LMFDB - Embedded newform 288.2.bc.a.205.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (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			205.24
Character	$\chi$	$=$	288.205
Dual form			288.2.bc.a.229.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0274977 - 1.41395i) q^{2} +(-0.523386 + 1.65108i) q^{3} +(-1.99849 + 0.0777604i) q^{4} +(-0.720492 - 0.552853i) q^{5} +(2.34893 + 0.694639i) q^{6} +(-0.375828 - 1.40261i) q^{7} +(0.164903 + 2.82362i) q^{8} +(-2.45213 - 1.72831i) q^{9} +O(q^{10})$	\(q+(-0.0274977 - 1.41395i) q^{2} +(-0.523386 + 1.65108i) q^{3} +(-1.99849 + 0.0777604i) q^{4} +(-0.720492 - 0.552853i) q^{5} +(2.34893 + 0.694639i) q^{6} +(-0.375828 - 1.40261i) q^{7} +(0.164903 + 2.82362i) q^{8} +(-2.45213 - 1.72831i) q^{9} +(-0.761892 + 1.03394i) q^{10} +(-4.59604 - 0.605081i) q^{11} +(0.917592 - 3.34036i) q^{12} +(-0.606629 - 4.60781i) q^{13} +(-1.97288 + 0.569969i) q^{14} +(1.28990 - 0.900234i) q^{15} +(3.98791 - 0.310807i) q^{16} +2.96949i q^{17} +(-2.37630 + 3.51471i) q^{18} +(-6.72261 - 2.78460i) q^{19} +(1.48288 + 1.04884i) q^{20} +(2.51252 + 0.113584i) q^{21} +(-0.729171 + 6.51520i) q^{22} +(-1.45707 + 5.43786i) q^{23} +(-4.74833 - 1.20557i) q^{24} +(-1.08063 - 4.03298i) q^{25} +(-6.49851 + 0.984445i) q^{26} +(4.13698 - 3.14410i) q^{27} +(0.860154 + 2.77387i) q^{28} +(-3.06838 - 3.99879i) q^{29} +(-1.30835 - 1.79909i) q^{30} +(4.46478 + 7.73323i) q^{31} +(-0.549122 - 5.63014i) q^{32} +(3.40454 - 7.27175i) q^{33} +(4.19870 - 0.0816541i) q^{34} +(-0.504655 + 1.21834i) q^{35} +(5.03495 + 3.26332i) q^{36} +(1.69709 - 0.702958i) q^{37} +(-3.75241 + 9.58198i) q^{38} +(7.92536 + 1.41007i) q^{39} +(1.44223 - 2.12556i) q^{40} +(-0.422584 + 1.57711i) q^{41} +(0.0915129 - 3.55569i) q^{42} +(6.75491 + 0.889301i) q^{43} +(9.23219 + 0.851856i) q^{44} +(0.811244 + 2.60090i) q^{45} +(7.72891 + 1.91069i) q^{46} +(-4.19677 - 2.42300i) q^{47} +(-1.57405 + 6.74703i) q^{48} +(4.23612 - 2.44572i) q^{49} +(-5.67270 + 1.63885i) q^{50} +(-4.90287 - 1.55419i) q^{51} +(1.57065 + 9.16148i) q^{52} +(0.809156 + 1.95348i) q^{53} +(-4.55934 - 5.76302i) q^{54} +(2.97689 + 2.97689i) q^{55} +(3.89845 - 1.29249i) q^{56} +(8.11611 - 9.64215i) q^{57} +(-5.56970 + 4.44848i) q^{58} +(-1.09037 - 0.836667i) q^{59} +(-2.50785 + 1.89941i) q^{60} +(0.841022 + 1.09604i) q^{61} +(10.8116 - 6.52561i) q^{62} +(-1.50256 + 4.08893i) q^{63} +(-7.94561 + 0.931244i) q^{64} +(-2.11037 + 3.65526i) q^{65} +(-10.3755 - 4.61388i) q^{66} +(-5.80185 + 0.763828i) q^{67} +(-0.230909 - 5.93449i) q^{68} +(-8.21573 - 5.25184i) q^{69} +(1.73655 + 0.680053i) q^{70} +(8.61020 - 8.61020i) q^{71} +(4.47571 - 7.20889i) q^{72} +(-10.3860 - 10.3860i) q^{73} +(-1.04061 - 2.38026i) q^{74} +(7.22436 + 0.326592i) q^{75} +(13.6516 + 5.04223i) q^{76} +(0.878629 + 6.67385i) q^{77} +(1.77583 - 11.2448i) q^{78} +(7.01911 + 4.05249i) q^{79} +(-3.04508 - 1.98079i) q^{80} +(3.02592 + 8.47607i) q^{81} +(2.24156 + 0.554145i) q^{82} +(-7.43962 + 5.70862i) q^{83} +(-5.03008 - 0.0316211i) q^{84} +(1.64169 - 2.13949i) q^{85} +(1.07168 - 9.57553i) q^{86} +(8.20828 - 2.97323i) q^{87} +(0.950615 - 13.0772i) q^{88} +(-7.32348 + 7.32348i) q^{89} +(3.65522 - 1.21857i) q^{90} +(-6.23496 + 2.58260i) q^{91} +(2.48909 - 10.9808i) q^{92} +(-15.1050 + 3.32425i) q^{93} +(-3.31060 + 6.00063i) q^{94} +(3.30411 + 5.72289i) q^{95} +(9.58322 + 2.04009i) q^{96} +(4.10503 - 7.11012i) q^{97} +(-3.57460 - 5.92239i) q^{98} +(10.2243 + 9.42710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.0274977	−	1.41395i	−0.0194438	−	0.999811i
$2$	−0.0274977	−	1.41395i	−0.0194438	−	0.999811i
$3$	−0.523386	+	1.65108i	−0.302177	+	0.953252i
$3$	−0.523386	+	1.65108i	−0.302177	+	0.953252i
$4$	−1.99849	+	0.0777604i	−0.999244	+	0.0388802i
$5$	−0.720492	−	0.552853i	−0.322214	−	0.247243i	0.434970	−	0.900445i	$-0.356759\pi$
$5$	−0.720492	−	0.552853i	−0.322214	−	0.247243i	−0.757184	+	0.653201i	$0.773425\pi$
$6$	2.34893	+	0.694639i	0.958947	+	0.283585i
$7$	−0.375828	−	1.40261i	−0.142050	−	0.530136i	−0.999869	−	0.0161849i	$-0.994848\pi$
$7$	−0.375828	−	1.40261i	−0.142050	−	0.530136i	0.857820	−	0.513951i	$-0.171819\pi$
$8$	0.164903	+	2.82362i	0.0583019	+	0.998299i
$9$	−2.45213	−	1.72831i	−0.817378	−	0.576102i
$10$	−0.761892	+	1.03394i	−0.240931	+	0.326960i
$11$	−4.59604	−	0.605081i	−1.38576	−	0.182439i	−0.599519	−	0.800360i	$-0.704642\pi$
$11$	−4.59604	−	0.605081i	−1.38576	−	0.182439i	−0.786240	+	0.617922i	$0.787975\pi$
$12$	0.917592	−	3.34036i	0.264886	−	0.964280i
$13$	−0.606629	−	4.60781i	−0.168249	−	1.27798i	−0.842186	−	0.539187i	$-0.818732\pi$
$13$	−0.606629	−	4.60781i	−0.168249	−	1.27798i	0.673937	−	0.738789i	$-0.264602\pi$
$14$	−1.97288	+	0.569969i	−0.527274	+	0.152330i
$15$	1.28990	−	0.900234i	0.333051	−	0.232440i
$16$	3.98791	−	0.310807i	0.996977	−	0.0777016i
$17$			2.96949i			0.720208i	0.932912	+	0.360104i	$0.117259\pi$
$17$			2.96949i			0.720208i	−0.932912	+	0.360104i	$0.882741\pi$
$18$	−2.37630	+	3.51471i	−0.560100	+	0.828425i
$19$	−6.72261	−	2.78460i	−1.54227	−	0.638830i	−0.560374	−	0.828240i	$-0.689343\pi$
$19$	−6.72261	−	2.78460i	−1.54227	−	0.638830i	−0.981898	+	0.189409i	$0.939343\pi$
$20$	1.48288	+	1.04884i	0.331583	+	0.234529i
$21$	2.51252	+	0.113584i	0.548277	+	0.0247860i
$22$	−0.729171	+	6.51520i	−0.155460	+	1.38904i
$23$	−1.45707	+	5.43786i	−0.303820	+	1.13387i	0.630136	+	0.776485i	$0.282999\pi$
$23$	−1.45707	+	5.43786i	−0.303820	+	1.13387i	−0.933956	+	0.357387i	$0.883668\pi$
$24$	−4.74833	−	1.20557i	−0.969248	−	0.246087i
$25$	−1.08063	−	4.03298i	−0.216127	−	0.806596i
$26$	−6.49851	+	0.984445i	−1.27446	+	0.193066i
$27$	4.13698	−	3.14410i	0.796163	−	0.605082i
$28$	0.860154	+	2.77387i	0.162554	+	0.524212i
$29$	−3.06838	−	3.99879i	−0.569784	−	0.742557i	0.416223	−	0.909263i	$-0.363354\pi$
$29$	−3.06838	−	3.99879i	−0.569784	−	0.742557i	−0.986007	+	0.166706i	$0.946687\pi$
$30$	−1.30835	−	1.79909i	−0.238871	−	0.328468i
$31$	4.46478	+	7.73323i	0.801899	+	1.38893i	0.918365	+	0.395735i	$0.129510\pi$
$31$	4.46478	+	7.73323i	0.801899	+	1.38893i	−0.116466	+	0.993195i	$0.537157\pi$
$32$	−0.549122	−	5.63014i	−0.0970719	−	0.995277i
$33$	3.40454	−	7.27175i	0.592655	−	1.26585i
$34$	4.19870	−	0.0816541i	0.720071	−	0.0140036i
$35$	−0.504655	+	1.21834i	−0.0853022	+	0.205938i
$36$	5.03495	+	3.26332i	0.839159	+	0.543886i
$37$	1.69709	−	0.702958i	0.279000	−	0.115566i	−0.238796	−	0.971070i	$-0.576753\pi$
$37$	1.69709	−	0.702958i	0.279000	−	0.115566i	0.517796	+	0.855504i	$0.326753\pi$
$38$	−3.75241	+	9.58198i	−0.608722	+	1.55440i
$39$	7.92536	+	1.41007i	1.26907	+	0.225792i
$40$	1.44223	−	2.12556i	0.228037	−	0.336080i
$41$	−0.422584	+	1.57711i	−0.0659966	+	0.246303i	−0.991041	−	0.133556i	$-0.957361\pi$
$41$	−0.422584	+	1.57711i	−0.0659966	+	0.246303i	0.925045	+	0.379858i	$0.124027\pi$
$42$	0.0915129	−	3.55569i	0.0141208	−	0.548655i
$43$	6.75491	+	0.889301i	1.03011	+	0.135617i	0.626588	−	0.779351i	$-0.284451\pi$
$43$	6.75491	+	0.889301i	1.03011	+	0.135617i	0.403526	+	0.914968i	$0.367784\pi$
$44$	9.23219	+	0.851856i	1.39180	+	0.128422i
$45$	0.811244	+	2.60090i	0.120933	+	0.387719i
$46$	7.72891	+	1.91069i	1.13956	+	0.281716i
$47$	−4.19677	−	2.42300i	−0.612161	−	0.353432i	0.161649	−	0.986848i	$-0.448319\pi$
$47$	−4.19677	−	2.42300i	−0.612161	−	0.353432i	−0.773811	+	0.633417i	$0.781652\pi$
$48$	−1.57405	+	6.74703i	−0.227194	+	0.973849i
$49$	4.23612	−	2.44572i	0.605159	−	0.349389i
$50$	−5.67270	+	1.63885i	−0.802241	+	0.231769i
$51$	−4.90287	−	1.55419i	−0.686539	−	0.217630i
$52$	1.57065	+	9.16148i	0.217809	+	1.27047i
$53$	0.809156	+	1.95348i	0.111146	+	0.268330i	0.969659	−	0.244462i	$-0.0786112\pi$
$53$	0.809156	+	1.95348i	0.111146	+	0.268330i	−0.858513	+	0.512792i	$0.828611\pi$
$54$	−4.55934	−	5.76302i	−0.620448	−	0.784247i
$55$	2.97689	+	2.97689i	0.401404	+	0.401404i
$56$	3.89845	−	1.29249i	0.520952	−	0.172716i
$57$	8.11611	−	9.64215i	1.07501	−	1.27713i
$58$	−5.56970	+	4.44848i	−0.731338	+	0.584114i
$59$	−1.09037	−	0.836667i	−0.141954	−	0.108925i	0.535344	−	0.844634i	$-0.320182\pi$
$59$	−1.09037	−	0.836667i	−0.141954	−	0.108925i	−0.677297	+	0.735710i	$0.736849\pi$
$60$	−2.50785	+	1.89941i	−0.323762	+	0.245213i
$61$	0.841022	+	1.09604i	0.107682	+	0.140334i	0.844085	−	0.536209i	$-0.180144\pi$
$61$	0.841022	+	1.09604i	0.107682	+	0.140334i	−0.736403	+	0.676543i	$0.763477\pi$
$62$	10.8116	−	6.52561i	1.37307	−	0.828753i
$63$	−1.50256	+	4.08893i	−0.189304	+	0.515156i
$64$	−7.94561	+	0.931244i	−0.993202	+	0.116406i
$65$	−2.11037	+	3.65526i	−0.261759	+	0.453380i
$66$	−10.3755	−	4.61388i	−1.27713	−	0.567930i
$67$	−5.80185	+	0.763828i	−0.708809	+	0.0933165i	−0.476307	−	0.879279i	$-0.658025\pi$
$67$	−5.80185	+	0.763828i	−0.708809	+	0.0933165i	−0.232503	+	0.972596i	$0.574691\pi$
$68$	−0.230909	−	5.93449i	−0.0280018	−	0.719663i
$69$	−8.21573	−	5.25184i	−0.989058	−	0.632247i
$70$	1.73655	+	0.680053i	0.207558	+	0.0812819i
$71$	8.61020	−	8.61020i	1.02184	−	1.02184i	0.0220868	−	0.999756i	$-0.492969\pi$
$71$	8.61020	−	8.61020i	1.02184	−	1.02184i	0.999756	−	0.0220868i	$-0.00703103\pi$
$72$	4.47571	−	7.20889i	0.527467	−	0.849575i
$73$	−10.3860	−	10.3860i	−1.21559	−	1.21559i	−0.969162	−	0.246423i	$-0.920745\pi$
$73$	−10.3860	−	10.3860i	−1.21559	−	1.21559i	−0.246423	−	0.969162i	$-0.579255\pi$
$74$	−1.04061	−	2.38026i	−0.120969	−	0.276700i
$75$	7.22436	+	0.326592i	0.834197	+	0.0377116i
