LMFDB - Embedded newform 912.3.be.e.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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.e.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-0.764419 - 1.32401i) q^{5} +1.67282 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-0.764419 - 1.32401i) q^{5} +1.67282 q^{7} +(1.50000 - 2.59808i) q^{9} -13.3641 q^{11} +(14.2345 + 8.21826i) q^{13} +(-2.29326 - 1.32401i) q^{15} +(10.8784 + 18.8420i) q^{17} +(15.2633 - 11.3151i) q^{19} +(2.50924 - 1.44871i) q^{21} +(-6.82209 + 11.8162i) q^{23} +(11.3313 - 19.6264i) q^{25} -5.19615i q^{27} +(42.6168 + 24.6048i) q^{29} -42.5492i q^{31} +(-20.0462 + 11.5737i) q^{33} +(-1.27874 - 2.21484i) q^{35} -27.6769i q^{37} +28.4689 q^{39} +(58.0924 - 33.5396i) q^{41} +(4.45551 + 7.71718i) q^{43} -4.58651 q^{45} +(11.8930 - 20.5992i) q^{47} -46.2017 q^{49} +(32.6353 + 18.8420i) q^{51} +(-32.3368 - 18.6697i) q^{53} +(10.2158 + 17.6943i) q^{55} +(13.0957 - 30.1911i) q^{57} +(-11.7806 + 6.80155i) q^{59} +(5.79193 - 10.0319i) q^{61} +(2.50924 - 4.34612i) q^{63} -25.1288i q^{65} +(86.0083 + 49.6569i) q^{67} +23.6324i q^{69} +(-16.1110 + 9.30169i) q^{71} +(-5.33528 - 9.24098i) q^{73} -39.2529i q^{75} -22.3558 q^{77} +(74.6873 - 43.1208i) q^{79} +(-4.50000 - 7.79423i) q^{81} -7.23820 q^{83} +(16.6314 - 28.8064i) q^{85} +85.2337 q^{87} +(81.0831 + 46.8134i) q^{89} +(23.8117 + 13.7477i) q^{91} +(-36.8487 - 63.8238i) q^{93} +(-26.6489 - 11.5593i) q^{95} +(-118.938 + 68.6687i) q^{97} +(-20.0462 + 34.7210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9	$ 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9} + 20 q^{11} + 21 q^{13} + 12 q^{15} - 2 q^{17} + 10 q^{19} - 15 q^{21} + 2 q^{23} - 5 q^{25} + 114 q^{29} + 30 q^{33} - 32 q^{35} + 42 q^{39} + 48 q^{41} + 21 q^{43} + 24 q^{45} - 46 q^{47} - 240 q^{49} - 6 q^{51} - 18 q^{53} + 140 q^{55} - 3 q^{57} + 144 q^{59} + 19 q^{61} - 15 q^{63} - 201 q^{67} - 204 q^{71} + 51 q^{73} - 220 q^{77} - 153 q^{79} - 27 q^{81} - 52 q^{83} - 92 q^{85} + 228 q^{87} + 216 q^{89} + 57 q^{91} - 15 q^{93} + 248 q^{95} + 12 q^{97} + 30 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9 + 20 * q^11 + 21 * q^13 + 12 * q^15 - 2 * q^17 + 10 * q^19 - 15 * q^21 + 2 * q^23 - 5 * q^25 + 114 * q^29 + 30 * q^33 - 32 * q^35 + 42 * q^39 + 48 * q^41 + 21 * q^43 + 24 * q^45 - 46 * q^47 - 240 * q^49 - 6 * q^51 - 18 * q^53 + 140 * q^55 - 3 * q^57 + 144 * q^59 + 19 * q^61 - 15 * q^63 - 201 * q^67 - 204 * q^71 + 51 * q^73 - 220 * q^77 - 153 * q^79 - 27 * q^81 - 52 * q^83 - 92 * q^85 + 228 * q^87 + 216 * q^89 + 57 * q^91 - 15 * q^93 + 248 * q^95 + 12 * q^97 + 30 * 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
$5$	−0.764419	−	1.32401i	−0.152884	−	0.264802i	0.779403	−	0.626523i	$-0.215523\pi$
$5$	−0.764419	−	1.32401i	−0.152884	−	0.264802i	−0.932286	+	0.361721i	$0.882189\pi$
$6$		0			0
$7$	1.67282			0.238975			0.119487	−	0.992836i	$-0.461875\pi$
$7$	1.67282			0.238975			0.119487	+	0.992836i	$0.461875\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−13.3641			−1.21492			−0.607460	−	0.794350i	$-0.707811\pi$
$11$	−13.3641			−1.21492			−0.607460	+	0.794350i	$0.707811\pi$
$12$		0			0
$13$	14.2345	+	8.21826i	1.09496	+	0.632174i	0.934892	−	0.354932i	$-0.115496\pi$
$13$	14.2345	+	8.21826i	1.09496	+	0.632174i	0.160066	+	0.987106i	$0.448829\pi$
$14$		0			0
$15$	−2.29326	−	1.32401i	−0.152884	−	0.0882675i
$16$		0			0
$17$	10.8784	+	18.8420i	0.639908	+	1.10835i	0.985453	+	0.169951i	$0.0543609\pi$
$17$	10.8784	+	18.8420i	0.639908	+	1.10835i	−0.345544	+	0.938402i	$0.612306\pi$
$18$		0			0
$19$	15.2633	−	11.3151i	0.803331	−	0.595533i
$19$	15.2633	−	11.3151i	0.803331	−	0.595533i
$20$		0			0
$21$	2.50924	−	1.44871i	0.119487	−	0.0689861i
$22$		0			0
$23$	−6.82209	+	11.8162i	−0.296613	+	0.513748i	−0.975359	−	0.220625i	$-0.929190\pi$
$23$	−6.82209	+	11.8162i	−0.296613	+	0.513748i	0.678746	+	0.734373i	$0.262524\pi$
$24$		0			0
$25$	11.3313	−	19.6264i	0.453253	−	0.785057i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	42.6168	+	24.6048i	1.46955	+	0.848443i	0.999417	−	0.0341544i	$-0.0108738\pi$
$29$	42.6168	+	24.6048i	1.46955	+	0.848443i	0.470130	+	0.882597i	$0.344207\pi$
$30$		0			0
$31$		−	42.5492i		−	1.37255i	−0.727340	−	0.686277i	$-0.759244\pi$
$31$		−	42.5492i		−	1.37255i	0.727340	−	0.686277i	$-0.240756\pi$
$32$		0			0
$33$	−20.0462	+	11.5737i	−0.607460	+	0.350717i
$34$		0			0
$35$	−1.27874	−	2.21484i	−0.0365354	−	0.0632811i
$36$		0			0
$37$		−	27.6769i		−	0.748024i	−0.927424	−	0.374012i	$-0.877982\pi$
$37$		−	27.6769i		−	0.748024i	0.927424	−	0.374012i	$-0.122018\pi$
$38$		0			0
$39$	28.4689			0.729972
$40$		0			0
$41$	58.0924	−	33.5396i	1.41689	−	0.818040i	0.420863	−	0.907124i	$-0.361727\pi$
$41$	58.0924	−	33.5396i	1.41689	−	0.818040i	0.996024	+	0.0890844i	$0.0283941\pi$
$42$		0			0
$43$	4.45551	+	7.71718i	0.103617	+	0.179469i	0.913172	−	0.407574i	$-0.133625\pi$
$43$	4.45551	+	7.71718i	0.103617	+	0.179469i	−0.809556	+	0.587043i	$0.800292\pi$
$44$		0			0
$45$	−4.58651			−0.101922
$46$		0			0
$47$	11.8930	−	20.5992i	0.253042	−	0.438281i	−0.711320	−	0.702868i	$-0.751902\pi$
$47$	11.8930	−	20.5992i	0.253042	−	0.438281i	0.964362	+	0.264587i	$0.0852357\pi$
$48$		0			0
$49$	−46.2017			−0.942891
$50$		0			0
$51$	32.6353	+	18.8420i	0.639908	+	0.369451i
$52$		0			0
$53$	−32.3368	−	18.6697i	−0.610128	−	0.352258i	0.162887	−	0.986645i	$-0.447919\pi$
$53$	−32.3368	−	18.6697i	−0.610128	−	0.352258i	−0.773016	+	0.634387i	$0.781253\pi$
$54$		0			0
$55$	10.2158	+	17.6943i	0.185741	+	0.321714i
$56$		0			0
$57$	13.0957	−	30.1911i	0.229750	−	0.529668i
$58$		0			0
$59$	−11.7806	+	6.80155i	−0.199672	+	0.115280i	−0.596502	−	0.802611i	$-0.703443\pi$
$59$	−11.7806	+	6.80155i	−0.199672	+	0.115280i	0.396831	+	0.917892i	$0.370110\pi$
$60$		0			0
$61$	5.79193	−	10.0319i	0.0949496	−	0.164458i	−0.814638	−	0.579970i	$-0.803064\pi$
$61$	5.79193	−	10.0319i	0.0949496	−	0.164458i	0.909588	+	0.415512i	$0.136398\pi$
$62$		0			0
$63$	2.50924	−	4.34612i	0.0398291	−	0.0689861i
$64$		0			0
$65$		−	25.1288i		−	0.386597i
$66$		0			0
$67$	86.0083	+	49.6569i	1.28371	+	0.741148i	0.977524	−	0.210825i	$-0.0676150\pi$
$67$	86.0083	+	49.6569i	1.28371	+	0.741148i	0.306182	+	0.951973i	$0.400948\pi$
$68$		0			0
$69$			23.6324i			0.342499i
$70$		0			0
$71$	−16.1110	+	9.30169i	−0.226915	+	0.131010i	−0.609148	−	0.793056i	$-0.708489\pi$
$71$	−16.1110	+	9.30169i	−0.226915	+	0.131010i	0.382233	+	0.924066i	$0.375155\pi$
$72$		0			0
