LMFDB - Embedded newform 216.3.u.a.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(41,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("216.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.u (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.2
Character	$\chi$	$=$	216.65
Dual form			216.3.u.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.83313 - 0.986589i) q^{3} +(-0.258656 + 0.710651i) q^{5} +(0.583550 - 3.30948i) q^{7} +(7.05328 + 5.59028i) q^{9} +O(q^{10})$	\(q+(-2.83313 - 0.986589i) q^{3} +(-0.258656 + 0.710651i) q^{5} +(0.583550 - 3.30948i) q^{7} +(7.05328 + 5.59028i) q^{9} +(-2.88727 - 7.93270i) q^{11} +(-17.2862 + 14.5049i) q^{13} +(1.43393 - 1.75818i) q^{15} +(-14.1752 + 8.18408i) q^{17} +(-13.9823 + 24.2180i) q^{19} +(-4.91837 + 8.80047i) q^{21} +(-12.5271 + 2.20887i) q^{23} +(18.7130 + 15.7021i) q^{25} +(-14.4676 - 22.7967i) q^{27} +(-11.9834 + 14.2812i) q^{29} +(-2.56209 - 14.5303i) q^{31} +(0.353692 + 25.3229i) q^{33} +(2.20095 + 1.27072i) q^{35} +(11.0410 + 19.1236i) q^{37} +(63.2846 - 24.0398i) q^{39} +(-35.1298 - 41.8661i) q^{41} +(-28.7132 + 10.4507i) q^{43} +(-5.79711 + 3.56647i) q^{45} +(-21.1991 - 3.73797i) q^{47} +(35.4328 + 12.8965i) q^{49} +(48.2347 - 9.20144i) q^{51} -59.3670i q^{53} +6.38419 q^{55} +(63.5070 - 54.8182i) q^{57} +(17.4521 - 47.9492i) q^{59} +(0.441832 - 2.50575i) q^{61} +(22.6169 - 20.0805i) q^{63} +(-5.83672 - 16.0363i) q^{65} +(-31.0457 + 26.0504i) q^{67} +(37.6702 + 6.10110i) q^{69} +(54.0385 - 31.1992i) q^{71} +(-33.8962 + 58.7100i) q^{73} +(-37.5249 - 62.9481i) q^{75} +(-27.9380 + 4.92622i) q^{77} +(33.0560 + 27.7373i) q^{79} +(18.4976 + 78.8596i) q^{81} +(-33.9331 + 40.4398i) q^{83} +(-2.14952 - 12.1905i) q^{85} +(48.0403 - 28.6380i) q^{87} +(42.5429 + 24.5622i) q^{89} +(37.9162 + 65.6728i) q^{91} +(-7.07673 + 43.6941i) q^{93} +(-13.5940 - 16.2007i) q^{95} +(170.372 - 62.0104i) q^{97} +(23.9813 - 72.0922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q+O(q^{10}) $ 108 * q	$ 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) $ 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{18}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−2.83313	−	0.986589i	−0.944378	−	0.328863i
$3$	−2.83313	−	0.986589i	−0.944378	−	0.328863i
$4$		0			0
$5$	−0.258656	+	0.710651i	−0.0517312	+	0.142130i	−0.962867	−	0.269976i	$-0.912984\pi$
$5$	−0.258656	+	0.710651i	−0.0517312	+	0.142130i	0.911136	+	0.412106i	$0.135207\pi$
$6$		0			0
$7$	0.583550	−	3.30948i	0.0833644	−	0.472783i	−0.914333	−	0.404963i	$-0.867285\pi$
$7$	0.583550	−	3.30948i	0.0833644	−	0.472783i	0.997698	−	0.0678201i	$-0.0216044\pi$
$8$		0			0
$9$	7.05328	+	5.59028i	0.783698	+	0.621142i
$10$		0			0
$11$	−2.88727	−	7.93270i	−0.262479	−	0.721155i	−0.998999	−	0.0447389i	$-0.985754\pi$
$11$	−2.88727	−	7.93270i	−0.262479	−	0.721155i	0.736520	−	0.676416i	$-0.236468\pi$
$12$		0			0
$13$	−17.2862	+	14.5049i	−1.32971	+	1.11576i	−0.345566	+	0.938394i	$0.612313\pi$
$13$	−17.2862	+	14.5049i	−1.32971	+	1.11576i	−0.984145	+	0.177366i	$0.943243\pi$
$14$		0			0
$15$	1.43393	−	1.75818i	0.0955951	−	0.117212i
$16$		0			0
$17$	−14.1752	+	8.18408i	−0.833838	+	0.481417i	−0.855165	−	0.518356i	$-0.826544\pi$
$17$	−14.1752	+	8.18408i	−0.833838	+	0.481417i	0.0213270	+	0.999773i	$0.493211\pi$
$18$		0			0
$19$	−13.9823	+	24.2180i	−0.735910	+	1.27463i	0.218412	+	0.975857i	$0.429912\pi$
$19$	−13.9823	+	24.2180i	−0.735910	+	1.27463i	−0.954323	+	0.298778i	$0.903421\pi$
$20$		0			0
$21$	−4.91837	+	8.80047i	−0.234208	+	0.419070i
$22$		0			0
$23$	−12.5271	+	2.20887i	−0.544657	+	0.0960377i	−0.439205	−	0.898387i	$-0.644740\pi$
$23$	−12.5271	+	2.20887i	−0.544657	+	0.0960377i	−0.105452	+	0.994424i	$0.533629\pi$
$24$		0			0
$25$	18.7130	+	15.7021i	0.748520	+	0.628082i
$26$		0			0
$27$	−14.4676	−	22.7967i	−0.535836	−	0.844322i
$28$		0			0
$29$	−11.9834	+	14.2812i	−0.413220	+	0.492457i	−0.932004	−	0.362449i	$-0.881941\pi$
$29$	−11.9834	+	14.2812i	−0.413220	+	0.492457i	0.518783	+	0.854906i	$0.326385\pi$
$30$		0			0
$31$	−2.56209	−	14.5303i	−0.0826480	−	0.468720i	−0.997839	−	0.0657006i	$-0.979072\pi$
$31$	−2.56209	−	14.5303i	−0.0826480	−	0.468720i	0.915191	−	0.403020i	$-0.132039\pi$
$32$		0			0
$33$	0.353692	+	25.3229i	0.0107179	+	0.767362i
$34$		0			0
$35$	2.20095	+	1.27072i	0.0628842	+	0.0363062i
$36$		0			0
$37$	11.0410	+	19.1236i	0.298406	+	0.516854i	0.975771	−	0.218792i	$-0.0702117\pi$
$37$	11.0410	+	19.1236i	0.298406	+	0.516854i	−0.677365	+	0.735647i	$0.736878\pi$
$38$		0			0
$39$	63.2846	−	24.0398i	1.62268	−	0.616406i
$40$		0			0
$41$	−35.1298	−	41.8661i	−0.856825	−	1.02112i	−0.999508	−	0.0313564i	$-0.990017\pi$
$41$	−35.1298	−	41.8661i	−0.856825	−	1.02112i	0.142683	−	0.989768i	$-0.454427\pi$
$42$		0			0
$43$	−28.7132	+	10.4507i	−0.667748	+	0.243041i	−0.653578	−	0.756859i	$-0.726733\pi$
$43$	−28.7132	+	10.4507i	−0.667748	+	0.243041i	−0.0141702	+	0.999900i	$0.504511\pi$
$44$		0			0
$45$	−5.79711	+	3.56647i	−0.128825	+	0.0792548i
$46$		0			0
$47$	−21.1991	−	3.73797i	−0.451044	−	0.0795313i	−0.0564885	−	0.998403i	$-0.517990\pi$
$47$	−21.1991	−	3.73797i	−0.451044	−	0.0795313i	−0.394556	+	0.918872i	$0.629102\pi$
$48$		0			0
$49$	35.4328	+	12.8965i	0.723119	+	0.263194i
$50$		0			0
$51$	48.2347	−	9.20144i	0.945778	−	0.180420i
$52$		0			0
$53$		−	59.3670i		−	1.12013i	−0.828448	−	0.560066i	$-0.810776\pi$
$53$		−	59.3670i		−	1.12013i	0.828448	−	0.560066i	$-0.189224\pi$
$54$		0			0
$55$	6.38419			0.116076
$56$		0			0
$57$	63.5070	−	54.8182i	1.11416	−	0.961722i
$58$		0			0
$59$	17.4521	−	47.9492i	0.295798	−	0.812699i	−0.699392	−	0.714738i	$-0.746546\pi$
$59$	17.4521	−	47.9492i	0.295798	−	0.812699i	0.995190	−	0.0979608i	$-0.0312320\pi$
$60$		0			0
$61$	0.441832	−	2.50575i	0.00724315	−	0.0410779i	−0.980972	−	0.194149i	$-0.937805\pi$
$61$	0.441832	−	2.50575i	0.00724315	−	0.0410779i	0.988215	+	0.153071i	$0.0489165\pi$
$62$		0			0
$63$	22.6169	−	20.0805i	0.358998	−	0.318738i
$64$		0			0
$65$	−5.83672	−	16.0363i	−0.0897957	−	0.246712i
$66$		0			0
$67$	−31.0457	+	26.0504i	−0.463368	+	0.388812i	−0.844369	−	0.535763i	$-0.820024\pi$
$67$	−31.0457	+	26.0504i	−0.463368	+	0.388812i	0.381000	+	0.924575i	$0.375580\pi$
$68$		0			0
$69$	37.6702	+	6.10110i	0.545945	+	0.0884217i
$70$		0			0
$71$	54.0385	−	31.1992i	0.761106	−	0.439425i	−0.0685868	−	0.997645i	$-0.521849\pi$
$71$	54.0385	−	31.1992i	0.761106	−	0.439425i	0.829693	+	0.558220i	$0.188516\pi$
$72$		0			0
$73$	−33.8962	+	58.7100i	−0.464332	+	0.804246i	−0.999171	−	0.0407074i	$-0.987039\pi$
$73$	−33.8962	+	58.7100i	−0.464332	+	0.804246i	0.534839	+	0.844954i	$0.320372\pi$
$74$		0			0
$75$	−37.5249	−	62.9481i	−0.500332	−	0.839308i
$76$		0			0
$77$	−27.9380	+	4.92622i	−0.362831	+	0.0639769i
$78$		0			0
