LMFDB - Embedded newform 1050.3.q.b.199.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.22986704741655040229376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 $ x^16 - 31x^12 + 880x^8 - 2511*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.5
Root			$-2.22431 + 0.596002i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.b.649.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.647280 - 1.12112i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.22960 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(15.1826 - 26.2970i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-28.9470 + 16.7125i) q^{19} +(-0.974040 - 12.0852i) q^{21} -1.83078i q^{22} +(30.9462 - 17.8668i) q^{23} +(4.24264 + 2.44949i) q^{24} +(3.95544 - 2.28367i) q^{26} +5.19615 q^{27} +(1.12472 + 13.9547i) q^{28} +32.8033 q^{29} +(39.5125 + 22.8125i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(1.12112 + 1.94184i) q^{33} -42.9428i q^{34} -6.00000 q^{36} +(34.6873 - 20.0267i) q^{37} +(-23.6351 + 40.9372i) q^{38} +(-2.79692 + 4.84440i) q^{39} +42.2993i q^{41} +(-9.73845 - 14.1125i) q^{42} +55.4597i q^{43} +(-1.29456 - 2.24224i) q^{44} +(25.2675 - 43.7646i) q^{46} +(-30.3745 - 52.6102i) q^{47} +6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(26.2970 + 45.5477i) q^{51} +(3.22960 - 5.59383i) q^{52} +(47.3438 + 27.3340i) q^{53} +(6.36396 - 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} -57.8939i q^{57} +(40.1757 - 23.1954i) q^{58} +(-11.4277 - 6.59780i) q^{59} +(34.1684 - 19.7271i) q^{61} +64.5236 q^{62} +(18.9713 + 9.00500i) q^{63} -8.00000 q^{64} +(2.74618 + 1.58551i) q^{66} +(34.7163 + 20.0434i) q^{67} +(-30.3651 - 52.5940i) q^{68} +61.8924i q^{69} +46.4480 q^{71} +(-7.34847 + 4.24264i) q^{72} +(68.2001 - 118.126i) q^{73} +(28.3220 - 49.0552i) q^{74} +66.8501i q^{76} +(0.728012 + 9.03263i) q^{77} +7.91088i q^{78} +(-21.1511 - 36.6348i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(29.9101 + 51.8059i) q^{82} +1.53725 q^{83} +(-21.9062 - 10.3981i) q^{84} +(39.2160 + 67.9240i) q^{86} +(-28.4085 + 49.2050i) q^{87} +(-3.17101 - 1.83078i) q^{88} +(30.2844 - 17.4847i) q^{89} +(-18.6070 + 12.8400i) q^{91} -71.4672i q^{92} +(-68.4376 + 39.5125i) q^{93} +(-74.4020 - 42.9560i) q^{94} +(8.48528 - 4.89898i) q^{96} -150.516 q^{97} +(-11.0982 - 68.4020i) q^{98} -3.88368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^9	$ 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−5.76140	+	3.97571i	−0.823057	+	0.567958i
$7$	−5.76140	+	3.97571i	−0.823057	+	0.567958i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.647280	−	1.12112i	0.0588436	−	0.101920i	−0.835103	−	0.550094i	$-0.814592\pi$
$11$	0.647280	−	1.12112i	0.0588436	−	0.101920i	0.893947	+	0.448174i	$0.147925\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	3.22960			0.248431			0.124215	−	0.992255i	$-0.460359\pi$
$13$	3.22960			0.248431			0.124215	+	0.992255i	$0.460359\pi$
$14$	−4.24500	+	8.94315i	−0.303214	+	0.638797i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	15.1826	−	26.2970i	0.893092	−	1.54688i	0.0569439	−	0.998377i	$-0.481864\pi$
$17$	15.1826	−	26.2970i	0.893092	−	1.54688i	0.836148	−	0.548504i	$-0.184802\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	−28.9470	+	16.7125i	−1.52352	+	0.879607i	−0.523912	+	0.851773i	$0.675528\pi$
$19$	−28.9470	+	16.7125i	−1.52352	+	0.879607i	−0.999613	+	0.0278345i	$0.991139\pi$
$20$		0			0
$21$	−0.974040	−	12.0852i	−0.0463829	−	0.575484i
$22$		−	1.83078i		−	0.0832175i
$23$	30.9462	−	17.8668i	1.34549	−	0.776818i	0.357881	−	0.933767i	$-0.383499\pi$
$23$	30.9462	−	17.8668i	1.34549	−	0.776818i	0.987607	+	0.156950i	$0.0501660\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	3.95544	−	2.28367i	0.152132	−	0.0878336i
$27$	5.19615			0.192450
$28$	1.12472	+	13.9547i	0.0401687	+	0.498384i
$29$	32.8033			1.13115			0.565574	−	0.824697i	$-0.308655\pi$
$29$	32.8033			1.13115			0.565574	+	0.824697i	$0.308655\pi$
$30$		0			0
$31$	39.5125	+	22.8125i	1.27460	+	0.735888i	0.975849	−	0.218444i	$-0.0700981\pi$
$31$	39.5125	+	22.8125i	1.27460	+	0.735888i	0.298747	+	0.954332i	$0.403431\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	1.12112	+	1.94184i	0.0339734	+	0.0588436i
$34$		−	42.9428i		−	1.26302i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	34.6873	−	20.0267i	0.937494	−	0.541262i	0.0483201	−	0.998832i	$-0.484613\pi$
$37$	34.6873	−	20.0267i	0.937494	−	0.541262i	0.889174	+	0.457570i	$0.151280\pi$
$38$	−23.6351	+	40.9372i	−0.621976	+	1.07729i
$39$	−2.79692	+	4.84440i	−0.0717158	+	0.124215i
$40$		0			0
$41$			42.2993i			1.03169i	0.856682	+	0.515845i	$0.172522\pi$
$41$			42.2993i			1.03169i	−0.856682	+	0.515845i	$0.827478\pi$
$42$	−9.73845	−	14.1125i	−0.231868	−	0.336012i
$43$			55.4597i			1.28976i	0.764283	+	0.644881i	$0.223093\pi$
$43$			55.4597i			1.28976i	−0.764283	+	0.644881i	$0.776907\pi$
$44$	−1.29456	−	2.24224i	−0.0294218	−	0.0509601i
$45$		0			0
$46$	25.2675	−	43.7646i	0.549293	−	0.951403i
$47$	−30.3745	−	52.6102i	−0.646266	−	1.11937i	−0.984008	−	0.178127i	$-0.942996\pi$
$47$	−30.3745	−	52.6102i	−0.646266	−	1.11937i	0.337741	−	0.941239i	$-0.390337\pi$
$48$	6.92820			0.144338
$49$	17.3875	−	45.8113i	0.354847	−	0.934924i
$50$		0			0
$51$	26.2970	+	45.5477i	0.515627	+	0.893092i
$52$	3.22960	−	5.59383i	0.0621077	−	0.107574i
$53$	47.3438	+	27.3340i	0.893280	+	0.515735i	0.875014	−	0.484098i	$-0.160852\pi$
$53$	47.3438	+	27.3340i	0.893280	+	0.515735i	0.0182660	+	0.999833i	$0.494185\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	11.2450	+	16.2957i	0.200804	+	0.290995i
$57$		−	57.8939i		−	1.01568i
$58$	40.1757	−	23.1954i	0.692684	−	0.399921i
$59$	−11.4277	−	6.59780i	−0.193690	−	0.111827i	0.400019	−	0.916507i	$-0.369004\pi$
$59$	−11.4277	−	6.59780i	−0.193690	−	0.111827i	−0.593709	+	0.804680i	$0.702337\pi$
$60$		0			0
$61$	34.1684	−	19.7271i	0.560137	−	0.323395i	−0.193064	−	0.981186i	$-0.561842\pi$
$61$	34.1684	−	19.7271i	0.560137	−	0.323395i	0.753200	+	0.657791i	$0.228509\pi$
$62$	64.5236			1.04070
$63$	18.9713	+	9.00500i	0.301132	+	0.142937i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	2.74618	+	1.58551i	0.0416087	+	0.0240228i
$67$	34.7163	+	20.0434i	0.518153	+	0.299156i	0.736179	−	0.676787i	$-0.236628\pi$
$67$	34.7163	+	20.0434i	0.518153	+	0.299156i	−0.218026	+	0.975943i	$0.569962\pi$
$68$	−30.3651	−	52.5940i	−0.446546	−	0.773440i
$69$			61.8924i			0.896992i
$70$		0			0
$71$	46.4480			0.654198			0.327099	−	0.944990i	$-0.393929\pi$
$71$	46.4480			0.654198			0.327099	+	0.944990i	$0.393929\pi$
$72$	−7.34847	+	4.24264i	−0.102062	+	0.0589256i
$73$	68.2001	−	118.126i	0.934247	−	1.61816i	0.158277	−	0.987395i	$-0.449406\pi$
$73$	68.2001	−	118.126i	0.934247	−	1.61816i	0.775970	−	0.630769i	$-0.217261\pi$
$74$	28.3220	−	49.0552i	0.382730	−	0.662908i
$75$		0			0
$76$			66.8501i			0.879607i
$77$	0.728012	+	9.03263i	0.00945470	+	0.117307i
$78$			7.91088i			0.101422i
$79$	−21.1511	−	36.6348i	−0.267736	−	0.463732i	0.700541	−	0.713612i	$-0.252942\pi$
$79$	−21.1511	−	36.6348i	−0.267736	−	0.463732i	−0.968277	+	0.249880i	$0.919609\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	29.9101	+	51.8059i	0.364758	+	0.631779i
$83$	1.53725			0.0185211			0.00926054	−	0.999957i	$-0.497052\pi$
$83$	1.53725			0.0185211			0.00926054	+	0.999957i	$0.497052\pi$
$84$	−21.9062	−	10.3981i	−0.260788	−	0.123787i
$85$		0			0
$86$	39.2160	+	67.9240i	0.456000	+	0.789814i
$87$	−28.4085	+	49.2050i	−0.326534	+	0.565574i
$88$	−3.17101	−	1.83078i	−0.0360342	−	0.0208044i
