LMFDB - Embedded newform 135.3.r.a.97.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(7,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([32, 9]))

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

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

chi := DirichletCharacter("135.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.r (of order $36$, degree $12$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			97.27
Character	$\chi$	$=$	135.97
Dual form			135.3.r.a.103.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.205868 + 2.35308i) q^{2} +(-2.50133 - 1.65630i) q^{3} +(-1.55539 + 0.274257i) q^{4} +(4.64198 + 1.85797i) q^{5} +(3.38248 - 6.22682i) q^{6} +(-2.93406 + 2.05445i) q^{7} +(1.47984 + 5.52284i) q^{8} +(3.51332 + 8.28593i) q^{9} +(-3.41632 + 11.3055i) q^{10} +(3.30286 - 1.20214i) q^{11} +(4.34480 + 1.89019i) q^{12} +(-1.27699 + 14.5961i) q^{13} +(-5.43832 - 6.48114i) q^{14} +(-8.53376 - 12.3359i) q^{15} +(-18.6276 + 6.77989i) q^{16} +(-1.65433 + 6.17406i) q^{17} +(-18.7742 + 9.97294i) q^{18} +(1.16951 + 0.675215i) q^{19} +(-7.72965 - 1.61677i) q^{20} +(10.7418 - 0.279168i) q^{21} +(3.50870 + 7.52443i) q^{22} +(-4.93199 - 3.45342i) q^{23} +(5.44593 - 16.2655i) q^{24} +(18.0959 + 17.2493i) q^{25} -34.6088 q^{26} +(4.93604 - 26.5450i) q^{27} +(4.00016 - 4.00016i) q^{28} +(36.1603 - 43.0941i) q^{29} +(27.2706 - 22.6202i) q^{30} +(1.46325 + 8.29852i) q^{31} +(-10.1229 - 21.7087i) q^{32} +(-10.2527 - 2.46358i) q^{33} +(-14.8687 - 2.62174i) q^{34} +(-17.4369 + 4.08532i) q^{35} +(-7.73706 - 11.9243i) q^{36} +(-5.71940 + 21.3451i) q^{37} +(-1.34807 + 2.89095i) q^{38} +(27.3698 - 34.3946i) q^{39} +(-3.39188 + 28.3864i) q^{40} +(16.5803 - 13.9125i) q^{41} +(2.86831 + 25.2190i) q^{42} +(19.5707 - 41.9694i) q^{43} +(-4.80755 + 2.77564i) q^{44} +(0.913732 + 44.9907i) q^{45} +(7.11084 - 12.3163i) q^{46} +(37.1779 - 26.0322i) q^{47} +(57.8234 + 13.8942i) q^{48} +(-12.3711 + 33.9892i) q^{49} +(-36.8637 + 46.1322i) q^{50} +(14.3642 - 12.7033i) q^{51} +(-2.01687 - 23.0529i) q^{52} +(-51.1073 + 51.1073i) q^{53} +(63.4787 + 6.15016i) q^{54} +(17.5654 + 0.556295i) q^{55} +(-15.6883 - 13.1641i) q^{56} +(-1.80696 - 3.62599i) q^{57} +(108.848 + 76.2164i) q^{58} +(28.7190 - 78.9047i) q^{59} +(16.6566 + 16.8467i) q^{60} +(16.5080 - 93.6215i) q^{61} +(-19.2259 + 5.15156i) q^{62} +(-27.3313 - 17.0935i) q^{63} +(-19.6708 + 11.3569i) q^{64} +(-33.0469 + 65.3822i) q^{65} +(3.68632 - 24.6326i) q^{66} +(-72.9564 - 6.38285i) q^{67} +(0.879855 - 10.0568i) q^{68} +(6.61664 + 16.8070i) q^{69} +(-13.2028 - 40.1895i) q^{70} +(-27.8020 - 48.1545i) q^{71} +(-40.5627 + 31.6653i) q^{72} +(-34.7929 - 129.849i) q^{73} +(-51.4043 - 9.06396i) q^{74} +(-16.6938 - 73.1185i) q^{75} +(-2.00422 - 0.729477i) q^{76} +(-7.22105 + 10.3127i) q^{77} +(86.5680 + 57.3227i) q^{78} +(-24.0782 + 28.6953i) q^{79} +(-99.0658 - 3.13742i) q^{80} +(-56.3132 + 58.2222i) q^{81} +(36.1506 + 36.1506i) q^{82} +(4.86489 - 0.425622i) q^{83} +(-16.6312 + 3.38025i) q^{84} +(-19.1506 + 25.5861i) q^{85} +(102.787 + 37.4112i) q^{86} +(-161.826 + 47.9003i) q^{87} +(11.5270 + 16.4622i) q^{88} +(79.3775 + 45.8286i) q^{89} +(-105.679 + 11.4122i) q^{90} +(-26.2402 - 45.4494i) q^{91} +(8.61830 + 4.01878i) q^{92} +(10.0848 - 23.1809i) q^{93} +(68.9097 + 82.1234i) q^{94} +(4.17429 + 5.30724i) q^{95} +(-10.6354 + 71.0673i) q^{96} +(48.9432 + 22.8226i) q^{97} +(-82.5262 - 22.1128i) q^{98} +(21.5649 + 23.1438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23}+ \cdots - 1032 q^{98}+O(q^{100}) $ 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.205868	+	2.35308i	0.102934	+	1.17654i	0.855420	+	0.517934i	$0.173299\pi$
$2$	0.205868	+	2.35308i	0.102934	+	1.17654i	−0.752486	+	0.658608i	$0.771146\pi$
$3$	−2.50133	−	1.65630i	−0.833777	−	0.552101i
$3$	−2.50133	−	1.65630i	−0.833777	−	0.552101i
$4$	−1.55539	+	0.274257i	−0.388848	+	0.0685644i
$5$	4.64198	+	1.85797i	0.928395	+	0.371594i
$5$	4.64198	+	1.85797i	0.928395	+	0.371594i
$6$	3.38248	−	6.22682i	0.563746	−	1.03780i
$7$	−2.93406	+	2.05445i	−0.419151	+	0.293493i	−0.764062	−	0.645143i	$-0.776798\pi$
$7$	−2.93406	+	2.05445i	−0.419151	+	0.293493i	0.344911	+	0.938635i	$0.387909\pi$
$8$	1.47984	+	5.52284i	0.184980	+	0.690355i
$9$	3.51332	+	8.28593i	0.390369	+	0.920659i
$10$	−3.41632	+	11.3055i	−0.341632	+	1.13055i
$11$	3.30286	−	1.20214i	0.300260	−	0.109286i	−0.187497	−	0.982265i	$-0.560037\pi$
$11$	3.30286	−	1.20214i	0.300260	−	0.109286i	0.487757	+	0.872979i	$0.337815\pi$
$12$	4.34480	+	1.89019i	0.362067	+	0.157516i
$13$	−1.27699	+	14.5961i	−0.0982304	+	1.12278i	0.773834	+	0.633388i	$0.218336\pi$
$13$	−1.27699	+	14.5961i	−0.0982304	+	1.12278i	−0.872065	+	0.489390i	$0.837219\pi$
$14$	−5.43832	−	6.48114i	−0.388452	−	0.462938i
$15$	−8.53376	−	12.3359i	−0.568917	−	0.822395i
$16$	−18.6276	+	6.77989i	−1.16423	+	0.423743i
$17$	−1.65433	+	6.17406i	−0.0973137	+	0.363180i	−0.997360	−	0.0726143i	$-0.976866\pi$
$17$	−1.65433	+	6.17406i	−0.0973137	+	0.363180i	0.900046	+	0.435794i	$0.143532\pi$
$18$	−18.7742	+	9.97294i	−1.04301	+	0.554052i
$19$	1.16951	+	0.675215i	0.0615530	+	0.0355376i	0.530461	−	0.847710i	$-0.322019\pi$
$19$	1.16951	+	0.675215i	0.0615530	+	0.0355376i	−0.468908	+	0.883247i	$0.655352\pi$
$20$	−7.72965	−	1.61677i	−0.386483	−	0.0808387i
$21$	10.7418	−	0.279168i	0.511516	−	0.0132937i
$22$	3.50870	+	7.52443i	0.159486	+	0.342020i
$23$	−4.93199	−	3.45342i	−0.214434	−	0.150149i	0.461425	−	0.887179i	$-0.347338\pi$
$23$	−4.93199	−	3.45342i	−0.214434	−	0.150149i	−0.675859	+	0.737031i	$0.736227\pi$
$24$	5.44593	−	16.2655i	0.226914	−	0.677730i
$25$	18.0959	+	17.2493i	0.723836	+	0.689972i
$26$	−34.6088			−1.33111
$27$	4.93604	−	26.5450i	0.182816	−	0.983147i
$28$	4.00016	−	4.00016i	0.142863	−	0.142863i
$29$	36.1603	−	43.0941i	1.24691	−	1.48600i	0.436981	−	0.899471i	$-0.356048\pi$
$29$	36.1603	−	43.0941i	1.24691	−	1.48600i	0.809925	−	0.586534i	$-0.199508\pi$
$30$	27.2706	−	22.6202i	0.909021	−	0.754008i
$31$	1.46325	+	8.29852i	0.0472017	+	0.267694i	0.999271	−	0.0381899i	$-0.0121592\pi$
$31$	1.46325	+	8.29852i	0.0472017	+	0.267694i	−0.952069	+	0.305884i	$0.901048\pi$
$32$	−10.1229	−	21.7087i	−0.316342	−	0.678397i
$33$	−10.2527	−	2.46358i	−0.310687	−	0.0746540i
$34$	−14.8687	−	2.62174i	−0.437313	−	0.0771101i
$35$	−17.4369	+	4.08532i	−0.498198	+	0.116723i
$36$	−7.73706	−	11.9243i	−0.214918	−	0.331231i
$37$	−5.71940	+	21.3451i	−0.154578	+	0.576895i	0.844563	+	0.535457i	$0.179861\pi$
$37$	−5.71940	+	21.3451i	−0.154578	+	0.576895i	−0.999141	+	0.0414379i	$0.986806\pi$
$38$	−1.34807	+	2.89095i	−0.0354756	+	0.0760777i
$39$	27.3698	−	34.3946i	0.701790	−	0.881914i
$40$	−3.39188	+	28.3864i	−0.0847971	+	0.709660i
$41$	16.5803	−	13.9125i	0.404397	−	0.339329i	−0.417793	−	0.908542i	$-0.637196\pi$
$41$	16.5803	−	13.9125i	0.404397	−	0.339329i	0.822190	+	0.569213i	$0.192752\pi$
$42$	2.86831	+	25.2190i	0.0682931	+	0.600452i
$43$	19.5707	−	41.9694i	0.455132	−	0.976033i	−0.536132	−	0.844134i	$-0.680115\pi$
$43$	19.5707	−	41.9694i	0.455132	−	0.976033i	0.991263	−	0.131898i	$-0.0421073\pi$
$44$	−4.80755	+	2.77564i	−0.109262	+	0.0630827i
$45$	0.913732	+	44.9907i	0.0203052	+	0.999794i
$46$	7.11084	−	12.3163i	0.154584	−	0.267746i
$47$	37.1779	−	26.0322i	0.791018	−	0.553877i	−0.106781	−	0.994283i	$-0.534054\pi$
$47$	37.1779	−	26.0322i	0.791018	−	0.553877i	0.897799	+	0.440406i	$0.145165\pi$
$48$	57.8234	+	13.8942i	1.20465	+	0.289463i
$49$	−12.3711	+	33.9892i	−0.252470	+	0.693657i
$50$	−36.8637	+	46.1322i	−0.737274	+	0.922645i
$51$	14.3642	−	12.7033i	0.281650	−	0.249084i
$52$	−2.01687	−	23.0529i	−0.0387859	−	0.443325i
$53$	−51.1073	+	51.1073i	−0.964289	+	0.964289i	−0.999384	−	0.0350953i	$-0.988827\pi$
$53$	−51.1073	+	51.1073i	−0.964289	+	0.964289i	0.0350953	+	0.999384i	$0.488827\pi$
$54$	63.4787	+	6.15016i	1.17553	+	0.113892i
$55$	17.5654	+	0.556295i	0.319370	+	0.0101145i
$56$	−15.6883	−	13.1641i	−0.280149	−	0.235073i
$57$	−1.80696	−	3.62599i	−0.0317011	−	0.0636139i
$58$	108.848	+	76.2164i	1.87670	+	1.31408i
$59$	28.7190	−	78.9047i	0.486762	−	1.33737i	−0.416834	−	0.908983i	$-0.636860\pi$
$59$	28.7190	−	78.9047i	0.486762	−	1.33737i	0.903596	−	0.428385i	$-0.140917\pi$
$60$	16.6566	+	16.8467i	0.277609	+	0.280779i
$61$	16.5080	−	93.6215i	0.270623	−	1.53478i	−0.481908	−	0.876222i	$-0.660056\pi$
$61$	16.5080	−	93.6215i	0.270623	−	1.53478i	0.752531	−	0.658557i	$-0.228833\pi$
$62$	−19.2259	+	5.15156i	−0.310095	+	0.0830896i
$63$	−27.3313	−	17.0935i	−0.433830	−	0.271325i
$64$	−19.6708	+	11.3569i	−0.307356	+	0.177452i
$65$	−33.0469	+	65.3822i	−0.508414	+	1.00588i
$66$	3.68632	−	24.6326i	0.0558533	−	0.373221i
$67$	−72.9564	−	6.38285i	−1.08890	−	0.0952665i	−0.471463	−	0.881886i	$-0.656274\pi$
$67$	−72.9564	−	6.38285i	−1.08890	−	0.0952665i	−0.617438	+	0.786619i	$0.711829\pi$
$68$	0.879855	−	10.0568i	0.0129390	−	0.147894i
$69$	6.61664	+	16.8070i	0.0958933	+	0.243580i
$70$	−13.2028	−	40.1895i	−0.188611	−	0.574136i
$71$	−27.8020	−	48.1545i	−0.391578	−	0.678232i	0.601080	−	0.799189i	$-0.294737\pi$
$71$	−27.8020	−	48.1545i	−0.391578	−	0.678232i	−0.992658	+	0.120956i	$0.961404\pi$
$72$	−40.5627	+	31.6653i	−0.563371	+	0.439796i
$73$	−34.7929	−	129.849i	−0.476616	−	1.77875i	−0.615165	−	0.788398i	$-0.710911\pi$
$73$	−34.7929	−	129.849i	−0.476616	−	1.77875i	0.138550	−	0.990355i	$-0.455756\pi$