$73$	−5.33528	−	9.24098i	−0.0730860	−	0.126589i	0.827166	−	0.561957i	$-0.189951\pi$
$73$	−5.33528	−	9.24098i	−0.0730860	−	0.126589i	−0.900252	+	0.435368i	$0.856618\pi$
$74$		0			0
$75$		−	39.2529i		−	0.523372i
$76$		0			0
$77$	−22.3558			−0.290335
$78$		0			0
$79$	74.6873	−	43.1208i	0.945409	−	0.545832i	0.0537574	−	0.998554i	$-0.482880\pi$
$79$	74.6873	−	43.1208i	0.945409	−	0.545832i	0.891652	+	0.452722i	$0.149547\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−7.23820			−0.0872073			−0.0436036	−	0.999049i	$-0.513884\pi$
$83$	−7.23820			−0.0872073			−0.0436036	+	0.999049i	$0.513884\pi$
$84$		0			0
$85$	16.6314	−	28.8064i	0.195663	−	0.338898i
$86$		0			0
$87$	85.2337			0.979697
$88$		0			0
$89$	81.0831	+	46.8134i	0.911046	+	0.525993i	0.880768	−	0.473549i	$-0.157027\pi$
$89$	81.0831	+	46.8134i	0.911046	+	0.525993i	0.0302786	+	0.999541i	$0.490361\pi$
$90$		0			0
$91$	23.8117	+	13.7477i	0.261667	+	0.151074i
$92$		0			0
$93$	−36.8487	−	63.8238i	−0.396222	−	0.686277i
$94$		0			0
$95$	−26.6489	−	11.5593i	−0.280515	−	0.121677i
$96$		0			0
$97$	−118.938	+	68.6687i	−1.22616	+	0.707924i	−0.966225	−	0.257701i	$-0.917035\pi$
$97$	−118.938	+	68.6687i	−1.22616	+	0.707924i	−0.259937	+	0.965626i	$0.583702\pi$
$98$		0			0
$99$	−20.0462	+	34.7210i	−0.202487	+	0.350717i
$100$		0			0
$101$	61.3994	−	106.347i	0.607915	−	1.05294i	−0.383669	−	0.923471i	$-0.625340\pi$
$101$	61.3994	−	106.347i	0.607915	−	1.05294i	0.991584	−	0.129468i	$-0.0413270\pi$
$102$		0			0
$103$		−	93.0920i		−	0.903806i	−0.892067	−	0.451903i	$-0.850745\pi$
$103$		−	93.0920i		−	0.903806i	0.892067	−	0.451903i	$-0.149255\pi$
$104$		0			0
$105$	−3.83621	−	2.21484i	−0.0365354	−	0.0210937i
$106$		0			0
$107$		−	4.08500i		−	0.0381775i	−0.999818	−	0.0190888i	$-0.993923\pi$
$107$		−	4.08500i		−	0.0381775i	0.999818	−	0.0190888i	$-0.00607651\pi$
$108$		0			0
$109$	136.536	−	78.8292i	1.25263	−	0.723204i	0.280995	−	0.959709i	$-0.409335\pi$
$109$	136.536	−	78.8292i	1.25263	−	0.723204i	0.971630	+	0.236506i	$0.0760021\pi$
$110$		0			0
$111$	−23.9689	−	41.5154i	−0.215936	−	0.374012i
$112$		0			0
$113$			44.1317i			0.390546i	0.980749	+	0.195273i	$0.0625593\pi$
$113$			44.1317i			0.390546i	−0.980749	+	0.195273i	$0.937441\pi$
$114$		0			0
$115$	20.8597			0.181389
$116$		0			0
$117$	42.7034	−	24.6548i	0.364986	−	0.210725i
$118$		0			0
$119$	18.1977	+	31.5194i	0.152922	+	0.264869i
$120$		0			0
$121$	57.5997			0.476030
$122$		0			0
$123$	58.0924	−	100.619i	0.472296	−	0.818040i
$124$		0			0
$125$	−72.8684			−0.582948
$126$		0			0
$127$	−78.4015	−	45.2651i	−0.617334	−	0.356418i	0.158496	−	0.987360i	$-0.449335\pi$
$127$	−78.4015	−	45.2651i	−0.617334	−	0.356418i	−0.775830	+	0.630941i	$0.782669\pi$
$128$		0			0
$129$	13.3665	+	7.71718i	0.103617	+	0.0598231i
$130$		0			0
$131$	82.8374	+	143.479i	0.632346	+	1.09526i	0.987071	+	0.160285i	$0.0512414\pi$
$131$	82.8374	+	143.479i	0.632346	+	1.09526i	−0.354724	+	0.934971i	$0.615425\pi$
$132$		0			0
$133$	25.5328	−	18.9282i	0.191976	−	0.142317i
$134$		0			0
$135$	−6.87977	+	3.97204i	−0.0509612	+	0.0294225i
$136$		0			0
$137$	−110.639	+	191.633i	−0.807585	+	1.39878i	0.106948	+	0.994265i	$0.465892\pi$
$137$	−110.639	+	191.633i	−0.807585	+	1.39878i	−0.914532	+	0.404513i	$0.867441\pi$
$138$		0			0
$139$	−97.9640	+	169.679i	−0.704777	+	1.22071i	0.261995	+	0.965069i	$0.415620\pi$
$139$	−97.9640	+	169.679i	−0.704777	+	1.22071i	−0.966772	+	0.255640i	$0.917714\pi$
$140$		0			0
$141$		−	41.1984i		−	0.292187i
$142$		0			0
$143$	−190.231	−	109.830i	−1.33029	−	0.768041i
$144$		0			0
$145$		−	75.2336i		−	0.518852i
$146$		0			0
$147$	−69.3025	+	40.0118i	−0.471446	+	0.272189i
$148$		0			0
$149$	68.0154	+	117.806i	0.456480	+	0.790646i	0.998772	−	0.0495441i	$-0.0157768\pi$
$149$	68.0154	+	117.806i	0.456480	+	0.790646i	−0.542292	+	0.840190i	$0.682443\pi$
$150$		0			0
$151$		−	178.257i		−	1.18051i	−0.807217	−	0.590255i	$-0.799027\pi$
$151$		−	178.257i		−	1.18051i	0.807217	−	0.590255i	$-0.200973\pi$
$152$		0			0
$153$	65.2706			0.426605
$154$		0			0
$155$	−56.3356	+	32.5254i	−0.363456	+	0.209841i
$156$		0			0
$157$	17.6086	+	30.4989i	0.112156	+	0.194261i	0.916640	−	0.399715i	$-0.130891\pi$
$157$	17.6086	+	30.4989i	0.112156	+	0.194261i	−0.804483	+	0.593976i	$0.797558\pi$
$158$		0			0
$159$	−64.6736			−0.406752
$160$		0			0
$161$	−11.4122	+	19.7664i	−0.0708830	+	0.122773i
$162$		0			0
$163$	136.657			0.838389			0.419195	−	0.907896i	$-0.362313\pi$
$163$	136.657			0.838389			0.419195	+	0.907896i	$0.362313\pi$
$164$		0			0
$165$	30.6473	+	17.6943i	0.185741	+	0.107238i
$166$		0			0
$167$	58.8850	+	33.9973i	0.352605	+	0.203577i	0.665832	−	0.746102i	$-0.268077\pi$
$167$	58.8850	+	33.9973i	0.352605	+	0.203577i	−0.313227	+	0.949678i	$0.601410\pi$
$168$		0			0
$169$	50.5797	+	87.6067i	0.299288	+	0.518383i
$170$		0			0
$171$	−6.50262	−	56.6279i	−0.0380270	−	0.331157i
$172$		0			0
$173$	48.3896	−	27.9377i	0.279709	−	0.161490i	−0.353583	−	0.935403i	$-0.615037\pi$
$173$	48.3896	−	27.9377i	0.279709	−	0.161490i	0.633292	+	0.773913i	$0.281703\pi$
$174$		0			0
$175$	18.9553	−	32.8316i	0.108316	−	0.187609i
$176$		0			0
$177$	−11.7806	+	20.4046i	−0.0665572	+	0.115280i
$178$		0			0
$179$			121.689i			0.679826i	0.940457	+	0.339913i	$0.110398\pi$
$179$			121.689i			0.679826i	−0.940457	+	0.339913i	$0.889602\pi$
$180$		0			0
$181$	122.621	+	70.7950i	0.677462	+	0.391133i	0.798898	−	0.601467i	$-0.205417\pi$
$181$	122.621	+	70.7950i	0.677462	+	0.391133i	−0.121436	+	0.992599i	$0.538750\pi$
$182$		0			0
$183$		−	20.0638i		−	0.109638i
$184$		0			0
$185$	−36.6445	+	21.1567i	−0.198079	+	0.114361i
$186$		0			0
$187$	−145.381	−	251.807i	−0.777437	−	1.34656i
$188$		0			0
$189$		−	8.69225i		−	0.0459907i
$190$		0			0
$191$	54.9450			0.287670			0.143835	−	0.989602i	$-0.454057\pi$
$191$	54.9450			0.287670			0.143835	+	0.989602i	$0.454057\pi$
$192$		0			0
$193$	315.753	−	182.300i	1.63603	−	0.944561i	0.653845	−	0.756629i	$-0.273155\pi$
$193$	315.753	−	182.300i	1.63603	−	0.944561i	0.982182	−	0.187932i	$-0.0601784\pi$
$194$		0			0
$195$	−21.7622	−	37.6932i	−0.111601	−	0.193298i
$196$		0			0
$197$	−191.628			−0.972730			−0.486365	−	0.873756i	$-0.661678\pi$
$197$	−191.628			−0.972730			−0.486365	+	0.873756i	$0.661678\pi$
$198$		0			0
$199$	−33.7914	+	58.5284i	−0.169806	+	0.294113i	−0.938352	−	0.345682i	$-0.887647\pi$
$199$	−33.7914	+	58.5284i	−0.169806	+	0.294113i	0.768546	+	0.639795i	$0.220981\pi$
$200$		0			0
$201$	172.017			0.855804
$202$		0			0
$203$	71.2905	+	41.1596i	0.351185	+	0.202756i
