LMFDB - Embedded newform 45.3.k.a.7.9

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			7.9
Character	$\chi$	$=$	45.7
Dual form			45.3.k.a.13.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.40598 - 0.644680i) q^{2} +(-0.325974 + 2.98224i) q^{3} +(1.90902 - 1.10217i) q^{4} +(0.360208 - 4.98701i) q^{5} +(1.13830 + 7.38535i) q^{6} +(-0.0658171 + 0.0176356i) 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} +(2.66465 + 6.05242i) q^{12} +(-12.6403 - 3.38696i) q^{13} +(-0.146985 + 0.0848619i) q^{14} +(14.7550 + 2.69986i) q^{15} +(-9.97912 + 17.2843i) q^{16} +(13.6029 + 13.6029i) q^{17} +(-22.3959 + 0.987258i) q^{18} +5.80704i q^{19} +(-4.80889 - 9.91729i) q^{20} +(-0.0311390 - 0.202031i) q^{21} +(5.96060 - 22.2453i) q^{22} +(43.8013 + 11.7365i) q^{23} +(-8.40093 - 10.4628i) q^{24} +(-24.7405 - 3.59273i) q^{25} -32.5958 q^{26} +(8.66274 - 25.5726i) q^{27} +(-0.106208 + 0.106208i) q^{28} +(-6.37222 - 3.67900i) q^{29} +(37.2408 - 3.01646i) q^{30} +(-8.35363 - 14.4689i) q^{31} +(-8.23618 + 30.7378i) q^{32} +(22.3722 + 16.3967i) 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} +(3.74368 + 13.9716i) q^{38} +(14.2211 - 36.5923i) q^{39} +(14.6331 + 16.9116i) q^{40} +(-31.1567 - 53.9649i) q^{41} +(-0.205165 - 0.466007i) q^{42} +(-2.59980 - 9.70259i) q^{43} -20.3810i q^{44} +(-12.8614 + 43.1229i) q^{45} +112.951 q^{46} +(-44.6476 + 11.9633i) q^{47} +(-48.2931 - 35.3944i) q^{48} +(-42.4312 + 24.4977i) q^{49} +(-61.8413 + 7.30568i) q^{50} +(-45.0012 + 36.1329i) q^{51} +(-27.8636 + 7.46602i) 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} +(-17.3180 - 1.89294i) q^{57} +(-17.7032 - 4.74356i) q^{58} +(-16.3509 + 9.44022i) q^{59} +(31.1433 - 11.1085i) q^{60} +(2.69547 - 4.66870i) q^{61} +(-29.4265 - 29.4265i) q^{62} +(0.612655 - 0.0270071i) q^{63} -0.568692i q^{64} +(-21.4439 + 61.8173i) q^{65} +(64.3977 + 25.0273i) q^{66} +(12.8379 - 47.9117i) q^{67} +(40.9609 + 10.9754i) q^{68} +(-49.2792 + 126.800i) q^{69} +(0.370262 + 0.763584i) q^{70} +56.4200 q^{71} +(33.9412 - 21.6430i) q^{72} +(-54.7135 + 54.7135i) q^{73} +(110.031 + 63.5264i) q^{74} +(18.7791 - 72.6109i) q^{75} +(6.40036 + 11.0857i) q^{76} +(-0.163056 + 0.608534i) q^{77} +(10.6254 - 97.2084i) 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} +(-16.0841 - 60.0267i) q^{83} +(-0.282117 - 0.351360i) q^{84} +(72.7376 - 62.9379i) q^{85} +(-12.5101 - 21.6682i) q^{86} +(13.0488 - 17.8042i) q^{87} +(10.7032 + 39.9449i) q^{88} -59.1599i q^{89} +(-3.14373 + 112.044i) q^{90} +0.891679 q^{91} +(96.5530 - 25.8713i) q^{92} +(45.8728 - 20.1960i) q^{93} +(-99.7085 + 57.5668i) q^{94} +(28.9598 + 2.09175i) q^{95} +(-88.9828 - 34.5820i) q^{96} +(-150.251 + 40.2595i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.40598	−	0.644680i	1.20299	−	0.322340i	0.398981	−	0.916959i	$-0.369364\pi$
$2$	2.40598	−	0.644680i	1.20299	−	0.322340i	0.804008	+	0.594619i	$0.202697\pi$
$3$	−0.325974	+	2.98224i	−0.108658	+	0.994079i
$3$	−0.325974	+	2.98224i	−0.108658	+	0.994079i
$4$	1.90902	−	1.10217i	0.477254	−	0.275543i
$5$	0.360208	−	4.98701i	0.0720417	−	0.997402i
$5$	0.360208	−	4.98701i	0.0720417	−	0.997402i
$6$	1.13830	+	7.38535i	0.189717	+	1.23089i
$7$	−0.0658171	+	0.0176356i	−0.00940244	+	0.00251938i	−0.263517	−	0.964655i	$-0.584883\pi$
$7$	−0.0658171	+	0.0176356i	−0.00940244	+	0.00251938i	0.254115	+	0.967174i	$0.418216\pi$
$8$	−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	$0.0286037\pi$
$12$	2.66465	+	6.05242i	0.222054	+	0.504368i
$13$	−12.6403	−	3.38696i	−0.972331	−	0.260535i	−0.262519	−	0.964927i	$-0.584553\pi$
$13$	−12.6403	−	3.38696i	−0.972331	−	0.260535i	−0.709812	+	0.704391i	$0.751220\pi$
$14$	−0.146985	+	0.0848619i	−0.0104989	+	0.00606156i
$15$	14.7550	+	2.69986i	0.983668	+	0.179991i
$16$	−9.97912	+	17.2843i	−0.623695	+	1.08027i
$17$	13.6029	+	13.6029i	0.800170	+	0.800170i	0.983122	−	0.182952i	$-0.0585652\pi$
$17$	13.6029	+	13.6029i	0.800170	+	0.800170i	−0.182952	+	0.983122i	$0.558565\pi$
$18$	−22.3959	+	0.987258i	−1.24422	+	0.0548477i
$19$			5.80704i			0.305634i	0.988255	+	0.152817i	$0.0488345\pi$
$19$			5.80704i			0.305634i	−0.988255	+	0.152817i	$0.951166\pi$
$20$	−4.80889	−	9.91729i	−0.240445	−	0.495865i
$21$	−0.0311390	−	0.202031i	−0.00148281	−	0.00962052i
$22$	5.96060	−	22.2453i	0.270936	−	1.01115i
$23$	43.8013	+	11.7365i	1.90440	+	0.510283i	0.995676	+	0.0928936i	$0.0296117\pi$
$23$	43.8013	+	11.7365i	1.90440	+	0.510283i	0.908728	+	0.417390i	$0.137055\pi$
$24$	−8.40093	−	10.4628i	−0.350039	−	0.435952i
$25$	−24.7405	−	3.59273i	−0.989620	−	0.143709i
$26$	−32.5958			−1.25368
$27$	8.66274	−	25.5726i	0.320842	−	0.947133i
$28$	−0.106208	+	0.106208i	−0.00379316	+	0.00379316i
$29$	−6.37222	−	3.67900i	−0.219732	−	0.126862i	0.386094	−	0.922459i	$-0.373824\pi$
$29$	−6.37222	−	3.67900i	−0.219732	−	0.126862i	−0.605826	+	0.795597i	$0.707157\pi$
$30$	37.2408	−	3.01646i	1.24136	−	0.100549i
$31$	−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	$0.920183\pi$
$32$	−8.23618	+	30.7378i	−0.257381	+	0.960558i
$33$	22.3722	+	16.3967i	0.677946	+	0.496871i
$34$	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	0.999690	−	0.0248806i	$-0.00792055\pi$
$37$	36.0680	+	36.0680i	0.974810	+	0.974810i	−0.0248806	+	0.999690i	$0.507921\pi$
$38$	3.74368	+	13.9716i	0.0985180	+	0.367674i
$39$	14.2211	−	36.5923i	0.364644	−	0.938265i
$40$	14.6331	+	16.9116i	0.365828	+	0.422789i
$41$	−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	$-0.441428\pi$
$42$	−0.205165	−	0.466007i	−0.00488488	−	0.0110954i
$43$	−2.59980	−	9.70259i	−0.0604605	−	0.225642i	0.929084	−	0.369868i	$-0.120597\pi$
$43$	−2.59980	−	9.70259i	−0.0604605	−	0.225642i	−0.989545	+	0.144227i	$0.953931\pi$
$44$		−	20.3810i		−	0.463204i
$45$	−12.8614	+	43.1229i	−0.285808	+	0.958287i
$46$	112.951			2.45546
$47$	−44.6476	+	11.9633i	−0.949948	+	0.254538i	−0.700340	−	0.713809i	$-0.746968\pi$
$47$	−44.6476	+	11.9633i	−0.949948	+	0.254538i	−0.249608	+	0.968347i	$0.580302\pi$
$48$	−48.2931	−	35.3944i	−1.00611	−	0.737382i
$49$	−42.4312	+	24.4977i	−0.865943	+	0.499953i
$50$	−61.8413	+	7.30568i	−1.23683	+	0.146114i
$51$	−45.0012	+	36.1329i	−0.882377	+	0.708488i
$52$	−27.8636	+	7.46602i	−0.535838	+	0.143577i
$53$	28.0258	−	28.0258i	0.528789	−	0.528789i	−0.391423	−	0.920211i	$-0.628017\pi$
$53$	28.0258	−	28.0258i	0.528789	−	0.528789i	0.920211	+	0.391423i	$0.128017\pi$
$54$	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
$57$	−17.3180	−	1.89294i	−0.303824	−	0.0332096i
$58$	−17.7032	−	4.74356i	−0.305228	−	0.0817855i
$59$	−16.3509	+	9.44022i	−0.277135	+	0.160004i	−0.632126	−	0.774866i	$-0.717817\pi$
$59$	−16.3509	+	9.44022i	−0.277135	+	0.160004i	0.354991	+	0.934870i	$0.384484\pi$
$60$	31.1433	−	11.1085i	0.519055	−	0.185141i
$61$	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
$63$	0.612655	−	0.0270071i	0.00972468	−	0.000428684i
$64$		−	0.568692i		−	0.00888582i
$65$	−21.4439	+	61.8173i	−0.329907	+	0.951035i
$66$	64.3977	+	25.0273i	0.975722	+	0.379202i
$67$	12.8379	−	47.9117i	0.191610	−	0.715100i	−0.801508	−	0.597984i	$-0.795969\pi$
$67$	12.8379	−	47.9117i	0.191610	−	0.715100i	0.993118	−	0.117116i	$-0.0373648\pi$
$68$	40.9609	+	10.9754i	0.602366	+	0.161403i
$69$	−49.2792	+	126.800i	−0.714191	+	1.83768i
$70$	0.370262	+	0.763584i	0.00528945	+	0.0109083i
$71$	56.4200			0.794648			0.397324	−	0.917678i	$-0.369939\pi$
$71$	56.4200			0.794648			0.397324	+	0.917678i	$0.369939\pi$
$72$	33.9412	−	21.6430i	0.471405	−	0.300597i
$73$	−54.7135	+	54.7135i	−0.749500	+	0.749500i	−0.974385	−	0.224885i	$-0.927799\pi$
$73$	−54.7135	+	54.7135i	−0.749500	+	0.749500i	0.224885	+	0.974385i	$0.427799\pi$
$74$	110.031	+	63.5264i	1.48691	+	0.858465i
$75$	18.7791	−	72.6109i	0.250388	−	0.968146i
$76$	6.40036	+	11.0857i	0.0842152	+	0.145865i
$77$	−0.163056	+	0.608534i	−0.00211761	+	0.00790303i
$78$	10.6254	−	97.2084i	0.136223	−	1.24626i
$79$	40.9692	+	23.6536i	0.518597	+	0.299412i	0.736361	−	0.676589i	$-0.236543\pi$
$79$	40.9692	+	23.6536i	0.518597	+	0.299412i	−0.217763	+	0.976002i	$0.569876\pi$
