LMFDB - Embedded newform 216.3.j.a.125.13

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			125.13
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.467688 + 1.94455i) q^{2} +(-3.56254 + 1.81888i) q^{4} +(1.89538 - 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +O(q^{10})$	\(q+(0.467688 + 1.94455i) q^{2} +(-3.56254 + 1.81888i) q^{4} +(1.89538 - 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +(7.27021 + 2.15029i) q^{10} +(-3.47103 - 6.01200i) q^{11} +(-14.6939 - 8.48351i) q^{13} +(16.5537 - 15.7218i) q^{14} +(9.38332 - 12.9597i) q^{16} +22.9919i q^{17} -21.7334i q^{19} +(-0.781157 + 15.1429i) q^{20} +(10.0673 - 9.56132i) q^{22} +(13.7369 + 7.93101i) q^{23} +(5.31504 + 9.20592i) q^{25} +(9.62445 - 32.5406i) q^{26} +(38.3137 + 24.8366i) q^{28} +(-6.57213 - 11.3833i) q^{29} +(3.45597 - 5.98592i) q^{31} +(29.5892 + 12.1852i) q^{32} +(-44.7088 + 10.7530i) q^{34} -43.2712 q^{35} -1.75177i q^{37} +(42.2616 - 10.1644i) q^{38} +(-29.8115 + 5.56317i) q^{40} +(-33.1748 - 19.1535i) q^{41} +(10.9120 - 6.30005i) q^{43} +(23.3008 + 15.1046i) q^{44} +(-8.99764 + 30.4213i) q^{46} +(28.8738 - 16.6703i) q^{47} +(-40.6498 + 70.4076i) q^{49} +(-15.4156 + 14.6409i) q^{50} +(67.7780 + 3.49637i) q^{52} +1.96807 q^{53} -26.3157 q^{55} +(-30.3770 + 86.1186i) q^{56} +(19.0616 - 18.1036i) q^{58} +(-10.5216 + 18.2239i) q^{59} +(48.0654 - 27.7506i) q^{61} +(13.2562 + 3.92076i) q^{62} +(-9.85628 + 63.2365i) q^{64} +(-55.7011 + 32.1590i) q^{65} +(-75.4627 - 43.5684i) q^{67} +(-41.8195 - 81.9093i) q^{68} +(-20.2374 - 84.1429i) q^{70} -38.7491i q^{71} +31.7926 q^{73} +(3.40640 - 0.819283i) q^{74} +(39.5305 + 77.4259i) q^{76} +(-39.6214 + 68.6263i) q^{77} +(-68.7491 - 119.077i) q^{79} +(-24.7603 - 55.3681i) q^{80} +(21.7294 - 73.4679i) q^{82} +(-33.5423 - 58.0970i) q^{83} +(75.4800 + 43.5784i) q^{85} +(17.3542 + 18.2725i) q^{86} +(-18.4740 + 52.3737i) q^{88} +159.426i q^{89} +193.677i q^{91} +(-63.3638 - 3.26866i) q^{92} +(45.9201 + 48.3499i) q^{94} +(-71.3485 - 41.1931i) q^{95} +(42.5296 + 73.6635i) q^{97} +(-155.922 - 46.1168i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.467688	+	1.94455i	0.233844	+	0.972274i
$2$	0.467688	+	1.94455i	0.233844	+	0.972274i
$3$		0			0
$3$		0			0
$4$	−3.56254	+	1.81888i	−0.890634	+	0.454721i
$5$	1.89538	−	3.28290i	0.379077	−	0.656580i	−0.611851	−	0.790973i	$-0.709575\pi$
$5$	1.89538	−	3.28290i	0.379077	−	0.656580i	0.990928	+	0.134393i	$0.0429083\pi$
$6$		0			0
$7$	−5.70744	−	9.88558i	−0.815349	−	1.41223i	−0.909077	−	0.416628i	$-0.863212\pi$
$7$	−5.70744	−	9.88558i	−0.815349	−	1.41223i	0.0937277	−	0.995598i	$-0.470122\pi$
$8$	−5.20306	−	6.07685i	−0.650383	−	0.759607i
$9$		0			0
$10$	7.27021	+	2.15029i	0.727021	+	0.215029i
$11$	−3.47103	−	6.01200i	−0.315548	−	0.546545i	0.664006	−	0.747727i	$-0.268855\pi$
$11$	−3.47103	−	6.01200i	−0.315548	−	0.546545i	−0.979554	+	0.201182i	$0.935522\pi$
$12$		0			0
$13$	−14.6939	−	8.48351i	−1.13030	−	0.652578i	−0.186288	−	0.982495i	$-0.559646\pi$
$13$	−14.6939	−	8.48351i	−1.13030	−	0.652578i	−0.944010	+	0.329917i	$0.892979\pi$
$14$	16.5537	−	15.7218i	1.18241	−	1.12298i
$15$		0			0
$16$	9.38332	−	12.9597i	0.586458	−	0.809980i
$17$			22.9919i			1.35246i	0.736690	+	0.676231i	$0.236388\pi$
$17$			22.9919i			1.35246i	−0.736690	+	0.676231i	$0.763612\pi$
$18$		0			0
$19$		−	21.7334i		−	1.14386i	−0.820302	−	0.571931i	$-0.806194\pi$
$19$		−	21.7334i		−	1.14386i	0.820302	−	0.571931i	$-0.193806\pi$
$20$	−0.781157	+	15.1429i	−0.0390579	+	0.757147i
$21$		0			0
$22$	10.0673	−	9.56132i	0.457603	−	0.434605i
$23$	13.7369	+	7.93101i	0.597257	+	0.344826i	0.767962	−	0.640496i	$-0.221271\pi$
$23$	13.7369	+	7.93101i	0.597257	+	0.344826i	−0.170705	+	0.985322i	$0.554604\pi$
$24$		0			0
$25$	5.31504	+	9.20592i	0.212602	+	0.368237i
$26$	9.62445	−	32.5406i	0.370171	−	1.25156i
$27$		0			0
$28$	38.3137	+	24.8366i	1.36835	+	0.887020i
$29$	−6.57213	−	11.3833i	−0.226625	−	0.392526i	0.730181	−	0.683254i	$-0.239436\pi$
$29$	−6.57213	−	11.3833i	−0.226625	−	0.392526i	−0.956806	+	0.290728i	$0.906103\pi$
$30$		0			0
$31$	3.45597	−	5.98592i	0.111483	−	0.193094i	−0.804885	−	0.593430i	$-0.797773\pi$
$31$	3.45597	−	5.98592i	0.111483	−	0.193094i	0.916368	+	0.400336i	$0.131107\pi$
$32$	29.5892	+	12.1852i	0.924662	+	0.380789i
$33$		0			0
$34$	−44.7088	+	10.7530i	−1.31496	+	0.316265i
$35$	−43.2712			−1.23632
$36$		0			0
$37$		−	1.75177i		−	0.0473452i	−0.999720	−	0.0236726i	$-0.992464\pi$
$37$		−	1.75177i		−	0.0473452i	0.999720	−	0.0236726i	$-0.00753592\pi$
$38$	42.2616	−	10.1644i	1.11215	−	0.267485i
$39$		0			0
$40$	−29.8115	+	5.56317i	−0.745288	+	0.139079i
$41$	−33.1748	−	19.1535i	−0.809142	−	0.467159i	0.0375156	−	0.999296i	$-0.488056\pi$
$41$	−33.1748	−	19.1535i	−0.809142	−	0.467159i	−0.846658	+	0.532137i	$0.821389\pi$
$42$		0			0
$43$	10.9120	−	6.30005i	0.253768	−	0.146513i	−0.367721	−	0.929936i	$-0.619862\pi$
$43$	10.9120	−	6.30005i	0.253768	−	0.146513i	0.621488	+	0.783424i	$0.286528\pi$
$44$	23.3008	+	15.1046i	0.529563	+	0.343285i
$45$		0			0
$46$	−8.99764	+	30.4213i	−0.195601	+	0.661333i
$47$	28.8738	−	16.6703i	0.614335	−	0.354687i	−0.160325	−	0.987064i	$-0.551254\pi$
$47$	28.8738	−	16.6703i	0.614335	−	0.354687i	0.774660	+	0.632378i	$0.217921\pi$
$48$		0			0
$49$	−40.6498	+	70.4076i	−0.829589	+	1.43689i
$50$	−15.4156	+	14.6409i	−0.308312	+	0.292817i
$51$		0			0
$52$	67.7780	+	3.49637i	1.30342	+	0.0672378i
$53$	1.96807			0.0371334			0.0185667	−	0.999828i	$-0.494090\pi$
$53$	1.96807			0.0371334			0.0185667	+	0.999828i	$0.494090\pi$
$54$		0			0
$55$	−26.3157			−0.478468
$56$	−30.3770	+	86.1186i	−0.542447	+	1.53783i
$57$		0			0
$58$	19.0616	−	18.1036i	0.328648	−	0.312132i
$59$	−10.5216	+	18.2239i	−0.178332	+	0.308880i	−0.941309	−	0.337545i	$-0.890404\pi$
$59$	−10.5216	+	18.2239i	−0.178332	+	0.308880i	0.762977	+	0.646425i	$0.223737\pi$
$60$		0			0
$61$	48.0654	−	27.7506i	0.787958	−	0.454928i	−0.0512853	−	0.998684i	$-0.516332\pi$
$61$	48.0654	−	27.7506i	0.787958	−	0.454928i	0.839243	+	0.543756i	$0.182998\pi$
$62$	13.2562	+	3.92076i	0.213810	+	0.0632381i
$63$		0			0
$64$	−9.85628	+	63.2365i	−0.154004	+	0.988070i
$65$	−55.7011	+	32.1590i	−0.856939	+	0.494754i
$66$		0			0
$67$	−75.4627	−	43.5684i	−1.12631	−	0.650275i	−0.183305	−	0.983056i	$-0.558680\pi$
$67$	−75.4627	−	43.5684i	−1.12631	−	0.650275i	−0.943004	+	0.332781i	$0.892013\pi$
$68$	−41.8195	−	81.9093i	−0.614993	−	1.20455i
$69$		0			0
$70$	−20.2374	−	84.1429i	−0.289106	−	1.20204i
$71$		−	38.7491i		−	0.545762i	−0.962048	−	0.272881i	$-0.912023\pi$
$71$		−	38.7491i		−	0.545762i	0.962048	−	0.272881i	$-0.0879765\pi$
$72$		0			0
$73$	31.7926			0.435515			0.217758	−	0.976003i	$-0.430126\pi$
$73$	31.7926			0.435515			0.217758	+	0.976003i	$0.430126\pi$
$74$	3.40640	−	0.819283i	0.0460325	−	0.0110714i
$75$		0			0
$76$	39.5305	+	77.4259i	0.520138	+	1.01876i
$77$	−39.6214	+	68.6263i	−0.514564	+	0.891250i
$78$		0			0
$79$	−68.7491	−	119.077i	−0.870241	−	1.50730i	−0.861747	−	0.507338i	$-0.830629\pi$
$79$	−68.7491	−	119.077i	−0.870241	−	1.50730i	−0.00849443	−	0.999964i	$-0.502704\pi$
$80$	−24.7603	−	55.3681i	−0.309504	−	0.692101i
$81$		0			0
$82$	21.7294	−	73.4679i	0.264993	−	0.895950i
$83$	−33.5423	−	58.0970i	−0.404124	−	0.699964i	0.590095	−	0.807334i	$-0.299090\pi$
$83$	−33.5423	−	58.0970i	−0.404124	−	0.699964i	−0.994219	+	0.107370i	$0.965757\pi$
$84$		0			0
$85$	75.4800	+	43.5784i	0.888000	+	0.512687i
