LMFDB - Embedded newform 105.3.o.b.44.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(44,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("105.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.10
Character	$\chi$	$=$	105.44
Dual form			105.3.o.b.74.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0859580 + 0.148884i) q^{2} +(2.40718 + 1.79039i) q^{3} +(1.98522 + 3.43851i) q^{4} +(-1.39092 - 4.80264i) q^{5} +(-0.473476 + 0.204491i) q^{6} +(6.99566 - 0.246384i) q^{7} -1.37025 q^{8} +(2.58900 + 8.61957i) q^{9} +O(q^{10})$	\(q+(-0.0859580 + 0.148884i) q^{2} +(2.40718 + 1.79039i) q^{3} +(1.98522 + 3.43851i) q^{4} +(-1.39092 - 4.80264i) q^{5} +(-0.473476 + 0.204491i) q^{6} +(6.99566 - 0.246384i) q^{7} -1.37025 q^{8} +(2.58900 + 8.61957i) q^{9} +(0.834595 + 0.205740i) q^{10} +(-10.0440 + 5.79890i) q^{11} +(-1.37749 + 11.8314i) q^{12} -7.34521i q^{13} +(-0.564650 + 1.06272i) q^{14} +(5.25042 - 14.0511i) q^{15} +(-7.82311 + 13.5500i) q^{16} +(2.30611 + 3.99429i) q^{17} +(-1.50586 - 0.355461i) q^{18} +(5.93904 - 10.2867i) q^{19} +(13.7526 - 14.3170i) q^{20} +(17.2809 + 11.9319i) q^{21} -1.99385i q^{22} +(11.8464 - 20.5186i) q^{23} +(-3.29843 - 2.45328i) q^{24} +(-21.1307 + 13.3601i) q^{25} +(1.09358 + 0.631380i) q^{26} +(-9.20022 + 25.3842i) q^{27} +(14.7351 + 23.5655i) q^{28} -32.7592i q^{29} +(1.64066 + 1.98950i) q^{30} +(-23.4865 - 40.6798i) q^{31} +(-4.08541 - 7.07614i) q^{32} +(-34.5599 - 4.02368i) q^{33} -0.792913 q^{34} +(-10.9137 - 33.2549i) q^{35} +(-24.4987 + 26.0141i) q^{36} +(-41.2822 - 23.8343i) q^{37} +(1.02102 + 1.76845i) q^{38} +(13.1508 - 17.6812i) q^{39} +(1.90590 + 6.58080i) q^{40} +70.7266i q^{41} +(-3.26189 + 1.54721i) q^{42} -14.1244i q^{43} +(-39.8791 - 23.0242i) q^{44} +(37.7956 - 24.4232i) q^{45} +(2.03658 + 3.52747i) q^{46} +(26.1140 - 45.2307i) q^{47} +(-43.0914 + 18.6109i) q^{48} +(48.8786 - 3.44723i) q^{49} +(-0.172755 - 4.29442i) q^{50} +(-1.60014 + 13.7438i) q^{51} +(25.2566 - 14.5819i) q^{52} +(11.5105 + 19.9368i) q^{53} +(-2.98845 - 3.55173i) q^{54} +(41.8204 + 40.1718i) q^{55} +(-9.58578 + 0.337606i) q^{56} +(32.7136 - 14.1288i) q^{57} +(4.87730 + 2.81591i) q^{58} +(1.09721 - 0.633473i) q^{59} +(58.7380 - 9.84095i) q^{60} +(-32.3278 + 55.9933i) q^{61} +8.07541 q^{62} +(20.2355 + 59.6617i) q^{63} -61.1802 q^{64} +(-35.2764 + 10.2166i) q^{65} +(3.56976 - 4.79954i) q^{66} +(-17.1764 + 9.91678i) q^{67} +(-9.15627 + 15.8591i) q^{68} +(65.2526 - 28.1821i) q^{69} +(5.88923 + 1.23366i) q^{70} +48.1993i q^{71} +(-3.54757 - 11.8109i) q^{72} +(107.763 - 62.2168i) q^{73} +(7.09706 - 4.09749i) q^{74} +(-74.7852 - 5.67196i) q^{75} +47.1613 q^{76} +(-68.8356 + 43.0418i) q^{77} +(1.50203 + 3.47778i) q^{78} +(-34.4509 + 59.6707i) q^{79} +(75.9571 + 18.7246i) q^{80} +(-67.5941 + 44.6322i) q^{81} +(-10.5300 - 6.07951i) q^{82} -35.8731 q^{83} +(-6.72137 + 83.1080i) q^{84} +(15.9756 - 16.6311i) q^{85} +(2.10289 + 1.21410i) q^{86} +(58.6517 - 78.8571i) q^{87} +(13.7627 - 7.94592i) q^{88} +(110.539 + 63.8196i) q^{89} +(0.387373 + 7.72651i) q^{90} +(-1.80974 - 51.3846i) q^{91} +94.0709 q^{92} +(16.2966 - 139.974i) q^{93} +(4.48941 + 7.77588i) q^{94} +(-57.6641 - 14.2151i) q^{95} +(2.83474 - 24.3480i) q^{96} +26.9526i q^{97} +(-3.68827 + 7.57354i) q^{98} +(-75.9879 - 71.5615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9}+O(q^{10}) $ 40 * q - 44 * q^4 + 80 * q^6 + 12 * q^9	$ 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9} + 62 q^{10} + 84 q^{15} - 116 q^{16} - 56 q^{19} + 36 q^{21} - 12 q^{24} - 6 q^{25} - 20 q^{30} - 444 q^{31} + 256 q^{34} - 688 q^{36} + 168 q^{39} + 54 q^{40} - 40 q^{45} + 304 q^{46} + 156 q^{49} + 156 q^{51} - 140 q^{54} - 500 q^{55} - 130 q^{60} + 288 q^{61} + 472 q^{64} + 340 q^{66} - 272 q^{69} + 710 q^{70} - 524 q^{75} + 400 q^{76} - 340 q^{79} + 496 q^{84} + 896 q^{85} + 1356 q^{90} - 656 q^{91} - 560 q^{94} + 472 q^{96} - 336 q^{99}+O(q^{100}) $ 40 * q - 44 * q^4 + 80 * q^6 + 12 * q^9 + 62 * q^10 + 84 * q^15 - 116 * q^16 - 56 * q^19 + 36 * q^21 - 12 * q^24 - 6 * q^25 - 20 * q^30 - 444 * q^31 + 256 * q^34 - 688 * q^36 + 168 * q^39 + 54 * q^40 - 40 * q^45 + 304 * q^46 + 156 * q^49 + 156 * q^51 - 140 * q^54 - 500 * q^55 - 130 * q^60 + 288 * q^61 + 472 * q^64 + 340 * q^66 - 272 * q^69 + 710 * q^70 - 524 * q^75 + 400 * q^76 - 340 * q^79 + 496 * q^84 + 896 * q^85 + 1356 * q^90 - 656 * q^91 - 560 * q^94 + 472 * q^96 - 336 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.0859580	+	0.148884i	−0.0429790	+	0.0744418i	−0.886715	−	0.462317i	$-0.847018\pi$
$2$	−0.0859580	+	0.148884i	−0.0429790	+	0.0744418i	0.843736	+	0.536759i	$0.180352\pi$
$3$	2.40718	+	1.79039i	0.802392	+	0.596797i
$3$	2.40718	+	1.79039i	0.802392	+	0.596797i
$4$	1.98522	+	3.43851i	0.496306	+	0.859627i
$5$	−1.39092	−	4.80264i	−0.278183	−	0.960528i
$5$	−1.39092	−	4.80264i	−0.278183	−	0.960528i
$6$	−0.473476	+	0.204491i	−0.0789126	+	0.0340818i
$7$	6.99566	−	0.246384i	0.999380	−	0.0351977i
$7$	6.99566	−	0.246384i	0.999380	−	0.0351977i
$8$	−1.37025			−0.171281
$9$	2.58900	+	8.61957i	0.287667	+	0.957730i
$10$	0.834595	+	0.205740i	0.0834595	+	0.0205740i
$11$	−10.0440	+	5.79890i	−0.913089	+	0.527172i	−0.881424	−	0.472326i	$-0.843414\pi$
$11$	−10.0440	+	5.79890i	−0.913089	+	0.527172i	−0.0316655	+	0.999499i	$0.510081\pi$
$12$	−1.37749	+	11.8314i	−0.114791	+	0.985951i
$13$		−	7.34521i		−	0.565016i	−0.959265	−	0.282508i	$-0.908834\pi$
$13$		−	7.34521i		−	0.565016i	0.959265	−	0.282508i	$-0.0911665\pi$
$14$	−0.564650	+	1.06272i	−0.0403322	+	0.0759084i
$15$	5.25042	−	14.0511i	0.350028	−	0.936739i
$16$	−7.82311	+	13.5500i	−0.488944	+	0.846876i
$17$	2.30611	+	3.99429i	0.135653	+	0.234958i	0.925847	−	0.377899i	$-0.123353\pi$
$17$	2.30611	+	3.99429i	0.135653	+	0.234958i	−0.790194	+	0.612857i	$0.790020\pi$
$18$	−1.50586	−	0.355461i	−0.0836588	−	0.0197478i
$19$	5.93904	−	10.2867i	0.312581	−	0.541406i	−0.666339	−	0.745649i	$-0.732140\pi$
$19$	5.93904	−	10.2867i	0.312581	−	0.541406i	0.978920	+	0.204242i	$0.0654730\pi$
$20$	13.7526	−	14.3170i	0.687631	−	0.715849i
$21$	17.2809	+	11.9319i	0.822901	+	0.568185i
$22$		−	1.99385i		−	0.0906293i
$23$	11.8464	−	20.5186i	0.515061	−	0.892111i	−0.484786	−	0.874633i	$-0.661103\pi$
$23$	11.8464	−	20.5186i	0.515061	−	0.892111i	0.999847	−	0.0174789i	$-0.00556398\pi$
$24$	−3.29843	−	2.45328i	−0.137434	−	0.102220i
$25$	−21.1307	+	13.3601i	−0.845228	+	0.534406i
$26$	1.09358	+	0.631380i	0.0420608	+	0.0242838i
$27$	−9.20022	+	25.3842i	−0.340749	+	0.940154i
$28$	14.7351	+	23.5655i	0.526255	+	0.841625i
$29$		−	32.7592i		−	1.12963i	−0.825219	−	0.564813i	$-0.808948\pi$
$29$		−	32.7592i		−	1.12963i	0.825219	−	0.564813i	$-0.191052\pi$
$30$	1.64066	+	1.98950i	0.0546887	+	0.0663168i
$31$	−23.4865	−	40.6798i	−0.757629	−	1.31225i	−0.944057	−	0.329784i	$-0.893024\pi$
$31$	−23.4865	−	40.6798i	−0.757629	−	1.31225i	0.186427	−	0.982469i	$-0.440309\pi$
$32$	−4.08541	−	7.07614i	−0.127669	−	0.221129i
$33$	−34.5599	−	4.02368i	−1.04727	−	0.121930i
$34$	−0.792913			−0.0233210
$35$	−10.9137	−	33.2549i	−0.311819	−	0.950141i
$36$	−24.4987	+	26.0141i	−0.680520	+	0.722613i
$37$	−41.2822	−	23.8343i	−1.11573	−	0.644170i	−0.175426	−	0.984493i	$-0.556130\pi$
$37$	−41.2822	−	23.8343i	−1.11573	−	0.644170i	−0.940309	+	0.340323i	$0.889464\pi$
$38$	1.02102	+	1.76845i	0.0268688	+	0.0465382i
$39$	13.1508	−	17.6812i	0.337200	−	0.453365i
$40$	1.90590	+	6.58080i	0.0476475	+	0.164520i
$41$			70.7266i			1.72504i	0.506024	+	0.862520i	$0.331115\pi$
$41$			70.7266i			1.72504i	−0.506024	+	0.862520i	$0.668885\pi$
$42$	−3.26189	+	1.54721i	−0.0776641	+	0.0368382i
$43$		−	14.1244i		−	0.328474i	−0.986421	−	0.164237i	$-0.947484\pi$
$43$		−	14.1244i		−	0.328474i	0.986421	−	0.164237i	$-0.0525162\pi$
$44$	−39.8791	−	23.0242i	−0.906343	−	0.523277i
$45$	37.7956	−	24.4232i	0.839903	−	0.542737i
$46$	2.03658	+	3.52747i	0.0442736	+	0.0766841i
$47$	26.1140	−	45.2307i	0.555616	−	0.962356i	−0.442239	−	0.896897i	$-0.645816\pi$
$47$	26.1140	−	45.2307i	0.555616	−	0.962356i	0.997855	−	0.0654585i	$-0.0208510\pi$
$48$	−43.0914	+	18.6109i	−0.897738	+	0.387727i
$49$	48.8786	−	3.44723i	0.997522	−	0.0703517i
$50$	−0.172755	−	4.29442i	−0.00345509	−	0.0858885i
$51$	−1.60014	+	13.7438i	−0.0313753	+	0.269486i
$52$	25.2566	−	14.5819i	0.485703	−	0.280421i
$53$	11.5105	+	19.9368i	0.217179	+	0.376166i	0.953945	−	0.299983i	$-0.0969810\pi$
$53$	11.5105	+	19.9368i	0.217179	+	0.376166i	−0.736765	+	0.676149i	$0.763648\pi$
$54$	−2.98845	−	3.55173i	−0.0553417	−	0.0657728i
$55$	41.8204	+	40.1718i	0.760370	+	0.730397i
$56$	−9.58578	+	0.337606i	−0.171175	+	0.00602868i
$57$	32.7136	−	14.1288i	0.573922	−	0.247873i
$58$	4.87730	+	2.81591i	0.0840914	+	0.0485502i
$59$	1.09721	−	0.633473i	0.0185967	−	0.0107368i	−0.490673	−	0.871344i	$-0.663249\pi$
$59$	1.09721	−	0.633473i	0.0185967	−	0.0107368i	0.509270	+	0.860607i	$0.329916\pi$
$60$	58.7380	−	9.84095i	0.978967	−	0.164016i
$61$	−32.3278	+	55.9933i	−0.529963	+	0.917923i	0.469426	+	0.882972i	$0.344461\pi$
$61$	−32.3278	+	55.9933i	−0.529963	+	0.917923i	−0.999389	+	0.0349515i	$0.988872\pi$
$62$	8.07541			0.130249
$63$	20.2355	+	59.6617i	0.321199	+	0.947012i
$64$	−61.1802			−0.955940
$65$	−35.2764	+	10.2166i	−0.542714	+	0.157178i
