LMFDB - Embedded newform 1386.2.bk.c.703.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

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.bk (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.1
Root			$1.60599 - 0.430324i$ of defining polynomial
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.c.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.09005 + 0.629341i) q^{5} +(2.11465 + 1.59005i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.09005 + 0.629341i) q^{5} +(2.11465 + 1.59005i) q^{7} +1.00000i q^{8} +(0.629341 - 1.09005i) q^{10} +(-1.45007 + 2.98283i) q^{11} -4.08338 q^{13} +(-2.62636 - 0.319700i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.60096 - 2.77294i) q^{17} +(3.81407 + 6.60616i) q^{19} +1.25868i q^{20} +(-0.235617 - 3.30824i) q^{22} +(-4.12636 - 7.14707i) q^{23} +(-1.70786 + 2.95810i) q^{25} +(3.53631 - 2.04169i) q^{26} +(2.43435 - 1.03631i) q^{28} +3.54386i q^{29} +(-7.95304 - 4.59169i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.20191i q^{34} +(-3.30576 - 0.402401i) q^{35} +(0.154122 + 0.266948i) q^{37} +(-6.60616 - 3.81407i) q^{38} +(-0.629341 - 1.09005i) q^{40} +6.05276 q^{41} -7.57607i q^{43} +(1.85817 + 2.74722i) q^{44} +(7.14707 + 4.12636i) q^{46} +(-4.07263 + 2.35133i) q^{47} +(1.94348 + 6.72480i) q^{49} -3.41572i q^{50} +(-2.04169 + 3.53631i) q^{52} +(-2.39830 + 4.15397i) q^{53} +(-0.296567 - 4.16403i) q^{55} +(-1.59005 + 2.11465i) q^{56} +(-1.77193 - 3.06907i) q^{58} +(-2.36710 - 1.36664i) q^{59} +(-0.755050 - 1.30779i) q^{61} +9.18338 q^{62} -1.00000 q^{64} +(4.45110 - 2.56984i) q^{65} +(-1.69044 + 2.92792i) q^{67} +(-1.60096 - 2.77294i) q^{68} +(3.06407 - 1.30439i) q^{70} -3.50810 q^{71} +(0.483428 - 0.837321i) q^{73} +(-0.266948 - 0.154122i) q^{74} +7.62813 q^{76} +(-7.80925 + 4.00195i) q^{77} +(-13.5212 + 7.80647i) q^{79} +(1.09005 + 0.629341i) q^{80} +(-5.24185 + 3.02638i) q^{82} +1.32998 q^{83} +4.03019i q^{85} +(3.78804 + 6.56107i) q^{86} +(-2.98283 - 1.45007i) q^{88} +(-9.22296 + 5.32488i) q^{89} +(-8.63492 - 6.49279i) q^{91} -8.25273 q^{92} +(2.35133 - 4.07263i) q^{94} +(-8.31505 - 4.80070i) q^{95} -10.6748i q^{97} +(-5.04550 - 4.85211i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5	$ 16 q + 8 q^{4} + 12 q^{5} - 8 q^{11} + 8 q^{14} - 8 q^{16} - 8 q^{22} - 16 q^{23} + 36 q^{26} - 12 q^{31} - 16 q^{37} - 12 q^{38} + 8 q^{44} - 24 q^{47} + 8 q^{49} + 28 q^{53} + 4 q^{56} - 12 q^{58} - 60 q^{59} - 16 q^{64} + 12 q^{67} + 60 q^{70} - 8 q^{71} - 44 q^{77} - 12 q^{80} - 20 q^{86} - 4 q^{88} - 96 q^{89} - 36 q^{91} - 32 q^{92}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 - 8 * q^11 + 8 * q^14 - 8 * q^16 - 8 * q^22 - 16 * q^23 + 36 * q^26 - 12 * q^31 - 16 * q^37 - 12 * q^38 + 8 * q^44 - 24 * q^47 + 8 * q^49 + 28 * q^53 + 4 * q^56 - 12 * q^58 - 60 * q^59 - 16 * q^64 + 12 * q^67 + 60 * q^70 - 8 * q^71 - 44 * q^77 - 12 * q^80 - 20 * q^86 - 4 * q^88 - 96 * q^89 - 36 * q^91 - 32 * q^92

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.09005	+	0.629341i	−0.487486	+	0.281450i	−0.723531	−	0.690292i	$-0.757482\pi$
$5$	−1.09005	+	0.629341i	−0.487486	+	0.281450i	0.236045	+	0.971742i	$0.424149\pi$
$6$		0			0
$7$	2.11465	+	1.59005i	0.799262	+	0.600983i
$7$	2.11465	+	1.59005i	0.799262	+	0.600983i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.629341	−	1.09005i	0.199015	−	0.344704i
$11$	−1.45007	+	2.98283i	−0.437213	+	0.899358i
$11$	−1.45007	+	2.98283i	−0.437213	+	0.899358i
$12$		0			0
$13$	−4.08338			−1.13253			−0.566263	−	0.824224i	$-0.691612\pi$
$13$	−4.08338			−1.13253			−0.566263	+	0.824224i	$0.691612\pi$
$14$	−2.62636	−	0.319700i	−0.701926	−	0.0854435i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.60096	−	2.77294i	0.388289	−	0.672537i	−0.603930	−	0.797037i	$-0.706400\pi$
$17$	1.60096	−	2.77294i	0.388289	−	0.672537i	0.992220	+	0.124501i	$0.0397329\pi$
$18$		0			0
$19$	3.81407	+	6.60616i	0.875007	+	1.51556i	0.856756	+	0.515723i	$0.172476\pi$
$19$	3.81407	+	6.60616i	0.875007	+	1.51556i	0.0182510	+	0.999833i	$0.494190\pi$
$20$			1.25868i			0.281450i
$21$		0			0
$22$	−0.235617	−	3.30824i	−0.0502337	−	0.705320i
$23$	−4.12636	−	7.14707i	−0.860407	−	1.49027i	−0.871537	−	0.490330i	$-0.836876\pi$
$23$	−4.12636	−	7.14707i	−0.860407	−	1.49027i	0.0111305	−	0.999938i	$-0.496457\pi$
$24$		0			0
$25$	−1.70786	+	2.95810i	−0.341572	+	0.591620i
$26$	3.53631	−	2.04169i	0.693528	−	0.400409i
$27$		0			0
$28$	2.43435	−	1.03631i	0.460049	−	0.195845i
$29$			3.54386i			0.658079i	0.944316	+	0.329039i	$0.106725\pi$
$29$			3.54386i			0.658079i	−0.944316	+	0.329039i	$0.893275\pi$
$30$		0			0
$31$	−7.95304	−	4.59169i	−1.42841	−	0.824692i	−0.431413	−	0.902155i	$-0.641985\pi$
$31$	−7.95304	−	4.59169i	−1.42841	−	0.824692i	−0.996995	+	0.0774626i	$0.975318\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			3.20191i			0.549124i
$35$	−3.30576	−	0.402401i	−0.558775	−	0.0680182i
$36$		0			0
$37$	0.154122	+	0.266948i	0.0253376	+	0.0438860i	0.878416	−	0.477896i	$-0.158601\pi$
$37$	0.154122	+	0.266948i	0.0253376	+	0.0438860i	−0.853079	+	0.521782i	$0.825267\pi$
$38$	−6.60616	−	3.81407i	−1.07166	−	0.618723i
$39$		0			0
$40$	−0.629341	−	1.09005i	−0.0995076	−	0.172352i
$41$	6.05276			0.945283			0.472641	−	0.881255i	$-0.343301\pi$
$41$	6.05276			0.945283			0.472641	+	0.881255i	$0.343301\pi$
$42$		0			0
$43$		−	7.57607i		−	1.15534i	−0.816270	−	0.577670i	$-0.803962\pi$
$43$		−	7.57607i		−	1.15534i	0.816270	−	0.577670i	$-0.196038\pi$
$44$	1.85817	+	2.74722i	0.280130	+	0.414158i
$45$		0			0
$46$	7.14707	+	4.12636i	1.05378	+	0.608399i
$47$	−4.07263	+	2.35133i	−0.594054	+	0.342977i	−0.766699	−	0.642007i	$-0.778102\pi$
$47$	−4.07263	+	2.35133i	−0.594054	+	0.342977i	0.172645	+	0.984984i	$0.444769\pi$
$48$		0			0
$49$	1.94348	+	6.72480i	0.277640	+	0.960685i
$50$		−	3.41572i		−	0.483056i
$51$		0			0
$52$	−2.04169	+	3.53631i	−0.283132	+	0.490399i
$53$	−2.39830	+	4.15397i	−0.329431	+	0.570592i	−0.982399	−	0.186794i	$-0.940190\pi$
$53$	−2.39830	+	4.15397i	−0.329431	+	0.570592i	0.652968	+	0.757386i	$0.273524\pi$
$54$		0			0
$55$	−0.296567	−	4.16403i	−0.0399891	−	0.561478i
$56$	−1.59005	+	2.11465i	−0.212479	+	0.282582i
$57$		0			0
$58$	−1.77193	−	3.06907i	−0.232666	−	0.402989i
$59$	−2.36710	−	1.36664i	−0.308170	−	0.177922i	0.337938	−	0.941169i	$-0.390271\pi$
$59$	−2.36710	−	1.36664i	−0.308170	−	0.177922i	−0.646107	+	0.763247i	$0.723604\pi$
$60$		0			0
$61$	−0.755050	−	1.30779i	−0.0966743	−	0.167445i	0.813632	−	0.581380i	$-0.197487\pi$
$61$	−0.755050	−	1.30779i	−0.0966743	−	0.167445i	−0.910306	+	0.413936i	$0.864154\pi$
$62$	9.18338			1.16629
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.45110	−	2.56984i	0.552090	−	0.318750i
$66$		0			0
$67$	−1.69044	+	2.92792i	−0.206520	+	0.357703i	−0.950616	−	0.310370i	$-0.899547\pi$
$67$	−1.69044	+	2.92792i	−0.206520	+	0.357703i	0.744096	+	0.668073i	$0.232880\pi$
$68$	−1.60096	−	2.77294i	−0.194145	−	0.336268i
$69$		0			0
$70$	3.06407	−	1.30439i	0.366227	−	0.155904i
$71$	−3.50810			−0.416334			−0.208167	−	0.978093i	$-0.566750\pi$
$71$	−3.50810			−0.416334			−0.208167	+	0.978093i	$0.566750\pi$
$72$		0			0
$73$	0.483428	−	0.837321i	0.0565809	−	0.0980011i	−0.836348	−	0.548200i	$-0.815313\pi$
$73$	0.483428	−	0.837321i	0.0565809	−	0.0980011i	0.892929	+	0.450198i	$0.148647\pi$
$74$	−0.266948	−	0.154122i	−0.0310321	−	0.0179164i
$75$		0			0
$76$	7.62813			0.875007
