LMFDB - Embedded newform 81.3.f.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,3,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, 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("81.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not 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:	$2.20709014132$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	81.71
Dual form			81.3.f.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14332 + 0.201599i) q^{2} +(-2.49222 + 0.907094i) q^{4} +(3.46013 - 4.12362i) q^{5} +(9.89907 + 3.60297i) q^{7} +(6.68824 - 3.86146i) q^{8} +(-3.12473 + 5.41219i) q^{10} +(7.54888 + 8.99640i) q^{11} +(1.95057 - 11.0622i) q^{13} +(-12.0442 - 2.12372i) q^{14} +(1.25834 - 1.05588i) q^{16} +(-2.73630 - 1.57980i) q^{17} +(2.26051 + 3.91532i) q^{19} +(-4.88289 + 13.4156i) q^{20} +(-10.4445 - 8.76396i) q^{22} +(-6.80880 - 18.7070i) q^{23} +(-0.690550 - 3.91630i) q^{25} +13.0409i q^{26} -27.9389 q^{28} +(-24.9744 + 4.40366i) q^{29} +(-20.7874 + 7.56598i) q^{31} +(-21.0826 + 25.1253i) q^{32} +(3.44696 + 1.25459i) q^{34} +(49.1093 - 28.3533i) q^{35} +(-8.82807 + 15.2907i) q^{37} +(-3.37382 - 4.02076i) q^{38} +(7.21898 - 40.9409i) q^{40} +(12.2557 + 2.16101i) q^{41} +(27.9211 - 23.4286i) q^{43} +(-26.9741 - 15.5735i) q^{44} +(11.5560 + 20.0156i) q^{46} +(4.24091 - 11.6518i) q^{47} +(47.4740 + 39.8354i) q^{49} +(1.57905 + 4.33839i) q^{50} +(5.17323 + 29.3388i) q^{52} +84.6210i q^{53} +63.2178 q^{55} +(80.1200 - 14.1273i) q^{56} +(27.6661 - 10.0696i) q^{58} +(43.8854 - 52.3006i) q^{59} +(-73.3637 - 26.7022i) q^{61} +(22.2414 - 12.8411i) q^{62} +(15.7537 - 27.2863i) q^{64} +(-38.8672 - 46.3201i) q^{65} +(-16.8654 + 95.6483i) q^{67} +(8.25249 + 1.45514i) q^{68} +(-50.4319 + 42.3174i) q^{70} +(-105.364 - 60.8322i) q^{71} +(-45.5705 - 78.9304i) q^{73} +(7.01076 - 19.2619i) q^{74} +(-9.18525 - 7.70734i) q^{76} +(42.3131 + 116.254i) q^{77} +(-3.54032 - 20.0781i) q^{79} -8.84240i q^{80} -14.4479 q^{82} +(-31.1219 + 5.48763i) q^{83} +(-15.9824 + 5.81713i) q^{85} +(-27.1997 + 32.4154i) q^{86} +(85.2279 + 31.0204i) q^{88} +(-59.7756 + 34.5114i) q^{89} +(59.1656 - 102.478i) q^{91} +(33.9381 + 40.4458i) q^{92} +(-2.49974 + 14.1767i) q^{94} +(23.9669 + 4.22602i) q^{95} +(-61.1335 + 51.2971i) q^{97} +(-62.3089 - 35.9741i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) $ 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

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

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	−0.452004	−	0.892016i	$-0.649291\pi$
$2$	−1.14332	+	0.201599i	−0.571662	+	0.100799i	−0.119658	+	0.992815i	$0.538180\pi$
$3$		0			0
$3$		0			0
$4$	−2.49222	+	0.907094i	−0.623055	+	0.226774i
$5$	3.46013	−	4.12362i	0.692026	−	0.824724i	−0.299574	−	0.954073i	$-0.596844\pi$
$5$	3.46013	−	4.12362i	0.692026	−	0.824724i	0.991599	+	0.129349i	$0.0412889\pi$
$6$		0			0
$7$	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
$9$		0			0
$10$	−3.12473	+	5.41219i	−0.312473	+	0.541219i
$11$	7.54888	+	8.99640i	0.686262	+	0.817855i	0.990898	−	0.134614i	$-0.0429794\pi$
$11$	7.54888	+	8.99640i	0.686262	+	0.817855i	−0.304636	+	0.952469i	$0.598535\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	1.25834	−	1.05588i	0.0786465	−	0.0659923i
$17$	−2.73630	−	1.57980i	−0.160959	−	0.0929296i	0.417357	−	0.908743i	$-0.362956\pi$
$17$	−2.73630	−	1.57980i	−0.160959	−	0.0929296i	−0.578316	+	0.815813i	$0.696290\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	−10.4445	−	8.76396i	−0.474749	−	0.398362i
$23$	−6.80880	−	18.7070i	−0.296035	−	0.813349i	−0.995153	−	0.0983427i	$-0.968646\pi$
$23$	−6.80880	−	18.7070i	−0.296035	−	0.813349i	0.699118	−	0.715007i	$-0.253576\pi$
$24$		0			0
$25$	−0.690550	−	3.91630i	−0.0276220	−	0.156652i
$26$			13.0409i			0.501575i
$27$		0			0
$28$	−27.9389			−0.997818
$29$	−24.9744	+	4.40366i	−0.861187	+	0.151851i	−0.586763	−	0.809758i	$-0.699598\pi$
$29$	−24.9744	+	4.40366i	−0.861187	+	0.151851i	−0.274424	+	0.961609i	$0.588487\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	3.44696	+	1.25459i	0.101381	+	0.0368998i
$35$	49.1093	−	28.3533i	1.40312	−	0.810093i
$36$		0			0
$37$	−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
$39$		0			0
$40$	7.21898	−	40.9409i	0.180475	−	1.02352i
$41$	12.2557	+	2.16101i	0.298920	+	0.0527076i	0.321096	−	0.947046i	$-0.395949\pi$
$41$	12.2557	+	2.16101i	0.298920	+	0.0527076i	−0.0221770	+	0.999754i	$0.507060\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	11.5560	+	20.0156i	0.251217	+	0.435121i
$47$	4.24091	−	11.6518i	0.0902320	−	0.247910i	−0.886365	−	0.462987i	$-0.846778\pi$
$47$	4.24091	−	11.6518i	0.0902320	−	0.247910i	0.976597	+	0.215076i	$0.0690000\pi$
$48$		0			0
$49$	47.4740	+	39.8354i	0.968857	+	0.812967i
$50$	1.57905	+	4.33839i	0.0315809	+	0.0867679i
$51$		0			0
$52$	5.17323	+	29.3388i	0.0994852	+	0.564209i
$53$			84.6210i			1.59662i	0.602245	+	0.798311i	$0.294273\pi$
$53$			84.6210i			1.59662i	−0.602245	+	0.798311i	$0.705727\pi$
$54$		0			0
$55$	63.2178			1.14942
$56$	80.1200	−	14.1273i	1.43071	−	0.252274i
$57$		0			0
$58$	27.6661	−	10.0696i	0.477002	−	0.173614i
$59$	43.8854	−	52.3006i	0.743820	−	0.886451i	−0.252890	−	0.967495i	$-0.581381\pi$
$59$	43.8854	−	52.3006i	0.743820	−	0.886451i	0.996711	+	0.0810443i	$0.0258255\pi$
$60$		0			0
$61$	−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
$63$		0			0
$64$	15.7537	−	27.2863i	0.246152	−	0.426348i
$65$	−38.8672	−	46.3201i	−0.597956	−	0.712617i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−50.4319	+	42.3174i	−0.720455	+	0.604534i
$71$	−105.364	−	60.8322i	−1.48401	−	0.856791i	−0.484171	−	0.874973i	$-0.660879\pi$
$71$	−105.364	−	60.8322i	−1.48401	−	0.856791i	−0.999835	+	0.0181820i	$0.994212\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	−9.18525	−	7.70734i	−0.120859	−	0.101412i
$77$	42.3131	+	116.254i	0.549521	+	1.50980i
