LMFDB - Embedded newform 684.3.s.a.445.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.3
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.96123 - 0.480768i) q^{3} +(-0.920304 - 1.59401i) q^{5} +(3.31490 + 5.74157i) q^{7} +(8.53772 + 2.84733i) q^{9} +O(q^{10})$	\(q+(-2.96123 - 0.480768i) q^{3} +(-0.920304 - 1.59401i) q^{5} +(3.31490 + 5.74157i) q^{7} +(8.53772 + 2.84733i) q^{9} +(-7.65648 - 13.2614i) q^{11} +2.53444i q^{13} +(1.95888 + 5.16269i) q^{15} +(-12.9506 + 22.4311i) q^{17} +(7.42625 - 17.4886i) q^{19} +(-7.05580 - 18.5958i) q^{21} +5.08329 q^{23} +(10.8061 - 18.7167i) q^{25} +(-23.9132 - 12.5362i) q^{27} +(-12.8830 - 7.43798i) q^{29} +(34.8501 + 20.1207i) q^{31} +(16.2969 + 42.9510i) q^{33} +(6.10143 - 10.5680i) q^{35} +17.0230i q^{37} +(1.21848 - 7.50505i) q^{39} +(-46.5938 + 26.9009i) q^{41} -50.4200 q^{43} +(-3.31862 - 16.2297i) q^{45} +(-32.3041 + 55.9524i) q^{47} +(2.52290 - 4.36980i) q^{49} +(49.1338 - 60.1974i) q^{51} +(-88.6168 + 51.1629i) q^{53} +(-14.0926 + 24.4091i) q^{55} +(-30.3988 + 48.2174i) q^{57} +(47.8066 - 27.6012i) q^{59} +(-41.5863 + 72.0295i) q^{61} +(11.9535 + 58.4586i) q^{63} +(4.03993 - 2.33245i) q^{65} +111.101i q^{67} +(-15.0528 - 2.44388i) q^{69} +(83.8226 + 48.3950i) q^{71} +(-66.6462 + 115.435i) q^{73} +(-40.9976 + 50.2291i) q^{75} +(50.7609 - 87.9205i) q^{77} +33.4509i q^{79} +(64.7855 + 48.6194i) q^{81} +(-45.0486 - 78.0264i) q^{83} +47.6740 q^{85} +(34.5734 + 28.2193i) q^{87} +(-26.4870 + 15.2923i) q^{89} +(-14.5517 + 8.40140i) q^{91} +(-93.5256 - 76.3368i) q^{93} +(-34.7115 + 4.25727i) q^{95} -79.5927i q^{97} +(-27.6093 - 135.023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−2.96123	−	0.480768i	−0.987075	−	0.160256i
$3$	−2.96123	−	0.480768i	−0.987075	−	0.160256i
$4$		0			0
$5$	−0.920304	−	1.59401i	−0.184061	−	0.318803i	0.759199	−	0.650859i	$-0.225591\pi$
$5$	−0.920304	−	1.59401i	−0.184061	−	0.318803i	−0.943260	+	0.332056i	$0.892258\pi$
$6$		0			0
$7$	3.31490	+	5.74157i	0.473557	+	0.820225i	0.999542	−	0.0302694i	$-0.00963651\pi$
$7$	3.31490	+	5.74157i	0.473557	+	0.820225i	−0.525985	+	0.850494i	$0.676303\pi$
$8$		0			0
$9$	8.53772	+	2.84733i	0.948636	+	0.316370i
$10$		0			0
$11$	−7.65648	−	13.2614i	−0.696044	−	1.20558i	−0.969828	−	0.243792i	$-0.921609\pi$
$11$	−7.65648	−	13.2614i	−0.696044	−	1.20558i	0.273784	−	0.961791i	$-0.411725\pi$
$12$		0			0
$13$			2.53444i			0.194957i	0.995238	+	0.0974784i	$0.0310777\pi$
$13$			2.53444i			0.194957i	−0.995238	+	0.0974784i	$0.968922\pi$
$14$		0			0
$15$	1.95888	+	5.16269i	0.130592	+	0.344179i
$16$		0			0
$17$	−12.9506	+	22.4311i	−0.761800	+	1.31948i	0.180121	+	0.983644i	$0.442351\pi$
$17$	−12.9506	+	22.4311i	−0.761800	+	1.31948i	−0.941922	+	0.335833i	$0.890982\pi$
$18$		0			0
$19$	7.42625	−	17.4886i	0.390856	−	0.920452i
$19$	7.42625	−	17.4886i	0.390856	−	0.920452i
$20$		0			0
$21$	−7.05580	−	18.5958i	−0.335990	−	0.885514i
$22$		0			0
$23$	5.08329			0.221013			0.110506	−	0.993875i	$-0.464753\pi$
$23$	5.08329			0.221013			0.110506	+	0.993875i	$0.464753\pi$
$24$		0			0
$25$	10.8061	−	18.7167i	0.432243	−	0.748667i
$26$		0			0
$27$	−23.9132	−	12.5362i	−0.885675	−	0.464305i
$28$		0			0
$29$	−12.8830	−	7.43798i	−0.444240	−	0.256482i	0.261155	−	0.965297i	$-0.415897\pi$
$29$	−12.8830	−	7.43798i	−0.444240	−	0.256482i	−0.705394	+	0.708815i	$0.749230\pi$
$30$		0			0
$31$	34.8501	+	20.1207i	1.12420	+	0.649055i	0.942469	−	0.334294i	$-0.108498\pi$
$31$	34.8501	+	20.1207i	1.12420	+	0.649055i	0.181728	+	0.983349i	$0.441831\pi$
$32$		0			0
$33$	16.2969	+	42.9510i	0.493846	+	1.30155i
$34$		0			0
$35$	6.10143	−	10.5680i	0.174326	−	0.301942i
$36$		0			0
$37$			17.0230i			0.460082i	0.973181	+	0.230041i	$0.0738861\pi$
$37$			17.0230i			0.460082i	−0.973181	+	0.230041i	$0.926114\pi$
$38$		0			0
$39$	1.21848	−	7.50505i	0.0312430	−	0.192437i
$40$		0			0
$41$	−46.5938	+	26.9009i	−1.13643	+	0.656121i	−0.945545	−	0.325491i	$-0.894470\pi$
$41$	−46.5938	+	26.9009i	−1.13643	+	0.656121i	−0.190889	+	0.981612i	$0.561137\pi$
$42$		0			0
$43$	−50.4200			−1.17256			−0.586279	−	0.810109i	$-0.699408\pi$
$43$	−50.4200			−1.17256			−0.586279	+	0.810109i	$0.699408\pi$
$44$		0			0
$45$	−3.31862	−	16.2297i	−0.0737472	−	0.360659i
$46$		0			0
$47$	−32.3041	+	55.9524i	−0.687322	+	1.19048i	0.285380	+	0.958415i	$0.407880\pi$
$47$	−32.3041	+	55.9524i	−0.687322	+	1.19048i	−0.972701	+	0.232061i	$0.925453\pi$
$48$		0			0
$49$	2.52290	−	4.36980i	0.0514878	−	0.0891795i
$50$		0			0
$51$	49.1338	−	60.1974i	0.963409	−	1.18034i
$52$		0			0
$53$	−88.6168	+	51.1629i	−1.67201	+	0.965338i	−0.705506	+	0.708704i	$0.749280\pi$
$53$	−88.6168	+	51.1629i	−1.67201	+	0.965338i	−0.966509	+	0.256634i	$0.917387\pi$
$54$		0			0
$55$	−14.0926	+	24.4091i	−0.256229	+	0.443801i
$56$		0			0
$57$	−30.3988	+	48.2174i	−0.533312	+	0.845919i
$58$		0			0
$59$	47.8066	−	27.6012i	0.810281	−	0.467816i	−0.0367722	−	0.999324i	$-0.511708\pi$
$59$	47.8066	−	27.6012i	0.810281	−	0.467816i	0.847054	+	0.531508i	$0.178374\pi$
$60$		0			0
$61$	−41.5863	+	72.0295i	−0.681742	+	1.18081i	0.292707	+	0.956202i	$0.405444\pi$
$61$	−41.5863	+	72.0295i	−0.681742	+	1.18081i	−0.974449	+	0.224609i	$0.927889\pi$
$62$		0			0
$63$	11.9535	+	58.4586i	0.189739	+	0.927914i
$64$		0			0
$65$	4.03993	−	2.33245i	0.0621527	−	0.0358839i
$66$		0			0
$67$			111.101i			1.65822i	0.559086	+	0.829110i	$0.311152\pi$
$67$			111.101i			1.65822i	−0.559086	+	0.829110i	$0.688848\pi$
$68$		0			0
$69$	−15.0528	−	2.44388i	−0.218156	−	0.0354186i
$70$		0			0
$71$	83.8226	+	48.3950i	1.18060	+	0.681620i	0.956153	−	0.292866i	$-0.0946091\pi$
$71$	83.8226	+	48.3950i	1.18060	+	0.681620i	0.224447	+	0.974486i	$0.427942\pi$
$72$		0			0
$73$	−66.6462	+	115.435i	−0.912961	+	1.58130i	−0.103102	+	0.994671i	$0.532877\pi$
$73$	−66.6462	+	115.435i	−0.912961	+	1.58130i	−0.809859	+	0.586624i	$0.800456\pi$
$74$		0			0
$75$	−40.9976	+	50.2291i	−0.546635	+	0.669721i
$76$		0			0
$77$	50.7609	−	87.9205i	0.659232	−	1.14182i
$78$		0			0
$79$			33.4509i			0.423429i	0.977332	+	0.211715i	$0.0679048\pi$
$79$			33.4509i			0.423429i	−0.977332	+	0.211715i	$0.932095\pi$
$80$		0			0
$81$	64.7855	+	48.6194i	0.799820	+	0.600239i
$82$		0			0
$83$	−45.0486	−	78.0264i	−0.542754	−	0.940077i	−0.998745	−	0.0500924i	$-0.984048\pi$
$83$	−45.0486	−	78.0264i	−0.542754	−	0.940077i	0.455991	−	0.889984i	$-0.349285\pi$
$84$		0			0
$85$	47.6740			0.560870
$86$		0			0
$87$	34.5734	+	28.2193i	0.397396	+	0.324359i
