LMFDB - Embedded newform 441.2.f.c.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.2
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	441.295
Dual form			441.2.f.c.148.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673648 + 1.16679i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(1.26604 + 2.19285i) q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(2.81908 + 1.02606i) q^{9} +O(q^{10})$	\(q+(-0.673648 + 1.16679i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(1.26604 + 2.19285i) q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(2.81908 + 1.02606i) q^{9} -3.41147 q^{10} +(-0.233956 + 0.405223i) q^{11} +(-0.109470 - 0.300767i) q^{12} +(2.91147 + 5.04282i) q^{13} +(-1.50000 - 4.12122i) q^{15} +(1.79813 - 3.11446i) q^{16} -3.87939 q^{17} +(-3.09627 + 2.59808i) q^{18} +2.18479 q^{19} +(-0.233956 + 0.405223i) q^{20} +(-0.315207 - 0.545955i) q^{22} +(0.0530334 + 0.0918566i) q^{23} +(5.02094 + 0.885328i) q^{24} +(-0.705737 + 1.22237i) q^{25} -7.84524 q^{26} +(-4.50000 - 2.59808i) q^{27} +(-4.39053 + 7.60462i) q^{29} +(5.81908 + 1.02606i) q^{30} +(-3.84002 - 6.65111i) q^{31} +(-0.520945 - 0.902302i) q^{32} +(0.520945 - 0.620838i) q^{33} +(2.61334 - 4.52644i) q^{34} +(0.0962667 + 0.545955i) q^{36} -7.68004 q^{37} +(-1.47178 + 2.54920i) q^{38} +(-3.44949 - 9.47740i) q^{39} +(-3.72668 - 6.45480i) q^{40} +(-1.11334 - 1.92836i) q^{41} +(-0.613341 + 1.06234i) q^{43} -0.0864665 q^{44} +(1.31908 + 7.48086i) q^{45} -0.142903 q^{46} +(-2.66637 + 4.61830i) q^{47} +(-4.00387 + 4.77163i) q^{48} +(-0.950837 - 1.64690i) q^{50} +(6.61721 + 1.16679i) q^{51} +(-0.538019 + 0.931876i) q^{52} -0.716881 q^{53} +(6.06283 - 3.50038i) q^{54} -1.18479 q^{55} +(-3.72668 - 0.657115i) q^{57} +(-5.91534 - 10.2457i) q^{58} +(0.368241 + 0.637812i) q^{59} +(0.520945 - 0.620838i) q^{60} +(0.479055 - 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(-7.37211 + 12.7689i) q^{65} +(0.373455 + 1.02606i) q^{66} +(4.81908 + 8.34689i) q^{67} +(-0.358441 - 0.620838i) q^{68} +(-0.0628336 - 0.172634i) q^{69} +13.2344 q^{71} +(-8.29813 - 3.02027i) q^{72} +10.2686 q^{73} +(5.17365 - 8.96102i) q^{74} +(1.57145 - 1.87278i) q^{75} +(0.201867 + 0.349643i) q^{76} +(13.3819 + 2.35959i) q^{78} +(6.31908 - 10.9450i) q^{79} +9.10607 q^{80} +(6.89440 + 5.78509i) q^{81} +3.00000 q^{82} +(-1.36571 + 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +(-0.826352 - 1.43128i) q^{86} +(9.77631 - 11.6510i) q^{87} +(0.688663 - 1.19280i) q^{88} +8.11381 q^{89} +(-9.61721 - 3.50038i) q^{90} +(-0.00980018 + 0.0169744i) q^{92} +(4.54963 + 12.5000i) q^{93} +(-3.59240 - 6.22221i) q^{94} +(2.76604 + 4.79093i) q^{95} +(0.617211 + 1.69577i) q^{96} +(-6.80200 + 11.7814i) q^{97} +(-1.07532 + 0.902302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} - 18 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} - 12 q^{17} + 9 q^{18} + 6 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} + 27 q^{24} + 6 q^{25} + 6 q^{26} - 27 q^{27} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 9 q^{34} - 27 q^{36} - 6 q^{37} + 6 q^{38} - 18 q^{39} - 9 q^{40} + 3 q^{43} + 30 q^{44} - 9 q^{45} + 3 q^{47} + 6 q^{50} + 9 q^{51} - 21 q^{52} + 12 q^{53} + 27 q^{54} - 9 q^{57} + 9 q^{58} - 3 q^{59} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} - 36 q^{66} + 12 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 36 q^{72} + 42 q^{73} + 30 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} + 30 q^{80} + 18 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} - 9 q^{87} - 27 q^{88} - 24 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 - 18 * q^12 - 3 * q^13 - 9 * q^15 - 3 * q^16 - 12 * q^17 + 9 * q^18 + 6 * q^19 - 6 * q^20 - 9 * q^22 - 12 * q^23 + 27 * q^24 + 6 * q^25 + 6 * q^26 - 27 * q^27 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 9 * q^34 - 27 * q^36 - 6 * q^37 + 6 * q^38 - 18 * q^39 - 9 * q^40 + 3 * q^43 + 30 * q^44 - 9 * q^45 + 3 * q^47 + 6 * q^50 + 9 * q^51 - 21 * q^52 + 12 * q^53 + 27 * q^54 - 9 * q^57 + 9 * q^58 - 3 * q^59 + 6 * q^61 + 60 * q^62 + 24 * q^64 - 15 * q^65 - 36 * q^66 + 12 * q^67 + 6 * q^68 + 9 * q^69 + 18 * q^71 - 36 * q^72 + 42 * q^73 + 30 * q^74 + 9 * q^75 + 15 * q^76 + 54 * q^78 + 21 * q^79 + 30 * q^80 + 18 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 - 9 * q^87 - 27 * q^88 - 24 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 27 * q^96 - 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.673648	+	1.16679i	−0.476341	+	0.825047i	−0.999633	−	0.0271067i	$-0.991371\pi$
$2$	−0.673648	+	1.16679i	−0.476341	+	0.825047i	0.523291	+	0.852154i	$0.324704\pi$
$3$	−1.70574	−	0.300767i	−0.984808	−	0.173648i
$3$	−1.70574	−	0.300767i	−0.984808	−	0.173648i
$4$	0.0923963	+	0.160035i	0.0461981	+	0.0800175i
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	0.996938	+	0.0782003i	$0.0249174\pi$
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	−0.430745	+	0.902473i	$0.641749\pi$
$6$	1.50000	−	1.78763i	0.612372	−	0.729797i
$7$		0			0
$7$		0			0
$8$	−2.94356			−1.04071
$9$	2.81908	+	1.02606i	0.939693	+	0.342020i
$10$	−3.41147			−1.07880
$11$	−0.233956	+	0.405223i	−0.0705403	+	0.122179i	−0.899138	−	0.437665i	$-0.855806\pi$
$11$	−0.233956	+	0.405223i	−0.0705403	+	0.122179i	0.828598	+	0.559844i	$0.189139\pi$
$12$	−0.109470	−	0.300767i	−0.0316014	−	0.0868241i
$13$	2.91147	+	5.04282i	0.807498	+	1.39863i	0.914592	+	0.404378i	$0.132512\pi$
$13$	2.91147	+	5.04282i	0.807498	+	1.39863i	−0.107094	+	0.994249i	$0.534155\pi$
$14$		0			0
$15$	−1.50000	−	4.12122i	−0.387298	−	1.06409i
$16$	1.79813	−	3.11446i	0.449533	−	0.778615i
$17$	−3.87939			−0.940889			−0.470445	−	0.882430i	$-0.655906\pi$
$17$	−3.87939			−0.940889			−0.470445	+	0.882430i	$0.655906\pi$
$18$	−3.09627	+	2.59808i	−0.729797	+	0.612372i
$19$	2.18479			0.501226			0.250613	−	0.968087i	$-0.419368\pi$
$19$	2.18479			0.501226			0.250613	+	0.968087i	$0.419368\pi$
$20$	−0.233956	+	0.405223i	−0.0523141	+	0.0906106i
$21$		0			0
$22$	−0.315207	−	0.545955i	−0.0672025	−	0.116398i
$23$	0.0530334	+	0.0918566i	0.0110582	+	0.0191534i	0.871502	−	0.490393i	$-0.163147\pi$
$23$	0.0530334	+	0.0918566i	0.0110582	+	0.0191534i	−0.860443	+	0.509546i	$0.829813\pi$
$24$	5.02094	+	0.885328i	1.02490	+	0.180717i
$25$	−0.705737	+	1.22237i	−0.141147	+	0.244474i
$26$	−7.84524			−1.53858
$27$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$28$		0			0
$29$	−4.39053	+	7.60462i	−0.815301	+	1.41214i	0.0938108	+	0.995590i	$0.470095\pi$
$29$	−4.39053	+	7.60462i	−0.815301	+	1.41214i	−0.909112	+	0.416552i	$0.863238\pi$
$30$	5.81908	+	1.02606i	1.06241	+	0.187332i
$31$	−3.84002	−	6.65111i	−0.689688	−	1.19458i	−0.971939	−	0.235235i	$-0.924414\pi$
$31$	−3.84002	−	6.65111i	−0.689688	−	1.19458i	0.282250	−	0.959341i	$-0.408919\pi$
$32$	−0.520945	−	0.902302i	−0.0920909	−	0.159506i
$33$	0.520945	−	0.620838i	0.0906848	−	0.108074i
$34$	2.61334	−	4.52644i	0.448184	−	0.776278i
$35$		0			0
$36$	0.0962667	+	0.545955i	0.0160444	+	0.0909926i
$37$	−7.68004			−1.26259			−0.631296	−	0.775542i	$-0.717477\pi$
$37$	−7.68004			−1.26259			−0.631296	+	0.775542i	$0.717477\pi$
$38$	−1.47178	+	2.54920i	−0.238754	+	0.413535i
$39$	−3.44949	−	9.47740i	−0.552361	−	1.51760i
$40$	−3.72668	−	6.45480i	−0.589240	−	1.02059i
$41$	−1.11334	−	1.92836i	−0.173875	−	0.301160i	0.765897	−	0.642964i	$-0.222295\pi$
$41$	−1.11334	−	1.92836i	−0.173875	−	0.301160i	−0.939771	+	0.341804i	$0.888962\pi$
$42$		0			0
$43$	−0.613341	+	1.06234i	−0.0935336	+	0.162005i	−0.908996	−	0.416806i	$-0.863150\pi$
$43$	−0.613341	+	1.06234i	−0.0935336	+	0.162005i	0.815462	+	0.578811i	$0.196483\pi$
$44$	−0.0864665			−0.0130353
$45$	1.31908	+	7.48086i	0.196637	+	1.11518i
$46$	−0.142903			−0.0210700
$47$	−2.66637	+	4.61830i	−0.388931	+	0.673648i	−0.992306	−	0.123810i	$-0.960489\pi$
$47$	−2.66637	+	4.61830i	−0.388931	+	0.673648i	0.603375	+	0.797457i	$0.293822\pi$
$48$	−4.00387	+	4.77163i	−0.577909	+	0.688725i
$49$		0			0
$50$	−0.950837	−	1.64690i	−0.134469	−	0.232907i
$51$	6.61721	+	1.16679i	0.926595	+	0.163384i
$52$	−0.538019	+	0.931876i	−0.0746098	+	0.129228i
$53$	−0.716881			−0.0984712			−0.0492356	−	0.998787i	$-0.515679\pi$
$53$	−0.716881			−0.0984712			−0.0492356	+	0.998787i	$0.515679\pi$
$54$	6.06283	−	3.50038i	0.825047	−	0.476341i
$55$	−1.18479			−0.159757
$56$		0			0
$57$	−3.72668	−	0.657115i	−0.493611	−	0.0870369i
$58$	−5.91534	−	10.2457i	−0.776723	−	1.34532i
$59$	0.368241	+	0.637812i	0.0479409	+	0.0830360i	0.889000	−	0.457907i	$-0.151401\pi$
$59$	0.368241	+	0.637812i	0.0479409	+	0.0830360i	−0.841059	+	0.540943i	$0.818067\pi$
$60$	0.520945	−	0.620838i	0.0672537	−	0.0801498i
$61$	0.479055	−	0.829748i	0.0613368	−	0.106238i	−0.833726	−	0.552178i	$-0.813797\pi$
