LMFDB - Embedded newform 27.3.f.a.14.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,3,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.735696713773$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.4
Character	$\chi$	$=$	27.14
Dual form			27.3.f.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14332 - 0.201599i) q^{2} +(1.10490 - 2.78912i) q^{3} +(-2.49222 + 0.907094i) q^{4} +(-3.46013 + 4.12362i) q^{5} +(0.700975 - 3.41162i) q^{6} +(9.89907 + 3.60297i) q^{7} +(-6.68824 + 3.86146i) q^{8} +(-6.55839 - 6.16340i) q^{9} +(-3.12473 + 5.41219i) q^{10} +(-7.54888 - 8.99640i) q^{11} +(-0.223658 + 7.95335i) q^{12} +(1.95057 - 11.0622i) q^{13} +(12.0442 + 2.12372i) q^{14} +(7.67818 + 14.2069i) q^{15} +(1.25834 - 1.05588i) q^{16} +(2.73630 + 1.57980i) q^{17} +(-8.74091 - 5.72460i) q^{18} +(2.26051 + 3.91532i) q^{19} +(4.88289 - 13.4156i) q^{20} +(20.9866 - 23.6288i) q^{21} +(-10.4445 - 8.76396i) q^{22} +(6.80880 + 18.7070i) q^{23} +(3.38024 + 22.9208i) q^{24} +(-0.690550 - 3.91630i) q^{25} -13.0409i q^{26} +(-24.4368 + 11.4822i) q^{27} -27.9389 q^{28} +(24.9744 - 4.40366i) q^{29} +(11.6428 + 14.6952i) q^{30} +(-20.7874 + 7.56598i) q^{31} +(21.0826 - 25.1253i) q^{32} +(-33.4328 + 11.1146i) q^{33} +(3.44696 + 1.25459i) q^{34} +(-49.1093 + 28.3533i) q^{35} +(21.9358 + 9.41147i) q^{36} +(-8.82807 + 15.2907i) q^{37} +(3.37382 + 4.02076i) q^{38} +(-28.6987 - 17.6630i) q^{39} +(7.21898 - 40.9409i) q^{40} +(-12.2557 - 2.16101i) q^{41} +(19.2309 - 31.2462i) q^{42} +(27.9211 - 23.4286i) q^{43} +(26.9741 + 15.5735i) q^{44} +(48.1084 - 5.71818i) q^{45} +(11.5560 + 20.0156i) q^{46} +(-4.24091 + 11.6518i) q^{47} +(-1.55462 - 4.67631i) q^{48} +(47.4740 + 39.8354i) q^{49} +(-1.57905 - 4.33839i) q^{50} +(7.42960 - 5.88634i) q^{51} +(5.17323 + 29.3388i) q^{52} -84.6210i q^{53} +(-25.6244 + 18.0543i) q^{54} +63.2178 q^{55} +(-80.1200 + 14.1273i) q^{56} +(13.4179 - 1.97880i) q^{57} +(27.6661 - 10.0696i) q^{58} +(-43.8854 + 52.3006i) q^{59} +(-32.0227 - 28.4419i) q^{60} +(-73.3637 - 26.7022i) q^{61} +(-22.2414 + 12.8411i) q^{62} +(-42.7155 - 84.6415i) q^{63} +(15.7537 - 27.2863i) q^{64} +(38.8672 + 46.3201i) q^{65} +(-35.9839 + 19.4476i) q^{66} +(-16.8654 + 95.6483i) q^{67} +(-8.25249 - 1.45514i) q^{68} +(59.6992 + 1.67882i) q^{69} +(-50.4319 + 42.3174i) q^{70} +(105.364 + 60.8322i) q^{71} +(67.6638 + 15.8973i) q^{72} +(-45.5705 - 78.9304i) q^{73} +(-7.01076 + 19.2619i) q^{74} +(-11.6860 - 2.40109i) q^{75} +(-9.18525 - 7.70734i) q^{76} +(-42.3131 - 116.254i) q^{77} +(-36.3728 - 14.4089i) q^{78} +(-3.54032 - 20.0781i) q^{79} +8.84240i q^{80} +(5.02506 + 80.8440i) q^{81} -14.4479 q^{82} +(31.1219 - 5.48763i) q^{83} +(-30.8697 + 77.9250i) q^{84} +(-15.9824 + 5.81713i) q^{85} +(27.1997 - 32.4154i) q^{86} +(15.3119 - 74.5223i) q^{87} +(85.2279 + 31.0204i) q^{88} +(59.7756 - 34.5114i) q^{89} +(53.8507 - 16.2363i) q^{90} +(59.1656 - 102.478i) q^{91} +(-33.9381 - 40.4458i) q^{92} +(-1.86551 + 66.3381i) q^{93} +(-2.49974 + 14.1767i) q^{94} +(-23.9669 - 4.22602i) q^{95} +(-46.7833 - 86.5629i) q^{96} +(-61.1335 + 51.2971i) q^{97} +(62.3089 + 35.9741i) q^{98} +(-5.93989 + 105.529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) $ 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	1.14332	−	0.201599i	0.571662	−	0.100799i	0.119658	−	0.992815i	$-0.461820\pi$
$2$	1.14332	−	0.201599i	0.571662	−	0.100799i	0.452004	+	0.892016i	$0.350709\pi$
$3$	1.10490	−	2.78912i	0.368300	−	0.929707i
$3$	1.10490	−	2.78912i	0.368300	−	0.929707i
$4$	−2.49222	+	0.907094i	−0.623055	+	0.226774i
$5$	−3.46013	+	4.12362i	−0.692026	+	0.824724i	−0.991599	−	0.129349i	$-0.958711\pi$
$5$	−3.46013	+	4.12362i	−0.692026	+	0.824724i	0.299574	+	0.954073i	$0.403156\pi$
$6$	0.700975	−	3.41162i	0.116829	−	0.568603i
$7$	9.89907	+	3.60297i	1.41415	+	0.514709i	0.932346	−	0.361568i	$-0.117759\pi$
$7$	9.89907	+	3.60297i	1.41415	+	0.514709i	0.481807	+	0.876278i	$0.339981\pi$
$8$	−6.68824	+	3.86146i	−0.836030	+	0.482682i
$9$	−6.55839	−	6.16340i	−0.728710	−	0.684822i
$10$	−3.12473	+	5.41219i	−0.312473	+	0.541219i
$11$	−7.54888	−	8.99640i	−0.686262	−	0.817855i	0.304636	−	0.952469i	$-0.401465\pi$
$11$	−7.54888	−	8.99640i	−0.686262	−	0.817855i	−0.990898	+	0.134614i	$0.957021\pi$
$12$	−0.223658	+	7.95335i	−0.0186382	+	0.662780i
$13$	1.95057	−	11.0622i	0.150044	−	0.850940i	−0.813134	−	0.582076i	$-0.802241\pi$
$13$	1.95057	−	11.0622i	0.150044	−	0.850940i	0.963178	−	0.268864i	$-0.0866482\pi$
$14$	12.0442	+	2.12372i	0.860300	+	0.151694i
$15$	7.67818	+	14.2069i	0.511879	+	0.947127i
$16$	1.25834	−	1.05588i	0.0786465	−	0.0659923i
$17$	2.73630	+	1.57980i	0.160959	+	0.0929296i	0.578316	−	0.815813i	$-0.303710\pi$
$17$	2.73630	+	1.57980i	0.160959	+	0.0929296i	−0.417357	+	0.908743i	$0.637044\pi$
$18$	−8.74091	−	5.72460i	−0.485606	−	0.318033i
$19$	2.26051	+	3.91532i	0.118974	+	0.206069i	0.919361	−	0.393414i	$-0.128706\pi$
$19$	2.26051	+	3.91532i	0.118974	+	0.206069i	−0.800387	+	0.599483i	$0.795373\pi$
$20$	4.88289	−	13.4156i	0.244145	−	0.670782i
$21$	20.9866	−	23.6288i	0.999361	−	1.12518i
$22$	−10.4445	−	8.76396i	−0.474749	−	0.398362i
$23$	6.80880	+	18.7070i	0.296035	+	0.813349i	0.995153	+	0.0983427i	$0.0313541\pi$
$23$	6.80880	+	18.7070i	0.296035	+	0.813349i	−0.699118	+	0.715007i	$0.746424\pi$
$24$	3.38024	+	22.9208i	0.140843	+	0.955035i
$25$	−0.690550	−	3.91630i	−0.0276220	−	0.156652i
$26$		−	13.0409i		−	0.501575i
$27$	−24.4368	+	11.4822i	−0.905068	+	0.425267i
$28$	−27.9389			−0.997818
$29$	24.9744	−	4.40366i	0.861187	−	0.151851i	0.274424	−	0.961609i	$-0.411513\pi$
$29$	24.9744	−	4.40366i	0.861187	−	0.151851i	0.586763	+	0.809758i	$0.300402\pi$
$30$	11.6428	+	14.6952i	0.388092	+	0.489840i
$31$	−20.7874	+	7.56598i	−0.670560	+	0.244064i	−0.654789	−	0.755812i	$-0.727243\pi$
$31$	−20.7874	+	7.56598i	−0.670560	+	0.244064i	−0.0157712	+	0.999876i	$0.505020\pi$
$32$	21.0826	−	25.1253i	0.658832	−	0.785165i
$33$	−33.4328	+	11.1146i	−1.01312	+	0.336807i
$34$	3.44696	+	1.25459i	0.101381	+	0.0368998i
$35$	−49.1093	+	28.3533i	−1.40312	+	0.810093i
$36$	21.9358	+	9.41147i	0.609326	+	0.261430i
$37$	−8.82807	+	15.2907i	−0.238596	+	0.413261i	−0.960312	−	0.278929i	$-0.910021\pi$
$37$	−8.82807	+	15.2907i	−0.238596	+	0.413261i	0.721715	+	0.692190i	$0.243354\pi$
$38$	3.37382	+	4.02076i	0.0887847	+	0.105810i
$39$	−28.6987	−	17.6630i	−0.735864	−	0.452898i
$40$	7.21898	−	40.9409i	0.180475	−	1.02352i
$41$	−12.2557	−	2.16101i	−0.298920	−	0.0527076i	0.0221770	−	0.999754i	$-0.492940\pi$
$41$	−12.2557	−	2.16101i	−0.298920	−	0.0527076i	−0.321096	+	0.947046i	$0.604051\pi$
$42$	19.2309	−	31.2462i	0.457880	−	0.743958i
$43$	27.9211	−	23.4286i	0.649329	−	0.544851i	−0.257539	−	0.966268i	$-0.582911\pi$
$43$	27.9211	−	23.4286i	0.649329	−	0.544851i	0.906867	+	0.421417i	$0.138467\pi$
$44$	26.9741	+	15.5735i	0.613047	+	0.353943i
$45$	48.1084	−	5.71818i	1.06908	−	0.127071i
$46$	11.5560	+	20.0156i	0.251217	+	0.435121i
$47$	−4.24091	+	11.6518i	−0.0902320	+	0.247910i	−0.976597	−	0.215076i	$-0.931000\pi$
$47$	−4.24091	+	11.6518i	−0.0902320	+	0.247910i	0.886365	+	0.462987i	$0.153222\pi$
$48$	−1.55462	−	4.67631i	−0.0323880	−	0.0974232i
$49$	47.4740	+	39.8354i	0.968857	+	0.812967i
$50$	−1.57905	−	4.33839i	−0.0315809	−	0.0867679i
$51$	7.42960	−	5.88634i	0.145678	−	0.115419i
$52$	5.17323	+	29.3388i	0.0994852	+	0.564209i
$53$		−	84.6210i		−	1.59662i	−0.602245	−	0.798311i	$-0.705727\pi$
$53$		−	84.6210i		−	1.59662i	0.602245	−	0.798311i	$-0.294273\pi$
$54$	−25.6244	+	18.0543i	−0.474526	+	0.334340i
$55$	63.2178			1.14942
$56$	−80.1200	+	14.1273i	−1.43071	+	0.252274i
$57$	13.4179	−	1.97880i	0.235402	−	0.0347158i
$58$	27.6661	−	10.0696i	0.477002	−	0.173614i
$59$	−43.8854	+	52.3006i	−0.743820	+	0.886451i	−0.996711	−	0.0810443i	$-0.974174\pi$
$59$	−43.8854	+	52.3006i	−0.743820	+	0.886451i	0.252890	+	0.967495i	$0.418619\pi$
$60$	−32.0227	−	28.4419i	−0.533712	−	0.474032i
$61$	−73.3637	−	26.7022i	−1.20268	−	0.437741i	−0.338523	−	0.940958i	$-0.609927\pi$
$61$	−73.3637	−	26.7022i	−1.20268	−	0.437741i	−0.864160	+	0.503217i	$0.832150\pi$
$62$	−22.2414	+	12.8411i	−0.358733	+	0.207114i
$63$	−42.7155	−	84.6415i	−0.678023	−	1.34352i
$64$	15.7537	−	27.2863i	0.246152	−	0.426348i
$65$	38.8672	+	46.3201i	0.597956	+	0.712617i
$66$	−35.9839	+	19.4476i	−0.545210	+	0.294661i
$67$	−16.8654	+	95.6483i	−0.251722	+	1.42759i	0.552627	+	0.833429i	$0.313625\pi$
$67$	−16.8654	+	95.6483i	−0.251722	+	1.42759i	−0.804349	+	0.594157i	$0.797486\pi$
$68$	−8.25249	−	1.45514i	−0.121360	−	0.0213991i
$69$	59.6992	+	1.67882i	0.865206	+	0.0243307i
$70$	−50.4319	+	42.3174i	−0.720455	+	0.604534i
$71$	105.364	+	60.8322i	1.48401	+	0.856791i	0.999835	−	0.0181820i	$-0.00578784\pi$
$71$	105.364	+	60.8322i	1.48401	+	0.856791i	0.484171	+	0.874973i	$0.339121\pi$
$72$	67.6638	+	15.8973i	0.939775	+	0.220796i
$73$	−45.5705	−	78.9304i	−0.624254	−	1.08124i	−0.988685	−	0.150009i	$-0.952070\pi$
$73$	−45.5705	−	78.9304i	−0.624254	−	1.08124i	0.364431	−	0.931230i	$-0.381263\pi$
$74$	−7.01076	+	19.2619i	−0.0947401	+	0.260296i
$75$	−11.6860	−	2.40109i	−0.155814	−	0.0320146i
$76$	−9.18525	−	7.70734i	−0.120859	−	0.101412i
$77$	−42.3131	−	116.254i	−0.549521	−	1.50980i
$78$	−36.3728	−	14.4089i	−0.466317	−	0.184730i
$79$	−3.54032	−	20.0781i	−0.0448142	−	0.254154i	0.954167	−	0.299273i	$-0.0967442\pi$
$79$	−3.54032	−	20.0781i	−0.0448142	−	0.254154i	−0.998982	+	0.0451196i	$0.985633\pi$
