LMFDB - Embedded newform 1350.3.k.a.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,3,Mod(449,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1350.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1350.k (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:	$36.7848356886$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.449
Dual form			1350.3.k.a.899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-5.49794 + 3.17423i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-5.49794 + 3.17423i) q^{7} +2.82843 q^{8} +(-8.17423 + 4.71940i) q^{11} +(-17.0580 - 9.84847i) q^{13} +(7.77526 + 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702 q^{17} -4.69694 q^{19} +(11.5601 + 6.67423i) q^{22} +(4.71940 - 8.17423i) q^{23} +27.8557i q^{26} -12.6969i q^{28} +(-2.84847 + 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(1.34847 + 2.33562i) q^{34} -17.3031i q^{37} +(3.32124 + 5.75255i) q^{38} +(53.5454 + 30.9145i) q^{41} +(0.826701 - 0.477296i) q^{43} -18.8776i q^{44} -13.3485 q^{46} +(-7.05501 - 12.2196i) q^{47} +(-4.34847 + 7.53177i) q^{49} +(34.1161 - 19.6969i) q^{52} +9.53512 q^{53} +(-15.5505 + 8.97809i) q^{56} +(4.02834 + 2.32577i) q^{58} +(79.2650 + 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470 q^{62} +8.00000 q^{64} +(26.8075 + 15.4773i) q^{67} +(1.90702 - 3.30306i) q^{68} +85.9026i q^{71} -96.0908i q^{73} +(-21.1918 + 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(29.9609 - 51.8939i) q^{77} +(14.8712 + 25.7576i) q^{79} -87.4393i q^{82} +(43.9530 + 76.1288i) q^{83} +(-1.16913 - 0.674999i) q^{86} +(-23.1202 + 13.3485i) q^{88} +41.3766i q^{89} +125.045 q^{91} +(9.43879 + 16.3485i) q^{92} +(-9.97730 + 17.2812i) q^{94} +(-83.0333 + 47.9393i) q^{97} +12.2993 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} - 36 q^{11} + 72 q^{14} - 16 q^{16} + 80 q^{19} + 36 q^{29} + 76 q^{31} - 48 q^{34} + 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{56} + 252 q^{59} + 124 q^{61} + 64 q^{64} + 144 q^{74} - 80 q^{76} - 28 q^{79} + 216 q^{86} + 824 q^{91} - 168 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 - 36 * q^11 + 72 * q^14 - 16 * q^16 + 80 * q^19 + 36 * q^29 + 76 * q^31 - 48 * q^34 + 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^56 + 252 * q^59 + 124 * q^61 + 64 * q^64 + 144 * q^74 - 80 * q^76 - 28 * q^79 + 216 * q^86 + 824 * q^91 - 168 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−5.49794	+	3.17423i	−0.785419	+	0.453462i	−0.838347	−	0.545136i	$-0.816478\pi$
$7$	−5.49794	+	3.17423i	−0.785419	+	0.453462i	0.0529281	+	0.998598i	$0.483145\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$		0			0
$11$	−8.17423	+	4.71940i	−0.743112	+	0.429036i	−0.823200	−	0.567752i	$-0.807813\pi$
$11$	−8.17423	+	4.71940i	−0.743112	+	0.429036i	0.0800876	+	0.996788i	$0.474480\pi$
$12$		0			0
$13$	−17.0580	−	9.84847i	−1.31216	−	0.757575i	−0.329704	−	0.944084i	$-0.606949\pi$
$13$	−17.0580	−	9.84847i	−1.31216	−	0.757575i	−0.982453	+	0.186510i	$0.940282\pi$
$14$	7.77526	+	4.48905i	0.555375	+	0.320646i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−1.90702			−0.112178			−0.0560889	−	0.998426i	$-0.517863\pi$
$17$	−1.90702			−0.112178			−0.0560889	+	0.998426i	$0.517863\pi$
$18$		0			0
$19$	−4.69694			−0.247207			−0.123604	−	0.992332i	$-0.539445\pi$
$19$	−4.69694			−0.247207			−0.123604	+	0.992332i	$0.539445\pi$
$20$		0			0
$21$		0			0
$22$	11.5601	+	6.67423i	0.525460	+	0.303374i
$23$	4.71940	−	8.17423i	0.205191	−	0.355402i	−0.745002	−	0.667062i	$-0.767552\pi$
$23$	4.71940	−	8.17423i	0.205191	−	0.355402i	0.950194	+	0.311660i	$0.100885\pi$
$24$		0			0
$25$		0			0
$26$			27.8557i			1.07137i
$27$		0			0
$28$		−	12.6969i		−	0.453462i
$29$	−2.84847	+	1.64456i	−0.0982231	+	0.0567091i	−0.548307	−	0.836277i	$-0.684727\pi$
$29$	−2.84847	+	1.64456i	−0.0982231	+	0.0567091i	0.450084	+	0.892986i	$0.351394\pi$
$30$		0			0
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	−0.318061	−	0.948070i	$-0.603032\pi$
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	0.980083	−	0.198587i	$-0.0636351\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.34847	+	2.33562i	0.0396609	+	0.0686946i
$35$		0			0
$36$		0			0
$37$		−	17.3031i		−	0.467650i	−0.972279	−	0.233825i	$-0.924876\pi$
$37$		−	17.3031i		−	0.467650i	0.972279	−	0.233825i	$-0.0751243\pi$
$38$	3.32124	+	5.75255i	0.0874010	+	0.151383i
$39$		0			0
$40$		0			0
$41$	53.5454	+	30.9145i	1.30599	+	0.754011i	0.981424	−	0.191853i	$-0.0614498\pi$
$41$	53.5454	+	30.9145i	1.30599	+	0.754011i	0.324562	+	0.945864i	$0.394783\pi$
$42$		0			0
$43$	0.826701	−	0.477296i	0.0192256	−	0.0110999i	−0.490356	−	0.871522i	$-0.663133\pi$
$43$	0.826701	−	0.477296i	0.0192256	−	0.0110999i	0.509582	+	0.860422i	$0.329800\pi$
$44$		−	18.8776i		−	0.429036i
$45$		0			0
$46$	−13.3485			−0.290184
$47$	−7.05501	−	12.2196i	−0.150107	−	0.259992i	0.781160	−	0.624331i	$-0.214628\pi$
$47$	−7.05501	−	12.2196i	−0.150107	−	0.259992i	−0.931267	+	0.364339i	$0.881295\pi$
$48$		0			0
$49$	−4.34847	+	7.53177i	−0.0887443	+	0.153710i
$50$		0			0
$51$		0			0
$52$	34.1161	−	19.6969i	0.656079	−	0.378787i
$53$	9.53512			0.179908			0.0899539	−	0.995946i	$-0.471328\pi$
$53$	9.53512			0.179908			0.0899539	+	0.995946i	$0.471328\pi$
$54$		0			0
$55$		0			0
$56$	−15.5505	+	8.97809i	−0.277688	+	0.160323i
$57$		0			0
$58$	4.02834	+	2.32577i	0.0694542	+	0.0400994i
$59$	79.2650	+	45.7637i	1.34348	+	0.775656i	0.987316	−	0.158769i	$-0.0507526\pi$
$59$	79.2650	+	45.7637i	1.34348	+	0.775656i	0.356160	+	0.934425i	$0.384086\pi$
$60$		0			0
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	0.990297	+	0.138968i	$0.0443786\pi$
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	−0.374798	+	0.927106i	$0.622288\pi$
$62$	−58.0470			−0.936241
$63$		0			0
$64$	8.00000			0.125000
$65$		0			0
$66$		0			0
$67$	26.8075	+	15.4773i	0.400111	+	0.231004i	0.686532	−	0.727100i	$-0.259132\pi$
$67$	26.8075	+	15.4773i	0.400111	+	0.231004i	−0.286421	+	0.958104i	$0.592465\pi$
$68$	1.90702	−	3.30306i	0.0280445	−	0.0485744i
$69$		0			0
$70$		0			0
$71$			85.9026i			1.20990i	0.796265	+	0.604948i	$0.206806\pi$
$71$			85.9026i			1.20990i	−0.796265	+	0.604948i	$0.793194\pi$
$72$		0			0
$73$		−	96.0908i		−	1.31631i	−0.752881	−	0.658156i	$-0.771337\pi$
$73$		−	96.0908i		−	1.31631i	0.752881	−	0.658156i	$-0.228663\pi$
$74$	−21.1918	+	12.2351i	−0.286376	+	0.165339i
$75$		0			0
$76$	4.69694	−	8.13534i	0.0618018	−	0.107044i
$77$	29.9609	−	51.8939i	0.389103	−	0.673946i
$78$		0			0
$79$	14.8712	+	25.7576i	0.188243	+	0.326046i	0.944664	−	0.328038i	$-0.106388\pi$
$79$	14.8712	+	25.7576i	0.188243	+	0.326046i	−0.756422	+	0.654084i	$0.773054\pi$
$80$		0			0
$81$		0			0
$82$		−	87.4393i		−	1.06633i