$78$		0			0
$79$	−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
$81$		0			0
$82$	−14.4479			−0.176194
$83$	−31.1219	+	5.48763i	−0.374963	+	0.0661161i	−0.357954	−	0.933739i	$-0.616526\pi$
$83$	−31.1219	+	5.48763i	−0.374963	+	0.0661161i	−0.0170090	+	0.999855i	$0.505414\pi$
$84$		0			0
$85$	−15.9824	+	5.81713i	−0.188029	+	0.0684369i
$86$	−27.1997	+	32.4154i	−0.316276	+	0.376923i
$87$		0			0
$88$	85.2279	+	31.0204i	0.968499	+	0.352505i
$89$	−59.7756	+	34.5114i	−0.671636	+	0.387769i	−0.796696	−	0.604380i	$-0.793421\pi$
$89$	−59.7756	+	34.5114i	−0.671636	+	0.387769i	0.125060	+	0.992149i	$0.460088\pi$
$90$		0			0
$91$	59.1656	−	102.478i	0.650171	−	1.12613i
$92$	33.9381	+	40.4458i	0.368892	+	0.439629i
$93$		0			0
$94$	−2.49974	+	14.1767i	−0.0265930	+	0.150816i
$95$	23.9669	+	4.22602i	0.252283	+	0.0444844i
$96$		0			0
$97$	−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
$99$		0			0
$100$	5.27346	+	9.13390i	0.0527346	+	0.0913390i
$101$	1.63372	−	4.48862i	0.0161755	−	0.0444417i	−0.931342	−	0.364145i	$-0.881361\pi$
$101$	1.63372	−	4.48862i	0.0161755	−	0.0444417i	0.947518	+	0.319704i	$0.103583\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	−17.0595	−	96.7493i	−0.160939	−	0.912729i
$107$			158.133i			1.47788i	0.673773	+	0.738938i	$0.264672\pi$
$107$			158.133i			1.47788i	−0.673773	+	0.738938i	$0.735328\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	16.2607	−	5.91842i	0.145185	−	0.0528430i
$113$	11.5806	−	13.8012i	0.102483	−	0.122134i	−0.712365	−	0.701809i	$-0.752376\pi$
$113$	11.5806	−	13.8012i	0.102483	−	0.122134i	0.814848	+	0.579675i	$0.196820\pi$
$114$		0			0
$115$	−100.700	−	36.6518i	−0.875652	−	0.318711i
$116$	58.2473	−	33.6291i	0.502131	−	0.289906i
$117$		0			0
$118$	−39.6315	+	68.6438i	−0.335860	+	0.581727i
$119$	−21.3948	−	25.4974i	−0.179788	−	0.214264i
$120$		0			0
$121$	−2.93828	+	16.6638i	−0.0242833	+	0.137717i
$122$	89.2617	+	15.7392i	0.731653	+	0.129010i
$123$		0			0
$124$	44.9437	−	37.7122i	0.362449	−	0.304131i
$125$	98.0067	+	56.5842i	0.784054	+	0.452674i
$126$		0			0
$127$	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
$129$		0			0
$130$	53.7759	+	45.1233i	0.413661	+	0.347102i
$131$	−33.6955	−	92.5776i	−0.257217	−	0.706699i	−0.999336	−	0.0364307i	$-0.988401\pi$
$131$	−33.6955	−	92.5776i	−0.257217	−	0.706699i	0.742119	−	0.670268i	$-0.233821\pi$
$132$		0			0
$133$	8.27018	+	46.9025i	0.0621818	+	0.352651i
$134$		−	112.757i		−	0.841471i
$135$		0			0
$136$	−24.4014			−0.179422
$137$	64.6590	−	11.4011i	0.471963	−	0.0832199i	0.0673925	−	0.997727i	$-0.478532\pi$
$137$	64.6590	−	11.4011i	0.471963	−	0.0832199i	0.404571	+	0.914507i	$0.367421\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	132.729	+	48.3096i	0.934714	+	0.340208i
$143$	114.245	−	65.9593i	0.798915	−	0.461254i
$144$		0			0
$145$	−68.2557	+	118.222i	−0.470729	+	0.815326i
$146$	68.0142	+	81.0562i	0.465851	+	0.555179i
$147$		0			0
$148$	8.13142	−	46.1156i	0.0549420	−	0.311592i
$149$	−198.691	−	35.0346i	−1.33350	−	0.235132i	−0.538953	−	0.842336i	$-0.681180\pi$
$149$	−198.691	−	35.0346i	−1.33350	−	0.235132i	−0.794546	+	0.607204i	$0.792291\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−71.8144	−	124.386i	−0.466327	−	0.807703i
$155$	−40.7277	+	111.898i	−0.262759	+	0.721926i
$156$		0			0
$157$	−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
$159$		0			0
$160$	30.6586	+	173.873i	0.191616	+	1.08671i
$161$		−	209.714i		−	1.30257i
$162$		0			0
$163$	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
$165$		0			0
$166$	34.4762	−	12.5483i	0.207688	−	0.0755921i
$167$	106.672	−	127.127i	0.638757	−	0.761241i	−0.345416	−	0.938450i	$-0.612262\pi$
$167$	106.672	−	127.127i	0.638757	−	0.761241i	0.984173	+	0.177208i	$0.0567067\pi$
$168$		0			0
$169$	40.2401	+	14.6462i	0.238107	+	0.0866639i
$170$	17.1004	−	9.87292i	0.100591	−	0.0580760i
$171$		0			0
$172$	−48.3337	+	83.7164i	−0.281010	+	0.486723i
$173$	7.00006	+	8.34234i	0.0404628	+	0.0482216i	0.785896	−	0.618358i	$-0.212202\pi$
$173$	7.00006	+	8.34234i	0.0404628	+	0.0482216i	−0.745434	+	0.666580i	$0.767757\pi$
$174$		0			0
$175$	7.27451	−	41.2558i	0.0415686	−	0.235747i
$176$	18.9982	+	3.34989i	0.107944	+	0.0190335i
$177$		0			0
$178$	61.3854	−	51.5085i	0.344862	−	0.289374i
$179$	244.720	+	141.289i	1.36715	+	0.789326i	0.990564	−	0.137054i	$-0.0437633\pi$
$179$	244.720	+	141.289i	1.36715	+	0.789326i	0.376590	+	0.926380i	$0.377097\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−117.775	−	98.8252i	−0.640083	−	0.537094i
$185$	32.5066	+	89.3112i	0.175711	+	0.482763i
$186$		0			0
$187$	−6.44344	−	36.5426i	−0.0344569	−	0.195415i
$188$			32.8857i			0.174924i
$189$		0			0
$190$	−28.2539			−0.148705
$191$	−106.979	+	18.8633i	−0.560100	+	0.0987607i	−0.446529	−	0.894769i	$-0.647340\pi$
$191$	−106.979	+	18.8633i	−0.560100	+	0.0987607i	−0.113571	+	0.993530i	$0.536229\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−154.450	−	56.2152i	−0.788011	−	0.286812i
$197$	−253.494	+	146.355i	−1.28677	+	0.742918i	−0.978077	−	0.208243i	$-0.933225\pi$
$197$	−253.494	+	146.355i	−1.28677	+	0.742918i	−0.308694	+	0.951161i	$0.599892\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	−0.962975	+	5.46130i	−0.00476720	+	0.0270361i
$203$	−263.090	−	46.3898i	−1.29601	−	0.228521i
$204$		0			0
$205$	51.3175	−	43.0605i	0.250329	−	0.210051i
$206$	72.6848	+	41.9646i	0.352839	+	0.203712i
$207$		0			0
$208$	−9.22585	−	15.9796i	−0.0443550	−	0.0768252i
$209$	−18.1595	+	49.8927i	−0.0868874	+	0.238721i
$210$		0			0
$211$	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
$213$		0			0
$214$	−31.8794	−	180.797i	−0.148969	−	0.844846i
$215$		−	196.202i		−	0.912568i
$216$		0			0
$217$	−233.036			−1.07390
$218$	21.2416	−	3.74547i	0.0974387	−	0.0171811i
$219$		0			0
$220$	−157.553	+	57.3445i	−0.716149	+	0.260657i
$221$	−22.8135	+	27.1880i	−0.103228	+	0.123023i
$222$		0			0