$80$			8.84240i			0.110530i
$81$	5.02506	+	80.8440i	0.0620378	+	0.998074i
$82$	−14.4479			−0.176194
$83$	31.1219	−	5.48763i	0.374963	−	0.0661161i	0.0170090	−	0.999855i	$-0.494586\pi$
$83$	31.1219	−	5.48763i	0.374963	−	0.0661161i	0.357954	+	0.933739i	$0.383474\pi$
$84$	−30.8697	+	77.9250i	−0.367496	+	0.927678i
$85$	−15.9824	+	5.81713i	−0.188029	+	0.0684369i
$86$	27.1997	−	32.4154i	0.316276	−	0.376923i
$87$	15.3119	−	74.5223i	0.175999	−	0.856578i
$88$	85.2279	+	31.0204i	0.968499	+	0.352505i
$89$	59.7756	−	34.5114i	0.671636	−	0.387769i	−0.125060	−	0.992149i	$-0.539912\pi$
$89$	59.7756	−	34.5114i	0.671636	−	0.387769i	0.796696	+	0.604380i	$0.206579\pi$
$90$	53.8507	−	16.2363i	0.598341	−	0.180404i
$91$	59.1656	−	102.478i	0.650171	−	1.12613i
$92$	−33.9381	−	40.4458i	−0.368892	−	0.439629i
$93$	−1.86551	+	66.3381i	−0.0200592	+	0.713313i
$94$	−2.49974	+	14.1767i	−0.0265930	+	0.150816i
$95$	−23.9669	−	4.22602i	−0.252283	−	0.0444844i
$96$	−46.7833	−	86.5629i	−0.487326	−	0.901696i
$97$	−61.1335	+	51.2971i	−0.630243	+	0.528836i	−0.901004	−	0.433810i	$-0.857169\pi$
$97$	−61.1335	+	51.2971i	−0.630243	+	0.528836i	0.270762	+	0.962646i	$0.412724\pi$
$98$	62.3089	+	35.9741i	0.635806	+	0.367083i
$99$	−5.93989	+	105.529i	−0.0599989	+	1.06595i
$100$	5.27346	+	9.13390i	0.0527346	+	0.0913390i
$101$	−1.63372	+	4.48862i	−0.0161755	+	0.0444417i	−0.947518	−	0.319704i	$-0.896417\pi$
$101$	−1.63372	+	4.48862i	−0.0161755	+	0.0444417i	0.931342	+	0.364145i	$0.118639\pi$
$102$	7.30776	−	8.22780i	0.0716447	−	0.0806647i
$103$	−55.3795	−	46.4689i	−0.537665	−	0.451154i	0.333074	−	0.942901i	$-0.391914\pi$
$103$	−55.3795	−	46.4689i	−0.537665	−	0.451154i	−0.870738	+	0.491746i	$0.836359\pi$
$104$	29.6704	+	81.5188i	0.285293	+	0.783835i
$105$	24.8199	+	168.299i	0.236380	+	1.60285i
$106$	−17.0595	−	96.7493i	−0.160939	−	0.912729i
$107$		−	158.133i		−	1.47788i	−0.673773	−	0.738938i	$-0.735328\pi$
$107$		−	158.133i		−	1.47788i	0.673773	−	0.738938i	$-0.264672\pi$
$108$	50.4865	−	50.7827i	0.467468	−	0.470211i
$109$	−18.5788			−0.170448			−0.0852240	−	0.996362i	$-0.527161\pi$
$109$	−18.5788			−0.170448			−0.0852240	+	0.996362i	$0.527161\pi$
$110$	72.2785	−	12.7447i	0.657077	−	0.115860i
$111$	32.8934	+	41.5172i	0.296337	+	0.374029i
$112$	16.2607	−	5.91842i	0.145185	−	0.0528430i
$113$	−11.5806	+	13.8012i	−0.102483	+	0.122134i	−0.814848	−	0.579675i	$-0.803180\pi$
$113$	−11.5806	+	13.8012i	−0.102483	+	0.122134i	0.712365	+	0.701809i	$0.247624\pi$
$114$	14.9421	−	4.96746i	0.131071	−	0.0435742i
$115$	−100.700	−	36.6518i	−0.875652	−	0.318711i
$116$	−58.2473	+	33.6291i	−0.502131	+	0.289906i
$117$	−80.9734	+	60.5283i	−0.692081	+	0.517336i
$118$	−39.6315	+	68.6438i	−0.335860	+	0.581727i
$119$	21.3948	+	25.4974i	0.179788	+	0.214264i
$120$	−106.213	−	65.3702i	−0.885107	−	0.544752i
$121$	−2.93828	+	16.6638i	−0.0242833	+	0.137717i
$122$	−89.2617	−	15.7392i	−0.731653	−	0.129010i
$123$	−19.5686	+	31.7949i	−0.159095	+	0.258495i
$124$	44.9437	−	37.7122i	0.362449	−	0.304131i
$125$	−98.0067	−	56.5842i	−0.784054	−	0.452674i
$126$	−65.9013	−	88.1614i	−0.523026	−	0.699693i
$127$	78.1067	+	135.285i	0.615013	+	1.06523i	0.990382	+	0.138359i	$0.0441827\pi$
$127$	78.1067	+	135.285i	0.615013	+	1.06523i	−0.375369	+	0.926876i	$0.622484\pi$
$128$	−32.3605	+	88.9098i	−0.252817	+	0.694608i
$129$	−34.4952	−	103.762i	−0.267405	−	0.804354i
$130$	53.7759	+	45.1233i	0.413661	+	0.347102i
$131$	33.6955	+	92.5776i	0.257217	+	0.706699i	0.999336	+	0.0364307i	$0.0115988\pi$
$131$	33.6955	+	92.5776i	0.257217	+	0.706699i	−0.742119	+	0.670268i	$0.766179\pi$
$132$	73.2400	−	58.0268i	0.554848	−	0.439597i
$133$	8.27018	+	46.9025i	0.0621818	+	0.352651i
$134$			112.757i			0.841471i
$135$	37.2062	−	140.498i	0.275602	−	1.04073i
$136$	−24.4014			−0.179422
$137$	−64.6590	+	11.4011i	−0.471963	+	0.0832199i	−0.404571	−	0.914507i	$-0.632579\pi$
$137$	−64.6590	+	11.4011i	−0.471963	+	0.0832199i	−0.0673925	+	0.997727i	$0.521468\pi$
$138$	68.5941	−	10.1159i	0.497058	−	0.0733034i
$139$	117.744	−	42.8553i	0.847080	−	0.308312i	0.118231	−	0.992986i	$-0.462278\pi$
$139$	117.744	−	42.8553i	0.847080	−	0.308312i	0.728849	+	0.684674i	$0.240056\pi$
$140$	96.6721	−	115.209i	0.690515	−	0.822924i
$141$	27.8125	+	24.7025i	0.197252	+	0.175195i
$142$	132.729	+	48.3096i	0.934714	+	0.340208i
$143$	−114.245	+	65.9593i	−0.798915	+	0.461254i
$144$	−14.7605	−	0.830824i	−0.102503	−	0.00576961i
$145$	−68.2557	+	118.222i	−0.470729	+	0.815326i
$146$	−68.0142	−	81.0562i	−0.465851	−	0.555179i
$147$	163.560	−	88.3966i	1.11265	−	0.601337i
$148$	8.13142	−	46.1156i	0.0549420	−	0.311592i
$149$	198.691	+	35.0346i	1.33350	+	0.235132i	0.794546	−	0.607204i	$-0.207709\pi$
$149$	198.691	+	35.0346i	1.33350	+	0.235132i	0.538953	+	0.842336i	$0.318820\pi$
$150$	−13.8450	−	0.389338i	−0.0922999	−	0.00259559i
$151$	98.1613	−	82.3671i	0.650075	−	0.545478i	−0.257019	−	0.966406i	$-0.582740\pi$
$151$	98.1613	−	82.3671i	0.650075	−	0.545478i	0.907094	+	0.420929i	$0.138296\pi$
$152$	−30.2377	−	17.4577i	−0.198932	−	0.114853i
$153$	−8.20877	−	27.2259i	−0.0536521	−	0.177947i
$154$	−71.8144	−	124.386i	−0.466327	−	0.807703i
$155$	40.7277	−	111.898i	0.262759	−	0.721926i
$156$	87.5455	+	17.9877i	0.561189	+	0.115306i
$157$	−106.439	−	89.3129i	−0.677955	−	0.568872i	0.237453	−	0.971399i	$-0.423687\pi$
$157$	−106.439	−	89.3129i	−0.677955	−	0.568872i	−0.915408	+	0.402527i	$0.868132\pi$
$158$	−8.09547	−	22.2421i	−0.0512371	−	0.140773i
$159$	−236.018	−	93.4977i	−1.48439	−	0.588036i
$160$	30.6586	+	173.873i	0.191616	+	1.08671i
$161$			209.714i			1.30257i
$162$	22.0433	+	91.4179i	0.136070	+	0.564308i
$163$	39.8569			0.244521			0.122261	−	0.992498i	$-0.460986\pi$
$163$	39.8569			0.244521			0.122261	+	0.992498i	$0.460986\pi$
$164$	32.5042	−	5.73136i	0.198196	−	0.0349473i
$165$	69.8494	−	176.322i	0.423329	−	1.06862i
$166$	34.4762	−	12.5483i	0.207688	−	0.0755921i
$167$	−106.672	+	127.127i	−0.638757	+	0.761241i	−0.984173	−	0.177208i	$-0.943293\pi$
$167$	−106.672	+	127.127i	−0.638757	+	0.761241i	0.345416	+	0.938450i	$0.387738\pi$
$168$	−49.1218	+	239.074i	−0.292391	+	1.42306i
$169$	40.2401	+	14.6462i	0.238107	+	0.0866639i
$170$	−17.1004	+	9.87292i	−0.100591	+	0.0580760i
$171$	9.30634	−	39.6106i	0.0544231	−	0.231641i
$172$	−48.3337	+	83.7164i	−0.281010	+	0.486723i
$173$	−7.00006	−	8.34234i	−0.0404628	−	0.0482216i	0.745434	−	0.666580i	$-0.232243\pi$
$173$	−7.00006	−	8.34234i	−0.0404628	−	0.0482216i	−0.785896	+	0.618358i	$0.787798\pi$
$174$	2.48282	−	88.2901i	0.0142691	−	0.507414i
$175$	7.27451	−	41.2558i	0.0415686	−	0.235747i
$176$	−18.9982	−	3.34989i	−0.107944	−	0.0190335i
$177$	97.3837	+	180.189i	0.550191	+	1.01801i
$178$	61.3854	−	51.5085i	0.344862	−	0.289374i
$179$	−244.720	−	141.289i	−1.36715	−	0.789326i	−0.376590	−	0.926380i	$-0.622903\pi$
$179$	−244.720	−	141.289i	−1.36715	−	0.789326i	−0.990564	+	0.137054i	$0.956237\pi$
$180$	−114.710	+	57.8898i	−0.637277	+	0.321610i
$181$	54.3996	+	94.2228i	0.300550	+	0.520568i	0.976261	−	0.216599i	$-0.0694964\pi$
$181$	54.3996	+	94.2228i	0.300550	+	0.520568i	−0.675711	+	0.737167i	$0.736163\pi$
$182$	46.9861	−	129.093i	0.258165	−	0.709303i
$183$	−155.535	+	175.117i	−0.849919	+	0.956923i
$184$	−117.775	−	98.8252i	−0.640083	−	0.537094i
$185$	−32.5066	−	89.3112i	−0.175711	−	0.482763i
$186$	11.2408	+	76.2221i	0.0604345	+	0.409796i
$187$	−6.44344	−	36.5426i	−0.0344569	−	0.195415i
$188$		−	32.8857i		−	0.174924i
$189$	−283.272	+	25.6182i	−1.49879	+	0.135546i
$190$	−28.2539			−0.148705
$191$	106.979	−	18.8633i	0.560100	−	0.0987607i	0.113571	−	0.993530i	$-0.463771\pi$
$191$	106.979	−	18.8633i	0.560100	−	0.0987607i	0.446529	+	0.894769i	$0.352660\pi$
$192$	−58.6984	−	74.0877i	−0.305721	−	0.385873i
$193$	−188.040	+	68.4410i	−0.974301	+	0.354617i	−0.779622	−	0.626250i	$-0.784589\pi$
$193$	−188.040	+	68.4410i	−0.974301	+	0.354617i	−0.194679	+	0.980867i	$0.562367\pi$
$194$	−59.5540	+	70.9737i	−0.306980	+	0.365844i
$195$	172.137	−	57.2262i	0.882752	−	0.293468i
$196$	−154.450	−	56.2152i	−0.788011	−	0.286812i
$197$	253.494	−	146.355i	1.28677	−	0.742918i	0.308694	−	0.951161i	$-0.400108\pi$
$197$	253.494	−	146.355i	1.28677	−	0.742918i	0.978077	+	0.208243i	$0.0667746\pi$
$198$	14.4833	+	121.851i	0.0731478	+	0.615409i
$199$	41.1548	−	71.2822i	0.206808	−	0.358202i	−0.743899	−	0.668292i	$-0.767026\pi$
$199$	41.1548	−	71.2822i	0.206808	−	0.358202i	0.950707	+	0.310090i	$0.100359\pi$
$200$	19.7412	+	23.5267i	0.0987060	+	0.117633i
$201$	248.140	+	152.721i	1.23453	+	0.759807i
$202$	−0.962975	+	5.46130i	−0.00476720	+	0.0270361i
$203$	263.090	+	46.3898i	1.29601	+	0.228521i
$204$	−13.1767	+	21.4094i	−0.0645918	+	0.104948i
$205$	51.3175	−	43.0605i	0.250329	−	0.210051i
$206$	−72.6848	−	41.9646i	−0.352839	−	0.203712i
$207$	70.6441	−	164.653i	0.341276	−	0.795427i
$208$	−9.22585	−	15.9796i	−0.0443550	−	0.0768252i
$209$	18.1595	−	49.8927i	0.0868874	−	0.238721i
$210$	62.3061	+	187.417i	0.296696	+	0.892462i
$211$	88.7425	+	74.4638i	0.420581	+	0.352909i	0.828384	−	0.560161i	$-0.189261\pi$
$211$	88.7425	+	74.4638i	0.420581	+	0.352909i	−0.407803	+	0.913070i	$0.633705\pi$
$212$	76.7592	+	210.894i	0.362072	+	0.994784i
$213$	286.085	−	226.661i	1.34312	−	1.06413i
$214$	−31.8794	−	180.797i	−0.148969	−	0.844846i
$215$			196.202i			0.912568i
$216$	119.101	−	171.158i	0.551395	−	0.792396i
$217$	−233.036			−1.07390
