LMFDB - Embedded newform 570.2.bi.a.47.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			47.38
Character	$\chi$	$=$	570.47
Dual form			570.2.bi.a.473.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(1.50626 + 0.855093i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.97892 - 1.04110i) q^{5} +(0.743394 + 1.56441i) q^{6} +(-2.09813 + 0.562193i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(1.53763 + 2.57598i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(1.50626 + 0.855093i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.97892 - 1.04110i) q^{5} +(0.743394 + 1.56441i) q^{6} +(-2.09813 + 0.562193i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(1.53763 + 2.57598i) q^{9} +(2.21818 + 0.282241i) q^{10} +(2.25218 - 1.30030i) q^{11} +(-0.288353 + 1.70788i) q^{12} +(-2.88829 + 0.252692i) q^{13} +(-2.04115 - 0.742919i) q^{14} +(3.87100 + 0.123992i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(1.92052 + 1.34476i) q^{17} +(-0.217968 + 2.99207i) q^{18} +(3.59309 + 2.46774i) q^{19} +(1.65514 + 1.50350i) q^{20} +(-3.64106 - 0.947290i) q^{21} +(2.59070 + 0.226657i) q^{22} +(-5.73853 - 2.67592i) q^{23} +(-1.21580 + 1.23362i) q^{24} +(2.83222 - 4.12050i) q^{25} +(-2.51089 - 1.44966i) q^{26} +(0.113370 + 5.19492i) q^{27} +(-1.24589 - 1.77932i) q^{28} +(-0.986495 + 5.59469i) q^{29} +(3.09982 + 2.32188i) q^{30} +(4.45573 - 7.71755i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(4.50425 - 0.0327612i) q^{33} +(0.801875 + 2.20313i) q^{34} +(-3.56673 + 3.29690i) q^{35} +(-1.89473 + 2.32594i) q^{36} +(-8.53429 - 8.53429i) q^{37} +(1.52785 + 4.08236i) q^{38} +(-4.56659 - 2.08913i) q^{39} +(0.493443 + 2.18094i) q^{40} +(-3.23906 - 3.86016i) q^{41} +(-2.43924 - 2.86440i) q^{42} +(7.06928 - 3.29646i) q^{43} +(1.99217 + 1.67163i) q^{44} +(5.72470 + 3.49683i) q^{45} +(-3.16588 - 5.48347i) q^{46} +(1.86125 + 2.65814i) q^{47} +(-1.70350 + 0.313166i) q^{48} +(-1.97607 + 1.14089i) q^{49} +(4.68344 - 1.75082i) q^{50} +(1.74291 + 3.66779i) q^{51} +(-1.22531 - 2.62768i) q^{52} +(-7.30907 - 3.40827i) q^{53} +(-2.88681 + 4.32045i) q^{54} +(3.10314 - 4.91793i) q^{55} -2.17215i q^{56} +(3.30197 + 6.78948i) q^{57} +(-4.01707 + 4.01707i) q^{58} +(-0.302793 - 1.71723i) q^{59} +(1.20745 + 3.67996i) q^{60} +(-6.68929 + 2.43470i) q^{61} +(8.07653 - 3.76615i) q^{62} +(-4.67436 - 4.54031i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-5.45260 + 3.50705i) q^{65} +(3.70845 + 2.55669i) q^{66} +(-1.51120 + 1.05816i) q^{67} +(-0.606808 + 2.26464i) q^{68} +(-6.35555 - 8.93761i) q^{69} +(-4.81272 + 0.654868i) q^{70} +(-4.61510 + 12.6799i) q^{71} +(-2.88618 + 0.818526i) q^{72} +(1.25518 - 14.3468i) q^{73} +(-2.09581 - 11.8859i) q^{74} +(7.78947 - 3.78472i) q^{75} +(-1.09001 + 4.22041i) q^{76} +(-3.99436 + 3.99436i) q^{77} +(-2.54245 - 4.33060i) q^{78} +(7.19735 + 8.57747i) q^{79} +(-0.846732 + 2.06955i) q^{80} +(-4.27137 + 7.92183i) q^{81} +(-0.439185 - 5.01990i) q^{82} +(6.93717 - 1.85881i) q^{83} +(-0.355155 - 3.74547i) q^{84} +(5.20059 + 0.661722i) q^{85} +(7.68159 + 1.35447i) q^{86} +(-6.26990 + 7.58351i) q^{87} +(0.673084 + 2.51198i) q^{88} +(0.349266 + 0.293069i) q^{89} +(2.68370 + 6.14799i) q^{90} +(5.91796 - 2.15396i) q^{91} +(0.551850 - 6.30767i) q^{92} +(13.3107 - 7.81457i) q^{93} +3.24499i q^{94} +(9.67958 + 1.14269i) q^{95} +(-1.57505 - 0.720560i) q^{96} +(-1.74306 + 2.48935i) q^{97} +(-2.27309 - 0.198869i) q^{98} +(6.81258 + 3.80220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	1.50626	+	0.855093i	0.869639	+	0.493688i
$3$	1.50626	+	0.855093i	0.869639	+	0.493688i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	1.97892	−	1.04110i	0.884999	−	0.465594i
$5$	1.97892	−	1.04110i	0.884999	−	0.465594i
$6$	0.743394	+	1.56441i	0.303489	+	0.638666i
$7$	−2.09813	+	0.562193i	−0.793020	+	0.212489i	−0.632517	−	0.774546i	$-0.717978\pi$
$7$	−2.09813	+	0.562193i	−0.793020	+	0.212489i	−0.160503	+	0.987035i	$0.551312\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	1.53763	+	2.57598i	0.512544	+	0.858661i
$10$	2.21818	+	0.282241i	0.701451	+	0.0892526i
$11$	2.25218	−	1.30030i	0.679059	−	0.392055i	−0.120442	−	0.992720i	$-0.538431\pi$
$11$	2.25218	−	1.30030i	0.679059	−	0.392055i	0.799500	+	0.600666i	$0.205098\pi$
$12$	−0.288353	+	1.70788i	−0.0832404	+	0.493022i
$13$	−2.88829	+	0.252692i	−0.801067	+	0.0700843i	−0.480334	−	0.877085i	$-0.659485\pi$
$13$	−2.88829	+	0.252692i	−0.801067	+	0.0700843i	−0.320733	+	0.947170i	$0.603929\pi$
$14$	−2.04115	−	0.742919i	−0.545521	−	0.198553i
$15$	3.87100	+	0.123992i	0.999487	+	0.0320146i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	1.92052	+	1.34476i	0.465795	+	0.326153i	0.782803	−	0.622270i	$-0.213789\pi$
$17$	1.92052	+	1.34476i	0.465795	+	0.326153i	−0.317008	+	0.948423i	$0.602678\pi$
$18$	−0.217968	+	2.99207i	−0.0513754	+	0.705238i
$19$	3.59309	+	2.46774i	0.824310	+	0.566138i
$19$	3.59309	+	2.46774i	0.824310	+	0.566138i
$20$	1.65514	+	1.50350i	0.370101	+	0.336192i
$21$	−3.64106	−	0.947290i	−0.794545	−	0.206716i
$22$	2.59070	+	0.226657i	0.552339	+	0.0483234i
$23$	−5.73853	−	2.67592i	−1.19657	−	0.557968i	−0.280834	−	0.959756i	$-0.590611\pi$
$23$	−5.73853	−	2.67592i	−1.19657	−	0.557968i	−0.915733	+	0.401788i	$0.868389\pi$
$24$	−1.21580	+	1.23362i	−0.248175	+	0.251812i
$25$	2.83222	−	4.12050i	0.566445	−	0.824100i
$26$	−2.51089	−	1.44966i	−0.492425	−	0.284302i
$27$	0.113370	+	5.19492i	0.0218181	+	0.999762i
$28$	−1.24589	−	1.77932i	−0.235452	−	0.336260i
$29$	−0.986495	+	5.59469i	−0.183188	+	1.03891i	0.745075	+	0.666981i	$0.232414\pi$
$29$	−0.986495	+	5.59469i	−0.183188	+	1.03891i	−0.928262	+	0.371927i	$0.878697\pi$
$30$	3.09982	+	2.32188i	0.565947	+	0.423916i
$31$	4.45573	−	7.71755i	0.800273	−	1.38611i	−0.119163	−	0.992875i	$-0.538021\pi$
$31$	4.45573	−	7.71755i	0.800273	−	1.38611i	0.919436	−	0.393239i	$-0.128645\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	4.50425	−	0.0327612i	0.784089	−	0.00570299i
$34$	0.801875	+	2.20313i	0.137520	+	0.377834i
$35$	−3.56673	+	3.29690i	−0.602888	+	0.557278i
$36$	−1.89473	+	2.32594i	−0.315788	+	0.387657i
$37$	−8.53429	−	8.53429i	−1.40303	−	1.40303i	−0.790273	−	0.612755i	$-0.790061\pi$
$37$	−8.53429	−	8.53429i	−1.40303	−	1.40303i	−0.612755	−	0.790273i	$-0.709939\pi$
$38$	1.52785	+	4.08236i	0.247849	+	0.662247i
$39$	−4.56659	−	2.08913i	−0.731239	−	0.334529i
$40$	0.493443	+	2.18094i	0.0780203	+	0.344837i
$41$	−3.23906	−	3.86016i	−0.505856	−	0.602856i	0.451320	−	0.892362i	$-0.350953\pi$
$41$	−3.23906	−	3.86016i	−0.505856	−	0.602856i	−0.957176	+	0.289507i	$0.906509\pi$
$42$	−2.43924	−	2.86440i	−0.376383	−	0.441987i
$43$	7.06928	−	3.29646i	1.07806	−	0.502705i	0.199281	−	0.979942i	$-0.436139\pi$
$43$	7.06928	−	3.29646i	1.07806	−	0.502705i	0.878775	+	0.477237i	$0.158362\pi$
$44$	1.99217	+	1.67163i	0.300331	+	0.252008i
$45$	5.72470	+	3.49683i	0.853388	+	0.521276i
$46$	−3.16588	−	5.48347i	−0.466784	−	0.808494i
$47$	1.86125	+	2.65814i	0.271491	+	0.387730i	0.931627	−	0.363417i	$-0.118390\pi$
$47$	1.86125	+	2.65814i	0.271491	+	0.387730i	−0.660135	+	0.751147i	$0.729501\pi$
$48$	−1.70350	+	0.313166i	−0.245880	+	0.0452016i
$49$	−1.97607	+	1.14089i	−0.282296	+	0.162984i
$50$	4.68344	−	1.75082i	0.662339	−	0.247603i
$51$	1.74291	+	3.66779i	0.244056	+	0.513593i
$52$	−1.22531	−	2.62768i	−0.169919	−	0.364393i
