LMFDB - Embedded newform 224.3.o.c.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(79,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("224.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} + 2x^{10} - 12x^{9} + 12x^{8} - 12x^{7} + 148x^{6} - 48x^{5} + 192x^{4} - 768x^{3} + 512x^{2} + 4096 $ x^12 + 2x^10 - 12x^9 + 12x^8 - 12x^7 + 148x^6 - 48x^5 + 192x^4 - 768x^3 + 512*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Root			$-1.61320 + 1.18220i$ of defining polynomial
Character	$\chi$	$=$	224.79
Dual form			224.3.o.c.207.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.717214 - 1.24225i) q^{3} +(2.27256 + 1.31206i) q^{5} +(-5.39122 - 4.46483i) q^{7} +(3.47121 - 6.01231i) q^{9} +O(q^{10})$	\(q+(-0.717214 - 1.24225i) q^{3} +(2.27256 + 1.31206i) q^{5} +(-5.39122 - 4.46483i) q^{7} +(3.47121 - 6.01231i) q^{9} +(-2.75399 - 4.77006i) q^{11} +6.22525i q^{13} -3.76412i q^{15} +(-10.5368 - 18.2502i) q^{17} +(12.6229 - 21.8634i) q^{19} +(-1.67978 + 9.89949i) q^{21} +(12.5463 + 7.24359i) q^{23} +(-9.05697 - 15.6871i) q^{25} -22.8682 q^{27} -29.9514i q^{29} +(-23.5249 + 13.5821i) q^{31} +(-3.95041 + 6.84230i) q^{33} +(-6.39374 - 17.2202i) q^{35} +(-31.5708 - 18.2274i) q^{37} +(7.73332 - 4.46483i) q^{39} +37.4338 q^{41} +28.9008 q^{43} +(15.7771 - 9.10890i) q^{45} +(51.8379 + 29.9287i) q^{47} +(9.13053 + 48.1418i) q^{49} +(-15.1143 + 26.1787i) q^{51} +(-36.5373 + 21.0948i) q^{53} -14.4537i q^{55} -36.2131 q^{57} +(14.6430 + 25.3625i) q^{59} +(92.2850 + 53.2808i) q^{61} +(-45.5580 + 16.9153i) q^{63} +(-8.16793 + 14.1473i) q^{65} +(56.4293 + 97.7384i) q^{67} -20.7808i q^{69} -94.6530i q^{71} +(32.3682 + 56.0634i) q^{73} +(-12.9916 + 22.5021i) q^{75} +(-6.45012 + 38.0126i) q^{77} +(-46.8433 - 27.0450i) q^{79} +(-14.8395 - 25.7027i) q^{81} -91.8824 q^{83} -55.2997i q^{85} +(-37.2071 + 21.4815i) q^{87} +(-36.1385 + 62.5938i) q^{89} +(27.7947 - 33.5617i) q^{91} +(33.7448 + 19.4826i) q^{93} +(57.3724 - 33.1240i) q^{95} +97.4646 q^{97} -38.2388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 8 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 8 * q^9	$ 12 q - 6 q^{3} - 8 q^{9} + 14 q^{11} - 82 q^{17} + 94 q^{19} + 116 q^{25} + 60 q^{27} + 146 q^{33} - 270 q^{35} + 120 q^{41} - 40 q^{43} - 204 q^{49} + 106 q^{51} - 372 q^{57} - 62 q^{59} - 64 q^{65} + 178 q^{67} + 54 q^{73} - 140 q^{75} + 206 q^{81} + 392 q^{83} - 26 q^{89} + 88 q^{91} - 184 q^{97} - 872 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 - 8 * q^9 + 14 * q^11 - 82 * q^17 + 94 * q^19 + 116 * q^25 + 60 * q^27 + 146 * q^33 - 270 * q^35 + 120 * q^41 - 40 * q^43 - 204 * q^49 + 106 * q^51 - 372 * q^57 - 62 * q^59 - 64 * q^65 + 178 * q^67 + 54 * q^73 - 140 * q^75 + 206 * q^81 + 392 * q^83 - 26 * q^89 + 88 * q^91 - 184 * q^97 - 872 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.717214	−	1.24225i	−0.239071	−	0.414084i	0.721377	−	0.692543i	$-0.243510\pi$
$3$	−0.717214	−	1.24225i	−0.239071	−	0.414084i	−0.960448	+	0.278459i	$0.910176\pi$
$4$		0			0
$5$	2.27256	+	1.31206i	0.454513	+	0.262413i	0.709734	−	0.704470i	$-0.248815\pi$
$5$	2.27256	+	1.31206i	0.454513	+	0.262413i	−0.255222	+	0.966883i	$0.582148\pi$
$6$		0			0
$7$	−5.39122	−	4.46483i	−0.770174	−	0.637833i
$7$	−5.39122	−	4.46483i	−0.770174	−	0.637833i
$8$		0			0
$9$	3.47121	−	6.01231i	0.385690	−	0.668034i
$10$		0			0
$11$	−2.75399	−	4.77006i	−0.250363	−	0.433642i	0.713263	−	0.700897i	$-0.247217\pi$
$11$	−2.75399	−	4.77006i	−0.250363	−	0.433642i	−0.963626	+	0.267255i	$0.913883\pi$
$12$		0			0
$13$			6.22525i			0.478865i	0.970913	+	0.239433i	$0.0769614\pi$
$13$			6.22525i			0.478865i	−0.970913	+	0.239433i	$0.923039\pi$
$14$		0			0
$15$		−	3.76412i		−	0.250942i
$16$		0			0
$17$	−10.5368	−	18.2502i	−0.619811	−	1.07354i	−0.989520	−	0.144396i	$-0.953876\pi$
$17$	−10.5368	−	18.2502i	−0.619811	−	1.07354i	0.369709	−	0.929147i	$-0.379457\pi$
$18$		0			0
$19$	12.6229	−	21.8634i	0.664361	−	1.15071i	−0.315098	−	0.949059i	$-0.602037\pi$
$19$	12.6229	−	21.8634i	0.664361	−	1.15071i	0.979458	−	0.201647i	$-0.0646294\pi$
$20$		0			0
$21$	−1.67978	+	9.89949i	−0.0799897	+	0.471404i
$22$		0			0
$23$	12.5463	+	7.24359i	0.545490	+	0.314939i	0.747301	−	0.664486i	$-0.231349\pi$
$23$	12.5463	+	7.24359i	0.545490	+	0.314939i	−0.201811	+	0.979424i	$0.564683\pi$
$24$		0			0
$25$	−9.05697	−	15.6871i	−0.362279	−	0.627485i
$26$		0			0
$27$	−22.8682			−0.846972
$28$		0			0
$29$		−	29.9514i		−	1.03281i	−0.856346	−	0.516403i	$-0.827271\pi$
$29$		−	29.9514i		−	1.03281i	0.856346	−	0.516403i	$-0.172729\pi$
$30$		0			0
$31$	−23.5249	+	13.5821i	−0.758868	+	0.438133i	−0.828889	−	0.559413i	$-0.811027\pi$
$31$	−23.5249	+	13.5821i	−0.758868	+	0.438133i	0.0700212	+	0.997546i	$0.477693\pi$
$32$		0			0
$33$	−3.95041	+	6.84230i	−0.119709	+	0.207343i
$34$		0			0
$35$	−6.39374	−	17.2202i	−0.182678	−	0.492007i
$36$		0			0
$37$	−31.5708	−	18.2274i	−0.853264	−	0.492632i	0.00848686	−	0.999964i	$-0.497299\pi$
$37$	−31.5708	−	18.2274i	−0.853264	−	0.492632i	−0.861751	+	0.507332i	$0.830632\pi$
$38$		0			0
$39$	7.73332	−	4.46483i	0.198290	−	0.114483i
$40$		0			0
$41$	37.4338			0.913020			0.456510	−	0.889718i	$-0.349099\pi$
$41$	37.4338			0.913020			0.456510	+	0.889718i	$0.349099\pi$
$42$		0			0
$43$	28.9008			0.672112			0.336056	−	0.941842i	$-0.390907\pi$
$43$	28.9008			0.672112			0.336056	+	0.941842i	$0.390907\pi$
$44$		0			0
$45$	15.7771	−	9.10890i	0.350602	−	0.202420i
$46$		0			0
$47$	51.8379	+	29.9287i	1.10293	+	0.636780i	0.936990	−	0.349355i	$-0.113599\pi$
$47$	51.8379	+	29.9287i	1.10293	+	0.636780i	0.165945	+	0.986135i	$0.446933\pi$
$48$		0			0
$49$	9.13053	+	48.1418i	0.186337	+	0.982486i
$50$		0			0
$51$	−15.1143	+	26.1787i	−0.296358	+	0.513307i
$52$		0			0
$53$	−36.5373	+	21.0948i	−0.689383	+	0.398015i	−0.803381	−	0.595466i	$-0.796968\pi$
$53$	−36.5373	+	21.0948i	−0.689383	+	0.398015i	0.113998	+	0.993481i	$0.463634\pi$
$54$		0			0
$55$		−	14.4537i		−	0.262794i
$56$		0			0
$57$	−36.2131			−0.635318
$58$		0			0
$59$	14.6430	+	25.3625i	0.248187	+	0.429873i	0.963023	−	0.269420i	$-0.0868319\pi$
$59$	14.6430	+	25.3625i	0.248187	+	0.429873i	−0.714836	+	0.699292i	$0.753499\pi$
$60$		0			0
$61$	92.2850	+	53.2808i	1.51287	+	0.873455i	0.999887	+	0.0150554i	$0.00479246\pi$
$61$	92.2850	+	53.2808i	1.51287	+	0.873455i	0.512982	+	0.858400i	$0.328541\pi$
$62$		0			0
$63$	−45.5580	+	16.9153i	−0.723143	+	0.268497i
$64$		0			0
$65$	−8.16793	+	14.1473i	−0.125660	+	0.217650i
$66$		0			0
$67$	56.4293	+	97.7384i	0.842228	+	1.45878i	0.888007	+	0.459831i	$0.152090\pi$
$67$	56.4293	+	97.7384i	0.842228	+	1.45878i	−0.0457783	+	0.998952i	$0.514577\pi$
$68$		0			0
$69$		−	20.7808i		−	0.301171i
$70$		0			0
