LMFDB - Embedded newform 252.4.b.e.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.e.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} -16.6517i q^{5} +(-15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +O(q^{10})$	\(q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} -16.6517i q^{5} +(-15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +(-0.813380 + 47.0912i) q^{10} +64.0450i q^{11} -28.6879i q^{13} +(43.0668 - 29.8204i) q^{14} +(63.8473 + 4.41779i) q^{16} +82.9041i q^{17} +17.1236 q^{19} +(4.60049 - 133.134i) q^{20} +(3.12838 - 181.120i) q^{22} -95.0501i q^{23} -152.281 q^{25} +(-1.40131 + 81.1296i) q^{26} +(-123.250 + 82.2285i) q^{28} +197.365 q^{29} +153.515 q^{31} +(-180.345 - 15.6123i) q^{32} +(4.04958 - 234.453i) q^{34} +(179.913 + 250.476i) q^{35} +10.7262 q^{37} +(-48.4255 - 0.836427i) q^{38} +(-19.5134 + 376.280i) q^{40} +41.1342i q^{41} +412.497i q^{43} +(-17.6941 + 512.055i) q^{44} +(-4.64287 + 268.802i) q^{46} +477.704 q^{47} +(109.526 - 325.043i) q^{49} +(430.650 + 7.43838i) q^{50} +(7.92580 - 229.367i) q^{52} +35.2304 q^{53} +1066.46 q^{55} +(352.567 - 226.522i) q^{56} +(-558.149 - 9.64060i) q^{58} +494.608 q^{59} +294.084i q^{61} +(-434.141 - 7.49867i) q^{62} +(509.254 + 52.9608i) q^{64} -477.704 q^{65} +207.870i q^{67} +(-22.9045 + 662.837i) q^{68} +(-496.561 - 717.136i) q^{70} +534.040i q^{71} +582.270i q^{73} +(-30.3338 - 0.523939i) q^{74} +(136.907 + 4.73084i) q^{76} +(-691.973 - 963.368i) q^{77} +311.277i q^{79} +(73.5639 - 1063.17i) q^{80} +(2.00926 - 116.328i) q^{82} -1319.63 q^{83} +1380.50 q^{85} +(20.1490 - 1166.54i) q^{86} +(75.0512 - 1447.23i) q^{88} -616.091i q^{89} +(309.958 + 431.525i) q^{91} +(26.2601 - 759.948i) q^{92} +(-1350.95 - 23.3342i) q^{94} -285.137i q^{95} -104.076i q^{97} +(-325.618 + 913.873i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 101 q^{14} + 41 q^{16} + 84 q^{19} + 172 q^{20} - 182 q^{22} - 216 q^{25} + 300 q^{26} - 379 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} + 1759 q^{56} - 570 q^{58} + 1168 q^{59} - 384 q^{62} + 2705 q^{64} - 280 q^{65} + 1552 q^{68} + 2592 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} - 3137 q^{98}+O(q^{100}) $ 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8 - 56 * q^10 - 101 * q^14 + 41 * q^16 + 84 * q^19 + 172 * q^20 - 182 * q^22 - 216 * q^25 + 300 * q^26 - 379 * 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 + 1759 * q^56 - 570 * q^58 + 1168 * q^59 - 384 * q^62 + 2705 * q^64 - 280 * q^65 + 1552 * q^68 + 2592 * 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 - 3137 * 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	$-0.732598\pi$
$5$		−	16.6517i		−	1.48938i	0.667412	−	0.744689i	$-0.267402\pi$
$6$		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	$-0.901002\pi$
$13$		−	28.6879i		−	0.612046i	0.952024	−	0.306023i	$-0.0989985\pi$
$14$	43.0668	−	29.8204i	0.822148	−	0.569274i
$15$		0			0
$16$	63.8473	+	4.41779i	0.997615	+	0.0690280i
$17$			82.9041i			1.18278i	0.806387	+	0.591388i	$0.201420\pi$
$17$			82.9041i			1.18278i	−0.806387	+	0.591388i	$0.798580\pi$
$18$		0			0
$19$	17.1236			0.206759			0.103379	−	0.994642i	$-0.467034\pi$
$19$	17.1236			0.206759			0.103379	+	0.994642i	$0.467034\pi$
$20$	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
$28$	−123.250	+	82.2285i	−0.831857	+	0.554990i
