LMFDB - Embedded newform 336.3.bh.b.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.3.bh.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +6.92820i q^{13} -3.00000 q^{15} +(-15.0000 - 8.66025i) q^{17} +(-9.00000 + 5.19615i) q^{19} +(7.50000 + 9.52628i) q^{21} +(18.0000 + 31.1769i) q^{23} +(-11.0000 + 19.0526i) q^{25} -5.19615i q^{27} -51.0000 q^{29} +(10.5000 + 6.06218i) q^{31} +(4.50000 - 2.59808i) q^{33} +(-12.0000 + 1.73205i) q^{35} +(-11.0000 - 19.0526i) q^{37} +(6.00000 - 10.3923i) q^{39} +24.2487i q^{41} -10.0000 q^{43} +(4.50000 + 2.59808i) q^{45} +(-78.0000 + 45.0333i) q^{47} +(35.5000 + 33.7750i) q^{49} +(15.0000 + 25.9808i) q^{51} +(-25.5000 + 44.1673i) q^{53} +5.19615i q^{55} +18.0000 q^{57} +(-64.5000 - 37.2391i) q^{59} +(60.0000 - 34.6410i) q^{61} +(-3.00000 - 20.7846i) q^{63} +(6.00000 + 10.3923i) q^{65} +(34.0000 - 58.8897i) q^{67} -62.3538i q^{69} +(-18.0000 - 10.3923i) q^{73} +(33.0000 - 19.0526i) q^{75} +(16.5000 - 12.9904i) q^{77} +(62.5000 + 108.253i) q^{79} +(-4.50000 + 7.79423i) q^{81} -154.153i q^{83} -30.0000 q^{85} +(76.5000 + 44.1673i) q^{87} +(63.0000 - 36.3731i) q^{89} +(18.0000 - 45.0333i) q^{91} +(-10.5000 - 18.1865i) q^{93} +(-9.00000 + 15.5885i) q^{95} -147.224i q^{97} -9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 3 q^{5} - 13 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 3 * q^5 - 13 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} + 3 q^{5} - 13 q^{7} + 3 q^{9} - 3 q^{11} - 6 q^{15} - 30 q^{17} - 18 q^{19} + 15 q^{21} + 36 q^{23} - 22 q^{25} - 102 q^{29} + 21 q^{31} + 9 q^{33} - 24 q^{35} - 22 q^{37} + 12 q^{39} - 20 q^{43} + 9 q^{45} - 156 q^{47} + 71 q^{49} + 30 q^{51} - 51 q^{53} + 36 q^{57} - 129 q^{59} + 120 q^{61} - 6 q^{63} + 12 q^{65} + 68 q^{67} - 36 q^{73} + 66 q^{75} + 33 q^{77} + 125 q^{79} - 9 q^{81} - 60 q^{85} + 153 q^{87} + 126 q^{89} + 36 q^{91} - 21 q^{93} - 18 q^{95} - 18 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 3 * q^5 - 13 * q^7 + 3 * q^9 - 3 * q^11 - 6 * q^15 - 30 * q^17 - 18 * q^19 + 15 * q^21 + 36 * q^23 - 22 * q^25 - 102 * q^29 + 21 * q^31 + 9 * q^33 - 24 * q^35 - 22 * q^37 + 12 * q^39 - 20 * q^43 + 9 * q^45 - 156 * q^47 + 71 * q^49 + 30 * q^51 - 51 * q^53 + 36 * q^57 - 129 * q^59 + 120 * q^61 - 6 * q^63 + 12 * q^65 + 68 * q^67 - 36 * q^73 + 66 * q^75 + 33 * q^77 + 125 * q^79 - 9 * q^81 - 60 * q^85 + 153 * q^87 + 126 * q^89 + 36 * q^91 - 21 * q^93 - 18 * q^95 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			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
$5$	1.50000	−	0.866025i	0.300000	−	0.173205i	−0.342443	−	0.939539i	$-0.611254\pi$
$5$	1.50000	−	0.866025i	0.300000	−	0.173205i	0.642443	+	0.766334i	$0.277921\pi$
$6$		0			0
$7$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$7$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.136364	+	0.236189i	−0.926118	−	0.377235i	$-0.876875\pi$
$11$	−1.50000	+	2.59808i	−0.136364	+	0.236189i	0.789754	+	0.613424i	$0.210208\pi$
$12$		0			0
$13$			6.92820i			0.532939i	0.963843	+	0.266469i	$0.0858571\pi$
$13$			6.92820i			0.532939i	−0.963843	+	0.266469i	$0.914143\pi$
$14$		0			0
$15$	−3.00000			−0.200000
$16$		0			0
$17$	−15.0000	−	8.66025i	−0.882353	−	0.509427i	−0.0109194	−	0.999940i	$-0.503476\pi$
$17$	−15.0000	−	8.66025i	−0.882353	−	0.509427i	−0.871433	+	0.490514i	$0.836809\pi$
$18$		0			0
$19$	−9.00000	+	5.19615i	−0.473684	+	0.273482i	−0.717781	−	0.696269i	$-0.754842\pi$
$19$	−9.00000	+	5.19615i	−0.473684	+	0.273482i	0.244096	+	0.969751i	$0.421509\pi$
$20$		0			0
$21$	7.50000	+	9.52628i	0.357143	+	0.453632i
$22$		0			0
$23$	18.0000	+	31.1769i	0.782609	+	1.35552i	0.930417	+	0.366502i	$0.119445\pi$
$23$	18.0000	+	31.1769i	0.782609	+	1.35552i	−0.147809	+	0.989016i	$0.547222\pi$
$24$		0			0
$25$	−11.0000	+	19.0526i	−0.440000	+	0.762102i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−51.0000			−1.75862			−0.879310	−	0.476249i	$-0.841996\pi$
$29$	−51.0000			−1.75862			−0.879310	+	0.476249i	$0.841996\pi$
$30$		0			0
$31$	10.5000	+	6.06218i	0.338710	+	0.195554i	0.659701	−	0.751528i	$-0.270683\pi$
$31$	10.5000	+	6.06218i	0.338710	+	0.195554i	−0.320992	+	0.947082i	$0.604016\pi$
$32$		0			0
$33$	4.50000	−	2.59808i	0.136364	−	0.0787296i
$34$		0			0
$35$	−12.0000	+	1.73205i	−0.342857	+	0.0494872i
$36$		0			0
$37$	−11.0000	−	19.0526i	−0.297297	−	0.514934i	0.678219	−	0.734859i	$-0.262752\pi$
$37$	−11.0000	−	19.0526i	−0.297297	−	0.514934i	−0.975517	+	0.219925i	$0.929419\pi$
$38$		0			0
$39$	6.00000	−	10.3923i	0.153846	−	0.266469i
$40$		0			0
$41$			24.2487i			0.591432i	0.955276	+	0.295716i	$0.0955582\pi$
$41$			24.2487i			0.591432i	−0.955276	+	0.295716i	$0.904442\pi$
$42$		0			0
$43$	−10.0000			−0.232558			−0.116279	−	0.993217i	$-0.537097\pi$
$43$	−10.0000			−0.232558			−0.116279	+	0.993217i	$0.537097\pi$
$44$		0			0
$45$	4.50000	+	2.59808i	0.100000	+	0.0577350i
$46$		0			0
$47$	−78.0000	+	45.0333i	−1.65957	+	0.958156i	−0.686664	+	0.726975i	$0.740925\pi$
$47$	−78.0000	+	45.0333i	−1.65957	+	0.958156i	−0.972911	+	0.231180i	$0.925741\pi$
$48$		0			0
$49$	35.5000	+	33.7750i	0.724490	+	0.689286i
$50$		0			0
$51$	15.0000	+	25.9808i	0.294118	+	0.509427i
$52$		0			0
$53$	−25.5000	+	44.1673i	−0.481132	+	0.833345i	−0.999766	−	0.0216515i	$-0.993108\pi$
$53$	−25.5000	+	44.1673i	−0.481132	+	0.833345i	0.518634	+	0.854997i	$0.326441\pi$
$54$		0			0
$55$			5.19615i			0.0944755i
$56$		0			0
$57$	18.0000			0.315789
$58$		0			0
$59$	−64.5000	−	37.2391i	−1.09322	−	0.631171i	−0.158788	−	0.987313i	$-0.550759\pi$
$59$	−64.5000	−	37.2391i	−1.09322	−	0.631171i	−0.934432	+	0.356142i	$0.884092\pi$
$60$		0			0
$61$	60.0000	−	34.6410i	0.983607	−	0.567886i	0.0802495	−	0.996775i	$-0.474428\pi$
$61$	60.0000	−	34.6410i	0.983607	−	0.567886i	0.903357	+	0.428889i	$0.141095\pi$
$62$		0			0
$63$	−3.00000	−	20.7846i	−0.0476190	−	0.329914i
$64$		0			0
$65$	6.00000	+	10.3923i	0.0923077	+	0.159882i
$66$		0			0
$67$	34.0000	−	58.8897i	0.507463	−	0.878951i	−0.492500	−	0.870312i	$-0.663917\pi$
$67$	34.0000	−	58.8897i	0.507463	−	0.878951i	0.999963	−	0.00863871i	$-0.00274982\pi$
$68$		0			0
$69$		−	62.3538i		−	0.903679i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−18.0000	−	10.3923i	−0.246575	−	0.142360i	0.371620	−	0.928385i	$-0.378803\pi$
$73$	−18.0000	−	10.3923i	−0.246575	−	0.142360i	−0.618195	+	0.786025i	$0.712136\pi$
$74$		0			0
$75$	33.0000	−	19.0526i	0.440000	−	0.254034i
$76$		0			0
$77$	16.5000	−	12.9904i	0.214286	−	0.168706i
$78$		0			0
$79$	62.5000	+	108.253i	0.791139	+	1.37029i	0.925262	+	0.379329i	$0.123845\pi$