$86$	17.3542	+	18.2725i	0.201793	+	0.212470i
$87$		0			0
$88$	−18.4740	+	52.3737i	−0.209932	+	0.595156i
$89$			159.426i			1.79130i	0.444762	+	0.895649i	$0.353288\pi$
$89$			159.426i			1.79130i	−0.444762	+	0.895649i	$0.646712\pi$
$90$		0			0
$91$			193.677i			2.12832i
$92$	−63.3638	−	3.26866i	−0.688737	−	0.0355289i
$93$		0			0
$94$	45.9201	+	48.3499i	0.488511	+	0.514361i
$95$	−71.3485	−	41.1931i	−0.751037	−	0.433611i
$96$		0			0
$97$	42.5296	+	73.6635i	0.438450	+	0.759418i	0.997570	−	0.0696690i	$-0.0221943\pi$
$97$	42.5296	+	73.6635i	0.438450	+	0.759418i	−0.559120	+	0.829087i	$0.688861\pi$
$98$	−155.922	−	46.1168i	−1.59104	−	0.470579i
$99$		0			0
$100$	−35.6795	−	23.1290i	−0.356795	−	0.231290i
$101$	14.8145	+	25.6594i	0.146678	+	0.254053i	0.929998	−	0.367565i	$-0.119809\pi$
$101$	14.8145	+	25.6594i	0.146678	+	0.254053i	−0.783320	+	0.621619i	$0.786475\pi$
$102$		0			0
$103$	1.31615	−	2.27965i	0.0127782	−	0.0221325i	−0.859566	−	0.511025i	$-0.829266\pi$
$103$	1.31615	−	2.27965i	0.0127782	−	0.0221325i	0.872344	+	0.488893i	$0.162599\pi$
$104$	24.9001	+	133.433i	0.239424	+	1.28301i
$105$		0			0
$106$	0.920442	+	3.82700i	0.00868341	+	0.0361038i
$107$	204.119			1.90766			0.953828	−	0.300352i	$-0.0971041\pi$
$107$	204.119			1.90766			0.953828	+	0.300352i	$0.0971041\pi$
$108$		0			0
$109$		−	106.708i		−	0.978974i	−0.872011	−	0.489487i	$-0.837184\pi$
$109$		−	106.708i		−	0.978974i	0.872011	−	0.489487i	$-0.162816\pi$
$110$	−12.3075	−	51.1722i	−0.111887	−	0.465202i
$111$		0			0
$112$	−181.669	−	18.7930i	−1.62204	−	0.167795i
$113$	−65.8775	−	38.0344i	−0.582986	−	0.336587i	0.179333	−	0.983788i	$-0.442606\pi$
$113$	−65.8775	−	38.0344i	−0.582986	−	0.336587i	−0.762319	+	0.647201i	$0.775939\pi$
$114$		0			0
$115$	52.0734	−	30.0646i	0.452812	−	0.261431i
$116$	44.1183	+	28.5993i	0.380330	+	0.246546i
$117$		0			0
$118$	−40.3582	−	11.9366i	−0.342018	−	0.101158i
$119$	227.288	−	131.225i	1.90998	−	1.10273i
$120$		0			0
$121$	36.4039	−	63.0535i	0.300859	−	0.521103i
$122$	76.4420	+	80.4869i	0.626574	+	0.659729i
$123$		0			0
$124$	−1.42433	+	27.6110i	−0.0114866	+	0.222670i
$125$	135.065			1.08052
$126$		0			0
$127$	196.308			1.54573			0.772865	−	0.634570i	$-0.218823\pi$
$127$	196.308			1.54573			0.772865	+	0.634570i	$0.218823\pi$
$128$	−127.576	+	10.4089i	−0.996688	+	0.0813198i
$129$		0			0
$130$	−88.5855	−	93.2730i	−0.681427	−	0.717485i
$131$	8.60811	−	14.9097i	0.0657108	−	0.113814i	−0.831298	−	0.555827i	$-0.812402\pi$
$131$	8.60811	−	14.9097i	0.0657108	−	0.113814i	0.897009	+	0.442012i	$0.145735\pi$
$132$		0			0
$133$	−214.847	+	124.042i	−1.61539	+	0.932647i
$134$	49.4279	−	167.117i	0.368865	−	1.24714i
$135$		0			0
$136$	139.718	−	119.628i	1.02734	−	0.879618i
$137$	158.315	−	91.4032i	1.15558	−	0.667176i	0.205342	−	0.978690i	$-0.434169\pi$
$137$	158.315	−	91.4032i	1.15558	−	0.667176i	0.950242	+	0.311514i	$0.100836\pi$
$138$		0			0
$139$	−84.6463	−	48.8706i	−0.608966	−	0.351587i	0.163595	−	0.986528i	$-0.447691\pi$
$139$	−84.6463	−	48.8706i	−0.608966	−	0.351587i	−0.772561	+	0.634941i	$0.781024\pi$
$140$	154.155	−	78.7053i	1.10111	−	0.562180i
$141$		0			0
$142$	75.3495	−	18.1225i	0.530630	−	0.127623i
$143$			117.786i			0.823678i
$144$		0			0
$145$	−49.8268			−0.343633
$146$	14.8690	+	61.8222i	0.101843	+	0.423440i
$147$		0			0
$148$	3.18627	+	6.24075i	0.0215288	+	0.0421672i
$149$	−14.1349	+	24.4823i	−0.0948650	+	0.164311i	−0.909552	−	0.415590i	$-0.863575\pi$
$149$	−14.1349	+	24.4823i	−0.0948650	+	0.164311i	0.814687	+	0.579901i	$0.196909\pi$
$150$		0			0
$151$	22.1105	+	38.2965i	0.146427	+	0.253619i	0.929904	−	0.367801i	$-0.119889\pi$
$151$	22.1105	+	38.2965i	0.146427	+	0.253619i	−0.783477	+	0.621420i	$0.786556\pi$
$152$	−132.071	+	113.080i	−0.868885	+	0.743948i
$153$		0			0
$154$	−151.978	−	44.9500i	−0.986867	−	0.291883i
$155$	−13.1008	−	22.6912i	−0.0845212	−	0.146395i
$156$		0			0
$157$	199.188	+	115.001i	1.26871	+	0.732492i	0.974744	−	0.223324i	$-0.0716907\pi$
$157$	199.188	+	115.001i	1.26871	+	0.732492i	0.293968	+	0.955815i	$0.405024\pi$
$158$	199.398	−	189.377i	1.26201	−	1.19859i
$159$		0			0
$160$	96.0858	−	74.0427i	0.600536	−	0.462767i
$161$		−	181.063i		−	1.12462i
$162$		0			0
$163$			38.2483i			0.234652i	0.993093	+	0.117326i	$0.0374322\pi$
$163$			38.2483i			0.234652i	−0.993093	+	0.117326i	$0.962568\pi$
$164$	153.025	+	7.89386i	0.933077	+	0.0481333i
$165$		0			0
$166$	97.2851	−	92.3959i	0.586055	−	0.556602i
$167$	−19.3179	−	11.1532i	−0.115676	−	0.0667857i	0.441046	−	0.897485i	$-0.354608\pi$
$167$	−19.3179	−	11.1532i	−0.115676	−	0.0667857i	−0.556722	+	0.830699i	$0.687941\pi$
$168$		0			0
$169$	59.4400	+	102.953i	0.351716	+	0.609190i
$170$	−49.4392	+	167.156i	−0.290819	+	0.983268i
$171$		0			0
$172$	−27.4153	+	42.2918i	−0.159392	+	0.245883i
$173$	−63.8618	−	110.612i	−0.369143	−	0.639375i	0.620289	−	0.784374i	$-0.287015\pi$
$173$	−63.8618	−	110.612i	−0.369143	−	0.639375i	−0.989432	+	0.144999i	$0.953682\pi$
$174$		0			0
$175$	60.6706	−	105.085i	0.346689	−	0.600483i
$176$	−110.483	−	11.4291i	−0.627746	−	0.0649381i
$177$		0			0
$178$	−310.011	+	74.5614i	−1.74163	+	0.418884i
$179$	−103.043			−0.575660			−0.287830	−	0.957682i	$-0.592934\pi$
$179$	−103.043			−0.575660			−0.287830	+	0.957682i	$0.592934\pi$
$180$		0			0
$181$		−	71.5305i		−	0.395196i	−0.980283	−	0.197598i	$-0.936686\pi$
$181$		−	71.5305i		−	0.395196i	0.980283	−	0.197598i	$-0.0633141\pi$
$182$	−376.614	+	90.5803i	−2.06931	+	0.497694i
$183$		0			0
$184$	−23.2784	−	124.743i	−0.126513	−	0.677949i
$185$	−5.75089	−	3.32028i	−0.0310859	−	0.0179475i
$186$		0			0
$187$	138.227	−	79.8054i	0.739182	−	0.426767i
$188$	−72.5425	+	111.906i	−0.385865	+	0.595247i
$189$		0			0
$190$	46.7331	−	158.006i	0.245964	−	0.831611i
$191$	−150.886	+	87.1141i	−0.789979	+	0.456095i	−0.839955	−	0.542656i	$-0.817419\pi$
$191$	−150.886	+	87.1141i	−0.789979	+	0.456095i	0.0499759	+	0.998750i	$0.484086\pi$
$192$		0			0
$193$	104.945	−	181.771i	0.543759	−	0.941818i	−0.454925	−	0.890530i	$-0.650334\pi$
$193$	104.945	−	181.771i	0.543759	−	0.941818i	0.998684	−	0.0512883i	$-0.0163327\pi$
$194$	−123.352	+	117.152i	−0.635833	+	0.603879i
$195$		0			0
$196$	16.7533	−	324.767i	0.0854760	−	1.65697i
$197$	75.9883			0.385727			0.192864	−	0.981226i	$-0.438223\pi$
$197$	75.9883			0.385727			0.192864	+	0.981226i	$0.438223\pi$
$198$		0			0
$199$	−278.786			−1.40094			−0.700468	−	0.713684i	$-0.747025\pi$
$199$	−278.786			−1.40094			−0.700468	+	0.713684i	$0.747025\pi$
$200$	28.2885	−	80.1977i	0.141443	−	0.400989i
$201$		0			0
$202$	−42.9674	+	40.8080i	−0.212710	+	0.202020i
$203$	−75.0201	+	129.939i	−0.369557	+	0.640092i
$204$		0			0
$205$	−125.758	+	72.6065i	−0.613454	+	0.354178i
$206$	5.04843	+	1.49316i	0.0245070	+	0.00724836i
$207$		0			0
$208$	−247.821	+	110.824i	−1.19145	+	0.532809i
$209$	−130.661	+	75.4371i	−0.625172	+	0.360943i
$210$		0			0
$211$	132.352	+	76.4132i	0.627259	+	0.362148i	0.779690	−	0.626166i	$-0.215377\pi$
$211$	132.352	+	76.4132i	0.627259	+	0.362148i	−0.152431	+	0.988314i	$0.548710\pi$
$212$	−7.01131	+	3.57969i	−0.0330722	+	0.0168853i
$213$		0			0
$214$	95.4641	+	396.920i	0.446094	+	1.85477i
$215$		−	47.7640i		−	0.222158i
$216$		0			0
$217$	−78.8990			−0.363590
$218$	207.499	−	49.9061i	0.951831	−	0.228927i
$219$		0			0
$220$	93.7507	−	47.8652i	0.426139	−	0.217569i
$221$	195.052	−	337.839i	0.882587	−	1.52869i
$222$		0			0
