LMFDB - Embedded newform 66.3.g.a.59.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(5,66)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("66.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.g (of order $10$, 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:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.6
Character	$\chi$	$=$	66.59
Dual form			66.3.g.a.47.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.831254 - 1.14412i) q^{2} +(1.02326 - 2.82009i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(3.31466 + 4.56224i) q^{5} +(-2.37594 - 3.51495i) q^{6} +(-1.24997 - 3.84700i) q^{7} +(-2.68999 - 0.874032i) q^{8} +(-6.90587 - 5.77140i) q^{9} +7.97508 q^{10} +(-10.5955 + 2.95553i) q^{11} +(-5.99655 - 0.203448i) q^{12} +(16.9796 + 12.3364i) q^{13} +(-5.44049 - 1.76772i) q^{14} +(16.2577 - 4.67928i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(11.8269 + 16.2783i) q^{17} +(-12.3437 + 3.10366i) q^{18} +(-3.25301 + 10.0117i) q^{19} +(6.62932 - 9.12447i) q^{20} +(-12.1280 - 0.411471i) q^{21} +(-5.42607 + 14.5794i) q^{22} -21.5005i q^{23} +(-5.21742 + 6.69167i) q^{24} +(-2.10161 + 6.46810i) q^{25} +(28.2287 - 9.17205i) q^{26} +(-23.3424 + 13.5695i) q^{27} +(-6.54492 + 4.75516i) q^{28} +(-27.9234 + 9.07286i) q^{29} +(8.16061 - 22.4905i) q^{30} +(15.6952 + 11.4033i) q^{31} +5.65685i q^{32} +(-2.50713 + 32.9046i) q^{33} +28.4556 q^{34} +(13.4077 - 18.4542i) q^{35} +(-6.70979 + 16.7027i) q^{36} +(-13.4612 - 41.4293i) q^{37} +(8.75057 + 12.0441i) q^{38} +(52.1643 - 35.2606i) q^{39} +(-4.92887 - 15.1695i) q^{40} +(-53.4514 - 17.3674i) q^{41} +(-10.5522 + 13.5338i) q^{42} -7.63681 q^{43} +(12.1701 + 18.3272i) q^{44} +(3.43989 - 50.6364i) q^{45} +(-24.5992 - 17.8724i) q^{46} +(-36.8620 - 11.9772i) q^{47} +(3.31909 + 11.5319i) q^{48} +(26.4048 - 19.1842i) q^{49} +(5.65333 + 7.78114i) q^{50} +(58.0085 - 16.6960i) q^{51} +(12.9712 - 39.9214i) q^{52} +(-13.2137 + 18.1871i) q^{53} +(-3.87825 + 37.9863i) q^{54} +(-48.6043 - 38.5427i) q^{55} +11.4409i q^{56} +(24.9053 + 19.4184i) q^{57} +(-12.8310 + 39.4897i) q^{58} +(100.895 - 32.7829i) q^{59} +(-18.9483 - 28.0320i) q^{60} +(-29.3348 + 21.3130i) q^{61} +(26.0935 - 8.47828i) q^{62} +(-13.5705 + 33.7810i) q^{63} +(6.47214 + 4.70228i) q^{64} +118.356i q^{65} +(35.5629 + 30.2206i) q^{66} -27.9454 q^{67} +(23.6538 - 32.5567i) q^{68} +(-60.6335 - 22.0007i) q^{69} +(-9.96859 - 30.6802i) q^{70} +(-57.4186 - 79.0299i) q^{71} +(13.5324 + 21.5610i) q^{72} +(6.13612 + 18.8850i) q^{73} +(-58.5899 - 19.0370i) q^{74} +(16.0902 + 12.5453i) q^{75} +21.0539 q^{76} +(24.6140 + 37.0667i) q^{77} +(3.01931 - 88.9929i) q^{78} +(27.5593 + 20.0230i) q^{79} +(-21.4529 - 6.97048i) q^{80} +(14.3820 + 79.7130i) q^{81} +(-64.3021 + 46.7182i) q^{82} +(52.3490 + 72.0522i) q^{83} +(6.71283 + 23.3231i) q^{84} +(-35.0635 + 107.914i) q^{85} +(-6.34812 + 8.73744i) q^{86} +(-2.98666 + 88.0306i) q^{87} +(31.0851 + 1.31047i) q^{88} +44.9681i q^{89} +(-55.0748 - 46.0274i) q^{90} +(26.2342 - 80.7406i) q^{91} +(-40.8964 + 13.2880i) q^{92} +(48.2186 - 32.5935i) q^{93} +(-44.3450 + 32.2186i) q^{94} +(-56.4585 + 18.3445i) q^{95} +(15.9529 + 5.78845i) q^{96} +(-148.040 - 107.557i) q^{97} -46.1573i q^{98} +(90.2287 + 40.7404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.831254	−	1.14412i	0.415627	−	0.572061i
$2$	0.831254	−	1.14412i	0.415627	−	0.572061i
$3$	1.02326	−	2.82009i	0.341088	−	0.940031i
$3$	1.02326	−	2.82009i	0.341088	−	0.940031i
$4$	−0.618034	−	1.90211i	−0.154508	−	0.475528i
$5$	3.31466	+	4.56224i	0.662932	+	0.912447i	0.999574	−	0.0291853i	$-0.00929130\pi$
$5$	3.31466	+	4.56224i	0.662932	+	0.912447i	−0.336642	+	0.941633i	$0.609291\pi$
$6$	−2.37594	−	3.51495i	−0.395990	−	0.585826i
$7$	−1.24997	−	3.84700i	−0.178567	−	0.549572i	0.821212	−	0.570624i	$-0.193299\pi$
$7$	−1.24997	−	3.84700i	−0.178567	−	0.549572i	−0.999778	+	0.0210517i	$0.993299\pi$
$8$	−2.68999	−	0.874032i	−0.336249	−	0.109254i
$9$	−6.90587	−	5.77140i	−0.767318	−	0.641266i
$10$	7.97508			0.797508
$11$	−10.5955	+	2.95553i	−0.963228	+	0.268684i
$11$	−10.5955	+	2.95553i	−0.963228	+	0.268684i
$12$	−5.99655	−	0.203448i	−0.499712	−	0.0169540i
$13$	16.9796	+	12.3364i	1.30612	+	0.948952i	0.999995	−	0.00303880i	$-0.000967283\pi$
$13$	16.9796	+	12.3364i	1.30612	+	0.948952i	0.306125	+	0.951991i	$0.400967\pi$
$14$	−5.44049	−	1.76772i	−0.388606	−	0.126266i
$15$	16.2577	−	4.67928i	1.08385	−	0.311952i
$16$	−3.23607	+	2.35114i	−0.202254	+	0.146946i
$17$	11.8269	+	16.2783i	0.695701	+	0.957550i	0.999988	+	0.00496931i	$0.00158179\pi$
$17$	11.8269	+	16.2783i	0.695701	+	0.957550i	−0.304287	+	0.952580i	$0.598418\pi$
$18$	−12.3437	+	3.10366i	−0.685762	+	0.172426i
$19$	−3.25301	+	10.0117i	−0.171211	+	0.526933i	−0.999440	−	0.0334564i	$-0.989349\pi$
$19$	−3.25301	+	10.0117i	−0.171211	+	0.526933i	0.828229	+	0.560389i	$0.189349\pi$
$20$	6.62932	−	9.12447i	0.331466	−	0.456224i
$21$	−12.1280	−	0.411471i	−0.577522	−	0.0195939i
$22$	−5.42607	+	14.5794i	−0.246640	+	0.662698i
$23$		−	21.5005i		−	0.934805i	−0.884045	−	0.467402i	$-0.845190\pi$
$23$		−	21.5005i		−	0.934805i	0.884045	−	0.467402i	$-0.154810\pi$
$24$	−5.21742	+	6.69167i	−0.217393	+	0.278820i
$25$	−2.10161	+	6.46810i	−0.0840645	+	0.258724i
$26$	28.2287	−	9.17205i	1.08572	−	0.352771i
$27$	−23.3424	+	13.5695i	−0.864533	+	0.502575i
$28$	−6.54492	+	4.75516i	−0.233747	+	0.169827i
$29$	−27.9234	+	9.07286i	−0.962876	+	0.312857i	−0.747937	−	0.663770i	$-0.768955\pi$
$29$	−27.9234	+	9.07286i	−0.962876	+	0.312857i	−0.214939	+	0.976627i	$0.568955\pi$
$30$	8.16061	−	22.4905i	0.272020	−	0.749683i
$31$	15.6952	+	11.4033i	0.506298	+	0.367847i	0.811418	−	0.584467i	$-0.198696\pi$
$31$	15.6952	+	11.4033i	0.506298	+	0.367847i	−0.305119	+	0.952314i	$0.598696\pi$
$32$			5.65685i			0.176777i
$33$	−2.50713	+	32.9046i	−0.0759736	+	0.997110i
$34$	28.4556			0.836929
$35$	13.4077	−	18.4542i	0.383078	−	0.527262i
$36$	−6.70979	+	16.7027i	−0.186383	+	0.463963i
$37$	−13.4612	−	41.4293i	−0.363817	−	1.11971i	−0.950719	−	0.310054i	$-0.899653\pi$
$37$	−13.4612	−	41.4293i	−0.363817	−	1.11971i	0.586902	−	0.809658i	$-0.300347\pi$
$38$	8.75057	+	12.0441i	0.230278	+	0.316951i
$39$	52.1643	−	35.2606i	1.33755	−	0.904119i
$40$	−4.92887	−	15.1695i	−0.123222	−	0.379238i
$41$	−53.4514	−	17.3674i	−1.30369	−	0.423595i	−0.426828	−	0.904333i	$-0.640369\pi$
$41$	−53.4514	−	17.3674i	−1.30369	−	0.423595i	−0.876864	+	0.480738i	$0.840369\pi$
$42$	−10.5522	+	13.5338i	−0.251243	+	0.322234i
$43$	−7.63681			−0.177600			−0.0888001	−	0.996049i	$-0.528303\pi$
$43$	−7.63681			−0.177600			−0.0888001	+	0.996049i	$0.528303\pi$
$44$	12.1701	+	18.3272i	0.276594	+	0.416528i
$45$	3.43989	−	50.6364i	0.0764420	−	1.12525i
$46$	−24.5992	−	17.8724i	−0.534766	−	0.388530i
$47$	−36.8620	−	11.9772i	−0.784298	−	0.254834i	−0.110624	−	0.993862i	$-0.535285\pi$
$47$	−36.8620	−	11.9772i	−0.784298	−	0.254834i	−0.673674	+	0.739029i	$0.735285\pi$
$48$	3.31909	+	11.5319i	0.0691477	+	0.240247i
$49$	26.4048	−	19.1842i	0.538874	−	0.391515i
$50$	5.65333	+	7.78114i	0.113067	+	0.155623i
$51$	58.0085	−	16.6960i	1.13742	−	0.327372i
$52$	12.9712	−	39.9214i	0.249447	−	0.767719i
$53$	−13.2137	+	18.1871i	−0.249315	+	0.343152i	−0.915271	−	0.402838i	$-0.868024\pi$
$53$	−13.2137	+	18.1871i	−0.249315	+	0.343152i	0.665956	+	0.745991i	$0.268024\pi$
$54$	−3.87825	+	37.9863i	−0.0718194	+	0.703450i
$55$	−48.6043	−	38.5427i	−0.883715	−	0.700776i
$56$			11.4409i			0.204302i
$57$	24.9053	+	19.4184i	0.436936	+	0.340674i
$58$	−12.8310	+	39.4897i	−0.221224	+	0.680856i
$59$	100.895	−	32.7829i	1.71009	−	0.555642i	0.719742	−	0.694242i	$-0.244260\pi$
$59$	100.895	−	32.7829i	1.71009	−	0.555642i	0.990348	+	0.138600i	$0.0442602\pi$
$60$	−18.9483	−	28.0320i	−0.315806	−	0.467201i
$61$	−29.3348	+	21.3130i	−0.480899	+	0.349393i	−0.801674	−	0.597762i	$-0.796057\pi$
$61$	−29.3348	+	21.3130i	−0.480899	+	0.349393i	0.320775	+	0.947155i	$0.396057\pi$
$62$	26.0935	−	8.47828i	0.420862	−	0.136746i
$63$	−13.5705	+	33.7810i	−0.215405	+	0.536206i
$64$	6.47214	+	4.70228i	0.101127	+	0.0734732i
$65$			118.356i			1.82086i
$66$	35.5629	+	30.2206i	0.538831	+	0.457887i
$67$	−27.9454			−0.417095			−0.208548	−	0.978012i	$-0.566874\pi$
$67$	−27.9454			−0.417095			−0.208548	+	0.978012i	$0.566874\pi$
$68$	23.6538	−	32.5567i	0.347850	−	0.478775i
$69$	−60.6335	−	22.0007i	−0.878746	−	0.318850i
$70$	−9.96859	−	30.6802i	−0.142408	−	0.438288i
$71$	−57.4186	−	79.0299i	−0.808712	−	1.11310i	−0.991521	−	0.129948i	$-0.958519\pi$
$71$	−57.4186	−	79.0299i	−0.808712	−	1.11310i	0.182809	−	0.983148i	$-0.441481\pi$
$72$	13.5324	+	21.5610i	0.187949	+	0.299458i
$73$	6.13612	+	18.8850i	0.0840564	+	0.258699i	0.984247	−	0.176796i	$-0.0565733\pi$
$73$	6.13612	+	18.8850i	0.0840564	+	0.258699i	−0.900191	+	0.435495i	$0.856573\pi$
$74$	−58.5899	−	19.0370i	−0.791756	−	0.257257i
$75$	16.0902	+	12.5453i	0.214535	+	0.167271i
$76$	21.0539			0.277025
$77$	24.6140	+	37.0667i	0.319662	+	0.481385i
$78$	3.01931	−	88.9929i	0.0387091	−	1.14094i
