LMFDB - Embedded newform 336.3.be.f.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(79,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.79"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,9,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.1364138928.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 35x^{4} + 364x^{2} + 972 $ x^6 + 35x^4 + 364x^2 + 972
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$4.07390i$ of defining polynomial
Character	$\chi$	$=$	336.79
Dual form			336.3.be.f.319.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{3} +(-2.29832 + 3.98081i) q^{5} +(4.95955 - 4.93992i) q^{7} +(1.50000 - 2.59808i) q^{9} +(0.161228 - 0.0930852i) q^{11} +13.7090 q^{13} +7.96163i q^{15} +(-11.6528 - 20.1833i) q^{17} +(28.5074 + 16.4587i) q^{19} +(3.16123 - 11.7050i) q^{21} +(21.4911 + 12.4079i) q^{23} +(1.93542 + 3.35224i) q^{25} -5.19615i q^{27} +24.0641 q^{29} +(1.08871 - 0.628570i) q^{31} +(0.161228 - 0.279256i) q^{33} +(8.26626 + 31.0966i) q^{35} +(17.7736 - 30.7848i) q^{37} +(20.5636 - 11.8724i) q^{39} -77.2563 q^{41} -41.9125i q^{43} +(6.89497 + 11.9424i) q^{45} +(52.3787 + 30.2408i) q^{47} +(0.194309 - 48.9996i) q^{49} +(-34.9585 - 20.1833i) q^{51} +(-17.2983 - 29.9616i) q^{53} +0.855760i q^{55} +57.0147 q^{57} +(-1.78257 + 1.02917i) q^{59} +(-15.5484 + 26.9306i) q^{61} +(-5.39497 - 20.2952i) q^{63} +(-31.5078 + 54.5731i) q^{65} +(-65.3950 + 37.7558i) q^{67} +42.9821 q^{69} +30.7190i q^{71} +(22.7736 + 39.4451i) q^{73} +(5.80626 + 3.35224i) q^{75} +(0.339786 - 1.25812i) q^{77} +(0.943915 + 0.544970i) q^{79} +(-4.50000 - 7.79423i) q^{81} -39.4358i q^{83} +107.128 q^{85} +(36.0962 - 20.8401i) q^{87} +(-76.1113 + 131.829i) q^{89} +(67.9907 - 67.7216i) q^{91} +(1.08871 - 1.88571i) q^{93} +(-131.038 + 75.6550i) q^{95} -25.9359 q^{97} -0.558511i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + q^{5} + 11 q^{7} + 9 q^{9} - 3 q^{11} - 44 q^{13} + 8 q^{17} + 30 q^{19} + 15 q^{21} - 24 q^{23} - 14 q^{25} + 34 q^{29} + 39 q^{31} - 3 q^{33} + 90 q^{35} + 6 q^{37} - 66 q^{39} - 136 q^{41}+ \cdots - 266 q^{97}+O(q^{100}) $ 6 * q + 9 * q^3 + q^5 + 11 * q^7 + 9 * q^9 - 3 * q^11 - 44 * q^13 + 8 * q^17 + 30 * q^19 + 15 * q^21 - 24 * q^23 - 14 * q^25 + 34 * q^29 + 39 * q^31 - 3 * q^33 + 90 * q^35 + 6 * q^37 - 66 * q^39 - 136 * q^41 - 3 * q^45 + 258 * q^47 + 157 * q^49 + 24 * q^51 - 89 * q^53 + 60 * q^57 - 63 * q^59 - 50 * q^61 + 12 * q^63 - 184 * q^65 - 348 * q^67 - 48 * q^69 + 36 * q^73 - 42 * q^75 + 221 * q^77 - 3 * q^79 - 27 * q^81 + 536 * q^85 + 51 * q^87 - 202 * q^89 + 62 * q^91 + 39 * q^93 - 432 * q^95 - 266 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	−2.29832	+	3.98081i	−0.459665	+	0.796163i	−0.998943	−	0.0459650i	$-0.985364\pi$
$5$	−2.29832	+	3.98081i	−0.459665	+	0.796163i	0.539278	+	0.842128i	$0.318697\pi$
$6$		0			0
$7$	4.95955	−	4.93992i	0.708507	−	0.705703i
$7$	4.95955	−	4.93992i	0.708507	−	0.705703i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	0.161228	−	0.0930852i	0.0146571	−	0.00846229i	−0.492654	−	0.870226i	$-0.663973\pi$
$11$	0.161228	−	0.0930852i	0.0146571	−	0.00846229i	0.507311	+	0.861763i	$0.330640\pi$
$12$		0			0
$13$	13.7090			1.05454			0.527271	−	0.849697i	$-0.323215\pi$
$13$	13.7090			1.05454			0.527271	+	0.849697i	$0.323215\pi$
$14$		0			0
$15$			7.96163i			0.530775i
$16$		0			0
$17$	−11.6528	−	20.1833i	−0.685462	−	1.18725i	−0.973292	−	0.229573i	$-0.926267\pi$
$17$	−11.6528	−	20.1833i	−0.685462	−	1.18725i	0.287830	−	0.957682i	$-0.407066\pi$
$18$		0			0
$19$	28.5074	+	16.4587i	1.50039	+	0.866249i	1.00000		0.000447947i	$0.000142586\pi$
$19$	28.5074	+	16.4587i	1.50039	+	0.866249i	0.500388	+	0.865801i	$0.333191\pi$
$20$		0			0
$21$	3.16123	−	11.7050i	0.150535	−	0.557380i
$22$		0			0
$23$	21.4911	+	12.4079i	0.934394	+	0.539472i	0.888198	−	0.459460i	$-0.151957\pi$
$23$	21.4911	+	12.4079i	0.934394	+	0.539472i	0.0461952	+	0.998932i	$0.485290\pi$
$24$		0			0
$25$	1.93542	+	3.35224i	0.0774167	+	0.134090i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	24.0641			0.829798			0.414899	−	0.909868i	$-0.363817\pi$
$29$	24.0641			0.829798			0.414899	+	0.909868i	$0.363817\pi$
$30$		0			0
$31$	1.08871	−	0.628570i	0.0351198	−	0.0202764i	−0.482337	−	0.875986i	$-0.660212\pi$
$31$	1.08871	−	0.628570i	0.0351198	−	0.0202764i	0.517457	+	0.855709i	$0.326879\pi$
$32$		0			0
$33$	0.161228	−	0.279256i	0.00488571	−	0.00846229i
$34$		0			0
$35$	8.26626	+	31.0966i	0.236179	+	0.888474i
$36$		0			0
$37$	17.7736	−	30.7848i	0.480368	−	0.832022i	−0.519378	−	0.854545i	$-0.673836\pi$
$37$	17.7736	−	30.7848i	0.480368	−	0.832022i	0.999746	+	0.0225223i	$0.00716968\pi$
$38$		0			0
$39$	20.5636	−	11.8724i	0.527271	−	0.304420i
$40$		0			0
$41$	−77.2563			−1.88430			−0.942150	−	0.335192i	$-0.891199\pi$
$41$	−77.2563			−1.88430			−0.942150	+	0.335192i	$0.891199\pi$
$42$		0			0
$43$		−	41.9125i		−	0.974710i	−0.873204	−	0.487355i	$-0.837962\pi$
$43$		−	41.9125i		−	0.974710i	0.873204	−	0.487355i	$-0.162038\pi$
$44$		0			0
$45$	6.89497	+	11.9424i	0.153222	+	0.265388i
$46$		0			0
$47$	52.3787	+	30.2408i	1.11444	+	0.643422i	0.939976	−	0.341242i	$-0.110847\pi$
$47$	52.3787	+	30.2408i	1.11444	+	0.643422i	0.174464	+	0.984664i	$0.444181\pi$
$48$		0			0
$49$	0.194309	−	48.9996i	0.00396548	−	0.999992i
$50$		0			0
$51$	−34.9585	−	20.1833i	−0.685462	−	0.395751i
$52$		0			0
$53$	−17.2983	−	29.9616i	−0.326383	−	0.565313i	0.655408	−	0.755275i	$-0.272497\pi$
$53$	−17.2983	−	29.9616i	−0.326383	−	0.565313i	−0.981791	+	0.189962i	$0.939163\pi$
$54$		0			0
$55$			0.855760i			0.0155593i
$56$		0			0
$57$	57.0147			1.00026
$58$		0			0
$59$	−1.78257	+	1.02917i	−0.0302131	+	0.0174435i	−0.515030	−	0.857172i	$-0.672219\pi$
$59$	−1.78257	+	1.02917i	−0.0302131	+	0.0174435i	0.484817	+	0.874615i	$0.338886\pi$
$60$		0			0
$61$	−15.5484	+	26.9306i	−0.254891	+	0.441485i	−0.964866	−	0.262742i	$-0.915373\pi$
$61$	−15.5484	+	26.9306i	−0.254891	+	0.441485i	0.709975	+	0.704227i	$0.248706\pi$
$62$		0			0
$63$	−5.39497	−	20.2952i	−0.0856345	−	0.322146i
$64$		0			0
$65$	−31.5078	+	54.5731i	−0.484736	+	0.839587i
$66$		0			0
$67$	−65.3950	+	37.7558i	−0.976044	+	0.563519i	−0.901074	−	0.433666i	$-0.857220\pi$
$67$	−65.3950	+	37.7558i	−0.976044	+	0.563519i	−0.0749708	+	0.997186i	$0.523886\pi$
$68$		0			0
$69$	42.9821			0.622929
$70$		0			0
$71$			30.7190i			0.432662i	0.976320	+	0.216331i	$0.0694091\pi$
$71$			30.7190i			0.432662i	−0.976320	+	0.216331i	$0.930591\pi$
$72$		0			0
$73$	22.7736	+	39.4451i	0.311967	+	0.540344i	0.978788	−	0.204875i	$-0.0656787\pi$