$74$	−51.4043	−	9.06396i	−0.694652	−	0.122486i
$75$	−16.6938	−	73.1185i	−0.222583	−	0.974914i
$76$	−2.00422	−	0.729477i	−0.0263714	−	0.00959839i
$77$	−7.22105	+	10.3127i	−0.0937798	+	0.133931i
$78$	86.5680	+	57.3227i	1.10985	+	0.734906i
$79$	−24.0782	+	28.6953i	−0.304788	+	0.363232i	−0.896598	−	0.442845i	$-0.853969\pi$
$79$	−24.0782	+	28.6953i	−0.304788	+	0.363232i	0.591810	+	0.806077i	$0.298414\pi$
$80$	−99.0658	−	3.13742i	−1.23832	−	0.0392177i
$81$	−56.3132	+	58.2222i	−0.695225	+	0.718792i
$82$	36.1506	+	36.1506i	0.440861	+	0.440861i
$83$	4.86489	−	0.425622i	0.0586131	−	0.00512798i	−0.0578115	−	0.998328i	$-0.518412\pi$
$83$	4.86489	−	0.425622i	0.0586131	−	0.00512798i	0.116425	+	0.993200i	$0.462857\pi$
$84$	−16.6312	+	3.38025i	−0.197991	+	0.0402410i
$85$	−19.1506	+	25.5861i	−0.225301	+	0.301013i
$86$	102.787	+	37.4112i	1.19519	+	0.435014i
$87$	−161.826	+	47.9003i	−1.86007	+	0.550578i
$88$	11.5270	+	16.4622i	0.130988	+	0.187070i
$89$	79.3775	+	45.8286i	0.891882	+	0.514928i	0.874557	−	0.484922i	$-0.161152\pi$
$89$	79.3775	+	45.8286i	0.891882	+	0.514928i	0.0173241	+	0.999850i	$0.494485\pi$
$90$	−105.679	+	11.4122i	−1.17421	+	0.126803i
$91$	−26.2402	−	45.4494i	−0.288354	−	0.499444i
$92$	8.61830	+	4.01878i	0.0936772	+	0.0436824i
$93$	10.0848	−	23.1809i	0.108439	−	0.249257i
$94$	68.9097	+	82.1234i	0.733082	+	0.873654i
$95$	4.17429	+	5.30724i	0.0439399	+	0.0558657i
$96$	−10.6354	+	71.0673i	−0.110785	+	0.740284i
$97$	48.9432	+	22.8226i	0.504569	+	0.235284i	0.658199	−	0.752844i	$-0.271319\pi$
$97$	48.9432	+	22.8226i	0.504569	+	0.235284i	−0.153630	+	0.988128i	$0.549096\pi$
$98$	−82.5262	−	22.1128i	−0.842104	−	0.225641i
$99$	21.5649	+	23.1438i	0.217827	+	0.233775i
$100$	−32.8770	−	21.8665i	−0.328770	−	0.218665i
$101$	15.1212	−	85.7564i	0.149714	−	0.849073i	−0.813746	−	0.581221i	$-0.802575\pi$
$101$	15.1212	−	85.7564i	0.149714	−	0.849073i	0.963460	−	0.267852i	$-0.0863138\pi$
$102$	32.8490	+	31.1849i	0.322049	+	0.305734i
$103$	61.4201	−	28.6406i	0.596311	−	0.278064i	−0.100939	−	0.994893i	$-0.532185\pi$
$103$	61.4201	−	28.6406i	0.596311	−	0.278064i	0.697250	+	0.716828i	$0.254407\pi$
$104$	−82.5018	+	14.5473i	−0.793286	+	0.139878i
$105$	50.3821	+	18.6621i	0.479829	+	0.177735i
$106$	−130.781	−	109.738i	−1.23378	−	1.03527i
$107$	129.856	+	129.856i	1.21361	+	1.21361i	0.969831	+	0.243779i	$0.0783873\pi$
$107$	129.856	+	129.856i	1.21361	+	1.21361i	0.243779	+	0.969831i	$0.421613\pi$
$108$	−0.397323	+	42.6416i	−0.00367891	+	0.394829i
$109$			143.122i			1.31304i	0.754308	+	0.656521i	$0.227973\pi$
$109$			143.122i			1.31304i	−0.754308	+	0.656521i	$0.772027\pi$
$110$	2.30714	+	41.4473i	0.0209740	+	0.376793i
$111$	49.6601	−	43.9181i	0.447388	−	0.395659i
$112$	40.7255	−	58.1621i	0.363621	−	0.519304i
$113$	141.780	−	66.1129i	1.25469	−	0.585070i	0.322337	−	0.946625i	$-0.395532\pi$
$113$	141.780	−	66.1129i	1.25469	−	0.585070i	0.932351	+	0.361555i	$0.117754\pi$
$114$	8.16027	−	4.99841i	0.0715813	−	0.0438457i
$115$	−16.4778	−	25.1942i	−0.143286	−	0.219080i
$116$	−44.4245	+	76.9455i	−0.382970	+	0.663323i
$117$	−125.429	+	40.6997i	−1.07204	+	0.347861i
$118$	191.582	+	51.3342i	1.62357	+	0.435035i
$119$	−7.83038	−	21.5138i	−0.0658015	−	0.180788i
$120$	55.5007	−	65.3858i	0.462506	−	0.544882i
$121$	−83.2276	+	69.8363i	−0.687832	+	0.577159i
$122$	223.698	+	19.5710i	1.83359	+	0.160418i
$123$	−64.5161	+	7.33781i	−0.524521	+	0.0596570i
$124$	−4.55186	−	12.5061i	−0.0367085	−	0.100856i
$125$	51.9521	+	113.692i	0.415616	+	0.909540i
$126$	34.5957	−	67.8318i	0.274569	−	0.538348i
$127$	−21.4186	+	5.73910i	−0.168651	+	0.0451898i	−0.342156	−	0.939643i	$-0.611157\pi$
$127$	−21.4186	+	5.73910i	−0.168651	+	0.0451898i	0.173506	+	0.984833i	$0.444491\pi$
$128$	−85.7287	−	122.433i	−0.669755	−	0.956510i
$129$	−118.467	+	72.5644i	−0.918347	+	0.562515i
$130$	−160.653	−	64.3021i	−1.23579	−	0.494631i
$131$	40.7506	+	231.108i	0.311073	+	1.76418i	0.593441	+	0.804877i	$0.297769\pi$
$131$	40.7506	+	231.108i	0.311073	+	1.76418i	−0.282368	+	0.959306i	$0.591120\pi$
$132$	16.6226	+	1.01997i	0.125929	+	0.00772701i
$133$	−4.81859	+	0.421572i	−0.0362300	+	0.00316972i
$134$		−	172.986i		−	1.29094i
$135$	72.2327	−	114.050i	0.535057	−	0.844816i
$136$	−36.5465			−0.268724
$137$	2.01043	+	22.9793i	0.0146746	+	0.167732i	0.999996	−	0.00298038i	$-0.000948687\pi$
$137$	2.01043	+	22.9793i	0.0146746	+	0.167732i	−0.985321	+	0.170712i	$0.945393\pi$
$138$	−38.1862	+	19.0295i	−0.276711	+	0.137895i
$139$	−139.754	+	24.6424i	−1.00543	+	0.177284i	−0.652033	−	0.758191i	$-0.726083\pi$
$139$	−139.754	+	24.6424i	−1.00543	+	0.177284i	−0.353394	+	0.935475i	$0.614972\pi$
$140$	26.0008	−	11.1365i	0.185720	−	0.0795463i
$141$	−136.111	+	3.53738i	−0.965329	+	0.0250878i
$142$	107.588	−	75.3339i	0.757662	−	0.530521i
$143$	13.3289	+	49.7441i	0.0932090	+	0.347861i
$144$	−121.622	−	130.527i	−0.844600	−	0.906438i
$145$	247.923	−	132.857i	1.70981	−	0.916257i
$146$	298.383	−	108.602i	2.04372	−	0.743853i
$147$	87.2405	−	64.5280i	0.593473	−	0.438966i
$148$	3.04186	−	34.7686i	0.0205531	−	0.234923i
$149$	135.284	+	161.225i	0.907946	+	1.08205i	0.996299	+	0.0859583i	$0.0273952\pi$
$149$	135.284	+	161.225i	0.907946	+	1.08205i	−0.0883531	+	0.996089i	$0.528160\pi$
$150$	168.617	−	54.3346i	1.12412	−	0.362230i
$151$	−238.024	+	86.6336i	−1.57632	+	0.573732i	−0.974399	−	0.224826i	$-0.927819\pi$
$151$	−238.024	+	86.6336i	−1.57632	+	0.573732i	−0.601917	+	0.798558i	$0.705596\pi$
$152$	−1.99842	+	7.45821i	−0.0131475	+	0.0490672i
$153$	−56.9700	+	7.98373i	−0.372353	+	0.0521812i
$154$	−25.7533	−	14.8687i	−0.167229	−	0.0965498i
$155$	−8.62601	+	41.2402i	−0.0556517	+	0.266066i
$156$	−33.1378	+	61.0035i	−0.212422	+	0.391048i
$157$	−37.1814	−	79.7357i	−0.236824	−	0.507871i	0.751594	−	0.659626i	$-0.229285\pi$
$157$	−37.1814	−	79.7357i	−0.236824	−	0.507871i	−0.988418	+	0.151755i	$0.951508\pi$
$158$	−72.4795	−	50.7507i	−0.458731	−	0.321207i
$159$	212.485	−	43.1871i	1.33639	−	0.271617i
$160$	−6.65631	−	119.579i	−0.0416020	−	0.747371i
$161$	21.5656			0.133948
$162$	−148.595	−	120.524i	−0.917252	−	0.743973i
$163$	88.1454	−	88.1454i	0.540769	−	0.540769i	−0.382985	−	0.923754i	$-0.625104\pi$
$163$	88.1454	−	88.1454i	0.540769	−	0.540769i	0.923754	+	0.382985i	$0.125104\pi$
$164$	−21.9732	+	26.1867i	−0.133983	+	0.159675i
$165$	−43.0154	−	30.4850i	−0.260699	−	0.184758i
$166$	2.00305	+	11.3599i	0.0120666	+	0.0684329i
$167$	−103.200	−	221.312i	−0.617962	−	1.32522i	−0.927317	−	0.374278i	$-0.877891\pi$
$167$	−103.200	−	221.312i	−0.617962	−	1.32522i	0.309354	−	0.950947i	$-0.399887\pi$
$168$	17.4380	+	58.9124i	0.103798	+	0.350669i
$169$	−44.9835	−	7.93180i	−0.266174	−	0.0469337i
$170$	−64.1488	−	39.7956i	−0.377346	−	0.234092i
$171$	−1.48593	+	12.0627i	−0.00868968	+	0.0705420i
$172$	−18.9296	+	70.6463i	−0.110056	+	0.410734i
$173$	56.9867	−	122.208i	0.329403	−	0.706407i	−0.669949	−	0.742407i	$-0.733684\pi$
$173$	56.9867	−	122.208i	0.329403	−	0.706407i	0.999352	+	0.0360004i	$0.0114618\pi$
$174$	−146.028	−	370.928i	−0.839243	−	2.13177i
$175$	−88.5322	−	13.4334i	−0.505898	−	0.0767620i
$176$	−53.3740	+	44.7861i	−0.303261	+	0.254467i
$177$	−202.526	+	149.799i	−1.14421	+	0.846325i
$178$	−91.4973	+	196.216i	−0.514030	+	1.10234i
$179$	241.899	−	139.661i	1.35139	−	0.780227i	0.362949	−	0.931809i	$-0.381770\pi$
$179$	241.899	−	139.661i	1.35139	−	0.780227i	0.988445	+	0.151582i	$0.0484367\pi$
$180$	−13.7603	−	69.7276i	−0.0764459	−	0.387376i
$181$	54.3285	−	94.0998i	0.300158	−	0.519888i	−0.676014	−	0.736889i	$-0.736294\pi$
$181$	54.3285	−	94.0998i	0.300158	−	0.519888i	0.976171	+	0.217001i	$0.0696274\pi$
$182$	101.544	−	71.1020i	0.557935	−	0.390670i
$183$	−196.358	+	206.836i	−1.07299	+	1.13025i
$184$	11.7741	−	32.3491i	0.0639897	−	0.175810i
$185$	−66.2079	+	88.4570i	−0.357881	+	0.478146i
$186$	56.6228	+	18.9581i	0.304424	+	0.101925i
$187$	1.95807	+	22.3808i	0.0104709	+	0.119683i
$188$	−50.6866	+	50.6866i	−0.269610	+	0.269610i
$189$	40.0527	+	88.0253i	0.211919	+	0.465743i
$190$	−11.6290	+	10.9151i	−0.0612054	+	0.0574476i
$191$	−97.1273	−	81.4995i	−0.508520	−	0.426699i	0.352088	−	0.935967i	$-0.385472\pi$
$191$	−97.1273	−	81.4995i	−0.508520	−	0.426699i	−0.860608	+	0.509268i	$0.829916\pi$
$192$	68.0137	+	4.17334i	0.354238	+	0.0217361i
$193$	−74.9327	−	52.4685i	−0.388253	−	0.271857i	0.363111	−	0.931746i	$-0.381715\pi$
$193$	−74.9327	−	52.4685i	−0.388253	−	0.271857i	−0.751363	+	0.659889i	$0.770603\pi$
$194$	−43.6276	+	119.866i	−0.224885	+	0.617865i
$195$	190.954	−	108.807i	0.979252	−	0.557984i
$196$	9.92004	−	56.2594i	0.0506125	−	0.287038i
$197$	−68.0511	+	18.2342i	−0.345437	+	0.0925596i	−0.427366	−	0.904079i	$-0.640559\pi$
$197$	−68.0511	+	18.2342i	−0.345437	+	0.0925596i	0.0819292	+	0.996638i	$0.473892\pi$
$198$	−50.0197	+	55.5085i	−0.252625	+	0.280346i
$199$	214.694	−	123.954i	1.07886	−	0.622883i	0.148274	−	0.988946i	$-0.452628\pi$
$199$	214.694	−	123.954i	1.07886	−	0.622883i	0.930590	+	0.366064i	$0.119295\pi$
$200$	−68.4861	+	125.467i	−0.342431	+	0.627335i
$201$	171.916	+	136.804i	0.855304	+	0.680615i
$202$	204.905	+	17.9269i	1.01438	+	0.0887468i
$203$	−17.5616	+	200.730i	−0.0865104	+	0.988818i
$204$	−18.8579	+	23.6981i	−0.0924407	+	0.116167i
$205$	102.814	−	33.7759i	0.501533	−	0.164760i
$206$	80.0383	+	138.630i	0.388535	+	0.672963i
$207$	11.2871	−	52.9991i	0.0545272	−	0.256034i
