LMFDB - Embedded newform 252.4.b.f.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.b (of order $2$, degree $1$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 $ x^12 - x^11 - 2x^10 - 6x^9 + 56x^7 - 448x^6 + 448x^5 - 3072x^3 - 8192x^2 - 32768x + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.1
Root			$2.82801 - 0.0488466i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.f.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} +16.6517i q^{5} +(15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +O(q^{10})$	\(q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} +16.6517i q^{5} +(15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +(0.813380 - 47.0912i) q^{10} +64.0450i q^{11} +28.6879i q^{13} +(-42.0112 - 31.2899i) q^{14} +(63.8473 + 4.41779i) q^{16} -82.9041i q^{17} -17.1236 q^{19} +(-4.60049 + 133.134i) q^{20} +(3.12838 - 181.120i) q^{22} -95.0501i q^{23} -152.281 q^{25} +(1.40131 - 81.1296i) q^{26} +(117.280 + 90.5401i) q^{28} +197.365 q^{29} -153.515 q^{31} +(-180.345 - 15.6123i) q^{32} +(-4.04958 + 234.453i) q^{34} +(-179.913 + 250.476i) q^{35} +10.7262 q^{37} +(48.4255 + 0.836427i) q^{38} +(19.5134 - 376.280i) q^{40} -41.1342i q^{41} +412.497i q^{43} +(-17.6941 + 512.055i) q^{44} +(-4.64287 + 268.802i) q^{46} -477.704 q^{47} +(109.526 + 325.043i) q^{49} +(430.650 + 7.43838i) q^{50} +(-7.92580 + 229.367i) q^{52} +35.2304 q^{53} -1066.46 q^{55} +(-327.245 - 261.776i) q^{56} +(-558.149 - 9.64060i) q^{58} -494.608 q^{59} -294.084i q^{61} +(434.141 + 7.49867i) q^{62} +(509.254 + 52.9608i) q^{64} -477.704 q^{65} +207.870i q^{67} +(22.9045 - 662.837i) q^{68} +(521.031 - 699.560i) q^{70} +534.040i q^{71} -582.270i q^{73} +(-30.3338 - 0.523939i) q^{74} +(-136.907 - 4.73084i) q^{76} +(-691.973 + 963.368i) q^{77} +311.277i q^{79} +(-73.5639 + 1063.17i) q^{80} +(-2.00926 + 116.328i) q^{82} +1319.63 q^{83} +1380.50 q^{85} +(20.1490 - 1166.54i) q^{86} +(75.0512 - 1447.23i) q^{88} +616.091i q^{89} +(-309.958 + 431.525i) q^{91} +(26.2601 - 759.948i) q^{92} +(1350.95 + 23.3342i) q^{94} -285.137i q^{95} +104.076i q^{97} +(-293.864 - 924.573i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8}+O(q^{10}) $ 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8	$ 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8} + 56 q^{10} - 69 q^{14} + 41 q^{16} - 84 q^{19} - 172 q^{20} - 182 q^{22} - 216 q^{25} - 300 q^{26} + 309 q^{28} - 200 q^{29} - 384 q^{31} + 159 q^{32} - 164 q^{34} - 84 q^{35} - 244 q^{37} - 268 q^{38} - 316 q^{40} - 190 q^{44} + 894 q^{46} - 280 q^{47} - 424 q^{49} + 1771 q^{50} - 796 q^{52} + 16 q^{53} + 212 q^{55} + 7 q^{56} - 570 q^{58} - 1168 q^{59} + 384 q^{62} + 2705 q^{64} - 280 q^{65} - 1552 q^{68} + 968 q^{70} - 1622 q^{74} - 788 q^{76} - 968 q^{77} + 3060 q^{80} - 2540 q^{82} + 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} + 1648 q^{91} - 4298 q^{92} + 4256 q^{94} - 97 q^{98}+O(q^{100}) $ 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8 + 56 * q^10 - 69 * q^14 + 41 * q^16 - 84 * q^19 - 172 * q^20 - 182 * q^22 - 216 * q^25 - 300 * q^26 + 309 * q^28 - 200 * q^29 - 384 * q^31 + 159 * q^32 - 164 * q^34 - 84 * q^35 - 244 * q^37 - 268 * q^38 - 316 * q^40 - 190 * q^44 + 894 * q^46 - 280 * q^47 - 424 * q^49 + 1771 * q^50 - 796 * q^52 + 16 * q^53 + 212 * q^55 + 7 * q^56 - 570 * q^58 - 1168 * q^59 + 384 * q^62 + 2705 * q^64 - 280 * q^65 - 1552 * q^68 + 968 * q^70 - 1622 * q^74 - 788 * q^76 - 968 * q^77 + 3060 * q^80 - 2540 * q^82 + 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 + 1648 * q^91 - 4298 * q^92 + 4256 * q^94 - 97 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−2.82801	−	0.0488466i	−0.999851	−	0.0172699i
$2$	−2.82801	−	0.0488466i	−0.999851	−	0.0172699i
$3$		0			0
$3$		0			0
$4$	7.99523	+	0.276277i	0.999404	+	0.0345346i
$5$			16.6517i			1.48938i	0.667412	+	0.744689i	$0.267402\pi$
$5$			16.6517i			1.48938i	−0.667412	+	0.744689i	$0.732598\pi$
$6$		0			0
$7$	15.0420	+	10.8045i	0.812194	+	0.583387i
$7$	15.0420	+	10.8045i	0.812194	+	0.583387i
$8$	−22.5971	−	1.17185i	−0.998658	−	0.0517890i
$9$		0			0
$10$	0.813380	−	47.0912i	0.0257213	−	1.48916i
$11$			64.0450i			1.75548i	0.479136	+	0.877741i	$0.340950\pi$
$11$			64.0450i			1.75548i	−0.479136	+	0.877741i	$0.659050\pi$
$12$		0			0
$13$			28.6879i			0.612046i	0.952024	+	0.306023i	$0.0989985\pi$
$13$			28.6879i			0.612046i	−0.952024	+	0.306023i	$0.901002\pi$
$14$	−42.0112	−	31.2899i	−0.801998	−	0.597327i
$15$		0			0
$16$	63.8473	+	4.41779i	0.997615	+	0.0690280i
$17$		−	82.9041i		−	1.18278i	−0.806387	−	0.591388i	$-0.798580\pi$
$17$		−	82.9041i		−	1.18278i	0.806387	−	0.591388i	$-0.201420\pi$
$18$		0			0
$19$	−17.1236			−0.206759			−0.103379	−	0.994642i	$-0.532966\pi$
$19$	−17.1236			−0.206759			−0.103379	+	0.994642i	$0.532966\pi$
$20$	−4.60049	+	133.134i	−0.0514350	+	1.48849i
$21$		0			0
$22$	3.12838	−	181.120i	0.0303169	−	1.75522i
$23$		−	95.0501i		−	0.861710i	−0.902421	−	0.430855i	$-0.858212\pi$
$23$		−	95.0501i		−	0.861710i	0.902421	−	0.430855i	$-0.141788\pi$
$24$		0			0
$25$	−152.281			−1.21824
$26$	1.40131	−	81.1296i	0.0105700	−	0.611955i
$27$		0			0
$28$	117.280	+	90.5401i	0.791563	+	0.611088i
$29$	197.365			1.26378			0.631892	−	0.775056i	$-0.282278\pi$
$29$	197.365			1.26378			0.631892	+	0.775056i	$0.282278\pi$
$30$		0			0
$31$	−153.515			−0.889422			−0.444711	−	0.895674i	$-0.646694\pi$
$31$	−153.515			−0.889422			−0.444711	+	0.895674i	$0.646694\pi$
$32$	−180.345	−	15.6123i	−0.996274	−	0.0862463i
$33$		0			0
$34$	−4.04958	+	234.453i	−0.0204264	+	1.18260i
$35$	−179.913	+	250.476i	−0.868883	+	1.20966i
$36$		0			0
$37$	10.7262			0.0476589			0.0238294	−	0.999716i	$-0.492414\pi$
$37$	10.7262			0.0476589			0.0238294	+	0.999716i	$0.492414\pi$
$38$	48.4255	+	0.836427i	0.206728	+	0.00357069i
$39$		0			0
$40$	19.5134	−	376.280i	0.0771333	−	1.48738i
$41$		−	41.1342i		−	0.156685i	−0.996927	−	0.0783425i	$-0.975037\pi$
$41$		−	41.1342i		−	0.156685i	0.996927	−	0.0783425i	$-0.0249628\pi$
$42$		0			0
$43$			412.497i			1.46291i	0.681890	+	0.731455i	$0.261158\pi$
$43$			412.497i			1.46291i	−0.681890	+	0.731455i	$0.738842\pi$
$44$	−17.6941	+	512.055i	−0.0606248	+	1.75443i
$45$		0			0
$46$	−4.64287	+	268.802i	−0.0148816	+	0.861581i
$47$	−477.704			−1.48256			−0.741280	−	0.671196i	$-0.765781\pi$
$47$	−477.704			−1.48256			−0.741280	+	0.671196i	$0.765781\pi$
$48$		0			0
$49$	109.526	+	325.043i	0.319319	+	0.947647i
$50$	430.650	+	7.43838i	1.21806	+	0.0210389i
$51$		0			0
$52$	−7.92580	+	229.367i	−0.0211368	+	0.611681i
$53$	35.2304			0.0913069			0.0456534	−	0.998957i	$-0.485463\pi$
$53$	35.2304			0.0913069			0.0456534	+	0.998957i	$0.485463\pi$
$54$		0			0
$55$	−1066.46			−2.61457
$56$	−327.245	−	261.776i	−0.780891	−	0.624667i
$57$		0			0
$58$	−558.149	−	9.64060i	−1.26360	−	0.0218254i
$59$	−494.608			−1.09140			−0.545699	−	0.837981i	$-0.683736\pi$
$59$	−494.608			−1.09140			−0.545699	+	0.837981i	$0.683736\pi$
$60$		0			0
