LMFDB - Embedded newform 216.3.j.a.125.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(125,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("216.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.j (of order $6$, degree $2$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.11
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.390748 + 1.96146i) q^{2} +(-3.69463 + 1.53287i) q^{4} +(3.47699 - 6.02232i) q^{5} +(2.29534 + 3.97565i) q^{7} +(-4.45034 - 6.64790i) q^{8} +O(q^{10})$	\(q+(0.390748 + 1.96146i) q^{2} +(-3.69463 + 1.53287i) q^{4} +(3.47699 - 6.02232i) q^{5} +(2.29534 + 3.97565i) q^{7} +(-4.45034 - 6.64790i) q^{8} +(13.1711 + 4.46675i) q^{10} +(7.77003 + 13.4581i) q^{11} +(19.3855 + 11.1922i) q^{13} +(-6.90117 + 6.05570i) q^{14} +(11.3006 - 11.3268i) q^{16} -9.17185i q^{17} +4.53461i q^{19} +(-3.61474 + 27.5800i) q^{20} +(-23.3614 + 20.4993i) q^{22} +(2.69533 + 1.55615i) q^{23} +(-11.6789 - 20.2284i) q^{25} +(-14.3782 + 42.3973i) q^{26} +(-14.5746 - 11.1701i) q^{28} +(-6.42846 - 11.1344i) q^{29} +(-2.17666 + 3.77008i) q^{31} +(26.6327 + 17.7397i) q^{32} +(17.9902 - 3.58388i) q^{34} +31.9235 q^{35} +23.0374i q^{37} +(-8.89444 + 1.77189i) q^{38} +(-55.5095 + 3.68669i) q^{40} +(-60.6979 - 35.0439i) q^{41} +(51.7345 - 29.8689i) q^{43} +(-49.3370 - 37.8122i) q^{44} +(-1.99913 + 5.89484i) q^{46} +(-32.1187 + 18.5438i) q^{47} +(13.9628 - 24.1843i) q^{49} +(35.1136 - 30.8118i) q^{50} +(-88.7787 - 11.6357i) q^{52} +24.3319 q^{53} +108.065 q^{55} +(16.2147 - 32.9522i) q^{56} +(19.3278 - 16.9599i) q^{58} +(20.7560 - 35.9504i) q^{59} +(-34.6245 + 19.9904i) q^{61} +(-8.24537 - 2.79626i) q^{62} +(-24.3890 + 59.1707i) q^{64} +(134.807 - 77.8306i) q^{65} +(-24.3421 - 14.0539i) q^{67} +(14.0593 + 33.8866i) q^{68} +(12.4741 + 62.6167i) q^{70} +59.8148i q^{71} -53.8883 q^{73} +(-45.1869 + 9.00183i) q^{74} +(-6.95098 - 16.7537i) q^{76} +(-35.6698 + 61.7819i) q^{77} +(-0.557280 - 0.965237i) q^{79} +(-28.9215 - 107.439i) q^{80} +(45.0196 - 132.750i) q^{82} +(-39.8750 - 69.0655i) q^{83} +(-55.2358 - 31.8904i) q^{85} +(78.8017 + 89.8037i) q^{86} +(54.8887 - 111.547i) q^{88} -10.6605i q^{89} +102.760i q^{91} +(-12.3436 - 1.61780i) q^{92} +(-48.9231 - 55.7536i) q^{94} +(27.3089 + 15.7668i) q^{95} +(-72.6276 - 125.795i) q^{97} +(52.8923 + 17.9375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.390748	+	1.96146i	0.195374	+	0.980729i
$2$	0.390748	+	1.96146i	0.195374	+	0.980729i
$3$		0			0
$3$		0			0
$4$	−3.69463	+	1.53287i	−0.923658	+	0.383218i
$5$	3.47699	−	6.02232i	0.695397	−	1.20446i	−0.274649	−	0.961544i	$-0.588562\pi$
$5$	3.47699	−	6.02232i	0.695397	−	1.20446i	0.970047	−	0.242919i	$-0.0781049\pi$
$6$		0			0
$7$	2.29534	+	3.97565i	0.327906	+	0.567951i	0.982096	−	0.188380i	$-0.0603236\pi$
$7$	2.29534	+	3.97565i	0.327906	+	0.567951i	−0.654190	+	0.756330i	$0.726990\pi$
$8$	−4.45034	−	6.64790i	−0.556292	−	0.830987i
$9$		0			0
$10$	13.1711	+	4.46675i	1.31711	+	0.446675i
$11$	7.77003	+	13.4581i	0.706367	+	1.22346i	0.966196	+	0.257809i	$0.0830004\pi$
$11$	7.77003	+	13.4581i	0.706367	+	1.22346i	−0.259829	+	0.965655i	$0.583666\pi$
$12$		0			0
$13$	19.3855	+	11.1922i	1.49120	+	0.860942i	0.999949	−	0.0100786i	$-0.00320818\pi$
$13$	19.3855	+	11.1922i	1.49120	+	0.860942i	0.491246	+	0.871021i	$0.336542\pi$
$14$	−6.90117	+	6.05570i	−0.492941	+	0.432550i
$15$		0			0
$16$	11.3006	−	11.3268i	0.706288	−	0.707925i
$17$		−	9.17185i		−	0.539520i	−0.962928	−	0.269760i	$-0.913056\pi$
$17$		−	9.17185i		−	0.539520i	0.962928	−	0.269760i	$-0.0869444\pi$
$18$		0			0
$19$			4.53461i			0.238664i	0.992854	+	0.119332i	$0.0380752\pi$
$19$			4.53461i			0.238664i	−0.992854	+	0.119332i	$0.961925\pi$
$20$	−3.61474	+	27.5800i	−0.180737	+	1.37900i
$21$		0			0
$22$	−23.3614	+	20.4993i	−1.06188	+	0.931787i
$23$	2.69533	+	1.55615i	0.117188	+	0.0676587i	0.557448	−	0.830212i	$-0.311780\pi$
$23$	2.69533	+	1.55615i	0.117188	+	0.0676587i	−0.440260	+	0.897870i	$0.645114\pi$
$24$		0			0
$25$	−11.6789	−	20.2284i	−0.467155	−	0.809136i
$26$	−14.3782	+	42.3973i	−0.553010	+	1.63066i
$27$		0			0
$28$	−14.5746	−	11.1701i	−0.520522	−	0.398932i
$29$	−6.42846	−	11.1344i	−0.221671	−	0.383946i	0.733644	−	0.679534i	$-0.237818\pi$
$29$	−6.42846	−	11.1344i	−0.221671	−	0.383946i	−0.955316	+	0.295588i	$0.904484\pi$
$30$		0			0
$31$	−2.17666	+	3.77008i	−0.0702147	+	0.121615i	−0.898995	−	0.437958i	$-0.855702\pi$
$31$	−2.17666	+	3.77008i	−0.0702147	+	0.121615i	0.828781	+	0.559574i	$0.189035\pi$
$32$	26.6327	+	17.7397i	0.832273	+	0.554366i
$33$		0			0
$34$	17.9902	−	3.58388i	0.529123	−	0.105408i
$35$	31.9235			0.912101
$36$		0			0
$37$			23.0374i			0.622633i	0.950306	+	0.311316i	$0.100770\pi$
$37$			23.0374i			0.622633i	−0.950306	+	0.311316i	$0.899230\pi$
$38$	−8.89444	+	1.77189i	−0.234064	+	0.0466287i
$39$		0			0
$40$	−55.5095	+	3.68669i	−1.38774	+	0.0921673i
$41$	−60.6979	−	35.0439i	−1.48044	−	0.854730i	−0.480682	−	0.876895i	$-0.659611\pi$
$41$	−60.6979	−	35.0439i	−1.48044	−	0.854730i	−0.999754	+	0.0221647i	$0.992944\pi$
$42$		0			0
$43$	51.7345	−	29.8689i	1.20313	−	0.694626i	0.241878	−	0.970307i	$-0.422237\pi$
$43$	51.7345	−	29.8689i	1.20313	−	0.694626i	0.961249	+	0.275681i	$0.0889034\pi$
$44$	−49.3370	−	37.8122i	−1.12129	−	0.859369i
$45$		0			0
$46$	−1.99913	+	5.89484i	−0.0434593	+	0.128149i
$47$	−32.1187	+	18.5438i	−0.683377	+	0.394548i	−0.801126	−	0.598495i	$-0.795765\pi$
$47$	−32.1187	+	18.5438i	−0.683377	+	0.394548i	0.117749	+	0.993043i	$0.462432\pi$
$48$		0			0
$49$	13.9628	−	24.1843i	0.284955	−	0.493556i
$50$	35.1136	−	30.8118i	0.702273	−	0.616236i
$51$		0			0
$52$	−88.7787	−	11.6357i	−1.70728	−	0.223763i
$53$	24.3319			0.459092			0.229546	−	0.973298i	$-0.426276\pi$
$53$	24.3319			0.459092			0.229546	+	0.973298i	$0.426276\pi$
$54$		0			0
$55$	108.065			1.96482
$56$	16.2147	−	32.9522i	0.289548	−	0.588432i
$57$		0			0
$58$	19.3278	−	16.9599i	0.333238	−	0.292412i
$59$	20.7560	−	35.9504i	0.351796	−	0.609329i	−0.634768	−	0.772703i	$-0.718904\pi$
$59$	20.7560	−	35.9504i	0.351796	−	0.609329i	0.986564	+	0.163374i	$0.0522377\pi$
$60$		0			0
$61$	−34.6245	+	19.9904i	−0.567614	+	0.327712i	−0.756196	−	0.654345i	$-0.772944\pi$
$61$	−34.6245	+	19.9904i	−0.567614	+	0.327712i	0.188582	+	0.982057i	$0.439611\pi$
$62$	−8.24537	−	2.79626i	−0.132990	−	0.0451010i
$63$		0			0
$64$	−24.3890	+	59.1707i	−0.381078	+	0.924543i
$65$	134.807	−	77.8306i	2.07395	−	1.19739i
$66$		0			0
$67$	−24.3421	−	14.0539i	−0.363315	−	0.209760i	0.307219	−	0.951639i	$-0.400602\pi$
$67$	−24.3421	−	14.0539i	−0.363315	−	0.209760i	−0.670534	+	0.741879i	$0.733935\pi$
$68$	14.0593	+	33.8866i	0.206754	+	0.498332i
$69$		0			0
$70$	12.4741	+	62.6167i	0.178201	+	0.894524i
$71$			59.8148i			0.842462i	0.906953	+	0.421231i	$0.138402\pi$
$71$			59.8148i			0.842462i	−0.906953	+	0.421231i	$0.861598\pi$
$72$		0			0
$73$	−53.8883			−0.738196			−0.369098	−	0.929390i	$-0.620333\pi$
$73$	−53.8883			−0.738196			−0.369098	+	0.929390i	$0.620333\pi$
$74$	−45.1869	+	9.00183i	−0.610634	+	0.121646i
$75$		0			0
$76$	−6.95098	−	16.7537i	−0.0914603	−	0.220444i
$77$	−35.6698	+	61.7819i	−0.463244	+	0.802363i
$78$		0			0
$79$	−0.557280	−	0.965237i	−0.00705418	−	0.0122182i	0.862477	−	0.506097i	$-0.168912\pi$
$79$	−0.557280	−	0.965237i	−0.00705418	−	0.0122182i	−0.869531	+	0.493878i	$0.835579\pi$
$80$	−28.9215	−	107.439i	−0.361519	−	1.34299i
$81$		0			0
$82$	45.0196	−	132.750i	0.549020	−	1.61890i