$88$		0			0
$89$	−26.4870	+	15.2923i	−0.297606	+	0.171823i	−0.641367	−	0.767234i	$-0.721632\pi$
$89$	−26.4870	+	15.2923i	−0.297606	+	0.171823i	0.343761	+	0.939057i	$0.388299\pi$
$90$		0			0
$91$	−14.5517	+	8.40140i	−0.159908	+	0.0923231i
$92$		0			0
$93$	−93.5256	−	76.3368i	−1.00565	−	0.820826i
$94$		0			0
$95$	−34.7115	+	4.25727i	−0.365384	+	0.0448134i
$96$		0			0
$97$		−	79.5927i		−	0.820544i	−0.911963	−	0.410272i	$-0.865434\pi$
$97$		−	79.5927i		−	0.820544i	0.911963	−	0.410272i	$-0.134566\pi$
$98$		0			0
$99$	−27.6093	−	135.023i	−0.278882	−	1.36387i
$100$		0			0
$101$	−61.3987	+	106.346i	−0.607908	+	1.05293i	0.383677	+	0.923467i	$0.374658\pi$
$101$	−61.3987	+	106.346i	−0.607908	+	1.05293i	−0.991585	+	0.129460i	$0.958676\pi$
$102$		0			0
$103$	−57.5120	−	33.2045i	−0.558369	−	0.322374i	0.194122	−	0.980977i	$-0.437814\pi$
$103$	−57.5120	−	33.2045i	−0.558369	−	0.322374i	−0.752490	+	0.658603i	$0.771148\pi$
$104$		0			0
$105$	−23.1485	+	28.3608i	−0.220462	+	0.270103i
$106$		0			0
$107$		−	14.3363i		−	0.133984i	−0.997753	−	0.0669922i	$-0.978660\pi$
$107$		−	14.3363i		−	0.133984i	0.997753	−	0.0669922i	$-0.0213403\pi$
$108$		0			0
$109$	20.7750	+	11.9944i	0.190596	+	0.110041i	0.592262	−	0.805746i	$-0.298235\pi$
$109$	20.7750	+	11.9944i	0.190596	+	0.110041i	−0.401665	+	0.915786i	$0.631569\pi$
$110$		0			0
$111$	8.18414	−	50.4091i	0.0737310	−	0.454136i
$112$		0			0
$113$	−41.1529	−	23.7596i	−0.364185	−	0.210262i	0.306730	−	0.951797i	$-0.400765\pi$
$113$	−41.1529	−	23.7596i	−0.364185	−	0.210262i	−0.670915	+	0.741534i	$0.734098\pi$
$114$		0			0
$115$	−4.67817	−	8.10283i	−0.0406797	−	0.0704594i
$116$		0			0
$117$	−7.21638	+	21.6383i	−0.0616784	+	0.184943i
$118$		0			0
$119$	−171.720			−1.44302
$120$		0			0
$121$	−56.7434	+	98.2824i	−0.468954	+	0.812251i
$122$		0			0
$123$	150.908	−	57.2590i	1.22689	−	0.465520i
$124$		0			0
$125$	−85.7947			−0.686358
$126$		0			0
$127$	145.228	−	83.8477i	1.14353	−	0.660218i	0.196228	−	0.980558i	$-0.437131\pi$
$127$	145.228	−	83.8477i	1.14353	−	0.660218i	0.947302	+	0.320341i	$0.103797\pi$
$128$		0			0
$129$	149.305	+	24.2403i	1.15740	+	0.187910i
$130$		0			0
$131$	−118.141	−	204.627i	−0.901842	−	1.56204i	−0.825102	−	0.564984i	$-0.808882\pi$
$131$	−118.141	−	204.627i	−0.901842	−	1.56204i	−0.0767398	−	0.997051i	$-0.524451\pi$
$132$		0			0
$133$	125.029	−	15.3345i	0.940070	−	0.115297i
$134$		0			0
$135$	2.02449	+	49.6552i	0.0149962	+	0.367816i
$136$		0			0
$137$	15.6168	−	27.0491i	0.113991	−	0.197439i	−0.803385	−	0.595460i	$-0.796970\pi$
$137$	15.6168	−	27.0491i	0.113991	−	0.197439i	0.917376	+	0.398021i	$0.130303\pi$
$138$		0			0
$139$	34.3740			0.247295			0.123648	−	0.992326i	$-0.460541\pi$
$139$	34.3740			0.247295			0.123648	+	0.992326i	$0.460541\pi$
$140$		0			0
$141$	122.560	−	150.157i	0.869219	−	1.06494i
$142$		0			0
$143$	33.6102	−	19.4049i	0.235037	−	0.135698i
$144$		0			0
$145$			27.3808i			0.188833i
$146$		0			0
$147$	−9.57175	+	11.7270i	−0.0651139	+	0.0797757i
$148$		0			0
$149$	112.018	+	194.021i	0.751799	+	1.30215i	0.946950	+	0.321381i	$0.104147\pi$
$149$	112.018	+	194.021i	0.751799	+	1.30215i	−0.195151	+	0.980773i	$0.562520\pi$
$150$		0			0
$151$	−10.4885	+	6.05557i	−0.0694606	+	0.0401031i	−0.534328	−	0.845277i	$-0.679435\pi$
$151$	−10.4885	+	6.05557i	−0.0694606	+	0.0401031i	0.464867	+	0.885380i	$0.346102\pi$
$152$		0			0
$153$	−174.437	+	154.636i	−1.14011	+	1.01069i
$154$		0			0
$155$		−	74.0687i		−	0.477863i
$156$		0			0
$157$	97.9548	+	169.663i	0.623916	+	1.08065i	0.988749	+	0.149582i	$0.0477927\pi$
$157$	97.9548	+	169.663i	0.623916	+	1.08065i	−0.364833	+	0.931073i	$0.618874\pi$
$158$		0			0
$159$	287.012	−	108.901i	1.80511	−	0.684911i
$160$		0			0
$161$	16.8506	+	29.1861i	0.104662	+	0.181280i
$162$		0			0
$163$	−314.591			−1.93001			−0.965003	−	0.262239i	$-0.915539\pi$
$163$	−314.591			−1.93001			−0.965003	+	0.262239i	$0.915539\pi$
$164$		0			0
$165$	53.4664	−	65.5055i	0.324039	−	0.397003i
$166$		0			0
$167$			103.021i			0.616890i	0.951242	+	0.308445i	$0.0998085\pi$
$167$			103.021i			0.616890i	−0.951242	+	0.308445i	$0.900191\pi$
$168$		0			0
$169$	162.577			0.961992
$170$		0			0
$171$	113.199	−	128.168i	0.661983	−	0.749519i
$172$		0			0
$173$		−	40.6365i		−	0.234893i	−0.993079	−	0.117447i	$-0.962529\pi$
$173$		−	40.6365i		−	0.234893i	0.993079	−	0.117447i	$-0.0374709\pi$
$174$		0			0
$175$	143.284			0.818767
$176$		0			0
$177$	−154.836	+	58.7494i	−0.874779	+	0.331917i
$178$		0			0
$179$		−	74.3147i		−	0.415166i	−0.978217	−	0.207583i	$-0.933440\pi$
$179$		−	74.3147i		−	0.415166i	0.978217	−	0.207583i	$-0.0665597\pi$
$180$		0			0
$181$	−85.8009	+	49.5372i	−0.474038	+	0.273686i	−0.717929	−	0.696117i	$-0.754910\pi$
$181$	−85.8009	+	49.5372i	−0.474038	+	0.273686i	0.243890	+	0.969803i	$0.421576\pi$
$182$		0			0
$183$	157.776	−	193.302i	0.862163	−	1.05630i
$184$		0			0
$185$	27.1349	−	15.6664i	0.146675	−	0.0846831i
$186$		0			0
$187$	396.624			2.12099
$188$		0			0
$189$	−7.29214	−	178.856i	−0.0385828	−	0.946327i
$190$		0			0
$191$	−166.239	−	287.934i	−0.870359	−	1.50751i	−0.861626	−	0.507544i	$-0.830553\pi$
$191$	−166.239	−	287.934i	−0.870359	−	1.50751i	−0.00873349	−	0.999962i	$-0.502780\pi$
$192$		0			0
$193$	−229.030	+	132.231i	−1.18669	+	0.685133i	−0.957552	−	0.288262i	$-0.906923\pi$
$193$	−229.030	+	132.231i	−1.18669	+	0.685133i	−0.229134	+	0.973395i	$0.573589\pi$
$194$		0			0
$195$	−13.0845	+	4.96465i	−0.0671001	+	0.0254598i
$196$		0			0
$197$	36.4851			0.185203			0.0926017	−	0.995703i	$-0.470482\pi$
$197$	36.4851			0.185203			0.0926017	+	0.995703i	$0.470482\pi$
$198$		0			0
$199$	−151.188	−	261.866i	−0.759740	−	1.31591i	−0.942983	−	0.332841i	$-0.891993\pi$
$199$	−151.188	−	261.866i	−0.759740	−	1.31591i	0.183243	−	0.983068i	$-0.441341\pi$
$200$		0			0
$201$	53.4137	−	328.994i	0.265740	−	1.63679i
$202$		0			0
$203$		−	98.6246i		−	0.485835i
$204$		0			0
$205$	85.7609	+	49.5141i	0.418346	+	0.241532i
$206$		0			0
$207$	43.3997	+	14.4738i	0.209660	+	0.0699217i
$208$		0			0
$209$	−288.782	+	35.4184i	−1.38173	+	0.169466i
$210$		0			0
$211$	249.001	−	143.761i	1.18010	−	0.681330i	0.224061	−	0.974575i	$-0.428068\pi$
$211$	249.001	−	143.761i	1.18010	−	0.681330i	0.956037	+	0.293245i	$0.0947351\pi$
$212$		0			0
$213$	−224.951	−	183.608i	−1.05611	−	0.862009i
$214$		0			0
$215$	46.4017	+	80.3702i	0.215822	+	0.373815i
$216$		0			0
$217$			266.792i			1.22946i
$218$		0			0
