LMFDB - Embedded newform 216.3.j.a.125.6

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			125.6
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45018 - 1.37730i) q^{2} +(0.206068 + 3.99469i) q^{4} +(-1.89538 + 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(5.20306 - 6.07685i) q^{8} +O(q^{10})$	\(q+(-1.45018 - 1.37730i) q^{2} +(0.206068 + 3.99469i) q^{4} +(-1.89538 + 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(5.20306 - 6.07685i) q^{8} +(7.27021 - 2.15029i) q^{10} +(3.47103 + 6.01200i) q^{11} +(14.6939 + 8.48351i) q^{13} +(-5.33861 + 22.1968i) q^{14} +(-15.9151 + 1.64636i) q^{16} +22.9919i q^{17} +21.7334i q^{19} +(-13.5047 - 6.89497i) q^{20} +(3.24672 - 13.4992i) q^{22} +(13.7369 + 7.93101i) q^{23} +(5.31504 + 9.20592i) q^{25} +(-9.62445 - 32.5406i) q^{26} +(38.3137 - 24.8366i) q^{28} +(6.57213 + 11.3833i) q^{29} +(3.45597 - 5.98592i) q^{31} +(25.3473 + 19.5324i) q^{32} +(31.6668 - 33.3424i) q^{34} +43.2712 q^{35} +1.75177i q^{37} +(29.9335 - 31.5174i) q^{38} +(10.0879 + 28.5991i) q^{40} +(-33.1748 - 19.1535i) q^{41} +(-10.9120 + 6.30005i) q^{43} +(-23.3008 + 15.1046i) q^{44} +(-8.99764 - 30.4213i) q^{46} +(28.8738 - 16.6703i) q^{47} +(-40.6498 + 70.4076i) q^{49} +(4.97156 - 20.6707i) q^{50} +(-30.8610 + 60.4456i) q^{52} -1.96807 q^{53} -26.3157 q^{55} +(-89.7694 - 16.7520i) q^{56} +(6.14741 - 25.5596i) q^{58} +(10.5216 - 18.2239i) q^{59} +(-48.0654 + 27.7506i) q^{61} +(-13.2562 + 3.92076i) q^{62} +(-9.85628 - 63.2365i) q^{64} +(-55.7011 + 32.1590i) q^{65} +(75.4627 + 43.5684i) q^{67} +(-91.8453 + 4.73789i) q^{68} +(-62.7512 - 59.5976i) q^{70} -38.7491i q^{71} +31.7926 q^{73} +(2.41272 - 2.54039i) q^{74} +(-86.8181 + 4.47856i) q^{76} +(39.6214 - 68.6263i) q^{77} +(-68.7491 - 119.077i) q^{79} +(24.7603 - 55.3681i) q^{80} +(21.7294 + 73.4679i) q^{82} +(33.5423 + 58.0970i) q^{83} +(-75.4800 - 43.5784i) q^{85} +(24.5015 + 5.89291i) q^{86} +(54.5940 + 10.1879i) q^{88} +159.426i q^{89} -193.677i q^{91} +(-28.8512 + 56.5090i) q^{92} +(-64.8323 - 15.5930i) q^{94} +(-71.3485 - 41.1931i) q^{95} +(42.5296 + 73.6635i) q^{97} +(155.922 - 46.1168i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.45018	−	1.37730i	−0.725092	−	0.688652i
$2$	−1.45018	−	1.37730i	−0.725092	−	0.688652i
$3$		0			0
$3$		0			0
$4$	0.206068	+	3.99469i	0.0515171	+	0.998672i
$5$	−1.89538	+	3.28290i	−0.379077	+	0.656580i	−0.990928	−	0.134393i	$-0.957092\pi$
$5$	−1.89538	+	3.28290i	−0.379077	+	0.656580i	0.611851	+	0.790973i	$0.290425\pi$
$6$		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	0.979554	−	0.201182i	$-0.0644784\pi$
$11$	3.47103	+	6.01200i	0.315548	+	0.546545i	−0.664006	+	0.747727i	$0.731145\pi$
$12$		0			0
$13$	14.6939	+	8.48351i	1.13030	+	0.652578i	0.944010	−	0.329917i	$-0.107021\pi$
$13$	14.6939	+	8.48351i	1.13030	+	0.652578i	0.186288	+	0.982495i	$0.440354\pi$
$14$	−5.33861	+	22.1968i	−0.381329	+	1.58549i
$15$		0			0
$16$	−15.9151	+	1.64636i	−0.994692	+	0.102897i
$17$			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	$0.193806\pi$
$19$			21.7334i			1.14386i	−0.820302	+	0.571931i	$0.806194\pi$
$20$	−13.5047	−	6.89497i	−0.675237	−	0.344748i
$21$		0			0
$22$	3.24672	−	13.4992i	0.147578	−	0.613598i
$23$	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	0.956806	−	0.290728i	$-0.0938975\pi$
$29$	6.57213	+	11.3833i	0.226625	+	0.392526i	−0.730181	+	0.683254i	$0.760564\pi$
$30$		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	$0.131107\pi$
$32$	25.3473	+	19.5324i	0.792104	+	0.610386i
$33$		0			0
$34$	31.6668	−	33.3424i	0.931376	−	0.980660i
$35$	43.2712			1.23632
$36$		0			0
$37$			1.75177i			0.0473452i	0.999720	+	0.0236726i	$0.00753592\pi$
$37$			1.75177i			0.0473452i	−0.999720	+	0.0236726i	$0.992464\pi$
$38$	29.9335	−	31.5174i	0.787723	−	0.829405i
$39$		0			0
$40$	10.0879	+	28.5991i	0.252198	+	0.714978i
$41$	−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	−0.621488	−	0.783424i	$-0.713472\pi$
$43$	−10.9120	+	6.30005i	−0.253768	+	0.146513i	0.367721	+	0.929936i	$0.380138\pi$
$44$	−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
$50$	4.97156	−	20.6707i	0.0994312	−	0.413414i
$51$		0			0
$52$	−30.8610	+	60.4456i	−0.593482	+	1.16242i
$53$	−1.96807			−0.0371334			−0.0185667	−	0.999828i	$-0.505910\pi$
$53$	−1.96807			−0.0371334			−0.0185667	+	0.999828i	$0.505910\pi$
$54$		0			0
$55$	−26.3157			−0.478468
$56$	−89.7694	−	16.7520i	−1.60303	−	0.299143i
$57$		0			0
$58$	6.14741	−	25.5596i	0.105990	−	0.440683i
$59$	10.5216	−	18.2239i	0.178332	−	0.308880i	−0.762977	−	0.646425i	$-0.776263\pi$
$59$	10.5216	−	18.2239i	0.178332	−	0.308880i	0.941309	+	0.337545i	$0.109596\pi$
$60$		0			0
