} +(7.15429 + 3.71700i) q^{65} +(2.91329 + 5.04596i) q^{67} +(-2.60564 + 1.50437i) q^{68} +(-5.51347 - 8.00157i) q^{70} +(-2.52520 - 1.45793i) q^{71} +7.67804 q^{73} +(-3.74165 + 6.48073i) q^{74} +(-0.585872 + 0.338254i) q^{76} -10.2393i q^{77} -3.74519 q^{79} +(0.960230 - 2.01940i) q^{80} +(-2.60564 - 1.50437i) q^{82} +10.3557 q^{83} +(0.535898 + 6.70637i) q^{85} -6.83247i q^{86} +(2.04055 - 1.17811i) q^{88} +(-4.15208 + 2.39720i) q^{89} +(0.553049 - 15.6587i) q^{91} -6.44791i q^{92} +(-2.80764 - 4.86298i) q^{94} +(0.120495 + 1.50791i) q^{95} +(8.17066 - 14.1520i) q^{97} +(-5.94234 + 10.2924i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 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 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * 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 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * 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	$-0.526610\pi$
$7$	2.17283	−	3.76344i	0.821251	−	1.42245i	0.904751	−	0.425940i	$-0.140057\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.960230	−	2.01940i	0.303651	−	0.638589i
$11$	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	0.781511	−	0.623891i	$-0.214449\pi$
$17$	2.60564	+	1.50437i	0.631962	+	0.364863i	−0.149550	+	0.988754i	$0.547782\pi$
$18$		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	$0.641941\pi$
$20$	−2.22896	+	0.178114i	−0.498411	+	0.0398275i
$21$		0			0
$22$	−2.04055	−	1.17811i	−0.435047	−	0.251175i
$23$	−5.58405	+	3.22396i	−1.16436	+	0.672241i	−0.952344	−	0.305026i	$-0.901335\pi$
$23$	−5.58405	+	3.22396i	−1.16436	+	0.672241i	−0.212012	+	0.977267i	$0.568002\pi$
$24$		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
$35$	9.68629	−	0.774021i	1.63728	−	0.130833i
$36$		0			0
$37$	−3.74165	−	6.48073i	−0.615123	−	1.06542i	−0.990363	−	0.138497i	$-0.955773\pi$
$37$	−3.74165	−	6.48073i	−0.615123	−	1.06542i	0.375240	−	0.926928i	$-0.377560\pi$
$38$		−	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	0.877961	−	0.478731i	$-0.158903\pi$
$43$	5.91710	+	3.41624i	0.902349	+	0.520971i	0.0243872	+	0.999703i	$0.492237\pi$
$44$			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	$-0.365690\pi$
$47$	5.61529			0.819074			0.409537	+	0.912294i	$0.365690\pi$
$48$		0			0
$49$	−5.94234	−	10.2924i	−0.848906	−	1.47035i
$50$	4.93655	−	0.794019i	0.698134	−	0.112291i
$51$		0			0
$52$	−0.127265	+	3.60330i	−0.0176485	+	0.499688i
$53$		−	9.43400i		−	1.29586i	−0.761700	−	0.647930i	$-0.775635\pi$
$53$		−	9.43400i		−	1.29586i	0.761700	−	0.647930i	$-0.224365\pi$
$54$		0			0
$55$	4.75816	+	2.26252i	0.641590	+	0.305078i
$56$	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
$65$	7.15429	+	3.71700i	0.887381	+	0.461037i
$66$		0			0
$67$	2.91329	+	5.04596i	0.355915	+	0.616463i	0.987274	−	0.159028i	$-0.0508360\pi$
$67$	2.91329	+	5.04596i	0.355915	+	0.616463i	−0.631359	+	0.775490i	$0.717503\pi$
$68$	−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	$-0.351665\pi$
$73$	7.67804			0.898647			0.449323	+	0.893369i	$0.351665\pi$
$74$	−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	$0.567569\pi$
$80$	0.960230	−	2.01940i	0.107357	−	0.225775i
$81$		0			0
$82$	−2.60564	−	1.50437i	−0.287745	−	0.166130i
$83$	10.3557			1.13668			0.568341	−	0.822793i	$-0.307585\pi$
$83$	10.3557			1.13668			0.568341	+	0.822793i	$0.307585\pi$
$84$		0			0
$85$	0.535898	+	6.70637i	0.0581263	+	0.727408i
$86$		−	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
$95$	0.120495	+	1.50791i	0.0123626	+	0.154708i
$96$		0			0
$97$	8.17066	−	14.1520i	0.829605	−	1.43692i	−0.0687436	−	0.997634i	$-0.521899\pi$