$80$	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
$83$	−16.0841	−	60.0267i	−0.193784	−	0.723213i	−0.992578	−	0.121608i	$-0.961195\pi$
$83$	−16.0841	−	60.0267i	−0.193784	−	0.723213i	0.798794	−	0.601605i	$-0.205472\pi$
$84$	−0.282117	−	0.351360i	−0.00335854	−	0.00418285i
$85$	72.7376	−	62.9379i	0.855737	−	0.740445i
$86$	−12.5101	−	21.6682i	−0.145467	−	0.251956i
$87$	13.0488	−	17.8042i	0.149987	−	0.204646i
$88$	10.7032	+	39.9449i	0.121627	+	0.453919i
$89$		−	59.1599i		−	0.664718i	−0.943153	−	0.332359i	$-0.892156\pi$
$89$		−	59.1599i		−	0.664718i	0.943153	−	0.332359i	$-0.107844\pi$
$90$	−3.14373	+	112.044i	−0.0349304	+	1.24494i
$91$	0.891679			0.00979867
$92$	96.5530	−	25.8713i	1.04949	−	0.281210i
$93$	45.8728	−	20.1960i	0.493256	−	0.217162i
$94$	−99.7085	+	57.5668i	−1.06073	+	0.612412i
$95$	28.9598	+	2.09175i	0.304840	+	0.0220184i
$96$	−88.9828	−	34.5820i	−0.926904	−	0.360229i
$97$	−150.251	+	40.2595i	−1.54898	+	0.415047i	−0.929153	−	0.369695i	$-0.879462\pi$
$97$	−150.251	+	40.2595i	−1.54898	+	0.415047i	−0.619823	+	0.784742i	$0.712796\pi$
$98$	−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	$0.0785451\pi$
$102$	−84.9779	+	115.946i	−0.833116	+	1.13673i
$103$	88.3218	+	23.6658i	0.857493	+	0.229765i	0.660672	−	0.750675i	$-0.270271\pi$
$103$	88.3218	+	23.6658i	0.857493	+	0.229765i	0.196821	+	0.980439i	$0.436938\pi$
$104$	50.6892	−	29.2654i	0.487397	−	0.281399i
$105$	−1.01875	+	0.0825172i	−0.00970234	+	0.000785878i
$106$	49.3618	−	85.4971i	0.465677	−	0.806576i
$107$	−14.6336	−	14.6336i	−0.136762	−	0.136762i	0.635411	−	0.772174i	$-0.280831\pi$
$107$	−14.6336	−	14.6336i	−0.136762	−	0.136762i	−0.772174	+	0.635411i	$0.780831\pi$
$108$	−11.6480	−	58.3663i	−0.107852	−	0.540429i
$109$		−	112.055i		−	1.02803i	−0.857781	−	0.514015i	$-0.828157\pi$
$109$		−	112.055i		−	1.02803i	0.857781	−	0.514015i	$-0.171843\pi$
$110$	−108.790	−	37.7385i	−0.989003	−	0.343077i
$111$	−119.320	+	95.8060i	−1.07496	+	0.863117i
$112$	0.351976	−	1.31359i	0.00314264	−	0.0117285i
$113$	−35.8191	−	9.59771i	−0.316984	−	0.0849355i	0.0968194	−	0.995302i	$-0.469133\pi$
$113$	−35.8191	−	9.59771i	−0.316984	−	0.0849355i	−0.413803	+	0.910366i	$0.635800\pi$
$114$	−42.8870	+	6.61017i	−0.376202	+	0.0579840i
$115$	74.3077	−	214.210i	0.646154	−	1.86269i
$116$	−16.2196			−0.139824
$117$	104.491	+	54.3389i	0.893088	+	0.464435i
$118$	−33.2541	+	33.2541i	−0.281814	+	0.281814i
$119$	−1.13520	−	0.655407i	−0.00953948	−	0.00550762i
$120$	−55.2044	+	38.1267i	−0.460036	+	0.317723i
$121$	17.7573	+	30.7565i	0.146754	+	0.254186i
$122$	3.47543	−	12.9705i	0.0284872	−	0.106316i
$123$	171.092	−	75.3254i	1.39100	−	0.612402i
$124$	−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	0.975580	+	0.219643i	$0.0704892\pi$
$127$	151.793	+	151.793i	1.19522	+	1.19522i	0.219643	+	0.975580i	$0.429511\pi$
$128$	−33.3113	−	124.320i	−0.260245	−	0.971247i
$129$	29.7829	−	4.59044i	0.230875	−	0.0355848i
$130$	−11.7413	+	162.556i	−0.0903176	+	1.25043i
$131$	−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	$0.835159\pi$
$132$	60.7809	+	6.64367i	0.460462	+	0.0503308i
$133$	−0.102411	−	0.382203i	−0.000770006	−	0.00287370i
$134$		−	123.551i		−	0.922021i
$135$	−124.410	−	52.4126i	−0.921558	−	0.388242i
$136$	−86.0434			−0.632672
$137$	67.4699	−	18.0785i	0.492481	−	0.131960i	−0.00402717	−	0.999992i	$-0.501282\pi$
$137$	67.4699	−	18.0785i	0.492481	−	0.131960i	0.496508	+	0.868032i	$0.334615\pi$
$138$	−36.8192	+	336.847i	−0.266805	+	2.44092i
$139$	106.332	−	61.3909i	0.764980	−	0.441661i	−0.0661012	−	0.997813i	$-0.521056\pi$
$139$	106.332	−	61.3909i	0.764980	−	0.441661i	0.831081	+	0.556152i	$0.187723\pi$
$140$	0.491405	+	0.567919i	0.00351004	+	0.00405657i
$141$	−21.1234	−	137.049i	−0.149811	−	0.971981i
$142$	135.745	−	36.3728i	0.955953	−	0.256147i
$143$	−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
$147$	−59.2264	−	134.526i	−0.402901	−	0.915140i
$148$	108.607	+	29.1013i	0.733834	+	0.196630i
$149$	23.0090	−	13.2842i	0.154423	−	0.0891560i	−0.420797	−	0.907155i	$-0.638250\pi$
$149$	23.0090	−	13.2842i	0.154423	−	0.0891560i	0.575220	+	0.817999i	$0.304916\pi$
$150$	−1.62865	−	186.807i	−0.0108577	−	1.24538i
$151$	−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
$153$	−93.0876	−	145.983i	−0.608415	−	0.954136i
$154$			1.56924i			0.0101899i
$155$	−75.1656	+	36.4478i	−0.484940	+	0.235147i
$156$	−13.1826	−	85.5295i	−0.0845042	−	0.548266i
$157$	−44.6968	+	166.811i	−0.284693	+	1.06249i	0.664370	+	0.747404i	$0.268700\pi$
$157$	−44.6968	+	166.811i	−0.284693	+	1.06249i	−0.949063	+	0.315086i	$0.897967\pi$
$158$	113.820	+	30.4980i	0.720379	+	0.193025i
$159$	74.4439	+	92.7152i	0.468201	+	0.583115i
$160$	150.323	+	52.1459i	0.939520	+	0.325912i
$161$	−3.08985			−0.0191916
$162$	198.723	+	34.8680i	1.22669	+	0.215235i
$163$	−65.0824	+	65.0824i	−0.399278	+	0.399278i	−0.877978	−	0.478700i	$-0.841108\pi$
$163$	−65.0824	+	65.0824i	−0.399278	+	0.399278i	0.478700	+	0.877978i	$0.341108\pi$
$164$	−118.957	−	68.6800i	−0.725349	−	0.418780i
$165$	89.8294	−	105.664i	0.544420	−	0.640389i
$166$	−77.3960	−	134.054i	−0.466241	−	0.807553i
$167$	−51.7034	+	192.960i	−0.309601	+	1.15545i	0.619311	+	0.785146i	$0.287412\pi$
$167$	−51.7034	+	192.960i	−0.309601	+	1.15545i	−0.928912	+	0.370301i	$0.879255\pi$
$168$	0.737444	+	0.540478i	0.00438955	+	0.00321713i
$169$	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
$173$	8.94958	+	33.4003i	0.0517317	+	0.193065i	0.986956	−	0.160991i	$-0.0514689\pi$
$173$	8.94958	+	33.4003i	0.0517317	+	0.193065i	−0.935224	+	0.354056i	$0.884802\pi$
$174$	19.9172	−	51.2489i	0.114467	−	0.294534i
$175$	1.69171	−	0.199852i	0.00966690	−	0.00114201i
$176$	92.2653	+	159.808i	0.524235	+	0.908001i
$177$	−22.8230	−	51.8397i	−0.128944	−	0.292879i
$178$	−38.1392	−	142.337i	−0.214265	−	0.799648i
$179$			185.962i			1.03890i	0.854502	+	0.519448i	$0.173862\pi$
$179$			185.962i			1.03890i	−0.854502	+	0.519448i	$0.826138\pi$
$180$	22.9762	+	96.4978i	0.127646	+	0.536099i
$181$	−97.7851			−0.540249			−0.270125	−	0.962825i	$-0.587065\pi$
$181$	−97.7851			−0.540249			−0.270125	+	0.962825i	$0.587065\pi$
$182$	2.14536	−	0.574847i	0.0117877	−	0.00315850i
$183$	13.0445	+	9.56041i	0.0712814	+	0.0522427i
$184$	−175.649	+	101.411i	−0.954613	+	0.551146i
$185$	192.863	−	166.879i	1.04250	−	0.902050i
$186$	97.3490	−	78.1645i	0.523382	−	0.420239i
$187$	171.805	−	46.0350i	0.918744	−	0.246177i
$188$	−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	$0.282906\pi$
$192$	1.69598	+	0.185379i	0.00883321	+	0.000965515i
$193$	−89.2148	−	23.9050i	−0.462253	−	0.123860i	0.0201740	−	0.999796i	$-0.493578\pi$
$193$	−89.2148	−	23.9050i	−0.462253	−	0.123860i	−0.482427	+	0.875936i	$0.660245\pi$
$194$	−335.545	+	193.727i	−1.72961	+	0.998594i
$195$	−177.364	−	84.1017i	−0.909557	−	0.431291i
$196$	−54.0013	+	93.5329i	−0.275517	+	0.477209i
$197$	−170.623	−	170.623i	−0.866107	−	0.866107i	0.125932	−	0.992039i	$-0.459808\pi$
$197$	−170.623	−	170.623i	−0.866107	−	0.866107i	−0.992039	+	0.125932i	$0.959808\pi$
$198$	−95.6294	+	183.891i	−0.482977	+	0.928742i
$199$		−	36.4196i		−	0.183013i	−0.995804	−	0.0915066i	$-0.970832\pi$
$199$		−	36.4196i		−	0.183013i	0.995804	−	0.0915066i	$-0.0291683\pi$
$200$	89.6092	−	66.8838i	0.448046	−	0.334419i
$201$	138.699	+	53.9036i	0.690046	+	0.268177i
$202$	35.5931	−	132.835i	0.176204	−	0.657601i
$203$	0.484283	+	0.129763i	0.00238563	+	0.000639227i
$204$	−46.0835	+	118.577i	−0.225900	+	0.581261i
$205$	−280.346	+	135.940i	−1.36754	+	0.663121i
$206$	227.757			1.10562
$207$	−362.084	−	188.296i	−1.74920	−	0.909641i
$208$	184.681	−	184.681i	0.887887	−	0.887887i
$209$	46.4977	+	26.8455i	0.222477	+	0.128447i
$210$	−2.39788	+	0.855300i	−0.0114185	+	0.00407286i
$211$	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	$0.681619\pi$
$212$	22.6125	−	84.3909i	0.106663	−	0.398070i
$213$	−18.3914	+	168.258i	−0.0863448	+	0.789943i
$214$	−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
$218$	−72.2398	−	269.603i	−0.331375	−	1.23671i
$219$	−145.334	−	181.004i	−0.663623	−	0.826502i
$220$	−101.640	−	7.34140i	−0.462001	−	0.0333700i