$71$		−	94.6530i		−	1.33314i	−0.745442	−	0.666571i	$-0.767761\pi$
$71$		−	94.6530i		−	1.33314i	0.745442	−	0.666571i	$-0.232239\pi$
$72$		0			0
$73$	32.3682	+	56.0634i	0.443401	+	0.767992i	0.997939	−	0.0641656i	$-0.0204386\pi$
$73$	32.3682	+	56.0634i	0.443401	+	0.767992i	−0.554539	+	0.832158i	$0.687105\pi$
$74$		0			0
$75$	−12.9916	+	22.5021i	−0.173221	+	0.300028i
$76$		0			0
$77$	−6.45012	+	38.0126i	−0.0837678	+	0.493670i
$78$		0			0
$79$	−46.8433	−	27.0450i	−0.592953	−	0.342342i	0.173311	−	0.984867i	$-0.444553\pi$
$79$	−46.8433	−	27.0450i	−0.592953	−	0.342342i	−0.766264	+	0.642525i	$0.777887\pi$
$80$		0			0
$81$	−14.8395	−	25.7027i	−0.183203	−	0.317317i
$82$		0			0
$83$	−91.8824			−1.10702			−0.553508	−	0.832844i	$-0.686711\pi$
$83$	−91.8824			−1.10702			−0.553508	+	0.832844i	$0.686711\pi$
$84$		0			0
$85$		−	55.2997i		−	0.650585i
$86$		0			0
$87$	−37.2071	+	21.4815i	−0.427668	+	0.246914i
$88$		0			0
$89$	−36.1385	+	62.5938i	−0.406051	+	0.703301i	−0.994443	−	0.105275i	$-0.966428\pi$
$89$	−36.1385	+	62.5938i	−0.406051	+	0.703301i	0.588392	+	0.808576i	$0.299761\pi$
$90$		0			0
$91$	27.7947	−	33.5617i	0.305436	−	0.368810i
$92$		0			0
$93$	33.7448	+	19.4826i	0.362847	+	0.209490i
$94$		0			0
$95$	57.3724	−	33.1240i	0.603920	−	0.348674i
$96$		0			0
$97$	97.4646			1.00479			0.502395	−	0.864638i	$-0.332452\pi$
$97$	97.4646			1.00479			0.502395	+	0.864638i	$0.332452\pi$
$98$		0			0
$99$	−38.2388			−0.386250
$100$		0			0
$101$	−167.533	+	96.7250i	−1.65874	+	0.957673i	−0.685441	+	0.728128i	$0.740391\pi$
$101$	−167.533	+	96.7250i	−1.65874	+	0.957673i	−0.973298	+	0.229546i	$0.926276\pi$
$102$		0			0
$103$	79.1012	+	45.6691i	0.767973	+	0.443389i	0.832151	−	0.554549i	$-0.187109\pi$
$103$	79.1012	+	45.6691i	0.767973	+	0.443389i	−0.0641781	+	0.997938i	$0.520443\pi$
$104$		0			0
$105$	−16.8062	+	20.2932i	−0.160059	+	0.193269i
$106$		0			0
$107$	−1.72143	+	2.98160i	−0.0160881	+	0.0278654i	−0.873957	−	0.486003i	$-0.838455\pi$
$107$	−1.72143	+	2.98160i	−0.0160881	+	0.0278654i	0.857869	+	0.513868i	$0.171788\pi$
$108$		0			0
$109$	167.840	−	96.9024i	1.53981	−	0.889012i	0.540966	−	0.841045i	$-0.318059\pi$
$109$	167.840	−	96.9024i	1.53981	−	0.889012i	0.998849	−	0.0479679i	$-0.0152745\pi$
$110$		0			0
$111$			52.2917i			0.471097i
$112$		0			0
$113$	−41.5646			−0.367828			−0.183914	−	0.982942i	$-0.558877\pi$
$113$	−41.5646			−0.367828			−0.183914	+	0.982942i	$0.558877\pi$
$114$		0			0
$115$	19.0081	+	32.9230i	0.165288	+	0.286287i
$116$		0			0
$117$	37.4281	+	21.6091i	0.319898	+	0.184693i
$118$		0			0
$119$	−24.6782	+	145.436i	−0.207379	+	1.22215i
$120$		0			0
$121$	45.3310	−	78.5156i	0.374637	−	0.648890i
$122$		0			0
$123$	−26.8481	−	46.5022i	−0.218277	−	0.378067i
$124$		0			0
$125$		−	113.137i		−	0.905093i
$126$		0			0
$127$		−	70.9794i		−	0.558893i	−0.960161	−	0.279446i	$-0.909849\pi$
$127$		−	70.9794i		−	0.558893i	0.960161	−	0.279446i	$-0.0901509\pi$
$128$		0			0
$129$	−20.7281	−	35.9021i	−0.160683	−	0.278311i
$130$		0			0
$131$	84.6252	−	146.575i	0.645994	−	1.11889i	−0.338077	−	0.941119i	$-0.609776\pi$
$131$	84.6252	−	146.575i	0.645994	−	1.11889i	0.984071	−	0.177776i	$-0.0568903\pi$
$132$		0			0
$133$	−165.669	+	61.5116i	−1.24563	+	0.462493i
$134$		0			0
$135$	−51.9695	−	30.0046i	−0.384959	−	0.222256i
$136$		0			0
$137$	−48.4716	−	83.9554i	−0.353808	−	0.612813i	0.633106	−	0.774066i	$-0.281780\pi$
$137$	−48.4716	−	83.9554i	−0.353808	−	0.612813i	−0.986913	+	0.161253i	$0.948447\pi$
$138$		0			0
$139$	97.6033			0.702182			0.351091	−	0.936341i	$-0.385811\pi$
$139$	97.6033			0.702182			0.351091	+	0.936341i	$0.385811\pi$
$140$		0			0
$141$		−	85.8610i		−	0.608943i
$142$		0			0
$143$	29.6948	−	17.1443i	0.207656	−	0.119890i
$144$		0			0
$145$	39.2981	−	68.0663i	0.271021	−	0.469423i
$146$		0			0
$147$	53.2557	−	45.8704i	0.362283	−	0.312043i
$148$		0			0
$149$	−118.934	−	68.6665i	−0.798214	−	0.460849i	0.0446321	−	0.999003i	$-0.485788\pi$
$149$	−118.934	−	68.6665i	−0.798214	−	0.460849i	−0.842846	+	0.538154i	$0.819122\pi$
$150$		0			0
$151$	41.5059	−	23.9635i	0.274874	−	0.158698i	−0.356227	−	0.934400i	$-0.615937\pi$
$151$	41.5059	−	23.9635i	0.274874	−	0.158698i	0.631100	+	0.775701i	$0.282604\pi$
$152$		0			0
$153$	−146.301			−0.956219
$154$		0			0
$155$	−71.2824			−0.459887
$156$		0			0
$157$	−47.5524	+	27.4544i	−0.302882	+	0.174869i	−0.643737	−	0.765247i	$-0.722617\pi$
$157$	−47.5524	+	27.4544i	−0.302882	+	0.174869i	0.340855	+	0.940116i	$0.389283\pi$
$158$		0			0
$159$	52.4101	+	30.2590i	0.329623	+	0.190308i
$160$		0			0
$161$	−35.2983	−	95.0688i	−0.219244	−	0.590489i
$162$		0			0
$163$	−4.07026	+	7.04990i	−0.0249709	+	0.0432509i	−0.878241	−	0.478219i	$-0.841283\pi$
$163$	−4.07026	+	7.04990i	−0.0249709	+	0.0432509i	0.853270	+	0.521470i	$0.174616\pi$
$164$		0			0
$165$	−17.9551	+	10.3664i	−0.108819	+	0.0628265i
$166$		0			0
$167$		−	12.1877i		−	0.0729802i	−0.999334	−	0.0364901i	$-0.988382\pi$
$167$		−	12.1877i		−	0.0729802i	0.999334	−	0.0364901i	$-0.0116177\pi$
$168$		0			0
$169$	130.246			0.770688
$170$		0			0
$171$	−87.6331	−	151.785i	−0.512474	−	0.887631i
$172$		0			0
$173$	229.411	+	132.450i	1.32607	+	0.765609i	0.984690	−	0.174314i	$-0.0557709\pi$
$173$	229.411	+	132.450i	1.32607	+	0.765609i	0.341384	+	0.939924i	$0.389104\pi$
$174$		0			0
$175$	−21.2123	+	125.011i	−0.121213	+	0.714347i
$176$		0			0
$177$	21.0044	−	36.3807i	0.118669	−	0.205540i
$178$		0			0
$179$	−118.385	−	205.049i	−0.661369	−	1.14552i	−0.980256	−	0.197731i	$-0.936643\pi$
$179$	−118.385	−	205.049i	−0.661369	−	1.14552i	0.318888	−	0.947793i	$-0.396691\pi$
$180$		0			0
$181$			19.7435i			0.109080i	0.998512	+	0.0545402i	$0.0173693\pi$
$181$			19.7435i			0.109080i	−0.998512	+	0.0545402i	$0.982631\pi$
$182$		0			0
$183$		−	152.855i		−	0.835272i
$184$		0			0
$185$	−47.8310	−	82.8458i	−0.258546	−	0.447815i
$186$		0			0
$187$	−58.0365	+	100.522i	−0.310355	+	0.537551i
$188$		0			0
$189$	123.288	+	102.103i	0.652316	+	0.540227i
$190$		0			0
$191$	−139.204	−	80.3697i	−0.728819	−	0.420784i	0.0891711	−	0.996016i	$-0.471578\pi$
$191$	−139.204	−	80.3697i	−0.728819	−	0.420784i	−0.817990	+	0.575233i	$0.804912\pi$
$192$		0			0
$193$	84.9196	+	147.085i	0.439998	+	0.762099i	0.997689	−	0.0679499i	$-0.0216458\pi$
$193$	84.9196	+	147.085i	0.439998	+	0.762099i	−0.557691	+	0.830049i	$0.688312\pi$
$194$		0			0
$195$	23.4326			0.120167
$196$		0			0
$197$		−	47.2927i		−	0.240064i	−0.992770	−	0.120032i	$-0.961700\pi$
$197$		−	47.2927i		−	0.240064i	0.992770	−	0.120032i	$-0.0382998\pi$
$198$		0			0
$199$	−243.806	+	140.761i	−1.22516	+	0.707344i	−0.966013	−	0.258495i	$-0.916773\pi$
$199$	−243.806	+	140.761i	−1.22516	+	0.707344i	−0.259143	+	0.965839i	$0.583440\pi$