$29$	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	$-0.353306\pi$
$31$	153.515			0.889422			0.444711	+	0.895674i	$0.353306\pi$
$32$	−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	$0.0249628\pi$
$41$			41.1342i			0.156685i	−0.996927	+	0.0783425i	$0.975037\pi$
$42$		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	$-0.234219\pi$
$47$	477.704			1.48256			0.741280	+	0.671196i	$0.234219\pi$
$48$		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
$56$	352.567	−	226.522i	0.841317	−	0.540542i
$57$		0			0
$58$	−558.149	−	9.64060i	−1.26360	−	0.0218254i
$59$	494.608			1.09140			0.545699	−	0.837981i	$-0.316264\pi$
$59$	494.608			1.09140			0.545699	+	0.837981i	$0.316264\pi$
$60$		0			0
$61$			294.084i			0.617273i	0.951180	+	0.308636i	$0.0998727\pi$
$61$			294.084i			0.617273i	−0.951180	+	0.308636i	$0.900127\pi$
$62$	−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
$70$	−496.561	−	717.136i	−0.847863	−	1.22449i
$71$			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	$0.154585\pi$
$73$			582.270i			0.933555i	−0.884375	+	0.466778i	$0.845415\pi$
$74$	−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	$-0.837553\pi$
$83$	−1319.63			−1.74515			−0.872577	+	0.488477i	$0.837553\pi$
$84$		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	$-0.880424\pi$
$89$		−	616.091i		−	0.733770i	0.930266	−	0.366885i	$-0.119576\pi$
$90$		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	$-0.982653\pi$
$97$		−	104.076i		−	0.108941i	0.998515	−	0.0544706i	$-0.0173471\pi$
$98$	−325.618	+	913.873i	−0.335637	+	0.941991i
$99$		0			0
$100$	−1217.52	−	42.0716i	−1.21752	−	0.0420716i
$101$			1754.34i			1.72835i	0.503196	+	0.864173i	$0.332158\pi$
$101$			1754.34i			1.72835i	−0.503196	+	0.864173i	$0.667842\pi$
$102$		0			0
$103$	−310.370			−0.296910			−0.148455	−	0.988919i	$-0.547430\pi$
$103$	−310.370			−0.296910			−0.148455	+	0.988919i	$0.547430\pi$
$104$	−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
$112$	−1008.13	+	623.385i	−0.850527	+	0.525931i
$113$	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	$-0.456987\pi$
$131$	403.984			0.269437			0.134719	+	0.990884i	$0.456987\pi$
$132$		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	$-0.318400\pi$
$139$	1770.10			1.08013			0.540065	+	0.841623i	$0.318400\pi$
$140$	1369.25	+	2052.32i	0.826590	+	1.23895i
$141$		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
$154$	1909.85	+	2758.21i	0.999349	+	1.44327i
$155$		−	2556.29i		−	1.32468i
$156$		0			0
$157$			758.016i			0.385327i	0.981265	+	0.192663i	$0.0617125\pi$
$157$			758.016i			0.385327i	−0.981265	+	0.192663i	$0.938287\pi$
$158$	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	$-0.632232\pi$
$167$	−1741.92			−0.807148			−0.403574	+	0.914947i	$0.632232\pi$
$168$		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	$-0.798981\pi$
$173$		−	2686.73i		−	1.18074i	0.807131	−	0.590372i	$-0.201019\pi$
$174$		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	$0.107143\pi$
$181$			1608.53i			0.660558i	−0.943883	+	0.330279i	$0.892857\pi$
$182$	−855.485	−	1235.50i	−0.348422	−	0.503193i
$183$		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
$196$	965.490	−	2568.53i	0.351855	−	0.936054i
$197$	−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	$-0.514329\pi$
$199$	−252.660			−0.0900029			−0.0450015	+	0.998987i	$0.514329\pi$