$79$	33.0560	+	27.7373i	0.418430	+	0.351105i	0.827566	−	0.561369i	$-0.189725\pi$
$79$	33.0560	+	27.7373i	0.418430	+	0.351105i	−0.409135	+	0.912474i	$0.634170\pi$
$80$		0			0
$81$	18.4976	+	78.8596i	0.228365	+	0.973576i
$82$		0			0
$83$	−33.9331	+	40.4398i	−0.408832	+	0.487227i	−0.930692	−	0.365804i	$-0.880794\pi$
$83$	−33.9331	+	40.4398i	−0.408832	+	0.487227i	0.521860	+	0.853031i	$0.325238\pi$
$84$		0			0
$85$	−2.14952	−	12.1905i	−0.0252884	−	0.143418i
$86$		0			0
$87$	48.0403	−	28.6380i	0.552187	−	0.329172i
$88$		0			0
$89$	42.5429	+	24.5622i	0.478011	+	0.275980i	0.719587	−	0.694402i	$-0.244331\pi$
$89$	42.5429	+	24.5622i	0.478011	+	0.275980i	−0.241576	+	0.970382i	$0.577664\pi$
$90$		0			0
$91$	37.9162	+	65.6728i	0.416662	+	0.721679i
$92$		0			0
$93$	−7.07673	+	43.6941i	−0.0760939	+	0.469829i
$94$		0			0
$95$	−13.5940	−	16.2007i	−0.143095	−	0.170533i
$96$		0			0
$97$	170.372	−	62.0104i	1.75642	−	0.639283i	0.756523	−	0.653967i	$-0.226897\pi$
$97$	170.372	−	62.0104i	1.75642	−	0.639283i	0.999892	+	0.0146843i	$0.00467431\pi$
$98$		0			0
$99$	23.9813	−	72.0922i	0.242235	−	0.728204i
$100$		0			0
$101$	−153.161	−	27.0065i	−1.51645	−	0.267391i	−0.647414	−	0.762139i	$-0.724149\pi$
$101$	−153.161	−	27.0065i	−1.51645	−	0.267391i	−0.869037	+	0.494748i	$0.835260\pi$
$102$		0			0
$103$	−172.864	−	62.9174i	−1.67829	−	0.610848i	−0.685218	−	0.728338i	$-0.740293\pi$
$103$	−172.864	−	62.9174i	−1.67829	−	0.610848i	−0.993074	+	0.117489i	$0.962515\pi$
$104$		0			0
$105$	−4.98190	−	5.77154i	−0.0474466	−	0.0549670i
$106$		0			0
$107$			127.069i			1.18756i	0.804627	+	0.593780i	$0.202365\pi$
$107$			127.069i			1.18756i	−0.804627	+	0.593780i	$0.797635\pi$
$108$		0			0
$109$	−6.77637			−0.0621685			−0.0310842	−	0.999517i	$-0.509896\pi$
$109$	−6.77637			−0.0621685			−0.0310842	+	0.999517i	$0.509896\pi$
$110$		0			0
$111$	−12.4135	−	65.0727i	−0.111834	−	0.586241i
$112$		0			0
$113$	70.6710	−	194.167i	0.625407	−	1.71829i	−0.0679420	−	0.997689i	$-0.521643\pi$
$113$	70.6710	−	194.167i	0.625407	−	1.71829i	0.693349	−	0.720602i	$-0.256134\pi$
$114$		0			0
$115$	1.67048	−	9.47374i	0.0145259	−	0.0823804i
$116$		0			0
$117$	−203.011	+	5.67212i	−1.73514	+	0.0484797i
$118$		0			0
$119$	18.8131	+	51.6885i	0.158093	+	0.434357i
$120$		0			0
$121$	38.0999	−	31.9696i	0.314875	−	0.264212i
$122$		0			0
$123$	58.2228	+	153.271i	0.473356	+	1.24611i
$124$		0			0
$125$	−32.3724	+	18.6902i	−0.258979	+	0.149522i
$126$		0			0
$127$	−76.5739	+	132.630i	−0.602944	+	1.04433i	0.389429	+	0.921057i	$0.372673\pi$
$127$	−76.5739	+	132.630i	−0.602944	+	1.04433i	−0.992373	+	0.123273i	$0.960661\pi$
$128$		0			0
$129$	91.6588	−	1.28022i	0.710534	−	0.00992421i
$130$		0			0
$131$	5.01721	−	0.884670i	0.0382994	−	0.00675321i	−0.154466	−	0.987998i	$-0.549366\pi$
$131$	5.01721	−	0.884670i	0.0382994	−	0.00675321i	0.192765	+	0.981245i	$0.438254\pi$
$132$		0			0
$133$	71.9898	+	60.4066i	0.541276	+	0.454185i
$134$		0			0
$135$	19.9426	−	4.38490i	0.147723	−	0.0324808i
$136$		0			0
$137$	−31.5083	+	37.5501i	−0.229987	+	0.274088i	−0.868680	−	0.495374i	$-0.835031\pi$
$137$	−31.5083	+	37.5501i	−0.229987	+	0.274088i	0.638693	+	0.769462i	$0.279476\pi$
$138$		0			0
$139$	−7.33099	−	41.5761i	−0.0527409	−	0.299109i	0.947015	−	0.321189i	$-0.104082\pi$
$139$	−7.33099	−	41.5761i	−0.0527409	−	0.299109i	−0.999756	+	0.0220798i	$0.992971\pi$
$140$		0			0
$141$	56.3720	+	31.5050i	0.399801	+	0.223439i
$142$		0			0
$143$	164.973	+	95.2472i	1.15366	+	0.666064i
$144$		0			0
$145$	−7.04941	−	12.2099i	−0.0486166	−	0.0842065i
$146$		0			0
$147$	−87.6623	−	71.4951i	−0.596342	−	0.486361i
$148$		0			0
$149$	−104.818	−	124.917i	−0.703475	−	0.838368i	0.289440	−	0.957196i	$-0.406531\pi$
$149$	−104.818	−	124.917i	−0.703475	−	0.838368i	−0.992915	+	0.118828i	$0.962086\pi$
$150$		0			0
$151$	−137.594	+	50.0802i	−0.911221	+	0.331657i	−0.754740	−	0.656024i	$-0.772237\pi$
$151$	−137.594	+	50.0802i	−0.911221	+	0.331657i	−0.156481	+	0.987681i	$0.550015\pi$
$152$		0			0
$153$	−145.733	−	21.5189i	−0.952505	−	0.140646i
$154$		0			0
$155$	10.9887	+	1.93760i	0.0708948	+	0.0125007i
$156$		0			0
$157$	−190.596	−	69.3713i	−1.21399	−	0.441855i	−0.345902	−	0.938271i	$-0.612427\pi$
$157$	−190.596	−	69.3713i	−1.21399	−	0.441855i	−0.868085	+	0.496415i	$0.834649\pi$
$158$		0			0
$159$	−58.5708	+	168.195i	−0.368370	+	1.05783i
$160$		0			0
$161$			42.7472i			0.265511i
$162$		0			0
$163$	7.45992			0.0457664			0.0228832	−	0.999738i	$-0.492715\pi$
$163$	7.45992			0.0457664			0.0228832	+	0.999738i	$0.492715\pi$
$164$		0			0
$165$	−18.0873	−	6.29858i	−0.109620	−	0.0381732i
$166$		0			0
$167$	−99.7352	+	274.020i	−0.597217	+	1.64084i	0.159576	+	0.987186i	$0.448987\pi$
$167$	−99.7352	+	274.020i	−0.597217	+	1.64084i	−0.756793	+	0.653655i	$0.773235\pi$
$168$		0			0
$169$	59.0761	−	335.037i	0.349563	−	1.98247i
$170$		0			0
$171$	−234.007	+	92.6518i	−1.36846	+	0.541823i
$172$		0			0
$173$	91.4538	+	251.267i	0.528635	+	1.45241i	0.860679	+	0.509148i	$0.170040\pi$
$173$	91.4538	+	251.267i	0.528635	+	1.45241i	−0.332044	+	0.943264i	$0.607738\pi$
$174$		0			0
$175$	62.8856	−	52.7673i	0.359346	−	0.301527i
$176$		0			0
$177$	−96.7503	+	118.629i	−0.546612	+	0.670218i
$178$		0			0
$179$	295.228	−	170.450i	1.64932	−	0.952235i	0.671977	−	0.740572i	$-0.265445\pi$
$179$	295.228	−	170.450i	1.64932	−	0.952235i	0.977343	−	0.211663i	$-0.0678880\pi$
$180$		0			0
$181$	23.2685	−	40.3023i	0.128555	−	0.222664i	−0.794562	−	0.607183i	$-0.792299\pi$
$181$	23.2685	−	40.3023i	0.128555	−	0.222664i	0.923117	+	0.384519i	$0.125633\pi$
$182$		0			0
$183$	−3.72392	+	6.66323i	−0.0203493	+	0.0364111i
$184$		0			0
$185$	−16.4460	+	2.89988i	−0.0888975	+	0.0156750i
$186$		0			0
$187$	105.850	+	88.8184i	0.566041	+	0.474965i
$188$		0			0
$189$	−83.8877	+	34.5771i	−0.443851	+	0.182948i
$190$		0			0
$191$	−192.955	+	229.955i	−1.01023	+	1.20395i	−0.0313560	+	0.999508i	$0.509983\pi$
$191$	−192.955	+	229.955i	−1.01023	+	1.20395i	−0.978879	+	0.204442i	$0.934462\pi$
$192$		0			0
$193$	0.892119	+	5.05946i	0.00462238	+	0.0262148i	0.987032	−	0.160525i	$-0.0513189\pi$
$193$	0.892119	+	5.05946i	0.00462238	+	0.0262148i	−0.982409	+	0.186740i	$0.940208\pi$
$194$		0			0
$195$	0.715002	+	51.1913i	0.00366668	+	0.262519i
$196$		0			0
$197$	−74.7338	−	43.1476i	−0.379359	−	0.219023i	0.298180	−	0.954510i	$-0.403620\pi$
$197$	−74.7338	−	43.1476i	−0.379359	−	0.219023i	−0.677540	+	0.735486i	$0.736954\pi$
$198$		0			0
$199$	50.9893	+	88.3161i	0.256228	+	0.443800i	0.965228	−	0.261408i	$-0.0841869\pi$
$199$	50.9893	+	88.3161i	0.256228	+	0.443800i	−0.709000	+	0.705208i	$0.750854\pi$
$200$		0			0
$201$	113.658	−	43.1750i	0.565461	−	0.214801i
$202$		0			0
$203$	40.2706	+	47.9926i	0.198377	+	0.236417i
$204$		0			0
$205$	38.8387	−	14.1361i	0.189457	−	0.0689568i
