LMFDB - Embedded newform 1386.2.ba.a.1187.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(989,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("1386.989");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1187.15
Character	$\chi$	$=$	1386.1187
Dual form			1386.2.ba.a.989.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.42143 - 1.39801i) q^{5} +(-2.62875 + 0.299420i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.42143 - 1.39801i) q^{5} +(-2.62875 + 0.299420i) q^{7} +1.00000 q^{8} +(-2.42143 - 1.39801i) q^{10} +(-1.36985 + 3.02052i) q^{11} -3.20191i q^{13} +(1.57368 + 2.12686i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.05881 - 3.56596i) q^{17} +(1.82770 - 1.05522i) q^{19} +2.79602i q^{20} +(3.30077 - 0.323937i) q^{22} +(0.902766 - 0.521212i) q^{23} +(1.40887 - 2.44023i) q^{25} +(-2.77293 + 1.60095i) q^{26} +(1.05507 - 2.42628i) q^{28} -9.40956 q^{29} +(3.58777 - 6.21420i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.11761 q^{34} +(-5.94674 + 4.40005i) q^{35} +(-4.60502 - 7.97612i) q^{37} +(-1.82770 - 1.05522i) q^{38} +(2.42143 - 1.39801i) q^{40} +0.110771 q^{41} -4.20415i q^{43} +(-1.93092 - 2.69658i) q^{44} +(-0.902766 - 0.521212i) q^{46} +(7.27267 - 4.19888i) q^{47} +(6.82070 - 1.57420i) q^{49} -2.81773 q^{50} +(2.77293 + 1.60095i) q^{52} +(-10.3301 - 5.96410i) q^{53} +(0.905736 + 9.22901i) q^{55} +(-2.62875 + 0.299420i) q^{56} +(4.70478 + 8.14891i) q^{58} +(6.34962 + 3.66595i) q^{59} +(9.21987 - 5.32310i) q^{61} -7.17555 q^{62} +1.00000 q^{64} +(-4.47630 - 7.75318i) q^{65} +(-3.97143 + 6.87872i) q^{67} +(2.05881 + 3.56596i) q^{68} +(6.78392 + 2.95000i) q^{70} +11.0925i q^{71} +(-5.46860 - 3.15730i) q^{73} +(-4.60502 + 7.97612i) q^{74} +2.11045i q^{76} +(2.69658 - 8.35036i) q^{77} +(12.4344 - 7.17899i) q^{79} +(-2.42143 - 1.39801i) q^{80} +(-0.0553856 - 0.0959306i) q^{82} -14.2335 q^{83} -11.5129i q^{85} +(-3.64090 + 2.10208i) q^{86} +(-1.36985 + 3.02052i) q^{88} +(10.3472 - 5.97394i) q^{89} +(0.958715 + 8.41703i) q^{91} +1.04242i q^{92} +(-7.27267 - 4.19888i) q^{94} +(2.95043 - 5.11029i) q^{95} -17.6911 q^{97} +(-4.77365 - 5.11979i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−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
$5$	2.42143	−	1.39801i	1.08289	−	0.625209i	0.151219	−	0.988500i	$-0.451680\pi$
$5$	2.42143	−	1.39801i	1.08289	−	0.625209i	0.931676	+	0.363291i	$0.118347\pi$
$6$		0			0
$7$	−2.62875	+	0.299420i	−0.993576	+	0.113170i
$7$	−2.62875	+	0.299420i	−0.993576	+	0.113170i
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.42143	−	1.39801i	−0.765722	−	0.442090i
$11$	−1.36985	+	3.02052i	−0.413024	+	0.910720i
$11$	−1.36985	+	3.02052i	−0.413024	+	0.910720i
$12$		0			0
$13$		−	3.20191i		−	0.888050i	−0.896015	−	0.444025i	$-0.853550\pi$
$13$		−	3.20191i		−	0.888050i	0.896015	−	0.444025i	$-0.146450\pi$
$14$	1.57368	+	2.12686i	0.420584	+	0.568427i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.05881	−	3.56596i	0.499334	−	0.864872i	−0.500666	−	0.865641i	$-0.666911\pi$
$17$	2.05881	−	3.56596i	0.499334	−	0.864872i	1.00000		0.000768905i	$0.000244750\pi$
$18$		0			0
$19$	1.82770	−	1.05522i	0.419304	−	0.242085i	−0.275476	−	0.961308i	$-0.588835\pi$
$19$	1.82770	−	1.05522i	0.419304	−	0.242085i	0.694779	+	0.719223i	$0.255502\pi$
$20$			2.79602i			0.625209i
$21$		0			0
$22$	3.30077	−	0.323937i	0.703726	−	0.0690637i
$23$	0.902766	−	0.521212i	0.188240	−	0.108680i	−0.402919	−	0.915236i	$-0.632004\pi$
$23$	0.902766	−	0.521212i	0.188240	−	0.108680i	0.591158	+	0.806556i	$0.298671\pi$
$24$		0			0
$25$	1.40887	−	2.44023i	0.281773	−	0.488046i
$26$	−2.77293	+	1.60095i	−0.543817	+	0.313973i
$27$		0			0
$28$	1.05507	−	2.42628i	0.199390	−	0.458523i
$29$	−9.40956			−1.74731			−0.873655	−	0.486545i	$-0.838257\pi$
$29$	−9.40956			−1.74731			−0.873655	+	0.486545i	$0.838257\pi$
$30$		0			0
$31$	3.58777	−	6.21420i	0.644383	−	1.11610i	−0.340061	−	0.940404i	$-0.610448\pi$
$31$	3.58777	−	6.21420i	0.644383	−	1.11610i	0.984444	−	0.175701i	$-0.0562191\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−4.11761			−0.706165
$35$	−5.94674	+	4.40005i	−1.00518	+	0.743744i
$36$		0			0
$37$	−4.60502	−	7.97612i	−0.757060	−	1.31127i	−0.944344	−	0.328961i	$-0.893302\pi$
$37$	−4.60502	−	7.97612i	−0.757060	−	1.31127i	0.187284	−	0.982306i	$-0.440032\pi$
$38$	−1.82770	−	1.05522i	−0.296492	−	0.171180i
$39$		0			0
$40$	2.42143	−	1.39801i	0.382861	−	0.221045i
$41$	0.110771			0.0172995			0.00864977	−	0.999963i	$-0.497247\pi$
$41$	0.110771			0.0172995			0.00864977	+	0.999963i	$0.497247\pi$
$42$		0			0
$43$		−	4.20415i		−	0.641127i	−0.947227	−	0.320564i	$-0.896128\pi$
$43$		−	4.20415i		−	0.641127i	0.947227	−	0.320564i	$-0.103872\pi$
$44$	−1.93092	−	2.69658i	−0.291097	−	0.406525i
$45$		0			0
$46$	−0.902766	−	0.521212i	−0.133106	−	0.0768485i
$47$	7.27267	−	4.19888i	1.06083	−	0.612469i	0.135167	−	0.990823i	$-0.456843\pi$
$47$	7.27267	−	4.19888i	1.06083	−	0.612469i	0.925661	+	0.378353i	$0.123510\pi$
$48$		0			0
$49$	6.82070	−	1.57420i	0.974385	−	0.224886i
$50$	−2.81773			−0.398488
$51$		0			0
$52$	2.77293	+	1.60095i	0.384537	+	0.222012i
$53$	−10.3301	−	5.96410i	−1.41895	−	0.819232i	−0.422745	−	0.906249i	$-0.638933\pi$
$53$	−10.3301	−	5.96410i	−1.41895	−	0.819232i	−0.996207	+	0.0870162i	$0.972267\pi$
$54$		0			0
$55$	0.905736	+	9.22901i	0.122129	+	1.24444i
$56$	−2.62875	+	0.299420i	−0.351282	+	0.0400117i
$57$		0			0
$58$	4.70478	+	8.14891i	0.617768	+	1.07000i
$59$	6.34962	+	3.66595i	0.826650	+	0.477266i	0.852704	−	0.522394i	$-0.174961\pi$
$59$	6.34962	+	3.66595i	0.826650	+	0.477266i	−0.0260545	+	0.999661i	$0.508294\pi$
$60$		0			0
$61$	9.21987	−	5.32310i	1.18048	−	0.681553i	0.224357	−	0.974507i	$-0.427972\pi$
$61$	9.21987	−	5.32310i	1.18048	−	0.681553i	0.956126	+	0.292954i	$0.0946383\pi$
$62$	−7.17555			−0.911295
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.47630	−	7.75318i	−0.555217	−	0.961664i
$66$		0			0
$67$	−3.97143	+	6.87872i	−0.485188	+	0.840370i	−0.999855	−	0.0170201i	$-0.994582\pi$
$67$	−3.97143	+	6.87872i	−0.485188	+	0.840370i	0.514667	+	0.857390i	$0.327915\pi$
$68$	2.05881	+	3.56596i	0.249667	+	0.432436i
$69$		0			0
$70$	6.78392	+	2.95000i	0.810834	+	0.352593i
$71$			11.0925i			1.31643i	0.752828	+	0.658217i	$0.228689\pi$
$71$			11.0925i			1.31643i	−0.752828	+	0.658217i	$0.771311\pi$
$72$		0			0
$73$	−5.46860	−	3.15730i	−0.640052	−	0.369534i	0.144583	−	0.989493i	$-0.453816\pi$
$73$	−5.46860	−	3.15730i	−0.640052	−	0.369534i	−0.784634	+	0.619959i	$0.787149\pi$
$74$	−4.60502	+	7.97612i	−0.535322	+	0.927205i
$75$		0			0
$76$			2.11045i			0.242085i
$77$	2.69658	−	8.35036i	0.307304	−	0.951611i
$78$		0			0
$79$	12.4344	−	7.17899i	1.39898	−	0.807700i	0.404692	−	0.914453i	$-0.367379\pi$
$79$	12.4344	−	7.17899i	1.39898	−	0.807700i	0.994286	+	0.106753i	$0.0340455\pi$
$80$	−2.42143	−	1.39801i	−0.270724	−	0.156302i
$81$		0			0
$82$	−0.0553856	−	0.0959306i	−0.00611631	−	0.0105938i
$83$	−14.2335			−1.56234			−0.781168	−	0.624321i	$-0.785376\pi$
$83$	−14.2335			−1.56234			−0.781168	+	0.624321i	$0.785376\pi$
$84$		0			0