$200$	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	$-0.593465\pi$
$223$	−1927.65			−0.578857			−0.289428	+	0.957200i	$0.593465\pi$
$224$	2881.44	−	1713.69i	0.859483	−	0.511165i
$225$		0			0
$226$	−4372.06	−	75.5161i	−1.28684	−	0.0222268i
$227$	−4063.72			−1.18819			−0.594093	−	0.804396i	$-0.702489\pi$
$227$	−4063.72			−1.18819			−0.594093	+	0.804396i	$0.702489\pi$
$228$		0			0
$229$			4096.49i			1.18211i	0.806631	+	0.591056i	$0.201289\pi$
$229$			4096.49i			1.18211i	−0.806631	+	0.591056i	$0.798711\pi$
$230$	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
$238$	2472.23	+	3570.41i	0.673324	+	0.972418i
$239$			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	$-0.804086\pi$
$241$		−	4320.12i		−	1.15470i	0.816496	−	0.577351i	$-0.195914\pi$
$242$	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	$-0.445026\pi$
$251$	1366.74			0.343698			0.171849	+	0.985123i	$0.445026\pi$
$252$		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	$0.259238\pi$
$257$			5993.21i			1.45465i	−0.686291	+	0.727327i	$0.740762\pi$
$258$		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
$266$	737.456	−	510.631i	0.169986	−	0.117702i
$267$		0			0
$268$	−57.4298	+	1661.97i	−0.0130899	+	0.378810i
$269$		−	7442.41i		−	1.68688i	−0.537220	−	0.843442i	$-0.680526\pi$
$269$		−	7442.41i		−	1.68688i	0.537220	−	0.843442i	$-0.319474\pi$
$270$		0			0
$271$	−5619.33			−1.25959			−0.629797	−	0.776760i	$-0.716862\pi$
$271$	−5619.33			−1.25959			−0.629797	+	0.776760i	$0.716862\pi$
$272$	−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
$280$	−3771.99	−	5870.86i	−0.805070	−	1.25304i
$281$	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	$-0.376720\pi$
$283$	3596.17			0.755371			0.377686	+	0.925934i	$0.376720\pi$
$284$	−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	$-0.866140\pi$
$293$		−	4095.02i		−	0.816497i	0.912871	−	0.408248i	$-0.133860\pi$
$294$		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	$-0.696024\pi$
$307$	−6214.27			−1.15527			−0.577633	+	0.816296i	$0.696024\pi$
$308$	−5266.33	−	7893.52i	−0.974275	−	1.46031i
$309$		0			0
$310$	−124.866	+	7229.20i	−0.0228771	+	1.32449i
$311$	−4044.93			−0.737514			−0.368757	−	0.929526i	$-0.620216\pi$
$311$	−4044.93			−0.737514			−0.368757	+	0.929526i	$0.620216\pi$
$312$		0			0
$313$			6931.84i			1.25179i	0.779907	+	0.625896i	$0.215266\pi$
$313$			6931.84i			1.25179i	−0.779907	+	0.625896i	$0.784734\pi$
$314$	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
$322$	−2834.43	−	4093.50i	−0.490549	−	0.708453i
$323$			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	$-0.767389\pi$
$349$		−	8703.25i		−	1.33488i	0.744662	−	0.667442i	$-0.232611\pi$
$350$	−6558.23	+	4541.06i	−1.00158	+	0.693514i
$351$		0			0
$352$	999.887	−	11550.2i	0.151404	−	1.74894i
$353$			1402.85i			0.211519i	0.994392	+	0.105760i	$0.0337274\pi$
$353$			1402.85i			0.211519i	−0.994392	+	0.105760i	$0.966273\pi$
$354$		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
$364$	2358.97	+	3535.78i	0.339680	+	0.509135i
$365$	9695.81			1.39042
$366$		0			0
$367$	−1036.73			−0.147458			−0.0737289	−	0.997278i	$-0.523490\pi$
$367$	−1036.73			−0.147458			−0.0737289	+	0.997278i	$0.523490\pi$
$368$	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	$-0.611477\pi$
$383$	−5143.39			−0.686201			−0.343101	+	0.939299i	$0.611477\pi$