$73$	22.7736	+	39.4451i	0.311967	+	0.540344i	−0.666821	+	0.745218i	$0.732345\pi$
$74$		0			0
$75$	5.80626	+	3.35224i	0.0774167	+	0.0446966i
$76$		0			0
$77$	0.339786	−	1.25812i	0.00441281	−	0.0163392i
$78$		0			0
$79$	0.943915	+	0.544970i	0.0119483	+	0.00689835i	0.505962	−	0.862556i	$-0.331138\pi$
$79$	0.943915	+	0.544970i	0.0119483	+	0.00689835i	−0.494014	+	0.869454i	$0.664471\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	39.4358i		−	0.475130i	−0.971372	−	0.237565i	$-0.923651\pi$
$83$		−	39.4358i		−	0.475130i	0.971372	−	0.237565i	$-0.0763493\pi$
$84$		0			0
$85$	107.128			1.26033
$86$		0			0
$87$	36.0962	−	20.8401i	0.414899	−	0.239542i
$88$		0			0
$89$	−76.1113	+	131.829i	−0.855183	+	1.48122i	0.0212925	+	0.999773i	$0.493222\pi$
$89$	−76.1113	+	131.829i	−0.855183	+	1.48122i	−0.876475	+	0.481447i	$0.840111\pi$
$90$		0			0
$91$	67.9907	−	67.7216i	0.747151	−	0.744194i
$92$		0			0
$93$	1.08871	−	1.88571i	0.0117066	−	0.0202764i
$94$		0			0
$95$	−131.038	+	75.6550i	−1.37935	+	0.796368i
$96$		0			0
$97$	−25.9359			−0.267380			−0.133690	−	0.991023i	$-0.542683\pi$
$97$	−25.9359			−0.267380			−0.133690	+	0.991023i	$0.542683\pi$
$98$		0			0
$99$		−	0.558511i		−	0.00564153i
$100$		0			0
$101$	32.6134	+	56.4881i	0.322905	+	0.559288i	0.981086	−	0.193572i	$-0.0620072\pi$
$101$	32.6134	+	56.4881i	0.322905	+	0.559288i	−0.658181	+	0.752860i	$0.728674\pi$
$102$		0			0
$103$	−120.084	−	69.3306i	−1.16586	−	0.673112i	−0.213162	−	0.977017i	$-0.568376\pi$
$103$	−120.084	−	69.3306i	−1.16586	−	0.673112i	−0.952703	+	0.303904i	$0.901710\pi$
$104$		0			0
$105$	39.3298	+	39.4861i	0.374570	+	0.376058i
$106$		0			0
$107$	−75.5872	−	43.6403i	−0.706423	−	0.407853i	0.103312	−	0.994649i	$-0.467056\pi$
$107$	−75.5872	−	43.6403i	−0.706423	−	0.407853i	−0.809735	+	0.586796i	$0.800389\pi$
$108$		0			0
$109$	−32.3073	−	55.9578i	−0.296397	−	0.513375i	0.678912	−	0.734220i	$-0.262452\pi$
$109$	−32.3073	−	55.9578i	−0.296397	−	0.513375i	−0.975309	+	0.220845i	$0.929118\pi$
$110$		0			0
$111$		−	61.5696i		−	0.554681i
$112$		0			0
$113$	−187.299			−1.65752			−0.828758	−	0.559607i	$-0.810952\pi$
$113$	−187.299			−1.65752			−0.828758	+	0.559607i	$0.810952\pi$
$114$		0			0
$115$	−98.7868	+	57.0346i	−0.859015	+	0.495953i
$116$		0			0
$117$	20.5636	−	35.6171i	0.175757	−	0.304420i
$118$		0			0
$119$	−157.497	−	42.5361i	−1.32350	−	0.357446i
$120$		0			0
$121$	−60.4827	+	104.759i	−0.499857	+	0.865777i
$122$		0			0
$123$	−115.884	+	66.9059i	−0.942150	+	0.543951i
$124$		0			0
$125$	−132.709			−1.06167
$126$		0			0
$127$		−	153.264i		−	1.20680i	−0.797437	−	0.603402i	$-0.793811\pi$
$127$		−	153.264i		−	1.20680i	0.797437	−	0.603402i	$-0.206189\pi$
$128$		0			0
$129$	−36.2973	−	62.8688i	−0.281374	−	0.487355i
$130$		0			0
$131$	167.531	+	96.7241i	1.27886	+	0.738352i	0.976639	−	0.214885i	$-0.0689377\pi$
$131$	167.531	+	96.7241i	1.27886	+	0.738352i	0.302224	+	0.953237i	$0.402271\pi$
$132$		0			0
$133$	222.689	−	59.1963i	1.67435	−	0.445085i
$134$		0			0
$135$	20.6849	+	11.9424i	0.153222	+	0.0884625i
$136$		0			0
$137$	−108.451	−	187.842i	−0.791611	−	1.37111i	−0.924969	−	0.380043i	$-0.875909\pi$
$137$	−108.451	−	187.842i	−0.791611	−	1.37111i	0.133358	−	0.991068i	$-0.457424\pi$
$138$		0			0
$139$		−	0.732659i		−	0.00527093i	−0.999997	−	0.00263546i	$-0.999161\pi$
$139$		−	0.732659i		−	0.00527093i	0.999997	−	0.00263546i	$-0.000838895\pi$
$140$		0			0
$141$	104.757			0.742960
$142$		0			0
$143$	2.21029	−	1.27611i	0.0154566	−	0.00892384i
$144$		0			0
$145$	−55.3072	+	95.7948i	−0.381429	+	0.660654i
$146$		0			0
$147$	−42.1434	−	73.6677i	−0.286690	−	0.501141i
$148$		0			0
$149$	−74.5137	+	129.062i	−0.500092	+	0.866185i	0.499908	+	0.866079i	$0.333367\pi$
$149$	−74.5137	+	129.062i	−0.500092	+	0.866185i	−1.00000		0.000106336i	$0.999966\pi$
$150$		0			0
$151$	−35.8891	+	20.7206i	−0.237676	+	0.137222i	−0.614108	−	0.789222i	$-0.710484\pi$
$151$	−35.8891	+	20.7206i	−0.237676	+	0.137222i	0.376432	+	0.926444i	$0.377151\pi$
$152$		0			0
$153$	−69.9171			−0.456974
$154$		0			0
$155$			5.77863i			0.0372815i
$156$		0			0
$157$	108.224	+	187.449i	0.689324	+	1.19394i	0.972057	+	0.234746i	$0.0754257\pi$
$157$	108.224	+	187.449i	0.689324	+	1.19394i	−0.282733	+	0.959199i	$0.591241\pi$
$158$		0			0
$159$	−51.8950	−	29.9616i	−0.326383	−	0.188438i
$160$		0			0
$161$	167.880	−	44.6267i	1.04273	−	0.277185i
$162$		0			0
$163$	92.1419	+	53.1981i	0.565288	+	0.326369i	0.755265	−	0.655420i	$-0.227508\pi$
$163$	92.1419	+	53.1981i	0.565288	+	0.326369i	−0.189977	+	0.981788i	$0.560841\pi$
$164$		0			0
$165$	0.741110	+	1.28364i	0.00449158	+	0.00777964i
$166$		0			0
$167$			266.346i			1.59489i	0.603394	+	0.797443i	$0.293815\pi$
$167$			266.346i			1.59489i	−0.603394	+	0.797443i	$0.706185\pi$
$168$		0			0
$169$	18.9379			0.112059
$170$		0			0
$171$	85.5221	−	49.3762i	0.500129	−	0.288750i
$172$		0			0
$173$	63.1981	−	109.462i	0.365307	−	0.632730i	−0.623519	−	0.781809i	$-0.714297\pi$
$173$	63.1981	−	109.462i	0.365307	−	0.632730i	0.988825	+	0.149079i	$0.0476308\pi$
$174$		0			0
$175$	26.1586	+	7.06480i	0.149478	+	0.0403703i
$176$		0			0
$177$	−1.78257	+	3.08751i	−0.0100710	+	0.0174435i
$178$		0			0
$179$	138.665	−	80.0585i	0.774667	−	0.447254i	−0.0598702	−	0.998206i	$-0.519069\pi$
$179$	138.665	−	80.0585i	0.774667	−	0.447254i	0.834537	+	0.550952i	$0.185735\pi$
$180$		0			0
$181$	−108.709			−0.600604			−0.300302	−	0.953844i	$-0.597087\pi$
$181$	−108.709			−0.600604			−0.300302	+	0.953844i	$0.597087\pi$
$182$		0			0
$183$			53.8612i			0.294323i
$184$		0			0
$185$	81.6991	+	141.507i	0.441617	+	0.764902i
$186$		0			0
$187$	−3.75754	−	2.16942i	−0.0200938	−	0.0116012i
$188$		0			0
$189$	−25.6686	−	25.7706i	−0.135813	−	0.136352i
$190$		0			0
$191$	−19.6656	−	11.3539i	−0.102961	−	0.0594446i	0.447635	−	0.894216i	$-0.352266\pi$
$191$	−19.6656	−	11.3539i	−0.102961	−	0.0594446i	−0.550596	+	0.834772i	$0.685600\pi$
$192$		0			0
$193$	−147.353	−	255.223i	−0.763487	−	1.32240i	−0.941043	−	0.338287i	$-0.890152\pi$
$193$	−147.353	−	255.223i	−0.763487	−	1.32240i	0.177556	−	0.984111i	$-0.443181\pi$
$194$		0			0
$195$			109.146i			0.559725i
$196$		0			0
$197$	296.976			1.50749			0.753746	−	0.657166i	$-0.228245\pi$
$197$	296.976			1.50749			0.753746	+	0.657166i	$0.228245\pi$
$198$		0			0
$199$	223.142	−	128.831i	1.12131	−	0.647391i	0.179579	−	0.983744i	$-0.442527\pi$
$199$	223.142	−	128.831i	1.12131	−	0.647391i	0.941736	+	0.336352i	$0.109193\pi$
$200$		0			0
$201$	−65.3950	+	113.267i	−0.325348	+	0.563519i
$202$		0			0