$66$	3.56976	−	4.79954i	0.0540873	−	0.0727203i
$67$	−17.1764	+	9.91678i	−0.256364	+	0.148012i	−0.622675	−	0.782481i	$-0.713954\pi$
$67$	−17.1764	+	9.91678i	−0.256364	+	0.148012i	0.366311	+	0.930493i	$0.380621\pi$
$68$	−9.15627	+	15.8591i	−0.134651	+	0.233222i
$69$	65.2526	−	28.1821i	0.945690	−	0.408437i
$70$	5.88923	+	1.23366i	0.0841319	+	0.0176237i
$71$			48.1993i			0.678863i	0.940631	+	0.339432i	$0.110235\pi$
$71$			48.1993i			0.678863i	−0.940631	+	0.339432i	$0.889765\pi$
$72$	−3.54757	−	11.8109i	−0.0492718	−	0.164041i
$73$	107.763	−	62.2168i	1.47620	−	0.852285i	0.476562	−	0.879141i	$-0.341883\pi$
$73$	107.763	−	62.2168i	1.47620	−	0.852285i	0.999639	+	0.0268558i	$0.00854949\pi$
$74$	7.09706	−	4.09749i	0.0959063	−	0.0553715i
$75$	−74.7852	−	5.67196i	−0.997136	−	0.0756262i
$76$	47.1613			0.620543
$77$	−68.8356	+	43.0418i	−0.893968	+	0.558984i
$78$	1.50203	+	3.47778i	0.0192568	+	0.0445869i
$79$	−34.4509	+	59.6707i	−0.436087	+	0.755325i	−0.997384	−	0.0722896i	$-0.976969\pi$
$79$	−34.4509	+	59.6707i	−0.436087	+	0.755325i	0.561296	+	0.827615i	$0.310303\pi$
$80$	75.9571	+	18.7246i	0.949464	+	0.234058i
$81$	−67.5941	+	44.6322i	−0.834495	+	0.551015i
$82$	−10.5300	−	6.07951i	−0.128415	−	0.0741404i
$83$	−35.8731			−0.432206			−0.216103	−	0.976371i	$-0.569335\pi$
$83$	−35.8731			−0.432206			−0.216103	+	0.976371i	$0.569335\pi$
$84$	−6.72137	+	83.1080i	−0.0800163	+	0.989381i
$85$	15.9756	−	16.6311i	0.187948	−	0.195660i
$86$	2.10289	+	1.21410i	0.0244522	+	0.0141175i
$87$	58.6517	−	78.8571i	0.674158	−	0.906404i
$88$	13.7627	−	7.94592i	0.156395	−	0.0902945i
$89$	110.539	+	63.8196i	1.24201	+	0.717074i	0.969503	−	0.245080i	$-0.0788143\pi$
$89$	110.539	+	63.8196i	1.24201	+	0.717074i	0.272506	+	0.962154i	$0.412148\pi$
$90$	0.387373	+	7.72651i	0.00430414	+	0.0858501i
$91$	−1.80974	−	51.3846i	−0.0198873	−	0.564666i
$92$	94.0709			1.02251
$93$	16.2966	−	139.974i	0.175232	−	1.50509i
$94$	4.48941	+	7.77588i	0.0477597	+	0.0827221i
$95$	−57.6641	−	14.2151i	−0.606991	−	0.149633i
$96$	2.83474	−	24.3480i	0.0295286	−	0.253625i
$97$			26.9526i			0.277862i	0.990302	+	0.138931i	$0.0443666\pi$
$97$			26.9526i			0.277862i	−0.990302	+	0.138931i	$0.955633\pi$
$98$	−3.68827	+	7.57354i	−0.0376354	+	0.0772810i
$99$	−75.9879	−	71.5615i	−0.767555	−	0.722843i
$100$	−87.8881	−	46.1352i	−0.878881	−	0.461352i
$101$	15.8571	−	9.15508i	0.157001	−	0.0906444i	−0.419441	−	0.907782i	$-0.637774\pi$
$101$	15.8571	−	9.15508i	0.157001	−	0.0906444i	0.576442	+	0.817138i	$0.304441\pi$
$102$	−1.90868	−	1.41962i	−0.0187126	−	0.0139179i
$103$	26.9167	+	15.5404i	0.261327	+	0.150877i	0.624940	−	0.780673i	$-0.285123\pi$
$103$	26.9167	+	15.5404i	0.261327	+	0.150877i	−0.363613	+	0.931550i	$0.618457\pi$
$104$			10.0648i			0.0967765i
$105$	33.2682	−	99.5903i	0.316840	−	0.948479i
$106$	−3.95768			−0.0373366
$107$	−91.2333	+	158.021i	−0.852648	+	1.47683i	0.0261619	+	0.999658i	$0.491671\pi$
$107$	−91.2333	+	158.021i	−0.852648	+	1.47683i	−0.878810	+	0.477172i	$0.841662\pi$
$108$	−105.548	+	18.7582i	−0.977297	+	0.173687i
$109$	17.0498	+	29.5311i	0.156420	+	0.270928i	0.933575	−	0.358381i	$-0.116671\pi$
$109$	17.0498	+	29.5311i	0.156420	+	0.270928i	−0.777155	+	0.629309i	$0.783338\pi$
$110$	−9.57572	+	2.77327i	−0.0870520	+	0.0252116i
$111$	−56.7009	−	131.285i	−0.510819	−	1.18274i
$112$	−51.3893	+	96.7188i	−0.458833	+	0.863561i
$113$	−64.0417			−0.566740			−0.283370	−	0.959011i	$-0.591453\pi$
$113$	−64.0417			−0.566740			−0.283370	+	0.959011i	$0.591453\pi$
$114$	−0.708453	+	6.08499i	−0.00621450	+	0.0533771i
$115$	−115.021	−	28.3544i	−1.00018	−	0.246560i
$116$	112.643	−	65.0342i	0.971057	−	0.560640i
$117$	63.3126	−	19.0168i	0.541134	−	0.162537i
$118$			0.217808i			0.00184583i
$119$	17.1169	+	27.3745i	0.143839	+	0.230038i
$120$	−7.19437	+	19.2535i	−0.0599530	+	0.160445i
$121$	6.75440	−	11.6990i	0.0558215	−	0.0966857i
$122$	−5.55766	−	9.62615i	−0.0455546	−	0.0789028i
$123$	−126.628	+	170.251i	−1.02950	+	1.38416i
$124$	93.2519	−	161.517i	0.752031	−	1.30256i
$125$	93.5550	+	82.9003i	0.748440	+	0.663202i
$126$	−10.6221	−	2.11567i	−0.0843020	−	0.0167910i
$127$			131.997i			1.03934i	0.854366	+	0.519672i	$0.173946\pi$
$127$			131.997i			1.03934i	−0.854366	+	0.519672i	$0.826054\pi$
$128$	21.6006	−	37.4133i	0.168754	−	0.292291i
$129$	25.2882	−	33.9999i	0.196032	−	0.263565i
$130$	1.51121	−	6.13028i	0.0116247	−	0.0471560i
$131$	−69.4990	−	40.1253i	−0.530527	−	0.306300i	0.210704	−	0.977550i	$-0.432424\pi$
$131$	−69.4990	−	40.1253i	−0.530527	−	0.306300i	−0.741231	+	0.671250i	$0.765758\pi$
$132$	−54.7737	−	126.822i	−0.414952	−	0.960776i
$133$	39.0131	−	73.4257i	0.293331	−	0.552073i
$134$		−	3.40971i		−	0.0254456i
$135$	134.708	+	8.87805i	0.997835	+	0.0657633i
$136$	−3.15993	−	5.47317i	−0.0232348	−	0.0402439i
$137$	−77.7452	−	134.659i	−0.567483	−	0.982909i	−0.996814	−	0.0797620i	$-0.974584\pi$
$137$	−77.7452	−	134.659i	−0.567483	−	0.982909i	0.429331	−	0.903147i	$-0.358749\pi$
$138$	−1.41313	+	12.1375i	−0.0102400	+	0.0879530i
$139$	−131.310			−0.944678			−0.472339	−	0.881417i	$-0.656590\pi$
$139$	−131.310			−0.944678			−0.472339	+	0.881417i	$0.656590\pi$
$140$	92.6813	−	103.545i	0.662009	−	0.739609i
$141$	143.842	−	62.1242i	1.02015	−	0.440597i
$142$	−7.17608	−	4.14311i	−0.0505358	−	0.0291768i
$143$	42.5941	+	73.7752i	0.297861	+	0.515911i
$144$	−137.049	−	32.3508i	−0.951732	−	0.224658i
$145$	−157.330	+	45.5653i	−1.08504	+	0.314243i
$146$			21.3921i			0.146521i
$147$	123.831	+	79.2137i	0.842390	+	0.538868i
$148$		−	189.265i		−	1.27882i
$149$	−81.9236	−	47.2986i	−0.549823	−	0.317440i	0.199228	−	0.979953i	$-0.436157\pi$
$149$	−81.9236	−	47.2986i	−0.549823	−	0.317440i	−0.749050	+	0.662513i	$0.769490\pi$
$150$	7.27285	−	10.6467i	0.0484856	−	0.0709783i
$151$	14.8293	+	25.6851i	0.0982074	+	0.170100i	0.910943	−	0.412533i	$-0.135356\pi$
$151$	14.8293	+	25.6851i	0.0982074	+	0.170100i	−0.812735	+	0.582633i	$0.802022\pi$
$152$	−8.13795	+	14.0953i	−0.0535392	+	0.0927325i
$153$	−28.4586	+	30.2189i	−0.186004	+	0.197509i
$154$	−0.491251	−	13.9483i	−0.00318994	−	0.0905732i
$155$	−162.703	+	169.379i	−1.04970	+	1.09277i
$156$	86.9043	+	10.1179i	0.557079	+	0.0648586i
$157$	−39.7991	+	22.9780i	−0.253497	+	0.146357i	−0.621365	−	0.783522i	$-0.713421\pi$
$157$	−39.7991	+	22.9780i	−0.253497	+	0.146357i	0.367867	+	0.929878i	$0.380088\pi$
$158$	−5.92266	−	10.2583i	−0.0374852	−	0.0649262i
$159$	−7.98680	+	68.5997i	−0.0502314	+	0.431444i
$160$	−28.3017	+	29.4631i	−0.176885	+	0.184144i
$161$	77.8180	−	146.460i	0.483341	−	0.909688i
$162$	−0.834748	−	13.9001i	−0.00515277	−	0.0858034i
$163$	184.229	+	106.364i	1.13024	+	0.652542i	0.943994	−	0.329962i	$-0.107036\pi$
$163$	184.229	+	106.364i	1.13024	+	0.652542i	0.186242	+	0.982504i	$0.440369\pi$
$164$	−243.194	+	140.408i	−1.48289	+	0.856147i
$165$	28.7457	+	171.576i	0.174216	+	1.03985i
$166$	3.08358	−	5.34092i	0.0185758	−	0.0321742i
$167$	11.5544			0.0691879			0.0345940	−	0.999401i	$-0.488986\pi$
$167$	11.5544			0.0691879			0.0345940	+	0.999401i	$0.488986\pi$
$168$	−23.6791	−	16.3496i	−0.140947	−	0.0973191i
$169$	115.048			0.680756
$170$	1.10288	+	3.80808i	0.00648751	+	0.0224004i
$171$	104.043	+	24.5597i	0.608441	+	0.143624i
$172$	48.5668	−	28.0401i	0.282365	−	0.163024i
$173$	−1.95332	+	3.38324i	−0.0112908	+	0.0195563i	−0.871616	−	0.490190i	$-0.836927\pi$
$173$	−1.95332	+	3.38324i	−0.0112908	+	0.0195563i	0.860325	+	0.509746i	$0.170261\pi$
$174$	6.69895	+	15.5107i	0.0384997	+	0.0891418i
$175$	−144.532	+	98.6693i	−0.825894	+	0.563825i
$176$		−	181.462i		−	1.03103i
$177$	3.77534	+	0.439548i	0.0213296	+	0.00248332i
$178$	−19.0034	+	10.9716i	−0.106761	+	0.0616382i
$179$	190.707	−	110.105i	1.06540	−	0.615110i	0.138480	−	0.990365i	$-0.455778\pi$
$179$	190.707	−	110.105i	1.06540	−	0.615110i	0.926921	+	0.375256i	$0.122445\pi$
$180$	159.012	+	81.4751i	0.883400	+	0.452639i
$181$	77.8562			0.430145			0.215072	−	0.976598i	$-0.431001\pi$
$181$	77.8562			0.430145			0.215072	+	0.976598i	$0.431001\pi$
$182$	7.80589	+	4.14748i	0.0428895	+	0.0227883i
$183$	−178.069	+	76.9065i	−0.973052	+	0.420254i
$184$	−16.2325	+	28.1155i	−0.0882200	+	0.152802i
$185$	−57.0474	+	231.415i	−0.308364	+	1.25089i
$186$	19.4389	+	14.4581i	0.104510	+	0.0777319i
$187$	−46.3250	−	26.7457i	−0.247727	−	0.143025i
$188$	207.368			1.10302
$189$	−58.1074	+	179.846i	−0.307446	+	0.951565i
$190$	7.07309	−	7.36334i	0.0372268	−	0.0387544i
$191$	−205.885	−	118.868i	−1.07793	−	0.622345i	−0.147594	−	0.989048i	$-0.547153\pi$
$191$	−205.885	−	118.868i	−1.07793	−	0.622345i	−0.930338	+	0.366703i	$0.880486\pi$
$192$	−147.271	−	109.536i	−0.767039	−	0.570502i
$193$	182.727	−	105.498i	0.946773	−	0.546620i	0.0546961	−	0.998503i	$-0.482581\pi$
$193$	182.727	−	105.498i	0.946773	−	0.546620i	0.892077	+	0.451883i	$0.149248\pi$
$194$	−4.01279	−	2.31679i	−0.0206845	−	0.0119422i
$195$	−103.208	−	38.5654i	−0.529273	−	0.197771i
$196$	108.888	+	161.226i	0.555552	+	0.822581i
$197$	378.734			1.92251			0.961253	−	0.275667i	$-0.0888987\pi$
$197$	378.734			1.92251			0.961253	+	0.275667i	$0.0888987\pi$
$198$	17.1861	−	5.16207i	0.0867985	−	0.0260711i
$199$	95.2314	+	164.946i	0.478550	+	0.828873i	0.999698	−	0.0245938i	$-0.00782923\pi$
$199$	95.2314	+	164.946i	0.478550	+	0.828873i	−0.521148	+	0.853467i	$0.674496\pi$