$219$	252.852	−	309.786i	1.15457	−	1.41455i
$220$		0			0
$221$	−56.8503	−	32.8225i	−0.257241	−	0.148518i
$222$		0			0
$223$			414.250i			1.85762i	0.370552	+	0.928812i	$0.379169\pi$
$223$			414.250i			1.85762i	−0.370552	+	0.928812i	$0.620831\pi$
$224$		0			0
$225$	145.552	−	129.029i	0.646897	−	0.573464i
$226$		0			0
$227$	235.073	−	135.719i	1.03556	−	0.597882i	0.116989	−	0.993133i	$-0.462676\pi$
$227$	235.073	−	135.719i	1.03556	−	0.597882i	0.918573	+	0.395251i	$0.129343\pi$
$228$		0			0
$229$	−23.6064	+	40.8875i	−0.103085	+	0.178548i	−0.912954	−	0.408062i	$-0.866205\pi$
$229$	−23.6064	+	40.8875i	−0.103085	+	0.178548i	0.809869	+	0.586610i	$0.199538\pi$
$230$		0			0
$231$	−192.584	+	235.948i	−0.833696	+	1.02142i
$232$		0			0
$233$	140.000	−	242.488i	0.600860	−	1.04072i	−0.391832	−	0.920037i	$-0.628158\pi$
$233$	140.000	−	242.488i	0.600860	−	1.04072i	0.992691	−	0.120682i	$-0.0385083\pi$
$234$		0			0
$235$	118.918			0.506036
$236$		0			0
$237$	16.0821	−	99.0558i	0.0678572	−	0.417957i
$238$		0			0
$239$	−116.760	+	202.234i	−0.488534	+	0.846166i	−0.999913	−	0.0131891i	$-0.995802\pi$
$239$	−116.760	+	202.234i	−0.488534	+	0.846166i	0.511379	+	0.859356i	$0.329135\pi$
$240$		0			0
$241$	88.3112	+	50.9865i	0.366436	+	0.211562i	0.671900	−	0.740641i	$-0.265478\pi$
$241$	88.3112	+	50.9865i	0.366436	+	0.211562i	−0.305464	+	0.952204i	$0.598812\pi$
$242$		0			0
$243$	−168.470	−	175.120i	−0.693291	−	0.720658i
$244$		0			0
$245$	−9.28735			−0.0379076
$246$		0			0
$247$	44.3237	+	18.8214i	0.179448	+	0.0761999i
$248$		0			0
$249$	95.8863	+	252.712i	0.385086	+	1.01491i
$250$		0			0
$251$	−32.2790	−	55.9089i	−0.128602	−	0.222745i	0.794533	−	0.607220i	$-0.207716\pi$
$251$	−32.2790	−	55.9089i	−0.128602	−	0.222745i	−0.923135	+	0.384476i	$0.874382\pi$
$252$		0			0
$253$	−38.9201	−	67.4116i	−0.153834	−	0.266449i
$254$		0			0
$255$	−141.173	−	22.9201i	−0.553621	−	0.0898829i
$256$		0			0
$257$			135.701i			0.528018i	0.964520	+	0.264009i	$0.0850449\pi$
$257$			135.701i			0.528018i	−0.964520	+	0.264009i	$0.914955\pi$
$258$		0			0
$259$	−97.7390	+	56.4296i	−0.377371	+	0.217875i
$260$		0			0
$261$	−88.8128	−	100.185i	−0.340279	−	0.383852i
$262$		0			0
$263$	−343.580			−1.30639			−0.653195	−	0.757190i	$-0.726572\pi$
$263$	−343.580			−1.30639			−0.653195	+	0.757190i	$0.726572\pi$
$264$		0			0
$265$	163.109	+	94.1709i	0.615505	+	0.355362i
$266$		0			0
$267$	85.7859	−	32.5497i	0.321296	−	0.121909i
$268$		0			0
$269$	406.540	+	234.716i	1.51130	+	0.872550i	0.999913	+	0.0132004i	$0.00420193\pi$
$269$	406.540	+	234.716i	1.51130	+	0.872550i	0.511388	+	0.859350i	$0.329131\pi$
$270$		0			0
$271$	−5.21532	+	9.03320i	−0.0192447	+	0.0333328i	−0.875487	−	0.483241i	$-0.839459\pi$
$271$	−5.21532	+	9.03320i	−0.0192447	+	0.0333328i	0.856243	+	0.516574i	$0.172793\pi$
$272$		0			0
$273$	47.1299	−	17.8825i	0.172637	−	0.0655036i
$274$		0			0
$275$	−330.946			−1.20344
$276$		0			0
$277$	−239.373	−	414.607i	−0.864163	−	1.49677i	−0.867875	−	0.496782i	$-0.834515\pi$
$277$	−239.373	−	414.607i	−0.864163	−	1.49677i	0.00371208	−	0.999993i	$-0.498818\pi$
$278$		0			0
$279$	240.250	+	271.015i	0.861112	+	0.971379i
$280$		0			0
$281$	−225.326	−	130.092i	−0.801873	−	0.462962i	0.0422526	−	0.999107i	$-0.486547\pi$
$281$	−225.326	−	130.092i	−0.801873	−	0.462962i	−0.844126	+	0.536145i	$0.819880\pi$
$282$		0			0
$283$	135.474	+	234.648i	0.478707	+	0.829145i	0.999702	−	0.0244150i	$-0.00777232\pi$
$283$	135.474	+	234.648i	0.478707	+	0.829145i	−0.520995	+	0.853560i	$0.674439\pi$
$284$		0			0
$285$	104.835	+	4.08143i	0.367843	+	0.0143208i
$286$		0			0
$287$	−308.907	−	178.348i	−1.07633	−	0.621421i
$288$		0			0
$289$	−190.936	−	330.712i	−0.660680	−	1.14433i
$290$		0			0
$291$	−38.2657	+	235.692i	−0.131497	+	0.809938i
$292$		0			0
$293$	196.791	+	113.617i	0.671641	+	0.387772i	0.796698	−	0.604377i	$-0.206578\pi$
$293$	196.791	+	113.617i	0.671641	+	0.387772i	−0.125057	+	0.992150i	$0.539911\pi$
$294$		0			0
$295$	−87.9932	−	50.8029i	−0.298282	−	0.172213i
$296$		0			0
$297$	16.8428	+	413.107i	0.0567097	+	1.39093i
$298$		0			0
$299$			12.8833i			0.0430879i
$300$		0			0
$301$	−167.137	−	289.490i	−0.555273	−	0.961761i
$302$		0			0
$303$	232.943	−	285.395i	0.768789	−	0.941898i
$304$		0			0
$305$	153.088			0.501928
$306$		0			0
$307$	429.650	+	248.058i	1.39951	+	0.808008i	0.994341	−	0.106233i	$-0.0338790\pi$
$307$	429.650	+	248.058i	1.39951	+	0.808008i	0.405170	+	0.914241i	$0.367212\pi$
$308$		0			0
$309$	154.342	+	125.976i	0.499489	+	0.407690i
$310$		0			0
$311$	−86.7171	+	150.198i	−0.278833	+	0.482953i	−0.971095	−	0.238693i	$-0.923281\pi$
$311$	−86.7171	+	150.198i	−0.278833	+	0.482953i	0.692262	+	0.721646i	$0.256614\pi$
$312$		0			0
$313$	105.550	−	182.818i	0.337221	−	0.584084i	−0.646688	−	0.762755i	$-0.723846\pi$
$313$	105.550	−	182.818i	0.337221	−	0.584084i	0.983909	+	0.178671i	$0.0571797\pi$
$314$		0			0
$315$	82.1828	−	72.8537i	0.260898	−	0.231282i
$316$		0			0
$317$	−143.794	−	83.0192i	−0.453607	−	0.261890i	0.255745	−	0.966744i	$-0.417679\pi$
$317$	−143.794	−	83.0192i	−0.453607	−	0.261890i	−0.709352	+	0.704854i	$0.751013\pi$
$318$		0			0
$319$			227.795i			0.714091i
$320$		0			0
$321$	−6.89246	+	42.4531i	−0.0214718	+	0.132253i
$322$		0			0
$323$	296.114	+	393.067i	0.916761	+	1.21693i
$324$		0			0
$325$	47.4363	+	27.3873i	0.145958	+	0.0842688i
$326$		0			0
$327$	−55.7529	−	45.5062i	−0.170498	−	0.139163i
$328$		0			0
$329$	−428.339			−1.30194
$330$		0			0
$331$	−182.184	+	105.184i	−0.550404	+	0.317776i	−0.749285	−	0.662248i	$-0.769603\pi$
$331$	−182.184	+	105.184i	−0.550404	+	0.317776i	0.198881	+	0.980024i	$0.436269\pi$
$332$		0			0
$333$	−48.4702	+	145.338i	−0.145556	+	0.436450i
$334$		0			0
$335$	177.096	−	102.246i	0.528645	−	0.305213i
$336$		0			0
$337$	−178.809	+	103.235i	−0.530590	+	0.306336i	−0.741257	−	0.671222i	$-0.765770\pi$
$337$	−178.809	+	103.235i	−0.530590	+	0.306336i	0.210667	+	0.977558i	$0.432437\pi$
$338$		0			0
$339$	110.440	+	90.1427i	0.325782	+	0.265908i
$340$		0			0
$341$		−	616.215i		−	1.80708i
$342$		0			0
$343$	358.313			1.04464
$344$		0			0
$345$	9.95754	+	26.2434i	0.0288624	+	0.0760679i
$346$		0			0
$347$	76.2543	+	132.076i	0.219753	+	0.380624i	0.954732	−	0.297466i	$-0.0961415\pi$
$347$	76.2543	+	132.076i	0.219753	+	0.380624i	−0.734979	+	0.678090i	$0.762808\pi$
$348$		0			0
$349$	22.5332	+	39.0287i	0.0645651	+	0.111830i	0.896501	−	0.443042i	$-0.146101\pi$