$83$	43.9530	+	76.1288i	0.529554	+	0.917215i	0.999406	+	0.0344693i	$0.0109741\pi$
$83$	43.9530	+	76.1288i	0.529554	+	0.917215i	−0.469852	+	0.882745i	$0.655693\pi$
$84$		0			0
$85$		0			0
$86$	−1.16913	−	0.674999i	−0.0135946	−	0.00784882i
$87$		0			0
$88$	−23.1202	+	13.3485i	−0.262730	+	0.151687i
$89$			41.3766i			0.464905i	0.972608	+	0.232453i	$0.0746751\pi$
$89$			41.3766i			0.464905i	−0.972608	+	0.232453i	$0.925325\pi$
$90$		0			0
$91$	125.045			1.37413
$92$	9.43879	+	16.3485i	0.102596	+	0.177701i
$93$		0			0
$94$	−9.97730	+	17.2812i	−0.106141	+	0.183842i
$95$		0			0
$96$		0			0
$97$	−83.0333	+	47.9393i	−0.856013	+	0.494219i	−0.862675	−	0.505758i	$-0.831213\pi$
$97$	−83.0333	+	47.9393i	−0.856013	+	0.494219i	0.00666202	+	0.999978i	$0.497879\pi$
$98$	12.2993			0.125503
$99$		0			0
$100$		0			0
$101$	136.772	−	78.9656i	1.35418	−	0.781838i	0.365350	−	0.930870i	$-0.380949\pi$
$101$	136.772	−	78.9656i	1.35418	−	0.781838i	0.988832	+	0.149032i	$0.0476159\pi$
$102$		0			0
$103$	−25.2327	−	14.5681i	−0.244978	−	0.141438i	0.372485	−	0.928038i	$-0.378506\pi$
$103$	−25.2327	−	14.5681i	−0.244978	−	0.141438i	−0.617462	+	0.786600i	$0.711839\pi$
$104$	−48.2474	−	27.8557i	−0.463918	−	0.267843i
$105$		0			0
$106$	−6.74235	−	11.6781i	−0.0636070	−	0.110171i
$107$	171.805			1.60566			0.802829	−	0.596210i	$-0.203327\pi$
$107$	171.805			1.60566			0.802829	+	0.596210i	$0.203327\pi$
$108$		0			0
$109$	−116.272			−1.06672			−0.533360	−	0.845888i	$-0.679071\pi$
$109$	−116.272			−1.06672			−0.533360	+	0.845888i	$0.679071\pi$
$110$		0			0
$111$		0			0
$112$	21.9917	+	12.6969i	0.196355	+	0.113366i
$113$	101.132	−	175.166i	0.894976	−	1.55014i	0.0611424	−	0.998129i	$-0.480526\pi$
$113$	101.132	−	175.166i	0.894976	−	1.55014i	0.833834	−	0.552015i	$-0.186141\pi$
$114$		0			0
$115$		0			0
$116$		−	6.57826i		−	0.0567091i
$117$		0			0
$118$		−	129.439i		−	1.09694i
$119$	10.4847	−	6.05334i	0.0881067	−	0.0508684i
$120$		0			0
$121$	−15.9546	+	27.6342i	−0.131856	+	0.228382i
$122$	53.0972	−	91.9671i	0.435223	−	0.753829i
$123$		0			0
$124$	41.0454	+	71.0927i	0.331011	+	0.573328i
$125$		0			0
$126$		0			0
$127$		−	10.0908i		−	0.0794552i	−0.999211	−	0.0397276i	$-0.987351\pi$
$127$		−	10.0908i		−	0.0794552i	0.999211	−	0.0397276i	$-0.0126490\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−4.29567	−	2.48010i	−0.0327913	−	0.0189321i	0.483515	−	0.875336i	$-0.339360\pi$
$131$	−4.29567	−	2.48010i	−0.0327913	−	0.0189321i	−0.516306	+	0.856404i	$0.672693\pi$
$132$		0			0
$133$	25.8235	−	14.9092i	0.194161	−	0.112099i
$134$		−	43.7764i		−	0.326690i
$135$		0			0
$136$	−5.39388			−0.0396609
$137$	117.342	+	203.242i	0.856511	+	1.48352i	0.875236	+	0.483696i	$0.160706\pi$
$137$	117.342	+	203.242i	0.856511	+	1.48352i	−0.0187249	+	0.999825i	$0.505961\pi$
$138$		0			0
$139$	53.2650	−	92.2578i	0.383202	−	0.663725i	−0.608316	−	0.793695i	$-0.708155\pi$
$139$	53.2650	−	92.2578i	0.383202	−	0.663725i	0.991518	+	0.129970i	$0.0414881\pi$
$140$		0			0
$141$		0			0
$142$	105.209	−	60.7423i	0.740907	−	0.427763i
$143$	185.915			1.30011
$144$		0			0
$145$		0			0
$146$	−117.687	+	67.9465i	−0.806074	+	0.465387i
$147$		0			0
$148$	29.9698	+	17.3031i	0.202499	+	0.116913i
$149$	−91.0301	−	52.5563i	−0.610940	−	0.352727i	0.162393	−	0.986726i	$-0.448079\pi$
$149$	−91.0301	−	52.5563i	−0.610940	−	0.352727i	−0.773333	+	0.634000i	$0.781412\pi$
$150$		0			0
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.756828	+	0.653614i	$0.226748\pi$
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.187632	+	0.982239i	$0.439919\pi$
$152$	−13.2849			−0.0874010
$153$		0			0
$154$	−84.7423			−0.550275
$155$		0			0
$156$		0			0
$157$	−170.764	−	98.5908i	−1.08767	−	0.627967i	−0.154715	−	0.987959i	$-0.549446\pi$
$157$	−170.764	−	98.5908i	−1.08767	−	0.627967i	−0.932955	+	0.359992i	$0.882779\pi$
$158$	21.0310	−	36.4268i	0.133108	−	0.230549i
$159$		0			0
$160$		0			0
$161$			59.9219i			0.372186i
$162$		0			0
$163$		−	249.060i		−	1.52798i	−0.645230	−	0.763988i	$-0.723238\pi$
$163$		−	249.060i		−	1.52798i	0.645230	−	0.763988i	$-0.276762\pi$
$164$	−107.091	+	61.8289i	−0.652993	+	0.377006i
$165$		0			0
$166$	62.1589	−	107.662i	0.374451	−	0.648569i
$167$	24.2182	−	41.9472i	0.145019	−	0.251181i	−0.784361	−	0.620305i	$-0.787009\pi$
$167$	24.2182	−	41.9472i	0.145019	−	0.251181i	0.929380	+	0.369124i	$0.120342\pi$
$168$		0			0
$169$	109.485	+	189.633i	0.647838	+	1.12209i
$170$		0			0
$171$		0			0
$172$			1.90918i			0.0110999i
$173$	−50.2206	−	86.9847i	−0.290293	−	0.502802i	0.683586	−	0.729870i	$-0.260419\pi$
$173$	−50.2206	−	86.9847i	−0.290293	−	0.502802i	−0.973879	+	0.227068i	$0.927086\pi$
$174$		0			0
$175$		0			0
$176$	32.6969	+	18.8776i	0.185778	+	0.107259i
$177$		0			0
$178$	50.6757	−	29.2577i	0.284695	−	0.164369i
$179$		−	285.071i		−	1.59257i	−0.604919	−	0.796287i	$-0.706794\pi$
$179$		−	285.071i		−	1.59257i	0.604919	−	0.796287i	$-0.293206\pi$
$180$		0			0
$181$	37.1214			0.205091			0.102545	−	0.994728i	$-0.467301\pi$
$181$	37.1214			0.205091			0.102545	+	0.994728i	$0.467301\pi$
$182$	−88.4205	−	153.149i	−0.485827	−	0.841476i
$183$		0			0
$184$	13.3485	−	23.1202i	0.0725460	−	0.125653i
$185$		0			0
$186$		0			0
$187$	15.5885	−	9.00000i	0.0833607	−	0.0481283i
$188$	28.2201			0.150107
$189$		0			0
$190$		0			0
$191$	15.5227	−	8.96204i	0.0812707	−	0.0469217i	−0.458814	−	0.888532i	$-0.651726\pi$
$191$	15.5227	−	8.96204i	0.0812707	−	0.0469217i	0.540085	+	0.841611i	$0.318392\pi$
$192$		0			0
$193$	82.6657	+	47.7270i	0.428319	+	0.247290i	0.698630	−	0.715483i	$-0.253793\pi$
$193$	82.6657	+	47.7270i	0.428319	+	0.247290i	−0.270311	+	0.962773i	$0.587127\pi$
$194$	117.427	+	67.7964i	0.605293	+	0.349466i
$195$		0			0
$196$	−8.69694	−	15.0635i	−0.0443721	−	0.0768548i
$197$	−160.363			−0.814026			−0.407013	−	0.913422i	$-0.633430\pi$
$197$	−160.363			−0.814026			−0.407013	+	0.913422i	$0.633430\pi$
$198$		0			0
$199$	−6.51531			−0.0327402			−0.0163701	−	0.999866i	$-0.505211\pi$
$199$	−6.51531			−0.0327402			−0.0163701	+	0.999866i	$0.505211\pi$
$200$		0			0
$201$		0			0
$202$	−193.425	−	111.674i	−0.957552	−	0.552843i
$203$	10.4405	−	18.0834i	0.0514309	−	0.0890809i
$204$		0			0
$205$		0			0
$206$			41.2048i			0.200024i
$207$		0			0
$208$			78.7878i			0.378787i
$209$	38.3939	−	22.1667i	0.183703	−	0.106061i
$210$		0			0
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	−0.622961	−	0.782253i	$-0.714071\pi$
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	0.988931	+	0.148374i	$0.0474040\pi$
$212$	−9.53512	+	16.5153i	−0.0449770	+	0.0779024i
$213$		0			0
$214$	−121.485	−	210.418i	−0.567685	−	0.983260i
$215$		0			0
$216$		0			0
$217$			260.576i			1.20081i
$218$	82.2170	+	142.404i	0.377142	+	0.653230i
$219$		0			0
$220$		0			0