$61$	0.479055	−	0.829748i	0.0613368	−	0.106238i	0.895063	+	0.445939i	$0.147130\pi$
$62$	10.3473			1.31411
$63$		0			0
$64$	8.59627			1.07453
$65$	−7.37211	+	12.7689i	−0.914398	+	1.58378i
$66$	0.373455	+	1.02606i	0.0459692	+	0.126299i
$67$	4.81908	+	8.34689i	0.588744	+	1.01973i	0.994397	+	0.105708i	$0.0337107\pi$
$67$	4.81908	+	8.34689i	0.588744	+	1.01973i	−0.405653	+	0.914027i	$0.632956\pi$
$68$	−0.358441	−	0.620838i	−0.0434673	−	0.0752876i
$69$	−0.0628336	−	0.172634i	−0.00756428	−	0.0207827i
$70$		0			0
$71$	13.2344			1.57064			0.785318	−	0.619092i	$-0.212499\pi$
$71$	13.2344			1.57064			0.785318	+	0.619092i	$0.212499\pi$
$72$	−8.29813	−	3.02027i	−0.977944	−	0.355943i
$73$	10.2686			1.20185			0.600923	−	0.799307i	$-0.294800\pi$
$73$	10.2686			1.20185			0.600923	+	0.799307i	$0.294800\pi$
$74$	5.17365	−	8.96102i	0.601424	−	1.04170i
$75$	1.57145	−	1.87278i	0.181456	−	0.216250i
$76$	0.201867	+	0.349643i	0.0231557	+	0.0401068i
$77$		0			0
$78$	13.3819	+	2.35959i	1.51520	+	0.267171i
$79$	6.31908	−	10.9450i	0.710952	−	1.23140i	−0.253548	−	0.967323i	$-0.581598\pi$
$79$	6.31908	−	10.9450i	0.710952	−	1.23140i	0.964500	−	0.264082i	$-0.0850689\pi$
$80$	9.10607			1.01809
$81$	6.89440	+	5.78509i	0.766044	+	0.642788i
$82$	3.00000			0.331295
$83$	−1.36571	+	2.36549i	−0.149907	+	0.259646i	−0.931193	−	0.364527i	$-0.881231\pi$
$83$	−1.36571	+	2.36549i	−0.149907	+	0.259646i	0.781286	+	0.624173i	$0.214564\pi$
$84$		0			0
$85$	−4.91147	−	8.50692i	−0.532724	−	0.922705i
$86$	−0.826352	−	1.43128i	−0.0891078	−	0.154339i
$87$	9.77631	−	11.6510i	1.04813	−	1.24911i
$88$	0.688663	−	1.19280i	0.0734117	−	0.127153i
$89$	8.11381			0.860062			0.430031	−	0.902814i	$-0.358503\pi$
$89$	8.11381			0.860062			0.430031	+	0.902814i	$0.358503\pi$
$90$	−9.61721	−	3.50038i	−1.01374	−	0.368972i
$91$		0			0
$92$	−0.00980018	+	0.0169744i	−0.00102174	+	0.00176970i
$93$	4.54963	+	12.5000i	0.471775	+	1.29619i
$94$	−3.59240	−	6.22221i	−0.370527	−	0.641772i
$95$	2.76604	+	4.79093i	0.283790	+	0.491539i
$96$	0.617211	+	1.69577i	0.0629939	+	0.173074i
$97$	−6.80200	+	11.7814i	−0.690639	+	1.19622i	0.280990	+	0.959711i	$0.409337\pi$
$97$	−6.80200	+	11.7814i	−0.690639	+	1.19622i	−0.971629	+	0.236511i	$0.923996\pi$
$98$		0			0
$99$	−1.07532	+	0.902302i	−0.108074	+	0.0906848i
$100$	−0.260830			−0.0260830
$101$	−4.78699	+	8.29131i	−0.476323	+	0.825016i	−0.999632	−	0.0271271i	$-0.991364\pi$
$101$	−4.78699	+	8.29131i	−0.476323	+	0.825016i	0.523309	+	0.852143i	$0.324697\pi$
$102$	−5.81908	+	6.93491i	−0.576175	+	0.686658i
$103$	1.52094	+	2.63435i	0.149863	+	0.259571i	0.931177	−	0.364568i	$-0.118783\pi$
$103$	1.52094	+	2.63435i	0.149863	+	0.259571i	−0.781314	+	0.624139i	$0.785450\pi$
$104$	−8.57011	−	14.8439i	−0.840368	−	1.45556i
$105$		0			0
$106$	0.482926	−	0.836452i	0.0469059	−	0.0812434i
$107$	−6.51754			−0.630074			−0.315037	−	0.949079i	$-0.602017\pi$
$107$	−6.51754			−0.630074			−0.315037	+	0.949079i	$0.602017\pi$
$108$		−	0.960210i		−	0.0923963i
$109$	10.6382			1.01895			0.509475	−	0.860485i	$-0.329840\pi$
$109$	10.6382			1.01895			0.509475	+	0.860485i	$0.329840\pi$
$110$	0.798133	−	1.38241i	0.0760990	−	0.131807i
$111$	13.1001	+	2.30991i	1.24341	+	0.219247i
$112$		0			0
$113$	−2.58853	−	4.48346i	−0.243508	−	0.421768i	0.718203	−	0.695834i	$-0.244965\pi$
$113$	−2.58853	−	4.48346i	−0.243508	−	0.421768i	−0.961711	+	0.274065i	$0.911632\pi$
$114$	3.27719	−	3.90560i	0.306937	−	0.365793i
$115$	−0.134285	+	0.232589i	−0.0125222	+	0.0216890i
$116$	−1.62267			−0.150662
$117$	3.03343	+	17.2035i	0.280441	+	1.59046i
$118$	−0.992259			−0.0913449
$119$		0			0
$120$	4.41534	+	12.1311i	0.403064	+	1.10741i
$121$	5.39053	+	9.33667i	0.490048	+	0.848788i
$122$	0.645430	+	1.11792i	0.0584345	+	0.101211i
$123$	1.31908	+	3.62414i	0.118937	+	0.326777i
$124$	0.709607	−	1.22908i	0.0637246	−	0.110374i
$125$	9.08647			0.812718
$126$		0			0
$127$	−8.88207			−0.788157			−0.394078	−	0.919077i	$-0.628936\pi$
$127$	−8.88207			−0.788157			−0.394078	+	0.919077i	$0.628936\pi$
$128$	−4.74897	+	8.22546i	−0.419754	+	0.727035i
$129$	1.36571	−	1.62760i	0.120244	−	0.143302i
$130$	−9.93242	−	17.2035i	−0.871131	−	1.50884i
$131$	5.68139	+	9.84045i	0.496385	+	0.859764i	0.999991	−	0.00416893i	$-0.00132701\pi$
$131$	5.68139	+	9.84045i	0.496385	+	0.859764i	−0.503606	+	0.863933i	$0.667994\pi$
$132$	0.147489	+	0.0260063i	0.0128373	+	0.00226356i
$133$		0			0
$134$	−12.9855			−1.12177
$135$		−	13.1571i		−	1.13238i
$136$	11.4192			0.979190
$137$	2.86231	−	4.95767i	0.244544	−	0.423562i	−0.717459	−	0.696600i	$-0.754695\pi$
$137$	2.86231	−	4.95767i	0.244544	−	0.423562i	0.962003	+	0.273038i	$0.0880285\pi$
$138$	0.243756	+	0.0429807i	0.0207499	+	0.00365876i
$139$	−0.461981	−	0.800175i	−0.0391847	−	0.0678700i	0.845768	−	0.533551i	$-0.179143\pi$
$139$	−0.461981	−	0.800175i	−0.0391847	−	0.0678700i	−0.884953	+	0.465681i	$0.845809\pi$
$140$		0			0
$141$	5.93717	−	7.07564i	0.500000	−	0.595876i
$142$	−8.91534	+	15.4418i	−0.748159	+	1.29585i
$143$	−2.72462			−0.227844
$144$	8.26470	−	6.93491i	0.688725	−	0.577909i
$145$	−22.2344			−1.84647
$146$	−6.91740	+	11.9813i	−0.572488	+	0.991579i
$147$		0			0
$148$	−0.709607	−	1.22908i	−0.0583294	−	0.101029i
$149$	−4.36231	−	7.55574i	−0.357374	−	0.618991i	0.630147	−	0.776476i	$-0.282995\pi$
$149$	−4.36231	−	7.55574i	−0.357374	−	0.618991i	−0.987521	+	0.157485i	$0.949661\pi$
$150$	1.12654	+	3.09516i	0.0919820	+	0.252718i
$151$	−9.21348	+	15.9582i	−0.749782	+	1.29866i	0.198145	+	0.980173i	$0.436508\pi$
$151$	−9.21348	+	15.9582i	−0.749782	+	1.29866i	−0.947927	+	0.318488i	$0.896825\pi$
$152$	−6.43107			−0.521629
$153$	−10.9363	−	3.98048i	−0.884147	−	0.321803i
$154$		0			0
$155$	9.72328	−	16.8412i	0.780992	−	1.35272i
$156$	1.19800	−	1.42772i	0.0959165	−	0.114309i
$157$	2.46198	+	4.26428i	0.196488	+	0.340326i	0.947387	−	0.320090i	$-0.103713\pi$
$157$	2.46198	+	4.26428i	0.196488	+	0.340326i	−0.750900	+	0.660416i	$0.770380\pi$
$158$	8.51367	+	14.7461i	0.677311	+	1.17314i
$159$	1.22281	+	0.215615i	0.0969752	+	0.0170994i
$160$	1.31908	−	2.28471i	0.104282	−	0.180622i
$161$		0			0
$162$	−11.3944	+	4.14722i	−0.895229	+	0.325837i
$163$	7.63816			0.598267			0.299133	−	0.954211i	$-0.403302\pi$
$163$	7.63816			0.598267			0.299133	+	0.954211i	$0.403302\pi$
$164$	0.205737	−	0.356347i	0.0160654	−	0.0278260i
$165$	2.02094	+	0.356347i	0.157330	+	0.0277416i
$166$	−1.84002	−	3.18701i	−0.142813	−	0.247360i
$167$	−2.82770	−	4.89771i	−0.218814	−	0.378996i	0.735632	−	0.677382i	$-0.236885\pi$
$167$	−2.82770	−	4.89771i	−0.218814	−	0.378996i	−0.954446	+	0.298385i	$0.903552\pi$
$168$		0			0
$169$	−10.4534	+	18.1058i	−0.804105	+	1.39275i
$170$	13.2344			1.01503
$171$	6.15910	+	2.24173i	0.470998	+	0.171429i
$172$	−0.226682			−0.0172843
$173$	10.5346	−	18.2465i	0.800932	−	1.38725i	−0.118071	−	0.993005i	$-0.537671\pi$
$173$	10.5346	−	18.2465i	0.800932	−	1.38725i	0.919003	−	0.394250i	$-0.128995\pi$
$174$	7.00846	+	19.2556i	0.531310	+	1.45976i
$175$		0			0
$176$	0.841367	+	1.45729i	0.0634204	+	0.109847i
$177$	−0.436289	−	1.19869i	−0.0327935	−	0.0900994i
$178$	−5.46585	+	9.46713i	−0.409683	+	0.709592i
$179$	−5.12061			−0.382733			−0.191366	−	0.981519i	$-0.561292\pi$
$179$	−5.12061			−0.382733			−0.191366	+	0.981519i	$0.561292\pi$
$180$	−1.07532	+	0.902302i	−0.0801498	+	0.0672537i
$181$	0.319955			0.0237821			0.0118910	−	0.999929i	$-0.496215\pi$
$181$	0.319955			0.0237821			0.0118910	+	0.999929i	$0.496215\pi$
$182$		0			0
$183$	−1.06670	+	1.27125i	−0.0788530	+	0.0939734i
$184$	−0.156107	−	0.270386i	−0.0115084	−	0.0199331i
$185$	−9.72328	−	16.8412i	−0.714870	−	1.23819i
$186$	−17.6498	−	3.11213i	−1.29414	−	0.228192i
$187$	0.907604	−	1.57202i	0.0663706	−	0.114957i
$188$	−0.985452			−0.0718715
$189$		0			0
$190$	−7.45336			−0.540724
$191$	7.78359	−	13.4816i	0.563200	−	0.975492i	−0.434014	−	0.900906i	$-0.642903\pi$
$191$	7.78359	−	13.4816i	0.563200	−	0.975492i	0.997215	−	0.0745858i	$-0.0237635\pi$
$192$	−14.6630	−	2.58548i	−1.05821	−	0.186591i
$193$	−3.02094	−	5.23243i	−0.217452	−	0.376639i	0.736576	−	0.676355i	$-0.236441\pi$
$193$	−3.02094	−	5.23243i	−0.217452	−	0.376639i	−0.954028	+	0.299716i	$0.903108\pi$
$194$	−9.16431	−	15.8731i	−0.657959	−	1.13962i
$195$	16.4153	−	19.5630i	1.17553	−	1.40094i
$196$		0			0
$197$	25.2344			1.79788			0.898939	−	0.438074i	$-0.144339\pi$
$197$	25.2344			1.79788			0.898939	+	0.438074i	$0.144339\pi$
$198$	−0.328411	−	1.86251i	−0.0233392	−	0.132363i
$199$	−3.04189			−0.215634			−0.107817	−	0.994171i	$-0.534386\pi$
$199$	−3.04189			−0.215634			−0.107817	+	0.994171i	$0.534386\pi$
$200$	2.07738	−	3.59813i	0.146893	−	0.254426i