$79$	27.5593	+	20.0230i	0.348852	+	0.253456i	0.748387	−	0.663262i	$-0.230828\pi$
$79$	27.5593	+	20.0230i	0.348852	+	0.253456i	−0.399535	+	0.916718i	$0.630828\pi$
$80$	−21.4529	−	6.97048i	−0.268162	−	0.0871310i
$81$	14.3820	+	79.7130i	0.177555	+	0.984111i
$82$	−64.3021	+	46.7182i	−0.784172	+	0.569734i
$83$	52.3490	+	72.0522i	0.630711	+	0.868099i	0.998078	−	0.0619773i	$-0.0197406\pi$
$83$	52.3490	+	72.0522i	0.630711	+	0.868099i	−0.367367	+	0.930076i	$0.619741\pi$
$84$	6.71283	+	23.3231i	0.0799146	+	0.277655i
$85$	−35.0635	+	107.914i	−0.412512	+	1.26958i
$86$	−6.34812	+	8.73744i	−0.0738154	+	0.101598i
$87$	−2.98666	+	88.0306i	−0.0343294	+	1.01185i
$88$	31.0851	+	1.31047i	0.353240	+	0.0148917i
$89$			44.9681i			0.505259i	0.967563	+	0.252630i	$0.0812954\pi$
$89$			44.9681i			0.505259i	−0.967563	+	0.252630i	$0.918705\pi$
$90$	−55.0748	−	46.0274i	−0.611943	−	0.511415i
$91$	26.2342	−	80.7406i	0.288288	−	0.887259i
$92$	−40.8964	+	13.2880i	−0.444526	+	0.144435i
$93$	48.2186	−	32.5935i	0.518480	−	0.350468i
$94$	−44.3450	+	32.2186i	−0.471756	+	0.342751i
$95$	−56.4585	+	18.3445i	−0.594300	+	0.193100i
$96$	15.9529	+	5.78845i	0.166176	+	0.0602964i
$97$	−148.040	−	107.557i	−1.52618	−	1.10884i	−0.958314	−	0.285718i	$-0.907768\pi$
$97$	−148.040	−	107.557i	−1.52618	−	1.10884i	−0.567869	−	0.823119i	$-0.692232\pi$
$98$		−	46.1573i		−	0.470993i
$99$	90.2287	+	40.7404i	0.911401	+	0.411519i
$100$	13.6019			0.136019
$101$	100.252	−	137.985i	0.992597	−	1.36619i	0.0628383	−	0.998024i	$-0.479985\pi$
$101$	100.252	−	137.985i	0.992597	−	1.36619i	0.929759	−	0.368169i	$-0.120015\pi$
$102$	29.1176	−	80.2475i	0.285466	−	0.786740i
$103$	21.9087	+	67.4280i	0.212706	+	0.654641i	0.999309	+	0.0371816i	$0.0118380\pi$
$103$	21.9087	+	67.4280i	0.212706	+	0.654641i	−0.786603	+	0.617459i	$0.788162\pi$
$104$	−34.8926	−	48.0255i	−0.335505	−	0.461783i
$105$	−38.3228	−	56.6945i	−0.364979	−	0.539948i
$106$	9.82433	+	30.2362i	0.0926823	+	0.285247i
$107$	−84.1874	−	27.3541i	−0.786798	−	0.255646i	−0.112058	−	0.993702i	$-0.535744\pi$
$107$	−84.1874	−	27.3541i	−0.786798	−	0.255646i	−0.674740	+	0.738056i	$0.735744\pi$
$108$	40.2372	+	36.0135i	0.372567	+	0.333458i
$109$	122.131			1.12047			0.560234	−	0.828334i	$-0.310711\pi$
$109$	122.131			1.12047			0.560234	+	0.828334i	$0.310711\pi$
$110$	−84.5001	+	23.5706i	−0.768182	+	0.214278i
$111$	−130.609	−	4.43124i	−1.17666	−	0.0399210i
$112$	13.0898	+	9.51032i	0.116873	+	0.0849136i
$113$	122.728	+	39.8768i	1.08609	+	0.352892i	0.796735	−	0.604329i	$-0.206559\pi$
$113$	122.728	+	39.8768i	1.08609	+	0.352892i	0.289356	+	0.957222i	$0.406559\pi$
$114$	42.9197	−	12.3531i	0.376489	−	0.108361i
$115$	98.0904	−	71.2669i	0.852960	−	0.619712i
$116$	34.5152	+	47.5061i	0.297545	+	0.409536i
$117$	−46.0605	−	183.189i	−0.393679	−	1.56572i
$118$	46.3620	−	142.688i	0.392898	−	1.20922i
$119$	47.8396	−	65.8456i	0.402014	−	0.553324i
$120$	−47.8230	−	1.62251i	−0.398525	−	0.0135209i
$121$	103.530	−	62.6306i	0.855617	−	0.517609i
$122$			51.2791i			0.420321i
$123$	−103.673	+	132.966i	−0.842866	+	1.08103i
$124$	11.9901	−	36.9017i	0.0966944	−	0.297595i
$125$	97.6056	−	31.7140i	0.780845	−	0.253712i
$126$	27.3690	+	43.6068i	0.217215	+	0.346086i
$127$	−3.82636	+	2.78001i	−0.0301288	+	0.0218899i	−0.602748	−	0.797932i	$-0.705927\pi$
$127$	−3.82636	+	2.78001i	−0.0301288	+	0.0218899i	0.572619	+	0.819822i	$0.305927\pi$
$128$	10.7600	−	3.49613i	0.0840623	−	0.0273135i
$129$	−7.81446	+	21.5365i	−0.0605772	+	0.166950i
$130$	135.413	+	98.3836i	1.04164	+	0.756797i
$131$		−	82.4708i		−	0.629548i	−0.949167	−	0.314774i	$-0.898071\pi$
$131$		−	82.4708i		−	0.629548i	0.949167	−	0.314774i	$-0.101929\pi$
$132$	64.1378	−	15.5673i	0.485892	−	0.117934i
$133$	42.5813			0.320160
$134$	−23.2297	+	31.9729i	−0.173356	+	0.238604i
$135$	−139.280	−	61.5152i	−1.03170	−	0.455668i
$136$	−17.5865	−	54.1257i	−0.129313	−	0.397983i
$137$	41.4798	+	57.0921i	0.302772	+	0.416730i	0.933110	−	0.359590i	$-0.117084\pi$
$137$	41.4798	+	57.0921i	0.302772	+	0.416730i	−0.630338	+	0.776321i	$0.717084\pi$
$138$	−75.5733	+	51.0840i	−0.547632	+	0.370174i
$139$	79.8398	+	245.722i	0.574387	+	1.76778i	0.638257	+	0.769823i	$0.279656\pi$
$139$	79.8398	+	245.722i	0.574387	+	1.76778i	−0.0638699	+	0.997958i	$0.520344\pi$
$140$	−43.3883	−	14.0977i	−0.309917	−	0.100698i
$141$	−71.4963	+	91.6985i	−0.507066	+	0.650344i
$142$	−138.149			−0.972882
$143$	−216.368	−	80.5267i	−1.51306	−	0.563124i
$144$	35.9172	+	2.43997i	0.249425	+	0.0169442i
$145$	−133.949	−	97.3197i	−0.923787	−	0.671171i
$146$	26.7075	+	8.67778i	0.182928	+	0.0594368i
$147$	−27.0822	−	94.0945i	−0.184233	−	0.640099i
$148$	−70.4838	+	51.2095i	−0.476242	+	0.346010i
$149$	−32.5506	−	44.8020i	−0.218460	−	0.300685i	0.685695	−	0.727889i	$-0.259498\pi$
$149$	−32.5506	−	44.8020i	−0.218460	−	0.300685i	−0.904155	+	0.427204i	$0.859498\pi$
$150$	27.7284	−	7.98077i	0.184856	−	0.0532051i
$151$	−8.70590	+	26.7940i	−0.0576549	+	0.177444i	−0.975737	−	0.218948i	$-0.929738\pi$
$151$	−8.70590	+	26.7940i	−0.0576549	+	0.177444i	0.918082	+	0.396391i	$0.129738\pi$
$152$	17.5011	−	24.0883i	0.115139	−	0.158475i
$153$	12.2737	−	180.674i	0.0802206	−	1.18087i
$154$	62.8693	+	2.65040i	0.408242	+	0.0172104i
$155$			109.403i			0.705828i
$156$	−99.3090	−	77.4302i	−0.636596	−	0.496347i
$157$	−70.7523	+	217.753i	−0.450651	+	1.38696i	0.425514	+	0.904952i	$0.360093\pi$
$157$	−70.7523	+	217.753i	−0.450651	+	1.38696i	−0.876165	+	0.482010i	$0.839907\pi$
$158$	45.8176	−	14.8870i	0.289985	−	0.0942218i
$159$	37.7682	+	55.8740i	0.237536	+	0.351409i
$160$	−25.8079	+	18.7505i	−0.161299	+	0.117191i
$161$	−82.7126	+	26.8749i	−0.513743	+	0.166925i
$162$	103.156	+	49.8070i	0.636768	+	0.307451i
$163$	−61.7634	−	44.8737i	−0.378916	−	0.275299i	0.381982	−	0.924170i	$-0.375242\pi$
$163$	−61.7634	−	44.8737i	−0.378916	−	0.275299i	−0.760899	+	0.648871i	$0.775242\pi$
$164$			112.404i			0.685391i
$165$	−158.429	+	97.6295i	−0.960175	+	0.591694i
$166$	125.952			0.758746
$167$	−36.1481	+	49.7536i	−0.216456	+	0.297925i	−0.903412	−	0.428773i	$-0.858946\pi$
$167$	−36.1481	+	49.7536i	−0.216456	+	0.297925i	0.686957	+	0.726698i	$0.258946\pi$
$168$	32.2645	+	11.7071i	0.192051	+	0.0696850i
$169$	83.8957	+	258.204i	0.496424	+	1.52784i
$170$	94.3206	+	129.821i	0.554827	+	0.763654i
$171$	80.2465	−	50.3652i	0.469278	−	0.294534i
$172$	4.71981	+	14.5261i	0.0274407	+	0.0844539i
$173$	98.4104	+	31.9755i	0.568846	+	0.184829i	0.579298	−	0.815116i	$-0.303327\pi$
$173$	98.4104	+	31.9755i	0.568846	+	0.184829i	−0.0104515	+	0.999945i	$0.503327\pi$
$174$	98.2351	+	76.5929i	0.564570	+	0.440189i
$175$	27.5098			0.157199
$176$	27.3389	−	34.4758i	0.155335	−	0.195885i
$177$	10.7916	−	318.080i	0.0609698	−	1.79706i
$178$	51.4490	+	37.3799i	0.289039	+	0.209999i
$179$	180.570	+	58.6707i	1.00877	+	0.327769i	0.766365	−	0.642406i	$-0.222064\pi$
$179$	180.570	+	58.6707i	1.00877	+	0.327769i	0.242405	+	0.970175i	$0.422064\pi$
$180$	−98.4421	+	24.7520i	−0.546901	+	0.137511i
$181$	114.896	−	83.4770i	0.634786	−	0.461199i	−0.223269	−	0.974757i	$-0.571673\pi$
$181$	114.896	−	83.4770i	0.634786	−	0.461199i	0.858055	+	0.513558i	$0.171673\pi$
$182$	−70.5698	−	97.1311i	−0.387746	−	0.533687i
$183$	30.0874	+	104.536i	0.164412	+	0.571234i
$184$	−18.7921	+	57.8362i	−0.102131	+	0.314327i
$185$	144.391	−	198.737i	0.780493	−	1.07426i
$186$	2.79093	−	82.2616i	0.0150050	−	0.442266i
$187$	−173.423	−	137.523i	−0.927397	−	0.735415i
$188$			77.5180i			0.412330i
$189$	81.3793	+	72.8368i	0.430578	+	0.385380i
$190$	−25.9430	+	79.8443i	−0.136542	+	0.420233i
$191$	−289.190	+	93.9635i	−1.51408	+	0.491955i	−0.944088	−	0.329693i	$-0.893055\pi$
$191$	−289.190	+	93.9635i	−1.51408	+	0.491955i	−0.569995	+	0.821648i	$0.693055\pi$
$192$	19.8836	−	13.4404i	0.103560	−	0.0700019i
$193$	76.0544	−	55.2568i	0.394064	−	0.286305i	−0.373055	−	0.927809i	$-0.621690\pi$
$193$	76.0544	−	55.2568i	0.394064	−	0.286305i	0.767119	+	0.641505i	$0.221690\pi$
$194$	−246.117	+	79.9683i	−1.26865	+	0.412208i
$195$	333.774	+	121.109i	1.71166	+	0.621072i
$196$	−52.8096	−	38.3684i	−0.269437	−	0.195757i
$197$		−	202.364i		−	1.02723i	−0.858021	−	0.513614i	$-0.828306\pi$
$197$		−	202.364i		−	1.02723i	0.858021	−	0.513614i	$-0.171694\pi$
$198$	121.615	−	69.3671i	0.614217	−	0.350339i
$199$	−159.417			−0.801090			−0.400545	−	0.916277i	$-0.631179\pi$
$199$	−159.417			−0.801090			−0.400545	+	0.916277i	$0.631179\pi$
$200$	11.3067	−	15.5623i	0.0565333	−	0.0778114i
$201$	−28.5955	+	78.8086i	−0.142266	+	0.392083i
$202$	−74.5372	−	229.402i	−0.368996	−	1.13565i
$203$	69.8067	+	96.0807i	0.343875	+	0.473304i
$204$	−67.6089	−	100.020i	−0.331416	−	0.490294i
$205$	−97.9389	−	301.425i	−0.477751	−	1.47036i
$206$	95.3576	+	30.9836i	0.462901	+	0.150406i
$207$	−124.088	+	148.480i	−0.599459	+	0.717293i
$208$	−83.9516			−0.403614
$209$	4.87734	−	115.694i	0.0233366	−	0.553558i
$210$	−96.7215	−	3.28152i	−0.460579	−	0.0156263i
$211$	139.991	+	101.709i	0.663463	+	0.482034i	0.867831	−	0.496860i	$-0.165514\pi$
