LMFDB - Embedded newform 99.3.l.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(26,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("99.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.l (of order $10$, degree $4$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	99.53
Dual form			99.3.l.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.84833 - 0.925479i) q^{2} +(4.02041 + 2.92100i) q^{4} +(-1.53284 + 0.498051i) q^{5} +(2.69388 + 1.95722i) q^{7} +(-1.70668 - 2.34904i) q^{8} +O(q^{10})$	\(q+(-2.84833 - 0.925479i) q^{2} +(4.02041 + 2.92100i) q^{4} +(-1.53284 + 0.498051i) q^{5} +(2.69388 + 1.95722i) q^{7} +(-1.70668 - 2.34904i) q^{8} +4.82698 q^{10} +(9.45670 - 5.61879i) q^{11} +(2.33725 - 7.19331i) q^{13} +(-5.86169 - 8.06793i) q^{14} +(-3.45544 - 10.6348i) q^{16} +(26.9649 - 8.76142i) q^{17} +(21.0884 - 15.3216i) q^{19} +(-7.61747 - 2.47507i) q^{20} +(-32.1359 + 7.25218i) q^{22} +19.5656i q^{23} +(-18.1239 + 13.1678i) q^{25} +(-13.3145 + 18.3259i) q^{26} +(5.11347 + 15.7376i) q^{28} +(1.26543 - 1.74171i) q^{29} +(-2.85173 + 8.77673i) q^{31} +45.1036i q^{32} -84.9135 q^{34} +(-5.10409 - 1.65842i) q^{35} +(54.6363 + 39.6956i) q^{37} +(-74.2465 + 24.1241i) q^{38} +(3.78602 + 2.75070i) q^{40} +(-17.0809 - 23.5098i) q^{41} +0.719802 q^{43} +(54.4323 + 5.03321i) q^{44} +(18.1076 - 55.7293i) q^{46} +(-14.4154 - 19.8410i) q^{47} +(-11.7156 - 36.0568i) q^{49} +(63.8093 - 20.7329i) q^{50} +(30.4084 - 22.0930i) q^{52} +(5.50829 + 1.78975i) q^{53} +(-11.6972 + 13.3226i) q^{55} -9.66837i q^{56} +(-5.21628 + 3.78985i) q^{58} +(43.4900 - 59.8589i) q^{59} +(22.3006 + 68.6343i) q^{61} +(16.2454 - 22.3598i) q^{62} +(27.9206 - 85.9309i) q^{64} +12.1903i q^{65} -79.8310 q^{67} +(134.002 + 43.5399i) q^{68} +(13.0033 + 9.44745i) q^{70} +(-102.505 + 33.3059i) q^{71} +(73.1189 + 53.1240i) q^{73} +(-118.885 - 163.631i) q^{74} +129.538 q^{76} +(36.4724 + 3.37250i) q^{77} +(35.4758 - 109.183i) q^{79} +(10.5933 + 14.5804i) q^{80} +(26.8942 + 82.7718i) q^{82} +(-119.598 + 38.8596i) q^{83} +(-36.9693 + 26.8598i) q^{85} +(-2.05023 - 0.666161i) q^{86} +(-29.3383 - 12.6247i) q^{88} -83.3041i q^{89} +(20.3751 - 14.8034i) q^{91} +(-57.1511 + 78.6618i) q^{92} +(22.6973 + 69.8550i) q^{94} +(-24.6942 + 33.9887i) q^{95} +(-24.1118 + 74.2085i) q^{97} +113.544i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^7	$ 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−2.84833	−	0.925479i	−1.42417	−	0.462739i	−0.507243	−	0.861803i	$-0.669335\pi$
$2$	−2.84833	−	0.925479i	−1.42417	−	0.462739i	−0.916923	+	0.399064i	$0.869335\pi$
$3$		0			0
$3$		0			0
$4$	4.02041	+	2.92100i	1.00510	+	0.730250i
$5$	−1.53284	+	0.498051i	−0.306569	+	0.0996102i	−0.458261	−	0.888817i	$-0.651528\pi$
$5$	−1.53284	+	0.498051i	−0.306569	+	0.0996102i	0.151693	+	0.988428i	$0.451528\pi$
$6$		0			0
$7$	2.69388	+	1.95722i	0.384840	+	0.279602i	0.763338	−	0.646000i	$-0.223559\pi$
$7$	2.69388	+	1.95722i	0.384840	+	0.279602i	−0.378498	+	0.925602i	$0.623559\pi$
$8$	−1.70668	−	2.34904i	−0.213335	−	0.293630i
$9$		0			0
$10$	4.82698			0.482698
$11$	9.45670	−	5.61879i	0.859700	−	0.510799i
$11$	9.45670	−	5.61879i	0.859700	−	0.510799i
$12$		0			0
$13$	2.33725	−	7.19331i	0.179788	−	0.553332i	−0.820031	−	0.572319i	$-0.806044\pi$
$13$	2.33725	−	7.19331i	0.179788	−	0.553332i	0.999820	+	0.0189869i	$0.00604407\pi$
$14$	−5.86169	−	8.06793i	−0.418692	−	0.576280i
$15$		0			0
$16$	−3.45544	−	10.6348i	−0.215965	−	0.664673i
$17$	26.9649	−	8.76142i	1.58617	−	0.515378i	0.622533	−	0.782593i	$-0.286104\pi$
$17$	26.9649	−	8.76142i	1.58617	−	0.515378i	0.963637	+	0.267215i	$0.0861035\pi$
$18$		0			0
$19$	21.0884	−	15.3216i	1.10991	−	0.806400i	0.127264	−	0.991869i	$-0.459380\pi$
$19$	21.0884	−	15.3216i	1.10991	−	0.806400i	0.982650	+	0.185469i	$0.0593804\pi$
$20$	−7.61747	−	2.47507i	−0.380874	−	0.123753i
$21$		0			0
$22$	−32.1359	+	7.25218i	−1.46072	+	0.329645i
$23$			19.5656i			0.850679i	0.905034	+	0.425339i	$0.139845\pi$
$23$			19.5656i			0.850679i	−0.905034	+	0.425339i	$0.860155\pi$
$24$		0			0
$25$	−18.1239	+	13.1678i	−0.724955	+	0.526710i
$26$	−13.3145	+	18.3259i	−0.512097	+	0.704841i
$27$		0			0
$28$	5.11347	+	15.7376i	0.182624	+	0.562058i
$29$	1.26543	−	1.74171i	0.0436355	−	0.0600591i	−0.786642	−	0.617410i	$-0.788182\pi$
$29$	1.26543	−	1.74171i	0.0436355	−	0.0600591i	0.830277	+	0.557351i	$0.188182\pi$
$30$		0			0
$31$	−2.85173	+	8.77673i	−0.0919914	+	0.283120i	−0.986458	−	0.164015i	$-0.947556\pi$
$31$	−2.85173	+	8.77673i	−0.0919914	+	0.283120i	0.894467	+	0.447135i	$0.147556\pi$
$32$			45.1036i			1.40949i
$33$		0			0
$34$	−84.9135			−2.49745
$35$	−5.10409	−	1.65842i	−0.145831	−	0.0473834i
$36$		0			0
$37$	54.6363	+	39.6956i	1.47666	+	1.07285i	0.978615	+	0.205701i	$0.0659475\pi$
$37$	54.6363	+	39.6956i	1.47666	+	1.07285i	0.498042	+	0.867153i	$0.334052\pi$
$38$	−74.2465	+	24.1241i	−1.95385	+	0.634846i
$39$		0			0
$40$	3.78602	+	2.75070i	0.0946504	+	0.0687676i
$41$	−17.0809	−	23.5098i	−0.416607	−	0.573410i	0.548207	−	0.836343i	$-0.315310\pi$
$41$	−17.0809	−	23.5098i	−0.416607	−	0.573410i	−0.964814	+	0.262932i	$0.915310\pi$
$42$		0			0
$43$	0.719802			0.0167396			0.00836979	−	0.999965i	$-0.497336\pi$
$43$	0.719802			0.0167396			0.00836979	+	0.999965i	$0.497336\pi$
$44$	54.4323	+	5.03321i	1.23710	+	0.114391i
$45$		0			0
$46$	18.1076	−	55.7293i	0.393643	−	1.21151i
$47$	−14.4154	−	19.8410i	−0.306710	−	0.422150i	0.627642	−	0.778502i	$-0.284020\pi$
$47$	−14.4154	−	19.8410i	−0.306710	−	0.422150i	−0.934352	+	0.356352i	$0.884020\pi$
$48$		0			0
$49$	−11.7156	−	36.0568i	−0.239093	−	0.735853i
$50$	63.8093	−	20.7329i	1.27619	−	0.414658i
$51$		0			0
$52$	30.4084	−	22.0930i	0.584776	−	0.424865i
$53$	5.50829	+	1.78975i	0.103930	+	0.0337689i	0.360520	−	0.932751i	$-0.382599\pi$
$53$	5.50829	+	1.78975i	0.103930	+	0.0337689i	−0.256590	+	0.966520i	$0.582599\pi$
$54$		0			0
$55$	−11.6972	+	13.3226i	−0.212676	+	0.242230i
$56$		−	9.66837i		−	0.172650i
$57$		0			0
$58$	−5.21628	+	3.78985i	−0.0899359	+	0.0653423i
$59$	43.4900	−	59.8589i	0.737119	−	1.01456i	−0.261660	−	0.965160i	$-0.584270\pi$
$59$	43.4900	−	59.8589i	0.737119	−	1.01456i	0.998779	−	0.0493973i	$-0.0157300\pi$
$60$		0			0
$61$	22.3006	+	68.6343i	0.365584	+	1.12515i	0.949614	+	0.313421i	$0.101475\pi$
$61$	22.3006	+	68.6343i	0.365584	+	1.12515i	−0.584030	+	0.811732i	$0.698525\pi$
$62$	16.2454	−	22.3598i	0.262022	−	0.360642i
$63$		0			0
$64$	27.9206	−	85.9309i	0.436260	−	1.34267i
$65$			12.1903i			0.187543i
$66$		0			0
$67$	−79.8310			−1.19151			−0.595754	−	0.803167i	$-0.703146\pi$
$67$	−79.8310			−1.19151			−0.595754	+	0.803167i	$0.703146\pi$
$68$	134.002	+	43.5399i	1.97062	+	0.640293i
$69$		0			0
$70$	13.0033	+	9.44745i	0.185761	+	0.134964i
$71$	−102.505	+	33.3059i	−1.44373	+	0.469097i	−0.923059	−	0.384658i	$-0.874319\pi$
$71$	−102.505	+	33.3059i	−1.44373	+	0.469097i	−0.520674	+	0.853755i	$0.674319\pi$
$72$		0			0
$73$	73.1189	+	53.1240i	1.00163	+	0.727726i	0.962437	−	0.271506i	$-0.0875216\pi$
$73$	73.1189	+	53.1240i	1.00163	+	0.727726i	0.0391919	+	0.999232i	$0.487522\pi$
$74$	−118.885	−	163.631i	−1.60655	−	2.21123i
$75$		0			0
$76$	129.538			1.70445
$77$	36.4724	+	3.37250i	0.473667	+	0.0437987i
$78$		0			0
$79$	35.4758	−	109.183i	0.449060	−	1.38206i	−0.428909	−	0.903348i	$-0.641102\pi$
