LMFDB - Embedded newform 882.3.n.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,3,Mod(19,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	882.n (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:	$24.0327593166$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.19
Dual form			882.3.n.b.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} -2.82843 q^{8} +(-8.12132 + 4.68885i) q^{10} +(-2.37868 - 4.11999i) q^{11} +15.2913i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-3.25736 + 1.88064i) q^{17} +(-3.62132 - 2.09077i) q^{19} +13.2621i q^{20} -6.72792 q^{22} +(-13.8640 + 24.0131i) q^{23} +(9.48528 + 16.4290i) q^{25} +(18.7279 + 10.8126i) q^{26} -3.51472 q^{29} +(42.3198 - 24.4334i) q^{31} +(2.82843 + 4.89898i) q^{32} +5.31925i q^{34} +(1.47056 - 2.54709i) q^{37} +(-5.12132 + 2.95680i) q^{38} +(16.2426 + 9.37769i) q^{40} +27.9590i q^{41} -10.4853 q^{43} +(-4.75736 + 8.23999i) q^{44} +(19.6066 + 33.9596i) q^{46} +(45.6213 + 26.3395i) q^{47} +26.8284 q^{50} +(26.4853 - 15.2913i) q^{52} +(27.9853 + 48.4719i) q^{53} +31.5462i q^{55} +(-2.48528 + 4.30463i) q^{58} +(33.5330 - 19.3603i) q^{59} +(78.3823 + 45.2540i) q^{61} -69.1080i q^{62} +8.00000 q^{64} +(50.6985 - 87.8124i) q^{65} +(17.3198 + 29.9988i) q^{67} +(6.51472 + 3.76127i) q^{68} -36.4264 q^{71} +(-45.5589 + 26.3034i) q^{73} +(-2.07969 - 3.60213i) q^{74} +8.36308i q^{76} +(16.8934 - 29.2602i) q^{79} +(22.9706 - 13.2621i) q^{80} +(34.2426 + 19.7700i) q^{82} +127.577i q^{83} +24.9411 q^{85} +(-7.41421 + 12.8418i) q^{86} +(6.72792 + 11.6531i) q^{88} +(-43.5883 - 25.1657i) q^{89} +55.4558 q^{92} +(64.5183 - 37.2497i) q^{94} +(13.8640 + 24.0131i) q^{95} +101.792i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 6 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 - 6 * q^5	$ 4 q - 4 q^{4} - 6 q^{5} - 24 q^{10} - 18 q^{11} - 8 q^{16} - 30 q^{17} - 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} + 24 q^{26} - 48 q^{29} + 42 q^{31} - 62 q^{37} - 12 q^{38} + 48 q^{40} - 8 q^{43} - 36 q^{44} + 36 q^{46} + 174 q^{47} + 96 q^{50} + 72 q^{52} + 78 q^{53} + 24 q^{58} - 78 q^{59} + 42 q^{61} + 32 q^{64} + 84 q^{65} - 58 q^{67} + 60 q^{68} + 24 q^{71} - 318 q^{73} - 96 q^{74} + 110 q^{79} + 24 q^{80} + 120 q^{82} - 36 q^{85} - 24 q^{86} - 24 q^{88} - 378 q^{89} + 120 q^{92} + 12 q^{94} + 30 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 6 * q^5 - 24 * q^10 - 18 * q^11 - 8 * q^16 - 30 * q^17 - 6 * q^19 + 24 * q^22 - 30 * q^23 + 4 * q^25 + 24 * q^26 - 48 * q^29 + 42 * q^31 - 62 * q^37 - 12 * q^38 + 48 * q^40 - 8 * q^43 - 36 * q^44 + 36 * q^46 + 174 * q^47 + 96 * q^50 + 72 * q^52 + 78 * q^53 + 24 * q^58 - 78 * q^59 + 42 * q^61 + 32 * q^64 + 84 * q^65 - 58 * q^67 + 60 * q^68 + 24 * q^71 - 318 * q^73 - 96 * q^74 + 110 * q^79 + 24 * q^80 + 120 * q^82 - 36 * q^85 - 24 * q^86 - 24 * q^88 - 378 * q^89 + 120 * q^92 + 12 * q^94 + 30 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−5.74264	−	3.31552i	−1.14853	−	0.663103i	−0.200000	−	0.979796i	$-0.564094\pi$
$5$	−5.74264	−	3.31552i	−1.14853	−	0.663103i	−0.948528	+	0.316693i	$0.897428\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−8.12132	+	4.68885i	−0.812132	+	0.468885i
$11$	−2.37868	−	4.11999i	−0.216244	−	0.374545i	0.737413	−	0.675442i	$-0.236047\pi$
$11$	−2.37868	−	4.11999i	−0.216244	−	0.374545i	−0.953657	+	0.300897i	$0.902714\pi$
$12$		0			0
$13$			15.2913i			1.17625i	0.808769	+	0.588126i	$0.200134\pi$
$13$			15.2913i			1.17625i	−0.808769	+	0.588126i	$0.799866\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−3.25736	+	1.88064i	−0.191609	+	0.110626i	−0.592736	−	0.805397i	$-0.701952\pi$
$17$	−3.25736	+	1.88064i	−0.191609	+	0.110626i	0.401126	+	0.916023i	$0.368619\pi$
$18$		0			0
$19$	−3.62132	−	2.09077i	−0.190596	−	0.110041i	0.401666	−	0.915786i	$-0.368431\pi$
$19$	−3.62132	−	2.09077i	−0.190596	−	0.110041i	−0.592261	+	0.805746i	$0.701765\pi$
$20$			13.2621i			0.663103i
$21$		0			0
$22$	−6.72792			−0.305815
$23$	−13.8640	+	24.0131i	−0.602781	+	1.04405i	0.389617	+	0.920977i	$0.372607\pi$
$23$	−13.8640	+	24.0131i	−0.602781	+	1.04405i	−0.992398	+	0.123070i	$0.960726\pi$
$24$		0			0
$25$	9.48528	+	16.4290i	0.379411	+	0.657160i
$26$	18.7279	+	10.8126i	0.720305	+	0.415868i
$27$		0			0
$28$		0			0
$29$	−3.51472			−0.121197			−0.0605986	−	0.998162i	$-0.519301\pi$
$29$	−3.51472			−0.121197			−0.0605986	+	0.998162i	$0.519301\pi$
$30$		0			0
$31$	42.3198	−	24.4334i	1.36516	−	0.788173i	0.374850	−	0.927085i	$-0.377694\pi$
$31$	42.3198	−	24.4334i	1.36516	−	0.788173i	0.990305	+	0.138913i	$0.0443607\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$			5.31925i			0.156448i
$35$		0			0
$36$		0			0
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	−0.845469	−	0.534025i	$-0.820679\pi$
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	0.885214	+	0.465185i	$0.154012\pi$
$38$	−5.12132	+	2.95680i	−0.134772	+	0.0778104i
$39$		0			0
$40$	16.2426	+	9.37769i	0.406066	+	0.234442i
$41$			27.9590i			0.681927i	0.940077	+	0.340963i	$0.110753\pi$
$41$			27.9590i			0.681927i	−0.940077	+	0.340963i	$0.889247\pi$
$42$		0			0
$43$	−10.4853			−0.243844			−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−10.4853			−0.243844			−0.121922	+	0.992540i	$0.538906\pi$
$44$	−4.75736	+	8.23999i	−0.108122	+	0.187272i
$45$		0			0
$46$	19.6066	+	33.9596i	0.426230	+	0.738253i
$47$	45.6213	+	26.3395i	0.970666	+	0.560415i	0.899439	−	0.437046i	$-0.143975\pi$
$47$	45.6213	+	26.3395i	0.970666	+	0.560415i	0.0712271	+	0.997460i	$0.477309\pi$
$48$		0			0
$49$		0			0
$50$	26.8284			0.536569
$51$		0			0
$52$	26.4853	−	15.2913i	0.509332	−	0.294063i
$53$	27.9853	+	48.4719i	0.528024	+	0.914565i	0.999466	+	0.0326677i	$0.0104003\pi$
$53$	27.9853	+	48.4719i	0.528024	+	0.914565i	−0.471442	+	0.881897i	$0.656266\pi$
$54$		0			0
$55$			31.5462i			0.573567i
$56$		0			0
$57$		0			0
$58$	−2.48528	+	4.30463i	−0.0428497	+	0.0742178i
$59$	33.5330	−	19.3603i	0.568356	−	0.328141i	−0.188136	−	0.982143i	$-0.560245\pi$
$59$	33.5330	−	19.3603i	0.568356	−	0.328141i	0.756492	+	0.654002i	$0.226911\pi$
$60$		0			0
$61$	78.3823	+	45.2540i	1.28495	+	0.741869i	0.977750	−	0.209774i	$-0.0672729\pi$
$61$	78.3823	+	45.2540i	1.28495	+	0.741869i	0.307205	+	0.951643i	$0.400606\pi$
$62$		−	69.1080i		−	1.11464i
$63$		0			0
$64$	8.00000			0.125000
$65$	50.6985	−	87.8124i	0.779977	−	1.35096i
$66$		0			0
$67$	17.3198	+	29.9988i	0.258505	+	0.447743i	0.965842	−	0.259134i	$-0.0834370\pi$
$67$	17.3198	+	29.9988i	0.258505	+	0.447743i	−0.707337	+	0.706877i	$0.750104\pi$
$68$	6.51472	+	3.76127i	0.0958047	+	0.0553129i
$69$		0			0
$70$		0			0
$71$	−36.4264			−0.513048			−0.256524	−	0.966538i	$-0.582577\pi$
$71$	−36.4264			−0.513048			−0.256524	+	0.966538i	$0.582577\pi$
$72$		0			0
$73$	−45.5589	+	26.3034i	−0.624094	+	0.360321i	−0.778461	−	0.627693i	$-0.783999\pi$
$73$	−45.5589	+	26.3034i	−0.624094	+	0.360321i	0.154367	+	0.988014i	$0.450666\pi$
$74$	−2.07969	−	3.60213i	−0.0281039	−	0.0486774i
$75$		0			0
$76$			8.36308i			0.110041i