$218$	−21.2416	+	3.74547i	−0.0974387	+	0.0171811i
$219$	−270.497	+	39.8915i	−1.23515	+	0.182153i
$220$	−157.553	+	57.3445i	−0.716149	+	0.260657i
$221$	22.8135	−	27.1880i	0.103228	−	0.123023i
$222$	45.9776	+	40.8364i	0.207106	+	0.183948i
$223$	186.281	+	67.8007i	0.835341	+	0.304039i	0.724049	−	0.689749i	$-0.242279\pi$
$223$	186.281	+	67.8007i	0.835341	+	0.304039i	0.111292	+	0.993788i	$0.464501\pi$
$224$	299.224	−	172.757i	1.33582	−	0.771236i
$225$	−19.6088	+	29.9408i	−0.0871504	+	0.133070i
$226$	−10.4580	+	18.1138i	−0.0462745	+	0.0801498i
$227$	−3.31155	−	3.94655i	−0.0145883	−	0.0173857i	0.758701	−	0.651439i	$-0.225834\pi$
$227$	−3.31155	−	3.94655i	−0.0145883	−	0.0173857i	−0.773289	+	0.634053i	$0.781390\pi$
$228$	−31.6455	+	17.1029i	−0.138796	+	0.0750129i
$229$	61.3581	−	347.979i	0.267939	−	1.51956i	−0.492594	−	0.870259i	$-0.663951\pi$
$229$	61.3581	−	347.979i	0.267939	−	1.51956i	0.760533	−	0.649299i	$-0.224938\pi$
$230$	−122.522	−	21.6039i	−0.532703	−	0.0939300i
$231$	−370.999	−	10.4330i	−1.60606	−	0.0451643i
$232$	−150.030	+	125.890i	−0.646683	+	0.542631i
$233$	121.729	+	70.2803i	0.522442	+	0.301632i	0.737933	−	0.674874i	$-0.235802\pi$
$233$	121.729	+	70.2803i	0.522442	+	0.301632i	−0.215491	+	0.976506i	$0.569135\pi$
$234$	−80.3765	+	85.5276i	−0.343489	+	0.365503i
$235$	−33.3735	−	57.8046i	−0.142015	−	0.245977i
$236$	61.9306	−	170.153i	0.262418	−	0.720987i
$237$	−59.9121	−	12.3100i	−0.252794	−	0.0519407i
$238$	29.6015	+	24.8386i	0.124376	+	0.104364i
$239$	−50.5074	−	138.768i	−0.211328	−	0.580619i	0.788060	−	0.615598i	$-0.211086\pi$
$239$	−50.5074	−	138.768i	−0.211328	−	0.580619i	−0.999388	+	0.0349794i	$0.988863\pi$
$240$	24.6625	+	9.76996i	0.102761	+	0.0407082i
$241$	52.8609	+	299.789i	0.219340	+	1.24394i	0.873215	+	0.487335i	$0.162031\pi$
$241$	52.8609	+	299.789i	0.219340	+	1.24394i	−0.653875	+	0.756602i	$0.726858\pi$
$242$			19.6445i			0.0811755i
$243$	231.036	+	75.3090i	0.950765	+	0.309913i
$244$	207.060			0.848606
$245$	−328.532	+	57.9291i	−1.34095	+	0.236445i
$246$	−15.9635	+	40.2970i	−0.0648922	+	0.163809i
$247$	47.7214	−	17.3692i	0.193204	−	0.0703205i
$248$	109.815	−	130.873i	0.442803	−	0.527712i
$249$	19.0809	−	92.8661i	0.0766302	−	0.372956i
$250$	−123.461	−	44.9361i	−0.493843	−	0.179744i
$251$	−108.072	+	62.3955i	−0.430567	+	0.248588i	−0.699588	−	0.714546i	$-0.746633\pi$
$251$	−108.072	+	62.3955i	−0.430567	+	0.248588i	0.269021	+	0.963134i	$0.413300\pi$
$252$	183.234	+	172.198i	0.727120	+	0.683327i
$253$	116.897	−	202.472i	0.462044	−	0.800284i
$254$	116.575	+	138.928i	0.458955	+	0.546961i
$255$	−1.43430	+	51.0043i	−0.00562472	+	0.200017i
$256$	−40.9593	+	232.292i	−0.159997	+	0.907390i
$257$	−450.088	−	79.3627i	−1.75132	−	0.308804i	−0.796199	−	0.605035i	$-0.793159\pi$
$257$	−450.088	−	79.3627i	−1.75132	−	0.308804i	−0.955116	+	0.296231i	$0.904270\pi$
$258$	−60.3575	−	111.679i	−0.233944	−	0.432865i
$259$	−142.481	+	119.556i	−0.550121	+	0.461606i
$260$	−138.882	−	80.1837i	−0.534163	−	0.308399i
$261$	−190.934	−	125.046i	−0.731547	−	0.479105i
$262$	57.1884	+	99.0533i	0.218276	+	0.378066i
$263$	−160.047	+	439.726i	−0.608545	+	1.67196i	0.124863	+	0.992174i	$0.460151\pi$
$263$	−160.047	+	439.726i	−0.608545	+	1.67196i	−0.733408	+	0.679789i	$0.762071\pi$
$264$	180.688	−	203.437i	0.684425	−	0.770593i
$265$	348.945	+	292.799i	1.31677	+	1.10490i
$266$	18.9110	+	51.9576i	0.0710940	+	0.195329i
$267$	−30.2106	−	204.853i	−0.113148	−	0.767240i
$268$	−44.7298	−	253.675i	−0.166902	−	0.946549i
$269$			317.049i			1.17862i	0.807907	+	0.589310i	$0.200601\pi$
$269$			317.049i			1.17862i	−0.807907	+	0.589310i	$0.799399\pi$
$270$	14.2145	−	168.136i	0.0526464	−	0.622725i
$271$	115.698			0.426931			0.213465	−	0.976951i	$-0.431525\pi$
$271$	115.698			0.426931			0.213465	+	0.976951i	$0.431525\pi$
$272$	5.11128	−	0.901257i	0.0187915	−	0.00331344i
$273$	−220.451	−	278.248i	−0.807513	−	1.01922i
$274$	−71.6277	+	26.0704i	−0.261415	+	0.0951473i
$275$	−30.0198	+	35.7762i	−0.109163	+	0.130095i
$276$	−150.307	+	49.9689i	−0.544589	+	0.181047i
$277$	108.352	+	39.4370i	0.391163	+	0.142372i	0.530112	−	0.847928i	$-0.322150\pi$
$277$	108.352	+	39.4370i	0.391163	+	0.142372i	−0.138949	+	0.990300i	$0.544372\pi$
$278$	125.980	−	72.7347i	0.453166	−	0.261635i
$279$	182.964	+	78.5001i	0.655785	+	0.281362i
$280$	218.970	−	379.267i	0.782035	−	1.35452i
$281$	−52.4463	−	62.5031i	−0.186642	−	0.222431i	0.664607	−	0.747193i	$-0.268599\pi$
$281$	−52.4463	−	62.5031i	−0.186642	−	0.222431i	−0.851249	+	0.524762i	$0.824154\pi$
$282$	36.7787	+	22.6360i	0.130421	+	0.0802694i
$283$	−72.4355	+	410.802i	−0.255956	+	1.45160i	0.537652	+	0.843167i	$0.319311\pi$
$283$	−72.4355	+	410.802i	−0.255956	+	1.45160i	−0.793608	+	0.608430i	$0.791800\pi$
$284$	−317.772	−	56.0318i	−1.11892	−	0.197295i
$285$	−38.2679	+	62.1773i	−0.134273	+	0.218166i
$286$	−117.322	+	98.4445i	−0.410215	+	0.344211i
$287$	−113.534	−	65.5489i	−0.395589	−	0.228393i
$288$	−293.125	+	34.8410i	−1.01780	+	0.120976i
$289$	−139.508	−	241.636i	−0.482728	−	0.836110i
$290$	−54.2049	+	148.927i	−0.186913	+	0.513540i
$291$	75.5275	+	227.187i	0.259545	+	0.780712i
$292$	185.169	+	155.375i	0.634141	+	0.532107i
$293$	−118.282	−	324.977i	−0.403693	−	1.10914i	−0.960448	−	0.278460i	$-0.910176\pi$
$293$	−118.282	−	324.977i	−0.403693	−	1.10914i	0.556755	−	0.830676i	$-0.312046\pi$
$294$	169.181	−	134.039i	0.575446	−	0.455917i
$295$	−63.8186	−	361.933i	−0.216334	−	1.22689i
$296$		−	136.357i		−	0.460665i
$297$	287.769	+	133.166i	0.968920	+	0.448369i
$298$	234.232			0.786012
$299$	220.222	−	38.8311i	0.736529	−	0.129870i
$300$	31.3022	−	4.61628i	0.104341	−	0.0153876i
$301$	360.806	−	131.323i	1.19869	−	0.436287i
$302$	95.6252	−	113.962i	0.316640	−	0.377356i
$303$	10.7142	+	9.51612i	0.0353604	+	0.0314063i
$304$	6.97859	+	2.54000i	0.0229559	+	0.00835526i
$305$	363.957	−	210.131i	1.19330	−	0.688954i
$306$	−14.8740	−	29.4731i	−0.0486078	−	0.0963174i
$307$	−288.668	+	499.988i	−0.940286	+	1.62862i	−0.175362	+	0.984504i	$0.556110\pi$
$307$	−288.668	+	499.988i	−0.940286	+	1.62862i	−0.764925	+	0.644120i	$0.777224\pi$
$308$	210.907	+	251.350i	0.684764	+	0.816070i
$309$	−190.796	+	103.117i	−0.617463	+	0.333711i
$310$	24.0064	−	136.147i	0.0774399	−	0.439184i
$311$	442.280	+	77.9859i	1.42212	+	0.250759i	0.831202	−	0.555971i	$-0.187653\pi$
$311$	442.280	+	77.9859i	1.42212	+	0.250759i	0.590921	+	0.806730i	$0.298765\pi$
$312$	260.149	+	7.31570i	0.833810	+	0.0234478i
$313$	8.30206	−	6.96625i	0.0265241	−	0.0222564i	−0.629429	−	0.777058i	$-0.716711\pi$
$313$	8.30206	−	6.96625i	0.0265241	−	0.0222564i	0.655953	+	0.754801i	$0.272267\pi$
$314$	−139.700	−	80.6557i	−0.444904	−	0.256865i
$315$	496.830	+	116.728i	1.57724	+	0.370566i
$316$	27.0360	+	46.8278i	0.0855570	+	0.148189i
$317$	−74.6402	+	205.072i	−0.235458	+	0.646916i	0.764539	+	0.644577i	$0.222967\pi$
$317$	−74.6402	+	205.072i	−0.235458	+	0.646916i	−0.999997	+	0.00233841i	$0.999256\pi$
$318$	−288.694	−	59.3172i	−0.907844	−	0.186532i
$319$	−228.146	−	191.437i	−0.715191	−	0.600117i
$320$	58.0083	+	159.376i	0.181276	+	0.498051i
$321$	−441.051	−	174.721i	−1.37399	−	0.544302i
$322$	42.2781	+	239.771i	0.131299	+	0.744631i
$323$			14.2846i			0.0442249i
$324$	−85.8567	−	196.923i	−0.264990	−	0.607787i
$325$	−44.6700			−0.137446
$326$	45.5694	−	8.03512i	0.139784	−	0.0246476i
$327$	−20.5277	+	51.8186i	−0.0627760	+	0.158467i
$328$	90.3137	−	32.8715i	0.275347	−	0.100218i
$329$	−83.9620	+	100.062i	−0.255204	+	0.304140i
$330$	44.3141	−	215.675i	0.134285	−	0.653561i
$331$	−564.453	−	205.444i	−1.70530	−	0.620677i	−0.708885	−	0.705324i	$-0.750802\pi$
$331$	−564.453	−	205.444i	−1.70530	−	0.620677i	−0.996411	+	0.0846470i	$0.973024\pi$
$332$	−72.5849	+	41.9069i	−0.218629	+	0.126226i
$333$	152.140	−	45.8713i	0.456878	−	0.137752i
$334$	−96.3325	+	166.853i	−0.288421	+	0.499559i
$335$	−336.061	−	400.502i	−1.00317	−	1.19553i
$336$	1.45928	−	51.8924i	0.00434309	−	0.154442i
$337$	78.0147	−	442.443i	0.231498	−	1.31289i	−0.618368	−	0.785889i	$-0.712206\pi$
$337$	78.0147	−	442.443i	0.231498	−	1.31289i	0.849865	−	0.527000i	$-0.176683\pi$
$338$	48.9602	+	8.63300i	0.144853	+	0.0255414i
$339$	25.6978	+	47.5485i	0.0758047	+	0.140261i
$340$	34.5551	−	28.9952i	0.101633	−	0.0852799i
$341$	224.988	+	129.897i	0.659789	+	0.380929i
$342$	2.65471	−	47.1639i	0.00776232	−	0.137906i
$343$	68.3305	+	118.352i	0.199214	+	0.345049i
$344$	−96.2747	+	264.512i	−0.279868	+	0.768932i
$345$	−213.490	+	240.368i	−0.618811	+	0.696719i
$346$	−9.68515	−	8.12680i	−0.0279918	−	0.0234879i
$347$	−80.7717	−	221.918i	−0.232771	−	0.639534i	0.767227	−	0.641376i	$-0.221636\pi$
$347$	−80.7717	−	221.918i	−0.232771	−	0.639534i	−0.999998	+	0.00184170i	$0.999414\pi$
$348$	29.4382	+	199.615i	0.0845925	+	0.573607i
$349$	41.6381	+	236.141i	0.119307	+	0.676622i	0.984527	+	0.175231i	$0.0560672\pi$
$349$	41.6381	+	236.141i	0.119307	+	0.676622i	−0.865221	+	0.501391i	$0.832822\pi$
$350$		−	48.6353i		−	0.138958i
$351$	79.3531	+	292.722i	0.226077	+	0.833967i
$352$	−385.187			−1.09428
$353$	25.2020	−	4.44379i	0.0713937	−	0.0125886i	−0.137837	−	0.990455i	$-0.544015\pi$
$353$	25.2020	−	4.44379i	0.0713937	−	0.0125886i	0.209231	+	0.977866i	$0.432904\pi$
$354$	147.667	+	186.382i	0.417139	+	0.526502i
$355$	−615.423	+	223.996i	−1.73359	+	0.630974i
$356$	−117.669	+	140.232i	−0.330530	+	0.393911i
$357$	94.7544	−	31.5007i	0.265418	−	0.0882374i
