LMFDB - Embedded newform 441.2.g.b.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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			79.2
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	441.79
Dual form			441.2.g.b.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673648 - 1.16679i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.0923963 - 0.160035i) q^{4} -2.53209 q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})$	\(q+(-0.673648 - 1.16679i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.0923963 - 0.160035i) q^{4} -2.53209 q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-2.29813 + 1.92836i) q^{9} +(1.70574 + 2.95442i) q^{10} +0.467911 q^{11} +(0.315207 + 0.0555796i) q^{12} +(2.91147 + 5.04282i) q^{13} +(-1.50000 - 4.12122i) q^{15} +(1.79813 + 3.11446i) q^{16} +(1.93969 + 3.35965i) q^{17} +(3.79813 + 1.38241i) q^{18} +(-1.09240 + 1.89209i) q^{19} +(-0.233956 + 0.405223i) q^{20} +(-0.315207 - 0.545955i) q^{22} -0.106067 q^{23} +(-1.74376 - 4.79093i) q^{24} +1.41147 q^{25} +(3.92262 - 6.79417i) q^{26} +(-4.50000 - 2.59808i) q^{27} +(-4.39053 + 7.60462i) q^{29} +(-3.79813 + 4.52644i) q^{30} +(-3.84002 + 6.65111i) q^{31} +(-0.520945 + 0.902302i) q^{32} +(0.277189 + 0.761570i) q^{33} +(2.61334 - 4.52644i) q^{34} +(0.0962667 + 0.545955i) q^{36} +(3.84002 - 6.65111i) q^{37} +2.94356 q^{38} +(-6.48293 + 7.72605i) q^{39} +7.45336 q^{40} +(-1.11334 - 1.92836i) q^{41} +(-0.613341 + 1.06234i) q^{43} +(0.0432332 - 0.0748822i) q^{44} +(5.81908 - 4.88279i) q^{45} +(0.0714517 + 0.123758i) q^{46} +(-2.66637 - 4.61830i) q^{47} +(-4.00387 + 4.77163i) q^{48} +(-0.950837 - 1.64690i) q^{50} +(-4.31908 + 5.14728i) q^{51} +1.07604 q^{52} +(0.358441 + 0.620838i) q^{53} +7.00076i q^{54} -1.18479 q^{55} +(-3.72668 - 0.657115i) q^{57} +11.8307 q^{58} +(0.368241 - 0.637812i) q^{59} +(-0.798133 - 0.140732i) q^{60} +(0.479055 + 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(-7.37211 - 12.7689i) q^{65} +(0.701867 - 0.836452i) q^{66} +(4.81908 - 8.34689i) q^{67} +0.716881 q^{68} +(-0.0628336 - 0.172634i) q^{69} +13.2344 q^{71} +(6.76470 - 5.67626i) q^{72} +(-5.13429 - 8.89284i) q^{73} -10.3473 q^{74} +(0.836152 + 2.29731i) q^{75} +(0.201867 + 0.349643i) q^{76} +(13.3819 + 2.35959i) q^{78} +(6.31908 + 10.9450i) q^{79} +(-4.55303 - 7.88609i) q^{80} +(1.56283 - 8.86327i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-1.36571 + 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +1.65270 q^{86} +(-14.9782 - 2.64106i) q^{87} -1.37733 q^{88} +(-4.05690 + 7.02676i) q^{89} +(-9.61721 - 3.50038i) q^{90} +(-0.00980018 + 0.0169744i) q^{92} +(-13.1001 - 2.30991i) q^{93} +(-3.59240 + 6.22221i) q^{94} +(2.76604 - 4.79093i) q^{95} +(-1.77719 - 0.313366i) 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} - 6 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 9 q^{6} + 12 q^{8} + 12 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} + 6 q^{17} + 9 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} + 24 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} - 3 q^{31} - 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} - 12 q^{38} - 18 q^{39} + 18 q^{40} + 3 q^{43} - 15 q^{44} + 18 q^{45} + 3 q^{47} + 6 q^{50} - 9 q^{51} + 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} - 3 q^{59} + 9 q^{60} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} + 18 q^{66} + 12 q^{67} - 12 q^{68} + 9 q^{69} + 18 q^{71} + 45 q^{72} - 21 q^{73} - 60 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} + 12 q^{86} - 36 q^{87} + 54 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8 + 12 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 - 3 * q^16 + 6 * q^17 + 9 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 + 24 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 - 3 * q^31 - 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 - 12 * q^38 - 18 * q^39 + 18 * q^40 + 3 * q^43 - 15 * q^44 + 18 * q^45 + 3 * q^47 + 6 * q^50 - 9 * q^51 + 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 - 3 * q^59 + 9 * q^60 + 6 * q^61 + 60 * q^62 + 24 * q^64 - 15 * q^65 + 18 * q^66 + 12 * q^67 - 12 * q^68 + 9 * q^69 + 18 * q^71 + 45 * q^72 - 21 * q^73 - 60 * q^74 + 9 * q^75 + 15 * q^76 + 54 * q^78 + 21 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 + 12 * q^86 - 36 * q^87 + 54 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.523291	−	0.852154i	$-0.324704\pi$
$2$	−0.673648	−	1.16679i	−0.476341	−	0.825047i	−0.999633	+	0.0271067i	$0.991371\pi$
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$4$	0.0923963	−	0.160035i	0.0461981	−	0.0800175i
$5$	−2.53209			−1.13238			−0.566192	−	0.824273i	$-0.691584\pi$
$5$	−2.53209			−1.13238			−0.566192	+	0.824273i	$0.691584\pi$
$6$	1.50000	−	1.78763i	0.612372	−	0.729797i
$7$		0			0
$7$		0			0
$8$	−2.94356			−1.04071
$9$	−2.29813	+	1.92836i	−0.766044	+	0.642788i
$10$	1.70574	+	2.95442i	0.539401	+	0.934271i
$11$	0.467911			0.141081			0.0705403	−	0.997509i	$-0.477528\pi$
$11$	0.467911			0.141081			0.0705403	+	0.997509i	$0.477528\pi$
$12$	0.315207	+	0.0555796i	0.0909926	+	0.0160444i
$13$	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
$17$	1.93969	+	3.35965i	0.470445	+	0.814834i	0.999429	−	0.0337978i	$-0.0107602\pi$
$17$	1.93969	+	3.35965i	0.470445	+	0.814834i	−0.528984	+	0.848632i	$0.677427\pi$
$18$	3.79813	+	1.38241i	0.895229	+	0.325837i
$19$	−1.09240	+	1.89209i	−0.250613	+	0.434074i	−0.963695	−	0.267007i	$-0.913965\pi$
$19$	−1.09240	+	1.89209i	−0.250613	+	0.434074i	0.713082	+	0.701081i	$0.247299\pi$
$20$	−0.233956	+	0.405223i	−0.0523141	+	0.0906106i
$21$		0			0
$22$	−0.315207	−	0.545955i	−0.0672025	−	0.116398i
$23$	−0.106067			−0.0221165			−0.0110582	−	0.999939i	$-0.503520\pi$
$23$	−0.106067			−0.0221165			−0.0110582	+	0.999939i	$0.503520\pi$
$24$	−1.74376	−	4.79093i	−0.355943	−	0.977944i
$25$	1.41147			0.282295
$26$	3.92262	−	6.79417i	0.769289	−	1.33245i
$27$	−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	$0.863238\pi$
$30$	−3.79813	+	4.52644i	−0.693441	+	0.826411i
$31$	−3.84002	+	6.65111i	−0.689688	+	1.19458i	0.282250	+	0.959341i	$0.408919\pi$
$31$	−3.84002	+	6.65111i	−0.689688	+	1.19458i	−0.971939	+	0.235235i	$0.924414\pi$
$32$	−0.520945	+	0.902302i	−0.0920909	+	0.159506i
$33$	0.277189	+	0.761570i	0.0482524	+	0.132572i
$34$	2.61334	−	4.52644i	0.448184	−	0.776278i
$35$		0			0
$36$	0.0962667	+	0.545955i	0.0160444	+	0.0909926i
$37$	3.84002	−	6.65111i	0.631296	−	1.09344i	−0.355991	−	0.934489i	$-0.615857\pi$
$37$	3.84002	−	6.65111i	0.631296	−	1.09344i	0.987287	−	0.158947i	$-0.0508099\pi$
$38$	2.94356			0.477509
$39$	−6.48293	+	7.72605i	−1.03810	+	1.23716i
$40$	7.45336			1.17848
$41$	−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	$0.196483\pi$
$44$	0.0432332	−	0.0748822i	0.00651766	−	0.0112889i
$45$	5.81908	−	4.88279i	0.867457	−	0.727883i
$46$	0.0714517	+	0.123758i	0.0105350	+	0.0182471i
$47$	−2.66637	−	4.61830i	−0.388931	−	0.673648i	0.603375	−	0.797457i	$-0.293822\pi$
$47$	−2.66637	−	4.61830i	−0.388931	−	0.673648i	−0.992306	+	0.123810i	$0.960489\pi$
$48$	−4.00387	+	4.77163i	−0.577909	+	0.688725i
$49$		0			0
$50$	−0.950837	−	1.64690i	−0.134469	−	0.232907i