$53$	−7.30907	−	3.40827i	−1.00398	−	0.468162i	−0.150119	−	0.988668i	$-0.547966\pi$
$53$	−7.30907	−	3.40827i	−1.00398	−	0.468162i	−0.853858	+	0.520506i	$0.825744\pi$
$54$	−2.88681	+	4.32045i	−0.392846	+	0.587939i
$55$	3.10314	−	4.91793i	0.418428	−	0.663133i
$56$		−	2.17215i		−	0.290266i
$57$	3.30197	+	6.78948i	0.437357	+	0.899288i
$58$	−4.01707	+	4.01707i	−0.527467	+	0.527467i
$59$	−0.302793	−	1.71723i	−0.0394203	−	0.223564i	0.958733	−	0.284308i	$-0.0917638\pi$
$59$	−0.302793	−	1.71723i	−0.0394203	−	0.223564i	−0.998153	+	0.0607440i	$0.980653\pi$
$60$	1.20745	+	3.67996i	0.155880	+	0.475080i
$61$	−6.68929	+	2.43470i	−0.856476	+	0.311732i	−0.732678	−	0.680576i	$-0.761730\pi$
$61$	−6.68929	+	2.43470i	−0.856476	+	0.311732i	−0.123798	+	0.992307i	$0.539508\pi$
$62$	8.07653	−	3.76615i	1.02572	−	0.478301i
$63$	−4.67436	−	4.54031i	−0.588914	−	0.572025i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−5.45260	+	3.50705i	−0.676312	+	0.434996i
$66$	3.70845	+	2.55669i	0.456479	+	0.314707i
$67$	−1.51120	+	1.05816i	−0.184623	+	0.129274i	−0.662234	−	0.749297i	$-0.730392\pi$
$67$	−1.51120	+	1.05816i	−0.184623	+	0.129274i	0.477611	+	0.878571i	$0.341503\pi$
$68$	−0.606808	+	2.26464i	−0.0735863	+	0.274628i
$69$	−6.35555	−	8.93761i	−0.765119	−	1.07596i
$70$	−4.81272	+	0.654868i	−0.575230	+	0.0782717i
$71$	−4.61510	+	12.6799i	−0.547711	+	1.50482i	0.289081	+	0.957305i	$0.406650\pi$
$71$	−4.61510	+	12.6799i	−0.547711	+	1.50482i	−0.836792	+	0.547520i	$0.815572\pi$
$72$	−2.88618	+	0.818526i	−0.340139	+	0.0964642i
$73$	1.25518	−	14.3468i	0.146908	−	1.67917i	−0.462739	−	0.886495i	$-0.653133\pi$
$73$	1.25518	−	14.3468i	0.146908	−	1.67917i	0.609647	−	0.792673i	$-0.291311\pi$
$74$	−2.09581	−	11.8859i	−0.243633	−	1.38171i
$75$	7.78947	−	3.78472i	0.899451	−	0.437022i
$76$	−1.09001	+	4.22041i	−0.125033	+	0.484115i
$77$	−3.99436	+	3.99436i	−0.455200	+	0.455200i
$78$	−2.54245	−	4.33060i	−0.287876	−	0.490344i
$79$	7.19735	+	8.57747i	0.809765	+	0.965040i	0.999860	−	0.0167253i	$-0.00532409\pi$
$79$	7.19735	+	8.57747i	0.809765	+	0.965040i	−0.190095	+	0.981766i	$0.560880\pi$
$80$	−0.846732	+	2.06955i	−0.0946676	+	0.231383i
$81$	−4.27137	+	7.92183i	−0.474597	+	0.880203i
$82$	−0.439185	−	5.01990i	−0.0484998	−	0.554356i
$83$	6.93717	−	1.85881i	0.761454	−	0.204031i	0.142861	−	0.989743i	$-0.454370\pi$
$83$	6.93717	−	1.85881i	0.761454	−	0.204031i	0.618593	+	0.785712i	$0.287703\pi$
$84$	−0.355155	−	3.74547i	−0.0387505	−	0.408664i
$85$	5.20059	+	0.661722i	0.564083	+	0.0717739i
$86$	7.68159	+	1.35447i	0.828327	+	0.146056i
$87$	−6.26990	+	7.58351i	−0.672203	+	0.813038i
$88$	0.673084	+	2.51198i	0.0717510	+	0.267778i
$89$	0.349266	+	0.293069i	0.0370221	+	0.0310652i	0.661111	−	0.750288i	$-0.270085\pi$
$89$	0.349266	+	0.293069i	0.0370221	+	0.0310652i	−0.624089	+	0.781353i	$0.714530\pi$
$90$	2.68370	+	6.14799i	0.282887	+	0.648055i
$91$	5.91796	−	2.15396i	0.620370	−	0.225796i
$92$	0.551850	−	6.30767i	0.0575343	−	0.657621i
$93$	13.3107	−	7.81457i	1.38026	−	0.810333i
$94$			3.24499i			0.334695i
$95$	9.67958	+	1.14269i	0.993104	+	0.117238i
$96$	−1.57505	−	0.720560i	−0.160753	−	0.0735418i
$97$	−1.74306	+	2.48935i	−0.176981	+	0.252755i	−0.897835	−	0.440331i	$-0.854861\pi$
$97$	−1.74306	+	2.48935i	−0.176981	+	0.252755i	0.720854	+	0.693087i	$0.243750\pi$
$98$	−2.27309	−	0.198869i	−0.229617	−	0.0200888i
$99$	6.81258	+	3.80220i	0.684690	+	0.382136i
$100$	4.84068	+	1.25213i	0.484068	+	0.125213i
$101$	−1.75004	+	2.08562i	−0.174136	+	0.207527i	−0.846052	−	0.533100i	$-0.821027\pi$
$101$	−1.75004	+	2.08562i	−0.174136	+	0.207527i	0.671917	+	0.740627i	$0.265471\pi$
$102$	−0.676052	+	4.00417i	−0.0669391	+	0.396472i
$103$	0.0720466	+	0.0193048i	0.00709897	+	0.00190216i	0.262367	−	0.964968i	$-0.415497\pi$
$103$	0.0720466	+	0.0193048i	0.00709897	+	0.00190216i	−0.255268	+	0.966870i	$0.582164\pi$
$104$	0.503462	−	2.85527i	0.0493685	−	0.279983i
$105$	−8.19158	+	1.91610i	−0.799417	+	0.186992i
$106$	−4.03233	−	6.98420i	−0.391655	−	0.678366i
$107$	−3.00016	−	11.1967i	−0.290036	−	1.08243i	−0.945080	−	0.326839i	$-0.894016\pi$
$107$	−3.00016	−	11.1967i	−0.290036	−	1.08243i	0.655044	−	0.755591i	$-0.272650\pi$
$108$	−4.84285	+	1.88330i	−0.466003	+	0.181221i
$109$	6.96202	−	19.1280i	0.666841	−	1.83213i	0.124022	−	0.992279i	$-0.460421\pi$
$109$	6.96202	−	19.1280i	0.666841	−	1.83213i	0.542819	−	0.839850i	$-0.317357\pi$
$110$	5.36275	−	2.24864i	0.511318	−	0.214400i
$111$	−5.55724	−	20.1525i	−0.527470	−	1.91279i
$112$	1.24589	−	1.77932i	0.117726	−	0.168130i
$113$	−2.83693	−	2.83693i	−0.266876	−	0.266876i	0.560964	−	0.827840i	$-0.310430\pi$
$113$	−2.83693	−	2.83693i	−0.266876	−	0.266876i	−0.827840	+	0.560964i	$0.810430\pi$
$114$	−1.18947	+	7.45555i	−0.111404	+	0.698276i
$115$	−14.1420	+	0.678956i	−1.31875	+	0.0633130i
$116$	−5.59469	+	0.986495i	−0.519454	+	0.0915938i
$117$	−5.09206	−	7.05163i	−0.470761	−	0.651924i
$118$	0.736927	−	1.58034i	0.0678396	−	0.145482i
$119$	−4.78553	−	1.74179i	−0.438689	−	0.159670i
$120$	−1.12166	+	3.70701i	−0.102393	+	0.338402i
$121$	−2.11845	+	3.66926i	−0.192586	+	0.333569i
$122$	−6.87603	−	1.84243i	−0.622527	−	0.166806i
$123$	−1.57807	−	8.58409i	−0.142289	−	0.774002i
$124$	8.77608	+	1.54746i	0.788115	+	0.138966i
$125$	1.31489	−	11.1028i	0.117607	−	0.993060i
$126$	−1.22480	−	6.40031i	−0.109114	−	0.570185i
$127$	0.310136	+	3.54487i	0.0275201	+	0.314556i	0.997461	+	0.0712153i	$0.0226877\pi$
$127$	0.310136	+	3.54487i	0.0275201	+	0.314556i	−0.969941	+	0.243341i	$0.921757\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	13.4669	+	1.07957i	1.18570	+	0.0950506i
$130$	−6.47807	−	0.254676i	−0.568165	−	0.0223366i
$131$	9.36795	−	1.65182i	0.818482	−	0.144320i	0.251296	−	0.967910i	$-0.419143\pi$
$131$	9.36795	−	1.65182i	0.818482	−	0.144320i	0.567186	+	0.823590i	$0.308032\pi$
$132$	1.57133	+	4.22140i	0.136767	+	0.367426i
$133$	−8.92612	−	3.15764i	−0.773993	−	0.273802i
$134$	−1.84484			−0.159370
$135$	5.63277	+	10.1623i	0.484792	+	0.874630i
$136$	−1.79601	+	1.50703i	−0.154007	+	0.129227i
$137$	−0.542028	+	1.16238i	−0.0463086	+	0.0993090i	−0.928101	−	0.372329i	$-0.878559\pi$
$137$	−0.542028	+	1.16238i	−0.0463086	+	0.0993090i	0.881792	+	0.471638i	$0.156337\pi$
$138$	−0.0797648	−	10.9667i	−0.00679003	−	0.933544i
$139$	−6.74939	+	8.04362i	−0.572476	+	0.682251i	−0.972137	−	0.234412i	$-0.924683\pi$
$139$	−6.74939	+	8.04362i	−0.572476	+	0.682251i	0.399661	+	0.916663i	$0.369128\pi$
$140$	−4.31797	−	2.22403i	−0.364935	−	0.187965i
$141$	0.530568	+	5.59539i	0.0446819	+	0.471217i
$142$	−11.0533	+	7.73964i	−0.927576	+	0.649496i
$143$	−6.17638	+	4.32475i	−0.516495	+	0.361653i
$144$	−2.83370	−	0.984946i	−0.236142	−	0.0820788i
$145$	3.87244	+	12.0985i	0.321588	+	1.00472i
$146$	9.25718	−	11.0323i	0.766130	−	0.913038i
$147$	−3.95204	+	0.0287447i	−0.325959	+	0.00237083i
$148$	5.10071	−	10.9385i	0.419276	−	0.899139i
$149$	8.91219	−	7.47821i	0.730115	−	0.612639i	−0.200048	−	0.979786i	$-0.564110\pi$
$149$	8.91219	−	7.47821i	0.730115	−	0.612639i	0.930163	+	0.367147i	$0.119665\pi$
$150$	8.55159	+	1.36759i	0.698234	+	0.111663i
$151$	8.65440			0.704285			0.352143	−	0.935946i	$-0.385453\pi$
$151$	8.65440			0.704285			0.352143	+	0.935946i	$0.385453\pi$
$152$	−3.31361	+	2.83196i	−0.268769	+	0.229702i
$153$	−0.511031	+	7.01499i	−0.0413144	+	0.567128i
