LMFDB - Embedded newform 45.3.k.a.43.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(7,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	45.43
Dual form			45.3.k.a.22.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.644680 - 2.40598i) q^{2} +(-2.98224 - 0.325974i) q^{3} +(-1.90902 + 1.10217i) q^{4} +(-4.49898 - 2.18155i) q^{5} +(1.13830 + 7.38535i) q^{6} +(0.0176356 + 0.0658171i) q^{7} +(-3.16269 - 3.16269i) q^{8} +(8.78748 + 1.94426i) q^{9} +(-2.34837 + 12.2309i) q^{10} +(4.62292 - 8.00713i) q^{11} +(6.05242 - 2.66465i) q^{12} +(3.38696 - 12.6403i) q^{13} +(0.146985 - 0.0848619i) q^{14} +(12.7059 + 7.97246i) q^{15} +(-9.97912 + 17.2843i) q^{16} +(13.6029 - 13.6029i) q^{17} +(-0.987258 - 22.3959i) q^{18} -5.80704i q^{19} +(10.9931 - 0.794023i) q^{20} +(-0.0311390 - 0.202031i) q^{21} +(-22.2453 - 5.96060i) q^{22} +(-11.7365 + 43.8013i) q^{23} +(8.40093 + 10.4628i) q^{24} +(15.4816 + 19.6295i) q^{25} -32.5958 q^{26} +(-25.5726 - 8.66274i) q^{27} +(-0.106208 - 0.106208i) q^{28} +(6.37222 + 3.67900i) q^{29} +(10.9903 - 35.7098i) q^{30} +(-8.35363 - 14.4689i) q^{31} +(30.7378 + 8.23618i) q^{32} +(-16.3967 + 22.3722i) q^{33} +(-41.4978 - 23.9587i) q^{34} +(0.0642412 - 0.334583i) q^{35} +(-18.9184 + 5.97368i) q^{36} +(36.0680 - 36.0680i) q^{37} +(-13.9716 + 3.74368i) q^{38} +(-14.2211 + 36.5923i) q^{39} +(7.32929 + 21.1284i) q^{40} +(-31.1567 - 53.9649i) q^{41} +(-0.466007 + 0.205165i) q^{42} +(9.70259 - 2.59980i) q^{43} +20.3810i q^{44} +(-35.2932 - 27.9176i) q^{45} +112.951 q^{46} +(11.9633 + 44.6476i) q^{47} +(35.3944 - 48.2931i) q^{48} +(42.4312 - 24.4977i) q^{49} +(37.2475 - 49.9033i) q^{50} +(-45.0012 + 36.1329i) q^{51} +(7.46602 + 27.8636i) q^{52} +(28.0258 + 28.0258i) q^{53} +(-4.35625 + 67.1118i) q^{54} +(-38.2664 + 25.9388i) q^{55} +(0.152383 - 0.263935i) q^{56} +(-1.89294 + 17.3180i) q^{57} +(4.74356 - 17.7032i) q^{58} +(16.3509 - 9.44022i) q^{59} +(-33.0428 - 1.21549i) q^{60} +(2.69547 - 4.66870i) q^{61} +(-29.4265 + 29.4265i) q^{62} +(0.0270071 + 0.612655i) q^{63} +0.568692i q^{64} +(-42.8134 + 49.4796i) q^{65} +(64.3977 + 25.0273i) q^{66} +(-47.9117 - 12.8379i) q^{67} +(-10.9754 + 40.9609i) q^{68} +(49.2792 - 126.800i) q^{69} +(-0.846414 + 0.0611359i) q^{70} +56.4200 q^{71} +(-21.6430 - 33.9412i) q^{72} +(-54.7135 - 54.7135i) q^{73} +(-110.031 - 63.5264i) q^{74} +(-39.7712 - 63.5866i) q^{75} +(6.40036 + 11.0857i) q^{76} +(0.608534 + 0.163056i) q^{77} +(97.2084 + 10.6254i) q^{78} +(-40.9692 - 23.6536i) q^{79} +(82.6026 - 55.9919i) q^{80} +(73.4397 + 34.1704i) q^{81} +(-109.752 + 109.752i) q^{82} +(60.0267 - 16.0841i) q^{83} +(0.282117 + 0.351360i) q^{84} +(-90.8746 + 31.5237i) q^{85} +(-12.5101 - 21.6682i) q^{86} +(-17.8042 - 13.0488i) q^{87} +(-39.9449 + 10.7032i) q^{88} +59.1599i q^{89} +(-44.4163 + 102.913i) q^{90} +0.891679 q^{91} +(-25.8713 - 96.5530i) q^{92} +(20.1960 + 45.8728i) q^{93} +(99.7085 - 57.5668i) q^{94} +(-12.6684 + 26.1258i) q^{95} +(-88.9828 - 34.5820i) q^{96} +(40.2595 + 150.251i) q^{97} +(-86.2954 - 86.2954i) q^{98} +(56.1918 - 61.3743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.644680	−	2.40598i	−0.322340	−	1.20299i	−0.916959	−	0.398981i	$-0.869364\pi$
$2$	−0.644680	−	2.40598i	−0.322340	−	1.20299i	0.594619	−	0.804008i	$-0.297303\pi$
$3$	−2.98224	−	0.325974i	−0.994079	−	0.108658i
$3$	−2.98224	−	0.325974i	−0.994079	−	0.108658i
$4$	−1.90902	+	1.10217i	−0.477254	+	0.275543i
$5$	−4.49898	−	2.18155i	−0.899796	−	0.436311i
$5$	−4.49898	−	2.18155i	−0.899796	−	0.436311i
$6$	1.13830	+	7.38535i	0.189717	+	1.23089i
$7$	0.0176356	+	0.0658171i	0.00251938	+	0.00940244i	0.967174	−	0.254115i	$-0.0817841\pi$
$7$	0.0176356	+	0.0658171i	0.00251938	+	0.00940244i	−0.964655	+	0.263517i	$0.915117\pi$
$8$	−3.16269	−	3.16269i	−0.395336	−	0.395336i
$9$	8.78748	+	1.94426i	0.976387	+	0.216029i
$10$	−2.34837	+	12.2309i	−0.234837	+	1.22309i
$11$	4.62292	−	8.00713i	0.420265	−	0.727921i	−0.575700	−	0.817661i	$-0.695270\pi$
$11$	4.62292	−	8.00713i	0.420265	−	0.727921i	0.995965	+	0.0897404i	$0.0286037\pi$
$12$	6.05242	−	2.66465i	0.504368	−	0.222054i
$13$	3.38696	−	12.6403i	0.260535	−	0.972331i	−0.704391	−	0.709812i	$-0.748780\pi$
$13$	3.38696	−	12.6403i	0.260535	−	0.972331i	0.964927	−	0.262519i	$-0.0845534\pi$
$14$	0.146985	−	0.0848619i	0.0104989	−	0.00606156i
$15$	12.7059	+	7.97246i	0.847060	+	0.531498i
$16$	−9.97912	+	17.2843i	−0.623695	+	1.08027i
$17$	13.6029	−	13.6029i	0.800170	−	0.800170i	−0.182952	−	0.983122i	$-0.558565\pi$
$17$	13.6029	−	13.6029i	0.800170	−	0.800170i	0.983122	+	0.182952i	$0.0585652\pi$
$18$	−0.987258	−	22.3959i	−0.0548477	−	1.24422i
$19$		−	5.80704i		−	0.305634i	−0.988255	−	0.152817i	$-0.951166\pi$
$19$		−	5.80704i		−	0.305634i	0.988255	−	0.152817i	$-0.0488345\pi$
$20$	10.9931	−	0.794023i	0.549654	−	0.0397011i
$21$	−0.0311390	−	0.202031i	−0.00148281	−	0.00962052i
$22$	−22.2453	−	5.96060i	−1.01115	−	0.270936i
$23$	−11.7365	+	43.8013i	−0.510283	+	1.90440i	−0.0928936	+	0.995676i	$0.529612\pi$
$23$	−11.7365	+	43.8013i	−0.510283	+	1.90440i	−0.417390	+	0.908728i	$0.637055\pi$
$24$	8.40093	+	10.4628i	0.350039	+	0.435952i
$25$	15.4816	+	19.6295i	0.619266	+	0.785182i
$26$	−32.5958			−1.25368
$27$	−25.5726	−	8.66274i	−0.947133	−	0.320842i
$28$	−0.106208	−	0.106208i	−0.00379316	−	0.00379316i
$29$	6.37222	+	3.67900i	0.219732	+	0.126862i	0.605826	−	0.795597i	$-0.292843\pi$
$29$	6.37222	+	3.67900i	0.219732	+	0.126862i	−0.386094	+	0.922459i	$0.626176\pi$
$30$	10.9903	−	35.7098i	0.366345	−	1.19033i
$31$	−8.35363	−	14.4689i	−0.269472	−	0.466739i	0.699254	−	0.714874i	$-0.253516\pi$
$31$	−8.35363	−	14.4689i	−0.269472	−	0.466739i	−0.968726	+	0.248135i	$0.920183\pi$
$32$	30.7378	+	8.23618i	0.960558	+	0.257381i
$33$	−16.3967	+	22.3722i	−0.496871	+	0.677946i
$34$	−41.4978	−	23.9587i	−1.22052	−	0.704669i
$35$	0.0642412	−	0.334583i	0.00183546	−	0.00955951i
$36$	−18.9184	+	5.97368i	−0.525510	+	0.165936i
$37$	36.0680	−	36.0680i	0.974810	−	0.974810i	−0.0248806	−	0.999690i	$-0.507921\pi$
$37$	36.0680	−	36.0680i	0.974810	−	0.974810i	0.999690	+	0.0248806i	$0.00792055\pi$
$38$	−13.9716	+	3.74368i	−0.367674	+	0.0985180i
$39$	−14.2211	+	36.5923i	−0.364644	+	0.938265i
$40$	7.32929	+	21.1284i	0.183232	+	0.528211i
$41$	−31.1567	−	53.9649i	−0.759919	−	1.31622i	−0.942892	−	0.333100i	$-0.891905\pi$
$41$	−31.1567	−	53.9649i	−0.759919	−	1.31622i	0.182973	−	0.983118i	$-0.441428\pi$
$42$	−0.466007	+	0.205165i	−0.0110954	+	0.00488488i
$43$	9.70259	−	2.59980i	0.225642	−	0.0604605i	−0.144227	−	0.989545i	$-0.546069\pi$
$43$	9.70259	−	2.59980i	0.225642	−	0.0604605i	0.369868	+	0.929084i	$0.379403\pi$
$44$			20.3810i			0.463204i
$45$	−35.2932	−	27.9176i	−0.784293	−	0.620390i
$46$	112.951			2.45546
$47$	11.9633	+	44.6476i	0.254538	+	0.949948i	0.968347	+	0.249608i	$0.0803017\pi$
$47$	11.9633	+	44.6476i	0.254538	+	0.949948i	−0.713809	+	0.700340i	$0.753032\pi$
$48$	35.3944	−	48.2931i	0.737382	−	1.00611i
$49$	42.4312	−	24.4977i	0.865943	−	0.499953i
$50$	37.2475	−	49.9033i	0.744951	−	0.998065i
$51$	−45.0012	+	36.1329i	−0.882377	+	0.708488i
$52$	7.46602	+	27.8636i	0.143577	+	0.535838i
$53$	28.0258	+	28.0258i	0.528789	+	0.528789i	0.920211	−	0.391423i	$-0.128017\pi$
$53$	28.0258	+	28.0258i	0.528789	+	0.528789i	−0.391423	+	0.920211i	$0.628017\pi$
$54$	−4.35625	+	67.1118i	−0.0806712	+	1.24281i
$55$	−38.2664	+	25.9388i	−0.695753	+	0.471614i
$56$	0.152383	−	0.263935i	0.00272112	−	0.00471312i
$57$	−1.89294	+	17.3180i	−0.0332096	+	0.303824i
$58$	4.74356	−	17.7032i	0.0817855	−	0.305228i
$59$	16.3509	−	9.44022i	0.277135	−	0.160004i	−0.354991	−	0.934870i	$-0.615516\pi$
$59$	16.3509	−	9.44022i	0.277135	−	0.160004i	0.632126	+	0.774866i	$0.282183\pi$
$60$	−33.0428	−	1.21549i	−0.550713	−	0.0202582i
$61$	2.69547	−	4.66870i	0.0441881	−	0.0765360i	−0.843085	−	0.537780i	$-0.819263\pi$
$61$	2.69547	−	4.66870i	0.0441881	−	0.0765360i	0.887274	+	0.461244i	$0.152597\pi$
$62$	−29.4265	+	29.4265i	−0.474621	+	0.474621i
$63$	0.0270071	+	0.612655i	0.000428684	+	0.00972468i
$64$			0.568692i			0.00888582i
$65$	−42.8134	+	49.4796i	−0.658667	+	0.761225i
$66$	64.3977	+	25.0273i	0.975722	+	0.379202i
$67$	−47.9117	−	12.8379i	−0.715100	−	0.191610i	−0.117116	−	0.993118i	$-0.537365\pi$
$67$	−47.9117	−	12.8379i	−0.715100	−	0.191610i	−0.597984	+	0.801508i	$0.704031\pi$
$68$	−10.9754	+	40.9609i	−0.161403	+	0.602366i
$69$	49.2792	−	126.800i	0.714191	−	1.83768i
$70$	−0.846414	+	0.0611359i	−0.0120916	+	0.000873370i
$71$	56.4200			0.794648			0.397324	−	0.917678i	$-0.369939\pi$
$71$	56.4200			0.794648			0.397324	+	0.917678i	$0.369939\pi$
$72$	−21.6430	−	33.9412i	−0.300597	−	0.471405i
$73$	−54.7135	−	54.7135i	−0.749500	−	0.749500i	0.224885	−	0.974385i	$-0.427799\pi$
$73$	−54.7135	−	54.7135i	−0.749500	−	0.749500i	−0.974385	+	0.224885i	$0.927799\pi$
$74$	−110.031	−	63.5264i	−1.48691	−	0.858465i
$75$	−39.7712	−	63.5866i	−0.530283	−	0.847821i
$76$	6.40036	+	11.0857i	0.0842152	+	0.145865i
$77$	0.608534	+	0.163056i	0.00790303	+	0.00211761i
$78$	97.2084	+	10.6254i	1.24626	+	0.136223i
$79$	−40.9692	−	23.6536i	−0.518597	−	0.299412i	0.217763	−	0.976002i	$-0.430124\pi$
$79$	−40.9692	−	23.6536i	−0.518597	−	0.299412i	−0.736361	+	0.676589i	$0.763457\pi$