$221$	−125.872	−	218.017i	−0.569558	−	0.986503i
$222$	−225.318	+	307.431i	−1.01495	+	1.38482i
$223$	−24.7802	−	92.4808i	−0.111122	−	0.414712i	0.887846	−	0.460141i	$-0.152201\pi$
$223$	−24.7802	−	92.4808i	−0.111122	−	0.414712i	−0.998968	+	0.0454290i	$0.985535\pi$
$224$		−	2.16833i		−	0.00968002i
$225$	210.421	+	79.6731i	0.935207	+	0.354102i
$226$	−92.3675			−0.408706
$227$	318.219	−	85.2664i	1.40184	−	0.375623i	0.522837	−	0.852433i	$-0.324874\pi$
$227$	318.219	−	85.2664i	1.40184	−	0.375623i	0.879007	+	0.476810i	$0.158207\pi$
$228$	−35.1467	+	15.4737i	−0.154152	+	0.0678672i
$229$	360.256	−	207.994i	1.57317	−	0.908269i	0.577391	−	0.816468i	$-0.304071\pi$
$229$	360.256	−	207.994i	1.57317	−	0.908269i	0.995777	−	0.0918017i	$-0.0292626\pi$
$230$	40.6860	−	563.289i	0.176896	−	2.44908i
$231$	−1.76164	−	0.684638i	−0.00762615	−	0.00296380i
$232$	31.7889	−	8.51781i	0.137021	−	0.0367147i
$233$	−22.0213	+	22.0213i	−0.0945121	+	0.0945121i	−0.752782	−	0.658270i	$-0.771289\pi$
$233$	−22.0213	+	22.0213i	−0.0945121	+	0.0945121i	0.658270	+	0.752782i	$0.271289\pi$
$234$	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
$237$	−83.8955	+	114.469i	−0.353989	+	0.482993i
$238$	−3.15379	−	0.845055i	−0.0132512	−	0.00355065i
$239$	−267.552	+	154.471i	−1.11946	+	0.646323i	−0.941264	−	0.337672i	$-0.890361\pi$
$239$	−267.552	+	154.471i	−1.11946	+	0.646323i	−0.178200	+	0.983994i	$0.557027\pi$
$240$	−193.908	+	228.089i	−0.807948	+	0.950370i
$241$	−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
$243$	−125.844	+	207.876i	−0.517875	+	0.855457i
$244$		−	11.8835i		−	0.0487028i
$245$	106.886	+	220.429i	0.436270	+	0.899711i
$246$	363.084	−	291.531i	1.47595	−	1.18509i
$247$	19.6682	−	73.4028i	0.0796284	−	0.297177i
$248$	72.1806	+	19.3407i	0.291051	+	0.0779868i
$249$	184.257	−	28.3995i	0.739987	−	0.114054i
$250$	14.1578	+	311.034i	0.0566311	+	1.24414i
$251$	275.877			1.09911			0.549556	−	0.835457i	$-0.314797\pi$
$251$	275.877			1.09911			0.549556	+	0.835457i	$0.314797\pi$
$252$	1.13980	−	0.726807i	0.00452302	−	0.00288416i
$253$	296.465	−	296.465i	1.17180	−	1.17180i
$254$	463.070	+	267.353i	1.82311	+	1.05257i
$255$	163.985	+	237.437i	0.643079	+	0.931125i
$256$	−159.155	−	275.665i	−0.621701	−	1.07682i
$257$	1.65593	−	6.18001i	0.00644330	−	0.0240467i	−0.962629	−	0.270822i	$-0.912704\pi$
$257$	1.65593	−	6.18001i	0.00644330	−	0.0240467i	0.969073	+	0.246776i	$0.0793711\pi$
$258$	68.6977	−	30.2449i	0.266270	−	0.117228i
$259$	−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
$263$	54.9964	+	205.249i	0.209112	+	0.780416i	0.988157	+	0.153448i	$0.0490377\pi$
$263$	54.9964	+	205.249i	0.209112	+	0.780416i	−0.779045	+	0.626968i	$0.784296\pi$
$264$	−122.614	+	18.8985i	−0.464447	+	0.0715852i
$265$	−129.670	−	149.860i	−0.489320	−	0.565509i
$266$	−0.492797	−	0.853549i	−0.00185262	−	0.00320883i
$267$	176.429	+	19.2846i	0.660782	+	0.0722269i
$268$	−28.2991	−	105.614i	−0.105594	−	0.394081i
$269$		−	349.046i		−	1.29757i	−0.760973	−	0.648784i	$-0.775278\pi$
$269$		−	349.046i		−	1.29757i	0.760973	−	0.648784i	$-0.224722\pi$
$270$	−333.118	−	45.8989i	−1.23377	−	0.169996i
$271$	−202.277			−0.746409			−0.373205	−	0.927749i	$-0.621741\pi$
$271$	−202.277			−0.746409			−0.373205	+	0.927749i	$0.621741\pi$
$272$	−370.862	+	99.3722i	−1.36346	+	0.365339i
$273$	−0.290664	+	2.65920i	−0.00106470	+	0.00974065i
$274$	150.676	−	86.9930i	0.549913	−	0.317493i
$275$	−143.141	+	181.491i	−0.520512	+	0.659969i
$276$	45.6806	+	296.377i	0.165509	+	1.07383i
$277$	−234.373	+	62.8000i	−0.846112	+	0.226715i	−0.655730	−	0.754995i	$-0.727639\pi$
$277$	−234.373	+	62.8000i	−0.846112	+	0.226715i	−0.190381	+	0.981710i	$0.560972\pi$
$278$	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	$0.000444772\pi$
$282$	−139.175	−	316.120i	−0.493530	−	1.12099i
$283$	−372.686	−	99.8610i	−1.31691	−	0.352866i	−0.469092	−	0.883149i	$-0.655419\pi$
$283$	−372.686	−	99.8610i	−1.31691	−	0.352866i	−0.847820	+	0.530283i	$0.822086\pi$
$284$	107.707	−	62.1845i	0.379249	−	0.218959i
$285$	−15.6782	+	85.6831i	−0.0550113	+	0.300642i
$286$	−150.688	+	260.999i	−0.526880	+	0.912583i
$287$	3.00235	+	3.00235i	0.0104611	+	0.0104611i
$288$	132.138	−	254.095i	0.458812	−	0.882274i
$289$			81.0774i			0.280545i
$290$	−30.0330	+	86.5774i	−0.103562	+	0.298543i
$291$	−71.0857	−	461.207i	−0.244281	−	1.58490i
$292$	−44.1453	+	164.753i	−0.151183	+	0.564222i
$293$	40.8052	+	10.9337i	0.139267	+	0.0373164i	0.327779	−	0.944754i	$-0.393700\pi$
$293$	40.8052	+	10.9337i	0.139267	+	0.0373164i	−0.188512	+	0.982071i	$0.560367\pi$
$294$	−229.223	−	285.484i	−0.779672	−	0.971032i
$295$	41.1887	+	84.9427i	0.139623	+	0.287941i
$296$	−228.143			−0.770755
$297$	−164.716	−	187.584i	−0.554598	−	0.631595i
$298$	46.7950	−	46.7950i	0.157030	−	0.157030i
$299$	−513.910	−	296.706i	−1.71876	−	0.992329i
$300$	−44.1800	−	159.313i	−0.147267	−	0.531044i
$301$	0.342223	+	0.592747i	0.00113695	+	0.00196926i
$302$	−63.4899	+	236.948i	−0.210232	+	0.784595i
$303$	133.593	+	97.9115i	0.440902	+	0.323140i
$304$	−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	0.554769	−	0.832004i	$-0.312806\pi$
$307$	−85.1111	−	85.1111i	−0.277235	−	0.277235i	−0.832004	+	0.554769i	$0.812806\pi$
$308$	0.359431	+	1.34142i	0.00116699	+	0.00435525i
$309$	−99.3675	+	255.682i	−0.321578	+	0.827450i
$310$	−157.350	+	136.150i	−0.507580	+	0.439195i
$311$	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	$0.572759\pi$
$312$	70.7531	+	160.707i	0.226773	+	0.515087i
$313$	76.9018	+	287.001i	0.245693	+	0.916937i	0.973034	+	0.230661i	$0.0740890\pi$
$313$	76.9018	+	287.001i	0.245693	+	0.916937i	−0.727342	+	0.686276i	$0.759244\pi$
$314$			430.158i			1.36993i
$315$	0.0859989	−	3.06504i	0.000273012	−	0.00973029i
$316$	104.281			0.330004
$317$	85.3965	−	22.8819i	0.269389	−	0.0721827i	−0.121596	−	0.992580i	$-0.538801\pi$
$317$	85.3965	−	22.8819i	0.269389	−	0.0721827i	0.390985	+	0.920397i	$0.372134\pi$
$318$	238.882	+	175.078i	0.751201	+	0.550561i
$319$	−58.9165	+	34.0155i	−0.184691	+	0.106632i
$320$	−2.83607	−	0.204848i	−0.00886273	−	0.000640149i
$321$	48.4109	−	38.8706i	0.150813	−	0.121092i
$322$	−7.43412	+	1.99197i	−0.0230873	+	0.00618623i
$323$	−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
$327$	334.176	+	36.5271i	1.02194	+	0.111704i
$328$	269.213	+	72.1354i	0.820771	+	0.219925i
$329$	2.72759	−	1.57478i	0.00829055	−	0.00478655i
$330$	148.008	−	312.137i	0.448509	−	0.945869i
$331$	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
$333$	−246.821	−	387.072i	−0.741204	−	1.16238i
$334$			497.589i			1.48979i
$335$	−234.312	−	81.2809i	−0.699438	−	0.242630i
$336$	3.80271	+	1.47787i	0.0113176	+	0.00439843i
$337$	7.58184	−	28.2958i	0.0224980	−	0.0839638i	−0.953764	−	0.300556i	$-0.902828\pi$
$337$	7.58184	−	28.2958i	0.0224980	−	0.0839638i	0.976262	+	0.216593i	$0.0694943\pi$
$338$	5.41056	+	1.44975i	0.0160076	+	0.00428921i
$339$	40.2988	−	103.693i	0.118875	−	0.305878i
$340$	69.4890	−	200.319i	0.204379	−	0.589173i
$341$	−154.473			−0.452999
$342$	−5.73305	−	130.054i	−0.0167633	−	0.380275i
$343$	4.72156	−	4.72156i	0.0137655	−	0.0137655i
$344$	38.9086	+	22.4639i	0.113107	+	0.0653021i
$345$	614.602	+	291.430i	1.78146	+	0.844725i
$346$	43.0650	+	74.5907i	0.124465	+	0.215580i
$347$	87.3943	−	326.160i	0.251857	−	0.939942i	−0.717956	−	0.696089i	$-0.754922\pi$
$347$	87.3943	−	326.160i	0.251857	−	0.939942i	0.969812	−	0.243853i	$-0.0784114\pi$
$348$	5.28716	−	48.3706i	0.0151930	−	0.138996i
$349$	51.4915	+	29.7286i	0.147540	+	0.0851823i	0.571953	−	0.820287i	$-0.306186\pi$
$349$	51.4915	+	29.7286i	0.147540	+	0.0851823i	−0.424413	+	0.905469i	$0.639519\pi$
$350$	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
$353$	−137.840	−	514.426i	−0.390482	−	1.45730i	−0.829342	−	0.558742i	$-0.811284\pi$
$353$	−137.840	−	514.426i	−0.390482	−	1.45730i	0.438860	−	0.898555i	$-0.355382\pi$
$354$	−88.3316	−	110.012i	−0.249524	−	0.310767i
$355$	20.3230	−	281.367i	0.0572478	−	0.792583i
$356$	−65.2043	−	112.937i	−0.183158	−	0.317239i
$357$	2.32462	−	3.17178i	0.00651155	−	0.00888455i