$77$		0			0
$78$		0			0
$79$	16.8934	−	29.2602i	0.213840	−	0.370383i	−0.739073	−	0.673626i	$-0.764736\pi$
$79$	16.8934	−	29.2602i	0.213840	−	0.370383i	0.952913	+	0.303243i	$0.0980694\pi$
$80$	22.9706	−	13.2621i	0.287132	−	0.165776i
$81$		0			0
$82$	34.2426	+	19.7700i	0.417593	+	0.241098i
$83$			127.577i			1.53708i	0.639803	+	0.768539i	$0.279016\pi$
$83$			127.577i			1.53708i	−0.639803	+	0.768539i	$0.720984\pi$
$84$		0			0
$85$	24.9411			0.293425
$86$	−7.41421	+	12.8418i	−0.0862118	+	0.149323i
$87$		0			0
$88$	6.72792	+	11.6531i	0.0764537	+	0.132422i
$89$	−43.5883	−	25.1657i	−0.489756	−	0.282761i	0.234717	−	0.972064i	$-0.424584\pi$
$89$	−43.5883	−	25.1657i	−0.489756	−	0.282761i	−0.724473	+	0.689303i	$0.757917\pi$
$90$		0			0
$91$		0			0
$92$	55.4558			0.602781
$93$		0			0
$94$	64.5183	−	37.2497i	0.686365	−	0.396273i
$95$	13.8640	+	24.0131i	0.145936	+	0.252769i
$96$		0			0
$97$			101.792i			1.04940i	0.851287	+	0.524700i	$0.175823\pi$
$97$			101.792i			1.04940i	−0.851287	+	0.524700i	$0.824177\pi$
$98$		0			0
$99$		0			0
$100$	18.9706	−	32.8580i	0.189706	−	0.328580i
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	−0.733541	−	0.679646i	$-0.762134\pi$
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	0.221820	+	0.975088i	$0.428800\pi$
$102$		0			0
$103$	−104.077	−	60.0890i	−1.01046	−	0.583388i	−0.0991322	−	0.995074i	$-0.531607\pi$
$103$	−104.077	−	60.0890i	−1.01046	−	0.583388i	−0.911326	+	0.411686i	$0.864940\pi$
$104$		−	43.2503i		−	0.415868i
$105$		0			0
$106$	79.1543			0.746739
$107$	−56.8051	+	98.3893i	−0.530889	+	0.919526i	0.468462	+	0.883484i	$0.344808\pi$
$107$	−56.8051	+	98.3893i	−0.530889	+	0.919526i	−0.999350	+	0.0360423i	$0.988525\pi$
$108$		0			0
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	0.978862	+	0.204524i	$0.0655645\pi$
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	−0.312308	+	0.949981i	$0.601102\pi$
$110$	38.6360	+	22.3065i	0.351237	+	0.202787i
$111$		0			0
$112$		0			0
$113$	−34.5442			−0.305700			−0.152850	−	0.988249i	$-0.548845\pi$
$113$	−34.5442			−0.305700			−0.152850	+	0.988249i	$0.548845\pi$
$114$		0			0
$115$	159.231	−	91.9323i	1.38462	−	0.799412i
$116$	3.51472	+	6.08767i	0.0302993	+	0.0524799i
$117$		0			0
$118$		−	54.7592i		−	0.464061i
$119$		0			0
$120$		0			0
$121$	49.1838	−	85.1888i	0.406477	−	0.704040i
$122$	110.849	−	63.9988i	0.908600	−	0.524581i
$123$		0			0
$124$	−84.6396	−	48.8667i	−0.682578	−	0.394086i
$125$			39.9814i			0.319851i
$126$		0			0
$127$	−247.338			−1.94754			−0.973772	−	0.227526i	$-0.926936\pi$
$127$	−247.338			−1.94754			−0.973772	+	0.227526i	$0.926936\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−71.6985	−	124.185i	−0.551527	−	0.955272i
$131$	−127.864	−	73.8223i	−0.976061	−	0.563529i	−0.0749822	−	0.997185i	$-0.523890\pi$
$131$	−127.864	−	73.8223i	−0.976061	−	0.563529i	−0.901079	+	0.433656i	$0.857223\pi$
$132$		0			0
$133$		0			0
$134$	48.9878			0.365581
$135$		0			0
$136$	9.21320	−	5.31925i	0.0677441	−	0.0391121i
$137$	−16.2868	−	28.2096i	−0.118882	−	0.205909i	0.800443	−	0.599409i	$-0.204598\pi$
$137$	−16.2868	−	28.2096i	−0.118882	−	0.205909i	−0.919325	+	0.393500i	$0.871264\pi$
$138$		0			0
$139$			68.5857i			0.493422i	0.969089	+	0.246711i	$0.0793499\pi$
$139$			68.5857i			0.493422i	−0.969089	+	0.246711i	$0.920650\pi$
$140$		0			0
$141$		0			0
$142$	−25.7574	+	44.6131i	−0.181390	+	0.314176i
$143$	63.0000	−	36.3731i	0.440559	−	0.254357i
$144$		0			0
$145$	20.1838	+	11.6531i	0.139198	+	0.0803662i
$146$			74.3973i			0.509571i
$147$		0			0
$148$	−5.88225			−0.0397449
$149$	46.1985	−	80.0181i	0.310057	−	0.537034i	−0.668317	−	0.743876i	$-0.732985\pi$
$149$	46.1985	−	80.0181i	0.310057	−	0.537034i	0.978374	+	0.206842i	$0.0663185\pi$
$150$		0			0
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	0.977022	−	0.213136i	$-0.0683678\pi$
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	−0.673093	+	0.739558i	$0.735035\pi$
$152$	10.2426	+	5.91359i	0.0673858	+	0.0389052i
$153$		0			0
$154$		0			0
$155$	−324.037			−2.09056
$156$		0			0
$157$	−7.32338	+	4.22815i	−0.0466457	+	0.0269309i	−0.523142	−	0.852246i	$-0.675240\pi$
$157$	−7.32338	+	4.22815i	−0.0466457	+	0.0269309i	0.476496	+	0.879177i	$0.341907\pi$
$158$	−23.8909	−	41.3802i	−0.151208	−	0.261900i
$159$		0			0
$160$		−	37.5108i		−	0.234442i
$161$		0			0
$162$		0			0
$163$	−110.989	+	192.238i	−0.680913	+	1.17938i	0.293789	+	0.955870i	$0.405084\pi$
$163$	−110.989	+	192.238i	−0.680913	+	1.17938i	−0.974703	+	0.223506i	$0.928250\pi$
$164$	48.4264	−	27.9590i	0.295283	−	0.170482i
$165$		0			0
$166$	156.250	+	90.2109i	0.941264	+	0.543439i
$167$		−	168.841i		−	1.01102i	−0.862820	−	0.505511i	$-0.831304\pi$
$167$		−	168.841i		−	1.01102i	0.862820	−	0.505511i	$-0.168696\pi$
$168$		0			0
$169$	−64.8234			−0.383570
$170$	17.6360	−	30.5465i	0.103741	−	0.179685i
$171$		0			0
$172$	10.4853	+	18.1610i	0.0609609	+	0.105587i
$173$	−142.323	−	82.1704i	−0.822678	−	0.474974i	0.0286608	−	0.999589i	$-0.490876\pi$
$173$	−142.323	−	82.1704i	−0.822678	−	0.474974i	−0.851339	+	0.524616i	$0.824209\pi$
$174$		0			0
$175$		0			0
$176$	19.0294			0.108122
$177$		0			0
$178$	−61.6432	+	35.5897i	−0.346310	+	0.199942i
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	0.999799	+	0.0200614i	$0.00638618\pi$
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	−0.482526	+	0.875882i	$0.660280\pi$
$180$		0			0
$181$		−	155.086i		−	0.856830i	−0.903582	−	0.428415i	$-0.859072\pi$
$181$		−	155.086i		−	0.856830i	0.903582	−	0.428415i	$-0.140928\pi$
$182$		0			0
$183$		0			0
$184$	39.2132	−	67.9193i	0.213115	−	0.369126i
$185$	−16.8898	+	9.75135i	−0.0912964	+	0.0527100i
$186$		0			0
$187$	15.4964	+	8.94687i	0.0828686	+	0.0478442i
$188$		−	105.358i		−	0.560415i
$189$		0			0
$190$	39.2132			0.206385
$191$	124.048	−	214.857i	0.649465	−	1.12491i	−0.333786	−	0.942649i	$-0.608326\pi$
$191$	124.048	−	214.857i	0.649465	−	1.12491i	0.983251	−	0.182257i	$-0.0583402\pi$
$192$		0			0
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	0.593866	−	0.804564i	$-0.297601\pi$
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	−0.993706	+	0.112021i	$0.964268\pi$
$194$	124.669	+	71.9777i	0.642624	+	0.371019i
$195$		0			0
$196$		0			0
$197$	181.103			0.919303			0.459651	−	0.888099i	$-0.347974\pi$
$197$	181.103			0.919303			0.459651	+	0.888099i	$0.347974\pi$
$198$		0			0
$199$	−301.989	+	174.353i	−1.51753	+	0.876147i	−0.517744	+	0.855535i	$0.673228\pi$
$199$	−301.989	+	174.353i	−1.51753	+	0.876147i	−0.999788	+	0.0206121i	$0.993439\pi$
$200$	−26.8284	−	46.4682i	−0.134142	−	0.232341i
$201$		0			0
$202$			84.3992i			0.417818i
$203$		0			0
$204$		0			0
$205$	92.6985	−	160.558i	0.452188	−	0.783212i
$206$	−147.187	+	84.9786i	−0.714502	+	0.412518i
$207$		0			0
$208$	−52.9706	−	30.5826i	−0.254666	−	0.147032i
$209$			19.8931i			0.0951823i
$210$		0			0
$211$	364.073			1.72547			0.862733	−	0.505660i	$-0.168751\pi$
$211$	364.073			1.72547			0.862733	+	0.505660i	$0.168751\pi$
$212$	55.9706	−	96.9439i	0.264012	−	0.457282i