$77$	−7.80925	+	4.00195i	−0.889946	+	0.456065i
$78$		0			0
$79$	−13.5212	+	7.80647i	−1.52125	+	0.878296i	−0.521568	+	0.853210i	$0.674653\pi$
$79$	−13.5212	+	7.80647i	−1.52125	+	0.878296i	−0.999685	+	0.0250865i	$0.992014\pi$
$80$	1.09005	+	0.629341i	0.121871	+	0.0703625i
$81$		0			0
$82$	−5.24185	+	3.02638i	−0.578865	+	0.334208i
$83$	1.32998			0.145984			0.0729921	−	0.997333i	$-0.476745\pi$
$83$	1.32998			0.145984			0.0729921	+	0.997333i	$0.476745\pi$
$84$		0			0
$85$			4.03019i			0.437136i
$86$	3.78804	+	6.56107i	0.408474	+	0.707498i
$87$		0			0
$88$	−2.98283	−	1.45007i	−0.317971	−	0.154578i
$89$	−9.22296	+	5.32488i	−0.977631	+	0.564436i	−0.901554	−	0.432666i	$-0.857573\pi$
$89$	−9.22296	+	5.32488i	−0.977631	+	0.564436i	−0.0760772	+	0.997102i	$0.524240\pi$
$90$		0			0
$91$	−8.63492	−	6.49279i	−0.905186	−	0.680629i
$92$	−8.25273			−0.860407
$93$		0			0
$94$	2.35133	−	4.07263i	0.242521	−	0.420059i
$95$	−8.31505	−	4.80070i	−0.853106	−	0.492541i
$96$		0			0
$97$		−	10.6748i		−	1.08386i	−0.840424	−	0.541930i	$-0.817694\pi$
$97$		−	10.6748i		−	1.08386i	0.840424	−	0.541930i	$-0.182306\pi$
$98$	−5.04550	−	4.85211i	−0.509672	−	0.490137i
$99$		0			0
$100$	1.70786	+	2.95810i	0.170786	+	0.295810i
$101$	−5.03242	+	8.71642i	−0.500745	+	0.867316i	0.499255	+	0.866455i	$0.333607\pi$
$101$	−5.03242	+	8.71642i	−0.500745	+	0.867316i	−1.00000		0.000860457i	$0.999726\pi$
$102$		0			0
$103$	2.49868	−	1.44261i	0.246202	−	0.142145i	−0.371822	−	0.928304i	$-0.621267\pi$
$103$	2.49868	−	1.44261i	0.246202	−	0.142145i	0.618024	+	0.786159i	$0.287933\pi$
$104$		−	4.08338i		−	0.400409i
$105$		0			0
$106$		−	4.79659i		−	0.465886i
$107$	−14.1162	+	8.15002i	−1.36467	+	0.787892i	−0.990241	−	0.139364i	$-0.955494\pi$
$107$	−14.1162	+	8.15002i	−1.36467	+	0.787892i	−0.374428	+	0.927256i	$0.622161\pi$
$108$		0			0
$109$	−9.96227	−	5.75172i	−0.954213	−	0.550915i	−0.0598257	−	0.998209i	$-0.519054\pi$
$109$	−9.96227	−	5.75172i	−0.954213	−	0.550915i	−0.894387	+	0.447294i	$0.852388\pi$
$110$	2.33885	+	3.45787i	0.223001	+	0.329695i
$111$		0			0
$112$	0.319700	−	2.62636i	0.0302088	−	0.248168i
$113$	−0.558958			−0.0525824			−0.0262912	−	0.999654i	$-0.508370\pi$
$113$	−0.558958			−0.0525824			−0.0262912	+	0.999654i	$0.508370\pi$
$114$		0			0
$115$	8.99589	+	5.19378i	0.838872	+	0.484323i
$116$	3.06907	+	1.77193i	0.284956	+	0.164520i
$117$		0			0
$118$	2.73329			0.251619
$119$	7.79458	−	3.31819i	0.714528	−	0.304178i
$120$		0			0
$121$	−6.79458	−	8.65064i	−0.617689	−	0.786422i
$122$	1.30779	+	0.755050i	0.118401	+	0.0683590i
$123$		0			0
$124$	−7.95304	+	4.59169i	−0.714204	+	0.412346i
$125$		−	10.5927i		−	0.947441i
$126$		0			0
$127$			11.2829i			1.00120i	0.865679	+	0.500599i	$0.166887\pi$
$127$			11.2829i			1.00120i	−0.865679	+	0.500599i	$0.833113\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.56984	+	4.45110i	−0.225390	+	0.390387i
$131$	3.51694	+	6.09152i	0.307276	+	0.532218i	0.977766	−	0.209701i	$-0.0672490\pi$
$131$	3.51694	+	6.09152i	0.307276	+	0.532218i	−0.670489	+	0.741919i	$0.733916\pi$
$132$		0			0
$133$	−2.43871	+	20.0343i	−0.211463	+	1.73719i
$134$		−	3.38087i		−	0.292063i
$135$		0			0
$136$	2.77294	+	1.60096i	0.237778	+	0.137281i
$137$	4.54487	−	7.87195i	0.388294	−	0.672546i	−0.603926	−	0.797041i	$-0.706398\pi$
$137$	4.54487	−	7.87195i	0.388294	−	0.672546i	0.992220	+	0.124495i	$0.0397310\pi$
$138$		0			0
$139$	7.86546			0.667140			0.333570	−	0.942725i	$-0.391747\pi$
$139$	7.86546			0.667140			0.333570	+	0.942725i	$0.391747\pi$
$140$	−2.00137	+	2.66167i	−0.169147	+	0.224952i
$141$		0			0
$142$	3.03810	−	1.75405i	0.254952	−	0.147196i
$143$	5.92120	−	12.1801i	0.495156	−	1.01855i
$144$		0			0
$145$	−2.23030	−	3.86299i	−0.185216	−	0.320804i
$146$			0.966855i			0.0800175i
$147$		0			0
$148$	0.308245			0.0253376
$149$	−5.39617	+	3.11548i	−0.442072	+	0.255230i	−0.704476	−	0.709728i	$-0.748818\pi$
$149$	−5.39617	+	3.11548i	−0.442072	+	0.255230i	0.262404	+	0.964958i	$0.415485\pi$
$150$		0			0
$151$	−15.1642	−	8.75506i	−1.23405	−	0.712476i	−0.266175	−	0.963925i	$-0.585760\pi$
$151$	−15.1642	−	8.75506i	−1.23405	−	0.712476i	−0.967871	+	0.251448i	$0.919093\pi$
$152$	−6.60616	+	3.81407i	−0.535830	+	0.309362i
$153$		0			0
$154$	4.76203	−	7.37042i	0.383735	−	0.593925i
$155$	11.5590			0.928438
$156$		0			0
$157$	−6.73252	−	3.88702i	−0.537314	−	0.310218i	0.206676	−	0.978409i	$-0.433735\pi$
$157$	−6.73252	−	3.88702i	−0.537314	−	0.310218i	−0.743989	+	0.668191i	$0.767069\pi$
$158$	7.80647	−	13.5212i	0.621049	−	1.07569i
$159$		0			0
$160$	−1.25868			−0.0995076
$161$	2.63840	−	21.6747i	0.207935	−	1.70820i
$162$		0			0
$163$	9.10616	+	15.7723i	0.713249	+	1.23538i	0.963631	+	0.267237i	$0.0861105\pi$
$163$	9.10616	+	15.7723i	0.713249	+	1.23538i	−0.250382	+	0.968147i	$0.580556\pi$
$164$	3.02638	−	5.24185i	0.236321	−	0.409319i
$165$		0			0
$166$	−1.15180	+	0.664990i	−0.0893967	+	0.0516132i
$167$	14.3653			1.11162			0.555809	−	0.831310i	$-0.312409\pi$
$167$	14.3653			1.11162			0.555809	+	0.831310i	$0.312409\pi$
$168$		0			0
$169$	3.67402			0.282617
$170$	−2.01510	−	3.49025i	−0.154551	−	0.267690i
$171$		0			0
$172$	−6.56107	−	3.78804i	−0.500277	−	0.288835i
$173$	2.38160	+	4.12505i	0.181069	+	0.313621i	0.942245	−	0.334924i	$-0.108711\pi$
$173$	2.38160	+	4.12505i	0.181069	+	0.313621i	−0.761176	+	0.648546i	$0.775377\pi$
$174$		0			0
$175$	−8.31505	+	3.53976i	−0.628559	+	0.267580i
$176$	3.30824	−	0.235617i	0.249368	−	0.0177603i
$177$		0			0
$178$	5.32488	−	9.22296i	0.399116	−	0.691290i
$179$	−1.94526	+	3.36928i	−0.145395	+	0.251832i	−0.929520	−	0.368771i	$-0.879779\pi$
$179$	−1.94526	+	3.36928i	−0.145395	+	0.251832i	0.784125	+	0.620603i	$0.213112\pi$
$180$		0			0
$181$		−	13.0698i		−	0.971474i	−0.874105	−	0.485737i	$-0.838551\pi$
$181$		−	13.0698i		−	0.971474i	0.874105	−	0.485737i	$-0.161449\pi$
$182$	10.7245	+	1.30546i	0.794949	+	0.0967670i
$183$		0			0
$184$	7.14707	−	4.12636i	0.526889	−	0.304200i
$185$	−0.336003	−	0.193991i	−0.0247034	−	0.0142625i
$186$		0			0
$187$	5.94971	+	8.79635i	0.435086	+	0.643253i
$188$			4.70267i			0.342977i
$189$		0			0
$190$	9.60139			0.696558
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	8.12582	+	4.69144i	0.584909	+	0.337698i	0.763082	−	0.646302i	$-0.223685\pi$
$193$	8.12582	+	4.69144i	0.584909	+	0.337698i	−0.178173	+	0.983999i	$0.557019\pi$
$194$	5.33739	+	9.24463i	0.383202	+	0.663726i
$195$		0			0
$196$	6.79558	+	1.67930i	0.485399	+	0.119950i
$197$		−	17.3471i		−	1.23593i	−0.786205	−	0.617966i	$-0.787957\pi$
$197$		−	17.3471i		−	1.23593i	0.786205	−	0.617966i	$-0.212043\pi$
$198$		0			0
$199$	2.53353	+	1.46273i	0.179597	+	0.103690i	0.587103	−	0.809512i	$-0.300268\pi$
$199$	2.53353	+	1.46273i	0.179597	+	0.103690i	−0.407506	+	0.913202i	$0.633602\pi$
$200$	−2.95810	−	1.70786i	−0.209169	−	0.120764i
$201$		0			0
$202$		−	10.0648i		−	0.708160i
$203$	−5.63492	+	7.49402i	−0.395494	+	0.525977i
$204$		0			0
$205$	−6.59782	+	3.80925i	−0.460812	+	0.266050i
$206$	−1.44261	+	2.49868i	−0.100512	+	0.174091i
$207$		0			0
$208$	2.04169	+	3.53631i	0.141566	+	0.245199i
$209$	−25.2357	+	1.79732i	−1.74559	+	0.124323i
$210$		0			0
$211$			0.252729i			0.0173986i	0.999962	+	0.00869931i	$0.00276911\pi$
$211$			0.252729i			0.0173986i	−0.999962	+	0.00869931i	$0.997231\pi$
$212$	2.39830	+	4.15397i	0.164716	+	0.285296i
$213$		0			0
$214$	8.15002	−	14.1162i	0.557124	−	0.964967i