$200$		0			0
$201$	80.9438	−	140.199i	0.402705	−	0.697506i
$202$		0			0
$203$	−133.728	+	161.474i	−0.658758	+	0.795440i
$204$		0			0
$205$	85.0707	+	49.1156i	0.414979	+	0.239588i
$206$		0			0
$207$	87.1014	−	50.2880i	0.420780	−	0.242937i
$208$		0			0
$209$	−139.053			−0.665326
$210$		0			0
$211$	105.459			0.499804			0.249902	−	0.968271i	$-0.419602\pi$
$211$	105.459			0.499804			0.249902	+	0.968271i	$0.419602\pi$
$212$		0			0
$213$	−117.583	+	67.8865i	−0.552032	+	0.318716i
$214$		0			0
$215$	65.6789	+	37.9197i	0.305483	+	0.176371i
$216$		0			0
$217$	187.470	+	31.8106i	0.863916	+	0.146593i
$218$		0			0
$219$	46.4299	−	80.4190i	0.212009	−	0.367210i
$220$		0			0
$221$	113.612	−	65.5941i	0.514083	−	0.296806i
$222$		0			0
$223$		−	386.423i		−	1.73284i	−0.499316	−	0.866420i	$-0.666415\pi$
$223$		−	386.423i		−	1.73284i	0.499316	−	0.866420i	$-0.333585\pi$
$224$		0			0
$225$	−125.755			−0.558909
$226$		0			0
$227$	71.6708	+	124.137i	0.315730	+	0.546861i	0.979592	−	0.200994i	$-0.0644172\pi$
$227$	71.6708	+	124.137i	0.315730	+	0.546861i	−0.663862	+	0.747855i	$0.731084\pi$
$228$		0			0
$229$	−154.383	−	89.1332i	−0.674163	−	0.389228i	0.123489	−	0.992346i	$-0.460592\pi$
$229$	−154.383	−	89.1332i	−0.674163	−	0.389228i	−0.797652	+	0.603118i	$0.793925\pi$
$230$		0			0
$231$	51.8473	−	19.2505i	0.224447	−	0.0833354i
$232$		0			0
$233$	−172.708	+	299.139i	−0.741235	+	1.28386i	0.210699	+	0.977551i	$0.432426\pi$
$233$	−172.708	+	299.139i	−0.741235	+	1.28386i	−0.951933	+	0.306305i	$0.900907\pi$
$234$		0			0
$235$	78.5366	+	136.029i	0.334199	+	0.578849i
$236$		0			0
$237$			77.5882i			0.327376i
$238$		0			0
$239$			140.165i			0.586464i	0.956041	+	0.293232i	$0.0947308\pi$
$239$			140.165i			0.586464i	−0.956041	+	0.293232i	$0.905269\pi$
$240$		0			0
$241$	109.775	+	190.135i	0.455496	+	0.788943i	0.998717	−	0.0506475i	$-0.0161285\pi$
$241$	109.775	+	190.135i	0.455496	+	0.788943i	−0.543220	+	0.839590i	$0.682795\pi$
$242$		0			0
$243$	−124.193	+	215.109i	−0.511083	+	0.885222i
$244$		0			0
$245$	−42.4154	+	121.385i	−0.173124	+	0.495449i
$246$		0			0
$247$	136.105	+	78.5803i	0.551033	+	0.318139i
$248$		0			0
$249$	65.8993	+	114.141i	0.264656	+	0.458398i
$250$		0			0
$251$	207.856			0.828113			0.414057	−	0.910251i	$-0.364112\pi$
$251$	207.856			0.828113			0.414057	+	0.910251i	$0.364112\pi$
$252$		0			0
$253$		−	79.7953i		−	0.315396i
$254$		0			0
$255$	−68.6962	+	39.6617i	−0.269397	+	0.155536i
$256$		0			0
$257$	14.7596	−	25.5643i	0.0574302	−	0.0994720i	−0.835881	−	0.548911i	$-0.815043\pi$
$257$	14.7596	−	25.5643i	0.0574302	−	0.0994720i	0.893311	+	0.449439i	$0.148376\pi$
$258$		0			0
$259$	88.8227	+	239.226i	0.342945	+	0.923653i
$260$		0			0
$261$	−180.077	−	103.967i	−0.689950	−	0.398343i
$262$		0			0
$263$	2.50134	−	1.44415i	0.00951079	−	0.00549106i	−0.495237	−	0.868758i	$-0.664919\pi$
$263$	2.50134	−	1.44415i	0.00951079	−	0.00549106i	0.504748	+	0.863267i	$0.331585\pi$
$264$		0			0
$265$	−110.711			−0.417778
$266$		0			0
$267$	103.676			0.388300
$268$		0			0
$269$	309.676	−	178.791i	1.15121	−	0.664652i	0.202029	−	0.979380i	$-0.435247\pi$
$269$	309.676	−	178.791i	1.15121	−	0.664652i	0.949182	+	0.314728i	$0.101913\pi$
$270$		0			0
$271$	294.743	+	170.170i	1.08761	+	0.627934i	0.932940	−	0.360031i	$-0.117234\pi$
$271$	294.743	+	170.170i	1.08761	+	0.627934i	0.154674	+	0.987966i	$0.450567\pi$
$272$		0			0
$273$	−61.6268	−	10.4571i	−0.225739	−	0.0383043i
$274$		0			0
$275$	−49.8857	+	86.4046i	−0.181403	+	0.314198i
$276$		0			0
$277$	−11.2603	+	6.50111i	−0.0406507	+	0.0234697i	−0.520188	−	0.854052i	$-0.674138\pi$
$277$	−11.2603	+	6.50111i	−0.0406507	+	0.0234697i	0.479537	+	0.877522i	$0.340805\pi$
$278$		0			0
$279$			188.585i			0.675933i
$280$		0			0
$281$	232.300			0.826689			0.413344	−	0.910575i	$-0.364361\pi$
$281$	232.300			0.826689			0.413344	+	0.910575i	$0.364361\pi$
$282$		0			0
$283$	6.07204	+	10.5171i	0.0214560	+	0.0371628i	0.876554	−	0.481303i	$-0.159836\pi$
$283$	6.07204	+	10.5171i	0.0214560	+	0.0371628i	−0.855098	+	0.518466i	$0.826503\pi$
$284$		0			0
$285$	−82.2966	−	47.5140i	−0.288760	−	0.166716i
$286$		0			0
$287$	−201.814	−	167.136i	−0.703185	−	0.582354i
$288$		0			0
$289$	−77.5475	+	134.316i	−0.268330	+	0.464762i
$290$		0			0
$291$	−69.9029	−	121.075i	−0.240216	−	0.416067i
$292$		0			0
$293$			84.6048i			0.288753i	0.989523	+	0.144377i	$0.0461177\pi$
$293$			84.6048i			0.288753i	−0.989523	+	0.144377i	$0.953882\pi$
$294$		0			0
$295$			76.8505i			0.260510i
$296$		0			0
$297$	62.9790	+	109.083i	0.212051	+	0.367282i
$298$		0			0
$299$	−45.0931	+	78.1036i	−0.150813	+	0.261216i
$300$		0			0
$301$	−155.811	−	129.037i	−0.517643	−	0.428695i
$302$		0			0
$303$	240.313	+	138.745i	0.793114	+	0.457904i
$304$		0			0
$305$	139.816	+	242.168i	0.458412	+	0.793992i
$306$		0			0
$307$	97.3710			0.317169			0.158585	−	0.987345i	$-0.449307\pi$
$307$	97.3710			0.317169			0.158585	+	0.987345i	$0.449307\pi$
$308$		0			0
$309$		−	131.018i		−	0.424007i
$310$		0			0
$311$	86.7666	−	50.0947i	0.278992	−	0.161076i	−0.353975	−	0.935255i	$-0.615170\pi$
$311$	86.7666	−	50.0947i	0.278992	−	0.161076i	0.632967	+	0.774179i	$0.281837\pi$
$312$		0			0
$313$	−70.9257	+	122.847i	−0.226600	+	0.392482i	−0.956798	−	0.290753i	$-0.906094\pi$
$313$	−70.9257	+	122.847i	−0.226600	+	0.392482i	0.730199	+	0.683235i	$0.239428\pi$
$314$		0			0
$315$	−125.727	−	21.3339i	−0.399135	−	0.0677267i
$316$		0			0
$317$	−24.9036	−	14.3781i	−0.0785604	−	0.0453569i	0.460205	−	0.887813i	$-0.347776\pi$
$317$	−24.9036	−	14.3781i	−0.0785604	−	0.0453569i	−0.538766	+	0.842456i	$0.681109\pi$
$318$		0			0
$319$	−142.870	+	82.4859i	−0.447867	+	0.258576i
$320$		0			0
$321$	4.93853			0.0153848
$322$		0			0
$323$	−532.017			−1.64711
$324$		0			0
$325$	97.6563	−	56.3819i	0.300481	−	0.173483i
$326$		0			0
$327$	−240.754	−	138.999i	−0.736251	−	0.425075i
$328$		0			0
$329$	−145.843	−	392.800i	−0.443293	−	1.19392i
$330$		0			0
$331$	140.896	−	244.039i	0.425668	−	0.737278i	−0.570815	−	0.821079i	$-0.693373\pi$
$331$	140.896	−	244.039i	0.425668	−	0.737278i	0.996483	+	0.0838009i	$0.0267060\pi$
$332$		0			0
$333$	−219.177	+	126.542i	−0.658190	+	0.380006i
$334$		0			0
$335$			296.156i			0.884046i
$336$		0			0
$337$	−22.7495			−0.0675058			−0.0337529	−	0.999430i	$-0.510746\pi$
$337$	−22.7495			−0.0675058			−0.0337529	+	0.999430i	$0.510746\pi$
$338$		0			0
$339$	29.8107	+	51.6337i	0.0879372	+	0.152312i
$340$		0			0
$341$	129.575	+	74.8101i	0.379985	+	0.219385i
$342$		0			0
$343$	165.720	−	300.309i	0.483150	−	0.875538i
$344$		0			0
$345$	27.2658	−	47.2257i	0.0790312	−	0.136886i
$346$		0			0
$347$	−40.0334	−	69.3399i	−0.115370	−	0.199827i	0.802558	−	0.596575i	$-0.203472\pi$