$223$	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
$225$		0			0
$226$	−10.4580	+	18.1138i	−0.0462745	+	0.0801498i
$227$	3.31155	+	3.94655i	0.0145883	+	0.0173857i	0.773289	−	0.634053i	$-0.218610\pi$
$227$	3.31155	+	3.94655i	0.0145883	+	0.0173857i	−0.758701	+	0.651439i	$0.774166\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−150.030	+	125.890i	−0.646683	+	0.542631i
$233$	−121.729	−	70.2803i	−0.522442	−	0.301632i	0.215491	−	0.976506i	$-0.430865\pi$
$233$	−121.729	−	70.2803i	−0.522442	−	0.301632i	−0.737933	+	0.674874i	$0.764198\pi$
$234$		0			0
$235$	−33.3735	−	57.8046i	−0.142015	−	0.245977i
$236$	−61.9306	+	170.153i	−0.262418	+	0.720987i
$237$		0			0
$238$	29.6015	+	24.8386i	0.124376	+	0.104364i
$239$	50.5074	+	138.768i	0.211328	+	0.580619i	0.999388	−	0.0349794i	$-0.0111366\pi$
$239$	50.5074	+	138.768i	0.211328	+	0.580619i	−0.788060	+	0.615598i	$0.788914\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	207.060			0.848606
$245$	328.532	−	57.9291i	1.34095	−	0.236445i
$246$		0			0
$247$	47.7214	−	17.3692i	0.193204	−	0.0703205i
$248$	−109.815	+	130.873i	−0.442803	+	0.527712i
$249$		0			0
$250$	−123.461	−	44.9361i	−0.493843	−	0.179744i
$251$	108.072	−	62.3955i	0.430567	−	0.248588i	−0.269021	−	0.963134i	$-0.586700\pi$
$251$	108.072	−	62.3955i	0.430567	−	0.248588i	0.699588	+	0.714546i	$0.253367\pi$
$252$		0			0
$253$	116.897	−	202.472i	0.462044	−	0.800284i
$254$	−116.575	−	138.928i	−0.458955	−	0.546961i
$255$		0			0
$256$	−40.9593	+	232.292i	−0.159997	+	0.907390i
$257$	450.088	+	79.3627i	1.75132	+	0.308804i	0.955116	−	0.296231i	$-0.0957298\pi$
$257$	450.088	+	79.3627i	1.75132	+	0.308804i	0.796199	+	0.605035i	$0.206841\pi$
$258$		0			0
$259$	−142.481	+	119.556i	−0.550121	+	0.461606i
$260$	138.882	+	80.1837i	0.534163	+	0.308399i
$261$		0			0
$262$	57.1884	+	99.0533i	0.218276	+	0.378066i
$263$	160.047	−	439.726i	0.608545	−	1.67196i	−0.124863	−	0.992174i	$-0.539849\pi$
$263$	160.047	−	439.726i	0.608545	−	1.67196i	0.733408	−	0.679789i	$-0.237929\pi$
$264$		0			0
$265$	348.945	+	292.799i	1.31677	+	1.10490i
$266$	−18.9110	−	51.9576i	−0.0710940	−	0.195329i
$267$		0			0
$268$	−44.7298	−	253.675i	−0.166902	−	0.946549i
$269$		−	317.049i		−	1.17862i	−0.807907	−	0.589310i	$-0.799399\pi$
$269$		−	317.049i		−	1.17862i	0.807907	−	0.589310i	$-0.200601\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	−71.6277	+	26.0704i	−0.261415	+	0.0951473i
$275$	30.0198	−	35.7762i	0.109163	−	0.130095i
$276$		0			0
$277$	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
$279$		0			0
$280$	218.970	−	379.267i	0.782035	−	1.35452i
$281$	52.4463	+	62.5031i	0.186642	+	0.222431i	0.851249	−	0.524762i	$-0.175846\pi$
$281$	52.4463	+	62.5031i	0.186642	+	0.222431i	−0.664607	+	0.747193i	$0.731401\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	−117.322	+	98.4445i	−0.410215	+	0.344211i
$287$	113.534	+	65.5489i	0.395589	+	0.228393i
$288$		0			0
$289$	−139.508	−	241.636i	−0.482728	−	0.836110i
$290$	54.2049	−	148.927i	0.186913	−	0.513540i
$291$		0			0
$292$	185.169	+	155.375i	0.634141	+	0.532107i
$293$	118.282	+	324.977i	0.403693	+	1.10914i	0.960448	+	0.278460i	$0.0898238\pi$
$293$	118.282	+	324.977i	0.403693	+	1.10914i	−0.556755	+	0.830676i	$0.687954\pi$
$294$		0			0
$295$	−63.8186	−	361.933i	−0.216334	−	1.22689i
$296$			136.357i			0.460665i
$297$		0			0
$298$	234.232			0.786012
$299$	−220.222	+	38.8311i	−0.736529	+	0.129870i
$300$		0			0
$301$	360.806	−	131.323i	1.19869	−	0.436287i
$302$	−95.6252	+	113.962i	−0.316640	+	0.377356i
$303$		0			0
$304$	6.97859	+	2.54000i	0.0229559	+	0.00835526i
$305$	−363.957	+	210.131i	−1.19330	+	0.688954i
$306$		0			0
$307$	−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
$309$		0			0
$310$	24.0064	−	136.147i	0.0774399	−	0.439184i
$311$	−442.280	−	77.9859i	−1.42212	−	0.250759i	−0.590921	−	0.806730i	$-0.701235\pi$
$311$	−442.280	−	77.9859i	−1.42212	−	0.250759i	−0.831202	+	0.555971i	$0.812347\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	27.0360	+	46.8278i	0.0855570	+	0.148189i
$317$	74.6402	−	205.072i	0.235458	−	0.646916i	−0.764539	−	0.644577i	$-0.777033\pi$
$317$	74.6402	−	205.072i	0.235458	−	0.646916i	0.999997	−	0.00233841i	$-0.000744341\pi$
$318$		0			0
$319$	−228.146	−	191.437i	−0.715191	−	0.600117i
$320$	−58.0083	−	159.376i	−0.181276	−	0.498051i
$321$		0			0
$322$	42.2781	+	239.771i	0.131299	+	0.744631i
$323$		−	14.2846i		−	0.0442249i
$324$		0			0
$325$	−44.6700			−0.137446
$326$	−45.5694	+	8.03512i	−0.139784	+	0.0246476i
$327$		0			0
$328$	90.3137	−	32.8715i	0.275347	−	0.100218i
$329$	83.9620	−	100.062i	0.255204	−	0.304140i
$330$		0			0
$331$	−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
$333$		0			0
$334$	−96.3325	+	166.853i	−0.288421	+	0.499559i
$335$	336.061	+	400.502i	1.00317	+	1.19553i
$336$		0			0
$337$	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
$339$		0			0
$340$	34.5551	−	28.9952i	0.101633	−	0.0852799i
$341$	−224.988	−	129.897i	−0.659789	−	0.380929i
$342$		0			0
$343$	68.3305	+	118.352i	0.199214	+	0.345049i
$344$	96.2747	−	264.512i	0.279868	−	0.768932i
$345$		0			0
$346$	−9.68515	−	8.12680i	−0.0279918	−	0.0234879i
$347$	80.7717	+	221.918i	0.232771	+	0.639534i	0.999998	−	0.00184170i	$-0.000586231\pi$
$347$	80.7717	+	221.918i	0.232771	+	0.639534i	−0.767227	+	0.641376i	$0.778364\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	−385.187			−1.09428
$353$	−25.2020	+	4.44379i	−0.0713937	+	0.0125886i	−0.209231	−	0.977866i	$-0.567096\pi$
$353$	−25.2020	+	4.44379i	−0.0713937	+	0.0125886i	0.137837	+	0.990455i	$0.455985\pi$
$354$		0			0
$355$	−615.423	+	223.996i	−1.73359	+	0.630974i
$356$	117.669	−	140.232i	0.330530	−	0.393911i
$357$		0			0
$358$	−308.279	−	112.204i	−0.861114	−	0.313420i
$359$	−16.7796	+	9.68773i	−0.0467399	+	0.0269853i	−0.523188	−	0.852217i	$-0.675257\pi$
$359$	−16.7796	+	9.68773i	−0.0467399	+	0.0269853i	0.476448	+	0.879203i	$0.341924\pi$