$206$		0			0
$207$	−100.705	−	54.4503i	−0.486500	−	0.263045i
$208$		0			0
$209$	232.485	+	40.9934i	1.11237	+	0.196141i
$210$		0			0
$211$	−96.2973	−	35.0494i	−0.456385	−	0.166111i	0.103590	−	0.994620i	$-0.466967\pi$
$211$	−96.2973	−	35.0494i	−0.456385	−	0.166111i	−0.559975	+	0.828509i	$0.689189\pi$
$212$		0			0
$213$	−183.879	+	35.0775i	−0.863282	+	0.164683i
$214$		0			0
$215$		−	23.1082i		−	0.107480i
$216$		0			0
$217$	−49.5829			−0.228493
$218$		0			0
$219$	153.955	−	132.892i	0.702992	−	0.606811i
$220$		0			0
$221$	126.328	−	347.082i	0.571618	−	1.57051i
$222$		0			0
$223$	73.5704	−	417.238i	0.329912	−	1.87102i	−0.142719	−	0.989763i	$-0.545584\pi$
$223$	73.5704	−	417.238i	0.329912	−	1.87102i	0.472631	−	0.881261i	$-0.343304\pi$
$224$		0			0
$225$	44.2091	+	215.362i	0.196485	+	0.957164i
$226$		0			0
$227$	−68.9646	−	189.479i	−0.303809	−	0.834708i	−0.993830	−	0.110918i	$-0.964621\pi$
$227$	−68.9646	−	189.479i	−0.303809	−	0.834708i	0.690021	−	0.723789i	$-0.257601\pi$
$228$		0			0
$229$	23.6130	−	19.8137i	0.103114	−	0.0865225i	−0.589773	−	0.807569i	$-0.700783\pi$
$229$	23.6130	−	19.8137i	0.103114	−	0.0865225i	0.692887	+	0.721046i	$0.256338\pi$
$230$		0			0
$231$	84.0122	+	13.6067i	0.363689	+	0.0589034i
$232$		0			0
$233$	106.811	−	61.6675i	0.458417	−	0.264667i	−0.252961	−	0.967476i	$-0.581405\pi$
$233$	106.811	−	61.6675i	0.458417	−	0.264667i	0.711379	+	0.702809i	$0.248071\pi$
$234$		0			0
$235$	8.13966	−	14.0983i	0.0346368	−	0.0599928i
$236$		0			0
$237$	−66.2867	−	111.196i	−0.279691	−	0.469182i
$238$		0			0
$239$	264.195	−	46.5847i	1.10542	−	0.194915i	0.408988	−	0.912540i	$-0.365882\pi$
$239$	264.195	−	46.5847i	1.10542	−	0.194915i	0.696430	+	0.717625i	$0.254771\pi$
$240$		0			0
$241$	263.512	+	221.113i	1.09341	+	0.917480i	0.996964	−	0.0778584i	$-0.0248082\pi$
$241$	263.512	+	221.113i	1.09341	+	0.917480i	0.0964455	+	0.995338i	$0.469253\pi$
$242$		0			0
$243$	25.3959	−	241.669i	0.104510	−	0.994524i
$244$		0			0
$245$	−18.3298	+	21.8446i	−0.0748156	+	0.0891617i
$246$		0			0
$247$	−109.579	−	621.451i	−0.443638	−	2.51599i
$248$		0			0
$249$	136.034	−	81.0935i	0.546323	−	0.325677i
$250$		0			0
$251$	401.828	+	231.996i	1.60091	+	0.924286i	0.991306	+	0.131580i	$0.0420050\pi$
$251$	401.828	+	231.996i	1.60091	+	0.924286i	0.609604	+	0.792706i	$0.291328\pi$
$252$		0			0
$253$	53.6914	+	92.9963i	0.212219	+	0.367574i
$254$		0			0
$255$	−5.93717	+	36.6580i	−0.0232830	+	0.143757i
$256$		0			0
$257$	134.254	+	159.998i	0.522389	+	0.622559i	0.961144	−	0.276048i	$-0.0890247\pi$
$257$	134.254	+	159.998i	0.522389	+	0.622559i	−0.438755	+	0.898607i	$0.644580\pi$
$258$		0			0
$259$	69.7322	−	25.3804i	0.269236	−	0.0979940i
$260$		0			0
$261$	−164.358	+	33.7392i	−0.629726	+	0.129269i
$262$		0			0
$263$	−261.142	−	46.0463i	−0.992935	−	0.175081i	−0.346500	−	0.938050i	$-0.612630\pi$
$263$	−261.142	−	46.0463i	−0.992935	−	0.175081i	−0.646435	+	0.762969i	$0.723741\pi$
$264$		0			0
$265$	42.1892	+	15.3556i	0.159205	+	0.0579457i
$266$		0			0
$267$	−96.2970	−	111.560i	−0.360663	−	0.417829i
$268$		0			0
$269$			505.050i			1.87751i	0.344584	+	0.938756i	$0.388020\pi$
$269$			505.050i			1.87751i	−0.344584	+	0.938756i	$0.611980\pi$
$270$		0			0
$271$	73.4358			0.270981			0.135490	−	0.990779i	$-0.456739\pi$
$271$	73.4358			0.270981			0.135490	+	0.990779i	$0.456739\pi$
$272$		0			0
$273$	−42.6296	−	223.467i	−0.156152	−	0.818562i
$274$		0			0
$275$	70.5304	−	193.781i	0.256474	−	0.704657i
$276$		0			0
$277$	74.5469	−	422.776i	0.269122	−	1.52627i	−0.487912	−	0.872893i	$-0.662241\pi$
$277$	74.5469	−	422.776i	0.269122	−	1.52627i	0.757034	−	0.653375i	$-0.226648\pi$
$278$		0			0
$279$	63.1574	−	116.809i	0.226371	−	0.418671i
$280$		0			0
$281$	34.6570	+	95.2192i	0.123334	+	0.338858i	0.985959	−	0.166986i	$-0.0534033\pi$
$281$	34.6570	+	95.2192i	0.123334	+	0.338858i	−0.862625	+	0.505844i	$0.831181\pi$
$282$		0			0
$283$	4.98672	−	4.18436i	0.0176209	−	0.0147857i	−0.633935	−	0.773387i	$-0.718561\pi$
$283$	4.98672	−	4.18436i	0.0176209	−	0.0147857i	0.651556	+	0.758601i	$0.274117\pi$
$284$		0			0
$285$	22.5301	+	59.3103i	0.0790531	+	0.208106i
$286$		0			0
$287$	−159.055	+	91.8305i	−0.554199	+	0.319967i
$288$		0			0
$289$	−10.5416	+	18.2586i	−0.0364762	+	0.0631787i
$290$		0			0
$291$	−543.866	+	7.59632i	−1.86896	+	0.0261042i
$292$		0			0
$293$	−51.1859	+	9.02545i	−0.174696	+	0.0308036i	−0.260312	−	0.965525i	$-0.583825\pi$
$293$	−51.1859	+	9.02545i	−0.174696	+	0.0308036i	0.0856159	+	0.996328i	$0.472714\pi$
$294$		0			0
$295$	29.5611	+	24.8047i	0.100207	+	0.0840838i
$296$		0			0
$297$	−139.068	+	180.587i	−0.468241	+	0.608038i
$298$		0			0
$299$	184.507	−	219.887i	0.617081	−	0.735409i
$300$		0			0
$301$	17.8309	+	101.124i	0.0592390	+	0.335961i
$302$		0			0
$303$	407.283	+	227.621i	1.34417	+	0.751223i
$304$		0			0
$305$	1.66643	+	0.962116i	0.00546372	+	0.00315448i
$306$		0			0
$307$	143.423	+	248.416i	0.467176	+	0.809172i	0.999297	−	0.0374964i	$-0.0119383\pi$
$307$	143.423	+	248.416i	0.467176	+	0.809172i	−0.532121	+	0.846668i	$0.678605\pi$
$308$		0			0
$309$	427.673	+	348.799i	1.38406	+	1.12880i
$310$		0			0
$311$	−316.696	−	377.424i	−1.01832	−	1.21358i	−0.976736	−	0.214447i	$-0.931205\pi$
$311$	−316.696	−	377.424i	−1.01832	−	1.21358i	−0.0415808	−	0.999135i	$-0.513239\pi$
$312$		0			0
$313$	−113.878	+	41.4483i	−0.363829	+	0.132423i	−0.517464	−	0.855705i	$-0.673124\pi$
$313$	−113.878	+	41.4483i	−0.363829	+	0.132423i	0.153636	+	0.988128i	$0.450902\pi$
$314$		0			0
$315$	8.42024	+	21.2666i	0.0267309	+	0.0675131i
$316$		0			0
$317$	216.405	+	38.1580i	0.682666	+	0.120372i	0.504217	−	0.863577i	$-0.331781\pi$
$317$	216.405	+	38.1580i	0.682666	+	0.120372i	0.178448	+	0.983949i	$0.442892\pi$
$318$		0			0
$319$	147.888	+	53.8269i	0.463599	+	0.168736i
$320$		0			0
$321$	125.365	−	360.003i	0.390545	−	1.12151i
$322$		0			0
$323$		−	457.729i		−	1.41712i
$324$		0			0
$325$	−551.234			−1.69610
$326$		0			0
$327$	19.1983	+	6.68549i	0.0587105	+	0.0204449i
$328$		0			0
$329$	−24.7415	+	67.9766i	−0.0752020	+	0.206616i
$330$		0			0
$331$	−71.2645	+	404.161i	−0.215301	+	1.22103i	0.665083	+	0.746769i	$0.268396\pi$
$331$	−71.2645	+	404.161i	−0.215301	+	1.22103i	−0.880384	+	0.474261i	$0.842715\pi$
$332$		0			0
$333$	−29.0309	+	196.607i	−0.0871797	+	0.590410i
$334$		0			0
$335$	−10.4826	−	28.8007i	−0.0312914	−	0.0859723i
$336$		0			0
$337$	−497.277	+	417.265i	−1.47560	+	1.23817i	−0.564864	+	0.825184i	$0.691071\pi$
$337$	−497.277	+	417.265i	−1.47560	+	1.23817i	−0.910735	+	0.412990i	$0.864484\pi$
$338$		0			0
$339$	−391.783	+	480.377i	−1.15570	+	1.41704i
$340$		0			0
$341$	−107.867	+	62.2772i	−0.316326	+	0.182631i
$342$		0			0
$343$	145.691	−	252.343i	0.424754	−	0.735695i
$344$		0			0
$345$	−14.0794	+	25.1923i	−0.0408098	+	0.0730211i