$79$	62.5000	+	108.253i	0.791139	+	1.37029i	−0.134123	+	0.990965i	$0.542822\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	154.153i		−	1.85726i	−0.371008	−	0.928630i	$-0.620988\pi$
$83$		−	154.153i		−	1.85726i	0.371008	−	0.928630i	$-0.379012\pi$
$84$		0			0
$85$	−30.0000			−0.352941
$86$		0			0
$87$	76.5000	+	44.1673i	0.879310	+	0.507670i
$88$		0			0
$89$	63.0000	−	36.3731i	0.707865	−	0.408686i	−0.102405	−	0.994743i	$-0.532654\pi$
$89$	63.0000	−	36.3731i	0.707865	−	0.408686i	0.810270	+	0.586057i	$0.199320\pi$
$90$		0			0
$91$	18.0000	−	45.0333i	0.197802	−	0.494872i
$92$		0			0
$93$	−10.5000	−	18.1865i	−0.112903	−	0.195554i
$94$		0			0
$95$	−9.00000	+	15.5885i	−0.0947368	+	0.164089i
$96$		0			0
$97$		−	147.224i		−	1.51778i	−0.651221	−	0.758888i	$-0.725743\pi$
$97$		−	147.224i		−	1.51778i	0.651221	−	0.758888i	$-0.274257\pi$
$98$		0			0
$99$	−9.00000			−0.0909091
$100$		0			0
$101$	18.0000	+	10.3923i	0.178218	+	0.102894i	0.586455	−	0.809982i	$-0.300523\pi$
$101$	18.0000	+	10.3923i	0.178218	+	0.102894i	−0.408237	+	0.912876i	$0.633856\pi$
$102$		0			0
$103$	132.000	−	76.2102i	1.28155	−	0.739905i	0.304421	−	0.952538i	$-0.401537\pi$
$103$	132.000	−	76.2102i	1.28155	−	0.739905i	0.977132	+	0.212632i	$0.0682037\pi$
$104$		0			0
$105$	19.5000	+	7.79423i	0.185714	+	0.0742307i
$106$		0			0
$107$	−16.5000	−	28.5788i	−0.154206	−	0.267092i	0.778564	−	0.627565i	$-0.215948\pi$
$107$	−16.5000	−	28.5788i	−0.154206	−	0.267092i	−0.932769	+	0.360473i	$0.882615\pi$
$108$		0			0
$109$	16.0000	−	27.7128i	0.146789	−	0.254246i	−0.783250	−	0.621707i	$-0.786440\pi$
$109$	16.0000	−	27.7128i	0.146789	−	0.254246i	0.930039	+	0.367461i	$0.119773\pi$
$110$		0			0
$111$			38.1051i			0.343289i
$112$		0			0
$113$	−186.000			−1.64602			−0.823009	−	0.568029i	$-0.807706\pi$
$113$	−186.000			−1.64602			−0.823009	+	0.568029i	$0.807706\pi$
$114$		0			0
$115$	54.0000	+	31.1769i	0.469565	+	0.271104i
$116$		0			0
$117$	−18.0000	+	10.3923i	−0.153846	+	0.0888231i
$118$		0			0
$119$	75.0000	+	95.2628i	0.630252	+	0.800528i
$120$		0			0
$121$	56.0000	+	96.9948i	0.462810	+	0.801610i
$122$		0			0
$123$	21.0000	−	36.3731i	0.170732	−	0.295716i
$124$		0			0
$125$			81.4064i			0.651251i
$126$		0			0
$127$	−131.000			−1.03150			−0.515748	−	0.856740i	$-0.672486\pi$
$127$	−131.000			−1.03150			−0.515748	+	0.856740i	$0.672486\pi$
$128$		0			0
$129$	15.0000	+	8.66025i	0.116279	+	0.0671338i
$130$		0			0
$131$	−85.5000	+	49.3634i	−0.652672	+	0.376820i	−0.789479	−	0.613777i	$-0.789649\pi$
$131$	−85.5000	+	49.3634i	−0.652672	+	0.376820i	0.136807	+	0.990598i	$0.456316\pi$
$132$		0			0
$133$	72.0000	−	10.3923i	0.541353	−	0.0781376i
$134$		0			0
$135$	−4.50000	−	7.79423i	−0.0333333	−	0.0577350i
$136$		0			0
$137$	72.0000	−	124.708i	0.525547	−	0.910275i	−0.474010	−	0.880520i	$-0.657194\pi$
$137$	72.0000	−	124.708i	0.525547	−	0.910275i	0.999557	−	0.0297553i	$-0.00947280\pi$
$138$		0			0
$139$		−	148.956i		−	1.07163i	−0.844336	−	0.535814i	$-0.820005\pi$
$139$		−	148.956i		−	1.07163i	0.844336	−	0.535814i	$-0.179995\pi$
$140$		0			0
$141$	156.000			1.10638
$142$		0			0
$143$	−18.0000	−	10.3923i	−0.125874	−	0.0726735i
$144$		0			0
$145$	−76.5000	+	44.1673i	−0.527586	+	0.304602i
$146$		0			0
$147$	−24.0000	−	81.4064i	−0.163265	−	0.553785i
$148$		0			0
$149$	75.0000	+	129.904i	0.503356	+	0.871838i	0.999992	+	0.00387918i	$0.00123478\pi$
$149$	75.0000	+	129.904i	0.503356	+	0.871838i	−0.496637	+	0.867958i	$0.665432\pi$
$150$		0			0
$151$	−116.500	+	201.784i	−0.771523	+	1.33632i	0.165205	+	0.986259i	$0.447171\pi$
$151$	−116.500	+	201.784i	−0.771523	+	1.33632i	−0.936728	+	0.350058i	$0.886162\pi$
$152$		0			0
$153$		−	51.9615i		−	0.339618i
$154$		0			0
$155$	21.0000			0.135484
$156$		0			0
$157$	126.000	+	72.7461i	0.802548	+	0.463351i	0.844361	−	0.535774i	$-0.179980\pi$
$157$	126.000	+	72.7461i	0.802548	+	0.463351i	−0.0418135	+	0.999125i	$0.513314\pi$
$158$		0			0
$159$	76.5000	−	44.1673i	0.481132	−	0.277782i
$160$		0			0
$161$	−36.0000	−	249.415i	−0.223602	−	1.54916i
$162$		0			0
$163$	−74.0000	−	128.172i	−0.453988	−	0.786330i	0.544642	−	0.838669i	$-0.316666\pi$
$163$	−74.0000	−	128.172i	−0.453988	−	0.786330i	−0.998629	+	0.0523391i	$0.983332\pi$
$164$		0			0
$165$	4.50000	−	7.79423i	0.0272727	−	0.0472377i
$166$		0			0
$167$		−	27.7128i		−	0.165945i	−0.996552	−	0.0829725i	$-0.973559\pi$
$167$		−	27.7128i		−	0.165945i	0.996552	−	0.0829725i	$-0.0264414\pi$
$168$		0			0
$169$	121.000			0.715976
$170$		0			0
$171$	−27.0000	−	15.5885i	−0.157895	−	0.0911606i
$172$		0			0
$173$	−162.000	+	93.5307i	−0.936416	+	0.540640i	−0.888835	−	0.458227i	$-0.848485\pi$
$173$	−162.000	+	93.5307i	−0.936416	+	0.540640i	−0.0475811	+	0.998867i	$0.515151\pi$
$174$		0			0
$175$	121.000	−	95.2628i	0.691429	−	0.544359i
$176$		0			0
$177$	64.5000	+	111.717i	0.364407	+	0.631171i
$178$		0			0
$179$	−81.0000	+	140.296i	−0.452514	+	0.783777i	−0.998541	−	0.0539901i	$-0.982806\pi$
$179$	−81.0000	+	140.296i	−0.452514	+	0.783777i	0.546028	+	0.837767i	$0.316139\pi$
$180$		0			0
$181$		−	259.808i		−	1.43540i	−0.696352	−	0.717701i	$-0.745195\pi$
$181$		−	259.808i		−	1.43540i	0.696352	−	0.717701i	$-0.254805\pi$
$182$		0			0
$183$	−120.000			−0.655738
$184$		0			0
$185$	−33.0000	−	19.0526i	−0.178378	−	0.102987i
$186$		0			0
$187$	45.0000	−	25.9808i	0.240642	−	0.138935i
$188$		0			0
$189$	−13.5000	+	33.7750i	−0.0714286	+	0.178704i
$190$		0			0
$191$	48.0000	+	83.1384i	0.251309	+	0.435280i	0.963886	−	0.266314i	$-0.0858057\pi$
$191$	48.0000	+	83.1384i	0.251309	+	0.435280i	−0.712578	+	0.701593i	$0.752472\pi$
$192$		0			0
$193$	−147.500	+	255.477i	−0.764249	+	1.32372i	0.176394	+	0.984320i	$0.443557\pi$
$193$	−147.500	+	255.477i	−0.764249	+	1.32372i	−0.940643	+	0.339398i	$0.889777\pi$
$194$		0			0
$195$		−	20.7846i		−	0.106588i
$196$		0			0
$197$	−330.000			−1.67513			−0.837563	−	0.546340i	$-0.816021\pi$
$197$	−330.000			−1.67513			−0.837563	+	0.546340i	$0.816021\pi$
$198$		0			0
$199$	102.000	+	58.8897i	0.512563	+	0.295928i	0.733886	−	0.679272i	$-0.237704\pi$
$199$	102.000	+	58.8897i	0.512563	+	0.295928i	−0.221324	+	0.975200i	$0.571038\pi$
$200$		0			0
$201$	−102.000	+	58.8897i	−0.507463	+	0.292984i
$202$		0			0
$203$	331.500	+	132.502i	1.63300	+	0.652719i
$204$		0			0
$205$	21.0000	+	36.3731i	0.102439	+	0.177430i
$206$		0			0
$207$	−54.0000	+	93.5307i	−0.260870	+	0.451839i
$208$		0			0
$209$		−	31.1769i		−	0.149172i
$210$		0			0
$211$	−220.000			−1.04265			−0.521327	−	0.853357i	$-0.674563\pi$
$211$	−220.000			−1.04265			−0.521327	+	0.853357i	$0.674563\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.0000	+	8.66025i	−0.0697674	+	0.0402803i
$216$		0			0
