LMFDB - Embedded newform 882.3.n.a.19.1

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:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.19
Dual form			882.3.n.a.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.12132 - 2.95680i) q^{5} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.12132 - 2.95680i) q^{5} +2.82843 q^{8} +(7.24264 - 4.18154i) q^{10} +(-0.878680 - 1.52192i) q^{11} +18.7554i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-20.3345 + 11.7401i) q^{17} +(19.9706 + 11.5300i) q^{19} +11.8272i q^{20} +2.48528 q^{22} +(9.36396 - 16.2189i) q^{23} +(4.98528 + 8.63476i) q^{25} +(-22.9706 - 13.2621i) q^{26} -30.0000 q^{29} +(7.45584 - 4.30463i) q^{31} +(-2.82843 - 4.89898i) q^{32} -33.2061i q^{34} +(35.4558 - 61.4113i) q^{37} +(-28.2426 + 16.3059i) q^{38} +(-14.4853 - 8.36308i) q^{40} -41.3951i q^{41} +10.4264 q^{43} +(-1.75736 + 3.04384i) q^{44} +(13.2426 + 22.9369i) q^{46} +(33.5147 + 19.3497i) q^{47} -14.1005 q^{50} +(32.4853 - 18.7554i) q^{52} +(-18.5147 - 32.0684i) q^{53} +10.3923i q^{55} +(21.2132 - 36.7423i) q^{58} +(84.4264 - 48.7436i) q^{59} +(-14.4853 - 8.36308i) q^{61} +12.1753i q^{62} +8.00000 q^{64} +(55.4558 - 96.0523i) q^{65} +(-30.4853 - 52.8021i) q^{67} +(40.6690 + 23.4803i) q^{68} +110.610 q^{71} +(-49.1543 + 28.3793i) q^{73} +(50.1421 + 86.8487i) q^{74} -46.1200i q^{76} +(34.9117 - 60.4688i) q^{79} +(20.4853 - 11.8272i) q^{80} +(50.6985 + 29.2708i) q^{82} -6.43583i q^{83} +138.853 q^{85} +(-7.37258 + 12.7697i) q^{86} +(-2.48528 - 4.30463i) q^{88} +(-36.4523 - 21.0457i) q^{89} -37.4558 q^{92} +(-47.3970 + 27.3647i) q^{94} +(-68.1838 - 118.098i) q^{95} +51.7153i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 12 q^{10} - 12 q^{11} - 8 q^{16} + 12 q^{17} + 12 q^{19} - 24 q^{22} + 12 q^{23} - 14 q^{25} - 24 q^{26} - 120 q^{29} - 72 q^{31} + 40 q^{37} - 96 q^{38} - 24 q^{40} - 128 q^{43} - 24 q^{44} + 36 q^{46} + 168 q^{47} - 96 q^{50} + 96 q^{52} - 108 q^{53} + 168 q^{59} - 24 q^{61} + 32 q^{64} + 120 q^{65} - 88 q^{67} - 24 q^{68} + 120 q^{71} + 24 q^{73} + 144 q^{74} - 64 q^{79} + 48 q^{80} + 84 q^{82} + 216 q^{85} - 120 q^{86} + 24 q^{88} - 324 q^{89} - 48 q^{92} + 48 q^{94} - 120 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 12 * q^5 + 12 * q^10 - 12 * q^11 - 8 * q^16 + 12 * q^17 + 12 * q^19 - 24 * q^22 + 12 * q^23 - 14 * q^25 - 24 * q^26 - 120 * q^29 - 72 * q^31 + 40 * q^37 - 96 * q^38 - 24 * q^40 - 128 * q^43 - 24 * q^44 + 36 * q^46 + 168 * q^47 - 96 * q^50 + 96 * q^52 - 108 * q^53 + 168 * q^59 - 24 * q^61 + 32 * q^64 + 120 * q^65 - 88 * q^67 - 24 * q^68 + 120 * q^71 + 24 * q^73 + 144 * q^74 - 64 * q^79 + 48 * q^80 + 84 * q^82 + 216 * q^85 - 120 * q^86 + 24 * q^88 - 324 * q^89 - 48 * q^92 + 48 * q^94 - 120 * 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
$5$	−5.12132	−	2.95680i	−1.02426	−	0.591359i	−0.108928	−	0.994050i	$-0.534742\pi$
$5$	−5.12132	−	2.95680i	−1.02426	−	0.591359i	−0.915336	+	0.402691i	$0.868075\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.82843			0.353553
$9$		0			0
$10$	7.24264	−	4.18154i	0.724264	−	0.418154i
$11$	−0.878680	−	1.52192i	−0.0798800	−	0.138356i	0.823318	−	0.567580i	$-0.192120\pi$
$11$	−0.878680	−	1.52192i	−0.0798800	−	0.138356i	−0.903198	+	0.429224i	$0.858787\pi$
$12$		0			0
$13$			18.7554i			1.44272i	0.692559	+	0.721361i	$0.256483\pi$
$13$			18.7554i			1.44272i	−0.692559	+	0.721361i	$0.743517\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−20.3345	+	11.7401i	−1.19615	+	0.690597i	−0.959694	−	0.281046i	$-0.909319\pi$
$17$	−20.3345	+	11.7401i	−1.19615	+	0.690597i	−0.236454	+	0.971643i	$0.575985\pi$
$18$		0			0
$19$	19.9706	+	11.5300i	1.05108	+	0.606843i	0.922952	−	0.384915i	$-0.125769\pi$
$19$	19.9706	+	11.5300i	1.05108	+	0.606843i	0.128130	+	0.991757i	$0.459102\pi$
$20$			11.8272i			0.591359i
$21$		0			0
$22$	2.48528			0.112967
$23$	9.36396	−	16.2189i	0.407129	−	0.705168i	−0.587438	−	0.809269i	$-0.699863\pi$
$23$	9.36396	−	16.2189i	0.407129	−	0.705168i	0.994567	+	0.104102i	$0.0331967\pi$
$24$		0			0
$25$	4.98528	+	8.63476i	0.199411	+	0.345390i
$26$	−22.9706	−	13.2621i	−0.883483	−	0.510079i
$27$		0			0
$28$		0			0
$29$	−30.0000			−1.03448			−0.517241	−	0.855840i	$-0.673041\pi$
$29$	−30.0000			−1.03448			−0.517241	+	0.855840i	$0.673041\pi$
$30$		0			0
$31$	7.45584	−	4.30463i	0.240511	−	0.138859i	−0.374901	−	0.927065i	$-0.622323\pi$
$31$	7.45584	−	4.30463i	0.240511	−	0.138859i	0.615412	+	0.788206i	$0.288990\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$		0			0
$34$		−	33.2061i		−	0.976651i
$35$		0			0
$36$		0			0
$37$	35.4558	−	61.4113i	0.958266	−	1.65977i	0.231556	−	0.972822i	$-0.425619\pi$
$37$	35.4558	−	61.4113i	0.958266	−	1.65977i	0.726711	−	0.686944i	$-0.241048\pi$
$38$	−28.2426	+	16.3059i	−0.743227	+	0.429103i
$39$		0			0
$40$	−14.4853	−	8.36308i	−0.362132	−	0.209077i
$41$		−	41.3951i		−	1.00964i	−0.863225	−	0.504819i	$-0.831559\pi$
$41$		−	41.3951i		−	1.00964i	0.863225	−	0.504819i	$-0.168441\pi$
$42$		0			0
$43$	10.4264			0.242475			0.121237	−	0.992624i	$-0.461314\pi$
$43$	10.4264			0.242475			0.121237	+	0.992624i	$0.461314\pi$
$44$	−1.75736	+	3.04384i	−0.0399400	+	0.0691781i
$45$		0			0
$46$	13.2426	+	22.9369i	0.287883	+	0.498629i
$47$	33.5147	+	19.3497i	0.713079	+	0.411696i	0.812200	−	0.583379i	$-0.198270\pi$
$47$	33.5147	+	19.3497i	0.713079	+	0.411696i	−0.0991210	+	0.995075i	$0.531603\pi$
$48$		0			0
$49$		0			0
$50$	−14.1005			−0.282010
$51$		0			0
$52$	32.4853	−	18.7554i	0.624717	−	0.360680i
$53$	−18.5147	−	32.0684i	−0.349334	−	0.605065i	0.636797	−	0.771031i	$-0.280259\pi$
$53$	−18.5147	−	32.0684i	−0.349334	−	0.605065i	−0.986131	+	0.165967i	$0.946926\pi$
$54$		0			0
$55$			10.3923i			0.188951i
$56$		0			0
$57$		0			0
$58$	21.2132	−	36.7423i	0.365745	−	0.633489i
$59$	84.4264	−	48.7436i	1.43096	−	0.826163i	0.433762	−	0.901027i	$-0.357186\pi$
$59$	84.4264	−	48.7436i	1.43096	−	0.826163i	0.997194	+	0.0748645i	$0.0238524\pi$
$60$		0			0
$61$	−14.4853	−	8.36308i	−0.237464	−	0.137100i	0.376547	−	0.926398i	$-0.377111\pi$
$61$	−14.4853	−	8.36308i	−0.237464	−	0.137100i	−0.614010	+	0.789298i	$0.710445\pi$
$62$			12.1753i			0.196376i
$63$		0			0
$64$	8.00000			0.125000
$65$	55.4558	−	96.0523i	0.853167	−	1.47773i
$66$		0			0
$67$	−30.4853	−	52.8021i	−0.455004	−	0.788090i	0.543684	−	0.839290i	$-0.317029\pi$
$67$	−30.4853	−	52.8021i	−0.455004	−	0.788090i	−0.998688	+	0.0511995i	$0.983696\pi$
$68$	40.6690	+	23.4803i	0.598074	+	0.345298i
$69$		0			0
$70$		0			0
$71$	110.610			1.55789			0.778945	−	0.627092i	$-0.215755\pi$
$71$	110.610			1.55789			0.778945	+	0.627092i	$0.215755\pi$
$72$		0			0
$73$	−49.1543	+	28.3793i	−0.673347	+	0.388757i	−0.797344	−	0.603526i	$-0.793762\pi$
$73$	−49.1543	+	28.3793i	−0.673347	+	0.388757i	0.123997	+	0.992283i	$0.460429\pi$
$74$	50.1421	+	86.8487i	0.677596	+	1.17363i
$75$		0			0
$76$		−	46.1200i		−	0.606843i
$77$		0			0
$78$		0			0