$358$	−308.279	−	112.204i	−0.861114	−	0.313420i
$359$	16.7796	−	9.68773i	0.0467399	−	0.0269853i	−0.476448	−	0.879203i	$-0.658076\pi$
$359$	16.7796	−	9.68773i	0.0467399	−	0.0269853i	0.523188	+	0.852217i	$0.324743\pi$
$360$	−299.680	+	224.013i	−0.832444	+	0.622258i
$361$	170.280	−	294.934i	0.471690	−	0.816992i
$362$	81.1916	+	96.7604i	0.224286	+	0.267294i
$363$	43.2308	+	26.6070i	0.119093	+	0.0732976i
$364$	−54.4967	+	309.066i	−0.149716	+	0.849083i
$365$	483.159	+	85.1939i	1.32372	+	0.233408i
$366$	−142.524	+	231.571i	−0.389409	+	0.632709i
$367$	299.305	−	251.147i	0.815545	−	0.684324i	−0.136379	−	0.990657i	$-0.543547\pi$
$367$	299.305	−	251.147i	0.815545	−	0.684324i	0.951924	+	0.306333i	$0.0991021\pi$
$368$	28.3201	+	16.3506i	0.0769569	+	0.0444311i
$369$	67.0585	+	89.7095i	0.181730	+	0.243115i
$370$	−55.1707	−	95.5584i	−0.149110	−	0.258266i
$371$	304.886	−	837.669i	0.821796	−	2.25787i
$372$	−55.5257	−	167.022i	−0.149263	−	0.448983i
$373$	−136.986	−	114.945i	−0.367255	−	0.308164i	0.440419	−	0.897792i	$-0.354830\pi$
$373$	−136.986	−	114.945i	−0.367255	−	0.308164i	−0.807675	+	0.589628i	$0.799274\pi$
$374$	−14.7339	−	40.4810i	−0.0393954	−	0.108238i
$375$	−266.108	+	210.833i	−0.709621	+	0.562221i
$376$	−16.6287	−	94.3061i	−0.0442253	−	0.250814i
$377$		−	284.862i		−	0.755603i
$378$	−318.707	+	86.3973i	−0.843140	+	0.228564i
$379$	3.48118			0.00918518			0.00459259	−	0.999989i	$-0.498538\pi$
$379$	3.48118			0.00918518			0.00459259	+	0.999989i	$0.498538\pi$
$380$	63.5643	−	11.2081i	0.167274	−	0.0294950i
$381$	463.626	−	68.3730i	1.21687	−	0.179457i
$382$	118.509	−	43.1337i	0.310233	−	0.112916i
$383$	11.0730	−	13.1963i	0.0289112	−	0.0344550i	−0.751395	−	0.659853i	$-0.770619\pi$
$383$	11.0730	−	13.1963i	0.0289112	−	0.0344550i	0.780306	+	0.625398i	$0.215063\pi$
$384$	212.225	+	188.494i	0.552670	+	0.490870i
$385$	625.797	+	227.772i	1.62545	+	0.591615i
$386$	−201.193	+	116.159i	−0.521226	+	0.300930i
$387$	−327.518	−	18.4350i	−0.846299	−	0.0476356i
$388$	105.827	−	183.298i	0.272750	−	0.472417i
$389$	203.618	+	242.662i	0.523439	+	0.623810i	0.961390	−	0.275189i	$-0.0887403\pi$
$389$	203.618	+	242.662i	0.523439	+	0.623810i	−0.437952	+	0.898999i	$0.644296\pi$
$390$	185.271	−	100.131i	0.475055	−	0.256745i
$391$	−10.9225	+	61.9446i	−0.0279348	+	0.158426i
$392$	−471.340	−	83.1100i	−1.20240	−	0.212015i
$393$	295.440	+	8.30814i	0.751756	+	0.0211403i
$394$	260.321	−	218.435i	0.660713	−	0.554404i
$395$	95.0446	+	54.8740i	0.240619	+	0.138922i
$396$	−80.9210	−	268.389i	−0.204346	−	0.677750i
$397$	−134.041	−	232.165i	−0.337634	−	0.584800i	0.646353	−	0.763039i	$-0.276293\pi$
$397$	−134.041	−	232.165i	−0.337634	−	0.584800i	−0.983987	+	0.178239i	$0.942960\pi$
$398$	32.6829	−	89.7955i	0.0821178	−	0.225617i
$399$	139.955	+	28.7560i	0.350763	+	0.0720703i
$400$	−5.00408	−	4.19892i	−0.0125102	−	0.0104973i
$401$	33.3356	+	91.5887i	0.0831311	+	0.228401i	0.974293	−	0.225285i	$-0.0723312\pi$
$401$	33.3356	+	91.5887i	0.0831311	+	0.228401i	−0.891162	+	0.453685i	$0.850109\pi$
$402$	314.493	+	124.585i	0.782321	+	0.309914i
$403$	43.1494	+	244.712i	0.107070	+	0.607227i
$404$		−	12.6686i		−	0.0313578i
$405$	−350.757	−	259.009i	−0.866067	−	0.639528i
$406$	310.149			0.763914
$407$	204.203	−	36.0065i	0.501727	−	0.0884680i
$408$	−26.9611	+	68.0584i	−0.0660810	+	0.166810i
$409$	380.898	−	138.636i	0.931292	−	0.338962i	0.168570	−	0.985690i	$-0.446085\pi$
$409$	380.898	−	138.636i	0.931292	−	0.338962i	0.762721	+	0.646727i	$0.223863\pi$
$410$	49.9916	−	59.5777i	0.121931	−	0.145311i
$411$	−39.6426	+	192.939i	−0.0964539	+	0.469437i
$412$	180.170	+	65.5764i	0.437305	+	0.159166i
$413$	−622.862	+	359.609i	−1.50814	+	0.870725i
$414$	47.5751	−	202.494i	0.114916	−	0.489116i
$415$	−85.0569	+	147.323i	−0.204956	+	0.354995i
$416$	−236.818	−	282.229i	−0.569275	−	0.678435i
$417$	10.5666	−	375.753i	0.0253397	−	0.901087i
$418$	10.7038	−	60.7045i	0.0256073	−	0.145226i
$419$	115.552	+	20.3750i	0.275781	+	0.0486277i	0.309828	−	0.950793i	$-0.399728\pi$
$419$	115.552	+	20.3750i	0.275781	+	0.0486277i	−0.0340470	+	0.999420i	$0.510840\pi$
$420$	−214.520	−	396.925i	−0.510762	−	0.945060i
$421$	−399.365	+	335.107i	−0.948610	+	0.795979i	−0.979063	−	0.203558i	$-0.934750\pi$
$421$	−399.365	+	335.107i	−0.948610	+	0.795979i	0.0304527	+	0.999536i	$0.490305\pi$
$422$	116.473	+	67.2459i	0.276003	+	0.159351i
$423$	99.6282	−	50.2787i	0.235528	−	0.118862i
$424$	326.760	+	565.966i	0.770661	+	1.33482i
$425$	4.29744	−	11.8071i	0.0101116	−	0.0277814i
$426$	281.394	−	316.821i	0.660549	−	0.743712i
$427$	−630.025	−	528.654i	−1.47547	−	1.23806i
$428$	143.441	+	394.102i	0.335143	+	0.920799i
$429$	57.7393	+	391.521i	0.134591	+	0.912636i
$430$	39.5541	+	224.323i	0.0919864	+	0.521681i
$431$			263.580i			0.611555i	0.952103	+	0.305777i	$0.0989163\pi$
$431$			263.580i			0.611555i	−0.952103	+	0.305777i	$0.901084\pi$
$432$	−18.6261	+	40.2509i	−0.0431161	+	0.0931733i
$433$	−702.013			−1.62128			−0.810639	−	0.585547i	$-0.800880\pi$
$433$	−702.013			−1.62128			−0.810639	+	0.585547i	$0.800880\pi$
$434$	−266.435	+	46.9797i	−0.613906	+	0.108248i
$435$	254.321	+	320.997i	0.584645	+	0.737924i
$436$	46.3025	−	16.8527i	0.106198	−	0.0386531i
$437$	−57.8526	+	68.9461i	−0.132386	+	0.157771i
$438$	−301.224	+	100.141i	−0.687727	+	0.228632i
$439$	416.204	+	151.486i	0.948073	+	0.345070i	0.769349	−	0.638829i	$-0.220581\pi$
$439$	416.204	+	151.486i	0.948073	+	0.345070i	0.178724	+	0.983899i	$0.442803\pi$
$440$	−422.816	+	244.113i	−0.960946	+	0.554802i
$441$	−65.8317	−	553.857i	−0.149278	−	1.25591i
$442$	20.6021	−	35.6839i	0.0466111	−	0.0807328i
$443$	−390.071	−	464.868i	−0.880520	−	1.04936i	−0.998412	−	0.0563369i	$-0.982058\pi$
$443$	−390.071	−	464.868i	−0.880520	−	1.04936i	0.117891	−	0.993026i	$-0.462387\pi$
$444$	−119.638	−	73.6326i	−0.269454	−	0.165839i
$445$	−64.5191	+	365.906i	−0.144987	+	0.822260i
$446$	226.648	+	39.9642i	0.508180	+	0.0896058i
$447$	317.250	−	515.464i	0.709731	−	1.15316i
$448$	254.259	−	213.348i	0.567542	−	0.476224i
$449$	347.745	+	200.771i	0.774488	+	0.447151i	0.834473	−	0.551048i	$-0.185772\pi$
$449$	347.745	+	200.771i	0.774488	+	0.447151i	−0.0599853	+	0.998199i	$0.519105\pi$
$450$	−16.3832	+	38.1852i	−0.0364072	+	0.0848560i
$451$	73.0755	+	126.570i	0.162030	+	0.280644i
$452$	16.3423	−	44.9002i	0.0361556	−	0.0993368i
$453$	−121.274	−	364.791i	−0.267712	−	0.805279i
$454$	−4.58180	−	3.84458i	−0.0100921	−	0.00846825i
$455$	217.859	+	598.563i	0.478811	+	1.31552i
$456$	−82.1013	+	65.0475i	−0.180047	+	0.142648i
$457$	−25.5458	−	144.878i	−0.0558990	−	0.317019i	0.944018	−	0.329894i	$-0.107013\pi$
$457$	−25.5458	−	144.878i	−0.0558990	−	0.317019i	−0.999917	+	0.0128747i	$0.995902\pi$
$458$		−	410.223i		−	0.895683i
$459$	−85.0061	−	7.18658i	−0.185198	−	0.0156570i
$460$	284.213			0.617855
$461$	−773.480	+	136.385i	−1.67783	+	0.295847i	−0.929868	−	0.367893i	$-0.880079\pi$
$461$	−773.480	+	136.385i	−1.67783	+	0.295847i	−0.747963	+	0.663740i	$0.768968\pi$
$462$	−426.276	+	62.8648i	−0.922675	+	0.136071i
$463$	336.835	−	122.598i	0.727506	−	0.264791i	0.0483975	−	0.998828i	$-0.484589\pi$
$463$	336.835	−	122.598i	0.727506	−	0.264791i	0.679109	+	0.734037i	$0.262366\pi$
$464$	26.7767	−	31.9112i	0.0577084	−	0.0687742i
$465$	−267.098	−	237.231i	−0.574405	−	0.510174i
$466$	153.344	+	55.8128i	0.329065	+	0.119770i
$467$	−88.2727	+	50.9643i	−0.189021	+	0.109131i	−0.591524	−	0.806287i	$-0.701474\pi$
$467$	−88.2727	+	50.9643i	−0.189021	+	0.109131i	0.402503	+	0.915419i	$0.368140\pi$
$468$	146.899	−	224.300i	0.313886	−	0.479274i
$469$	−511.569	+	886.063i	−1.09077	+	1.88926i
$470$	−49.8101	−	59.3613i	−0.105979	−	0.126301i
$471$	−366.709	+	198.189i	−0.778575	+	0.420784i
$472$	91.5597	−	519.261i	0.193982	−	1.10013i
$473$	−421.547	−	74.3300i	−0.891219	−	0.157146i
$474$	−70.9806	−	1.99606i	−0.149748	−	0.00421110i
$475$	13.7726	−	11.5566i	0.0289949	−	0.0243296i
$476$	−76.4491	−	44.1379i	−0.160607	−	0.0927267i
$477$	−521.553	+	554.978i	−1.09340	+	1.16348i
$478$	−85.7219	−	148.475i	−0.179334	−	0.310616i
$479$	43.2210	−	118.749i	0.0902318	−	0.247910i	−0.886365	−	0.462986i	$-0.846778\pi$
$479$	43.2210	−	118.749i	0.0902318	−	0.247910i	0.976597	+	0.215077i	$0.0690001\pi$
$480$	518.828	+	106.602i	1.08089	+	0.222088i
$481$	151.929	+	127.483i	0.315860	+	0.265038i
$482$	120.874	+	332.099i	0.250776	+	0.689003i
$483$	584.918	+	231.713i	1.21101	+	0.479737i
$484$	−7.79280	−	44.1952i	−0.0161008	−	0.0913123i
$485$		−	429.586i		−	0.885745i
$486$	279.331	+	39.5260i	0.574756	+	0.0813292i
$487$	454.010			0.932258			0.466129	−	0.884717i	$-0.345648\pi$
$487$	454.010			0.932258			0.466129	+	0.884717i	$0.345648\pi$
$488$	593.783	−	104.700i	1.21677	−	0.214549i
$489$	44.0379	−	111.166i	0.0900571	−	0.227333i
$490$	−363.940	+	132.463i	−0.742735	+	0.270334i
$491$	203.177	−	242.137i	0.413803	−	0.493151i	−0.518374	−	0.855154i	$-0.673463\pi$
$491$	203.177	−	242.137i	0.413803	−	0.493151i	0.932177	+	0.362003i	$0.117907\pi$
$492$	19.9284	−	96.9906i	0.0405048	−	0.197135i
$493$	75.2944	+	27.4049i	0.152727	+	0.0555881i
$494$	51.0594	−	29.4792i	0.103359	−	0.0596744i
$495$	−414.607	−	389.637i	−0.837591	−	0.787145i
$496$	−18.1689	+	31.4695i	−0.0366309	+	0.0634466i
$497$	823.833	+	981.806i	1.65761	+	1.97547i
$498$	3.09398	−	110.023i	0.00621280	−	0.220929i
$499$	21.2323	−	120.414i	0.0425497	−	0.241312i	−0.956114	−	0.292996i	$-0.905348\pi$