$217$	−52.5000	−	66.6840i	−0.241935	−	0.307299i
$218$		0			0
$219$	18.0000	+	31.1769i	0.0821918	+	0.142360i
$220$		0			0
$221$	60.0000	−	103.923i	0.271493	−	0.470240i
$222$		0			0
$223$			150.688i			0.675733i	0.941194	+	0.337866i	$0.109705\pi$
$223$			150.688i			0.675733i	−0.941194	+	0.337866i	$0.890295\pi$
$224$		0			0
$225$	−66.0000			−0.293333
$226$		0			0
$227$	−94.5000	−	54.5596i	−0.416300	−	0.240351i	0.277193	−	0.960814i	$-0.410596\pi$
$227$	−94.5000	−	54.5596i	−0.416300	−	0.240351i	−0.693493	+	0.720464i	$0.743929\pi$
$228$		0			0
$229$	−327.000	+	188.794i	−1.42795	+	0.824426i	−0.996959	−	0.0779313i	$-0.975169\pi$
$229$	−327.000	+	188.794i	−1.42795	+	0.824426i	−0.430989	+	0.902357i	$0.641835\pi$
$230$		0			0
$231$	−36.0000	+	5.19615i	−0.155844	+	0.0224942i
$232$		0			0
$233$	105.000	+	181.865i	0.450644	+	0.780538i	0.998426	−	0.0560830i	$-0.0178611\pi$
$233$	105.000	+	181.865i	0.450644	+	0.780538i	−0.547782	+	0.836621i	$0.684528\pi$
$234$		0			0
$235$	−78.0000	+	135.100i	−0.331915	+	0.574893i
$236$		0			0
$237$		−	216.506i		−	0.913529i
$238$		0			0
$239$	−120.000			−0.502092			−0.251046	−	0.967975i	$-0.580775\pi$
$239$	−120.000			−0.502092			−0.251046	+	0.967975i	$0.580775\pi$
$240$		0			0
$241$	−10.5000	−	6.06218i	−0.0435685	−	0.0251543i	0.478058	−	0.878329i	$-0.341341\pi$
$241$	−10.5000	−	6.06218i	−0.0435685	−	0.0251543i	−0.521626	+	0.853174i	$0.674674\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	82.5000	+	19.9186i	0.336735	+	0.0813003i
$246$		0			0
$247$	−36.0000	−	62.3538i	−0.145749	−	0.252445i
$248$		0			0
$249$	−133.500	+	231.229i	−0.536145	+	0.928630i
$250$		0			0
$251$		−	136.832i		−	0.545147i	−0.962135	−	0.272574i	$-0.912125\pi$
$251$		−	136.832i		−	0.545147i	0.962135	−	0.272574i	$-0.0878749\pi$
$252$		0			0
$253$	−108.000			−0.426877
$254$		0			0
$255$	45.0000	+	25.9808i	0.176471	+	0.101885i
$256$		0			0
$257$	117.000	−	67.5500i	0.455253	−	0.262840i	−0.254793	−	0.966996i	$-0.582007\pi$
$257$	117.000	−	67.5500i	0.455253	−	0.262840i	0.710046	+	0.704155i	$0.248674\pi$
$258$		0			0
$259$	22.0000	+	152.420i	0.0849421	+	0.588496i
$260$		0			0
$261$	−76.5000	−	132.502i	−0.293103	−	0.507670i
$262$		0			0
$263$	81.0000	−	140.296i	0.307985	−	0.533445i	−0.669937	−	0.742418i	$-0.733679\pi$
$263$	81.0000	−	140.296i	0.307985	−	0.533445i	0.977921	+	0.208973i	$0.0670121\pi$
$264$		0			0
$265$			88.3346i			0.333338i
$266$		0			0
$267$	−126.000			−0.471910
$268$		0			0
$269$	334.500	+	193.124i	1.24349	+	0.717932i	0.969804	−	0.243886i	$-0.0784223\pi$
$269$	334.500	+	193.124i	1.24349	+	0.717932i	0.273691	+	0.961818i	$0.411756\pi$
$270$		0			0
$271$	−187.500	+	108.253i	−0.691882	+	0.399458i	−0.804317	−	0.594201i	$-0.797468\pi$
$271$	−187.500	+	108.253i	−0.691882	+	0.399458i	0.112435	+	0.993659i	$0.464135\pi$
$272$		0			0
$273$	−66.0000	+	51.9615i	−0.241758	+	0.190335i
$274$		0			0
$275$	−33.0000	−	57.1577i	−0.120000	−	0.207846i
$276$		0			0
$277$	50.0000	−	86.6025i	0.180505	−	0.312645i	−0.761547	−	0.648109i	$-0.775560\pi$
$277$	50.0000	−	86.6025i	0.180505	−	0.312645i	0.942053	+	0.335465i	$0.108893\pi$
$278$		0			0
$279$			36.3731i			0.130369i
$280$		0			0
$281$	228.000			0.811388			0.405694	−	0.914009i	$-0.367030\pi$
$281$	228.000			0.811388			0.405694	+	0.914009i	$0.367030\pi$
$282$		0			0
$283$	−15.0000	−	8.66025i	−0.0530035	−	0.0306016i	0.473264	−	0.880921i	$-0.343076\pi$
$283$	−15.0000	−	8.66025i	−0.0530035	−	0.0306016i	−0.526268	+	0.850319i	$0.676409\pi$
$284$		0			0
$285$	27.0000	−	15.5885i	0.0947368	−	0.0546963i
$286$		0			0
$287$	63.0000	−	157.617i	0.219512	−	0.549187i
$288$		0			0
$289$	5.50000	+	9.52628i	0.0190311	+	0.0329629i
$290$		0			0
$291$	−127.500	+	220.836i	−0.438144	+	0.758888i
$292$		0			0
$293$			278.860i			0.951741i	0.879515	+	0.475871i	$0.157867\pi$
$293$			278.860i			0.951741i	−0.879515	+	0.475871i	$0.842133\pi$
$294$		0			0
$295$	−129.000			−0.437288
$296$		0			0
$297$	13.5000	+	7.79423i	0.0454545	+	0.0262432i
$298$		0			0
$299$	−216.000	+	124.708i	−0.722408	+	0.417082i
$300$		0			0
$301$	65.0000	+	25.9808i	0.215947	+	0.0863148i
$302$		0			0
$303$	−18.0000	−	31.1769i	−0.0594059	−	0.102894i
$304$		0			0
$305$	60.0000	−	103.923i	0.196721	−	0.340731i
$306$		0			0
$307$		−	27.7128i		−	0.0902697i	−0.998981	−	0.0451349i	$-0.985628\pi$
$307$		−	27.7128i		−	0.0902697i	0.998981	−	0.0451349i	$-0.0143718\pi$
$308$		0			0
$309$	−264.000			−0.854369
$310$		0			0
$311$	−57.0000	−	32.9090i	−0.183280	−	0.105817i	0.405553	−	0.914072i	$-0.367079\pi$
$311$	−57.0000	−	32.9090i	−0.183280	−	0.105817i	−0.588833	+	0.808255i	$0.700412\pi$
$312$		0			0
$313$	103.500	−	59.7558i	0.330671	−	0.190913i	−0.325468	−	0.945553i	$-0.605522\pi$
$313$	103.500	−	59.7558i	0.330671	−	0.190913i	0.656139	+	0.754640i	$0.272189\pi$
$314$		0			0
$315$	−22.5000	−	28.5788i	−0.0714286	−	0.0907265i
$316$		0			0
$317$	100.500	+	174.071i	0.317035	+	0.549120i	0.979868	−	0.199647i	$-0.0639795\pi$
$317$	100.500	+	174.071i	0.317035	+	0.549120i	−0.662833	+	0.748767i	$0.730646\pi$
$318$		0			0
$319$	76.5000	−	132.502i	0.239812	−	0.415366i
$320$		0			0
$321$			57.1577i			0.178061i
$322$		0			0
$323$	180.000			0.557276
$324$		0			0
$325$	−132.000	−	76.2102i	−0.406154	−	0.234493i
$326$		0			0
$327$	−48.0000	+	27.7128i	−0.146789	+	0.0847487i
$328$		0			0
$329$	624.000	−	90.0666i	1.89666	−	0.273759i
$330$		0			0
$331$	224.000	+	387.979i	0.676737	+	1.17214i	0.975958	+	0.217959i	$0.0699400\pi$
$331$	224.000	+	387.979i	0.676737	+	1.17214i	−0.299221	+	0.954184i	$0.596727\pi$
$332$		0			0
$333$	33.0000	−	57.1577i	0.0990991	−	0.171645i
$334$		0			0
$335$		−	117.779i		−	0.351580i
$336$		0			0
$337$	−293.000			−0.869436			−0.434718	−	0.900567i	$-0.643152\pi$
$337$	−293.000			−0.869436			−0.434718	+	0.900567i	$0.643152\pi$
$338$		0			0
$339$	279.000	+	161.081i	0.823009	+	0.475164i
$340$		0			0
$341$	−31.5000	+	18.1865i	−0.0923754	+	0.0533329i
$342$		0			0
$343$	−143.000	−	311.769i	−0.416910	−	0.908948i
$344$		0			0
$345$	−54.0000	−	93.5307i	−0.156522	−	0.271104i
$346$		0			0
$347$	195.000	−	337.750i	0.561960	−	0.973343i	−0.435366	−	0.900254i	$-0.643381\pi$
$347$	195.000	−	337.750i	0.561960	−	0.973343i	0.997325	−	0.0730890i	$-0.0232857\pi$
$348$		0			0
$349$		−	138.564i		−	0.397032i	−0.980098	−	0.198516i	$-0.936388\pi$
$349$		−	138.564i		−	0.397032i	0.980098	−	0.198516i	$-0.0636121\pi$
$350$		0			0
$351$	36.0000			0.102564
$352$		0			0
$353$	−438.000	−	252.879i	−1.24079	−	0.716372i	−0.271537	−	0.962428i	$-0.587532\pi$
$353$	−438.000	−	252.879i	−1.24079	−	0.716372i	−0.969256	+	0.246056i	$0.920865\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−30.0000	−	207.846i	−0.0840336	−	0.582202i
