LMFDB - Embedded newform 882.3.n.e.325.1

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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			325.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.325
Dual form			882.3.n.e.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24264 + 0.717439i) q^{5} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24264 + 0.717439i) q^{5} +2.82843 q^{8} +(1.75736 + 1.01461i) q^{10} +(3.00000 - 5.19615i) q^{11} +21.3280i q^{13} +(-2.00000 - 3.46410i) q^{16} +(-7.75736 - 4.47871i) q^{17} +(6.25736 - 3.61269i) q^{19} -2.86976i q^{20} -8.48528 q^{22} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} +(26.1213 - 15.0812i) q^{26} +33.9411 q^{29} +(-38.2279 - 22.0709i) q^{31} +(-2.82843 + 4.89898i) q^{32} +12.6677i q^{34} +(13.9853 + 24.2232i) q^{37} +(-8.84924 - 5.10911i) q^{38} +(-3.51472 + 2.02922i) q^{40} -54.8313i q^{41} -1.48528 q^{43} +(6.00000 + 10.3923i) q^{44} +(-26.4853 + 45.8739i) q^{46} +(-37.2426 + 21.5020i) q^{47} +32.4437 q^{50} +(-36.9411 - 21.3280i) q^{52} +(-42.7279 + 74.0069i) q^{53} +8.60927i q^{55} +(-24.0000 - 41.5692i) q^{58} +(-35.6985 - 20.6105i) q^{59} +(1.02944 - 0.594346i) q^{61} +62.4259i q^{62} +8.00000 q^{64} +(-15.3015 - 26.5030i) q^{65} +(-2.19848 + 3.80789i) q^{67} +(15.5147 - 8.95743i) q^{68} -137.397 q^{71} +(-68.3528 - 39.4635i) q^{73} +(19.7782 - 34.2568i) q^{74} +14.4508i q^{76} +(-49.1690 - 85.1633i) q^{79} +(4.97056 + 2.86976i) q^{80} +(-67.1543 + 38.7716i) q^{82} +110.401i q^{83} +12.8528 q^{85} +(1.05025 + 1.81909i) q^{86} +(8.48528 - 14.6969i) q^{88} +(-18.0000 + 10.3923i) q^{89} +74.9117 q^{92} +(52.6690 + 30.4085i) q^{94} +(-5.18377 + 8.97855i) q^{95} +10.9867i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 12 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 + 12 * q^5	$ 4 q - 4 q^{4} + 12 q^{5} + 24 q^{10} + 12 q^{11} - 8 q^{16} - 48 q^{17} + 42 q^{19} - 24 q^{23} + 22 q^{25} + 96 q^{26} - 102 q^{31} + 22 q^{37} + 24 q^{38} - 48 q^{40} + 28 q^{43} + 24 q^{44} - 72 q^{46} - 132 q^{47} + 192 q^{50} - 12 q^{52} - 120 q^{53} - 96 q^{58} - 24 q^{59} + 72 q^{61} + 32 q^{64} - 180 q^{65} + 110 q^{67} + 96 q^{68} - 312 q^{71} + 66 q^{73} + 48 q^{74} - 10 q^{79} - 48 q^{80} - 48 q^{82} - 288 q^{85} + 24 q^{86} - 72 q^{89} + 96 q^{92} + 24 q^{94} + 132 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 + 12 * q^5 + 24 * q^10 + 12 * q^11 - 8 * q^16 - 48 * q^17 + 42 * q^19 - 24 * q^23 + 22 * q^25 + 96 * q^26 - 102 * q^31 + 22 * q^37 + 24 * q^38 - 48 * q^40 + 28 * q^43 + 24 * q^44 - 72 * q^46 - 132 * q^47 + 192 * q^50 - 12 * q^52 - 120 * q^53 - 96 * q^58 - 24 * q^59 + 72 * q^61 + 32 * q^64 - 180 * q^65 + 110 * q^67 + 96 * q^68 - 312 * q^71 + 66 * q^73 + 48 * q^74 - 10 * q^79 - 48 * q^80 - 48 * q^82 - 288 * q^85 + 24 * q^86 - 72 * q^89 + 96 * q^92 + 24 * q^94 + 132 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.24264	+	0.717439i	−0.248528	+	0.143488i	−0.619090	−	0.785320i	$-0.712498\pi$
$5$	−1.24264	+	0.717439i	−0.248528	+	0.143488i	0.370562	+	0.928808i	$0.379165\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.82843			0.353553
$9$		0			0
$10$	1.75736	+	1.01461i	0.175736	+	0.101461i
$11$	3.00000	−	5.19615i	0.272727	−	0.472377i	−0.696832	−	0.717234i	$-0.745408\pi$
$11$	3.00000	−	5.19615i	0.272727	−	0.472377i	0.969559	+	0.244857i	$0.0787410\pi$
$12$		0			0
$13$			21.3280i			1.64061i	0.571924	+	0.820306i	$0.306197\pi$
$13$			21.3280i			1.64061i	−0.571924	+	0.820306i	$0.693803\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−7.75736	−	4.47871i	−0.456315	−	0.263454i	0.254178	−	0.967157i	$-0.418195\pi$
$17$	−7.75736	−	4.47871i	−0.456315	−	0.263454i	−0.710494	+	0.703704i	$0.751528\pi$
$18$		0			0
$19$	6.25736	−	3.61269i	0.329335	−	0.190141i	−0.326211	−	0.945297i	$-0.605772\pi$
$19$	6.25736	−	3.61269i	0.329335	−	0.190141i	0.655546	+	0.755156i	$0.272439\pi$
$20$		−	2.86976i		−	0.143488i
$21$		0			0
$22$	−8.48528			−0.385695
$23$	−18.7279	−	32.4377i	−0.814257	−	1.41034i	−0.909860	−	0.414916i	$-0.863811\pi$
$23$	−18.7279	−	32.4377i	−0.814257	−	1.41034i	0.0956024	−	0.995420i	$-0.469522\pi$
$24$		0			0
$25$	−11.4706	+	19.8676i	−0.458823	+	0.794704i
$26$	26.1213	−	15.0812i	1.00467	−	0.580044i
$27$		0			0
$28$		0			0
$29$	33.9411			1.17038			0.585192	−	0.810895i	$-0.301019\pi$
$29$	33.9411			1.17038			0.585192	+	0.810895i	$0.301019\pi$
$30$		0			0
$31$	−38.2279	−	22.0709i	−1.23316	−	0.711965i	−0.265472	−	0.964119i	$-0.585528\pi$
$31$	−38.2279	−	22.0709i	−1.23316	−	0.711965i	−0.967687	+	0.252154i	$0.918861\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$			12.6677i			0.372580i
$35$		0			0
$36$		0			0
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	0.990768	−	0.135566i	$-0.0432853\pi$
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	−0.612788	+	0.790248i	$0.709952\pi$
$38$	−8.84924	−	5.10911i	−0.232875	−	0.134450i
$39$		0			0
$40$	−3.51472	+	2.02922i	−0.0878680	+	0.0507306i
$41$		−	54.8313i		−	1.33735i	−0.743556	−	0.668674i	$-0.766862\pi$
$41$		−	54.8313i		−	1.33735i	0.743556	−	0.668674i	$-0.233138\pi$
$42$		0			0
$43$	−1.48528			−0.0345414			−0.0172707	−	0.999851i	$-0.505498\pi$
$43$	−1.48528			−0.0345414			−0.0172707	+	0.999851i	$0.505498\pi$
$44$	6.00000	+	10.3923i	0.136364	+	0.236189i
$45$		0			0
$46$	−26.4853	+	45.8739i	−0.575767	+	0.997258i
$47$	−37.2426	+	21.5020i	−0.792397	+	0.457490i	−0.840806	−	0.541337i	$-0.817918\pi$
$47$	−37.2426	+	21.5020i	−0.792397	+	0.457490i	0.0484090	+	0.998828i	$0.484585\pi$
$48$		0			0
$49$		0			0
$50$	32.4437			0.648873
$51$		0			0
$52$	−36.9411	−	21.3280i	−0.710406	−	0.410153i
$53$	−42.7279	+	74.0069i	−0.806187	+	1.39636i	0.109299	+	0.994009i	$0.465139\pi$
$53$	−42.7279	+	74.0069i	−0.806187	+	1.39636i	−0.915487	+	0.402348i	$0.868194\pi$
$54$		0			0
$55$			8.60927i			0.156532i
$56$		0			0
$57$		0			0
$58$	−24.0000	−	41.5692i	−0.413793	−	0.716711i
$59$	−35.6985	−	20.6105i	−0.605059	−	0.349331i	0.165970	−	0.986131i	$-0.446924\pi$
$59$	−35.6985	−	20.6105i	−0.605059	−	0.349331i	−0.771029	+	0.636800i	$0.780258\pi$
$60$		0			0
$61$	1.02944	−	0.594346i	0.0168760	−	0.00974337i	−0.491538	−	0.870856i	$-0.663565\pi$
$61$	1.02944	−	0.594346i	0.0168760	−	0.00974337i	0.508414	+	0.861113i	$0.330232\pi$
$62$			62.4259i			1.00687i
$63$		0			0
$64$	8.00000			0.125000
$65$	−15.3015	−	26.5030i	−0.235408	−	0.407738i
$66$		0			0
$67$	−2.19848	+	3.80789i	−0.0328132	+	0.0568341i	−0.881966	−	0.471314i	$-0.843780\pi$
$67$	−2.19848	+	3.80789i	−0.0328132	+	0.0568341i	0.849152	+	0.528148i	$0.177113\pi$
$68$	15.5147	−	8.95743i	0.228158	−	0.131727i
$69$		0			0
$70$		0			0
$71$	−137.397			−1.93517			−0.967584	−	0.252548i	$-0.918731\pi$
$71$	−137.397			−1.93517			−0.967584	+	0.252548i	$0.918731\pi$
$72$		0			0
$73$	−68.3528	−	39.4635i	−0.936340	−	0.540596i	−0.0475288	−	0.998870i	$-0.515135\pi$
$73$	−68.3528	−	39.4635i	−0.936340	−	0.540596i	−0.888811	+	0.458274i	$0.848468\pi$