$499$	21.2323	−	120.414i	0.0425497	−	0.241312i	0.998663	+	0.0516842i	$0.0164589\pi$
$500$	295.582	+	52.1190i	0.591163	+	0.104238i
$501$	236.711	+	437.985i	0.472477	+	0.874222i
$502$	−110.983	+	93.1256i	−0.221081	+	0.185509i
$503$	−391.041	−	225.768i	−0.777418	−	0.448843i	0.0580963	−	0.998311i	$-0.481497\pi$
$503$	−391.041	−	225.768i	−0.777418	−	0.448843i	−0.835515	+	0.549468i	$0.814830\pi$
$504$	612.531	+	401.159i	1.21534	+	0.795951i
$505$	−12.8565	−	22.2680i	−0.0254583	−	0.0440951i
$506$	92.8333	−	255.057i	0.183465	−	0.504066i
$507$	85.3113	−	96.0519i	0.168267	−	0.189452i
$508$	−317.375	−	266.309i	−0.624754	−	0.524231i
$509$	−170.911	−	469.573i	−0.335778	−	0.922541i	−0.986578	−	0.163292i	$-0.947789\pi$
$509$	−170.911	−	469.573i	−0.335778	−	0.922541i	0.650800	−	0.759249i	$-0.274434\pi$
$510$	8.64255	+	58.6037i	0.0169462	+	0.114909i
$511$	−166.722	−	945.527i	−0.326266	−	1.85035i
$512$		−	104.621i		−	0.204338i
$513$	−100.196	−	69.7223i	−0.195314	−	0.135911i
$514$	−530.596			−1.03229
$515$	383.240	−	67.5756i	0.744156	−	0.131215i
$516$	180.091	+	227.307i	0.349014	+	0.440517i
$517$	136.838	−	49.8051i	0.264678	−	0.0963348i
$518$	−138.800	+	165.415i	−0.267954	+	0.319335i
$519$	−31.0022	+	10.3066i	−0.0597344	+	0.0198585i
$520$	−438.816	−	159.716i	−0.843877	−	0.307146i
$521$	−595.632	+	343.888i	−1.14325	+	0.660054i	−0.947233	−	0.320546i	$-0.896133\pi$
$521$	−595.632	+	343.888i	−1.14325	+	0.660054i	−0.196015	+	0.980601i	$0.562800\pi$
$522$	−243.508	−	104.477i	−0.466491	−	0.200147i
$523$	260.218	−	450.711i	0.497549	−	0.861780i	−0.502447	−	0.864608i	$-0.667567\pi$
$523$	260.218	−	450.711i	0.497549	−	0.861780i	0.999996	+	0.00282784i	$0.000900130\pi$
$524$	−167.953	−	200.159i	−0.320521	−	0.381983i
$525$	−107.030	−	65.8730i	−0.203866	−	0.125472i
$526$	−94.3376	+	535.015i	−0.179349	+	1.01714i
$527$	−68.8332	−	12.1372i	−0.130613	−	0.0230306i
$528$	−30.3343	+	49.2869i	−0.0574514	+	0.0933465i
$529$	101.644	−	85.2896i	0.192144	−	0.161228i
$530$	457.985	+	264.418i	0.864123	+	0.498902i
$531$	610.167	−	72.5247i	1.14909	−	0.136581i
$532$	−63.1561	−	109.390i	−0.118715	−	0.205620i
$533$	−47.8111	+	131.360i	−0.0897020	+	0.246454i
$534$	−75.8387	−	228.123i	−0.142020	−	0.427197i
$535$	652.079	+	547.160i	1.21884	+	1.02273i
$536$	−256.542	−	704.844i	−0.478623	−	1.31501i
$537$	−664.465	+	526.444i	−1.23736	+	0.980343i
$538$	63.9168	+	362.490i	0.118804	+	0.673773i
$539$		−	727.808i		−	1.35029i
$540$	34.7189	+	383.902i	0.0642942	+	0.710930i
$541$	803.120			1.48451			0.742255	−	0.670117i	$-0.233756\pi$
$541$	803.120			1.48451			0.742255	+	0.670117i	$0.233756\pi$
$542$	132.281	−	23.3247i	0.244060	−	0.0430344i
$543$	322.905	−	47.6203i	0.594668	−	0.0876984i
$544$	97.3813	−	35.4439i	0.179010	−	0.0651542i
$545$	64.2851	−	76.6120i	0.117954	−	0.140572i
$546$	−308.142	−	273.685i	−0.564362	−	0.501254i
$547$	64.5461	+	23.4929i	0.118000	+	0.0429486i	0.400345	−	0.916364i	$-0.368890\pi$
$547$	64.5461	+	23.4929i	0.118000	+	0.0429486i	−0.282345	+	0.959313i	$0.591112\pi$
$548$	150.803	−	87.0659i	0.275187	−	0.158879i
$549$	316.572	+	627.293i	0.576633	+	1.14261i
$550$	−27.1099	+	46.9557i	−0.0492907	+	0.0853741i
$551$	73.6967	+	87.8283i	0.133751	+	0.159398i
$552$	−405.765	+	219.298i	−0.735082	+	0.397278i
$553$	37.2950	−	211.511i	0.0674412	−	0.382478i
$554$	131.832	+	23.2456i	0.237964	+	0.0419595i
$555$	−285.016	−	8.01501i	−0.513543	−	0.0144415i
$556$	−254.570	+	213.610i	−0.457861	+	0.384191i
$557$	575.120	+	332.045i	1.03253	+	0.596132i	0.917709	−	0.397254i	$-0.130037\pi$
$557$	575.120	+	332.045i	1.03253	+	0.596132i	0.114822	+	0.993386i	$0.463370\pi$
$558$	225.013	+	52.8658i	0.403249	+	0.0947415i
$559$	−204.710	−	354.569i	−0.366208	−	0.634291i
$560$	−31.8589	+	87.5315i	−0.0568908	+	0.156306i
$561$	−109.041	−	22.4043i	−0.194369	−	0.0399364i
$562$	−72.5637	−	60.8882i	−0.129117	−	0.108342i
$563$	−118.905	−	326.689i	−0.211199	−	0.580264i	0.788182	−	0.615442i	$-0.211022\pi$
$563$	−118.905	−	326.689i	−0.211199	−	0.580264i	−0.999381	+	0.0351778i	$0.988800\pi$
$564$	−91.7223	−	36.3354i	−0.162628	−	0.0644246i
$565$	−16.8406	−	95.5076i	−0.0298063	−	0.169040i
$566$			484.283i			0.855623i
$567$	−241.535	+	818.385i	−0.425987	+	1.44336i
$568$	−939.603			−1.65423
$569$	−385.078	+	67.8997i	−0.676763	+	0.119332i	−0.501457	−	0.865182i	$-0.667203\pi$
$569$	−385.078	+	67.8997i	−0.676763	+	0.119332i	−0.175306	+	0.984514i	$0.556091\pi$
$570$	−31.2178	+	78.8037i	−0.0547680	+	0.138252i
$571$	−804.118	+	292.675i	−1.40826	+	0.512566i	−0.930620	−	0.365988i	$-0.880731\pi$
$571$	−804.118	+	292.675i	−1.40826	+	0.512566i	−0.477644	+	0.878554i	$0.658509\pi$
$572$	224.892	−	268.016i	0.393168	−	0.468559i
$573$	65.5891	−	319.219i	0.114466	−	0.557102i
$574$	−143.021	−	52.0553i	−0.249165	−	0.0906887i
$575$	68.5606	−	39.5835i	0.119236	−	0.0688408i
$576$	−271.495	+	81.8576i	−0.471346	+	0.142114i
$577$	313.746	−	543.423i	0.543753	−	0.941808i	−0.454931	−	0.890527i	$-0.650336\pi$
$577$	313.746	−	543.423i	0.543753	−	0.941808i	0.998684	−	0.0512815i	$-0.0163306\pi$
$578$	−208.217	−	248.143i	−0.360237	−	0.429314i
$579$	−16.8752	+	600.087i	−0.0291454	+	1.03642i
$580$	62.8694	−	356.550i	0.108396	−	0.614742i
$581$	327.850	+	57.8088i	0.564285	+	0.0994987i
$582$	132.153	+	244.522i	0.227067	+	0.420141i
$583$	−761.285	+	638.794i	−1.30581	+	1.09570i
$584$	609.573	+	351.937i	1.04379	+	0.602632i
$585$	30.5829	−	543.339i	0.0522785	−	0.928785i
$586$	−200.750	−	347.709i	−0.342576	−	0.593359i
$587$	−254.654	+	699.655i	−0.433822	+	1.19192i	0.509626	+	0.860396i	$0.329784\pi$
$587$	−254.654	+	699.655i	−0.433822	+	1.19192i	−0.943448	+	0.331520i	$0.892439\pi$
$588$	−327.443	+	368.668i	−0.556876	+	0.626986i
$589$	−76.6133	−	64.2862i	−0.130073	−	0.109145i
$590$	−145.931	−	400.942i	−0.247340	−	0.679562i
$591$	−128.116	−	868.733i	−0.216778	−	1.46994i
$592$	5.03630	+	28.5623i	0.00850726	+	0.0482471i
$593$		−	625.722i		−	1.05518i	−0.849499	−	0.527591i	$-0.823096\pi$
$593$		−	625.722i		−	1.05518i	0.849499	−	0.527591i	$-0.176904\pi$
$594$	355.860	+	94.2376i	0.599091	+	0.158649i
$595$	−179.170			−0.301126
$596$	−526.963	+	92.9177i	−0.884165	+	0.155902i
$597$	−153.343	−	193.546i	−0.256856	−	0.324197i
$598$	243.957	−	88.7932i	0.407955	−	0.148484i
$599$	−368.344	+	438.975i	−0.614932	+	0.732847i	−0.980190	−	0.198059i	$-0.936536\pi$
$599$	−368.344	+	438.975i	−0.614932	+	0.732847i	0.365258	+	0.930906i	$0.380981\pi$
$600$	87.4307	−	29.0660i	0.145718	−	0.0484434i
$601$	−1063.24	−	386.989i	−1.76912	−	0.643908i	−0.999988	−	0.00482034i	$-0.998466\pi$
$601$	−1063.24	−	386.989i	−1.76912	−	0.643908i	−0.769134	−	0.639088i	$-0.779312\pi$
$602$	386.043	−	222.882i	0.641268	−	0.370236i
$603$	700.128	−	523.351i	1.16107	−	0.867912i
$604$	−169.925	+	294.319i	−0.281333	+	0.487283i
$605$	−58.5483	−	69.7752i	−0.0967741	−	0.115331i
$606$	14.1682	+	8.72004i	0.0233799	+	0.0143895i
$607$	−40.3687	+	228.942i	−0.0665052	+	0.377170i	0.933330	+	0.359019i	$0.116889\pi$
$607$	−40.3687	+	228.942i	−0.0665052	+	0.377170i	−0.999835	+	0.0181503i	$0.994222\pi$
$608$	146.031	+	25.7492i	0.240182	+	0.0423506i
$609$	420.075	−	682.533i	0.689778	−	1.12074i
$610$	373.759	−	313.621i	0.612720	−	0.514133i
$611$	120.623	+	69.6414i	0.197418	+	0.113979i
$612$	45.1545	+	60.4067i	0.0737819	+	0.0987038i
$613$	533.889	+	924.724i	0.870945	+	1.50852i	0.861020	+	0.508571i	$0.169826\pi$
$613$	533.889	+	924.724i	0.870945	+	1.50852i	0.00992514	+	0.999951i	$0.496841\pi$
$614$	−229.244	+	629.843i	−0.373362	+	1.02580i
$615$	−63.4002	−	190.708i	−0.103090	−	0.310095i
$616$	731.912	+	614.147i	1.18817	+	0.996991i
$617$	144.247	+	396.317i	0.233788	+	0.642328i	1.00000		0.000260046i	$-8.27751e-5\pi$
$617$	144.247	+	396.317i	0.233788	+	0.642328i	−0.766212	+	0.642588i	$0.777861\pi$
$618$	−197.354	+	156.360i	−0.319343	+	0.253010i
$619$	104.335	+	591.711i	0.168554	+	0.955915i	0.945324	+	0.326131i	$0.105745\pi$
$619$	104.335	+	591.711i	0.168554	+	0.955915i	−0.776771	+	0.629783i	$0.783144\pi$
$620$			315.820i			0.509386i
$621$	−381.184	−	378.960i	−0.613823	−	0.610242i
$622$	521.392			0.838250
$623$	716.066	−	126.262i	1.14938	−	0.202667i
$624$	−54.7628	+	8.07611i	−0.0877609	+	0.0129425i
$625$	665.870	−	242.357i	1.06539	−	0.387771i
$626$	8.08756	−	9.63837i	0.0129194	−	0.0153968i
$627$	−119.092	−	105.775i	−0.189940	−	0.168701i
$628$	346.285	+	126.037i	0.551409	+	0.200696i
$629$	−48.3124	+	27.8932i	−0.0768083	+	0.0443453i
$630$	591.571	+	33.2977i	0.939001	+	0.0528535i
$631$	554.621	−	960.632i	0.878956	−	1.52240i	0.0264679	−	0.999650i	$-0.491574\pi$
$631$	554.621	−	960.632i	0.878956	−	1.52240i	0.852488	−	0.522747i	$-0.175093\pi$
$632$	101.209	+	120.617i	0.160141	+	0.190849i
$633$	305.740	−	165.239i	0.483002	−	0.261040i
$634$	−43.9956	+	249.512i	−0.0693937	+	0.393551i
$635$	−828.122	−	146.020i	−1.30413	−	0.229953i
$636$	673.021	+	18.9262i	1.05821	+	0.0297581i
$637$	533.269	−	447.466i	0.837157	−	0.702458i
$638$	−299.439	−	172.881i	−0.469340	−	0.270973i
$639$	−316.089	−	1048.36i	−0.494661	−	1.64063i
$640$	−254.659	−	441.082i	−0.397904	−	0.689191i
$641$	−56.5257	+	155.303i	−0.0881837	+	0.242283i	−0.975943	−	0.218025i	$-0.930039\pi$
$641$	−56.5257	+	155.303i	−0.0881837	+	0.242283i	0.887760	+	0.460308i	$0.152261\pi$
$642$	−539.489	−	110.847i	−0.840325	−	0.172659i
$643$	608.717	+	510.774i	0.946683	+	0.794361i	0.978736	−	0.205125i	$-0.0657600\pi$