$346$		0			0
$347$	−392.388	+	69.1886i	−1.13080	+	0.199391i	−0.707579	−	0.706635i	$-0.750212\pi$
$347$	−392.388	+	69.1886i	−1.13080	+	0.199391i	−0.423223	+	0.906025i	$0.639101\pi$
$348$		0			0
$349$	108.191	+	90.7833i	0.310004	+	0.260124i	0.784494	−	0.620137i	$-0.212923\pi$
$349$	108.191	+	90.7833i	0.310004	+	0.260124i	−0.474490	+	0.880261i	$0.657367\pi$
$350$		0			0
$351$	580.753	+	184.219i	1.65457	+	0.524840i
$352$		0			0
$353$	−310.710	+	370.289i	−0.880197	+	1.04898i	0.118234	+	0.992986i	$0.462277\pi$
$353$	−310.710	+	370.289i	−0.880197	+	1.04898i	−0.998431	+	0.0559924i	$0.982168\pi$
$354$		0			0
$355$	8.19433	+	46.4724i	0.0230826	+	0.130908i
$356$		0			0
$357$	−2.30461	−	165.001i	−0.00645550	−	0.462188i
$358$		0			0
$359$	−46.5672	−	26.8856i	−0.129714	−	0.0748901i	0.433739	−	0.901038i	$-0.357194\pi$
$359$	−46.5672	−	26.8856i	−0.129714	−	0.0748901i	−0.563453	+	0.826148i	$0.690527\pi$
$360$		0			0
$361$	−210.509	−	364.613i	−0.583128	−	1.01001i
$362$		0			0
$363$	−139.483	+	52.9852i	−0.384251	+	0.145965i
$364$		0			0
$365$	−32.9549	−	39.2741i	−0.0902873	−	0.107600i
$366$		0			0
$367$	−529.054	+	192.560i	−1.44156	+	0.524687i	−0.940222	−	0.340562i	$-0.889383\pi$
$367$	−529.054	+	192.560i	−1.44156	+	0.524687i	−0.501343	+	0.865249i	$0.667160\pi$
$368$		0			0
$369$	−13.7375	−	491.679i	−0.0372290	−	1.33246i
$370$		0			0
$371$	−196.474	−	34.6436i	−0.529579	−	0.0933791i
$372$		0			0
$373$	389.269	+	141.682i	1.04362	+	0.379845i	0.806250	−	0.591575i	$-0.201494\pi$
$373$	389.269	+	141.682i	1.04362	+	0.379845i	0.237366	+	0.971420i	$0.423716\pi$
$374$		0			0
$375$	110.155	−	21.0136i	0.293746	−	0.0560362i
$376$		0			0
$377$		−	420.687i		−	1.11588i
$378$		0			0
$379$	495.375			1.30706			0.653529	−	0.756902i	$-0.273288\pi$
$379$	495.375			1.30706			0.653529	+	0.756902i	$0.273288\pi$
$380$		0			0
$381$	347.795	−	300.211i	0.912849	−	0.787956i
$382$		0			0
$383$	−220.564	+	605.995i	−0.575886	+	1.58223i	0.219164	+	0.975688i	$0.429667\pi$
$383$	−220.564	+	605.995i	−0.575886	+	1.58223i	−0.795049	+	0.606545i	$0.792555\pi$
$384$		0			0
$385$	3.72550	−	21.1284i	0.00967662	−	0.0548788i
$386$		0			0
$387$	−260.945	−	86.8026i	−0.674276	−	0.224296i
$388$		0			0
$389$	79.7045	+	218.986i	0.204896	+	0.562947i	0.998994	−	0.0448425i	$-0.0142786\pi$
$389$	79.7045	+	218.986i	0.204896	+	0.562947i	−0.794098	+	0.607790i	$0.792056\pi$
$390$		0			0
$391$	159.497	−	133.834i	0.407921	−	0.342287i
$392$		0			0
$393$	−15.0872	−	2.44354i	−0.0383899	−	0.00621767i
$394$		0			0
$395$	−28.2616	+	16.3169i	−0.0715485	+	0.0413085i
$396$		0			0
$397$	−175.994	+	304.831i	−0.443310	+	0.767835i	−0.997933	−	0.0642665i	$-0.979529\pi$
$397$	−175.994	+	304.831i	−0.443310	+	0.767835i	0.554623	+	0.832102i	$0.312863\pi$
$398$		0			0
$399$	−144.360	−	242.164i	−0.361805	−	0.606928i
$400$		0			0
$401$	218.176	−	38.4703i	0.544080	−	0.0959360i	0.105149	−	0.994457i	$-0.466468\pi$
$401$	218.176	−	38.4703i	0.544080	−	0.0959360i	0.438931	+	0.898521i	$0.355357\pi$
$402$		0			0
$403$	255.050	+	214.012i	0.632877	+	0.531047i
$404$		0			0
$405$	−60.8262	−	7.25217i	−0.150188	−	0.0179066i
$406$		0			0
$407$	119.824	−	142.800i	0.294407	−	0.350860i
$408$		0			0
$409$	73.1803	+	415.026i	0.178925	+	1.01473i	0.933515	+	0.358538i	$0.116725\pi$
$409$	73.1803	+	415.026i	0.178925	+	1.01473i	−0.754590	+	0.656196i	$0.772164\pi$
$410$		0			0
$411$	126.314	−	75.2987i	0.307332	−	0.183208i
$412$		0			0
$413$	−148.503	−	85.7382i	−0.359571	−	0.207598i
$414$		0			0
$415$	−19.9616	−	34.5746i	−0.0481003	−	0.0833122i
$416$		0			0
$417$	−20.2489	+	125.023i	−0.0485585	+	0.299816i
$418$		0			0
$419$	21.7857	+	25.9632i	0.0519946	+	0.0619647i	0.791415	−	0.611279i	$-0.209345\pi$
$419$	21.7857	+	25.9632i	0.0519946	+	0.0619647i	−0.739420	+	0.673244i	$0.764900\pi$
$420$		0			0
$421$	−525.190	+	191.153i	−1.24748	+	0.454046i	−0.879550	−	0.475807i	$-0.842156\pi$
$421$	−525.190	+	191.153i	−1.24748	+	0.454046i	−0.367932	+	0.929853i	$0.619934\pi$
$422$		0			0
$423$	−128.627	−	144.874i	−0.304082	−	0.342491i
$424$		0			0
$425$	−393.768	−	69.4319i	−0.926513	−	0.163369i
$426$		0			0
$427$	−8.03491	−	2.92447i	−0.0188171	−	0.00684887i
$428$		0			0
$429$	−373.420	−	432.608i	−0.870444	−	1.00841i
$430$		0			0
$431$			49.9125i			0.115806i	0.998322	+	0.0579032i	$0.0184415\pi$
$431$			49.9125i			0.115806i	−0.998322	+	0.0579032i	$0.981559\pi$
$432$		0			0
$433$	−194.509			−0.449212			−0.224606	−	0.974450i	$-0.572110\pi$
$433$	−194.509			−0.449212			−0.224606	+	0.974450i	$0.572110\pi$
$434$		0			0
$435$	7.92572	+	41.5472i	0.0182200	+	0.0955109i
$436$		0			0
$437$	121.663	−	334.267i	0.278406	−	0.764913i
$438$		0			0
$439$	16.6079	−	94.1882i	0.0378313	−	0.214552i	−0.960032	−	0.279891i	$-0.909702\pi$
$439$	16.6079	−	94.1882i	0.0378313	−	0.214552i	0.997863	+	0.0653389i	$0.0208129\pi$
$440$		0			0
$441$	177.823	+	289.042i	0.403226	+	0.655424i
$442$		0			0
$443$	−144.832	−	397.923i	−0.326935	−	0.898247i	−0.988883	−	0.148697i	$-0.952492\pi$
$443$	−144.832	−	397.923i	−0.326935	−	0.898247i	0.661948	−	0.749550i	$-0.269730\pi$
$444$		0			0
$445$	−28.4591	+	23.8800i	−0.0639531	+	0.0536630i
$446$		0			0
$447$	173.721	+	457.318i	0.388637	+	1.02308i
$448$		0			0
$449$	−419.265	+	242.063i	−0.933774	+	0.539115i	−0.888003	−	0.459837i	$-0.847908\pi$
$449$	−419.265	+	242.063i	−0.933774	+	0.539115i	−0.0457709	+	0.998952i	$0.514574\pi$
$450$		0			0
$451$	−230.682	+	399.553i	−0.511491	+	0.885928i
$452$		0			0
$453$	439.232	−	6.13486i	0.969606	−	0.0135427i
$454$		0			0
$455$	−56.4777	+	9.95854i	−0.124127	+	0.0218869i
$456$		0			0
$457$	358.118	+	300.497i	0.783628	+	0.657542i	0.944160	−	0.329489i	$-0.106876\pi$
$457$	358.118	+	300.497i	0.783628	+	0.657542i	−0.160531	+	0.987031i	$0.551321\pi$
$458$		0			0
$459$	391.651	+	204.745i	0.853271	+	0.446067i
$460$		0			0
$461$	424.591	−	506.008i	0.921022	−	1.09763i	−0.0739286	−	0.997264i	$-0.523554\pi$
$461$	424.591	−	506.008i	0.921022	−	1.09763i	0.994950	−	0.100368i	$-0.0320019\pi$
$462$		0			0
$463$	73.1284	+	414.732i	0.157945	+	0.895748i	0.956044	+	0.293223i	$0.0947278\pi$
$463$	73.1284	+	414.732i	0.157945	+	0.895748i	−0.798100	+	0.602526i	$0.794161\pi$
$464$		0			0
$465$	−29.2208	−	16.3308i	−0.0628404	−	0.0351200i
$466$		0			0
$467$	−651.750	−	376.288i	−1.39561	−	0.805756i	−0.401682	−	0.915779i	$-0.631574\pi$
$467$	−651.750	−	376.288i	−1.39561	−	0.805756i	−0.993929	+	0.110023i	$0.964908\pi$
$468$		0			0
$469$	68.0966	+	117.947i	0.145195	+	0.251486i
$470$		0			0
$471$	471.543	+	384.578i	1.00115	+	0.816514i
$472$		0			0
$473$	165.805	+	197.599i	0.350540	+	0.417757i
$474$		0			0
$475$	−641.924	+	233.641i	−1.35142	+	0.491876i
$476$		0			0
$477$	331.878	−	418.732i	0.695761	−	0.877845i
$478$		0			0