$74$	19.7782	−	34.2568i	0.267273	−	0.462930i
$75$		0			0
$76$			14.4508i			0.190141i
$77$		0			0
$78$		0			0
$79$	−49.1690	−	85.1633i	−0.622393	−	1.07802i	−0.989039	−	0.147656i	$-0.952827\pi$
$79$	−49.1690	−	85.1633i	−0.622393	−	1.07802i	0.366646	−	0.930361i	$-0.380506\pi$
$80$	4.97056	+	2.86976i	0.0621320	+	0.0358719i
$81$		0			0
$82$	−67.1543	+	38.7716i	−0.818955	+	0.472824i
$83$			110.401i			1.33013i	0.746784	+	0.665067i	$0.231597\pi$
$83$			110.401i			1.33013i	−0.746784	+	0.665067i	$0.768403\pi$
$84$		0			0
$85$	12.8528			0.151210
$86$	1.05025	+	1.81909i	0.0122122	+	0.0211522i
$87$		0			0
$88$	8.48528	−	14.6969i	0.0964237	−	0.167011i
$89$	−18.0000	+	10.3923i	−0.202247	+	0.116767i	−0.597703	−	0.801717i	$-0.703920\pi$
$89$	−18.0000	+	10.3923i	−0.202247	+	0.116767i	0.395456	+	0.918485i	$0.370587\pi$
$90$		0			0
$91$		0			0
$92$	74.9117			0.814257
$93$		0			0
$94$	52.6690	+	30.4085i	0.560309	+	0.323495i
$95$	−5.18377	+	8.97855i	−0.0545660	+	0.0945110i
$96$		0			0
$97$			10.9867i			0.113264i	0.998395	+	0.0566322i	$0.0180362\pi$
$97$			10.9867i			0.113264i	−0.998395	+	0.0566322i	$0.981964\pi$
$98$		0			0
$99$		0			0
$100$	−22.9411	−	39.7352i	−0.229411	−	0.397352i
$101$	−92.8234	−	53.5916i	−0.919043	−	0.530610i	−0.0357136	−	0.999362i	$-0.511370\pi$
$101$	−92.8234	−	53.5916i	−0.919043	−	0.530610i	−0.883330	+	0.468752i	$0.844704\pi$
$102$		0			0
$103$	−91.1102	+	52.6025i	−0.884565	+	0.510704i	−0.872161	−	0.489219i	$-0.837282\pi$
$103$	−91.1102	+	52.6025i	−0.884565	+	0.510704i	−0.0124040	+	0.999923i	$0.503948\pi$
$104$			60.3246i			0.580044i
$105$		0			0
$106$	120.853			1.14012
$107$	59.2721	+	102.662i	0.553945	+	0.959460i	0.997985	+	0.0634534i	$0.0202114\pi$
$107$	59.2721	+	102.662i	0.553945	+	0.959460i	−0.444040	+	0.896007i	$0.646455\pi$
$108$		0			0
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	0.490496	+	0.871444i	$0.336816\pi$
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	−0.999940	+	0.0109400i	$0.996518\pi$
$110$	10.5442	−	6.08767i	0.0958560	−	0.0553425i
$111$		0			0
$112$		0			0
$113$	−101.397			−0.897318			−0.448659	−	0.893703i	$-0.648098\pi$
$113$	−101.397			−0.897318			−0.448659	+	0.893703i	$0.648098\pi$
$114$		0			0
$115$	46.5442	+	26.8723i	0.404732	+	0.233672i
$116$	−33.9411	+	58.7878i	−0.292596	+	0.506791i
$117$		0			0
$118$			58.2954i			0.494029i
$119$		0			0
$120$		0			0
$121$	42.5000	+	73.6122i	0.351240	+	0.608365i
$122$	−1.45584	−	0.840532i	−0.0119331	−	0.00688961i
$123$		0			0
$124$	76.4558	−	44.1418i	0.616579	−	0.355982i
$125$		−	68.7897i		−	0.550317i
$126$		0			0
$127$	82.5736			0.650186			0.325093	−	0.945682i	$-0.394604\pi$
$127$	82.5736			0.650186			0.325093	+	0.945682i	$0.394604\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−21.6396	+	37.4809i	−0.166459	+	0.288315i
$131$	−52.4558	+	30.2854i	−0.400426	+	0.231186i	−0.686668	−	0.726971i	$-0.740927\pi$
$131$	−52.4558	+	30.2854i	−0.400426	+	0.231186i	0.286242	+	0.958157i	$0.407594\pi$
$132$		0			0
$133$		0			0
$134$	6.21825			0.0464049
$135$		0			0
$136$	−21.9411	−	12.6677i	−0.161332	−	0.0931450i
$137$	33.5147	−	58.0492i	0.244633	−	0.423717i	−0.717395	−	0.696666i	$-0.754666\pi$
$137$	33.5147	−	58.0492i	0.244633	−	0.423717i	0.962028	+	0.272949i	$0.0879992\pi$
$138$		0			0
$139$		−	91.5525i		−	0.658651i	−0.944216	−	0.329326i	$-0.893179\pi$
$139$		−	91.5525i		−	0.658651i	0.944216	−	0.329326i	$-0.106821\pi$
$140$		0			0
$141$		0			0
$142$	97.1543	+	168.276i	0.684185	+	1.18504i
$143$	110.823	+	63.9839i	0.774989	+	0.447440i
$144$		0			0
$145$	−42.1766	+	24.3507i	−0.290873	+	0.167936i
$146$			111.620i			0.764518i
$147$		0			0
$148$	−55.9411			−0.377981
$149$	40.5442	+	70.2245i	0.272108	+	0.471306i	0.969402	−	0.245480i	$-0.0789457\pi$
$149$	40.5442	+	70.2245i	0.272108	+	0.471306i	−0.697293	+	0.716786i	$0.745612\pi$
$150$		0			0
$151$	25.6030	−	44.3457i	0.169556	−	0.293680i	−0.768708	−	0.639600i	$-0.779100\pi$
$151$	25.6030	−	44.3457i	0.169556	−	0.293680i	0.938264	+	0.345920i	$0.112433\pi$
$152$	17.6985	−	10.2182i	0.116437	−	0.0672252i
$153$		0			0
$154$		0			0
$155$	63.3381			0.408633
$156$		0			0
$157$	−162.000	−	93.5307i	−1.03185	−	0.595737i	−0.114334	−	0.993442i	$-0.536473\pi$
$157$	−162.000	−	93.5307i	−1.03185	−	0.595737i	−0.917513	+	0.397705i	$0.869807\pi$
$158$	−69.5355	+	120.439i	−0.440098	+	0.762273i
$159$		0			0
$160$		−	8.11689i		−	0.0507306i
$161$		0			0
$162$		0			0
$163$	−41.9706	−	72.6951i	−0.257488	−	0.445982i	0.708080	−	0.706132i	$-0.249561\pi$
$163$	−41.9706	−	72.6951i	−0.257488	−	0.445982i	−0.965568	+	0.260149i	$0.916228\pi$
$164$	94.9706	+	54.8313i	0.579089	+	0.334337i
$165$		0			0
$166$	135.213	−	78.0654i	0.814537	−	0.470273i
$167$		−	127.620i		−	0.764190i	−0.924123	−	0.382095i	$-0.875203\pi$
$167$		−	127.620i		−	0.764190i	0.924123	−	0.382095i	$-0.124797\pi$
$168$		0			0
$169$	−285.882			−1.69161
$170$	−9.08831	−	15.7414i	−0.0534607	−	0.0925966i
$171$		0			0
$172$	1.48528	−	2.57258i	0.00863536	−	0.0149569i
$173$	−123.816	+	71.4853i	−0.715701	+	0.413210i	−0.813168	−	0.582029i	$-0.802259\pi$
$173$	−123.816	+	71.4853i	−0.715701	+	0.413210i	0.0974675	+	0.995239i	$0.468926\pi$
$174$		0			0
$175$		0			0
$176$	−24.0000			−0.136364
$177$		0			0
$178$	25.4558	+	14.6969i	0.143010	+	0.0825671i
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	−0.526670	−	0.850070i	$-0.676560\pi$
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	0.999517	+	0.0310748i	$0.00989300\pi$
$180$		0			0
$181$			209.969i			1.16005i	0.814600	+	0.580024i	$0.196957\pi$
$181$			209.969i			1.16005i	−0.814600	+	0.580024i	$0.803043\pi$
$182$		0			0
$183$		0			0
$184$	−52.9706	−	91.7477i	−0.287883	−	0.498629i
$185$	−34.7574	−	20.0672i	−0.187878	−	0.108471i
$186$		0			0
$187$	−46.5442	+	26.8723i	−0.248899	+	0.143702i
$188$		−	86.0082i		−	0.457490i
$189$		0			0
$190$	14.6619			0.0771679
$191$	33.3015	+	57.6799i	0.174353	+	0.301989i	0.939937	−	0.341347i	$-0.110883\pi$
$191$	33.3015	+	57.6799i	0.174353	+	0.301989i	−0.765584	+	0.643336i	$0.777550\pi$
$192$		0			0
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	−0.853060	−	0.521813i	$-0.825256\pi$
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	0.878433	+	0.477865i	$0.158589\pi$
$194$	13.4558	−	7.76874i	0.0693600	−	0.0400450i
$195$		0			0
$196$		0			0
$197$	267.161			1.35615			0.678075	−	0.734993i	$-0.262815\pi$
$197$	267.161			1.35615			0.678075	+	0.734993i	$0.262815\pi$
$198$		0			0
$199$	113.397	+	65.4698i	0.569834	+	0.328994i	0.757083	−	0.653319i	$-0.226624\pi$
$199$	113.397	+	65.4698i	0.569834	+	0.328994i	−0.187249	+	0.982312i	$0.559957\pi$
$200$	−32.4437	+	56.1941i	−0.162218	+	0.280970i
$201$		0			0
$202$			151.580i			0.750396i
$203$		0			0
$204$		0			0
$205$	39.3381	+	68.1356i	0.191893	+	0.332369i
$206$	128.849	+	74.3911i	0.625482	+	0.361122i
$207$		0			0
$208$	73.8823	−	42.6559i	0.355203	−	0.205077i
$209$		−	43.3523i		−	0.207427i
$210$		0			0
$211$	−23.0883			−0.109423			−0.0547116	−	0.998502i	$-0.517424\pi$