$384$		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
$392$	−2855.88	+	7216.67i	−0.367968	+	0.929838i
$393$		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	$-0.859149\pi$
$397$		−	6774.24i		−	0.856396i	0.903685	−	0.428198i	$-0.140851\pi$
$398$	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
$406$	8499.87	−	5885.50i	1.03902	−	0.719439i
$407$			686.961i			0.0836643i
$408$		0			0
$409$		−	11986.2i		−	1.44910i	−0.689223	−	0.724549i	$-0.742048\pi$
$409$		−	11986.2i		−	1.44910i	0.689223	−	0.724549i	$-0.257952\pi$
$410$	−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	$-0.576796\pi$
$419$	−4098.42			−0.477854			−0.238927	+	0.971038i	$0.576796\pi$
$420$		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	$0.0221762\pi$
$433$			1254.43i			0.139225i	−0.997574	+	0.0696123i	$0.977824\pi$
$434$	6611.39	−	4577.87i	0.731237	−	0.506325i
$435$		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	$-0.251821\pi$
$439$	12933.4			1.40610			0.703049	+	0.711141i	$0.251821\pi$
$440$	−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
$448$	−8232.43	+	4705.58i	−0.868182	+	0.496245i
$449$	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	$0.232053\pi$
$461$			13187.0i			1.33227i	−0.745830	+	0.666137i	$0.767947\pi$
$462$		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	$-0.692467\pi$
$467$	−11474.1			−1.13695			−0.568476	+	0.822700i	$0.692467\pi$
$468$		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
$476$	−6817.08	−	10217.9i	−0.656430	−	0.983901i
$477$		0			0
$478$	139.776	−	8092.42i	0.0133749	−	0.774349i
$479$	17924.0			1.70975			0.854873	−	0.518837i	$-0.173635\pi$
$479$	17924.0			1.70975			0.854873	+	0.518837i	$0.173635\pi$
$480$		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
$490$	15217.6	+	5422.11i	1.40298	+	0.499890i
$491$		−	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	$-0.262008\pi$
$503$	15340.8			1.35987			0.679935	+	0.733273i	$0.262008\pi$
$504$		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	$-0.890735\pi$
$509$		−	7729.91i		−	0.673128i	0.941661	−	0.336564i	$-0.109265\pi$
$510$		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
$518$	461.943	−	319.860i	0.0391827	−	0.0271309i
$519$		0			0
$520$	10794.7	+	559.798i	0.910344	+	0.0472092i
$521$		−	9454.94i		−	0.795064i	−0.917588	−	0.397532i	$-0.869867\pi$
$521$		−	9454.94i		−	0.795064i	0.917588	−	0.397532i	$-0.130133\pi$
$522$		0			0
$523$	20468.5			1.71133			0.855665	−	0.517531i	$-0.173149\pi$
$523$	20468.5			1.71133			0.855665	+	0.517531i	$0.173149\pi$
$524$	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
$532$	−2110.47	+	1408.04i	−0.171993	+	0.114749i
$533$	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
$560$	10380.4	+	16787.1i	0.783310	+	1.26676i
$561$		0			0
$562$	−14216.4	−	245.551i	−1.06705	−	0.0184305i
$563$	−21115.0			−1.58062			−0.790310	−	0.612707i	$-0.790081\pi$
$563$	−21115.0			−1.58062			−0.790310	+	0.612707i	$0.790081\pi$
$564$		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
$574$	1226.64	+	1771.52i	0.0891966	+	0.128818i
$575$			14474.3i			1.04977i
$576$		0			0
$577$		−	4516.90i		−	0.325894i	−0.986635	−	0.162947i	$-0.947900\pi$
$577$		−	4516.90i		−	0.325894i	0.986635	−	0.162947i	$-0.0521000\pi$
$578$	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	$-0.518247\pi$
$587$	−1629.66			−0.114588			−0.0572942	+	0.998357i	$0.518247\pi$