$61$	−48.0654	+	27.7506i	−0.787958	+	0.454928i	−0.839243	−	0.543756i	$-0.817002\pi$
$61$	−48.0654	+	27.7506i	−0.787958	+	0.454928i	0.0512853	+	0.998684i	$0.483668\pi$
$62$	−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	0.943004	−	0.332781i	$-0.107987\pi$
$67$	75.4627	+	43.5684i	1.12631	+	0.650275i	0.183305	+	0.983056i	$0.441320\pi$
$68$	−91.8453	+	4.73789i	−1.35067	+	0.0696749i
$69$		0			0
$70$	−62.7512	−	59.5976i	−0.896446	−	0.851394i
$71$		−	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	$0.430126\pi$
$74$	2.41272	−	2.54039i	0.0326044	−	0.0343296i
$75$		0			0
$76$	−86.8181	+	4.47856i	−1.14234	+	0.0589284i
$77$	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	0.994219	−	0.107370i	$-0.0342430\pi$
$83$	33.5423	+	58.0970i	0.404124	+	0.699964i	−0.590095	+	0.807334i	$0.700910\pi$
$84$		0			0
$85$	−75.4800	−	43.5784i	−0.888000	−	0.512687i
$86$	24.5015	+	5.89291i	0.284901	+	0.0685223i
$87$		0			0
$88$	54.5940	+	10.1879i	0.620386	+	0.115771i
$89$			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
$92$	−28.8512	+	56.5090i	−0.313600	+	0.614228i
$93$		0			0
$94$	−64.8323	−	15.5930i	−0.689705	−	0.165883i
$95$	−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	0.783320	−	0.621619i	$-0.213525\pi$
$101$	−14.8145	−	25.6594i	−0.146678	−	0.254053i	−0.929998	+	0.367565i	$0.880191\pi$
$102$		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	$0.162599\pi$
$104$	128.006	−	45.1523i	1.23083	−	0.434156i
$105$		0			0
$106$	2.85406	+	2.71063i	0.0269251	+	0.0255720i
$107$	−204.119			−1.90766			−0.953828	−	0.300352i	$-0.902896\pi$
$107$	−204.119			−1.90766			−0.953828	+	0.300352i	$0.902896\pi$
$108$		0			0
$109$			106.708i			0.978974i	0.872011	+	0.489487i	$0.162816\pi$
$109$			106.708i			0.978974i	−0.872011	+	0.489487i	$0.837184\pi$
$110$	38.1626	+	36.2447i	0.346933	+	0.329498i
$111$		0			0
$112$	107.110	+	147.933i	0.956336	+	1.32083i
$113$	−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
$122$	107.925	+	25.9572i	0.884629	+	0.212764i
$123$		0			0
$124$	24.6240	+	12.5720i	0.198581	+	0.101387i
$125$	−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	$0.218823\pi$
$128$	−72.8024	+	105.280i	−0.568769	+	0.822497i
$129$		0			0
$130$	125.070	+	30.0808i	0.962073	+	0.231391i
$131$	−8.60811	+	14.9097i	−0.0657108	+	0.113814i	−0.897009	−	0.442012i	$-0.854265\pi$
$131$	−8.60811	+	14.9097i	−0.0657108	+	0.113814i	0.831298	+	0.555827i	$0.187598\pi$
$132$		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	0.772561	−	0.634941i	$-0.218976\pi$
$139$	84.6463	+	48.8706i	0.608966	+	0.351587i	−0.163595	+	0.986528i	$0.552309\pi$
$140$	8.91682	+	172.855i	0.0636916	+	1.23468i
$141$		0			0
$142$	−53.3693	+	56.1933i	−0.375840	+	0.395728i
$143$			117.786i			0.823678i
$144$		0			0
$145$	−49.8268			−0.343633
$146$	−46.1051	−	43.7881i	−0.315789	−	0.299918i
$147$		0			0
$148$	−6.99778	+	0.360985i	−0.0472823	+	0.00243909i
$149$	14.1349	−	24.4823i	0.0948650	−	0.164311i	−0.814687	−	0.579901i	$-0.803091\pi$
$149$	14.1349	−	24.4823i	0.0948650	−	0.164311i	0.909552	+	0.415590i	$0.136425\pi$
$150$		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	−0.293968	−	0.955815i	$-0.594976\pi$
$157$	−199.188	−	115.001i	−1.26871	−	0.732492i	−0.974744	+	0.223324i	$0.928309\pi$
$158$	−64.3062	+	267.372i	−0.407001	+	1.69223i
$159$		0			0
$160$	−112.166	+	46.1914i	−0.701036	+	0.288696i
$161$		−	181.063i		−	1.12462i
$162$		0			0
$163$		−	38.2483i		−	0.234652i	−0.993093	−	0.117326i	$-0.962568\pi$
$163$		−	38.2483i		−	0.234652i	0.993093	−	0.117326i	$-0.0374322\pi$
$164$	69.6760	−	136.470i	0.424854	−	0.832135i
$165$		0			0
$166$	31.3747	−	130.449i	0.189004	−	0.785839i
$167$	−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	0.989432	−	0.144999i	$-0.0463179\pi$
$173$	63.8618	+	110.612i	0.369143	+	0.639375i	−0.620289	+	0.784374i	$0.712985\pi$
$174$		0			0
$175$	60.6706	−	105.085i	0.346689	−	0.600483i
$176$	−65.1395	−	89.9668i	−0.370111	−	0.511175i
$177$		0			0
$178$	219.577	−	231.196i	1.23358	−	1.29886i
$179$	103.043			0.575660			0.287830	−	0.957682i	$-0.407066\pi$
$179$	103.043			0.575660			0.287830	+	0.957682i	$0.407066\pi$
$180$		0			0
$181$			71.5305i			0.395196i	0.980283	+	0.197598i	$0.0633141\pi$
$181$			71.5305i			0.395196i	−0.980283	+	0.197598i	$0.936686\pi$
$182$	−266.752	+	280.867i	−1.46567	+	1.54322i
$183$		0			0
$184$	119.670	−	42.2116i	0.650378	−	0.229411i
$185$	−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	$-0.0163327\pi$
$194$	39.7812	−	165.402i	0.205058	−	0.852587i
$195$		0			0
$196$	−289.633	−	147.875i	−1.47772	−	0.754463i
$197$	−75.9883			−0.385727			−0.192864	−	0.981226i	$-0.561777\pi$