$204$		0			0
$205$	−88.8138	−	51.2766i	−0.433238	−	0.250130i
$206$		0			0
$207$	20.4663	+	35.4486i	0.0988709	+	0.171249i
$208$		0			0
$209$	−203.980	+	151.217i	−0.975983	+	0.723525i
$210$		0			0
$211$	−76.4694	+	44.1496i	−0.362414	+	0.209240i	−0.670139	−	0.742235i	$-0.733766\pi$
$211$	−76.4694	+	44.1496i	−0.362414	+	0.209240i	0.307725	+	0.951475i	$0.400432\pi$
$212$		0			0
$213$	−16.1110	+	27.9051i	−0.0756385	+	0.131010i
$214$		0			0
$215$	6.81176	−	11.7983i	0.0316826	−	0.0548758i
$216$		0			0
$217$		−	71.1773i		−	0.328006i
$218$		0			0
$219$	−16.0058	−	9.24098i	−0.0730860	−	0.0421962i
$220$		0			0
$221$			357.607i			1.61813i
$222$		0			0
$223$	−95.4499	+	55.1080i	−0.428027	+	0.247121i	−0.698506	−	0.715605i	$-0.746151\pi$
$223$	−95.4499	+	55.1080i	−0.428027	+	0.247121i	0.270479	+	0.962726i	$0.412818\pi$
$224$		0			0
$225$	−33.9940	−	58.8793i	−0.151084	−	0.261686i
$226$		0			0
$227$			35.3545i			0.155747i	0.996963	+	0.0778734i	$0.0248130\pi$
$227$			35.3545i			0.155747i	−0.996963	+	0.0778734i	$0.975187\pi$
$228$		0			0
$229$	−258.185			−1.12744			−0.563722	−	0.825964i	$-0.690631\pi$
$229$	−258.185			−1.12744			−0.563722	+	0.825964i	$0.690631\pi$
$230$		0			0
$231$	−33.5337	+	19.3607i	−0.145168	+	0.0838126i
$232$		0			0
$233$	−219.856	−	380.802i	−0.943589	−	1.63434i	−0.758553	−	0.651612i	$-0.774093\pi$
$233$	−219.856	−	380.802i	−0.943589	−	1.63434i	−0.185036	−	0.982732i	$-0.559240\pi$
$234$		0			0
$235$	−36.3648			−0.154744
$236$		0			0
$237$	74.6873	−	129.362i	0.315136	−	0.545832i
$238$		0			0
$239$	474.807			1.98664			0.993320	−	0.115391i	$-0.0368121\pi$
$239$	474.807			1.98664			0.993320	+	0.115391i	$0.0368121\pi$
$240$		0			0
$241$	141.352	+	81.6097i	0.586524	+	0.338630i	0.763722	−	0.645546i	$-0.223370\pi$
$241$	141.352	+	81.6097i	0.586524	+	0.338630i	−0.177198	+	0.984175i	$0.556703\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	35.3174	+	61.1715i	0.144153	+	0.249680i
$246$		0			0
$247$	310.255	−	35.6268i	1.25609	−	0.144238i
$248$		0			0
$249$	−10.8573	+	6.26847i	−0.0436036	+	0.0251746i
$250$		0			0
$251$	−218.317	+	378.136i	−0.869789	+	1.50652i	−0.00757655	+	0.999971i	$0.502412\pi$
$251$	−218.317	+	378.136i	−0.869789	+	1.50652i	−0.862212	+	0.506547i	$0.830922\pi$
$252$		0			0
$253$	91.1713	−	157.913i	0.360361	−	0.624163i
$254$		0			0
$255$		−	57.6127i		−	0.225932i
$256$		0			0
$257$	−273.079	−	157.662i	−1.06256	−	0.613471i	−0.136422	−	0.990651i	$-0.543560\pi$
$257$	−273.079	−	157.662i	−1.06256	−	0.613471i	−0.926140	+	0.377180i	$0.876894\pi$
$258$		0			0
$259$		−	46.2986i		−	0.178759i
$260$		0			0
$261$	127.851	−	73.8145i	0.489849	−	0.282814i
$262$		0			0
$263$	−87.1962	−	151.028i	−0.331544	−	0.574252i	0.651270	−	0.758846i	$-0.274236\pi$
$263$	−87.1962	−	151.028i	−0.331544	−	0.574252i	−0.982815	+	0.184594i	$0.940903\pi$
$264$		0			0
$265$			57.0858i			0.215418i
$266$		0			0
$267$	162.166			0.607364
$268$		0			0
$269$	−209.828	+	121.144i	−0.780028	+	0.450349i	−0.836440	−	0.548058i	$-0.815367\pi$
$269$	−209.828	+	121.144i	−0.780028	+	0.450349i	0.0564122	+	0.998408i	$0.482034\pi$
$270$		0			0
$271$	136.606	+	236.609i	0.504082	+	0.873095i	0.999989	+	0.00471973i	$0.00150234\pi$
$271$	136.606	+	236.609i	0.504082	+	0.873095i	−0.495907	+	0.868376i	$0.665164\pi$
$272$		0			0
$273$	47.6235			0.174445
$274$		0			0
$275$	−151.433	+	262.290i	−0.550666	+	0.953782i
$276$		0			0
$277$	−530.540			−1.91531			−0.957654	−	0.287923i	$-0.907035\pi$
$277$	−530.540			−1.91531			−0.957654	+	0.287923i	$0.907035\pi$
$278$		0			0
$279$	−110.546	−	63.8238i	−0.396222	−	0.228759i
$280$		0			0
$281$	−373.878	−	215.859i	−1.33053	−	0.768180i	−0.345147	−	0.938549i	$-0.612171\pi$
$281$	−373.878	−	215.859i	−1.33053	−	0.768180i	−0.985380	+	0.170368i	$0.945504\pi$
$282$		0			0
$283$	100.911	+	174.783i	0.356576	+	0.617608i	0.987386	−	0.158329i	$-0.0506107\pi$
$283$	100.911	+	174.783i	0.356576	+	0.617608i	−0.630810	+	0.775937i	$0.717277\pi$
$284$		0			0
$285$	−49.9840	+	5.73970i	−0.175382	+	0.0201393i
$286$		0			0
$287$	97.1783	−	56.1059i	0.338600	−	0.195491i
$288$		0			0
$289$	−92.1808	+	159.662i	−0.318965	+	0.552463i
$290$		0			0
$291$	−118.938	+	206.006i	−0.408720	+	0.707924i
$292$		0			0
$293$			328.951i			1.12270i	0.827578	+	0.561350i	$0.189718\pi$
$293$			328.951i			1.12270i	−0.827578	+	0.561350i	$0.810282\pi$
$294$		0			0
$295$	18.0107	+	10.3985i	0.0610531	+	0.0352490i
$296$		0			0
$297$			69.4420i			0.233811i
$298$		0			0
$299$	−194.217	+	112.132i	−0.649557	+	0.375022i
$300$		0			0
$301$	7.45329	+	12.9095i	0.0247618	+	0.0428886i
$302$		0			0
$303$		−	212.694i		−	0.701959i
$304$		0			0
$305$	−17.7098			−0.0580650
$306$		0			0
$307$	−348.399	+	201.148i	−1.13485	+	0.655205i	−0.945150	−	0.326637i	$-0.894085\pi$
$307$	−348.399	+	201.148i	−1.13485	+	0.655205i	−0.189699	+	0.981842i	$0.560751\pi$
$308$		0			0
$309$	−80.6201	−	139.638i	−0.260906	−	0.451903i
$310$		0			0
$311$	−499.959			−1.60758			−0.803792	−	0.594911i	$-0.797187\pi$
$311$	−499.959			−1.60758			−0.803792	+	0.594911i	$0.797187\pi$
$312$		0			0
$313$	−240.839	+	417.146i	−0.769454	+	1.33273i	0.168405	+	0.985718i	$0.446138\pi$
$313$	−240.839	+	417.146i	−0.769454	+	1.33273i	−0.937859	+	0.347016i	$0.887195\pi$
$314$		0			0
$315$	−7.67243			−0.0243569
$316$		0			0
$317$	−38.0365	−	21.9604i	−0.119989	−	0.0692756i	0.438804	−	0.898583i	$-0.355402\pi$
$317$	−38.0365	−	21.9604i	−0.119989	−	0.0692756i	−0.558793	+	0.829307i	$0.688735\pi$
$318$		0			0
$319$	−569.537	−	328.822i	−1.78538	−	1.03079i
$320$		0			0
$321$	−3.53771	−	6.12749i	−0.0110209	−	0.0190888i
$322$		0			0
$323$	379.240	+	164.500i	1.17412	+	0.509288i
$324$		0			0
$325$	322.590	−	186.248i	0.992586	−	0.573070i
$326$		0			0
$327$	136.536	−	236.488i	0.417542	−	0.723204i
$328$		0			0
$329$	19.8948	−	34.4588i	0.0604706	−	0.104738i
$330$		0			0
$331$			518.377i			1.56609i	0.621963	+	0.783046i	$0.286335\pi$
$331$			518.377i			1.56609i	−0.621963	+	0.783046i	$0.713665\pi$
$332$		0			0
$333$	−71.9067	−	41.5154i	−0.215936	−	0.124671i
$334$		0			0
$335$		−	151.835i		−	0.453238i
$336$		0			0
$337$	−39.4546	+	22.7791i	−0.117076	+	0.0675938i	−0.557394	−	0.830248i	$-0.688199\pi$
$337$	−39.4546	+	22.7791i	−0.117076	+	0.0675938i	0.440319	+	0.897842i	$0.354866\pi$
$338$		0			0
$339$	38.2192	+	66.1976i	0.112741	+	0.195273i
$340$		0			0
$341$			568.632i			1.66754i
$342$		0			0
$343$	−159.256			−0.464302
$344$		0			0
$345$	31.2896	−	18.0651i	0.0906945	−	0.0523625i
$346$		0			0