$154$	−5.56306	+	0.980918i	−0.448284	+	0.0790446i
$155$	0.782782	−	19.9113i	0.0628746	−	1.59931i
$156$	0.401279	−	5.00571i	0.0321281	−	0.400778i
$157$	4.23003	+	9.07132i	0.337593	+	0.723970i	0.999676	−	0.0254602i	$-0.00810512\pi$
$157$	4.23003	+	9.07132i	0.337593	+	0.723970i	−0.662083	+	0.749431i	$0.730327\pi$
$158$	0.975890	+	11.1545i	0.0776377	+	0.887403i
$159$	−8.09496	−	11.3837i	−0.641972	−	0.902784i
$160$	−1.88065	+	1.20961i	−0.148678	+	0.0956282i
$161$	13.5446	+	2.38828i	1.06746	+	0.188223i
$162$	−8.04268	+	4.03923i	−0.631892	+	0.317352i
$163$	−1.44712	−	0.387755i	−0.113347	−	0.0303714i	0.201699	−	0.979447i	$-0.435354\pi$
$163$	−1.44712	−	0.387755i	−0.113347	−	0.0303714i	−0.315047	+	0.949076i	$0.602020\pi$
$164$	2.51954	−	4.36397i	0.196743	−	0.340769i
$165$	8.87942	−	4.75420i	0.691262	−	0.370114i
$166$	6.74877	+	2.45635i	0.523806	+	0.190650i
$167$	−7.77903	+	16.6822i	−0.601960	+	1.29091i	0.335247	+	0.942130i	$0.391180\pi$
$167$	−7.77903	+	16.6822i	−0.601960	+	1.29091i	−0.937206	+	0.348776i	$0.886597\pi$
$168$	1.85739	−	3.27182i	0.143301	−	0.252426i
$169$	−4.52414	+	0.797729i	−0.348011	+	0.0613638i
$170$	3.88053	+	3.52499i	0.297623	+	0.270354i
$171$	−0.832005	+	13.0502i	−0.0636250	+	0.997974i
$172$	5.51550	+	5.51550i	0.420553	+	0.420553i
$173$	−6.94584	+	9.91968i	−0.528082	+	0.754179i	−0.991237	−	0.132098i	$-0.957829\pi$
$173$	−6.94584	+	9.91968i	−0.528082	+	0.754179i	0.463154	+	0.886278i	$0.346718\pi$
$174$	−9.48572	+	2.61578i	−0.719111	+	0.198302i
$175$	−3.62587	+	10.2376i	−0.274090	+	0.773891i
$176$	−0.889456	+	2.44376i	−0.0670453	+	0.184205i
$177$	1.01230	−	2.84550i	0.0760893	−	0.213881i
$178$	0.118004	+	0.440398i	0.00884480	+	0.0330093i
$179$	6.75938	+	11.7076i	0.505220	+	0.875066i	0.999982	+	0.00603755i	$0.00192183\pi$
$179$	6.75938	+	11.7076i	0.505220	+	0.875066i	−0.494762	+	0.869028i	$0.664745\pi$
$180$	−1.32798	+	6.57544i	−0.0989817	+	0.490105i
$181$	2.66125	−	15.0927i	0.197809	−	1.12183i	−0.710553	−	0.703644i	$-0.751555\pi$
$181$	2.66125	−	15.0927i	0.197809	−	1.12183i	0.908362	−	0.418186i	$-0.137334\pi$
$182$	6.08317	+	1.62998i	0.450914	+	0.120822i
$183$	−12.1577	−	2.05267i	−0.898723	−	0.151738i
$184$	4.06998	−	4.85042i	0.300043	−	0.357577i
$185$	−25.7737	−	8.00360i	−1.89492	−	0.588437i
$186$	15.3857	+	1.23339i	1.12814	+	0.0904363i
$187$	6.07396	+	0.531403i	0.444172	+	0.0388600i
$188$	−1.86125	+	2.65814i	−0.135746	+	0.193865i
$189$	−3.15841	−	10.8359i	−0.229741	−	0.788195i
$190$	7.27363	+	6.48802i	0.527684	+	0.470690i
$191$		−	1.19747i		−	0.0866457i	−0.999061	−	0.0433229i	$-0.986206\pi$
$191$		−	1.19747i		−	0.0866457i	0.999061	−	0.0433229i	$-0.0137944\pi$
$192$	−0.876912	−	1.49366i	−0.0632857	−	0.107796i
$193$	0.572119	−	6.53935i	0.0411821	−	0.470713i	−0.947402	−	0.320045i	$-0.896302\pi$
$193$	0.572119	−	6.53935i	0.0411821	−	0.470713i	0.988584	−	0.150668i	$-0.0481425\pi$
$194$	−2.85567	+	1.03938i	−0.205025	+	0.0746230i
$195$	−11.2119	+	0.620048i	−0.802900	+	0.0444025i
$196$	−1.74794	−	1.46669i	−0.124853	−	0.104764i
$197$	5.46802	+	20.4069i	0.389580	+	1.45393i	0.830818	+	0.556544i	$0.187873\pi$
$197$	5.46802	+	20.4069i	0.389580	+	1.45393i	−0.441238	+	0.897390i	$0.645461\pi$
$198$	3.39968	+	7.02211i	0.241605	+	0.499040i
$199$	−5.51687	−	0.972773i	−0.391080	−	0.0689580i	−0.0253495	−	0.999679i	$-0.508070\pi$
$199$	−5.51687	−	0.972773i	−0.391080	−	0.0689580i	−0.365731	+	0.930721i	$0.619181\pi$
$200$	3.24706	+	3.80218i	0.229602	+	0.268855i
$201$	−3.18108	+	0.301638i	−0.224376	+	0.0212759i
$202$	−2.62981	+	0.704656i	−0.185033	+	0.0495794i
$203$	−1.07550	−	12.2930i	−0.0754853	−	0.862800i
$204$	−2.85049	+	2.89225i	−0.199574	+	0.202498i
$205$	−10.4286	−	4.26675i	−0.728367	−	0.298003i
$206$	0.0479444	+	0.0571379i	0.00334044	+	0.00398098i
$207$	−1.93063	−	18.8969i	−0.134188	−	1.31343i
$208$	2.05013	−	2.05013i	0.142151	−	0.142151i
$209$	11.3011	+	0.885716i	0.781712	+	0.0612662i
$210$	−7.80918	−	3.12892i	−0.538885	−	0.215916i
$211$	−2.27631	−	12.9096i	−0.156707	−	0.888732i	−0.957208	−	0.289400i	$-0.906544\pi$
$211$	−2.27631	−	12.9096i	−0.156707	−	0.888732i	0.800501	−	0.599332i	$-0.204567\pi$
$212$	0.702882	−	8.03397i	0.0482741	−	0.551776i
$213$	−17.7940	+	15.1528i	−1.21923	+	1.03826i
$214$	3.96460	−	10.8927i	0.271015	−	0.744607i
$215$	10.5576	−	13.8832i	0.720021	−	0.946829i
$216$	−5.04725	−	1.23504i	−0.343422	−	0.0840336i
$217$	−5.00997	+	18.6974i	−0.340099	+	1.26927i
$218$	16.6743	−	11.6755i	1.12933	−	0.790764i
$219$	14.1585	−	20.5367i	0.956742	−	1.38774i
$220$	5.68268	+	1.23397i	0.383126	+	0.0831942i
$221$	−5.88684	−	3.39877i	−0.395991	−	0.228626i
$222$	7.00675	−	19.6954i	0.470262	−	1.32187i
$223$	6.33554	−	2.95431i	0.424259	−	0.197835i	−0.198749	−	0.980050i	$-0.563688\pi$
$223$	6.33554	−	2.95431i	0.424259	−	0.197835i	0.623008	+	0.782215i	$0.285910\pi$
$224$	2.04115	−	0.742919i	0.136380	−	0.0496383i
$225$	14.9693	+	0.959945i	0.997950	+	0.0639963i
$226$	−0.696680	−	3.95107i	−0.0463425	−	0.262821i
$227$	−1.54386	+	1.54386i	−0.102470	+	0.102470i	−0.756483	−	0.654013i	$-0.773084\pi$
$227$	−1.54386	+	1.54386i	−0.102470	+	0.102470i	0.654013	+	0.756483i	$0.273084\pi$
$228$	−5.25068	+	5.42498i	−0.347735	+	0.359278i
$229$			13.7017i			0.905435i	0.891654	+	0.452718i	$0.149545\pi$
$229$			13.7017i			0.905435i	−0.891654	+	0.452718i	$0.850455\pi$
$230$	−11.9739	−	7.55534i	−0.789533	−	0.498184i
$231$	−9.43210	+	2.60099i	−0.620586	+	0.171133i
$232$	−5.14873	−	2.40089i	−0.338031	−	0.157626i
$233$	9.31497	+	19.9760i	0.610244	+	1.30867i	0.932209	+	0.361920i	$0.117879\pi$
$233$	9.31497	+	19.9760i	0.610244	+	1.30867i	−0.321965	+	0.946752i	$0.604343\pi$
$234$	−0.126521	−	8.69704i	−0.00827092	−	0.568543i
$235$	6.45065	+	3.32249i	0.420794	+	0.216736i
$236$	1.51010	−	0.871859i	0.0982993	−	0.0567532i
$237$	3.50654	+	19.0743i	0.227774	+	1.23901i
$238$	−2.92103	−	4.17166i	−0.189342	−	0.270409i
$239$	10.8475	+	18.7884i	0.701667	+	1.21532i	0.967881	+	0.251409i	$0.0808939\pi$
$239$	10.8475	+	18.7884i	0.701667	+	1.21532i	−0.266214	+	0.963914i	$0.585773\pi$
$240$	−3.04506	+	2.39325i	−0.196558	+	0.154483i
$241$	−15.8632	−	13.3108i	−1.02184	−	0.857422i	−0.0319788	−	0.999489i	$-0.510181\pi$
$241$	−15.8632	−	13.3108i	−1.02184	−	0.857422i	−0.989857	+	0.142066i	$0.954625\pi$
$242$	−3.83993	+	1.79059i	−0.246840	+	0.115104i
$243$	−13.2077	+	8.27991i	−0.847274	+	0.531157i
$244$	−4.57574	−	5.45316i	−0.292932	−	0.349103i
$245$	−2.72271	+	4.31500i	−0.173947	+	0.275675i
$246$	3.63096	−	7.93682i	0.231501	−	0.506033i
$247$	−11.0014	−	6.21960i	−0.700005	−	0.395743i
$248$	6.30136	+	6.30136i	0.400136	+	0.400136i
$249$	12.0386	+	3.13208i	0.762918	+	0.198487i
$250$	7.44537	−	8.34065i	0.470886	−	0.527509i
$251$	−0.782708	−	2.15047i	−0.0494041	−	0.135737i	0.912537	−	0.408995i	$-0.134121\pi$
$251$	−0.782708	−	2.15047i	−0.0494041	−	0.135737i	−0.961941	+	0.273259i	$0.911899\pi$
$252$	2.66777	−	5.94534i	0.168054	−	0.374521i
$253$	−16.4037	+	1.43514i	−1.03129	+	0.0902264i
$254$	−1.77920	+	3.08167i	−0.111637	+	0.193361i
$255$	7.26760	+	5.44371i	0.455115	+	0.340898i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	3.28170	+	4.68676i	0.204707	+	0.292352i	0.908358	−	0.418194i	$-0.137337\pi$
$257$	3.28170	+	4.68676i	0.204707	+	0.292352i	−0.703651	+	0.710546i	$0.748448\pi$
$258$	10.4123	+	8.60865i	0.648239	+	0.535951i