$211$	−23.0883			−0.109423			−0.0547116	+	0.998502i	$0.517424\pi$
$212$	−85.4558	−	148.014i	−0.403094	−	0.698179i
$213$		0			0
$214$	83.8234	−	145.186i	0.391698	−	0.678441i
$215$	1.84567	−	1.06560i	0.00858452	−	0.00495627i
$216$		0			0
$217$		0			0
$218$	157.061			0.720463
$219$		0			0
$220$	−14.9117	−	8.60927i	−0.0677804	−	0.0391330i
$221$	95.5219	−	165.449i	0.432226	−	0.748637i
$222$		0			0
$223$		−	228.631i		−	1.02525i	−0.858613	−	0.512625i	$-0.828673\pi$
$223$		−	228.631i		−	1.02525i	0.858613	−	0.512625i	$-0.171327\pi$
$224$		0			0
$225$		0			0
$226$	71.6985	+	124.185i	0.317250	+	0.549493i
$227$	56.8234	+	32.8070i	0.250323	+	0.144524i	0.619912	−	0.784671i	$-0.287168\pi$
$227$	56.8234	+	32.8070i	0.250323	+	0.144524i	−0.369589	+	0.929195i	$0.620502\pi$
$228$		0			0
$229$	−80.9558	+	46.7399i	−0.353519	+	0.204104i	−0.666234	−	0.745743i	$-0.732095\pi$
$229$	−80.9558	+	46.7399i	−0.353519	+	0.204104i	0.312715	+	0.949847i	$0.398761\pi$
$230$		−	76.0063i		−	0.330462i
$231$		0			0
$232$	96.0000			0.413793
$233$	−118.757	−	205.694i	−0.509688	−	0.882806i	−0.999937	−	0.0112234i	$-0.996427\pi$
$233$	−118.757	−	205.694i	−0.509688	−	0.882806i	0.490249	−	0.871583i	$-0.336906\pi$
$234$		0			0
$235$	30.8528	−	53.4386i	0.131289	−	0.227398i
$236$	71.3970	−	41.2211i	0.302530	−	0.174666i
$237$		0			0
$238$		0			0
$239$	−366.853			−1.53495			−0.767475	−	0.641079i	$-0.778487\pi$
$239$	−366.853			−1.53495			−0.767475	+	0.641079i	$0.778487\pi$
$240$		0			0
$241$	364.617	+	210.512i	1.51293	+	0.873493i	0.999885	+	0.0151343i	$0.00481759\pi$
$241$	364.617	+	210.512i	1.51293	+	0.873493i	0.513049	+	0.858359i	$0.328516\pi$
$242$	60.1041	−	104.103i	0.248364	−	0.430179i
$243$		0			0
$244$			2.37738i			0.00974337i
$245$		0			0
$246$		0			0
$247$	77.0513	+	133.457i	0.311949	+	0.540311i
$248$	−108.125	−	62.4259i	−0.435987	−	0.251717i
$249$		0			0
$250$	−84.2498	+	48.6416i	−0.336999	+	0.194567i
$251$		−	146.621i		−	0.584148i	−0.956396	−	0.292074i	$-0.905655\pi$
$251$		−	146.621i		−	0.584148i	0.956396	−	0.292074i	$-0.0943454\pi$
$252$		0			0
$253$	−224.735			−0.888281
$254$	−58.3883	−	101.132i	−0.229875	−	0.398156i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	21.7279	−	12.5446i	0.0845444	−	0.0488118i	−0.457132	−	0.889399i	$-0.651123\pi$
$257$	21.7279	−	12.5446i	0.0845444	−	0.0488118i	0.541676	+	0.840587i	$0.317790\pi$
$258$		0			0
$259$		0			0
$260$	61.2061			0.235408
$261$		0			0
$262$	74.1838	+	42.8300i	0.283144	+	0.163473i
$263$	−45.3381	+	78.5279i	−0.172388	+	0.298585i	−0.939254	−	0.343222i	$-0.888482\pi$
$263$	−45.3381	+	78.5279i	−0.172388	+	0.298585i	0.766866	+	0.641807i	$0.221815\pi$
$264$		0			0
$265$		−	122.619i		−	0.462712i
$266$		0			0
$267$		0			0
$268$	−4.39697	−	7.61577i	−0.0164066	−	0.0284171i
$269$	−59.2355	−	34.1996i	−0.220206	−	0.127136i	0.385839	−	0.922566i	$-0.373912\pi$
$269$	−59.2355	−	34.1996i	−0.220206	−	0.127136i	−0.606046	+	0.795430i	$0.707245\pi$
$270$		0			0
$271$	106.971	−	61.7595i	0.394725	−	0.227895i	−0.289480	−	0.957184i	$-0.593482\pi$
$271$	106.971	−	61.7595i	0.394725	−	0.227895i	0.684206	+	0.729289i	$0.260149\pi$
$272$			35.8297i			0.131727i
$273$		0			0
$274$	−94.7939			−0.345963
$275$	68.8234	+	119.206i	0.250267	+	0.433475i
$276$		0			0
$277$	136.441	−	236.323i	0.492567	−	0.853151i	−0.507396	−	0.861713i	$-0.669392\pi$
$277$	136.441	−	236.323i	0.492567	−	0.853151i	0.999963	+	0.00856145i	$0.00272523\pi$
$278$	−112.128	+	64.7374i	−0.403340	+	0.232868i
$279$		0			0
$280$		0			0
$281$	−133.103			−0.473675			−0.236837	−	0.971549i	$-0.576111\pi$
$281$	−133.103			−0.473675			−0.236837	+	0.971549i	$0.576111\pi$
$282$		0			0
$283$	111.507	+	64.3787i	0.394018	+	0.227486i	0.683900	−	0.729576i	$-0.260283\pi$
$283$	111.507	+	64.3787i	0.394018	+	0.227486i	−0.289882	+	0.957063i	$0.593616\pi$
$284$	137.397	−	237.979i	0.483792	−	0.837953i
$285$		0			0
$286$		−	180.974i		−	0.632776i
$287$		0			0
$288$		0			0
$289$	−104.382	−	180.795i	−0.361184	−	0.625589i
$290$	59.6468	+	34.4371i	0.205678	+	0.118749i
$291$		0			0
$292$	136.706	−	78.9270i	0.468170	−	0.270298i
$293$		−	308.984i		−	1.05455i	−0.849694	−	0.527276i	$-0.823213\pi$
$293$		−	308.984i		−	1.05455i	0.849694	−	0.527276i	$-0.176787\pi$
$294$		0			0
$295$	59.1472			0.200499
$296$	39.5563	+	68.5136i	0.133636	+	0.231465i
$297$		0			0
$298$	57.3381	−	99.3125i	0.192410	−	0.333263i
$299$	691.831	−	399.429i	2.31381	−	1.33588i
$300$		0			0
$301$		0			0
$302$	−72.4163			−0.239789
$303$		0			0
$304$	−25.0294	−	14.4508i	−0.0823337	−	0.0475354i
$305$	−0.852814	+	1.47712i	−0.00279611	+	0.00484301i
$306$		0			0
$307$		−	606.090i		−	1.97423i	−0.160003	−	0.987117i	$-0.551150\pi$
$307$		−	606.090i		−	1.97423i	0.160003	−	0.987117i	$-0.448850\pi$
$308$		0			0
$309$		0			0
$310$	−44.7868	−	77.5730i	−0.144474	−	0.250236i
$311$	−176.044	−	101.639i	−0.566057	−	0.326813i	0.189516	−	0.981878i	$-0.439308\pi$
$311$	−176.044	−	101.639i	−0.566057	−	0.326813i	−0.755573	+	0.655064i	$0.772641\pi$
$312$		0			0
$313$	351.294	−	202.820i	1.12234	−	0.647986i	0.180346	−	0.983603i	$-0.442278\pi$
$313$	351.294	−	202.820i	1.12234	−	0.647986i	0.941999	+	0.335617i	$0.108945\pi$
$314$			264.545i			0.842500i
$315$		0			0
$316$	196.676			0.622393
$317$	−13.0294	−	22.5676i	−0.0411023	−	0.0711913i	0.844742	−	0.535173i	$-0.179754\pi$
$317$	−13.0294	−	22.5676i	−0.0411023	−	0.0711913i	−0.885845	+	0.463982i	$0.846420\pi$
$318$		0			0
$319$	101.823	−	176.363i	0.319196	−	0.552863i
$320$	−9.94113	+	5.73951i	−0.0310660	+	0.0179360i
$321$		0			0
$322$		0			0
$323$	−64.7208			−0.200374
$324$		0			0
$325$	−423.735	−	244.644i	−1.30380	−	0.752750i
$326$	−59.3553	+	102.806i	−0.182072	+	0.315357i
$327$		0			0
$328$		−	155.086i		−	0.472824i
$329$		0			0
$330$		0			0
$331$	54.3162	+	94.0785i	0.164097	+	0.284225i	0.936334	−	0.351110i	$-0.114196\pi$
$331$	54.3162	+	94.0785i	0.164097	+	0.284225i	−0.772237	+	0.635335i	$0.780862\pi$
$332$	−191.220	−	110.401i	−0.575965	−	0.332533i
$333$		0			0
$334$	−156.302	+	90.2407i	−0.467969	+	0.270182i
$335$		−	6.30911i		−	0.0188332i
$336$		0			0
$337$	441.735			1.31079			0.655393	−	0.755288i	$-0.272503\pi$
$337$	441.735			1.31079			0.655393	+	0.755288i	$0.272503\pi$
$338$	202.149	+	350.133i	0.598075	+	1.03590i
$339$		0			0
$340$	−12.8528	+	22.2617i	−0.0378024	+	0.0654757i
$341$	−229.368	+	132.425i	−0.672632	+	0.388344i
$342$		0			0
$343$		0			0
$344$	−4.20101			−0.0122122
$345$		0			0
$346$	175.103	+	101.096i	0.506077	+	0.292184i
$347$	17.0955	−	29.6102i	0.0492664	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$347$	17.0955	−	29.6102i	0.0492664	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$348$		0			0
$349$		−	221.787i		−	0.635493i	−0.948176	−	0.317746i	$-0.897074\pi$
$349$		−	221.787i		−	0.635493i	0.948176	−	0.317746i	$-0.102926\pi$
$350$		0			0
$351$		0			0
$352$	16.9706	+	29.3939i	0.0482118	+	0.0835053i