$79$	34.9117	−	60.4688i	0.441920	−	0.765428i	−0.555912	−	0.831241i	$-0.687631\pi$
$79$	34.9117	−	60.4688i	0.441920	−	0.765428i	0.997832	+	0.0658132i	$0.0209641\pi$
$80$	20.4853	−	11.8272i	0.256066	−	0.147840i
$81$		0			0
$82$	50.6985	+	29.2708i	0.618274	+	0.356961i
$83$		−	6.43583i		−	0.0775401i	−0.999248	−	0.0387701i	$-0.987656\pi$
$83$		−	6.43583i		−	0.0775401i	0.999248	−	0.0387701i	$-0.0123440\pi$
$84$		0			0
$85$	138.853			1.63356
$86$	−7.37258	+	12.7697i	−0.0857277	+	0.148485i
$87$		0			0
$88$	−2.48528	−	4.30463i	−0.0282418	−	0.0489163i
$89$	−36.4523	−	21.0457i	−0.409576	−	0.236469i	0.281031	−	0.959699i	$-0.409323\pi$
$89$	−36.4523	−	21.0457i	−0.409576	−	0.236469i	−0.690608	+	0.723230i	$0.742657\pi$
$90$		0			0
$91$		0			0
$92$	−37.4558			−0.407129
$93$		0			0
$94$	−47.3970	+	27.3647i	−0.504223	+	0.291113i
$95$	−68.1838	−	118.098i	−0.717724	−	1.24313i
$96$		0			0
$97$			51.7153i			0.533148i	0.963814	+	0.266574i	$0.0858916\pi$
$97$			51.7153i			0.533148i	−0.963814	+	0.266574i	$0.914108\pi$
$98$		0			0
$99$		0			0
$100$	9.97056	−	17.2695i	0.0997056	−	0.172695i
$101$	−5.72435	+	3.30496i	−0.0566767	+	0.0327223i	−0.528071	−	0.849200i	$-0.677084\pi$
$101$	−5.72435	+	3.30496i	−0.0566767	+	0.0327223i	0.471394	+	0.881923i	$0.343751\pi$
$102$		0			0
$103$	−152.309	−	87.9354i	−1.47872	−	0.853742i	−0.479014	−	0.877807i	$-0.659006\pi$
$103$	−152.309	−	87.9354i	−1.47872	−	0.853742i	−0.999710	+	0.0240648i	$0.992339\pi$
$104$			53.0482i			0.510079i
$105$		0			0
$106$	52.3675			0.494033
$107$	−23.1213	+	40.0473i	−0.216087	+	0.374274i	−0.953608	−	0.301050i	$-0.902663\pi$
$107$	−23.1213	+	40.0473i	−0.216087	+	0.374274i	0.737521	+	0.675324i	$0.235996\pi$
$108$		0			0
$109$	17.9706	+	31.1259i	0.164868	+	0.285559i	0.936608	−	0.350378i	$-0.113947\pi$
$109$	17.9706	+	31.1259i	0.164868	+	0.285559i	−0.771741	+	0.635937i	$0.780614\pi$
$110$	−12.7279	−	7.34847i	−0.115708	−	0.0668043i
$111$		0			0
$112$		0			0
$113$	73.0294			0.646278			0.323139	−	0.946351i	$-0.395262\pi$
$113$	73.0294			0.646278			0.323139	+	0.946351i	$0.395262\pi$
$114$		0			0
$115$	−95.9117	+	55.3746i	−0.834015	+	0.481519i
$116$	30.0000	+	51.9615i	0.258621	+	0.447944i
$117$		0			0
$118$			137.868i			1.16837i
$119$		0			0
$120$		0			0
$121$	58.9558	−	102.115i	0.487238	−	0.843922i
$122$	20.4853	−	11.8272i	0.167912	−	0.0969441i
$123$		0			0
$124$	−14.9117	−	8.60927i	−0.120256	−	0.0694296i
$125$			88.8780i			0.711024i
$126$		0			0
$127$	89.9411			0.708198			0.354099	−	0.935208i	$-0.384788\pi$
$127$	89.9411			0.708198			0.354099	+	0.935208i	$0.384788\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	78.4264	+	135.839i	0.603280	+	1.04491i
$131$	10.5442	+	6.08767i	0.0804897	+	0.0464708i	0.539705	−	0.841854i	$-0.318536\pi$
$131$	10.5442	+	6.08767i	0.0804897	+	0.0464708i	−0.459215	+	0.888325i	$0.651869\pi$
$132$		0			0
$133$		0			0
$134$	86.2254			0.643473
$135$		0			0
$136$	−57.5147	+	33.2061i	−0.422902	+	0.244163i
$137$	82.8823	+	143.556i	0.604980	+	1.04786i	0.992055	+	0.125808i	$0.0401522\pi$
$137$	82.8823	+	143.556i	0.604980	+	1.04786i	−0.387075	+	0.922048i	$0.626514\pi$
$138$		0			0
$139$		−	220.514i		−	1.58643i	−0.608941	−	0.793215i	$-0.708406\pi$
$139$		−	220.514i		−	1.58643i	0.608941	−	0.793215i	$-0.291594\pi$
$140$		0			0
$141$		0			0
$142$	−78.2132	+	135.469i	−0.550797	+	0.954009i
$143$	28.5442	−	16.4800i	0.199609	−	0.115245i
$144$		0			0
$145$	153.640	+	88.7039i	1.05958	+	0.611751i
$146$		−	80.2687i		−	0.549786i
$147$		0			0
$148$	−141.823			−0.958266
$149$	105.426	−	182.604i	0.707560	−	1.22553i	−0.258200	−	0.966091i	$-0.583129\pi$
$149$	105.426	−	182.604i	0.707560	−	1.22553i	0.965760	−	0.259438i	$-0.0835373\pi$
$150$		0			0
$151$	36.1838	+	62.6721i	0.239628	+	0.415047i	0.960607	−	0.277909i	$-0.0896413\pi$
$151$	36.1838	+	62.6721i	0.239628	+	0.415047i	−0.720980	+	0.692956i	$0.756308\pi$
$152$	56.4853	+	32.6118i	0.371614	+	0.214551i
$153$		0			0
$154$		0			0
$155$	−50.9117			−0.328463
$156$		0			0
$157$	202.368	−	116.837i	1.28897	−	0.744184i	0.310495	−	0.950575i	$-0.399505\pi$
$157$	202.368	−	116.837i	1.28897	−	0.744184i	0.978470	+	0.206390i	$0.0661717\pi$
$158$	49.3726	+	85.5158i	0.312485	+	0.541239i
$159$		0			0
$160$			33.4523i			0.209077i
$161$		0			0
$162$		0			0
$163$	36.5442	−	63.2963i	0.224197	−	0.388321i	−0.731881	−	0.681432i	$-0.761357\pi$
$163$	36.5442	−	63.2963i	0.224197	−	0.388321i	0.956078	+	0.293111i	$0.0946907\pi$
$164$	−71.6985	+	41.3951i	−0.437186	+	0.252409i
$165$		0			0
$166$	7.88225	+	4.55082i	0.0474834	+	0.0274146i
$167$			39.3958i			0.235903i	0.993019	+	0.117951i	$0.0376327\pi$
$167$			39.3958i			0.235903i	−0.993019	+	0.117951i	$0.962367\pi$
$168$		0			0
$169$	−182.765			−1.08145
$170$	−98.1838	+	170.059i	−0.577552	+	1.00035i
$171$		0			0
$172$	−10.4264	−	18.0591i	−0.0606186	−	0.104995i
$173$	20.6360	+	11.9142i	0.119283	+	0.0688683i	0.558455	−	0.829535i	$-0.311394\pi$
$173$	20.6360	+	11.9142i	0.119283	+	0.0688683i	−0.439171	+	0.898403i	$0.644728\pi$
$174$		0			0
$175$		0			0
$176$	7.02944			0.0399400
$177$		0			0
$178$	51.5513	−	29.7632i	0.289614	−	0.167209i
$179$	−6.45227	−	11.1757i	−0.0360462	−	0.0624339i	0.847439	−	0.530892i	$-0.178143\pi$
$179$	−6.45227	−	11.1757i	−0.0360462	−	0.0624339i	−0.883486	+	0.468458i	$0.844810\pi$
$180$		0			0
$181$			65.3678i			0.361148i	0.983561	+	0.180574i	$0.0577955\pi$
$181$			65.3678i			0.361148i	−0.983561	+	0.180574i	$0.942204\pi$
$182$		0			0
$183$		0			0
$184$	26.4853	−	45.8739i	0.143942	−	0.249314i
$185$	−363.161	+	209.671i	−1.96303	+	1.13336i
$186$		0			0
$187$	35.7351	+	20.6316i	0.191097	+	0.110330i
$188$		−	77.3989i		−	0.411696i
$189$		0			0
$190$	192.853			1.01501
$191$	−50.0330	+	86.6597i	−0.261953	+	0.453716i	−0.966761	−	0.255682i	$-0.917700\pi$
$191$	−50.0330	+	86.6597i	−0.261953	+	0.453716i	0.704808	+	0.709398i	$0.251033\pi$
$192$		0			0
$193$	−39.4558	−	68.3395i	−0.204434	−	0.354091i	0.745518	−	0.666486i	$-0.232202\pi$
$193$	−39.4558	−	68.3395i	−0.204434	−	0.354091i	−0.949952	+	0.312395i	$0.898869\pi$
$194$	−63.3381	−	36.5683i	−0.326485	−	0.188496i
$195$		0			0
$196$		0			0
$197$	183.941			0.933711			0.466856	−	0.884334i	$-0.345387\pi$
$197$	183.941			0.933711			0.466856	+	0.884334i	$0.345387\pi$
$198$		0			0
$199$	147.250	−	85.0147i	0.739949	−	0.427210i	−0.0821020	−	0.996624i	$-0.526163\pi$
$199$	147.250	−	85.0147i	0.739949	−	0.427210i	0.822051	+	0.569414i	$0.192830\pi$
$200$	14.1005	+	24.4228i	0.0705025	+	0.122114i
$201$		0			0
$202$		−	9.34783i		−	0.0462764i
$203$		0			0
$204$		0			0
$205$	−122.397	+	211.998i	−0.597058	+	1.03414i
$206$	215.397	−	124.359i	1.04562	−	0.603687i
$207$		0			0
$208$	−64.9706	−	37.5108i	−0.312358	−	0.180340i
$209$		−	40.5247i		−	0.193898i
$210$		0			0
$211$	21.5736			0.102245			0.0511223	−	0.998692i	$-0.483720\pi$
$211$	21.5736			0.102245			0.0511223	+	0.998692i	$0.483720\pi$
$212$	−37.0294	+	64.1369i	−0.174667	+	0.302532i
$213$		0			0
$214$	−32.6985	−	56.6354i	−0.152797	−	0.264652i