$51$	−4.31908	+	5.14728i	−0.604792	+	0.720763i
$52$	1.07604			0.149220
$53$	0.358441	+	0.620838i	0.0492356	+	0.0852786i	0.889593	−	0.456754i	$-0.150988\pi$
$53$	0.358441	+	0.620838i	0.0492356	+	0.0852786i	−0.840357	+	0.542033i	$0.817655\pi$
$54$			7.00076i			0.952682i
$55$	−1.18479			−0.159757
$56$		0			0
$57$	−3.72668	−	0.657115i	−0.493611	−	0.0870369i
$58$	11.8307			1.55345
$59$	0.368241	−	0.637812i	0.0479409	−	0.0830360i	−0.841059	−	0.540943i	$-0.818067\pi$
$59$	0.368241	−	0.637812i	0.0479409	−	0.0830360i	0.889000	+	0.457907i	$0.151401\pi$
$60$	−0.798133	−	0.140732i	−0.103039	−	0.0181685i
$61$	0.479055	+	0.829748i	0.0613368	+	0.106238i	0.895063	−	0.445939i	$-0.147130\pi$
$61$	0.479055	+	0.829748i	0.0613368	+	0.106238i	−0.833726	+	0.552178i	$0.813797\pi$
$62$	10.3473			1.31411
$63$		0			0
$64$	8.59627			1.07453
$65$	−7.37211	−	12.7689i	−0.914398	−	1.58378i
$66$	0.701867	−	0.836452i	0.0863938	−	0.102960i
$67$	4.81908	−	8.34689i	0.588744	−	1.01973i	−0.405653	−	0.914027i	$-0.632956\pi$
$67$	4.81908	−	8.34689i	0.588744	−	1.01973i	0.994397	−	0.105708i	$-0.0337107\pi$
$68$	0.716881			0.0869346
$69$	−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	$0.212499\pi$
$72$	6.76470	−	5.67626i	0.797228	−	0.668953i
$73$	−5.13429	−	8.89284i	−0.600923	−	1.04083i	−0.992682	−	0.120761i	$-0.961467\pi$
$73$	−5.13429	−	8.89284i	−0.600923	−	1.04083i	0.391759	−	0.920068i	$-0.371867\pi$
$74$	−10.3473			−1.20285
$75$	0.836152	+	2.29731i	0.0965505	+	0.265270i
$76$	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	0.964500	+	0.264082i	$0.0850689\pi$
$79$	6.31908	+	10.9450i	0.710952	+	1.23140i	−0.253548	+	0.967323i	$0.581598\pi$
$80$	−4.55303	−	7.88609i	−0.509045	−	0.881691i
$81$	1.56283	−	8.86327i	0.173648	−	0.984808i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	−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
$86$	1.65270			0.178216
$87$	−14.9782	−	2.64106i	−1.60583	−	0.283151i
$88$	−1.37733			−0.146823
$89$	−4.05690	+	7.02676i	−0.430031	+	0.744835i	−0.996875	−	0.0789894i	$-0.974831\pi$
$89$	−4.05690	+	7.02676i	−0.430031	+	0.744835i	0.566845	+	0.823825i	$0.308164\pi$
$90$	−9.61721	−	3.50038i	−1.01374	−	0.368972i
$91$		0			0
$92$	−0.00980018	+	0.0169744i	−0.00102174	+	0.00176970i
$93$	−13.1001	−	2.30991i	−1.35842	−	0.239526i
$94$	−3.59240	+	6.22221i	−0.370527	+	0.641772i
$95$	2.76604	−	4.79093i	0.283790	−	0.491539i
$96$	−1.77719	−	0.313366i	−0.181384	−	0.0319828i
$97$	−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
$100$	0.130415	−	0.225885i	0.0130415	−	0.0225885i
$101$	9.57398			0.952646			0.476323	−	0.879270i	$-0.341969\pi$
$101$	9.57398			0.952646			0.476323	+	0.879270i	$0.341969\pi$
$102$	8.91534	+	1.57202i	0.882751	+	0.155653i
$103$	−3.04189			−0.299726			−0.149863	−	0.988707i	$-0.547883\pi$
$103$	−3.04189			−0.299726			−0.149863	+	0.988707i	$0.547883\pi$
$104$	−8.57011	−	14.8439i	−0.840368	−	1.45556i
$105$		0			0
$106$	0.482926	−	0.836452i	0.0469059	−	0.0812434i
$107$	3.25877	−	5.64436i	0.315037	−	0.545660i	−0.664408	−	0.747370i	$-0.731316\pi$
$107$	3.25877	−	5.64436i	0.315037	−	0.545660i	0.979445	+	0.201709i	$0.0646497\pi$
$108$	−0.831566	+	0.480105i	−0.0800175	+	0.0461981i
$109$	−5.31908	−	9.21291i	−0.509475	−	0.882437i	−0.999940	−	0.0109759i	$-0.996506\pi$
$109$	−5.31908	−	9.21291i	−0.509475	−	0.882437i	0.490465	−	0.871461i	$-0.336827\pi$
$110$	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	$0.911632\pi$
$114$	1.74376	+	4.79093i	0.163318	+	0.448712i
$115$	0.268571			0.0250443
$116$	0.811337	+	1.40528i	0.0753308	+	0.130477i
$117$	−16.4153	−	5.97470i	−1.51760	−	0.552361i
$118$	−0.992259			−0.0913449
$119$		0			0
$120$	4.41534	+	12.1311i	0.403064	+	1.10741i
$121$	−10.7811			−0.980096
$122$	0.645430	−	1.11792i	0.0584345	−	0.101211i
$123$	2.47906	−	2.95442i	0.223529	−	0.266391i
$124$	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
$129$	−2.09240	−	0.368946i	−0.184225	−	0.0324839i
$130$	−9.93242	+	17.2035i	−0.871131	+	1.50884i
$131$	−11.3628			−0.992771			−0.496385	−	0.868102i	$-0.665340\pi$
$131$	−11.3628			−0.992771			−0.496385	+	0.868102i	$0.665340\pi$
$132$	0.147489	+	0.0260063i	0.0128373	+	0.00226356i
$133$		0			0
$134$	−12.9855			−1.12177
$135$	11.3944	+	6.57856i	0.980674	+	0.566192i
$136$	−5.70961	−	9.88933i	−0.489595	−	0.848003i
$137$	−5.72462			−0.489087			−0.244544	−	0.969638i	$-0.578638\pi$
$137$	−5.72462			−0.489087			−0.244544	+	0.969638i	$0.578638\pi$
$138$	−0.159100	+	0.189608i	−0.0135435	+	0.0161405i
$139$	−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
$143$	1.36231	+	2.35959i	0.113922	+	0.197319i
$144$	−10.1382	−	3.68999i	−0.844846	−	0.307499i
$145$	11.1172	−	19.2556i	0.923234	−	1.59909i
$146$	−6.91740	+	11.9813i	−0.572488	+	0.991579i
$147$		0			0
$148$	−0.709607	−	1.22908i	−0.0583294	−	0.101029i
$149$	8.72462			0.714749			0.357374	−	0.933961i	$-0.383672\pi$
$149$	8.72462			0.714749			0.357374	+	0.933961i	$0.383672\pi$
$150$	2.11721	−	2.52319i	0.172870	−	0.206018i
$151$	18.4270			1.49956			0.749782	−	0.661685i	$-0.230158\pi$
$151$	18.4270			1.49956			0.749782	+	0.661685i	$0.230158\pi$
$152$	3.21554	−	5.56947i	0.260815	−	0.451744i
$153$	−10.9363	−	3.98048i	−0.884147	−	0.321803i
$154$		0			0
$155$	9.72328	−	16.8412i	0.780992	−	1.35272i
$156$	0.637441	+	1.75135i	0.0510361	+	0.140220i
$157$	2.46198	−	4.26428i	0.196488	−	0.340326i	−0.750900	−	0.660416i	$-0.770380\pi$
$157$	2.46198	−	4.26428i	0.196488	−	0.340326i	0.947387	+	0.320090i	$0.103713\pi$
$158$	8.51367	−	14.7461i	0.677311	−	1.17314i
$159$	−0.798133	+	0.951178i	−0.0632961	+	0.0754333i
$160$	1.31908	−	2.28471i	0.104282	−	0.180622i
$161$		0			0
$162$	−11.3944	+	4.14722i	−0.895229	+	0.325837i
$163$	−3.81908	+	6.61484i	−0.299133	+	0.518114i	−0.975938	−	0.218049i	$-0.930031\pi$
$163$	−3.81908	+	6.61484i	−0.299133	+	0.518114i	0.676805	+	0.736163i	$0.263364\pi$
$164$	−0.411474			−0.0321307
$165$	−0.701867	−	1.92836i	−0.0546402	−	0.150123i
$166$	3.68004			0.285627
$167$	−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
$170$	−6.61721	+	11.4613i	−0.507517	+	0.879045i
$171$	−1.13816	−	6.45480i	−0.0870369	−	0.493611i
$172$	0.113341	+	0.196312i	0.00864215	+	0.0149687i
$173$	10.5346	+	18.2465i	0.800932	+	1.38725i	0.919003	+	0.394250i	$0.128995\pi$
$173$	10.5346	+	18.2465i	0.800932	+	1.38725i	−0.118071	+	0.993005i	$0.537671\pi$
$174$	7.00846	+	19.2556i	0.531310	+	1.45976i
$175$		0			0
$176$	0.841367	+	1.45729i	0.0634204	+	0.109847i
$177$	1.25624	+	0.221510i	0.0944251	+	0.0166497i
$178$	10.9317			0.819366
$179$	2.56031	+	4.43458i	0.191366	+	0.331456i	0.945703	−	0.325031i	$-0.105375\pi$
$179$	2.56031	+	4.43458i	0.191366	+	0.331456i	−0.754337	+	0.656487i	$0.772041\pi$
$180$	−0.243756	−	1.38241i	−0.0181685	−	0.103039i
$181$	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
$184$	0.312214			0.0230168
$185$	−9.72328	+	16.8412i	−0.714870	+	1.23819i
$186$	6.12970	+	16.8412i	0.449451	+	1.23486i
$187$	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	0.997215	+	0.0745858i	$0.0237635\pi$
$191$	7.78359	+	13.4816i	0.563200	+	0.975492i	−0.434014	+	0.900906i	$0.642903\pi$
$192$	5.09240	+	13.9912i	0.367512	+	1.00973i
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	−0.954028	−	0.299716i	$-0.903108\pi$