$76$	13.6516	+	5.04223i	1.56594	+	0.578383i
$77$	0.878629	+	6.67385i	0.100129	+	0.760556i
$78$	1.77583	−	11.2448i	0.201073	−	1.27322i
$79$	7.01911	+	4.05249i	0.789712	+	0.455940i	0.839861	−	0.542801i	$-0.182636\pi$
$79$	7.01911	+	4.05249i	0.789712	+	0.455940i	−0.0501492	+	0.998742i	$0.515970\pi$
$80$	−3.04508	−	1.98079i	−0.340451	−	0.221459i
$81$	3.02592	+	8.47607i	0.336213	+	0.941786i
$82$	2.24156	+	0.554145i	0.247539	+	0.0611950i
$83$	−7.43962	+	5.70862i	−0.816604	+	0.626603i	−0.930253	−	0.366918i	$-0.880413\pi$
$83$	−7.43962	+	5.70862i	−0.816604	+	0.626603i	0.113649	+	0.993521i	$0.463746\pi$
$84$	−5.03008	−	0.0316211i	−0.548826	−	0.00345015i
$85$	1.64169	−	2.13949i	0.178066	−	0.232061i
$86$	1.07168	−	9.57553i	0.115562	−	1.03256i
$87$	8.20828	−	2.97323i	0.880019	−	0.318764i
$88$	0.950615	−	13.0772i	0.101336	−	1.39404i
$89$	−7.32348	+	7.32348i	−0.776287	+	0.776287i	−0.979197	−	0.202910i	$-0.934960\pi$
$89$	−7.32348	+	7.32348i	−0.776287	+	0.776287i	0.202910	+	0.979197i	$0.434960\pi$
$90$	3.65522	−	1.21857i	0.385294	−	0.128449i
$91$	−6.23496	+	2.58260i	−0.653601	+	0.270731i
$92$	2.48909	−	10.9808i	0.259505	−	1.14483i
$93$	−15.1050	+	3.32425i	−1.56631	+	0.344709i
$94$	−3.31060	+	6.00063i	−0.341462	+	0.618918i
$95$	3.30411	+	5.72289i	0.338995	+	0.587156i
$96$	9.58322	+	2.04009i	0.978083	+	0.208216i
$97$	4.10503	−	7.11012i	0.416803	−	0.721923i	−0.578813	−	0.815460i	$-0.696484\pi$
$97$	4.10503	−	7.11012i	0.416803	−	0.721923i	0.995616	+	0.0935369i	$0.0298173\pi$
$98$	−3.57460	−	5.92239i	−0.361089	−	0.598251i
$99$	10.2243	+	9.42710i	1.02759	+	0.947460i
$100$	2.47324	+	7.97583i	0.247324	+	0.797583i
$101$	−0.166243	+	1.26274i	−0.0165418	+	0.125647i	−0.997723	−	0.0674402i	$-0.978517\pi$
$101$	−0.166243	+	1.26274i	−0.0165418	+	0.125647i	0.981182	+	0.193088i	$0.0618501\pi$
$102$	−2.06272	+	6.97513i	−0.204240	+	0.690641i
$103$	−6.96285	−	1.86569i	−0.686070	−	0.183832i	−0.101087	−	0.994878i	$-0.532232\pi$
$103$	−6.96285	−	1.86569i	−0.686070	−	0.183832i	−0.584983	+	0.811046i	$0.698899\pi$
$104$	12.9106	−	2.47273i	1.26599	−	0.242471i
$105$	−1.74746	−	1.47089i	−0.170534	−	0.143544i
$106$	2.73986	−	1.19782i	0.266119	−	0.116342i
$107$	−5.13149	−	12.3885i	−0.496080	−	1.19764i	−0.951578	−	0.307406i	$-0.900539\pi$
$107$	−5.13149	−	12.3885i	−0.496080	−	1.19764i	0.455499	−	0.890236i	$-0.349461\pi$
$108$	−8.02323	+	6.60514i	−0.772035	+	0.635580i
$109$	1.02860	+	0.426060i	0.0985220	+	0.0408092i	0.431400	−	0.902161i	$-0.358020\pi$
$109$	1.02860	+	0.426060i	0.0985220	+	0.0408092i	−0.332878	+	0.942970i	$0.608020\pi$
$110$	4.12731	−	4.29102i	0.393523	−	0.409133i
$111$	0.272406	+	3.16995i	0.0258557	+	0.300878i
$112$	−1.93471	−	5.47666i	−0.182812	−	0.517496i
$113$	7.98790	−	4.61182i	0.751438	−	0.433843i	−0.0747750	−	0.997200i	$-0.523824\pi$
$113$	7.98790	−	4.61182i	0.751438	−	0.433843i	0.826213	+	0.563357i	$0.190491\pi$
$114$	−13.8567	−	11.2106i	−1.29779	−	1.04997i
$115$	4.05614	−	3.11239i	0.378237	−	0.290232i
$116$	6.44307	+	7.75294i	0.598224	+	0.719842i
$117$	−6.47616	+	12.3474i	−0.598721	+	1.14152i
$118$	−1.15302	+	1.56472i	−0.106144	+	0.144045i
$119$	4.16503	−	1.11602i	0.381808	−	0.102305i
$120$	2.75462	+	3.49373i	0.251462	+	0.318932i
$121$	10.1323	+	2.71494i	0.921119	+	0.246813i
$122$	1.52662	−	1.21930i	0.138213	−	0.110390i
$123$	−2.38275	−	1.52316i	−0.214846	−	0.137338i
$124$	−9.52415	−	15.1076i	−0.855294	−	1.35670i
$125$	−3.18874	+	7.69831i	−0.285210	+	0.688558i
$126$	5.82284	+	2.01210i	0.518740	+	0.179252i
$127$	−17.0663			−1.51439			−0.757193	−	0.653192i	$-0.773430\pi$
$127$	−17.0663			−1.51439			−0.757193	+	0.653192i	$0.773430\pi$
$128$	1.53522	+	11.2091i	0.135695	+	0.990751i
$129$	−5.00373	+	10.6875i	−0.440554	+	0.940978i
$130$	5.22638	+	2.88344i	0.458384	+	0.252894i
$131$	2.61422	−	0.344169i	0.228406	−	0.0300702i	−0.0154546	−	0.999881i	$-0.504920\pi$
$131$	2.61422	−	0.344169i	0.228406	−	0.0300702i	0.243860	+	0.969810i	$0.421586\pi$
$132$	−6.23848	+	14.7972i	−0.542990	+	1.28793i
$133$	−1.37915	+	10.4757i	−0.119588	+	0.908360i
$134$	1.23955	+	8.18250i	0.107081	+	0.706861i
$135$	−4.71889	−	0.0218454i	−0.406137	−	0.00188016i
$136$	−8.38470	+	0.489678i	−0.718982	+	0.0419895i
$137$	0.00132436		0.000354861i	0.000113148		3.03178e-5i	−0.258762	−	0.965941i	$-0.583315\pi$
$137$	0.00132436		0.000354861i	0.000113148		3.03178e-5i	0.258876	+	0.965911i	$0.416648\pi$
$138$	−7.19991	+	11.7610i	−0.612897	+	1.00116i
$139$	−1.32737	+	1.72986i	−0.112586	+	0.146725i	−0.846247	−	0.532791i	$-0.821143\pi$
$139$	−1.32737	+	1.72986i	−0.112586	+	0.146725i	0.733661	+	0.679515i	$0.237810\pi$
$140$	0.913808	−	2.47409i	0.0772308	−	0.209099i
$141$	6.19711	−	5.66103i	0.521890	−	0.476745i
$142$	−12.4111	−	11.9376i	−1.04152	−	1.00178i
$143$			21.5447i			1.80166i
$144$	−10.3160	−	6.13018i	−0.859671	−	0.510848i
$145$			4.57746i			0.380137i
$146$	−14.3996	+	14.9708i	−1.19172	+	1.23899i
$147$	1.82096	+	8.27422i	0.150190	+	0.682447i
$148$	−3.33695	+	1.53682i	−0.274296	+	0.126326i
$149$	−1.82492	+	2.37828i	−0.149503	+	0.194836i	−0.862101	−	0.506736i	$-0.830852\pi$
$149$	−1.82492	+	2.37828i	−0.149503	+	0.194836i	0.712598	+	0.701573i	$0.247518\pi$
$150$	0.263131	−	10.2238i	0.0214846	−	0.834773i
$151$	−17.3295	+	4.64343i	−1.41025	+	0.377877i	−0.882016	−	0.471219i	$-0.843814\pi$
$151$	−17.3295	+	4.64343i	−1.41025	+	0.377877i	−0.528239	+	0.849096i	$0.677147\pi$
$152$	6.75405	−	19.4413i	0.547826	−	1.57689i
$153$	5.13219	−	7.28159i	0.414913	−	0.588682i
$154$	9.41231	−	1.42585i	0.758465	−	0.114898i
$155$	1.05850	−	8.04010i	0.0850207	−	0.645796i
$156$	−15.9484	−	2.20173i	−1.27689	−	0.176279i
$157$	10.9297	−	1.43892i	0.872282	−	0.114838i	0.318922	−	0.947781i	$-0.396679\pi$
$157$	10.9297	−	1.43892i	0.872282	−	0.114838i	0.553359	+	0.832943i	$0.313346\pi$
$158$	5.53699	−	10.0361i	0.440499	−	0.798428i
$159$	−3.64885	+	0.313560i	−0.289372	+	0.0248669i
$160$	−2.71700	+	4.36005i	−0.214798	+	0.344692i
$161$	8.17479			0.644264
$162$	11.9015	−	4.51156i	0.935071	−	0.354462i
$163$	−1.00365	+	2.42302i	−0.0786116	+	0.189785i	−0.958299	−	0.285767i	$-0.907752\pi$
$163$	−1.00365	+	2.42302i	−0.0786116	+	0.189785i	0.879688	+	0.475552i	$0.157752\pi$
$164$	0.721893	−	3.18469i	0.0563704	−	0.248682i
$165$	−6.47315	+	3.35702i	−0.503934	+	0.261344i
$166$	8.27626	+	10.3622i	0.642362	+	0.804267i
$167$	6.14172	+	1.64567i	0.475261	+	0.127346i	0.488495	−	0.872567i	$-0.337546\pi$
$167$	6.14172	+	1.64567i	0.475261	+	0.127346i	−0.0132343	+	0.999912i	$0.504213\pi$
$168$	0.0936048	+	7.11313i	0.00722177	+	0.548790i
$169$	−8.30686	+	2.22582i	−0.638989	+	0.171217i
$170$	−3.07027	−	2.26243i	−0.235479	−	0.173521i
$171$	11.6721	+	18.4469i	0.892588	+	1.41067i
$172$	−13.5688	−	1.25199i	−1.03461	−	0.0954635i
$173$	8.77819	−	6.73574i	0.667394	−	0.512109i	−0.218595	−	0.975816i	$-0.570147\pi$
$173$	8.77819	−	6.73574i	0.667394	−	0.512109i	0.885989	+	0.463706i	$0.153481\pi$
$174$	−4.42970	−	11.5243i	−0.335815	−	0.873655i
$175$	−5.25055	+	3.03141i	−0.396905	+	0.229153i
$176$	−18.5167	−	0.984525i	−1.39575	−	0.0742113i
$177$	1.95209	−	1.36238i	0.146728	−	0.102403i
$178$	10.5564	+	10.1536i	0.791234	+	0.761046i
$179$	−16.1533	−	6.69093i	−1.20736	−	0.500103i	−0.313987	−	0.949427i	$-0.601665\pi$
$179$	−16.1533	−	6.69093i	−1.20736	−	0.500103i	−0.893369	+	0.449324i	$0.851665\pi$
$180$	−1.82351	−	5.13478i	−0.135916	−	0.382724i
$181$	1.20649	+	2.91273i	0.0896779	+	0.216502i	0.962355	−	0.271797i	$-0.0876178\pi$
$181$	1.20649	+	2.91273i	0.0896779	+	0.216502i	−0.872677	+	0.488298i	$0.837618\pi$
$182$	3.82311	+	8.74488i	0.283388	+	0.648214i
$183$	−2.24983	+	0.814942i	−0.166312	+	0.0602423i
$184$	−15.5947	−	3.21749i	−1.14966	−	0.237196i
$185$	−1.61137	−	0.431766i	−0.118470	−	0.0317440i
$186$	5.11566	+	21.2662i	0.375099	+	1.55932i
$187$	1.79678	−	13.6479i	0.131394	−	0.998034i
$188$	8.57560	+	4.51600i	0.625440	+	0.329363i
$189$	−5.96473	−	4.62093i	−0.433870	−	0.336123i
$190$	8.00101	−	4.82920i	0.580454	−	0.350347i
$191$	9.29221	−	16.0946i	0.672361	−	1.16456i	−0.304872	−	0.952393i	$-0.598614\pi$
$191$	9.29221	−	16.0946i	0.672361	−	1.16456i	0.977233	−	0.212170i	$-0.0680531\pi$
$192$	2.62106	−	13.6062i	0.189159	−	0.981946i
$193$	−6.50863	−	11.2733i	−0.468502	−	0.811469i	0.530850	−	0.847466i	$-0.321873\pi$
$193$	−6.50863	−	11.2733i	−0.468502	−	0.811469i	−0.999352	+	0.0359969i	$0.988539\pi$
$194$	−10.1662	−	5.60878i	−0.729891	−	0.402687i
$195$	−4.93060	−	5.39750i	−0.353087	−	0.386523i
$196$	−8.27564	+	5.21715i	−0.591117	+	0.372653i
$197$	−18.3755	+	7.61139i	−1.30920	+	0.542289i	−0.924651	−	0.380815i	$-0.875643\pi$
$197$	−18.3755	+	7.61139i	−1.30920	+	0.542289i	−0.384550	+	0.923104i	$0.625643\pi$
$198$	13.0483	−	14.7159i	0.927300	−	1.04581i
$199$	10.0690	−	10.0690i	0.713772	−	0.713772i	−0.253550	−	0.967322i	$-0.581598\pi$
$199$	10.0690	−	10.0690i	0.713772	−	0.713772i	0.967322	+	0.253550i	$0.0815983\pi$
$200$	11.2094	−	3.71634i	0.792623	−	0.262785i
$201$	1.77547	−	9.97910i	0.125232	−	0.703872i
$202$	1.79002	+	0.200336i	0.125945	+	0.0140956i
$203$	−4.45555	+	5.80659i	−0.312719	+	0.407543i
$204$	9.91918	+	2.72478i	0.694482	+	0.190773i
$205$	1.17638	−	0.902665i	0.0821616	−	0.0630448i
$206$	−2.44652	+	9.89639i	−0.170457	+	0.689515i
$207$	12.9712	−	10.8161i	0.901561	−	0.751771i
$208$	−3.85132	−	18.1870i	−0.267041	−	1.26104i
$209$	29.2125	+	16.8658i	2.02067	+	1.16663i