$213$		0			0
$214$	80.3345	+	139.143i	0.375395	+	0.650203i
$215$	60.2132	+	34.7641i	0.280061	+	0.161694i
$216$		0			0
$217$		0			0
$218$	205.497			0.942649
$219$		0			0
$220$	54.6396	−	31.5462i	0.248362	−	0.143392i
$221$	−28.7574	−	49.8092i	−0.130124	−	0.225381i
$222$		0			0
$223$			123.231i			0.552603i	0.961071	+	0.276302i	$0.0891089\pi$
$223$			123.231i			0.552603i	−0.961071	+	0.276302i	$0.910891\pi$
$224$		0			0
$225$		0			0
$226$	−24.4264	+	42.3078i	−0.108081	+	0.187203i
$227$	−66.1432	+	38.1878i	−0.291380	+	0.168228i	−0.638564	−	0.769569i	$-0.720471\pi$
$227$	−66.1432	+	38.1878i	−0.291380	+	0.168228i	0.347184	+	0.937797i	$0.387138\pi$
$228$		0			0
$229$	−309.419	−	178.643i	−1.35117	−	0.780101i	−0.362760	−	0.931883i	$-0.618166\pi$
$229$	−309.419	−	178.643i	−1.35117	−	0.780101i	−0.988414	+	0.151782i	$0.951499\pi$
$230$		−	260.024i		−	1.13054i
$231$		0			0
$232$	9.94113			0.0428497
$233$	−136.537	+	236.488i	−0.585994	+	1.01497i	0.408757	+	0.912643i	$0.365962\pi$
$233$	−136.537	+	236.488i	−0.585994	+	1.01497i	−0.994751	+	0.102328i	$0.967371\pi$
$234$		0			0
$235$	−174.658	−	302.516i	−0.743225	−	1.28730i
$236$	−67.0660	−	38.7206i	−0.284178	−	0.164070i
$237$		0			0
$238$		0			0
$239$	265.103			1.10922			0.554608	−	0.832112i	$-0.312868\pi$
$239$	265.103			1.10922			0.554608	+	0.832112i	$0.312868\pi$
$240$		0			0
$241$	75.8970	−	43.8191i	0.314925	−	0.181822i	−0.334203	−	0.942501i	$-0.608467\pi$
$241$	75.8970	−	43.8191i	0.314925	−	0.181822i	0.649128	+	0.760679i	$0.275134\pi$
$242$	−69.5563	−	120.475i	−0.287423	−	0.497831i
$243$		0			0
$244$		−	181.016i		−	0.741869i
$245$		0			0
$246$		0			0
$247$	31.9706	−	55.3746i	0.129435	−	0.224189i
$248$	−119.698	+	69.1080i	−0.482655	+	0.278661i
$249$		0			0
$250$	48.9670	+	28.2711i	0.195868	+	0.113084i
$251$			495.655i			1.97472i	0.158491	+	0.987360i	$0.449337\pi$
$251$			495.655i			1.97472i	−0.158491	+	0.987360i	$0.550663\pi$
$252$		0			0
$253$	131.912			0.521390
$254$	−174.894	+	302.926i	−0.688561	+	1.19262i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	346.875	+	200.268i	1.34971	+	0.779254i	0.988208	−	0.153119i	$-0.0489317\pi$
$257$	346.875	+	200.268i	1.34971	+	0.779254i	0.361499	+	0.932372i	$0.382265\pi$
$258$		0			0
$259$		0			0
$260$	−202.794			−0.779977
$261$		0			0
$262$	−180.827	+	104.400i	−0.690179	+	0.398475i
$263$	−16.1726	−	28.0118i	−0.0614928	−	0.106509i	0.833640	−	0.552308i	$-0.186253\pi$
$263$	−16.1726	−	28.0118i	−0.0614928	−	0.106509i	−0.895133	+	0.445799i	$0.852919\pi$
$264$		0			0
$265$		−	371.142i		−	1.40054i
$266$		0			0
$267$		0			0
$268$	34.6396	−	59.9976i	0.129252	−	0.223872i
$269$	−265.838	+	153.482i	−0.988246	+	0.570564i	−0.904749	−	0.425944i	$-0.859942\pi$
$269$	−265.838	+	153.482i	−0.988246	+	0.570564i	−0.0834963	+	0.996508i	$0.526609\pi$
$270$		0			0
$271$	65.8051	+	37.9926i	0.242823	+	0.140194i	0.616474	−	0.787376i	$-0.288561\pi$
$271$	65.8051	+	37.9926i	0.242823	+	0.140194i	−0.373650	+	0.927570i	$0.621894\pi$
$272$		−	15.0451i		−	0.0553129i
$273$		0			0
$274$	−46.0660			−0.168124
$275$	45.1249	−	78.1586i	0.164091	−	0.284213i
$276$		0			0
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	−0.999996	−	0.00294398i	$-0.999063\pi$
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	0.497448	−	0.867494i	$-0.334270\pi$
$278$	84.0000	+	48.4974i	0.302158	+	0.174451i
$279$		0			0
$280$		0			0
$281$	−394.690			−1.40459			−0.702296	−	0.711885i	$-0.747842\pi$
$281$	−394.690			−1.40459			−0.702296	+	0.711885i	$0.747842\pi$
$282$		0			0
$283$	−126.783	+	73.1981i	−0.447996	+	0.258650i	−0.706983	−	0.707230i	$-0.749944\pi$
$283$	−126.783	+	73.1981i	−0.447996	+	0.258650i	0.258988	+	0.965881i	$0.416611\pi$
$284$	36.4264	+	63.0924i	0.128262	+	0.222156i
$285$		0			0
$286$		−	102.879i		−	0.359715i
$287$		0			0
$288$		0			0
$289$	−137.426	+	238.030i	−0.475524	+	0.823632i
$290$	28.5442	−	16.4800i	0.0984281	−	0.0568275i
$291$		0			0
$292$	91.1177	+	52.6069i	0.312047	+	0.180160i
$293$		−	299.678i		−	1.02279i	−0.859345	−	0.511396i	$-0.829128\pi$
$293$		−	299.678i		−	1.02279i	0.859345	−	0.511396i	$-0.170872\pi$
$294$		0			0
$295$	−256.757			−0.870364
$296$	−4.15938	+	7.20426i	−0.0140520	+	0.0243387i
$297$		0			0
$298$	−65.3345	−	113.163i	−0.219243	−	0.379741i
$299$	−367.191	−	211.998i	−1.22806	−	0.709023i
$300$		0			0
$301$		0			0
$302$	129.806			0.429822
$303$		0			0
$304$	14.4853	−	8.36308i	0.0476490	−	0.0275101i
$305$	−300.081	−	519.755i	−0.983871	−	1.70412i
$306$		0			0
$307$		−	20.9886i		−	0.0683666i	−0.999416	−	0.0341833i	$-0.989117\pi$
$307$		−	20.9886i		−	0.0683666i	0.999416	−	0.0341833i	$-0.0108830\pi$
$308$		0			0
$309$		0			0
$310$	−229.128	+	396.862i	−0.739124	+	1.28020i
$311$	157.651	−	91.0197i	0.506916	−	0.292668i	−0.224649	−	0.974440i	$-0.572124\pi$
$311$	157.651	−	91.0197i	0.506916	−	0.292668i	0.731565	+	0.681772i	$0.238790\pi$
$312$		0			0
$313$	84.8087	+	48.9643i	0.270954	+	0.156435i	0.629321	−	0.777145i	$-0.283333\pi$
$313$	84.8087	+	48.9643i	0.270954	+	0.156435i	−0.358367	+	0.933581i	$0.616666\pi$
$314$			11.9590i			0.0380861i
$315$		0			0
$316$	−67.5736			−0.213840
$317$	−240.985	+	417.399i	−0.760206	+	1.31672i	0.182538	+	0.983199i	$0.441569\pi$
$317$	−240.985	+	417.399i	−0.760206	+	1.31672i	−0.942744	+	0.333517i	$0.891765\pi$
$318$		0			0
$319$	8.36039	+	14.4806i	0.0262081	+	0.0453938i
$320$	−45.9411	−	26.5241i	−0.143566	−	0.0828879i
$321$		0			0
$322$		0			0
$323$	15.7279			0.0486933
$324$		0			0
$325$	−251.220	+	145.042i	−0.772986	+	0.446283i
$326$	156.962	+	271.866i	0.481478	+	0.833945i
$327$		0			0
$328$		−	79.0800i		−	0.241098i
$329$		0			0
$330$		0			0
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	−0.984412	−	0.175879i	$-0.943723\pi$
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	0.644522	+	0.764586i	$0.277056\pi$
$332$	220.971	−	127.577i	0.665574	−	0.384269i
$333$		0			0
$334$	−206.787	−	119.388i	−0.619122	−	0.357450i
$335$		−	229.696i		−	0.685661i
$336$		0			0
$337$	−264.368			−0.784473			−0.392237	−	0.919864i	$-0.628299\pi$
$337$	−264.368			−0.784473			−0.392237	+	0.919864i	$0.628299\pi$
$338$	−45.8370	+	79.3921i	−0.135613	+	0.234888i
$339$		0			0
$340$	−24.9411	−	43.1993i	−0.0733563	−	0.127057i
$341$	−201.331	−	116.238i	−0.590412	−	0.340875i
$342$		0			0
$343$		0			0
$344$	29.6569			0.0862118
$345$		0			0
$346$	−201.276	+	116.207i	−0.581722	+	0.335857i
$347$	−95.6285	−	165.633i	−0.275586	−	0.477330i	0.694697	−	0.719303i	$-0.255539\pi$
$347$	−95.6285	−	165.633i	−0.275586	−	0.477330i	−0.970283	+	0.241973i	$0.922205\pi$
$348$		0			0
$349$			135.448i			0.388104i	0.980991	+	0.194052i	$0.0621630\pi$
$349$			135.448i			0.388104i	−0.980991	+	0.194052i	$0.937837\pi$
$350$		0			0
$351$		0			0
$352$	13.4558	−	23.3062i	0.0382268	−	0.0662108i
$353$	−301.802	+	174.245i	−0.854962	+	0.493612i	−0.862322	−	0.506360i	$-0.830991\pi$
$353$	−301.802	+	174.245i	−0.854962	+	0.493612i	0.00736010	+	0.999973i	$0.497657\pi$
$354$		0			0
$355$	209.184	+	120.772i	0.589250	+	0.340204i