$347$	−40.0334	−	69.3399i	−0.115370	−	0.199827i	−0.917928	+	0.396748i	$0.870139\pi$
$348$		0			0
$349$			222.628i			0.637903i	0.947771	+	0.318951i	$0.103331\pi$
$349$			222.628i			0.637903i	−0.947771	+	0.318951i	$0.896669\pi$
$350$		0			0
$351$		−	142.360i		−	0.405585i
$352$		0			0
$353$	−162.239	−	281.006i	−0.459601	−	0.796052i	0.539339	−	0.842089i	$-0.318674\pi$
$353$	−162.239	−	281.006i	−0.459601	−	0.796052i	−0.998940	+	0.0460367i	$0.985341\pi$
$354$		0			0
$355$	124.191	−	215.105i	0.349834	−	0.605929i
$356$		0			0
$357$	198.368	−	73.6523i	0.555651	−	0.206309i
$358$		0			0
$359$	−114.236	−	65.9541i	−0.318206	−	0.183716i	0.332387	−	0.943143i	$-0.392146\pi$
$359$	−114.236	−	65.9541i	−0.318206	−	0.183716i	−0.650593	+	0.759427i	$0.725479\pi$
$360$		0			0
$361$	−138.173	−	239.322i	−0.382750	−	0.662942i
$362$		0			0
$363$	−130.048			−0.358259
$364$		0			0
$365$			169.877i			0.465416i
$366$		0			0
$367$	165.468	−	95.5332i	0.450868	−	0.260309i	−0.257329	−	0.966324i	$-0.582842\pi$
$367$	165.468	−	95.5332i	0.450868	−	0.260309i	0.708197	+	0.706015i	$0.249509\pi$
$368$		0			0
$369$	129.941	−	225.064i	0.352143	−	0.609929i
$370$		0			0
$371$	291.165	+	49.4061i	0.784813	+	0.133170i
$372$		0			0
$373$	385.278	+	222.440i	1.03292	+	0.596354i	0.917819	−	0.397000i	$-0.129949\pi$
$373$	385.278	+	222.440i	1.03292	+	0.596354i	0.115098	+	0.993354i	$0.463282\pi$
$374$		0			0
$375$	−140.544	+	81.1431i	−0.374784	+	0.216382i
$376$		0			0
$377$	186.455			0.494574
$378$		0			0
$379$	253.564			0.669034			0.334517	−	0.942390i	$-0.391427\pi$
$379$	253.564			0.669034			0.334517	+	0.942390i	$0.391427\pi$
$380$		0			0
$381$	−88.1742	+	50.9074i	−0.231428	+	0.133615i
$382$		0			0
$383$	−547.948	−	316.358i	−1.43067	−	0.826000i	−0.433501	−	0.901153i	$-0.642722\pi$
$383$	−547.948	−	316.358i	−1.43067	−	0.826000i	−0.997172	+	0.0751535i	$0.976055\pi$
$384$		0			0
$385$	−64.5332	+	77.9230i	−0.167619	+	0.202397i
$386$		0			0
$387$	100.321	−	173.761i	0.259227	−	0.448994i
$388$		0			0
$389$	−116.434	+	67.2230i	−0.299315	+	0.172810i	−0.642135	−	0.766591i	$-0.721951\pi$
$389$	−116.434	+	67.2230i	−0.299315	+	0.172810i	0.342820	+	0.939401i	$0.388618\pi$
$390$		0			0
$391$		−	305.297i		−	0.780810i
$392$		0			0
$393$	−242.778			−0.617755
$394$		0			0
$395$	−70.9696	−	122.923i	−0.179670	−	0.311197i
$396$		0			0
$397$	−270.162	−	155.978i	−0.680509	−	0.392892i	0.119538	−	0.992830i	$-0.461859\pi$
$397$	−270.162	−	155.978i	−0.680509	−	0.392892i	−0.800047	+	0.599938i	$0.795192\pi$
$398$		0			0
$399$	195.233	+	161.686i	0.489306	+	0.405227i
$400$		0			0
$401$	319.775	−	553.866i	0.797444	−	1.38121i	−0.123832	−	0.992303i	$-0.539518\pi$
$401$	319.775	−	553.866i	0.797444	−	1.38121i	0.921276	−	0.388910i	$-0.127148\pi$
$402$		0			0
$403$	−84.5520	−	146.448i	−0.209806	−	0.363395i
$404$		0			0
$405$		−	77.8813i		−	0.192299i
$406$		0			0
$407$			200.793i			0.493348i
$408$		0			0
$409$	−51.6414	−	89.4456i	−0.126263	−	0.218693i	0.795963	−	0.605345i	$-0.206965\pi$
$409$	−51.6414	−	89.4456i	−0.126263	−	0.218693i	−0.922226	+	0.386652i	$0.873632\pi$
$410$		0			0
$411$	−69.5291	+	120.428i	−0.169170	+	0.293012i
$412$		0			0
$413$	34.2954	−	202.114i	0.0830397	−	0.489379i
$414$		0			0
$415$	−208.808	−	120.556i	−0.503153	−	0.290496i
$416$		0			0
$417$	−70.0024	−	121.248i	−0.167871	−	0.290762i
$418$		0			0
$419$	55.0511			0.131387			0.0656934	−	0.997840i	$-0.479074\pi$
$419$	55.0511			0.131387			0.0656934	+	0.997840i	$0.479074\pi$
$420$		0			0
$421$			513.922i			1.22072i	0.792125	+	0.610358i	$0.208975\pi$
$421$			513.922i			1.22072i	−0.792125	+	0.610358i	$0.791025\pi$
$422$		0			0
$423$	359.881	−	207.777i	0.850782	−	0.491199i
$424$		0			0
$425$	−190.863	+	330.584i	−0.449089	+	0.777844i
$426$		0			0
$427$	−259.639	−	699.285i	−0.608054	−	1.63767i
$428$		0			0
$429$	−42.5950	−	24.5923i	−0.0992891	−	0.0573246i
$430$		0			0
$431$	−277.403	+	160.159i	−0.643627	+	0.371598i	−0.786011	−	0.618213i	$-0.787857\pi$
$431$	−277.403	+	160.159i	−0.643627	+	0.371598i	0.142383	+	0.989812i	$0.454524\pi$
$432$		0			0
$433$	−37.1029			−0.0856880			−0.0428440	−	0.999082i	$-0.513642\pi$
$433$	−37.1029			−0.0856880			−0.0428440	+	0.999082i	$0.513642\pi$
$434$		0			0
$435$	−112.741			−0.259174
$436$		0			0
$437$	316.739	−	182.870i	0.724804	−	0.418466i
$438$		0			0
$439$	88.7426	+	51.2356i	0.202147	+	0.116710i	0.597657	−	0.801752i	$-0.296099\pi$
$439$	88.7426	+	51.2356i	0.202147	+	0.116710i	−0.395509	+	0.918462i	$0.629432\pi$
$440$		0			0
$441$	321.137	+	112.215i	0.728203	+	0.254455i
$442$		0			0
$443$	−173.497	+	300.505i	−0.391641	+	0.678342i	−0.992666	−	0.120888i	$-0.961426\pi$
$443$	−173.497	+	300.505i	−0.391641	+	0.678342i	0.601025	+	0.799230i	$0.294759\pi$
$444$		0			0
$445$	−164.254	+	94.8322i	−0.369110	+	0.213106i
$446$		0			0
$447$			196.994i			0.440703i
$448$		0			0
$449$	249.728			0.556187			0.278094	−	0.960554i	$-0.410297\pi$
$449$	249.728			0.556187			0.278094	+	0.960554i	$0.410297\pi$
$450$		0			0
$451$	−103.093	−	178.562i	−0.228587	−	0.395924i
$452$		0			0
$453$	−59.5372	−	34.3738i	−0.131429	−	0.0758805i
$454$		0			0
$455$	107.200	−	39.8026i	0.235605	−	0.0874782i
$456$		0			0
$457$	135.736	−	235.101i	0.297015	−	0.514445i	−0.678437	−	0.734659i	$-0.737342\pi$
$457$	135.736	−	235.101i	0.297015	−	0.514445i	0.975452	+	0.220214i	$0.0706756\pi$
$458$		0			0
$459$	240.958	+	417.351i	0.524962	+	0.909261i
$460$		0			0
$461$		−	276.405i		−	0.599577i	−0.954006	−	0.299788i	$-0.903084\pi$
$461$		−	276.405i		−	0.599577i	0.954006	−	0.299788i	$-0.0969161\pi$
$462$		0			0
$463$			796.625i			1.72057i	0.509811	+	0.860286i	$0.329715\pi$
$463$			796.625i			1.72057i	−0.509811	+	0.860286i	$0.670285\pi$
$464$		0			0
$465$	51.1247	+	88.5507i	0.109946	+	0.190432i
$466$		0			0
$467$	378.294	−	655.224i	0.810051	−	1.40305i	−0.102776	−	0.994704i	$-0.532773\pi$
$467$	378.294	−	655.224i	0.810051	−	1.40305i	0.912828	−	0.408345i	$-0.133894\pi$
$468$		0			0
$469$	132.163	−	778.877i	0.281797	−	1.66072i
$470$		0			0
$471$	68.2105	+	39.3814i	0.144821	+	0.0836123i
$472$		0			0
$473$	−79.5927	−	137.859i	−0.168272	−	0.291456i
$474$		0			0
$475$	−457.299			−0.962735
$476$		0			0
$477$			292.898i			0.614042i
$478$		0			0
$479$	446.732	−	257.921i	0.932635	−	0.538457i	0.0449907	−	0.998987i	$-0.485674\pi$
$479$	446.732	−	257.921i	0.932635	−	0.538457i	0.887644	+	0.460531i	$0.152341\pi$
$480$		0			0
$481$	113.470	−	196.536i	0.235904	−	0.408598i
$482$		0			0
$483$	−92.7829	+	112.034i	−0.192097	+	0.231954i
$484$		0			0
$485$	221.494	+	127.880i	0.456689	+	0.263670i
$486$		0			0
$487$	−115.410	+	66.6319i	−0.236981	+	0.136821i	−0.613788	−	0.789471i	$-0.710355\pi$