$61$		−	294.084i		−	0.617273i	−0.951180	−	0.308636i	$-0.900127\pi$
$61$		−	294.084i		−	0.617273i	0.951180	−	0.308636i	$-0.0998727\pi$
$62$	434.141	+	7.49867i	0.889289	+	0.0153602i
$63$		0			0
$64$	509.254	+	52.9608i	0.994636	+	0.103439i
$65$	−477.704			−0.911567
$66$		0			0
$67$			207.870i			0.379036i	0.981877	+	0.189518i	$0.0606926\pi$
$67$			207.870i			0.379036i	−0.981877	+	0.189518i	$0.939307\pi$
$68$	22.9045	−	662.837i	0.0408467	−	1.18207i
$69$		0			0
$70$	521.031	−	699.560i	0.889645	−	1.19448i
$71$			534.040i			0.892660i	0.894869	+	0.446330i	$0.147269\pi$
$71$			534.040i			0.892660i	−0.894869	+	0.446330i	$0.852731\pi$
$72$		0			0
$73$		−	582.270i		−	0.933555i	−0.884375	−	0.466778i	$-0.845415\pi$
$73$		−	582.270i		−	0.933555i	0.884375	−	0.466778i	$-0.154585\pi$
$74$	−30.3338	−	0.523939i	−0.0476518	−	0.000823063i
$75$		0			0
$76$	−136.907	−	4.73084i	−0.206635	−	0.00714032i
$77$	−691.973	+	963.368i	−1.02413	+	1.42579i
$78$		0			0
$79$			311.277i			0.443309i	0.975125	+	0.221654i	$0.0711457\pi$
$79$			311.277i			0.443309i	−0.975125	+	0.221654i	$0.928854\pi$
$80$	−73.5639	+	1063.17i	−0.102809	+	1.48582i
$81$		0			0
$82$	−2.00926	+	116.328i	−0.00270593	+	0.156662i
$83$	1319.63			1.74515			0.872577	−	0.488477i	$-0.162447\pi$
$83$	1319.63			1.74515			0.872577	+	0.488477i	$0.162447\pi$
$84$		0			0
$85$	1380.50			1.76160
$86$	20.1490	−	1166.54i	0.0252643	−	1.46269i
$87$		0			0
$88$	75.0512	−	1447.23i	0.0909146	−	1.75313i
$89$			616.091i			0.733770i	0.930266	+	0.366885i	$0.119576\pi$
$89$			616.091i			0.733770i	−0.930266	+	0.366885i	$0.880424\pi$
$90$		0			0
$91$	−309.958	+	431.525i	−0.357060	+	0.497100i
$92$	26.2601	−	759.948i	0.0297588	−	0.861196i
$93$		0			0
$94$	1350.95	+	23.3342i	1.48234	+	0.0256036i
$95$		−	285.137i		−	0.307941i
$96$		0			0
$97$			104.076i			0.108941i	0.998515	+	0.0544706i	$0.0173471\pi$
$97$			104.076i			0.108941i	−0.998515	+	0.0544706i	$0.982653\pi$
$98$	−293.864	−	924.573i	−0.302906	−	0.953021i
$99$		0			0
$100$	−1217.52	−	42.0716i	−1.21752	−	0.0420716i
$101$		−	1754.34i		−	1.72835i	−0.503196	−	0.864173i	$-0.667842\pi$
$101$		−	1754.34i		−	1.72835i	0.503196	−	0.864173i	$-0.332158\pi$
$102$		0			0
$103$	310.370			0.296910			0.148455	−	0.988919i	$-0.452570\pi$
$103$	310.370			0.296910			0.148455	+	0.988919i	$0.452570\pi$
$104$	33.6180	−	648.263i	0.0316973	−	0.611225i
$105$		0			0
$106$	−99.6317	−	1.72088i	−0.0912932	−	0.00157686i
$107$			482.444i			0.435884i	0.975962	+	0.217942i	$0.0699344\pi$
$107$			482.444i			0.435884i	−0.975962	+	0.217942i	$0.930066\pi$
$108$		0			0
$109$	−72.5584			−0.0637600			−0.0318800	−	0.999492i	$-0.510149\pi$
$109$	−72.5584			−0.0637600			−0.0318800	+	0.999492i	$0.510149\pi$
$110$	3015.96	+	52.0930i	2.61418	+	0.0451533i
$111$		0			0
$112$	912.663	+	756.290i	0.769987	+	0.638060i
$113$	1545.99			1.28703			0.643514	−	0.765434i	$-0.277476\pi$
$113$	1545.99			1.28703			0.643514	+	0.765434i	$0.277476\pi$
$114$		0			0
$115$	1582.75			1.28341
$116$	1577.98	+	54.5273i	1.26303	+	0.0436443i
$117$		0			0
$118$	1398.75	+	24.1599i	1.09124	+	0.0188483i
$119$	895.736	−	1247.05i	0.690017	−	0.960645i
$120$		0			0
$121$	−2770.76			−2.08172
$122$	−14.3650	+	831.672i	−0.0106602	+	0.617181i
$123$		0			0
$124$	−1227.39	−	42.4126i	−0.888892	−	0.0307158i
$125$		−	454.269i		−	0.325048i
$126$		0			0
$127$		−	1982.75i		−	1.38536i	−0.721246	−	0.692679i	$-0.756430\pi$
$127$		−	1982.75i		−	1.38536i	0.721246	−	0.692679i	$-0.243570\pi$
$128$	−1437.58	−	174.649i	−0.992701	−	0.120601i
$129$		0			0
$130$	1350.95	+	23.3342i	0.911432	+	0.0157426i
$131$	−403.984			−0.269437			−0.134719	−	0.990884i	$-0.543013\pi$
$131$	−403.984			−0.269437			−0.134719	+	0.990884i	$0.543013\pi$
$132$		0			0
$133$	−257.573	−	185.011i	−0.167928	−	0.120620i
$134$	10.1538	−	587.859i	0.00654590	−	0.378980i
$135$		0			0
$136$	−97.1513	+	1873.39i	−0.0612548	+	1.18119i
$137$	1366.78			0.852350			0.426175	−	0.904641i	$-0.359861\pi$
$137$	1366.78			0.852350			0.426175	+	0.904641i	$0.359861\pi$
$138$		0			0
$139$	−1770.10			−1.08013			−0.540065	−	0.841623i	$-0.681600\pi$
$139$	−1770.10			−1.08013			−0.540065	+	0.841623i	$0.681600\pi$
$140$	−1507.65	+	1952.91i	−0.910140	+	1.17894i
$141$		0			0
$142$	26.0860	−	1510.27i	0.0154161	−	0.892527i
$143$	−1837.32			−1.07444
$144$		0			0
$145$			3286.47i			1.88225i
$146$	−28.4419	+	1646.66i	−0.0161224	+	0.933416i
$147$		0			0
$148$	85.7585	+	2.96340i	0.0476305	+	0.00164588i
$149$	−1991.97			−1.09522			−0.547612	−	0.836732i	$-0.684463\pi$
$149$	−1991.97			−1.09522			−0.547612	+	0.836732i	$0.684463\pi$
$150$		0			0
$151$			1117.45i			0.602229i	0.953588	+	0.301115i	$0.0973586\pi$
$151$			1117.45i			0.602229i	−0.953588	+	0.301115i	$0.902641\pi$
$152$	386.942	+	20.0663i	0.206481	+	0.0107078i
$153$		0			0
$154$	2003.96	−	2690.61i	1.04860	−	1.40789i
$155$		−	2556.29i		−	1.32468i
$156$		0			0
$157$		−	758.016i		−	0.385327i	−0.981265	−	0.192663i	$-0.938287\pi$
$157$		−	758.016i		−	0.385327i	0.981265	−	0.192663i	$-0.0617125\pi$
$158$	15.2048	−	880.293i	0.00765588	−	0.443243i
$159$		0			0
$160$	259.971	−	3003.06i	0.128453	−	1.48383i
$161$	1026.97	−	1429.75i	0.502710	−	0.699876i
$162$		0			0
$163$			147.846i			0.0710443i	0.999369	+	0.0355222i	$0.0113094\pi$
$163$			147.846i			0.0710443i	−0.999369	+	0.0355222i	$0.988691\pi$
$164$	11.3644	−	328.877i	0.00541105	−	0.156591i
$165$		0			0
$166$	−3731.91	−	64.4592i	−1.74489	−	0.0301386i
$167$	1741.92			0.807148			0.403574	−	0.914947i	$-0.367768\pi$
$167$	1741.92			0.807148			0.403574	+	0.914947i	$0.367768\pi$
$168$		0			0
$169$	1374.00			0.625400
$170$	−3904.06	−	67.4326i	−1.76134	−	0.0304226i
$171$		0			0
$172$	−113.963	+	3298.00i	−0.0505210	+	1.46204i
$173$			2686.73i			1.18074i	0.807131	+	0.590372i	$0.201019\pi$
$173$			2686.73i			1.18074i	−0.807131	+	0.590372i	$0.798981\pi$
$174$		0			0
$175$	−2290.61	−	1645.31i	−0.989451	−	0.710708i
$176$	−282.937	+	4089.10i	−0.121177	+	1.75129i
$177$		0			0
$178$	30.0939	−	1742.31i	0.0126721	−	0.733661i
$179$			1032.53i			0.431146i	0.976488	+	0.215573i	$0.0691619\pi$
$179$			1032.53i			0.431146i	−0.976488	+	0.215573i	$0.930838\pi$
$180$		0			0
$181$		−	1608.53i		−	0.660558i	−0.943883	−	0.330279i	$-0.892857\pi$
$181$		−	1608.53i		−	0.660558i	0.943883	−	0.330279i	$-0.107143\pi$
$182$	897.642	−	1205.22i	0.365591	−	0.490860i
$183$		0			0
$184$	−111.385	+	2147.85i	−0.0446271	+	0.860553i
$185$			178.610i			0.0709821i
$186$		0			0
$187$	5309.60			2.07634
$188$	−3819.35	−	131.978i	−1.48167	−	0.0511996i
$189$		0			0
$190$	−13.9280	+	806.369i	−0.00531811	+	0.307896i
$191$			1970.43i			0.746469i	0.927737	+	0.373235i	$0.121751\pi$
$191$			1970.43i			0.746469i	−0.927737	+	0.373235i	$0.878249\pi$
$192$		0			0
$193$	966.622			0.360513			0.180256	−	0.983620i	$-0.442307\pi$
$193$	966.622			0.360513			0.180256	+	0.983620i	$0.442307\pi$
$194$	5.08374	−	294.327i	0.00188140	−	0.108925i
$195$		0			0
$196$	785.887	+	2629.05i	0.286402	+	0.958110i
