LMFDB - Embedded newform 288.2.bf.a.227.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			227.7
Character	$\chi$	$=$	288.227
Dual form			288.2.bf.a.203.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31275 + 0.526004i) q^{2} +(1.63480 + 0.572226i) q^{3} +(1.44664 - 1.38103i) q^{4} +(1.23257 + 0.945783i) q^{5} +(-2.44708 + 0.108718i) q^{6} +(-4.39511 + 1.17766i) q^{7} +(-1.17266 + 2.57388i) q^{8} +(2.34512 + 1.87094i) q^{9} +O(q^{10})$	\(q+(-1.31275 + 0.526004i) q^{2} +(1.63480 + 0.572226i) q^{3} +(1.44664 - 1.38103i) q^{4} +(1.23257 + 0.945783i) q^{5} +(-2.44708 + 0.108718i) q^{6} +(-4.39511 + 1.17766i) q^{7} +(-1.17266 + 2.57388i) q^{8} +(2.34512 + 1.87094i) q^{9} +(-2.11554 - 0.593244i) q^{10} +(-0.647702 + 4.91978i) q^{11} +(3.15522 - 1.42989i) q^{12} +(-1.11076 + 0.146234i) q^{13} +(5.15023 - 3.85782i) q^{14} +(1.47380 + 2.25147i) q^{15} +(0.185536 - 3.99569i) q^{16} +4.08402 q^{17} +(-4.06268 - 1.22255i) q^{18} +(2.37867 + 0.985278i) q^{19} +(3.08923 - 0.334001i) q^{20} +(-7.85899 - 0.589751i) q^{21} +(-1.73755 - 6.79916i) q^{22} +(1.43586 - 5.35870i) q^{23} +(-3.38990 + 3.53675i) q^{24} +(-0.669376 - 2.49815i) q^{25} +(1.38123 - 0.776232i) q^{26} +(2.76318 + 4.40055i) q^{27} +(-4.73175 + 7.77341i) q^{28} +(5.76810 + 7.51713i) q^{29} +(-3.11901 - 2.18040i) q^{30} +(0.512694 - 0.296004i) q^{31} +(1.85819 + 5.34295i) q^{32} +(-3.87409 + 7.67221i) q^{33} +(-5.36130 + 2.14821i) q^{34} +(-6.53108 - 2.70526i) q^{35} +(5.97636 - 0.532081i) q^{36} +(-1.95073 - 4.70947i) q^{37} +(-3.64087 - 0.0422366i) q^{38} +(-1.89954 - 0.396542i) q^{39} +(-3.87971 + 2.06341i) q^{40} +(-4.67789 - 1.25344i) q^{41} +(10.6271 - 3.35966i) q^{42} +(-2.65553 - 0.349608i) q^{43} +(5.85736 + 8.01165i) q^{44} +(1.12101 + 4.52404i) q^{45} +(0.933768 + 7.78992i) q^{46} +(-2.20325 - 1.27205i) q^{47} +(2.58975 - 6.42598i) q^{48} +(11.8679 - 6.85192i) q^{49} +(2.19276 + 2.92735i) q^{50} +(6.67653 + 2.33698i) q^{51} +(-1.40491 + 1.74553i) q^{52} +(-2.74153 - 6.61863i) q^{53} +(-5.94208 - 4.32339i) q^{54} +(-5.45138 + 5.45138i) q^{55} +(2.12278 - 12.6935i) q^{56} +(3.32484 + 2.97187i) q^{57} +(-11.5261 - 6.83409i) q^{58} +(-0.387332 + 0.504781i) q^{59} +(5.24139 + 1.22172i) q^{60} +(9.82581 - 7.53961i) q^{61} +(-0.517341 + 0.658259i) q^{62} +(-12.5104 - 5.46124i) q^{63} +(-5.24975 - 6.03656i) q^{64} +(-1.50739 - 0.870292i) q^{65} +(1.05011 - 12.1095i) q^{66} +(9.52916 - 1.25454i) q^{67} +(5.90810 - 5.64013i) q^{68} +(5.41373 - 7.93875i) q^{69} +(9.99667 + 0.115968i) q^{70} +(-1.64564 + 1.64564i) q^{71} +(-7.56561 + 3.84208i) q^{72} +(-0.361810 - 0.361810i) q^{73} +(5.03802 + 5.15628i) q^{74} +(0.335210 - 4.46699i) q^{75} +(4.80178 - 1.85966i) q^{76} +(-2.94714 - 22.3857i) q^{77} +(2.70221 - 0.478605i) q^{78} +(-3.24123 + 5.61397i) q^{79} +(4.00774 - 4.74949i) q^{80} +(1.99913 + 8.77516i) q^{81} +(6.80022 - 0.815134i) q^{82} +(-7.37393 - 9.60989i) q^{83} +(-12.1836 + 10.0003i) q^{84} +(5.03383 + 3.86259i) q^{85} +(3.66996 - 0.937872i) q^{86} +(5.12816 + 15.5896i) q^{87} +(-11.9034 - 7.43633i) q^{88} +(2.45638 + 2.45638i) q^{89} +(-3.85126 - 5.34929i) q^{90} +(4.70968 - 1.95082i) q^{91} +(-5.32333 - 9.73507i) q^{92} +(1.00753 - 0.190529i) q^{93} +(3.56142 + 0.510966i) q^{94} +(2.00002 + 3.46413i) q^{95} +(-0.0196182 + 9.79794i) q^{96} +(8.51749 - 14.7527i) q^{97} +(-11.9755 + 15.2374i) q^{98} +(-10.7236 + 10.3256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.31275	+	0.526004i	−0.928256	+	0.371941i
$2$	−1.31275	+	0.526004i	−0.928256	+	0.371941i
$3$	1.63480	+	0.572226i	0.943850	+	0.330375i
$3$	1.63480	+	0.572226i	0.943850	+	0.330375i
$4$	1.44664	−	1.38103i	0.723320	−	0.690513i
$5$	1.23257	+	0.945783i	0.551221	+	0.422967i	0.846457	−	0.532458i	$-0.178731\pi$
$5$	1.23257	+	0.945783i	0.551221	+	0.422967i	−0.295236	+	0.955425i	$0.595398\pi$
$6$	−2.44708	+	0.108718i	−0.999015	+	0.0443838i
$7$	−4.39511	+	1.17766i	−1.66119	+	0.445116i	−0.962716	−	0.270516i	$-0.912806\pi$
$7$	−4.39511	+	1.17766i	−1.66119	+	0.445116i	−0.698478	+	0.715631i	$0.746139\pi$
$8$	−1.17266	+	2.57388i	−0.414597	+	0.910005i
$9$	2.34512	+	1.87094i	0.781705	+	0.623648i
$10$	−2.11554	−	0.593244i	−0.668993	−	0.187600i
$11$	−0.647702	+	4.91978i	−0.195289	+	1.48337i	0.560280	+	0.828303i	$0.310693\pi$
$11$	−0.647702	+	4.91978i	−0.195289	+	1.48337i	−0.755570	+	0.655068i	$0.772640\pi$
$12$	3.15522	−	1.42989i	0.910834	−	0.412774i
$13$	−1.11076	+	0.146234i	−0.308069	+	0.0405580i	−0.282976	−	0.959127i	$-0.591322\pi$
$13$	−1.11076	+	0.146234i	−0.308069	+	0.0405580i	−0.0250932	+	0.999685i	$0.507988\pi$
$14$	5.15023	−	3.85782i	1.37646	−	1.03105i
$15$	1.47380	+	2.25147i	0.380532	+	0.581327i
$16$	0.185536	−	3.99569i	0.0463840	−	0.998924i
$17$	4.08402			0.990519			0.495260	−	0.868745i	$-0.335073\pi$
$17$	4.08402			0.990519			0.495260	+	0.868745i	$0.335073\pi$
$18$	−4.06268	−	1.22255i	−0.957583	−	0.288158i
$19$	2.37867	+	0.985278i	0.545705	+	0.226038i	0.638466	−	0.769650i	$-0.279569\pi$
$19$	2.37867	+	0.985278i	0.545705	+	0.226038i	−0.0927611	+	0.995688i	$0.529569\pi$
$20$	3.08923	−	0.334001i	0.690773	−	0.0746848i
$21$	−7.85899	−	0.589751i	−1.71497	−	0.128694i
$22$	−1.73755	−	6.79916i	−0.370447	−	1.44958i
$23$	1.43586	−	5.35870i	0.299397	−	1.11737i	−0.638264	−	0.769817i	$-0.720347\pi$
$23$	1.43586	−	5.35870i	0.299397	−	1.11737i	0.937662	−	0.347549i	$-0.112986\pi$
$24$	−3.38990	+	3.53675i	−0.691960	+	0.721936i
$25$	−0.669376	−	2.49815i	−0.133875	−	0.499629i
$26$	1.38123	−	0.776232i	0.270882	−	0.152232i
$27$	2.76318	+	4.40055i	0.531775	+	0.846886i
$28$	−4.73175	+	7.77341i	−0.894217	+	1.46904i
$29$	5.76810	+	7.51713i	1.07111	+	1.39590i	0.912752	+	0.408514i	$0.133953\pi$
$29$	5.76810	+	7.51713i	1.07111	+	1.39590i	0.158356	+	0.987382i	$0.449381\pi$
$30$	−3.11901	−	2.18040i	−0.569451	−	0.398085i
$31$	0.512694	−	0.296004i	0.0920825	−	0.0531639i	−0.453252	−	0.891383i	$-0.649736\pi$
$31$	0.512694	−	0.296004i	0.0920825	−	0.0531639i	0.545334	+	0.838219i	$0.316403\pi$
$32$	1.85819	+	5.34295i	0.328484	+	0.944509i
$33$	−3.87409	+	7.67221i	−0.674392	+	1.33556i
$34$	−5.36130	+	2.14821i	−0.919456	+	0.368415i
$35$	−6.53108	−	2.70526i	−1.10395	−	0.457273i
$36$	5.97636	−	0.532081i	0.996060	−	0.0886801i
$37$	−1.95073	−	4.70947i	−0.320698	−	0.774233i	−0.999214	−	0.0396471i	$-0.987377\pi$
$37$	−1.95073	−	4.70947i	−0.320698	−	0.774233i	0.678516	−	0.734586i	$-0.262623\pi$
$38$	−3.64087	−	0.0422366i	−0.590627	−	0.00685168i
$39$	−1.89954	−	0.396542i	−0.304170	−	0.0634975i
$40$	−3.87971	+	2.06341i	−0.613437	+	0.326253i
$41$	−4.67789	−	1.25344i	−0.730563	−	0.195754i	−0.125683	−	0.992070i	$-0.540112\pi$
$41$	−4.67789	−	1.25344i	−0.730563	−	0.195754i	−0.604880	+	0.796317i	$0.706779\pi$
$42$	10.6271	−	3.35966i	1.63980	−	0.518407i
$43$	−2.65553	−	0.349608i	−0.404965	−	0.0533147i	−0.0747075	−	0.997205i	$-0.523802\pi$
$43$	−2.65553	−	0.349608i	−0.404965	−	0.0533147i	−0.330258	+	0.943891i	$0.607136\pi$
$44$	5.85736	+	8.01165i	0.883030	+	1.20780i
$45$	1.12101	+	4.52404i	0.167110	+	0.674403i
$46$	0.933768	+	7.78992i	0.137677	+	1.14856i
$47$	−2.20325	−	1.27205i	−0.321377	−	0.185547i	0.330629	−	0.943761i	$-0.392739\pi$
$47$	−2.20325	−	1.27205i	−0.321377	−	0.185547i	−0.652006	+	0.758214i	$0.726072\pi$
$48$	2.58975	−	6.42598i	0.373799	−	0.927510i
$49$	11.8679	−	6.85192i	1.69541	−	0.978846i
$50$	2.19276	+	2.92735i	0.310103	+	0.413990i
$51$	6.67653	+	2.33698i	0.934902	+	0.327243i
$52$	−1.40491	+	1.74553i	−0.194827	+	0.242062i
$53$	−2.74153	−	6.61863i	−0.376578	−	0.909139i	−0.992602	−	0.121412i	$-0.961258\pi$
$53$	−2.74153	−	6.61863i	−0.376578	−	0.909139i	0.616024	−	0.787727i	$-0.288742\pi$
$54$	−5.94208	−	4.32339i	−0.808615	−	0.588339i
$55$	−5.45138	+	5.45138i	−0.735064	+	0.735064i
$56$	2.12278	−	12.6935i	0.283668	−	1.69624i
$57$	3.32484	+	2.97187i	0.440386	+	0.393633i
$58$	−11.5261	−	6.83409i	−1.51345	−	0.897360i
$59$	−0.387332	+	0.504781i	−0.0504264	+	0.0657170i	−0.817886	−	0.575381i	$-0.804854\pi$
$59$	−0.387332	+	0.504781i	−0.0504264	+	0.0657170i	0.767459	+	0.641098i	$0.221521\pi$
$60$	5.24139	+	1.22172i	0.676660	+	0.157723i
$61$	9.82581	−	7.53961i	1.25807	−	0.965348i	0.258066	−	0.966127i	$-0.416915\pi$
$61$	9.82581	−	7.53961i	1.25807	−	0.965348i	1.00000		0.000779171i	$0.000248018\pi$
$62$	−0.517341	+	0.658259i	−0.0657024	+	0.0835990i
$63$	−12.5104	−	5.46124i	−1.57616	−	0.688051i
$64$	−5.24975	−	6.03656i	−0.656219	−	0.754570i
$65$	−1.50739	−	0.870292i	−0.186969	−	0.107946i
$66$	1.05011	−	12.1095i	0.129259	−	1.49058i
$67$	9.52916	−	1.25454i	1.16417	−	0.153266i	0.476424	−	0.879216i	$-0.341933\pi$
$67$	9.52916	−	1.25454i	1.16417	−	0.153266i	0.687748	+	0.725949i	$0.258599\pi$
$68$	5.90810	−	5.64013i	0.716463	−	0.683966i
$69$	5.41373	−	7.93875i	0.651736	−	0.955713i
$70$	9.99667	+	0.115968i	1.19483	+	0.0138609i
$71$	−1.64564	+	1.64564i	−0.195301	+	0.195301i	−0.797982	−	0.602681i	$-0.794099\pi$
$71$	−1.64564	+	1.64564i	−0.195301	+	0.195301i	0.602681	+	0.797982i	$0.294099\pi$
$72$	−7.56561	+	3.84208i	−0.891616	+	0.452793i
$73$	−0.361810	−	0.361810i	−0.0423466	−	0.0423466i	0.685616	−	0.727963i	$-0.259533\pi$
$73$	−0.361810	−	0.361810i	−0.0423466	−	0.0423466i	−0.727963	+	0.685616i	$0.759533\pi$
$74$	5.03802	+	5.15628i	0.585658	+	0.599406i
$75$	0.335210	−	4.46699i	0.0387067	−	0.515804i
$76$	4.80178	−	1.85966i	0.550802	−	0.213318i
$77$	−2.94714	−	22.3857i	−0.335858	−	2.55109i