$210$	−2.03171	+	2.51125i	−0.140201	+	0.173293i
$211$	−2.89019	−	21.9531i	−0.198969	−	1.51132i	−0.741312	−	0.671160i	$-0.765796\pi$
$211$	−2.89019	−	21.9531i	−0.198969	−	1.51132i	0.542344	−	0.840157i	$-0.317537\pi$
$212$	−1.76899	−	3.84108i	−0.121495	−	0.263806i
$213$	9.70968	+	18.7226i	0.665296	+	1.28285i
$214$	−17.3756	+	7.59630i	−1.18777	+	0.519273i
$215$	−4.37520	−	4.37520i	−0.298386	−	0.298386i
$216$	9.55993	+	11.1628i	0.650471	+	0.759531i
$217$	9.16870	−	9.16870i	0.622412	−	0.622412i
$218$	0.574142	−	1.46610i	0.0388858	−	0.0992969i
$219$	22.5839	−	11.7122i	1.52608	−	0.791437i
$220$	−6.18076	−	5.71780i	−0.416707	−	0.385494i
$221$	13.6828	−	1.80138i	0.920408	−	0.121174i
$222$	4.47465	−	0.472334i	0.300319	−	0.0317010i
$223$	7.40653	−	12.8285i	0.495978	−	0.859059i	−0.504012	−	0.863697i	$-0.668143\pi$
$223$	7.40653	−	12.8285i	0.495978	−	0.859059i	0.999989	+	0.00463837i	$0.00147644\pi$
$224$	−7.69050	+	2.88616i	−0.513843	+	0.192840i
$225$	−4.32036	+	11.7571i	−0.288024	+	0.783804i
$226$	−6.74051	−	11.1676i	−0.448372	−	0.742861i
$227$	−8.77860	−	11.4405i	−0.582656	−	0.759332i	0.405280	−	0.914192i	$-0.367174\pi$
$227$	−8.77860	−	11.4405i	−0.582656	−	0.759332i	−0.987936	+	0.154860i	$0.950507\pi$
$228$	−15.4702	+	19.9008i	−1.02454	+	1.31796i
$229$	14.4869	+	11.1162i	0.957320	+	0.734577i	0.964139	−	0.265399i	$-0.0855038\pi$
$229$	14.4869	+	11.1162i	0.957320	+	0.734577i	−0.00681866	+	0.999977i	$0.502170\pi$
$230$	−4.51228	−	5.64958i	−0.297531	−	0.372522i
$231$	−11.4789	−	2.04231i	−0.755258	−	0.134374i
$232$	10.7851	−	9.32334i	0.708074	−	0.612107i
$233$	−10.0421	−	10.0421i	−0.657882	−	0.657882i	0.296997	−	0.954879i	$-0.404015\pi$
$233$	−10.0421	−	10.0421i	−0.657882	−	0.657882i	−0.954879	+	0.296997i	$0.904015\pi$
$234$	17.6366	+	8.81742i	1.15294	+	0.576413i
$235$	1.68417	+	4.06595i	0.109863	+	0.265233i
$236$	2.24414	+	1.58728i	0.146081	+	0.103323i
$237$	−10.3647	+	9.46811i	−0.673259	+	0.615020i
$238$	−1.69252	−	5.85844i	−0.109710	−	0.379747i
$239$	7.27308	−	4.19911i	0.470456	−	0.271618i	−0.245974	−	0.969276i	$-0.579108\pi$
$239$	7.27308	−	4.19911i	0.470456	−	0.271618i	0.716431	+	0.697658i	$0.245775\pi$
$240$	4.86420	−	3.99096i	0.313983	−	0.257615i
$241$	−20.8530	−	12.0395i	−1.34326	−	0.775531i	−0.355975	−	0.934495i	$-0.615851\pi$
$241$	−20.8530	−	12.0395i	−1.34326	−	0.775531i	−0.987284	+	0.158964i	$0.949184\pi$
$242$	3.56017	−	14.4012i	0.228856	−	0.925744i
$243$	−15.5784	+	0.559781i	−0.999355	+	0.0359100i
$244$	−1.76600	−	2.12503i	−0.113057	−	0.136041i
$245$	−4.40421	−	0.579825i	−0.281375	−	0.0370437i
$246$	−2.08814	+	3.41097i	−0.133135	+	0.217475i
$247$	−8.75275	+	32.6657i	−0.556924	+	2.07847i
$248$	−21.0994	+	13.8821i	−1.33981	+	0.881512i
$249$	−5.53160	−	15.2712i	−0.350551	−	0.967775i
$250$	10.9727	+	4.29703i	0.693973	+	0.271768i
$251$	−15.9339	+	6.60002i	−1.00574	+	0.416589i	−0.823897	−	0.566739i	$-0.808205\pi$
$251$	−15.9339	+	6.60002i	−1.00574	+	0.416589i	−0.181838	+	0.983328i	$0.558205\pi$
$252$	2.68488	−	8.28851i	0.169132	−	0.522127i
$253$	9.98710	−	24.1110i	0.627884	−	1.51584i
$254$	0.469282	+	24.1308i	0.0294454	+	1.51410i
$255$	2.67324	+	3.83035i	0.167405	+	0.239866i
$256$	15.8068	−	2.47893i	0.987925	−	0.154933i
$257$	3.31145	+	5.73560i	0.206563	+	0.357777i	0.950629	−	0.310328i	$-0.100439\pi$
$257$	3.31145	+	5.73560i	0.206563	+	0.357777i	−0.744067	+	0.668105i	$0.767106\pi$
$258$	15.2491	+	6.78113i	0.949366	+	0.422175i
$259$	−1.62379	−	2.11616i	−0.100897	−	0.131492i
$260$	3.93331	−	7.46910i	0.243933	−	0.463214i
$261$	0.612947	+	15.1087i	0.0379405	+	0.935203i
$262$	−0.558521	−	3.68690i	−0.0345056	−	0.227778i
$263$	−7.44739	−	27.7940i	−0.459226	−	1.71385i	−0.675358	−	0.737490i	$-0.736011\pi$
$263$	−7.44739	−	27.7940i	−0.459226	−	1.71385i	0.216133	−	0.976364i	$-0.430656\pi$
$264$	21.0940	+	8.41399i	1.29825	+	0.517845i
$265$	0.496994	−	1.85481i	0.0305301	−	0.113940i
$266$	14.8500	+	1.66199i	0.910513	+	0.101903i
$267$	−8.25865	−	15.9247i	−0.505421	−	0.974573i
$268$	11.5355	−	1.97766i	0.704645	−	0.120805i
$269$	27.2150	+	11.2728i	1.65933	+	0.687316i	0.998026	−	0.0628036i	$-0.0200042\pi$
$269$	27.2150	+	11.2728i	1.65933	+	0.687316i	0.661302	+	0.750120i	$0.270004\pi$
$270$	0.0988701	+	6.67285i	0.00601704	+	0.406097i
$271$			18.9559i			1.15149i	0.817629	+	0.575746i	$0.195288\pi$
$271$			18.9559i			1.15149i	−0.817629	+	0.575746i	$0.804712\pi$
$272$	0.922937	+	11.8421i	0.0559613	+	0.718030i
$273$	−1.00080	−	11.6461i	−0.0605710	−	0.704855i
$274$	−0.000538171	−	0.00186281i	−3.25121e−5	−	0.000112537i
$275$	2.52636	+	19.1896i	0.152345	+	1.15718i
$276$	16.8274	+	9.85688i	1.01289	+	0.593314i
$277$	−15.1422	−	1.99351i	−0.909807	−	0.119778i	−0.338928	−	0.940812i	$-0.610064\pi$
$277$	−15.1422	−	1.99351i	−0.909807	−	0.119778i	−0.570879	+	0.821034i	$0.693398\pi$
$278$	2.48243	+	1.82926i	0.148886	+	0.109712i
$279$	2.41714	−	26.6794i	0.144710	−	1.59726i
$280$	−3.52336	−	1.22404i	−0.210561	−	0.0731506i
$281$	5.37133	+	20.0461i	0.320427	+	1.19585i	0.918830	+	0.394653i	$0.129135\pi$
$281$	5.37133	+	20.0461i	0.320427	+	1.19585i	−0.598404	+	0.801195i	$0.704198\pi$
$282$	−8.17480	−	8.60671i	−0.486802	−	0.512522i
$283$	6.67645	+	5.12302i	0.396874	+	0.304532i	0.787848	−	0.615870i	$-0.211195\pi$
$283$	6.67645	+	5.12302i	0.396874	+	0.304532i	−0.390974	+	0.920402i	$0.627862\pi$
$284$	−16.5378	+	17.8769i	−0.981341	+	1.06080i
$285$	−11.1783	+	2.46007i	−0.662144	+	0.145722i
$286$	30.4631	−	0.592430i	1.80132	−	0.0350311i
$287$	2.37088			0.139949
$288$	−8.38408	+	14.7549i	−0.494037	+	0.869441i
$289$	8.18212			0.481301
$290$	6.47228	−	0.125869i	0.380065	−	0.00739131i
$291$	9.59086	+	10.4991i	0.562226	+	0.615467i
$292$	21.5638	+	19.9486i	1.26193	+	1.16740i
$293$	3.09607	+	2.37570i	0.180874	+	0.138790i	0.695230	−	0.718787i	$-0.255302\pi$
$293$	3.09607	+	2.37570i	0.180874	+	0.138790i	−0.514356	+	0.857577i	$0.671969\pi$
$294$	11.6492	−	2.80226i	0.679397	−	0.163431i
$295$	0.323046	+	1.20562i	0.0188085	+	0.0701941i
$296$	2.26474	+	4.67601i	0.131635	+	0.271788i
$297$	−20.9162	+	11.9472i	−1.21368	+	0.693247i
$298$	3.41294	+	2.51494i	0.197706	+	0.145686i
$299$	25.9405	+	3.41513i	1.50018	+	0.197502i
$300$	−14.4632	−	0.0909215i	−0.835033	−	0.00524935i
$301$	−1.29134	−	9.80871i	−0.0744317	−	0.565365i
$302$	7.04208	+	24.3753i	0.405226	+	1.40264i
$303$	−1.99788	−	0.935381i	−0.114775	−	0.0537362i
$304$	−27.6746	−	9.01528i	−1.58725	−	0.517062i
$305$		−	1.25465i		−	0.0718411i
$306$	−10.4369	−	7.05641i	−0.596638	−	0.403388i
$307$	−5.38302	−	2.22972i	−0.307225	−	0.127257i	0.223744	−	0.974648i	$-0.428172\pi$
$307$	−5.38302	−	2.22972i	−0.307225	−	0.127257i	−0.530969	+	0.847391i	$0.678172\pi$
$308$	−2.27489	−	13.2693i	−0.129624	−	0.756088i
$309$	6.72466	−	10.5197i	0.382553	−	0.598448i
$310$	−11.3974	−	1.27558i	−0.647327	−	0.0724479i
$311$	7.26892	−	27.1280i	0.412182	−	1.53829i	−0.378230	−	0.925711i	$-0.623467\pi$
$311$	7.26892	−	27.1280i	0.412182	−	1.53829i	0.790413	−	0.612574i	$-0.209866\pi$
$312$	−2.67458	+	22.6107i	−0.151418	+	1.28008i
$313$	3.69784	+	13.8005i	0.209014	+	0.780052i	0.988188	+	0.153244i	$0.0489721\pi$
$313$	3.69784	+	13.8005i	0.209014	+	0.780052i	−0.779174	+	0.626807i	$0.784361\pi$
$314$	−2.33509	−	15.4144i	−0.131777	−	0.869884i
$315$	3.34315	−	2.11535i	0.188365	−	0.119186i
$316$	−14.3427	−	7.55304i	−0.806842	−	0.424891i
$317$	−20.7408	−	27.0300i	−1.16492	−	1.51815i	−0.813137	−	0.582073i	$-0.802242\pi$
$317$	−20.7408	−	27.0300i	−1.16492	−	1.51815i	−0.351784	−	0.936081i	$-0.614425\pi$
$318$	0.543691	+	5.15065i	0.0304887	+	0.288834i
$319$	11.6828	+	20.2352i	0.654112	+	1.13296i
$320$	6.23959	+	3.72180i	0.348804	+	0.208055i
$321$	23.1402	−	1.98853i	1.29156	−	0.110989i
$322$	−0.224788	−	11.5587i	−0.0125269	−	0.644142i
$323$	8.26884	−	19.9627i	0.460090	−	1.11076i
$324$	−6.70637	−	16.7040i	−0.372576	−	0.928002i
$325$	−17.9276	+	7.42587i	−0.994447	+	0.411913i
$326$	3.45361	+	1.35247i	0.191278	+	0.0749066i
$327$	−1.24181	+	1.47531i	−0.0686725	+	0.0815847i
$328$	−4.52283	−	0.933146i	−0.249731	−	0.0515244i
$329$	−1.82126	+	6.79705i	−0.100410	+	0.374734i
$330$	4.92465	+	9.06037i	0.271093	+	0.498757i
$331$	9.17113	+	1.20740i	0.504091	+	0.0663648i	0.378283	−	0.925690i	$-0.376514\pi$
$331$	9.17113	+	1.20740i	0.504091	+	0.0663648i	0.125808	+	0.992055i	$0.459848\pi$
$332$	14.4241	−	11.9871i	0.791625	−	0.657879i
$333$	−5.37642	−	1.20934i	−0.294626	−	0.0662716i
$334$	2.15800	−	8.72932i	0.118081	−	0.477647i
$335$	4.60247	+	2.65724i	0.251460	+	0.145180i
$336$	10.0550	−	0.327946i	0.548545	−	0.0178909i
$337$	−21.7957	+	12.5838i	−1.18729	+	0.685482i	−0.957690	−	0.287803i	$-0.907075\pi$
$337$	−21.7957	+	12.5838i	−1.18729	+	0.685482i	−0.229600	+	0.973285i	$0.573742\pi$
$338$	3.37560	+	11.6842i	0.183609	+	0.635539i
$339$	3.43372	+	15.6024i	0.186494	+	0.847408i
$340$	−3.11453	+	4.40341i	−0.168909	+	0.238809i
$341$	−15.8411	−	38.2438i	−0.857844	−	2.07102i
$342$	25.7620	−	17.0110i	1.39305	−	0.919848i
$343$	−12.2099	−	12.2099i	−0.659273	−	0.659273i
$344$	−1.39714	+	19.2199i	−0.0753288	+	1.03627i
$345$	3.01587	+	8.32600i	0.162369	+	0.448257i
$346$	−9.76536	−	12.2267i	−0.524989	−	0.657310i
$347$	−9.34827	−	7.17318i	−0.501841	−	0.385076i	0.326591	−	0.945166i	$-0.394100\pi$
$347$	−9.34827	−	7.17318i	−0.501841	−	0.385076i	−0.828432	+	0.560089i	$0.810767\pi$
$348$	−16.1729	+	6.58025i	−0.866960	+	0.352738i