$221$	32.5301	+	18.7813i	0.147195	+	0.0849831i
$222$		0			0
$223$	80.3437	−	46.3865i	0.360286	−	0.208011i	−0.308920	−	0.951088i	$-0.599968\pi$
$223$	80.3437	−	46.3865i	0.360286	−	0.208011i	0.669206	+	0.743077i	$0.266634\pi$
$224$		−	35.9124i		−	0.160323i
$225$		0			0
$226$	−286.045			−1.26569
$227$	84.9010	+	147.053i	0.374013	+	0.647810i	0.990179	−	0.139807i	$-0.0446482\pi$
$227$	84.9010	+	147.053i	0.374013	+	0.647810i	−0.616166	+	0.787617i	$0.711315\pi$
$228$		0			0
$229$	203.772	−	352.944i	0.889836	−	1.54124i	0.0497675	−	0.998761i	$-0.484152\pi$
$229$	203.772	−	352.944i	0.889836	−	1.54124i	0.840068	−	0.542480i	$-0.182515\pi$
$230$		0			0
$231$		0			0
$232$	−8.05669	+	4.65153i	−0.0347271	+	0.0200497i
$233$	15.2562			0.0654772			0.0327386	−	0.999464i	$-0.489577\pi$
$233$	15.2562			0.0654772			0.0327386	+	0.999464i	$0.489577\pi$
$234$		0			0
$235$		0			0
$236$	−158.530	+	91.5274i	−0.671738	+	0.387828i
$237$		0			0
$238$	−14.8276	−	8.56072i	−0.0623008	−	0.0359694i
$239$	48.9620	+	28.2682i	0.204862	+	0.118277i	0.598921	−	0.800808i	$-0.295596\pi$
$239$	48.9620	+	28.2682i	0.204862	+	0.118277i	−0.394059	+	0.919085i	$0.628930\pi$
$240$		0			0
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	0.765348	−	0.643617i	$-0.222567\pi$
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	−0.940062	+	0.341003i	$0.889233\pi$
$242$	45.1264			0.186473
$243$		0			0
$244$	−150.182			−0.615498
$245$		0			0
$246$		0			0
$247$	80.1206	+	46.2577i	0.324375	+	0.187278i
$248$	58.0470	−	100.540i	0.234060	−	0.405404i
$249$		0			0
$250$		0			0
$251$		−	218.903i		−	0.872123i	−0.899917	−	0.436062i	$-0.856373\pi$
$251$		−	218.903i		−	0.872123i	0.899917	−	0.436062i	$-0.143627\pi$
$252$		0			0
$253$			89.0908i			0.352138i
$254$	−12.3587	+	7.13528i	−0.0486562	+	0.0280917i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	6.41212	−	11.1061i	0.0249499	−	0.0432145i	−0.853281	−	0.521452i	$-0.825391\pi$
$257$	6.41212	−	11.1061i	0.0249499	−	0.0432145i	0.878231	+	0.478237i	$0.158724\pi$
$258$		0			0
$259$	54.9240	+	95.1311i	0.212062	+	0.367302i
$260$		0			0
$261$		0			0
$262$			7.01479i			0.0267740i
$263$	−168.232	−	291.386i	−0.639666	−	1.10793i	−0.985506	−	0.169640i	$-0.945739\pi$
$263$	−168.232	−	291.386i	−0.639666	−	1.10793i	0.345840	−	0.938293i	$-0.387594\pi$
$264$		0			0
$265$		0			0
$266$	−36.5199	−	21.0848i	−0.137293	−	0.0792661i
$267$		0			0
$268$	−53.6149	+	30.9546i	−0.200056	+	0.115502i
$269$			60.4468i			0.224709i	0.993668	+	0.112355i	$0.0358393\pi$
$269$			60.4468i			0.224709i	−0.993668	+	0.112355i	$0.964161\pi$
$270$		0			0
$271$	274.636			1.01342			0.506708	−	0.862118i	$-0.330862\pi$
$271$	274.636			1.01342			0.506708	+	0.862118i	$0.330862\pi$
$272$	3.81405	+	6.60612i	0.0140222	+	0.0242872i
$273$		0			0
$274$	165.947	−	287.428i	0.605645	−	1.04901i
$275$		0			0
$276$		0			0
$277$	42.4352	−	24.5000i	0.153196	−	0.0884477i	−0.421442	−	0.906855i	$-0.638476\pi$
$277$	42.4352	−	24.5000i	0.153196	−	0.0884477i	0.574638	+	0.818407i	$0.305143\pi$
$278$	−150.656			−0.541929
$279$		0			0
$280$		0			0
$281$	297.121	−	171.543i	1.05737	−	0.610473i	0.132666	−	0.991161i	$-0.457646\pi$
$281$	297.121	−	171.543i	1.05737	−	0.610473i	0.924704	+	0.380688i	$0.124313\pi$
$282$		0			0
$283$	297.401	+	171.704i	1.05089	+	0.606729i	0.922897	−	0.385047i	$-0.125815\pi$
$283$	297.401	+	171.704i	1.05089	+	0.606729i	0.127988	+	0.991776i	$0.459148\pi$
$284$	−148.788	−	85.9026i	−0.523901	−	0.302474i
$285$		0			0
$286$	−131.462	−	227.699i	−0.459657	−	0.796150i
$287$	−392.519			−1.36766
$288$		0			0
$289$	−285.363			−0.987416
$290$		0			0
$291$		0			0
$292$	166.434	+	96.0908i	0.569980	+	0.329078i
$293$	−143.226	+	248.076i	−0.488828	+	0.846674i	−0.999917	−	0.0128532i	$-0.995909\pi$
$293$	−143.226	+	248.076i	−0.488828	+	0.846674i	0.511090	+	0.859527i	$0.329242\pi$
$294$		0			0
$295$		0			0
$296$		−	48.9404i		−	0.165339i
$297$		0			0
$298$			148.652i			0.498831i
$299$	−161.007	+	92.9577i	−0.538486	+	0.310895i
$300$		0			0
$301$	−3.03010	+	5.24829i	−0.0100668	+	0.0174362i
$302$	201.686	−	349.330i	0.667834	−	1.15672i
$303$		0			0
$304$	9.39388	+	16.2707i	0.0309009	+	0.0535219i
$305$		0			0
$306$		0			0
$307$		−	154.091i		−	0.501924i	−0.967997	−	0.250962i	$-0.919253\pi$
$307$		−	154.091i		−	0.501924i	0.967997	−	0.250962i	$-0.0807470\pi$
$308$	59.9219	+	103.788i	0.194552	+	0.336973i
$309$		0			0
$310$		0			0
$311$	62.3411	+	35.9926i	0.200454	+	0.115732i	0.596867	−	0.802340i	$-0.296412\pi$
$311$	62.3411	+	35.9926i	0.200454	+	0.115732i	−0.396413	+	0.918072i	$0.629745\pi$
$312$		0			0
$313$	−318.356	+	183.803i	−1.01711	+	0.587230i	−0.913266	−	0.407363i	$-0.866448\pi$
$313$	−318.356	+	183.803i	−1.01711	+	0.587230i	−0.103846	+	0.994593i	$0.533115\pi$
$314$			278.857i			0.888079i
$315$		0			0
$316$	−59.4847			−0.188243
$317$	−53.7987	−	93.1821i	−0.169712	−	0.293950i	0.768607	−	0.639722i	$-0.220950\pi$
$317$	−53.7987	−	93.1821i	−0.169712	−	0.293950i	−0.938319	+	0.345772i	$0.887617\pi$
$318$		0			0
$319$	15.5227	−	26.8861i	0.0486605	−	0.0842825i
$320$		0			0
$321$		0			0
$322$	73.3890	−	42.3712i	0.227916	−	0.131587i
$323$	8.95717			0.0277312
$324$		0			0
$325$		0			0
$326$	−305.035	+	176.112i	−0.935691	+	0.540221i
$327$		0			0
$328$	151.449	+	87.4393i	0.461736	+	0.266583i
$329$	77.5760	+	44.7885i	0.235793	+	0.136135i
$330$		0			0
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	0.852744	−	0.522329i	$-0.174937\pi$
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	−0.878722	+	0.477334i	$0.841603\pi$
$332$	−175.812			−0.529554
$333$		0			0
$334$	−68.4995			−0.205088
$335$		0			0
$336$		0			0
$337$	315.574	+	182.197i	0.936422	+	0.540644i	0.888837	−	0.458223i	$-0.151514\pi$
$337$	315.574	+	182.197i	0.936422	+	0.540644i	0.0475854	+	0.998867i	$0.484847\pi$
$338$	154.835	−	268.182i	0.458091	−	0.793437i
$339$		0			0
$340$		0			0
$341$			387.419i			1.13613i
$342$		0			0
$343$		−	366.287i		−	1.06789i
$344$	2.33826	−	1.35000i	0.00679728	−	0.00392441i
$345$		0			0
$346$	−71.0227	+	123.015i	−0.205268	+	0.355534i
$347$	−291.697	+	505.234i	−0.840626	+	1.45601i	0.0487402	+	0.998811i	$0.484479\pi$
$347$	−291.697	+	505.234i	−0.840626	+	1.45601i	−0.889366	+	0.457196i	$0.848854\pi$
$348$		0			0
$349$	156.379	+	270.856i	0.448076	+	0.776091i	0.998261	−	0.0589524i	$-0.0187760\pi$
$349$	156.379	+	270.856i	0.448076	+	0.776091i	−0.550185	+	0.835043i	$0.685443\pi$
$350$		0			0
$351$		0			0
$352$		−	53.3939i		−	0.151687i
$353$	18.8078	+	32.5760i	0.0532798	+	0.0922834i	0.891435	−	0.453148i	$-0.149699\pi$
$353$	18.8078	+	32.5760i	0.0532798	+	0.0922834i	−0.838155	+	0.545431i	$0.816366\pi$
$354$		0			0
$355$		0			0
$356$	−71.6663	−	41.3766i	−0.201310	−	0.116226i
$357$		0			0
$358$	−349.139	+	201.576i	−0.975249	+	0.563060i