$223$	119.959	+	207.776i	0.537934	+	0.931729i	0.999015	+	0.0443711i	$0.0141284\pi$
$223$	119.959	+	207.776i	0.537934	+	0.931729i	−0.461081	+	0.887358i	$0.652538\pi$
$224$	−48.4204	−	362.053i	−0.216163	−	1.61631i
$225$		0			0
$226$	43.1496	−	145.890i	0.190927	−	0.645532i
$227$	134.662	+	233.242i	0.593227	+	1.02750i	0.993795	+	0.111231i	$0.0354795\pi$
$227$	134.662	+	233.242i	0.593227	+	1.02750i	−0.400568	+	0.916267i	$0.631187\pi$
$228$		0			0
$229$	−3.17890	−	1.83534i	−0.0138816	−	0.00801457i	0.493043	−	0.870005i	$-0.335884\pi$
$229$	−3.17890	−	1.83534i	−0.0138816	−	0.00801457i	−0.506925	+	0.861990i	$0.669218\pi$
$230$	82.8162	+	87.1984i	0.360070	+	0.379124i
$231$		0			0
$232$	−34.9792	+	99.1657i	−0.150772	+	0.427438i
$233$		−	22.7345i		−	0.0975731i	−0.998809	−	0.0487865i	$-0.984465\pi$
$233$		−	22.7345i		−	0.0975731i	0.998809	−	0.0487865i	$-0.0155354\pi$
$234$		0			0
$235$		−	126.386i		−	0.537814i
$236$	4.33634	−	84.0610i	0.0183743	−	0.356191i
$237$		0			0
$238$	361.473	+	380.600i	1.51879	+	1.59916i
$239$	−67.2142	−	38.8061i	−0.281231	−	0.162369i	0.352750	−	0.935718i	$-0.385247\pi$
$239$	−67.2142	−	38.8061i	−0.281231	−	0.162369i	−0.633981	+	0.773349i	$0.718580\pi$
$240$		0			0
$241$	−99.9215	−	173.069i	−0.414612	−	0.718129i	0.580776	−	0.814064i	$-0.302749\pi$
$241$	−99.9215	−	173.069i	−0.414612	−	0.718129i	−0.995388	+	0.0959348i	$0.969416\pi$
$242$	139.636	+	41.2999i	0.577009	+	0.170661i
$243$		0			0
$244$	−120.760	+	186.288i	−0.494917	+	0.763475i
$245$	154.094	+	266.899i	0.628955	+	1.08938i
$246$		0			0
$247$	−184.375	+	319.348i	−0.746459	+	1.29290i
$248$	−54.3572	+	10.1437i	−0.219182	+	0.0409019i
$249$		0			0
$250$	63.1684	+	262.641i	0.252674	+	1.05056i
$251$	−250.203			−0.996825			−0.498412	−	0.866940i	$-0.666083\pi$
$251$	−250.203			−0.996825			−0.498412	+	0.866940i	$0.666083\pi$
$252$		0			0
$253$		−	110.115i		−	0.435237i
$254$	91.8108	+	381.730i	0.361460	+	1.50287i
$255$		0			0
$256$	−79.9065	−	243.210i	−0.312135	−	0.950038i
$257$	287.367	+	165.911i	1.11816	+	0.645570i	0.940930	−	0.338600i	$-0.109953\pi$
$257$	287.367	+	165.911i	1.11816	+	0.645570i	0.177229	+	0.984170i	$0.443287\pi$
$258$		0			0
$259$	−17.3173	+	9.99814i	−0.0668621	+	0.0386029i
$260$	139.943	−	215.881i	0.538244	−	0.830313i
$261$		0			0
$262$	33.0185	+	9.76580i	0.126025	+	0.0372741i
$263$	−301.212	+	173.905i	−1.14529	+	0.661235i	−0.947736	−	0.319057i	$-0.896634\pi$
$263$	−301.212	+	173.905i	−1.14529	+	0.661235i	−0.197557	+	0.980291i	$0.563301\pi$
$264$		0			0
$265$	3.73024	−	6.46097i	0.0140764	−	0.0243810i
$266$	−341.687	−	359.768i	−1.28454	−	1.35251i
$267$		0			0
$268$	348.085	+	17.9562i	1.29882	+	0.0670006i
$269$	−507.709			−1.88740			−0.943698	−	0.330809i	$-0.892678\pi$
$269$	−507.709			−1.88740			−0.943698	+	0.330809i	$0.892678\pi$
$270$		0			0
$271$	85.0065			0.313677			0.156839	−	0.987624i	$-0.449870\pi$
$271$	85.0065			0.313677			0.156839	+	0.987624i	$0.449870\pi$
$272$	297.967	+	215.740i	1.09547	+	0.793162i
$273$		0			0
$274$	251.780	+	265.103i	0.918905	+	0.967529i
$275$	36.8973	−	63.9080i	0.134172	−	0.232393i
$276$		0			0
$277$	−159.497	+	92.0857i	−0.575802	+	0.332439i	−0.759463	−	0.650550i	$-0.774538\pi$
$277$	−159.497	+	92.0857i	−0.575802	+	0.332439i	0.183661	+	0.982990i	$0.441205\pi$
$278$	55.4431	−	187.455i	0.199436	−	0.674299i
$279$		0			0
$280$	225.143	+	262.953i	0.804081	+	0.939117i
$281$	244.767	−	141.316i	0.871057	−	0.502905i	0.00335771	−	0.999994i	$-0.498931\pi$
$281$	244.767	−	141.316i	0.871057	−	0.502905i	0.867699	+	0.497089i	$0.165598\pi$
$282$		0			0
$283$	−210.985	−	121.812i	−0.745529	−	0.430431i	0.0785474	−	0.996910i	$-0.474972\pi$
$283$	−210.985	−	121.812i	−0.745529	−	0.430431i	−0.824076	+	0.566479i	$0.808305\pi$
$284$	70.4801	+	138.045i	0.248169	+	0.486074i
$285$		0			0
$286$	−229.041	+	55.0871i	−0.800841	+	0.192612i
$287$			437.270i			1.52359i
$288$		0			0
$289$	−239.626			−0.829154
$290$	−23.3034	−	96.8906i	−0.0803566	−	0.334106i
$291$		0			0
$292$	−113.262	+	57.8270i	−0.387884	+	0.198038i
$293$	−285.189	+	493.962i	−0.973342	+	1.68588i	−0.288039	+	0.957619i	$0.593003\pi$
$293$	−285.189	+	493.962i	−0.973342	+	1.68588i	−0.685303	+	0.728258i	$0.740330\pi$
$294$		0			0
$295$	39.8849	+	69.0827i	0.135203	+	0.234179i
$296$	−10.6453	+	9.11458i	−0.0359637	+	0.0307925i
$297$		0			0
$298$	−54.2178	−	16.0359i	−0.181939	−	0.0538116i
$299$	−134.566	−	233.074i	−0.450052	−	0.779513i
$300$		0			0
$301$	−124.559	−	71.9143i	−0.413818	−	0.238918i
$302$	−64.1286	+	60.9058i	−0.212346	+	0.201675i
$303$		0			0
$304$	−281.658	−	203.931i	−0.926505	−	0.670827i
$305$		−	210.392i		−	0.689810i
$306$		0			0
$307$			147.169i			0.479377i	0.970850	+	0.239688i	$0.0770453\pi$
$307$			147.169i			0.479377i	−0.970850	+	0.239688i	$0.922955\pi$
$308$	16.3294	−	316.550i	0.0530176	−	1.02776i
$309$		0			0
$310$	37.9971	−	36.0875i	0.122571	−	0.116411i
$311$	140.255	+	80.9762i	0.450981	+	0.260374i	0.708244	−	0.705967i	$-0.249488\pi$
$311$	140.255	+	80.9762i	0.450981	+	0.260374i	−0.257264	+	0.966341i	$0.582821\pi$
$312$		0			0
$313$	−217.298	−	376.370i	−0.694241	−	1.20246i	−0.970436	−	0.241359i	$-0.922407\pi$
$313$	−217.298	−	376.370i	−0.694241	−	1.20246i	0.276195	−	0.961102i	$-0.410927\pi$
$314$	−130.468	+	441.115i	−0.415502	+	1.40483i
$315$		0			0
$316$	461.508	+	299.169i	1.46047	+	0.946738i
$317$	−303.122	−	525.022i	−0.956219	−	1.65622i	−0.731553	−	0.681785i	$-0.761204\pi$
$317$	−303.122	−	525.022i	−0.956219	−	1.65622i	−0.224667	−	0.974436i	$-0.572129\pi$
$318$		0			0
$319$	−45.6241	+	79.0232i	−0.143022	+	0.247722i
$320$	188.918	+	152.215i	0.590368	+	0.475671i
$321$		0			0
$322$	352.086	−	84.6810i	1.09343	−	0.262985i
$323$	499.691			1.54703
$324$		0			0
$325$		−	180.361i		−	0.554957i
$326$	−74.3756	+	17.8883i	−0.228146	+	0.0548720i
$327$		0			0
$328$	56.2177	+	301.255i	0.171396	+	0.918462i
$329$	−329.591	−	190.289i	−1.00180	−	0.578387i
$330$		0			0
$331$	339.693	−	196.122i	1.02626	−	0.592514i	0.110352	−	0.993893i	$-0.464802\pi$
$331$	339.693	−	196.122i	1.02626	−	0.592514i	0.915912	+	0.401379i	$0.131469\pi$
$332$	225.167	+	145.963i	0.678215	+	0.439648i
$333$		0			0
$334$	12.6532	−	42.7808i	0.0378838	−	0.128086i
$335$	−286.062	+	165.158i	−0.853916	+	0.493008i
$336$		0			0
$337$	3.96893	−	6.87439i	0.0117772	−	0.0203988i	−0.860077	−	0.510165i	$-0.829584\pi$
$337$	3.96893	−	6.87439i	0.0117772	−	0.0203988i	0.871854	+	0.489766i	$0.162918\pi$
$338$	−172.398	+	163.734i	−0.510053	+	0.484419i
$339$		0			0
$340$	−348.164	−	17.9603i	−1.02401	−	0.0528243i
$341$	−47.9831			−0.140713
$342$		0			0
$343$	368.697			1.07492
$344$	−95.0603	−	33.5311i	−0.276338	−	0.0974741i
$345$		0			0
$346$	185.223	−	175.914i	0.535325	−	0.508422i
$347$	108.377	−	187.715i	0.312326	−	0.540965i	−0.666539	−	0.745470i	$-0.732225\pi$
$347$	108.377	−	187.715i	0.312326	−	0.540965i	0.978866	+	0.204505i	$0.0655584\pi$
$348$		0			0
$349$	434.379	−	250.789i	1.24464	−	0.718593i	0.274605	−	0.961557i	$-0.411453\pi$
$349$	434.379	−	250.789i	1.24464	−	0.718593i	0.970035	+	0.242964i	$0.0781197\pi$
$350$	232.717	+	68.8301i	0.664906	+	0.196658i
$351$		0			0
$352$	−29.4473	−	220.185i	−0.0836570	−	0.625527i
$353$	140.586	−	81.1674i	0.398261	−	0.229936i	−0.287472	−	0.957789i	$-0.592815\pi$
$353$	140.586	−	81.1674i	0.398261	−	0.229936i	0.685733	+	0.727853i	$0.259482\pi$
$354$		0			0
$355$	−127.209	−	73.4444i	−0.358337	−	0.206886i