$347$	94.0195	+	162.847i	0.270949	+	0.469298i	0.969105	−	0.246648i	$-0.0793290\pi$
$347$	94.0195	+	162.847i	0.270949	+	0.469298i	−0.698156	+	0.715946i	$0.745996\pi$
$348$		0			0
$349$	−17.4375			−0.0499643			−0.0249821	−	0.999688i	$-0.507953\pi$
$349$	−17.4375			−0.0499643			−0.0249821	+	0.999688i	$0.507953\pi$
$350$		0			0
$351$	42.7034	−	73.9644i	0.121662	−	0.210725i
$352$		0			0
$353$	−191.459			−0.542378			−0.271189	−	0.962526i	$-0.587417\pi$
$353$	−191.459			−0.542378			−0.271189	+	0.962526i	$0.587417\pi$
$354$		0			0
$355$	24.6311	+	14.2208i	0.0693834	+	0.0400585i
$356$		0			0
$357$	54.5931	+	31.5194i	0.152922	+	0.0882895i
$358$		0			0
$359$	−65.3306	−	113.156i	−0.181979	−	0.315197i	0.760575	−	0.649250i	$-0.224917\pi$
$359$	−65.3306	−	113.156i	−0.181979	−	0.315197i	−0.942554	+	0.334053i	$0.891584\pi$
$360$		0			0
$361$	104.936	−	345.412i	0.290681	−	0.956820i
$362$		0			0
$363$	86.3995	−	49.8828i	0.238015	−	0.137418i
$364$		0			0
$365$	−8.15678	+	14.1280i	−0.0223473	+	0.0387067i
$366$		0			0
$367$	243.815	−	422.300i	0.664346	−	1.15068i	−0.315116	−	0.949053i	$-0.602043\pi$
$367$	243.815	−	422.300i	0.664346	−	1.15068i	0.979462	−	0.201628i	$-0.0646233\pi$
$368$		0			0
$369$		−	201.238i		−	0.545360i
$370$		0			0
$371$	−54.0938	−	31.2311i	−0.145805	−	0.0841808i
$372$		0			0
$373$			216.022i			0.579147i	0.957156	+	0.289574i	$0.0935135\pi$
$373$			216.022i			0.579147i	−0.957156	+	0.289574i	$0.906486\pi$
$374$		0			0
$375$	−109.303	+	63.1059i	−0.291474	+	0.168282i
$376$		0			0
$377$	404.418	+	700.473i	1.07273	+	1.85802i
$378$		0			0
$379$		−	292.805i		−	0.772573i	−0.922379	−	0.386287i	$-0.873758\pi$
$379$		−	292.805i		−	0.772573i	0.922379	−	0.386287i	$-0.126242\pi$
$380$		0			0
$381$	−156.803			−0.411556
$382$		0			0
$383$	−585.063	+	337.786i	−1.52758	+	0.881948i	−0.528116	+	0.849172i	$0.677102\pi$
$383$	−585.063	+	337.786i	−1.52758	+	0.881948i	−0.999463	+	0.0327761i	$0.989565\pi$
$384$		0			0
$385$	17.0892	+	29.5994i	0.0443875	+	0.0768815i
$386$		0			0
$387$	26.7331			0.0690777
$388$		0			0
$389$	114.756	−	198.763i	0.295003	−	0.510960i	−0.679983	−	0.733228i	$-0.738013\pi$
$389$	114.756	−	198.763i	0.295003	−	0.510960i	0.974986	+	0.222268i	$0.0713461\pi$
$390$		0			0
$391$	−296.855			−0.759220
$392$		0			0
$393$	248.512	+	143.479i	0.632346	+	0.365085i
$394$		0			0
$395$	−114.185	−	65.9246i	−0.289075	−	0.166898i
$396$		0			0
$397$	−190.690	−	330.284i	−0.480327	−	0.831951i	0.519418	−	0.854520i	$-0.326149\pi$
$397$	−190.690	−	330.284i	−0.480327	−	0.831951i	−0.999745	+	0.0225695i	$0.992815\pi$
$398$		0			0
$399$	21.9069	−	50.5044i	0.0549045	−	0.126577i
$400$		0			0
$401$	395.218	−	228.179i	0.985581	−	0.569025i	0.0816306	−	0.996663i	$-0.473987\pi$
$401$	395.218	−	228.179i	0.985581	−	0.569025i	0.903950	+	0.427637i	$0.140654\pi$
$402$		0			0
$403$	349.680	−	605.664i	0.867693	−	1.50289i
$404$		0			0
$405$	−6.87977	+	11.9161i	−0.0169871	+	0.0294225i
$406$		0			0
$407$			369.877i			0.908790i
$408$		0			0
$409$	−39.6757	−	22.9068i	−0.0970065	−	0.0560067i	0.450712	−	0.892669i	$-0.351170\pi$
$409$	−39.6757	−	22.9068i	−0.0970065	−	0.0560067i	−0.547718	+	0.836663i	$0.684504\pi$
$410$		0			0
$411$			383.265i			0.932518i
$412$		0			0
$413$	−19.7069	+	11.3778i	−0.0477165	+	0.0275491i
$414$		0			0
$415$	5.53302	+	9.58347i	0.0133326	+	0.0230927i
$416$		0			0
$417$			339.357i			0.813807i
$418$		0			0
$419$	−212.009			−0.505989			−0.252995	−	0.967468i	$-0.581415\pi$
$419$	−212.009			−0.505989			−0.252995	+	0.967468i	$0.581415\pi$
$420$		0			0
$421$	294.940	−	170.284i	0.700571	−	0.404475i	−0.106989	−	0.994260i	$-0.534121\pi$
$421$	294.940	−	170.284i	0.700571	−	0.404475i	0.807560	+	0.589785i	$0.200788\pi$
$422$		0			0
$423$	−35.6789	−	61.7976i	−0.0843472	−	0.146094i
$424$		0			0
$425$	493.069			1.16016
$426$		0			0
$427$	9.68887	−	16.7816i	0.0226906	−	0.0393012i
$428$		0			0
$429$	−380.462			−0.886857
$430$		0			0
$431$	−665.265	−	384.091i	−1.54354	−	0.891162i	−0.998612	−	0.0526786i	$-0.983224\pi$
$431$	−665.265	−	384.091i	−1.54354	−	0.891162i	−0.544927	−	0.838484i	$-0.683443\pi$
$432$		0			0
$433$	−477.168	−	275.493i	−1.10200	−	0.636242i	−0.165257	−	0.986251i	$-0.552845\pi$
$433$	−477.168	−	275.493i	−1.10200	−	0.636242i	−0.936747	+	0.350009i	$0.886179\pi$
$434$		0			0
$435$	−65.1542	−	112.850i	−0.149780	−	0.259426i
$436$		0			0
$437$	29.5743	+	257.547i	0.0676758	+	0.589353i
$438$		0			0
$439$	717.509	−	414.254i	1.63442	−	0.943631i	0.651708	−	0.758470i	$-0.274053\pi$
$439$	717.509	−	414.254i	1.63442	−	0.943631i	0.982708	−	0.185161i	$-0.0592807\pi$
$440$		0			0
$441$	−69.3025	+	120.035i	−0.157149	+	0.272189i
$442$		0			0
$443$	−211.725	+	366.719i	−0.477935	+	0.827807i	−0.999680	−	0.0252941i	$-0.991948\pi$
$443$	−211.725	+	366.719i	−0.477935	+	0.827807i	0.521745	+	0.853101i	$0.325281\pi$
$444$		0			0
$445$		−	143.140i		−	0.321663i
$446$		0			0
$447$	204.046	+	117.806i	0.456480	+	0.263549i
$448$		0			0
$449$		−	60.0968i		−	0.133846i	−0.997758	−	0.0669230i	$-0.978682\pi$
$449$		−	60.0968i		−	0.133846i	0.997758	−	0.0669230i	$-0.0213182\pi$
$450$		0			0
$451$	−776.353	+	448.228i	−1.72140	+	0.993853i
$452$		0			0
$453$	−154.375	−	267.385i	−0.340784	−	0.590255i
$454$		0			0
$455$		−	42.0360i		−	0.0923868i
$456$		0			0
$457$	35.8562			0.0784599			0.0392299	−	0.999230i	$-0.487510\pi$
$457$	35.8562			0.0784599			0.0392299	+	0.999230i	$0.487510\pi$
$458$		0			0
$459$	97.9059	−	56.5260i	0.213303	−	0.123150i
$460$		0			0
$461$	10.8422	+	18.7793i	0.0235190	+	0.0407360i	0.877545	−	0.479494i	$-0.159180\pi$
$461$	10.8422	+	18.7793i	0.0235190	+	0.0407360i	−0.854026	+	0.520230i	$0.825846\pi$
$462$		0			0
$463$	153.576			0.331697			0.165848	−	0.986151i	$-0.446964\pi$
$463$	153.576			0.331697			0.165848	+	0.986151i	$0.446964\pi$
$464$		0			0
$465$	−56.3356	+	97.5761i	−0.121152	+	0.209841i
$466$		0			0
$467$	67.0282			0.143529			0.0717646	−	0.997422i	$-0.477137\pi$
$467$	67.0282			0.143529			0.0717646	+	0.997422i	$0.477137\pi$
$468$		0			0
$469$	143.877	+	83.0673i	0.306773	+	0.177116i
$470$		0			0
$471$	52.8257	+	30.4989i	0.112156	+	0.0647536i
$472$		0			0
$473$	−59.5440	−	103.133i	−0.125886	−	0.218041i
$474$		0			0
$475$	−49.1222	−	427.779i	−0.103415	−	0.900588i
$476$		0			0
$477$	−97.0104	+	56.0090i	−0.203376	+	0.117419i
$478$		0			0
$479$	166.925	−	289.123i	0.348487	−	0.603597i	−0.637494	−	0.770455i	$-0.720029\pi$
$479$	166.925	−	289.123i	0.348487	−	0.603597i	0.985981	+	0.166859i	$0.0533623\pi$
$480$		0			0
$481$	227.456	−	393.966i	0.472882	−	0.819055i
$482$		0			0