$200$	28.9543	−	18.3067i	0.144771	−	0.0915335i
$201$	−59.1015	−	6.88096i	−0.294037	−	0.0342336i
$202$			3.14781i			0.0155832i
$203$	−8.07132	−	229.172i	−0.0397602	−	1.12893i
$204$	−50.4348	+	21.7824i	−0.247229	+	0.106777i
$205$	339.674	−	98.3748i	1.65695	−	0.479877i
$206$	−4.62741	+	2.67164i	−0.0224632	+	0.0129691i
$207$	207.532	+	48.9883i	1.00257	+	0.236658i
$208$	99.5278	+	57.4624i	0.478499	+	0.276262i
$209$			137.760i			0.659137i
$210$	11.9677	+	13.5137i	0.0569890	+	0.0643508i
$211$	56.9073			0.269703			0.134851	−	0.990866i	$-0.456944\pi$
$211$	56.9073			0.269703			0.134851	+	0.990866i	$0.456944\pi$
$212$	−45.7018	+	79.1579i	−0.215575	+	0.373386i
$213$	−86.2955	+	116.024i	−0.405143	+	0.544715i
$214$	−15.6845	−	27.1663i	−0.0732919	−	0.126945i
$215$	−67.8344	+	19.6459i	−0.315509	+	0.0913761i
$216$	12.6066	−	34.7826i	0.0583637	−	0.161030i
$217$	−174.327	−	278.796i	−0.803348	−	1.28477i
$218$	−5.86227			−0.0268911
$219$	370.796	+	43.1704i	1.69313	+	0.197125i
$220$	−55.1084	+	223.550i	−0.250493	+	1.01613i
$221$	29.3389	−	16.9388i	0.132755	−	0.0766464i
$222$	24.4200	+	2.84313i	0.110000	+	0.0128069i
$223$		−	105.559i		−	0.473357i	−0.971588	−	0.236679i	$-0.923941\pi$
$223$		−	105.559i		−	0.473357i	0.971588	−	0.236679i	$-0.0760589\pi$
$224$	−30.3236	−	48.4957i	−0.135373	−	0.216499i
$225$	−169.866	−	147.548i	−0.754961	−	0.655770i
$226$	5.50489	−	9.53475i	0.0243579	−	0.0421892i
$227$	−193.360	−	334.909i	−0.851805	−	1.47537i	−0.879577	−	0.475756i	$-0.842175\pi$
$227$	−193.360	−	334.909i	−0.851805	−	1.47537i	0.0277721	−	0.999614i	$-0.491159\pi$
$228$	113.526	+	84.4371i	0.497919	+	0.370338i
$229$	−14.0913	+	24.4068i	−0.0615340	+	0.106580i	−0.895151	−	0.445762i	$-0.852933\pi$
$229$	−14.0913	+	24.4068i	−0.0615340	+	0.106580i	0.833617	+	0.552343i	$0.186266\pi$
$230$	14.1084	−	14.6874i	0.0613410	−	0.0638582i
$231$	−242.761	−	19.6333i	−1.05091	−	0.0849927i
$232$			44.8881i			0.193483i
$233$	−171.016	+	296.208i	−0.733974	+	1.27128i	0.221199	+	0.975229i	$0.429003\pi$
$233$	−171.016	+	296.208i	−0.733974	+	1.27128i	−0.955172	+	0.296051i	$0.904330\pi$
$234$	−2.61094	+	11.0609i	−0.0111579	+	0.0472686i
$235$	−253.549	−	62.5038i	−1.07893	−	0.265974i
$236$	4.35640	+	2.51517i	0.0184593	+	0.0106575i
$237$	−189.763	+	81.9574i	−0.800689	+	0.345812i
$238$	−5.54695	+	0.195361i	−0.0233065	+	0.000820844i
$239$			105.588i			0.441791i	0.975298	+	0.220895i	$0.0708979\pi$
$239$			105.588i			0.441791i	−0.975298	+	0.220895i	$0.929102\pi$
$240$	149.318	+	181.066i	0.622158	+	0.754443i
$241$	−9.53578	−	16.5165i	−0.0395675	−	0.0685330i	0.845563	−	0.533875i	$-0.179265\pi$
$241$	−9.53578	−	16.5165i	−0.0395675	−	0.0685330i	−0.885131	+	0.465342i	$0.845931\pi$
$242$	1.16119	+	2.01124i	0.00479830	+	0.00831090i
$243$	−242.620	−	13.5823i	−0.998437	−	0.0558941i
$244$	−256.711			−1.05210
$245$	−84.5419	−	229.951i	−0.345069	−	0.938577i
$246$	−14.4629	−	33.4873i	−0.0587924	−	0.136127i
$247$	−75.5582	−	43.6235i	−0.305904	−	0.176614i
$248$	32.1823	+	55.7414i	0.129767	+	0.224764i
$249$	−86.3529	−	64.2269i	−0.346799	−	0.257939i
$250$	−20.3843	+	6.80287i	−0.0815372	+	0.0272115i
$251$		−	222.387i		−	0.886003i	−0.896521	−	0.443001i	$-0.853914\pi$
$251$		−	222.387i		−	0.886003i	0.896521	−	0.443001i	$-0.146086\pi$
$252$	−164.975	+	188.022i	−0.654664	+	0.746118i
$253$			274.784i			1.08610i
$254$	−19.6521	−	11.3462i	−0.0773706	−	0.0446699i
$255$	68.2322	−	11.4316i	0.267577	−	0.0448298i
$256$	−118.647	−	205.502i	−0.463464	−	0.802744i
$257$	182.147	−	315.488i	0.708743	−	1.22758i	−0.256581	−	0.966523i	$-0.582596\pi$
$257$	182.147	−	315.488i	0.708743	−	1.22758i	0.965324	−	0.261056i	$-0.0840707\pi$
$258$	2.88831	+	6.68756i	0.0111950	+	0.0259208i
$259$	−294.669	−	156.565i	−1.13772	−	0.604499i
$260$	−105.161	−	101.016i	−0.404467	−	0.388523i
$261$	282.370	−	84.8136i	1.08188	−	0.324956i
$262$	11.9480	−	6.89817i	0.0456030	−	0.0263289i
$263$	−181.221	−	313.884i	−0.689054	−	1.19348i	−0.972144	−	0.234383i	$-0.924693\pi$
$263$	−181.221	−	313.884i	−0.689054	−	1.19348i	0.283090	−	0.959093i	$-0.408640\pi$
$264$	47.3556	+	5.51344i	0.179377	+	0.0208842i
$265$	79.7390	−	83.0112i	0.300902	−	0.313250i
$266$	7.57840	+	12.1199i	0.0284902	+	0.0455636i
$267$	151.824	+	351.533i	0.568631	+	1.31660i
$268$	−68.1978	−	39.3740i	−0.254470	−	0.146918i
$269$	274.148	−	158.279i	1.01914	−	0.588399i	0.105283	−	0.994442i	$-0.466425\pi$
$269$	274.148	−	158.279i	1.01914	−	0.588399i	0.913854	+	0.406043i	$0.133092\pi$
$270$	−12.9010	+	19.2926i	−0.0477815	+	0.0714542i
$271$	24.8208	−	42.9910i	0.0915898	−	0.158638i	−0.816590	−	0.577218i	$-0.804138\pi$
$271$	24.8208	−	42.9910i	0.0915898	−	0.158638i	0.908180	+	0.418579i	$0.137472\pi$
$272$	−72.1637			−0.265308
$273$	87.6422	−	126.932i	0.321034	−	0.464953i
$274$	26.7313			0.0975594
$275$	134.762	−	256.724i	0.490045	−	0.933541i
$276$	226.445	+	168.424i	0.820454	+	0.610231i
$277$	−95.4077	+	55.0836i	−0.344432	+	0.198858i	−0.662230	−	0.749300i	$-0.730390\pi$
$277$	−95.4077	+	55.0836i	−0.344432	+	0.198858i	0.317798	+	0.948158i	$0.397057\pi$
$278$	11.2872	−	19.5499i	0.0406013	−	0.0703235i
$279$	289.836	−	307.764i	1.03884	−	1.10310i
$280$	14.9544	+	45.5675i	0.0534087	+	0.162741i
$281$			400.249i			1.42437i	0.701990	+	0.712187i	$0.252295\pi$
$281$			400.249i			1.42437i	−0.701990	+	0.712187i	$0.747705\pi$
$282$	−3.11507	+	26.7557i	−0.0110463	+	0.0948784i
$283$	−277.081	+	159.973i	−0.979086	+	0.565276i	−0.901994	−	0.431748i	$-0.857897\pi$
$283$	−277.081	+	159.973i	−0.979086	+	0.565276i	−0.0770921	+	0.997024i	$0.524564\pi$
$284$	−165.734	+	95.6863i	−0.583569	+	0.336924i
$285$	−113.357	−	137.460i	−0.397745	−	0.482314i
$286$	−14.6452			−0.0512071
$287$	17.4259	+	494.779i	0.0607173	+	1.72397i
$288$	50.4161	−	53.5346i	0.175056	−	0.185884i
$289$	133.864	−	231.859i	0.463196	−	0.802280i
$290$	6.73989	−	27.3406i	0.0232410	−	0.0942780i
$291$	−48.2556	+	64.8796i	−0.165827	+	0.222954i
$292$	427.866	+	247.028i	1.46529	+	0.845988i
$293$	328.719			1.12191			0.560954	−	0.827847i	$-0.310434\pi$
$293$	328.719			1.12191			0.560954	+	0.827847i	$0.310434\pi$
$294$	−22.4379	+	11.6274i	−0.0763194	+	0.0395490i
$295$	−4.56847	−	4.38838i	−0.0154863	−	0.0148759i
$296$	56.5668	+	32.6588i	0.191104	+	0.110334i
$297$	−54.7933	−	308.309i	−0.184489	−	1.03808i
$298$	14.0840	−	8.13138i	0.0472616	−	0.0272865i
$299$	−150.713	−	87.0143i	−0.504058	−	0.291018i
$300$	−128.962	−	268.410i	−0.429874	−	0.894698i
$301$	−3.48002	−	98.8095i	−0.0115615	−	0.328271i
$302$	−5.09879			−0.0168834
$303$	54.5619	+	6.35244i	0.180072	+	0.0209651i
$304$	92.9235	+	160.948i	0.305669	+	0.529435i
$305$	313.881	+	77.3765i	1.02912	+	0.253694i
$306$	−2.05285	−	6.83457i	−0.00670867	−	0.0223352i
$307$		−	433.637i		−	1.41250i	−0.707963	−	0.706250i	$-0.750386\pi$
$307$		−	433.637i		−	1.41250i	0.707963	−	0.706250i	$-0.249614\pi$
$308$	−284.653	−	151.244i	−0.924199	−	0.491052i
$309$	36.9700	+	85.5998i	0.119644	+	0.277022i
$310$	−11.2322	−	38.7833i	−0.0362330	−	0.125107i
$311$	−310.113	+	179.044i	−0.997148	+	0.575704i	−0.907403	−	0.420261i	$-0.861939\pi$
$311$	−310.113	+	179.044i	−0.997148	+	0.575704i	−0.0897451	+	0.995965i	$0.528605\pi$
$312$	−18.0198	+	24.2276i	−0.0577559	+	0.0776527i
$313$	−193.637	−	111.796i	−0.618647	−	0.357176i	0.157695	−	0.987488i	$-0.449594\pi$
$313$	−193.637	−	111.796i	−0.618647	−	0.357176i	−0.776342	+	0.630312i	$0.782927\pi$
$314$		−	7.90057i		−	0.0251610i
$315$	258.388	−	180.168i	0.820279	−	0.571963i
$316$	−273.571			−0.865730
$317$	−268.012	+	464.210i	−0.845462	+	1.46438i	0.0397565	+	0.999209i	$0.487342\pi$
$317$	−268.012	+	464.210i	−0.845462	+	1.46438i	−0.885219	+	0.465175i	$0.845992\pi$
$318$	−9.52683	−	7.08579i	−0.0299586	−	0.0222824i
$319$	189.967	+	329.033i	0.595508	+	1.03145i
$320$	85.0965	+	293.826i	0.265927	+	0.918207i
$321$	−502.534	+	217.041i	−1.56553	+	0.676139i
$322$	15.1164	+	24.1752i	0.0469452	+	0.0750782i
$323$	54.7843			0.169611
$324$	−287.658	−	143.818i	−0.887832	−	0.443883i
$325$	98.1332	+	155.210i	0.301948	+	0.477568i
$326$	−31.6718	+	18.2857i	−0.0971528	+	0.0560912i
$327$	−11.8304	+	101.613i	−0.0361785	+	0.310742i
$328$		−	96.9129i		−	0.295466i
$329$	171.540	−	322.853i	0.521399	−	0.981316i
$330$	−28.0157	−	10.4685i	−0.0848961	−	0.0317228i
$331$	−107.615	+	186.394i	−0.325120	+	0.563124i	−0.981537	−	0.191274i	$-0.938738\pi$
$331$	−107.615	+	186.394i	−0.325120	+	0.563124i	0.656417	+	0.754398i	$0.272071\pi$
$332$	−71.2161	−	123.350i	−0.214506	−	0.371536i
$333$	98.5617	−	417.542i	0.295981	−	1.25388i
$334$	−0.993191	+	1.72026i	−0.00297363	+	0.00515047i
$335$	71.5177	+	68.6985i	0.213486	+	0.205070i
$336$	−296.868	+	140.812i	−0.883535	+	0.419085i
$337$			203.340i			0.603381i	0.953406	+	0.301691i	$0.0975510\pi$
$337$			203.340i			0.603381i	−0.953406	+	0.301691i	$0.902449\pi$
$338$	−9.88928	+	17.1287i	−0.0292582	+	0.0506767i
$339$	−154.160	−	114.660i	−0.454748	−	0.338229i
$340$	88.9013	+	21.9155i	0.261474	+	0.0644575i
$341$	471.796	+	272.392i	1.38357	+	0.798802i
$342$	−12.5999	+	13.3792i	−0.0368418	+	0.0391206i
$343$	341.089	−	36.1586i	0.994428	−	0.105419i
$344$			19.3539i			0.0562613i
$345$	−226.110	−	274.186i	−0.655390	−	0.794741i
$346$	−0.335806	−	0.581633i	−0.000970538	−	0.00168102i