$80$	82.6026	−	55.9919i	1.03253	−	0.699899i
$81$	73.4397	+	34.1704i	0.906663	+	0.421856i
$82$	−109.752	+	109.752i	−1.33844	+	1.33844i
$83$	60.0267	−	16.0841i	0.723213	−	0.193784i	0.121608	−	0.992578i	$-0.461195\pi$
$83$	60.0267	−	16.0841i	0.723213	−	0.193784i	0.601605	+	0.798794i	$0.294528\pi$
$84$	0.282117	+	0.351360i	0.00335854	+	0.00418285i
$85$	−90.8746	+	31.5237i	−1.06911	+	0.370867i
$86$	−12.5101	−	21.6682i	−0.145467	−	0.251956i
$87$	−17.8042	−	13.0488i	−0.204646	−	0.149987i
$88$	−39.9449	+	10.7032i	−0.453919	+	0.121627i
$89$			59.1599i			0.664718i	0.943153	+	0.332359i	$0.107844\pi$
$89$			59.1599i			0.664718i	−0.943153	+	0.332359i	$0.892156\pi$
$90$	−44.4163	+	102.913i	−0.493514	+	1.14347i
$91$	0.891679			0.00979867
$92$	−25.8713	−	96.5530i	−0.281210	−	1.04949i
$93$	20.1960	+	45.8728i	0.217162	+	0.493256i
$94$	99.7085	−	57.5668i	1.06073	−	0.612412i
$95$	−12.6684	+	26.1258i	−0.133351	+	0.275008i
$96$	−88.9828	−	34.5820i	−0.926904	−	0.360229i
$97$	40.2595	+	150.251i	0.415047	+	1.54898i	0.784742	+	0.619823i	$0.212796\pi$
$97$	40.2595	+	150.251i	0.415047	+	1.54898i	−0.369695	+	0.929153i	$0.620538\pi$
$98$	−86.2954	−	86.2954i	−0.880566	−	0.880566i
$99$	56.1918	−	61.3743i	0.567594	−	0.619943i
$100$	−51.1898	−	20.4097i	−0.511898	−	0.204097i
$101$	27.6053	−	47.8137i	0.273319	−	0.473403i	−0.696390	−	0.717663i	$-0.745212\pi$
$101$	27.6053	−	47.8137i	0.273319	−	0.473403i	0.969710	+	0.244260i	$0.0785451\pi$
$102$	115.946	+	84.9779i	1.13673	+	0.833116i
$103$	−23.6658	+	88.3218i	−0.229765	+	0.857493i	0.750675	+	0.660672i	$0.229729\pi$
$103$	−23.6658	+	88.3218i	−0.229765	+	0.857493i	−0.980439	+	0.196821i	$0.936938\pi$
$104$	−50.6892	+	29.2654i	−0.487397	+	0.281399i
$105$	−0.300648	+	0.976864i	−0.00286331	+	0.00930347i
$106$	49.3618	−	85.4971i	0.465677	−	0.806576i
$107$	−14.6336	+	14.6336i	−0.136762	+	0.136762i	−0.772174	−	0.635411i	$-0.780831\pi$
$107$	−14.6336	+	14.6336i	−0.136762	+	0.136762i	0.635411	+	0.772174i	$0.280831\pi$
$108$	58.3663	−	11.6480i	0.540429	−	0.107852i
$109$			112.055i			1.02803i	0.857781	+	0.514015i	$0.171843\pi$
$109$			112.055i			1.02803i	−0.857781	+	0.514015i	$0.828157\pi$
$110$	87.0777	+	75.3459i	0.791615	+	0.684963i
$111$	−119.320	+	95.8060i	−1.07496	+	0.863117i
$112$	−1.31359	−	0.351976i	−0.0117285	−	0.00314264i
$113$	9.59771	−	35.8191i	0.0849355	−	0.316984i	−0.910366	−	0.413803i	$-0.864200\pi$
$113$	9.59771	−	35.8191i	0.0849355	−	0.316984i	0.995302	+	0.0968194i	$0.0308669\pi$
$114$	42.8870	−	6.61017i	0.376202	−	0.0579840i
$115$	148.357	−	171.457i	1.29006	−	1.49093i
$116$	−16.2196			−0.139824
$117$	54.3389	−	104.491i	0.464435	−	0.893088i
$118$	−33.2541	−	33.2541i	−0.281814	−	0.281814i
$119$	1.13520	+	0.655407i	0.00953948	+	0.00550762i
$120$	−14.9704	−	65.3992i	−0.124753	−	0.544993i
$121$	17.7573	+	30.7565i	0.146754	+	0.254186i
$122$	−12.9705	−	3.47543i	−0.106316	−	0.0284872i
$123$	75.3254	+	171.092i	0.612402	+	1.39100i
$124$	31.8944	+	18.4143i	0.257213	+	0.148502i
$125$	−26.8287	−	122.087i	−0.214629	−	0.976696i
$126$	1.45662	−	0.459945i	0.0115605	−	0.00365035i
$127$	151.793	−	151.793i	1.19522	−	1.19522i	0.219643	−	0.975580i	$-0.429511\pi$
$127$	151.793	−	151.793i	1.19522	−	1.19522i	0.975580	−	0.219643i	$-0.0704892\pi$
$128$	124.320	−	33.3113i	0.971247	−	0.260245i
$129$	−29.7829	+	4.59044i	−0.230875	+	0.0355848i
$130$	146.648	+	71.1095i	1.12806	+	0.546996i
$131$	−0.751448	−	1.30155i	−0.00573624	−	0.00993547i	0.863143	−	0.504960i	$-0.168493\pi$
$131$	−0.751448	−	1.30155i	−0.00573624	−	0.00993547i	−0.868879	+	0.495024i	$0.835159\pi$
$132$	6.64367	−	60.7809i	0.0503308	−	0.460462i
$133$	0.382203	−	0.102411i	0.00287370	−	0.000770006i
$134$			123.551i			0.922021i
$135$	96.1523	+	94.7615i	0.712239	+	0.701937i
$136$	−86.0434			−0.632672
$137$	−18.0785	−	67.4699i	−0.131960	−	0.492481i	0.868032	−	0.496508i	$-0.165385\pi$
$137$	−18.0785	−	67.4699i	−0.131960	−	0.492481i	−0.999992	+	0.00402717i	$0.998718\pi$
$138$	−336.847	−	36.8192i	−2.44092	−	0.266805i
$139$	−106.332	+	61.3909i	−0.764980	+	0.441661i	−0.831081	−	0.556152i	$-0.812277\pi$
$139$	−106.332	+	61.3909i	−0.764980	+	0.441661i	0.0661012	+	0.997813i	$0.478944\pi$
$140$	0.246130	+	0.709529i	0.00175807	+	0.00506806i
$141$	−21.1234	−	137.049i	−0.149811	−	0.971981i
$142$	−36.3728	−	135.745i	−0.256147	−	0.955953i
$143$	−85.5549	−	85.5549i	−0.598286	−	0.598286i
$144$	−121.297	+	132.484i	−0.842338	+	0.920027i
$145$	−20.6426	−	30.4531i	−0.142362	−	0.210021i
$146$	−96.3668	+	166.912i	−0.660047	+	1.14323i
$147$	−134.526	+	59.2264i	−0.915140	+	0.402901i
$148$	−29.1013	+	108.607i	−0.196630	+	0.733834i
$149$	−23.0090	+	13.2842i	−0.154423	+	0.0891560i	−0.575220	−	0.817999i	$-0.695084\pi$
$149$	−23.0090	+	13.2842i	−0.154423	+	0.0891560i	0.420797	+	0.907155i	$0.361750\pi$
$150$	−127.348	+	136.682i	−0.848988	+	0.911211i
$151$	−49.2414	+	85.2887i	−0.326102	+	0.564826i	−0.981735	−	0.190254i	$-0.939069\pi$
$151$	−49.2414	+	85.2887i	−0.326102	+	0.564826i	0.655633	+	0.755080i	$0.272402\pi$
$152$	−18.3659	+	18.3659i	−0.120828	+	0.120828i
$153$	145.983	−	93.0876i	0.954136	−	0.608415i
$154$		−	1.56924i		−	0.0101899i
$155$	6.01810	+	83.3193i	0.0388264	+	0.537544i
$156$	−13.1826	−	85.5295i	−0.0845042	−	0.548266i
$157$	166.811	+	44.6968i	1.06249	+	0.284693i	0.747404	−	0.664370i	$-0.231300\pi$
$157$	166.811	+	44.6968i	1.06249	+	0.284693i	0.315086	+	0.949063i	$0.397967\pi$
$158$	−30.4980	+	113.820i	−0.193025	+	0.720379i
$159$	−74.4439	−	92.7152i	−0.468201	−	0.583115i
$160$	−120.321	−	104.111i	−0.752008	−	0.650692i
$161$	−3.08985			−0.0191916
$162$	34.8680	−	198.723i	0.215235	−	1.22669i
$163$	−65.0824	−	65.0824i	−0.399278	−	0.399278i	0.478700	−	0.877978i	$-0.341108\pi$
$163$	−65.0824	−	65.0824i	−0.399278	−	0.399278i	−0.877978	+	0.478700i	$0.841108\pi$
$164$	118.957	+	68.6800i	0.725349	+	0.418780i
$165$	122.575	−	64.8817i	0.742878	−	0.393222i
$166$	−77.3960	−	134.054i	−0.466241	−	0.807553i
$167$	192.960	+	51.7034i	1.15545	+	0.309601i	0.785146	−	0.619311i	$-0.212588\pi$
$167$	192.960	+	51.7034i	1.15545	+	0.309601i	0.370301	+	0.928912i	$0.379255\pi$
$168$	−0.540478	+	0.737444i	−0.00321713	+	0.00438955i
$169$	−1.94752	−	1.12440i	−0.0115238	−	0.00665325i
$170$	134.430	+	198.320i	0.790767	+	1.16659i
$171$	11.2904	−	51.0293i	0.0660258	−	0.298417i
$172$	−15.6570	+	15.6570i	−0.0910290	+	0.0910290i
$173$	−33.4003	+	8.94958i	−0.193065	+	0.0517317i	−0.354056	−	0.935224i	$-0.615198\pi$
$173$	−33.4003	+	8.94958i	−0.193065	+	0.0517317i	0.160991	+	0.986956i	$0.448531\pi$
$174$	−19.9172	+	51.2489i	−0.114467	+	0.294534i
$175$	−1.01893	+	1.36514i	−0.00582246	+	0.00780077i
$176$	92.2653	+	159.808i	0.524235	+	0.908001i
$177$	−51.8397	+	22.8230i	−0.292879	+	0.128944i
$178$	142.337	−	38.1392i	0.799648	−	0.214265i
$179$		−	185.962i		−	1.03890i	−0.854502	−	0.519448i	$-0.826138\pi$
$179$		−	185.962i		−	1.03890i	0.854502	−	0.519448i	$-0.173862\pi$
$180$	98.1452	+	14.3960i	0.545251	+	0.0799776i
$181$	−97.7851			−0.540249			−0.270125	−	0.962825i	$-0.587065\pi$
$181$	−97.7851			−0.540249			−0.270125	+	0.962825i	$0.587065\pi$
$182$	−0.574847	−	2.14536i	−0.00315850	−	0.0117877i
$183$	−9.56041	+	13.0445i	−0.0522427	+	0.0712814i
$184$	175.649	−	101.411i	0.954613	−	0.551146i
$185$	−240.953	+	83.5848i	−1.30245	+	0.451810i
$186$	97.3490	−	78.1645i	0.523382	−	0.420239i
$187$	−46.0350	−	171.805i	−0.246177	−	0.918744i
$188$	−72.0473	−	72.0473i	−0.383231	−	0.383231i
$189$	0.119168	−	1.83589i	0.000630518	−	0.00971368i
$190$	71.0251	+	13.6371i	0.373816	+	0.0717741i
$191$	−68.2090	+	118.141i	−0.357115	+	0.618542i	−0.987478	−	0.157759i	$-0.949573\pi$
$191$	−68.2090	+	118.141i	−0.357115	+	0.618542i	0.630362	+	0.776301i	$0.282906\pi$
$192$	0.185379	−	1.69598i	0.000965515	−	0.00883321i
$193$	23.9050	−	89.2148i	0.123860	−	0.462253i	−0.875936	−	0.482427i	$-0.839755\pi$
$193$	23.9050	−	89.2148i	0.123860	−	0.462253i	0.999796	+	0.0201740i	$0.00642202\pi$
$194$	335.545	−	193.727i	1.72961	−	0.998594i
$195$	143.809	−	133.604i	0.737481	−	0.685149i
$196$	−54.0013	+	93.5329i	−0.275517	+	0.477209i
$197$	−170.623	+	170.623i	−0.866107	+	0.866107i	−0.992039	−	0.125932i	$-0.959808\pi$
$197$	−170.623	+	170.623i	−0.866107	+	0.866107i	0.125932	+	0.992039i	$0.459808\pi$
$198$	−183.891	−	95.6294i	−0.928742	−	0.482977i
$199$			36.4196i			0.183013i	0.995804	+	0.0915066i	$0.0291683\pi$
$199$			36.4196i			0.183013i	−0.995804	+	0.0915066i	$0.970832\pi$
$200$	13.1185	−	111.046i	0.0655925	−	0.555229i
$201$	138.699	+	53.9036i	0.690046	+	0.268177i
$202$	−132.835	−	35.5931i	−0.657601	−	0.176204i
$203$	−0.129763	+	0.484283i	−0.000639227	+	0.00238563i
$204$	46.0835	−	118.577i	0.225900	−	0.581261i
$205$	22.4458	+	310.757i	0.109492	+	1.51589i
$206$	227.757			1.10562
$207$	−188.296	+	362.084i	−0.909641	+	1.74920i
$208$	184.681	+	184.681i	0.887887	+	0.887887i
$209$	−46.4977	−	26.8455i	−0.222477	−	0.128447i
$210$	2.54414	+	0.0935869i	0.0121149	+	0.000445652i
$211$	96.8033	+	167.668i	0.458784	+	0.794636i	0.998897	−	0.0469559i	$-0.0149520\pi$
$211$	96.8033	+	167.668i	0.458784	+	0.794636i	−0.540113	+	0.841592i	$0.681619\pi$
$212$	−84.3909	−	22.6125i	−0.398070	−	0.106663i
$213$	−168.258	−	18.3914i	−0.789943	−	0.0863448i