$85$		−	11.5129i		−	1.24875i
$86$	−3.64090	+	2.10208i	−0.392609	+	0.226673i
$87$		0			0
$88$	−1.36985	+	3.02052i	−0.146026	+	0.321988i
$89$	10.3472	−	5.97394i	1.09680	−	0.633236i	0.161419	−	0.986886i	$-0.448393\pi$
$89$	10.3472	−	5.97394i	1.09680	−	0.633236i	0.935378	+	0.353650i	$0.115060\pi$
$90$		0			0
$91$	0.958715	+	8.41703i	0.100501	+	0.882344i
$92$			1.04242i			0.108680i
$93$		0			0
$94$	−7.27267	−	4.19888i	−0.750119	−	0.433081i
$95$	2.95043	−	5.11029i	0.302708	−	0.524305i
$96$		0			0
$97$	−17.6911			−1.79626			−0.898129	−	0.439733i	$-0.855073\pi$
$97$	−17.6911			−1.79626			−0.898129	+	0.439733i	$0.855073\pi$
$98$	−4.77365	−	5.11979i	−0.482211	−	0.517177i
$99$		0			0
$100$	1.40887	+	2.44023i	0.140887	+	0.244023i
$101$	−0.117005	+	0.202659i	−0.0116425	+	0.0201653i	−0.871788	−	0.489883i	$-0.837039\pi$
$101$	−0.117005	+	0.202659i	−0.0116425	+	0.0201653i	0.860145	+	0.510049i	$0.170373\pi$
$102$		0			0
$103$	−6.27192	−	10.8633i	−0.617991	−	1.07039i	−0.989852	−	0.142103i	$-0.954614\pi$
$103$	−6.27192	−	10.8633i	−0.617991	−	1.07039i	0.371861	−	0.928288i	$-0.378720\pi$
$104$		−	3.20191i		−	0.313973i
$105$		0			0
$106$			11.9282i			1.15857i
$107$	6.54545	+	11.3370i	0.632772	+	1.09599i	0.986982	+	0.160828i	$0.0514164\pi$
$107$	6.54545	+	11.3370i	0.632772	+	1.09599i	−0.354210	+	0.935166i	$0.615250\pi$
$108$		0			0
$109$	−5.63480	−	3.25325i	−0.539716	−	0.311605i	0.205248	−	0.978710i	$-0.434200\pi$
$109$	−5.63480	−	3.25325i	−0.539716	−	0.311605i	−0.744964	+	0.667105i	$0.767533\pi$
$110$	7.53969	−	5.39890i	0.718881	−	0.514765i
$111$		0			0
$112$	1.57368	+	2.12686i	0.148699	+	0.200969i
$113$			0.871772i			0.0820094i	0.999159	+	0.0410047i	$0.0130559\pi$
$113$			0.871772i			0.0820094i	−0.999159	+	0.0410047i	$0.986944\pi$
$114$		0			0
$115$	1.45732	−	2.52415i	0.135896	−	0.235378i
$116$	4.70478	−	8.14891i	0.436828	−	0.756608i
$117$		0			0
$118$		−	7.33191i		−	0.674957i
$119$	−4.34438	+	9.99047i	−0.398248	+	0.915825i
$120$		0			0
$121$	−7.24705	−	8.27528i	−0.658822	−	0.752299i
$122$	−9.21987	−	5.32310i	−0.834728	−	0.481931i
$123$		0			0
$124$	3.58777	+	6.21420i	0.322192	+	0.558052i
$125$			6.10167i			0.545750i
$126$		0			0
$127$		−	9.15849i		−	0.812685i	−0.913721	−	0.406342i	$-0.866804\pi$
$127$		−	9.15849i		−	0.812685i	0.913721	−	0.406342i	$-0.133196\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−4.47630	+	7.75318i	−0.392598	+	0.679999i
$131$	−3.87340	−	6.70892i	−0.338420	−	0.586161i	0.645716	−	0.763578i	$-0.276559\pi$
$131$	−3.87340	−	6.70892i	−0.338420	−	0.586161i	−0.984136	+	0.177417i	$0.943226\pi$
$132$		0			0
$133$	−4.48862	+	3.32118i	−0.389213	+	0.287982i
$134$	7.94287			0.686159
$135$		0			0
$136$	2.05881	−	3.56596i	0.176541	−	0.305778i
$137$	−6.78091	−	3.91496i	−0.579333	−	0.334478i	0.181536	−	0.983384i	$-0.441893\pi$
$137$	−6.78091	−	3.91496i	−0.579333	−	0.334478i	−0.760868	+	0.648907i	$0.775227\pi$
$138$		0			0
$139$		−	3.11030i		−	0.263812i	−0.991262	−	0.131906i	$-0.957890\pi$
$139$		−	3.11030i		−	0.263812i	0.991262	−	0.131906i	$-0.0421097\pi$
$140$	−0.837184	−	7.35005i	−0.0707550	−	0.621193i
$141$		0			0
$142$	9.60636	−	5.54624i	0.806148	−	0.465430i
$143$	9.67142	+	4.38612i	0.808765	+	0.366786i
$144$		0			0
$145$	−22.7845	+	13.1547i	−1.89215	+	1.09243i
$146$			6.31460i			0.522600i
$147$		0			0
$148$	9.21003			0.757060
$149$	4.08541	+	7.07613i	0.334690	+	0.579699i	0.983425	−	0.181314i	$-0.0580352\pi$
$149$	4.08541	+	7.07613i	0.334690	+	0.579699i	−0.648736	+	0.761014i	$0.724702\pi$
$150$		0			0
$151$	−5.93139	−	3.42449i	−0.482690	−	0.278681i	0.238847	−	0.971057i	$-0.423231\pi$
$151$	−5.93139	−	3.42449i	−0.482690	−	0.278681i	−0.721537	+	0.692376i	$0.756564\pi$
$152$	1.82770	−	1.05522i	0.148246	−	0.0855900i
$153$		0			0
$154$	−8.57991	+	1.83987i	−0.691389	+	0.148261i
$155$		−	20.0630i		−	1.61150i
$156$		0			0
$157$	4.04332	−	7.00324i	0.322692	−	0.558920i	−0.658350	−	0.752712i	$-0.728745\pi$
$157$	4.04332	−	7.00324i	0.322692	−	0.558920i	0.981043	+	0.193792i	$0.0620787\pi$
$158$	−12.4344	−	7.17899i	−0.989226	−	0.571130i
$159$		0			0
$160$			2.79602i			0.221045i
$161$	−2.21709	+	1.64044i	−0.174731	+	0.129285i
$162$		0			0
$163$	−0.682357	−	1.18188i	−0.0534463	−	0.0925717i	0.838064	−	0.545571i	$-0.183687\pi$
$163$	−0.682357	−	1.18188i	−0.0534463	−	0.0925717i	−0.891511	+	0.453000i	$0.850354\pi$
$164$	−0.0553856	+	0.0959306i	−0.00432489	+	0.00749092i
$165$		0			0
$166$	7.11677	+	12.3266i	0.552369	+	0.956731i
$167$	7.34655			0.568493			0.284247	−	0.958751i	$-0.408257\pi$
$167$	7.34655			0.568493			0.284247	+	0.958751i	$0.408257\pi$
$168$		0			0
$169$	2.74778			0.211368
$170$	−9.97049	+	5.75647i	−0.764702	+	0.441501i
$171$		0			0
$172$	3.64090	+	2.10208i	0.277616	+	0.160282i
$173$	−0.327674	−	0.567548i	−0.0249126	−	0.0431498i	0.853300	−	0.521420i	$-0.174597\pi$
$173$	−0.327674	−	0.567548i	−0.0249126	−	0.0431498i	−0.878213	+	0.478270i	$0.841264\pi$
$174$		0			0
$175$	−2.97291	+	6.83660i	−0.224731	+	0.516799i
$176$	3.30077	−	0.323937i	0.248805	−	0.0244177i
$177$		0			0
$178$	−10.3472	−	5.97394i	−0.775553	−	0.447765i
$179$	3.55106	+	2.05021i	0.265419	+	0.153240i	0.626804	−	0.779177i	$-0.284363\pi$
$179$	3.55106	+	2.05021i	0.265419	+	0.153240i	−0.361385	+	0.932417i	$0.617696\pi$
$180$		0			0
$181$	−11.0064			−0.818102			−0.409051	−	0.912511i	$-0.634140\pi$
$181$	−11.0064			−0.818102			−0.409051	+	0.912511i	$0.634140\pi$
$182$	6.81000	−	5.03879i	0.504791	−	0.373500i
$183$		0			0
$184$	0.902766	−	0.521212i	0.0665528	−	0.0384243i
$185$	−22.3014	−	12.8757i	−1.63963	−	0.946642i
$186$		0			0
$187$	7.95079	+	11.1035i	0.581419	+	0.811966i
$188$			8.39776i			0.612469i
$189$		0			0
$190$	−5.90086			−0.428093
$191$	−18.8331	+	10.8733i	−1.36271	+	0.786763i	−0.989984	−	0.141178i	$-0.954911\pi$
$191$	−18.8331	+	10.8733i	−1.36271	+	0.786763i	−0.372728	+	0.927940i	$0.621578\pi$
$192$		0			0
$193$	19.3131	+	11.1504i	1.39019	+	0.802625i	0.993336	−	0.115257i	$-0.0367692\pi$
$193$	19.3131	+	11.1504i	1.39019	+	0.802625i	0.396852	+	0.917882i	$0.370102\pi$
$194$	8.84554	+	15.3209i	0.635073	+	1.09998i
$195$		0			0
$196$	−2.04705	+	6.69400i	−0.146218	+	0.478143i
$197$	11.0036			0.783972			0.391986	−	0.919971i	$-0.371788\pi$
$197$	11.0036			0.783972			0.391986	+	0.919971i	$0.371788\pi$
$198$		0			0
$199$	−8.22506	+	14.2462i	−0.583059	+	1.00989i	0.412055	+	0.911159i	$0.364811\pi$
$199$	−8.22506	+	14.2462i	−0.583059	+	1.00989i	−0.995114	+	0.0987290i	$0.968522\pi$
$200$	1.40887	−	2.44023i	0.0996219	−	0.172550i
$201$		0			0
$202$	0.234010			0.0164649
$203$	24.7354	−	2.81741i	1.73609	−	0.197743i
$204$		0			0
$205$	0.268224	−	0.154859i	0.0187336	−	0.0108158i
$206$	−6.27192	+	10.8633i	−0.436986	+	0.756881i
$207$		0			0
$208$	−2.77293	+	1.60095i	−0.192268	+	0.111006i
$209$	0.683653	+	6.96610i	0.0472893	+	0.481855i
$210$		0			0
$211$			0.618822i			0.0426015i	0.999773	+	0.0213007i	$0.00678075\pi$
$211$			0.618822i			0.0426015i	−0.999773	+	0.0213007i	$0.993219\pi$
$212$	10.3301	−	5.96410i	0.709476	−	0.409616i
$213$		0			0
$214$	6.54545	−	11.3370i	0.447438	−	0.774985i
$215$	−5.87745	−	10.1800i	−0.400839	−	0.694273i