$78$	2.70221	−	0.478605i	0.305965	−	0.0541913i
$79$	−3.24123	+	5.61397i	−0.364667	+	0.631622i	−0.988723	−	0.149758i	$-0.952150\pi$
$79$	−3.24123	+	5.61397i	−0.364667	+	0.631622i	0.624056	+	0.781380i	$0.285484\pi$
$80$	4.00774	−	4.74949i	0.448079	−	0.531009i
$81$	1.99913	+	8.77516i	0.222126	+	0.975018i
$82$	6.80022	−	0.815134i	0.750959	−	0.0900165i
$83$	−7.37393	−	9.60989i	−0.809394	−	1.05482i	−0.997358	−	0.0726465i	$-0.976856\pi$
$83$	−7.37393	−	9.60989i	−0.809394	−	1.05482i	0.187964	−	0.982176i	$-0.439811\pi$
$84$	−12.1836	+	10.0003i	−1.32934	+	1.09112i
$85$	5.03383	+	3.86259i	0.545995	+	0.418957i
$86$	3.66996	−	0.937872i	0.395741	−	0.101133i
$87$	5.12816	+	15.5896i	0.549797	+	1.67138i
$88$	−11.9034	−	7.43633i	−1.26891	−	0.792715i
$89$	2.45638	+	2.45638i	0.260376	+	0.260376i	0.825207	−	0.564831i	$-0.191059\pi$
$89$	2.45638	+	2.45638i	0.260376	+	0.260376i	−0.564831	+	0.825207i	$0.691059\pi$
$90$	−3.85126	−	5.34929i	−0.405959	−	0.563864i
$91$	4.70968	−	1.95082i	0.493709	−	0.204501i
$92$	−5.32333	−	9.73507i	−0.554996	−	1.01495i
$93$	1.00753	−	0.190529i	0.104476	−	0.0197570i
$94$	3.56142	+	0.510966i	0.367333	+	0.0527021i
$95$	2.00002	+	3.46413i	0.205197	+	0.355412i
$96$	−0.0196182	+	9.79794i	−0.00200227	+	0.999998i
$97$	8.51749	−	14.7527i	0.864820	−	1.49791i	−0.00240483	−	0.999997i	$-0.500765\pi$
$97$	8.51749	−	14.7527i	0.864820	−	1.49791i	0.867225	−	0.497916i	$-0.165901\pi$
$98$	−11.9755	+	15.2374i	−1.20970	+	1.53921i
$99$	−10.7236	+	10.3256i	−1.07776	+	1.03777i
$100$	−4.41835	−	2.68949i	−0.441835	−	0.268949i
$101$	−0.526559	+	3.99961i	−0.0523945	+	0.397976i	0.945073	+	0.326858i	$0.105990\pi$
$101$	−0.526559	+	3.99961i	−0.0523945	+	0.397976i	−0.997468	+	0.0711178i	$0.977343\pi$
$102$	−9.99390	+	0.444005i	−0.989543	+	0.0439630i
$103$	−4.11044	+	15.3404i	−0.405013	+	1.51153i	0.399018	+	0.916943i	$0.369351\pi$
$103$	−4.11044	+	15.3404i	−0.405013	+	1.51153i	−0.804031	+	0.594587i	$0.797316\pi$
$104$	0.926148	−	3.03044i	0.0908163	−	0.297160i
$105$	−9.12896	−	8.15980i	−0.890896	−	0.796315i
$106$	7.08038	+	7.24658i	0.687707	+	0.703850i
$107$	2.60587	−	1.07939i	0.251919	−	0.104348i	−0.253150	−	0.967427i	$-0.581467\pi$
$107$	2.60587	−	1.07939i	0.251919	−	0.104348i	0.505070	+	0.863079i	$0.331467\pi$
$108$	10.0746	+	2.54998i	0.969429	+	0.245372i
$109$	−0.946606	+	2.28531i	−0.0906684	+	0.218893i	−0.962708	−	0.270542i	$-0.912797\pi$
$109$	−0.946606	+	2.28531i	−0.0906684	+	0.218893i	0.872040	+	0.489435i	$0.162797\pi$
$110$	4.28887	−	10.0238i	0.408928	−	0.955729i
$111$	−0.494160	−	8.81528i	−0.0469036	−	0.836710i
$112$	3.89014	+	17.7800i	0.367584	+	1.68005i
$113$	8.13956	+	14.0981i	0.765705	+	1.32624i	0.939873	+	0.341525i	$0.110943\pi$
$113$	8.13956	+	14.0981i	0.765705	+	1.32624i	−0.174167	+	0.984716i	$0.555723\pi$
$114$	−5.92791	−	2.15245i	−0.555200	−	0.201595i
$115$	6.83796	−	5.24695i	0.637643	−	0.489281i
$116$	18.7257	+	2.90869i	1.73864	+	0.270065i
$117$	−2.87845	−	1.73523i	−0.266113	−	0.160422i
$118$	0.242955	−	0.866392i	0.0223658	−	0.0797578i
$119$	−17.9497	+	4.80960i	−1.64544	+	0.440896i
$120$	−7.52327	+	1.15318i	−0.686778	+	0.105270i
$121$	−13.1596	−	3.52610i	−1.19633	−	0.320554i
$122$	−8.93300	+	15.0661i	−0.808756	+	1.36402i
$123$	−6.93014	−	4.72592i	−0.624870	−	0.426122i
$124$	0.332894	−	1.13625i	0.0298948	−	0.102039i
$125$	4.51037	−	10.8890i	0.403420	−	0.973942i
$126$	19.2957	+	0.588754i	1.71899	+	0.0524504i
$127$		−	21.9679i		−	1.94934i	−0.223651	−	0.974669i	$-0.571798\pi$
$127$		−	21.9679i		−	1.94934i	0.223651	−	0.974669i	$-0.428202\pi$
$128$	10.0669	+	5.16313i	0.889795	+	0.456360i
$129$	−4.14120	−	2.09110i	−0.364613	−	0.184111i
$130$	2.43661	+	0.349586i	0.213705	+	0.0306607i
$131$	0.425820	+	3.23442i	0.0372040	+	0.282593i	0.999927	+	0.0121025i	$0.00385244\pi$
$131$	0.425820	+	3.23442i	0.0372040	+	0.282593i	−0.962723	+	0.270490i	$0.912814\pi$
$132$	4.99111	+	16.4491i	0.434420	+	1.43171i
$133$	−11.6148	−	1.52912i	−1.00713	−	0.132592i
$134$	−11.8495	+	6.65927i	−1.02364	+	0.575274i
$135$	−0.756152	+	8.03734i	−0.0650792	+	0.691744i
$136$	−4.78915	+	10.5118i	−0.410666	+	0.901378i
$137$	−0.899631	−	3.35747i	−0.0768606	−	0.286848i	0.916788	−	0.399374i	$-0.130772\pi$
$137$	−0.899631	−	3.35747i	−0.0768606	−	0.286848i	−0.993649	+	0.112526i	$0.964106\pi$
$138$	−2.93107	+	13.2693i	−0.249509	+	1.12955i
$139$	9.94055	−	12.9548i	0.843146	−	1.09881i	−0.150759	−	0.988571i	$-0.548172\pi$
$139$	9.94055	−	12.9548i	0.843146	−	1.09881i	0.993905	−	0.110239i	$-0.0351617\pi$
$140$	−13.1842	+	5.10605i	−1.11427	+	0.431540i
$141$	−2.87397	−	3.34029i	−0.242032	−	0.281304i
$142$	1.29471	−	3.02593i	0.108649	−	0.253930i
$143$		−	5.55941i		−	0.464901i
$144$	7.91083	−	9.02324i	0.659236	−	0.751936i
$145$			14.7207i			1.22249i
$146$	0.665280	+	0.284654i	0.0550590	+	0.0235581i
$147$	23.3224	−	4.41039i	1.92360	−	0.363763i
$148$	−9.32590	−	4.11891i	−0.766585	−	0.338572i
$149$	−6.06859	+	7.90874i	−0.497158	+	0.647910i	−0.972777	−	0.231742i	$-0.925557\pi$
$149$	−6.06859	+	7.90874i	−0.497158	+	0.647910i	0.475619	+	0.879651i	$0.342224\pi$
$150$	1.90961	+	6.04038i	0.155919	+	0.493195i
$151$	1.15942	+	4.32703i	0.0943526	+	0.352129i	0.996921	−	0.0784188i	$-0.0249871\pi$
$151$	1.15942	+	4.32703i	0.0943526	+	0.352129i	−0.902568	+	0.430548i	$0.858320\pi$
$152$	−5.32536	+	4.96703i	−0.431944	+	0.402880i
$153$	9.57749	+	7.64097i	0.774294	+	0.617736i
$154$	15.6439	+	27.8368i	1.26062	+	2.24315i
$155$	0.911885	+	0.120052i	0.0732444	+	0.00964281i
$156$	−3.29559	+	2.04966i	−0.263858	+	0.164104i
$157$	1.01101	+	7.67935i	0.0806870	+	0.612879i	0.983242	+	0.182305i	$0.0583557\pi$
$157$	1.01101	+	7.67935i	0.0806870	+	0.612879i	−0.902555	+	0.430574i	$0.858311\pi$
$158$	1.30196	−	9.07466i	0.103579	−	0.721941i
$159$	−0.694486	−	12.3889i	−0.0550763	−	0.982503i
$160$	−2.76293	+	8.34299i	−0.218429	+	0.659572i
$161$			25.2430i			1.98943i
$162$	−7.24013	−	10.4681i	−0.568839	−	0.822449i
$163$	−4.51520	+	10.9007i	−0.353658	+	0.853806i	0.642504	+	0.766282i	$0.277895\pi$
$163$	−4.51520	+	10.9007i	−0.353658	+	0.853806i	−0.996162	+	0.0875240i	$0.972105\pi$
$164$	−8.49825	+	4.64701i	−0.663602	+	0.362871i
$165$	−12.0313	+	5.79248i	−0.936637	+	0.450944i
$166$	14.7350	+	8.73670i	1.14366	+	0.678099i
$167$	0.875847	+	0.234682i	0.0677751	+	0.0181603i	0.292547	−	0.956251i	$-0.405497\pi$
$167$	0.875847	+	0.234682i	0.0677751	+	0.0181603i	−0.224772	+	0.974411i	$0.572164\pi$
$168$	10.7338	−	19.5366i	0.828134	−	1.50728i
$169$	−11.3446	+	3.03979i	−0.872664	+	0.233830i
$170$	−8.63991	−	2.42282i	−0.662651	−	0.185822i
$171$	3.73486	+	6.76096i	0.285612	+	0.517023i
$172$	−4.32442	+	3.16160i	−0.329734	+	0.241070i
$173$	−0.836588	+	0.641936i	−0.0636046	+	0.0488055i	−0.640074	−	0.768313i	$-0.721096\pi$
$173$	−0.836588	+	0.641936i	−0.0636046	+	0.0488055i	0.576470	+	0.817118i	$0.304430\pi$
$174$	−14.9322	−	17.7679i	−1.13201	−	1.34698i
$175$	5.88396	+	10.1913i	0.444785	+	0.770391i
$176$	19.5378	+	3.50082i	1.47272	+	0.263884i
$177$	−0.922058	+	0.603573i	−0.0693062	+	0.0453673i
$178$	−4.51669	−	1.93256i	−0.338540	−	0.144851i
$179$	8.10504	−	19.5673i	0.605799	−	1.46253i	−0.261730	−	0.965141i	$-0.584293\pi$
$179$	8.10504	−	19.5673i	0.605799	−	1.46253i	0.867529	−	0.497387i	$-0.165707\pi$
$180$	7.86950	+	4.99651i	0.586558	+	0.372418i
$181$	4.74472	−	1.96533i	0.352672	−	0.146082i	−0.199312	−	0.979936i	$-0.563871\pi$
$181$	4.74472	−	1.96533i	0.352672	−	0.146082i	0.551984	+	0.833854i	$0.313871\pi$
$182$	−5.15652	+	5.03825i	−0.382226	+	0.373460i
$183$	20.3776	−	6.70314i	1.50635	−	0.495510i
$184$	12.1089	+	9.97965i	0.892680	+	0.735710i
$185$	2.04973	−	7.64971i	0.150699	−	0.562418i
$186$	−1.22242	+	0.780083i	−0.0896322	+	0.0571985i
$187$	−2.64523	+	20.0925i	−0.193438	+	1.46931i
$188$	−4.94404	+	1.20255i	−0.360581	+	0.0877050i
$189$	−17.3268	−	16.0868i	−1.26034	−	1.17014i
$190$	−4.44767	−	3.49553i	−0.322668	−	0.253592i
$191$	−2.81155	+	4.86975i	−0.203437	+	0.352363i	−0.949634	−	0.313363i	$-0.898544\pi$
$191$	−2.81155	+	4.86975i	−0.203437	+	0.352363i	0.746197	+	0.665725i	$0.231878\pi$
$192$	−5.12800	−	12.8726i	−0.370081	−	0.928999i
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	0.885187	−	0.465236i	$-0.154031\pi$
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	−0.845500	+	0.533976i	$0.820697\pi$
$194$	−3.42137	+	23.8469i	−0.245640	+	1.71211i
$195$	−1.96627	−	2.28532i	−0.140808	−	0.163655i
$196$	7.70587	−	26.3021i	0.550419	−	1.87872i
$197$	7.02701	−	2.91068i	0.500653	−	0.207377i	−0.118042	−	0.993009i	$-0.537662\pi$
$197$	7.02701	−	2.91068i	0.500653	−	0.207377i	0.618695	+	0.785631i	$0.287662\pi$
$198$	8.64608	−	19.1957i	0.614450	−	1.36418i
$199$	1.84792	+	1.84792i	0.130996	+	0.130996i	0.769565	−	0.638569i	$-0.220473\pi$
$199$	1.84792	+	1.84792i	0.130996	+	0.130996i	−0.638569	+	0.769565i	$0.720473\pi$
$200$	7.21489	+	1.20657i	0.510170	+	0.0853175i
$201$	16.2961	+	3.40192i	1.14944	+	0.239953i
$202$	−1.41257	−	5.52747i	−0.0993879	−	0.388911i
$203$	−34.2040	−	26.2457i	−2.40065	−	1.84209i
$204$	12.8860	−	5.83969i	0.902198	−	0.408860i
$205$	−4.58034	−	5.96921i	−0.319905	−	0.416908i
$206$	−2.67310	−	22.3002i	−0.186243	−	1.55373i
$207$	13.3931	−	9.88036i	0.930884	−	0.686732i
$208$	0.378221	+	4.46538i	0.0262249	+	0.309619i
$209$	−6.38803	+	11.0644i	−0.441869	+	0.765340i
$210$	16.2762	+	5.90994i	1.12316	+	0.407825i