$214$	44.6420	+	25.7741i	0.208607	+	0.120440i
$215$	−49.3234	−	9.47028i	−0.229411	−	0.0440478i
$216$	53.4805	+	108.276i	0.247595	+	0.501276i
$217$	0.804980	−	0.804980i	0.00370959	−	0.00370959i
$218$	269.603	−	72.2398i	1.23671	−	0.331375i
$219$	145.334	+	181.004i	0.663623	+	0.826502i
$220$	44.4622	−	91.6936i	0.202101	−	0.416789i
$221$	−125.872	−	218.017i	−0.569558	−	0.986503i
$222$	307.431	+	225.318i	1.38482	+	1.01495i
$223$	92.4808	−	24.7802i	0.414712	−	0.111122i	−0.0454290	−	0.998968i	$-0.514465\pi$
$223$	92.4808	−	24.7802i	0.414712	−	0.111122i	0.460141	+	0.887846i	$0.347799\pi$
$224$			2.16833i			0.00968002i
$225$	97.8797	+	202.595i	0.435021	+	0.900420i
$226$	−92.3675			−0.408706
$227$	−85.2664	−	318.219i	−0.375623	−	1.40184i	−0.852433	−	0.522837i	$-0.824874\pi$
$227$	−85.2664	−	318.219i	−0.375623	−	1.40184i	0.476810	−	0.879007i	$-0.341793\pi$
$228$	−15.4737	−	35.1467i	−0.0678672	−	0.154152i
$229$	−360.256	+	207.994i	−1.57317	+	0.908269i	−0.577391	+	0.816468i	$0.695929\pi$
$229$	−360.256	+	207.994i	−1.57317	+	0.908269i	−0.995777	+	0.0918017i	$0.970737\pi$
$230$	−508.165	−	246.409i	−2.20941	−	1.07134i
$231$	−1.76164	−	0.684638i	−0.00762615	−	0.00296380i
$232$	−8.51781	−	31.7889i	−0.0367147	−	0.137021i
$233$	−22.0213	−	22.0213i	−0.0945121	−	0.0945121i	0.658270	−	0.752782i	$-0.271289\pi$
$233$	−22.0213	−	22.0213i	−0.0945121	−	0.0945121i	−0.752782	+	0.658270i	$0.771289\pi$
$234$	−286.435	−	63.3748i	−1.22408	−	0.270833i
$235$	43.5785	−	226.967i	0.185441	−	0.965817i
$236$	−20.8095	+	36.0431i	−0.0881758	+	0.152725i
$237$	114.469	+	83.8955i	0.482993	+	0.353989i
$238$	0.845055	−	3.15379i	0.00355065	−	0.0132512i
$239$	267.552	−	154.471i	1.11946	−	0.646323i	0.178200	−	0.983994i	$-0.442973\pi$
$239$	267.552	−	154.471i	1.11946	−	0.646323i	0.941264	+	0.337672i	$0.109639\pi$
$240$	−264.593	+	140.055i	−1.10247	+	0.583562i
$241$	−12.8569	+	22.2688i	−0.0533481	+	0.0924016i	−0.891466	−	0.453087i	$-0.850323\pi$
$241$	−12.8569	+	22.2688i	−0.0533481	+	0.0924016i	0.838118	+	0.545489i	$0.183656\pi$
$242$	62.5517	−	62.5517i	0.258478	−	0.258478i
$243$	−207.876	−	125.844i	−0.855457	−	0.517875i
$244$			11.8835i			0.0487028i
$245$	−244.340	+	17.6485i	−0.997307	+	0.0720349i
$246$	363.084	−	291.531i	1.47595	−	1.18509i
$247$	−73.4028	−	19.6682i	−0.297177	−	0.0796284i
$248$	−19.3407	+	72.1806i	−0.0779868	+	0.291051i
$249$	−184.257	+	28.3995i	−0.739987	+	0.114054i
$250$	−276.443	+	143.256i	−1.10577	+	0.573025i
$251$	275.877			1.09911			0.549556	−	0.835457i	$-0.314797\pi$
$251$	275.877			1.09911			0.549556	+	0.835457i	$0.314797\pi$
$252$	−0.726807	−	1.13980i	−0.00288416	−	0.00452302i
$253$	296.465	+	296.465i	1.17180	+	1.17180i
$254$	−463.070	−	267.353i	−1.82311	−	1.05257i
$255$	281.286	−	64.3884i	1.10308	−	0.252503i
$256$	−159.155	−	275.665i	−0.621701	−	1.07682i
$257$	−6.18001	−	1.65593i	−0.0240467	−	0.00644330i	0.246776	−	0.969073i	$-0.420629\pi$
$257$	−6.18001	−	1.65593i	−0.0240467	−	0.00644330i	−0.270822	+	0.962629i	$0.587296\pi$
$258$	30.2449	+	68.6977i	0.117228	+	0.266270i
$259$	3.00997	+	1.73781i	0.0116215	+	0.00670968i
$260$	27.1964	−	141.645i	0.104602	−	0.544789i
$261$	48.8428	+	44.7185i	0.187137	+	0.171335i
$262$	−2.64705	+	2.64705i	−0.0101032	+	0.0101032i
$263$	−205.249	+	54.9964i	−0.780416	+	0.209112i	−0.626968	−	0.779045i	$-0.715704\pi$
$263$	−205.249	+	54.9964i	−0.780416	+	0.209112i	−0.153448	+	0.988157i	$0.549038\pi$
$264$	122.614	−	18.8985i	0.464447	−	0.0715852i
$265$	−64.9477	−	187.227i	−0.245086	−	0.706518i
$266$	−0.492797	−	0.853549i	−0.00185262	−	0.00320883i
$267$	19.2846	−	176.429i	0.0722269	−	0.660782i
$268$	105.614	−	28.2991i	0.394081	−	0.105594i
$269$			349.046i			1.29757i	0.760973	+	0.648784i	$0.224722\pi$
$269$			349.046i			1.29757i	−0.760973	+	0.648784i	$0.775278\pi$
$270$	166.007	−	292.431i	0.614839	−	1.08308i
$271$	−202.277			−0.746409			−0.373205	−	0.927749i	$-0.621741\pi$
$271$	−202.277			−0.746409			−0.373205	+	0.927749i	$0.621741\pi$
$272$	99.3722	+	370.862i	0.365339	+	1.36346i
$273$	−2.65920	−	0.290664i	−0.00974065	−	0.00106470i
$274$	−150.676	+	86.9930i	−0.549913	+	0.317493i
$275$	228.747	−	33.2177i	0.831806	−	0.120792i
$276$	45.6806	+	296.377i	0.165509	+	1.07383i
$277$	62.8000	+	234.373i	0.226715	+	0.846112i	0.981710	+	0.190381i	$0.0609725\pi$
$277$	62.8000	+	234.373i	0.226715	+	0.846112i	−0.754995	+	0.655730i	$0.772361\pi$
$278$	216.255	+	216.255i	0.777897	+	0.777897i
$279$	−45.2760	−	143.387i	−0.162280	−	0.513932i
$280$	−1.26136	+	0.855006i	−0.00450484	+	0.00305359i
$281$	140.160	−	242.764i	0.498789	−	0.863929i	−0.501210	−	0.865326i	$-0.667111\pi$
$281$	140.160	−	242.764i	0.498789	−	0.863929i	0.999999	+	0.00139729i	$0.000444772\pi$
$282$	−316.120	+	139.175i	−1.12099	+	0.493530i
$283$	99.8610	−	372.686i	0.352866	−	1.31691i	−0.530283	−	0.847820i	$-0.677914\pi$
$283$	99.8610	−	372.686i	0.352866	−	1.31691i	0.883149	−	0.469092i	$-0.155419\pi$
$284$	−107.707	+	62.1845i	−0.379249	+	0.218959i
$285$	46.2964	−	73.7837i	0.162444	−	0.258890i
$286$	−150.688	+	260.999i	−0.526880	+	0.912583i
$287$	3.00235	−	3.00235i	0.0104611	−	0.0104611i
$288$	254.095	+	132.138i	0.882274	+	0.458812i
$289$		−	81.0774i		−	0.280545i
$290$	−59.9617	+	69.2980i	−0.206764	+	0.238959i
$291$	−71.0857	−	461.207i	−0.244281	−	1.58490i
$292$	164.753	+	44.1453i	0.564222	+	0.151183i
$293$	−10.9337	+	40.8052i	−0.0373164	+	0.139267i	−0.982071	−	0.188512i	$-0.939633\pi$
$293$	−10.9337	+	40.8052i	−0.0373164	+	0.139267i	0.944754	+	0.327779i	$0.106300\pi$
$294$	229.223	+	285.484i	0.779672	+	0.971032i
$295$	−94.1569	+	6.80090i	−0.319176	+	0.0230539i
$296$	−228.143			−0.770755
$297$	−187.584	+	164.716i	−0.631595	+	0.554598i
$298$	46.7950	+	46.7950i	0.157030	+	0.157030i
$299$	513.910	+	296.706i	1.71876	+	0.992329i
$300$	146.007	+	77.5531i	0.486691	+	0.258510i
$301$	0.342223	+	0.592747i	0.00113695	+	0.00196926i
$302$	236.948	+	63.4899i	0.784595	+	0.210232i
$303$	−97.9115	+	133.593i	−0.323140	+	0.440902i
$304$	100.371	+	57.9492i	0.330168	+	0.190622i
$305$	−22.3119	+	15.1240i	−0.0731537	+	0.0495870i
$306$	−318.079	−	291.220i	−1.03947	−	0.951698i
$307$	−85.1111	+	85.1111i	−0.277235	+	0.277235i	−0.832004	−	0.554769i	$-0.812806\pi$
$307$	−85.1111	+	85.1111i	−0.277235	+	0.277235i	0.554769	+	0.832004i	$0.312806\pi$
$308$	−1.34142	+	0.359431i	−0.00435525	+	0.00116699i
$309$	99.3675	−	255.682i	0.321578	−	0.827450i
$310$	196.585	−	68.1937i	0.634144	−	0.219980i
$311$	227.093	+	393.336i	0.730202	+	1.26475i	0.956797	+	0.290758i	$0.0939074\pi$
$311$	227.093	+	393.336i	0.730202	+	1.26475i	−0.226595	+	0.973989i	$0.572759\pi$
$312$	160.707	−	70.7531i	0.515087	−	0.226773i
$313$	−287.001	+	76.9018i	−0.916937	+	0.245693i	−0.686276	−	0.727342i	$-0.740756\pi$
$313$	−287.001	+	76.9018i	−0.916937	+	0.245693i	−0.230661	+	0.973034i	$0.574089\pi$
$314$		−	430.158i		−	1.36993i
$315$	1.21503	−	2.81524i	0.00385725	−	0.00893726i
$316$	104.281			0.330004
$317$	−22.8819	−	85.3965i	−0.0721827	−	0.269389i	0.920397	−	0.390985i	$-0.127866\pi$
$317$	−22.8819	−	85.3965i	−0.0721827	−	0.269389i	−0.992580	+	0.121596i	$0.961199\pi$
$318$	−175.078	+	238.882i	−0.550561	+	0.751201i
$319$	58.9165	−	34.0155i	0.184691	−	0.106632i
$320$	1.24063	−	2.55854i	0.00387698	−	0.00799542i
$321$	48.4109	−	38.8706i	0.150813	−	0.121092i
$322$	1.99197	+	7.43412i	0.00618623	+	0.0230873i
$323$	−78.9926	−	78.9926i	−0.244559	−	0.244559i
$324$	−177.859	+	15.7113i	−0.548948	+	0.0484917i
$325$	300.559	−	129.208i	0.924797	−	0.397564i
$326$	−114.629	+	198.544i	−0.351624	+	0.609031i
$327$	36.5271	−	334.176i	0.111704	−	1.02194i
$328$	−72.1354	+	269.213i	−0.219925	+	0.820771i
$329$	−2.72759	+	1.57478i	−0.00829055	+	0.00478655i
$330$	−235.125	−	253.084i	−0.712501	−	0.766922i
$331$	223.152	−	386.510i	0.674175	−	1.16770i	−0.302535	−	0.953138i	$-0.597833\pi$
$331$	223.152	−	386.510i	0.674175	−	1.16770i	0.976709	−	0.214566i	$-0.0688338\pi$
$332$	−96.8645	+	96.8645i	−0.291761	+	0.291761i
$333$	387.072	−	246.821i	1.16238	−	0.741204i
$334$		−	497.589i		−	1.48979i
$335$	187.547	+	162.279i	0.559842	+	0.484416i
$336$	3.80271	+	1.47787i	0.0113176	+	0.00439843i
$337$	−28.2958	−	7.58184i	−0.0839638	−	0.0224980i	0.216593	−	0.976262i	$-0.430506\pi$
$337$	−28.2958	−	7.58184i	−0.0839638	−	0.0224980i	−0.300556	+	0.953764i	$0.597172\pi$
$338$	−1.44975	+	5.41056i	−0.00428921	+	0.0160076i
$339$	−40.2988	+	103.693i	−0.118875	+	0.305878i
$340$	138.737	−	160.339i	0.408049	−	0.471584i
$341$	−154.473			−0.452999
$342$	−130.054	+	5.73305i	−0.380275	+	0.0167633i
$343$	4.72156	+	4.72156i	0.0137655	+	0.0137655i
$344$	−38.9086	−	22.4639i	−0.113107	−	0.0653021i
$345$	−498.327	+	462.966i	−1.44443	+	1.34193i
$346$	43.0650	+	74.5907i	0.124465	+	0.215580i
$347$	−326.160	−	87.3943i	−0.939942	−	0.251857i	−0.243853	−	0.969812i	$-0.578411\pi$
$347$	−326.160	−	87.3943i	−0.939942	−	0.251857i	−0.696089	+	0.717956i	$0.745078\pi$
$348$	48.3706	+	5.28716i	0.138996	+	0.0151930i
$349$	−51.4915	−	29.7286i	−0.147540	−	0.0851823i	0.424413	−	0.905469i	$-0.360481\pi$
$349$	−51.4915	−	29.7286i	−0.147540	−	0.0851823i	−0.571953	+	0.820287i	$0.693814\pi$
$350$	3.94137	+	1.57145i	0.0112611	+	0.00448985i
$351$	−196.113	+	293.905i	−0.558727	+	0.837336i