$259$	22.7040	+	13.1082i	1.41076	+	0.814501i
$260$	−5.16045	−	3.92429i	−0.320038	−	0.243374i
$261$	−15.9287	+	6.06139i	−0.985961	+	0.375190i
$262$	8.62122	+	4.02014i	0.532621	+	0.248365i
$263$	−9.02087	−	0.789224i	−0.556250	−	0.0486656i	−0.194435	−	0.980915i	$-0.562287\pi$
$263$	−9.02087	−	0.789224i	−0.556250	−	0.0486656i	−0.361815	+	0.932250i	$0.617843\pi$
$264$	−1.13414	+	4.35925i	−0.0698015	+	0.268293i
$265$	−18.0124	+	0.864774i	−1.10649	+	0.0531227i
$266$	−5.50070	−	7.70640i	−0.337270	−	0.472510i
$267$	0.275484	+	0.740092i	0.0168593	+	0.0452929i
$268$	−1.51120	−	1.05816i	−0.0923114	−	0.0646371i
$269$	−4.39791	+	3.69028i	−0.268145	+	0.225001i	−0.766939	−	0.641720i	$-0.778221\pi$
$269$	−4.39791	+	3.69028i	−0.268145	+	0.225001i	0.498794	+	0.866721i	$0.333777\pi$
$270$	−1.21474	+	11.5553i	−0.0739270	+	0.703232i
$271$	24.1237	+	8.78030i	1.46541	+	0.533365i	0.946850	−	0.321676i	$-0.104246\pi$
$271$	24.1237	+	8.78030i	1.46541	+	0.533365i	0.518560	+	0.855041i	$0.326468\pi$
$272$	−2.33560	+	0.204339i	−0.141617	+	0.0123899i
$273$	10.7558	+	1.81598i	0.650971	+	0.109908i
$274$	−1.11072	+	0.641274i	−0.0671010	+	0.0387408i
$275$	1.02081	−	12.9629i	0.0615571	−	0.781689i
$276$	6.22488	−	9.02911i	0.374693	−	0.543489i
$277$	2.21816	−	8.27827i	0.133276	−	0.497393i	−0.866723	−	0.498790i	$-0.833778\pi$
$277$	2.21816	−	8.27827i	0.133276	−	0.497393i	0.999999	+	0.00139686i	$0.000444636\pi$
$278$	−10.1424	+	2.71765i	−0.608301	+	0.162994i
$279$	26.7316	−	0.388879i	1.60038	−	0.0232816i
$280$	−2.26142	−	4.29850i	−0.135146	−	0.256885i
$281$	3.98212	+	10.9408i	0.237553	+	0.652672i	0.999984	+	0.00560262i	$0.00178338\pi$
$281$	3.98212	+	10.9408i	0.237553	+	0.652672i	−0.762431	+	0.647069i	$0.775994\pi$
$282$	−2.77477	+	4.88780i	−0.165235	+	0.291064i
$283$	8.51244	+	5.96047i	0.506012	+	0.354313i	0.798538	−	0.601944i	$-0.205607\pi$
$283$	8.51244	+	5.96047i	0.506012	+	0.354313i	−0.292526	+	0.956257i	$0.594496\pi$
$284$	−13.4936			−0.800701
$285$	13.6028	+	9.99813i	0.805763	+	0.592238i
$286$	−7.53996			−0.445847
$287$	8.96613	+	6.27815i	0.529254	+	0.370588i
$288$	−1.75629	−	2.43217i	−0.103491	−	0.143317i
$289$	−3.93433	−	10.8095i	−0.231431	−	0.635851i
$290$	−3.76728	+	12.1316i	−0.221222	+	0.712393i
$291$	−4.75413	+	2.25913i	−0.278692	+	0.132432i
$292$	13.9109	−	3.72741i	0.814073	−	0.218130i
$293$	−5.89850	+	22.0135i	−0.344594	+	1.28604i	0.548491	+	0.836156i	$0.315202\pi$
$293$	−5.89850	+	22.0135i	−0.344594	+	1.28604i	−0.893086	+	0.449887i	$0.851464\pi$
$294$	−3.25381	−	2.24325i	−0.189766	−	0.130829i
$295$	−2.38701	−	3.08301i	−0.138977	−	0.179500i
$296$	10.4523	−	6.03465i	0.607529	−	0.350757i
$297$	7.01027	+	11.5525i	0.406777	+	0.670343i
$298$	11.5898	−	1.01397i	0.671377	−	0.0587379i
$299$	17.2507	+	6.27875i	0.997635	+	0.363109i
$300$	6.22063	+	6.02526i	0.359148	+	0.347868i
$301$	−12.9791	+	10.8907i	−0.748100	+	0.627731i
$302$	7.08927	+	4.96396i	0.407942	+	0.285644i
$303$	−4.41941	+	1.64503i	−0.253889	+	0.0945047i
$304$	−4.33870	+	0.419193i	−0.248841	+	0.0240424i
$305$	−10.7028	+	11.7823i	−0.612839	+	0.674652i
$306$	−4.44224	+	5.45323i	−0.253946	+	0.311740i
$307$	−8.32684	−	0.728504i	−0.475238	−	0.0415779i	−0.152979	−	0.988229i	$-0.548887\pi$
$307$	−8.32684	−	0.728504i	−0.475238	−	0.0415779i	−0.322259	+	0.946652i	$0.604442\pi$
$308$	−5.11963	−	2.38732i	−0.291718	−	0.136030i
$309$	0.0920135	+	0.0906846i	0.00523446	+	0.00515887i
$310$	12.0618	−	15.8614i	0.685067	−	0.900865i
$311$	23.7604	+	13.7181i	1.34733	+	0.777879i	0.987870	−	0.155282i	$-0.0496287\pi$
$311$	23.7604	+	13.7181i	1.34733	+	0.777879i	0.359457	+	0.933162i	$0.382962\pi$
$312$	3.19987	−	3.87028i	0.181157	−	0.219111i
$313$	8.25681	+	11.7919i	0.466702	+	0.666520i	0.981648	−	0.190703i	$-0.0610768\pi$
$313$	8.25681	+	11.7919i	0.466702	+	0.666520i	−0.514946	+	0.857223i	$0.672188\pi$
$314$	−1.73806	+	9.85704i	−0.0980845	+	0.556265i
$315$	−13.9771	−	4.11842i	−0.787520	−	0.232047i
$316$	−5.59854	+	9.69696i	−0.314943	+	0.545497i
$317$	−27.7630	+	2.42894i	−1.55932	+	0.136423i	−0.833914	−	0.551894i	$-0.813905\pi$
$317$	−27.7630	+	2.42894i	−1.55932	+	0.136423i	−0.725409	+	0.688318i	$0.758350\pi$
$318$	−0.101595	−	13.9680i	−0.00569717	−	0.783288i
$319$	5.05300	+	13.8830i	0.282914	+	0.777299i
$320$	−2.23434	−	0.0878399i	−0.124904	−	0.00491040i
$321$	5.05524	−	19.4306i	0.282156	−	1.08451i
$322$	9.72522	+	9.72522i	0.541966	+	0.541966i
$323$	3.58208	+	9.57121i	0.199312	+	0.532556i
$324$	−8.90498	−	1.30435i	−0.494721	−	0.0724638i
$325$	−7.13906	+	12.6169i	−0.396004	+	0.699858i
$326$	−0.963006	−	1.14767i	−0.0533360	−	0.0635634i
$327$	26.8428	−	22.8585i	1.48441	−	1.26408i
$328$	4.56696	−	2.12961i	0.252168	−	0.117588i
$329$	−5.39954	−	4.53075i	−0.297686	−	0.249788i
$330$	10.0005	+	1.19861i	0.550509	+	0.0659816i
$331$	12.1854	+	21.1057i	0.669769	+	1.16007i	0.977969	+	0.208752i	$0.0669401\pi$
$331$	12.1854	+	21.1057i	0.669769	+	1.16007i	−0.308200	+	0.951322i	$0.599727\pi$
$332$	4.11936	+	5.88306i	0.226079	+	0.322875i
$333$	8.86157	−	35.1068i	0.485611	−	1.92384i
$334$	−15.9407	+	9.20338i	−0.872237	+	0.503586i
$335$	−1.88890	+	3.66731i	−0.103202	+	0.200367i
$336$	3.39812	−	1.61476i	0.185383	−	0.0880925i
$337$	7.09199	+	15.2088i	0.386325	+	0.828477i	0.999264	+	0.0383470i	$0.0122092\pi$
$337$	7.09199	+	15.2088i	0.386325	+	0.828477i	−0.612939	+	0.790130i	$0.710013\pi$
$338$	−4.16352	−	1.94148i	−0.226466	−	0.105603i
$339$	−1.84731	−	6.69898i	−0.100332	−	0.363839i
$340$	1.15689	+	5.11328i	0.0627412	+	0.277306i
$341$		−	23.1751i		−	1.25500i
$342$	−8.16683	+	10.2129i	−0.441611	+	0.552249i
$343$	14.2563	−	14.2563i	0.769765	−	0.769765i
$344$	1.35447	+	7.68159i	0.0730282	+	0.414163i
$345$	−21.8821	−	11.0700i	−1.17809	−	0.595990i
$346$	−11.3794	+	4.14176i	−0.611760	+	0.222662i
$347$	−7.41555	+	3.45793i	−0.398087	+	0.185631i	−0.611344	−	0.791365i	$-0.709371\pi$
$347$	−7.41555	+	3.45793i	−0.398087	+	0.185631i	0.213256	+	0.976996i	$0.431593\pi$
$348$	−9.27060	−	3.29806i	−0.496956	−	0.176795i
$349$	−1.24138	−	0.716712i	−0.0664496	−	0.0383647i	0.466407	−	0.884570i	$-0.345548\pi$
$349$	−1.24138	−	0.716712i	−0.0664496	−	0.0383647i	−0.532857	+	0.846205i	$0.678882\pi$
$350$	−8.84219	+	6.30645i	−0.472635	+	0.337094i
$351$	−1.64016	−	14.9758i	−0.0875453	−	0.799347i
$352$	−2.13028	+	1.49164i	−0.113545	+	0.0795047i
$353$	−1.91569	+	7.14944i	−0.101962	+	0.380526i	−0.997983	−	0.0634854i	$-0.979778\pi$
$353$	−1.91569	+	7.14944i	−0.101962	+	0.380526i	0.896021	+	0.444011i	$0.146445\pi$
$354$	2.46134	−	1.75027i	0.130819	−	0.0930257i
$355$	4.06812	+	29.8972i	0.215913	+	1.58678i
$356$	−0.155939	+	0.428438i	−0.00826473	+	0.0227072i
$357$	−5.71886	−	6.71566i	−0.302674	−	0.355431i
$358$	−1.17824	+	13.4673i	−0.0622718	+	0.711770i
$359$	0.704206	+	3.99375i	0.0371666	+	0.210782i	0.997735	−	0.0672599i	$-0.0214257\pi$
$359$	0.704206	+	3.99375i	0.0371666	+	0.210782i	−0.960569	+	0.278042i	$0.910315\pi$
$360$	−4.85934	+	4.62459i	−0.256110	+	0.243737i
$361$	6.82053	+	17.7336i	0.358975	+	0.933347i
$362$	10.8368	−	10.8368i	0.569568	−	0.569568i
$363$	−6.32849	+	3.71539i	−0.332160	+	0.195007i
$364$	4.04812	+	4.82436i	0.212179	+	0.252865i
$365$	−12.4526	−	29.6979i	−0.651797	−	1.55446i
$366$	−8.78164	−	8.65482i	−0.459024	−	0.452395i
$367$	−0.0269063	−	0.307540i	−0.00140450	−	0.0160535i	0.995460	−	0.0951797i	$-0.0303426\pi$