$349$	17.4783	+	22.7782i	0.935591	+	1.21929i	0.975481	+	0.220082i	$0.0706326\pi$
$349$	17.4783	+	22.7782i	0.935591	+	1.21929i	−0.0398898	+	0.999204i	$0.512701\pi$
$350$	4.43063	+	7.34064i	0.236827	+	0.392374i
$351$	−16.9970	−	17.1551i	−0.907234	−	0.915673i
$352$	−0.882900	+	26.2086i	−0.0470587	+	1.39692i
$353$	−0.660212	+	1.14352i	−0.0351395	+	0.0608634i	−0.883060	−	0.469259i	$-0.844521\pi$
$353$	−0.660212	+	1.14352i	−0.0351395	+	0.0608634i	0.847921	+	0.530123i	$0.177854\pi$
$354$	−1.98001	−	2.72268i	−0.105236	−	0.144709i
$355$	−10.9638	+	1.44341i	−0.581896	+	0.0766080i
$356$	14.0664	−	15.2054i	0.745518	−	0.805882i
$357$	−0.337286	+	7.46091i	−0.0178511	+	0.394873i
$358$	−9.01643	+	23.0239i	−0.476533	+	1.21685i
$359$	11.9308	−	11.9308i	0.629681	−	0.629681i	−0.318307	−	0.947988i	$-0.603114\pi$
$359$	11.9308	−	11.9308i	0.629681	−	0.629681i	0.947988	+	0.318307i	$0.103114\pi$
$360$	−7.21016	+	2.71954i	−0.380009	+	0.143332i
$361$	24.0045	+	24.0045i	1.26339	+	1.26339i
$362$	4.08527	−	1.78601i	0.214717	−	0.0938705i
$363$	−9.78570	+	15.3083i	−0.513616	+	0.803477i
$364$	12.2597	−	5.64614i	0.642581	−	0.295938i
$365$	1.74109	+	13.2249i	0.0911330	+	0.692224i
$366$	1.21415	+	3.15873i	0.0634646	+	0.165110i
$367$	13.7260	+	7.92470i	0.716490	+	0.413666i	0.813459	−	0.581622i	$-0.197582\pi$
$367$	13.7260	+	7.92470i	0.716490	+	0.413666i	−0.0969693	+	0.995287i	$0.530915\pi$
$368$	−4.12054	+	22.1385i	−0.214798	+	1.15405i
$369$	3.76195	−	3.13692i	0.195839	−	0.163302i
$370$	−0.566185	+	2.29027i	−0.0294345	+	0.119065i
$371$	2.43586	−	1.86910i	0.126463	−	0.0970388i
$372$	29.9286	−	7.81804i	1.55173	−	0.405347i
$373$	3.19353	−	4.16189i	0.165355	−	0.215495i	−0.703325	−	0.710868i	$-0.748302\pi$
$373$	3.19353	−	4.16189i	0.165355	−	0.215495i	0.868680	+	0.495374i	$0.164969\pi$
$374$	−19.3468	−	2.16527i	−1.00040	−	0.111963i
$375$	−11.0416	−	9.29406i	−0.570185	−	0.479943i
$376$	6.14958	−	12.2496i	0.317140	−	0.631726i
$377$	−16.5643	+	16.5643i	−0.853105	+	0.853105i
$378$	−6.36973	+	8.56087i	−0.327623	+	0.440324i
$379$	4.77373	−	1.97734i	0.245210	−	0.101569i	−0.256694	−	0.966493i	$-0.582633\pi$
$379$	4.77373	−	1.97734i	0.245210	−	0.101569i	0.501904	+	0.864923i	$0.332633\pi$
$380$	−7.04824	−	11.1802i	−0.361567	−	0.573532i
$381$	8.93224	−	28.1778i	0.457613	−	1.44359i
$382$	−23.0124	−	12.6961i	−1.17742	−	0.649590i
$383$	−7.78312	−	13.4808i	−0.397699	−	0.688835i	0.595743	−	0.803175i	$-0.296858\pi$
$383$	−7.78312	−	13.4808i	−0.397699	−	0.688835i	−0.993442	+	0.114341i	$0.963524\pi$
$384$	−19.3106	−	3.33190i	−0.985439	−	0.170031i
$385$	3.05661	−	5.29421i	0.155779	−	0.269818i
$386$	−15.7608	+	9.51285i	−0.802206	+	0.484191i
$387$	−15.0270	−	13.8552i	−0.763863	−	0.704301i
$388$	−7.65097	+	14.5287i	−0.388419	+	0.737583i
$389$	1.99277	−	15.1366i	0.101037	−	0.767454i	−0.863657	−	0.504081i	$-0.831831\pi$
$389$	1.99277	−	15.1366i	0.101037	−	0.767454i	0.964694	−	0.263374i	$-0.0848352\pi$
$390$	−7.49620	+	7.12002i	−0.379585	+	0.360536i
$391$	−16.1477	−	4.32676i	−0.816623	−	0.218814i
$392$	7.60433	+	11.5579i	0.384077	+	0.583760i
$393$	−0.799997	+	4.49642i	−0.0403545	+	0.226815i
$394$	11.2674	+	25.7727i	0.567642	+	1.29841i
$395$	−2.81678	−	6.80032i	−0.141728	−	0.342161i
$396$	−21.1663	−	18.0449i	−1.06365	−	0.906791i
$397$	32.7009	+	13.5451i	1.64121	+	0.679811i	0.996419	−	0.0845483i	$-0.0269447\pi$
$397$	32.7009	+	13.5451i	1.64121	+	0.679811i	0.644790	+	0.764360i	$0.276945\pi$
$398$	−14.5139	−	13.9601i	−0.727516	−	0.699759i
$399$	−16.5744	−	7.75994i	−0.829759	−	0.388483i
$400$	−5.56294	−	15.7473i	−0.278147	−	0.787364i
$401$	−13.6610	+	7.88721i	−0.682200	+	0.393868i	−0.800683	−	0.599088i	$-0.795530\pi$
$401$	−13.6610	+	7.88721i	−0.682200	+	0.393868i	0.118483	+	0.992956i	$0.462197\pi$
$402$	−14.1587	−	2.23601i	−0.706174	−	0.111522i
$403$	32.9248	−	25.2641i	1.64010	−	1.25849i
$404$	0.234043	−	2.53650i	0.0116441	−	0.126195i
$405$	2.50587	−	7.77983i	0.124518	−	0.386583i
$406$	8.33273	+	6.14025i	0.413546	+	0.304735i
$407$	−8.22525	+	2.20395i	−0.407710	+	0.109246i
$408$	3.57994	−	14.1001i	0.177233	−	0.698060i
$409$	−26.4913	−	7.09833i	−1.30991	−	0.350990i	−0.464722	−	0.885457i	$-0.653846\pi$
$409$	−26.4913	−	7.09833i	−1.30991	−	0.350990i	−0.845189	+	0.534467i	$0.820512\pi$
$410$	−1.30867	−	1.63851i	−0.0646304	−	0.0809203i
$411$	−0.000107247		0.00237235i	−5.29011e−6		0.000117019i
$412$	14.0602	+	3.18712i	0.692698	+	0.157018i
$413$	−0.763726	+	1.84380i	−0.0375805	+	0.0907274i
$414$	−15.6501	−	18.0432i	−0.769158	−	0.886774i
$415$	8.51621			0.418044
$416$	−25.6095	+	5.94566i	−1.25561	+	0.291510i
$417$	−2.16141	−	3.09697i	−0.105845	−	0.151659i
$418$	23.0441	−	41.7687i	1.12712	−	2.04297i
$419$	8.36151	−	1.10081i	0.408487	−	0.0537783i	0.0765168	−	0.997068i	$-0.475620\pi$
$419$	8.36151	−	1.10081i	0.408487	−	0.0537783i	0.331970	+	0.943290i	$0.392287\pi$
$420$	3.60665	+	2.80367i	0.175986	+	0.136805i
$421$	−2.00163	+	15.2039i	−0.0975535	+	0.740992i	0.870840	+	0.491566i	$0.163575\pi$
$421$	−2.00163	+	15.2039i	−0.0975535	+	0.740992i	−0.968394	+	0.249426i	$0.919758\pi$
$422$	−30.9611	+	4.69023i	−1.50716	+	0.228317i
$423$	6.10334	+	13.1948i	0.296755	+	0.641554i
$424$	−5.38243	+	2.60688i	−0.261394	+	0.126601i
$425$	11.9759	−	3.20893i	0.580916	−	0.155656i
$426$	26.2057	−	14.2438i	1.26967	−	0.690114i
$427$	1.22124	−	1.59155i	0.0590998	−	0.0770203i
$428$	11.2186	+	24.3593i	0.542269	+	1.17745i
$429$	−35.5721	−	11.2762i	−1.71744	−	0.544421i
$430$	−6.06600	+	6.30661i	−0.292528	+	0.304132i
$431$			29.5801i			1.42482i	0.701762	+	0.712412i	$0.252397\pi$
$431$			29.5801i			1.42482i	−0.701762	+	0.712412i	$0.747603\pi$
$432$	15.5207	−	13.8242i	0.746740	−	0.665116i
$433$			24.8594i			1.19467i	0.801994	+	0.597333i	$0.203773\pi$
$433$			24.8594i			1.19467i	−0.801994	+	0.597333i	$0.796227\pi$
$434$	−13.2162	−	12.7119i	−0.634396	−	0.610192i
$435$	−7.55775	−	2.39578i	−0.362367	−	0.114869i
$436$	−2.08878	−	0.771492i	−0.100034	−	0.0369478i
$437$	24.9376	−	32.4993i	1.19292	−	1.55465i
$438$	−17.1814	−	31.6104i	−0.820960	−	1.51040i
$439$	2.61213	−	0.699918i	0.124670	−	0.0334053i	−0.195944	−	0.980615i	$-0.562777\pi$
$439$	2.61213	−	0.699918i	0.124670	−	0.0334053i	0.320615	+	0.947210i	$0.396111\pi$
$440$	−7.91470	+	8.89649i	−0.377318	+	0.424124i
$441$	−14.6145	−	1.32406i	−0.695927	−	0.0630506i
$442$	−2.92330	−	19.2973i	−0.139047	−	0.917878i
$443$	−1.42427	+	10.8184i	−0.0676692	+	0.513998i	0.923722	+	0.383064i	$0.125131\pi$
$443$	−1.42427	+	10.8184i	−0.0676692	+	0.513998i	−0.991391	+	0.130934i	$0.958202\pi$
$444$	−0.790898	−	6.31393i	−0.0375343	−	0.299646i
$445$	9.32531	−	1.22770i	0.442062	−	0.0581986i
$446$	−18.3424	−	10.1197i	−0.868540	−	0.479181i
$447$	−2.97159	−	4.25784i	−0.140551	−	0.201389i
$448$	4.29235	+	10.7946i	0.202795	+	0.509997i
$449$	0.319692			0.0150872			0.00754359	−	0.999972i	$-0.497599\pi$
$449$	0.319692			0.0150872			0.00754359	+	0.999972i	$0.497599\pi$
$450$	16.7427	+	5.78546i	0.789256	+	0.272729i
$451$	2.89649	−	6.99275i	0.136390	−	0.329276i
$452$	−15.6051	+	9.83780i	−0.734002	+	0.462731i
$453$	1.40335	−	31.0427i	0.0659352	−	1.45851i
$454$	−15.9349	+	12.7271i	−0.747860	+	0.597310i
$455$	5.92004	+	1.58627i	0.277536	+	0.0743654i
$456$	28.5641	+	21.3268i	1.33764	+	0.998717i
$457$	−16.6150	+	4.45196i	−0.777215	+	0.208254i	−0.625556	−	0.780179i	$-0.715128\pi$
$457$	−16.6150	+	4.45196i	−0.777215	+	0.208254i	−0.151658	+	0.988433i	$0.548461\pi$
$458$	15.3193	−	20.7893i	0.715825	−	0.971422i
$459$	9.33638	+	12.2847i	0.435785	+	0.573403i
$460$	−7.86413	+	6.53547i	−0.366667	+	0.304718i
$461$	11.2398	−	8.62456i	0.523487	−	0.401686i	−0.312932	−	0.949775i	$-0.601311\pi$
$461$	11.2398	−	8.62456i	0.523487	−	0.401686i	0.836420	+	0.548089i	$0.184645\pi$
$462$	−2.57208	+	16.2867i	−0.119664	+	0.757728i
$463$	16.2750	−	9.39636i	0.756362	−	0.436686i	−0.0716262	−	0.997432i	$-0.522819\pi$
$463$	16.2750	−	9.39636i	0.756362	−	0.436686i	0.827988	+	0.560746i	$0.189486\pi$
$464$	−13.4793	−	14.9931i	−0.625759	−	0.696039i
$465$	12.7208	+	5.95574i	0.589915	+	0.276191i
$466$	−13.9229	+	14.4752i	−0.644966	+	0.670549i
$467$	7.90006	+	3.27231i	0.365571	+	0.151425i	0.557905	−	0.829905i	$-0.311605\pi$
$467$	7.90006	+	3.27231i	0.365571	+	0.151425i	−0.192333	+	0.981330i	$0.561605\pi$
$468$	11.9824	−	25.1797i	0.553886	−	1.16393i
$469$	3.25185	+	7.85066i	0.150156	+	0.362510i
$470$	5.70272	−	2.49313i	0.263047	−	0.115000i
$471$	−3.34466	+	18.7989i	−0.154114	+	0.866205i
$472$	2.18262	−	3.21674i	0.100463	−	0.148063i
$473$	−30.5078	−	8.17453i	−1.40275	−	0.375865i
$474$	13.6724	+	14.3948i	0.627994	+	0.661173i
$475$	−3.96554	+	30.1213i	−0.181951	+	1.38206i
$476$	−8.23698	+	2.55422i	−0.377542	+	0.117073i
$477$	1.39204	−	6.18865i	0.0637373	−	0.283359i
$478$	−6.13731	−	10.1683i	−0.280714	−	0.465086i
$479$	−11.2038	+	19.4055i	−0.511912	+	0.886658i	0.487992	+	0.872848i	$0.337729\pi$
$479$	−11.2038	+	19.4055i	−0.511912	+	0.886658i	−0.999905	+	0.0138104i	$0.995604\pi$
$480$	−5.77676	−	6.76798i	−0.263672	−	0.308914i
$481$	−4.26860	−	7.39343i	−0.194631	−	0.337111i
$482$	−16.4498	+	29.8161i	−0.749266	+	1.35808i
$483$	−4.27857	+	13.4972i	−0.194682	+	0.614146i
$484$	−20.4604	−	4.63789i	−0.930019	−	0.210813i
$485$	−6.88849	+	2.85331i	−0.312790	+	0.129562i
$486$	1.21987	+	22.0116i	0.0553344	+	0.998468i
$487$	−11.1545	+	11.1545i	−0.505459	+	0.505459i	−0.913129	−	0.407670i	$-0.866341\pi$
