LMFDB - Embedded newform 912.3.be.j.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$3.62416 - 6.27723i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.j.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-3.62416 - 6.27723i) q^{5} +0.758627 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-3.62416 - 6.27723i) q^{5} +0.758627 q^{7} +(1.50000 - 2.59808i) q^{9} +14.9189 q^{11} +(11.3543 + 6.55539i) q^{13} +(-10.8725 - 6.27723i) q^{15} +(-5.54250 - 9.59990i) q^{17} +(-12.6949 - 14.1365i) q^{19} +(1.13794 - 0.656990i) q^{21} +(13.5247 - 23.4255i) q^{23} +(-13.7690 + 23.8487i) q^{25} -5.19615i q^{27} +(46.0416 + 26.5821i) q^{29} +3.15697i q^{31} +(22.3783 - 12.9201i) q^{33} +(-2.74938 - 4.76207i) q^{35} -13.0777i q^{37} +22.7085 q^{39} +(-46.1794 + 26.6617i) q^{41} +(-36.4549 - 63.1417i) q^{43} -21.7450 q^{45} +(34.5847 - 59.9024i) q^{47} -48.4245 q^{49} +(-16.6275 - 9.59990i) q^{51} +(-45.2399 - 26.1192i) q^{53} +(-54.0684 - 93.6491i) q^{55} +(-31.2849 - 10.2106i) q^{57} +(-74.2621 + 42.8752i) q^{59} +(-31.9467 + 55.3333i) q^{61} +(1.13794 - 1.97097i) q^{63} -95.0311i q^{65} +(-9.93978 - 5.73873i) q^{67} -46.8511i q^{69} +(95.5318 - 55.1553i) q^{71} +(-20.5645 - 35.6188i) q^{73} +47.6974i q^{75} +11.3179 q^{77} +(-28.6077 + 16.5167i) q^{79} +(-4.50000 - 7.79423i) q^{81} -62.5274 q^{83} +(-40.1738 + 69.5831i) q^{85} +92.0831 q^{87} +(90.1436 + 52.0444i) q^{89} +(8.61365 + 4.97309i) q^{91} +(2.73402 + 4.73546i) q^{93} +(-42.7295 + 130.922i) q^{95} +(58.1738 - 33.5867i) q^{97} +(22.3783 - 38.7604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	−3.62416	−	6.27723i	−0.724832	−	1.25545i	−0.959043	−	0.283260i	$-0.908584\pi$
$5$	−3.62416	−	6.27723i	−0.724832	−	1.25545i	0.234212	−	0.972186i	$-0.424749\pi$
$6$		0			0
$7$	0.758627			0.108375			0.0541876	−	0.998531i	$-0.482743\pi$
$7$	0.758627			0.108375			0.0541876	+	0.998531i	$0.482743\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	14.9189			1.35626			0.678131	−	0.734942i	$-0.262790\pi$
$11$	14.9189			1.35626			0.678131	+	0.734942i	$0.262790\pi$
$12$		0			0
$13$	11.3543	+	6.55539i	0.873405	+	0.504261i	0.868478	−	0.495727i	$-0.165098\pi$
$13$	11.3543	+	6.55539i	0.873405	+	0.504261i	0.00492686	+	0.999988i	$0.498432\pi$
$14$		0			0
$15$	−10.8725	−	6.27723i	−0.724832	−	0.418482i
$16$		0			0
$17$	−5.54250	−	9.59990i	−0.326030	−	0.564700i	0.655691	−	0.755030i	$-0.272378\pi$
$17$	−5.54250	−	9.59990i	−0.326030	−	0.564700i	−0.981720	+	0.190330i	$0.939044\pi$
$18$		0			0
$19$	−12.6949	−	14.1365i	−0.668152	−	0.744024i
$19$	−12.6949	−	14.1365i	−0.668152	−	0.744024i
$20$		0			0
$21$	1.13794	−	0.656990i	0.0541876	−	0.0312852i
$22$		0			0
$23$	13.5247	−	23.4255i	0.588032	−	1.01850i	−0.406458	−	0.913669i	$-0.633236\pi$
$23$	13.5247	−	23.4255i	0.588032	−	1.01850i	0.994490	−	0.104832i	$-0.0334304\pi$
$24$		0			0
$25$	−13.7690	+	23.8487i	−0.550762	+	0.953948i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	46.0416	+	26.5821i	1.58764	+	0.916625i	0.993695	+	0.112120i	$0.0357639\pi$
$29$	46.0416	+	26.5821i	1.58764	+	0.916625i	0.593946	+	0.804505i	$0.297569\pi$
$30$		0			0
$31$			3.15697i			0.101838i	0.998703	+	0.0509189i	$0.0162150\pi$
$31$			3.15697i			0.101838i	−0.998703	+	0.0509189i	$0.983785\pi$
$32$		0			0
$33$	22.3783	−	12.9201i	0.678131	−	0.391519i
$34$		0			0
$35$	−2.74938	−	4.76207i	−0.0785538	−	0.136059i
$36$		0			0
$37$		−	13.0777i		−	0.353450i	−0.984260	−	0.176725i	$-0.943450\pi$
$37$		−	13.0777i		−	0.353450i	0.984260	−	0.176725i	$-0.0565503\pi$
$38$		0			0
$39$	22.7085			0.582270
$40$		0			0
$41$	−46.1794	+	26.6617i	−1.12633	+	0.650285i	−0.943008	−	0.332769i	$-0.892017\pi$
$41$	−46.1794	+	26.6617i	−1.12633	+	0.650285i	−0.183318	+	0.983054i	$0.558684\pi$
$42$		0			0
$43$	−36.4549	−	63.1417i	−0.847787	−	1.46841i	−0.883178	−	0.469037i	$-0.844601\pi$
$43$	−36.4549	−	63.1417i	−0.847787	−	1.46841i	0.0353910	−	0.999374i	$-0.488732\pi$
$44$		0			0
$45$	−21.7450			−0.483221
$46$		0			0
$47$	34.5847	−	59.9024i	0.735845	−	1.27452i	−0.218507	−	0.975835i	$-0.570119\pi$
$47$	34.5847	−	59.9024i	0.735845	−	1.27452i	0.954352	−	0.298685i	$-0.0965479\pi$
$48$		0			0
$49$	−48.4245			−0.988255
$50$		0			0
$51$	−16.6275	−	9.59990i	−0.326030	−	0.188233i
$52$		0			0
$53$	−45.2399	−	26.1192i	−0.853582	−	0.492816i	0.00827561	−	0.999966i	$-0.497366\pi$
$53$	−45.2399	−	26.1192i	−0.853582	−	0.492816i	−0.861858	+	0.507150i	$0.830699\pi$
$54$		0			0
$55$	−54.0684	−	93.6491i	−0.983061	−	1.70271i
$56$		0			0
$57$	−31.2849	−	10.2106i	−0.548858	−	0.179133i
$58$		0			0
$59$	−74.2621	+	42.8752i	−1.25868	+	0.726699i	−0.972818	−	0.231572i	$-0.925613\pi$
$59$	−74.2621	+	42.8752i	−1.25868	+	0.726699i	−0.285862	+	0.958271i	$0.592280\pi$
$60$		0			0
$61$	−31.9467	+	55.3333i	−0.523717	+	0.907104i	0.475902	+	0.879498i	$0.342122\pi$
$61$	−31.9467	+	55.3333i	−0.523717	+	0.907104i	−0.999619	+	0.0276056i	$0.991212\pi$
$62$		0			0
$63$	1.13794	−	1.97097i	0.0180625	−	0.0312852i
$64$		0			0
$65$		−	95.0311i		−	1.46202i
$66$		0			0
$67$	−9.93978	−	5.73873i	−0.148355	−	0.0856527i	0.423985	−	0.905669i	$-0.360631\pi$
$67$	−9.93978	−	5.73873i	−0.148355	−	0.0856527i	−0.572340	+	0.820016i	$0.693964\pi$
$68$		0			0
$69$		−	46.8511i		−	0.679001i
$70$		0			0
$71$	95.5318	−	55.1553i	1.34552	−	0.776835i	0.357907	−	0.933757i	$-0.383490\pi$
$71$	95.5318	−	55.1553i	1.34552	−	0.776835i	0.987611	+	0.156922i	$0.0501571\pi$
$72$		0			0
$73$	−20.5645	−	35.6188i	−0.281706	−	0.487929i	0.690099	−	0.723715i	$-0.257567\pi$
$73$	−20.5645	−	35.6188i	−0.281706	−	0.487929i	−0.971805	+	0.235786i	$0.924234\pi$
$74$		0			0
$75$			47.6974i			0.635965i
$76$		0			0
$77$	11.3179			0.146985
$78$		0			0
$79$	−28.6077	+	16.5167i	−0.362123	+	0.209072i	−0.670012	−	0.742351i	$-0.733711\pi$
$79$	−28.6077	+	16.5167i	−0.362123	+	0.209072i	0.307889	+	0.951422i	$0.400378\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−62.5274			−0.753342			−0.376671	−	0.926347i	$-0.622931\pi$
$83$	−62.5274			−0.753342			−0.376671	+	0.926347i	$0.622931\pi$
$84$		0			0
$85$	−40.1738	+	69.5831i	−0.472633	+	0.818625i
$86$		0			0
$87$	92.0831			1.05843
$88$		0			0
$89$	90.1436	+	52.0444i	1.01285	+	0.584769i	0.912025	−	0.410135i	$-0.134519\pi$