$367$	−0.0269063	−	0.307540i	−0.00140450	−	0.0160535i	−0.996865	+	0.0791262i	$0.974787\pi$
$368$	6.11602	−	1.63878i	0.318820	−	0.0854274i
$369$	4.96322	−	14.2793i	0.258375	−	0.743349i
$370$	−16.5219	−	21.3393i	−0.858932	−	1.10938i
$371$	17.2515	+	3.04191i	0.895654	+	0.157928i
$372$	11.8958	+	9.83523i	0.616770	+	0.509933i
$373$	6.84410	+	25.5425i	0.354374	+	1.32254i	0.881270	+	0.472612i	$0.156689\pi$
$373$	6.84410	+	25.5425i	0.354374	+	1.32254i	−0.526896	+	0.849930i	$0.676644\pi$
$374$	4.67070	+	3.91918i	0.241516	+	0.202656i
$375$	11.4744	−	15.5993i	0.592538	−	0.805543i
$376$	−3.04929	+	1.10985i	−0.157255	+	0.0572362i
$377$	1.43555	−	16.4084i	0.0739344	−	0.845074i
$378$	3.62799	−	10.6878i	0.186604	−	0.549723i
$379$		−	26.2505i		−	1.34840i	−0.738549	−	0.674200i	$-0.764489\pi$
$379$		−	26.2505i		−	1.34840i	0.738549	−	0.674200i	$-0.235511\pi$
$380$	2.23683	+	9.48665i	0.114747	+	0.486655i
$381$	−2.56404	+	5.60468i	−0.131360	+	0.287137i
$382$	0.686839	−	0.980908i	0.0351418	−	0.0501876i
$383$	−19.0517	−	1.66681i	−0.973497	−	0.0851699i	−0.410705	−	0.911768i	$-0.634717\pi$
$383$	−19.0517	−	1.66681i	−0.973497	−	0.0851699i	−0.562792	+	0.826598i	$0.690273\pi$
$384$	0.138405	−	1.72651i	0.00706293	−	0.0881057i
$385$	−3.74598	+	12.0630i	−0.190913	+	0.614789i
$386$	4.21947	−	5.02857i	0.214766	−	0.255948i
$387$	19.3616	+	13.1416i	0.984204	+	0.668025i
$388$	−2.93539	−	0.786535i	−0.149022	−	0.0399303i
$389$	−6.21080	+	35.2232i	−0.314900	+	1.78589i	0.257880	+	0.966177i	$0.416976\pi$
$389$	−6.21080	+	35.2232i	−0.314900	+	1.78589i	−0.572780	+	0.819709i	$0.694135\pi$
$390$	−9.53989	−	5.92296i	−0.483071	−	0.299921i
$391$	−7.42250	−	12.8561i	−0.375372	−	0.650163i
$392$	−0.590566	−	2.20402i	−0.0298281	−	0.111320i
$393$	15.5230	+	5.52239i	0.783033	+	0.278568i
$394$	−7.22580	+	19.8527i	−0.364030	+	1.00017i
$395$	23.1729	+	9.48094i	1.16596	+	0.477038i
$396$	−1.24286	+	7.70216i	−0.0624562	+	0.387048i
$397$	−6.03261	+	8.61546i	−0.302768	+	0.432397i	−0.941490	−	0.337040i	$-0.890574\pi$
$397$	−6.03261	+	8.61546i	−0.302768	+	0.432397i	0.638722	+	0.769437i	$0.279463\pi$
$398$	−3.96119	−	3.96119i	−0.198557	−	0.198557i
$399$	−10.7450	−	12.3889i	−0.537922	−	0.620220i
$400$	0.478996	+	4.97700i	0.0239498	+	0.248850i
$401$	−22.0628	+	3.89027i	−1.10176	+	0.194271i	−0.694821	−	0.719182i	$-0.744517\pi$
$401$	−22.0628	+	3.89027i	−1.10176	+	0.194271i	−0.406943	+	0.913453i	$0.633405\pi$
$402$	−2.77880	−	1.57751i	−0.138594	−	0.0786789i
$403$	−10.9193	+	23.4164i	−0.543928	+	1.16646i
$404$	−2.55839	−	0.931178i	−0.127285	−	0.0463278i
$405$	−0.205272	+	20.1236i	−0.0102001	+	0.999948i
$406$	6.16999	−	10.6867i	0.306211	−	0.530373i
$407$	−30.3179	−	8.12365i	−1.50280	−	0.402675i
$408$	−3.99391	+	0.734225i	−0.197728	+	0.0363496i
$409$	−4.54384	−	0.801202i	−0.224678	−	0.0396169i	0.0601755	−	0.998188i	$-0.480834\pi$
$409$	−4.54384	−	0.801202i	−0.224678	−	0.0396169i	−0.284854	+	0.958571i	$0.591945\pi$
$410$	−6.09533	−	9.47674i	−0.301027	−	0.468023i
$411$	−1.81038	+	1.28737i	−0.0892994	+	0.0635010i
$412$	0.00650079	+	0.0743043i	0.000320271	+	0.00366071i
$413$	1.60071	+	3.43274i	0.0787660	+	0.168914i
$414$	9.25736	−	16.5868i	0.454974	−	0.815198i
$415$	11.7929	−	10.9007i	0.578890	−	0.535095i
$416$	2.85527	−	0.503462i	0.139991	−	0.0246842i
$417$	−17.0444	+	6.34441i	−0.834667	+	0.310687i
$418$	8.74928	+	7.20757i	0.427941	+	0.352534i
$419$	2.80237			0.136905			0.0684523	−	0.997654i	$-0.478194\pi$
$419$	2.80237			0.136905			0.0684523	+	0.997654i	$0.478194\pi$
$420$	−4.60223	−	7.04222i	−0.224566	−	0.343625i
$421$	2.54127	−	2.13238i	0.123854	−	0.103926i	−0.578757	−	0.815500i	$-0.696462\pi$
$421$	2.54127	−	2.13238i	0.123854	−	0.103926i	0.702611	+	0.711574i	$0.252018\pi$
$422$	5.53999	−	11.8805i	0.269682	−	0.578336i
$423$	−3.98540	+	8.88179i	−0.193777	+	0.431847i
$424$	5.18386	−	6.17789i	0.251751	−	0.300025i
$425$	10.9805	−	4.10484i	0.532630	−	0.199114i
$426$	−23.2673	+	2.20626i	−1.12730	+	0.106894i
$427$	12.6663	−	8.86901i	0.612963	−	0.429201i
$428$	9.49539	−	6.64874i	0.458977	−	0.321379i
$429$	−13.0013	+	1.23281i	−0.627708	+	0.0595208i
$430$	16.6114	−	5.31691i	0.801071	−	0.256404i
$431$	23.9311	−	28.5199i	1.15272	−	1.37376i	0.237210	−	0.971458i	$-0.423767\pi$
$431$	23.9311	−	28.5199i	1.15272	−	1.37376i	0.915509	−	0.402298i	$-0.131788\pi$
$432$	−3.42607	−	3.90666i	−0.164837	−	0.187959i
$433$	15.4653	−	33.1655i	0.743215	−	1.59383i	−0.0600405	−	0.998196i	$-0.519123\pi$
$433$	15.4653	−	33.1655i	0.743215	−	1.59383i	0.803256	−	0.595634i	$-0.203099\pi$
$434$	−14.8283	+	12.4425i	−0.711783	+	0.597257i
$435$	−4.51242	+	21.5347i	−0.216354	+	1.03251i
$436$	20.3556			0.974856
$437$	−14.0156	−	23.7760i	−0.670455	−	1.13736i
$438$	23.3773	−	8.70172i	1.11701	−	0.415784i
$439$	−35.6338	+	6.28320i	−1.70071	+	0.299881i	−0.937942	−	0.346793i	$-0.887271\pi$
$439$	−35.6338	+	6.28320i	−1.70071	+	0.299881i	−0.762766	+	0.646674i	$0.776159\pi$
$440$	3.94720	+	4.27026i	0.188175	+	0.203577i
$441$	−5.97737	−	3.33606i	−0.284637	−	0.158860i
$442$	−2.87276	−	6.16066i	−0.136643	−	0.293033i
$443$	−0.559720	−	6.39763i	−0.0265931	−	0.303961i	−0.997830	−	0.0658447i	$-0.979026\pi$
$443$	−0.559720	−	6.39763i	−0.0265931	−	0.303961i	0.971237	−	0.238116i	$-0.0765298\pi$
$444$	17.0364	−	12.1146i	0.808513	−	0.574935i
$445$	0.996282	+	0.216338i	0.0472283	+	0.0102554i
$446$	6.88429	+	1.21389i	0.325981	+	0.0574792i
$447$	19.8186	−	3.64338i	0.937389	−	0.172326i
$448$	2.09813	+	0.562193i	0.0991275	+	0.0265611i
$449$	2.20685	−	3.82237i	0.104148	−	0.180389i	−0.809242	−	0.587475i	$-0.800122\pi$
$449$	2.20685	−	3.82237i	0.104148	−	0.180389i	0.913390	+	0.407087i	$0.133455\pi$
$450$	11.7115	+	9.37235i	0.552085	+	0.441817i
$451$	−12.3143	−	4.48204i	−0.579858	−	0.211051i
$452$	1.69555	−	3.63613i	0.0797521	−	0.171029i
$453$	13.0358	+	7.40032i	0.612474	+	0.347697i
$454$	−2.15018	+	0.379135i	−0.100913	+	0.0177937i
$455$	9.46866	−	10.4237i	0.443897	−	0.488670i
$456$	−7.41274	+	1.43221i	−0.347134	+	0.0670696i
$457$	−3.51929	−	3.51929i	−0.164625	−	0.164625i	0.619987	−	0.784612i	$-0.287138\pi$
$457$	−3.51929	−	3.51929i	−0.164625	−	0.164625i	−0.784612	+	0.619987i	$0.787138\pi$
$458$	−7.85899	+	11.2238i	−0.367226	+	0.524454i
$459$	−6.76821	+	10.1294i	−0.315913	+	0.472800i
$460$	−5.47485	−	13.0569i	−0.255266	−	0.608781i
$461$	13.6328	−	37.4557i	0.634941	−	1.74449i	−0.0321222	−	0.999484i	$-0.510227\pi$
$461$	13.6328	−	37.4557i	0.634941	−	1.74449i	0.667063	−	0.745001i	$-0.267551\pi$
$462$	−9.21819	−	3.27942i	−0.428869	−	0.152572i
$463$	−7.49172	−	27.9595i	−0.348170	−	1.29939i	−0.888865	−	0.458169i	$-0.848505\pi$
$463$	−7.49172	−	27.9595i	−0.348170	−	1.29939i	0.540695	−	0.841219i	$-0.318161\pi$
$464$	−2.84050	−	4.91989i	−0.131867	−	0.228400i
$465$	18.2050	−	29.3222i	0.844239	−	1.35978i
$466$	−3.82739	+	21.7062i	−0.177301	+	1.00552i
$467$	−27.9290	−	7.48354i	−1.29240	−	0.346297i	−0.453827	−	0.891090i	$-0.649942\pi$
$467$	−27.9290	−	7.48354i	−1.29240	−	0.346297i	−0.838571	+	0.544792i	$0.816608\pi$
$468$	4.88478	−	7.19677i	0.225799	−	0.332671i
$469$	2.57582	−	3.06974i	0.118940	−	0.141747i
$470$	3.37836	+	6.42157i	0.155832	+	0.296205i
$471$	−1.38530	+	17.2808i	−0.0638315	+	0.796259i
$472$	1.73708	+	0.151975i	0.0799557	+	0.00699521i
$473$	11.6349	−	16.6164i	0.534975	−	0.764023i