$360$		0			0
$361$	170.280	−	294.934i	0.471690	−	0.816992i
$362$	−81.1916	−	96.7604i	−0.224286	−	0.267294i
$363$		0			0
$364$	−54.4967	+	309.066i	−0.149716	+	0.849083i
$365$	−483.159	−	85.1939i	−1.32372	−	0.233408i
$366$		0			0
$367$	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
$369$		0			0
$370$	−55.1707	−	95.5584i	−0.149110	−	0.258266i
$371$	−304.886	+	837.669i	−0.821796	+	2.25787i
$372$		0			0
$373$	−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
$375$		0			0
$376$	−16.6287	−	94.3061i	−0.0442253	−	0.250814i
$377$			284.862i			0.755603i
$378$		0			0
$379$	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
$381$		0			0
$382$	118.509	−	43.1337i	0.310233	−	0.112916i
$383$	−11.0730	+	13.1963i	−0.0289112	+	0.0344550i	−0.780306	−	0.625398i	$-0.784937\pi$
$383$	−11.0730	+	13.1963i	−0.0289112	+	0.0344550i	0.751395	+	0.659853i	$0.229381\pi$
$384$		0			0
$385$	625.797	+	227.772i	1.62545	+	0.591615i
$386$	201.193	−	116.159i	0.521226	−	0.300930i
$387$		0			0
$388$	105.827	−	183.298i	0.272750	−	0.472417i
$389$	−203.618	−	242.662i	−0.523439	−	0.623810i	0.437952	−	0.898999i	$-0.355704\pi$
$389$	−203.618	−	242.662i	−0.523439	−	0.623810i	−0.961390	+	0.275189i	$0.911260\pi$
$390$		0			0
$391$	−10.9225	+	61.9446i	−0.0279348	+	0.158426i
$392$	471.340	+	83.1100i	1.20240	+	0.212015i
$393$		0			0
$394$	260.321	−	218.435i	0.660713	−	0.554404i
$395$	−95.0446	−	54.8740i	−0.240619	−	0.138922i
$396$		0			0
$397$	−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
$399$		0			0
$400$	−5.00408	−	4.19892i	−0.0125102	−	0.0104973i
$401$	−33.3356	−	91.5887i	−0.0831311	−	0.228401i	0.891162	−	0.453685i	$-0.149891\pi$
$401$	−33.3356	−	91.5887i	−0.0831311	−	0.228401i	−0.974293	+	0.225285i	$0.927669\pi$
$402$		0			0
$403$	43.1494	+	244.712i	0.107070	+	0.607227i
$404$			12.6686i			0.0313578i
$405$		0			0
$406$	310.149			0.763914
$407$	−204.203	+	36.0065i	−0.501727	+	0.0884680i
$408$		0			0
$409$	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
$411$		0			0
$412$	180.170	+	65.5764i	0.437305	+	0.159166i
$413$	622.862	−	359.609i	1.50814	−	0.870725i
$414$		0			0
$415$	−85.0569	+	147.323i	−0.204956	+	0.354995i
$416$	236.818	+	282.229i	0.569275	+	0.678435i
$417$		0			0
$418$	10.7038	−	60.7045i	0.0256073	−	0.145226i
$419$	−115.552	−	20.3750i	−0.275781	−	0.0486277i	0.0340470	−	0.999420i	$-0.489160\pi$
$419$	−115.552	−	20.3750i	−0.275781	−	0.0486277i	−0.309828	+	0.950793i	$0.600272\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	326.760	+	565.966i	0.770661	+	1.33482i
$425$	−4.29744	+	11.8071i	−0.0101116	+	0.0277814i
$426$		0			0
$427$	−630.025	−	528.654i	−1.47547	−	1.23806i
$428$	−143.441	−	394.102i	−0.335143	−	0.920799i
$429$		0			0
$430$	39.5541	+	224.323i	0.0919864	+	0.521681i
$431$		−	263.580i		−	0.611555i	−0.952103	−	0.305777i	$-0.901084\pi$
$431$		−	263.580i		−	0.611555i	0.952103	−	0.305777i	$-0.0989163\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	46.3025	−	16.8527i	0.106198	−	0.0386531i
$437$	57.8526	−	68.9461i	0.132386	−	0.157771i
$438$		0			0
$439$	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
$441$		0			0
$442$	20.6021	−	35.6839i	0.0466111	−	0.0807328i
$443$	390.071	+	464.868i	0.880520	+	1.04936i	0.998412	+	0.0563369i	$0.0179421\pi$
$443$	390.071	+	464.868i	0.880520	+	1.04936i	−0.117891	+	0.993026i	$0.537613\pi$
$444$		0			0
$445$	−64.5191	+	365.906i	−0.144987	+	0.822260i
$446$	−226.648	−	39.9642i	−0.508180	−	0.0896058i
$447$		0			0
$448$	254.259	−	213.348i	0.567542	−	0.476224i
$449$	−347.745	−	200.771i	−0.774488	−	0.447151i	0.0599853	−	0.998199i	$-0.480895\pi$
$449$	−347.745	−	200.771i	−0.774488	−	0.447151i	−0.834473	+	0.551048i	$0.814228\pi$
$450$		0			0
$451$	73.0755	+	126.570i	0.162030	+	0.280644i
$452$	−16.3423	+	44.9002i	−0.0361556	+	0.0993368i
$453$		0			0
$454$	−4.58180	−	3.84458i	−0.0100921	−	0.00846825i
$455$	−217.859	−	598.563i	−0.478811	−	1.31552i
$456$		0			0
$457$	−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
$459$		0			0
$460$	284.213			0.617855
$461$	773.480	−	136.385i	1.67783	−	0.295847i	0.747963	−	0.663740i	$-0.231032\pi$
$461$	773.480	−	136.385i	1.67783	−	0.295847i	0.929868	+	0.367893i	$0.119921\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	153.344	+	55.8128i	0.329065	+	0.119770i
$467$	88.2727	−	50.9643i	0.189021	−	0.109131i	−0.402503	−	0.915419i	$-0.631860\pi$
$467$	88.2727	−	50.9643i	0.189021	−	0.109131i	0.591524	+	0.806287i	$0.298526\pi$
$468$		0			0
$469$	−511.569	+	886.063i	−1.09077	+	1.88926i
$470$	49.8101	+	59.3613i	0.105979	+	0.126301i
$471$		0			0
$472$	91.5597	−	519.261i	0.193982	−	1.10013i
$473$	421.547	+	74.3300i	0.891219	+	0.157146i
$474$		0			0
$475$	13.7726	−	11.5566i	0.0289949	−	0.0243296i
$476$	76.4491	+	44.1379i	0.160607	+	0.0927267i
$477$		0			0
$478$	−85.7219	−	148.475i	−0.179334	−	0.310616i
$479$	−43.2210	+	118.749i	−0.0902318	+	0.247910i	−0.976597	−	0.215077i	$-0.931000\pi$
$479$	−43.2210	+	118.749i	−0.0902318	+	0.247910i	0.886365	+	0.462986i	$0.153222\pi$
$480$		0			0
$481$	151.929	+	127.483i	0.315860	+	0.265038i
$482$	−120.874	−	332.099i	−0.250776	−	0.689003i
$483$		0			0
$484$	−7.79280	−	44.1952i	−0.0161008	−	0.0913123i
$485$			429.586i			0.885745i
$486$		0			0
$487$	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
$489$		0			0
$490$	−363.940	+	132.463i	−0.742735	+	0.270334i
$491$	−203.177	+	242.137i	−0.413803	+	0.493151i	−0.932177	−	0.362003i	$-0.882093\pi$
$491$	−203.177	+	242.137i	−0.413803	+	0.493151i	0.518374	+	0.855154i	$0.326537\pi$
$492$		0			0
$493$	75.2944	+	27.4049i	0.152727	+	0.0555881i
$494$	−51.0594	+	29.4792i	−0.103359	+	0.0596744i
$495$		0			0
$496$	−18.1689	+	31.4695i	−0.0366309	+	0.0634466i
$497$	−823.833	−	981.806i	−1.65761	−	1.97547i
$498$		0			0
$499$	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
$501$		0			0
$502$	−110.983	+	93.1256i	−0.221081	+	0.185509i