$79$	35.4758	−	109.183i	0.449060	−	1.38206i	0.877969	−	0.478717i	$-0.158898\pi$
$80$	10.5933	+	14.5804i	0.132416	+	0.182256i
$81$		0			0
$82$	26.8942	+	82.7718i	0.327978	+	1.00941i
$83$	−119.598	+	38.8596i	−1.44093	+	0.468188i	−0.922188	−	0.386741i	$-0.873601\pi$
$83$	−119.598	+	38.8596i	−1.44093	+	0.468188i	−0.518746	+	0.854929i	$0.673601\pi$
$84$		0			0
$85$	−36.9693	+	26.8598i	−0.434933	+	0.315998i
$86$	−2.05023	−	0.666161i	−0.0238399	−	0.00774606i
$87$		0			0
$88$	−29.3383	−	12.6247i	−0.333390	−	0.143463i
$89$		−	83.3041i		−	0.936001i	−0.883728	−	0.468000i	$-0.844975\pi$
$89$		−	83.3041i		−	0.936001i	0.883728	−	0.468000i	$-0.155025\pi$
$90$		0			0
$91$	20.3751	−	14.8034i	0.223902	−	0.162675i
$92$	−57.1511	+	78.6618i	−0.621208	+	0.855020i
$93$		0			0
$94$	22.6973	+	69.8550i	0.241460	+	0.743138i
$95$	−24.6942	+	33.9887i	−0.259939	+	0.357776i
$96$		0			0
$97$	−24.1118	+	74.2085i	−0.248575	+	0.765036i	0.746452	+	0.665439i	$0.231756\pi$
$97$	−24.1118	+	74.2085i	−0.248575	+	0.765036i	−0.995028	+	0.0995976i	$0.968244\pi$
$98$			113.544i			1.15861i
$99$		0			0
$100$	−111.328			−1.11328
$101$	37.0777	+	12.0473i	0.367106	+	0.119280i	0.486760	−	0.873536i	$-0.338179\pi$
$101$	37.0777	+	12.0473i	0.367106	+	0.119280i	−0.119654	+	0.992816i	$0.538179\pi$
$102$		0			0
$103$	−24.3898	−	17.7202i	−0.236794	−	0.172041i	0.463060	−	0.886327i	$-0.346752\pi$
$103$	−24.3898	−	17.7202i	−0.236794	−	0.172041i	−0.699854	+	0.714286i	$0.746752\pi$
$104$	−20.8863	+	6.78638i	−0.200830	+	0.0652537i
$105$		0			0
$106$	−14.0331	−	10.1956i	−0.132387	−	0.0961850i
$107$	29.2449	+	40.2522i	0.273317	+	0.376188i	0.923506	−	0.383584i	$-0.125310\pi$
$107$	29.2449	+	40.2522i	0.273317	+	0.376188i	−0.650189	+	0.759772i	$0.725310\pi$
$108$		0			0
$109$	−149.823			−1.37453			−0.687263	−	0.726409i	$-0.741188\pi$
$109$	−149.823			−1.37453			−0.687263	+	0.726409i	$0.741188\pi$
$110$	45.6473	−	27.1218i	0.414976	−	0.246562i
$111$		0			0
$112$	11.5060	−	35.4118i	0.102732	−	0.316177i
$113$	74.9246	+	103.125i	0.663050	+	0.912609i	0.999578	−	0.0290640i	$-0.00925266\pi$
$113$	74.9246	+	103.125i	0.663050	+	0.912609i	−0.336528	+	0.941673i	$0.609253\pi$
$114$		0			0
$115$	−9.74467	−	29.9910i	−0.0847363	−	0.260791i
$116$	10.1751	−	3.30609i	0.0877164	−	0.0285008i
$117$		0			0
$118$	−179.272	+	130.249i	−1.51926	+	1.10380i
$119$	89.7881	+	29.1739i	0.754522	+	0.245159i
$120$		0			0
$121$	57.8585	−	106.270i	0.478169	−	0.878268i
$122$		−	216.132i		−	1.77157i
$123$		0			0
$124$	−37.1020	+	26.9562i	−0.299210	+	0.217388i
$125$	44.9066	−	61.8086i	0.359253	−	0.494469i
$126$		0			0
$127$	−73.5383	−	226.328i	−0.579042	−	1.78211i	−0.621983	−	0.783030i	$-0.713673\pi$
$127$	−73.5383	−	226.328i	−0.579042	−	1.78211i	0.0429415	−	0.999078i	$-0.486327\pi$
$128$	−53.0096	+	72.9614i	−0.414137	+	0.570011i
$129$		0			0
$130$	11.2819	−	34.7220i	0.0867835	−	0.267092i
$131$			148.535i			1.13386i	0.823767	+	0.566929i	$0.191869\pi$
$131$			148.535i			1.13386i	−0.823767	+	0.566929i	$0.808131\pi$
$132$		0			0
$133$	86.7972			0.652610
$134$	227.385	+	73.8819i	1.69690	+	0.551357i
$135$		0			0
$136$	−66.6014	−	48.3887i	−0.489716	−	0.355800i
$137$	−19.1720	+	6.22935i	−0.139941	+	0.0454697i	−0.378150	−	0.925744i	$-0.623440\pi$
$137$	−19.1720	+	6.22935i	−0.139941	+	0.0454697i	0.238209	+	0.971214i	$0.423440\pi$
$138$		0			0
$139$	−120.445	−	87.5083i	−0.866509	−	0.629556i	0.0631388	−	0.998005i	$-0.479889\pi$
$139$	−120.445	−	87.5083i	−0.866509	−	0.629556i	−0.929648	+	0.368449i	$0.879889\pi$
$140$	−15.6763	−	21.5766i	−0.111973	−	0.154118i
$141$		0			0
$142$	322.792			2.27319
$143$	−18.3150	−	81.1575i	−0.128077	−	0.567535i
$144$		0			0
$145$	−1.07224	+	3.30003i	−0.00739478	+	0.0227588i
$146$	−159.102	−	218.985i	−1.08974	−	1.49990i
$147$		0			0
$148$	103.710	+	319.185i	0.700741	+	2.15666i
$149$	42.7009	−	13.8744i	0.286583	−	0.0931166i	−0.162198	−	0.986758i	$-0.551858\pi$
$149$	42.7009	−	13.8744i	0.286583	−	0.0931166i	0.448781	+	0.893642i	$0.351858\pi$
$150$		0			0
$151$	−37.6538	+	27.3571i	−0.249363	+	0.181173i	−0.705444	−	0.708765i	$-0.749253\pi$
$151$	−37.6538	+	27.3571i	−0.249363	+	0.181173i	0.456081	+	0.889938i	$0.349253\pi$
$152$	−71.9822	−	23.3884i	−0.473567	−	0.153871i
$153$		0			0
$154$	−100.764	−	43.3604i	−0.654313	−	0.281561i
$155$		−	14.8737i		−	0.0959591i
$156$		0			0
$157$	−14.7026	+	10.6820i	−0.0936468	+	0.0680384i	−0.633623	−	0.773642i	$-0.718433\pi$
$157$	−14.7026	+	10.6820i	−0.0936468	+	0.0680384i	0.539977	+	0.841680i	$0.318433\pi$
$158$	−202.093	+	278.158i	−1.27907	+	1.76049i
$159$		0			0
$160$	−22.4639	−	69.1367i	−0.140399	−	0.432105i
$161$	−38.2941	+	52.7073i	−0.237852	+	0.327375i
$162$		0			0
$163$	−43.0033	+	132.351i	−0.263824	+	0.811967i	0.728138	+	0.685431i	$0.240386\pi$
$163$	−43.0033	+	132.351i	−0.263824	+	0.811967i	−0.991962	+	0.126536i	$0.959614\pi$
$164$		−	144.412i		−	0.880564i
$165$		0			0
$166$	376.617			2.26878
$167$	−138.107	−	44.8735i	−0.826985	−	0.268704i	−0.135210	−	0.990817i	$-0.543171\pi$
$167$	−138.107	−	44.8735i	−0.826985	−	0.268704i	−0.691775	+	0.722113i	$0.743171\pi$
$168$		0			0
$169$	90.4429	+	65.7106i	0.535165	+	0.388820i
$170$	130.159	−	42.2912i	0.765642	−	0.248772i
$171$		0			0
$172$	2.89390	+	2.10254i	0.0168250	+	0.0122241i
$173$	170.702	+	234.952i	0.986719	+	1.35810i	0.933130	+	0.359539i	$0.117066\pi$
$173$	170.702	+	234.952i	0.986719	+	1.35810i	0.0535891	+	0.998563i	$0.482934\pi$
$174$		0			0
$175$	−74.5956			−0.426261
$176$	−92.4316	−	81.1544i	−0.525179	−	0.461105i
$177$		0			0
$178$	−77.0961	+	237.278i	−0.433124	+	1.33302i
$179$	−86.0584	−	118.449i	−0.480773	−	0.661727i	0.497880	−	0.867246i	$-0.334112\pi$
$179$	−86.0584	−	118.449i	−0.480773	−	0.661727i	−0.978653	+	0.205519i	$0.934112\pi$
$180$		0			0
$181$	69.0532	+	212.524i	0.381509	+	1.17417i	0.938981	+	0.343969i	$0.111772\pi$
$181$	69.0532	+	212.524i	0.381509	+	1.17417i	−0.557471	+	0.830196i	$0.688228\pi$
$182$	−71.7353	+	23.3082i	−0.394150	+	0.128067i
$183$		0			0
$184$	45.9605	−	33.3922i	0.249785	−	0.181479i
$185$	−103.519	−	33.6355i	−0.559564	−	0.181813i
$186$		0			0
$187$	205.770	−	234.364i	1.10038	−	1.25328i
$188$		−	121.876i		−	0.648279i
$189$		0			0
$190$	101.793	−	73.9571i	0.535754	−	0.389248i
$191$	−13.6471	+	18.7836i	−0.0714506	+	0.0983433i	−0.843247	−	0.537527i	$-0.819359\pi$
$191$	−13.6471	+	18.7836i	−0.0714506	+	0.0983433i	0.771796	+	0.635870i	$0.219359\pi$
$192$		0			0
$193$	−38.7623	−	119.298i	−0.200841	−	0.618124i	−0.999859	−	0.0168170i	$-0.994647\pi$
$193$	−38.7623	−	119.298i	−0.200841	−	0.618124i	0.799018	−	0.601307i	$-0.205353\pi$
$194$	137.357	−	189.056i	0.708025	−	0.974513i
$195$		0			0
$196$	58.2205	−	179.184i	0.297043	−	0.914205i
$197$		−	12.3847i		−	0.0628665i	−0.999506	−	0.0314333i	$-0.989993\pi$
$197$		−	12.3847i		−	0.0628665i	0.999506	−	0.0314333i	$-0.0100072\pi$
$198$		0			0
$199$	112.611			0.565885			0.282943	−	0.959137i	$-0.408689\pi$
$199$	112.611			0.565885			0.282943	+	0.959137i	$0.408689\pi$
$200$	61.8633	+	20.1006i	0.309316	+	0.100503i
$201$		0			0
$202$	−94.4601	−	68.6293i	−0.467625	−	0.339749i
$203$	6.81782	−	2.21525i	0.0335853	−	0.0109125i
$204$		0			0
$205$	37.8914	+	27.5297i	0.184836	+	0.134291i
$206$	53.0705	+	73.0453i	0.257624	+	0.354589i
$207$		0			0
$208$	−84.5754			−0.406613
$209$	113.338	−	263.383i	0.542286	−	1.26021i
$210$		0			0