$358$	119.886	+	447.421i	0.334878	+	1.24978i
$359$		−	342.196i		−	0.953192i	−0.879122	−	0.476596i	$-0.841870\pi$
$359$		−	342.196i		−	0.953192i	0.879122	−	0.476596i	$-0.158130\pi$
$360$	−95.7078	−	177.061i	−0.265855	−	0.491836i
$361$	327.278			0.906588
$362$	−235.269	+	63.0401i	−0.649914	+	0.174144i
$363$	−97.5117	+	42.9306i	−0.268627	+	0.118266i
$364$	1.70223	−	0.982783i	0.00467646	−	0.00269995i
$365$	253.148	+	292.565i	0.693557	+	0.801548i
$366$	37.5482	+	14.5926i	0.102591	+	0.0398705i
$367$	355.509	−	95.2584i	0.968690	−	0.259560i	0.260416	−	0.965497i	$-0.416140\pi$
$367$	355.509	−	95.2584i	0.968690	−	0.259560i	0.708275	+	0.705937i	$0.249474\pi$
$368$	−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
$372$	65.3125	−	89.1142i	0.175571	−	0.239554i
$373$	−321.501	−	86.1459i	−0.861933	−	0.230954i	−0.199337	−	0.979931i	$-0.563879\pi$
$373$	−321.501	−	86.1459i	−0.861933	−	0.230954i	−0.662596	+	0.748977i	$0.730545\pi$
$374$	383.681	−	221.519i	1.02589	−	0.592296i
$375$	−355.347	−	119.807i	−0.947592	−	0.319484i
$376$	103.370	−	179.042i	0.274921	−	0.476177i
$377$	68.0862	+	68.0862i	0.180600	+	0.180600i
$378$	0.896843	+	4.49392i	0.00237260	+	0.0118887i
$379$		−	203.700i		−	0.537466i	−0.963215	−	0.268733i	$-0.913395\pi$
$379$		−	203.700i		−	0.537466i	0.963215	−	0.268733i	$-0.0866049\pi$
$380$	57.5901	−	27.9254i	0.151553	−	0.0734880i
$381$	−502.164	+	403.203i	−1.31802	+	1.05828i
$382$	−87.9460	+	328.219i	−0.230225	+	0.859212i
$383$	19.9865	+	5.35538i	0.0521842	+	0.0139827i	0.284817	−	0.958582i	$-0.408067\pi$
$383$	19.9865	+	5.35538i	0.0521842	+	0.0139827i	−0.232633	+	0.972565i	$0.574734\pi$
$384$	381.609	−	58.8174i	0.993774	−	0.153170i
$385$	2.97603	+	1.03236i	0.00772994	+	0.00268146i
$386$	−230.060			−0.596010
$387$	3.98132	+	90.3161i	0.0102876	+	0.233375i
$388$	−242.458	+	242.458i	−0.624892	+	0.624892i
$389$	160.439	+	92.6297i	0.412440	+	0.238123i	0.691838	−	0.722053i	$-0.256801\pi$
$389$	160.439	+	92.6297i	0.412440	+	0.238123i	−0.279397	+	0.960176i	$0.590135\pi$
$390$	−480.952	−	88.0042i	−1.23321	−	0.225652i
$391$	436.174	+	755.475i	1.11553	+	1.93216i
$392$	56.7182	−	211.675i	0.144689	−	0.539988i
$393$	4.12647	−	1.81673i	0.0104999	−	0.00462271i
$394$	−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	0.343501	−	0.939152i	$-0.388387\pi$
$397$	−236.474	−	236.474i	−0.595652	−	0.595652i	−0.939152	+	0.343501i	$0.888387\pi$
$398$	−23.4790	−	87.6248i	−0.0589925	−	0.220163i
$399$	1.17320	−	0.180825i	0.00294036	−	0.000453197i
$400$	308.986	−	391.771i	0.772466	−	0.979428i
$401$	−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	$0.860385\pi$
$402$	368.458	+	40.2743i	0.916562	+	0.100185i
$403$	56.5868	+	211.185i	0.140414	+	0.524032i
$404$		−	121.703i		−	0.301245i
$405$	196.861	−	353.936i	0.486078	−	0.873916i
$406$	1.24883			0.00307593
$407$	455.540	−	122.062i	1.11926	−	0.299906i
$408$	28.0479	−	256.602i	0.0687449	−	0.628926i
$409$	−326.511	+	188.511i	−0.798315	+	0.460907i	−0.842882	−	0.538099i	$-0.819143\pi$
$409$	−326.511	+	188.511i	−0.798315	+	0.460907i	0.0445668	+	0.999006i	$0.485809\pi$
$410$	−586.870	+	507.802i	−1.43139	+	1.23854i
$411$	31.9210	+	207.104i	0.0776666	+	0.503904i
$412$	194.691	−	52.1674i	0.472552	−	0.126620i
$413$	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
$417$	148.421	+	337.120i	0.355925	+	0.808440i
$418$	129.179	+	34.6135i	0.309041	+	0.0828074i
$419$	198.025	−	114.330i	0.472613	−	0.272863i	−0.244720	−	0.969594i	$-0.578696\pi$
$419$	198.025	−	114.330i	0.472613	−	0.272863i	0.717333	+	0.696731i	$0.245363\pi$
$420$	−1.85386	+	1.28036i	−0.00441394	+	0.00304847i
$421$	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
$423$	415.599	−	18.3205i	0.982504	−	0.0433108i
$424$			177.274i			0.418098i
$425$	−287.671	−	385.414i	−0.676873	−	0.906856i
$426$	64.2230	+	416.681i	0.150758	+	0.978125i
$427$	−0.0950727	+	0.354816i	−0.000222653	+	0.000830951i
$428$	−44.0644	−	11.8070i	−0.102954	−	0.0275865i
$429$	−227.256	−	283.034i	−0.529735	−	0.659752i
$430$	−112.566	+	54.5831i	−0.261781	+	0.126937i
$431$	46.4787			0.107839			0.0539196	−	0.998545i	$-0.482829\pi$
$431$	46.4787			0.107839			0.0539196	+	0.998545i	$0.482829\pi$
$432$	355.559	+	404.922i	0.823053	+	0.937319i
$433$	−430.638	+	430.638i	−0.994544	+	0.994544i	−0.999985	−	0.00544093i	$-0.998268\pi$
$433$	−430.638	+	430.638i	−0.994544	+	0.994544i	0.00544093	+	0.999985i	$0.498268\pi$
$434$	2.45572	+	1.41781i	0.00565834	+	0.00326684i
$435$	−84.0895	−	71.4879i	−0.193309	−	0.164340i
$436$	−123.504	−	213.916i	−0.283266	−	0.490632i
$437$	−68.1545	+	254.356i	−0.155960	+	0.582050i
$438$	−466.359	−	341.798i	−1.06475	−	0.780360i
$439$	−335.332	−	193.604i	−0.763855	−	0.441012i	0.0668232	−	0.997765i	$-0.478714\pi$
$439$	−335.332	−	193.604i	−0.763855	−	0.441012i	−0.830678	+	0.556753i	$0.812047\pi$
$440$	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
$443$	189.882	+	708.648i	0.428627	+	1.59966i	0.755874	+	0.654717i	$0.227212\pi$
$443$	189.882	+	708.648i	0.428627	+	1.59966i	−0.327247	+	0.944939i	$0.606121\pi$
$444$	−122.190	+	314.407i	−0.275203	+	0.708124i
$445$	−295.031	−	21.3099i	−0.662990	−	0.0478874i
$446$	−119.241	−	206.531i	−0.267357	−	0.463075i
$447$	32.1164	+	72.9486i	0.0718489	+	0.163196i
$448$	0.0100292	+	0.0374297i	2.23867e−5	+	8.35483e-5i
$449$			141.098i			0.314250i	0.987579	+	0.157125i	$0.0502226\pi$
$449$			141.098i			0.314250i	−0.987579	+	0.157125i	$0.949777\pi$
$450$	557.633	+	56.0371i	1.23918	+	0.124527i
$451$	−576.139			−1.27747
$452$	−78.9577	+	21.1566i	−0.174685	+	0.0468067i
$453$	−238.300	−	174.652i	−0.526048	−	0.385544i
$454$	710.657	−	410.298i	1.56532	−	0.903740i
$455$	0.321190	−	4.44681i	0.000705913	−	0.00977321i
$456$	60.7582	−	48.7846i	0.133242	−	0.106984i
$457$	−709.254	+	190.044i	−1.55198	+	0.415851i	−0.930113	−	0.367273i	$-0.880291\pi$
$457$	−709.254	+	190.044i	−1.55198	+	0.415851i	−0.621865	+	0.783124i	$0.713625\pi$
$458$	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	$0.921450\pi$
$462$	−4.67984	−	0.511530i	−0.0101295	−	0.00110721i
$463$	268.091	+	71.8346i	0.579029	+	0.155150i	0.536434	−	0.843942i	$-0.319771\pi$
$463$	268.091	+	71.8346i	0.579029	+	0.155150i	0.0425948	+	0.999092i	$0.486438\pi$
$464$	127.178	−	73.4265i	0.274091	−	0.158247i
$465$	−84.1940	−	236.043i	−0.181062	−	0.507619i
$466$	−38.7861	+	67.1795i	−0.0832320	+	0.144162i
$467$	−57.4439	−	57.4439i	−0.123006	−	0.123006i	0.642924	−	0.765930i	$-0.277721\pi$
$467$	−57.4439	−	57.4439i	−0.123006	−	0.123006i	−0.765930	+	0.642924i	$0.777721\pi$
$468$	259.366	−	11.4334i	0.554202	−	0.0244304i
$469$			3.37981i			0.00720642i
$470$	251.170	+	517.983i	0.534404	+	1.10209i
$471$	−482.900	−	187.673i	−1.02526	−	0.398456i
$472$	21.8565	−	81.5694i	0.0463061	−	0.172817i
$473$	−89.7086	−	24.0373i	−0.189659	−	0.0508189i
$474$	−128.055	+	329.497i	−0.270157	+	0.695140i
$475$	20.8631	−	143.669i	0.0439223	−	0.302461i
$476$	−2.88948			−0.00607034
$477$	−300.766	+	191.787i	−0.630536	+	0.402068i
$478$	−544.139	+	544.139i	−1.13837	+	1.13837i
$479$	419.328	+	242.099i	0.875423	+	0.505426i	0.869147	−	0.494554i	$-0.164669\pi$
$479$	419.328	+	242.099i	0.875423	+	0.505426i	0.00627671	+	0.999980i	$0.498002\pi$
$480$	−204.513	+	431.301i	−0.426069	+	0.898544i
$481$	−333.749	−	578.071i	−0.693866	−	1.20181i
$482$	−16.5771	+	61.8668i	−0.0343924	+	0.128354i
$483$	1.00721	−	9.21467i	0.00208532	−	0.0190780i
$484$	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	0.520714	−	0.853731i	$-0.325666\pi$
$487$	−162.179	−	162.179i	−0.333017	−	0.333017i	−0.853731	+	0.520714i	$0.825666\pi$
$488$	6.24069	+	23.2906i	0.0127883	+	0.0477266i
$489$	−172.876	−	215.306i	−0.353530	−	0.440299i
$490$	399.272	+	461.440i	0.814840	+	0.941715i
$491$	−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	$-0.464248\pi$
$492$	243.597	−	332.371i	0.495116	−	0.675550i
$493$	−36.6356	−	136.726i	−0.0743115	−	0.277334i
$494$		−	189.285i		−	0.383168i
$495$	285.833	+	302.336i	0.577441	+	0.610780i
$496$	333.448			0.672274
$497$	−3.71340	+	0.995002i	−0.00747163	+	0.00200202i
$498$	425.009	−	187.115i	0.853433	−	0.375733i