$83$	−39.8750	−	69.0655i	−0.480422	−	0.832114i	0.519326	−	0.854576i	$-0.326183\pi$
$83$	−39.8750	−	69.0655i	−0.480422	−	0.832114i	−0.999748	+	0.0224616i	$0.992850\pi$
$84$		0			0
$85$	−55.2358	−	31.8904i	−0.649833	−	0.375181i
$86$	78.8017	+	89.8037i	0.916299	+	1.04423i
$87$		0			0
$88$	54.8887	−	111.547i	0.623736	−	1.26758i
$89$		−	10.6605i		−	0.119781i	−0.998205	−	0.0598905i	$-0.980925\pi$
$89$		−	10.6605i		−	0.119781i	0.998205	−	0.0598905i	$-0.0190751\pi$
$90$		0			0
$91$			102.760i			1.12923i
$92$	−12.3436	−	1.61780i	−0.134170	−	0.0175848i
$93$		0			0
$94$	−48.9231	−	55.7536i	−0.520459	−	0.593123i
$95$	27.3089	+	15.7668i	0.287462	+	0.165966i
$96$		0			0
$97$	−72.6276	−	125.795i	−0.748738	−	1.29685i	−0.948428	−	0.316993i	$-0.897327\pi$
$97$	−72.6276	−	125.795i	−0.748738	−	1.29685i	0.199690	−	0.979859i	$-0.436006\pi$
$98$	52.8923	+	17.9375i	0.539718	+	0.183035i
$99$		0			0
$100$	74.1567	+	56.8342i	0.741567	+	0.568342i
$101$	−47.7840	−	82.7643i	−0.473109	−	0.819449i	0.526417	−	0.850226i	$-0.323535\pi$
$101$	−47.7840	−	82.7643i	−0.473109	−	0.819449i	−0.999526	+	0.0307777i	$0.990202\pi$
$102$		0			0
$103$	−51.3053	+	88.8633i	−0.498109	+	0.862751i	−0.999998	−	0.00218165i	$-0.999306\pi$
$103$	−51.3053	+	88.8633i	−0.498109	+	0.862751i	0.501888	+	0.864933i	$0.332639\pi$
$104$	−11.8673	−	178.682i	−0.114108	−	1.71810i
$105$		0			0
$106$	9.50765	+	47.7260i	0.0896948	+	0.450245i
$107$	23.2763			0.217536			0.108768	−	0.994067i	$-0.465310\pi$
$107$	23.2763			0.217536			0.108768	+	0.994067i	$0.465310\pi$
$108$		0			0
$109$		−	83.5260i		−	0.766294i	−0.923687	−	0.383147i	$-0.874840\pi$
$109$		−	83.5260i		−	0.766294i	0.923687	−	0.383147i	$-0.125160\pi$
$110$	42.2263	+	211.965i	0.383876	+	1.92696i
$111$		0			0
$112$	70.9702	+	18.9284i	0.633663	+	0.169003i
$113$	−22.9401	−	13.2445i	−0.203010	−	0.117208i	0.395049	−	0.918660i	$-0.370728\pi$
$113$	−22.9401	−	13.2445i	−0.203010	−	0.117208i	−0.598059	+	0.801452i	$0.704061\pi$
$114$		0			0
$115$	18.7433	−	10.8214i	0.162985	−	0.0940994i
$116$	40.8185	+	31.2836i	0.351883	+	0.269686i
$117$		0			0
$118$	78.6255	+	26.6644i	0.666318	+	0.225969i
$119$	36.4641	−	21.0526i	0.306421	−	0.176912i
$120$		0			0
$121$	−60.2469	+	104.351i	−0.497908	+	0.862402i
$122$	−52.7399	−	60.1032i	−0.432294	−	0.492649i
$123$		0			0
$124$	2.26289	−	17.2656i	0.0182491	−	0.139239i
$125$	11.4202			0.0913620
$126$		0			0
$127$	−10.6813			−0.0841046			−0.0420523	−	0.999115i	$-0.513390\pi$
$127$	−10.6813			−0.0841046			−0.0420523	+	0.999115i	$0.513390\pi$
$128$	−125.591	−	24.7172i	−0.981179	−	0.193103i
$129$		0			0
$130$	205.337	+	234.005i	1.57951	+	1.80004i
$131$	−119.843	+	207.575i	−0.914835	+	1.58454i	−0.107691	+	0.994184i	$0.534346\pi$
$131$	−119.843	+	207.575i	−0.914835	+	1.58454i	−0.807143	+	0.590356i	$0.798988\pi$
$132$		0			0
$133$	−18.0280	+	10.4085i	−0.135549	+	0.0782594i
$134$	18.0545	−	53.2375i	0.134735	−	0.397295i
$135$		0			0
$136$	−60.9735	+	40.8178i	−0.448334	+	0.300131i
$137$	−109.882	+	63.4404i	−0.802058	+	0.463069i	−0.844190	−	0.536043i	$-0.819918\pi$
$137$	−109.882	+	63.4404i	−0.802058	+	0.463069i	0.0421320	+	0.999112i	$0.486585\pi$
$138$		0			0
$139$	−131.623	−	75.9927i	−0.946930	−	0.546710i	−0.0548041	−	0.998497i	$-0.517453\pi$
$139$	−131.623	−	75.9927i	−0.946930	−	0.546710i	−0.892126	+	0.451787i	$0.850787\pi$
$140$	−117.946	+	48.9347i	−0.842469	+	0.349534i
$141$		0			0
$142$	−117.324	+	23.3725i	−0.826226	+	0.164595i
$143$			347.857i			2.43256i
$144$		0			0
$145$	−89.4067			−0.616598
$146$	−21.0568	−	105.700i	−0.144225	−	0.723970i
$147$		0			0
$148$	−35.3134	−	85.1147i	−0.238604	−	0.575100i
$149$	−49.0244	+	84.9127i	−0.329023	+	0.569884i	−0.982318	−	0.187219i	$-0.940053\pi$
$149$	−49.0244	+	84.9127i	−0.329023	+	0.569884i	0.653296	+	0.757103i	$0.273386\pi$
$150$		0			0
$151$	99.7733	+	172.812i	0.660750	+	1.14445i	0.980419	+	0.196924i	$0.0630951\pi$
$151$	99.7733	+	172.812i	0.660750	+	1.14445i	−0.319668	+	0.947529i	$0.603572\pi$
$152$	30.1456	−	20.1805i	0.198326	−	0.132767i
$153$		0			0
$154$	−135.121	−	45.8236i	−0.877406	−	0.297556i
$155$	15.1364	+	26.2170i	0.0976542	+	0.169142i
$156$		0			0
$157$	193.810	+	111.896i	1.23446	+	0.712716i	0.967957	−	0.251118i	$-0.0807982\pi$
$157$	193.810	+	111.896i	1.23446	+	0.712716i	0.266504	+	0.963834i	$0.414131\pi$
$158$	1.67552	−	1.47025i	0.0106045	−	0.00930536i
$159$		0			0
$160$	199.436	−	98.7100i	1.24647	−	0.616937i
$161$			14.2876i			0.0887429i
$162$		0			0
$163$		−	143.924i		−	0.882972i	−0.897268	−	0.441486i	$-0.854451\pi$
$163$		−	143.924i		−	0.882972i	0.897268	−	0.441486i	$-0.145549\pi$
$164$	277.974	+	36.4323i	1.69496	+	0.222148i
$165$		0			0
$166$	119.888	−	105.200i	0.722217	−	0.633737i
$167$	−232.808	−	134.412i	−1.39406	−	0.804863i	−0.400301	−	0.916384i	$-0.631094\pi$
$167$	−232.808	−	134.412i	−1.39406	−	0.804863i	−0.993762	+	0.111521i	$0.964428\pi$
$168$		0			0
$169$	166.033	+	287.577i	0.982443	+	1.70164i
$170$	40.9684	−	120.804i	0.240990	−	0.710610i
$171$		0			0
$172$	−145.355	+	189.657i	−0.845084	+	1.10266i
$173$	68.3117	+	118.319i	0.394865	+	0.683926i	0.993084	−	0.117406i	$-0.0374580\pi$
$173$	68.3117	+	118.319i	0.394865	+	0.683926i	−0.598219	+	0.801333i	$0.704125\pi$
$174$		0			0
$175$	53.6141	−	92.8623i	0.306366	−	0.530642i
$176$	240.243	+	64.0750i	1.36502	+	0.364062i
$177$		0			0
$178$	20.9101	−	4.16558i	0.117473	−	0.0234021i
$179$	78.4371			0.438196			0.219098	−	0.975703i	$-0.429689\pi$
$179$	78.4371			0.438196			0.219098	+	0.975703i	$0.429689\pi$
$180$		0			0
$181$		−	237.123i		−	1.31007i	−0.755597	−	0.655037i	$-0.772653\pi$
$181$		−	237.123i		−	1.31007i	0.755597	−	0.655037i	$-0.227347\pi$
$182$	−201.560	+	40.1534i	−1.10747	+	0.220623i
$183$		0			0
$184$	−1.65001	−	24.8437i	−0.00896742	−	0.135020i
$185$	138.739	+	80.1008i	0.749938	+	0.432977i
$186$		0			0
$187$	123.436	−	71.2656i	0.660083	−	0.381099i
$188$	90.2416	−	117.746i	0.480009	−	0.626310i
$189$		0			0
$190$	−20.2550	+	59.7260i	−0.106605	+	0.314347i
$191$	220.726	−	127.436i	1.15563	−	0.667205i	0.205379	−	0.978682i	$-0.434157\pi$
$191$	220.726	−	127.436i	1.15563	−	0.667205i	0.950254	+	0.311477i	$0.100824\pi$
$192$		0			0
$193$	147.201	−	254.960i	0.762699	−	1.32103i	−0.178755	−	0.983894i	$-0.557207\pi$
$193$	147.201	−	254.960i	0.762699	−	1.32103i	0.941454	−	0.337140i	$-0.109460\pi$
$194$	218.362	−	191.610i	1.12558	−	0.987680i
$195$		0			0
$196$	−14.5160	+	110.755i	−0.0740610	+	0.565077i
$197$	−212.853			−1.08047			−0.540237	−	0.841513i	$-0.681665\pi$
$197$	−212.853			−1.08047			−0.540237	+	0.841513i	$0.681665\pi$
$198$		0			0
$199$	−206.128			−1.03582			−0.517909	−	0.855435i	$-0.673290\pi$
$199$	−206.128			−1.03582			−0.517909	+	0.855435i	$0.673290\pi$
$200$	−82.5014	+	167.663i	−0.412507	+	0.838315i
$201$		0			0
$202$	143.667	−	126.066i	0.711224	−	0.624091i
$203$	29.5111	−	51.1147i	0.145375	−	0.251796i
$204$		0			0
$205$	−422.091	+	243.695i	−2.05898	+	1.18875i
$206$	−194.349	−	65.9099i	−0.943442	−	0.319951i
$207$		0			0
$208$	345.841	−	93.0970i	1.66270	−	0.447582i
$209$	−61.0272	+	35.2341i	−0.291996	+	0.168584i
$210$		0			0
$211$	7.29372	+	4.21103i	0.0345674	+	0.0199575i	0.517184	−	0.855874i	$-0.326980\pi$
$211$	7.29372	+	4.21103i	0.0345674	+	0.0199575i	−0.482617	+	0.875832i	$0.660314\pi$
$212$	−89.8974	+	37.2977i	−0.424044	+	0.175933i
$213$		0			0
$214$	9.09518	+	45.6555i	0.0425008	+	0.213343i
$215$		−	415.415i		−	1.93216i
$216$		0			0