$97$	8.17066	−	14.1520i	0.829605	−	1.43692i	0.898349	−	0.439283i	$-0.144768\pi$
$98$	−5.94234	+	10.2924i	−0.600267	+	1.03969i
$99$		0			0
$100$	−3.15592	−	3.87817i	−0.315592	−	0.387817i
$101$	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	$0.0591702\pi$
$103$			3.75144i			0.369640i	−0.982772	+	0.184820i	$0.940830\pi$
$104$	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	0.397728	−	0.917503i	$-0.369799\pi$
$107$	14.3904	−	8.30831i	1.39117	−	0.803194i	0.993445	+	0.114309i	$0.0364654\pi$
$108$		0			0
$109$			11.1116i			1.06430i	0.846652	+	0.532148i	$0.178615\pi$
$109$			11.1116i			1.06430i	−0.846652	+	0.532148i	$0.821385\pi$
$110$	−0.419677	−	5.25194i	−0.0400146	−	0.500753i
$111$		0			0
$112$	−4.34565			−0.410625
$113$	−13.5620	−	7.83002i	−1.27581	−	0.736587i	−0.299731	−	0.954024i	$-0.596897\pi$
$113$	−13.5620	−	7.83002i	−1.27581	−	0.736587i	−0.976074	+	0.217437i	$0.930230\pi$
$114$		0			0
$115$	−13.0209	−	6.19148i	−1.21420	−	0.577358i
$116$	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	−0.921382	−	0.388658i	$-0.872939\pi$
$127$	−11.7820	+	6.80236i	−1.04549	+	0.603611i	−0.124103	+	0.992269i	$0.539605\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.358130	−	8.05430i	−0.0314101	−	0.706409i
$131$	−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	$0.344584\pi$
$137$	−6.20689	+	10.7506i	−0.530290	+	0.918489i	−0.999375	+	0.0353365i	$0.988750\pi$
$138$		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	$0.936220\pi$
$140$	−4.17283	+	8.77559i	−0.352668	+	0.741673i
$141$		0			0
$142$			2.91585i			0.244693i
$143$	4.50479	−	7.20280i	0.376710	−	0.602329i
$144$		0			0
$145$	9.26852	−	19.4920i	0.769709	−	1.61872i
$146$	−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	$0.0571600\pi$
$157$			4.47595i			0.357220i	−0.983920	+	0.178610i	$0.942840\pi$
$158$	1.87260	+	3.24343i	0.148976	+	0.258033i
$159$		0			0
$160$	−2.22896	+	0.178114i	−0.176215	+	0.0140811i
$161$			28.0204i			2.20831i
$162$		0			0
$163$	−3.87774	+	6.71645i	−0.303728	+	0.526073i	−0.976977	−	0.213343i	$-0.931565\pi$
$163$	−3.87774	+	6.71645i	−0.303728	+	0.526073i	0.673249	+	0.739416i	$0.264898\pi$
$164$			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	0.878844	−	0.477108i	$-0.158315\pi$
$167$	0.339021	+	0.587202i	0.0262342	+	0.0454390i	−0.852610	+	0.522547i	$0.824982\pi$
$168$		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	0.523579	−	0.851977i	$-0.324596\pi$
$173$	0.625226	+	0.360974i	0.0475350	+	0.0274444i	−0.476044	+	0.879421i	$0.657930\pi$
$174$		0			0
$175$	13.7145	+	16.8532i	1.03672	+	1.27398i
$176$	−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
$185$	7.18569	−	15.1117i	0.528302	−	1.11104i
$186$		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	$-0.863753\pi$
$193$	−11.3135	−	19.5955i	−0.814363	−	1.41052i	0.0954215	−	0.995437i	$-0.469580\pi$
$194$	−16.3413			−1.17324
$195$		0			0
$196$	11.8847			0.848906
$197$	−0.823770	−	1.42681i	−0.0586912	−	0.101656i	0.835187	−	0.549966i	$-0.185359\pi$
$197$	−0.823770	−	1.42681i	−0.0586912	−	0.101656i	−0.893878	+	0.448310i	$0.852026\pi$
$198$		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
$205$	6.07583	+	2.88908i	0.424355	+	0.201782i
$206$	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
$215$	1.21696	+	15.2293i	0.0829959	+	1.03863i
$216$		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	0.777919	−	0.628364i	$-0.216275\pi$
$223$	−2.31792	−	4.01476i	−0.155220	−	0.268848i	−0.933139	+	0.359516i	$0.882942\pi$
$224$	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	$0.367615\pi$