$89$	30.2844	−	17.4847i	0.340274	−	0.196457i	−0.320119	−	0.947377i	$-0.603723\pi$
$89$	30.2844	−	17.4847i	0.340274	−	0.196457i	0.660393	+	0.750920i	$0.270390\pi$
$90$		0			0
$91$	−18.6070	+	12.8400i	−0.204473	+	0.141098i
$92$		−	71.4672i		−	0.776818i
$93$	−68.4376	+	39.5125i	−0.735888	+	0.424865i
$94$	−74.4020	−	42.9560i	−0.791511	−	0.456979i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	−150.516			−1.55172			−0.775858	−	0.630907i	$-0.782683\pi$
$97$	−150.516			−1.55172			−0.775858	+	0.630907i	$0.782683\pi$
$98$	−11.0982	−	68.4020i	−0.113247	−	0.697979i
$99$	−3.88368			−0.0392291
$100$		0			0
$101$	103.806	+	59.9325i	1.02778	+	0.593391i	0.916349	−	0.400381i	$-0.131122\pi$
$101$	103.806	+	59.9325i	1.02778	+	0.593391i	0.111434	+	0.993772i	$0.464456\pi$
$102$	64.4142	+	37.1895i	0.631511	+	0.364603i
$103$	49.8245	+	86.2986i	0.483733	+	0.837851i	0.999825	−	0.0186825i	$-0.00594715\pi$
$103$	49.8245	+	86.2986i	0.483733	+	0.837851i	−0.516092	+	0.856533i	$0.672614\pi$
$104$		−	9.13469i		−	0.0878336i
$105$		0			0
$106$	77.3122			0.729360
$107$	40.6950	−	23.4953i	0.380327	−	0.219582i	−0.297634	−	0.954680i	$-0.596197\pi$
$107$	40.6950	−	23.4953i	0.380327	−	0.219582i	0.677961	+	0.735098i	$0.262864\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	−29.0802	+	50.3683i	−0.266791	+	0.462095i	−0.968031	−	0.250830i	$-0.919297\pi$
$109$	−29.0802	+	50.3683i	−0.266791	+	0.462095i	0.701241	+	0.712925i	$0.252630\pi$
$110$		0			0
$111$			69.3746i			0.624996i
$112$	25.2951	+	12.0067i	0.225849	+	0.107202i
$113$		−	211.102i		−	1.86816i	−0.357068	−	0.934078i	$-0.616224\pi$
$113$		−	211.102i		−	1.86816i	0.357068	−	0.934078i	$-0.383776\pi$
$114$	−40.9372	−	70.9053i	−0.359098	−	0.621976i
$115$		0			0
$116$	32.8033	−	56.8170i	0.282787	−	0.489802i
$117$	−4.84440	−	8.39075i	−0.0414052	−	0.0717158i
$118$	−18.6614			−0.158148
$119$	17.0762	+	211.869i	0.143498	+	1.78041i
$120$		0			0
$121$	59.6621	+	103.338i	0.493075	+	0.854031i
$122$	27.8983	−	48.3213i	0.228675	−	0.396077i
$123$	−63.4490	−	36.6323i	−0.515845	−	0.297823i
$124$	79.0250	−	45.6251i	0.637298	−	0.367944i
$125$		0			0
$126$	29.6025	−	2.38590i	0.234940	−	0.0189357i
$127$		−	90.2615i		−	0.710720i	−0.934729	−	0.355360i	$-0.884358\pi$
$127$		−	90.2615i		−	0.710720i	0.934729	−	0.355360i	$-0.115642\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−83.1896	−	48.0296i	−0.644881	−	0.372322i
$130$		0			0
$131$	−174.806	+	100.924i	−1.33440	+	0.770414i	−0.985970	−	0.166923i	$-0.946617\pi$
$131$	−174.806	+	100.924i	−1.33440	+	0.770414i	−0.348426	+	0.937336i	$0.613284\pi$
$132$	4.48449			0.0339734
$133$	100.331	−	211.372i	0.754368	−	1.58927i
$134$	56.6914			0.423070
$135$		0			0
$136$	−74.3791	−	42.9428i	−0.546905	−	0.315756i
$137$	−0.00352554	−	0.00203547i	−2.57339e−5	−	1.48575e-5i	0.499987	−	0.866033i	$-0.333338\pi$
$137$	−0.00352554	−	0.00203547i	−2.57339e−5	−	1.48575e-5i	−0.500013	+	0.866018i	$0.666671\pi$
$138$	43.7646	+	75.8024i	0.317134	+	0.549293i
$139$		−	115.950i		−	0.834169i	−0.908868	−	0.417085i	$-0.863052\pi$
$139$		−	115.950i		−	0.834169i	0.908868	−	0.417085i	$-0.136948\pi$
$140$		0			0
$141$	105.220			0.746244
$142$	56.8870	−	32.8437i	0.400613	−	0.231294i
$143$	2.09046	−	3.62078i	0.0146186	−	0.0253201i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$		−	192.899i		−	1.32123i
$147$	53.6589	+	65.7550i	0.365027	+	0.447313i
$148$		−	80.1068i		−	0.541262i
$149$	−2.59675	−	4.49770i	−0.0174278	−	0.0301859i	0.857180	−	0.515017i	$-0.172214\pi$
$149$	−2.59675	−	4.49770i	−0.0174278	−	0.0301859i	−0.874608	+	0.484831i	$0.838881\pi$
$150$		0			0
$151$	80.3710	−	139.207i	0.532258	−	0.921899i	−0.467032	−	0.884240i	$-0.654677\pi$
$151$	80.3710	−	139.207i	0.532258	−	0.921899i	0.999291	−	0.0376583i	$-0.0119898\pi$
$152$	47.2702	+	81.8744i	0.310988	+	0.538647i
$153$	−91.0954			−0.595395
$154$	7.27866	+	10.5479i	0.0472640	+	0.0684928i
$155$		0			0
$156$	5.59383	+	9.68881i	0.0358579	+	0.0621077i
$157$	−47.6157	+	82.4728i	−0.303285	+	0.525305i	−0.976878	−	0.213798i	$-0.931417\pi$
$157$	−47.6157	+	82.4728i	−0.303285	+	0.525305i	0.673593	+	0.739102i	$0.264750\pi$
$158$	−51.8095	−	29.9122i	−0.327908	−	0.189318i
$159$	−82.0019	+	47.3438i	−0.515735	+	0.297760i
$160$		0			0
$161$	−107.260	+	225.971i	−0.666214	+	1.40355i
$162$			12.7279i			0.0785674i
$163$	213.473	−	123.249i	1.30965	−	0.756128i	0.327615	−	0.944811i	$-0.393755\pi$
$163$	213.473	−	123.249i	1.30965	−	0.756128i	0.982038	+	0.188683i	$0.0604218\pi$
$164$	73.2645	+	42.2993i	0.446735	+	0.257923i
$165$		0			0
$166$	1.88274	−	1.08700i	0.0113418	−	0.00654819i
$167$	−14.9445			−0.0894879			−0.0447439	−	0.998998i	$-0.514247\pi$
$167$	−14.9445			−0.0894879			−0.0447439	+	0.998998i	$0.514247\pi$
$168$	−34.1820	+	2.75500i	−0.203464	+	0.0163988i
$169$	−158.570			−0.938282
$170$		0			0
$171$	86.8409	+	50.1376i	0.507841	+	0.293202i
$172$	96.0591	+	55.4597i	0.558483	+	0.322440i
$173$	83.8331	+	145.203i	0.484584	+	0.839325i	0.999843	−	0.0177099i	$-0.00563752\pi$
$173$	83.8331	+	145.203i	0.484584	+	0.839325i	−0.515259	+	0.857035i	$0.672304\pi$
$174$			80.3513i			0.461789i
$175$		0			0
$176$	−5.17824			−0.0294218
$177$	19.7934	−	11.4277i	0.111827	−	0.0645635i
$178$	24.7271	−	42.8286i	0.138916	−	0.240610i
$179$	33.4724	−	57.9759i	0.186997	−	0.323888i	−0.757251	−	0.653124i	$-0.773458\pi$
$179$	33.4724	−	57.9759i	0.186997	−	0.323888i	0.944248	+	0.329236i	$0.106791\pi$
$180$		0			0
$181$		−	24.9109i		−	0.137629i	−0.997629	−	0.0688146i	$-0.978078\pi$
$181$		−	24.9109i		−	0.137629i	0.997629	−	0.0688146i	$-0.0219217\pi$
$182$	−13.7097	+	28.8828i	−0.0753278	+	0.158697i
$183$			68.3367i			0.373425i
$184$	−50.5350	−	87.5291i	−0.274647	−	0.475702i
$185$		0			0
$186$	−55.8791	+	96.7854i	−0.300425	+	0.520352i
$187$	−19.6547	−	34.0430i	−0.105106	−	0.182048i
$188$	−121.498			−0.646266
$189$	−29.9371	+	20.6584i	−0.158397	+	0.109304i
$190$		0			0
$191$	6.80231	+	11.7819i	0.0356142	+	0.0616856i	0.883283	−	0.468840i	$-0.155328\pi$
$191$	6.80231	+	11.7819i	0.0356142	+	0.0616856i	−0.847669	+	0.530526i	$0.821995\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	157.978	+	91.2089i	0.818541	+	0.472585i	0.849913	−	0.526923i	$-0.176654\pi$
$193$	157.978	+	91.2089i	0.818541	+	0.472585i	−0.0313718	+	0.999508i	$0.509988\pi$
$194$	−184.344	+	106.431i	−0.950228	+	0.548615i
$195$		0			0
$196$	−61.9600	−	75.9273i	−0.316122	−	0.387384i
$197$		−	286.679i		−	1.45522i	−0.685989	−	0.727612i	$-0.740630\pi$
$197$		−	286.679i		−	1.45522i	0.685989	−	0.727612i	$-0.259370\pi$
$198$	−4.75652	+	2.74618i	−0.0240228	+	0.0138696i
$199$	2.74117	+	1.58262i	0.0137747	+	0.00795285i	0.506872	−	0.862022i	$-0.330802\pi$
$199$	2.74117	+	1.58262i	0.0137747	+	0.00795285i	−0.493097	+	0.869974i	$0.664135\pi$
$200$		0			0
$201$	−60.1303	+	34.7163i	−0.299156	+	0.172718i
$202$	169.515			0.839181
$203$	−188.993	+	130.416i	−0.931000	+	0.642445i
$204$	105.188			0.515627
$205$		0			0
$206$	122.045	+	70.4625i	0.592450	+	0.342051i
$207$	−92.8387	−	53.6004i	−0.448496	−	0.258939i
$208$	−6.45920	−	11.1877i	−0.0310539	−	0.0537869i
$209$			43.2708i			0.207037i
$210$		0			0
$211$	−179.324			−0.849878			−0.424939	−	0.905222i	$-0.639705\pi$
$211$	−179.324			−0.849878			−0.424939	+	0.905222i	$0.639705\pi$
$212$	94.6877	−	54.6679i	0.446640	−	0.257868i
$213$	−40.2252	+	69.6720i	−0.188851	+	0.327099i
$214$	33.2273	−	57.5514i	0.155268	−	0.268932i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−318.343	+	25.6578i	−1.46702	+	0.118239i
$218$			82.2512i			0.377299i
$219$	118.126	+	204.600i	0.539388	+	0.934247i
$220$		0			0