$503$	391.041	+	225.768i	0.777418	+	0.448843i	0.835515	−	0.549468i	$-0.185170\pi$
$503$	391.041	+	225.768i	0.777418	+	0.448843i	−0.0580963	+	0.998311i	$0.518503\pi$
$504$		0			0
$505$	−12.8565	−	22.2680i	−0.0254583	−	0.0440951i
$506$	−92.8333	+	255.057i	−0.183465	+	0.504066i
$507$		0			0
$508$	−317.375	−	266.309i	−0.624754	−	0.524231i
$509$	170.911	+	469.573i	0.335778	+	0.922541i	0.986578	+	0.163292i	$0.0522113\pi$
$509$	170.911	+	469.573i	0.335778	+	0.922541i	−0.650800	+	0.759249i	$0.725566\pi$
$510$		0			0
$511$	−166.722	−	945.527i	−0.326266	−	1.85035i
$512$			104.621i			0.204338i
$513$		0			0
$514$	−530.596			−1.03229
$515$	−383.240	+	67.5756i	−0.744156	+	0.131215i
$516$		0			0
$517$	136.838	−	49.8051i	0.264678	−	0.0963348i
$518$	138.800	−	165.415i	0.267954	−	0.319335i
$519$		0			0
$520$	−438.816	−	159.716i	−0.843877	−	0.307146i
$521$	595.632	−	343.888i	1.14325	−	0.660054i	0.196015	−	0.980601i	$-0.437200\pi$
$521$	595.632	−	343.888i	1.14325	−	0.660054i	0.947233	+	0.320546i	$0.103867\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	−94.3376	+	535.015i	−0.179349	+	1.01714i
$527$	68.8332	+	12.1372i	0.130613	+	0.0230306i
$528$		0			0
$529$	101.644	−	85.2896i	0.192144	−	0.161228i
$530$	−457.985	−	264.418i	−0.864123	−	0.498902i
$531$		0			0
$532$	−63.1561	−	109.390i	−0.118715	−	0.205620i
$533$	47.8111	−	131.360i	0.0897020	−	0.246454i
$534$		0			0
$535$	652.079	+	547.160i	1.21884	+	1.02273i
$536$	256.542	+	704.844i	0.478623	+	1.31501i
$537$		0			0
$538$	63.9168	+	362.490i	0.118804	+	0.673773i
$539$			727.808i			1.35029i
$540$		0			0
$541$	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
$543$		0			0
$544$	97.3813	−	35.4439i	0.179010	−	0.0651542i
$545$	−64.2851	+	76.6120i	−0.117954	+	0.140572i
$546$		0			0
$547$	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
$549$		0			0
$550$	−27.1099	+	46.9557i	−0.0492907	+	0.0853741i
$551$	−73.6967	−	87.8283i	−0.133751	−	0.159398i
$552$		0			0
$553$	37.2950	−	211.511i	0.0674412	−	0.382478i
$554$	−131.832	−	23.2456i	−0.237964	−	0.0419595i
$555$		0			0
$556$	−254.570	+	213.610i	−0.457861	+	0.384191i
$557$	−575.120	−	332.045i	−1.03253	−	0.596132i	−0.114822	−	0.993386i	$-0.536630\pi$
$557$	−575.120	−	332.045i	−1.03253	−	0.596132i	−0.917709	+	0.397254i	$0.869963\pi$
$558$		0			0
$559$	−204.710	−	354.569i	−0.366208	−	0.634291i
$560$	31.8589	−	87.5315i	0.0568908	−	0.156306i
$561$		0			0
$562$	−72.5637	−	60.8882i	−0.129117	−	0.108342i
$563$	118.905	+	326.689i	0.211199	+	0.580264i	0.999381	−	0.0351778i	$-0.0111997\pi$
$563$	118.905	+	326.689i	0.211199	+	0.580264i	−0.788182	+	0.615442i	$0.788978\pi$
$564$		0			0
$565$	−16.8406	−	95.5076i	−0.0298063	−	0.169040i
$566$		−	484.283i		−	0.855623i
$567$		0			0
$568$	−939.603			−1.65423
$569$	385.078	−	67.8997i	0.676763	−	0.119332i	0.175306	−	0.984514i	$-0.443909\pi$
$569$	385.078	−	67.8997i	0.676763	−	0.119332i	0.501457	+	0.865182i	$0.332797\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−143.021	−	52.0553i	−0.249165	−	0.0906887i
$575$	−68.5606	+	39.5835i	−0.119236	+	0.0688408i
$576$		0			0
$577$	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
$579$		0			0
$580$	62.8694	−	356.550i	0.108396	−	0.614742i
$581$	−327.850	−	57.8088i	−0.564285	−	0.0994987i
$582$		0			0
$583$	−761.285	+	638.794i	−1.30581	+	1.09570i
$584$	−609.573	−	351.937i	−1.04379	−	0.602632i
$585$		0			0
$586$	−200.750	−	347.709i	−0.342576	−	0.593359i
$587$	254.654	−	699.655i	0.433822	−	1.19192i	−0.509626	−	0.860396i	$-0.670216\pi$
$587$	254.654	−	699.655i	0.433822	−	1.19192i	0.943448	−	0.331520i	$-0.107561\pi$
$588$		0			0
$589$	−76.6133	−	64.2862i	−0.130073	−	0.109145i
$590$	145.931	+	400.942i	0.247340	+	0.679562i
$591$		0			0
$592$	5.03630	+	28.5623i	0.00850726	+	0.0482471i
$593$			625.722i			1.05518i	0.849499	+	0.527591i	$0.176904\pi$
$593$			625.722i			1.05518i	−0.849499	+	0.527591i	$0.823096\pi$
$594$		0			0
$595$	−179.170			−0.301126
$596$	526.963	−	92.9177i	0.884165	−	0.155902i
$597$		0			0
$598$	243.957	−	88.7932i	0.407955	−	0.148484i
$599$	368.344	−	438.975i	0.614932	−	0.732847i	−0.365258	−	0.930906i	$-0.619019\pi$
$599$	368.344	−	438.975i	0.614932	−	0.732847i	0.980190	+	0.198059i	$0.0634638\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−169.925	+	294.319i	−0.281333	+	0.487283i
$605$	58.5483	+	69.7752i	0.0967741	+	0.115331i
$606$		0			0
$607$	−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
$609$		0			0
$610$	373.759	−	313.621i	0.612720	−	0.514133i
$611$	−120.623	−	69.6414i	−0.197418	−	0.113979i
$612$		0			0
$613$	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
$615$		0			0
$616$	731.912	+	614.147i	1.18817	+	0.996991i
$617$	−144.247	−	396.317i	−0.233788	−	0.642328i	0.766212	−	0.642588i	$-0.222139\pi$
$617$	−144.247	−	396.317i	−0.233788	−	0.642328i	−1.00000		0.000260046i	$0.999917\pi$
$618$		0			0
$619$	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
$621$		0			0
$622$	521.392			0.838250
$623$	−716.066	+	126.262i	−1.14938	+	0.202667i
$624$		0			0
$625$	665.870	−	242.357i	1.06539	−	0.387771i
$626$	−8.08756	+	9.63837i	−0.0129194	+	0.0153968i
$627$		0			0
$628$	346.285	+	126.037i	0.551409	+	0.200696i
$629$	48.3124	−	27.8932i	0.0768083	−	0.0443453i
$630$		0			0
$631$	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
$633$		0			0
$634$	−43.9956	+	249.512i	−0.0693937	+	0.393551i
$635$	828.122	+	146.020i	1.30413	+	0.229953i
$636$		0			0
$637$	533.269	−	447.466i	0.837157	−	0.702458i
$638$	299.439	+	172.881i	0.469340	+	0.270973i
$639$		0			0
$640$	−254.659	−	441.082i	−0.397904	−	0.689191i
$641$	56.5257	−	155.303i	0.0881837	−	0.242283i	−0.887760	−	0.460308i	$-0.847739\pi$
$641$	56.5257	−	155.303i	0.0881837	−	0.242283i	0.975943	+	0.218025i	$0.0699614\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	2.87977	+	16.3320i	0.00445785	+	0.0252817i
$647$			222.504i			0.343900i	0.985106	+	0.171950i	$0.0550068\pi$