$211$	47.5609	−	146.377i	0.225407	−	0.693732i	−0.772843	−	0.634597i	$-0.781166\pi$
$211$	47.5609	−	146.377i	0.225407	−	0.693732i	0.998250	−	0.0591343i	$-0.0188340\pi$
$212$	16.9177	+	23.2853i	0.0798006	+	0.109836i
$213$		0			0
$214$	−46.0467	−	141.717i	−0.215171	−	0.662229i
$215$	−1.10334	+	0.358498i	−0.00513183	+	0.00166743i
$216$		0			0
$217$	−24.8602	+	18.0620i	−0.114563	+	0.0832349i
$218$	426.746	+	138.658i	1.95755	+	0.636047i
$219$		0			0
$220$	−85.9430	+	19.3950i	−0.390650	+	0.0881589i
$221$		−	214.445i		−	0.970337i
$222$		0			0
$223$	−228.453	+	165.981i	−1.02445	+	0.744310i	−0.967191	−	0.254049i	$-0.918237\pi$
$223$	−228.453	+	165.981i	−1.02445	+	0.744310i	−0.0572631	+	0.998359i	$0.518237\pi$
$224$	−88.2774	+	121.503i	−0.394096	+	0.542426i
$225$		0			0
$226$	−117.970	−	363.075i	−0.521992	−	1.60653i
$227$	−119.241	+	164.121i	−0.525290	+	0.723000i	−0.986404	−	0.164341i	$-0.947450\pi$
$227$	−119.241	+	164.121i	−0.525290	+	0.723000i	0.461113	+	0.887341i	$0.347450\pi$
$228$		0			0
$229$	−129.515	+	398.606i	−0.565568	+	1.74064i	0.100690	+	0.994918i	$0.467895\pi$
$229$	−129.515	+	398.606i	−0.565568	+	1.74064i	−0.666258	+	0.745721i	$0.732105\pi$
$230$			94.4428i			0.410621i
$231$		0			0
$232$	−6.25105			−0.0269442
$233$	−105.683	−	34.3384i	−0.453574	−	0.147375i	0.0733156	−	0.997309i	$-0.476642\pi$
$233$	−105.683	−	34.3384i	−0.453574	−	0.147375i	−0.526890	+	0.849934i	$0.676642\pi$
$234$		0			0
$235$	31.9783	+	23.2336i	0.136078	+	0.0988665i
$236$	349.696	−	113.623i	1.48176	−	0.481453i
$237$		0			0
$238$	−228.746	−	166.194i	−0.961119	−	0.698294i
$239$	184.598	+	254.077i	0.772375	+	1.06308i	0.996083	+	0.0884262i	$0.0281837\pi$
$239$	184.598	+	254.077i	0.772375	+	1.06308i	−0.223708	+	0.974656i	$0.571816\pi$
$240$		0			0
$241$	−104.293			−0.432753			−0.216376	−	0.976310i	$-0.569424\pi$
$241$	−104.293			−0.432753			−0.216376	+	0.976310i	$0.569424\pi$
$242$	−263.151	+	249.146i	−1.08740	+	1.02953i
$243$		0			0
$244$	−110.823	+	341.079i	−0.454193	+	1.39786i
$245$	35.9162	+	49.4345i	0.146597	+	0.201773i
$246$		0			0
$247$	−60.9243	−	187.506i	−0.246657	−	0.759132i
$248$	25.4839	−	8.28023i	0.102758	−	0.0333880i
$249$		0			0
$250$	−185.111	+	134.491i	−0.740446	+	0.537965i
$251$	−317.213	−	103.069i	−1.26380	−	0.410632i	−0.400950	−	0.916100i	$-0.631320\pi$
$251$	−317.213	−	103.069i	−1.26380	−	0.410632i	−0.862845	+	0.505468i	$0.831320\pi$
$252$		0			0
$253$	109.935	+	185.026i	0.434525	+	0.731329i
$254$			712.714i			2.80596i
$255$		0			0
$256$	−73.8756	+	53.6738i	−0.288577	+	0.209663i
$257$	180.443	−	248.359i	0.702114	−	0.966377i	−0.297817	−	0.954623i	$-0.596258\pi$
$257$	180.443	−	248.359i	0.702114	−	0.966377i	0.999931	−	0.0117541i	$-0.00374153\pi$
$258$		0			0
$259$	69.4906	+	213.870i	0.268304	+	0.825753i
$260$	−35.6079	+	49.0100i	−0.136953	+	0.188500i
$261$		0			0
$262$	137.466	−	423.078i	0.524681	−	1.61480i
$263$		−	249.060i		−	0.946997i	−0.880794	−	0.473499i	$-0.842991\pi$
$263$		−	249.060i		−	0.946997i	0.880794	−	0.473499i	$-0.157009\pi$
$264$		0			0
$265$	−9.33473			−0.0352254
$266$	−247.227	−	80.3289i	−0.929425	−	0.301988i
$267$		0			0
$268$	−320.953	−	233.186i	−1.19759	−	0.870098i
$269$	−187.289	+	60.8538i	−0.696241	+	0.226222i	−0.635692	−	0.771943i	$-0.719285\pi$
$269$	−187.289	+	60.8538i	−0.696241	+	0.226222i	−0.0605488	+	0.998165i	$0.519285\pi$
$270$		0			0
$271$	374.950	+	272.417i	1.38358	+	1.00523i	0.996536	+	0.0831675i	$0.0265037\pi$
$271$	374.950	+	272.417i	1.38358	+	1.00523i	0.387043	+	0.922061i	$0.373496\pi$
$272$	−186.351	−	256.491i	−0.685115	−	0.942980i
$273$		0			0
$274$	60.3733			0.220340
$275$	−97.4053	+	226.358i	−0.354201	+	0.823119i
$276$		0			0
$277$	−7.24800	+	22.3070i	−0.0261661	+	0.0805308i	−0.963287	−	0.268475i	$-0.913480\pi$
$277$	−7.24800	+	22.3070i	−0.0261661	+	0.0805308i	0.937121	+	0.349005i	$0.113480\pi$
$278$	262.080	+	360.722i	0.942732	+	1.29756i
$279$		0			0
$280$	4.81534	+	14.8201i	0.0171977	+	0.0529289i
$281$	−250.553	+	81.4096i	−0.891647	+	0.289714i	−0.718785	−	0.695232i	$-0.755302\pi$
$281$	−250.553	+	81.4096i	−0.891647	+	0.289714i	−0.172862	+	0.984946i	$0.555302\pi$
$282$		0			0
$283$	28.9820	−	21.0566i	0.102410	−	0.0744050i	−0.535402	−	0.844597i	$-0.679840\pi$
$283$	28.9820	−	21.0566i	0.102410	−	0.0744050i	0.637812	+	0.770192i	$0.279840\pi$
$284$	−509.399	−	165.514i	−1.79366	−	0.582795i
$285$		0			0
$286$	−22.9424	+	248.114i	−0.0802181	+	0.867530i
$287$		−	96.7636i		−	0.337155i
$288$		0			0
$289$	416.537	−	302.632i	1.44130	−	1.04717i
$290$	6.10821	−	8.40723i	0.0210628	−	0.0289904i
$291$		0			0
$292$	138.793	+	427.161i	0.475318	+	1.46288i
$293$	67.1224	−	92.3860i	0.229087	−	0.315311i	−0.678964	−	0.734172i	$-0.737571\pi$
$293$	67.1224	−	92.3860i	0.229087	−	0.315311i	0.908050	+	0.418861i	$0.137571\pi$
$294$		0			0
$295$	−36.8506	+	113.415i	−0.124917	+	0.384456i
$296$		−	196.091i		−	0.662469i
$297$		0			0
$298$	−134.467			−0.451231
$299$	140.742	+	45.7297i	0.470707	+	0.152942i
$300$		0			0
$301$	1.93906	+	1.40881i	0.00644205	+	0.00468042i
$302$	132.569	−	43.0743i	0.438970	−	0.142630i
$303$		0			0
$304$	−235.811	−	171.327i	−0.775695	−	0.563575i
$305$	−68.3668	−	94.0988i	−0.224153	−	0.308521i
$306$		0			0
$307$	−224.438			−0.731070			−0.365535	−	0.930798i	$-0.619114\pi$
$307$	−224.438			−0.731070			−0.365535	+	0.930798i	$0.619114\pi$
$308$	136.783	+	120.095i	0.444100	+	0.389918i
$309$		0			0
$310$	−13.7653	+	42.3651i	−0.0444041	+	0.136662i
$311$	100.614	+	138.483i	0.323518	+	0.445284i	0.939537	−	0.342447i	$-0.111256\pi$
$311$	100.614	+	138.483i	0.323518	+	0.445284i	−0.616020	+	0.787731i	$0.711256\pi$
$312$		0			0
$313$	−84.7045	−	260.694i	−0.270621	−	0.832887i	−0.990345	−	0.138626i	$-0.955731\pi$
$313$	−84.7045	−	260.694i	−0.270621	−	0.832887i	0.719723	−	0.694261i	$-0.244269\pi$
$314$	51.7637	−	16.8191i	0.164853	−	0.0535639i
$315$		0			0
$316$	461.551	−	335.337i	1.46060	−	1.06119i
$317$	588.275	+	191.142i	1.85576	+	0.602972i	0.995685	+	0.0927984i	$0.0295812\pi$
$317$	588.275	+	191.142i	1.85576	+	0.602972i	0.860072	+	0.510173i	$0.170419\pi$
$318$		0			0
$319$	2.18047	−	23.5811i	0.00683534	−	0.0739218i
$320$			145.625i			0.455077i
$321$		0			0
$322$	157.854	−	114.688i	0.490229	−	0.356172i
$323$	434.407	−	597.909i	1.34491	−	1.85111i
$324$		0			0
$325$	52.3598	+	161.147i	0.161107	+	0.495837i
$326$	244.975	−	337.180i	0.751459	−	1.03429i
$327$		0			0
$328$	−26.0740	+	80.2475i	−0.0794939	+	0.244657i
$329$		−	81.6633i		−	0.248217i
$330$		0			0
$331$	−160.328			−0.484376			−0.242188	−	0.970229i	$-0.577865\pi$
$331$	−160.328			−0.484376			−0.242188	+	0.970229i	$0.577865\pi$
$332$	−594.340	−	193.113i	−1.79018	−	0.581665i
$333$		0			0
$334$	351.844	+	255.629i	1.05342	+	0.765357i
$335$	122.368	−	39.7599i	0.365279	−	0.118686i
$336$		0			0
$337$	88.9953	+	64.6588i	0.264081	+	0.191866i	0.711944	−	0.702236i	$-0.247815\pi$
$337$	88.9953	+	64.6588i	0.264081	+	0.191866i	−0.447863	+	0.894102i	$0.647815\pi$
$338$	−196.797	−	270.868i	−0.582241	−	0.801386i
$339$		0			0
$340$	−227.089			−0.667910
$341$	22.3466	+	99.0222i	0.0655325	+	0.290388i
$342$		0			0
$343$	89.4301	−	275.238i	0.260729	−	0.802442i
$344$	−1.22847	−	1.69085i	−0.00357114	−	0.00491525i
$345$		0			0
$346$	−268.774	−	827.202i	−0.776804	−	2.39076i
$347$	210.883	−	68.5202i	0.607733	−	0.197464i	0.0110468	−	0.999939i	$-0.496484\pi$