$197$	−1068.53			−0.386443			−0.193222	−	0.981155i	$-0.561894\pi$
$197$	−1068.53			−0.386443			−0.193222	+	0.981155i	$0.561894\pi$
$198$		0			0
$199$	252.660			0.0900029			0.0450015	−	0.998987i	$-0.485671\pi$
$199$	252.660			0.0900029			0.0450015	+	0.998987i	$0.485671\pi$
$200$	3441.09	+	178.450i	1.21661	+	0.0630916i
$201$		0			0
$202$	−85.6932	+	4961.27i	−0.0298483	+	1.72809i
$203$	2968.77	+	2132.43i	1.02644	+	0.737276i
$204$		0			0
$205$	684.956			0.233363
$206$	−877.728	−	15.1605i	−0.296865	−	0.00512759i
$207$		0			0
$208$	−126.737	+	1831.65i	−0.0422483	+	0.610586i
$209$		−	1096.68i		−	0.362961i
$210$		0			0
$211$			4606.20i			1.50286i	0.659811	+	0.751432i	$0.270636\pi$
$211$			4606.20i			1.50286i	−0.659811	+	0.751432i	$0.729364\pi$
$212$	281.675	+	9.73333i	0.0912524	+	0.00315324i
$213$		0			0
$214$	23.5657	−	1364.35i	0.00752766	−	0.435819i
$215$	−6868.79			−2.17883
$216$		0			0
$217$	−2309.18	−	1658.65i	−0.722383	−	0.518877i
$218$	205.196	+	3.54423i	0.0637505	+	0.00110113i
$219$		0			0
$220$	−8526.60	−	294.638i	−2.61301	−	0.0902932i
$221$	2378.35			0.723914
$222$		0			0
$223$	1927.65			0.578857			0.289428	−	0.957200i	$-0.406535\pi$
$223$	1927.65			0.578857			0.289428	+	0.957200i	$0.406535\pi$
$224$	−2544.07	−	2183.37i	−0.758853	−	0.651262i
$225$		0			0
$226$	−4372.06	−	75.5161i	−1.28684	−	0.0222268i
$227$	4063.72			1.18819			0.594093	−	0.804396i	$-0.297511\pi$
$227$	4063.72			1.18819			0.594093	+	0.804396i	$0.297511\pi$
$228$		0			0
$229$		−	4096.49i		−	1.18211i	−0.806631	−	0.591056i	$-0.798711\pi$
$229$		−	4096.49i		−	1.18211i	0.806631	−	0.591056i	$-0.201289\pi$
$230$	−4476.03	−	77.3119i	−1.28322	−	0.0221643i
$231$		0			0
$232$	−4459.87	−	231.282i	−1.26209	−	0.0654501i
$233$	−1950.08			−0.548301			−0.274150	−	0.961687i	$-0.588397\pi$
$233$	−1950.08			−0.548301			−0.274150	+	0.961687i	$0.588397\pi$
$234$		0			0
$235$		−	7954.60i		−	2.20809i
$236$	−3954.51	−	136.649i	−1.09075	−	0.0376910i
$237$		0			0
$238$	−2594.06	+	3482.90i	−0.706504	+	0.948585i
$239$			2861.53i			0.774465i	0.921982	+	0.387232i	$0.126569\pi$
$239$			2861.53i			0.774465i	−0.921982	+	0.387232i	$0.873431\pi$
$240$		0			0
$241$			4320.12i			1.15470i	0.816496	+	0.577351i	$0.195914\pi$
$241$			4320.12i			1.15470i	−0.816496	+	0.577351i	$0.804086\pi$
$242$	7835.74	+	135.342i	2.08141	+	0.0359510i
$243$		0			0
$244$	81.2487	−	2351.27i	0.0213173	−	0.616905i
$245$	−5412.53	+	1823.81i	−1.41140	+	0.475586i
$246$		0			0
$247$		−	491.239i		−	0.126546i
$248$	3468.98	+	179.897i	0.888229	+	0.0460623i
$249$		0			0
$250$	−22.1895	+	1284.67i	−0.00561354	+	0.325000i
$251$	−1366.74			−0.343698			−0.171849	−	0.985123i	$-0.554974\pi$
$251$	−1366.74			−0.343698			−0.171849	+	0.985123i	$0.554974\pi$
$252$		0			0
$253$	6087.49			1.51272
$254$	−96.8504	+	5607.22i	−0.0239249	+	1.38515i
$255$		0			0
$256$	4056.97	+	564.128i	0.990470	+	0.137727i
$257$		−	5993.21i		−	1.45465i	−0.686291	−	0.727327i	$-0.740762\pi$
$257$		−	5993.21i		−	1.45465i	0.686291	−	0.727327i	$-0.259238\pi$
$258$		0			0
$259$	161.344	+	115.891i	0.0387083	+	0.0278036i
$260$	−3819.35	−	131.978i	−0.911024	−	0.0314806i
$261$		0			0
$262$	1142.47	+	19.7332i	0.269397	+	0.00465314i
$263$		−	1636.95i		−	0.383798i	−0.981415	−	0.191899i	$-0.938535\pi$
$263$		−	1636.95i		−	0.383798i	0.981415	−	0.191899i	$-0.0614646\pi$
$264$		0			0
$265$			586.647i			0.135990i
$266$	719.381	+	535.794i	0.165820	+	0.123502i
$267$		0			0
$268$	−57.4298	+	1661.97i	−0.0130899	+	0.378810i
$269$			7442.41i			1.68688i	0.537220	+	0.843442i	$0.319474\pi$
$269$			7442.41i			1.68688i	−0.537220	+	0.843442i	$0.680526\pi$
$270$		0			0
$271$	5619.33			1.25959			0.629797	−	0.776760i	$-0.283138\pi$
$271$	5619.33			1.25959			0.629797	+	0.776760i	$0.283138\pi$
$272$	366.253	−	5293.21i	0.0816447	−	1.17996i
$273$		0			0
$274$	−3865.26	−	66.7625i	−0.852223	−	0.0147200i
$275$		−	9752.81i		−	2.13861i
$276$		0			0
$277$	−698.240			−0.151456			−0.0757278	−	0.997129i	$-0.524128\pi$
$277$	−698.240			−0.151456			−0.0757278	+	0.997129i	$0.524128\pi$
$278$	5005.86	+	86.4634i	1.07997	+	0.0186537i
$279$		0			0
$280$	4359.03	−	5449.19i	0.930365	−	1.16304i
$281$	5026.99			1.06721			0.533604	−	0.845735i	$-0.320837\pi$
$281$	5026.99			1.06721			0.533604	+	0.845735i	$0.320837\pi$
$282$		0			0
$283$	−3596.17			−0.755371			−0.377686	−	0.925934i	$-0.623280\pi$
$283$	−3596.17			−0.755371			−0.377686	+	0.925934i	$0.623280\pi$
$284$	−147.543	+	4269.77i	−0.0308276	+	0.892127i
$285$		0			0
$286$	5195.95	+	89.7467i	1.07428	+	0.0185554i
$287$	444.434	−	618.743i	0.0914080	−	0.127259i
$288$		0			0
$289$	−1960.10			−0.398961
$290$	160.533	−	9294.16i	0.0325062	−	1.88197i
$291$		0			0
$292$	160.868	−	4655.38i	0.0322399	−	0.932999i
$293$			4095.02i			0.816497i	0.912871	+	0.408248i	$0.133860\pi$
$293$			4095.02i			0.816497i	−0.912871	+	0.408248i	$0.866140\pi$
$294$		0			0
$295$		−	8236.09i		−	1.62550i
$296$	−242.381	−	12.5695i	−0.0475949	−	0.00246821i
$297$		0			0
$298$	5633.30	+	97.3008i	1.09506	+	0.0189144i
$299$	2726.79			0.527406
$300$		0			0
$301$	−4456.81	+	6204.79i	−0.853443	+	1.18817i
$302$	54.5835	−	3160.15i	0.0104004	−	0.602139i
$303$		0			0
$304$	−1093.29	−	75.6482i	−0.206265	−	0.0142721i
$305$	4897.02			0.919352
$306$		0			0
$307$	6214.27			1.15527			0.577633	−	0.816296i	$-0.303976\pi$
$307$	6214.27			1.15527			0.577633	+	0.816296i	$0.303976\pi$
$308$	−5798.64	+	7511.17i	−1.07275	+	1.38957i
$309$		0			0
$310$	−124.866	+	7229.20i	−0.0228771	+	1.32449i
$311$	4044.93			0.737514			0.368757	−	0.929526i	$-0.379784\pi$
$311$	4044.93			0.737514			0.368757	+	0.929526i	$0.379784\pi$
$312$		0			0
$313$		−	6931.84i		−	1.25179i	−0.779907	−	0.625896i	$-0.784734\pi$
$313$		−	6931.84i		−	1.25179i	0.779907	−	0.625896i	$-0.215266\pi$
$314$	−37.0265	+	2143.67i	−0.00665454	+	0.385269i
$315$		0			0
$316$	−85.9986	+	2488.73i	−0.0153095	+	0.443044i
$317$	−3966.39			−0.702759			−0.351379	−	0.936233i	$-0.614287\pi$
$317$	−3966.39			−0.702759			−0.351379	+	0.936233i	$0.614287\pi$
$318$		0			0
$319$			12640.2i			2.21855i
$320$	−881.889	+	8479.96i	−0.154060	+	1.48139i
$321$		0			0
$322$	−2974.11	+	3993.17i	−0.514722	+	0.691090i
$323$			1419.61i			0.244549i
$324$		0			0
$325$		−	4368.61i		−	0.745622i
$326$	7.22179	−	418.110i	0.00122693	−	0.0710337i
$327$		0			0
$328$	−48.2032	+	929.512i	−0.00811455	+	0.156475i
$329$	−7185.65	−	5161.34i	−1.20413	−	0.864906i
$330$		0			0
$331$		−	9949.84i		−	1.65224i	−0.563491	−	0.826122i	$-0.690542\pi$
$331$		−	9949.84i		−	1.65224i	0.563491	−	0.826122i	$-0.309458\pi$
$332$	10550.7	+	364.582i	1.74411	+	0.0602681i
$333$		0			0
$334$	−4926.15	−	85.0867i	−0.807027	−	0.0139393i
$335$	−3461.41			−0.564528
$336$		0			0
$337$	4947.26			0.799686			0.399843	−	0.916584i	$-0.369065\pi$
$337$	4947.26			0.799686			0.399843	+	0.916584i	$0.369065\pi$
$338$	−3885.69	−	67.1153i	−0.625306	−	0.0108006i
$339$		0			0
$340$	11037.4	+	381.399i	1.76055	+	0.0608361i
$341$		−	9831.86i		−	1.56136i
$342$		0			0