$197$	−75.9883			−0.385727			−0.192864	+	0.981226i	$0.561777\pi$
$198$		0			0
$199$	−278.786			−1.40094			−0.700468	−	0.713684i	$-0.747025\pi$
$199$	−278.786			−1.40094			−0.700468	+	0.713684i	$0.747025\pi$
$200$	83.5975	+	15.6003i	0.417988	+	0.0780013i
$201$		0			0
$202$	−13.8571	+	57.6149i	−0.0685994	+	0.285222i
$203$	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	0.152431	−	0.988314i	$-0.451290\pi$
$211$	−132.352	−	76.4132i	−0.627259	−	0.362148i	−0.779690	+	0.626166i	$0.784623\pi$
$212$	−0.405557	−	7.86182i	−0.00191300	−	0.0370840i
$213$		0			0
$214$	296.011	+	281.134i	1.38323	+	1.31371i
$215$		−	47.7640i		−	0.222158i
$216$		0			0
$217$	−78.8990			−0.363590
$218$	146.970	−	154.747i	0.674173	−	0.709847i
$219$		0			0
$220$	−5.42284	−	105.123i	−0.0246493	−	0.477832i
$221$	−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	$-0.964521\pi$
$227$	−134.662	−	233.242i	−0.593227	−	1.02750i	0.400568	−	0.916267i	$-0.368813\pi$
$228$		0			0
$229$	3.17890	+	1.83534i	0.0138816	+	0.00801457i	0.506925	−	0.861990i	$-0.330782\pi$
$229$	3.17890	+	1.83534i	0.0138816	+	0.00801457i	−0.493043	+	0.870005i	$0.664116\pi$
$230$	116.924	+	28.1217i	0.508366	+	0.122268i
$231$		0			0
$232$	103.370	+	19.2900i	0.445559	+	0.0831464i
$233$		−	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
$236$	74.9672	+	38.2751i	0.317657	+	0.162183i
$237$		0			0
$238$	−510.346	−	122.744i	−2.14431	−	0.515733i
$239$	−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
$248$	−18.3939	−	52.1465i	−0.0741690	−	0.210268i
$249$		0			0
$250$	195.870	+	186.026i	0.783479	+	0.744104i
$251$	250.203			0.996825			0.498412	−	0.866940i	$-0.333917\pi$
$251$	250.203			0.996825			0.498412	+	0.866940i	$0.333917\pi$
$252$		0			0
$253$			110.115i			0.435237i
$254$	−284.682	−	270.375i	−1.12080	−	1.06447i
$255$		0			0
$256$	250.579	−	52.4038i	0.978824	−	0.204702i
$257$	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
$266$	−482.411	−	116.026i	−1.81358	−	0.436188i
$267$		0			0
$268$	−158.492	+	310.428i	−0.591387	+	1.15831i
$269$	507.709			1.88740			0.943698	−	0.330809i	$-0.107322\pi$
$269$	507.709			1.88740			0.943698	+	0.330809i	$0.107322\pi$
$270$		0			0
$271$	85.0065			0.313677			0.156839	−	0.987624i	$-0.449870\pi$
$271$	85.0065			0.313677			0.156839	+	0.987624i	$0.449870\pi$
$272$	−37.8528	−	365.917i	−0.139165	−	1.34528i
$273$		0			0
$274$	−355.476	−	85.4963i	−1.29736	−	0.312030i
$275$	−36.8973	+	63.9080i	−0.134172	+	0.232393i
$276$		0			0
$277$	159.497	−	92.0857i	0.575802	−	0.332439i	−0.183661	−	0.982990i	$-0.558795\pi$
$277$	159.497	−	92.0857i	0.575802	−	0.332439i	0.759463	+	0.650550i	$0.225462\pi$
$278$	−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	0.824076	−	0.566479i	$-0.191695\pi$
$283$	210.985	+	121.812i	0.745529	+	0.430431i	−0.0785474	+	0.996910i	$0.525028\pi$
$284$	154.791	−	7.98497i	0.545037	−	0.0281161i
$285$		0			0
$286$	162.227	−	170.811i	0.567228	−	0.597243i
$287$			437.270i			1.52359i
$288$		0			0
$289$	−239.626			−0.829154
$290$	72.2581	+	68.6267i	0.249166	+	0.236644i
$291$		0			0
$292$	6.55145	+	127.002i	0.0224365	+	0.434937i
$293$	285.189	−	493.962i	0.973342	−	1.68588i	0.288039	−	0.957619i	$-0.406997\pi$
$293$	285.189	−	493.962i	0.973342	−	1.68588i	0.685303	−	0.728258i	$-0.259670\pi$
$294$		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
$302$	20.6816	−	85.9899i	0.0684822	−	0.284735i
$303$		0			0
$304$	−35.7809	−	345.888i	−0.117700	−	1.13779i
$305$		−	210.392i		−	0.689810i
$306$		0			0
$307$		−	147.169i		−	0.479377i	−0.970850	−	0.239688i	$-0.922955\pi$
$307$		−	147.169i		−	0.479377i	0.970850	−	0.239688i	$-0.0770453\pi$
$308$	282.305	+	144.133i	0.916575	+	0.467966i
$309$		0			0
$310$	12.2542	−	50.9502i	0.0395295	−	0.164355i
$311$	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	$0.238796\pi$
$317$	303.122	+	525.022i	0.956219	+	1.65622i	0.224667	+	0.974436i	$0.427871\pi$
$318$		0			0
$319$	−45.6241	+	79.0232i	−0.143022	+	0.247722i
$320$	226.281	+	87.5002i	0.707127	+	0.273438i
$321$		0			0
$322$	−249.379	+	262.575i	−0.774469	+	0.815450i
$323$	−499.691			−1.54703
$324$		0			0
$325$			180.361i			0.554957i
$326$	−52.6795	+	55.4670i	−0.161594	+	0.170144i
$327$		0			0
$328$	−289.004	+	101.942i	−0.881109	+	0.310798i
$329$	−329.591	−	190.289i	−1.00180	−	0.578387i
$330$		0			0
$331$	−339.693	+	196.122i	−1.02626	+	0.592514i	−0.915912	−	0.401379i	$-0.868531\pi$
$331$	−339.693	+	196.122i	−1.02626	+	0.592514i	−0.110352	+	0.993893i	$0.535198\pi$
$332$	−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	$0.162918\pi$
$338$	55.5987	−	231.168i	0.164493	−	0.683928i
$339$		0			0
$340$	158.528	−	310.499i	0.466259	−	0.913233i
$341$	47.9831			0.140713