$487$	−11.1545	+	11.1545i	−0.505459	+	0.505459i	0.407670	+	0.913129i	$0.366341\pi$
$488$	−2.95611	+	2.55546i	−0.133817	+	0.115680i
$489$	−3.47530	−	2.92527i	−0.157158	−	0.132285i
$490$	−0.698736	+	6.24326i	−0.0315657	+	0.282042i
$491$	0.740341	−	0.964831i	0.0334111	−	0.0435422i	−0.776349	−	0.630303i	$-0.782931\pi$
$491$	0.740341	−	0.964831i	0.0334111	−	0.0435422i	0.809760	+	0.586761i	$0.199597\pi$
$492$	4.88035	+	2.85872i	0.220023	+	0.128881i
$493$	11.8744	−	9.11153i	0.534795	−	0.410363i
$494$	46.4282	+	11.4777i	2.08891	+	0.516406i
$495$	−2.15476	−	12.4447i	−0.0968492	−	0.559348i
$496$	20.2087	+	29.4517i	0.907396	+	1.32242i
$497$	−15.3127	−	8.84078i	−0.686868	−	0.396563i
$498$	−21.4406	+	8.24131i	−0.960776	+	0.369302i
$499$	1.67710	+	12.7388i	0.0750772	+	0.570268i	0.987097	+	0.160122i	$0.0511888\pi$
$499$	1.67710	+	12.7388i	0.0750772	+	0.570268i	−0.912020	+	0.410146i	$0.865478\pi$
$500$	5.77404	−	15.6329i	0.258223	−	0.699126i
$501$	−5.93162	+	9.27916i	−0.265005	+	0.414562i
$502$	9.77021	+	22.3481i	0.436066	+	0.997446i
$503$	11.3606	+	11.3606i	0.506546	+	0.506546i	0.913465	−	0.406918i	$-0.133397\pi$
$503$	11.3606	+	11.3606i	0.506546	+	0.506546i	−0.406918	+	0.913465i	$0.633397\pi$
$504$	−11.7933	−	3.56836i	−0.525317	−	0.158948i
$505$	0.817886	−	0.817886i	0.0363954	−	0.0363954i
$506$	−34.3663	−	13.4582i	−1.52777	−	0.598291i
$507$	0.672693	−	14.8803i	0.0298753	−	0.660855i
$508$	34.1067	−	1.32708i	1.51324	−	0.0588796i
$509$	1.88647	−	0.248358i	0.0836163	−	0.0110083i	−0.0886019	−	0.996067i	$-0.528240\pi$
$509$	1.88647	−	0.248358i	0.0836163	−	0.0110083i	0.172218	+	0.985059i	$0.444907\pi$
$510$	5.34240	−	3.88514i	0.236565	−	0.172037i
$511$	−10.6641	+	18.4708i	−0.471752	+	0.817099i
$512$	−3.93973	−	22.2818i	−0.174113	−	0.984726i
$513$	−36.5664	+	9.61672i	−1.61445	+	0.424589i
$514$	8.01877	−	4.83993i	0.353693	−	0.213480i
$515$	3.98522	+	5.19364i	0.175610	+	0.228859i
$516$	9.16884	−	21.7478i	0.403636	−	0.957395i
$517$	17.8224	+	13.6756i	0.783829	+	0.601453i
$518$	−2.94749	+	2.35414i	−0.129505	+	0.103435i
$519$	6.52687	+	18.0189i	0.286498	+	0.790942i
$520$	−10.6691	−	5.35610i	−0.467870	−	0.234881i
$521$	30.8949	+	30.8949i	1.35353	+	1.35353i	0.881678	+	0.471851i	$0.156414\pi$
$521$	30.8949	+	30.8949i	1.35353	+	1.35353i	0.471851	+	0.881678i	$0.343586\pi$
$522$	21.3460	−	1.28213i	0.934289	−	0.0561172i
$523$	9.11094	+	21.9958i	0.398394	+	0.961807i	0.988047	+	0.154151i	$0.0492642\pi$
$523$	9.11094	+	21.9958i	0.398394	+	0.961807i	−0.589654	+	0.807656i	$0.700736\pi$
$524$	−5.19773	+	0.891100i	−0.227064	+	0.0389279i
$525$	−2.25703	−	10.2557i	−0.0985050	−	0.447595i
$526$	−39.0945	+	11.2945i	−1.70460	+	0.492463i
$527$	−22.9638	+	13.2581i	−1.00032	+	0.577533i
$528$	11.3169	−	30.0572i	0.492504	−	1.30807i
$529$	−7.52867	−	4.34668i	−0.327334	−	0.188986i
$530$	−2.63626	−	0.651720i	−0.114512	−	0.0283089i
$531$	1.22771	+	3.93610i	0.0532779	+	0.170812i
$532$	1.94163	−	21.0428i	0.0841802	−	0.912322i
$533$	7.52335	+	0.990468i	0.325873	+	0.0429019i
$534$	−22.2895	+	12.1152i	−0.964562	+	0.524275i
$535$	−3.15183	+	11.7628i	−0.136265	+	0.508549i
$536$	−3.11350	−	16.2562i	−0.134483	−	0.702163i
$537$	19.5017	−	23.1685i	0.841560	−	0.999795i
$538$	15.1908	−	38.7905i	0.654923	−	1.67238i
$539$	−20.9492	+	8.67745i	−0.902347	+	0.373764i
$540$	9.43234	−	0.323285i	0.405903	−	0.0139120i
$541$	−9.40824	+	22.7135i	−0.404492	+	0.976530i	0.582069	+	0.813139i	$0.302243\pi$
$541$	−9.40824	+	22.7135i	−0.404492	+	0.976530i	−0.986561	+	0.163391i	$0.947757\pi$
$542$	26.8027	−	0.521244i	1.15127	−	0.0223894i
$543$	−5.44061	+	0.467533i	−0.233479	+	0.0200638i
$544$	16.7187	−	1.63061i	0.716806	−	0.0699119i
$545$	−0.505549	−	0.875637i	−0.0216554	−	0.0375082i
$546$	−16.4395	+	1.73531i	−0.703544	+	0.0742646i
$547$	7.06835	+	9.21165i	0.302221	+	0.393862i	0.919633	−	0.392778i	$-0.128486\pi$
$547$	7.06835	+	9.21165i	0.302221	+	0.393862i	−0.617413	+	0.786639i	$0.711819\pi$
$548$	−0.00261912		0.000812167i	−0.000111883		3.46941e-5i
$549$	−0.168005	−	4.14118i	−0.00717026	−	0.176741i
$550$	27.0636	−	4.09981i	1.15400	−	0.174816i
$551$	9.49251	+	35.4265i	0.404394	+	1.50922i
$552$	13.4744	−	24.0641i	0.573508	−	1.02424i
$553$	3.04607	−	11.3681i	0.129532	−	0.483421i
$554$	−2.40234	+	21.4651i	−0.102066	+	0.911964i
$555$	1.55625	−	2.43452i	0.0660591	−	0.103340i
$556$	2.51821	−	3.56032i	0.106796	−	0.150991i
$557$	−31.1741	−	12.9127i	−1.32089	−	0.547130i	−0.392846	−	0.919604i	$-0.628510\pi$
$557$	−31.1741	−	12.9127i	−1.32089	−	0.547130i	−0.928043	+	0.372474i	$0.878510\pi$
$558$	−37.7897	−	2.68408i	−1.59977	−	0.113626i
$559$		−	31.6648i		−	1.33928i
$560$	−1.63385	+	5.01549i	−0.0690426	+	0.211943i
$561$	21.5934	+	10.1098i	0.911674	+	0.426834i
$562$	28.1964	−	8.14599i	1.18939	−	0.343618i
$563$	5.62575	+	42.7318i	0.237097	+	1.80093i	0.533428	+	0.845846i	$0.320904\pi$
$563$	5.62575	+	42.7318i	0.237097	+	1.80093i	−0.296331	+	0.955085i	$0.595763\pi$
$564$	−11.9446	+	11.7954i	−0.502960	+	0.496676i
$565$	−8.30487	−	1.09336i	−0.349389	−	0.0459979i
$566$	7.06009	−	9.58102i	0.296758	−	0.402720i
$567$	10.7514	−	7.42972i	0.451516	−	0.312019i
$568$	25.7317	+	22.8921i	1.07968	+	0.960529i
$569$	0.0486029	+	0.181388i	0.00203754	+	0.00760420i	0.966937	−	0.255015i	$-0.0820804\pi$
$569$	0.0486029	+	0.181388i	0.00203754	+	0.00760420i	−0.964900	+	0.262619i	$0.915414\pi$
$570$	3.78579	+	15.7378i	0.158569	+	0.659186i
$571$	22.0081	+	16.8874i	0.921010	+	0.706716i	0.956215	−	0.292665i	$-0.0945419\pi$
$571$	22.0081	+	16.8874i	0.921010	+	0.706716i	−0.0352055	+	0.999380i	$0.511209\pi$
$572$	−1.67533	−	43.0569i	−0.0700490	−	1.80030i
$573$	21.7100	+	23.7659i	0.906950	+	0.992834i
$574$	−0.0651936	−	3.35230i	−0.00272113	−	0.139922i
$575$	23.5053			0.980240
$576$	21.0932	+	11.4489i	0.878883	+	0.477038i
$577$	−14.9045			−0.620481			−0.310240	−	0.950658i	$-0.600410\pi$
$577$	−14.9045			−0.620481			−0.310240	+	0.950658i	$0.600410\pi$
$578$	−0.224989	−	11.5691i	−0.00935831	−	0.481210i
$579$	22.0196	−	4.84600i	0.915105	−	0.201393i
$580$	−0.355945	−	9.14800i	−0.0147798	−	0.379850i
$581$	10.8030	+	8.28941i	0.448183	+	0.343903i
$582$	14.5814	−	13.8497i	0.604418	−	0.574087i
$583$	−2.53691	−	9.46786i	−0.105068	−	0.392119i
$584$	27.6133	−	31.0387i	1.14265	−	1.28439i
$585$	11.4923	−	5.31584i	0.475149	−	0.219783i
$586$	3.27398	−	4.44300i	0.135247	−	0.183539i
$587$	−34.9651	−	4.60324i	−1.44316	−	0.189996i	−0.632070	−	0.774912i	$-0.717794\pi$
$587$	−34.9651	−	4.60324i	−1.44316	−	0.189996i	−0.811094	+	0.584915i	$0.801128\pi$
$588$	−4.28257	−	16.3943i	−0.176610	−	0.676091i
$589$	−8.48107	−	64.4201i	−0.349456	−	2.65438i
$590$	1.69580	−	0.489921i	0.0698151	−	0.0201697i
$591$	−2.94952	−	34.3231i	−0.121327	−	1.41187i
$592$	6.54935	−	3.33080i	0.269177	−	0.136895i
$593$		−	18.8010i		−	0.772063i	−0.922486	−	0.386032i	$-0.873846\pi$
$593$		−	18.8010i		−	0.772063i	0.922486	−	0.386032i	$-0.126154\pi$
$594$	17.4679	+	29.2459i	0.716715	+	1.19997i
$595$	−3.61786	−	1.49857i	−0.148318	−	0.0614353i
$596$	3.46214	−	4.89487i	0.141815	−	0.200501i
$597$	11.3547	+	21.8947i	0.464719	+	0.896090i
$598$	4.11551	−	36.7724i	0.168296	−	1.50373i
$599$	10.7198	−	40.0067i	0.437997	−	1.63463i	−0.295793	−	0.955252i	$-0.595584\pi$
$599$	10.7198	−	40.0067i	0.437997	−	1.63463i	0.733790	−	0.679376i	$-0.237750\pi$
$600$	0.269146	+	20.4527i	0.0109878	+	0.834977i
$601$	7.10376	+	26.5116i	0.289768	+	1.08143i	0.945284	+	0.326249i	$0.105785\pi$
$601$	7.10376	+	26.5116i	0.289768	+	1.08143i	−0.655515	+	0.755182i	$0.727549\pi$
$602$	−13.8335	+	2.09560i	−0.563811	+	0.0854105i
$603$	15.5470	+	8.15436i	0.633125	+	0.332071i
$604$	34.2717	−	10.6274i	1.39450	−	0.432422i
$605$	−5.79928	−	7.55777i	−0.235774	−	0.307267i
$606$	−1.26764	+	2.85061i	−0.0514944	+	0.115798i
$607$	−6.17311	−	10.6921i	−0.250559	−	0.433981i	0.713121	−	0.701041i	$-0.247281\pi$
$607$	−6.17311	−	10.6921i	−0.250559	−	0.433981i	−0.963680	+	0.267060i	$0.913948\pi$
$608$	−11.9861	+	39.3783i	−0.486102	+	1.59700i
$609$	−7.25518	−	10.3956i	−0.293995	−	0.421250i
$610$	−1.77401	+	0.0344999i	−0.0718275	+	0.00139686i
$611$	−8.61886	+	20.8078i	−0.348682	+	0.841792i
$612$	−9.69040	+	14.9513i	−0.391711	+	0.604369i
$613$	15.0335	−	6.22710i	0.607199	−	0.251510i	−0.0578313	−	0.998326i	$-0.518419\pi$
$613$	15.0335	−	6.22710i	0.607199	−	0.251510i	0.665030	+	0.746816i	$0.268419\pi$
$614$	−3.00468	+	7.67261i	−0.121259	+	0.309641i
$615$	0.874673	+	2.41473i	0.0352702	+	0.0973714i
$616$	−18.6995	+	3.58145i	−0.753425	+	0.144301i
$617$	8.57996	−	32.0208i	0.345416	−	1.28911i	−0.546709	−	0.837322i	$-0.684120\pi$
$617$	8.57996	−	32.0208i	0.345416	−	1.28911i	0.892125	−	0.451788i	$-0.149214\pi$
$618$	−15.0593	−	9.21904i	−0.605773	−	0.370844i
$619$	−41.3276	−	5.44088i	−1.66110	−	0.218688i	−0.759267	−	0.650779i	$-0.774442\pi$
$619$	−41.3276	−	5.44088i	−1.66110	−	0.218688i	−0.901830	+	0.432091i	$0.857776\pi$
$620$	−1.49020	+	16.1503i	−0.0598477	+	0.648613i
$621$	11.0693	+	27.0775i	0.444195	+	1.08658i
$622$	−38.5574	−	9.53190i	−1.54601	−	0.382194i
$623$	13.0243	+	7.51960i	0.521809	+	0.301267i
$624$	32.0439	+	3.15997i	1.28278	+	0.126500i
$625$	−11.5258	+	6.65445i	−0.461034	+	0.266178i
$626$	19.4115	−	5.60803i	0.775840	−	0.224142i
$627$	−43.1363	+	39.4048i	−1.72270	+	1.57368i
$628$	−21.7309	+	3.72555i	−0.867157	+	0.148666i
$629$	2.08743	+	5.03950i	0.0832312	+	0.200938i
$630$	−3.08292	−	4.66887i	−0.122826	−	0.186012i