$343$	−1864.42	+	6072.69i	−0.293496	+	0.955960i
$344$	483.385	−	9321.21i	0.0757627	−	1.46095i
$345$		0			0
$346$	131.238	−	7598.10i	0.0203913	−	1.18057i
$347$		−	5246.44i		−	0.811653i	−0.913950	−	0.405826i	$-0.866984\pi$
$347$		−	5246.44i		−	0.811653i	0.913950	−	0.405826i	$-0.133016\pi$
$348$		0			0
$349$			8703.25i			1.33488i	0.744662	+	0.667442i	$0.232611\pi$
$349$			8703.25i			1.33488i	−0.744662	+	0.667442i	$0.767389\pi$
$350$	6397.49	+	4764.84i	0.977030	+	0.727690i
$351$		0			0
$352$	999.887	−	11550.2i	0.151404	−	1.74894i
$353$		−	1402.85i		−	0.211519i	−0.994392	−	0.105760i	$-0.966273\pi$
$353$		−	1402.85i		−	0.211519i	0.994392	−	0.105760i	$-0.0337274\pi$
$354$		0			0
$355$	−8892.69			−1.32951
$356$	−170.212	+	4925.79i	−0.0253404	+	0.733332i
$357$		0			0
$358$	50.4356	−	2920.01i	0.00744583	−	0.431081i
$359$			9556.07i			1.40487i	0.711746	+	0.702437i	$0.247905\pi$
$359$			9556.07i			1.40487i	−0.711746	+	0.702437i	$0.752095\pi$
$360$		0			0
$361$	−6565.78			−0.957251
$362$	−78.5711	+	4548.93i	−0.0114077	+	0.660459i
$363$		0			0
$364$	−2597.41	+	3364.51i	−0.374014	+	0.484473i
$365$	9695.81			1.39042
$366$		0			0
$367$	1036.73			0.147458			0.0737289	−	0.997278i	$-0.476510\pi$
$367$	1036.73			0.147458			0.0737289	+	0.997278i	$0.476510\pi$
$368$	419.912	−	6068.70i	0.0594821	−	0.859654i
$369$		0			0
$370$	8.72449	−	505.111i	0.00122585	−	0.0709715i
$371$	529.937	+	380.646i	0.0741589	+	0.0532672i
$372$		0			0
$373$	10769.4			1.49496			0.747481	−	0.664283i	$-0.231263\pi$
$373$	10769.4			1.49496			0.747481	+	0.664283i	$0.231263\pi$
$374$	−15015.6	−	259.356i	−2.07603	−	0.0358582i
$375$		0			0
$376$	10794.7	+	559.798i	1.48057	+	0.0767803i
$377$			5661.99i			0.773494i
$378$		0			0
$379$			3268.34i			0.442963i	0.975165	+	0.221482i	$0.0710893\pi$
$379$			3268.34i			0.442963i	−0.975165	+	0.221482i	$0.928911\pi$
$380$	78.7767	−	2279.74i	0.0106346	−	0.307758i
$381$		0			0
$382$	96.2489	−	5572.40i	0.0128914	−	0.746358i
$383$	5143.39			0.686201			0.343101	−	0.939299i	$-0.388523\pi$
$383$	5143.39			0.686201			0.343101	+	0.939299i	$0.388523\pi$
$384$		0			0
$385$	−16041.8	−	11522.6i	−2.12354	−	1.52531i
$386$	−2733.61	−	47.2161i	−0.360459	−	0.00622601i
$387$		0			0
$388$	−28.7537	+	832.109i	−0.00376224	+	0.108876i
$389$	5140.27			0.669979			0.334990	−	0.942222i	$-0.391267\pi$
$389$	5140.27			0.669979			0.334990	+	0.942222i	$0.391267\pi$
$390$		0			0
$391$	−7880.05			−1.01921
$392$	−2094.07	−	7473.36i	−0.269813	−	0.962913i
$393$		0			0
$394$	3021.80	+	52.1938i	0.386386	+	0.00667382i
$395$	−5183.30			−0.660254
$396$		0			0
$397$			6774.24i			0.856396i	0.903685	+	0.428198i	$0.140851\pi$
$397$			6774.24i			0.856396i	−0.903685	+	0.428198i	$0.859149\pi$
$398$	−714.523	−	12.3416i	−0.0899895	−	0.00155434i
$399$		0			0
$400$	−9722.71	−	672.743i	−1.21534	−	0.0840929i
$401$	8827.27			1.09928			0.549642	−	0.835401i	$-0.314764\pi$
$401$	8827.27			1.09928			0.549642	+	0.835401i	$0.314764\pi$
$402$		0			0
$403$		−	4404.02i		−	0.544367i
$404$	484.682	−	14026.3i	0.0596877	−	1.72731i
$405$		0			0
$406$	−8291.54	−	6175.53i	−1.01355	−	0.754892i
$407$			686.961i			0.0836643i
$408$		0			0
$409$			11986.2i			1.44910i	0.689223	+	0.724549i	$0.257952\pi$
$409$			11986.2i			1.44910i	−0.689223	+	0.724549i	$0.742048\pi$
$410$	−1937.06	−	33.4577i	−0.233328	−	0.00403015i
$411$		0			0
$412$	2481.48	+	85.7480i	0.296732	+	0.0102536i
$413$	−7439.92	−	5343.98i	−0.886427	−	0.636708i
$414$		0			0
$415$			21974.1i			2.59919i
$416$	447.883	−	5173.72i	0.0527867	−	0.609766i
$417$		0			0
$418$	−53.5690	+	3101.41i	−0.00626828	+	0.362907i
$419$	4098.42			0.477854			0.238927	−	0.971038i	$-0.423204\pi$
$419$	4098.42			0.477854			0.238927	+	0.971038i	$0.423204\pi$
$420$		0			0
$421$	318.996			0.0369285			0.0184643	−	0.999830i	$-0.494122\pi$
$421$	318.996			0.0369285			0.0184643	+	0.999830i	$0.494122\pi$
$422$	224.997	−	13026.4i	0.0259542	−	1.50264i
$423$		0			0
$424$	−796.102	−	41.2847i	−0.0911843	−	0.00472869i
$425$			12624.7i			1.44091i
$426$		0			0
$427$	3177.43	−	4423.63i	0.360109	−	0.501346i
$428$	−133.288	+	3857.25i	−0.0150531	+	0.435624i
$429$		0			0
$430$	19425.0	+	335.517i	2.17850	+	0.0376280i
$431$			9939.59i			1.11084i	0.831569	+	0.555422i	$0.187443\pi$
$431$			9939.59i			1.11084i	−0.831569	+	0.555422i	$0.812557\pi$
$432$		0			0
$433$		−	1254.43i		−	0.139225i	−0.997574	−	0.0696123i	$-0.977824\pi$
$433$		−	1254.43i		−	0.139225i	0.997574	−	0.0696123i	$-0.0221762\pi$
$434$	6449.35	+	4803.46i	0.713315	+	0.531275i
$435$		0			0
$436$	−580.121	−	20.0462i	−0.0637220	−	0.00220192i
$437$			1627.60i			0.178166i
$438$		0			0
$439$	−12933.4			−1.40610			−0.703049	−	0.711141i	$-0.748179\pi$
$439$	−12933.4			−1.40610			−0.703049	+	0.711141i	$0.748179\pi$
$440$	24098.9	+	1249.73i	2.61107	+	0.135406i
$441$		0			0
$442$	−6725.98	−	116.174i	−0.723806	−	0.0125019i
$443$			596.175i			0.0639394i	0.999489	+	0.0319697i	$0.0101780\pi$
$443$			596.175i			0.0639394i	−0.999489	+	0.0319697i	$0.989822\pi$
$444$		0			0
$445$	−10259.0			−1.09286
$446$	−5451.41	−	94.1591i	−0.578770	−	0.00999677i
$447$		0			0
$448$	7088.00	+	6298.86i	0.747492	+	0.664270i
$449$	3428.69			0.360378			0.180189	−	0.983632i	$-0.442329\pi$
$449$	3428.69			0.360378			0.180189	+	0.983632i	$0.442329\pi$
$450$		0			0
$451$	2634.44			0.275058
$452$	12360.5	+	427.120i	1.28626	+	0.0444470i
$453$		0			0
$454$	−11492.2	−	198.499i	−1.18801	−	0.0205198i
$455$	−7185.65	−	5161.34i	−0.740370	−	0.531797i
$456$		0			0
$457$	19011.5			1.94600			0.973000	−	0.230807i	$-0.0741367\pi$
$457$	19011.5			1.94600			0.973000	+	0.230807i	$0.0741367\pi$
$458$	−200.099	+	11584.9i	−0.0204149	+	1.18194i
$459$		0			0
$460$	12654.5	+	437.277i	1.28265	+	0.0443221i
$461$		−	13187.0i		−	1.33227i	−0.745830	−	0.666137i	$-0.767947\pi$
$461$		−	13187.0i		−	1.33227i	0.745830	−	0.666137i	$-0.232053\pi$
$462$		0			0
$463$			7425.75i			0.745364i	0.927959	+	0.372682i	$0.121562\pi$
$463$			7425.75i			0.745364i	−0.927959	+	0.372682i	$0.878438\pi$
$464$	12601.2	+	871.917i	1.26077	+	0.0872365i
$465$		0			0
$466$	5514.84	+	95.2548i	0.548219	+	0.00946908i
$467$	11474.1			1.13695			0.568476	−	0.822700i	$-0.307533\pi$
$467$	11474.1			1.13695			0.568476	+	0.822700i	$0.307533\pi$
$468$		0			0
$469$	−2245.93	+	3126.80i	−0.221125	+	0.307851i
$470$	−388.555	+	22495.7i	−0.0381334	+	2.20776i
$471$		0			0
$472$	11176.7	+	579.607i	1.08993	+	0.0565224i
$473$	−26418.4			−2.56811
$474$		0			0
$475$	2607.58			0.251882
$476$	7506.15	−	9722.96i	0.722781	−	0.936242i
$477$		0			0
$478$	139.776	−	8092.42i	0.0133749	−	0.774349i
$479$	−17924.0			−1.70975			−0.854873	−	0.518837i	$-0.826365\pi$
$479$	−17924.0			−1.70975			−0.854873	+	0.518837i	$0.826365\pi$
$480$		0			0
$481$			307.713i			0.0291694i
$482$	211.023	−	12217.3i	0.0199415	−	1.15453i
$483$		0			0
$484$	−22152.9	−	765.497i	−2.08047	−	0.0718912i
$485$	−1733.04			−0.162254
$486$		0			0
$487$		−	8161.93i		−	0.759450i	−0.925099	−	0.379725i	$-0.876019\pi$