$356$	−289.977	−	567.959i	−0.814541	−	1.59539i
$357$		0			0
$358$	−48.1920	−	200.372i	−0.134615	−	0.559699i
$359$		−	245.739i		−	0.684509i	−0.939607	−	0.342255i	$-0.888809\pi$
$359$		−	245.739i		−	0.684509i	0.939607	−	0.342255i	$-0.111191\pi$
$360$		0			0
$361$	−111.340			−0.308420
$362$	139.094	−	33.4540i	0.384239	−	0.0924142i
$363$		0			0
$364$	−352.275	−	689.980i	−0.967790	−	1.89555i
$365$	60.2592	−	104.372i	0.165094	−	0.285951i
$366$		0			0
$367$	13.1011	+	22.6918i	0.0356979	+	0.0618305i	0.883322	−	0.468766i	$-0.155301\pi$
$367$	13.1011	+	22.6918i	0.0356979	+	0.0618305i	−0.847624	+	0.530597i	$0.821968\pi$
$368$	231.681	−	103.607i	0.629568	−	0.281540i
$369$		0			0
$370$	3.76682	−	12.7357i	0.0101806	−	0.0344209i
$371$	−11.2326	−	19.4555i	−0.0302767	−	0.0524407i
$372$		0			0
$373$	19.4643	+	11.2377i	0.0521831	+	0.0301279i	0.525865	−	0.850568i	$-0.323742\pi$
$373$	19.4643	+	11.2377i	0.0521831	+	0.0301279i	−0.473681	+	0.880696i	$0.657075\pi$
$374$	219.832	+	231.465i	0.587787	+	0.618890i
$375$		0			0
$376$	−251.535	−	88.7251i	−0.668976	−	0.235971i
$377$			223.019i			0.591562i
$378$		0			0
$379$			170.148i			0.448940i	0.974481	+	0.224470i	$0.0720650\pi$
$379$			170.148i			0.448940i	−0.974481	+	0.224470i	$0.927935\pi$
$380$	329.107	+	16.9772i	0.866071	+	0.0446768i
$381$		0			0
$382$	−239.965	−	252.663i	−0.628181	−	0.661421i
$383$	−83.5469	−	48.2358i	−0.218138	−	0.125942i	0.386950	−	0.922101i	$-0.373529\pi$
$383$	−83.5469	−	48.2358i	−0.218138	−	0.125942i	−0.605088	+	0.796159i	$0.706862\pi$
$384$		0			0
$385$	150.195	+	260.146i	0.390118	+	0.675704i
$386$	402.544	+	119.059i	1.04286	+	0.308444i
$387$		0			0
$388$	−285.499	−	185.072i	−0.735822	−	0.476991i
$389$	55.8230	+	96.6882i	0.143504	+	0.248556i	0.928814	−	0.370547i	$-0.120830\pi$
$389$	55.8230	+	96.6882i	0.143504	+	0.248556i	−0.785310	+	0.619103i	$0.787496\pi$
$390$		0			0
$391$	−182.349	+	315.837i	−0.466365	+	0.807767i
$392$	639.360	−	119.312i	1.63102	−	0.304367i
$393$		0			0
$394$	35.5388	+	147.763i	0.0902000	+	0.375033i
$395$	−521.223			−1.31955
$396$		0			0
$397$		−	582.265i		−	1.46666i	−0.679871	−	0.733332i	$-0.737964\pi$
$397$		−	582.265i		−	1.46666i	0.679871	−	0.733332i	$-0.262036\pi$
$398$	−130.385	−	542.113i	−0.327601	−	1.36209i
$399$		0			0
$400$	169.179	+	17.5009i	0.422946	+	0.0437523i
$401$	530.337	+	306.190i	1.32254	+	0.763567i	0.984133	−	0.177434i	$-0.0567795\pi$
$401$	530.337	+	306.190i	1.32254	+	0.763567i	0.338404	+	0.941001i	$0.390113\pi$
$402$		0			0
$403$	−101.563	+	58.6375i	−0.252018	+	0.145503i
$404$	−99.4485	−	64.4667i	−0.246160	−	0.159571i
$405$		0			0
$406$	−287.758	−	85.1095i	−0.708763	−	0.209629i
$407$	−10.5316	+	6.08045i	−0.0258763	+	0.0149397i
$408$		0			0
$409$	169.968	−	294.393i	0.415569	−	0.719786i	−0.579919	−	0.814674i	$-0.696916\pi$
$409$	169.968	−	294.393i	0.415569	−	0.719786i	0.995488	+	0.0948878i	$0.0302492\pi$
$410$	−200.002	−	210.586i	−0.487811	−	0.513623i
$411$		0			0
$412$	−0.542436	+	10.5153i	−0.00131659	+	0.0255225i
$413$	240.206			0.581612
$414$		0			0
$415$	−254.302			−0.612776
$416$	−331.406	−	430.069i	−0.796649	−	1.03382i
$417$		0			0
$418$	−207.800	−	218.796i	−0.497129	−	0.523434i
$419$	38.4222	−	66.5492i	0.0916998	−	0.158829i	−0.816527	−	0.577308i	$-0.804103\pi$
$419$	38.4222	−	66.5492i	0.0916998	−	0.158829i	0.908226	+	0.418479i	$0.137437\pi$
$420$		0			0
$421$	−697.260	+	402.563i	−1.65620	+	0.956207i	−0.681755	+	0.731581i	$0.738783\pi$
$421$	−697.260	+	402.563i	−1.65620	+	0.956207i	−0.974445	+	0.224627i	$0.927884\pi$
$422$	−86.6900	+	293.102i	−0.205426	+	0.694554i
$423$		0			0
$424$	−10.2400	−	11.9597i	−0.0241509	−	0.0282067i
$425$	−211.661	+	122.203i	−0.498027	+	0.287536i
$426$		0			0
$427$	−548.661	−	316.770i	−1.28492	−	0.741850i
$428$	−727.182	+	371.269i	−1.69902	+	0.867452i
$429$		0			0
$430$	92.8795	−	22.3387i	0.215999	−	0.0519504i
$431$		−	713.531i		−	1.65552i	−0.561080	−	0.827762i	$-0.689614\pi$
$431$		−	713.531i		−	1.65552i	0.561080	−	0.827762i	$-0.310386\pi$
$432$		0			0
$433$	488.389			1.12792			0.563960	−	0.825802i	$-0.309277\pi$
$433$	488.389			1.12792			0.563960	+	0.825802i	$0.309277\pi$
$434$	−36.9001	−	153.423i	−0.0850233	−	0.353509i
$435$		0			0
$436$	194.090	+	380.152i	0.445160	+	0.871908i
$437$	172.368	−	298.549i	0.394434	−	0.683179i
$438$		0			0
$439$	−190.893	−	330.636i	−0.434836	−	0.753158i	0.562446	−	0.826834i	$-0.309860\pi$
$439$	−190.893	−	330.636i	−0.434836	−	0.753158i	−0.997282	+	0.0736756i	$0.976527\pi$
$440$	136.922	+	159.917i	0.311187	+	0.363447i
$441$		0			0
$442$	748.169	+	221.284i	1.69269	+	0.500643i
$443$	271.361	+	470.011i	0.612554	+	1.06097i	0.990808	+	0.135272i	$0.0431910\pi$
$443$	271.361	+	470.011i	0.612554	+	1.06097i	−0.378255	+	0.925702i	$0.623476\pi$
$444$		0			0
$445$	523.378	+	302.173i	1.17613	+	0.679039i
$446$	−347.926	+	330.441i	−0.780103	+	0.740899i
$447$		0			0
$448$	681.384	−	263.484i	1.52095	−	0.588133i
$449$		−	131.985i		−	0.293953i	−0.989140	−	0.146976i	$-0.953046\pi$
$449$		−	131.985i		−	0.293953i	0.989140	−	0.146976i	$-0.0469542\pi$
$450$		0			0
$451$			265.929i			0.589644i
$452$	303.871	+	15.6754i	0.672281	+	0.0346800i
$453$		0			0
$454$	−390.571	+	370.942i	−0.860288	+	0.817053i
$455$	635.821	+	367.092i	1.39741	+	0.806795i
$456$		0			0
$457$	127.088	+	220.122i	0.278091	+	0.481668i	0.970910	−	0.239443i	$-0.0769649\pi$
$457$	127.088	+	220.122i	0.278091	+	0.481668i	−0.692819	+	0.721111i	$0.743632\pi$
$458$	2.08217	−	7.03988i	0.00454622	−	0.0153709i
$459$		0			0
$460$	−130.829	+	201.822i	−0.284412	+	0.438743i
$461$	247.923	+	429.415i	0.537794	+	0.931487i	0.999022	+	0.0442051i	$0.0140755\pi$
$461$	247.923	+	429.415i	0.537794	+	0.931487i	−0.461228	+	0.887281i	$0.652591\pi$
$462$		0			0
$463$	188.880	−	327.149i	0.407947	−	0.706586i	−0.586712	−	0.809796i	$-0.699578\pi$
$463$	188.880	−	327.149i	0.407947	−	0.706586i	0.994660	+	0.103210i	$0.0329113\pi$
$464$	−209.192	−	21.6401i	−0.450844	−	0.0466383i
$465$		0			0
$466$	44.2084	−	10.6327i	0.0948678	−	0.0228169i
$467$	−134.451			−0.287904			−0.143952	−	0.989585i	$-0.545981\pi$
$467$	−134.451			−0.287904			−0.143952	+	0.989585i	$0.545981\pi$
$468$		0			0
$469$			994.658i			2.12081i
$470$	245.764	−	59.1093i	0.522903	−	0.125765i
$471$		0			0
$472$	165.489	−	30.8821i	0.350612	−	0.0654282i
$473$	−75.7517	−	43.7353i	−0.160152	−	0.0924636i
$474$		0			0
$475$	200.076	−	115.514i	0.421212	−	0.243187i
$476$	−571.039	+	880.903i	−1.19966	+	1.85064i
$477$		0			0
$478$	44.0251	−	148.850i	0.0921028	−	0.311402i
$479$	266.094	−	153.630i	0.555521	−	0.320730i	−0.195825	−	0.980639i	$-0.562738\pi$
$479$	266.094	−	153.630i	0.555521	−	0.320730i	0.751346	+	0.659909i	$0.229405\pi$
$480$		0			0
$481$	−14.8612	+	25.7403i	−0.0308964	+	0.0535142i
$482$	289.809	−	275.244i	0.601264	−	0.571047i
$483$		0			0
$484$	−15.0034	+	290.845i	−0.0309988	+	0.600919i
$485$	322.440			0.664825
$486$		0			0
$487$	489.926			1.00601			0.503005	−	0.864284i	$-0.332228\pi$
$487$	489.926			1.00601			0.503005	+	0.864284i	$0.332228\pi$
$488$	−418.724	−	147.698i	−0.858040	−	0.302661i
$489$		0			0
$490$	−446.930	+	424.469i	−0.912101	+	0.866263i
$491$	45.0122	−	77.9634i	0.0916745	−	0.158785i	−0.816541	−	0.577287i	$-0.804111\pi$
$491$	45.0122	−	77.9634i	0.0916745	−	0.158785i	0.908216	+	0.418502i	$0.137445\pi$
$492$		0			0
$493$	261.722	−	151.105i	0.530877	−	0.306502i
$494$	−707.217	−	209.172i	−1.43161	−	0.423425i