$216$		0			0
$217$	−7.57072	+	17.4099i	−0.513934	+	1.18186i
$218$			6.50650i			0.440676i
$219$		0			0
$220$	−8.44543	−	3.83012i	−0.569391	−	0.258226i
$221$	−11.4179	−	6.59211i	−0.768049	−	0.443433i
$222$		0			0
$223$	10.3553			0.693443			0.346722	−	0.937968i	$-0.387295\pi$
$223$	10.3553			0.693443			0.346722	+	0.937968i	$0.387295\pi$
$224$	1.05507	−	2.42628i	0.0704949	−	0.162112i
$225$		0			0
$226$	0.754977	−	0.435886i	0.0502203	−	0.0289947i
$227$	6.46564	−	11.1988i	0.429140	−	0.743292i	−0.567657	−	0.823265i	$-0.692150\pi$
$227$	6.46564	−	11.1988i	0.429140	−	0.743292i	0.996797	+	0.0799731i	$0.0254834\pi$
$228$		0			0
$229$	−2.73849	−	4.74320i	−0.180964	−	0.313439i	0.761245	−	0.648465i	$-0.224589\pi$
$229$	−2.73849	−	4.74320i	−0.180964	−	0.313439i	−0.942209	+	0.335025i	$0.891255\pi$
$230$	−2.91464			−0.192186
$231$		0			0
$232$	−9.40956			−0.617768
$233$	13.7588	+	23.8310i	0.901372	+	1.56122i	0.825715	+	0.564088i	$0.190772\pi$
$233$	13.7588	+	23.8310i	0.901372	+	1.56122i	0.0756568	+	0.997134i	$0.475895\pi$
$234$		0			0
$235$	11.7402	−	20.3345i	0.765843	−	1.32648i
$236$	−6.34962	+	3.66595i	−0.413325	+	0.238633i
$237$		0			0
$238$	10.8242	−	1.23290i	0.701628	−	0.0799167i
$239$	13.3339			0.862499			0.431249	−	0.902233i	$-0.358073\pi$
$239$	13.3339			0.862499			0.431249	+	0.902233i	$0.358073\pi$
$240$		0			0
$241$	15.7035	+	9.06641i	1.01155	+	0.584019i	0.911645	−	0.410978i	$-0.134813\pi$
$241$	15.7035	+	9.06641i	1.01155	+	0.584019i	0.0999053	+	0.994997i	$0.468146\pi$
$242$	−3.54308	+	10.4138i	−0.227758	+	0.669422i
$243$		0			0
$244$			10.6462i			0.681553i
$245$	14.3151	−	13.3472i	0.914555	−	0.852722i
$246$		0			0
$247$	−3.37873	−	5.85213i	−0.214984	−	0.372362i
$248$	3.58777	−	6.21420i	0.227824	−	0.394602i
$249$		0			0
$250$	5.28420	−	3.05083i	0.334202	−	0.192952i
$251$			18.5540i			1.17112i	0.810630	+	0.585559i	$0.199125\pi$
$251$			18.5540i			1.17112i	−0.810630	+	0.585559i	$0.800875\pi$
$252$		0			0
$253$	0.337680	+	3.44080i	0.0212298	+	0.216321i
$254$	−7.93149	+	4.57925i	−0.497666	+	0.287327i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.4582	−	13.5436i	1.46328	−	0.844826i	0.464120	−	0.885773i	$-0.346371\pi$
$257$	23.4582	−	13.5436i	1.46328	−	0.844826i	0.999161	+	0.0409470i	$0.0130375\pi$
$258$		0			0
$259$	14.4937	+	19.5884i	0.900593	+	1.21717i
$260$	8.95260			0.555217
$261$		0			0
$262$	−3.87340	+	6.70892i	−0.239299	+	0.414478i
$263$	−5.53418	+	9.58548i	−0.341252	+	0.591066i	−0.984665	−	0.174453i	$-0.944184\pi$
$263$	−5.53418	+	9.58548i	−0.341252	+	0.591066i	0.643414	+	0.765519i	$0.277518\pi$
$264$		0			0
$265$	−33.3515			−2.04877
$266$	5.12053	+	2.22667i	0.313960	+	0.136526i
$267$		0			0
$268$	−3.97143	−	6.87872i	−0.242594	−	0.420185i
$269$	8.44523	+	4.87586i	0.514915	+	0.297286i	0.734852	−	0.678228i	$-0.237252\pi$
$269$	8.44523	+	4.87586i	0.514915	+	0.297286i	−0.219937	+	0.975514i	$0.570585\pi$
$270$		0			0
$271$	−2.91324	+	1.68196i	−0.176967	+	0.102172i	−0.585867	−	0.810407i	$-0.699246\pi$
$271$	−2.91324	+	1.68196i	−0.176967	+	0.102172i	0.408900	+	0.912579i	$0.365912\pi$
$272$	−4.11761			−0.249667
$273$		0			0
$274$			7.82992i			0.473023i
$275$	5.44082	+	7.59824i	0.328094	+	0.458191i
$276$		0			0
$277$	14.3722	+	8.29777i	0.863539	+	0.498564i	0.865196	−	0.501434i	$-0.167194\pi$
$277$	14.3722	+	8.29777i	0.863539	+	0.498564i	−0.00165684	+	0.999999i	$0.500527\pi$
$278$	−2.69360	+	1.55515i	−0.161551	+	0.0932716i
$279$		0			0
$280$	−5.94674	+	4.40005i	−0.355386	+	0.262953i
$281$	5.58641			0.333257			0.166629	−	0.986020i	$-0.446712\pi$
$281$	5.58641			0.333257			0.166629	+	0.986020i	$0.446712\pi$
$282$		0			0
$283$	2.33852	+	1.35014i	0.139010	+	0.0802577i	0.567892	−	0.823103i	$-0.307759\pi$
$283$	2.33852	+	1.35014i	0.139010	+	0.0802577i	−0.428882	+	0.903361i	$0.641092\pi$
$284$	−9.60636	−	5.54624i	−0.570033	−	0.329109i
$285$		0			0
$286$	−1.03722	−	10.5688i	−0.0613320	−	0.624944i
$287$	−0.291190	+	0.0331671i	−0.0171884	+	0.00195779i
$288$		0			0
$289$	0.0226302	+	0.0391967i	0.00133119	+	0.00230569i
$290$	22.7845	+	13.1547i	1.33795	+	0.772468i
$291$		0			0
$292$	5.46860	−	3.15730i	0.320026	−	0.184767i
$293$	15.8185			0.924125			0.462062	−	0.886847i	$-0.347110\pi$
$293$	15.8185			0.924125			0.462062	+	0.886847i	$0.347110\pi$
$294$		0			0
$295$	20.5002			1.19357
$296$	−4.60502	−	7.97612i	−0.267661	−	0.463603i
$297$		0			0
$298$	4.08541	−	7.07613i	0.236661	−	0.409909i
$299$	−1.66887	−	2.89057i	−0.0965134	−	0.167166i
$300$		0			0
$301$	1.25881	+	11.0517i	0.0725564	+	0.637008i
$302$			6.84898i			0.394115i
$303$		0			0
$304$	−1.82770	−	1.05522i	−0.104826	−	0.0605213i
$305$	14.8835	−	25.7790i	0.852226	−	1.47610i
$306$		0			0
$307$			12.2813i			0.700932i	0.936575	+	0.350466i	$0.113977\pi$
$307$			12.2813i			0.700932i	−0.936575	+	0.350466i	$0.886023\pi$
$308$	5.88333	+	6.51049i	0.335234	+	0.370969i
$309$		0			0
$310$	−17.3750	+	10.0315i	−0.986836	+	0.569750i
$311$	−17.6592	−	10.1956i	−1.00136	−	0.578137i	−0.0927112	−	0.995693i	$-0.529553\pi$
$311$	−17.6592	−	10.1956i	−1.00136	−	0.578137i	−0.908651	+	0.417556i	$0.862887\pi$
$312$		0			0
$313$	1.62210	+	2.80957i	0.0916867	+	0.158806i	0.908221	−	0.418491i	$-0.137441\pi$
$313$	1.62210	+	2.80957i	0.0916867	+	0.158806i	−0.816534	+	0.577297i	$0.804108\pi$
$314$	−8.08665			−0.456356
$315$		0			0
$316$			14.3580i			0.807700i
$317$	9.57584	−	5.52861i	0.537833	−	0.310518i	−0.206368	−	0.978475i	$-0.566164\pi$
$317$	9.57584	−	5.52861i	0.537833	−	0.310518i	0.744200	+	0.667957i	$0.232831\pi$
$318$		0			0
$319$	12.8896	−	28.4217i	0.721681	−	1.59131i
$320$	2.42143	−	1.39801i	0.135362	−	0.0781512i
$321$		0			0
$322$	2.52921	+	1.09983i	0.140947	+	0.0612913i
$323$		−	8.69001i		−	0.483525i
$324$		0			0
$325$	−7.81339	−	4.51106i	−0.433409	−	0.250229i
$326$	−0.682357	+	1.18188i	−0.0377922	+	0.0654581i
$327$		0			0
$328$	0.110771			0.00611631
$329$	−17.8608	+	13.2154i	−0.984700	+	0.728589i
$330$		0			0
$331$	7.27038	+	12.5927i	0.399616	+	0.692156i	0.993678	−	0.112263i	$-0.0358100\pi$
$331$	7.27038	+	12.5927i	0.399616	+	0.692156i	−0.594062	+	0.804419i	$0.702477\pi$
$332$	7.11677	−	12.3266i	0.390584	−	0.676511i
$333$		0			0
$334$	−3.67328	−	6.36230i	−0.200993	−	0.348130i
$335$			22.2084i			1.21338i
$336$		0			0
$337$		−	20.0460i		−	1.09198i	−0.837793	−	0.545988i	$-0.816154\pi$
$337$		−	20.0460i		−	1.09198i	0.837793	−	0.545988i	$-0.183846\pi$
$338$	−1.37389	−	2.37965i	−0.0747299	−	0.129436i
$339$		0			0
$340$	9.97049	+	5.75647i	0.540726	+	0.312188i
$341$	13.8554	+	19.3494i	0.750313	+	1.04783i
$342$		0			0
$343$	−17.4586	+	6.18044i	−0.942675	+	0.333713i
$344$		−	4.20415i		−	0.226673i
$345$		0			0
$346$	−0.327674	+	0.567548i	−0.0176158	+	0.0305115i
$347$	6.04444	−	10.4693i	0.324482	−	0.562020i	−0.656925	−	0.753956i	$-0.728143\pi$
$347$	6.04444	−	10.4693i	0.324482	−	0.562020i	0.981407	+	0.191936i	$0.0614766\pi$
$348$		0			0
$349$			4.92511i			0.263635i	0.991274	+	0.131818i	$0.0420813\pi$
$349$			4.92511i			0.263635i	−0.991274	+	0.131818i	$0.957919\pi$
$350$	7.40713	−	0.843685i	0.395928	−	0.0450969i
$351$		0			0