$201$	−5.70961	−	15.6870i	−0.402725	−	1.10648i
$202$	−6.44949	−	11.1708i	−0.453785	−	0.785978i
$203$		0			0
$204$	0.424678	+	1.16679i	0.0297334	+	0.0816918i
$205$	2.81908	−	4.88279i	0.196893	−	0.341029i
$206$	−4.09833			−0.285544
$207$	0.0552549	+	0.313366i	0.00384048	+	0.0217805i
$208$	20.9409			1.45199
$209$	−0.511144	+	0.885328i	−0.0353566	+	0.0612394i
$210$		0			0
$211$	2.72668	+	4.72275i	0.187713	+	0.325128i	0.944487	−	0.328548i	$-0.106559\pi$
$211$	2.72668	+	4.72275i	0.187713	+	0.325128i	−0.756775	+	0.653676i	$0.773226\pi$
$212$	−0.0662372	−	0.114726i	−0.00454919	−	0.00787942i
$213$	−22.5744	−	3.98048i	−1.54678	−	0.272738i
$214$	4.39053	−	7.60462i	0.300130	−	0.519841i
$215$	−3.10607			−0.211832
$216$	13.2460	+	7.64760i	0.901278	+	0.520353i
$217$		0			0
$218$	−7.16637	+	12.4125i	−0.485368	+	0.840682i
$219$	−17.5155	−	3.08845i	−1.18359	−	0.208698i
$220$	−0.109470	−	0.189608i	−0.00738049	−	0.0127834i
$221$	−11.2947	−	19.5630i	−0.759766	−	1.31595i
$222$	−11.5201	+	13.7291i	−0.773176	+	0.921436i
$223$	7.09627	−	12.2911i	0.475201	−	0.823073i	−0.524395	−	0.851475i	$-0.675709\pi$
$223$	7.09627	−	12.2911i	0.475201	−	0.823073i	0.999597	+	0.0284023i	$0.00904195\pi$
$224$		0			0
$225$	−3.24376	+	2.72183i	−0.216250	+	0.181456i
$226$	6.97502			0.463972
$227$	−1.44697	+	2.50622i	−0.0960385	+	0.166344i	−0.910042	−	0.414517i	$-0.863951\pi$
$227$	−1.44697	+	2.50622i	−0.0960385	+	0.166344i	0.814003	+	0.580861i	$0.197284\pi$
$228$	−0.239170	−	0.657115i	−0.0158394	−	0.0435185i
$229$	4.58378	+	7.93934i	0.302905	+	0.524646i	0.976793	−	0.214187i	$-0.0687103\pi$
$229$	4.58378	+	7.93934i	0.302905	+	0.524646i	−0.673888	+	0.738834i	$0.735377\pi$
$230$	−0.180922	−	0.313366i	−0.0119297	−	0.0206628i
$231$		0			0
$232$	12.9238	−	22.3847i	0.848489	−	1.46963i
$233$	13.2713			0.869429			0.434715	−	0.900568i	$-0.356849\pi$
$233$	13.2713			0.869429			0.434715	+	0.900568i	$0.356849\pi$
$234$	−22.1163	−	8.04969i	−1.44579	−	0.526225i
$235$	−13.5030			−0.880838
$236$	−0.0680482	+	0.117863i	−0.00442956	+	0.00767222i
$237$	−14.0706	+	16.7687i	−0.913982	+	1.08924i
$238$		0			0
$239$	−4.76857	−	8.25941i	−0.308453	−	0.534257i	0.669571	−	0.742748i	$-0.266478\pi$
$239$	−4.76857	−	8.25941i	−0.308453	−	0.534257i	−0.978024	+	0.208491i	$0.933145\pi$
$240$	−15.5326	−	2.73881i	−1.00262	−	0.176789i
$241$	−4.47906	+	7.75795i	−0.288521	+	0.499734i	−0.973457	−	0.228870i	$-0.926497\pi$
$241$	−4.47906	+	7.75795i	−0.288521	+	0.499734i	0.684936	+	0.728604i	$0.259830\pi$
$242$	−14.5253			−0.933720
$243$	−10.0201	−	11.9415i	−0.642788	−	0.766044i
$244$	0.177052			0.0113346
$245$		0			0
$246$	−5.11721	−	0.902302i	−0.326261	−	0.0575287i
$247$	6.36097	+	11.0175i	0.404739	+	0.701028i
$248$	11.3033	+	19.5780i	0.717763	+	1.24320i
$249$	3.04101	−	3.62414i	0.192716	−	0.229670i
$250$	−6.12108	+	10.6020i	−0.387131	+	0.670531i
$251$	24.9982			1.57788			0.788938	−	0.614473i	$-0.210631\pi$
$251$	24.9982			1.57788			0.788938	+	0.614473i	$0.210631\pi$
$252$		0			0
$253$	−0.0496299			−0.00312020
$254$	5.98339	−	10.3635i	0.375431	−	0.650266i
$255$	5.81908	+	15.9878i	0.364405	+	1.00119i
$256$	2.19800	+	3.80704i	0.137375	+	0.237940i
$257$	5.42602	+	9.39815i	0.338466	+	0.586240i	0.984144	−	0.177369i	$-0.0567587\pi$
$257$	5.42602	+	9.39815i	0.338466	+	0.586240i	−0.645678	+	0.763609i	$0.723425\pi$
$258$	0.979055	+	2.68993i	0.0609533	+	0.167468i
$259$		0			0
$260$	−2.72462			−0.168974
$261$	−20.1800	+	16.9331i	−1.24911	+	1.04813i
$262$	−15.3090			−0.945795
$263$	−13.0437	+	22.5924i	−0.804309	+	1.39310i	0.112448	+	0.993658i	$0.464131\pi$
$263$	−13.0437	+	22.5924i	−0.804309	+	1.39310i	−0.916757	+	0.399446i	$0.869202\pi$
$264$	−1.53343	+	1.82747i	−0.0943763	+	0.112473i
$265$	−0.907604	−	1.57202i	−0.0557537	−	0.0965682i
$266$		0			0
$267$	−13.8400	−	2.44037i	−0.846996	−	0.149348i
$268$	−0.890530	+	1.54244i	−0.0543978	+	0.0942197i
$269$	7.63310			0.465399			0.232699	−	0.972549i	$-0.425244\pi$
$269$	7.63310			0.465399			0.232699	+	0.972549i	$0.425244\pi$
$270$	15.3516	+	8.86327i	0.934271	+	0.539401i
$271$	−3.40373			−0.206762			−0.103381	−	0.994642i	$-0.532966\pi$
$271$	−3.40373			−0.206762			−0.103381	+	0.994642i	$0.532966\pi$
$272$	−6.97565	+	12.0822i	−0.422961	+	0.732590i
$273$		0			0
$274$	3.85638	+	6.67945i	0.232973	+	0.403520i
$275$	−0.330222	−	0.571962i	−0.0199131	−	0.0344906i
$276$	0.0218219	−	0.0260063i	0.00131352	−	0.00156540i
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	−0.767185	−	0.641426i	$-0.778343\pi$
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	0.939084	+	0.343689i	$0.111676\pi$
$278$	1.24485			0.0746612
$279$	−4.00088	−	22.6901i	−0.239526	−	1.35842i
$280$		0			0
$281$	−14.1887	+	24.5755i	−0.846425	+	1.46605i	0.0379535	+	0.999280i	$0.487916\pi$
$281$	−14.1887	+	24.5755i	−0.846425	+	1.46605i	−0.884378	+	0.466771i	$0.845417\pi$
$282$	4.25624	+	11.6939i	0.253456	+	0.696364i
$283$	2.28564	+	3.95885i	0.135867	+	0.235329i	0.925929	−	0.377699i	$-0.123285\pi$
$283$	2.28564	+	3.95885i	0.135867	+	0.235329i	−0.790061	+	0.613028i	$0.789951\pi$
$284$	1.22281	+	2.11797i	0.0725605	+	0.125678i
$285$	−3.27719	−	9.00400i	−0.194124	−	0.533351i
$286$	1.83544	−	3.17907i	0.108532	−	0.187982i
$287$		0			0
$288$	−0.542766	−	3.07818i	−0.0319828	−	0.181384i
$289$	−1.95037			−0.114728
$290$	14.9782	−	25.9430i	0.879549	−	1.52342i
$291$	15.1459	−	18.0502i	0.887868	−	1.05812i
$292$	0.948778	+	1.64333i	0.0555230	+	0.0961687i
$293$	2.16385	+	3.74789i	0.126413	+	0.218954i	0.922285	−	0.386512i	$-0.126320\pi$
$293$	2.16385	+	3.74789i	0.126413	+	0.218954i	−0.795871	+	0.605466i	$0.792987\pi$
$294$		0			0
$295$	−0.932419	+	1.61500i	−0.0542875	+	0.0940287i
$296$	22.6067			1.31399
$297$	2.10560	−	1.21567i	0.122179	−	0.0705403i
$298$	11.7547			0.680929
$299$	−0.308811	+	0.534876i	−0.0178590	+	0.0309327i
$300$	0.444907	+	0.0784491i	0.0256867	+	0.00452926i
$301$		0			0
$302$	−12.4133	−	21.5004i	−0.714304	−	1.23721i
$303$	10.6591	−	12.7030i	0.612349	−	0.729769i
$304$	3.92855	−	6.80445i	0.225318	−	0.390262i
$305$	2.42602			0.138914
$306$	12.0116	−	10.0789i	0.686658	−	0.576175i
$307$	−12.3773			−0.706411			−0.353206	−	0.935546i	$-0.614908\pi$
$307$	−12.3773			−0.706411			−0.353206	+	0.935546i	$0.614908\pi$
$308$		0			0
$309$	−1.80200	−	4.95096i	−0.102512	−	0.281651i
$310$	13.1001	+	22.6901i	0.744038	+	1.28871i
$311$	−10.9927	−	19.0400i	−0.623340	−	1.07966i	−0.988859	−	0.148853i	$-0.952442\pi$
$311$	−10.9927	−	19.0400i	−0.623340	−	1.07966i	0.365519	−	0.930804i	$-0.380892\pi$
$312$	10.1538	+	27.8973i	0.574846	+	1.57938i
$313$	−6.94491	+	12.0289i	−0.392549	+	0.679915i	−0.992785	−	0.119908i	$-0.961740\pi$
$313$	−6.94491	+	12.0289i	−0.392549	+	0.679915i	0.600236	+	0.799823i	$0.295073\pi$
$314$	−6.63404			−0.374380
$315$		0			0
$316$	2.33544			0.131379
$317$	3.09105	−	5.35386i	0.173611	−	0.300703i	−0.766069	−	0.642759i	$-0.777790\pi$
$317$	3.09105	−	5.35386i	0.173611	−	0.300703i	0.939680	+	0.342056i	$0.111123\pi$
$318$	−1.07532	+	1.28152i	−0.0603011	+	0.0718640i
$319$	−2.05438	−	3.55829i	−0.115023	−	0.199226i
$320$	10.8833	+	18.8504i	0.608392	+	1.05377i
$321$	11.1172	+	1.96026i	0.620502	+	0.109411i
$322$		0			0
$323$	−8.47565			−0.471598
$324$	−0.288800	+	1.63787i	−0.0160444	+	0.0909926i
$325$	−8.21894			−0.455905
$326$	−5.14543	+	8.91215i	−0.284979	+	0.493598i
$327$	−18.1459	−	3.19961i	−1.00347	−	0.176939i
$328$	3.27719	+	5.67626i	0.180952	+	0.313419i
$329$		0			0
$330$	−1.77719	+	2.11797i	−0.0978310	+	0.116590i
$331$	−5.36571	+	9.29369i	−0.294926	+	0.510827i	−0.974968	−	0.222346i	$-0.928628\pi$
$331$	−5.36571	+	9.29369i	−0.294926	+	0.510827i	0.680041	+	0.733174i	$0.261962\pi$
$332$	−0.504748			−0.0277016
$333$	−21.6506	−	7.88019i	−1.18645	−	0.431832i
$334$	7.61949			0.416920
$335$	−12.2023	+	21.1351i	−0.666685	+	1.15473i
$336$		0			0
$337$	9.29726	+	16.1033i	0.506454	+	0.877204i	0.999972	+	0.00746831i	$0.00237726\pi$
$337$	9.29726	+	16.1033i	0.506454	+	0.877204i	−0.493518	+	0.869735i	$0.664289\pi$
$338$	−14.0838	−	24.3938i	−0.766057	−	1.32685i
$339$	3.06687	+	8.42615i	0.166569	+	0.457645i
$340$	0.907604	−	1.57202i	0.0492217	−	0.0852545i
$341$	3.59358			0.194603
$342$	−6.76470	+	5.67626i	−0.365793	+	0.306937i
$343$		0			0
$344$	1.80541	−	3.12706i	0.0973410	−	0.168600i
$345$	0.299011	−	0.356347i	0.0160982	−	0.0191851i
$346$	14.1932	+	24.5834i	0.763034	+	1.32161i
$347$	10.2062	+	17.6777i	0.547898	+	0.948987i	0.998418	+	0.0562207i	$0.0179050\pi$
$347$	10.2062	+	17.6777i	0.547898	+	0.948987i	−0.450521	+	0.892766i	$0.648762\pi$
$348$	2.76786	+	0.488048i	0.148373	+	0.0261621i
$349$	−1.78106	+	3.08489i	−0.0953379	+	0.165130i	−0.909750	−	0.415157i	$-0.863726\pi$