$352$	208.047	−	208.047i	0.591042	−	0.591042i
$353$	514.426	−	137.840i	1.45730	−	0.390482i	0.558742	−	0.829342i	$-0.311284\pi$
$353$	514.426	−	137.840i	1.45730	−	0.390482i	0.898555	+	0.438860i	$0.144618\pi$
$354$	88.3316	+	110.012i	0.249524	+	0.310767i
$355$	−253.832	−	123.083i	−0.715021	−	0.346713i
$356$	−65.2043	−	112.937i	−0.183158	−	0.317239i
$357$	−3.17178	−	2.32462i	−0.00888455	−	0.00651155i
$358$	−447.421	+	119.886i	−1.24978	+	0.334878i
$359$			342.196i			0.953192i	0.879122	+	0.476596i	$0.158130\pi$
$359$			342.196i			0.953192i	−0.879122	+	0.476596i	$0.841870\pi$
$360$	23.3268	+	199.916i	0.0647966	+	0.555322i
$361$	327.278			0.906588
$362$	63.0401	+	235.269i	0.174144	+	0.649914i
$363$	−42.9306	−	97.5117i	−0.118266	−	0.268627i
$364$	−1.70223	+	0.982783i	−0.00467646	+	0.00269995i
$365$	126.795	+	365.516i	0.347382	+	1.00141i
$366$	37.5482	+	14.5926i	0.102591	+	0.0398705i
$367$	−95.2584	−	355.509i	−0.259560	−	0.968690i	−0.965497	−	0.260416i	$-0.916140\pi$
$367$	−95.2584	−	355.509i	−0.259560	−	0.968690i	0.705937	−	0.708275i	$-0.250526\pi$
$368$	−639.956	−	639.956i	−1.73901	−	1.73901i
$369$	−168.867	−	534.793i	−0.457633	−	1.44930i
$370$	356.441	+	525.843i	0.963354	+	1.42120i
$371$	−1.35032	+	2.33883i	−0.00363968	+	0.00630412i
$372$	−89.1142	−	65.3125i	−0.239554	−	0.175571i
$373$	86.1459	−	321.501i	0.230954	−	0.861933i	−0.748977	−	0.662596i	$-0.769455\pi$
$373$	86.1459	−	321.501i	0.230954	−	0.861933i	0.979931	−	0.199337i	$-0.0638787\pi$
$374$	−383.681	+	221.519i	−1.02589	+	0.592296i
$375$	40.2124	+	372.838i	0.107233	+	0.994234i
$376$	103.370	−	179.042i	0.274921	−	0.476177i
$377$	68.0862	−	68.0862i	0.180600	−	0.180600i
$378$	−4.49392	+	0.896843i	−0.0118887	+	0.00237260i
$379$			203.700i			0.537466i	0.963215	+	0.268733i	$0.0866049\pi$
$379$			203.700i			0.537466i	−0.963215	+	0.268733i	$0.913395\pi$
$380$	−4.61092	−	63.8373i	−0.0121340	−	0.167993i
$381$	−502.164	+	403.203i	−1.31802	+	1.05828i
$382$	328.219	+	87.9460i	0.859212	+	0.230225i
$383$	−5.35538	+	19.9865i	−0.0139827	+	0.0521842i	−0.972565	−	0.232633i	$-0.925266\pi$
$383$	−5.35538	+	19.9865i	−0.0139827	+	0.0521842i	0.958582	+	0.284817i	$0.0919327\pi$
$384$	−381.609	+	58.8174i	−0.993774	+	0.153170i
$385$	−2.38206	−	2.06114i	−0.00618718	−	0.00535360i
$386$	−230.060			−0.596010
$387$	90.3161	−	3.98132i	0.233375	−	0.0102876i
$388$	−242.458	−	242.458i	−0.624892	−	0.624892i
$389$	−160.439	−	92.6297i	−0.412440	−	0.238123i	0.279397	−	0.960176i	$-0.409865\pi$
$389$	−160.439	−	92.6297i	−0.412440	−	0.238123i	−0.691838	+	0.722053i	$0.743199\pi$
$390$	−414.159	−	259.869i	−1.06195	−	0.666330i
$391$	436.174	+	755.475i	1.11553	+	1.93216i
$392$	−211.675	−	56.7182i	−0.539988	−	0.144689i
$393$	1.81673	+	4.12647i	0.00462271	+	0.0104999i
$394$	520.513	+	300.518i	1.32110	+	0.762737i
$395$	132.718	+	195.793i	0.335995	+	0.495680i
$396$	−39.6260	+	179.098i	−0.100066	+	0.452266i
$397$	−236.474	+	236.474i	−0.595652	+	0.595652i	−0.939152	−	0.343501i	$-0.888387\pi$
$397$	−236.474	+	236.474i	−0.595652	+	0.595652i	0.343501	+	0.939152i	$0.388387\pi$
$398$	87.6248	−	23.4790i	0.220163	−	0.0589925i
$399$	−1.17320	+	0.180825i	−0.00294036	+	0.000453197i
$400$	−493.777	+	71.7045i	−1.23444	+	0.179261i
$401$	−34.0375	−	58.9547i	−0.0848816	−	0.147019i	0.820459	−	0.571705i	$-0.193718\pi$
$401$	−34.0375	−	58.9547i	−0.0848816	−	0.147019i	−0.905341	+	0.424686i	$0.860385\pi$
$402$	40.2743	−	368.458i	0.100185	−	0.916562i
$403$	−211.185	+	56.5868i	−0.524032	+	0.140414i
$404$			121.703i			0.301245i
$405$	−255.859	−	313.944i	−0.631751	−	0.775171i
$406$	1.24883			0.00307593
$407$	−122.062	−	455.540i	−0.299906	−	1.11926i
$408$	256.602	+	28.0479i	0.628926	+	0.0687449i
$409$	326.511	−	188.511i	0.798315	−	0.460907i	−0.0445668	−	0.999006i	$-0.514191\pi$
$409$	326.511	−	188.511i	0.798315	−	0.460907i	0.842882	+	0.538099i	$0.180857\pi$
$410$	733.204	−	254.343i	1.78830	−	0.620348i
$411$	31.9210	+	207.104i	0.0776666	+	0.503904i
$412$	−52.1674	−	194.691i	−0.126620	−	0.472552i
$413$	0.909687	+	0.909687i	0.00220263	+	0.00220263i
$414$	992.557	+	219.607i	2.39748	+	0.530451i
$415$	−305.147	−	58.5894i	−0.735295	−	0.141179i
$416$	208.216	−	360.640i	0.500518	−	0.866923i
$417$	337.120	−	148.421i	0.808440	−	0.355925i
$418$	−34.6135	+	129.179i	−0.0828074	+	0.309041i
$419$	−198.025	+	114.330i	−0.472613	+	0.272863i	−0.717333	−	0.696731i	$-0.754637\pi$
$419$	−198.025	+	114.330i	−0.472613	+	0.272863i	0.244720	+	0.969594i	$0.421304\pi$
$420$	−0.502730	−	2.19622i	−0.00119698	−	0.00522908i
$421$	204.894	−	354.887i	0.486684	−	0.842961i	−0.513199	−	0.858270i	$-0.671540\pi$
$421$	204.894	−	354.887i	0.486684	−	0.842961i	0.999883	+	0.0153086i	$0.00487306\pi$
$422$	340.999	−	340.999i	0.808055	−	0.808055i
$423$	18.3205	+	415.599i	0.0433108	+	0.982504i
$424$		−	177.274i		−	0.418098i
$425$	477.614	+	56.4234i	1.12380	+	0.132761i
$426$	64.2230	+	416.681i	0.150758	+	0.978125i
$427$	0.354816	+	0.0950727i	0.000830951	+	0.000222653i
$428$	11.8070	−	44.0644i	0.0275865	−	0.102954i
$429$	227.256	+	283.034i	0.529735	+	0.659752i
$430$	9.01251	+	124.776i	0.0209593	+	0.290177i
$431$	46.4787			0.107839			0.0539196	−	0.998545i	$-0.482829\pi$
$431$	46.4787			0.107839			0.0539196	+	0.998545i	$0.482829\pi$
$432$	404.922	−	355.559i	0.937319	−	0.823053i
$433$	−430.638	−	430.638i	−0.994544	−	0.994544i	0.00544093	−	0.999985i	$-0.498268\pi$
$433$	−430.638	−	430.638i	−0.994544	−	0.994544i	−0.999985	+	0.00544093i	$0.998268\pi$
$434$	−2.45572	−	1.41781i	−0.00565834	−	0.00326684i
$435$	51.6341	+	97.5474i	0.118699	+	0.224247i
$436$	−123.504	−	213.916i	−0.283266	−	0.490632i
$437$	254.356	+	68.1545i	0.582050	+	0.155960i
$438$	341.798	−	466.359i	0.780360	−	1.06475i
$439$	335.332	+	193.604i	0.763855	+	0.441012i	0.830678	−	0.556753i	$-0.187953\pi$
$439$	335.332	+	193.604i	0.763855	+	0.441012i	−0.0668232	+	0.997765i	$0.521286\pi$
$440$	203.061	+	38.9885i	0.461502	+	0.0886101i
$441$	420.494	−	132.775i	0.953500	−	0.301078i
$442$	−443.397	+	443.397i	−1.00316	+	1.00316i
$443$	−708.648	+	189.882i	−1.59966	+	0.428627i	−0.944939	−	0.327247i	$-0.893879\pi$
$443$	−708.648	+	189.882i	−1.59966	+	0.428627i	−0.654717	+	0.755874i	$0.727212\pi$
$444$	122.190	−	314.407i	0.275203	−	0.708124i
$445$	129.060	−	266.159i	0.290024	−	0.598110i
$446$	−119.241	−	206.531i	−0.267357	−	0.463075i
$447$	72.9486	−	32.1164i	0.163196	−	0.0718489i
$448$	−0.0374297	+	0.0100292i	−8.35483e−5	+	2.23867e-5i
$449$		−	141.098i		−	0.314250i	−0.987579	−	0.157125i	$-0.949777\pi$
$449$		−	141.098i		−	0.314250i	0.987579	−	0.157125i	$-0.0502226\pi$
$450$	424.337	−	366.105i	0.942971	−	0.813567i
$451$	−576.139			−1.27747
$452$	21.1566	+	78.9577i	0.0468067	+	0.174685i
$453$	174.652	−	238.300i	0.385544	−	0.526048i
$454$	−710.657	+	410.298i	−1.56532	+	0.903740i
$455$	−4.01165	−	1.94525i	−0.00881680	−	0.00427527i
$456$	60.7582	−	48.7846i	0.133242	−	0.106984i
$457$	190.044	+	709.254i	0.415851	+	1.55198i	0.783124	+	0.621865i	$0.213625\pi$
$457$	190.044	+	709.254i	0.415851	+	1.55198i	−0.367273	+	0.930113i	$0.619709\pi$
$458$	732.678	+	732.678i	1.59973	+	1.59973i
$459$	−465.699	+	230.023i	−1.01460	+	0.501139i
$460$	−94.2412	+	490.830i	−0.204872	+	1.06702i
$461$	−321.041	+	556.060i	−0.696402	+	1.20620i	0.273304	+	0.961928i	$0.411883\pi$
$461$	−321.041	+	556.060i	−0.696402	+	1.20620i	−0.969706	+	0.244275i	$0.921450\pi$
$462$	−0.511530	+	4.67984i	−0.00110721	+	0.0101295i
$463$	−71.8346	+	268.091i	−0.155150	+	0.579029i	0.843942	+	0.536434i	$0.180229\pi$
$463$	−71.8346	+	268.091i	−0.155150	+	0.579029i	−0.999092	+	0.0425948i	$0.986438\pi$
$464$	−127.178	+	73.4265i	−0.274091	+	0.158247i
$465$	9.21251	−	250.440i	0.0198118	−	0.538580i
$466$	−38.7861	+	67.1795i	−0.0832320	+	0.144162i
$467$	−57.4439	+	57.4439i	−0.123006	+	0.123006i	−0.765930	−	0.642924i	$-0.777721\pi$
$467$	−57.4439	+	57.4439i	−0.123006	+	0.123006i	0.642924	+	0.765930i	$0.277721\pi$
$468$	11.4334	+	259.366i	0.0244304	+	0.554202i
$469$		−	3.37981i		−	0.00720642i
$470$	−574.172	+	41.4721i	−1.22164	+	0.0882384i
$471$	−482.900	−	187.673i	−1.02526	−	0.398456i
$472$	−81.5694	−	21.8565i	−0.172817	−	0.0463061i
$473$	24.0373	−	89.7086i	0.0508189	−	0.189659i
$474$	128.055	−	329.497i	0.270157	−	0.695140i
$475$	113.990	−	89.9026i	0.239978	−	0.189269i
$476$	−2.88948			−0.00607034
$477$	191.787	+	300.766i	0.402068	+	0.630536i
$478$	−544.139	−	544.139i	−1.13837	−	1.13837i
$479$	−419.328	−	242.099i	−0.875423	−	0.505426i	−0.00627671	−	0.999980i	$-0.501998\pi$
$479$	−419.328	−	242.099i	−0.875423	−	0.505426i	−0.869147	+	0.494554i	$0.835331\pi$
$480$	324.889	+	349.704i	0.676853	+	0.728551i
$481$	−333.749	−	578.071i	−0.693866	−	1.20181i
$482$	61.8668	+	16.5771i	0.128354	+	0.0343924i
$483$	9.21467	+	1.00721i	0.0190780	+	0.00208532i
$484$	−67.7979	−	39.1431i	−0.140078	−	0.0808742i
$485$	146.653	−	763.803i	0.302378	−	1.57485i
$486$	−168.763	+	581.274i	−0.347250	+	1.19604i
$487$	−162.179	+	162.179i	−0.333017	+	0.333017i	−0.853731	−	0.520714i	$-0.825666\pi$
$487$	−162.179	+	162.179i	−0.333017	+	0.333017i	0.520714	+	0.853731i	$0.325666\pi$
$488$	−23.2906	+	6.24069i	−0.0477266	+	0.0127883i
$489$	172.876	+	215.306i	0.353530	+	0.440299i