$349$	22.5332	+	39.0287i	0.0645651	+	0.111830i	−0.831936	+	0.554872i	$0.812767\pi$
$350$		0			0
$351$	31.7723	−	60.6066i	0.0905195	−	0.172668i
$352$		0			0
$353$	−87.1767	−	150.995i	−0.246960	−	0.427747i	0.715721	−	0.698386i	$-0.246098\pi$
$353$	−87.1767	−	150.995i	−0.246960	−	0.427747i	−0.962681	+	0.270640i	$0.912765\pi$
$354$		0			0
$355$		−	178.153i		−	0.501838i
$356$		0			0
$357$	508.501	+	82.5574i	1.42437	+	0.231253i
$358$		0			0
$359$	−85.1783	+	147.533i	−0.237265	+	0.410956i	−0.959929	−	0.280244i	$-0.909584\pi$
$359$	−85.1783	+	147.533i	−0.237265	+	0.410956i	0.722663	+	0.691200i	$0.242918\pi$
$360$		0			0
$361$	−250.701	−	259.749i	−0.694464	−	0.719528i
$362$		0			0
$363$	215.281	−	263.756i	0.593061	−	0.726601i
$364$		0			0
$365$	245.339			0.672161
$366$		0			0
$367$	206.861	−	358.293i	0.563653	−	0.976276i	−0.433520	−	0.901144i	$-0.642729\pi$
$367$	206.861	−	358.293i	0.563653	−	0.976276i	0.997174	−	0.0751323i	$-0.0239379\pi$
$368$		0			0
$369$	−474.401	+	97.0050i	−1.28564	+	0.262886i
$370$		0			0
$371$	−587.511	−	339.200i	−1.58359	−	0.914285i
$372$		0			0
$373$	−37.5725	−	21.6925i	−0.100731	−	0.0581568i	0.448788	−	0.893638i	$-0.351856\pi$
$373$	−37.5725	−	21.6925i	−0.100731	−	0.0581568i	−0.549519	+	0.835481i	$0.685189\pi$
$374$		0			0
$375$	254.058	+	41.2474i	0.677487	+	0.109993i
$376$		0			0
$377$	18.8511	−	32.6511i	0.0500029	−	0.0866076i
$378$		0			0
$379$			151.050i			0.398548i	0.979944	+	0.199274i	$0.0638583\pi$
$379$			151.050i			0.398548i	−0.979944	+	0.199274i	$0.936142\pi$
$380$		0			0
$381$	−470.365	+	178.471i	−1.23455	+	0.468427i
$382$		0			0
$383$	150.175	−	86.7033i	0.392101	−	0.226379i	−0.290969	−	0.956732i	$-0.593978\pi$
$383$	150.175	−	86.7033i	0.392101	−	0.226379i	0.683070	+	0.730353i	$0.260644\pi$
$384$		0			0
$385$	−186.862			−0.485355
$386$		0			0
$387$	−430.472	−	143.562i	−1.11233	−	0.370962i
$388$		0			0
$389$	−42.1929	+	73.0802i	−0.108465	+	0.187867i	−0.915149	−	0.403117i	$-0.867927\pi$
$389$	−42.1929	+	73.0802i	−0.108465	+	0.187867i	0.806684	+	0.590984i	$0.201260\pi$
$390$		0			0
$391$	−65.8317	+	114.024i	−0.168367	+	0.291621i
$392$		0			0
$393$	251.465	+	662.744i	0.639860	+	1.68637i
$394$		0			0
$395$	53.3212	−	30.7850i	0.134990	−	0.0779368i
$396$		0			0
$397$	−277.537	+	480.708i	−0.699085	+	1.21085i	0.269699	+	0.962945i	$0.413076\pi$
$397$	−277.537	+	480.708i	−0.699085	+	1.21085i	−0.968784	+	0.247906i	$0.920258\pi$
$398$		0			0
$399$	−377.612	−	14.7011i	−0.946397	−	0.0368450i
$400$		0			0
$401$	271.836	−	156.944i	0.677894	−	0.391382i	−0.121167	−	0.992632i	$-0.538664\pi$
$401$	271.836	−	156.944i	0.677894	−	0.391382i	0.799061	+	0.601250i	$0.205330\pi$
$402$		0			0
$403$	−50.9947	+	88.3254i	−0.126538	+	0.219170i
$404$		0			0
$405$	17.8776	−	148.013i	0.0441423	−	0.365465i
$406$		0			0
$407$	225.750	−	130.337i	0.554667	−	0.320237i
$408$		0			0
$409$			100.493i			0.245705i	0.992425	+	0.122852i	$0.0392042\pi$
$409$			100.493i			0.245705i	−0.992425	+	0.122852i	$0.960796\pi$
$410$		0			0
$411$	−59.2493	+	72.5905i	−0.144159	+	0.176619i
$412$		0			0
$413$	316.948	+	182.990i	0.767429	+	0.443075i
$414$		0			0
$415$	−82.9167	+	143.616i	−0.199799	+	0.346063i
$416$		0			0
$417$	−101.789	−	16.5259i	−0.244099	−	0.0396305i
$418$		0			0
$419$	−229.603	+	397.685i	−0.547980	+	0.949129i	0.450433	+	0.892810i	$0.351270\pi$
$419$	−229.603	+	397.685i	−0.547980	+	0.949129i	−0.998413	+	0.0563185i	$0.982064\pi$
$420$		0			0
$421$		−	77.2913i		−	0.183590i	−0.995778	−	0.0917949i	$-0.970740\pi$
$421$		−	77.2913i		−	0.183590i	0.995778	−	0.0917949i	$-0.0292604\pi$
$422$		0			0
$423$	−435.118	+	385.725i	−1.02865	+	0.911880i
$424$		0			0
$425$	279.891	+	484.785i	0.658566	+	1.14067i
$426$		0			0
$427$	−551.417			−1.29137
$428$		0			0
$429$	−108.857	+	41.3035i	−0.253745	+	0.0962785i
$430$		0			0
$431$	353.010	−	203.810i	0.819049	−	0.472878i	−0.0310396	−	0.999518i	$-0.509882\pi$
$431$	353.010	−	203.810i	0.819049	−	0.472878i	0.850088	+	0.526640i	$0.176548\pi$
$432$		0			0
$433$	539.985	−	311.760i	1.24708	−	0.720001i	0.276553	−	0.960999i	$-0.410808\pi$
$433$	539.985	−	311.760i	1.24708	−	0.720001i	0.970526	+	0.240998i	$0.0774746\pi$
$434$		0			0
$435$	13.1638	−	81.0808i	0.0302617	−	0.186393i
$436$		0			0
$437$	37.7498	−	88.8995i	0.0863840	−	0.203431i
$438$		0			0
$439$			463.843i			1.05659i	0.849061	+	0.528294i	$0.177168\pi$
$439$			463.843i			1.05659i	−0.849061	+	0.528294i	$0.822832\pi$
$440$		0			0
$441$	33.9821	−	30.1246i	0.0770569	−	0.0683097i
$442$		0			0
$443$	39.5266	−	68.4622i	0.0892249	−	0.154542i	−0.817959	−	0.575277i	$-0.804894\pi$
$443$	39.5266	−	68.4622i	0.0892249	−	0.154542i	0.907184	+	0.420735i	$0.138228\pi$
$444$		0			0
$445$	48.7521	+	28.1470i	0.109555	+	0.0632518i
$446$		0			0
$447$	−238.432	−	628.395i	−0.533404	−	1.40581i
$448$		0			0
$449$		−	368.400i		−	0.820491i	−0.911975	−	0.410245i	$-0.865443\pi$
$449$		−	368.400i		−	0.820491i	0.911975	−	0.410245i	$-0.134557\pi$
$450$		0			0
$451$	713.489	+	411.933i	1.58202	+	0.913377i
$452$		0			0
$453$	33.9703	−	12.8893i	0.0749896	−	0.0284533i
$454$		0			0
$455$	26.7839	+	15.4637i	0.0588657	+	0.0339861i
$456$		0			0
$457$	−333.410	−	577.483i	−0.729562	−	1.26364i	−0.957068	−	0.289862i	$-0.906390\pi$
$457$	−333.410	−	577.483i	−0.729562	−	1.26364i	0.227506	−	0.973777i	$-0.426943\pi$
$458$		0			0
$459$	590.893	−	374.048i	1.28735	−	0.814920i
$460$		0			0
$461$	−634.642			−1.37666			−0.688332	−	0.725396i	$-0.741657\pi$
$461$	−634.642			−1.37666			−0.688332	+	0.725396i	$0.741657\pi$
$462$		0			0
$463$	−187.291	+	324.397i	−0.404516	+	0.700642i	−0.994265	−	0.106944i	$-0.965893\pi$
$463$	−187.291	+	324.397i	−0.404516	+	0.700642i	0.589749	+	0.807587i	$0.299227\pi$
$464$		0			0
$465$	−35.6099	+	219.334i	−0.0765804	+	0.471686i
$466$		0			0
$467$	246.992			0.528890			0.264445	−	0.964401i	$-0.414811\pi$
$467$	246.992			0.528890			0.264445	+	0.964401i	$0.414811\pi$
$468$		0			0
$469$	−637.893	+	368.287i	−1.36011	+	0.785261i
$470$		0			0
$471$	−208.498	−	549.503i	−0.442671	−	1.16667i
$472$		0			0
$473$	386.040	+	668.641i	0.816152	+	1.41362i
$474$		0			0
$475$	−247.080	−	327.978i	−0.520168	−	0.690480i
$476$		0			0
$477$	−902.263	+	184.494i	−1.89154	+	0.386780i
$478$		0			0
$479$	254.438	−	440.699i	0.531185	−	0.920040i	−0.468152	−	0.883648i	$-0.655080\pi$
$479$	254.438	−	440.699i	0.531185	−	0.920040i	0.999338	−	0.0363920i	$-0.0115865\pi$
$480$		0			0
$481$	−43.1438			−0.0896961