$495$		0			0
$496$	−45.1471	−	100.956i	−0.0910223	−	0.203540i
$497$	−383.058	+	221.158i	−0.770740	+	0.444987i
$498$		0			0
$499$	471.622	+	272.291i	0.945134	+	0.545673i	0.891566	−	0.452891i	$-0.149607\pi$
$499$	471.622	+	272.291i	0.945134	+	0.545673i	0.0535679	+	0.998564i	$0.482941\pi$
$500$	−481.175	+	245.668i	−0.962350	+	0.491336i
$501$		0			0
$502$	−117.017	−	486.532i	−0.233101	−	0.969187i
$503$		−	59.9114i		−	0.119108i	−0.998225	−	0.0595541i	$-0.981032\pi$
$503$		−	59.9114i		−	0.119108i	0.998225	−	0.0595541i	$-0.0189679\pi$
$504$		0			0
$505$	112.316			0.222409
$506$	214.124	−	51.4994i	0.423170	−	0.101778i
$507$		0			0
$508$	−699.353	+	357.061i	−1.37668	+	0.702876i
$509$	328.303	−	568.638i	0.644996	−	1.11717i	−0.339306	−	0.940676i	$-0.610192\pi$
$509$	328.303	−	568.638i	0.644996	−	1.11717i	0.984302	−	0.176490i	$-0.0564744\pi$
$510$		0			0
$511$	−181.454	−	314.288i	−0.355097	−	0.615046i
$512$	435.562	−	269.128i	0.850706	−	0.525641i
$513$		0			0
$514$	−188.225	+	636.394i	−0.366196	+	1.23812i
$515$	−4.98924	−	8.64161i	−0.00968784	−	0.0167798i
$516$		0			0
$517$	−200.443	−	115.726i	−0.387705	−	0.223841i
$518$	−27.5410	−	28.9983i	−0.0531679	−	0.0559813i
$519$		0			0
$520$	485.242	+	171.162i	0.933157	+	0.329157i
$521$		−	657.693i		−	1.26237i	−0.775634	−	0.631184i	$-0.782569\pi$
$521$		−	657.693i		−	1.26237i	0.775634	−	0.631184i	$-0.217431\pi$
$522$		0			0
$523$			534.207i			1.02143i	0.859750	+	0.510714i	$0.170619\pi$
$523$			534.207i			1.02143i	−0.859750	+	0.510714i	$0.829381\pi$
$524$	−3.54772	+	68.7734i	−0.00677045	+	0.131247i
$525$		0			0
$526$	−479.039	−	504.388i	−0.910721	−	0.958912i
$527$	137.627	+	79.4592i	0.261152	+	0.150776i
$528$		0			0
$529$	−138.698	−	240.232i	−0.262190	−	0.454126i
$530$	14.3083	+	4.23192i	0.0269967	+	0.00798475i
$531$		0			0
$532$	539.783	−	832.686i	1.01463	−	1.56520i
$533$	324.978	+	562.878i	0.609715	+	1.05606i
$534$		0			0
$535$	386.884	−	670.103i	0.723148	−	1.25253i
$536$	127.878	+	685.265i	0.238579	+	1.27848i
$537$		0			0
$538$	−237.450	−	987.265i	−0.441356	−	1.83507i
$539$	564.387			1.04710
$540$		0			0
$541$		−	41.7800i		−	0.0772273i	−0.999254	−	0.0386137i	$-0.987706\pi$
$541$		−	41.7800i		−	0.0772273i	0.999254	−	0.0386137i	$-0.0122942\pi$
$542$	39.7565	+	165.299i	0.0733515	+	0.304980i
$543$		0			0
$544$	−280.161	+	680.310i	−0.515002	+	1.25057i
$545$	−350.312	−	202.253i	−0.642775	−	0.371106i
$546$		0			0
$547$	72.1250	−	41.6414i	0.131855	−	0.0761268i	−0.432621	−	0.901576i	$-0.642411\pi$
$547$	72.1250	−	41.6414i	0.131855	−	0.0761268i	0.564477	+	0.825449i	$0.309078\pi$
$548$	−397.751	+	613.584i	−0.725823	+	1.11968i
$549$		0			0
$550$	141.529	+	41.8596i	0.257325	+	0.0761083i
$551$	−247.397	+	142.835i	−0.448996	+	0.259228i
$552$		0			0
$553$	−784.763	+	1359.25i	−1.41910	+	2.45796i
$554$	−253.660	−	267.083i	−0.457870	−	0.482098i
$555$		0			0
$556$	390.445	+	20.1414i	0.702240	+	0.0362255i
$557$	−233.457			−0.419133			−0.209566	−	0.977794i	$-0.567205\pi$
$557$	−233.457			−0.419133			−0.209566	+	0.977794i	$0.567205\pi$
$558$		0			0
$559$	−213.786			−0.382444
$560$	−406.028	+	560.781i	−0.725049	+	1.00139i
$561$		0			0
$562$	389.271	+	409.869i	0.692653	+	0.729305i
$563$	−314.155	+	544.133i	−0.558002	+	0.966488i	0.439661	+	0.898164i	$0.355099\pi$
$563$	−314.155	+	544.133i	−0.558002	+	0.966488i	−0.997663	+	0.0683244i	$0.978235\pi$
$564$		0			0
$565$	−249.726	+	144.179i	−0.441993	+	0.255185i
$566$	138.194	−	467.240i	0.244160	−	0.825512i
$567$		0			0
$568$	−235.473	+	201.614i	−0.414565	+	0.354954i
$569$	−584.843	+	337.660i	−1.02784	+	0.593426i	−0.916366	−	0.400341i	$-0.868892\pi$
$569$	−584.843	+	337.660i	−1.02784	+	0.593426i	−0.111478	+	0.993767i	$0.535558\pi$
$570$		0			0
$571$	637.313	+	367.953i	1.11613	+	0.644400i	0.940411	−	0.340039i	$-0.110440\pi$
$571$	637.313	+	367.953i	1.11613	+	0.644400i	0.175723	+	0.984440i	$0.443774\pi$
$572$	−214.239	−	419.617i	−0.374544	−	0.733596i
$573$		0			0
$574$	−850.293	+	204.506i	−1.48135	+	0.356282i
$575$			168.615i			0.293243i
$576$		0			0
$577$	180.595			0.312990			0.156495	−	0.987679i	$-0.449981\pi$
$577$	180.595			0.312990			0.156495	+	0.987679i	$0.449981\pi$
$578$	−112.070	−	465.964i	−0.193893	−	0.806165i
$579$		0			0
$580$	177.510	−	90.6292i	0.306051	−	0.156257i
$581$	−382.882	+	663.171i	−0.659005	+	1.14143i
$582$		0			0
$583$	−6.83122	−	11.8320i	−0.0117174	−	0.0202951i
$584$	−165.419	−	193.199i	−0.283251	−	0.330820i
$585$		0			0
$586$	−1093.91	−	323.544i	−1.86674	−	0.552123i
$587$	134.034	+	232.154i	0.228338	+	0.395493i	0.957316	−	0.289045i	$-0.0933376\pi$
$587$	134.034	+	232.154i	0.228338	+	0.395493i	−0.728978	+	0.684537i	$0.760004\pi$
$588$		0			0
$589$	−130.094	−	75.1099i	−0.220873	−	0.127521i
$590$	−115.681	+	109.867i	−0.196070	+	0.186216i
$591$		0			0
$592$	−22.7024	−	16.4374i	−0.0383486	−	0.0277660i
$593$			195.220i			0.329208i	0.986360	+	0.164604i	$0.0526345\pi$
$593$			195.220i			0.329208i	−0.986360	+	0.164604i	$0.947365\pi$
$594$		0			0
$595$		−	994.885i		−	1.67208i
$596$	5.82551	−	112.929i	0.00977434	−	0.189478i
$597$		0			0
$598$	390.290	−	370.675i	0.652658	−	0.619858i
$599$	−733.133	−	423.274i	−1.22393	−	0.706635i	−0.258175	−	0.966098i	$-0.583121\pi$
$599$	−733.133	−	423.274i	−1.22393	−	0.706635i	−0.965753	+	0.259463i	$0.916454\pi$
$600$		0			0
$601$	400.778	+	694.167i	0.666851	+	1.15502i	0.978780	+	0.204915i	$0.0656918\pi$
$601$	400.778	+	694.167i	0.666851	+	1.15502i	−0.311928	+	0.950106i	$0.600975\pi$
$602$	81.5860	−	275.845i	0.135525	−	0.458214i
$603$		0			0
$604$	−148.426	−	96.2163i	−0.245739	−	0.159298i
$605$	−137.999	−	239.021i	−0.228097	−	0.395076i
$606$		0			0
$607$	−269.066	+	466.036i	−0.443272	+	0.767770i	−0.997930	−	0.0643086i	$-0.979516\pi$
$607$	−269.066	+	466.036i	−0.443272	+	0.767770i	0.554658	+	0.832078i	$0.312849\pi$
$608$	264.826	−	643.073i	0.435570	−	1.05769i
$609$		0			0
$610$	409.117	−	98.3978i	0.670684	−	0.161308i
$611$	−565.690			−0.925843
$612$		0			0
$613$			977.999i			1.59543i	0.603034	+	0.797715i	$0.293958\pi$
$613$			977.999i			1.59543i	−0.603034	+	0.797715i	$0.706042\pi$
$614$	−286.177	+	68.8290i	−0.466086	+	0.112099i
$615$		0			0
$616$	623.184	−	116.293i	1.01166	−	0.188788i
$617$	174.494	+	100.744i	0.282810	+	0.163280i	0.634695	−	0.772763i	$-0.281126\pi$
$617$	174.494	+	100.744i	0.282810	+	0.163280i	−0.351885	+	0.936043i	$0.614459\pi$
$618$		0			0
$619$	−646.869	+	373.470i	−1.04502	+	0.603344i	−0.921252	−	0.388967i	$-0.872832\pi$
$619$	−646.869	+	373.470i	−1.04502	+	0.603344i	−0.123771	+	0.992311i	$0.539499\pi$
$620$	87.9447	+	57.0095i	0.141846	+	0.0919508i
$621$		0			0
$622$	−91.8666	+	310.604i	−0.147696	+	0.499364i
$623$	1576.01	−	909.912i	2.52972	−	1.46053i
$624$		0			0
$625$	123.125	−	213.258i	0.196999	−	0.341213i
$626$	630.243	−	598.569i	1.00678	−	0.956181i
$627$		0			0
$628$	−918.788	−	47.3962i	−1.46304	−	0.0754717i
$629$	40.2765			0.0640326
$630$		0			0
$631$	−700.521			−1.11018			−0.555088	−	0.831792i	$-0.687315\pi$
$631$	−700.521			−1.11018			−0.555088	+	0.831792i	$0.687315\pi$
$632$	−365.907	+	1037.34i	−0.578967	+	1.64136i
$633$		0			0
$634$	879.164	−	834.981i	1.38669	−	1.31700i
$635$	372.079	−	644.459i	0.585950	−	1.01490i
$636$		0			0
$637$	1194.61	−	689.707i	1.87536	−	1.08274i
$638$	−175.002	−	51.7600i	−0.274298	−	0.0811285i
$639$		0			0
$640$	−207.634	+	438.549i	−0.324428	+	0.685232i