$479$	−458.812	−	80.9009i	−0.957854	−	0.168895i	−0.327196	−	0.944957i	$-0.606104\pi$
$479$	−458.812	−	80.9009i	−0.957854	−	0.168895i	−0.630658	+	0.776061i	$0.717215\pi$
$480$		0			0
$481$	−468.244	−	170.427i	−0.973479	−	0.354318i
$482$		0			0
$483$	42.1739	−	121.108i	0.0873166	−	0.250742i
$484$		0			0
$485$			137.115i			0.282711i
$486$		0			0
$487$	329.233			0.676042			0.338021	−	0.941139i	$-0.390242\pi$
$487$	329.233			0.676042			0.338021	+	0.941139i	$0.390242\pi$
$488$		0			0
$489$	−21.1349	−	7.35987i	−0.0432207	−	0.0150509i
$490$		0			0
$491$	−58.9581	+	161.986i	−0.120078	+	0.329911i	−0.985140	−	0.171754i	$-0.945057\pi$
$491$	−58.9581	+	161.986i	−0.120078	+	0.329911i	0.865062	+	0.501665i	$0.167279\pi$
$492$		0			0
$493$	52.9886	−	300.513i	0.107482	−	0.609560i
$494$		0			0
$495$	45.0295	+	35.6894i	0.0909687	+	0.0720998i
$496$		0			0
$497$	−71.7187	−	197.046i	−0.144303	−	0.396470i
$498$		0			0
$499$	401.698	−	337.065i	0.805007	−	0.675481i	−0.144404	−	0.989519i	$-0.546126\pi$
$499$	401.698	−	337.065i	0.805007	−	0.675481i	0.949410	+	0.314038i	$0.101682\pi$
$500$		0			0
$501$	552.909	−	677.938i	1.10361	−	1.35317i
$502$		0			0
$503$	121.808	−	70.3262i	0.242164	−	0.139813i	−0.374007	−	0.927426i	$-0.622016\pi$
$503$	121.808	−	70.3262i	0.242164	−	0.139813i	0.616171	+	0.787612i	$0.288683\pi$
$504$		0			0
$505$	58.8083	−	101.859i	0.116452	−	0.201701i
$506$		0			0
$507$	−497.915	+	890.921i	−0.982080	+	1.75724i
$508$		0			0
$509$	−167.676	+	29.5659i	−0.329423	+	0.0580862i	−0.335914	−	0.941893i	$-0.609045\pi$
$509$	−167.676	+	29.5659i	−0.329423	+	0.0580862i	0.00649053	+	0.999979i	$0.497934\pi$
$510$		0			0
$511$	174.519	+	146.439i	0.341525	+	0.286574i
$512$		0			0
$513$	754.381	−	31.6264i	1.47053	−	0.0616498i
$514$		0			0
$515$	89.4246	−	106.572i	0.173640	−	0.206936i
$516$		0			0
$517$	31.5552	+	178.959i	0.0610352	+	0.346148i
$518$		0			0
$519$	−11.2032	−	802.101i	−0.0215860	−	1.54547i
$520$		0			0
$521$	−286.746	−	165.553i	−0.550375	−	0.317759i	0.198898	−	0.980020i	$-0.436264\pi$
$521$	−286.746	−	165.553i	−0.550375	−	0.317759i	−0.749273	+	0.662261i	$0.769597\pi$
$522$		0			0
$523$	248.864	+	431.044i	0.475838	+	0.824176i	0.999617	−	0.0276781i	$-0.00881134\pi$
$523$	248.864	+	431.044i	0.475838	+	0.824176i	−0.523778	+	0.851855i	$0.675478\pi$
$524$		0			0
$525$	−230.223	+	87.4545i	−0.438520	+	0.166580i
$526$		0			0
$527$	155.236	+	185.003i	0.294565	+	0.351049i
$528$		0			0
$529$	−345.048	+	125.587i	−0.652265	+	0.237405i
$530$		0			0
$531$	391.144	−	240.638i	0.736618	−	0.453178i
$532$		0			0
$533$	1214.53	+	214.154i	2.27866	+	0.401789i
$534$		0			0
$535$	−90.3017	−	32.8671i	−0.168788	−	0.0614339i
$536$		0			0
$537$	−1004.59	+	191.639i	−1.87074	+	0.356869i
$538$		0			0
$539$		−	318.314i		−	0.590563i
$540$		0			0
$541$	372.605			0.688733			0.344367	−	0.938835i	$-0.388094\pi$
$541$	372.605			0.688733			0.344367	+	0.938835i	$0.388094\pi$
$542$		0			0
$543$	−105.685	+	91.2252i	−0.194631	+	0.168002i
$544$		0			0
$545$	1.75275	−	4.81563i	0.00321605	−	0.00883602i
$546$		0			0
$547$	116.127	−	658.586i	0.212297	−	1.20400i	−0.673239	−	0.739425i	$-0.735097\pi$
$547$	116.127	−	658.586i	0.212297	−	1.20400i	0.885536	−	0.464571i	$-0.153792\pi$
$548$		0			0
$549$	17.1242	−	15.2038i	0.0311917	−	0.0276937i
$550$		0			0
$551$	−178.309	−	489.899i	−0.323609	−	0.889109i
$552$		0			0
$553$	111.086	−	93.2120i	0.200878	−	0.168557i
$554$		0			0
$555$	49.4548	+	8.00974i	0.0891078	+	0.0144320i
$556$		0			0
$557$	−326.274	+	188.374i	−0.585770	+	0.338195i	−0.763423	−	0.645899i	$-0.776483\pi$
$557$	−326.274	+	188.374i	−0.585770	+	0.338195i	0.177653	+	0.984093i	$0.443150\pi$
$558$		0			0
$559$	344.756	−	597.135i	0.616737	−	1.06822i
$560$		0			0
$561$	−212.259	−	356.064i	−0.378358	−	0.634696i
$562$		0			0
$563$	692.827	−	122.164i	1.23060	−	0.216988i	0.479716	−	0.877424i	$-0.340740\pi$
$563$	692.827	−	122.164i	1.23060	−	0.216988i	0.750882	+	0.660436i	$0.229629\pi$
$564$		0			0
$565$	119.705	+	100.445i	0.211868	+	0.177778i
$566$		0			0
$567$	271.779	−	15.1988i	0.479327	−	0.0268057i
$568$		0			0
$569$	261.878	−	312.094i	0.460243	−	0.548496i	−0.485149	−	0.874431i	$-0.661235\pi$
$569$	261.878	−	312.094i	0.460243	−	0.548496i	0.945392	+	0.325935i	$0.105679\pi$
$570$		0			0
$571$	113.307	+	642.596i	0.198436	+	1.12539i	0.907440	+	0.420182i	$0.138034\pi$
$571$	113.307	+	642.596i	0.198436	+	1.12539i	−0.709004	+	0.705205i	$0.750855\pi$
$572$		0			0
$573$	773.537	−	461.125i	1.34998	−	0.804755i
$574$		0			0
$575$	−269.103	−	155.367i	−0.468006	−	0.270203i
$576$		0			0
$577$	−538.144	−	932.094i	−0.932659	−	1.61541i	−0.778755	−	0.627328i	$-0.784149\pi$
$577$	−538.144	−	932.094i	−0.932659	−	1.61541i	−0.153904	−	0.988086i	$-0.549185\pi$
$578$		0			0
$579$	2.46412	−	15.2143i	0.00425581	−	0.0262768i
$580$		0			0
$581$	114.033	+	135.899i	0.196271	+	0.233906i
$582$		0			0
$583$	−470.941	+	171.408i	−0.807789	+	0.294011i
$584$		0			0
$585$	48.4791	−	145.737i	0.0828703	−	0.249123i
$586$		0			0
$587$	531.377	+	93.6961i	0.905242	+	0.159619i	0.606842	−	0.794822i	$-0.292436\pi$
$587$	531.377	+	93.6961i	0.905242	+	0.159619i	0.298400	+	0.954441i	$0.403547\pi$
$588$		0			0
$589$	387.720	+	141.119i	0.658268	+	0.239590i
$590$		0			0
$591$	169.162	+	195.974i	0.286230	+	0.331598i
$592$		0			0
$593$		−	357.622i		−	0.603073i	−0.953455	−	0.301536i	$-0.902501\pi$
$593$		−	357.622i		−	0.603073i	0.953455	−	0.301536i	$-0.0974995\pi$
$594$		0			0
$595$	−41.5986			−0.0699136
$596$		0			0
$597$	−57.3278	−	300.517i	−0.0960265	−	0.503378i
$598$		0			0
$599$	−367.828	+	1010.60i	−0.614070	+	1.68714i	0.106980	+	0.994261i	$0.465882\pi$
$599$	−367.828	+	1010.60i	−0.614070	+	1.68714i	−0.721050	+	0.692883i	$0.756340\pi$
$600$		0			0
$601$	67.6118	−	383.446i	0.112499	−	0.638013i	−0.875459	−	0.483292i	$-0.839441\pi$
$601$	67.6118	−	383.446i	0.112499	−	0.638013i	0.987958	−	0.154721i	$-0.0494479\pi$
$602$		0			0
$603$	−364.603	+	10.1870i	−0.604648	+	0.0168939i
$604$		0			0
$605$	12.8645	+	35.3449i	0.0212636	+	0.0584213i
$606$		0			0
$607$	−36.2664	+	30.4311i	−0.0597469	+	0.0501336i	−0.672172	−	0.740395i	$-0.734639\pi$
$607$	−36.2664	+	30.4311i	−0.0597469	+	0.0501336i	0.612425	+	0.790529i	$0.290194\pi$
$608$		0			0
$609$	−66.7429	−	175.700i	−0.109594	−	0.288506i
$610$		0			0
$611$	420.671	−	242.875i	0.688496	−	0.397504i
$612$		0			0
$613$	495.834	−	858.810i	0.808865	−	1.40099i	−0.104786	−	0.994495i	$-0.533416\pi$
$613$	495.834	−	858.810i	0.808865	−	1.40099i	0.913651	−	0.406500i	$-0.133251\pi$
$614$		0			0
$615$	−123.982	+	1.73169i	−0.201597	+	0.00281575i
$616$		0			0
$617$	−644.903	+	113.714i	−1.04522	+	0.184301i	−0.669792	−	0.742549i	$-0.733617\pi$
$617$	−644.903	+	113.714i	−1.04522	+	0.184301i	−0.375432	+	0.926850i	$0.622505\pi$
$618$		0			0