$89$	90.1436	+	52.0444i	1.01285	+	0.584769i	0.100825	+	0.994904i	$0.467852\pi$
$90$		0			0
$91$	8.61365	+	4.97309i	0.0946555	+	0.0546494i
$92$		0			0
$93$	2.73402	+	4.73546i	0.0293980	+	0.0509189i
$94$		0			0
$95$	−42.7295	+	130.922i	−0.449784	+	1.37812i
$96$		0			0
$97$	58.1738	−	33.5867i	0.599730	−	0.346254i	−0.169205	−	0.985581i	$-0.554120\pi$
$97$	58.1738	−	33.5867i	0.599730	−	0.346254i	0.768935	+	0.639327i	$0.220787\pi$
$98$		0			0
$99$	22.3783	−	38.7604i	0.226044	−	0.391519i
$100$		0			0
$101$	84.3492	−	146.097i	0.835140	−	1.44651i	−0.0587756	−	0.998271i	$-0.518720\pi$
$101$	84.3492	−	146.097i	0.835140	−	1.44651i	0.893916	−	0.448234i	$-0.147947\pi$
$102$		0			0
$103$		−	137.387i		−	1.33386i	−0.745121	−	0.666929i	$-0.767608\pi$
$103$		−	137.387i		−	1.33386i	0.745121	−	0.666929i	$-0.232392\pi$
$104$		0			0
$105$	−8.24815	−	4.76207i	−0.0785538	−	0.0453531i
$106$		0			0
$107$			78.9509i			0.737859i	0.929457	+	0.368930i	$0.120276\pi$
$107$			78.9509i			0.737859i	−0.929457	+	0.368930i	$0.879724\pi$
$108$		0			0
$109$	−45.8176	+	26.4528i	−0.420345	+	0.242686i	−0.695225	−	0.718792i	$-0.744695\pi$
$109$	−45.8176	+	26.4528i	−0.420345	+	0.242686i	0.274880	+	0.961479i	$0.411362\pi$
$110$		0			0
$111$	−11.3256	−	19.6165i	−0.102032	−	0.176725i
$112$		0			0
$113$			121.938i			1.07910i	0.841955	+	0.539548i	$0.181405\pi$
$113$			121.938i			1.07910i	−0.841955	+	0.539548i	$0.818595\pi$
$114$		0			0
$115$	−196.063			−1.70490
$116$		0			0
$117$	34.0628	−	19.6662i	0.291135	−	0.168087i
$118$		0			0
$119$	−4.20469	−	7.28274i	−0.0353335	−	0.0611995i
$120$		0			0
$121$	101.573			0.839444
$122$		0			0
$123$	−46.1794	+	79.9850i	−0.375442	+	0.650285i
$124$		0			0
$125$	18.3969			0.147175
$126$		0			0
$127$	67.2677	+	38.8370i	0.529667	+	0.305803i	0.740881	−	0.671636i	$-0.234408\pi$
$127$	67.2677	+	38.8370i	0.529667	+	0.305803i	−0.211214	+	0.977440i	$0.567742\pi$
$128$		0			0
$129$	−109.365	−	63.1417i	−0.847787	−	0.489470i
$130$		0			0
$131$	34.7058	+	60.1121i	0.264929	+	0.458871i	0.967545	−	0.252698i	$-0.0813180\pi$
$131$	34.7058	+	60.1121i	0.264929	+	0.458871i	−0.702616	+	0.711570i	$0.747985\pi$
$132$		0			0
$133$	−9.63069	−	10.7243i	−0.0724112	−	0.0806338i
$134$		0			0
$135$	−32.6174	+	18.8317i	−0.241611	+	0.139494i
$136$		0			0
$137$	41.7089	−	72.2419i	0.304445	−	0.527313i	−0.672693	−	0.739922i	$-0.734863\pi$
$137$	41.7089	−	72.2419i	0.304445	−	0.527313i	0.977138	+	0.212608i	$0.0681958\pi$
$138$		0			0
$139$	45.2514	−	78.3777i	0.325549	−	0.563868i	−0.656074	−	0.754697i	$-0.727784\pi$
$139$	45.2514	−	78.3777i	0.325549	−	0.563868i	0.981623	+	0.190828i	$0.0611174\pi$
$140$		0			0
$141$		−	119.805i		−	0.849680i
$142$		0			0
$143$	169.393	+	97.7990i	1.18457	+	0.683909i
$144$		0			0
$145$		−	385.351i		−	2.65759i
$146$		0			0
$147$	−72.6367	+	41.9368i	−0.494127	+	0.285285i
$148$		0			0
$149$	−47.1071	−	81.5919i	−0.316155	−	0.547597i	0.663527	−	0.748152i	$-0.269059\pi$
$149$	−47.1071	−	81.5919i	−0.316155	−	0.547597i	−0.979682	+	0.200555i	$0.935725\pi$
$150$		0			0
$151$		−	17.6258i		−	0.116727i	−0.998295	−	0.0583637i	$-0.981412\pi$
$151$		−	17.6258i		−	0.116727i	0.998295	−	0.0583637i	$-0.0185883\pi$
$152$		0			0
$153$	−33.2550			−0.217353
$154$		0			0
$155$	19.8170	−	11.4414i	0.127852	−	0.0738152i
$156$		0			0
$157$	49.4004	+	85.5640i	0.314652	+	0.544994i	0.979364	−	0.202107i	$-0.0647788\pi$
$157$	49.4004	+	85.5640i	0.314652	+	0.544994i	−0.664711	+	0.747100i	$0.731445\pi$
$158$		0			0
$159$	−90.4797			−0.569055
$160$		0			0
$161$	10.2602	−	17.7712i	0.0637281	−	0.110380i
$162$		0			0
$163$	195.798			1.20122			0.600608	−	0.799544i	$-0.294925\pi$
$163$	195.798			1.20122			0.600608	+	0.799544i	$0.294925\pi$
$164$		0			0
$165$	−162.205	−	93.6491i	−0.983061	−	0.567570i
$166$		0			0
$167$	128.377	+	74.1183i	0.768723	+	0.443822i	0.832419	−	0.554147i	$-0.186955\pi$
$167$	128.377	+	74.1183i	0.768723	+	0.443822i	−0.0636959	+	0.997969i	$0.520289\pi$
$168$		0			0
$169$	1.44626	+	2.50499i	0.00855773	+	0.0148224i
$170$		0			0
$171$	−55.7700	+	11.7776i	−0.326140	+	0.0688749i
$172$		0			0
$173$	−86.9398	+	50.1947i	−0.502542	+	0.290143i	−0.729763	−	0.683700i	$-0.760370\pi$
$173$	−86.9398	+	50.1947i	−0.502542	+	0.290143i	0.227220	+	0.973843i	$0.427036\pi$
$174$		0			0
$175$	−10.4456	+	18.0923i	−0.0596890	+	0.103384i
$176$		0			0
$177$	−74.2621	+	128.626i	−0.419560	+	0.726699i
$178$		0			0
$179$		−	49.9107i		−	0.278831i	−0.990234	−	0.139415i	$-0.955478\pi$
$179$		−	49.9107i		−	0.278831i	0.990234	−	0.139415i	$-0.0445223\pi$
$180$		0			0
$181$	280.566	+	161.985i	1.55009	+	0.894944i	0.998134	+	0.0610696i	$0.0194512\pi$
$181$	280.566	+	161.985i	1.55009	+	0.894944i	0.551955	+	0.833874i	$0.313882\pi$
$182$		0			0
$183$			110.667i			0.604736i
$184$		0			0
$185$	−82.0914	+	47.3955i	−0.443737	+	0.256192i
$186$		0			0
$187$	−82.6879	−	143.220i	−0.442181	−	0.765880i
$188$		0			0
$189$		−	3.94194i		−	0.0208568i
$190$		0			0
$191$	183.415			0.960288			0.480144	−	0.877190i	$-0.340584\pi$
$191$	183.415			0.960288			0.480144	+	0.877190i	$0.340584\pi$
$192$		0			0
$193$	−138.682	+	80.0678i	−0.718557	+	0.414859i	−0.814221	−	0.580554i	$-0.802836\pi$
$193$	−138.682	+	80.0678i	−0.718557	+	0.414859i	0.0956641	+	0.995414i	$0.469503\pi$
$194$		0			0
$195$	−82.2993	−	142.547i	−0.422048	−	0.731008i
$196$		0			0
$197$	21.9594			0.111469			0.0557345	−	0.998446i	$-0.482250\pi$
$197$	21.9594			0.111469			0.0557345	+	0.998446i	$0.482250\pi$
$198$		0			0
$199$	−101.025	+	174.980i	−0.507661	+	0.879295i	0.492300	+	0.870426i	$0.336156\pi$
$199$	−101.025	+	174.980i	−0.507661	+	0.879295i	−0.999961	+	0.00886891i	$0.997177\pi$
$200$		0			0
$201$	−19.8796			−0.0989033
$202$		0			0
$203$	34.9284	+	20.1659i	0.172061	+	0.0993394i
$204$		0			0
$205$	334.723	+	193.252i	1.63279	+	0.942694i
$206$		0			0
$207$	−40.5742	−	70.2766i	−0.196011	−	0.339500i
$208$		0			0
$209$	−189.394	−	210.900i	−0.906189	−	1.00909i
$210$		0			0
$211$	136.069	−	78.5593i	0.644875	−	0.372319i	−0.141615	−	0.989922i	$-0.545229\pi$
$211$	136.069	−	78.5593i	0.644875	−	0.372319i	0.786490	+	0.617603i	$0.211896\pi$
$212$		0			0
$213$	95.5318	−	165.466i	0.448506	−	0.776835i
$214$		0			0
$215$	−264.236	+	457.671i	−1.22901	+	2.12870i
$216$		0			0
$217$			2.39496i			0.0110367i