$487$	−115.410	+	66.6319i	−0.236981	+	0.136821i	0.376807	+	0.926292i	$0.377022\pi$
$488$		0			0
$489$	11.6770			0.0238793
$490$		0			0
$491$	595.369			1.21256			0.606282	−	0.795249i	$-0.292660\pi$
$491$	595.369			1.21256			0.606282	+	0.795249i	$0.292660\pi$
$492$		0			0
$493$	−546.619	+	315.591i	−1.10876	+	0.640144i
$494$		0			0
$495$	−86.9000	−	50.1717i	−0.175556	−	0.101357i
$496$		0			0
$497$	−422.610	+	510.295i	−0.850322	+	1.02675i
$498$		0			0
$499$	−191.203	+	331.173i	−0.383172	+	0.663673i	−0.991514	−	0.130002i	$-0.958502\pi$
$499$	−191.203	+	331.173i	−0.383172	+	0.663673i	0.608342	+	0.793675i	$0.291835\pi$
$500$		0			0
$501$	−15.1402	+	8.74119i	−0.0302199	+	0.0174475i
$502$		0			0
$503$			513.765i			1.02140i	0.859758	+	0.510701i	$0.170614\pi$
$503$			513.765i			1.02140i	−0.859758	+	0.510701i	$0.829386\pi$
$504$		0			0
$505$	−507.638			−1.00522
$506$		0			0
$507$	−93.4145	−	161.799i	−0.184249	−	0.319129i
$508$		0			0
$509$	−732.796	−	423.080i	−1.43968	−	0.831199i	−0.441851	−	0.897088i	$-0.645678\pi$
$509$	−732.796	−	423.080i	−1.43968	−	0.831199i	−0.997827	+	0.0658897i	$0.979011\pi$
$510$		0			0
$511$	75.8095	−	446.769i	0.148355	−	0.874304i
$512$		0			0
$513$	−288.662	+	499.978i	−0.562695	+	0.974616i
$514$		0			0
$515$	119.842	+	207.572i	0.232702	+	0.403052i
$516$		0			0
$517$		−	329.693i		−	0.637705i
$518$		0			0
$519$		−	379.981i		−	0.732141i
$520$		0			0
$521$	141.818	+	245.636i	0.272204	+	0.471471i	0.969426	−	0.245385i	$-0.0789142\pi$
$521$	141.818	+	245.636i	0.272204	+	0.471471i	−0.697222	+	0.716855i	$0.745581\pi$
$522$		0			0
$523$	−448.840	+	777.415i	−0.858204	+	1.48645i	0.0154372	+	0.999881i	$0.495086\pi$
$523$	−448.840	+	777.415i	−0.858204	+	1.48645i	−0.873641	+	0.486571i	$0.838247\pi$
$524$		0			0
$525$	170.508	−	63.3084i	0.324778	−	0.120587i
$526$		0			0
$527$	495.754	+	286.223i	0.940709	+	0.543118i
$528$		0			0
$529$	−159.561	−	276.367i	−0.301627	−	0.522434i
$530$		0			0
$531$	203.316			0.382893
$532$		0			0
$533$			233.035i			0.437213i
$534$		0			0
$535$	−7.82410	+	4.51725i	−0.0146245	+	0.00844345i
$536$		0			0
$537$	−169.815	+	294.128i	−0.316228	+	0.547724i
$538$		0			0
$539$	204.494	−	176.135i	0.379395	−	0.326782i
$540$		0			0
$541$	104.490	+	60.3276i	0.193143	+	0.111511i	0.593453	−	0.804869i	$-0.297764\pi$
$541$	104.490	+	60.3276i	0.193143	+	0.111511i	−0.400310	+	0.916380i	$0.631098\pi$
$542$		0			0
$543$	24.5264	−	14.1603i	0.0451684	−	0.0260780i
$544$		0			0
$545$	508.569			0.933153
$546$		0			0
$547$	−65.8090			−0.120309			−0.0601545	−	0.998189i	$-0.519159\pi$
$547$	−65.8090			−0.120309			−0.0601545	+	0.998189i	$0.519159\pi$
$548$		0			0
$549$	640.681	−	369.897i	1.16700	−	0.673765i
$550$		0			0
$551$	−654.839	−	378.071i	−1.18846	−	0.686155i
$552$		0			0
$553$	131.791	+	354.953i	0.238321	+	0.641868i
$554$		0			0
$555$	−68.6102	+	118.836i	−0.123622	+	0.214119i
$556$		0			0
$557$	−394.697	+	227.878i	−0.708612	+	0.409117i	−0.810547	−	0.585674i	$-0.800830\pi$
$557$	−394.697	+	227.878i	−0.708612	+	0.409117i	0.101935	+	0.994791i	$0.467497\pi$
$558$		0			0
$559$			179.915i			0.321851i
$560$		0			0
$561$	166.498			0.296788
$562$		0			0
$563$	413.897	+	716.891i	0.735164	+	1.27334i	0.954651	+	0.297726i	$0.0962283\pi$
$563$	413.897	+	716.891i	0.735164	+	1.27334i	−0.219487	+	0.975615i	$0.570438\pi$
$564$		0			0
$565$	−94.4582	−	54.5355i	−0.167183	−	0.0965229i
$566$		0			0
$567$	−34.7554	+	204.825i	−0.0612971	+	0.361243i
$568$		0			0
$569$	23.9051	−	41.4049i	0.0420126	−	0.0727679i	−0.844255	−	0.535942i	$-0.819956\pi$
$569$	23.9051	−	41.4049i	0.0420126	−	0.0727679i	0.886267	+	0.463175i	$0.153290\pi$
$570$		0			0
$571$	249.237	+	431.692i	0.436493	+	0.756028i	0.997416	−	0.0718399i	$-0.0228871\pi$
$571$	249.237	+	431.692i	0.436493	+	0.756028i	−0.560923	+	0.827868i	$0.689554\pi$
$572$		0			0
$573$			230.569i			0.402389i
$574$		0			0
$575$		−	262.420i		−	0.456383i
$576$		0			0
$577$	−107.802	−	186.719i	−0.186832	−	0.323603i	0.757360	−	0.652997i	$-0.226489\pi$
$577$	−107.802	−	186.719i	−0.186832	−	0.323603i	−0.944192	+	0.329395i	$0.893155\pi$
$578$		0			0
$579$	121.811	−	210.983i	0.210382	−	0.364392i
$580$		0			0
$581$	495.358	+	410.240i	0.852596	+	0.706092i
$582$		0			0
$583$	201.247	+	116.190i	0.345192	+	0.199297i
$584$		0			0
$585$	56.7051	+	98.2162i	0.0969319	+	0.167891i
$586$		0			0
$587$	−302.330			−0.515042			−0.257521	−	0.966273i	$-0.582906\pi$
$587$	−302.330			−0.515042			−0.257521	+	0.966273i	$0.582906\pi$
$588$		0			0
$589$			685.780i			1.16431i
$590$		0			0
$591$	−58.7494	+	33.9190i	−0.0994067	+	0.0573925i
$592$		0			0
$593$	−426.339	+	738.440i	−0.718952	+	1.24526i	0.242463	+	0.970161i	$0.422045\pi$
$593$	−426.339	+	738.440i	−0.718952	+	1.24526i	−0.961415	+	0.275101i	$0.911289\pi$
$594$		0			0
$595$	−246.904	+	298.133i	−0.414965	+	0.501064i
$596$		0			0
$597$	349.722	+	201.912i	0.585799	+	0.338211i
$598$		0			0
$599$	275.095	−	158.826i	0.459257	−	0.265152i	−0.252475	−	0.967604i	$-0.581244\pi$
$599$	275.095	−	158.826i	0.459257	−	0.265152i	0.711732	+	0.702451i	$0.247911\pi$
$600$		0			0
$601$	279.540			0.465125			0.232562	−	0.972581i	$-0.425289\pi$
$601$	279.540			0.465125			0.232562	+	0.972581i	$0.425289\pi$
$602$		0			0
$603$	783.511			1.29936
$604$		0			0
$605$	206.035	−	118.954i	0.340554	−	0.196619i
$606$		0			0
$607$	−827.056	−	477.501i	−1.36253	−	0.786657i	−0.372570	−	0.928004i	$-0.621524\pi$
$607$	−827.056	−	477.501i	−1.36253	−	0.786657i	−0.989960	+	0.141346i	$0.954857\pi$
$608$		0			0
$609$	296.503	+	50.3118i	0.486869	+	0.0826138i
$610$		0			0
$611$	−186.313	+	322.704i	−0.304932	+	0.528157i
$612$		0			0
$613$	915.014	−	528.284i	1.49268	−	0.861800i	0.492717	−	0.870189i	$-0.336004\pi$
$613$	915.014	−	528.284i	1.49268	−	0.861800i	0.999965	+	0.00838891i	$0.00267030\pi$
$614$		0			0
$615$		−	140.906i		−	0.229115i
$616$		0			0
$617$	974.782			1.57987			0.789937	−	0.613188i	$-0.210113\pi$
$617$	974.782			1.57987			0.789937	+	0.613188i	$0.210113\pi$
$618$		0			0
$619$	−180.385	−	312.435i	−0.291413	−	0.504742i	0.682731	−	0.730670i	$-0.260792\pi$
$619$	−180.385	−	312.435i	−0.291413	−	0.504742i	−0.974144	+	0.225928i	$0.927459\pi$
$620$		0			0
$621$	−286.911	−	165.648i	−0.462015	−	0.266744i
$622$		0			0
$623$	474.301	−	176.104i	0.761319	−	0.282671i
$624$		0			0
$625$	−77.9818	+	135.068i	−0.124771	+	0.216110i
$626$		0			0
$627$	99.7308	+	172.739i	0.159060	+	0.275500i
$628$		0			0
$629$			768.232i			1.22135i
$630$		0			0
$631$			1180.39i			1.87067i	0.353760	+	0.935336i	$0.384903\pi$
$631$			1180.39i			1.87067i	−0.353760	+	0.935336i	$0.615097\pi$
$632$		0			0
$633$	−75.6363	−	131.006i	−0.119489	−	0.206961i
$634$		0			0
$635$	93.1295	−	161.305i	0.146661	−	0.254024i