$211$	0.141909	+	1.07790i	0.00976940	+	0.0742060i	0.995635	−	0.0933318i	$-0.0297517\pi$
$211$	0.141909	+	1.07790i	0.00976940	+	0.0742060i	−0.985866	+	0.167538i	$0.946418\pi$
$212$	−13.1065	−	5.78866i	−0.900159	−	0.397567i
$213$	−3.63196	+	1.74861i	−0.248858	+	0.119813i
$214$	−2.85311	+	2.78767i	−0.195034	+	0.190561i
$215$	−2.94247	−	2.94247i	−0.200675	−	0.200675i
$216$	−14.5668	+	1.95178i	−0.991143	+	0.132802i
$217$	−1.90475	+	1.90475i	−0.129303	+	0.129303i
$218$	0.0405788	−	3.49796i	0.00274834	−	0.236912i
$219$	−0.384448	−	0.798522i	−0.0259786	−	0.0539591i
$220$	−0.357690	+	15.4147i	−0.0241155	+	1.03926i
$221$	−4.53635	+	0.597222i	−0.305148	+	0.0401735i
$222$	5.28558	+	11.3124i	0.354745	+	0.759236i
$223$	−5.00046	−	2.88701i	−0.334855	−	0.193329i	0.323139	−	0.946351i	$-0.395262\pi$
$223$	−5.00046	−	2.88701i	−0.334855	−	0.193329i	−0.657995	+	0.753023i	$0.728595\pi$
$224$	−14.4591	−	21.2945i	−0.966092	−	1.42280i
$225$	3.10413	−	7.11081i	0.206942	−	0.474054i
$226$	−18.1009	−	14.2259i	−1.20405	−	0.946294i
$227$	4.88016	−	3.74468i	0.323908	−	0.248543i	−0.433988	−	0.900918i	$-0.642894\pi$
$227$	4.88016	−	3.74468i	0.323908	−	0.248543i	0.757896	+	0.652375i	$0.226227\pi$
$228$	8.91408	−	0.292471i	0.590349	−	0.0193693i
$229$	9.03017	−	11.7684i	0.596731	−	0.777675i	−0.393166	−	0.919468i	$-0.628620\pi$
$229$	9.03017	−	11.7684i	0.596731	−	0.777675i	0.989896	+	0.141793i	$0.0452868\pi$
$230$	−6.21664	+	10.4847i	−0.409913	+	0.691344i
$231$	7.99173	−	38.2826i	0.525817	−	2.51881i
$232$	−26.1122	+	6.03140i	−1.71435	+	0.395981i
$233$	−14.8047	+	14.8047i	−0.969888	+	0.969888i	−0.999560	−	0.0296721i	$-0.990554\pi$
$233$	−14.8047	+	14.8047i	−0.969888	+	0.969888i	0.0296721	+	0.999560i	$0.490554\pi$
$234$	4.69143	+	0.763854i	0.306689	+	0.0499347i
$235$	−1.51258	−	3.65168i	−0.0986695	−	0.238209i
$236$	0.136785	+	1.26515i	0.00890398	+	0.0823545i
$237$	−8.51121	+	7.32299i	−0.552863	+	0.475679i
$238$	21.0336	−	15.7554i	1.36341	−	1.02127i
$239$	5.86397	−	3.38557i	0.379309	−	0.218994i	−0.298209	−	0.954501i	$-0.596389\pi$
$239$	5.86397	−	3.38557i	0.379309	−	0.218994i	0.677518	+	0.735507i	$0.263056\pi$
$240$	9.26962	−	5.47111i	0.598352	−	0.353159i
$241$	−25.0688	−	14.4735i	−1.61482	−	0.932318i	−0.988231	−	0.152970i	$-0.951116\pi$
$241$	−25.0688	−	14.4735i	−1.61482	−	0.932318i	−0.626592	−	0.779348i	$-0.715551\pi$
$242$	19.1300	−	2.29309i	1.22972	−	0.147406i
$243$	−1.75320	+	15.4896i	−0.112468	+	0.993655i
$244$	3.80202	−	24.4768i	0.243399	−	1.56697i
$245$	21.1084	+	2.77897i	1.34857	+	0.177542i
$246$	11.5834	+	2.55868i	0.738532	+	0.163136i
$247$	−2.78621	−	0.746563i	−0.177282	−	0.0475027i
$248$	0.160666	+	1.66673i	0.0102023	+	0.105837i
$249$	−6.55584	−	19.9298i	−0.415459	−	1.26300i
$250$	−0.193349	+	16.6670i	−0.0122285	+	1.05412i
$251$	−1.10999	−	2.67976i	−0.0700622	−	0.169145i	0.884969	−	0.465649i	$-0.154179\pi$
$251$	−1.10999	−	2.67976i	−0.0700622	−	0.169145i	−0.955032	+	0.296504i	$0.904179\pi$
$252$	−25.6401	+	9.37670i	−1.61518	+	0.590677i
$253$	25.4337	+	10.5350i	1.59900	+	0.662327i
$254$	11.5552	+	28.8385i	0.725039	+	1.80949i
$255$	6.01901	+	9.19503i	0.376925	+	0.575815i
$256$	−15.9312	−	1.48269i	−0.995697	−	0.0926682i
$257$	−19.8010	+	11.4321i	−1.23515	+	0.713115i	−0.968099	−	0.250567i	$-0.919383\pi$
$257$	−19.8010	+	11.4321i	−1.23515	+	0.713115i	−0.267052	+	0.963682i	$0.586050\pi$
$258$	6.53630	+	0.566813i	0.406932	+	0.0352883i
$259$	14.1198	+	18.4013i	0.877364	+	1.14340i
$260$	−3.38255	+	0.822745i	−0.209777	+	0.0510245i
$261$	−0.537282	+	28.4203i	−0.0332569	+	1.75917i
$262$	−2.26031	−	4.02201i	−0.139643	−	0.248481i
$263$	0.158349	+	0.590968i	0.00976425	+	0.0364407i	0.970636	−	0.240553i	$-0.0773287\pi$
$263$	0.158349	+	0.590968i	0.00976425	+	0.0364407i	−0.960872	+	0.276993i	$0.910662\pi$
$264$	−15.2044	−	18.9683i	−0.935767	−	1.16742i
$265$	2.88067	−	10.7508i	0.176958	−	0.660417i
$266$	16.0517	−	4.10209i	0.984196	−	0.251515i
$267$	2.61008	+	5.42129i	0.159734	+	0.331778i
$268$	12.0527	−	14.9749i	0.736237	−	0.914737i
$269$	1.42907	+	0.591941i	0.0871321	+	0.0360913i	0.425824	−	0.904806i	$-0.359984\pi$
$269$	1.42907	+	0.591941i	0.0871321	+	0.0360913i	−0.338692	+	0.940897i	$0.609984\pi$
$270$	−3.23503	−	10.9488i	−0.196878	−	0.666322i
$271$	12.8060			0.777912			0.388956	−	0.921256i	$-0.372836\pi$
$271$	12.8060			0.777912			0.388956	+	0.921256i	$0.372836\pi$
$272$	0.757732	−	16.3185i	0.0459443	−	0.989453i
$273$	8.81568	−	0.494182i	0.533549	−	0.0299092i
$274$	2.94703	+	3.93432i	0.178037	+	0.237681i
$275$	12.7239	−	1.67513i	0.767280	−	0.101014i
$276$	−3.13190	−	18.9610i	−0.188518	−	1.14132i
$277$	−1.37192	+	10.4208i	−0.0824309	+	0.626125i	0.899505	+	0.436911i	$0.143927\pi$
$277$	−1.37192	+	10.4208i	−0.0824309	+	0.626125i	−0.981936	+	0.189214i	$0.939406\pi$
$278$	−6.23523	+	22.2352i	−0.373964	+	1.33358i
$279$	1.75613	+	0.265058i	0.105137	+	0.0158686i
$280$	14.6217	−	13.6379i	0.873816	−	0.815020i
$281$	7.83178	−	2.09852i	0.467205	−	0.125187i	−0.0175337	−	0.999846i	$-0.505581\pi$
$281$	7.83178	−	2.09852i	0.467205	−	0.125187i	0.484738	+	0.874659i	$0.338915\pi$
$282$	5.52981	+	2.87326i	0.329296	+	0.171100i
$283$	−9.18149	−	7.04520i	−0.545783	−	0.418794i	0.298723	−	0.954340i	$-0.403439\pi$
$283$	−9.18149	−	7.04520i	−0.545783	−	0.418794i	−0.844506	+	0.535546i	$0.820106\pi$
$284$	−0.107978	+	4.65332i	−0.00640731	+	0.276124i
$285$	1.28735	+	6.80761i	0.0762563	+	0.403248i
$286$	2.92427	+	7.29813i	0.172916	+	0.431547i
$287$	22.0359			1.30074
$288$	−5.63871	+	16.0064i	−0.332264	+	0.943186i
$289$	−0.320814			−0.0188714
$290$	−7.74316	−	19.3247i	−0.454694	−	1.13478i
$291$	22.3663	−	19.2438i	1.31113	−	1.12809i
$292$	−1.02308	−	0.0237400i	−0.0598711	−	0.00138928i
$293$	−2.29923	−	1.76426i	−0.134322	−	0.103069i	0.539415	−	0.842040i	$-0.318645\pi$
$293$	−2.29923	−	1.76426i	−0.134322	−	0.103069i	−0.673737	+	0.738971i	$0.735312\pi$
$294$	−28.2967	+	18.0574i	−1.65030	+	1.05313i
$295$	−0.954827	+	0.255845i	−0.0555922	+	0.0148959i
$296$	14.4092	+	0.501649i	0.837516	+	0.0291577i
$297$	−23.4395	+	10.7440i	−1.36010	+	0.623431i
$298$	3.80653	−	13.5743i	0.220507	−	0.786340i
$299$	−0.811268	+	6.16219i	−0.0469168	+	0.356369i
$300$	−5.68411	−	6.92507i	−0.328172	−	0.399819i
$301$	12.0831	−	1.59077i	0.696457	−	0.0916903i
$302$	−3.79807	−	5.07046i	−0.218554	−	0.291772i
$303$	−3.14949	+	6.23723i	−0.180934	+	0.358320i
$304$	4.37820	−	9.32165i	0.251107	−	0.534633i
$305$	19.2418			1.10178
$306$	−16.5921	−	4.99291i	−0.948505	−	0.285426i
$307$	−25.8180	−	10.6941i	−1.47351	−	0.610347i	−0.505852	−	0.862620i	$-0.668822\pi$
$307$	−25.8180	−	10.6941i	−1.47351	−	0.610347i	−0.967656	+	0.252273i	$0.918822\pi$
$308$	−35.1787	−	28.3141i	−2.00450	−	1.61334i
$309$	−15.4979	+	22.7262i	−0.881643	+	1.29285i
$310$	−1.26023	+	0.322056i	−0.0715761	+	0.0182916i
$311$	−8.69628	+	32.4549i	−0.493121	+	1.84035i	0.0471908	+	0.998886i	$0.484973\pi$
$311$	−8.69628	+	32.4549i	−0.493121	+	1.84035i	−0.540311	+	0.841465i	$0.681694\pi$
$312$	3.24816	−	4.42419i	0.183891	−	0.250471i
$313$	3.01691	+	11.2593i	0.170526	+	0.636412i	0.997271	+	0.0738342i	$0.0235236\pi$
$313$	3.01691	+	11.2593i	0.170526	+	0.636412i	−0.826745	+	0.562578i	$0.809810\pi$
$314$	−5.36657	−	9.54930i	−0.302853	−	0.538898i
$315$	−10.2547	−	18.5634i	−0.577789	−	1.04593i
$316$	3.06415	+	12.5976i	0.172372	+	0.708672i
$317$	15.9632	+	20.8036i	0.896582	+	1.16845i	0.985033	+	0.172368i	$0.0551420\pi$
$317$	15.9632	+	20.8036i	0.896582	+	1.16845i	−0.0884501	+	0.996081i	$0.528191\pi$
$318$	7.42829	+	15.8982i	0.416558	+	0.891530i
$319$	−40.7187	+	23.5089i	−2.27981	+	1.31625i
$320$	−0.761401	−	12.4056i	−0.0425636	−	0.693494i
$321$	4.87773	−	0.273431i	0.272248	−	0.0152615i
$322$	−13.2779	−	33.1378i	−0.739950	−	1.84670i
$323$	9.71454	+	4.02389i	0.540531	+	0.223895i
$324$	15.0107	+	9.93365i	0.833931	+	0.551869i
$325$	1.10883	+	2.67695i	0.0615068	+	0.148491i
$326$	0.193556	−	16.6849i	0.0107201	−	0.924091i
$327$	−2.85522	+	3.19434i	−0.157894	+	0.176647i
$328$	8.71176	−	10.5705i	0.481026	−	0.583658i
$329$	11.1816	+	2.99609i	0.616460	+	0.165180i
$330$	12.7473	−	13.9326i	0.701715	−	0.766965i
$331$	33.4239	+	4.40034i	1.83714	+	0.241864i	0.967689	−	0.252149i	$-0.0811372\pi$
$331$	33.4239	+	4.40034i	1.83714	+	0.241864i	0.869454	+	0.494013i	$0.164471\pi$
$332$	−23.9389	−	3.71847i	−1.31382	−	0.204078i
$333$	4.23648	−	14.6940i	0.232158	−	0.805224i
$334$	−1.27321	+	0.152619i	−0.0696672	+	0.00835092i
$335$	12.9319	+	7.46621i	0.706543	+	0.407923i
$336$	−3.81459	+	31.2927i	−0.208103	+	1.70716i
$337$	−2.73282	+	1.57779i	−0.148866	+	0.0859478i	−0.572583	−	0.819847i	$-0.694058\pi$
$337$	−2.73282	+	1.57779i	−0.148866	+	0.0859478i	0.423717	+	0.905795i	$0.360725\pi$
$338$	13.2938	−	9.95781i	0.723086	−	0.541633i
$339$	5.23921	+	27.7052i	0.284555	+	1.50474i
$340$	12.6165	−	1.36406i	0.684224	−	0.0739768i
$341$	1.12420	+	2.71407i	0.0608790	+	0.146975i
$342$	−8.45924	−	6.91092i	−0.457423	−	0.373699i
$343$	−21.5692	+	21.5692i	−1.16463	+	1.16463i
$344$	4.01388	−	6.42507i	0.216414	−	0.346416i
$345$	14.1811	−	4.66484i	0.763486	−	0.251146i
$346$	0.760572	−	1.28275i	0.0408886	−	0.0689612i
$347$	−15.6447	+	20.3886i	−0.839853	+	1.09452i	0.154458	+	0.987999i	$0.450637\pi$
$347$	−15.6447	+	20.3886i	−0.839853	+	1.09452i	−0.994311	+	0.106518i	$0.966030\pi$
$348$	28.9483	+	15.4704i	1.55179	+	0.829303i
$349$	−9.63369	+	7.39219i	−0.515680	+	0.395695i	−0.833554	−	0.552438i	$-0.813698\pi$