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	0.736576	+	0.676355i	$0.236441\pi$
$194$	18.3286			1.31592
$195$	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	$0.144339\pi$
$198$	1.77719	+	0.646844i	0.126299	+	0.0459692i
$199$	1.52094	+	2.63435i	0.107817	+	0.186744i	0.914886	−	0.403713i	$-0.132281\pi$
$199$	1.52094	+	2.63435i	0.107817	+	0.186744i	−0.807069	+	0.590458i	$0.798947\pi$
$200$	−4.15476			−0.293786
$201$	16.4402	+	2.89884i	1.15960	+	0.204469i
$202$	−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
$206$	2.04916	+	3.54925i	0.142772	+	0.247288i
$207$	0.243756	−	0.204535i	0.0169422	−	0.0142162i
$208$	−10.4704	+	18.1353i	−0.725994	+	1.25746i
$209$	−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	$0.773226\pi$
$212$	0.132474			0.00909837
$213$	7.84002	+	21.5403i	0.537189	+	1.47592i
$214$	−8.78106			−0.600261
$215$	1.55303	−	2.68993i	0.105916	−	0.183452i
$216$	13.2460	+	7.64760i	0.901278	+	0.520353i
$217$		0			0
$218$	−7.16637	+	12.4125i	−0.485368	+	0.840682i
$219$	11.4324	−	13.6246i	0.772531	−	0.920667i
$220$	−0.109470	+	0.189608i	−0.00738049	+	0.0127834i
$221$	−11.2947	+	19.5630i	−0.759766	+	1.31595i
$222$	−6.12970	−	16.8412i	−0.411399	−	1.13031i
$223$	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
$226$	−3.48751	+	6.04055i	−0.231986	+	0.401811i
$227$	2.89393			0.192077			0.0960385	−	0.995378i	$-0.469383\pi$
$227$	2.89393			0.192077			0.0960385	+	0.995378i	$0.469383\pi$
$228$	−0.449493	+	0.535685i	−0.0297684	+	0.0354766i
$229$	−9.16756			−0.605809			−0.302905	−	0.953021i	$-0.597956\pi$
$229$	−9.16756			−0.605809			−0.302905	+	0.953021i	$0.597956\pi$
$230$	−0.180922	−	0.313366i	−0.0119297	−	0.0206628i
$231$		0			0
$232$	12.9238	−	22.3847i	0.848489	−	1.46963i
$233$	−6.63563	+	11.4932i	−0.434715	+	0.752948i	−0.997272	−	0.0738103i	$-0.976484\pi$
$233$	−6.63563	+	11.4932i	−0.434715	+	0.752948i	0.562558	+	0.826758i	$0.309817\pi$
$234$	4.08693	+	23.1782i	0.267171	+	1.51520i
$235$	6.75150	+	11.6939i	0.440419	+	0.762828i
$236$	−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	$0.933145\pi$
$240$	10.1382	−	12.0822i	0.654415	−	0.779902i
$241$	8.95811			0.577043			0.288521	−	0.957473i	$-0.406836\pi$
$241$	8.95811			0.577043			0.288521	+	0.957473i	$0.406836\pi$
$242$	7.26264	+	12.5793i	0.466860	+	0.808626i
$243$	15.3516	−	2.70691i	0.984808	−	0.173648i
$244$	0.177052			0.0113346
$245$		0			0
$246$	−5.11721	−	0.902302i	−0.326261	−	0.0575287i
$247$	−12.7219			−0.809477
$248$	11.3033	−	19.5780i	0.717763	−	1.24320i
$249$	−4.65910	−	0.821525i	−0.295258	−	0.0520620i
$250$	−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
$255$	10.9363	−	13.0334i	0.684857	−	0.816181i
$256$	2.19800	−	3.80704i	0.137375	−	0.237940i
$257$	−10.8520			−0.676932			−0.338466	−	0.940979i	$-0.609908\pi$
$257$	−10.8520			−0.676932			−0.338466	+	0.940979i	$0.609908\pi$
$258$	0.979055	+	2.68993i	0.0609533	+	0.167468i
$259$		0			0
$260$	−2.72462			−0.168974
$261$	−4.57444	−	25.9430i	−0.283151	−	1.60583i
$262$	7.65451	+	13.2580i	0.472897	+	0.819082i
$263$	26.0874			1.60862			0.804309	−	0.594211i	$-0.202536\pi$
$263$	26.0874			1.60862			0.804309	+	0.594211i	$0.202536\pi$
$264$	−0.815923	−	2.24173i	−0.0502166	−	0.137969i
$265$	−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
$269$	−3.81655	−	6.61046i	−0.232699	−	0.403047i	0.725902	−	0.687798i	$-0.241422\pi$
$269$	−3.81655	−	6.61046i	−0.232699	−	0.403047i	−0.958602	+	0.284751i	$0.908089\pi$
$270$		−	17.7265i		−	1.07880i
$271$	1.70187	−	2.94772i	0.103381	−	0.179061i	−0.809695	−	0.586852i	$-0.800367\pi$
$271$	1.70187	−	2.94772i	0.103381	−	0.179061i	0.913076	+	0.407790i	$0.133701\pi$
$272$	−6.97565	+	12.0822i	−0.422961	+	0.732590i
$273$		0			0
$274$	3.85638	+	6.67945i	0.232973	+	0.403520i
$275$	0.660444			0.0398263
$276$	−0.0334331	−	0.00589515i	−0.00201243	−	0.000354846i
$277$	−5.72193			−0.343798			−0.171899	−	0.985115i	$-0.554990\pi$
$277$	−5.72193			−0.343798			−0.171899	+	0.985115i	$0.554990\pi$
$278$	−0.622426	+	1.07807i	−0.0373306	+	0.0646585i
$279$	−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	$0.845417\pi$
$282$	−12.2554	−	2.16095i	−0.729796	−	0.128683i
$283$	2.28564	−	3.95885i	0.135867	−	0.235329i	−0.790061	−	0.613028i	$-0.789951\pi$
$283$	2.28564	−	3.95885i	0.135867	−	0.235329i	0.925929	+	0.377699i	$0.123285\pi$
$284$	1.22281	−	2.11797i	0.0725605	−	0.125678i
$285$	9.43629	+	1.66387i	0.558958	+	0.0985593i
$286$	1.83544	−	3.17907i	0.108532	−	0.187982i
$287$		0			0
$288$	−0.542766	−	3.07818i	−0.0319828	−	0.181384i
$289$	0.975185	−	1.68907i	0.0573638	−	0.0993571i
$290$	−29.9564			−1.75910
$291$	−23.2049	−	4.09164i	−1.36029	−	0.239856i
$292$	−1.89756			−0.111046
$293$	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
$296$	−11.3033	+	19.5780i	−0.656994	+	1.13795i
$297$	−2.10560	−	1.21567i	−0.122179	−	0.0705403i
$298$	−5.87733	−	10.1798i	−0.340464	−	0.589702i
$299$	−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
$303$	5.67159	+	15.5826i	0.325824	+	0.895195i
$304$	−7.85710			−0.450635
$305$	−1.21301	−	2.10100i	−0.0694568	−	0.120303i
$306$	2.72281	+	15.4418i	0.155653	+	0.882751i
$307$	−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
$310$	−26.2003			−1.48808
$311$	−10.9927	+	19.0400i	−0.623340	+	1.07966i	0.365519	+	0.930804i	$0.380892\pi$
$311$	−10.9927	+	19.0400i	−0.623340	+	1.07966i	−0.988859	+	0.148853i	$0.952442\pi$
$312$	19.0829	−	22.7421i	1.08036	−	1.28752i
$313$	−6.94491	−	12.0289i	−0.392549	−	0.679915i	0.600236	−	0.799823i	$-0.295073\pi$
$313$	−6.94491	−	12.0289i	−0.392549	−	0.679915i	−0.992785	+	0.119908i	$0.961740\pi$
$314$	−6.63404			−0.374380
$315$		0			0
$316$	2.33544			0.131379
$317$	3.09105	+	5.35386i	0.173611	+	0.300703i	0.939680	−	0.342056i	$-0.111123\pi$
$317$	3.09105	+	5.35386i	0.173611	+	0.300703i	−0.766069	+	0.642759i	$0.777790\pi$
$318$	1.64749	+	0.290497i	0.0923866	+	0.0162903i
$319$	−2.05438	+	3.55829i	−0.115023	+	0.199226i
$320$	−21.7665			−1.21678
$321$	11.1172	+	1.96026i	0.620502	+	0.109411i
$322$		0			0
$323$	−8.47565			−0.471598
$324$	−1.27403	−	1.06904i	−0.0707796	−	0.0593912i
$325$	4.10947	+	7.11781i	0.227952	+	0.394825i
$326$	10.2909			0.569958
$327$	11.8439	−	14.1150i	0.654969	−	0.780561i
$328$	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	0.680041	−	0.733174i	$-0.261962\pi$
$331$	−5.36571	−	9.29369i	−0.294926	−	0.510827i	−0.974968	+	0.222346i	$0.928628\pi$
$332$	0.252374	+	0.437124i	0.0138508	+	0.0239903i
$333$	4.00088	+	22.6901i	0.219247	+	1.24341i
$334$	−3.80974	+	6.59867i	−0.208460	+	0.361063i
$335$	−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	$0.664289\pi$
$338$	28.1676			1.53211
$339$	5.76382	−	6.86906i	0.313048	−	0.373076i
$340$	−1.81521			−0.0984434
$341$	−1.79679	+	3.11213i	−0.0973016	+	0.168531i
$342$	−6.76470	+	5.67626i	−0.365793	+	0.306937i
$343$		0			0
$344$	1.80541	−	3.12706i	0.0973410	−	0.168600i
$345$	0.159100	+	0.437124i	0.00856567	+	0.0235340i
$346$	14.1932	−	24.5834i	0.763034	−	1.32161i
$347$	10.2062	−	17.6777i	0.547898	−	0.948987i	−0.450521	−	0.892766i	$-0.648762\pi$
$347$	10.2062	−	17.6777i	0.547898	−	0.948987i	0.998418	−	0.0562207i	$-0.0179050\pi$
$348$	−1.80659	+	2.15301i	−0.0968434	+	0.115413i