$490$	199.983	+	576.500i	0.408129	+	1.17653i
$491$	−395.023	−	684.199i	−0.804527	−	1.39348i	−0.916610	−	0.399783i	$-0.869086\pi$
$491$	−395.023	−	684.199i	−0.804527	−	1.39348i	0.112083	−	0.993699i	$-0.464248\pi$
$492$	−332.371	−	243.597i	−0.675550	−	0.495116i
$493$	136.726	−	36.6356i	0.277334	−	0.0743115i
$494$			189.285i			0.383168i
$495$	−386.697	+	153.536i	−0.781206	+	0.310175i
$496$	333.448			0.672274
$497$	0.995002	+	3.71340i	0.00200202	+	0.00747163i
$498$	187.115	+	425.009i	0.375733	+	0.853433i
$499$	422.362	−	243.851i	0.846418	−	0.488680i	−0.0130228	−	0.999915i	$-0.504145\pi$
$499$	422.362	−	243.851i	0.846418	−	0.488680i	0.859441	+	0.511236i	$0.170812\pi$
$500$	185.777	+	203.496i	0.371554	+	0.406992i
$501$	−558.597	−	217.091i	−1.11496	−	0.433316i
$502$	−177.852	−	663.754i	−0.354288	−	1.32222i
$503$	346.274	+	346.274i	0.688418	+	0.688418i	0.961882	−	0.273465i	$-0.0881696\pi$
$503$	346.274	+	346.274i	0.688418	+	0.688418i	−0.273465	+	0.961882i	$0.588170\pi$
$504$	1.85222	−	2.02305i	0.00367504	−	0.00401399i
$505$	−228.504	+	154.891i	−0.452483	+	0.306714i
$506$	522.164	−	904.415i	1.03194	−	1.78738i
$507$	5.44143	+	3.98806i	0.0107326	+	0.00786600i
$508$	−122.474	+	457.078i	−0.241090	+	0.899760i
$509$	−362.182	+	209.106i	−0.711557	+	0.410818i	−0.811637	−	0.584162i	$-0.801423\pi$
$509$	−362.182	+	209.106i	−0.711557	+	0.410818i	0.100080	+	0.994979i	$0.468090\pi$
$510$	−336.256	−	635.257i	−0.659326	−	1.24560i
$511$	2.63618	−	4.56599i	0.00515886	−	0.00893540i
$512$	−196.607	+	196.607i	−0.383998	+	0.383998i
$513$	−50.3049	+	148.501i	−0.0980603	+	0.289476i
$514$			15.9365i			0.0310049i
$515$	299.151	−	345.730i	0.580875	−	0.671320i
$516$	51.7966	−	41.5891i	0.100381	−	0.0805990i
$517$	412.804	+	110.610i	0.798460	+	0.213947i
$518$	2.24066	−	8.36225i	0.00432559	−	0.0161433i
$519$	102.525	−	15.8022i	0.197543	−	0.0304473i
$520$	291.894	−	21.0833i	0.561335	−	0.0405449i
$521$	−17.3149			−0.0332341			−0.0166170	−	0.999862i	$-0.505290\pi$
$521$	−17.3149			−0.0332341			−0.0166170	+	0.999862i	$0.505290\pi$
$522$	76.1036	−	146.344i	0.145792	−	0.280352i
$523$	577.571	+	577.571i	1.10434	+	1.10434i	0.993880	+	0.110462i	$0.0352329\pi$
$523$	577.571	+	577.571i	1.10434	+	1.10434i	0.110462	+	0.993880i	$0.464767\pi$
$524$	2.86905	+	1.65645i	0.00547529	+	0.00316116i
$525$	3.48369	−	3.73901i	0.00663560	−	0.00712193i
$526$	264.640	+	458.370i	0.503118	+	0.871427i
$527$	−310.453	−	83.1855i	−0.589094	−	0.157847i
$528$	−223.064	−	506.662i	−0.422469	−	0.959587i
$529$	−1322.68	−	763.649i	−2.50034	−	1.44357i
$530$	−408.594	+	276.964i	−0.770932	+	0.522574i
$531$	162.038	−	51.1652i	0.305156	−	0.0963564i
$532$	−0.616757	+	0.616757i	−0.00115932	+	0.00115932i
$533$	−787.659	+	211.053i	−1.47778	+	0.395971i
$534$	−436.916	+	67.3418i	−0.818195	+	0.126108i
$535$	97.7600	−	33.9122i	0.182729	−	0.0633873i
$536$	110.927	+	192.132i	0.206954	+	0.358455i
$537$	−60.6189	+	554.584i	−0.112884	+	1.03274i
$538$	839.797	−	225.023i	1.56096	−	0.418258i
$539$		−	453.003i		−	0.840451i
$540$	−288.000	−	74.9250i	−0.533333	−	0.138750i
$541$	846.162			1.56407			0.782035	−	0.623234i	$-0.214182\pi$
$541$	846.162			1.56407			0.782035	+	0.623234i	$0.214182\pi$
$542$	130.404	+	486.674i	0.240598	+	0.897922i
$543$	291.618	+	31.8754i	0.537050	+	0.0587024i
$544$	530.160	−	306.088i	0.974558	−	0.562661i
$545$	244.455	−	504.135i	0.448541	−	0.925018i
$546$	1.01500	+	6.58536i	0.00185897	+	0.0120611i
$547$	−17.6950	−	66.0385i	−0.0323491	−	0.120728i	0.947863	−	0.318677i	$-0.103239\pi$
$547$	−17.6950	−	66.0385i	−0.0323491	−	0.120728i	−0.980212	+	0.197949i	$0.936572\pi$
$548$	108.876	+	108.876i	0.198678	+	0.198678i
$549$	32.7636	−	35.7854i	0.0596787	−	0.0651828i
$550$	−227.389	−	528.944i	−0.413435	−	0.961717i
$551$	21.3641	−	37.0038i	0.0387734	−	0.0671575i
$552$	−556.884	+	245.174i	−1.00885	+	0.444156i
$553$	0.834291	−	3.11362i	0.00150866	−	0.00563041i
$554$	523.410	−	302.191i	0.944784	−	0.545471i
$555$	745.826	−	170.725i	1.34383	−	0.307613i
$556$	135.327	−	234.392i	0.243393	−	0.421569i
$557$	367.003	−	367.003i	0.658893	−	0.658893i	−0.296225	−	0.955118i	$-0.595728\pi$
$557$	367.003	−	367.003i	0.658893	−	0.658893i	0.955118	+	0.296225i	$0.0957279\pi$
$558$	−315.797	+	201.372i	−0.565945	+	0.360881i
$559$		−	131.449i		−	0.235151i
$560$	5.14197	+	4.44921i	0.00918210	+	0.00794502i
$561$	81.2835	+	527.370i	0.144890	+	0.940053i
$562$	−674.443	−	180.716i	−1.20008	−	0.321560i
$563$	81.4441	−	303.953i	0.144661	−	0.539882i	−0.855109	−	0.518448i	$-0.826510\pi$
$563$	81.4441	−	303.953i	0.144661	−	0.539882i	0.999770	−	0.0214341i	$-0.00682321\pi$
$564$	191.377	+	238.348i	0.339320	+	0.422603i
$565$	−121.321	+	140.212i	−0.214728	+	0.248162i
$566$	−961.053			−1.69797
$567$	−0.953838	+	5.43620i	−0.00168225	+	0.00958765i
$568$	−178.439	−	178.439i	−0.314153	−	0.314153i
$569$	882.789	+	509.679i	1.55148	+	0.895745i	0.998022	+	0.0628645i	$0.0200236\pi$
$569$	882.789	+	509.679i	1.55148	+	0.895745i	0.553453	+	0.832880i	$0.313310\pi$
$570$	−207.368	−	63.8214i	−0.363804	−	0.111967i
$571$	443.096	+	767.465i	0.776000	+	1.34407i	0.934231	+	0.356669i	$0.116088\pi$
$571$	443.096	+	767.465i	0.776000	+	1.34407i	−0.158231	+	0.987402i	$0.550579\pi$
$572$	257.622	+	69.0296i	0.450388	+	0.120681i
$573$	241.927	−	330.092i	0.422210	−	0.576076i
$574$	−9.15913	−	5.28803i	−0.0159567	−	0.00921259i
$575$	−1041.50	+	447.733i	−1.81130	+	0.778667i
$576$	−1.10569	+	4.99737i	−0.00191960	+	0.00867600i
$577$	194.509	−	194.509i	0.337105	−	0.337105i	−0.518172	−	0.855277i	$-0.673387\pi$
$577$	194.509	−	194.509i	0.337105	−	0.337105i	0.855277	+	0.518172i	$0.173387\pi$
$578$	−195.070	+	52.2689i	−0.337492	+	0.0904307i
$579$	−100.372	+	258.267i	−0.173354	+	0.446058i
$580$	72.9715	+	35.3839i	0.125813	+	0.0610067i
$581$	2.11722	+	3.66713i	0.00364409	+	0.00631175i
$582$	−1063.83	+	468.361i	−1.82788	+	0.804745i
$583$	353.967	−	94.8452i	0.607147	−	0.162685i
$584$			346.084i			0.592609i
$585$	−472.423	+	351.561i	−0.807561	+	0.600959i
$586$	105.225			0.179565
$587$	207.853	+	775.720i	0.354095	+	1.32150i	0.881620	+	0.471960i	$0.156453\pi$
$587$	207.853	+	775.720i	0.354095	+	1.32150i	−0.527526	+	0.849539i	$0.676880\pi$
$588$	191.534	−	261.334i	0.325738	−	0.444446i
$589$	−84.0216	+	48.5099i	−0.142651	+	0.0823598i
$590$	77.0639	+	222.155i	0.130617	+	0.376534i
$591$	564.457	−	453.220i	0.955089	−	0.766870i
$592$	263.485	+	983.338i	0.445075	+	1.66104i
$593$	572.308	+	572.308i	0.965106	+	0.965106i	0.999411	−	0.0343049i	$-0.0109217\pi$
$593$	572.308	+	572.308i	0.965106	+	0.965106i	−0.0343049	+	0.999411i	$0.510922\pi$
$594$	517.234	+	345.133i	0.870764	+	0.581032i
$595$	−3.67743	−	5.42516i	−0.00618055	−	0.00911791i
$596$	29.2830	−	50.7197i	0.0491326	−	0.0851001i
$597$	11.8718	−	108.612i	0.0198858	−	0.181930i
$598$	382.561	−	1427.74i	0.639734	−	2.38752i
$599$	−263.198	+	151.957i	−0.439396	+	0.253685i	−0.703341	−	0.710852i	$-0.748309\pi$
$599$	−263.198	+	151.957i	−0.439396	+	0.253685i	0.263945	+	0.964538i	$0.414976\pi$
$600$	−75.3205	+	326.888i	−0.125534	+	0.544814i
$601$	−52.0948	+	90.2308i	−0.0866801	+	0.150134i	−0.906106	−	0.423051i	$-0.860959\pi$
$601$	−52.0948	+	90.2308i	−0.0866801	+	0.150134i	0.819426	+	0.573185i	$0.194292\pi$
$602$	1.20551	−	1.20551i	0.00200251	−	0.00200251i
$603$	−396.063	−	205.966i	−0.656821	−	0.341568i
$604$		−	217.090i		−	0.359420i
$605$	−12.7926	−	177.111i	−0.0211449	−	0.292746i
$606$	384.544	+	149.448i	0.634561	+	0.246614i
$607$	−283.439	−	75.9472i	−0.466950	−	0.125119i	0.0176696	−	0.999844i	$-0.494375\pi$
$607$	−283.439	−	75.9472i	−0.466950	−	0.125119i	−0.484620	+	0.874725i	$0.661042\pi$
$608$	47.8279	−	178.496i	0.0786642	−	0.293579i
$609$	0.544848	−	1.40195i	0.000894660	−	0.00230205i
$610$	50.7721	+	43.9317i	0.0832330	+	0.0720193i
$611$	604.878			0.989980
$612$	−176.085	+	338.604i	−0.287721	+	0.553274i
$613$	610.767	+	610.767i	0.996357	+	0.996357i	0.999993	−	0.00363596i	$-0.00115736\pi$
$613$	610.767	+	610.767i	0.996357	+	0.996357i	−0.00363596	+	0.999993i	$0.501157\pi$
$614$	259.645	+	149.906i	0.422874	+	0.244147i
$615$	34.3600	−	934.068i	0.0558699	−	1.51881i
$616$	−1.40891	−	2.44030i	−0.00228719	−	0.00396152i
$617$	972.818	+	260.666i	1.57669	+	0.422473i	0.937899	−	0.346908i	$-0.112768\pi$
$617$	972.818	+	260.666i	1.57669	+	0.422473i	0.638791	+	0.769381i	$0.279435\pi$
$618$	−679.226	−	74.2429i	−1.09907	−	0.120134i
$619$	−189.444	−	109.376i	−0.306049	−	0.176697i	0.339108	−	0.940747i	$-0.389875\pi$
$619$	−189.444	−	109.376i	−0.306049	−	0.176697i	−0.645157	+	0.764050i	$0.723208\pi$
$620$	−103.321	−	152.425i	−0.166646	−	0.245847i
$621$	679.572	−	1018.44i	1.09432	−	1.64000i
$622$	799.956	−	799.956i	1.28610	−	1.28610i
$623$	−3.89373	+	1.04332i	−0.00624997	+	0.00167467i
$624$	−490.560	−	610.962i	−0.786154	−	0.979106i
$625$	−145.638	+	607.795i	−0.233020	+	0.972472i
$626$	370.048	+	640.942i	0.591131	+	1.02387i
$627$	129.916	+	95.2166i	0.207203	+	0.151861i
$628$	−367.708	+	98.5271i	−0.585523	+	0.156890i
$629$		−	981.257i		−	1.56003i
$630$	−7.55671	−	1.10842i	−0.0119948	−	0.00175940i
$631$	−427.714			−0.677835			−0.338917	−	0.940816i	$-0.610061\pi$
$631$	−427.714			−0.677835			−0.338917	+	0.940816i	$0.610061\pi$