$483$			39.5329i			0.0818486i
$484$		0			0
$485$	181.836	+	104.983i	0.374920	+	0.216460i
$486$		0			0
$487$		−	130.381i		−	0.267723i	−0.991000	−	0.133862i	$-0.957262\pi$
$487$		−	130.381i		−	0.267723i	0.991000	−	0.133862i	$-0.0427378\pi$
$488$		0			0
$489$	204.986	−	118.349i	0.419195	−	0.242022i
$490$		0			0
$491$	−385.973	−	668.524i	−0.786095	−	1.36156i	−0.928343	−	0.371725i	$-0.878766\pi$
$491$	−385.973	−	668.524i	−0.786095	−	1.36156i	0.142248	−	0.989831i	$-0.454567\pi$
$492$		0			0
$493$			1070.65i			2.17170i
$494$		0			0
$495$	61.2947			0.123828
$496$		0			0
$497$	−26.9509	+	15.5601i	−0.0542271	+	0.0313080i
$498$		0			0
$499$	441.323	+	764.394i	0.884416	+	1.53185i	0.846382	+	0.532576i	$0.178776\pi$
$499$	441.323	+	764.394i	0.884416	+	1.53185i	0.0380335	+	0.999276i	$0.487891\pi$
$500$		0			0
$501$	117.770			0.235070
$502$		0			0
$503$	−239.319	+	414.512i	−0.475783	+	0.824080i	−0.999615	−	0.0277415i	$-0.991168\pi$
$503$	−239.319	+	414.512i	−0.475783	+	0.824080i	0.523832	+	0.851821i	$0.324502\pi$
$504$		0			0
$505$	−187.739			−0.371761
$506$		0			0
$507$	151.739	+	87.6067i	0.299288	+	0.172794i
$508$		0			0
$509$	−220.589	−	127.357i	−0.433377	−	0.250210i	0.267407	−	0.963584i	$-0.413833\pi$
$509$	−220.589	−	127.357i	−0.433377	−	0.250210i	−0.700784	+	0.713373i	$0.747166\pi$
$510$		0			0
$511$	−8.92499	−	15.4585i	−0.0174657	−	0.0302515i
$512$		0			0
$513$	−58.7951	−	79.3104i	−0.114610	−	0.154601i
$514$		0			0
$515$	−123.255	+	71.1613i	−0.239330	+	0.138177i
$516$		0			0
$517$	−158.939	+	275.290i	−0.307425	+	0.532476i
$518$		0			0
$519$	48.3896	−	83.8132i	0.0932362	−	0.161490i
$520$		0			0
$521$		−	623.420i		−	1.19658i	−0.801279	−	0.598291i	$-0.795847\pi$
$521$		−	623.420i		−	1.19658i	0.801279	−	0.598291i	$-0.204153\pi$
$522$		0			0
$523$	472.852	+	273.001i	0.904115	+	0.521991i	0.878533	−	0.477682i	$-0.158523\pi$
$523$	472.852	+	273.001i	0.904115	+	0.521991i	0.0255821	+	0.999673i	$0.491856\pi$
$524$		0			0
$525$		−	65.6631i		−	0.125073i
$526$		0			0
$527$	801.712	−	462.869i	1.52127	−	0.878308i
$528$		0			0
$529$	171.418	+	296.905i	0.324042	+	0.561257i
$530$		0			0
$531$			40.8093i			0.0768537i
$532$		0			0
$533$	1102.55			2.06857
$534$		0			0
$535$	−5.40858	+	3.12265i	−0.0101095	+	0.00583672i
$536$		0			0
$537$	105.386	+	182.533i	0.196249	+	0.339913i
$538$		0			0
$539$	617.444			1.14554
$540$		0			0
$541$	198.902	−	344.509i	0.367657	−	0.636801i	−0.621542	−	0.783381i	$-0.713493\pi$
$541$	198.902	−	344.509i	0.367657	−	0.636801i	0.989199	+	0.146580i	$0.0468267\pi$
$542$		0			0
$543$	245.241			0.451641
$544$		0			0
$545$	−208.742	−	120.517i	−0.383012	−	0.221132i
$546$		0			0
$547$	364.014	+	210.163i	0.665473	+	0.384211i	0.794359	−	0.607448i	$-0.207807\pi$
$547$	364.014	+	210.163i	0.665473	+	0.384211i	−0.128886	+	0.991659i	$0.541140\pi$
$548$		0			0
$549$	−17.3758	−	30.0957i	−0.0316499	−	0.0548192i
$550$		0			0
$551$	928.880	−	106.664i	1.68581	−	0.193583i
$552$		0			0
$553$	124.939	−	72.1334i	0.225929	−	0.130440i
$554$		0			0
$555$	−36.6445	+	63.4702i	−0.0660262	+	0.114361i
$556$		0			0
$557$	199.353	−	345.290i	0.357906	−	0.619911i	−0.629705	−	0.776834i	$-0.716824\pi$
$557$	199.353	−	345.290i	0.357906	−	0.619911i	0.987611	+	0.156923i	$0.0501576\pi$
$558$		0			0
$559$			146.466i			0.262015i
$560$		0			0
$561$	−436.142	−	251.807i	−0.777437	−	0.448853i
$562$		0			0
$563$			105.735i			0.187806i	0.995581	+	0.0939028i	$0.0299343\pi$
$563$			105.735i			0.187806i	−0.995581	+	0.0939028i	$0.970066\pi$
$564$		0			0
$565$	58.4309	−	33.7351i	0.103418	−	0.0597082i
$566$		0			0
$567$	−7.52771	−	13.0384i	−0.0132764	−	0.0229954i
$568$		0			0
$569$		−	221.061i		−	0.388508i	−0.980951	−	0.194254i	$-0.937771\pi$
$569$		−	221.061i		−	0.388508i	0.980951	−	0.194254i	$-0.0622286\pi$
$570$		0			0
$571$	516.662			0.904837			0.452419	−	0.891806i	$-0.350561\pi$
$571$	516.662			0.904837			0.452419	+	0.891806i	$0.350561\pi$
$572$		0			0
$573$	82.4175	−	47.5838i	0.143835	−	0.0830432i
$574$		0			0
$575$	154.607	+	267.787i	0.268881	+	0.465716i
$576$		0			0
$577$	333.786			0.578484			0.289242	−	0.957256i	$-0.406597\pi$
$577$	333.786			0.578484			0.289242	+	0.957256i	$0.406597\pi$
$578$		0			0
$579$	315.753	−	546.901i	0.545342	−	0.944561i
$580$		0			0
$581$	−12.1082			−0.0208403
$582$		0			0
$583$	432.153	+	249.504i	0.741257	+	0.427965i
$584$		0			0
$585$	−65.2865	−	37.6932i	−0.111601	−	0.0644328i
$586$		0			0
$587$	−305.631	−	529.369i	−0.520667	−	0.901821i	−0.999711	−	0.0240308i	$-0.992350\pi$
$587$	−305.631	−	529.369i	−0.520667	−	0.901821i	0.479044	−	0.877791i	$-0.340983\pi$
$588$		0			0
$589$	−481.449	−	649.440i	−0.817401	−	1.10262i
$590$		0			0
$591$	−287.442	+	165.955i	−0.486365	+	0.280803i
$592$		0			0
$593$	346.490	−	600.138i	0.584300	−	1.01204i	−0.410663	−	0.911787i	$-0.634703\pi$
$593$	346.490	−	600.138i	0.584300	−	1.01204i	0.994962	−	0.100249i	$-0.0319641\pi$
$594$		0			0
$595$	27.8213	−	48.1880i	0.0467585	−	0.0809882i
$596$		0			0
$597$			117.057i			0.196075i
$598$		0			0
$599$	−774.830	−	447.348i	−1.29354	−	0.746825i	−0.314259	−	0.949337i	$-0.601756\pi$
$599$	−774.830	−	447.348i	−1.29354	−	0.746825i	−0.979280	+	0.202512i	$0.935089\pi$
$600$		0			0
$601$			517.412i			0.860919i	0.902610	+	0.430460i	$0.141648\pi$
$601$			517.412i			0.860919i	−0.902610	+	0.430460i	$0.858352\pi$
$602$		0			0
$603$	258.025	−	148.971i	0.427902	−	0.247049i
$604$		0			0
$605$	−44.0303	−	76.2626i	−0.0727773	−	0.126054i
$606$		0			0
$607$		−	219.019i		−	0.360822i	−0.983591	−	0.180411i	$-0.942257\pi$
$607$		−	219.019i		−	0.360822i	0.983591	−	0.180411i	$-0.0577427\pi$
$608$		0			0
$609$	142.581			0.234123
$610$		0			0
$611$	338.579	−	195.479i	0.554140	−	0.319933i
$612$		0			0
$613$	−237.343	−	411.091i	−0.387183	−	0.670621i	0.604886	−	0.796312i	$-0.293219\pi$
$613$	−237.343	−	411.091i	−0.387183	−	0.670621i	−0.992069	+	0.125691i	$0.959885\pi$
$614$		0			0
$615$	−177.628			−0.288825
$616$		0			0
$617$	155.471	−	269.284i	0.251979	−	0.436441i	−0.712092	−	0.702087i	$-0.752252\pi$
$617$	155.471	−	269.284i	0.251979	−	0.436441i	0.964071	+	0.265646i	$0.0855852\pi$
$618$		0			0
$619$	487.156			0.787005			0.393503	−	0.919323i	$-0.371263\pi$
$619$	487.156			0.787005			0.393503	+	0.919323i	$0.371263\pi$
$620$		0			0
$621$	61.3988	+	35.4486i	0.0988709	+	0.0570831i
$622$		0			0
$623$	135.638	+	78.3105i	0.217717	+	0.125699i
$624$		0			0
$625$	−227.581	−	394.182i	−0.364130	−	0.630692i
$626$		0			0
$627$	−175.013	+	403.477i	−0.279128	+	0.643504i
$628$		0			0