$215$	−53.3970	−	30.8288i	−0.248358	−	0.143390i
$216$		0			0
$217$		0			0
$218$	−50.8284			−0.233158
$219$		0			0
$220$	18.0000	−	10.3923i	0.0818182	−	0.0472377i
$221$	−220.191	−	381.382i	−0.996339	−	1.72571i
$222$		0			0
$223$		−	119.359i		−	0.535240i	−0.963525	−	0.267620i	$-0.913763\pi$
$223$		−	119.359i		−	0.535240i	0.963525	−	0.267620i	$-0.0862372\pi$
$224$		0			0
$225$		0			0
$226$	−51.6396	+	89.4424i	−0.228494	+	0.395763i
$227$	147.088	−	84.9215i	0.647966	−	0.374103i	−0.139710	−	0.990192i	$-0.544617\pi$
$227$	147.088	−	84.9215i	0.647966	−	0.374103i	0.787677	+	0.616089i	$0.211284\pi$
$228$		0			0
$229$	95.2721	+	55.0054i	0.416035	+	0.240198i	0.693380	−	0.720573i	$-0.256121\pi$
$229$	95.2721	+	55.0054i	0.416035	+	0.240198i	−0.277344	+	0.960771i	$0.589454\pi$
$230$		−	156.623i		−	0.680970i
$231$		0			0
$232$	−84.8528			−0.365745
$233$	28.6325	−	49.5929i	0.122886	−	0.212845i	−0.798019	−	0.602633i	$-0.794118\pi$
$233$	28.6325	−	49.5929i	0.122886	−	0.212845i	0.920905	+	0.389788i	$0.127452\pi$
$234$		0			0
$235$	−114.426	−	198.192i	−0.486921	−	0.843372i
$236$	−168.853	−	97.4872i	−0.715478	−	0.413081i
$237$		0			0
$238$		0			0
$239$	−281.522			−1.17792			−0.588958	−	0.808164i	$-0.700462\pi$
$239$	−281.522			−1.17792			−0.588958	+	0.808164i	$0.700462\pi$
$240$		0			0
$241$	145.757	−	84.1531i	0.604802	−	0.349183i	−0.166126	−	0.986105i	$-0.553126\pi$
$241$	145.757	−	84.1531i	0.604802	−	0.349183i	0.770928	+	0.636922i	$0.219793\pi$
$242$	83.3762	+	144.412i	0.344530	+	0.596743i
$243$		0			0
$244$			33.4523i			0.137100i
$245$		0			0
$246$		0			0
$247$	−216.250	+	374.556i	−0.875505	+	1.51642i
$248$	21.0883	−	12.1753i	0.0850335	−	0.0490941i
$249$		0			0
$250$	−108.853	−	62.8462i	−0.435411	−	0.251385i
$251$		−	106.096i		−	0.422695i	−0.977411	−	0.211348i	$-0.932215\pi$
$251$		−	106.096i		−	0.422695i	0.977411	−	0.211348i	$-0.0677852\pi$
$252$		0			0
$253$	−32.9117			−0.130086
$254$	−63.5980	+	110.155i	−0.250386	+	0.433681i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−251.548	−	145.231i	−0.978785	−	0.565102i	−0.0768819	−	0.997040i	$-0.524496\pi$
$257$	−251.548	−	145.231i	−0.978785	−	0.565102i	−0.901903	+	0.431938i	$0.857830\pi$
$258$		0			0
$259$		0			0
$260$	−221.823			−0.853167
$261$		0			0
$262$	−14.9117	+	8.60927i	−0.0569148	+	0.0328598i
$263$	−44.5111	−	77.0956i	−0.169244	−	0.293139i	0.768910	−	0.639357i	$-0.220799\pi$
$263$	−44.5111	−	77.0956i	−0.169244	−	0.293139i	−0.938154	+	0.346218i	$0.887466\pi$
$264$		0			0
$265$			218.977i			0.826328i
$266$		0			0
$267$		0			0
$268$	−60.9706	+	105.604i	−0.227502	+	0.394045i
$269$	−165.842	+	95.7490i	−0.616513	+	0.355944i	−0.775510	−	0.631335i	$-0.782507\pi$
$269$	−165.842	+	95.7490i	−0.616513	+	0.355944i	0.158997	+	0.987279i	$0.449174\pi$
$270$		0			0
$271$	188.309	+	108.720i	0.694866	+	0.401181i	0.805432	−	0.592688i	$-0.201933\pi$
$271$	188.309	+	108.720i	0.694866	+	0.401181i	−0.110566	+	0.993869i	$0.535266\pi$
$272$		−	93.9211i		−	0.345298i
$273$		0			0
$274$	−234.426			−0.855571
$275$	8.76093	−	15.1744i	0.0318579	−	0.0551796i
$276$		0			0
$277$	−145.338	−	251.733i	−0.524686	−	0.908783i	−0.999587	−	0.0287438i	$-0.990849\pi$
$277$	−145.338	−	251.733i	−0.524686	−	0.908783i	0.474901	−	0.880039i	$-0.342484\pi$
$278$	270.073	+	155.927i	0.971486	+	0.560888i
$279$		0			0
$280$		0			0
$281$	−18.8528			−0.0670919			−0.0335459	−	0.999437i	$-0.510680\pi$
$281$	−18.8528			−0.0670919			−0.0335459	+	0.999437i	$0.510680\pi$
$282$		0			0
$283$	−347.912	+	200.867i	−1.22937	+	0.709777i	−0.966898	−	0.255163i	$-0.917871\pi$
$283$	−347.912	+	200.867i	−1.22937	+	0.709777i	−0.262472	+	0.964940i	$0.584538\pi$
$284$	−110.610	−	191.582i	−0.389472	−	0.674586i
$285$		0			0
$286$			46.6124i			0.162980i
$287$		0			0
$288$		0			0
$289$	131.162	−	227.179i	0.453847	−	0.786087i
$290$	−217.279	+	125.446i	−0.749239	+	0.432573i
$291$		0			0
$292$	98.3087	+	56.7585i	0.336673	+	0.194379i
$293$			280.893i			0.958679i	0.877629	+	0.479340i	$0.159124\pi$
$293$			280.893i			0.958679i	−0.877629	+	0.479340i	$0.840876\pi$
$294$		0			0
$295$	−576.500			−1.95424
$296$	100.284	−	173.697i	0.338798	−	0.586816i
$297$		0			0
$298$	149.095	+	258.241i	0.500320	+	0.866580i
$299$	304.191	+	175.625i	1.01736	+	0.587374i
$300$		0			0
$301$		0			0
$302$	−102.343			−0.338885
$303$		0			0
$304$	−79.8823	+	46.1200i	−0.262771	+	0.151711i
$305$	49.4558	+	85.6600i	0.162150	+	0.280853i
$306$		0			0
$307$			152.318i			0.496151i	0.968741	+	0.248076i	$0.0797982\pi$
$307$			152.318i			0.496151i	−0.968741	+	0.248076i	$0.920202\pi$
$308$		0			0
$309$		0			0
$310$	36.0000	−	62.3538i	0.116129	−	0.201141i
$311$	245.220	−	141.578i	0.788490	−	0.455235i	−0.0509408	−	0.998702i	$-0.516222\pi$
$311$	245.220	−	141.578i	0.788490	−	0.455235i	0.839431	+	0.543467i	$0.182889\pi$
$312$		0			0
$313$	−42.0732	−	24.2910i	−0.134419	−	0.0776069i	0.431282	−	0.902217i	$-0.358061\pi$
$313$	−42.0732	−	24.2910i	−0.134419	−	0.0776069i	−0.565702	+	0.824610i	$0.691395\pi$
$314$			330.465i			1.05244i
$315$		0			0
$316$	−139.647			−0.441920
$317$	−289.014	+	500.587i	−0.911717	+	1.57914i	−0.100079	+	0.994980i	$0.531910\pi$
$317$	−289.014	+	500.587i	−0.911717	+	1.57914i	−0.811638	+	0.584161i	$0.801424\pi$
$318$		0			0
$319$	26.3604	+	45.6575i	0.0826345	+	0.143127i
$320$	−40.9706	−	23.6544i	−0.128033	−	0.0739199i
$321$		0			0
$322$		0			0
$323$	−541.456			−1.67633
$324$		0			0
$325$	−161.948	+	93.5009i	−0.498302	+	0.287695i
$326$	51.6812	+	89.5145i	0.158531	+	0.274584i
$327$		0			0
$328$		−	117.083i		−	0.356961i
$329$		0			0
$330$		0			0
$331$	−166.184	+	287.839i	−0.502066	+	0.869603i	0.497931	+	0.867216i	$0.334093\pi$
$331$	−166.184	+	287.839i	−0.502066	+	0.869603i	−0.999997	+	0.00238698i	$0.999240\pi$
$332$	−11.1472	+	6.43583i	−0.0335759	+	0.0193850i
$333$		0			0
$334$	−48.2498	−	27.8570i	−0.144460	−	0.0834043i
$335$			360.555i			1.07628i
$336$		0			0
$337$	88.1766			0.261652			0.130826	−	0.991405i	$-0.458237\pi$
$337$	88.1766			0.261652			0.130826	+	0.991405i	$0.458237\pi$
$338$	129.234	−	223.840i	0.382349	−	0.662248i
$339$		0			0
$340$	−138.853	−	240.500i	−0.408391	−	0.707353i
$341$	−13.1026	−	7.56479i	−0.0384240	−	0.0221841i
$342$		0			0
$343$		0			0
$344$	29.4903			0.0857277
$345$		0			0
$346$	−29.1838	+	16.8493i	−0.0843461	+	0.0486973i
$347$	−160.040	−	277.198i	−0.461211	−	0.798841i	0.537811	−	0.843066i	$-0.319251\pi$
$347$	−160.040	−	277.198i	−0.461211	−	0.798841i	−0.999022	+	0.0442250i	$0.985918\pi$
$348$		0			0
$349$		−	333.046i		−	0.954287i	−0.878825	−	0.477143i	$-0.841672\pi$
$349$		−	333.046i		−	0.954287i	0.878825	−	0.477143i	$-0.158328\pi$
$350$		0			0
$351$		0			0
$352$	−4.97056	+	8.60927i	−0.0141209	+	0.0244581i
$353$	567.864	−	327.856i	1.60868	−	0.928771i	0.619012	−	0.785381i	$-0.287533\pi$
$353$	567.864	−	327.856i	1.60868	−	0.928771i	0.989666	−	0.143390i	$-0.0458002\pi$
$354$		0			0
$355$	−566.470	−	327.052i	−1.59569	−	0.921272i