$632$	54.7639	+	204.382i	0.0866517	+	0.323389i
$633$	−234.035	−	531.582i	−0.369724	−	0.839782i
$634$	−190.711	+	110.107i	−0.300805	+	0.173670i
$635$	−1014.06	+	351.770i	−1.59695	+	0.553968i
$636$	244.303	+	94.9450i	0.384124	+	0.149285i
$637$	−165.945	−	619.316i	−0.260511	−	0.972239i
$638$	−119.823	−	119.823i	−0.187810	−	0.187810i
$639$	495.790	+	109.695i	0.775884	+	0.171667i
$640$	−631.982	−	121.343i	−0.987472	−	0.189598i
$641$	−256.912	+	444.984i	−0.400798	+	0.694203i	−0.993822	−	0.110982i	$-0.964600\pi$
$641$	−256.912	+	444.984i	−0.400798	+	0.694203i	0.593024	+	0.805185i	$0.297934\pi$
$642$	−124.731	−	91.4165i	−0.194286	−	0.142393i
$643$	−50.3713	+	187.988i	−0.0783379	+	0.292361i	−0.993969	−	0.109657i	$-0.965025\pi$
$643$	−50.3713	+	187.988i	−0.0783379	+	0.292361i	0.915632	+	0.402019i	$0.131691\pi$
$644$	5.89858	−	3.40555i	0.00915929	−	0.00528812i
$645$	144.007	+	44.3208i	0.223267	+	0.0687143i
$646$	−139.129	+	240.979i	−0.215371	+	0.373033i
$647$	−139.726	+	139.726i	−0.215960	+	0.215960i	−0.806794	−	0.590833i	$-0.798799\pi$
$647$	−139.726	+	139.726i	−0.215960	+	0.215960i	0.590833	+	0.806794i	$0.298799\pi$
$648$	−124.197	−	340.337i	−0.191661	−	0.525211i
$649$		−	174.565i		−	0.268976i
$650$	−504.636	−	639.841i	−0.776364	−	0.984370i
$651$	−2.66304	+	2.13824i	−0.00409070	+	0.00328455i
$652$	195.975	+	52.5114i	0.300576	+	0.0805390i
$653$	−166.789	+	622.466i	−0.255420	+	0.953240i	0.712437	+	0.701737i	$0.247592\pi$
$653$	−166.789	+	622.466i	−0.255420	+	0.953240i	−0.967856	+	0.251503i	$0.919075\pi$
$654$	−827.568	+	127.553i	−1.26539	+	0.195035i
$655$	0.541356	+	7.49495i	0.000826498	+	0.0114427i
$656$	1243.66			1.89583
$657$	−374.417	−	587.172i	−0.569888	−	0.893716i
$658$	5.54730	+	5.54730i	0.00843054	+	0.00843054i
$659$	210.200	+	121.359i	0.318968	+	0.184156i	0.650932	−	0.759136i	$-0.274378\pi$
$659$	210.200	+	121.359i	0.318968	+	0.184156i	−0.331965	+	0.943292i	$0.607711\pi$
$660$	−162.487	+	258.959i	−0.246192	+	0.392362i
$661$	−331.364	−	573.939i	−0.501307	−	0.868288i	−0.999999	−	0.00150927i	$-0.999520\pi$
$661$	−331.364	−	573.939i	−0.501307	−	0.868288i	0.498692	−	0.866779i	$-0.333814\pi$
$662$	−1073.80	−	287.723i	−1.62205	−	0.434627i
$663$	304.313	+	691.210i	0.458994	+	1.04255i
$664$	−240.715	−	138.977i	−0.362522	−	0.209302i
$665$	−1.94294	−	0.373051i	−0.00292171	−	0.000560979i
$666$	−843.384	−	772.167i	−1.26634	−	1.15941i
$667$	−235.933	+	235.933i	−0.353722	+	0.353722i
$668$	−425.349	+	113.972i	−0.636750	+	0.170617i
$669$	−283.877	+	43.7540i	−0.424331	+	0.0654021i
$670$	269.533	−	555.853i	0.402288	−	0.829631i
$671$	−24.9219	−	43.1660i	−0.0371414	−	0.0643308i
$672$	0.706817	−	6.46646i	0.00105181	−	0.00962271i
$673$	−467.643	+	125.305i	−0.694864	+	0.186188i	−0.588929	−	0.808185i	$-0.700450\pi$
$673$	−467.643	+	125.305i	−0.694864	+	0.186188i	−0.105935	+	0.994373i	$0.533784\pi$
$674$			72.9670i			0.108260i
$675$	−225.860	−	636.091i	−0.334607	−	0.942358i
$676$	4.95712			0.00733302
$677$	−113.880	−	425.004i	−0.168212	−	0.627776i	−0.997609	−	0.0691156i	$-0.977982\pi$
$677$	−113.880	−	425.004i	−0.168212	−	0.627776i	0.829397	−	0.558660i	$-0.188684\pi$
$678$	275.462	+	30.1094i	0.406286	+	0.0444091i
$679$	−9.17906	+	5.29953i	−0.0135185	+	0.00780490i
$680$	387.108	+	187.708i	0.569276	+	0.276042i
$681$	150.554	+	976.798i	0.221077	+	1.43436i
$682$	99.5854	+	371.658i	0.146020	+	0.544953i
$683$	−336.034	−	336.034i	−0.491998	−	0.491998i	0.416938	−	0.908935i	$-0.363103\pi$
$683$	−336.034	−	336.034i	−0.491998	−	0.491998i	−0.908935	+	0.416938i	$0.863103\pi$
$684$	34.6894	+	109.860i	0.0507155	+	0.160614i
$685$	−65.8544	+	342.985i	−0.0961379	+	0.500708i
$686$	8.31607	−	14.4039i	0.0121226	−	0.0209969i
$687$	1142.17	−	502.853i	1.66254	−	0.731954i
$688$	−51.8875	+	193.647i	−0.0754179	+	0.281463i
$689$	449.177	−	259.332i	0.651926	−	0.376389i
$690$	1435.15	+	900.499i	2.07992	+	1.30507i
$691$	−465.054	+	805.496i	−0.673015	+	1.16570i	0.304029	+	0.952663i	$0.401668\pi$
$691$	−465.054	+	805.496i	−0.673015	+	1.16570i	−0.977045	+	0.213034i	$0.931665\pi$
$692$	53.8977	−	53.8977i	0.0778869	−	0.0778869i
$693$	5.03045	+	2.61600i	0.00725895	+	0.00377489i
$694$			841.075i			1.21192i
$695$	612.314	−	44.2270i	0.881027	−	0.0636360i
$696$	15.0398	+	97.5786i	0.0216089	+	0.140199i
$697$	−1157.90	−	310.258i	−1.66126	−	0.445134i
$698$	−38.3309	+	143.053i	−0.0549153	+	0.204947i
$699$	58.4944	+	72.8512i	0.0836830	+	0.104222i
$700$	0.440541	−	3.72910i	0.000629345	−	0.00532729i
$701$	−1057.58			−1.50868			−0.754338	−	0.656486i	$-0.772042\pi$
$701$	−1057.58			−1.50868			−0.754338	+	0.656486i	$0.772042\pi$
$702$	833.559	+	282.369i	1.18741	+	0.402235i
$703$	−209.448	−	209.448i	−0.297935	−	0.297935i
$704$	4.55359	+	2.62902i	0.00646817	+	0.00373440i
$705$	−203.947	+	662.664i	−0.289286	+	0.939949i
$706$	−663.280	−	1148.83i	−0.939490	−	1.62724i
$707$	3.63379	+	0.973672i	0.00513974	+	0.00137719i
$708$	73.8079	−	100.706i	0.104248	−	0.142240i
$709$	450.749	+	260.240i	0.635754	+	0.367053i	0.782977	−	0.622051i	$-0.213700\pi$
$709$	450.749	+	260.240i	0.635754	+	0.367053i	−0.147223	+	0.989103i	$0.547034\pi$
$710$	−132.495	+	690.065i	−0.186613	+	0.971922i
$711$	−314.027	−	287.510i	−0.441670	−	0.404374i
$712$	187.104	−	187.104i	0.262787	−	0.262787i
$713$	731.800	−	196.085i	1.02637	−	0.275014i
$714$	−3.54821	+	9.12988i	−0.00496948	+	0.0127870i
$715$	198.267	+	571.552i	0.277297	+	0.799374i
$716$	204.962	+	355.005i	0.286260	+	0.495817i
$717$	−848.257	+	373.455i	−1.18306	+	0.520857i
$718$	823.316	−	220.607i	1.14668	−	0.307252i
$719$		−	1211.89i		−	1.68553i	−0.538285	−	0.842763i	$-0.680928\pi$
$719$		−	1211.89i		−	1.68553i	0.538285	−	0.842763i	$-0.319072\pi$
$720$	834.732	−	331.427i	1.15935	−	0.460315i
$721$	−6.23044			−0.00864139
$722$	−210.990	−	787.424i	−0.292230	−	1.09062i
$723$	45.6013	−	62.2198i	0.0630724	−	0.0860578i
$724$	186.673	−	107.776i	0.257836	−	0.148862i
$725$	26.4353	+	182.041i	0.0364625	+	0.251091i
$726$	−206.934	+	166.154i	−0.285034	+	0.228862i
$727$	53.9360	+	201.292i	0.0741899	+	0.276880i	0.993048	−	0.117707i	$-0.0375543\pi$
$727$	53.9360	+	201.292i	0.0741899	+	0.276880i	−0.918859	+	0.394587i	$0.870888\pi$
$728$	−2.82010	−	2.82010i	−0.00387377	−	0.00387377i
$729$	578.914	+	443.057i	0.794120	+	0.607761i
$730$	797.680	−	540.705i	1.09271	−	0.740692i
$731$	96.6185	−	167.348i	0.132173	−	0.228930i
$732$	3.87371	−	35.4394i	0.00529195	−	0.0484145i
$733$	−189.606	+	707.621i	−0.258672	+	0.965376i	0.707339	+	0.706874i	$0.249895\pi$
$733$	−189.606	+	707.621i	−0.258672	+	0.965376i	−0.966011	+	0.258502i	$0.916771\pi$
$734$	−793.936	+	458.379i	−1.08166	+	0.624495i
$735$	734.434	+	27.0164i	0.999229	+	0.0367570i
$736$	−721.511	+	1249.69i	−0.980313	+	1.69795i
$737$	−324.286	+	324.286i	−0.440009	+	0.440009i
$738$	−1177.83	+	751.059i	−1.59598	+	1.01770i
$739$			1243.93i			1.68326i	0.540056	+	0.841629i	$0.318403\pi$
$739$			1243.93i			1.68326i	−0.540056	+	0.841629i	$0.681597\pi$
$740$	367.859	−	425.137i	0.497107	−	0.574509i
$741$	212.493	+	82.5827i	0.286766	+	0.111448i
$742$	6.49769	+	1.74105i	0.00875700	+	0.00234643i
$743$	332.161	−	1239.64i	0.447054	−	1.66843i	−0.263400	−	0.964687i	$-0.584844\pi$
$743$	332.161	−	1239.64i	0.447054	−	1.66843i	0.710455	−	0.703743i	$-0.248489\pi$
$744$	81.2077	−	208.955i	0.109150	−	0.280854i
$745$	132.497	−	9.57019i	0.177849	−	0.0128459i
$746$	−829.060			−1.11134
$747$	558.755	−	24.6311i	0.747999	−	0.0329733i
$748$	277.240	+	277.240i	0.370642	+	0.370642i
$749$	−1.22121	−	0.705066i	−0.00163045	−	0.000941343i
$750$	871.115	−	337.111i	1.16149	−	0.449481i
$751$	−470.274	−	814.539i	−0.626198	−	1.08461i	−0.988308	−	0.152471i	$-0.951277\pi$
$751$	−470.274	−	814.539i	−0.626198	−	1.08461i	0.362110	−	0.932135i	$-0.382056\pi$
$752$	−891.087	−	238.766i	−1.18496	−	0.317508i
$753$	−822.731	−	89.9287i	−1.09260	−	0.119427i
$754$	−207.708	−	119.920i	−0.275474	−	0.159045i
$755$	407.598	−	276.289i	0.539865	−	0.365946i
$756$	1.79597	+	3.63608i	0.00237562	+	0.00480963i
$757$	872.169	−	872.169i	1.15214	−	1.15214i	0.166015	−	0.986123i	$-0.446910\pi$
$757$	872.169	−	872.169i	1.15214	−	1.15214i	0.986123	−	0.166015i	$-0.0530901\pi$
$758$	490.097	−	131.321i	0.646566	−	0.173247i
$759$	−787.490	−	980.770i	−1.03754	−	1.29219i
$760$	122.694	−	42.5615i	0.161439	−	0.0560020i
$761$	−229.806	−	398.036i	−0.301979	−	0.523043i	0.674605	−	0.738179i	$-0.264314\pi$
$761$	−229.806	−	398.036i	−0.301979	−	0.523043i	−0.976584	+	0.215136i	$0.930981\pi$
$762$	1293.83	+	948.260i	1.69794	+	1.24444i
$763$	−7.37515	+	1.97617i	−0.00966599	+	0.00259000i
$764$		−	300.712i		−	0.393602i
$765$	−859.849	+	100.330i	−1.12399	+	0.131150i
$766$	51.5397			0.0672842
$767$	−63.9473	−	238.655i	−0.0833733	−	0.311153i
$768$	384.779	+	873.980i	0.501015	+	1.13799i
$769$	775.372	−	447.661i	1.00829	−	0.582134i	0.0975969	−	0.995226i	$-0.468884\pi$
$769$	775.372	−	447.661i	1.00829	−	0.582134i	0.910689	+	0.413092i	$0.135551\pi$
$770$	−3.42338	+	7.05997i	−0.00444594	+	0.00916879i
$771$	17.8905	+	6.95289i	0.0232042	+	0.00901802i
$772$	52.6949	+	196.660i	0.0682576	+	0.254741i
$773$	94.0446	+	94.0446i	0.121662	+	0.121662i	0.765316	−	0.643654i	$-0.222583\pi$