$218$		0			0
$219$	−61.6936	−	35.6188i	−0.281706	−	0.162643i
$220$		0			0
$221$		−	145.333i		−	0.657616i
$222$		0			0
$223$	92.6527	−	53.4931i	0.415483	−	0.239879i	−0.277660	−	0.960679i	$-0.589559\pi$
$223$	92.6527	−	53.4931i	0.415483	−	0.239879i	0.693143	+	0.720800i	$0.256225\pi$
$224$		0			0
$225$	41.3071	+	71.5461i	0.183587	+	0.317983i
$226$		0			0
$227$			26.3993i			0.116296i	0.998308	+	0.0581482i	$0.0185196\pi$
$227$			26.3993i			0.116296i	−0.998308	+	0.0581482i	$0.981480\pi$
$228$		0			0
$229$	−236.493			−1.03272			−0.516361	−	0.856371i	$-0.672714\pi$
$229$	−236.493			−1.03272			−0.516361	+	0.856371i	$0.672714\pi$
$230$		0			0
$231$	16.9768	−	9.80155i	0.0734926	−	0.0424310i
$232$		0			0
$233$	158.465	+	274.469i	0.680107	+	1.17798i	0.974948	+	0.222433i	$0.0714000\pi$
$233$	158.465	+	274.469i	0.680107	+	1.17798i	−0.294841	+	0.955546i	$0.595267\pi$
$234$		0			0
$235$	−501.362			−2.13345
$236$		0			0
$237$	−28.6077	+	49.5500i	−0.120708	+	0.209072i
$238$		0			0
$239$	129.902			0.543522			0.271761	−	0.962365i	$-0.412394\pi$
$239$	129.902			0.543522			0.271761	+	0.962365i	$0.412394\pi$
$240$		0			0
$241$	−220.332	−	127.209i	−0.914240	−	0.527837i	−0.0324471	−	0.999473i	$-0.510330\pi$
$241$	−220.332	−	127.209i	−0.914240	−	0.527837i	−0.881793	+	0.471637i	$0.843663\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	175.498	+	303.971i	0.716318	+	1.24070i
$246$		0			0
$247$	−51.4712	−	243.729i	−0.208386	−	0.986758i
$248$		0			0
$249$	−93.7911	+	54.1503i	−0.376671	+	0.217471i
$250$		0			0
$251$	127.898	−	221.525i	0.509552	−	0.882570i	−0.490387	−	0.871505i	$-0.663145\pi$
$251$	127.898	−	221.525i	0.509552	−	0.882570i	0.999939	−	0.0110650i	$-0.00352216\pi$
$252$		0			0
$253$	201.774	−	349.482i	0.797525	−	1.38135i
$254$		0			0
$255$			139.166i			0.545750i
$256$		0			0
$257$	115.452	+	66.6562i	0.449229	+	0.259363i	0.707505	−	0.706709i	$-0.249821\pi$
$257$	115.452	+	66.6562i	0.449229	+	0.259363i	−0.258275	+	0.966071i	$0.583154\pi$
$258$		0			0
$259$		−	9.92106i		−	0.0383052i
$260$		0			0
$261$	138.125	−	79.7463i	0.529213	−	0.305542i
$262$		0			0
$263$	−69.0463	−	119.592i	−0.262534	−	0.454721i	0.704381	−	0.709822i	$-0.251225\pi$
$263$	−69.0463	−	119.592i	−0.262534	−	0.454721i	−0.966914	+	0.255101i	$0.917891\pi$
$264$		0			0
$265$			378.641i			1.42883i
$266$		0			0
$267$	180.287			0.675233
$268$		0			0
$269$	−326.589	+	188.556i	−1.21408	+	0.700952i	−0.963646	−	0.267181i	$-0.913908\pi$
$269$	−326.589	+	188.556i	−1.21408	+	0.700952i	−0.250438	+	0.968133i	$0.580575\pi$
$270$		0			0
$271$	−68.7341	−	119.051i	−0.253632	−	0.439303i	0.710891	−	0.703302i	$-0.248292\pi$
$271$	−68.7341	−	119.051i	−0.253632	−	0.439303i	−0.964523	+	0.263999i	$0.914958\pi$
$272$		0			0
$273$	17.2273			0.0631037
$274$		0			0
$275$	−205.419	+	355.796i	−0.746977	+	1.29380i
$276$		0			0
$277$	−390.819			−1.41090			−0.705449	−	0.708761i	$-0.749254\pi$
$277$	−390.819			−1.41090			−0.705449	+	0.708761i	$0.749254\pi$
$278$		0			0
$279$	8.20205	+	4.73546i	0.0293980	+	0.0169730i
$280$		0			0
$281$	315.805	+	182.330i	1.12386	+	0.648862i	0.942384	−	0.334533i	$-0.108579\pi$
$281$	315.805	+	182.330i	1.12386	+	0.648862i	0.181478	+	0.983395i	$0.441912\pi$
$282$		0			0
$283$	−17.7513	−	30.7462i	−0.0627255	−	0.108644i	0.832957	−	0.553337i	$-0.186646\pi$
$283$	−17.7513	−	30.7462i	−0.0627255	−	0.108644i	−0.895683	+	0.444694i	$0.853313\pi$
$284$		0			0
$285$	49.2872	+	233.387i	0.172937	+	0.818902i
$286$		0			0
$287$	−35.0329	+	20.2263i	−0.122066	+	0.0704748i
$288$		0			0
$289$	83.0613	−	143.866i	0.287409	−	0.497808i
$290$		0			0
$291$	58.1738	−	100.760i	0.199910	−	0.346254i
$292$		0			0
$293$			361.441i			1.23359i	0.787125	+	0.616793i	$0.211569\pi$
$293$			361.441i			1.23359i	−0.787125	+	0.616793i	$0.788431\pi$
$294$		0			0
$295$	538.275	+	310.773i	1.82466	+	1.05347i
$296$		0			0
$297$		−	77.5207i		−	0.261013i
$298$		0			0
$299$	307.127	−	177.320i	1.02718	−	0.593043i
$300$		0			0
$301$	−27.6556	−	47.9010i	−0.0918792	−	0.159139i
$302$		0			0
$303$		−	292.194i		−	0.964337i
$304$		0			0
$305$	463.120			1.51843
$306$		0			0
$307$	−168.160	+	97.0872i	−0.547752	+	0.316245i	−0.748215	−	0.663456i	$-0.769089\pi$
$307$	−168.160	+	97.0872i	−0.547752	+	0.316245i	0.200463	+	0.979701i	$0.435755\pi$
$308$		0			0
$309$	−118.981	−	206.081i	−0.385052	−	0.666929i
$310$		0			0
$311$	551.466			1.77320			0.886601	−	0.462535i	$-0.153060\pi$
$311$	551.466			1.77320			0.886601	+	0.462535i	$0.153060\pi$
$312$		0			0
$313$	−85.7856	+	148.585i	−0.274075	+	0.474713i	−0.969901	−	0.243498i	$-0.921705\pi$
$313$	−85.7856	+	148.585i	−0.274075	+	0.474713i	0.695826	+	0.718210i	$0.255038\pi$
$314$		0			0
$315$	−16.4963			−0.0523692
$316$		0			0
$317$	468.637	+	270.568i	1.47835	+	0.853526i	0.999700	−	0.0244796i	$-0.00779288\pi$
$317$	468.637	+	270.568i	1.47835	+	0.853526i	0.478650	+	0.878006i	$0.341126\pi$
$318$		0			0
$319$	686.888	+	396.575i	2.15325	+	1.24318i
$320$		0			0
$321$	68.3735	+	118.426i	0.213002	+	0.368930i
$322$		0			0
$323$	−65.3471	+	200.221i	−0.202313	+	0.619880i
$324$		0			0
$325$	−312.675	+	180.523i	−0.962077	+	0.555455i
$326$		0			0
$327$	−45.8176	+	79.3585i	−0.140115	+	0.242686i
$328$		0			0
$329$	26.2369	−	45.4436i	0.0797474	−	0.138126i
$330$		0			0
$331$			367.637i			1.11069i	0.831621	+	0.555343i	$0.187413\pi$
$331$			367.637i			1.11069i	−0.831621	+	0.555343i	$0.812587\pi$
$332$		0			0
$333$	−33.9767	−	19.6165i	−0.102032	−	0.0589083i
$334$		0			0
$335$			83.1923i			0.248335i
$336$		0			0
$337$	150.652	−	86.9788i	0.447038	−	0.258097i	−0.259541	−	0.965732i	$-0.583571\pi$
$337$	150.652	−	86.9788i	0.447038	−	0.258097i	0.706578	+	0.707635i	$0.250238\pi$
$338$		0			0
$339$	105.601	+	182.907i	0.311508	+	0.539548i
$340$		0			0
$341$			47.0984i			0.138119i
$342$		0			0
$343$	−73.9088			−0.215478
$344$		0			0
$345$	−294.095	+	169.796i	−0.852448	+	0.492161i
$346$		0			0
$347$	−314.074	−	543.993i	−0.905113	−	1.56770i	−0.820765	−	0.571266i	$-0.806453\pi$
$347$	−314.074	−	543.993i	−0.905113	−	1.56770i	−0.0843479	−	0.996436i	$-0.526881\pi$
$348$		0			0
$349$	−229.618			−0.657931			−0.328966	−	0.944342i	$-0.606700\pi$
$349$	−229.618			−0.657931			−0.328966	+	0.944342i	$0.606700\pi$
$350$		0			0