$227$	−8.89213	+	15.4016i	−0.590192	+	1.02224i	−0.994206	+	0.107489i	$0.965719\pi$
$228$		0			0
$229$			15.3361i			1.01344i	0.862111	+	0.506720i	$0.169142\pi$
$229$			15.3361i			1.01344i	−0.862111	+	0.506720i	$0.830858\pi$
$230$	1.14846	+	14.3722i	0.0757274	+	0.947672i
$231$		0			0
$232$	−4.82620	−	8.35922i	−0.316855	−	0.548809i
$233$			7.75548i			0.508079i	0.967194	+	0.254039i	$0.0817593\pi$
$233$			7.75548i			0.508079i	−0.967194	+	0.254039i	$0.918241\pi$
$234$		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
$245$	11.4120	−	23.9999i	0.729088	−	1.53330i
$246$		0			0
$247$	2.43766	+	0.0860957i	0.155105	+	0.00547814i
$248$			7.11493i			0.451798i
$249$		0			0
$250$	7.72518	+	8.08218i	0.488583	+	0.511162i
$251$	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	−0.0632261	−	0.997999i	$-0.520139\pi$
$257$	12.3353	−	7.12178i	0.769454	−	0.444244i	0.832680	+	0.553755i	$0.186806\pi$
$258$		0			0
$259$	−32.5198			−2.02068
$260$	−6.79616	+	4.33730i	−0.421480	+	0.268988i
$261$		0			0
$262$	5.10611	+	8.84404i	0.315457	+	0.546387i
$263$	13.3385	−	7.70101i	0.822490	−	0.474865i	−0.0287845	−	0.999586i	$-0.509164\pi$
$263$	13.3385	−	7.70101i	0.822490	−	0.474865i	0.851274	+	0.524721i	$0.175830\pi$
$264$		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
$275$	1.87089	+	11.6316i	0.112819	+	0.701414i
$276$		0			0
$277$	−12.3861	−	7.15114i	−0.744211	−	0.429671i	0.0793871	−	0.996844i	$-0.474704\pi$
$277$	−12.3861	−	7.15114i	−0.744211	−	0.429671i	−0.823599	+	0.567173i	$0.808037\pi$
$278$	15.6183			0.936723
$279$		0			0
$280$	9.68629	−	0.774021i	0.578867	−	0.0462566i
$281$			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	−0.0721756	−	0.997392i	$-0.522994\pi$
$283$	12.7095	−	7.33785i	0.755503	−	0.436190i	0.827679	+	0.561202i	$0.189661\pi$
$284$	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
$290$	−21.5148	+	1.71923i	−1.26339	+	0.100956i
$291$		0			0
$292$	−3.83902	+	6.64938i	−0.224662	+	0.389125i
$293$	−3.43198	+	5.94436i	−0.200498	+	0.347273i	−0.948689	−	0.316210i	$-0.897589\pi$
$293$	−3.43198	+	5.94436i	−0.200498	+	0.347273i	0.748191	+	0.663484i	$0.230923\pi$
$294$		0			0
$295$	0.938596	+	11.7458i	0.0546472	+	0.683868i
$296$	−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
$305$	9.61333	−	0.768190i	0.550458	−	0.0439865i
$306$		0			0
$307$	−10.9917			−0.627328			−0.313664	−	0.949534i	$-0.601557\pi$
$307$	−10.9917			−0.627328			−0.313664	+	0.949534i	$0.601557\pi$
$308$	8.86753	+	5.11967i	0.505275	+	0.291720i
$309$		0			0
$310$	14.3678	+	6.83197i	0.816039	+	0.388030i
$311$	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	$-0.868814\pi$
$313$		−	14.1734i		−	0.801130i	0.916268	−	0.400565i	$-0.131186\pi$
$314$	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	$-0.528716\pi$
$317$	−3.20808			−0.180184			−0.0900920	+	0.995933i	$0.528716\pi$
$318$		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
$325$	2.23284	+	17.8889i	0.123856	+	0.992300i
$326$	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
$335$	−5.59485	+	11.7662i	−0.305680	+	0.642854i
$336$		0			0
$337$		−	0.772078i		−	0.0420578i	−0.999779	−	0.0210289i	$-0.993306\pi$
$337$		−	0.772078i		−	0.0420578i	0.999779	−	0.0210289i	$-0.00669420\pi$
$338$	−12.9676	−	0.917149i	−0.705345	−	0.0498863i
$339$		0			0
$340$	−6.07583	−	2.88908i	−0.329508	−	0.156682i
$341$	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	0.953565	−	0.301188i	$-0.0973830\pi$
$347$	21.7856	+	12.5779i	1.16951	+	0.675218i	0.215946	+	0.976405i	$0.430716\pi$
$348$		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	0.948559	−	0.316599i	$-0.102541\pi$