$208$	−75.1728	−	280.549i	−0.361408	−	1.34879i
$209$	4.67442	+	0.824227i	0.0223657	+	0.00394367i
$210$	−33.5415	+	122.395i	−0.159721	+	0.582834i
$211$	291.396	+	106.059i	1.38102	+	0.502651i	0.922488	−	0.386025i	$-0.126152\pi$
$211$	291.396	+	106.059i	1.38102	+	0.502651i	0.458535	+	0.888676i	$0.348374\pi$
$212$	65.4753	−	93.5084i	0.308846	−	0.441077i
$213$	−10.2164	+	166.499i	−0.0479644	+	0.781685i
$214$	−278.829	+	332.296i	−1.30294	+	1.55279i
$215$	168.824	−	158.459i	0.785230	−	0.737020i
$216$	153.908	−	12.0213i	0.712538	−	0.0556544i
$217$	−21.3421	−	21.3421i	−0.0983509	−	0.0983509i
$218$	−336.777	+	29.4642i	−1.54485	+	0.135157i
$219$	−128.041	+	382.423i	−0.584661	+	1.74622i
$220$	−27.4736	+	3.95217i	−0.124880	+	0.0179644i
$221$	−88.0047	−	32.0311i	−0.398211	−	0.144937i
$222$	113.566	+	107.813i	0.511561	+	0.485644i
$223$	32.0347	+	45.7503i	0.143653	+	0.205158i	0.884531	−	0.466482i	$-0.154479\pi$
$223$	32.0347	+	45.7503i	0.143653	+	0.205158i	−0.740877	+	0.671641i	$0.765590\pi$
$224$	74.3007	+	42.8975i	0.331700	+	0.191507i
$225$	−79.3499	+	210.544i	−0.352666	+	0.935749i
$226$	184.757	+	320.009i	0.817510	+	1.41597i
$227$	−237.363	−	110.684i	−1.04565	−	0.487596i	−0.177619	−	0.984099i	$-0.556839\pi$
$227$	−237.363	−	110.684i	−1.04565	−	0.487596i	−0.868035	+	0.496503i	$0.834617\pi$
$228$	3.80499	+	5.14427i	0.0166885	+	0.0225626i
$229$	−147.760	−	176.093i	−0.645240	−	0.768967i	0.339948	−	0.940444i	$-0.389590\pi$
$229$	−147.760	−	176.093i	−0.645240	−	0.768967i	−0.985188	+	0.171477i	$0.945146\pi$
$230$	55.8917	−	43.9604i	0.243008	−	0.191132i
$231$	35.1432	−	13.8353i	0.152135	−	0.0598930i
$232$	291.513	+	135.935i	1.25652	+	0.585927i
$233$	−303.670	−	81.3682i	−1.30331	−	0.349220i	−0.460606	−	0.887605i	$-0.652368\pi$
$233$	−303.670	−	81.3682i	−1.30331	−	0.349220i	−0.842699	+	0.538385i	$0.819035\pi$
$234$	−121.592	−	286.766i	−0.519622	−	1.22550i
$235$	220.946	−	51.7656i	0.940195	−	0.220279i
$236$	−23.0290	+	130.604i	−0.0975806	+	0.553407i
$237$	107.756	−	31.8956i	0.454666	−	0.134581i
$238$	49.0117	−	22.8545i	0.205932	−	0.0960275i
$239$	−205.885	+	36.3030i	−0.861443	+	0.151896i	−0.586880	−	0.809674i	$-0.699644\pi$
$239$	−205.885	+	36.3030i	−0.861443	+	0.151896i	−0.274562	+	0.961569i	$0.588533\pi$
$240$	242.600	+	171.931i	1.01083	+	0.716378i
$241$	77.9550	+	65.4120i	0.323465	+	0.271419i	0.790031	−	0.613067i	$-0.210065\pi$
$241$	77.9550	+	65.4120i	0.323465	+	0.271419i	−0.466566	+	0.884486i	$0.654509\pi$
$242$	−181.465	−	181.465i	−0.749853	−	0.749853i
$243$	237.292	−	52.3612i	0.976509	−	0.215478i
$244$			150.146i			0.615351i
$245$	−120.577	+	134.792i	−0.492151	+	0.550171i
$246$	−30.5483	−	150.301i	−0.124180	−	0.610980i
$247$	−11.3490	+	16.2080i	−0.0459472	+	0.0656195i
$248$	−43.6660	+	20.3618i	−0.176073	+	0.0821040i
$249$	−12.8737	−	6.99311i	−0.0517014	−	0.0280848i
$250$	−256.833	+	145.653i	−1.02733	+	0.582613i
$251$	−81.4048	+	140.997i	−0.324322	+	0.561742i	−0.981375	−	0.192102i	$-0.938469\pi$
$251$	−81.4048	+	140.997i	−0.324322	+	0.561742i	0.657053	+	0.753844i	$0.271803\pi$
$252$	47.1989	+	19.0912i	0.187297	+	0.0757588i
$253$	−20.4412	−	5.47720i	−0.0807952	−	0.0216490i
$254$	−17.9140	−	49.2183i	−0.0705276	−	0.193773i
$255$	90.2804	−	32.2802i	0.354041	−	0.126589i
$256$	200.848	−	168.531i	0.784561	−	0.658325i
$257$	111.162	+	9.72540i	0.432536	+	0.0378420i	0.301345	−	0.953515i	$-0.402564\pi$
$257$	111.162	+	9.72540i	0.432536	+	0.0378420i	0.131191	+	0.991357i	$0.458120\pi$
$258$	−195.139	−	263.824i	−0.756352	−	1.02257i
$259$	−27.0714	−	74.3780i	−0.104523	−	0.287174i
$260$	33.4693	−	110.758i	0.128728	−	0.425994i
$261$	484.117	+	148.218i	1.85486	+	0.567885i
$262$	−535.427	+	143.467i	−2.04362	+	0.547585i
$263$	−173.306	−	247.506i	−0.658957	−	0.941088i	−0.999999	−	0.00104015i	$-0.999669\pi$
$263$	−173.306	−	247.506i	−0.658957	−	0.941088i	0.341043	−	0.940048i	$-0.389220\pi$
$264$	−1.56634	−	60.2696i	−0.00593309	−	0.228294i
$265$	−332.195	+	142.283i	−1.25356	+	0.536917i
$266$	−1.98399	−	11.2518i	−0.00745861	−	0.0422999i
$267$	−122.643	−	246.106i	−0.459338	−	0.921744i
$268$	115.226	−	10.0810i	0.429949	−	0.0376156i
$269$			119.721i			0.445060i	0.974926	+	0.222530i	$0.0714315\pi$
$269$			119.721i			0.445060i	−0.974926	+	0.222530i	$0.928568\pi$
$270$	283.240	+	146.490i	1.04904	+	0.542557i
$271$	−141.433			−0.521894			−0.260947	−	0.965353i	$-0.584035\pi$
$271$	−141.433			−0.521894			−0.260947	+	0.965353i	$0.584035\pi$
$272$	−11.0432	−	126.224i	−0.0405999	−	0.464059i
$273$	−9.64251	+	157.146i	−0.0353205	+	0.575625i
$274$	−53.6583	+	9.46140i	−0.195833	+	0.0345307i
$275$	80.5044	+	35.2182i	0.292743	+	0.128066i
$276$	−14.9009	−	24.3268i	−0.0539888	−	0.0881407i
$277$	−25.4895	+	17.8479i	−0.0920198	+	0.0644329i	−0.618681	−	0.785642i	$-0.712333\pi$
$277$	−25.4895	+	17.8479i	−0.0920198	+	0.0644329i	0.526661	+	0.850075i	$0.323444\pi$
$278$	−86.7567	−	323.780i	−0.312074	−	1.16468i
$279$	−63.6200	+	41.2797i	−0.228029	+	0.147956i
$280$	−48.3664	−	90.2558i	−0.172737	−	0.322342i
$281$	−193.860	+	70.5593i	−0.689894	+	0.251101i	−0.663090	−	0.748540i	$-0.730755\pi$
$281$	−193.860	+	70.5593i	−0.689894	+	0.251101i	−0.0268039	+	0.999641i	$0.508533\pi$
$282$	−36.3448	−	319.553i	−0.128882	−	1.13317i
$283$	2.87663	−	32.8800i	0.0101648	−	0.116184i	−0.989417	−	0.145099i	$-0.953650\pi$
$283$	2.87663	−	32.8800i	0.0101648	−	0.116184i	0.999582	+	0.0289155i	$0.00920537\pi$
$284$	56.4497	+	67.2742i	0.198767	+	0.236881i
$285$	−1.65089	−	20.1891i	−0.00579260	−	0.0708388i
$286$	−114.308	+	41.6047i	−0.399679	+	0.145471i
$287$	−20.0650	+	74.8834i	−0.0699127	+	0.260918i
$288$	144.312	−	160.147i	0.501082	−	0.556067i
$289$	214.899	+	124.072i	0.743596	+	0.429315i
$290$	363.664	+	556.032i	1.25401	+	1.91735i
$291$	−84.6220	−	138.152i	−0.290797	−	0.474748i
$292$	89.7287	+	192.424i	0.307290	+	0.658986i
$293$	106.365	+	74.4778i	0.363022	+	0.254190i	0.740829	−	0.671694i	$-0.234433\pi$
$293$	106.365	+	74.4778i	0.363022	+	0.254190i	−0.377807	+	0.925884i	$0.623322\pi$
$294$	169.800	+	192.000i	0.577551	+	0.653061i
$295$	279.915	−	312.915i	0.948865	−	1.06073i
$296$	−126.349			−0.426856
$297$	−15.6078	−	93.6082i	−0.0525515	−	0.315179i
$298$	−351.525	+	351.525i	−1.17962	+	1.17962i
$299$	56.7046	−	67.5779i	0.189648	−	0.226013i
$300$	46.0186	+	109.150i	0.153395	+	0.363832i
$301$	28.8026	+	163.348i	0.0956897	+	0.542683i
$302$	−252.858	−	542.255i	−0.837277	−	1.79555i
$303$	−179.862	+	189.460i	−0.593603	+	0.625280i
$304$	−26.3630	−	4.64851i	−0.0867203	−	0.0152911i
$305$	250.576	−	403.917i	0.821560	−	1.32432i
$306$	−30.5147	−	132.412i	−0.0997212	−	0.432718i
$307$	−109.109	+	407.200i	−0.355404	+	1.32639i	0.524571	+	0.851366i	$0.324226\pi$
$307$	−109.109	+	407.200i	−0.355404	+	1.32639i	−0.879975	+	0.475019i	$0.842441\pi$
$308$	8.40321	−	18.0207i	0.0272832	−	0.0585089i
$309$	−201.070	−	30.0905i	−0.650710	−	0.0973803i
$310$	−98.8175	−	11.8077i	−0.318766	−	0.0380893i
$311$	−331.968	+	278.554i	−1.06742	+	0.895672i	−0.994816	−	0.101689i	$-0.967575\pi$
$311$	−331.968	+	278.554i	−1.06742	+	0.895672i	−0.0726038	+	0.997361i	$0.523131\pi$
$312$	230.459	+	100.260i	0.738651	+	0.321348i
$313$	228.281	−	489.550i	0.729332	−	1.56406i	−0.0934003	−	0.995629i	$-0.529774\pi$
$313$	228.281	−	489.550i	0.729332	−	1.56406i	0.822732	−	0.568429i	$-0.192449\pi$
$314$	179.970	−	103.906i	0.573154	−	0.330911i
$315$	−95.1121	−	130.128i	−0.301943	−	0.413105i
$316$	29.5812	−	51.2361i	0.0936113	−	0.162140i
$317$	−271.226	+	189.915i	−0.855603	+	0.599100i	−0.916944	−	0.399017i	$-0.869351\pi$
$317$	−271.226	+	189.915i	−0.855603	+	0.599100i	0.0613401	+	0.998117i	$0.480463\pi$
$318$	145.367	+	491.105i	0.457128	+	1.54436i
$319$	67.6271	−	185.804i	0.211997	−	0.582457i
$320$	−112.412	+	16.1709i	−0.351288	+	0.0505340i
$321$	−109.732	−	539.895i	−0.341845	−	1.68192i
$322$	4.43967	+	50.7457i	0.0137878	+	0.157595i
$323$	−6.10357	+	6.10357i	−0.0188965	+	0.0188965i
$324$	71.6212	−	106.003i	0.221053	−	0.327169i
$325$	−274.881	+	242.103i	−0.845789	+	0.744931i
$326$	225.560	+	189.267i	0.691901	+	0.580574i
$327$	237.053	−	357.994i	0.724932	−	1.09478i
$328$	101.373	+	70.9819i	0.309063	+	0.216408i
$329$	−55.6001	+	152.760i	−0.168997	+	0.464316i
$330$	62.8784	−	107.495i	0.190541	−	0.325742i
$331$	−38.9001	+	220.613i	−0.117523	+	0.666505i	0.867947	+	0.496656i	$0.165439\pi$
$331$	−38.9001	+	220.613i	−0.117523	+	0.666505i	−0.985470	+	0.169849i	$0.945672\pi$
$332$	−7.45007	+	1.99624i	−0.0224400	+	0.00601277i
$333$	−196.958	+	27.6015i	−0.591466	+	0.0828875i
$334$	499.521	−	288.399i	1.49557	−	0.863469i
$335$	−326.803	−	165.180i	−0.975530	−	0.493074i
$336$	−198.202	+	78.0288i	−0.589887	+	0.232229i
$337$	−154.344	−	13.5034i	−0.457996	−	0.0400694i	−0.144176	−	0.989552i	$-0.546053\pi$
$337$	−154.344	−	13.5034i	−0.457996	−	0.0400694i	−0.313820	+	0.949483i	$0.601609\pi$
$338$	9.40353	−	107.483i	0.0278211	−	0.317996i
$339$	−464.141	−	69.4598i	−1.36915	−	0.204896i
$340$	22.7695	−	45.0486i	0.0669691	−	0.132496i
$341$	14.8089	+	25.6498i	0.0434279	+	0.0752194i
$342$	−28.6904	−	1.01321i	−0.0838901	−	0.00296259i
$343$	−78.9568	−	294.671i	−0.230195	−	0.859099i
$344$	260.752	+	45.9776i	0.757999	+	0.133656i
$345$	−0.512653	+	90.3113i	−0.00148595	+	0.261772i
$346$	299.298	+	108.936i	0.865024	+	0.314843i
$347$	155.096	−	221.500i	0.446962	−	0.638328i	−0.530935	−	0.847412i	$-0.678159\pi$