$211$	139.991	+	101.709i	0.663463	+	0.482034i	−0.204368	+	0.978894i	$0.565514\pi$
$212$	42.7604	+	13.8937i	0.201700	+	0.0655363i
$213$	−281.626	+	81.0574i	−1.32219	+	0.380551i
$214$	−101.278	+	73.5825i	−0.473260	+	0.343843i
$215$	−25.3134	−	34.8409i	−0.117737	−	0.162051i
$216$	74.6511	−	16.1000i	0.345607	−	0.0745369i
$217$	24.2499	−	74.6334i	0.111751	−	0.343933i
$218$	101.522	−	139.733i	0.465697	−	0.640977i
$219$	59.5364	+	2.01992i	0.271856	+	0.00922338i
$220$	−43.2734	+	116.272i	−0.196697	+	0.528507i
$221$			422.301i			1.91086i
$222$	−113.639	+	145.749i	−0.511888	+	0.656528i
$223$	96.6507	−	297.460i	0.433411	−	1.33390i	−0.461295	−	0.887247i	$-0.652615\pi$
$223$	96.6507	−	297.460i	0.433411	−	1.33390i	0.894706	−	0.446656i	$-0.147385\pi$
$224$	21.7619	−	7.07088i	0.0971515	−	0.0315664i
$225$	51.8434	−	32.5386i	0.230415	−	0.144616i
$226$	147.642	−	107.268i	0.653285	−	0.474639i
$227$	142.562	−	46.3213i	0.628028	−	0.204059i	0.0223264	−	0.999751i	$-0.492893\pi$
$227$	142.562	−	46.3213i	0.628028	−	0.204059i	0.605701	+	0.795692i	$0.292893\pi$
$228$	21.5437	−	59.3740i	0.0944898	−	0.260412i
$229$	−66.8573	−	48.5747i	−0.291953	−	0.212117i	0.432161	−	0.901796i	$-0.357751\pi$
$229$	−66.8573	−	48.5747i	−0.291953	−	0.212117i	−0.724114	+	0.689680i	$0.757751\pi$
$230$		−	171.468i		−	0.745514i
$231$	129.718	−	31.4848i	0.561550	−	0.136298i
$232$	83.0438			0.357947
$233$	−106.571	+	146.683i	−0.457387	+	0.629539i	−0.973964	−	0.226701i	$-0.927206\pi$
$233$	−106.571	+	146.683i	−0.457387	+	0.629539i	0.516577	+	0.856241i	$0.327206\pi$
$234$	−247.879	−	99.5779i	−1.05931	−	0.425547i
$235$	−67.5421	−	207.873i	−0.287413	−	0.884567i
$236$	−124.713	−	171.653i	−0.528447	−	0.727345i
$237$	84.6672	−	57.2311i	0.357246	−	0.241481i
$238$	−35.5686	−	109.469i	−0.149448	−	0.459953i
$239$	−147.850	−	48.0393i	−0.618619	−	0.201001i	−0.0170917	−	0.999854i	$-0.505441\pi$
$239$	−147.850	−	48.0393i	−0.618619	−	0.201001i	−0.601527	+	0.798853i	$0.705441\pi$
$240$	−41.6094	+	53.3666i	−0.173372	+	0.222361i
$241$	−8.20602			−0.0340499			−0.0170249	−	0.999855i	$-0.505419\pi$
$241$	−8.20602			−0.0340499			−0.0170249	+	0.999855i	$0.505419\pi$
$242$	14.4023	−	170.513i	0.0595138	−	0.704598i
$243$	239.515	+	41.0089i	0.985657	+	0.168761i
$244$	58.6696	+	42.6260i	0.240449	+	0.174697i
$245$	175.046	+	56.8758i	0.714473	+	0.232146i
$246$	65.9518	+	229.143i	0.268097	+	0.931476i
$247$	−178.743	+	129.864i	−0.723656	+	0.525767i
$248$	−32.2533	−	44.3929i	−0.130054	−	0.179003i
$249$	256.761	−	73.9007i	1.03117	−	0.296790i
$250$	44.8504	−	138.035i	0.179401	−	0.552141i
$251$	−87.4201	+	120.324i	−0.348287	+	0.479377i	−0.946839	−	0.321708i	$-0.895743\pi$
$251$	−87.4201	+	120.324i	−0.348287	+	0.479377i	0.598552	+	0.801084i	$0.295743\pi$
$252$	72.6422	+	4.93482i	0.288263	+	0.0195826i
$253$	63.5453	+	227.809i	0.251167	+	0.900430i
$254$			6.68872i			0.0263336i
$255$	268.449	+	209.307i	1.05274	+	0.820812i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−179.297	+	58.2572i	−0.697654	+	0.226682i	−0.636308	−	0.771435i	$-0.719539\pi$
$257$	−179.297	+	58.2572i	−0.697654	+	0.226682i	−0.0613460	+	0.998117i	$0.519539\pi$
$258$	18.1446	+	26.8430i	0.0703280	+	0.104043i
$259$	−142.553	+	103.571i	−0.550397	+	0.399887i
$260$	225.126	−	73.1479i	0.865869	−	0.281338i
$261$	245.198	+	98.5011i	0.939457	+	0.377399i
$262$	−94.3567	−	68.5542i	−0.360140	−	0.261657i
$263$		−	225.855i		−	0.858765i	−0.903123	−	0.429383i	$-0.858731\pi$
$263$		−	225.855i		−	0.858765i	0.903123	−	0.429383i	$-0.141269\pi$
$264$	35.5039	−	86.3219i	0.134484	−	0.326977i
$265$	−126.773			−0.478387
$266$	35.3959	−	48.7183i	0.133067	−	0.183151i
$267$	126.814	+	46.0142i	0.474959	+	0.172338i
$268$	17.2712	+	53.1553i	0.0644447	+	0.198341i
$269$	−58.6740	−	80.7579i	−0.218119	−	0.300215i	0.685910	−	0.727687i	$-0.259404\pi$
$269$	−58.6740	−	80.7579i	−0.218119	−	0.300215i	−0.904029	+	0.427471i	$0.859404\pi$
$270$	−186.158	+	108.218i	−0.689472	+	0.400808i
$271$	−52.5846	−	161.839i	−0.194039	−	0.597191i	−0.999986	−	0.00520380i	$-0.998344\pi$
$271$	−52.5846	−	161.839i	−0.194039	−	0.597191i	0.805947	−	0.591987i	$-0.201656\pi$
$272$	−76.5454	−	24.8711i	−0.281417	−	0.0914379i
$273$	−200.852	−	156.602i	−0.735720	−	0.573633i
$274$	99.8006			0.364236
$275$	3.15102	−	74.7442i	0.0114583	−	0.271797i
$276$	−4.37423	+	128.929i	−0.0158487	+	0.467134i
$277$	−66.8096	−	48.5400i	−0.241190	−	0.175235i	0.460623	−	0.887596i	$-0.347626\pi$
$277$	−66.8096	−	48.5400i	−0.241190	−	0.175235i	−0.701813	+	0.712361i	$0.747626\pi$
$278$	347.503	+	112.911i	1.25001	+	0.406153i
$279$	−42.5765	−	169.333i	−0.152604	−	0.606928i
$280$	−52.1962	+	37.9228i	−0.186415	+	0.135439i
$281$	2.65837	+	3.65893i	0.00946038	+	0.0130211i	0.813721	−	0.581256i	$-0.197438\pi$
$281$	2.65837	+	3.65893i	0.00946038	+	0.0130211i	−0.804261	+	0.594277i	$0.797438\pi$
$282$	45.4827	+	158.025i	0.161286	+	0.560373i
$283$	−126.009	+	387.817i	−0.445262	+	1.37038i	0.436934	+	0.899494i	$0.356064\pi$
$283$	−126.009	+	387.817i	−0.445262	+	1.37038i	−0.882196	+	0.470883i	$0.843936\pi$
$284$	−114.837	+	158.060i	−0.404356	+	0.556548i
$285$	−6.03873	+	177.989i	−0.0211885	+	0.624524i
$286$	−271.989	+	180.613i	−0.951010	+	0.631515i
$287$			227.336i			0.792113i
$288$	32.6480	−	39.0655i	0.113361	−	0.135644i
$289$	−35.8028	+	110.190i	−0.123885	+	0.381279i
$290$	−222.691	+	72.3568i	−0.767902	+	0.249506i
$291$	−454.805	+	307.427i	−1.56290	+	1.05645i
$292$	32.1291	−	23.3432i	0.110031	−	0.0799424i
$293$	−121.156	+	39.3658i	−0.413500	+	0.134354i	−0.508377	−	0.861135i	$-0.669754\pi$
$293$	−121.156	+	39.3658i	−0.413500	+	0.134354i	0.0948767	+	0.995489i	$0.469754\pi$
$294$	−130.168	−	47.2311i	−0.442748	−	0.160650i
$295$	483.997	+	351.644i	1.64067	+	1.19201i
$296$			123.210i			0.416251i
$297$	207.220	−	212.765i	0.697709	−	0.716381i
$298$	−78.3168			−0.262808
$299$	265.238	−	365.069i	0.887085	−	1.22097i
$300$	13.9184	−	38.3587i	0.0463945	−	0.127862i
$301$	9.54576	+	29.3788i	0.0317135	+	0.0976041i
$302$	23.4188	+	32.2332i	0.0775457	+	0.106733i
$303$	−286.548	−	423.916i	−0.945702	−	1.39906i
$304$	−13.0120	−	40.0469i	−0.0428027	−	0.131733i
$305$	−194.470	−	63.1871i	−0.637606	−	0.207171i
$306$	−196.510	−	164.229i	−0.642191	−	0.536694i
$307$	−153.177			−0.498947			−0.249473	−	0.968382i	$-0.580257\pi$
$307$	−153.177			−0.498947			−0.249473	+	0.968382i	$0.580257\pi$
$308$	55.2927	−	69.7270i	0.179522	−	0.226386i
$309$	212.572	+	7.21202i	0.687934	+	0.0233399i
$310$	125.171	+	90.9420i	0.403777	+	0.293361i
$311$	30.6291	+	9.95201i	0.0984860	+	0.0320000i	0.357845	−	0.933781i	$-0.383511\pi$
$311$	30.6291	+	9.95201i	0.0984860	+	0.0320000i	−0.259360	+	0.965781i	$0.583511\pi$
$312$	−171.141	+	49.2576i	−0.548528	+	0.157877i
$313$	198.484	−	144.207i	0.634133	−	0.460725i	−0.223696	−	0.974659i	$-0.571812\pi$
$313$	198.484	−	144.207i	0.634133	−	0.460725i	0.857830	+	0.513934i	$0.171812\pi$
$314$	190.323	+	261.957i	0.606125	+	0.834259i
$315$	−199.098	+	50.0606i	−0.632058	+	0.158922i
$316$	21.0535	−	64.7959i	0.0666248	−	0.205050i
$317$	20.3067	−	27.9497i	0.0640589	−	0.0881694i	−0.775786	−	0.630997i	$-0.782646\pi$
$317$	20.3067	−	27.9497i	0.0640589	−	0.0881694i	0.839844	+	0.542827i	$0.182646\pi$
$318$	95.3217	+	3.23403i	0.299754	+	0.0101699i
$319$	269.048	−	178.660i	0.843410	−	0.560063i
$320$			45.1139i			0.140981i
$321$	−163.287	+	209.426i	−0.508683	+	0.652417i
$322$	−38.0069	+	116.973i	−0.118034	+	0.363271i
$323$	−201.447	+	65.4542i	−0.623676	+	0.202645i
$324$	142.735	−	76.6214i	0.440539	−	0.236486i
$325$	−115.477	+	83.8993i	−0.355315	+	0.258152i
$326$	−102.682	+	33.3634i	−0.314976	+	0.102342i
$327$	124.972	−	344.421i	0.382178	−	1.05328i
$328$	128.604	+	93.4364i	0.392086	+	0.284867i
$329$			156.779i			0.476533i
$330$	−19.9946	+	262.417i	−0.0605896	+	0.795203i
$331$	58.5743			0.176962			0.0884808	−	0.996078i	$-0.471799\pi$
$331$	58.5743			0.176962			0.0884808	+	0.996078i	$0.471799\pi$
$332$	104.698	−	144.104i	0.315355	−	0.434049i
$333$	−146.144	+	363.795i	−0.438871	+	1.09248i
$334$	26.8759	+	82.7157i	0.0804669	+	0.247652i
$335$	−92.6294	−	127.493i	−0.276506	−	0.380577i
$336$	40.2143	−	27.1830i	0.119686	−	0.0809018i
$337$	98.4177	+	302.898i	0.292041	+	0.898808i	0.984199	+	0.177063i	$0.0566597\pi$
$337$	98.4177	+	302.898i	0.292041	+	0.898808i	−0.692159	+	0.721745i	$0.743340\pi$
$338$	365.156	+	118.646i	1.08034	+	0.351025i
$339$	238.040	−	305.301i	0.702182	−	0.900592i
$340$	226.936			0.667458
$341$	−200.002	−	74.4357i	−0.586516	−	0.218286i
$342$	9.08118	−	133.678i	0.0265532	−	0.390872i
$343$	−267.157	−	194.101i	−0.778884	−	0.565893i
$344$	20.5430	+	6.67481i	0.0597179	+	0.0194035i
$345$	−100.607	−	349.549i	−0.291614	−	1.01319i
$346$	118.388	−	86.0138i	0.342162	−	0.248595i
$347$	29.8163	+	41.0386i	0.0859260	+	0.118267i	0.849816	−	0.527080i	$-0.176713\pi$
$347$	29.8163	+	41.0386i	0.0859260	+	0.118267i	−0.763890	+	0.645346i	$0.776713\pi$
$348$	169.290	−	48.7249i	0.486465	−	0.140014i