$215$	4.76793	+	8.25830i	0.325170	+	0.563212i
$216$		0			0
$217$	−9.51686	−	22.3556i	−0.646047	−	1.51759i
$218$	11.5034			0.779111
$219$		0			0
$220$	−3.75444	−	1.82518i	−0.253124	−	0.123054i
$221$	−6.53732	+	11.3230i	−0.439748	+	0.761666i
$222$		0			0
$223$			19.0370i			1.27482i	0.770527	+	0.637408i	$0.219993\pi$
$223$			19.0370i			1.27482i	−0.770527	+	0.637408i	$0.780007\pi$
$224$	1.03631	+	2.43435i	0.0692416	+	0.162652i
$225$		0			0
$226$	0.484072	−	0.279479i	0.0322000	−	0.0185907i
$227$	−9.20350	+	15.9409i	−0.610858	+	1.05804i	0.380238	+	0.924888i	$0.375842\pi$
$227$	−9.20350	+	15.9409i	−0.610858	+	1.05804i	−0.991096	+	0.133148i	$0.957491\pi$
$228$		0			0
$229$	−4.59674	+	2.65393i	−0.303761	+	0.175377i	−0.644131	−	0.764915i	$-0.722781\pi$
$229$	−4.59674	+	2.65393i	−0.303761	+	0.175377i	0.340370	+	0.940292i	$0.389448\pi$
$230$	−10.3876			−0.684936
$231$		0			0
$232$	−3.54386			−0.232666
$233$	−18.4629	+	10.6596i	−1.20955	+	0.698332i	−0.962660	−	0.270712i	$-0.912741\pi$
$233$	−18.4629	+	10.6596i	−1.20955	+	0.698332i	−0.246887	+	0.969044i	$0.579408\pi$
$234$		0			0
$235$	2.95958	−	5.12614i	0.193062	−	0.334393i
$236$	−2.36710	+	1.36664i	−0.154085	+	0.0889609i
$237$		0			0
$238$	−5.09121	+	6.77092i	−0.330014	+	0.438894i
$239$		−	7.25163i		−	0.469069i	−0.972108	−	0.234535i	$-0.924643\pi$
$239$		−	7.25163i		−	0.469069i	0.972108	−	0.234535i	$-0.0753566\pi$
$240$		0			0
$241$	−1.77705	+	3.07794i	−0.114470	+	0.198267i	−0.917568	−	0.397580i	$-0.869850\pi$
$241$	−1.77705	+	3.07794i	−0.114470	+	0.198267i	0.803098	+	0.595847i	$0.203184\pi$
$242$	10.2096	+	4.09439i	0.656298	+	0.263197i
$243$		0			0
$244$	−1.51010			−0.0966743
$245$	−6.35068	−	6.10726i	−0.405730	−	0.390179i
$246$		0			0
$247$	−15.5743	−	26.9755i	−0.990968	−	1.71641i
$248$	4.59169	−	7.95304i	0.291573	−	0.505019i
$249$		0			0
$250$	5.29636	+	9.17356i	0.334971	+	0.580187i
$251$		−	0.735728i		−	0.0464387i	−0.999730	−	0.0232194i	$-0.992608\pi$
$251$		−	0.735728i		−	0.0464387i	0.999730	−	0.0232194i	$-0.00739162\pi$
$252$		0			0
$253$	27.3021	−	1.94448i	1.71647	−	0.122249i
$254$	−5.64146	−	9.77130i	−0.353977	−	0.613106i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.0352	−	8.10325i	0.875494	−	0.505467i	0.00632378	−	0.999980i	$-0.497987\pi$
$257$	14.0352	−	8.10325i	0.875494	−	0.505467i	0.869170	+	0.494513i	$0.164654\pi$
$258$		0			0
$259$	−0.0985460	+	0.809564i	−0.00612335	+	0.0503038i
$260$		−	5.13968i		−	0.318750i
$261$		0			0
$262$	−6.09152	−	3.51694i	−0.376335	−	0.217277i
$263$	21.0462	+	12.1510i	1.29776	+	0.749264i	0.980017	−	0.198911i	$-0.0637406\pi$
$263$	21.0462	+	12.1510i	1.29776	+	0.749264i	0.317746	+	0.948176i	$0.397074\pi$
$264$		0			0
$265$		−	6.03738i		−	0.370874i
$266$	−7.90514	−	18.5695i	−0.484695	−	1.13857i
$267$		0			0
$268$	1.69044	+	2.92792i	0.103260	+	0.178851i
$269$	23.4246	+	13.5242i	1.42822	+	0.824586i	0.996981	−	0.0776498i	$-0.0247416\pi$
$269$	23.4246	+	13.5242i	1.42822	+	0.824586i	0.431244	+	0.902236i	$0.358075\pi$
$270$		0			0
$271$	−5.22166	−	9.04417i	−0.317193	−	0.549394i	0.662708	−	0.748878i	$-0.269407\pi$
$271$	−5.22166	−	9.04417i	−0.317193	−	0.549394i	−0.979901	+	0.199483i	$0.936074\pi$
$272$	−3.20191			−0.194145
$273$		0			0
$274$			9.08974i			0.549131i
$275$	−6.34700	−	9.38372i	−0.382738	−	0.565859i
$276$		0			0
$277$	17.6675	+	10.2003i	1.06153	+	0.612877i	0.925856	−	0.377876i	$-0.123345\pi$
$277$	17.6675	+	10.2003i	1.06153	+	0.612877i	0.135678	+	0.990753i	$0.456679\pi$
$278$	−6.81169	+	3.93273i	−0.408538	+	0.235869i
$279$		0			0
$280$	0.402401	−	3.30576i	0.0240481	−	0.197557i
$281$		−	9.99535i		−	0.596272i	−0.954523	−	0.298136i	$-0.903635\pi$
$281$		−	9.99535i		−	0.596272i	0.954523	−	0.298136i	$-0.0963650\pi$
$282$		0			0
$283$	−1.74448	+	3.02153i	−0.103699	+	0.179611i	−0.913206	−	0.407499i	$-0.866401\pi$
$283$	−1.74448	+	3.02153i	−0.103699	+	0.179611i	0.809507	+	0.587110i	$0.199734\pi$
$284$	−1.75405	+	3.03810i	−0.104084	+	0.180278i
$285$		0			0
$286$	0.962115	+	13.5088i	0.0568911	+	0.798794i
$287$	12.7995	+	9.62420i	0.755529	+	0.568099i
$288$		0			0
$289$	3.37387	+	5.84372i	0.198463	+	0.343748i
$290$	3.86299	+	2.23030i	0.226843	+	0.130968i
$291$		0			0
$292$	−0.483428	−	0.837321i	−0.0282905	−	0.0490005i
$293$	17.3549			1.01388			0.506942	−	0.861980i	$-0.330776\pi$
$293$	17.3549			1.01388			0.506942	+	0.861980i	$0.330776\pi$
$294$		0			0
$295$	3.44034			0.200304
$296$	−0.266948	+	0.154122i	−0.0155160	+	0.00895819i
$297$		0			0
$298$	3.11548	−	5.39617i	0.180475	−	0.312592i
$299$	16.8495	+	29.1842i	0.974433	+	1.68777i
$300$		0			0
$301$	12.0463	−	16.0207i	0.694339	−	0.923419i
$302$	17.5101			1.00759
$303$		0			0
$304$	3.81407	−	6.60616i	0.218752	−	0.378889i
$305$	1.64609	+	0.950368i	0.0942546	+	0.0544179i
$306$		0			0
$307$	22.6829			1.29458			0.647290	−	0.762244i	$-0.275902\pi$
$307$	22.6829			1.29458			0.647290	+	0.762244i	$0.275902\pi$
$308$	−0.438830	+	8.76398i	−0.0250047	+	0.499374i
$309$		0			0
$310$	−10.0104	+	5.77948i	−0.568550	+	0.328252i
$311$	−5.75141	−	3.32058i	−0.326133	−	0.188293i	0.327990	−	0.944681i	$-0.393629\pi$
$311$	−5.75141	−	3.32058i	−0.326133	−	0.188293i	−0.654123	+	0.756388i	$0.726962\pi$
$312$		0			0
$313$	−0.435583	+	0.251484i	−0.0246206	+	0.0142147i	−0.512260	−	0.858831i	$-0.671191\pi$
$313$	−0.435583	+	0.251484i	−0.0246206	+	0.0142147i	0.487639	+	0.873045i	$0.337858\pi$
$314$	7.77404			0.438715
$315$		0			0
$316$			15.6129i			0.878296i
$317$	−5.27437	−	9.13547i	−0.296238	−	0.513099i	0.679034	−	0.734107i	$-0.262399\pi$
$317$	−5.27437	−	9.13547i	−0.296238	−	0.513099i	−0.975272	+	0.221008i	$0.929065\pi$
$318$		0			0
$319$	−10.5707	−	5.13886i	−0.591848	−	0.287721i
$320$	1.09005	−	0.629341i	0.0609357	−	0.0351812i
$321$		0			0
$322$	8.55242	+	20.0900i	0.476608	+	1.11957i
$323$	24.4246			1.35902
$324$		0			0
$325$	6.97385	−	12.0791i	0.386839	−	0.670025i
$326$	−15.7723	−	9.10616i	−0.873548	−	0.504343i
$327$		0			0
$328$			6.05276i			0.334208i
$329$	−12.3509	−	1.50344i	−0.680928	−	0.0828875i
$330$		0			0
$331$	2.89029	+	5.00613i	0.158865	+	0.275162i	0.934460	−	0.356069i	$-0.115883\pi$
$331$	2.89029	+	5.00613i	0.158865	+	0.275162i	−0.775595	+	0.631231i	$0.782550\pi$
$332$	0.664990	−	1.15180i	0.0364960	−	0.0632130i
$333$		0			0
$334$	−12.4407	+	7.18264i	−0.680724	+	0.393016i
$335$		−	4.25544i		−	0.232500i
$336$		0			0
$337$			11.1226i			0.605885i	0.953009	+	0.302943i	$0.0979690\pi$
$337$			11.1226i			0.605885i	−0.953009	+	0.302943i	$0.902031\pi$
$338$	−3.18180	+	1.83701i	−0.173067	+	0.0999202i
$339$		0			0
$340$	3.49025	+	2.01510i	0.189285	+	0.109284i
$341$	25.2287	−	17.0643i	1.36621	−	0.924084i
$342$		0			0
$343$	−6.58300	+	17.3108i	−0.355449	+	0.934696i
$344$	7.57607			0.408474
$345$		0			0
$346$	−4.12505	−	2.38160i	−0.221764	−	0.128035i
$347$	12.7058	+	7.33569i	0.682083	+	0.393801i	0.800639	−	0.599147i	$-0.204493\pi$
$347$	12.7058	+	7.33569i	0.682083	+	0.393801i	−0.118557	+	0.992947i	$0.537827\pi$
$348$		0			0
$349$	24.6769			1.32093			0.660463	−	0.750859i	$-0.270360\pi$
$349$	24.6769			1.32093			0.660463	+	0.750859i	$0.270360\pi$
$350$	5.43117	−	7.22304i	0.290308	−	0.386088i
$351$		0			0
$352$	−2.74722	+	1.85817i	−0.146427	+	0.0990409i
$353$	16.6664	+	9.62237i	0.887065	+	0.512147i	0.872981	−	0.487754i	$-0.162184\pi$
$353$	16.6664	+	9.62237i	0.887065	+	0.512147i	0.0140834	+	0.999901i	$0.495517\pi$
$354$		0			0