$351$	34.0628	−	58.9985i	0.0970450	−	0.168087i
$352$		0			0
$353$	610.268			1.72881			0.864403	−	0.502800i	$-0.167697\pi$
$353$	610.268			1.72881			0.864403	+	0.502800i	$0.167697\pi$
$354$		0			0
$355$	−692.445	−	399.783i	−1.95055	−	1.12615i
$356$		0			0
$357$	−12.6141	−	7.28274i	−0.0353335	−	0.0203998i
$358$		0			0
$359$	206.043	+	356.876i	0.573935	+	0.994085i	0.996156	+	0.0875919i	$0.0279171\pi$
$359$	206.043	+	356.876i	0.573935	+	0.994085i	−0.422221	+	0.906493i	$0.638750\pi$
$360$		0			0
$361$	−38.6792	+	358.922i	−0.107145	+	0.994243i
$362$		0			0
$363$	152.359	−	87.9645i	0.419722	−	0.242327i
$364$		0			0
$365$	−149.058	+	258.177i	−0.408379	+	0.707333i
$366$		0			0
$367$	160.898	−	278.683i	0.438413	−	0.759354i	−0.559154	−	0.829064i	$-0.688874\pi$
$367$	160.898	−	278.683i	0.438413	−	0.759354i	0.997567	+	0.0697097i	$0.0222073\pi$
$368$		0			0
$369$			159.970i			0.433523i
$370$		0			0
$371$	−34.3202	−	19.8148i	−0.0925072	−	0.0534091i
$372$		0			0
$373$			18.9450i			0.0507910i	0.999677	+	0.0253955i	$0.00808450\pi$
$373$			18.9450i			0.0507910i	−0.999677	+	0.0253955i	$0.991915\pi$
$374$		0			0
$375$	27.5954	−	15.9322i	0.0735877	−	0.0424859i
$376$		0			0
$377$	348.512	+	603.641i	0.924436	+	1.60117i
$378$		0			0
$379$			300.409i			0.792636i	0.918113	+	0.396318i	$0.129712\pi$
$379$			300.409i			0.792636i	−0.918113	+	0.396318i	$0.870288\pi$
$380$		0			0
$381$	134.535			0.353111
$382$		0			0
$383$	378.682	−	218.632i	0.988726	−	0.570841i	0.0838330	−	0.996480i	$-0.473284\pi$
$383$	378.682	−	218.632i	0.988726	−	0.570841i	0.904893	+	0.425638i	$0.139950\pi$
$384$		0			0
$385$	−41.0177	−	71.0447i	−0.106539	−	0.184532i
$386$		0			0
$387$	−218.729			−0.565192
$388$		0			0
$389$	159.849	−	276.867i	0.410923	−	0.711740i	−0.584068	−	0.811705i	$-0.698540\pi$
$389$	159.849	−	276.867i	0.410923	−	0.711740i	0.994991	+	0.0999649i	$0.0318731\pi$
$390$		0			0
$391$	−299.844			−0.766863
$392$		0			0
$393$	104.117	+	60.1121i	0.264929	+	0.152957i
$394$		0			0
$395$	207.358	+	119.718i	0.524957	+	0.303084i
$396$		0			0
$397$	208.513	+	361.156i	0.525223	+	0.909713i	0.999568	+	0.0293740i	$0.00935139\pi$
$397$	208.513	+	361.156i	0.525223	+	0.909713i	−0.474346	+	0.880339i	$0.657315\pi$
$398$		0			0
$399$	−23.7336	−	7.74603i	−0.0594826	−	0.0194136i
$400$		0			0
$401$	−491.597	+	283.824i	−1.22593	+	0.707790i	−0.966176	−	0.257885i	$-0.916974\pi$
$401$	−491.597	+	283.824i	−1.22593	+	0.707790i	−0.259752	+	0.965675i	$0.583641\pi$
$402$		0			0
$403$	−20.6952	+	35.8451i	−0.0513528	+	0.0889456i
$404$		0			0
$405$	−32.6174	+	56.4950i	−0.0805369	+	0.139494i
$406$		0			0
$407$		−	195.104i		−	0.479370i
$408$		0			0
$409$	−456.222	−	263.400i	−1.11546	−	0.644009i	−0.175219	−	0.984529i	$-0.556063\pi$
$409$	−456.222	−	263.400i	−1.11546	−	0.644009i	−0.940237	+	0.340520i	$0.889397\pi$
$410$		0			0
$411$		−	144.484i		−	0.351542i
$412$		0			0
$413$	−56.3372	+	32.5263i	−0.136410	+	0.0787562i
$414$		0			0
$415$	226.609	+	392.499i	0.546046	+	0.945780i
$416$		0			0
$417$		−	156.755i		−	0.375912i
$418$		0			0
$419$	153.284			0.365832			0.182916	−	0.983129i	$-0.441446\pi$
$419$	153.284			0.365832			0.182916	+	0.983129i	$0.441446\pi$
$420$		0			0
$421$	−416.944	+	240.723i	−0.990366	+	0.571788i	−0.905384	−	0.424594i	$-0.860417\pi$
$421$	−416.944	+	240.723i	−0.990366	+	0.571788i	−0.0849823	+	0.996382i	$0.527083\pi$
$422$		0			0
$423$	−103.754	−	179.707i	−0.245282	−	0.424840i
$424$		0			0
$425$	305.260			0.718259
$426$		0			0
$427$	−24.2356	+	41.9773i	−0.0567579	+	0.0983076i
$428$		0			0
$429$	338.786			0.789710
$430$		0			0
$431$	−442.352	−	255.392i	−1.02634	−	0.592557i	−0.110405	−	0.993887i	$-0.535215\pi$
$431$	−442.352	−	255.392i	−1.02634	−	0.592557i	−0.915933	+	0.401330i	$0.868548\pi$
$432$		0			0
$433$	−172.028	−	99.3206i	−0.397294	−	0.229378i	0.288022	−	0.957624i	$-0.407002\pi$
$433$	−172.028	−	99.3206i	−0.397294	−	0.229378i	−0.685316	+	0.728246i	$0.740336\pi$
$434$		0			0
$435$	−333.724	−	578.027i	−0.767181	−	1.32880i
$436$		0			0
$437$	−502.849	+	106.193i	−1.15068	+	0.243004i
$438$		0			0
$439$	−323.049	+	186.513i	−0.735875	+	0.424858i	−0.820568	−	0.571549i	$-0.806343\pi$
$439$	−323.049	+	186.513i	−0.735875	+	0.424858i	0.0846924	+	0.996407i	$0.473009\pi$
$440$		0			0
$441$	−72.6367	+	125.811i	−0.164709	+	0.285285i
$442$		0			0
$443$	−177.651	+	307.700i	−0.401017	+	0.694583i	−0.993849	−	0.110744i	$-0.964677\pi$
$443$	−177.651	+	307.700i	−0.401017	+	0.694583i	0.592832	+	0.805326i	$0.298010\pi$
$444$		0			0
$445$		−	754.469i		−	1.69544i
$446$		0			0
$447$	−141.321	−	81.5919i	−0.316155	−	0.182532i
$448$		0			0
$449$		−	430.528i		−	0.958859i	−0.877580	−	0.479429i	$-0.840844\pi$
$449$		−	430.528i		−	0.958859i	0.877580	−	0.479429i	$-0.159156\pi$
$450$		0			0
$451$	−688.944	+	397.762i	−1.52759	+	0.881956i
$452$		0			0
$453$	−15.2644	−	26.4388i	−0.0336963	−	0.0583637i
$454$		0			0
$455$		−	72.0931i		−	0.158446i
$456$		0			0
$457$	865.465			1.89380			0.946898	−	0.321533i	$-0.104198\pi$
$457$	865.465			1.89380			0.946898	+	0.321533i	$0.104198\pi$
$458$		0			0
$459$	−49.8825	+	28.7997i	−0.108677	+	0.0627444i
$460$		0			0
$461$	−312.309	−	540.934i	−0.677459	−	1.17339i	−0.975744	−	0.218916i	$-0.929748\pi$
$461$	−312.309	−	540.934i	−0.677459	−	1.17339i	0.298285	−	0.954477i	$-0.403586\pi$
$462$		0			0
$463$	340.873			0.736227			0.368114	−	0.929781i	$-0.380004\pi$
$463$	340.873			0.736227			0.368114	+	0.929781i	$0.380004\pi$
$464$		0			0
$465$	19.8170	−	34.3241i	0.0426172	−	0.0738152i
$466$		0			0
$467$	−269.969			−0.578092			−0.289046	−	0.957315i	$-0.593338\pi$
$467$	−269.969			−0.578092			−0.289046	+	0.957315i	$0.593338\pi$
$468$		0			0
$469$	−7.54058	−	4.35356i	−0.0160780	−	0.00928264i
$470$		0			0
$471$	148.201	+	85.5640i	0.314652	+	0.181665i
$472$		0			0
$473$	−543.865	−	942.002i	−1.14982	−	1.99155i
$474$		0			0
$475$	511.933	−	108.111i	1.07775	−	0.227602i
$476$		0			0
$477$	−135.720	+	78.3577i	−0.284527	+	0.164272i
$478$		0			0
$479$	422.492	−	731.777i	0.882028	−	1.52772i	0.0329464	−	0.999457i	$-0.489511\pi$
$479$	422.492	−	731.777i	0.882028	−	1.52772i	0.849082	−	0.528261i	$-0.177156\pi$
$480$		0			0
$481$	85.7291	−	148.487i	0.178231	−	0.308705i
$482$		0			0
$483$		−	35.5425i		−	0.0735869i