$353$	387.448	+	223.693i	1.09759	+	0.633692i	0.935586	−	0.353099i	$-0.114872\pi$
$353$	387.448	+	223.693i	1.09759	+	0.633692i	0.162000	+	0.986791i	$0.448206\pi$
$354$		0			0
$355$	170.735	−	98.5739i	0.480944	−	0.277673i
$356$		−	41.5692i		−	0.116767i
$357$		0			0
$358$	−239.397			−0.668707
$359$	145.882	+	252.675i	0.406357	+	0.703831i	0.994478	−	0.104941i	$-0.0334655\pi$
$359$	145.882	+	252.675i	0.406357	+	0.703831i	−0.588121	+	0.808773i	$0.700132\pi$
$360$		0			0
$361$	−154.397	+	267.423i	−0.427692	+	0.740785i
$362$	257.158	−	148.470i	0.710381	−	0.410139i
$363$		0			0
$364$		0			0
$365$	113.251			0.310276
$366$		0			0
$367$	363.169	+	209.676i	0.989561	+	0.571324i	0.905143	−	0.425107i	$-0.139763\pi$
$367$	363.169	+	209.676i	0.989561	+	0.571324i	0.0844183	+	0.996430i	$0.473097\pi$
$368$	−74.9117	+	129.751i	−0.203564	+	0.352584i
$369$		0			0
$370$			56.7585i			0.153401i
$371$		0			0
$372$		0			0
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	0.844225	−	0.535988i	$-0.180061\pi$
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	−0.886292	+	0.463127i	$0.846728\pi$
$374$	65.8234	+	38.0031i	0.175998	+	0.101613i
$375$		0			0
$376$	−105.338	+	60.8170i	−0.280155	+	0.161747i
$377$			723.895i			1.92015i
$378$		0			0
$379$	206.779			0.545590			0.272795	−	0.962072i	$-0.412052\pi$
$379$	206.779			0.545590			0.272795	+	0.962072i	$0.412052\pi$
$380$	−10.3675	−	17.9571i	−0.0272830	−	0.0472555i
$381$		0			0
$382$	47.0955	−	81.5717i	0.123287	−	0.213539i
$383$	−431.772	+	249.283i	−1.12734	+	0.650871i	−0.943265	−	0.332041i	$-0.892263\pi$
$383$	−431.772	+	249.283i	−1.12734	+	0.650871i	−0.184076	+	0.982912i	$0.558929\pi$
$384$		0			0
$385$		0			0
$386$	−13.8507			−0.0358827
$387$		0			0
$388$	−19.0294	−	10.9867i	−0.0490449	−	0.0283161i
$389$	−324.213	+	561.554i	−0.833453	+	1.44358i	0.0618308	+	0.998087i	$0.480306\pi$
$389$	−324.213	+	561.554i	−0.833453	+	1.44358i	−0.895284	+	0.445496i	$0.853027\pi$
$390$		0			0
$391$			335.508i			0.858077i
$392$		0			0
$393$		0			0
$394$	−188.912	−	327.205i	−0.479471	−	0.830469i
$395$	122.199	+	70.5516i	0.309364	+	0.178612i
$396$		0			0
$397$	−65.6026	+	37.8757i	−0.165246	+	0.0954047i	−0.580342	−	0.814373i	$-0.697081\pi$
$397$	−65.6026	+	37.8757i	−0.165246	+	0.0954047i	0.415096	+	0.909777i	$0.363748\pi$
$398$		−	185.176i		−	0.465268i
$399$		0			0
$400$	91.7645			0.229411
$401$	−282.125	−	488.655i	−0.703553	−	1.21859i	−0.967211	−	0.253974i	$-0.918262\pi$
$401$	−282.125	−	488.655i	−0.703553	−	1.21859i	0.263658	−	0.964616i	$-0.415071\pi$
$402$		0			0
$403$	470.727	−	815.324i	1.16806	−	2.02314i
$404$	185.647	−	107.183i	0.459522	−	0.265305i
$405$		0			0
$406$		0			0
$407$	167.823			0.412342
$408$		0			0
$409$	309.559	+	178.724i	0.756868	+	0.436978i	0.828170	−	0.560477i	$-0.189382\pi$
$409$	309.559	+	178.724i	0.756868	+	0.436978i	−0.0713023	+	0.997455i	$0.522716\pi$
$410$	55.6325	−	96.3583i	0.135689	−	0.235020i
$411$		0			0
$412$		−	210.410i		−	0.510704i
$413$		0			0
$414$		0			0
$415$	−79.2061	−	137.189i	−0.190858	−	0.330576i
$416$	−104.485	−	60.3246i	−0.251167	−	0.145011i
$417$		0			0
$418$	−53.0955	+	30.6547i	−0.127023	+	0.0733365i
$419$		−	502.175i		−	1.19851i	−0.800559	−	0.599254i	$-0.795464\pi$
$419$		−	502.175i		−	1.19851i	0.800559	−	0.599254i	$-0.204536\pi$
$420$		0			0
$421$	33.7939			0.0802706			0.0401353	−	0.999194i	$-0.487221\pi$
$421$	33.7939			0.0802706			0.0401353	+	0.999194i	$0.487221\pi$
$422$	16.3259	+	28.2773i	0.0386870	+	0.0670078i
$423$		0			0
$424$	−120.853	+	209.323i	−0.285030	+	0.493687i
$425$	177.963	−	102.747i	0.418735	−	0.241757i
$426$		0			0
$427$		0			0
$428$	−237.088			−0.553945
$429$		0			0
$430$	−2.61017	−	1.50698i	−0.00607017	−	0.00350461i
$431$	251.860	−	436.234i	0.584362	−	1.01214i	−0.410593	−	0.911819i	$-0.634678\pi$
$431$	251.860	−	436.234i	0.584362	−	1.01214i	0.994955	−	0.100326i	$-0.0319884\pi$
$432$		0			0
$433$			837.548i			1.93429i	0.254224	+	0.967145i	$0.418180\pi$
$433$			837.548i			1.93429i	−0.254224	+	0.967145i	$0.581820\pi$
$434$		0			0
$435$		0			0
$436$	−111.059	−	192.360i	−0.254722	−	0.441192i
$437$	−234.375	−	135.316i	−0.536326	−	0.309648i
$438$		0			0
$439$	164.558	−	95.0079i	0.374848	−	0.216419i	−0.300726	−	0.953711i	$-0.597229\pi$
$439$	164.558	−	95.0079i	0.374848	−	0.216419i	0.675575	+	0.737292i	$0.263896\pi$
$440$			24.3507i			0.0553425i
$441$		0			0
$442$	−270.177			−0.611259
$443$	−84.7279	−	146.753i	−0.191259	−	0.331271i	0.754408	−	0.656405i	$-0.227924\pi$
$443$	−84.7279	−	146.753i	−0.191259	−	0.331271i	−0.945668	+	0.325134i	$0.894591\pi$
$444$		0			0
$445$	14.9117	−	25.8278i	0.0335094	−	0.0580400i
$446$	−280.014	+	161.666i	−0.627835	+	0.362481i
$447$		0			0
$448$		0			0
$449$	−18.1035			−0.0403195			−0.0201598	−	0.999797i	$-0.506417\pi$
$449$	−18.1035			−0.0403195			−0.0201598	+	0.999797i	$0.506417\pi$
$450$		0			0
$451$	−284.912	−	164.494i	−0.631733	−	0.364731i
$452$	101.397	−	175.625i	0.224330	−	0.388550i
$453$		0			0
$454$		−	92.7922i		−	0.204388i
$455$		0			0
$456$		0			0
$457$	164.412	+	284.769i	0.359763	+	0.623128i	0.987921	−	0.154958i	$-0.0495242\pi$
$457$	164.412	+	284.769i	0.359763	+	0.623128i	−0.628158	+	0.778086i	$0.716191\pi$
$458$	114.489	+	66.1002i	0.249976	+	0.144324i
$459$		0			0
$460$	−93.0883	+	53.7446i	−0.202366	+	0.116836i
$461$			794.331i			1.72306i	0.507706	+	0.861530i	$0.330494\pi$
$461$			794.331i			1.72306i	−0.507706	+	0.861530i	$0.669506\pi$
$462$		0			0
$463$	−403.396			−0.871266			−0.435633	−	0.900124i	$-0.643475\pi$
$463$	−403.396			−0.871266			−0.435633	+	0.900124i	$0.643475\pi$
$464$	−67.8823	−	117.576i	−0.146298	−	0.253395i
$465$		0			0
$466$	−167.948	+	290.895i	−0.360404	+	0.624238i
$467$	−2.44870	+	1.41376i	−0.00524347	+	0.00302732i	−0.502619	−	0.864508i	$-0.667630\pi$
$467$	−2.44870	+	1.41376i	−0.00524347	+	0.00302732i	0.497376	+	0.867535i	$0.334297\pi$
$468$		0			0
$469$		0			0
$470$	−87.2649			−0.185670
$471$		0			0
$472$	−100.971	−	58.2954i	−0.213921	−	0.123507i
$473$	−4.45584	+	7.71775i	−0.00942039	+	0.0163166i
$474$		0			0
$475$			165.758i			0.348965i
$476$		0			0
$477$		0			0
$478$	259.404	+	449.301i	0.542686	+	0.939960i
$479$	328.669	+	189.757i	0.686157	+	0.396153i	0.802171	−	0.597095i	$-0.203678\pi$
$479$	328.669	+	189.757i	0.686157	+	0.396153i	−0.116014	+	0.993248i	$0.537012\pi$
$480$		0			0
$481$	−516.632	+	298.278i	−1.07408	+	0.620120i
$482$		−	595.418i		−	1.23531i
$483$		0			0
$484$	−170.000			−0.351240
$485$	−7.88225	−	13.6525i	−0.0162521	−	0.0281494i
$486$		0			0
$487$	−287.757	+	498.410i	−0.590877	+	1.02343i	0.403238	+	0.915095i	$0.367885\pi$
$487$	−287.757	+	498.410i	−0.590877	+	1.02343i	−0.994115	+	0.108333i	$0.965449\pi$
$488$	2.91169	−	1.68106i	0.00596657	−	0.00344480i
$489$		0			0
$490$		0			0
$491$	−238.441			−0.485623			−0.242811	−	0.970074i	$-0.578070\pi$
$491$	−238.441			−0.485623			−0.242811	+	0.970074i	$0.578070\pi$
$492$		0			0
$493$	−263.294	−	152.013i	−0.534064	−	0.308342i