$773$	94.0446	+	94.0446i	0.121662	+	0.121662i	−0.643654	+	0.765316i	$0.722583\pi$
$774$	−67.8039	−	214.732i	−0.0876020	−	0.277431i
$775$	154.690	−	387.981i	0.199600	−	0.500620i
$776$	347.868	−	602.524i	0.448283	−	0.776449i
$777$	−8.40996	−	6.16372i	−0.0108236	−	0.00793272i
$778$	−119.433	+	445.730i	−0.153513	+	0.572918i
$779$	−313.377	+	180.928i	−0.402281	+	0.232257i
$780$	−127.279	+	413.554i	−0.163178	+	0.530198i
$781$	260.825	−	451.762i	0.333963	−	0.578441i
$782$	1536.46	−	1536.46i	1.96479	−	1.96479i
$783$	−131.084	−	149.283i	−0.167412	−	0.190655i
$784$			977.861i			1.24727i
$785$	−652.970	−	564.997i	−0.831809	−	0.719742i
$786$	8.75699	−	7.03126i	0.0111412	−	0.00894562i
$787$	899.963	+	241.144i	1.14354	+	0.306410i	0.780372	−	0.625315i	$-0.215030\pi$
$787$	899.963	+	241.144i	1.14354	+	0.306410i	0.363164	+	0.931725i	$0.381696\pi$
$788$	137.666	−	513.778i	0.174704	−	0.652003i
$789$	630.030	−	97.1064i	0.798517	−	0.123075i
$790$	385.514	−	445.541i	0.487993	−	0.563976i
$791$	2.52677			0.00319440
$792$	−371.825	+	16.3908i	−0.469476	+	0.0206955i
$793$	−49.8843	−	49.8843i	−0.0629058	−	0.0629058i
$794$	721.400	+	416.501i	0.908565	+	0.524560i
$795$	132.658	+	579.527i	0.166866	+	0.728965i
$796$	−40.1407	−	69.5257i	−0.0504280	−	0.0873438i
$797$	163.649	+	43.8496i	0.205331	+	0.0550183i	0.360019	−	0.932945i	$-0.382770\pi$
$797$	163.649	+	43.8496i	0.205331	+	0.0550183i	−0.154687	+	0.987963i	$0.549437\pi$
$798$	1.19140	+	2.70612i	0.00149298	+	0.00339113i
$799$	770.071	+	444.601i	0.963793	+	0.556446i
$800$	314.200	+	730.879i	0.392750	+	0.913599i
$801$	−115.022	+	519.866i	−0.143598	+	0.649022i
$802$	−119.900	+	119.900i	−0.149502	+	0.149502i
$803$	−691.034	+	185.162i	−0.860565	+	0.230588i
$804$	−324.190	+	49.9674i	−0.403222	+	0.0621485i
$805$	13.9012	+	6.74068i	0.0172686	+	0.00837352i
$806$	272.293	+	471.626i	0.337833	+	0.585144i
$807$	113.780	−	1040.94i	0.140991	−	1.28989i
$808$	−238.527	+	63.9130i	−0.295206	+	0.0791003i
$809$			1540.82i			1.90459i	0.305175	+	0.952296i	$0.401285\pi$
$809$			1540.82i			1.90459i	−0.305175	+	0.952296i	$0.598715\pi$
$810$	−590.396	+	817.985i	−0.728884	+	1.00986i
$811$	−895.419			−1.10409			−0.552046	−	0.833813i	$-0.686153\pi$
$811$	−895.419			−1.10409			−0.552046	+	0.833813i	$0.686153\pi$
$812$	−0.286042	−	1.06752i	−0.000352269	−	0.00131469i
$813$	603.238	+	65.9370i	0.741990	+	0.0811033i
$814$	−1017.33	+	587.355i	−1.24979	+	0.721566i
$815$	150.824	+	434.785i	0.185060	+	0.533479i
$816$	−175.460	−	1138.39i	−0.215025	−	1.39509i
$817$	−15.0972	−	56.3434i	−0.0184788	−	0.0689637i
$818$	−664.048	−	664.048i	−0.811795	−	0.811795i
$819$	7.83561	+	1.73366i	0.00956729	+	0.00211680i
$820$	−385.357	−	568.501i	−0.469947	−	0.693294i
$821$	−322.268	+	558.185i	−0.392531	+	0.679884i	−0.992783	−	0.119927i	$-0.961734\pi$
$821$	−322.268	+	558.185i	−0.392531	+	0.679884i	0.600251	+	0.799811i	$0.295067\pi$
$822$	477.710	−	210.317i	0.581156	−	0.255860i
$823$	−56.6061	+	211.257i	−0.0687802	+	0.256691i	−0.991751	−	0.128179i	$-0.959087\pi$
$823$	−56.6061	+	211.257i	−0.0687802	+	0.256691i	0.922971	+	0.384870i	$0.125754\pi$
$824$	354.182	−	204.487i	0.429832	−	0.248164i
$825$	−693.005	+	24.4978i	−0.840006	+	0.0296943i
$826$	1.60223	−	2.77514i	0.00193975	−	0.00335974i
$827$	−982.768	+	982.768i	−1.18835	+	1.18835i	−0.210831	+	0.977522i	$0.567617\pi$
$827$	−982.768	+	982.768i	−1.18835	+	1.18835i	−0.977522	+	0.210831i	$0.932383\pi$
$828$	−39.6191	−	898.759i	−0.0478492	−	1.08546i
$829$			763.031i			0.920424i	0.887809	+	0.460212i	$0.152227\pi$
$829$			763.031i			0.920424i	−0.887809	+	0.460212i	$0.847773\pi$
$830$	55.7574	+	771.949i	0.0671776	+	0.930059i
$831$	−110.885	−	719.427i	−0.133436	−	0.865736i
$832$	7.18844	+	1.92614i	0.00863996	+	0.00231507i
$833$	243.948	−	910.427i	0.292855	−	1.09295i
$834$	−574.431	−	715.418i	−0.688766	−	0.857816i
$835$	−755.327	−	653.564i	−0.904584	−	0.782711i
$836$	118.353			0.141571
$837$	88.2834	+	442.373i	0.105476	+	0.528522i
$838$	402.737	+	402.737i	0.480593	+	0.480593i
$839$	−946.477	−	546.449i	−1.12810	−	0.651309i	−0.184644	−	0.982805i	$-0.559113\pi$
$839$	−946.477	−	546.449i	−1.12810	−	0.651309i	−0.943457	+	0.331496i	$0.892447\pi$
$840$	4.04037	−	2.13866i	0.00480997	−	0.00254603i
$841$	−393.430	−	681.440i	−0.467812	−	0.810274i
$842$	−985.940	−	264.182i	−1.17095	−	0.313755i
$843$	−497.125	+	678.291i	−0.589709	+	0.804616i
$844$	−369.598	−	213.388i	−0.437913	−	0.252829i
$845$	6.30890	+	9.30726i	0.00746615	+	0.0110145i
$846$	988.112	−	312.007i	1.16798	−	0.368803i
$847$	−1.71114	+	1.71114i	−0.00202024	+	0.00202024i
$848$	−764.080	+	204.735i	−0.901038	+	0.241432i
$849$	−419.295	+	1078.89i	−0.493870	+	1.27077i
$850$	−172.154	−	1185.50i	−0.202535	−	1.39471i
$851$	1156.51	+	2003.14i	1.35900	+	2.35386i
$852$	341.478	−	150.339i	0.400795	−	0.176455i
$853$	−1588.02	+	425.510i	−1.86169	+	0.498839i	−0.999964	−	0.00853057i	$-0.997285\pi$
$853$	−1588.02	+	425.510i	−1.86169	+	0.498839i	−0.861729	+	0.507369i	$0.830618\pi$
$854$		−	0.914971i		−	0.00107140i
$855$	−162.119	+	204.949i	−0.189612	+	0.239707i
$856$	92.5628			0.108134
$857$	85.2695	+	318.230i	0.0994977	+	0.371330i	0.997663	−	0.0683276i	$-0.0217663\pi$
$857$	85.2695	+	318.230i	0.0994977	+	0.371330i	−0.898165	+	0.439658i	$0.855100\pi$
$858$	534.465	−	729.240i	0.622920	−	0.849930i
$859$	1361.73	−	786.197i	1.58525	−	0.915247i	0.591180	−	0.806540i	$-0.298662\pi$
$859$	1361.73	−	786.197i	1.58525	−	0.915247i	0.994074	−	0.108707i	$-0.0346710\pi$
$860$	104.597	−	36.2839i	0.121624	−	0.0421906i
$861$	−9.93239	+	7.97502i	−0.0115359	+	0.00926251i
$862$	−29.9639	−	111.827i	−0.0347609	−	0.129729i
$863$	458.505	+	458.505i	0.531292	+	0.531292i	0.920957	−	0.389665i	$-0.127409\pi$
$863$	458.505	+	458.505i	0.531292	+	0.531292i	−0.389665	+	0.920957i	$0.627409\pi$
$864$	−714.698	−	476.895i	−0.827197	−	0.551961i
$865$	169.791	+	32.6006i	0.196290	+	0.0376885i
$866$	−758.481	+	1313.73i	−0.875844	+	1.51701i
$867$	−26.4291	+	241.792i	−0.0304834	+	0.278883i
$868$	−0.649494	+	2.42395i	−0.000748265	+	0.00279256i
$869$	−378.794	+	218.697i	−0.435897	+	0.251665i
$870$	201.409	−	187.117i	0.231505	−	0.215077i
$871$	−324.550	+	562.137i	−0.372618	+	0.645393i
$872$	354.396	−	354.396i	0.406418	−	0.406418i
$873$	61.6532	+	1398.60i	0.0706222	+	1.60206i
$874$		−	655.913i		−	0.750472i
$875$	7.56226	−	3.91887i	0.00864259	−	0.00447870i
$876$	−476.941	−	185.357i	−0.544454	−	0.211595i
$877$	−1041.72	−	279.129i	−1.18783	−	0.318277i	−0.389800	−	0.920900i	$-0.627456\pi$
$877$	−1041.72	−	279.129i	−1.18783	−	0.318277i	−0.798026	+	0.602623i	$0.794122\pi$
$878$	249.625	−	931.615i	0.284311	−	1.06106i
$879$	45.9083	−	118.127i	0.0522279	−	0.134387i
$880$	−66.4695	−	920.256i	−0.0755335	−	1.04574i
$881$	1585.15			1.79927			0.899633	−	0.436647i	$-0.143834\pi$
$881$	1585.15			1.79927			0.899633	+	0.436647i	$0.143834\pi$
$882$	−590.539	−	926.101i	−0.669545	−	1.05000i
$883$	−1004.45	−	1004.45i	−1.13755	−	1.13755i	−0.988889	−	0.148657i	$-0.952505\pi$
$883$	−1004.45	−	1004.45i	−1.13755	−	1.13755i	−0.148657	−	0.988889i	$-0.547495\pi$
$884$	480.584	+	277.466i	0.543648	+	0.313875i
$885$	283.015	+	10.4108i	0.319791	+	0.0117636i
$886$	913.702	+	1582.58i	1.03127	+	1.78621i
$887$	−302.408	−	81.0299i	−0.340933	−	0.0913528i	0.0842901	−	0.996441i	$-0.473138\pi$
$887$	−302.408	−	81.0299i	−0.340933	−	0.0913528i	−0.425223	+	0.905088i	$0.639804\pi$
$888$	680.378	+	74.3688i	0.766191	+	0.0837487i
$889$	12.6676	+	7.31362i	0.0142492	+	0.00822680i
$890$	−723.576	−	138.929i	−0.813006	−	0.156100i
$891$	613.112	−	430.074i	0.688117	−	0.482687i
$892$	−149.235	+	149.235i	−0.167304	+	0.167304i
$893$	259.270	−	69.4713i	0.290336	−	0.0777954i
$894$	−124.300	−	154.808i	−0.139038	−	0.173163i
$895$	−405.687	+	836.641i	−0.453281	+	0.934794i
$896$	4.38491	+	7.59489i	0.00489387	+	0.00847644i
$897$	−1435.88	−	1052.37i	−1.60076	−	1.17321i
$898$	−339.479	+	90.9632i	−0.378039	+	0.101295i
$899$		−	122.932i		−	0.136743i
$900$	−410.148	−	278.876i	−0.455720	−	0.309863i
$901$	762.464			0.846242
$902$	371.425	+	1386.18i	0.411779	+	1.53678i
$903$	−0.827369	−	1.87927i	−0.000916245	−	0.00208114i
$904$	−143.639	+	82.9302i	−0.158893	+	0.0917370i
$905$	439.933	+	213.324i	0.486114	+	0.235717i
$906$	−685.938	−	266.581i	−0.757106	−	0.294239i
$907$	95.9237	+	357.992i	0.105759	+	0.394699i	0.998430	−	0.0560100i	$-0.0178379\pi$
$907$	95.9237	+	357.992i	0.105759	+	0.394699i	−0.892671	+	0.450709i	$0.851171\pi$
$908$	513.506	+	513.506i	0.565536	+	0.565536i
$909$	335.543	−	366.490i	0.369134	−	0.403180i
$910$	−2.09399	+	10.9060i	−0.00230109	+	0.0119846i
$911$	490.084	−	848.851i	0.537963	−	0.931779i	−0.461051	−	0.887374i	$-0.652527\pi$
$911$	490.084	−	848.851i	0.537963	−	0.931779i	0.999014	−	0.0444052i	$-0.0141393\pi$
$912$	−280.440	−	205.537i	−0.307500	−	0.225369i
$913$	148.711	−	554.997i	0.162882	−	0.607883i
$914$	1583.93	−	914.484i	1.73297	−	1.00053i
$915$	71.4694	−	37.8304i	0.0781086	−	0.0413447i
$916$	458.489	−	794.127i	0.500534	−	0.866951i
$917$	0.0724117	−	0.0724117i	7.89659e−5	−	7.89659e-5i
$918$	853.657	+	972.172i	0.929909	+	1.05901i
$919$		−	1321.17i		−	1.43762i	−0.695205	−	0.718811i	$-0.744687\pi$
$919$		−	1321.17i		−	1.43762i	0.695205	−	0.718811i	$-0.255313\pi$