$347$	155.096	−	221.500i	0.446962	−	0.638328i	0.977898	+	0.209084i	$0.0670482\pi$
$348$	238.565	−	118.886i	0.685533	−	0.341625i
$349$	84.5706	−	100.787i	0.242323	−	0.288789i	−0.631151	−	0.775660i	$-0.717417\pi$
$349$	84.5706	−	100.787i	0.242323	−	0.288789i	0.873474	+	0.486871i	$0.161862\pi$
$350$	13.3838	−	211.089i	0.0382395	−	0.603112i
$351$	381.150	+	105.945i	1.08590	+	0.301837i
$352$	−59.5316	−	59.5316i	−0.169124	−	0.169124i
$353$	560.875	−	49.0702i	1.58888	−	0.139009i	0.741855	−	0.670561i	$-0.233946\pi$
$353$	560.875	−	49.0702i	1.58888	−	0.139009i	0.847026	+	0.531552i	$0.178391\pi$
$354$	−394.184	−	445.721i	−1.11352	−	1.25910i
$355$	−39.5867	−	275.187i	−0.111512	−	0.775176i
$356$	−136.032	−	49.5116i	−0.382112	−	0.139077i
$357$	−16.0470	+	66.7826i	−0.0449496	+	0.187066i
$358$	378.433	+	540.458i	1.05707	+	1.50966i
$359$	8.33750	+	4.81366i	0.0232242	+	0.0134085i	0.511567	−	0.859243i	$-0.329065\pi$
$359$	8.33750	+	4.81366i	0.0232242	+	0.0134085i	−0.488343	+	0.872652i	$0.662398\pi$
$360$	−247.124	+	71.6255i	−0.686457	+	0.198960i
$361$	−179.588	−	311.056i	−0.497474	−	0.861651i
$362$	232.609	+	108.467i	0.642567	+	0.299634i
$363$	323.850	−	36.8334i	0.892149	−	0.101470i
$364$	53.2786	+	63.4950i	0.146370	+	0.174437i
$365$	79.7475	−	667.400i	0.218486	−	1.82849i
$366$	−527.127	−	419.465i	−1.44024	−	1.14608i
$367$	374.566	+	174.663i	1.02062	+	0.475921i	0.859566	−	0.511025i	$-0.170734\pi$
$367$	374.566	+	174.663i	1.02062	+	0.475921i	0.161051	+	0.986946i	$0.448512\pi$
$368$	115.285	+	30.8905i	0.313274	+	0.0839416i
$369$	173.530	+	88.5039i	0.470270	+	0.239848i
$370$	−221.777	−	137.582i	−0.599397	−	0.371844i
$371$	44.9544	−	254.949i	0.121171	−	0.687194i
$372$	−9.32824	+	38.8212i	−0.0250759	+	0.104358i
$373$	−86.4264	+	40.3013i	−0.231706	+	0.108046i	−0.535004	−	0.844849i	$-0.679690\pi$
$373$	−86.4264	+	40.3013i	−0.231706	+	0.108046i	0.303298	+	0.952896i	$0.401912\pi$
$374$	−52.2608	+	9.21499i	−0.139735	+	0.0246390i
$375$	58.3600	−	370.431i	0.155627	−	0.987816i
$376$	198.789	+	166.804i	0.528694	+	0.443627i
$377$	582.831	+	582.831i	1.54597	+	1.54597i
$378$	−198.885	+	112.369i	−0.526152	+	0.297272i
$379$			597.153i			1.57560i	0.615931	+	0.787800i	$0.288780\pi$
$379$			597.153i			1.57560i	−0.615931	+	0.787800i	$0.711220\pi$
$380$	−7.94821	−	7.11000i	−0.0209163	−	0.0187105i
$381$	63.0808	+	21.1204i	0.165566	+	0.0554340i
$382$	171.780	−	245.327i	0.449685	−	0.642217i
$383$	248.482	−	115.869i	0.648778	−	0.302530i	−0.0702309	−	0.997531i	$-0.522374\pi$
$383$	248.482	−	115.869i	0.648778	−	0.302530i	0.719009	+	0.695000i	$0.244596\pi$
$384$	11.6492	+	448.239i	0.0303365	+	1.16729i
$385$	−52.6807	+	34.4549i	−0.136833	+	0.0894933i
$386$	108.036	−	187.125i	0.279887	−	0.484779i
$387$	416.513	+	14.7092i	1.07626	+	0.0380083i
$388$	−82.3851	−	22.0750i	−0.212333	−	0.0568944i
$389$	51.2144	+	140.710i	0.131657	+	0.361724i	0.987952	−	0.154764i	$-0.0494616\pi$
$389$	51.2144	+	140.710i	0.131657	+	0.361724i	−0.856295	+	0.516487i	$0.827239\pi$
$390$	295.343	+	426.931i	0.757290	+	1.09470i
$391$	29.4808	−	24.7373i	0.0753984	−	0.0632667i
$392$	−206.024	−	18.0248i	−0.525572	−	0.0459816i
$393$	280.854	−	645.573i	0.714642	−	1.64268i
$394$	−56.9162	−	156.376i	−0.144457	−	0.396894i
$395$	−165.086	+	88.4664i	−0.417938	+	0.223966i
$396$	−39.8892	−	30.0833i	−0.100730	−	0.0759679i
$397$	−408.658	+	109.500i	−1.02937	+	0.275818i	−0.733700	−	0.679473i	$-0.762208\pi$
$397$	−408.658	+	109.500i	−1.02937	+	0.275818i	−0.295666	+	0.955291i	$0.595542\pi$
$398$	335.872	+	479.675i	0.843899	+	1.20521i
$399$	12.7512	+	6.92656i	0.0319578	+	0.0173598i
$400$	−454.032	−	198.625i	−1.13508	−	0.496562i
$401$	−99.4097	−	563.780i	−0.247904	−	1.40594i	−0.813650	−	0.581356i	$-0.802523\pi$
$401$	−99.4097	−	563.780i	−0.247904	−	1.40594i	0.565745	−	0.824580i	$-0.308589\pi$
$402$	−286.518	+	432.696i	−0.712732	+	1.07636i
$403$	−122.995	+	10.7606i	−0.305198	+	0.0267013i
$404$			137.532i			0.340425i
$405$	−369.580	+	165.638i	−0.912542	+	0.408982i
$406$	−475.950			−1.17229
$407$	6.76948	+	77.3755i	0.0166326	+	0.190112i
$408$	91.4149	+	60.5321i	0.224056	+	0.148363i
$409$	198.382	−	34.9800i	0.485041	−	0.0855257i	0.0742199	−	0.997242i	$-0.476353\pi$
$409$	198.382	−	34.9800i	0.485041	−	0.0855257i	0.410821	+	0.911716i	$0.365242\pi$
$410$	100.644	+	234.977i	0.245472	+	0.573115i
$411$	33.0319	−	60.8086i	0.0803696	−	0.147953i
$412$	−87.6773	+	61.3923i	−0.212809	+	0.149010i
$413$	77.8426	+	290.513i	0.188481	+	0.703420i
$414$	127.035	+	15.6487i	0.306848	+	0.0377988i
$415$	23.3735	+	7.06308i	0.0563216	+	0.0170195i
$416$	329.790	−	120.034i	0.792764	−	0.288542i
$417$	390.387	+	169.837i	0.936180	+	0.407282i
$418$	−0.977160	+	11.1690i	−0.00233770	+	0.0267201i
$419$	−139.993	−	166.838i	−0.334113	−	0.398180i	0.572664	−	0.819790i	$-0.305910\pi$
$419$	−139.993	−	166.838i	−0.334113	−	0.398180i	−0.906778	+	0.421609i	$0.861465\pi$
$420$	−83.4821	−	15.2093i	−0.198767	−	0.0362125i
$421$	−398.010	+	144.864i	−0.945392	+	0.344094i	−0.768293	−	0.640099i	$-0.778893\pi$
$421$	−398.010	+	144.864i	−0.945392	+	0.344094i	−0.177099	+	0.984193i	$0.556671\pi$
$422$	−189.578	+	707.513i	−0.449236	+	1.67657i
$423$	346.319	+	216.594i	0.818720	+	0.512042i
$424$	−357.888	−	206.627i	−0.844076	−	0.487327i
$425$	−136.435	+	83.1890i	−0.321023	+	0.195739i
$426$	−393.889	+	10.2367i	−0.924622	+	0.0240299i
$427$	143.905	+	308.606i	0.337015	+	0.722730i
$428$	−237.591	−	166.363i	−0.555120	−	0.388699i
$429$	49.0514	−	146.503i	0.114339	−	0.341499i
$430$	407.624	+	364.636i	0.947962	+	0.847991i
$431$	−222.552			−0.516362			−0.258181	−	0.966097i	$-0.583123\pi$
$431$	−222.552			−0.516362			−0.258181	+	0.966097i	$0.583123\pi$
$432$	88.0254	+	527.935i	0.203763	+	1.22207i
$433$	−280.953	+	280.953i	−0.648851	+	0.648851i	−0.952715	−	0.303864i	$-0.901723\pi$
$433$	−280.953	+	280.953i	−0.648851	+	0.648851i	0.303864	+	0.952715i	$0.401723\pi$
$434$	45.8262	−	54.6135i	0.105590	−	0.125838i
$435$	−840.189	−	78.3152i	−1.93147	−	0.180035i
$436$	−39.2522	−	222.610i	−0.0900279	−	0.510573i
$437$	−3.43620	−	7.36895i	−0.00786315	−	0.0168626i
$438$	−926.233	−	222.562i	−2.11469	−	0.508132i
$439$	−89.7832	−	15.8312i	−0.204518	−	0.0360620i	0.0704507	−	0.997515i	$-0.477556\pi$
$439$	−89.7832	−	15.8312i	−0.204518	−	0.0360620i	−0.274968	+	0.961453i	$0.588667\pi$
$440$	22.9216	+	97.8339i	0.0520945	+	0.222350i
$441$	−325.095	+	16.9091i	−0.737178	+	0.0383427i
$442$	57.2545	−	213.677i	0.129535	−	0.483431i
$443$	−208.641	+	447.431i	−0.470972	+	1.01000i	0.517088	+	0.855932i	$0.327016\pi$
$443$	−208.641	+	447.431i	−0.470972	+	1.01000i	−0.988060	+	0.154070i	$0.950762\pi$
$444$	−65.1960	+	81.9295i	−0.146838	+	0.184526i
$445$	283.320	+	360.216i	0.636675	+	0.809475i
$446$	−101.059	+	84.7989i	−0.226590	+	0.190132i
$447$	−71.3522	−	627.349i	−0.159625	−	1.40346i
$448$	34.3830	−	73.7345i	0.0767477	−	0.164586i
$449$	221.384	−	127.816i	0.493061	−	0.284669i	−0.232783	−	0.972529i	$-0.574783\pi$
$449$	221.384	−	127.816i	0.493061	−	0.284669i	0.725843	+	0.687860i	$0.241450\pi$
$450$	−511.762	−	143.373i	−1.13725	−	0.318606i
$451$	38.0375	−	65.8829i	0.0843404	−	0.146082i
$452$	−202.391	+	141.716i	−0.447768	+	0.313530i
$453$	738.868	+	177.540i	1.63105	+	0.391921i
$454$	211.584	−	581.322i	0.466044	−	1.28045i
$455$	−37.3629	−	259.728i	−0.0821162	−	0.570832i
$456$	17.3518	−	15.3455i	0.0380521	−	0.0336523i
$457$	−44.4391	−	507.942i	−0.0972410	−	1.11147i	−0.875399	−	0.483401i	$-0.839401\pi$
$457$	−44.4391	−	507.942i	−0.0972410	−	1.11147i	0.778158	−	0.628069i	$-0.216154\pi$
$458$	383.943	−	383.943i	0.838304	−	0.838304i
$459$	155.724	+	74.3897i	0.339269	+	0.162069i
$460$	32.5392	+	34.6676i	0.0707374	+	0.0753644i
$461$	180.017	+	151.052i	0.390492	+	0.327661i	0.816805	−	0.576914i	$-0.195743\pi$
$461$	180.017	+	151.052i	0.390492	+	0.327661i	−0.426313	+	0.904576i	$0.640188\pi$
$462$	39.7905	+	79.8467i	0.0861266	+	0.172828i
$463$	−110.063	−	77.0668i	−0.237717	−	0.166451i	0.448648	−	0.893709i	$-0.351906\pi$
$463$	−110.063	−	77.0668i	−0.237717	−	0.166451i	−0.686365	+	0.727258i	$0.740795\pi$
$464$	−381.406	+	1047.90i	−0.821995	+	2.25841i
$465$	89.8828	−	88.8681i	0.193296	−	0.191114i
$466$	128.950	−	731.312i	0.276717	−	1.56934i
$467$	26.9991	−	7.23439i	0.0578140	−	0.0154912i	−0.229796	−	0.973239i	$-0.573806\pi$
$467$	26.9991	−	7.23439i	0.0578140	−	0.0154912i	0.287610	+	0.957748i	$0.407139\pi$
$468$	183.929	−	97.7038i	0.393010	−	0.208769i
$469$	227.171	−	131.157i	0.484374	−	0.279654i
$470$	167.295	+	509.247i	0.355946	+	1.08350i
$471$	−39.0636	+	261.029i	−0.0829376	+	0.554202i
$472$	478.278	+	41.8439i	1.01330	+	0.0886523i
$473$	14.1859	−	162.146i	0.0299914	−	0.342803i
$474$	97.2366	+	246.992i	0.205141	+	0.521081i
$475$	9.51628	+	32.3918i	0.0200343	+	0.0681932i
$476$	18.0796	+	31.3148i	0.0379824	+	0.0657874i
$477$	−603.028	−	243.915i	−1.26421	−	0.511353i
$478$	−127.809	−	476.991i	−0.267383	−	0.997888i
$479$	−397.592	−	70.1063i	−0.830047	−	0.146360i	−0.257548	−	0.966265i	$-0.582915\pi$
$479$	−397.592	−	70.1063i	−0.830047	−	0.146360i	−0.572499	+	0.819906i	$0.694026\pi$
$480$	−181.410	+	310.132i	−0.377938	+	0.646109i
$481$	−304.252	−	110.739i	−0.632541	−	0.230226i
$482$	−137.872	+	196.901i	−0.286040	+	0.408508i
$483$	−53.9428	−	35.7192i	−0.111683	−	0.0739528i
$484$	110.298	−	131.449i	0.227889	−	0.271588i
$485$	184.790	+	196.877i	0.381009	+	0.405932i