$349$	−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
$352$	−0.243756	+	0.422197i	−0.0129922	+	0.0225032i
$353$	−10.0223			−0.533433			−0.266716	−	0.963775i	$-0.585939\pi$
$353$	−10.0223			−0.533433			−0.266716	+	0.963775i	$0.585939\pi$
$354$	−0.587811	−	1.61500i	−0.0312418	−	0.0858361i
$355$	−33.5107			−1.77857
$356$	0.749686	+	1.29849i	0.0397333	+	0.0688200i
$357$		0			0
$358$	3.44949	−	5.97470i	0.182311	−	0.315773i
$359$	−4.74035	+	8.21053i	−0.250186	+	0.433335i	−0.963577	−	0.267431i	$-0.913825\pi$
$359$	−4.74035	+	8.21053i	−0.250186	+	0.433335i	0.713391	+	0.700766i	$0.247159\pi$
$360$	−17.1288	+	14.3728i	−0.902768	+	0.757512i
$361$	7.11334	+	12.3207i	0.374386	+	0.648456i
$362$	−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
$366$	2.20187	+	0.388249i	0.115093	+	0.0202941i
$367$	−16.1334			−0.842157			−0.421079	−	0.907024i	$-0.638348\pi$
$367$	−16.1334			−0.842157			−0.421079	+	0.907024i	$0.638348\pi$
$368$	−0.190722	−	0.330341i	−0.00994209	−	0.0172202i
$369$	6.27719	+	2.28471i	0.326777	+	0.118937i
$370$	26.2003			1.36209
$371$		0			0
$372$	−1.58007	+	1.88305i	−0.0819228	+	0.0976318i
$373$	14.0496			0.727462			0.363731	−	0.931504i	$-0.381503\pi$
$373$	14.0496			0.727462			0.363731	+	0.931504i	$0.381503\pi$
$374$	1.22281	−	2.11797i	0.0632301	−	0.109518i
$375$	5.38279	+	14.7891i	0.277966	+	0.763705i
$376$	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
$381$	−5.26171	−	14.4564i	−0.269565	−	0.740625i
$382$	10.4868	−	18.1637i	0.536551	−	0.929334i
$383$	32.0205			1.63617			0.818086	−	0.575095i	$-0.195035\pi$
$383$	32.0205			1.63617			0.818086	+	0.575095i	$0.195035\pi$
$384$	10.5744	−	12.6021i	0.539625	−	0.643100i
$385$		0			0
$386$	8.14022			0.414326
$387$	−0.639033	−	3.62414i	−0.0324839	−	0.184225i
$388$	1.25696	+	2.17712i	0.0638124	+	0.110526i
$389$	−30.0428			−1.52323			−0.761616	−	0.648029i	$-0.775594\pi$
$389$	−30.0428			−1.52323			−0.761616	+	0.648029i	$0.775594\pi$
$390$	−33.8842	−	5.97470i	−1.71579	−	0.302541i
$391$	−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
$395$	−16.0005	−	27.7136i	−0.805071	−	1.39442i
$396$	0.0450442	+	0.255459i	0.00226356	+	0.0128373i
$397$	−6.15998	+	10.6694i	−0.309160	+	0.535482i	−0.978179	−	0.207764i	$-0.933381\pi$
$397$	−6.15998	+	10.6694i	−0.309160	+	0.535482i	0.669019	+	0.743246i	$0.266715\pi$
$398$	2.04916	−	3.54925i	0.102715	−	0.177908i
$399$		0			0
$400$	2.53802	+	4.39598i	0.126901	+	0.219799i
$401$	20.9760			1.04749			0.523745	−	0.851875i	$-0.324535\pi$
$401$	20.9760			1.04749			0.523745	+	0.851875i	$0.324535\pi$
$402$	−7.69253	−	21.1351i	−0.383669	−	1.05412i
$403$	−44.7205			−2.22769
$404$	0.884600	−	1.53217i	0.0440105	−	0.0762284i
$405$	−3.95723	+	22.4426i	−0.196637	+	1.11518i
$406$		0			0
$407$	1.79679	−	3.11213i	0.0890635	−	0.154263i
$408$	12.7135	−	15.1513i	0.629411	−	0.750103i
$409$	12.8307	−	22.2234i	0.634437	−	1.09888i	−0.352197	−	0.935926i	$-0.614565\pi$
$409$	12.8307	−	22.2234i	0.634437	−	1.09888i	0.986634	−	0.162951i	$-0.0521012\pi$
$410$	3.79813	−	6.57856i	0.187576	−	0.324892i
$411$	−3.39124	−	9.31737i	−0.167278	−	0.459592i
$412$	−0.281059	+	0.486809i	−0.0138468	+	0.0239833i
$413$		0			0
$414$	−0.402856	−	0.146628i	−0.0197993	−	0.00720635i
$415$	3.45811	−	5.98962i	0.169752	−	0.294019i
$416$	−6.06687			−0.297453
$417$	1.02869	−	1.22594i	0.0503749	−	0.0600345i
$418$	1.37733			0.0673672
$419$	−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	$0.270147\pi$
$422$	3.67365	−	6.36295i	0.178830	−	0.309743i
$423$	15.0334	+	5.47172i	0.730951	+	0.266044i
$424$	−1.05509	−	1.82747i	−0.0512398	−	0.0887500i
$425$	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
$429$	−3.03343	+	3.61510i	−0.146456	+	0.174539i
$430$	−4.18479			−0.201809
$431$	−8.86349	−	15.3520i	−0.426939	−	0.739481i	0.569660	−	0.821881i	$-0.307075\pi$
$431$	−8.86349	−	15.3520i	−0.426939	−	0.739481i	−0.996599	+	0.0823997i	$0.973742\pi$
$432$		−	18.6867i		−	0.899067i
$433$	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
$436$	−1.96585			−0.0941472
$437$	0.115867	−	0.200688i	0.00554267	−	0.00960019i
$438$	−23.5985	−	4.16106i	−1.12758	−	0.198823i
$439$	14.9277	+	25.8555i	0.712459	+	1.23401i	0.963931	+	0.266151i	$0.0857518\pi$
$439$	14.9277	+	25.8555i	0.712459	+	1.23401i	−0.251473	+	0.967864i	$0.580915\pi$
$440$	3.48751			0.166261
$441$		0			0
$442$	30.4347			1.44763
$443$	−5.33275	−	9.23659i	−0.253367	−	0.438844i	0.711084	−	0.703107i	$-0.248205\pi$
$443$	−5.33275	−	9.23659i	−0.253367	−	0.438844i	−0.964451	+	0.264263i	$0.914871\pi$
$444$	1.58007	−	1.88305i	0.0749868	−	0.0893658i
$445$	10.2724	−	17.7924i	0.486960	−	0.843440i
$446$	−19.1215			−0.905432
$447$	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	$0.473272\pi$
$450$	5.36097	+	1.95123i	0.252718	+	0.0919820i
$451$	−0.520945	−	0.902302i	−0.0245303	−	0.0424878i
$452$	−0.956680			−0.0449985
$453$	10.9161	+	29.9916i	0.512881	+	1.40913i
$454$	−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	0.801283	−	0.598285i	$-0.204151\pi$
$457$	−2.51161	−	4.35024i	−0.117488	−	0.203496i	−0.918772	+	0.394789i	$0.870818\pi$
$458$	6.17571	+	10.6966i	0.288572	+	0.499821i
$459$		−	20.1579i		−	0.940889i
$460$	0.0248149	−	0.0429807i	0.00115700	−	0.00200399i
$461$	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	$0.726027\pi$
$464$	−31.5790			−1.46602
$465$	33.1707	+	5.84889i	1.53825	+	0.271236i
$466$	17.8803			0.828290
$467$	−1.68433	+	2.91734i	−0.0779413	+	0.134998i	−0.902362	−	0.430980i	$-0.858168\pi$
$467$	−1.68433	+	2.91734i	−0.0779413	+	0.134998i	0.824420	+	0.565978i	$0.191501\pi$
$468$	−2.47288	+	2.07499i	−0.114309	+	0.0959165i
$469$		0			0
$470$	9.09627	−	15.7552i	0.419579	−	0.726733i
$471$	8.39899	+	1.48097i	0.387005	+	0.0682394i
$472$	−1.08394	+	1.87744i	−0.0498924	+	0.0864162i
$473$	−0.286989	+	0.497079i	−0.0131958	+	0.0228557i
$474$	29.0442	+	5.12127i	1.33404	+	0.235228i
$475$	−1.54189	+	2.67063i	−0.0707467	+	0.122537i
$476$		0			0
$477$	−2.02094	−	0.735564i	−0.0925327	−	0.0336791i
$478$	−6.42468	+	11.1279i	−0.293858	+	0.508977i
$479$	36.7665			1.67990			0.839952	−	0.542660i	$-0.182583\pi$
$479$	36.7665			1.67990			0.839952	+	0.542660i	$0.182583\pi$
$480$	4.50000	+	0.793471i	0.205396	+	0.0362168i
$481$	44.7205			2.03908
$482$	−6.03462	−	10.4523i	−0.274869	−	0.476087i
$483$		0			0
$484$	−0.996130	+	1.72535i	−0.0452786	+	0.0784249i
$485$	17.2233	−	29.8316i	0.782069	−	1.35458i
$486$	−13.5000	−	16.0887i	−0.612372	−	0.729797i
$487$	18.7087	+	32.4045i	0.847773	+	1.46839i	0.883191	+	0.469014i	$0.155391\pi$
$487$	18.7087	+	32.4045i	0.847773	+	1.46839i	−0.0354172	+	0.999373i	$0.511276\pi$
$488$	−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	$0.627779\pi$
$492$	−0.243756	−	0.669713i	−0.0109894	−	0.0301930i
$493$	−34.0651			−1.53422
$494$	8.57011	+	14.8439i	0.385587	+	0.667857i
$495$	2.72281	−	2.28471i	0.122381	−	0.102690i
$496$	−27.6195			−1.24015
$497$		0			0
$498$	2.18004	+	5.98962i	0.0976901	+	0.268401i
$499$	33.7452			1.51064			0.755320	−	0.655356i	$-0.227481\pi$
$499$	33.7452			1.51064			0.755320	+	0.655356i	$0.227481\pi$
$500$	0.839556	−	1.45415i	0.0375461	−	0.0650317i
$501$	6.29638	−	7.50373i	0.281301	−	0.335242i
$502$	−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