$920$	−1011.47	+	73.0581i	−1.09943	+	0.0794110i
$921$	281.565	−	226.077i	0.305717	−	0.245470i
$922$	1544.84	+	413.938i	1.67553	+	0.448956i
$923$	191.092	−	713.166i	0.207034	−	0.772661i
$924$	4.11759	−	0.634643i	0.00445626	−	0.000686843i
$925$	1266.39	+	149.606i	1.36907	+	0.161736i
$926$	691.330			0.746577
$927$	−379.683	+	730.114i	−0.409583	+	0.787609i
$928$	165.567	+	165.567i	0.178413	+	0.178413i
$929$	−672.297	−	388.151i	−0.723678	−	0.417816i	0.0924267	−	0.995719i	$-0.470538\pi$
$929$	−672.297	−	388.151i	−0.723678	−	0.417816i	−0.816105	+	0.577904i	$0.803871\pi$
$930$	−608.491	+	139.288i	−0.654292	+	0.149772i
$931$	−142.259	−	246.400i	−0.152802	−	0.264662i
$932$	66.3103	+	17.7678i	0.0711484	+	0.0190642i
$933$	−549.027	−	1247.05i	−0.588454	−	1.33660i
$934$	175.242	+	101.176i	0.187625	+	0.108325i
$935$	−167.691	+	873.376i	−0.179349	+	0.934092i
$936$	−502.331	+	158.616i	−0.536678	+	0.169462i
$937$	295.586	−	295.586i	0.315459	−	0.315459i	−0.531561	−	0.847020i	$-0.678394\pi$
$937$	295.586	−	295.586i	0.315459	−	0.315459i	0.847020	+	0.531561i	$0.178394\pi$
$938$	−8.13175	+	2.17890i	−0.00866925	+	0.00232292i
$939$	880.974	−	135.784i	0.938205	−	0.144605i
$940$	166.964	+	481.315i	0.177622	+	0.512037i
$941$	−48.8020	−	84.5275i	−0.0518618	−	0.0898273i	0.838929	−	0.544241i	$-0.183182\pi$
$941$	−48.8020	−	84.5275i	−0.0518618	−	0.0898273i	−0.890791	+	0.454413i	$0.849849\pi$
$942$	−140.220	+	1282.83i	−0.148854	+	1.36182i
$943$	2729.40	−	731.341i	2.89438	−	0.775548i
$944$			376.820i			0.399174i
$945$	−4.54122	+	7.99964i	−0.00480552	+	0.00846523i
$946$	−231.333			−0.244538
$947$	47.4532	+	177.098i	0.0501090	+	0.187009i	0.986444	−	0.164099i	$-0.0524716\pi$
$947$	47.4532	+	177.098i	0.0501090	+	0.187009i	−0.936335	+	0.351108i	$0.885805\pi$
$948$	−310.991	−	33.9929i	−0.328050	−	0.0358575i
$949$	−876.908	+	506.283i	−0.924034	+	0.533491i
$950$	−289.790	−	216.298i	−0.305042	−	0.227682i
$951$	40.4023	+	262.131i	0.0424840	+	0.275638i
$952$	−1.51743	−	5.66313i	−0.00159394	−	0.00594866i
$953$	−16.8810	−	16.8810i	−0.0177135	−	0.0177135i	0.698195	−	0.715908i	$-0.253987\pi$
$953$	−16.8810	−	16.8810i	−0.0177135	−	0.0177135i	−0.715908	+	0.698195i	$0.753987\pi$
$954$	599.995	−	655.332i	0.628925	−	0.686931i
$955$	564.603	−	382.714i	0.591207	−	0.400748i
$956$	−340.507	+	589.776i	−0.356179	+	0.616920i
$957$	−186.791	+	82.2369i	−0.195184	+	0.0859320i
$958$	−312.153	+	1164.97i	−0.325838	+	1.21604i
$959$	4.12185	−	2.37975i	0.00429807	−	0.00248149i
$960$	−4.53388	+	7.22575i	−0.00472279	+	0.00752682i
$961$	340.934	−	590.514i	0.354770	−	0.614479i
$962$	−1175.66	+	1175.66i	−1.22210	+	1.22210i
$963$	−157.044	+	100.141i	−0.163078	+	0.103988i
$964$		−	56.6819i		−	0.0587987i
$965$	−302.175	+	349.226i	−0.313135	+	0.361892i
$966$	−3.51719	−	22.8196i	−0.00364098	−	0.0236228i
$967$	1161.19	+	311.140i	1.20082	+	0.321758i	0.803153	−	0.595772i	$-0.203154\pi$
$967$	1161.19	+	311.140i	1.20082	+	0.321758i	0.397665	+	0.917531i	$0.369821\pi$
$968$	41.1125	−	153.434i	0.0424716	−	0.158506i
$969$	209.825	+	261.324i	0.216538	+	0.269684i
$970$	−1932.24	+	139.564i	−1.99200	+	0.143881i
$971$	−608.975			−0.627163			−0.313582	−	0.949561i	$-0.601529\pi$
$971$	−608.975			−0.627163			−0.313582	+	0.949561i	$0.601529\pi$
$972$	535.540	+	11.1225i	0.550967	+	0.0114429i
$973$	−5.91580	−	5.91580i	−0.00607996	−	0.00607996i
$974$	494.753	+	285.646i	0.507960	+	0.293271i
$975$	−938.457	+	287.355i	−0.962520	+	0.294723i
$976$	53.7969	+	93.1790i	0.0551198	+	0.0954702i
$977$	85.2493	+	22.8425i	0.0872562	+	0.0233802i	0.302183	−	0.953250i	$-0.402285\pi$
$977$	85.2493	+	22.8425i	0.0872562	+	0.0233802i	−0.214927	+	0.976630i	$0.568951\pi$
$978$	406.572	−	554.739i	0.415718	−	0.567218i
$979$	473.701	+	273.491i	0.483862	+	0.279358i
$980$	446.998	−	302.996i	0.456120	−	0.309180i
$981$	−217.865	+	984.684i	−0.222085	+	1.00376i
$982$	−1391.51	+	1391.51i	−1.41701	+	1.41701i
$983$	1378.97	−	369.494i	1.40282	−	0.375884i	0.523461	−	0.852049i	$-0.324640\pi$
$983$	1378.97	−	369.494i	1.40282	−	0.375884i	0.879356	+	0.476166i	$0.157974\pi$
$984$	302.881	−	779.343i	0.307806	−	0.792015i
$985$	1139.85	−	395.406i	1.15721	−	0.401428i
$986$	−176.289	−	305.341i	−0.178792	−	0.309676i
$987$	8.64766	−	3.80723i	0.00876156	−	0.00385738i
$988$	161.805	−	43.3555i	0.163770	−	0.0438821i
$989$			455.499i			0.460565i
$990$	618.701	+	831.403i	0.624951	+	0.839801i
$991$	14.7275			0.0148613			0.00743063	−	0.999972i	$-0.497635\pi$
$991$	14.7275			0.0148613			0.00743063	+	0.999972i	$0.497635\pi$
$992$	−137.604	−	513.545i	−0.138714	−	0.517687i
$993$	−791.484	+	1079.92i	−0.797063	+	1.08754i
$994$	8.29290	−	4.78791i	0.00834296	−	0.00481681i
$995$	79.4514	−	163.851i	0.0798506	−	0.164675i
$996$	320.448	−	257.298i	0.321735	−	0.258331i
$997$	−59.6878	−	222.758i	−0.0598674	−	0.223428i	0.929510	−	0.368796i	$-0.120230\pi$
$997$	−59.6878	−	222.758i	−0.0598674	−	0.223428i	−0.989378	+	0.145368i	$0.953563\pi$
$998$	−858.989	−	858.989i	−0.860710	−	0.860710i
$999$	−1234.80	+	609.903i	−1.23603	+	0.610514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.43.2	yes	40
3.2	odd	2		135.3.l.a.73.9		40
5.2	odd	4	inner	45.3.k.a.7.9	✓	40
5.3	odd	4		225.3.o.b.7.2		40
5.4	even	2		225.3.o.b.43.9		40
9.2	odd	6		405.3.g.g.163.9		20
9.4	even	3	inner	45.3.k.a.13.9	yes	40
9.5	odd	6		135.3.l.a.118.2		40
9.7	even	3		405.3.g.h.163.2		20
15.2	even	4		135.3.l.a.127.2		40
45.2	even	12		405.3.g.g.82.9		20
45.4	even	6		225.3.o.b.193.2		40
45.7	odd	12		405.3.g.h.82.2		20
45.13	odd	12		225.3.o.b.157.9		40
45.22	odd	12	inner	45.3.k.a.22.2	yes	40
45.32	even	12		135.3.l.a.37.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.9	✓	40	5.2	odd	4	inner
45.3.k.a.13.9	yes	40	9.4	even	3	inner
45.3.k.a.22.2	yes	40	45.22	odd	12	inner
45.3.k.a.43.2	yes	40	1.1	even	1	trivial
135.3.l.a.37.9		40	45.32	even	12
135.3.l.a.73.9		40	3.2	odd	2
135.3.l.a.118.2		40	9.5	odd	6
135.3.l.a.127.2		40	15.2	even	4
225.3.o.b.7.2		40	5.3	odd	4
225.3.o.b.43.9		40	5.4	even	2
225.3.o.b.157.9		40	45.13	odd	12
225.3.o.b.193.2		40	45.4	even	6
405.3.g.g.82.9		20	45.2	even	12
405.3.g.g.163.9		20	9.2	odd	6
405.3.g.h.82.2		20	45.7	odd	12
405.3.g.h.163.2		20	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.644680 - 2.40598i) q^{2} +(-2.98224 - 0.325974i) q^{3} +(-1.90902 + 1.10217i) q^{4} +(-4.49898 - 2.18155i) q^{5} +(1.13830 + 7.38535i) q^{6} +(0.0176356 + 0.0658171i) q^{7} +(-3.16269 - 3.16269i) q^{8} +(8.78748 + 1.94426i) q^{9} +(-2.34837 + 12.2309i) q^{10} +(4.62292 - 8.00713i) q^{11} +(6.05242 - 2.66465i) q^{12} +(3.38696 - 12.6403i) q^{13} +(0.146985 - 0.0848619i) q^{14} +(12.7059 + 7.97246i) q^{15} +(-9.97912 + 17.2843i) q^{16} +(13.6029 - 13.6029i) q^{17} +(-0.987258 - 22.3959i) q^{18} -5.80704i q^{19} +(10.9931 - 0.794023i) q^{20} +(-0.0311390 - 0.202031i) q^{21} +(-22.2453 - 5.96060i) q^{22} +(-11.7365 + 43.8013i) q^{23} +(8.40093 + 10.4628i) q^{24} +(15.4816 + 19.6295i) q^{25} -32.5958 q^{26} +(-25.5726 - 8.66274i) q^{27} +(-0.106208 - 0.106208i) q^{28} +(6.37222 + 3.67900i) q^{29} +(10.9903 - 35.7098i) q^{30} +(-8.35363 - 14.4689i) q^{31} +(30.7378 + 8.23618i) q^{32} +(-16.3967 + 22.3722i) q^{33} +(-41.4978 - 23.9587i) q^{34} +(0.0642412 - 0.334583i) q^{35} +(-18.9184 + 5.97368i) q^{36} +(36.0680 - 36.0680i) q^{37} +(-13.9716 + 3.74368i) q^{38} +(-14.2211 + 36.5923i) q^{39} +(7.32929 + 21.1284i) q^{40} +(-31.1567 - 53.9649i) q^{41} +(-0.466007 + 0.205165i) q^{42} +(9.70259 - 2.59980i) q^{43} +20.3810i q^{44} +(-35.2932 - 27.9176i) q^{45} +112.951 q^{46} +(11.9633 + 44.6476i) q^{47} +(35.3944 - 48.2931i) q^{48} +(42.4312 - 24.4977i) q^{49} +(37.2475 - 49.9033i) q^{50} +(-45.0012 + 36.1329i) q^{51} +(7.46602 + 27.8636i) q^{52} +(28.0258 + 28.0258i) q^{53} +(-4.35625 + 67.1118i) q^{54} +(-38.2664 + 25.9388i) q^{55} +(0.152383 - 0.263935i) q^{56} +(-1.89294 + 17.3180i) q^{57} +(4.74356 - 17.7032i) q^{58} +(16.3509 - 9.44022i) q^{59} +(-33.0428 - 1.21549i) q^{60} +(2.69547 - 4.66870i) q^{61} +(-29.4265 + 29.4265i) q^{62} +(0.0270071 + 0.612655i) q^{63} +0.568692i q^{64} +(-42.8134 + 49.4796i) q^{65} +(64.3977 + 25.0273i) q^{66} +(-47.9117 - 12.8379i) q^{67} +(-10.9754 + 40.9609i) q^{68} +(49.2792 - 126.800i) q^{69} +(-0.846414 + 0.0611359i) q^{70} +56.4200 q^{71} +(-21.6430 - 33.9412i) q^{72} +(-54.7135 - 54.7135i) q^{73} +(-110.031 - 63.5264i) q^{74} +(-39.7712 - 63.5866i) q^{75} +(6.40036 + 11.0857i) q^{76} +(0.608534 + 0.163056i) q^{77} +(97.2084 + 10.6254i) q^{78} +(-40.9692 - 23.6536i) q^{79} +(82.6026 - 55.9919i) q^{80} +(73.4397 + 34.1704i) q^{81} +(-109.752 + 109.752i) q^{82} +(60.0267 - 16.0841i) q^{83} +(0.282117 + 0.351360i) q^{84} +(-90.8746 + 31.5237i) q^{85} +(-12.5101 - 21.6682i) q^{86} +(-17.8042 - 13.0488i) q^{87} +(-39.9449 + 10.7032i) q^{88} +59.1599i q^{89} +(-44.4163 + 102.913i) q^{90} +0.891679 q^{91} +(-25.8713 - 96.5530i) q^{92} +(20.1960 + 45.8728i) q^{93} +(99.7085 - 57.5668i) q^{94} +(-12.6684 + 26.1258i) q^{95} +(-88.9828 - 34.5820i) q^{96} +(40.2595 + 150.251i) q^{97} +(-86.2954 - 86.2954i) q^{98} +(56.1918 - 61.3743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

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