$482$		0			0
$483$	−35.8667	−	94.5278i	−0.0742581	−	0.195710i
$484$		0			0
$485$	−126.872	+	73.2495i	−0.261591	+	0.151030i
$486$		0			0
$487$		−	358.976i		−	0.737118i	−0.929604	−	0.368559i	$-0.879851\pi$
$487$		−	358.976i		−	0.737118i	0.929604	−	0.368559i	$-0.120149\pi$
$488$		0			0
$489$	931.575	+	151.245i	1.90506	+	0.309295i
$490$		0			0
$491$	248.985	+	431.254i	0.507097	+	0.878318i	0.999966	+	0.00821480i	$0.00261488\pi$
$491$	248.985	+	431.254i	0.507097	+	0.878318i	−0.492869	+	0.870104i	$0.664052\pi$
$492$		0			0
$493$	333.684	−	192.653i	0.676844	−	0.390776i
$494$		0			0
$495$	−189.819	+	168.272i	−0.383473	+	0.339943i
$496$		0			0
$497$			641.698i			1.29114i
$498$		0			0
$499$	−377.629	−	654.073i	−0.756772	−	1.31077i	−0.944489	−	0.328544i	$-0.893442\pi$
$499$	−377.629	−	654.073i	−0.756772	−	1.31077i	0.187717	−	0.982223i	$-0.439891\pi$
$500$		0			0
$501$	49.5290	−	305.067i	0.0988603	−	0.608917i
$502$		0			0
$503$	34.5273	+	59.8030i	0.0686427	+	0.118893i	0.898304	−	0.439374i	$-0.144800\pi$
$503$	34.5273	+	59.8030i	0.0686427	+	0.118893i	−0.829661	+	0.558267i	$0.811466\pi$
$504$		0			0
$505$	226.022			0.447568
$506$		0			0
$507$	−481.426	−	78.1617i	−0.949559	−	0.154165i
$508$		0			0
$509$			414.128i			0.813611i	0.913515	+	0.406806i	$0.133357\pi$
$509$			414.128i			0.813611i	−0.913515	+	0.406806i	$0.866643\pi$
$510$		0			0
$511$	−883.701			−1.72936
$512$		0			0
$513$	−396.827	+	325.111i	−0.773542	+	0.633745i
$514$		0			0
$515$			122.233i			0.237346i
$516$		0			0
$517$	989.343			1.91362
$518$		0			0
$519$	−19.5368	+	120.334i	−0.0376431	+	0.231857i
$520$		0			0
$521$			395.573i			0.759258i	0.925139	+	0.379629i	$0.123948\pi$
$521$			395.573i			0.759258i	−0.925139	+	0.379629i	$0.876052\pi$
$522$		0			0
$523$	−430.932	+	248.799i	−0.823962	+	0.475715i	−0.851781	−	0.523898i	$-0.824477\pi$
$523$	−430.932	+	248.799i	−0.823962	+	0.475715i	0.0278188	+	0.999613i	$0.491144\pi$
$524$		0			0
$525$	−424.297	−	68.8865i	−0.808185	−	0.131212i
$526$		0			0
$527$	−902.660	+	521.151i	−1.71283	+	0.988901i
$528$		0			0
$529$	−503.160			−0.951153
$530$		0			0
$531$	486.749	−	99.5300i	0.916665	−	0.187439i
$532$		0			0
$533$	−68.1788	−	118.089i	−0.127915	−	0.221556i
$534$		0			0
$535$	−22.8523	+	13.1938i	−0.0427146	+	0.0246613i
$536$		0			0
$537$	−35.7282	+	220.063i	−0.0665329	+	0.409800i
$538$		0			0
$539$	−77.2662			−0.143351
$540$		0			0
$541$	−116.908	−	202.490i	−0.216095	−	0.374288i	0.737515	−	0.675330i	$-0.235999\pi$
$541$	−116.908	−	202.490i	−0.216095	−	0.374288i	−0.953611	+	0.301042i	$0.902666\pi$
$542$		0			0
$543$	277.892	−	105.440i	0.511772	−	0.194181i
$544$		0			0
$545$		−	44.1541i		−	0.0810168i
$546$		0			0
$547$	331.612	+	191.456i	0.606238	+	0.350012i	0.771492	−	0.636239i	$-0.219511\pi$
$547$	331.612	+	191.456i	0.606238	+	0.350012i	−0.165254	+	0.986251i	$0.552844\pi$
$548$		0			0
$549$	−560.144	+	496.558i	−1.02030	+	0.904478i
$550$		0			0
$551$	−225.752	+	170.068i	−0.409713	+	0.308654i
$552$		0			0
$553$	−192.061	+	110.886i	−0.347307	+	0.200518i
$554$		0			0
$555$	−87.8846	+	33.3460i	−0.158351	+	0.0600830i
$556$		0			0
$557$	440.741	+	763.386i	0.791277	+	1.37053i	0.925177	+	0.379537i	$0.123917\pi$
$557$	440.741	+	763.386i	0.791277	+	1.37053i	−0.133900	+	0.990995i	$0.542750\pi$
$558$		0			0
$559$		−	127.786i		−	0.228598i
$560$		0			0
$561$	−1174.49	−	190.684i	−2.09357	−	0.339901i
$562$		0			0
$563$	−51.5358	−	29.7542i	−0.0915379	−	0.0528494i	0.453532	−	0.891240i	$-0.350164\pi$
$563$	−51.5358	−	29.7542i	−0.0915379	−	0.0528494i	−0.545070	+	0.838390i	$0.683497\pi$
$564$		0			0
$565$			87.4644i			0.154804i
$566$		0			0
$567$	−64.3946	+	533.139i	−0.113571	+	0.940280i
$568$		0			0
$569$	791.507	−	456.977i	1.39105	−	0.803123i	0.397618	−	0.917551i	$-0.369837\pi$
$569$	791.507	−	456.977i	1.39105	−	0.803123i	0.993432	+	0.114428i	$0.0365034\pi$
$570$		0			0
$571$	14.0632	−	24.3582i	0.0246291	−	0.0426588i	−0.853448	−	0.521178i	$-0.825493\pi$
$571$	14.0632	−	24.3582i	0.0246291	−	0.0426588i	0.878077	+	0.478519i	$0.158826\pi$
$572$		0			0
$573$	353.841	+	932.559i	0.617523	+	1.62750i
$574$		0			0
$575$	54.9304	−	95.1423i	0.0955312	−	0.165465i
$576$		0			0
$577$	696.198			1.20658			0.603291	−	0.797521i	$-0.293856\pi$
$577$	696.198			1.20658			0.603291	+	0.797521i	$0.293856\pi$
$578$		0			0
$579$	741.783	−	281.455i	1.28115	−	0.486105i
$580$		0			0
$581$	298.663	−	517.299i	0.514049	−	0.890360i
$582$		0			0
$583$	1356.99	+	783.456i	2.32759	+	1.34383i
$584$		0			0
$585$	41.1330	−	8.41085i	0.0703129	−	0.0143775i
$586$		0			0
$587$	−249.452			−0.424961			−0.212481	−	0.977165i	$-0.568154\pi$
$587$	−249.452			−0.424961			−0.212481	+	0.977165i	$0.568154\pi$
$588$		0			0
$589$	610.689	−	460.058i	1.03682	−	0.781082i
$590$		0			0
$591$	−108.041	−	17.5409i	−0.182810	−	0.0296800i
$592$		0			0
$593$	98.5298	+	170.659i	0.166155	+	0.287789i	0.937065	−	0.349156i	$-0.113532\pi$
$593$	98.5298	+	170.659i	0.166155	+	0.287789i	−0.770910	+	0.636944i	$0.780198\pi$
$594$		0			0
$595$	158.034	+	273.724i	0.265604	+	0.460040i
$596$		0			0
$597$	321.806	+	848.131i	0.539039	+	1.42065i
$598$		0			0
$599$			350.250i			0.584724i	0.956308	+	0.292362i	$0.0944412\pi$
$599$			350.250i			0.584724i	−0.956308	+	0.292362i	$0.905559\pi$
$600$		0			0
$601$	−718.814	+	415.008i	−1.19603	+	0.690528i	−0.959668	−	0.281137i	$-0.909289\pi$
$601$	−718.814	+	415.008i	−1.19603	+	0.690528i	−0.236362	+	0.971665i	$0.575955\pi$
$602$		0			0
$603$	−316.340	+	948.547i	−0.524610	+	1.57305i
$604$		0			0
$605$	208.885			0.345264
$606$		0			0
$607$	−812.587	−	469.147i	−1.33869	−	0.772895i	−0.352080	−	0.935970i	$-0.614525\pi$
$607$	−812.587	−	469.147i	−1.33869	−	0.772895i	−0.986614	+	0.163075i	$0.947859\pi$
$608$		0			0
$609$	−47.4156	+	292.050i	−0.0778581	+	0.479556i
$610$		0			0
$611$	−141.808	−	81.8728i	−0.232091	−	0.133998i
$612$		0			0
$613$	89.8809	−	155.678i	0.146625	−	0.253961i	−0.783353	−	0.621577i	$-0.786492\pi$
$613$	89.8809	−	155.678i	0.146625	−	0.253961i	0.929978	+	0.367615i	$0.119826\pi$
$614$		0			0
$615$	−230.153	−	187.854i	−0.374232	−	0.305453i
$616$		0			0
$617$	−121.557			−0.197013			−0.0985067	−	0.995136i	$-0.531407\pi$
$617$	−121.557			−0.197013			−0.0985067	+	0.995136i	$0.531407\pi$
$618$		0			0
$619$	156.050	+	270.287i	0.252101	+	0.436651i	0.964104	−	0.265525i	$-0.0855452\pi$
$619$	156.050	+	270.287i	0.252101	+	0.436651i	−0.712003	+	0.702176i	$0.752212\pi$
$620$		0			0