$507$	−35.6614	−	6.28806i	−1.58378	−	0.279263i
$508$	−0.820670	+	1.42144i	−0.0364114	+	0.0630663i
$509$	7.93851			0.351868			0.175934	−	0.984402i	$-0.443705\pi$
$509$	7.93851			0.351868			0.175934	+	0.984402i	$0.443705\pi$
$510$	−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
$514$	7.31046	+	12.6621i	0.322451	+	0.558501i
$515$	7.70233			0.339405
$516$	−0.252374	+	0.300767i	−0.0111101	+	0.0132405i
$517$	−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
$521$	−7.33750	−	12.7089i	−0.321462	−	0.556788i	0.659328	−	0.751855i	$-0.270841\pi$
$521$	−7.33750	−	12.7089i	−0.321462	−	0.556788i	−0.980790	+	0.195067i	$0.937507\pi$
$522$	−27.1885	+	22.8139i	−1.19001	+	0.998536i
$523$	14.1716	−	24.5459i	0.619680	−	1.07332i	−0.369864	−	0.929086i	$-0.620596\pi$
$523$	14.1716	−	24.5459i	0.619680	−	1.07332i	0.989544	−	0.144232i	$-0.0460711\pi$
$524$	−1.04988	+	1.81844i	−0.0458641	+	0.0794390i
$525$		0			0
$526$	−17.5737	−	30.4386i	−0.766251	−	1.32719i
$527$	−29.7939			−1.29784
$528$	−1.87346	+	2.23270i	−0.0815317	+	0.0971657i
$529$	−22.9887			−0.999511
$530$	−1.22281	+	2.11797i	−0.0531155	+	0.0919988i
$531$	0.383666	+	2.17588i	0.0166497	+	0.0944251i
$532$		0			0
$533$	6.48293	−	11.2288i	0.280807	−	0.486371i
$534$	6.47590	+	17.7924i	0.280240	+	0.769952i
$535$	−8.25150	+	14.2920i	−0.356743	+	0.617898i
$536$	−14.1853	+	24.5696i	−0.612710	+	1.06124i
$537$	−5.70099	+	6.79417i	−0.246016	+	0.293190i
$538$	−5.14203	+	8.90625i	−0.221688	+	0.383976i
$539$		0			0
$540$	2.10560	−	1.21567i	0.0906106	−	0.0523141i
$541$	−5.64290	+	9.77380i	−0.242607	+	0.420208i	−0.961456	−	0.274958i	$-0.911336\pi$
$541$	−5.64290	+	9.77380i	−0.242607	+	0.420208i	0.718849	+	0.695166i	$0.244669\pi$
$542$	−4.58584			−0.196979
$543$	0.189540	+	0.520758i	0.00813395	+	0.0223478i
$544$	−4.04189			−0.173295
$545$	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	$-0.0482812\pi$
$548$	−0.528934	+	0.916140i	−0.0225949	+	0.0391356i
$549$	−2.70099	−	0.983080i	−0.115275	−	0.0419568i
$550$	−0.444907	−	0.770602i	−0.0189709	−	0.0328586i
$551$	−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
$555$	−33.1707	−	5.84889i	−1.40802	−	0.248272i
$556$	−0.170741			−0.00724105
$557$	0.387841	+	0.671761i	0.0164334	+	0.0284634i	0.874125	−	0.485701i	$-0.161436\pi$
$557$	0.387841	+	0.671761i	0.0164334	+	0.0284634i	−0.857692	+	0.514164i	$0.828102\pi$
$558$	−23.7795	+	19.9533i	−1.00667	+	0.844692i
$559$	−7.14290			−0.302113
$560$		0			0
$561$	−2.02094	+	2.40847i	−0.0853243	+	0.101686i
$562$	38.2327			1.61275
$563$	12.4761	−	21.6093i	0.525806	−	0.910722i	−0.473742	−	0.880663i	$-0.657097\pi$
$563$	12.4761	−	21.6093i	0.525806	−	0.910722i	0.999548	−	0.0300588i	$-0.00956944\pi$
$564$	−0.583778	−	1.60392i	−0.0245815	−	0.0675371i
$565$	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	0.999732	+	0.0231391i	$0.00736608\pi$
$569$	12.4017	+	21.4803i	0.519905	+	0.900502i	−0.479827	+	0.877363i	$0.659301\pi$
$570$	−4.41534	−	12.1311i	−0.184938	−	0.508114i
$571$	−4.39827	+	7.61803i	−0.184062	+	0.318805i	−0.943260	−	0.332055i	$-0.892258\pi$
$571$	−4.39827	+	7.61803i	−0.184062	+	0.318805i	0.759198	+	0.650860i	$0.225591\pi$
$572$	0.503490			0.0210520
$573$	−17.3316	+	20.6550i	−0.724037	+	0.862873i
$574$		0			0
$575$	−0.149711			−0.00624336
$576$	−19.7554	+	16.5767i	−0.823140	+	0.690697i
$577$	−6.43717	−	11.1495i	−0.267983	−	0.464160i	0.700358	−	0.713792i	$-0.253024\pi$
$577$	−6.43717	−	11.1495i	−0.267983	−	0.464160i	−0.968341	+	0.249632i	$0.919690\pi$
$578$	−2.62773			−0.109299
$579$	−10.3059	−	1.81720i	−0.428298	−	0.0755204i
$580$	−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
$584$	15.1131	+	26.1766i	0.625384	+	1.08320i
$585$	41.5651	+	15.1285i	1.71851	+	0.625485i
$586$	2.91534	−	5.04952i	0.120432	−	0.208594i
$587$	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
$590$	2.51249			0.103438
$591$	14.9488	+	41.0714i	0.614911	+	1.68945i
$592$	27.6195			1.13515
$593$	1.88026	−	3.25671i	0.0772131	−	0.133737i	−0.824833	−	0.565376i	$-0.808731\pi$
$593$	1.88026	−	3.25671i	0.0772131	−	0.133737i	0.902047	+	0.431639i	$0.142064\pi$
$594$			3.27573i			0.134405i
$595$		0			0
$596$	0.806123	−	1.39625i	0.0330201	−	0.0571924i
$597$	−3.38666	+	4.03606i	−0.138607	+	0.165185i
$598$	−0.416060	+	0.720637i	−0.0170139	+	0.0294690i
$599$	1.84524	−	3.19604i	0.0753943	−	0.130587i	−0.825863	−	0.563870i	$-0.809312\pi$
$599$	1.84524	−	3.19604i	0.0753943	−	0.130587i	0.901258	+	0.433283i	$0.142645\pi$
$600$	−2.46127	−	6.76227i	−0.100481	−	0.276069i
$601$	−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
$604$	1.70258	−	2.94896i	0.0692771	−	0.119991i
$605$	27.2986			1.10985
$606$	14.3610	−	17.1147i	0.583374	−	0.695239i
$607$	−24.3946			−0.990145			−0.495072	−	0.868852i	$-0.664858\pi$
$607$	−24.3946			−0.990145			−0.495072	+	0.868852i	$0.664858\pi$
$608$	−1.13816	−	1.97134i	−0.0461583	−	0.0799485i
$609$		0			0
$610$	−1.63429	+	2.83067i	−0.0661703	+	0.114610i
$611$	15.5262	−	26.8921i	0.628121	−	1.08794i
$612$	−1.64749	+	1.38241i	−0.0665958	+	0.0558805i
$613$	−21.0107	−	36.3917i	−0.848616	−	1.46985i	−0.882444	−	0.470418i	$-0.844103\pi$
$613$	−21.0107	−	36.3917i	−0.848616	−	1.46985i	0.0338284	−	0.999428i	$-0.489230\pi$
$614$	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	$-0.550545\pi$
$618$	−4.56283	+	5.43777i	−0.183544	+	0.218739i
$619$	27.2094			1.09364			0.546820	−	0.837250i	$-0.315838\pi$
$619$	27.2094			1.09364			0.546820	+	0.837250i	$0.315838\pi$
$620$	−1.79679	−	3.11213i	−0.0721608	−	0.124986i
$621$	0.477301	+	0.275570i	0.0191534	+	0.0110582i
$622$	29.6209			1.18769
$623$		0			0
$624$	−35.7196	−	6.29833i	−1.42993	−	0.252135i
$625$	−30.0651			−1.20260
$626$	−9.35685	+	16.2065i	−0.373975	+	0.647743i
$627$	−1.74376	−	0.307471i	−0.0696389	−	0.0122792i
$628$	−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
$633$	−6.07145	+	7.23567i	−0.241319	+	0.287592i
$634$	4.16456	−	7.21324i	0.165396	−	0.286474i
$635$	22.4902			0.892496
$636$	0.0784773	+	0.215615i	0.00311183	+	0.00854968i
$637$		0			0
$638$	5.53571			0.219161
$639$	−30.4145	+	25.5208i	−1.20318	+	1.00959i
$640$	12.0248	+	20.8276i	0.475323	+	0.823283i
$641$	−0.279000			−0.0110198			−0.00550991	−	0.999985i	$-0.501754\pi$
$641$	−0.279000			−0.0110198			−0.00550991	+	0.999985i	$0.501754\pi$
$642$	−5.20187	−	14.2920i	−0.205301	−	0.564061i
$643$	−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
$647$	11.2285	+	19.4483i	0.441438	+	0.764592i	0.997796	−	0.0663498i	$-0.0211353\pi$
$647$	11.2285	+	19.4483i	0.441438	+	0.764592i	−0.556359	+	0.830942i	$0.687802\pi$
$648$	−4.60030	+	26.0896i	−0.180717	+	1.02490i
$649$	0.172304	−	0.298439i	0.00676352	−	0.0117148i
$650$	5.53667	−	9.58980i	0.217166	−	0.376143i
$651$		0			0
$652$	0.705737	+	1.22237i	0.0276388	+	0.0478718i
$653$	−50.5313			−1.97744			−0.988721	−	0.149771i	$-0.952146\pi$
$653$	−50.5313			−1.97744			−0.988721	+	0.149771i	$0.952146\pi$
$654$	−24.4479	−	4.31082i	−0.955989	−	0.168567i
$655$	28.7716			1.12420
$656$	4.00387	−	6.93491i	0.156325	−	0.270763i
$657$	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	$0.150089\pi$
$660$	−0.373455	−	0.0658503i	−0.0145367	−	0.00256322i
$661$	−17.3050	+	29.9731i	−0.673086	+	1.16582i	0.303938	+	0.952692i	$0.401698\pi$