$484$		0			0
$485$	−421.662	−	243.447i	−0.869407	−	0.501952i
$486$		0			0
$487$			453.462i			0.931134i	0.885013	+	0.465567i	$0.154150\pi$
$487$			453.462i			0.931134i	−0.885013	+	0.465567i	$0.845850\pi$
$488$		0			0
$489$	293.697	−	169.566i	0.600608	−	0.346761i
$490$		0			0
$491$	417.201	+	722.613i	0.849696	+	1.47172i	0.881480	+	0.472222i	$0.156548\pi$
$491$	417.201	+	722.613i	0.849696	+	1.47172i	−0.0317836	+	0.999495i	$0.510119\pi$
$492$		0			0
$493$		−	589.326i		−	1.19539i
$494$		0			0
$495$	−324.410			−0.655374
$496$		0			0
$497$	72.4730	−	41.8423i	0.145821	−	0.0841897i
$498$		0			0
$499$	230.228	+	398.767i	0.461379	+	0.799132i	0.999030	−	0.0440354i	$-0.0140214\pi$
$499$	230.228	+	398.767i	0.461379	+	0.799132i	−0.537651	+	0.843168i	$0.680688\pi$
$500$		0			0
$501$	256.753			0.512482
$502$		0			0
$503$	−156.554	+	271.160i	−0.311241	+	0.539085i	−0.978631	−	0.205623i	$-0.934078\pi$
$503$	−156.554	+	271.160i	−0.311241	+	0.539085i	0.667390	+	0.744708i	$0.267411\pi$
$504$		0			0
$505$	−1222.78			−2.42134
$506$		0			0
$507$	4.33877	+	2.50499i	0.00855773	+	0.00494081i
$508$		0			0
$509$	437.303	+	252.477i	0.859141	+	0.496025i	0.863725	−	0.503964i	$-0.168126\pi$
$509$	437.303	+	252.477i	0.859141	+	0.496025i	−0.00458350	+	0.999989i	$0.501459\pi$
$510$		0			0
$511$	−15.6008	−	27.0214i	−0.0305300	−	0.0528795i
$512$		0			0
$513$	−73.4552	+	65.9646i	−0.143188	+	0.128586i
$514$		0			0
$515$	−862.411	+	497.914i	−1.67459	+	0.966822i
$516$		0			0
$517$	515.965	−	893.677i	0.997997	−	1.72858i
$518$		0			0
$519$	−86.9398	+	150.584i	−0.167514	+	0.290143i
$520$		0			0
$521$			875.937i			1.68126i	0.541610	+	0.840630i	$0.317815\pi$
$521$			875.937i			1.68126i	−0.541610	+	0.840630i	$0.682185\pi$
$522$		0			0
$523$	44.8796	+	25.9113i	0.0858119	+	0.0495435i	0.542292	−	0.840190i	$-0.317557\pi$
$523$	44.8796	+	25.9113i	0.0858119	+	0.0495435i	−0.456480	+	0.889734i	$0.650890\pi$
$524$		0			0
$525$			36.1845i			0.0689229i
$526$		0			0
$527$	30.3066	−	17.4975i	0.0575078	−	0.0332021i
$528$		0			0
$529$	−101.337	−	175.521i	−0.191563	−	0.331797i
$530$		0			0
$531$			257.251i			0.484466i
$532$		0			0
$533$	−699.111			−1.31165
$534$		0			0
$535$	495.593	−	286.131i	0.926342	−	0.534824i
$536$		0			0
$537$	−43.2240	−	74.8661i	−0.0804916	−	0.139415i
$538$		0			0
$539$	−722.439			−1.34033
$540$		0			0
$541$	279.493	−	484.096i	0.516623	−	0.894818i	−0.483191	−	0.875515i	$-0.660522\pi$
$541$	279.493	−	484.096i	0.516623	−	0.894818i	0.999814	−	0.0193023i	$-0.00614451\pi$
$542$		0			0
$543$	561.132			1.03339
$544$		0			0
$545$	332.101	+	191.738i	0.609359	+	0.351814i
$546$		0			0
$547$	583.965	+	337.152i	1.06758	+	0.616366i	0.927518	−	0.373777i	$-0.121938\pi$
$547$	583.965	+	337.152i	1.06758	+	0.616366i	0.140059	+	0.990143i	$0.455271\pi$
$548$		0			0
$549$	95.8401	+	166.000i	0.174572	+	0.302368i
$550$		0			0
$551$	−208.716	−	988.322i	−0.378795	−	1.79369i
$552$		0			0
$553$	−21.7026	+	12.5300i	−0.0392452	+	0.0226582i
$554$		0			0
$555$	−82.0914	+	142.186i	−0.147912	+	0.256192i
$556$		0			0
$557$	−71.2198	+	123.356i	−0.127863	+	0.221465i	−0.922848	−	0.385163i	$-0.874145\pi$
$557$	−71.2198	+	123.356i	−0.127863	+	0.221465i	0.794985	+	0.606629i	$0.207478\pi$
$558$		0			0
$559$		−	955.903i		−	1.71002i
$560$		0			0
$561$	−248.064	−	143.220i	−0.442181	−	0.255293i
$562$		0			0
$563$		−	364.262i		−	0.647001i	−0.946228	−	0.323501i	$-0.895140\pi$
$563$		−	364.262i		−	0.647001i	0.946228	−	0.323501i	$-0.104860\pi$
$564$		0			0
$565$	765.432	−	441.922i	1.35475	−	0.782164i
$566$		0			0
$567$	−3.41382	−	5.91291i	−0.00602085	−	0.0104284i
$568$		0			0
$569$		−	980.551i		−	1.72329i	−0.507513	−	0.861644i	$-0.669435\pi$
$569$		−	980.551i		−	1.72329i	0.507513	−	0.861644i	$-0.330565\pi$
$570$		0			0
$571$	−424.679			−0.743746			−0.371873	−	0.928284i	$-0.621284\pi$
$571$	−424.679			−0.743746			−0.371873	+	0.928284i	$0.621284\pi$
$572$		0			0
$573$	275.122	−	158.842i	0.480144	−	0.277211i
$574$		0			0
$575$	372.445	+	645.094i	0.647731	+	1.12190i
$576$		0			0
$577$	463.717			0.803669			0.401835	−	0.915712i	$-0.368373\pi$
$577$	463.717			0.803669			0.401835	+	0.915712i	$0.368373\pi$
$578$		0			0
$579$	−138.682	+	240.204i	−0.239519	+	0.414859i
$580$		0			0
$581$	−47.4350			−0.0816437
$582$		0			0
$583$	−674.928	−	389.670i	−1.15768	−	0.668387i
$584$		0			0
$585$	−246.898	−	142.547i	−0.422048	−	0.243669i
$586$		0			0
$587$	−399.893	−	692.635i	−0.681249	−	1.17996i	−0.974600	−	0.223953i	$-0.928104\pi$
$587$	−399.893	−	692.635i	−0.681249	−	1.17996i	0.293351	−	0.956005i	$-0.405230\pi$
$588$		0			0
$589$	44.6284	−	40.0774i	0.0757698	−	0.0680432i
$590$		0			0
$591$	32.9391	−	19.0174i	0.0557345	−	0.0321784i
$592$		0			0
$593$	−4.68634	+	8.11698i	−0.00790276	+	0.0136880i	−0.869950	−	0.493140i	$-0.835849\pi$
$593$	−4.68634	+	8.11698i	−0.00790276	+	0.0136880i	0.862047	+	0.506828i	$0.169182\pi$
$594$		0			0
$595$	−30.4769	+	52.7876i	−0.0512218	+	0.0887187i
$596$		0			0
$597$			349.959i			0.586196i
$598$		0			0
$599$	577.466	+	333.400i	0.964050	+	0.556595i	0.897417	−	0.441183i	$-0.145441\pi$
$599$	577.466	+	333.400i	0.964050	+	0.556595i	0.0666330	+	0.997778i	$0.478774\pi$
$600$		0			0
$601$		−	411.529i		−	0.684741i	−0.939565	−	0.342370i	$-0.888770\pi$
$601$		−	411.529i		−	0.684741i	0.939565	−	0.342370i	$-0.111230\pi$
$602$		0			0
$603$	−29.8193	+	17.2162i	−0.0494516	+	0.0285509i
$604$		0			0
$605$	−368.116	−	637.595i	−0.608456	−	1.05388i
$606$		0			0
$607$			824.043i			1.35757i	0.734338	+	0.678784i	$0.237493\pi$
$607$			824.043i			1.35757i	−0.734338	+	0.678784i	$0.762507\pi$
$608$		0			0
$609$	69.8567			0.114707
$610$		0			0
$611$	785.368	−	453.432i	1.28538	−	0.742115i
$612$		0			0
$613$	38.5035	+	66.6901i	0.0628116	+	0.108793i	0.895721	−	0.444616i	$-0.146660\pi$
$613$	38.5035	+	66.6901i	0.0628116	+	0.108793i	−0.832910	+	0.553409i	$0.813327\pi$
$614$		0			0
$615$	669.446			1.08853
$616$		0			0
$617$	431.616	−	747.581i	0.699540	−	1.21164i	−0.269087	−	0.963116i	$-0.586722\pi$
$617$	431.616	−	747.581i	0.699540	−	1.21164i	0.968626	−	0.248522i	$-0.0799449\pi$
$618$		0			0
$619$	−841.177			−1.35893			−0.679465	−	0.733708i	$-0.737788\pi$
$619$	−841.177			−1.35893			−0.679465	+	0.733708i	$0.737788\pi$