$474$	−8.06817	+	17.6360i	−0.370583	+	0.810049i
$475$	20.3447	−	7.81611i	0.933481	−	0.358628i
$476$		−	5.09266i		−	0.233422i
$477$	−2.45901	−	24.0687i	−0.112590	−	1.10203i
$478$	−1.89085	+	21.6125i	−0.0864853	+	0.988531i
$479$	−25.9950	+	9.46142i	−1.18774	+	0.432303i	−0.858931	−	0.512092i	$-0.828871\pi$
$479$	−25.9950	+	9.46142i	−1.18774	+	0.432303i	−0.328813	+	0.944395i	$0.606648\pi$
$480$	−3.86707	+	0.213860i	−0.176507	+	0.00976131i
$481$	26.8060	+	22.4929i	1.22225	+	1.02559i
$482$	−5.35959	−	20.0023i	−0.244123	−	0.911079i
$483$	18.3595	+	15.1792i	0.835385	+	0.690680i
$484$	−4.17253	−	0.735730i	−0.189660	−	0.0334423i
$485$	−0.857714	+	6.74092i	−0.0389468	+	0.306090i
$486$	−15.5683	−	0.793112i	−0.706191	−	0.0359763i
$487$	−6.06171	+	1.62423i	−0.274682	+	0.0736009i	−0.393531	−	0.919311i	$-0.628746\pi$
$487$	−6.06171	+	1.62423i	−0.274682	+	0.0736009i	0.118848	+	0.992912i	$0.462080\pi$
$488$	−0.620426	−	7.09151i	−0.0280854	−	0.321017i
$489$	−1.84818	−	1.82148i	−0.0835774	−	0.0823704i
$490$	−4.70529	+	1.97296i	−0.212564	+	0.0891294i
$491$	8.45195	+	10.0726i	0.381431	+	0.454572i	0.922265	−	0.386557i	$-0.126336\pi$
$491$	8.45195	+	10.0726i	0.381431	+	0.454572i	−0.540834	+	0.841129i	$0.681891\pi$
$492$	7.52668	−	4.41883i	0.339329	−	0.199216i
$493$	−9.41813	+	9.41813i	−0.424171	+	0.424171i
$494$	−5.44444	−	11.4050i	−0.244957	−	0.513134i
$495$	17.4400	+	0.431672i	0.783869	+	0.0194022i
$496$	1.54746	+	8.77608i	0.0694830	+	0.394058i
$497$	2.55455	−	29.1987i	0.114587	−	1.30974i
$498$	8.06499	+	9.47073i	0.361401	+	0.424393i
$499$	6.14121	−	16.8728i	0.274918	−	0.755331i	−0.723001	−	0.690847i	$-0.757238\pi$
$499$	6.14121	−	16.8728i	0.274918	−	0.755331i	0.997919	−	0.0644840i	$-0.0205401\pi$
$500$	10.8829	−	2.56177i	0.486698	−	0.114566i
$501$	−25.9821	+	18.4759i	−1.16079	+	0.825442i
$502$	0.592303	−	2.21051i	0.0264358	−	0.0986597i
$503$	19.1070	−	13.3789i	0.851941	−	0.596535i	−0.0639544	−	0.997953i	$-0.520371\pi$
$503$	19.1070	−	13.3789i	0.851941	−	0.596535i	0.915895	+	0.401417i	$0.131482\pi$
$504$	5.59542	−	3.33997i	0.249240	−	0.148774i
$505$	−1.29185	+	5.94923i	−0.0574866	+	0.264737i
$506$	−14.2603	−	8.23319i	−0.633948	−	0.366010i
$507$	−7.49667	−	2.66698i	−0.332939	−	0.118445i
$508$	−3.22501	+	1.50385i	−0.143087	+	0.0667225i
$509$	−0.963495	+	0.350684i	−0.0427062	+	0.0155438i	−0.363285	−	0.931678i	$-0.618345\pi$
$509$	−0.963495	+	0.350684i	−0.0427062	+	0.0155438i	0.320579	+	0.947222i	$0.396123\pi$
$510$	2.83089	+	8.62775i	0.125354	+	0.382043i
$511$	5.43214	+	30.8072i	0.240304	+	1.36283i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−12.4123	+	18.9455i	−0.548019	+	0.836466i
$514$			5.72148i			0.252364i
$515$	0.162673	−	0.0368050i	0.00716821	−	0.00162182i
$516$	3.59151	+	13.0240i	0.158107	+	0.573351i
$517$	7.64825	+	3.56644i	0.336370	+	0.156852i
$518$	11.0795	+	23.7601i	0.486805	+	1.04396i
$519$	−18.9445	+	9.00228i	−0.831570	+	0.395156i
$520$	−1.97631	−	6.17450i	−0.0866671	−	0.270770i
$521$	−3.60995	+	2.08420i	−0.158155	+	0.0913106i	−0.576989	−	0.816752i	$-0.695772\pi$
$521$	−3.60995	+	2.08420i	−0.158155	+	0.0913106i	0.418834	+	0.908063i	$0.362439\pi$
$522$	−16.5247	−	4.17112i	−0.723266	−	0.182565i
$523$	5.57787	+	7.96602i	0.243903	+	0.348330i	0.922374	−	0.386297i	$-0.126246\pi$
$523$	5.57787	+	7.96602i	0.243903	+	0.348330i	−0.678471	+	0.734627i	$0.737357\pi$
$524$	4.75623	+	8.23804i	0.207777	+	0.359880i
$525$	−14.2156	+	12.3200i	−0.620420	+	0.537691i
$526$	−6.93678	−	5.82065i	−0.302458	−	0.253792i
$527$	18.9356	−	8.82983i	0.824849	−	0.384633i
$528$	−3.42939	+	2.92037i	−0.149245	+	0.127093i
$529$	10.9861	+	13.0927i	0.477655	+	0.569248i
$530$	−15.2509	−	9.62310i	−0.662457	−	0.418001i
$531$	3.95796	−	3.42045i	0.171761	−	0.148435i
$532$	−0.0857040	−	9.46779i	−0.00371574	−	0.410481i
$533$	10.3308	+	10.3308i	0.447475	+	0.447475i
$534$	−0.198836	+	0.764259i	−0.00860449	+	0.0330727i
$535$	−17.5940	−	19.0340i	−0.760655	−	0.822910i
$536$	−0.630972	−	1.73358i	−0.0272538	−	0.0748793i
$537$	0.170303	+	23.4145i	0.00734913	+	1.01041i
$538$	−5.71922	+	0.500367i	−0.246573	+	0.0215723i
$539$	−2.96698	+	5.13896i	−0.127797	+	0.221351i
$540$	−7.62289	+	8.76878i	−0.328037	+	0.377348i
$541$	4.92882	−	27.9527i	0.211907	−	1.20178i	−0.674288	−	0.738468i	$-0.735549\pi$
$541$	4.92882	−	27.9527i	0.211907	−	1.20178i	0.886195	−	0.463313i	$-0.153339\pi$
$542$	14.7248	+	21.0292i	0.632484	+	0.903281i
$543$	16.9142	−	20.4579i	0.725856	−	0.877931i
$544$	−2.03042	−	1.17226i	−0.0870535	−	0.0502604i
$545$	−6.13688	−	45.1009i	−0.262875	−	1.93191i
$546$	7.76904	+	7.65684i	0.332484	+	0.327683i
$547$	4.37290	+	2.03912i	0.186972	+	0.0871863i	0.513850	−	0.857880i	$-0.328219\pi$
$547$	4.37290	+	2.03912i	0.186972	+	0.0871863i	−0.326878	+	0.945067i	$0.605997\pi$
$548$	−1.27767	−	0.111781i	−0.0545792	−	0.00477506i
$549$	−16.5574	−	13.4878i	−0.706654	−	0.575646i
$550$	8.27138	−	10.0330i	0.352693	−	0.427810i
$551$	−17.3508	+	17.6678i	−0.739169	+	0.752673i
$552$	10.2780	−	3.82577i	0.437461	−	0.162836i
$553$	−19.9232	−	13.9504i	−0.847221	−	0.593230i
$554$	6.56523	−	5.50888i	0.278930	−	0.234050i
$555$	−31.9780	−	34.0944i	−1.35739	−	1.44723i
$556$	−9.86696	−	3.59128i	−0.418452	−	0.152304i
$557$	16.2137	−	1.41851i	0.686995	−	0.0601043i	0.261687	−	0.965153i	$-0.415721\pi$
$557$	16.2137	−	1.41851i	0.686995	−	0.0601043i	0.425308	+	0.905049i	$0.360166\pi$
$558$	22.1203	+	15.0140i	0.936425	+	0.635595i
$559$	−19.5851	+	11.3075i	−0.828363	+	0.478255i
$560$	0.613070	−	4.81822i	0.0259069	−	0.203607i
$561$	8.69457	+	5.99423i	0.367085	+	0.253077i
$562$	−3.01341	+	11.2462i	−0.127113	+	0.474393i
$563$	16.3792	−	4.38880i	0.690302	−	0.184966i	0.103419	−	0.994638i	$-0.467022\pi$
$563$	16.3792	−	4.38880i	0.690302	−	0.184966i	0.586882	+	0.809672i	$0.300355\pi$
$564$	−5.07648	+	2.41231i	−0.213758	+	0.101576i
$565$	−8.56757	−	2.66052i	−0.360440	−	0.111929i
$566$	3.55419	+	9.76507i	0.149394	+	0.410456i
$567$	4.50831	−	19.0224i	0.189331	−	0.798866i
$568$	−11.0533	−	7.73964i	−0.463788	−	0.324748i
$569$	15.5246			0.650824			0.325412	−	0.945572i	$-0.394497\pi$
$569$	15.5246			0.650824			0.325412	+	0.945572i	$0.394497\pi$
$570$	5.40811	+	15.9923i	0.226521	+	0.669842i
$571$	−34.2466			−1.43318			−0.716588	−	0.697497i	$-0.754297\pi$
$571$	−34.2466			−1.43318			−0.716588	+	0.697497i	$0.754297\pi$
$572$	−6.17638	−	4.32475i	−0.258247	−	0.180827i
$573$	1.02395	−	1.80370i	0.0427760	−	0.0753505i
$574$	3.74363	+	10.2855i	0.156256	+	0.429310i
$575$	−27.2789	+	16.0668i	−1.13761	+	0.670032i
$576$	−0.0436381	−	2.99968i	−0.00181825	−	0.124987i
$577$	−2.01953	+	0.541132i	−0.0840743	+	0.0225276i	−0.300611	−	0.953747i	$-0.597191\pi$
$577$	−2.01953	+	0.541132i	−0.0840743	+	0.0225276i	0.216537	+	0.976274i	$0.430524\pi$
$578$	2.97725	−	11.1112i	0.123837	−	0.462166i
$579$	6.45351	−	9.36075i	0.268199	−	0.389019i
$580$	−10.0444	+	7.77682i	−0.417071	+	0.322915i
$581$	−13.5101	+	7.80007i	−0.560494	+	0.323601i
$582$	−5.19014	−	0.876288i	−0.215138	−	0.0363233i
$583$	−20.8931	+	1.82791i	−0.865305	+	0.0757044i
$584$	13.5331	+	4.92564i	0.560003	+	0.203825i
$585$	−17.4182	−	8.65325i	−0.720154	−	0.357768i
$586$	−17.4582	+	14.6492i	−0.721192	+	0.605152i
$587$	9.48906	+	6.64431i	0.391656	+	0.274240i	0.752773	−	0.658280i	$-0.228716\pi$
$587$	9.48906	+	6.64431i	0.391656	+	0.274240i	−0.361117	+	0.932520i	$0.617605\pi$