$356$			84.1829i			0.236469i
$357$		0			0
$358$	18.2498			0.0509770
$359$	−48.8787	+	84.6604i	−0.136152	+	0.235823i	−0.926037	−	0.377433i	$-0.876807\pi$
$359$	−48.8787	+	84.6604i	−0.136152	+	0.235823i	0.789885	+	0.613255i	$0.210140\pi$
$360$		0			0
$361$	85.3823	+	147.886i	0.236516	+	0.409658i
$362$	−80.0589	−	46.2220i	−0.221157	−	0.127685i
$363$		0			0
$364$		0			0
$365$	335.647			0.919580
$366$		0			0
$367$	−278.044	+	160.529i	−0.757612	+	0.437408i	−0.828438	−	0.560081i	$-0.810770\pi$
$367$	−278.044	+	160.529i	−0.757612	+	0.437408i	0.0708255	+	0.997489i	$0.477437\pi$
$368$	37.4558	+	64.8754i	0.101782	+	0.176292i
$369$		0			0
$370$		−	593.040i		−	1.60281i
$371$		0			0
$372$		0			0
$373$	−93.7351	+	162.354i	−0.251300	+	0.435265i	−0.963884	−	0.266322i	$-0.914192\pi$
$373$	−93.7351	+	162.354i	−0.251300	+	0.435265i	0.712584	+	0.701587i	$0.247525\pi$
$374$	−50.5370	+	29.1776i	−0.135126	+	0.0780149i
$375$		0			0
$376$	94.7939	+	54.7293i	0.252112	+	0.145557i
$377$		−	562.662i		−	1.49247i
$378$		0			0
$379$	−357.103			−0.942223			−0.471112	−	0.882074i	$-0.656147\pi$
$379$	−357.103			−0.942223			−0.471112	+	0.882074i	$0.656147\pi$
$380$	−136.368	+	236.195i	−0.358862	+	0.621567i
$381$		0			0
$382$	−70.7574	−	122.555i	−0.185229	−	0.320826i
$383$	538.867	+	311.115i	1.40696	+	0.812311i	0.995094	−	0.0989320i	$-0.0315426\pi$
$383$	538.867	+	311.115i	1.40696	+	0.812311i	0.411870	+	0.911243i	$0.364876\pi$
$384$		0			0
$385$		0			0
$386$	111.598			0.289114
$387$		0			0
$388$	89.5736	−	51.7153i	0.230860	−	0.133287i
$389$	113.735	+	196.995i	0.292378	+	0.506414i	0.974372	−	0.224945i	$-0.0722201\pi$
$389$	113.735	+	196.995i	0.292378	+	0.506414i	−0.681994	+	0.731358i	$0.738887\pi$
$390$		0			0
$391$			439.737i			1.12465i
$392$		0			0
$393$		0			0
$394$	−130.066	+	225.281i	−0.330117	+	0.571779i
$395$	−357.588	+	206.453i	−0.905286	+	0.522667i
$396$		0			0
$397$	−623.823	−	360.165i	−1.57134	−	0.907216i	−0.996005	−	0.0893004i	$-0.971537\pi$
$397$	−623.823	−	360.165i	−1.57134	−	0.907216i	−0.575339	−	0.817915i	$-0.695130\pi$
$398$			240.458i			0.604166i
$399$		0			0
$400$	−39.8823			−0.0997056
$401$	348.588	−	603.772i	0.869296	−	1.50567i	0.00657959	−	0.999978i	$-0.497906\pi$
$401$	348.588	−	603.772i	0.869296	−	1.50567i	0.862717	−	0.505687i	$-0.168761\pi$
$402$		0			0
$403$	80.7351	+	139.837i	0.200335	+	0.346991i
$404$	11.4487	+	6.60991i	0.0283384	+	0.0163612i
$405$		0			0
$406$		0			0
$407$	−124.617			−0.306185
$408$		0			0
$409$	88.6690	−	51.1931i	0.216795	−	0.125166i	−0.387671	−	0.921798i	$-0.626720\pi$
$409$	88.6690	−	51.1931i	0.216795	−	0.125166i	0.604465	+	0.796632i	$0.293387\pi$
$410$	−173.095	−	299.810i	−0.422184	−	0.731244i
$411$		0			0
$412$			351.742i			0.853742i
$413$		0			0
$414$		0			0
$415$	−19.0294	+	32.9600i	−0.0458541	+	0.0794216i
$416$	91.8823	−	53.0482i	0.220871	−	0.127520i
$417$		0			0
$418$	49.6325	+	28.6553i	0.118738	+	0.0685534i
$419$		−	391.426i		−	0.934191i	−0.884207	−	0.467095i	$-0.845300\pi$
$419$		−	391.426i		−	0.934191i	0.884207	−	0.467095i	$-0.154700\pi$
$420$		0			0
$421$	354.441			0.841902			0.420951	−	0.907083i	$-0.361696\pi$
$421$	354.441			0.841902			0.420951	+	0.907083i	$0.361696\pi$
$422$	−15.2548	+	26.4221i	−0.0361489	+	0.0626117i
$423$		0			0
$424$	−52.3675	−	90.7032i	−0.123508	−	0.213923i
$425$	−202.747	−	117.056i	−0.477051	−	0.275425i
$426$		0			0
$427$		0			0
$428$	92.4853			0.216087
$429$		0			0
$430$	75.5147	−	43.5984i	0.175616	−	0.101392i
$431$	292.643	+	506.873i	0.678987	+	1.17604i	0.975286	+	0.220944i	$0.0709139\pi$
$431$	292.643	+	506.873i	0.678987	+	1.17604i	−0.296300	+	0.955095i	$0.595753\pi$
$432$		0			0
$433$		−	392.207i		−	0.905789i	−0.891564	−	0.452895i	$-0.850391\pi$
$433$		−	392.207i		−	0.905789i	0.891564	−	0.452895i	$-0.149609\pi$
$434$		0			0
$435$		0			0
$436$	35.9411	−	62.2519i	0.0824338	−	0.142779i
$437$	374.007	−	215.933i	0.855852	−	0.494126i
$438$		0			0
$439$	339.926	+	196.256i	0.774319	+	0.447053i	0.834413	−	0.551140i	$-0.185807\pi$
$439$	339.926	+	196.256i	0.774319	+	0.447053i	−0.0600943	+	0.998193i	$0.519140\pi$
$440$			29.3939i			0.0668043i
$441$		0			0
$442$	622.794			1.40904
$443$	−407.371	+	705.587i	−0.919574	+	1.59275i	−0.119510	+	0.992833i	$0.538132\pi$
$443$	−407.371	+	705.587i	−0.919574	+	1.59275i	−0.800064	+	0.599915i	$0.795201\pi$
$444$		0			0
$445$	124.456	+	215.564i	0.279676	+	0.484413i
$446$	146.184	+	84.3992i	0.327766	+	0.189236i
$447$		0			0
$448$		0			0
$449$	−180.323			−0.401610			−0.200805	−	0.979631i	$-0.564356\pi$
$449$	−180.323			−0.401610			−0.200805	+	0.979631i	$0.564356\pi$
$450$		0			0
$451$	−63.0000	+	36.3731i	−0.139690	+	0.0806498i
$452$	−73.0294	−	126.491i	−0.161570	−	0.279847i
$453$		0			0
$454$			240.194i			0.529062i
$455$		0			0
$456$		0			0
$457$	−140.088	+	242.640i	−0.306539	+	0.530941i	−0.977603	−	0.210459i	$-0.932504\pi$
$457$	−140.088	+	242.640i	−0.306539	+	0.530941i	0.671064	+	0.741400i	$0.265838\pi$
$458$	−134.735	+	77.7893i	−0.294181	+	0.169846i
$459$		0			0
$460$	191.823	+	110.749i	0.417007	+	0.240759i
$461$		−	406.297i		−	0.881338i	−0.897670	−	0.440669i	$-0.854741\pi$
$461$		−	406.297i		−	0.881338i	0.897670	−	0.440669i	$-0.145259\pi$
$462$		0			0
$463$	457.470			0.988056			0.494028	−	0.869446i	$-0.335524\pi$
$463$	457.470			0.988056			0.494028	+	0.869446i	$0.335524\pi$
$464$	60.0000	−	103.923i	0.129310	−	0.223972i
$465$		0			0
$466$	40.4924	+	70.1349i	0.0868936	+	0.150504i
$467$	−557.470	−	321.856i	−1.19373	−	0.689198i	−0.234577	−	0.972098i	$-0.575370\pi$
$467$	−557.470	−	321.856i	−1.19373	−	0.689198i	−0.959150	+	0.282899i	$0.908704\pi$
$468$		0			0
$469$		0			0
$470$	323.647			0.688610
$471$		0			0
$472$	238.794	−	137.868i	0.505919	−	0.292093i
$473$	−9.16147	−	15.8681i	−0.0193689	−	0.0335479i
$474$		0			0
$475$			229.921i			0.484045i
$476$		0			0
$477$		0			0
$478$	199.066	−	344.792i	0.416456	−	0.721323i
$479$	−145.955	+	84.2674i	−0.304709	+	0.175924i	−0.644556	−	0.764557i	$-0.722958\pi$
$479$	−145.955	+	84.2674i	−0.304709	+	0.175924i	0.339848	+	0.940481i	$0.389624\pi$
$480$		0			0
$481$	1151.79	+	664.988i	2.39458	+	1.38251i
$482$			238.021i			0.493819i
$483$		0			0
$484$	−235.823			−0.487238
$485$	152.912	−	264.851i	0.315282	−	0.546084i
$486$		0			0
$487$	1.38983	+	2.40725i	0.00285385	+	0.00494302i	0.867449	−	0.497526i	$-0.165758\pi$
$487$	1.38983	+	2.40725i	0.00285385	+	0.00494302i	−0.864595	+	0.502469i	$0.832425\pi$
$488$	−40.9706	−	23.6544i	−0.0839561	−	0.0484721i
$489$		0			0
$490$		0			0
$491$	247.477			0.504027			0.252014	−	0.967724i	$-0.418907\pi$
$491$	247.477			0.504027			0.252014	+	0.967724i	$0.418907\pi$
$492$		0			0
$493$	610.036	−	352.204i	1.23739	−	0.714410i
$494$	−305.823	−	529.702i	−0.619076	−	1.07227i
$495$		0			0
$496$			34.4371i			0.0694296i
$497$		0			0
$498$		0			0
$499$	241.713	−	418.659i	0.484394	−	0.838996i	−0.515445	−	0.856923i	$-0.672373\pi$