$629$	521.488	−	301.081i	0.829075	−	0.478667i
$630$		0			0
$631$	−304.100	+	526.717i	−0.481934	+	0.834734i	−0.999785	−	0.0207369i	$-0.993399\pi$
$631$	−304.100	+	526.717i	−0.481934	+	0.834734i	0.517851	+	0.855471i	$0.326732\pi$
$632$		0			0
$633$	−76.4694	+	132.449i	−0.120805	+	0.209240i
$634$		0			0
$635$			138.406i			0.217962i
$636$		0			0
$637$	−657.655	−	379.697i	−1.03243	−	0.596071i
$638$		0			0
$639$			55.8101i			0.0873398i
$640$		0			0
$641$	−345.251	+	199.331i	−0.538613	+	0.310969i	−0.744517	−	0.667604i	$-0.767320\pi$
$641$	−345.251	+	199.331i	−0.538613	+	0.310969i	0.205903	+	0.978572i	$0.433987\pi$
$642$		0			0
$643$	−105.542	−	182.804i	−0.164140	−	0.284299i	0.772210	−	0.635368i	$-0.219152\pi$
$643$	−105.542	−	182.804i	−0.164140	−	0.284299i	−0.936349	+	0.351069i	$0.885818\pi$
$644$		0			0
$645$		−	23.5966i		−	0.0365839i
$646$		0			0
$647$	859.605			1.32860			0.664301	−	0.747465i	$-0.268729\pi$
$647$	859.605			1.32860			0.664301	+	0.747465i	$0.268729\pi$
$648$		0			0
$649$	157.438	−	90.8967i	0.242585	−	0.140057i
$650$		0			0
$651$	−61.6413	−	106.766i	−0.0946871	−	0.164003i
$652$		0			0
$653$	−971.150			−1.48721			−0.743606	−	0.668618i	$-0.766886\pi$
$653$	−971.150			−1.48721			−0.743606	+	0.668618i	$0.766886\pi$
$654$		0			0
$655$	126.645	−	219.355i	0.193351	−	0.334894i
$656$		0			0
$657$	−32.0117			−0.0487240
$658$		0			0
$659$	769.270	+	444.138i	1.16733	+	0.673958i	0.953050	−	0.302814i	$-0.0979261\pi$
$659$	769.270	+	444.138i	1.16733	+	0.673958i	0.214280	+	0.976772i	$0.431259\pi$
$660$		0			0
$661$	439.175	+	253.558i	0.664409	+	0.383597i	0.793955	−	0.607977i	$-0.208019\pi$
$661$	439.175	+	253.558i	0.664409	+	0.383597i	−0.129546	+	0.991573i	$0.541352\pi$
$662$		0			0
$663$	309.697	+	536.411i	0.467115	+	0.809067i
$664$		0			0
$665$	−44.5789	−	19.3366i	−0.0670360	−	0.0290777i
$666$		0			0
$667$	−581.472	+	335.713i	−0.871772	+	0.503318i
$668$		0			0
$669$	−95.4499	+	165.324i	−0.142676	+	0.247121i
$670$		0			0
$671$	−77.4040	+	134.068i	−0.115356	+	0.199803i
$672$		0			0
$673$			955.112i			1.41919i	0.704612	+	0.709593i	$0.251121\pi$
$673$			955.112i			1.41919i	−0.704612	+	0.709593i	$0.748879\pi$
$674$		0			0
$675$	−101.982	−	58.8793i	−0.151084	−	0.0872286i
$676$		0			0
$677$			1243.14i			1.83624i	0.396298	+	0.918122i	$0.370295\pi$
$677$			1243.14i			1.83624i	−0.396298	+	0.918122i	$0.629705\pi$
$678$		0			0
$679$	−198.962	+	114.871i	−0.293022	+	0.169176i
$680$		0			0
$681$	30.6179	+	53.0318i	0.0449602	+	0.0778734i
$682$		0			0
$683$			86.0288i			0.125957i	0.998015	+	0.0629786i	$0.0200600\pi$
$683$			86.0288i			0.125957i	−0.998015	+	0.0629786i	$0.979940\pi$
$684$		0			0
$685$	338.298			0.493866
$686$		0			0
$687$	−387.277	+	223.595i	−0.563722	+	0.325465i
$688$		0			0
$689$	−306.864	−	531.505i	−0.445377	−	0.771415i
$690$		0			0
$691$	−482.988			−0.698970			−0.349485	−	0.936942i	$-0.613643\pi$
$691$	−482.988			−0.698970			−0.349485	+	0.936942i	$0.613643\pi$
$692$		0			0
$693$	−33.5337	+	58.0821i	−0.0483892	+	0.0838126i
$694$		0			0
$695$	299.542			0.430996
$696$		0			0
$697$	1263.91	+	729.718i	1.81335	+	1.04694i
$698$		0			0
$699$	−659.569	−	380.802i	−0.943589	−	0.544781i
$700$		0			0
$701$	280.255	+	485.416i	0.399794	+	0.692463i	0.993700	−	0.112071i	$-0.0357485\pi$
$701$	280.255	+	485.416i	0.399794	+	0.692463i	−0.593907	+	0.804534i	$0.702415\pi$
$702$		0			0
$703$	−313.168	−	422.441i	−0.445473	−	0.600911i
$704$		0			0
$705$	−54.5472	+	31.4928i	−0.0773719	+	0.0446707i
$706$		0			0
$707$	102.710	−	177.899i	0.145276	−	0.251626i
$708$		0			0
$709$	−143.453	+	248.468i	−0.202331	+	0.350448i	−0.949279	−	0.314434i	$-0.898185\pi$
$709$	−143.453	+	248.468i	−0.202331	+	0.350448i	0.746948	+	0.664883i	$0.231519\pi$
$710$		0			0
$711$		−	258.725i		−	0.363888i
$712$		0			0
$713$	502.770	+	290.274i	0.705147	+	0.407117i
$714$		0			0
$715$			335.824i			0.469684i
$716$		0			0
$717$	712.211	−	411.195i	0.993320	−	0.573494i
$718$		0			0
$719$	−516.409	−	894.447i	−0.718233	−	1.24402i	−0.961699	−	0.274107i	$-0.911618\pi$
$719$	−516.409	−	894.447i	−0.718233	−	1.24402i	0.243466	−	0.969909i	$-0.421715\pi$
$720$		0			0
$721$		−	155.727i		−	0.215987i
$722$		0			0
$723$	282.704			0.391016
$724$		0			0
$725$	965.811	−	557.611i	1.33215	−	0.769119i
$726$		0			0
$727$	−578.109	−	1001.31i	−0.795198	−	1.37732i	−0.922713	−	0.385487i	$-0.874033\pi$
$727$	−578.109	−	1001.31i	−0.795198	−	1.37732i	0.127515	−	0.991837i	$-0.459300\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−96.9381	+	167.902i	−0.132610	+	0.229688i
$732$		0			0
$733$	342.819			0.467692			0.233846	−	0.972274i	$-0.424869\pi$
$733$	342.819			0.467692			0.233846	+	0.972274i	$0.424869\pi$
$734$		0			0
$735$	105.952	+	61.1715i	0.144153	+	0.0832266i
$736$		0			0
$737$	−1149.43	−	663.621i	−1.55960	−	0.900435i
$738$		0			0
$739$	26.8369	+	46.4829i	0.0363152	+	0.0628997i	0.883612	−	0.468220i	$-0.155105\pi$
$739$	26.8369	+	46.4829i	0.0363152	+	0.0628997i	−0.847297	+	0.531120i	$0.821771\pi$
$740$		0			0
$741$	434.529	−	322.129i	0.586409	−	0.434722i
$742$		0			0
$743$	769.551	−	444.300i	1.03573	−	0.597982i	0.117113	−	0.993119i	$-0.462636\pi$
$743$	769.551	−	444.300i	1.03573	−	0.597982i	0.918622	+	0.395137i	$0.129303\pi$
$744$		0			0
$745$	103.985	−	180.107i	0.139577	−	0.241754i
$746$		0			0
$747$	−10.8573	+	18.8054i	−0.0145345	+	0.0251746i
$748$		0			0
$749$		−	6.83348i		−	0.00912347i
$750$		0			0
$751$	137.952	+	79.6464i	0.183690	+	0.106054i	0.589025	−	0.808114i	$-0.299512\pi$
$751$	137.952	+	79.6464i	0.183690	+	0.106054i	−0.405335	+	0.914168i	$0.632845\pi$
$752$		0			0
$753$			756.272i			1.00435i
$754$		0			0
$755$	−236.014	+	136.263i	−0.312602	+	0.180481i
$756$		0			0
$757$	−557.688	−	965.943i	−0.736708	−	1.27601i	−0.953970	−	0.299902i	$-0.903046\pi$
$757$	−557.688	−	965.943i	−0.736708	−	1.27601i	0.217262	−	0.976113i	$-0.430287\pi$
$758$		0			0
$759$		−	315.827i		−	0.416109i
$760$		0			0
$761$	235.790			0.309843			0.154921	−	0.987927i	$-0.450488\pi$
$761$	235.790			0.309843			0.154921	+	0.987927i	$0.450488\pi$
$762$		0			0
$763$	228.401	−	131.867i	0.299346	−	0.172827i
$764$		0			0
$765$	−49.8941	−	86.4191i	−0.0652210	−	0.112966i
$766$		0			0
$767$	−223.588			−0.291509
$768$		0			0
$769$	−204.338	+	353.924i	−0.265719	+	0.460239i	−0.967752	−	0.251906i	$-0.918943\pi$
$769$	−204.338	+	353.924i	−0.265719	+	0.460239i	0.702033	+	0.712145i	$0.252276\pi$
$770$		0			0
$771$	−546.157			−0.708375
$772$		0			0
$773$	305.197	+	176.206i	0.394822	+	0.227950i	0.684247	−	0.729250i	$-0.260131\pi$