$342$		0			0
$343$	368.697			1.07492
$344$	−18.4914	+	99.0902i	−0.0537540	+	0.288053i
$345$		0			0
$346$	59.7348	−	248.365i	0.172644	−	0.717817i
$347$	−108.377	+	187.715i	−0.312326	+	0.540965i	−0.978866	−	0.204505i	$-0.934442\pi$
$347$	−108.377	+	187.715i	−0.312326	+	0.540965i	0.666539	+	0.745470i	$0.267775\pi$
$348$		0			0
$349$	−434.379	+	250.789i	−1.24464	+	0.718593i	−0.970035	−	0.242964i	$-0.921880\pi$
$349$	−434.379	+	250.789i	−1.24464	+	0.718593i	−0.274605	+	0.961557i	$0.588547\pi$
$350$	−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
$356$	−636.855	+	32.8526i	−1.78892	+	0.0922825i
$357$		0			0
$358$	−149.431	−	141.922i	−0.417406	−	0.396429i
$359$		−	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
$362$	98.5192	−	103.732i	0.272153	−	0.286554i
$363$		0			0
$364$	773.678	−	39.9106i	2.12549	−	0.109645i
$365$	−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	0.473681	−	0.880696i	$-0.342925\pi$
$373$	−19.4643	−	11.2377i	−0.0521831	−	0.0301279i	−0.525865	+	0.850568i	$0.676258\pi$
$374$	310.371	+	74.6480i	0.829868	+	0.199594i
$375$		0			0
$376$	48.9292	−	262.198i	0.130131	−	0.697335i
$377$			223.019i			0.591562i
$378$		0			0
$379$		−	170.148i		−	0.448940i	−0.974481	−	0.224470i	$-0.927935\pi$
$379$		−	170.148i		−	0.448940i	0.974481	−	0.224470i	$-0.0720650\pi$
$380$	149.851	−	293.504i	0.394344	−	0.772378i
$381$		0			0
$382$	338.795	+	81.4844i	0.886898	+	0.213310i
$383$	−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	0.785310	−	0.619103i	$-0.212504\pi$
$389$	−55.8230	−	96.6882i	−0.143504	−	0.248556i	−0.928814	+	0.370547i	$0.879170\pi$
$390$		0			0
$391$	−182.349	+	315.837i	−0.466365	+	0.807767i
$392$	216.353	+	613.358i	0.551921	+	1.56469i
$393$		0			0
$394$	110.197	+	104.659i	0.279688	+	0.265632i
$395$	521.223			1.31955
$396$		0			0
$397$			582.265i			1.46666i	0.679871	+	0.733332i	$0.262036\pi$
$397$			582.265i			1.46666i	−0.679871	+	0.733332i	$0.737964\pi$
$398$	404.292	+	383.973i	1.01581	+	0.964758i
$399$		0			0
$400$	−99.7455	−	137.762i	−0.249364	−	0.344406i
$401$	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	$0.0302492\pi$
$410$	−282.374	−	67.9144i	−0.688716	−	0.165645i
$411$		0			0
$412$	9.37770	+	4.78787i	0.0227614	+	0.0116210i
$413$	−240.206			−0.581612
$414$		0			0
$415$	−254.302			−0.612776
$416$	206.747	+	502.040i	0.496989	+	1.20683i
$417$		0			0
$418$	293.382	+	70.5621i	0.701872	+	0.168809i
$419$	−38.4222	+	66.5492i	−0.0916998	+	0.158829i	−0.908226	−	0.418479i	$-0.862563\pi$
$419$	−38.4222	+	66.5492i	−0.0916998	+	0.158829i	0.816527	+	0.577308i	$0.195897\pi$
$420$		0			0
$421$	697.260	−	402.563i	1.65620	−	0.956207i	0.681755	−	0.731581i	$-0.261217\pi$
$421$	697.260	−	402.563i	1.65620	−	0.956207i	0.974445	−	0.224627i	$-0.0721162\pi$
$422$	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
$428$	−42.0625	−	815.393i	−0.0982769	−	1.90512i
$429$		0			0
$430$	−65.7856	+	69.2666i	−0.152990	+	0.161085i
$431$		−	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	$0.309277\pi$
$434$	114.418	+	108.668i	0.263636	+	0.250387i
$435$		0			0
$436$	−426.266	+	21.9892i	−0.977674	+	0.0504339i
$437$	−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	$-0.956809\pi$
$443$	−271.361	−	470.011i	−0.612554	−	1.06097i	0.378255	−	0.925702i	$-0.376524\pi$
$444$		0			0
$445$	−523.378	−	302.173i	−1.17613	−	0.679039i
$446$	112.207	−	466.533i	0.251585	−	1.04604i
$447$		0			0
$448$	−568.875	+	458.354i	−1.26981	+	1.02311i
$449$		−	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
$452$	138.360	−	270.998i	0.306107	−	0.599552i
$453$		0			0
$454$	−125.960	+	523.715i	−0.277445	+	1.15356i
$455$	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	$-0.985924\pi$
$461$	−247.923	−	429.415i	−0.537794	−	0.931487i	0.461228	−	0.887281i	$-0.347409\pi$
$462$		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	$0.0329113\pi$
$464$	−123.337	−	170.345i	−0.265812	−	0.367124i
$465$		0			0
$466$	−31.3124	+	32.9693i	−0.0671939	+	0.0707495i
$467$	134.451			0.287904			0.143952	−	0.989585i	$-0.454019\pi$
$467$	134.451			0.287904			0.143952	+	0.989585i	$0.454019\pi$
$468$		0			0
$469$		−	994.658i		−	2.12081i
$470$	174.072	−	183.283i	0.370367	−	0.389965i
$471$		0			0
$472$	−55.9997	−	158.759i	−0.118643	−	0.336353i
$473$	−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
$482$	−93.4641	+	388.604i	−0.193909	+	0.806233i
$483$		0			0
$484$	259.381	+	132.429i	0.535910	+	0.273614i
$485$	−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	$0.332228\pi$
$488$	−81.4512	+	436.475i	−0.166908	+	0.894415i
$489$		0			0
$490$	−144.136	+	599.287i	−0.294155	+	1.22303i
$491$	−45.0122	+	77.9634i	−0.0916745	+	0.158785i	−0.908216	−	0.418502i	$-0.862555\pi$