$641$	−271.932	+	157.000i	−0.424231	+	0.244930i	−0.696886	−	0.717182i	$-0.745432\pi$
$641$	−271.932	+	157.000i	−0.424231	+	0.244930i	0.272655	+	0.962112i	$0.412098\pi$
$642$		0			0
$643$	−31.2886	−	18.0645i	−0.0486603	−	0.0280940i	0.475472	−	0.879731i	$-0.342277\pi$
$643$	−31.2886	−	18.0645i	−0.0486603	−	0.0280940i	−0.524133	+	0.851637i	$0.675610\pi$
$644$	329.333	+	645.044i	0.511386	+	1.00162i
$645$		0			0
$646$	233.699	+	971.673i	0.361764	+	1.50414i
$647$		−	750.073i		−	1.15931i	−0.814862	−	0.579655i	$-0.803187\pi$
$647$		−	750.073i		−	1.15931i	0.814862	−	0.579655i	$-0.196813\pi$
$648$		0			0
$649$	146.083			0.225089
$650$	350.720	−	84.3526i	0.539570	−	0.129773i
$651$		0			0
$652$	−69.5692	−	136.261i	−0.106701	−	0.208989i
$653$	10.5807	−	18.3264i	0.0162033	−	0.0280649i	−0.857810	−	0.513967i	$-0.828175\pi$
$653$	10.5807	−	18.3264i	0.0162033	−	0.0280649i	0.874013	+	0.485902i	$0.161509\pi$
$654$		0			0
$655$	−32.6313	−	56.5191i	−0.0498188	−	0.0862888i
$656$	−559.513	+	250.212i	−0.852917	+	0.381420i
$657$		0			0
$658$	215.881	−	729.901i	0.328087	−	1.10927i
$659$	−566.376	−	980.992i	−0.859448	−	1.48861i	−0.872457	−	0.488691i	$-0.837474\pi$
$659$	−566.376	−	980.992i	−0.859448	−	1.48861i	0.0130092	−	0.999915i	$-0.495859\pi$
$660$		0			0
$661$	−478.603	−	276.322i	−0.724060	−	0.418036i	0.0921855	−	0.995742i	$-0.470615\pi$
$661$	−478.603	−	276.322i	−0.724060	−	0.418036i	−0.816245	+	0.577706i	$0.803948\pi$
$662$	540.239	+	568.826i	0.816071	+	0.859254i
$663$		0			0
$664$	−178.524	+	506.114i	−0.268862	+	0.762220i
$665$			940.429i			1.41418i
$666$		0			0
$667$		−	208.494i		−	0.312585i
$668$	89.1072	+	4.59665i	0.133394	+	0.00688121i
$669$		0			0
$670$	−454.945	−	479.018i	−0.679022	−	0.714953i
$671$	−333.673	−	192.646i	−0.497277	−	0.287103i
$672$		0			0
$673$	82.2812	+	142.515i	0.122260	+	0.211761i	0.920659	−	0.390368i	$-0.127652\pi$
$673$	82.2812	+	142.515i	0.122260	+	0.211761i	−0.798398	+	0.602130i	$0.794319\pi$
$674$	15.2238	+	4.50271i	0.0225872	+	0.00668057i
$675$		0			0
$676$	−399.017	−	258.659i	−0.590261	−	0.382632i
$677$	303.242	+	525.230i	0.447920	+	0.775819i	0.998250	−	0.0591273i	$-0.0188318\pi$
$677$	303.242	+	525.230i	0.447920	+	0.775819i	−0.550331	+	0.834947i	$0.685498\pi$
$678$		0			0
$679$	485.471	−	840.861i	0.714980	−	1.23838i
$680$	−127.908	−	685.422i	−0.188099	−	1.00797i
$681$		0			0
$682$	−22.4411	−	93.3054i	−0.0329048	−	0.136811i
$683$	−117.424			−0.171924			−0.0859619	−	0.996298i	$-0.527396\pi$
$683$	−117.424			−0.171924			−0.0859619	+	0.996298i	$0.527396\pi$
$684$		0			0
$685$		−	692.976i		−	1.01164i
$686$	172.435	+	716.950i	0.251363	+	1.04512i
$687$		0			0
$688$	20.7443	−	200.531i	0.0301516	−	0.291470i
$689$	−28.9185	−	16.6961i	−0.0419718	−	0.0242324i
$690$		0			0
$691$	−787.615	+	454.730i	−1.13982	+	0.658075i	−0.946386	−	0.323038i	$-0.895296\pi$
$691$	−787.615	+	454.730i	−1.13982	+	0.658075i	−0.193434	+	0.981113i	$0.561962\pi$
$692$	428.700	+	277.901i	0.619508	+	0.401592i
$693$		0			0
$694$	415.708	+	122.953i	0.599002	+	0.177165i
$695$	−320.874	+	185.257i	−0.461690	+	0.266557i
$696$		0			0
$697$	440.375	−	762.751i	0.631814	−	1.09433i
$698$	690.825	+	727.381i	0.989721	+	1.04209i
$699$		0			0
$700$	−25.0046	+	484.720i	−0.0357208	+	0.692458i
$701$	−190.527			−0.271793			−0.135896	−	0.990723i	$-0.543391\pi$
$701$	−190.527			−0.271793			−0.135896	+	0.990723i	$0.543391\pi$
$702$		0			0
$703$	−38.0719			−0.0541564
$704$	414.389	−	160.240i	0.588621	−	0.227613i
$705$		0			0
$706$	223.584	+	235.415i	0.316692	+	0.333450i
$707$	169.105	−	292.899i	0.239187	−	0.414284i
$708$		0			0
$709$	890.120	−	513.911i	1.25546	−	0.724839i	0.283270	−	0.959040i	$-0.408581\pi$
$709$	890.120	−	513.911i	1.25546	−	0.724839i	0.972188	+	0.234201i	$0.0752474\pi$
$710$	83.3219	−	281.714i	0.117355	−	0.396780i
$711$		0			0
$712$	968.805	−	829.501i	1.36068	−	1.16503i
$713$	94.9487	−	54.8186i	0.133168	−	0.0768845i
$714$		0			0
$715$	386.680	+	223.250i	0.540811	+	0.312237i
$716$	367.095	−	187.423i	0.512702	−	0.261764i
$717$		0			0
$718$	477.851	−	114.929i	0.665531	−	0.160068i
$719$			548.905i			0.763428i	0.924281	+	0.381714i	$0.124666\pi$
$719$			548.905i			0.763428i	−0.924281	+	0.381714i	$0.875334\pi$
$720$		0			0
$721$	−30.0475			−0.0416748
$722$	−52.0723	−	216.505i	−0.0721222	−	0.299869i
$723$		0			0
$724$	130.106	+	254.830i	0.179704	+	0.351975i
$725$	69.8623	−	121.005i	0.0963617	−	0.166903i
$726$		0			0
$727$	−180.113	−	311.965i	−0.247749	−	0.429113i	0.715152	−	0.698969i	$-0.246357\pi$
$727$	−180.113	−	311.965i	−0.247749	−	0.429113i	−0.962901	+	0.269856i	$0.913024\pi$
$728$	1176.94	−	1007.71i	1.61668	−	1.38422i
$729$		0			0
$730$	231.139	+	68.3634i	0.316628	+	0.0936484i
$731$	144.850	+	250.887i	0.198153	+	0.343211i
$732$		0			0
$733$	−557.115	−	321.651i	−0.760048	−	0.438814i	0.0692647	−	0.997598i	$-0.477935\pi$
$733$	−557.115	−	321.651i	−0.760048	−	0.438814i	−0.829313	+	0.558784i	$0.811268\pi$
$734$	−37.9981	+	36.0885i	−0.0517685	+	0.0491668i
$735$		0			0
$736$	309.823	+	402.060i	0.420955	+	0.546276i
$737$			604.909i			0.820772i
$738$		0			0
$739$		−	948.427i		−	1.28339i	−0.766959	−	0.641696i	$-0.778231\pi$
$739$		−	948.427i		−	1.28339i	0.766959	−	0.641696i	$-0.221769\pi$
$740$	26.5270	+	1.36841i	0.0358473	+	0.00184920i
$741$		0			0
$742$	32.5788	−	30.9415i	0.0439067	−	0.0417001i
$743$	832.510	+	480.650i	1.12047	+	0.646904i	0.941521	−	0.336954i	$-0.109397\pi$
$743$	832.510	+	480.650i	1.12047	+	0.646904i	0.178950	+	0.983858i	$0.442730\pi$
$744$		0			0
$745$	53.5821	+	92.8068i	0.0719222	+	0.124573i
$746$	−12.7491	+	43.1050i	−0.0170899	+	0.0577815i
$747$		0			0
$748$	−347.282	+	535.728i	−0.464280	+	0.716214i
$749$	−1165.00	−	2017.84i	−1.55541	−	2.69404i
$750$		0			0
$751$	−80.1757	+	138.868i	−0.106759	+	0.184911i	−0.914455	−	0.404687i	$-0.867381\pi$
$751$	−80.1757	+	138.868i	−0.106759	+	0.184911i	0.807697	+	0.589598i	$0.200714\pi$
$752$	54.8905	−	530.617i	0.0729927	−	0.705608i
$753$		0			0
$754$	−433.671	+	104.303i	−0.575160	+	0.138333i
$755$	167.632			0.222029
$756$		0			0
$757$		−	43.6832i		−	0.0577057i	−0.999584	−	0.0288529i	$-0.990815\pi$
$757$		−	43.6832i		−	0.0577057i	0.999584	−	0.0288529i	$-0.00918543\pi$
$758$	−330.861	+	79.5763i	−0.436493	+	0.104982i
$759$		0			0
$760$	120.906	+	647.905i	0.159087	+	0.852506i
$761$	787.821	+	454.849i	1.03524	+	0.597699i	0.918483	−	0.395461i	$-0.129415\pi$
$761$	787.821	+	454.849i	1.03524	+	0.597699i	0.116762	+	0.993160i	$0.462749\pi$
$762$		0			0
$763$	−1054.87	+	609.031i	−1.38253	+	0.798206i
$764$	379.087	−	584.791i	0.496187	−	0.765434i
$765$		0			0
$766$	54.7230	−	185.020i	0.0714400	−	0.241541i
$767$	309.206	−	178.520i	0.403137	−	0.232751i
$768$		0			0
$769$	−407.652	+	706.074i	−0.530106	+	0.918171i	0.469277	+	0.883051i	$0.344515\pi$
$769$	−407.652	+	706.074i	−0.530106	+	0.918171i	−0.999383	+	0.0351200i	$0.988819\pi$
$770$	−435.622	+	413.730i	−0.565743	+	0.537311i
$771$		0			0
$772$	−43.2519	+	838.449i	−0.0560258	+	1.08607i
$773$	−199.902			−0.258606			−0.129303	−	0.991605i	$-0.541274\pi$
$773$	−199.902			−0.258606			−0.129303	+	0.991605i	$0.541274\pi$
$774$		0			0
$775$	73.4745			0.0948058
$776$	226.358	−	641.722i	0.291698	−	0.826962i
$777$		0			0
$778$	−161.907	+	153.770i	−0.208107	+	0.197648i
$779$	−416.270	+	721.001i	−0.534365	+	0.925547i
$780$		0			0
$781$	−232.959	+	134.499i	−0.298284	+	0.172214i
$782$	−699.443	−	206.872i	−0.894428	−	0.264543i