$349$	−1.78106	+	3.08489i	−0.0953379	+	0.165130i	0.814412	+	0.580288i	$0.197060\pi$
$350$		0			0
$351$		−	30.2569i		−	1.61500i
$352$	0.487511			0.0259844
$353$	5.01114	−	8.67956i	0.266716	−	0.461966i	−0.701296	−	0.712871i	$-0.747395\pi$
$353$	5.01114	−	8.67956i	0.266716	−	0.461966i	0.968012	+	0.250904i	$0.0807280\pi$
$354$	1.69253	+	0.298439i	0.0899571	+	0.0158619i
$355$	16.7554	+	29.0211i	0.889283	+	1.54028i
$356$	0.749686	+	1.29849i	0.0397333	+	0.0688200i
$357$		0			0
$358$	3.44949	−	5.97470i	0.182311	−	0.315773i
$359$	9.48070			0.500372			0.250186	−	0.968198i	$-0.419508\pi$
$359$	9.48070			0.500372			0.250186	+	0.968198i	$0.419508\pi$
$360$	−3.88279	−	22.0204i	−0.204641	−	1.16058i
$361$	−14.2267			−0.748773
$362$	−0.215537	+	0.373321i	−0.0113284	+	0.0196213i
$363$	−6.38666	−	17.5472i	−0.335213	−	0.920989i
$364$		0			0
$365$	13.0005	+	22.5175i	0.680476	+	1.17862i
$366$	−0.764700	−	2.10100i	−0.0399715	−	0.109821i
$367$	8.06670	−	13.9719i	0.421079	−	0.729329i	−0.574967	−	0.818177i	$-0.694985\pi$
$367$	8.06670	−	13.9719i	0.421079	−	0.729329i	0.996045	+	0.0888474i	$0.0283183\pi$
$368$	0.381445			0.0198842
$369$	−1.15998	−	6.57856i	−0.0603860	−	0.342466i
$370$	26.2003			1.36209
$371$		0			0
$372$	−1.58007	+	1.88305i	−0.0819228	+	0.0976318i
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	0.624841	−	0.780752i	$-0.285164\pi$
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	−0.988572	+	0.150752i	$0.951831\pi$
$374$	1.22281	+	2.11797i	0.0632301	+	0.109518i
$375$	−15.4991	−	2.73291i	−0.800371	−	0.141127i
$376$	7.84864	−	13.5942i	0.404763	−	0.701070i
$377$	−51.1317			−2.63341
$378$		0			0
$379$	16.0574			0.824812			0.412406	−	0.911000i	$-0.364689\pi$
$379$	16.0574			0.824812			0.412406	+	0.911000i	$0.364689\pi$
$380$	−0.511144	+	0.885328i	−0.0262212	+	0.0454164i
$381$	15.1505	+	2.67144i	0.776183	+	0.136862i
$382$	10.4868	+	18.1637i	0.536551	+	0.929334i
$383$	−16.0103	−	27.7306i	−0.818086	−	1.41697i	−0.907090	−	0.420936i	$-0.861702\pi$
$383$	−16.0103	−	27.7306i	−0.818086	−	1.41697i	0.0890039	−	0.996031i	$-0.471632\pi$
$384$	10.5744	−	12.6021i	0.539625	−	0.643100i
$385$		0			0
$386$	8.14022			0.414326
$387$	−2.81908	+	2.36549i	−0.143302	+	0.120244i
$388$	−2.51392			−0.127625
$389$	15.0214	−	26.0178i	0.761616	−	1.31916i	−0.180402	−	0.983593i	$-0.557740\pi$
$389$	15.0214	−	26.0178i	0.761616	−	1.31916i	0.942017	−	0.335564i	$-0.108927\pi$
$390$	11.7679	+	32.3319i	0.595889	+	1.63719i
$391$	−0.205737	−	0.356347i	−0.0104046	−	0.0180212i
$392$		0			0
$393$	−6.73127	−	18.4940i	−0.339548	−	0.932899i
$394$	−16.9991	+	29.4433i	−0.856403	+	1.48333i
$395$	32.0009			1.61014
$396$	−0.243756	−	0.0887198i	−0.0122492	−	0.00445834i
$397$	12.3200			0.618321			0.309160	−	0.951010i	$-0.399952\pi$
$397$	12.3200			0.618321			0.309160	+	0.951010i	$0.399952\pi$
$398$	2.04916	−	3.54925i	0.102715	−	0.177908i
$399$		0			0
$400$	2.53802	+	4.39598i	0.126901	+	0.219799i
$401$	−10.4880	−	18.1657i	−0.523745	−	0.907152i	−0.999618	−	0.0276385i	$-0.991201\pi$
$401$	−10.4880	−	18.1657i	−0.523745	−	0.907152i	0.475873	−	0.879514i	$-0.342132\pi$
$402$	22.1498	+	3.90560i	1.10473	+	0.194794i
$403$	22.3603	−	38.7291i	1.11384	−	1.92923i
$404$	−1.76920			−0.0880210
$405$	−3.95723	+	22.4426i	−0.196637	+	1.11518i
$406$		0			0
$407$	1.79679	−	3.11213i	0.0890635	−	0.154263i
$408$	−19.4782	−	3.43453i	−0.964314	−	0.170034i
$409$	12.8307	+	22.2234i	0.634437	+	1.09888i	0.986634	+	0.162951i	$0.0521012\pi$
$409$	12.8307	+	22.2234i	0.634437	+	1.09888i	−0.352197	+	0.935926i	$0.614565\pi$
$410$	3.79813	+	6.57856i	0.187576	+	0.324892i
$411$	−6.37346	+	7.59559i	−0.314379	+	0.374663i
$412$	−0.281059	+	0.486809i	−0.0138468	+	0.0239833i
$413$		0			0
$414$	−0.402856	−	0.146628i	−0.0197993	−	0.00720635i
$415$	−6.91622			−0.339504
$416$	3.03343	−	5.25406i	0.148726	−	0.257601i
$417$	0.547352	+	1.50384i	0.0268039	+	0.0736432i
$418$	−0.688663	−	1.19280i	−0.0336836	−	0.0583417i
$419$	−0.739885	−	1.28152i	−0.0361458	−	0.0626063i	0.847387	−	0.530976i	$-0.178175\pi$
$419$	−0.739885	−	1.28152i	−0.0361458	−	0.0626063i	−0.883532	+	0.468370i	$0.844841\pi$
$420$		0			0
$421$	−6.55350	+	11.3510i	−0.319398	+	0.553214i	−0.980363	−	0.197203i	$-0.936814\pi$
$421$	−6.55350	+	11.3510i	−0.319398	+	0.553214i	0.660965	+	0.750417i	$0.270147\pi$
$422$	−7.34730			−0.357661
$423$	−12.2554	+	10.2835i	−0.595876	+	0.500000i
$424$	2.11019			0.102480
$425$	2.73783	−	4.74205i	0.132804	−	0.230023i
$426$	19.8516	−	23.6583i	0.961815	−	1.14625i
$427$		0			0
$428$	−0.602196	−	1.04303i	−0.0291083	−	0.0504170i
$429$	4.64749	+	0.819478i	0.224383	+	0.0395648i
$430$	2.09240	−	3.62414i	0.100904	−	0.174771i
$431$	17.7270			0.853879			0.426939	−	0.904280i	$-0.359592\pi$
$431$	17.7270			0.853879			0.426939	+	0.904280i	$0.359592\pi$
$432$	−16.1832	+	9.34337i	−0.778615	+	0.449533i
$433$	5.83843			0.280577			0.140289	−	0.990111i	$-0.455197\pi$
$433$	5.83843			0.280577			0.140289	+	0.990111i	$0.455197\pi$
$434$		0			0
$435$	37.9261	+	6.68739i	1.81842	+	0.320636i
$436$	0.982926	+	1.70248i	0.0470736	+	0.0815339i
$437$	0.115867	+	0.200688i	0.00554267	+	0.00960019i
$438$	15.4029	−	18.3564i	0.735977	−	0.877103i
$439$	14.9277	−	25.8555i	0.712459	−	1.23401i	−0.251473	−	0.967864i	$-0.580915\pi$
$439$	14.9277	−	25.8555i	0.712459	−	1.23401i	0.963931	−	0.266151i	$-0.0857518\pi$
$440$	3.48751			0.166261
$441$		0			0
$442$	30.4347			1.44763
$443$	−5.33275	+	9.23659i	−0.253367	+	0.438844i	−0.964451	−	0.264263i	$-0.914871\pi$
$443$	−5.33275	+	9.23659i	−0.253367	+	0.438844i	0.711084	+	0.703107i	$0.248205\pi$
$444$	0.840738	+	2.30991i	0.0398996	+	0.109623i
$445$	10.2724	+	17.7924i	0.486960	+	0.843440i
$446$	9.56077	+	16.5597i	0.452716	+	0.784127i
$447$	5.16843	+	14.2002i	0.244459	+	0.671644i
$448$		0			0
$449$	3.55438			0.167741			0.0838707	−	0.996477i	$-0.473272\pi$
$449$	3.55438			0.167741			0.0838707	+	0.996477i	$0.473272\pi$
$450$	−0.990667	−	5.61835i	−0.0467005	−	0.264852i
$451$	1.04189			0.0490606
$452$	0.478340	−	0.828510i	0.0224992	−	0.0389698i
$453$	20.5155	−	24.4494i	0.963901	−	1.14873i
$454$	−1.94949	−	3.37662i	−0.0914942	−	0.158473i
$455$		0			0
$456$	10.9697	+	1.93426i	0.513704	+	0.0905799i
$457$	−2.51161	+	4.35024i	−0.117488	+	0.203496i	−0.918772	−	0.394789i	$-0.870818\pi$
$457$	−2.51161	+	4.35024i	−0.117488	+	0.203496i	0.801283	+	0.598285i	$0.204151\pi$
$458$	−12.3514			−0.577144
$459$	17.4572	+	10.0789i	0.814834	+	0.470445i
$460$	−0.0496299			−0.00231400
$461$	9.23055	−	15.9878i	0.429910	−	0.744625i	−0.566955	−	0.823749i	$-0.691879\pi$
$461$	9.23055	−	15.9878i	0.429910	−	0.744625i	0.996865	+	0.0791233i	$0.0252121\pi$
$462$		0			0
$463$	7.11721	+	12.3274i	0.330765	+	0.572902i	0.982662	−	0.185406i	$-0.0593600\pi$
$463$	7.11721	+	12.3274i	0.330765	+	0.572902i	−0.651897	+	0.758307i	$0.726027\pi$
$464$	15.7895	+	27.3482i	0.733010	+	1.26961i
$465$	−21.6506	+	25.8022i	−1.00402	+	1.19655i
$466$	−8.94016	+	15.4848i	−0.414145	+	0.717320i
$467$	3.36865			0.155883			0.0779413	−	0.996958i	$-0.475165\pi$
$467$	3.36865			0.155883			0.0779413	+	0.996958i	$0.475165\pi$
$468$	−2.47288	+	2.07499i	−0.114309	+	0.0959165i
$469$		0			0
$470$	9.09627	−	15.7552i	0.419579	−	0.726733i
$471$	−2.91694	−	8.01422i	−0.134405	−	0.369276i
$472$	−1.08394	−	1.87744i	−0.0498924	−	0.0864162i
$473$	−0.286989	−	0.497079i	−0.0131958	−	0.0228557i
$474$	−10.0869	−	27.7136i	−0.463308	−	1.27293i
$475$	−1.54189	+	2.67063i	−0.0707467	+	0.122537i
$476$		0			0
$477$	−2.02094	−	0.735564i	−0.0925327	−	0.0336791i
$478$	12.8494			0.587716
$479$	−18.3833	+	31.8407i	−0.839952	+	1.45484i	0.0499812	+	0.998750i	$0.484084\pi$
$479$	−18.3833	+	31.8407i	−0.839952	+	1.45484i	−0.889934	+	0.456090i	$0.849249\pi$
$480$	−2.93717	+	3.50038i	−0.134063	+	0.159770i
$481$	−22.3603	−	38.7291i	−1.01954	−	1.76589i
$482$	−6.03462	−	10.4523i	−0.274869	−	0.476087i
$483$		0			0
$484$	−0.996130	+	1.72535i	−0.0452786	+	0.0784249i
$485$	−34.4466			−1.56414
$486$	20.6832	−	3.64701i	0.938209	−	0.165432i
$487$	−37.4175			−1.69555			−0.847773	−	0.530358i	$-0.822057\pi$
$487$	−37.4175			−1.69555			−0.847773	+	0.530358i	$0.822057\pi$
$488$	−1.41013	+	2.44242i	−0.0638336	+	0.110563i
$489$	−13.0287	−	2.29731i	−0.589178	−	0.103888i
$490$		0			0
$491$	13.3353	+	23.0974i	0.601813	+	1.04237i	0.992547	+	0.121866i	$0.0388879\pi$
$491$	13.3353	+	23.0974i	0.601813	+	1.04237i	−0.390734	+	0.920504i	$0.627779\pi$
$492$	−0.458111	+	0.545955i	−0.0206532	+	0.0246136i
$493$	17.0326	−	29.5013i	0.767108	−	1.32867i
$494$	−17.1402			−0.771175
$495$	−3.34002	−	1.21567i	−0.150123	−	0.0546402i
$496$	−27.6195			−1.24015
$497$		0			0
$498$	2.18004	+	5.98962i	0.0976901	+	0.268401i