$619$	569.579	+	477.933i	0.920160	+	0.772106i	0.974025	−	0.226443i	$-0.0727096\pi$
$619$	569.579	+	477.933i	0.920160	+	0.772106i	−0.0538648	+	0.998548i	$0.517154\pi$
$620$		0			0
$621$	231.592	+	253.620i	0.372934	+	0.408405i
$622$		0			0
$623$	106.114	−	126.462i	0.170327	−	0.202988i
$624$		0			0
$625$	101.138	+	573.584i	0.161821	+	0.917734i
$626$		0			0
$627$	−618.218	−	345.507i	−0.985993	−	0.551048i
$628$		0			0
$629$	−313.018	−	180.721i	−0.497645	−	0.287315i
$630$		0			0
$631$	−431.802	−	747.903i	−0.684314	−	1.18527i	−0.973652	−	0.228040i	$-0.926768\pi$
$631$	−431.802	−	747.903i	−0.684314	−	1.18527i	0.289338	−	0.957227i	$-0.406565\pi$
$632$		0			0
$633$	238.244	+	194.305i	0.376372	+	0.306960i
$634$		0			0
$635$	−74.4473	−	88.7228i	−0.117240	−	0.139721i
$636$		0			0
$637$	−799.562	+	291.017i	−1.25520	+	0.456855i
$638$		0			0
$639$	555.561	+	82.0339i	0.869422	+	0.128379i
$640$		0			0
$641$	−4.97964	−	0.878046i	−0.00776856	−	0.00136981i	0.169763	−	0.985485i	$-0.445700\pi$
$641$	−4.97964	−	0.878046i	−0.00776856	−	0.00136981i	−0.177531	+	0.984115i	$0.556811\pi$
$642$		0			0
$643$	845.246	+	307.645i	1.31454	+	0.478452i	0.901703	−	0.432355i	$-0.142317\pi$
$643$	845.246	+	307.645i	1.31454	+	0.478452i	0.412832	+	0.910807i	$0.364540\pi$
$644$		0			0
$645$	−22.7983	+	65.4686i	−0.0353462	+	0.101502i
$646$		0			0
$647$			1018.11i			1.57358i	0.617219	+	0.786791i	$0.288259\pi$
$647$			1018.11i			1.57358i	−0.617219	+	0.786791i	$0.711741\pi$
$648$		0			0
$649$	−430.756			−0.663723
$650$		0			0
$651$	140.475	+	48.9180i	0.215783	+	0.0751428i
$652$		0			0
$653$	194.625	−	534.729i	0.298048	−	0.818880i	−0.696778	−	0.717287i	$-0.745384\pi$
$653$	194.625	−	534.729i	0.298048	−	0.818880i	0.994826	−	0.101594i	$-0.0323941\pi$
$654$		0			0
$655$	−0.669040	+	3.79431i	−0.00102144	+	0.00579285i
$656$		0			0
$657$	−567.285	+	224.609i	−0.863447	+	0.341870i
$658$		0			0
$659$	4.28665	+	11.7775i	0.00650477	+	0.0178717i	0.942903	−	0.333069i	$-0.108084\pi$
$659$	4.28665	+	11.7775i	0.00650477	+	0.0178717i	−0.936398	+	0.350941i	$0.885862\pi$
$660$		0			0
$661$	317.814	−	266.678i	0.480808	−	0.403446i	−0.369911	−	0.929067i	$-0.620612\pi$
$661$	317.814	−	266.678i	0.480808	−	0.403446i	0.850718	+	0.525622i	$0.176167\pi$
$662$		0			0
$663$	−700.331	+	858.697i	−1.05631	+	1.29517i
$664$		0			0
$665$	−61.5486	+	35.5351i	−0.0925542	+	0.0534362i
$666$		0			0
$667$	118.572	−	205.372i	0.177769	−	0.307905i
$668$		0			0
$669$	−620.078	+	1109.51i	−0.926872	+	1.65846i
$670$		0			0
$671$	−21.1531	+	3.72986i	−0.0315247	+	0.00555866i
$672$		0			0
$673$	−54.0487	−	45.3523i	−0.0803102	−	0.0673882i	0.601749	−	0.798685i	$-0.294471\pi$
$673$	−54.0487	−	45.3523i	−0.0803102	−	0.0673882i	−0.682059	+	0.731297i	$0.738915\pi$
$674$		0			0
$675$	87.2235	−	653.765i	0.129220	−	0.968541i
$676$		0			0
$677$	−307.143	+	366.039i	−0.453683	+	0.540678i	−0.943599	−	0.331092i	$-0.892583\pi$
$677$	−307.143	+	366.039i	−0.453683	+	0.540678i	0.489916	+	0.871770i	$0.337028\pi$
$678$		0			0
$679$	−105.801	−	600.030i	−0.155819	−	0.883696i
$680$		0			0
$681$	8.44821	+	604.858i	0.0124056	+	0.888191i
$682$		0			0
$683$	274.743	+	158.623i	0.402259	+	0.232244i	0.687458	−	0.726224i	$-0.258726\pi$
$683$	274.743	+	158.623i	0.402259	+	0.232244i	−0.285199	+	0.958468i	$0.592060\pi$
$684$		0			0
$685$	−18.5352	−	32.1039i	−0.0270587	−	0.0468671i
$686$		0			0
$687$	−86.4467	+	32.8384i	−0.125832	+	0.0477997i
$688$		0			0
$689$	861.111	+	1026.23i	1.24980	+	1.48945i
$690$		0			0
$691$	−1022.89	+	372.302i	−1.48031	+	0.538788i	−0.950878	−	0.309566i	$-0.899816\pi$
$691$	−1022.89	+	372.302i	−1.48031	+	0.538788i	−0.529429	+	0.848354i	$0.677594\pi$
$692$		0			0
$693$	−224.593	−	121.435i	−0.324089	−	0.175231i
$694$		0			0
$695$	31.4423	+	5.54413i	0.0452407	+	0.00797716i
$696$		0			0
$697$	840.610	+	305.957i	1.20604	+	0.438963i
$698$		0			0
$699$	−363.451	+	69.3334i	−0.519958	+	0.0991893i
$700$		0			0
$701$		−	97.5617i		−	0.139175i	−0.997576	−	0.0695875i	$-0.977832\pi$
$701$		−	97.5617i		−	0.139175i	0.997576	−	0.0695875i	$-0.0221683\pi$
$702$		0			0
$703$	−617.515			−0.878400
$704$		0			0
$705$	−36.9700	+	31.9119i	−0.0524397	+	0.0452651i
$706$		0			0
$707$	−178.755	+	491.125i	−0.252836	+	0.694661i
$708$		0			0
$709$	−73.6524	+	417.703i	−0.103882	+	0.589144i	0.887779	+	0.460270i	$0.152247\pi$
$709$	−73.6524	+	417.703i	−0.103882	+	0.589144i	−0.991661	+	0.128874i	$0.958864\pi$
$710$		0			0
$711$	78.0942	+	380.431i	0.109837	+	0.535065i
$712$		0			0
$713$	64.1911	+	176.364i	0.0900296	+	0.247354i
$714$		0			0
$715$	−110.359	+	92.6020i	−0.154348	+	0.129513i
$716$		0			0
$717$	−794.459	−	128.671i	−1.10803	−	0.179458i
$718$		0			0
$719$	−277.619	+	160.283i	−0.386118	+	0.222925i	−0.680477	−	0.732770i	$-0.738227\pi$
$719$	−277.619	+	160.283i	−0.386118	+	0.222925i	0.294359	+	0.955695i	$0.404894\pi$
$720$		0			0
$721$	−309.099	+	535.375i	−0.428708	+	0.742545i
$722$		0			0
$723$	−528.416	−	886.419i	−0.730867	−	1.22603i
$724$		0			0
$725$	−448.490	+	79.0809i	−0.618607	+	0.109077i
$726$		0			0
$727$	−500.981	−	420.373i	−0.689108	−	0.578230i	0.229544	−	0.973298i	$-0.426276\pi$
$727$	−500.981	−	420.373i	−0.689108	−	0.578230i	−0.918652	+	0.395068i	$0.870721\pi$
$728$		0			0
$729$	−310.378	+	659.626i	−0.425759	+	0.904837i
$730$		0			0
$731$	321.487	−	383.133i	0.439790	−	0.524121i
$732$		0			0
$733$	−119.592	−	678.241i	−0.163154	−	0.925295i	−0.950947	−	0.309354i	$-0.899887\pi$
$733$	−119.592	−	678.241i	−0.163154	−	0.925295i	0.787793	−	0.615941i	$-0.211224\pi$
$734$		0			0
$735$	73.4825	−	43.8047i	0.0999761	−	0.0595982i
$736$		0			0
$737$	296.287	+	171.062i	0.402018	+	0.232105i
$738$		0			0
$739$	−319.184	−	552.843i	−0.431913	−	0.748096i	0.565125	−	0.825006i	$-0.308828\pi$
$739$	−319.184	−	552.843i	−0.431913	−	0.748096i	−0.997038	+	0.0769096i	$0.975495\pi$
$740$		0			0
$741$	−302.666	+	1868.76i	−0.408456	+	2.52194i
$742$		0			0
$743$	−170.316	−	202.975i	−0.229227	−	0.273183i	0.639155	−	0.769078i	$-0.279284\pi$
$743$	−170.316	−	202.975i	−0.229227	−	0.273183i	−0.868382	+	0.495896i	$0.834840\pi$
$744$		0			0
$745$	115.884	−	42.1783i	0.155549	−	0.0566152i
$746$		0			0
$747$	−465.409	+	95.5384i	−0.623038	+	0.127896i
$748$		0			0
$749$	420.532	+	74.1511i	0.561458	+	0.0990002i
$750$		0			0
$751$	−250.994	−	91.3545i	−0.334214	−	0.121644i	0.169462	−	0.985537i	$-0.445797\pi$
$751$	−250.994	−	91.3545i	−0.334214	−	0.121644i	−0.503675	+	0.863893i	$0.668019\pi$
$752$		0			0
$753$	−909.549	−	1053.71i	−1.20790	−	1.39936i
$754$		0			0
$755$		−	110.735i		−	0.146669i
$756$		0			0
$757$	1333.87			1.76205			0.881024	−	0.473072i	$-0.156855\pi$
$757$	1333.87			1.76205			0.881024	+	0.473072i	$0.156855\pi$
$758$		0			0
$759$	−60.3658	−	316.442i	−0.0795333	−	0.416920i
$760$		0			0