$203$	119.347	−	118.875i	0.587918	−	0.585591i
$204$		0			0
$205$	177.560	−	307.543i	0.866146	−	1.50021i
$206$		0			0
$207$	64.4732	−	37.2236i	0.311465	−	0.179824i
$208$		0			0
$209$	6.12826			0.0293218
$210$		0			0
$211$			84.2895i			0.399476i	0.979849	+	0.199738i	$0.0640091\pi$
$211$			84.2895i			0.399476i	−0.979849	+	0.199738i	$0.935991\pi$
$212$		0			0
$213$	26.6035	+	46.0785i	0.124899	+	0.216331i
$214$		0			0
$215$	166.846	+	96.3285i	0.776027	+	0.448040i
$216$		0			0
$217$	2.29445	−	8.49559i	0.0105735	−	0.0391502i
$218$		0			0
$219$	68.3209	+	39.4451i	0.311967	+	0.180115i
$220$		0			0
$221$	−159.749	−	276.694i	−0.722848	−	1.25201i
$222$		0			0
$223$			170.727i			0.765591i	0.923833	+	0.382795i	$0.125039\pi$
$223$			170.727i			0.765591i	−0.923833	+	0.382795i	$0.874961\pi$
$224$		0			0
$225$	11.6125			0.0516112
$226$		0			0
$227$	66.4950	−	38.3909i	0.292930	−	0.169123i	−0.346333	−	0.938112i	$-0.612573\pi$
$227$	66.4950	−	38.3909i	0.292930	−	0.169123i	0.639262	+	0.768989i	$0.279240\pi$
$228$		0			0
$229$	−190.772	+	330.426i	−0.833064	+	1.44291i	0.0625335	+	0.998043i	$0.480082\pi$
$229$	−190.772	+	330.426i	−0.833064	+	1.44291i	−0.895597	+	0.444866i	$0.853251\pi$
$230$		0			0
$231$	−0.579882	−	2.18144i	−0.00251031	−	0.00944346i
$232$		0			0
$233$	13.4090	−	23.2251i	0.0575495	−	0.0996786i	−0.835815	−	0.549011i	$-0.815005\pi$
$233$	13.4090	−	23.2251i	0.0575495	−	0.0996786i	0.893365	+	0.449332i	$0.148338\pi$
$234$		0			0
$235$	−240.766	+	139.006i	−1.02454	+	0.591517i
$236$		0			0
$237$	1.88783			0.00796553
$238$		0			0
$239$		−	429.135i		−	1.79554i	−0.440460	−	0.897772i	$-0.645185\pi$
$239$		−	429.135i		−	1.79554i	0.440460	−	0.897772i	$-0.354815\pi$
$240$		0			0
$241$	−143.915	−	249.269i	−0.597159	−	1.03431i	−0.993238	−	0.116094i	$-0.962963\pi$
$241$	−143.915	−	249.269i	−0.597159	−	1.03431i	0.396079	−	0.918216i	$-0.370371\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	194.612	+	113.390i	0.794334	+	0.462818i
$246$		0			0
$247$	390.809	+	225.634i	1.58222	+	0.913496i
$248$		0			0
$249$	−34.1524	−	59.1537i	−0.137158	−	0.237565i
$250$		0			0
$251$		−	112.212i		−	0.447060i	−0.974697	−	0.223530i	$-0.928242\pi$
$251$		−	112.212i		−	0.447060i	0.974697	−	0.223530i	$-0.0717581\pi$
$252$		0			0
$253$	4.61996			0.0182607
$254$		0			0
$255$	160.692	−	92.7756i	0.630165	−	0.363826i
$256$		0			0
$257$	−5.42828	+	9.40205i	−0.0211217	+	0.0365839i	−0.876393	−	0.481597i	$-0.840057\pi$
$257$	−5.42828	+	9.40205i	−0.0211217	+	0.0365839i	0.855271	+	0.518180i	$0.173390\pi$
$258$		0			0
$259$	−63.9255	−	240.479i	−0.246816	−	0.928491i
$260$		0			0
$261$	36.0962	−	62.5204i	0.138300	−	0.239542i
$262$		0			0
$263$	32.3048	−	18.6512i	0.122832	−	0.0709170i	−0.437325	−	0.899303i	$-0.644074\pi$
$263$	32.3048	−	18.6512i	0.122832	−	0.0709170i	0.560157	+	0.828386i	$0.310741\pi$
$264$		0			0
$265$	159.029			0.600108
$266$		0			0
$267$			263.657i			0.987480i
$268$		0			0
$269$	−15.3346	−	26.5603i	−0.0570059	−	0.0987372i	0.836114	−	0.548556i	$-0.184822\pi$
$269$	−15.3346	−	26.5603i	−0.0570059	−	0.0987372i	−0.893120	+	0.449818i	$0.851489\pi$
$270$		0			0
$271$	268.261	+	154.881i	0.989894	+	0.571515i	0.905243	−	0.424895i	$-0.139689\pi$
$271$	268.261	+	154.881i	0.989894	+	0.571515i	0.0846512	+	0.996411i	$0.473022\pi$
$272$		0			0
$273$	43.3374	−	160.464i	0.158745	−	0.587781i
$274$		0			0
$275$	0.624089	+	0.360318i	0.00226941	+	0.00131025i
$276$		0			0
$277$	−145.499	−	252.012i	−0.525269	−	0.909792i	−0.999567	−	0.0294279i	$-0.990631\pi$
$277$	−145.499	−	252.012i	−0.525269	−	0.909792i	0.474298	−	0.880364i	$-0.342702\pi$
$278$		0			0
$279$		−	3.77142i		−	0.0135176i
$280$		0			0
$281$	433.358			1.54220			0.771100	−	0.636714i	$-0.219707\pi$
$281$	433.358			1.54220			0.771100	+	0.636714i	$0.219707\pi$
$282$		0			0
$283$	93.4602	−	53.9593i	0.330248	−	0.190669i	−0.325703	−	0.945472i	$-0.605601\pi$
$283$	93.4602	−	53.9593i	0.330248	−	0.190669i	0.655951	+	0.754803i	$0.272268\pi$
$284$		0			0
$285$	−131.038	+	226.965i	−0.459784	+	0.796368i
$286$		0			0
$287$	−383.157	+	381.640i	−1.33504	+	1.32976i
$288$		0			0
$289$	−127.078	+	220.105i	−0.439715	+	0.761609i
$290$		0			0
$291$	−38.9038	+	22.4611i	−0.133690	+	0.0771860i
$292$		0			0
$293$	134.703			0.459736			0.229868	−	0.973222i	$-0.426171\pi$
$293$	134.703			0.459736			0.229868	+	0.973222i	$0.426171\pi$
$294$		0			0
$295$		−	9.46145i		−	0.0320727i
$296$		0			0
$297$	−0.483685	−	0.837767i	−0.00162857	−	0.00282076i
$298$		0			0
$299$	294.622	+	170.100i	0.985357	+	0.568896i
$300$		0			0
$301$	−207.045	−	207.867i	−0.687856	−	0.690589i
$302$		0			0
$303$	97.8402	+	56.4881i	0.322905	+	0.186429i
$304$		0			0
$305$	−71.4704	−	123.790i	−0.234329	−	0.405870i
$306$		0			0
$307$			532.540i			1.73466i	0.497736	+	0.867329i	$0.334165\pi$
$307$			532.540i			1.73466i	−0.497736	+	0.867329i	$0.665835\pi$
$308$		0			0
$309$	−240.168			−0.777243
$310$		0			0
$311$	−443.216	+	255.891i	−1.42513	+	0.822799i	−0.996731	−	0.0807901i	$-0.974256\pi$
$311$	−443.216	+	255.891i	−1.42513	+	0.822799i	−0.428399	+	0.903590i	$0.640922\pi$
$312$		0			0
$313$	−43.6965	+	75.6845i	−0.139605	+	0.241803i	−0.927347	−	0.374202i	$-0.877917\pi$
$313$	−43.6965	+	75.6845i	−0.139605	+	0.241803i	0.787742	+	0.616005i	$0.211250\pi$
$314$		0			0
$315$	93.1907	+	25.1685i	0.295843	+	0.0799001i
$316$		0			0
$317$	71.6108	−	124.034i	0.225902	−	0.391273i	−0.730688	−	0.682712i	$-0.760801\pi$
$317$	71.6108	−	124.034i	0.225902	−	0.391273i	0.956590	+	0.291439i	$0.0941339\pi$
$318$		0			0
$319$	3.87982	−	2.24002i	0.0121624	−	0.00702199i
$320$		0			0
$321$	−151.174			−0.470949
$322$		0			0
$323$		−	767.164i		−	2.37512i
$324$		0			0
$325$	26.5327	+	45.9561i	0.0816392	+	0.141403i
$326$		0			0
$327$	−96.9218	−	55.9578i	−0.296397	−	0.171125i
$328$		0			0
$329$	409.162	−	108.766i	1.24365	−	0.330595i
$330$		0			0
$331$	−528.430	−	305.089i	−1.59647	−	0.921720i	−0.992161	−	0.124966i	$-0.960118\pi$
$331$	−528.430	−	305.089i	−1.59647	−	0.921720i	−0.604304	−	0.796754i	$-0.706549\pi$
$332$		0			0
$333$	−53.3209	−	92.3545i	−0.160123	−	0.277341i
$334$		0			0
$335$		−	347.100i		−	1.03612i
$336$		0			0
$337$	243.994			0.724018			0.362009	−	0.932175i	$-0.382091\pi$
$337$	243.994			0.724018			0.362009	+	0.932175i	$0.382091\pi$
$338$		0			0
$339$	−280.949	+	162.206i	−0.828758	+	0.478484i
$340$		0			0
$341$	0.117021	−	0.202687i	0.000343170	−	0.000594389i
$342$		0			0
$343$	−241.091	−	243.976i	−0.702888	−	0.711300i
$344$		0			0
$345$	−98.7868	+	171.104i	−0.286338	+	0.495953i
$346$		0			0