$499$	241.713	−	418.659i	0.484394	−	0.838996i	0.999839	+	0.0179271i	$0.00570668\pi$
$500$	153.941	−	88.8780i	0.307882	−	0.177756i
$501$		0			0
$502$	129.941	+	75.0215i	0.258847	+	0.149445i
$503$		−	58.7033i		−	0.116706i	−0.998296	−	0.0583532i	$-0.981415\pi$
$503$		−	58.7033i		−	0.116706i	0.998296	−	0.0583532i	$-0.0185849\pi$
$504$		0			0
$505$	39.0883			0.0774026
$506$	23.2721	−	40.3084i	0.0459922	−	0.0796609i
$507$		0			0
$508$	−89.9411	−	155.783i	−0.177049	−	0.306659i
$509$	59.6512	+	34.4396i	0.117193	+	0.0676614i	0.557451	−	0.830210i	$-0.311780\pi$
$509$	59.6512	+	34.4396i	0.117193	+	0.0676614i	−0.440258	+	0.897871i	$0.645113\pi$
$510$		0			0
$511$		0			0
$512$	22.6274			0.0441942
$513$		0			0
$514$	355.742	−	205.388i	0.692105	−	0.399587i
$515$	520.014	+	900.691i	1.00974	+	1.74891i
$516$		0			0
$517$		−	68.0089i		−	0.131545i
$518$		0			0
$519$		0			0
$520$	156.853	−	271.677i	0.301640	−	0.522456i
$521$	−253.503	+	146.360i	−0.486570	+	0.280922i	−0.723151	−	0.690690i	$-0.757307\pi$
$521$	−253.503	+	146.360i	−0.486570	+	0.280922i	0.236580	+	0.971612i	$0.423973\pi$
$522$		0			0
$523$	−426.999	−	246.528i	−0.816442	−	0.471373i	0.0327460	−	0.999464i	$-0.489575\pi$
$523$	−426.999	−	246.528i	−0.816442	−	0.471373i	−0.849188	+	0.528091i	$0.822908\pi$
$524$		−	24.3507i		−	0.0464708i
$525$		0			0
$526$	125.897			0.239347
$527$	−101.074	+	175.065i	−0.191791	+	0.332192i
$528$		0			0
$529$	89.1325	+	154.382i	0.168492	+	0.291837i
$530$	−268.191	−	154.840i	−0.506021	−	0.292151i
$531$		0			0
$532$		0			0
$533$	776.382			1.45663
$534$		0			0
$535$	236.823	−	136.730i	0.442661	−	0.255570i
$536$	−86.2254	−	149.347i	−0.160868	−	0.278632i
$537$		0			0
$538$		−	270.819i		−	0.503381i
$539$		0			0
$540$		0			0
$541$	518.926	−	898.806i	0.959198	−	1.66138i	0.234742	−	0.972058i	$-0.424575\pi$
$541$	518.926	−	898.806i	0.959198	−	1.66138i	0.724456	−	0.689322i	$-0.242091\pi$
$542$	−266.309	+	153.753i	−0.491344	+	0.283678i
$543$		0			0
$544$	115.029	+	66.4123i	0.211451	+	0.122081i
$545$		−	212.541i		−	0.389984i
$546$		0			0
$547$	−130.530			−0.238629			−0.119314	−	0.992857i	$-0.538070\pi$
$547$	−130.530			−0.238629			−0.119314	+	0.992857i	$0.538070\pi$
$548$	165.765	−	287.113i	0.302490	−	0.523928i
$549$		0			0
$550$	12.3898	+	21.4598i	0.0225270	+	0.0390178i
$551$	−599.117	−	345.900i	−1.08733	−	0.627768i
$552$		0			0
$553$		0			0
$554$	411.078			0.742018
$555$		0			0
$556$	−381.941	+	220.514i	−0.686944	+	0.396608i
$557$	332.574	+	576.034i	0.597080	+	1.03417i	0.993250	+	0.115996i	$0.0370059\pi$
$557$	332.574	+	576.034i	0.597080	+	1.03417i	−0.396170	+	0.918177i	$0.629661\pi$
$558$		0			0
$559$			195.551i			0.349823i
$560$		0			0
$561$		0			0
$562$	13.3310	−	23.0899i	0.0237206	−	0.0410852i
$563$	−718.191	+	414.648i	−1.27565	+	0.736497i	−0.976045	−	0.217567i	$-0.930188\pi$
$563$	−718.191	+	414.648i	−1.27565	+	0.736497i	−0.299604	+	0.954064i	$0.596855\pi$
$564$		0			0
$565$	−374.007	−	215.933i	−0.661960	−	0.382183i
$566$		−	568.137i		−	1.00378i
$567$		0			0
$568$	312.853			0.550797
$569$	353.485	−	612.254i	0.621240	−	1.07602i	−0.368016	−	0.929820i	$-0.619963\pi$
$569$	353.485	−	612.254i	0.621240	−	1.07602i	0.989255	−	0.146199i	$-0.0467039\pi$
$570$		0			0
$571$	183.456	+	317.755i	0.321289	+	0.556488i	0.980754	−	0.195246i	$-0.0625507\pi$
$571$	183.456	+	317.755i	0.321289	+	0.556488i	−0.659466	+	0.751735i	$0.729217\pi$
$572$	−57.0883	−	32.9600i	−0.0998047	−	0.0576223i
$573$		0			0
$574$		0			0
$575$	186.728			0.324744
$576$		0			0
$577$	−338.059	+	195.178i	−0.585891	+	0.338264i	−0.763471	−	0.645842i	$-0.776506\pi$
$577$	−338.059	+	195.178i	−0.585891	+	0.338264i	0.177580	+	0.984106i	$0.443173\pi$
$578$	185.491	+	321.280i	0.320919	+	0.555847i
$579$		0			0
$580$		−	354.815i		−	0.611751i
$581$		0			0
$582$		0			0
$583$	−32.5370	+	56.3558i	−0.0558096	+	0.0966651i
$584$	−139.029	+	80.2687i	−0.238064	+	0.137446i
$585$		0			0
$586$	−344.022	−	198.621i	−0.587069	−	0.338944i
$587$			702.499i			1.19676i	0.801212	+	0.598381i	$0.204189\pi$
$587$			702.499i			1.19676i	−0.801212	+	0.598381i	$0.795811\pi$
$588$		0			0
$589$	198.530			0.337063
$590$	407.647	−	706.065i	0.690927	−	1.19672i
$591$		0			0
$592$	141.823	+	245.645i	0.239567	+	0.414941i
$593$	816.245	+	471.259i	1.37647	+	0.794704i	0.991732	−	0.128323i	$-0.0409594\pi$
$593$	816.245	+	471.259i	1.37647	+	0.794704i	0.384735	+	0.923027i	$0.374293\pi$
$594$		0			0
$595$		0			0
$596$	−421.706			−0.707560
$597$		0			0
$598$	−430.191	+	248.371i	−0.719383	+	0.415336i
$599$	−476.054	−	824.550i	−0.794749	−	1.37655i	−0.922999	−	0.384803i	$-0.874269\pi$
$599$	−476.054	−	824.550i	−0.794749	−	1.37655i	0.128250	−	0.991742i	$-0.459064\pi$
$600$		0			0
$601$			729.804i			1.21432i	0.794581	+	0.607158i	$0.207690\pi$
$601$			729.804i			1.21432i	−0.794581	+	0.607158i	$0.792310\pi$
$602$		0			0
$603$		0			0
$604$	72.3675	−	125.344i	0.119814	−	0.207524i
$605$	−603.864	+	348.641i	−0.998122	+	0.576266i
$606$		0			0
$607$	871.514	+	503.169i	1.43577	+	0.828944i	0.997552	−	0.0699241i	$-0.0222757\pi$
$607$	871.514	+	503.169i	1.43577	+	0.828944i	0.438220	+	0.898868i	$0.355609\pi$
$608$		−	130.447i		−	0.214551i
$609$		0			0
$610$	−139.882			−0.229315
$611$	−362.912	+	628.581i	−0.593963	+	1.02877i
$612$		0			0
$613$	99.7939	+	172.848i	0.162796	+	0.281971i	0.935870	−	0.352344i	$-0.114615\pi$
$613$	99.7939	+	172.848i	0.162796	+	0.281971i	−0.773074	+	0.634315i	$0.781282\pi$
$614$	−186.551	−	107.705i	−0.303829	−	0.175416i
$615$		0			0
$616$		0			0
$617$	353.294			0.572599			0.286299	−	0.958140i	$-0.407575\pi$
$617$	353.294			0.572599			0.286299	+	0.958140i	$0.407575\pi$
$618$		0			0
$619$	−48.6762	+	28.1032i	−0.0786368	+	0.0454010i	−0.538803	−	0.842432i	$-0.681123\pi$
$619$	−48.6762	+	28.1032i	−0.0786368	+	0.0454010i	0.460166	+	0.887833i	$0.347790\pi$
$620$	50.9117	+	88.1816i	0.0821156	+	0.142228i
$621$		0			0
$622$			400.443i			0.643799i
$623$		0			0
$624$		0			0
$625$	387.426	−	671.041i	0.619882	−	1.07367i
$626$	59.5004	−	34.3526i	0.0950486	−	0.0548763i
$627$		0			0
$628$	−404.735	−	233.674i	−0.644483	−	0.372092i
$629$			1665.03i			2.64710i
$630$		0			0
$631$	807.322			1.27943			0.639716	−	0.768611i	$-0.279052\pi$
$631$	807.322			1.27943			0.639716	+	0.768611i	$0.279052\pi$
$632$	98.7452	−	171.032i	0.156242	−	0.270620i
$633$		0			0
$634$	−408.728	−	707.938i	−0.644681	−	1.11662i
$635$	−460.617	−	265.938i	−0.725382	−	0.418799i
$636$		0			0
$637$		0			0
$638$	−74.5584			−0.116863
$639$		0			0
$640$	57.9411	−	33.4523i	0.0905330	−	0.0522693i
$641$	508.176	+	880.186i	0.792786	+	1.37315i	0.924236	+	0.381823i	$0.124703\pi$
$641$	508.176	+	880.186i	0.792786	+	1.37315i	−0.131450	+	0.991323i	$0.541963\pi$
$642$		0			0
$643$		−	404.688i		−	0.629375i	−0.949195	−	0.314687i	$-0.898100\pi$
$643$		−	404.688i		−	0.629375i	0.949195	−	0.314687i	$-0.101900\pi$
$644$		0			0
$645$		0			0
$646$	382.867	−	663.145i	0.592674	−	1.02654i
$647$	814.587	−	470.302i	1.25902	−	0.726896i	0.286137	−	0.958189i	$-0.407629\pi$