$773$	305.197	+	176.206i	0.394822	+	0.227950i	−0.289426	+	0.957201i	$0.593464\pi$
$774$		0			0
$775$	−835.089	−	482.139i	−1.07753	−	0.622114i
$776$		0			0
$777$	−40.0957	−	69.4479i	−0.0516033	−	0.0893795i
$778$		0			0
$779$	507.175	−	1169.25i	0.651059	−	1.50096i
$780$		0			0
$781$	215.309	−	124.309i	0.275684	−	0.159166i
$782$		0			0
$783$	127.851	−	221.444i	0.163283	−	0.282814i
$784$		0			0
$785$	26.9206	−	46.6279i	0.0342938	−	0.0593986i
$786$		0			0
$787$		−	229.730i		−	0.291906i	−0.989292	−	0.145953i	$-0.953375\pi$
$787$		−	229.730i		−	0.291906i	0.989292	−	0.145953i	$-0.0466248\pi$
$788$		0			0
$789$	−261.589	−	151.028i	−0.331544	−	0.191417i
$790$		0			0
$791$			73.8246i			0.0933307i
$792$		0			0
$793$	164.890	−	95.1992i	0.207932	−	0.120049i
$794$		0			0
$795$	49.4377	+	85.6286i	0.0621858	+	0.107709i
$796$		0			0
$797$		−	318.880i		−	0.400100i	−0.979786	−	0.200050i	$-0.935890\pi$
$797$		−	318.880i		−	0.400100i	0.979786	−	0.200050i	$-0.0641105\pi$
$798$		0			0
$799$	517.507			0.647693
$800$		0			0
$801$	243.249	−	140.440i	0.303682	−	0.175331i
$802$		0			0
$803$	71.3013	+	123.498i	0.0887937	+	0.153795i
$804$		0			0
$805$	34.8947			0.0433474
$806$		0			0
$807$	−209.828	+	363.432i	−0.260009	+	0.450349i
$808$		0			0
$809$	271.092			0.335096			0.167548	−	0.985864i	$-0.446415\pi$
$809$	271.092			0.335096			0.167548	+	0.985864i	$0.446415\pi$
$810$		0			0
$811$	−677.502	−	391.156i	−0.835391	−	0.482313i	0.0203038	−	0.999794i	$-0.493537\pi$
$811$	−677.502	−	391.156i	−0.835391	−	0.482313i	−0.855695	+	0.517481i	$0.826870\pi$
$812$		0			0
$813$	409.819	+	236.609i	0.504082	+	0.291032i
$814$		0			0
$815$	−104.463	−	180.936i	−0.128176	−	0.222007i
$816$		0			0
$817$	155.327	+	67.3748i	0.190118	+	0.0824661i
$818$		0			0
$819$	71.4352	−	41.2431i	0.0872224	−	0.0503579i
$820$		0			0
$821$	60.0903	−	104.079i	0.0731916	−	0.126772i	−0.827107	−	0.562045i	$-0.810015\pi$
$821$	60.0903	−	104.079i	0.0731916	−	0.126772i	0.900298	+	0.435273i	$0.143348\pi$
$822$		0			0
$823$	−521.288	+	902.897i	−0.633400	+	1.09708i	0.353452	+	0.935453i	$0.385008\pi$
$823$	−521.288	+	902.897i	−0.633400	+	1.09708i	−0.986852	+	0.161628i	$0.948326\pi$
$824$		0			0
$825$			524.580i			0.635855i
$826$		0			0
$827$	−173.617	−	100.238i	−0.209936	−	0.121207i	0.391346	−	0.920244i	$-0.372010\pi$
$827$	−173.617	−	100.238i	−0.209936	−	0.121207i	−0.601282	+	0.799037i	$0.705343\pi$
$828$		0			0
$829$		−	1068.85i		−	1.28933i	−0.764465	−	0.644665i	$-0.776997\pi$
$829$		−	1068.85i		−	1.28933i	0.764465	−	0.644665i	$-0.223003\pi$
$830$		0			0
$831$	−795.810	+	459.461i	−0.957654	+	0.552902i
$832$		0			0
$833$	−502.602	−	870.532i	−0.603364	−	1.04506i
$834$		0			0
$835$		−	103.953i		−	0.124494i
$836$		0			0
$837$	−221.092			−0.264148
$838$		0			0
$839$	276.256	−	159.496i	0.329268	−	0.190103i	−0.326248	−	0.945284i	$-0.605784\pi$
$839$	276.256	−	159.496i	0.329268	−	0.190103i	0.655516	+	0.755181i	$0.272451\pi$
$840$		0			0
$841$	790.297	+	1368.83i	0.939711	+	1.62763i
$842$		0			0
$843$	−747.756			−0.887018
$844$		0			0
$845$	77.3282	−	133.936i	0.0915126	−	0.158505i
$846$		0			0
$847$	96.3541			0.113759
$848$		0			0
$849$	302.733	+	174.783i	0.356576	+	0.205869i
$850$		0			0
$851$	327.036	+	188.814i	0.384296	+	0.221874i
$852$		0			0
$853$	690.204	+	1195.47i	0.809149	+	1.40149i	0.913454	+	0.406941i	$0.133405\pi$
$853$	690.204	+	1195.47i	0.809149	+	1.40149i	−0.104306	+	0.994545i	$0.533262\pi$
$854$		0			0
$855$	−70.0052	+	51.8969i	−0.0818775	+	0.0606982i
$856$		0			0
$857$	−329.128	+	190.022i	−0.384047	+	0.221730i	−0.679578	−	0.733604i	$-0.737837\pi$
$857$	−329.128	+	190.022i	−0.384047	+	0.221730i	0.295531	+	0.955333i	$0.404504\pi$
$858$		0			0
$859$	235.815	−	408.444i	0.274523	−	0.475487i	−0.695492	−	0.718534i	$-0.744813\pi$
$859$	235.815	−	408.444i	0.274523	−	0.475487i	0.970015	+	0.243047i	$0.0781468\pi$
$860$		0			0
$861$	97.1783	−	168.318i	0.112867	−	0.195491i
$862$		0			0
$863$			255.574i			0.296147i	0.988976	+	0.148073i	$0.0473071\pi$
$863$			255.574i			0.296147i	−0.988976	+	0.148073i	$0.952693\pi$
$864$		0			0
$865$	−73.9798	−	42.7123i	−0.0855258	−	0.0493783i
$866$		0			0
$867$			319.324i			0.368309i
$868$		0			0
$869$	−998.130	+	576.271i	−1.14860	+	0.663143i
$870$		0			0
$871$	816.187	+	1413.68i	0.937069	+	1.62305i
$872$		0			0
$873$			412.012i			0.471950i
$874$		0			0
$875$	−121.896			−0.139310
$876$		0			0
$877$	−879.977	+	508.055i	−1.00339	+	0.579310i	−0.909251	−	0.416249i	$-0.863345\pi$
$877$	−879.977	+	508.055i	−1.00339	+	0.579310i	−0.0941434	+	0.995559i	$0.530011\pi$
$878$		0			0
$879$	284.880	+	493.427i	0.324096	+	0.561350i
$880$		0			0
$881$	−1218.43			−1.38301			−0.691506	−	0.722371i	$-0.743052\pi$
$881$	−1218.43			−1.38301			−0.691506	+	0.722371i	$0.743052\pi$
$882$		0			0
$883$	239.852	−	415.435i	0.271633	−	0.470481i	−0.697647	−	0.716441i	$-0.745770\pi$
$883$	239.852	−	415.435i	0.271633	−	0.470481i	0.969280	+	0.245960i	$0.0791031\pi$
$884$		0			0
$885$	36.0213			0.0407021
$886$		0			0
$887$	830.055	+	479.232i	0.935800	+	0.540284i	0.888641	−	0.458603i	$-0.151650\pi$
$887$	830.055	+	479.232i	0.935800	+	0.540284i	0.0471588	+	0.998887i	$0.484983\pi$
$888$		0			0
$889$	−131.152	−	75.7205i	−0.147527	−	0.0851750i
$890$		0			0
$891$	60.1385	+	104.163i	0.0674955	+	0.116906i
$892$		0			0
$893$	−51.5569	−	448.982i	−0.0577345	−	0.502779i
$894$		0			0
$895$	161.117	−	93.0212i	0.180019	−	0.103934i
$896$		0			0
$897$	−194.217	+	336.395i	−0.216519	+	0.375022i
$898$		0			0
$899$	1046.92	−	1813.31i	1.16453	−	2.01703i
$900$		0			0
$901$		−	812.387i		−	0.901651i
$902$		0			0
$903$	22.3599	+	12.9095i	0.0247618	+	0.0142962i
$904$		0			0
$905$		−	216.468i		−	0.239191i
$906$		0			0
$907$	−681.648	+	393.550i	−0.751541	+	0.433903i	−0.826251	−	0.563303i	$-0.809530\pi$
$907$	−681.648	+	393.550i	−0.751541	+	0.433903i	0.0747092	+	0.997205i	$0.476197\pi$
$908$		0			0
$909$	−184.198	−	319.040i	−0.202638	−	0.350980i
$910$		0			0
$911$			1379.47i			1.51423i	0.653280	+	0.757116i	$0.273392\pi$
$911$			1379.47i			1.51423i	−0.653280	+	0.757116i	$0.726608\pi$
$912$		0			0
$913$	96.7322			0.105950
$914$		0			0
$915$	−26.5647	+	15.3372i	−0.0290325	+	0.0167619i
$916$		0			0
$917$	138.572	+	240.014i	0.151115	+	0.261739i
$918$		0			0
$919$	−1449.67			−1.57745			−0.788723	−	0.614749i	$-0.789257\pi$
$919$	−1449.67			−1.57745			−0.788723	+	0.614749i	$0.789257\pi$
$920$		0			0
$921$	−348.399	+	603.444i	−0.378283	+	0.655205i
$922$		0			0
$923$	−305.775			−0.331284