$486$	172.061	+	547.588i	0.354035	+	1.12672i
$487$	198.013	+	198.013i	0.406597	+	0.406597i	0.880550	−	0.473953i	$-0.157173\pi$
$487$	198.013	+	198.013i	0.406597	+	0.406597i	−0.473953	+	0.880550i	$0.657173\pi$
$488$	541.486	−	47.3739i	1.10960	−	0.0970776i
$489$	−366.476	+	74.4853i	−0.749440	+	0.152322i
$490$	−342.000	−	255.979i	−0.697959	−	0.522405i
$491$	−508.696	−	185.150i	−1.03604	−	0.377088i	−0.232663	−	0.972557i	$-0.574744\pi$
$491$	−508.696	−	185.150i	−1.03604	−	0.377088i	−0.803378	+	0.595470i	$0.796966\pi$
$492$	98.3353	−	29.1072i	0.199869	−	0.0591609i
$493$	206.244	+	294.548i	0.418346	+	0.597460i
$494$	−40.4752	−	23.3684i	−0.0819336	−	0.0473044i
$495$	57.1032	+	147.500i	0.115360	+	0.297979i
$496$	−83.5199	−	144.661i	−0.168387	−	0.291655i
$497$	180.504	+	84.1702i	0.363186	+	0.169357i
$498$	13.8051	−	31.7324i	0.0277211	−	0.0637198i
$499$	−183.346	−	218.504i	−0.367427	−	0.437883i	0.550377	−	0.834916i	$-0.314484\pi$
$499$	−183.346	−	218.504i	−0.367427	−	0.437883i	−0.917804	+	0.397033i	$0.870040\pi$
$500$	−111.987	−	162.588i	−0.223974	−	0.325176i
$501$	−108.424	+	724.506i	−0.216415	+	1.44612i
$502$	−348.537	−	162.525i	−0.694297	−	0.323756i
$503$	−793.904	−	212.726i	−1.57834	−	0.422914i	−0.639927	−	0.768435i	$-0.721036\pi$
$503$	−793.904	−	212.726i	−1.57834	−	0.422914i	−0.938411	+	0.345521i	$0.887702\pi$
$504$	53.9585	−	176.242i	0.107061	−	0.349686i
$505$	229.525	−	369.984i	0.454505	−	0.732642i
$506$	8.68012	−	49.2274i	0.0171544	−	0.0972874i
$507$	99.3811	+	94.3464i	0.196018	+	0.186088i
$508$	31.7404	−	14.8008i	0.0624810	−	0.0291354i
$509$	460.147	−	81.1364i	0.904022	−	0.159403i	0.297734	−	0.954649i	$-0.403769\pi$
$509$	460.147	−	81.1364i	0.904022	−	0.159403i	0.606288	+	0.795245i	$0.292658\pi$
$510$	94.5439	+	205.792i	0.185380	+	0.403513i
$511$	368.853	+	309.504i	0.721825	+	0.605683i
$512$	15.1697	+	15.1697i	0.0296284	+	0.0296284i
$513$	23.6963	−	27.7116i	0.0461916	−	0.0540188i
$514$			263.575i			0.512792i
$515$	338.324	−	18.8326i	0.656940	−	0.0365682i
$516$	164.361	−	145.357i	0.318529	−	0.281699i
$517$	91.4989	−	130.674i	0.176980	−	0.252754i
$518$	169.445	−	79.0133i	0.327113	−	0.152535i
$519$	−344.957	+	211.296i	−0.664657	+	0.407122i
$520$	−410.000	−	85.7576i	−0.788461	−	0.164919i
$521$	113.109	−	195.911i	0.217100	−	0.376029i	−0.736820	−	0.676089i	$-0.763673\pi$
$521$	113.109	−	195.911i	0.217100	−	0.376029i	0.953920	+	0.300060i	$0.0970068\pi$
$522$	−249.105	+	1169.68i	−0.477213	+	2.24077i
$523$	−1.77194	−	0.474790i	−0.00338803	−	0.000907820i	0.257125	−	0.966378i	$-0.417225\pi$
$523$	−1.77194	−	0.474790i	−0.00338803	−	0.000907820i	−0.260513	+	0.965470i	$0.583892\pi$
$524$	−126.766	−	348.287i	−0.241920	−	0.664671i
$525$	199.199	+	180.238i	0.379426	+	0.343310i
$526$	546.725	−	458.756i	1.03940	−	0.872161i
$527$	−53.6562	−	4.69431i	−0.101814	−	0.00890761i
$528$	207.685	−	23.6213i	0.393344	−	0.0447374i
$529$	−168.530	−	463.033i	−0.318583	−	0.875299i
$530$	−403.192	−	752.391i	−0.760740	−	1.41960i
$531$	754.698	−	39.2540i	1.42128	−	0.0739246i
$532$	7.37918	−	1.97725i	0.0138706	−	0.00371663i
$533$	181.896	+	259.774i	0.341268	+	0.487381i
$534$	553.859	−	339.255i	1.03719	−	0.635309i
$535$	361.521	+	844.059i	0.675740	+	1.57768i
$536$	−72.7123	−	412.372i	−0.135657	−	0.769351i
$537$	−836.391	−	51.3212i	−1.55753	−	0.0955702i
$538$	−281.714	+	24.6468i	−0.523632	+	0.0458118i
$539$			127.133i			0.235869i
$540$	−81.0711	+	197.203i	−0.150132	+	0.365191i
$541$	−234.130			−0.432773			−0.216386	−	0.976308i	$-0.569427\pi$
$541$	−234.130			−0.432773			−0.216386	+	0.976308i	$0.569427\pi$
$542$	−29.1166	−	332.804i	−0.0537207	−	0.614030i
$543$	−291.751	+	145.390i	−0.537295	+	0.267753i
$544$	150.777	−	26.5861i	0.277164	−	0.0488716i
$545$	−265.915	+	664.367i	−0.487918	+	1.21902i
$546$	−371.762	+	9.66167i	−0.680883	+	0.0176954i
$547$	264.852	−	185.452i	0.484191	−	0.339034i	−0.305859	−	0.952077i	$-0.598944\pi$
$547$	264.852	−	185.452i	0.484191	−	0.339034i	0.790050	+	0.613043i	$0.210055\pi$
$548$	−9.42924	−	35.1904i	−0.0172066	−	0.0642160i
$549$	833.739	−	192.138i	1.51865	−	0.349978i
$550$	−66.2981	+	196.684i	−0.120542	+	0.357607i
$551$	71.3874	−	25.9829i	0.129560	−	0.0471559i
$552$	−83.0309	+	61.4143i	−0.150418	+	0.111258i
$553$	11.6938	−	133.661i	0.0211462	−	0.241702i
$554$	−47.2451	−	56.3045i	−0.0852800	−	0.101633i
$555$	312.120	−	111.600i	0.562378	−	0.201081i
$556$	210.614	−	76.6573i	0.378803	−	0.137873i
$557$	−1.77258	+	6.61538i	−0.00318238	+	0.0118768i	−0.967499	−	0.252876i	$-0.918624\pi$
$557$	−1.77258	+	6.61538i	−0.00318238	+	0.0118768i	0.964316	+	0.264753i	$0.0852903\pi$
$558$	−110.232	−	141.205i	−0.197548	−	0.253056i
$559$	587.599	+	339.250i	1.05116	+	0.606888i
$560$	297.110	−	194.320i	0.530554	−	0.347000i
$561$	32.1716	−	59.2250i	0.0573470	−	0.105570i
$562$	−205.942	−	441.643i	−0.366444	−	0.785842i
$563$	517.684	+	362.486i	0.919510	+	0.643847i	0.934470	−	0.356041i	$-0.115874\pi$
$563$	517.684	+	362.486i	0.919510	+	0.643847i	−0.0149610	+	0.999888i	$0.504762\pi$
$564$	210.736	−	42.8316i	0.373646	−	0.0759425i
$565$	780.974	−	43.4724i	1.38225	−	0.0769424i
$566$	77.9617			0.137742
$567$	45.6117	−	286.520i	0.0804439	−	0.505326i
$568$	224.807	−	224.807i	0.395787	−	0.395787i
$569$	−76.5081	+	91.1789i	−0.134461	+	0.160244i	−0.829073	−	0.559140i	$-0.811131\pi$
$569$	−76.5081	+	91.1789i	−0.134461	+	0.160244i	0.694613	+	0.719384i	$0.255576\pi$
$570$	47.1667	−	8.04097i	0.0827486	−	0.0141070i
$571$	0.263528	+	1.49454i	0.000461520	+	0.00261741i	0.985038	−	0.172339i	$-0.0551326\pi$
$571$	0.263528	+	1.49454i	0.000461520	+	0.00261741i	−0.984576	+	0.174957i	$0.944021\pi$
$572$	−34.3743	−	73.7160i	−0.0600950	−	0.128874i
$573$	107.960	+	364.730i	0.188411	+	0.636526i
$574$	−180.338	−	31.7984i	−0.314177	−	0.0553979i
$575$	−29.6798	−	147.566i	−0.0516170	−	0.256637i
$576$	−163.212	−	123.090i	−0.283355	−	0.213698i
$577$	108.806	−	406.071i	0.188573	−	0.703763i	−0.805265	−	0.592915i	$-0.797977\pi$
$577$	108.806	−	406.071i	0.188573	−	0.703763i	0.993837	−	0.110847i	$-0.0353565\pi$
$578$	−247.711	+	531.218i	−0.428566	+	0.919063i
$579$	100.528	+	255.352i	0.173623	+	0.441023i
$580$	−349.180	+	274.640i	−0.602034	+	0.473517i
$581$	−13.3994	+	11.2435i	−0.0230627	+	0.0193519i
$582$	307.661	−	227.564i	0.528628	−	0.391003i
$583$	−107.362	+	230.239i	−0.184154	+	0.394921i
$584$	665.647	−	384.312i	1.13981	−	0.658068i
$585$	−657.857	−	44.1160i	−1.12454	−	0.0754119i
$586$	−153.355	+	265.619i	−0.261698	+	0.453275i
$587$	246.684	−	172.730i	0.420246	−	0.294259i	−0.344262	−	0.938874i	$-0.611871\pi$
$587$	246.684	−	172.730i	0.420246	−	0.294259i	0.764508	+	0.644614i	$0.222982\pi$
$588$	−117.996	+	124.293i	−0.200673	+	0.211382i
$589$	−3.89200	+	10.6932i	−0.00660781	+	0.0181548i
$590$	793.941	+	594.245i	1.34566	+	1.00720i
$591$	200.420	+	67.1034i	0.339120	+	0.113542i
$592$	−38.1788	−	436.385i	−0.0644911	−	0.737137i
$593$	−31.7465	+	31.7465i	−0.0535355	+	0.0535355i	−0.733368	−	0.679832i	$-0.762053\pi$
$593$	−31.7465	+	31.7465i	−0.0535355	+	0.0535355i	0.679832	+	0.733368i	$0.262053\pi$
$594$	217.055	−	55.9974i	0.365412	−	0.0942717i
$595$	3.62353	−	114.415i	0.00608997	−	0.192294i
$596$	−254.637	−	213.665i	−0.427243	−	0.358499i
$597$	−742.326	−	45.5493i	−1.24343	−	0.0762970i
$598$	170.690	+	119.519i	0.285435	+	0.199864i
$599$	−16.1057	+	44.2501i	−0.0268877	+	0.0738734i	−0.952410	−	0.304819i	$-0.901404\pi$
$599$	−16.1057	+	44.2501i	−0.0268877	+	0.0738734i	0.925523	+	0.378693i	$0.123626\pi$
$600$	379.118	−	200.401i	0.631863	−	0.334001i
$601$	160.281	−	908.998i	0.266690	−	1.51248i	−0.497489	−	0.867471i	$-0.665744\pi$
$601$	160.281	−	908.998i	0.266690	−	1.51248i	0.764179	−	0.645005i	$-0.223145\pi$
$602$	−378.441	+	101.403i	−0.628640	+	0.168443i
$603$	−203.431	−	626.936i	−0.337365	−	1.03970i
$604$	346.460	−	200.029i	0.573610	−	0.331174i
$605$	−516.094	+	169.544i	−0.853049	+	0.280238i
$606$	−482.843	−	384.226i	−0.796770	−	0.634036i
$607$	−134.360	−	11.7550i	−0.221351	−	0.0193657i	−0.0240591	−	0.999711i	$-0.507659\pi$
$607$	−134.360	−	11.7550i	−0.221351	−	0.0193657i	−0.197291	+	0.980345i	$0.563215\pi$
$608$	2.81920	−	32.2236i	0.00463684	−	0.0529994i
$609$	376.397	−	473.005i	0.618058	−	0.776692i
$610$	1002.04	+	506.472i	1.64268	+	0.830282i
$611$	332.493	+	575.896i	0.544179	+	0.942546i
$612$	86.4211	−	28.0423i	0.141211	−	0.0458207i
$613$	193.130	+	720.773i	0.315058	+	1.17581i	0.923936	+	0.382548i	$0.124953\pi$
$613$	193.130	+	720.773i	0.315058	+	1.17581i	−0.608878	+	0.793264i	$0.708380\pi$
$614$	−980.639	−	172.913i	−1.59713	−	0.281617i
$615$	−313.116	−	85.8070i	−0.509131	−	0.139524i
$616$	−67.6415	−	24.6195i	−0.109808	−	0.0399667i
$617$	277.352	−	396.100i	0.449518	−	0.641978i	−0.528883	−	0.848695i	$-0.677389\pi$
$617$	277.352	−	396.100i	0.449518	−	0.641978i	0.978401	+	0.206717i	$0.0662779\pi$
$618$	29.4117	−	479.328i	0.0475918	−	0.775612i
$619$	−710.594	+	846.852i	−1.14797	+	1.36810i	−0.229164	+	0.973388i	$0.573599\pi$
$619$	−710.594	+	846.852i	−1.14797	+	1.36810i	−0.918806	+	0.394710i	$0.870845\pi$
$620$	2.10639	−	66.5104i	0.00339740	−	0.107275i
$621$	−116.015	+	113.873i	−0.186820	+	0.183371i
$622$	−723.802	−	723.802i	−1.16367	−	1.16367i
$623$	−327.051	+	28.6132i	−0.524961	+	0.0459281i
$624$	−276.642	+	826.254i	−0.443336	+	1.32413i
$625$	29.9230	+	624.283i	0.0478768	+	0.998853i
$626$	1198.95	+	436.381i	1.91525	+	0.697095i