$353$	3.75948	+	6.51161i	0.200097	+	0.346578i	−0.748462	+	0.663177i	$0.769208\pi$
$354$		0			0
$355$	−0.519354	−	6.49932i	−0.0275644	−	0.344948i
$356$		−	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	−0.660155	−	0.751130i	$-0.729509\pi$
$367$	−6.50838	+	3.75761i	−0.339735	+	0.196146i	0.320420	+	0.947276i	$0.396176\pi$
$368$	5.58405	+	3.22396i	0.291089	+	0.168060i
$369$		0			0
$370$	−16.6800	+	1.33288i	−0.867151	+	0.0692931i
$371$	−35.5043	−	20.4984i	−1.84329	−	1.06423i
$372$		0			0
$373$	−19.8135	−	11.4393i	−1.02590	−	0.592305i	−0.110095	−	0.993921i	$-0.535115\pi$
$373$	−19.8135	−	11.4393i	−1.02590	−	0.592305i	−0.915808	+	0.401616i	$0.868449\pi$
$374$	−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	$0.567334\pi$
$380$	−1.36614	−	0.649603i	−0.0700813	−	0.0333239i
$381$		0			0
$382$	−0.586882			−0.0300275
$383$	6.84652	−	11.8585i	0.349841	−	0.605942i	−0.636380	−	0.771376i	$-0.719569\pi$
$383$	6.84652	−	11.8585i	0.349841	−	0.605942i	0.986221	+	0.165434i	$0.0529024\pi$
$384$		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	$0.427300\pi$
$397$	−14.5517	+	25.2043i	−0.730328	+	1.26497i	−0.956743	+	0.290934i	$0.906034\pi$
$398$	10.2733			0.514954
$399$		0			0
$400$	4.93655	−	0.794019i	0.246828	−	0.0397009i
$401$	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	$0.458448\pi$
$410$	−0.535898	−	6.70637i	−0.0264661	−	0.331204i
$411$		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
$425$	−11.6684	+	9.49533i	−0.566000	+	0.460591i
$426$		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	0.570168	−	0.821528i	$-0.306878\pi$
$433$	2.99201	+	1.72744i	0.143787	+	0.0830155i	−0.426381	+	0.904544i	$0.640212\pi$
$434$		−	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	$-0.363064\pi$
$440$	4.75816	+	2.26252i	0.226836	+	0.107861i
$441$		0			0
$442$	−5.08909	−	9.58038i	−0.242064	−	0.455692i
$443$			13.1629i			0.625390i	0.949854	+	0.312695i	$0.101232\pi$
$443$			13.1629i			0.625390i	−0.949854	+	0.312695i	$0.898768\pi$
$444$		0			0
$445$	−9.68180	−	4.60373i	−0.458961	−	0.218238i
$446$	−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
$455$	29.5338	−	18.8484i	1.38456	−	0.883626i
$456$		0			0
$457$	−5.38493	−	9.32698i	−0.251897	−	0.436298i	0.712151	−	0.702026i	$-0.247721\pi$
$457$	−5.38493	−	9.32698i	−0.251897	−	0.436298i	−0.964048	+	0.265728i	$0.914388\pi$
$458$	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	$-0.744976\pi$
$463$	−29.9462			−1.39172			−0.695860	+	0.718178i	$0.744976\pi$
$464$	−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	$0.169085\pi$
$467$			21.8940i			1.01313i	−0.862201	+	0.506566i	$0.830915\pi$
$468$		0			0
$469$	25.3203			1.16918
$470$	5.39197	−	11.3395i	0.248713	−	0.523051i
$471$		0			0
$472$	4.56364	+	2.63482i	0.210059	+	0.121277i
$473$	16.0989			0.740227
$474$		0			0
$475$	−2.62361	+	2.13500i	−0.120379	+	0.0979605i
$476$			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
$485$	36.4242	−	2.91062i	1.65394	−	0.132164i
$486$		0			0
$487$	10.8587	−	18.8079i	0.492056	−	0.852265i	−0.507902	−	0.861415i	$-0.669579\pi$
$487$	10.8587	−	18.8079i	0.492056	−	0.852265i	0.999958	+	0.00914916i	$0.00291231\pi$
$488$	2.15646	−	3.73509i	0.0976183	−	0.169080i
$489$		0			0
$490$	−26.4905	+	2.11683i	−1.19672	+	0.0956285i
$491$	−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	$-0.0754347\pi$
$500$	3.13679	−	10.7313i	0.140281	−	0.479918i
$501$		0			0
$502$	−7.12807			−0.318142
$503$	7.14818	+	4.12700i	0.318722	+	0.184014i	0.650823	−	0.759230i	$-0.274424\pi$