$359$		−	294.028i		−	0.819019i	−0.912306	−	0.409510i	$-0.865700\pi$
$359$		−	294.028i		−	0.819019i	0.912306	−	0.409510i	$-0.134300\pi$
$360$		0			0
$361$	−338.939			−0.938889
$362$	−26.2488	−	45.4643i	−0.0725105	−	0.125592i
$363$		0			0
$364$	−125.045	+	216.585i	−0.343531	+	0.595014i
$365$		0			0
$366$		0			0
$367$	28.7755	−	16.6135i	0.0784072	−	0.0452684i	−0.460284	−	0.887772i	$-0.652252\pi$
$367$	28.7755	−	16.6135i	0.0784072	−	0.0452684i	0.538691	+	0.842503i	$0.318919\pi$
$368$	−37.7552			−0.102596
$369$		0			0
$370$		0			0
$371$	−52.4235	+	30.2667i	−0.141303	+	0.0815814i
$372$		0			0
$373$	194.881	+	112.515i	0.522470	+	0.301648i	0.737945	−	0.674861i	$-0.235797\pi$
$373$	194.881	+	112.515i	0.522470	+	0.301648i	−0.215475	+	0.976509i	$0.569130\pi$
$374$	−22.0454	−	12.7279i	−0.0589449	−	0.0340319i
$375$		0			0
$376$	−19.9546	−	34.5624i	−0.0530707	−	0.0919212i
$377$	64.7858			0.171846
$378$		0			0
$379$	166.334			0.438875			0.219438	−	0.975627i	$-0.429578\pi$
$379$	166.334			0.438875			0.219438	+	0.975627i	$0.429578\pi$
$380$		0			0
$381$		0			0
$382$	−21.9524	−	12.6742i	−0.0574671	−	0.0331786i
$383$	−368.493	+	638.249i	−0.962124	+	1.66645i	−0.244972	+	0.969530i	$0.578779\pi$
$383$	−368.493	+	638.249i	−0.962124	+	1.66645i	−0.717152	+	0.696917i	$0.754555\pi$
$384$		0			0
$385$		0			0
$386$		−	134.992i		−	0.349721i
$387$		0			0
$388$		−	191.757i		−	0.494219i
$389$	−146.682	+	84.6867i	−0.377074	+	0.217704i	−0.676544	−	0.736402i	$-0.736523\pi$
$389$	−146.682	+	84.6867i	−0.377074	+	0.217704i	0.299471	+	0.954106i	$0.403190\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	−12.2993	+	21.3031i	−0.0313758	+	0.0543445i
$393$		0			0
$394$	113.394	+	196.404i	0.287802	+	0.498487i
$395$		0			0
$396$		0			0
$397$			256.272i			0.645523i	0.946480	+	0.322761i	$0.104611\pi$
$397$			256.272i			0.645523i	−0.946480	+	0.322761i	$0.895389\pi$
$398$	4.60702	+	7.97959i	0.0115754	+	0.0200492i
$399$		0			0
$400$		0			0
$401$	−226.364	−	130.691i	−0.564498	−	0.325913i	0.190451	−	0.981697i	$-0.439005\pi$
$401$	−226.364	−	130.691i	−0.564498	−	0.325913i	−0.754949	+	0.655784i	$0.772338\pi$
$402$		0			0
$403$	−700.155	+	404.234i	−1.73736	+	1.00306i
$404$			315.862i			0.781838i
$405$		0			0
$406$	−29.5301			−0.0727342
$407$	81.6600	+	141.439i	0.200639	+	0.347517i
$408$		0			0
$409$	−221.894	+	384.331i	−0.542528	+	0.939686i	0.456230	+	0.889862i	$0.349199\pi$
$409$	−221.894	+	384.331i	−0.542528	+	0.939686i	−0.998758	+	0.0498240i	$0.984134\pi$
$410$		0			0
$411$		0			0
$412$	50.4654	−	29.1362i	0.122489	−	0.0707190i
$413$	−581.059			−1.40692
$414$		0			0
$415$		0			0
$416$	96.4949	−	55.7114i	0.231959	−	0.133922i
$417$		0			0
$418$	−54.2971	−	31.3485i	−0.129897	−	0.0749963i
$419$	9.32525	+	5.38394i	0.0222560	+	0.0128495i	0.511087	−	0.859529i	$-0.329243\pi$
$419$	9.32525	+	5.38394i	0.0222560	+	0.0128495i	−0.488831	+	0.872379i	$0.662576\pi$
$420$		0			0
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	0.674571	−	0.738210i	$-0.264328\pi$
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	−0.976594	+	0.215091i	$0.930995\pi$
$422$	−218.410			−0.517560
$423$		0			0
$424$	26.9694			0.0636070
$425$		0			0
$426$		0			0
$427$	−412.844	−	238.356i	−0.966849	−	0.558210i
$428$	−171.805	+	297.576i	−0.401414	+	0.695270i
$429$		0			0
$430$		0			0
$431$		−	698.663i		−	1.62103i	−0.585719	−	0.810514i	$-0.699188\pi$
$431$		−	698.663i		−	1.62103i	0.585719	−	0.810514i	$-0.300812\pi$
$432$		0			0
$433$			211.728i			0.488978i	0.969652	+	0.244489i	$0.0786202\pi$
$433$			211.728i			0.488978i	−0.969652	+	0.244489i	$0.921380\pi$
$434$	319.139	−	184.255i	0.735342	−	0.424550i
$435$		0			0
$436$	116.272	−	201.390i	0.266680	−	0.461903i
$437$	−22.1667	+	38.3939i	−0.0507247	+	0.0878578i
$438$		0			0
$439$	139.931	+	242.368i	0.318750	+	0.552092i	0.980228	−	0.197874i	$-0.0634035\pi$
$439$	139.931	+	242.368i	0.318750	+	0.552092i	−0.661477	+	0.749965i	$0.730070\pi$
$440$		0			0
$441$		0			0
$442$		−	53.1214i		−	0.120184i
$443$	275.627	+	477.400i	0.622183	+	1.07765i	0.989078	+	0.147391i	$0.0470874\pi$
$443$	275.627	+	477.400i	0.622183	+	1.07765i	−0.366895	+	0.930262i	$0.619579\pi$
$444$		0			0
$445$		0			0
$446$	−113.623	−	65.6004i	−0.254761	−	0.147086i
$447$		0			0
$448$	−43.9835	+	25.3939i	−0.0981774	+	0.0566828i
$449$			542.865i			1.20905i	0.796585	+	0.604527i	$0.206638\pi$
$449$			542.865i			1.20905i	−0.796585	+	0.604527i	$0.793362\pi$
$450$		0			0
$451$	−583.590			−1.29399
$452$	202.265	+	350.333i	0.447488	+	0.775072i
$453$		0			0
$454$	120.068	−	207.964i	0.264467	−	0.458071i
$455$		0			0
$456$		0			0
$457$	−79.9898	+	46.1821i	−0.175032	+	0.101055i	−0.584957	−	0.811065i	$-0.698888\pi$
$457$	−79.9898	+	46.1821i	−0.175032	+	0.101055i	0.409924	+	0.912120i	$0.365555\pi$
$458$	−576.356			−1.25842
$459$		0			0
$460$		0			0
$461$	199.030	−	114.910i	0.431736	−	0.249263i	−0.268350	−	0.963321i	$-0.586478\pi$
$461$	199.030	−	114.910i	0.431736	−	0.249263i	0.700086	+	0.714059i	$0.253145\pi$
$462$		0			0
$463$	442.368	+	255.401i	0.955438	+	0.551623i	0.894766	−	0.446535i	$-0.147342\pi$
$463$	442.368	+	255.401i	0.955438	+	0.551623i	0.0606723	+	0.998158i	$0.480676\pi$
$464$	11.3939	+	6.57826i	0.0245558	+	0.0141773i
$465$		0			0
$466$	−10.7878	−	18.6849i	−0.0231497	−	0.0400964i
$467$	833.657			1.78513			0.892567	−	0.450915i	$-0.148902\pi$
$467$	833.657			1.78513			0.892567	+	0.450915i	$0.148902\pi$
$468$		0			0
$469$	−196.514			−0.419007
$470$		0			0
$471$		0			0
$472$	224.195	+	129.439i	0.474990	+	0.274236i
$473$	−4.50510	+	7.80306i	−0.00952452	+	0.0164970i
$474$		0			0
$475$		0			0
$476$			24.2134i			0.0508684i
$477$		0			0
$478$		−	79.9546i		−	0.167269i
$479$	569.144	−	328.595i	1.18819	−	0.686003i	0.230296	−	0.973121i	$-0.426031\pi$
$479$	569.144	−	328.595i	1.18819	−	0.686003i	0.957895	+	0.287118i	$0.0926972\pi$
$480$		0			0
$481$	−170.409	+	295.156i	−0.354280	+	0.613631i
$482$	−59.5471	+	103.139i	−0.123542	+	0.213980i
$483$		0			0
$484$	−31.9092	−	55.2683i	−0.0659281	−	0.114191i
$485$		0			0
$486$		0			0
$487$			351.666i			0.722107i	0.932545	+	0.361054i	$0.117583\pi$
$487$			351.666i			0.722107i	−0.932545	+	0.361054i	$0.882417\pi$
$488$	106.194	+	183.934i	0.217612	+	0.376914i
$489$		0			0
$490$		0			0
$491$	−212.539	−	122.709i	−0.432869	−	0.249917i	0.267699	−	0.963503i	$-0.413737\pi$
$491$	−212.539	−	122.709i	−0.432869	−	0.249917i	−0.700568	+	0.713586i	$0.747070\pi$
$492$		0			0
$493$	5.43210	−	3.13622i	0.0110185	−	0.00636151i
$494$		−	130.836i		−	0.264851i
$495$		0			0
$496$	−164.182			−0.331011
$497$	−272.675	−	472.287i	−0.548642	−	0.950276i
$498$		0			0
$499$	315.113	−	545.792i	0.631489	−	1.09377i	−0.355758	−	0.934578i	$-0.615777\pi$