$487$		−	8161.93i		−	0.759450i	0.925099	−	0.379725i	$-0.123981\pi$
$488$	−344.623	+	6645.44i	−0.0319679	+	0.616445i
$489$		0			0
$490$	15395.8	−	4893.35i	1.41941	−	0.451141i
$491$		−	17622.4i		−	1.61973i	−0.586616	−	0.809865i	$-0.699540\pi$
$491$		−	17622.4i		−	1.61973i	0.586616	−	0.809865i	$-0.300460\pi$
$492$		0			0
$493$		−	16362.4i		−	1.49478i
$494$	−23.9953	+	1389.23i	−0.00218543	+	0.126527i
$495$		0			0
$496$	−9801.52	−	678.196i	−0.887301	−	0.0613950i
$497$	−5770.02	+	8033.05i	−0.520766	+	0.725013i
$498$		0			0
$499$		−	6772.04i		−	0.607531i	−0.952747	−	0.303766i	$-0.901756\pi$
$499$		−	6772.04i		−	0.607531i	0.952747	−	0.303766i	$-0.0982440\pi$
$500$	125.504	−	3631.98i	0.0112254	−	0.324854i
$501$		0			0
$502$	3865.16	+	66.7608i	0.343647	+	0.00593561i
$503$	−15340.8			−1.35987			−0.679935	−	0.733273i	$-0.737992\pi$
$503$	−15340.8			−1.35987			−0.679935	+	0.733273i	$0.737992\pi$
$504$		0			0
$505$	29212.7			2.57416
$506$	−17215.4	−	297.353i	−1.51249	−	0.0261244i
$507$		0			0
$508$	547.787	−	15852.5i	0.0478428	−	1.38453i
$509$			7729.91i			0.673128i	0.941661	+	0.336564i	$0.109265\pi$
$509$			7729.91i			0.673128i	−0.941661	+	0.336564i	$0.890735\pi$
$510$		0			0
$511$	6291.12	−	8758.53i	0.544624	−	0.758228i
$512$	−11445.6	−	1793.53i	−0.987944	−	0.154811i
$513$		0			0
$514$	−292.748	+	16948.8i	−0.0251217	+	1.45444i
$515$			5168.20i			0.442210i
$516$		0			0
$517$		−	30594.6i		−	2.60261i
$518$	−450.621	−	335.622i	−0.0382223	−	0.0284679i
$519$		0			0
$520$	10794.7	+	559.798i	0.910344	+	0.0472092i
$521$			9454.94i			0.795064i	0.917588	+	0.397532i	$0.130133\pi$
$521$			9454.94i			0.795064i	−0.917588	+	0.397532i	$0.869867\pi$
$522$		0			0
$523$	−20468.5			−1.71133			−0.855665	−	0.517531i	$-0.826851\pi$
$523$	−20468.5			−1.71133			−0.855665	+	0.517531i	$0.826851\pi$
$524$	−3229.95	−	111.611i	−0.269276	−	0.00930490i
$525$		0			0
$526$	−79.9596	+	4629.32i	−0.00662814	+	0.383741i
$527$			12727.0i			1.05199i
$528$		0			0
$529$	3132.47			0.257456
$530$	28.6557	−	1659.04i	0.00234853	−	0.135970i
$531$		0			0
$532$	−2008.24	−	1550.37i	−0.163662	−	0.126348i
$533$	1180.05			0.0958984
$534$		0			0
$535$	−8033.53			−0.649196
$536$	243.593	−	4697.26i	0.0196299	−	0.378528i
$537$		0			0
$538$	363.536	−	21047.2i	0.0291323	−	1.68663i
$539$	−20817.4	+	7014.62i	−1.66358	+	0.560559i
$540$		0			0
$541$	−14593.7			−1.15976			−0.579882	−	0.814700i	$-0.696901\pi$
$541$	−14593.7			−1.15976			−0.579882	+	0.814700i	$0.696901\pi$
$542$	−15891.5	−	274.485i	−1.25941	−	0.0217530i
$543$		0			0
$544$	−1294.32	+	14951.3i	−0.102010	+	1.17837i
$545$		−	1208.22i		−	0.0949627i
$546$		0			0
$547$			8758.57i			0.684624i	0.939586	+	0.342312i	$0.111210\pi$
$547$			8758.57i			0.684624i	−0.939586	+	0.342312i	$0.888790\pi$
$548$	10927.7	+	377.610i	0.851842	+	0.0294356i
$549$		0			0
$550$	−476.391	+	27581.0i	−0.0369334	+	2.13829i
$551$	−3379.59			−0.261298
$552$		0			0
$553$	−3363.19	+	4682.24i	−0.258621	+	0.360053i
$554$	1974.63	+	34.1066i	0.151433	+	0.00261562i
$555$		0			0
$556$	−14152.4	−	489.038i	−1.07949	−	0.0373019i
$557$	3314.26			0.252118			0.126059	−	0.992023i	$-0.459767\pi$
$557$	3314.26			0.252118			0.126059	+	0.992023i	$0.459767\pi$
$558$		0			0
$559$	−11833.7			−0.895369
$560$	−12593.5	+	15197.4i	−0.950312	+	1.14680i
$561$		0			0
$562$	−14216.4	−	245.551i	−1.06705	−	0.0184305i
$563$	21115.0			1.58062			0.790310	−	0.612707i	$-0.209919\pi$
$563$	21115.0			1.58062			0.790310	+	0.612707i	$0.209919\pi$
$564$		0			0
$565$			25743.4i			1.91687i
$566$	10170.0	+	175.660i	0.755259	+	0.0130452i
$567$		0			0
$568$	625.815	−	12067.7i	0.0462299	−	0.891462i
$569$	8726.10			0.642912			0.321456	−	0.946924i	$-0.395828\pi$
$569$	8726.10			0.642912			0.321456	+	0.946924i	$0.395828\pi$
$570$		0			0
$571$			19948.3i			1.46202i	0.682369	+	0.731008i	$0.260950\pi$
$571$			19948.3i			1.46202i	−0.682369	+	0.731008i	$0.739050\pi$
$572$	−14689.8	−	507.608i	−1.07379	−	0.0371052i
$573$		0			0
$574$	−1287.08	+	1728.10i	−0.0935921	+	0.125661i
$575$			14474.3i			1.04977i
$576$		0			0
$577$			4516.90i			0.325894i	0.986635	+	0.162947i	$0.0521000\pi$
$577$			4516.90i			0.325894i	−0.986635	+	0.162947i	$0.947900\pi$
$578$	5543.16	+	95.7439i	0.398902	+	0.00689001i
$579$		0			0
$580$	−907.975	+	26276.1i	−0.0650028	+	1.88113i
$581$	19849.9	+	14257.9i	1.41740	+	1.01810i
$582$		0			0
$583$			2256.33i			0.160288i
$584$	−682.334	+	13157.6i	−0.0483479	+	0.932303i
$585$		0			0
$586$	200.028	−	11580.7i	0.0141008	−	0.816375i
$587$	1629.66			0.114588			0.0572942	−	0.998357i	$-0.481753\pi$
$587$	1629.66			0.114588			0.0572942	+	0.998357i	$0.481753\pi$
$588$		0			0
$589$	2628.72			0.183896
$590$	−402.305	+	23291.7i	−0.0280722	+	1.62526i
$591$		0			0
$592$	684.840	+	47.3862i	0.0475452	+	0.00328980i
$593$		−	6205.32i		−	0.429717i	−0.976645	−	0.214858i	$-0.931071\pi$
$593$		−	6205.32i		−	0.429717i	0.976645	−	0.214858i	$-0.0689290\pi$
$594$		0			0
$595$	20765.5	+	14915.6i	1.43076	+	1.02770i
$596$	−15926.2	−	550.334i	−1.09457	−	0.0378231i
$597$		0			0
$598$	−7711.38	−	133.194i	−0.527327	−	0.00910823i
$599$		−	752.600i		−	0.0513362i	−0.999671	−	0.0256681i	$-0.991829\pi$
$599$		−	752.600i		−	0.0513362i	0.999671	−	0.0256681i	$-0.00817131\pi$
$600$		0			0
$601$			21945.7i			1.48949i	0.667348	+	0.744746i	$0.267430\pi$
$601$			21945.7i			1.48949i	−0.667348	+	0.744746i	$0.732570\pi$
$602$	12907.0	−	17329.5i	0.873835	−	1.17325i
$603$		0			0
$604$	−308.725	+	8934.25i	−0.0207977	+	0.601870i
$605$		−	46138.1i		−	3.10046i
$606$		0			0
$607$	1770.10			0.118363			0.0591815	−	0.998247i	$-0.481151\pi$
$607$	1770.10			0.118363			0.0591815	+	0.998247i	$0.481151\pi$
$608$	3088.14	+	267.337i	0.205988	+	0.0178322i
$609$		0			0
$610$	−13848.8	−	239.202i	−0.919215	−	0.0158771i
$611$		−	13704.3i		−	0.907395i
$612$		0			0
$613$	−22582.9			−1.48795			−0.743977	−	0.668205i	$-0.767063\pi$
$613$	−22582.9			−1.48795			−0.743977	+	0.668205i	$0.767063\pi$
$614$	−17574.0	−	303.546i	−1.15509	−	0.0199513i
$615$		0			0
$616$	16765.5	−	20958.4i	1.09659	−	1.37084i
$617$	−12035.2			−0.785279			−0.392639	−	0.919692i	$-0.628438\pi$
$617$	−12035.2			−0.785279			−0.392639	+	0.919692i	$0.628438\pi$
$618$		0			0
$619$	875.313			0.0568365			0.0284183	−	0.999596i	$-0.490953\pi$
$619$	875.313			0.0568365			0.0284183	+	0.999596i	$0.490953\pi$
$620$	706.243	−	20438.1i	0.0457474	−	1.32389i
$621$		0			0
$622$	−11439.1	−	197.581i	−0.737404	−	0.0127368i
$623$	−6656.54	+	9267.27i	−0.428072	+	0.595964i
$624$		0			0
$625$	−11470.7			−0.734125
$626$	−338.596	+	19603.3i	−0.0216183	+	1.25160i
$627$		0			0
$628$	209.422	−	6060.51i	0.0133071	−	0.385097i
$629$		−	889.248i		−	0.0563698i
$630$		0			0
$631$		−	18162.8i		−	1.14588i	−0.819597	−	0.572940i	$-0.805803\pi$
$631$		−	18162.8i		−	1.14588i	0.819597	−	0.572940i	$-0.194197\pi$
$632$	364.770	−	7033.94i	0.0229585	−	0.442714i
$633$		0			0
$634$	11217.0	+	193.744i	0.702654	+	0.0121365i
$635$	33016.2			2.06332
$636$		0			0