$355$	3.82400	−	2.20779i	0.202957	−	0.117177i
$356$			10.6498i			0.564436i
$357$		0			0
$358$		−	3.89051i		−	0.205620i
$359$	−2.85275	+	1.64703i	−0.150562	+	0.0869271i	−0.573388	−	0.819284i	$-0.694371\pi$
$359$	−2.85275	+	1.64703i	−0.150562	+	0.0869271i	0.422826	+	0.906211i	$0.361038\pi$
$360$		0			0
$361$	−19.5942	+	33.9381i	−1.03127	+	1.78622i
$362$	6.53492	+	11.3188i	0.343468	+	0.594904i
$363$		0			0
$364$	−9.94038	+	4.23167i	−0.521017	+	0.221800i
$365$			1.21696i			0.0636988i
$366$		0			0
$367$	26.7957	+	15.4705i	1.39873	+	0.807555i	0.994259	−	0.106998i	$-0.0341238\pi$
$367$	26.7957	+	15.4705i	1.39873	+	0.807555i	0.404467	+	0.914553i	$0.367457\pi$
$368$	−4.12636	+	7.14707i	−0.215102	+	0.372567i
$369$		0			0
$370$	0.387982			0.0201702
$371$	−11.6766	+	4.97077i	−0.606218	+	0.258070i
$372$		0			0
$373$	0.832767	−	0.480798i	0.0431191	−	0.0248948i	−0.478286	−	0.878204i	$-0.658742\pi$
$373$	0.832767	−	0.480798i	0.0431191	−	0.0248948i	0.521405	+	0.853310i	$0.325408\pi$
$374$	−9.55077	−	4.64301i	−0.493859	−	0.240084i
$375$		0			0
$376$	−2.35133	−	4.07263i	−0.121261	−	0.210030i
$377$		−	14.4709i		−	0.745292i
$378$		0			0
$379$	−1.41216			−0.0725379			−0.0362689	−	0.999342i	$-0.511547\pi$
$379$	−1.41216			−0.0725379			−0.0362689	+	0.999342i	$0.511547\pi$
$380$	−8.31505	+	4.80070i	−0.426553	+	0.246271i
$381$		0			0
$382$	−5.19615	−	3.00000i	−0.265858	−	0.153493i
$383$	−3.27426	+	1.89039i	−0.167307	+	0.0965946i	−0.581315	−	0.813678i	$-0.697462\pi$
$383$	−3.27426	+	1.89039i	−0.167307	+	0.0965946i	0.414009	+	0.910273i	$0.364128\pi$
$384$		0			0
$385$	5.99388	−	9.27702i	0.305477	−	0.472800i
$386$	−9.38289			−0.477576
$387$		0			0
$388$	−9.24463	−	5.33739i	−0.469325	−	0.270965i
$389$	−1.68943	+	2.92618i	−0.0856574	+	0.148363i	−0.905671	−	0.423981i	$-0.860632\pi$
$389$	−1.68943	+	2.92618i	−0.0856574	+	0.148363i	0.820014	+	0.572344i	$0.193966\pi$
$390$		0			0
$391$	−26.4245			−1.33635
$392$	−6.72480	+	1.94348i	−0.339654	+	0.0981604i
$393$		0			0
$394$	8.67356	+	15.0230i	0.436968	+	0.756850i
$395$	9.82586	−	17.0189i	0.494393	−	0.856313i
$396$		0			0
$397$	−9.98525	+	5.76499i	−0.501145	+	0.289336i	−0.729186	−	0.684315i	$-0.760101\pi$
$397$	−9.98525	+	5.76499i	−0.501145	+	0.289336i	0.228041	+	0.973652i	$0.426768\pi$
$398$	−2.92547			−0.146640
$399$		0			0
$400$	3.41572			0.170786
$401$	13.0261	+	22.5619i	0.650494	+	1.12669i	0.983003	+	0.183588i	$0.0587714\pi$
$401$	13.0261	+	22.5619i	0.650494	+	1.12669i	−0.332509	+	0.943100i	$0.607895\pi$
$402$		0			0
$403$	32.4753	+	18.7496i	1.61771	+	0.933986i
$404$	5.03242	+	8.71642i	0.250372	+	0.433658i
$405$		0			0
$406$	1.13297	−	9.30747i	0.0562285	−	0.461922i
$407$	−1.01975	+	0.0726278i	−0.0505471	+	0.00360003i
$408$		0			0
$409$	17.5109	−	30.3297i	0.865856	−	1.49971i	−0.000338063	−	1.00000i	$-0.500108\pi$
$409$	17.5109	−	30.3297i	0.865856	−	1.49971i	0.866194	−	0.499707i	$-0.166559\pi$
$410$	3.80925	−	6.59782i	0.188126	−	0.325843i
$411$		0			0
$412$		−	2.88523i		−	0.142145i
$413$	−2.83254	−	6.65377i	−0.139380	−	0.327411i
$414$		0			0
$415$	−1.44974	+	0.837011i	−0.0711652	+	0.0410872i
$416$	−3.53631	−	2.04169i	−0.173382	−	0.100102i
$417$		0			0
$418$	20.9561	−	14.1744i	1.02500	−	0.693292i
$419$			12.1242i			0.592307i	0.955140	+	0.296154i	$0.0957040\pi$
$419$			12.1242i			0.592307i	−0.955140	+	0.296154i	$0.904296\pi$
$420$		0			0
$421$	18.6940			0.911089			0.455545	−	0.890213i	$-0.349445\pi$
$421$	18.6940			0.911089			0.455545	+	0.890213i	$0.349445\pi$
$422$	−0.126365	−	0.218870i	−0.00615134	−	0.0106544i
$423$		0			0
$424$	−4.15397	−	2.39830i	−0.201735	−	0.116472i
$425$	5.46842	+	9.47158i	0.265257	+	0.459439i
$426$		0			0
$427$	0.482779	−	3.96607i	0.0233633	−	0.191932i
$428$			16.3000i			0.787892i
$429$		0			0
$430$	−8.25830	−	4.76793i	−0.398251	−	0.229930i
$431$	−29.3945	−	16.9709i	−1.41588	−	0.817461i	−0.419949	−	0.907548i	$-0.637952\pi$
$431$	−29.3945	−	16.9709i	−1.41588	−	0.817461i	−0.995934	+	0.0900869i	$0.971286\pi$
$432$		0			0
$433$		−	27.0949i		−	1.30210i	−0.759037	−	0.651048i	$-0.774330\pi$
$433$		−	27.0949i		−	1.30210i	0.759037	−	0.651048i	$-0.225670\pi$
$434$	19.4196	+	14.6020i	0.932172	+	0.700920i
$435$		0			0
$436$	−9.96227	+	5.75172i	−0.477106	+	0.275458i
$437$	31.4765	−	54.5188i	1.50572	−	2.60799i
$438$		0			0
$439$	10.2269	+	17.7135i	0.488104	+	0.845421i	0.999906	−	0.0136821i	$-0.00435529\pi$
$439$	10.2269	+	17.7135i	0.488104	+	0.845421i	−0.511802	+	0.859103i	$0.671022\pi$
$440$	4.16403	−	0.296567i	0.198512	−	0.0141383i
$441$		0			0
$442$		−	13.0746i		−	0.621897i
$443$	−1.79868	−	3.11541i	−0.0854579	−	0.148017i	0.820128	−	0.572180i	$-0.193902\pi$
$443$	−1.79868	−	3.11541i	−0.0854579	−	0.148017i	−0.905586	+	0.424162i	$0.860569\pi$
$444$		0			0
$445$	6.70233	−	11.6088i	0.317721	−	0.550309i
$446$	−9.51852	−	16.4866i	−0.450715	−	0.780662i
$447$		0			0
$448$	−2.11465	−	1.59005i	−0.0999078	−	0.0751228i
$449$	−37.0664			−1.74927			−0.874637	−	0.484779i	$-0.838900\pi$
$449$	−37.0664			−1.74927			−0.874637	+	0.484779i	$0.838900\pi$
$450$		0			0
$451$	−8.77694	+	18.0544i	−0.413290	+	0.850148i
$452$	−0.279479	+	0.484072i	−0.0131456	+	0.0227688i
$453$		0			0
$454$		−	18.4070i		−	0.863883i
$455$	13.4987	+	1.64316i	0.632828	+	0.0770324i
$456$		0			0
$457$	15.7194	−	9.07561i	0.735323	−	0.424539i	−0.0850431	−	0.996377i	$-0.527103\pi$
$457$	15.7194	−	9.07561i	0.735323	−	0.424539i	0.820366	+	0.571838i	$0.193769\pi$
$458$	2.65393	−	4.59674i	0.124010	−	0.214792i
$459$		0			0
$460$	8.99589	−	5.19378i	0.419436	−	0.242161i
$461$	22.4278			1.04457			0.522284	−	0.852772i	$-0.325080\pi$
$461$	22.4278			1.04457			0.522284	+	0.852772i	$0.325080\pi$
$462$		0			0
$463$	−15.6274			−0.726267			−0.363134	−	0.931737i	$-0.618293\pi$
$463$	−15.6274			−0.726267			−0.363134	+	0.931737i	$0.618293\pi$
$464$	3.06907	−	1.77193i	0.142478	−	0.0822598i
$465$		0			0
$466$	10.6596	−	18.4629i	0.493796	−	0.855279i
$467$	5.27860	−	3.04760i	0.244264	−	0.141026i	−0.372871	−	0.927883i	$-0.621626\pi$
$467$	5.27860	−	3.04760i	0.244264	−	0.141026i	0.617135	+	0.786857i	$0.288293\pi$
$468$		0			0
$469$	−8.23022	+	3.50365i	−0.380036	+	0.161783i
$470$			5.91916i			0.273031i
$471$		0			0
$472$	1.36664	−	2.36710i	0.0629048	−	0.108954i
$473$	22.5982	+	10.9858i	1.03906	+	0.505130i
$474$		0			0
$475$	−26.0556			−1.19551
$476$	1.02365	−	8.40939i	0.0469190	−	0.385444i
$477$		0			0
$478$	3.62582	+	6.28010i	0.165841	+	0.287245i
$479$	15.3138	−	26.5242i	0.699704	−	1.21192i	−0.268865	−	0.963178i	$-0.586648\pi$
$479$	15.3138	−	26.5242i	0.699704	−	1.21192i	0.968569	−	0.248745i	$-0.0800182\pi$
$480$		0			0
$481$	−0.629341	−	1.09005i	−0.0286955	−	0.0497020i
$482$		−	3.55410i		−	0.161885i
$483$		0			0
$484$	−10.8890	+	1.55896i	−0.494953	+	0.0708617i
$485$	6.71808	+	11.6361i	0.305052	+	0.528366i
$486$		0			0
$487$	1.58726	−	2.74922i	0.0719258	−	0.124579i	−0.827819	−	0.560995i	$-0.810419\pi$
$487$	1.58726	−	2.74922i	0.0719258	−	0.124579i	0.899745	+	0.436415i	$0.143752\pi$
$488$	1.30779	−	0.755050i	0.0592007	−	0.0341795i
$489$		0			0
$490$	8.55348	+	2.11370i	0.386407	+	0.0954874i
$491$			32.6507i			1.47351i	0.676162	+	0.736753i	$0.263642\pi$
$491$			32.6507i			1.47351i	−0.676162	+	0.736753i	$0.736358\pi$
$492$		0			0
$493$	9.82691	+	5.67357i	0.442582	+	0.255525i
$494$	26.9755	+	15.5743i	1.21368	+	0.700721i
$495$		0			0
$496$			9.18338i			0.412346i