$356$			100.663i			0.282761i
$357$		0			0
$358$	261.889			0.731535
$359$	152.415	−	263.991i	0.424555	−	0.735351i	−0.571824	−	0.820377i	$-0.693764\pi$
$359$	152.415	−	263.991i	0.424555	−	0.735351i	0.996379	+	0.0850256i	$0.0270972\pi$
$360$		0			0
$361$	−171.757	−	297.492i	−0.475782	−	0.824079i
$362$	−189.941	−	109.663i	−0.524699	−	0.302935i
$363$		0			0
$364$		0			0
$365$	348.838			0.955720
$366$		0			0
$367$	82.2761	−	47.5021i	0.224186	−	0.129434i	−0.383701	−	0.923457i	$-0.625351\pi$
$367$	82.2761	−	47.5021i	0.224186	−	0.129434i	0.607887	+	0.794024i	$0.292017\pi$
$368$	−55.4558	−	96.0523i	−0.150695	−	0.261012i
$369$		0			0
$370$			27.5810i			0.0745432i
$371$		0			0
$372$		0			0
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	−0.984412	−	0.175879i	$-0.943723\pi$
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	0.644521	+	0.764586i	$0.277057\pi$
$374$	21.9153	−	12.6528i	0.0585970	−	0.0338310i
$375$		0			0
$376$	−129.037	−	74.4993i	−0.343182	−	0.198136i
$377$		−	53.7446i		−	0.142559i
$378$		0			0
$379$	508.250			1.34103			0.670514	−	0.741897i	$-0.266074\pi$
$379$	508.250			1.34103			0.670514	+	0.741897i	$0.266074\pi$
$380$	27.7279	−	48.0262i	0.0729682	−	0.126385i
$381$		0			0
$382$	−175.430	−	303.854i	−0.459241	−	0.795428i
$383$	413.753	+	238.881i	1.08030	+	0.623709i	0.930976	−	0.365080i	$-0.118958\pi$
$383$	413.753	+	238.881i	1.08030	+	0.623709i	0.149320	+	0.988789i	$0.452292\pi$
$384$		0			0
$385$		0			0
$386$	−218.267			−0.565459
$387$		0			0
$388$	176.309	−	101.792i	0.454404	−	0.262350i
$389$	85.1102	+	147.415i	0.218792	+	0.378959i	0.954439	−	0.298406i	$-0.0964550\pi$
$389$	85.1102	+	147.415i	0.218792	+	0.378959i	−0.735647	+	0.677365i	$0.763122\pi$
$390$		0			0
$391$		−	104.292i		−	0.266732i
$392$		0			0
$393$		0			0
$394$	128.059	−	221.804i	0.325023	−	0.562956i
$395$	−194.025	+	112.021i	−0.491204	+	0.283597i
$396$		0			0
$397$	−211.786	−	122.275i	−0.533467	−	0.307997i	0.208960	−	0.977924i	$-0.432992\pi$
$397$	−211.786	−	122.275i	−0.533467	−	0.307997i	−0.742427	+	0.669927i	$0.766325\pi$
$398$			493.146i			1.23906i
$399$		0			0
$400$	−75.8823			−0.189706
$401$	−208.786	+	361.629i	−0.520664	+	0.901817i	0.479047	+	0.877789i	$0.340982\pi$
$401$	−208.786	+	361.629i	−0.520664	+	0.901817i	−0.999711	+	0.0240277i	$0.992351\pi$
$402$		0			0
$403$	373.617	+	647.124i	0.927090	+	1.60577i
$404$	103.368	+	59.6793i	0.255860	+	0.147721i
$405$		0			0
$406$		0			0
$407$	−13.9920			−0.0343784
$408$		0			0
$409$	−266.919	+	154.106i	−0.652614	+	0.376787i	−0.789457	−	0.613806i	$-0.789638\pi$
$409$	−266.919	+	154.106i	−0.652614	+	0.376787i	0.136843	+	0.990593i	$0.456304\pi$
$410$	−131.095	−	227.064i	−0.319745	−	0.553815i
$411$		0			0
$412$			240.356i			0.583388i
$413$		0			0
$414$		0			0
$415$	422.985	−	732.631i	1.01924	−	1.76538i
$416$	−74.9117	+	43.2503i	−0.180076	+	0.103967i
$417$		0			0
$418$	24.3640	+	14.0665i	0.0582870	+	0.0336520i
$419$			103.142i			0.246163i	0.992397	+	0.123081i	$0.0392776\pi$
$419$			103.142i			0.246163i	−0.992397	+	0.123081i	$0.960722\pi$
$420$		0			0
$421$	−165.220			−0.392447			−0.196224	−	0.980559i	$-0.562868\pi$
$421$	−165.220			−0.392447			−0.196224	+	0.980559i	$0.562868\pi$
$422$	257.439	−	445.897i	0.610044	−	1.05663i
$423$		0			0
$424$	−79.1543	−	137.099i	−0.186685	−	0.323347i
$425$	−61.7939	−	35.6767i	−0.145398	−	0.0839453i
$426$		0			0
$427$		0			0
$428$	227.220			0.530889
$429$		0			0
$430$	85.1543	−	49.1639i	0.198033	−	0.114335i
$431$	297.268	+	514.883i	0.689717	+	1.19463i	0.971929	+	0.235273i	$0.0755984\pi$
$431$	297.268	+	514.883i	0.689717	+	1.19463i	−0.282212	+	0.959352i	$0.591068\pi$
$432$		0			0
$433$		−	40.6267i		−	0.0938261i	−0.998899	−	0.0469131i	$-0.985062\pi$
$433$		−	40.6267i		−	0.0938261i	0.998899	−	0.0469131i	$-0.0149384\pi$
$434$		0			0
$435$		0			0
$436$	145.309	−	251.682i	0.333277	−	0.577252i
$437$	100.412	−	57.9727i	0.229775	−	0.132661i
$438$		0			0
$439$	−126.959	−	73.3001i	−0.289201	−	0.166971i	0.348380	−	0.937353i	$-0.386732\pi$
$439$	−126.959	−	73.3001i	−0.289201	−	0.166971i	−0.637582	+	0.770383i	$0.720065\pi$
$440$		−	89.2261i		−	0.202787i
$441$		0			0
$442$	−81.3381			−0.184023
$443$	53.6802	−	92.9768i	0.121174	−	0.209880i	−0.799057	−	0.601256i	$-0.794667\pi$
$443$	53.6802	−	92.9768i	0.121174	−	0.209880i	0.920231	+	0.391376i	$0.128001\pi$
$444$		0			0
$445$	166.875	+	289.035i	0.374999	+	0.649518i
$446$	150.926	+	87.1372i	0.338399	+	0.195375i
$447$		0			0
$448$		0			0
$449$	−135.161			−0.301028			−0.150514	−	0.988608i	$-0.548093\pi$
$449$	−135.161			−0.301028			−0.150514	+	0.988608i	$0.548093\pi$
$450$		0			0
$451$	115.191	−	66.5055i	0.255412	−	0.147462i
$452$	34.5442	+	59.8322i	0.0764251	+	0.132372i
$453$		0			0
$454$			108.011i			0.237910i
$455$		0			0
$456$		0			0
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	−0.940080	−	0.340954i	$-0.889250\pi$
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	0.765315	+	0.643656i	$0.222583\pi$
$458$	−437.584	+	252.639i	−0.955424	+	0.551614i
$459$		0			0
$460$	−318.463	−	183.865i	−0.692311	−	0.399706i
$461$		−	310.250i		−	0.672993i	−0.941685	−	0.336497i	$-0.890758\pi$
$461$		−	310.250i		−	0.672993i	0.941685	−	0.336497i	$-0.109242\pi$
$462$		0			0
$463$	−326.014			−0.704135			−0.352067	−	0.935975i	$-0.614521\pi$
$463$	−326.014			−0.704135			−0.352067	+	0.935975i	$0.614521\pi$
$464$	7.02944	−	12.1753i	0.0151496	−	0.0262400i
$465$		0			0
$466$	193.092	+	334.445i	0.414360	+	0.717693i
$467$	515.769	+	297.779i	1.10443	+	0.637643i	0.937381	−	0.348306i	$-0.113243\pi$
$467$	515.769	+	297.779i	1.10443	+	0.637643i	0.167048	+	0.985949i	$0.446576\pi$
$468$		0			0
$469$		0			0
$470$	−494.007			−1.05108
$471$		0			0
$472$	−94.8457	+	54.7592i	−0.200944	+	0.116015i
$473$	24.9411	+	43.1993i	0.0527297	+	0.0913304i
$474$		0			0
$475$		−	79.3262i		−	0.167002i
$476$		0			0
$477$		0			0
$478$	187.456	−	324.683i	0.392167	−	0.679253i
$479$	438.798	−	253.340i	0.916071	−	0.528894i	0.0336914	−	0.999432i	$-0.489274\pi$
$479$	438.798	−	253.340i	0.916071	−	0.528894i	0.882379	+	0.470539i	$0.155940\pi$
$480$		0			0
$481$	38.9483	+	22.4868i	0.0809735	+	0.0467501i
$482$		−	123.939i		−	0.257135i
$483$		0			0
$484$	−196.735			−0.406477
$485$	337.492	−	584.554i	0.695861	−	1.20527i
$486$		0			0
$487$	−105.651	−	182.992i	−0.216942	−	0.375755i	0.736930	−	0.675970i	$-0.236275\pi$
$487$	−105.651	−	182.992i	−0.216942	−	0.375755i	−0.953872	+	0.300215i	$0.902942\pi$
$488$	−221.698	−	127.998i	−0.454300	−	0.262290i
$489$		0			0
$490$		0			0
$491$	784.161			1.59707			0.798534	−	0.601949i	$-0.205609\pi$
$491$	784.161			1.59707			0.798534	+	0.601949i	$0.205609\pi$
$492$		0			0
$493$	11.4487	−	6.60991i	0.0232225	−	0.0134075i
$494$	−45.2132	−	78.3116i	−0.0915247	−	0.158525i
$495$		0			0
$496$			195.467i			0.394086i
$497$		0			0
$498$		0			0
$499$	85.7462	−	148.517i	0.171836	−	0.297629i	−0.767226	−	0.641377i	$-0.778363\pi$
$499$	85.7462	−	148.517i	0.171836	−	0.297629i	0.939062	+	0.343748i	$0.111697\pi$