$221$	49.0336	−	84.9288i	0.221872	−	0.384293i
$222$	49.0552	+	84.9661i	0.220969	+	0.382730i
$223$	−71.3345			−0.319886			−0.159943	−	0.987126i	$-0.551131\pi$
$223$	−71.3345			−0.319886			−0.159943	+	0.987126i	$0.551131\pi$
$224$	39.4700	−	3.18120i	0.176205	−	0.0142018i
$225$		0			0
$226$	−149.271	−	258.546i	−0.660493	−	1.14401i
$227$	−71.2698	+	123.443i	−0.313964	+	0.543802i	−0.979217	−	0.202817i	$-0.934990\pi$
$227$	−71.2698	+	123.443i	−0.313964	+	0.543802i	0.665253	+	0.746618i	$0.268324\pi$
$228$	−100.275	−	57.8939i	−0.439804	−	0.253921i
$229$	−109.001	+	62.9320i	−0.475989	+	0.274812i	−0.718743	−	0.695276i	$-0.755282\pi$
$229$	−109.001	+	62.9320i	−0.475989	+	0.274812i	0.242755	+	0.970088i	$0.421949\pi$
$230$		0			0
$231$	−14.1794	−	6.73047i	−0.0613828	−	0.0291362i
$232$		−	92.7817i		−	0.399921i
$233$	142.258	−	82.1326i	0.610549	−	0.352500i	−0.162631	−	0.986687i	$-0.551998\pi$
$233$	142.258	−	82.1326i	0.610549	−	0.352500i	0.773180	+	0.634186i	$0.218665\pi$
$234$	−11.8663	−	6.85102i	−0.0507108	−	0.0292779i
$235$		0			0
$236$	−22.8555	+	13.1956i	−0.0968452	+	0.0559136i
$237$	73.2697			0.309155
$238$	170.728	+	247.411i	0.717344	+	1.03954i
$239$	50.4246			0.210982			0.105491	−	0.994420i	$-0.466359\pi$
$239$	50.4246			0.210982			0.105491	+	0.994420i	$0.466359\pi$
$240$		0			0
$241$	−169.006	−	97.5757i	−0.701270	−	0.404879i	0.106550	−	0.994307i	$-0.466020\pi$
$241$	−169.006	−	97.5757i	−0.701270	−	0.404879i	−0.807820	+	0.589429i	$0.799353\pi$
$242$	146.142	+	84.3749i	0.603891	+	0.348657i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$		−	78.9084i		−	0.323395i
$245$		0			0
$246$	−103.612			−0.421186
$247$	−93.4872	+	53.9748i	−0.378491	+	0.218522i
$248$	64.5236	−	111.758i	0.260176	−	0.450638i
$249$	−1.33130	+	2.30587i	−0.00534657	+	0.00926054i
$250$		0			0
$251$			328.725i			1.30966i	0.755775	+	0.654832i	$0.227260\pi$
$251$			328.725i			1.30966i	−0.755775	+	0.654832i	$0.772740\pi$
$252$	34.5684	−	23.8542i	0.137176	−	0.0946597i
$253$		−	46.2593i		−	0.182843i
$254$	−63.8245	−	110.547i	−0.251278	−	0.435225i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	201.596	+	349.175i	0.784420	+	1.35866i	0.929345	+	0.369213i	$0.120373\pi$
$257$	201.596	+	349.175i	0.784420	+	1.35866i	−0.144924	+	0.989443i	$0.546294\pi$
$258$	−135.848			−0.526543
$259$	−120.227	+	253.288i	−0.464197	+	0.977947i
$260$		0			0
$261$	−49.2050	−	85.2255i	−0.188525	−	0.326534i
$262$	−142.728	+	247.213i	−0.544765	+	0.943560i
$263$	−431.240	−	248.977i	−1.63970	−	0.946679i	−0.980937	−	0.194326i	$-0.937748\pi$
$263$	−431.240	−	248.977i	−1.63970	−	0.946679i	−0.658759	−	0.752354i	$-0.728919\pi$
$264$	5.49235	−	3.17101i	0.0208044	−	0.0120114i
$265$		0			0
$266$	−26.5830	−	329.822i	−0.0999360	−	1.23993i
$267$			60.5688i			0.226849i
$268$	69.4325	−	40.0869i	0.259077	−	0.149578i
$269$	155.357	+	89.6952i	0.577534	+	0.333439i	0.760153	−	0.649745i	$-0.225124\pi$
$269$	155.357	+	89.6952i	0.577534	+	0.333439i	−0.182619	+	0.983184i	$0.558457\pi$
$270$		0			0
$271$	−126.057	+	72.7792i	−0.465156	+	0.268558i	−0.714210	−	0.699932i	$-0.753214\pi$
$271$	−126.057	+	72.7792i	−0.465156	+	0.268558i	0.249054	+	0.968490i	$0.419880\pi$
$272$	−121.461			−0.446546
$273$	−3.14576	−	39.0303i	−0.0115229	−	0.142968i
$274$	−0.00575719			−2.10116e−5
$275$		0			0
$276$	107.201	+	61.8924i	0.388409	+	0.224248i
$277$	−185.057	−	106.843i	−0.668076	−	0.385714i	0.127271	−	0.991868i	$-0.459378\pi$
$277$	−185.057	−	106.843i	−0.668076	−	0.385714i	−0.795347	+	0.606154i	$0.792712\pi$
$278$	−81.9887	−	142.009i	−0.294923	−	0.510822i
$279$		−	136.875i		−	0.490592i
$280$		0			0
$281$	−349.479			−1.24370			−0.621849	−	0.783137i	$-0.713618\pi$
$281$	−349.479			−1.24370			−0.621849	+	0.783137i	$0.713618\pi$
$282$	128.868	−	74.4020i	0.456979	−	0.263837i
$283$	47.1253	−	81.6234i	0.166521	−	0.288422i	−0.770674	−	0.637230i	$-0.780080\pi$
$283$	47.1253	−	81.6234i	0.166521	−	0.288422i	0.937194	+	0.348808i	$0.113413\pi$
$284$	46.4480	−	80.4503i	0.163549	−	0.283276i
$285$		0			0
$286$		−	5.91271i		−	0.0206738i
$287$	−168.170	−	243.703i	−0.585957	−	0.849140i
$288$			16.9706i			0.0589256i
$289$	−316.521	−	548.230i	−1.09523	−	1.89699i
$290$		0			0
$291$	130.351	−	225.775i	0.447942	−	0.775858i
$292$	−136.400	−	236.252i	−0.467124	−	0.809082i
$293$	−195.931			−0.668707			−0.334354	−	0.942448i	$-0.608518\pi$
$293$	−195.931			−0.668707			−0.334354	+	0.942448i	$0.608518\pi$
$294$	112.214	+	42.5905i	0.381681	+	0.144866i
$295$		0			0
$296$	−56.6441	−	98.1104i	−0.191365	−	0.331454i
$297$	3.36337	−	5.82552i	0.0113245	−	0.0196145i
$298$	−6.36070	−	3.67235i	−0.0213446	−	0.0123233i
$299$	99.9440	−	57.7027i	0.334261	−	0.192986i
$300$		0			0
$301$	−220.492	−	319.526i	−0.732531	−	1.06155i
$302$		−	227.324i		−	0.752727i
$303$	−179.797	+	103.806i	−0.593391	+	0.342594i
$304$	115.788	+	66.8501i	0.380881	+	0.219902i
$305$		0			0
$306$	−111.569	+	64.4142i	−0.364603	+	0.210504i
$307$	−452.419			−1.47368			−0.736839	−	0.676069i	$-0.763682\pi$
$307$	−452.419			−1.47368			−0.736839	+	0.676069i	$0.763682\pi$
$308$	16.3730	+	7.77168i	0.0531590	+	0.0252327i
$309$	−172.597			−0.558567
$310$		0			0
$311$	−56.8889	−	32.8448i	−0.182922	−	0.105610i	0.405743	−	0.913987i	$-0.367013\pi$
$311$	−56.8889	−	32.8448i	−0.182922	−	0.105610i	−0.588665	+	0.808377i	$0.700346\pi$
$312$	13.7020	+	7.91088i	0.0439168	+	0.0253554i
$313$	177.290	+	307.075i	0.566422	+	0.981071i	0.996916	+	0.0784776i	$0.0250059\pi$
$313$	177.290	+	307.075i	0.566422	+	0.981071i	−0.430494	+	0.902593i	$0.641661\pi$
$314$			134.678i			0.428909i
$315$		0			0
$316$	−84.6045			−0.267736
$317$	−116.792	+	67.4299i	−0.368429	+	0.212713i	−0.672772	−	0.739850i	$-0.734896\pi$
$317$	−116.792	+	67.4299i	−0.368429	+	0.212713i	0.304343	+	0.952563i	$0.401563\pi$
$318$	−66.9543	+	115.968i	−0.210548	+	0.364680i
$319$	21.2329	−	36.7765i	0.0665609	−	0.115287i
$320$		0			0
$321$			81.3900i			0.253551i
$322$	28.4190	+	352.601i	0.0882576	+	1.09504i
$323$			1014.96i			3.14228i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	174.300	−	301.897i	0.534664	−	0.926064i
$327$	−50.3683	−	87.2405i	−0.154032	−	0.266791i
$328$	119.641			0.364758
$329$	384.162	+	182.348i	1.16767	+	0.554250i
$330$		0			0
$331$	90.2612	+	156.337i	0.272692	+	0.472317i	0.969550	−	0.244892i	$-0.0787525\pi$
$331$	90.2612	+	156.337i	0.272692	+	0.472317i	−0.696858	+	0.717209i	$0.745419\pi$
$332$	1.53725	−	2.66259i	0.00463027	−	0.00801986i
$333$	−104.062	−	60.0801i	−0.312498	−	0.180421i
$334$	−18.3032	+	10.5673i	−0.0547999	+	0.0316387i
$335$		0			0
$336$	−39.9162	+	27.5445i	−0.118798	+	0.0819777i
$337$			5.84677i			0.0173495i	0.999962	+	0.00867473i	$0.00276129\pi$
$337$			5.84677i			0.0173495i	−0.999962	+	0.00867473i	$0.997239\pi$
$338$	−194.207	+	112.126i	−0.574578	+	0.331733i
$339$	316.653	+	182.819i	0.934078	+	0.539290i
$340$		0			0
$341$	51.1513	−	29.5322i	0.150004	−	0.0866047i
$342$	141.811			0.414651
$343$	81.9559	+	333.065i	0.238938	+	0.971035i
$344$	156.864			0.456000
$345$		0			0
$346$	205.348	+	118.558i	0.593492	+	0.342653i
$347$	339.718	+	196.136i	0.979014	+	0.565234i	0.901972	−	0.431794i	$-0.142119\pi$
$347$	339.718	+	196.136i	0.979014	+	0.565234i	0.0770414	+	0.997028i	$0.475453\pi$
$348$	56.8170	+	98.4099i	0.163267	+	0.282787i
$349$		−	230.853i		−	0.661471i	−0.943724	−	0.330735i	$-0.892703\pi$
$349$		−	230.853i		−	0.661471i	0.943724	−	0.330735i	$-0.107297\pi$
$350$		0			0
$351$	16.7815			0.0478106
$352$	−6.34202	+	3.66157i	−0.0180171	+	0.0104022i
$353$	62.8188	−	108.805i	0.177957	−	0.308230i	−0.763224	−	0.646134i	$-0.776385\pi$