$631$	−3.36566	−	3.36566i	−0.133985	−	0.133985i	0.636934	−	0.770919i	$-0.280202\pi$
$631$	−3.36566	−	3.36566i	−0.133985	−	0.133985i	−0.770919	+	0.636934i	$0.780202\pi$
$632$	−10.2852	+	20.4875i	−0.409123	+	0.814951i
$633$	37.7591	+	6.71804i	1.50079	+	0.267018i
$634$	−37.6486	+	30.0697i	−1.49522	+	1.19422i
$635$	12.2961	+	9.43513i	0.487956	+	0.374422i
$636$	7.26779	−	0.910381i	0.288187	−	0.0360990i
$637$	−13.8392	−	18.0356i	−0.548328	−	0.714595i
$638$	28.2903	−	17.0753i	1.12002	−	0.676018i
$639$	−35.9944	+	6.23231i	−1.42392	+	0.246546i
$640$	5.09085	−	8.92479i	0.201234	−	0.352783i
$641$	3.34820	−	5.79926i	0.132246	−	0.229057i	−0.792296	−	0.610137i	$-0.791114\pi$
$641$	3.34820	−	5.79926i	0.132246	−	0.229057i	0.924542	+	0.381080i	$0.124448\pi$
$642$	−3.44797	−	32.6643i	−0.136081	−	1.28916i
$643$	9.30824	−	1.22545i	0.367081	−	0.0483271i	0.0552704	−	0.998471i	$-0.482398\pi$
$643$	9.30824	−	1.22545i	0.367081	−	0.0483271i	0.311811	+	0.950144i	$0.399065\pi$
$644$	−16.3372	+	0.635675i	−0.643777	+	0.0250491i
$645$	9.51374	−	4.93389i	0.374603	−	0.194272i
$646$	−28.4536	−	11.1428i	−1.11949	−	0.438406i
$647$	−17.3236	+	17.3236i	−0.681063	+	0.681063i	−0.960240	−	0.279177i	$-0.909938\pi$
$647$	−17.3236	+	17.3236i	−0.681063	+	0.681063i	0.279177	+	0.960240i	$0.409938\pi$
$648$	−23.4342	+	9.94177i	−0.920582	+	0.390550i
$649$	4.50512	+	4.50512i	0.176841	+	0.176841i
$650$	10.9928	+	25.1445i	0.431171	+	0.986249i
$651$	10.3395	+	19.9370i	0.405237	+	0.781394i
$652$	1.81736	−	4.92041i	0.0711733	−	0.192698i
$653$	2.88176	+	21.8891i	0.112772	+	0.856587i	0.950549	+	0.310575i	$0.100522\pi$
$653$	2.88176	+	21.8891i	0.112772	+	0.856587i	−0.837777	+	0.546012i	$0.816145\pi$
$654$	2.12015	+	1.71529i	0.0829045	+	0.0670732i
$655$	−2.07380	−	1.19731i	−0.0810301	−	0.0467827i
$656$	−1.19505	+	6.42069i	−0.0466589	+	0.250686i
$657$	7.51766	+	43.4179i	0.293292	+	1.69389i
$658$	9.66074	+	2.38827i	0.376615	+	0.0931043i
$659$	25.6164	−	19.6562i	0.997873	−	0.765695i	0.0256309	−	0.999671i	$-0.491841\pi$
$659$	25.6164	−	19.6562i	0.997873	−	0.765695i	0.972242	+	0.233976i	$0.0751739\pi$
$660$	12.6755	−	7.21232i	0.493392	−	0.280739i
$661$	−16.4041	+	21.3782i	−0.638044	+	0.831515i	−0.994711	−	0.102716i	$-0.967247\pi$
$661$	−16.4041	+	21.3782i	−0.638044	+	0.831515i	0.356666	+	0.934232i	$0.383913\pi$
$662$	1.45502	−	13.0007i	0.0565508	−	0.505286i
$663$	−4.18719	+	23.5343i	−0.162617	+	0.913997i
$664$	−17.3458	−	20.0653i	−0.673146	−	0.778683i
$665$	6.78520	−	6.78520i	0.263119	−	0.263119i
$666$	−1.56211	+	7.63522i	−0.0605305	+	0.295859i
$667$	26.2157	−	10.8589i	1.01508	−	0.420458i
$668$	−12.4021	−	2.81127i	−0.479853	−	0.108771i
$669$	17.3044	+	18.9430i	0.669026	+	0.732379i
$670$	3.63063	−	6.58071i	0.140264	−	0.254235i
$671$	−3.20218	−	5.54634i	−0.123619	−	0.214114i
$672$	−0.740188	−	14.2082i	−0.0285534	−	0.548094i
$673$	13.3347	−	23.0964i	0.514016	−	0.890302i	−0.485852	−	0.874041i	$-0.661491\pi$
$673$	13.3347	−	23.0964i	0.514016	−	0.890302i	0.999868	−	0.0162604i	$-0.00517608\pi$
$674$	18.3921	+	30.4720i	0.708438	+	1.17374i
$675$	−17.1506	−	13.2867i	−0.660129	−	0.511407i
$676$	16.4281	−	5.09421i	0.631849	−	0.195931i
$677$	4.38064	−	33.2743i	0.168362	−	1.27883i	−0.673519	−	0.739170i	$-0.735218\pi$
$677$	4.38064	−	33.2743i	0.168362	−	1.27883i	0.841880	−	0.539664i	$-0.181449\pi$
$678$	21.9666	−	5.28413i	0.843621	−	0.202936i
$679$	−11.5155	−	3.08557i	−0.441924	−	0.118413i
$680$	6.31183	+	4.28270i	0.242048	+	0.164234i
$681$	23.4838	−	8.50638i	0.899900	−	0.325965i
$682$	−53.6391	+	23.4501i	−2.05395	+	0.897950i
$683$	−6.73316	−	16.2553i	−0.257637	−	0.621992i	0.741144	−	0.671346i	$-0.234284\pi$
$683$	−6.73316	−	16.2553i	−0.257637	−	0.621992i	−0.998781	+	0.0493546i	$0.984284\pi$
$684$	−24.7610	−	35.9583i	−0.946761	−	1.37490i
$685$	−0.00115037		0.000476501i	−4.39536e−5		1.82062e-5i
$686$	−16.9284	+	17.5999i	−0.646329	+	0.671967i
$687$	−25.9359	+	18.1010i	−0.989517	+	0.690594i
$688$	27.2144	+	1.44698i	1.03754	+	0.0551655i
$689$	8.51038	−	4.91347i	0.324220	−	0.187188i
$690$	11.6896	−	4.49323i	0.445015	−	0.171054i
$691$	8.65609	−	6.64205i	0.329293	−	0.252676i	−0.430861	−	0.902418i	$-0.641790\pi$
$691$	8.65609	−	6.64205i	0.329293	−	0.252676i	0.760154	+	0.649743i	$0.225123\pi$
$692$	−17.0193	+	14.1439i	−0.646978	+	0.537670i
$693$	9.37994	−	17.8837i	0.356314	−	0.679346i
$694$	−9.88543	+	13.4152i	−0.375246	+	0.509234i
$695$	1.91271	−	0.512510i	0.0725534	−	0.0194406i
$696$	9.74883	+	22.6867i	0.369529	+	0.859938i
$697$	−4.68320	−	1.25486i	−0.177389	−	0.0475312i
$698$	31.7265	−	25.3397i	1.20086	−	0.959122i
$699$	21.8363	−	11.3245i	0.825924	−	0.428330i
$700$	10.2574	−	6.46652i	0.387695	−	0.244411i
$701$	5.28075	−	12.7489i	0.199451	−	0.481518i	−0.792232	−	0.610220i	$-0.791081\pi$
$701$	5.28075	−	12.7489i	0.199451	−	0.481518i	0.991683	+	0.128702i	$0.0410811\pi$
$702$	−23.7890	+	24.5046i	−0.897860	+	0.924867i
$703$	−13.3663			−0.504121
$704$	37.0819	+	0.527697i	1.39758	+	0.0198883i
$705$	−7.59468	+	0.652641i	−0.286032	+	0.0245799i
$706$	1.63503	+	0.902060i	0.0615352	+	0.0339495i
$707$	1.83361	−	0.241399i	0.0689599	−	0.00907874i
$708$	−3.79528	+	2.87450i	−0.142635	+	0.108030i
$709$	1.93584	−	14.7042i	0.0727021	−	0.552227i	−0.915870	−	0.401476i	$-0.868497\pi$
$709$	1.93584	−	14.7042i	0.0727021	−	0.552227i	0.988572	−	0.150751i	$-0.0481693\pi$
$710$	2.34237	+	15.4625i	0.0879078	+	0.580296i
$711$	−10.2079	−	22.0684i	−0.382825	−	0.827630i
$712$	−21.8864	−	19.4710i	−0.820226	−	0.729708i
$713$	−48.5577	+	13.0110i	−1.81850	+	0.487266i
$714$	10.5586	+	0.271747i	0.395146	+	0.0101699i
$715$	11.9111	−	15.5228i	0.445449	−	0.580520i
$716$	32.8025	+	12.1156i	1.22589	+	0.452783i
$717$	3.12645	+	14.2062i	0.116759	+	0.530540i
$718$	−17.1975	−	16.5414i	−0.641805	−	0.617319i
$719$			16.3364i			0.609244i	0.952473	+	0.304622i	$0.0985301\pi$
$719$			16.3364i			0.609244i	−0.952473	+	0.304622i	$0.901470\pi$
$720$	4.04354	+	10.1200i	0.150694	+	0.377150i
$721$			10.4673i			0.389824i
$722$	33.2810	−	34.6011i	1.23859	−	1.28772i
$723$	30.7923	−	28.1287i	1.14518	−	1.04612i
$724$	−2.63766	−	5.72724i	−0.0980277	−	0.212851i
$725$	−12.8112	+	16.6959i	−0.475798	+	0.620072i
$726$	21.9142	+	13.4155i	0.813312	+	0.497896i
$727$	−6.97849	+	1.86988i	−0.258818	+	0.0693500i	−0.385895	−	0.922543i	$-0.626107\pi$
$727$	−6.97849	+	1.86988i	−0.258818	+	0.0693500i	0.127077	+	0.991893i	$0.459440\pi$
$728$	−8.32045	−	17.1793i	−0.308376	−	0.636705i
$729$	7.22928	−	26.0142i	0.267751	−	0.963488i
$730$	18.6514	−	2.82547i	0.690321	−	0.104575i
$731$	−2.64077	+	20.0587i	−0.0976725	+	0.741896i
$732$	4.43289	−	1.80360i	0.163844	−	0.0666630i
$733$	2.92779	−	0.385450i	0.108140	−	0.0142369i	−0.0762618	−	0.997088i	$-0.524298\pi$
$733$	2.92779	−	0.385450i	0.108140	−	0.0142369i	0.184402	+	0.982851i	$0.440965\pi$
$734$	10.8277	−	19.6257i	0.399656	−	0.724398i
$735$	3.26244	−	6.96823i	0.120337	−	0.257027i
$736$	31.4160	+	5.21746i	1.15801	+	0.192318i
$737$	27.1277			0.999263
$738$	−4.53888	−	5.23294i	−0.167078	−	0.192627i
$739$	5.13318	−	12.3926i	0.188827	−	0.455869i	−0.800907	−	0.598788i	$-0.795649\pi$
$739$	5.13318	−	12.3926i	0.188827	−	0.455869i	0.989734	+	0.142920i	$0.0456490\pi$
$740$	3.25388	+	0.737578i	0.119615	+	0.0271139i
$741$	−49.3527	−	31.5483i	−1.81301	−	1.15895i
$742$	−2.70979	−	3.39277i	−0.0994793	−	0.124553i
$743$	−4.40792	−	1.18110i	−0.161711	−	0.0433303i	0.177055	−	0.984201i	$-0.443343\pi$
$743$	−4.40792	−	1.18110i	−0.161711	−	0.0433303i	−0.338766	+	0.940871i	$0.610010\pi$
$744$	−11.8773	−	42.1025i	−0.435442	−	1.54355i
$745$	2.62967	−	0.704619i	0.0963438	−	0.0258152i
$746$	−5.97250	−	4.40104i	−0.218669	−	0.161133i
$747$	28.1092	−	1.14037i	1.02846	−	0.0417239i
$748$	−2.52958	+	27.4149i	−0.0924906	+	1.00239i
$749$	−15.4477	+	11.8534i	−0.564445	+	0.433114i
$750$	−12.8377	+	15.8678i	−0.468766	+	0.579409i
$751$	36.8063	−	21.2501i	1.34308	−	0.775429i	0.355823	−	0.934553i	$-0.384201\pi$
$751$	36.8063	−	21.2501i	1.34308	−	0.775429i	0.987259	+	0.159125i	$0.0508672\pi$
$752$	−17.4894	−	8.35833i	−0.637773	−	0.304797i
$753$	−2.55760	−	29.7624i	−0.0932042	−	1.08460i
$754$	23.8765	+	22.9655i	0.869531	+	0.836356i
$755$	15.0529	+	6.23511i	0.547831	+	0.226919i
$756$	12.2798	+	8.77105i	0.446611	+	0.319000i
$757$	−5.84444	−	14.1097i	−0.212420	−	0.512827i	0.781374	−	0.624063i	$-0.214519\pi$
$757$	−5.84444	−	14.1097i	−0.212420	−	0.512827i	−0.993794	+	0.111236i	$0.964519\pi$
$758$	−2.92713	−	6.69543i	−0.106318	−	0.243189i
$759$	34.5821	+	29.1089i	1.25525	+	1.05658i
$760$	−15.6144	+	10.2733i	−0.566393	+	0.372651i
$761$	−35.7993	−	9.59240i	−1.29772	−	0.347724i	−0.457135	−	0.889397i	$-0.651125\pi$
$761$	−35.7993	−	9.59240i	−1.29772	−	0.347724i	−0.840589	+	0.541673i	$0.817791\pi$
$762$	−40.0875	−	11.8549i	−1.45222	−	0.429457i
$763$	0.211019	−	1.60285i	0.00763940	−	0.0580270i
$764$	−17.3189	+	32.8874i	−0.626574	+	1.18982i
$765$	−7.72335	+	2.40898i	−0.279238	+	0.0870969i
$766$	−18.8470	+	11.3756i	−0.680972	+	0.411017i
$767$	−3.19375	+	5.53174i	−0.115320	+	0.199740i
$768$	−4.18014	+	27.3957i	−0.150838	+	0.988559i
$769$	−10.8009	−	18.7078i	−0.389492	−	0.674619i	0.602890	−	0.797825i	$-0.294016\pi$
$769$	−10.8009	−	18.7078i	−0.389492	−	0.674619i	−0.992381	+	0.123205i	$0.960683\pi$
$770$	−7.56978	−	4.17631i	−0.272796	−	0.150504i
$771$	−11.2031	+	2.46554i	−0.403470	+	0.0887942i