$661$	−17.3050	+	29.9731i	−0.673086	+	1.16582i	−0.977024	+	0.213128i	$0.931635\pi$
$662$	−7.22921	+	12.5214i	−0.280971	+	0.486656i
$663$	−38.5317	−	6.79417i	−1.49645	−	0.263864i
$664$	4.02007	−	6.96296i	0.156009	−	0.270215i
$665$		0			0
$666$	23.7795	−	19.9533i	0.921436	−	0.773176i
$667$	0.465690	−	0.806598i	0.0180316	−	0.0312316i
$668$	−1.04507			−0.0404351
$669$	24.2087	+	4.26865i	0.935964	+	0.165036i
$670$	32.8803			1.27028
$671$	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	$0.269763\pi$
$674$	12.5262	−	21.6959i	0.482490	−	0.835697i
$675$	−6.35163	−	3.66712i	−0.244474	−	0.141147i
$676$	1.93170	+	3.34581i	0.0742963	+	0.128685i
$677$	−21.8790	−	37.8955i	−0.840877	−	1.45644i	−0.889154	−	0.457608i	$-0.848706\pi$
$677$	−21.8790	−	37.8955i	−0.840877	−	1.45644i	0.0482766	−	0.998834i	$-0.484627\pi$
$678$	−11.8976	−	2.09786i	−0.456923	−	0.0805678i
$679$		0			0
$680$	14.4572	+	25.0407i	0.554410	+	0.960266i
$681$	1.71436	+	4.71015i	0.0656942	+	0.180493i
$682$	4.84161			0.185395
$683$	−14.1206	−	24.4576i	−0.540310	−	0.935845i	−0.998886	−	0.0471895i	$-0.984974\pi$
$683$	−14.1206	−	24.4576i	−0.540310	−	0.935845i	0.458576	−	0.888655i	$-0.348360\pi$
$684$	−1.13816	−	0.414255i	−0.0435185	−	0.0158394i
$685$	14.4953			0.553835
$686$		0			0
$687$	−5.43083	−	14.9211i	−0.207199	−	0.569274i
$688$	−4.41147			−0.168186
$689$	−2.08718	+	3.61510i	−0.0795153	+	0.137725i
$690$	0.402856	−	0.480105i	0.0153365	−	0.0182773i
$691$	−14.5326	−	25.1711i	−0.552844	−	0.957555i	−0.998068	−	0.0621351i	$-0.980209\pi$
$691$	−14.5326	−	25.1711i	−0.552844	−	0.957555i	0.445223	−	0.895420i	$-0.353124\pi$
$692$	3.89344			0.148006
$693$		0			0
$694$	−27.5016			−1.04395
$695$	1.16978	+	2.02611i	0.0443722	+	0.0768549i
$696$	44.0892	+	7.77412i	1.67120	+	0.294677i
$697$	4.31908	−	7.48086i	0.163597	−	0.283358i
$698$	4.79923			0.181654
$699$	−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
$703$	8.38965	+	14.5313i	0.316422	+	0.548059i
$704$	4.02229			0.151596
$705$	−15.0334	+	17.9161i	−0.566192	+	0.674761i
$706$	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	0.985680	−	0.168626i	$-0.0539329\pi$
$709$	9.23442	+	15.9945i	0.346806	+	0.600686i	−0.638874	+	0.769311i	$0.720600\pi$
$710$	22.5744	+	39.1001i	0.847204	+	1.46740i
$711$	−35.6279	−	12.9675i	−1.33615	−	0.486320i
$712$	11.9418	−	20.6837i	0.447536	−	0.775155i
$713$	0.407299	−	0.705463i	0.0152535	−	0.0264198i
$714$		0			0
$715$	−3.44949	−	5.97470i	−0.129004	−	0.223441i
$716$	0.946251			0.0353631
$717$	10.6181	−	12.6541i	0.396540	−	0.472578i
$718$	12.7733			0.476696
$719$	−16.8885	+	29.2517i	−0.629834	+	1.09090i	0.357751	+	0.933817i	$0.383544\pi$
$719$	−16.8885	+	29.2517i	−0.629834	+	1.09090i	−0.987585	+	0.157087i	$0.949790\pi$
$720$	25.6707	+	9.34337i	0.956691	+	0.348207i
$721$		0			0
$722$	9.58378	−	16.5996i	0.356671	−	0.617773i
$723$	5.30675	+	14.5802i	0.197360	+	0.542243i
$724$	0.0295627	−	0.0512040i	0.00109869	−	0.00190298i
$725$	−6.19712	+	10.7337i	−0.230155	+	0.398641i
$726$	−16.1716	+	19.2725i	−0.600184	+	0.715271i
$727$	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
$730$	17.5155	−	30.3377i	0.648277	−	1.12285i
$731$	−4.75877			−0.176009
$732$	0.104885	+	0.288169i	0.00387665	+	0.0106510i
$733$	13.6364			0.503672			0.251836	−	0.967770i	$-0.418966\pi$
$733$	13.6364			0.503672			0.251836	+	0.967770i	$0.418966\pi$
$734$	10.8682	+	18.8243i	0.401154	+	0.694819i
$735$		0			0
$736$	0.0552549	−	0.0957044i	0.00203672	−	0.00352771i
$737$	2.25490	−	3.90560i	0.0830603	−	0.143865i
$738$	−1.56283	−	8.86327i	−0.0575287	−	0.326261i
$739$	16.0209	+	27.7491i	0.589340	+	1.02077i	0.994319	+	0.106441i	$0.0339455\pi$
$739$	16.0209	+	27.7491i	0.589340	+	1.02077i	−0.404979	+	0.914326i	$0.632721\pi$
$740$	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	$-0.379184\pi$
$744$	38.5611	+	6.79936i	1.41372	+	0.249277i
$745$	−22.0915			−0.809371
$746$	−9.46451	−	16.3930i	−0.346520	−	0.600191i
$747$	−1.42292	−	8.06980i	−0.0520620	−	0.295258i
$748$	0.335437			0.0122648
$749$		0			0
$750$	13.6297	−	16.2432i	0.497686	−	0.593119i
$751$	26.1165			0.953004			0.476502	−	0.879173i	$-0.341904\pi$
$751$	26.1165			0.953004			0.476502	+	0.879173i	$0.341904\pi$
$752$	9.58899	−	16.6086i	0.349675	−	0.605654i
$753$	14.8089	+	40.6870i	0.539665	+	1.48272i
$754$	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
$759$	−0.0294005	−	0.0807773i	−0.00106717	−	0.00293203i
$760$	−8.14203	+	14.1024i	−0.295342	+	0.511548i
$761$	−40.7648			−1.47772			−0.738861	−	0.673858i	$-0.764636\pi$
$761$	−40.7648			−1.47772			−0.738861	+	0.673858i	$0.764636\pi$
$762$	−13.3231	+	15.8779i	−0.482645	+	0.575194i
$763$		0			0
$764$	2.87670			0.104075
$765$	27.6917	+	10.0789i	1.00119	+	0.364405i
$766$	−21.5706	−	37.3613i	−0.779377	−	1.34992i
$767$	4.28850			0.154849
$768$	7.49841	+	1.32217i	0.270575	+	0.0477098i
$769$	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
$773$	12.4513	+	21.5663i	0.447842	+	0.775686i	0.998245	−	0.0592135i	$-0.0188593\pi$
$773$	12.4513	+	21.5663i	0.447842	+	0.775686i	−0.550403	+	0.834899i	$0.685526\pi$
$774$	−3.79813	+	3.18701i	−0.136521	+	0.114555i
$775$	−5.42009	+	9.38788i	−0.194695	+	0.337222i
$776$	20.0221	−	34.6793i	0.718752	−	1.24492i
$777$		0			0
$778$	20.2383	+	35.0538i	0.725578	+	1.25674i
$779$	4.86484			0.174301
$780$	−1.61406	−	4.43458i	−0.0577925	−	0.158784i
$781$	6.19253			0.221586
$782$	−0.277189	+	0.480105i	−0.00991225	+	0.0171685i
$783$	39.5148	−	22.8139i	1.41214	−	0.815301i
$784$		0			0
$785$	−6.23396	+	10.7975i	−0.222499	+	0.385380i
$786$	−17.0442	+	20.3124i	−0.607945	+	0.724521i
$787$	−15.3525	+	26.5913i	−0.547258	+	0.947879i	0.451203	+	0.892421i	$0.350995\pi$
$787$	−15.3525	+	26.5913i	−0.547258	+	0.947879i	−0.998461	+	0.0554572i	$0.982338\pi$
$788$	2.33157	−	4.03839i	0.0830586	−	0.143862i
$789$	15.4541	+	42.4597i	0.550180	+	1.51161i
$790$	−21.5574	+	37.3385i	−0.766977	+	1.32844i
$791$		0			0
$792$	3.16528	−	2.65598i	0.112473	−	0.0943763i
$793$	−2.78952	+	4.83158i	−0.0990586	+	0.171575i
$794$	16.5986			0.589063
$795$	2.02094	−	2.40847i	0.0716755	−	0.0854196i
$796$	0.562118			0.0199238
$797$	−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
$800$	−0.735300	+	1.27358i	−0.0259968	+	0.0450277i
$801$	−4.22684	−	23.9716i	−0.149348	−	0.846996i
$802$	−14.1304	−	24.4746i	−0.498962	−	0.864228i
$803$	−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
$807$	8.49825	−	10.1278i	0.299152	−	0.356516i
$808$	−28.1816			−0.991425
$809$	−8.49407	−	14.7122i	−0.298636	−	0.517252i	0.677188	−	0.735810i	$-0.263198\pi$
$809$	−8.49407	−	14.7122i	−0.298636	−	0.517252i	−0.975824	+	0.218558i	$0.929865\pi$
$810$	28.8516	−	10.5011i	1.01374	−	0.368972i
$811$	−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
$814$	−4.84161			−0.169699
$815$	9.67024	−	16.7494i	0.338734	−	0.586704i
$816$	−23.7973	−	4.19610i	−0.833071	−	0.146893i
$817$	−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	0.784709	−	0.619864i	$-0.212812\pi$
$821$	−4.13934	−	7.16954i	−0.144464	−	0.250219i	−0.929173	+	0.369646i	$0.879479\pi$
$822$	−8.58693	+	10.2335i	−0.299504	+	0.356935i
$823$	−27.2763	+	47.2440i	−0.950792	+	1.64682i	−0.207077	+	0.978325i	$0.566395\pi$