$347$	9.76578	+	16.9148i	0.0281435	+	0.0487459i	0.879754	−	0.475429i	$-0.157707\pi$
$347$	9.76578	+	16.9148i	0.0281435	+	0.0487459i	−0.851611	+	0.524175i	$0.824374\pi$
$348$	387.587	+	45.1253i	1.11376	+	0.129670i
$349$	−19.4121			−0.0556219			−0.0278110	−	0.999613i	$-0.508854\pi$
$349$	−19.4121			−0.0556219			−0.0278110	+	0.999613i	$0.508854\pi$
$350$	−2.26661	−	29.9998i	−0.00647603	−	0.0857137i
$351$	186.452	+	67.5776i	0.531203	+	0.192529i
$352$	82.0676	+	47.3817i	0.233146	+	0.134607i
$353$	160.280	+	277.612i	0.454050	+	0.786437i	0.998633	−	0.0522696i	$-0.0166455\pi$
$353$	160.280	+	277.612i	0.454050	+	0.786437i	−0.544583	+	0.838707i	$0.683312\pi$
$354$	−0.389962	+	0.524303i	−0.00110159	+	0.00148108i
$355$	231.484	−	67.0412i	0.652067	−	0.188848i
$356$			506.784i			1.42355i
$357$	−7.80778	+	96.5413i	−0.0218705	+	0.270424i
$358$			37.8575i			0.105747i
$359$	−16.9213	−	9.76951i	−0.0471345	−	0.0272131i	0.476248	−	0.879311i	$-0.341997\pi$
$359$	−16.9213	−	9.76951i	−0.0471345	−	0.0272131i	−0.523382	+	0.852098i	$0.675330\pi$
$360$	−51.7893	+	33.4658i	−0.143859	+	0.0929604i
$361$	109.956	+	190.449i	0.304586	+	0.527558i
$362$	−6.69236	+	11.5915i	−0.0184872	+	0.0320207i
$363$	37.2048	−	16.0685i	0.102492	−	0.0442657i
$364$	173.094	−	108.233i	0.475532	−	0.297343i
$365$	−448.694	−	431.007i	−1.22930	−	1.18084i
$366$	3.85629	−	33.1222i	0.0105363	−	0.0904979i
$367$	369.737	−	213.468i	1.00746	−	0.581656i	0.0970116	−	0.995283i	$-0.469072\pi$
$367$	369.737	−	213.468i	1.00746	−	0.581656i	0.910446	+	0.413627i	$0.135738\pi$
$368$	185.351	+	321.038i	0.503672	+	0.872385i
$369$	−609.633	+	183.111i	−1.65212	+	0.496237i
$370$	−29.5502	−	28.3854i	−0.0798654	−	0.0767172i
$371$	85.4357	+	136.635i	0.230285	+	0.368288i
$372$	513.652	−	221.843i	1.38079	−	0.596351i
$373$	−194.156	−	112.096i	−0.520525	−	0.300525i	0.216625	−	0.976255i	$-0.430495\pi$
$373$	−194.156	−	112.096i	−0.520525	−	0.300525i	−0.737149	+	0.675730i	$0.763829\pi$
$374$	7.96400	−	4.59802i	0.0212941	−	0.0122942i
$375$	76.7796	+	367.056i	0.204746	+	0.978815i
$376$	−35.7826	+	61.9772i	−0.0951664	+	0.164833i
$377$	−240.623			−0.638258
$378$	−21.7813	−	24.1104i	−0.0576225	−	0.0637842i
$379$	441.863			1.16586			0.582932	−	0.812521i	$-0.301905\pi$
$379$	441.863			1.16586			0.582932	+	0.812521i	$0.301905\pi$
$380$	−65.5974	−	226.499i	−0.172625	−	0.596049i
$381$	−236.326	+	317.739i	−0.620277	+	0.833961i
$382$	35.3949	−	20.4353i	0.0926569	−	0.0534955i
$383$	−71.4848	+	123.815i	−0.186644	+	0.323277i	−0.944129	−	0.329575i	$-0.893095\pi$
$383$	−71.4848	+	123.815i	−0.186644	+	0.323277i	0.757485	+	0.652853i	$0.226428\pi$
$384$	118.981	−	51.3869i	0.309846	−	0.133820i
$385$	302.459	+	270.725i	0.785607	+	0.703181i
$386$			36.2734i			0.0939726i
$387$	121.746	−	36.5681i	0.314590	−	0.0944912i
$388$	−92.6766	+	53.5069i	−0.238857	+	0.137904i
$389$	35.6423	−	20.5781i	0.0916256	−	0.0529000i	−0.453487	−	0.891263i	$-0.649820\pi$
$389$	35.6423	−	20.5781i	0.0916256	−	0.0529000i	0.545113	+	0.838363i	$0.316487\pi$
$390$	14.6133	−	12.0510i	0.0374701	−	0.0309000i
$391$	109.276			0.279479
$392$	−66.9757	+	4.72356i	−0.170856	+	0.0120499i
$393$	−95.4565	−	221.019i	−0.242892	−	0.562389i
$394$	−32.5552	+	56.3872i	−0.0826274	+	0.143115i
$395$	334.495	+	82.4582i	0.846823	+	0.208755i
$396$	95.2117	−	403.350i	0.240434	−	1.01856i
$397$	−326.923	−	188.749i	−0.823484	−	0.475439i	0.0281322	−	0.999604i	$-0.491044\pi$
$397$	−326.923	−	188.749i	−0.823484	−	0.475439i	−0.851617	+	0.524165i	$0.824377\pi$
$398$	−32.7436			−0.0822704
$399$	225.372	−	106.900i	0.564842	−	0.267920i
$400$	−15.7225	−	390.839i	−0.0393063	−	0.977098i
$401$	81.6070	+	47.1158i	0.203509	+	0.117496i	0.598291	−	0.801279i	$-0.295847\pi$
$401$	81.6070	+	47.1158i	0.203509	+	0.117496i	−0.394782	+	0.918775i	$0.629180\pi$
$402$	6.10471	−	8.20777i	0.0151858	−	0.0204173i
$403$	−298.802	+	172.513i	−0.741444	+	0.428073i
$404$	62.9596	+	36.3497i	0.155841	+	0.0899746i
$405$	308.370	+	262.551i	0.761408	+	0.648273i
$406$	34.8138	+	18.4975i	0.0857482	+	0.0455603i
$407$	552.850			1.35835
$408$	2.19258	−	18.8324i	0.00537398	−	0.0461578i
$409$	−264.873	−	458.773i	−0.647611	−	1.12169i	−0.983692	−	0.179862i	$-0.942435\pi$
$409$	−264.873	−	458.773i	−0.647611	−	1.12169i	0.336081	−	0.941833i	$-0.390898\pi$
$410$	−14.5513	+	59.0280i	−0.0354910	+	0.143971i
$411$	53.9451	−	463.341i	0.131253	−	1.12735i
$412$			123.404i			0.299525i
$413$	7.51962	−	4.70190i	0.0182073	−	0.0113847i
$414$	−25.1325	+	26.6871i	−0.0607066	+	0.0644616i
$415$	49.8965	+	172.286i	0.120233	+	0.415146i
$416$	−51.9757	+	30.0082i	−0.124942	+	0.0721351i
$417$	−316.087	−	235.097i	−0.758002	−	0.563781i
$418$	−20.5101	−	11.8415i	−0.0490673	−	0.0283290i
$419$			208.590i			0.497828i	0.968526	+	0.248914i	$0.0800736\pi$
$419$			208.590i			0.497828i	−0.968526	+	0.248914i	$0.919926\pi$
$420$	408.487	−	83.3160i	0.972587	−	0.198371i
$421$	−382.542			−0.908650			−0.454325	−	0.890836i	$-0.650120\pi$
$421$	−382.542			−0.908650			−0.454325	+	0.890836i	$0.650120\pi$
$422$	−4.89164	+	8.47256i	−0.0115916	+	0.0200772i
$423$	457.479	+	107.989i	1.08151	+	0.255293i
$424$	−15.7722	−	27.3183i	−0.0371987	−	0.0644300i
$425$	−102.094	−	53.5923i	−0.240221	−	0.126100i
$426$	−9.85631	−	22.8212i	−0.0231369	−	0.0535709i
$427$	−212.358	+	399.675i	−0.497326	+	0.936008i
$428$	−724.474			−1.69270
$429$	−29.5548	+	253.850i	−0.0688923	+	0.591725i
$430$	2.90596	−	11.7881i	0.00675804	−	0.0274143i
$431$	−403.517	+	232.971i	−0.936234	+	0.540535i	−0.888778	−	0.458338i	$-0.848445\pi$
$431$	−403.517	+	232.971i	−0.936234	+	0.540535i	−0.0474561	+	0.998873i	$0.515111\pi$
$432$	−271.982	−	323.246i	−0.629587	−	0.748255i
$433$			769.033i			1.77606i	0.459788	+	0.888029i	$0.347926\pi$
$433$			769.033i			1.77606i	−0.459788	+	0.888029i	$0.652074\pi$
$434$	56.4928	−	1.98965i	0.130168	−	0.00458444i
$435$	−460.302	−	171.999i	−1.05817	−	0.395401i
$436$	−67.6953	+	117.252i	−0.155265	+	0.268926i
$437$	−140.713	−	243.721i	−0.321997	−	0.557714i
$438$	−38.3003	+	51.4946i	−0.0874435	+	0.117568i
$439$	−129.054	+	223.528i	−0.293973	+	0.509176i	−0.974745	−	0.223319i	$-0.928311\pi$
$439$	−129.054	+	223.528i	−0.293973	+	0.509176i	0.680773	+	0.732495i	$0.261644\pi$
$440$	−57.3042	−	55.0453i	−0.130237	−	0.125103i
$441$	156.261	+	412.388i	0.354332	+	0.935120i
$442$			5.82412i			0.0131767i
$443$	202.227	−	350.267i	0.456493	−	0.790670i	−0.542279	−	0.840198i	$-0.682439\pi$
$443$	202.227	−	350.267i	0.456493	−	0.790670i	0.998773	+	0.0495286i	$0.0157719\pi$
$444$	338.859	−	455.595i	0.763196	−	1.02612i
$445$	152.752	−	619.646i	0.343263	−	1.39246i
$446$	15.7160	+	9.07361i	0.0352376	+	0.0203444i
$447$	−112.522	−	260.531i	−0.251726	−	0.582844i
$448$	−427.996	+	15.0738i	−0.955348	+	0.0336469i
$449$			24.0690i			0.0536058i	0.999641	+	0.0268029i	$0.00853266\pi$
$449$			24.0690i			0.0536058i	−0.999641	+	0.0268029i	$0.991467\pi$
$450$	36.5689	−	12.6073i	0.0812641	−	0.0280163i
$451$	−410.136	−	710.377i	−0.909393	−	1.57511i
$452$	−127.137	−	220.208i	−0.281276	−	0.487185i
$453$	−10.2896	+	88.3789i	−0.0227144	+	0.195097i
$454$	66.4833			0.146439
$455$	−244.265	+	80.1633i	−0.536846	+	0.176183i
$456$	−44.8257	+	19.3599i	−0.0983019	+	0.0424559i
$457$	−183.663	−	106.038i	−0.401888	−	0.232030i	0.285410	−	0.958405i	$-0.407870\pi$
$457$	−183.663	−	106.038i	−0.401888	−	0.232030i	−0.687298	+	0.726375i	$0.741204\pi$
$458$	−2.42252	−	4.19592i	−0.00528934	−	0.00916140i
$459$	−122.609	+	21.7902i	−0.267121	+	0.0474733i
$460$	−130.845	−	451.789i	−0.284445	−	0.982150i
$461$		−	315.604i		−	0.684608i	−0.939589	−	0.342304i	$-0.888793\pi$
$461$		−	315.604i		−	0.684608i	0.939589	−	0.342304i	$-0.111207\pi$
$462$	23.7903	−	34.4555i	0.0514942	−	0.0745790i
$463$		−	612.544i		−	1.32299i	−0.749950	−	0.661495i	$-0.769922\pi$
$463$		−	612.544i		−	1.32299i	0.749950	−	0.661495i	$-0.230078\pi$
$464$	443.887	+	256.278i	0.956654	+	0.552324i
$465$	−694.910	+	116.425i	−1.49443	+	0.250376i
$466$	−29.4003	−	50.9229i	−0.0630909	−	0.109277i
$467$	201.374	−	348.790i	0.431208	−	0.746874i	−0.565770	−	0.824563i	$-0.691421\pi$
$467$	201.374	−	348.790i	0.431208	−	0.746874i	0.996978	+	0.0776892i	$0.0247542\pi$
$468$	191.079	+	179.948i	0.408288	+	0.384505i
$469$	−117.717	+	73.6064i	−0.250995	+	0.156943i
$470$	31.1004	−	32.3766i	0.0661710	−	0.0688864i
$471$	−136.943	−	15.9438i	−0.290749	−	0.0338509i
$472$	−1.50344	+	0.868014i	−0.00318526	+	0.00183901i
$473$	81.9059	+	141.865i	0.173163	+	0.299926i
$474$	4.10956	−	35.2975i	0.00866995	−	0.0744673i
$475$	11.9360	+	296.712i	0.0251285	+	0.624657i
$476$	−60.1467	+	113.201i	−0.126359	+	0.237817i
$477$	−142.046	+	150.832i	−0.297790	+	0.316210i
$478$	−15.7203	−	9.07612i	−0.0328877	−	0.0189877i
$479$	232.441	−	134.200i	0.485263	−	0.280167i	−0.237344	−	0.971426i	$-0.576277\pi$
$479$	232.441	−	134.200i	0.485263	−	0.280167i	0.722607	+	0.691259i	$0.242944\pi$
$480$	−120.878	+	20.2518i	−0.251828	+	0.0421912i
$481$	−175.068	+	303.226i	−0.363967	+	0.630408i
$482$	3.27870			0.00680229
$483$	449.542	−	213.230i	0.930728	−	0.441470i
$484$	53.6359			0.110818
$485$	129.443	−	37.4888i	0.266894	−	0.0772965i
$486$	22.8773	−	34.9546i	0.0470726	−	0.0719231i
$487$	60.9309	−	35.1785i	0.125115	−	0.0722351i	−0.436136	−	0.899881i	$-0.643653\pi$