$347$	210.883	−	68.5202i	0.607733	−	0.197464i	0.596686	+	0.802475i	$0.296484\pi$
$348$		0			0
$349$	377.286	−	274.115i	1.08105	−	0.785429i	0.103184	−	0.994662i	$-0.467097\pi$
$349$	377.286	−	274.115i	1.08105	−	0.785429i	0.977866	+	0.209234i	$0.0670969\pi$
$350$	212.473	+	69.0367i	0.607066	+	0.197248i
$351$		0			0
$352$	253.427	+	426.531i	0.719964	+	1.21174i
$353$			494.404i			1.40058i	0.713860	+	0.700289i	$0.246945\pi$
$353$			494.404i			1.40058i	−0.713860	+	0.700289i	$0.753055\pi$
$354$		0			0
$355$	140.536	−	102.106i	0.395877	−	0.287621i
$356$	243.331	−	334.917i	0.683515	−	0.940777i
$357$		0			0
$358$	135.501	+	417.028i	0.378493	+	1.16488i
$359$	−16.5578	+	22.7898i	−0.0461219	+	0.0634814i	−0.831455	−	0.555592i	$-0.812492\pi$
$359$	−16.5578	+	22.7898i	−0.0461219	+	0.0634814i	0.785333	+	0.619073i	$0.212492\pi$
$360$		0			0
$361$	98.4129	−	302.884i	0.272612	−	0.839013i
$362$		−	669.246i		−	1.84875i
$363$		0			0
$364$	125.157			0.343838
$365$	−138.538	−	45.0138i	−0.379557	−	0.123326i
$366$		0			0
$367$	−24.1068	−	17.5146i	−0.0656861	−	0.0477238i	0.554458	−	0.832212i	$-0.312926\pi$
$367$	−24.1068	−	17.5146i	−0.0656861	−	0.0477238i	−0.620144	+	0.784488i	$0.712926\pi$
$368$	208.076	−	67.6079i	0.565423	−	0.183717i
$369$		0			0
$370$	263.729	+	191.610i	0.712780	+	0.517865i
$371$	11.3357	+	15.6023i	0.0305545	+	0.0420547i
$372$		0			0
$373$	−313.887			−0.841520			−0.420760	−	0.907172i	$-0.638237\pi$
$373$	−313.887			−0.841520			−0.420760	+	0.907172i	$0.638237\pi$
$374$	−803.001	+	477.110i	−2.14706	+	1.27570i
$375$		0			0
$376$	−22.0051	+	67.7246i	−0.0585241	+	0.180119i
$377$	−9.57107	−	13.1735i	−0.0253875	−	0.0349428i
$378$		0			0
$379$	−9.70792	−	29.8779i	−0.0256146	−	0.0788335i	0.937432	−	0.348168i	$-0.113196\pi$
$379$	−9.70792	−	29.8779i	−0.0256146	−	0.0788335i	−0.963047	+	0.269335i	$0.913196\pi$
$380$	−198.562	+	64.5167i	−0.522532	+	0.169781i
$381$		0			0
$382$	56.2551	−	40.8718i	0.147265	−	0.106994i
$383$	−451.654	−	146.751i	−1.17925	−	0.383163i	−0.347164	−	0.937804i	$-0.612855\pi$
$383$	−451.654	−	146.751i	−1.17925	−	0.383163i	−0.832089	+	0.554642i	$0.812855\pi$
$384$		0			0
$385$	−57.5861	+	12.9956i	−0.149574	+	0.0337548i
$386$			375.674i			0.973249i
$387$		0			0
$388$	−313.703	+	227.918i	−0.808512	+	0.587418i
$389$	24.8910	−	34.2595i	0.0639871	−	0.0880706i	−0.775824	−	0.630949i	$-0.782666\pi$
$389$	24.8910	−	34.2595i	0.0639871	−	0.0880706i	0.839811	+	0.542879i	$0.182666\pi$
$390$		0			0
$391$	171.423	+	527.584i	0.438421	+	1.34932i
$392$	−64.7042	+	89.0577i	−0.165062	+	0.227188i
$393$		0			0
$394$	−11.4618	+	35.2757i	−0.0290908	+	0.0895323i
$395$			185.029i			0.468429i
$396$		0			0
$397$	−560.270			−1.41126			−0.705630	−	0.708580i	$-0.749336\pi$
$397$	−560.270			−1.41126			−0.705630	+	0.708580i	$0.749336\pi$
$398$	−320.754	−	104.219i	−0.805915	−	0.261858i
$399$		0			0
$400$	202.662	+	147.243i	0.506655	+	0.368107i
$401$	−537.622	+	174.684i	−1.34070	+	0.435621i	−0.889555	−	0.456828i	$-0.848986\pi$
$401$	−537.622	+	174.684i	−1.34070	+	0.435621i	−0.451149	+	0.892449i	$0.648986\pi$
$402$		0			0
$403$	56.4686	+	41.0268i	0.140121	+	0.101804i
$404$	113.878	+	156.739i	0.281875	+	0.387968i
$405$		0			0
$406$	−21.4696			−0.0528807
$407$	739.720	+	68.3999i	1.81750	+	0.168059i
$408$		0			0
$409$	53.8474	−	165.725i	0.131656	−	0.405196i	−0.863399	−	0.504522i	$-0.831669\pi$
$409$	53.8474	−	165.725i	0.131656	−	0.405196i	0.995055	+	0.0993261i	$0.0316687\pi$
$410$	−82.4492	−	113.482i	−0.201096	−	0.276784i
$411$		0			0
$412$	−46.2962	−	142.485i	−0.112370	−	0.345838i
$413$	234.314	−	76.1331i	0.567345	−	0.184342i
$414$		0			0
$415$	163.970	−	119.131i	0.395109	−	0.287063i
$416$	324.444	+	105.418i	0.779914	+	0.253409i
$417$		0			0
$418$	−566.579	+	645.310i	−1.35545	+	1.54380i
$419$			279.267i			0.666508i	0.942837	+	0.333254i	$0.108147\pi$
$419$			279.267i			0.666508i	−0.942837	+	0.333254i	$0.891853\pi$
$420$		0			0
$421$	−313.096	+	227.478i	−0.743696	+	0.540327i	−0.893867	−	0.448333i	$-0.852018\pi$
$421$	−313.096	+	227.478i	−0.743696	+	0.540327i	0.150170	+	0.988660i	$0.452018\pi$
$422$	−270.938	+	372.915i	−0.642034	+	0.883684i
$423$		0			0
$424$	−5.19668	−	15.9937i	−0.0122563	−	0.0377211i
$425$	−373.340	+	513.858i	−0.878447	+	1.20908i
$426$		0			0
$427$	−74.2570	+	228.540i	−0.173904	+	0.535222i
$428$			247.255i			0.577698i
$429$		0			0
$430$	3.47447			0.00808017
$431$	−304.315	−	98.8779i	−0.706067	−	0.229415i	−0.0660949	−	0.997813i	$-0.521054\pi$
$431$	−304.315	−	98.8779i	−0.706067	−	0.229415i	−0.639972	+	0.768398i	$0.721054\pi$
$432$		0			0
$433$	−425.660	−	309.260i	−0.983049	−	0.714227i	−0.0246608	−	0.999696i	$-0.507851\pi$
$433$	−425.660	−	309.260i	−0.983049	−	0.714227i	−0.958388	+	0.285469i	$0.907851\pi$
$434$	87.5260	−	28.4389i	0.201673	−	0.0655275i
$435$		0			0
$436$	−602.351	−	437.634i	−1.38154	−	1.00375i
$437$	299.776	+	412.607i	0.685987	+	0.944180i
$438$		0			0
$439$	22.7817			0.0518946			0.0259473	−	0.999663i	$-0.491740\pi$
$439$	22.7817			0.0518946			0.0259473	+	0.999663i	$0.491740\pi$
$440$	51.2588	+	4.73976i	0.116497	+	0.0107722i
$441$		0			0
$442$	−198.464	+	610.809i	−0.449013	+	1.38192i
$443$	−35.2684	−	48.5428i	−0.0796127	−	0.109577i	0.767353	−	0.641225i	$-0.221573\pi$
$443$	−35.2684	−	48.5428i	−0.0796127	−	0.109577i	−0.846966	+	0.531647i	$0.821573\pi$
$444$		0			0
$445$	41.4897	+	127.692i	0.0932352	+	0.286949i
$446$	804.323	−	261.340i	1.80341	−	0.585965i
$447$		0			0
$448$	243.400	−	176.840i	0.543304	−	0.394733i
$449$	−723.967	−	235.231i	−1.61240	−	0.523900i	−0.642267	−	0.766481i	$-0.722006\pi$
$449$	−723.967	−	235.231i	−1.61240	−	0.523900i	−0.970131	+	0.242581i	$0.922006\pi$
$450$		0			0
$451$	−293.626	−	126.352i	−0.651055	−	0.280159i
$452$			633.459i			1.40146i
$453$		0			0
$454$	491.528	−	357.116i	1.08266	−	0.786599i
$455$	−23.8590	+	32.8391i	−0.0524374	+	0.0721739i
$456$		0			0
$457$	−243.795	−	750.325i	−0.533469	−	1.64185i	−0.746934	−	0.664898i	$-0.768475\pi$
$457$	−243.795	−	750.325i	−0.533469	−	1.64185i	0.213465	−	0.976951i	$-0.431525\pi$
$458$	737.804	−	1015.50i	1.61093	−	2.21725i
$459$		0			0
$460$	48.4262	−	149.040i	0.105274	−	0.324001i
$461$		−	726.842i		−	1.57666i	−0.615250	−	0.788332i	$-0.710945\pi$
$461$		−	726.842i		−	1.57666i	0.615250	−	0.788332i	$-0.289055\pi$
$462$		0			0
$463$	301.548			0.651291			0.325646	−	0.945492i	$-0.394418\pi$
$463$	301.548			0.651291			0.325646	+	0.945492i	$0.394418\pi$
$464$	−22.8953	−	7.43915i	−0.0493434	−	0.0160326i
$465$		0			0
$466$	269.240	+	195.614i	0.577769	+	0.419773i
$467$	278.170	−	90.3828i	0.595652	−	0.193539i	0.00435192	−	0.999991i	$-0.498615\pi$
$467$	278.170	−	90.3828i	0.595652	−	0.193539i	0.591300	+	0.806451i	$0.298615\pi$
$468$		0			0
$469$	−215.055	−	156.246i	−0.458539	−	0.333148i
$470$	−69.5827	−	95.7724i	−0.148048	−	0.203771i
$471$		0			0
$472$	−214.835			−0.455158
$473$	6.80695	−	4.04441i	0.0143910	−	0.00855055i
$474$		0			0
$475$	−180.452	+	555.373i	−0.379898	+	1.16921i
$476$	275.768	+	379.562i	0.579345	+	0.797400i
$477$		0			0
$478$	−290.652	−	894.536i	−0.608059	−	1.87141i
$479$	−472.561	+	153.544i	−0.986557	+	0.320552i	−0.757481	−	0.652857i	$-0.773570\pi$
$479$	−472.561	+	153.544i	−0.986557	+	0.320552i	−0.229076	+	0.973409i	$0.573570\pi$
$480$		0			0
$481$	413.242	−	300.238i	0.859130	−	0.624194i
$482$	297.062	+	96.5214i	0.616312	+	0.200252i