$823$	−27.2763	+	47.2440i	−0.950792	+	1.64682i	−0.743716	+	0.668496i	$0.766938\pi$
$824$	8.95399			0.311927
$825$	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	$0.686948\pi$
$828$	−0.0102107	−	0.0579078i	−0.000354846	−	0.00201243i
$829$	−0.176174	−	0.305143i	−0.00611879	−	0.0105981i	0.862950	−	0.505290i	$-0.168614\pi$
$829$	−0.176174	−	0.305143i	−0.00611879	−	0.0105981i	−0.869069	+	0.494692i	$0.835281\pi$
$830$	−9.31820			−0.323439
$831$	−3.38965	−	9.31299i	−0.117586	−	0.323064i
$832$	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
$836$	0.0944557	+	0.163602i	0.00326682	+	0.00565829i
$837$	34.5602	−	19.9533i	1.19458	−	0.689688i
$838$	−0.996845	+	1.72659i	−0.0344354	+	0.0596439i
$839$	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
$842$	17.6590			0.608570
$843$	−48.4043	−	8.53498i	−1.66713	−	0.293960i
$844$	1.00774			0.0346879
$845$	26.4688	−	45.8454i	0.910556	−	1.57713i
$846$	−3.74288	−	21.2269i	−0.128683	−	0.729796i
$847$		0			0
$848$	−1.28905	+	2.23270i	−0.0442661	+	0.0766711i
$849$	7.79742	+	1.37490i	0.267607	+	0.0471863i
$850$	3.68866	−	6.38895i	0.126520	−	0.219139i
$851$	−0.407299	+	0.705463i	−0.0139620	+	0.0241829i
$852$	4.17159	+	0.735564i	0.142916	+	0.0252000i
$853$	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
$856$	−9.59240	+	16.6145i	−0.327861	+	0.567873i
$857$	−16.4074			−0.560465			−0.280232	−	0.959932i	$-0.590411\pi$
$857$	−16.4074			−0.560465			−0.280232	+	0.959932i	$0.590411\pi$
$858$	6.26155	+	1.10408i	0.213766	+	0.0376926i
$859$	26.8324			0.915511			0.457756	−	0.889078i	$-0.348653\pi$
$859$	26.8324			0.915511			0.457756	+	0.889078i	$0.348653\pi$
$860$	−0.286989	−	0.497079i	−0.00978624	−	0.0169503i
$861$		0			0
$862$	−11.9418	+	20.6837i	−0.406738	+	0.704490i
$863$	−7.25284	+	12.5623i	−0.246890	+	0.427625i	−0.962661	−	0.270709i	$-0.912742\pi$
$863$	−7.25284	+	12.5623i	−0.246890	+	0.427625i	0.715772	+	0.698334i	$0.246075\pi$
$864$	4.68850	−	2.70691i	0.159506	−	0.0920909i
$865$	−26.6746	−	46.2017i	−0.906963	−	1.57091i
$866$	−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
$870$	−17.7460	−	48.7568i	−0.601647	−	1.65301i
$871$	56.1225			1.90164
$872$	15.6570	+	27.1188i	0.530214	+	0.918358i
$873$	−7.08693	−	40.1920i	−0.239856	−	1.36029i
$874$	−0.312214			−0.0105608
$875$		0			0
$876$	−1.12410	−	3.08845i	−0.0379800	−	0.104349i
$877$	18.9145			0.638696			0.319348	−	0.947637i	$-0.396536\pi$
$877$	18.9145			0.638696			0.319348	+	0.947637i	$0.396536\pi$
$878$	20.1120	−	34.8350i	0.678747	−	1.17562i
$879$	−4.81820	+	5.74211i	−0.162514	+	0.193676i
$880$	−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
$885$	−3.18092	−	0.560882i	−0.106926	−	0.0188539i
$886$	−7.18479	+	12.4444i	−0.241378	+	0.418079i
$887$	38.9600			1.30815			0.654074	−	0.756431i	$-0.273058\pi$
$887$	38.9600			1.30815			0.654074	+	0.756431i	$0.273058\pi$
$888$	−38.5611	−	6.79936i	−1.29403	−	0.228172i
$889$		0			0
$890$	−27.6800			−0.927837
$891$	0.731267	−	4.14722i	0.0244984	−	0.138937i
$892$	−1.31134	−	2.27130i	−0.0439068	−	0.0760488i
$893$	11.6509			0.389884
$894$	13.0869	−	15.5964i	0.437693	−	0.521622i
$895$	−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
$899$	−33.7195	−	58.4038i	−1.12461	−	1.94788i
$900$	0.135878	+	0.770602i	0.00452926	+	0.0256867i
$901$	−1.39053	+	2.40847i	−0.0463253	+	0.0802377i
$902$	−0.701867	+	1.21567i	−0.0233696	+	0.0404773i
$903$		0			0
$904$	7.61949	+	13.1973i	0.253420	+	0.438937i
$905$	−0.810155			−0.0269305
$906$	27.6404	−	32.9406i	0.918292	−	1.09438i
$907$	34.5276			1.14647			0.573236	−	0.819390i	$-0.305688\pi$
$907$	34.5276			1.14647			0.573236	+	0.819390i	$0.305688\pi$
$908$	0.267389	−	0.463131i	0.00887360	−	0.0153695i
$909$	−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	$0.886553\pi$
$912$	−4.65451	−	12.7882i	−0.154126	−	0.423459i
$913$	−0.639033	+	1.10684i	−0.0211489	+	0.0366310i
$914$	−3.38388	+	5.86106i	−0.111929	+	0.193867i
$915$	2.70099	−	3.21891i	0.0892920	−	0.106414i
$916$	−0.847048	+	1.46713i	−0.0279873	+	0.0484753i
$917$		0			0
$918$	−23.5201	+	13.5793i	−0.776278	+	0.448184i
$919$	4.97818	−	8.62246i	0.164215	−	0.284429i	−0.772161	−	0.635427i	$-0.780824\pi$
$919$	4.97818	−	8.62246i	0.164215	−	0.284429i	0.936376	+	0.350998i	$0.114158\pi$
$920$	−0.790555			−0.0260638
$921$	−7.33228	−	20.1453i	−0.241607	−	0.663809i
$922$	−24.8726			−0.819135
$923$	38.5317	+	66.7388i	1.26829	+	2.19674i
$924$		0			0
$925$	5.42009	−	9.38788i	0.178212	−	0.308671i
$926$	9.58899	−	16.6086i	0.315114	−	0.545793i
$927$	6.99067	−	5.86587i	0.229604	−	0.192660i
$928$	−4.57444	−	7.92317i	−0.150164	−	0.260091i
$929$	4.52300	+	7.83407i	0.148395	+	0.257028i	0.930634	−	0.365950i	$-0.119256\pi$
$929$	4.52300	+	7.83407i	0.148395	+	0.257028i	−0.782239	+	0.622978i	$0.785923\pi$
$930$	−15.5209	−	42.6434i	−0.508952	−	1.39833i
$931$		0			0
$932$	1.22621	+	2.12387i	0.0401660	+	0.0695696i
$933$	−37.5014	−	6.61251i	−1.22774	−	0.216484i
$934$	4.53857			0.148507
$935$	−2.29813	−	3.98048i	−0.0751570	−	0.130176i
$936$	48.3196	+	17.5869i	1.57938	+	0.574846i
$937$	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
$940$	2.49525			0.0813862
$941$	−29.7690	+	51.5615i	−0.970443	+	1.68086i	−0.276223	+	0.961094i	$0.589083\pi$
$941$	−29.7690	+	51.5615i	−0.970443	+	1.68086i	−0.694220	+	0.719763i	$0.744251\pi$
$942$	−3.92998	−	10.7975i	−0.128046	−	0.351802i
$943$	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	0.787172	−	0.616733i	$-0.211544\pi$
$947$	−4.32429	−	7.48989i	−0.140521	−	0.243389i	−0.927693	+	0.373344i	$0.878211\pi$
$948$	1.38350	+	3.80115i	0.0449341	+	0.123455i
$949$	29.8967	−	51.7826i	0.970487	−	1.68093i
$950$	4.15476			0.134798
$951$	−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	$0.480487\pi$
$954$	0.503155	+	2.85353i	0.0162903	+	0.0923866i
$955$	−19.7087	−	34.1365i	−0.637760	−	1.10463i
$956$	−1.76239			−0.0569998
$957$	−7.00846	−	1.23578i	−0.226551	−	0.0399471i
$958$	−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
$962$	−30.1259	−	52.1796i	−0.971298	−	1.68234i
$963$	3.39528	+	19.2556i	0.109411	+	0.620502i
$964$	0.827696	−	1.43361i	0.0266583	−	0.0461735i
$965$	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	$0.655607\pi$
$968$	31.7347			1.01999
$969$	−5.02094	−	13.7949i	−0.161296	−	0.443157i
$970$	−46.4097			−1.49013
$971$	−27.7285	+	48.0272i	−0.889850	+	1.54126i	−0.0497974	+	0.998759i	$0.515858\pi$
$971$	−27.7285	+	48.0272i	−0.889850	+	1.54126i	−0.840052	+	0.542506i	$0.817476\pi$
$972$	0.985234	−	2.70691i	0.0316014	−	0.0868241i
$973$		0			0
$974$	25.2062	−	43.6584i	0.807659	−	1.39891i
$975$	−9.15048	+	10.9051i	−0.293050	+	0.349243i
$976$	−1.72281	+	2.98400i	−0.0551458	+	0.0955154i
$977$	−28.2743	+	48.9724i	−0.904573	+	1.56677i	−0.0830847	+	0.996542i	$0.526477\pi$
$977$	−28.2743	+	48.9724i	−0.904573	+	1.56677i	−0.821489	+	0.570225i	$0.806856\pi$
$978$	6.09627	+	16.7494i	0.194937	+	0.535585i
$979$	−1.89827	+	3.28790i	−0.0606690	+	0.105082i
$980$		0			0
$981$	29.9898	+	10.9154i	0.957500	+	0.348502i
$982$	17.9666	−	31.1190i	0.573336	−	0.993047i
$983$	−28.9973			−0.924871			−0.462435	−	0.886653i	$-0.653024\pi$
$983$	−28.9973			−0.924871			−0.462435	+	0.886653i	$0.653024\pi$
$984$	−7.29726	+	8.69653i	−0.232628	+	0.277235i