$487$	60.9309	−	35.1785i	0.125115	−	0.0722351i	0.561251	+	0.827645i	$0.310320\pi$
$488$	44.2970	−	76.7247i	0.0907726	−	0.157223i
$489$	253.037	+	585.879i	0.517458	+	1.19812i
$490$	41.5030	+	7.17926i	0.0847001	+	0.0146516i
$491$		−	573.554i		−	1.16814i	−0.811705	−	0.584068i	$-0.801460\pi$
$491$		−	573.554i		−	1.16814i	0.811705	−	0.584068i	$-0.198540\pi$
$492$	−836.796	−	97.4250i	−1.70080	−	0.198018i
$493$	130.850	−	75.5461i	0.265415	−	0.153238i
$494$	12.9897	−	7.49958i	0.0262948	−	0.0151813i
$495$	−237.991	+	464.479i	−0.480790	+	0.938341i
$496$	734.950			1.48175
$497$	11.8755	+	337.186i	0.0238944	+	0.678443i
$498$	16.9851	−	7.33572i	0.0341065	−	0.0147304i
$499$	−19.6456	+	34.0272i	−0.0393700	+	0.0681909i	−0.885039	−	0.465517i	$-0.845868\pi$
$499$	−19.6456	+	34.0272i	−0.0393700	+	0.0681909i	0.845669	+	0.533708i	$0.179202\pi$
$500$	−99.3256	+	486.265i	−0.198651	+	0.972530i
$501$	27.8135	+	20.6869i	0.0555159	+	0.0412911i
$502$	33.1097	+	19.1159i	0.0659556	+	0.0380795i
$503$	−377.200			−0.749901			−0.374951	−	0.927045i	$-0.622340\pi$
$503$	−377.200			−0.749901			−0.374951	+	0.927045i	$0.622340\pi$
$504$	−27.7276	−	81.7513i	−0.0550152	−	0.162205i
$505$	−66.0244	−	63.4218i	−0.130741	−	0.125588i
$506$	−40.9108	−	23.6199i	−0.0808515	−	0.0466796i
$507$	276.940	+	205.981i	0.546234	+	0.406273i
$508$	−453.871	+	262.043i	−0.893447	+	0.515832i
$509$	−581.066	−	335.479i	−1.14158	−	0.659094i	−0.194762	−	0.980851i	$-0.562393\pi$
$509$	−581.066	−	335.479i	−1.14158	−	0.659094i	−0.946822	+	0.321757i	$0.895727\pi$
$510$	−4.16312	+	11.1413i	−0.00816299	+	0.0218457i
$511$	738.542	−	461.799i	1.44529	−	0.903716i
$512$	213.599			0.417186
$513$	206.479	+	245.398i	0.402494	+	0.478358i
$514$	31.3140	+	54.2374i	0.0609221	+	0.105520i
$515$	37.1959	−	150.887i	0.0722250	−	0.292984i
$516$	167.112	+	19.4562i	0.323860	+	0.0377058i
$517$			605.729i			1.17162i
$518$	48.6391	−	30.4133i	0.0938979	−	0.0587129i
$519$	−10.7593	+	4.64686i	−0.0207308	+	0.00895350i
$520$	48.3374	−	13.9992i	0.0929565	−	0.0269216i
$521$	663.160	−	382.876i	1.27286	−	0.734886i	0.297335	−	0.954773i	$-0.403902\pi$
$521$	663.160	−	382.876i	1.27286	−	0.734886i	0.975525	+	0.219887i	$0.0705689\pi$
$522$	−11.6446	+	49.3307i	−0.0223077	+	0.0945032i
$523$	−169.809	−	98.0393i	−0.324683	−	0.187456i	0.328795	−	0.944401i	$-0.393357\pi$
$523$	−169.809	−	98.0393i	−0.324683	−	0.187456i	−0.653478	+	0.756946i	$0.726691\pi$
$524$		−	318.630i		−	0.608073i
$525$	−524.570	−	21.2533i	−0.999180	−	0.0404824i
$526$	62.3096			0.118459
$527$	108.325	−	187.624i	0.205550	−	0.356023i
$528$	324.887	−	436.810i	0.615316	−	0.827292i
$529$	−16.1743	−	28.0146i	−0.0305752	−	0.0529577i
$530$	5.50480	+	19.0073i	0.0103864	+	0.0358628i
$531$	8.30094	+	7.81740i	0.0156327	+	0.0147220i
$532$	329.924	−	11.6198i	0.620159	−	0.0218417i
$533$	519.502			0.974676
$534$	−65.3879	−	7.61287i	−0.122449	−	0.0142563i
$535$	885.815	+	218.367i	1.65573	+	0.408163i
$536$	23.5359	−	13.5884i	0.0439102	−	0.0253516i
$537$	656.195	+	76.3983i	1.22197	+	0.142269i
$538$			54.4215i			0.101155i
$539$	−470.946	+	318.066i	−0.873740	+	0.590104i
$540$	236.898	+	480.818i	0.438699	+	0.890404i
$541$	−422.140	+	731.167i	−0.780295	+	1.35151i	0.151475	+	0.988461i	$0.451598\pi$
$541$	−422.140	+	731.167i	−0.780295	+	1.35151i	−0.931770	+	0.363050i	$0.881736\pi$
$542$	4.26710	+	7.39083i	0.00787288	+	0.0136362i
$543$	187.414	+	139.393i	0.345145	+	0.256709i
$544$	18.8428	−	32.6367i	0.0346375	−	0.0599938i
$545$	118.113	−	122.959i	0.216720	−	0.225614i
$546$	11.3646	+	23.9593i	0.0208142	+	0.0438815i
$547$		−	160.122i		−	0.292727i	−0.989231	−	0.146363i	$-0.953243\pi$
$547$		−	160.122i		−	0.292727i	0.989231	−	0.146363i	$-0.0467569\pi$
$548$	308.683	−	534.654i	0.563290	−	0.975647i
$549$	−566.335	−	133.685i	−1.03158	−	0.243506i
$550$	26.6381	+	42.1313i	0.0484329	+	0.0766024i
$551$	−336.985	−	194.558i	−0.611587	−	0.353100i
$552$	−89.4122	+	38.6165i	−0.161979	+	0.0699574i
$553$	−226.305	+	425.924i	−0.409231	+	0.770206i
$554$		−	18.9395i		−	0.0341868i
$555$	−551.646	+	454.920i	−0.993957	+	0.819675i
$556$	−260.680	−	451.511i	−0.468849	−	0.812070i
$557$	142.397	+	246.638i	0.255649	+	0.442797i	0.965072	−	0.261986i	$-0.0843775\pi$
$557$	142.397	+	246.638i	0.255649	+	0.442797i	−0.709422	+	0.704784i	$0.751044\pi$
$558$	20.9073	+	69.6066i	0.0374682	+	0.124743i
$559$	−103.747			−0.185593
$560$	535.984	+	112.276i	0.957114	+	0.200494i
$561$	−63.6271	−	147.322i	−0.113417	−	0.262605i
$562$	−59.5905	−	34.4046i	−0.106033	−	0.0612181i
$563$	−90.7228	−	157.136i	−0.161142	−	0.279106i	0.774137	−	0.633018i	$-0.218184\pi$
$563$	−90.7228	−	157.136i	−0.161142	−	0.279106i	−0.935278	+	0.353913i	$0.884851\pi$
$564$	499.172	+	371.270i	0.885057	+	0.658280i
$565$	89.0767	+	307.569i	0.157658	+	0.544370i
$566$		−	55.0038i		−	0.0971799i
$567$	−461.869	+	328.886i	−0.814584	+	0.580046i
$568$		−	66.0449i		−	0.116276i
$569$	−350.000	−	202.073i	−0.615115	−	0.355137i	0.159850	−	0.987141i	$-0.448899\pi$
$569$	−350.000	−	202.073i	−0.615115	−	0.355137i	−0.774965	+	0.632005i	$0.782232\pi$
$570$	30.2094	−	5.06128i	0.0529990	−	0.00887944i
$571$	369.018	+	639.158i	0.646267	+	1.11937i	0.984007	+	0.178127i	$0.0570039\pi$
$571$	369.018	+	639.158i	0.646267	+	1.11937i	−0.337741	+	0.941239i	$0.609663\pi$
$572$	−169.118	+	292.920i	−0.295660	+	0.512099i
$573$	−282.782	−	654.751i	−0.493511	−	1.14267i
$574$	−75.1624	−	39.9358i	−0.130945	−	0.0695746i
$575$	23.8084	+	591.841i	0.0414059	+	1.02929i
$576$	−158.396	−	527.347i	−0.274992	−	0.915533i
$577$	569.531	−	328.819i	0.987056	−	0.569877i	0.0826627	−	0.996578i	$-0.473658\pi$
$577$	569.531	−	328.819i	0.987056	−	0.569877i	0.904393	+	0.426701i	$0.140324\pi$
$578$	23.0133	+	39.8602i	0.0398154	+	0.0689623i
$579$	628.739	+	73.2017i	1.08590	+	0.126428i
$580$	−469.013	−	450.525i	−0.808642	−	0.776767i
$581$	−250.956	+	8.83855i	−0.431938	+	0.0152126i
$582$	−5.51155	−	12.7614i	−0.00947002	−	0.0219268i
$583$	−231.223	−	133.496i	−0.396608	−	0.228982i
$584$	−147.661	+	85.2524i	−0.252845	+	0.145980i
$585$	−179.393	−	277.617i	−0.306655	−	0.474559i
$586$	−28.2560	+	48.9409i	−0.0482185	+	0.0835168i
$587$	−339.097			−0.577679			−0.288839	−	0.957378i	$-0.593269\pi$
$587$	−339.097			−0.577679			−0.288839	+	0.957378i	$0.593269\pi$
$588$	−26.5440	+	583.051i	−0.0451428	+	0.991584i
$589$	−557.949			−0.947283
$590$	1.04605	−	0.302953i	0.00177297	−	0.000513480i
$591$	911.679	+	678.081i	1.54260	+	1.14735i
$592$	645.910	−	372.916i	1.09106	−	0.629926i
$593$	−163.991	+	284.041i	−0.276545	+	0.478990i	−0.970524	−	0.241006i	$-0.922523\pi$
$593$	−163.991	+	284.041i	−0.276545	+	0.478990i	0.693979	+	0.719995i	$0.255856\pi$
$594$	50.6121	+	18.3438i	0.0852056	+	0.0308818i
$595$	107.662	−	120.282i	0.180944	−	0.202154i
$596$		−	375.593i		−	0.630190i
$597$	−66.0783	+	567.555i	−0.110684	+	0.950678i
$598$	25.9100	−	14.9591i	0.0433278	−	0.0250153i
$599$	−726.655	+	419.534i	−1.21311	+	0.700391i	−0.963436	−	0.267938i	$-0.913658\pi$
$599$	−726.655	+	419.534i	−1.21311	+	0.700391i	−0.249677	+	0.968329i	$0.580324\pi$
$600$	102.474	+	7.77199i	0.170790	+	0.0129533i
$601$	347.260			0.577804			0.288902	−	0.957359i	$-0.406710\pi$
$601$	347.260			0.577804			0.288902	+	0.957359i	$0.406710\pi$
$602$	15.0102	+	7.97534i	0.0249340	+	0.0132481i
$603$	−129.948	−	122.378i	−0.215503	−	0.202949i
$604$	−58.8790	+	101.981i	−0.0974818	+	0.168843i
$605$	−65.5807	−	16.1667i	−0.108398	−	0.0267218i
$606$	−5.63581	+	7.57733i	−0.00930001	+	0.0125038i
$607$	277.758	+	160.363i	0.457591	+	0.264190i	0.711031	−	0.703161i	$-0.248229\pi$
$607$	277.758	+	160.363i	0.457591	+	0.264190i	−0.253440	+	0.967351i	$0.581562\pi$
$608$	−97.0537			−0.159628
$609$	390.878	−	566.109i	0.641837	−	0.929571i
$610$	−38.5007	+	40.0806i	−0.0631159	+	0.0657059i
$611$	−332.229	−	191.813i	−0.543747	−	0.313932i
$612$	−160.405	−	37.8638i	−0.262099	−	0.0618690i
$613$	−220.529	+	127.323i	−0.359754	+	0.207704i	−0.668973	−	0.743287i	$-0.733266\pi$
$613$	−220.529	+	127.323i	−0.359754	+	0.207704i	0.309219	+	0.950991i	$0.399932\pi$
$614$	64.5615	+	37.2746i	0.105149	+	0.0607078i
$615$	993.786	+	371.344i	1.61591	+	0.603812i
$616$	94.3217	−	58.9779i	0.153120	−	0.0957433i
$617$	126.508			0.205037			0.102519	−	0.994731i	$-0.467310\pi$
$617$	126.508			0.205037			0.102519	+	0.994731i	$0.467310\pi$
$618$	−15.9223	−	1.85377i	−0.0257642	−	0.00299963i
$619$	183.100	+	317.138i	0.295799	+	0.512339i	0.975170	−	0.221456i	$-0.0710808\pi$
$619$	183.100	+	317.138i	0.295799	+	0.512339i	−0.679372	+	0.733794i	$0.737748\pi$
$620$	−905.414	−	223.198i	−1.46034	−	0.359997i
$621$	411.857	+	489.486i	0.663216	+	0.788222i
$622$		−	61.5610i		−	0.0989727i
$623$	789.016	+	419.225i	1.26648	+	0.672914i
$624$	136.701	+	316.516i	0.219072	+	0.507237i
$625$	268.013	−	564.619i	0.428821	−	0.903390i
$626$	33.2892	−	19.2195i	0.0531777	−	0.0307021i
$627$	−246.643	+	331.612i	−0.393371	+	0.528886i
$628$	−158.020	−	91.2329i	−0.251624	−	0.145275i
$629$		−	219.858i		−	0.349535i
$630$	4.61361	+	53.9566i	0.00732320	+	0.0856454i
$631$	66.0739			0.104713			0.0523565	−	0.998628i	$-0.483327\pi$
$631$	66.0739			0.104713			0.0523565	+	0.998628i	$0.483327\pi$
$632$	47.2062	−	81.7636i	0.0746934	−	0.129373i
$633$	136.986	+	101.886i	0.216408	+	0.160958i