$353$	62.8188	−	108.805i	0.177957	−	0.308230i	0.941181	+	0.337904i	$0.109718\pi$
$354$	16.1613	−	27.9921i	0.0456533	−	0.0790738i
$355$		0			0
$356$		−	69.9388i		−	0.196457i
$357$	−332.592	−	157.870i	−0.931630	−	0.442212i
$358$		−	94.6743i		−	0.264453i
$359$	215.984	+	374.096i	0.601628	+	1.04205i	0.992575	+	0.121637i	$0.0388143\pi$
$359$	215.984	+	374.096i	0.601628	+	1.04205i	−0.390947	+	0.920413i	$0.627852\pi$
$360$		0			0
$361$	378.118	−	654.919i	1.04742	−	1.81418i
$362$	−17.6147	−	30.5095i	−0.0486593	−	0.0842803i
$363$	−206.675			−0.569354
$364$	3.63241	+	45.0683i	0.00997916	+	0.123814i
$365$		0			0
$366$	48.3213	+	83.6950i	0.132026	+	0.228675i
$367$	−236.049	+	408.849i	−0.643185	+	1.11403i	0.341532	+	0.939870i	$0.389054\pi$
$367$	−236.049	+	408.849i	−0.643185	+	1.11403i	−0.984717	+	0.174159i	$0.944279\pi$
$368$	−123.785	−	71.4672i	−0.336372	−	0.194204i
$369$	109.897	−	63.4490i	0.297823	−	0.171948i
$370$		0			0
$371$	−381.439	+	30.7432i	−1.02814	+	0.0828658i
$372$			158.050i			0.424865i
$373$	75.7963	−	43.7610i	0.203207	−	0.117322i	−0.394943	−	0.918705i	$-0.629236\pi$
$373$	75.7963	−	43.7610i	0.203207	−	0.117322i	0.598151	+	0.801384i	$0.295902\pi$
$374$	−48.1441	−	27.7960i	−0.128728	−	0.0743209i
$375$		0			0
$376$	−148.804	+	85.9121i	−0.395756	+	0.228490i
$377$	105.942			0.281012
$378$	−22.0577	+	46.4700i	−0.0583536	+	0.122936i
$379$	359.658			0.948965			0.474483	−	0.880265i	$-0.342635\pi$
$379$	359.658			0.948965			0.474483	+	0.880265i	$0.342635\pi$
$380$		0			0
$381$	135.392	+	78.1687i	0.355360	+	0.205167i
$382$	16.6622	+	9.61992i	0.0436183	+	0.0251830i
$383$	242.085	+	419.304i	0.632077	+	1.09479i	0.987126	+	0.159942i	$0.0511306\pi$
$383$	242.085	+	419.304i	0.632077	+	1.09479i	−0.355050	+	0.934847i	$0.615536\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	257.978			0.668336
$387$	144.089	−	83.1896i	0.372322	−	0.214960i
$388$	−150.516	+	260.702i	−0.387929	+	0.671913i
$389$	−179.791	+	311.407i	−0.462188	+	0.800533i	−0.999070	−	0.0431246i	$-0.986269\pi$
$389$	−179.791	+	311.407i	−0.462188	+	0.800533i	0.536882	+	0.843657i	$0.319602\pi$
$390$		0			0
$391$		−	1085.06i		−	2.77508i
$392$	−129.574	−	49.1793i	−0.330546	−	0.125457i
$393$		−	349.612i		−	0.889597i
$394$	−202.713	−	351.109i	−0.514499	−	0.891139i
$395$		0			0
$396$	−3.88368	+	6.72673i	−0.00980727	+	0.0169867i
$397$	−90.6969	−	157.092i	−0.228456	−	0.395697i	0.728895	−	0.684626i	$-0.240034\pi$
$397$	−90.6969	−	157.092i	−0.228456	−	0.395697i	−0.957351	+	0.288929i	$0.906701\pi$
$398$	4.47632			0.0112470
$399$	230.169	+	333.550i	0.576865	+	0.835965i
$400$		0			0
$401$	132.742	+	229.916i	0.331027	+	0.573355i	0.982713	−	0.185133i	$-0.0592716\pi$
$401$	132.742	+	229.916i	0.331027	+	0.573355i	−0.651687	+	0.758488i	$0.725938\pi$
$402$	−49.0962	+	85.0371i	−0.122130	+	0.211535i
$403$	127.610	+	73.6754i	0.316649	+	0.182817i
$404$	207.612	−	119.865i	0.513891	−	0.296695i
$405$		0			0
$406$	−139.250	+	293.365i	−0.342980	+	0.722574i
$407$		−	51.8516i		−	0.127399i
$408$	128.828	−	74.3791i	0.315756	−	0.182302i
$409$	492.567	+	284.384i	1.20432	+	0.695315i	0.961513	−	0.274759i	$-0.0885981\pi$
$409$	492.567	+	284.384i	1.20432	+	0.695315i	0.242808	+	0.970074i	$0.421931\pi$
$410$		0			0
$411$	0.00610642	−	0.00352554i	1.48575e−5	−	8.57797e-6i
$412$	199.298			0.483733
$413$	92.0707	−	7.42071i	0.222931	−	0.0179678i
$414$	−151.605			−0.366195
$415$		0			0
$416$	−15.8218	−	9.13469i	−0.0380331	−	0.0219584i
$417$	173.924	+	100.415i	0.417085	+	0.240804i
$418$	30.5970	+	52.9956i	0.0731987	+	0.126784i
$419$		−	556.041i		−	1.32707i	−0.748146	−	0.663534i	$-0.769056\pi$
$419$		−	556.041i		−	1.32707i	0.748146	−	0.663534i	$-0.230944\pi$
$420$		0			0
$421$	−476.267			−1.13128			−0.565638	−	0.824654i	$-0.691370\pi$
$421$	−476.267			−1.13128			−0.565638	+	0.824654i	$0.691370\pi$
$422$	−219.627	+	126.801i	−0.520442	+	0.300477i
$423$	−91.1235	+	157.831i	−0.215422	+	0.373122i
$424$	77.3122	−	133.909i	0.182340	−	0.315822i
$425$		0			0
$426$			113.774i			0.267075i
$427$	−118.428	+	249.499i	−0.277350	+	0.584307i
$428$		−	93.9810i		−	0.219582i
$429$	3.62078	+	6.27137i	0.00844004	+	0.0146186i
$430$		0			0
$431$	−229.808	+	398.039i	−0.533196	+	0.923523i	0.466052	+	0.884757i	$0.345676\pi$
$431$	−229.808	+	398.039i	−0.533196	+	0.923523i	−0.999248	+	0.0387660i	$0.987657\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	65.9185			0.152237			0.0761183	−	0.997099i	$-0.475747\pi$
$433$	65.9185			0.152237			0.0761183	+	0.997099i	$0.475747\pi$
$434$	−371.746	+	256.527i	−0.856559	+	0.591076i
$435$		0			0
$436$	58.1604	+	100.737i	0.133395	+	0.231047i
$437$	−597.199	+	1034.38i	−1.36659	+	2.36700i
$438$	289.348	+	167.055i	0.660613	+	0.381405i
$439$	307.619	−	177.604i	0.700727	−	0.404565i	−0.106891	−	0.994271i	$-0.534090\pi$
$439$	307.619	−	177.604i	0.700727	−	0.404565i	0.807618	+	0.589706i	$0.200756\pi$
$440$		0			0
$441$	−145.102	+	23.5429i	−0.329031	+	0.0533852i
$442$		−	138.688i		−	0.313774i
$443$	−656.650	+	379.117i	−1.48228	+	0.855795i	−0.999798	−	0.0201113i	$-0.993598\pi$
$443$	−656.650	+	379.117i	−1.48228	+	0.855795i	−0.482482	+	0.875906i	$0.660265\pi$
$444$	120.160	+	69.3746i	0.270631	+	0.156249i
$445$		0			0
$446$	−87.3666	+	50.4411i	−0.195889	+	0.113097i
$447$	8.99539			0.0201239
$448$	46.0912	−	31.8057i	0.102882	−	0.0709948i
$449$	−668.104			−1.48798			−0.743992	−	0.668189i	$-0.767070\pi$
$449$	−668.104			−1.48798			−0.743992	+	0.668189i	$0.767070\pi$
$450$		0			0
$451$	47.4227	+	27.3795i	0.105150	+	0.0607084i
$452$	−365.639	−	211.102i	−0.808936	−	0.467039i
$453$	139.207	+	241.113i	0.307300	+	0.532258i
$454$			201.581i			0.444012i
$455$		0			0
$456$	−163.749			−0.359098
$457$	645.475	−	372.665i	1.41242	−	0.815460i	0.416802	−	0.908997i	$-0.363151\pi$
$457$	645.475	−	372.665i	1.41242	−	0.815460i	0.995616	+	0.0935379i	$0.0298176\pi$
$458$	−88.9993	+	154.151i	−0.194322	+	0.336575i
$459$	78.8909	−	136.643i	0.171876	−	0.297697i
$460$		0			0
$461$		−	592.937i		−	1.28620i	−0.765783	−	0.643099i	$-0.777648\pi$
$461$		−	592.937i		−	1.28620i	0.765783	−	0.643099i	$-0.222352\pi$
$462$	−22.1253	+	1.78326i	−0.0478903	+	0.00385987i
$463$		−	529.829i		−	1.14434i	−0.820136	−	0.572169i	$-0.806102\pi$
$463$		−	529.829i		−	1.14434i	0.820136	−	0.572169i	$-0.193898\pi$
$464$	−65.6066	−	113.634i	−0.141394	−	0.244901i
$465$		0			0
$466$	116.153	−	201.183i	0.249255	−	0.431723i
$467$	83.6375	+	144.864i	0.179095	+	0.310202i	0.941571	−	0.336815i	$-0.109350\pi$
$467$	83.6375	+	144.864i	0.179095	+	0.310202i	−0.762476	+	0.647017i	$0.776016\pi$
$468$	−19.3776			−0.0414052
$469$	−279.701	+	22.5434i	−0.596378	+	0.0480669i
$470$		0			0
$471$	−82.4728	−	142.847i	−0.175102	−	0.303285i
$472$	−18.6614	+	32.3225i	−0.0395369	+	0.0684799i
$473$	62.1771	+	35.8980i	0.131453	+	0.0758943i
$474$	89.7367	−	51.8095i	0.189318	−	0.109303i
$475$		0			0
$476$	384.044	+	182.292i	0.806815	+	0.382966i
$477$		−	164.004i		−	0.343824i
$478$	61.7573	−	35.6556i	0.129199	−	0.0745933i
$479$	−221.195	−	127.707i	−0.461785	−	0.266612i	0.251009	−	0.967985i	$-0.419237\pi$
$479$	−221.195	−	127.707i	−0.461785	−	0.266612i	−0.712795	+	0.701373i	$0.752571\pi$
$480$		0			0
$481$	112.026	−	64.6783i	0.232902	−	0.134466i
$482$	−275.986			−0.572585
$483$	−246.066	−	356.587i	−0.509454	−	0.738276i
$484$	238.648			0.493075
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	525.531	+	303.415i	1.07912	+	0.623030i	0.930659	−	0.365889i	$-0.119235\pi$
$487$	525.531	+	303.415i	1.07912	+	0.623030i	0.148460	+	0.988918i	$0.452568\pi$