$499$	315.113	−	545.792i	0.631489	−	1.09377i	0.987247	−	0.159193i	$-0.0508892\pi$
$500$		0			0
$501$		0			0
$502$	−268.100	+	154.788i	−0.534064	+	0.308342i
$503$	286.891			0.570360			0.285180	−	0.958474i	$-0.407947\pi$
$503$	286.891			0.570360			0.285180	+	0.958474i	$0.407947\pi$
$504$		0			0
$505$		0			0
$506$	109.114	−	62.9967i	0.215639	−	0.124499i
$507$		0			0
$508$	17.4778	+	10.0908i	0.0344051	+	0.0198638i
$509$	755.454	+	436.161i	1.48419	+	0.856898i	0.999838	−	0.0179741i	$-0.00572163\pi$
$509$	755.454	+	436.161i	1.48419	+	0.856898i	0.484353	+	0.874873i	$0.339055\pi$
$510$		0			0
$511$	305.015	+	528.301i	0.596898	+	1.03386i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−18.1362			−0.0352845
$515$		0			0
$516$		0			0
$517$	115.339	+	66.5908i	0.223092	+	0.128802i
$518$	77.6742	−	134.536i	0.149950	−	0.259721i
$519$		0			0
$520$		0			0
$521$		−	206.132i		−	0.395646i	−0.980238	−	0.197823i	$-0.936613\pi$
$521$		−	206.132i		−	0.395646i	0.980238	−	0.197823i	$-0.0633872\pi$
$522$		0			0
$523$			884.817i			1.69181i	0.533333	+	0.845906i	$0.320939\pi$
$523$			884.817i			1.69181i	−0.533333	+	0.845906i	$0.679061\pi$
$524$	8.59133	−	4.96021i	0.0163957	−	0.00946604i
$525$		0			0
$526$	−237.916	+	412.083i	−0.452312	+	0.783427i
$527$	−39.1373	+	67.7878i	−0.0742643	+	0.128630i
$528$		0			0
$529$	219.955	+	380.973i	0.415793	+	0.720175i
$530$		0			0
$531$		0			0
$532$			59.6367i			0.112099i
$533$	−608.920	−	1054.68i	−1.14244	−	1.97876i
$534$		0			0
$535$		0			0
$536$	75.8230	+	43.7764i	0.141461	+	0.0816724i
$537$		0			0
$538$	74.0319	−	42.7423i	0.137606	−	0.0794467i
$539$		−	82.0886i		−	0.152298i
$540$		0			0
$541$	−509.151			−0.941129			−0.470565	−	0.882365i	$-0.655950\pi$
$541$	−509.151			−0.941129			−0.470565	+	0.882365i	$0.655950\pi$
$542$	−194.197	−	336.359i	−0.358297	−	0.620588i
$543$		0			0
$544$	5.39388	−	9.34247i	0.00991521	−	0.0171737i
$545$		0			0
$546$		0			0
$547$	−474.620	+	274.022i	−0.867679	+	0.500955i	−0.866576	−	0.499045i	$-0.833684\pi$
$547$	−474.620	+	274.022i	−0.867679	+	0.500955i	−0.00110267	+	0.999999i	$0.500351\pi$
$548$	−469.368			−0.856511
$549$		0			0
$550$		0			0
$551$	13.3791	−	7.72442i	0.0242815	−	0.0140189i
$552$		0			0
$553$	−163.522	−	94.4092i	−0.295699	−	0.170722i
$554$	−60.0125	−	34.6482i	−0.108326	−	0.0625419i
$555$		0			0
$556$	106.530	+	184.516i	0.191601	+	0.331862i
$557$	406.542			0.729879			0.364939	−	0.931031i	$-0.381090\pi$
$557$	406.542			0.729879			0.364939	+	0.931031i	$0.381090\pi$
$558$		0			0
$559$	−18.8025			−0.0336360
$560$		0			0
$561$		0			0
$562$	−420.192	−	242.598i	−0.747673	−	0.431669i
$563$	−303.236	+	525.220i	−0.538607	+	0.932895i	0.460372	+	0.887726i	$0.347716\pi$
$563$	−303.236	+	525.220i	−0.538607	+	0.932895i	−0.998979	+	0.0451687i	$0.985617\pi$
$564$		0			0
$565$		0			0
$566$		−	485.653i		−	0.858045i
$567$		0			0
$568$			242.969i			0.427763i
$569$	−224.954	+	129.877i	−0.395350	+	0.228255i	−0.684476	−	0.729036i	$-0.739969\pi$
$569$	−224.954	+	129.877i	−0.395350	+	0.228255i	0.289126	+	0.957291i	$0.406635\pi$
$570$		0			0
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	−0.825004	−	0.565126i	$-0.808827\pi$
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	0.901916	+	0.431911i	$0.142161\pi$
$572$	−185.915	+	322.015i	−0.325027	+	0.562963i
$573$		0			0
$574$	277.553	+	480.736i	0.483541	+	0.837518i
$575$		0			0
$576$		0			0
$577$			132.091i			0.228927i	0.993427	+	0.114463i	$0.0365149\pi$
$577$			132.091i			0.228927i	−0.993427	+	0.114463i	$0.963485\pi$
$578$	201.782	+	349.497i	0.349104	+	0.604666i
$579$		0			0
$580$		0			0
$581$	−483.302	−	279.034i	−0.831844	−	0.480266i
$582$		0			0
$583$	−77.9423	+	45.0000i	−0.133692	+	0.0771870i
$584$		−	271.786i		−	0.465387i
$585$		0			0
$586$	405.106			0.691306
$587$	−283.833	−	491.614i	−0.483532	−	0.837502i	0.516289	−	0.856414i	$-0.327313\pi$
$587$	−283.833	−	491.614i	−0.483532	−	0.837502i	−0.999821	+	0.0189125i	$0.993980\pi$
$588$		0			0
$589$	−96.3939	+	166.959i	−0.163657	+	0.283462i
$590$		0			0
$591$		0			0
$592$	−59.9396	+	34.6061i	−0.101249	+	0.0584563i
$593$	−77.0321			−0.129902			−0.0649512	−	0.997888i	$-0.520689\pi$
$593$	−77.0321			−0.129902			−0.0649512	+	0.997888i	$0.520689\pi$
$594$		0			0
$595$		0			0
$596$	182.060	−	105.113i	0.305470	−	0.176363i
$597$		0			0
$598$	227.699	+	131.462i	0.380767	+	0.219836i
$599$	−764.917	−	441.625i	−1.27699	−	0.737270i	−0.300696	−	0.953720i	$-0.597219\pi$
$599$	−764.917	−	441.625i	−1.27699	−	0.737270i	−0.976294	+	0.216450i	$0.930552\pi$
$600$		0			0
$601$	397.545	+	688.569i	0.661473	+	1.14571i	0.980229	+	0.197868i	$0.0634018\pi$
$601$	397.545	+	688.569i	0.661473	+	1.14571i	−0.318755	+	0.947837i	$0.603265\pi$
$602$	8.57042			0.0142366
$603$		0			0
$604$	−570.454			−0.944460
$605$		0			0
$606$		0			0
$607$	−256.987	−	148.372i	−0.423373	−	0.244434i	0.273147	−	0.961972i	$-0.411936\pi$
$607$	−256.987	−	148.372i	−0.423373	−	0.244434i	−0.696519	+	0.717538i	$0.745269\pi$
$608$	13.2849	−	23.0102i	0.0218502	−	0.0378457i
$609$		0			0
$610$		0			0
$611$			277.924i			0.454868i
$612$		0			0
$613$		−	517.181i		−	0.843688i	−0.906668	−	0.421844i	$-0.861383\pi$
$613$		−	517.181i		−	0.843688i	0.906668	−	0.421844i	$-0.138617\pi$
$614$	−188.722	+	108.959i	−0.307365	+	0.177457i
$615$		0			0
$616$	84.7423	−	146.778i	0.137569	−	0.238276i
$617$	132.738	−	229.909i	0.215134	−	0.372623i	−0.738180	−	0.674604i	$-0.764314\pi$
$617$	132.738	−	229.909i	0.215134	−	0.372623i	0.953314	+	0.301981i	$0.0976478\pi$
$618$		0			0
$619$	−98.5227	−	170.646i	−0.159164	−	0.275681i	0.775403	−	0.631466i	$-0.217547\pi$
$619$	−98.5227	−	170.646i	−0.159164	−	0.275681i	−0.934568	+	0.355786i	$0.884213\pi$
$620$		0			0
$621$		0			0
$622$		−	101.803i		−	0.163670i
$623$	−131.339	−	227.486i	−0.210817	−	0.365146i
$624$		0			0
$625$		0			0
$626$	450.224	+	259.937i	0.719207	+	0.415234i
$627$		0			0
$628$	341.529	−	197.182i	0.543835	−	0.313983i
$629$			32.9973i			0.0524600i
$630$		0			0
$631$	−160.879			−0.254958			−0.127479	−	0.991841i	$-0.540689\pi$
$631$	−160.879			−0.254958			−0.127479	+	0.991841i	$0.540689\pi$
$632$	42.0620	+	72.8536i	0.0665538	+	0.115275i
$633$		0			0
$634$	−76.0829	+	131.779i	−0.120005	+	0.207854i
$635$		0			0
$636$		0			0
$637$	148.353	−	85.6515i	0.232893	−	0.134461i
$638$	−43.9048			−0.0688164
$639$		0			0
$640$		0			0
$641$	267.894	−	154.669i	0.417931	−	0.241293i	−0.276261	−	0.961083i	$-0.589095\pi$
$641$	267.894	−	154.669i	0.417931	−	0.241293i	0.694192	+	0.719790i	$0.255762\pi$
$642$		0			0
$643$	−341.726	−	197.296i	−0.531456	−	0.306836i	0.210153	−	0.977668i	$-0.432604\pi$
$643$	−341.726	−	197.296i	−0.531456	−	0.306836i	−0.741609	+	0.670832i	$0.765937\pi$
$644$	−103.788	−	59.9219i	−0.161161	−	0.0930464i