$783$		0			0
$784$	531.029	+	1187.47i	0.677333	+	1.51462i
$785$	755.075	−	435.943i	0.961879	−	0.555341i
$786$		0			0
$787$	−950.172	−	548.582i	−1.20733	−	0.697055i	−0.245158	−	0.969483i	$-0.578840\pi$
$787$	−950.172	−	548.582i	−1.20733	−	0.697055i	−0.962176	+	0.272428i	$0.912173\pi$
$788$	−270.711	+	138.214i	−0.343542	+	0.175398i
$789$		0			0
$790$	−243.770	−	1013.54i	−0.308570	−	1.28297i
$791$			868.316i			1.09774i
$792$		0			0
$793$	−941.690			−1.18750
$794$	1132.24	−	272.319i	1.42600	−	0.342971i
$795$		0			0
$796$	993.186	−	507.080i	1.24772	−	0.637035i
$797$	−297.651	+	515.547i	−0.373465	+	0.646860i	−0.990096	−	0.140392i	$-0.955164\pi$
$797$	−297.651	+	515.547i	−0.373465	+	0.646860i	0.616631	+	0.787252i	$0.288497\pi$
$798$		0			0
$799$	383.281	+	663.862i	0.479700	+	0.830866i
$800$	45.0914	+	337.161i	0.0563642	+	0.421451i
$801$		0			0
$802$	−347.370	+	1174.47i	−0.433129	+	1.46442i
$803$	−110.353	−	191.137i	−0.137426	−	0.238029i
$804$		0			0
$805$	−594.412	−	343.184i	−0.738400	−	0.426316i
$806$	−161.523	−	170.070i	−0.200401	−	0.211006i
$807$		0			0
$808$	78.8478	−	223.533i	0.0975839	−	0.276649i
$809$		−	578.133i		−	0.714627i	−0.933985	−	0.357313i	$-0.883693\pi$
$809$		−	578.133i		−	0.714627i	0.933985	−	0.357313i	$-0.116307\pi$
$810$		0			0
$811$		−	870.431i		−	1.07328i	−0.843811	−	0.536641i	$-0.819693\pi$
$811$		−	870.431i		−	1.07328i	0.843811	−	0.536641i	$-0.180307\pi$
$812$	30.9185	−	599.364i	0.0380770	−	0.738133i
$813$		0			0
$814$	−16.7492	−	17.6355i	−0.0205765	−	0.0216653i
$815$	125.565	+	72.4951i	0.154068	+	0.0889511i
$816$		0			0
$817$	−136.921	−	237.155i	−0.167590	−	0.290275i
$818$	651.952	+	192.826i	0.797008	+	0.235729i
$819$		0			0
$820$	315.955	−	487.403i	0.385311	−	0.594393i
$821$	610.012	+	1056.57i	0.743011	+	1.28693i	0.951118	+	0.308826i	$0.0999362\pi$
$821$	610.012	+	1056.57i	0.743011	+	1.28693i	−0.208108	+	0.978106i	$0.566731\pi$
$822$		0			0
$823$	184.322	−	319.255i	0.223964	−	0.387916i	−0.732044	−	0.681257i	$-0.761434\pi$
$823$	184.322	−	319.255i	0.223964	−	0.387916i	0.956008	+	0.293341i	$0.0947670\pi$
$824$	−20.7011	+	3.86307i	−0.0251227	+	0.00468819i
$825$		0			0
$826$	112.341	+	467.092i	0.136007	+	0.565486i
$827$	754.669			0.912538			0.456269	−	0.889842i	$-0.349185\pi$
$827$	754.669			0.912538			0.456269	+	0.889842i	$0.349185\pi$
$828$		0			0
$829$		−	257.000i		−	0.310012i	−0.987914	−	0.155006i	$-0.950460\pi$
$829$		−	257.000i		−	0.310012i	0.987914	−	0.155006i	$-0.0495397\pi$
$830$	−118.934	−	494.503i	−0.143294	−	0.595787i
$831$		0			0
$832$	681.294	−	845.573i	0.818864	−	1.01631i
$833$	−1618.80	−	934.615i	−1.94334	−	1.12199i
$834$		0			0
$835$	−73.2297	+	42.2792i	−0.0877003	+	0.0506338i
$836$	328.273	−	506.405i	0.392671	−	0.605747i
$837$		0			0
$838$	147.378	+	43.5896i	0.175868	+	0.0520162i
$839$	−1439.78	+	831.258i	−1.71607	+	0.990773i	−0.790268	+	0.612762i	$0.790059\pi$
$839$	−1439.78	+	831.258i	−1.71607	+	0.990773i	−0.925801	+	0.378011i	$0.876608\pi$
$840$		0			0
$841$	334.114	−	578.703i	0.397282	−	0.688113i
$842$	−1108.90	−	1167.58i	−1.31699	−	1.38668i
$843$		0			0
$844$	−610.494	−	31.4927i	−0.723334	−	0.0373136i
$845$	450.646			0.533309
$846$		0			0
$847$	−831.094			−0.981221
$848$	18.4670	−	25.5055i	0.0217771	−	0.0300773i
$849$		0			0
$850$	−336.620	−	354.433i	−0.396024	−	0.416980i
$851$	13.8933	−	24.0639i	0.0163259	−	0.0282772i
$852$		0			0
$853$	−435.489	+	251.429i	−0.510538	+	0.294759i	−0.733055	−	0.680170i	$-0.761906\pi$
$853$	−435.489	+	251.429i	−0.510538	+	0.294759i	0.222517	+	0.974929i	$0.428573\pi$
$854$	359.372	−	1215.05i	0.420810	−	1.42277i
$855$		0			0
$856$	−1062.05	−	1240.40i	−1.24071	−	1.44907i
$857$	−270.221	+	156.012i	−0.315310	+	0.182045i	−0.649300	−	0.760532i	$-0.724938\pi$
$857$	−270.221	+	156.012i	−0.315310	+	0.182045i	0.333990	+	0.942577i	$0.391605\pi$
$858$		0			0
$859$	890.067	+	513.880i	1.03617	+	0.598231i	0.918745	−	0.394852i	$-0.129204\pi$
$859$	890.067	+	513.880i	1.03617	+	0.598231i	0.117421	+	0.993082i	$0.462537\pi$
$860$	86.8772	+	170.161i	0.101020	+	0.197862i
$861$		0			0
$862$	1387.49	−	333.710i	1.60962	−	0.387134i
$863$			749.389i			0.868354i	0.900828	+	0.434177i	$0.142961\pi$
$863$			749.389i			0.868354i	−0.900828	+	0.434177i	$0.857039\pi$
$864$		0			0
$865$	−484.170			−0.559734
$866$	228.414	+	949.697i	0.263757	+	1.09665i
$867$		0			0
$868$	281.081	−	143.508i	0.323826	−	0.165332i
$869$	−477.260	+	826.638i	−0.549206	+	0.951252i
$870$		0			0
$871$	739.227	+	1280.38i	0.848710	+	1.47001i
$872$	−648.450	+	555.209i	−0.743635	+	0.636708i
$873$		0			0
$874$	661.158	+	195.549i	0.756474	+	0.223740i
$875$	−770.878	−	1335.20i	−0.881003	−	1.52594i
$876$		0			0
$877$	1288.44	+	743.881i	1.46914	+	0.848211i	0.999402	−	0.0345923i	$-0.0110133\pi$
$877$	1288.44	+	743.881i	1.46914	+	0.848211i	0.469743	+	0.882803i	$0.344347\pi$
$878$	553.660	−	525.836i	0.630593	−	0.598901i
$879$		0			0
$880$	−246.929	+	341.043i	−0.280601	+	0.387549i
$881$			970.067i			1.10110i	0.834803	+	0.550549i	$0.185582\pi$
$881$			970.067i			1.10110i	−0.834803	+	0.550549i	$0.814418\pi$
$882$		0			0
$883$		−	468.838i		−	0.530960i	−0.964116	−	0.265480i	$-0.914470\pi$
$883$		−	468.838i		−	0.530960i	0.964116	−	0.265480i	$-0.0855305\pi$
$884$	−80.3880	+	1558.34i	−0.0909366	+	1.76283i
$885$		0			0
$886$	−787.048	+	747.494i	−0.888316	+	0.843672i
$887$	−358.011	−	206.698i	−0.403620	−	0.233030i	0.284425	−	0.958698i	$-0.408197\pi$
$887$	−358.011	−	206.698i	−0.403620	−	0.233030i	−0.688045	+	0.725668i	$0.741531\pi$
$888$		0			0
$889$	−1120.42	−	1940.62i	−1.26031	−	2.18292i
$890$	−342.811	+	1159.06i	−0.385181	+	1.30231i
$891$		0			0
$892$	−805.279	−	522.016i	−0.902779	−	0.585220i
$893$	−362.301	−	627.524i	−0.405713	−	0.702715i
$894$		0			0
$895$	−195.306	+	338.280i	−0.218219	+	0.377967i
$896$	831.032	+	1201.76i	0.927491	+	1.34124i
$897$		0			0
$898$	256.651	−	61.7277i	0.285803	−	0.0687391i
$899$	−90.8523			−0.101059
$900$		0			0
$901$			45.2495i			0.0502215i
$902$	−517.112	+	124.372i	−0.573295	+	0.137885i
$903$		0			0
$904$	111.635	+	598.223i	0.123490	+	0.661751i
$905$	−234.828	−	135.578i	−0.259478	−	0.149810i
$906$		0			0
$907$	1337.74	−	772.343i	1.47490	−	0.851536i	0.475304	−	0.879822i	$-0.342338\pi$
$907$	1337.74	−	772.343i	1.47490	−	0.851536i	0.999600	+	0.0282854i	$0.00900473\pi$
$908$	−903.980	−	585.998i	−0.995573	−	0.645373i
$909$		0			0
$910$	−416.461	+	1408.07i	−0.457650	+	1.54733i
$911$	−73.7841	+	42.5993i	−0.0809924	+	0.0467610i	−0.539949	−	0.841698i	$-0.681557\pi$
$911$	−73.7841	+	42.5993i	−0.0809924	+	0.0467610i	0.458957	+	0.888459i	$0.348223\pi$
$912$		0			0
$913$	−232.853	+	403.313i	−0.255041	+	0.441744i
$914$	−368.601	+	350.077i	−0.403284	+	0.383016i
$915$		0			0
$916$	14.6632	+	0.756410i	0.0160079	+	0.000825775i
$917$	−196.521			−0.214309
$918$		0			0
$919$	−125.501			−0.136563			−0.0682815	−	0.997666i	$-0.521752\pi$
$919$	−125.501			−0.136563			−0.0682815	+	0.997666i	$0.521752\pi$
$920$	−453.639	−	160.014i	−0.493086	−	0.173929i
$921$		0			0
$922$	−719.068	+	682.931i	−0.779900	+	0.740706i
$923$	−328.729	+	569.375i	−0.356152	+	0.616874i
$924$		0			0
$925$	16.1267	−	9.31074i	0.0174342	−	0.0100657i
$926$	724.494	+	214.282i	0.782391	+	0.231406i
$927$		0			0
$928$	−55.7562	−	416.904i	−0.0600821	−	0.449250i
$929$	1474.21	−	851.134i	1.58688	−	0.916183i	0.593059	−	0.805159i	$-0.297920\pi$
$929$	1474.21	−	851.134i	1.58688	−	0.916183i	0.993818	−	0.111024i	$-0.0354131\pi$