$347$	312.604	−	180.482i	0.900875	−	0.520121i	0.0233911	−	0.999726i	$-0.492554\pi$
$347$	312.604	−	180.482i	0.900875	−	0.520121i	0.877484	+	0.479606i	$0.159220\pi$
$348$		0			0
$349$	−375.119			−1.07484			−0.537420	−	0.843314i	$-0.680601\pi$
$349$	−375.119			−1.07484			−0.537420	+	0.843314i	$0.680601\pi$
$350$		0			0
$351$		−	71.2343i		−	0.202947i
$352$		0			0
$353$	76.8294	+	133.072i	0.217647	+	0.376976i	0.954088	−	0.299526i	$-0.0968285\pi$
$353$	76.8294	+	133.072i	0.217647	+	0.376976i	−0.736441	+	0.676502i	$0.763495\pi$
$354$		0			0
$355$	−122.287	−	70.6022i	−0.344469	−	0.198880i
$356$		0			0
$357$	−273.083	+	72.5923i	−0.764938	+	0.203340i
$358$		0			0
$359$	46.9502	+	27.1067i	0.130780	+	0.0755061i	0.563963	−	0.825800i	$-0.309276\pi$
$359$	46.9502	+	27.1067i	0.130780	+	0.0755061i	−0.433182	+	0.901306i	$0.642609\pi$
$360$		0			0
$361$	361.280	+	625.755i	1.00078	+	1.73339i
$362$		0			0
$363$			209.518i			0.577185i
$364$		0			0
$365$	−209.365			−0.573602
$366$		0			0
$367$	130.929	−	75.5921i	0.356756	−	0.205973i	−0.310901	−	0.950442i	$-0.600631\pi$
$367$	130.929	−	75.5921i	0.356756	−	0.205973i	0.667657	+	0.744469i	$0.267297\pi$
$368$		0			0
$369$	−115.884	+	200.718i	−0.314050	+	0.543951i
$370$		0			0
$371$	−233.800	−	63.1436i	−0.630188	−	0.170198i
$372$		0			0
$373$	−316.054	+	547.422i	−0.847330	+	1.46762i	0.0362517	+	0.999343i	$0.488458\pi$
$373$	−316.054	+	547.422i	−0.847330	+	1.46762i	−0.883582	+	0.468276i	$0.844875\pi$
$374$		0			0
$375$	−199.064	+	114.929i	−0.530836	+	0.306478i
$376$		0			0
$377$	329.896			0.875056
$378$		0			0
$379$			316.045i			0.833892i	0.908931	+	0.416946i	$0.136900\pi$
$379$			316.045i			0.833892i	−0.908931	+	0.416946i	$0.863100\pi$
$380$		0			0
$381$	−132.731	−	229.896i	−0.348375	−	0.603402i
$382$		0			0
$383$	−237.606	−	137.182i	−0.620380	−	0.358177i	0.156637	−	0.987656i	$-0.449935\pi$
$383$	−237.606	−	137.182i	−0.620380	−	0.358177i	−0.777017	+	0.629480i	$0.783268\pi$
$384$		0			0
$385$	4.22739	+	4.24419i	0.0109802	+	0.0110239i
$386$		0			0
$387$	−108.892	−	62.8688i	−0.281374	−	0.162452i
$388$		0			0
$389$	117.536	+	203.579i	0.302150	+	0.523338i	0.976623	−	0.214961i	$-0.0689625\pi$
$389$	117.536	+	203.579i	0.302150	+	0.523338i	−0.674473	+	0.738299i	$0.735629\pi$
$390$		0			0
$391$		−	578.348i		−	1.47915i
$392$		0			0
$393$	335.062			0.852575
$394$		0			0
$395$	−4.33884	+	2.50503i	−0.0109844	+	0.00634186i
$396$		0			0
$397$	−284.092	+	492.061i	−0.715596	+	1.23945i	0.247133	+	0.968982i	$0.420512\pi$
$397$	−284.092	+	492.061i	−0.715596	+	1.23945i	−0.962729	+	0.270468i	$0.912822\pi$
$398$		0			0
$399$	282.768	−	281.648i	0.708691	−	0.705886i
$400$		0			0
$401$	115.696	−	200.391i	0.288519	−	0.499729i	−0.684938	−	0.728602i	$-0.740171\pi$
$401$	115.696	−	200.391i	0.288519	−	0.499729i	0.973456	+	0.228873i	$0.0735040\pi$
$402$		0			0
$403$	14.9252	−	8.61709i	0.0370353	−	0.0213824i
$404$		0			0
$405$	41.3698			0.102148
$406$		0			0
$407$		−	6.61785i		−	0.0162601i
$408$		0			0
$409$	−33.8249	−	58.5865i	−0.0827016	−	0.143243i	0.821708	−	0.569909i	$-0.193021\pi$
$409$	−33.8249	−	58.5865i	−0.0827016	−	0.143243i	−0.904409	+	0.426666i	$0.859688\pi$
$410$		0			0
$411$	−325.352	−	187.842i	−0.791611	−	0.457037i
$412$		0			0
$413$	−3.75675	+	13.9100i	−0.00909624	+	0.0336804i
$414$		0			0
$415$	156.987	+	90.6362i	0.378281	+	0.218400i
$416$		0			0
$417$	−0.634501	−	1.09899i	−0.00152159	−	0.00263546i
$418$		0			0
$419$		−	111.646i		−	0.266459i	−0.991085	−	0.133229i	$-0.957465\pi$
$419$		−	111.646i		−	0.266459i	0.991085	−	0.133229i	$-0.0425347\pi$
$420$		0			0
$421$	509.147			1.20937			0.604687	−	0.796463i	$-0.293298\pi$
$421$	509.147			1.20937			0.604687	+	0.796463i	$0.293298\pi$
$422$		0			0
$423$	157.136	−	90.7225i	0.371480	−	0.214474i
$424$		0			0
$425$	45.1063	−	78.1263i	0.106132	−	0.183827i
$426$		0			0
$427$	55.9220	+	210.371i	0.130965	+	0.492673i
$428$		0			0
$429$	2.21029	−	3.82833i	0.00515218	−	0.00892384i
$430$		0			0
$431$	−659.682	+	380.868i	−1.53059	+	0.883684i	−0.531251	+	0.847215i	$0.678278\pi$
$431$	−659.682	+	380.868i	−1.53059	+	0.883684i	−0.999335	+	0.0364694i	$0.988389\pi$
$432$		0			0
$433$	−218.413			−0.504418			−0.252209	−	0.967673i	$-0.581157\pi$
$433$	−218.413			−0.504418			−0.252209	+	0.967673i	$0.581157\pi$
$434$		0			0
$435$			191.590i			0.440436i
$436$		0			0
$437$	408.436	+	707.431i	0.934635	+	1.61884i
$438$		0			0
$439$	−562.488	−	324.753i	−1.28129	−	0.739756i	−0.304210	−	0.952605i	$-0.598392\pi$
$439$	−562.488	−	324.753i	−1.28129	−	0.739756i	−0.977085	+	0.212849i	$0.931726\pi$
$440$		0			0
$441$	−127.013	−	74.0043i	−0.288012	−	0.167810i
$442$		0			0
$443$	−653.200	−	377.125i	−1.47449	−	0.851298i	−0.474904	−	0.880038i	$-0.657517\pi$
$443$	−653.200	−	377.125i	−1.47449	−	0.851298i	−0.999587	+	0.0287397i	$0.990851\pi$
$444$		0			0
$445$	−349.857	−	605.969i	−0.786195	−	1.36173i
$446$		0			0
$447$			258.123i			0.577457i
$448$		0			0
$449$	−566.657			−1.26204			−0.631021	−	0.775766i	$-0.717364\pi$
$449$	−566.657			−1.26204			−0.631021	+	0.775766i	$0.717364\pi$
$450$		0			0
$451$	−12.4559	+	7.19142i	−0.0276184	+	0.0159455i
$452$		0			0
$453$	−35.8891	+	62.1617i	−0.0792253	+	0.137222i
$454$		0			0
$455$	113.322	+	426.305i	0.249060	+	0.936933i
$456$		0			0
$457$	350.908	−	607.791i	0.767852	−	1.32996i	−0.170873	−	0.985293i	$-0.554659\pi$
$457$	350.908	−	607.791i	0.767852	−	1.32996i	0.938725	−	0.344666i	$-0.112008\pi$
$458$		0			0
$459$	−104.876	+	60.5500i	−0.228487	+	0.131917i
$460$		0			0
$461$	−475.670			−1.03182			−0.515911	−	0.856642i	$-0.672546\pi$
$461$	−475.670			−1.03182			−0.515911	+	0.856642i	$0.672546\pi$
$462$		0			0
$463$			564.736i			1.21973i	0.792505	+	0.609866i	$0.208777\pi$
$463$			564.736i			1.21973i	−0.792505	+	0.609866i	$0.791223\pi$
$464$		0			0
$465$	5.00444	+	8.66794i	0.0107622	+	0.0186407i
$466$		0			0
$467$	674.760	+	389.573i	1.44488	+	0.834203i	0.998170	−	0.0604753i	$-0.0192616\pi$
$467$	674.760	+	389.573i	1.44488	+	0.834203i	0.446712	+	0.894678i	$0.352595\pi$
$468$		0			0
$469$	−137.819	+	510.298i	−0.293857	+	1.08806i
$470$		0			0
$471$	324.672	+	187.449i	0.689324	+	0.397981i
$472$		0			0
$473$	−3.90144	−	6.75749i	−0.00824828	−	0.0142864i
$474$		0			0
$475$			127.418i			0.268249i
$476$		0			0
$477$	−103.790			−0.217589
$478$		0			0
$479$	−204.157	+	117.870i	−0.426214	+	0.246075i	−0.697732	−	0.716358i	$-0.745808\pi$
$479$	−204.157	+	117.870i	−0.426214	+	0.246075i	0.271518	+	0.962433i	$0.412474\pi$
$480$		0			0
$481$	243.659	−	422.031i	0.506568	−	0.877402i
$482$		0			0
$483$	213.172	−	212.328i	0.441350	−	0.439603i