$627$	−10.3271	−	9.80393i	−0.0164707	−	0.0156363i
$628$	79.6997	+	113.823i	0.126910	+	0.181247i
$629$	−122.324	−	70.6239i	−0.194474	−	0.112280i
$630$	286.622	−	250.596i	0.454955	−	0.397771i
$631$	468.867	+	812.101i	0.743054	+	1.28701i	0.951099	+	0.308887i	$0.0999566\pi$
$631$	468.867	+	812.101i	0.743054	+	1.28701i	−0.208045	+	0.978119i	$0.566710\pi$
$632$	−194.112	−	90.5158i	−0.307139	−	0.143221i
$633$	−553.211	−	747.930i	−0.873951	−	1.18156i
$634$	−502.722	−	599.121i	−0.792937	−	0.944986i
$635$	−110.088	−	13.1544i	−0.173367	−	0.0207155i
$636$	−318.654	+	125.449i	−0.501028	+	0.197246i
$637$	−480.313	−	223.973i	−0.754023	−	0.351607i
$638$	451.134	+	120.881i	0.707107	+	0.189469i
$639$	301.327	−	399.547i	0.471561	−	0.625270i
$640$	−170.473	−	727.613i	−0.266364	−	1.13690i
$641$	144.211	−	817.859i	0.224977	−	1.27591i	−0.637751	−	0.770243i	$-0.720135\pi$
$641$	144.211	−	817.859i	0.224977	−	1.27591i	0.862728	−	0.505668i	$-0.168754\pi$
$642$	1247.83	−	369.356i	1.94366	−	0.575321i
$643$	−492.087	+	229.464i	−0.765299	+	0.356865i	−0.765753	−	0.643135i	$-0.777633\pi$
$643$	−492.087	+	229.464i	−0.765299	+	0.356865i	0.000453650		1.00000i	$0.499856\pi$
$644$	−33.5430	+	5.91453i	−0.0520854	+	0.00918406i
$645$	−684.743	+	116.735i	−1.06162	+	0.180984i
$646$	−15.6187	−	13.1057i	−0.0241776	−	0.0202874i
$647$	−396.580	−	396.580i	−0.612952	−	0.612952i	0.330762	−	0.943714i	$-0.392694\pi$
$647$	−396.580	−	396.580i	−0.612952	−	0.612952i	−0.943714	+	0.330762i	$0.892694\pi$
$648$	−404.886	−	224.849i	−0.624825	−	0.346990i
$649$		−	295.136i		−	0.454755i
$650$	−626.277	−	596.978i	−0.963503	−	0.918427i
$651$	18.0347	+	88.7329i	0.0277031	+	0.136302i
$652$	−112.926	+	161.275i	−0.173199	+	0.247355i
$653$	190.492	−	88.8280i	0.291719	−	0.136031i	−0.271250	−	0.962509i	$-0.587437\pi$
$653$	190.492	−	88.8280i	0.291719	−	0.136031i	0.562969	+	0.826478i	$0.309659\pi$
$654$	891.192	+	484.105i	1.36268	+	0.740222i
$655$	−240.228	+	1148.51i	−0.366761	+	1.75345i
$656$	−214.526	+	371.569i	−0.327021	+	0.566416i
$657$	953.681	−	744.493i	1.45157	−	1.13317i
$658$	−370.904	−	99.3833i	−0.563683	−	0.151038i
$659$	−280.075	−	769.498i	−0.424999	−	1.16768i	−0.948812	−	0.315842i	$-0.897713\pi$
$659$	−280.075	−	769.498i	−0.424999	−	1.16768i	0.523812	−	0.851834i	$-0.324509\pi$
$660$	75.2665	+	35.6189i	0.114040	+	0.0539680i
$661$	−160.592	+	134.752i	−0.242952	+	0.203861i	−0.756130	−	0.654421i	$-0.772912\pi$
$661$	−160.592	+	134.752i	−0.242952	+	0.203861i	0.513178	+	0.858282i	$0.328468\pi$
$662$	−527.130	−	46.1179i	−0.796269	−	0.0696645i
$663$	167.076	+	225.883i	0.252000	+	0.340698i
$664$	9.54990	+	26.2381i	0.0143824	+	0.0395153i
$665$	−23.1511	−	6.99587i	−0.0348136	−	0.0105201i
$666$	−105.496	−	457.777i	−0.158403	−	0.687352i
$667$	−327.164	+	87.6634i	−0.490501	+	0.131429i
$668$	221.213	+	315.924i	0.331156	+	0.472940i
$669$	−4.35302	−	167.496i	−0.00650676	−	0.250367i
$670$	321.404	−	802.999i	0.479707	−	1.19851i
$671$	−58.0228	−	329.064i	−0.0864722	−	0.490408i
$672$	−114.799	−	230.365i	−0.170832	−	0.342806i
$673$	−1158.65	+	101.369i	−1.72162	+	0.150622i	−0.904678	−	0.426097i	$-0.859888\pi$
$673$	−1158.65	+	101.369i	−1.72162	+	0.150622i	−0.816943	+	0.576719i	$0.804333\pi$
$674$		−	365.965i		−	0.542975i
$675$	547.204	−	395.212i	0.810673	−	0.585499i
$676$	72.1423			0.106719
$677$	97.9291	+	1119.33i	0.144652	+	1.65337i	0.628196	+	0.778055i	$0.283794\pi$
$677$	97.9291	+	1119.33i	0.144652	+	1.65337i	−0.483545	+	0.875320i	$0.660651\pi$
$678$	67.8929	−	1106.46i	0.100137	−	1.63195i
$679$	−190.490	+	33.5885i	−0.280545	+	0.0494676i
$680$	−169.648	−	67.9023i	−0.249482	−	0.0998563i
$681$	410.398	+	670.004i	0.602640	+	0.983854i
$682$	−57.3075	+	40.1271i	−0.0840286	+	0.0588374i
$683$	22.5930	+	84.3181i	0.0330790	+	0.123453i	0.980491	−	0.196564i	$-0.0629783\pi$
$683$	22.5930	+	84.3181i	0.0330790	+	0.123453i	−0.947412	+	0.320016i	$0.896312\pi$
$684$	−0.997072	−	19.1697i	−0.00145771	−	0.0280259i
$685$	−33.3624	+	110.405i	−0.0487043	+	0.161175i
$686$	677.131	−	246.455i	0.987071	−	0.359265i
$687$	77.9323	+	685.203i	0.113439	+	0.997384i
$688$	−80.0063	+	914.477i	−0.116288	+	1.32918i
$689$	−680.704	−	811.232i	−0.987960	−	1.17740i
$690$	−212.616	+	17.3859i	−0.308139	+	0.0251970i
$691$	−890.562	+	324.138i	−1.28880	+	0.469086i	−0.893334	−	0.449394i	$-0.851640\pi$
$691$	−890.562	+	324.138i	−1.28880	+	0.469086i	−0.395469	+	0.918479i	$0.629418\pi$
$692$	−55.1201	+	205.711i	−0.0796533	+	0.297270i
$693$	−110.820	−	23.6012i	−0.159914	−	0.0340566i
$694$	553.137	+	319.354i	0.797028	+	0.460164i
$695$	−694.521	−	145.269i	−0.999311	−	0.209021i
$696$	−504.022	−	822.853i	−0.724170	−	1.18226i
$697$	58.4673	+	125.383i	0.0838842	+	0.179890i
$698$	254.571	+	178.253i	0.364716	+	0.255377i
$699$	624.809	+	706.499i	0.893862	+	1.01073i
$700$	141.386	−	3.38651i	0.201981	−	0.00483787i
$701$	312.401			0.445651			0.222825	−	0.974858i	$-0.428472\pi$
$701$	312.401			0.445651			0.222825	+	0.974858i	$0.428472\pi$
$702$	−170.830	+	918.689i	−0.243348	+	1.30867i
$703$	−21.1014	+	21.1014i	−0.0300162	+	0.0300162i
$704$	−51.3172	+	61.1575i	−0.0728938	+	0.0868714i
$705$	−638.398	−	236.470i	−0.905530	−	0.335419i
$706$	230.933	+	1309.68i	0.327100	+	1.85508i
$707$	131.816	+	282.680i	0.186444	+	0.399830i
$708$	273.923	−	288.541i	0.386897	−	0.407544i
$709$	837.243	+	147.629i	1.18088	+	0.208221i	0.729417	−	0.684069i	$-0.239791\pi$
$709$	837.243	+	147.629i	1.18088	+	0.208221i	0.451462	+	0.892290i	$0.350903\pi$
$710$	639.389	−	149.803i	0.900548	−	0.210990i
$711$	−322.362	−	98.6948i	−0.453392	−	0.138811i
$712$	−135.638	+	506.208i	−0.190503	+	0.710966i
$713$	21.4415	−	45.9814i	0.0300722	−	0.0644901i
$714$	−160.449	−	24.0115i	−0.224718	−	0.0336296i
$715$	−30.5506	+	255.676i	−0.0427282	+	0.357588i
$716$	−337.945	+	283.570i	−0.471991	+	0.396047i
$717$	575.115	+	250.202i	0.802113	+	0.348956i
$718$	−9.61051	+	20.6098i	−0.0133851	+	0.0287045i
$719$	−228.610	+	131.988i	−0.317956	+	0.183572i	−0.650481	−	0.759522i	$-0.725433\pi$
$719$	−228.610	+	131.988i	−0.317956	+	0.183572i	0.332525	+	0.943094i	$0.392099\pi$
$720$	−322.053	−	831.874i	−0.447296	−	1.15538i
$721$	−121.369	+	210.218i	−0.168335	+	0.291564i
$722$	694.969	−	486.623i	0.962561	−	0.673992i
$723$	−86.6491	−	292.734i	−0.119847	−	0.404888i
$724$	−58.6946	+	161.262i	−0.0810698	+	0.222738i
$725$	1397.70	−	156.087i	1.92786	−	0.215293i
$726$	153.343	+	754.463i	0.211216	+	1.03921i
$727$	−50.9264	−	582.092i	−0.0700501	−	0.800676i	−0.947238	−	0.320530i	$-0.896139\pi$
$727$	−50.9264	−	582.092i	−0.0700501	−	0.800676i	0.877188	−	0.480146i	$-0.159416\pi$
$728$	212.178	−	212.178i	0.291454	−	0.291454i
$729$	−680.271	−	262.054i	−0.933156	−	0.359471i
$730$	1586.87	+	50.2561i	2.17379	+	0.0688440i
$731$	226.745	+	190.262i	0.310185	+	0.260276i
$732$	248.687	−	375.564i	0.339736	−	0.513065i
$733$	−787.798	−	551.622i	−1.07476	−	0.752554i	−0.104476	−	0.994527i	$-0.533317\pi$
$733$	−787.798	−	551.622i	−1.07476	−	0.752554i	−0.970283	+	0.241973i	$0.922205\pi$
$734$	−333.886	+	917.344i	−0.454885	+	1.24979i
$735$	524.860	−	137.447i	0.714095	−	0.187003i
$736$	−25.0430	+	142.026i	−0.0340258	+	0.192970i
$737$	−248.638	+	66.6223i	−0.337365	+	0.0903967i
$738$	−172.533	+	426.550i	−0.233784	+	0.577981i
$739$	−625.369	+	361.057i	−0.846236	+	0.488575i	−0.859379	−	0.511339i	$-0.829150\pi$
$739$	−625.369	+	361.057i	−0.846236	+	0.488575i	0.0131429	+	0.999914i	$0.495816\pi$
$740$	78.7192	−	155.743i	0.106377	−	0.210464i
$741$	55.2329	−	21.7443i	0.0745383	−	0.0293445i
$742$	609.171	+	53.2956i	0.820986	+	0.0718269i
$743$	−100.027	+	1143.31i	−0.134626	+	1.53878i	0.565494	+	0.824752i	$0.308685\pi$
$743$	−100.027	+	1143.31i	−0.134626	+	1.53878i	−0.700120	+	0.714025i	$0.746870\pi$
$744$	142.948	+	21.3926i	0.192135	+	0.0287535i
$745$	328.433	+	999.756i	0.440850	+	1.34195i
$746$	−112.625	−	195.072i	−0.150972	−	0.261491i
$747$	20.6186	+	38.8147i	0.0276018	+	0.0519608i
$748$	−9.18367	−	34.2739i	−0.0122776	−	0.0458207i
$749$	−647.789	−	114.223i	−0.864872	−	0.152500i
$750$	883.670	+	61.0660i	1.17823	+	0.0814214i
$751$	1206.84	+	439.255i	1.60698	+	0.584894i	0.980840	−	0.194815i	$-0.0624106\pi$
$751$	1206.84	+	439.255i	1.60698	+	0.584894i	0.626142	+	0.779709i	$0.284633\pi$
$752$	−516.039	+	736.980i	−0.686222	+	0.980026i
$753$	437.155	−	217.850i	0.580550	−	0.289309i
$754$	−1251.46	+	1491.44i	−1.65977	+	1.97803i
$755$	−1265.86	−	40.0899i	−1.67664	−	0.0530992i
$756$	−86.4392	−	125.929i	−0.114338	−	0.166573i
$757$	337.827	+	337.827i	0.446271	+	0.446271i	0.894113	−	0.447842i	$-0.147807\pi$
$757$	337.827	+	337.827i	0.446271	+	0.446271i	−0.447842	+	0.894113i	$0.647807\pi$
$758$	−1405.15	+	122.935i	−1.85376	+	0.162183i
$759$	42.0583	+	47.5571i	0.0554128	+	0.0626576i
$760$	−23.1337	+	30.9078i	−0.0304391	+	0.0406682i
$761$	−684.518	−	249.144i	−0.899497	−	0.327390i	−0.149446	−	0.988770i	$-0.547749\pi$
$761$	−684.518	−	249.144i	−0.899497	−	0.327390i	−0.750051	+	0.661380i	$0.769971\pi$
$762$	−36.7116	+	152.782i	−0.0481780	+	0.200502i
$763$	−294.036	−	419.927i	−0.385368	−	0.550363i
$764$	173.423	+	100.126i	0.226993	+	0.131055i
$765$	−279.287	−	68.7882i	−0.365081	−	0.0899193i
$766$	323.804	+	560.846i	0.422721	+	0.732174i
$767$	1115.03	+	519.946i	1.45375	+	0.677896i
$768$	−781.525	+	88.8876i	−1.01761	+	0.115739i
$769$	−699.977	−	834.200i	−0.910243	−	1.08479i	−0.996078	−	0.0884764i	$-0.971800\pi$