$588$	−1.37869	−	3.70387i	−0.0568561	−	0.152745i
$589$	35.0547	−	16.7342i	1.44440	−	0.689523i
$590$	−0.186979	−	3.89458i	−0.00769780	−	0.160337i
$591$	−9.21356	+	35.4138i	−0.378995	+	1.45673i
$592$	12.0234	+	1.05191i	0.494158	+	0.0432332i
$593$	−29.0922	−	13.5659i	−1.19468	−	0.557086i	−0.279501	−	0.960145i	$-0.590169\pi$
$593$	−29.0922	−	13.5659i	−1.19468	−	0.557086i	−0.915174	+	0.403059i	$0.867947\pi$
$594$	−0.883756	+	13.4842i	−0.0362609	+	0.553262i
$595$	−11.2836	+	1.53536i	−0.462581	+	0.0629434i
$596$	10.0754	+	5.81702i	0.412703	+	0.238274i
$597$	−7.47802	−	6.18268i	−0.306055	−	0.253040i
$598$	10.5296	+	15.0379i	0.430588	+	0.614944i
$599$	8.01234	−	45.4402i	0.327375	−	1.85664i	−0.165052	−	0.986285i	$-0.552779\pi$
$599$	8.01234	−	45.4402i	0.327375	−	1.85664i	0.492428	−	0.870353i	$-0.336110\pi$
$600$	1.63970	+	8.50361i	0.0669404	+	0.347158i
$601$	−15.6832	+	27.1642i	−0.639733	+	1.10805i	0.345758	+	0.938324i	$0.387622\pi$
$601$	−15.6832	+	27.1642i	−0.639733	+	1.10805i	−0.985491	+	0.169726i	$0.945712\pi$
$602$	−16.8785	+	1.47668i	−0.687915	+	0.0601848i
$603$	−5.04946	−	2.26578i	−0.205630	−	0.0922696i
$604$	2.95998	+	8.13248i	0.120440	+	0.330906i
$605$	−0.372169	+	9.46668i	−0.0151308	+	0.384875i
$606$	−4.56372	−	1.18734i	−0.185389	−	0.0482323i
$607$	−30.2517	−	30.2517i	−1.22788	−	1.22788i	−0.964765	−	0.263112i	$-0.915251\pi$
$607$	−30.2517	−	30.2517i	−1.22788	−	1.22788i	−0.263112	−	0.964765i	$-0.584749\pi$
$608$	−3.79449	−	2.14519i	−0.153887	−	0.0869990i
$609$	8.89169	−	19.4361i	0.360309	−	0.787591i
$610$	−15.5252	+	3.51262i	−0.628599	+	0.142222i
$611$	−6.04752	−	7.20715i	−0.244656	−	0.291570i
$612$	−6.76672	+	1.91906i	−0.273528	+	0.0775732i
$613$	34.5736	−	16.1219i	1.39642	−	0.651159i	0.428756	−	0.903420i	$-0.358952\pi$
$613$	34.5736	−	16.1219i	1.39642	−	0.651159i	0.967659	+	0.252261i	$0.0811743\pi$
$614$	−6.40309	−	5.37283i	−0.258408	−	0.216830i
$615$	−12.0598	−	15.3443i	−0.486296	−	0.618741i
$616$	−2.82444	−	4.89208i	−0.113800	−	0.197107i
$617$	−8.92594	−	12.7476i	−0.359345	−	0.513198i	0.598252	−	0.801308i	$-0.295862\pi$
$617$	−8.92594	−	12.7476i	−0.359345	−	0.513198i	−0.957597	+	0.288110i	$0.906973\pi$
$618$	0.0233585	+	0.127061i	0.000939615	+	0.00511115i
$619$	−15.2646	+	8.81303i	−0.613537	+	0.354225i	−0.774348	−	0.632760i	$-0.781922\pi$
$619$	−15.2646	+	8.81303i	−0.613537	+	0.354225i	0.160812	+	0.986985i	$0.448589\pi$
$620$	18.9782	−	6.07448i	0.762182	−	0.243957i
$621$	13.2506	−	30.1146i	0.531729	−	1.20846i
$622$	11.5950	+	24.8656i	0.464917	+	0.997018i
$623$	−0.897568	−	0.418543i	−0.0359603	−	0.0167686i
$624$	4.84108	−	1.33498i	0.193798	−	0.0534418i
$625$	−8.95701	−	23.3403i	−0.358281	−	0.933614i
$626$			14.3953i			0.575352i
$627$	16.2650	+	10.9976i	0.649561	+	0.439201i
$628$	−7.07750	+	7.07750i	−0.282423	+	0.282423i
$629$	−4.91369	−	27.8669i	−0.195922	−	1.11113i
$630$	−9.08713	−	11.3905i	−0.362040	−	0.453810i
$631$	35.8068	−	13.0326i	1.42544	−	0.518819i	0.489822	−	0.871822i	$-0.337062\pi$
$631$	35.8068	−	13.0326i	1.42544	−	0.518819i	0.935622	+	0.353003i	$0.114839\pi$
$632$	−10.1480	+	4.73209i	−0.403666	+	0.188233i
$633$	7.61017	−	21.3916i	0.302477	−	0.850240i
$634$	−24.1353	−	13.9345i	−0.958534	−	0.553410i
$635$	4.30429	+	6.69211i	0.170811	+	0.265568i
$636$	7.92851	−	11.5002i	0.314386	−	0.456013i
$637$	5.41917	−	3.79454i	0.214715	−	0.150345i
$638$	−3.82379	+	14.2706i	−0.151385	+	0.564977i
$639$	−39.7595	+	7.60859i	−1.57286	+	0.300991i
$640$	−1.77988	−	1.35352i	−0.0703560	−	0.0535026i
$641$	−12.5898	+	34.5902i	−0.497268	+	1.36623i	0.396637	+	0.917975i	$0.370177\pi$
$641$	−12.5898	+	34.5902i	−0.497268	+	1.36623i	−0.893905	+	0.448256i	$0.852045\pi$
$642$	15.2860	−	13.0171i	0.603288	−	0.513742i
$643$	−3.28386	+	37.5346i	−0.129503	+	1.48022i	0.602062	+	0.798450i	$0.294346\pi$
$643$	−3.28386	+	37.5346i	−0.129503	+	1.48022i	−0.731564	+	0.681772i	$0.761209\pi$
$644$	2.38828	+	13.5446i	0.0941113	+	0.533732i
$645$	27.7739	−	11.8841i	1.09360	−	0.467934i
$646$	−2.55555	+	9.89487i	−0.100547	+	0.389308i
$647$	29.7444	−	29.7444i	1.16937	−	1.16937i	0.187015	−	0.982357i	$-0.440119\pi$
$647$	29.7444	−	29.7444i	1.16937	−	1.16937i	0.982357	−	0.187015i	$-0.0598814\pi$
$648$	−6.54639	−	6.17615i	−0.257166	−	0.242622i
$649$	−2.91485	−	3.47379i	−0.114418	−	0.136358i
$650$	−13.0847	+	6.24034i	−0.513225	+	0.244766i
$651$	−23.5344	+	23.8792i	−0.922384	+	0.935900i
$652$	−0.130574	−	1.49247i	−0.00511368	−	0.0584497i
$653$	17.9182	−	4.80116i	0.701192	−	0.187884i	0.109428	−	0.993995i	$-0.465098\pi$
$653$	17.9182	−	4.80116i	0.701192	−	0.187884i	0.591764	+	0.806111i	$0.298432\pi$
$654$	35.0995	−	3.32822i	1.37250	−	0.130144i
$655$	16.8187	−	13.0218i	0.657161	−	0.508803i
$656$	4.96252	+	0.875027i	0.193754	+	0.0341641i
$657$	38.8872	−	18.8268i	1.51713	−	0.734504i
$658$	−1.82431	−	6.80843i	−0.0711191	−	0.265420i
$659$	−16.7820	−	14.0817i	−0.653733	−	0.548547i	0.254468	−	0.967081i	$-0.418100\pi$
$659$	−16.7820	−	14.0817i	−0.653733	−	0.548547i	−0.908201	+	0.418534i	$0.862544\pi$
$660$	7.50443	+	6.71789i	0.292109	+	0.261494i
$661$	2.78248	−	1.01274i	0.108226	−	0.0393910i	−0.287340	−	0.957829i	$-0.592771\pi$
$661$	2.78248	−	1.01274i	0.108226	−	0.0393910i	0.395566	+	0.918438i	$0.370549\pi$
$662$	−2.12405	+	24.2780i	−0.0825536	+	0.943592i
$663$	−5.96084	−	10.1532i	−0.231500	−	0.394318i
$664$			7.18189i			0.278711i
$665$	−20.9515	+	3.04428i	−0.812463	+	0.118052i
$666$	27.3954	−	23.6750i	1.06155	−	0.917387i
$667$	20.6320	−	29.4655i	0.798874	−	1.14091i
$668$	−18.3367	−	1.60425i	−0.709469	−	0.0620705i
$669$	12.0692	+	0.967516i	0.466621	+	0.0374063i
$670$	−3.65078	+	1.92066i	−0.141042	+	0.0742016i
$671$	−11.8997	+	14.1815i	−0.459381	+	0.547469i
$672$	3.70977	+	0.626346i	0.143107	+	0.0241618i
$673$	24.3814	+	6.53299i	0.939836	+	0.251828i	0.696044	−	0.717999i	$-0.254942\pi$
$673$	24.3814	+	6.53299i	0.939836	+	0.251828i	0.243792	+	0.969828i	$0.421609\pi$
$674$	−2.91400	+	16.5261i	−0.112243	+	0.636563i
$675$	21.7267	+	14.2460i	0.836262	+	0.548330i
$676$	−2.29697	−	3.97847i	−0.0883449	−	0.153018i
$677$	−1.04283	−	3.89189i	−0.0400792	−	0.149578i	0.942987	−	0.332831i	$-0.108004\pi$
$677$	−1.04283	−	3.89189i	−0.0400792	−	0.149578i	−0.983066	+	0.183253i	$0.941337\pi$
$678$	2.32915	−	6.54706i	0.0894504	−	0.251438i
$679$	2.25768	−	6.20294i	0.0866419	−	0.238047i
$680$	−1.98519	+	4.85212i	−0.0761284	+	0.186070i
$681$	−3.64561	+	1.00531i	−0.139700	+	0.0385237i
$682$	13.2927	−	18.9839i	0.509004	−	0.726933i
$683$	2.48258	+	2.48258i	0.0949933	+	0.0949933i	0.753006	−	0.658013i	$-0.228603\pi$
$683$	2.48258	+	2.48258i	0.0949933	+	0.0949933i	−0.658013	+	0.753006i	$0.728603\pi$
$684$	−12.5477	+	3.68160i	−0.479775	+	0.140770i
$685$	0.137528	+	2.86456i	0.00525466	+	0.109449i
$686$	19.8551	−	3.50099i	0.758071	−	0.133668i
$687$	−11.7162	+	20.6383i	−0.447003	+	0.787402i
$688$	−3.29646	+	7.06928i	−0.125676	+	0.269514i
$689$	21.9719	+	7.99713i	0.837064	+	0.304666i
$690$	−11.5752	−	21.6191i	−0.440661	−	0.823023i
$691$	6.24786	−	10.8216i	0.237680	−	0.411674i	−0.722368	−	0.691509i	$-0.756946\pi$
$691$	6.24786	−	10.8216i	0.237680	−	0.411674i	0.960048	+	0.279835i	$0.0902797\pi$
$692$	−11.6971	−	3.13422i	−0.444656	−	0.119145i
$693$	−16.4313	−	4.14754i	−0.624172	−	0.157552i