$497$	−7.41839	−	5.57805i	−0.332760	−	0.250210i
$498$		0			0
$499$	−14.2274	−	24.6426i	−0.636906	−	1.10315i	−0.986108	−	0.166106i	$-0.946881\pi$
$499$	−14.2274	−	24.6426i	−0.636906	−	1.10315i	0.349202	−	0.937048i	$-0.386453\pi$
$500$	−9.17356	−	5.29636i	−0.410254	−	0.236860i
$501$		0			0
$502$	0.367864	+	0.637159i	0.0164186	+	0.0284378i
$503$	−22.5058			−1.00348			−0.501741	−	0.865018i	$-0.667307\pi$
$503$	−22.5058			−1.00348			−0.501741	+	0.865018i	$0.667307\pi$
$504$		0			0
$505$		−	12.6684i		−	0.563739i
$506$	−22.6720	+	15.3350i	−1.00789	+	0.681724i
$507$		0			0
$508$	9.77130	+	5.64146i	0.433531	+	0.250299i
$509$	11.6437	−	6.72249i	0.516098	−	0.297969i	−0.219239	−	0.975671i	$-0.570357\pi$
$509$	11.6437	−	6.72249i	0.516098	−	0.297969i	0.735337	+	0.677702i	$0.237024\pi$
$510$		0			0
$511$	2.35366	−	1.00197i	0.104120	−	0.0443244i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−8.10325	+	14.0352i	−0.357419	+	0.619068i
$515$	−1.81579	+	3.14505i	−0.0800134	+	0.138587i
$516$		0			0
$517$	−1.10803	−	15.5576i	−0.0487310	−	0.684221i
$518$	−0.319439	−	0.750376i	−0.0140353	−	0.0329696i
$519$		0			0
$520$	2.56984	+	4.45110i	0.112695	+	0.195193i
$521$	−34.2339	−	19.7649i	−1.49981	−	0.865918i	−0.499813	−	0.866133i	$-0.666598\pi$
$521$	−34.2339	−	19.7649i	−1.49981	−	0.865918i	−1.00000		0.000215610i	$0.999931\pi$
$522$		0			0
$523$	14.8061	+	25.6449i	0.647425	+	1.12137i	0.983736	+	0.179622i	$0.0574875\pi$
$523$	14.8061	+	25.6449i	0.647425	+	1.12137i	−0.336310	+	0.941751i	$0.609179\pi$
$524$	7.03388			0.307276
$525$		0			0
$526$	−24.3021			−1.05962
$527$	−25.4650	+	14.7022i	−1.10927	+	0.640438i
$528$		0			0
$529$	−22.5538	+	39.0643i	−0.980599	+	1.69845i
$530$	3.01869	+	5.22853i	0.131124	+	0.227113i
$531$		0			0
$532$	16.1308	+	12.1291i	0.699360	+	0.525864i
$533$	−24.7158			−1.07056
$534$		0			0
$535$	10.2583	−	17.7679i	0.443504	−	0.768172i
$536$	−2.92792	−	1.69044i	−0.126467	−	0.0730157i
$537$		0			0
$538$	−27.0484			−1.16614
$539$	−22.8771	−	3.95437i	−0.985388	−	0.170327i
$540$		0			0
$541$	−15.1111	+	8.72442i	−0.649679	+	0.375092i	−0.788333	−	0.615249i	$-0.789056\pi$
$541$	−15.1111	+	8.72442i	−0.649679	+	0.375092i	0.138654	+	0.990341i	$0.455722\pi$
$542$	9.04417	+	5.22166i	0.388480	+	0.224289i
$543$		0			0
$544$	2.77294	−	1.60096i	0.118889	−	0.0686405i
$545$	14.4792			0.620220
$546$		0			0
$547$		−	1.16878i		−	0.0499734i	−0.999688	−	0.0249867i	$-0.992046\pi$
$547$		−	1.16878i		−	0.0499734i	0.999688	−	0.0249867i	$-0.00795434\pi$
$548$	−4.54487	−	7.87195i	−0.194147	−	0.336273i
$549$		0			0
$550$	10.1885	+	4.95304i	0.434440	+	0.211198i
$551$	−23.4113	+	13.5165i	−0.997355	+	0.575823i
$552$		0			0
$553$	−41.0053	−	4.99146i	−1.74372	−	0.212258i
$554$	−20.4006			−0.866739
$555$		0			0
$556$	3.93273	−	6.81169i	0.166785	−	0.288880i
$557$	4.20151	+	2.42574i	0.178024	+	0.102782i	0.586364	−	0.810048i	$-0.300559\pi$
$557$	4.20151	+	2.42574i	0.178024	+	0.102782i	−0.408340	+	0.912830i	$0.633892\pi$
$558$		0			0
$559$			30.9360i			1.30845i
$560$	1.30439	+	3.06407i	0.0551205	+	0.129481i
$561$		0			0
$562$	4.99767	+	8.65622i	0.210814	+	0.365141i
$563$	−13.0572	+	22.6158i	−0.550297	+	0.953143i	0.447956	+	0.894056i	$0.352152\pi$
$563$	−13.0572	+	22.6158i	−0.550297	+	0.953143i	−0.998253	+	0.0590869i	$0.981181\pi$
$564$		0			0
$565$	0.609293	−	0.351776i	0.0256332	−	0.0147993i
$566$		−	3.48896i		−	0.146652i
$567$		0			0
$568$		−	3.50810i		−	0.147196i
$569$	−6.47913	+	3.74073i	−0.271619	+	0.156820i	−0.629623	−	0.776901i	$-0.716791\pi$
$569$	−6.47913	+	3.74073i	−0.271619	+	0.156820i	0.358004	+	0.933720i	$0.383457\pi$
$570$		0			0
$571$	28.5249	+	16.4688i	1.19373	+	0.689199i	0.959150	−	0.282898i	$-0.0912958\pi$
$571$	28.5249	+	16.4688i	1.19373	+	0.689199i	0.234578	+	0.972097i	$0.424629\pi$
$572$	−7.58763	−	11.2179i	−0.317255	−	0.469045i
$573$		0			0
$574$	−15.8968	−	1.93507i	−0.663518	−	0.0807682i
$575$	28.1890			1.17556
$576$		0			0
$577$	1.34703	+	0.777711i	0.0560778	+	0.0323765i	0.527777	−	0.849383i	$-0.323026\pi$
$577$	1.34703	+	0.777711i	0.0560778	+	0.0323765i	−0.471699	+	0.881760i	$0.656359\pi$
$578$	−5.84372	−	3.37387i	−0.243067	−	0.140335i
$579$		0			0
$580$	−4.46060			−0.185216
$581$	2.81244	+	2.11473i	0.116680	+	0.0877340i
$582$		0			0
$583$	−8.91290	−	13.1773i	−0.369134	−	0.545747i
$584$	0.837321	+	0.483428i	0.0346486	+	0.0200044i
$585$		0			0
$586$	−15.0298	+	8.67744i	−0.620874	+	0.358462i
$587$		−	42.8124i		−	1.76706i	−0.468376	−	0.883529i	$-0.655161\pi$
$587$		−	42.8124i		−	1.76706i	0.468376	−	0.883529i	$-0.344839\pi$
$588$		0			0
$589$		−	70.0520i		−	2.88644i
$590$	−2.97942	+	1.72017i	−0.122661	+	0.0708183i
$591$		0			0
$592$	0.154122	−	0.266948i	0.00633439	−	0.0109715i
$593$	−16.7711	−	29.0484i	−0.688707	−	1.19288i	−0.972256	−	0.233918i	$-0.924845\pi$
$593$	−16.7711	−	29.0484i	−0.688707	−	1.19288i	0.283549	−	0.958958i	$-0.408488\pi$
$594$		0			0
$595$	−6.40821	+	8.52244i	−0.262711	+	0.349386i
$596$			6.23096i			0.255230i
$597$		0			0
$598$	−29.1842	−	16.8495i	−1.19343	−	0.689029i
$599$	7.00856	−	12.1392i	0.286362	−	0.495993i	−0.686577	−	0.727057i	$-0.740887\pi$
$599$	7.00856	−	12.1392i	0.286362	−	0.495993i	0.972939	+	0.231064i	$0.0742207\pi$
$600$		0			0
$601$	−36.1513			−1.47464			−0.737322	−	0.675542i	$-0.763910\pi$
$601$	−36.1513			−1.47464			−0.737322	+	0.675542i	$0.763910\pi$
$602$	−2.42207	+	19.8975i	−0.0987163	+	0.810963i
$603$		0			0
$604$	−15.1642	+	8.75506i	−0.617023	+	0.356238i
$605$	12.8506	+	5.15353i	0.522453	+	0.209521i
$606$		0			0
$607$	14.8196	+	25.6684i	0.601511	+	1.04185i	0.992593	+	0.121491i	$0.0387676\pi$
$607$	14.8196	+	25.6684i	0.601511	+	1.04185i	−0.391082	+	0.920356i	$0.627899\pi$
$608$			7.62813i			0.309362i
$609$		0			0
$610$	−1.90074			−0.0769586
$611$	16.6301	−	9.60139i	0.672782	−	0.388431i
$612$		0			0
$613$	−28.9964	−	16.7411i	−1.17115	−	0.676166i	−0.217202	−	0.976127i	$-0.569693\pi$
$613$	−28.9964	−	16.7411i	−1.17115	−	0.676166i	−0.953951	+	0.299961i	$0.903026\pi$
$614$	−19.6439	+	11.3414i	−0.792765	+	0.457703i
$615$		0			0
$616$	−4.00195	−	7.80925i	−0.161243	−	0.314644i
$617$	−8.79395			−0.354031			−0.177016	−	0.984208i	$-0.556644\pi$
$617$	−8.79395			−0.354031			−0.177016	+	0.984208i	$0.556644\pi$
$618$		0			0
$619$	24.2445	+	13.9976i	0.974469	+	0.562610i	0.900596	−	0.434657i	$-0.143131\pi$
$619$	24.2445	+	13.9976i	0.974469	+	0.562610i	0.0738736	+	0.997268i	$0.476464\pi$
$620$	5.77948	−	10.0104i	0.232109	−	0.402025i
$621$		0			0
$622$	6.64116			0.266286
$623$	−27.9701	−	3.40473i	−1.12060	−	0.136408i
$624$		0			0
$625$	−1.87286	−	3.24390i	−0.0749146	−	0.129756i
$626$	0.251484	−	0.435583i	0.0100513	−	0.0174094i
$627$		0			0
$628$	−6.73252	+	3.88702i	−0.268657	+	0.155109i
$629$	0.986974			0.0393532
$630$		0			0
$631$	−0.154087			−0.00613412			−0.00306706	−	0.999995i	$-0.500976\pi$
$631$	−0.154087			−0.00613412			−0.00306706	+	0.999995i	$0.500976\pi$
$632$	−7.80647	−	13.5212i	−0.310525	−	0.537844i
$633$		0			0
$634$	9.13547	+	5.27437i	0.362816	+	0.209472i
$635$	−7.10081	−	12.2990i	−0.281787	−	0.488069i
$636$		0			0
$637$	−7.93596	−	27.4599i	−0.314434	−	1.08800i
$638$	11.7240	−	0.834995i	0.464156	−	0.0330578i
$639$		0			0
$640$	−0.629341	+	1.09005i	−0.0248769	+	0.0430880i
$641$	−9.92017	+	17.1822i	−0.391823	+	0.678658i	−0.992690	−	0.120691i	$-0.961489\pi$
$641$	−9.92017	+	17.1822i	−0.391823	+	0.678658i	0.600867	+	0.799349i	$0.294822\pi$