$503$	7.14818	+	4.12700i	0.318722	+	0.184014i	−0.332101	+	0.943244i	$0.607757\pi$
$504$		0			0
$505$	−11.7515	+	24.7138i	−0.522936	+	1.09975i
$506$	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
$520$	7.15429	+	3.71700i	0.313737	+	0.163001i
$521$	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	−0.558338	−	0.829614i	$-0.688561\pi$
$523$	−2.72235	+	1.57175i	−0.119040	+	0.0687279i	0.439298	+	0.898342i	$0.355227\pi$
$524$	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
$530$	−19.0510	−	9.05881i	−0.827522	−	0.393490i
$531$		0			0
$532$			2.93986i			0.127459i
$533$	5.75231	−	9.19748i	0.249160	−	0.398387i
$534$		0			0
$535$	33.5555	+	15.9558i	1.45073	+	0.689828i
$536$	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	$0.337428\pi$
$547$			40.8067i			1.74477i	−0.488820	+	0.872385i	$0.662572\pi$
$548$	−6.20689	−	10.7506i	−0.265145	−	0.459245i
$549$		0			0
$550$	9.13785	−	7.43606i	0.389639	−	0.317075i
$551$		−	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	$0.0127731\pi$
$557$	12.6109	+	21.8427i	0.534340	+	0.925504i	−0.464855	+	0.885387i	$0.653894\pi$
$558$		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	−0.343912	−	0.939002i	$-0.611752\pi$
$563$	−31.5356	−	18.2071i	−1.32907	−	0.767337i	−0.985155	+	0.171664i	$0.945086\pi$
$564$		0			0
$565$	−2.78927	−	34.9057i	−0.117346	−	1.46849i
$566$	−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
$575$	−5.11976	−	31.8304i	−0.213509	−	1.32742i
$576$		0			0
$577$	−31.1697			−1.29761			−0.648806	−	0.760954i	$-0.724731\pi$
$577$	−31.1697			−1.29761			−0.648806	+	0.760954i	$0.724731\pi$
$578$	−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	0.979282	−	0.202503i	$-0.0649076\pi$
$587$	7.61411	+	13.1880i	0.314268	+	0.544328i	−0.665014	+	0.746831i	$0.731574\pi$
$588$		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	$-0.600976\pi$
$593$	−15.1921			−0.623865			−0.311933	+	0.950104i	$0.600976\pi$
$594$		0			0
$595$	26.4035	+	12.5549i	1.08244	+	0.514703i
$596$	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
$605$	−12.1438	+	0.970399i	−0.493716	+	0.0394523i
$606$		0			0
$607$	37.6094	+	21.7138i	1.52652	+	0.881335i	0.999504	+	0.0314772i	$0.0100212\pi$
$607$	37.6094	+	21.7138i	1.52652	+	0.881335i	0.527012	+	0.849858i	$0.323312\pi$
$608$	−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	$-0.937481\pi$
$613$	−16.3258	−	28.2771i	−0.659392	−	1.14210i	0.321382	−	0.946950i	$-0.395853\pi$
$614$	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	−0.946784	−	0.321869i	$-0.895689\pi$
$617$	−4.83488	+	8.37426i	−0.194645	+	0.337135i	0.752139	+	0.659004i	$0.229022\pi$
$618$		0			0
$619$		−	5.20064i		−	0.209031i	−0.994523	−	0.104516i	$-0.966671\pi$
$619$		−	5.20064i		−	0.209031i	0.994523	−	0.104516i	$-0.0333292\pi$
$620$	−1.26727	−	15.8589i	−0.0508947	−	0.636909i
$621$		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
$635$	−27.4733	−	13.0637i	−1.09024	−	0.518415i
$636$		0			0
$637$	−36.3305	−	22.7219i	−1.43947	−	0.900276i
$638$			22.7432i			0.900413i
$639$		0			0
$640$	0.960230	−	2.01940i	0.0379564	−	0.0798236i
$641$	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	−0.943683	−	0.330851i	$-0.892664\pi$
$643$	−4.69916	+	8.13918i	−0.185317	+	0.320978i	0.758367	+	0.651828i	$0.225998\pi$
$644$	−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	−0.990165	−	0.139905i	$-0.955320\pi$
$647$	−34.6972	+	20.0324i	−1.36409	+	0.787555i	−0.373921	+	0.927461i	$0.621987\pi$
$648$		0			0
$649$	12.4165			0.487389
$650$	14.3759	−	10.8782i	0.563868	−	0.426677i
$651$		0			0
$652$	−3.87774	−	6.71645i	−0.151864	−	0.263036i