$494$	108.967	−	188.736i	0.220581	−	0.382057i
$495$		0			0
$496$			176.567i			0.355982i
$497$		0			0
$498$		0			0
$499$	143.287	+	248.180i	0.287148	+	0.497355i	0.973128	−	0.230266i	$-0.0739595\pi$
$499$	143.287	+	248.180i	0.287148	+	0.497355i	−0.685980	+	0.727620i	$0.740626\pi$
$500$	119.147	+	68.7897i	0.238294	+	0.137579i
$501$		0			0
$502$	−179.574	+	103.677i	−0.357716	+	0.206528i
$503$		−	25.4374i		−	0.0505714i	−0.999680	−	0.0252857i	$-0.991950\pi$
$503$		−	25.4374i		−	0.0505714i	0.999680	−	0.0252857i	$-0.00804954\pi$
$504$		0			0
$505$	153.795			0.304544
$506$	158.912	+	275.243i	0.314055	+	0.543959i
$507$		0			0
$508$	−82.5736	+	143.022i	−0.162546	+	0.281539i
$509$	−697.889	+	402.926i	−1.37110	+	0.791603i	−0.991066	−	0.133370i	$-0.957420\pi$
$509$	−697.889	+	402.926i	−1.37110	+	0.791603i	−0.380031	+	0.924974i	$0.624087\pi$
$510$		0			0
$511$		0			0
$512$	22.6274			0.0441942
$513$		0			0
$514$	−30.7279	−	17.7408i	−0.0597819	−	0.0345151i
$515$	75.4781	−	130.732i	0.146559	−	0.253848i
$516$		0			0
$517$			258.025i			0.499080i
$518$		0			0
$519$		0			0
$520$	−43.2792	−	74.9618i	−0.0832293	−	0.144157i
$521$	−661.706	−	382.036i	−1.27007	−	0.733274i	−0.295068	−	0.955476i	$-0.595342\pi$
$521$	−661.706	−	382.036i	−1.27007	−	0.733274i	−0.975001	+	0.222202i	$0.928676\pi$
$522$		0			0
$523$	153.096	−	88.3900i	0.292726	−	0.169006i	−0.346444	−	0.938071i	$-0.612611\pi$
$523$	153.096	−	88.3900i	0.292726	−	0.169006i	0.639171	+	0.769065i	$0.279278\pi$
$524$		−	121.142i		−	0.231186i
$525$		0			0
$526$	128.235			0.243794
$527$	197.698	+	342.424i	0.375139	+	0.649761i
$528$		0			0
$529$	−436.970	+	756.854i	−0.826030	+	1.43073i
$530$	−150.177	+	86.7045i	−0.283352	+	0.163593i
$531$		0			0
$532$		0			0
$533$	1169.44			2.19407
$534$		0			0
$535$	−147.308	−	85.0482i	−0.275342	−	0.158969i
$536$	−6.21825	+	10.7703i	−0.0116012	+	0.0200939i
$537$		0			0
$538$			96.7312i			0.179798i
$539$		0			0
$540$		0			0
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	0.857979	−	0.513685i	$-0.171720\pi$
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	−0.873854	+	0.486189i	$0.838387\pi$
$542$	−151.279	−	87.3411i	−0.279113	−	0.161146i
$543$		0			0
$544$	43.8823	−	25.3354i	0.0806659	−	0.0465725i
$545$		−	159.356i		−	0.292396i
$546$		0			0
$547$	212.676			0.388805			0.194402	−	0.980922i	$-0.437723\pi$
$547$	212.676			0.388805			0.194402	+	0.980922i	$0.437723\pi$
$548$	67.0294	+	116.098i	0.122316	+	0.211858i
$549$		0			0
$550$	97.3310	−	168.582i	0.176965	−	0.306513i
$551$	212.382	−	122.619i	0.385448	−	0.222538i
$552$		0			0
$553$		0			0
$554$	−385.914			−0.696595
$555$		0			0
$556$	158.574	+	91.5525i	0.285204	+	0.164663i
$557$	−440.823	+	763.528i	−0.791424	+	1.37079i	0.133661	+	0.991027i	$0.457327\pi$
$557$	−440.823	+	763.528i	−0.791424	+	1.37079i	−0.925085	+	0.379760i	$0.876007\pi$
$558$		0			0
$559$		−	31.6780i		−	0.0566691i
$560$		0			0
$561$		0			0
$562$	94.1177	+	163.017i	0.167469	+	0.290065i
$563$	664.301	+	383.534i	1.17993	+	0.681233i	0.955998	−	0.293372i	$-0.0947774\pi$
$563$	664.301	+	383.534i	1.17993	+	0.681233i	0.223932	+	0.974605i	$0.428111\pi$
$564$		0			0
$565$	126.000	−	72.7461i	0.223009	−	0.128754i
$566$		−	182.090i		−	0.321714i
$567$		0			0
$568$	−388.617			−0.684185
$569$	−14.6468	−	25.3689i	−0.0257412	−	0.0445851i	0.852868	−	0.522127i	$-0.174861\pi$
$569$	−14.6468	−	25.3689i	−0.0257412	−	0.0445851i	−0.878609	+	0.477542i	$0.841528\pi$
$570$		0			0
$571$	−482.521	+	835.752i	−0.845046	+	1.46366i	0.0405347	+	0.999178i	$0.487094\pi$
$571$	−482.521	+	835.752i	−0.845046	+	1.46366i	−0.885581	+	0.464485i	$0.846239\pi$
$572$	−221.647	+	127.968i	−0.387494	+	0.223720i
$573$		0			0
$574$		0			0
$575$	859.279			1.49440
$576$		0			0
$577$	−227.883	−	131.568i	−0.394944	−	0.228021i	0.289356	−	0.957222i	$-0.406559\pi$
$577$	−227.883	−	131.568i	−0.394944	−	0.228021i	−0.684300	+	0.729201i	$0.739892\pi$
$578$	−147.619	+	255.683i	−0.255396	+	0.442359i
$579$		0			0
$580$		−	97.4027i		−	0.167936i
$581$		0			0
$582$		0			0
$583$	256.368	+	444.042i	0.439738	+	0.761649i
$584$	−193.331	−	111.620i	−0.331046	−	0.191130i
$585$		0			0
$586$	−378.426	+	218.485i	−0.645779	+	0.372841i
$587$			436.477i			0.743572i	0.928318	+	0.371786i	$0.121254\pi$
$587$			436.477i			0.743572i	−0.928318	+	0.371786i	$0.878746\pi$
$588$		0			0
$589$	−318.941			−0.541496
$590$	−41.8234	−	72.4402i	−0.0708871	−	0.122780i
$591$		0			0
$592$	55.9411	−	96.8929i	0.0944951	−	0.163670i
$593$	603.603	−	348.490i	1.01788	−	0.587673i	0.104391	−	0.994536i	$-0.466711\pi$
$593$	603.603	−	348.490i	1.01788	−	0.587673i	0.913489	+	0.406863i	$0.133377\pi$
$594$		0			0
$595$		0			0
$596$	−162.177			−0.272108
$597$		0			0
$598$	−978.396	−	564.877i	−1.63611	−	0.944611i
$599$	199.206	−	345.035i	0.332564	−	0.576018i	−0.650450	−	0.759549i	$-0.725419\pi$
$599$	199.206	−	345.035i	0.332564	−	0.576018i	0.983014	+	0.183531i	$0.0587528\pi$
$600$		0			0
$601$		−	36.1691i		−	0.0601816i	−0.999547	−	0.0300908i	$-0.990420\pi$
$601$		−	36.1691i		−	0.0601816i	0.999547	−	0.0300908i	$-0.00957964\pi$
$602$		0			0
$603$		0			0
$604$	51.2061	+	88.6915i	0.0847782	+	0.146840i
$605$	−105.624	−	60.9823i	−0.174586	−	0.100797i
$606$		0			0
$607$	−27.3457	+	15.7880i	−0.0450505	+	0.0260099i	−0.522356	−	0.852727i	$-0.674947\pi$
$607$	−27.3457	+	15.7880i	−0.0450505	+	0.0260099i	0.477306	+	0.878737i	$0.341613\pi$
$608$			40.8729i			0.0672252i
$609$		0			0
$610$	2.41212			0.00395430
$611$	−458.595	−	794.310i	−0.750565	−	1.30002i
$612$		0			0
$613$	204.632	−	354.434i	0.333821	−	0.578195i	−0.649436	−	0.760416i	$-0.724995\pi$
$613$	204.632	−	354.434i	0.333821	−	0.578195i	0.983258	+	0.182220i	$0.0583285\pi$
$614$	−742.305	+	428.570i	−1.20897	+	0.697997i
$615$		0			0
$616$		0			0
$617$	−1227.38			−1.98927			−0.994636	−	0.103436i	$-0.967016\pi$
$617$	−1227.38			−1.98927			−0.994636	+	0.103436i	$0.967016\pi$
$618$		0			0
$619$	−412.022	−	237.881i	−0.665625	−	0.384299i	0.128792	−	0.991672i	$-0.458890\pi$
$619$	−412.022	−	237.881i	−0.665625	−	0.384299i	−0.794417	+	0.607373i	$0.792223\pi$
$620$	−63.3381	+	109.705i	−0.102158	+	0.176943i
$621$		0			0
$622$			287.478i			0.462184i
$623$		0			0
$624$		0			0
$625$	−237.412	−	411.209i	−0.379859	−	0.657935i
$626$	−496.805	−	286.830i	−0.793618	−	0.458195i
$627$		0			0
$628$	324.000	−	187.061i	0.515924	−	0.297869i
$629$		−	250.544i		−	0.398322i
$630$		0			0
$631$	−54.9420			−0.0870713			−0.0435357	−	0.999052i	$-0.513862\pi$
$631$	−54.9420			−0.0870713			−0.0435357	+	0.999052i	$0.513862\pi$
$632$	−139.071	−	240.878i	−0.220049	−	0.381136i
$633$		0			0
$634$	−18.4264	+	31.9155i	−0.0290637	+	0.0503399i
$635$	−102.609	+	59.2415i	−0.161589	+	0.0932937i
$636$		0			0
$637$		0			0
$638$	−288.000			−0.451411
$639$		0			0
$640$	14.0589	+	8.11689i	0.0219670	+	0.0126826i
$641$	−114.551	+	198.409i	−0.178707	+	0.309530i	−0.941438	−	0.337186i	$-0.890525\pi$
$641$	−114.551	+	198.409i	−0.178707	+	0.309530i	0.762731	+	0.646716i	$0.223858\pi$