$484$		0			0
$485$	59.6090	−	103.246i	0.122905	−	0.212878i
$486$		0			0
$487$	−304.438	+	175.767i	−0.625129	+	0.360919i	−0.778863	−	0.627194i	$-0.784203\pi$
$487$	−304.438	+	175.767i	−0.625129	+	0.360919i	0.153734	+	0.988112i	$0.450870\pi$
$488$		0			0
$489$	184.284			0.376858
$490$		0			0
$491$		−	586.350i		−	1.19420i	−0.802169	−	0.597098i	$-0.796320\pi$
$491$		−	586.350i		−	1.19420i	0.802169	−	0.597098i	$-0.203680\pi$
$492$		0			0
$493$	−280.416	−	485.694i	−0.568794	−	0.985181i
$494$		0			0
$495$	2.22333	+	1.28364i	0.00449158	+	0.00259321i
$496$		0			0
$497$	151.750	+	152.353i	0.305331	+	0.306544i
$498$		0			0
$499$	−253.489	−	146.352i	−0.507994	−	0.293291i	0.224014	−	0.974586i	$-0.428084\pi$
$499$	−253.489	−	146.352i	−0.507994	−	0.293291i	−0.732009	+	0.681295i	$0.761417\pi$
$500$		0			0
$501$	230.662	+	399.519i	0.460404	+	0.797443i
$502$		0			0
$503$		−	577.054i		−	1.14722i	−0.819127	−	0.573612i	$-0.805542\pi$
$503$		−	577.054i		−	1.14722i	0.819127	−	0.573612i	$-0.194458\pi$
$504$		0			0
$505$	−299.825			−0.593712
$506$		0			0
$507$	28.4068	−	16.4007i	0.0560293	−	0.0323485i
$508$		0			0
$509$	410.890	−	711.683i	0.807250	−	1.39820i	−0.107512	−	0.994204i	$-0.534288\pi$
$509$	410.890	−	711.683i	0.807250	−	1.39820i	0.914762	−	0.403994i	$-0.132378\pi$
$510$		0			0
$511$	307.803	+	83.1299i	0.602354	+	0.162681i
$512$		0			0
$513$	85.5221	−	148.129i	0.166710	−	0.288750i
$514$		0			0
$515$	551.984	−	318.688i	1.07181	−	0.618812i
$516$		0			0
$517$	11.2599			0.0217793
$518$		0			0
$519$		−	218.925i		−	0.421820i
$520$		0			0
$521$	45.0485	+	78.0263i	0.0864654	+	0.149763i	0.906015	−	0.423246i	$-0.139109\pi$
$521$	45.0485	+	78.0263i	0.0864654	+	0.149763i	−0.819549	+	0.573009i	$0.805776\pi$
$522$		0			0
$523$	130.787	+	75.5102i	0.250072	+	0.144379i	0.619797	−	0.784762i	$-0.287215\pi$
$523$	130.787	+	75.5102i	0.250072	+	0.144379i	−0.369725	+	0.929141i	$0.620548\pi$
$524$		0			0
$525$	45.3563	−	12.0568i	0.0863929	−	0.0229654i
$526$		0			0
$527$	−25.3732	−	14.6493i	−0.0481466	−	0.0277974i
$528$		0			0
$529$	43.4102	+	75.1887i	0.0820609	+	0.142134i
$530$		0			0
$531$			6.17501i			0.0116290i
$532$		0			0
$533$	−1059.11			−1.98707
$534$		0			0
$535$	347.448	−	200.599i	0.649435	−	0.374952i
$536$		0			0
$537$	138.665	−	240.175i	0.258222	−	0.447254i
$538$		0			0
$539$	−4.52981	−	7.91822i	−0.00840411	−	0.0146906i
$540$		0			0
$541$	−271.652	+	470.515i	−0.502129	+	0.869714i	0.497868	+	0.867253i	$0.334117\pi$
$541$	−271.652	+	470.515i	−0.502129	+	0.869714i	−0.999997	+	0.00246052i	$0.999217\pi$
$542$		0			0
$543$	−163.064	+	94.1450i	−0.300302	+	0.173379i
$544$		0			0
$545$	297.010			0.544973
$546$		0			0
$547$			908.509i			1.66089i	0.557097	+	0.830447i	$0.311915\pi$
$547$			908.509i			1.66089i	−0.557097	+	0.830447i	$0.688085\pi$
$548$		0			0
$549$	46.6451	+	80.7918i	0.0849638	+	0.147162i
$550$		0			0
$551$	686.005	+	396.065i	1.24502	+	0.718812i
$552$		0			0
$553$	7.37350	−	1.96006i	0.0133336	−	0.00354442i
$554$		0			0
$555$	245.097	+	141.507i	0.441617	+	0.254967i
$556$		0			0
$557$	297.094	+	514.583i	0.533383	+	0.923847i	0.999240	+	0.0389864i	$0.0124129\pi$
$557$	297.094	+	514.583i	0.533383	+	0.923847i	−0.465857	+	0.884860i	$0.654254\pi$
$558$		0			0
$559$		−	574.581i		−	1.02787i
$560$		0			0
$561$	−7.51508			−0.0133959
$562$		0			0
$563$	−606.259	+	350.024i	−1.07684	+	0.621712i	−0.930041	−	0.367455i	$-0.880229\pi$
$563$	−606.259	+	350.024i	−1.07684	+	0.621712i	−0.146796	+	0.989167i	$0.546896\pi$
$564$		0			0
$565$	430.475	−	745.604i	0.761902	−	1.31965i
$566$		0			0
$567$	−60.8209	−	16.4262i	−0.107268	−	0.0289704i
$568$		0			0
$569$	−416.677	+	721.705i	−0.732297	+	1.26837i	0.223603	+	0.974680i	$0.428218\pi$
$569$	−416.677	+	721.705i	−0.732297	+	1.26837i	−0.955899	+	0.293694i	$0.905115\pi$
$570$		0			0
$571$	796.086	−	459.621i	1.39420	−	0.804940i	0.400420	−	0.916332i	$-0.368864\pi$
$571$	796.086	−	459.621i	1.39420	−	0.804940i	0.993777	+	0.111392i	$0.0355309\pi$
$572$		0			0
$573$	−39.3311			−0.0686407
$574$		0			0
$575$			96.0577i			0.167057i
$576$		0			0
$577$	−5.50000	−	9.52628i	−0.00953206	−	0.0165100i	0.861220	−	0.508232i	$-0.169701\pi$
$577$	−5.50000	−	9.52628i	−0.00953206	−	0.0165100i	−0.870752	+	0.491722i	$0.836368\pi$
$578$		0			0
$579$	−442.059	−	255.223i	−0.763487	−	0.440799i
$580$		0			0
$581$	−194.810	−	195.584i	−0.335301	−	0.336633i
$582$		0			0
$583$	−5.57796	−	3.22044i	−0.00956769	−	0.00552391i
$584$		0			0
$585$	94.5235	+	163.719i	0.161579	+	0.279862i
$586$		0			0
$587$			965.911i			1.64550i	0.568401	+	0.822752i	$0.307562\pi$
$587$			965.911i			1.64550i	−0.568401	+	0.822752i	$0.692438\pi$
$588$		0			0
$589$	41.3819			0.0702578
$590$		0			0
$591$	445.464	−	257.189i	0.753746	−	0.435175i
$592$		0			0
$593$	513.816	−	889.955i	0.866468	−	1.50077i	0.000886063	−	1.00000i	$-0.499718\pi$
$593$	513.816	−	889.955i	0.866468	−	1.50077i	0.865582	−	0.500767i	$-0.166949\pi$
$594$		0			0
$595$	531.307	−	529.204i	0.892953	−	0.889419i
$596$		0			0
$597$	223.142	−	386.493i	0.373772	−	0.647391i
$598$		0			0
$599$	695.499	−	401.547i	1.16110	−	0.670362i	0.209533	−	0.977802i	$-0.432806\pi$
$599$	695.499	−	401.547i	1.16110	−	0.670362i	0.951567	+	0.307440i	$0.0994724\pi$
$600$		0			0
$601$	702.916			1.16958			0.584789	−	0.811186i	$-0.301177\pi$
$601$	702.916			1.16958			0.584789	+	0.811186i	$0.301177\pi$
$602$		0			0
$603$			226.535i			0.375680i
$604$		0			0
$605$	−278.017	−	481.540i	−0.459533	−	0.795935i
$606$		0			0
$607$	−185.611	−	107.162i	−0.305783	−	0.176544i	0.339255	−	0.940695i	$-0.389825\pi$
$607$	−185.611	−	107.162i	−0.305783	−	0.176544i	−0.645038	+	0.764150i	$0.723159\pi$
$608$		0			0
$609$	76.0722	−	281.670i	0.124913	−	0.462513i
$610$		0			0
$611$	718.061	+	414.573i	1.17522	+	0.678515i
$612$		0			0
$613$	369.332	+	639.701i	0.602498	+	1.04356i	0.992441	+	0.122719i	$0.0391614\pi$
$613$	369.332	+	639.701i	0.602498	+	1.04356i	−0.389943	+	0.920839i	$0.627505\pi$
$614$		0			0
$615$		−	615.086i		−	1.00014i
$616$		0			0
$617$	32.2398			0.0522526			0.0261263	−	0.999659i	$-0.491683\pi$
$617$	32.2398			0.0522526			0.0261263	+	0.999659i	$0.491683\pi$
$618$		0			0
$619$	354.274	−	204.540i	0.572332	−	0.330436i	−0.185748	−	0.982597i	$-0.559471\pi$
$619$	354.274	−	204.540i	0.572332	−	0.330436i	0.758080	+	0.652161i	$0.226137\pi$
$620$		0			0
$621$	64.4732	−	111.671i	0.103822	−	0.179824i
$622$		0			0
$623$	273.745	+	1029.79i	0.439399	+	1.65296i
$624$		0			0
$625$	256.623	−	444.484i	0.410597	−	0.711174i
$626$		0			0
$627$	9.19239	−	5.30723i	0.0146609	−	0.00846448i