$653$	27.1900	−	15.6981i	1.06403	−	0.614316i	0.137483	−	0.990504i	$-0.456099\pi$
$653$	27.1900	−	15.6981i	1.06403	−	0.614316i	0.926543	+	0.376189i	$0.122766\pi$
$654$		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
$665$	5.93675	+	2.82295i	0.230217	+	0.109469i
$666$		0			0
$667$	53.8995	+	31.1189i	2.08700	+	1.20493i
$668$	−0.678042			−0.0262342
$669$		0			0
$670$	12.9872	−	1.03779i	0.501740	−	0.0400935i
$671$		−	10.1622i		−	0.392308i
$672$		0			0
$673$	−7.44817	+	4.30020i	−0.287106	+	0.165761i	−0.636636	−	0.771164i	$-0.719675\pi$
$673$	−7.44817	+	4.30020i	−0.287106	+	0.165761i	0.349530	+	0.936925i	$0.386341\pi$
$674$	−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	$-0.834500\pi$
$677$		−	25.8539i		−	0.993646i	0.867852	−	0.496823i	$-0.165500\pi$
$678$		0			0
$679$	−35.5068	−	61.4997i	−1.36263	−	2.36014i
$680$	0.535898	+	6.70637i	0.0205508	+	0.257177i
$681$		0			0
$682$	8.38219	−	14.5184i	0.320971	−	0.555938i
$683$	10.4524	−	18.1041i	0.399950	−	0.692734i	−0.593769	−	0.804636i	$-0.702361\pi$
$683$	10.4524	−	18.1041i	0.399950	−	0.692734i	0.993719	+	0.111901i	$0.0356941\pi$
$684$		0			0
$685$	−27.6698	+	2.21107i	−1.05721	+	0.0844805i
$686$	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
$695$	−34.8126	+	2.78184i	−1.32052	+	0.105521i
$696$		0			0
$697$	9.05251			0.342888
$698$	23.6602	+	13.6602i	0.895551	+	0.517046i
$699$		0			0
$700$	−21.4525	+	3.45053i	−0.810829	+	0.130418i
$701$	−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
$715$	18.9778	−	0.843835i	0.709728	−	0.0315577i
$716$	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
$725$	47.6495	−	7.66418i	1.76966	−	0.284640i
$726$		0			0
$727$		−	28.2602i		−	1.04811i	−0.851684	−	0.524056i	$-0.824418\pi$
$727$		−	28.2602i		−	1.04811i	0.851684	−	0.524056i	$-0.175582\pi$
$728$	0.553049	−	15.6587i	0.0204974	−	0.580350i
$729$		0			0
$730$	7.37269	−	15.5050i	0.272875	−	0.573866i
$731$	10.2786	+	17.8030i	0.380166	+	0.658468i
$732$		0			0
$733$	5.28165			0.195082			0.0975410	−	0.995232i	$-0.468902\pi$
$733$	5.28165			0.195082			0.0975410	+	0.995232i	$0.468902\pi$
$734$	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	0.643904	−	0.765106i	$-0.277314\pi$
$743$	−9.28543	−	16.0828i	−0.340650	−	0.590022i	−0.984553	+	0.175084i	$0.943980\pi$
$744$		0			0
$745$	−3.47794	−	43.5238i	−0.127422	−	1.59459i
$746$			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	−0.409200	−	0.912445i	$-0.634192\pi$
$757$	4.85341	−	2.80211i	0.176400	−	0.101845i	0.585600	+	0.810600i	$0.300859\pi$
$758$	22.6152	+	13.0569i	0.821421	+	0.474247i
$759$		0			0
$760$	0.120495	+	1.50791i	0.00437083	+	0.0546976i
$761$	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	$0.293250\pi$
$770$	−20.6773	−	9.83213i	−0.745158	−	0.354325i
$771$		0			0
$772$	22.6270			0.814363
$773$	−10.6748	+	18.4893i	−0.383945	+	0.665013i	−0.991622	−	0.129172i	$-0.958768\pi$
$773$	−10.6748	+	18.4893i	−0.383945	+	0.665013i	0.607677	+	0.794184i	$0.292102\pi$
$774$		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	−0.984950	−	0.172841i	$-0.944705\pi$
$787$	−9.61648	+	16.6562i	−0.342791	+	0.593731i	0.642159	+	0.766571i	$0.278039\pi$
$788$	1.64754			0.0586912
$789$		0			0
$790$	−3.59625	+	7.56302i	−0.127949	+	0.269080i
$791$	−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	0.108543	−	0.994092i	$-0.465381\pi$
$797$	−19.7080	−	11.3784i	−0.698094	−	0.403044i	−0.806637	+	0.591047i	$0.798715\pi$
$798$		0			0
$799$	14.6314	+	8.44747i	0.517623	+	0.298850i
$800$	−3.15592	−	3.87817i	−0.111578	−	0.137114i
$801$		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