$217$	−19.9847			−0.0920954
$218$	163.833	−	32.6377i	0.751526	−	0.149714i
$219$		0			0
$220$	−399.261	+	165.650i	−1.81482	+	0.752956i
$221$	102.654	−	177.801i	0.464496	−	0.804530i
$222$		0			0
$223$	−217.164	−	376.140i	−0.973831	−	1.68672i	−0.683740	−	0.729726i	$-0.739648\pi$
$223$	−217.164	−	376.140i	−0.973831	−	1.68672i	−0.290091	−	0.956999i	$-0.593686\pi$
$224$	−9.39571	+	146.601i	−0.0419451	+	0.654470i
$225$		0			0
$226$	17.0147	−	50.1714i	0.0752862	−	0.221997i
$227$	−29.4669	−	51.0382i	−0.129810	−	0.224838i	0.793793	−	0.608188i	$-0.208103\pi$
$227$	−29.4669	−	51.0382i	−0.129810	−	0.224838i	−0.923603	+	0.383351i	$0.874770\pi$
$228$		0			0
$229$	150.597	+	86.9472i	0.657628	+	0.379682i	0.791373	−	0.611334i	$-0.209367\pi$
$229$	150.597	+	86.9472i	0.657628	+	0.379682i	−0.133744	+	0.991016i	$0.542700\pi$
$230$	28.5497	+	32.5357i	0.124129	+	0.141459i
$231$		0			0
$232$	−45.4117	+	92.2877i	−0.195740	+	0.397792i
$233$			124.652i			0.534987i	0.963560	+	0.267494i	$0.0861954\pi$
$233$			124.652i			0.534987i	−0.963560	+	0.267494i	$0.913805\pi$
$234$		0			0
$235$			257.906i			1.09747i
$236$	−21.5783	+	164.640i	−0.0914334	+	0.697626i
$237$		0			0
$238$	55.5420	+	63.2965i	0.233370	+	0.265952i
$239$	111.522	+	64.3874i	0.466621	+	0.269404i	0.714824	−	0.699304i	$-0.246507\pi$
$239$	111.522	+	64.3874i	0.466621	+	0.269404i	−0.248203	+	0.968708i	$0.579840\pi$
$240$		0			0
$241$	131.126	+	227.117i	0.544092	+	0.942395i	0.998663	+	0.0516849i	$0.0164591\pi$
$241$	131.126	+	227.117i	0.544092	+	0.942395i	−0.454571	+	0.890710i	$0.650208\pi$
$242$	−228.221	−	77.3969i	−0.943061	−	0.319822i
$243$		0			0
$244$	97.2818	−	126.932i	0.398696	−	0.520214i
$245$	−97.0968	−	168.177i	−0.396314	−	0.686435i
$246$		0			0
$247$	−50.7525	+	87.9059i	−0.205476	+	0.355894i
$248$	34.7499	−	2.30793i	0.140121	−	0.00930619i
$249$		0			0
$250$	4.46244	+	22.4003i	0.0178498	+	0.0896013i
$251$	−227.156			−0.905005			−0.452503	−	0.891763i	$-0.649469\pi$
$251$	−227.156			−0.905005			−0.452503	+	0.891763i	$0.649469\pi$
$252$		0			0
$253$			48.3654i			0.191167i
$254$	−4.17369	−	20.9509i	−0.0164319	−	0.0824838i
$255$		0			0
$256$	−0.592754	−	255.999i	−0.00231545	−	0.999997i
$257$	−15.0254	−	8.67493i	−0.0584647	−	0.0337546i	0.470483	−	0.882409i	$-0.344080\pi$
$257$	−15.0254	−	8.67493i	−0.0584647	−	0.0337546i	−0.528947	+	0.848655i	$0.677413\pi$
$258$		0			0
$259$	−91.5888	+	52.8788i	−0.353625	+	0.204165i
$260$	−378.756	+	494.197i	−1.45675	+	1.90076i
$261$		0			0
$262$	−453.978	−	153.958i	−1.73274	−	0.587626i
$263$	−40.5408	+	23.4062i	−0.154147	+	0.0889970i	−0.575090	−	0.818090i	$-0.695033\pi$
$263$	−40.5408	+	23.4062i	−0.154147	+	0.0889970i	0.420942	+	0.907087i	$0.361699\pi$
$264$		0			0
$265$	84.6017	−	146.534i	0.319252	−	0.552960i
$266$	−27.4602	−	31.2941i	−0.103234	−	0.117647i
$267$		0			0
$268$	111.478	+	14.6107i	0.415962	+	0.0545175i
$269$	474.565			1.76418			0.882091	−	0.471079i	$-0.156135\pi$
$269$	474.565			1.76418			0.882091	+	0.471079i	$0.156135\pi$
$270$		0			0
$271$	10.2990			0.0380036			0.0190018	−	0.999819i	$-0.493951\pi$
$271$	10.2990			0.0380036			0.0190018	+	0.999819i	$0.493951\pi$
$272$	−103.888	−	103.647i	−0.381940	−	0.381057i
$273$		0			0
$274$	−167.372	−	190.740i	−0.610846	−	0.696130i
$275$	181.490	−	314.351i	0.659965	−	1.14309i
$276$		0			0
$277$	333.475	−	192.532i	1.20388	−	0.695060i	0.242464	−	0.970160i	$-0.422044\pi$
$277$	333.475	−	192.532i	1.20388	−	0.695060i	0.961416	+	0.275100i	$0.0887110\pi$
$278$	97.6249	−	287.868i	0.351169	−	1.03549i
$279$		0			0
$280$	−142.070	−	212.224i	−0.507394	−	0.757944i
$281$	−9.19798	+	5.31046i	−0.0327330	+	0.0188984i	−0.516277	−	0.856422i	$-0.672683\pi$
$281$	−9.19798	+	5.31046i	−0.0327330	+	0.0188984i	0.483544	+	0.875320i	$0.339349\pi$
$282$		0			0
$283$	−326.705	−	188.623i	−1.15443	−	0.666512i	−0.204470	−	0.978873i	$-0.565547\pi$
$283$	−326.705	−	188.623i	−1.15443	−	0.666512i	−0.949964	+	0.312360i	$0.898880\pi$
$284$	−91.6884	−	220.994i	−0.322847	−	0.778146i
$285$		0			0
$286$	−682.306	+	135.924i	−2.38569	+	0.475260i
$287$		−	321.752i		−	1.12109i
$288$		0			0
$289$	204.877			0.708918
$290$	−34.9355	−	175.367i	−0.120467	−	0.604715i
$291$		0			0
$292$	199.098	−	82.6040i	0.681841	−	0.282890i
$293$	124.349	−	215.379i	0.424399	−	0.735080i	−0.571965	−	0.820278i	$-0.693819\pi$
$293$	124.349	−	215.379i	0.424399	−	0.735080i	0.996364	+	0.0851974i	$0.0271521\pi$
$294$		0			0
$295$	−144.336	−	249.998i	−0.489276	−	0.847451i
$296$	153.150	−	102.524i	0.517400	−	0.346366i
$297$		0			0
$298$	−185.709	−	62.9797i	−0.623184	−	0.211341i
$299$	34.8336	+	60.3336i	0.116500	+	0.201785i
$300$		0			0
$301$	237.497	+	137.119i	0.789026	+	0.455544i
$302$	−299.978	+	263.227i	−0.993305	+	0.871613i
$303$		0			0
$304$	51.3626	+	51.2438i	0.168956	+	0.168565i
$305$			278.026i			0.911561i
$306$		0			0
$307$			557.648i			1.81644i	0.418488	+	0.908222i	$0.362560\pi$
$307$			557.648i			1.81644i	−0.418488	+	0.908222i	$0.637440\pi$
$308$	37.0830	−	282.939i	0.120399	−	0.918632i
$309$		0			0
$310$	−45.5090	+	39.9337i	−0.146803	+	0.128818i
$311$	124.423	+	71.8354i	0.400072	+	0.230982i	0.686515	−	0.727115i	$-0.259140\pi$
$311$	124.423	+	71.8354i	0.400072	+	0.230982i	−0.286443	+	0.958097i	$0.592473\pi$
$312$		0			0
$313$	−135.455	−	234.614i	−0.432763	−	0.749567i	0.564347	−	0.825537i	$-0.309128\pi$
$313$	−135.455	−	234.614i	−0.432763	−	0.749567i	−0.997110	+	0.0759706i	$0.975794\pi$
$314$	−143.749	+	423.874i	−0.457799	+	1.34992i
$315$		0			0
$316$	3.53853	+	2.71196i	0.0111979	+	0.00858214i
$317$	152.700	+	264.483i	0.481702	+	0.834332i	0.999779	−	0.0210014i	$-0.00668543\pi$
$317$	152.700	+	264.483i	0.481702	+	0.834332i	−0.518077	+	0.855334i	$0.673352\pi$
$318$		0			0
$319$	99.8988	−	173.030i	0.313162	−	0.542413i
$320$	271.545	+	352.614i	0.848577	+	1.10192i
$321$		0			0
$322$	−28.0245	+	5.58286i	−0.0870327	+	0.0173381i
$323$	41.5908			0.128764
$324$		0			0
$325$		−	522.851i		−	1.60877i
$326$	282.302	−	56.2383i	0.865956	−	0.172510i
$327$		0			0
$328$	37.1575	+	559.471i	0.113285	+	1.70570i
$329$	−147.447	−	85.1286i	−0.448167	−	0.258750i
$330$		0			0
$331$	371.718	−	214.612i	1.12302	−	0.648373i	0.180846	−	0.983511i	$-0.442116\pi$
$331$	371.718	−	214.612i	1.12302	−	0.648373i	0.942169	+	0.335138i	$0.108783\pi$
$332$	253.192	+	194.048i	0.762627	+	0.584483i
$333$		0			0
$334$	172.674	−	509.165i	0.516988	−	1.52445i
$335$	−169.274	+	97.7305i	−0.505296	+	0.291733i
$336$		0			0
$337$	−233.725	+	404.823i	−0.693545	+	1.20125i	0.277124	+	0.960834i	$0.410619\pi$
$337$	−233.725	+	404.823i	−0.693545	+	1.20125i	−0.970669	+	0.240421i	$0.922715\pi$
$338$	−499.194	+	438.037i	−1.47690	+	1.29597i
$339$		0			0
$340$	252.960	+	33.1538i	0.743999	+	0.0975113i
$341$	−67.6507			−0.198389
$342$		0			0
$343$	353.141			1.02957
$344$	−428.801	−	210.999i	−1.24651	−	0.613368i
$345$		0			0
$346$	−205.386	+	180.224i	−0.593600	+	0.520877i
$347$	−111.555	+	193.219i	−0.321484	+	0.556826i	−0.980794	−	0.195045i	$-0.937515\pi$
$347$	−111.555	+	193.219i	−0.321484	+	0.556826i	0.659311	+	0.751871i	$0.270848\pi$
$348$		0			0
$349$	−42.4023	+	24.4810i	−0.121497	+	0.0701461i	−0.559517	−	0.828819i	$-0.689013\pi$
$349$	−42.4023	+	24.4810i	−0.121497	+	0.0701461i	0.438020	+	0.898965i	$0.355680\pi$
$350$	203.095	+	68.8759i	0.580272	+	0.196788i
$351$		0			0
$352$	−31.8057	+	496.264i	−0.0903570	+	1.40984i
$353$	−32.8296	+	18.9542i	−0.0930017	+	0.0536945i	−0.545780	−	0.837929i	$-0.683766\pi$