$349$	−9.63369	+	7.39219i	−0.515680	+	0.395695i	0.317874	+	0.948133i	$0.397031\pi$
$350$	−13.0849	−	10.2837i	−0.699415	−	0.549687i
$351$	−3.71274	−	4.48387i	−0.198171	−	0.239331i
$352$	−27.4897	+	5.68124i	−1.46521	+	0.302811i
$353$	−3.33343	−	1.92456i	−0.177421	−	0.102434i	0.408660	−	0.912687i	$-0.365996\pi$
$353$	−3.33343	−	1.92456i	−0.177421	−	0.102434i	−0.586080	+	0.810253i	$0.699330\pi$
$354$	0.892953	−	1.27735i	0.0474599	−	0.0678903i
$355$	−3.58478	+	0.471945i	−0.190260	+	0.0250483i
$356$	6.94583	+	0.161174i	0.368128	+	0.00854223i
$357$	−32.0962	−	2.40855i	−1.69871	−	0.127474i
$358$	−0.347444	+	29.9503i	−0.0183630	+	1.58292i
$359$	14.3336	−	14.3336i	0.756497	−	0.756497i	−0.219186	−	0.975683i	$-0.570340\pi$
$359$	14.3336	−	14.3336i	0.756497	−	0.756497i	0.975683	+	0.219186i	$0.0703402\pi$
$360$	−12.9589	−	2.41980i	−0.682994	−	0.127535i
$361$	−8.74772	−	8.74772i	−0.460406	−	0.460406i
$362$	−5.19487	+	5.07573i	−0.273036	+	0.266774i
$363$	−19.4955	−	13.2947i	−1.02325	−	0.697791i
$364$	4.11909	−	9.32632i	0.215899	−	0.488832i
$365$	−0.103762	−	0.788149i	−0.00543114	−	0.0412536i
$366$	−23.2248	+	19.5182i	−1.21398	+	1.02023i
$367$	4.67472	−	8.09686i	0.244019	−	0.422652i	−0.717837	−	0.696212i	$-0.754868\pi$
$367$	4.67472	−	8.09686i	0.244019	−	0.422652i	0.961855	+	0.273559i	$0.0882009\pi$
$368$	−21.1453	−	6.73149i	−1.10228	−	0.350903i
$369$	−8.62508	−	11.6915i	−0.449004	−	0.608636i
$370$	1.33298	+	11.1203i	0.0692984	+	0.578119i
$371$	19.8438	+	25.8610i	1.03024	+	1.34264i
$372$	1.19441	−	1.66705i	0.0619272	−	0.0864327i
$373$	−4.50562	−	3.45728i	−0.233292	−	0.179011i	0.485500	−	0.874237i	$-0.338638\pi$
$373$	−4.50562	−	3.45728i	−0.233292	−	0.179011i	−0.718791	+	0.695226i	$0.755304\pi$
$374$	−7.09619	−	27.7679i	−0.366935	−	1.43584i
$375$	13.6045	−	15.2203i	0.702533	−	0.785975i
$376$	5.85776	−	4.17924i	0.302091	−	0.215528i
$377$	−7.50622	−	7.50622i	−0.386590	−	0.386590i
$378$	31.2076	+	12.0040i	1.60514	+	0.617418i
$379$	21.3058	−	8.82516i	1.09441	−	0.453318i	0.238865	−	0.971053i	$-0.423225\pi$
$379$	21.3058	−	8.82516i	1.09441	−	0.453318i	0.855541	+	0.517735i	$0.173225\pi$
$380$	7.67736	+	2.24928i	0.393840	+	0.115385i
$381$	12.5706	−	35.9131i	0.644012	−	1.83988i
$382$	1.12937	−	7.87167i	0.0577834	−	0.402750i
$383$	11.6397	+	20.1606i	0.594762	+	1.03016i	0.993580	+	0.113128i	$0.0360871\pi$
$383$	11.6397	+	20.1606i	0.594762	+	1.03016i	−0.398818	+	0.917030i	$0.630580\pi$
$384$	13.5028	+	14.2012i	0.689063	+	0.724701i
$385$	17.5395	−	30.3793i	0.893896	−	1.54827i
$386$	−1.22610	−	0.963622i	−0.0624069	−	0.0490471i
$387$	−5.57344	−	5.78823i	−0.283314	−	0.294232i
$388$	−8.05215	−	33.1048i	−0.408786	−	1.68064i
$389$	0.359571	−	2.73121i	0.0182310	−	0.138478i	−0.979909	−	0.199447i	$-0.936086\pi$
$389$	0.359571	−	2.73121i	0.0182310	−	0.138478i	0.998140	+	0.0609685i	$0.0194189\pi$
$390$	3.78332	+	1.96579i	0.191576	+	0.0995417i
$391$	5.86407	−	21.8850i	0.296559	−	1.10677i
$392$	3.71911	+	38.5815i	0.187843	+	1.94866i
$393$	−1.15469	+	5.53128i	−0.0582465	+	0.279016i
$394$	−7.69369	+	7.51724i	−0.387603	+	0.378713i
$395$	−9.30464	+	3.85411i	−0.468167	+	0.193921i
$396$	−1.25318	+	29.7470i	−0.0629746	+	1.49485i
$397$	−7.43673	+	17.9539i	−0.373239	+	0.901078i	0.619958	+	0.784635i	$0.287149\pi$
$397$	−7.43673	+	17.9539i	−0.373239	+	0.901078i	−0.993197	+	0.116444i	$0.962851\pi$
$398$	−3.39788	−	1.45385i	−0.170321	−	0.0728751i
$399$	−18.1129	−	9.14612i	−0.906779	−	0.457879i
$400$	−10.1060	+	2.21113i	−0.505301	+	0.110556i
$401$	−10.3222	−	17.8787i	−0.515468	−	0.892817i	−0.999839	−	0.0179544i	$-0.994285\pi$
$401$	−10.3222	−	17.8787i	−0.515468	−	0.892817i	0.484370	−	0.874863i	$-0.339049\pi$
$402$	−23.1822	+	4.10594i	−1.15622	+	0.204786i
$403$	−0.526193	+	0.403762i	−0.0262115	+	0.0201128i
$404$	4.76182	+	6.51319i	0.236909	+	0.324043i
$405$	−5.83533	+	12.7067i	−0.289960	+	0.631402i
$406$	58.7068	+	16.4626i	2.91357	+	0.817027i
$407$	24.4331	−	6.54683i	1.21110	−	0.324514i
$408$	−13.8444	+	14.4441i	−0.685400	+	0.715092i
$409$	−18.4213	−	4.93596i	−0.910873	−	0.244068i	−0.227193	−	0.973850i	$-0.572955\pi$
$409$	−18.4213	−	4.93596i	−0.910873	−	0.244068i	−0.683680	+	0.729782i	$0.739622\pi$
$410$	9.15268	+	5.42682i	0.452018	+	0.268012i
$411$	0.450517	−	6.00357i	0.0222224	−	0.296134i
$412$	15.2391	+	27.8686i	0.750777	+	1.37299i
$413$	1.10790	−	2.67472i	0.0545164	−	0.131614i
$414$	−12.3847	+	20.0153i	−0.608675	+	0.983698i
$415$		−	18.8190i		−	0.923787i
$416$	−2.84532	−	5.66300i	−0.139503	−	0.277651i
$417$	23.6638	−	15.4902i	1.15882	−	0.758557i
$418$	2.56599	−	17.8849i	0.125507	−	0.874781i
$419$	−3.80400	−	28.8942i	−0.185837	−	1.41158i	−0.789214	−	0.614119i	$-0.789512\pi$
$419$	−3.80400	−	28.8942i	−0.185837	−	1.41158i	0.603376	−	0.797457i	$-0.293822\pi$
$420$	−24.4752	+	0.803032i	−1.19427	+	0.0391839i
$421$	−26.5497	−	3.49534i	−1.29395	−	0.170352i	−0.548072	−	0.836431i	$-0.684638\pi$
$421$	−26.5497	−	3.49534i	−1.29395	−	0.170352i	−0.745881	+	0.666079i	$0.767971\pi$
$422$	−0.753273	−	1.34038i	−0.0366687	−	0.0652485i
$423$	−2.78695	−	7.10526i	−0.135506	−	0.345469i
$424$	20.2505	+	0.705011i	0.983450	+	0.0342383i
$425$	−2.73374	−	10.2025i	−0.132606	−	0.494892i
$426$	3.84810	−	4.20592i	0.186441	−	0.203777i
$427$	−34.3063	+	44.7089i	−1.66020	+	2.16361i
$428$	2.27910	−	5.16027i	0.110164	−	0.249431i
$429$	3.18124	−	9.08850i	0.153592	−	0.438797i
$430$	5.41049	+	2.31499i	0.260917	+	0.111639i
$431$			0.846314i			0.0407655i	0.999792	+	0.0203828i	$0.00648848\pi$
$431$			0.846314i			0.0407655i	−0.999792	+	0.0203828i	$0.993512\pi$
$432$	18.0959	−	10.2244i	0.870640	−	0.491920i
$433$			35.1194i			1.68773i	0.536554	+	0.843866i	$0.319726\pi$
$433$			35.1194i			1.68773i	−0.536554	+	0.843866i	$0.680274\pi$
$434$	1.49856	−	3.50237i	0.0719332	−	0.168119i
$435$	−8.42358	+	24.0654i	−0.403880	+	1.15385i
$436$	1.78667	+	4.61331i	0.0855661	+	0.220937i
$437$	8.69525	−	11.3319i	0.415950	−	0.542077i
$438$	0.924711	+	0.846041i	0.0441844	+	0.0404254i
$439$	1.64799	+	6.15039i	0.0786544	+	0.293542i	0.994037	−	0.109043i	$-0.0347785\pi$
$439$	1.64799	+	6.15039i	0.0786544	+	0.293542i	−0.915383	+	0.402585i	$0.868112\pi$
$440$	−7.63863	−	20.4238i	−0.364157	−	0.973668i
$441$	40.6511	+	6.13560i	1.93577	+	0.292171i
$442$	5.64097	−	3.17014i	0.268314	−	0.150788i
$443$	−19.9204	−	2.62257i	−0.946447	−	0.124602i	−0.358525	−	0.933520i	$-0.616720\pi$
$443$	−19.9204	−	2.62257i	−0.946447	−	0.124602i	−0.587922	+	0.808918i	$0.700054\pi$
$444$	−12.8890	−	12.0701i	−0.611685	−	0.572821i
$445$	0.704455	+	5.35086i	0.0333944	+	0.253655i
$446$	8.08294	+	1.15968i	0.382738	+	0.0549124i
$447$	−14.4465	+	9.45658i	−0.683296	+	0.447281i
$448$	30.1823	+	20.3489i	1.42598	+	0.961394i
$449$			2.52101i			0.118974i	0.998229	+	0.0594870i	$0.0189465\pi$
$449$			2.52101i			0.118974i	−0.998229	+	0.0594870i	$0.981054\pi$
$450$	−0.334644	+	10.9675i	−0.0157752	+	0.517014i
$451$	9.19651	−	22.2023i	0.433047	−	1.04547i
$452$	31.2449	+	9.15398i	1.46964	+	0.430567i
$453$	−0.580616	+	7.73726i	−0.0272797	+	0.363528i
$454$	−4.43673	+	7.48282i	−0.208226	+	0.351186i
$455$	7.65005	+	2.04983i	0.358640	+	0.0960973i
$456$	−11.5481	+	5.07278i	−0.540791	+	0.237555i
$457$	21.2878	−	5.70405i	0.995801	−	0.266824i	0.276116	−	0.961124i	$-0.410953\pi$
$457$	21.2878	−	5.70405i	0.995801	−	0.266824i	0.719686	+	0.694300i	$0.244286\pi$
$458$	−5.66419	+	20.1988i	−0.264670	+	0.943830i
$459$	11.2849	+	17.9719i	0.526733	+	0.838857i
$460$	2.64589	−	17.0339i	0.123365	−	0.794208i
$461$	0.552658	−	0.424069i	0.0257398	−	0.0197509i	−0.595811	−	0.803124i	$-0.703169\pi$
$461$	0.552658	−	0.424069i	0.0257398	−	0.0197509i	0.621551	+	0.783374i	$0.286503\pi$
$462$	9.64560	+	54.4592i	0.448754	+	2.53367i
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	0.640798	−	0.767710i	$-0.278604\pi$
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	−0.985255	+	0.171092i	$0.945270\pi$
$464$	31.1063	−	21.6528i	1.44408	−	1.00521i
$465$	1.42205	+	0.718065i	0.0659460	+	0.0332995i
$466$	11.6476	−	27.2222i	0.539564	−	1.26105i
$467$	0.222565	−	0.537320i	0.0102991	−	0.0248642i	−0.918646	−	0.395081i	$-0.870717\pi$
$467$	0.222565	−	0.537320i	0.0102991	−	0.0248642i	0.928945	+	0.370217i	$0.120717\pi$
$468$	−6.56048	+	1.46496i	−0.303258	+	0.0677178i
$469$	−40.4042	+	16.7360i	−1.86569	+	0.772796i
$470$	3.90644	+	3.99813i	0.180190	+	0.184420i
$471$	−2.74153	+	13.1327i	−0.126323	+	0.605123i
$472$	−0.845041	−	1.58888i	−0.0388962	−	0.0731343i
$473$	3.43999	−	12.8382i	0.158171	−	0.590302i
$474$	7.32120	−	14.0902i	0.336274	−	0.647184i
$475$	0.869143	−	6.60179i	0.0398790	−	0.302911i
$476$	−19.3245	+	31.7467i	−0.885739	+	1.45511i
$477$	5.95390	−	20.6507i	0.272610	−	0.945531i
$478$	−5.91713	+	7.52888i	−0.270643	+	0.344363i
$479$	18.1501	−	31.4369i	0.829300	−	1.43639i	−0.0692877	−	0.997597i	$-0.522073\pi$
$479$	18.1501	−	31.4369i	0.829300	−	1.43639i	0.898588	−	0.438793i	$-0.144594\pi$
$480$	−9.29090	+	12.0581i	−0.424070	+	0.550373i
$481$	2.85547	+	4.94582i	0.130198	+	0.225510i
$482$	40.5222	+	5.81382i	1.84574	+	0.264812i
$483$	−14.4447	+	41.2672i	−0.657257	+	1.87772i
$484$	−23.9068	+	13.0727i	−1.08667	+	0.594215i
$485$	24.4513	−	10.1280i	1.11027	−	0.459891i
$486$	−5.84604	−	21.2561i	−0.265182	−	0.964198i
$487$	5.14815	+	5.14815i	0.233285	+	0.233285i	0.814062	−	0.580777i	$-0.197251\pi$
$487$	5.14815	+	5.14815i	0.233285	+	0.233285i	−0.580777	+	0.814062i	$0.697251\pi$