$645$		0			0
$646$	−6.33368	−	10.9703i	−0.00980445	−	0.0169818i
$647$	−418.736			−0.647196			−0.323598	−	0.946195i	$-0.604892\pi$
$647$	−418.736			−0.647196			−0.323598	+	0.946195i	$0.604892\pi$
$648$		0			0
$649$	−863.908			−1.33114
$650$		0			0
$651$		0			0
$652$	431.385	+	249.060i	0.661633	+	0.381994i
$653$	−265.363	+	459.621i	−0.406375	+	0.703861i	−0.994480	−	0.104923i	$-0.966540\pi$
$653$	−265.363	+	459.621i	−0.406375	+	0.703861i	0.588106	+	0.808784i	$0.299874\pi$
$654$		0			0
$655$		0			0
$656$		−	247.316i		−	0.377006i
$657$		0			0
$658$		−	126.681i		−	0.192524i
$659$	310.204	−	179.096i	0.470719	−	0.271770i	−0.245822	−	0.969315i	$-0.579058\pi$
$659$	310.204	−	179.096i	0.470719	−	0.271770i	0.716541	+	0.697545i	$0.245724\pi$
$660$		0			0
$661$	111.136	−	192.493i	0.168133	−	0.291214i	−0.769631	−	0.638489i	$-0.779560\pi$
$661$	111.136	−	192.493i	0.168133	−	0.291214i	0.937763	+	0.347275i	$0.112893\pi$
$662$	−12.1604	+	21.0625i	−0.0183692	+	0.0318165i
$663$		0			0
$664$	124.318	+	215.325i	0.187226	+	0.324284i
$665$		0			0
$666$		0			0
$667$			31.0454i			0.0465448i
$668$	48.4365	+	83.8944i	0.0725097	+	0.125590i
$669$		0			0
$670$		0			0
$671$	−613.810	−	354.383i	−0.914769	−	0.528142i
$672$		0			0
$673$	−250.464	+	144.606i	−0.372161	+	0.214867i	−0.674402	−	0.738364i	$-0.735599\pi$
$673$	−250.464	+	144.606i	−0.372161	+	0.214867i	0.302241	+	0.953231i	$0.402265\pi$
$674$		−	515.331i		−	0.764586i
$675$		0			0
$676$	−437.939			−0.647838
$677$	232.226	+	402.227i	0.343022	+	0.594131i	0.984992	−	0.172598i	$-0.0552163\pi$
$677$	232.226	+	402.227i	0.343022	+	0.594131i	−0.641971	+	0.766729i	$0.721883\pi$
$678$		0			0
$679$	304.341	−	527.134i	0.448220	−	0.776339i
$680$		0			0
$681$		0			0
$682$	474.490	−	273.947i	0.695733	−	0.401681i
$683$	1126.36			1.64913			0.824565	−	0.565767i	$-0.191420\pi$
$683$	1126.36			1.64913			0.824565	+	0.565767i	$0.191420\pi$
$684$		0			0
$685$		0			0
$686$	−448.608	+	259.004i	−0.653948	+	0.377557i
$687$		0			0
$688$	−3.30680	−	1.90918i	−0.00480640	−	0.00277498i
$689$	−162.650	−	93.9063i	−0.236067	−	0.136294i
$690$		0			0
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	−0.947409	−	0.320025i	$-0.896309\pi$
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	0.196554	−	0.980493i	$-0.437025\pi$
$692$	200.883			0.290293
$693$		0			0
$694$	825.044			1.18882
$695$		0			0
$696$		0			0
$697$	−102.112	−	58.9546i	−0.146503	−	0.0845833i
$698$	221.153	−	383.048i	0.316838	−	0.548779i
$699$		0			0
$700$		0			0
$701$			778.180i			1.11010i	0.831817	+	0.555050i	$0.187301\pi$
$701$			778.180i			1.11010i	−0.831817	+	0.555050i	$0.812699\pi$
$702$		0			0
$703$			81.2714i			0.115607i
$704$	−65.3939	+	37.7552i	−0.0928890	+	0.0536295i
$705$		0			0
$706$	26.5982	−	46.0695i	0.0376745	−	0.0652542i
$707$	−501.311	+	868.296i	−0.709068	+	1.22814i
$708$		0			0
$709$	−586.014	−	1015.01i	−0.826536	−	1.43160i	−0.900739	−	0.434360i	$-0.856975\pi$
$709$	−586.014	−	1015.01i	−0.826536	−	1.43160i	0.0742031	−	0.997243i	$-0.476359\pi$
$710$		0			0
$711$		0			0
$712$			117.031i			0.164369i
$713$	−193.710	−	335.515i	−0.271682	−	0.470568i
$714$		0			0
$715$		0			0
$716$	493.757	+	285.071i	0.689605	+	0.398144i
$717$		0			0
$718$	−360.109	+	207.909i	−0.501545	+	0.289567i
$719$			515.416i			0.716851i	0.933558	+	0.358426i	$0.116686\pi$
$719$			515.416i			0.716851i	−0.933558	+	0.358426i	$0.883314\pi$
$720$		0			0
$721$	184.970			0.256547
$722$	239.666	+	415.114i	0.331947	+	0.574949i
$723$		0			0
$724$	−37.1214	+	64.2962i	−0.0512727	+	0.0888069i
$725$		0			0
$726$		0			0
$727$	728.681	−	420.704i	1.00231	−	0.578685i	0.0933809	−	0.995630i	$-0.470233\pi$
$727$	728.681	−	420.704i	1.00231	−	0.578685i	0.908932	+	0.416945i	$0.136899\pi$
$728$	353.682			0.485827
$729$		0			0
$730$		0			0
$731$	−1.57654	+	0.910215i	−0.00215669	+	0.00124516i
$732$		0			0
$733$	−525.125	−	303.181i	−0.716405	−	0.413617i	0.0970229	−	0.995282i	$-0.469068\pi$
$733$	−525.125	−	303.181i	−0.716405	−	0.413617i	−0.813428	+	0.581665i	$0.802401\pi$
$734$	−40.6946	−	23.4951i	−0.0554423	−	0.0320096i
$735$		0			0
$736$	26.6969	+	46.2405i	0.0362730	+	0.0628267i
$737$	−292.174			−0.396437
$738$		0			0
$739$	389.362			0.526877			0.263439	−	0.964676i	$-0.415143\pi$
$739$	389.362			0.526877			0.263439	+	0.964676i	$0.415143\pi$
$740$		0			0
$741$		0			0
$742$	74.1380	+	42.8036i	0.0999164	+	0.0576868i
$743$	522.375	−	904.779i	0.703061	−	1.21774i	−0.264325	−	0.964434i	$-0.585149\pi$
$743$	522.375	−	904.779i	0.703061	−	1.21774i	0.967387	−	0.253304i	$-0.0815174\pi$
$744$		0			0
$745$		0			0
$746$		−	318.240i		−	0.426595i
$747$		0			0
$748$			36.0000i			0.0481283i
$749$	−944.574	+	545.350i	−1.26111	+	0.728105i
$750$		0			0
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	−0.0117826	−	0.999931i	$-0.503751\pi$
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	0.871857	−	0.489761i	$-0.162916\pi$
$752$	−28.2201	+	48.8786i	−0.0375267	+	0.0649981i
$753$		0			0
$754$	−45.8105	−	79.3460i	−0.0607566	−	0.105233i
$755$		0			0
$756$		0			0
$757$		−	1042.36i		−	1.37697i	−0.725252	−	0.688483i	$-0.758277\pi$
$757$		−	1042.36i		−	1.37697i	0.725252	−	0.688483i	$-0.241723\pi$
$758$	−117.616	−	203.716i	−0.155166	−	0.268755i
$759$		0			0
$760$		0			0
$761$	281.607	+	162.586i	0.370048	+	0.213647i	0.673479	−	0.739206i	$-0.264799\pi$
$761$	281.607	+	162.586i	0.370048	+	0.213647i	−0.303431	+	0.952853i	$0.598132\pi$
$762$		0			0
$763$	639.258	−	369.076i	0.837822	−	0.483717i
$764$			35.8481i			0.0469217i
$765$		0			0
$766$	1042.26			1.36065
$767$	−901.405	−	1561.28i	−1.17523	−	2.03557i
$768$		0			0
$769$	171.348	−	296.783i	0.222819	−	0.385934i	−0.732844	−	0.680397i	$-0.761807\pi$
$769$	171.348	−	296.783i	0.222819	−	0.385934i	0.955663	+	0.294463i	$0.0951407\pi$
$770$		0			0
$771$		0			0
$772$	−165.331	+	95.4541i	−0.214160	+	0.123645i
$773$	532.579			0.688977			0.344488	−	0.938791i	$-0.388052\pi$
$773$	532.579			0.688977			0.344488	+	0.938791i	$0.388052\pi$
$774$		0			0
$775$		0			0
$776$	−234.854	+	135.593i	−0.302646	+	0.174733i
$777$		0			0
$778$	207.439	+	119.765i	0.266631	+	0.153940i
$779$	−251.499	−	145.203i	−0.322849	−	0.186397i
$780$		0			0
$781$	−405.409	−	702.188i	−0.519089	−	0.899089i
$782$	25.4558			0.0325522
$783$		0			0
$784$	34.7878			0.0443721
$785$		0			0
$786$		0			0
$787$	−90.0264	−	51.9768i	−0.114392	−	0.0660442i	0.441712	−	0.897157i	$-0.354371\pi$
$787$	−90.0264	−	51.9768i	−0.114392	−	0.0660442i	−0.556104	+	0.831113i	$0.687704\pi$
$788$	160.363	−	277.757i	0.203507	−	0.352484i
$789$		0			0
$790$		0			0
$791$			1284.07i			1.62335i
$792$		0			0
$793$		−	1479.06i		−	1.86514i
$794$	313.868	−	181.212i	0.395300	−	0.228227i
$795$		0			0
$796$	6.51531	−	11.2848i	0.00818506	−	0.0141769i