$642$		0			0
$643$			854.640i			1.32914i	0.747224	+	0.664572i	$0.231386\pi$
$643$			854.640i			1.32914i	−0.747224	+	0.664572i	$0.768614\pi$
$644$		0			0
$645$		0			0
$646$	45.7645	+	79.2664i	0.0708429	+	0.122703i
$647$	868.632	+	501.505i	1.34255	+	0.775124i	0.987182	−	0.159601i	$-0.0510207\pi$
$647$	868.632	+	501.505i	1.34255	+	0.775124i	0.355372	+	0.934725i	$0.384354\pi$
$648$		0			0
$649$	−214.191	+	123.663i	−0.330032	+	0.190544i
$650$			691.957i			1.06455i
$651$		0			0
$652$	167.882			0.257488
$653$	635.382	+	1100.51i	0.973020	+	1.68532i	0.686321	+	0.727299i	$0.259224\pi$
$653$	635.382	+	1100.51i	0.973020	+	1.68532i	0.286698	+	0.958021i	$0.407442\pi$
$654$		0			0
$655$	43.4558	−	75.2677i	0.0663448	−	0.114913i
$656$	−189.941	+	109.663i	−0.289544	+	0.167169i
$657$		0			0
$658$		0			0
$659$	783.308			1.18863			0.594315	−	0.804232i	$-0.297423\pi$
$659$	783.308			1.18863			0.594315	+	0.804232i	$0.297423\pi$
$660$		0			0
$661$	−72.5589	−	41.8919i	−0.109771	−	0.0633765i	0.444109	−	0.895973i	$-0.353520\pi$
$661$	−72.5589	−	41.8919i	−0.109771	−	0.0633765i	−0.553881	+	0.832596i	$0.686854\pi$
$662$	76.8148	−	133.047i	0.116034	−	0.200977i
$663$		0			0
$664$			312.262i			0.470273i
$665$		0			0
$666$		0			0
$667$	−635.647	−	1100.97i	−0.952994	−	1.65063i
$668$	221.044	+	127.620i	0.330904	+	0.191047i
$669$		0			0
$670$	−7.72706	+	4.46122i	−0.0115329	+	0.00665853i
$671$		−	7.13215i		−	0.0106291i
$672$		0			0
$673$	415.676			0.617647			0.308823	−	0.951119i	$-0.400065\pi$
$673$	415.676			0.617647			0.308823	+	0.951119i	$0.400065\pi$
$674$	−312.354	−	541.013i	−0.463433	−	0.802690i
$675$		0			0
$676$	285.882	−	495.163i	0.422903	−	0.732489i
$677$	685.279	−	395.646i	1.01223	−	0.584411i	0.100386	−	0.994949i	$-0.467992\pi$
$677$	685.279	−	395.646i	1.01223	−	0.584411i	0.911844	+	0.410538i	$0.134659\pi$
$678$		0			0
$679$		0			0
$680$	36.3532			0.0534607
$681$		0			0
$682$	324.375	+	187.278i	0.475623	+	0.274601i
$683$	−164.080	+	284.195i	−0.240235	+	0.416099i	−0.960781	−	0.277308i	$-0.910558\pi$
$683$	−164.080	+	284.195i	−0.240235	+	0.416099i	0.720546	+	0.693407i	$0.243891\pi$
$684$		0			0
$685$			96.1791i			0.140407i
$686$		0			0
$687$		0			0
$688$	2.97056	+	5.14517i	0.00431768	+	0.00747844i
$689$	−1578.42	−	911.300i	−2.29088	−	1.32264i
$690$		0			0
$691$	−875.182	+	505.287i	−1.26654	+	0.731240i	−0.974333	−	0.225113i	$-0.927725\pi$
$691$	−875.182	+	505.287i	−1.26654	+	0.731240i	−0.292212	+	0.956353i	$0.594391\pi$
$692$		−	285.941i		−	0.413210i
$693$		0			0
$694$	−48.3532			−0.0696733
$695$	65.6833	+	113.767i	0.0945084	+	0.163693i
$696$		0			0
$697$	−245.574	+	425.346i	−0.352329	+	0.610252i
$698$	−271.632	+	156.827i	−0.389158	+	0.224681i
$699$		0			0
$700$		0			0
$701$	0.103464			0.000147594			7.37972e−5	−	1.00000i	$-0.499977\pi$
$701$	0.103464			0.000147594			7.37972e−5		1.00000i	$0.499977\pi$
$702$		0			0
$703$	175.022	+	101.049i	0.248964	+	0.143740i
$704$	24.0000	−	41.5692i	0.0340909	−	0.0590472i
$705$		0			0
$706$		−	632.700i		−	0.896175i
$707$		0			0
$708$		0			0
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	−0.881286	−	0.472584i	$-0.843321\pi$
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	0.0313734	−	0.999508i	$-0.490012\pi$
$710$	−241.456	−	139.405i	−0.340079	−	0.196345i
$711$		0			0
$712$	−50.9117	+	29.3939i	−0.0715052	+	0.0412835i
$713$			1653.37i			2.31889i
$714$		0			0
$715$	−183.618			−0.256809
$716$	169.279	+	293.200i	0.236423	+	0.409498i
$717$		0			0
$718$	206.309	−	357.337i	0.287338	−	0.497684i
$719$	850.925	−	491.282i	1.18348	−	0.683285i	0.226666	−	0.973973i	$-0.427217\pi$
$719$	850.925	−	491.282i	1.18348	−	0.683285i	0.956818	+	0.290688i	$0.0938840\pi$
$720$		0			0
$721$		0			0
$722$	436.701			0.604848
$723$		0			0
$724$	−363.676	−	209.969i	−0.502315	−	0.290012i
$725$	−389.324	+	674.329i	−0.536998	+	0.930108i
$726$		0			0
$727$			630.440i			0.867181i	0.901110	+	0.433590i	$0.142753\pi$
$727$			630.440i			0.867181i	−0.901110	+	0.433590i	$0.857247\pi$
$728$		0			0
$729$		0			0
$730$	−80.0803	−	138.703i	−0.109699	−	0.190004i
$731$	11.5219	+	6.65215i	0.0157618	+	0.00910007i
$732$		0			0
$733$	−258.486	+	149.237i	−0.352641	+	0.203597i	−0.665848	−	0.746088i	$-0.731930\pi$
$733$	−258.486	+	149.237i	−0.352641	+	0.203597i	0.313207	+	0.949685i	$0.398597\pi$
$734$		−	593.053i		−	0.807974i
$735$		0			0
$736$	211.882			0.287883
$737$	13.1909	+	22.8473i	0.0178981	+	0.0310004i
$738$		0			0
$739$	−172.684	+	299.097i	−0.233672	+	0.404732i	−0.958886	−	0.283792i	$-0.908408\pi$
$739$	−172.684	+	299.097i	−0.233672	+	0.404732i	0.725214	+	0.688524i	$0.241741\pi$
$740$	69.5147	−	40.1343i	0.0939388	−	0.0542356i
$741$		0			0
$742$		0			0
$743$	−683.616			−0.920076			−0.460038	−	0.887899i	$-0.652164\pi$
$743$	−683.616			−0.920076			−0.460038	+	0.887899i	$0.652164\pi$
$744$		0			0
$745$	−100.764	−	58.1759i	−0.135253	−	0.0780885i
$746$	−22.1903	+	38.4347i	−0.0297457	+	0.0515211i
$747$		0			0
$748$		−	107.489i		−	0.143702i
$749$		0			0
$750$		0			0
$751$	289.169	+	500.855i	0.385045	+	0.666918i	0.991775	−	0.127990i	$-0.0408525\pi$
$751$	289.169	+	500.855i	0.385045	+	0.666918i	−0.606730	+	0.794908i	$0.707519\pi$
$752$	148.971	+	86.0082i	0.198099	+	0.114373i
$753$		0			0
$754$	886.587	−	511.871i	1.17584	−	0.678874i
$755$			73.4744i			0.0973171i
$756$		0			0
$757$	1204.82			1.59158			0.795788	−	0.605576i	$-0.207057\pi$
$757$	1204.82			1.59158			0.795788	+	0.605576i	$0.207057\pi$
$758$	−146.215	−	253.251i	−0.192895	−	0.334105i
$759$		0			0
$760$	−14.6619	+	25.3952i	−0.0192920	+	0.0334147i
$761$	−202.669	+	117.011i	−0.266319	+	0.153760i	−0.627214	−	0.778847i	$-0.715805\pi$
$761$	−202.669	+	117.011i	−0.266319	+	0.153760i	0.360894	+	0.932607i	$0.382471\pi$
$762$		0			0
$763$		0			0
$764$	−133.206			−0.174353
$765$		0			0
$766$	610.617	+	352.540i	0.797151	+	0.460235i
$767$	439.581	−	761.376i	0.573117	−	0.992668i
$768$		0			0
$769$		−	1290.16i		−	1.67771i	−0.544358	−	0.838853i	$-0.683226\pi$
$769$		−	1290.16i		−	1.67771i	0.544358	−	0.838853i	$-0.316774\pi$
$770$		0			0
$771$		0			0
$772$	9.79394	+	16.9636i	0.0126864	+	0.0219736i
$773$	345.646	+	199.559i	0.447149	+	0.258161i	0.706625	−	0.707588i	$-0.250217\pi$
$773$	345.646	+	199.559i	0.447149	+	0.258161i	−0.259477	+	0.965749i	$0.583550\pi$
$774$		0			0
$775$	876.992	−	506.331i	1.13160	−	0.653331i
$776$			31.0749i			0.0400450i
$777$		0			0
$778$	917.013			1.17868
$779$	−198.088	−	343.099i	−0.254285	−	0.440435i
$780$		0			0
$781$	−412.191	+	713.936i	−0.527773	+	0.914130i
$782$	410.912	−	237.240i	0.525463	−	0.303376i
$783$		0			0
$784$		0			0
$785$	268.410			0.341924
$786$		0			0
$787$	1348.16	+	778.361i	1.71304	+	0.989023i	0.930401	+	0.366544i	$0.119459\pi$
$787$	1348.16	+	778.361i	1.71304	+	0.989023i	0.782637	+	0.622478i	$0.213874\pi$
$788$	−267.161	+	462.737i	−0.339037	+	0.587230i
$789$		0			0
$790$		−	199.550i		−	0.252595i
$791$		0			0
$792$		0			0