$769$	−699.977	−	834.200i	−0.910243	−	1.08479i	0.0858349	−	0.996309i	$-0.472644\pi$
$770$	−91.9206	−	116.869i	−0.119377	−	0.151778i
$771$	−261.944	−	208.444i	−0.339746	−	0.270356i
$772$	130.940	+	61.0581i	0.169611	+	0.0790909i
$773$	668.219	+	179.049i	0.864449	+	0.231628i	0.663686	−	0.748011i	$-0.268991\pi$
$773$	668.219	+	179.049i	0.864449	+	0.231628i	0.200763	+	0.979640i	$0.435658\pi$
$774$	51.1348	+	983.119i	0.0660657	+	1.27018i
$775$	−116.665	+	175.409i	−0.150535	+	0.226334i
$776$	−53.6174	+	304.079i	−0.0690946	+	0.391855i
$777$	−55.4781	+	230.882i	−0.0714003	+	0.297146i
$778$	−320.560	+	149.480i	−0.412031	+	0.192133i
$779$	28.7847	−	5.07551i	0.0369508	−	0.00651542i
$780$	−267.167	+	221.608i	−0.342522	+	0.284113i
$781$	−149.715	−	125.626i	−0.191696	−	0.160852i
$782$	64.2781	+	64.2781i	0.0821970	+	0.0821970i
$783$	−965.444	−	1172.59i	−1.23301	−	1.49756i
$784$		−	717.012i		−	0.914556i
$785$	−24.4485	−	439.213i	−0.0311446	−	0.559507i
$786$	1576.91	+	527.971i	2.00624	+	0.671719i
$787$	−656.999	+	938.292i	−0.834815	+	1.19224i	0.144421	+	0.989516i	$0.453868\pi$
$787$	−656.999	+	938.292i	−0.834815	+	1.19224i	−0.979236	+	0.202723i	$0.935021\pi$
$788$	100.845	−	47.0249i	0.127976	−	0.0596763i
$789$	23.5496	+	906.142i	0.0298474	+	1.14847i
$790$	−242.155	−	370.248i	−0.306525	−	0.468668i
$791$	−280.164	+	485.258i	−0.354190	+	0.613475i
$792$	−95.9068	+	153.348i	−0.121094	+	0.193622i
$793$	1345.43	+	360.507i	1.69663	+	0.454611i
$794$	−341.792	−	939.065i	−0.430468	−	1.18270i
$795$	1066.59	+	194.318i	1.34163	+	0.244425i
$796$	−299.938	+	251.678i	−0.376807	+	0.316178i
$797$	760.933	+	66.5730i	0.954746	+	0.0835295i	0.553870	−	0.832603i	$-0.313150\pi$
$797$	760.933	+	66.5730i	0.954746	+	0.0835295i	0.400876	+	0.916132i	$0.368706\pi$
$798$	−13.6737	+	31.4305i	−0.0171350	+	0.0393866i
$799$	99.2198	+	272.604i	0.124180	+	0.341182i
$800$	191.276	−	567.452i	0.239095	−	0.709315i
$801$	−100.854	+	818.726i	−0.125910	+	1.02213i
$802$	1306.16	−	349.984i	1.62862	−	0.436389i
$803$	−271.013	−	387.047i	−0.337501	−	0.482002i
$804$	−304.916	−	165.634i	−0.379249	−	0.206012i
$805$	100.107	+	40.0683i	0.124357	+	0.0497742i
$806$	−50.6414	−	287.202i	−0.0628305	−	0.356329i
$807$	198.295	−	299.462i	0.245718	−	0.371081i
$808$	495.996	−	43.3940i	0.613856	−	0.0537054i
$809$		−	983.045i		−	1.21514i	−0.794267	−	0.607568i	$-0.792145\pi$
$809$		−	983.045i		−	1.21514i	0.794267	−	0.607568i	$-0.207855\pi$
$810$	−465.844	−	835.552i	−0.575116	−	1.03155i
$811$	1259.96			1.55358			0.776792	−	0.629757i	$-0.216845\pi$
$811$	1259.96			1.55358			0.776792	+	0.629757i	$0.216845\pi$
$812$	−27.7366	−	317.030i	−0.0341583	−	0.390431i
$813$	353.771	+	234.256i	0.435143	+	0.288138i
$814$	−180.677	+	31.8583i	−0.221962	+	0.0391380i
$815$	572.940	−	245.397i	0.702994	−	0.301101i
$816$	−181.443	+	334.019i	−0.222356	+	0.409337i
$817$	51.2264	−	35.8691i	0.0627006	−	0.0439034i
$818$	123.151	+	459.607i	0.150552	+	0.561867i
$819$	284.400	−	377.103i	0.347253	−	0.460443i
$820$	−150.653	+	80.7323i	−0.183723	+	0.0984540i
$821$	−837.346	+	304.769i	−1.01991	+	0.371217i	−0.797230	−	0.603675i	$-0.793702\pi$
$821$	−837.346	+	304.769i	−1.01991	+	0.371217i	−0.222679	+	0.974892i	$0.571480\pi$
$822$	149.888	+	65.2083i	0.182346	+	0.0793288i
$823$	−47.6180	+	544.277i	−0.0578591	+	0.661333i	0.910785	+	0.412881i	$0.135477\pi$
$823$	−47.6180	+	544.277i	−0.0578591	+	0.661333i	−0.968644	+	0.248452i	$0.920078\pi$
$824$	249.070	+	296.830i	0.302269	+	0.360230i
$825$	−143.036	−	221.432i	−0.173377	−	0.268403i
$826$	−667.575	+	242.978i	−0.808203	+	0.294162i
$827$	99.0791	−	369.768i	0.119805	−	0.447120i	−0.879796	−	0.475351i	$-0.842321\pi$
$827$	99.0791	−	369.768i	0.119805	−	0.447120i	0.999601	+	0.0282316i	$0.00898759\pi$
$828$	−3.02050	+	85.5299i	−0.00364795	+	0.103297i
$829$	−272.496	−	157.326i	−0.328705	−	0.189778i	0.326561	−	0.945176i	$-0.394110\pi$
$829$	−272.496	−	157.326i	−0.328705	−	0.189778i	−0.655266	+	0.755398i	$0.727443\pi$
$830$	−11.8082	+	56.4538i	−0.0142267	+	0.0680167i
$831$	93.3192	−	2.42526i	0.112297	−	0.00291848i
$832$	−140.648	−	301.620i	−0.169048	−	0.362524i
$833$	−189.385	−	132.609i	−0.227353	−	0.159195i
$834$	−319.271	+	953.577i	−0.382819	+	1.14338i
$835$	−67.8588	−	1219.07i	−0.0812680	−	1.45996i
$836$	−7.49661			−0.00896724
$837$	227.507	+	2.11984i	0.271812	+	0.00253267i
$838$	363.763	−	363.763i	0.434084	−	0.434084i
$839$	−156.428	+	186.423i	−0.186446	+	0.222197i	−0.851168	−	0.524893i	$-0.824105\pi$
$839$	−156.428	+	186.423i	−0.186446	+	0.222197i	0.664723	+	0.747090i	$0.268550\pi$
$840$	−28.5105	+	305.869i	−0.0339411	+	0.364130i
$841$	−403.501	−	2288.37i	−0.479787	−	2.72101i
$842$	−422.814	−	906.728i	−0.502155	−	1.07687i
$843$	601.776	+	144.599i	0.713851	+	0.171529i
$844$	−482.322	−	85.0465i	−0.571472	−	0.100766i
$845$	−194.075	−	120.397i	−0.229675	−	0.142482i
$846$	−438.367	+	859.507i	−0.518164	+	1.01597i
$847$	100.720	−	375.891i	0.118913	−	0.443791i
$848$	605.505	−	1298.51i	0.714038	−	1.53126i
$849$	−61.6547	+	77.4793i	−0.0726204	+	0.0912595i
$850$	−223.838	−	303.917i	−0.263339	−	0.357549i
$851$	101.922	−	85.5224i	0.119767	−	0.100496i
$852$	−29.7730	−	261.773i	−0.0349449	−	0.307245i
$853$	543.503	−	1165.55i	0.637167	−	1.36641i	−0.276921	−	0.960893i	$-0.589314\pi$
$853$	543.503	−	1165.55i	0.637167	−	1.36641i	0.914088	−	0.405516i	$-0.132908\pi$
$854$	−696.550	+	402.153i	−0.815632	+	0.470905i
$855$	−29.3098	+	53.2339i	−0.0342804	+	0.0622619i
$856$	−525.009	+	909.342i	−0.613328	+	1.06232i
$857$	778.374	−	545.023i	0.908254	−	0.635967i	−0.0232370	−	0.999730i	$-0.507397\pi$
$857$	778.374	−	545.023i	0.908254	−	0.635967i	0.931491	+	0.363763i	$0.118508\pi$
$858$	354.832	+	85.2616i	0.413558	+	0.0993725i
$859$	162.636	−	446.840i	0.189332	−	0.520186i	−0.808314	−	0.588751i	$-0.799620\pi$
$859$	162.636	−	446.840i	0.189332	−	0.520186i	0.997647	+	0.0685649i	$0.0218420\pi$
$860$	−219.129	+	292.768i	−0.254802	+	0.340428i
$861$	174.219	−	154.075i	0.202345	−	0.178948i
$862$	−45.8164	−	523.684i	−0.0531513	−	0.607522i
$863$	−1127.92	+	1127.92i	−1.30698	+	1.30698i	−0.383398	+	0.923583i	$0.625246\pi$
$863$	−1127.92	+	1127.92i	−1.30698	+	1.30698i	−0.923583	+	0.383398i	$0.874754\pi$
$864$	−626.224	+	161.558i	−0.724796	+	0.186988i
$865$	491.590	−	461.409i	0.568313	−	0.533421i
$866$	−718.944	−	603.266i	−0.830189	−	0.696612i
$867$	−332.033	−	666.284i	−0.382968	−	0.768493i
$868$	39.0486	+	27.3422i	0.0449869	+	0.0315002i
$869$	−45.0312	+	123.722i	−0.0518196	+	0.142373i
$870$	11.3142	−	1993.16i	0.0130048	−	2.29099i
$871$	186.330	−	1056.73i	0.213926	−	1.21324i
$872$	−790.437	+	211.797i	−0.906465	+	0.242887i
$873$	−17.1534	+	485.723i	−0.0196488	+	0.556384i
$874$	16.6323	−	9.60269i	0.0190301	−	0.0109871i
$875$	−386.006	−	226.848i	−0.441150	−	0.259254i
$876$	94.2711	−	629.934i	0.107615	−	0.719102i
$877$	−308.611	−	27.0000i	−0.351894	−	0.0307868i	−0.0901616	−	0.995927i	$-0.528738\pi$
$877$	−308.611	−	27.0000i	−0.351894	−	0.0307868i	−0.261733	+	0.965140i	$0.584294\pi$
$878$	18.7686	−	214.527i	0.0213766	−	0.244336i
$879$	−142.697	−	362.467i	−0.162340	−	0.412363i
$880$	−330.972	+	108.729i	−0.376105	+	0.123555i
$881$	253.650	+	439.334i	0.287911	+	0.498677i	0.973311	−	0.229490i	$-0.0737059\pi$
$881$	253.650	+	439.334i	0.287911	+	0.498677i	−0.685400	+	0.728167i	$0.740373\pi$
$882$	−106.715	−	761.496i	−0.120993	−	0.863374i
$883$	−164.139	−	612.574i	−0.185888	−	0.693742i	−0.994439	−	0.105316i	$-0.966415\pi$
$883$	−164.139	−	612.574i	−0.185888	−	0.693742i	0.808551	−	0.588426i	$-0.200252\pi$
$884$	145.667	+	25.6849i	0.164781	+	0.0290554i
$885$	−1218.44	+	319.079i	−1.37677	+	0.360541i
$886$	−1095.80	−	398.837i	−1.23679	−	0.450154i
$887$	−978.326	+	1397.19i	−1.10296	+	1.57519i	−0.326307	+	0.945264i	$0.605804\pi$
$887$	−978.326	+	1397.19i	−1.10296	+	1.57519i	−0.776654	+	0.629928i	$0.783085\pi$
$888$	316.042	+	209.273i	0.355903	+	0.235668i
$889$	51.0528	−	60.8424i	0.0574272	−	0.0684391i
$890$	−789.292	+	740.833i	−0.886845	+	0.832397i
$891$	−116.003	+	259.996i	−0.130195	+	0.291803i
$892$	−62.3739	−	62.3739i	−0.0699259	−	0.0699259i
$893$	61.0571	−	5.34180i	0.0683730	−	0.00598186i
$894$	1461.51	−	297.049i	1.63480	−	0.332269i
$895$	1382.38	−	198.860i	1.54456	−	0.222190i
$896$	503.066	+	183.101i	0.561457	+	0.204354i
$897$	−253.767	+	75.1147i	−0.282906	+	0.0837400i
$898$	346.338	+	494.622i	0.385677	+	0.550804i
$899$	410.529	+	237.019i	0.456651	+	0.263647i
$900$	65.6770	−	349.240i	0.0729744	−	0.388044i
$901$	−230.991	−	400.088i	−0.256372	−	0.444049i
$902$	162.859	+	75.9423i	0.180553	+	0.0841933i
$903$	198.508	−	456.292i	0.219832	−	0.505307i
$904$	574.943	+	685.190i	0.635998	+	0.757953i
$905$	427.026	−	335.868i	0.471852	−	0.371125i
$906$	−265.658	+	1775.17i	−0.293221	+	1.95935i
$907$	−476.312	−	222.108i	−0.525151	−	0.244882i	0.141917	−	0.989879i	$-0.454673\pi$
$907$	−476.312	−	222.108i	−0.525151	−	0.244882i	−0.667068	+	0.744997i	$0.732451\pi$
$908$	399.549	+	107.059i	0.440032	+	0.117906i
$909$	763.697	−	175.996i	0.840150	−	0.193615i
$910$	603.471	−	141.388i	0.663155	−	0.155371i
$911$	22.4735	−	127.454i	0.0246691	−	0.139905i	−0.969986	−	0.243162i	$-0.921815\pi$
$911$	22.4735	−	127.454i	0.0246691	−	0.139905i	0.994655	+	0.103257i	$0.0329264\pi$
$912$	58.2432	+	55.2926i	0.0638632	+	0.0606278i
$913$	15.5564	−	7.25406i	0.0170388	−	0.00794530i