$772$	13.8840	+	22.0234i	0.499698	+	0.792640i
$773$	44.3905	−	18.3871i	1.59661	−	0.661339i	0.605682	−	0.795706i	$-0.292900\pi$
$773$	44.3905	−	18.3871i	1.59661	−	0.661339i	0.990932	+	0.134367i	$0.0429002\pi$
$774$	−19.1773	+	21.6283i	−0.689316	+	0.777413i
$775$	26.3632	−	26.3632i	0.946992	−	0.946992i
$776$	20.7532	+	10.4185i	0.744996	+	0.374004i
$777$	4.34382	−	1.57343i	0.155834	−	0.0564467i
$778$	−21.4571	−	2.40144i	−0.769274	−	0.0860959i
$779$	7.23247	−	9.42554i	0.259130	−	0.337705i
$780$	10.2735	+	10.4034i	0.367849	+	0.372503i
$781$	−44.7827	+	34.3630i	−1.60245	+	1.22960i
$782$	−5.67378	+	22.9509i	−0.202894	+	0.820723i
$783$	−25.2664	−	6.89564i	−0.902949	−	0.246430i
$784$	16.1331	−	11.0699i	0.576182	−	0.395354i
$785$	−8.67024	−	5.00576i	−0.309454	−	0.178663i
$786$	6.37970	+	1.00751i	0.227556	+	0.0359367i
$787$	2.22532	+	16.9030i	0.0793242	+	0.602527i	0.984227	+	0.176909i	$0.0566098\pi$
$787$	2.22532	+	16.9030i	0.0793242	+	0.602527i	−0.904903	+	0.425618i	$0.860057\pi$
$788$	36.1314	−	16.6401i	1.28713	−	0.592781i
$789$	49.7881	+	2.25077i	1.77250	+	0.0801297i
$790$	−9.53783	+	4.16977i	−0.339341	+	0.148354i
$791$	−9.47064	−	9.47064i	−0.336737	−	0.336737i
$792$	−24.9325	+	30.4242i	−0.885938	+	1.08108i
$793$	4.54016	−	4.54016i	0.161226	−	0.161226i
$794$	18.2529	−	46.6097i	0.647771	−	1.65412i
$795$	2.80232	+	1.79136i	0.0993879	+	0.0635329i
$796$	−19.3398	+	20.9057i	−0.685481	+	0.740984i
$797$	−13.5344	+	1.78184i	−0.479415	+	0.0631162i	−0.366361	−	0.930473i	$-0.619397\pi$
$797$	−13.5344	+	1.78184i	−0.479415	+	0.0631162i	−0.113054	+	0.993589i	$0.536063\pi$
$798$	−10.5164	+	23.6487i	−0.372276	+	0.837155i
$799$	7.19509	−	12.4623i	0.254544	−	0.440883i
$800$	−22.1128	+	8.29871i	−0.781806	+	0.293404i
$801$	30.6154	−	5.30094i	1.08174	−	0.187300i
$802$	11.5277	+	19.0991i	0.407058	+	0.674413i
$803$	41.4500	+	54.0187i	1.46274	+	1.90628i
$804$	−2.77227	+	20.0812i	−0.0977704	+	0.708209i
$805$	−5.88987	−	4.51946i	−0.207591	−	0.159290i
$806$	−36.6274	−	45.8592i	−1.29014	−	1.61532i
$807$	−32.8563	+	39.0341i	−1.15660	+	1.37407i
$808$	−3.59291	−	0.261177i	−0.126398	−	0.00918816i
$809$	−11.4237	−	11.4237i	−0.401637	−	0.401637i	0.477173	−	0.878809i	$-0.341662\pi$
$809$	−11.4237	−	11.4237i	−0.401637	−	0.401637i	−0.878809	+	0.477173i	$0.841662\pi$
$810$	−11.0692	−	3.32924i	−0.388931	−	0.116977i
$811$	−20.4744	−	49.4296i	−0.718953	−	1.73571i	−0.676311	−	0.736616i	$-0.736423\pi$
$811$	−20.4744	−	49.4296i	−0.718953	−	1.73571i	−0.0426419	−	0.999090i	$-0.513577\pi$
$812$	8.45285	−	11.9509i	0.296637	−	0.419393i
$813$	−31.2978	−	9.92128i	−1.09766	−	0.347954i
$814$	3.34244	+	11.5695i	0.117152	+	0.405509i
$815$	2.06269	−	1.19089i	0.0722529	−	0.0417152i
$816$	−20.0352	−	4.67412i	−0.701374	−	0.163627i
$817$	−42.9343	−	24.7881i	−1.50208	−	0.867227i
$818$	−9.30821	+	37.6525i	−0.325454	+	1.31649i
$819$	19.7525	+	4.44302i	0.690208	+	0.155252i
$820$	−2.28078	+	1.89544i	−0.0796483	+	0.0661916i
$821$	−35.1012	−	4.62115i	−1.22504	−	0.161279i	−0.509882	−	0.860244i	$-0.670311\pi$
$821$	−35.1012	−	4.62115i	−1.22504	−	0.161279i	−0.715156	+	0.698965i	$0.753644\pi$
$822$	0.00335733		8.64075e-5i	0.000117100		3.01381e-6i
$823$	4.49431	−	16.7730i	0.156662	−	0.584670i	−0.842296	−	0.539016i	$-0.818796\pi$
$823$	4.49431	−	16.7730i	0.156662	−	0.584670i	0.998957	−	0.0456537i	$-0.0145371\pi$
$824$	4.11980	−	19.9681i	0.143520	−	0.695621i
$825$	−33.0059	−	5.87235i	−1.14912	−	0.204449i
$826$	2.62803	+	1.02917i	0.0914409	+	0.0358093i
$827$	−7.35316	+	3.04578i	−0.255694	+	0.105912i	−0.506849	−	0.862035i	$-0.669190\pi$
$827$	−7.35316	+	3.04578i	−0.255694	+	0.105912i	0.251154	+	0.967947i	$0.419190\pi$
$828$	−25.0817	+	22.6245i	−0.871651	+	0.786255i
$829$	−10.6878	+	25.8026i	−0.371203	+	0.896163i	0.622344	+	0.782743i	$0.286180\pi$
$829$	−10.6878	+	25.8026i	−0.371203	+	0.896163i	−0.993547	+	0.113419i	$0.963820\pi$
$830$	−0.234176	−	12.0415i	−0.00812836	−	0.417965i
$831$	11.2167	−	23.9576i	0.389102	−	0.831081i
$832$	9.11104	+	36.0469i	0.315868	+	1.24970i
$833$	7.26255	+	12.5791i	0.251633	+	0.435840i
$834$	−4.31952	+	3.14128i	−0.149573	+	0.108774i
$835$	−3.51525	−	4.58116i	−0.121650	−	0.158538i
$836$	−59.6923	−	31.4346i	−2.06450	−	1.08719i
$837$	42.7848	+	17.9545i	1.47886	+	0.620599i
$838$	−1.78641	−	11.7925i	−0.0617106	−	0.407364i
$839$	−2.13371	−	7.96313i	−0.0736640	−	0.274918i	0.919263	−	0.393644i	$-0.128786\pi$
$839$	−2.13371	−	7.96313i	−0.0736640	−	0.274918i	−0.992927	+	0.118726i	$0.962119\pi$
$840$	3.86507	−	5.17670i	0.133358	−	0.178613i
$841$	0.930377	−	3.47222i	0.0320820	−	0.119732i
$842$	21.5525	+	2.41213i	0.742749	+	0.0831274i
$843$	−35.9089	−	1.62334i	−1.23677	−	0.0559108i
$844$	7.48309	+	43.6484i	0.257579	+	1.50244i
$845$	7.21557	+	2.98879i	0.248223	+	0.102817i
$846$	18.4889	−	8.99263i	0.635663	−	0.309173i
$847$		−	15.2320i		−	0.523378i
$848$	3.83399	+	7.53879i	0.131660	+	0.258883i
$849$	−11.9529	+	8.34204i	−0.410222	+	0.286298i
$850$	−4.86657	−	16.8450i	−0.166922	−	0.577780i
$851$	1.34981	+	10.2528i	0.0462708	+	0.351461i
$852$	−20.8605	−	36.6618i	−0.714670	−	1.25601i
$853$	13.5663	+	1.78604i	0.464502	+	0.0611528i	0.359145	−	0.933282i	$-0.383068\pi$
$853$	13.5663	+	1.78604i	0.464502	+	0.0611528i	0.105356	+	0.994435i	$0.466402\pi$
$854$	−2.28394	−	1.68300i	−0.0781549	−	0.0575911i
$855$	1.78878	−	19.7438i	0.0611749	−	0.675224i
$856$	34.1342	−	16.5323i	1.16668	−	0.565061i
$857$	7.69456	+	28.7165i	0.262841	+	0.980936i	0.963559	+	0.267498i	$0.0861967\pi$
$857$	7.69456	+	28.7165i	0.262841	+	0.980936i	−0.700717	+	0.713439i	$0.747137\pi$
$858$	−14.9658	+	50.6071i	−0.510925	+	1.72770i
$859$	−5.17408	−	3.97021i	−0.176537	−	0.135462i	0.516713	−	0.856159i	$-0.327155\pi$
$859$	−5.17408	−	3.97021i	−0.176537	−	0.135462i	−0.693250	+	0.720697i	$0.743822\pi$
$860$	9.08401	+	8.40358i	0.309762	+	0.286560i
$861$	−1.24089	+	3.91451i	−0.0422893	+	0.133406i
$862$	41.8247	−	0.813383i	1.42455	−	0.0277039i
$863$	10.7733			0.366729			0.183364	−	0.983045i	$-0.441301\pi$
$863$	10.7733			0.366729			0.183364	+	0.983045i	$0.441301\pi$
$864$	−19.9734	−	21.5653i	−0.679510	−	0.733666i
$865$	−10.0485			−0.341659
$866$	35.1498	−	0.683575i	1.19444	−	0.0232288i
$867$	−4.28241	+	13.5093i	−0.145438	+	0.458801i
$868$	−17.6106	+	19.0365i	−0.597742	+	0.646141i
$869$	−29.8081	−	22.8725i	−1.01117	−	0.775898i
$870$	−3.17968	+	10.7521i	−0.107801	+	0.364532i
$871$	7.03915	+	26.2705i	0.238512	+	0.890141i
$872$	−1.03341	+	2.97463i	−0.0349957	+	0.100734i
$873$	−22.3545	+	10.3402i	−0.756587	+	0.349963i
$874$	−46.6379	−	34.3667i	−1.57755	−	1.16247i
$875$	11.9961	+	1.57932i	0.405543	+	0.0533908i
$876$	−44.2230	+	25.1628i	−1.49416	+	0.850173i
$877$	−3.17186	−	24.0927i	−0.107106	−	0.813552i	−0.957708	−	0.287742i	$-0.907096\pi$
$877$	−3.17186	−	24.0927i	−0.107106	−	0.813552i	0.850602	−	0.525810i	$-0.176238\pi$
$878$	−1.06147	−	3.67416i	−0.0358230	−	0.123997i
$879$	−5.54291	+	3.86845i	−0.186958	+	0.130480i
$880$	12.7968	+	10.9463i	0.431380	+	0.369001i
$881$		−	48.0709i		−	1.61955i	−0.586740	−	0.809776i	$-0.699589\pi$
$881$		−	48.0709i		−	1.61955i	0.586740	−	0.809776i	$-0.300411\pi$
$882$	−1.47029	+	20.7005i	−0.0495072	+	0.697022i
$883$	−46.9201	−	19.4350i	−1.57899	−	0.654038i	−0.590735	−	0.806866i	$-0.701162\pi$
$883$	−46.9201	−	19.4350i	−1.57899	−	0.654038i	−0.988253	+	0.152827i	$0.951162\pi$
$884$	−27.2049	+	4.66402i	−0.915001	+	0.156868i
$885$	−2.15966	−	0.0976319i	−0.0725961	−	0.00328186i
$886$	15.3358	+	1.71636i	0.515217	+	0.0576623i
$887$	−4.91413	+	18.3398i	−0.165000	+	0.615789i	0.833040	+	0.553213i	$0.186598\pi$
$887$	−4.91413	+	18.3398i	−0.165000	+	0.615789i	−0.998040	+	0.0625763i	$0.980068\pi$
$888$	−8.90580	+	1.29191i	−0.298859	+	0.0433535i
$889$	6.41397	+	23.9373i	0.215118	+	0.802830i
$890$	−1.99233	−	13.1517i	−0.0667829	−	0.440847i
$891$	−8.77856	−	40.7873i	−0.294093	−	1.36643i
$892$	−13.8043	+	26.2135i	−0.462202	+	0.877693i
$893$	21.4661	+	27.9752i	0.718337	+	0.936155i
$894$	−5.93865	+	4.31875i	−0.198618	+	0.144441i
$895$	7.93924	+	13.7512i	0.265380	+	0.459651i
$896$	15.1449	−	6.36598i	0.505957	−	0.212673i
$897$	−19.2156	+	41.0424i	−0.641589	+	1.37037i
$898$	−0.00879078	−	0.452027i	−0.000293352	−	0.0150843i
$899$	17.2239	−	41.5822i	0.574450	−	1.38685i
$900$	7.71995	−	23.8323i	0.257332	−	0.794410i
$901$	−5.80083	+	2.40278i	−0.193254	+	0.0800483i
$902$	−9.96702	−	3.90320i	−0.331865	−	0.129962i
$903$	16.8708	+	3.00164i	0.561427	+	0.0998882i
$904$	14.3392	+	21.7943i	0.476916	+	0.724866i
$905$	0.741043	−	2.76561i	0.0246331	−	0.0919320i
$906$	−43.9313	−	1.13066i	−1.45952	−	0.0375637i
$907$	−0.717482	−	0.0944582i	−0.0238236	−	0.00313643i	0.118605	−	0.992942i	$-0.462158\pi$
$907$	−0.717482	−	0.0944582i	−0.0238236	−	0.00313643i	−0.142429	+	0.989805i	$0.545491\pi$
$908$	18.4335	+	22.1811i	0.611739	+	0.736104i
$909$	2.59005	−	2.80909i	0.0859065	−	0.0931716i
$910$	2.08011	−	8.41423i	0.0689550	−	0.278929i
$911$	−46.1861	−	26.6656i	−1.53021	−	0.883469i	−0.999351	−	0.0360110i	$-0.988535\pi$
$911$	−46.1861	−	26.6656i	−1.53021	−	0.883469i	−0.530862	−	0.847458i	$-0.678132\pi$
$912$	29.3695	−	40.9745i	0.972520	−	1.35680i
$913$	37.6470	−	21.7355i	1.24593	−	0.719340i
$914$	6.75171	+	23.3702i	0.223327	+	0.773019i
$915$	2.07153	+	0.656666i	0.0684826	+	0.0217087i
$916$	−29.8162	−	21.0890i	−0.985157	−	0.696801i
$917$	−1.46523	−	3.53738i	−0.0483862	−	0.116815i
$918$	17.1132	−	13.5389i	0.564821	−	0.446852i