$643$	608.717	+	510.774i	0.946683	+	0.794361i	−0.0320527	+	0.999486i	$0.510204\pi$
$644$	−190.230	−	522.654i	−0.295389	−	0.811574i
$645$	547.231	+	216.784i	0.848421	+	0.336099i
$646$	2.87977	+	16.3320i	0.00445785	+	0.0252817i
$647$		−	222.504i		−	0.343900i	−0.985106	−	0.171950i	$-0.944993\pi$
$647$		−	222.504i		−	0.343900i	0.985106	−	0.171950i	$-0.0550068\pi$
$648$	−345.784	−	521.300i	−0.533618	−	0.804475i
$649$	801.803			1.23544
$650$	−51.0723	+	9.00542i	−0.0785728	+	0.0138545i
$651$	−257.481	+	649.964i	−0.395516	+	0.998409i
$652$	−99.3323	+	36.1540i	−0.152350	+	0.0554509i
$653$	−299.851	+	357.348i	−0.459190	+	0.547241i	−0.945106	−	0.326764i	$-0.894042\pi$
$653$	−299.851	+	357.348i	−0.459190	+	0.547241i	0.485916	+	0.874006i	$0.338486\pi$
$654$	−13.0233	+	63.3839i	−0.0199133	+	0.0969172i
$655$	−498.345	−	181.383i	−0.760833	−	0.276920i
$656$	−17.7037	+	10.2212i	−0.0269873	+	0.0155811i
$657$	−187.610	+	798.526i	−0.285556	+	1.21541i
$658$	−75.8234	+	131.330i	−0.115233	+	0.199590i
$659$	−133.876	−	159.547i	−0.203150	−	0.242104i	0.654845	−	0.755764i	$-0.272734\pi$
$659$	−133.876	−	159.547i	−0.203150	−	0.242104i	−0.857994	+	0.513659i	$0.828290\pi$
$660$	−14.1392	+	502.794i	−0.0214230	+	0.761809i
$661$	−110.055	+	624.153i	−0.166498	+	0.944256i	0.781009	+	0.624520i	$0.214705\pi$
$661$	−110.055	+	624.153i	−0.166498	+	0.944256i	−0.947507	+	0.319736i	$0.896406\pi$
$662$	−686.770	−	121.096i	−1.03742	−	0.182925i
$663$	−50.6241	−	93.6695i	−0.0763561	−	0.141281i
$664$	−186.961	+	156.879i	−0.281567	+	0.236263i
$665$	−222.024	−	128.186i	−0.333871	−	0.192760i
$666$	164.698	−	83.1171i	0.247295	−	0.124800i
$667$	252.425	+	437.214i	0.378449	+	0.655493i
$668$	150.535	−	413.591i	0.225352	−	0.619149i
$669$	394.926	−	444.647i	0.590323	−	0.664645i
$670$	−464.967	−	390.154i	−0.693981	−	0.582319i
$671$	313.590	+	861.581i	0.467347	+	1.28403i
$672$	−151.228	−	1025.45i	−0.225041	−	1.52597i
$673$	19.1049	+	108.349i	0.0283877	+	0.160994i	0.995706	−	0.0925699i	$-0.0295082\pi$
$673$	19.1049	+	108.349i	0.0283877	+	0.160994i	−0.967319	+	0.253564i	$0.918397\pi$
$674$		−	521.584i		−	0.773864i
$675$	61.8427	+	87.7730i	0.0916188	+	0.130034i
$676$	−113.573			−0.168007
$677$	−140.866	+	24.8384i	−0.208073	+	0.0366890i	−0.276713	−	0.960953i	$-0.589245\pi$
$677$	−140.866	+	24.8384i	−0.208073	+	0.0366890i	0.0686398	+	0.997642i	$0.478134\pi$
$678$	38.9666	+	49.1827i	0.0574729	+	0.0725409i
$679$	−789.987	+	287.532i	−1.16346	+	0.423463i
$680$	84.4318	−	100.622i	0.124164	−	0.147973i
$681$	−14.6663	+	4.87577i	−0.0215365	+	0.00715972i
$682$	283.421	+	103.157i	0.415574	+	0.151257i
$683$	784.050	−	452.671i	1.14795	−	0.662769i	0.199563	−	0.979885i	$-0.436048\pi$
$683$	784.050	−	452.671i	1.14795	−	0.662769i	0.948387	+	0.317116i	$0.102714\pi$
$684$	12.7371	+	107.160i	0.0186215	+	0.156667i
$685$	176.714	−	306.078i	0.257977	−	0.446830i
$686$	101.984	+	121.539i	0.148664	+	0.177171i
$687$	−902.761	−	555.617i	−1.31406	−	0.808758i
$688$	10.3967	−	58.9625i	0.0151115	−	0.0857013i
$689$	−936.096	−	165.059i	−1.35863	−	0.239563i
$690$	−195.630	+	317.858i	−0.283522	+	0.460664i
$691$	407.543	−	341.969i	0.589788	−	0.494891i	−0.298357	−	0.954454i	$-0.596439\pi$
$691$	407.543	−	341.969i	0.589788	−	0.494891i	0.888145	+	0.459564i	$0.151994\pi$
$692$	25.0130	+	14.4413i	0.0361459	+	0.0208689i
$693$	−439.016	+	1023.23i	−0.633500	+	1.47653i
$694$	−137.087	−	237.441i	−0.197531	−	0.342134i
$695$	−230.690	+	633.817i	−0.331929	+	0.911967i
$696$	185.355	+	557.549i	0.266315	+	0.801077i
$697$	−30.1213	−	25.2748i	−0.0432156	−	0.0362622i
$698$	95.2117	+	261.592i	0.136406	+	0.374773i
$699$	330.519	−	261.864i	0.472845	−	0.374627i
$700$	19.2932	+	109.417i	0.0275617	+	0.156310i
$701$			905.026i			1.29105i	0.763739	+	0.645525i	$0.223361\pi$
$701$			905.026i			1.29105i	−0.763739	+	0.645525i	$0.776639\pi$
$702$	149.739	+	318.679i	0.213303	+	0.453959i
$703$	−79.8237			−0.113547
$704$	−364.401	+	64.2538i	−0.517616	+	0.0912696i
$705$	−198.098	+	29.2144i	−0.280991	+	0.0414389i
$706$	27.9182	−	10.1614i	0.0395442	−	0.0143929i
$707$	−32.3447	+	38.5469i	−0.0457492	+	0.0545217i
$708$	−406.150	−	360.734i	−0.573658	−	0.509511i
$709$	341.922	+	124.450i	0.482260	+	0.175528i	0.571698	−	0.820464i	$-0.306285\pi$
$709$	341.922	+	124.450i	0.482260	+	0.175528i	−0.0894380	+	0.995992i	$0.528507\pi$
$710$	−658.471	+	380.168i	−0.927424	+	0.535449i
$711$	−100.531	+	153.501i	−0.141393	+	0.215894i
$712$	−266.529	+	461.642i	−0.374338	+	0.648373i
$713$	−283.074	−	337.355i	−0.397019	−	0.473148i
$714$	101.984	−	55.1180i	0.142835	−	0.0771960i
$715$	123.311	−	699.329i	0.172462	−	0.978083i
$716$	738.060	+	130.140i	1.03081	+	0.181760i
$717$	−442.846	−	12.4534i	−0.617638	−	0.0173687i
$718$	17.2315	−	14.4590i	0.0239994	−	0.0201379i
$719$	−389.328	−	224.778i	−0.541485	−	0.312626i	0.204196	−	0.978930i	$-0.434542\pi$
$719$	−389.328	−	224.778i	−0.541485	−	0.312626i	−0.745680	+	0.666304i	$0.767875\pi$
$720$	54.4992	−	57.9919i	0.0756934	−	0.0805444i
$721$	−380.779	−	659.529i	−0.528127	−	0.914742i
$722$	135.227	−	371.534i	0.187295	−	0.514589i
$723$	894.553	+	183.801i	1.23728	+	0.254220i
$724$	−221.045	−	185.479i	−0.305310	−	0.256186i
$725$	−34.4922	−	94.7665i	−0.0475754	−	0.130712i
$726$	54.7908	+	21.7052i	0.0754695	+	0.0298969i
$727$	100.606	+	570.564i	0.138385	+	0.784820i	0.972443	+	0.233142i	$0.0749009\pi$
$727$	100.606	+	570.564i	0.138385	+	0.784820i	−0.834058	+	0.551677i	$0.813988\pi$
$728$			913.862i			1.25530i
$729$	465.317	−	561.178i	0.638295	−	0.769792i
$730$	569.582			0.780250
$731$	113.413	−	19.9978i	0.155148	−	0.0273568i
$732$	228.780	−	577.515i	0.312542	−	0.788955i
$733$	−879.854	+	320.241i	−1.20035	+	0.436891i	−0.863345	−	0.504613i	$-0.831635\pi$
$733$	−879.854	+	320.241i	−1.20035	+	0.436891i	−0.337002	+	0.941504i	$0.609413\pi$
$734$	291.572	−	347.482i	0.397237	−	0.473409i
$735$	−201.424	+	980.321i	−0.274046	+	1.33377i
$736$	613.567	+	223.320i	0.833650	+	0.303424i
$737$	987.805	−	570.310i	1.34031	−	0.773826i
$738$	94.7550	+	89.0482i	0.128394	+	0.120661i
$739$	−263.918	+	457.119i	−0.357128	+	0.618564i	−0.987480	−	0.157746i	$-0.949577\pi$
$739$	−263.918	+	457.119i	−0.357128	+	0.618564i	0.630352	+	0.776310i	$0.282911\pi$
$740$	162.027	+	193.097i	0.218956	+	0.260942i
$741$	4.28263	−	152.292i	0.00577953	−	0.205522i
$742$	179.711	−	1019.19i	0.242198	−	1.37357i
$743$	−36.2725	−	6.39582i	−0.0488190	−	0.00860811i	0.149185	−	0.988809i	$-0.452335\pi$
$743$	−36.2725	−	6.39582i	−0.0488190	−	0.00860811i	−0.198004	+	0.980201i	$0.563446\pi$
$744$	−243.685	−	450.889i	−0.327534	−	0.606034i
$745$	−831.967	+	698.103i	−1.11673	+	0.937051i
$746$	−179.793	−	103.803i	−0.241009	−	0.139146i
$747$	−237.932	−	155.827i	−0.318517	−	0.208603i
$748$	49.2061	+	85.2274i	0.0657835	+	0.113940i
$749$	569.747	−	1565.37i	0.760677	−	2.08994i
$750$	−261.744	+	294.697i	−0.348992	+	0.392930i
$751$	75.4565	+	63.3155i	0.100475	+	0.0843082i	0.691641	−	0.722241i	$-0.256888\pi$
$751$	75.4565	+	63.3155i	0.100475	+	0.0843082i	−0.591167	+	0.806550i	$0.701332\pi$
$752$	6.96633	+	19.1398i	0.00926374	+	0.0254519i
$753$	54.6197	+	370.367i	0.0725362	+	0.491856i
$754$	−57.4279	−	325.690i	−0.0761644	−	0.431950i
$755$			689.781i			0.913617i
$756$	682.738	−	320.801i	0.903093	−	0.424339i
$757$	−1385.09			−1.82971			−0.914857	−	0.403779i	$-0.867697\pi$
$757$	−1385.09			−1.82971			−0.914857	+	0.403779i	$0.867697\pi$
$758$	3.98012	−	0.701803i	0.00525082	−	0.000925861i
$759$	−435.559	−	549.752i	−0.573859	−	0.724310i
$760$	176.615	−	64.2827i	0.232388	−	0.0845825i
$761$	935.204	−	1114.53i	1.22891	−	1.46456i	0.389541	−	0.921009i	$-0.372634\pi$
$761$	935.204	−	1114.53i	1.22891	−	1.46456i	0.839374	−	0.543555i	$-0.182922\pi$
$762$	516.291	−	171.639i	0.677547	−	0.225248i
$763$	−183.913	−	66.9389i	−0.241039	−	0.0877312i
$764$	−249.505	+	144.052i	−0.326577	+	0.188549i
$765$	140.672	+	60.3551i	0.183886	+	0.0788956i
$766$	9.99966	−	17.3199i	0.0130544	−	0.0226109i
$767$	492.959	+	587.486i	0.642711	+	0.765953i
$768$	602.634	+	370.900i	0.784680	+	0.482942i
$769$	−17.3763	+	98.5458i	−0.0225959	+	0.128148i	−0.994019	−	0.109206i	$-0.965169\pi$
$769$	−17.3763	+	98.5458i	−0.0225959	+	0.128148i	0.971423	+	0.237354i	$0.0762802\pi$
$770$	761.408	+	134.257i	0.988842	+	0.174360i
$771$	−718.654	+	1167.66i	−0.932106	+	1.51448i
$772$	406.555	−	341.140i	0.526626	−	0.441891i
$773$	−547.928	−	316.347i	−0.708834	−	0.409245i	0.101795	−	0.994805i	$-0.467541\pi$
$773$	−547.928	−	316.347i	−0.708834	−	0.409245i	−0.810629	+	0.585560i	$0.800875\pi$
$774$	−378.175	+	44.9501i	−0.488599	+	0.0580750i
$775$	43.9854	+	76.1850i	0.0567554	+	0.0983032i
$776$	210.794	−	579.152i	0.271642	−	0.746330i
$777$	176.029	+	529.495i	0.226549	+	0.681461i
$778$	281.722	+	236.392i	0.362110	+	0.303846i
$779$	−19.2431	−	52.8699i	−0.0247023	−	0.0678690i
$780$	−377.093	+	298.765i	−0.483453	+	0.383031i
$781$	−248.112	−	1407.12i	−0.317686	−	1.80168i
$782$			73.0247i			0.0933820i
$783$	−559.732	+	394.373i	−0.714856	+	0.503670i
$784$	101.800			0.129847
$785$	736.585	−	129.880i	0.938325	−	0.165452i
$786$	339.459	−	50.0616i	0.431882	−	0.0636915i
$787$	766.476	−	278.974i	0.973921	−	0.354478i	0.194447	−	0.980913i	$-0.437709\pi$
$787$	766.476	−	278.974i	0.973921	−	0.354478i	0.779474	+	0.626435i	$0.215487\pi$
$788$	−499.005	+	594.691i	−0.633256	+	0.754685i
$789$	1049.61	+	932.244i	1.33031	+	1.18155i