$628$		0			0
$629$	−828.453			−1.31710
$630$		0			0
$631$			428.212i			0.678625i	0.940674	+	0.339312i	$0.110194\pi$
$631$			428.212i			0.678625i	−0.940674	+	0.339312i	$0.889806\pi$
$632$		0			0
$633$	72.9968	+	126.434i	0.115319	+	0.199738i
$634$		0			0
$635$	610.116	+	352.251i	0.960813	+	0.554726i
$636$		0			0
$637$	2.66379	−	671.738i	0.00418177	−	1.05453i
$638$		0			0
$639$	79.8104	+	46.0785i	0.124899	+	0.0721104i
$640$		0			0
$641$	−432.657	−	749.385i	−0.674973	−	1.16909i	−0.976477	−	0.215622i	$-0.930822\pi$
$641$	−432.657	−	749.385i	−0.674973	−	1.16909i	0.301504	−	0.953465i	$-0.402511\pi$
$642$		0			0
$643$		−	43.7834i		−	0.0680924i	−0.999420	−	0.0340462i	$-0.989161\pi$
$643$		−	43.7834i		−	0.0680924i	0.999420	−	0.0340462i	$-0.0108393\pi$
$644$		0			0
$645$	333.692			0.517352
$646$		0			0
$647$	−377.136	+	217.740i	−0.582900	+	0.336538i	−0.762285	−	0.647241i	$-0.775923\pi$
$647$	−377.136	+	217.740i	−0.582900	+	0.336538i	0.179385	+	0.983779i	$0.442589\pi$
$648$		0			0
$649$	−0.191601	+	0.331862i	−0.000295225	+	0.000511344i
$650$		0			0
$651$	−3.91572	−	14.7304i	−0.00601493	−	0.0226274i
$652$		0			0
$653$	−335.432	+	580.986i	−0.513679	+	0.889718i	0.486195	+	0.873850i	$0.338384\pi$
$653$	−335.432	+	580.986i	−0.513679	+	0.889718i	−0.999874	+	0.0158676i	$0.994949\pi$
$654$		0			0
$655$	−770.081	+	444.607i	−1.17570	+	0.678789i
$656$		0			0
$657$	136.642			0.207978
$658$		0			0
$659$			18.6391i			0.0282839i	0.999900	+	0.0141419i	$0.00450167\pi$
$659$			18.6391i			0.0282839i	−0.999900	+	0.0141419i	$0.995498\pi$
$660$		0			0
$661$	129.755	+	224.742i	0.196301	+	0.340003i	0.947326	−	0.320270i	$-0.103774\pi$
$661$	129.755	+	224.742i	0.196301	+	0.340003i	−0.751025	+	0.660273i	$0.770440\pi$
$662$		0			0
$663$	−479.248	−	276.694i	−0.722848	−	0.417336i
$664$		0			0
$665$	−276.161	+	1022.53i	−0.415280	+	1.53765i
$666$		0			0
$667$	517.164	+	298.584i	0.775358	+	0.447653i
$668$		0			0
$669$	147.854	+	256.090i	0.221007	+	0.382795i
$670$		0			0
$671$			5.78930i			0.00862787i
$672$		0			0
$673$	−5.29772			−0.00787179			−0.00393590	−	0.999992i	$-0.501253\pi$
$673$	−5.29772			−0.00787179			−0.00393590	+	0.999992i	$0.501253\pi$
$674$		0			0
$675$	17.4188	−	10.0567i	0.0258056	−	0.0148989i
$676$		0			0
$677$	312.667	−	541.556i	0.461843	−	0.799935i	−0.537210	−	0.843448i	$-0.680522\pi$
$677$	312.667	−	541.556i	0.461843	−	0.799935i	0.999053	+	0.0435135i	$0.0138552\pi$
$678$		0			0
$679$	−128.630	+	128.121i	−0.189441	+	0.188691i
$680$		0			0
$681$	66.4950	−	115.173i	0.0976432	−	0.169123i
$682$		0			0
$683$	597.735	−	345.103i	0.875162	−	0.505275i	0.00610161	−	0.999981i	$-0.498058\pi$
$683$	597.735	−	345.103i	0.875162	−	0.505275i	0.869060	+	0.494707i	$0.164724\pi$
$684$		0			0
$685$	997.019			1.45550
$686$		0			0
$687$			660.852i			0.961939i
$688$		0			0
$689$	−237.143	−	410.745i	−0.344185	−	0.596146i
$690$		0			0
$691$	−909.589	−	525.151i	−1.31634	−	0.759987i	−0.333200	−	0.942856i	$-0.608128\pi$
$691$	−909.589	−	525.151i	−1.31634	−	0.759987i	−0.983137	+	0.182869i	$0.941462\pi$
$692$		0			0
$693$	−2.75900	−	2.76997i	−0.00398125	−	0.00399707i
$694$		0			0
$695$	2.91658	+	1.68389i	0.00419651	+	0.00242286i
$696$		0			0
$697$	900.256	+	1559.29i	1.29162	+	2.23714i
$698$		0			0
$699$		−	46.4502i		−	0.0664524i
$700$		0			0
$701$	−865.251			−1.23431			−0.617155	−	0.786842i	$-0.711715\pi$
$701$	−865.251			−1.23431			−0.617155	+	0.786842i	$0.711715\pi$
$702$		0			0
$703$	1013.36	−	585.063i	1.44148	−	0.832237i
$704$		0			0
$705$	−240.766	+	417.019i	−0.341512	+	0.591517i
$706$		0			0
$707$	440.795	+	119.048i	0.623472	+	0.168384i
$708$		0			0
$709$	601.050	−	1041.05i	0.847744	−	1.46834i	−0.0354731	−	0.999371i	$-0.511294\pi$
$709$	601.050	−	1041.05i	0.847744	−	1.46834i	0.883217	−	0.468965i	$-0.155373\pi$
$710$		0			0
$711$	2.83175	−	1.63491i	0.00398276	−	0.00229945i
$712$		0			0
$713$	31.1968			0.0437543
$714$		0			0
$715$			11.7317i			0.0164079i
$716$		0			0
$717$	−371.642	−	643.703i	−0.518329	−	0.897772i
$718$		0			0
$719$	−268.331	−	154.921i	−0.373200	−	0.215467i	0.301656	−	0.953417i	$-0.402461\pi$
$719$	−268.331	−	154.921i	−0.373200	−	0.215467i	−0.674855	+	0.737950i	$0.735794\pi$
$720$		0			0
$721$	−938.051	+	249.358i	−1.30104	+	0.345850i
$722$		0			0
$723$	−431.746	−	249.269i	−0.597159	−	0.344770i
$724$		0			0
$725$	46.5742	+	80.6688i	0.0642402	+	0.111267i
$726$		0			0
$727$		−	753.887i		−	1.03698i	−0.855083	−	0.518492i	$-0.826494\pi$
$727$		−	753.887i		−	1.03698i	0.855083	−	0.518492i	$-0.173506\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−845.934	+	488.400i	−1.15723	+	0.668126i
$732$		0			0
$733$	−194.286	+	336.512i	−0.265055	+	0.459089i	−0.967578	−	0.252572i	$-0.918724\pi$
$733$	−194.286	+	336.512i	−0.265055	+	0.459089i	0.702523	+	0.711661i	$0.252057\pi$
$734$		0			0
$735$	390.117	+	1.54701i	0.530771	+	0.00210478i
$736$		0			0
$737$	−7.02902	+	12.1746i	−0.00953734	+	0.0165191i
$738$		0			0
$739$	363.390	−	209.803i	0.491732	−	0.283902i	−0.233561	−	0.972342i	$-0.575038\pi$
$739$	363.390	−	209.803i	0.491732	−	0.283902i	0.725293	+	0.688441i	$0.241704\pi$
$740$		0			0
$741$	781.618			1.05481
$742$		0			0
$743$			86.3362i			0.116199i	0.998311	+	0.0580997i	$0.0185041\pi$
$743$			86.3362i			0.116199i	−0.998311	+	0.0580997i	$0.981496\pi$
$744$		0			0
$745$	−342.513	−	593.250i	−0.459749	−	0.796309i
$746$		0			0
$747$	−102.457	−	59.1537i	−0.137158	−	0.0791883i
$748$		0			0
$749$	−590.459	+	156.959i	−0.788329	+	0.209558i
$750$		0			0
$751$	438.068	+	252.919i	0.583314	+	0.336776i	0.762449	−	0.647048i	$-0.223997\pi$
$751$	438.068	+	252.919i	0.583314	+	0.336776i	−0.179136	+	0.983824i	$0.557330\pi$
$752$		0			0
$753$	−97.1785	−	168.318i	−0.129055	−	0.223530i
$754$		0			0
$755$		−	190.490i		−	0.252305i
$756$		0			0
$757$	−240.329			−0.317475			−0.158737	−	0.987321i	$-0.550742\pi$
$757$	−240.329			−0.317475			−0.158737	+	0.987321i	$0.550742\pi$
$758$		0			0
$759$	6.92993	−	4.00100i	0.00913035	−	0.00527141i
$760$		0			0
$761$	−250.415	+	433.732i	−0.329061	+	0.569950i	−0.982326	−	0.187179i	$-0.940065\pi$
$761$	−250.415	+	433.732i	−0.329061	+	0.569950i	0.653265	+	0.757129i	$0.273399\pi$
$762$		0			0
$763$	−436.657	−	117.930i	−0.572290	−	0.154561i
$764$		0			0
$765$	160.692	−	278.327i	0.210055	−	0.363826i
$766$		0			0
$767$	−24.4374	+	14.1089i	−0.0318610	+	0.0183949i
$768$		0			0
$769$	−713.336			−0.927615			−0.463807	−	0.885936i	$-0.653517\pi$
$769$	−713.336			−0.927615			−0.463807	+	0.885936i	$0.653517\pi$
$770$		0			0
$771$			18.8041i			0.0243892i
$772$		0			0