$634$	−46.0755	−	79.8050i	−0.0726742	−	0.125875i
$635$	633.932	−	183.596i	0.998319	−	0.289128i
$636$	−251.736	+	108.723i	−0.395811	+	0.170948i
$637$	−25.3207	−	359.024i	−0.0397499	−	0.563617i
$638$	−65.3167			−0.102377
$639$	−415.457	+	124.788i	−0.650168	+	0.195287i
$640$	−209.727	−	51.7010i	−0.327698	−	0.0807827i
$641$	803.605	−	463.961i	1.25367	−	0.723809i	0.281837	−	0.959462i	$-0.409056\pi$
$641$	803.605	−	463.961i	1.25367	−	0.723809i	0.971837	+	0.235654i	$0.0757231\pi$
$642$	10.8830	−	93.4754i	0.0169517	−	0.145600i
$643$		−	455.224i		−	0.707968i	−0.935251	−	0.353984i	$-0.884827\pi$
$643$		−	455.224i		−	0.707968i	0.935251	−	0.353984i	$-0.115173\pi$
$644$	658.089	−	23.1775i	1.02188	−	0.0359900i
$645$	−198.463	−	74.1590i	−0.307695	−	0.114975i
$646$	−4.70914	+	8.15648i	−0.00728970	+	0.0126261i
$647$	−321.902	−	557.551i	−0.497530	−	0.861747i	0.502466	−	0.864597i	$-0.332426\pi$
$647$	−321.902	−	557.551i	−0.497530	−	0.861747i	−0.999996	+	0.00284968i	$0.999093\pi$
$648$	92.6206	−	61.1571i	0.142933	−	0.0943783i
$649$	−7.34689	+	12.7252i	−0.0113203	+	0.0196074i
$650$	−31.5435	+	1.26892i	−0.0485284	+	0.00195218i
$651$	79.5183	−	983.223i	0.122148	−	1.51033i
$652$			844.628i			1.29544i
$653$	285.108	−	493.822i	0.436613	−	0.756236i	−0.560813	−	0.827943i	$-0.689511\pi$
$653$	285.108	−	493.822i	0.436613	−	0.756236i	0.997426	+	0.0717069i	$0.0228446\pi$
$654$	−14.1115	−	10.4958i	−0.0215772	−	0.0160485i
$655$	−96.0398	+	389.590i	−0.146626	+	0.594793i
$656$	−958.347	−	553.302i	−1.46089	−	0.843448i
$657$	815.280	+	767.789i	1.24091	+	1.16863i
$658$	33.3222	+	53.2913i	0.0506417	+	0.0809899i
$659$			629.009i			0.954491i	0.878770	+	0.477245i	$0.158365\pi$
$659$			629.009i			0.954491i	−0.878770	+	0.477245i	$0.841635\pi$
$660$	−532.897	+	439.458i	−0.807420	+	0.665845i
$661$	−199.704	−	345.897i	−0.302124	−	0.523294i	0.674493	−	0.738281i	$-0.264362\pi$
$661$	−199.704	−	345.897i	−0.302124	−	0.523294i	−0.976617	+	0.214987i	$0.931029\pi$
$662$	−18.5007	−	32.0441i	−0.0279466	−	0.0484050i
$663$	100.951	+	11.7534i	0.152264	+	0.0177275i
$664$	49.1550			0.0740286
$665$	−406.901	−	85.2366i	−0.611882	−	0.128175i
$666$	53.6930	+	50.5653i	0.0806201	+	0.0759238i
$667$	−672.171	−	388.078i	−1.00775	−	0.581826i
$668$	22.9380	+	39.7298i	0.0343384	+	0.0594758i
$669$	188.991	−	254.098i	0.282498	−	0.379818i
$670$	−16.3756	+	4.74262i	−0.0244412	+	0.00707854i
$671$		−	749.861i		−	1.11753i
$672$	13.8320	−	171.029i	0.0205833	−	0.254507i
$673$			1005.37i			1.49387i	0.664900	+	0.746933i	$0.268474\pi$
$673$			1005.37i			1.49387i	−0.664900	+	0.746933i	$0.731526\pi$
$674$	−30.2739	−	17.4787i	−0.0449168	−	0.0259327i
$675$	−144.729	−	659.301i	−0.214414	−	0.976743i
$676$	228.396	+	395.593i	0.337863	+	0.585196i
$677$	−134.300	+	232.614i	−0.198375	+	0.343595i	−0.948002	−	0.318266i	$-0.896900\pi$
$677$	−134.300	+	232.614i	−0.198375	+	0.343595i	0.749627	+	0.661861i	$0.230233\pi$
$678$	30.3222	−	13.0959i	0.0447230	−	0.0193155i
$679$	6.64067	+	188.551i	0.00978008	+	0.277689i
$680$	−21.8904	+	22.7887i	−0.0321918	+	0.0335129i
$681$	134.167	−	1152.37i	0.197014	−	1.69218i
$682$	−81.1093	+	46.8285i	−0.118929	+	0.0686634i
$683$	−158.562	−	274.638i	−0.232156	−	0.402105i	0.726287	−	0.687392i	$-0.241245\pi$
$683$	−158.562	−	274.638i	−0.232156	−	0.402105i	−0.958442	+	0.285287i	$0.907911\pi$
$684$	122.101	+	406.510i	0.178510	+	0.594313i
$685$	−538.580	+	560.681i	−0.786247	+	0.818512i
$686$	−23.9359	+	53.8906i	−0.0348920	+	0.0785578i
$687$	−77.6180	+	33.5226i	−0.112981	+	0.0487957i
$688$	191.386	+	110.497i	0.278177	+	0.160606i
$689$	146.440	−	84.5471i	0.212540	−	0.122710i
$690$	60.2577	−	10.0956i	0.0873300	−	0.0146312i
$691$	449.553	−	778.648i	0.650583	−	1.12684i	−0.332399	−	0.943139i	$-0.607858\pi$
$691$	449.553	−	778.648i	0.650583	−	1.12684i	0.982982	−	0.183704i	$-0.0588087\pi$
$692$	−15.5111			−0.0224148
$693$	−549.217	−	481.898i	−0.792522	−	0.695379i
$694$	−3.35779			−0.00483831
$695$	182.642	+	630.636i	0.262794	+	0.907389i
$696$	−80.3673	+	108.054i	−0.115470	+	0.155250i
$697$	−282.503	+	163.103i	−0.405313	+	0.234007i
$698$	1.66862	−	2.89014i	0.00239057	−	0.00414060i
$699$	−941.994	+	406.840i	−1.34763	+	0.582032i
$700$	−626.202	−	301.092i	−0.894575	−	0.430131i
$701$			430.110i			0.613566i	0.951779	+	0.306783i	$0.0992526\pi$
$701$			430.110i			0.613566i	−0.951779	+	0.306783i	$0.900747\pi$
$702$	−26.0882	+	21.9508i	−0.0371627	+	0.0312690i
$703$	−490.353	+	283.106i	−0.697515	+	0.402711i
$704$	614.492	−	354.777i	0.872859	−	0.503945i
$705$	−498.432	−	604.410i	−0.706995	−	0.857319i
$706$	−55.1092			−0.0780584
$707$	108.675	−	67.9528i	0.153713	−	0.0961143i
$708$	5.98349	+	13.8541i	0.00845126	+	0.0195680i
$709$	354.562	−	614.119i	0.500087	−	0.866176i	−0.499913	−	0.866076i	$-0.666635\pi$
$709$	354.562	−	614.119i	0.500087	−	0.866176i	1.00000		0.000100361i	$-3.19460e-5\pi$
$710$	−9.91654	+	40.2269i	−0.0139670	+	0.0566575i
$711$	−603.529	−	142.464i	−0.848846	−	0.200372i
$712$	−151.465	−	87.4486i	−0.212732	−	0.122821i
$713$	−1112.92			−1.56090
$714$	−13.7023	−	9.46094i	−0.0191908	−	0.0132506i
$715$	295.071	−	307.180i	0.412687	−	0.429622i
$716$	757.191	+	437.164i	1.05753	+	0.610565i
$717$	−189.044	+	254.169i	−0.263659	+	0.354489i
$718$	2.90904	−	1.67953i	0.00405159	−	0.00233918i
$719$	740.112	+	427.304i	1.02936	+	0.594303i	0.916802	−	0.399342i	$-0.130761\pi$
$719$	740.112	+	427.304i	1.02936	+	0.594303i	0.112561	+	0.993645i	$0.464095\pi$
$720$	35.2551	+	703.196i	0.0489654	+	0.976662i
$721$	192.129	+	102.083i	0.266476	+	0.141586i
$722$	−37.8062			−0.0523632
$723$	6.61659	−	56.8308i	0.00915158	−	0.0786041i
$724$	154.562	+	267.709i	0.213483	+	0.369764i
$725$	437.667	+	692.224i	0.603679	+	0.954792i
$726$	−0.805715	+	6.92039i	−0.00110980	+	0.00953222i
$727$		−	1136.87i		−	1.56378i	−0.623413	−	0.781892i	$-0.714255\pi$
$727$		−	1136.87i		−	1.56378i	0.623413	−	0.781892i	$-0.285745\pi$
$728$	2.47979	+	70.4096i	0.00340631	+	0.0967165i
$729$	−559.712	−	467.080i	−0.767781	−	0.640713i
$730$	102.739	−	29.7547i	0.140738	−	0.0407598i
$731$	56.4170	−	32.5724i	0.0771778	−	0.0445586i
$732$	−617.949	−	459.613i	−0.844193	−	0.627887i
$733$	−158.068	−	91.2606i	−0.215645	−	0.124503i	0.388287	−	0.921539i	$-0.373067\pi$
$733$	−158.068	−	91.2606i	−0.215645	−	0.124503i	−0.603932	+	0.797036i	$0.706400\pi$
$734$			73.3970i			0.0999960i
$735$	208.196	−	704.897i	0.283259	−	0.959043i
$736$	−193.590			−0.263029
$737$	115.013	−	199.208i	0.156055	−	0.270296i
$738$	25.1406	−	106.504i	0.0340658	−	0.144315i
$739$	−692.467	−	1199.39i	−0.937032	−	1.62299i	−0.770969	−	0.636872i	$-0.780228\pi$
$739$	−692.467	−	1199.39i	−0.937032	−	1.62299i	−0.166063	−	0.986115i	$-0.553105\pi$
$740$	−908.974	+	263.252i	−1.22834	+	0.355747i
$741$	−103.779	−	240.288i	−0.140052	−	0.324276i
$742$	−27.6866	+	0.975107i	−0.0373135	+	0.00131416i
$743$	82.8544			0.111513			0.0557566	−	0.998444i	$-0.482243\pi$
$743$	82.8544			0.111513			0.0557566	+	0.998444i	$0.482243\pi$
$744$	−22.3303	+	191.798i	−0.0300139	+	0.257793i
$745$	−113.209	+	459.238i	−0.151959	+	0.616427i
$746$	33.3785	−	19.2711i	0.0447432	−	0.0258325i
$747$	−92.8756	−	309.211i	−0.124331	−	0.413937i
$748$		−	212.385i		−	0.283937i
$749$	−599.304	+	1127.94i	−0.800139	+	1.50593i
$750$	−61.2484	−	20.1201i	−0.0816645	−	0.0268268i
$751$	−193.183	+	334.603i	−0.257234	+	0.445543i	−0.965500	−	0.260403i	$-0.916145\pi$
$751$	−193.183	+	334.603i	−0.257234	+	0.445543i	0.708266	+	0.705946i	$0.249478\pi$
$752$	408.585	+	707.689i	0.543331	+	0.941076i
$753$	398.159	−	535.324i	0.528764	−	0.710922i
$754$	20.6835	−	35.8248i	0.0274317	−	0.0475130i
$755$	102.730	−	106.946i	0.136066	−	0.141650i
$756$	−733.757	+	157.232i	−0.970578	+	0.207978i
$757$		−	1387.66i		−	1.83311i	−0.399908	−	0.916555i	$-0.630958\pi$
$757$		−	1387.66i		−	1.83311i	0.399908	−	0.916555i	$-0.369042\pi$
$758$	−37.9816	+	65.7861i	−0.0501077	+	0.0867891i
$759$	−491.971	+	661.454i	−0.648183	+	0.871481i
$760$	79.0141	+	19.4782i	0.103966	+	0.0256292i
$761$	500.579	+	289.009i	0.657791	+	0.379776i	0.791435	−	0.611254i	$-0.209334\pi$
$761$	500.579	+	289.009i	0.657791	+	0.379776i	−0.133644	+	0.991029i	$0.542668\pi$
$762$	−26.9921	−	62.4972i	−0.0354227	−	0.0820173i
$763$	126.551	+	202.389i	0.165859	+	0.265254i
$764$		−	943.916i		−	1.23549i
$765$	184.714	+	94.6444i	0.241456	+	0.123718i
$766$	−12.2894	−	21.2858i	−0.0160436	−	0.0277883i
$767$	−4.65299	−	8.05922i	−0.00606649	−	0.0105075i
$768$	82.3255	−	707.105i	0.107195	−	0.920709i
$769$	622.200			0.809103			0.404551	−	0.914515i	$-0.367428\pi$
$769$	622.200			0.809103			0.404551	+	0.914515i	$0.367428\pi$
$770$	−66.3052	+	21.7602i	−0.0861107	+	0.0282600i
$771$	1003.31	−	433.321i	1.30131	−	0.562024i
$772$	725.508	+	418.872i	0.939778	+	0.542581i
$773$	−511.015	−	885.105i	−0.661081	−	1.14503i	−0.980332	−	0.197355i	$-0.936765\pi$
$773$	−511.015	−	885.105i	−0.661081	−	1.14503i	0.319251	−	0.947670i	$-0.396569\pi$
$774$	−5.02067	+	21.2693i	−0.00648666	+	0.0274798i
$775$	1039.77	+	545.810i	1.34164	+	0.704271i
$776$		−	36.9317i		−	0.0475924i
$777$	−429.006	−	904.452i	−0.552132	−	1.16403i
$778$			7.07541i			0.00909436i
$779$	727.545	+	420.048i	0.933947	+	0.539215i
$780$	−72.2839	−	431.443i	−0.0926716	−	0.553132i