$790$	119.729	+	43.5779i	0.151556	+	0.0551619i
$791$	−164.362	+	94.8944i	−0.207790	+	0.119968i
$792$	−367.767	−	728.738i	−0.464353	−	0.920124i
$793$	−438.486	+	759.481i	−0.552946	+	0.957731i
$794$	−200.056	−	238.418i	−0.251960	−	0.300275i
$795$	1202.20	−	649.735i	1.51220	−	0.817277i
$796$	−37.9072	+	214.982i	−0.0476221	+	0.270078i
$797$	1233.67	+	217.529i	1.54789	+	0.272934i	0.881323	−	0.472514i	$-0.156653\pi$
$797$	1233.67	+	217.529i	1.54789	+	0.272934i	0.666564	+	0.745448i	$0.267764\pi$
$798$	165.811	+	4.66280i	0.207783	+	0.00584311i
$799$	−30.0119	+	25.1830i	−0.0375618	+	0.0315181i
$800$	−112.957	−	65.2156i	−0.141196	−	0.0815196i
$801$	−604.740	−	142.081i	−0.754981	−	0.177380i
$802$	56.5776	+	97.9952i	0.0705456	+	0.122189i
$803$	−366.084	+	1005.81i	−0.455895	+	1.25256i
$804$	−756.953	−	155.529i	−0.941483	−	0.193444i
$805$	−864.781	−	725.637i	−1.07426	−	0.901413i
$806$	98.6675	+	271.087i	0.122416	+	0.336336i
$807$	884.288	+	350.307i	1.09577	+	0.434086i
$808$	−6.40587	−	36.3295i	−0.00792806	−	0.0449622i
$809$		−	1021.88i		−	1.26313i	−0.775321	−	0.631567i	$-0.782412\pi$
$809$		−	1021.88i		−	1.26313i	0.775321	−	0.631567i	$-0.217588\pi$
$810$	−453.245	−	225.419i	−0.559562	−	0.278295i
$811$	−365.788			−0.451034			−0.225517	−	0.974239i	$-0.572407\pi$
$811$	−365.788			−0.451034			−0.225517	+	0.974239i	$0.572407\pi$
$812$	−697.758	+	123.034i	−0.859308	+	0.151519i
$813$	127.835	−	322.696i	0.157239	−	0.396921i
$814$	226.211	−	82.3342i	0.277901	−	0.101148i
$815$	−137.910	+	164.355i	−0.169215	+	0.201662i
$816$	3.13374	−	15.2518i	0.00384037	−	0.0186909i
$817$	154.846	+	56.3595i	0.189531	+	0.0689835i
$818$	407.542	−	235.294i	0.498217	−	0.287646i
$819$	−1019.64	+	307.429i	−1.24498	+	0.375371i
$820$	−88.8346	+	153.866i	−0.108335	+	0.187641i
$821$	−6.23245	−	7.42755i	−0.00759129	−	0.00904695i	0.762235	−	0.647300i	$-0.224102\pi$
$821$	−6.23245	−	7.42755i	−0.00759129	−	0.00904695i	−0.769827	+	0.638253i	$0.779657\pi$
$822$	−6.42805	+	228.584i	−0.00782001	+	0.278082i
$823$	0.155222	−	0.880308i	0.000188605	−	0.00106963i	−0.984713	−	0.174183i	$-0.944272\pi$
$823$	0.155222	−	0.880308i	0.000188605	−	0.00106963i	0.984902	+	0.173113i	$0.0553827\pi$
$824$	549.829	+	96.9497i	0.667268	+	0.117657i
$825$	66.6153	+	123.258i	0.0807458	+	0.149403i
$826$	−639.636	+	536.719i	−0.774378	+	0.649780i
$827$	−583.611	−	336.948i	−0.705696	−	0.407434i	0.103769	−	0.994601i	$-0.466910\pi$
$827$	−583.611	−	336.948i	−0.705696	−	0.407434i	−0.809465	+	0.587168i	$0.800243\pi$
$828$	−26.7044	+	474.434i	−0.0322517	+	0.572988i
$829$	−14.4804	−	25.0808i	−0.0174673	−	0.0302542i	0.857160	−	0.515051i	$-0.172227\pi$
$829$	−14.4804	−	25.0808i	−0.0174673	−	0.0302542i	−0.874627	+	0.484797i	$0.838894\pi$
$830$	−67.5475	+	185.585i	−0.0813825	+	0.223597i
$831$	229.713	−	258.633i	0.276429	−	0.311231i
$832$	−271.118	−	227.495i	−0.325863	−	0.273431i
$833$	66.9709	+	184.001i	0.0803972	+	0.220890i
$834$	−63.6704	−	431.738i	−0.0763434	−	0.517672i
$835$	−155.124	−	879.753i	−0.185778	−	1.05360i
$836$			140.816i			0.168440i
$837$	421.103	−	423.574i	0.503110	−	0.506062i
$838$	136.221			0.162555
$839$	629.012	−	110.912i	0.749716	−	0.132195i	0.214282	−	0.976772i	$-0.431259\pi$
$839$	629.012	−	110.912i	0.749716	−	0.132195i	0.535434	+	0.844577i	$0.320148\pi$
$840$	−815.882	−	1029.79i	−0.971288	−	1.22593i
$841$	−185.952	+	67.6809i	−0.221108	+	0.0804767i
$842$	−389.047	+	463.648i	−0.462051	+	0.550650i
$843$	−232.277	+	77.2195i	−0.275536	+	0.0916008i
$844$	−288.712	−	105.082i	−0.342075	−	0.124505i
$845$	−199.631	+	115.257i	−0.236250	+	0.136399i
$846$	103.771	−	77.5698i	0.122661	−	0.0916900i
$847$	−89.1253	+	154.370i	−0.105225	+	0.182254i
$848$	−89.3493	−	106.482i	−0.105365	−	0.125569i
$849$	1065.74	+	655.926i	1.25529	+	0.772587i
$850$	2.53306	−	14.3657i	0.00298008	−	0.0169008i
$851$	−346.151	−	61.0358i	−0.406758	−	0.0717225i
$852$	−507.386	+	824.395i	−0.595523	+	0.967600i
$853$	595.279	−	499.498i	0.697865	−	0.585578i	−0.223300	−	0.974750i	$-0.571683\pi$
$853$	595.279	−	499.498i	0.697865	−	0.585578i	0.921165	+	0.389171i	$0.127239\pi$
$854$	−826.899	−	477.410i	−0.968266	−	0.559029i
$855$	131.138	+	175.434i	0.153378	+	0.205185i
$856$	610.623	+	1057.63i	0.713345	+	1.23555i
$857$	368.296	−	1011.88i	0.429750	−	1.18073i	−0.516215	−	0.856459i	$-0.672659\pi$
$857$	368.296	−	1011.88i	0.429750	−	1.18073i	0.945965	−	0.324269i	$-0.105118\pi$
$858$	144.945	+	435.995i	0.168934	+	0.508153i
$859$	−62.0374	−	52.0556i	−0.0722205	−	0.0606002i	0.605963	−	0.795493i	$-0.292788\pi$
$859$	−62.0374	−	52.0556i	−0.0722205	−	0.0606002i	−0.678183	+	0.734893i	$0.737232\pi$
$860$	−177.974	−	488.979i	−0.206946	−	0.568580i
$861$	−308.267	+	244.235i	−0.358034	+	0.283664i
$862$	53.1375	+	301.358i	0.0616444	+	0.349603i
$863$			1599.17i			1.85304i	0.376244	+	0.926520i	$0.377215\pi$
$863$			1599.17i			1.85304i	−0.376244	+	0.926520i	$0.622785\pi$
$864$	−226.698	+	856.057i	−0.262382	+	0.990807i
$865$	58.6217			0.0677708
$866$	−802.629	+	141.525i	−0.926823	+	0.163424i
$867$	−828.094	+	122.123i	−0.955126	+	0.140857i
$868$	580.776	−	211.385i	0.669097	−	0.243531i
$869$	−153.906	+	183.418i	−0.177107	+	0.211067i
$870$	355.484	+	315.733i	0.408602	+	0.362912i
$871$	1025.19	+	373.137i	1.17702	+	0.428400i
$872$	124.260	−	71.7413i	0.142500	−	0.0822722i
$873$	717.103	+	40.3635i	0.821423	+	0.0462354i
$874$	−52.2449	+	90.4908i	−0.0597767	+	0.103536i
$875$	−766.304	−	913.245i	−0.875776	−	1.04371i
$876$	637.954	−	344.785i	0.728258	−	0.393590i
$877$	−65.7402	+	372.831i	−0.0749603	+	0.425121i	0.924115	+	0.382116i	$0.124804\pi$
$877$	−65.7402	+	372.831i	−0.0749603	+	0.425121i	−0.999075	+	0.0430055i	$0.986307\pi$
$878$	506.396	+	89.2913i	0.576761	+	0.101698i
$879$	−1037.09	−	29.1642i	−1.17985	−	0.0331789i
$880$	79.5498	−	66.7502i	0.0903975	−	0.0758525i
$881$	−1046.81	−	604.374i	−1.18820	−	0.686009i	−0.230305	−	0.973119i	$-0.573972\pi$
$881$	−1046.81	−	604.374i	−1.18820	−	0.686009i	−0.957898	+	0.287109i	$0.907306\pi$
$882$	−186.924	−	619.967i	−0.211932	−	0.702910i
$883$	298.144	+	516.401i	0.337649	+	0.584826i	0.983990	−	0.178223i	$-0.0570349\pi$
$883$	298.144	+	516.401i	0.337649	+	0.584826i	−0.646341	+	0.763049i	$0.723702\pi$
$884$	−32.1941	+	88.4525i	−0.0364186	+	0.100059i
$885$	−1079.99	−	221.902i	−1.22033	−	0.250737i
$886$	−539.694	−	452.857i	−0.609136	−	0.511126i
$887$	34.7360	+	95.4364i	0.0391612	+	0.107595i	0.957732	−	0.287662i	$-0.0928779\pi$
$887$	34.7360	+	95.4364i	0.0391612	+	0.107595i	−0.918571	+	0.395256i	$0.870656\pi$
$888$	−380.316	−	150.661i	−0.428283	−	0.169663i
$889$	285.757	+	1620.61i	0.321436	+	1.82296i
$890$			431.356i			0.484670i
$891$	689.371	−	655.489i	0.773705	−	0.735678i
$892$	−525.755			−0.589412
$893$	−55.2071	+	9.73450i	−0.0618220	+	0.0109009i
$894$	258.802	−	653.301i	0.289488	−	0.730761i
$895$	1429.39	−	520.255i	1.59708	−	0.581290i
$896$	−640.678	+	763.531i	−0.715043	+	0.852155i
$897$	135.019	−	657.131i	0.150523	−	0.732588i
$898$	438.061	+	159.441i	0.487818	+	0.177551i
$899$	−485.835	+	280.497i	−0.540417	+	0.312010i
$900$	21.7104	−	92.4062i	0.0241227	−	0.102674i
$901$	133.684	−	231.548i	0.148373	−	0.256990i
$902$	109.065	+	129.979i	0.120915	+	0.144101i
$903$	32.3796	−	1151.43i	0.0358578	−	1.27511i
$904$	24.1609	−	137.023i	0.0267267	−	0.151575i
$905$	−576.769	−	101.700i	−0.637313	−	0.112376i
$906$	−212.197	−	392.626i	−0.234213	−	0.433362i
$907$	1321.91	−	1109.21i	1.45745	−	1.22295i	0.530547	−	0.847656i	$-0.321987\pi$
$907$	1321.91	−	1109.21i	1.45745	−	1.22295i	0.926906	−	0.375293i	$-0.122458\pi$
$908$	11.8330	+	6.83179i	0.0130319	+	0.00752400i
$909$	38.3797	−	19.3688i	0.0422219	−	0.0213078i
$910$	369.753	+	640.431i	0.406322	+	0.703771i
$911$	106.953	−	293.850i	0.117401	−	0.322558i	−0.867048	−	0.498224i	$-0.833986\pi$
$911$	106.953	−	293.850i	0.117401	−	0.322558i	0.984450	+	0.175666i	$0.0562080\pi$
$912$	14.7950	−	16.6577i	0.0162226	−	0.0182650i
$913$	−284.305	−	238.560i	−0.311396	−	0.261292i
$914$	−58.4144	−	160.492i	−0.0639107	−	0.175593i
$915$	−183.944	−	1247.30i	−0.201032	−	1.36316i
$916$	162.732	+	922.898i	0.177655	+	1.00753i
$917$			1037.84i			1.13177i
$918$	−98.6384	+	8.92054i	−0.107449	+	0.00971737i
$919$	198.504			0.216000			0.108000	−	0.994151i	$-0.465555\pi$
$919$	198.504			0.216000			0.108000	+	0.994151i	$0.465555\pi$
$920$	815.035	−	143.713i	0.885908	−	0.156209i
$921$	1075.58	+	1357.57i	1.16784	+	1.47401i
$922$	−856.844	+	311.866i	−0.929332	+	0.338249i
$923$	878.459	−	1046.91i	0.951743	−	1.13424i
$924$	934.076	−	310.530i	1.01090	−	0.336072i
$925$	65.9791	+	24.0144i	0.0713287	+	0.0259615i
$926$	360.397	−	208.075i	0.389197	−	0.224703i
$927$	76.7941	+	646.087i	0.0828416	+	0.696966i
$928$	415.883	−	720.330i	0.448149	−	0.776218i
$929$	854.746	+	1018.65i	0.920071	+	1.09650i	0.995056	+	0.0993136i	$0.0316647\pi$
$929$	854.746	+	1018.65i	0.920071	+	1.09650i	−0.0749849	+	0.997185i	$0.523891\pi$
$930$	−353.206	−	217.385i	−0.379791	−	0.233748i
$931$	−48.6528	+	275.924i	−0.0522587	+	0.296374i
$932$	−367.127	−	64.7343i	−0.393913	−	0.0694574i
$933$	706.187	−	1147.41i	0.756899	−	1.22980i
$934$	−90.6501	+	76.0644i	−0.0970557	+	0.0814394i
$935$	172.983	+	99.8717i	0.185008	+	0.106815i
$936$	307.843	−	717.503i	0.328892	−	0.766563i
$937$	−675.671	−	1170.30i	−0.721100	−	1.24898i	−0.960559	−	0.278076i	$-0.910303\pi$