$488$	7.88378	+	34.1319i	0.356882	+	1.54508i
$489$	−13.6191	+	15.2366i	−0.615876	+	0.689025i
$490$	−29.1719	+	7.45499i	−1.31785	+	0.336782i
$491$	−17.1385	−	13.1508i	−0.773449	−	0.593488i	0.144814	−	0.989459i	$-0.453741\pi$
$491$	−17.1385	−	13.1508i	−0.773449	−	0.593488i	−0.918263	+	0.395971i	$0.870408\pi$
$492$	−16.5520	+	2.73400i	−0.746224	+	0.123258i
$493$	23.5570	+	30.7001i	1.06095	+	1.38266i
$494$	4.05030	−	0.485505i	0.182232	−	0.0218439i
$495$	−22.9834	+	2.58489i	−1.03303	+	0.116182i
$496$	−1.08762	−	2.10349i	−0.0488355	−	0.0944494i
$497$	5.29475	−	9.17077i	0.237502	−	0.411365i
$498$	19.0893	+	22.7145i	0.855413	+	1.01786i
$499$	−4.42483	−	33.6099i	−0.198083	−	1.50459i	−0.744810	−	0.667277i	$-0.767460\pi$
$499$	−4.42483	−	33.6099i	−0.198083	−	1.50459i	0.546727	−	0.837311i	$-0.315873\pi$
$500$	−8.51310	−	21.9814i	−0.380718	−	0.983038i
$501$	1.29754	+	0.884840i	0.0579698	+	0.0395317i
$502$	2.86671	+	2.93401i	0.127948	+	0.130951i
$503$	−8.18706	−	8.18706i	−0.365043	−	0.365043i	0.500623	−	0.865666i	$-0.333104\pi$
$503$	−8.18706	−	8.18706i	−0.365043	−	0.365043i	−0.865666	+	0.500623i	$0.833104\pi$
$504$	28.7270	−	25.7961i	1.27960	−	1.14905i
$505$	−4.43178	+	4.43178i	−0.197212	+	0.197212i
$506$	−38.9295	−	0.451609i	−1.73063	−	0.0200765i
$507$	−20.2856	−	1.52226i	−0.900916	−	0.0676061i
$508$	−30.3383	−	31.7797i	−1.34604	−	1.41000i
$509$	−20.5911	+	2.71087i	−0.912683	+	0.120157i	−0.572219	−	0.820101i	$-0.693917\pi$
$509$	−20.5911	+	2.71087i	−0.912683	+	0.120157i	−0.340464	+	0.940258i	$0.610584\pi$
$510$	−12.7381	−	8.90479i	−0.564052	−	0.394311i
$511$	2.01628	+	1.16410i	0.0891951	+	0.0514968i
$512$	21.6936	−	6.43344i	0.958729	−	0.284321i
$513$	2.23694	+	13.1900i	0.0987633	+	0.582351i
$514$	19.9805	−	25.4229i	0.881301	−	1.12136i
$515$	−19.5750	+	15.0204i	−0.862579	+	0.661880i
$516$	−8.87870	+	2.69403i	−0.390863	+	0.118598i
$517$	7.68525	−	10.0156i	0.337997	−	0.440486i
$518$	−28.2150	−	16.7293i	−1.23970	−	0.735044i
$519$	−1.73498	+	0.570718i	−0.0761573	+	0.0250517i
$520$	4.00768	−	2.85929i	0.175748	−	0.125388i
$521$	20.7314	−	20.7314i	0.908261	−	0.908261i	−0.0878707	−	0.996132i	$-0.528006\pi$
$521$	20.7314	−	20.7314i	0.908261	−	0.908261i	0.996132	+	0.0878707i	$0.0280062\pi$
$522$	−14.2439	−	37.5915i	−0.623437	−	1.64533i
$523$	−5.99966	−	14.4845i	−0.262347	−	0.633361i	0.736736	−	0.676181i	$-0.236366\pi$
$523$	−5.99966	−	14.4845i	−0.262347	−	0.633361i	−0.999083	+	0.0428191i	$0.986366\pi$
$524$	5.08283	+	4.09098i	0.222044	+	0.178715i
$525$	3.78734	+	20.0277i	0.165293	+	0.874079i
$526$	−0.518725	−	0.692503i	−0.0226175	−	0.0301946i
$527$	2.09385	−	1.20888i	0.0912095	−	0.0526598i
$528$	29.9370	+	16.9031i	1.30284	+	0.735615i
$529$	−6.73541	−	3.88869i	−0.292844	−	0.169073i
$530$	1.87336	+	15.6284i	0.0813734	+	0.678854i
$531$	−1.85276	+	0.459093i	−0.0804028	+	0.0199229i
$532$	−18.9143	+	13.8283i	−0.820037	+	0.599533i
$533$	5.37930	+	0.708198i	0.233003	+	0.0306755i
$534$	−6.27801	−	5.74390i	−0.271676	−	0.248563i
$535$	4.23278	+	1.13417i	0.182999	+	0.0490345i
$536$	−7.94540	+	25.9981i	−0.343189	+	1.12295i
$537$	24.4470	−	27.3506i	1.05497	−	1.18027i
$538$	−2.18738	−	0.0253751i	−0.0943047	−	0.00109400i
$539$	26.0231	+	62.8254i	1.12090	+	2.70608i
$540$	10.0059	+	12.6714i	0.430585	+	0.545291i
$541$	−4.63048	−	1.91801i	−0.199080	−	0.0824617i	0.280916	−	0.959732i	$-0.409362\pi$
$541$	−4.63048	−	1.91801i	−0.199080	−	0.0824617i	−0.479996	+	0.877271i	$0.659362\pi$
$542$	−16.8112	+	6.73603i	−0.722102	+	0.289337i
$543$	8.88126	−	0.497858i	0.381131	−	0.0213651i
$544$	7.58887	+	21.8207i	0.325370	+	0.935555i
$545$	−3.32816	+	1.92152i	−0.142563	+	0.0823087i
$546$	−11.3129	+	5.28582i	−0.484146	+	0.226212i
$547$	−19.8489	−	25.8676i	−0.848679	−	1.10602i	−0.993189	−	0.116517i	$-0.962827\pi$
$547$	−19.8489	−	25.8676i	−0.848679	−	1.10602i	0.144510	−	0.989503i	$-0.453840\pi$
$548$	−5.93819	−	3.61463i	−0.253667	−	0.154410i
$549$	37.1488	+	0.702294i	1.58547	+	0.0299732i
$550$	−15.8222	+	8.89185i	−0.674661	+	0.379150i
$551$	6.31395	+	23.5640i	0.268983	+	1.00386i
$552$	14.0850	+	23.2437i	0.599496	+	0.989319i
$553$	7.63417	−	28.4911i	0.324638	−	1.21156i
$554$	−3.68038	−	14.4016i	−0.156364	−	0.611864i
$555$	7.72826	−	11.3328i	0.328046	−	0.481051i
$556$	−3.51048	−	32.4691i	−0.148878	−	1.37699i
$557$	−29.0633	−	12.0384i	−1.23145	−	0.510083i	−0.330418	−	0.943835i	$-0.607190\pi$
$557$	−29.0633	−	12.0384i	−1.23145	−	0.510083i	−0.901033	+	0.433751i	$0.857190\pi$
$558$	−2.44479	+	0.575776i	−0.103496	+	0.0243745i
$559$	3.00078			0.126920
$560$	−12.0212	+	25.5943i	−0.507986	+	1.08156i
$561$	−15.8218	+	31.3334i	−0.667999	+	1.32290i
$562$	−9.17736	+	6.87438i	−0.387124	+	0.289978i
$563$	0.314743	−	0.0414367i	0.0132648	−	0.00174635i	−0.123891	−	0.992296i	$-0.539537\pi$
$563$	0.314743	−	0.0414367i	0.0132648	−	0.00174635i	0.137156	+	0.990550i	$0.456204\pi$
$564$	−8.77063	−	0.863182i	−0.369310	−	0.0363465i
$565$	−3.30121	+	25.0752i	−0.138883	+	1.05492i
$566$	15.7588	+	4.41911i	0.662393	+	0.185749i
$567$	−19.1206	−	36.2135i	−0.802990	−	1.52082i
$568$	−2.30591	−	6.16546i	−0.0967540	−	0.258697i
$569$	−42.7781	+	11.4624i	−1.79335	+	0.480527i	−0.992909	−	0.118881i	$-0.962069\pi$
$569$	−42.7781	+	11.4624i	−1.79335	+	0.480527i	−0.800444	+	0.599408i	$0.795403\pi$
$570$	−5.27080	−	8.25955i	−0.220770	−	0.345955i
$571$	−5.09120	−	3.90662i	−0.213060	−	0.163487i	0.496718	−	0.867912i	$-0.334538\pi$
$571$	−5.09120	−	3.90662i	−0.213060	−	0.163487i	−0.709778	+	0.704425i	$0.751205\pi$
$572$	−7.67768	−	8.04246i	−0.321020	−	0.336272i
$573$	−7.38291	+	6.35221i	−0.308426	+	0.265367i
$574$	−28.9277	+	11.5910i	−1.20742	+	0.483798i
$575$	−14.3480			−0.598351
$576$	−1.01720	−	23.9784i	−0.0423834	−	0.999101i
$577$	6.71403			0.279509			0.139754	−	0.990186i	$-0.455369\pi$
$577$	6.71403			0.279509			0.139754	+	0.990186i	$0.455369\pi$
$578$	0.421149	−	0.168749i	0.0175175	−	0.00701904i
$579$	0.354888	+	1.87667i	0.0147487	+	0.0779918i
$580$	20.3297	+	21.2956i	0.844145	+	0.884252i
$581$	43.7264	+	33.5525i	1.81408	+	1.39199i
$582$	−19.2391	+	37.0271i	−0.797485	+	1.53482i
$583$	34.3380	−	9.20083i	1.42213	−	0.381059i
$584$	1.35553	−	0.506978i	0.0560924	−	0.0209789i
$585$	−1.90674	−	4.86118i	−0.0788338	−	0.200985i
$586$	3.94633	+	1.10663i	0.163021	+	0.0457147i
$587$	1.37700	−	10.4594i	0.0568349	−	0.431704i	−0.939245	−	0.343247i	$-0.888473\pi$
$587$	1.37700	−	10.4594i	0.0568349	−	0.431704i	0.996080	−	0.0884568i	$-0.0281935\pi$
$588$	27.6483	−	38.5891i	1.14020	−	1.59139i
$589$	1.51118	−	0.198950i	0.0622670	−	0.00819760i
$590$	1.11888	−	0.838104i	0.0460634	−	0.0345042i
$591$	13.1533	−	0.737336i	0.541054	−	0.0303299i
$592$	−19.1795	+	6.92073i	−0.788274	+	0.284440i
$593$	13.6954			0.562403			0.281202	−	0.959649i	$-0.409267\pi$
$593$	13.6954			0.562403			0.281202	+	0.959649i	$0.409267\pi$
$594$	25.1188	−	26.4335i	1.03064	−	1.08458i
$595$	−26.6730	−	11.0483i	−1.09349	−	0.452938i
$596$	2.14311	+	19.8220i	0.0877851	+	0.811940i
$597$	1.96355	+	4.07841i	0.0803627	+	0.166918i
$598$	−2.17634	−	8.51617i	−0.0889972	−	0.348252i
$599$	10.5998	−	39.5590i	0.433096	−	1.61634i	−0.312485	−	0.949923i	$-0.601161\pi$
$599$	10.5998	−	39.5590i	0.433096	−	1.61634i	0.745581	−	0.666415i	$-0.232172\pi$
$600$	11.1044	+	6.10104i	0.453337	+	0.249074i
$601$	−6.05516	−	22.5982i	−0.246995	−	0.921798i	−0.972370	−	0.233444i	$-0.925000\pi$
$601$	−6.05516	−	22.5982i	−0.246995	−	0.921798i	0.725375	−	0.688354i	$-0.241666\pi$
$602$	−15.0253	+	8.44403i	−0.612387	+	0.344153i
$603$	24.6942	+	14.8865i	1.00562	+	0.606225i
$604$	7.65301	+	4.65846i	0.311397	+	0.189550i
$605$	−12.8852	−	16.7923i	−0.523856	−	0.682703i
$606$	0.853701	−	9.84459i	0.0346792	−	0.399909i
$607$	16.3379	−	9.43267i	0.663133	−	0.382860i	−0.130337	−	0.991470i	$-0.541606\pi$
$607$	16.3379	−	9.43267i	0.663133	−	0.382860i	0.793470	+	0.608610i	$0.208272\pi$
$608$	−0.844277	+	14.5400i	−0.0342399	+	0.589674i
$609$	−40.8982	−	62.4788i	−1.65728	−	2.53177i
$610$	−25.2597	+	10.1213i	−1.02274	+	0.409798i
$611$	2.63329	+	1.09075i	0.106532	+	0.0441269i
$612$	24.4076	−	2.17303i	0.986617	−	0.0878394i
$613$	−9.88791	−	23.8715i	−0.399369	−	0.964162i	−0.987816	−	0.155626i	$-0.950260\pi$
$613$	−9.88791	−	23.8715i	−0.399369	−	0.964162i	0.588447	−	0.808536i	$-0.299740\pi$
$614$	39.5178	+	0.458433i	1.59481	+	0.0185009i
$615$	−4.07218	−	12.3794i	−0.164206	−	0.499187i
$616$	61.0743	+	18.6652i	2.46075	+	0.752042i
$617$	1.01203	+	0.271173i	0.0407428	+	0.0109170i	0.279133	−	0.960252i	$-0.409953\pi$
$617$	1.01203	+	0.271173i	0.0407428	+	0.0109170i	−0.238390	+	0.971169i	$0.576620\pi$
$618$	8.39078	−	37.9859i	0.337527	−	1.52802i
$619$	8.02100	+	1.05599i	0.322391	+	0.0424436i	0.289985	−	0.957031i	$-0.406350\pi$
$619$	8.02100	+	1.05599i	0.322391	+	0.0424436i	0.0324062	+	0.999475i	$0.489683\pi$
$620$	1.48496	−	1.08567i	0.0596376	−	0.0436014i
$621$	27.5488	−	8.48850i	1.10549	−	0.340632i
$622$	−5.65536	−	47.1796i	−0.226759	−	1.89173i
$623$	−13.6889	−	7.90327i	−0.548433	−	0.316638i
$624$	−1.93689	+	7.51642i	−0.0775377	+	0.300897i
$625$	4.65908	−	2.68992i	0.186363	−	0.107597i
$626$	−9.88288	−	13.1937i	−0.394999	−	0.527328i
$627$	−16.7745	+	14.4326i	−0.669907	+	0.576384i
$628$	12.0679	+	9.71303i	0.481563	+	0.387592i
$629$	−7.96680	−	19.2336i	−0.317657	−	0.766892i
$630$	23.2264	+	18.9752i	0.925361	+	0.755989i