$349$	151.663	−	466.770i	0.434564	−	1.33745i	−0.458968	−	0.888453i	$-0.651781\pi$
$349$	151.663	−	466.770i	0.434564	−	1.33745i	0.893533	−	0.448998i	$-0.148219\pi$
$350$	22.8676	−	31.4745i	0.0653360	−	0.0899273i
$351$	−563.743	−	57.5559i	−1.60611	−	0.163977i
$352$	−16.7190	−	59.9373i	−0.0474971	−	0.170276i
$353$			359.397i			1.01812i	0.860731	+	0.509060i	$0.170007\pi$
$353$			359.397i			1.01812i	−0.860731	+	0.509060i	$0.829993\pi$
$354$	−354.952	−	276.752i	−1.00269	−	0.781786i
$355$	170.230	−	523.914i	0.479521	−	1.47581i
$356$	85.5343	−	27.7918i	0.240265	−	0.0780668i
$357$	−136.738	−	202.290i	−0.383020	−	0.566637i
$358$	217.226	−	157.824i	0.606776	−	0.440849i
$359$	23.4437	−	7.61733i	0.0653029	−	0.0212182i	−0.276183	−	0.961105i	$-0.589070\pi$
$359$	23.4437	−	7.61733i	0.0653029	−	0.0212182i	0.341486	+	0.939887i	$0.389070\pi$
$360$	−53.5111	+	133.205i	−0.148642	+	0.370014i
$361$	202.403	+	147.054i	0.560672	+	0.407352i
$362$		−	200.846i		−	0.554823i
$363$	−70.6862	−	356.051i	−0.194728	−	0.980857i
$364$	−169.791			−0.466460
$365$	−65.8188	+	90.5918i	−0.180325	+	0.248197i
$366$	144.612	+	52.4721i	0.395115	+	0.143366i
$367$	111.647	+	343.615i	0.304216	+	0.936281i	0.979968	+	0.199153i	$0.0638189\pi$
$367$	111.647	+	343.615i	0.304216	+	0.936281i	−0.675752	+	0.737129i	$0.736181\pi$
$368$	50.5507	+	69.5771i	0.137366	+	0.189068i
$369$	268.894	+	428.426i	0.728709	+	1.16105i
$370$	−107.354	−	330.402i	−0.290147	−	0.892980i
$371$	86.4825	+	28.0999i	0.233106	+	0.0757409i
$372$	−91.7974	−	71.5734i	−0.246767	−	0.192402i
$373$	−76.6743			−0.205561			−0.102781	−	0.994704i	$-0.532774\pi$
$373$	−76.6743			−0.205561			−0.102781	+	0.994704i	$0.532774\pi$
$374$	−301.502	+	84.1013i	−0.806154	+	0.224870i
$375$	10.4398	−	307.709i	0.0278394	−	0.820557i
$376$	88.6901	+	64.4371i	0.235878	+	0.171375i
$377$	−586.054	−	190.420i	−1.55452	−	0.505094i
$378$	150.981	−	32.5620i	0.399421	−	0.0861429i
$379$	150.923	−	109.652i	0.398213	−	0.289318i	−0.370600	−	0.928793i	$-0.620848\pi$
$379$	150.923	−	109.652i	0.398213	−	0.289318i	0.768813	+	0.639474i	$0.220848\pi$
$380$	69.7865	+	96.0529i	0.183649	+	0.252771i
$381$	3.92453	+	13.6354i	0.0103006	+	0.0357884i
$382$	−132.884	+	408.976i	−0.347865	+	1.07062i
$383$	198.180	−	272.771i	0.517441	−	0.712196i	−0.467711	−	0.883881i	$-0.654921\pi$
$383$	198.180	−	272.771i	0.517441	−	0.712196i	0.985152	+	0.171686i	$0.0549213\pi$
$384$	1.15087	−	33.9216i	0.00299707	−	0.0883375i
$385$	−87.5200	+	235.158i	−0.227325	+	0.610800i
$386$		−	132.948i		−	0.344425i
$387$	52.7387	+	44.0750i	0.136276	+	0.113889i
$388$	−113.092	+	348.062i	−0.291475	+	0.897068i
$389$	705.064	−	229.089i	1.81251	−	0.588919i	0.812523	−	0.582929i	$-0.198093\pi$
$389$	705.064	−	229.089i	1.81251	−	0.588919i	0.999982	−	0.00598950i	$-0.00190653\pi$
$390$	416.015	−	281.206i	1.06670	−	0.721042i
$391$	349.993	−	254.285i	0.895122	−	0.650344i
$392$	−87.7964	+	28.5268i	−0.223970	+	0.0727724i
$393$	−232.575	−	84.3893i	−0.591795	−	0.214731i
$394$	−231.529	−	168.216i	−0.587637	−	0.426944i
$395$			192.102i			0.486333i
$396$	21.7285	−	196.804i	0.0548700	−	0.496980i
$397$	176.069			0.443500			0.221750	−	0.975104i	$-0.428823\pi$
$397$	176.069			0.443500			0.221750	+	0.975104i	$0.428823\pi$
$398$	−132.516	+	182.392i	−0.332955	+	0.458273i
$399$	43.5719	−	120.083i	0.109203	−	0.300961i
$400$	−8.40645	−	25.8724i	−0.0210161	−	0.0646810i
$401$	214.238	+	294.874i	0.534260	+	0.735346i	0.987772	−	0.155904i	$-0.0498290\pi$
$401$	214.238	+	294.874i	0.534260	+	0.735346i	−0.453512	+	0.891250i	$0.649829\pi$
$402$	66.3966	+	98.2267i	0.165166	+	0.244345i
$403$	125.824	+	387.245i	0.312217	+	0.960906i
$404$	−324.423	−	105.412i	−0.803028	−	0.260920i
$405$	−315.998	+	329.835i	−0.780242	+	0.814408i
$406$	167.955			0.413683
$407$	265.074	+	399.180i	0.651287	+	0.980787i
$408$	−170.635	−	5.78923i	−0.418224	−	0.0141893i
$409$	−585.125	−	425.118i	−1.43062	−	1.03941i	−0.989900	−	0.141765i	$-0.954722\pi$
$409$	−585.125	−	425.118i	−1.43062	−	1.03941i	−0.440722	−	0.897644i	$-0.645278\pi$
$410$	−426.279	−	138.506i	−1.03970	−	0.337821i
$411$	203.450	−	58.5568i	0.495012	−	0.142474i
$412$	114.715	−	83.3456i	0.278435	−	0.202295i
$413$	−252.232	−	347.167i	−0.610731	−	0.840599i
$414$	66.7303	+	265.396i	0.161184	+	0.641053i
$415$	−155.200	+	477.657i	−0.373976	+	1.15098i
$416$	−69.7851	+	96.0510i	−0.167753	+	0.230892i
$417$	774.655	+	26.2821i	1.85769	+	0.0630266i
$418$	−128.314	−	101.751i	−0.306970	−	0.243424i
$419$		−	602.254i		−	1.43736i	−0.695341	−	0.718680i	$-0.744747\pi$
$419$		−	602.254i		−	1.43736i	0.695341	−	0.718680i	$-0.255253\pi$
$420$	−84.1546	+	107.933i	−0.200368	+	0.256984i
$421$	7.05641	−	21.7174i	0.0167611	−	0.0515853i	−0.942326	−	0.334696i	$-0.891366\pi$
$421$	7.05641	−	21.7174i	0.0167611	−	0.0515853i	0.959087	+	0.283111i	$0.0913664\pi$
$422$	232.736	−	75.6204i	0.551506	−	0.179195i
$423$	185.439	+	295.458i	0.438390	+	0.698482i
$424$	51.4408	−	37.3740i	0.121323	−	0.0881461i
$425$	−130.146	+	42.2869i	−0.306225	+	0.0994985i
$426$	−141.363	+	389.594i	−0.331838	+	0.914540i
$427$	118.659	+	86.2106i	0.277889	+	0.201898i
$428$			177.040i			0.413644i
$429$	−448.494	+	527.778i	−1.04544	+	1.23025i
$430$	−60.9041			−0.141638
$431$	119.827	−	164.928i	0.278021	−	0.382663i	−0.647056	−	0.762442i	$-0.724000\pi$
$431$	119.827	−	164.928i	0.278021	−	0.382663i	0.925077	+	0.379779i	$0.124000\pi$
$432$	43.6337	−	98.7932i	0.101004	−	0.228688i
$433$	129.442	+	398.382i	0.298943	+	0.920051i	0.981869	+	0.189563i	$0.0607071\pi$
$433$	129.442	+	398.382i	0.298943	+	0.920051i	−0.682926	+	0.730488i	$0.739293\pi$
$434$	−65.2320	−	89.7841i	−0.150304	−	0.206876i
$435$	−411.516	+	278.165i	−0.946014	+	0.639461i
$436$	−75.4811	−	232.307i	−0.173122	−	0.532814i
$437$	215.257	+	69.9413i	0.492579	+	0.160049i
$438$	51.8009	−	66.4379i	0.118267	−	0.151685i
$439$	−699.480			−1.59335			−0.796674	−	0.604409i	$-0.793409\pi$
$439$	−699.480			−1.59335			−0.796674	+	0.604409i	$0.793409\pi$
$440$	97.0578	+	146.161i	0.220586	+	0.332185i
$441$	−293.068	−	19.9090i	−0.664553	−	0.0451452i
$442$	483.164	+	351.039i	1.09313	+	0.794206i
$443$	89.7362	+	29.1570i	0.202565	+	0.0658173i	0.408542	−	0.912739i	$-0.366037\pi$
$443$	89.7362	+	29.1570i	0.202565	+	0.0658173i	−0.205977	+	0.978557i	$0.566037\pi$
$444$	72.2921	+	251.172i	0.162820	+	0.565702i
$445$	−205.155	+	149.054i	−0.461022	+	0.334952i
$446$	−259.990	−	357.845i	−0.582937	−	0.802344i
$447$	−159.654	+	45.9514i	−0.357167	+	0.102800i
$448$	9.99974	−	30.7760i	0.0223208	−	0.0686965i
$449$	−205.908	+	283.409i	−0.458593	+	0.631200i	−0.974216	−	0.225616i	$-0.927561\pi$
$449$	−205.908	+	283.409i	−0.458593	+	0.631200i	0.515623	+	0.856816i	$0.327561\pi$
$450$	5.86692	−	86.3631i	0.0130376	−	0.191918i
$451$	617.674	+	26.0395i	1.36957	+	0.0577373i
$452$		−	258.088i		−	0.570992i
$453$	66.6532	+	51.9688i	0.147137	+	0.114721i
$454$	65.5082	−	201.614i	0.144291	−	0.444083i
$455$	455.315	−	147.941i	1.00069	−	0.325145i
$456$	−50.0229	−	74.0035i	−0.109699	−	0.162288i
$457$	−549.667	+	399.356i	−1.20277	+	0.873865i	−0.994555	−	0.104218i	$-0.966766\pi$
$457$	−549.667	+	399.356i	−1.20277	+	0.873865i	−0.208217	+	0.978083i	$0.566766\pi$
$458$	−111.151	+	36.1151i	−0.242687	+	0.0788539i
$459$	−496.958	−	219.490i	−1.08270	−	0.478192i
$460$	−196.181	−	142.534i	−0.426480	−	0.309856i
$461$		−	98.3560i		−	0.213354i	−0.994294	−	0.106677i	$-0.965979\pi$
$461$		−	98.3560i		−	0.213354i	0.994294	−	0.106677i	$-0.0340210\pi$
$462$	71.8062	−	174.585i	0.155425	−	0.377890i
$463$	−476.548			−1.02926			−0.514631	−	0.857412i	$-0.672071\pi$
$463$	−476.548			−1.02926			−0.514631	+	0.857412i	$0.672071\pi$
$464$	69.0305	−	95.0123i	0.148773	−	0.204768i
$465$	308.528	+	111.948i	0.663501	+	0.240749i
$466$	79.2353	+	243.861i	0.170033	+	0.523307i
$467$	282.702	+	389.106i	0.605358	+	0.833204i	0.996186	−	0.0872598i	$-0.0278110\pi$
$467$	282.702	+	389.106i	0.605358	+	0.833204i	−0.390827	+	0.920464i	$0.627811\pi$
$468$	−319.980	+	200.829i	−0.683717	+	0.429123i
$469$	34.9308	+	107.506i	0.0744793	+	0.229224i
$470$	−293.977	−	95.5190i	−0.625484	−	0.203232i
$471$	541.686	+	422.347i	1.15008	+	0.896702i
$472$	−300.061			−0.635723
$473$	80.9159	−	22.5708i	0.171069	−	0.0477184i
$474$	4.90060	−	144.443i	0.0103388	−	0.304733i
$475$	−57.9203	−	42.0816i	−0.121937	−	0.0885928i
$476$	−154.812	−	50.3015i	−0.325236	−	0.105676i
$477$	196.217	−	49.3361i	0.411356	−	0.103430i
$478$	−177.864	+	129.225i	−0.372100	+	0.270346i
$479$	523.348	+	720.327i	1.09258	+	1.50381i	0.844863	+	0.534983i	$0.179682\pi$
$479$	523.348	+	720.327i	1.09258	+	1.50381i	0.247722	+	0.968831i	$0.420318\pi$
$480$	26.4700	+	91.9675i	0.0551459	+	0.191599i
$481$	282.523	−	869.515i	0.587365	−	1.80772i
$482$	−6.82129	+	9.38870i	−0.0141521	+	0.0194786i
$483$	−8.84684	+	260.757i	−0.0183164	+	0.539870i
$484$	−183.115	−	158.217i	−0.378338	−	0.326895i
$485$		−	1031.91i		−	2.12764i
$486$	246.017	−	239.945i	0.506207	−	0.493715i
$487$	−37.9160	+	116.693i	−0.0778562	+	0.239617i	−0.982408	−	0.186747i	$-0.940206\pi$