$491$	−45.0122	+	77.9634i	−0.0916745	+	0.158785i	0.816541	+	0.577287i	$0.195889\pi$
$492$		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	−0.0535679	−	0.998564i	$-0.517059\pi$
$499$	−471.622	−	272.291i	−0.945134	−	0.545673i	−0.891566	+	0.452891i	$0.850393\pi$
$500$	−27.8327	−	539.544i	−0.0556654	−	1.07909i
$501$		0			0
$502$	−362.840	−	344.605i	−0.722790	−	0.686465i
$503$		−	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
$506$	151.662	−	159.687i	0.299727	−	0.315587i
$507$		0			0
$508$	40.4528	+	784.188i	0.0796315	+	1.54368i
$509$	−328.303	+	568.638i	−0.644996	+	1.11717i	0.339306	+	0.940676i	$0.389808\pi$
$509$	−328.303	+	568.638i	−0.644996	+	1.11717i	−0.984302	+	0.176490i	$0.943526\pi$
$510$		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
$518$	−38.8837	−	9.35202i	−0.0750651	−	0.0180541i
$519$		0			0
$520$	−94.3905	+	505.813i	−0.181520	+	0.972716i
$521$		−	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	$-0.829381\pi$
$523$		−	534.207i		−	1.02143i	0.859750	−	0.510714i	$-0.170619\pi$
$524$	−61.3334	−	31.3143i	−0.117048	−	0.0597601i
$525$		0			0
$526$	676.332	+	162.666i	1.28580	+	0.309252i
$527$	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
$536$	657.396	−	231.887i	1.22649	−	0.432624i
$537$		0			0
$538$	−736.272	−	699.270i	−1.36854	−	1.29976i
$539$	−564.387			−1.04710
$540$		0			0
$541$			41.7800i			0.0772273i	0.999254	+	0.0386137i	$0.0122942\pi$
$541$			41.7800i			0.0772273i	−0.999254	+	0.0386137i	$0.987706\pi$
$542$	−123.275	−	117.080i	−0.227445	−	0.216014i
$543$		0			0
$544$	−449.085	+	582.782i	−0.825525	+	1.07129i
$545$	−350.312	−	202.253i	−0.642775	−	0.371106i
$546$		0			0
$547$	−72.1250	+	41.6414i	−0.131855	+	0.0761268i	−0.564477	−	0.825449i	$-0.690922\pi$
$547$	−72.1250	+	41.6414i	−0.131855	+	0.0761268i	0.432621	+	0.901576i	$0.357589\pi$
$548$	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
$554$	−358.130	−	86.1348i	−0.646445	−	0.155478i
$555$		0			0
$556$	−177.780	+	348.206i	−0.319748	+	0.626270i
$557$	233.457			0.419133			0.209566	−	0.977794i	$-0.432795\pi$
$557$	233.457			0.419133			0.209566	+	0.977794i	$0.432795\pi$
$558$		0			0
$559$	−213.786			−0.382444
$560$	−688.664	+	71.2399i	−1.22976	+	0.127214i
$561$		0			0
$562$	−549.593	−	132.184i	−0.977923	−	0.235203i
$563$	314.155	−	544.133i	0.558002	−	0.966488i	−0.439661	−	0.898164i	$-0.644901\pi$
$563$	314.155	−	544.133i	0.558002	−	0.966488i	0.997663	−	0.0683244i	$-0.0217653\pi$
$564$		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	−0.175723	−	0.984440i	$-0.556226\pi$
$571$	−637.313	−	367.953i	−1.11613	−	0.644400i	−0.940411	+	0.340039i	$0.889560\pi$
$572$	−470.518	+	24.2720i	−0.822585	+	0.0424335i
$573$		0			0
$574$	602.254	−	634.122i	1.04922	−	1.10474i
$575$			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	$0.449981\pi$
$578$	347.501	+	330.037i	0.601213	+	0.570999i
$579$		0			0
$580$	−10.2677	−	199.043i	−0.0177030	−	0.343177i
$581$	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	0.728978	−	0.684537i	$-0.239996\pi$
$587$	−134.034	−	232.154i	−0.228338	−	0.395493i	−0.957316	+	0.289045i	$0.906662\pi$
$588$		0			0
$589$	130.094	+	75.1099i	0.220873	+	0.127521i
$590$	37.3074	−	155.116i	0.0632329	−	0.262909i
$591$		0			0
$592$	−2.88404	−	27.8796i	−0.00487170	−	0.0470939i
$593$			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
$596$	100.712	+	51.4194i	0.168980	+	0.0862742i
$597$		0			0
$598$	125.869	−	523.339i	0.210484	−	0.875148i
$599$	−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	$0.312849\pi$
$608$	−424.504	+	550.883i	−0.698198	+	0.906057i
$609$		0			0
$610$	−289.774	+	305.107i	−0.475039	+	0.500176i
$611$	565.690			0.925843
$612$		0			0
$613$		−	977.999i		−	1.59543i	−0.603034	−	0.797715i	$-0.706042\pi$
$613$		−	977.999i		−	1.59543i	0.603034	−	0.797715i	$-0.293958\pi$
$614$	−202.696	+	213.422i	−0.330124	+	0.347592i
$615$		0			0
$616$	−210.879	−	597.840i	−0.342336	−	0.970520i
$617$	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	0.123771	−	0.992311i	$-0.460501\pi$
$619$	646.869	−	373.470i	1.04502	−	0.603344i	0.921252	+	0.388967i	$0.127168\pi$
$620$	−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
$626$	−203.255	+	845.091i	−0.324688	+	1.34999i
$627$		0			0
$628$	418.348	−	819.392i	0.666158	−	1.30476i
$629$	−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	$0.687315\pi$
$632$	−1081.32	−	201.786i	−1.71095	−	0.319282i
$633$		0			0
$634$	283.533	−	1178.87i	0.447212	−	1.85941i
$635$	−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	0.524133	−	0.851637i	$-0.324390\pi$
$643$	31.2886	+	18.0645i	0.0486603	+	0.0280940i	−0.475472	+	0.879731i	$0.657723\pi$