$937$	−675.671	−	1170.30i	−0.721100	−	1.24898i	0.239459	−	0.970906i	$-0.423030\pi$
$938$	−406.260	+	1116.19i	−0.433113	+	1.18997i
$939$	−10.2568	−	30.8524i	−0.0109231	−	0.0328567i
$940$	135.608	+	113.789i	0.144264	+	0.121052i
$941$	265.840	+	730.391i	0.282508	+	0.776186i	0.997062	+	0.0766044i	$0.0244078\pi$
$941$	265.840	+	730.391i	0.282508	+	0.776186i	−0.714553	+	0.699581i	$0.753370\pi$
$942$	−379.313	+	300.523i	−0.402667	+	0.319027i
$943$	−43.0206	−	243.982i	−0.0456210	−	0.258729i
$944$			112.150i			0.118803i
$945$	874.517	−	1256.75i	0.925415	−	1.32989i
$946$	−496.949			−0.525316
$947$	−270.124	+	47.6301i	−0.285242	+	0.0502958i	−0.314438	−	0.949278i	$-0.601816\pi$
$947$	−270.124	+	47.6301i	−0.285242	+	0.0502958i	0.0291967	+	0.999574i	$0.490705\pi$
$948$	160.480	−	23.6668i	0.169283	−	0.0249649i
$949$	−962.034	+	350.152i	−1.01373	+	0.368969i
$950$	13.4167	−	15.9894i	0.0141229	−	0.0168310i
$951$	489.501	+	434.765i	0.514723	+	0.457166i
$952$	−241.551	−	87.9173i	−0.253730	−	0.0923501i
$953$	858.313	−	495.548i	0.900644	−	0.519987i	0.0232347	−	0.999730i	$-0.492603\pi$
$953$	858.313	−	495.548i	0.900644	−	0.519987i	0.877409	+	0.479743i	$0.159270\pi$
$954$	−484.421	+	739.664i	−0.507779	+	0.775329i
$955$	−292.376	+	506.410i	−0.306153	+	0.530272i
$956$	251.751	+	300.025i	0.263338	+	0.313834i
$957$	−786.020	+	424.808i	−0.821338	+	0.443896i
$958$	25.4760	−	144.482i	0.0265929	−	0.150816i
$959$	−681.141	−	120.104i	−0.710262	−	0.125238i
$960$	508.613	+	14.3028i	0.529806	+	0.0148988i
$961$	−361.298	+	303.165i	−0.375961	+	0.315468i
$962$	199.405	+	115.126i	0.207281	+	0.119674i
$963$	−974.635	+	1037.10i	−1.01208	+	1.07694i
$964$	−403.678	−	699.190i	−0.418753	−	0.725301i
$965$	368.418	−	1012.22i	0.381780	−	1.04893i
$966$	715.464	+	147.004i	0.740646	+	0.152178i
$967$	239.352	+	200.840i	0.247520	+	0.207694i	0.758104	−	0.652134i	$-0.226126\pi$
$967$	239.352	+	200.840i	0.247520	+	0.207694i	−0.510583	+	0.859828i	$0.670571\pi$
$968$	−44.6946	−	122.797i	−0.0461721	−	0.126857i
$969$	39.8416	+	15.7831i	0.0411162	+	0.0162880i
$970$	−86.6041	−	491.156i	−0.0892826	−	0.506347i
$971$		−	487.838i		−	0.502407i	−0.967934	−	0.251204i	$-0.919174\pi$
$971$		−	487.838i		−	0.502407i	0.967934	−	0.251204i	$-0.0808264\pi$
$972$	−644.105	+	21.8847i	−0.662659	+	0.0225151i
$973$	1319.96			1.35659
$974$	519.080	−	91.5279i	0.532937	−	0.0939711i
$975$	−49.3558	+	124.590i	−0.0506214	+	0.127785i
$976$	−120.511	+	43.8624i	−0.123474	+	0.0449410i
$977$	−413.839	+	493.194i	−0.423582	+	0.504805i	−0.935059	−	0.354492i	$-0.884654\pi$
$977$	−413.839	+	493.194i	−0.423582	+	0.504805i	0.511478	+	0.859297i	$0.329098\pi$
$978$	27.9387	−	135.977i	0.0285672	−	0.139035i
$979$	−761.718	−	277.243i	−0.778057	−	0.283190i
$980$	766.227	−	442.382i	0.781865	−	0.451410i
$981$	121.847	+	114.509i	0.124207	+	0.116726i
$982$	183.483	−	317.802i	0.186846	−	0.323627i
$983$	−989.779	−	1179.57i	−1.00690	−	1.19997i	−0.979726	−	0.200341i	$-0.935795\pi$
$983$	−989.779	−	1179.57i	−1.00690	−	1.19997i	−0.0271699	−	0.999631i	$-0.508650\pi$
$984$	8.10498	−	288.216i	0.00823676	−	0.292902i
$985$	−273.610	+	1551.72i	−0.277777	+	1.57535i
$986$	91.6108	+	16.1534i	0.0929115	+	0.0163828i
$987$	186.316	+	344.739i	0.188770	+	0.349279i
$988$	−103.177	+	86.5756i	−0.104430	+	0.0876271i
$989$	628.389	+	362.801i	0.635378	+	0.366836i
$990$	−552.581	−	361.897i	−0.558163	−	0.365552i
$991$	−155.571	−	269.456i	−0.156984	−	0.271903i	0.776796	−	0.629752i	$-0.216844\pi$
$991$	−155.571	−	269.456i	−0.156984	−	0.271903i	−0.933780	+	0.357849i	$0.883510\pi$
$992$	−248.155	+	681.799i	−0.250156	+	0.687297i
$993$	−1196.67	+	1347.33i	−1.20511	+	1.35683i
$994$	1139.84	+	956.439i	1.14672	+	0.962213i
$995$	151.540	+	416.352i	0.152301	+	0.418445i
$996$	36.6844	+	248.751i	0.0368318	+	0.249750i
$997$	−8.37502	−	47.4971i	−0.00840022	−	0.0476400i	0.980320	−	0.197417i	$-0.0632554\pi$
$997$	−8.37502	−	47.4971i	−0.00840022	−	0.0476400i	−0.988720	+	0.149777i	$0.952144\pi$
$998$		−	141.953i		−	0.142238i
$999$	40.1592	−	475.021i	0.0401994	−	0.475496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.3.f.a.14.4	yes	30
3.2	odd	2		81.3.f.a.71.2		30
4.3	odd	2		432.3.bc.a.257.3		30
9.2	odd	6		243.3.f.a.134.4		30
9.4	even	3		243.3.f.c.53.2		30
9.5	odd	6		243.3.f.b.53.4		30
9.7	even	3		243.3.f.d.134.2		30
27.2	odd	18	inner	27.3.f.a.2.4	✓	30
27.5	odd	18		729.3.b.a.728.19		30
27.7	even	9		243.3.f.a.107.4		30
27.11	odd	18		243.3.f.c.188.2		30
27.16	even	9		243.3.f.b.188.4		30
27.20	odd	18		243.3.f.d.107.2		30
27.22	even	9		729.3.b.a.728.12		30
27.25	even	9		81.3.f.a.8.2		30
108.83	even	18		432.3.bc.a.353.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.4	✓	30	27.2	odd	18	inner
27.3.f.a.14.4	yes	30	1.1	even	1	trivial
81.3.f.a.8.2		30	27.25	even	9
81.3.f.a.71.2		30	3.2	odd	2
243.3.f.a.107.4		30	27.7	even	9
243.3.f.a.134.4		30	9.2	odd	6
243.3.f.b.53.4		30	9.5	odd	6
243.3.f.b.188.4		30	27.16	even	9
243.3.f.c.53.2		30	9.4	even	3
243.3.f.c.188.2		30	27.11	odd	18
243.3.f.d.107.2		30	27.20	odd	18
243.3.f.d.134.2		30	9.7	even	3
432.3.bc.a.257.3		30	4.3	odd	2
432.3.bc.a.353.3		30	108.83	even	18
729.3.b.a.728.12		30	27.22	even	9
729.3.b.a.728.19		30	27.5	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14332 - 0.201599i) q^{2} +(1.10490 - 2.78912i) q^{3} +(-2.49222 + 0.907094i) q^{4} +(-3.46013 + 4.12362i) q^{5} +(0.700975 - 3.41162i) q^{6} +(9.89907 + 3.60297i) q^{7} +(-6.68824 + 3.86146i) q^{8} +(-6.55839 - 6.16340i) q^{9} +(-3.12473 + 5.41219i) q^{10} +(-7.54888 - 8.99640i) q^{11} +(-0.223658 + 7.95335i) q^{12} +(1.95057 - 11.0622i) q^{13} +(12.0442 + 2.12372i) q^{14} +(7.67818 + 14.2069i) q^{15} +(1.25834 - 1.05588i) q^{16} +(2.73630 + 1.57980i) q^{17} +(-8.74091 - 5.72460i) q^{18} +(2.26051 + 3.91532i) q^{19} +(4.88289 - 13.4156i) q^{20} +(20.9866 - 23.6288i) q^{21} +(-10.4445 - 8.76396i) q^{22} +(6.80880 + 18.7070i) q^{23} +(3.38024 + 22.9208i) q^{24} +(-0.690550 - 3.91630i) q^{25} -13.0409i q^{26} +(-24.4368 + 11.4822i) q^{27} -27.9389 q^{28} +(24.9744 - 4.40366i) q^{29} +(11.6428 + 14.6952i) q^{30} +(-20.7874 + 7.56598i) q^{31} +(21.0826 - 25.1253i) q^{32} +(-33.4328 + 11.1146i) q^{33} +(3.44696 + 1.25459i) q^{34} +(-49.1093 + 28.3533i) q^{35} +(21.9358 + 9.41147i) q^{36} +(-8.82807 + 15.2907i) q^{37} +(3.37382 + 4.02076i) q^{38} +(-28.6987 - 17.6630i) q^{39} +(7.21898 - 40.9409i) q^{40} +(-12.2557 - 2.16101i) q^{41} +(19.2309 - 31.2462i) q^{42} +(27.9211 - 23.4286i) q^{43} +(26.9741 + 15.5735i) q^{44} +(48.1084 - 5.71818i) q^{45} +(11.5560 + 20.0156i) q^{46} +(-4.24091 + 11.6518i) q^{47} +(-1.55462 - 4.67631i) q^{48} +(47.4740 + 39.8354i) q^{49} +(-1.57905 - 4.33839i) q^{50} +(7.42960 - 5.88634i) q^{51} +(5.17323 + 29.3388i) q^{52} -84.6210i q^{53} +(-25.6244 + 18.0543i) q^{54} +63.2178 q^{55} +(-80.1200 + 14.1273i) q^{56} +(13.4179 - 1.97880i) q^{57} +(27.6661 - 10.0696i) q^{58} +(-43.8854 + 52.3006i) q^{59} +(-32.0227 - 28.4419i) q^{60} +(-73.3637 - 26.7022i) q^{61} +(-22.2414 + 12.8411i) q^{62} +(-42.7155 - 84.6415i) q^{63} +(15.7537 - 27.2863i) q^{64} +(38.8672 + 46.3201i) q^{65} +(-35.9839 + 19.4476i) q^{66} +(-16.8654 + 95.6483i) q^{67} +(-8.25249 - 1.45514i) q^{68} +(59.6992 + 1.67882i) q^{69} +(-50.4319 + 42.3174i) q^{70} +(105.364 + 60.8322i) q^{71} +(67.6638 + 15.8973i) q^{72} +(-45.5705 - 78.9304i) q^{73} +(-7.01076 + 19.2619i) q^{74} +(-11.6860 - 2.40109i) q^{75} +(-9.18525 - 7.70734i) q^{76} +(-42.3131 - 116.254i) q^{77} +(-36.3728 - 14.4089i) q^{78} +(-3.54032 - 20.0781i) q^{79} +8.84240i q^{80} +(5.02506 + 80.8440i) q^{81} -14.4479 q^{82} +(31.1219 - 5.48763i) q^{83} +(-30.8697 + 77.9250i) q^{84} +(-15.9824 + 5.81713i) q^{85} +(27.1997 - 32.4154i) q^{86} +(15.3119 - 74.5223i) q^{87} +(85.2279 + 31.0204i) q^{88} +(59.7756 - 34.5114i) q^{89} +(53.8507 - 16.2363i) q^{90} +(59.1656 - 102.478i) q^{91} +(-33.9381 - 40.4458i) q^{92} +(-1.86551 + 66.3381i) q^{93} +(-2.49974 + 14.1767i) q^{94} +(-23.9669 - 4.22602i) q^{95} +(-46.7833 - 86.5629i) q^{96} +(-61.1335 + 51.2971i) q^{97} +(62.3089 + 35.9741i) q^{98} +(-5.93989 + 105.529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20}+ \cdots + 513 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 15 * q^5 - 18 * q^6 - 6 * q^7 - 9 * q^8 - 3 * q^10 - 6 * q^11 - 15 * q^12 - 6 * q^13 - 15 * q^14 - 9 * q^15 - 18 * q^16 - 9 * q^17 + 63 * q^18 - 3 * q^19 + 213 * q^20 + 132 * q^21 - 42 * q^22 + 120 * q^23 + 144 * q^24 - 15 * q^25 - 90 * q^27 - 12 * q^28 - 168 * q^29 - 243 * q^30 + 39 * q^31 - 360 * q^32 - 207 * q^33 + 54 * q^34 - 252 * q^35 - 360 * q^36 - 3 * q^37 - 84 * q^38 + 15 * q^39 - 33 * q^40 + 228 * q^41 + 486 * q^42 - 96 * q^43 + 639 * q^44 + 477 * q^45 - 3 * q^46 + 399 * q^47 + 453 * q^48 - 78 * q^49 + 303 * q^50 + 36 * q^51 - 9 * q^52 - 54 * q^54 - 12 * q^55 - 393 * q^56 - 192 * q^57 + 129 * q^58 - 474 * q^59 - 846 * q^60 + 138 * q^61 - 900 * q^62 - 585 * q^63 - 51 * q^64 - 411 * q^65 - 423 * q^66 + 354 * q^67 + 99 * q^68 + 99 * q^69 + 489 * q^70 + 315 * q^71 + 720 * q^72 - 66 * q^73 + 321 * q^74 + 255 * q^75 + 258 * q^76 + 201 * q^77 + 180 * q^78 + 30 * q^79 + 36 * q^81 - 12 * q^82 - 33 * q^83 - 588 * q^84 - 261 * q^85 - 258 * q^86 - 279 * q^87 - 642 * q^88 + 72 * q^89 + 288 * q^90 + 96 * q^91 - 3 * q^92 + 591 * q^93 - 861 * q^94 + 681 * q^95 + 270 * q^96 - 582 * q^97 + 882 * q^98 + 513 * q^99

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