$773$	105.072	+	181.990i	0.135928	+	0.235434i	0.925951	−	0.377643i	$-0.123265\pi$
$773$	105.072	+	181.990i	0.135928	+	0.235434i	−0.790024	+	0.613076i	$0.789932\pi$
$774$		0			0
$775$	4.21424	+	2.43309i	0.00543773	+	0.00313947i
$776$		0			0
$777$	−304.149	−	305.358i	−0.391441	−	0.392996i
$778$		0			0
$779$	−2202.37	−	1271.54i	−2.82718	−	1.63227i
$780$		0			0
$781$	2.85949	+	4.95278i	0.00366132	+	0.00634158i
$782$		0			0
$783$		−	125.041i		−	0.159695i
$784$		0			0
$785$	−994.934			−1.26743
$786$		0			0
$787$	−1284.22	+	741.445i	−1.63179	+	0.942116i	−0.648253	+	0.761425i	$0.724500\pi$
$787$	−1284.22	+	741.445i	−1.63179	+	0.942116i	−0.983540	+	0.180691i	$0.942167\pi$
$788$		0			0
$789$	32.3048	−	55.9535i	0.0409440	−	0.0709170i
$790$		0			0
$791$	−928.921	+	925.245i	−1.17436	+	1.16972i
$792$		0			0
$793$	−213.153	+	369.193i	−0.268794	+	0.465564i
$794$		0			0
$795$	238.543	−	137.723i	0.300054	−	0.173236i
$796$		0			0
$797$	445.840			0.559398			0.279699	−	0.960088i	$-0.409765\pi$
$797$	445.840			0.559398			0.279699	+	0.960088i	$0.409765\pi$
$798$		0			0
$799$		−	1409.57i		−	1.76416i
$800$		0			0
$801$	228.334	+	395.486i	0.285061	+	0.493740i
$802$		0			0
$803$	7.34351	+	4.23978i	0.00914509	+	0.00527992i
$804$		0			0
$805$	−208.192	+	770.865i	−0.258623	+	0.957596i
$806$		0			0
$807$	−46.0038	−	26.5603i	−0.0570059	−	0.0329124i
$808$		0			0
$809$	84.1885	+	145.819i	0.104065	+	0.180246i	0.913356	−	0.407162i	$-0.133482\pi$
$809$	84.1885	+	145.819i	0.104065	+	0.180246i	−0.809291	+	0.587408i	$0.800148\pi$
$810$		0			0
$811$			1142.96i			1.40932i	0.709545	+	0.704660i	$0.248900\pi$
$811$			1142.96i			1.40932i	−0.709545	+	0.704660i	$0.751100\pi$
$812$		0			0
$813$	536.522			0.659929
$814$		0			0
$815$	−423.544	+	244.533i	−0.519685	+	0.300041i
$816$		0			0
$817$	689.827	−	1194.82i	0.844342	−	1.46244i
$818$		0			0
$819$	−73.9599	−	278.228i	−0.0903051	−	0.339716i
$820$		0			0
$821$	−72.4494	+	125.486i	−0.0882454	+	0.152845i	−0.906770	−	0.421627i	$-0.861459\pi$
$821$	−72.4494	+	125.486i	−0.0882454	+	0.152845i	0.818524	+	0.574472i	$0.194793\pi$
$822$		0			0
$823$	−7.54995	+	4.35897i	−0.00917370	+	0.00529644i	−0.504580	−	0.863365i	$-0.668353\pi$
$823$	−7.54995	+	4.35897i	−0.00917370	+	0.00529644i	0.495406	+	0.868661i	$0.335019\pi$
$824$		0			0
$825$	1.24818			0.00151294
$826$		0			0
$827$			227.873i			0.275541i	0.990464	+	0.137771i	$0.0439937\pi$
$827$			227.873i			0.275541i	−0.990464	+	0.137771i	$0.956006\pi$
$828$		0			0
$829$	27.2629	+	47.2207i	0.0328865	+	0.0569611i	0.882000	−	0.471249i	$-0.156197\pi$
$829$	27.2629	+	47.2207i	0.0328865	+	0.0569611i	−0.849114	+	0.528210i	$0.822863\pi$
$830$		0			0
$831$	−436.498	−	252.012i	−0.525269	−	0.303264i
$832$		0			0
$833$	−991.239	+	567.063i	−1.18996	+	0.680748i
$834$		0			0
$835$	−1060.27	−	612.149i	−1.26979	−	0.733113i
$836$		0			0
$837$	−3.26614	−	5.65713i	−0.00390220	−	0.00675881i
$838$		0			0
$839$		−	1009.63i		−	1.20337i	−0.798732	−	0.601687i	$-0.794496\pi$
$839$		−	1009.63i		−	1.20337i	0.798732	−	0.601687i	$-0.205504\pi$
$840$		0			0
$841$	−261.918			−0.311436
$842$		0			0
$843$	650.037	−	375.299i	0.771100	−	0.445195i
$844$		0			0
$845$	−43.5254	+	75.3882i	−0.0515094	+	0.0892168i
$846$		0			0
$847$	217.535	+	818.338i	0.256830	+	0.966160i
$848$		0			0
$849$	93.4602	−	161.878i	0.110083	−	0.190669i
$850$		0			0
$851$	763.948	−	441.066i	0.897706	−	0.518291i
$852$		0			0
$853$	1153.22			1.35196			0.675978	−	0.736921i	$-0.263721\pi$
$853$	1153.22			1.35196			0.675978	+	0.736921i	$0.263721\pi$
$854$		0			0
$855$			453.930i			0.530912i
$856$		0			0
$857$	255.480	+	442.503i	0.298109	+	0.516340i	0.975703	−	0.219096i	$-0.0703107\pi$
$857$	255.480	+	442.503i	0.298109	+	0.516340i	−0.677594	+	0.735436i	$0.736977\pi$
$858$		0			0
$859$	−500.132	−	288.751i	−0.582226	−	0.336148i	0.179792	−	0.983705i	$-0.442458\pi$
$859$	−500.132	−	288.751i	−0.582226	−	0.336148i	−0.762017	+	0.647557i	$0.775791\pi$
$860$		0			0
$861$	−244.225	+	904.284i	−0.283652	+	1.05027i
$862$		0			0
$863$	645.308	+	372.569i	0.747750	+	0.431714i	0.824880	−	0.565307i	$-0.191242\pi$
$863$	645.308	+	372.569i	0.747750	+	0.431714i	−0.0771303	+	0.997021i	$0.524576\pi$
$864$		0			0
$865$	290.499	+	503.159i	0.335837	+	0.581687i
$866$		0			0
$867$			440.210i			0.507739i
$868$		0			0
$869$	0.202915			0.000233503
$870$		0			0
$871$	−896.503	+	517.596i	−1.02928	+	0.594255i
$872$		0			0
$873$	−38.9038	+	67.3834i	−0.0445633	+	0.0771860i
$874$		0			0
$875$	−658.177	+	655.573i	−0.752203	+	0.749226i
$876$		0			0
$877$	282.403	−	489.137i	0.322011	−	0.557739i	−0.658892	−	0.752237i	$-0.728975\pi$
$877$	282.403	−	489.137i	0.322011	−	0.557739i	0.980903	+	0.194499i	$0.0623080\pi$
$878$		0			0
$879$	202.054	−	116.656i	0.229868	−	0.132714i
$880$		0			0
$881$	−743.531			−0.843963			−0.421981	−	0.906605i	$-0.638665\pi$
$881$	−743.531			−0.843963			−0.421981	+	0.906605i	$0.638665\pi$
$882$		0			0
$883$		−	715.022i		−	0.809764i	−0.914369	−	0.404882i	$-0.867313\pi$
$883$		−	715.022i		−	0.809764i	0.914369	−	0.404882i	$-0.132687\pi$
$884$		0			0
$885$	−8.19386	−	14.1922i	−0.00925860	−	0.0160364i
$886$		0			0
$887$	1278.48	+	738.131i	1.44135	+	0.832166i	0.997940	−	0.0641509i	$-0.0204339\pi$
$887$	1278.48	+	738.131i	1.44135	+	0.832166i	0.443414	+	0.896317i	$0.353767\pi$
$888$		0			0
$889$	−757.113	−	760.122i	−0.851646	−	0.855030i
$890$		0			0
$891$	−1.45106	−	0.837767i	−0.00162857	−	0.000940255i
$892$		0			0
$893$	995.452	+	1724.17i	1.11473	+	1.93076i
$894$		0			0
$895$			736.001i			0.822347i
$896$		0			0
$897$	589.244			0.656905
$898$		0			0
$899$	26.1990	−	15.1260i	0.0291424	−	0.0168253i
$900$		0			0
$901$	−403.149	+	698.275i	−0.447447	+	0.775000i
$902$		0			0
$903$	−490.585	−	132.495i	−0.543284	−	0.146728i
$904$		0			0
$905$	249.849	−	432.751i	0.276076	−	0.478178i
$906$		0			0
$907$	1.66164	−	0.959350i	0.00183202	−	0.00105772i	−0.499084	−	0.866554i	$-0.666330\pi$
$907$	1.66164	−	0.959350i	0.00183202	−	0.00105772i	0.500916	+	0.865496i	$0.332997\pi$
$908$		0			0
$909$	195.680			0.215270
$910$		0			0
$911$		−	1568.49i		−	1.72172i	−0.508840	−	0.860861i	$-0.669926\pi$
$911$		−	1568.49i		−	1.72172i	0.508840	−	0.860861i	$-0.330074\pi$
$912$		0			0
$913$	−3.67089	−	6.35817i	−0.00402069	−	0.00696404i
$914$		0			0
$915$	−214.411	−	123.790i	−0.234329	−	0.135290i
$916$		0			0
$917$	1308.69	−	347.882i	1.42714	−	0.379370i
$918$		0			0
$919$	366.523	+	211.612i	0.398828	+	0.230264i	0.685978	−	0.727622i	$-0.259374\pi$
$919$	366.523	+	211.612i	0.398828	+	0.230264i	−0.287150	+	0.957886i	$0.592708\pi$