$500$	69.2498	−	39.9814i	0.138500	−	0.0799628i
$501$		0			0
$502$	607.051	+	350.481i	1.20926	+	0.698169i
$503$			20.0883i			0.0399370i	0.999801	+	0.0199685i	$0.00635659\pi$
$503$			20.0883i			0.0399370i	−0.999801	+	0.0199685i	$0.993643\pi$
$504$		0			0
$505$	395.735			0.783634
$506$	93.2756	−	161.558i	0.184339	−	0.319285i
$507$		0			0
$508$	247.338	+	428.402i	0.486886	+	0.843311i
$509$	−412.890	−	238.382i	−0.811178	−	0.468334i	0.0361865	−	0.999345i	$-0.488479\pi$
$509$	−412.890	−	238.382i	−0.811178	−	0.468334i	−0.847365	+	0.531011i	$0.821812\pi$
$510$		0			0
$511$		0			0
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	490.555	−	283.222i	0.954387	−	0.551016i
$515$	398.452	+	690.139i	0.773693	+	1.34008i
$516$		0			0
$517$		−	250.613i		−	0.484744i
$518$		0			0
$519$		0			0
$520$	−143.397	+	248.371i	−0.275763	+	0.477636i
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.423707	−	0.905799i	$-0.360729\pi$
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.996299	+	0.0859587i	$0.0273953\pi$
$522$		0			0
$523$	513.554	+	296.501i	0.981940	+	0.566923i	0.902855	−	0.429945i	$-0.141467\pi$
$523$	513.554	+	296.501i	0.981940	+	0.566923i	0.0790845	+	0.996868i	$0.474800\pi$
$524$			295.289i			0.563529i
$525$		0			0
$526$	−45.7431			−0.0869640
$527$	−91.9005	+	159.176i	−0.174384	+	0.302043i
$528$		0			0
$529$	−119.919	−	207.706i	−0.226690	−	0.392638i
$530$	−454.555	−	262.437i	−0.857651	−	0.495165i
$531$		0			0
$532$		0			0
$533$	−427.529			−0.802118
$534$		0			0
$535$	652.422	−	376.676i	1.21948	−	0.704068i
$536$	−48.9878	−	84.8494i	−0.0913952	−	0.158301i
$537$		0			0
$538$			434.112i			0.806899i
$539$		0			0
$540$		0			0
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	0.135352	+	0.990798i	$0.456783\pi$
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	−0.925732	+	0.378180i	$0.876550\pi$
$542$	93.0624	−	53.7296i	0.171702	−	0.0991322i
$543$		0			0
$544$	−18.4264	−	10.6385i	−0.0338721	−	0.0195560i
$545$		−	963.546i		−	1.76797i
$546$		0			0
$547$	415.897			0.760323			0.380161	−	0.924920i	$-0.375868\pi$
$547$	415.897			0.760323			0.380161	+	0.924920i	$0.375868\pi$
$548$	−32.5736	+	56.4191i	−0.0594409	+	0.102955i
$549$		0			0
$550$	−63.8162	−	110.533i	−0.116030	−	0.200969i
$551$	12.7279	+	7.34847i	0.0230997	+	0.0133366i
$552$		0			0
$553$		0			0
$554$	−393.733			−0.710709
$555$		0			0
$556$	118.794	−	68.5857i	0.213658	−	0.123356i
$557$	−292.110	−	505.950i	−0.524435	−	0.908348i	−0.999595	−	0.0284485i	$-0.990943\pi$
$557$	−292.110	−	505.950i	−0.524435	−	0.908348i	0.475160	−	0.879899i	$-0.342390\pi$
$558$		0			0
$559$		−	160.333i		−	0.286822i
$560$		0			0
$561$		0			0
$562$	−279.088	+	483.395i	−0.496598	+	0.860134i
$563$	789.076	−	455.573i	1.40156	−	0.809189i	0.407004	−	0.913426i	$-0.366573\pi$
$563$	789.076	−	455.573i	1.40156	−	0.809189i	0.994552	+	0.104237i	$0.0332402\pi$
$564$		0			0
$565$	198.375	+	114.532i	0.351106	+	0.202711i
$566$			207.035i			0.365787i
$567$		0			0
$568$	103.029			0.181390
$569$	350.000	−	606.217i	0.615113	−	1.06541i	−0.375251	−	0.926923i	$-0.622444\pi$
$569$	350.000	−	606.217i	0.615113	−	1.06541i	0.990365	−	0.138485i	$-0.0442231\pi$
$570$		0			0
$571$	281.231	+	487.107i	0.492525	+	0.853077i	0.999963	−	0.00861055i	$-0.00274086\pi$
$571$	281.231	+	487.107i	0.492525	+	0.853077i	−0.507438	+	0.861688i	$0.669408\pi$
$572$	−126.000	−	72.7461i	−0.220280	−	0.127179i
$573$		0			0
$574$		0			0
$575$	−526.014			−0.914807
$576$		0			0
$577$	573.014	−	330.830i	0.993092	−	0.573362i	0.0868946	−	0.996218i	$-0.472306\pi$
$577$	573.014	−	330.830i	0.993092	−	0.573362i	0.906197	+	0.422856i	$0.138972\pi$
$578$	194.350	+	336.625i	0.336246	+	0.582395i
$579$		0			0
$580$		−	46.6124i		−	0.0803662i
$581$		0			0
$582$		0			0
$583$	133.136	−	230.598i	0.228364	−	0.395538i
$584$	128.860	−	74.3973i	0.220651	−	0.127393i
$585$		0			0
$586$	−367.029	−	211.905i	−0.626330	−	0.361612i
$587$			823.029i			1.40209i	0.713116	+	0.701046i	$0.247283\pi$
$587$			823.029i			1.40209i	−0.713116	+	0.701046i	$0.752717\pi$
$588$		0			0
$589$	−204.338			−0.346924
$590$	−181.555	+	314.462i	−0.307720	+	0.532987i
$591$		0			0
$592$	5.88225	+	10.1884i	0.00993623	+	0.0172101i
$593$	−538.890	−	311.128i	−0.908752	−	0.524668i	−0.0287225	−	0.999587i	$-0.509144\pi$
$593$	−538.890	−	311.128i	−0.908752	−	0.524668i	−0.880029	+	0.474919i	$0.842477\pi$
$594$		0			0
$595$		0			0
$596$	−184.794			−0.310057
$597$		0			0
$598$	−519.286	+	299.810i	−0.868372	+	0.501355i
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	0.568619	−	0.822601i	$-0.307478\pi$
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	−0.996703	+	0.0811377i	$0.974145\pi$
$600$		0			0
$601$			680.160i			1.13171i	0.824504	+	0.565857i	$0.191454\pi$
$601$			680.160i			1.13171i	−0.824504	+	0.565857i	$0.808546\pi$
$602$		0			0
$603$		0			0
$604$	91.7868	−	158.979i	0.151965	−	0.263211i
$605$	−564.889	+	326.139i	−0.933701	+	0.539073i
$606$		0			0
$607$	−33.5482	−	19.3690i	−0.0552688	−	0.0319095i	0.472111	−	0.881539i	$-0.343492\pi$
$607$	−33.5482	−	19.3690i	−0.0552688	−	0.0319095i	−0.527380	+	0.849630i	$0.676825\pi$
$608$		−	23.6544i		−	0.0389052i
$609$		0			0
$610$	−848.756			−1.39140
$611$	−402.765	+	697.609i	−0.659189	+	1.14175i
$612$		0			0
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	0.654784	−	0.755816i	$-0.272760\pi$
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	−0.981948	+	0.189151i	$0.939426\pi$
$614$	−25.7056	−	14.8412i	−0.0418658	−	0.0241713i
$615$		0			0
$616$		0			0
$617$	959.044			1.55437			0.777183	−	0.629275i	$-0.216648\pi$
$617$	959.044			1.55437			0.777183	+	0.629275i	$0.216648\pi$
$618$		0			0
$619$	869.951	−	502.267i	1.40541	−	0.811416i	0.410473	−	0.911873i	$-0.365364\pi$
$619$	869.951	−	502.267i	1.40541	−	0.811416i	0.994941	+	0.100457i	$0.0320303\pi$
$620$	324.037	+	561.248i	0.522640	+	0.905238i
$621$		0			0
$622$		−	257.443i		−	0.413895i
$623$		0			0
$624$		0			0
$625$	369.691	−	640.323i	0.591505	−	1.02452i
$626$	119.938	−	69.2460i	0.191594	−	0.110617i
$627$		0			0
$628$	14.6468	+	8.45631i	0.0233229	+	0.0134655i
$629$			11.0624i			0.0175873i
$630$		0			0
$631$	−386.514			−0.612542			−0.306271	−	0.951944i	$-0.599081\pi$
$631$	−386.514			−0.612542			−0.306271	+	0.951944i	$0.599081\pi$
$632$	−47.7817	+	82.7604i	−0.0756040	+	0.130950i
$633$		0			0
$634$	340.805	+	590.291i	0.537547	+	0.931058i
$635$	1420.37	+	820.053i	2.23681	+	1.29142i
$636$		0			0
$637$		0			0
$638$	23.6468			0.0370639
$639$		0			0
$640$	−64.9706	+	37.5108i	−0.101517	+	0.0586106i
$641$	−496.074	−	859.225i	−0.773906	−	1.34044i	−0.935407	−	0.353572i	$-0.884967\pi$
$641$	−496.074	−	859.225i	−0.773906	−	1.34044i	0.161502	−	0.986872i	$-0.448366\pi$
$642$		0			0
$643$			944.986i			1.46965i	0.678256	+	0.734826i	$0.262736\pi$
$643$			944.986i			1.46965i	−0.678256	+	0.734826i	$0.737264\pi$
$644$		0			0
$645$		0			0
$646$	11.1213	−	19.2627i	0.0172157	−	0.0298184i
$647$	2.50357	−	1.44544i	0.00386951	−	0.00223406i	−0.498064	−	0.867140i	$-0.665956\pi$