$499$	−422.362	+	243.851i	−0.846418	+	0.488680i	−0.859441	−	0.511236i	$-0.829188\pi$
$499$	−422.362	+	243.851i	−0.846418	+	0.488680i	0.0130228	+	0.999915i	$0.495855\pi$
$500$	83.3443	+	262.636i	0.166689	+	0.525272i
$501$	−558.597	−	217.091i	−1.11496	−	0.433316i
$502$	663.754	−	177.852i	1.32222	−	0.354288i
$503$	346.274	−	346.274i	0.688418	−	0.688418i	−0.273465	−	0.961882i	$-0.588170\pi$
$503$	346.274	−	346.274i	0.688418	−	0.688418i	0.961882	+	0.273465i	$0.0881696\pi$
$504$	−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
$507$	−3.98806	+	5.44143i	−0.00786600	+	0.0107326i
$508$	457.078	+	122.474i	0.899760	+	0.241090i
$509$	362.182	−	209.106i	0.711557	−	0.410818i	−0.100080	−	0.994979i	$-0.531910\pi$
$509$	362.182	−	209.106i	0.711557	−	0.410818i	0.811637	+	0.584162i	$0.198577\pi$
$510$	547.615	+	465.550i	1.07376	+	0.912843i
$511$	2.63618	−	4.56599i	0.00515886	−	0.00893540i
$512$	−196.607	−	196.607i	−0.383998	−	0.383998i
$513$	148.501	+	50.3049i	0.289476	+	0.0980603i
$514$		−	15.9365i		−	0.0310049i
$515$	149.836	−	431.937i	0.290943	−	0.838712i
$516$	51.7966	−	41.5891i	0.100381	−	0.0805990i
$517$	−110.610	+	412.804i	−0.213947	+	0.798460i
$518$	−8.36225	−	2.24066i	−0.0161433	−	0.00432559i
$519$	−102.525	+	15.8022i	−0.197543	+	0.0304473i
$520$	−127.688	−	263.329i	−0.245554	−	0.506403i
$521$	−17.3149			−0.0332341			−0.0166170	−	0.999862i	$-0.505290\pi$
$521$	−17.3149			−0.0332341			−0.0166170	+	0.999862i	$0.505290\pi$
$522$	146.344	+	76.1036i	0.280352	+	0.145792i
$523$	577.571	−	577.571i	1.10434	−	1.10434i	0.110462	−	0.993880i	$-0.464767\pi$
$523$	577.571	−	577.571i	1.10434	−	1.10434i	0.993880	−	0.110462i	$-0.0352329\pi$
$524$	−2.86905	−	1.65645i	−0.00547529	−	0.00316116i
$525$	0.0445528	+	5.11022i	8.48625e−5	+	0.00973375i
$526$	264.640	+	458.370i	0.503118	+	0.871427i
$527$	83.1855	−	310.453i	0.157847	−	0.589094i
$528$	−506.662	+	223.064i	−0.959587	+	0.422469i
$529$	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
$533$	211.053	+	787.659i	0.395971	+	1.47778i
$534$	436.916	−	67.3418i	0.818195	−	0.126108i
$535$	−78.2488	+	67.7066i	−0.146260	+	0.126554i
$536$	110.927	+	192.132i	0.206954	+	0.358455i
$537$	−554.584	−	60.6189i	−1.03274	−	0.112884i
$538$	−225.023	−	839.797i	−0.418258	−	1.56096i
$539$			453.003i			0.840451i
$540$	−295.269	+	37.0648i	−0.546794	+	0.0686386i
$541$	846.162			1.56407			0.782035	−	0.623234i	$-0.214182\pi$
$541$	846.162			1.56407			0.782035	+	0.623234i	$0.214182\pi$
$542$	−486.674	+	130.404i	−0.897922	+	0.240598i
$543$	31.8754	−	291.618i	0.0587024	−	0.537050i
$544$	−530.160	+	306.088i	−0.974558	+	0.562661i
$545$	−558.821	−	40.3633i	−1.02536	−	0.0740611i
$546$	1.01500	+	6.58536i	0.00185897	+	0.0120611i
$547$	66.0385	−	17.6950i	0.120728	−	0.0323491i	−0.197949	−	0.980212i	$-0.563428\pi$
$547$	66.0385	−	17.6950i	0.120728	−	0.0323491i	0.318677	+	0.947863i	$0.396761\pi$
$548$	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
$552$	−245.174	−	556.884i	−0.444156	−	1.00885i
$553$	−3.11362	−	0.834291i	−0.00563041	−	0.00150866i
$554$	−523.410	+	302.191i	−0.944784	+	0.545471i
$555$	434.805	+	629.562i	0.783433	+	1.13435i
$556$	135.327	−	234.392i	0.243393	−	0.421569i
$557$	367.003	+	367.003i	0.658893	+	0.658893i	0.955118	−	0.296225i	$-0.0957279\pi$
$557$	367.003	+	367.003i	0.658893	+	0.658893i	−0.296225	+	0.955118i	$0.595728\pi$
$558$	201.372	+	315.797i	0.360881	+	0.565945i
$559$			131.449i			0.235151i
$560$	−6.42411	−	2.22848i	−0.0114716	−	0.00397942i
$561$	81.2835	+	527.370i	0.144890	+	0.940053i
$562$	180.716	−	674.443i	0.321560	−	1.20008i
$563$	−303.953	−	81.4441i	−0.539882	−	0.144661i	−0.0214341	−	0.999770i	$-0.506823\pi$
$563$	−303.953	−	81.4441i	−0.539882	−	0.144661i	−0.518448	+	0.855109i	$0.673490\pi$
$564$	−191.377	−	238.348i	−0.339320	−	0.422603i
$565$	−60.7662	+	175.173i	−0.107551	+	0.310041i
$566$	−961.053			−1.69797
$567$	−5.43620	−	0.953838i	−0.00958765	−	0.00168225i
$568$	−178.439	+	178.439i	−0.314153	+	0.314153i
$569$	−882.789	−	509.679i	−1.55148	−	0.895745i	−0.998022	−	0.0628645i	$-0.979976\pi$
$569$	−882.789	−	509.679i	−1.55148	−	0.895745i	−0.553453	−	0.832880i	$-0.686690\pi$
$570$	17.5167	+	216.259i	0.0307311	+	0.379402i
$571$	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	$0.550579\pi$
$572$	−69.0296	+	257.622i	−0.120681	+	0.450388i
$573$	−330.092	−	241.927i	−0.576076	−	0.422210i
$574$	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	0.855277	−	0.518172i	$-0.173387\pi$
$577$	194.509	+	194.509i	0.337105	+	0.337105i	−0.518172	+	0.855277i	$0.673387\pi$
$578$	52.2689	+	195.070i	0.0904307	+	0.337492i
$579$	100.372	−	258.267i	0.173354	−	0.446058i
$580$	−5.84243	+	80.8871i	−0.0100732	+	0.139461i
$581$	2.11722	+	3.66713i	0.00364409	+	0.00631175i
$582$	−468.361	−	1063.83i	−0.804745	−	1.82788i
$583$	−94.8452	−	353.967i	−0.162685	−	0.607147i
$584$		−	346.084i		−	0.592609i
$585$	308.627	−	501.526i	0.527568	−	0.857309i
$586$	105.225			0.179565
$587$	−775.720	+	207.853i	−1.32150	+	0.354095i	−0.849539	−	0.527526i	$-0.823120\pi$
$587$	−775.720	+	207.853i	−1.32150	+	0.354095i	−0.471960	+	0.881620i	$0.656453\pi$
$588$	−261.334	−	191.534i	−0.444446	−	0.325738i
$589$	84.0216	−	48.5099i	0.142651	−	0.0823598i
$590$	153.860	+	177.817i	0.260780	+	0.301384i
$591$	564.457	−	453.220i	0.955089	−	0.766870i
$592$	−983.338	+	263.485i	−1.66104	+	0.445075i
$593$	572.308	−	572.308i	0.965106	−	0.965106i	−0.0343049	−	0.999411i	$-0.510922\pi$
$593$	572.308	−	572.308i	0.965106	−	0.965106i	0.999411	+	0.0343049i	$0.0109217\pi$
$594$	−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
$597$	108.612	+	11.8718i	0.181930	+	0.0198858i
$598$	−1427.74	−	382.561i	−2.38752	−	0.639734i
$599$	263.198	−	151.957i	0.439396	−	0.253685i	−0.263945	−	0.964538i	$-0.585024\pi$
$599$	263.198	−	151.957i	0.439396	−	0.253685i	0.703341	+	0.710852i	$0.251691\pi$
$600$	170.253	+	289.038i	0.283755	+	0.481730i
$601$	−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
$603$	−205.966	+	396.063i	−0.341568	+	0.656821i
$604$			217.090i			0.359420i
$605$	159.779	−	77.4770i	0.264098	−	0.128061i
$606$	384.544	+	149.448i	0.634561	+	0.246614i
$607$	75.9472	−	283.439i	0.125119	−	0.466950i	−0.874725	−	0.484620i	$-0.838958\pi$
$607$	75.9472	−	283.439i	0.125119	−	0.466950i	0.999844	+	0.0176696i	$0.00562469\pi$
$608$	−178.496	−	47.8279i	−0.293579	−	0.0786642i
$609$	−0.544848	+	1.40195i	−0.000894660	+	0.00230205i
$610$	−63.4321	−	22.0041i	−0.103987	−	0.0360723i
$611$	604.878			0.989980
$612$	−338.604	−	176.085i	−0.553274	−	0.287721i
$613$	610.767	−	610.767i	0.996357	−	0.996357i	−0.00363596	−	0.999993i	$-0.501157\pi$
$613$	610.767	−	610.767i	0.996357	−	0.996357i	0.999993	+	0.00363596i	$0.00115736\pi$
$614$	−259.645	−	149.906i	−0.422874	−	0.244147i
$615$	−314.019	−	880.372i	−0.510601	−	1.43150i
$616$	−1.40891	−	2.44030i	−0.00228719	−	0.00396152i
$617$	−260.666	+	972.818i	−0.422473	+	1.57669i	0.346908	+	0.937899i	$0.387232\pi$
$617$	−260.666	+	972.818i	−0.422473	+	1.57669i	−0.769381	+	0.638791i	$0.779435\pi$
$618$	−74.2429	+	679.226i	−0.120134	+	1.09907i
$619$	189.444	+	109.376i	0.306049	+	0.176697i	0.645157	−	0.764050i	$-0.276792\pi$
$619$	189.444	+	109.376i	0.306049	+	0.176697i	−0.339108	+	0.940747i	$0.610125\pi$
$620$	−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
$623$	1.04332	+	3.89373i	0.00167467	+	0.00624997i
$624$	490.560	+	610.962i	0.786154	+	0.979106i
$625$	599.185	+	177.772i	0.958695	+	0.284435i
$626$	370.048	+	640.942i	0.591131	+	1.02387i
$627$	−95.2166	+	129.916i	−0.151861	+	0.207203i
$628$	98.5271	+	367.708i	0.156890	+	0.585523i
$629$			981.257i			1.56003i
$630$	−1.76906	−	7.42986i	−0.00280803	−	0.0117934i
$631$	−427.714			−0.677835			−0.338917	−	0.940816i	$-0.610061\pi$
$631$	−427.714			−0.677835			−0.338917	+	0.940816i	$0.610061\pi$
$632$	−204.382	+	54.7639i	−0.323389	+	0.0866517i
$633$	−531.582	+	234.035i	−0.839782	+	0.369724i
$634$	190.711	−	110.107i	0.300805	−	0.173670i
$635$	811.672	−	702.317i	1.27822	−	1.10601i
$636$	244.303	+	94.9450i	0.384124	+	0.149285i