$483$		0			0
$484$	543.031	−	258.246i	1.12196	−	0.533566i
$485$		−	125.759i		−	0.259297i
$486$		0			0
$487$	−559.612	+	406.582i	−1.14910	+	0.834870i	−0.988361	−	0.152127i	$-0.951388\pi$
$487$	−559.612	+	406.582i	−1.14910	+	0.834870i	−0.160739	+	0.986997i	$0.551388\pi$
$488$	123.165	−	169.522i	0.252387	−	0.347381i
$489$		0			0
$490$	−56.5508	−	174.045i	−0.115410	−	0.355195i
$491$	174.127	−	239.665i	0.354638	−	0.488117i	−0.594007	−	0.804460i	$-0.702455\pi$
$491$	174.127	−	239.665i	0.354638	−	0.488117i	0.948645	+	0.316343i	$0.102455\pi$
$492$		0			0
$493$	18.8623	−	58.0521i	0.0382602	−	0.117753i
$494$			590.462i			1.19527i
$495$		0			0
$496$	103.192			0.208049
$497$	−341.323	−	110.903i	−0.686766	−	0.223144i
$498$		0			0
$499$	108.411	+	78.7653i	0.217257	+	0.157846i	0.691091	−	0.722768i	$-0.257130\pi$
$499$	108.411	+	78.7653i	0.217257	+	0.157846i	−0.473834	+	0.880614i	$0.657130\pi$
$500$	361.086	−	117.324i	0.722172	−	0.234648i
$501$		0			0
$502$	808.139	+	587.147i	1.60984	+	1.16962i
$503$	111.681	+	153.716i	0.222030	+	0.305598i	0.905471	−	0.424408i	$-0.139518\pi$
$503$	111.681	+	153.716i	0.222030	+	0.305598i	−0.683442	+	0.730005i	$0.739518\pi$
$504$		0			0
$505$	−62.8345			−0.124425
$506$	−141.893	−	628.758i	−0.280422	−	1.24261i
$507$		0			0
$508$	365.449	−	1124.74i	0.719388	−	2.21405i
$509$	70.0055	+	96.3543i	0.137535	+	0.189301i	0.872229	−	0.489098i	$-0.162674\pi$
$509$	70.0055	+	96.3543i	0.137535	+	0.189301i	−0.734693	+	0.678399i	$0.762674\pi$
$510$		0			0
$511$	92.9982	+	286.219i	0.181992	+	0.560115i
$512$	603.181	−	195.985i	1.17809	−	0.382784i
$513$		0			0
$514$	−743.813	+	540.412i	−1.44711	+	1.05139i
$515$	46.2113	+	15.0150i	0.0897307	+	0.0291553i
$516$		0			0
$517$	−247.804	−	106.634i	−0.479312	−	0.206255i
$518$		−	673.485i		−	1.30016i
$519$		0			0
$520$	28.6355	−	20.8049i	0.0550683	−	0.0400095i
$521$	−374.594	+	515.584i	−0.718990	+	0.989605i	0.280567	+	0.959835i	$0.409478\pi$
$521$	−374.594	+	515.584i	−0.718990	+	0.989605i	−0.999557	+	0.0297704i	$0.990522\pi$
$522$		0			0
$523$	40.0788	+	123.350i	0.0766325	+	0.235851i	0.982033	−	0.188707i	$-0.0604297\pi$
$523$	40.0788	+	123.350i	0.0766325	+	0.235851i	−0.905401	+	0.424558i	$0.860430\pi$
$524$	−433.872	+	597.173i	−0.828000	+	1.13964i
$525$		0			0
$526$	−230.500	+	709.406i	−0.438213	+	1.34868i
$527$			261.649i			0.496487i
$528$		0			0
$529$	146.187			0.276346
$530$	26.5884	+	8.63910i	0.0501668	+	0.0163002i
$531$		0			0
$532$	348.960	+	253.535i	0.655940	+	0.476569i
$533$	−209.036	+	67.9199i	−0.392187	+	0.127429i
$534$		0			0
$535$	−64.8755	−	47.1348i	−0.121263	−	0.0881025i
$536$	136.246	+	187.526i	0.254190	+	0.349863i
$537$		0			0
$538$	589.779			1.09624
$539$	−313.386	−	275.151i	−0.581421	−	0.510484i
$540$		0			0
$541$	−152.652	+	469.814i	−0.282166	+	0.868417i	0.705068	+	0.709140i	$0.250916\pi$
$541$	−152.652	+	469.814i	−0.282166	+	0.868417i	−0.987234	+	0.159278i	$0.949084\pi$
$542$	−815.865	−	1122.94i	−1.50529	−	2.07185i
$543$		0			0
$544$	395.172	+	1216.21i	0.726418	+	2.23569i
$545$	229.656	−	74.6197i	0.421387	−	0.136917i
$546$		0			0
$547$	85.8592	−	62.3803i	0.156964	−	0.114041i	−0.506531	−	0.862222i	$-0.669072\pi$
$547$	85.8592	−	62.3803i	0.156964	−	0.114041i	0.663495	+	0.748181i	$0.269072\pi$
$548$	−95.2752	−	30.9568i	−0.173860	−	0.0564905i
$549$		0			0
$550$	486.932	−	554.595i	0.885331	−	1.00836i
$551$		−	56.1183i		−	0.101848i
$552$		0			0
$553$	309.262	−	224.692i	0.559245	−	0.406315i
$554$	41.2894	−	56.8300i	0.0745296	−	0.102581i
$555$		0			0
$556$	−228.626	−	703.639i	−0.411198	−	1.26554i
$557$	−486.473	+	669.572i	−0.873380	+	1.20210i	0.104830	+	0.994490i	$0.466570\pi$
$557$	−486.473	+	669.572i	−0.873380	+	1.20210i	−0.978211	+	0.207615i	$0.933430\pi$
$558$		0			0
$559$	1.68236	−	5.17776i	0.00300958	−	0.00926254i
$560$			60.0113i			0.107163i
$561$		0			0
$562$	789.001			1.40392
$563$	447.869	+	145.521i	0.795504	+	0.258475i	0.678446	−	0.734650i	$-0.262654\pi$
$563$	447.869	+	145.521i	0.795504	+	0.258475i	0.117058	+	0.993125i	$0.462654\pi$
$564$		0			0
$565$	−166.209	−	120.758i	−0.294176	−	0.213731i
$566$	−102.038	+	33.1540i	−0.180279	+	0.0585760i
$567$		0			0
$568$	253.180	+	183.946i	0.445740	+	0.323849i
$569$	−117.601	−	161.863i	−0.206679	−	0.284470i	0.693076	−	0.720865i	$-0.256255\pi$
$569$	−117.601	−	161.863i	−0.206679	−	0.284470i	−0.899755	+	0.436395i	$0.856255\pi$
$570$		0			0
$571$	658.692			1.15358			0.576788	−	0.816894i	$-0.304306\pi$
$571$	658.692			1.15358			0.576788	+	0.816894i	$0.304306\pi$
$572$	163.427	−	379.785i	0.285712	−	0.663960i
$573$		0			0
$574$	−89.5526	+	275.615i	−0.156015	+	0.480165i
$575$	−257.635	−	354.604i	−0.448061	−	0.616703i
$576$		0			0
$577$	−31.2037	−	96.0352i	−0.0540792	−	0.166439i	0.920369	−	0.391051i	$-0.127888\pi$
$577$	−31.2037	−	96.0352i	−0.0540792	−	0.166439i	−0.974448	+	0.224612i	$0.927888\pi$
$578$	−1466.51	+	476.499i	−2.53722	+	0.824394i
$579$		0			0
$580$	−13.9502	+	10.1354i	−0.0240521	+	0.0174749i
$581$	−398.238	−	129.395i	−0.685435	−	0.222711i
$582$		0			0
$583$	62.1465	−	14.0247i	0.106598	−	0.0240562i
$584$		−	262.425i		−	0.449358i
$585$		0			0
$586$	−276.688	+	201.026i	−0.472164	+	0.343047i
$587$	−205.366	+	282.662i	−0.349857	+	0.481537i	−0.947288	−	0.320383i	$-0.896188\pi$
$587$	−205.366	+	282.662i	−0.349857	+	0.481537i	0.597431	+	0.801921i	$0.296188\pi$
$588$		0			0
$589$	74.3352	+	228.780i	0.126206	+	0.388421i
$590$	209.926	−	288.938i	0.355806	−	0.489725i
$591$		0			0
$592$	233.361	−	718.210i	0.394190	−	1.21319i
$593$		−	670.238i		−	1.13025i	−0.825005	−	0.565125i	$-0.808828\pi$
$593$		−	670.238i		−	1.13025i	0.825005	−	0.565125i	$-0.191172\pi$
$594$		0			0
$595$	−152.161			−0.255733
$596$	212.202	+	68.9488i	0.356044	+	0.115686i
$597$		0			0
$598$	−358.557	−	260.507i	−0.599593	−	0.435630i
$599$	733.577	−	238.354i	1.22467	−	0.397919i	0.375889	−	0.926665i	$-0.377338\pi$
$599$	733.577	−	238.354i	1.22467	−	0.397919i	0.848780	+	0.528746i	$0.177338\pi$
$600$		0			0
$601$	150.252	+	109.165i	0.250004	+	0.181638i	0.705728	−	0.708482i	$-0.250620\pi$
$601$	150.252	+	109.165i	0.250004	+	0.181638i	−0.455725	+	0.890121i	$0.650620\pi$
$602$	−4.21926	−	5.80731i	−0.00700873	−	0.00964669i
$603$		0			0
$604$	−231.294			−0.382937
$605$	−35.7600	+	191.712i	−0.0591074	+	0.316880i
$606$		0			0
$607$	−150.857	+	464.292i	−0.248530	+	0.764895i	0.746506	+	0.665378i	$0.231730\pi$
$607$	−150.857	+	464.292i	−0.248530	+	0.764895i	−0.995036	+	0.0995170i	$0.968270\pi$
$608$	691.059	+	951.161i	1.13661	+	1.56441i
$609$		0			0
$610$	107.645	+	331.297i	0.176467	+	0.543109i
$611$	−176.415	+	57.3207i	−0.288732	+	0.0938146i
$612$		0			0
$613$	−412.972	+	300.041i	−0.673689	+	0.489464i	−0.871258	−	0.490825i	$-0.836695\pi$
$613$	−412.972	+	300.041i	−0.673689	+	0.489464i	0.197569	+	0.980289i	$0.436695\pi$
$614$	639.275	+	207.713i	1.04116	+	0.338295i
$615$		0			0
$616$	−54.3245	−	91.4309i	−0.0881891	−	0.148427i
$617$		−	1142.14i		−	1.85111i	−0.378608	−	0.925557i	$-0.623597\pi$
$617$		−	1142.14i		−	1.85111i	0.378608	−	0.925557i	$-0.376403\pi$
$618$		0			0
$619$	734.760	−	533.834i	1.18701	−	0.862414i	0.194066	−	0.980989i	$-0.437832\pi$
$619$	734.760	−	533.834i	1.18701	−	0.862414i	0.992945	+	0.118575i	$0.0378325\pi$
$620$	43.4460	−	59.7983i	0.0700742	−	0.0964488i
$621$		0			0
$622$	−158.419	−	487.562i	−0.254692	−	0.783862i