$647$	2.50357	−	1.44544i	0.00386951	−	0.00223406i	0.501934	+	0.864906i	$0.332622\pi$
$648$		0			0
$649$	−159.529	−	92.1039i	−0.245807	−	0.141917i
$650$			410.241i			0.631140i
$651$		0			0
$652$	443.955			0.680913
$653$	−161.529	+	279.777i	−0.247365	+	0.428449i	−0.962794	−	0.270237i	$-0.912898\pi$
$653$	−161.529	+	279.777i	−0.247365	+	0.428449i	0.715429	+	0.698686i	$0.246231\pi$
$654$		0			0
$655$	489.518	+	847.870i	0.747356	+	1.29446i
$656$	−96.8528	−	55.9180i	−0.147641	−	0.0852409i
$657$		0			0
$658$		0			0
$659$	−295.955			−0.449098			−0.224549	−	0.974463i	$-0.572091\pi$
$659$	−295.955			−0.449098			−0.224549	+	0.974463i	$0.572091\pi$
$660$		0			0
$661$	−17.9710	+	10.3756i	−0.0271876	+	0.0156968i	−0.513532	−	0.858070i	$-0.671663\pi$
$661$	−17.9710	+	10.3756i	−0.0271876	+	0.0156968i	0.486345	+	0.873767i	$0.338330\pi$
$662$	159.104	+	275.576i	0.240338	+	0.416278i
$663$		0			0
$664$		−	360.843i		−	0.543439i
$665$		0			0
$666$		0			0
$667$	48.7279	−	84.3992i	0.0730554	−	0.126536i
$668$	−292.441	+	168.841i	−0.437785	+	0.252756i
$669$		0			0
$670$	−281.319	−	162.420i	−0.419880	−	0.242418i
$671$		−	430.579i		−	0.641698i
$672$		0			0
$673$	627.044			0.931714			0.465857	−	0.884860i	$-0.345746\pi$
$673$	627.044			0.931714			0.465857	+	0.884860i	$0.345746\pi$
$674$	−186.936	+	323.783i	−0.277353	+	0.480390i
$675$		0			0
$676$	64.8234	+	112.277i	0.0958926	+	0.166091i
$677$	−94.6097	−	54.6230i	−0.139749	−	0.0806838i	0.428496	−	0.903544i	$-0.359044\pi$
$677$	−94.6097	−	54.6230i	−0.139749	−	0.0806838i	−0.568244	+	0.822860i	$0.692377\pi$
$678$		0			0
$679$		0			0
$680$	−70.5442			−0.103741
$681$		0			0
$682$	−284.724	+	164.386i	−0.417484	+	0.241035i
$683$	396.783	+	687.248i	0.580941	+	1.00622i	0.995368	+	0.0961370i	$0.0306487\pi$
$683$	396.783	+	687.248i	0.580941	+	1.00622i	−0.414427	+	0.910083i	$0.636018\pi$
$684$		0			0
$685$			215.996i			0.315323i
$686$		0			0
$687$		0			0
$688$	20.9706	−	36.3221i	0.0304805	−	0.0527937i
$689$	−741.198	+	427.931i	−1.07576	+	0.621090i
$690$		0			0
$691$	−159.253	−	91.9447i	−0.230467	−	0.133060i	0.380320	−	0.924855i	$-0.375814\pi$
$691$	−159.253	−	91.9447i	−0.230467	−	0.133060i	−0.610788	+	0.791794i	$0.709147\pi$
$692$			328.682i			0.474974i
$693$		0			0
$694$	−270.478			−0.389738
$695$	227.397	−	393.863i	0.327190	−	0.566710i
$696$		0			0
$697$	−52.5807	−	91.0725i	−0.0754386	−	0.130664i
$698$	165.889	+	95.7763i	0.237664	+	0.137215i
$699$		0			0
$700$		0			0
$701$	1043.82			1.48905			0.744525	−	0.667595i	$-0.232676\pi$
$701$	1043.82			1.48905			0.744525	+	0.667595i	$0.232676\pi$
$702$		0			0
$703$	−10.6508	+	6.14922i	−0.0151504	+	0.00874711i
$704$	−19.0294	−	32.9600i	−0.0270305	−	0.0468181i
$705$		0			0
$706$			492.840i			0.698073i
$707$		0			0
$708$		0			0
$709$	490.279	−	849.188i	0.691507	−	1.19773i	−0.279836	−	0.960048i	$-0.590280\pi$
$709$	490.279	−	849.188i	0.691507	−	1.19773i	0.971344	−	0.237678i	$-0.0763864\pi$
$710$	295.831	−	170.798i	0.416663	−	0.240560i
$711$		0			0
$712$	123.286	+	71.1794i	0.173155	+	0.0999711i
$713$			1354.97i			1.90038i
$714$		0			0
$715$	−482.382			−0.674660
$716$	185.184	−	320.748i	0.258637	−	0.447972i
$717$		0			0
$718$	−215.548	−	373.340i	−0.300206	−	0.519972i
$719$	−674.187	−	389.242i	−0.937673	−	0.541366i	−0.0484429	−	0.998826i	$-0.515426\pi$
$719$	−674.187	−	389.242i	−0.937673	−	0.541366i	−0.889230	+	0.457460i	$0.848759\pi$
$720$		0			0
$721$		0			0
$722$	−485.803			−0.672858
$723$		0			0
$724$	−268.617	+	155.086i	−0.371018	+	0.214208i
$725$	−33.3381	−	57.7433i	−0.0459836	−	0.0796459i
$726$		0			0
$727$		−	735.255i		−	1.01135i	−0.862723	−	0.505677i	$-0.831243\pi$
$727$		−	735.255i		−	1.01135i	0.862723	−	0.505677i	$-0.168757\pi$
$728$		0			0
$729$		0			0
$730$	246.665	−	427.237i	0.337898	−	0.585256i
$731$	34.1543	−	19.7190i	0.0467227	−	0.0269754i
$732$		0			0
$733$	414.705	+	239.430i	0.565764	+	0.326644i	0.755456	−	0.655200i	$-0.227415\pi$
$733$	414.705	+	239.430i	0.565764	+	0.326644i	−0.189692	+	0.981844i	$0.560749\pi$
$734$		−	134.356i		−	0.183047i
$735$		0			0
$736$	−156.853			−0.213115
$737$	82.3965	−	142.715i	0.111800	−	0.193643i
$738$		0			0
$739$	9.95227	+	17.2378i	0.0134672	+	0.0233259i	0.872680	−	0.488292i	$-0.162380\pi$
$739$	9.95227	+	17.2378i	0.0134672	+	0.0233259i	−0.859213	+	0.511618i	$0.829046\pi$
$740$	33.7797	+	19.5027i	0.0456482	+	0.0263550i
$741$		0			0
$742$		0			0
$743$	−43.3095			−0.0582901			−0.0291450	−	0.999575i	$-0.509278\pi$
$743$	−43.3095			−0.0582901			−0.0291450	+	0.999575i	$0.509278\pi$
$744$		0			0
$745$	−530.603	+	306.344i	−0.712218	+	0.411199i
$746$	179.293	+	310.544i	0.240339	+	0.416279i
$747$		0			0
$748$		−	35.7875i		−	0.0478442i
$749$		0			0
$750$		0			0
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	−0.931235	−	0.364420i	$-0.881267\pi$
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	0.781215	+	0.624263i	$0.214600\pi$
$752$	−182.485	+	105.358i	−0.242667	+	0.140104i
$753$		0			0
$754$	−65.8234	−	38.0031i	−0.0872989	−	0.0504020i
$755$		−	608.641i		−	0.806147i
$756$		0			0
$757$	935.779			1.23617			0.618084	−	0.786112i	$-0.287909\pi$
$757$	935.779			1.23617			0.618084	+	0.786112i	$0.287909\pi$
$758$	359.387	−	622.476i	0.474125	−	0.821209i
$759$		0			0
$760$	−39.2132	−	67.9193i	−0.0515963	−	0.0893674i
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.992191	+	0.124724i	$0.0398046\pi$
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.604110	+	0.796901i	$0.293529\pi$
$762$		0			0
$763$		0			0
$764$	−496.191			−0.649465
$765$		0			0
$766$	585.136	−	337.828i	0.763885	−	0.441029i
$767$	296.044	+	512.763i	0.385976	+	0.668530i
$768$		0			0
$769$			1.72330i			0.00224097i	0.999999	+	0.00112048i	$0.000356661\pi$
$769$			1.72330i			0.00224097i	−0.999999	+	0.00112048i	$0.999643\pi$
$770$		0			0
$771$		0			0
$772$	−154.338	+	267.321i	−0.199920	+	0.346271i
$773$	194.213	−	112.129i	0.251245	−	0.145057i	−0.369089	−	0.929394i	$-0.620330\pi$
$773$	194.213	−	112.129i	0.251245	−	0.145057i	0.620334	+	0.784337i	$0.286997\pi$
$774$		0			0
$775$	802.831	+	463.514i	1.03591	+	0.598083i
$776$		−	287.911i		−	0.371019i
$777$		0			0
$778$	240.728			0.309419
$779$	58.4558	−	101.248i	0.0750396	−	0.129972i
$780$		0			0
$781$	86.6468	+	150.077i	0.110943	+	0.192160i
$782$	−127.731	−	73.7458i	−0.163340	−	0.0943041i
$783$		0			0
$784$		0			0
$785$	56.0740			0.0714319
$786$		0			0
$787$	−60.7979	+	35.1017i	−0.0772528	+	0.0446019i	−0.538129	−	0.842863i	$-0.680869\pi$
$787$	−60.7979	+	35.1017i	−0.0772528	+	0.0446019i	0.460876	+	0.887465i	$0.347535\pi$
$788$	−181.103	−	313.679i	−0.229826	−	0.398070i
$789$		0			0
$790$			316.842i			0.401066i
$791$		0			0
$792$		0			0
$793$	−691.992	+	1198.57i	−0.872625	+	1.51143i
$794$	−299.511	+	172.923i	−0.377218	+	0.217787i
$795$		0			0
$796$	603.978	+	348.707i	0.758766	+	0.438074i
$797$		−	1305.38i		−	1.63787i	−0.573889	−	0.818933i	$-0.694566\pi$
$797$		−	1305.38i		−	1.63787i	0.573889	−	0.818933i	$-0.305434\pi$
$798$		0			0
$799$	−198.140			−0.247985