$631$	−2.84039	+	2.84039i	−0.113074	+	0.113074i	−0.761380	−	0.648306i	$-0.775478\pi$
$631$	−2.84039	+	2.84039i	−0.113074	+	0.113074i	0.648306	+	0.761380i	$0.275478\pi$
$632$	−10.6489	−	14.9258i	−0.423589	−	0.593717i
$633$	−0.384813	+	1.84336i	−0.0152949	+	0.0732669i
$634$	−31.8985	−	18.9133i	−1.26685	−	0.751145i
$635$	20.7769	−	27.0770i	0.824506	−	1.07452i
$636$	−18.1140	−	16.9632i	−0.718269	−	0.672633i
$637$	−12.1804	+	9.34632i	−0.482603	+	0.370315i
$638$	41.0878	−	52.2796i	1.62668	−	2.06977i
$639$	−6.93812	+	0.780314i	−0.274468	+	0.0308687i
$640$	7.52492	+	15.8850i	0.297449	+	0.627909i
$641$	−18.8927	−	10.9077i	−0.746215	−	0.430828i	0.0781094	−	0.996945i	$-0.475112\pi$
$641$	−18.8927	−	10.9077i	−0.746215	−	0.430828i	−0.824325	+	0.566117i	$0.808445\pi$
$642$	−6.25942	+	2.92465i	−0.247040	+	0.115427i
$643$	−3.20671	+	0.422172i	−0.126460	+	0.0166488i	−0.193491	−	0.981102i	$-0.561981\pi$
$643$	−3.20671	+	0.422172i	−0.126460	+	0.0166488i	0.0670303	+	0.997751i	$0.478648\pi$
$644$	34.8613	+	36.5176i	1.37373	+	1.43899i
$645$	−3.12658	−	6.49410i	−0.123109	−	0.255705i
$646$	−14.8694	−	0.172495i	−0.585028	−	0.00678672i
$647$	−16.3835	+	16.3835i	−0.644101	+	0.644101i	−0.951561	−	0.307460i	$-0.900521\pi$
$647$	−16.3835	+	16.3835i	−0.644101	+	0.644101i	0.307460	+	0.951561i	$0.400521\pi$
$648$	−24.9305	−	5.14472i	−0.979364	−	0.202104i
$649$	−2.23254	−	2.23254i	−0.0876349	−	0.0876349i
$650$	−2.86370	−	2.93093i	−0.112324	−	0.114960i
$651$	−4.20382	+	2.02393i	−0.164761	+	0.0793241i
$652$	8.52222	+	22.0050i	0.333756	+	0.861781i
$653$	3.15272	+	23.9473i	0.123375	+	0.937129i	0.935421	+	0.353535i	$0.115021\pi$
$653$	3.15272	+	23.9473i	0.123375	+	0.937129i	−0.812046	+	0.583594i	$0.801646\pi$
$654$	2.06796	−	5.69524i	0.0808638	−	0.222701i
$655$	−2.53421	+	4.38938i	−0.0990197	+	0.171507i
$656$	−5.87627	+	18.4589i	−0.229430	+	0.720697i
$657$	−0.171560	−	1.52541i	−0.00669318	−	0.0595120i
$658$	−16.2546	+	1.94842i	−0.633670	+	0.0759572i
$659$	−4.31241	−	5.62005i	−0.167988	−	0.218926i	0.701772	−	0.712402i	$-0.252393\pi$
$659$	−4.31241	−	5.62005i	−0.167988	−	0.218926i	−0.869759	+	0.493476i	$0.835726\pi$
$660$	−9.40543	+	24.9952i	−0.366106	+	0.972937i
$661$	30.6268	+	23.5008i	1.19125	+	0.914075i	0.997751	−	0.0670263i	$-0.0213511\pi$
$661$	30.6268	+	23.5008i	1.19125	+	0.914075i	0.193495	+	0.981101i	$0.438018\pi$
$662$	−46.1919	+	11.8045i	−1.79530	+	0.458796i
$663$	−7.75776	−	1.61948i	−0.301286	−	0.0628955i
$664$	33.3818	−	7.71053i	1.29547	−	0.299227i
$665$	−12.8699	−	12.8699i	−0.499072	−	0.499072i
$666$	2.16762	+	21.5179i	0.0839937	+	0.833803i
$667$	48.5642	−	20.1160i	1.88041	−	0.778893i
$668$	1.59114	−	0.870066i	0.0615630	−	0.0336639i
$669$	−6.52270	−	7.58107i	−0.252182	−	0.293101i
$670$	−20.9036	−	2.99909i	−0.807576	−	0.115865i
$671$	30.7291	+	53.2243i	1.18628	+	2.05470i
$672$	−11.4525	−	43.0861i	−0.441788	−	1.66208i
$673$	−4.86626	+	8.42860i	−0.187580	+	0.324899i	−0.944443	−	0.328675i	$-0.893398\pi$
$673$	−4.86626	+	8.42860i	−0.187580	+	0.324899i	0.756863	+	0.653574i	$0.226731\pi$
$674$	2.75759	−	3.50872i	0.106218	−	0.135151i
$675$	9.14360	−	9.84846i	0.351938	−	0.379067i
$676$	−12.2136	+	20.0647i	−0.469753	+	0.771720i
$677$	3.48507	−	26.4718i	0.133942	−	1.01739i	−0.784023	−	0.620732i	$-0.786836\pi$
$677$	3.48507	−	26.4718i	0.133942	−	1.01739i	0.917965	−	0.396661i	$-0.129831\pi$
$678$	−21.4508	−	33.6143i	−0.823814	−	1.29095i
$679$	−20.0615	+	74.8706i	−0.769890	+	2.87327i
$680$	−15.8448	+	8.42699i	−0.607621	+	0.323160i
$681$	10.1209	−	3.32923i	0.387832	−	0.127576i
$682$	−2.90341	−	2.97156i	−0.111177	−	0.113787i
$683$	−13.9691	+	5.78620i	−0.534513	+	0.221403i	−0.633579	−	0.773678i	$-0.718415\pi$
$683$	−13.9691	+	5.78620i	−0.534513	+	0.221403i	0.0990653	+	0.995081i	$0.468415\pi$
$684$	14.7401	+	4.62273i	0.563600	+	0.176755i
$685$	2.06658	−	4.98916i	0.0789599	−	0.190626i
$686$	16.9696	−	39.6606i	0.647901	−	1.51425i
$687$	21.4966	−	14.0716i	0.820148	−	0.536863i
$688$	−1.88962	+	10.5458i	−0.0720412	+	0.402056i
$689$	4.01304	+	6.95080i	0.152885	+	0.264804i
$690$	−16.1626	+	13.5831i	−0.615299	+	0.517100i
$691$	−26.7099	+	20.4952i	−1.01609	+	0.779676i	−0.975611	−	0.219504i	$-0.929556\pi$
$691$	−26.7099	+	20.4952i	−1.01609	+	0.779676i	−0.0404818	+	0.999180i	$0.512889\pi$
$692$	−0.323711	+	2.08400i	−0.0123056	+	0.0792218i
$693$	34.9711	−	58.0111i	1.32844	−	2.20366i
$694$	9.81318	−	34.9944i	0.372503	−	1.32837i
$695$	24.5048	−	6.56604i	0.929520	−	0.249064i
$696$	−46.1394	−	5.08198i	−1.74891	−	0.192632i
$697$	−19.1046	−	5.11905i	−0.723637	−	0.193898i
$698$	8.75834	−	14.7715i	0.331508	−	0.559109i
$699$	−32.6743	+	15.7310i	−1.23585	+	0.595002i
$700$	22.5864	+	6.61727i	0.853687	+	0.250109i
$701$	−8.97900	+	21.6772i	−0.339132	+	0.818737i	0.658667	+	0.752434i	$0.271120\pi$
$701$	−8.97900	+	21.6772i	−0.339132	+	0.818737i	−0.997800	+	0.0663032i	$0.978880\pi$
$702$	7.23244	+	3.93330i	0.272971	+	0.148453i
$703$		−	13.1243i		−	0.494993i
$704$	33.0989	−	21.9178i	1.24746	−	0.826057i
$705$	−0.383167	−	6.83529i	−0.0144309	−	0.257432i
$706$	5.38829	+	0.773071i	0.202791	+	0.0290949i
$707$	−2.39592	−	18.1988i	−0.0901078	−	0.684437i
$708$	−0.500337	+	2.14654i	−0.0188038	+	0.0806719i
$709$	29.6997	+	3.91003i	1.11539	+	0.146844i	0.665615	−	0.746295i	$-0.268169\pi$
$709$	29.6997	+	3.91003i	1.11539	+	0.146844i	0.449779	+	0.893140i	$0.351503\pi$
$710$	4.45769	−	2.50516i	0.167294	−	0.0940168i
$711$	−18.1045	+	7.10126i	−0.678972	+	0.266318i
$712$	−9.20294	+	3.44195i	−0.344895	+	0.128993i
$713$	−0.850040	−	3.17239i	−0.0318343	−	0.118807i
$714$	43.4013	−	13.7209i	1.62425	−	0.513492i
$715$	5.25799	−	6.85235i	0.196638	−	0.256263i
$716$	−15.2979	−	39.5001i	−0.571708	−	1.47619i
$717$	11.5237	−	2.17919i	0.430361	−	0.0813835i
$718$	−11.2769	+	26.3560i	−0.420851	+	0.983595i
$719$			40.2309i			1.50036i	0.661234	+	0.750180i	$0.270033\pi$
$719$			40.2309i			1.50036i	−0.661234	+	0.750180i	$0.729967\pi$
$720$	18.2847	−	3.63983i	0.681429	−	0.135648i
$721$		−	72.2632i		−	2.69122i
$722$	16.0849	+	6.88226i	0.598619	+	0.256131i
$723$	−32.7003	−	38.0062i	−1.21614	−	1.41346i
$724$	4.14973	−	9.39570i	0.154224	−	0.349188i
$725$	14.9179	−	19.4413i	0.554035	−	0.722033i
$726$	32.5858	+	7.19795i	1.20937	+	0.267141i
$727$	3.89504	+	14.5365i	0.144459	+	0.539129i	0.999779	+	0.0210282i	$0.00669397\pi$
$727$	3.89504	+	14.5365i	0.144459	+	0.539129i	−0.855320	+	0.518100i	$0.826639\pi$
$728$	−0.501671	+	14.4098i	−0.0185932	+	0.534063i
$729$	−11.7296	+	24.3190i	−0.434431	+	0.900705i
$730$	0.550783	+	0.980065i	0.0203854	+	0.0362738i
$731$	−10.8452	−	1.42780i	−0.401126	−	0.0528092i
$732$	20.2218	−	37.8390i	0.747418	−	1.39857i
$733$	0.172177	+	1.30781i	0.00635950	+	0.0483052i	0.994330	−	0.106335i	$-0.0339115\pi$
$733$	0.172177	+	1.30781i	0.00635950	+	0.0483052i	−0.987971	+	0.154640i	$0.950578\pi$
$734$	−1.87778	+	13.0881i	−0.0693101	+	0.483090i
$735$	32.9177	+	16.6218i	1.21419	+	0.613105i
$736$	31.2994	−	2.28574i	1.15371	−	0.0842535i
$737$			47.6940i			1.75683i
$738$	17.4724	+	10.8113i	0.643167	+	0.397968i
$739$	−11.4907	+	27.7409i	−0.422691	+	1.02047i	0.558860	+	0.829262i	$0.311239\pi$
$739$	−11.4907	+	27.7409i	−0.422691	+	1.02047i	−0.981550	+	0.191204i	$0.938761\pi$
$740$	−7.59922	−	13.8971i	−0.279353	−	0.510868i
$741$	−4.12768	−	2.81482i	−0.151634	−	0.103405i
$742$	−39.6530	−	23.5112i	−1.45571	−	0.863122i
$743$	5.46342	+	1.46392i	0.200433	+	0.0537060i	0.357639	−	0.933860i	$-0.383582\pi$
$743$	5.46342	+	1.46392i	0.200433	+	0.0537060i	−0.157206	+	0.987566i	$0.550249\pi$
$744$	−0.691087	+	2.81669i	−0.0253365	+	0.103265i
$745$	−14.9599	+	4.00849i	−0.548089	+	0.146860i
$746$	7.73330	+	2.16858i	0.283136	+	0.0793975i
$747$	0.686861	−	36.3325i	0.0251309	−	1.32934i
$748$	23.9215	+	32.7197i	0.874658	+	1.19635i
$749$	−10.1819	+	7.81287i	−0.372040	+	0.285476i
$750$	−9.85339	+	27.1366i	−0.359795	+	0.990887i
$751$	−26.9412	−	46.6635i	−0.983099	−	1.70278i	−0.650098	−	0.759850i	$-0.725272\pi$
$751$	−26.9412	−	46.6635i	−0.983099	−	1.70278i	−0.333001	−	0.942927i	$-0.608061\pi$
$752$	−5.49149	+	8.56751i	−0.200254	+	0.312425i
$753$	−0.281185	−	5.01603i	−0.0102469	−	0.182794i
$754$	13.8021	+	5.90551i	0.502643	+	0.215066i
$755$	−2.66336	+	6.42992i	−0.0969296	+	0.234009i
$756$	−47.2820	+	0.657053i	−1.71963	+	0.0238968i
$757$	34.5808	−	14.3238i	1.25686	−	0.520609i	0.347916	−	0.937526i	$-0.386889\pi$
$757$	34.5808	−	14.3238i	1.25686	−	0.520609i	0.908945	+	0.416917i	$0.136889\pi$
$758$	−23.3272	+	22.7922i	−0.847283	+	0.827850i
$759$	35.5505	+	31.7763i	1.29040	+	1.15341i
$760$	−11.2616	+	1.08557i	−0.408501	+	0.0393779i
$761$	−5.54843	+	20.7070i	−0.201130	+	0.750629i	0.789464	+	0.613797i	$0.210359\pi$
$761$	−5.54843	+	20.7070i	−0.201130	+	0.750629i	−0.990594	+	0.136832i	$0.956308\pi$
$762$	2.38830	+	53.7572i	0.0865190	+	1.94742i
$763$	1.46910	−	11.1590i	0.0531852	−	0.403981i
$764$	2.65795	+	10.9276i	0.0961612	+	0.395347i
$765$	4.57821	+	18.4762i	0.165526	+	0.668010i
$766$	−25.8846	−	20.3433i	−0.935250	−	0.735035i
$767$	0.356416	−	0.617331i	0.0128695	−	0.0222905i
$768$	−25.1957	−	11.5401i	−0.909173	−	0.416418i
$769$	23.0680	+	39.9550i	0.831854	+	1.44081i	0.896566	+	0.442910i	$0.146054\pi$
$769$	23.0680	+	39.9550i	0.831854	+	1.44081i	−0.0647118	+	0.997904i	$0.520613\pi$
$770$	−7.04540	+	49.1064i	−0.253899	+	1.76967i
$771$	−38.9123	+	7.35852i	−1.40139	+	0.265011i