$815$	−17.2867	+	1.38136i	−0.605526	+	0.0483869i
$816$		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	0.431646	−	0.902043i	$-0.357933\pi$
$823$	−3.83623	−	2.21485i	−0.133723	−	0.0772047i	−0.565369	+	0.824838i	$0.691266\pi$
$824$			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	$-0.245364\pi$
$827$	41.2574			1.43466			0.717330	+	0.696734i	$0.245364\pi$
$828$		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	$0.566851\pi$
$830$	9.94382	−	20.9122i	0.345155	−	0.725873i
$831$		0			0
$832$	3.18419	−	1.69144i	0.110392	−	0.0586400i
$833$		−	35.7579i		−	1.23894i
$834$		0			0
$835$	−0.651076	+	1.36923i	−0.0225314	+	0.0473843i
$836$	−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
$845$	29.0677	−	0.265420i	0.999958	−	0.00913072i
$846$		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	$-0.237178\pi$
$853$	42.9336			1.47002			0.735009	+	0.678058i	$0.237178\pi$
$854$	−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	$0.268153\pi$
$857$			43.6929i			1.49252i	−0.665654	+	0.746261i	$0.731847\pi$
$858$		0			0
$859$	−50.5362			−1.72427			−0.862137	−	0.506676i	$-0.830874\pi$
$859$	−50.5362			−1.72427			−0.862137	+	0.506676i	$0.830874\pi$
$860$	−13.7975	−	6.56075i	−0.470490	−	0.223720i
$861$		0			0
$862$	7.45678	+	4.30517i	0.253979	+	0.146635i
$863$	−9.24937			−0.314852			−0.157426	−	0.987531i	$-0.550320\pi$
$863$	−9.24937			−0.314852			−0.157426	+	0.987531i	$0.550320\pi$
$864$		0			0
$865$	0.128589	+	1.60920i	0.00437216	+	0.0547143i
$866$		−	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
$875$	−13.6314	+	46.6344i	−0.460825	+	1.57653i
$876$		0			0
$877$	−28.4654	+	49.3035i	−0.961208	+	1.66486i	−0.241731	+	0.970343i	$0.577715\pi$
$877$	−28.4654	+	49.3035i	−0.961208	+	1.66486i	−0.719476	+	0.694517i	$0.755618\pi$
$878$	−12.1229	+	20.9974i	−0.409127	+	0.708628i
$879$		0			0
$880$	−0.419677	−	5.25194i	−0.0141473	−	0.177043i
$881$	−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	$-0.998985\pi$
$883$		−	0.189481i		−	0.00637654i	0.999995	−	0.00318827i	$-0.00101486\pi$
$884$	−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	−0.737580	−	0.675260i	$-0.764032\pi$
$887$	−15.5339	+	8.96852i	−0.521578	+	0.301133i	0.216002	+	0.976393i	$0.430698\pi$
$888$		0			0
$889$			59.1213i			1.98287i
$890$	0.853950	+	10.6865i	0.0286245	+	0.358214i
$891$		0			0
$892$	4.63585			0.155220
$893$	3.28984	+	1.89939i	0.110090	+	0.0635607i
$894$		0			0
$895$	6.11999	−	12.8705i	0.204569	−	0.430215i
$896$	−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	−0.892842	−	0.450371i	$-0.851292\pi$
$907$	−28.5874	+	16.5050i	−0.949230	+	0.548038i	−0.0563882	+	0.998409i	$0.517958\pi$
$908$	−8.89213	−	15.4016i	−0.295096	−	0.511121i
$909$		0			0
$910$	−31.0901	−	16.1528i	−1.03063	−	0.535460i
$911$	−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	$0.0651764\pi$
$920$	−13.0209	−	6.19148i	−0.429286	−	0.204127i
$921$		0			0
$922$			11.8915i			0.391626i
$923$	−10.5067	−	0.371086i	−0.345832	−	0.0122144i
$924$		0			0
$925$	36.9417	−	5.94188i	1.21463	−	0.195368i
$926$	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	$-0.774727\pi$
$937$		−	39.7996i		−	1.30020i	0.759850	−	0.650099i	$-0.225273\pi$
$938$	−12.6601	−	21.9280i	−0.413368	−	0.715974i
$939$		0			0
$940$	−12.5163	+	1.00016i	−0.408236	+	0.0326217i
$941$			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	0.784058	−	0.620688i	$-0.213147\pi$
$947$	−4.47761	−	7.75545i	−0.145503	−	0.252018i	−0.929560	+	0.368670i	$0.879813\pi$
$948$		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	0.316351	−	0.948642i	$-0.397542\pi$