$588$		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	$0.0689290\pi$
$593$			6205.32i			0.429717i	−0.976645	+	0.214858i	$0.931071\pi$
$594$		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	$-0.732570\pi$
$601$		−	21945.7i		−	1.48949i	0.667348	−	0.744746i	$-0.267430\pi$
$602$	12300.8	+	17764.9i	0.832796	+	1.20273i
$603$		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	$-0.518849\pi$
$607$	−1770.10			−0.118363			−0.0591815	+	0.998247i	$0.518849\pi$
$608$	−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
$616$	14507.6	+	22580.2i	0.948911	+	1.47692i
$617$	−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	$-0.509047\pi$
$619$	−875.313			−0.0568365			−0.0284183	+	0.999596i	$0.509047\pi$
$620$	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	$-0.748476\pi$
$643$	−22947.8			−1.40742			−0.703712	+	0.710485i	$0.748476\pi$
$644$	7815.83	+	11714.9i	0.478241	+	0.716819i
$645$		0			0
$646$	69.3432	−	4014.67i	0.00422333	−	0.244513i
$647$	8556.53			0.519926			0.259963	−	0.965619i	$-0.416290\pi$
$647$	8556.53			0.519926			0.259963	+	0.965619i	$0.416290\pi$
$648$		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
$658$	20573.2	−	14245.3i	1.21888	−	0.843982i
$659$			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	$-0.948651\pi$
$661$		−	5459.18i		−	0.321237i	0.987017	−	0.160618i	$-0.0513488\pi$
$662$	−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	$-0.837275\pi$
$677$		−	17235.8i		−	0.978474i	0.872151	−	0.489237i	$-0.162725\pi$
$678$		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
$686$	−4975.96	−	17264.7i	−0.276943	−	0.960886i
$687$		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	$-0.657300\pi$
$691$	−17230.7			−0.948604			−0.474302	+	0.880362i	$0.657300\pi$
$692$	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
$700$	18768.5	−	12521.8i	1.01340	−	0.676114i
$701$	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	$-0.133332\pi$
$719$	35225.3			1.82709			0.913547	+	0.406733i	$0.133332\pi$
$720$		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	$-0.605679\pi$
$727$	−12778.0			−0.651872			−0.325936	+	0.945392i	$0.605679\pi$
$728$	−6498.46	−	10114.4i	−0.330836	−	0.514925i
$729$		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	$-0.921201\pi$
$733$		−	9725.54i		−	0.490069i	0.969514	−	0.245035i	$-0.0787994\pi$
$734$	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
$742$	1517.26	−	1050.58i	0.0750678	−	0.0519786i
$743$		−	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	$0.128190\pi$
$761$			16455.3i			0.783843i	−0.919999	+	0.391922i	$0.871810\pi$
$762$		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	$0.271510\pi$
$769$			32125.7i			1.50648i	−0.657746	+	0.753240i	$0.728490\pi$
$770$	45929.0	−	31802.3i	2.14957	−	1.48841i
$771$		0			0
$772$	7728.36	+	267.055i	0.360298	+	0.0124502i
$773$		−	302.967i		−	0.0140970i	−0.999975	−	0.00704850i	$-0.997756\pi$
$773$		−	302.967i		−	0.0140970i	0.999975	−	0.00704850i	$-0.00224363\pi$
$774$		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
$784$	8428.94	−	20269.3i	0.383971	−	0.923345i
$785$	12622.3			0.573897
$786$		0			0
$787$	−23519.9			−1.06531			−0.532653	−	0.846334i	$-0.678805\pi$
$787$	−23519.9			−1.06531			−0.532653	+	0.846334i	$0.678805\pi$
$788$	−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	$0.0512207\pi$