$772$	2.11644	+	0.620064i	0.0761722	+	0.0223166i
$773$	3.48172	−	1.44218i	0.125229	−	0.0518715i	−0.319189	−	0.947691i	$-0.603411\pi$
$773$	3.48172	−	1.44218i	0.125229	−	0.0518715i	0.444418	+	0.895820i	$0.353411\pi$
$774$	10.3612	+	4.66687i	0.372425	+	0.167747i
$775$	−1.08265	−	1.08265i	−0.0388898	−	0.0388898i
$776$	27.9837	+	39.2229i	1.00456	+	1.40802i
$777$	12.5533	+	38.1621i	0.450348	+	1.36906i
$778$	0.964601	+	3.77455i	0.0345826	+	0.135324i
$779$	−9.89218	−	7.59054i	−0.354424	−	0.271959i
$780$	−6.00057	−	0.590561i	−0.214855	−	0.0211455i
$781$	−7.03031	−	9.16208i	−0.251564	−	0.327845i
$782$	3.81352	+	31.8142i	0.136371	+	1.13767i
$783$	−17.1412	+	46.1540i	−0.612576	+	1.64941i
$784$	−25.1763	−	48.6917i	−0.899153	−	1.73899i
$785$	−6.01686	+	10.4215i	−0.214751	+	0.371960i
$786$	−1.39365	−	7.86858i	−0.0497099	−	0.280663i
$787$	0.488356	+	3.70943i	0.0174080	+	0.132227i	0.997942	−	0.0641222i	$-0.0204247\pi$
$787$	0.488356	+	3.70943i	0.0174080	+	0.132227i	−0.980534	+	0.196349i	$0.937091\pi$
$788$	6.14582	−	13.9152i	0.218936	−	0.495708i
$789$	−0.0792982	+	1.05672i	−0.00282309	+	0.0376204i
$790$	10.1874	−	9.95376i	0.362452	−	0.354139i
$791$	−52.3771	−	52.3771i	−1.86232	−	1.86232i
$792$	−14.0019	−	39.7097i	−0.497537	−	1.41102i
$793$	−9.81155	+	9.81155i	−0.348418	+	0.348418i
$794$	0.318795	−	27.4807i	0.0113136	−	0.975255i
$795$	10.8612	−	15.9270i	0.385207	−	0.564872i
$796$	5.22531	+	0.121251i	0.185206	+	0.00429762i
$797$	−29.0768	+	3.82803i	−1.02995	+	0.135596i	−0.626514	−	0.779410i	$-0.715519\pi$
$797$	−29.0768	+	3.82803i	−1.02995	+	0.135596i	−0.403439	+	0.915006i	$0.632185\pi$
$798$	28.5887	+	2.47914i	1.01203	+	0.0877607i
$799$	−8.99811	−	5.19506i	−0.318330	−	0.183788i
$800$	12.1037	−	8.21847i	0.427929	−	0.290567i
$801$	1.16474	+	10.3563i	0.0411542	+	0.365920i
$802$	22.9548	+	18.0407i	0.810562	+	0.637040i
$803$	2.01437	−	1.54568i	0.0710856	−	0.0545459i
$804$	28.2728	−	17.5840i	0.997103	−	0.620140i
$805$	−23.8744	+	31.1137i	−0.841462	+	1.09662i
$806$	0.478381	−	0.806819i	0.0168503	−	0.0284190i
$807$	1.99752	+	1.78545i	0.0703159	+	0.0628510i
$808$	−9.67706	−	6.04547i	−0.340438	−	0.212679i
$809$	14.3467	−	14.3467i	0.504404	−	0.504404i	−0.408400	−	0.912803i	$-0.633913\pi$
$809$	14.3467	−	14.3467i	0.504404	−	0.504404i	0.912803	+	0.408400i	$0.133913\pi$
$810$	0.976561	−	19.7502i	0.0343129	−	0.693951i
$811$	13.2334	+	31.9483i	0.464688	+	1.12186i	0.966451	+	0.256851i	$0.0826848\pi$
$811$	13.2334	+	31.9483i	0.464688	+	1.12186i	−0.501763	+	0.865005i	$0.667315\pi$
$812$	−85.7269	+	9.26860i	−3.00842	+	0.325264i
$813$	20.9353	+	7.32795i	0.734232	+	0.257002i
$814$	−28.6309	+	21.4463i	−1.00351	+	0.751691i
$815$	−15.8750	+	9.16541i	−0.556075	+	0.321050i
$816$	10.5766	−	26.2438i	0.370255	−	0.918716i
$817$	−5.97219	−	3.44804i	−0.208940	−	0.120632i
$818$	26.7789	−	3.20995i	0.936303	−	0.112233i
$819$	14.6946	+	4.23667i	0.513472	+	0.148041i
$820$	−14.8697	−	2.30974i	−0.519274	−	0.0806596i
$821$	−27.9809	−	3.68375i	−0.976540	−	0.128564i	−0.374670	−	0.927158i	$-0.622244\pi$
$821$	−27.9809	−	3.68375i	−0.976540	−	0.128564i	−0.601870	+	0.798594i	$0.705577\pi$
$822$	2.56648	+	8.11817i	0.0895163	+	0.283154i
$823$	−20.7098	−	5.54918i	−0.721899	−	0.193432i	−0.120880	−	0.992667i	$-0.538572\pi$
$823$	−20.7098	−	5.54918i	−0.721899	−	0.193432i	−0.601019	+	0.799235i	$0.705238\pi$
$824$	−34.6642	−	28.5687i	−1.20758	−	0.995239i
$825$	21.7595	+	4.54244i	0.757570	+	0.158148i
$826$	−0.0474932	+	4.09400i	−0.00165250	+	0.142449i
$827$	1.83537	+	4.43098i	0.0638222	+	0.154080i	0.952573	−	0.304310i	$-0.0984260\pi$
$827$	1.83537	+	4.43098i	0.0638222	+	0.154080i	−0.888751	+	0.458391i	$0.848426\pi$
$828$	5.72996	−	32.7895i	0.199130	−	1.13951i
$829$	31.7765	+	13.1623i	1.10364	+	0.457144i	0.858744	−	0.512405i	$-0.171245\pi$
$829$	31.7765	+	13.1623i	1.10364	+	0.457144i	0.244899	+	0.969549i	$0.421245\pi$
$830$	9.89885	+	24.7047i	0.343594	+	0.857511i
$831$	−8.20587	+	16.2508i	−0.284658	+	0.563735i
$832$	6.71396	+	5.93747i	0.232765	+	0.205845i
$833$	48.4686	−	27.9834i	1.67934	−	0.969566i
$834$	−22.9169	+	32.7820i	−0.793546	+	1.13515i
$835$	0.857582	+	1.11762i	0.0296779	+	0.0386769i
$836$	6.03903	+	24.8282i	0.208864	+	0.858702i
$837$	2.71925	+	1.43822i	0.0939909	+	0.0497122i
$838$	20.1922	+	35.9301i	0.697527	+	1.24118i
$839$	−1.62295	−	6.05695i	−0.0560306	−	0.209109i	0.932235	−	0.361853i	$-0.117856\pi$
$839$	−1.62295	−	6.05695i	−0.0560306	−	0.209109i	−0.988266	+	0.152744i	$0.951189\pi$
$840$	31.7075	−	13.9282i	1.09401	−	0.480570i
$841$	−15.7305	+	58.7072i	−0.542432	+	2.02439i
$842$	36.6918	−	9.37673i	1.26448	−	0.323144i
$843$	14.0042	+	1.05090i	0.482330	+	0.0361948i
$844$	1.69390	+	1.36336i	0.0583066	+	0.0469288i
$845$	−16.8580	−	6.98282i	−0.579933	−	0.240216i
$846$	7.39596	+	7.86150i	0.254278	+	0.270284i
$847$	61.9903			2.13001
$848$	−26.9547	+	9.72631i	−0.925628	+	0.334003i
$849$	−10.9784	−	16.7714i	−0.376778	−	0.575591i
$850$	8.95527	+	11.9554i	0.307163	+	0.410066i
$851$	−28.0376	+	3.69122i	−0.961118	+	0.126534i
$852$	−2.83927	+	7.54544i	−0.0972718	+	0.258503i
$853$	6.08693	−	46.2348i	0.208412	−	1.58305i	−0.492829	−	0.870126i	$-0.664037\pi$
$853$	6.08693	−	46.2348i	0.208412	−	1.58305i	0.701242	−	0.712924i	$-0.252629\pi$
$854$	21.5187	−	76.7370i	0.736355	−	2.62589i
$855$	−1.79093	+	11.8657i	−0.0612484	+	0.405799i
$856$	−0.277575	+	7.97297i	−0.00948733	+	0.272510i
$857$	−9.74444	+	2.61101i	−0.332864	+	0.0891906i	−0.421380	−	0.906884i	$-0.638454\pi$
$857$	−9.74444	+	2.61101i	−0.332864	+	0.0891906i	0.0885163	+	0.996075i	$0.471787\pi$
$858$	0.604406	+	13.6043i	0.0206341	+	0.464443i
$859$	14.2715	+	10.9509i	0.486937	+	0.373640i	0.822855	−	0.568251i	$-0.192380\pi$
$859$	14.2715	+	10.9509i	0.486937	+	0.373640i	−0.335918	+	0.941891i	$0.609047\pi$
$860$	−8.32033	−	0.193069i	−0.283721	−	0.00658360i
$861$	36.0243	+	12.6095i	1.22770	+	0.429732i
$862$	−0.445164	−	1.11100i	−0.0151624	−	0.0378408i
$863$	−0.213637			−0.00727230			−0.00363615	−	0.999993i	$-0.501157\pi$
$863$	−0.213637			−0.00727230			−0.00363615	+	0.999993i	$0.501157\pi$
$864$	−18.3774	+	22.9406i	−0.625212	+	0.780455i
$865$	−1.63828			−0.0557033
$866$	−18.4729	−	46.1031i	−0.627736	−	1.56665i
$867$	−0.524465	−	0.183578i	−0.0178118	−	0.00623463i
$868$	−0.124979	+	5.38600i	−0.00424207	+	0.182813i
$869$	−25.5202	−	19.5823i	−0.865713	−	0.664285i
$870$	−1.60040	−	36.0228i	−0.0542588	−	1.22129i
$871$	−10.4011	+	2.78698i	−0.352429	+	0.0944331i
$872$	−4.77208	−	5.11634i	−0.161603	−	0.173261i
$873$	47.5761	−	18.6611i	1.61021	−	0.631582i
$874$	−5.45411	+	19.4497i	−0.184488	+	0.657896i
$875$	−6.99996	+	53.1700i	−0.236642	+	1.79747i
$876$	−1.65894	−	0.624241i	−0.0560503	−	0.0210912i
$877$	32.0647	−	4.22140i	1.08275	−	0.142546i	0.432025	−	0.901862i	$-0.357799\pi$
$877$	32.0647	−	4.22140i	1.08275	−	0.142546i	0.650723	+	0.759315i	$0.274466\pi$
$878$	−5.39853	−	7.20709i	−0.182192	−	0.243228i
$879$	−2.74921	−	4.19988i	−0.0927287	−	0.141659i
$880$	20.7706	+	22.7935i	0.700178	+	0.768369i
$881$	−40.2583			−1.35634			−0.678168	−	0.734907i	$-0.737226\pi$
$881$	−40.2583			−1.35634			−0.678168	+	0.734907i	$0.737226\pi$
$882$	−56.5922	+	13.3281i	−1.90556	+	0.448781i
$883$	25.3073	+	10.4826i	0.851660	+	0.352769i	0.765440	−	0.643507i	$-0.222521\pi$
$883$	25.3073	+	10.4826i	0.851660	+	0.352769i	0.0862196	+	0.996276i	$0.472521\pi$
$884$	−5.73769	+	7.12879i	−0.192979	+	0.239767i
$885$	−1.70735	−	0.128122i	−0.0573919	−	0.00430678i
$886$	27.5300	−	7.03542i	0.924890	−	0.236359i
$887$	−0.474768	+	1.77186i	−0.0159411	+	0.0594931i	−0.973438	−	0.228950i	$-0.926471\pi$
$887$	−0.474768	+	1.77186i	−0.0159411	+	0.0594931i	0.957497	+	0.288443i	$0.0931375\pi$
$888$	23.2690	+	9.06539i	0.780856	+	0.304215i
$889$	25.8709	+	96.5514i	0.867681	+	3.23823i
$890$	−3.73935	−	6.65382i	−0.125343	−	0.223036i
$891$	−44.4668	+	4.15161i	−1.48969	+	0.139084i
$892$	−11.2209	+	2.72929i	−0.375704	+	0.0913833i
$893$	−3.98749	−	5.19660i	−0.133436	−	0.173898i
$894$	13.9905	−	20.0131i	0.467912	−	0.669337i
$895$	28.4964	−	16.4524i	0.952530	−	0.549944i
$896$	−50.3254	−	10.8371i	−1.68126	−	0.362041i
$897$	−4.85242	+	9.60970i	−0.162018	+	0.320859i
$898$	−1.32606	−	3.30947i	−0.0442513	−	0.110438i
$899$	5.18237	+	2.14661i	0.172842	+	0.0715933i
$900$	−5.32965	−	14.5737i	−0.177655	−	0.485789i
$901$	−11.1964	−	27.0306i	−0.373008	−	0.900520i
$902$	−0.394233	+	33.9836i	−0.0131265	+	1.13153i
$903$	20.6636	+	4.31367i	0.687643	+	0.143550i
$904$	−45.8319	+	4.41801i	−1.52435	+	0.146941i
$905$	7.70696	+	2.06507i	0.256188	+	0.0686454i
$906$	−3.30762	−	10.4625i	−0.109888	−	0.347594i
$907$	56.6006	+	7.45161i	1.87939	+	0.247427i	0.981315	−	0.192410i	$-0.0616303\pi$
$907$	56.6006	+	7.45161i	1.87939	+	0.247427i	0.898078	+	0.439836i	$0.144964\pi$
$908$	1.88834	−	12.1568i	0.0626667	−	0.403438i
$909$	−8.71789	+	8.39438i	−0.289154	+	0.278424i
$910$	−11.1208	+	1.33304i	−0.368652	+	0.0441899i
$911$	−3.88028	−	2.24028i	−0.128559	−	0.0742237i	0.434341	−	0.900748i	$-0.356981\pi$
$911$	−3.88028	−	2.24028i	−0.128559	−	0.0742237i	−0.562900	+	0.826525i	$0.690315\pi$
$912$	12.4916	−	12.7337i	0.413637	−	0.421654i
$913$	52.0547	−	30.0538i	1.72276	−	0.994635i
$914$	−24.9453	+	18.6855i	−0.825116	+	0.618060i
$915$	31.4564	+	11.0107i	1.03992	+	0.364001i
$916$	−3.18898	−	29.4955i	−0.105367	−	0.974558i
$917$	−5.68059	−	13.7142i	−0.187590	−	0.452881i
$918$	−24.2675	−	17.6568i	−0.800948	−	0.582761i