$499$	−16.8726	−	29.2242i	−0.755320	−	1.30825i	−0.945215	−	0.326449i	$-0.894148\pi$
$499$	−16.8726	−	29.2242i	−0.755320	−	1.30825i	0.189895	−	0.981804i	$-0.439185\pi$
$500$	0.839556	+	1.45415i	0.0375461	+	0.0650317i
$501$	3.35023	+	9.20469i	0.149677	+	0.411235i
$502$	−16.8400	+	29.1678i	−0.751607	+	1.30182i
$503$	32.0401			1.42860			0.714299	−	0.699840i	$-0.246745\pi$
$503$	32.0401			1.42860			0.714299	+	0.699840i	$0.246745\pi$
$504$		0			0
$505$	−24.2422			−1.07876
$506$	0.0334331	−	0.0579078i	0.00148628	−	0.00257431i
$507$	23.2763	−	27.7396i	1.03374	−	1.23196i
$508$	−0.820670	−	1.42144i	−0.0364114	−	0.0630663i
$509$	−3.96926	−	6.87495i	−0.175934	−	0.304727i	0.764550	−	0.644564i	$-0.222961\pi$
$509$	−3.96926	−	6.87495i	−0.175934	−	0.304727i	−0.940484	+	0.339838i	$0.889628\pi$
$510$	−22.5744	−	3.98048i	−0.999613	−	0.176259i
$511$		0			0
$512$	−24.9186			−1.10126
$513$	−9.83157	−	5.67626i	−0.434074	−	0.250613i
$514$	−14.6209			−0.644901
$515$	−3.85117	+	6.67042i	−0.169703	+	0.293934i
$516$	0.386659	+	0.0681784i	0.0170217	+	0.00300139i
$517$	−1.24763	−	2.16095i	−0.0548705	−	0.0950386i
$518$		0			0
$519$	−23.4572	+	27.9552i	−1.02966	+	1.22710i
$520$	21.7003	−	37.5860i	0.951620	−	1.64825i
$521$	14.6750			0.642923			0.321462	−	0.946923i	$-0.395826\pi$
$521$	14.6750			0.642923			0.321462	+	0.946923i	$0.395826\pi$
$522$	−6.16313	−	34.9529i	−0.269753	−	1.52985i
$523$	−28.3432			−1.23936			−0.619680	−	0.784854i	$-0.712738\pi$
$523$	−28.3432			−1.23936			−0.619680	+	0.784854i	$0.712738\pi$
$524$	−1.04988	+	1.81844i	−0.0458641	+	0.0794390i
$525$		0			0
$526$	−17.5737	−	30.4386i	−0.766251	−	1.32719i
$527$	14.8969	+	25.8022i	0.648920	+	1.12396i
$528$	−0.996845	−	2.73881i	−0.0433821	−	0.119191i
$529$	11.4944	−	19.9088i	0.499755	−	0.865602i
$530$	2.44562			0.106231
$531$	0.383666	+	2.17588i	0.0166497	+	0.0944251i
$532$		0			0
$533$	6.48293	−	11.2288i	0.280807	−	0.486371i
$534$	12.1707	−	14.5045i	0.526678	−	0.627671i
$535$	−8.25150	−	14.2920i	−0.356743	−	0.617898i
$536$	−14.1853	−	24.5696i	−0.612710	−	1.06124i
$537$	8.73442	+	1.54011i	0.376918	+	0.0664608i
$538$	−5.14203	+	8.90625i	−0.221688	+	0.383976i
$539$		0			0
$540$	2.10560	−	1.21567i	0.0906106	−	0.0523141i
$541$	11.2858			0.485215			0.242607	−	0.970125i	$-0.421997\pi$
$541$	11.2858			0.485215			0.242607	+	0.970125i	$0.421997\pi$
$542$	2.29292	−	3.97145i	0.0984893	−	0.170588i
$543$	−0.545759	−	0.0962321i	−0.0234208	−	0.00412972i
$544$	2.02094	+	3.50038i	0.0866473	+	0.150077i
$545$	13.4684	+	23.3279i	0.576922	+	0.999258i
$546$		0			0
$547$	14.6202	−	25.3229i	0.625115	−	1.08273i	−0.363404	−	0.931632i	$-0.618385\pi$
$547$	14.6202	−	25.3229i	0.625115	−	1.08273i	0.988519	−	0.151099i	$-0.0482812\pi$
$548$	1.05787			0.0451899
$549$	2.20187	−	1.84759i	0.0939734	−	0.0788530i
$550$	0.889814			0.0379418
$551$	−9.59240	+	16.6145i	−0.408650	+	0.707802i
$552$	0.184955	+	0.508159i	0.00787219	+	0.0216287i
$553$		0			0
$554$	3.85457	+	6.67631i	0.163765	+	0.283649i
$555$	11.5201	+	31.6511i	0.489000	+	1.34352i
$556$	0.0853707	−	0.147866i	0.00362052	−	0.00627093i
$557$	−0.775682			−0.0328667			−0.0164334	−	0.999865i	$-0.505231\pi$
$557$	−0.775682			−0.0328667			−0.0164334	+	0.999865i	$0.505231\pi$
$558$	29.1698	+	10.6170i	1.23486	+	0.449451i
$559$	−7.14290			−0.302113
$560$		0			0
$561$	−2.02094	+	2.40847i	−0.0853243	+	0.101686i
$562$	−19.1163	−	33.1105i	−0.806374	−	1.39668i
$563$	12.4761	+	21.6093i	0.525806	+	0.910722i	0.999548	+	0.0300588i	$0.00956944\pi$
$563$	12.4761	+	21.6093i	0.525806	+	0.910722i	−0.473742	+	0.880663i	$0.657097\pi$
$564$	1.68092	+	0.296392i	0.0707796	+	0.0124804i
$565$	6.55438	−	11.3525i	0.275745	−	0.477604i
$566$	−6.15888			−0.258877
$567$		0			0
$568$	−38.9564			−1.63457
$569$	12.4017	−	21.4803i	0.519905	−	0.900502i	−0.479827	−	0.877363i	$-0.659301\pi$
$569$	12.4017	−	21.4803i	0.519905	−	0.900502i	0.999732	−	0.0231391i	$-0.00736608\pi$
$570$	12.7135	+	2.24173i	0.532509	+	0.0938957i
$571$	−4.39827	−	7.61803i	−0.184062	−	0.318805i	0.759198	−	0.650860i	$-0.225591\pi$
$571$	−4.39827	−	7.61803i	−0.184062	−	0.318805i	−0.943260	+	0.332055i	$0.892258\pi$
$572$	−0.251745	−	0.436035i	−0.0105260	−	0.0182315i
$573$	−17.3316	+	20.6550i	−0.724037	+	0.862873i
$574$		0			0
$575$	−0.149711			−0.00624336
$576$	24.2335	+	8.82029i	1.00973	+	0.367512i
$577$	12.8743			0.535965			0.267983	−	0.963424i	$-0.413643\pi$
$577$	12.8743			0.535965			0.267983	+	0.963424i	$0.413643\pi$
$578$	1.31386	−	2.27568i	0.0546495	−	0.0946557i
$579$	3.57919	+	9.83375i	0.148746	+	0.408677i
$580$	−2.05438	−	3.55829i	−0.0853034	−	0.147750i
$581$		0			0
$582$	10.8578	+	29.8316i	0.450071	+	1.23656i
$583$	0.167718	−	0.290497i	0.00694619	−	0.0120311i
$584$	−30.2262			−1.25077
$585$	−33.8842	+	28.4322i	−1.40094	+	1.17553i
$586$	−5.83069			−0.240864
$587$	22.4315	−	38.8526i	0.925849	−	1.60362i	0.135658	−	0.990756i	$-0.456685\pi$
$587$	22.4315	−	38.8526i	0.925849	−	1.60362i	0.790190	−	0.612861i	$-0.209982\pi$
$588$		0			0
$589$	−8.38965	−	14.5313i	−0.345690	−	0.598752i
$590$	−1.25624	−	2.17588i	−0.0517188	−	0.0895795i
$591$	−43.0433	−	7.58969i	−1.77056	−	0.312198i
$592$	−13.8097	+	23.9192i	−0.567577	+	0.983072i
$593$	−3.76053			−0.154426			−0.0772131	−	0.997015i	$-0.524602\pi$
$593$	−3.76053			−0.154426			−0.0772131	+	0.997015i	$0.524602\pi$
$594$			3.27573i			0.134405i
$595$		0			0
$596$	0.806123	−	1.39625i	0.0330201	−	0.0571924i
$597$	5.18866	+	0.914901i	0.212358	+	0.0374444i
$598$	−0.416060	−	0.720637i	−0.0170139	−	0.0294690i
$599$	1.84524	+	3.19604i	0.0753943	+	0.130587i	0.901258	−	0.433283i	$-0.142645\pi$
$599$	1.84524	+	3.19604i	0.0753943	+	0.130587i	−0.825863	+	0.563870i	$0.809312\pi$
$600$	−4.62567	+	5.51266i	−0.188842	+	0.225053i
$601$	−10.9285	+	18.9288i	−0.445785	+	0.772122i	−0.998107	−	0.0615091i	$-0.980409\pi$
$601$	−10.9285	+	18.9288i	−0.445785	+	0.772122i	0.552322	+	0.833631i	$0.313742\pi$
$602$		0			0
$603$	5.02094	+	28.4752i	0.204469	+	1.15960i
$604$	−3.40516			−0.138554
$605$	−13.6493	+	23.6413i	−0.554923	+	0.961155i
$606$	7.64131	+	20.9943i	0.310407	+	0.852836i
$607$	12.1973	+	21.1263i	0.495072	+	0.857490i	0.999984	−	0.00568063i	$-0.00180821\pi$
$607$	12.1973	+	21.1263i	0.495072	+	0.857490i	−0.504911	+	0.863171i	$0.668475\pi$
$608$	−1.13816	−	1.97134i	−0.0461583	−	0.0799485i
$609$		0			0
$610$	−1.63429	+	2.83067i	−0.0661703	+	0.114610i
$611$	−31.0523			−1.25624
$612$	−0.373455	−	2.11797i	−0.0150960	−	0.0856139i
$613$	42.0215			1.69723			0.848616	−	0.529010i	$-0.177437\pi$
$613$	42.0215			1.69723			0.848616	+	0.529010i	$0.177437\pi$
$614$	8.33796	−	14.4418i	0.336493	−	0.582823i
$615$	−6.27719	+	7.48086i	−0.253121	+	0.301657i
$616$		0			0
$617$	−23.2049	−	40.1920i	−0.934192	−	1.61807i	−0.776068	−	0.630650i	$-0.782788\pi$
$617$	−23.2049	−	40.1920i	−0.934192	−	1.61807i	−0.158125	−	0.987419i	$-0.550545\pi$
$618$	6.99067	+	1.23264i	0.281206	+	0.0495842i
$619$	−13.6047	+	23.5641i	−0.546820	+	0.947120i	0.451670	+	0.892185i	$0.350828\pi$
$619$	−13.6047	+	23.5641i	−0.546820	+	0.947120i	−0.998490	+	0.0549349i	$0.982505\pi$
$620$	3.59358			0.144322
$621$		−	0.551139i		−	0.0221165i
$622$	29.6209			1.18769
$623$		0			0
$624$	−35.7196	−	6.29833i	−1.42993	−	0.252135i
$625$	15.0326	+	26.0372i	0.601302	+	1.04149i
$626$	−9.35685	−	16.2065i	−0.373975	−	0.647743i
$627$	1.13816	−	1.35640i	0.0454536	−	0.0541694i
$628$	−0.454956	+	0.788006i	−0.0181547	+	0.0314449i
$629$	29.7939			1.18796
$630$		0			0
$631$	−29.6023			−1.17845			−0.589224	−	0.807970i	$-0.700566\pi$
$631$	−29.6023			−1.17845			−0.589224	+	0.807970i	$0.700566\pi$
$632$	−18.6006	+	32.2172i	−0.739892	+	1.28153i
$633$	−3.23055	−	8.87587i	−0.128403	−	0.352784i
$634$	4.16456	+	7.21324i	0.165396	+	0.286474i
$635$	−11.2451	−	19.4771i	−0.446248	−	0.772925i
$636$	0.0784773	+	0.215615i	0.00311183	+	0.00854968i
$637$		0			0
$638$	5.53571			0.219161
$639$	37.3089	+	13.5793i	1.47592	+	0.537189i
$640$	−24.0496			−0.950645
$641$	0.139500	−	0.241621i	0.00550991	−	0.00954345i	−0.863257	−	0.504764i	$-0.831579\pi$
$641$	0.139500	−	0.241621i	0.00550991	−	0.00954345i	0.868767	+	0.495221i	$0.164913\pi$
$642$	−9.77631	+	11.6510i	−0.385840	+	0.459826i
$643$	−9.12196	−	15.7997i	−0.359735	−	0.623079i	0.628181	−	0.778067i	$-0.283800\pi$
$643$	−9.12196	−	15.7997i	−0.359735	−	0.623079i	−0.987916	+	0.154988i	$0.950466\pi$
$644$		0			0
$645$	5.29813	+	0.934204i	0.208614	+	0.0367842i
$646$	5.70961	−	9.88933i	0.224642	−	0.389090i
$647$	−22.4570			−0.882875			−0.441438	−	0.897292i	$-0.645531\pi$
$647$	−22.4570			−0.882875			−0.441438	+	0.897292i	$0.645531\pi$
$648$	−20.2941	−	17.0288i	−0.797228	−	0.668953i
$649$	−0.344608			−0.0135270
$650$	5.53667	−	9.58980i	0.217166	−	0.376143i
$651$		0			0