$797$	552.138	−	956.331i	0.692770	−	1.19991i	−0.278156	−	0.960536i	$-0.589723\pi$
$797$	552.138	−	956.331i	0.692770	−	1.19991i	0.970927	−	0.239378i	$-0.0769434\pi$
$798$		0			0
$799$	13.4541	+	23.3031i	0.0168386	+	0.0291654i
$800$		0			0
$801$		0			0
$802$			369.650i			0.460911i
$803$	453.491	+	785.469i	0.564746	+	0.978168i
$804$		0			0
$805$		0			0
$806$	990.168	+	571.674i	1.22850	+	0.709273i
$807$		0			0
$808$	386.851	−	223.348i	0.478776	−	0.276421i
$809$			256.465i			0.317015i	0.987358	+	0.158508i	$0.0506683\pi$
$809$			256.465i			0.317015i	−0.987358	+	0.158508i	$0.949332\pi$
$810$		0			0
$811$	735.362			0.906735			0.453368	−	0.891324i	$-0.350222\pi$
$811$	735.362			0.906735			0.453368	+	0.891324i	$0.350222\pi$
$812$	20.8809	+	36.1668i	0.0257154	+	0.0445404i
$813$		0			0
$814$	115.485	−	200.025i	0.141873	−	0.245731i
$815$		0			0
$816$		0			0
$817$	−3.88296	+	2.24183i	−0.00475271	+	0.00274398i
$818$	627.611			0.767250
$819$		0			0
$820$		0			0
$821$	−1078.45	+	622.645i	−1.31358	+	0.758398i	−0.982688	−	0.185269i	$-0.940684\pi$
$821$	−1078.45	+	622.645i	−1.31358	+	0.758398i	−0.330896	+	0.943667i	$0.607351\pi$
$822$		0			0
$823$	1335.63	+	771.129i	1.62288	+	0.936973i	0.986143	+	0.165896i	$0.0530516\pi$
$823$	1335.63	+	771.129i	1.62288	+	0.936973i	0.636742	+	0.771077i	$0.280282\pi$
$824$	−71.3689	−	41.2048i	−0.0866127	−	0.0500059i
$825$		0			0
$826$	410.871	+	711.649i	0.497422	+	0.861560i
$827$	955.707			1.15563			0.577815	−	0.816167i	$-0.303905\pi$
$827$	955.707			1.15563			0.577815	+	0.816167i	$0.303905\pi$
$828$		0			0
$829$	−1082.88			−1.30625			−0.653123	−	0.757252i	$-0.726542\pi$
$829$	−1082.88			−1.30625			−0.653123	+	0.757252i	$0.726542\pi$
$830$		0			0
$831$		0			0
$832$	−136.464	−	78.7878i	−0.164020	−	0.0946968i
$833$	8.29263	−	14.3633i	0.00995514	−	0.0172428i
$834$		0			0
$835$		0			0
$836$			88.6669i			0.106061i
$837$		0			0
$838$		−	15.2281i		−	0.0181719i
$839$	903.778	−	521.797i	1.07721	−	0.621927i	0.147067	−	0.989127i	$-0.453017\pi$
$839$	903.778	−	521.797i	1.07721	−	0.621927i	0.930142	+	0.367200i	$0.119683\pi$
$840$		0			0
$841$	−415.091	+	718.958i	−0.493568	+	0.854885i
$842$	−179.819	+	311.456i	−0.213562	+	0.369901i
$843$		0			0
$844$	154.439	+	267.497i	0.182985	+	0.316939i
$845$		0			0
$846$		0			0
$847$		−	202.574i		−	0.239167i
$848$	−19.0702	−	33.0306i	−0.0224885	−	0.0389512i
$849$		0			0
$850$		0			0
$851$	−141.439	−	81.6600i	−0.166204	−	0.0959577i
$852$		0			0
$853$	410.338	−	236.909i	0.481053	−	0.277736i	−0.239802	−	0.970822i	$-0.577083\pi$
$853$	410.338	−	236.909i	0.481053	−	0.277736i	0.720855	+	0.693086i	$0.243749\pi$
$854$			674.172i			0.789429i
$855$		0			0
$856$	485.939			0.567685
$857$	458.381	+	793.939i	0.534867	+	0.926417i	0.999170	+	0.0407403i	$0.0129716\pi$
$857$	458.381	+	793.939i	0.534867	+	0.926417i	−0.464303	+	0.885677i	$0.653695\pi$
$858$		0			0
$859$	478.901	−	829.480i	0.557510	−	0.965635i	−0.440194	−	0.897903i	$-0.645090\pi$
$859$	478.901	−	829.480i	0.557510	−	0.965635i	0.997704	−	0.0677322i	$-0.0215764\pi$
$860$		0			0
$861$		0			0
$862$	−855.684	+	494.030i	−0.992673	+	0.573120i
$863$	524.200			0.607416			0.303708	−	0.952765i	$-0.401775\pi$
$863$	524.200			0.607416			0.303708	+	0.952765i	$0.401775\pi$
$864$		0			0
$865$		0			0
$866$	259.312	−	149.714i	0.299437	−	0.172880i
$867$		0			0
$868$	−451.330	−	260.576i	−0.519965	−	0.300202i
$869$	−243.121	−	140.366i	−0.279771	−	0.161526i
$870$		0			0
$871$	−304.855	−	528.025i	−0.350006	−	0.606228i
$872$	−328.868			−0.377142
$873$		0			0
$874$	62.6969			0.0717356
$875$		0			0
$876$		0			0
$877$	872.742	+	503.878i	0.995145	+	0.574547i	0.906808	−	0.421543i	$-0.138511\pi$
$877$	872.742	+	503.878i	0.995145	+	0.574547i	0.0883370	+	0.996091i	$0.471845\pi$
$878$	197.893	−	342.760i	0.225390	−	0.390388i
$879$		0			0
$880$		0			0
$881$			1536.71i			1.74428i	0.489254	+	0.872141i	$0.337269\pi$
$881$			1536.71i			1.74428i	−0.489254	+	0.872141i	$0.662731\pi$
$882$		0			0
$883$		−	294.213i		−	0.333197i	−0.986025	−	0.166599i	$-0.946722\pi$
$883$		−	294.213i		−	0.333197i	0.986025	−	0.166599i	$-0.0532784\pi$
$884$	−65.0602	+	37.5625i	−0.0735975	+	0.0424915i
$885$		0			0
$886$	389.796	−	675.146i	0.439950	−	0.762016i
$887$	287.402	−	497.794i	0.324015	−	0.561211i	−0.657297	−	0.753631i	$-0.728300\pi$
$887$	287.402	−	497.794i	0.324015	−	0.561211i	0.981313	+	0.192420i	$0.0616337\pi$
$888$		0			0
$889$	32.0306	+	55.4787i	0.0360299	+	0.0624057i
$890$		0			0
$891$		0			0
$892$			185.546i			0.208011i
$893$	33.1370	+	57.3949i	0.0371075	+	0.0642720i
$894$		0			0
$895$		0			0
$896$	62.2020	+	35.9124i	0.0694219	+	0.0400808i
$897$		0			0
$898$	664.872	−	383.864i	0.740391	−	0.427465i
$899$			135.004i			0.150171i
$900$		0			0
$901$	−18.1837			−0.0201817
$902$	412.661	+	714.749i	0.457495	+	0.792405i
$903$		0			0
$904$	286.045	−	495.445i	0.316422	−	0.548059i
$905$		0			0
$906$		0			0
$907$	441.737	−	255.037i	0.487031	−	0.281187i	−0.236311	−	0.971677i	$-0.575938\pi$
$907$	441.737	−	255.037i	0.487031	−	0.281187i	0.723342	+	0.690490i	$0.242605\pi$
$908$	−339.604			−0.374013
$909$		0			0
$910$		0			0
$911$	803.127	−	463.685i	0.881588	−	0.508985i	0.0104064	−	0.999946i	$-0.496687\pi$
$911$	803.127	−	463.685i	0.881588	−	0.508985i	0.871182	+	0.490961i	$0.163354\pi$
$912$		0			0
$913$	−718.564	−	414.863i	−0.787036	−	0.454396i
$914$	113.123	+	65.3114i	0.123767	+	0.0714567i
$915$		0			0
$916$	407.545	+	705.888i	0.444918	+	0.770621i
$917$	31.4897			0.0343399
$918$		0			0
$919$	1240.63			1.34998			0.674991	−	0.737826i	$-0.264147\pi$
$919$	1240.63			1.34998			0.674991	+	0.737826i	$0.264147\pi$
$920$		0			0
$921$		0			0
$922$	−281.471	−	162.507i	−0.305283	−	0.176255i
$923$	846.010	−	1465.33i	0.916587	−	1.58757i
$924$		0			0
$925$		0			0
$926$		−	722.384i		−	0.780112i
$927$		0			0
$928$		−	18.6061i		−	0.0200497i
$929$	293.576	−	169.496i	0.316013	−	0.182450i	−0.333601	−	0.942714i	$-0.608264\pi$
$929$	293.576	−	169.496i	0.316013	−	0.182450i	0.649614	+	0.760264i	$0.274931\pi$
$930$		0			0
$931$	20.4245	−	35.3763i	0.0219382	−	0.0379981i
$932$	−15.2562	+	26.4245i	−0.0163693	+	0.0283525i
$933$		0			0
$934$	−589.485	−	1021.02i	−0.631140	−	1.09317i
$935$		0			0
$936$		0			0
$937$		−	1322.21i		−	1.41111i	−0.708655	−	0.705556i	$-0.750698\pi$
$937$		−	1322.21i		−	1.41111i	0.708655	−	0.705556i	$-0.249302\pi$
$938$	138.957	+	240.680i	0.148141	+	0.256588i
$939$		0			0
$940$		0			0
$941$	310.984	+	179.547i	0.330482	+	0.190804i	0.656055	−	0.754713i	$-0.272224\pi$
$941$	310.984	+	179.547i	0.330482	+	0.190804i	−0.325573	+	0.945517i	$0.605557\pi$
$942$		0			0
$943$	505.404	−	291.795i	0.535953	−	0.309433i
$944$		−	366.110i		−	0.387828i
$945$		0			0
$946$	12.7423			0.0134697