$919$	12.8420	−	12.8420i	0.423620	−	0.423620i	−0.462828	−	0.886448i	$-0.653165\pi$
$919$	12.8420	−	12.8420i	0.423620	−	0.423620i	0.886448	+	0.462828i	$0.153165\pi$
$920$	5.48646	+	23.7530i	0.180883	+	0.783113i
$921$	−36.0876	−	32.2565i	−1.18913	−	1.06289i
$922$	−0.502441	+	0.847398i	−0.0165470	+	0.0279076i
$923$	1.58726	−	2.06856i	0.0522453	−	0.0680874i
$924$	−41.3080	−	66.4179i	−1.35893	−	2.18499i
$925$	−10.4592	+	8.02561i	−0.343896	+	0.263881i
$926$	16.4826	+	12.9540i	0.541651	+	0.425696i
$927$	−38.3404	+	28.2845i	−1.25926	+	0.928985i
$928$	−29.4455	+	44.7869i	−0.966594	+	1.47020i
$929$	−37.2662	−	21.5156i	−1.22266	−	0.705905i	−0.257178	−	0.966364i	$-0.582793\pi$
$929$	−37.2662	−	21.5156i	−1.22266	−	0.705905i	−0.965485	+	0.260459i	$0.916126\pi$
$930$	−2.24450	−	0.194638i	−0.0736002	−	0.00638244i
$931$	34.9809	−	4.60532i	1.14645	−	0.150933i
$932$	−0.971403	+	41.8627i	−0.0318194	+	1.37126i
$933$	−32.7882	+	48.0810i	−1.07344	+	1.57410i
$934$	−0.00954085	+	0.822438i	−0.000312186	+	0.0269110i
$935$	−22.2635	+	22.2635i	−0.728096	+	0.728096i
$936$	7.84172	−	5.37397i	0.256315	−	0.175654i
$937$	30.0408	+	30.0408i	0.981392	+	0.981392i	0.999830	−	0.0184383i	$-0.00586941\pi$
$937$	30.0408	+	30.0408i	0.981392	+	0.981392i	−0.0184383	+	0.999830i	$0.505869\pi$
$938$	44.2376	−	43.2230i	1.44441	−	1.41128i
$939$	−1.51081	+	20.1330i	−0.0493034	+	0.657015i
$940$	−7.23122	−	3.19376i	−0.235856	−	0.104169i
$941$	−2.79738	−	21.2482i	−0.0911920	−	0.692672i	−0.974582	−	0.224033i	$-0.928078\pi$
$941$	−2.79738	−	21.2482i	−0.0911920	−	0.692672i	0.883390	−	0.468639i	$-0.155256\pi$
$942$	−3.30889	−	18.6820i	−0.107809	−	0.608694i
$943$	−13.4336	+	23.2676i	−0.437458	+	0.757699i
$944$	1.94509	+	1.64132i	0.0633072	+	0.0534203i
$945$	−6.14193	−	36.2155i	−0.199797	−	1.17809i
$946$	2.23709	+	18.6629i	0.0727342	+	0.606782i
$947$	−7.88938	−	10.2816i	−0.256370	−	0.334108i	0.647381	−	0.762167i	$-0.275864\pi$
$947$	−7.88938	−	10.2816i	−0.256370	−	0.334108i	−0.903751	+	0.428058i	$0.859198\pi$
$948$	−2.19943	+	22.3479i	−0.0714340	+	0.725827i
$949$	0.454792	+	0.348974i	0.0147632	+	0.0113282i
$950$	2.33160	+	9.12370i	0.0756471	+	0.296012i
$951$	14.1922	+	43.1443i	0.460213	+	1.39905i
$952$	8.66945	−	51.8404i	0.280979	−	1.68016i
$953$	−17.4567	−	17.4567i	−0.565477	−	0.565477i	0.365381	−	0.930858i	$-0.380939\pi$
$953$	−17.4567	−	17.4567i	−0.565477	−	0.565477i	−0.930858	+	0.365381i	$0.880939\pi$
$954$	3.04635	+	30.2411i	0.0986292	+	0.979090i
$955$	−8.07116	+	3.34318i	−0.261176	+	0.108183i
$956$	3.80751	−	12.9960i	0.123144	−	0.420320i
$957$	−80.0191	+	15.1320i	−2.58665	+	0.489149i
$958$	−7.29068	+	50.8160i	−0.235551	+	1.64179i
$959$	7.90794	+	13.6970i	0.255361	+	0.442298i
$960$	5.85407	−	20.7163i	0.188939	−	0.668616i
$961$	−15.3248	+	26.5433i	−0.494347	+	0.856234i
$962$	−6.35005	−	4.99065i	−0.204734	−	0.160905i
$963$	8.13055	+	2.34416i	0.262003	+	0.0755394i
$964$	−56.2537	+	13.6827i	−1.81181	+	0.440691i
$965$	−0.223614	+	1.69852i	−0.00719839	+	0.0546772i
$966$	−2.74436	−	61.7716i	−0.0882984	−	1.98747i
$967$	11.5775	−	43.2077i	0.372306	−	1.38947i	−0.484935	−	0.874550i	$-0.661157\pi$
$967$	11.5775	−	43.2077i	0.372306	−	1.38947i	0.857241	−	0.514915i	$-0.172177\pi$
$968$	24.5074	−	29.7363i	0.787699	−	0.955762i
$969$	13.5787	+	12.1372i	0.436211	+	0.389902i
$970$	−26.7711	+	26.1571i	−0.859568	+	0.839853i
$971$	35.1496	−	14.5595i	1.12801	−	0.467235i	0.260903	−	0.965365i	$-0.415980\pi$
$971$	35.1496	−	14.5595i	1.12801	−	0.467235i	0.867103	+	0.498130i	$0.165980\pi$
$972$	18.8552	+	24.8290i	0.604781	+	0.796391i
$973$	−28.4334	+	68.6443i	−0.911532	+	2.20063i
$974$	−9.46620	−	4.05030i	−0.303317	−	0.129780i
$975$	0.280889	+	5.01077i	0.00899566	+	0.160473i
$976$	−28.3029	−	40.6598i	−0.905955	−	1.30149i
$977$	3.00365	+	5.20247i	0.0960952	+	0.166442i	0.910065	−	0.414465i	$-0.136031\pi$
$977$	3.00365	+	5.20247i	0.0960952	+	0.166442i	−0.813970	+	0.580907i	$0.802698\pi$
$978$	9.86395	−	27.1656i	0.315414	−	0.868661i
$979$	−13.6759	+	10.4939i	−0.437083	+	0.335386i
$980$	34.3741	−	25.1311i	1.09804	−	0.802782i
$981$	−6.49559	+	3.58827i	−0.207388	+	0.114565i
$982$	29.4160	+	8.24887i	0.938701	+	0.263232i
$983$	27.9412	−	7.48681i	0.891184	−	0.238792i	0.215958	−	0.976403i	$-0.430713\pi$
$983$	27.9412	−	7.48681i	0.891184	−	0.238792i	0.675226	+	0.737611i	$0.264046\pi$
$984$	20.2906	−	12.2955i	0.646842	−	0.391966i
$985$	11.4141	+	3.05841i	0.363685	+	0.0974490i
$986$	−47.0729	−	27.9105i	−1.49911	−	0.888853i
$987$	16.5651	+	11.2964i	0.527274	+	0.359568i
$988$	−5.06167	+	2.76782i	−0.161033	+	0.0880561i
$989$	−5.68642	+	13.7282i	−0.180818	+	0.436532i
$990$	28.8118	−	15.4826i	0.915700	−	0.492071i
$991$		−	36.4148i		−	1.15675i	−0.815770	−	0.578377i	$-0.803686\pi$
$991$		−	36.4148i		−	1.15675i	0.815770	−	0.578377i	$-0.196314\pi$
$992$	2.53422	+	2.18927i	0.0804614	+	0.0695093i
$993$	52.1232	+	26.3197i	1.65408	+	0.835229i
$994$	−2.12684	+	14.8240i	−0.0674591	+	0.470189i
$995$	0.529958	+	4.02543i	0.0168008	+	0.127615i
$996$	−37.0075	−	19.7774i	−1.17263	−	0.626671i
$997$	38.7999	+	5.10810i	1.22880	+	0.161775i	0.716844	−	0.697234i	$-0.245586\pi$
$997$	38.7999	+	5.10810i	1.22880	+	0.161775i	0.511960	+	0.859009i	$0.328919\pi$
$998$	23.4877	+	41.7941i	0.743489	+	1.32297i
$999$	15.3340	−	21.5974i	0.485148	−	0.683312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.227.7	yes	368
3.2	odd	2		864.2.bn.a.35.40		368
9.4	even	3		864.2.bn.a.611.24		368
9.5	odd	6	inner	288.2.bf.a.131.23	yes	368
32.11	odd	8	inner	288.2.bf.a.11.23	✓	368
96.11	even	8		864.2.bn.a.683.24		368
288.139	odd	24		864.2.bn.a.395.40		368
288.203	even	24	inner	288.2.bf.a.203.7	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.23	✓	368	32.11	odd	8	inner
288.2.bf.a.131.23	yes	368	9.5	odd	6	inner
288.2.bf.a.203.7	yes	368	288.203	even	24	inner
288.2.bf.a.227.7	yes	368	1.1	even	1	trivial
864.2.bn.a.35.40		368	3.2	odd	2
864.2.bn.a.395.40		368	288.139	odd	24
864.2.bn.a.611.24		368	9.4	even	3
864.2.bn.a.683.24		368	96.11	even	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31275 + 0.526004i) q^{2} +(1.63480 + 0.572226i) q^{3} +(1.44664 - 1.38103i) q^{4} +(1.23257 + 0.945783i) q^{5} +(-2.44708 + 0.108718i) q^{6} +(-4.39511 + 1.17766i) q^{7} +(-1.17266 + 2.57388i) q^{8} +(2.34512 + 1.87094i) q^{9} +O(q^{10})\)	\(q+(-1.31275 + 0.526004i) q^{2} +(1.63480 + 0.572226i) q^{3} +(1.44664 - 1.38103i) q^{4} +(1.23257 + 0.945783i) q^{5} +(-2.44708 + 0.108718i) q^{6} +(-4.39511 + 1.17766i) q^{7} +(-1.17266 + 2.57388i) q^{8} +(2.34512 + 1.87094i) q^{9} +(-2.11554 - 0.593244i) q^{10} +(-0.647702 + 4.91978i) q^{11} +(3.15522 - 1.42989i) q^{12} +(-1.11076 + 0.146234i) q^{13} +(5.15023 - 3.85782i) q^{14} +(1.47380 + 2.25147i) q^{15} +(0.185536 - 3.99569i) q^{16} +4.08402 q^{17} +(-4.06268 - 1.22255i) q^{18} +(2.37867 + 0.985278i) q^{19} +(3.08923 - 0.334001i) q^{20} +(-7.85899 - 0.589751i) q^{21} +(-1.73755 - 6.79916i) q^{22} +(1.43586 - 5.35870i) q^{23} +(-3.38990 + 3.53675i) q^{24} +(-0.669376 - 2.49815i) q^{25} +(1.38123 - 0.776232i) q^{26} +(2.76318 + 4.40055i) q^{27} +(-4.73175 + 7.77341i) q^{28} +(5.76810 + 7.51713i) q^{29} +(-3.11901 - 2.18040i) q^{30} +(0.512694 - 0.296004i) q^{31} +(1.85819 + 5.34295i) q^{32} +(-3.87409 + 7.67221i) q^{33} +(-5.36130 + 2.14821i) q^{34} +(-6.53108 - 2.70526i) q^{35} +(5.97636 - 0.532081i) q^{36} +(-1.95073 - 4.70947i) q^{37} +(-3.64087 - 0.0422366i) q^{38} +(-1.89954 - 0.396542i) q^{39} +(-3.87971 + 2.06341i) q^{40} +(-4.67789 - 1.25344i) q^{41} +(10.6271 - 3.35966i) q^{42} +(-2.65553 - 0.349608i) q^{43} +(5.85736 + 8.01165i) q^{44} +(1.12101 + 4.52404i) q^{45} +(0.933768 + 7.78992i) q^{46} +(-2.20325 - 1.27205i) q^{47} +(2.58975 - 6.42598i) q^{48} +(11.8679 - 6.85192i) q^{49} +(2.19276 + 2.92735i) q^{50} +(6.67653 + 2.33698i) q^{51} +(-1.40491 + 1.74553i) q^{52} +(-2.74153 - 6.61863i) q^{53} +(-5.94208 - 4.32339i) q^{54} +(-5.45138 + 5.45138i) q^{55} +(2.12278 - 12.6935i) q^{56} +(3.32484 + 2.97187i) q^{57} +(-11.5261 - 6.83409i) q^{58} +(-0.387332 + 0.504781i) q^{59} +(5.24139 + 1.22172i) q^{60} +(9.82581 - 7.53961i) q^{61} +(-0.517341 + 0.658259i) q^{62} +(-12.5104 - 5.46124i) q^{63} +(-5.24975 - 6.03656i) q^{64} +(-1.50739 - 0.870292i) q^{65} +(1.05011 - 12.1095i) q^{66} +(9.52916 - 1.25454i) q^{67} +(5.90810 - 5.64013i) q^{68} +(5.41373 - 7.93875i) q^{69} +(9.99667 + 0.115968i) q^{70} +(-1.64564 + 1.64564i) q^{71} +(-7.56561 + 3.84208i) q^{72} +(-0.361810 - 0.361810i) q^{73} +(5.03802 + 5.15628i) q^{74} +(0.335210 - 4.46699i) q^{75} +(4.80178 - 1.85966i) q^{76} +(-2.94714 - 22.3857i) q^{77} +(2.70221 - 0.478605i) q^{78} +(-3.24123 + 5.61397i) q^{79} +(4.00774 - 4.74949i) q^{80} +(1.99913 + 8.77516i) q^{81} +(6.80022 - 0.815134i) q^{82} +(-7.37393 - 9.60989i) q^{83} +(-12.1836 + 10.0003i) q^{84} +(5.03383 + 3.86259i) q^{85} +(3.66996 - 0.937872i) q^{86} +(5.12816 + 15.5896i) q^{87} +(-11.9034 - 7.43633i) q^{88} +(2.45638 + 2.45638i) q^{89} +(-3.85126 - 5.34929i) q^{90} +(4.70968 - 1.95082i) q^{91} +(-5.32333 - 9.73507i) q^{92} +(1.00753 - 0.190529i) q^{93} +(3.56142 + 0.510966i) q^{94} +(2.00002 + 3.46413i) q^{95} +(-0.0196182 + 9.79794i) q^{96} +(8.51749 - 14.7527i) q^{97} +(-11.9755 + 15.2374i) q^{98} +(-10.7236 + 10.3256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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