$985$	−63.8958			−2.03589
$986$	22.9479	+	39.7469i	0.730810	+	1.26580i
$987$		0			0
$988$	−1.17546	+	2.03596i	−0.0373963	+	0.0647724i
$989$	0.0650551	−	0.112679i	0.00206863	−	0.00358298i
$990$	−4.50000	−	1.63787i	−0.143019	−	0.0520548i
$991$	−3.40461	−	5.89696i	−0.108151	−	0.187323i	0.806870	−	0.590729i	$-0.201160\pi$
$991$	−3.40461	−	5.89696i	−0.108151	−	0.187323i	−0.915021	+	0.403406i	$0.867826\pi$
$992$	−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
$996$	−0.561956	+	0.669713i	−0.0178063	+	0.0212207i
$997$	38.9377			1.23317			0.616585	−	0.787289i	$-0.288516\pi$
$997$	38.9377			1.23317			0.616585	+	0.787289i	$0.288516\pi$
$998$	−22.7324	−	39.3736i	−0.719580	−	1.24635i
$999$	−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.g.b.79.2		6
3.2	odd	2		1323.2.g.e.667.2		6
7.2	even	3		441.2.f.c.295.2		6
7.3	odd	6		441.2.h.d.214.2		6
7.4	even	3		441.2.h.e.214.2		6
7.5	odd	6		63.2.f.a.43.2	yes	6
7.6	odd	2		441.2.g.c.79.2		6
9.4	even	3		441.2.h.e.373.2		6
9.5	odd	6		1323.2.h.b.226.2		6
21.2	odd	6		1323.2.f.d.883.2		6
21.5	even	6		189.2.f.b.127.2		6
21.11	odd	6		1323.2.h.b.802.2		6
21.17	even	6		1323.2.h.c.802.2		6
21.20	even	2		1323.2.g.d.667.2		6
28.19	even	6		1008.2.r.h.673.1		6
63.2	odd	6		3969.2.a.l.1.2		3
63.4	even	3	inner	441.2.g.b.67.2		6
63.5	even	6		189.2.f.b.64.2		6
63.13	odd	6		441.2.h.d.373.2		6
63.16	even	3		3969.2.a.q.1.2		3
63.23	odd	6		1323.2.f.d.442.2		6
63.31	odd	6		441.2.g.c.67.2		6
63.32	odd	6		1323.2.g.e.361.2		6
63.40	odd	6		63.2.f.a.22.2	✓	6
63.41	even	6		1323.2.h.c.226.2		6
63.47	even	6		567.2.a.c.1.2		3
63.58	even	3		441.2.f.c.148.2		6
63.59	even	6		1323.2.g.d.361.2		6
63.61	odd	6		567.2.a.h.1.2		3
84.47	odd	6		3024.2.r.k.2017.3		6
252.47	odd	6		9072.2.a.bs.1.1		3
252.103	even	6		1008.2.r.h.337.1		6
252.131	odd	6		3024.2.r.k.1009.3		6
252.187	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	63.40	odd	6
63.2.f.a.43.2	yes	6	7.5	odd	6
189.2.f.b.64.2		6	63.5	even	6
189.2.f.b.127.2		6	21.5	even	6
441.2.f.c.148.2		6	63.58	even	3
441.2.f.c.295.2		6	7.2	even	3
441.2.g.b.67.2		6	63.4	even	3	inner
441.2.g.b.79.2		6	1.1	even	1	trivial
441.2.g.c.67.2		6	63.31	odd	6
441.2.g.c.79.2		6	7.6	odd	2
441.2.h.d.214.2		6	7.3	odd	6
441.2.h.d.373.2		6	63.13	odd	6
441.2.h.e.214.2		6	7.4	even	3
441.2.h.e.373.2		6	9.4	even	3
567.2.a.c.1.2		3	63.47	even	6
567.2.a.h.1.2		3	63.61	odd	6
1008.2.r.h.337.1		6	252.103	even	6
1008.2.r.h.673.1		6	28.19	even	6
1323.2.f.d.442.2		6	63.23	odd	6
1323.2.f.d.883.2		6	21.2	odd	6
1323.2.g.d.361.2		6	63.59	even	6
1323.2.g.d.667.2		6	21.20	even	2
1323.2.g.e.361.2		6	63.32	odd	6
1323.2.g.e.667.2		6	3.2	odd	2
1323.2.h.b.226.2		6	9.5	odd	6
1323.2.h.b.802.2		6	21.11	odd	6
1323.2.h.c.226.2		6	63.41	even	6
1323.2.h.c.802.2		6	21.17	even	6
3024.2.r.k.1009.3		6	252.131	odd	6
3024.2.r.k.2017.3		6	84.47	odd	6
3969.2.a.l.1.2		3	63.2	odd	6
3969.2.a.q.1.2		3	63.16	even	3
9072.2.a.bs.1.1		3	252.47	odd	6
9072.2.a.ca.1.3		3	252.187	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.673648 - 1.16679i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.0923963 - 0.160035i) q^{4} -2.53209 q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\)	\(q+(-0.673648 - 1.16679i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.0923963 - 0.160035i) q^{4} -2.53209 q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-2.29813 + 1.92836i) q^{9} +(1.70574 + 2.95442i) q^{10} +0.467911 q^{11} +(0.315207 + 0.0555796i) q^{12} +(2.91147 + 5.04282i) q^{13} +(-1.50000 - 4.12122i) q^{15} +(1.79813 + 3.11446i) q^{16} +(1.93969 + 3.35965i) q^{17} +(3.79813 + 1.38241i) q^{18} +(-1.09240 + 1.89209i) q^{19} +(-0.233956 + 0.405223i) q^{20} +(-0.315207 - 0.545955i) q^{22} -0.106067 q^{23} +(-1.74376 - 4.79093i) q^{24} +1.41147 q^{25} +(3.92262 - 6.79417i) q^{26} +(-4.50000 - 2.59808i) q^{27} +(-4.39053 + 7.60462i) q^{29} +(-3.79813 + 4.52644i) q^{30} +(-3.84002 + 6.65111i) q^{31} +(-0.520945 + 0.902302i) q^{32} +(0.277189 + 0.761570i) q^{33} +(2.61334 - 4.52644i) q^{34} +(0.0962667 + 0.545955i) q^{36} +(3.84002 - 6.65111i) q^{37} +2.94356 q^{38} +(-6.48293 + 7.72605i) q^{39} +7.45336 q^{40} +(-1.11334 - 1.92836i) q^{41} +(-0.613341 + 1.06234i) q^{43} +(0.0432332 - 0.0748822i) q^{44} +(5.81908 - 4.88279i) q^{45} +(0.0714517 + 0.123758i) q^{46} +(-2.66637 - 4.61830i) q^{47} +(-4.00387 + 4.77163i) q^{48} +(-0.950837 - 1.64690i) q^{50} +(-4.31908 + 5.14728i) q^{51} +1.07604 q^{52} +(0.358441 + 0.620838i) q^{53} +7.00076i q^{54} -1.18479 q^{55} +(-3.72668 - 0.657115i) q^{57} +11.8307 q^{58} +(0.368241 - 0.637812i) q^{59} +(-0.798133 - 0.140732i) q^{60} +(0.479055 + 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(-7.37211 - 12.7689i) q^{65} +(0.701867 - 0.836452i) q^{66} +(4.81908 - 8.34689i) q^{67} +0.716881 q^{68} +(-0.0628336 - 0.172634i) q^{69} +13.2344 q^{71} +(6.76470 - 5.67626i) q^{72} +(-5.13429 - 8.89284i) q^{73} -10.3473 q^{74} +(0.836152 + 2.29731i) q^{75} +(0.201867 + 0.349643i) q^{76} +(13.3819 + 2.35959i) q^{78} +(6.31908 + 10.9450i) q^{79} +(-4.55303 - 7.88609i) q^{80} +(1.56283 - 8.86327i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-1.36571 + 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +1.65270 q^{86} +(-14.9782 - 2.64106i) q^{87} -1.37733 q^{88} +(-4.05690 + 7.02676i) q^{89} +(-9.61721 - 3.50038i) q^{90} +(-0.00980018 + 0.0169744i) q^{92} +(-13.1001 - 2.30991i) q^{93} +(-3.59240 + 6.22221i) q^{94} +(2.76604 - 4.79093i) q^{95} +(-1.77719 - 0.313366i) q^{96} +(-6.80200 + 11.7814i) q^{97} +(-1.07532 + 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 9 q^{6} + 12 q^{8} + 12 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} + 6 q^{17} + 9 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} + 24 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} - 3 q^{31} - 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} - 12 q^{38} - 18 q^{39} + 18 q^{40} + 3 q^{43} - 15 q^{44} + 18 q^{45} + 3 q^{47} + 6 q^{50} - 9 q^{51} + 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} - 3 q^{59} + 9 q^{60} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} + 18 q^{66} + 12 q^{67} - 12 q^{68} + 9 q^{69} + 18 q^{71} + 45 q^{72} - 21 q^{73} - 60 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} + 12 q^{86} - 36 q^{87} + 54 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 9 * q^6 + 12 * q^8 + 12 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 - 3 * q^16 + 6 * q^17 + 9 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 + 24 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 - 3 * q^31 - 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 - 12 * q^38 - 18 * q^39 + 18 * q^40 + 3 * q^43 - 15 * q^44 + 18 * q^45 + 3 * q^47 + 6 * q^50 - 9 * q^51 + 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 - 3 * q^59 + 9 * q^60 + 6 * q^61 + 60 * q^62 + 24 * q^64 - 15 * q^65 + 18 * q^66 + 12 * q^67 - 12 * q^68 + 9 * q^69 + 18 * q^71 + 45 * q^72 - 21 * q^73 - 60 * q^74 + 9 * q^75 + 15 * q^76 + 54 * q^78 + 21 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 + 12 * q^86 - 36 * q^87 + 54 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 3 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more