$623$	163.044	−	224.411i	0.261708	−	0.360210i
$624$		0			0
$625$	135.017	−	415.538i	0.216027	−	0.664862i
$626$			820.934i			1.31140i
$627$		0			0
$628$	−90.3126			−0.143810
$629$	1821.05	+	591.696i	2.89515	+	0.940693i
$630$		0			0
$631$	−764.038	−	555.106i	−1.21084	−	0.879724i	−0.215530	−	0.976497i	$-0.569148\pi$
$631$	−764.038	−	555.106i	−1.21084	−	0.879724i	−0.995306	+	0.0967735i	$0.969148\pi$
$632$	−317.022	+	103.007i	−0.501617	+	0.162985i
$633$		0			0
$634$	−1498.70	−	1088.87i	−2.36389	−	1.71746i
$635$	225.446	+	310.299i	0.355032	+	0.488660i
$636$		0			0
$637$	−286.750			−0.450157
$638$	−28.0345	+	65.1487i	−0.0439412	+	0.102114i
$639$		0			0
$640$	44.9169	−	138.240i	0.0701826	−	0.216000i
$641$	211.062	+	290.502i	0.329270	+	0.453202i	0.941269	−	0.337657i	$-0.109634\pi$
$641$	211.062	+	290.502i	0.329270	+	0.453202i	−0.611999	+	0.790859i	$0.709634\pi$
$642$		0			0
$643$	286.813	+	882.719i	0.446054	+	1.37281i	0.881324	+	0.472513i	$0.156653\pi$
$643$	286.813	+	882.719i	0.446054	+	1.37281i	−0.435269	+	0.900300i	$0.643347\pi$
$644$	−307.916	+	100.048i	−0.478131	+	0.155354i
$645$		0			0
$646$	−1790.69	+	1301.01i	−2.77196	+	2.01395i
$647$	414.935	+	134.821i	0.641322	+	0.208378i	0.611584	−	0.791180i	$-0.290533\pi$
$647$	414.935	+	134.821i	0.641322	+	0.208378i	0.0297382	+	0.999558i	$0.490533\pi$
$648$		0			0
$649$	74.9381	−	810.429i	0.115467	−	1.24873i
$650$		−	507.458i		−	0.780705i
$651$		0			0
$652$	−559.487	+	406.491i	−0.858110	+	0.623453i
$653$	−143.077	+	196.928i	−0.219107	+	0.301575i	−0.904394	−	0.426698i	$-0.859677\pi$
$653$	−143.077	+	196.928i	−0.219107	+	0.301575i	0.685287	+	0.728273i	$0.259677\pi$
$654$		0			0
$655$	−73.9782	−	227.682i	−0.112944	−	0.347605i
$656$	−190.999	+	262.888i	−0.291158	+	0.400744i
$657$		0			0
$658$	−75.5777	+	232.604i	−0.114860	+	0.353502i
$659$		−	348.053i		−	0.528153i	−0.964502	−	0.264076i	$-0.914933\pi$
$659$		−	348.053i		−	0.528153i	0.964502	−	0.264076i	$-0.0850671\pi$
$660$		0			0
$661$	601.901			0.910592			0.455296	−	0.890340i	$-0.349533\pi$
$661$	601.901			0.910592			0.455296	+	0.890340i	$0.349533\pi$
$662$	456.669	+	148.381i	0.689832	+	0.224140i
$663$		0			0
$664$	295.398	+	214.619i	0.444876	+	0.323221i
$665$	−133.046	+	43.2294i	−0.200070	+	0.0650066i
$666$		0			0
$667$	34.0777	+	24.7589i	0.0510910	+	0.0371198i
$668$	−424.170	−	583.819i	−0.634984	−	0.873981i
$669$		0			0
$670$	−385.343			−0.575138
$671$	596.532	+	523.752i	0.889020	+	0.780555i
$672$		0			0
$673$	228.328	−	702.722i	0.339269	−	1.04416i	−0.625312	−	0.780375i	$-0.715028\pi$
$673$	228.328	−	702.722i	0.339269	−	1.04416i	0.964581	−	0.263788i	$-0.0849719\pi$
$674$	−193.648	−	266.533i	−0.287311	−	0.395450i
$675$		0			0
$676$	171.677	+	528.367i	0.253960	+	0.781608i
$677$	−40.0554	+	13.0148i	−0.0591661	+	0.0192242i	−0.338451	−	0.940984i	$-0.609903\pi$
$677$	−40.0554	+	13.0148i	−0.0591661	+	0.0192242i	0.279284	+	0.960208i	$0.409903\pi$
$678$		0			0
$679$	−210.196	+	152.717i	−0.309568	+	0.224914i
$680$	126.190	+	41.0015i	0.185573	+	0.0602963i
$681$		0			0
$682$	27.9925	−	302.729i	0.0410448	−	0.443885i
$683$		−	543.110i		−	0.795183i	−0.917562	−	0.397592i	$-0.869846\pi$
$683$		−	543.110i		−	0.795183i	0.917562	−	0.397592i	$-0.130154\pi$
$684$		0			0
$685$	26.2851	−	19.0972i	0.0383724	−	0.0278792i
$686$	−509.453	+	701.202i	−0.742643	+	1.02216i
$687$		0			0
$688$	−2.48724	−	7.65492i	−0.00361517	−	0.0111263i
$689$	25.7485	−	35.4398i	0.0373708	−	0.0514365i
$690$		0			0
$691$	−132.313	+	407.217i	−0.191480	+	0.589315i	0.808519	+	0.588469i	$0.200269\pi$
$691$	−132.313	+	407.217i	−0.191480	+	0.589315i	−1.00000		0.000845986i	$0.999731\pi$
$692$			1443.22i			2.08558i
$693$		0			0
$694$	−664.080			−0.956887
$695$	228.207	+	74.1488i	0.328355	+	0.106689i
$696$		0			0
$697$	−666.564	−	484.287i	−0.956333	−	0.694816i
$698$	−1328.32	+	431.599i	−1.90304	+	0.618336i
$699$		0			0
$700$	−299.905	−	217.894i	−0.428436	−	0.311277i
$701$	−1.63437	−	2.24952i	−0.00233149	−	0.00320902i	0.807850	−	0.589389i	$-0.200631\pi$
$701$	−1.63437	−	2.24952i	−0.00233149	−	0.00320902i	−0.810181	+	0.586180i	$0.800631\pi$
$702$		0			0
$703$	1760.39			2.50411
$704$	−218.790	−	969.503i	−0.310781	−	1.37713i
$705$		0			0
$706$	457.560	−	1408.23i	0.648103	−	1.99465i
$707$	76.3037	+	105.023i	0.107926	+	0.148547i
$708$		0			0
$709$	332.968	+	1024.77i	0.469631	+	1.44537i	0.853064	+	0.521806i	$0.174742\pi$
$709$	332.968	+	1024.77i	0.469631	+	1.44537i	−0.383433	+	0.923568i	$0.625258\pi$
$710$	−494.790	+	160.767i	−0.696888	+	0.226433i
$711$		0			0
$712$	−195.685	+	142.173i	−0.274838	+	0.199682i
$713$	−171.722	−	55.7959i	−0.240844	−	0.0782551i
$714$		0			0
$715$	68.4946	+	115.280i	0.0957967	+	0.161231i
$716$		−	727.591i		−	1.01619i
$717$		0			0
$718$	68.2535	−	49.5891i	0.0950606	−	0.0690656i
$719$	630.939	−	868.413i	0.877523	−	1.20781i	−0.0995782	−	0.995030i	$-0.531749\pi$
$719$	630.939	−	868.413i	0.877523	−	1.20781i	0.977101	−	0.212777i	$-0.0682506\pi$
$720$		0			0
$721$	−31.0208	−	95.4722i	−0.0430247	−	0.132416i
$722$	−560.625	+	771.634i	−0.776489	+	1.06875i
$723$		0			0
$724$	−343.160	+	1056.14i	−0.473978	+	1.45875i
$725$			48.2295i			0.0665234i
$726$		0			0
$727$	−212.371			−0.292119			−0.146060	−	0.989276i	$-0.546659\pi$
$727$	−212.371			−0.292119			−0.146060	+	0.989276i	$0.546659\pi$
$728$	−69.5476	−	22.5974i	−0.0955325	−	0.0310404i
$729$		0			0
$730$	352.944	+	256.429i	0.483484	+	0.351272i
$731$	19.4094	−	6.30649i	0.0265518	−	0.00862721i
$732$		0			0
$733$	762.274	+	553.825i	1.03994	+	0.755559i	0.970273	−	0.242011i	$-0.0778072\pi$
$733$	762.274	+	553.825i	1.03994	+	0.755559i	0.0696644	+	0.997570i	$0.477807\pi$
$734$	52.4548	+	72.1978i	0.0714642	+	0.0983621i
$735$		0			0
$736$	−882.479			−1.19902
$737$	−754.938	+	448.553i	−1.02434	+	0.608620i
$738$		0			0
$739$	−222.759	+	685.580i	−0.301432	+	0.927714i	0.679552	+	0.733627i	$0.262174\pi$
$739$	−222.759	+	685.580i	−0.301432	+	0.927714i	−0.980984	+	0.194086i	$0.937826\pi$
$740$	−317.941	−	437.609i	−0.429650	−	0.591363i
$741$		0			0
$742$	−17.8483	−	54.9314i	−0.0240543	−	0.0740316i
$743$	−795.619	+	258.512i	−1.07082	+	0.347931i	−0.790807	−	0.612066i	$-0.790339\pi$
$743$	−795.619	+	258.512i	−1.07082	+	0.347931i	−0.280013	+	0.959996i	$0.590339\pi$
$744$		0			0
$745$	−58.5437	+	42.5345i	−0.0785822	+	0.0570933i
$746$	894.054	+	290.496i	1.19846	+	0.389405i
$747$		0			0
$748$	1511.86	−	341.185i	2.02120	−	0.456130i
$749$			165.673i			0.221192i
$750$		0			0
$751$	28.5315	−	20.7293i	0.0379913	−	0.0276023i	−0.568628	−	0.822595i	$-0.692525\pi$
$751$	28.5315	−	20.7293i	0.0379913	−	0.0276023i	0.606619	+	0.794993i	$0.292525\pi$
$752$	−161.193	+	221.864i	−0.214353	+	0.295031i
$753$		0			0
$754$	15.0698	+	46.3802i	0.0199865	+	0.0615122i
$755$	44.0922	−	60.6877i	0.0584002	−	0.0803810i
$756$		0			0
$757$	140.510	−	432.445i	0.185614	−	0.571262i	−0.814344	−	0.580382i	$-0.802903\pi$
$757$	140.510	−	432.445i	0.185614	−	0.571262i	0.999958	+	0.00912038i	$0.00290315\pi$
$758$			94.0866i			0.124125i
$759$		0			0
$760$	121.986			0.160508
$761$	−99.5654	−	32.3508i	−0.130835	−	0.0425108i	0.242868	−	0.970059i	$-0.421912\pi$
$761$	−99.5654	−	32.3508i	−0.130835	−	0.0425108i	−0.373703	+	0.927549i	$0.621912\pi$
$762$		0			0
$763$	−403.605	−	293.237i	−0.528972	−	0.384320i
$764$	−109.734	+	35.6546i	−0.143630	+	0.0466683i