$642$		0			0
$643$		−	25.2948i		−	0.997529i	−0.866737	−	0.498765i	$-0.833787\pi$
$643$		−	25.2948i		−	0.997529i	0.866737	−	0.498765i	$-0.166213\pi$
$644$	−17.4516	−	13.1223i	−0.687690	−	0.517089i
$645$		0			0
$646$	−21.1523	+	12.2123i	−0.832228	+	0.480487i
$647$	−0.813596	−	0.469730i	−0.0319857	−	0.0184670i	0.483922	−	0.875111i	$-0.339212\pi$
$647$	−0.813596	−	0.469730i	−0.0319857	−	0.0184670i	−0.515908	+	0.856644i	$0.672545\pi$
$648$		0			0
$649$	7.50893	−	5.07892i	0.294751	−	0.199365i
$650$			13.9477i			0.547073i
$651$		0			0
$652$	18.2123			0.713249
$653$	−5.50375	−	9.53278i	−0.215379	−	0.373047i	0.738011	−	0.674789i	$-0.235765\pi$
$653$	−5.50375	−	9.53278i	−0.215379	−	0.373047i	−0.953390	+	0.301742i	$0.902432\pi$
$654$		0			0
$655$	−7.66729	−	4.42671i	−0.299586	−	0.172966i
$656$	−3.02638	−	5.24185i	−0.118160	−	0.204660i
$657$		0			0
$658$	11.4479	−	4.87344i	0.446287	−	0.189986i
$659$		−	29.9068i		−	1.16500i	−0.812830	−	0.582501i	$-0.802074\pi$
$659$		−	29.9068i		−	1.16500i	0.812830	−	0.582501i	$-0.197926\pi$
$660$		0			0
$661$	2.32896	+	1.34463i	0.0905861	+	0.0522999i	0.544609	−	0.838690i	$-0.316678\pi$
$661$	2.32896	+	1.34463i	0.0905861	+	0.0522999i	−0.454023	+	0.890990i	$0.650011\pi$
$662$	−5.00613	−	2.89029i	−0.194569	−	0.112334i
$663$		0			0
$664$			1.32998i			0.0516132i
$665$	−9.95006	−	23.3731i	−0.385847	−	0.906371i
$666$		0			0
$667$	25.3282	−	14.6233i	0.980713	−	0.566215i
$668$	7.18264	−	12.4407i	0.277905	−	0.481345i
$669$		0			0
$670$	2.12772	+	3.68532i	0.0822011	+	0.142376i
$671$	4.99578	−	0.355806i	0.192860	−	0.0137357i
$672$		0			0
$673$		−	3.56361i		−	0.137367i	−0.997638	−	0.0686836i	$-0.978120\pi$
$673$		−	3.56361i		−	0.137367i	0.997638	−	0.0686836i	$-0.0218799\pi$
$674$	−5.56129	−	9.63243i	−0.214213	−	0.371027i
$675$		0			0
$676$	1.83701	−	3.18180i	0.0706543	−	0.122377i
$677$	15.5901	+	27.0029i	0.599178	+	1.03781i	0.992943	+	0.118595i	$0.0378390\pi$
$677$	15.5901	+	27.0029i	0.599178	+	1.03781i	−0.393765	+	0.919211i	$0.628828\pi$
$678$		0			0
$679$	16.9734	−	22.5734i	0.651381	−	0.866288i
$680$	−4.03019			−0.154551
$681$		0			0
$682$	−13.3166	+	27.3925i	−0.509918	+	1.04891i
$683$	−7.79993	+	13.5099i	−0.298456	+	0.516941i	−0.975783	−	0.218741i	$-0.929805\pi$
$683$	−7.79993	+	13.5099i	−0.298456	+	0.516941i	0.677327	+	0.735682i	$0.263138\pi$
$684$		0			0
$685$			11.4411i			0.437142i
$686$	−2.95436	−	18.2831i	−0.112798	−	0.698052i
$687$		0			0
$688$	−6.56107	+	3.78804i	−0.250138	+	0.144417i
$689$	9.79316	−	16.9623i	0.373090	−	0.646210i
$690$		0			0
$691$	−31.8902	+	18.4118i	−1.21316	+	0.700419i	−0.963447	−	0.267901i	$-0.913670\pi$
$691$	−31.8902	+	18.4118i	−1.21316	+	0.700419i	−0.249714	+	0.968320i	$0.580337\pi$
$692$	4.76319			0.181069
$693$		0			0
$694$	−14.6714			−0.556918
$695$	−8.57375	+	4.95006i	−0.325221	+	0.187766i
$696$		0			0
$697$	9.69021	−	16.7839i	0.367043	−	0.635737i
$698$	−21.3708	+	12.3385i	−0.808899	+	0.467018i
$699$		0			0
$700$	−1.09201	+	8.97092i	−0.0412739	+	0.339069i
$701$			15.6940i			0.592754i	0.955071	+	0.296377i	$0.0957784\pi$
$701$			15.6940i			0.592754i	−0.955071	+	0.296377i	$0.904222\pi$
$702$		0			0
$703$	−1.17567	+	2.03631i	−0.0443411	+	0.0768010i
$704$	1.45007	−	2.98283i	0.0546516	−	0.112420i
$705$		0			0
$706$	−19.2447			−0.724285
$707$	−24.5014	+	10.4303i	−0.921468	+	0.392273i
$708$		0			0
$709$	12.1733	+	21.0847i	0.457176	+	0.791852i	0.998810	−	0.0487621i	$-0.0155276\pi$
$709$	12.1733	+	21.0847i	0.457176	+	0.791852i	−0.541634	+	0.840614i	$0.682194\pi$
$710$	−2.20779	+	3.82400i	−0.0828569	+	0.143512i
$711$		0			0
$712$	−5.32488	−	9.22296i	−0.199558	−	0.345645i
$713$			75.7880i			2.83828i
$714$		0			0
$715$	1.21100	+	17.0033i	0.0452887	+	0.635888i
$716$	1.94526	+	3.36928i	0.0726976	+	0.125916i
$717$		0			0
$718$	1.64703	−	2.85275i	0.0614668	−	0.106464i
$719$	−36.9070	+	21.3083i	−1.37640	+	0.794665i	−0.991724	−	0.128386i	$-0.959020\pi$
$719$	−36.9070	+	21.3083i	−1.37640	+	0.794665i	−0.384676	+	0.923051i	$0.625687\pi$
$720$		0			0
$721$	7.57766	+	0.922408i	0.282207	+	0.0343523i
$722$		−	39.1884i		−	1.45844i
$723$		0			0
$724$	−11.3188	−	6.53492i	−0.420661	−	0.242868i
$725$	−10.4831	−	6.05242i	−0.389332	−	0.224781i
$726$		0			0
$727$			23.2698i			0.863031i	0.902106	+	0.431515i	$0.142021\pi$
$727$			23.2698i			0.863031i	−0.902106	+	0.431515i	$0.857979\pi$
$728$	6.49279	−	8.63492i	0.240639	−	0.320031i
$729$		0			0
$730$	−0.608482	−	1.05392i	−0.0225209	−	0.0390074i
$731$	−21.0080	−	12.1290i	−0.777008	−	0.448606i
$732$		0			0
$733$	−18.8378	−	32.6281i	−0.695791	−	1.20515i	−0.969913	−	0.243450i	$-0.921721\pi$
$733$	−18.8378	−	32.6281i	−0.695791	−	1.20515i	0.274122	−	0.961695i	$-0.411613\pi$
$734$	−30.9410			−1.14205
$735$		0			0
$736$		−	8.25273i		−	0.304200i
$737$	−6.28225	−	9.28799i	−0.231410	−	0.342127i
$738$		0			0
$739$	0.479784	+	0.277003i	0.0176491	+	0.0101897i	0.508799	−	0.860886i	$-0.330090\pi$
$739$	0.479784	+	0.277003i	0.0176491	+	0.0101897i	−0.491149	+	0.871075i	$0.663423\pi$
$740$	−0.336003	+	0.193991i	−0.0123517	+	0.00713126i
$741$		0			0
$742$	7.62682	−	10.1431i	0.279990	−	0.372365i
$743$			20.1974i			0.740972i	0.928838	+	0.370486i	$0.120809\pi$
$743$			20.1974i			0.740972i	−0.928838	+	0.370486i	$0.879191\pi$
$744$		0			0
$745$	3.92140	−	6.79207i	0.143669	−	0.248842i
$746$	−0.480798	+	0.832767i	−0.0176033	+	0.0304898i
$747$		0			0
$748$	10.5927	−	0.754426i	0.387308	−	0.0275845i
$749$	−42.8098	−	5.21112i	−1.56424	−	0.190410i
$750$		0			0
$751$	−3.70031	−	6.40913i	−0.135026	−	0.233872i	0.790581	−	0.612357i	$-0.209779\pi$
$751$	−3.70031	−	6.40913i	−0.135026	−	0.233872i	−0.925607	+	0.378485i	$0.876445\pi$
$752$	4.07263	+	2.35133i	0.148513	+	0.0857443i
$753$		0			0
$754$	7.23547	+	12.5322i	0.263500	+	0.456396i
$755$	22.0397			0.802106
$756$		0			0
$757$	−29.1994			−1.06127			−0.530636	−	0.847600i	$-0.678047\pi$
$757$	−29.1994			−1.06127			−0.530636	+	0.847600i	$0.678047\pi$
$758$	1.22297	−	0.706081i	0.0444202	−	0.0256460i
$759$		0			0
$760$	4.80070	−	8.31505i	0.174140	−	0.301619i
$761$	25.4831	+	44.1380i	0.923761	+	1.60000i	0.793541	+	0.608517i	$0.208235\pi$
$761$	25.4831	+	44.1380i	0.923761	+	1.60000i	0.130220	+	0.991485i	$0.458432\pi$
$762$		0			0
$763$	−11.9212	−	28.0034i	−0.431576	−	1.01379i
$764$	6.00000			0.217072
$765$		0			0
$766$	1.89039	−	3.27426i	0.0683027	−	0.118304i
$767$	9.66576	+	5.58053i	0.349010	+	0.201501i
$768$		0			0
$769$	32.9963			1.18988			0.594938	−	0.803771i	$-0.297176\pi$
$769$	32.9963			1.18988			0.594938	+	0.803771i	$0.297176\pi$
$770$	−0.552347	+	11.0311i	−0.0199052	+	0.397532i
$771$		0			0
$772$	8.12582	−	4.69144i	0.292455	−	0.168849i
$773$	28.1797	+	16.2696i	1.01355	+	0.585175i	0.912230	−	0.409678i	$-0.134359\pi$
$773$	28.1797	+	16.2696i	1.01355	+	0.585175i	0.101323	+	0.994854i	$0.467692\pi$
$774$		0			0
$775$	27.1654	−	15.6839i	0.975808	−	0.563383i
$776$	10.6748			0.383202
$777$		0			0
$778$		−	3.37886i		−	0.121138i
$779$	23.0856	+	39.9855i	0.827129	+	1.43263i
$780$		0			0
$781$	5.08699	−	10.4641i	0.182027	−	0.374434i
$782$	22.8843	−	13.2123i	0.818341	−	0.472470i
$783$		0			0
$784$	4.85211	−	5.04550i	0.173290	−	0.180196i
$785$	9.78505			0.349243
$786$		0			0
$787$	−10.0577	+	17.4205i	−0.358519	+	0.620973i	−0.987714	−	0.156275i	$-0.950051\pi$
$787$	−10.0577	+	17.4205i	−0.358519	+	0.620973i	0.629195	+	0.777248i	$0.283385\pi$