$920$		0			0
$921$	461.193	+	798.810i	0.500753	+	0.867329i
$922$		0			0
$923$			421.128i			0.456260i
$924$		0			0
$925$	137.598			0.148754
$926$		0			0
$927$	−360.252	+	207.992i	−0.388622	+	0.224371i
$928$		0			0
$929$	−141.536	+	245.148i	−0.152353	+	0.263884i	−0.932092	−	0.362221i	$-0.882018\pi$
$929$	−141.536	+	245.148i	−0.152353	+	0.263884i	0.779739	+	0.626105i	$0.215352\pi$
$930$		0			0
$931$	812.011	−	1393.65i	0.872192	−	1.49694i
$932$		0			0
$933$	−443.216	+	767.672i	−0.475043	+	0.822799i
$934$		0			0
$935$	17.2721	−	9.97204i	0.0184728	−	0.0106653i
$936$		0			0
$937$	−480.799			−0.513126			−0.256563	−	0.966528i	$-0.582590\pi$
$937$	−480.799			−0.513126			−0.256563	+	0.966528i	$0.582590\pi$
$938$		0			0
$939$			151.369i			0.161202i
$940$		0			0
$941$	−240.048	−	415.776i	−0.255099	−	0.441844i	0.709823	−	0.704380i	$-0.248775\pi$
$941$	−240.048	−	415.776i	−0.255099	−	0.441844i	−0.964922	+	0.262535i	$0.915441\pi$
$942$		0			0
$943$	−1660.32	−	958.586i	−1.76068	−	1.01653i
$944$		0			0
$945$	161.583	−	42.9527i	0.170987	−	0.0454526i
$946$		0			0
$947$	284.108	+	164.030i	0.300008	+	0.173210i	0.642446	−	0.766331i	$-0.277920\pi$
$947$	284.108	+	164.030i	0.300008	+	0.173210i	−0.342439	+	0.939540i	$0.611253\pi$
$948$		0			0
$949$	312.205	+	540.754i	0.328983	+	0.569815i
$950$		0			0
$951$		−	248.067i		−	0.260849i
$952$		0			0
$953$	−882.514			−0.926038			−0.463019	−	0.886348i	$-0.653234\pi$
$953$	−882.514			−0.926038			−0.463019	+	0.886348i	$0.653234\pi$
$954$		0			0
$955$	90.3956	−	52.1899i	0.0946551	−	0.0546491i
$956$		0			0
$957$	3.87982	−	6.72005i	0.00405415	−	0.00702199i
$958$		0			0
$959$	−1465.79	−	395.875i	−1.52846	−	0.412799i
$960$		0			0
$961$	−479.710	+	830.882i	−0.499178	+	0.864601i
$962$		0			0
$963$	−226.762	+	130.921i	−0.235474	+	0.135951i
$964$		0			0
$965$	1354.66			1.40379
$966$		0			0
$967$			1428.30i			1.47704i	0.674231	+	0.738520i	$0.264475\pi$
$967$			1428.30i			1.47704i	−0.674231	+	0.738520i	$0.735525\pi$
$968$		0			0
$969$	−664.384	−	1150.75i	−0.685639	−	1.18756i
$970$		0			0
$971$	−959.579	−	554.013i	−0.988238	−	0.570560i	−0.0834910	−	0.996509i	$-0.526607\pi$
$971$	−959.579	−	554.013i	−0.988238	−	0.570560i	−0.904747	+	0.425949i	$0.859940\pi$
$972$		0			0
$973$	−3.61928	−	3.63366i	−0.00371971	−	0.00373449i
$974$		0			0
$975$	79.5982	+	45.9561i	0.0816392	+	0.0471344i
$976$		0			0
$977$	181.175	+	313.804i	0.185440	+	0.321191i	0.943725	−	0.330732i	$-0.107296\pi$
$977$	181.175	+	313.804i	0.185440	+	0.321191i	−0.758285	+	0.651923i	$0.773962\pi$
$978$		0			0
$979$			28.3393i			0.0289472i
$980$		0			0
$981$	−193.844			−0.197598
$982$		0			0
$983$	1139.99	−	658.175i	1.15971	−	0.669558i	0.208474	−	0.978028i	$-0.433150\pi$
$983$	1139.99	−	658.175i	1.15971	−	0.669558i	0.951234	+	0.308470i	$0.0998170\pi$
$984$		0			0
$985$	−682.546	+	1182.21i	−0.692941	+	1.20021i
$986$		0			0
$987$	519.549	−	517.493i	0.526392	−	0.524309i
$988$		0			0
$989$	520.045	−	900.744i	0.525829	−	0.910763i
$990$		0			0
$991$	1231.66	−	711.100i	1.24285	−	0.717558i	0.273174	−	0.961965i	$-0.411927\pi$
$991$	1231.66	−	711.100i	1.24285	−	0.717558i	0.969673	+	0.244407i	$0.0785933\pi$
$992$		0			0
$993$	−1056.86			−1.06431
$994$		0			0
$995$			1184.38i			1.19033i
$996$		0			0
$997$	−660.969	−	1144.83i	−0.662958	−	1.14828i	−0.979835	−	0.199811i	$-0.935967\pi$
$997$	−660.969	−	1144.83i	−0.662958	−	1.14828i	0.316876	−	0.948467i	$-0.397366\pi$
$998$		0			0
$999$	−159.963	−	92.3545i	−0.160123	−	0.0924469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.be.f.79.1	yes	6
3.2	odd	2		1008.3.cd.i.415.3		6
4.3	odd	2		336.3.be.d.79.1	✓	6
7.2	even	3		2352.3.m.n.1471.6		6
7.4	even	3		336.3.be.d.319.1	yes	6
7.5	odd	6		2352.3.m.o.1471.1		6
12.11	even	2		1008.3.cd.h.415.3		6
21.11	odd	6		1008.3.cd.h.991.3		6
28.11	odd	6	inner	336.3.be.f.319.1	yes	6
28.19	even	6		2352.3.m.o.1471.4		6
28.23	odd	6		2352.3.m.n.1471.3		6
84.11	even	6		1008.3.cd.i.991.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.be.d.79.1	✓	6	4.3	odd	2
336.3.be.d.319.1	yes	6	7.4	even	3
336.3.be.f.79.1	yes	6	1.1	even	1	trivial
336.3.be.f.319.1	yes	6	28.11	odd	6	inner
1008.3.cd.h.415.3		6	12.11	even	2
1008.3.cd.h.991.3		6	21.11	odd	6
1008.3.cd.i.415.3		6	3.2	odd	2
1008.3.cd.i.991.3		6	84.11	even	6
2352.3.m.n.1471.3		6	28.23	odd	6
2352.3.m.n.1471.6		6	7.2	even	3
2352.3.m.o.1471.1		6	7.5	odd	6
2352.3.m.o.1471.4		6	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-2.29832 + 3.98081i) q^{5} +(4.95955 - 4.93992i) q^{7} +(1.50000 - 2.59808i) q^{9} +(0.161228 - 0.0930852i) q^{11} +13.7090 q^{13} +7.96163i q^{15} +(-11.6528 - 20.1833i) q^{17} +(28.5074 + 16.4587i) q^{19} +(3.16123 - 11.7050i) q^{21} +(21.4911 + 12.4079i) q^{23} +(1.93542 + 3.35224i) q^{25} -5.19615i q^{27} +24.0641 q^{29} +(1.08871 - 0.628570i) q^{31} +(0.161228 - 0.279256i) q^{33} +(8.26626 + 31.0966i) q^{35} +(17.7736 - 30.7848i) q^{37} +(20.5636 - 11.8724i) q^{39} -77.2563 q^{41} -41.9125i q^{43} +(6.89497 + 11.9424i) q^{45} +(52.3787 + 30.2408i) q^{47} +(0.194309 - 48.9996i) q^{49} +(-34.9585 - 20.1833i) q^{51} +(-17.2983 - 29.9616i) q^{53} +0.855760i q^{55} +57.0147 q^{57} +(-1.78257 + 1.02917i) q^{59} +(-15.5484 + 26.9306i) q^{61} +(-5.39497 - 20.2952i) q^{63} +(-31.5078 + 54.5731i) q^{65} +(-65.3950 + 37.7558i) q^{67} +42.9821 q^{69} +30.7190i q^{71} +(22.7736 + 39.4451i) q^{73} +(5.80626 + 3.35224i) q^{75} +(0.339786 - 1.25812i) q^{77} +(0.943915 + 0.544970i) q^{79} +(-4.50000 - 7.79423i) q^{81} -39.4358i q^{83} +107.128 q^{85} +(36.0962 - 20.8401i) q^{87} +(-76.1113 + 131.829i) q^{89} +(67.9907 - 67.7216i) q^{91} +(1.08871 - 1.88571i) q^{93} +(-131.038 + 75.6550i) q^{95} -25.9359 q^{97} -0.558511i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + q^{5} + 11 q^{7} + 9 q^{9} - 3 q^{11} - 44 q^{13} + 8 q^{17} + 30 q^{19} + 15 q^{21} - 24 q^{23} - 14 q^{25} + 34 q^{29} + 39 q^{31} - 3 q^{33} + 90 q^{35} + 6 q^{37} - 66 q^{39} - 136 q^{41}+ \cdots - 266 q^{97}+O(q^{100}) \) 6 * q + 9 * q^3 + q^5 + 11 * q^7 + 9 * q^9 - 3 * q^11 - 44 * q^13 + 8 * q^17 + 30 * q^19 + 15 * q^21 - 24 * q^23 - 14 * q^25 + 34 * q^29 + 39 * q^31 - 3 * q^33 + 90 * q^35 + 6 * q^37 - 66 * q^39 - 136 * q^41 - 3 * q^45 + 258 * q^47 + 157 * q^49 + 24 * q^51 - 89 * q^53 + 60 * q^57 - 63 * q^59 - 50 * q^61 + 12 * q^63 - 184 * q^65 - 348 * q^67 - 48 * q^69 + 36 * q^73 - 42 * q^75 + 221 * q^77 - 3 * q^79 - 27 * q^81 + 536 * q^85 + 51 * q^87 - 202 * q^89 + 62 * q^91 + 39 * q^93 - 432 * q^95 - 266 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more