$953$	−10.7128	−	6.18504i	−0.347022	−	0.200353i	−0.663373	+	0.748289i	$0.730876\pi$
$954$		0			0
$955$	1.30814	−	0.104532i	0.0423304	−	0.00338257i
$956$	−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
$965$	21.7271	−	45.6928i	0.699421	−	1.47090i
$966$		0			0
$967$	−6.35606			−0.204397			−0.102198	−	0.994764i	$-0.532588\pi$
$967$	−6.35606			−0.204397			−0.102198	+	0.994764i	$0.532588\pi$
$968$	−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	$-0.878367\pi$
$977$	−24.5952	−	42.6002i	−0.786871	−	1.36290i	0.141005	−	0.990009i	$-0.454967\pi$
$978$		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	$-0.614942\pi$
$983$	−22.1542			−0.706609			−0.353304	+	0.935508i	$0.614942\pi$
$984$		0			0
$985$	1.58202	−	3.32703i	0.0504073	−	0.106008i
$986$	−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
$995$	−22.8988	+	1.82982i	−0.725941	+	0.0580091i
$996$		0			0
$997$	41.0355	+	23.6919i	1.29961	+	0.750329i	0.980336	−	0.197335i	$-0.0632286\pi$
$997$	41.0355	+	23.6919i	1.29961	+	0.750329i	0.319271	+	0.947663i	$0.396562\pi$
$998$	−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.c.829.5		12
3.2	odd	2		390.2.x.b.49.4	yes	12
5.4	even	2		1170.2.bj.d.829.2		12
13.4	even	6		1170.2.bj.d.199.2		12
15.2	even	4		1950.2.bc.i.751.3		12
15.8	even	4		1950.2.bc.j.751.4		12
15.14	odd	2		390.2.x.a.49.3	✓	12
39.17	odd	6		390.2.x.a.199.3	yes	12
65.4	even	6	inner	1170.2.bj.c.199.5		12
195.17	even	12		1950.2.bc.i.901.3		12
195.134	odd	6		390.2.x.b.199.4	yes	12
195.173	even	12		1950.2.bc.j.901.4		12

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

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.26873 + 1.84128i) q^{5} +(2.17283 - 3.76344i) q^{7} +1.00000 q^{8} +(0.960230 - 2.01940i) q^{10} +(2.04055 - 1.17811i) q^{11} +(3.18419 - 1.69144i) q^{13} -4.34565 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.60564 + 1.50437i) q^{17} +(0.585872 + 0.338254i) q^{19} +(-2.22896 + 0.178114i) q^{20} +(-2.04055 - 1.17811i) q^{22} +(-5.58405 + 3.22396i) q^{23} +(-1.78064 + 4.67219i) q^{25} +(-3.05692 - 1.91187i) q^{26} +(2.17283 + 3.76344i) q^{28} +(-4.82620 - 8.35922i) q^{29} +7.11493i q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00874i q^{34} +(9.68629 - 0.774021i) q^{35} +(-3.74165 - 6.48073i) q^{37} -0.676507i q^{38} +(1.26873 + 1.84128i) q^{40} +(2.60564 - 1.50437i) q^{41} +(5.91710 + 3.41624i) q^{43} +2.35623i q^{44} +(5.58405 + 3.22396i) q^{46} +5.61529 q^{47} +(-5.94234 - 10.2924i) q^{49} +(4.93655 - 0.794019i) q^{50} +(-0.127265 + 3.60330i) q^{52} -9.43400i q^{53} +(4.75816 + 2.26252i) q^{55} +(2.17283 - 3.76344i) q^{56} +(-4.82620 + 8.35922i) q^{58} +(4.56364 + 2.63482i) q^{59} +(2.15646 - 3.73509i) q^{61} +(6.16171 - 3.55746i) q^{62} +1.00000 q^{64} +(7.15429 + 3.71700i) q^{65} +(2.91329 + 5.04596i) q^{67} +(-2.60564 + 1.50437i) q^{68} +(-5.51347 - 8.00157i) q^{70} +(-2.52520 - 1.45793i) q^{71} +7.67804 q^{73} +(-3.74165 + 6.48073i) q^{74} +(-0.585872 + 0.338254i) q^{76} -10.2393i q^{77} -3.74519 q^{79} +(0.960230 - 2.01940i) q^{80} +(-2.60564 - 1.50437i) q^{82} +10.3557 q^{83} +(0.535898 + 6.70637i) q^{85} -6.83247i q^{86} +(2.04055 - 1.17811i) q^{88} +(-4.15208 + 2.39720i) q^{89} +(0.553049 - 15.6587i) q^{91} -6.44791i q^{92} +(-2.80764 - 4.86298i) q^{94} +(0.120495 + 1.50791i) q^{95} +(8.17066 - 14.1520i) q^{97} +(-5.94234 + 10.2924i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29}+ \cdots + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * 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 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more