$788$	−15.0230	−	8.67356i	−0.535174	−	0.308983i
$789$		0			0
$790$			19.6517i			0.699177i
$791$	−1.18200	−	0.888772i	−0.0420271	−	0.0316011i
$792$		0			0
$793$	3.08316	+	5.34019i	0.109486	+	0.189636i
$794$	5.76499	−	9.98525i	0.204592	−	0.354363i
$795$		0			0
$796$	2.53353	−	1.46273i	0.0897985	−	0.0518452i
$797$		−	31.1568i		−	1.10363i	−0.833966	−	0.551816i	$-0.813935\pi$
$797$		−	31.1568i		−	1.10363i	0.833966	−	0.551816i	$-0.186065\pi$
$798$		0			0
$799$			15.0575i			0.532697i
$800$	−2.95810	+	1.70786i	−0.104585	+	0.0603819i
$801$		0			0
$802$	−22.5619	−	13.0261i	−0.796689	−	0.459969i
$803$	1.79658	+	2.65616i	0.0634001	+	0.0937339i
$804$		0			0
$805$	10.7648	+	25.2870i	0.379409	+	0.891248i
$806$	−37.4993			−1.32086
$807$		0			0
$808$	−8.71642	−	5.03242i	−0.306642	−	0.177040i
$809$	−12.6960	−	7.33001i	−0.446366	−	0.257709i	0.259928	−	0.965628i	$-0.416301\pi$
$809$	−12.6960	−	7.33001i	−0.446366	−	0.257709i	−0.706294	+	0.707918i	$0.749634\pi$
$810$		0			0
$811$	45.7501			1.60650			0.803251	−	0.595640i	$-0.203102\pi$
$811$	45.7501			1.60650			0.803251	+	0.595640i	$0.203102\pi$
$812$	3.67255	+	8.62700i	0.128881	+	0.302748i
$813$		0			0
$814$	0.846815	−	0.572772i	0.0296809	−	0.0200757i
$815$	−19.8523	−	11.4618i	−0.695397	−	0.401488i
$816$		0			0
$817$	50.0487	−	28.8956i	1.75098	−	1.01093i
$818$			35.0217i			1.22451i
$819$		0			0
$820$			7.61851i			0.266050i
$821$	6.11121	−	3.52831i	0.213283	−	0.123139i	−0.389553	−	0.921004i	$-0.627371\pi$
$821$	6.11121	−	3.52831i	0.213283	−	0.123139i	0.602836	+	0.797865i	$0.294037\pi$
$822$		0			0
$823$	14.2038	−	24.6016i	0.495112	−	0.857559i	−0.504872	−	0.863194i	$-0.668460\pi$
$823$	14.2038	−	24.6016i	0.495112	−	0.857559i	0.999984	+	0.00563530i	$0.00179378\pi$
$824$	1.44261	+	2.49868i	0.0502559	+	0.0870457i
$825$		0			0
$826$	5.77994	+	4.34606i	0.201110	+	0.151219i
$827$		−	0.161893i		−	0.00562957i	−0.999996	−	0.00281478i	$-0.999104\pi$
$827$		−	0.161893i		−	0.00562957i	0.999996	−	0.00281478i	$-0.000895975\pi$
$828$		0			0
$829$	−21.0966	−	12.1801i	−0.732715	−	0.423033i	0.0866997	−	0.996234i	$-0.472368\pi$
$829$	−21.0966	−	12.1801i	−0.732715	−	0.423033i	−0.819415	+	0.573201i	$0.805701\pi$
$830$	0.837011	−	1.44974i	0.0290531	−	0.0503214i
$831$		0			0
$832$	4.08338			0.141566
$833$	21.7589	+	5.37697i	0.753900	+	0.186301i
$834$		0			0
$835$	−15.6589	+	9.04066i	−0.541898	+	0.312865i
$836$	−11.0613	+	22.7534i	−0.382564	+	0.786944i
$837$		0			0
$838$	−6.06211	−	10.4999i	−0.209412	−	0.362713i
$839$		−	3.31341i		−	0.114392i	−0.998363	−	0.0571958i	$-0.981784\pi$
$839$		−	3.31341i		−	0.114392i	0.998363	−	0.0571958i	$-0.0182159\pi$
$840$		0			0
$841$	16.4410			0.566932
$842$	−16.1895	+	9.34699i	−0.557926	+	0.322119i
$843$		0			0
$844$	0.218870	+	0.126365i	0.00753382	+	0.00434965i
$845$	−4.00487	+	2.31221i	−0.137772	+	0.0795425i
$846$		0			0
$847$	−0.613188	−	29.0968i	−0.0210694	−	0.999778i
$848$	4.79659			0.164716
$849$		0			0
$850$	−9.47158	−	5.46842i	−0.324873	−	0.187565i
$851$	1.27193	−	2.20305i	0.0436012	−	0.0755196i
$852$		0			0
$853$	17.0905			0.585169			0.292584	−	0.956240i	$-0.405485\pi$
$853$	17.0905			0.585169			0.292584	+	0.956240i	$0.405485\pi$
$854$	1.56494	+	3.67611i	0.0535511	+	0.125794i
$855$		0			0
$856$	−8.15002	−	14.1162i	−0.278562	−	0.482483i
$857$	11.2484	−	19.4827i	0.384237	−	0.665517i	−0.607426	−	0.794376i	$-0.707798\pi$
$857$	11.2484	−	19.4827i	0.384237	−	0.665517i	0.991663	+	0.128859i	$0.0411314\pi$
$858$		0			0
$859$	−33.3698	+	19.2661i	−1.13856	+	0.657350i	−0.946074	−	0.323950i	$-0.894989\pi$
$859$	−33.3698	+	19.2661i	−1.13856	+	0.657350i	−0.192489	+	0.981299i	$0.561656\pi$
$860$	9.53587			0.325170
$861$		0			0
$862$	33.9418			1.15606
$863$	−12.8730	−	22.2967i	−0.438202	−	0.758989i	0.559348	−	0.828933i	$-0.311051\pi$
$863$	−12.8730	−	22.2967i	−0.438202	−	0.758989i	−0.997551	+	0.0699437i	$0.977718\pi$
$864$		0			0
$865$	−5.19212	−	2.99767i	−0.176537	−	0.101924i
$866$	13.5474	+	23.4648i	0.460360	+	0.797368i
$867$		0			0
$868$	−24.1189	−	2.93593i	−0.818649	−	0.0996519i
$869$	−3.67867	−	51.6514i	−0.124790	−	1.75215i
$870$		0			0
$871$	6.90270	−	11.9558i	0.233889	−	0.405108i
$872$	5.75172	−	9.96227i	0.194778	−	0.337365i
$873$		0			0
$874$			62.9529i			2.12941i
$875$	16.8430	−	22.3999i	0.569396	−	0.757254i
$876$		0			0
$877$	−14.7676	+	8.52609i	−0.498667	+	0.287906i	−0.728163	−	0.685404i	$-0.759626\pi$
$877$	−14.7676	+	8.52609i	−0.498667	+	0.287906i	0.229496	+	0.973310i	$0.426292\pi$
$878$	−17.7135	−	10.2269i	−0.597803	−	0.345142i
$879$		0			0
$880$	−3.45787	+	2.33885i	−0.116565	+	0.0788426i
$881$		−	38.3968i		−	1.29362i	−0.762651	−	0.646811i	$-0.776102\pi$
$881$		−	38.3968i		−	1.29362i	0.762651	−	0.646811i	$-0.223898\pi$
$882$		0			0
$883$	−35.3727			−1.19038			−0.595192	−	0.803583i	$-0.702924\pi$
$883$	−35.3727			−1.19038			−0.595192	+	0.803583i	$0.702924\pi$
$884$	6.53732	+	11.3230i	0.219874	+	0.380833i
$885$		0			0
$886$	3.11541	+	1.79868i	0.104664	+	0.0604279i
$887$	−1.05289	−	1.82365i	−0.0353525	−	0.0612322i	0.847808	−	0.530304i	$-0.177922\pi$
$887$	−1.05289	−	1.82365i	−0.0353525	−	0.0612322i	−0.883160	+	0.469071i	$0.844589\pi$
$888$		0			0
$889$	−17.9404	+	23.8594i	−0.601702	+	0.800219i
$890$			13.4047i			0.449325i
$891$		0			0
$892$	16.4866	+	9.51852i	0.552011	+	0.318704i
$893$	−31.0665	−	17.9363i	−1.03960	−	0.600215i
$894$		0			0
$895$		−	4.89692i		−	0.163686i
$896$	2.62636	+	0.319700i	0.0877407	+	0.0106804i
$897$		0			0
$898$	32.1005	−	18.5332i	1.07121	−	0.618461i
$899$	16.2723	−	28.1845i	0.542712	−	0.940005i
$900$		0			0
$901$	7.67914	+	13.3007i	0.255829	+	0.443109i
$902$	−1.42613	−	20.0240i	−0.0474851	−	0.666727i
$903$		0			0
$904$		−	0.558958i		−	0.0185907i
$905$	8.22539	+	14.2468i	0.273421	+	0.473579i
$906$		0			0
$907$	−25.2204	+	43.6831i	−0.837431	+	1.45047i	0.0546043	+	0.998508i	$0.482610\pi$
$907$	−25.2204	+	43.6831i	−0.837431	+	1.45047i	−0.892035	+	0.451965i	$0.850723\pi$
$908$	9.20350	+	15.9409i	0.305429	+	0.529018i
$909$		0			0
$910$	−12.5118	+	5.32632i	−0.414761	+	0.176566i
$911$	1.24825			0.0413565			0.0206782	−	0.999786i	$-0.493417\pi$
$911$	1.24825			0.0413565			0.0206782	+	0.999786i	$0.493417\pi$
$912$		0			0
$913$	−1.92857	+	3.96711i	−0.0638262	+	0.131292i
$914$	−9.07561	+	15.7194i	−0.300195	+	0.519952i
$915$		0			0
$916$			5.30786i			0.175377i
$917$	−2.24873	+	18.4735i	−0.0742597	+	0.610050i
$918$		0			0
$919$	−14.0660	+	8.12103i	−0.463996	+	0.267888i	−0.713723	−	0.700428i	$-0.752992\pi$
$919$	−14.0660	+	8.12103i	−0.463996	+	0.267888i	0.249727	+	0.968316i	$0.419659\pi$
$920$	−5.19378	+	8.99589i	−0.171234	+	0.296586i
$921$		0			0
$922$	−19.4231	+	11.2139i	−0.639665	+	0.369311i
$923$	14.3249			0.471510
$924$		0			0
$925$	−1.05288			−0.0346184
$926$	13.5337	−	7.81370i	0.444746	−	0.256774i
$927$		0			0
$928$	−1.77193	+	3.06907i	−0.0581665	+	0.100747i
$929$	20.7072	−	11.9553i	0.679382	−	0.392242i	−0.120240	−	0.992745i	$-0.538366\pi$
$929$	20.7072	−	11.9553i	0.679382	−	0.392242i	0.799622	+	0.600503i	$0.205033\pi$
$930$		0			0
$931$	−37.0125	+	38.4877i	−1.21304	+	1.26138i
$932$			21.3192i			0.698332i
$933$		0			0
$934$	−3.04760	+	5.27860i	−0.0997206	+	0.172721i
$935$	−12.0214	−	5.84407i	−0.393142	−	0.191122i
$936$		0			0
$937$	28.2482			0.922827			0.461414	−	0.887185i	$-0.347342\pi$
$937$	28.2482			0.922827			0.461414	+	0.887185i	$0.347342\pi$
$938$	5.37576	−	7.14936i	0.175525	−	0.233435i