$353$	−32.8296	+	18.9542i	−0.0930017	+	0.0536945i	0.452778	+	0.891623i	$0.350433\pi$
$354$		0			0
$355$	360.224	+	207.975i	1.01471	+	0.585846i
$356$	16.3412	+	39.3866i	0.0459022	+	0.110637i
$357$		0			0
$358$	30.6492	+	153.851i	0.0856122	+	0.429752i
$359$		−	538.228i		−	1.49924i	−0.661868	−	0.749621i	$-0.730236\pi$
$359$		−	538.228i		−	1.49924i	0.661868	−	0.749621i	$-0.269764\pi$
$360$		0			0
$361$	340.437			0.943040
$362$	465.107	−	92.6555i	1.28483	−	0.255955i
$363$		0			0
$364$	−157.518	−	379.661i	−0.432743	−	1.04303i
$365$	−187.369	+	324.533i	−0.513340	+	0.889130i
$366$		0			0
$367$	58.2868	+	100.956i	0.158820	+	0.275084i	0.934443	−	0.356112i	$-0.115898\pi$
$367$	58.2868	+	100.956i	0.158820	+	0.275084i	−0.775624	+	0.631196i	$0.782564\pi$
$368$	48.0851	−	12.9440i	0.130666	−	0.0351740i
$369$		0			0
$370$	−102.902	+	303.429i	−0.278114	+	0.820079i
$371$	55.8501	+	96.7352i	0.150539	+	0.260742i
$372$		0			0
$373$	−117.381	−	67.7702i	−0.314695	−	0.181689i	0.334330	−	0.942456i	$-0.391490\pi$
$373$	−117.381	−	67.7702i	−0.314695	−	0.181689i	−0.649026	+	0.760767i	$0.724823\pi$
$374$	188.017	+	214.267i	0.502718	+	0.572906i
$375$		0			0
$376$	266.216	+	130.996i	0.708021	+	0.348394i
$377$		−	287.796i		−	0.763384i
$378$		0			0
$379$			292.521i			0.771822i	0.922536	+	0.385911i	$0.126113\pi$
$379$			292.521i			0.771822i	−0.922536	+	0.385911i	$0.873887\pi$
$380$	−125.065	−	16.3914i	−0.329117	−	0.0431353i
$381$		0			0
$382$	336.209	+	383.149i	0.880128	+	1.00301i
$383$	−230.166	−	132.886i	−0.600956	−	0.346962i	0.168462	−	0.985708i	$-0.446120\pi$
$383$	−230.166	−	132.886i	−0.600956	−	0.346962i	−0.769417	+	0.638746i	$0.779453\pi$
$384$		0			0
$385$	248.047	+	429.630i	0.644278	+	1.11592i
$386$	557.611	+	189.103i	1.44459	+	0.489905i
$387$		0			0
$388$	461.159	+	353.436i	1.18855	+	0.910918i
$389$	70.7571	+	122.555i	0.181895	+	0.315051i	0.942526	−	0.334133i	$-0.108444\pi$
$389$	70.7571	+	122.555i	0.181895	+	0.315051i	−0.760631	+	0.649185i	$0.775110\pi$
$390$		0			0
$391$	14.2728	−	24.7212i	0.0365033	−	0.0632255i
$392$	−222.913	+	14.8049i	−0.568657	+	0.0377676i
$393$		0			0
$394$	−83.1721	−	417.503i	−0.211097	−	1.05965i
$395$	−7.75062			−0.0196218
$396$		0			0
$397$			371.596i			0.936009i	0.883726	+	0.468004i	$0.155027\pi$
$397$			371.596i			0.936009i	−0.883726	+	0.468004i	$0.844973\pi$
$398$	−80.5442	−	404.311i	−0.202372	−	1.01586i
$399$		0			0
$400$	−361.101	−	96.3088i	−0.902753	−	0.240772i
$401$	25.8599	+	14.9302i	0.0644885	+	0.0372325i	0.531898	−	0.846809i	$-0.321479\pi$
$401$	25.8599	+	14.9302i	0.0644885	+	0.0372325i	−0.467409	+	0.884041i	$0.654812\pi$
$402$		0			0
$403$	−84.3913	+	48.7233i	−0.209408	+	0.120902i
$404$	303.411	+	232.537i	0.751018	+	0.575586i
$405$		0			0
$406$	111.791	+	37.9117i	0.275347	+	0.0933787i
$407$	−310.040	+	179.001i	−0.761768	+	0.439807i
$408$		0			0
$409$	180.690	−	312.965i	0.441785	−	0.765195i	−0.556037	−	0.831158i	$-0.687679\pi$
$409$	180.690	−	312.965i	0.441785	−	0.765195i	0.997822	+	0.0659631i	$0.0210120\pi$
$410$	−642.928	−	732.691i	−1.56812	−	1.78705i
$411$		0			0
$412$	53.3379	−	406.962i	0.129461	−	0.987771i
$413$	190.568			0.461425
$414$		0			0
$415$	−554.579			−1.33634
$416$	317.742	+	641.974i	0.763804	+	1.54321i
$417$		0			0
$418$	−92.9564	−	105.935i	−0.222384	−	0.253432i
$419$	98.1870	−	170.065i	0.234336	−	0.405883i	−0.724743	−	0.689019i	$-0.758042\pi$
$419$	98.1870	−	170.065i	0.234336	−	0.405883i	0.959080	+	0.283136i	$0.0913749\pi$
$420$		0			0
$421$	−82.7053	+	47.7499i	−0.196450	+	0.113420i	−0.594998	−	0.803727i	$-0.702847\pi$
$421$	−82.7053	+	47.7499i	−0.196450	+	0.113420i	0.398549	+	0.917147i	$0.369514\pi$
$422$	−5.40975	+	15.9518i	−0.0128193	+	0.0378004i
$423$		0			0
$424$	−108.285	−	161.756i	−0.255389	−	0.381500i
$425$	−185.532	+	107.117i	−0.436545	+	0.252040i
$426$		0			0
$427$	−158.950	−	91.7699i	−0.372249	−	0.214918i
$428$	−85.9974	+	35.6796i	−0.200928	+	0.0833636i
$429$		0			0
$430$	814.819	−	162.323i	1.89493	−	0.377495i
$431$			237.261i			0.550490i	0.961374	+	0.275245i	$0.0887589\pi$
$431$			237.261i			0.550490i	−0.961374	+	0.275245i	$0.911241\pi$
$432$		0			0
$433$	−180.685			−0.417287			−0.208644	−	0.977992i	$-0.566905\pi$
$433$	−180.685			−0.417287			−0.208644	+	0.977992i	$0.566905\pi$
$434$	−7.80899	−	39.1991i	−0.0179931	−	0.0903206i
$435$		0			0
$436$	128.035	+	308.598i	0.293658	+	0.707793i
$437$	−7.05653	+	12.2223i	−0.0161477	+	0.0279686i
$438$		0			0
$439$	93.0216	+	161.118i	0.211894	+	0.367012i	0.952307	−	0.305140i	$-0.0987034\pi$
$439$	93.0216	+	161.118i	0.211894	+	0.367012i	−0.740413	+	0.672152i	$0.765370\pi$
$440$	−480.927	−	718.406i	−1.09301	−	1.63274i
$441$		0			0
$442$	388.861	+	131.875i	0.879777	+	0.298360i
$443$	−141.006	−	244.230i	−0.318299	−	0.551310i	0.661834	−	0.749650i	$-0.269778\pi$
$443$	−141.006	−	244.230i	−0.318299	−	0.551310i	−0.980133	+	0.198340i	$0.936445\pi$
$444$		0			0
$445$	−64.2009	−	37.0664i	−0.144272	−	0.0832954i
$446$	652.925	−	572.935i	1.46396	−	1.28461i
$447$		0			0
$448$	−291.224	+	38.8549i	−0.650053	+	0.0867298i
$449$			158.722i			0.353502i	0.984256	+	0.176751i	$0.0565588\pi$
$449$			158.722i			0.353502i	−0.984256	+	0.176751i	$0.943441\pi$
$450$		0			0
$451$		−	1089.17i		−	2.41501i
$452$	105.057	+	13.7692i	0.232428	+	0.0304629i
$453$		0			0
$454$	88.5950	−	77.7411i	0.195143	−	0.171236i
$455$	618.855	+	357.296i	1.36012	+	0.785266i
$456$		0			0
$457$	−213.180	−	369.239i	−0.466477	−	0.807963i	0.532789	−	0.846248i	$-0.321144\pi$
$457$	−213.180	−	369.239i	−0.466477	−	0.807963i	−0.999267	+	0.0382852i	$0.987810\pi$
$458$	−111.698	+	329.364i	−0.243881	+	0.719135i
$459$		0			0
$460$	−52.6616	+	68.7122i	−0.114482	+	0.149374i
$461$	203.028	+	351.655i	0.440408	+	0.762808i	0.997720	−	0.0674949i	$-0.0215006\pi$
$461$	203.028	+	351.655i	0.440408	+	0.762808i	−0.557312	+	0.830303i	$0.688167\pi$
$462$		0			0
$463$	−357.640	+	619.450i	−0.772440	+	1.33790i	0.163783	+	0.986496i	$0.447630\pi$
$463$	−357.640	+	619.450i	−0.772440	+	1.33790i	−0.936222	+	0.351408i	$0.885703\pi$
$464$	−198.763	−	53.0118i	−0.428368	−	0.114250i
$465$		0			0
$466$	−244.500	+	48.7076i	−0.524677	+	0.104523i
$467$	−419.019			−0.897256			−0.448628	−	0.893719i	$-0.648087\pi$
$467$	−419.019			−0.897256			−0.448628	+	0.893719i	$0.648087\pi$
$468$		0			0
$469$		−	129.034i		−	0.275126i
$470$	−505.871	+	100.776i	−1.07632	+	0.214417i
$471$		0			0
$472$	−331.365	+	22.0078i	−0.702045	+	0.0466267i
$473$	803.957	+	464.165i	1.69970	+	0.981321i
$474$		0			0
$475$	91.7279	−	52.9591i	0.193111	−	0.111493i
$476$	−102.451	+	133.676i	−0.215232	+	0.280832i
$477$		0			0
$478$	−82.7161	+	243.906i	−0.173046	+	0.510263i
$479$	27.1481	−	15.6740i	0.0566766	−	0.0327223i	−0.471394	−	0.881923i	$-0.656249\pi$
$479$	27.1481	−	15.6740i	0.0566766	−	0.0327223i	0.528071	+	0.849201i	$0.322916\pi$
$480$		0			0
$481$	−257.840	+	446.593i	−0.536051	+	0.928467i
$482$	−394.244	+	345.944i	−0.817933	+	0.717727i
$483$		0			0
$484$	62.6337	−	477.888i	0.129409	−	0.987372i
$485$	−1010.10			−2.08268
$486$		0			0
$487$	156.973			0.322327			0.161163	−	0.986928i	$-0.448475\pi$
$487$	156.973			0.322327			0.161163	+	0.986928i	$0.448475\pi$
$488$	286.985	+	141.216i	0.588084	+	0.289376i
$489$		0			0
$490$	291.931	−	256.166i	0.595777	−	0.522788i
$491$	15.1335	−	26.2120i	0.0308218	−	0.0533849i	−0.850203	−	0.526455i	$-0.823521\pi$
$491$	15.1335	−	26.2120i	0.0308218	−	0.0533849i	0.881025	+	0.473070i	$0.156854\pi$