$352$	−1.93092	−	2.69658i	−0.102918	−	0.143728i
$353$	−8.28001	−	4.78047i	−0.440700	−	0.254438i	0.263194	−	0.964743i	$-0.415224\pi$
$353$	−8.28001	−	4.78047i	−0.440700	−	0.254438i	−0.703895	+	0.710304i	$0.748557\pi$
$354$		0			0
$355$	15.5074	+	26.8596i	0.823047	+	1.42556i
$356$			11.9479i			0.633236i
$357$		0			0
$358$		−	4.10041i		−	0.216714i
$359$	−4.14103	−	7.17248i	−0.218555	−	0.378549i	0.735811	−	0.677187i	$-0.236801\pi$
$359$	−4.14103	−	7.17248i	−0.218555	−	0.378549i	−0.954366	+	0.298638i	$0.903468\pi$
$360$		0			0
$361$	−7.27300	+	12.5972i	−0.382790	+	0.663011i
$362$	5.50322	+	9.53186i	0.289243	+	0.500983i
$363$		0			0
$364$	−7.76872	−	3.37824i	−0.407191	−	0.177068i
$365$	−17.6558			−0.924144
$366$		0			0
$367$	18.6919	−	32.3753i	0.975710	−	1.68998i	0.298138	−	0.954523i	$-0.403634\pi$
$367$	18.6919	−	32.3753i	0.975710	−	1.68998i	0.677572	−	0.735457i	$-0.263032\pi$
$368$	−0.902766	−	0.521212i	−0.0470599	−	0.0271701i
$369$		0			0
$370$			25.7514i			1.33875i
$371$	28.9411	+	12.5851i	1.50255	+	0.653386i
$372$		0			0
$373$	20.6889	−	11.9447i	1.07123	−	0.618475i	0.142713	−	0.989764i	$-0.454417\pi$
$373$	20.6889	−	11.9447i	1.07123	−	0.618475i	0.928517	+	0.371289i	$0.121084\pi$
$374$	5.64049	−	12.4373i	0.291663	−	0.643119i
$375$		0			0
$376$	7.27267	−	4.19888i	0.375059	−	0.216541i
$377$			30.1285i			1.55170i
$378$		0			0
$379$	17.9926			0.924217			0.462109	−	0.886823i	$-0.347093\pi$
$379$	17.9926			0.924217			0.462109	+	0.886823i	$0.347093\pi$
$380$	2.95043	+	5.11029i	0.151354	+	0.262153i
$381$		0			0
$382$	18.8331	+	10.8733i	0.963583	+	0.556325i
$383$	−14.6369	+	8.45064i	−0.747913	+	0.431808i	−0.824939	−	0.565221i	$-0.808791\pi$
$383$	−14.6369	+	8.45064i	−0.747913	+	0.431808i	0.0770265	+	0.997029i	$0.475457\pi$
$384$		0			0
$385$	−5.14431	−	23.9896i	−0.262178	−	1.22262i
$386$		−	22.3009i		−	1.13508i
$387$		0			0
$388$	8.84554	−	15.3209i	0.449064	−	0.777802i
$389$	9.20118	+	5.31230i	0.466518	+	0.269344i	0.714781	−	0.699348i	$-0.246526\pi$
$389$	9.20118	+	5.31230i	0.466518	+	0.269344i	−0.248263	+	0.968693i	$0.579860\pi$
$390$		0			0
$391$		−	4.29230i		−	0.217071i
$392$	6.82070	−	1.57420i	0.344497	−	0.0795092i
$393$		0			0
$394$	−5.50179	−	9.52937i	−0.277176	−	0.480083i
$395$	20.0726	−	34.7668i	1.00996	−	1.74931i
$396$		0			0
$397$	11.4791	+	19.8824i	0.576120	+	0.997870i	0.995919	+	0.0902525i	$0.0287674\pi$
$397$	11.4791	+	19.8824i	0.576120	+	0.997870i	−0.419799	+	0.907617i	$0.637899\pi$
$398$	16.4501			0.824570
$399$		0			0
$400$	−2.81773			−0.140887
$401$	8.28001	−	4.78047i	0.413484	−	0.238725i	−0.278802	−	0.960349i	$-0.589937\pi$
$401$	8.28001	−	4.78047i	0.413484	−	0.238725i	0.692286	+	0.721624i	$0.256604\pi$
$402$		0			0
$403$	−19.8973	−	11.4877i	−0.991156	−	0.572244i
$404$	−0.117005	−	0.202659i	−0.00582123	−	0.0100827i
$405$		0			0
$406$	−14.8077	−	20.0128i	−0.734891	−	0.993218i
$407$	30.4002	−	2.98347i	1.50688	−	0.147885i
$408$		0			0
$409$	−11.3509	−	6.55346i	−0.561267	−	0.324048i	0.192387	−	0.981319i	$-0.438377\pi$
$409$	−11.3509	−	6.55346i	−0.561267	−	0.324048i	−0.753654	+	0.657271i	$0.771711\pi$
$410$	−0.268224	−	0.154859i	−0.0132466	−	0.00764795i
$411$		0			0
$412$	12.5438			0.617991
$413$	−17.7892	−	7.73569i	−0.875351	−	0.380648i
$414$		0			0
$415$	−34.4655	+	19.8987i	−1.69184	+	0.976786i
$416$	2.77293	+	1.60095i	0.135954	+	0.0784932i
$417$		0			0
$418$	5.69099	−	4.07511i	0.278356	−	0.199320i
$419$			4.51379i			0.220513i	0.993903	+	0.110256i	$0.0351672\pi$
$419$			4.51379i			0.220513i	−0.993903	+	0.110256i	$0.964833\pi$
$420$		0			0
$421$	−37.3188			−1.81881			−0.909403	−	0.415917i	$-0.863461\pi$
$421$	−37.3188			−1.81881			−0.909403	+	0.415917i	$0.863461\pi$
$422$	0.535916	−	0.309411i	0.0260880	−	0.0150619i
$423$		0			0
$424$	−10.3301	−	5.96410i	−0.501675	−	0.289642i
$425$	−5.80117	−	10.0479i	−0.281398	−	0.487395i
$426$		0			0
$427$	−22.6429	+	16.7537i	−1.09577	+	0.810770i
$428$	−13.0909			−0.632772
$429$		0			0
$430$	−5.87745	+	10.1800i	−0.283436	+	0.490925i
$431$	−13.8494	+	23.9878i	−0.667100	+	1.15545i	0.311611	+	0.950210i	$0.399131\pi$
$431$	−13.8494	+	23.9878i	−0.667100	+	1.15545i	−0.978711	+	0.205242i	$0.934202\pi$
$432$		0			0
$433$	8.18187			0.393196			0.196598	−	0.980484i	$-0.437011\pi$
$433$	8.18187			0.393196			0.196598	+	0.980484i	$0.437011\pi$
$434$	18.8627	−	2.14850i	0.905441	−	0.103131i
$435$		0			0
$436$	5.63480	−	3.25325i	0.269858	−	0.155802i
$437$	1.09999	−	1.90524i	0.0526197	−	0.0911400i
$438$		0			0
$439$	1.16163	−	0.670668i	0.0554416	−	0.0320092i	−0.472023	−	0.881586i	$-0.656476\pi$
$439$	1.16163	−	0.670668i	0.0554416	−	0.0320092i	0.527465	+	0.849577i	$0.323143\pi$
$440$	0.905736	+	9.22901i	0.0431793	+	0.439976i
$441$		0			0
$442$			13.1842i			0.627109i
$443$	−23.5122	+	13.5748i	−1.11710	+	0.644958i	−0.940659	−	0.339354i	$-0.889792\pi$
$443$	−23.5122	+	13.5748i	−1.11710	+	0.644958i	−0.176441	+	0.984311i	$0.556458\pi$
$444$		0			0
$445$	16.7033	−	28.9309i	0.791810	−	1.37146i
$446$	−5.17766	−	8.96797i	−0.245169	−	0.424646i
$447$		0			0
$448$	−2.62875	+	0.299420i	−0.124197	+	0.0141463i
$449$		−	37.3766i		−	1.76391i	−0.471334	−	0.881955i	$-0.656227\pi$
$449$		−	37.3766i		−	1.76391i	0.471334	−	0.881955i	$-0.343773\pi$
$450$		0			0
$451$	−0.151739	+	0.334586i	−0.00714513	+	0.0157550i
$452$	−0.754977	−	0.435886i	−0.0355111	−	0.0205024i
$453$		0			0
$454$	−12.9313			−0.606895
$455$	14.0886	+	19.0409i	0.660481	+	0.892652i
$456$		0			0
$457$	20.4149	−	11.7865i	0.954967	−	0.551350i	0.0603464	−	0.998177i	$-0.480779\pi$
$457$	20.4149	−	11.7865i	0.954967	−	0.551350i	0.894620	+	0.446827i	$0.147446\pi$
$458$	−2.73849	+	4.74320i	−0.127961	+	0.221635i
$459$		0			0
$460$	1.45732	+	2.52415i	0.0679479	+	0.117689i
$461$	38.3140			1.78446			0.892231	−	0.451580i	$-0.149139\pi$
$461$	38.3140			1.78446			0.892231	+	0.451580i	$0.149139\pi$
$462$		0			0
$463$	−9.80424			−0.455642			−0.227821	−	0.973703i	$-0.573160\pi$
$463$	−9.80424			−0.455642			−0.227821	+	0.973703i	$0.573160\pi$
$464$	4.70478	+	8.14891i	0.218414	+	0.378304i
$465$		0			0
$466$	13.7588	−	23.8310i	0.637366	−	1.10395i
$467$	10.8457	−	6.26175i	0.501878	−	0.289759i	−0.227611	−	0.973752i	$-0.573091\pi$
$467$	10.8457	−	6.26175i	0.501878	−	0.289759i	0.729489	+	0.683993i	$0.239758\pi$
$468$		0			0
$469$	8.38029	−	19.2716i	0.386966	−	0.889880i
$470$	−23.4803			−1.08307
$471$		0			0
$472$	6.34962	+	3.66595i	0.292265	+	0.168739i
$473$	12.6987	+	5.75904i	0.583887	+	0.264801i
$474$		0			0
$475$		−	5.94668i		−	0.272852i
$476$	−6.47982	−	8.75758i	−0.297002	−	0.401403i
$477$		0			0
$478$	−6.66695	−	11.5475i	−0.304939	−	0.528170i
$479$	−7.84197	+	13.5827i	−0.358309	+	0.620609i	−0.987678	−	0.156497i	$-0.949980\pi$
$479$	−7.84197	+	13.5827i	−0.358309	+	0.620609i	0.629370	+	0.777106i	$0.283313\pi$
$480$		0			0
$481$	−25.5388	+	14.7448i	−1.16447	+	0.672307i
$482$		−	18.1328i		−	0.825928i
$483$		0			0
$484$	10.7901	−	2.13848i	0.490460	−	0.0972038i
$485$	−42.8376	+	24.7323i	−1.94516	+	1.12304i
$486$		0			0
$487$	19.0262	−	32.9544i	0.862161	−	1.49331i	−0.00767777	−	0.999971i	$-0.502444\pi$