$939$		0			0
$940$	−2.95958	−	5.12614i	−0.0965309	−	0.167196i
$941$	−29.3512	+	50.8377i	−0.956821	+	1.65726i	−0.226677	+	0.973970i	$0.572786\pi$
$941$	−29.3512	+	50.8377i	−0.956821	+	1.65726i	−0.730144	+	0.683293i	$0.760547\pi$
$942$		0			0
$943$	−24.9759	−	43.2595i	−0.813327	−	1.40872i
$944$			2.73329i			0.0889609i
$945$		0			0
$946$	−25.0635	+	1.78505i	−0.814885	+	0.0580371i
$947$	−22.1672	−	38.3948i	−0.720338	−	1.24766i	−0.960864	−	0.277020i	$-0.910653\pi$
$947$	−22.1672	−	38.3948i	−0.720338	−	1.24766i	0.240526	−	0.970643i	$-0.422680\pi$
$948$		0			0
$949$	−1.97402	+	3.41910i	−0.0640794	+	0.110989i
$950$	22.5648	−	13.0278i	0.732098	−	0.422677i
$951$		0			0
$952$	3.31819	+	7.79458i	0.107543	+	0.252624i
$953$			13.9238i			0.451037i	0.974239	+	0.225518i	$0.0724075\pi$
$953$			13.9238i			0.451037i	−0.974239	+	0.225518i	$0.927592\pi$
$954$		0			0
$955$	−6.54031	−	3.77605i	−0.211639	−	0.122190i
$956$	−6.28010	−	3.62582i	−0.203113	−	0.117267i
$957$		0			0
$958$			30.6275i			0.989531i
$959$	22.1276	−	9.41982i	0.714537	−	0.304182i
$960$		0			0
$961$	26.6672	+	46.1890i	0.860233	+	1.48997i
$962$	1.09005	+	0.629341i	0.0351447	+	0.0202908i
$963$		0			0
$964$	1.77705	+	3.07794i	0.0572349	+	0.0991337i
$965$	−11.8101			−0.380180
$966$		0			0
$967$			29.3085i			0.942499i	0.882000	+	0.471250i	$0.156197\pi$
$967$			29.3085i			0.942499i	−0.882000	+	0.471250i	$0.843803\pi$
$968$	8.65064	−	6.79458i	0.278042	−	0.218386i
$969$		0			0
$970$	−11.6361	−	6.71808i	−0.373611	−	0.215705i
$971$	0.0286574	−	0.0165453i	0.000919659	−	0.000530965i	−0.499540	−	0.866291i	$-0.666498\pi$
$971$	0.0286574	−	0.0165453i	0.000919659	−	0.000530965i	0.500460	+	0.865760i	$0.333164\pi$
$972$		0			0
$973$	16.6327	+	12.5065i	0.533219	+	0.400939i
$974$			3.17453i			0.101718i
$975$		0			0
$976$	−0.755050	+	1.30779i	−0.0241686	+	0.0418612i
$977$	21.0948	−	36.5373i	0.674883	−	1.16893i	−0.301620	−	0.953428i	$-0.597527\pi$
$977$	21.0948	−	36.5373i	0.674883	−	1.16893i	0.976503	−	0.215503i	$-0.0691392\pi$
$978$		0			0
$979$	−2.50926	−	35.2320i	−0.0801964	−	1.12602i
$980$	−8.46438	+	2.44622i	−0.270385	+	0.0781416i
$981$		0			0
$982$	−16.3254	−	28.2763i	−0.520963	−	0.902335i
$983$	44.0056	+	25.4067i	1.40356	+	0.810347i	0.994756	−	0.102274i	$-0.0326120\pi$
$983$	44.0056	+	25.4067i	1.40356	+	0.810347i	0.408806	+	0.912621i	$0.365945\pi$
$984$		0			0
$985$	10.9173	+	18.9092i	0.347853	+	0.602499i
$986$	−11.3471			−0.361367
$987$		0			0
$988$	−31.1486			−0.990968
$989$	−54.1467	+	31.2616i	−1.72177	+	0.994062i
$990$		0			0
$991$	−23.2614	+	40.2899i	−0.738923	+	1.27985i	0.214058	+	0.976821i	$0.431332\pi$
$991$	−23.2614	+	40.2899i	−0.738923	+	1.27985i	−0.952981	+	0.303030i	$0.902002\pi$
$992$	−4.59169	−	7.95304i	−0.145786	−	0.252509i
$993$		0			0
$994$	9.21354	+	1.12154i	0.292236	+	0.0355731i
$995$	−3.68223			−0.116735
$996$		0			0
$997$	2.26888	−	3.92981i	0.0718560	−	0.124458i	−0.827859	−	0.560937i	$-0.810441\pi$
$997$	2.26888	−	3.92981i	0.0718560	−	0.124458i	0.899715	+	0.436478i	$0.143774\pi$
$998$	24.6426	+	14.2274i	0.780048	+	0.450361i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.c.703.1		16
3.2	odd	2		154.2.i.a.87.6	yes	16
7.5	odd	6	inner	1386.2.bk.c.901.5		16
11.10	odd	2	inner	1386.2.bk.c.703.5		16
12.11	even	2		1232.2.bn.b.241.5		16
21.2	odd	6		1078.2.i.c.901.3		16
21.5	even	6		154.2.i.a.131.2	yes	16
21.11	odd	6		1078.2.c.b.1077.13		16
21.17	even	6		1078.2.c.b.1077.12		16
21.20	even	2		1078.2.i.c.1011.7		16
33.32	even	2		154.2.i.a.87.2	✓	16
77.54	even	6	inner	1386.2.bk.c.901.1		16
84.47	odd	6		1232.2.bn.b.593.6		16
132.131	odd	2		1232.2.bn.b.241.6		16
231.32	even	6		1078.2.c.b.1077.5		16
231.65	even	6		1078.2.i.c.901.7		16
231.131	odd	6		154.2.i.a.131.6	yes	16
231.164	odd	6		1078.2.c.b.1077.4		16
231.230	odd	2		1078.2.i.c.1011.3		16
924.131	even	6		1232.2.bn.b.593.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.2	✓	16	33.32	even	2
154.2.i.a.87.6	yes	16	3.2	odd	2
154.2.i.a.131.2	yes	16	21.5	even	6
154.2.i.a.131.6	yes	16	231.131	odd	6
1078.2.c.b.1077.4		16	231.164	odd	6
1078.2.c.b.1077.5		16	231.32	even	6
1078.2.c.b.1077.12		16	21.17	even	6
1078.2.c.b.1077.13		16	21.11	odd	6
1078.2.i.c.901.3		16	21.2	odd	6
1078.2.i.c.901.7		16	231.65	even	6
1078.2.i.c.1011.3		16	231.230	odd	2
1078.2.i.c.1011.7		16	21.20	even	2
1232.2.bn.b.241.5		16	12.11	even	2
1232.2.bn.b.241.6		16	132.131	odd	2
1232.2.bn.b.593.5		16	924.131	even	6
1232.2.bn.b.593.6		16	84.47	odd	6
1386.2.bk.c.703.1		16	1.1	even	1	trivial
1386.2.bk.c.703.5		16	11.10	odd	2	inner
1386.2.bk.c.901.1		16	77.54	even	6	inner
1386.2.bk.c.901.5		16	7.5	odd	6	inner

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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.09005 + 0.629341i) q^{5} +(2.11465 + 1.59005i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.09005 + 0.629341i) q^{5} +(2.11465 + 1.59005i) q^{7} +1.00000i q^{8} +(0.629341 - 1.09005i) q^{10} +(-1.45007 + 2.98283i) q^{11} -4.08338 q^{13} +(-2.62636 - 0.319700i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.60096 - 2.77294i) q^{17} +(3.81407 + 6.60616i) q^{19} +1.25868i q^{20} +(-0.235617 - 3.30824i) q^{22} +(-4.12636 - 7.14707i) q^{23} +(-1.70786 + 2.95810i) q^{25} +(3.53631 - 2.04169i) q^{26} +(2.43435 - 1.03631i) q^{28} +3.54386i q^{29} +(-7.95304 - 4.59169i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.20191i q^{34} +(-3.30576 - 0.402401i) q^{35} +(0.154122 + 0.266948i) q^{37} +(-6.60616 - 3.81407i) q^{38} +(-0.629341 - 1.09005i) q^{40} +6.05276 q^{41} -7.57607i q^{43} +(1.85817 + 2.74722i) q^{44} +(7.14707 + 4.12636i) q^{46} +(-4.07263 + 2.35133i) q^{47} +(1.94348 + 6.72480i) q^{49} -3.41572i q^{50} +(-2.04169 + 3.53631i) q^{52} +(-2.39830 + 4.15397i) q^{53} +(-0.296567 - 4.16403i) q^{55} +(-1.59005 + 2.11465i) q^{56} +(-1.77193 - 3.06907i) q^{58} +(-2.36710 - 1.36664i) q^{59} +(-0.755050 - 1.30779i) q^{61} +9.18338 q^{62} -1.00000 q^{64} +(4.45110 - 2.56984i) q^{65} +(-1.69044 + 2.92792i) q^{67} +(-1.60096 - 2.77294i) q^{68} +(3.06407 - 1.30439i) q^{70} -3.50810 q^{71} +(0.483428 - 0.837321i) q^{73} +(-0.266948 - 0.154122i) q^{74} +7.62813 q^{76} +(-7.80925 + 4.00195i) q^{77} +(-13.5212 + 7.80647i) q^{79} +(1.09005 + 0.629341i) q^{80} +(-5.24185 + 3.02638i) q^{82} +1.32998 q^{83} +4.03019i q^{85} +(3.78804 + 6.56107i) q^{86} +(-2.98283 - 1.45007i) q^{88} +(-9.22296 + 5.32488i) q^{89} +(-8.63492 - 6.49279i) q^{91} -8.25273 q^{92} +(2.35133 - 4.07263i) q^{94} +(-8.31505 - 4.80070i) q^{95} -10.6748i q^{97} +(-5.04550 - 4.85211i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5	\( 16 q + 8 q^{4} + 12 q^{5} - 8 q^{11} + 8 q^{14} - 8 q^{16} - 8 q^{22} - 16 q^{23} + 36 q^{26} - 12 q^{31} - 16 q^{37} - 12 q^{38} + 8 q^{44} - 24 q^{47} + 8 q^{49} + 28 q^{53} + 4 q^{56} - 12 q^{58} - 60 q^{59} - 16 q^{64} + 12 q^{67} + 60 q^{70} - 8 q^{71} - 44 q^{77} - 12 q^{80} - 20 q^{86} - 4 q^{88} - 96 q^{89} - 36 q^{91} - 32 q^{92}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 - 8 * q^11 + 8 * q^14 - 8 * q^16 - 8 * q^22 - 16 * q^23 + 36 * q^26 - 12 * q^31 - 16 * q^37 - 12 * q^38 + 8 * q^44 - 24 * q^47 + 8 * q^49 + 28 * q^53 + 4 * q^56 - 12 * q^58 - 60 * q^59 - 16 * q^64 + 12 * q^67 + 60 * q^70 - 8 * q^71 - 44 * q^77 - 12 * q^80 - 20 * q^86 - 4 * q^88 - 96 * q^89 - 36 * q^91 - 32 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more