$781$	−279.503	−	484.113i	−0.357878	−	0.619863i
$782$	−9.39316	+	16.2694i	−0.0120117	+	0.0208049i
$783$	831.564	+	301.391i	1.06202	+	0.384919i
$784$	−335.672	+	689.274i	−0.428153	+	0.879176i
$785$	165.712	+	159.180i	0.211098	+	0.202777i
$786$	41.1113	+	4.78644i	0.0523045	+	0.00608961i
$787$	−1151.46	+	664.796i	−1.46310	+	0.844722i	−0.999153	−	0.0411411i	$-0.986901\pi$
$787$	−1151.46	+	664.796i	−1.46310	+	0.844722i	−0.463947	+	0.885863i	$0.653567\pi$
$788$	751.871	+	1302.28i	0.954151	+	1.65264i
$789$	125.744	−	1080.03i	0.159371	−	1.36886i
$790$	−41.0292	+	42.7129i	−0.0519357	+	0.0540670i
$791$	−448.014	+	15.7788i	−0.566389	+	0.0199479i
$792$	104.122	+	98.0569i	0.131467	+	0.123809i
$793$	411.283	+	237.454i	0.518642	+	0.299438i
$794$	56.2033	−	32.4490i	0.0707850	−	0.0408678i
$795$	340.568	−	57.0587i	0.428388	−	0.0717720i
$796$	−378.111	+	654.908i	−0.475014	+	0.822748i
$797$	133.172			0.167092			0.0835458	−	0.996504i	$-0.473376\pi$
$797$	133.172			0.167092			0.0835458	+	0.996504i	$0.473376\pi$
$798$	−3.45685	+	42.7431i	−0.00433190	+	0.0535628i
$799$	240.886			0.301485
$800$	180.866	+	94.9420i	0.226082	+	0.118678i
$801$	−263.912	+	1118.03i	−0.329479	+	1.39579i
$802$	−14.0295	+	8.09996i	−0.0174932	+	0.0100997i
$803$	−721.578	+	1249.81i	−0.898602	+	1.55643i
$804$	−93.6694	−	216.881i	−0.116504	−	0.269753i
$805$	−811.632	−	170.018i	−1.00824	−	0.211203i
$806$		−	59.3156i		−	0.0735926i
$807$	943.305	+	109.825i	1.16890	+	0.136091i
$808$	−21.7281	+	12.5447i	−0.0268912	+	0.0155256i
$809$	−347.381	+	200.561i	−0.429396	+	0.247912i	−0.699089	−	0.715034i	$-0.746411\pi$
$809$	−347.381	+	200.561i	−0.429396	+	0.247912i	0.269693	+	0.962946i	$0.413078\pi$
$810$	−65.5963	+	23.3430i	−0.0809831	+	0.0288185i
$811$	−393.851			−0.485636			−0.242818	−	0.970072i	$-0.578072\pi$
$811$	−393.851			−0.485636			−0.242818	+	0.970072i	$0.578072\pi$
$812$	771.986	−	482.711i	0.950722	−	0.594472i
$813$	136.719	−	59.0479i	0.168166	−	0.0726296i
$814$	−47.5219	+	82.3103i	−0.0583807	+	0.101118i
$815$	254.583	−	1032.73i	0.312372	−	1.26715i
$816$	−173.711	−	129.201i	−0.212881	−	0.158335i
$817$	−145.294	−	83.8854i	−0.177838	−	0.102675i
$818$	91.0717			0.111335
$819$	438.228	−	148.634i	0.535077	−	0.181483i
$820$	1012.59	+	972.677i	1.23487	+	1.18619i
$821$	1249.35	+	721.310i	1.52174	+	0.878575i	0.999670	+	0.0256698i	$0.00817183\pi$
$821$	1249.35	+	721.310i	1.52174	+	0.878575i	0.522066	+	0.852905i	$0.325161\pi$
$822$	64.3469	+	47.8594i	0.0782809	+	0.0582231i
$823$	819.737	−	473.275i	0.996035	−	0.575061i	0.0889621	−	0.996035i	$-0.471645\pi$
$823$	819.737	−	473.275i	0.996035	−	0.575061i	0.907073	+	0.420974i	$0.138312\pi$
$824$	−36.8825	−	21.2941i	−0.0447603	−	0.0258424i
$825$	784.033	−	376.703i	0.950343	−	0.456609i
$826$	0.0536644	+	1.52371i	6.49690e−5	+	0.00184469i
$827$	−1302.22			−1.57463			−0.787313	−	0.616554i	$-0.788528\pi$
$827$	−1302.22			−1.57463			−0.787313	+	0.616554i	$0.788528\pi$
$828$	243.550	+	810.851i	0.294142	+	0.979289i
$829$	431.724	+	747.768i	0.520777	+	0.902012i	0.999708	+	0.0241599i	$0.00769107\pi$
$829$	431.724	+	747.768i	0.520777	+	0.902012i	−0.478931	+	0.877853i	$0.658976\pi$
$830$	−29.9395	−	7.38055i	−0.0360717	−	0.00889223i
$831$	−328.284	−	38.2209i	−0.395047	−	0.0459939i
$832$			449.381i			0.540122i
$833$	126.489	+	187.286i	0.151847	+	0.224833i
$834$	62.1722	−	26.8517i	0.0745470	−	0.0321963i
$835$	−16.0712	−	55.4916i	−0.0192469	−	0.0664569i
$836$	−473.687	+	273.483i	−0.566611	+	0.327133i
$837$	1248.70	−	221.922i	1.49188	−	0.265140i
$838$	−31.0556	−	17.9300i	−0.0370592	−	0.0213961i
$839$		−	1072.55i		−	1.27836i	−0.769057	−	0.639181i	$-0.779274\pi$
$839$		−	1072.55i		−	1.27836i	0.769057	−	0.639181i	$-0.220726\pi$
$840$	−45.5856	+	136.463i	−0.0542686	+	0.162456i
$841$	−232.163			−0.276056
$842$	32.8825	−	56.9542i	0.0390529	−	0.0676415i
$843$	−716.602	+	963.470i	−0.850062	+	1.14291i
$844$	112.974	+	195.676i	0.133855	+	0.231844i
$845$	−160.022	−	552.533i	−0.189375	−	0.653886i
$846$	−55.4017	+	58.8286i	−0.0654866	+	0.0695373i
$847$	44.3691	−	83.5062i	0.0523838	−	0.0985905i
$848$	−360.192			−0.424754
$849$	−953.398	−	111.001i	−1.12297	−	0.130743i
$850$	16.7548	−	10.5934i	0.0197115	−	0.0124629i
$851$	−978.090	+	564.701i	−1.14934	+	0.663573i
$852$	−570.266	−	66.3939i	−0.669326	−	0.0779271i
$853$		−	328.468i		−	0.385074i	−0.981290	−	0.192537i	$-0.938328\pi$
$853$		−	328.468i		−	0.385074i	0.981290	−	0.192537i	$-0.0616715\pi$
$854$	−41.2512	−	65.9720i	−0.0483035	−	0.0772505i
$855$	−26.7645	−	533.843i	−0.0313035	−	0.624378i
$856$	125.012	−	216.527i	0.146042	−	0.252953i
$857$	404.874	+	701.262i	0.472431	+	0.818275i	0.999502	−	0.0315461i	$-0.0100431\pi$
$857$	404.874	+	701.262i	0.472431	+	0.818275i	−0.527071	+	0.849821i	$0.676710\pi$
$858$	−35.2536	−	26.2207i	−0.0410882	−	0.0305602i
$859$	288.964	−	500.501i	0.336396	−	0.582655i	−0.647356	−	0.762188i	$-0.724125\pi$
$859$	288.964	−	500.501i	0.336396	−	0.582655i	0.983752	+	0.179533i	$0.0574585\pi$
$860$	−202.219	−	194.247i	−0.235138	−	0.225869i
$861$	−843.901	+	1222.22i	−0.980141	+	1.41954i
$862$		−	80.1027i		−	0.0929266i
$863$	−270.895	+	469.205i	−0.313900	+	0.543690i	−0.979203	−	0.202883i	$-0.934969\pi$
$863$	−270.895	+	469.205i	−0.313900	+	0.543690i	0.665303	+	0.746573i	$0.268302\pi$
$864$	217.208	−	38.6027i	0.251399	−	0.0446791i
$865$	18.9654	+	4.67526i	0.0219253	+	0.00540493i
$866$	−114.496	−	66.1045i	−0.132213	−	0.0763332i
$867$	737.352	−	318.457i	0.850463	−	0.367309i
$868$	612.564	−	1152.89i	0.705718	−	1.32822i
$869$		−	799.109i		−	0.919573i
$870$	65.1745	−	53.7467i	0.0749132	−	0.0617778i
$871$	72.8409	+	126.164i	0.0836290	+	0.144850i
$872$	−23.3624	−	40.4649i	−0.0267918	−	0.0464047i
$873$	−232.320	+	69.7803i	−0.266117	+	0.0799316i
$874$	48.3814			0.0553563
$875$	674.905	+	556.892i	0.771320	+	0.636448i
$876$	587.671	+	1360.69i	0.670858	+	1.55330i
$877$	1078.25	+	622.527i	1.22947	+	0.709837i	0.966920	−	0.255080i	$-0.0821018\pi$
$877$	1078.25	+	622.527i	1.22947	+	0.709837i	0.262554	+	0.964917i	$0.415435\pi$
$878$	−22.1864	−	38.4281i	−0.0252693	−	0.0437677i
$879$	791.285	+	588.536i	0.900211	+	0.669551i
$880$	−871.494	+	252.398i	−0.990335	+	0.286816i
$881$			1358.85i			1.54239i	0.636596	+	0.771197i	$0.280342\pi$
$881$			1358.85i			1.54239i	−0.636596	+	0.771197i	$0.719658\pi$
$882$	−74.8296	−	12.1834i	−0.0848408	−	0.0138134i
$883$		−	130.644i		−	0.147954i	−0.997260	−	0.0739771i	$-0.976431\pi$
$883$		−	130.644i		−	0.147954i	0.997260	−	0.0739771i	$-0.0235692\pi$
$884$	116.489	+	67.2548i	0.131775	+	0.0760800i
$885$	−3.14019	−	18.7430i	−0.00354824	−	0.0211785i
$886$	34.7660	+	60.2164i	0.0392392	+	0.0679644i
$887$	−131.126	+	227.117i	−0.147831	+	0.256050i	−0.930425	−	0.366481i	$-0.880562\pi$
$887$	−131.126	+	227.117i	−0.147831	+	0.256050i	0.782595	+	0.622532i	$0.213896\pi$
$888$	77.6941	+	179.892i	0.0874934	+	0.202581i
$889$	32.5218	+	923.404i	0.0365825	+	1.03870i
$890$	79.1248	+	76.0058i	0.0889042	+	0.0853997i
$891$	420.097	−	840.256i	0.471489	−	0.943049i
$892$	362.964	−	209.557i	0.406910	−	0.234930i
$893$	−310.184	−	537.254i	−0.347350	−	0.601629i
$894$	48.4610	+	5.64213i	0.0542069	+	0.00631110i
$895$	−794.050	−	762.750i	−0.887207	−	0.852234i
$896$	141.892	−	267.053i	0.158362	−	0.298050i
$897$	−207.004	−	479.294i	−0.230773	−	0.534330i
$898$	−3.58348	−	2.06892i	−0.00399051	−	0.00230392i
$899$	−1332.64	+	769.398i	−1.48236	+	0.855838i
$900$	170.123	−	877.002i	0.189026	−	0.974447i
$901$	−53.0889	+	91.9527i	−0.0589222	+	0.102056i
$902$	141.018			0.156339
$903$	168.531	−	244.083i	0.186634	−	0.270302i
$904$	87.7529			0.0970718
$905$	−108.292	−	373.915i	−0.119659	−	0.413166i
$906$	−12.2737	−	9.12883i	−0.0135471	−	0.0100760i
$907$	−605.517	+	349.595i	−0.667604	+	0.385441i	−0.795168	−	0.606389i	$-0.792617\pi$
$907$	−605.517	+	349.595i	−0.667604	+	0.385441i	0.127564	+	0.991830i	$0.459284\pi$
$908$	767.724	−	1329.74i	0.845512	−	1.46447i
$909$	119.967	+	112.979i	0.131977	+	0.124289i
$910$	9.06150	−	43.2577i	0.00995769	−	0.0475359i
$911$			932.168i			1.02324i	0.859213	+	0.511618i	$0.170954\pi$
$911$			932.168i			1.02324i	−0.859213	+	0.511618i	$0.829046\pi$
$912$	−64.4769	+	553.800i	−0.0706983	+	0.607237i
$913$	360.309	−	208.024i	0.394643	−	0.227847i
$914$	31.5746	−	18.2296i	0.0345455	−	0.0199448i
$915$	617.033	+	748.229i	0.674353	+	0.817736i
$916$	−111.897			−0.122159
$917$	−496.078	−	263.579i	−0.540979	−	0.287437i
$918$	7.29497	−	20.1274i	0.00794659	−	0.0219253i
$919$	421.415	−	729.912i	0.458558	−	0.794246i	−0.540327	−	0.841455i	$-0.681699\pi$
$919$	421.415	−	729.912i	0.458558	−	0.794246i	0.998885	+	0.0472093i	$0.0150328\pi$
$920$	157.607	+	38.8525i	0.171312	+	0.0422309i
$921$	776.380	−	1043.84i	0.842975	−	1.13338i
$922$	46.9883	+	27.1287i	0.0509634	+	0.0294237i
$923$	354.034			0.383569
$924$	−414.425	−	873.712i	−0.448512	−	0.945576i
$925$	1190.75	−	47.9011i	1.28730	−	0.0517850i
$926$	91.1978	+	52.6531i	0.0984857	+	0.0568608i
$927$	−64.2639	+	272.245i	−0.0693246	+	0.293684i
$928$	−231.808	+	133.835i	−0.249793	+	0.144218i
$929$	498.241	+	287.660i	0.536320	+	0.309645i	0.743586	−	0.668640i	$-0.233123\pi$
$929$	498.241	+	287.660i	0.536320	+	0.309645i	−0.207266	+	0.978285i	$0.566457\pi$
$930$	42.3993	−	113.468i	0.0455906	−	0.122009i