$637$	619.316	−	165.945i	0.972239	−	0.260511i
$638$	−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	$0.297934\pi$
$642$	91.4165	−	124.731i	0.142393	−	0.194286i
$643$	187.988	+	50.3713i	0.292361	+	0.0783379i	0.402019	−	0.915632i	$-0.368309\pi$
$643$	187.988	+	50.3713i	0.292361	+	0.0783379i	−0.109657	+	0.993969i	$0.534975\pi$
$644$	−5.89858	+	3.40555i	−0.00915929	+	0.00528812i
$645$	−12.1645	−	150.181i	−0.0188597	−	0.232839i
$646$	−139.129	+	240.979i	−0.215371	+	0.373033i
$647$	−139.726	−	139.726i	−0.215960	−	0.215960i	0.590833	−	0.806794i	$-0.298799\pi$
$647$	−139.726	−	139.726i	−0.215960	−	0.215960i	−0.806794	+	0.590833i	$0.798799\pi$
$648$	−340.337	+	124.197i	−0.525211	+	0.191661i
$649$			174.565i			0.268976i
$650$	806.436	+	117.108i	1.24067	+	0.180166i
$651$	−2.66304	+	2.13824i	−0.00409070	+	0.00328455i
$652$	−52.5114	+	195.975i	−0.0805390	+	0.300576i
$653$	622.466	+	166.789i	0.953240	+	0.255420i	0.701737	−	0.712437i	$-0.252408\pi$
$653$	622.466	+	166.789i	0.953240	+	0.255420i	0.251503	+	0.967856i	$0.419075\pi$
$654$	827.568	−	127.553i	1.26539	−	0.195035i
$655$	−6.76150	+	3.27865i	−0.0103229	+	0.00500557i
$656$	1243.66			1.89583
$657$	587.172	−	374.417i	0.893716	−	0.569888i
$658$	5.54730	−	5.54730i	0.00843054	−	0.00843054i
$659$	−210.200	−	121.359i	−0.318968	−	0.184156i	0.331965	−	0.943292i	$-0.392289\pi$
$659$	−210.200	−	121.359i	−0.318968	−	0.184156i	−0.650932	+	0.759136i	$0.725622\pi$
$660$	55.0258	−	300.722i	0.0833725	−	0.455639i
$661$	−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	$-0.333814\pi$
$662$	287.723	−	1073.80i	0.434627	−	1.62205i
$663$	691.210	−	304.313i	1.04255	−	0.458994i
$664$	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
$668$	113.972	+	425.349i	0.170617	+	0.636750i
$669$	283.877	−	43.7540i	0.424331	−	0.0654021i
$670$	−616.149	−	44.5041i	−0.919625	−	0.0664240i
$671$	−24.9219	−	43.1660i	−0.0371414	−	0.0643308i
$672$	6.46646	+	0.706817i	0.00962271	+	0.00105181i
$673$	125.305	+	467.643i	0.186188	+	0.694864i	0.994373	+	0.105935i	$0.0337835\pi$
$673$	125.305	+	467.643i	0.186188	+	0.694864i	−0.808185	+	0.588929i	$0.799550\pi$
$674$		−	72.9670i		−	0.108260i
$675$	−306.196	+	601.556i	−0.453624	+	0.891193i
$676$	4.95712			0.00733302
$677$	425.004	−	113.880i	0.627776	−	0.168212i	0.0691156	−	0.997609i	$-0.477982\pi$
$677$	425.004	−	113.880i	0.627776	−	0.168212i	0.558660	+	0.829397i	$0.311316\pi$
$678$	30.1094	−	275.462i	0.0444091	−	0.406286i
$679$	9.17906	−	5.29953i	0.0135185	−	0.00780490i
$680$	−30.9936	+	429.099i	−0.0455788	+	0.631028i
$681$	150.554	+	976.798i	0.221077	+	1.43436i
$682$	−371.658	+	99.5854i	−0.544953	+	0.146020i
$683$	−336.034	+	336.034i	−0.491998	+	0.491998i	−0.908935	−	0.416938i	$-0.863103\pi$
$683$	−336.034	+	336.034i	−0.491998	+	0.491998i	0.416938	+	0.908935i	$0.363103\pi$
$684$	−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
$687$	502.853	+	1142.17i	0.731954	+	1.66254i
$688$	193.647	+	51.8875i	0.281463	+	0.0754179i
$689$	−449.177	+	259.332i	−0.651926	+	0.376389i
$690$	1666.60	+	304.953i	2.41536	+	0.441960i
$691$	−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
$693$	2.61600	−	5.03045i	0.00377489	−	0.00725895i
$694$		−	841.075i		−	1.21192i
$695$	−267.855	−	552.393i	−0.385403	−	0.794810i
$696$	15.0398	+	97.5786i	0.0216089	+	0.140199i
$697$	310.258	−	1157.90i	0.445134	−	1.66126i
$698$	143.053	+	38.3309i	0.204947	+	0.0549153i
$699$	−58.4944	−	72.8512i	−0.0836830	−	0.104222i
$700$	3.00923	−	2.24607i	0.00429889	−	0.00320867i
$701$	−1057.58			−1.50868			−0.754338	−	0.656486i	$-0.772042\pi$
$701$	−1057.58			−1.50868			−0.754338	+	0.656486i	$0.772042\pi$
$702$	−282.369	+	833.559i	−0.402235	+	1.18741i
$703$	−209.448	+	209.448i	−0.297935	+	0.297935i
$704$	−4.55359	−	2.62902i	−0.00646817	−	0.00373440i
$705$	−691.075	+	55.9762i	−0.980248	+	0.0793989i
$706$	−663.280	−	1148.83i	−0.939490	−	1.62724i
$707$	−0.973672	+	3.63379i	−0.00137719	+	0.00513974i
$708$	−100.706	−	73.8079i	−0.142240	−	0.104248i
$709$	−450.749	−	260.240i	−0.635754	−	0.367053i	0.147223	−	0.989103i	$-0.452966\pi$
$709$	−450.749	−	260.240i	−0.635754	−	0.367053i	−0.782977	+	0.622051i	$0.786300\pi$
$710$	−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
$713$	−196.085	−	731.800i	−0.275014	−	1.02637i
$714$	3.54821	−	9.12988i	0.00496948	−	0.0127870i
$715$	395.845	+	457.481i	0.553630	+	0.639833i
$716$	204.962	+	355.005i	0.286260	+	0.495817i
$717$	−373.455	−	848.257i	−0.520857	−	1.18306i
$718$	−220.607	−	823.316i	−0.307252	−	1.14668i
$719$			1211.89i			1.68553i	0.538285	+	0.842763i	$0.319072\pi$
$719$			1211.89i			1.68553i	−0.538285	+	0.842763i	$0.680928\pi$
$720$	−617.006	−	652.629i	−0.856953	−	0.906430i
$721$	−6.23044			−0.00864139
$722$	787.424	−	210.990i	1.09062	−	0.292230i
$723$	−62.2198	−	45.6013i	−0.0860578	−	0.0630724i
$724$	−186.673	+	107.776i	−0.257836	+	0.148862i
$725$	144.434	+	113.914i	0.199220	+	0.157123i
$726$	−206.934	+	166.154i	−0.285034	+	0.228862i
$727$	−201.292	+	53.9360i	−0.276880	+	0.0741899i	−0.394587	−	0.918859i	$-0.629112\pi$
$727$	−201.292	+	53.9360i	−0.276880	+	0.0741899i	0.117707	+	0.993048i	$0.462446\pi$
$728$	−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
$732$	35.4394	+	3.87371i	0.0484145	+	0.00529195i
$733$	707.621	+	189.606i	0.965376	+	0.258672i	0.706874	−	0.707339i	$-0.250105\pi$
$733$	707.621	+	189.606i	0.965376	+	0.258672i	0.258502	+	0.966011i	$0.416771\pi$
$734$	793.936	−	458.379i	1.08166	−	0.624495i
$735$	−692.214	+	246.905i	−0.941788	+	0.335926i
$736$	−721.511	+	1249.69i	−0.980313	+	1.69795i
$737$	−324.286	−	324.286i	−0.440009	−	0.440009i
$738$	751.059	+	1177.83i	1.01770	+	1.59598i
$739$		−	1243.93i		−	1.68326i	−0.540056	−	0.841629i	$-0.681597\pi$
$739$		−	1243.93i		−	1.68326i	0.540056	−	0.841629i	$-0.318403\pi$
$740$	184.250	−	531.144i	0.248986	−	0.717762i
$741$	212.493	+	82.5827i	0.286766	+	0.111448i
$742$	−1.74105	+	6.49769i	−0.00234643	+	0.00875700i
$743$	−1239.64	−	332.161i	−1.66843	−	0.447054i	−0.703743	−	0.710455i	$-0.748489\pi$
$743$	−1239.64	−	332.161i	−1.66843	−	0.447054i	−0.964687	+	0.263400i	$0.915156\pi$
$744$	−81.2077	+	208.955i	−0.109150	+	0.280854i
$745$	−57.9606	−	119.531i	−0.0777995	−	0.160444i
$746$	−829.060			−1.11134
$747$	24.6311	+	558.755i	0.0329733	+	0.747999i
$748$	277.240	−	277.240i	0.370642	−	0.370642i
$749$	1.22121	+	0.705066i	0.00163045	+	0.000941343i
$750$	−932.194	−	59.1673i	−1.24292	−	0.0788897i
$751$	−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	$-0.382056\pi$
$752$	238.766	−	891.087i	0.317508	−	1.18496i
$753$	−89.9287	+	822.731i	−0.119427	+	1.09260i
$754$	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	0.986123	+	0.166015i	$0.0530901\pi$
$757$	872.169	+	872.169i	1.15214	+	1.15214i	0.166015	+	0.986123i	$0.446910\pi$
$758$	−131.321	−	490.097i	−0.173247	−	0.646566i
$759$	787.490	+	980.770i	1.03754	+	1.29219i
$760$	−98.2063	+	84.9752i	−0.129219	+	0.111809i
$761$	−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	$0.930981\pi$
$762$	−948.260	+	1293.83i	−1.24444	+	1.69794i
$763$	1.97617	+	7.37515i	0.00259000	+	0.00966599i
$764$			300.712i			0.393602i
$765$	−761.548	+	411.644i	−0.995488	+	0.538097i
$766$	51.5397			0.0672842
$767$	238.655	−	63.9473i	0.311153	−	0.0833733i
$768$	873.980	−	384.779i	1.13799	−	0.501015i
$769$	−775.372	+	447.661i	−1.00829	+	0.582134i	−0.910689	−	0.413092i	$-0.864449\pi$
$769$	−775.372	+	447.661i	−1.00829	+	0.582134i	−0.0975969	+	0.995226i	$0.531116\pi$
$770$	7.82580	+	0.565253i	0.0101634	+	0.000734094i
$771$	17.8905	+	6.95289i	0.0232042	+	0.00901802i
$772$	−196.660	+	52.6949i	−0.254741	+	0.0682576i
$773$	94.0446	−	94.0446i	0.121662	−	0.121662i	−0.643654	−	0.765316i	$-0.722583\pi$
$773$	94.0446	−	94.0446i	0.121662	−	0.121662i	0.765316	+	0.643654i	$0.222583\pi$
$774$	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
$777$	6.16372	−	8.40996i	0.00793272	−	0.0108236i
$778$	445.730	+	119.433i	0.572918	+	0.153513i
$779$	313.377	−	180.928i	0.402281	−	0.232257i
$780$	−431.285	+	34.9335i	−0.552929	+	0.0447866i
$781$	260.825	−	451.762i	0.333963	−	0.578441i