$647$			222.504i			0.343900i	−0.985106	+	0.171950i	$0.944993\pi$
$648$		0			0
$649$	801.803			1.23544
$650$	51.0723	−	9.00542i	0.0785728	−	0.0138545i
$651$		0			0
$652$	−99.3323	+	36.1540i	−0.152350	+	0.0554509i
$653$	299.851	−	357.348i	0.459190	−	0.547241i	−0.485916	−	0.874006i	$-0.661514\pi$
$653$	299.851	−	357.348i	0.459190	−	0.547241i	0.945106	+	0.326764i	$0.105958\pi$
$654$		0			0
$655$	−498.345	−	181.383i	−0.760833	−	0.276920i
$656$	17.7037	−	10.2212i	0.0269873	−	0.0155811i
$657$		0			0
$658$	−75.8234	+	131.330i	−0.115233	+	0.199590i
$659$	133.876	+	159.547i	0.203150	+	0.242104i	0.857994	−	0.513659i	$-0.171710\pi$
$659$	133.876	+	159.547i	0.203150	+	0.242104i	−0.654845	+	0.755764i	$0.727266\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	−186.961	+	156.879i	−0.281567	+	0.236263i
$665$	222.024	+	128.186i	0.333871	+	0.192760i
$666$		0			0
$667$	252.425	+	437.214i	0.378449	+	0.655493i
$668$	−150.535	+	413.591i	−0.225352	+	0.619149i
$669$		0			0
$670$	−464.967	−	390.154i	−0.693981	−	0.582319i
$671$	−313.590	−	861.581i	−0.467347	−	1.28403i
$672$		0			0
$673$	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
$675$		0			0
$676$	−113.573			−0.168007
$677$	140.866	−	24.8384i	0.208073	−	0.0366890i	−0.0686398	−	0.997642i	$-0.521866\pi$
$677$	140.866	−	24.8384i	0.208073	−	0.0366890i	0.276713	+	0.960953i	$0.410755\pi$
$678$		0			0
$679$	−789.987	+	287.532i	−1.16346	+	0.423463i
$680$	−84.4318	+	100.622i	−0.124164	+	0.147973i
$681$		0			0
$682$	283.421	+	103.157i	0.415574	+	0.151257i
$683$	−784.050	+	452.671i	−1.14795	+	0.662769i	−0.948387	−	0.317116i	$-0.897286\pi$
$683$	−784.050	+	452.671i	−1.14795	+	0.662769i	−0.199563	+	0.979885i	$0.563952\pi$
$684$		0			0
$685$	176.714	−	306.078i	0.257977	−	0.446830i
$686$	−101.984	−	121.539i	−0.148664	−	0.177171i
$687$		0			0
$688$	10.3967	−	58.9625i	0.0151115	−	0.0857013i
$689$	936.096	+	165.059i	1.35863	+	0.239563i
$690$		0			0
$691$	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
$693$		0			0
$694$	−137.087	−	237.441i	−0.197531	−	0.342134i
$695$	230.690	−	633.817i	0.331929	−	0.911967i
$696$		0			0
$697$	−30.1213	−	25.2748i	−0.0432156	−	0.0362622i
$698$	−95.2117	−	261.592i	−0.136406	−	0.374773i
$699$		0			0
$700$	19.2932	+	109.417i	0.0275617	+	0.156310i
$701$		−	905.026i		−	1.29105i	−0.763739	−	0.645525i	$-0.776639\pi$
$701$		−	905.026i		−	1.29105i	0.763739	−	0.645525i	$-0.223361\pi$
$702$		0			0
$703$	−79.8237			−0.113547
$704$	364.401	−	64.2538i	0.517616	−	0.0912696i
$705$		0			0
$706$	27.9182	−	10.1614i	0.0395442	−	0.0143929i
$707$	32.3447	−	38.5469i	0.0457492	−	0.0545217i
$708$		0			0
$709$	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
$711$		0			0
$712$	−266.529	+	461.642i	−0.374338	+	0.648373i
$713$	283.074	+	337.355i	0.397019	+	0.473148i
$714$		0			0
$715$	123.311	−	699.329i	0.172462	−	0.978083i
$716$	−738.060	−	130.140i	−1.03081	−	0.181760i
$717$		0			0
$718$	17.2315	−	14.4590i	0.0239994	−	0.0201379i
$719$	389.328	+	224.778i	0.541485	+	0.312626i	0.745680	−	0.666304i	$-0.232125\pi$
$719$	389.328	+	224.778i	0.541485	+	0.312626i	−0.204196	+	0.978930i	$0.565458\pi$
$720$		0			0
$721$	−380.779	−	659.529i	−0.528127	−	0.914742i
$722$	−135.227	+	371.534i	−0.187295	+	0.514589i
$723$		0			0
$724$	−221.045	−	185.479i	−0.305310	−	0.256186i
$725$	34.4922	+	94.7665i	0.0475754	+	0.130712i
$726$		0			0
$727$	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
$729$		0			0
$730$	569.582			0.780250
$731$	−113.413	+	19.9978i	−0.155148	+	0.0273568i
$732$		0			0
$733$	−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
$735$		0			0
$736$	613.567	+	223.320i	0.833650	+	0.303424i
$737$	−987.805	+	570.310i	−1.34031	+	0.773826i
$738$		0			0
$739$	−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
$741$		0			0
$742$	179.711	−	1019.19i	0.242198	−	1.37357i
$743$	36.2725	+	6.39582i	0.0488190	+	0.00860811i	0.198004	−	0.980201i	$-0.436554\pi$
$743$	36.2725	+	6.39582i	0.0488190	+	0.00860811i	−0.149185	+	0.988809i	$0.547665\pi$
$744$		0			0
$745$	−831.967	+	698.103i	−1.11673	+	0.937051i
$746$	179.793	+	103.803i	0.241009	+	0.139146i
$747$		0			0
$748$	49.2061	+	85.2274i	0.0657835	+	0.113940i
$749$	−569.747	+	1565.37i	−0.760677	+	2.08994i
$750$		0			0
$751$	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
$753$		0			0
$754$	−57.4279	−	325.690i	−0.0761644	−	0.431950i
$755$		−	689.781i		−	0.913617i
$756$		0			0
$757$	−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
$759$		0			0
$760$	176.615	−	64.2827i	0.232388	−	0.0845825i
$761$	−935.204	+	1114.53i	−1.22891	+	1.46456i	−0.389541	+	0.921009i	$0.627366\pi$
$761$	−935.204	+	1114.53i	−1.22891	+	1.46456i	−0.839374	+	0.543555i	$0.817078\pi$
$762$		0			0
$763$	−183.913	−	66.9389i	−0.241039	−	0.0877312i
$764$	249.505	−	144.052i	0.326577	−	0.188549i
$765$		0			0
$766$	9.99966	−	17.3199i	0.0130544	−	0.0226109i
$767$	−492.959	−	587.486i	−0.642711	−	0.765953i
$768$		0			0
$769$	−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
$771$		0			0
$772$	406.555	−	341.140i	0.526626	−	0.441891i
$773$	547.928	+	316.347i	0.708834	+	0.409245i	0.810629	−	0.585560i	$-0.199125\pi$
$773$	547.928	+	316.347i	0.708834	+	0.409245i	−0.101795	+	0.994805i	$0.532459\pi$
$774$		0			0
$775$	43.9854	+	76.1850i	0.0567554	+	0.0983032i
$776$	−210.794	+	579.152i	−0.271642	+	0.746330i
$777$		0			0
$778$	281.722	+	236.392i	0.362110	+	0.303846i
$779$	19.2431	+	52.8699i	0.0247023	+	0.0678690i
$780$		0			0
$781$	−248.112	−	1407.12i	−0.317686	−	1.80168i
$782$		−	73.0247i		−	0.0933820i
$783$		0			0
$784$	101.800			0.129847
$785$	−736.585	+	129.880i	−0.938325	+	0.165452i
$786$		0			0
$787$	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
$789$		0			0
$790$	119.729	+	43.5779i	0.151556	+	0.0551619i
$791$	164.362	−	94.8944i	0.207790	−	0.119968i
$792$		0			0
$793$	−438.486	+	759.481i	−0.552946	+	0.957731i