$488$	−55.7967	−	96.6427i	−0.114337	−	0.198038i
$489$			426.947i			0.873102i
$490$		0			0
$491$	707.855			1.44166			0.720830	−	0.693112i	$-0.243761\pi$
$491$	707.855			1.44166			0.720830	+	0.693112i	$0.243761\pi$
$492$	−126.898	+	73.2645i	−0.257923	+	0.148912i
$493$	498.038	−	862.628i	1.01022	−	1.74975i
$494$	−76.3319	+	132.211i	−0.154518	+	0.267633i
$495$		0			0
$496$		−	182.500i		−	0.367944i
$497$	−267.606	+	184.664i	−0.538442	+	0.371557i
$498$			3.76548i			0.00756120i
$499$	330.115	+	571.776i	0.661553	+	1.14584i	0.980208	+	0.197972i	$0.0634357\pi$
$499$	330.115	+	571.776i	0.661553	+	1.14584i	−0.318655	+	0.947871i	$0.603231\pi$
$500$		0			0
$501$	12.9423	−	22.4167i	0.0258329	−	0.0447439i
$502$	232.444	+	402.605i	0.463036	+	0.802002i
$503$	254.083			0.505136			0.252568	−	0.967579i	$-0.418725\pi$
$503$	254.083			0.505136			0.252568	+	0.967579i	$0.418725\pi$
$504$	25.4700	−	53.6589i	0.0505357	−	0.106466i
$505$		0			0
$506$	−32.7103	−	56.6559i	−0.0646448	−	0.111968i
$507$	137.325	−	237.855i	0.270859	−	0.469141i
$508$	−156.337	−	90.2615i	−0.307751	−	0.177680i
$509$	−222.003	+	128.174i	−0.436156	+	0.251815i	−0.701966	−	0.712211i	$-0.747694\pi$
$509$	−222.003	+	128.174i	−0.436156	+	0.251815i	0.265810	+	0.964026i	$0.414361\pi$
$510$		0			0
$511$	76.7063	+	951.715i	0.150110	+	1.86246i
$512$			22.6274i			0.0441942i
$513$	−150.413	+	86.8409i	−0.293202	+	0.169280i
$514$	493.807	+	285.100i	0.960715	+	0.554669i
$515$		0			0
$516$	−166.379	+	96.0591i	−0.322440	+	0.186161i
$517$	−78.6433			−0.152115
$518$	31.8545	+	395.227i	0.0614952	+	0.762986i
$519$	−290.406			−0.559550
$520$		0			0
$521$	164.700	+	95.0898i	0.316124	+	0.182514i	0.649663	−	0.760222i	$-0.274910\pi$
$521$	164.700	+	95.0898i	0.316124	+	0.182514i	−0.333540	+	0.942736i	$0.608243\pi$
$522$	−120.527	−	69.5863i	−0.230895	−	0.133307i
$523$	−173.610	−	300.701i	−0.331950	−	0.574954i	0.650944	−	0.759126i	$-0.274373\pi$
$523$	−173.610	−	300.701i	−0.331950	−	0.574954i	−0.982894	+	0.184171i	$0.941040\pi$
$524$			403.697i			0.770414i
$525$		0			0
$526$	−704.212			−1.33881
$527$	1199.80	−	692.706i	2.27666	−	1.31443i
$528$	4.48449	−	7.76736i	0.00849335	−	0.0147109i
$529$	373.946	−	647.693i	0.706891	−	1.22437i
$530$		0			0
$531$			39.5868i			0.0745515i
$532$	−265.777	−	385.151i	−0.499580	−	0.723967i
$533$			136.610i			0.256304i
$534$	42.8286	+	74.1813i	0.0802033	+	0.138916i
$535$		0			0
$536$	56.6914	−	98.1924i	0.105768	−	0.183195i
$537$	57.9759	+	100.417i	0.107963	+	0.186997i
$538$	253.696			0.471554
$539$	−40.1055	−	49.1462i	−0.0744072	−	0.0911804i
$540$		0			0
$541$	−216.672	−	375.287i	−0.400503	−	0.693691i	0.593284	−	0.804993i	$-0.297831\pi$
$541$	−216.672	−	375.287i	−0.400503	−	0.693691i	−0.993787	+	0.111302i	$0.964498\pi$
$542$	−102.925	+	178.272i	−0.189899	+	0.328915i
$543$	37.3663	+	21.5735i	0.0688146	+	0.0397301i
$544$	−148.758	+	85.8856i	−0.273452	+	0.157878i
$545$		0			0
$546$	−31.4513	−	45.5777i	−0.0576032	−	0.0834757i
$547$		−	718.061i		−	1.31272i	−0.754446	−	0.656362i	$-0.772094\pi$
$547$		−	718.061i		−	1.31272i	0.754446	−	0.656362i	$-0.227906\pi$
$548$	−0.00705109	+	0.00407095i	−1.28670e−5	+	7.42874e-6i
$549$	−102.505	−	59.1813i	−0.186712	−	0.107798i
$550$		0			0
$551$	−949.556	+	548.226i	−1.72333	+	0.994966i
$552$	175.058			0.317134
$553$	267.510	+	126.977i	0.483742	+	0.229615i
$554$	−302.197			−0.545482
$555$		0			0
$556$	−200.830	−	115.950i	−0.361206	−	0.208542i
$557$	858.396	+	495.595i	1.54111	+	0.889758i	0.998769	+	0.0495971i	$0.0157937\pi$
$557$	858.396	+	495.595i	1.54111	+	0.889758i	0.542337	+	0.840161i	$0.317540\pi$
$558$	−96.7854	−	167.637i	−0.173451	−	0.300425i
$559$			179.113i			0.320417i
$560$		0			0
$561$	68.0860			0.121365
$562$	−428.023	+	247.119i	−0.761606	+	0.439713i
$563$	290.108	−	502.481i	0.515289	−	0.892506i	−0.484554	−	0.874762i	$-0.661018\pi$
$563$	290.108	−	502.481i	0.515289	−	0.892506i	0.999843	−	0.0177449i	$-0.00564868\pi$
$564$	105.220	−	182.247i	0.186561	−	0.323133i
$565$		0			0
$566$		−	133.291i		−	0.235496i
$567$	−5.06126	−	62.7964i	−0.00892639	−	0.110752i
$568$		−	131.375i		−	0.231294i
$569$	−106.770	−	184.931i	−0.187645	−	0.325010i	0.756820	−	0.653624i	$-0.226752\pi$
$569$	−106.770	−	184.931i	−0.187645	−	0.325010i	−0.944465	+	0.328613i	$0.893419\pi$
$570$		0			0
$571$	378.751	−	656.016i	0.663311	−	1.14889i	−0.316429	−	0.948616i	$-0.602484\pi$
$571$	378.751	−	656.016i	0.663311	−	1.14889i	0.979740	−	0.200273i	$-0.0641828\pi$
$572$	−4.18091	−	7.24156i	−0.00730929	−	0.0126601i
$573$	−23.5639			−0.0411237
$574$	−378.289	−	179.560i	−0.659040	−	0.312823i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−90.7836	+	157.242i	−0.157337	+	0.272516i	−0.933908	−	0.357514i	$-0.883624\pi$
$577$	−90.7836	+	157.242i	−0.157337	+	0.272516i	0.776570	+	0.630031i	$0.216958\pi$
$578$	−775.314	−	447.628i	−1.34137	−	0.774442i
$579$	−273.627	+	157.978i	−0.472585	+	0.272847i
$580$		0			0
$581$	−8.85671	+	6.11165i	−0.0152439	+	0.0105192i
$582$		−	368.689i		−	0.633486i
$583$	61.2894	−	35.3855i	0.105128	−	0.0606955i
$584$	−334.111	−	192.899i	−0.572107	−	0.330306i
$585$		0			0
$586$	−239.966	+	138.544i	−0.409498	+	0.236424i
$587$	156.397			0.266434			0.133217	−	0.991087i	$-0.457469\pi$
$587$	156.397			0.266434			0.133217	+	0.991087i	$0.457469\pi$
$588$	167.550	−	27.1850i	0.284949	−	0.0462329i
$589$	−1525.02			−2.58917
$590$		0			0
$591$	430.019	+	248.271i	0.727612	+	0.420087i
$592$	−138.749	−	80.1068i	−0.234373	−	0.135316i
$593$	−105.889	−	183.404i	−0.178564	−	0.309282i	0.762825	−	0.646605i	$-0.223812\pi$
$593$	−105.889	−	183.404i	−0.178564	−	0.309282i	−0.941389	+	0.337323i	$0.890479\pi$
$594$		−	9.51303i		−	0.0160152i
$595$		0			0
$596$	−10.3870			−0.0174278
$597$	−4.74785	+	2.74117i	−0.00795285	+	0.00459158i
$598$	81.6039	−	141.342i	0.136461	−	0.236358i
$599$	264.528	−	458.175i	0.441616	−	0.764901i	−0.556194	−	0.831053i	$-0.687739\pi$
$599$	264.528	−	458.175i	0.441616	−	0.764901i	0.997810	+	0.0661519i	$0.0210722\pi$
$600$		0			0
$601$			899.473i			1.49663i	0.663345	+	0.748314i	$0.269136\pi$
$601$			899.473i			1.49663i	−0.663345	+	0.748314i	$0.730864\pi$
$602$	−495.985	−	235.427i	−0.823895	−	0.391074i
$603$		−	120.261i		−	0.199437i
$604$	−160.742	−	278.413i	−0.266129	−	0.460949i
$605$		0			0
$606$	−146.804	+	254.272i	−0.242251	+	0.419591i
$607$	−268.038	−	464.255i	−0.441578	−	0.764835i	0.556229	−	0.831029i	$-0.312248\pi$
$607$	−268.038	−	464.255i	−0.441578	−	0.764835i	−0.997807	+	0.0661939i	$0.978914\pi$
$608$	189.081			0.310988
$609$	−31.9517	−	396.433i	−0.0524659	−	0.650958i
$610$		0			0
$611$	−98.0976	−	169.910i	−0.160552	−	0.278085i
$612$	−91.0954	+	157.782i	−0.148849	+	0.257813i
$613$	−717.977	−	414.524i	−1.17125	−	0.676222i	−0.217276	−	0.976110i	$-0.569717\pi$
$613$	−717.977	−	414.524i	−1.17125	−	0.676222i	−0.953974	+	0.299888i	$0.903051\pi$
$614$	−554.098	+	319.908i	−0.902439	+	0.521024i
$615$		0			0
$616$	25.5481	−	2.05913i	0.0414742	−	0.00334274i
$617$		−	404.320i		−	0.655300i	−0.944799	−	0.327650i	$-0.893743\pi$
$617$		−	404.320i		−	0.655300i	0.944799	−	0.327650i	$-0.106257\pi$
$618$	−211.388	+	122.045i	−0.342051	+	0.197483i
$619$	346.662	+	200.145i	0.560036	+	0.323337i	0.753160	−	0.657838i	$-0.228529\pi$
$619$	346.662	+	200.145i	0.560036	+	0.323337i	−0.193124	+	0.981174i	$0.561862\pi$
$620$		0			0
$621$	160.801	−	92.8387i	0.258939	−	0.149499i
$622$	−92.8991			−0.149355
$623$	−104.966	+	221.138i	−0.168485	+	0.354957i
$624$	22.3753			0.0358579
$625$		0			0
$626$	434.270	+	250.726i	0.693722	+	0.400521i
$627$	−64.9061	−	37.4736i	−0.103519	−	0.0597665i