$930$		0			0
$931$	1530.19	+	883.458i	1.64360	+	0.948935i
$932$	41.3515	+	80.9926i	0.0443685	+	0.0869019i
$933$		0			0
$934$	−62.8812	−	261.447i	−0.0673246	−	0.279922i
$935$		−	605.047i		−	0.647109i
$936$		0			0
$937$	1629.91			1.73950			0.869748	−	0.493496i	$-0.164281\pi$
$937$	1629.91			1.73950			0.869748	+	0.493496i	$0.164281\pi$
$938$	−1934.16	+	465.189i	−2.06200	+	0.495938i
$939$		0			0
$940$	229.882	+	450.256i	0.244555	+	0.478995i
$941$	847.730	−	1468.31i	0.900882	−	1.56037i	0.0745304	−	0.997219i	$-0.476254\pi$
$941$	847.730	−	1468.31i	0.900882	−	1.56037i	0.826352	−	0.563155i	$-0.190412\pi$
$942$		0			0
$943$	−303.813	−	526.220i	−0.322177	−	0.558027i
$944$	137.449	+	307.358i	0.145603	+	0.325591i
$945$		0			0
$946$	49.6172	−	167.757i	0.0524495	−	0.177333i
$947$	759.787	+	1315.99i	0.802310	+	1.38964i	0.918092	+	0.396367i	$0.129729\pi$
$947$	759.787	+	1315.99i	0.802310	+	1.38964i	−0.115783	+	0.993275i	$0.536938\pi$
$948$		0			0
$949$	−467.156	−	269.713i	−0.492262	−	0.284207i
$950$	318.195	+	335.033i	0.334942	+	0.352666i
$951$		0			0
$952$	−1980.03	−	698.425i	−2.07986	−	0.733639i
$953$		−	330.801i		−	0.347115i	−0.984824	−	0.173558i	$-0.944474\pi$
$953$		−	330.801i		−	0.347115i	0.984824	−	0.173558i	$-0.0555263\pi$
$954$		0			0
$955$			660.459i			0.691580i
$956$	310.037	+	15.9934i	0.324306	+	0.0167295i
$957$		0			0
$958$	423.190	+	445.583i	0.441743	+	0.465118i
$959$	−1807.15	−	1043.36i	−1.88441	−	1.08796i
$960$		0			0
$961$	456.613	+	790.876i	0.475143	+	0.822972i
$962$	−57.0037	−	16.8598i	−0.0592554	−	0.0175258i
$963$		0			0
$964$	670.766	+	434.819i	0.695816	+	0.451057i
$965$	−397.824	−	689.051i	−0.412253	−	0.714043i
$966$		0			0
$967$	−272.891	+	472.661i	−0.282204	+	0.488791i	−0.971927	−	0.235281i	$-0.924399\pi$
$967$	−272.891	+	472.661i	−0.282204	+	0.488791i	0.689723	+	0.724073i	$0.257732\pi$
$968$	−572.579	+	106.850i	−0.591507	+	0.110382i
$969$		0			0
$970$	150.801	+	627.000i	0.155465	+	0.646392i
$971$	−661.647			−0.681408			−0.340704	−	0.940171i	$-0.610665\pi$
$971$	−661.647			−0.681408			−0.340704	+	0.940171i	$0.610665\pi$
$972$		0			0
$973$			1115.70i			1.14666i
$974$	229.133	+	952.686i	0.235249	+	0.978117i
$975$		0			0
$976$	91.3748	−	883.305i	0.0936217	−	0.905026i
$977$	−137.933	−	79.6354i	−0.141180	−	0.0815102i	0.427746	−	0.903899i	$-0.359308\pi$
$977$	−137.933	−	79.6354i	−0.141180	−	0.0815102i	−0.568926	+	0.822389i	$0.692641\pi$
$978$		0			0
$979$	958.466	−	553.370i	0.979025	−	0.565240i
$980$	−1034.42	−	670.557i	−1.05553	−	0.684242i
$981$		0			0
$982$	172.655	+	51.0658i	0.175820	+	0.0520019i
$983$	488.957	−	282.299i	0.497413	−	0.287181i	−0.230232	−	0.973136i	$-0.573948\pi$
$983$	488.957	−	282.299i	0.497413	−	0.287181i	0.727644	+	0.685955i	$0.240615\pi$
$984$		0			0
$985$	144.027	−	249.462i	0.146220	−	0.253261i
$986$	416.236	+	438.261i	0.422146	+	0.444484i
$987$		0			0
$988$	75.9879	−	1473.04i	0.0769108	−	1.49094i
$989$	199.863			0.202086
$990$		0			0
$991$	259.373			0.261729			0.130864	−	0.991400i	$-0.458225\pi$
$991$	259.373			0.261729			0.130864	+	0.991400i	$0.458225\pi$
$992$	175.199	−	135.007i	0.176612	−	0.136095i
$993$		0			0
$994$	−609.205	−	641.441i	−0.612882	−	0.645313i
$995$	−528.407	+	915.228i	−0.531062	+	0.919827i
$996$		0			0
$997$	−1549.08	+	894.362i	−1.55374	+	0.897053i	−0.555909	+	0.831243i	$0.687630\pi$
$997$	−1549.08	+	894.362i	−1.55374	+	0.897053i	−0.997832	+	0.0658097i	$0.979037\pi$
$998$	−308.911	+	1044.44i	−0.309530	+	1.04653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.j.a.125.13		44
3.2	odd	2		72.3.j.a.5.10	✓	44
4.3	odd	2		864.3.n.a.17.17		44
8.3	odd	2		864.3.n.a.17.6		44
8.5	even	2	inner	216.3.j.a.125.6		44
9.2	odd	6	inner	216.3.j.a.197.6		44
9.4	even	3		648.3.h.a.485.3		44
9.5	odd	6		648.3.h.a.485.42		44
9.7	even	3		72.3.j.a.29.17	yes	44
12.11	even	2		288.3.n.a.113.16		44
24.5	odd	2		72.3.j.a.5.17	yes	44
24.11	even	2		288.3.n.a.113.7		44
36.7	odd	6		288.3.n.a.209.7		44
36.11	even	6		864.3.n.a.305.6		44
36.23	even	6		2592.3.h.a.1457.33		44
36.31	odd	6		2592.3.h.a.1457.12		44
72.5	odd	6		648.3.h.a.485.4		44
72.11	even	6		864.3.n.a.305.17		44
72.13	even	6		648.3.h.a.485.41		44
72.29	odd	6	inner	216.3.j.a.197.13		44
72.43	odd	6		288.3.n.a.209.16		44
72.59	even	6		2592.3.h.a.1457.11		44
72.61	even	6		72.3.j.a.29.10	yes	44
72.67	odd	6		2592.3.h.a.1457.34		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.10	✓	44	3.2	odd	2
72.3.j.a.5.17	yes	44	24.5	odd	2
72.3.j.a.29.10	yes	44	72.61	even	6
72.3.j.a.29.17	yes	44	9.7	even	3
216.3.j.a.125.6		44	8.5	even	2	inner
216.3.j.a.125.13		44	1.1	even	1	trivial
216.3.j.a.197.6		44	9.2	odd	6	inner
216.3.j.a.197.13		44	72.29	odd	6	inner
288.3.n.a.113.7		44	24.11	even	2
288.3.n.a.113.16		44	12.11	even	2
288.3.n.a.209.7		44	36.7	odd	6
288.3.n.a.209.16		44	72.43	odd	6
648.3.h.a.485.3		44	9.4	even	3
648.3.h.a.485.4		44	72.5	odd	6
648.3.h.a.485.41		44	72.13	even	6
648.3.h.a.485.42		44	9.5	odd	6
864.3.n.a.17.6		44	8.3	odd	2
864.3.n.a.17.17		44	4.3	odd	2
864.3.n.a.305.6		44	36.11	even	6
864.3.n.a.305.17		44	72.11	even	6
2592.3.h.a.1457.11		44	72.59	even	6
2592.3.h.a.1457.12		44	36.31	odd	6
2592.3.h.a.1457.33		44	36.23	even	6
2592.3.h.a.1457.34		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)

\(f(q)\)	\(=\)	\(q+(0.467688 + 1.94455i) q^{2} +(-3.56254 + 1.81888i) q^{4} +(1.89538 - 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +O(q^{10})\)	\(q+(0.467688 + 1.94455i) q^{2} +(-3.56254 + 1.81888i) q^{4} +(1.89538 - 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +(7.27021 + 2.15029i) q^{10} +(-3.47103 - 6.01200i) q^{11} +(-14.6939 - 8.48351i) q^{13} +(16.5537 - 15.7218i) q^{14} +(9.38332 - 12.9597i) q^{16} +22.9919i q^{17} -21.7334i q^{19} +(-0.781157 + 15.1429i) q^{20} +(10.0673 - 9.56132i) q^{22} +(13.7369 + 7.93101i) q^{23} +(5.31504 + 9.20592i) q^{25} +(9.62445 - 32.5406i) q^{26} +(38.3137 + 24.8366i) q^{28} +(-6.57213 - 11.3833i) q^{29} +(3.45597 - 5.98592i) q^{31} +(29.5892 + 12.1852i) q^{32} +(-44.7088 + 10.7530i) q^{34} -43.2712 q^{35} -1.75177i q^{37} +(42.2616 - 10.1644i) q^{38} +(-29.8115 + 5.56317i) q^{40} +(-33.1748 - 19.1535i) q^{41} +(10.9120 - 6.30005i) q^{43} +(23.3008 + 15.1046i) q^{44} +(-8.99764 + 30.4213i) q^{46} +(28.8738 - 16.6703i) q^{47} +(-40.6498 + 70.4076i) q^{49} +(-15.4156 + 14.6409i) q^{50} +(67.7780 + 3.49637i) q^{52} +1.96807 q^{53} -26.3157 q^{55} +(-30.3770 + 86.1186i) q^{56} +(19.0616 - 18.1036i) q^{58} +(-10.5216 + 18.2239i) q^{59} +(48.0654 - 27.7506i) q^{61} +(13.2562 + 3.92076i) q^{62} +(-9.85628 + 63.2365i) q^{64} +(-55.7011 + 32.1590i) q^{65} +(-75.4627 - 43.5684i) q^{67} +(-41.8195 - 81.9093i) q^{68} +(-20.2374 - 84.1429i) q^{70} -38.7491i q^{71} +31.7926 q^{73} +(3.40640 - 0.819283i) q^{74} +(39.5305 + 77.4259i) q^{76} +(-39.6214 + 68.6263i) q^{77} +(-68.7491 - 119.077i) q^{79} +(-24.7603 - 55.3681i) q^{80} +(21.7294 - 73.4679i) q^{82} +(-33.5423 - 58.0970i) q^{83} +(75.4800 + 43.5784i) q^{85} +(17.3542 + 18.2725i) q^{86} +(-18.4740 + 52.3737i) q^{88} +159.426i q^{89} +193.677i q^{91} +(-63.3638 - 3.26866i) q^{92} +(45.9201 + 48.3499i) q^{94} +(-71.3485 - 41.1931i) q^{95} +(42.5296 + 73.6635i) q^{97} +(-155.922 - 46.1168i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 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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