$637$	−9324.81	+	3142.09i	−0.580004	+	0.195438i
$638$	617.432	−	35746.7i	0.0383141	−	2.21822i
$639$		0			0
$640$	2908.20	−	23938.3i	0.179620	−	1.47851i
$641$	−2528.87			−0.155826			−0.0779128	−	0.996960i	$-0.524826\pi$
$641$	−2528.87			−0.155826			−0.0779128	+	0.996960i	$0.524826\pi$
$642$		0			0
$643$	22947.8			1.40742			0.703712	−	0.710485i	$-0.251524\pi$
$643$	22947.8			1.40742			0.703712	+	0.710485i	$0.251524\pi$
$644$	8605.85	−	11147.4i	0.526580	−	0.682097i
$645$		0			0
$646$	69.3432	−	4014.67i	0.00422333	−	0.244513i
$647$	−8556.53			−0.519926			−0.259963	−	0.965619i	$-0.583710\pi$
$647$	−8556.53			−0.519926			−0.259963	+	0.965619i	$0.583710\pi$
$648$		0			0
$649$		−	31677.2i		−	1.91593i
$650$	−213.392	+	12354.5i	−0.0128768	+	0.745510i
$651$		0			0
$652$	−40.8465	+	1182.07i	−0.00245349	+	0.0710019i
$653$	18532.9			1.11064			0.555319	−	0.831637i	$-0.312596\pi$
$653$	18532.9			1.11064			0.555319	+	0.831637i	$0.312596\pi$
$654$		0			0
$655$		−	6727.04i		−	0.401293i
$656$	181.722	−	2626.31i	0.0108156	−	0.156311i
$657$		0			0
$658$	20068.9	+	14947.3i	1.18901	+	0.885572i
$659$			20893.8i			1.23506i	0.786546	+	0.617532i	$0.211867\pi$
$659$			20893.8i			1.23506i	−0.786546	+	0.617532i	$0.788133\pi$
$660$		0			0
$661$			5459.18i			0.321237i	0.987017	+	0.160618i	$0.0513488\pi$
$661$			5459.18i			0.321237i	−0.987017	+	0.160618i	$0.948651\pi$
$662$	−486.015	+	28138.2i	−0.0285340	+	1.65200i
$663$		0			0
$664$	−29819.7	−	1546.40i	−1.74281	−	0.0903797i
$665$	3080.76	−	4289.04i	0.179649	−	0.250108i
$666$		0			0
$667$		−	18759.6i		−	1.08902i
$668$	13927.0	+	481.251i	0.806666	+	0.0278745i
$669$		0			0
$670$	9788.87	+	169.078i	0.564444	+	0.00974932i
$671$	18834.6			1.08361
$672$		0			0
$673$	1716.03			0.0982882			0.0491441	−	0.998792i	$-0.484351\pi$
$673$	1716.03			0.0982882			0.0491441	+	0.998792i	$0.484351\pi$
$674$	−13990.9	−	241.656i	−0.799567	−	0.0138105i
$675$		0			0
$676$	10985.5	+	379.605i	0.625027	+	0.0215979i
$677$			17235.8i			0.978474i	0.872151	+	0.489237i	$0.162725\pi$
$677$			17235.8i			0.978474i	−0.872151	+	0.489237i	$0.837275\pi$
$678$		0			0
$679$	−1124.48	+	1565.51i	−0.0635548	+	0.0884813i
$680$	−31195.2	−	1617.74i	−1.75924	−	0.0912315i
$681$		0			0
$682$	−480.253	+	27804.6i	−0.0269645	+	1.56113i
$683$		−	19454.4i		−	1.08990i	−0.838468	−	0.544951i	$-0.816548\pi$
$683$		−	19454.4i		−	1.08990i	0.838468	−	0.544951i	$-0.183452\pi$
$684$		0			0
$685$			22759.3i			1.26947i
$686$	5569.22	−	17082.5i	0.309962	−	0.950749i
$687$		0			0
$688$	−1822.32	+	26336.8i	−0.100982	+	1.45942i
$689$			1010.69i			0.0558840i
$690$		0			0
$691$	17230.7			0.948604			0.474302	−	0.880362i	$-0.342700\pi$
$691$	17230.7			0.948604			0.474302	+	0.880362i	$0.342700\pi$
$692$	−742.282	+	21481.1i	−0.0407765	+	1.18004i
$693$		0			0
$694$	−256.270	+	14837.0i	−0.0140171	+	0.811532i
$695$		−	29475.3i		−	1.60872i
$696$		0			0
$697$	−3410.20			−0.185323
$698$	425.124	−	24612.8i	0.0230533	−	1.33468i
$699$		0			0
$700$	−17859.4	−	13787.5i	−0.964317	−	0.744454i
$701$	22169.2			1.19447			0.597233	−	0.802068i	$-0.296267\pi$
$701$	22169.2			1.19447			0.597233	+	0.802068i	$0.296267\pi$
$702$		0			0
$703$	−183.671			−0.00985388
$704$	−3391.87	+	32615.2i	−0.181585	+	1.74607i
$705$		0			0
$706$	−68.5245	+	3967.27i	−0.00365291	+	0.211488i
$707$	18954.7	−	26388.8i	1.00829	−	1.40375i
$708$		0			0
$709$	15665.5			0.829800			0.414900	−	0.909867i	$-0.363817\pi$
$709$	15665.5			0.829800			0.414900	+	0.909867i	$0.363817\pi$
$710$	25148.6	+	434.377i	1.32931	+	0.0229604i
$711$		0			0
$712$	721.967	−	13921.8i	0.0380012	−	0.732785i
$713$			14591.6i			0.766424i
$714$		0			0
$715$		−	30594.6i		−	1.60024i
$716$	−285.265	+	8255.33i	−0.0148894	+	0.430889i
$717$		0			0
$718$	466.781	−	27024.6i	0.0242620	−	1.40466i
$719$	−35225.3			−1.82709			−0.913547	−	0.406733i	$-0.866668\pi$
$719$	−35225.3			−1.82709			−0.913547	+	0.406733i	$0.866668\pi$
$720$		0			0
$721$	4668.60	+	3353.39i	0.241148	+	0.173213i
$722$	18568.1	+	320.716i	0.957108	+	0.0165316i
$723$		0			0
$724$	444.399	−	12860.5i	0.0228121	−	0.660164i
$725$	−30054.8			−1.53960
$726$		0			0
$727$	12778.0			0.651872			0.325936	−	0.945392i	$-0.394321\pi$
$727$	12778.0			0.651872			0.325936	+	0.945392i	$0.394321\pi$
$728$	7509.82	−	9387.97i	0.382325	−	0.477941i
$729$		0			0
$730$	−27419.8	−	473.607i	−1.39021	−	0.0240123i
$731$	34197.7			1.73030
$732$		0			0
$733$			9725.54i			0.490069i	0.969514	+	0.245035i	$0.0787994\pi$
$733$			9725.54i			0.490069i	−0.969514	+	0.245035i	$0.921201\pi$
$734$	−2931.88	−	50.6408i	−0.147436	−	0.00254658i
$735$		0			0
$736$	−1483.95	+	17141.8i	−0.0743193	+	0.858499i
$737$	−13313.1			−0.665391
$738$		0			0
$739$		−	18977.4i		−	0.944648i	−0.881425	−	0.472324i	$-0.843415\pi$
$739$		−	18977.4i		−	0.944648i	0.881425	−	0.472324i	$-0.156585\pi$
$740$	−49.3458	+	1428.03i	−0.00245134	+	0.0709397i
$741$		0			0
$742$	−1480.07	−	1102.35i	−0.0732279	−	0.0545400i
$743$		−	18688.2i		−	0.922752i	−0.887205	−	0.461376i	$-0.847356\pi$
$743$		−	18688.2i		−	0.922752i	0.887205	−	0.461376i	$-0.152644\pi$
$744$		0			0
$745$		−	33169.7i		−	1.63120i
$746$	−30456.1	−	526.051i	−1.49474	−	0.0258178i
$747$		0			0
$748$	42451.4	+	1466.92i	2.07510	+	0.0717056i
$749$	−5212.56	+	7256.95i	−0.254289	+	0.354023i
$750$		0			0
$751$		−	19229.5i		−	0.934345i	−0.884166	−	0.467173i	$-0.845273\pi$
$751$		−	19229.5i		−	0.934345i	0.884166	−	0.467173i	$-0.154727\pi$
$752$	−30500.1	−	2110.40i	−1.47902	−	0.102338i
$753$		0			0
$754$	276.569	−	16012.1i	0.0133581	−	0.773379i
$755$	−18607.4			−0.896946
$756$		0			0
$757$	35890.6			1.72321			0.861603	−	0.507584i	$-0.169461\pi$
$757$	35890.6			1.72321			0.861603	+	0.507584i	$0.169461\pi$
$758$	159.647	−	9242.87i	0.00764992	−	0.442897i
$759$		0			0
$760$	−334.138	+	6443.26i	−0.0159480	+	0.307528i
$761$		−	16455.3i		−	0.783843i	−0.919999	−	0.391922i	$-0.871810\pi$
$761$		−	16455.3i		−	0.783843i	0.919999	−	0.391922i	$-0.128190\pi$
$762$		0			0
$763$	−1091.43	−	783.956i	−0.0517855	−	0.0371968i
$764$	−544.385	+	15754.1i	−0.0257790	+	0.746024i
$765$		0			0
$766$	−14545.5	−	251.237i	−0.686099	−	0.0118506i
$767$		−	14189.3i		−	0.667986i
$768$		0			0
$769$		−	32125.7i		−	1.50648i	−0.657746	−	0.753240i	$-0.728490\pi$
$769$		−	32125.7i		−	1.50648i	0.657746	−	0.753240i	$-0.271510\pi$
$770$	44803.3	+	33369.4i	2.09688	+	1.56175i
$771$		0			0
$772$	7728.36	+	267.055i	0.360298	+	0.0124502i
$773$			302.967i			0.0140970i	0.999975	+	0.00704850i	$0.00224363\pi$
$773$			302.967i			0.0140970i	−0.999975	+	0.00704850i	$0.997756\pi$
$774$		0			0
$775$	23377.3			1.08353
$776$	121.961	−	2351.80i	0.00564195	−	0.108795i
$777$		0			0
$778$	−14536.7	−	251.084i	−0.669879	−	0.0115704i
$779$			704.364i			0.0323959i
$780$		0			0
$781$	−34202.6			−1.56705
$782$	22284.8	+	384.913i	1.01906	+	0.0176016i
$783$		0			0
$784$	5557.00	+	21237.0i	0.253143	+	0.967429i
$785$	12622.3			0.573897
$786$		0			0
$787$	23519.9			1.06531			0.532653	−	0.846334i	$-0.321195\pi$