$487$	19.0262	−	32.9544i	0.862161	−	1.49331i	0.869839	−	0.493336i	$-0.164223\pi$
$488$	9.21987	−	5.32310i	0.417364	−	0.240965i
$489$		0			0
$490$	−18.7166	−	5.72359i	−0.845528	−	0.258565i
$491$	3.63565			0.164075			0.0820373	−	0.996629i	$-0.473857\pi$
$491$	3.63565			0.164075			0.0820373	+	0.996629i	$0.473857\pi$
$492$		0			0
$493$	−19.3725	+	33.5541i	−0.872492	+	1.51120i
$494$	−3.37873	+	5.85213i	−0.152016	+	0.263300i
$495$		0			0
$496$	−7.17555			−0.322192
$497$	−3.32131	−	29.1594i	−0.148981	−	1.30798i
$498$		0			0
$499$	9.18656	+	15.9116i	0.411247	+	0.712301i	0.995026	−	0.0996117i	$-0.0317601\pi$
$499$	9.18656	+	15.9116i	0.411247	+	0.712301i	−0.583779	+	0.811912i	$0.698427\pi$
$500$	−5.28420	−	3.05083i	−0.236316	−	0.136437i
$501$		0			0
$502$	16.0682	−	9.27699i	0.717160	−	0.414053i
$503$	−34.2342			−1.52643			−0.763213	−	0.646146i	$-0.776380\pi$
$503$	−34.2342			−1.52643			−0.763213	+	0.646146i	$0.776380\pi$
$504$		0			0
$505$			0.654298i			0.0291159i
$506$	2.81098	−	2.01284i	0.124963	−	0.0894816i
$507$		0			0
$508$	7.93149	+	4.57925i	0.351903	+	0.203171i
$509$	−9.23009	+	5.32899i	−0.409116	+	0.236203i	−0.690410	−	0.723418i	$-0.742570\pi$
$509$	−9.23009	+	5.32899i	−0.409116	+	0.236203i	0.281294	+	0.959622i	$0.409237\pi$
$510$		0			0
$511$	15.3210	+	6.66236i	0.677760	+	0.294725i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−23.4582	−	13.5436i	−1.03470	−	0.597382i
$515$	−30.3740	−	17.5364i	−1.33844	−	0.772747i
$516$		0			0
$517$	2.72035	+	27.7190i	0.119641	+	1.21908i
$518$	9.71725	−	22.3461i	0.426951	−	0.981831i
$519$		0			0
$520$	−4.47630	−	7.75318i	−0.196299	−	0.339999i
$521$	18.3680	+	10.6048i	0.804716	+	0.464603i	0.845118	−	0.534581i	$-0.179530\pi$
$521$	18.3680	+	10.6048i	0.804716	+	0.464603i	−0.0404016	+	0.999184i	$0.512864\pi$
$522$		0			0
$523$	−18.1257	+	10.4649i	−0.792583	+	0.457598i	−0.840871	−	0.541236i	$-0.817957\pi$
$523$	−18.1257	+	10.4649i	−0.792583	+	0.457598i	0.0482882	+	0.998833i	$0.484623\pi$
$524$	7.74679			0.338420
$525$		0			0
$526$	11.0684			0.482603
$527$	−14.7731	−	25.5877i	−0.643525	−	1.11462i
$528$		0			0
$529$	−10.9567	+	18.9775i	−0.476377	+	0.825110i
$530$	16.6758	+	28.8833i	0.724348	+	1.25461i
$531$		0			0
$532$	−0.631910	−	5.54785i	−0.0273968	−	0.240530i
$533$		−	0.354679i		−	0.0153629i
$534$		0			0
$535$	31.6986	+	18.3012i	1.37045	+	0.791230i
$536$	−3.97143	+	6.87872i	−0.171540	+	0.297116i
$537$		0			0
$538$		−	9.75172i		−	0.420426i
$539$	−4.58839	+	22.7584i	−0.197636	+	0.980275i
$540$		0			0
$541$	0.708020	−	0.408775i	0.0304402	−	0.0175746i	−0.484703	−	0.874679i	$-0.661072\pi$
$541$	0.708020	−	0.408775i	0.0304402	−	0.0175746i	0.515143	+	0.857104i	$0.327739\pi$
$542$	2.91324	+	1.68196i	0.125134	+	0.0722463i
$543$		0			0
$544$	2.05881	+	3.56596i	0.0882706	+	0.152889i
$545$	−18.1923			−0.779273
$546$		0			0
$547$			16.2530i			0.694930i	0.937693	+	0.347465i	$0.112957\pi$
$547$			16.2530i			0.694930i	−0.937693	+	0.347465i	$0.887043\pi$
$548$	6.78091	−	3.91496i	0.289666	−	0.167239i
$549$		0			0
$550$	3.85986	−	8.51101i	0.164585	−	0.362911i
$551$	−17.1979	+	9.92919i	−0.732654	+	0.422998i
$552$		0			0
$553$	−30.5374	+	22.5949i	−1.29858	+	0.960833i
$554$		−	16.5955i		−	0.705077i
$555$		0			0
$556$	2.69360	+	1.55515i	0.114234	+	0.0659530i
$557$	3.81751	−	6.61212i	0.161753	−	0.280165i	−0.773744	−	0.633498i	$-0.781619\pi$
$557$	3.81751	−	6.61212i	0.161753	−	0.280165i	0.935498	+	0.353333i	$0.114952\pi$
$558$		0			0
$559$	−13.4613			−0.569353
$560$	6.78392	+	2.95000i	0.286673	+	0.124660i
$561$		0			0
$562$	−2.79320	−	4.83797i	−0.117824	−	0.204078i
$563$	−22.5824	+	39.1138i	−0.951734	+	1.64845i	−0.210061	+	0.977688i	$0.567366\pi$
$563$	−22.5824	+	39.1138i	−0.951734	+	1.64845i	−0.741672	+	0.670763i	$0.765967\pi$
$564$		0			0
$565$	1.21875	+	2.11093i	0.0512731	+	0.0888075i
$566$		−	2.70029i		−	0.113502i
$567$		0			0
$568$			11.0925i			0.465430i
$569$	16.3937	+	28.3948i	0.687261	+	1.19037i	0.972720	+	0.231981i	$0.0745207\pi$
$569$	16.3937	+	28.3948i	0.687261	+	1.19037i	−0.285459	+	0.958391i	$0.592146\pi$
$570$		0			0
$571$	4.58774	+	2.64873i	0.191991	+	0.110846i	0.592914	−	0.805266i	$-0.297977\pi$
$571$	4.58774	+	2.64873i	0.191991	+	0.110846i	−0.400923	+	0.916112i	$0.631311\pi$
$572$	−8.63420	+	6.18263i	−0.361014	+	0.258509i
$573$		0			0
$574$	0.174319	+	0.235594i	0.00727592	+	0.00983352i
$575$		−	2.93727i		−	0.122493i
$576$		0			0
$577$	−6.83877	+	11.8451i	−0.284702	+	0.493118i	−0.972537	−	0.232749i	$-0.925228\pi$
$577$	−6.83877	+	11.8451i	−0.284702	+	0.493118i	0.687835	+	0.725867i	$0.258561\pi$
$578$	0.0226302	−	0.0391967i	0.000941294	−	0.00163037i
$579$		0			0
$580$		−	26.3093i		−	1.09243i
$581$	37.4165	−	4.26181i	1.55230	−	0.176810i
$582$		0			0
$583$	32.1653	−	23.0324i	1.33215	−	0.953906i
$584$	−5.46860	−	3.15730i	−0.226292	−	0.130650i
$585$		0			0
$586$	−7.90923	−	13.6992i	−0.326727	−	0.565909i
$587$			24.5620i			1.01378i	0.862011	+	0.506890i	$0.169205\pi$
$587$			24.5620i			1.01378i	−0.862011	+	0.506890i	$0.830795\pi$
$588$		0			0
$589$		−	15.1436i		−	0.623982i
$590$	−10.2501	−	17.7537i	−0.421989	−	0.730907i
$591$		0			0
$592$	−4.60502	+	7.97612i	−0.189265	+	0.327817i
$593$	2.76466	+	4.78853i	0.113531	+	0.196641i	0.917192	−	0.398447i	$-0.130451\pi$
$593$	2.76466	+	4.78853i	0.113531	+	0.196641i	−0.803661	+	0.595088i	$0.797117\pi$
$594$		0			0
$595$	3.44720	+	30.2647i	0.141321	+	1.24073i
$596$	−8.17082			−0.334690
$597$		0			0
$598$	−1.66887	+	2.89057i	−0.0682453	+	0.118204i
$599$	−20.9741	−	12.1094i	−0.856977	−	0.494776i	0.00602174	−	0.999982i	$-0.498083\pi$
$599$	−20.9741	−	12.1094i	−0.856977	−	0.494776i	−0.862999	+	0.505206i	$0.831417\pi$
$600$		0			0
$601$		−	16.7793i		−	0.684443i	−0.939619	−	0.342222i	$-0.888821\pi$
$601$		−	16.7793i		−	0.684443i	0.939619	−	0.342222i	$-0.111179\pi$
$602$	8.94163	−	6.61600i	0.364434	−	0.269648i
$603$		0			0
$604$	5.93139	−	3.42449i	0.241345	−	0.139341i
$605$	−29.1171	−	9.90653i	−1.18378	−	0.402758i
$606$		0			0
$607$	30.9524	−	17.8704i	1.25632	−	0.725337i	0.283963	−	0.958835i	$-0.408351\pi$
$607$	30.9524	−	17.8704i	1.25632	−	0.725337i	0.972357	+	0.233498i	$0.0750174\pi$
$608$			2.11045i			0.0855900i
$609$		0			0
$610$	−29.7670			−1.20523
$611$	−13.4444	−	23.2864i	−0.543903	−	0.942068i
$612$		0			0
$613$	7.82971	+	4.52049i	0.316239	+	0.182581i	0.649715	−	0.760178i	$-0.274888\pi$
$613$	7.82971	+	4.52049i	0.316239	+	0.182581i	−0.333476	+	0.942759i	$0.608222\pi$
$614$	10.6359	−	6.14066i	0.429231	−	0.247817i
$615$		0			0
$616$	2.69658	−	8.35036i	0.108648	−	0.336445i
$617$			11.5919i			0.466672i	0.972396	+	0.233336i	$0.0749643\pi$
$617$			11.5919i			0.466672i	−0.972396	+	0.233336i	$0.925036\pi$
$618$		0			0
$619$	0.200558	−	0.347377i	0.00806111	−	0.0139622i	−0.861967	−	0.506965i	$-0.830767\pi$
$619$	0.200558	−	0.347377i	0.00806111	−	0.0139622i	0.870028	+	0.493003i	$0.164101\pi$
$620$	17.3750	+	10.0315i	0.697799	+	0.402874i
$621$		0			0
$622$			20.3911i			0.817609i
$623$	−25.4114	+	18.8022i	−1.01809	+	0.753292i
$624$		0			0
$625$	15.5745	+	26.9759i	0.622981	+	1.07903i