$487$	−37.9160	+	116.693i	−0.0778562	+	0.239617i	0.904552	+	0.426364i	$0.140206\pi$
$488$	97.5387	−	31.6923i	0.199874	−	0.0649431i
$489$	−189.748	+	128.261i	−0.388033	+	0.262292i
$490$	210.580	−	152.996i	0.429756	−	0.312236i
$491$	−43.4997	+	14.1339i	−0.0885940	+	0.0287859i	−0.352979	−	0.935631i	$-0.614831\pi$
$491$	−43.4997	+	14.1339i	−0.0885940	+	0.0287859i	0.264385	+	0.964417i	$0.414831\pi$
$492$	316.990	+	115.019i	0.644290	+	0.233779i
$493$	−477.939	−	347.243i	−0.969450	−	0.704347i
$494$			312.454i			0.632499i
$495$	113.210	+	546.685i	0.228707	+	1.10441i
$496$	−77.6016			−0.156455
$497$	−232.257	+	319.674i	−0.467318	+	0.643208i
$498$	128.882	−	355.196i	0.258799	−	0.713245i
$499$	−267.175	−	822.281i	−0.535421	−	1.64786i	−0.742737	−	0.669583i	$-0.766473\pi$
$499$	−267.175	−	822.281i	−0.535421	−	1.64786i	0.207315	−	0.978274i	$-0.433527\pi$
$500$	−120.647	−	166.057i	−0.241294	−	0.332113i
$501$	103.321	+	152.852i	0.206229	+	0.305094i
$502$	64.9965	+	200.039i	0.129475	+	0.398484i
$503$	33.5539	+	10.9023i	0.0667075	+	0.0216746i	0.342181	−	0.939634i	$-0.388835\pi$
$503$	33.5539	+	10.9023i	0.0667075	+	0.0216746i	−0.275473	+	0.961309i	$0.588835\pi$
$504$	66.0302	−	79.0095i	0.131012	−	0.156765i
$505$	961.825			1.90460
$506$	313.464	+	116.663i	0.619493	+	0.230560i
$507$	814.008	+	27.6172i	1.60554	+	0.0544719i
$508$	7.65272	+	5.56003i	0.0150644	+	0.0109449i
$509$	−239.674	−	77.8749i	−0.470873	−	0.152996i	0.0639621	−	0.997952i	$-0.479626\pi$
$509$	−239.674	−	77.8749i	−0.470873	−	0.152996i	−0.534835	+	0.844956i	$0.679626\pi$
$510$	462.623	−	133.152i	0.907103	−	0.261082i
$511$	64.9808	−	47.2113i	0.127164	−	0.0923901i
$512$	−13.3001	−	18.3060i	−0.0259767	−	0.0357538i
$513$	−59.9215	−	277.840i	−0.116806	−	0.541598i
$514$	−82.3881	+	253.564i	−0.160288	+	0.493316i
$515$	−235.003	+	323.454i	−0.456316	+	0.628065i
$516$	45.7945	+	1.55369i	0.0887490	+	0.00301103i
$517$	425.970	+	17.9578i	0.823927	+	0.0347346i
$518$			249.191i			0.481065i
$519$	190.874	−	244.807i	0.367772	−	0.471690i
$520$	103.447	−	318.376i	0.198936	−	0.612262i
$521$	190.709	−	61.9652i	0.366045	−	0.118935i	−0.120219	−	0.992747i	$-0.538360\pi$
$521$	190.709	−	61.9652i	0.366045	−	0.118935i	0.486263	+	0.873812i	$0.338360\pi$
$522$	316.519	−	198.658i	0.606359	−	0.380570i
$523$	−206.580	+	150.089i	−0.394991	+	0.286978i	−0.767498	−	0.641052i	$-0.778498\pi$
$523$	−206.580	+	150.089i	−0.394991	+	0.286978i	0.372506	+	0.928030i	$0.378498\pi$
$524$	−156.869	+	50.9698i	−0.299368	+	0.0972705i
$525$	28.1497	−	77.5801i	0.0536185	−	0.147772i
$526$	−258.406	−	187.743i	−0.491266	−	0.356926i
$527$			390.358i			0.740717i
$528$	−69.2502	−	112.376i	−0.131156	−	0.212834i
$529$	66.7281			0.126140
$530$	−105.380	+	145.043i	−0.198831	+	0.273667i
$531$	−885.972	−	355.913i	−1.66850	−	0.670269i
$532$	−26.3167	−	80.9945i	−0.0494675	−	0.152245i
$533$	−693.330	−	954.288i	−1.30081	−	1.79041i
$534$	158.061	−	106.842i	0.295994	−	0.200078i
$535$	−154.256	−	474.752i	−0.288330	−	0.887388i
$536$	75.1729	+	24.4252i	0.140248	+	0.0455693i
$537$	350.227	−	449.188i	0.652192	−	0.836477i
$538$	−141.170			−0.262398
$539$	−223.073	+	281.307i	−0.413864	+	0.521905i
$540$	−30.9293	+	302.944i	−0.0572766	+	0.561007i
$541$	−570.240	−	414.304i	−1.05405	−	0.765811i	−0.0810702	−	0.996708i	$-0.525834\pi$
$541$	−570.240	−	414.304i	−1.05405	−	0.765811i	−0.972978	+	0.230898i	$0.925834\pi$
$542$	−228.875	−	74.3659i	−0.422278	−	0.137206i
$543$	−117.844	−	409.437i	−0.217024	−	0.754028i
$544$	−92.0842	+	66.9031i	−0.169272	+	0.122984i
$545$	404.823	+	557.191i	0.742794	+	1.02237i
$546$	−346.130	+	99.6230i	−0.633938	+	0.182460i
$547$	44.1358	−	135.836i	0.0806871	−	0.248329i	−0.902573	−	0.430537i	$-0.858324\pi$
$547$	44.1358	−	135.836i	0.0806871	−	0.248329i	0.983260	+	0.182208i	$0.0583243\pi$
$548$	82.9596	−	114.184i	0.151386	−	0.208365i
$549$	325.588	+	22.1182i	0.593057	+	0.0402882i
$550$	−82.8973	−	65.7366i	−0.150722	−	0.119521i
$551$		−	309.076i		−	0.560936i
$552$	143.874	+	112.177i	0.260642	+	0.203220i
$553$	42.5804	−	131.049i	0.0769989	−	0.236978i
$554$	−111.072	+	36.0893i	−0.200490	+	0.0651432i
$555$	−412.708	−	610.557i	−0.743618	−	1.10010i
$556$	418.047	−	303.729i	0.751882	−	0.546275i
$557$	596.721	−	193.886i	1.07131	−	0.348090i	0.280313	−	0.959909i	$-0.409562\pi$
$557$	596.721	−	193.886i	1.07131	−	0.348090i	0.790998	+	0.611818i	$0.209562\pi$
$558$	−229.130	−	92.0459i	−0.410626	−	0.164957i
$559$	−129.670	−	94.2105i	−0.231967	−	0.168534i
$560$			91.2424i			0.162933i
$561$	−565.284	+	348.348i	−1.00764	+	0.620941i
$562$	6.39604			0.0113809
$563$	−96.5581	+	132.901i	−0.171506	+	0.236058i	−0.886114	−	0.463467i	$-0.846605\pi$
$563$	−96.5581	+	132.901i	−0.171506	+	0.236058i	0.714608	+	0.699525i	$0.246605\pi$
$564$	218.608	+	79.3213i	0.387603	+	0.140641i
$565$	224.875	+	692.093i	0.398008	+	1.22494i
$566$	338.964	+	466.544i	0.598876	+	0.824283i
$567$	288.679	−	154.966i	0.509134	−	0.273309i
$568$	85.3809	+	262.776i	0.150319	+	0.462633i
$569$	−670.068	−	217.718i	−1.17762	−	0.382633i	−0.346141	−	0.938183i	$-0.612508\pi$
$569$	−670.068	−	217.718i	−1.17762	−	0.382633i	−0.831484	+	0.555549i	$0.812508\pi$
$570$	198.622	+	154.863i	0.348460	+	0.271690i
$571$	−686.225			−1.20179			−0.600897	−	0.799326i	$-0.705190\pi$
$571$	−686.225			−1.20179			−0.600897	+	0.799326i	$0.705190\pi$
$572$	−19.4482	+	461.324i	−0.0340004	+	0.806511i
$573$	−30.9314	+	911.692i	−0.0539815	+	1.59109i
$574$	260.101	+	188.974i	0.453137	+	0.329223i
$575$	139.067	+	45.1858i	0.241856	+	0.0785839i
$576$	−17.5570	−	69.8266i	−0.0304808	−	0.121227i
$577$	−259.540	+	188.567i	−0.449810	+	0.326806i	−0.789521	−	0.613724i	$-0.789671\pi$
$577$	−259.540	+	188.567i	−0.449810	+	0.326806i	0.339711	+	0.940530i	$0.389671\pi$
$578$	96.3093	+	132.558i	0.166625	+	0.229340i
$579$	−78.0056	−	271.023i	−0.134725	−	0.468088i
$580$	−102.328	+	314.933i	−0.176428	+	0.542988i
$581$	211.751	−	291.450i	0.364459	−	0.501635i
$582$	−26.3244	+	775.902i	−0.0452310	+	1.33317i
$583$	86.2534	−	231.755i	0.147947	−	0.397521i
$584$		−	56.1638i		−	0.0961708i
$585$	683.078	−	817.349i	1.16765	−	1.39718i
$586$	−55.6717	+	171.340i	−0.0950029	+	0.292389i
$587$	−468.265	+	152.149i	−0.797726	+	0.259197i	−0.679391	−	0.733777i	$-0.737756\pi$
$587$	−468.265	+	152.149i	−0.797726	+	0.259197i	−0.118336	+	0.992974i	$0.537756\pi$
$588$	−162.241	+	109.667i	−0.275920	+	0.186509i
$589$	−165.223	+	120.042i	−0.280515	+	0.203806i
$590$	804.648	−	261.446i	1.36381	−	0.443129i
$591$	−570.685	−	207.071i	−0.965626	−	0.350375i
$592$	140.968	+	102.419i	0.238121	+	0.173005i
$593$			490.333i			0.826869i	0.910534	+	0.413434i	$0.135671\pi$
$593$			490.333i			0.826869i	−0.910534	+	0.413434i	$0.864329\pi$
$594$	−71.1775	−	413.947i	−0.119827	−	0.696880i
$595$	458.975			0.771387
$596$	−65.1012	+	89.6041i	−0.109230	+	0.150342i
$597$	−163.125	+	449.571i	−0.273242	+	0.753050i
$598$	−197.204	−	606.931i	−0.329772	−	1.01493i
$599$	−132.418	−	182.258i	−0.221065	−	0.304270i	0.684051	−	0.729434i	$-0.260216\pi$
$599$	−132.418	−	182.258i	−0.221065	−	0.304270i	−0.905116	+	0.425164i	$0.860216\pi$
$600$	−32.3174	−	47.8101i	−0.0538623	−	0.0796836i
$601$	39.5997	+	121.875i	0.0658897	+	0.202788i	0.978581	−	0.205862i	$-0.0659998\pi$
$601$	39.5997	+	121.875i	0.0658897	+	0.202788i	−0.912691	+	0.408650i	$0.866000\pi$
$602$	41.5479	+	13.4997i	0.0690165	+	0.0224248i
$603$	192.987	+	161.284i	0.320045	+	0.267469i
$604$	56.3457			0.0932877
$605$	628.901	+	264.728i	1.03951	+	0.437567i
$606$	−723.206	−	24.5366i	−1.19341	−	0.0404894i
$607$	435.915	+	316.711i	0.718146	+	0.521764i	0.885791	−	0.464083i	$-0.153616\pi$
$607$	435.915	+	316.711i	0.718146	+	0.521764i	−0.167645	+	0.985847i	$0.553616\pi$
$608$	−56.6349	−	18.4018i	−0.0931495	−	0.0302661i
$609$	342.387	−	98.5457i	0.562212	−	0.161816i
$610$	−233.948	+	169.973i	−0.383521	+	0.278644i
$611$	−478.146	−	658.111i	−0.782562	−	1.07710i
$612$	−351.248	+	88.3165i	−0.573934	+	0.144308i
$613$	205.844	−	633.523i	0.335798	−	1.03348i	−0.630529	−	0.776165i	$-0.717162\pi$
$613$	205.844	−	633.523i	0.335798	−	1.03348i	0.966328	−	0.257315i	$-0.0828378\pi$
$614$	−127.329	+	175.253i	−0.207376	+	0.285428i
$615$	−950.264	−	32.2401i	−1.54514	−	0.0524229i
$616$	−33.8140	−	121.223i	−0.0548928	−	0.196790i
$617$		−	819.028i		−	1.32744i	−0.747983	−	0.663718i	$-0.768978\pi$
$617$		−	819.028i		−	1.32744i	0.747983	−	0.663718i	$-0.231022\pi$
$618$	184.953	−	237.213i	0.299276	−	0.383840i
$619$	−325.530	+	1001.88i	−0.525896	+	1.61854i	0.236642	+	0.971597i	$0.423953\pi$
$619$	−325.530	+	1001.88i	−0.525896	+	1.61854i	−0.762538	+	0.646944i	$0.776047\pi$
$620$	208.098	−	67.6150i	0.335641	−	0.109056i
$621$	291.752	+	501.874i	0.469810	+	0.808170i
$622$	36.8469	−	26.7708i	0.0592394	−	0.0430399i
$623$	172.992	−	56.2086i	0.277676	−	0.0902225i
$624$	−85.9046	+	236.751i	−0.137668	+	0.379409i
$625$	605.768	+	440.117i	0.969230	+	0.704186i
$626$		−	346.962i		−	0.554253i
$627$	−321.276	−	132.140i	−0.512403	−	0.210749i