$644$	723.291	−	37.3114i	1.12312	−	0.0579369i
$645$		0			0
$646$	724.644	+	688.226i	1.12174	+	1.06537i
$647$		−	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
$650$	248.412	−	261.556i	0.382172	−	0.402395i
$651$		0			0
$652$	152.790	−	7.88176i	0.234340	−	0.0120886i
$653$	−10.5807	+	18.3264i	−0.0162033	+	0.0280649i	−0.874013	−	0.485902i	$-0.838491\pi$
$653$	−10.5807	+	18.3264i	−0.0162033	+	0.0280649i	0.857810	+	0.513967i	$0.171825\pi$
$654$		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	$0.162526\pi$
$659$	566.376	+	980.992i	0.859448	+	1.48861i	−0.0130092	+	0.999915i	$0.504141\pi$
$660$		0			0
$661$	478.603	+	276.322i	0.724060	+	0.418036i	0.816245	−	0.577706i	$-0.196052\pi$
$661$	478.603	+	276.322i	0.724060	+	0.418036i	−0.0921855	+	0.995742i	$0.529385\pi$
$662$	762.737	+	183.448i	1.15217	+	0.277111i
$663$		0			0
$664$	527.570	+	98.4506i	0.794533	+	0.148269i
$665$			940.429i			1.41418i
$666$		0			0
$667$			208.494i			0.312585i
$668$	40.5728	−	79.4674i	0.0607377	−	0.118963i
$669$		0			0
$670$	642.315	+	154.485i	0.958679	+	0.230574i
$671$	−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	0.550331	−	0.834947i	$-0.314502\pi$
$677$	−303.242	−	525.230i	−0.447920	−	0.775819i	−0.998250	+	0.0591273i	$0.981168\pi$
$678$		0			0
$679$	485.471	−	840.861i	0.714980	−	1.23838i
$680$	−657.547	+	231.940i	−0.966980	+	0.341088i
$681$		0			0
$682$	−69.5843	−	66.0873i	−0.102030	−	0.0969021i
$683$	117.424			0.171924			0.0859619	−	0.996298i	$-0.472604\pi$
$683$	117.424			0.171924			0.0859619	+	0.996298i	$0.472604\pi$
$684$		0			0
$685$			692.976i			1.01164i
$686$	−534.679	−	507.808i	−0.779415	−	0.740245i
$687$		0			0
$688$	163.293	−	118.231i	0.237345	−	0.171847i
$689$	−28.9185	−	16.6961i	−0.0419718	−	0.0242324i
$690$		0			0
$691$	787.615	−	454.730i	1.13982	−	0.658075i	0.193434	−	0.981113i	$-0.438038\pi$
$691$	787.615	−	454.730i	1.13982	−	0.658075i	0.946386	+	0.323038i	$0.104704\pi$
$692$	−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
$698$	975.343	+	234.582i	1.39734	+	0.336077i
$699$		0			0
$700$	432.282	+	220.706i	0.617546	+	0.315294i
$701$	190.527			0.271793			0.135896	−	0.990723i	$-0.456609\pi$
$701$	190.527			0.271793			0.135896	+	0.990723i	$0.456609\pi$
$702$		0			0
$703$	−38.0719			−0.0541564
$704$	345.966	−	278.751i	0.491429	−	0.395954i
$705$		0			0
$706$	−315.668	−	75.9220i	−0.447122	−	0.107538i
$707$	−169.105	+	292.899i	−0.239187	+	0.414284i
$708$		0			0
$709$	−890.120	+	513.911i	−1.25546	+	0.724839i	−0.972188	−	0.234201i	$-0.924753\pi$
$709$	−890.120	+	513.911i	−1.25546	+	0.724839i	−0.283270	+	0.959040i	$0.591419\pi$
$710$	−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
$716$	21.2339	+	411.625i	0.0296563	+	0.574895i
$717$		0			0
$718$	−338.457	+	356.367i	−0.471389	+	0.496332i
$719$			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
$722$	161.463	+	153.349i	0.223633	+	0.212394i
$723$		0			0
$724$	−285.742	+	14.7402i	−0.394671	+	0.0203594i
$725$	−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	0.829313	−	0.558784i	$-0.188732\pi$
$733$	557.115	+	321.651i	0.760048	+	0.438814i	−0.0692647	+	0.997598i	$0.522065\pi$
$734$	12.2545	−	50.9515i	0.0166955	−	0.0694163i
$735$		0			0
$736$	193.282	+	469.344i	0.262612	+	0.637696i
$737$			604.909i			0.820772i
$738$		0			0
$739$			948.427i			1.28339i	0.766959	+	0.641696i	$0.221769\pi$
$739$			948.427i			1.28339i	−0.766959	+	0.641696i	$0.778231\pi$
$740$	12.0784	−	23.6572i	0.0163222	−	0.0319692i
$741$		0			0
$742$	10.5067	−	43.6848i	0.0141600	−	0.0588744i
$743$	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	$0.200714\pi$
$752$	−432.083	+	312.845i	−0.574578	+	0.416018i
$753$		0			0
$754$	307.165	−	323.418i	0.407380	−	0.428937i
$755$	−167.632			−0.222029
$756$		0			0
$757$			43.6832i			0.0577057i	0.999584	+	0.0288529i	$0.00918543\pi$
$757$			43.6832i			0.0577057i	−0.999584	+	0.0288529i	$0.990815\pi$
$758$	−234.346	+	246.746i	−0.309163	+	0.325523i
$759$		0			0
$760$	−621.555	+	219.244i	−0.817836	+	0.288479i
$761$	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	$0.988819\pi$
$770$	140.489	−	584.125i	0.182454	−	0.758603i
$771$		0			0
$772$	747.744	+	381.767i	0.968580	+	0.494517i
$773$	199.902			0.258606			0.129303	−	0.991605i	$-0.458726\pi$
$773$	199.902			0.258606			0.129303	+	0.991605i	$0.458726\pi$
$774$		0			0
$775$	73.4745			0.0948058
$776$	668.927	+	124.829i	0.862019	+	0.160863i
$777$		0			0
$778$	−52.2155	+	217.101i	−0.0671150	+	0.279050i
$779$	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	0.962176	−	0.272428i	$-0.0878267\pi$
$787$	950.172	+	548.582i	1.20733	+	0.697055i	0.245158	+	0.969483i	$0.421160\pi$