$652$	0.705737	+	1.22237i	0.0276388	+	0.0478718i
$653$	25.2656	+	43.7614i	0.988721	+	1.71251i	0.624066	+	0.781372i	$0.285480\pi$
$653$	25.2656	+	43.7614i	0.988721	+	1.71251i	0.364655	+	0.931143i	$0.381187\pi$
$654$	15.9572	−	19.0171i	0.623977	−	0.743627i
$655$	−14.3858	+	24.9169i	−0.562099	+	0.973584i
$656$	−8.00774			−0.312650
$657$	28.9479	+	10.5362i	1.12937	+	0.411055i
$658$		0			0
$659$	1.33631	−	2.31456i	0.0520554	−	0.0901626i	−0.838824	−	0.544403i	$-0.816756\pi$
$659$	1.33631	−	2.31456i	0.0520554	−	0.0901626i	0.890879	+	0.454241i	$0.150089\pi$
$660$	0.129700	+	0.356347i	0.00504855	+	0.0138708i
$661$	−17.3050	−	29.9731i	−0.673086	−	1.16582i	−0.977024	−	0.213128i	$-0.931635\pi$
$661$	−17.3050	−	29.9731i	−0.673086	−	1.16582i	0.303938	−	0.952692i	$-0.401698\pi$
$662$	−7.22921	−	12.5214i	−0.280971	−	0.486656i
$663$	13.3819	+	36.7665i	0.519710	+	1.42789i
$664$	4.02007	−	6.96296i	0.156009	−	0.270215i
$665$		0			0
$666$	23.7795	−	19.9533i	0.921436	−	0.773176i
$667$	−0.931379			−0.0360631
$668$	0.522537	−	0.905061i	0.0202176	−	0.0350179i
$669$	−15.8011	+	18.8310i	−0.610907	+	0.728050i
$670$	−16.4402	−	28.4752i	−0.635139	−	1.10009i
$671$	0.224155	+	0.388249i	0.00865342	+	0.0149882i
$672$		0			0
$673$	−8.25624	+	14.3002i	−0.318255	+	0.551234i	−0.980124	−	0.198386i	$-0.936430\pi$
$673$	−8.25624	+	14.3002i	−0.318255	+	0.551234i	0.661869	+	0.749619i	$0.269763\pi$
$674$	−25.0523			−0.964979
$675$	6.35163	−	3.66712i	0.244474	−	0.141147i
$676$	−3.86341			−0.148593
$677$	−21.8790	+	37.8955i	−0.840877	+	1.45644i	0.0482766	+	0.998834i	$0.484627\pi$
$677$	−21.8790	+	37.8955i	−0.840877	+	1.45644i	−0.889154	+	0.457608i	$0.848706\pi$
$678$	−11.8976	−	2.09786i	−0.456923	−	0.0805678i
$679$		0			0
$680$	14.4572	+	25.0407i	0.554410	+	0.960266i
$681$	3.22193	−	3.83975i	0.123465	−	0.147140i
$682$	−2.42081	+	4.19296i	−0.0926975	+	0.160557i
$683$	28.2412			1.08062			0.540310	−	0.841466i	$-0.318307\pi$
$683$	28.2412			1.08062			0.540310	+	0.841466i	$0.318307\pi$
$684$	0.210323	+	1.19280i	0.00804189	+	0.0456078i
$685$	14.4953			0.553835
$686$		0			0
$687$	−5.43083	−	14.9211i	−0.207199	−	0.569274i
$688$	2.20574	+	3.82045i	0.0840929	+	0.145653i
$689$	−2.08718	−	3.61510i	−0.0795153	−	0.137725i
$690$	0.214355	+	0.588936i	0.00816036	+	0.0224204i
$691$	−14.5326	+	25.1711i	−0.552844	+	0.957555i	0.445223	+	0.895420i	$0.353124\pi$
$691$	−14.5326	+	25.1711i	−0.552844	+	0.957555i	−0.998068	+	0.0621351i	$0.980209\pi$
$692$	3.89344			0.148006
$693$		0			0
$694$	−27.5016			−1.04395
$695$	1.16978	−	2.02611i	0.0443722	−	0.0768549i
$696$	−28.7772	+	34.2953i	−1.09080	+	1.29996i
$697$	4.31908	+	7.48086i	0.163597	+	0.283358i
$698$	−2.39961	−	4.15625i	−0.0908268	−	0.157317i
$699$	−22.6373	−	3.99156i	−0.856221	−	0.150975i
$700$		0			0
$701$	−1.10876			−0.0418771			−0.0209386	−	0.999781i	$-0.506665\pi$
$701$	−1.10876			−0.0418771			−0.0209386	+	0.999781i	$0.506665\pi$
$702$	35.3036	+	20.3825i	1.33245	+	0.769289i
$703$	−16.7793			−0.632843
$704$	−2.01114	+	3.48340i	−0.0757979	+	0.131286i
$705$	23.0326	+	4.06126i	0.867456	+	0.152956i
$706$	6.75150	+	11.6939i	0.254096	+	0.440107i
$707$		0			0
$708$	0.151522	−	0.180576i	0.00569453	−	0.00678648i
$709$	9.23442	−	15.9945i	0.346806	−	0.600686i	−0.638874	−	0.769311i	$-0.720600\pi$
$709$	9.23442	−	15.9945i	0.346806	−	0.600686i	0.985680	+	0.168626i	$0.0539329\pi$
$710$	−45.1489			−1.69441
$711$	29.0442	−	24.3709i	1.08924	−	0.913982i
$712$	−23.8835			−0.895072
$713$	0.407299	−	0.705463i	0.0152535	−	0.0264198i
$714$		0			0
$715$	−3.44949	−	5.97470i	−0.129004	−	0.223441i
$716$	−0.473126	−	0.819478i	−0.0176815	−	0.0306253i
$717$	5.64977	+	15.5226i	0.210994	+	0.579702i
$718$	−6.38666	+	11.0620i	−0.238348	+	0.412831i
$719$	33.7769			1.25967			0.629834	−	0.776730i	$-0.283123\pi$
$719$	33.7769			1.25967			0.629834	+	0.776730i	$0.283123\pi$
$720$	25.6707	+	9.34337i	0.956691	+	0.348207i
$721$		0			0
$722$	9.58378	−	16.5996i	0.356671	−	0.617773i
$723$	9.97343	−	11.8859i	0.370916	−	0.442040i
$724$	0.0295627	+	0.0512040i	0.00109869	+	0.00190298i
$725$	−6.19712	−	10.7337i	−0.230155	−	0.398641i
$726$	24.7763	+	4.36873i	0.919535	+	0.162139i
$727$	8.40214	−	14.5529i	0.311618	−	0.539738i	−0.667095	−	0.744973i	$-0.732462\pi$
$727$	8.40214	−	14.5529i	0.311618	−	0.539738i	0.978713	+	0.205234i	$0.0657957\pi$
$728$		0			0
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	−35.0310			−1.29655
$731$	2.37939	−	4.12122i	0.0880047	−	0.152429i
$732$	−0.302004	−	0.0532514i	−0.0111624	−	0.00196823i
$733$	−6.81820	−	11.8095i	−0.251836	−	0.436193i	0.712195	−	0.701981i	$-0.247701\pi$
$733$	−6.81820	−	11.8095i	−0.251836	−	0.436193i	−0.964031	+	0.265789i	$0.914368\pi$
$734$	10.8682	+	18.8243i	0.401154	+	0.694819i
$735$		0			0
$736$	0.0552549	−	0.0957044i	0.00203672	−	0.00352771i
$737$	−4.50980			−0.166121
$738$	8.45723	+	3.07818i	0.311315	+	0.113309i
$739$	−32.0419			−1.17868			−0.589340	−	0.807885i	$-0.700612\pi$
$739$	−32.0419			−1.17868			−0.589340	+	0.807885i	$0.700612\pi$
$740$	1.79679	−	3.11213i	0.0660513	−	0.114404i
$741$	−7.53643	−	20.7062i	−0.276858	−	0.760660i
$742$		0			0
$743$	−16.8764	−	29.2309i	−0.619137	−	1.07238i	−0.989644	−	0.143547i	$-0.954149\pi$
$743$	−16.8764	−	29.2309i	−0.619137	−	1.07238i	0.370507	−	0.928830i	$-0.379184\pi$
$744$	−13.3921	−	36.7946i	−0.490979	−	1.34895i
$745$	11.0458	−	19.1318i	0.404685	−	0.700936i
$746$	18.9290			0.693040
$747$	−6.27719	+	5.26719i	−0.229670	+	0.192716i
$748$	0.335437			0.0122648
$749$		0			0
$750$	13.6297	−	16.2432i	0.497686	−	0.593119i
$751$	−13.0582	−	22.6175i	−0.476502	−	0.825326i	0.523135	−	0.852250i	$-0.324762\pi$
$751$	−13.0582	−	22.6175i	−0.476502	−	0.825326i	−0.999637	+	0.0269236i	$0.991429\pi$
$752$	9.58899	+	16.6086i	0.349675	+	0.605654i
$753$	−42.6404	−	7.51866i	−1.55390	−	0.273995i
$754$	34.4447	−	59.6600i	1.25440	−	2.17269i
$755$	−46.6587			−1.69808
$756$		0			0
$757$	35.6536			1.29585			0.647927	−	0.761703i	$-0.275636\pi$
$757$	35.6536			1.29585			0.647927	+	0.761703i	$0.275636\pi$
$758$	−10.8170	+	18.7356i	−0.392892	+	0.680509i
$759$	0.0846555	+	0.0149270i	0.00307280	+	0.000541817i
$760$	−8.14203	−	14.1024i	−0.295342	−	0.511548i
$761$	20.3824	+	35.3033i	0.738861	+	1.27974i	0.953009	+	0.302943i	$0.0979692\pi$
$761$	20.3824	+	35.3033i	0.738861	+	1.27974i	−0.214148	+	0.976801i	$0.568698\pi$
$762$	−13.3231	+	15.8779i	−0.482645	+	0.575194i
$763$		0			0
$764$	2.87670			0.104075
$765$	−5.11721	−	29.0211i	−0.185013	−	1.04926i
$766$	43.1411			1.55875
$767$	−2.14425	+	3.71395i	−0.0774243	+	0.134103i
$768$	−2.60417	−	7.15490i	−0.0939699	−	0.258180i
$769$	19.7135	+	34.1447i	0.710886	+	1.23129i	0.964525	+	0.263992i	$0.0850392\pi$
$769$	19.7135	+	34.1447i	0.710886	+	1.23129i	−0.253639	+	0.967299i	$0.581627\pi$
$770$		0			0
$771$	−6.42871	−	17.6627i	−0.231524	−	0.636108i
$772$	0.558248	−	0.966914i	0.0200918	−	0.0348000i
$773$	−24.9026			−0.895685			−0.447842	−	0.894113i	$-0.647807\pi$
$773$	−24.9026			−0.895685			−0.447842	+	0.894113i	$0.647807\pi$
$774$	−0.860967	−	4.88279i	−0.0309468	−	0.175508i
$775$	10.8402			0.389391
$776$	20.0221	−	34.6793i	0.718752	−	1.24492i
$777$		0			0
$778$	20.2383	+	35.0538i	0.725578	+	1.25674i
$779$	−2.43242	−	4.21307i	−0.0871504	−	0.150949i
$780$	4.64749	+	0.819478i	0.166407	+	0.0293420i
$781$	−3.09627	+	5.36289i	−0.110793	+	0.191899i
$782$	0.554378			0.0198245
$783$	39.5148	−	22.8139i	1.41214	−	0.815301i
$784$		0			0
$785$	−6.23396	+	10.7975i	−0.222499	+	0.385380i
$786$	26.1132	+	4.60446i	0.931426	+	0.164236i
$787$	−15.3525	−	26.5913i	−0.547258	−	0.947879i	−0.998461	−	0.0554572i	$-0.982338\pi$
$787$	−15.3525	−	26.5913i	−0.547258	−	0.947879i	0.451203	−	0.892421i	$-0.350995\pi$
$788$	2.33157	+	4.03839i	0.0830586	+	0.143862i
$789$	29.0442	−	34.6135i	1.03400	−	1.23227i
$790$	−21.5574	+	37.3385i	−0.766977	+	1.32844i
$791$		0			0
$792$	3.16528	−	2.65598i	0.112473	−	0.0943763i
$793$	5.57903			0.198117
$794$	−8.29932	+	14.3748i	−0.294532	+	0.510144i
$795$	1.07532	+	2.95442i	0.0381377	+	0.104783i
$796$	−0.281059	−	0.486809i	−0.00996188	−	0.0172545i
$797$	−5.50686	−	9.53817i	−0.195063	−	0.337859i	0.751858	−	0.659325i	$-0.229158\pi$
$797$	−5.50686	−	9.53817i	−0.195063	−	0.337859i	−0.946921	+	0.321466i	$0.895825\pi$
$798$		0			0
$799$	10.3439	−	17.9161i	0.365941	−	0.633828i
$800$	1.47060			0.0519935
$801$	22.8735	+	8.32526i	0.808194	+	0.294158i
$802$	28.2608			0.997925
$803$	−2.40239	+	4.16106i	−0.0847785	+	0.146841i
$804$	1.98293	−	2.36316i	0.0699324	−	0.0833422i
$805$		0			0
$806$	30.1259	+	52.1796i	1.06114	+	1.83795i
$807$	−13.0201	−	2.29579i	−0.458328	−	0.0808156i
$808$	14.0908	−	24.4060i	0.495713	−	0.858600i