$620$		0			0
$621$	−121.723	−	70.2766i	−0.196011	−	0.113167i
$622$		0			0
$623$	68.3853	+	39.4823i	0.109768	+	0.0633745i
$624$		0			0
$625$	277.553	+	480.736i	0.444085	+	0.769177i
$626$		0			0
$627$	−466.735	−	152.330i	−0.744394	−	0.242951i
$628$		0			0
$629$	−125.544	+	72.4829i	−0.199593	+	0.115235i
$630$		0			0
$631$	57.3026	−	99.2510i	0.0908124	−	0.157292i	−0.817041	−	0.576580i	$-0.804387\pi$
$631$	57.3026	−	99.2510i	0.0908124	−	0.157292i	0.907853	+	0.419288i	$0.137720\pi$
$632$		0			0
$633$	136.069	−	235.678i	0.214958	−	0.372319i
$634$		0			0
$635$		−	563.006i		−	0.886624i
$636$		0			0
$637$	−549.825	−	317.441i	−0.863147	−	0.498338i
$638$		0			0
$639$		−	330.932i		−	0.517890i
$640$		0			0
$641$	603.188	−	348.251i	0.941011	−	0.543293i	0.0507337	−	0.998712i	$-0.483844\pi$
$641$	603.188	−	348.251i	0.941011	−	0.543293i	0.890277	+	0.455419i	$0.150511\pi$
$642$		0			0
$643$	127.186	+	220.293i	0.197802	+	0.342602i	0.947815	−	0.318820i	$-0.103287\pi$
$643$	127.186	+	220.293i	0.197802	+	0.342602i	−0.750014	+	0.661422i	$0.769953\pi$
$644$		0			0
$645$			915.342i			1.41913i
$646$		0			0
$647$	−293.312			−0.453342			−0.226671	−	0.973971i	$-0.572784\pi$
$647$	−293.312			−0.453342			−0.226671	+	0.973971i	$0.572784\pi$
$648$		0			0
$649$	−1107.91	+	639.650i	−1.70710	+	0.985594i
$650$		0			0
$651$	2.07410	+	3.59244i	0.00318602	+	0.00551835i
$652$		0			0
$653$	836.036			1.28030			0.640150	−	0.768250i	$-0.278872\pi$
$653$	836.036			1.28030			0.640150	+	0.768250i	$0.278872\pi$
$654$		0			0
$655$	251.558	−	435.712i	0.384059	−	0.665209i
$656$		0			0
$657$	−123.387			−0.187804
$658$		0			0
$659$	−706.747	−	408.041i	−1.07245	−	0.619182i	−0.143603	−	0.989635i	$-0.545869\pi$
$659$	−706.747	−	408.041i	−1.07245	−	0.619182i	−0.928851	+	0.370454i	$0.879202\pi$
$660$		0			0
$661$	663.013	+	382.791i	1.00305	+	0.579108i	0.909148	−	0.416474i	$-0.136734\pi$
$661$	663.013	+	382.791i	1.00305	+	0.579108i	0.0938973	+	0.995582i	$0.470067\pi$
$662$		0			0
$663$	−125.862	−	218.000i	−0.189837	−	0.328808i
$664$		0			0
$665$	−32.4157	+	99.3206i	−0.0487454	+	0.149354i
$666$		0			0
$667$	1245.40	−	719.032i	1.86717	−	1.07801i
$668$		0			0
$669$	92.6527	−	160.479i	0.138494	−	0.239879i
$670$		0			0
$671$	−476.609	+	825.511i	−0.710296	+	1.23027i
$672$		0			0
$673$		−	637.277i		−	0.946920i	−0.880815	−	0.473460i	$-0.843005\pi$
$673$		−	637.277i		−	0.946920i	0.880815	−	0.473460i	$-0.156995\pi$
$674$		0			0
$675$	123.921	+	71.5461i	0.183587	+	0.105994i
$676$		0			0
$677$			813.175i			1.20114i	0.799571	+	0.600572i	$0.205060\pi$
$677$			813.175i			1.20114i	−0.799571	+	0.600572i	$0.794940\pi$
$678$		0			0
$679$	44.1322	−	25.4797i	0.0649959	−	0.0375254i
$680$		0			0
$681$	22.8624	+	39.5989i	0.0335719	+	0.0581482i
$682$		0			0
$683$		−	417.020i		−	0.610571i	−0.952261	−	0.305285i	$-0.901248\pi$
$683$		−	417.020i		−	0.610571i	0.952261	−	0.305285i	$-0.0987519\pi$
$684$		0			0
$685$	−604.639			−0.882684
$686$		0			0
$687$	−354.740	+	204.809i	−0.516361	+	0.298121i
$688$		0			0
$689$	−342.444	−	593.130i	−0.497015	−	0.860856i
$690$		0			0
$691$	985.879			1.42674			0.713371	−	0.700786i	$-0.247167\pi$
$691$	985.879			1.42674			0.713371	+	0.700786i	$0.247167\pi$
$692$		0			0
$693$	16.9768	−	29.4047i	0.0244975	−	0.0424310i
$694$		0			0
$695$	−655.993			−0.943874
$696$		0			0
$697$	511.899	+	295.545i	0.734432	+	0.424024i
$698$		0			0
$699$	475.395	+	274.469i	0.680107	+	0.392660i
$700$		0			0
$701$	146.242	+	253.298i	0.208619	+	0.361338i	0.951280	−	0.308330i	$-0.0997699\pi$
$701$	146.242	+	253.298i	0.208619	+	0.361338i	−0.742661	+	0.669668i	$0.766437\pi$
$702$		0			0
$703$	−184.872	+	166.019i	−0.262975	+	0.236159i
$704$		0			0
$705$	−752.042	+	434.192i	−1.06673	+	0.615875i
$706$		0			0
$707$	63.9896	−	110.833i	0.0905086	−	0.156765i
$708$		0			0
$709$	−65.4799	+	113.415i	−0.0923553	+	0.159964i	−0.908502	−	0.417881i	$-0.862773\pi$
$709$	−65.4799	+	113.415i	−0.0923553	+	0.159964i	0.816146	+	0.577845i	$0.196106\pi$
$710$		0			0
$711$			99.1001i			0.139381i
$712$		0			0
$713$	73.9537	+	42.6972i	0.103722	+	0.0598839i
$714$		0			0
$715$		−	1417.76i		−	1.98288i
$716$		0			0
$717$	194.853	−	112.498i	0.271761	−	0.156901i
$718$		0			0
$719$	−161.512	−	279.747i	−0.224634	−	0.389078i	0.731575	−	0.681761i	$-0.238785\pi$
$719$	−161.512	−	279.747i	−0.224634	−	0.389078i	−0.956210	+	0.292682i	$0.905452\pi$
$720$		0			0
$721$		−	104.226i		−	0.144557i
$722$		0			0
$723$	−440.664			−0.609493
$724$		0			0
$725$	−1267.90	+	732.021i	−1.74882	+	1.00968i
$726$		0			0
$727$	−530.172	−	918.286i	−0.729261	−	1.26312i	−0.957196	−	0.289440i	$-0.906531\pi$
$727$	−530.172	−	918.286i	−0.729261	−	1.26312i	0.227936	−	0.973676i	$-0.426802\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−404.102	+	699.926i	−0.552808	+	0.957491i
$732$		0			0
$733$	−1.88434			−0.00257072			−0.00128536	−	0.999999i	$-0.500409\pi$
$733$	−1.88434			−0.00257072			−0.00128536	+	0.999999i	$0.500409\pi$
$734$		0			0
$735$	526.494	+	303.971i	0.716318	+	0.413567i
$736$		0			0
$737$	−148.290	−	85.6154i	−0.201208	−	0.116167i
$738$		0			0
$739$	407.412	+	705.658i	0.551302	+	0.954882i	0.998181	+	0.0602883i	$0.0192020\pi$
$739$	407.412	+	705.658i	0.551302	+	0.954882i	−0.446879	+	0.894594i	$0.647465\pi$
$740$		0			0
$741$	−288.283	−	321.018i	−0.389045	−	0.433223i
$742$		0			0
$743$	240.341	−	138.761i	0.323473	−	0.186758i	−0.329466	−	0.944167i	$-0.606869\pi$
$743$	240.341	−	138.761i	0.323473	−	0.186758i	0.652940	+	0.757410i	$0.273535\pi$
$744$		0			0
$745$	−341.447	+	591.404i	−0.458319	+	0.793831i
$746$		0			0
$747$	−93.7911	+	162.451i	−0.125557	+	0.217471i
$748$		0			0
$749$			59.8943i			0.0799657i
$750$		0			0
$751$	1076.10	+	621.288i	1.43289	+	0.827282i	0.997341	−	0.0728816i	$-0.0232195\pi$
$751$	1076.10	+	621.288i	1.43289	+	0.827282i	0.435553	+	0.900163i	$0.356553\pi$
$752$		0			0
$753$		−	443.050i		−	0.588380i
$754$		0			0
$755$	−110.641	+	63.8788i	−0.146545	+	0.0846077i
$756$		0			0
$757$	−52.3310	−	90.6400i	−0.0691295	−	0.119736i	0.829389	−	0.558672i	$-0.188689\pi$
$757$	−52.3310	−	90.6400i	−0.0691295	−	0.119736i	−0.898518	+	0.438936i	$0.855356\pi$
$758$		0			0
$759$		−	698.965i		−	0.920902i
$760$		0			0
$761$	−1312.08			−1.72416			−0.862079	−	0.506773i	$-0.830838\pi$