$492$		0			0
$493$	−102.123	+	58.9609i	−0.207147	+	0.119596i
$494$	−192.255	−	65.1998i	−0.389180	−	0.131983i
$495$		0			0
$496$	18.1054	+	67.2587i	0.0365028	+	0.135602i
$497$	−237.803	+	137.296i	−0.478477	+	0.276249i
$498$		0			0
$499$	−92.1565	−	53.2066i	−0.184682	−	0.106626i	0.404808	−	0.914402i	$-0.367338\pi$
$499$	−92.1565	−	53.2066i	−0.184682	−	0.106626i	−0.589491	+	0.807775i	$0.700672\pi$
$500$	−42.1936	+	17.5058i	−0.0843872	+	0.0350116i
$501$		0			0
$502$	−88.7609	−	445.557i	−0.176815	−	0.887565i
$503$			895.530i			1.78038i	0.455592	+	0.890189i	$0.349428\pi$
$503$			895.530i			1.78038i	−0.455592	+	0.890189i	$0.650572\pi$
$504$		0			0
$505$	−664.577			−1.31599
$506$	−94.8666	+	18.8987i	−0.187483	+	0.0373492i
$507$		0			0
$508$	39.4634	−	16.3730i	0.0776839	−	0.0322304i
$509$	136.924	−	237.160i	0.269006	−	0.465932i	−0.699599	−	0.714535i	$-0.746638\pi$
$509$	136.924	−	237.160i	0.269006	−	0.465932i	0.968605	+	0.248603i	$0.0799715\pi$
$510$		0			0
$511$	−123.692	−	214.241i	−0.242059	−	0.419259i
$512$	501.900	−	101.194i	0.980274	−	0.197644i
$513$		0			0
$514$	11.1444	−	32.8614i	0.0216816	−	0.0639328i
$515$	356.775	+	617.953i	0.692768	+	1.19991i
$516$		0			0
$517$	−499.127	−	288.171i	−0.965430	−	0.557391i
$518$	−139.508	−	158.985i	−0.269320	−	0.306921i
$519$		0			0
$520$	−1117.34	−	549.807i	−2.14874	−	1.05732i
$521$		−	575.650i		−	1.10489i	−0.833548	−	0.552447i	$-0.813694\pi$
$521$		−	575.650i		−	1.10489i	0.833548	−	0.552447i	$-0.186306\pi$
$522$		0			0
$523$			83.4381i			0.159537i	0.996813	+	0.0797687i	$0.0254182\pi$
$523$			83.4381i			0.159537i	−0.996813	+	0.0797687i	$0.974582\pi$
$524$	124.591	−	950.617i	0.237770	−	1.81415i
$525$		0			0
$526$	−61.7515	−	70.3730i	−0.117398	−	0.133789i
$527$	34.5786	+	19.9639i	0.0656140	+	0.0378823i
$528$		0			0
$529$	−259.657	−	449.739i	−0.490845	−	0.850168i
$530$	320.479	+	108.685i	0.604677	+	0.205065i
$531$		0			0
$532$	50.6521	−	66.0902i	0.0952107	−	0.124230i
$533$	−784.441	−	1358.69i	−1.47175	−	2.54914i
$534$		0			0
$535$	80.9314	−	140.177i	0.151274	−	0.262014i
$536$	14.9015	+	224.368i	0.0278014	+	0.418597i
$537$		0			0
$538$	185.435	+	930.839i	0.344676	+	1.73018i
$539$	433.965			0.805130
$540$		0			0
$541$			995.189i			1.83954i	0.392463	+	0.919768i	$0.371623\pi$
$541$			995.189i			1.83954i	−0.392463	+	0.919768i	$0.628377\pi$
$542$	4.02430	+	20.2010i	0.00742492	+	0.0372712i
$543$		0			0
$544$	162.706	−	244.271i	0.299092	−	0.449028i
$545$	−503.020	−	290.419i	−0.922973	−	0.532879i
$546$		0			0
$547$	−447.270	+	258.231i	−0.817678	+	0.472087i	−0.849615	−	0.527403i	$-0.823166\pi$
$547$	−447.270	+	258.231i	−0.817678	+	0.472087i	0.0319370	+	0.999490i	$0.489832\pi$
$548$	308.727	−	402.824i	0.563371	−	0.735080i
$549$		0			0
$550$	687.503	+	233.154i	1.25000	+	0.423916i
$551$	50.4903	−	29.1506i	0.0916339	−	0.0529049i
$552$		0			0
$553$	2.55830	−	4.43111i	0.00462622	−	0.00801285i
$554$	507.947	+	578.865i	0.916873	+	1.04488i
$555$		0			0
$556$	602.787	+	79.0034i	1.08415	+	0.142092i
$557$	−440.448			−0.790751			−0.395376	−	0.918520i	$-0.629386\pi$
$557$	−440.448			−0.790751			−0.395376	+	0.918520i	$0.629386\pi$
$558$		0			0
$559$	1337.20			2.39213
$560$	360.755	−	361.591i	0.644206	−	0.645699i
$561$		0			0
$562$	−14.0103	−	15.9664i	−0.0249294	−	0.0284100i
$563$	−129.798	+	224.816i	−0.230547	+	0.399319i	−0.957969	−	0.286871i	$-0.907385\pi$
$563$	−129.798	+	224.816i	−0.230547	+	0.399319i	0.727422	+	0.686190i	$0.240718\pi$
$564$		0			0
$565$	−159.525	+	92.1019i	−0.282345	+	0.163012i
$566$	242.317	−	714.521i	0.428121	−	1.26241i
$567$		0			0
$568$	397.642	−	266.196i	0.700075	−	0.468655i
$569$	892.111	−	515.060i	1.56786	−	0.905203i	0.571438	−	0.820645i	$-0.306386\pi$
$569$	892.111	−	515.060i	1.56786	−	0.905203i	0.996419	−	0.0845575i	$-0.0269477\pi$
$570$		0			0
$571$	−683.633	−	394.696i	−1.19726	−	0.691236i	−0.237313	−	0.971433i	$-0.576267\pi$
$571$	−683.633	−	394.696i	−1.19726	−	0.691236i	−0.959942	+	0.280197i	$0.909600\pi$
$572$	−533.220	−	1285.20i	−0.932203	−	2.24686i
$573$		0			0
$574$	631.102	−	125.724i	1.09948	−	0.219031i
$575$		−	72.6963i		−	0.126428i
$576$		0			0
$577$	−100.099			−0.173482			−0.0867411	−	0.996231i	$-0.527645\pi$
$577$	−100.099			−0.173482			−0.0867411	+	0.996231i	$0.527645\pi$
$578$	80.0554	+	401.858i	0.138504	+	0.695256i
$579$		0			0
$580$	330.325	−	137.049i	0.569526	−	0.236292i
$581$	183.054	−	317.058i	0.315067	−	0.545711i
$582$		0			0
$583$	189.060	+	327.461i	0.324288	+	0.561683i
$584$	239.821	+	358.244i	0.410653	+	0.613431i
$585$		0			0
$586$	471.045	+	159.746i	0.803831	+	0.272604i
$587$	64.4085	+	111.559i	0.109725	+	0.190049i	0.915659	−	0.401957i	$-0.131670\pi$
$587$	64.4085	+	111.559i	0.109725	+	0.190049i	−0.805934	+	0.592005i	$0.798336\pi$
$588$		0			0
$589$	−17.0958	−	9.87028i	−0.0290252	−	0.0167577i
$590$	433.961	−	380.796i	0.735528	−	0.645417i
$591$		0			0
$592$	260.940	+	260.337i	0.440777	+	0.439758i
$593$		−	845.625i		−	1.42601i	−0.701158	−	0.713006i	$-0.747333\pi$
$593$		−	845.625i		−	1.42601i	0.701158	−	0.713006i	$-0.252667\pi$
$594$		0			0
$595$		−	292.798i		−	0.492097i
$596$	50.9666	−	388.869i	0.0855145	−	0.652465i
$597$		0			0
$598$	−104.731	+	91.9000i	−0.175135	+	0.153679i
$599$	404.246	+	233.391i	0.674868	+	0.389635i	0.797919	−	0.602765i	$-0.205934\pi$
$599$	404.246	+	233.391i	0.674868	+	0.389635i	−0.123051	+	0.992400i	$0.539268\pi$
$600$		0			0
$601$	−101.377	−	175.589i	−0.168680	−	0.292162i	0.769276	−	0.638916i	$-0.220617\pi$
$601$	−101.377	−	175.589i	−0.168680	−	0.292162i	−0.937956	+	0.346754i	$0.887284\pi$
$602$	−176.151	+	519.419i	−0.292610	+	0.862822i
$603$		0			0
$604$	−633.525	−	485.538i	−1.04888	−	0.803872i
$605$	418.955	+	725.652i	0.692488	+	1.19942i
$606$		0			0
$607$	−162.045	+	280.671i	−0.266961	+	0.462390i	−0.968076	−	0.250659i	$-0.919353\pi$
$607$	−162.045	+	280.671i	−0.266961	+	0.462390i	0.701115	+	0.713049i	$0.252686\pi$
$608$	−80.4427	+	120.769i	−0.132307	+	0.198633i
$609$		0			0
$610$	−545.336	+	108.638i	−0.893994	+	0.178095i
$611$	−830.185			−1.35873
$612$		0			0
$613$		−	901.063i		−	1.46992i	−0.678108	−	0.734962i	$-0.737200\pi$
$613$		−	901.063i		−	1.46992i	0.678108	−	0.734962i	$-0.262800\pi$
$614$	−1093.80	+	217.900i	−1.78144	+	0.354886i
$615$		0			0
$616$	569.463	−	37.8212i	0.924452	−	0.0613980i
$617$	−210.860	−	121.740i	−0.341751	−	0.197310i	0.319295	−	0.947655i	$-0.396554\pi$
$617$	−210.860	−	121.740i	−0.341751	−	0.197310i	−0.661046	+	0.750345i	$0.729887\pi$
$618$		0			0
$619$	−216.653	+	125.085i	−0.350005	+	0.202075i	−0.664687	−	0.747122i	$-0.731435\pi$
$619$	−216.653	+	125.085i	−0.350005	+	0.202075i	0.314683	+	0.949197i	$0.398102\pi$
$620$	−96.1108	−	73.6600i	−0.155017	−	0.118806i
$621$		0			0
$622$	−92.2841	+	272.119i	−0.148367	+	0.437490i
$623$	42.3825	−	24.4695i	0.0680297	−	0.0392769i
$624$		0			0
$625$	331.680	−	574.486i	0.530688	−	0.919178i
$626$	407.258	−	357.364i	0.650571	−	0.570869i
$627$		0			0
$628$	−887.581	−	116.330i	−1.41334	−	0.185238i
$629$	211.296			0.335923
$630$		0			0
$631$	−839.956			−1.33115			−0.665575	−	0.746331i	$-0.731814\pi$
$631$	−839.956			−1.33115			−0.665575	+	0.746331i	$0.731814\pi$
$632$	−3.93671	+	8.00037i	−0.00622898	+	0.0126588i
$633$		0			0
$634$	−459.106	+	402.860i	−0.724142	+	0.635426i
$635$	−37.1387	+	64.3261i	−0.0584861	+	0.101301i
$636$		0			0
$637$	541.352	−	312.550i	0.849847	−	0.490659i
$638$	378.426	+	128.336i	0.593144	+	0.201154i