$794$	200.056	+	238.418i	0.251960	+	0.300275i
$795$		0			0
$796$	−37.9072	+	214.982i	−0.0476221	+	0.270078i
$797$	−1233.67	−	217.529i	−1.54789	−	0.272934i	−0.666564	−	0.745448i	$-0.732236\pi$
$797$	−1233.67	−	217.529i	−1.54789	−	0.272934i	−0.881323	+	0.472514i	$0.843347\pi$
$798$		0			0
$799$	−30.0119	+	25.1830i	−0.0375618	+	0.0315181i
$800$	112.957	+	65.2156i	0.141196	+	0.0815196i
$801$		0			0
$802$	56.5776	+	97.9952i	0.0705456	+	0.122189i
$803$	366.084	−	1005.81i	0.455895	−	1.25256i
$804$		0			0
$805$	−864.781	−	725.637i	−1.07426	−	0.901413i
$806$	−98.6675	−	271.087i	−0.122416	−	0.336336i
$807$		0			0
$808$	−6.40587	−	36.3295i	−0.00792806	−	0.0449622i
$809$			1021.88i			1.26313i	0.775321	+	0.631567i	$0.217588\pi$
$809$			1021.88i			1.26313i	−0.775321	+	0.631567i	$0.782412\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	226.211	−	82.3342i	0.277901	−	0.101148i
$815$	137.910	−	164.355i	0.169215	−	0.201662i
$816$		0			0
$817$	154.846	+	56.3595i	0.189531	+	0.0689835i
$818$	−407.542	+	235.294i	−0.498217	+	0.287646i
$819$		0			0
$820$	−88.8346	+	153.866i	−0.108335	+	0.187641i
$821$	6.23245	+	7.42755i	0.00759129	+	0.00904695i	0.769827	−	0.638253i	$-0.220343\pi$
$821$	6.23245	+	7.42755i	0.00759129	+	0.00904695i	−0.762235	+	0.647300i	$0.775898\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	−639.636	+	536.719i	−0.774378	+	0.649780i
$827$	583.611	+	336.948i	0.705696	+	0.407434i	0.809465	−	0.587168i	$-0.199757\pi$
$827$	583.611	+	336.948i	0.705696	+	0.407434i	−0.103769	+	0.994601i	$0.533090\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	−271.118	−	227.495i	−0.325863	−	0.273431i
$833$	−66.9709	−	184.001i	−0.0803972	−	0.220890i
$834$		0			0
$835$	−155.124	−	879.753i	−0.185778	−	1.05360i
$836$		−	140.816i		−	0.168440i
$837$		0			0
$838$	136.221			0.162555
$839$	−629.012	+	110.912i	−0.749716	+	0.132195i	−0.535434	−	0.844577i	$-0.679852\pi$
$839$	−629.012	+	110.912i	−0.749716	+	0.132195i	−0.214282	+	0.976772i	$0.568741\pi$
$840$		0			0
$841$	−185.952	+	67.6809i	−0.221108	+	0.0804767i
$842$	389.047	−	463.648i	0.462051	−	0.550650i
$843$		0			0
$844$	−288.712	−	105.082i	−0.342075	−	0.124505i
$845$	199.631	−	115.257i	0.236250	−	0.136399i
$846$		0			0
$847$	−89.1253	+	154.370i	−0.105225	+	0.182254i
$848$	89.3493	+	106.482i	0.105365	+	0.125569i
$849$		0			0
$850$	2.53306	−	14.3657i	0.00298008	−	0.0169008i
$851$	346.151	+	61.0358i	0.406758	+	0.0717225i
$852$		0			0
$853$	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
$855$		0			0
$856$	610.623	+	1057.63i	0.713345	+	1.23555i
$857$	−368.296	+	1011.88i	−0.429750	+	1.18073i	0.516215	+	0.856459i	$0.327341\pi$
$857$	−368.296	+	1011.88i	−0.429750	+	1.18073i	−0.945965	+	0.324269i	$0.894882\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	53.1375	+	301.358i	0.0616444	+	0.349603i
$863$		−	1599.17i		−	1.85304i	−0.376244	−	0.926520i	$-0.622785\pi$
$863$		−	1599.17i		−	1.85304i	0.376244	−	0.926520i	$-0.377215\pi$
$864$		0			0
$865$	58.6217			0.0677708
$866$	802.629	−	141.525i	0.926823	−	0.163424i
$867$		0			0
$868$	580.776	−	211.385i	0.669097	−	0.243531i
$869$	153.906	−	183.418i	0.177107	−	0.211067i
$870$		0			0
$871$	1025.19	+	373.137i	1.17702	+	0.428400i
$872$	−124.260	+	71.7413i	−0.142500	+	0.0822722i
$873$		0			0
$874$	−52.2449	+	90.4908i	−0.0597767	+	0.103536i
$875$	766.304	+	913.245i	0.875776	+	1.04371i
$876$		0			0
$877$	−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
$879$		0			0
$880$	79.5498	−	66.7502i	0.0903975	−	0.0758525i
$881$	1046.81	+	604.374i	1.18820	+	0.686009i	0.957898	−	0.287109i	$-0.0926943\pi$
$881$	1046.81	+	604.374i	1.18820	+	0.686009i	0.230305	+	0.973119i	$0.426028\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−539.694	−	452.857i	−0.609136	−	0.511126i
$887$	−34.7360	−	95.4364i	−0.0391612	−	0.107595i	0.918571	−	0.395256i	$-0.129344\pi$
$887$	−34.7360	−	95.4364i	−0.0391612	−	0.107595i	−0.957732	+	0.287662i	$0.907122\pi$
$888$		0			0
$889$	285.757	+	1620.61i	0.321436	+	1.82296i
$890$		−	431.356i		−	0.484670i
$891$		0			0
$892$	−525.755			−0.589412
$893$	55.2071	−	9.73450i	0.0618220	−	0.0109009i
$894$		0			0
$895$	1429.39	−	520.255i	1.59708	−	0.581290i
$896$	640.678	−	763.531i	0.715043	−	0.852155i
$897$		0			0
$898$	438.061	+	159.441i	0.487818	+	0.177551i
$899$	485.835	−	280.497i	0.540417	−	0.312010i
$900$		0			0
$901$	133.684	−	231.548i	0.148373	−	0.256990i
$902$	−109.065	−	129.979i	−0.120915	−	0.144101i
$903$		0			0
$904$	24.1609	−	137.023i	0.0267267	−	0.151575i
$905$	576.769	+	101.700i	0.637313	+	0.112376i
$906$		0			0
$907$	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
$909$		0			0
$910$	369.753	+	640.431i	0.406322	+	0.703771i
$911$	−106.953	+	293.850i	−0.117401	+	0.322558i	−0.984450	−	0.175666i	$-0.943792\pi$
$911$	−106.953	+	293.850i	−0.117401	+	0.322558i	0.867048	+	0.498224i	$0.166014\pi$
$912$		0			0
$913$	−284.305	−	238.560i	−0.311396	−	0.261292i
$914$	58.4144	+	160.492i	0.0639107	+	0.175593i
$915$		0			0
$916$	162.732	+	922.898i	0.177655	+	1.00753i
$917$		−	1037.84i		−	1.13177i
$918$		0			0
$919$	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
$921$		0			0
$922$	−856.844	+	311.866i	−0.929332	+	0.338249i
$923$	−878.459	+	1046.91i	−0.951743	+	1.13424i
$924$		0			0
$925$	65.9791	+	24.0144i	0.0713287	+	0.0259615i
$926$	−360.397	+	208.075i	−0.389197	+	0.224703i
$927$		0			0
$928$	415.883	−	720.330i	0.448149	−	0.776218i
$929$	−854.746	−	1018.65i	−0.920071	−	1.09650i	−0.995056	−	0.0993136i	$-0.968335\pi$
$929$	−854.746	−	1018.65i	−0.920071	−	1.09650i	0.0749849	−	0.997185i	$-0.476109\pi$
$930$		0			0
$931$	−48.6528	+	275.924i	−0.0522587	+	0.296374i
$932$	367.127	+	64.7343i	0.393913	+	0.0694574i
$933$		0			0
$934$	−90.6501	+	76.0644i	−0.0970557	+	0.0814394i
$935$	−172.983	−	99.8717i	−0.185008	−	0.106815i
$936$		0			0
$937$	−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
$939$		0			0