$628$	95.2314	+	164.946i	0.151642	+	0.262652i
$629$		−	1216.23i		−	1.93359i
$630$		0			0
$631$	334.639			0.530331			0.265165	−	0.964203i	$-0.414573\pi$
$631$	334.639			0.530331			0.265165	+	0.964203i	$0.414573\pi$
$632$	−103.619	+	59.8244i	−0.163954	+	0.0946589i
$633$	155.299	−	268.987i	0.245339	−	0.424939i
$634$	−95.3603	+	165.169i	−0.150411	+	0.260519i
$635$		0			0
$636$			189.375i			0.297760i
$637$	56.1547	−	147.952i	0.0881550	−	0.232264i
$638$		−	60.0558i		−	0.0941313i
$639$	−69.6720	−	120.676i	−0.109033	−	0.188851i
$640$		0			0
$641$	36.0084	−	62.3683i	0.0561753	−	0.0972984i	−0.836570	−	0.547860i	$-0.815443\pi$
$641$	36.0084	−	62.3683i	0.0561753	−	0.0972984i	0.892746	+	0.450561i	$0.148776\pi$
$642$	57.5514	+	99.6819i	0.0896439	+	0.155268i
$643$	−1254.20			−1.95054			−0.975269	−	0.221020i	$-0.929061\pi$
$643$	−1254.20			−1.95054			−0.975269	+	0.221020i	$0.929061\pi$
$644$	284.133	+	411.751i	0.441200	+	0.639366i
$645$		0			0
$646$	717.683	+	1243.06i	1.11096	+	1.92425i
$647$	73.1699	−	126.734i	0.113091	−	0.195879i	−0.803924	−	0.594732i	$-0.797258\pi$
$647$	73.1699	−	126.734i	0.113091	−	0.195879i	0.917015	+	0.398853i	$0.130591\pi$
$648$	22.0454	+	12.7279i	0.0340207	+	0.0196419i
$649$	−14.7939	+	8.54125i	−0.0227949	+	0.0131606i
$650$		0			0
$651$	237.207	−	499.735i	0.364373	−	0.767642i
$652$		−	492.996i		−	0.756128i
$653$	687.082	−	396.687i	1.05219	−	0.607484i	0.128930	−	0.991654i	$-0.458846\pi$
$653$	687.082	−	396.687i	1.05219	−	0.607484i	0.923262	+	0.384170i	$0.125512\pi$
$654$	−123.377	−	71.2316i	−0.188649	−	0.108917i
$655$		0			0
$656$	146.529	−	84.5986i	0.223368	−	0.128961i
$657$	−409.200			−0.622832
$658$	599.441	−	48.3137i	0.911004	−	0.0734251i
$659$	−35.5649			−0.0539680			−0.0269840	−	0.999636i	$-0.508590\pi$
$659$	−35.5649			−0.0539680			−0.0269840	+	0.999636i	$0.508590\pi$
$660$		0			0
$661$	193.509	+	111.723i	0.292752	+	0.169021i	0.639182	−	0.769055i	$-0.279273\pi$
$661$	193.509	+	111.723i	0.292752	+	0.169021i	−0.346430	+	0.938076i	$0.612606\pi$
$662$	221.094	+	127.649i	0.333979	+	0.192823i
$663$	84.9288	+	147.101i	0.128098	+	0.221872i
$664$		−	4.34800i		−	0.00654819i
$665$		0			0
$666$	−169.932			−0.255154
$667$	1015.14	−	586.090i	1.52195	−	0.878696i
$668$	−14.9445	+	25.8846i	−0.0223720	+	0.0387494i
$669$	61.7775	−	107.002i	0.0923431	−	0.159943i
$670$		0			0
$671$		−	51.0759i		−	0.0761190i
$672$	−29.4102	+	61.9600i	−0.0437652	+	0.0922024i
$673$			216.920i			0.322318i	0.986928	+	0.161159i	$0.0515232\pi$
$673$			216.920i			0.322318i	−0.986928	+	0.161159i	$0.948477\pi$
$674$	4.13429	+	7.16080i	0.00613396	+	0.0106243i
$675$		0			0
$676$	−158.570	+	274.651i	−0.234571	+	0.406288i
$677$	−23.4825	−	40.6729i	−0.0346861	−	0.0600781i	0.848161	−	0.529738i	$-0.177710\pi$
$677$	−23.4825	−	40.6729i	−0.0346861	−	0.0600781i	−0.882847	+	0.469660i	$0.844376\pi$
$678$	517.091			0.762672
$679$	867.186	−	598.410i	1.27715	−	0.881310i
$680$		0			0
$681$	−123.443	−	213.809i	−0.181267	−	0.313964i
$682$	41.7648	−	72.3388i	0.0612388	−	0.106069i
$683$	−51.1993	−	29.5599i	−0.0749623	−	0.0432795i	0.462050	−	0.886854i	$-0.347114\pi$
$683$	−51.1993	−	29.5599i	−0.0749623	−	0.0432795i	−0.537013	+	0.843574i	$0.680447\pi$
$684$	173.682	−	100.275i	0.253921	−	0.146601i
$685$		0			0
$686$	335.888	+	349.968i	0.489632	+	0.510157i
$687$		−	218.003i		−	0.317326i
$688$	192.118	−	110.919i	0.279242	−	0.161220i
$689$	152.902	+	88.2779i	0.221918	+	0.128125i
$690$		0			0
$691$	916.389	−	529.078i	1.32618	−	0.765669i	0.341472	−	0.939892i	$-0.389075\pi$
$691$	916.389	−	529.078i	1.32618	−	0.765669i	0.984706	+	0.174222i	$0.0557412\pi$
$692$	335.332			0.484584
$693$	22.3754	−	15.4404i	0.0322878	−	0.0222805i
$694$	554.757			0.799361
$695$		0			0
$696$	139.173	+	80.3513i	0.199961	+	0.115447i
$697$	1112.34	+	642.212i	1.59590	+	0.921395i
$698$	−163.238	−	282.736i	−0.233865	−	0.405066i
$699$			284.516i			0.407032i
$700$		0			0
$701$	−394.358			−0.562565			−0.281283	−	0.959625i	$-0.590760\pi$
$701$	−394.358			−0.562565			−0.281283	+	0.959625i	$0.590760\pi$
$702$	20.5531	−	11.8663i	0.0292779	−	0.0169036i
$703$	−669.394	+	1159.42i	−0.952197	+	1.64925i
$704$	−5.17824	+	8.96898i	−0.00735546	+	0.0127400i
$705$		0			0
$706$		−	177.678i		−	0.251669i
$707$	−836.342	+	67.4075i	−1.18295	+	0.0953430i
$708$		−	45.7109i		−	0.0645635i
$709$	−20.7217	−	35.8911i	−0.0292267	−	0.0506221i	0.851042	−	0.525097i	$-0.175971\pi$
$709$	−20.7217	−	35.8911i	−0.0292267	−	0.0506221i	−0.880269	+	0.474475i	$0.842638\pi$
$710$		0			0
$711$	−63.4534	+	109.905i	−0.0892453	+	0.154577i
$712$	−49.4542	−	85.6572i	−0.0694581	−	0.120305i
$713$	1630.35			2.28660
$714$	−518.971	+	41.8280i	−0.726850	+	0.0585826i
$715$		0			0
$716$	−66.9449	−	115.952i	−0.0934984	−	0.161944i
$717$	−43.6690	+	75.6369i	−0.0609051	+	0.105491i
$718$	529.052	+	305.448i	0.736841	+	0.425415i
$719$	−556.327	+	321.195i	−0.773751	+	0.446725i	−0.834211	−	0.551445i	$-0.814077\pi$
$719$	−556.327	+	321.195i	−0.773751	+	0.446725i	0.0604602	+	0.998171i	$0.480743\pi$
$720$		0			0
$721$	−630.157	−	299.113i	−0.874004	−	0.414859i
$722$		−	1069.48i		−	1.48127i
$723$	292.727	−	169.006i	0.404879	−	0.233757i
$724$	−43.1469	−	24.9109i	−0.0595952	−	0.0344073i
$725$		0			0
$726$	−253.125	+	146.142i	−0.348657	+	0.201297i
$727$	979.168			1.34686			0.673431	−	0.739250i	$-0.264820\pi$
$727$	979.168			1.34686			0.673431	+	0.739250i	$0.264820\pi$
$728$	36.3169	+	52.6286i	0.0498858	+	0.0722921i
$729$	27.0000			0.0370370
$730$		0			0
$731$	1458.42	+	842.021i	1.99511	+	1.15188i
$732$	118.363	+	68.3367i	0.161698	+	0.0933562i
$733$	−618.862	−	1071.90i	−0.844286	−	1.46235i	−0.886240	−	0.463227i	$-0.846692\pi$
$733$	−618.862	−	1071.90i	−0.844286	−	1.46235i	0.0419537	−	0.999120i	$-0.486642\pi$
$734$			667.647i			0.909601i
$735$		0			0
$736$	−202.140			−0.274647
$737$	44.9423	−	25.9474i	0.0609800	−	0.0352068i
$738$	89.7304	−	155.418i	0.121586	−	0.210593i
$739$	−477.274	+	826.662i	−0.645837	+	1.11862i	0.338271	+	0.941049i	$0.390158\pi$
$739$	−477.274	+	826.662i	−0.645837	+	1.11862i	−0.984108	+	0.177574i	$0.943175\pi$
$740$		0			0
$741$		−	186.974i		−	0.252327i
$742$	−445.426	+	307.370i	−0.600305	+	0.414246i
$743$			401.194i			0.539964i	0.962865	+	0.269982i	$0.0870178\pi$
$743$			401.194i			0.539964i	−0.962865	+	0.269982i	$0.912982\pi$
$744$	111.758	+	193.571i	0.150213	+	0.260176i
$745$		0			0
$746$	61.8874	−	107.192i	0.0829590	−	0.143689i
$747$	−2.30587	−	3.99389i	−0.00308685	−	0.00534657i
$748$	−78.6190			−0.105106
$749$	−141.050	+	297.157i	−0.188318	+	0.396738i
$750$		0			0
$751$	420.870	+	728.968i	0.560412	+	0.970662i	0.997460	+	0.0712243i	$0.0226906\pi$
$751$	420.870	+	728.968i	0.560412	+	0.970662i	−0.437048	+	0.899438i	$0.643976\pi$
$752$	−121.498	+	210.441i	−0.161567	+	0.279841i
$753$	−493.088	−	284.685i	−0.654832	−	0.378067i
$754$	129.751	−	74.9120i	0.172084	−	0.0993528i
$755$		0			0
$756$	5.84424	+	72.5110i	0.00773048	+	0.0959140i
$757$			1287.18i			1.70037i	0.526487	+	0.850183i	$0.323509\pi$
$757$			1287.18i			1.70037i	−0.526487	+	0.850183i	$0.676491\pi$
$758$	440.489	−	254.317i	0.581120	−	0.335510i
$759$	69.3890	+	40.0617i	0.0914216	+	0.0527823i
$760$		0			0
$761$	−1237.18	+	714.288i	−1.62573	+	0.938618i	−0.640387	+	0.768052i	$0.721226\pi$
$761$	−1237.18	+	714.288i	−1.62573	+	0.938618i	−0.985346	+	0.170565i	$0.945441\pi$
$762$	221.095			0.290150
$763$	−32.7072	−	405.807i	−0.0428666	−	0.531857i
$764$	27.2092			0.0356142
$765$		0			0
$766$	592.986	+	342.361i	0.774133	+	0.446946i