$639$		0			0
$640$	−585.532	+	670.407i	−0.914894	+	1.04751i
$641$	−807.530	+	466.228i	−1.25980	+	0.727344i	−0.973035	−	0.230658i	$-0.925912\pi$
$641$	−807.530	+	466.228i	−1.25980	+	0.727344i	−0.286762	+	0.958002i	$0.592579\pi$
$642$		0			0
$643$	137.674	+	79.4863i	0.214112	+	0.123618i	0.603221	−	0.797574i	$-0.293884\pi$
$643$	137.674	+	79.4863i	0.214112	+	0.123618i	−0.389109	+	0.921192i	$0.627217\pi$
$644$	−21.9011	−	52.7874i	−0.0340079	−	0.0819681i
$645$		0			0
$646$	16.2515	+	81.5785i	0.0251571	+	0.126283i
$647$			169.902i			0.262600i	0.991343	+	0.131300i	$0.0419152\pi$
$647$			169.902i			0.262600i	−0.991343	+	0.131300i	$0.958085\pi$
$648$		0			0
$649$	645.098			0.993988
$650$	1025.55	−	204.303i	1.57777	−	0.314313i
$651$		0			0
$652$	220.618	+	531.748i	0.338371	+	0.815564i
$653$	−93.3433	+	161.675i	−0.142945	+	0.247589i	−0.928605	−	0.371071i	$-0.878991\pi$
$653$	−93.3433	+	161.675i	−0.142945	+	0.247589i	0.785659	+	0.618660i	$0.212324\pi$
$654$		0			0
$655$	833.387	+	1443.47i	1.27235	+	2.20377i
$656$	−1082.86	+	291.495i	−1.65070	+	0.444352i
$657$		0			0
$658$	109.361	−	322.475i	0.166203	−	0.490084i
$659$	−47.0020	−	81.4099i	−0.0713232	−	0.123535i	0.828158	−	0.560494i	$-0.189389\pi$
$659$	−47.0020	−	81.4099i	−0.0713232	−	0.123535i	−0.899481	+	0.436959i	$0.856056\pi$
$660$		0			0
$661$	307.644	+	177.619i	0.465423	+	0.268712i	0.714322	−	0.699817i	$-0.246735\pi$
$661$	307.644	+	177.619i	0.465423	+	0.268712i	−0.248899	+	0.968529i	$0.580069\pi$
$662$	566.200	+	645.250i	0.855287	+	0.974698i
$663$		0			0
$664$	−281.683	+	572.449i	−0.424222	+	0.862123i
$665$			144.761i			0.217685i
$666$		0			0
$667$		−	40.0146i		−	0.0599919i
$668$	1066.18	+	139.737i	1.59608	+	0.209187i
$669$		0			0
$670$	−257.838	−	293.836i	−0.384833	−	0.438561i
$671$	−538.067	−	310.653i	−0.801888	−	0.462970i
$672$		0			0
$673$	−371.462	−	643.391i	−0.551949	−	0.956004i	−0.998134	−	0.0610631i	$-0.980551\pi$
$673$	−371.462	−	643.391i	−0.551949	−	0.956004i	0.446185	−	0.894941i	$-0.352782\pi$
$674$	−885.370	−	300.257i	−1.31361	−	0.445485i
$675$		0			0
$676$	−1054.25	−	807.985i	−1.55954	−	1.19524i
$677$	363.885	+	630.267i	0.537496	+	0.930971i	0.999038	+	0.0438525i	$0.0139632\pi$
$677$	363.885	+	630.267i	0.537496	+	0.930971i	−0.461542	+	0.887119i	$0.652704\pi$
$678$		0			0
$679$	333.411	−	577.484i	0.491032	−	0.850492i
$680$	33.8138	+	509.125i	0.0497262	+	0.748713i
$681$		0			0
$682$	−26.4344	−	132.694i	−0.0387601	−	0.194566i
$683$	839.650			1.22936			0.614678	−	0.788778i	$-0.289286\pi$
$683$	839.650			1.22936			0.614678	+	0.788778i	$0.289286\pi$
$684$		0			0
$685$			882.326i			1.28807i
$686$	137.989	+	692.672i	0.201151	+	1.00973i
$687$		0			0
$688$	246.311	−	923.522i	0.358011	−	1.34233i
$689$	471.687	+	272.329i	0.684597	+	0.395252i
$690$		0			0
$691$	624.218	−	360.393i	0.903355	−	0.521552i	0.0250679	−	0.999686i	$-0.492020\pi$
$691$	624.218	−	360.393i	0.903355	−	0.521552i	0.878287	+	0.478133i	$0.158686\pi$
$692$	−433.755	−	332.433i	−0.626813	−	0.480395i
$693$		0			0
$694$	−422.580	−	143.310i	−0.608905	−	0.206499i
$695$	−915.305	+	528.451i	−1.31699	+	0.760362i
$696$		0			0
$697$	−321.418	+	556.712i	−0.461144	+	0.798726i
$698$	−64.5870	−	73.6044i	−0.0925316	−	0.105450i
$699$		0			0
$700$	−55.7382	+	425.275i	−0.0796259	+	0.607536i
$701$	482.229			0.687916			0.343958	−	0.938985i	$-0.388232\pi$
$701$	482.229			0.687916			0.343958	+	0.938985i	$0.388232\pi$
$702$		0			0
$703$	−104.466			−0.148600
$704$	−985.829	+	131.529i	−1.40033	+	0.186831i
$705$		0			0
$706$	−50.0059	−	56.9875i	−0.0708299	−	0.0807189i
$707$	219.362	−	379.945i	0.310271	−	0.537405i
$708$		0			0
$709$	406.899	−	234.923i	0.573906	−	0.331345i	−0.184802	−	0.982776i	$-0.559164\pi$
$709$	406.899	−	234.923i	0.573906	−	0.331345i	0.758708	+	0.651431i	$0.225831\pi$
$710$	−267.178	+	787.829i	−0.376307	+	1.10962i
$711$		0			0
$712$	−70.8699	+	47.4428i	−0.0995364	+	0.0666332i
$713$	−11.7336	+	6.77440i	−0.0164567	+	0.00950127i
$714$		0			0
$715$	2094.90	+	1209.49i	2.92993	+	1.69160i
$716$	−289.796	+	120.234i	−0.404743	+	0.167925i
$717$		0			0
$718$	1055.71	−	210.312i	1.47035	−	0.292913i
$719$			933.168i			1.29787i	0.760844	+	0.648934i	$0.224785\pi$
$719$			933.168i			1.29787i	−0.760844	+	0.648934i	$0.775215\pi$
$720$		0			0
$721$	−471.053			−0.653333
$722$	133.025	+	667.753i	0.184246	+	0.924866i
$723$		0			0
$724$	363.480	+	876.083i	0.502044	+	1.21006i
$725$	−150.154	+	260.075i	−0.207109	+	0.358724i
$726$		0			0
$727$	−411.433	−	712.622i	−0.565932	−	0.980223i	−0.996962	−	0.0778855i	$-0.975183\pi$
$727$	−411.433	−	712.622i	−0.565932	−	0.980223i	0.431030	−	0.902337i	$-0.358150\pi$
$728$	683.140	−	457.318i	0.938378	−	0.628184i
$729$		0			0
$730$	−709.771	−	240.706i	−0.972289	−	0.329734i
$731$	−273.953	−	474.501i	−0.374765	−	0.649112i
$732$		0			0
$733$	−747.781	−	431.731i	−1.02016	−	0.588992i	−0.106013	−	0.994365i	$-0.533809\pi$
$733$	−747.781	−	431.731i	−1.02016	−	0.588992i	−0.914152	+	0.405372i	$0.867142\pi$
$734$	−175.245	+	153.775i	−0.238753	+	0.209503i
$735$		0			0
$736$	44.1783	+	89.2590i	0.0600249	+	0.121276i
$737$		−	436.797i		−	0.592669i
$738$		0			0
$739$			377.321i			0.510583i	0.966864	+	0.255292i	$0.0821714\pi$
$739$			377.321i			0.510583i	−0.966864	+	0.255292i	$0.917829\pi$
$740$	−635.372	−	83.2742i	−0.858611	−	0.112533i
$741$		0			0
$742$	−167.919	+	147.347i	−0.226306	+	0.198581i
$743$	−670.266	−	386.978i	−0.902108	−	0.520832i	−0.0242246	−	0.999707i	$-0.507712\pi$
$743$	−670.266	−	386.978i	−0.902108	−	0.520832i	−0.877884	+	0.478874i	$0.841045\pi$
$744$		0			0
$745$	340.914	+	590.481i	0.457603	+	0.792592i
$746$	87.0617	−	256.720i	0.116705	−	0.344128i
$747$		0			0
$748$	−346.808	+	452.511i	−0.463647	+	0.604961i
$749$	53.4272	+	92.5386i	0.0713313	+	0.123549i
$750$		0			0
$751$	598.825	−	1037.20i	0.797370	−	1.38109i	−0.123953	−	0.992288i	$-0.539557\pi$
$751$	598.825	−	1037.20i	0.797370	−	1.38109i	0.921323	−	0.388798i	$-0.127109\pi$
$752$	−152.920	+	573.358i	−0.203351	+	0.762444i
$753$		0			0
$754$	564.499	−	112.456i	0.748673	−	0.149146i
$755$	1387.64			1.83794
$756$		0			0
$757$		−	400.054i		−	0.528473i	−0.964458	−	0.264236i	$-0.914880\pi$
$757$		−	400.054i		−	0.528473i	0.964458	−	0.264236i	$-0.0851199\pi$
$758$	−573.767	+	114.302i	−0.756948	+	0.150794i
$759$		0			0
$760$	−16.7177	−	251.714i	−0.0219970	−	0.331202i
$761$	−539.091	−	311.245i	−0.708399	−	0.408994i	0.102069	−	0.994777i	$-0.467454\pi$
$761$	−539.091	−	311.245i	−0.708399	−	0.408994i	−0.810468	+	0.585783i	$0.800787\pi$
$762$		0			0
$763$	332.071	−	191.721i	0.435217	−	0.251273i
$764$	−620.157	+	809.174i	−0.811724	+	1.05913i
$765$		0			0
$766$	170.714	−	503.386i	0.222864	−	0.657162i
$767$	804.731	−	464.612i	1.04919	−	0.605752i
$768$		0			0
$769$	−85.2885	+	147.724i	−0.110908	+	0.192099i	−0.916137	−	0.400866i	$-0.868709\pi$
$769$	−85.2885	+	147.724i	−0.110908	+	0.192099i	0.805228	+	0.592965i	$0.202043\pi$
$770$	−745.777	+	654.411i	−0.968541	+	0.849884i
$771$		0			0
$772$	−153.033	+	1167.62i	−0.198229	+	1.51246i
$773$	−26.7288			−0.0345780			−0.0172890	−	0.999851i	$-0.505504\pi$
$773$	−26.7288			−0.0345780			−0.0172890	+	0.999851i	$0.505504\pi$
$774$		0			0
$775$	101.683			0.131204
$776$	−513.053	+	1042.65i	−0.661150	+	1.34362i
$777$		0			0
$778$	−212.738	+	186.675i	−0.273442	+	0.239942i
$779$	158.911	−	275.241i	0.203993	−	0.353326i
$780$		0			0
$781$	−804.993	+	464.763i	−1.03072	+	0.595087i