$782$	1536.46	+	1536.46i	1.96479	+	1.96479i
$783$	−149.283	+	131.084i	−0.190655	+	0.167412i
$784$		−	977.861i		−	1.24727i
$785$	815.787	+	282.990i	1.03922	+	0.360497i
$786$	8.75699	−	7.03126i	0.0111412	−	0.00894562i
$787$	−241.144	+	899.963i	−0.306410	+	1.14354i	0.625315	+	0.780372i	$0.284970\pi$
$787$	−241.144	+	899.963i	−0.306410	+	1.14354i	−0.931725	+	0.363164i	$0.881696\pi$
$788$	−513.778	−	137.666i	−0.652003	−	0.174704i
$789$	−630.030	+	97.1064i	−0.798517	+	0.123075i
$790$	193.093	−	556.635i	0.244421	−	0.704602i
$791$	2.52677			0.00319440
$792$	−16.3908	−	371.825i	−0.0206955	−	0.469476i
$793$	−49.8843	+	49.8843i	−0.0629058	+	0.0629058i
$794$	−721.400	−	416.501i	−0.908565	−	0.524560i
$795$	489.187	−	337.855i	0.615330	−	0.424975i
$796$	−40.1407	−	69.5257i	−0.0504280	−	0.0873438i
$797$	−43.8496	+	163.649i	−0.0550183	+	0.205331i	−0.987963	−	0.154687i	$-0.950563\pi$
$797$	−43.8496	+	163.649i	−0.0550183	+	0.205331i	0.932945	+	0.360019i	$0.117230\pi$
$798$	2.70612	−	1.19140i	0.00339113	−	0.00149298i
$799$	−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
$803$	185.162	+	691.034i	0.230588	+	0.860565i
$804$	324.190	−	49.9674i	0.403222	−	0.0621485i
$805$	−1.11299	+	15.4091i	−0.00138260	+	0.0191418i
$806$	272.293	+	471.626i	0.337833	+	0.585144i
$807$	1040.94	+	113.780i	1.28989	+	0.140991i
$808$	63.9130	+	238.527i	0.0791003	+	0.295206i
$809$		−	1540.82i		−	1.90459i	−0.305175	−	0.952296i	$-0.598715\pi$
$809$		−	1540.82i		−	1.90459i	0.305175	−	0.952296i	$-0.401285\pi$
$810$	245.469	−	978.474i	0.303048	−	1.20799i
$811$	−895.419			−1.10409			−0.552046	−	0.833813i	$-0.686153\pi$
$811$	−895.419			−1.10409			−0.552046	+	0.833813i	$0.686153\pi$
$812$	1.06752	−	0.286042i	0.00131469	−	0.000352269i
$813$	65.9370	−	603.238i	0.0811033	−	0.741990i
$814$	1017.33	−	587.355i	1.24979	−	0.721566i
$815$	301.123	+	348.010i	0.369476	+	0.427006i
$816$	−175.460	−	1138.39i	−0.215025	−	1.39509i
$817$	56.3434	−	15.0972i	0.0689637	−	0.0184788i
$818$	−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	$0.295067\pi$
$822$	210.317	+	477.710i	0.255860	+	0.581156i
$823$	211.257	+	56.6061i	0.256691	+	0.0687802i	0.384870	−	0.922971i	$-0.374246\pi$
$823$	211.257	+	56.6061i	0.256691	+	0.0687802i	−0.128179	+	0.991751i	$0.540913\pi$
$824$	−354.182	+	204.487i	−0.429832	+	0.248164i
$825$	−494.590	−	486.041i	−0.599504	−	0.589141i
$826$	1.60223	−	2.77514i	0.00193975	−	0.00335974i
$827$	−982.768	−	982.768i	−1.18835	−	1.18835i	−0.977522	−	0.210831i	$-0.932383\pi$
$827$	−982.768	−	982.768i	−1.18835	−	1.18835i	−0.210831	−	0.977522i	$-0.567617\pi$
$828$	−898.759	+	39.6191i	−1.08546	+	0.0478492i
$829$		−	763.031i		−	0.920424i	−0.887809	−	0.460212i	$-0.847773\pi$
$829$		−	763.031i		−	0.920424i	0.887809	−	0.460212i	$-0.152227\pi$
$830$	−696.406	+	337.687i	−0.839044	+	0.406852i
$831$	−110.885	−	719.427i	−0.133436	−	0.865736i
$832$	−1.92614	+	7.18844i	−0.00231507	+	0.00863996i
$833$	−910.427	−	243.948i	−1.09295	−	0.292855i
$834$	574.431	+	715.418i	0.688766	+	0.857816i
$835$	943.667	+	327.351i	1.13014	+	0.392037i
$836$	118.353			0.141571
$837$	−442.373	+	88.2834i	−0.528522	+	0.105476i
$838$	402.737	−	402.737i	0.480593	−	0.480593i
$839$	946.477	+	546.449i	1.12810	+	0.651309i	0.943457	−	0.331496i	$-0.107553\pi$
$839$	946.477	+	546.449i	1.12810	+	0.651309i	0.184644	+	0.982805i	$0.440887\pi$
$840$	2.96100	−	3.48295i	0.00352500	−	0.00414637i
$841$	−393.430	−	681.440i	−0.467812	−	0.810274i
$842$	264.182	−	985.940i	0.313755	−	1.17095i
$843$	678.291	+	497.125i	0.804616	+	0.589709i
$844$	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
$848$	204.735	+	764.080i	0.241432	+	0.901038i
$849$	419.295	−	1078.89i	0.493870	−	1.27077i
$850$	−940.598	−	741.842i	−1.10659	−	0.872755i
$851$	1156.51	+	2003.14i	1.35900	+	2.35386i
$852$	150.339	+	341.478i	0.176455	+	0.400795i
$853$	425.510	+	1588.02i	0.498839	+	1.86169i	0.507369	+	0.861729i	$0.330618\pi$
$853$	425.510	+	1588.02i	0.498839	+	1.86169i	−0.00853057	+	0.999964i	$0.502715\pi$
$854$			0.914971i			0.00107140i
$855$	−250.417	−	74.6866i	−0.292885	−	0.0873527i
$856$	92.5628			0.108134
$857$	−318.230	+	85.2695i	−0.371330	+	0.0994977i	−0.439658	−	0.898165i	$-0.644900\pi$
$857$	−318.230	+	85.2695i	−0.371330	+	0.0994977i	0.0683276	+	0.997663i	$0.478234\pi$
$858$	−729.240	−	534.465i	−0.849930	−	0.622920i
$859$	−1361.73	+	786.197i	−1.58525	+	0.915247i	−0.591180	+	0.806540i	$0.701338\pi$
$859$	−1361.73	+	786.197i	−1.58525	+	0.915247i	−0.994074	+	0.108707i	$0.965329\pi$
$860$	−83.7213	+	72.4417i	−0.0973503	+	0.0842346i
$861$	−9.93239	+	7.97502i	−0.0115359	+	0.00926251i
$862$	111.827	−	29.9639i	0.129729	−	0.0347609i
$863$	458.505	−	458.505i	0.531292	−	0.531292i	−0.389665	−	0.920957i	$-0.627409\pi$
$863$	458.505	−	458.505i	0.531292	−	0.531292i	0.920957	+	0.389665i	$0.127409\pi$
$864$	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
$867$	−241.792	−	26.4291i	−0.278883	−	0.0304834i
$868$	2.42395	+	0.649494i	0.00279256	+	0.000748265i
$869$	378.794	−	218.697i	0.435897	−	0.251665i
$870$	−248.404	−	117.788i	−0.285522	−	0.135388i
$871$	−324.550	+	562.137i	−0.372618	+	0.645393i
$872$	354.396	+	354.396i	0.406418	+	0.406418i
$873$	1398.60	−	61.6532i	1.60206	−	0.0706222i
$874$			655.913i			0.750472i
$875$	−0.387295	−	8.50854i	−0.000442622	−	0.00972405i
$876$	−476.941	−	185.357i	−0.544454	−	0.211595i
$877$	279.129	−	1041.72i	0.318277	−	1.18783i	−0.602623	−	0.798026i	$-0.705878\pi$
$877$	279.129	−	1041.72i	0.318277	−	1.18783i	0.920900	−	0.389800i	$-0.127456\pi$
$878$	−931.615	−	249.625i	−1.06106	−	0.284311i
$879$	−45.9083	+	118.127i	−0.0522279	+	0.134387i
$880$	830.199	−	402.564i	0.943408	−	0.457459i
$881$	1585.15			1.79927			0.899633	−	0.436647i	$-0.143834\pi$
$881$	1585.15			1.79927			0.899633	+	0.436647i	$0.143834\pi$
$882$	926.101	−	590.539i	1.05000	−	0.669545i
$883$	−1004.45	+	1004.45i	−1.13755	+	1.13755i	−0.148657	+	0.988889i	$0.547495\pi$
$883$	−1004.45	+	1004.45i	−1.13755	+	1.13755i	−0.988889	+	0.148657i	$0.952505\pi$
$884$	−480.584	−	277.466i	−0.543648	−	0.313875i
$885$	−266.746	+	95.1454i	−0.301408	+	0.107509i
$886$	913.702	+	1582.58i	1.03127	+	1.78621i
$887$	81.0299	−	302.408i	0.0913528	−	0.340933i	−0.905088	−	0.425223i	$-0.860196\pi$
$887$	81.0299	−	302.408i	0.0913528	−	0.340933i	0.996441	+	0.0842901i	$0.0268622\pi$
$888$	74.3688	−	680.378i	0.0837487	−	0.766191i
$889$	−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
$893$	−69.4713	−	259.270i	−0.0777954	−	0.290336i
$894$	124.300	+	154.808i	0.139038	+	0.173163i
$895$	927.395	+	66.9852i	1.03620	+	0.0748438i
$896$	4.38491	+	7.59489i	0.00489387	+	0.00847644i
$897$	1052.37	−	1435.88i	1.17321	−	1.60076i
$898$	90.9632	+	339.479i	0.101295	+	0.378039i
$899$			122.932i			0.136743i
$900$	489.511	−	79.8233i	0.543902	−	0.0886926i
$901$	762.464			0.846242
$902$	−1386.18	+	371.425i	−1.53678	+	0.411779i
$903$	−1.87927	+	0.827369i	−0.00208114	+	0.000916245i
$904$	143.639	−	82.9302i	0.158893	−	0.0917370i
$905$	−35.2230	+	487.655i	−0.0389205	+	0.538845i
$906$	−685.938	−	266.581i	−0.757106	−	0.294239i
$907$	−357.992	+	95.9237i	−0.394699	+	0.105759i	−0.450709	−	0.892671i	$-0.648829\pi$
$907$	−357.992	+	95.9237i	−0.394699	+	0.105759i	0.0560100	+	0.998430i	$0.482162\pi$
$908$	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	$-0.0141393\pi$
$912$	205.537	−	280.440i	0.225369	−	0.307500i
$913$	−554.997	−	148.711i	−0.607883	−	0.162882i
$914$	−1583.93	+	914.484i	−1.73297	+	1.00053i
$915$	52.3766	−	61.6093i	0.0572422	−	0.0673326i
$916$	458.489	−	794.127i	0.500534	−	0.866951i
$917$	0.0724117	+	0.0724117i	7.89659e−5	+	7.89659e-5i
$918$	972.172	−	853.657i	1.05901	−	0.929909i
$919$			1321.17i			1.43762i	0.695205	+	0.718811i	$0.255313\pi$
$919$			1321.17i			1.43762i	−0.695205	+	0.718811i	$0.744687\pi$
$920$	442.467	+	912.491i	0.480942	+	0.991838i
$921$	281.565	−	226.077i	0.305717	−	0.245470i
$922$	−413.938	+	1544.84i	−0.448956	+	1.67553i
$923$	−713.166	−	191.092i	−0.772661	−	0.207034i
$924$	−4.11759	+	0.634643i	−0.00445626	+	0.000686843i
$925$	−762.757	−	1021.92i	−0.824602	−	1.10478i