$797$			7210.03i			0.320442i	−0.987081	+	0.160221i	$0.948779\pi$
$798$		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	$-0.719929\pi$
$811$	−29435.6			−1.27450			−0.637252	+	0.770655i	$0.719929\pi$
$812$	−24325.2	+	16229.0i	−1.05129	+	0.701388i
$813$		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
$826$	21301.2	−	14749.4i	0.897291	−	0.621304i
$827$			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	$0.0784233\pi$
$829$			11642.7i			0.487778i	−0.969803	+	0.243889i	$0.921577\pi$
$830$	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	$-0.490027\pi$
$839$	1522.64			0.0626546			0.0313273	+	0.999509i	$0.490027\pi$
$840$		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	$-0.893682\pi$
$853$		−	16334.5i		−	0.655664i	0.944736	−	0.327832i	$-0.106318\pi$
$854$	8769.71	+	12665.3i	0.351397	+	0.507490i
$855$		0			0
$856$	565.353	−	10901.8i	0.0225740	−	0.435299i
$857$		−	40489.7i		−	1.61389i	−0.590627	−	0.806945i	$-0.701120\pi$
$857$		−	40489.7i		−	1.61389i	0.590627	−	0.806945i	$-0.298880\pi$
$858$		0			0
$859$	3963.14			0.157416			0.0787080	−	0.996898i	$-0.474921\pi$
$859$	3963.14			0.157416			0.0787080	+	0.996898i	$0.474921\pi$
$860$	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
$868$	−18920.6	+	12623.3i	−0.739872	+	0.493621i
$869$	−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	$0.0658732\pi$
$881$			10746.0i			0.410946i	−0.978663	+	0.205473i	$0.934127\pi$
$882$		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	$-0.313647\pi$
$887$	29194.6			1.10514			0.552569	+	0.833467i	$0.313647\pi$
$888$		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
$896$	23511.2	−	12905.3i	0.876623	−	0.481178i
$897$		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
$910$	−20573.2	+	14245.3i	−0.749443	+	0.518931i
$911$		−	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	$0.287772\pi$
$929$			44503.1i			1.57169i	−0.618423	+	0.785845i	$0.712228\pi$
$930$		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	$-0.886669\pi$
$937$		−	19995.0i		−	0.697128i	0.937285	−	0.348564i	$-0.113331\pi$
$938$	6198.78	+	8952.31i	0.215775	+	0.311624i
$939$		0			0
$940$	2197.67	−	63598.9i	0.0762555	−	2.20677i
$941$		−	5492.38i		−	0.190272i	−0.995464	−	0.0951362i	$-0.969671\pi$
$941$		−	5492.38i		−	0.190272i	0.995464	−	0.0951362i	$-0.0303287\pi$
$942$		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
$952$	18779.6	+	29229.3i	0.639340	+	0.995091i
$953$	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	$-0.202017\pi$
$971$	48730.8			1.61055			0.805276	+	0.592900i	$0.202017\pi$
$972$		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
$980$	−42770.6	−	16077.1i	−1.39414	−	0.524045i
$981$		0			0
$982$	−860.793	+	49836.2i	−0.0279725	+	1.61949i
$983$	8921.53			0.289474			0.144737	−	0.989470i	$-0.453766\pi$
$983$	8921.53			0.289474			0.144737	+	0.989470i	$0.453766\pi$
$984$		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
$994$	15925.3	+	22999.4i	0.508168	+	0.733898i
$995$			4207.23i			0.134048i
$996$		0			0
$997$			37847.7i			1.20225i	0.799153	+	0.601127i	$0.205281\pi$
$997$			37847.7i			1.20225i	−0.799153	+	0.601127i	$0.794719\pi$
$998$	−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.e.55.1		12
3.2	odd	2		84.4.b.b.55.12	yes	12
4.3	odd	2		252.4.b.f.55.2		12
7.6	odd	2		252.4.b.f.55.1		12
12.11	even	2		84.4.b.a.55.11	✓	12