$782$	54.0666	+	18.3357i	0.0691389	+	0.0234472i
$783$		0			0
$784$	−116.142	−	431.450i	−0.148141	−	0.550319i
$785$	1347.75	−	778.125i	1.71688	−	0.991242i
$786$		0			0
$787$	552.776	+	319.145i	0.702384	+	0.405522i	0.808235	−	0.588860i	$-0.200423\pi$
$787$	552.776	+	319.145i	0.702384	+	0.405522i	−0.105851	+	0.994382i	$0.533757\pi$
$788$	786.415	−	326.277i	0.997989	−	0.414057i
$789$		0			0
$790$	−3.02854	−	15.2025i	−0.00383360	−	0.0192437i
$791$		−	121.603i		−	0.153733i
$792$		0			0
$793$	−894.952			−1.12856
$794$	−728.869	+	145.200i	−0.917971	+	0.182872i
$795$		0			0
$796$	761.567	−	315.968i	0.956742	−	0.396945i
$797$	−391.164	+	677.516i	−0.490796	+	0.850083i	−0.999944	−	0.0105960i	$-0.996627\pi$
$797$	−391.164	+	677.516i	−0.490796	+	0.850083i	0.509148	+	0.860679i	$0.329960\pi$
$798$		0			0
$799$	170.081	+	294.588i	0.212867	+	0.368696i
$800$	47.8060	−	745.917i	0.0597575	−	0.932397i
$801$		0			0
$802$	−19.1803	+	56.5570i	−0.0239156	+	0.0705200i
$803$	−418.714	−	725.234i	−0.521437	−	0.903156i
$804$		0			0
$805$	86.0445	+	49.6778i	0.106888	+	0.0617116i
$806$	−128.544	−	146.491i	−0.159484	−	0.181751i
$807$		0			0
$808$	−337.554	+	685.992i	−0.417764	+	0.849000i
$809$			571.316i			0.706200i	0.935586	+	0.353100i	$0.114873\pi$
$809$			571.316i			0.706200i	−0.935586	+	0.353100i	$0.885127\pi$
$810$		0			0
$811$		−	554.157i		−	0.683301i	−0.939827	−	0.341651i	$-0.889014\pi$
$811$		−	554.157i		−	0.683301i	0.939827	−	0.341651i	$-0.110986\pi$
$812$	−30.6803	+	234.087i	−0.0377836	+	0.288284i
$813$		0			0
$814$	−472.251	−	538.185i	−0.580161	−	0.661161i
$815$	−866.759	−	500.424i	−1.06351	−	0.614017i
$816$		0			0
$817$	135.444	+	234.596i	0.165782	+	0.287143i
$818$	684.471	+	232.126i	0.836762	+	0.283772i
$819$		0			0
$820$	1185.92	−	1547.37i	1.44624	−	1.88704i
$821$	−425.017	−	736.150i	−0.517682	−	0.896651i	−0.999789	−	0.0205386i	$-0.993462\pi$
$821$	−425.017	−	736.150i	−0.517682	−	0.896651i	0.482108	−	0.876112i	$-0.339871\pi$
$822$		0			0
$823$	−299.122	+	518.094i	−0.363453	+	0.629519i	−0.988527	−	0.151047i	$-0.951736\pi$
$823$	−299.122	+	518.094i	−0.363453	+	0.629519i	0.625074	+	0.780566i	$0.285069\pi$
$824$	819.080	−	54.3996i	0.994029	−	0.0660190i
$825$		0			0
$826$	74.4643	+	373.792i	0.0901505	+	0.452533i
$827$	−667.626			−0.807287			−0.403643	−	0.914916i	$-0.632256\pi$
$827$	−667.626			−0.807287			−0.403643	+	0.914916i	$0.632256\pi$
$828$		0			0
$829$			1520.09i			1.83365i	0.399291	+	0.916824i	$0.369256\pi$
$829$			1520.09i			1.83365i	−0.399291	+	0.916824i	$0.630744\pi$
$830$	−216.701	−	1087.78i	−0.261085	−	1.31058i
$831$		0			0
$832$	−1135.05	+	874.089i	−1.36424	+	1.05059i
$833$	−221.814	−	128.065i	−0.266284	−	0.153739i
$834$		0			0
$835$	−1618.94	+	934.698i	−1.93886	+	1.11940i
$836$	171.464	−	223.724i	0.205100	−	0.267612i
$837$		0			0
$838$	371.941	+	126.137i	0.443844	+	0.150522i
$839$	719.550	−	415.432i	0.857628	−	0.495152i	−0.00558927	−	0.999984i	$-0.501779\pi$
$839$	719.550	−	415.432i	0.857628	−	0.495152i	0.863217	+	0.504833i	$0.168446\pi$
$840$		0			0
$841$	337.850	−	585.173i	0.401724	−	0.695806i
$842$	−125.976	−	143.565i	−0.149616	−	0.170504i
$843$		0			0
$844$	−33.4026	−	4.37786i	−0.0395765	−	0.00518704i
$845$	2309.18			2.73275
$846$		0			0
$847$	−553.149			−0.653069
$848$	274.965	−	275.603i	0.324251	−	0.325003i
$849$		0			0
$850$	−282.601	−	322.057i	−0.332472	−	0.378891i
$851$	−35.8497	+	62.0934i	−0.0421265	+	0.0729653i
$852$		0			0
$853$	1145.57	−	661.395i	1.34299	−	0.775376i	0.355745	−	0.934583i	$-0.384227\pi$
$853$	1145.57	−	661.395i	1.34299	−	0.775376i	0.987245	+	0.159207i	$0.0508939\pi$
$854$	117.893	−	347.633i	0.138048	−	0.407064i
$855$		0			0
$856$	−103.587	−	154.738i	−0.121013	−	0.180769i
$857$	−439.392	+	253.683i	−0.512709	+	0.296013i	−0.733947	−	0.679207i	$-0.762324\pi$
$857$	−439.392	+	253.683i	−0.512709	+	0.296013i	0.221237	+	0.975220i	$0.428990\pi$
$858$		0			0
$859$	−169.177	−	97.6744i	−0.196947	−	0.113707i	0.398284	−	0.917262i	$-0.369606\pi$
$859$	−169.177	−	97.6744i	−0.196947	−	0.113707i	−0.595230	+	0.803555i	$0.702939\pi$
$860$	636.778	+	1534.81i	0.740440	+	1.78466i
$861$		0			0
$862$	−465.378	+	92.7094i	−0.539881	+	0.107551i
$863$		−	772.315i		−	0.894919i	−0.894304	−	0.447460i	$-0.852329\pi$
$863$		−	772.315i		−	0.894919i	0.894304	−	0.447460i	$-0.147671\pi$
$864$		0			0
$865$	950.075			1.09835
$866$	−70.6026	−	354.407i	−0.0815272	−	0.409246i
$867$		0			0
$868$	73.8361	−	30.6340i	0.0850646	−	0.0352926i
$869$	8.66017	−	14.9999i	0.00996567	−	0.0172611i
$870$		0			0
$871$	−314.590	−	544.885i	−0.361182	−	0.625586i
$872$	−555.272	+	371.719i	−0.636780	+	0.426283i
$873$		0			0
$874$	−26.7308	−	9.06526i	−0.0305844	−	0.0103721i
$875$	26.2134	+	45.4030i	0.0299582	+	0.0518891i
$876$		0			0
$877$	879.427	+	507.737i	1.00277	+	0.578948i	0.909066	−	0.416653i	$-0.136797\pi$
$877$	879.427	+	507.737i	1.00277	+	0.578948i	0.0937011	+	0.995600i	$0.470130\pi$
$878$	−279.678	+	245.415i	−0.318540	+	0.279516i
$879$		0			0
$880$	1221.20	−	1224.03i	1.38773	−	1.39095i
$881$			743.678i			0.844130i	0.906566	+	0.422065i	$0.138695\pi$
$881$			743.678i			0.844130i	−0.906566	+	0.422065i	$0.861305\pi$
$882$		0			0
$883$		−	483.566i		−	0.547640i	−0.961781	−	0.273820i	$-0.911713\pi$
$883$		−	483.566i		−	0.547640i	0.961781	−	0.273820i	$-0.0882872\pi$
$884$	−106.721	+	814.265i	−0.120725	+	0.921114i
$885$		0			0
$886$	423.949	−	372.011i	0.478498	−	0.419877i
$887$	1096.70	+	633.179i	1.23641	+	0.713844i	0.968359	−	0.249560i	$-0.0802860\pi$
$887$	1096.70	+	633.179i	1.23641	+	0.713844i	0.268054	+	0.963404i	$0.413619\pi$
$888$		0			0
$889$	−24.5172	−	42.4651i	−0.0275784	−	0.0477672i
$890$	47.6178	−	140.411i	0.0535032	−	0.157765i
$891$		0			0
$892$	1378.92	+	1056.81i	1.54587	+	1.18477i
$893$	−84.0887	−	145.646i	−0.0941643	−	0.163097i
$894$		0			0
$895$	272.725	−	472.373i	0.304720	−	0.527791i
$896$	−190.007	−	556.040i	−0.212062	−	0.620581i
$897$		0			0
$898$	−311.327	+	62.0206i	−0.346690	+	0.0690652i
$899$	55.9702			0.0622583
$900$		0			0
$901$		−	223.168i		−	0.247690i
$902$	2136.36	−	425.592i	2.36847	−	0.471831i
$903$		0			0
$904$	14.0433	+	211.446i	0.0155346	+	0.233901i
$905$	−1428.03	−	824.474i	−1.57794	−	0.911021i
$906$		0			0
$907$	−1283.82	+	741.212i	−1.41545	+	0.817213i	−0.995895	−	0.0905144i	$-0.971149\pi$
$907$	−1283.82	+	741.212i	−1.41545	+	0.817213i	−0.419560	+	0.907728i	$0.637816\pi$
$908$	187.104	+	143.398i	0.206062	+	0.157928i
$909$		0			0
$910$	−459.005	+	1353.47i	−0.504401	+	1.48733i
$911$	982.545	−	567.273i	1.07853	−	0.622692i	0.148034	−	0.988982i	$-0.452706\pi$
$911$	982.545	−	567.273i	1.07853	−	0.622692i	0.930501	+	0.366290i	$0.119372\pi$
$912$		0			0
$913$	619.660	−	1073.28i	0.678708	−	1.17556i
$914$	640.947	−	562.423i	0.701255	−	0.615343i
$915$		0			0
$916$	−689.679	−	90.3918i	−0.752925	−	0.0986810i
$917$	−1100.33			−1.19992
$918$		0			0
$919$	−51.6557			−0.0562086			−0.0281043	−	0.999605i	$-0.508947\pi$
$919$	−51.6557			−0.0562086			−0.0281043	+	0.999605i	$0.508947\pi$
$920$	−155.354	−	76.4442i	−0.168863	−	0.0830916i
$921$		0			0
$922$	−610.423	+	535.639i	−0.662064	+	0.580953i
$923$	−669.462	+	1159.54i	−0.725311	+	1.25628i
$924$		0			0
$925$	466.010	−	269.051i	0.503794	−	0.290866i
$926$	−1354.77	−	459.446i	−1.46304	−	0.496162i
$927$		0			0
$928$	26.3141	−	410.579i	0.0283557	−	0.442435i
$929$	781.777	−	451.359i	0.841525	−	0.485855i	−0.0162571	−	0.999868i	$-0.505175\pi$