$761$	−73.6245	+	202.282i	−0.0967471	+	0.265810i	−0.978620	−	0.205677i	$-0.934060\pi$
$761$	−73.6245	+	202.282i	−0.0967471	+	0.265810i	0.881873	+	0.471487i	$0.156283\pi$
$762$		0			0
$763$	−3.95435	+	22.4262i	−0.00518264	+	0.0293922i
$764$		0			0
$765$	52.9872	−	97.9995i	0.0692643	−	0.128104i
$766$		0			0
$767$	393.817	+	1082.00i	0.513451	+	1.41069i
$768$		0			0
$769$	−110.829	+	92.9963i	−0.144121	+	0.120932i	−0.711998	−	0.702182i	$-0.752209\pi$
$769$	−110.829	+	92.9963i	−0.144121	+	0.120932i	0.567877	+	0.823113i	$0.307765\pi$
$770$		0			0
$771$	−222.507	−	585.748i	−0.288596	−	0.759726i
$772$		0			0
$773$	−399.274	+	230.521i	−0.516526	+	0.298216i	−0.735512	−	0.677512i	$-0.763058\pi$
$773$	−399.274	+	230.521i	−0.516526	+	0.298216i	0.218986	+	0.975728i	$0.429725\pi$
$774$		0			0
$775$	180.212	−	312.136i	0.232531	−	0.402756i
$776$		0			0
$777$	−222.601	+	3.10912i	−0.286487	+	0.00400144i
$778$		0			0
$779$	1505.11	−	265.392i	1.93211	−	0.340683i
$780$		0			0
$781$	−403.517	−	338.591i	−0.516667	−	0.433535i
$782$		0			0
$783$	498.936	+	66.5666i	0.637211	+	0.0850148i
$784$		0			0
$785$	98.5975	−	117.504i	0.125602	−	0.149687i
$786$		0			0
$787$	−121.532	−	689.242i	−0.154424	−	0.875784i	−0.959310	−	0.282354i	$-0.908885\pi$
$787$	−121.532	−	689.242i	−0.154424	−	0.875784i	0.804886	−	0.593430i	$-0.202226\pi$
$788$		0			0
$789$	694.421	+	388.095i	0.880128	+	0.491882i
$790$		0			0
$791$	−601.351	−	347.190i	−0.760242	−	0.438926i
$792$		0			0
$793$	28.7080	+	49.7238i	0.0362018	+	0.0627034i
$794$		0			0
$795$	−104.378	−	85.1279i	−0.131293	−	0.107079i
$796$		0			0
$797$	837.968	+	998.652i	1.05140	+	1.25301i	0.966512	+	0.256623i	$0.0826099\pi$
$797$	837.968	+	998.652i	1.05140	+	1.25301i	0.0848914	+	0.996390i	$0.472946\pi$
$798$		0			0
$799$	331.094	−	120.508i	0.414385	−	0.150824i
$800$		0			0
$801$	162.758	+	411.071i	0.203193	+	0.513197i
$802$		0			0
$803$	563.596	+	99.3773i	0.701864	+	0.123757i
$804$		0			0
$805$	−30.3783	−	11.0568i	−0.0377371	−	0.0137352i
$806$		0			0
$807$	498.277	−	1430.88i	0.617444	−	1.77308i
$808$		0			0
$809$			268.678i			0.332111i	0.986116	+	0.166055i	$0.0531031\pi$
$809$			268.678i			0.332111i	−0.986116	+	0.166055i	$0.946897\pi$
$810$		0			0
$811$	200.828			0.247630			0.123815	−	0.992305i	$-0.460487\pi$
$811$	200.828			0.247630			0.123815	+	0.992305i	$0.460487\pi$
$812$		0			0
$813$	−208.053	−	72.4510i	−0.255908	−	0.0891156i
$814$		0			0
$815$	−1.92955	+	5.30140i	−0.00236755	+	0.00650478i
$816$		0			0
$817$	148.380	−	841.502i	0.181615	−	1.02999i
$818$		0			0
$819$	−99.6954	+	675.171i	−0.121728	+	0.824384i
$820$		0			0
$821$	−268.844	−	738.643i	−0.327459	−	0.899687i	−0.988753	−	0.149560i	$-0.952214\pi$
$821$	−268.844	−	738.643i	−0.327459	−	0.899687i	0.661293	−	0.750127i	$-0.270008\pi$
$822$		0			0
$823$	−338.358	+	283.916i	−0.411127	+	0.344977i	−0.824776	−	0.565460i	$-0.808699\pi$
$823$	−338.358	+	283.916i	−0.411127	+	0.344977i	0.413648	+	0.910437i	$0.364254\pi$
$824$		0			0
$825$	−391.004	+	479.422i	−0.473944	+	0.581117i
$826$		0			0
$827$	−417.000	+	240.755i	−0.504233	+	0.291119i	−0.730460	−	0.682956i	$-0.760694\pi$
$827$	−417.000	+	240.755i	−0.504233	+	0.291119i	0.226227	+	0.974075i	$0.427361\pi$
$828$		0			0
$829$	−24.9177	+	43.1587i	−0.0300575	+	0.0520612i	−0.880663	−	0.473744i	$-0.842902\pi$
$829$	−24.9177	+	43.1587i	−0.0300575	+	0.0520612i	0.850605	+	0.525805i	$0.176236\pi$
$830$		0			0
$831$	−628.308	+	1124.23i	−0.756086	+	1.35287i
$832$		0			0
$833$	−607.815	+	107.174i	−0.729670	+	0.128660i
$834$		0			0
$835$	−168.936	−	141.754i	−0.202318	−	0.169765i
$836$		0			0
$837$	−294.176	+	268.626i	−0.351465	+	0.320939i
$838$		0			0
$839$	410.565	−	489.292i	0.489350	−	0.583185i	−0.463702	−	0.885991i	$-0.653479\pi$
$839$	410.565	−	489.292i	0.489350	−	0.583185i	0.953052	+	0.302806i	$0.0979235\pi$
$840$		0			0
$841$	85.6857	+	485.948i	0.101885	+	0.577821i
$842$		0			0
$843$	−4.24550	−	303.961i	−0.00503618	−	0.360570i
$844$		0			0
$845$	222.814	+	128.642i	0.263685	+	0.152239i
$846$		0			0
$847$	−83.5696	−	144.747i	−0.0986654	−	0.170893i
$848$		0			0
$849$	−18.2563	+	6.93499i	−0.0215033	+	0.00816842i
$850$		0			0
$851$	−180.554	−	215.175i	−0.212166	−	0.252850i
$852$		0			0
$853$	20.6728	−	7.52428i	0.0242354	−	0.00882096i	−0.329874	−	0.944025i	$-0.607006\pi$
$853$	20.6728	−	7.52428i	0.0242354	−	0.00882096i	0.354109	+	0.935204i	$0.384784\pi$
$854$		0			0
$855$	−5.31592	−	190.262i	−0.00621745	−	0.222529i
$856$		0			0
$857$	−1377.81	−	242.946i	−1.60772	−	0.283484i	−0.703545	−	0.710650i	$-0.748401\pi$
$857$	−1377.81	−	242.946i	−1.60772	−	0.283484i	−0.904173	+	0.427166i	$0.859512\pi$
$858$		0			0
$859$	−14.9330	−	5.43516i	−0.0173841	−	0.00632731i	0.333313	−	0.942816i	$-0.391833\pi$
$859$	−14.9330	−	5.43516i	−0.0173841	−	0.00632731i	−0.350698	+	0.936489i	$0.614055\pi$
$860$		0			0
$861$	541.223	−	103.246i	0.628598	−	0.119914i
$862$		0			0
$863$		−	285.988i		−	0.331388i	−0.986177	−	0.165694i	$-0.947014\pi$
$863$		−	285.988i		−	0.331388i	0.986177	−	0.165694i	$-0.0529864\pi$
$864$		0			0
$865$	−202.218			−0.233779
$866$		0			0
$867$	47.8796	−	41.3289i	0.0552245	−	0.0476689i
$868$		0			0
$869$	124.590	−	342.308i	0.143372	−	0.393911i
$870$		0			0
$871$	158.805	−	900.628i	0.182325	−	1.03402i
$872$		0			0
$873$	1548.34	+	515.051i	1.77358	+	0.589978i
$874$		0			0
$875$	42.9639	+	118.042i	0.0491017	+	0.134906i
$876$		0			0
$877$	597.399	−	501.277i	0.681185	−	0.571582i	−0.235168	−	0.971955i	$-0.575564\pi$
$877$	597.399	−	501.277i	0.681185	−	0.571582i	0.916352	+	0.400373i	$0.131119\pi$
$878$		0			0
$879$	153.921	+	24.9291i	0.175109	+	0.0283608i
$880$		0			0
$881$	655.943	−	378.709i	0.744544	−	0.429863i	−0.0791750	−	0.996861i	$-0.525229\pi$
$881$	655.943	−	378.709i	0.744544	−	0.429863i	0.823719	+	0.566998i	$0.191895\pi$
$882$		0			0
$883$	335.762	−	581.557i	0.380252	−	0.658615i	−0.610846	−	0.791749i	$-0.709171\pi$
$883$	335.762	−	581.557i	0.380252	−	0.658615i	0.991098	+	0.133134i	$0.0425041\pi$
$884$		0			0
$885$	−59.2785	−	99.4397i	−0.0669813	−	0.112361i
$886$		0			0
$887$	687.739	−	121.267i	0.775355	−	0.136716i	0.228050	−	0.973649i	$-0.426765\pi$
$887$	687.739	−	121.267i	0.775355	−	0.136716i	0.547305	+	0.836934i	$0.315654\pi$
$888$		0			0
$889$	394.251	+	330.816i	0.443477	+	0.372122i
$890$		0			0
$891$	572.162	−	374.425i	0.642158	−	0.420230i
$892$		0			0
$893$	386.938	−	461.135i	0.433301	−	0.516389i
$894$		0			0
$895$	44.7680	+	253.892i	0.0500202	+	0.283678i
$896$		0			0
$897$	−739.672	+	440.937i	−0.824607	+	0.491568i
$898$		0			0
$899$	238.214	+	137.533i	0.264976	+	0.152984i
$900$		0			0
$901$	485.864	+	841.542i	0.539250	+	0.934008i
$902$		0			0
$903$	49.2507	−	304.090i	0.0545412	−	0.336755i
$904$		0			0
$905$	22.6223	+	26.9602i	0.0249970	+	0.0297903i