$924$		0			0
$925$	−543.199	−	313.616i	−0.587242	−	0.339044i
$926$		0			0
$927$	−241.860	−	139.638i	−0.260906	−	0.150634i
$928$		0			0
$929$	−583.463	−	1010.59i	−0.628055	−	1.08782i	−0.987942	−	0.154827i	$-0.950518\pi$
$929$	−583.463	−	1010.59i	−0.628055	−	1.08782i	0.359886	−	0.932996i	$-0.382815\pi$
$930$		0			0
$931$	−705.189	+	522.778i	−0.757454	+	0.561523i
$932$		0			0
$933$	−749.938	+	432.977i	−0.803792	+	0.464069i
$934$		0			0
$935$	−222.263	+	384.972i	−0.237715	+	0.411734i
$936$		0			0
$937$	240.883	−	417.221i	0.257079	−	0.445274i	−0.708379	−	0.705832i	$-0.750573\pi$
$937$	240.883	−	417.221i	0.257079	−	0.445274i	0.965458	+	0.260558i	$0.0839067\pi$
$938$		0			0
$939$			834.292i			0.888489i
$940$		0			0
$941$	1362.72	+	786.767i	1.44816	+	0.836096i	0.998372	−	0.0570386i	$-0.0181658\pi$
$941$	1362.72	+	786.767i	1.44816	+	0.836096i	0.449789	+	0.893135i	$0.351499\pi$
$942$		0			0
$943$			915.242i			0.970564i
$944$		0			0
$945$	−11.5086	+	6.64452i	−0.0121785	+	0.00703123i
$946$		0			0
$947$	−807.221	−	1398.15i	−0.852398	−	1.47640i	−0.879038	−	0.476752i	$-0.841814\pi$
$947$	−807.221	−	1398.15i	−0.852398	−	1.47640i	0.0266393	−	0.999645i	$-0.491519\pi$
$948$		0			0
$949$		−	175.387i		−	0.184812i
$950$		0			0
$951$	−76.0730			−0.0799926
$952$		0			0
$953$	−357.227	+	206.245i	−0.374844	+	0.216416i	−0.675573	−	0.737293i	$-0.736104\pi$
$953$	−357.227	+	206.245i	−0.374844	+	0.216416i	0.300728	+	0.953710i	$0.402770\pi$
$954$		0			0
$955$	−42.0010	−	72.7478i	−0.0439801	−	0.0761757i
$956$		0			0
$957$	−1139.07			−1.19025
$958$		0			0
$959$	−185.080	+	320.567i	−0.192992	+	0.334273i
$960$		0			0
$961$	−849.433			−0.883905
$962$		0			0
$963$	−10.6131	−	6.12749i	−0.0110209	−	0.00636292i
$964$		0			0
$965$	−482.735	−	278.707i	−0.500244	−	0.288816i
$966$		0			0
$967$	887.106	+	1536.51i	0.917379	+	1.58895i	0.803380	+	0.595467i	$0.203033\pi$
$967$	887.106	+	1536.51i	0.917379	+	1.58895i	0.113999	+	0.993481i	$0.463634\pi$
$968$		0			0
$969$	711.322	−	81.6816i	0.734078	−	0.0842948i
$970$		0			0
$971$	−8.88359	+	5.12894i	−0.00914890	+	0.00528212i	−0.504567	−	0.863372i	$-0.668348\pi$
$971$	−8.88359	+	5.12894i	−0.00914890	+	0.00528212i	0.495419	+	0.868654i	$0.335015\pi$
$972$		0			0
$973$	−163.877	+	283.842i	−0.168424	+	0.291719i
$974$		0			0
$975$	322.590	−	558.743i	0.330862	−	0.573070i
$976$		0			0
$977$			808.461i			0.827494i	0.910392	+	0.413747i	$0.135780\pi$
$977$			808.461i			0.827494i	−0.910392	+	0.413747i	$0.864220\pi$
$978$		0			0
$979$	−1083.60	−	625.619i	−1.10685	−	0.639039i
$980$		0			0
$981$		−	472.975i		−	0.482136i
$982$		0			0
$983$	1142.18	−	659.438i	1.16193	−	0.670842i	0.210166	−	0.977666i	$-0.432599\pi$
$983$	1142.18	−	659.438i	1.16193	−	0.670842i	0.951766	+	0.306823i	$0.0992661\pi$
$984$		0			0
$985$	146.484	+	253.718i	0.148715	+	0.257581i
$986$		0			0
$987$		−	68.9177i		−	0.0698254i
$988$		0			0
$989$	−121.584			−0.122936
$990$		0			0
$991$	448.238	−	258.790i	0.452309	−	0.261141i	−0.256496	−	0.966545i	$-0.582568\pi$
$991$	448.238	−	258.790i	0.452309	−	0.261141i	0.708805	+	0.705405i	$0.249235\pi$
$992$		0			0
$993$	448.927	+	777.565i	0.452092	+	0.783046i
$994$		0			0
$995$	103.323			0.103842
$996$		0			0
$997$	−586.552	+	1015.94i	−0.588317	+	1.01899i	0.406136	+	0.913813i	$0.366876\pi$
$997$	−586.552	+	1015.94i	−0.588317	+	1.01899i	−0.994453	+	0.105182i	$0.966458\pi$
$998$		0			0
$999$	−143.813			−0.143957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.e.145.2		6
4.3	odd	2		228.3.l.d.145.2	✓	6
12.11	even	2		684.3.y.f.145.2		6
19.8	odd	6	inner	912.3.be.e.673.2		6
76.27	even	6		228.3.l.d.217.2	yes	6
228.179	odd	6		684.3.y.f.217.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.l.d.145.2	✓	6	4.3	odd	2
228.3.l.d.217.2	yes	6	76.27	even	6
684.3.y.f.145.2		6	12.11	even	2
684.3.y.f.217.2		6	228.179	odd	6
912.3.be.e.145.2		6	1.1	even	1	trivial
912.3.be.e.673.2		6	19.8	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-0.764419 - 1.32401i) q^{5} +1.67282 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-0.764419 - 1.32401i) q^{5} +1.67282 q^{7} +(1.50000 - 2.59808i) q^{9} -13.3641 q^{11} +(14.2345 + 8.21826i) q^{13} +(-2.29326 - 1.32401i) q^{15} +(10.8784 + 18.8420i) q^{17} +(15.2633 - 11.3151i) q^{19} +(2.50924 - 1.44871i) q^{21} +(-6.82209 + 11.8162i) q^{23} +(11.3313 - 19.6264i) q^{25} -5.19615i q^{27} +(42.6168 + 24.6048i) q^{29} -42.5492i q^{31} +(-20.0462 + 11.5737i) q^{33} +(-1.27874 - 2.21484i) q^{35} -27.6769i q^{37} +28.4689 q^{39} +(58.0924 - 33.5396i) q^{41} +(4.45551 + 7.71718i) q^{43} -4.58651 q^{45} +(11.8930 - 20.5992i) q^{47} -46.2017 q^{49} +(32.6353 + 18.8420i) q^{51} +(-32.3368 - 18.6697i) q^{53} +(10.2158 + 17.6943i) q^{55} +(13.0957 - 30.1911i) q^{57} +(-11.7806 + 6.80155i) q^{59} +(5.79193 - 10.0319i) q^{61} +(2.50924 - 4.34612i) q^{63} -25.1288i q^{65} +(86.0083 + 49.6569i) q^{67} +23.6324i q^{69} +(-16.1110 + 9.30169i) q^{71} +(-5.33528 - 9.24098i) q^{73} -39.2529i q^{75} -22.3558 q^{77} +(74.6873 - 43.1208i) q^{79} +(-4.50000 - 7.79423i) q^{81} -7.23820 q^{83} +(16.6314 - 28.8064i) q^{85} +85.2337 q^{87} +(81.0831 + 46.8134i) q^{89} +(23.8117 + 13.7477i) q^{91} +(-36.8487 - 63.8238i) q^{93} +(-26.6489 - 11.5593i) q^{95} +(-118.938 + 68.6687i) q^{97} +(-20.0462 + 34.7210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9	\( 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9} + 20 q^{11} + 21 q^{13} + 12 q^{15} - 2 q^{17} + 10 q^{19} - 15 q^{21} + 2 q^{23} - 5 q^{25} + 114 q^{29} + 30 q^{33} - 32 q^{35} + 42 q^{39} + 48 q^{41} + 21 q^{43} + 24 q^{45} - 46 q^{47} - 240 q^{49} - 6 q^{51} - 18 q^{53} + 140 q^{55} - 3 q^{57} + 144 q^{59} + 19 q^{61} - 15 q^{63} - 201 q^{67} - 204 q^{71} + 51 q^{73} - 220 q^{77} - 153 q^{79} - 27 q^{81} - 52 q^{83} - 92 q^{85} + 228 q^{87} + 216 q^{89} + 57 q^{91} - 15 q^{93} + 248 q^{95} + 12 q^{97} + 30 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9 + 20 * q^11 + 21 * q^13 + 12 * q^15 - 2 * q^17 + 10 * q^19 - 15 * q^21 + 2 * q^23 - 5 * q^25 + 114 * q^29 + 30 * q^33 - 32 * q^35 + 42 * q^39 + 48 * q^41 + 21 * q^43 + 24 * q^45 - 46 * q^47 - 240 * q^49 - 6 * q^51 - 18 * q^53 + 140 * q^55 - 3 * q^57 + 144 * q^59 + 19 * q^61 - 15 * q^63 - 201 * q^67 - 204 * q^71 + 51 * q^73 - 220 * q^77 - 153 * q^79 - 27 * q^81 - 52 * q^83 - 92 * q^85 + 228 * q^87 + 216 * q^89 + 57 * q^91 - 15 * q^93 + 248 * q^95 + 12 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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