$929$	781.777	−	451.359i	0.841525	−	0.485855i	0.857782	+	0.514013i	$0.171842\pi$
$930$		0			0
$931$	109.666	+	63.3158i	0.117794	+	0.0680084i
$932$	−191.076	−	460.543i	−0.205017	−	0.494145i
$933$		0			0
$934$	−163.731	−	821.887i	−0.175301	−	0.879965i
$935$		−	991.158i		−	1.06006i
$936$		0			0
$937$	1400.55			1.49471			0.747356	−	0.664424i	$-0.231323\pi$
$937$	1400.55			1.49471			0.747356	+	0.664424i	$0.231323\pi$
$938$	253.095	−	50.4199i	0.269824	−	0.0537526i
$939$		0			0
$940$	−395.336	−	952.866i	−0.420571	−	1.01369i
$941$	607.305	−	1051.88i	0.645383	−	1.11784i	−0.338830	−	0.940848i	$-0.610031\pi$
$941$	607.305	−	1051.88i	0.645383	−	1.11784i	0.984213	−	0.176989i	$-0.0566356\pi$
$942$		0			0
$943$	−109.067	−	188.910i	−0.115660	−	0.200329i
$944$	−172.648	−	641.360i	−0.182890	−	0.679407i
$945$		0			0
$946$	−596.295	+	1758.30i	−0.630333	+	1.85867i
$947$	9.83190	+	17.0293i	0.0103821	+	0.0179824i	0.871170	−	0.490982i	$-0.163362\pi$
$947$	9.83190	+	17.0293i	0.0103821	+	0.0179824i	−0.860788	+	0.508964i	$0.830029\pi$
$948$		0			0
$949$	−1044.65	−	603.132i	−1.10079	−	0.635544i
$950$	139.720	+	159.227i	0.147073	+	0.167607i
$951$		0			0
$952$	−302.233	−	148.719i	−0.317471	−	0.156217i
$953$			1678.28i			1.76105i	0.473997	+	0.880526i	$0.342811\pi$
$953$			1678.28i			1.76105i	−0.473997	+	0.880526i	$0.657189\pi$
$954$		0			0
$955$		−	1772.38i		−	1.85589i
$956$	−510.732	−	66.9384i	−0.534238	−	0.0700192i
$957$		0			0
$958$	41.3519	+	47.1253i	0.0431648	+	0.0491913i
$959$	−504.434	−	291.235i	−0.526000	−	0.303686i
$960$		0			0
$961$	471.024	+	815.838i	0.490140	+	0.848947i
$962$	−976.723	−	331.238i	−1.01530	−	0.344322i
$963$		0			0
$964$	−832.605	−	638.115i	−0.863698	−	0.661945i
$965$	−1023.63	−	1772.98i	−1.06076	−	1.83729i
$966$		0			0
$967$	122.729	−	212.572i	0.126917	−	0.219827i	−0.795564	−	0.605870i	$-0.792825\pi$
$967$	122.729	−	212.572i	0.126917	−	0.219827i	0.922481	+	0.386043i	$0.126158\pi$
$968$	961.831	−	63.8805i	0.993627	−	0.0659923i
$969$		0			0
$970$	−394.695	−	1981.27i	−0.406902	−	2.04255i
$971$	91.7515			0.0944918			0.0472459	−	0.998883i	$-0.484956\pi$
$971$	91.7515			0.0944918			0.0472459	+	0.998883i	$0.484956\pi$
$972$		0			0
$973$		−	697.718i		−	0.717079i
$974$	61.3370	+	307.896i	0.0629743	+	0.316115i
$975$		0			0
$976$	−164.850	+	618.088i	−0.168903	+	0.633287i
$977$	1148.46	+	663.066i	1.17550	+	0.678675i	0.954969	−	0.296705i	$-0.0958877\pi$
$977$	1148.46	+	663.066i	1.17550	+	0.678675i	0.220531	+	0.975380i	$0.429221\pi$
$978$		0			0
$979$	143.470	−	82.8325i	0.146548	−	0.0846093i
$980$	616.530	+	472.514i	0.629113	+	0.482157i
$981$		0			0
$982$	57.3271	+	19.4414i	0.0583779	+	0.0197978i
$983$	−1197.01	+	691.093i	−1.21771	+	0.703045i	−0.964427	−	0.264348i	$-0.914843\pi$
$983$	−1197.01	+	691.093i	−1.21771	+	0.703045i	−0.253282	+	0.967393i	$0.581510\pi$
$984$		0			0
$985$	−740.089	+	1281.87i	−0.751359	+	1.30139i
$986$	−155.554	−	177.272i	−0.157762	−	0.179789i
$987$		0			0
$988$	52.7632	−	402.577i	0.0534040	−	0.407466i
$989$	185.922			0.187990
$990$		0			0
$991$	−1113.50			−1.12362			−0.561808	−	0.827267i	$-0.689894\pi$
$991$	−1113.50			−1.12362			−0.561808	+	0.827267i	$0.689894\pi$
$992$	−124.850	+	61.7942i	−0.125857	+	0.0622925i
$993$		0			0
$994$	−362.220	−	412.792i	−0.364407	−	0.415284i
$995$	−716.704	+	1241.37i	−0.720306	+	1.24761i
$996$		0			0
$997$	603.984	−	348.711i	0.605802	−	0.349760i	−0.165519	−	0.986207i	$-0.552930\pi$
$997$	603.984	−	348.711i	0.605802	−	0.349760i	0.771321	+	0.636447i	$0.219597\pi$
$998$	68.3524	−	201.551i	0.0684894	−	0.201955i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.j.a.125.11		44
3.2	odd	2		72.3.j.a.5.12	✓	44
4.3	odd	2		864.3.n.a.17.19		44
8.3	odd	2		864.3.n.a.17.4		44
8.5	even	2	inner	216.3.j.a.125.5		44
9.2	odd	6	inner	216.3.j.a.197.5		44
9.4	even	3		648.3.h.a.485.5		44
9.5	odd	6		648.3.h.a.485.40		44
9.7	even	3		72.3.j.a.29.18	yes	44
12.11	even	2		288.3.n.a.113.12		44
24.5	odd	2		72.3.j.a.5.18	yes	44
24.11	even	2		288.3.n.a.113.11		44
36.7	odd	6		288.3.n.a.209.11		44
36.11	even	6		864.3.n.a.305.4		44
36.23	even	6		2592.3.h.a.1457.37		44
36.31	odd	6		2592.3.h.a.1457.8		44
72.5	odd	6		648.3.h.a.485.6		44
72.11	even	6		864.3.n.a.305.19		44
72.13	even	6		648.3.h.a.485.39		44
72.29	odd	6	inner	216.3.j.a.197.11		44
72.43	odd	6		288.3.n.a.209.12		44
72.59	even	6		2592.3.h.a.1457.7		44
72.61	even	6		72.3.j.a.29.12	yes	44
72.67	odd	6		2592.3.h.a.1457.38		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.12	✓	44	3.2	odd	2
72.3.j.a.5.18	yes	44	24.5	odd	2
72.3.j.a.29.12	yes	44	72.61	even	6
72.3.j.a.29.18	yes	44	9.7	even	3
216.3.j.a.125.5		44	8.5	even	2	inner
216.3.j.a.125.11		44	1.1	even	1	trivial
216.3.j.a.197.5		44	9.2	odd	6	inner
216.3.j.a.197.11		44	72.29	odd	6	inner
288.3.n.a.113.11		44	24.11	even	2
288.3.n.a.113.12		44	12.11	even	2
288.3.n.a.209.11		44	36.7	odd	6
288.3.n.a.209.12		44	72.43	odd	6
648.3.h.a.485.5		44	9.4	even	3
648.3.h.a.485.6		44	72.5	odd	6
648.3.h.a.485.39		44	72.13	even	6
648.3.h.a.485.40		44	9.5	odd	6
864.3.n.a.17.4		44	8.3	odd	2
864.3.n.a.17.19		44	4.3	odd	2
864.3.n.a.305.4		44	36.11	even	6
864.3.n.a.305.19		44	72.11	even	6
2592.3.h.a.1457.7		44	72.59	even	6
2592.3.h.a.1457.8		44	36.31	odd	6
2592.3.h.a.1457.37		44	36.23	even	6
2592.3.h.a.1457.38		44	72.67	odd	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.390748 + 1.96146i) q^{2} +(-3.69463 + 1.53287i) q^{4} +(3.47699 - 6.02232i) q^{5} +(2.29534 + 3.97565i) q^{7} +(-4.45034 - 6.64790i) q^{8} +O(q^{10})\)	\(q+(0.390748 + 1.96146i) q^{2} +(-3.69463 + 1.53287i) q^{4} +(3.47699 - 6.02232i) q^{5} +(2.29534 + 3.97565i) q^{7} +(-4.45034 - 6.64790i) q^{8} +(13.1711 + 4.46675i) q^{10} +(7.77003 + 13.4581i) q^{11} +(19.3855 + 11.1922i) q^{13} +(-6.90117 + 6.05570i) q^{14} +(11.3006 - 11.3268i) q^{16} -9.17185i q^{17} +4.53461i q^{19} +(-3.61474 + 27.5800i) q^{20} +(-23.3614 + 20.4993i) q^{22} +(2.69533 + 1.55615i) q^{23} +(-11.6789 - 20.2284i) q^{25} +(-14.3782 + 42.3973i) q^{26} +(-14.5746 - 11.1701i) q^{28} +(-6.42846 - 11.1344i) q^{29} +(-2.17666 + 3.77008i) q^{31} +(26.6327 + 17.7397i) q^{32} +(17.9902 - 3.58388i) q^{34} +31.9235 q^{35} +23.0374i q^{37} +(-8.89444 + 1.77189i) q^{38} +(-55.5095 + 3.68669i) q^{40} +(-60.6979 - 35.0439i) q^{41} +(51.7345 - 29.8689i) q^{43} +(-49.3370 - 37.8122i) q^{44} +(-1.99913 + 5.89484i) q^{46} +(-32.1187 + 18.5438i) q^{47} +(13.9628 - 24.1843i) q^{49} +(35.1136 - 30.8118i) q^{50} +(-88.7787 - 11.6357i) q^{52} +24.3319 q^{53} +108.065 q^{55} +(16.2147 - 32.9522i) q^{56} +(19.3278 - 16.9599i) q^{58} +(20.7560 - 35.9504i) q^{59} +(-34.6245 + 19.9904i) q^{61} +(-8.24537 - 2.79626i) q^{62} +(-24.3890 + 59.1707i) q^{64} +(134.807 - 77.8306i) q^{65} +(-24.3421 - 14.0539i) q^{67} +(14.0593 + 33.8866i) q^{68} +(12.4741 + 62.6167i) q^{70} +59.8148i q^{71} -53.8883 q^{73} +(-45.1869 + 9.00183i) q^{74} +(-6.95098 - 16.7537i) q^{76} +(-35.6698 + 61.7819i) q^{77} +(-0.557280 - 0.965237i) q^{79} +(-28.9215 - 107.439i) q^{80} +(45.0196 - 132.750i) q^{82} +(-39.8750 - 69.0655i) q^{83} +(-55.2358 - 31.8904i) q^{85} +(78.8017 + 89.8037i) q^{86} +(54.8887 - 111.547i) q^{88} -10.6605i q^{89} +102.760i q^{91} +(-12.3436 - 1.61780i) q^{92} +(-48.9231 - 55.7536i) q^{94} +(27.3089 + 15.7668i) q^{95} +(-72.6276 - 125.795i) q^{97} +(52.8923 + 17.9375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

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