$626$	1.62210	−	2.80957i	0.0648323	−	0.112293i
$627$		0			0
$628$	4.04332	+	7.00324i	0.161346	+	0.279460i
$629$	−37.9234			−1.51210
$630$		0			0
$631$	32.7927			1.30546			0.652728	−	0.757592i	$-0.273624\pi$
$631$	32.7927			1.30546			0.652728	+	0.757592i	$0.273624\pi$
$632$	12.4344	−	7.17899i	0.494613	−	0.285565i
$633$		0			0
$634$	−9.57584	−	5.52861i	−0.380305	−	0.219569i
$635$	−12.8037	−	22.1766i	−0.508098	−	0.880052i
$636$		0			0
$637$	−5.04045	−	21.8392i	−0.199710	−	0.865302i
$638$	−31.0588	+	3.04811i	−1.22963	+	0.120676i
$639$		0			0
$640$	−2.42143	−	1.39801i	−0.0957152	−	0.0552612i
$641$	−27.3662	−	15.7999i	−1.08090	−	0.624058i	−0.149761	−	0.988722i	$-0.547850\pi$
$641$	−27.3662	−	15.7999i	−1.08090	−	0.624058i	−0.931139	+	0.364664i	$0.881184\pi$
$642$		0			0
$643$	−4.86178			−0.191730			−0.0958650	−	0.995394i	$-0.530562\pi$
$643$	−4.86178			−0.191730			−0.0958650	+	0.995394i	$0.530562\pi$
$644$	−0.312123	−	2.74028i	−0.0122994	−	0.107982i
$645$		0			0
$646$	−7.52577	+	4.34501i	−0.296098	+	0.170952i
$647$	18.9738	+	10.9545i	0.745937	+	0.430667i	0.824224	−	0.566264i	$-0.191612\pi$
$647$	18.9738	+	10.9545i	0.745937	+	0.430667i	−0.0782867	+	0.996931i	$0.524945\pi$
$648$		0			0
$649$	−19.7711	+	14.1573i	−0.776082	+	0.555724i
$650$			9.02212i			0.353877i
$651$		0			0
$652$	1.36471			0.0534463
$653$	31.4813	−	18.1757i	1.23196	−	0.711271i	0.264520	−	0.964380i	$-0.414786\pi$
$653$	31.4813	−	18.1757i	1.23196	−	0.711271i	0.967438	+	0.253109i	$0.0814530\pi$
$654$		0			0
$655$	−18.7583	−	10.8301i	−0.732947	−	0.423167i
$656$	−0.0553856	−	0.0959306i	−0.00216244	−	0.00374546i
$657$		0			0
$658$	20.3753	+	8.86024i	0.794312	+	0.345408i
$659$	−1.25809			−0.0490083			−0.0245041	−	0.999700i	$-0.507801\pi$
$659$	−1.25809			−0.0490083			−0.0245041	+	0.999700i	$0.507801\pi$
$660$		0			0
$661$	−19.0453	+	32.9875i	−0.740778	+	1.28307i	0.211363	+	0.977408i	$0.432210\pi$
$661$	−19.0453	+	32.9875i	−0.740778	+	1.28307i	−0.952141	+	0.305658i	$0.901124\pi$
$662$	7.27038	−	12.5927i	0.282571	−	0.489428i
$663$		0			0
$664$	−14.2335			−0.552369
$665$	−6.22583	+	14.3171i	−0.241427	+	0.555194i
$666$		0			0
$667$	−8.49463	+	4.90437i	−0.328913	+	0.189898i
$668$	−3.67328	+	6.36230i	−0.142123	+	0.246165i
$669$		0			0
$670$	19.2331	−	11.1042i	0.743038	−	0.428993i
$671$	3.44870	+	35.1406i	0.133136	+	1.35659i
$672$		0			0
$673$		−	19.4116i		−	0.748263i	−0.927376	−	0.374131i	$-0.877941\pi$
$673$		−	19.4116i		−	0.748263i	0.927376	−	0.374131i	$-0.122059\pi$
$674$	−17.3604	+	10.0230i	−0.668696	+	0.386072i
$675$		0			0
$676$	−1.37389	+	2.37965i	−0.0528420	+	0.0915250i
$677$	−5.25697	−	9.10535i	−0.202042	−	0.349947i	0.747144	−	0.664662i	$-0.231424\pi$
$677$	−5.25697	−	9.10535i	−0.202042	−	0.349947i	−0.949186	+	0.314715i	$0.898091\pi$
$678$		0			0
$679$	46.5055	−	5.29706i	1.78472	−	0.203283i
$680$		−	11.5129i		−	0.441501i
$681$		0			0
$682$	9.82939	−	21.6739i	0.376387	−	0.829935i
$683$	−37.1706	−	21.4605i	−1.42230	−	0.821163i	−0.425800	−	0.904817i	$-0.640007\pi$
$683$	−37.1706	−	21.4605i	−1.42230	−	0.821163i	−0.996495	+	0.0836546i	$0.973341\pi$
$684$		0			0
$685$	−21.8926			−0.836474
$686$	14.0817	+	12.0294i	0.537642	+	0.459283i
$687$		0			0
$688$	−3.64090	+	2.10208i	−0.138808	+	0.0801409i
$689$	−19.0965	+	33.0761i	−0.727519	+	1.26010i
$690$		0			0
$691$	23.5279	+	40.7515i	0.895043	+	1.55026i	0.833751	+	0.552141i	$0.186189\pi$
$691$	23.5279	+	40.7515i	0.895043	+	1.55026i	0.0612926	+	0.998120i	$0.480478\pi$
$692$	0.655347			0.0249126
$693$		0			0
$694$	−12.0889			−0.458887
$695$	−4.34823	−	7.53135i	−0.164938	−	0.285680i
$696$		0			0
$697$	0.228056	−	0.395005i	0.00863825	−	0.0149619i
$698$	4.26527	−	2.46255i	0.161443	−	0.0932091i
$699$		0			0
$700$	−4.43422	−	5.99292i	−0.167598	−	0.226511i
$701$	1.94709			0.0735406			0.0367703	−	0.999324i	$-0.488293\pi$
$701$	1.94709			0.0735406			0.0367703	+	0.999324i	$0.488293\pi$
$702$		0			0
$703$	−16.8332	−	9.71865i	−0.634876	−	0.366546i
$704$	−1.36985	+	3.02052i	−0.0516280	+	0.113840i
$705$		0			0
$706$			9.56093i			0.359830i
$707$	0.246898	−	0.567774i	0.00928555	−	0.0213534i
$708$		0			0
$709$	−11.4549	−	19.8405i	−0.430199	−	0.745126i	0.566691	−	0.823930i	$-0.308223\pi$
$709$	−11.4549	−	19.8405i	−0.430199	−	0.745126i	−0.996890	+	0.0788042i	$0.974890\pi$
$710$	15.5074	−	26.8596i	0.581982	−	1.00802i
$711$		0			0
$712$	10.3472	−	5.97394i	0.387776	−	0.223883i
$713$		−	7.47996i		−	0.280127i
$714$		0			0
$715$	29.5505	−	2.90008i	1.10512	−	0.108457i
$716$	−3.55106	+	2.05021i	−0.132709	+	0.0766199i
$717$		0			0
$718$	−4.14103	+	7.17248i	−0.154542	+	0.267674i
$719$	−1.87531	+	1.08271i	−0.0699372	+	0.0403782i	−0.534561	−	0.845130i	$-0.679523\pi$
$719$	−1.87531	+	1.08271i	−0.0699372	+	0.0403782i	0.464624	+	0.885508i	$0.346190\pi$
$720$		0			0
$721$	19.7400	+	26.6790i	0.735157	+	0.993577i
$722$	14.5460			0.541346
$723$		0			0
$724$	5.50322	−	9.53186i	0.204526	−	0.354249i
$725$	−13.2568	+	22.9615i	−0.492345	+	0.852767i
$726$		0			0
$727$	19.8670			0.736825			0.368412	−	0.929662i	$-0.379901\pi$
$727$	19.8670			0.736825			0.368412	+	0.929662i	$0.379901\pi$
$728$	0.958715	+	8.41703i	0.0355323	+	0.311956i
$729$		0			0
$730$	8.82788	+	15.2903i	0.326734	+	0.565921i
$731$	−14.9918	−	8.65553i	−0.554493	−	0.320137i
$732$		0			0
$733$	−31.7695	+	18.3421i	−1.17343	+	0.677483i	−0.954487	−	0.298254i	$-0.903596\pi$
$733$	−31.7695	+	18.3421i	−1.17343	+	0.677483i	−0.218948	+	0.975737i	$0.570262\pi$
$734$	−37.3838			−1.37986
$735$		0			0
$736$			1.04242i			0.0384243i
$737$	−15.3371	−	21.4186i	−0.564948	−	0.788963i
$738$		0			0
$739$	−31.5162	−	18.1959i	−1.15934	−	0.669346i	−0.208195	−	0.978087i	$-0.566759\pi$
$739$	−31.5162	−	18.1959i	−1.15934	−	0.669346i	−0.951146	+	0.308742i	$0.900092\pi$
$740$	22.3014	−	12.8757i	0.819816	−	0.473321i
$741$		0			0
$742$	−3.57154	−	31.3563i	−0.131115	−	1.15113i
$743$	−0.143528			−0.00526553			−0.00263276	−	0.999997i	$-0.500838\pi$
$743$	−0.143528			−0.00526553			−0.00263276	+	0.999997i	$0.500838\pi$
$744$		0			0
$745$	19.7850	+	11.4229i	0.724867	+	0.418502i
$746$	−20.6889	−	11.9447i	−0.757474	−	0.437328i
$747$		0			0
$748$	−13.5913	+	1.33385i	−0.496947	+	0.0487704i
$749$	−20.6009	−	27.8425i	−0.752741	−	1.01734i
$750$		0			0
$751$	2.63144	+	4.55779i	0.0960226	+	0.166316i	0.910035	−	0.414532i	$-0.136055\pi$
$751$	2.63144	+	4.55779i	0.0960226	+	0.166316i	−0.814012	+	0.580848i	$0.802721\pi$
$752$	−7.27267	−	4.19888i	−0.265207	−	0.153117i
$753$		0			0
$754$	26.0921	−	15.0643i	0.950217	−	0.548608i
$755$	−19.1499			−0.696936
$756$		0			0
$757$	−13.6449			−0.495932			−0.247966	−	0.968769i	$-0.579762\pi$
$757$	−13.6449			−0.495932			−0.247966	+	0.968769i	$0.579762\pi$
$758$	−8.99630	−	15.5820i	−0.326760	−	0.565965i
$759$		0			0
$760$	2.95043	−	5.11029i	0.107023	−	0.185370i
$761$	−14.3603	−	24.8727i	−0.520559	−	0.901635i	−0.999714	−	0.0239048i	$-0.992390\pi$
$761$	−14.3603	−	24.8727i	−0.520559	−	0.901635i	0.479155	−	0.877730i	$-0.340943\pi$
$762$		0			0
$763$	15.7866	+	6.86483i	0.571513	+	0.248523i
$764$		−	21.7465i		−	0.786763i
$765$		0			0
$766$	14.6369	+	8.45064i	0.528854	+	0.305334i