$628$	457.918			0.729169
$629$	515.197	−	709.107i	0.819073	−	1.12736i
$630$	−108.226	+	269.406i	−0.171787	+	0.427628i
$631$	143.011	+	440.144i	0.226643	+	0.697534i	0.998121	+	0.0612783i	$0.0195177\pi$
$631$	143.011	+	440.144i	0.226643	+	0.697534i	−0.771478	+	0.636256i	$0.780482\pi$
$632$	−56.6337	−	77.9495i	−0.0896102	−	0.123338i
$633$	430.077	−	290.712i	0.679426	−	0.459260i
$634$	−15.0979	−	46.4666i	−0.0238138	−	0.0732912i
$635$	−25.3662	−	8.24196i	−0.0399467	−	0.0129795i
$636$	82.9367	−	106.371i	0.130404	−	0.167251i
$637$	685.006			1.07536
$638$	19.2379	−	456.335i	0.0301535	−	0.715259i
$639$	−59.5879	+	877.155i	−0.0932518	+	1.37270i
$640$	51.6158	+	37.5011i	0.0806497	+	0.0585954i
$641$	49.5760	+	16.1082i	0.0773416	+	0.0251298i	0.347432	−	0.937705i	$-0.387054\pi$
$641$	49.5760	+	16.1082i	0.0773416	+	0.0251298i	−0.270091	+	0.962835i	$0.587054\pi$
$642$	103.876	+	360.907i	0.161800	+	0.562160i
$643$	65.2909	−	47.4366i	0.101541	−	0.0737739i	−0.535856	−	0.844309i	$-0.680011\pi$
$643$	65.2909	−	47.4366i	0.101541	−	0.0737739i	0.637397	+	0.770535i	$0.280011\pi$
$644$	102.238	+	140.719i	0.158755	+	0.218508i
$645$	−124.157	+	35.7348i	−0.192491	+	0.0554027i
$646$	−92.5662	+	284.890i	−0.143291	+	0.441006i
$647$	−679.703	+	935.531i	−1.05055	+	1.44595i	−0.162211	+	0.986756i	$0.551862\pi$
$647$	−679.703	+	935.531i	−1.05055	+	1.44595i	−0.888335	+	0.459196i	$0.848138\pi$
$648$	30.9843	−	226.998i	0.0478153	−	0.350305i
$649$	−972.147	+	645.550i	−1.49791	+	0.994684i
$650$			201.862i			0.310557i
$651$	−185.659	−	144.756i	−0.285191	−	0.222360i
$652$	−47.1830	+	145.214i	−0.0723666	+	0.222721i
$653$	−623.268	+	202.512i	−0.954469	+	0.310126i	−0.744530	−	0.667589i	$-0.767326\pi$
$653$	−623.268	+	202.512i	−0.954469	+	0.310126i	−0.209939	+	0.977715i	$0.567326\pi$
$654$	−290.176	−	429.285i	−0.443695	−	0.656399i
$655$	376.251	−	273.363i	0.574429	−	0.417347i
$656$	213.805	−	69.4696i	0.325923	−	0.105899i
$657$	66.6178	−	165.831i	0.101397	−	0.252407i
$658$	179.375	+	130.323i	0.272606	+	0.198060i
$659$			550.890i			0.835949i	0.908459	+	0.417974i	$0.137260\pi$
$659$			550.890i			0.835949i	−0.908459	+	0.417974i	$0.862740\pi$
$660$	283.617	+	241.011i	0.429722	+	0.365169i
$661$	38.4015			0.0580960			0.0290480	−	0.999578i	$-0.490752\pi$
$661$	38.4015			0.0580960			0.0290480	+	0.999578i	$0.490752\pi$
$662$	48.6901	−	67.0162i	0.0735500	−	0.101233i
$663$	1190.93	+	432.125i	1.79627	+	0.651772i
$664$	−77.8425	−	239.575i	−0.117233	−	0.360805i
$665$	141.143	+	194.266i	0.212244	+	0.292129i
$666$	294.744	+	469.613i	0.442559	+	0.705125i
$667$	195.071	+	600.367i	0.292461	+	0.900101i
$668$	116.978	+	38.0083i	0.175116	+	0.0568987i
$669$	−739.967	−	576.944i	−1.10608	−	0.862398i
$670$	−222.867			−0.332637
$671$	247.826	−	312.522i	0.369339	−	0.465755i
$672$	2.32763	−	68.6061i	0.00346374	−	0.102092i
$673$	138.533	+	100.650i	0.205844	+	0.149554i	0.685931	−	0.727666i	$-0.259395\pi$
$673$	138.533	+	100.650i	0.205844	+	0.149554i	−0.480087	+	0.877221i	$0.659395\pi$
$674$	428.363	+	139.184i	0.635553	+	0.206504i
$675$	−38.7124	−	179.499i	−0.0573517	−	0.265924i
$676$	439.284	−	319.158i	0.649828	−	0.472127i
$677$	−437.228	−	601.793i	−0.645832	−	0.888911i	0.353078	−	0.935594i	$-0.385135\pi$
$677$	−437.228	−	601.793i	−0.645832	−	0.888911i	−0.998910	+	0.0466827i	$0.985135\pi$
$678$	−151.430	−	526.129i	−0.223348	−	0.776002i
$679$	−228.728	+	703.952i	−0.336860	+	1.03675i
$680$	188.641	−	259.642i	0.277413	−	0.381827i
$681$	15.2483	−	449.438i	0.0223910	−	0.659968i
$682$	−251.416	+	166.952i	−0.368645	+	0.244797i
$683$			373.222i			0.546444i	0.961951	+	0.273222i	$0.0880894\pi$
$683$			373.222i			0.546444i	−0.961951	+	0.273222i	$0.911911\pi$
$684$	−145.395	−	121.510i	−0.212566	−	0.177647i
$685$	−122.976	+	378.482i	−0.179527	+	0.552528i
$686$	−444.151	+	144.313i	−0.647451	+	0.210369i
$687$	−205.398	+	138.839i	−0.298978	+	0.202095i
$688$	24.7132	−	17.9552i	0.0359204	−	0.0260977i
$689$	−448.726	+	145.800i	−0.651271	+	0.211611i
$690$	−483.557	−	175.457i	−0.700807	−	0.254286i
$691$	−105.233	−	76.4562i	−0.152291	−	0.110646i	0.509031	−	0.860748i	$-0.330004\pi$
$691$	−105.233	−	76.4562i	−0.152291	−	0.110646i	−0.661321	+	0.750103i	$0.730004\pi$
$692$		−	206.950i		−	0.299060i
$693$	43.9457	−	398.034i	0.0634137	−	0.574364i
$694$	71.7382			0.103369
$695$	−856.399	+	1178.73i	−1.23223	+	1.69602i
$696$	84.9756	−	234.191i	0.122091	−	0.336482i
$697$	−349.452	−	1075.50i	−0.501366	−	1.54305i
$698$	−407.972	−	561.526i	−0.584488	−	0.804478i
$699$	304.609	+	450.636i	0.435778	+	0.644686i
$700$	−17.0020	−	52.3267i	−0.0242885	−	0.0747524i
$701$	653.822	+	212.440i	0.932699	+	0.303052i	0.735666	−	0.677345i	$-0.236869\pi$
$701$	653.822	+	212.440i	0.932699	+	0.303052i	0.197033	+	0.980397i	$0.436869\pi$
$702$	−534.464	+	597.148i	−0.761345	+	0.850638i
$703$	458.569			0.652303
$704$	−82.4733	−	30.6945i	−0.117150	−	0.0436002i
$705$	−655.336	−	22.2339i	−0.929554	−	0.0315374i
$706$	411.194	+	298.750i	0.582427	+	0.423158i
$707$	−656.143	−	213.194i	−0.928066	−	0.301547i
$708$	−611.693	+	176.057i	−0.863974	+	0.248668i
$709$	83.1869	−	60.4388i	0.117330	−	0.0852451i	−0.527573	−	0.849510i	$-0.676898\pi$
$709$	83.1869	−	60.4388i	0.117330	−	0.0852451i	0.644903	+	0.764265i	$0.276898\pi$
$710$	−457.918	−	630.270i	−0.644954	−	0.887704i
$711$	−74.7602	−	297.332i	−0.105148	−	0.418189i
$712$	39.3035	−	120.964i	0.0552016	−	0.169893i
$713$	245.176	−	337.456i	0.343865	−	0.473290i
$714$	−345.108	−	11.7087i	−0.483345	−	0.0163987i
$715$	−349.804	−	1254.04i	−0.489236	−	1.75390i
$716$		−	379.725i		−	0.530342i
$717$	−286.765	+	367.794i	−0.399951	+	0.512962i
$718$	10.7725	−	33.1544i	0.0150035	−	0.0461761i
$719$	884.332	−	287.337i	1.22995	−	0.399634i	0.379252	−	0.925293i	$-0.376181\pi$
$719$	884.332	−	287.337i	1.22995	−	0.399634i	0.850695	+	0.525659i	$0.176181\pi$
$720$	107.922	+	171.951i	0.149891	+	0.238820i
$721$	232.011	−	168.566i	0.321790	−	0.233794i
$722$	336.496	−	109.334i	0.466061	−	0.151432i
$723$	−8.39692	+	23.1418i	−0.0116140	+	0.0320080i
$724$	−229.793	−	166.954i	−0.317393	−	0.230600i
$725$		−	199.679i		−	0.275419i
$726$	−466.124	−	215.095i	−0.642045	−	0.296274i
$727$	574.556			0.790311			0.395156	−	0.918614i	$-0.370691\pi$
$727$	574.556			0.790311			0.395156	+	0.918614i	$0.370691\pi$
$728$	−141.140	+	194.262i	−0.193873	+	0.266844i
$729$	360.735	−	633.491i	0.494836	−	0.868986i
$730$	48.9360	+	150.610i	0.0670356	+	0.206314i
$731$	−90.3198	−	124.315i	−0.123557	−	0.170061i
$732$	180.244	−	121.836i	0.246235	−	0.166443i
$733$	−20.6685	−	63.6111i	−0.0281971	−	0.0867819i	0.935968	−	0.352086i	$-0.114528\pi$
$733$	−20.6685	−	63.6111i	−0.0281971	−	0.0867819i	−0.964165	+	0.265304i	$0.914528\pi$
$734$	485.945	+	157.893i	0.662051	+	0.215113i
$735$	339.513	−	435.447i	0.461923	−	0.592445i
$736$	121.625			0.165252
$737$	296.096	−	82.5933i	0.401758	−	0.112067i
$738$	713.691	+	48.4833i	0.967061	+	0.0656955i
$739$	820.326	+	596.002i	1.11005	+	0.806498i	0.982671	−	0.185356i	$-0.0593440\pi$
$739$	820.326	+	596.002i	1.11005	+	0.806498i	0.127378	+	0.991854i	$0.459344\pi$
$740$	−467.260	−	151.822i	−0.631432	−	0.205165i
$741$	183.329	+	636.958i	0.247407	+	0.859593i
$742$	104.039	−	75.5885i	0.140214	−	0.101871i
$743$	−18.5066	−	25.4722i	−0.0249079	−	0.0342828i	0.796381	−	0.604795i	$-0.206745\pi$
$743$	−18.5066	−	25.4722i	−0.0249079	−	0.0342828i	−0.821289	+	0.570512i	$0.806745\pi$
$744$	−158.196	+	45.5318i	−0.212629	+	0.0611986i
$745$	96.5034	−	297.007i	0.129535	−	0.398667i
$746$	−63.7358	+	87.7248i	−0.0854368	+	0.117594i
$747$	54.3268	−	799.710i	0.0727266	−	1.07056i
$748$	−154.402	+	414.864i	−0.206420	+	0.554631i
$749$			358.061i			0.478052i
$750$	−343.379	−	267.729i	−0.457838	−	0.356971i
$751$	418.114	−	1286.82i	0.556743	−	1.71348i	−0.134553	−	0.990906i	$-0.542960\pi$
$751$	418.114	−	1286.82i	0.556743	−	1.71348i	0.691296	−	0.722572i	$-0.257040\pi$
$752$	147.448	−	47.9087i	0.196074	−	0.0637084i
$753$	249.870	+	369.656i	0.331832	+	0.490911i
$754$	−705.024	+	512.230i	−0.935045	+	0.679350i
$755$	−151.098	+	49.0946i	−0.200129	+	0.0650259i
$756$	88.2487	−	199.808i	0.116731	−	0.264297i
$757$	−229.027	−	166.398i	−0.302545	−	0.219812i	0.426146	−	0.904654i	$-0.359871\pi$
$757$	−229.027	−	166.398i	−0.302545	−	0.219812i	−0.728691	+	0.684843i	$0.759871\pi$
$758$		−	263.822i		−	0.348051i
$759$	707.466	+	53.9046i	0.932103	+	0.0710205i
$760$	167.907			0.220930
$761$	−535.331	+	736.819i	−0.703457	+	0.968225i	0.296456	+	0.955046i	$0.404195\pi$
$761$	−535.331	+	736.819i	−0.703457	+	0.968225i	−0.999913	+	0.0131789i	$0.995805\pi$
$762$	18.8628	+	6.84432i	0.0247544	+	0.00898205i
$763$	−152.660	−	469.839i	−0.200078	−	0.615778i
$764$	357.458	+	491.999i	0.467877	+	0.643978i
$765$	864.960	−	542.876i	1.13067	−	0.709642i
$766$	−147.346	−	453.484i	−0.192357	−	0.592015i
$767$	2117.58	+	688.044i	2.76086	+	0.897059i
$768$	−37.8538	−	29.5142i	−0.0492888	−	0.0384300i
$769$	186.619			0.242678			0.121339	−	0.992611i	$-0.461281\pi$