$636$		0			0
$637$	−299.695	+	56.8398i	−0.470478	+	0.0892305i
$638$		0			0
$639$	−569.083	−	328.560i	−0.890584	−	0.514179i
$640$		0			0
$641$	238.773	+	413.567i	0.372501	+	0.645190i	0.989950	−	0.141421i	$-0.0451670\pi$
$641$	238.773	+	413.567i	0.372501	+	0.645190i	−0.617449	+	0.786611i	$0.711834\pi$
$642$		0			0
$643$	−1072.27			−1.66760			−0.833801	−	0.552066i	$-0.813840\pi$
$643$	−1072.27			−1.66760			−0.833801	+	0.552066i	$0.813840\pi$
$644$		0			0
$645$		−	108.786i		−	0.168661i
$646$		0			0
$647$	373.550	−	215.669i	0.577357	−	0.333337i	−0.182725	−	0.983164i	$-0.558492\pi$
$647$	373.550	−	215.669i	0.577357	−	0.333337i	0.760082	+	0.649827i	$0.225159\pi$
$648$		0			0
$649$	80.6537	−	139.696i	0.124274	−	0.215249i
$650$		0			0
$651$	−94.9392	−	255.700i	−0.145836	−	0.392780i
$652$		0			0
$653$	−874.317	−	504.787i	−1.33892	−	0.773028i	−0.352276	−	0.935896i	$-0.614592\pi$
$653$	−874.317	−	504.787i	−1.33892	−	0.773028i	−0.986648	+	0.162868i	$0.947926\pi$
$654$		0			0
$655$	384.632	−	222.068i	0.587225	−	0.339034i
$656$		0			0
$657$	449.428			0.684060
$658$		0			0
$659$	−986.016			−1.49623			−0.748115	−	0.663569i	$-0.769041\pi$
$659$	−986.016			−1.49623			−0.748115	+	0.663569i	$0.769041\pi$
$660$		0			0
$661$	264.228	−	152.552i	0.399740	−	0.230790i	−0.286632	−	0.958041i	$-0.592536\pi$
$661$	264.228	−	152.552i	0.399740	−	0.230790i	0.686372	+	0.727251i	$0.259202\pi$
$662$		0			0
$663$	−162.969	−	94.0899i	−0.245805	−	0.141915i
$664$		0			0
$665$	−457.201	−	77.5796i	−0.687520	−	0.116661i
$666$		0			0
$667$	216.955	−	375.778i	0.325270	−	0.563385i
$668$		0			0
$669$	−480.035	+	277.148i	−0.717540	+	0.414272i
$670$		0			0
$671$		−	586.940i		−	0.874724i
$672$		0			0
$673$	−959.704			−1.42601			−0.713005	−	0.701159i	$-0.752666\pi$
$673$	−959.704			−1.42601			−0.713005	+	0.701159i	$0.752666\pi$
$674$		0			0
$675$	207.117	+	358.737i	0.306840	+	0.531463i
$676$		0			0
$677$	−105.318	−	60.8054i	−0.155566	−	0.0898160i	0.420196	−	0.907433i	$-0.361961\pi$
$677$	−105.318	−	60.8054i	−0.155566	−	0.0898160i	−0.575762	+	0.817617i	$0.695295\pi$
$678$		0			0
$679$	−525.453	−	435.163i	−0.773863	−	0.640888i
$680$		0			0
$681$	102.807	−	178.066i	0.150964	−	0.261478i
$682$		0			0
$683$	−45.6786	−	79.1177i	−0.0668794	−	0.115838i	0.830647	−	0.556800i	$-0.187971\pi$
$683$	−45.6786	−	79.1177i	−0.0668794	−	0.115838i	−0.897526	+	0.440961i	$0.854638\pi$
$684$		0			0
$685$		−	254.392i		−	0.371375i
$686$		0			0
$687$			255.710i			0.372213i
$688$		0			0
$689$	−131.320	−	227.454i	−0.190596	−	0.330121i
$690$		0			0
$691$	378.521	−	655.617i	0.547787	−	0.948795i	−0.450639	−	0.892706i	$-0.648804\pi$
$691$	378.521	−	655.617i	0.547787	−	0.948795i	0.998426	−	0.0560887i	$-0.0178630\pi$
$692$		0			0
$693$	206.154	+	170.730i	0.297480	+	0.246363i
$694$		0			0
$695$	221.809	+	128.062i	0.319150	+	0.184262i
$696$		0			0
$697$	−394.432	−	683.176i	−0.565899	−	0.980167i
$698$		0			0
$699$	495.473			0.708832
$700$		0			0
$701$		−	513.435i		−	0.732433i	−0.930530	−	0.366216i	$-0.880653\pi$
$701$		−	513.435i		−	0.732433i	0.930530	−	0.366216i	$-0.119347\pi$
$702$		0			0
$703$	−797.026	+	460.163i	−1.13375	+	0.654571i
$704$		0			0
$705$	112.655	−	195.124i	0.159795	−	0.276772i
$706$		0			0
$707$	1335.07	+	226.539i	1.88835	+	0.320423i
$708$		0			0
$709$	353.678	+	204.196i	0.498841	+	0.288006i	0.728235	−	0.685328i	$-0.240341\pi$
$709$	353.678	+	204.196i	0.498841	+	0.288006i	−0.229394	+	0.973334i	$0.573674\pi$
$710$		0			0
$711$	−325.206	+	187.758i	−0.457392	+	0.264075i
$712$		0			0
$713$	−393.533			−0.551940
$714$		0			0
$715$	89.9777			0.125843
$716$		0			0
$717$	174.120	−	100.528i	0.242845	−	0.140207i
$718$		0			0
$719$	797.802	+	460.611i	1.10960	+	0.640628i	0.938726	−	0.344665i	$-0.112007\pi$
$719$	797.802	+	460.611i	1.10960	+	0.640628i	0.170874	+	0.985293i	$0.445341\pi$
$720$		0			0
$721$	−222.547	−	599.386i	−0.308665	−	0.831326i
$722$		0			0
$723$	157.464	−	272.735i	0.217792	−	0.377227i
$724$		0			0
$725$	−469.851	+	271.269i	−0.648070	+	0.374164i
$726$		0			0
$727$		−	404.650i		−	0.556603i	−0.960494	−	0.278301i	$-0.910229\pi$
$727$		−	404.650i		−	0.556603i	0.960494	−	0.278301i	$-0.0897714\pi$
$728$		0			0
$729$	89.1823			0.122335
$730$		0			0
$731$	−304.522	−	527.447i	−0.416582	−	0.721541i
$732$		0			0
$733$	181.337	+	104.695i	0.247390	+	0.142830i	0.618568	−	0.785731i	$-0.287713\pi$
$733$	181.337	+	104.695i	0.247390	+	0.142830i	−0.371179	+	0.928561i	$0.621046\pi$
$734$		0			0
$735$	181.212	−	34.3685i	0.246547	−	0.0467598i
$736$		0			0
$737$	310.812	−	538.342i	0.421726	−	0.730451i
$738$		0			0
$739$	−611.765	−	1059.61i	−0.827828	−	1.43384i	−0.899739	−	0.436429i	$-0.856243\pi$
$739$	−611.765	−	1059.61i	−0.827828	−	1.43384i	0.0719108	−	0.997411i	$-0.477090\pi$
$740$		0			0
$741$		−	225.436i		−	0.304232i
$742$		0			0
$743$			571.739i			0.769501i	0.923021	+	0.384750i	$0.125712\pi$
$743$			571.739i			0.769501i	−0.923021	+	0.384750i	$0.874288\pi$
$744$		0			0
$745$	−180.190	−	312.098i	−0.241866	−	0.418923i
$746$		0			0
$747$	−318.943	+	552.425i	−0.426965	+	0.739525i
$748$		0			0
$749$	22.5929	−	8.38858i	0.0301641	−	0.0111997i
$750$		0			0
$751$	1108.18	+	639.811i	1.47561	+	0.851945i	0.999622	−	0.0275052i	$-0.00875630\pi$
$751$	1108.18	+	639.811i	1.47561	+	0.851945i	0.475991	+	0.879450i	$0.342090\pi$
$752$		0			0
$753$	−149.078	−	258.210i	−0.197978	−	0.342908i
$754$		0			0
$755$	125.766			0.166578
$756$		0			0
$757$		−	159.036i		−	0.210087i	−0.994468	−	0.105043i	$-0.966502\pi$
$757$		−	159.036i		−	0.210087i	0.994468	−	0.105043i	$-0.0334981\pi$
$758$		0			0
$759$	−99.1257	+	57.2303i	−0.130600	+	0.0754022i
$760$		0			0
$761$	130.214	−	225.538i	0.171110	−	0.296371i	−0.767698	−	0.640811i	$-0.778598\pi$
$761$	130.214	−	225.538i	0.171110	−	0.296371i	0.938808	+	0.344441i	$0.111931\pi$
$762$		0			0
$763$	−1337.51	−	226.955i	−1.75297	−	0.297450i
$764$		0			0
$765$	−332.479	−	191.957i	−0.434613	−	0.250924i
$766$		0			0
$767$	−157.888	+	91.1565i	−0.205851	+	0.118848i
$768$		0			0
$769$	−556.399			−0.723536			−0.361768	−	0.932268i	$-0.617827\pi$
$769$	−556.399			−0.723536			−0.361768	+	0.932268i	$0.617827\pi$
$770$		0			0
$771$	−42.3430			−0.0549196
$772$		0			0
$773$	−90.2809	+	52.1237i	−0.116793	+	0.0674304i	−0.557258	−	0.830339i	$-0.688147\pi$
$773$	−90.2809	+	52.1237i	−0.116793	+	0.0674304i	0.440466	+	0.897770i	$0.354813\pi$
$774$		0			0
$775$	426.129	+	246.026i	0.549844	+	0.317452i
$776$		0			0
$777$	233.474	−	281.916i	0.300481	−	0.362827i
$778$		0			0
$779$	472.521	−	818.431i	0.606574	−	1.05062i
$780$		0			0
$781$	−451.501	+	260.674i	−0.578106	+	0.333769i
$782$		0			0
$783$			684.935i			0.874757i
$784$		0			0
$785$	−144.088			−0.183551