$914$	1186.08	−	209.138i	1.29768	−	0.228816i
$915$	−1295.78	+	595.302i	−1.41616	+	0.650603i
$916$	278.119	+	233.370i	0.303624	+	0.254771i
$917$	−594.364	−	594.364i	−0.648162	−	0.648162i
$918$	−142.986	+	381.747i	−0.155759	+	0.415846i
$919$		−	63.5001i		−	0.0690970i	−0.999403	−	0.0345485i	$-0.989001\pi$
$919$		−	63.5001i		−	0.0690970i	0.999403	−	0.0345485i	$-0.0109993\pi$
$920$	114.759	−	128.288i	0.124738	−	0.139443i
$921$	947.365	−	837.825i	1.02863	−	0.909691i
$922$	−318.378	+	454.691i	−0.345312	+	0.493157i
$923$	738.372	−	344.308i	0.799969	−	0.373032i
$924$	−50.8670	+	31.1576i	−0.0550509	+	0.0337203i
$925$	−471.686	+	287.603i	−0.509931	+	0.310922i
$926$	158.686	−	274.853i	0.171368	−	0.296817i
$927$	453.102	+	408.299i	0.488784	+	0.440451i
$928$	−1301.57	−	348.753i	−1.40255	−	0.375812i
$929$	159.618	+	438.546i	0.171817	+	0.472062i	0.995475	−	0.0950242i	$-0.0302928\pi$
$929$	159.618	+	438.546i	0.171817	+	0.472062i	−0.823658	+	0.567086i	$0.808071\pi$
$930$	227.618	+	193.207i	0.244751	+	0.207749i
$931$	−37.4180	+	31.3975i	−0.0401912	+	0.0337244i
$932$	494.642	+	43.2756i	0.530732	+	0.0464330i
$933$	1291.73	−	146.916i	1.38449	−	0.157467i
$934$	22.5814	+	62.0419i	0.0241771	+	0.0664260i
$935$	−32.4936	+	107.529i	−0.0347525	+	0.115005i
$936$	−410.393	−	632.495i	−0.438454	−	0.675742i
$937$	−702.528	+	188.242i	−0.749763	+	0.200898i	−0.613413	−	0.789762i	$-0.710204\pi$
$937$	−702.528	+	188.242i	−0.749763	+	0.200898i	−0.136350	+	0.990661i	$0.543537\pi$
$938$	355.392	+	507.552i	0.378883	+	0.541101i
$939$	−1381.85	+	846.424i	−1.47162	+	0.901410i
$940$	−329.460	+	141.112i	−0.350490	+	0.150119i
$941$	−117.348	−	665.516i	−0.124706	−	0.707243i	−0.981482	−	0.191554i	$-0.938647\pi$
$941$	−117.348	−	665.516i	−0.124706	−	0.707243i	0.856776	−	0.515689i	$-0.172464\pi$
$942$	−622.265	−	38.1824i	−0.660579	−	0.0405333i
$943$	−129.819	+	11.3577i	−0.137666	+	0.0120443i
$944$			1664.52i			1.76326i
$945$	22.3751	+	483.028i	0.0236774	+	0.511141i
$946$	384.463			0.406410
$947$	20.6901	+	236.489i	0.0218481	+	0.249725i	0.999263	+	0.0383939i	$0.0122242\pi$
$947$	20.6901	+	236.489i	0.0218481	+	0.249725i	−0.977415	+	0.211331i	$0.932220\pi$
$948$	−158.855	+	79.1631i	−0.167568	+	0.0835053i
$949$	1939.72	−	342.025i	2.04396	−	0.360406i
$950$	−74.2615	+	29.0610i	−0.0781700	+	0.0305906i
$951$	992.983	−	25.8065i	1.04415	−	0.0271362i
$952$	107.230	−	75.0829i	0.112636	−	0.0788686i
$953$	−23.5901	−	88.0396i	−0.0247535	−	0.0923815i	0.952444	−	0.304714i	$-0.0985608\pi$
$953$	−23.5901	−	88.0396i	−0.0247535	−	0.0923815i	−0.977198	+	0.212332i	$0.931894\pi$
$954$	449.809	−	1469.19i	0.471498	−	1.54003i
$955$	−299.439	−	558.778i	−0.313549	−	0.585108i
$956$	310.275	−	112.931i	0.324556	−	0.118129i
$957$	−476.905	+	352.746i	−0.498334	+	0.368596i
$958$	83.1143	−	950.001i	0.0867582	−	0.991650i
$959$	−53.1085	−	63.2922i	−0.0553790	−	0.0659981i
$960$	307.964	+	145.740i	0.320796	+	0.151812i
$961$	836.320	−	304.396i	0.870261	−	0.316749i
$962$	197.942	−	738.728i	0.205761	−	0.767909i
$963$	−619.754	+	1532.21i	−0.643565	+	1.59108i
$964$	−139.190	−	80.3615i	−0.144388	−	0.0833626i
$965$	−250.351	−	382.780i	−0.259431	−	0.396663i
$966$	72.9452	−	134.285i	0.0755126	−	0.139012i
$967$	535.715	+	1148.84i	0.553997	+	1.18805i	0.961489	+	0.274842i	$0.0886255\pi$
$967$	535.715	+	1148.84i	0.553997	+	1.18805i	−0.407492	+	0.913209i	$0.633597\pi$
$968$	−508.858	−	356.306i	−0.525680	−	0.368085i
$969$	25.3764	−	5.15768i	0.0261882	−	0.00532269i
$970$	−425.226	+	475.356i	−0.438377	+	0.490058i
$971$	515.541			0.530938			0.265469	−	0.964119i	$-0.414473\pi$
$971$	515.541			0.530938			0.265469	+	0.964119i	$0.414473\pi$
$972$	−354.721	+	146.521i	−0.364939	+	0.150742i
$973$	359.420	−	359.420i	0.369394	−	0.369394i
$974$	−425.176	+	506.705i	−0.436525	+	0.520231i
$975$	1088.56	−	150.292i	1.11648	−	0.154146i
$976$	327.239	+	1855.87i	0.335286	+	1.90150i
$977$	197.554	+	423.655i	0.202204	+	0.433628i	0.981094	−	0.193533i	$-0.0619945\pi$
$977$	197.554	+	423.655i	0.202204	+	0.433628i	−0.778890	+	0.627161i	$0.784217\pi$
$978$	−250.716	−	847.016i	−0.256356	−	0.866069i
$979$	317.265	+	55.9425i	0.324071	+	0.0571424i
$980$	150.577	−	242.723i	0.153650	−	0.247677i
$981$	−1185.89	+	502.831i	−1.20886	+	0.512570i
$982$	330.950	−	1235.12i	0.337016	−	1.25776i
$983$	126.088	−	270.396i	0.128268	−	0.275072i	−0.831677	−	0.555260i	$-0.812619\pi$
$983$	126.088	−	270.396i	0.128268	−	0.275072i	0.959945	+	0.280188i	$0.0903967\pi$
$984$	−135.999	−	345.453i	−0.138210	−	0.351070i
$985$	−349.770	−	41.7940i	−0.355097	−	0.0424304i
$986$	−650.636	+	545.949i	−0.659874	+	0.553700i
$987$	392.091	−	290.013i	0.397256	−	0.293833i
$988$	13.2069	−	28.3223i	0.0133673	−	0.0286663i
$989$	−241.460	+	139.407i	−0.244146	+	0.140958i
$990$	−335.324	+	164.734i	−0.338711	+	0.166398i
$991$	412.360	−	714.229i	0.416105	−	0.720716i	−0.579438	−	0.815016i	$-0.696728\pi$
$991$	412.360	−	714.229i	0.416105	−	0.720716i	0.995544	+	0.0943004i	$0.0300614\pi$
$992$	165.338	−	115.771i	0.166671	−	0.116704i
$993$	462.705	−	487.397i	0.465966	−	0.490832i
$994$	−160.900	+	442.068i	−0.161871	+	0.444737i
$995$	1226.91	−	176.495i	1.23307	−	0.177382i
$996$	21.9415	+	7.34632i	0.0220296	+	0.00737582i
$997$	−111.406	−	1273.37i	−0.111741	−	1.27720i	−0.820456	−	0.571709i	$-0.806281\pi$
$997$	−111.406	−	1273.37i	−0.111741	−	1.27720i	0.708716	−	0.705494i	$-0.249275\pi$
$998$	476.412	−	476.412i	0.477367	−	0.477367i
$999$	538.374	+	257.182i	0.538913	+	0.257439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.r.a.97.27	yes	408
3.2	odd	2		405.3.s.a.127.8		408
5.3	odd	4	inner	135.3.r.a.43.27	yes	408
15.8	even	4		405.3.s.a.208.8		408
27.5	odd	18		405.3.s.a.37.8		408
27.22	even	9	inner	135.3.r.a.22.27	✓	408
135.103	odd	36	inner	135.3.r.a.103.27	yes	408
135.113	even	36		405.3.s.a.118.8		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.27	✓	408	27.22	even	9	inner
135.3.r.a.43.27	yes	408	5.3	odd	4	inner
135.3.r.a.97.27	yes	408	1.1	even	1	trivial
135.3.r.a.103.27	yes	408	135.103	odd	36	inner
405.3.s.a.37.8		408	27.5	odd	18
405.3.s.a.118.8		408	135.113	even	36
405.3.s.a.127.8		408	3.2	odd	2
405.3.s.a.208.8		408	15.8	even	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.205868 + 2.35308i) q^{2} +(-2.50133 - 1.65630i) q^{3} +(-1.55539 + 0.274257i) q^{4} +(4.64198 + 1.85797i) q^{5} +(3.38248 - 6.22682i) q^{6} +(-2.93406 + 2.05445i) q^{7} +(1.47984 + 5.52284i) q^{8} +(3.51332 + 8.28593i) q^{9} +(-3.41632 + 11.3055i) q^{10} +(3.30286 - 1.20214i) q^{11} +(4.34480 + 1.89019i) q^{12} +(-1.27699 + 14.5961i) q^{13} +(-5.43832 - 6.48114i) q^{14} +(-8.53376 - 12.3359i) q^{15} +(-18.6276 + 6.77989i) q^{16} +(-1.65433 + 6.17406i) q^{17} +(-18.7742 + 9.97294i) q^{18} +(1.16951 + 0.675215i) q^{19} +(-7.72965 - 1.61677i) q^{20} +(10.7418 - 0.279168i) q^{21} +(3.50870 + 7.52443i) q^{22} +(-4.93199 - 3.45342i) q^{23} +(5.44593 - 16.2655i) q^{24} +(18.0959 + 17.2493i) q^{25} -34.6088 q^{26} +(4.93604 - 26.5450i) q^{27} +(4.00016 - 4.00016i) q^{28} +(36.1603 - 43.0941i) q^{29} +(27.2706 - 22.6202i) q^{30} +(1.46325 + 8.29852i) q^{31} +(-10.1229 - 21.7087i) q^{32} +(-10.2527 - 2.46358i) q^{33} +(-14.8687 - 2.62174i) q^{34} +(-17.4369 + 4.08532i) q^{35} +(-7.73706 - 11.9243i) q^{36} +(-5.71940 + 21.3451i) q^{37} +(-1.34807 + 2.89095i) q^{38} +(27.3698 - 34.3946i) q^{39} +(-3.39188 + 28.3864i) q^{40} +(16.5803 - 13.9125i) q^{41} +(2.86831 + 25.2190i) q^{42} +(19.5707 - 41.9694i) q^{43} +(-4.80755 + 2.77564i) q^{44} +(0.913732 + 44.9907i) q^{45} +(7.11084 - 12.3163i) q^{46} +(37.1779 - 26.0322i) q^{47} +(57.8234 + 13.8942i) q^{48} +(-12.3711 + 33.9892i) q^{49} +(-36.8637 + 46.1322i) q^{50} +(14.3642 - 12.7033i) q^{51} +(-2.01687 - 23.0529i) q^{52} +(-51.1073 + 51.1073i) q^{53} +(63.4787 + 6.15016i) q^{54} +(17.5654 + 0.556295i) q^{55} +(-15.6883 - 13.1641i) q^{56} +(-1.80696 - 3.62599i) q^{57} +(108.848 + 76.2164i) q^{58} +(28.7190 - 78.9047i) q^{59} +(16.6566 + 16.8467i) q^{60} +(16.5080 - 93.6215i) q^{61} +(-19.2259 + 5.15156i) q^{62} +(-27.3313 - 17.0935i) q^{63} +(-19.6708 + 11.3569i) q^{64} +(-33.0469 + 65.3822i) q^{65} +(3.68632 - 24.6326i) q^{66} +(-72.9564 - 6.38285i) q^{67} +(0.879855 - 10.0568i) q^{68} +(6.61664 + 16.8070i) q^{69} +(-13.2028 - 40.1895i) q^{70} +(-27.8020 - 48.1545i) q^{71} +(-40.5627 + 31.6653i) q^{72} +(-34.7929 - 129.849i) q^{73} +(-51.4043 - 9.06396i) q^{74} +(-16.6938 - 73.1185i) q^{75} +(-2.00422 - 0.729477i) q^{76} +(-7.22105 + 10.3127i) q^{77} +(86.5680 + 57.3227i) q^{78} +(-24.0782 + 28.6953i) q^{79} +(-99.0658 - 3.13742i) q^{80} +(-56.3132 + 58.2222i) q^{81} +(36.1506 + 36.1506i) q^{82} +(4.86489 - 0.425622i) q^{83} +(-16.6312 + 3.38025i) q^{84} +(-19.1506 + 25.5861i) q^{85} +(102.787 + 37.4112i) q^{86} +(-161.826 + 47.9003i) q^{87} +(11.5270 + 16.4622i) q^{88} +(79.3775 + 45.8286i) q^{89} +(-105.679 + 11.4122i) q^{90} +(-26.2402 - 45.4494i) q^{91} +(8.61830 + 4.01878i) q^{92} +(10.0848 - 23.1809i) q^{93} +(68.9097 + 82.1234i) q^{94} +(4.17429 + 5.30724i) q^{95} +(-10.6354 + 71.0673i) q^{96} +(48.9432 + 22.8226i) q^{97} +(-82.5262 - 22.1128i) q^{98} +(21.5649 + 23.1438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23}+ \cdots - 1032 q^{98}+O(q^{100}) \) 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

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