$793$	12.6762	+	21.9558i	0.0159851	+	0.0276870i
$794$	92.7761	+	53.5643i	0.116846	+	0.0674613i
$795$		0			0
$796$	−226.794	+	130.940i	−0.284917	+	0.164497i
$797$			600.232i			0.753114i	0.926393	+	0.376557i	$0.122892\pi$
$797$			600.232i			0.753114i	−0.926393	+	0.376557i	$0.877108\pi$
$798$		0			0
$799$	385.206			0.482110
$800$	−64.8873	−	112.388i	−0.0811091	−	0.140485i
$801$		0			0
$802$	−398.985	+	691.062i	−0.497487	+	0.861673i
$803$	−410.117	+	236.781i	−0.510731	+	0.294871i
$804$		0			0
$805$		0			0
$806$	−1331.42			−1.65188
$807$		0			0
$808$	−262.544	−	151.580i	−0.324931	−	0.187599i
$809$	−114.640	+	198.562i	−0.141705	+	0.245441i	−0.928139	−	0.372234i	$-0.878592\pi$
$809$	−114.640	+	198.562i	−0.141705	+	0.245441i	0.786434	+	0.617675i	$0.211925\pi$
$810$		0			0
$811$		−	529.955i		−	0.653459i	−0.945118	−	0.326729i	$-0.894053\pi$
$811$		−	529.955i		−	0.653459i	0.945118	−	0.326729i	$-0.105947\pi$
$812$		0			0
$813$		0			0
$814$	−118.669	−	205.541i	−0.145785	−	0.252507i
$815$	104.309	+	60.2226i	0.127986	+	0.0738928i
$816$		0			0
$817$	−9.29394	+	5.36586i	−0.0113757	+	0.00656776i
$818$		−	505.508i		−	0.617980i
$819$		0			0
$820$	−157.352			−0.191893
$821$	−151.669	−	262.698i	−0.184737	−	0.319974i	0.758751	−	0.651381i	$-0.225810\pi$
$821$	−151.669	−	262.698i	−0.184737	−	0.319974i	−0.943488	+	0.331407i	$0.892477\pi$
$822$		0			0
$823$	564.955	−	978.531i	0.686459	−	1.18898i	−0.286517	−	0.958075i	$-0.592498\pi$
$823$	564.955	−	978.531i	0.686459	−	1.18898i	0.972976	−	0.230906i	$-0.0741690\pi$
$824$	−257.698	+	148.782i	−0.312741	+	0.180561i
$825$		0			0
$826$		0			0
$827$	161.604			0.195410			0.0977049	−	0.995215i	$-0.468850\pi$
$827$	161.604			0.195410			0.0977049	+	0.995215i	$0.468850\pi$
$828$		0			0
$829$	−1325.32	−	765.175i	−1.59870	−	0.923010i	−0.991738	−	0.128279i	$-0.959055\pi$
$829$	−1325.32	−	765.175i	−1.59870	−	0.923010i	−0.606962	−	0.794731i	$-0.707612\pi$
$830$	−112.014	+	194.014i	−0.134957	+	0.233752i
$831$		0			0
$832$			170.624i			0.205077i
$833$		0			0
$834$		0			0
$835$	91.5593	+	158.585i	0.109652	+	0.189923i
$836$	75.0883	+	43.3523i	0.0898186	+	0.0518568i
$837$		0			0
$838$	−615.037	+	355.092i	−0.733934	+	0.423737i
$839$		−	218.629i		−	0.260583i	−0.991476	−	0.130291i	$-0.958409\pi$
$839$		−	218.629i		−	0.260583i	0.991476	−	0.130291i	$-0.0415913\pi$
$840$		0			0
$841$	311.000			0.369798
$842$	−23.8959	−	41.3890i	−0.0283800	−	0.0491555i
$843$		0			0
$844$	23.0883	−	39.9901i	0.0273558	−	0.0473817i
$845$	355.249	−	205.103i	0.420413	−	0.242726i
$846$		0			0
$847$		0			0
$848$	341.823			0.403094
$849$		0			0
$850$	−251.677	−	145.306i	−0.296091	−	0.170948i
$851$	523.831	−	907.301i	0.615547	−	1.06616i
$852$		0			0
$853$		−	762.730i		−	0.894174i	−0.894491	−	0.447087i	$-0.852461\pi$
$853$		−	762.730i		−	0.894174i	0.894491	−	0.447087i	$-0.147539\pi$
$854$		0			0
$855$		0			0
$856$	167.647	+	290.373i	0.195849	+	0.339220i
$857$	−795.015	−	459.002i	−0.927672	−	0.535592i	−0.0415977	−	0.999134i	$-0.513245\pi$
$857$	−795.015	−	459.002i	−0.927672	−	0.535592i	−0.886075	+	0.463543i	$0.846578\pi$
$858$		0			0
$859$	761.367	−	439.575i	0.886341	−	0.511729i	0.0135969	−	0.999908i	$-0.495672\pi$
$859$	761.367	−	439.575i	0.886341	−	0.511729i	0.872744	+	0.488179i	$0.162339\pi$
$860$			4.26239i			0.00495627i
$861$		0			0
$862$	−712.368			−0.826412
$863$	175.294	+	303.619i	0.203122	+	0.351818i	0.949533	−	0.313668i	$-0.101558\pi$
$863$	175.294	+	303.619i	0.203122	+	0.351818i	−0.746411	+	0.665486i	$0.768224\pi$
$864$		0			0
$865$	102.573	−	177.661i	0.118581	−	0.205389i
$866$	1025.78	−	592.236i	1.18451	−	0.683875i
$867$		0			0
$868$		0			0
$869$	−590.029			−0.678974
$870$		0			0
$871$	−81.2145	−	46.8892i	−0.0932428	−	0.0538338i
$872$	−157.061	+	272.038i	−0.180116	+	0.311970i
$873$		0			0
$874$			382.732i			0.437909i
$875$		0			0
$876$		0			0
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	0.865009	−	0.501756i	$-0.167313\pi$
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	−0.867038	+	0.498242i	$0.833979\pi$
$878$	−232.721	−	134.361i	−0.265058	−	0.153031i
$879$		0			0
$880$	29.8234	−	17.2185i	0.0338902	−	0.0195665i
$881$		−	488.565i		−	0.554557i	−0.960790	−	0.277279i	$-0.910567\pi$
$881$		−	488.565i		−	0.554557i	0.960790	−	0.277279i	$-0.0894325\pi$
$882$		0			0
$883$	−1162.16			−1.31615			−0.658075	−	0.752953i	$-0.728629\pi$
$883$	−1162.16			−1.31615			−0.658075	+	0.752953i	$0.728629\pi$
$884$	191.044	+	330.897i	0.216113	+	0.374318i
$885$		0			0
$886$	−119.823	+	207.540i	−0.135241	+	0.234244i
$887$	75.2801	−	43.4630i	0.0848704	−	0.0490000i	−0.456964	−	0.889485i	$-0.651063\pi$
$887$	75.2801	−	43.4630i	0.0848704	−	0.0490000i	0.541835	+	0.840485i	$0.317730\pi$
$888$		0			0
$889$		0			0
$890$	−42.1766			−0.0473895
$891$		0			0
$892$	396.000	+	228.631i	0.443946	+	0.256312i
$893$	−155.360	+	269.092i	−0.173976	+	0.301335i
$894$		0			0
$895$			242.895i			0.271391i
$896$		0			0
$897$		0			0
$898$	12.8011	+	22.1721i	0.0142551	+	0.0246906i
$899$	−1297.50	−	749.111i	−1.44327	−	0.833272i
$900$		0			0
$901$	662.912	−	382.732i	0.735751	−	0.424786i
$902$			465.259i			0.515808i
$903$		0			0
$904$	−286.794			−0.317250
$905$	−150.640	−	260.915i	−0.166453	−	0.288304i
$906$		0			0
$907$	230.448	−	399.148i	0.254077	−	0.440075i	−0.710567	−	0.703629i	$-0.751562\pi$
$907$	230.448	−	399.148i	0.254077	−	0.440075i	0.964645	+	0.263554i	$0.0848948\pi$
$908$	−113.647	+	65.6140i	−0.125162	+	0.0722621i
$909$		0			0
$910$		0			0
$911$	1184.28			1.29998			0.649988	−	0.759944i	$-0.274774\pi$
$911$	1184.28			1.29998			0.649988	+	0.759944i	$0.274774\pi$
$912$		0			0
$913$	573.661	+	331.203i	0.628325	+	0.362764i
$914$	232.513	−	402.725i	0.254391	−	0.440618i
$915$		0			0
$916$		−	186.960i		−	0.204104i
$917$		0			0
$918$		0			0
$919$	270.919	+	469.246i	0.294798	+	0.510605i	0.974938	−	0.222477i	$-0.0714143\pi$
$919$	270.919	+	469.246i	0.294798	+	0.510605i	−0.680140	+	0.733082i	$0.738081\pi$
$920$	131.647	+	76.0063i	0.143094	+	0.0826155i
$921$		0			0
$922$	972.853	−	561.677i	1.05515	−	0.609194i
$923$		−	2930.40i		−	3.17486i
$924$		0			0
$925$	−641.676			−0.693704
$926$	285.244	+	494.057i	0.308039	+	0.533539i
$927$		0			0
$928$	−96.0000	+	166.277i	−0.103448	+	0.179178i
$929$	−779.610	+	450.108i	−0.839193	+	0.484508i	−0.856990	−	0.515333i	$-0.827668\pi$
$929$	−779.610	+	450.108i	−0.839193	+	0.484508i	0.0177969	+	0.999842i	$0.494335\pi$
$930$		0			0
$931$		0			0
$932$	475.029			0.509688
$933$		0			0
$934$	3.46299	+	1.99936i	0.00370769	+	0.00214064i
$935$	38.5584	−	66.7852i	0.0412390	−	0.0714280i
$936$		0			0
$937$		−	233.964i		−	0.249695i	−0.992176	−	0.124847i	$-0.960156\pi$
$937$		−	233.964i		−	0.249695i	0.992176	−	0.124847i	$-0.0398441\pi$
$938$		0			0
$939$		0			0
$940$	61.7056	+	106.877i	0.0656443	+	0.113699i
$941$	1132.49	+	653.845i	1.20350	+	0.694840i	0.961331	−	0.275394i	$-0.0888083\pi$
$941$	1132.49	+	653.845i	1.20350	+	0.694840i	0.242167	+	0.970234i	$0.422142\pi$