$800$	−53.6569	+	92.9364i	−0.0670711	+	0.116170i
$801$		0			0
$802$	295.269	+	511.420i	0.368165	+	0.637681i
$803$	216.740	+	125.135i	0.269913	+	0.155834i
$804$		0			0
$805$		0			0
$806$	1056.75			1.31110
$807$		0			0
$808$	146.184	−	84.3992i	0.180921	−	0.104455i
$809$	381.382	+	660.573i	0.471424	+	0.816531i	0.999466	−	0.0326879i	$-0.0104067\pi$
$809$	381.382	+	660.573i	0.471424	+	0.816531i	−0.528041	+	0.849219i	$0.677073\pi$
$810$		0			0
$811$			1214.98i			1.49813i	0.662498	+	0.749064i	$0.269496\pi$
$811$			1214.98i			1.49813i	−0.662498	+	0.749064i	$0.730504\pi$
$812$		0			0
$813$		0			0
$814$	−9.89383	+	17.1366i	−0.0121546	+	0.0210524i
$815$	1274.74	−	735.970i	1.56410	−	0.903031i
$816$		0			0
$817$	37.9706	+	21.9223i	0.0464756	+	0.0268327i
$818$			435.877i			0.532857i
$819$		0			0
$820$	−370.794			−0.452188
$821$	−291.684	+	505.211i	−0.355279	+	0.615361i	−0.987166	−	0.159700i	$-0.948947\pi$
$821$	−291.684	+	505.211i	−0.355279	+	0.615361i	0.631887	+	0.775061i	$0.282281\pi$
$822$		0			0
$823$	−515.371	−	892.648i	−0.626210	−	1.08463i	−0.988306	−	0.152486i	$-0.951272\pi$
$823$	−515.371	−	892.648i	−0.626210	−	1.08463i	0.362096	−	0.932141i	$-0.382061\pi$
$824$	294.375	+	169.957i	0.357251	+	0.206259i
$825$		0			0
$826$		0			0
$827$	−152.102			−0.183920			−0.0919599	−	0.995763i	$-0.529313\pi$
$827$	−152.102			−0.183920			−0.0919599	+	0.995763i	$0.529313\pi$
$828$		0			0
$829$	−532.095	+	307.205i	−0.641852	+	0.370573i	−0.785327	−	0.619081i	$-0.787505\pi$
$829$	−532.095	+	307.205i	−0.641852	+	0.370573i	0.143476	+	0.989654i	$0.454172\pi$
$830$	−598.191	−	1036.10i	−0.720712	−	1.24831i
$831$		0			0
$832$			122.330i			0.147032i
$833$		0			0
$834$		0			0
$835$	−559.794	+	969.592i	−0.670412	+	1.16119i
$836$	34.4558	−	19.8931i	0.0412151	−	0.0237956i
$837$		0			0
$838$	126.323	+	72.9326i	0.150743	+	0.0870317i
$839$			1546.14i			1.84284i	0.388568	+	0.921420i	$0.372970\pi$
$839$			1546.14i			1.84284i	−0.388568	+	0.921420i	$0.627030\pi$
$840$		0			0
$841$	−828.647			−0.985311
$842$	−116.828	+	202.353i	−0.138751	+	0.240324i
$843$		0			0
$844$	−364.073	−	630.593i	−0.431366	−	0.747148i
$845$	372.257	+	214.923i	0.440541	+	0.254347i
$846$		0			0
$847$		0			0
$848$	−223.882			−0.264012
$849$		0			0
$850$	−87.3898	+	50.4545i	−0.102812	+	0.0593583i
$851$	40.7756	+	70.6255i	0.0479150	+	0.0829912i
$852$		0			0
$853$		−	1235.15i		−	1.44800i	−0.689798	−	0.724002i	$-0.742301\pi$
$853$		−	1235.15i		−	1.44800i	0.689798	−	0.724002i	$-0.257699\pi$
$854$		0			0
$855$		0			0
$856$	160.669	−	278.287i	0.187697	−	0.325102i
$857$	−953.219	+	550.341i	−1.11227	+	0.642172i	−0.939417	−	0.342775i	$-0.888633\pi$
$857$	−953.219	+	550.341i	−1.11227	+	0.642172i	−0.172857	+	0.984947i	$0.555300\pi$
$858$		0			0
$859$	−512.488	−	295.885i	−0.596610	−	0.344453i	0.171096	−	0.985254i	$-0.445269\pi$
$859$	−512.488	−	295.885i	−0.596610	−	0.344453i	−0.767707	+	0.640801i	$0.778602\pi$
$860$		−	139.056i		−	0.161694i
$861$		0			0
$862$	840.801			0.975407
$863$	−32.3635	+	56.0553i	−0.0375012	+	0.0649540i	−0.884167	−	0.467171i	$-0.845273\pi$
$863$	−32.3635	+	56.0553i	−0.0375012	+	0.0649540i	0.846666	+	0.532125i	$0.178606\pi$
$864$		0			0
$865$	544.875	+	943.751i	0.629913	+	1.09104i
$866$	−49.7574	−	28.7274i	−0.0574565	−	0.0331725i
$867$		0			0
$868$		0			0
$869$	−160.736			−0.184967
$870$		0			0
$871$	−458.720	+	264.842i	−0.526659	+	0.304067i
$872$	−205.497	−	355.932i	−0.235662	−	0.408179i
$873$		0			0
$874$		−	163.972i		−	0.187611i
$875$		0			0
$876$		0			0
$877$	152.096	−	263.438i	0.173427	−	0.300385i	−0.766188	−	0.642616i	$-0.777849\pi$
$877$	152.096	−	263.438i	0.173427	−	0.300385i	0.939616	+	0.342231i	$0.111182\pi$
$878$	−179.548	+	103.662i	−0.204496	+	0.118066i
$879$		0			0
$880$	−109.279	−	63.0924i	−0.124181	−	0.0716959i
$881$		−	863.732i		−	0.980400i	−0.871610	−	0.490200i	$-0.836924\pi$
$881$		−	863.732i		−	0.980400i	0.871610	−	0.490200i	$-0.163076\pi$
$882$		0			0
$883$	−567.456			−0.642645			−0.321323	−	0.946970i	$-0.604127\pi$
$883$	−567.456			−0.642645			−0.321323	+	0.946970i	$0.604127\pi$
$884$	−57.5147	+	99.6184i	−0.0650619	+	0.112691i
$885$		0			0
$886$	−75.9153	−	131.489i	−0.0856831	−	0.148408i
$887$	−770.555	−	444.880i	−0.868721	−	0.501556i	−0.00179783	−	0.999998i	$-0.500572\pi$
$887$	−770.555	−	444.880i	−0.868721	−	0.501556i	−0.866923	+	0.498442i	$0.833906\pi$
$888$		0			0
$889$		0			0
$890$	471.993			0.530329
$891$		0			0
$892$	213.442	−	123.231i	0.239284	−	0.138151i
$893$	−110.140	−	190.767i	−0.123337	−	0.213625i
$894$		0			0
$895$		−	1227.96i		−	1.37202i
$896$		0			0
$897$		0			0
$898$	−95.5736	+	165.538i	−0.106429	+	0.184341i
$899$	−148.742	+	85.8764i	−0.165453	+	0.0955243i
$900$		0			0
$901$	−182.316	−	105.260i	−0.202349	−	0.116826i
$902$		−	188.106i		−	0.208543i
$903$		0			0
$904$	97.7056			0.108081
$905$	−514.191	+	890.605i	−0.568167	+	0.984094i
$906$		0			0
$907$	−186.989	−	323.874i	−0.206162	−	0.357083i	0.744340	−	0.667800i	$-0.232764\pi$
$907$	−186.989	−	323.874i	−0.206162	−	0.357083i	−0.950502	+	0.310717i	$0.899431\pi$
$908$	132.286	+	76.3756i	0.145690	+	0.0841141i
$909$		0			0
$910$		0			0
$911$	−1133.75			−1.24451			−0.622256	−	0.782814i	$-0.713784\pi$
$911$	−1133.75			−1.24451			−0.622256	+	0.782814i	$0.713784\pi$
$912$		0			0
$913$	525.618	−	303.466i	0.575704	−	0.332383i
$914$	112.950	+	195.635i	0.123577	+	0.214042i
$915$		0			0
$916$			714.572i			0.780101i
$917$		0			0
$918$		0			0
$919$	−228.151	+	395.169i	−0.248260	+	0.429999i	−0.963043	−	0.269347i	$-0.913192\pi$
$919$	−228.151	+	395.169i	−0.248260	+	0.429999i	0.714783	+	0.699346i	$0.246525\pi$
$920$	−450.375	+	260.024i	−0.489538	+	0.282635i
$921$		0			0
$922$	−379.977	−	219.380i	−0.412122	−	0.237939i
$923$		−	557.007i		−	0.603474i
$924$		0			0
$925$	55.7948			0.0603187
$926$	−230.527	+	399.284i	−0.248949	+	0.431193i
$927$		0			0
$928$	−9.94113	−	17.2185i	−0.0107124	−	0.0185545i
$929$	−824.058	−	475.770i	−0.887037	−	0.512131i	−0.0140650	−	0.999901i	$-0.504477\pi$
$929$	−824.058	−	475.770i	−0.887037	−	0.512131i	−0.872972	+	0.487770i	$0.837811\pi$
$930$		0			0
$931$		0			0
$932$	546.146			0.585994
$933$		0			0
$934$	729.407	−	421.123i	0.780949	−	0.450881i
$935$	−59.3269	−	102.757i	−0.0634513	−	0.109901i
$936$		0			0
$937$		−	1295.71i		−	1.38283i	−0.722460	−	0.691413i	$-0.756989\pi$
$937$		−	1295.71i		−	1.38283i	0.722460	−	0.691413i	$-0.243011\pi$
$938$		0			0
$939$		0			0
$940$	−349.316	+	605.033i	−0.371613	+	0.643652i
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.970866	−	0.239622i	$-0.922977\pi$
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.277915	+	0.960606i	$0.589643\pi$
$942$		0			0
$943$	−671.382	−	387.622i	−0.711964	−	0.411052i
$944$			154.882i			0.164070i
$945$		0			0
$946$	70.5442			0.0745710
$947$	−354.731	+	614.412i	−0.374584	+	0.648799i	−0.990265	−	0.139197i	$-0.955548\pi$
$947$	−354.731	+	614.412i	−0.374584	+	0.648799i	0.615681	+	0.787996i	$0.288881\pi$
$948$		0			0
$949$	−402.213	−	696.654i	−0.423828	−	0.734092i