$787$	23519.9			1.06531			0.532653	+	0.846334i	$0.321195\pi$
$788$	−8543.11	−	295.209i	−0.386213	−	0.0133457i
$789$		0			0
$790$	14658.4	+	253.187i	0.660156	+	0.0114025i
$791$	23254.8	+	16703.6i	1.04532	+	0.750835i
$792$		0			0
$793$	8436.67			0.377800
$794$	330.898	−	19157.6i	0.0147898	−	0.856269i
$795$		0			0
$796$	2020.07	+	69.8040i	0.0899492	+	0.00310821i
$797$		−	7210.03i		−	0.320442i	−0.987081	−	0.160221i	$-0.948779\pi$
$797$		−	7210.03i		−	0.320442i	0.987081	−	0.160221i	$-0.0512207\pi$
$798$		0			0
$799$			39603.6i			1.75354i
$800$	27463.0	+	2377.44i	1.21370	+	0.105069i
$801$		0			0
$802$	−24963.6	−	431.181i	−1.09912	−	0.0189845i
$803$	37291.5			1.63884
$804$		0			0
$805$	23807.8	+	17100.8i	1.04238	+	0.748725i
$806$	−215.121	+	12454.6i	−0.00940115	+	0.544286i
$807$		0			0
$808$	−2055.82	+	39642.8i	−0.0895093	+	1.72603i
$809$	−40393.4			−1.75544			−0.877722	−	0.479170i	$-0.840938\pi$
$809$	−40393.4			−1.75544			−0.877722	+	0.479170i	$0.840938\pi$
$810$		0			0
$811$	29435.6			1.27450			0.637252	−	0.770655i	$-0.280071\pi$
$811$	29435.6			1.27450			0.637252	+	0.770655i	$0.280071\pi$
$812$	23146.9	+	17869.4i	1.00036	+	0.772284i
$813$		0			0
$814$	33.5557	−	1942.73i	0.00144487	−	0.0836518i
$815$	−2461.90			−0.105812
$816$		0			0
$817$		−	7063.41i		−	0.302469i
$818$	585.486	−	33897.1i	0.0250257	−	1.44888i
$819$		0			0
$820$	5476.38	+	189.237i	0.233224	+	0.00805909i
$821$	−12341.4			−0.524624			−0.262312	−	0.964983i	$-0.584485\pi$
$821$	−12341.4			−0.524624			−0.262312	+	0.964983i	$0.584485\pi$
$822$		0			0
$823$		−	22102.8i		−	0.936153i	−0.883688	−	0.468077i	$-0.844947\pi$
$823$		−	22102.8i		−	0.936153i	0.883688	−	0.468077i	$-0.155053\pi$
$824$	−7013.45	−	363.708i	−0.296511	−	0.0153766i
$825$		0			0
$826$	20779.1	+	15476.2i	0.875299	+	0.651921i
$827$			3867.63i			0.162625i	0.996689	+	0.0813124i	$0.0259111\pi$
$827$			3867.63i			0.162625i	−0.996689	+	0.0813124i	$0.974089\pi$
$828$		0			0
$829$		−	11642.7i		−	0.487778i	−0.969803	−	0.243889i	$-0.921577\pi$
$829$		−	11642.7i		−	0.487778i	0.969803	−	0.243889i	$-0.0784233\pi$
$830$	1073.36	−	62142.8i	0.0448877	−	2.59880i
$831$		0			0
$832$	−1519.33	+	14609.4i	−0.0633094	+	0.608763i
$833$	26947.4	−	9080.19i	1.12086	−	0.377683i
$834$		0			0
$835$			29006.0i			1.20215i
$836$	302.987	−	8768.19i	0.0125347	−	0.362744i
$837$		0			0
$838$	−11590.3	−	200.193i	−0.477782	−	0.00825247i
$839$	−1522.64			−0.0626546			−0.0313273	−	0.999509i	$-0.509973\pi$
$839$	−1522.64			−0.0626546			−0.0313273	+	0.999509i	$0.509973\pi$
$840$		0			0
$841$	14563.9			0.597152
$842$	−902.122	−	15.5819i	−0.0369230	−	0.000637751i
$843$		0			0
$844$	−1272.59	+	36827.7i	−0.0519008	+	1.50197i
$845$			22879.5i			0.931456i
$846$		0			0
$847$	−41678.0	−	29936.7i	−1.69076	−	1.21445i
$848$	2249.37	+	155.640i	0.0910891	+	0.00630273i
$849$		0			0
$850$	616.672	−	35702.7i	0.0248843	−	1.44070i
$851$		−	1019.53i		−	0.0410681i
$852$		0			0
$853$			16334.5i			0.655664i	0.944736	+	0.327832i	$0.106318\pi$
$853$			16334.5i			0.655664i	−0.944736	+	0.327832i	$0.893682\pi$
$854$	−9201.87	+	12354.8i	−0.368714	+	0.495052i
$855$		0			0
$856$	565.353	−	10901.8i	0.0225740	−	0.435299i
$857$			40489.7i			1.61389i	0.590627	+	0.806945i	$0.298880\pi$
$857$			40489.7i			1.61389i	−0.590627	+	0.806945i	$0.701120\pi$
$858$		0			0
$859$	−3963.14			−0.157416			−0.0787080	−	0.996898i	$-0.525079\pi$
$859$	−3963.14			−0.157416			−0.0787080	+	0.996898i	$0.525079\pi$
$860$	−54917.5	−	1897.69i	−2.17753	−	0.0752448i
$861$		0			0
$862$	485.515	−	28109.2i	0.0191841	−	1.11068i
$863$			38486.3i			1.51806i	0.651054	+	0.759031i	$0.274327\pi$
$863$			38486.3i			1.51806i	−0.651054	+	0.759031i	$0.725673\pi$
$864$		0			0
$865$	−44738.8			−1.75857
$866$	−61.2748	+	3547.55i	−0.00240439	+	0.139204i
$867$		0			0
$868$	−18004.2	−	13899.2i	−0.704033	−	0.543515i
$869$	−19935.7			−0.778221
$870$		0			0
$871$	−5963.37			−0.231988
$872$	1639.61	+	85.0277i	0.0636744	+	0.00330207i
$873$		0			0
$874$	79.5025	−	4602.85i	0.00307690	−	0.178139i
$875$	4908.14	−	6833.13i	0.189629	−	0.264002i
$876$		0			0
$877$	−7715.19			−0.297062			−0.148531	−	0.988908i	$-0.547454\pi$
$877$	−7715.19			−0.297062			−0.148531	+	0.988908i	$0.547454\pi$
$878$	36575.7	+	631.752i	1.40589	+	0.0242831i
$879$		0			0
$880$	−68090.7	−	4711.40i	−2.60834	−	0.180479i
$881$		−	10746.0i		−	0.410946i	−0.978663	−	0.205473i	$-0.934127\pi$
$881$		−	10746.0i		−	0.410946i	0.978663	−	0.205473i	$-0.0658732\pi$
$882$		0			0
$883$		−	3332.31i		−	0.127000i	−0.997982	−	0.0635000i	$-0.979774\pi$
$883$		−	3332.31i		−	0.127000i	0.997982	−	0.0635000i	$-0.0202263\pi$
$884$	19015.4	+	657.082i	0.723482	+	0.0250001i
$885$		0			0
$886$	29.1211	−	1685.99i	0.00110422	−	0.0639298i
$887$	−29194.6			−1.10514			−0.552569	−	0.833467i	$-0.686353\pi$
$887$	−29194.6			−1.10514			−0.552569	+	0.833467i	$0.686353\pi$
$888$		0			0
$889$	21422.6	−	29824.6i	0.808200	−	1.12518i
$890$	29012.5	+	501.116i	1.09270	+	0.0188735i
$891$		0			0
$892$	15412.0	+	532.565i	0.578511	+	0.0199906i
$893$	8179.99			0.306532
$894$		0			0
$895$	−17193.5			−0.642139
$896$	−19737.2	−	18159.4i	−0.735909	−	0.677080i
$897$		0			0
$898$	−9696.35	−	167.480i	−0.360324	−	0.00622368i
$899$	−30298.5			−1.12404
$900$		0			0
$901$		−	2920.74i		−	0.107996i
$902$	−7450.21	−	128.683i	−0.275017	−	0.00475021i
$903$		0			0
$904$	−34934.7	−	1811.67i	−1.28530	−	0.0666539i
$905$	26784.8			0.983820
$906$		0			0
$907$			42775.0i			1.56595i	0.622051	+	0.782976i	$0.286299\pi$
$907$			42775.0i			1.56595i	−0.622051	+	0.782976i	$0.713701\pi$
$908$	32490.3	+	1122.71i	1.18748	+	0.0410335i
$909$		0			0
$910$	20068.9	+	14947.3i	0.731075	+	0.544504i
$911$		−	43757.7i		−	1.59139i	−0.605697	−	0.795696i	$-0.707105\pi$
$911$		−	43757.7i		−	1.59139i	0.605697	−	0.795696i	$-0.292895\pi$
$912$		0			0
$913$			84515.5i			3.06359i
$914$	−53764.7	−	928.647i	−1.94571	−	0.0336071i
$915$		0			0
$916$	1131.76	−	32752.3i	0.0408237	−	1.18141i
$917$	−6076.75	−	4364.84i	−0.218835	−	0.157186i
$918$		0			0
$919$			2327.16i			0.0835322i	0.999127	+	0.0417661i	$0.0132984\pi$
$919$			2327.16i			0.0835322i	−0.999127	+	0.0417661i	$0.986702\pi$
$920$	−35765.5	−	1854.75i	−1.28169	−	0.0664666i
$921$		0			0
$922$	−644.138	+	37292.8i	−0.0230082	+	1.33207i
$923$	−15320.5			−0.546349
$924$		0			0
$925$	−1633.39			−0.0580602
$926$	362.722	−	21000.0i	0.0128723	−	0.745253i
$927$		0			0
$928$	−35593.8	−	3081.31i	−1.25908	−	0.108997i
$929$		−	44503.1i		−	1.57169i	−0.618423	−	0.785845i	$-0.712228\pi$
$929$		−	44503.1i		−	1.57169i	0.618423	−	0.785845i	$-0.287772\pi$
$930$		0			0
$931$	−1875.48	−	5565.89i	−0.0660219	−	0.195934i
$932$	−15591.3	−	538.762i	−0.547974	−	0.0189353i
$933$		0			0
$934$	−32448.7	−	560.469i	−1.13678	−	0.0196350i
$935$			88414.0i			3.09246i
$936$		0			0
$937$			19995.0i			0.697128i	0.937285	+	0.348564i	$0.113331\pi$
$937$			19995.0i			0.697128i	−0.937285	+	0.348564i	$0.886669\pi$