$786$		0			0
$787$	18.1655	+	31.4635i	0.0230819	+	0.0399791i	0.877336	−	0.479877i	$-0.159319\pi$
$787$	18.1655	+	31.4635i	0.0230819	+	0.0399791i	−0.854254	+	0.519856i	$0.825985\pi$
$788$		0			0
$789$	−3.58799	−	2.07153i	−0.00454752	−	0.00262551i
$790$		0			0
$791$	224.084	+	185.579i	0.283292	+	0.234613i
$792$		0			0
$793$	−331.686	+	574.497i	−0.418267	+	0.724460i
$794$		0			0
$795$	79.4035	+	137.531i	0.0998786	+	0.172995i
$796$		0			0
$797$			17.3808i			0.0218077i	0.999941	+	0.0109039i	$0.00347087\pi$
$797$			17.3808i			0.0218077i	−0.999941	+	0.0109039i	$0.996529\pi$
$798$		0			0
$799$		−	1261.41i		−	1.57873i
$800$		0			0
$801$	250.889	+	434.552i	0.313219	+	0.542512i
$802$		0			0
$803$	178.284	−	308.797i	0.222022	−	0.384554i
$804$		0			0
$805$	44.5188	−	262.363i	0.0553029	−	0.325917i
$806$		0			0
$807$	−444.207	−	256.463i	−0.550443	−	0.317798i
$808$		0			0
$809$	395.110	+	684.350i	0.488393	+	0.845921i	0.999911	−	0.0133513i	$-0.00424997\pi$
$809$	395.110	+	684.350i	0.488393	+	0.845921i	−0.511518	+	0.859273i	$0.670917\pi$
$810$		0			0
$811$	1088.07			1.34163			0.670817	−	0.741623i	$-0.265944\pi$
$811$	1088.07			1.34163			0.670817	+	0.741623i	$0.265944\pi$
$812$		0			0
$813$		−	488.194i		−	0.600484i
$814$		0			0
$815$	−18.4999	+	10.6809i	−0.0226992	+	0.0131054i
$816$		0			0
$817$	364.811	−	631.871i	0.446525	−	0.773403i
$818$		0			0
$819$	−105.302	−	283.610i	−0.128574	−	0.346288i
$820$		0			0
$821$	−615.199	−	355.185i	−0.749329	−	0.432625i	0.0761224	−	0.997098i	$-0.475746\pi$
$821$	−615.199	−	355.185i	−0.749329	−	0.432625i	−0.825451	+	0.564473i	$0.809079\pi$
$822$		0			0
$823$	10.5957	−	6.11742i	0.0128745	−	0.00743307i	−0.493549	−	0.869718i	$-0.664301\pi$
$823$	10.5957	−	6.11742i	0.0128745	−	0.00743307i	0.506423	+	0.862285i	$0.330967\pi$
$824$		0			0
$825$	143.115			0.173473
$826$		0			0
$827$	−50.6323			−0.0612240			−0.0306120	−	0.999531i	$-0.509746\pi$
$827$	−50.6323			−0.0612240			−0.0306120	+	0.999531i	$0.509746\pi$
$828$		0			0
$829$	−703.863	+	406.375i	−0.849050	+	0.490199i	−0.860330	−	0.509737i	$-0.829743\pi$
$829$	−703.863	+	406.375i	−0.849050	+	0.490199i	0.0112800	+	0.999936i	$0.496409\pi$
$830$		0			0
$831$	16.1520	+	9.32538i	0.0194369	+	0.0112219i
$832$		0			0
$833$	782.393	−	673.894i	0.939247	−	0.808996i
$834$		0			0
$835$	15.9910	−	27.6973i	0.0191510	−	0.0331704i
$836$		0			0
$837$	537.973	−	310.599i	0.642740	−	0.371086i
$838$		0			0
$839$		−	247.088i		−	0.294503i	−0.989099	−	0.147252i	$-0.952957\pi$
$839$		−	247.088i		−	0.294503i	0.989099	−	0.147252i	$-0.0470427\pi$
$840$		0			0
$841$	−56.0837			−0.0666869
$842$		0			0
$843$	−166.608	−	288.574i	−0.197638	−	0.342318i
$844$		0			0
$845$	295.993	+	170.892i	0.350287	+	0.202239i
$846$		0			0
$847$	−594.949	+	220.900i	−0.702419	+	0.260803i
$848$		0			0
$849$	8.70990	−	15.0860i	0.0102590	−	0.0177691i
$850$		0			0
$851$	−264.064	−	457.371i	−0.310298	−	0.537452i
$852$		0			0
$853$		−	659.254i		−	0.772866i	−0.922318	−	0.386433i	$-0.873707\pi$
$853$		−	659.254i		−	0.772866i	0.922318	−	0.386433i	$-0.126293\pi$
$854$		0			0
$855$		−	459.921i		−	0.537919i
$856$		0			0
$857$	52.1741	+	90.3682i	0.0608799	+	0.105447i	0.894859	−	0.446349i	$-0.147276\pi$
$857$	52.1741	+	90.3682i	0.0608799	+	0.105447i	−0.833979	+	0.551796i	$0.813943\pi$
$858$		0			0
$859$	−675.738	+	1170.41i	−0.786657	+	1.36253i	0.141348	+	0.989960i	$0.454856\pi$
$859$	−675.738	+	1170.41i	−0.786657	+	1.36253i	−0.928004	+	0.372569i	$0.878477\pi$
$860$		0			0
$861$	−62.8807	+	370.576i	−0.0730322	+	0.430401i
$862$		0			0
$863$	−1129.48	−	652.105i	−1.30878	−	0.755625i	−0.326889	−	0.945063i	$-0.606000\pi$
$863$	−1129.48	−	652.105i	−1.30878	−	0.755625i	−0.981893	+	0.189437i	$0.939334\pi$
$864$		0			0
$865$	347.567	+	602.004i	0.401812	+	0.695958i
$866$		0			0
$867$	222.473			0.256600
$868$		0			0
$869$			297.927i			0.342839i
$870$		0			0
$871$	−608.446	+	351.286i	−0.698560	+	0.403314i
$872$		0			0
$873$	338.320	−	585.987i	0.387537	−	0.671234i
$874$		0			0
$875$	−505.136	+	609.944i	−0.577298	+	0.697079i
$876$		0			0
$877$	1043.59	+	602.517i	1.18995	+	0.687021i	0.958296	−	0.285777i	$-0.0922516\pi$
$877$	1043.59	+	602.517i	1.18995	+	0.687021i	0.231658	+	0.972797i	$0.425585\pi$
$878$		0			0
$879$	105.100	−	60.6797i	0.119568	−	0.0690327i
$880$		0			0
$881$	−485.495			−0.551073			−0.275536	−	0.961291i	$-0.588855\pi$
$881$	−485.495			−0.551073			−0.275536	+	0.961291i	$0.588855\pi$
$882$		0			0
$883$	−355.597			−0.402714			−0.201357	−	0.979518i	$-0.564535\pi$
$883$	−355.597			−0.402714			−0.201357	+	0.979518i	$0.564535\pi$
$884$		0			0
$885$	95.4676	−	55.1182i	0.107873	−	0.0622805i
$886$		0			0
$887$	596.239	+	344.239i	0.672197	+	0.388093i	0.796909	−	0.604100i	$-0.206467\pi$
$887$	596.239	+	344.239i	0.672197	+	0.388093i	−0.124712	+	0.992193i	$0.539801\pi$
$888$		0			0
$889$	−316.911	+	382.666i	−0.356480	+	0.430445i
$890$		0			0
$891$	−81.7356	+	141.570i	−0.0917346	+	0.158889i
$892$		0			0
$893$	1308.69	−	755.570i	1.46549	−	0.846103i
$894$		0			0
$895$		−	621.315i		−	0.694207i
$896$		0			0
$897$	129.366			0.144220
$898$		0			0
$899$	406.803	+	704.603i	0.452506	+	0.783763i
$900$		0			0
$901$	769.971	+	444.543i	0.854574	+	0.493388i
$902$		0			0
$903$	−48.5471	+	286.103i	−0.0537620	+	0.316836i
$904$		0			0
$905$	−25.9048	+	44.8684i	−0.0286241	+	0.0495784i
$906$		0			0
$907$	101.105	+	175.119i	0.111472	+	0.193075i	0.916364	−	0.400346i	$-0.131110\pi$
$907$	101.105	+	175.119i	0.111472	+	0.193075i	−0.804892	+	0.593421i	$0.797777\pi$
$908$		0			0
$909$			1343.01i			1.47746i
$910$		0			0
$911$		−	402.691i		−	0.442032i	−0.975270	−	0.221016i	$-0.929063\pi$
$911$		−	402.691i		−	0.442032i	0.975270	−	0.221016i	$-0.0709373\pi$
$912$		0			0
$913$	253.044	+	438.284i	0.277156	+	0.480049i
$914$		0			0
$915$	200.555	−	347.372i	0.219186	−	0.379642i
$916$		0			0
$917$	−1110.67	+	412.382i	−1.21120	+	0.449708i
$918$		0			0
$919$	49.5319	+	28.5973i	0.0538976	+	0.0311178i	0.526707	−	0.850047i	$-0.323427\pi$
$919$	49.5319	+	28.5973i	0.0538976	+	0.0311178i	−0.472809	+	0.881165i	$0.656760\pi$
$920$		0			0
$921$	−69.8358	−	120.959i	−0.0758261	−	0.131335i
$922$		0			0
$923$	589.238			0.638395
$924$		0			0
$925$			660.340i			0.713881i
$926$		0			0
$927$	549.154	−	317.054i	0.592399	−	0.342022i
$928$		0			0
$929$	−327.576	+	567.378i	−0.352611	+	0.610740i	−0.986706	−	0.162515i	$-0.948039\pi$
$929$	−327.576	+	567.378i	−0.352611	+	0.610740i	0.634095	+	0.773255i	$0.281373\pi$
$930$		0			0
$931$	1167.80	+	408.062i	1.25435	+	0.438305i
$932$		0			0
$933$	−124.460	−	71.8573i	−0.133398	−	0.0770174i
$934$		0			0
$935$	−263.783	+	152.295i	−0.282121	+	0.162883i
$936$		0			0