$950$	−97.1543	−	56.0921i	−0.102268	−	0.0590443i
$951$		0			0
$952$		0			0
$953$	−936.603			−0.982794			−0.491397	−	0.870936i	$-0.663514\pi$
$953$	−936.603			−0.982794			−0.491397	+	0.870936i	$0.663514\pi$
$954$		0			0
$955$	−1424.72	+	822.564i	−1.49186	+	0.861324i
$956$	−265.103	−	459.171i	−0.277304	−	0.480305i
$957$		0			0
$958$		−	716.554i		−	0.747969i
$959$		0			0
$960$		0			0
$961$	713.477	−	1235.78i	0.742432	−	1.28593i
$962$	55.0812	−	31.8011i	0.0572569	−	0.0330573i
$963$		0			0
$964$	−151.794	−	87.6383i	−0.157463	−	0.0909111i
$965$			1023.42i			1.06054i
$966$		0			0
$967$	1374.37			1.42127			0.710635	−	0.703561i	$-0.248408\pi$
$967$	1374.37			1.42127			0.710635	+	0.703561i	$0.248408\pi$
$968$	−139.113	+	240.950i	−0.143711	+	0.248916i
$969$		0			0
$970$	−477.286	−	826.684i	−0.492048	−	0.852252i
$971$	−27.2466	−	15.7309i	−0.0280604	−	0.0162007i	0.485904	−	0.874012i	$-0.338490\pi$
$971$	−27.2466	−	15.7309i	−0.0280604	−	0.0162007i	−0.513965	+	0.857811i	$0.671824\pi$
$972$		0			0
$973$		0			0
$974$	−298.825			−0.306802
$975$		0			0
$976$	−313.529	+	181.016i	−0.321239	+	0.185467i
$977$	−270.949	−	469.297i	−0.277327	−	0.480345i	0.693392	−	0.720560i	$-0.256115\pi$
$977$	−270.949	−	469.297i	−0.277327	−	0.480345i	−0.970720	+	0.240215i	$0.922782\pi$
$978$		0			0
$979$			239.445i			0.244581i
$980$		0			0
$981$		0			0
$982$	554.485	−	960.397i	0.564649	−	0.978001i
$983$	19.4161	−	11.2099i	0.0197519	−	0.0114038i	−0.490092	−	0.871671i	$-0.663037\pi$
$983$	19.4161	−	11.2099i	0.0197519	−	0.0114038i	0.509843	+	0.860267i	$0.329703\pi$
$984$		0			0
$985$	−1040.01	−	600.448i	−1.05584	−	0.609592i
$986$		−	18.6957i		−	0.0189611i
$987$		0			0
$988$	−127.882			−0.129435
$989$	145.368	−	251.784i	0.146984	−	0.254584i
$990$		0			0
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	0.642726	−	0.766097i	$-0.277804\pi$
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	−0.984822	+	0.173568i	$0.944470\pi$
$992$	239.397	+	138.216i	0.241328	+	0.139331i
$993$		0			0
$994$		0			0
$995$	2312.28			2.32390
$996$		0			0
$997$	−758.779	+	438.081i	−0.761062	+	0.439400i	−0.829677	−	0.558244i	$-0.811475\pi$
$997$	−758.779	+	438.081i	−0.761062	+	0.439400i	0.0686147	+	0.997643i	$0.478142\pi$
$998$	−121.263	−	210.034i	−0.121506	−	0.210455i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.n.b.19.2		4
3.2	odd	2		98.3.d.a.19.1		4
7.2	even	3		882.3.c.f.685.2		4
7.3	odd	6	inner	882.3.n.b.325.2		4
7.4	even	3		126.3.n.c.73.2		4
7.5	odd	6		882.3.c.f.685.1		4
7.6	odd	2		126.3.n.c.19.2		4
12.11	even	2		784.3.s.c.705.2		4
21.2	odd	6		98.3.b.b.97.3		4
21.5	even	6		98.3.b.b.97.4		4
21.11	odd	6		14.3.d.a.3.1	✓	4
21.17	even	6		98.3.d.a.31.1		4
21.20	even	2		14.3.d.a.5.1	yes	4
28.11	odd	6		1008.3.cg.l.577.2		4
28.27	even	2		1008.3.cg.l.145.2		4
84.11	even	6		112.3.s.b.17.1		4
84.23	even	6		784.3.c.e.97.3		4
84.47	odd	6		784.3.c.e.97.2		4
84.59	odd	6		784.3.s.c.129.2		4
84.83	odd	2		112.3.s.b.33.1		4
105.32	even	12		350.3.i.a.199.3		8
105.53	even	12		350.3.i.a.199.2		8
105.62	odd	4		350.3.i.a.299.2		8
105.74	odd	6		350.3.k.a.101.2		4
105.83	odd	4		350.3.i.a.299.3		8
105.104	even	2		350.3.k.a.201.2		4
168.11	even	6		448.3.s.c.129.2		4
168.53	odd	6		448.3.s.d.129.1		4
168.83	odd	2		448.3.s.c.257.2		4
168.125	even	2		448.3.s.d.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.1	✓	4	21.11	odd	6
14.3.d.a.5.1	yes	4	21.20	even	2
98.3.b.b.97.3		4	21.2	odd	6
98.3.b.b.97.4		4	21.5	even	6
98.3.d.a.19.1		4	3.2	odd	2
98.3.d.a.31.1		4	21.17	even	6
112.3.s.b.17.1		4	84.11	even	6
112.3.s.b.33.1		4	84.83	odd	2
126.3.n.c.19.2		4	7.6	odd	2
126.3.n.c.73.2		4	7.4	even	3
350.3.i.a.199.2		8	105.53	even	12
350.3.i.a.199.3		8	105.32	even	12
350.3.i.a.299.2		8	105.62	odd	4
350.3.i.a.299.3		8	105.83	odd	4
350.3.k.a.101.2		4	105.74	odd	6
350.3.k.a.201.2		4	105.104	even	2
448.3.s.c.129.2		4	168.11	even	6
448.3.s.c.257.2		4	168.83	odd	2
448.3.s.d.129.1		4	168.53	odd	6
448.3.s.d.257.1		4	168.125	even	2
784.3.c.e.97.2		4	84.47	odd	6
784.3.c.e.97.3		4	84.23	even	6
784.3.s.c.129.2		4	84.59	odd	6
784.3.s.c.705.2		4	12.11	even	2
882.3.c.f.685.1		4	7.5	odd	6
882.3.c.f.685.2		4	7.2	even	3
882.3.n.b.19.2		4	1.1	even	1	trivial
882.3.n.b.325.2		4	7.3	odd	6	inner
1008.3.cg.l.145.2		4	28.27	even	2
1008.3.cg.l.577.2		4	28.11	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	882.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} -2.82843 q^{8} +(-8.12132 + 4.68885i) q^{10} +(-2.37868 - 4.11999i) q^{11} +15.2913i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-3.25736 + 1.88064i) q^{17} +(-3.62132 - 2.09077i) q^{19} +13.2621i q^{20} -6.72792 q^{22} +(-13.8640 + 24.0131i) q^{23} +(9.48528 + 16.4290i) q^{25} +(18.7279 + 10.8126i) q^{26} -3.51472 q^{29} +(42.3198 - 24.4334i) q^{31} +(2.82843 + 4.89898i) q^{32} +5.31925i q^{34} +(1.47056 - 2.54709i) q^{37} +(-5.12132 + 2.95680i) q^{38} +(16.2426 + 9.37769i) q^{40} +27.9590i q^{41} -10.4853 q^{43} +(-4.75736 + 8.23999i) q^{44} +(19.6066 + 33.9596i) q^{46} +(45.6213 + 26.3395i) q^{47} +26.8284 q^{50} +(26.4853 - 15.2913i) q^{52} +(27.9853 + 48.4719i) q^{53} +31.5462i q^{55} +(-2.48528 + 4.30463i) q^{58} +(33.5330 - 19.3603i) q^{59} +(78.3823 + 45.2540i) q^{61} -69.1080i q^{62} +8.00000 q^{64} +(50.6985 - 87.8124i) q^{65} +(17.3198 + 29.9988i) q^{67} +(6.51472 + 3.76127i) q^{68} -36.4264 q^{71} +(-45.5589 + 26.3034i) q^{73} +(-2.07969 - 3.60213i) q^{74} +8.36308i q^{76} +(16.8934 - 29.2602i) q^{79} +(22.9706 - 13.2621i) q^{80} +(34.2426 + 19.7700i) q^{82} +127.577i q^{83} +24.9411 q^{85} +(-7.41421 + 12.8418i) q^{86} +(6.72792 + 11.6531i) q^{88} +(-43.5883 - 25.1657i) q^{89} +55.4558 q^{92} +(64.5183 - 37.2497i) q^{94} +(13.8640 + 24.0131i) q^{95} +101.792i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 6 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 - 6 * q^5	\( 4 q - 4 q^{4} - 6 q^{5} - 24 q^{10} - 18 q^{11} - 8 q^{16} - 30 q^{17} - 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} + 24 q^{26} - 48 q^{29} + 42 q^{31} - 62 q^{37} - 12 q^{38} + 48 q^{40} - 8 q^{43} - 36 q^{44} + 36 q^{46} + 174 q^{47} + 96 q^{50} + 72 q^{52} + 78 q^{53} + 24 q^{58} - 78 q^{59} + 42 q^{61} + 32 q^{64} + 84 q^{65} - 58 q^{67} + 60 q^{68} + 24 q^{71} - 318 q^{73} - 96 q^{74} + 110 q^{79} + 24 q^{80} + 120 q^{82} - 36 q^{85} - 24 q^{86} - 24 q^{88} - 378 q^{89} + 120 q^{92} + 12 q^{94} + 30 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 6 * q^5 - 24 * q^10 - 18 * q^11 - 8 * q^16 - 30 * q^17 - 6 * q^19 + 24 * q^22 - 30 * q^23 + 4 * q^25 + 24 * q^26 - 48 * q^29 + 42 * q^31 - 62 * q^37 - 12 * q^38 + 48 * q^40 - 8 * q^43 - 36 * q^44 + 36 * q^46 + 174 * q^47 + 96 * q^50 + 72 * q^52 + 78 * q^53 + 24 * q^58 - 78 * q^59 + 42 * q^61 + 32 * q^64 + 84 * q^65 - 58 * q^67 + 60 * q^68 + 24 * q^71 - 318 * q^73 - 96 * q^74 + 110 * q^79 + 24 * q^80 + 120 * q^82 - 36 * q^85 - 24 * q^86 - 24 * q^88 - 378 * q^89 + 120 * q^92 + 12 * q^94 + 30 * q^95

Introduction

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