$647$	814.587	−	470.302i	1.25902	−	0.726896i	0.972884	+	0.231292i	$0.0742953\pi$
$648$		0			0
$649$	−148.368	−	85.6600i	−0.228609	−	0.131988i
$650$		−	264.460i		−	0.406862i
$651$		0			0
$652$	−146.177			−0.224197
$653$	365.985	−	633.904i	0.560467	−	0.970757i	−0.436989	−	0.899467i	$-0.643955\pi$
$653$	365.985	−	633.904i	0.560467	−	0.970757i	0.997456	−	0.0712901i	$-0.0227116\pi$
$654$		0			0
$655$	−36.0000	−	62.3538i	−0.0549618	−	0.0951967i
$656$	143.397	+	82.7903i	0.218593	+	0.126205i
$657$		0			0
$658$		0			0
$659$	−904.316			−1.37225			−0.686127	−	0.727481i	$-0.740691\pi$
$659$	−904.316			−1.37225			−0.686127	+	0.727481i	$0.740691\pi$
$660$		0			0
$661$	−290.881	+	167.940i	−0.440063	+	0.254070i	−0.703624	−	0.710572i	$-0.748436\pi$
$661$	−290.881	+	167.940i	−0.440063	+	0.254070i	0.263562	+	0.964643i	$0.415103\pi$
$662$	−235.019	−	407.065i	−0.355014	−	0.614902i
$663$		0			0
$664$		−	18.2033i		−	0.0274146i
$665$		0			0
$666$		0			0
$667$	−280.919	+	486.566i	−0.421168	+	0.729484i
$668$	68.2355	−	39.3958i	0.102149	−	0.0589757i
$669$		0			0
$670$	−441.588	−	254.951i	−0.659086	−	0.380524i
$671$			29.3939i			0.0438061i
$672$		0			0
$673$	1191.44			1.77034			0.885171	−	0.465266i	$-0.154041\pi$
$673$	1191.44			1.77034			0.885171	+	0.465266i	$0.154041\pi$
$674$	−62.3503	+	107.994i	−0.0925078	+	0.160228i
$675$		0			0
$676$	182.765	+	316.557i	0.270362	+	0.468280i
$677$	1048.82	+	605.536i	1.54922	+	0.894441i	0.998202	+	0.0599456i	$0.0190927\pi$
$677$	1048.82	+	605.536i	1.54922	+	0.894441i	0.551015	+	0.834495i	$0.314241\pi$
$678$		0			0
$679$		0			0
$680$	392.735			0.577552
$681$		0			0
$682$	18.5299	−	10.6982i	0.0271699	−	0.0156865i
$683$	−616.945	−	1068.58i	−0.903287	−	1.56454i	−0.823201	−	0.567750i	$-0.807814\pi$
$683$	−616.945	−	1068.58i	−0.903287	−	1.56454i	−0.0800856	−	0.996788i	$-0.525519\pi$
$684$		0			0
$685$		−	980.264i		−	1.43104i
$686$		0			0
$687$		0			0
$688$	−20.8528	+	36.1181i	−0.0303093	+	0.0524973i
$689$	601.456	−	347.251i	0.872940	−	0.503992i
$690$		0			0
$691$	75.0883	+	43.3523i	0.108666	+	0.0627384i	0.553348	−	0.832950i	$-0.313350\pi$
$691$	75.0883	+	43.3523i	0.108666	+	0.0627384i	−0.444682	+	0.895689i	$0.646683\pi$
$692$		−	47.6569i		−	0.0688683i
$693$		0			0
$694$	452.662			0.652251
$695$	−652.014	+	1129.32i	−0.938150	+	1.62492i
$696$		0			0
$697$	485.985	+	841.750i	0.697252	+	1.20768i
$698$	407.897	+	235.499i	0.584379	+	0.337391i
$699$		0			0
$700$		0			0
$701$	149.147			0.212763			0.106382	−	0.994325i	$-0.466073\pi$
$701$	149.147			0.212763			0.106382	+	0.994325i	$0.466073\pi$
$702$		0			0
$703$	1416.15	−	817.612i	2.01443	−	1.16303i
$704$	−7.02944	−	12.1753i	−0.00998500	−	0.0172945i
$705$		0			0
$706$			927.317i			1.31348i
$707$		0			0
$708$		0			0
$709$	−94.8234	+	164.239i	−0.133742	+	0.231649i	−0.925116	−	0.379684i	$-0.876033\pi$
$709$	−94.8234	+	164.239i	−0.133742	+	0.231649i	0.791374	+	0.611332i	$0.209366\pi$
$710$	801.110	−	462.521i	1.12832	−	0.651438i
$711$		0			0
$712$	−103.103	−	59.5263i	−0.144807	−	0.0836044i
$713$		−	161.234i		−	0.226134i
$714$		0			0
$715$	−194.912			−0.272604
$716$	−12.9045	+	22.3513i	−0.0180231	+	0.0312169i
$717$		0			0
$718$	−69.1249	−	119.728i	−0.0962742	−	0.166752i
$719$	−10.3978	−	6.00319i	−0.0144615	−	0.00834937i	0.492752	−	0.870170i	$-0.335991\pi$
$719$	−10.3978	−	6.00319i	−0.0144615	−	0.00834937i	−0.507213	+	0.861821i	$0.669324\pi$
$720$		0			0
$721$		0			0
$722$	−241.497			−0.334484
$723$		0			0
$724$	113.220	−	65.3678i	0.156382	−	0.0902870i
$725$	−149.558	−	259.043i	−0.206288	−	0.357300i
$726$		0			0
$727$		−	417.169i		−	0.573823i	−0.957957	−	0.286911i	$-0.907371\pi$
$727$		−	417.169i		−	0.573823i	0.957957	−	0.286911i	$-0.0926286\pi$
$728$		0			0
$729$		0			0
$730$	−237.338	+	411.082i	−0.325121	+	0.563126i
$731$	−212.016	+	122.408i	−0.290036	+	0.167452i
$732$		0			0
$733$	−1114.57	−	643.495i	−1.52055	−	0.877892i	−0.999706	−	0.0242419i	$-0.992283\pi$
$733$	−1114.57	−	643.495i	−1.52055	−	0.877892i	−0.520847	−	0.853650i	$-0.674384\pi$
$734$		−	454.043i		−	0.618588i
$735$		0			0
$736$	−105.941			−0.143942
$737$	−53.5736	+	92.7922i	−0.0726914	+	0.125905i
$738$		0			0
$739$	−666.735	−	1154.82i	−0.902213	−	1.56268i	−0.824616	−	0.565693i	$-0.808609\pi$
$739$	−666.735	−	1154.82i	−0.902213	−	1.56268i	−0.0775967	−	0.996985i	$-0.524725\pi$
$740$	726.323	+	419.343i	0.981517	+	0.566679i
$741$		0			0
$742$		0			0
$743$	776.476			1.04506			0.522528	−	0.852622i	$-0.324989\pi$
$743$	776.476			1.04506			0.522528	+	0.852622i	$0.324989\pi$
$744$		0			0
$745$	−1079.84	+	623.449i	−1.44946	+	0.836844i
$746$	−132.561	−	229.603i	−0.177696	−	0.307779i
$747$		0			0
$748$		−	82.5266i		−	0.110330i
$749$		0			0
$750$		0			0
$751$	−24.4193	+	42.2954i	−0.0325157	+	0.0563188i	−0.881825	−	0.471576i	$-0.843685\pi$
$751$	−24.4193	+	42.2954i	−0.0325157	+	0.0563188i	0.849310	+	0.527895i	$0.177019\pi$
$752$	−134.059	+	77.3989i	−0.178270	+	0.102924i
$753$		0			0
$754$	689.117	+	397.862i	0.913948	+	0.527668i
$755$		−	427.952i		−	0.566824i
$756$		0			0
$757$	−1279.47			−1.69019			−0.845093	−	0.534620i	$-0.820455\pi$
$757$	−1279.47			−1.69019			−0.845093	+	0.534620i	$0.820455\pi$
$758$	252.510	−	437.360i	0.333126	−	0.576992i
$759$		0			0
$760$	−192.853	−	334.031i	−0.253754	−	0.439514i
$761$	−1139.80	−	658.062i	−1.49776	−	0.864734i	−0.497766	−	0.867311i	$-0.665846\pi$
$761$	−1139.80	−	658.062i	−1.49776	−	0.864734i	−0.999997	+	0.00257751i	$0.999180\pi$
$762$		0			0
$763$		0			0
$764$	200.132			0.261953
$765$		0			0
$766$	−762.073	+	439.983i	−0.994874	+	0.574391i
$767$	914.205	+	1583.45i	1.19192	+	2.06447i
$768$		0			0
$769$		−	110.324i		−	0.143464i	−0.997424	−	0.0717320i	$-0.977147\pi$
$769$		−	110.324i		−	0.143464i	0.997424	−	0.0717320i	$-0.0228526\pi$
$770$		0			0
$771$		0			0
$772$	−78.9117	+	136.679i	−0.102217	+	0.177045i
$773$	621.489	−	358.817i	0.803996	−	0.464187i	−0.0408706	−	0.999164i	$-0.513013\pi$
$773$	621.489	−	358.817i	0.803996	−	0.464187i	0.844867	+	0.534977i	$0.179680\pi$
$774$		0			0
$775$	74.3390	+	42.9196i	0.0959212	+	0.0553802i
$776$			146.273i			0.188496i
$777$		0			0
$778$	−321.691			−0.413485
$779$	477.286	−	826.684i	0.612691	−	1.06121i
$780$		0			0
$781$	−97.1909	−	168.340i	−0.124444	−	0.215544i
$782$	−538.566	−	310.941i	−0.688703	−	0.397623i
$783$		0			0
$784$		0			0
$785$	−1381.85			−1.76032
$786$		0			0
$787$	−300.676	+	173.595i	−0.382054	+	0.220579i	−0.678711	−	0.734405i	$-0.737461\pi$
$787$	−300.676	+	173.595i	−0.382054	+	0.220579i	0.296658	+	0.954984i	$0.404128\pi$
$788$	−183.941	−	318.595i	−0.233428	−	0.404309i
$789$		0			0
$790$		−	583.939i		−	0.739163i
$791$		0			0
$792$		0			0
$793$	156.853	−	271.677i	0.197797	−	0.342594i
$794$	882.219	−	509.350i	1.11111	−	0.641498i
$795$		0			0
$796$	−294.500	−	170.029i	−0.369974	−	0.213605i
$797$		−	361.246i		−	0.453257i	−0.973981	−	0.226629i	$-0.927230\pi$