$906$		0			0
$907$	−63.4316	+	23.0872i	−0.0699356	+	0.0254545i	−0.376751	−	0.926315i	$-0.622959\pi$
$907$	−63.4316	+	23.0872i	−0.0699356	+	0.0254545i	0.306815	+	0.951769i	$0.400737\pi$
$908$		0			0
$909$	−929.317	−	1046.70i	−1.02235	−	1.15148i
$910$		0			0
$911$	864.718	+	152.473i	0.949197	+	0.167369i	0.626752	−	0.779219i	$-0.284384\pi$
$911$	864.718	+	152.473i	0.949197	+	0.167369i	0.322445	+	0.946588i	$0.395495\pi$
$912$		0			0
$913$	418.771	+	152.420i	0.458676	+	0.166944i
$914$		0			0
$915$	−3.77202	−	4.36989i	−0.00412242	−	0.00477584i
$916$		0			0
$917$		−	17.1206i		−	0.0186702i
$918$		0			0
$919$	−512.424			−0.557589			−0.278794	−	0.960351i	$-0.589935\pi$
$919$	−512.424			−0.557589			−0.278794	+	0.960351i	$0.589935\pi$
$920$		0			0
$921$	−161.252	−	845.294i	−0.175083	−	0.917801i
$922$		0			0
$923$	−481.583	+	1323.14i	−0.521758	+	1.43352i
$924$		0			0
$925$	−93.6696	+	531.227i	−0.101264	+	0.574299i
$926$		0			0
$927$	−867.534	−	1410.13i	−0.935851	−	1.52118i
$928$		0			0
$929$	−190.451	−	523.261i	−0.205007	−	0.563251i	0.793995	−	0.607924i	$-0.207998\pi$
$929$	−190.451	−	523.261i	−0.205007	−	0.563251i	−0.999002	+	0.0446729i	$0.985775\pi$
$930$		0			0
$931$	−807.760	+	677.791i	−0.867626	+	0.728025i
$932$		0			0
$933$	524.880	+	1381.74i	0.562573	+	1.48097i
$934$		0			0
$935$	−90.4975	+	52.2488i	−0.0967888	+	0.0558810i
$936$		0			0
$937$	880.267	−	1524.67i	0.939453	−	1.62718i	0.172959	−	0.984929i	$-0.444667\pi$
$937$	880.267	−	1524.67i	0.939453	−	1.62718i	0.766494	−	0.642251i	$-0.221999\pi$
$938$		0			0
$939$	363.525	−	5.07745i	0.387141	−	0.00540729i
$940$		0			0
$941$	−459.051	+	80.9431i	−0.487833	+	0.0860182i	−0.412154	−	0.911114i	$-0.635224\pi$
$941$	−459.051	+	80.9431i	−0.487833	+	0.0860182i	−0.0756790	+	0.997132i	$0.524112\pi$
$942$		0			0
$943$	532.552	+	446.864i	0.564742	+	0.473875i
$944$		0			0
$945$	−2.87422	−	68.5585i	−0.00304150	−	0.0725487i
$946$		0			0
$947$	−713.699	+	850.554i	−0.753642	+	0.898156i	−0.997428	−	0.0716733i	$-0.977166\pi$
$947$	−713.699	+	850.554i	−0.753642	+	0.898156i	0.243786	+	0.969829i	$0.421611\pi$
$948$		0			0
$949$	−265.643	−	1506.54i	−0.279919	−	1.58750i
$950$		0			0
$951$	−575.458	−	321.610i	−0.605108	−	0.338180i
$952$		0			0
$953$	51.8224	+	29.9197i	0.0543782	+	0.0313953i	0.526943	−	0.849901i	$-0.323338\pi$
$953$	51.8224	+	29.9197i	0.0543782	+	0.0313953i	−0.472564	+	0.881296i	$0.656672\pi$
$954$		0			0
$955$	−113.509	−	196.603i	−0.118857	−	0.205867i
$956$		0			0
$957$	−365.882	−	298.404i	−0.382322	−	0.311812i
$958$		0			0
$959$	105.885	+	126.188i	0.110411	+	0.131583i
$960$		0			0
$961$	698.479	−	254.225i	0.726825	−	0.264543i
$962$		0			0
$963$	−710.351	+	896.253i	−0.737643	+	0.930689i
$964$		0			0
$965$	−3.82626	−	0.674673i	−0.00396504	−	0.000699143i
$966$		0			0
$967$	572.099	+	208.227i	0.591623	+	0.215333i	0.620443	−	0.784251i	$-0.286953\pi$
$967$	572.099	+	208.227i	0.591623	+	0.215333i	−0.0288201	+	0.999585i	$0.509175\pi$
$968$		0			0
$969$	−451.591	+	1296.81i	−0.466038	+	1.33829i
$970$		0			0
$971$			30.2090i			0.0311113i	0.999879	+	0.0155556i	$0.00495171\pi$
$971$			30.2090i			0.0311113i	−0.999879	+	0.0155556i	$0.995048\pi$
$972$		0			0
$973$	−141.873			−0.145810
$974$		0			0
$975$	1561.72	+	543.841i	1.60176	+	0.557786i
$976$		0			0
$977$	223.451	−	613.927i	0.228712	−	0.628380i	−0.771255	−	0.636526i	$-0.780371\pi$
$977$	223.451	−	613.927i	0.228712	−	0.628380i	0.999967	+	0.00814601i	$0.00259298\pi$
$978$		0			0
$979$	72.0116	−	408.398i	0.0735563	−	0.417158i
$980$		0			0
$981$	−47.7956	−	37.8818i	−0.0487213	−	0.0386155i
$982$		0			0
$983$	427.204	+	1173.73i	0.434592	+	1.19403i	0.942964	+	0.332894i	$0.108025\pi$
$983$	427.204	+	1173.73i	0.434592	+	1.19403i	−0.508372	+	0.861137i	$0.669753\pi$
$984$		0			0
$985$	49.9932	−	41.9493i	0.0507545	−	0.0425881i
$986$		0			0
$987$	137.161	−	168.177i	0.138967	−	0.170392i
$988$		0			0
$989$	336.609	−	194.341i	0.340353	−	0.196503i
$990$		0			0
$991$	−796.030	+	1378.76i	−0.803259	+	1.39129i	0.114201	+	0.993458i	$0.463569\pi$
$991$	−796.030	+	1378.76i	−0.803259	+	1.39129i	−0.917460	+	0.397828i	$0.869764\pi$
$992$		0			0
$993$	600.643	−	1074.73i	0.604877	−	1.08231i
$994$		0			0
$995$	−75.9506	+	13.3921i	−0.0763323	+	0.0134594i
$996$		0			0
$997$	753.763	+	632.482i	0.756031	+	0.634385i	0.937090	−	0.349087i	$-0.113508\pi$
$997$	753.763	+	632.482i	0.756031	+	0.634385i	−0.181060	+	0.983472i	$0.557953\pi$
$998$		0			0
$999$	276.218	−	528.371i	0.276495	−	0.528900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.65.2	✓	108
4.3	odd	2		432.3.bc.d.65.17		108
27.5	odd	18	inner	216.3.u.a.113.2	yes	108
108.59	even	18		432.3.bc.d.113.17		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.65.2	✓	108	1.1	even	1	trivial
216.3.u.a.113.2	yes	108	27.5	odd	18	inner
432.3.bc.d.65.17		108	4.3	odd	2
432.3.bc.d.113.17		108	108.59	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.u (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.83313 - 0.986589i) q^{3} +(-0.258656 + 0.710651i) q^{5} +(0.583550 - 3.30948i) q^{7} +(7.05328 + 5.59028i) q^{9} +O(q^{10})\)	\(q+(-2.83313 - 0.986589i) q^{3} +(-0.258656 + 0.710651i) q^{5} +(0.583550 - 3.30948i) q^{7} +(7.05328 + 5.59028i) q^{9} +(-2.88727 - 7.93270i) q^{11} +(-17.2862 + 14.5049i) q^{13} +(1.43393 - 1.75818i) q^{15} +(-14.1752 + 8.18408i) q^{17} +(-13.9823 + 24.2180i) q^{19} +(-4.91837 + 8.80047i) q^{21} +(-12.5271 + 2.20887i) q^{23} +(18.7130 + 15.7021i) q^{25} +(-14.4676 - 22.7967i) q^{27} +(-11.9834 + 14.2812i) q^{29} +(-2.56209 - 14.5303i) q^{31} +(0.353692 + 25.3229i) q^{33} +(2.20095 + 1.27072i) q^{35} +(11.0410 + 19.1236i) q^{37} +(63.2846 - 24.0398i) q^{39} +(-35.1298 - 41.8661i) q^{41} +(-28.7132 + 10.4507i) q^{43} +(-5.79711 + 3.56647i) q^{45} +(-21.1991 - 3.73797i) q^{47} +(35.4328 + 12.8965i) q^{49} +(48.2347 - 9.20144i) q^{51} -59.3670i q^{53} +6.38419 q^{55} +(63.5070 - 54.8182i) q^{57} +(17.4521 - 47.9492i) q^{59} +(0.441832 - 2.50575i) q^{61} +(22.6169 - 20.0805i) q^{63} +(-5.83672 - 16.0363i) q^{65} +(-31.0457 + 26.0504i) q^{67} +(37.6702 + 6.10110i) q^{69} +(54.0385 - 31.1992i) q^{71} +(-33.8962 + 58.7100i) q^{73} +(-37.5249 - 62.9481i) q^{75} +(-27.9380 + 4.92622i) q^{77} +(33.0560 + 27.7373i) q^{79} +(18.4976 + 78.8596i) q^{81} +(-33.9331 + 40.4398i) q^{83} +(-2.14952 - 12.1905i) q^{85} +(48.0403 - 28.6380i) q^{87} +(42.5429 + 24.5622i) q^{89} +(37.9162 + 65.6728i) q^{91} +(-7.07673 + 43.6941i) q^{93} +(-13.5940 - 16.2007i) q^{95} +(170.372 - 62.0104i) q^{97} +(23.9813 - 72.0922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 108 * q	\( 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) \) 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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