21.20	even	2		84.4.b.a.55.12	yes	12
24.5	odd	2		1344.4.b.g.895.2		12
24.11	even	2		1344.4.b.h.895.2		12
28.27	even	2	inner	252.4.b.e.55.2		12
84.83	odd	2		84.4.b.b.55.11	yes	12
168.83	odd	2		1344.4.b.g.895.11		12
168.125	even	2		1344.4.b.h.895.11		12

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

\(f(q)\)	\(=\)	\(q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} -16.6517i q^{5} +(-15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +O(q^{10})\)	\(q+(-2.82801 - 0.0488466i) q^{2} +(7.99523 + 0.276277i) q^{4} -16.6517i q^{5} +(-15.0420 + 10.8045i) q^{7} +(-22.5971 - 1.17185i) q^{8} +(-0.813380 + 47.0912i) q^{10} +64.0450i q^{11} -28.6879i q^{13} +(43.0668 - 29.8204i) q^{14} +(63.8473 + 4.41779i) q^{16} +82.9041i q^{17} +17.1236 q^{19} +(4.60049 - 133.134i) q^{20} +(3.12838 - 181.120i) q^{22} -95.0501i q^{23} -152.281 q^{25} +(-1.40131 + 81.1296i) q^{26} +(-123.250 + 82.2285i) q^{28} +197.365 q^{29} +153.515 q^{31} +(-180.345 - 15.6123i) q^{32} +(4.04958 - 234.453i) q^{34} +(179.913 + 250.476i) q^{35} +10.7262 q^{37} +(-48.4255 - 0.836427i) q^{38} +(-19.5134 + 376.280i) q^{40} +41.1342i q^{41} +412.497i q^{43} +(-17.6941 + 512.055i) q^{44} +(-4.64287 + 268.802i) q^{46} +477.704 q^{47} +(109.526 - 325.043i) q^{49} +(430.650 + 7.43838i) q^{50} +(7.92580 - 229.367i) q^{52} +35.2304 q^{53} +1066.46 q^{55} +(352.567 - 226.522i) q^{56} +(-558.149 - 9.64060i) q^{58} +494.608 q^{59} +294.084i q^{61} +(-434.141 - 7.49867i) q^{62} +(509.254 + 52.9608i) q^{64} -477.704 q^{65} +207.870i q^{67} +(-22.9045 + 662.837i) q^{68} +(-496.561 - 717.136i) q^{70} +534.040i q^{71} +582.270i q^{73} +(-30.3338 - 0.523939i) q^{74} +(136.907 + 4.73084i) q^{76} +(-691.973 - 963.368i) q^{77} +311.277i q^{79} +(73.5639 - 1063.17i) q^{80} +(2.00926 - 116.328i) q^{82} -1319.63 q^{83} +1380.50 q^{85} +(20.1490 - 1166.54i) q^{86} +(75.0512 - 1447.23i) q^{88} -616.091i q^{89} +(309.958 + 431.525i) q^{91} +(26.2601 - 759.948i) q^{92} +(-1350.95 - 23.3342i) q^{94} -285.137i q^{95} -104.076i q^{97} +(-325.618 + 913.873i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8}+O(q^{10}) \) 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8	\( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8} - 56 q^{10} - 101 q^{14} + 41 q^{16} + 84 q^{19} + 172 q^{20} - 182 q^{22} - 216 q^{25} + 300 q^{26} - 379 q^{28} - 200 q^{29} + 384 q^{31} + 159 q^{32} + 164 q^{34} + 84 q^{35} - 244 q^{37} + 268 q^{38} + 316 q^{40} - 190 q^{44} + 894 q^{46} + 280 q^{47} - 424 q^{49} + 1771 q^{50} + 796 q^{52} + 16 q^{53} - 212 q^{55} + 1759 q^{56} - 570 q^{58} + 1168 q^{59} - 384 q^{62} + 2705 q^{64} - 280 q^{65} + 1552 q^{68} + 2592 q^{70} - 1622 q^{74} + 788 q^{76} - 968 q^{77} - 3060 q^{80} + 2540 q^{82} - 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} - 1648 q^{91} - 4298 q^{92} - 4256 q^{94} - 3137 q^{98}+O(q^{100}) \) 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8 - 56 * q^10 - 101 * q^14 + 41 * q^16 + 84 * q^19 + 172 * q^20 - 182 * q^22 - 216 * q^25 + 300 * q^26 - 379 * 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 + 1759 * q^56 - 570 * q^58 + 1168 * q^59 - 384 * q^62 + 2705 * q^64 - 280 * q^65 + 1552 * q^68 + 2592 * 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 - 3137 * q^98

Introduction

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