$809$	16.9881			0.597271			0.298636	−	0.954367i	$-0.403468\pi$
$809$	16.9881			0.597271			0.298636	+	0.954367i	$0.403468\pi$
$810$	−23.5201	−	19.7357i	−0.826411	−	0.693441i
$811$	−37.9796			−1.33364			−0.666822	−	0.745217i	$-0.732346\pi$
$811$	−37.9796			−1.33364			−0.666822	+	0.745217i	$0.732346\pi$
$812$		0			0
$813$	5.80587	+	1.02373i	0.203621	+	0.0359039i
$814$	2.42081	+	4.19296i	0.0848493	+	0.146963i
$815$	9.67024	+	16.7494i	0.338734	+	0.586704i
$816$	15.5326	−	18.5110i	0.543748	−	0.648014i
$817$	−1.34002	+	2.32099i	−0.0468814	+	0.0812011i
$818$	−34.5735			−1.20883
$819$		0			0
$820$	1.04189			0.0363843
$821$	−4.13934	+	7.16954i	−0.144464	+	0.250219i	−0.929173	−	0.369646i	$-0.879479\pi$
$821$	−4.13934	+	7.16954i	−0.144464	+	0.250219i	0.784709	+	0.619864i	$0.212812\pi$
$822$	−4.56901	−	12.5533i	−0.159363	−	0.437845i
$823$	−27.2763	−	47.2440i	−0.950792	−	1.64682i	−0.743716	−	0.668496i	$-0.766938\pi$
$823$	−27.2763	−	47.2440i	−0.950792	−	1.64682i	−0.207077	−	0.978325i	$-0.566395\pi$
$824$	−4.47700	−	7.75438i	−0.155964	−	0.270137i
$825$	0.391245	+	1.07494i	0.0136214	+	0.0374245i
$826$		0			0
$827$	−31.8708			−1.10826			−0.554129	−	0.832431i	$-0.686948\pi$
$827$	−31.8708			−1.10826			−0.554129	+	0.832431i	$0.686948\pi$
$828$	−0.0450442	+	0.0377966i	−0.00156540	+	0.00131352i
$829$	0.352349			0.0122376			0.00611879	−	0.999981i	$-0.498052\pi$
$829$	0.352349			0.0122376			0.00611879	+	0.999981i	$0.498052\pi$
$830$	4.65910	−	8.06980i	0.161720	−	0.280107i
$831$	−6.37046	+	7.59202i	−0.220989	+	0.263364i
$832$	25.0278	+	43.3494i	0.867683	+	1.50287i
$833$		0			0
$834$	−2.12339	−	0.374411i	−0.0735270	−	0.0129648i
$835$	7.15998	−	12.4014i	0.247781	−	0.429170i
$836$	−0.188911			−0.00653363
$837$			39.9067i			1.37938i
$838$	1.99369			0.0688709
$839$	12.5077	−	21.6640i	0.431815	−	0.747926i	−0.565215	−	0.824944i	$-0.691207\pi$
$839$	12.5077	−	21.6640i	0.431815	−	0.747926i	0.997030	+	0.0770182i	$0.0245399\pi$
$840$		0			0
$841$	−24.0535	−	41.6619i	−0.829431	−	1.43662i
$842$	−8.82951	−	15.2932i	−0.304285	−	0.527037i
$843$	31.5936	−	37.6518i	1.08814	−	1.29680i
$844$	−0.503870	+	0.872729i	−0.0173439	+	0.0300406i
$845$	−52.9377			−1.82111
$846$	−3.74288	−	21.2269i	−0.128683	−	0.729796i
$847$		0			0
$848$	−1.28905	+	2.23270i	−0.0442661	+	0.0766711i
$849$	−2.70801	−	7.44021i	−0.0929388	−	0.255347i
$850$	3.68866	+	6.38895i	0.126520	+	0.219139i
$851$	−0.407299	−	0.705463i	−0.0139620	−	0.0241829i
$852$	−1.44878	−	3.98048i	−0.0496343	−	0.136369i
$853$	19.5954	−	33.9402i	0.670933	−	1.16209i	−0.306706	−	0.951804i	$-0.599227\pi$
$853$	19.5954	−	33.9402i	0.670933	−	1.16209i	0.977640	−	0.210286i	$-0.0674397\pi$
$854$		0			0
$855$	2.88191	+	16.3441i	0.0985593	+	0.558958i
$856$	19.1848			0.655723
$857$	8.20368	−	14.2092i	0.280232	−	0.485377i	−0.691210	−	0.722654i	$-0.742922\pi$
$857$	8.20368	−	14.2092i	0.280232	−	0.485377i	0.971442	+	0.237278i	$0.0762552\pi$
$858$	−4.08693	+	4.87062i	−0.139526	+	0.166280i
$859$	−13.4162	−	23.2376i	−0.457756	−	0.792856i	0.541086	−	0.840967i	$-0.318013\pi$
$859$	−13.4162	−	23.2376i	−0.457756	−	0.792856i	−0.998842	+	0.0481111i	$0.984680\pi$
$860$	−0.286989	−	0.497079i	−0.00978624	−	0.0169503i
$861$		0			0
$862$	−11.9418	+	20.6837i	−0.406738	+	0.704490i
$863$	14.5057			0.493779			0.246890	−	0.969044i	$-0.420592\pi$
$863$	14.5057			0.493779			0.246890	+	0.969044i	$0.420592\pi$
$864$			5.41381i			0.184182i
$865$	53.3492			1.81393
$866$	−3.93305	+	6.81224i	−0.133650	+	0.231489i
$867$	3.32682	+	0.586608i	0.112985	+	0.0199222i
$868$		0			0
$869$	2.95677	+	5.12127i	0.100301	+	0.173727i
$870$	−33.3516	+	39.7469i	−1.13073	+	1.34755i
$871$	−28.0612	+	48.6035i	−0.950819	+	1.64687i
$872$	−31.3141			−1.06043
$873$	−31.2638	+	26.2335i	−1.05812	+	0.887868i
$874$	−0.312214			−0.0105608
$875$		0			0
$876$	−1.12410	−	3.08845i	−0.0379800	−	0.104349i
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270131\pi$
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	−0.980352	+	0.197255i	$0.936797\pi$
$878$	20.1120	+	34.8350i	0.678747	+	1.17562i
$879$	−2.56371	−	7.04374i	−0.0864718	−	0.237579i
$880$	−2.13041	+	3.68999i	−0.0718163	+	0.124389i
$881$	−53.8976			−1.81585			−0.907927	−	0.419128i	$-0.862336\pi$
$881$	−53.8976			−1.81585			−0.907927	+	0.419128i	$0.862336\pi$
$882$		0			0
$883$	43.4252			1.46137			0.730687	−	0.682712i	$-0.239200\pi$
$883$	43.4252			1.46137			0.730687	+	0.682712i	$0.239200\pi$
$884$	2.08718	−	3.61510i	0.0701995	−	0.121589i
$885$	2.07620	−	2.47432i	0.0697907	−	0.0831733i
$886$	−7.18479	−	12.4444i	−0.241378	−	0.418079i
$887$	−19.4800	−	33.7403i	−0.654074	−	1.13289i	−0.982125	−	0.188229i	$-0.939725\pi$
$887$	−19.4800	−	33.7403i	−0.654074	−	1.13289i	0.328051	−	0.944660i	$-0.393608\pi$
$888$	−38.5611	−	6.79936i	−1.29403	−	0.228172i
$889$		0			0
$890$	−27.6800			−0.927837
$891$	−3.95723	+	1.44032i	−0.132572	+	0.0482524i
$892$	2.62267			0.0878136
$893$	−5.82547	+	10.0900i	−0.194942	+	0.337650i
$894$	−20.0503	−	3.53542i	−0.670584	−	0.118242i
$895$	−6.48293	−	11.2288i	−0.216700	−	0.375336i
$896$		0			0
$897$	0.687623	−	0.819478i	0.0229591	−	0.0273616i
$898$	−2.39440	+	4.14722i	−0.0799022	+	0.138395i
$899$	67.4389			2.24921
$900$	−0.735300	−	0.267627i	−0.0245100	−	0.00892091i
$901$	2.78106			0.0926505
$902$	−0.701867	+	1.21567i	−0.0233696	+	0.0404773i
$903$		0			0
$904$	7.61949	+	13.1973i	0.253420	+	0.438937i
$905$	0.405078	+	0.701615i	0.0134652	+	0.0233225i
$906$	14.7072	+	40.4076i	0.488613	+	1.34245i
$907$	−17.2638	+	29.9018i	−0.573236	+	0.992874i	0.422995	+	0.906132i	$0.360979\pi$
$907$	−17.2638	+	29.9018i	−0.573236	+	0.992874i	−0.996231	+	0.0867416i	$0.972355\pi$
$908$	−0.534777			−0.0177472
$909$	−22.0023	+	18.4621i	−0.729769	+	0.612349i
$910$		0			0
$911$	−23.2631	+	40.2929i	−0.770741	+	1.33496i	0.166416	+	0.986056i	$0.446780\pi$
$911$	−23.2631	+	40.2929i	−0.770741	+	1.33496i	−0.937157	+	0.348907i	$0.886553\pi$
$912$	−8.74763	+	10.4250i	−0.289663	+	0.345207i
$913$	−0.639033	−	1.10684i	−0.0211489	−	0.0366310i
$914$	−3.38388	−	5.86106i	−0.111929	−	0.193867i
$915$	−4.13816	−	0.729669i	−0.136803	−	0.0241221i
$916$	−0.847048	+	1.46713i	−0.0279873	+	0.0484753i
$917$		0			0
$918$	−23.5201	+	13.5793i	−0.776278	+	0.448184i
$919$	−9.95636			−0.328430			−0.164215	−	0.986425i	$-0.552509\pi$
$919$	−9.95636			−0.328430			−0.164215	+	0.986425i	$0.552509\pi$
$920$	0.395277	−	0.684640i	0.0130319	−	0.0225719i
$921$	21.1125	+	3.72270i	0.695679	+	0.122667i
$922$	12.4363	+	21.5403i	0.409567	+	0.709391i
$923$	38.5317	+	66.7388i	1.26829	+	2.19674i
$924$		0			0
$925$	5.42009	−	9.38788i	0.178212	−	0.308671i
$926$	−19.1780			−0.630228
$927$	1.58466	+	8.98703i	0.0520469	+	0.295173i
$928$	9.14889			0.300327
$929$	4.52300	−	7.83407i	0.148395	−	0.257028i	−0.782239	−	0.622978i	$-0.785923\pi$
$929$	4.52300	−	7.83407i	0.148395	−	0.257028i	0.930634	+	0.365950i	$0.119256\pi$
$930$	−15.5209	−	42.6434i	−0.508952	−	1.39833i
$931$		0			0
$932$	1.22621	+	2.12387i	0.0401660	+	0.0695696i
$933$	13.0241	+	35.7834i	0.426390	+	1.17150i
$934$	−2.26929	+	3.93052i	−0.0742533	+	0.128610i
$935$	4.59627			0.150314
$936$	−8.92910	−	50.6395i	−0.291857	−	1.65520i
$937$	24.3928			0.796878			0.398439	−	0.917195i	$-0.369552\pi$
$937$	24.3928			0.796878			0.398439	+	0.917195i	$0.369552\pi$
$938$		0			0
$939$	15.4641	−	18.4294i	0.504652	−	0.601421i
$940$	−1.24763	−	2.16095i	−0.0406931	−	0.0704825i
$941$	−29.7690	−	51.5615i	−0.970443	−	1.68086i	−0.694220	−	0.719763i	$-0.744251\pi$
$941$	−29.7690	−	51.5615i	−0.970443	−	1.68086i	−0.276223	−	0.961094i	$-0.589083\pi$
$942$	11.3159	+	1.99530i	0.368693	+	0.0650105i
$943$	0.118089	−	0.204535i	0.00384549	−	0.00666059i
$944$	2.64858			0.0862041
$945$		0			0
$946$	0.773318			0.0251428
$947$	−4.32429	+	7.48989i	−0.140521	+	0.243389i	−0.927693	−	0.373344i	$-0.878211\pi$
$947$	−4.32429	+	7.48989i	−0.140521	+	0.243389i	0.787172	+	0.616733i	$0.211544\pi$
$948$	−3.98364	−	0.702423i	−0.129383	−	0.0228137i
$949$	29.8967	+	51.7826i	0.970487	+	1.68093i
$950$	−2.07738	−	3.59813i	−0.0673992	−	0.116739i
$951$	−6.88279	+	8.20259i	−0.223190	+	0.265987i
$952$		0			0
$953$	3.78249			0.122527			0.0612634	−	0.998122i	$-0.480487\pi$
$953$	3.78249			0.122527			0.0612634	+	0.998122i	$0.480487\pi$
$954$	2.21966	−	1.86251i	0.0718640	−	0.0603011i
$955$	39.4175			1.27552
$956$	0.881196	−	1.52628i	0.0284999	−	0.0493633i
$957$	2.43401	+	6.68739i	0.0786804	+	0.216173i
$958$	−24.7677	−	42.8989i	−0.800208	−	1.38600i
$959$		0			0
$960$	−12.8944	−	35.4271i	−0.416165	−	1.14340i
$961$	−13.9915	+	24.2341i	−0.451340	+	0.781744i
$962$	60.2518			1.94260
$963$	−18.3735	−	6.68739i	−0.592076	−	0.215498i
$964$	−1.65539			−0.0533166