$761$	−1312.08			−1.72416			−0.862079	+	0.506773i	$0.830838\pi$
$762$		0			0
$763$	−34.7585	+	20.0678i	−0.0455550	+	0.0263012i
$764$		0			0
$765$	120.521	+	208.749i	0.157544	+	0.272875i
$766$		0			0
$767$	−1124.26			−1.46578
$768$		0			0
$769$	311.446	−	539.440i	0.405001	−	0.701482i	−0.589321	−	0.807899i	$-0.700604\pi$
$769$	311.446	−	539.440i	0.405001	−	0.701482i	0.994322	+	0.106417i	$0.0339378\pi$
$770$		0			0
$771$	230.904			0.299486
$772$		0			0
$773$	−800.852	−	462.372i	−1.03603	−	0.598153i	−0.117325	−	0.993094i	$-0.537432\pi$
$773$	−800.852	−	462.372i	−1.03603	−	0.598153i	−0.918707	+	0.394941i	$0.870765\pi$
$774$		0			0
$775$	−75.2896	−	43.4685i	−0.0971479	−	0.0560884i
$776$		0			0
$777$	−8.59189	−	14.8816i	−0.0110578	−	0.0191526i
$778$		0			0
$779$	963.144	+	314.346i	1.23639	+	0.403525i
$780$		0			0
$781$	1425.23	−	822.855i	1.82487	−	1.05359i
$782$		0			0
$783$	138.125	−	239.239i	0.176404	−	0.305542i
$784$		0			0
$785$	358.070	−	620.195i	0.456140	−	0.790057i
$786$		0			0
$787$		−	490.780i		−	0.623609i	−0.950146	−	0.311804i	$-0.899067\pi$
$787$		−	490.780i		−	0.623609i	0.950146	−	0.311804i	$-0.100933\pi$
$788$		0			0
$789$	−207.139	−	119.592i	−0.262534	−	0.151574i
$790$		0			0
$791$			92.5054i			0.116947i
$792$		0			0
$793$	−725.463	+	418.846i	−0.914834	+	0.528179i
$794$		0			0
$795$	327.913	+	567.962i	0.412469	+	0.714417i
$796$		0			0
$797$			47.4031i			0.0594769i	0.999558	+	0.0297384i	$0.00946744\pi$
$797$			47.4031i			0.0594769i	−0.999558	+	0.0297384i	$0.990533\pi$
$798$		0			0
$799$	−766.743			−0.959629
$800$		0			0
$801$	270.431	−	156.133i	0.337616	−	0.194923i
$802$		0			0
$803$	−306.800	−	531.393i	−0.382067	−	0.661759i
$804$		0			0
$805$	−148.739			−0.184769
$806$		0			0
$807$	−326.589	+	565.668i	−0.404695	+	0.700952i
$808$		0			0
$809$	25.7002			0.0317679			0.0158840	−	0.999874i	$-0.494944\pi$
$809$	25.7002			0.0317679			0.0158840	+	0.999874i	$0.494944\pi$
$810$		0			0
$811$	−921.387	−	531.963i	−1.13611	−	0.655934i	−0.190647	−	0.981659i	$-0.561059\pi$
$811$	−921.387	−	531.963i	−1.13611	−	0.655934i	−0.945465	+	0.325724i	$0.894392\pi$
$812$		0			0
$813$	−206.202	−	119.051i	−0.253632	−	0.146434i
$814$		0			0
$815$	−709.604	−	1229.07i	−0.870679	−	1.50806i
$816$		0			0
$817$	−429.809	+	1316.92i	−0.526082	+	1.61190i
$818$		0			0
$819$	25.8410	−	14.9193i	0.0315518	−	0.0182165i
$820$		0			0
$821$	27.9746	−	48.4534i	0.0340738	−	0.0590175i	−0.848486	−	0.529218i	$-0.822485\pi$
$821$	27.9746	−	48.4534i	0.0340738	−	0.0590175i	0.882559	+	0.470201i	$0.155819\pi$
$822$		0			0
$823$	−649.232	+	1124.50i	−0.788861	+	1.36635i	0.137805	+	0.990459i	$0.455995\pi$
$823$	−649.232	+	1124.50i	−0.788861	+	1.36635i	−0.926665	+	0.375887i	$0.877338\pi$
$824$		0			0
$825$			711.591i			0.862535i
$826$		0			0
$827$	−157.293	−	90.8133i	−0.190197	−	0.109811i	0.401878	−	0.915693i	$-0.368358\pi$
$827$	−157.293	−	90.8133i	−0.190197	−	0.109811i	−0.592075	+	0.805883i	$0.701691\pi$
$828$		0			0
$829$			714.207i			0.861528i	0.902465	+	0.430764i	$0.141756\pi$
$829$			714.207i			0.861528i	−0.902465	+	0.430764i	$0.858244\pi$
$830$		0			0
$831$	−586.228	+	338.459i	−0.705449	+	0.407291i
$832$		0			0
$833$	268.393	+	464.870i	0.322200	+	0.558067i
$834$		0			0
$835$		−	1074.47i		−	1.28679i
$836$		0			0
$837$	16.4041			0.0195987
$838$		0			0
$839$	18.0652	−	10.4299i	0.0215318	−	0.0124314i	−0.489195	−	0.872174i	$-0.662710\pi$
$839$	18.0652	−	10.4299i	0.0215318	−	0.0124314i	0.510727	+	0.859743i	$0.329376\pi$
$840$		0			0
$841$	992.718	+	1719.44i	1.18040	+	2.04452i
$842$		0			0
$843$	631.610			0.749241
$844$		0			0
$845$	10.4829	−	18.1570i	0.0124058	−	0.0214875i
$846$		0			0
$847$	77.0558			0.0909750
$848$		0			0
$849$	−53.2539	−	30.7462i	−0.0627255	−	0.0362146i
$850$		0			0
$851$	−306.351	−	176.872i	−0.359989	−	0.207840i
$852$		0			0
$853$	832.408	+	1441.77i	0.975859	+	1.69024i	0.677071	+	0.735918i	$0.263249\pi$
$853$	832.408	+	1441.77i	0.975859	+	1.69024i	0.298788	+	0.954319i	$0.403418\pi$
$854$		0			0
$855$	276.050	+	307.397i	0.322865	+	0.359528i
$856$		0			0
$857$	−872.236	+	503.586i	−1.01778	+	0.587615i	−0.913460	−	0.406929i	$-0.866600\pi$
$857$	−872.236	+	503.586i	−1.01778	+	0.587615i	−0.104319	+	0.994544i	$0.533266\pi$
$858$		0			0
$859$	−489.607	+	848.025i	−0.569974	+	0.987223i	0.426594	+	0.904443i	$0.359713\pi$
$859$	−489.607	+	848.025i	−0.569974	+	0.987223i	−0.996568	+	0.0827802i	$0.973620\pi$
$860$		0			0
$861$	−35.0329	+	60.6788i	−0.0406886	+	0.0704748i
$862$		0			0
$863$		−	567.219i		−	0.657264i	−0.944458	−	0.328632i	$-0.893412\pi$
$863$		−	567.219i		−	0.657264i	0.944458	−	0.328632i	$-0.106588\pi$
$864$		0			0
$865$	630.167	+	363.827i	0.728517	+	0.420610i
$866$		0			0
$867$		−	287.733i		−	0.331872i
$868$		0			0
$869$	−426.795	+	246.410i	−0.491133	+	0.283556i
$870$		0			0
$871$	−75.2393	−	130.318i	−0.0863826	−	0.149619i
$872$		0			0
$873$		−	201.520i		−	0.230836i
$874$		0			0
$875$	13.9564			0.0159502
$876$		0			0
$877$	428.057	−	247.139i	0.488093	−	0.281800i	−0.235690	−	0.971828i	$-0.575735\pi$
$877$	428.057	−	247.139i	0.488093	−	0.281800i	0.723783	+	0.690028i	$0.242402\pi$
$878$		0			0
$879$	313.017	+	542.161i	0.356106	+	0.616793i
$880$		0			0
$881$	1065.60			1.20953			0.604766	−	0.796403i	$-0.293267\pi$
$881$	1065.60			1.20953			0.604766	+	0.796403i	$0.293267\pi$
$882$		0			0
$883$	686.080	−	1188.32i	0.776987	−	1.34578i	−0.156684	−	0.987649i	$-0.550080\pi$
$883$	686.080	−	1188.32i	0.776987	−	1.34578i	0.933671	−	0.358132i	$-0.116586\pi$
$884$		0			0
$885$	1076.55			1.21644
$886$		0			0
$887$	371.721	+	214.613i	0.419077	+	0.241954i	0.694682	−	0.719317i	$-0.255545\pi$
$887$	371.721	+	214.613i	0.419077	+	0.241954i	−0.275605	+	0.961271i	$0.588878\pi$
$888$		0			0
$889$	51.0311	+	29.4628i	0.0574028	+	0.0331415i
$890$		0			0
$891$	−67.1349	−	116.281i	−0.0753478	−	0.130506i
$892$		0			0
$893$	−1285.86	+	271.550i	−1.43993	+	0.304088i
$894$		0			0
$895$	−313.301	+	180.884i	−0.350057	+	0.202105i
$896$		0			0
$897$	307.127	−	531.959i	0.342393	−	0.593043i
$898$		0			0
$899$	−83.9190	+	145.352i	−0.0933470	+	0.161682i
$900$		0			0
$901$			579.064i			0.642690i
$902$		0			0
$903$	−82.9669	−	47.9010i	−0.0918792	−	0.0530465i
$904$		0			0