$621$	−121.558	−	63.7254i	−0.195745	−	0.102617i
$622$		0			0
$623$	−175.603	−	101.385i	−0.281867	−	0.162736i
$624$		0			0
$625$	−191.195	−	331.159i	−0.305912	−	0.529855i
$626$		0			0
$627$	872.178	+	33.9555i	1.39103	+	0.0541555i
$628$		0			0
$629$	−381.846	−	220.459i	−0.607068	−	0.350491i
$630$		0			0
$631$	−445.955	−	772.417i	−0.706744	−	1.22412i	−0.966059	−	0.258323i	$-0.916830\pi$
$631$	−445.955	−	772.417i	−0.706744	−	1.22412i	0.259315	−	0.965793i	$-0.416503\pi$
$632$		0			0
$633$	−806.463	+	305.996i	−1.27403	+	0.483406i
$634$		0			0
$635$	−267.309	−	154.331i	−0.420958	−	0.243040i
$636$		0			0
$637$	11.0750	+	6.39414i	0.0173862	+	0.0100379i
$638$		0			0
$639$	577.858	+	651.854i	0.904316	+	1.02012i
$640$		0			0
$641$			483.178i			0.753788i	0.926256	+	0.376894i	$0.123008\pi$
$641$			483.178i			0.753788i	−0.926256	+	0.376894i	$0.876992\pi$
$642$		0			0
$643$	−168.993	−	292.705i	−0.262820	−	0.455217i	0.704170	−	0.710031i	$-0.251319\pi$
$643$	−168.993	−	292.705i	−0.262820	−	0.455217i	−0.966990	+	0.254814i	$0.917986\pi$
$644$		0			0
$645$	−98.7666	−	260.303i	−0.153127	−	0.403570i
$646$		0			0
$647$	556.371			0.859924			0.429962	−	0.902847i	$-0.358527\pi$
$647$	556.371			0.859924			0.429962	+	0.902847i	$0.358527\pi$
$648$		0			0
$649$	−732.061	−	422.655i	−1.12798	−	0.651241i
$650$		0			0
$651$	128.265	−	790.033i	0.197028	−	1.21357i
$652$		0			0
$653$	11.4095	−	19.7619i	0.0174725	−	0.0302632i	−0.857157	−	0.515055i	$-0.827771\pi$
$653$	11.4095	−	19.7619i	0.0174725	−	0.0302632i	0.874629	+	0.484792i	$0.161105\pi$
$654$		0			0
$655$	−217.452	+	376.637i	−0.331987	+	0.575019i
$656$		0			0
$657$	−897.687	+	795.785i	−1.36634	+	1.21124i
$658$		0			0
$659$	215.748	+	124.562i	0.327387	+	0.189017i	0.654680	−	0.755906i	$-0.272803\pi$
$659$	215.748	+	124.562i	0.327387	+	0.189017i	−0.327294	+	0.944923i	$0.606137\pi$
$660$		0			0
$661$		−	948.636i		−	1.43515i	−0.696480	−	0.717577i	$-0.745251\pi$
$661$		−	948.636i		−	1.43515i	0.696480	−	0.717577i	$-0.254749\pi$
$662$		0			0
$663$	152.566	+	124.527i	0.230115	+	0.187823i
$664$		0			0
$665$	−139.508	−	185.186i	−0.209787	−	0.278475i
$666$		0			0
$667$	−65.4878	−	37.8094i	−0.0981826	−	0.0566858i
$668$		0			0
$669$	199.158	−	1226.69i	0.297695	−	1.83361i
$670$		0			0
$671$	1273.62			1.89809
$672$		0			0
$673$	−498.486	+	287.801i	−0.740692	+	0.427639i	−0.822321	−	0.569024i	$-0.807321\pi$
$673$	−498.486	+	287.801i	−0.740692	+	0.427639i	0.0816286	+	0.996663i	$0.473988\pi$
$674$		0			0
$675$	−493.045	+	312.109i	−0.730437	+	0.462383i
$676$		0			0
$677$	773.523	−	446.594i	1.14257	−	0.659666i	0.195508	−	0.980702i	$-0.437364\pi$
$677$	773.523	−	446.594i	1.14257	−	0.659666i	0.947067	+	0.321036i	$0.104031\pi$
$678$		0			0
$679$	456.987	−	263.842i	0.673030	−	0.388574i
$680$		0			0
$681$	−761.352	+	288.880i	−1.11799	+	0.424199i
$682$		0			0
$683$		−	711.769i		−	1.04212i	−0.853519	−	0.521061i	$-0.825536\pi$
$683$		−	711.769i		−	1.04212i	0.853519	−	0.521061i	$-0.174464\pi$
$684$		0			0
$685$	−57.4889			−0.0839253
$686$		0			0
$687$	89.5613	−	109.728i	0.130366	−	0.159720i
$688$		0			0
$689$	−129.669	−	224.594i	−0.188199	−	0.325971i
$690$		0			0
$691$	−25.8916	−	44.8455i	−0.0374697	−	0.0648995i	0.846682	−	0.532099i	$-0.178596\pi$
$691$	−25.8916	−	44.8455i	−0.0374697	−	0.0648995i	−0.884152	+	0.467199i	$0.845263\pi$
$692$		0			0
$693$	683.721	−	606.108i	0.986610	−	0.874614i
$694$		0			0
$695$	−31.6345	−	54.7926i	−0.0455173	−	0.0788383i
$696$		0			0
$697$		−	1393.53i		−	1.99933i
$698$		0			0
$699$	−531.153	+	650.753i	−0.759875	+	0.930977i
$700$		0			0
$701$	448.023	−	775.998i	0.639120	−	1.10699i	−0.346507	−	0.938048i	$-0.612632\pi$
$701$	448.023	−	775.998i	0.639120	−	1.10699i	0.985626	−	0.168940i	$-0.0540345\pi$
$702$		0			0
$703$	297.709	+	126.417i	0.423484	+	0.179826i
$704$		0			0
$705$	−352.144	−	57.1722i	−0.499495	−	0.0810953i
$706$		0			0
$707$	−814.122			−1.15152
$708$		0			0
$709$	305.107	−	528.460i	0.430334	−	0.745360i	−0.566568	−	0.824015i	$-0.691729\pi$
$709$	305.107	−	528.460i	0.430334	−	0.745360i	0.996902	+	0.0786550i	$0.0250626\pi$
$710$		0			0
$711$	−95.2457	+	285.595i	−0.133960	+	0.401680i
$712$		0			0
$713$	177.153	+	102.279i	0.248462	+	0.143449i
$714$		0			0
$715$	−61.8633	−	35.7168i	−0.0865220	−	0.0499535i
$716$		0			0
$717$	442.980	−	542.726i	0.617824	−	0.756940i
$718$		0			0
$719$	18.9204	−	32.7710i	0.0263148	−	0.0455786i	−0.852568	−	0.522616i	$-0.824956\pi$
$719$	18.9204	−	32.7710i	0.0263148	−	0.0455786i	0.878883	+	0.477038i	$0.158289\pi$
$720$		0			0
$721$		−	440.279i		−	0.610650i
$722$		0			0
$723$	−236.997	−	193.440i	−0.327796	−	0.267552i
$724$		0			0
$725$	−278.429	+	160.751i	−0.384039	+	0.221725i
$726$		0			0
$727$	178.913			0.246098			0.123049	−	0.992401i	$-0.460733\pi$
$727$	178.913			0.246098			0.123049	+	0.992401i	$0.460733\pi$
$728$		0			0
$729$	414.685	+	599.564i	0.568841	+	0.822448i
$730$		0			0
$731$	652.970	−	1130.98i	0.893256	−	1.54716i
$732$		0			0
$733$	220.426	−	381.790i	0.300718	−	0.520859i	−0.675581	−	0.737286i	$-0.736107\pi$
$733$	220.426	−	381.790i	0.300718	−	0.520859i	0.976299	+	0.216427i	$0.0694403\pi$
$734$		0			0
$735$	27.5019	+	4.46506i	0.0374176	+	0.00607492i
$736$		0			0
$737$	1473.35	−	850.640i	1.99912	−	1.15419i
$738$		0			0
$739$	129.576	−	224.433i	0.175340	−	0.303698i	−0.764939	−	0.644103i	$-0.777231\pi$
$739$	129.576	−	224.433i	0.175340	−	0.303698i	0.940279	+	0.340405i	$0.110564\pi$
$740$		0			0
$741$	−122.204	−	77.0438i	−0.164918	−	0.103973i
$742$		0			0
$743$	−583.576	+	336.928i	−0.785432	+	0.453470i	−0.838352	−	0.545129i	$-0.816481\pi$
$743$	−583.576	+	336.928i	−0.785432	+	0.453470i	0.0529197	+	0.998599i	$0.483147\pi$
$744$		0			0
$745$	206.181	−	357.117i	0.276754	−	0.479351i
$746$		0			0
$747$	−162.445	−	794.436i	−0.217464	−	1.06350i
$748$		0			0
$749$	82.3131	−	47.5235i	0.109897	−	0.0634493i
$750$		0			0
$751$			1015.51i			1.35220i	0.736808	+	0.676102i	$0.236332\pi$
$751$			1015.51i			1.35220i	−0.736808	+	0.676102i	$0.763668\pi$
$752$		0			0
$753$	68.7062	+	181.078i	0.0912434	+	0.240475i
$754$		0			0
$755$	19.3053	+	11.1459i	0.0255699	+	0.0147628i
$756$		0			0
$757$	190.298	−	329.606i	0.251385	−	0.435411i	−0.712523	−	0.701649i	$-0.752447\pi$
$757$	190.298	−	329.606i	0.251385	−	0.435411i	0.963907	+	0.266238i	$0.0857807\pi$
$758$		0			0
$759$	82.8419	+	218.333i	0.109146	+	0.287658i
$760$		0			0
$761$	−246.211	+	426.449i	−0.323536	+	0.560380i	−0.981215	−	0.192918i	$-0.938205\pi$