$919$	14.4428	+	14.4428i	0.476422	+	0.476422i	0.903986	−	0.427563i	$-0.140628\pi$
$919$	14.4428	+	14.4428i	0.476422	+	0.476422i	−0.427563	+	0.903986i	$0.640628\pi$
$920$	9.45705	+	10.9397i	0.311790	+	0.360673i
$921$	6.49884	−	7.72079i	0.214144	−	0.254409i
$922$	−12.5037	−	15.6552i	−0.411789	−	0.515578i
$923$	−44.8974	−	34.4510i	−1.47781	−	1.13397i
$924$	23.0993	+	3.18893i	0.759912	+	0.104908i
$925$	−4.66895	−	6.08469i	−0.153514	−	0.200063i
$926$	−13.7335	−	22.7535i	−0.451310	−	0.747728i
$927$	13.8494	+	16.6088i	0.454872	+	0.545506i
$928$	−20.8288	+	19.4712i	−0.683740	+	0.639175i
$929$	−10.1784	+	17.6295i	−0.333942	+	0.578404i	−0.983281	−	0.182095i	$-0.941712\pi$
$929$	−10.1784	+	17.6295i	−0.333942	+	0.578404i	0.649339	+	0.760499i	$0.275046\pi$
$930$	8.07130	−	18.1504i	0.264668	−	0.595174i
$931$	−35.2881	+	4.64577i	−1.15652	+	0.152259i
$932$	20.8500	+	19.2882i	0.682963	+	0.631806i
$933$	40.9860	+	26.2000i	1.34182	+	0.857749i
$934$	4.40964	−	11.2602i	0.144288	−	0.368446i
$935$	−8.83985	+	8.83985i	−0.289094	+	0.289094i
$936$	−35.9323	−	16.2501i	−1.17448	−	0.531150i
$937$	−5.27127	−	5.27127i	−0.172205	−	0.172205i	0.615742	−	0.787947i	$-0.288856\pi$
$937$	−5.27127	−	5.27127i	−0.172205	−	0.172205i	−0.787947	+	0.615742i	$0.788856\pi$
$938$	11.0110	−	4.81381i	0.359522	−	0.157177i
$939$	−24.7212	−	1.11757i	−0.806745	−	0.0364706i
$940$	−3.68197	−	7.99479i	−0.120092	−	0.260761i
$941$	3.03923	+	23.0852i	0.0990760	+	0.752557i	0.966804	+	0.255518i	$0.0822461\pi$
$941$	3.03923	+	23.0852i	0.0990760	+	0.752557i	−0.867728	+	0.497039i	$0.834421\pi$
$942$	26.6725	+	4.21225i	0.869038	+	0.137243i
$943$	−7.96034	−	4.59591i	−0.259224	−	0.149663i
$944$	−4.60832	−	2.99766i	−0.149988	−	0.0975654i
$945$	1.74285	+	6.62696i	0.0566948	+	0.215575i
$946$	−10.7195	+	43.3611i	−0.348520	+	1.40979i
$947$	10.6832	−	8.19752i	0.347158	−	0.266384i	−0.420433	−	0.907323i	$-0.638122\pi$
$947$	10.6832	−	8.19752i	0.347158	−	0.266384i	0.767591	+	0.640940i	$0.221455\pi$
$948$	19.9775	−	19.7279i	0.648838	−	0.640731i
$949$	−41.5561	+	54.1570i	−1.34897	+	1.75801i
$950$	42.6989	+	4.77879i	1.38533	+	0.155045i
$951$	55.4841	−	20.0977i	1.79920	−	0.651711i
$952$	3.83803	+	11.5764i	0.124391	+	0.375194i
$953$	18.6594	−	18.6594i	0.604437	−	0.604437i	−0.337050	−	0.941487i	$-0.609429\pi$
$953$	18.6594	−	18.6594i	0.604437	−	0.604437i	0.941487	+	0.337050i	$0.109429\pi$
$954$	−8.78870	−	1.79810i	−0.284545	−	0.0582157i
$955$	−15.5929	+	6.45879i	−0.504574	+	0.209002i
$956$	−14.2086	+	8.95743i	−0.459540	+	0.289704i
$957$	−39.5246	+	8.69843i	−1.27765	+	0.281180i
$958$	27.7464	+	15.3079i	0.896444	+	0.494576i
$959$	−0.000995461	−	0.00172419i	−3.21451e−5	−	5.56770e-5i
$960$	−9.41071	+	8.35413i	−0.303729	+	0.269628i
$961$	−24.3686	+	42.2076i	−0.786083	+	1.36154i
$962$	−10.3365	+	6.23887i	−0.333263	+	0.201149i
$963$	−8.82803	+	39.2471i	−0.284479	+	1.26472i
$964$	42.6106	+	22.4392i	1.37240	+	0.722719i
$965$	−1.54305	+	11.7206i	−0.0496725	+	0.377300i
$966$	19.2020	+	5.67853i	0.617815	+	0.182704i
$967$	−18.4246	−	4.93687i	−0.592496	−	0.158759i	−0.0499024	−	0.998754i	$-0.515891\pi$
$967$	−18.4246	−	4.93687i	−0.592496	−	0.158759i	−0.542594	+	0.839995i	$0.682558\pi$
$968$	−5.99511	+	29.0574i	−0.192690	+	0.933942i
$969$	28.6323	+	24.1007i	0.919802	+	0.774227i
$970$	4.22384	+	9.66149i	0.135619	+	0.310212i
$971$	8.21113	+	19.8234i	0.263508	+	0.636164i	0.999151	−	0.0412055i	$-0.0131198\pi$
$971$	8.21113	+	19.8234i	0.263508	+	0.636164i	−0.735643	+	0.677370i	$0.763120\pi$
$972$	31.0897	−	2.33010i	0.997203	−	0.0747379i
$973$	2.92517	+	1.21165i	0.0937768	+	0.0388436i
$974$	16.0786	+	15.4652i	0.515192	+	0.495536i
$975$	−2.87763	−	33.4866i	−0.0921580	−	1.07243i
$976$	3.69457	+	4.10952i	0.118260	+	0.131542i
$977$	12.9072	−	7.45199i	0.412938	−	0.238410i	−0.279113	−	0.960258i	$-0.590040\pi$
$977$	12.9072	−	7.45199i	0.412938	−	0.238410i	0.692052	+	0.721848i	$0.256707\pi$
$978$	−4.04062	+	4.99432i	−0.129205	+	0.159701i
$979$	38.0903	−	29.2277i	1.21737	−	0.934122i
$980$	8.84685	+	0.816300i	0.282602	+	0.0260758i
$981$	−1.78590	−	2.82249i	−0.0570195	−	0.0901152i
$982$	−1.38458	−	1.02027i	−0.0441836	−	0.0325582i
$983$	−20.6922	+	5.54447i	−0.659980	+	0.176841i	−0.573237	−	0.819390i	$-0.694313\pi$
$983$	−20.6922	+	5.54447i	−0.659980	+	0.176841i	−0.0867431	+	0.996231i	$0.527646\pi$
$984$	3.90788	−	6.97915i	0.124579	−	0.222487i
$985$	17.4474	+	4.67501i	0.555920	+	0.148958i
$986$	−13.2097	−	16.5392i	−0.420684	−	0.526715i
$987$	−10.2693	−	6.56454i	−0.326874	−	0.208951i
$988$	14.9522	−	65.9626i	0.475692	−	2.09855i
$989$	−14.6783	+	35.4365i	−0.466742	+	1.12681i
$990$	−17.5369	+	3.38891i	−0.557359	+	0.107707i
$991$	−41.0625			−1.30439			−0.652196	−	0.758050i	$-0.726152\pi$
$991$	−41.0625			−1.30439			−0.652196	+	0.758050i	$0.726152\pi$
$992$	41.0875	−	29.3838i	1.30453	−	0.932938i
$993$	−6.79356	+	14.5103i	−0.215587	+	0.460472i
$994$	−12.0793	+	21.8944i	−0.383133	+	0.694449i
$995$	−12.8213	+	1.68796i	−0.406462	+	0.0535118i
$996$	12.2423	+	30.0892i	0.387913	+	0.953413i
$997$	3.48506	−	26.4716i	0.110373	−	0.838366i	−0.843284	−	0.537469i	$-0.819381\pi$
$997$	3.48506	−	26.4716i	0.110373	−	0.838366i	0.953657	−	0.300897i	$-0.0972860\pi$
$998$	17.9659	−	2.72161i	0.568700	−	0.0861512i
$999$	4.81067	−	8.24395i	0.152203	−	0.260827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.205.24	yes	368
3.2	odd	2		864.2.bk.a.397.23		368
9.4	even	3	inner	288.2.bc.a.13.39	✓	368
9.5	odd	6		864.2.bk.a.685.8		368
32.5	even	8	inner	288.2.bc.a.133.39	yes	368
96.5	odd	8		864.2.bk.a.613.8		368
288.5	odd	24		864.2.bk.a.37.23		368
288.229	even	24	inner	288.2.bc.a.229.24	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.39	✓	368	9.4	even	3	inner
288.2.bc.a.133.39	yes	368	32.5	even	8	inner
288.2.bc.a.205.24	yes	368	1.1	even	1	trivial
288.2.bc.a.229.24	yes	368	288.229	even	24	inner
864.2.bk.a.37.23		368	288.5	odd	24
864.2.bk.a.397.23		368	3.2	odd	2
864.2.bk.a.613.8		368	96.5	odd	8
864.2.bk.a.685.8		368	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.0274977 - 1.41395i) q^{2} +(-0.523386 + 1.65108i) q^{3} +(-1.99849 + 0.0777604i) q^{4} +(-0.720492 - 0.552853i) q^{5} +(2.34893 + 0.694639i) q^{6} +(-0.375828 - 1.40261i) q^{7} +(0.164903 + 2.82362i) q^{8} +(-2.45213 - 1.72831i) q^{9} +O(q^{10})\)	\(q+(-0.0274977 - 1.41395i) q^{2} +(-0.523386 + 1.65108i) q^{3} +(-1.99849 + 0.0777604i) q^{4} +(-0.720492 - 0.552853i) q^{5} +(2.34893 + 0.694639i) q^{6} +(-0.375828 - 1.40261i) q^{7} +(0.164903 + 2.82362i) q^{8} +(-2.45213 - 1.72831i) q^{9} +(-0.761892 + 1.03394i) q^{10} +(-4.59604 - 0.605081i) q^{11} +(0.917592 - 3.34036i) q^{12} +(-0.606629 - 4.60781i) q^{13} +(-1.97288 + 0.569969i) q^{14} +(1.28990 - 0.900234i) q^{15} +(3.98791 - 0.310807i) q^{16} +2.96949i q^{17} +(-2.37630 + 3.51471i) q^{18} +(-6.72261 - 2.78460i) q^{19} +(1.48288 + 1.04884i) q^{20} +(2.51252 + 0.113584i) q^{21} +(-0.729171 + 6.51520i) q^{22} +(-1.45707 + 5.43786i) q^{23} +(-4.74833 - 1.20557i) q^{24} +(-1.08063 - 4.03298i) q^{25} +(-6.49851 + 0.984445i) q^{26} +(4.13698 - 3.14410i) q^{27} +(0.860154 + 2.77387i) q^{28} +(-3.06838 - 3.99879i) q^{29} +(-1.30835 - 1.79909i) q^{30} +(4.46478 + 7.73323i) q^{31} +(-0.549122 - 5.63014i) q^{32} +(3.40454 - 7.27175i) q^{33} +(4.19870 - 0.0816541i) q^{34} +(-0.504655 + 1.21834i) q^{35} +(5.03495 + 3.26332i) q^{36} +(1.69709 - 0.702958i) q^{37} +(-3.75241 + 9.58198i) q^{38} +(7.92536 + 1.41007i) q^{39} +(1.44223 - 2.12556i) q^{40} +(-0.422584 + 1.57711i) q^{41} +(0.0915129 - 3.55569i) q^{42} +(6.75491 + 0.889301i) q^{43} +(9.23219 + 0.851856i) q^{44} +(0.811244 + 2.60090i) q^{45} +(7.72891 + 1.91069i) q^{46} +(-4.19677 - 2.42300i) q^{47} +(-1.57405 + 6.74703i) q^{48} +(4.23612 - 2.44572i) q^{49} +(-5.67270 + 1.63885i) q^{50} +(-4.90287 - 1.55419i) q^{51} +(1.57065 + 9.16148i) q^{52} +(0.809156 + 1.95348i) q^{53} +(-4.55934 - 5.76302i) q^{54} +(2.97689 + 2.97689i) q^{55} +(3.89845 - 1.29249i) q^{56} +(8.11611 - 9.64215i) q^{57} +(-5.56970 + 4.44848i) q^{58} +(-1.09037 - 0.836667i) q^{59} +(-2.50785 + 1.89941i) q^{60} +(0.841022 + 1.09604i) q^{61} +(10.8116 - 6.52561i) q^{62} +(-1.50256 + 4.08893i) q^{63} +(-7.94561 + 0.931244i) q^{64} +(-2.11037 + 3.65526i) q^{65} +(-10.3755 - 4.61388i) q^{66} +(-5.80185 + 0.763828i) q^{67} +(-0.230909 - 5.93449i) q^{68} +(-8.21573 - 5.25184i) q^{69} +(1.73655 + 0.680053i) q^{70} +(8.61020 - 8.61020i) q^{71} +(4.47571 - 7.20889i) q^{72} +(-10.3860 - 10.3860i) q^{73} +(-1.04061 - 2.38026i) q^{74} +(7.22436 + 0.326592i) q^{75} +(13.6516 + 5.04223i) q^{76} +(0.878629 + 6.67385i) q^{77} +(1.77583 - 11.2448i) q^{78} +(7.01911 + 4.05249i) q^{79} +(-3.04508 - 1.98079i) q^{80} +(3.02592 + 8.47607i) q^{81} +(2.24156 + 0.554145i) q^{82} +(-7.43962 + 5.70862i) q^{83} +(-5.03008 - 0.0316211i) q^{84} +(1.64169 - 2.13949i) q^{85} +(1.07168 - 9.57553i) q^{86} +(8.20828 - 2.97323i) q^{87} +(0.950615 - 13.0772i) q^{88} +(-7.32348 + 7.32348i) q^{89} +(3.65522 - 1.21857i) q^{90} +(-6.23496 + 2.58260i) q^{91} +(2.48909 - 10.9808i) q^{92} +(-15.1050 + 3.32425i) q^{93} +(-3.31060 + 6.00063i) q^{94} +(3.30411 + 5.72289i) q^{95} +(9.58322 + 2.04009i) q^{96} +(4.10503 - 7.11012i) q^{97} +(-3.57460 - 5.92239i) q^{98} +(10.2243 + 9.42710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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