$931$	254.831	−	523.274i	0.273718	−	0.562056i
$932$	−1358.02			−1.45710
$933$	−1067.06	−	124.233i	−1.14368	−	0.133155i
$934$	34.6194	+	59.9626i	0.0370658	+	0.0641998i
$935$	−64.0160	+	259.683i	−0.0684663	+	0.277736i
$936$	−86.7539	+	26.0577i	−0.0926858	+	0.0278394i
$937$		−	23.2884i		−	0.0248542i	−0.999923	−	0.0124271i	$-0.996044\pi$
$937$		−	23.2884i		−	0.0248542i	0.999923	−	0.0124271i	$-0.00395577\pi$
$938$	−0.840096	−	23.8532i	−0.000895625	−	0.0254298i
$939$	−265.959	−	615.798i	−0.283236	−	0.655802i
$940$	−288.432	−	995.915i	−0.306842	−	1.05948i
$941$	338.756	−	195.581i	0.359996	−	0.207844i	−0.309083	−	0.951035i	$-0.600022\pi$
$941$	338.756	−	195.581i	0.359996	−	0.207844i	0.669079	+	0.743191i	$0.266689\pi$
$942$	14.1451	−	19.0181i	0.0150160	−	0.0201890i
$943$	1451.21	+	837.855i	1.53893	+	0.888500i
$944$			19.8229i			0.0209988i
$945$	944.557	+	28.9181i	0.999532	+	0.0306011i
$946$	−28.1619			−0.0297694
$947$	343.972	−	595.777i	0.363223	−	0.629120i	−0.625267	−	0.780411i	$-0.715010\pi$
$947$	343.972	−	595.777i	0.363223	−	0.629120i	0.988489	+	0.151291i	$0.0483431\pi$
$948$	−658.533	−	489.798i	−0.694655	−	0.516665i
$949$	−456.996	−	791.540i	−0.481555	−	0.834078i
$950$	−45.2016	−	23.7277i	−0.0475806	−	0.0249765i
$951$	−1476.27	+	637.590i	−1.55233	+	0.670441i
$952$	−23.4543	−	37.5099i	−0.0246369	−	0.0394011i
$953$	650.515			0.682597			0.341299	−	0.939955i	$-0.389133\pi$
$953$	650.515			0.682597			0.341299	+	0.939955i	$0.389133\pi$
$954$	−10.2464	−	34.1135i	−0.0107405	−	0.0357584i
$955$	−284.510	+	1154.13i	−0.297916	+	1.20851i
$956$	−363.065	+	209.616i	−0.379775	+	0.219263i
$957$	−131.813	+	1132.15i	−0.137735	+	1.18302i
$958$			46.1422i			0.0481651i
$959$	−577.057	−	922.871i	−0.601727	−	0.962326i
$960$	−321.221	+	859.648i	−0.334606	+	0.895467i
$961$	−622.732	+	1078.60i	−0.648004	+	1.12238i
$962$	−30.0970	−	52.1295i	−0.0312858	−	0.0541886i
$963$	−1598.28	−	377.276i	−1.65968	−	0.391772i
$964$	37.8613	−	65.5777i	0.0392752	−	0.0680266i
$965$	−760.825	−	730.835i	−0.788420	−	0.757342i
$966$	−6.89526	+	85.2582i	−0.00713795	+	0.0882590i
$967$			1283.37i			1.32717i	0.748100	+	0.663586i	$0.230966\pi$
$967$			1283.37i			1.32717i	−0.748100	+	0.663586i	$0.769034\pi$
$968$	−9.25519	+	16.0305i	−0.00956115	+	0.0165604i
$969$	131.875	+	98.0852i	0.136094	+	0.101223i
$970$	−5.54523	+	22.4945i	−0.00571674	+	0.0231902i
$971$	197.998	+	114.314i	0.203912	+	0.117728i	0.598479	−	0.801139i	$-0.295772\pi$
$971$	197.998	+	114.314i	0.203912	+	0.117728i	−0.394567	+	0.918867i	$0.629105\pi$
$972$	−434.952	−	861.215i	−0.447482	−	0.886023i
$973$	−918.602	+	32.3527i	−0.944092	+	0.0332504i
$974$			12.0955i			0.0124184i
$975$	−41.6618	+	549.313i	−0.0427300	+	0.563398i
$976$	−505.807	−	876.084i	−0.518245	−	0.897627i
$977$	757.438	+	1311.92i	0.775270	+	1.34281i	0.934643	+	0.355588i	$0.115719\pi$
$977$	757.438	+	1311.92i	0.775270	+	1.34281i	−0.159373	+	0.987218i	$0.550947\pi$
$978$	−108.978	−	12.6879i	−0.111430	−	0.0129733i
$979$	−1480.33			−1.51209
$980$	622.855	−	747.203i	0.635566	−	0.762452i
$981$	−210.404	+	223.418i	−0.214479	+	0.227745i
$982$	85.3928	+	49.3016i	0.0869581	+	0.0502053i
$983$	10.5805	+	18.3259i	0.0107635	+	0.0186429i	0.871357	−	0.490650i	$-0.163240\pi$
$983$	10.5805	+	18.3259i	0.0107635	+	0.0186429i	−0.860594	+	0.509292i	$0.829907\pi$
$984$	173.512	−	233.286i	0.176333	−	0.237080i
$985$	−526.787	−	1818.92i	−0.534809	−	1.84662i
$986$			25.9752i			0.0263440i
$987$	990.961	−	470.040i	1.00401	−	0.476231i
$988$		−	346.410i		−	0.350617i
$989$	−289.812	−	167.323i	−0.293036	−	0.169184i
$990$	−48.6960	−	75.3586i	−0.0491879	−	0.0761198i
$991$	439.883	+	761.900i	0.443878	+	0.768819i	0.997973	−	0.0636342i	$-0.0202691\pi$
$991$	439.883	+	761.900i	0.443878	+	0.768819i	−0.554095	+	0.832453i	$0.686936\pi$
$992$	−191.904	+	332.387i	−0.193452	+	0.335068i
$993$	−592.766	+	256.011i	−0.596944	+	0.257816i
$994$	−51.2222	−	27.2157i	−0.0515314	−	0.0273800i
$995$	659.716	−	686.788i	0.663031	−	0.690239i
$996$	49.4148	−	424.430i	0.0496132	−	0.426134i
$997$	−1155.75	+	667.271i	−1.15922	+	0.669279i	−0.951118	−	0.308827i	$-0.900063\pi$
$997$	−1155.75	+	667.271i	−1.15922	+	0.669279i	−0.208107	+	0.978106i	$0.566730\pi$
$998$	−3.37740	−	5.84982i	−0.00338417	−	0.00586155i
$999$	984.818	−	828.633i	0.985804	−	0.829463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.o.b.44.10	yes	40
3.2	odd	2	inner	105.3.o.b.44.12	yes	40
5.4	even	2	inner	105.3.o.b.44.11	yes	40
7.4	even	3	inner	105.3.o.b.74.9	yes	40
15.14	odd	2	inner	105.3.o.b.44.9	✓	40
21.11	odd	6	inner	105.3.o.b.74.11	yes	40
35.4	even	6	inner	105.3.o.b.74.12	yes	40
105.74	odd	6	inner	105.3.o.b.74.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.b.44.9	✓	40	15.14	odd	2	inner
105.3.o.b.44.10	yes	40	1.1	even	1	trivial
105.3.o.b.44.11	yes	40	5.4	even	2	inner
105.3.o.b.44.12	yes	40	3.2	odd	2	inner
105.3.o.b.74.9	yes	40	7.4	even	3	inner
105.3.o.b.74.10	yes	40	105.74	odd	6	inner
105.3.o.b.74.11	yes	40	21.11	odd	6	inner
105.3.o.b.74.12	yes	40	35.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0859580 + 0.148884i) q^{2} +(2.40718 + 1.79039i) q^{3} +(1.98522 + 3.43851i) q^{4} +(-1.39092 - 4.80264i) q^{5} +(-0.473476 + 0.204491i) q^{6} +(6.99566 - 0.246384i) q^{7} -1.37025 q^{8} +(2.58900 + 8.61957i) q^{9} +O(q^{10})\)	\(q+(-0.0859580 + 0.148884i) q^{2} +(2.40718 + 1.79039i) q^{3} +(1.98522 + 3.43851i) q^{4} +(-1.39092 - 4.80264i) q^{5} +(-0.473476 + 0.204491i) q^{6} +(6.99566 - 0.246384i) q^{7} -1.37025 q^{8} +(2.58900 + 8.61957i) q^{9} +(0.834595 + 0.205740i) q^{10} +(-10.0440 + 5.79890i) q^{11} +(-1.37749 + 11.8314i) q^{12} -7.34521i q^{13} +(-0.564650 + 1.06272i) q^{14} +(5.25042 - 14.0511i) q^{15} +(-7.82311 + 13.5500i) q^{16} +(2.30611 + 3.99429i) q^{17} +(-1.50586 - 0.355461i) q^{18} +(5.93904 - 10.2867i) q^{19} +(13.7526 - 14.3170i) q^{20} +(17.2809 + 11.9319i) q^{21} -1.99385i q^{22} +(11.8464 - 20.5186i) q^{23} +(-3.29843 - 2.45328i) q^{24} +(-21.1307 + 13.3601i) q^{25} +(1.09358 + 0.631380i) q^{26} +(-9.20022 + 25.3842i) q^{27} +(14.7351 + 23.5655i) q^{28} -32.7592i q^{29} +(1.64066 + 1.98950i) q^{30} +(-23.4865 - 40.6798i) q^{31} +(-4.08541 - 7.07614i) q^{32} +(-34.5599 - 4.02368i) q^{33} -0.792913 q^{34} +(-10.9137 - 33.2549i) q^{35} +(-24.4987 + 26.0141i) q^{36} +(-41.2822 - 23.8343i) q^{37} +(1.02102 + 1.76845i) q^{38} +(13.1508 - 17.6812i) q^{39} +(1.90590 + 6.58080i) q^{40} +70.7266i q^{41} +(-3.26189 + 1.54721i) q^{42} -14.1244i q^{43} +(-39.8791 - 23.0242i) q^{44} +(37.7956 - 24.4232i) q^{45} +(2.03658 + 3.52747i) q^{46} +(26.1140 - 45.2307i) q^{47} +(-43.0914 + 18.6109i) q^{48} +(48.8786 - 3.44723i) q^{49} +(-0.172755 - 4.29442i) q^{50} +(-1.60014 + 13.7438i) q^{51} +(25.2566 - 14.5819i) q^{52} +(11.5105 + 19.9368i) q^{53} +(-2.98845 - 3.55173i) q^{54} +(41.8204 + 40.1718i) q^{55} +(-9.58578 + 0.337606i) q^{56} +(32.7136 - 14.1288i) q^{57} +(4.87730 + 2.81591i) q^{58} +(1.09721 - 0.633473i) q^{59} +(58.7380 - 9.84095i) q^{60} +(-32.3278 + 55.9933i) q^{61} +8.07541 q^{62} +(20.2355 + 59.6617i) q^{63} -61.1802 q^{64} +(-35.2764 + 10.2166i) q^{65} +(3.56976 - 4.79954i) q^{66} +(-17.1764 + 9.91678i) q^{67} +(-9.15627 + 15.8591i) q^{68} +(65.2526 - 28.1821i) q^{69} +(5.88923 + 1.23366i) q^{70} +48.1993i q^{71} +(-3.54757 - 11.8109i) q^{72} +(107.763 - 62.2168i) q^{73} +(7.09706 - 4.09749i) q^{74} +(-74.7852 - 5.67196i) q^{75} +47.1613 q^{76} +(-68.8356 + 43.0418i) q^{77} +(1.50203 + 3.47778i) q^{78} +(-34.4509 + 59.6707i) q^{79} +(75.9571 + 18.7246i) q^{80} +(-67.5941 + 44.6322i) q^{81} +(-10.5300 - 6.07951i) q^{82} -35.8731 q^{83} +(-6.72137 + 83.1080i) q^{84} +(15.9756 - 16.6311i) q^{85} +(2.10289 + 1.21410i) q^{86} +(58.6517 - 78.8571i) q^{87} +(13.7627 - 7.94592i) q^{88} +(110.539 + 63.8196i) q^{89} +(0.387373 + 7.72651i) q^{90} +(-1.80974 - 51.3846i) q^{91} +94.0709 q^{92} +(16.2966 - 139.974i) q^{93} +(4.48941 + 7.77588i) q^{94} +(-57.6641 - 14.2151i) q^{95} +(2.83474 - 24.3480i) q^{96} +26.9526i q^{97} +(-3.68827 + 7.57354i) q^{98} +(-75.9879 - 71.5615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9}+O(q^{10}) \) 40 * q - 44 * q^4 + 80 * q^6 + 12 * q^9	\( 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9} + 62 q^{10} + 84 q^{15} - 116 q^{16} - 56 q^{19} + 36 q^{21} - 12 q^{24} - 6 q^{25} - 20 q^{30} - 444 q^{31} + 256 q^{34} - 688 q^{36} + 168 q^{39} + 54 q^{40} - 40 q^{45} + 304 q^{46} + 156 q^{49} + 156 q^{51} - 140 q^{54} - 500 q^{55} - 130 q^{60} + 288 q^{61} + 472 q^{64} + 340 q^{66} - 272 q^{69} + 710 q^{70} - 524 q^{75} + 400 q^{76} - 340 q^{79} + 496 q^{84} + 896 q^{85} + 1356 q^{90} - 656 q^{91} - 560 q^{94} + 472 q^{96} - 336 q^{99}+O(q^{100}) \) 40 * q - 44 * q^4 + 80 * q^6 + 12 * q^9 + 62 * q^10 + 84 * q^15 - 116 * q^16 - 56 * q^19 + 36 * q^21 - 12 * q^24 - 6 * q^25 - 20 * q^30 - 444 * q^31 + 256 * q^34 - 688 * q^36 + 168 * q^39 + 54 * q^40 - 40 * q^45 + 304 * q^46 + 156 * q^49 + 156 * q^51 - 140 * q^54 - 500 * q^55 - 130 * q^60 + 288 * q^61 + 472 * q^64 + 340 * q^66 - 272 * q^69 + 710 * q^70 - 524 * q^75 + 400 * q^76 - 340 * q^79 + 496 * q^84 + 896 * q^85 + 1356 * q^90 - 656 * q^91 - 560 * q^94 + 472 * q^96 - 336 * q^99

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