$767$	11.7380	−	20.3309i	0.423836	−	0.734106i
$768$		0			0
$769$		−	40.9742i		−	1.47757i	−0.673943	−	0.738783i	$-0.735401\pi$
$769$		−	40.9742i		−	1.47757i	0.673943	−	0.738783i	$-0.264599\pi$
$770$	−18.2035	+	16.4499i	−0.656007	+	0.592814i
$771$		0			0
$772$	−19.3131	+	11.1504i	−0.695094	+	0.401313i
$773$	−9.44578	−	5.45352i	−0.339741	−	0.196150i	0.320416	−	0.947277i	$-0.396177\pi$
$773$	−9.44578	−	5.45352i	−0.339741	−	0.196150i	−0.660158	+	0.751127i	$0.729510\pi$
$774$		0			0
$775$	−10.1094	−	17.5100i	−0.363140	−	0.628977i
$776$	−17.6911			−0.635073
$777$		0			0
$778$		−	10.6246i		−	0.380911i
$779$	0.202457	−	0.116888i	0.00725376	−	0.00418796i
$780$		0			0
$781$	−33.5050	−	15.1950i	−1.19890	−	0.543719i
$782$	−3.71724	+	2.14615i	−0.132928	+	0.0767462i
$783$		0			0
$784$	−4.77365	−	5.11979i	−0.170487	−	0.182850i
$785$		−	22.6104i		−	0.807001i
$786$		0			0
$787$	−16.7122	−	9.64880i	−0.595726	−	0.343943i	0.171632	−	0.985161i	$-0.445096\pi$
$787$	−16.7122	−	9.64880i	−0.595726	−	0.343943i	−0.767358	+	0.641219i	$0.778429\pi$
$788$	−5.50179	+	9.52937i	−0.195993	+	0.339470i
$789$		0			0
$790$	−40.1452			−1.42830
$791$	−0.261026	−	2.29167i	−0.00928102	−	0.0814826i
$792$		0			0
$793$	−17.0441	−	29.5212i	−0.605253	−	1.04833i
$794$	11.4791	−	19.8824i	0.407379	−	0.705600i
$795$		0			0
$796$	−8.22506	−	14.2462i	−0.291529	−	0.504944i
$797$		−	23.8010i		−	0.843075i	−0.906811	−	0.421538i	$-0.861491\pi$
$797$		−	23.8010i		−	0.843075i	0.906811	−	0.421538i	$-0.138509\pi$
$798$		0			0
$799$		−	34.5787i		−	1.22331i
$800$	1.40887	+	2.44023i	0.0498109	+	0.0862751i
$801$		0			0
$802$	−8.28001	−	4.78047i	−0.292377	−	0.168804i
$803$	17.0278	−	12.1930i	0.600899	−	0.430282i
$804$		0			0
$805$	−3.07515	+	7.07173i	−0.108385	+	0.249246i
$806$			22.9754i			0.809275i
$807$		0			0
$808$	−0.117005	+	0.202659i	−0.00411623	+	0.00712952i
$809$	10.7545	−	18.6274i	0.378109	−	0.654905i	−0.612678	−	0.790333i	$-0.709908\pi$
$809$	10.7545	−	18.6274i	0.378109	−	0.654905i	0.990787	+	0.135428i	$0.0432410\pi$
$810$		0			0
$811$		−	52.4205i		−	1.84073i	−0.391059	−	0.920366i	$-0.627891\pi$
$811$		−	52.4205i		−	1.84073i	0.391059	−	0.920366i	$-0.372109\pi$
$812$	−9.92776	+	22.8302i	−0.348396	+	0.801183i
$813$		0			0
$814$	−17.7839	−	24.8356i	−0.623324	−	0.870487i
$815$	−3.30455	−	1.90788i	−0.115753	−	0.0668302i
$816$		0			0
$817$	−4.43632	−	7.68394i	−0.155207	−	0.268827i
$818$			13.1069i			0.458273i
$819$		0			0
$820$			0.309718i			0.0108158i
$821$	−24.4907	−	42.4191i	−0.854731	−	1.48044i	−0.876894	−	0.480683i	$-0.840389\pi$
$821$	−24.4907	−	42.4191i	−0.854731	−	1.48044i	0.0221630	−	0.999754i	$-0.492945\pi$
$822$		0			0
$823$	−3.61437	+	6.26027i	−0.125989	+	0.218219i	−0.922119	−	0.386906i	$-0.873544\pi$
$823$	−3.61437	+	6.26027i	−0.125989	+	0.218219i	0.796130	+	0.605126i	$0.206877\pi$
$824$	−6.27192	−	10.8633i	−0.218493	−	0.378441i
$825$		0			0
$826$	2.19532	+	19.2738i	0.0763849	+	0.670620i
$827$	45.2699			1.57419			0.787095	−	0.616832i	$-0.211584\pi$
$827$	45.2699			1.57419			0.787095	+	0.616832i	$0.211584\pi$
$828$		0			0
$829$	24.5067	−	42.4468i	0.851152	−	1.47424i	−0.0290174	−	0.999579i	$-0.509238\pi$
$829$	24.5067	−	42.4468i	0.851152	−	1.47424i	0.880169	−	0.474660i	$-0.157429\pi$
$830$	34.4655	+	19.8987i	1.19631	+	0.690692i
$831$		0			0
$832$		−	3.20191i		−	0.111006i
$833$	8.42895	−	27.5633i	0.292046	−	0.955011i
$834$		0			0
$835$	17.7891	−	10.2706i	0.615618	−	0.355427i
$836$	−6.37465	−	2.89099i	−0.220472	−	0.0999869i
$837$		0			0
$838$	3.90905	−	2.25689i	0.135036	−	0.0779631i
$839$			2.44258i			0.0843273i	0.999111	+	0.0421637i	$0.0134251\pi$
$839$			2.44258i			0.0843273i	−0.999111	+	0.0421637i	$0.986575\pi$
$840$		0			0
$841$	59.5398			2.05309
$842$	18.6594	+	32.3190i	0.643045	+	1.11379i
$843$		0			0
$844$	−0.535916	−	0.309411i	−0.0184470	−	0.0106504i
$845$	6.65355	−	3.84143i	0.228889	−	0.132149i
$846$		0			0
$847$	21.5285	+	19.5838i	0.739728	+	0.672906i
$848$			11.9282i			0.409616i
$849$		0			0
$850$	−5.80117	+	10.0479i	−0.198978	+	0.344641i
$851$	−8.31450	−	4.80038i	−0.285017	−	0.164555i
$852$		0			0
$853$		−	37.5500i		−	1.28569i	−0.765997	−	0.642844i	$-0.777754\pi$
$853$		−	37.5500i		−	1.28569i	0.765997	−	0.642844i	$-0.222246\pi$
$854$	25.8306	+	11.2325i	0.883906	+	0.384368i
$855$		0			0
$856$	6.54545	+	11.3370i	0.223719	+	0.387492i
$857$	−21.4068	+	37.0777i	−0.731243	+	1.26655i	0.225109	+	0.974334i	$0.427726\pi$
$857$	−21.4068	+	37.0777i	−0.731243	+	1.26655i	−0.956352	+	0.292217i	$0.905607\pi$
$858$		0			0
$859$	−5.43313	−	9.41045i	−0.185376	−	0.321080i	0.758327	−	0.651874i	$-0.226017\pi$
$859$	−5.43313	−	9.41045i	−0.185376	−	0.321080i	−0.943703	+	0.330794i	$0.892684\pi$
$860$	11.7549			0.400839
$861$		0			0
$862$	27.6987			0.943422
$863$	−0.401363	+	0.231727i	−0.0136626	+	0.00788808i	−0.506816	−	0.862054i	$-0.669178\pi$
$863$	−0.401363	+	0.231727i	−0.0136626	+	0.00788808i	0.493153	+	0.869943i	$0.335844\pi$
$864$		0			0
$865$	−1.58687	−	0.916183i	−0.0539554	−	0.0311511i
$866$	−4.09094	−	7.08571i	−0.139016	−	0.240782i
$867$		0			0
$868$	−11.2920	−	15.2614i	−0.383276	−	0.518005i
$869$	4.65109	+	47.3924i	0.157777	+	1.60768i
$870$		0			0
$871$	22.0250	+	12.7162i	0.746290	+	0.430871i
$872$	−5.63480	−	3.25325i	−0.190818	−	0.110169i
$873$		0			0
$874$	−2.19998			−0.0744155
$875$	−1.82696	−	16.0398i	−0.0617625	−	0.542243i
$876$		0			0
$877$	−15.8492	+	9.15055i	−0.535190	+	0.308992i	−0.743127	−	0.669150i	$-0.766658\pi$
$877$	−15.8492	+	9.15055i	−0.535190	+	0.308992i	0.207937	+	0.978142i	$0.433325\pi$
$878$	−1.16163	−	0.670668i	−0.0392031	−	0.0226339i
$879$		0			0
$880$	7.53969	−	5.39890i	0.254163	−	0.181997i
$881$		−	26.3700i		−	0.888426i	−0.895921	−	0.444213i	$-0.853483\pi$
$881$		−	26.3700i		−	0.888426i	0.895921	−	0.444213i	$-0.146517\pi$
$882$		0			0
$883$	−10.2737			−0.345738			−0.172869	−	0.984945i	$-0.555304\pi$
$883$	−10.2737			−0.345738			−0.172869	+	0.984945i	$0.555304\pi$
$884$	11.4179	−	6.59211i	0.384024	−	0.221717i
$885$		0			0
$886$	23.5122	+	13.5748i	0.789909	+	0.456054i
$887$	−8.89664	−	15.4094i	−0.298720	−	0.517398i	0.677123	−	0.735870i	$-0.263226\pi$
$887$	−8.89664	−	15.4094i	−0.298720	−	0.517398i	−0.975843	+	0.218471i	$0.929893\pi$
$888$		0			0
$889$	2.74224	+	24.0754i	0.0919716	+	0.807464i
$890$	−33.4065			−1.11979
$891$		0			0
$892$	−5.17766	+	8.96797i	−0.173361	+	0.300270i
$893$	8.86152	−	15.3486i	0.296539	−	0.513621i
$894$		0			0
$895$	11.4648			0.383228
$896$	1.57368	+	2.12686i	0.0525730	+	0.0710533i
$897$		0			0
$898$	−32.3691	+	18.6883i	−1.08017	+	0.623636i
$899$	−33.7594	+	58.4729i	−1.12594	+	1.95018i
$900$		0			0
$901$	−42.5355	+	24.5579i	−1.41706	+	0.818141i
$902$	0.365630	−	0.0358829i	0.0121741	−	0.00119477i
$903$		0			0
$904$			0.871772i			0.0289947i
$905$	−26.6513	+	15.3871i	−0.885918	+	0.511485i
$906$		0			0
$907$	−16.7926	+	29.0857i	−0.557590	+	0.965775i	0.440107	+	0.897945i	$0.354941\pi$
$907$	−16.7926	+	29.0857i	−0.557590	+	0.965775i	−0.997697	+	0.0678291i	$0.978393\pi$
$908$	6.46564	+	11.1988i	0.214570	+	0.371646i
$909$		0			0