$797$		−	361.246i		−	0.453257i	0.973981	−	0.226629i	$-0.0727704\pi$
$798$		0			0
$799$	−908.674			−1.13726
$800$	28.2010	−	48.8456i	0.0352513	−	0.0610570i
$801$		0			0
$802$	492.978	+	853.862i	0.614685	+	1.06467i
$803$	86.3818	+	49.8726i	0.107574	+	0.0621078i
$804$		0			0
$805$		0			0
$806$	−228.353			−0.283317
$807$		0			0
$808$	−16.1909	+	9.34783i	−0.0200383	+	0.0115691i
$809$	−56.5736	−	97.9883i	−0.0699303	−	0.121123i	0.828940	−	0.559337i	$-0.188944\pi$
$809$	−56.5736	−	97.9883i	−0.0699303	−	0.121123i	−0.898870	+	0.438215i	$0.855611\pi$
$810$		0			0
$811$			134.182i			0.165453i	0.996572	+	0.0827264i	$0.0263628\pi$
$811$			134.182i			0.165453i	−0.996572	+	0.0827264i	$0.973637\pi$
$812$		0			0
$813$		0			0
$814$	88.1177	−	152.624i	0.108253	−	0.187499i
$815$	−374.309	+	216.107i	−0.459274	+	0.265162i
$816$		0			0
$817$	208.221	+	120.217i	0.254861	+	0.147144i
$818$			144.796i			0.177012i
$819$		0			0
$820$	489.588			0.597058
$821$	245.839	−	425.805i	0.299438	−	0.518642i	−0.676570	−	0.736379i	$-0.736534\pi$
$821$	245.839	−	425.805i	0.299438	−	0.518642i	0.976007	+	0.217737i	$0.0698675\pi$
$822$		0			0
$823$	470.926	+	815.668i	0.572207	+	0.991091i	0.996339	+	0.0854906i	$0.0272458\pi$
$823$	470.926	+	815.668i	0.572207	+	0.991091i	−0.424132	+	0.905600i	$0.639421\pi$
$824$	−430.794	−	248.719i	−0.522808	−	0.301843i
$825$		0			0
$826$		0			0
$827$	−966.978			−1.16926			−0.584630	−	0.811300i	$-0.698760\pi$
$827$	−966.978			−1.16926			−0.584630	+	0.811300i	$0.698760\pi$
$828$		0			0
$829$	−1026.70	+	592.764i	−1.23848	+	0.715035i	−0.968783	−	0.247911i	$-0.920256\pi$
$829$	−1026.70	+	592.764i	−1.23848	+	0.715035i	−0.269694	+	0.962946i	$0.586923\pi$
$830$	−26.9117	−	46.6124i	−0.0324237	−	0.0561595i
$831$		0			0
$832$			150.043i			0.180340i
$833$		0			0
$834$		0			0
$835$	116.485	−	201.758i	0.139503	−	0.241627i
$836$	−70.1909	+	40.5247i	−0.0839604	+	0.0484746i
$837$		0			0
$838$	479.397	+	276.780i	0.572073	+	0.330286i
$839$		−	1376.91i		−	1.64113i	−0.571550	−	0.820567i	$-0.693658\pi$
$839$		−	1376.91i		−	1.64113i	0.571550	−	0.820567i	$-0.306342\pi$
$840$		0			0
$841$	59.0000			0.0701546
$842$	−250.627	+	434.099i	−0.297657	+	0.515558i
$843$		0			0
$844$	−21.5736	−	37.3666i	−0.0255611	−	0.0442732i
$845$	935.996	+	540.397i	1.10769	+	0.639523i
$846$		0			0
$847$		0			0
$848$	148.118			0.174667
$849$		0			0
$850$	286.727	−	165.542i	0.337326	−	0.194755i
$851$	−664.014	−	1150.11i	−0.780275	−	1.35148i
$852$		0			0
$853$		−	175.006i		−	0.205165i	−0.994725	−	0.102582i	$-0.967289\pi$
$853$		−	175.006i		−	0.205165i	0.994725	−	0.102582i	$-0.0327105\pi$
$854$		0			0
$855$		0			0
$856$	−65.3970	+	113.271i	−0.0763983	+	0.132326i
$857$	53.4746	−	30.8736i	0.0623974	−	0.0360252i	−0.468477	−	0.883476i	$-0.655197\pi$
$857$	53.4746	−	30.8736i	0.0623974	−	0.0360252i	0.530874	+	0.847451i	$0.321864\pi$
$858$		0			0
$859$	165.676	+	95.6532i	0.192871	+	0.111354i	0.593326	−	0.804962i	$-0.297815\pi$
$859$	165.676	+	95.6532i	0.192871	+	0.111354i	−0.400455	+	0.916316i	$0.631148\pi$
$860$			123.315i			0.143390i
$861$		0			0
$862$	−827.720			−0.960232
$863$	−247.253	+	428.255i	−0.286504	+	0.496240i	−0.972973	−	0.230919i	$-0.925827\pi$
$863$	−247.253	+	428.255i	−0.286504	+	0.496240i	0.686468	+	0.727160i	$0.259160\pi$
$864$		0			0
$865$	−70.4558	−	122.033i	−0.0814518	−	0.141079i
$866$	480.353	+	277.332i	0.554680	+	0.320245i
$867$		0			0
$868$		0			0
$869$	−122.705			−0.141202
$870$		0			0
$871$	990.323	−	571.763i	1.13700	−	0.656445i
$872$	50.8284	+	88.0374i	0.0582895	+	0.100960i
$873$		0			0
$874$			610.751i			0.698800i
$875$		0			0
$876$		0			0
$877$	227.177	−	393.481i	0.259038	−	0.448668i	−0.706946	−	0.707267i	$-0.749928\pi$
$877$	227.177	−	393.481i	0.259038	−	0.448668i	0.965985	+	0.258600i	$0.0832611\pi$
$878$	−480.728	+	277.548i	−0.547526	+	0.316114i
$879$		0			0
$880$	−36.0000	−	20.7846i	−0.0409091	−	0.0236189i
$881$		−	143.493i		−	0.162875i	−0.996678	−	0.0814375i	$-0.974049\pi$
$881$		−	143.493i		−	0.162875i	0.996678	−	0.0814375i	$-0.0259511\pi$
$882$		0			0
$883$	−927.986			−1.05095			−0.525473	−	0.850810i	$-0.676112\pi$
$883$	−927.986			−1.05095			−0.525473	+	0.850810i	$0.676112\pi$
$884$	−440.382	+	762.764i	−0.498169	+	0.862855i
$885$		0			0
$886$	−576.110	−	997.851i	−0.650237	−	1.12624i
$887$	829.882	+	479.133i	0.935606	+	0.540172i	0.888580	−	0.458721i	$-0.151692\pi$
$887$	829.882	+	479.133i	0.935606	+	0.540172i	0.0470256	+	0.998894i	$0.485026\pi$
$888$		0			0
$889$		0			0
$890$	−352.014			−0.395522
$891$		0			0
$892$	−206.735	+	119.359i	−0.231766	+	0.133810i
$893$	446.205	+	772.850i	0.499670	+	0.865454i
$894$		0			0
$895$			76.3122i			0.0852650i
$896$		0			0
$897$		0			0
$898$	127.508	−	220.850i	0.141991	−	0.245935i
$899$	−223.675	+	129.139i	−0.248805	+	0.143647i
$900$		0			0
$901$	752.976	+	434.731i	0.835711	+	0.482498i
$902$		−	102.879i		−	0.114056i
$903$		0			0
$904$	206.558			0.228494
$905$	193.279	−	334.769i	0.213568	−	0.369911i
$906$		0			0
$907$	276.360	+	478.670i	0.304697	+	0.527751i	0.977194	−	0.212349i	$-0.0681114\pi$
$907$	276.360	+	478.670i	0.304697	+	0.527751i	−0.672497	+	0.740100i	$0.734778\pi$
$908$	−294.177	−	169.843i	−0.323983	−	0.187052i
$909$		0			0
$910$		0			0
$911$	−142.742			−0.156687			−0.0783437	−	0.996926i	$-0.524963\pi$
$911$	−142.742			−0.156687			−0.0783437	+	0.996926i	$0.524963\pi$
$912$		0			0
$913$	−9.79481	+	5.65503i	−0.0107282	+	0.00619390i
$914$	−198.115	−	343.145i	−0.216756	−	0.375432i
$915$		0			0
$916$		−	220.021i		−	0.240198i
$917$		0			0
$918$		0			0
$919$	−543.227	+	940.898i	−0.591107	+	1.02383i	0.402976	+	0.915210i	$0.367976\pi$
$919$	−543.227	+	940.898i	−0.591107	+	1.02383i	−0.994084	+	0.108617i	$0.965358\pi$
$920$	−271.279	+	156.623i	−0.294869	+	0.170243i
$921$		0			0
$922$	497.610	+	287.295i	0.539707	+	0.311600i
$923$			2074.54i			2.24760i
$924$		0			0
$925$	707.029			0.764356
$926$	−323.480	+	560.284i	−0.349331	+	0.605059i
$927$		0			0
$928$	84.8528	+	146.969i	0.0914362	+	0.158372i
$929$	−1342.99	−	775.374i	−1.44563	−	0.834633i	−0.447410	−	0.894329i	$-0.647654\pi$
$929$	−1342.99	−	775.374i	−1.44563	−	0.834633i	−0.998217	+	0.0596956i	$0.980987\pi$
$930$		0			0
$931$		0			0
$932$	−114.530			−0.122886
$933$		0			0
$934$	788.382	−	455.172i	0.844092	−	0.487337i
$935$	−122.007	−	211.323i	−0.130489	−	0.226013i
$936$		0			0
$937$			759.317i			0.810370i	0.914235	+	0.405185i	$0.132793\pi$
$937$			759.317i			0.810370i	−0.914235	+	0.405185i	$0.867207\pi$
$938$		0			0
$939$		0			0
$940$	−228.853	+	396.385i	−0.243460	+	0.421686i
$941$	−31.4817	+	18.1760i	−0.0334556	+	0.0193156i	−0.516635	−	0.856206i	$-0.672815\pi$
$941$	−31.4817	+	18.1760i	−0.0334556	+	0.0193156i	0.483179	+	0.875522i	$0.339482\pi$
$942$		0			0
$943$	−671.382	−	387.622i	−0.711964	−	0.411052i
$944$			389.949i			0.413081i
$945$		0			0
$946$	25.9126			0.0273917
$947$	46.2685	−	80.1394i	0.0488580	−	0.0846245i	−0.840562	−	0.541715i	$-0.817775\pi$