$769$	186.619			0.242678			0.121339	+	0.992611i	$0.461281\pi$
$770$	196.298	+	295.610i	0.254933	+	0.383909i
$771$	−19.1774	+	565.247i	−0.0248734	+	0.733135i
$772$	−152.109	−	110.514i	−0.197032	−	0.143152i
$773$	219.371	+	71.2781i	0.283792	+	0.0922097i	0.447454	−	0.894307i	$-0.352331\pi$
$773$	219.371	+	71.2781i	0.283792	+	0.0922097i	−0.163662	+	0.986516i	$0.552331\pi$
$774$	94.2665	−	23.7021i	0.121791	−	0.0306228i
$775$	−106.743	+	77.5532i	−0.137733	+	0.100069i
$776$	304.218	+	418.720i	0.392033	+	0.539587i
$777$	146.210	+	507.992i	0.188173	+	0.653787i
$778$	323.981	−	997.112i	0.416428	−	1.28163i
$779$	347.755	−	478.644i	0.446413	−	0.614434i
$780$	24.0792	−	709.726i	0.0308708	−	0.909905i
$781$	841.954	+	667.660i	1.07805	+	0.854878i
$782$		−	611.810i		−	0.782365i
$783$	528.685	−	590.690i	0.675204	−	0.754393i
$784$	−40.3430	+	124.163i	−0.0514579	+	0.158371i
$785$	−1227.96	+	398.989i	−1.56428	+	0.508266i
$786$	−289.881	+	195.946i	−0.368805	+	0.249295i
$787$	−1194.18	+	867.620i	−1.51738	+	1.10244i	−0.554610	+	0.832111i	$0.687132\pi$
$787$	−1194.18	+	867.620i	−1.51738	+	1.10244i	−0.962768	+	0.270329i	$0.912868\pi$
$788$	−384.919	+	125.068i	−0.488476	+	0.158715i
$789$	−636.933	−	231.109i	−0.807266	−	0.292914i
$790$	219.788	+	159.685i	0.278212	+	0.202133i
$791$		−	521.981i		−	0.659900i
$792$	−207.106	−	188.454i	−0.261498	−	0.237947i
$793$	−761.018			−0.959669
$794$	146.358	−	201.445i	0.184330	−	0.253709i
$795$	−129.722	+	357.511i	−0.163172	+	0.449699i
$796$	98.5250	+	303.229i	0.123775	+	0.380941i
$797$	616.341	+	848.320i	0.773326	+	1.06439i	0.995987	+	0.0894961i	$0.0285257\pi$
$797$	616.341	+	848.320i	0.773326	+	1.06439i	−0.222661	+	0.974896i	$0.571474\pi$
$798$	−101.171	−	149.671i	−0.126780	−	0.187558i
$799$	−240.995	−	741.705i	−0.301620	−	0.928292i
$800$	−36.5891	−	11.8885i	−0.0457364	−	0.0148607i
$801$	259.529	−	310.543i	0.324006	−	0.387695i
$802$	515.458			0.642716
$803$	−120.830	−	181.961i	−0.150474	−	0.226601i
$804$	167.576	+	5.68543i	0.208428	+	0.00707143i
$805$	−396.774	−	288.273i	−0.492887	−	0.358103i
$806$	547.647	+	177.941i	0.679463	+	0.220771i
$807$	−287.784	+	82.8297i	−0.356609	+	0.102639i
$808$	−390.282	+	283.556i	−0.483022	+	0.350936i
$809$	−828.391	−	1140.18i	−1.02397	−	1.40937i	−0.909383	−	0.415959i	$-0.863446\pi$
$809$	−828.391	−	1140.18i	−1.02397	−	1.40937i	−0.114586	−	0.993413i	$-0.536554\pi$
$810$	114.697	+	635.718i	0.141602	+	0.784836i
$811$	−278.285	+	856.472i	−0.343138	+	1.05607i	0.619436	+	0.785047i	$0.287361\pi$
$811$	−278.285	+	856.472i	−0.343138	+	1.05607i	−0.962573	+	0.271022i	$0.912639\pi$
$812$	139.613	−	192.161i	0.171938	−	0.236652i
$813$	−510.209	−	17.3101i	−0.627563	−	0.0212916i
$814$	677.055	+	28.5429i	0.831763	+	0.0350649i
$815$		−	430.520i		−	0.528246i
$816$	−148.465	+	190.415i	−0.181942	+	0.233352i
$817$	24.8426	−	76.4576i	0.0304071	−	0.0935834i
$818$	−972.774	+	316.074i	−1.18921	+	0.386398i
$819$	−647.156	+	406.175i	−0.790178	+	0.495941i
$820$	−512.815	+	372.582i	−0.625384	+	0.454368i
$821$	−136.546	+	44.3665i	−0.166317	+	0.0540396i	−0.390992	−	0.920394i	$-0.627868\pi$
$821$	−136.546	+	44.3665i	−0.166317	+	0.0540396i	0.224675	+	0.974434i	$0.427868\pi$
$822$	102.122	−	281.447i	0.124236	−	0.342393i
$823$	133.936	+	97.3105i	0.162742	+	0.118239i	0.666175	−	0.745795i	$-0.267930\pi$
$823$	133.936	+	97.3105i	0.162742	+	0.118239i	−0.503434	+	0.864034i	$0.667930\pi$
$824$		−	200.530i		−	0.243361i
$825$	−207.561	−	85.3692i	−0.251590	−	0.103478i
$826$	−606.871			−0.734710
$827$	−409.414	+	563.509i	−0.495059	+	0.681390i	−0.981311	−	0.192429i	$-0.938364\pi$
$827$	−409.414	+	563.509i	−0.495059	+	0.681390i	0.486252	+	0.873818i	$0.338364\pi$
$828$	359.116	+	144.264i	0.433715	+	0.174232i
$829$	−83.6927	−	257.580i	−0.100956	−	0.310711i	0.887804	−	0.460222i	$-0.152230\pi$
$829$	−83.6927	−	257.580i	−0.100956	−	0.310711i	−0.988760	+	0.149511i	$0.952230\pi$
$830$	417.487	+	574.622i	0.502997	+	0.692316i
$831$	−205.251	+	138.740i	−0.246993	+	0.166956i
$832$	51.8850	+	159.685i	0.0623617	+	0.191930i
$833$	624.575	+	202.937i	0.749789	+	0.243621i
$834$	674.005	−	864.454i	0.808160	−	1.03652i
$835$	−346.806			−0.415337
$836$	−223.077	+	62.2254i	−0.266838	+	0.0744323i
$837$	−521.102	−	53.2024i	−0.622583	−	0.0635632i
$838$	−689.053	−	500.626i	−0.822258	−	0.597406i
$839$	−828.196	−	269.097i	−0.987123	−	0.320736i	−0.229415	−	0.973329i	$-0.573681\pi$
$839$	−828.196	−	269.097i	−0.987123	−	0.320736i	−0.757709	+	0.652593i	$0.773681\pi$
$840$	53.5354	+	186.003i	0.0637326	+	0.221432i
$841$	17.0164	−	12.3632i	0.0202336	−	0.0147005i
$842$	−18.9817	−	26.1261i	−0.0225436	−	0.0310286i
$843$	13.0387	−	3.75280i	0.0154671	−	0.00445172i
$844$	106.943	−	329.138i	0.126710	−	0.389974i
$845$	−899.904	+	1238.61i	−1.06497	+	1.46581i
$846$	492.187	+	33.4358i	0.581781	+	0.0395222i
$847$	−370.349	−	319.993i	−0.437248	−	0.377796i
$848$		−	89.9219i		−	0.106040i
$849$	964.739	+	752.196i	1.13632	+	0.885979i
$850$	−59.8026	+	184.054i	−0.0703561	+	0.216534i
$851$	−890.752	+	289.423i	−1.04671	+	0.340097i
$852$	328.235	+	485.588i	0.385252	+	0.569939i
$853$	−732.575	+	532.247i	−0.858821	+	0.623970i	−0.927564	−	0.373664i	$-0.878101\pi$
$853$	−732.575	+	532.247i	−0.858821	+	0.623970i	0.0687427	+	0.997634i	$0.478101\pi$
$854$	197.271	−	64.0973i	0.230997	−	0.0750553i
$855$	495.768	+	199.160i	0.579845	+	0.232935i
$856$	202.555	+	147.165i	0.236630	+	0.171922i
$857$		−	1064.31i		−	1.24190i	−0.783849	−	0.620952i	$-0.786746\pi$
$857$		−	1064.31i		−	1.24190i	0.783849	−	0.620952i	$-0.213254\pi$
$858$	231.030	+	951.849i	0.269266	+	1.10938i
$859$	453.288			0.527693			0.263847	−	0.964565i	$-0.415009\pi$
$859$	453.288			0.527693			0.263847	+	0.964565i	$0.415009\pi$
$860$	−50.6268	+	69.6818i	−0.0588684	+	0.0810254i
$861$	641.110	+	232.625i	0.744611	+	0.270180i
$862$	−89.0910	−	274.194i	−0.103354	−	0.318090i
$863$	410.437	+	564.919i	0.475594	+	0.654599i	0.977651	−	0.210236i	$-0.0674232\pi$
$863$	410.437	+	564.919i	0.475594	+	0.654599i	−0.502057	+	0.864835i	$0.667423\pi$
$864$	−76.7609	−	132.045i	−0.0888436	−	0.152829i
$865$	180.317	+	554.959i	0.208459	+	0.641571i
$866$	563.397	+	183.059i	0.650574	+	0.211384i
$867$	274.110	+	213.720i	0.316159	+	0.246506i
$868$	−156.948			−0.180816
$869$	−351.184	−	130.702i	−0.404124	−	0.150405i
$870$	−23.8188	+	702.051i	−0.0273780	+	0.806955i
$871$	−474.500	−	344.745i	−0.544777	−	0.395803i
$872$	−328.532	−	106.746i	−0.376757	−	0.122416i
$873$	401.587	+	1597.17i	0.460008	+	1.82952i
$874$	258.955	−	188.142i	0.296287	−	0.215265i
$875$	−244.008	−	335.848i	−0.278866	−	0.383826i
$876$	−32.9534	−	114.493i	−0.0376180	−	0.130700i
$877$	−388.143	+	1194.58i	−0.442580	+	1.36212i	0.442535	+	0.896751i	$0.354079\pi$
$877$	−388.143	+	1194.58i	−0.442580	+	1.36212i	−0.885116	+	0.465371i	$0.845921\pi$
$878$	−581.445	+	800.291i	−0.662238	+	0.911493i
$879$	−12.9587	+	381.952i	−0.0147425	+	0.434530i
$880$	247.906	+	10.4511i	0.281711	+	0.0118762i
$881$			346.744i			0.393581i	0.980446	+	0.196790i	$0.0630518\pi$
$881$			346.744i			0.393581i	−0.980446	+	0.196790i	$0.936948\pi$
$882$	−266.392	+	318.756i	−0.302032	+	0.361401i
$883$	238.130	−	732.889i	0.269683	−	0.829999i	−0.720894	−	0.693045i	$-0.756269\pi$
$883$	238.130	−	732.889i	0.269683	−	0.829999i	0.990577	−	0.136954i	$-0.0437313\pi$
$884$	803.263	−	260.996i	0.908669	−	0.295244i
$885$	1486.93	−	1005.09i	1.68014	−	1.13570i
$886$	107.953	−	78.4323i	0.121843	−	0.0885240i
$887$	778.193	−	252.850i	0.877331	−	0.285062i	0.164482	−	0.986380i	$-0.447405\pi$
$887$	778.193	−	252.850i	0.877331	−	0.285062i	0.712849	+	0.701318i	$0.247405\pi$
$888$	347.464	+	126.076i	0.391289	+	0.141978i
$889$	15.4775	+	11.2451i	0.0174101	+	0.0126492i
$890$			358.624i			0.402948i
$891$	−387.978	−	802.094i	−0.435441	−	0.900217i
$892$	−625.537			−0.701274
$893$	239.825	−	330.090i	0.268561	−	0.369642i
$894$	−80.1387	+	220.861i	−0.0896406	+	0.247048i
$895$	330.858	+	1018.28i	0.369674	+	1.13774i
$896$	−26.8992	−	37.0236i	−0.0300215	−	0.0413210i
$897$	−758.122	−	1121.56i	−0.845175	−	1.25035i
$898$	153.092	+	471.169i	0.170481	+	0.524687i
$899$	−541.725	−	176.017i	−0.602586	−	0.195792i
$900$	−93.9331	−	78.5021i	−0.104370	−	0.0872246i
$901$	−452.333			−0.502034
$902$	543.237	−	685.050i	0.602258	−	0.759479i
$903$	92.6189	+	3.14233i	0.102568	+	0.00347987i
$904$	−295.285	−	214.537i	−0.326642	−	0.237320i
$905$	761.684	+	247.486i	0.841640	+	0.273465i
$906$	114.864	−	33.0602i	0.126782	−	0.0364903i
$907$	976.272	−	709.303i	1.07637	−	0.782032i	0.0993274	−	0.995055i	$-0.468331\pi$
$907$	976.272	−	709.303i	1.07637	−	0.782032i	0.977047	+	0.213023i	$0.0683309\pi$
$908$	−176.217	−	242.541i	−0.194071	−	0.267116i
$909$	−1488.70	+	374.313i	−1.63773	+	0.411786i
$910$	209.220	−	643.913i	0.229912	−	0.707596i
$911$	847.792	−	1166.89i	0.930616	−	1.28088i	−0.0290022	−	0.999579i	$-0.509233\pi$
$911$	847.792	−	1166.89i	0.930616	−	1.28088i	0.959619	−	0.281304i	$-0.0907670\pi$
$912$	−126.251	−	4.28337i	−0.138433	−	0.00469668i