$938$	6504.24	−	8732.89i	0.226408	−	0.303986i
$939$		0			0
$940$	2197.67	−	63598.9i	0.0762555	−	2.20677i
$941$			5492.38i			0.190272i	0.995464	+	0.0951362i	$0.0303287\pi$
$941$			5492.38i			0.190272i	−0.995464	+	0.0951362i	$0.969671\pi$
$942$		0			0
$943$	−3909.81			−0.135017
$944$	−31579.4	−	2185.07i	−1.08880	−	0.0753370i
$945$		0			0
$946$	74711.2	+	1290.45i	2.56773	+	0.0443510i
$947$			25553.9i			0.876863i	0.898765	+	0.438432i	$0.144466\pi$
$947$			25553.9i			0.876863i	−0.898765	+	0.438432i	$0.855534\pi$
$948$		0			0
$949$	16704.1			0.571379
$950$	−7374.26	−	127.371i	−0.251845	−	0.00434998i
$951$		0			0
$952$	−21702.4	+	27129.9i	−0.738842	+	0.923620i
$953$	39066.4			1.32790			0.663948	−	0.747779i	$-0.268880\pi$
$953$	39066.4			1.32790			0.663948	+	0.747779i	$0.268880\pi$
$954$		0			0
$955$	−32811.2			−1.11177
$956$	−790.574	+	22878.6i	−0.0267458	+	0.774003i
$957$		0			0
$958$	50689.2	+	875.526i	1.70949	+	0.0295271i
$959$	20559.2	+	14767.4i	0.692274	+	0.497250i
$960$		0			0
$961$	−6224.19			−0.208928
$962$	15.0307	−	870.214i	0.000503752	−	0.0291651i
$963$		0			0
$964$	−1193.55	+	34540.3i	−0.0398771	+	1.15401i
$965$			16095.9i			0.536939i
$966$		0			0
$967$			17718.4i			0.589229i	0.955616	+	0.294614i	$0.0951912\pi$
$967$			17718.4i			0.589229i	−0.955616	+	0.294614i	$0.904809\pi$
$968$	62611.1	+	3246.92i	2.07892	+	0.107810i
$969$		0			0
$970$	4901.05	+	84.6531i	0.162230	+	0.00280211i
$971$	−48730.8			−1.61055			−0.805276	−	0.592900i	$-0.797983\pi$
$971$	−48730.8			−1.61055			−0.805276	+	0.592900i	$0.797983\pi$
$972$		0			0
$973$	−26626.0	−	19125.0i	−0.877276	−	0.630134i
$974$	−398.682	+	23082.0i	−0.0131156	+	0.759337i
$975$		0			0
$976$	1299.20	−	18776.5i	0.0426091	−	0.615801i
$977$	−18189.4			−0.595629			−0.297815	−	0.954624i	$-0.596258\pi$
$977$	−18189.4			−0.595629			−0.297815	+	0.954624i	$0.596258\pi$
$978$		0			0
$979$	−39457.6			−1.28812
$980$	−43778.3	+	13086.4i	−1.42699	+	0.426560i
$981$		0			0
$982$	−860.793	+	49836.2i	−0.0279725	+	1.61949i
$983$	−8921.53			−0.289474			−0.144737	−	0.989470i	$-0.546234\pi$
$983$	−8921.53			−0.289474			−0.144737	+	0.989470i	$0.546234\pi$
$984$		0			0
$985$		−	17792.8i		−	0.575560i
$986$	−799.245	+	46272.9i	−0.0258146	+	1.49455i
$987$		0			0
$988$	135.718	−	3927.57i	0.00437020	−	0.126470i
$989$	39207.9			1.26060
$990$		0			0
$991$			38882.1i			1.24635i	0.782083	+	0.623174i	$0.214157\pi$
$991$			38882.1i			1.24635i	−0.782083	+	0.623174i	$0.785843\pi$
$992$	27685.6	+	2396.71i	0.886108	+	0.0767094i
$993$		0			0
$994$	16710.0	−	22435.7i	0.533209	−	0.715911i
$995$			4207.23i			0.134048i
$996$		0			0
$997$		−	37847.7i		−	1.20225i	−0.799153	−	0.601127i	$-0.794719\pi$
$997$		−	37847.7i		−	1.20225i	0.799153	−	0.601127i	$-0.205281\pi$
$998$	−330.791	+	19151.4i	−0.0104920	+	0.607441i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.f.55.1		12
3.2	odd	2		84.4.b.a.55.12	yes	12
4.3	odd	2		252.4.b.e.55.2		12
7.6	odd	2		252.4.b.e.55.1		12
12.11	even	2		84.4.b.b.55.11	yes	12
21.20	even	2		84.4.b.b.55.12	yes	12
24.5	odd	2		1344.4.b.h.895.11		12
24.11	even	2		1344.4.b.g.895.11		12
28.27	even	2	inner	252.4.b.f.55.2		12
84.83	odd	2		84.4.b.a.55.11	✓	12
168.83	odd	2		1344.4.b.h.895.2		12
168.125	even	2		1344.4.b.g.895.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.b.a.55.11	✓	12	84.83	odd	2
84.4.b.a.55.12	yes	12	3.2	odd	2
84.4.b.b.55.11	yes	12	12.11	even	2
84.4.b.b.55.12	yes	12	21.20	even	2
252.4.b.e.55.1		12	7.6	odd	2
252.4.b.e.55.2		12	4.3	odd	2
252.4.b.f.55.1		12	1.1	even	1	trivial
252.4.b.f.55.2		12	28.27	even	2	inner
1344.4.b.g.895.2		12	168.125	even	2
1344.4.b.g.895.11		12	24.11	even	2
1344.4.b.h.895.2		12	168.83	odd	2
1344.4.b.h.895.11		12	24.5	odd	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} +16.6517i q^{5} +(15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +O(q^{10})\)	\(q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} +16.6517i q^{5} +(15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +(0.813380 - 47.0912i) q^{10} +64.0450i q^{11} +28.6879i q^{13} +(-42.0112 - 31.2899i) q^{14} +(63.8473 + 4.41779i) q^{16} -82.9041i q^{17} -17.1236 q^{19} +(-4.60049 + 133.134i) q^{20} +(3.12838 - 181.120i) q^{22} -95.0501i q^{23} -152.281 q^{25} +(1.40131 - 81.1296i) q^{26} +(117.280 + 90.5401i) q^{28} +197.365 q^{29} -153.515 q^{31} +(-180.345 - 15.6123i) q^{32} +(-4.04958 + 234.453i) q^{34} +(-179.913 + 250.476i) q^{35} +10.7262 q^{37} +(48.4255 + 0.836427i) q^{38} +(19.5134 - 376.280i) q^{40} -41.1342i q^{41} +412.497i q^{43} +(-17.6941 + 512.055i) q^{44} +(-4.64287 + 268.802i) q^{46} -477.704 q^{47} +(109.526 + 325.043i) q^{49} +(430.650 + 7.43838i) q^{50} +(-7.92580 + 229.367i) q^{52} +35.2304 q^{53} -1066.46 q^{55} +(-327.245 - 261.776i) q^{56} +(-558.149 - 9.64060i) q^{58} -494.608 q^{59} -294.084i q^{61} +(434.141 + 7.49867i) q^{62} +(509.254 + 52.9608i) q^{64} -477.704 q^{65} +207.870i q^{67} +(22.9045 - 662.837i) q^{68} +(521.031 - 699.560i) q^{70} +534.040i q^{71} -582.270i q^{73} +(-30.3338 - 0.523939i) q^{74} +(-136.907 - 4.73084i) q^{76} +(-691.973 + 963.368i) q^{77} +311.277i q^{79} +(-73.5639 + 1063.17i) q^{80} +(-2.00926 + 116.328i) q^{82} +1319.63 q^{83} +1380.50 q^{85} +(20.1490 - 1166.54i) q^{86} +(75.0512 - 1447.23i) q^{88} +616.091i q^{89} +(-309.958 + 431.525i) q^{91} +(26.2601 - 759.948i) q^{92} +(1350.95 + 23.3342i) q^{94} -285.137i q^{95} +104.076i q^{97} +(-293.864 - 924.573i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8}+O(q^{10}) \) 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8	\( 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8} + 56 q^{10} - 69 q^{14} + 41 q^{16} - 84 q^{19} - 172 q^{20} - 182 q^{22} - 216 q^{25} - 300 q^{26} + 309 q^{28} - 200 q^{29} - 384 q^{31} + 159 q^{32} - 164 q^{34} - 84 q^{35} - 244 q^{37} - 268 q^{38} - 316 q^{40} - 190 q^{44} + 894 q^{46} - 280 q^{47} - 424 q^{49} + 1771 q^{50} - 796 q^{52} + 16 q^{53} + 212 q^{55} + 7 q^{56} - 570 q^{58} - 1168 q^{59} + 384 q^{62} + 2705 q^{64} - 280 q^{65} - 1552 q^{68} + 968 q^{70} - 1622 q^{74} - 788 q^{76} - 968 q^{77} + 3060 q^{80} - 2540 q^{82} + 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} + 1648 q^{91} - 4298 q^{92} + 4256 q^{94} - 97 q^{98}+O(q^{100}) \) 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8 + 56 * q^10 - 69 * q^14 + 41 * q^16 - 84 * q^19 - 172 * q^20 - 182 * q^22 - 216 * q^25 - 300 * q^26 + 309 * q^28 - 200 * q^29 - 384 * q^31 + 159 * q^32 - 164 * q^34 - 84 * q^35 - 244 * q^37 - 268 * q^38 - 316 * q^40 - 190 * q^44 + 894 * q^46 - 280 * q^47 - 424 * q^49 + 1771 * q^50 - 796 * q^52 + 16 * q^53 + 212 * q^55 + 7 * q^56 - 570 * q^58 - 1168 * q^59 + 384 * q^62 + 2705 * q^64 - 280 * q^65 - 1552 * q^68 + 968 * q^70 - 1622 * q^74 - 788 * q^76 - 968 * q^77 + 3060 * q^80 - 2540 * q^82 + 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 + 1648 * q^91 - 4298 * q^92 + 4256 * q^94 - 97 * q^98

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