$947$	46.2685	−	80.1394i	0.0488580	−	0.0846245i	0.889420	+	0.457091i	$0.151108\pi$
$948$		0			0
$949$	−532.264	−	921.908i	−0.560868	−	0.971452i
$950$	−281.595	−	162.579i	−0.296416	−	0.171136i
$951$		0			0
$952$		0			0
$953$	1361.29			1.42843			0.714215	−	0.699927i	$-0.246784\pi$
$953$	1361.29			1.42843			0.714215	+	0.699927i	$0.246784\pi$
$954$		0			0
$955$	512.470	−	295.875i	0.536618	−	0.309817i
$956$	281.522	+	487.610i	0.294479	+	0.510052i
$957$		0			0
$958$		−	238.344i		−	0.248794i
$959$		0			0
$960$		0			0
$961$	−443.440	+	768.061i	−0.461436	+	0.799231i
$962$	−1628.88	+	940.435i	−1.69322	+	0.977583i
$963$		0			0
$964$	−291.515	−	168.306i	−0.302401	−	0.174591i
$965$			466.651i			0.483577i
$966$		0			0
$967$	481.677			0.498115			0.249057	−	0.968489i	$-0.419879\pi$
$967$	481.677			0.498115			0.249057	+	0.968489i	$0.419879\pi$
$968$	166.752	−	288.823i	0.172265	−	0.298371i
$969$		0			0
$970$	216.250	+	374.556i	0.222938	+	0.386140i
$971$	−1236.12	−	713.672i	−1.27303	−	0.734987i	−0.297476	−	0.954729i	$-0.596145\pi$
$971$	−1236.12	−	713.672i	−1.27303	−	0.734987i	−0.975558	+	0.219743i	$0.929478\pi$
$972$		0			0
$973$		0			0
$974$	−3.93102			−0.00403596
$975$		0			0
$976$	57.9411	−	33.4523i	0.0593659	−	0.0342749i
$977$	−678.131	−	1174.56i	−0.694095	−	1.20221i	−0.970485	−	0.241163i	$-0.922471\pi$
$977$	−678.131	−	1174.56i	−0.694095	−	1.20221i	0.276389	−	0.961046i	$-0.410862\pi$
$978$		0			0
$979$			73.9698i			0.0755565i
$980$		0			0
$981$		0			0
$982$	−174.993	+	303.097i	−0.178200	+	0.308652i
$983$	−1139.26	+	657.754i	−1.15897	+	0.669129i	−0.951056	−	0.309019i	$-0.899999\pi$
$983$	−1139.26	+	657.754i	−1.15897	+	0.669129i	−0.207910	+	0.978148i	$0.566666\pi$
$984$		0			0
$985$	−942.021	−	543.876i	−0.956367	−	0.552159i
$986$			996.184i			1.01033i
$987$		0			0
$988$	864.999			0.875505
$989$	97.6325	−	169.104i	0.0987184	−	0.170985i
$990$		0			0
$991$	−521.640	−	903.506i	−0.526377	−	0.911712i	−0.999528	−	0.0307302i	$-0.990217\pi$
$991$	−521.640	−	903.506i	−0.526377	−	0.911712i	0.473151	−	0.880982i	$-0.343117\pi$
$992$	−42.1766	−	24.3507i	−0.0425168	−	0.0245471i
$993$		0			0
$994$		0			0
$995$	−1005.48			−1.01054
$996$		0			0
$997$	710.425	−	410.164i	0.712562	−	0.411398i	−0.0994467	−	0.995043i	$-0.531707\pi$
$997$	710.425	−	410.164i	0.712562	−	0.411398i	0.812009	+	0.583645i	$0.198374\pi$
$998$	341.833	+	592.073i	0.342519	+	0.593259i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.n.a.19.1		4
3.2	odd	2		294.3.g.b.19.2		4
7.2	even	3		126.3.c.b.55.4		4
7.3	odd	6	inner	882.3.n.a.325.1		4
7.4	even	3		882.3.n.d.325.1		4
7.5	odd	6		126.3.c.b.55.3		4
7.6	odd	2		882.3.n.d.19.1		4
21.2	odd	6		42.3.c.a.13.1	✓	4
21.5	even	6		42.3.c.a.13.2	yes	4
21.11	odd	6		294.3.g.c.31.2		4
21.17	even	6		294.3.g.b.31.2		4
21.20	even	2		294.3.g.c.19.2		4
28.19	even	6		1008.3.f.g.433.1		4
28.23	odd	6		1008.3.f.g.433.4		4
84.23	even	6		336.3.f.c.97.3		4
84.47	odd	6		336.3.f.c.97.2		4
105.2	even	12		1050.3.h.a.349.2		8
105.23	even	12		1050.3.h.a.349.7		8
105.44	odd	6		1050.3.f.a.601.4		4
105.47	odd	12		1050.3.h.a.349.3		8
105.68	odd	12		1050.3.h.a.349.6		8
105.89	even	6		1050.3.f.a.601.3		4
168.5	even	6		1344.3.f.f.769.1		4
168.107	even	6		1344.3.f.e.769.2		4
168.131	odd	6		1344.3.f.e.769.3		4
168.149	odd	6		1344.3.f.f.769.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.1	✓	4	21.2	odd	6
42.3.c.a.13.2	yes	4	21.5	even	6
126.3.c.b.55.3		4	7.5	odd	6
126.3.c.b.55.4		4	7.2	even	3
294.3.g.b.19.2		4	3.2	odd	2
294.3.g.b.31.2		4	21.17	even	6
294.3.g.c.19.2		4	21.20	even	2
294.3.g.c.31.2		4	21.11	odd	6
336.3.f.c.97.2		4	84.47	odd	6
336.3.f.c.97.3		4	84.23	even	6
882.3.n.a.19.1		4	1.1	even	1	trivial
882.3.n.a.325.1		4	7.3	odd	6	inner
882.3.n.d.19.1		4	7.6	odd	2
882.3.n.d.325.1		4	7.4	even	3
1008.3.f.g.433.1		4	28.19	even	6
1008.3.f.g.433.4		4	28.23	odd	6
1050.3.f.a.601.3		4	105.89	even	6
1050.3.f.a.601.4		4	105.44	odd	6
1050.3.h.a.349.2		8	105.2	even	12
1050.3.h.a.349.3		8	105.47	odd	12
1050.3.h.a.349.6		8	105.68	odd	12
1050.3.h.a.349.7		8	105.23	even	12
1344.3.f.e.769.2		4	168.107	even	6
1344.3.f.e.769.3		4	168.131	odd	6
1344.3.f.f.769.1		4	168.5	even	6
1344.3.f.f.769.4		4	168.149	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.12132 - 2.95680i) q^{5} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-5.12132 - 2.95680i) q^{5} +2.82843 q^{8} +(7.24264 - 4.18154i) q^{10} +(-0.878680 - 1.52192i) q^{11} +18.7554i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-20.3345 + 11.7401i) q^{17} +(19.9706 + 11.5300i) q^{19} +11.8272i q^{20} +2.48528 q^{22} +(9.36396 - 16.2189i) q^{23} +(4.98528 + 8.63476i) q^{25} +(-22.9706 - 13.2621i) q^{26} -30.0000 q^{29} +(7.45584 - 4.30463i) q^{31} +(-2.82843 - 4.89898i) q^{32} -33.2061i q^{34} +(35.4558 - 61.4113i) q^{37} +(-28.2426 + 16.3059i) q^{38} +(-14.4853 - 8.36308i) q^{40} -41.3951i q^{41} +10.4264 q^{43} +(-1.75736 + 3.04384i) q^{44} +(13.2426 + 22.9369i) q^{46} +(33.5147 + 19.3497i) q^{47} -14.1005 q^{50} +(32.4853 - 18.7554i) q^{52} +(-18.5147 - 32.0684i) q^{53} +10.3923i q^{55} +(21.2132 - 36.7423i) q^{58} +(84.4264 - 48.7436i) q^{59} +(-14.4853 - 8.36308i) q^{61} +12.1753i q^{62} +8.00000 q^{64} +(55.4558 - 96.0523i) q^{65} +(-30.4853 - 52.8021i) q^{67} +(40.6690 + 23.4803i) q^{68} +110.610 q^{71} +(-49.1543 + 28.3793i) q^{73} +(50.1421 + 86.8487i) q^{74} -46.1200i q^{76} +(34.9117 - 60.4688i) q^{79} +(20.4853 - 11.8272i) q^{80} +(50.6985 + 29.2708i) q^{82} -6.43583i q^{83} +138.853 q^{85} +(-7.37258 + 12.7697i) q^{86} +(-2.48528 - 4.30463i) q^{88} +(-36.4523 - 21.0457i) q^{89} -37.4558 q^{92} +(-47.3970 + 27.3647i) q^{94} +(-68.1838 - 118.098i) q^{95} +51.7153i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 12 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 - 12 * q^5	\( 4 q - 4 q^{4} - 12 q^{5} + 12 q^{10} - 12 q^{11} - 8 q^{16} + 12 q^{17} + 12 q^{19} - 24 q^{22} + 12 q^{23} - 14 q^{25} - 24 q^{26} - 120 q^{29} - 72 q^{31} + 40 q^{37} - 96 q^{38} - 24 q^{40} - 128 q^{43} - 24 q^{44} + 36 q^{46} + 168 q^{47} - 96 q^{50} + 96 q^{52} - 108 q^{53} + 168 q^{59} - 24 q^{61} + 32 q^{64} + 120 q^{65} - 88 q^{67} - 24 q^{68} + 120 q^{71} + 24 q^{73} + 144 q^{74} - 64 q^{79} + 48 q^{80} + 84 q^{82} + 216 q^{85} - 120 q^{86} + 24 q^{88} - 324 q^{89} - 48 q^{92} + 48 q^{94} - 120 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 12 * q^5 + 12 * q^10 - 12 * q^11 - 8 * q^16 + 12 * q^17 + 12 * q^19 - 24 * q^22 + 12 * q^23 - 14 * q^25 - 24 * q^26 - 120 * q^29 - 72 * q^31 + 40 * q^37 - 96 * q^38 - 24 * q^40 - 128 * q^43 - 24 * q^44 + 36 * q^46 + 168 * q^47 - 96 * q^50 + 96 * q^52 - 108 * q^53 + 168 * q^59 - 24 * q^61 + 32 * q^64 + 120 * q^65 - 88 * q^67 - 24 * q^68 + 120 * q^71 + 24 * q^73 + 144 * q^74 - 64 * q^79 + 48 * q^80 + 84 * q^82 + 216 * q^85 - 120 * q^86 + 24 * q^88 - 324 * q^89 - 48 * q^92 + 48 * q^94 - 120 * q^95

Introduction

L-functions

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