$910$	9.44564	−	21.7215i	0.313120	−	0.720061i
$911$		−	2.04771i		−	0.0678437i	−0.999424	−	0.0339218i	$-0.989200\pi$
$911$		−	2.04771i		−	0.0678437i	0.999424	−	0.0339218i	$-0.0107997\pi$
$912$		0			0
$913$	19.4978	−	42.9927i	0.645282	−	1.42285i
$914$	−20.4149	−	11.7865i	−0.675263	−	0.389864i
$915$		0			0
$916$	5.47697			0.180964
$917$	12.1910	+	16.4763i	0.402582	+	0.544096i
$918$		0			0
$919$	−37.2849	+	21.5264i	−1.22992	+	0.710092i	−0.967012	−	0.254731i	$-0.918013\pi$
$919$	−37.2849	+	21.5264i	−1.22992	+	0.710092i	−0.262903	+	0.964822i	$0.584680\pi$
$920$	1.45732	−	2.52415i	0.0480464	−	0.0832188i
$921$		0			0
$922$	−19.1570	−	33.1809i	−0.630902	−	1.09275i
$923$	35.5171			1.16906
$924$		0			0
$925$	−25.9514			−0.853277
$926$	4.90212	+	8.49072i	0.161094	+	0.279022i
$927$		0			0
$928$	4.70478	−	8.14891i	0.154442	−	0.267501i
$929$	11.1033	−	6.41047i	0.364286	−	0.210321i	−0.306673	−	0.951815i	$-0.599216\pi$
$929$	11.1033	−	6.41047i	0.364286	−	0.210321i	0.670959	+	0.741494i	$0.265883\pi$
$930$		0			0
$931$	10.8051	−	10.0745i	0.354122	−	0.330180i
$932$	−27.5177			−0.901372
$933$		0			0
$934$	−10.8457	−	6.26175i	−0.354881	−	0.204891i
$935$	34.7750	+	15.7709i	1.13726	+	0.515765i
$936$		0			0
$937$		−	47.4540i		−	1.55025i	−0.631805	−	0.775127i	$-0.717686\pi$
$937$		−	47.4540i		−	1.55025i	0.631805	−	0.775127i	$-0.282314\pi$
$938$	−20.8798	+	2.37825i	−0.681751	+	0.0776527i
$939$		0			0
$940$	11.7402	+	20.3345i	0.382922	+	0.663240i
$941$	−5.71859	+	9.90490i	−0.186421	+	0.322890i	−0.944054	−	0.329790i	$-0.893022\pi$
$941$	−5.71859	+	9.90490i	−0.186421	+	0.322890i	0.757634	+	0.652680i	$0.226355\pi$
$942$		0			0
$943$	0.100000	−	0.0577353i	0.00325646	−	0.00188012i
$944$		−	7.33191i		−	0.238633i
$945$		0			0
$946$	−1.36188	−	13.8769i	−0.0442786	−	0.451178i
$947$	−4.81239	+	2.77843i	−0.156382	+	0.0902869i	−0.576149	−	0.817345i	$-0.695445\pi$
$947$	−4.81239	+	2.77843i	−0.156382	+	0.0902869i	0.419767	+	0.907632i	$0.362112\pi$
$948$		0			0
$949$	−10.1094	+	17.5100i	−0.328165	+	0.568398i
$950$	−5.14998	+	2.97334i	−0.167087	+	0.0964679i
$951$		0			0
$952$	−4.34438	+	9.99047i	−0.140802	+	0.323793i
$953$	−25.6550			−0.831045			−0.415523	−	0.909583i	$-0.636401\pi$
$953$	−25.6550			−0.831045			−0.415523	+	0.909583i	$0.636401\pi$
$954$		0			0
$955$	−30.4019	+	52.6576i	−0.983782	+	1.70396i
$956$	−6.66695	+	11.5475i	−0.215625	+	0.373473i
$957$		0			0
$958$	15.6839			0.506725
$959$	18.9976	+	8.26113i	0.613464	+	0.266766i
$960$		0			0
$961$	−10.2442	−	17.7435i	−0.330459	−	0.572372i
$962$	25.5388	+	14.7448i	0.823404	+	0.475393i
$963$		0			0
$964$	−15.7035	+	9.06641i	−0.505775	+	0.292009i
$965$	62.3537			2.00724
$966$		0			0
$967$			44.1653i			1.42026i	0.704071	+	0.710130i	$0.251364\pi$
$967$			44.1653i			1.42026i	−0.704071	+	0.710130i	$0.748636\pi$
$968$	−7.24705	−	8.27528i	−0.232929	−	0.265978i
$969$		0			0
$970$	42.8376	+	24.7323i	1.37543	+	0.794107i
$971$	47.3097	−	27.3143i	1.51824	−	0.876557i	0.518472	−	0.855094i	$-0.326501\pi$
$971$	47.3097	−	27.3143i	1.51824	−	0.876557i	0.999770	−	0.0214630i	$-0.00683242\pi$
$972$		0			0
$973$	0.931285	+	8.17621i	0.0298556	+	0.262117i
$974$	−38.0525			−1.21928
$975$		0			0
$976$	−9.21987	−	5.32310i	−0.295121	−	0.170388i
$977$	−0.164978	−	0.0952499i	−0.00527810	−	0.00304731i	0.497359	−	0.867545i	$-0.334303\pi$
$977$	−0.164978	−	0.0952499i	−0.00527810	−	0.00304731i	−0.502637	+	0.864498i	$0.667637\pi$
$978$		0			0
$979$	3.87036	+	39.4371i	0.123697	+	1.26042i
$980$	4.40150	+	19.0708i	0.140601	+	0.609195i
$981$		0			0
$982$	−1.81783	−	3.14857i	−0.0580091	−	0.100475i
$983$	37.5517	+	21.6805i	1.19771	+	0.691500i	0.960045	−	0.279847i	$-0.0902837\pi$
$983$	37.5517	+	21.6805i	1.19771	+	0.691500i	0.237668	+	0.971346i	$0.423617\pi$
$984$		0			0
$985$	26.6443	−	15.3831i	0.848959	−	0.490147i
$986$	38.7449			1.23389
$987$		0			0
$988$	6.75746			0.214984
$989$	−2.19125	−	3.79536i	−0.0696778	−	0.120686i
$990$		0			0
$991$	−14.8052	+	25.6433i	−0.470302	+	0.814588i	−0.999423	−	0.0339589i	$-0.989188\pi$
$991$	−14.8052	+	25.6433i	−0.470302	+	0.814588i	0.529121	+	0.848546i	$0.322522\pi$
$992$	3.58777	+	6.21420i	0.113912	+	0.197301i
$993$		0			0
$994$	−23.5921	+	17.4560i	−0.748296	+	0.553672i
$995$			45.9949i			1.45814i
$996$		0			0
$997$	48.9359	+	28.2531i	1.54981	+	0.894786i	0.998155	+	0.0607158i	$0.0193383\pi$
$997$	48.9359	+	28.2531i	1.54981	+	0.894786i	0.551659	+	0.834070i	$0.313995\pi$
$998$	9.18656	−	15.9116i	0.290795	−	0.503673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.ba.a.1187.15	yes	32
3.2	odd	2		1386.2.ba.b.1187.2	yes	32
7.2	even	3	inner	1386.2.ba.a.989.2	✓	32
11.10	odd	2		1386.2.ba.b.1187.15	yes	32
21.2	odd	6		1386.2.ba.b.989.15	yes	32
33.32	even	2	inner	1386.2.ba.a.1187.2	yes	32
77.65	odd	6		1386.2.ba.b.989.2	yes	32
231.65	even	6	inner	1386.2.ba.a.989.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.2	✓	32	7.2	even	3	inner
1386.2.ba.a.989.15	yes	32	231.65	even	6	inner
1386.2.ba.a.1187.2	yes	32	33.32	even	2	inner
1386.2.ba.a.1187.15	yes	32	1.1	even	1	trivial
1386.2.ba.b.989.2	yes	32	77.65	odd	6
1386.2.ba.b.989.15	yes	32	21.2	odd	6
1386.2.ba.b.1187.2	yes	32	3.2	odd	2
1386.2.ba.b.1187.15	yes	32	11.10	odd	2

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.42143 - 1.39801i) q^{5} +(-2.62875 + 0.299420i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.42143 - 1.39801i) q^{5} +(-2.62875 + 0.299420i) q^{7} +1.00000 q^{8} +(-2.42143 - 1.39801i) q^{10} +(-1.36985 + 3.02052i) q^{11} -3.20191i q^{13} +(1.57368 + 2.12686i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.05881 - 3.56596i) q^{17} +(1.82770 - 1.05522i) q^{19} +2.79602i q^{20} +(3.30077 - 0.323937i) q^{22} +(0.902766 - 0.521212i) q^{23} +(1.40887 - 2.44023i) q^{25} +(-2.77293 + 1.60095i) q^{26} +(1.05507 - 2.42628i) q^{28} -9.40956 q^{29} +(3.58777 - 6.21420i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.11761 q^{34} +(-5.94674 + 4.40005i) q^{35} +(-4.60502 - 7.97612i) q^{37} +(-1.82770 - 1.05522i) q^{38} +(2.42143 - 1.39801i) q^{40} +0.110771 q^{41} -4.20415i q^{43} +(-1.93092 - 2.69658i) q^{44} +(-0.902766 - 0.521212i) q^{46} +(7.27267 - 4.19888i) q^{47} +(6.82070 - 1.57420i) q^{49} -2.81773 q^{50} +(2.77293 + 1.60095i) q^{52} +(-10.3301 - 5.96410i) q^{53} +(0.905736 + 9.22901i) q^{55} +(-2.62875 + 0.299420i) q^{56} +(4.70478 + 8.14891i) q^{58} +(6.34962 + 3.66595i) q^{59} +(9.21987 - 5.32310i) q^{61} -7.17555 q^{62} +1.00000 q^{64} +(-4.47630 - 7.75318i) q^{65} +(-3.97143 + 6.87872i) q^{67} +(2.05881 + 3.56596i) q^{68} +(6.78392 + 2.95000i) q^{70} +11.0925i q^{71} +(-5.46860 - 3.15730i) q^{73} +(-4.60502 + 7.97612i) q^{74} +2.11045i q^{76} +(2.69658 - 8.35036i) q^{77} +(12.4344 - 7.17899i) q^{79} +(-2.42143 - 1.39801i) q^{80} +(-0.0553856 - 0.0959306i) q^{82} -14.2335 q^{83} -11.5129i q^{85} +(-3.64090 + 2.10208i) q^{86} +(-1.36985 + 3.02052i) q^{88} +(10.3472 - 5.97394i) q^{89} +(0.958715 + 8.41703i) q^{91} +1.04242i q^{92} +(-7.27267 - 4.19888i) q^{94} +(2.95043 - 5.11029i) q^{95} -17.6911 q^{97} +(-4.77365 - 5.11979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more