$965$	7.64930	−	13.2490i	0.246240	−	0.426500i
$966$		0			0
$967$	16.4745	+	28.5346i	0.529783	+	0.917611i	0.999396	+	0.0347392i	$0.0110601\pi$
$967$	16.4745	+	28.5346i	0.529783	+	0.917611i	−0.469613	+	0.882872i	$0.655607\pi$
$968$	−15.8674	−	27.4831i	−0.509996	−	0.883340i
$969$	14.4572	+	2.54920i	0.464433	+	0.0818921i
$970$	23.2049	−	40.1920i	0.745063	−	1.29049i
$971$	55.4570			1.77970			0.889850	−	0.456254i	$-0.150809\pi$
$971$	55.4570			1.77970			0.889850	+	0.456254i	$0.150809\pi$
$972$	0.985234	−	2.70691i	0.0316014	−	0.0868241i
$973$		0			0
$974$	25.2062	−	43.6584i	0.807659	−	1.39891i
$975$	14.0194	+	2.47199i	0.448979	+	0.0791670i
$976$	−1.72281	−	2.98400i	−0.0551458	−	0.0955154i
$977$	−28.2743	−	48.9724i	−0.904573	−	1.56677i	−0.821489	−	0.570225i	$-0.806856\pi$
$977$	−28.2743	−	48.9724i	−0.904573	−	1.56677i	−0.0830847	−	0.996542i	$-0.526477\pi$
$978$	11.4572	−	13.6542i	0.366362	−	0.436613i
$979$	−1.89827	+	3.28790i	−0.0606690	+	0.105082i
$980$		0			0
$981$	29.9898	+	10.9154i	0.957500	+	0.348502i
$982$	−35.9331			−1.14667
$983$	14.4987	−	25.1124i	0.462435	−	0.800961i	−0.536646	−	0.843807i	$-0.680309\pi$
$983$	14.4987	−	25.1124i	0.462435	−	0.800961i	0.999082	+	0.0428458i	$0.0136424\pi$
$984$	−3.88279	−	10.6679i	−0.123779	−	0.340079i
$985$	31.9479	+	55.3354i	1.01794	+	1.76313i
$986$	22.9479	+	39.7469i	0.730810	+	1.26580i
$987$		0			0
$988$	−1.17546	+	2.03596i	−0.0373963	+	0.0647724i
$989$	−0.130110			−0.00413726
$990$	3.66843	−	3.07818i	0.116590	−	0.0978310i
$991$	6.80922			0.216302			0.108151	−	0.994134i	$-0.465507\pi$
$991$	6.80922			0.216302			0.108151	+	0.994134i	$0.465507\pi$
$992$	−4.00088	+	6.92972i	−0.127028	+	0.220019i
$993$	11.9477	−	14.2388i	0.379150	−	0.451853i
$994$		0			0
$995$	−3.85117	−	6.67042i	−0.122090	−	0.211466i
$996$	0.860967	+	0.151812i	0.0272808	+	0.00481034i
$997$	−19.4688	+	33.7210i	−0.616585	+	1.06796i	0.373520	+	0.927622i	$0.378151\pi$
$997$	−19.4688	+	33.7210i	−0.616585	+	1.06796i	−0.990104	+	0.140333i	$0.955183\pi$
$998$	45.4647			1.43916
$999$	34.5602	+	19.9533i	1.09344	+	0.631296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.c.295.2		6
3.2	odd	2		1323.2.f.d.883.2		6
7.2	even	3		441.2.h.e.214.2		6
7.3	odd	6		441.2.g.c.79.2		6
7.4	even	3		441.2.g.b.79.2		6
7.5	odd	6		441.2.h.d.214.2		6
7.6	odd	2		63.2.f.a.43.2	yes	6
9.2	odd	6		3969.2.a.l.1.2		3
9.4	even	3	inner	441.2.f.c.148.2		6
9.5	odd	6		1323.2.f.d.442.2		6
9.7	even	3		3969.2.a.q.1.2		3
21.2	odd	6		1323.2.h.b.802.2		6
21.5	even	6		1323.2.h.c.802.2		6
21.11	odd	6		1323.2.g.e.667.2		6
21.17	even	6		1323.2.g.d.667.2		6
21.20	even	2		189.2.f.b.127.2		6
28.27	even	2		1008.2.r.h.673.1		6
63.4	even	3		441.2.h.e.373.2		6
63.5	even	6		1323.2.g.d.361.2		6
63.13	odd	6		63.2.f.a.22.2	✓	6
63.20	even	6		567.2.a.c.1.2		3
63.23	odd	6		1323.2.g.e.361.2		6
63.31	odd	6		441.2.h.d.373.2		6
63.32	odd	6		1323.2.h.b.226.2		6
63.34	odd	6		567.2.a.h.1.2		3
63.40	odd	6		441.2.g.c.67.2		6
63.41	even	6		189.2.f.b.64.2		6
63.58	even	3		441.2.g.b.67.2		6
63.59	even	6		1323.2.h.c.226.2		6
84.83	odd	2		3024.2.r.k.2017.3		6
252.83	odd	6		9072.2.a.bs.1.1		3
252.139	even	6		1008.2.r.h.337.1		6
252.167	odd	6		3024.2.r.k.1009.3		6
252.223	even	6		9072.2.a.ca.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	63.13	odd	6
63.2.f.a.43.2	yes	6	7.6	odd	2
189.2.f.b.64.2		6	63.41	even	6
189.2.f.b.127.2		6	21.20	even	2
441.2.f.c.148.2		6	9.4	even	3	inner
441.2.f.c.295.2		6	1.1	even	1	trivial
441.2.g.b.67.2		6	63.58	even	3
441.2.g.b.79.2		6	7.4	even	3
441.2.g.c.67.2		6	63.40	odd	6
441.2.g.c.79.2		6	7.3	odd	6
441.2.h.d.214.2		6	7.5	odd	6
441.2.h.d.373.2		6	63.31	odd	6
441.2.h.e.214.2		6	7.2	even	3
441.2.h.e.373.2		6	63.4	even	3
567.2.a.c.1.2		3	63.20	even	6
567.2.a.h.1.2		3	63.34	odd	6
1008.2.r.h.337.1		6	252.139	even	6
1008.2.r.h.673.1		6	28.27	even	2
1323.2.f.d.442.2		6	9.5	odd	6
1323.2.f.d.883.2		6	3.2	odd	2
1323.2.g.d.361.2		6	63.5	even	6
1323.2.g.d.667.2		6	21.17	even	6
1323.2.g.e.361.2		6	63.23	odd	6
1323.2.g.e.667.2		6	21.11	odd	6
1323.2.h.b.226.2		6	63.32	odd	6
1323.2.h.b.802.2		6	21.2	odd	6
1323.2.h.c.226.2		6	63.59	even	6
1323.2.h.c.802.2		6	21.5	even	6
3024.2.r.k.1009.3		6	252.167	odd	6
3024.2.r.k.2017.3		6	84.83	odd	2
3969.2.a.l.1.2		3	9.2	odd	6
3969.2.a.q.1.2		3	9.7	even	3
9072.2.a.bs.1.1		3	252.83	odd	6
9072.2.a.ca.1.3		3	252.223	even	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.673648 + 1.16679i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(1.26604 + 2.19285i) q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(2.81908 + 1.02606i) q^{9} +O(q^{10})\)	\(q+(-0.673648 + 1.16679i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.0923963 + 0.160035i) q^{4} +(1.26604 + 2.19285i) q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(2.81908 + 1.02606i) q^{9} -3.41147 q^{10} +(-0.233956 + 0.405223i) q^{11} +(-0.109470 - 0.300767i) q^{12} +(2.91147 + 5.04282i) q^{13} +(-1.50000 - 4.12122i) q^{15} +(1.79813 - 3.11446i) q^{16} -3.87939 q^{17} +(-3.09627 + 2.59808i) q^{18} +2.18479 q^{19} +(-0.233956 + 0.405223i) q^{20} +(-0.315207 - 0.545955i) q^{22} +(0.0530334 + 0.0918566i) q^{23} +(5.02094 + 0.885328i) q^{24} +(-0.705737 + 1.22237i) q^{25} -7.84524 q^{26} +(-4.50000 - 2.59808i) q^{27} +(-4.39053 + 7.60462i) q^{29} +(5.81908 + 1.02606i) q^{30} +(-3.84002 - 6.65111i) q^{31} +(-0.520945 - 0.902302i) q^{32} +(0.520945 - 0.620838i) q^{33} +(2.61334 - 4.52644i) q^{34} +(0.0962667 + 0.545955i) q^{36} -7.68004 q^{37} +(-1.47178 + 2.54920i) q^{38} +(-3.44949 - 9.47740i) q^{39} +(-3.72668 - 6.45480i) q^{40} +(-1.11334 - 1.92836i) q^{41} +(-0.613341 + 1.06234i) q^{43} -0.0864665 q^{44} +(1.31908 + 7.48086i) q^{45} -0.142903 q^{46} +(-2.66637 + 4.61830i) q^{47} +(-4.00387 + 4.77163i) q^{48} +(-0.950837 - 1.64690i) q^{50} +(6.61721 + 1.16679i) q^{51} +(-0.538019 + 0.931876i) q^{52} -0.716881 q^{53} +(6.06283 - 3.50038i) q^{54} -1.18479 q^{55} +(-3.72668 - 0.657115i) q^{57} +(-5.91534 - 10.2457i) q^{58} +(0.368241 + 0.637812i) q^{59} +(0.520945 - 0.620838i) q^{60} +(0.479055 - 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(-7.37211 + 12.7689i) q^{65} +(0.373455 + 1.02606i) q^{66} +(4.81908 + 8.34689i) q^{67} +(-0.358441 - 0.620838i) q^{68} +(-0.0628336 - 0.172634i) q^{69} +13.2344 q^{71} +(-8.29813 - 3.02027i) q^{72} +10.2686 q^{73} +(5.17365 - 8.96102i) q^{74} +(1.57145 - 1.87278i) q^{75} +(0.201867 + 0.349643i) q^{76} +(13.3819 + 2.35959i) q^{78} +(6.31908 - 10.9450i) q^{79} +9.10607 q^{80} +(6.89440 + 5.78509i) q^{81} +3.00000 q^{82} +(-1.36571 + 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +(-0.826352 - 1.43128i) q^{86} +(9.77631 - 11.6510i) q^{87} +(0.688663 - 1.19280i) q^{88} +8.11381 q^{89} +(-9.61721 - 3.50038i) q^{90} +(-0.00980018 + 0.0169744i) q^{92} +(4.54963 + 12.5000i) q^{93} +(-3.59240 - 6.22221i) q^{94} +(2.76604 + 4.79093i) q^{95} +(0.617211 + 1.69577i) q^{96} +(-6.80200 + 11.7814i) q^{97} +(-1.07532 + 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} - 18 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} - 12 q^{17} + 9 q^{18} + 6 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} + 27 q^{24} + 6 q^{25} + 6 q^{26} - 27 q^{27} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 9 q^{34} - 27 q^{36} - 6 q^{37} + 6 q^{38} - 18 q^{39} - 9 q^{40} + 3 q^{43} + 30 q^{44} - 9 q^{45} + 3 q^{47} + 6 q^{50} + 9 q^{51} - 21 q^{52} + 12 q^{53} + 27 q^{54} - 9 q^{57} + 9 q^{58} - 3 q^{59} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} - 36 q^{66} + 12 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 36 q^{72} + 42 q^{73} + 30 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} + 30 q^{80} + 18 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} - 9 q^{87} - 27 q^{88} - 24 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 - 18 * q^12 - 3 * q^13 - 9 * q^15 - 3 * q^16 - 12 * q^17 + 9 * q^18 + 6 * q^19 - 6 * q^20 - 9 * q^22 - 12 * q^23 + 27 * q^24 + 6 * q^25 + 6 * q^26 - 27 * q^27 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 9 * q^34 - 27 * q^36 - 6 * q^37 + 6 * q^38 - 18 * q^39 - 9 * q^40 + 3 * q^43 + 30 * q^44 - 9 * q^45 + 3 * q^47 + 6 * q^50 + 9 * q^51 - 21 * q^52 + 12 * q^53 + 27 * q^54 - 9 * q^57 + 9 * q^58 - 3 * q^59 + 6 * q^61 + 60 * q^62 + 24 * q^64 - 15 * q^65 - 36 * q^66 + 12 * q^67 + 6 * q^68 + 9 * q^69 + 18 * q^71 - 36 * q^72 + 42 * q^73 + 30 * q^74 + 9 * q^75 + 15 * q^76 + 54 * q^78 + 21 * q^79 + 30 * q^80 + 18 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 - 9 * q^87 - 27 * q^88 - 24 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 27 * q^96 - 3 * q^97 + 18 * q^99

Introduction

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