$761$	−246.211	+	426.449i	−0.323536	+	0.560380i	0.657679	+	0.753298i	$0.271538\pi$
$762$		0			0
$763$			159.041i			0.208442i
$764$		0			0
$765$	407.027	+	135.743i	0.532062	+	0.177442i
$766$		0			0
$767$	69.9534	+	121.163i	0.0912039	+	0.157970i
$768$		0			0
$769$	280.145			0.364298			0.182149	−	0.983271i	$-0.441695\pi$
$769$	280.145			0.364298			0.182149	+	0.983271i	$0.441695\pi$
$770$		0			0
$771$	65.2406	−	401.840i	0.0846181	−	0.521194i
$772$		0			0
$773$	765.269	−	441.828i	0.989999	−	0.571576i	0.0847249	−	0.996404i	$-0.472999\pi$
$773$	765.269	−	441.828i	0.989999	−	0.571576i	0.905274	+	0.424828i	$0.139666\pi$
$774$		0			0
$775$	753.186	−	434.852i	0.971853	−	0.561100i
$776$		0			0
$777$	316.557	−	120.111i	0.407409	−	0.154583i
$778$		0			0
$779$	124.442	+	1014.63i	0.159746	+	1.30248i
$780$		0			0
$781$		−	1482.14i		−	1.89775i
$782$		0			0
$783$	214.829	+	339.370i	0.274366	+	0.433423i
$784$		0			0
$785$	180.296	−	312.283i	0.229677	−	0.397812i
$786$		0			0
$787$	119.325	+	68.8925i	0.151620	+	0.0875381i	0.573891	−	0.818932i	$-0.305433\pi$
$787$	119.325	+	68.8925i	0.151620	+	0.0875381i	−0.422270	+	0.906470i	$0.638767\pi$
$788$		0			0
$789$	1017.42	+	165.183i	1.28950	+	0.209357i
$790$		0			0
$791$		−	315.043i		−	0.398285i
$792$		0			0
$793$	−182.554	−	105.398i	−0.230207	−	0.132910i
$794$		0			0
$795$	−437.727	−	357.279i	−0.550601	−	0.449407i
$796$		0			0
$797$	658.196	+	380.010i	0.825842	+	0.476800i	0.852427	−	0.522846i	$-0.175130\pi$
$797$	658.196	+	380.010i	0.825842	+	0.476800i	−0.0265846	+	0.999647i	$0.508463\pi$
$798$		0			0
$799$	−836.716	−	1449.23i	−1.04720	−	1.81381i
$800$		0			0
$801$	−269.680	+	55.1440i	−0.336680	+	0.0688439i
$802$		0			0
$803$	2041.10			2.54184
$804$		0			0
$805$	31.0153	−	53.7201i	0.0385283	−	0.0667330i
$806$		0			0
$807$	−1091.01	−	890.499i	−1.35194	−	1.10347i
$808$		0			0
$809$	−195.804			−0.242032			−0.121016	−	0.992651i	$-0.538615\pi$
$809$	−195.804			−0.242032			−0.121016	+	0.992651i	$0.538615\pi$
$810$		0			0
$811$	−177.853	+	102.683i	−0.219301	+	0.126613i	−0.605626	−	0.795749i	$-0.707077\pi$
$811$	−177.853	+	102.683i	−0.219301	+	0.126613i	0.386326	+	0.922362i	$0.373744\pi$
$812$		0			0
$813$	19.7866	−	24.2420i	0.0243378	−	0.0298179i
$814$		0			0
$815$	289.519	+	501.462i	0.355238	+	0.615291i
$816$		0			0
$817$	−374.432	+	881.775i	−0.458301	+	1.07928i
$818$		0			0
$819$	−148.160	+	30.2955i	−0.180903	+	0.0369909i
$820$		0			0
$821$	−561.125	+	971.897i	−0.683465	+	1.18380i	0.290452	+	0.956890i	$0.406195\pi$
$821$	−561.125	+	971.897i	−0.683465	+	1.18380i	−0.973917	+	0.226906i	$0.927139\pi$
$822$		0			0
$823$	−166.971			−0.202881			−0.101441	−	0.994842i	$-0.532345\pi$
$823$	−166.971			−0.202881			−0.101441	+	0.994842i	$0.532345\pi$
$824$		0			0
$825$	980.007	+	159.108i	1.18789	+	0.192859i
$826$		0			0
$827$	−1227.81	+	708.877i	−1.48466	+	0.857167i	−0.999848	−	0.0174521i	$-0.994445\pi$
$827$	−1227.81	+	708.877i	−1.48466	+	0.857167i	−0.484810	+	0.874620i	$0.661111\pi$
$828$		0			0
$829$			1069.64i			1.29027i	0.764068	+	0.645136i	$0.223199\pi$
$829$			1069.64i			1.29027i	−0.764068	+	0.645136i	$0.776801\pi$
$830$		0			0
$831$	509.509	+	1342.83i	0.613127	+	1.61592i
$832$		0			0
$833$	65.3463	+	113.183i	0.0784469	+	0.135874i
$834$		0			0
$835$	164.216	−	94.8103i	0.196666	−	0.113545i
$836$		0			0
$837$	−581.140	−	918.041i	−0.694313	−	1.09682i
$838$		0			0
$839$		−	1040.50i		−	1.24016i	−0.784537	−	0.620082i	$-0.787099\pi$
$839$		−	1040.50i		−	1.24016i	0.784537	−	0.620082i	$-0.212901\pi$
$840$		0			0
$841$	−309.853	−	536.681i	−0.368434	−	0.638146i
$842$		0			0
$843$	604.698	+	493.562i	0.717317	+	0.585483i
$844$		0			0
$845$	−149.620	−	259.149i	−0.177065	−	0.306686i
$846$		0			0
$847$	−752.394			−0.888305
$848$		0			0
$849$	−288.358	−	759.977i	−0.339644	−	0.895144i
$850$		0			0
$851$			86.5330i			0.101684i
$852$		0			0
$853$	−59.2399			−0.0694489			−0.0347244	−	0.999397i	$-0.511055\pi$
$853$	−59.2399			−0.0694489			−0.0347244	+	0.999397i	$0.511055\pi$
$854$		0			0
$855$	−308.479	−	62.4875i	−0.360794	−	0.0730848i
$856$		0			0
$857$			498.443i			0.581614i	0.956782	+	0.290807i	$0.0939237\pi$
$857$			498.443i			0.581614i	−0.956782	+	0.290807i	$0.906076\pi$
$858$		0			0
$859$	−6.37734			−0.00742414			−0.00371207	−	0.999993i	$-0.501182\pi$
$859$	−6.37734			−0.00742414			−0.00371207	+	0.999993i	$0.501182\pi$
$860$		0			0
$861$	829.001	+	676.641i	0.962835	+	0.785878i
$862$		0			0
$863$		−	1182.43i		−	1.37014i	−0.728475	−	0.685072i	$-0.759771\pi$
$863$		−	1182.43i		−	1.37014i	0.728475	−	0.685072i	$-0.240229\pi$
$864$		0			0
$865$	−64.7752	+	37.3980i	−0.0748846	+	0.0432346i
$866$		0			0
$867$	406.410	+	1071.11i	0.468755	+	1.23542i
$868$		0			0
$869$	443.607	−	256.116i	0.510479	−	0.294725i
$870$		0			0
$871$	−281.578			−0.323281
$872$		0			0
$873$	226.627	−	679.541i	0.259595	−	0.778397i
$874$		0			0
$875$	−284.401	−	492.596i	−0.325029	−	0.562967i
$876$		0			0
$877$	−61.2740	+	35.3765i	−0.0698677	+	0.0403381i	−0.534527	−	0.845151i	$-0.679510\pi$
$877$	−61.2740	+	35.3765i	−0.0698677	+	0.0403381i	0.464659	+	0.885490i	$0.346177\pi$
$878$		0			0
$879$	−528.119	−	431.057i	−0.600818	−	0.490395i
$880$		0			0
$881$	1012.09			1.14880			0.574399	−	0.818576i	$-0.305236\pi$
$881$	1012.09			1.14880			0.574399	+	0.818576i	$0.305236\pi$
$882$		0			0
$883$	−222.537	−	385.445i	−0.252024	−	0.436518i	0.712059	−	0.702119i	$-0.247763\pi$
$883$	−222.537	−	385.445i	−0.252024	−	0.436518i	−0.964083	+	0.265602i	$0.914429\pi$
$884$		0			0
$885$	236.143	+	192.743i	0.266829	+	0.217789i
$886$		0			0
$887$			407.100i			0.458963i	0.973313	+	0.229481i	$0.0737030\pi$
$887$			407.100i			0.458963i	−0.973313	+	0.229481i	$0.926297\pi$
$888$		0			0
$889$	962.835	+	555.893i	1.08305	+	0.625301i
$890$		0			0
$891$	148.733	−	1231.40i	0.166928	−	1.38204i
$892$		0			0
$893$	738.629	+	980.470i	0.827132	+	1.09795i
$894$		0			0
$895$	−118.459	+	68.3922i	−0.132356	+	0.0764158i
$896$		0			0
$897$	6.19387	−	38.1503i	0.00690510	−	0.0425310i
$898$		0			0
$899$	−299.315	−	518.429i	−0.332942	−	0.576673i
$900$		0			0
$901$		−	2650.36i		−	2.94158i
$902$		0			0
$903$	355.753	+	937.600i	0.393968	+	1.03832i
$904$		0			0
$905$	157.926	+	91.1786i	0.174504	+	0.100750i
$906$		0			0
$907$			347.653i			0.383299i	0.981463	+	0.191650i	$0.0613838\pi$
$907$			347.653i			0.383299i	−0.981463	+	0.191650i	$0.938616\pi$
$908$		0			0