$358$		0			0
$359$	150.000	+	259.808i	0.417827	+	0.723698i	0.995721	−	0.0924142i	$-0.0294584\pi$
$359$	150.000	+	259.808i	0.417827	+	0.723698i	−0.577893	+	0.816112i	$0.696125\pi$
$360$		0			0
$361$	−126.500	+	219.104i	−0.350416	+	0.606937i
$362$		0			0
$363$		−	193.990i		−	0.534407i
$364$		0			0
$365$	−36.0000			−0.0986301
$366$		0			0
$367$	175.500	+	101.325i	0.478202	+	0.276090i	0.719667	−	0.694320i	$-0.244295\pi$
$367$	175.500	+	101.325i	0.478202	+	0.276090i	−0.241465	+	0.970410i	$0.577628\pi$
$368$		0			0
$369$	−63.0000	+	36.3731i	−0.170732	+	0.0985720i
$370$		0			0
$371$	280.500	−	220.836i	0.756065	−	0.595247i
$372$		0			0
$373$	−205.000	−	355.070i	−0.549598	−	0.951931i	−0.998302	−	0.0582510i	$-0.981448\pi$
$373$	−205.000	−	355.070i	−0.549598	−	0.951931i	0.448704	−	0.893680i	$-0.351886\pi$
$374$		0			0
$375$	70.5000	−	122.110i	0.188000	−	0.325626i
$376$		0			0
$377$		−	353.338i		−	0.937237i
$378$		0			0
$379$	374.000			0.986807			0.493404	−	0.869800i	$-0.335753\pi$
$379$	374.000			0.986807			0.493404	+	0.869800i	$0.335753\pi$
$380$		0			0
$381$	196.500	+	113.449i	0.515748	+	0.297767i
$382$		0			0
$383$	249.000	−	143.760i	0.650131	−	0.375353i	−0.138376	−	0.990380i	$-0.544188\pi$
$383$	249.000	−	143.760i	0.650131	−	0.375353i	0.788506	+	0.615027i	$0.210855\pi$
$384$		0			0
$385$	13.5000	−	33.7750i	0.0350649	−	0.0877272i
$386$		0			0
$387$	−15.0000	−	25.9808i	−0.0387597	−	0.0671338i
$388$		0			0
$389$	69.0000	−	119.512i	0.177378	−	0.307228i	−0.763604	−	0.645685i	$-0.776572\pi$
$389$	69.0000	−	119.512i	0.177378	−	0.307228i	0.940982	+	0.338458i	$0.109905\pi$
$390$		0			0
$391$		−	623.538i		−	1.59473i
$392$		0			0
$393$	171.000			0.435115
$394$		0			0
$395$	187.500	+	108.253i	0.474684	+	0.274059i
$396$		0			0
$397$	534.000	−	308.305i	1.34509	−	0.776587i	0.357539	−	0.933898i	$-0.383616\pi$
$397$	534.000	−	308.305i	1.34509	−	0.776587i	0.987549	+	0.157311i	$0.0502826\pi$
$398$		0			0
$399$	−117.000	−	46.7654i	−0.293233	−	0.117206i
$400$		0			0
$401$	−258.000	−	446.869i	−0.643392	−	1.11439i	−0.984671	−	0.174425i	$-0.944193\pi$
$401$	−258.000	−	446.869i	−0.643392	−	1.11439i	0.341279	−	0.939962i	$-0.389140\pi$
$402$		0			0
$403$	−42.0000	+	72.7461i	−0.104218	+	0.180511i
$404$		0			0
$405$			15.5885i			0.0384900i
$406$		0			0
$407$	66.0000			0.162162
$408$		0			0
$409$	226.500	+	130.770i	0.553790	+	0.319731i	0.750649	−	0.660701i	$-0.229741\pi$
$409$	226.500	+	130.770i	0.553790	+	0.319731i	−0.196859	+	0.980432i	$0.563074\pi$
$410$		0			0
$411$	−216.000	+	124.708i	−0.525547	+	0.303425i
$412$		0			0
$413$	322.500	+	409.630i	0.780872	+	0.991840i
$414$		0			0
$415$	−133.500	−	231.229i	−0.321687	−	0.557178i
$416$		0			0
$417$	−129.000	+	223.435i	−0.309353	+	0.535814i
$418$		0			0
$419$			533.472i			1.27320i	0.771193	+	0.636601i	$0.219660\pi$
$419$			533.472i			1.27320i	−0.771193	+	0.636601i	$0.780340\pi$
$420$		0			0
$421$	−76.0000			−0.180523			−0.0902613	−	0.995918i	$-0.528770\pi$
$421$	−76.0000			−0.180523			−0.0902613	+	0.995918i	$0.528770\pi$
$422$		0			0
$423$	−234.000	−	135.100i	−0.553191	−	0.319385i
$424$		0			0
$425$	330.000	−	190.526i	0.776471	−	0.448296i
$426$		0			0
$427$	−480.000	+	69.2820i	−1.12412	+	0.162253i
$428$		0			0
$429$	18.0000	+	31.1769i	0.0419580	+	0.0726735i
$430$		0			0
$431$	303.000	−	524.811i	0.703016	−	1.21766i	−0.264386	−	0.964417i	$-0.585169\pi$
$431$	303.000	−	524.811i	0.703016	−	1.21766i	0.967403	−	0.253243i	$-0.0814972\pi$
$432$		0			0
$433$			34.6410i			0.0800023i	0.999200	+	0.0400012i	$0.0127362\pi$
$433$			34.6410i			0.0800023i	−0.999200	+	0.0400012i	$0.987264\pi$
$434$		0			0
$435$	153.000			0.351724
$436$		0			0
$437$	−324.000	−	187.061i	−0.741419	−	0.428058i
$438$		0			0
$439$	−85.5000	+	49.3634i	−0.194761	+	0.112445i	−0.594209	−	0.804310i	$-0.702535\pi$
$439$	−85.5000	+	49.3634i	−0.194761	+	0.112445i	0.399449	+	0.916756i	$0.369202\pi$
$440$		0			0
$441$	−34.5000	+	142.894i	−0.0782313	+	0.324023i
$442$		0			0
$443$	310.500	+	537.802i	0.700903	+	1.21400i	0.968150	+	0.250371i	$0.0805527\pi$
$443$	310.500	+	537.802i	0.700903	+	1.21400i	−0.267247	+	0.963628i	$0.586114\pi$
$444$		0			0
$445$	63.0000	−	109.119i	0.141573	−	0.245212i
$446$		0			0
$447$		−	259.808i		−	0.581225i
$448$		0			0
$449$	504.000			1.12249			0.561247	−	0.827648i	$-0.310322\pi$
$449$	504.000			1.12249			0.561247	+	0.827648i	$0.310322\pi$
$450$		0			0
$451$	−63.0000	−	36.3731i	−0.139690	−	0.0806498i
$452$		0			0
$453$	349.500	−	201.784i	0.771523	−	0.445439i
$454$		0			0
$455$	−12.0000	−	83.1384i	−0.0263736	−	0.182722i
$456$		0			0
$457$	221.500	+	383.649i	0.484683	+	0.839495i	0.999845	−	0.0175975i	$-0.00560174\pi$
$457$	221.500	+	383.649i	0.484683	+	0.839495i	−0.515162	+	0.857093i	$0.672268\pi$
$458$		0			0
$459$	−45.0000	+	77.9423i	−0.0980392	+	0.169809i
$460$		0			0
$461$			180.133i			0.390745i	0.980729	+	0.195372i	$0.0625915\pi$
$461$			180.133i			0.390745i	−0.980729	+	0.195372i	$0.937408\pi$
$462$		0			0
$463$	−158.000			−0.341253			−0.170626	−	0.985336i	$-0.554579\pi$
$463$	−158.000			−0.341253			−0.170626	+	0.985336i	$0.554579\pi$
$464$		0			0
$465$	−31.5000	−	18.1865i	−0.0677419	−	0.0391108i
$466$		0			0
$467$	−18.0000	+	10.3923i	−0.0385439	+	0.0222533i	−0.519148	−	0.854684i	$-0.673751\pi$
$467$	−18.0000	+	10.3923i	−0.0385439	+	0.0222533i	0.480604	+	0.876938i	$0.340417\pi$
$468$		0			0
$469$	−374.000	+	294.449i	−0.797441	+	0.627822i
$470$		0			0
$471$	−126.000	−	218.238i	−0.267516	−	0.463351i
$472$		0			0
$473$	15.0000	−	25.9808i	0.0317125	−	0.0549276i
$474$		0			0
$475$		−	228.631i		−	0.481328i
$476$		0			0
$477$	−153.000			−0.320755
$478$		0			0
$479$	−357.000	−	206.114i	−0.745303	−	0.430301i	0.0786914	−	0.996899i	$-0.474926\pi$
$479$	−357.000	−	206.114i	−0.745303	−	0.430301i	−0.823994	+	0.566598i	$0.808259\pi$
$480$		0			0
$481$	132.000	−	76.2102i	0.274428	−	0.158441i
$482$		0			0
$483$	−162.000	+	405.300i	−0.335404	+	0.839130i
$484$		0			0
$485$	−127.500	−	220.836i	−0.262887	−	0.455333i
$486$		0			0
$487$	57.5000	−	99.5929i	0.118070	−	0.204503i	−0.800933	−	0.598754i	$-0.795663\pi$
$487$	57.5000	−	99.5929i	0.118070	−	0.204503i	0.919003	+	0.394251i	$0.128996\pi$
$488$		0			0
$489$			256.344i			0.524220i
$490$		0			0
$491$	−273.000			−0.556008			−0.278004	−	0.960580i	$-0.589673\pi$
$491$	−273.000			−0.556008			−0.278004	+	0.960580i	$0.589673\pi$
$492$		0			0
$493$	765.000	+	441.673i	1.55172	+	0.895888i
$494$		0			0
$495$	−13.5000	+	7.79423i	−0.0272727	+	0.0157459i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	233.000	+	403.568i	0.466934	+	0.808753i	0.999286	−	0.0377695i	$-0.0120253\pi$