$913$	−767.617	−	608.711i	−0.840763	−	0.666715i
$914$			960.853i			1.05126i
$915$	−377.187	+	483.766i	−0.412227	+	0.528706i
$916$	−51.0744	+	157.191i	−0.0557581	+	0.171606i
$917$	−317.266	+	103.086i	−0.345982	+	0.112416i
$918$	−664.222	+	386.129i	−0.723553	+	0.420620i
$919$	851.674	−	618.778i	0.926740	−	0.673316i	−0.0184523	−	0.999830i	$-0.505874\pi$
$919$	851.674	−	618.778i	0.926740	−	0.673316i	0.945193	+	0.326514i	$0.105874\pi$
$920$	−326.152	+	105.973i	−0.354513	+	0.115188i
$921$	−156.740	+	431.972i	−0.170185	+	0.469025i
$922$	−112.531	−	81.7588i	−0.122051	−	0.0886755i
$923$		−	2050.23i		−	2.22127i
$924$	−140.058	−	227.280i	−0.151578	−	0.245974i
$925$	296.259			0.320281
$926$	−396.132	+	545.230i	−0.427789	+	0.588801i
$927$	237.855	−	592.093i	0.256586	−	0.638719i
$928$	−51.3239	−	157.959i	−0.0553059	−	0.170214i
$929$	−59.0269	−	81.2435i	−0.0635381	−	0.0874527i	0.776065	−	0.630652i	$-0.217213\pi$
$929$	−59.0269	−	81.2435i	−0.0635381	−	0.0874527i	−0.839604	+	0.543200i	$0.817213\pi$
$930$	384.548	−	259.936i	0.413492	−	0.279501i
$931$	106.172	+	326.764i	0.114041	+	0.350982i
$932$	344.872	+	112.056i	0.370034	+	0.120231i
$933$	59.4073	−	76.1935i	0.0636734	−	0.0816651i
$934$	680.183			0.728247
$935$	52.5719	−	1247.04i	0.0562266	−	1.33373i
$936$	−36.2108	+	533.036i	−0.0386868	+	0.569483i
$937$	−550.771	−	400.159i	−0.587803	−	0.427064i	0.253726	−	0.967276i	$-0.418344\pi$
$937$	−550.771	−	400.159i	−0.587803	−	0.427064i	−0.841529	+	0.540213i	$0.818344\pi$
$938$	152.036	+	49.3996i	0.162086	+	0.0526648i
$939$	−203.576	−	707.304i	−0.216801	−	0.753253i
$940$	−353.655	+	256.946i	−0.376229	+	0.273346i
$941$	905.041	+	1245.68i	0.961787	+	1.32379i	0.946088	+	0.323909i	$0.104997\pi$
$941$	905.041	+	1245.68i	0.961787	+	1.32379i	0.0156984	+	0.999877i	$0.495003\pi$
$942$	933.495	−	268.678i	0.990972	−	0.285221i
$943$	−373.408	+	1149.23i	−0.395979	+	1.21870i
$944$	−249.427	+	343.307i	−0.264223	+	0.363672i
$945$	−62.5543	+	612.701i	−0.0661950	+	0.648361i
$946$	41.4379	−	111.340i	0.0438032	−	0.117695i
$947$		−	635.059i		−	0.670601i	−0.942111	−	0.335301i	$-0.891162\pi$
$947$		−	635.059i		−	0.670601i	0.942111	−	0.335301i	$-0.108838\pi$
$948$	−161.187	−	125.676i	−0.170029	−	0.132570i
$949$	−128.784	+	396.357i	−0.135705	+	0.417658i
$950$	−96.2929	+	31.2875i	−0.101361	+	0.0329342i
$951$	−58.0418	−	85.8666i	−0.0610324	−	0.0902909i
$952$	−186.239	+	135.311i	−0.195630	+	0.142133i
$953$	1354.43	−	440.079i	1.42122	−	0.461783i	0.505232	−	0.862983i	$-0.331407\pi$
$953$	1354.43	−	440.079i	1.42122	−	0.461783i	0.915990	+	0.401200i	$0.131407\pi$
$954$	106.659	−	265.507i	0.111802	−	0.278309i
$955$	−1387.25	−	1007.90i	−1.45262	−	1.05539i
$956$			310.917i			0.325227i
$957$	−228.532	−	941.556i	−0.238800	−	0.983862i
$958$	1259.18			1.31438
$959$	167.785	−	230.936i	0.174958	−	0.240810i
$960$	127.225	+	46.1634i	0.132526	+	0.0480868i
$961$	−180.659	−	556.011i	−0.187991	−	0.578576i
$962$	−759.984	−	1046.03i	−0.790004	−	1.08735i
$963$	423.515	+	674.783i	0.439787	+	0.700709i
$964$	5.07160	+	15.6088i	0.00526100	+	0.0161917i
$965$	504.189	+	163.821i	0.522476	+	0.169763i
$966$	290.984	+	226.877i	0.301226	+	0.234863i
$967$	−969.749			−1.00284			−0.501421	−	0.865203i	$-0.667189\pi$
$967$	−969.749			−1.00284			−0.501421	+	0.865203i	$0.667189\pi$
$968$	−333.236	+	77.9878i	−0.344252	+	0.0805659i
$969$	−21.5466	+	635.077i	−0.0222359	+	0.655395i
$970$	−1180.63	−	857.777i	−1.21714	−	0.884306i
$971$	1196.16	+	388.656i	1.23188	+	0.400264i	0.851397	−	0.524522i	$-0.175756\pi$
$971$	1196.16	+	388.656i	1.23188	+	0.400264i	0.380488	+	0.924786i	$0.375756\pi$
$972$	−70.0247	−	480.929i	−0.0720418	−	0.494783i
$973$	845.495	−	614.288i	0.868957	−	0.631334i
$974$	101.994	+	140.382i	0.104716	+	0.144130i
$975$	118.440	+	411.508i	0.121477	+	0.422060i
$976$	44.8196	−	137.941i	0.0459217	−	0.141333i
$977$	−795.131	+	1094.40i	−0.813850	+	1.12017i	0.176868	+	0.984235i	$0.443403\pi$
$977$	−795.131	+	1094.40i	−0.813850	+	1.12017i	−0.990718	+	0.135933i	$0.956597\pi$
$978$	−10.9828	+	323.713i	−0.0112298	+	0.330995i
$979$	−132.904	−	476.460i	−0.135755	−	0.486680i
$980$		−	368.108i		−	0.375621i
$981$	−843.420	−	704.867i	−0.859756	−	0.718518i
$982$	−19.9884	+	61.5178i	−0.0203547	+	0.0626454i
$983$	−451.820	+	146.805i	−0.459634	+	0.149344i	−0.529676	−	0.848200i	$-0.677686\pi$
$983$	−451.820	+	146.805i	−0.459634	+	0.149344i	0.0700425	+	0.997544i	$0.477686\pi$
$984$	395.095	−	267.066i	0.401520	−	0.271408i
$985$	923.232	−	670.767i	0.937291	−	0.680982i
$986$	−794.577	+	258.174i	−0.805859	+	0.261839i
$987$	442.132	+	160.426i	0.447956	+	0.162539i
$988$	357.486	+	259.729i	0.361828	+	0.262884i
$989$			164.195i			0.166021i
$990$	719.581	+	324.908i	0.726850	+	0.328190i
$991$	−947.231			−0.955833			−0.477917	−	0.878405i	$-0.658608\pi$
$991$	−947.231			−0.955833			−0.477917	+	0.878405i	$0.658608\pi$
$992$	−64.5066	+	88.7857i	−0.0650268	+	0.0895017i
$993$	59.9369	−	165.185i	0.0603594	−	0.166350i
$994$	172.682	+	531.461i	0.173724	+	0.534669i
$995$	−528.413	−	727.297i	−0.531068	−	0.730952i
$996$	−299.254	−	442.715i	−0.300456	−	0.444493i
$997$	−326.005	−	1003.34i	−0.326986	−	1.00636i	−0.970536	−	0.240955i	$-0.922539\pi$
$997$	−326.005	−	1003.34i	−0.326986	−	1.00636i	0.643550	−	0.765404i	$-0.277461\pi$
$998$	−1162.88	−	377.843i	−1.16521	−	0.378600i
$999$	876.394	+	784.398i	0.877271	+	0.785183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.g.a.59.6	yes	32
3.2	odd	2	inner	66.3.g.a.59.3	yes	32
11.3	even	5	inner	66.3.g.a.47.3	✓	32
11.5	even	5		726.3.c.h.485.16		16
11.6	odd	10		726.3.c.i.485.8		16
33.5	odd	10		726.3.c.h.485.8		16
33.14	odd	10	inner	66.3.g.a.47.6	yes	32
33.17	even	10		726.3.c.i.485.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.g.a.47.3	✓	32	11.3	even	5	inner
66.3.g.a.47.6	yes	32	33.14	odd	10	inner
66.3.g.a.59.3	yes	32	3.2	odd	2	inner
66.3.g.a.59.6	yes	32	1.1	even	1	trivial
726.3.c.h.485.8		16	33.5	odd	10
726.3.c.h.485.16		16	11.5	even	5
726.3.c.i.485.8		16	11.6	odd	10
726.3.c.i.485.16		16	33.17	even	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831254 - 1.14412i) q^{2} +(1.02326 - 2.82009i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(3.31466 + 4.56224i) q^{5} +(-2.37594 - 3.51495i) q^{6} +(-1.24997 - 3.84700i) q^{7} +(-2.68999 - 0.874032i) q^{8} +(-6.90587 - 5.77140i) q^{9} +7.97508 q^{10} +(-10.5955 + 2.95553i) q^{11} +(-5.99655 - 0.203448i) q^{12} +(16.9796 + 12.3364i) q^{13} +(-5.44049 - 1.76772i) q^{14} +(16.2577 - 4.67928i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(11.8269 + 16.2783i) q^{17} +(-12.3437 + 3.10366i) q^{18} +(-3.25301 + 10.0117i) q^{19} +(6.62932 - 9.12447i) q^{20} +(-12.1280 - 0.411471i) q^{21} +(-5.42607 + 14.5794i) q^{22} -21.5005i q^{23} +(-5.21742 + 6.69167i) q^{24} +(-2.10161 + 6.46810i) q^{25} +(28.2287 - 9.17205i) q^{26} +(-23.3424 + 13.5695i) q^{27} +(-6.54492 + 4.75516i) q^{28} +(-27.9234 + 9.07286i) q^{29} +(8.16061 - 22.4905i) q^{30} +(15.6952 + 11.4033i) q^{31} +5.65685i q^{32} +(-2.50713 + 32.9046i) q^{33} +28.4556 q^{34} +(13.4077 - 18.4542i) q^{35} +(-6.70979 + 16.7027i) q^{36} +(-13.4612 - 41.4293i) q^{37} +(8.75057 + 12.0441i) q^{38} +(52.1643 - 35.2606i) q^{39} +(-4.92887 - 15.1695i) q^{40} +(-53.4514 - 17.3674i) q^{41} +(-10.5522 + 13.5338i) q^{42} -7.63681 q^{43} +(12.1701 + 18.3272i) q^{44} +(3.43989 - 50.6364i) q^{45} +(-24.5992 - 17.8724i) q^{46} +(-36.8620 - 11.9772i) q^{47} +(3.31909 + 11.5319i) q^{48} +(26.4048 - 19.1842i) q^{49} +(5.65333 + 7.78114i) q^{50} +(58.0085 - 16.6960i) q^{51} +(12.9712 - 39.9214i) q^{52} +(-13.2137 + 18.1871i) q^{53} +(-3.87825 + 37.9863i) q^{54} +(-48.6043 - 38.5427i) q^{55} +11.4409i q^{56} +(24.9053 + 19.4184i) q^{57} +(-12.8310 + 39.4897i) q^{58} +(100.895 - 32.7829i) q^{59} +(-18.9483 - 28.0320i) q^{60} +(-29.3348 + 21.3130i) q^{61} +(26.0935 - 8.47828i) q^{62} +(-13.5705 + 33.7810i) q^{63} +(6.47214 + 4.70228i) q^{64} +118.356i q^{65} +(35.5629 + 30.2206i) q^{66} -27.9454 q^{67} +(23.6538 - 32.5567i) q^{68} +(-60.6335 - 22.0007i) q^{69} +(-9.96859 - 30.6802i) q^{70} +(-57.4186 - 79.0299i) q^{71} +(13.5324 + 21.5610i) q^{72} +(6.13612 + 18.8850i) q^{73} +(-58.5899 - 19.0370i) q^{74} +(16.0902 + 12.5453i) q^{75} +21.0539 q^{76} +(24.6140 + 37.0667i) q^{77} +(3.01931 - 88.9929i) q^{78} +(27.5593 + 20.0230i) q^{79} +(-21.4529 - 6.97048i) q^{80} +(14.3820 + 79.7130i) q^{81} +(-64.3021 + 46.7182i) q^{82} +(52.3490 + 72.0522i) q^{83} +(6.71283 + 23.3231i) q^{84} +(-35.0635 + 107.914i) q^{85} +(-6.34812 + 8.73744i) q^{86} +(-2.98666 + 88.0306i) q^{87} +(31.0851 + 1.31047i) q^{88} +44.9681i q^{89} +(-55.0748 - 46.0274i) q^{90} +(26.2342 - 80.7406i) q^{91} +(-40.8964 + 13.2880i) q^{92} +(48.2186 - 32.5935i) q^{93} +(-44.3450 + 32.2186i) q^{94} +(-56.4585 + 18.3445i) q^{95} +(15.9529 + 5.78845i) q^{96} +(-148.040 - 107.557i) q^{97} -46.1573i q^{98} +(90.2287 + 40.7404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

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