$937$	−1490.29			−1.59049			−0.795245	−	0.606288i	$-0.792658\pi$
$937$	−1490.29			−1.59049			−0.795245	+	0.606288i	$0.792658\pi$
$938$		0			0
$939$	203.475			0.216694
$940$		0			0
$941$	301.240	−	173.921i	0.320128	−	0.184826i	−0.331322	−	0.943518i	$-0.607495\pi$
$941$	301.240	−	173.921i	0.320128	−	0.184826i	0.651450	+	0.758692i	$0.274161\pi$
$942$		0			0
$943$	469.655	+	271.155i	0.498043	+	0.287545i
$944$		0			0
$945$	146.214	+	393.797i	0.154723	+	0.416716i
$946$		0			0
$947$	−716.497	+	1241.01i	−0.756596	+	1.31046i	0.187981	+	0.982173i	$0.439806\pi$
$947$	−716.497	+	1241.01i	−0.756596	+	1.31046i	−0.944577	+	0.328290i	$0.893528\pi$
$948$		0			0
$949$	−349.009	+	201.500i	−0.367765	+	0.212329i
$950$		0			0
$951$			41.2488i			0.0433741i
$952$		0			0
$953$	−67.7570			−0.0710986			−0.0355493	−	0.999368i	$-0.511318\pi$
$953$	−67.7570			−0.0710986			−0.0355493	+	0.999368i	$0.511318\pi$
$954$		0			0
$955$	−210.900	−	365.290i	−0.220838	−	0.382503i
$956$		0			0
$957$	204.936	+	118.320i	0.214145	+	0.123636i
$958$		0			0
$959$	−113.525	+	669.040i	−0.118379	+	0.697643i
$960$		0			0
$961$	−111.553	+	193.215i	−0.116080	+	0.201056i
$962$		0			0
$963$	11.9509	+	20.6995i	0.0124100	+	0.0214948i
$964$		0			0
$965$			445.680i			0.461845i
$966$		0			0
$967$		−	1272.02i		−	1.31543i	−0.753267	−	0.657715i	$-0.771523\pi$
$967$		−	1272.02i		−	1.31543i	0.753267	−	0.657715i	$-0.228477\pi$
$968$		0			0
$969$	381.570	+	660.898i	0.393777	+	0.682042i
$970$		0			0
$971$	−544.112	+	942.430i	−0.560363	+	0.970577i	0.437102	+	0.899412i	$0.356005\pi$
$971$	−544.112	+	942.430i	−0.560363	+	0.970577i	−0.997465	+	0.0711647i	$0.977328\pi$
$972$		0			0
$973$	−526.201	−	435.782i	−0.540802	−	0.447875i
$974$		0			0
$975$	−140.081	−	80.8757i	−0.143673	−	0.0829495i
$976$		0			0
$977$	222.510	+	385.398i	0.227748	+	0.394471i	0.957140	−	0.289625i	$-0.0935305\pi$
$977$	222.510	+	385.398i	0.227748	+	0.394471i	−0.729392	+	0.684096i	$0.760197\pi$
$978$		0			0
$979$	398.101			0.406641
$980$		0			0
$981$		−	1345.47i		−	1.37153i
$982$		0			0
$983$	898.398	−	518.691i	0.913935	−	0.527661i	0.0322401	−	0.999480i	$-0.489736\pi$
$983$	898.398	−	518.691i	0.913935	−	0.527661i	0.881695	+	0.471819i	$0.156403\pi$
$984$		0			0
$985$	62.0511	−	107.476i	0.0629960	−	0.109112i
$986$		0			0
$987$	−383.355	+	462.896i	−0.388404	+	0.468992i
$988$		0			0
$989$	362.597	+	209.346i	0.366630	+	0.211674i
$990$		0			0
$991$	57.7139	−	33.3211i	0.0582381	−	0.0336238i	−0.470598	−	0.882348i	$-0.655962\pi$
$991$	57.7139	−	33.3211i	0.0582381	−	0.0336238i	0.528836	+	0.848724i	$0.322629\pi$
$992$		0			0
$993$	−404.210			−0.407060
$994$		0			0
$995$	−738.752			−0.742465
$996$		0			0
$997$	−1642.43	+	948.258i	−1.64737	+	0.951111i	−0.669262	+	0.743027i	$0.733389\pi$
$997$	−1642.43	+	948.258i	−1.64737	+	0.951111i	−0.978111	+	0.208084i	$0.933277\pi$
$998$		0			0
$999$	721.968	+	416.828i	0.722691	+	0.417246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.o.c.79.4		12
4.3	odd	2		56.3.k.c.51.1	yes	12
7.2	even	3		1568.3.g.k.687.3		6
7.4	even	3	inner	224.3.o.c.207.3		12
7.5	odd	6		1568.3.g.i.687.4		6
8.3	odd	2	inner	224.3.o.c.79.3		12
8.5	even	2		56.3.k.c.51.6	yes	12
28.3	even	6		392.3.k.k.67.6		12
28.11	odd	6		56.3.k.c.11.6	yes	12
28.19	even	6		392.3.g.l.99.4		6
28.23	odd	6		392.3.g.k.99.4		6
28.27	even	2		392.3.k.k.275.1		12
56.5	odd	6		392.3.g.l.99.3		6
56.11	odd	6	inner	224.3.o.c.207.4		12
56.13	odd	2		392.3.k.k.275.6		12
56.19	even	6		1568.3.g.i.687.3		6
56.37	even	6		392.3.g.k.99.3		6
56.45	odd	6		392.3.k.k.67.1		12
56.51	odd	6		1568.3.g.k.687.4		6
56.53	even	6		56.3.k.c.11.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.c.11.1	✓	12	56.53	even	6
56.3.k.c.11.6	yes	12	28.11	odd	6
56.3.k.c.51.1	yes	12	4.3	odd	2
56.3.k.c.51.6	yes	12	8.5	even	2
224.3.o.c.79.3		12	8.3	odd	2	inner
224.3.o.c.79.4		12	1.1	even	1	trivial
224.3.o.c.207.3		12	7.4	even	3	inner
224.3.o.c.207.4		12	56.11	odd	6	inner
392.3.g.k.99.3		6	56.37	even	6
392.3.g.k.99.4		6	28.23	odd	6
392.3.g.l.99.3		6	56.5	odd	6
392.3.g.l.99.4		6	28.19	even	6
392.3.k.k.67.1		12	56.45	odd	6
392.3.k.k.67.6		12	28.3	even	6
392.3.k.k.275.1		12	28.27	even	2
392.3.k.k.275.6		12	56.13	odd	2
1568.3.g.i.687.3		6	56.19	even	6
1568.3.g.i.687.4		6	7.5	odd	6
1568.3.g.k.687.3		6	7.2	even	3
1568.3.g.k.687.4		6	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.717214 - 1.24225i) q^{3} +(2.27256 + 1.31206i) q^{5} +(-5.39122 - 4.46483i) q^{7} +(3.47121 - 6.01231i) q^{9} +O(q^{10})\)	\(q+(-0.717214 - 1.24225i) q^{3} +(2.27256 + 1.31206i) q^{5} +(-5.39122 - 4.46483i) q^{7} +(3.47121 - 6.01231i) q^{9} +(-2.75399 - 4.77006i) q^{11} +6.22525i q^{13} -3.76412i q^{15} +(-10.5368 - 18.2502i) q^{17} +(12.6229 - 21.8634i) q^{19} +(-1.67978 + 9.89949i) q^{21} +(12.5463 + 7.24359i) q^{23} +(-9.05697 - 15.6871i) q^{25} -22.8682 q^{27} -29.9514i q^{29} +(-23.5249 + 13.5821i) q^{31} +(-3.95041 + 6.84230i) q^{33} +(-6.39374 - 17.2202i) q^{35} +(-31.5708 - 18.2274i) q^{37} +(7.73332 - 4.46483i) q^{39} +37.4338 q^{41} +28.9008 q^{43} +(15.7771 - 9.10890i) q^{45} +(51.8379 + 29.9287i) q^{47} +(9.13053 + 48.1418i) q^{49} +(-15.1143 + 26.1787i) q^{51} +(-36.5373 + 21.0948i) q^{53} -14.4537i q^{55} -36.2131 q^{57} +(14.6430 + 25.3625i) q^{59} +(92.2850 + 53.2808i) q^{61} +(-45.5580 + 16.9153i) q^{63} +(-8.16793 + 14.1473i) q^{65} +(56.4293 + 97.7384i) q^{67} -20.7808i q^{69} -94.6530i q^{71} +(32.3682 + 56.0634i) q^{73} +(-12.9916 + 22.5021i) q^{75} +(-6.45012 + 38.0126i) q^{77} +(-46.8433 - 27.0450i) q^{79} +(-14.8395 - 25.7027i) q^{81} -91.8824 q^{83} -55.2997i q^{85} +(-37.2071 + 21.4815i) q^{87} +(-36.1385 + 62.5938i) q^{89} +(27.7947 - 33.5617i) q^{91} +(33.7448 + 19.4826i) q^{93} +(57.3724 - 33.1240i) q^{95} +97.4646 q^{97} -38.2388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 8 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 8 * q^9	\( 12 q - 6 q^{3} - 8 q^{9} + 14 q^{11} - 82 q^{17} + 94 q^{19} + 116 q^{25} + 60 q^{27} + 146 q^{33} - 270 q^{35} + 120 q^{41} - 40 q^{43} - 204 q^{49} + 106 q^{51} - 372 q^{57} - 62 q^{59} - 64 q^{65} + 178 q^{67} + 54 q^{73} - 140 q^{75} + 206 q^{81} + 392 q^{83} - 26 q^{89} + 88 q^{91} - 184 q^{97} - 872 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 - 8 * q^9 + 14 * q^11 - 82 * q^17 + 94 * q^19 + 116 * q^25 + 60 * q^27 + 146 * q^33 - 270 * q^35 + 120 * q^41 - 40 * q^43 - 204 * q^49 + 106 * q^51 - 372 * q^57 - 62 * q^59 - 64 * q^65 + 178 * q^67 + 54 * q^73 - 140 * q^75 + 206 * q^81 + 392 * q^83 - 26 * q^89 + 88 * q^91 - 184 * q^97 - 872 * q^99

Introduction

L-functions

Modular forms

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Database

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