$499$	233.000	+	403.568i	0.466934	+	0.808753i	−0.532353	+	0.846523i	$0.678692\pi$
$500$		0			0
$501$	−24.0000	+	41.5692i	−0.0479042	+	0.0829725i
$502$		0			0
$503$			723.997i			1.43936i	0.694307	+	0.719679i	$0.255711\pi$
$503$			723.997i			1.43936i	−0.694307	+	0.719679i	$0.744289\pi$
$504$		0			0
$505$	36.0000			0.0712871
$506$		0			0
$507$	−181.500	−	104.789i	−0.357988	−	0.206685i
$508$		0			0
$509$	−307.500	+	177.535i	−0.604126	+	0.348792i	−0.770663	−	0.637243i	$-0.780075\pi$
$509$	−307.500	+	177.535i	−0.604126	+	0.348792i	0.166537	+	0.986035i	$0.446741\pi$
$510$		0			0
$511$	90.0000	+	114.315i	0.176125	+	0.223709i
$512$		0			0
$513$	27.0000	+	46.7654i	0.0526316	+	0.0911606i
$514$		0			0
$515$	132.000	−	228.631i	0.256311	−	0.443943i
$516$		0			0
$517$		−	270.200i		−	0.522630i
$518$		0			0
$519$	324.000			0.624277
$520$		0			0
$521$	−795.000	−	458.993i	−1.52591	−	0.880986i	−0.999527	−	0.0307387i	$-0.990214\pi$
$521$	−795.000	−	458.993i	−1.52591	−	0.880986i	−0.526384	−	0.850247i	$-0.676453\pi$
$522$		0			0
$523$	−420.000	+	242.487i	−0.803059	+	0.463646i	−0.844540	−	0.535493i	$-0.820126\pi$
$523$	−420.000	+	242.487i	−0.803059	+	0.463646i	0.0414805	+	0.999139i	$0.486793\pi$
$524$		0			0
$525$	−264.000	+	38.1051i	−0.502857	+	0.0725812i
$526$		0			0
$527$	−105.000	−	181.865i	−0.199241	−	0.345096i
$528$		0			0
$529$	−383.500	+	664.241i	−0.724953	+	1.25565i
$530$		0			0
$531$		−	223.435i		−	0.420781i
$532$		0			0
$533$	−168.000			−0.315197
$534$		0			0
$535$	−49.5000	−	28.5788i	−0.0925234	−	0.0534184i
$536$		0			0
$537$	243.000	−	140.296i	0.452514	−	0.261259i
$538$		0			0
$539$	−141.000	+	41.5692i	−0.261596	+	0.0771229i
$540$		0			0
$541$	−31.0000	−	53.6936i	−0.0573013	−	0.0992488i	0.835952	−	0.548803i	$-0.184916\pi$
$541$	−31.0000	−	53.6936i	−0.0573013	−	0.0992488i	−0.893253	+	0.449554i	$0.851583\pi$
$542$		0			0
$543$	−225.000	+	389.711i	−0.414365	+	0.717701i
$544$		0			0
$545$		−	55.4256i		−	0.101698i
$546$		0			0
$547$	802.000			1.46618			0.733090	−	0.680132i	$-0.238078\pi$
$547$	802.000			1.46618			0.733090	+	0.680132i	$0.238078\pi$
$548$		0			0
$549$	180.000	+	103.923i	0.327869	+	0.189295i
$550$		0			0
$551$	459.000	−	265.004i	0.833031	−	0.480951i
$552$		0			0
$553$	−125.000	−	866.025i	−0.226040	−	1.56605i
$554$		0			0
$555$	33.0000	+	57.1577i	0.0594595	+	0.102987i
$556$		0			0
$557$	55.5000	−	96.1288i	0.0996409	−	0.172583i	−0.811895	−	0.583803i	$-0.801564\pi$
$557$	55.5000	−	96.1288i	0.0996409	−	0.172583i	0.911536	+	0.411220i	$0.134897\pi$
$558$		0			0
$559$		−	69.2820i		−	0.123939i
$560$		0			0
$561$	−90.0000			−0.160428
$562$		0			0
$563$	−166.500	−	96.1288i	−0.295737	−	0.170744i	0.344789	−	0.938680i	$-0.387950\pi$
$563$	−166.500	−	96.1288i	−0.295737	−	0.170744i	−0.640526	+	0.767936i	$0.721284\pi$
$564$		0			0
$565$	−279.000	+	161.081i	−0.493805	+	0.285099i
$566$		0			0
$567$	49.5000	−	38.9711i	0.0873016	−	0.0687322i
$568$		0			0
$569$	213.000	+	368.927i	0.374341	+	0.648378i	0.990228	−	0.139457i	$-0.0445356\pi$
$569$	213.000	+	368.927i	0.374341	+	0.648378i	−0.615887	+	0.787834i	$0.711202\pi$
$570$		0			0
$571$	−290.000	+	502.295i	−0.507881	+	0.879676i	0.492077	+	0.870551i	$0.336238\pi$
$571$	−290.000	+	502.295i	−0.507881	+	0.879676i	−0.999958	+	0.00912412i	$0.997096\pi$
$572$		0			0
$573$		−	166.277i		−	0.290187i
$574$		0			0
$575$	−792.000			−1.37739
$576$		0			0
$577$	−835.500	−	482.376i	−1.44801	−	0.836007i	−0.449644	−	0.893208i	$-0.648449\pi$
$577$	−835.500	−	482.376i	−1.44801	−	0.836007i	−0.998363	+	0.0572006i	$0.981783\pi$
$578$		0			0
$579$	442.500	−	255.477i	0.764249	−	0.441239i
$580$		0			0
$581$	−400.500	+	1001.99i	−0.689329	+	1.72460i
$582$		0			0
$583$	−76.5000	−	132.502i	−0.131218	−	0.227276i
$584$		0			0
$585$	−18.0000	+	31.1769i	−0.0307692	+	0.0532939i
$586$		0			0
$587$			1002.86i			1.70845i	0.519907	+	0.854223i	$0.325966\pi$
$587$			1002.86i			1.70845i	−0.519907	+	0.854223i	$0.674034\pi$
$588$		0			0
$589$	−126.000			−0.213922
$590$		0			0
$591$	495.000	+	285.788i	0.837563	+	0.483567i
$592$		0			0
$593$	−762.000	+	439.941i	−1.28499	+	0.741890i	−0.977756	−	0.209743i	$-0.932737\pi$
$593$	−762.000	+	439.941i	−1.28499	+	0.741890i	−0.307235	+	0.951634i	$0.599404\pi$
$594$		0			0
$595$	195.000	+	77.9423i	0.327731	+	0.130995i
$596$		0			0
$597$	−102.000	−	176.669i	−0.170854	−	0.295928i
$598$		0			0
$599$	−78.0000	+	135.100i	−0.130217	+	0.225543i	−0.923760	−	0.382972i	$-0.874901\pi$
$599$	−78.0000	+	135.100i	−0.130217	+	0.225543i	0.793543	+	0.608514i	$0.208234\pi$
$600$		0			0
$601$			1124.10i			1.87038i	0.354141	+	0.935192i	$0.384773\pi$
$601$			1124.10i			1.87038i	−0.354141	+	0.935192i	$0.615227\pi$
$602$		0			0
$603$	204.000			0.338308
$604$		0			0
$605$	168.000	+	96.9948i	0.277686	+	0.160322i
$606$		0			0
$607$	346.500	−	200.052i	0.570840	−	0.329575i	−0.186645	−	0.982427i	$-0.559761\pi$
$607$	346.500	−	200.052i	0.570840	−	0.329575i	0.757485	+	0.652853i	$0.226428\pi$
$608$		0			0
$609$	−382.500	−	485.840i	−0.628079	−	0.797767i
$610$		0			0
$611$	−312.000	−	540.400i	−0.510638	−	0.884451i
$612$		0			0
$613$	428.000	−	741.318i	0.698206	−	1.20933i	−0.270883	−	0.962612i	$-0.587315\pi$
$613$	428.000	−	741.318i	0.698206	−	1.20933i	0.969088	−	0.246715i	$-0.0793512\pi$
$614$		0			0
$615$		−	72.7461i		−	0.118286i
$616$		0			0
$617$	444.000			0.719611			0.359806	−	0.933027i	$-0.382843\pi$
$617$	444.000			0.719611			0.359806	+	0.933027i	$0.382843\pi$
$618$		0			0
$619$	222.000	+	128.172i	0.358643	+	0.207063i	0.668485	−	0.743725i	$-0.266943\pi$
$619$	222.000	+	128.172i	0.358643	+	0.207063i	−0.309842	+	0.950788i	$0.600276\pi$
$620$		0			0
$621$	162.000	−	93.5307i	0.260870	−	0.150613i
$622$		0			0
$623$	−504.000	+	72.7461i	−0.808989	+	0.116767i
$624$		0			0
$625$	−204.500	−	354.204i	−0.327200	−	0.566727i
$626$		0			0
$627$	−27.0000	+	46.7654i	−0.0430622	+	0.0745859i
$628$		0			0
$629$			381.051i			0.605805i
$630$		0			0
$631$	85.0000			0.134707			0.0673534	−	0.997729i	$-0.478545\pi$
$631$	85.0000			0.134707			0.0673534	+	0.997729i	$0.478545\pi$
$632$		0			0
$633$	330.000	+	190.526i	0.521327	+	0.300988i
$634$		0			0
$635$	−196.500	+	113.449i	−0.309449	+	0.178660i
$636$		0			0
$637$	−234.000	+	245.951i	−0.367347	+	0.386109i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	66.0000	−	114.315i	0.102964	−	0.178339i	−0.809940	−	0.586512i	$-0.800501\pi$
$641$	66.0000	−	114.315i	0.102964	−	0.178339i	0.912905	+	0.408173i	$0.133834\pi$
$642$		0			0
$643$			713.605i			1.10981i	0.831915	+	0.554903i	$0.187245\pi$
$643$			713.605i			1.10981i	−0.831915	+	0.554903i	$0.812755\pi$