$765$		0			0
$766$	1150.64	+	835.992i	1.50215	+	1.09137i
$767$	−328.937	−	452.742i	−0.428861	−	0.590277i
$768$		0			0
$769$	−93.7806			−0.121951			−0.0609757	−	0.998139i	$-0.519421\pi$
$769$	−93.7806			−0.121951			−0.0609757	+	0.998139i	$0.519421\pi$
$770$	176.051	+	16.2790i	0.228638	+	0.0211415i
$771$		0			0
$772$	192.629	−	592.852i	0.249520	−	0.767943i
$773$	210.854	+	290.216i	0.272774	+	0.375441i	0.923324	−	0.384023i	$-0.125462\pi$
$773$	210.854	+	290.216i	0.272774	+	0.375441i	−0.650550	+	0.759463i	$0.725462\pi$
$774$		0			0
$775$	−63.8855	−	196.619i	−0.0824329	−	0.253702i
$776$	215.470	−	70.0105i	0.277668	−	0.0902197i
$777$		0			0
$778$	−102.604	+	74.5463i	−0.131882	+	0.0958178i
$779$	−720.416	−	234.077i	−0.924796	−	0.300485i
$780$		0			0
$781$	−782.221	+	890.918i	−1.00156	+	1.14074i
$782$		−	1661.38i		−	2.12453i
$783$		0			0
$784$	−342.973	+	249.184i	−0.437465	+	0.317837i
$785$	17.2165	−	23.6965i	0.0219319	−	0.0301866i
$786$		0			0
$787$	85.5717	+	263.363i	0.108732	+	0.334641i	0.990588	−	0.136876i	$-0.0437063\pi$
$787$	85.5717	+	263.363i	0.108732	+	0.334641i	−0.881857	+	0.471518i	$0.843706\pi$
$788$	36.1757	−	49.7916i	0.0459083	−	0.0631873i
$789$		0			0
$790$	171.241	−	527.025i	0.216761	−	0.667120i
$791$			424.449i			0.536598i
$792$		0			0
$793$	545.830			0.688311
$794$	1595.84	+	518.519i	2.00987	+	0.653046i
$795$		0			0
$796$	452.743	+	328.937i	0.568773	+	0.413238i
$797$	502.740	−	163.350i	0.630790	−	0.204956i	0.0238652	−	0.999715i	$-0.492403\pi$
$797$	502.740	−	163.350i	0.630790	−	0.204956i	0.606925	+	0.794759i	$0.292403\pi$
$798$		0			0
$799$	−562.544	−	408.712i	−0.704061	−	0.511530i
$800$	−593.913	−	817.451i	−0.742392	−	1.02181i
$801$		0			0
$802$	1692.99			2.11096
$803$	989.956	+	91.5385i	1.23282	+	0.113996i
$804$		0			0
$805$	32.4480	−	99.8645i	0.0403080	−	0.124055i
$806$	−122.872	−	169.118i	−0.152446	−	0.209824i
$807$		0			0
$808$	−34.9802	−	107.658i	−0.0432923	−	0.133240i
$809$	1196.30	−	388.701i	1.47874	−	0.480470i	0.545001	−	0.838436i	$-0.316529\pi$
$809$	1196.30	−	388.701i	1.47874	−	0.480470i	0.933735	+	0.357965i	$0.116529\pi$
$810$		0			0
$811$	842.338	−	611.995i	1.03864	−	0.754617i	0.0686215	−	0.997643i	$-0.478140\pi$
$811$	842.338	−	611.995i	1.03864	−	0.754617i	0.970020	+	0.243026i	$0.0781399\pi$
$812$	33.8812	+	11.0087i	0.0417256	+	0.0135575i
$813$		0			0
$814$	−2043.67	−	879.421i	−2.51065	−	1.08037i
$815$		−	224.291i		−	0.275203i
$816$		0			0
$817$	15.1794	−	11.0285i	0.0185795	−	0.0134988i
$818$	−306.750	+	422.206i	−0.375000	+	0.516144i
$819$		0			0
$820$	71.9248	+	221.362i	0.0877132	+	0.269953i
$821$	256.077	−	352.460i	0.311908	−	0.429305i	−0.624067	−	0.781371i	$-0.714521\pi$
$821$	256.077	−	352.460i	0.311908	−	0.429305i	0.935975	+	0.352066i	$0.114521\pi$
$822$		0			0
$823$	181.461	−	558.480i	0.220487	−	0.678590i	−0.778231	−	0.627978i	$-0.783883\pi$
$823$	181.461	−	558.480i	0.220487	−	0.678590i	0.998718	−	0.0506122i	$-0.0161172\pi$
$824$			87.5354i			0.106232i
$825$		0			0
$826$	−737.862			−0.893296
$827$	−261.498	−	84.9657i	−0.316200	−	0.102740i	0.146617	−	0.989193i	$-0.453161\pi$
$827$	−261.498	−	84.9657i	−0.316200	−	0.102740i	−0.462817	+	0.886454i	$0.653161\pi$
$828$		0			0
$829$	741.496	+	538.729i	0.894447	+	0.649854i	0.937034	−	0.349239i	$-0.113560\pi$
$829$	741.496	+	538.729i	0.894447	+	0.649854i	−0.0425868	+	0.999093i	$0.513560\pi$
$830$	−577.295	+	187.575i	−0.695536	+	0.225993i
$831$		0			0
$832$	−552.870	−	401.684i	−0.664508	−	0.482793i
$833$	−631.817	−	869.622i	−0.758484	−	1.04396i
$834$		0			0
$835$	234.045			0.280293
$836$	1225.01	−	727.848i	1.46532	−	0.870632i
$837$		0			0
$838$	258.456	−	795.444i	0.308420	−	0.949218i
$839$	−622.365	−	856.612i	−0.741794	−	1.02099i	−0.998513	−	0.0545057i	$-0.982642\pi$
$839$	−622.365	−	856.612i	−0.741794	−	1.02099i	0.256720	−	0.966486i	$-0.417358\pi$
$840$		0			0
$841$	258.451	+	795.430i	0.307314	+	0.945815i
$842$	1102.33	−	358.168i	1.30918	−	0.425378i
$843$		0			0
$844$	618.783	−	449.572i	0.733155	−	0.532668i
$845$	−171.362	−	55.6789i	−0.202795	−	0.0658922i
$846$		0			0
$847$	363.858	−	173.038i	0.429584	−	0.204295i
$848$		−	64.7637i		−	0.0763723i
$849$		0			0
$850$	1538.96	−	1118.12i	1.81054	−	1.31544i
$851$	−776.669	+	1068.99i	−0.912654	+	1.25616i
$852$		0			0
$853$	−81.1273	−	249.684i	−0.0951082	−	0.292713i	0.892174	−	0.451693i	$-0.149180\pi$
$853$	−81.1273	−	249.684i	−0.0951082	−	0.292713i	−0.987282	+	0.158980i	$0.949180\pi$
$854$	423.017	−	582.233i	0.495336	−	0.681772i
$855$		0			0
$856$	44.6424	−	137.395i	0.0521523	−	0.160508i
$857$		−	139.937i		−	0.163287i	−0.996662	−	0.0816437i	$-0.973983\pi$
$857$		−	139.937i		−	0.163287i	0.996662	−	0.0816437i	$-0.0260169\pi$
$858$		0			0
$859$	−466.124			−0.542635			−0.271318	−	0.962490i	$-0.587459\pi$
$859$	−466.124			−0.542635			−0.271318	+	0.962490i	$0.587459\pi$
$860$	−5.48307	−	1.78156i	−0.00637566	−	0.00207158i
$861$		0			0
$862$	775.280	+	563.274i	0.899397	+	0.653450i
$863$	−212.481	+	69.0391i	−0.246212	+	0.0799990i	−0.429523	−	0.903056i	$-0.641318\pi$
$863$	−212.481	+	69.0391i	−0.246212	+	0.0799990i	0.183311	+	0.983055i	$0.441318\pi$
$864$		0			0
$865$	−378.678	−	275.126i	−0.437778	−	0.318064i
$866$	926.207	+	1274.81i	1.06952	+	1.47207i
$867$		0			0
$868$	−152.707			−0.175930
$869$	−277.993	−	1231.84i	−0.319900	−	1.41754i
$870$		0			0
$871$	−186.585	+	574.249i	−0.214219	+	0.659299i
$872$	255.700	+	351.941i	0.293234	+	0.403602i
$873$		0			0
$874$	−472.004	−	1452.68i	−0.540050	−	1.66210i
$875$	241.946	−	78.6129i	0.276509	−	0.0898433i
$876$		0			0
$877$	−360.882	+	262.196i	−0.411496	+	0.298969i	−0.774207	−	0.632932i	$-0.781851\pi$
$877$	−360.882	+	262.196i	−0.411496	+	0.298969i	0.362711	+	0.931902i	$0.381851\pi$
$878$	−64.8899	−	21.0840i	−0.0739065	−	0.0240137i
$879$		0			0
$880$	182.102	+	78.3614i	0.206934	+	0.0890470i
$881$			1631.61i			1.85200i	0.377522	+	0.926001i	$0.376776\pi$
$881$			1631.61i			1.85200i	−0.377522	+	0.926001i	$0.623224\pi$
$882$		0			0
$883$	−1206.42	+	876.515i	−1.36627	+	0.992656i	−0.368256	+	0.929724i	$0.620045\pi$
$883$	−1206.42	+	876.515i	−1.36627	+	0.992656i	−0.998018	+	0.0629318i	$0.979955\pi$
$884$	626.393	−	862.155i	0.708589	−	0.975289i
$885$		0			0
$886$	55.5308	+	170.906i	0.0626758	+	0.192896i
$887$	−366.280	+	504.141i	−0.412943	+	0.568367i	−0.963933	−	0.266145i	$-0.914250\pi$
$887$	−366.280	+	504.141i	−0.412943	+	0.568367i	0.550991	+	0.834511i	$0.314250\pi$
$888$		0			0
$889$	244.869	−	753.629i	0.275443	−	0.847727i
$890$		−	402.107i		−	0.451806i
$891$		0			0
$892$	−1403.31			−1.57321
$893$	−607.993	−	197.549i	−0.680843	−	0.221219i
$894$		0			0
$895$	190.908	+	138.703i	0.213305	+	0.154975i
$896$	−285.603	+	92.7979i	−0.318753	+	0.103569i
$897$		0			0
$898$	1844.40	+	1340.03i	2.05389	+	1.49224i
$899$	11.6779	+	16.0732i	0.0129899	+	0.0178790i
$900$		0			0
$901$	164.211			0.182254
$902$	719.407	+	631.636i	0.797569	+	0.700261i
$903$		0			0
$904$	114.372	−	352.002i	0.126518	−	0.389383i
$905$	−211.696	−	291.374i	−0.233918	−	0.321960i
$906$		0			0
$907$	−298.683	−	919.251i	−0.329308	−	1.01351i	−0.969458	−	0.245257i	$-0.921128\pi$
$907$	−298.683	−	919.251i	−0.329308	−	1.01351i	0.640150	−	0.768250i	$-0.278872\pi$
$908$	−958.795	+	311.531i	−1.05594	+	0.343096i
$909$		0			0
$910$	98.3504	−	71.4557i	0.108077	−	0.0785228i