$767$	−36.9070	−	21.3083i	−0.0481187	−	0.0277813i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$		−	1030.04i		−	1.33945i	−0.742608	−	0.669726i	$-0.766411\pi$
$769$		−	1030.04i		−	1.33945i	0.742608	−	0.669726i	$-0.233589\pi$
$770$		0			0
$771$	−698.349			−0.905771
$772$	315.957	−	182.418i	0.409271	−	0.236293i
$773$	374.310	−	648.324i	0.484231	−	0.838712i	−0.515605	−	0.856826i	$-0.672433\pi$
$773$	374.310	−	648.324i	0.484231	−	0.838712i	0.999836	+	0.0181142i	$0.00576625\pi$
$774$	117.648	−	203.772i	0.152000	−	0.263271i
$775$		0			0
$776$			425.725i			0.548615i
$777$	−275.813	−	399.695i	−0.354972	−	0.514408i
$778$			508.526i			0.653632i
$779$	−706.929	−	1224.44i	−0.907482	−	1.57181i
$780$		0			0
$781$	30.0649	−	52.0739i	0.0384954	−	0.0666759i
$782$	−767.250	−	1328.92i	−0.981139	−	1.69938i
$783$	170.451			0.217690
$784$	−193.470	+	31.3905i	−0.246773	+	0.0400389i
$785$		0			0
$786$	−247.213	−	428.185i	−0.314520	−	0.544765i
$787$	−80.7880	+	139.929i	−0.102653	+	0.177800i	−0.912777	−	0.408458i	$-0.866066\pi$
$787$	−80.7880	+	139.929i	−0.102653	+	0.177800i	0.810124	+	0.586259i	$0.199400\pi$
$788$	−496.543	−	286.679i	−0.630131	−	0.363806i
$789$	746.930	−	431.240i	0.946679	−	0.546566i
$790$		0			0
$791$	839.279	+	1216.24i	1.06103	+	1.53760i
$792$			10.9847i			0.0138696i
$793$	110.350	−	63.7107i	0.139155	−	0.0803414i
$794$	−222.161	−	128.265i	−0.279800	−	0.161543i
$795$		0			0
$796$	5.48235	−	3.16523i	0.00688737	−	0.00397643i
$797$	1350.55			1.69454			0.847269	−	0.531164i	$-0.178245\pi$
$797$	1350.55			1.69454			0.847269	+	0.531164i	$0.178245\pi$
$798$	517.754	+	245.760i	0.648815	+	0.307969i
$799$	−1844.65			−2.30870
$800$		0			0
$801$	−90.8531	−	52.4541i	−0.113425	−	0.0654857i
$802$	325.150	+	187.725i	0.405423	+	0.234071i
$803$	−88.2891	−	152.921i	−0.109949	−	0.190437i
$804$			138.865i			0.172718i
$805$		0			0
$806$	208.386			0.258543
$807$	−269.085	+	155.357i	−0.333439	+	0.192511i
$808$	169.515	−	293.608i	0.209795	−	0.363376i
$809$	644.079	−	1115.58i	0.796142	−	1.37896i	−0.125969	−	0.992034i	$-0.540204\pi$
$809$	644.079	−	1115.58i	0.796142	−	1.37896i	0.922111	−	0.386925i	$-0.126463\pi$
$810$		0			0
$811$			1097.00i			1.35265i	0.736605	+	0.676323i	$0.236428\pi$
$811$			1097.00i			1.35265i	−0.736605	+	0.676323i	$0.763572\pi$
$812$	36.8947	+	457.762i	0.0454368	+	0.563746i
$813$		−	252.114i		−	0.310104i
$814$	−36.6646	−	63.5049i	−0.0450425	−	0.0780159i
$815$		0			0
$816$	105.188	−	182.191i	0.128907	−	0.223273i
$817$	−926.873	−	1605.39i	−1.13448	−	1.96498i
$818$	804.359			0.983324
$819$	61.2697	+	29.0826i	0.0748104	+	0.0355099i
$820$		0			0
$821$	−448.083	−	776.103i	−0.545778	−	0.945315i	−0.998558	−	0.0536923i	$-0.982901\pi$
$821$	−448.083	−	776.103i	−0.545778	−	0.945315i	0.452780	−	0.891622i	$-0.350432\pi$
$822$	0.00498587	−	0.00863579i	6.06554e−6	−	1.05058e-5i
$823$	46.8742	+	27.0628i	0.0569553	+	0.0328832i	0.528207	−	0.849115i	$-0.322864\pi$
$823$	46.8742	+	27.0628i	0.0569553	+	0.0328832i	−0.471252	+	0.881999i	$0.656198\pi$
$824$	244.089	−	140.925i	0.296225	−	0.171026i
$825$		0			0
$826$	107.516	−	74.1923i	0.130164	−	0.0898212i
$827$			977.965i			1.18255i	0.806472	+	0.591273i	$0.201374\pi$
$827$			977.965i			1.18255i	−0.806472	+	0.591273i	$0.798626\pi$
$828$	−185.677	+	107.201i	−0.224248	+	0.129470i
$829$	667.395	+	385.321i	0.805061	+	0.464802i	0.845238	−	0.534391i	$-0.179459\pi$
$829$	667.395	+	385.321i	0.805061	+	0.464802i	−0.0401771	+	0.999193i	$0.512792\pi$
$830$		0			0
$831$	320.528	−	185.057i	0.385714	−	0.222692i
$832$	−25.8368			−0.0310539
$833$	−940.712	−	1152.77i	−1.12931	−	1.38388i
$834$	284.017			0.340548
$835$		0			0
$836$	74.9472	+	43.2708i	0.0896497	+	0.0517593i
$837$	205.313	+	118.537i	0.245296	+	0.141622i
$838$	−393.181	−	681.009i	−0.469189	−	0.812659i
$839$		−	148.387i		−	0.176862i	−0.996082	−	0.0884308i	$-0.971815\pi$
$839$		−	148.387i		−	0.176862i	0.996082	−	0.0884308i	$-0.0281852\pi$
$840$		0			0
$841$	235.056			0.279496
$842$	−583.306	+	336.772i	−0.692762	+	0.399966i
$843$	302.658	−	524.218i	0.359024	−	0.621849i
$844$	−179.324	+	310.599i	−0.212470	+	0.368008i
$845$		0			0
$846$			257.736i			0.304653i
$847$	−754.578	−	358.171i	−0.890883	−	0.422870i
$848$		−	218.672i		−	0.257868i
$849$	81.6234	+	141.376i	0.0961407	+	0.166521i
$850$		0			0
$851$	715.627	−	1239.50i	0.840924	−	1.45652i
$852$	80.4503	+	139.344i	0.0944253	+	0.163549i
$853$	−59.1817			−0.0693807			−0.0346903	−	0.999398i	$-0.511044\pi$
$853$	−59.1817			−0.0693807			−0.0346903	+	0.999398i	$0.511044\pi$
$854$	31.3780	+	389.314i	0.0367423	+	0.455872i
$855$		0			0
$856$	−66.4546	−	115.103i	−0.0776339	−	0.134466i
$857$	128.218	−	222.080i	0.149613	−	0.259137i	−0.781472	−	0.623941i	$-0.785531\pi$
$857$	128.218	−	222.080i	0.149613	−	0.259137i	0.931084	+	0.364804i	$0.118864\pi$
$858$	8.86906	+	5.12055i	0.0103369	+	0.00596801i
$859$	−26.1614	+	15.1043i	−0.0304556	+	0.0175836i	−0.515151	−	0.857100i	$-0.672264\pi$
$859$	−26.1614	+	15.1043i	−0.0304556	+	0.0175836i	0.484695	+	0.874683i	$0.338931\pi$
$860$		0			0
$861$	511.194	−	41.2012i	0.593721	−	0.0478528i
$862$			649.994i			0.754054i
$863$	−1114.24	+	643.310i	−1.29113	+	0.745434i	−0.978855	−	0.204558i	$-0.934424\pi$
$863$	−1114.24	+	643.310i	−1.29113	+	0.745434i	−0.312275	+	0.949992i	$0.601091\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	80.7333	−	46.6114i	0.0932255	−	0.0538238i
$867$	1096.46			1.26466
$868$	−273.903	+	577.045i	−0.315556	+	0.664798i
$869$	−54.7628			−0.0630182
$870$		0			0
$871$	112.120	+	64.7323i	0.128725	+	0.0743196i
$872$	142.463	+	82.2512i	0.163375	+	0.0943247i
$873$	225.775	+	391.053i	0.258619	+	0.447942i
$874$			1689.13i			1.93265i
$875$		0			0
$876$	472.504			0.539388
$877$	264.177	−	152.523i	0.301228	−	0.173914i	−0.341767	−	0.939785i	$-0.611025\pi$
$877$	264.177	−	152.523i	0.301228	−	0.173914i	0.642994	+	0.765871i	$0.277692\pi$
$878$	251.170	−	435.039i	0.286071	−	0.495489i
$879$	169.681	−	293.897i	0.193039	−	0.334354i
$880$		0			0
$881$		−	515.564i		−	0.585204i	−0.956234	−	0.292602i	$-0.905479\pi$
$881$		−	515.564i		−	0.585204i	0.956234	−	0.292602i	$-0.0945210\pi$
$882$	−161.066	+	131.437i	−0.182615	+	0.149022i
$883$			951.802i			1.07792i	0.842332	+	0.538960i	$0.181182\pi$
$883$			951.802i			1.07792i	−0.842332	+	0.538960i	$0.818818\pi$
$884$	−98.0673	−	169.858i	−0.110936	−	0.192147i
$885$		0			0
$886$	−536.152	+	928.643i	−0.605138	+	1.04813i
$887$	608.088	+	1053.24i	0.685556	+	1.18742i	0.973262	+	0.229699i	$0.0737742\pi$
$887$	608.088	+	1053.24i	0.685556	+	1.18742i	−0.287706	+	0.957719i	$0.592892\pi$
$888$	196.221			0.220969
$889$	358.853	+	520.033i	0.403659	+	0.584963i
$890$		0			0
$891$	5.82552	+	10.0901i	0.00653818	+	0.0113245i
$892$	−71.3345	+	123.555i	−0.0799715	+	0.138515i
$893$	1758.50	+	1015.27i	1.96920	+	1.13692i
$894$	11.0171	−	6.36070i	0.0123233	−	0.00711488i
$895$		0			0
$896$	33.9600	−	71.5452i	0.0379018	−	0.0798496i
$897$			199.888i			0.222841i
$898$	−818.257	+	472.421i	−0.911200	+	0.526081i
$899$	1296.14	+	748.327i	1.44176	+	0.832399i
$900$		0			0
$901$	1437.60	−	830.000i	1.59556	−	0.921198i
$902$	77.4409			0.0858547
$903$	670.240	−	54.0200i	0.742237	−	0.0598228i
$904$	−597.086			−0.660493
$905$		0			0
$906$	340.985	+	196.868i	0.376363	+	0.217294i
$907$	1188.52	+	686.190i	1.31038	+	0.756549i	0.982159	−	0.188052i	$-0.0602172\pi$
$907$	1188.52	+	686.190i	1.31038	+	0.756549i	0.328222	+	0.944601i	$0.393551\pi$
$908$	142.540	+	246.886i	0.156982	+	0.271901i
$909$		−	359.595i		−	0.395594i
$910$		0			0
$911$	−317.135			−0.348118			−0.174059	−	0.984735i	$-0.555688\pi$