$644$		0			0
$645$	30.0000			0.0465116
$646$		0			0
$647$	−864.000	−	498.831i	−1.33539	−	0.770990i	−0.349274	−	0.937021i	$-0.613572\pi$
$647$	−864.000	−	498.831i	−1.33539	−	0.770990i	−0.986121	+	0.166031i	$0.946905\pi$
$648$		0			0
$649$	193.500	−	111.717i	0.298151	−	0.172138i
$650$		0			0
$651$	21.0000	+	145.492i	0.0322581	+	0.223490i
$652$		0			0
$653$	187.500	+	324.760i	0.287136	+	0.497335i	0.973125	−	0.230278i	$-0.0739634\pi$
$653$	187.500	+	324.760i	0.287136	+	0.497335i	−0.685989	+	0.727612i	$0.740630\pi$
$654$		0			0
$655$	−85.5000	+	148.090i	−0.130534	+	0.226092i
$656$		0			0
$657$		−	62.3538i		−	0.0949069i
$658$		0			0
$659$	−1038.00			−1.57511			−0.787557	−	0.616242i	$-0.788654\pi$
$659$	−1038.00			−1.57511			−0.787557	+	0.616242i	$0.788654\pi$
$660$		0			0
$661$	387.000	+	223.435i	0.585477	+	0.338025i	0.763307	−	0.646036i	$-0.223574\pi$
$661$	387.000	+	223.435i	0.585477	+	0.338025i	−0.177830	+	0.984061i	$0.556908\pi$
$662$		0			0
$663$	−180.000	+	103.923i	−0.271493	+	0.156747i
$664$		0			0
$665$	99.0000	−	77.9423i	0.148872	−	0.117206i
$666$		0			0
$667$	−918.000	−	1590.02i	−1.37631	−	2.38384i
$668$		0			0
$669$	130.500	−	226.033i	0.195067	−	0.337866i
$670$		0			0
$671$			207.846i			0.309756i
$672$		0			0
$673$	1093.00			1.62407			0.812036	−	0.583608i	$-0.198359\pi$
$673$	1093.00			1.62407			0.812036	+	0.583608i	$0.198359\pi$
$674$		0			0
$675$	99.0000	+	57.1577i	0.146667	+	0.0846780i
$676$		0			0
$677$	−1048.50	+	605.352i	−1.54874	+	0.894168i	−0.550506	+	0.834831i	$0.685565\pi$
$677$	−1048.50	+	605.352i	−1.54874	+	0.894168i	−0.998238	+	0.0593371i	$0.981101\pi$
$678$		0			0
$679$	−382.500	+	956.958i	−0.563328	+	1.40936i
$680$		0			0
$681$	94.5000	+	163.679i	0.138767	+	0.240351i
$682$		0			0
$683$	−1.50000	+	2.59808i	−0.00219619	+	0.00380392i	−0.867121	−	0.498097i	$-0.834032\pi$
$683$	−1.50000	+	2.59808i	−0.00219619	+	0.00380392i	0.864925	+	0.501901i	$0.167366\pi$
$684$		0			0
$685$		−	249.415i		−	0.364110i
$686$		0			0
$687$	654.000			0.951965
$688$		0			0
$689$	−306.000	−	176.669i	−0.444122	−	0.256414i
$690$		0			0
$691$	987.000	−	569.845i	1.42836	−	0.824667i	0.431373	−	0.902174i	$-0.358029\pi$
$691$	987.000	−	569.845i	1.42836	−	0.824667i	0.996992	+	0.0775070i	$0.0246960\pi$
$692$		0			0
$693$	58.5000	+	23.3827i	0.0844156	+	0.0337412i
$694$		0			0
$695$	−129.000	−	223.435i	−0.185612	−	0.321489i
$696$		0			0
$697$	210.000	−	363.731i	0.301291	−	0.521852i
$698$		0			0
$699$		−	363.731i		−	0.520359i
$700$		0			0
$701$	447.000			0.637660			0.318830	−	0.947812i	$-0.396710\pi$
$701$	447.000			0.637660			0.318830	+	0.947812i	$0.396710\pi$
$702$		0			0
$703$	198.000	+	114.315i	0.281650	+	0.162611i
$704$		0			0
$705$	234.000	−	135.100i	0.331915	−	0.191631i
$706$		0			0
$707$	−90.0000	−	114.315i	−0.127298	−	0.161691i
$708$		0			0
$709$	211.000	+	365.463i	0.297602	+	0.515462i	0.975587	−	0.219614i	$-0.0704797\pi$
$709$	211.000	+	365.463i	0.297602	+	0.515462i	−0.677985	+	0.735076i	$0.737146\pi$
$710$		0			0
$711$	−187.500	+	324.760i	−0.263713	+	0.456764i
$712$		0			0
$713$			436.477i			0.612169i
$714$		0			0
$715$	−36.0000			−0.0503497
$716$		0			0
$717$	180.000	+	103.923i	0.251046	+	0.144941i
$718$		0			0
$719$	−147.000	+	84.8705i	−0.204451	+	0.118040i	−0.598730	−	0.800951i	$-0.704328\pi$
$719$	−147.000	+	84.8705i	−0.204451	+	0.118040i	0.394279	+	0.918991i	$0.370994\pi$
$720$		0			0
$721$	−1056.00	+	152.420i	−1.46463	+	0.211401i
$722$		0			0
$723$	10.5000	+	18.1865i	0.0145228	+	0.0251543i
$724$		0			0
$725$	561.000	−	971.681i	0.773793	−	1.34025i
$726$		0			0
$727$		−	50.2295i		−	0.0690914i	−0.999403	−	0.0345457i	$-0.989002\pi$
$727$		−	50.2295i		−	0.0690914i	0.999403	−	0.0345457i	$-0.0109984\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	150.000	+	86.6025i	0.205198	+	0.118471i
$732$		0			0
$733$	255.000	−	147.224i	0.347885	−	0.200852i	−0.315868	−	0.948803i	$-0.602296\pi$
$733$	255.000	−	147.224i	0.347885	−	0.200852i	0.663754	+	0.747951i	$0.268962\pi$
$734$		0			0
$735$	−106.500	−	101.325i	−0.144898	−	0.137857i
$736$		0			0
$737$	102.000	+	176.669i	0.138399	+	0.239714i
$738$		0			0
$739$	49.0000	−	84.8705i	0.0663058	−	0.114845i	−0.830967	−	0.556322i	$-0.812212\pi$
$739$	49.0000	−	84.8705i	0.0663058	−	0.114845i	0.897272	+	0.441477i	$0.145545\pi$
$740$		0			0
$741$			124.708i			0.168296i
$742$		0			0
$743$	180.000			0.242261			0.121131	−	0.992637i	$-0.461348\pi$
$743$	180.000			0.242261			0.121131	+	0.992637i	$0.461348\pi$
$744$		0			0
$745$	225.000	+	129.904i	0.302013	+	0.174368i
$746$		0			0
$747$	400.500	−	231.229i	0.536145	−	0.309543i
$748$		0			0
$749$	33.0000	+	228.631i	0.0440587	+	0.305248i
$750$		0			0
$751$	360.500	+	624.404i	0.480027	+	0.831431i	0.999737	−	0.0229117i	$-0.00729366\pi$
$751$	360.500	+	624.404i	0.480027	+	0.831431i	−0.519711	+	0.854342i	$0.673960\pi$
$752$		0			0
$753$	−118.500	+	205.248i	−0.157371	+	0.272574i
$754$		0			0
$755$			403.568i			0.534527i
$756$		0			0
$757$	−644.000			−0.850727			−0.425363	−	0.905023i	$-0.639854\pi$
$757$	−644.000			−0.850727			−0.425363	+	0.905023i	$0.639854\pi$
$758$		0			0
$759$	162.000	+	93.5307i	0.213439	+	0.123229i
$760$		0			0
$761$	−492.000	+	284.056i	−0.646518	+	0.373267i	−0.787121	−	0.616799i	$-0.788429\pi$
$761$	−492.000	+	284.056i	−0.646518	+	0.373267i	0.140603	+	0.990066i	$0.455096\pi$
$762$		0			0
$763$	−176.000	+	138.564i	−0.230668	+	0.181604i
$764$		0			0
$765$	−45.0000	−	77.9423i	−0.0588235	−	0.101885i
$766$		0			0
$767$	258.000	−	446.869i	0.336375	−	0.582619i
$768$		0			0
$769$		−	275.396i		−	0.358122i	−0.983838	−	0.179061i	$-0.942694\pi$
$769$		−	275.396i		−	0.358122i	0.983838	−	0.179061i	$-0.0573060\pi$
$770$		0			0
$771$	−234.000			−0.303502
$772$		0			0
$773$	−870.000	−	502.295i	−1.12549	−	0.649799i	−0.182690	−	0.983171i	$-0.558480\pi$
$773$	−870.000	−	502.295i	−1.12549	−	0.649799i	−0.942796	+	0.333372i	$0.891814\pi$
$774$		0			0
$775$	−231.000	+	133.368i	−0.298065	+	0.172088i
$776$		0			0
$777$	99.0000	−	247.683i	0.127413	−	0.318769i
$778$		0			0
$779$	−126.000	−	218.238i	−0.161746	−	0.280152i
$780$		0			0
$781$		0			0
$782$		0			0
$783$			265.004i			0.338447i
$784$		0			0
$785$	252.000			0.321019
$786$		0			0
$787$	−690.000	−	398.372i	−0.876747	−	0.506190i	−0.00716264	−	0.999974i	$-0.502280\pi$
$787$	−690.000	−	398.372i	−0.876747	−	0.506190i	−0.869585	+	0.493784i	$0.835613\pi$
$788$		0			0
$789$	−243.000	+	140.296i	−0.307985	+	0.177815i
$790$		0			0
$791$	1209.00	+	483.242i	1.52845	+	0.610926i
$792$		0			0
$793$	240.000	+	415.692i	0.302648	+	0.524202i
$794$		0			0
$795$	76.5000	−	132.502i	0.0962264	−	0.166669i