$926$	691.330			0.746577
$927$	−730.114	−	379.683i	−0.787609	−	0.409583i
$928$	165.567	−	165.567i	0.178413	−	0.178413i
$929$	672.297	+	388.151i	0.723678	+	0.417816i	0.816105	−	0.577904i	$-0.196129\pi$
$929$	672.297	+	388.151i	0.723678	+	0.417816i	−0.0924267	+	0.995719i	$0.529462\pi$
$930$	−354.741	−	513.636i	−0.381442	−	0.552297i
$931$	−142.259	−	246.400i	−0.152802	−	0.264662i
$932$	−17.7678	+	66.3103i	−0.0190642	+	0.0711484i
$933$	−1247.05	+	549.027i	−1.33660	+	0.588454i
$934$	−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	0.847020	−	0.531561i	$-0.178394\pi$
$937$	295.586	+	295.586i	0.315459	+	0.315459i	−0.531561	+	0.847020i	$0.678394\pi$
$938$	2.17890	+	8.13175i	0.00232292	+	0.00866925i
$939$	−880.974	+	135.784i	−0.938205	+	0.144605i
$940$	333.349	+	385.253i	0.354626	+	0.409843i
$941$	−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	$0.849849\pi$
$942$	−1282.83	−	140.220i	−1.36182	−	0.148854i
$943$	−731.341	−	2729.40i	−0.775548	−	2.89438i
$944$		−	376.820i		−	0.399174i
$945$	9.11265	+	1.25559i	0.00964301	+	0.00132867i
$946$	−231.333			−0.244538
$947$	−177.098	+	47.4532i	−0.187009	+	0.0501090i	−0.351108	−	0.936335i	$-0.614195\pi$
$947$	−177.098	+	47.4532i	−0.187009	+	0.0501090i	0.164099	+	0.986444i	$0.447528\pi$
$948$	−33.9929	+	310.991i	−0.0358575	+	0.328050i
$949$	876.908	−	506.283i	0.924034	−	0.533491i
$950$	−42.4244	−	359.115i	−0.0446573	−	0.378016i
$951$	40.4023	+	262.131i	0.0424840	+	0.275638i
$952$	5.66313	−	1.51743i	0.00594866	−	0.00159394i
$953$	−16.8810	+	16.8810i	−0.0177135	+	0.0177135i	−0.715908	−	0.698195i	$-0.753987\pi$
$953$	−16.8810	+	16.8810i	−0.0177135	+	0.0177135i	0.698195	+	0.715908i	$0.253987\pi$
$954$	−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
$957$	−82.2369	−	186.791i	−0.0859320	−	0.195184i
$958$	1164.97	+	312.153i	1.21604	+	0.325838i
$959$	−4.12185	+	2.37975i	−0.00429807	+	0.00248149i
$960$	1.53539	−	8.39107i	0.00159937	−	0.00874070i
$961$	340.934	−	590.514i	0.354770	−	0.614479i
$962$	−1175.66	−	1175.66i	−1.22210	−	1.22210i
$963$	100.141	+	157.044i	0.103988	+	0.163078i
$964$			56.6819i			0.0587987i
$965$	−151.351	+	436.304i	−0.156840	+	0.452129i
$966$	−3.51719	−	22.8196i	−0.00364098	−	0.0236228i
$967$	−311.140	+	1161.19i	−0.321758	+	1.20082i	0.595772	+	0.803153i	$0.296846\pi$
$967$	−311.140	+	1161.19i	−0.321758	+	1.20082i	−0.917531	+	0.397665i	$0.869821\pi$
$968$	−153.434	−	41.1125i	−0.158506	−	0.0424716i
$969$	−209.825	−	261.324i	−0.216538	−	0.269684i
$970$	845.253	+	1743.15i	0.871395	+	1.79706i
$971$	−608.975			−0.627163			−0.313582	−	0.949561i	$-0.601529\pi$
$971$	−608.975			−0.627163			−0.313582	+	0.949561i	$0.601529\pi$
$972$	−11.1225	+	535.540i	−0.0114429	+	0.550967i
$973$	−5.91580	+	5.91580i	−0.00607996	+	0.00607996i
$974$	−494.753	−	285.646i	−0.507960	−	0.293271i
$975$	−483.304	+	854.220i	−0.495696	+	0.876123i
$976$	53.7969	+	93.1790i	0.0551198	+	0.0954702i
$977$	−22.8425	+	85.2493i	−0.0233802	+	0.0872562i	−0.976630	−	0.214927i	$-0.931049\pi$
$977$	−22.8425	+	85.2493i	−0.0233802	+	0.0872562i	0.953250	+	0.302183i	$0.0977154\pi$
$978$	−554.739	−	406.572i	−0.567218	−	0.415718i
$979$	−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
$983$	−369.494	−	1378.97i	−0.375884	−	1.40282i	−0.852049	−	0.523461i	$-0.824640\pi$
$983$	−369.494	−	1378.97i	−0.375884	−	1.40282i	0.476166	−	0.879356i	$-0.342026\pi$
$984$	−302.881	+	779.343i	−0.307806	+	0.792015i
$985$	−912.359	+	789.439i	−0.926253	+	0.801461i
$986$	−176.289	−	305.341i	−0.178792	−	0.309676i
$987$	3.80723	+	8.64766i	0.00385738	+	0.00876156i
$988$	−43.3555	−	161.805i	−0.0438821	−	0.163770i
$989$		−	455.499i		−	0.460565i
$990$	882.619	+	543.143i	0.891534	+	0.548630i
$991$	14.7275			0.0148613			0.00743063	−	0.999972i	$-0.497635\pi$
$991$	14.7275			0.0148613			0.00743063	+	0.999972i	$0.497635\pi$
$992$	513.545	−	137.604i	0.517687	−	0.138714i
$993$	1079.92	+	791.484i	1.08754	+	0.797063i
$994$	−8.29290	+	4.78791i	−0.00834296	+	0.00481681i
$995$	−181.625	−	13.1187i	−0.182538	−	0.0131846i
$996$	320.448	−	257.298i	0.321735	−	0.258331i
$997$	222.758	−	59.6878i	0.223428	−	0.0598674i	−0.145368	−	0.989378i	$-0.546437\pi$
$997$	222.758	−	59.6878i	0.223428	−	0.0598674i	0.368796	+	0.929510i	$0.379770\pi$
$998$	−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.7.9	✓	40
3.2	odd	2		135.3.l.a.127.2		40
5.2	odd	4		225.3.o.b.43.9		40
5.3	odd	4	inner	45.3.k.a.43.2	yes	40
5.4	even	2		225.3.o.b.7.2		40
9.2	odd	6		405.3.g.g.82.9		20
9.4	even	3	inner	45.3.k.a.22.2	yes	40
9.5	odd	6		135.3.l.a.37.9		40
9.7	even	3		405.3.g.h.82.2		20
15.8	even	4		135.3.l.a.73.9		40
45.4	even	6		225.3.o.b.157.9		40
45.13	odd	12	inner	45.3.k.a.13.9	yes	40
45.22	odd	12		225.3.o.b.193.2		40
45.23	even	12		135.3.l.a.118.2		40
45.38	even	12		405.3.g.g.163.9		20
45.43	odd	12		405.3.g.h.163.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.9	✓	40	1.1	even	1	trivial
45.3.k.a.13.9	yes	40	45.13	odd	12	inner
45.3.k.a.22.2	yes	40	9.4	even	3	inner
45.3.k.a.43.2	yes	40	5.3	odd	4	inner
135.3.l.a.37.9		40	9.5	odd	6
135.3.l.a.73.9		40	15.8	even	4
135.3.l.a.118.2		40	45.23	even	12
135.3.l.a.127.2		40	3.2	odd	2
225.3.o.b.7.2		40	5.4	even	2
225.3.o.b.43.9		40	5.2	odd	4
225.3.o.b.157.9		40	45.4	even	6
225.3.o.b.193.2		40	45.22	odd	12
405.3.g.g.82.9		20	9.2	odd	6
405.3.g.g.163.9		20	45.38	even	12
405.3.g.h.82.2		20	9.7	even	3
405.3.g.h.163.2		20	45.43	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(2.40598 - 0.644680i) q^{2} +(-0.325974 + 2.98224i) q^{3} +(1.90902 - 1.10217i) q^{4} +(0.360208 - 4.98701i) q^{5} +(1.13830 + 7.38535i) q^{6} +(-0.0658171 + 0.0176356i) 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} +(2.66465 + 6.05242i) q^{12} +(-12.6403 - 3.38696i) q^{13} +(-0.146985 + 0.0848619i) q^{14} +(14.7550 + 2.69986i) q^{15} +(-9.97912 + 17.2843i) q^{16} +(13.6029 + 13.6029i) q^{17} +(-22.3959 + 0.987258i) q^{18} +5.80704i q^{19} +(-4.80889 - 9.91729i) q^{20} +(-0.0311390 - 0.202031i) q^{21} +(5.96060 - 22.2453i) q^{22} +(43.8013 + 11.7365i) q^{23} +(-8.40093 - 10.4628i) q^{24} +(-24.7405 - 3.59273i) q^{25} -32.5958 q^{26} +(8.66274 - 25.5726i) q^{27} +(-0.106208 + 0.106208i) q^{28} +(-6.37222 - 3.67900i) q^{29} +(37.2408 - 3.01646i) q^{30} +(-8.35363 - 14.4689i) q^{31} +(-8.23618 + 30.7378i) q^{32} +(22.3722 + 16.3967i) 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} +(3.74368 + 13.9716i) q^{38} +(14.2211 - 36.5923i) q^{39} +(14.6331 + 16.9116i) q^{40} +(-31.1567 - 53.9649i) q^{41} +(-0.205165 - 0.466007i) q^{42} +(-2.59980 - 9.70259i) q^{43} -20.3810i q^{44} +(-12.8614 + 43.1229i) q^{45} +112.951 q^{46} +(-44.6476 + 11.9633i) q^{47} +(-48.2931 - 35.3944i) q^{48} +(-42.4312 + 24.4977i) q^{49} +(-61.8413 + 7.30568i) q^{50} +(-45.0012 + 36.1329i) q^{51} +(-27.8636 + 7.46602i) 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} +(-17.3180 - 1.89294i) q^{57} +(-17.7032 - 4.74356i) q^{58} +(-16.3509 + 9.44022i) q^{59} +(31.1433 - 11.1085i) q^{60} +(2.69547 - 4.66870i) q^{61} +(-29.4265 - 29.4265i) q^{62} +(0.612655 - 0.0270071i) q^{63} -0.568692i q^{64} +(-21.4439 + 61.8173i) q^{65} +(64.3977 + 25.0273i) q^{66} +(12.8379 - 47.9117i) q^{67} +(40.9609 + 10.9754i) q^{68} +(-49.2792 + 126.800i) q^{69} +(0.370262 + 0.763584i) q^{70} +56.4200 q^{71} +(33.9412 - 21.6430i) q^{72} +(-54.7135 + 54.7135i) q^{73} +(110.031 + 63.5264i) q^{74} +(18.7791 - 72.6109i) q^{75} +(6.40036 + 11.0857i) q^{76} +(-0.163056 + 0.608534i) q^{77} +(10.6254 - 97.2084i) 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} +(-16.0841 - 60.0267i) q^{83} +(-0.282117 - 0.351360i) q^{84} +(72.7376 - 62.9379i) q^{85} +(-12.5101 - 21.6682i) q^{86} +(13.0488 - 17.8042i) q^{87} +(10.7032 + 39.9449i) q^{88} -59.1599i q^{89} +(-3.14373 + 112.044i) q^{90} +0.891679 q^{91} +(96.5530 - 25.8713i) q^{92} +(45.8728 - 20.1960i) q^{93} +(-99.7085 + 57.5668i) q^{94} +(28.9598 + 2.09175i) q^{95} +(-88.9828 - 34.5820i) q^{96} +(-150.251 + 40.2595i) 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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