$788$	−15.6588	−	303.549i	−0.0198715	−	0.385215i
$789$		0			0
$790$	−755.870	−	717.883i	−0.956797	−	0.908713i
$791$			868.316i			1.09774i
$792$		0			0
$793$	−941.690			−1.18750
$794$	801.956	−	844.392i	1.01002	−	1.06347i
$795$		0			0
$796$	−57.4490	−	1113.66i	−0.0721722	−	1.39908i
$797$	297.651	−	515.547i	0.373465	−	0.646860i	−0.616631	−	0.787252i	$-0.711503\pi$
$797$	297.651	−	515.547i	0.373465	−	0.646860i	0.990096	+	0.140392i	$0.0448364\pi$
$798$		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
$806$	−228.047	−	54.8481i	−0.282937	−	0.0680498i
$807$		0			0
$808$	−233.009	−	43.4821i	−0.288377	−	0.0538145i
$809$		−	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	$0.180307\pi$
$811$			870.431i			1.07328i	−0.843811	+	0.536641i	$0.819693\pi$
$812$	534.524	+	272.906i	0.658280	+	0.336091i
$813$		0			0
$814$	23.6474	+	5.68751i	0.0290509	+	0.00698711i
$815$	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	$-0.900064\pi$
$821$	−610.012	−	1056.57i	−0.743011	−	1.28693i	0.208108	−	0.978106i	$-0.433269\pi$
$822$		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	$0.0947670\pi$
$824$	−7.00504	−	19.8592i	−0.00850127	−	0.0241010i
$825$		0			0
$826$	348.343	+	330.836i	0.421722	+	0.400528i
$827$	−754.669			−0.912538			−0.456269	−	0.889842i	$-0.650815\pi$
$827$	−754.669			−0.912538			−0.456269	+	0.889842i	$0.650815\pi$
$828$		0			0
$829$			257.000i			0.310012i	0.987914	+	0.155006i	$0.0495397\pi$
$829$			257.000i			0.310012i	−0.987914	+	0.155006i	$0.950460\pi$
$830$	368.785	+	350.251i	0.444319	+	0.421990i
$831$		0			0
$832$	391.641	−	1012.80i	0.470722	−	1.21731i
$833$	−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
$842$	−1565.61	−	376.548i	−1.85939	−	0.447207i
$843$		0			0
$844$	277.974	−	544.450i	0.329353	−	0.645083i
$845$	−450.646			−0.533309
$846$		0			0
$847$	−831.094			−0.981221
$848$	31.3219	−	3.24014i	0.0369363	−	0.00382092i
$849$		0			0
$850$	475.258	+	114.305i	0.559127	+	0.134477i
$851$	−13.8933	+	24.0639i	−0.0163259	+	0.0282772i
$852$		0			0
$853$	435.489	−	251.429i	0.510538	−	0.294759i	−0.222517	−	0.974929i	$-0.571427\pi$
$853$	435.489	−	251.429i	0.510538	−	0.294759i	0.733055	+	0.680170i	$0.238094\pi$
$854$	−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	−0.117421	−	0.993082i	$-0.537463\pi$
$859$	−890.067	−	513.880i	−1.03617	−	0.598231i	−0.918745	+	0.394852i	$0.870796\pi$
$860$	190.802	−	9.84266i	0.221863	−	0.0114449i
$861$		0			0
$862$	−982.748	+	1034.75i	−1.14008	+	1.20041i
$863$			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
$866$	−708.255	−	672.661i	−0.817846	−	0.776744i
$867$		0			0
$868$	−16.2586	−	315.177i	−0.0187311	−	0.363107i
$869$	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	−0.469743	−	0.882803i	$-0.655653\pi$
$877$	−1288.44	−	743.881i	−1.46914	−	0.848211i	−0.999402	+	0.0345923i	$0.988987\pi$
$878$	−178.557	+	742.402i	−0.203368	+	0.845560i
$879$		0			0
$880$	418.816	−	43.3251i	0.475928	−	0.0492330i
$881$			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	$0.0855305\pi$
$883$			468.838i			0.530960i	−0.964116	+	0.265480i	$0.914470\pi$
$884$	−1389.76	−	709.553i	−1.57212	−	0.802662i
$885$		0			0
$886$	−253.825	+	1055.35i	−0.286484	+	1.19114i
$887$	−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
$896$	1456.27	+	118.817i	1.62530	+	0.132608i
$897$		0			0
$898$	−181.783	+	191.402i	−0.202431	+	0.213143i
$899$	90.8523			0.101059
$900$		0			0
$901$		−	45.2495i		−	0.0502215i
$902$	−366.265	+	385.646i	−0.406059	+	0.427546i
$903$		0			0
$904$	−573.894	+	202.432i	−0.634838	+	0.223930i
$905$	−234.828	−	135.578i	−0.259478	−	0.149810i
$906$		0			0
$907$	−1337.74	+	772.343i	−1.47490	+	0.851536i	−0.999600	−	0.0282854i	$-0.990995\pi$
$907$	−1337.74	+	772.343i	−1.47490	+	0.851536i	−0.475304	+	0.879822i	$0.657662\pi$
$908$	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
$914$	118.875	−	494.256i	0.130060	−	0.540762i
$915$		0			0
$916$	−6.67653	+	13.0769i	−0.00728879	+	0.0142761i
$917$	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	$0.521752\pi$
$920$	−88.2431	+	472.870i	−0.0959164	+	0.513990i
$921$		0			0
$922$	−231.901	+	964.197i	−0.251520	+	1.04577i
$923$	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
$932$	90.8174	−	4.68487i	0.0974435	−	0.00502668i
$933$		0			0
$934$	−194.979	−	185.180i	−0.208757	−	0.198266i
$935$		−	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	$0.164281\pi$
$938$	−1369.95	+	1442.44i	−1.46050	+	1.53778i
$939$		0			0
$940$	−504.874	+	26.0442i	−0.537100	+	0.0277066i
$941$	−847.730	+	1468.31i	−0.900882	+	1.56037i	−0.0745304	+	0.997219i	$0.523746\pi$
$941$	−847.730	+	1468.31i	−0.900882	+	1.56037i	−0.826352	+	0.563155i	$0.809588\pi$