$796$		0			0
$797$		−	545.596i		−	0.684562i	−0.939598	−	0.342281i	$-0.888801\pi$
$797$		−	545.596i		−	0.684562i	0.939598	−	0.342281i	$-0.111199\pi$
$798$		0			0
$799$	1560.00			1.95244
$800$		0			0
$801$	189.000	+	109.119i	0.235955	+	0.136229i
$802$		0			0
$803$	54.0000	−	31.1769i	0.0672478	−	0.0388255i
$804$		0			0
$805$	−270.000	−	342.946i	−0.335404	−	0.426020i
$806$		0			0
$807$	−334.500	−	579.371i	−0.414498	−	0.717932i
$808$		0			0
$809$	−24.0000	+	41.5692i	−0.0296663	+	0.0513835i	−0.880477	−	0.474088i	$-0.842778\pi$
$809$	−24.0000	+	41.5692i	−0.0296663	+	0.0513835i	0.850811	+	0.525472i	$0.176111\pi$
$810$		0			0
$811$		−	436.477i		−	0.538196i	−0.963113	−	0.269098i	$-0.913274\pi$
$811$		−	436.477i		−	0.538196i	0.963113	−	0.269098i	$-0.0867255\pi$
$812$		0			0
$813$	375.000			0.461255
$814$		0			0
$815$	−222.000	−	128.172i	−0.272393	−	0.157266i
$816$		0			0
$817$	90.0000	−	51.9615i	0.110159	−	0.0636004i
$818$		0			0
$819$	144.000	−	20.7846i	0.175824	−	0.0253780i
$820$		0			0
$821$	−595.500	−	1031.44i	−0.725335	−	1.25632i	−0.958836	−	0.283960i	$-0.908352\pi$
$821$	−595.500	−	1031.44i	−0.725335	−	1.25632i	0.233501	−	0.972357i	$-0.424982\pi$
$822$		0			0
$823$	−125.000	+	216.506i	−0.151883	+	0.263070i	−0.931920	−	0.362664i	$-0.881867\pi$
$823$	−125.000	+	216.506i	−0.151883	+	0.263070i	0.780036	+	0.625734i	$0.215200\pi$
$824$		0			0
$825$			114.315i			0.138564i
$826$		0			0
$827$	1137.00			1.37485			0.687424	−	0.726256i	$-0.258741\pi$
$827$	1137.00			1.37485			0.687424	+	0.726256i	$0.258741\pi$
$828$		0			0
$829$	63.0000	+	36.3731i	0.0759952	+	0.0438758i	0.537516	−	0.843253i	$-0.319363\pi$
$829$	63.0000	+	36.3731i	0.0759952	+	0.0438758i	−0.461521	+	0.887129i	$0.652696\pi$
$830$		0			0
$831$	−150.000	+	86.6025i	−0.180505	+	0.104215i
$832$		0			0
$833$	−240.000	−	814.064i	−0.288115	−	0.977268i
$834$		0			0
$835$	−24.0000	−	41.5692i	−0.0287425	−	0.0497835i
$836$		0			0
$837$	31.5000	−	54.5596i	0.0376344	−	0.0651847i
$838$		0			0
$839$			1416.82i			1.68870i	0.535794	+	0.844349i	$0.320012\pi$
$839$			1416.82i			1.68870i	−0.535794	+	0.844349i	$0.679988\pi$
$840$		0			0
$841$	1760.00			2.09275
$842$		0			0
$843$	−342.000	−	197.454i	−0.405694	−	0.234228i
$844$		0			0
$845$	181.500	−	104.789i	0.214793	−	0.124011i
$846$		0			0
$847$	−112.000	−	775.959i	−0.132231	−	0.916126i
$848$		0			0
$849$	15.0000	+	25.9808i	0.0176678	+	0.0306016i
$850$		0			0
$851$	396.000	−	685.892i	0.465335	−	0.805984i
$852$		0			0
$853$			872.954i			1.02339i	0.859166	+	0.511696i	$0.170983\pi$
$853$			872.954i			1.02339i	−0.859166	+	0.511696i	$0.829017\pi$
$854$		0			0
$855$	−54.0000			−0.0631579
$856$		0			0
$857$	−600.000	−	346.410i	−0.700117	−	0.404213i	0.107274	−	0.994229i	$-0.465788\pi$
$857$	−600.000	−	346.410i	−0.700117	−	0.404213i	−0.807391	+	0.590017i	$0.799121\pi$
$858$		0			0
$859$	771.000	−	445.137i	0.897555	−	0.518204i	0.0211491	−	0.999776i	$-0.493268\pi$
$859$	771.000	−	445.137i	0.897555	−	0.518204i	0.876406	+	0.481573i	$0.159934\pi$
$860$		0			0
$861$	−231.000	+	181.865i	−0.268293	+	0.211226i
$862$		0			0
$863$	315.000	+	545.596i	0.365006	+	0.632209i	0.988777	−	0.149398i	$-0.0477337\pi$
$863$	315.000	+	545.596i	0.365006	+	0.632209i	−0.623771	+	0.781607i	$0.714400\pi$
$864$		0			0
$865$	−162.000	+	280.592i	−0.187283	+	0.324384i
$866$		0			0
$867$		−	19.0526i		−	0.0219753i
$868$		0			0
$869$	−375.000			−0.431530
$870$		0			0
$871$	408.000	+	235.559i	0.468427	+	0.270447i
$872$		0			0
$873$	382.500	−	220.836i	0.438144	−	0.252963i
$874$		0			0
$875$	211.500	−	529.142i	0.241714	−	0.604733i
$876$		0			0
$877$	−820.000	−	1420.28i	−0.935006	−	1.61948i	−0.774624	−	0.632422i	$-0.782061\pi$
$877$	−820.000	−	1420.28i	−0.935006	−	1.61948i	−0.160382	−	0.987055i	$-0.551273\pi$
$878$		0			0
$879$	241.500	−	418.290i	0.274744	−	0.475871i
$880$		0			0
$881$			1267.86i			1.43912i	0.694432	+	0.719558i	$0.255656\pi$
$881$			1267.86i			1.43912i	−0.694432	+	0.719558i	$0.744344\pi$
$882$		0			0
$883$	−226.000			−0.255946			−0.127973	−	0.991778i	$-0.540847\pi$
$883$	−226.000			−0.255946			−0.127973	+	0.991778i	$0.540847\pi$
$884$		0			0
$885$	193.500	+	111.717i	0.218644	+	0.126234i
$886$		0			0
$887$	−6.00000	+	3.46410i	−0.00676437	+	0.00390541i	−0.503378	−	0.864066i	$-0.667910\pi$
$887$	−6.00000	+	3.46410i	−0.00676437	+	0.00390541i	0.496614	+	0.867972i	$0.334576\pi$
$888$		0			0
$889$	851.500	+	340.348i	0.957818	+	0.382844i
$890$		0			0
$891$	−13.5000	−	23.3827i	−0.0151515	−	0.0262432i
$892$		0			0
$893$	468.000	−	810.600i	0.524076	−	0.907727i
$894$		0			0
$895$			280.592i			0.313511i
$896$		0			0
$897$	432.000			0.481605
$898$		0			0
$899$	−535.500	−	309.171i	−0.595662	−	0.343906i
$900$		0			0
$901$	765.000	−	441.673i	0.849057	−	0.490203i
$902$		0			0
$903$	−75.0000	−	95.2628i	−0.0830565	−	0.105496i
$904$		0			0
$905$	−225.000	−	389.711i	−0.248619	−	0.430620i
$906$		0			0
$907$	572.000	−	990.733i	0.630650	−	1.09232i	−0.356768	−	0.934193i	$-0.616121\pi$
$907$	572.000	−	990.733i	0.630650	−	1.09232i	0.987419	−	0.158126i	$-0.0505452\pi$
$908$		0			0
$909$			62.3538i			0.0685961i
$910$		0			0
$911$	480.000			0.526894			0.263447	−	0.964674i	$-0.415141\pi$
$911$	480.000			0.526894			0.263447	+	0.964674i	$0.415141\pi$
$912$		0			0
$913$	400.500	+	231.229i	0.438664	+	0.253263i
$914$		0			0
$915$	−180.000	+	103.923i	−0.196721	+	0.113577i
$916$		0			0
$917$	684.000	−	98.7269i	0.745911	−	0.107663i
$918$		0			0
$919$	−871.000	−	1508.62i	−0.947769	−	1.64158i	−0.750109	−	0.661314i	$-0.769999\pi$
$919$	−871.000	−	1508.62i	−0.947769	−	1.64158i	−0.197660	−	0.980271i	$-0.563334\pi$
$920$		0			0
$921$	−24.0000	+	41.5692i	−0.0260586	+	0.0451349i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	484.000			0.523243
$926$		0			0
$927$	396.000	+	228.631i	0.427184	+	0.246635i
$928$		0			0
$929$	1005.00	−	580.237i	1.08181	−	0.624582i	0.150425	−	0.988621i	$-0.451936\pi$
$929$	1005.00	−	580.237i	1.08181	−	0.624582i	0.931384	+	0.364039i	$0.118603\pi$
$930$		0			0
$931$	−495.000	−	119.512i	−0.531686	−	0.128369i
$932$		0			0
$933$	57.0000	+	98.7269i	0.0610932	+	0.105817i
$934$		0			0
$935$	45.0000	−	77.9423i	0.0481283	−	0.0833607i
$936$		0			0
$937$		−	1331.95i		−	1.42150i	−0.703444	−	0.710751i	$-0.748355\pi$
$937$		−	1331.95i		−	1.42150i	0.703444	−	0.710751i	$-0.251645\pi$
$938$		0			0
$939$	−207.000			−0.220447
$940$		0			0
$941$	703.500	+	406.166i	0.747609	+	0.431632i	0.824829	−	0.565382i	$-0.191271\pi$
$941$	703.500	+	406.166i	0.747609	+	0.431632i	−0.0772204	+	0.997014i	$0.524605\pi$
$942$		0			0
$943$	−756.000	+	436.477i	−0.801697	+	0.462860i