$911$	−586.842	−	190.676i	−0.644173	−	0.209304i	−0.0313298	−	0.999509i	$-0.509974\pi$
$911$	−586.842	−	190.676i	−0.644173	−	0.209304i	−0.612843	+	0.790205i	$0.709974\pi$
$912$		0			0
$913$	−912.655	+	1039.48i	−0.999622	+	1.13853i
$914$			2362.80i			2.58512i
$915$		0			0
$916$	−1685.03	+	1224.25i	−1.83956	+	1.33652i
$917$	−290.716	+	400.136i	−0.317029	+	0.436353i
$918$		0			0
$919$	341.206	+	1050.12i	0.371279	+	1.14268i	0.945955	+	0.324299i	$0.105128\pi$
$919$	341.206	+	1050.12i	0.371279	+	1.14268i	−0.574676	+	0.818381i	$0.694872\pi$
$920$	−53.8192	+	74.0757i	−0.0584991	+	0.0805171i
$921$		0			0
$922$	−672.677	+	2070.29i	−0.729585	+	2.24543i
$923$			815.195i			0.883202i
$924$		0			0
$925$	−1512.92			−1.63559
$926$	−858.908	−	279.076i	−0.927546	−	0.301378i
$927$		0			0
$928$	78.5576	+	57.0754i	0.0846526	+	0.0615037i
$929$	−1025.82	+	333.308i	−1.10422	+	0.358782i	−0.803724	−	0.595002i	$-0.797151\pi$
$929$	−1025.82	+	333.308i	−1.10422	+	0.358782i	−0.300493	+	0.953784i	$0.597151\pi$
$930$		0			0
$931$	−799.509	−	580.878i	−0.858764	−	0.623929i
$932$	−324.586	−	446.754i	−0.348268	−	0.479350i
$933$		0			0
$934$	−875.967			−0.937866
$935$	−198.689	+	461.728i	−0.212501	+	0.493826i
$936$		0			0
$937$	−181.607	+	558.927i	−0.193817	+	0.596507i	0.806171	+	0.591682i	$0.201536\pi$
$937$	−181.607	+	558.927i	−0.193817	+	0.596507i	−0.999988	+	0.00482521i	$0.998464\pi$
$938$	467.944	+	644.070i	0.498875	+	0.686642i
$939$		0			0
$940$	60.7007	+	186.818i	0.0645752	+	0.198742i
$941$	1016.93	−	330.422i	1.08070	−	0.351139i	0.286051	−	0.958214i	$-0.407657\pi$
$941$	1016.93	−	330.422i	1.08070	−	0.351139i	0.794644	+	0.607075i	$0.207657\pi$
$942$		0			0
$943$	459.984	−	334.198i	0.487788	−	0.354399i
$944$	−786.862	−	255.667i	−0.833541	−	0.270834i
$945$		0			0
$946$	−23.1315	+	5.22013i	−0.0244519	+	0.00551811i
$947$			435.924i			0.460321i	0.973153	+	0.230160i	$0.0739251\pi$
$947$			435.924i			0.460321i	−0.973153	+	0.230160i	$0.926075\pi$
$948$		0			0
$949$	553.034	−	401.803i	0.582755	−	0.423396i
$950$	1027.97	−	1414.88i	1.08208	−	1.48935i
$951$		0			0
$952$	−84.7087	−	260.707i	−0.0889798	−	0.273852i
$953$	−394.390	+	542.832i	−0.413841	+	0.569603i	−0.964150	−	0.265358i	$-0.914510\pi$
$953$	−394.390	+	542.832i	−0.413841	+	0.569603i	0.550309	+	0.834961i	$0.314510\pi$
$954$		0			0
$955$	11.5636	−	35.5892i	0.0121085	−	0.0372662i
$956$			1560.70i			1.63253i
$957$		0			0
$958$	1488.11			1.55335
$959$	−63.8391	−	20.7426i	−0.0665684	−	0.0216294i
$960$		0			0
$961$	708.567	+	514.804i	0.737322	+	0.535696i
$962$	−1454.91	+	472.730i	−1.51238	+	0.491403i
$963$		0			0
$964$	−419.303	−	304.641i	−0.434961	−	0.316018i
$965$	118.833	+	163.560i	0.123143	+	0.169492i
$966$		0			0
$967$	−940.682			−0.972784			−0.486392	−	0.873741i	$-0.661687\pi$
$967$	−940.682			−0.972784			−0.486392	+	0.873741i	$0.661687\pi$
$968$	−348.380	+	45.4574i	−0.359896	+	0.0469601i
$969$		0			0
$970$	−116.387	+	358.203i	−0.119987	+	0.369282i
$971$	−633.408	−	871.812i	−0.652326	−	0.897849i	0.346872	−	0.937913i	$-0.387244\pi$
$971$	−633.408	−	871.812i	−0.652326	−	0.897849i	−0.999197	+	0.0400635i	$0.987244\pi$
$972$		0			0
$973$	−153.191	−	471.473i	−0.157442	−	0.484556i
$974$	1970.24	−	640.171i	2.02284	−	0.657259i
$975$		0			0
$976$	652.851	−	474.324i	0.668905	−	0.485988i
$977$	956.809	+	310.886i	0.979334	+	0.318205i	0.754578	−	0.656210i	$-0.227842\pi$
$977$	956.809	+	310.886i	0.979334	+	0.318205i	0.224756	+	0.974415i	$0.427842\pi$
$978$		0			0
$979$	−468.068	−	787.782i	−0.478108	−	0.804680i
$980$			303.658i			0.309855i
$981$		0			0
$982$	−717.777	+	521.495i	−0.730934	+	0.531054i
$983$	−689.954	+	949.640i	−0.701886	+	0.966063i	0.298048	+	0.954551i	$0.403665\pi$
$983$	−689.954	+	949.640i	−0.701886	+	0.966063i	−0.999934	+	0.0115123i	$0.996335\pi$
$984$		0			0
$985$	6.16822	+	18.9838i	0.00626215	+	0.0192729i
$986$	−107.452	+	147.895i	−0.108978	+	0.149995i
$987$		0			0
$988$	302.763	−	931.810i	0.306441	−	0.943127i
$989$			14.0834i			0.0142400i
$990$		0			0
$991$	−989.386			−0.998372			−0.499186	−	0.866495i	$-0.666368\pi$
$991$	−989.386			−0.998372			−0.499186	+	0.866495i	$0.666368\pi$
$992$	−395.862	−	128.623i	−0.399054	−	0.129661i
$993$		0			0
$994$	869.563	+	631.774i	0.874812	+	0.635588i
$995$	−172.615	+	56.0861i	−0.173483	+	0.0563680i
$996$		0			0
$997$	1185.69	+	861.453i	1.18926	+	0.864045i	0.993185	−	0.116545i	$-0.0371820\pi$
$997$	1185.69	+	861.453i	1.18926	+	0.864045i	0.196070	+	0.980590i	$0.437182\pi$
$998$	−235.895	−	324.682i	−0.236368	−	0.325333i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.53.2	✓	32
3.2	odd	2	inner	99.3.l.a.53.7	yes	32
11.4	even	5		1089.3.b.i.485.3		16
11.5	even	5	inner	99.3.l.a.71.7	yes	32
11.7	odd	10		1089.3.b.j.485.14		16
33.5	odd	10	inner	99.3.l.a.71.2	yes	32
33.26	odd	10		1089.3.b.i.485.14		16
33.29	even	10		1089.3.b.j.485.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.53.2	✓	32	1.1	even	1	trivial
99.3.l.a.53.7	yes	32	3.2	odd	2	inner
99.3.l.a.71.2	yes	32	33.5	odd	10	inner
99.3.l.a.71.7	yes	32	11.5	even	5	inner
1089.3.b.i.485.3		16	11.4	even	5
1089.3.b.i.485.14		16	33.26	odd	10
1089.3.b.j.485.3		16	33.29	even	10
1089.3.b.j.485.14		16	11.7	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.84833 - 0.925479i) q^{2} +(4.02041 + 2.92100i) q^{4} +(-1.53284 + 0.498051i) q^{5} +(2.69388 + 1.95722i) q^{7} +(-1.70668 - 2.34904i) q^{8} +O(q^{10})\)	\(q+(-2.84833 - 0.925479i) q^{2} +(4.02041 + 2.92100i) q^{4} +(-1.53284 + 0.498051i) q^{5} +(2.69388 + 1.95722i) q^{7} +(-1.70668 - 2.34904i) q^{8} +4.82698 q^{10} +(9.45670 - 5.61879i) q^{11} +(2.33725 - 7.19331i) q^{13} +(-5.86169 - 8.06793i) q^{14} +(-3.45544 - 10.6348i) q^{16} +(26.9649 - 8.76142i) q^{17} +(21.0884 - 15.3216i) q^{19} +(-7.61747 - 2.47507i) q^{20} +(-32.1359 + 7.25218i) q^{22} +19.5656i q^{23} +(-18.1239 + 13.1678i) q^{25} +(-13.3145 + 18.3259i) q^{26} +(5.11347 + 15.7376i) q^{28} +(1.26543 - 1.74171i) q^{29} +(-2.85173 + 8.77673i) q^{31} +45.1036i q^{32} -84.9135 q^{34} +(-5.10409 - 1.65842i) q^{35} +(54.6363 + 39.6956i) q^{37} +(-74.2465 + 24.1241i) q^{38} +(3.78602 + 2.75070i) q^{40} +(-17.0809 - 23.5098i) q^{41} +0.719802 q^{43} +(54.4323 + 5.03321i) q^{44} +(18.1076 - 55.7293i) q^{46} +(-14.4154 - 19.8410i) q^{47} +(-11.7156 - 36.0568i) q^{49} +(63.8093 - 20.7329i) q^{50} +(30.4084 - 22.0930i) q^{52} +(5.50829 + 1.78975i) q^{53} +(-11.6972 + 13.3226i) q^{55} -9.66837i q^{56} +(-5.21628 + 3.78985i) q^{58} +(43.4900 - 59.8589i) q^{59} +(22.3006 + 68.6343i) q^{61} +(16.2454 - 22.3598i) q^{62} +(27.9206 - 85.9309i) q^{64} +12.1903i q^{65} -79.8310 q^{67} +(134.002 + 43.5399i) q^{68} +(13.0033 + 9.44745i) q^{70} +(-102.505 + 33.3059i) q^{71} +(73.1189 + 53.1240i) q^{73} +(-118.885 - 163.631i) q^{74} +129.538 q^{76} +(36.4724 + 3.37250i) q^{77} +(35.4758 - 109.183i) q^{79} +(10.5933 + 14.5804i) q^{80} +(26.8942 + 82.7718i) q^{82} +(-119.598 + 38.8596i) q^{83} +(-36.9693 + 26.8598i) q^{85} +(-2.05023 - 0.666161i) q^{86} +(-29.3383 - 12.6247i) q^{88} -83.3041i q^{89} +(20.3751 - 14.8034i) q^{91} +(-57.1511 + 78.6618i) q^{92} +(22.6973 + 69.8550i) q^{94} +(-24.6942 + 33.9887i) q^{95} +(-24.1118 + 74.2085i) q^{97} +113.544i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^7	\( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

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