$909$	−827.006	+	733.128i	−0.909798	+	0.806521i
$910$		0			0
$911$	−261.179	+	150.792i	−0.286695	+	0.165523i	−0.636450	−	0.771318i	$-0.719598\pi$
$911$	−261.179	+	150.792i	−0.286695	+	0.165523i	0.349755	+	0.936841i	$0.386265\pi$
$912$		0			0
$913$	−689.827	+	1194.81i	−0.755560	+	1.30867i
$914$		0			0
$915$	−453.328	−	73.5998i	−0.495441	−	0.0804370i
$916$		0			0
$917$	783.252	−	1356.63i	0.854146	−	1.47943i
$918$		0			0
$919$	1364.04			1.48427			0.742135	−	0.670250i	$-0.233813\pi$
$919$	1364.04			1.48427			0.742135	+	0.670250i	$0.233813\pi$
$920$		0			0
$921$	−1153.03	−	941.119i	−1.25193	−	1.02185i
$922$		0			0
$923$	−122.654	+	212.443i	−0.132886	+	0.230166i
$924$		0			0
$925$	318.615	+	183.952i	0.344448	+	0.198867i
$926$		0			0
$927$	−396.477	−	447.247i	−0.427699	−	0.482467i
$928$		0			0
$929$	−1635.54			−1.76054			−0.880271	−	0.474471i	$-0.842639\pi$
$929$	−1635.54			−1.76054			−0.880271	+	0.474471i	$0.842639\pi$
$930$		0			0
$931$	−57.6859	−	76.5732i	−0.0619612	−	0.0822484i
$932$		0			0
$933$	328.999	−	403.080i	0.352625	−	0.432026i
$934$		0			0
$935$	−365.015	−	632.224i	−0.390390	−	0.676176i
$936$		0			0
$937$	339.778	+	588.513i	0.362624	+	0.628083i	0.988392	−	0.151927i	$-0.0485477\pi$
$937$	339.778	+	588.513i	0.362624	+	0.628083i	−0.625768	+	0.780009i	$0.715214\pi$
$938$		0			0
$939$	−400.451	+	490.621i	−0.426465	+	0.522493i
$940$		0			0
$941$		−	1113.24i		−	1.18304i	−0.806291	−	0.591520i	$-0.798528\pi$
$941$		−	1113.24i		−	1.18304i	0.806291	−	0.591520i	$-0.201472\pi$
$942$		0			0
$943$	−236.850	+	136.745i	−0.251166	+	0.145011i
$944$		0			0
$945$	−278.388	+	176.226i	−0.294590	+	0.186482i
$946$		0			0
$947$	−1477.40			−1.56009			−0.780043	−	0.625725i	$-0.784803\pi$
$947$	−1477.40			−1.56009			−0.780043	+	0.625725i	$0.784803\pi$
$948$		0			0
$949$	−292.562	−	168.911i	−0.308284	−	0.177988i
$950$		0			0
$951$	385.892	+	314.970i	0.405775	+	0.331199i
$952$		0			0
$953$	856.935	+	494.751i	0.899197	+	0.519152i	0.876940	−	0.480601i	$-0.159581\pi$
$953$	856.935	+	494.751i	0.899197	+	0.519152i	0.0222574	+	0.999752i	$0.492915\pi$
$954$		0			0
$955$	−305.980	+	529.973i	−0.320398	+	0.554946i
$956$		0			0
$957$	109.517	−	674.553i	0.114437	−	0.704862i
$958$		0			0
$959$	207.073			0.215926
$960$		0			0
$961$	329.186	+	570.167i	0.342546	+	0.593306i
$962$		0			0
$963$	40.8203	−	122.400i	0.0423886	−	0.127103i
$964$		0			0
$965$	421.555	+	243.385i	0.436845	+	0.252212i
$966$		0			0
$967$	−418.735	−	725.270i	−0.433025	−	0.750021i	0.564107	−	0.825702i	$-0.309220\pi$
$967$	−418.735	−	725.270i	−0.433025	−	0.750021i	−0.997132	+	0.0756805i	$0.975887\pi$
$968$		0			0
$969$	−687.886	−	1306.32i	−0.709893	−	1.34811i
$970$		0			0
$971$	107.490	+	62.0594i	0.110700	+	0.0639129i	0.554328	−	0.832298i	$-0.312975\pi$
$971$	107.490	+	62.0594i	0.110700	+	0.0639129i	−0.443628	+	0.896211i	$0.646309\pi$
$972$		0			0
$973$	113.946	+	197.361i	0.117108	+	0.202837i
$974$		0			0
$975$	−127.303	−	103.906i	−0.130567	−	0.106570i
$976$		0			0
$977$	444.691	+	256.743i	0.455160	+	0.262787i	0.710007	−	0.704195i	$-0.248692\pi$
$977$	444.691	+	256.743i	0.455160	+	0.262787i	−0.254847	+	0.966981i	$0.582025\pi$
$978$		0			0
$979$	405.594	+	234.170i	0.414294	+	0.239193i
$980$		0			0
$981$	143.219	+	161.558i	0.145993	+	0.164688i
$982$		0			0
$983$		−	801.456i		−	0.815316i	−0.913135	−	0.407658i	$-0.866345\pi$
$983$		−	801.456i		−	0.815316i	0.913135	−	0.407658i	$-0.133655\pi$
$984$		0			0
$985$	−33.5773	−	58.1577i	−0.0340887	−	0.0590433i
$986$		0			0
$987$	1268.41	+	205.932i	1.28512	+	0.208644i
$988$		0			0
$989$	−256.299			−0.259150
$990$		0			0
$991$	1285.82	+	742.366i	1.29749	+	0.749108i	0.979970	−	0.199143i	$-0.0638159\pi$
$991$	1285.82	+	742.366i	1.29749	+	0.749108i	0.317522	+	0.948251i	$0.397149\pi$
$992$		0			0
$993$	590.056	−	223.885i	0.594216	−	0.225463i
$994$		0			0
$995$	−278.278	+	481.992i	−0.279677	+	0.484414i
$996$		0			0
$997$	386.401	−	669.267i	0.387564	−	0.671281i	−0.604557	−	0.796562i	$-0.706650\pi$
$997$	386.401	−	669.267i	0.387564	−	0.671281i	0.992121	+	0.125281i	$0.0399832\pi$
$998$		0			0
$999$	213.405	−	407.076i	0.213619	−	0.407483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.3	✓	80
3.2	odd	2		2052.3.s.a.901.24		80
9.2	odd	6		2052.3.bl.a.1585.17		80
9.7	even	3		684.3.bl.a.673.12	yes	80
19.12	odd	6		684.3.bl.a.373.12	yes	80
57.50	even	6		2052.3.bl.a.145.17		80
171.88	odd	6	inner	684.3.s.a.601.3	yes	80
171.164	even	6		2052.3.s.a.829.24		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.3	✓	80	1.1	even	1	trivial
684.3.s.a.601.3	yes	80	171.88	odd	6	inner
684.3.bl.a.373.12	yes	80	19.12	odd	6
684.3.bl.a.673.12	yes	80	9.7	even	3
2052.3.s.a.829.24		80	171.164	even	6
2052.3.s.a.901.24		80	3.2	odd	2
2052.3.bl.a.145.17		80	57.50	even	6
2052.3.bl.a.1585.17		80	9.2	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.96123 - 0.480768i) q^{3} +(-0.920304 - 1.59401i) q^{5} +(3.31490 + 5.74157i) q^{7} +(8.53772 + 2.84733i) q^{9} +O(q^{10})\)	\(q+(-2.96123 - 0.480768i) q^{3} +(-0.920304 - 1.59401i) q^{5} +(3.31490 + 5.74157i) q^{7} +(8.53772 + 2.84733i) q^{9} +(-7.65648 - 13.2614i) q^{11} +2.53444i q^{13} +(1.95888 + 5.16269i) q^{15} +(-12.9506 + 22.4311i) q^{17} +(7.42625 - 17.4886i) q^{19} +(-7.05580 - 18.5958i) q^{21} +5.08329 q^{23} +(10.8061 - 18.7167i) q^{25} +(-23.9132 - 12.5362i) q^{27} +(-12.8830 - 7.43798i) q^{29} +(34.8501 + 20.1207i) q^{31} +(16.2969 + 42.9510i) q^{33} +(6.10143 - 10.5680i) q^{35} +17.0230i q^{37} +(1.21848 - 7.50505i) q^{39} +(-46.5938 + 26.9009i) q^{41} -50.4200 q^{43} +(-3.31862 - 16.2297i) q^{45} +(-32.3041 + 55.9524i) q^{47} +(2.52290 - 4.36980i) q^{49} +(49.1338 - 60.1974i) q^{51} +(-88.6168 + 51.1629i) q^{53} +(-14.0926 + 24.4091i) q^{55} +(-30.3988 + 48.2174i) q^{57} +(47.8066 - 27.6012i) q^{59} +(-41.5863 + 72.0295i) q^{61} +(11.9535 + 58.4586i) q^{63} +(4.03993 - 2.33245i) q^{65} +111.101i q^{67} +(-15.0528 - 2.44388i) q^{69} +(83.8226 + 48.3950i) q^{71} +(-66.6462 + 115.435i) q^{73} +(-40.9976 + 50.2291i) q^{75} +(50.7609 - 87.9205i) q^{77} +33.4509i q^{79} +(64.7855 + 48.6194i) q^{81} +(-45.0486 - 78.0264i) q^{83} +47.6740 q^{85} +(34.5734 + 28.2193i) q^{87} +(-26.4870 + 15.2923i) q^{89} +(-14.5517 + 8.40140i) q^{91} +(-93.5256 - 76.3368i) q^{93} +(-34.7115 + 4.25727i) q^{95} -79.5927i q^{97} +(-27.6093 - 135.023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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