$944$		0			0
$945$	9.00000	+	62.3538i	0.00952381	+	0.0659829i
$946$		0			0
$947$	−645.000	−	1117.17i	−0.681098	−	1.17970i	−0.974646	−	0.223752i	$-0.928169\pi$
$947$	−645.000	−	1117.17i	−0.681098	−	1.17970i	0.293548	−	0.955944i	$-0.405164\pi$
$948$		0			0
$949$	72.0000	−	124.708i	0.0758693	−	0.131410i
$950$		0			0
$951$		−	348.142i		−	0.366080i
$952$		0			0
$953$	174.000			0.182581			0.0912907	−	0.995824i	$-0.470901\pi$
$953$	174.000			0.182581			0.0912907	+	0.995824i	$0.470901\pi$
$954$		0			0
$955$	144.000	+	83.1384i	0.150785	+	0.0870560i
$956$		0			0
$957$	−229.500	+	132.502i	−0.239812	+	0.138455i
$958$		0			0
$959$	−792.000	+	623.538i	−0.825860	+	0.650196i
$960$		0			0
$961$	−407.000	−	704.945i	−0.423517	−	0.733553i
$962$		0			0
$963$	49.5000	−	85.7365i	0.0514019	−	0.0890306i
$964$		0			0
$965$			510.955i			0.529487i
$966$		0			0
$967$	−41.0000			−0.0423992			−0.0211996	−	0.999775i	$-0.506749\pi$
$967$	−41.0000			−0.0423992			−0.0211996	+	0.999775i	$0.506749\pi$
$968$		0			0
$969$	−270.000	−	155.885i	−0.278638	−	0.160872i
$970$		0			0
$971$	−853.500	+	492.768i	−0.878991	+	0.507486i	−0.870326	−	0.492477i	$-0.836092\pi$
$971$	−853.500	+	492.768i	−0.878991	+	0.507486i	−0.00866523	+	0.999962i	$0.502758\pi$
$972$		0			0
$973$	−387.000	+	968.216i	−0.397739	+	0.995084i
$974$		0			0
$975$	132.000	+	228.631i	0.135385	+	0.234493i
$976$		0			0
$977$	−639.000	+	1106.78i	−0.654043	+	1.13284i	0.328090	+	0.944647i	$0.393595\pi$
$977$	−639.000	+	1106.78i	−0.654043	+	1.13284i	−0.982133	+	0.188189i	$0.939738\pi$
$978$		0			0
$979$			218.238i			0.222920i
$980$		0			0
$981$	96.0000			0.0978593
$982$		0			0
$983$	201.000	+	116.047i	0.204476	+	0.118054i	0.598742	−	0.800942i	$-0.295668\pi$
$983$	201.000	+	116.047i	0.204476	+	0.118054i	−0.394266	+	0.918997i	$0.629001\pi$
$984$		0			0
$985$	−495.000	+	285.788i	−0.502538	+	0.290140i
$986$		0			0
$987$	−1014.00	−	405.300i	−1.02736	−	0.410638i
$988$		0			0
$989$	−180.000	−	311.769i	−0.182002	−	0.315237i
$990$		0			0
$991$	−416.500	+	721.399i	−0.420283	+	0.727951i	−0.995967	−	0.0897213i	$-0.971402\pi$
$991$	−416.500	+	721.399i	−0.420283	+	0.727951i	0.575684	+	0.817672i	$0.304736\pi$
$992$		0			0
$993$		−	775.959i		−	0.781429i
$994$		0			0
$995$	204.000			0.205025
$996$		0			0
$997$	1014.00	+	585.433i	1.01705	+	0.587195i	0.913248	−	0.407403i	$-0.133566\pi$
$997$	1014.00	+	585.433i	1.01705	+	0.587195i	0.103803	+	0.994598i	$0.466899\pi$
$998$		0			0
$999$	−99.0000	+	57.1577i	−0.0990991	+	0.0572149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.b.241.1		2
3.2	odd	2		1008.3.cg.b.577.1		2
4.3	odd	2		84.3.m.a.73.1	yes	2
7.3	odd	6		2352.3.f.c.97.1		2
7.4	even	3		2352.3.f.c.97.2		2
7.5	odd	6	inner	336.3.bh.b.145.1		2
12.11	even	2		252.3.z.b.73.1		2
20.3	even	4		2100.3.be.c.1249.1		4
20.7	even	4		2100.3.be.c.1249.2		4
20.19	odd	2		2100.3.bd.b.1501.1		2
21.5	even	6		1008.3.cg.b.145.1		2
28.3	even	6		588.3.d.a.97.2		2
28.11	odd	6		588.3.d.a.97.1		2
28.19	even	6		84.3.m.a.61.1	✓	2
28.23	odd	6		588.3.m.a.313.1		2
28.27	even	2		588.3.m.a.325.1		2
84.11	even	6		1764.3.d.c.685.1		2
84.23	even	6		1764.3.z.e.901.1		2
84.47	odd	6		252.3.z.b.145.1		2
84.59	odd	6		1764.3.d.c.685.2		2
84.83	odd	2		1764.3.z.e.325.1		2
140.19	even	6		2100.3.bd.b.901.1		2
140.47	odd	12		2100.3.be.c.649.1		4
140.103	odd	12		2100.3.be.c.649.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.m.a.61.1	✓	2	28.19	even	6
84.3.m.a.73.1	yes	2	4.3	odd	2
252.3.z.b.73.1		2	12.11	even	2
252.3.z.b.145.1		2	84.47	odd	6
336.3.bh.b.145.1		2	7.5	odd	6	inner
336.3.bh.b.241.1		2	1.1	even	1	trivial
588.3.d.a.97.1		2	28.11	odd	6
588.3.d.a.97.2		2	28.3	even	6
588.3.m.a.313.1		2	28.23	odd	6
588.3.m.a.325.1		2	28.27	even	2
1008.3.cg.b.145.1		2	21.5	even	6
1008.3.cg.b.577.1		2	3.2	odd	2
1764.3.d.c.685.1		2	84.11	even	6
1764.3.d.c.685.2		2	84.59	odd	6
1764.3.z.e.325.1		2	84.83	odd	2
1764.3.z.e.901.1		2	84.23	even	6
2100.3.bd.b.901.1		2	140.19	even	6
2100.3.bd.b.1501.1		2	20.19	odd	2
2100.3.be.c.649.1		4	140.47	odd	12
2100.3.be.c.649.2		4	140.103	odd	12
2100.3.be.c.1249.1		4	20.3	even	4
2100.3.be.c.1249.2		4	20.7	even	4
2352.3.f.c.97.1		2	7.3	odd	6
2352.3.f.c.97.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +6.92820i q^{13} -3.00000 q^{15} +(-15.0000 - 8.66025i) q^{17} +(-9.00000 + 5.19615i) q^{19} +(7.50000 + 9.52628i) q^{21} +(18.0000 + 31.1769i) q^{23} +(-11.0000 + 19.0526i) q^{25} -5.19615i q^{27} -51.0000 q^{29} +(10.5000 + 6.06218i) q^{31} +(4.50000 - 2.59808i) q^{33} +(-12.0000 + 1.73205i) q^{35} +(-11.0000 - 19.0526i) q^{37} +(6.00000 - 10.3923i) q^{39} +24.2487i q^{41} -10.0000 q^{43} +(4.50000 + 2.59808i) q^{45} +(-78.0000 + 45.0333i) q^{47} +(35.5000 + 33.7750i) q^{49} +(15.0000 + 25.9808i) q^{51} +(-25.5000 + 44.1673i) q^{53} +5.19615i q^{55} +18.0000 q^{57} +(-64.5000 - 37.2391i) q^{59} +(60.0000 - 34.6410i) q^{61} +(-3.00000 - 20.7846i) q^{63} +(6.00000 + 10.3923i) q^{65} +(34.0000 - 58.8897i) q^{67} -62.3538i q^{69} +(-18.0000 - 10.3923i) q^{73} +(33.0000 - 19.0526i) q^{75} +(16.5000 - 12.9904i) q^{77} +(62.5000 + 108.253i) q^{79} +(-4.50000 + 7.79423i) q^{81} -154.153i q^{83} -30.0000 q^{85} +(76.5000 + 44.1673i) q^{87} +(63.0000 - 36.3731i) q^{89} +(18.0000 - 45.0333i) q^{91} +(-10.5000 - 18.1865i) q^{93} +(-9.00000 + 15.5885i) q^{95} -147.224i q^{97} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 3 q^{5} - 13 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 3 * q^5 - 13 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} + 3 q^{5} - 13 q^{7} + 3 q^{9} - 3 q^{11} - 6 q^{15} - 30 q^{17} - 18 q^{19} + 15 q^{21} + 36 q^{23} - 22 q^{25} - 102 q^{29} + 21 q^{31} + 9 q^{33} - 24 q^{35} - 22 q^{37} + 12 q^{39} - 20 q^{43} + 9 q^{45} - 156 q^{47} + 71 q^{49} + 30 q^{51} - 51 q^{53} + 36 q^{57} - 129 q^{59} + 120 q^{61} - 6 q^{63} + 12 q^{65} + 68 q^{67} - 36 q^{73} + 66 q^{75} + 33 q^{77} + 125 q^{79} - 9 q^{81} - 60 q^{85} + 153 q^{87} + 126 q^{89} + 36 q^{91} - 21 q^{93} - 18 q^{95} - 18 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 3 * q^5 - 13 * q^7 + 3 * q^9 - 3 * q^11 - 6 * q^15 - 30 * q^17 - 18 * q^19 + 15 * q^21 + 36 * q^23 - 22 * q^25 - 102 * q^29 + 21 * q^31 + 9 * q^33 - 24 * q^35 - 22 * q^37 + 12 * q^39 - 20 * q^43 + 9 * q^45 - 156 * q^47 + 71 * q^49 + 30 * q^51 - 51 * q^53 + 36 * q^57 - 129 * q^59 + 120 * q^61 - 6 * q^63 + 12 * q^65 + 68 * q^67 - 36 * q^73 + 66 * q^75 + 33 * q^77 + 125 * q^79 - 9 * q^81 - 60 * q^85 + 153 * q^87 + 126 * q^89 + 36 * q^91 - 21 * q^93 - 18 * q^95 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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