$940$	135.608	+	113.789i	0.144264	+	0.121052i
$941$	−265.840	−	730.391i	−0.282508	−	0.776186i	−0.997062	−	0.0766044i	$-0.975592\pi$
$941$	−265.840	−	730.391i	−0.282508	−	0.776186i	0.714553	−	0.699581i	$-0.246630\pi$
$942$		0			0
$943$	−43.0206	−	243.982i	−0.0456210	−	0.258729i
$944$		−	112.150i		−	0.118803i
$945$		0			0
$946$	−496.949			−0.525316
$947$	270.124	−	47.6301i	0.285242	−	0.0502958i	−0.0291967	−	0.999574i	$-0.509295\pi$
$947$	270.124	−	47.6301i	0.285242	−	0.0502958i	0.314438	+	0.949278i	$0.398184\pi$
$948$		0			0
$949$	−962.034	+	350.152i	−1.01373	+	0.368969i
$950$	−13.4167	+	15.9894i	−0.0141229	+	0.0168310i
$951$		0			0
$952$	−241.551	−	87.9173i	−0.253730	−	0.0923501i
$953$	−858.313	+	495.548i	−0.900644	+	0.519987i	−0.877409	−	0.479743i	$-0.840730\pi$
$953$	−858.313	+	495.548i	−0.900644	+	0.519987i	−0.0232347	+	0.999730i	$0.507397\pi$
$954$		0			0
$955$	−292.376	+	506.410i	−0.306153	+	0.530272i
$956$	−251.751	−	300.025i	−0.263338	−	0.313834i
$957$		0			0
$958$	25.4760	−	144.482i	0.0265929	−	0.150816i
$959$	681.141	+	120.104i	0.710262	+	0.125238i
$960$		0			0
$961$	−361.298	+	303.165i	−0.375961	+	0.315468i
$962$	−199.405	−	115.126i	−0.207281	−	0.119674i
$963$		0			0
$964$	−403.678	−	699.190i	−0.418753	−	0.725301i
$965$	−368.418	+	1012.22i	−0.381780	+	1.04893i
$966$		0			0
$967$	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
$969$		0			0
$970$	−86.6041	−	491.156i	−0.0892826	−	0.506347i
$971$			487.838i			0.502407i	0.967934	+	0.251204i	$0.0808264\pi$
$971$			487.838i			0.502407i	−0.967934	+	0.251204i	$0.919174\pi$
$972$		0			0
$973$	1319.96			1.35659
$974$	−519.080	+	91.5279i	−0.532937	+	0.0939711i
$975$		0			0
$976$	−120.511	+	43.8624i	−0.123474	+	0.0449410i
$977$	413.839	−	493.194i	0.423582	−	0.504805i	−0.511478	−	0.859297i	$-0.670902\pi$
$977$	413.839	−	493.194i	0.423582	−	0.504805i	0.935059	+	0.354492i	$0.115346\pi$
$978$		0			0
$979$	−761.718	−	277.243i	−0.778057	−	0.283190i
$980$	−766.227	+	442.382i	−0.781865	+	0.451410i
$981$		0			0
$982$	183.483	−	317.802i	0.186846	−	0.323627i
$983$	989.779	+	1179.57i	1.00690	+	1.19997i	0.979726	+	0.200341i	$0.0642051\pi$
$983$	989.779	+	1179.57i	1.00690	+	1.19997i	0.0271699	+	0.999631i	$0.491350\pi$
$984$		0			0
$985$	−273.610	+	1551.72i	−0.277777	+	1.57535i
$986$	−91.6108	−	16.1534i	−0.0929115	−	0.0163828i
$987$		0			0
$988$	−103.177	+	86.5756i	−0.104430	+	0.0876271i
$989$	−628.389	−	362.801i	−0.635378	−	0.366836i
$990$		0			0
$991$	−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
$993$		0			0
$994$	1139.84	+	956.439i	1.14672	+	0.962213i
$995$	−151.540	−	416.352i	−0.152301	−	0.418445i
$996$		0			0
$997$	−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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.3.f.a.71.2		30
3.2	odd	2		27.3.f.a.14.4	yes	30
9.2	odd	6		243.3.f.d.134.2		30
9.4	even	3		243.3.f.b.53.4		30
9.5	odd	6		243.3.f.c.53.2		30
9.7	even	3		243.3.f.a.134.4		30
12.11	even	2		432.3.bc.a.257.3		30
27.2	odd	18	inner	81.3.f.a.8.2		30
27.5	odd	18		729.3.b.a.728.12		30
27.7	even	9		243.3.f.d.107.2		30
27.11	odd	18		243.3.f.b.188.4		30
27.16	even	9		243.3.f.c.188.2		30
27.20	odd	18		243.3.f.a.107.4		30
27.22	even	9		729.3.b.a.728.19		30
27.25	even	9		27.3.f.a.2.4	✓	30
108.79	odd	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	27.25	even	9
27.3.f.a.14.4	yes	30	3.2	odd	2
81.3.f.a.8.2		30	27.2	odd	18	inner
81.3.f.a.71.2		30	1.1	even	1	trivial
243.3.f.a.107.4		30	27.20	odd	18
243.3.f.a.134.4		30	9.7	even	3
243.3.f.b.53.4		30	9.4	even	3
243.3.f.b.188.4		30	27.11	odd	18
243.3.f.c.53.2		30	9.5	odd	6
243.3.f.c.188.2		30	27.16	even	9
243.3.f.d.107.2		30	27.7	even	9
243.3.f.d.134.2		30	9.2	odd	6
432.3.bc.a.257.3		30	12.11	even	2
432.3.bc.a.353.3		30	108.79	odd	18
729.3.b.a.728.12		30	27.5	odd	18
729.3.b.a.728.19		30	27.22	even	9

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.14332 + 0.201599i) q^{2} +(-2.49222 + 0.907094i) q^{4} +(3.46013 - 4.12362i) q^{5} +(9.89907 + 3.60297i) q^{7} +(6.68824 - 3.86146i) q^{8} +(-3.12473 + 5.41219i) q^{10} +(7.54888 + 8.99640i) q^{11} +(1.95057 - 11.0622i) q^{13} +(-12.0442 - 2.12372i) q^{14} +(1.25834 - 1.05588i) q^{16} +(-2.73630 - 1.57980i) q^{17} +(2.26051 + 3.91532i) q^{19} +(-4.88289 + 13.4156i) q^{20} +(-10.4445 - 8.76396i) q^{22} +(-6.80880 - 18.7070i) q^{23} +(-0.690550 - 3.91630i) q^{25} +13.0409i q^{26} -27.9389 q^{28} +(-24.9744 + 4.40366i) q^{29} +(-20.7874 + 7.56598i) q^{31} +(-21.0826 + 25.1253i) q^{32} +(3.44696 + 1.25459i) q^{34} +(49.1093 - 28.3533i) q^{35} +(-8.82807 + 15.2907i) q^{37} +(-3.37382 - 4.02076i) q^{38} +(7.21898 - 40.9409i) q^{40} +(12.2557 + 2.16101i) q^{41} +(27.9211 - 23.4286i) q^{43} +(-26.9741 - 15.5735i) q^{44} +(11.5560 + 20.0156i) q^{46} +(4.24091 - 11.6518i) q^{47} +(47.4740 + 39.8354i) q^{49} +(1.57905 + 4.33839i) q^{50} +(5.17323 + 29.3388i) q^{52} +84.6210i q^{53} +63.2178 q^{55} +(80.1200 - 14.1273i) q^{56} +(27.6661 - 10.0696i) q^{58} +(43.8854 - 52.3006i) q^{59} +(-73.3637 - 26.7022i) q^{61} +(22.2414 - 12.8411i) q^{62} +(15.7537 - 27.2863i) q^{64} +(-38.8672 - 46.3201i) q^{65} +(-16.8654 + 95.6483i) q^{67} +(8.25249 + 1.45514i) q^{68} +(-50.4319 + 42.3174i) q^{70} +(-105.364 - 60.8322i) q^{71} +(-45.5705 - 78.9304i) q^{73} +(7.01076 - 19.2619i) q^{74} +(-9.18525 - 7.70734i) q^{76} +(42.3131 + 116.254i) q^{77} +(-3.54032 - 20.0781i) q^{79} -8.84240i q^{80} -14.4479 q^{82} +(-31.1219 + 5.48763i) q^{83} +(-15.9824 + 5.81713i) q^{85} +(-27.1997 + 32.4154i) q^{86} +(85.2279 + 31.0204i) q^{88} +(-59.7756 + 34.5114i) q^{89} +(59.1656 - 102.478i) q^{91} +(33.9381 + 40.4458i) q^{92} +(-2.49974 + 14.1767i) q^{94} +(23.9669 + 4.22602i) q^{95} +(-61.1335 + 51.2971i) q^{97} +(-62.3089 - 35.9741i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) \) 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

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