$942$		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	$-0.870271\pi$
$947$	−759.787	−	1315.99i	−0.802310	−	1.38964i	0.115783	−	0.993275i	$-0.463062\pi$
$948$		0			0
$949$	467.156	+	269.713i	0.492262	+	0.284207i
$950$	449.244	+	108.049i	0.472889	+	0.113736i
$951$		0			0
$952$	385.160	−	2063.97i	0.404580	−	2.16803i
$953$		−	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
$956$	141.168	−	276.496i	0.147665	−	0.289222i
$957$		0			0
$958$	−597.481	−	143.702i	−0.623675	−	0.150002i
$959$	−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	$0.257732\pi$
$968$	−193.755	−	549.293i	−0.200160	−	0.567451i
$969$		0			0
$970$	467.597	+	444.098i	0.482059	+	0.457833i
$971$	661.647			0.681408			0.340704	−	0.940171i	$-0.389335\pi$
$971$	661.647			0.681408			0.340704	+	0.940171i	$0.389335\pi$
$972$		0			0
$973$		−	1115.70i		−	1.14666i
$974$	−710.484	−	674.778i	−0.729449	−	0.692790i
$975$		0			0
$976$	719.277	−	520.785i	0.736964	−	0.533592i
$977$	−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
$986$	587.664	+	141.340i	0.596008	+	0.143347i
$987$		0			0
$988$	−1313.69	−	670.715i	−1.32964	−	0.678861i
$989$	−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	$0.458225\pi$
$992$	204.519	−	84.2237i	0.206168	−	0.0849029i
$993$		0			0
$994$	860.106	+	206.866i	0.865298	+	0.208115i
$995$	528.407	−	915.228i	0.531062	−	0.919827i
$996$		0			0
$997$	1549.08	−	894.362i	1.55374	−	0.897053i	0.555909	−	0.831243i	$-0.312370\pi$
$997$	1549.08	−	894.362i	1.55374	−	0.897053i	0.997832	−	0.0658097i	$-0.0209630\pi$
$998$	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.125.6		44
3.2	odd	2		72.3.j.a.5.17	yes	44
4.3	odd	2		864.3.n.a.17.6		44
8.3	odd	2		864.3.n.a.17.17		44
8.5	even	2	inner	216.3.j.a.125.13		44
9.2	odd	6	inner	216.3.j.a.197.13		44
9.4	even	3		648.3.h.a.485.41		44
9.5	odd	6		648.3.h.a.485.4		44
9.7	even	3		72.3.j.a.29.10	yes	44
12.11	even	2		288.3.n.a.113.7		44
24.5	odd	2		72.3.j.a.5.10	✓	44
24.11	even	2		288.3.n.a.113.16		44
36.7	odd	6		288.3.n.a.209.16		44
36.11	even	6		864.3.n.a.305.17		44
36.23	even	6		2592.3.h.a.1457.11		44
36.31	odd	6		2592.3.h.a.1457.34		44
72.5	odd	6		648.3.h.a.485.42		44
72.11	even	6		864.3.n.a.305.6		44
72.13	even	6		648.3.h.a.485.3		44
72.29	odd	6	inner	216.3.j.a.197.6		44
72.43	odd	6		288.3.n.a.209.7		44
72.59	even	6		2592.3.h.a.1457.33		44
72.61	even	6		72.3.j.a.29.17	yes	44
72.67	odd	6		2592.3.h.a.1457.12		44

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

\(f(q)\)	\(=\)	\(q+(-1.45018 - 1.37730i) q^{2} +(0.206068 + 3.99469i) q^{4} +(-1.89538 + 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(5.20306 - 6.07685i) q^{8} +O(q^{10})\)	\(q+(-1.45018 - 1.37730i) q^{2} +(0.206068 + 3.99469i) q^{4} +(-1.89538 + 3.28290i) q^{5} +(-5.70744 - 9.88558i) q^{7} +(5.20306 - 6.07685i) q^{8} +(7.27021 - 2.15029i) q^{10} +(3.47103 + 6.01200i) q^{11} +(14.6939 + 8.48351i) q^{13} +(-5.33861 + 22.1968i) q^{14} +(-15.9151 + 1.64636i) q^{16} +22.9919i q^{17} +21.7334i q^{19} +(-13.5047 - 6.89497i) q^{20} +(3.24672 - 13.4992i) q^{22} +(13.7369 + 7.93101i) q^{23} +(5.31504 + 9.20592i) q^{25} +(-9.62445 - 32.5406i) q^{26} +(38.3137 - 24.8366i) q^{28} +(6.57213 + 11.3833i) q^{29} +(3.45597 - 5.98592i) q^{31} +(25.3473 + 19.5324i) q^{32} +(31.6668 - 33.3424i) q^{34} +43.2712 q^{35} +1.75177i q^{37} +(29.9335 - 31.5174i) q^{38} +(10.0879 + 28.5991i) q^{40} +(-33.1748 - 19.1535i) q^{41} +(-10.9120 + 6.30005i) q^{43} +(-23.3008 + 15.1046i) q^{44} +(-8.99764 - 30.4213i) q^{46} +(28.8738 - 16.6703i) q^{47} +(-40.6498 + 70.4076i) q^{49} +(4.97156 - 20.6707i) q^{50} +(-30.8610 + 60.4456i) q^{52} -1.96807 q^{53} -26.3157 q^{55} +(-89.7694 - 16.7520i) q^{56} +(6.14741 - 25.5596i) q^{58} +(10.5216 - 18.2239i) q^{59} +(-48.0654 + 27.7506i) q^{61} +(-13.2562 + 3.92076i) q^{62} +(-9.85628 - 63.2365i) q^{64} +(-55.7011 + 32.1590i) q^{65} +(75.4627 + 43.5684i) q^{67} +(-91.8453 + 4.73789i) q^{68} +(-62.7512 - 59.5976i) q^{70} -38.7491i q^{71} +31.7926 q^{73} +(2.41272 - 2.54039i) q^{74} +(-86.8181 + 4.47856i) q^{76} +(39.6214 - 68.6263i) q^{77} +(-68.7491 - 119.077i) q^{79} +(24.7603 - 55.3681i) q^{80} +(21.7294 + 73.4679i) q^{82} +(33.5423 + 58.0970i) q^{83} +(-75.4800 - 43.5784i) q^{85} +(24.5015 + 5.89291i) q^{86} +(54.5940 + 10.1879i) q^{88} +159.426i q^{89} -193.677i q^{91} +(-28.8512 + 56.5090i) q^{92} +(-64.8323 - 15.5930i) q^{94} +(-71.3485 - 41.1931i) q^{95} +(42.5296 + 73.6635i) q^{97} +(155.922 - 46.1168i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 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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