$942$		0			0
$943$	−1778.60	+	1026.88i	−1.88611	+	1.08895i
$944$			164.884i			0.174666i
$945$		0			0
$946$	12.6030			0.0133224
$947$	−563.881	−	976.671i	−0.595440	−	1.03133i	−0.993485	−	0.113966i	$-0.963645\pi$
$947$	−563.881	−	976.671i	−0.595440	−	1.03133i	0.398045	−	0.917366i	$-0.369689\pi$
$948$		0			0
$949$	841.677	−	1457.83i	0.886909	−	1.53617i
$950$	203.012	−	117.209i	0.213696	−	0.123378i
$951$		0			0
$952$		0			0
$953$	91.4255			0.0959345			0.0479672	−	0.998849i	$-0.484726\pi$
$953$	91.4255			0.0959345			0.0479672	+	0.998849i	$0.484726\pi$
$954$		0			0
$955$	−82.7636	−	47.7836i	−0.0866635	−	0.0500352i
$956$	366.853	−	635.408i	0.383737	−	0.664652i
$957$		0			0
$958$		−	536.714i		−	0.560245i
$959$		0			0
$960$		0			0
$961$	493.749	+	855.199i	0.513787	+	0.889905i
$962$	730.628	+	421.828i	0.759489	+	0.438491i
$963$		0			0
$964$	−729.235	+	421.024i	−0.756467	+	0.436747i
$965$			14.0531i			0.0145628i
$966$		0			0
$967$	−1098.19			−1.13567			−0.567834	−	0.823143i	$-0.692218\pi$
$967$	−1098.19			−1.13567			−0.567834	+	0.823143i	$0.692218\pi$
$968$	120.208	+	208.207i	0.124182	+	0.215089i
$969$		0			0
$970$	−11.1472	+	19.3075i	−0.0114919	+	0.0199046i
$971$	114.405	−	66.0517i	0.117822	−	0.0680245i	−0.439931	−	0.898032i	$-0.644997\pi$
$971$	114.405	−	66.0517i	0.117822	−	0.0680245i	0.557753	+	0.830007i	$0.311664\pi$
$972$		0			0
$973$		0			0
$974$	813.899			0.835626
$975$		0			0
$976$	−4.11775	−	2.37738i	−0.00421901	−	0.00243584i
$977$	224.117	−	388.182i	0.229393	−	0.397320i	−0.728235	−	0.685327i	$-0.759659\pi$
$977$	224.117	−	388.182i	0.229393	−	0.397320i	0.957628	+	0.288007i	$0.0929926\pi$
$978$		0			0
$979$			124.708i			0.127383i
$980$		0			0
$981$		0			0
$982$	168.603	+	292.029i	0.171694	+	0.297382i
$983$	1426.14	+	823.382i	1.45080	+	0.837621i	0.998527	−	0.0542567i	$-0.0172789\pi$
$983$	1426.14	+	823.382i	1.45080	+	0.837621i	0.452276	+	0.891878i	$0.350612\pi$
$984$		0			0
$985$	−331.986	+	191.672i	−0.337041	+	0.194591i
$986$			429.956i			0.436061i
$987$		0			0
$988$	−308.205			−0.311949
$989$	27.8162	+	48.1791i	0.0281256	+	0.0487150i
$990$		0			0
$991$	314.448	−	544.640i	0.317304	−	0.549587i	−0.662621	−	0.748955i	$-0.730556\pi$
$991$	314.448	−	544.640i	0.317304	−	0.549587i	0.979925	+	0.199369i	$0.0638891\pi$
$992$	216.250	−	124.852i	0.217994	−	0.125859i
$993$		0			0
$994$		0			0
$995$	−187.882			−0.188826
$996$		0			0
$997$	869.645	+	502.090i	0.872262	+	0.503601i	0.868099	−	0.496390i	$-0.165342\pi$
$997$	869.645	+	502.090i	0.872262	+	0.503601i	0.00416289	+	0.999991i	$0.498675\pi$
$998$	202.638	−	350.980i	0.203044	−	0.351683i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.n.e.325.1		4
3.2	odd	2		294.3.g.a.31.2		4
7.2	even	3		126.3.n.a.19.1		4
7.3	odd	6		882.3.c.b.685.4		4
7.4	even	3		882.3.c.b.685.3		4
7.5	odd	6	inner	882.3.n.e.19.1		4
7.6	odd	2		126.3.n.a.73.1		4
21.2	odd	6		42.3.g.a.19.2	✓	4
21.5	even	6		294.3.g.a.19.2		4
21.11	odd	6		294.3.c.a.97.2		4
21.17	even	6		294.3.c.a.97.1		4
21.20	even	2		42.3.g.a.31.2	yes	4
28.23	odd	6		1008.3.cg.h.145.2		4
28.27	even	2		1008.3.cg.h.577.2		4
84.11	even	6		2352.3.f.e.97.2		4
84.23	even	6		336.3.bh.e.145.1		4
84.59	odd	6		2352.3.f.e.97.3		4
84.83	odd	2		336.3.bh.e.241.1		4
105.2	even	12		1050.3.q.a.649.3		8
105.23	even	12		1050.3.q.a.649.2		8
105.44	odd	6		1050.3.p.a.901.1		4
105.62	odd	4		1050.3.q.a.199.2		8
105.83	odd	4		1050.3.q.a.199.3		8
105.104	even	2		1050.3.p.a.451.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.2	✓	4	21.2	odd	6
42.3.g.a.31.2	yes	4	21.20	even	2
126.3.n.a.19.1		4	7.2	even	3
126.3.n.a.73.1		4	7.6	odd	2
294.3.c.a.97.1		4	21.17	even	6
294.3.c.a.97.2		4	21.11	odd	6
294.3.g.a.19.2		4	21.5	even	6
294.3.g.a.31.2		4	3.2	odd	2
336.3.bh.e.145.1		4	84.23	even	6
336.3.bh.e.241.1		4	84.83	odd	2
882.3.c.b.685.3		4	7.4	even	3
882.3.c.b.685.4		4	7.3	odd	6
882.3.n.e.19.1		4	7.5	odd	6	inner
882.3.n.e.325.1		4	1.1	even	1	trivial
1008.3.cg.h.145.2		4	28.23	odd	6
1008.3.cg.h.577.2		4	28.27	even	2
1050.3.p.a.451.1		4	105.104	even	2
1050.3.p.a.901.1		4	105.44	odd	6
1050.3.q.a.199.2		8	105.62	odd	4
1050.3.q.a.199.3		8	105.83	odd	4
1050.3.q.a.649.2		8	105.23	even	12
1050.3.q.a.649.3		8	105.2	even	12
2352.3.f.e.97.2		4	84.11	even	6
2352.3.f.e.97.3		4	84.59	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24264 + 0.717439i) q^{5} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24264 + 0.717439i) q^{5} +2.82843 q^{8} +(1.75736 + 1.01461i) q^{10} +(3.00000 - 5.19615i) q^{11} +21.3280i q^{13} +(-2.00000 - 3.46410i) q^{16} +(-7.75736 - 4.47871i) q^{17} +(6.25736 - 3.61269i) q^{19} -2.86976i q^{20} -8.48528 q^{22} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} +(26.1213 - 15.0812i) q^{26} +33.9411 q^{29} +(-38.2279 - 22.0709i) q^{31} +(-2.82843 + 4.89898i) q^{32} +12.6677i q^{34} +(13.9853 + 24.2232i) q^{37} +(-8.84924 - 5.10911i) q^{38} +(-3.51472 + 2.02922i) q^{40} -54.8313i q^{41} -1.48528 q^{43} +(6.00000 + 10.3923i) q^{44} +(-26.4853 + 45.8739i) q^{46} +(-37.2426 + 21.5020i) q^{47} +32.4437 q^{50} +(-36.9411 - 21.3280i) q^{52} +(-42.7279 + 74.0069i) q^{53} +8.60927i q^{55} +(-24.0000 - 41.5692i) q^{58} +(-35.6985 - 20.6105i) q^{59} +(1.02944 - 0.594346i) q^{61} +62.4259i q^{62} +8.00000 q^{64} +(-15.3015 - 26.5030i) q^{65} +(-2.19848 + 3.80789i) q^{67} +(15.5147 - 8.95743i) q^{68} -137.397 q^{71} +(-68.3528 - 39.4635i) q^{73} +(19.7782 - 34.2568i) q^{74} +14.4508i q^{76} +(-49.1690 - 85.1633i) q^{79} +(4.97056 + 2.86976i) q^{80} +(-67.1543 + 38.7716i) q^{82} +110.401i q^{83} +12.8528 q^{85} +(1.05025 + 1.81909i) q^{86} +(8.48528 - 14.6969i) q^{88} +(-18.0000 + 10.3923i) q^{89} +74.9117 q^{92} +(52.6690 + 30.4085i) q^{94} +(-5.18377 + 8.97855i) q^{95} +10.9867i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 12 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 + 12 * q^5	\( 4 q - 4 q^{4} + 12 q^{5} + 24 q^{10} + 12 q^{11} - 8 q^{16} - 48 q^{17} + 42 q^{19} - 24 q^{23} + 22 q^{25} + 96 q^{26} - 102 q^{31} + 22 q^{37} + 24 q^{38} - 48 q^{40} + 28 q^{43} + 24 q^{44} - 72 q^{46} - 132 q^{47} + 192 q^{50} - 12 q^{52} - 120 q^{53} - 96 q^{58} - 24 q^{59} + 72 q^{61} + 32 q^{64} - 180 q^{65} + 110 q^{67} + 96 q^{68} - 312 q^{71} + 66 q^{73} + 48 q^{74} - 10 q^{79} - 48 q^{80} - 48 q^{82} - 288 q^{85} + 24 q^{86} - 72 q^{89} + 96 q^{92} + 24 q^{94} + 132 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 + 12 * q^5 + 24 * q^10 + 12 * q^11 - 8 * q^16 - 48 * q^17 + 42 * q^19 - 24 * q^23 + 22 * q^25 + 96 * q^26 - 102 * q^31 + 22 * q^37 + 24 * q^38 - 48 * q^40 + 28 * q^43 + 24 * q^44 - 72 * q^46 - 132 * q^47 + 192 * q^50 - 12 * q^52 - 120 * q^53 - 96 * q^58 - 24 * q^59 + 72 * q^61 + 32 * q^64 - 180 * q^65 + 110 * q^67 + 96 * q^68 - 312 * q^71 + 66 * q^73 + 48 * q^74 - 10 * q^79 - 48 * q^80 - 48 * q^82 - 288 * q^85 + 24 * q^86 - 72 * q^89 + 96 * q^92 + 24 * q^94 + 132 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more