$911$	−317.135			−0.348118			−0.174059	+	0.984735i	$0.555688\pi$
$912$	−200.550	+	115.788i	−0.219902	+	0.126960i
$913$	0.995031	−	1.72344i	0.00108985	−	0.00188767i
$914$	527.028	−	912.839i	0.576617	−	0.998730i
$915$		0			0
$916$			251.728i			0.274812i
$917$	605.882	−	1276.44i	0.660721	−	1.39198i
$918$		−	223.137i		−	0.243069i
$919$	451.409	+	781.863i	0.491195	+	0.850775i	0.999949	−	0.0101370i	$-0.00322675\pi$
$919$	451.409	+	781.863i	0.491195	+	0.850775i	−0.508753	+	0.860912i	$0.669893\pi$
$920$		0			0
$921$	391.806	−	678.628i	0.425414	−	0.736839i
$922$	−419.270	−	726.197i	−0.454740	−	0.787632i
$923$	150.009			0.162523
$924$	−25.8369	+	17.8290i	−0.0279621	+	0.0192955i
$925$		0			0
$926$	−374.645	−	648.905i	−0.404585	−	0.700761i
$927$	149.474	−	258.896i	0.161244	−	0.279284i
$928$	−160.703	−	92.7817i	−0.173171	−	0.0999803i
$929$	291.968	−	168.568i	0.314282	−	0.181451i	−0.334559	−	0.942375i	$-0.608587\pi$
$929$	291.968	−	168.568i	0.314282	−	0.181451i	0.648841	+	0.760924i	$0.275254\pi$
$930$		0			0
$931$	262.307	+	1616.69i	0.281748	+	1.73651i
$932$		−	328.530i		−	0.352500i
$933$	98.5344	−	56.8889i	0.105610	−	0.0609741i
$934$	204.869	+	118.281i	0.219346	+	0.126640i
$935$		0			0
$936$	−23.7326	+	13.7020i	−0.0253554	+	0.0146389i
$937$	−1577.72			−1.68380			−0.841900	−	0.539634i	$-0.818562\pi$
$937$	−1577.72			−1.68380			−0.841900	+	0.539634i	$0.818562\pi$
$938$	−326.622	+	225.388i	−0.348211	+	0.240286i
$939$	−614.150			−0.654047
$940$		0			0
$941$	−711.530	−	410.802i	−0.756142	−	0.436559i	0.0717667	−	0.997421i	$-0.477136\pi$
$941$	−711.530	−	410.802i	−0.756142	−	0.436559i	−0.827909	+	0.560863i	$0.810470\pi$
$942$	−202.016	−	116.634i	−0.214455	−	0.123815i
$943$	755.753	+	1309.00i	0.801435	+	1.38813i
$944$			52.7824i			0.0559136i
$945$		0			0
$946$	101.535			0.107331
$947$	−354.357	+	204.588i	−0.374189	+	0.216038i	−0.675287	−	0.737555i	$-0.735980\pi$
$947$	−354.357	+	204.588i	−0.374189	+	0.216038i	0.301098	+	0.953593i	$0.402647\pi$
$948$	73.2697	−	126.907i	0.0772887	−	0.133868i
$949$	220.259	−	381.500i	0.232096	−	0.402002i
$950$		0			0
$951$		−	233.584i		−	0.245619i
$952$	599.256	−	48.2988i	0.629470	−	0.0507340i
$953$			820.950i			0.861437i	0.902486	+	0.430719i	$0.141740\pi$
$953$			820.950i			0.861437i	−0.902486	+	0.430719i	$0.858260\pi$
$954$	−115.968	−	200.863i	−0.121560	−	0.210548i
$955$		0			0
$956$	50.4246	−	87.3380i	0.0527454	−	0.0913577i
$957$	36.7765	+	63.6988i	0.0384289	+	0.0665609i
$958$	−361.210			−0.377046
$959$	0.0284045	−	0.00228935i	2.96189e−5	−	2.38722e-6i
$960$		0			0
$961$	560.324	+	970.510i	0.583063	+	1.00990i
$962$	91.4689	−	158.429i	0.0950820	−	0.164687i
$963$	−122.085	−	70.4858i	−0.126776	−	0.0731940i
$964$	−338.012	+	195.151i	−0.350635	+	0.202439i
$965$		0			0
$966$	−553.514	−	262.733i	−0.572995	−	0.271981i
$967$		−	1627.11i		−	1.68263i	−0.540543	−	0.841317i	$-0.681781\pi$
$967$		−	1627.11i		−	1.68263i	0.540543	−	0.841317i	$-0.318219\pi$
$968$	292.283	−	168.750i	0.301945	−	0.174328i
$969$	−1522.44	−	878.978i	−1.57114	−	0.907098i
$970$		0			0
$971$	1074.33	−	620.263i	1.10641	−	0.638788i	0.168515	−	0.985699i	$-0.446103\pi$
$971$	1074.33	−	620.263i	1.10641	−	0.638788i	0.937898	+	0.346911i	$0.112769\pi$
$972$	−31.1769			−0.0320750
$973$	460.981	+	668.032i	0.473773	+	0.686569i
$974$	858.188			0.881097
$975$		0			0
$976$	−136.673	−	78.9084i	−0.140034	−	0.0808488i
$977$	622.459	+	359.377i	0.637113	+	0.367837i	0.783502	−	0.621390i	$-0.213432\pi$
$977$	622.459	+	359.377i	0.637113	+	0.367837i	−0.146389	+	0.989227i	$0.546765\pi$
$978$	301.897	+	522.901i	0.308688	+	0.534664i
$979$		−	45.2700i		−	0.0462410i
$980$		0			0
$981$	174.481			0.177860
$982$	866.941	−	500.529i	0.882832	−	0.509704i
$983$	201.047	−	348.223i	0.204524	−	0.354246i	−0.745457	−	0.666554i	$-0.767769\pi$
$983$	201.047	−	348.223i	0.204524	−	0.354246i	0.949981	+	0.312308i	$0.101102\pi$
$984$	−103.612	+	179.461i	−0.105296	+	0.182379i
$985$		0			0
$986$		−	1408.66i		−	1.42867i
$987$	−606.217	+	418.325i	−0.614202	+	0.423835i
$988$			215.899i			0.218522i
$989$	990.889	+	1716.27i	1.00191	+	1.73536i
$990$		0			0
$991$	298.270	−	516.618i	0.300979	−	0.521310i	−0.675379	−	0.737471i	$-0.736020\pi$
$991$	298.270	−	516.618i	0.300979	−	0.521310i	0.976358	+	0.216160i	$0.0693534\pi$
$992$	−129.047	−	223.516i	−0.130088	−	0.225319i
$993$	−312.674			−0.314878
$994$	−197.172	+	415.392i	−0.198362	+	0.417899i
$995$		0			0
$996$	2.66259	+	4.61175i	0.00267329	+	0.00463027i
$997$	−680.693	+	1178.99i	−0.682741	+	1.18254i	0.291400	+	0.956601i	$0.405879\pi$
$997$	−680.693	+	1178.99i	−0.682741	+	1.18254i	−0.974141	+	0.225941i	$0.927454\pi$
$998$	808.613	+	466.853i	0.810234	+	0.467789i
$999$	180.240	−	104.062i	0.180421	−	0.104166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.b.199.5		16
5.2	odd	4		1050.3.p.d.451.3	yes	8
5.3	odd	4		1050.3.p.c.451.2	✓	8
5.4	even	2	inner	1050.3.q.b.199.4		16
7.5	odd	6	inner	1050.3.q.b.649.4		16
35.12	even	12		1050.3.p.d.901.3	yes	8
35.19	odd	6	inner	1050.3.q.b.649.5		16
35.33	even	12		1050.3.p.c.901.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.2	✓	8	5.3	odd	4
1050.3.p.c.901.2	yes	8	35.33	even	12
1050.3.p.d.451.3	yes	8	5.2	odd	4
1050.3.p.d.901.3	yes	8	35.12	even	12
1050.3.q.b.199.4		16	5.4	even	2	inner
1050.3.q.b.199.5		16	1.1	even	1	trivial
1050.3.q.b.649.4		16	7.5	odd	6	inner
1050.3.q.b.649.5		16	35.19	odd	6	inner

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.647280 - 1.12112i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.22960 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(15.1826 - 26.2970i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-28.9470 + 16.7125i) q^{19} +(-0.974040 - 12.0852i) q^{21} -1.83078i q^{22} +(30.9462 - 17.8668i) q^{23} +(4.24264 + 2.44949i) q^{24} +(3.95544 - 2.28367i) q^{26} +5.19615 q^{27} +(1.12472 + 13.9547i) q^{28} +32.8033 q^{29} +(39.5125 + 22.8125i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(1.12112 + 1.94184i) q^{33} -42.9428i q^{34} -6.00000 q^{36} +(34.6873 - 20.0267i) q^{37} +(-23.6351 + 40.9372i) q^{38} +(-2.79692 + 4.84440i) q^{39} +42.2993i q^{41} +(-9.73845 - 14.1125i) q^{42} +55.4597i q^{43} +(-1.29456 - 2.24224i) q^{44} +(25.2675 - 43.7646i) q^{46} +(-30.3745 - 52.6102i) q^{47} +6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(26.2970 + 45.5477i) q^{51} +(3.22960 - 5.59383i) q^{52} +(47.3438 + 27.3340i) q^{53} +(6.36396 - 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} -57.8939i q^{57} +(40.1757 - 23.1954i) q^{58} +(-11.4277 - 6.59780i) q^{59} +(34.1684 - 19.7271i) q^{61} +64.5236 q^{62} +(18.9713 + 9.00500i) q^{63} -8.00000 q^{64} +(2.74618 + 1.58551i) q^{66} +(34.7163 + 20.0434i) q^{67} +(-30.3651 - 52.5940i) q^{68} +61.8924i q^{69} +46.4480 q^{71} +(-7.34847 + 4.24264i) q^{72} +(68.2001 - 118.126i) q^{73} +(28.3220 - 49.0552i) q^{74} +66.8501i q^{76} +(0.728012 + 9.03263i) q^{77} +7.91088i q^{78} +(-21.1511 - 36.6348i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(29.9101 + 51.8059i) q^{82} +1.53725 q^{83} +(-21.9062 - 10.3981i) q^{84} +(39.2160 + 67.9240i) q^{86} +(-28.4085 + 49.2050i) q^{87} +(-3.17101 - 1.83078i) q^{88} +(30.2844 - 17.4847i) q^{89} +(-18.6070 + 12.8400i) q^{91} -71.4672i q^{92} +(-68.4376 + 39.5125i) q^{93} +(-74.4020 - 42.9560i) q^{94} +(8.48528 - 4.89898i) q^{96} -150.516 q^{97} +(-11.0982 - 68.4020i) q^{98} -3.88368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^9	\( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

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