$905$		−	2348.23i		−	2.59473i
$906$		0			0
$907$	−45.4727	+	26.2537i	−0.0501353	+	0.0289456i	−0.524858	−	0.851190i	$-0.675882\pi$
$907$	−45.4727	+	26.2537i	−0.0501353	+	0.0289456i	0.474723	+	0.880135i	$0.342548\pi$
$908$		0			0
$909$	−253.048	−	438.291i	−0.278380	−	0.482169i
$910$		0			0
$911$		−	881.668i		−	0.967803i	−0.875123	−	0.483901i	$-0.839219\pi$
$911$		−	881.668i		−	0.967803i	0.875123	−	0.483901i	$-0.160781\pi$
$912$		0			0
$913$	−932.839			−1.02173
$914$		0			0
$915$	694.680	−	401.073i	0.759213	−	0.438332i
$916$		0			0
$917$	26.3287	+	45.6027i	0.0287118	+	0.0497303i
$918$		0			0
$919$	−492.946			−0.536394			−0.268197	−	0.963364i	$-0.586428\pi$
$919$	−492.946			−0.536394			−0.268197	+	0.963364i	$0.586428\pi$
$920$		0			0
$921$	−168.160	+	291.262i	−0.182584	+	0.316245i
$922$		0			0
$923$	1446.26			1.56691
$924$		0			0
$925$	311.885	+	180.067i	0.337173	+	0.194667i
$926$		0			0
$927$	−356.943	−	206.081i	−0.385052	−	0.222310i
$928$		0			0
$929$	432.798	+	749.628i	0.465875	+	0.806919i	0.999241	−	0.0389660i	$-0.0124064\pi$
$929$	432.798	+	749.628i	0.465875	+	0.806919i	−0.533366	+	0.845885i	$0.679073\pi$
$930$		0			0
$931$	614.744	+	684.551i	0.660305	+	0.735286i
$932$		0			0
$933$	827.199	−	477.583i	0.886601	−	0.511879i
$934$		0			0
$935$	−599.348	+	1038.10i	−0.641014	+	1.11027i
$936$		0			0
$937$	−812.808	+	1407.83i	−0.867458	+	1.50248i	−0.00287236	+	0.999996i	$0.500914\pi$
$937$	−812.808	+	1407.83i	−0.867458	+	1.50248i	−0.864586	+	0.502485i	$0.832419\pi$
$938$		0			0
$939$			297.170i			0.316475i
$940$		0			0
$941$	−1175.31	−	678.565i	−1.24900	−	0.721110i	−0.278090	−	0.960555i	$-0.589701\pi$
$941$	−1175.31	−	678.565i	−1.24900	−	0.721110i	−0.970910	+	0.239445i	$0.923035\pi$
$942$		0			0
$943$			1442.37i			1.52955i
$944$		0			0
$945$	−24.7445	+	14.2862i	−0.0261846	+	0.0151177i
$946$		0			0
$947$	167.820	+	290.672i	0.177212	+	0.306940i	0.940925	−	0.338616i	$-0.109959\pi$
$947$	167.820	+	290.672i	0.177212	+	0.306940i	−0.763713	+	0.645556i	$0.776626\pi$
$948$		0			0
$949$		−	539.234i		−	0.568213i
$950$		0			0
$951$	937.274			0.985567
$952$		0			0
$953$	710.377	−	410.136i	0.745412	−	0.430364i	−0.0786221	−	0.996904i	$-0.525052\pi$
$953$	710.377	−	410.136i	0.745412	−	0.430364i	0.824034	+	0.566541i	$0.191719\pi$
$954$		0			0
$955$	−664.725	−	1151.34i	−0.696047	−	1.20559i
$956$		0			0
$957$	1373.78			1.43550
$958$		0			0
$959$	31.6415	−	54.8047i	0.0329943	−	0.0571477i
$960$		0			0
$961$	951.034			0.989629
$962$		0			0
$963$	205.121	+	118.426i	0.213002	+	0.122977i
$964$		0			0
$965$	1005.21	+	580.357i	1.04167	+	0.601406i
$966$		0			0
$967$	−881.670	−	1527.10i	−0.911758	−	1.57921i	−0.811580	−	0.584242i	$-0.801392\pi$
$967$	−881.670	−	1527.10i	−0.911758	−	1.57921i	−0.100178	−	0.994970i	$-0.531941\pi$
$968$		0			0
$969$	75.3759	+	356.924i	0.0777874	+	0.368343i
$970$		0			0
$971$	892.776	−	515.444i	0.919439	−	0.530839i	0.0359832	−	0.999352i	$-0.488544\pi$
$971$	892.776	−	515.444i	0.919439	−	0.530839i	0.883456	+	0.468514i	$0.155210\pi$
$972$		0			0
$973$	34.3289	−	59.4594i	0.0352815	−	0.0611094i
$974$		0			0
$975$	−312.675	+	541.569i	−0.320692	+	0.555455i
$976$		0			0
$977$		−	1304.58i		−	1.33529i	−0.744481	−	0.667643i	$-0.767303\pi$
$977$		−	1304.58i		−	1.33529i	0.744481	−	0.667643i	$-0.232697\pi$
$978$		0			0
$979$	1344.84	+	776.444i	1.37369	+	0.793099i
$980$		0			0
$981$			158.717i			0.161791i
$982$		0			0
$983$	135.373	−	78.1579i	0.137715	−	0.0795096i	−0.429560	−	0.903038i	$-0.641331\pi$
$983$	135.373	−	78.1579i	0.137715	−	0.0795096i	0.567274	+	0.823529i	$0.307998\pi$
$984$		0			0
$985$	−79.5844	−	137.844i	−0.0807963	−	0.139943i
$986$		0			0
$987$		−	90.8872i		−	0.0920843i
$988$		0			0
$989$	−1972.17			−1.99410
$990$		0			0
$991$	51.2843	−	29.6090i	0.0517501	−	0.0298779i	−0.473902	−	0.880578i	$-0.657155\pi$
$991$	51.2843	−	29.6090i	0.0517501	−	0.0298779i	0.525652	+	0.850700i	$0.323821\pi$
$992$		0			0
$993$	318.383	+	551.456i	0.320627	+	0.555343i
$994$		0			0
$995$	1464.52			1.47188
$996$		0			0
$997$	73.1609	−	126.718i	0.0733811	−	0.127100i	−0.827000	−	0.562202i	$-0.809954\pi$
$997$	73.1609	−	126.718i	0.0733811	−	0.127100i	0.900381	+	0.435102i	$0.143288\pi$
$998$		0			0
$999$	−67.9535			−0.0680215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.j.145.2		20
4.3	odd	2		456.3.w.a.145.2	✓	20
12.11	even	2		1368.3.bv.c.145.9		20
19.8	odd	6	inner	912.3.be.j.673.2		20
76.27	even	6		456.3.w.a.217.2	yes	20
228.179	odd	6		1368.3.bv.c.217.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.2	✓	20	4.3	odd	2
456.3.w.a.217.2	yes	20	76.27	even	6
912.3.be.j.145.2		20	1.1	even	1	trivial
912.3.be.j.673.2		20	19.8	odd	6	inner
1368.3.bv.c.145.9		20	12.11	even	2
1368.3.bv.c.217.9		20	228.179	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.62416 - 6.27723i) q^{5} +0.758627 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-3.62416 - 6.27723i) q^{5} +0.758627 q^{7} +(1.50000 - 2.59808i) q^{9} +14.9189 q^{11} +(11.3543 + 6.55539i) q^{13} +(-10.8725 - 6.27723i) q^{15} +(-5.54250 - 9.59990i) q^{17} +(-12.6949 - 14.1365i) q^{19} +(1.13794 - 0.656990i) q^{21} +(13.5247 - 23.4255i) q^{23} +(-13.7690 + 23.8487i) q^{25} -5.19615i q^{27} +(46.0416 + 26.5821i) q^{29} +3.15697i q^{31} +(22.3783 - 12.9201i) q^{33} +(-2.74938 - 4.76207i) q^{35} -13.0777i q^{37} +22.7085 q^{39} +(-46.1794 + 26.6617i) q^{41} +(-36.4549 - 63.1417i) q^{43} -21.7450 q^{45} +(34.5847 - 59.9024i) q^{47} -48.4245 q^{49} +(-16.6275 - 9.59990i) q^{51} +(-45.2399 - 26.1192i) q^{53} +(-54.0684 - 93.6491i) q^{55} +(-31.2849 - 10.2106i) q^{57} +(-74.2621 + 42.8752i) q^{59} +(-31.9467 + 55.3333i) q^{61} +(1.13794 - 1.97097i) q^{63} -95.0311i q^{65} +(-9.93978 - 5.73873i) q^{67} -46.8511i q^{69} +(95.5318 - 55.1553i) q^{71} +(-20.5645 - 35.6188i) q^{73} +47.6974i q^{75} +11.3179 q^{77} +(-28.6077 + 16.5167i) q^{79} +(-4.50000 - 7.79423i) q^{81} -62.5274 q^{83} +(-40.1738 + 69.5831i) q^{85} +92.0831 q^{87} +(90.1436 + 52.0444i) q^{89} +(8.61365 + 4.97309i) q^{91} +(2.73402 + 4.73546i) q^{93} +(-42.7295 + 130.922i) q^{95} +(58.1738 - 33.5867i) q^{97} +(22.3783 - 38.7604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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