$947$	−387.896	−	671.855i	−0.409605	−	0.709457i	0.585240	−	0.810860i	$-0.301000\pi$
$947$	−387.896	−	671.855i	−0.409605	−	0.709457i	−0.994845	+	0.101403i	$0.967667\pi$
$948$		0			0
$949$	−946.347	+	1639.12i	−0.997205	+	1.72721i
$950$		0			0
$951$		0			0
$952$	29.6552	−	17.1214i	0.0311504	−	0.0179847i
$953$	465.082			0.488019			0.244010	−	0.969773i	$-0.421537\pi$
$953$	465.082			0.488019			0.244010	+	0.969773i	$0.421537\pi$
$954$		0			0
$955$		0			0
$956$	−97.9240	+	56.5364i	−0.102431	+	0.0591385i
$957$		0			0
$958$	−804.891	−	464.704i	−0.840178	−	0.485077i
$959$	−1290.28	−	744.942i	−1.34544	−	0.776791i
$960$		0			0
$961$	−361.863	−	626.765i	−0.376548	−	0.652200i
$962$	481.989			0.501028
$963$		0			0
$964$	168.424			0.174714
$965$		0			0
$966$		0			0
$967$	1060.21	+	612.113i	1.09639	+	0.633002i	0.935271	−	0.353933i	$-0.115156\pi$
$967$	1060.21	+	612.113i	1.09639	+	0.633002i	0.161121	+	0.986935i	$0.448489\pi$
$968$	−45.1264	+	78.1612i	−0.0466182	+	0.0807451i
$969$		0			0
$970$		0			0
$971$		−	658.702i		−	0.678375i	−0.940719	−	0.339188i	$-0.889848\pi$
$971$		−	658.702i		−	0.678375i	0.940719	−	0.339188i	$-0.110152\pi$
$972$		0			0
$973$			676.303i			0.695070i
$974$	430.702	−	248.666i	0.442199	−	0.255304i
$975$		0			0
$976$	150.182	−	260.122i	0.153875	−	0.266519i
$977$	−759.170	+	1314.92i	−0.777042	+	1.34588i	0.156597	+	0.987663i	$0.449948\pi$
$977$	−759.170	+	1314.92i	−0.777042	+	1.34588i	−0.933639	+	0.358214i	$0.883386\pi$
$978$		0			0
$979$	−195.272	−	338.222i	−0.199461	−	0.345477i
$980$		0			0
$981$		0			0
$982$			347.074i			0.353436i
$983$	−413.920	−	716.930i	−0.421078	−	0.729329i	0.574967	−	0.818177i	$-0.305015\pi$
$983$	−413.920	−	716.930i	−0.421078	−	0.729329i	−0.996045	+	0.0888477i	$0.971682\pi$
$984$		0			0
$985$		0			0
$986$	−7.68215	−	4.43529i	−0.00779122	−	0.00449826i
$987$		0			0
$988$	−160.241	+	92.5153i	−0.162187	+	0.0936390i
$989$		−	9.01020i		−	0.00911041i
$990$		0			0
$991$	429.546			0.433447			0.216723	−	0.976233i	$-0.430463\pi$
$991$	429.546			0.433447			0.216723	+	0.976233i	$0.430463\pi$
$992$	116.094	+	201.081i	0.117030	+	0.202702i
$993$		0			0
$994$	−385.621	+	667.915i	−0.387949	+	0.671947i
$995$		0			0
$996$		0			0
$997$	601.886	−	347.499i	0.603697	−	0.348545i	−0.166798	−	0.985991i	$-0.553343\pi$
$997$	601.886	−	347.499i	0.603697	−	0.348545i	0.770495	+	0.637447i	$0.220009\pi$
$998$	−891.274			−0.893060
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.3.k.a.449.2		8
3.2	odd	2		450.3.k.a.149.3		8
5.2	odd	4		54.3.d.a.17.2		4
5.3	odd	4		1350.3.i.b.1151.1		4
5.4	even	2	inner	1350.3.k.a.449.3		8
9.2	odd	6	inner	1350.3.k.a.899.3		8
9.7	even	3		450.3.k.a.299.2		8
15.2	even	4		18.3.d.a.5.1	✓	4
15.8	even	4		450.3.i.b.401.2		4
15.14	odd	2		450.3.k.a.149.2		8
20.7	even	4		432.3.q.d.17.2		4
40.27	even	4		1728.3.q.c.449.2		4
40.37	odd	4		1728.3.q.d.449.1		4
45.2	even	12		54.3.d.a.35.2		4
45.7	odd	12		18.3.d.a.11.1	yes	4
45.22	odd	12		162.3.b.a.161.3		4
45.29	odd	6	inner	1350.3.k.a.899.2		8
45.32	even	12		162.3.b.a.161.2		4
45.34	even	6		450.3.k.a.299.3		8
45.38	even	12		1350.3.i.b.251.1		4
45.43	odd	12		450.3.i.b.101.2		4
60.47	odd	4		144.3.q.c.113.1		4
120.77	even	4		576.3.q.f.257.1		4
120.107	odd	4		576.3.q.e.257.2		4
180.7	even	12		144.3.q.c.65.1		4
180.47	odd	12		432.3.q.d.305.2		4
180.67	even	12		1296.3.e.g.161.1		4
180.167	odd	12		1296.3.e.g.161.3		4
360.187	even	12		576.3.q.e.65.2		4
360.227	odd	12		1728.3.q.c.1601.2		4
360.277	odd	12		576.3.q.f.65.1		4
360.317	even	12		1728.3.q.d.1601.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.1	✓	4	15.2	even	4
18.3.d.a.11.1	yes	4	45.7	odd	12
54.3.d.a.17.2		4	5.2	odd	4
54.3.d.a.35.2		4	45.2	even	12
144.3.q.c.65.1		4	180.7	even	12
144.3.q.c.113.1		4	60.47	odd	4
162.3.b.a.161.2		4	45.32	even	12
162.3.b.a.161.3		4	45.22	odd	12
432.3.q.d.17.2		4	20.7	even	4
432.3.q.d.305.2		4	180.47	odd	12
450.3.i.b.101.2		4	45.43	odd	12
450.3.i.b.401.2		4	15.8	even	4
450.3.k.a.149.2		8	15.14	odd	2
450.3.k.a.149.3		8	3.2	odd	2
450.3.k.a.299.2		8	9.7	even	3
450.3.k.a.299.3		8	45.34	even	6
576.3.q.e.65.2		4	360.187	even	12
576.3.q.e.257.2		4	120.107	odd	4
576.3.q.f.65.1		4	360.277	odd	12
576.3.q.f.257.1		4	120.77	even	4
1296.3.e.g.161.1		4	180.67	even	12
1296.3.e.g.161.3		4	180.167	odd	12
1350.3.i.b.251.1		4	45.38	even	12
1350.3.i.b.1151.1		4	5.3	odd	4
1350.3.k.a.449.2		8	1.1	even	1	trivial
1350.3.k.a.449.3		8	5.4	even	2	inner
1350.3.k.a.899.2		8	45.29	odd	6	inner
1350.3.k.a.899.3		8	9.2	odd	6	inner
1728.3.q.c.449.2		4	40.27	even	4
1728.3.q.c.1601.2		4	360.227	odd	12
1728.3.q.d.449.1		4	40.37	odd	4
1728.3.q.d.1601.1		4	360.317	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1350.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-5.49794 + 3.17423i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-5.49794 + 3.17423i) q^{7} +2.82843 q^{8} +(-8.17423 + 4.71940i) q^{11} +(-17.0580 - 9.84847i) q^{13} +(7.77526 + 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702 q^{17} -4.69694 q^{19} +(11.5601 + 6.67423i) q^{22} +(4.71940 - 8.17423i) q^{23} +27.8557i q^{26} -12.6969i q^{28} +(-2.84847 + 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(1.34847 + 2.33562i) q^{34} -17.3031i q^{37} +(3.32124 + 5.75255i) q^{38} +(53.5454 + 30.9145i) q^{41} +(0.826701 - 0.477296i) q^{43} -18.8776i q^{44} -13.3485 q^{46} +(-7.05501 - 12.2196i) q^{47} +(-4.34847 + 7.53177i) q^{49} +(34.1161 - 19.6969i) q^{52} +9.53512 q^{53} +(-15.5505 + 8.97809i) q^{56} +(4.02834 + 2.32577i) q^{58} +(79.2650 + 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470 q^{62} +8.00000 q^{64} +(26.8075 + 15.4773i) q^{67} +(1.90702 - 3.30306i) q^{68} +85.9026i q^{71} -96.0908i q^{73} +(-21.1918 + 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(29.9609 - 51.8939i) q^{77} +(14.8712 + 25.7576i) q^{79} -87.4393i q^{82} +(43.9530 + 76.1288i) q^{83} +(-1.16913 - 0.674999i) q^{86} +(-23.1202 + 13.3485i) q^{88} +41.3766i q^{89} +125.045 q^{91} +(9.43879 + 16.3485i) q^{92} +(-9.97730 + 17.2812i) q^{94} +(-83.0333 + 47.9393i) q^{97} +12.2993 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} - 36 q^{11} + 72 q^{14} - 16 q^{16} + 80 q^{19} + 36 q^{29} + 76 q^{31} - 48 q^{34} + 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{56} + 252 q^{59} + 124 q^{61} + 64 q^{64} + 144 q^{74} - 80 q^{76} - 28 q^{79} + 216 q^{86} + 824 q^{91} - 168 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 - 36 * q^11 + 72 * q^14 - 16 * q^16 + 80 * q^19 + 36 * q^29 + 76 * q^31 - 48 * q^34 + 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^56 + 252 * q^59 + 124 * q^61 + 64 * q^64 + 144 * q^74 - 80 * q^76 - 28 * q^79 + 216 * q^86 + 824 * q^91 - 168 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more