$694$	−8.05785	−	1.42082i	−0.305872	−	0.0539334i
$695$	−4.98229	+	22.9444i	−0.188989	+	0.870332i
$696$	−5.70234	−	8.01901i	−0.216147	−	0.303960i
$697$	−1.02968	−	11.7693i	−0.0390019	−	0.445794i
$698$	−0.605791	−	1.29912i	−0.0229295	−	0.0491725i
$699$	−3.05059	+	38.0542i	−0.115384	+	1.43934i
$700$	−10.8603	+	0.0942683i	−0.410482	+	0.00356301i
$701$	47.6373	−	8.39974i	1.79924	−	0.317254i	0.828970	−	0.559293i	$-0.188927\pi$
$701$	47.6373	−	8.39974i	1.79924	−	0.317254i	0.970267	+	0.242039i	$0.0778161\pi$
$702$	7.24620	−	13.2082i	0.273490	−	0.498511i
$703$	−9.60403	−	51.7248i	−0.362223	−	1.95084i
$704$	−2.60060			−0.0980137
$705$	6.87531	+	10.5204i	0.258939	+	0.396223i
$706$	−5.66999	+	4.75768i	−0.213393	+	0.179058i
$707$	2.49930	−	5.35977i	0.0939959	−	0.201575i
$708$	3.02013	−	0.0219666i	0.113503	−	0.000825555i
$709$	7.82531	−	9.32584i	0.293886	−	0.350239i	−0.598817	−	0.800886i	$-0.704362\pi$
$709$	7.82531	−	9.32584i	0.293886	−	0.350239i	0.892702	+	0.450647i	$0.148807\pi$
$710$	−13.8159	+	26.8237i	−0.518502	+	1.00668i
$711$	−11.0285	+	31.7292i	−0.413602	+	1.18994i
$712$	−0.373479	+	0.261513i	−0.0139967	+	0.00980061i
$713$	−46.2209	+	32.3642i	−1.73099	+	1.21205i
$714$	−0.832669	−	8.78135i	−0.0311619	−	0.328634i
$715$	−7.72005	+	14.9885i	−0.288713	+	0.560539i
$716$	−8.68969	+	10.3560i	−0.324749	+	0.387021i
$717$	0.273304	+	37.5759i	0.0102067	+	1.40330i
$718$	−1.71387	+	3.67541i	−0.0639611	+	0.137165i
$719$	−11.1167	+	9.32805i	−0.414584	+	0.347877i	−0.826098	−	0.563526i	$-0.809445\pi$
$719$	−11.1167	+	9.32805i	−0.414584	+	0.347877i	0.411514	+	0.911403i	$0.365000\pi$
$720$	−6.63309	+	1.00104i	−0.247201	+	0.0373067i
$721$	−0.162017			−0.00603381
$722$	−4.58452	+	18.4386i	−0.170618	+	0.686214i
$723$	−12.5121	−	33.6139i	−0.465329	−	1.25012i
$724$	15.0927	−	2.66125i	0.560915	−	0.0989044i
$725$	20.2589	+	19.9103i	0.752398	+	0.739449i
$726$	−7.31506	−	0.586406i	−0.271487	−	0.0217636i
$727$	−15.6247	−	33.5073i	−0.579488	−	1.24272i	−0.949523	−	0.313699i	$-0.898432\pi$
$727$	−15.6247	−	33.5073i	−0.579488	−	1.24272i	0.370034	−	0.929018i	$-0.379346\pi$
$728$	0.548886	+	6.27379i	0.0203431	+	0.232522i
$729$	−26.9743	+	1.17790i	−0.999048	+	0.0436258i
$730$	6.83349	−	31.4696i	0.252919	−	1.16474i
$731$	18.0097	+	3.17559i	0.666112	+	0.117454i
$732$	−2.22930	−	12.1266i	−0.0823973	−	0.448210i
$733$	−20.7244	−	5.55307i	−0.765471	−	0.205107i	−0.145101	−	0.989417i	$-0.546351\pi$
$733$	−20.7244	−	5.55307i	−0.765471	−	0.205107i	−0.620370	+	0.784309i	$0.713018\pi$
$734$	0.154358	−	0.267355i	0.00569744	−	0.00986826i
$735$	−7.79083	+	4.17135i	−0.287369	+	0.153862i
$736$	5.94992	+	2.16559i	0.219317	+	0.0798248i
$737$	−2.02759	+	4.34817i	−0.0746871	+	0.160167i
$738$	12.2559	−	8.85010i	0.451145	−	0.325777i
$739$	−3.52287	+	0.621178i	−0.129591	+	0.0228504i	−0.238067	−	0.971249i	$-0.576514\pi$
$739$	−3.52287	+	0.621178i	−0.129591	+	0.0228504i	0.108476	+	0.994099i	$0.465403\pi$
$740$	−1.29419	−	26.9567i	−0.0475755	−	0.990949i
$741$	−11.2527	−	18.7756i	−0.413378	−	0.689738i
$742$	12.3868	+	12.3868i	0.454735	+	0.454735i
$743$	13.8890	−	19.8355i	0.509537	−	0.727694i	−0.479143	−	0.877737i	$-0.659052\pi$
$743$	13.8890	−	19.8355i	0.509537	−	0.727694i	0.988679	+	0.150043i	$0.0479413\pi$
$744$	4.10323	+	14.8797i	0.150432	+	0.545517i
$745$	9.85092	−	24.0772i	0.360910	−	0.882122i
$746$	−9.04423	+	24.8488i	−0.331133	+	0.909780i
$747$	15.4551	+	15.0119i	0.565472	+	0.549256i
$748$	1.57806	+	5.88941i	0.0576997	+	0.215338i
$749$	12.5895	+	21.8056i	0.460009	+	0.796760i
$750$	18.3467	−	6.19670i	0.669926	−	0.226272i
$751$	3.49041	−	19.7951i	0.127367	−	0.722334i	−0.852507	−	0.522716i	$-0.824919\pi$
$751$	3.49041	−	19.7951i	0.127367	−	0.722334i	0.979874	−	0.199618i	$-0.0639701\pi$
$752$	−3.13442	−	0.839865i	−0.114301	−	0.0306267i
$753$	0.659892	−	3.90845i	0.0240478	−	0.142432i
$754$	10.5874	−	12.6175i	0.385570	−	0.459504i
$755$	17.1263	−	9.01009i	0.623291	−	0.327911i
$756$	9.10217	−	6.67403i	0.331043	−	0.242732i
$757$	24.8122	+	2.17079i	0.901815	+	0.0788986i	0.528624	−	0.848856i	$-0.322708\pi$
$757$	24.8122	+	2.17079i	0.901815	+	0.0788986i	0.373191	+	0.927755i	$0.378264\pi$
$758$	15.0567	−	21.5032i	0.546884	−	0.781031i
$759$	−25.9354	−	11.8650i	−0.941396	−	0.430672i
$760$	−3.60901	+	9.05401i	−0.130913	+	0.328423i
$761$		−	18.6056i		−	0.674454i	−0.941423	−	0.337227i	$-0.890511\pi$
$761$		−	18.6056i		−	0.674454i	0.941423	−	0.337227i	$-0.109489\pi$
$762$	−5.31506	+	3.12041i	−0.192544	+	0.113041i
$763$	−3.85362	+	44.0471i	−0.139510	+	1.59461i
$764$	1.12525	−	0.409558i	0.0407102	−	0.0148173i
$765$	6.29201	+	14.4141i	0.227488	+	0.521143i
$766$	−14.6502	−	12.2930i	−0.529333	−	0.444163i
$767$	1.30848	+	4.88333i	0.0472466	+	0.176327i
$768$	1.10366	−	1.33489i	0.0398249	−	0.0481687i
$769$	27.0529	+	4.77016i	0.975554	+	0.172016i	0.638629	−	0.769515i	$-0.279502\pi$
$769$	27.0529	+	4.77016i	0.975554	+	0.172016i	0.336925	+	0.941531i	$0.390613\pi$
$770$	−9.98761	+	7.73286i	−0.359928	+	0.278673i
$771$	0.935483	+	9.86564i	0.0336906	+	0.355302i
$772$	6.34066	−	1.69897i	0.228205	−	0.0611474i
$773$	3.93998	+	45.0341i	0.141711	+	1.61977i	0.650937	+	0.759132i	$0.274376\pi$
$773$	3.93998	+	45.0341i	0.141711	+	1.61977i	−0.509226	+	0.860633i	$0.670068\pi$
$774$	8.32237	+	21.8703i	0.299141	+	0.786112i
$775$	−19.1805	−	40.2177i	−0.688985	−	1.44466i
$776$	−1.95339	−	2.32796i	−0.0701227	−	0.0835690i
$777$	22.9894	+	39.1583i	0.824741	+	1.40480i
$778$	−25.2908	+	25.2908i	−0.906718	+	0.906718i
$779$	−2.11235	−	21.8630i	−0.0756827	−	0.783324i
$780$	−4.41735	−	10.3237i	−0.158166	−	0.369646i
$781$	6.09358	+	34.5584i	0.218045	+	1.23660i
$782$	1.29383	−	14.7885i	0.0462671	−	0.528836i
$783$	−29.1758	−	4.49049i	−1.04266	−	0.160477i
$784$	0.780412	−	2.14416i	0.0278718	−	0.0765773i
$785$	17.8150	+	13.5475i	0.635845	+	0.483532i
$786$	9.54820	+	13.4273i	0.340573	+	0.478937i
$787$	−7.64970	+	28.5491i	−0.272682	+	1.01766i	0.684696	+	0.728828i	$0.259935\pi$
$787$	−7.64970	+	28.5491i	−0.272682	+	1.01766i	−0.957379	+	0.288836i	$0.906732\pi$
$788$	−17.3061	+	12.1178i	−0.616503	+	0.431680i
$789$	−12.9129	−	8.90245i	−0.459712	−	0.316936i
$790$	13.5441	+	21.0578i	0.481878	+	0.749202i
$791$	7.54716	+	4.35735i	0.268346	+	0.154930i
$792$	−5.43587	+	5.59636i	−0.193155	+	0.198858i
$793$	18.7054	−	8.72246i	0.664247	−	0.309743i
$794$	−9.88325	+	3.59721i	−0.350743	+	0.127660i
$795$	−27.8708	−	14.0997i	−0.988475	−	0.500064i
$796$	−0.972773	−	5.51687i	−0.0344790	−	0.195540i
$797$	−0.838849	+	0.838849i	−0.0297135	+	0.0297135i	−0.721807	−	0.692094i	$-0.756688\pi$
$797$	−0.838849	+	0.838849i	−0.0297135	+	0.0297135i	0.692094	+	0.721807i	$0.256688\pi$
$798$	−1.69580	−	16.3114i	−0.0600307	−	0.577419i
$799$			7.60796i			0.269150i
$800$	−2.46232	+	4.35166i	−0.0870562	+	0.153855i
$801$	−0.217897	+	1.35033i	−0.00769903	+	0.0477117i
$802$	−20.3042	−	9.46799i	−0.716965	−	0.334326i
$803$	−15.8282	−	33.9438i	−0.558566	−	1.19785i
$804$	−1.37144	−	2.88607i	−0.0483670	−	0.101784i
$805$	29.2901	−	9.37507i	1.03234	−	0.330428i
$806$	−22.3757	+	12.9186i	−0.788149	+	0.455038i
$807$	−9.77993	+	1.79790i	−0.344270	+	0.0632892i
$808$	−1.56161	−	2.23021i	−0.0549372	−	0.0784584i
$809$	−2.51647	−	4.35865i	−0.0884742	−	0.153242i	0.818392	−	0.574660i	$-0.194866\pi$
$809$	−2.51647	−	4.35865i	−0.0884742	−	0.153242i	−0.906866	+	0.421418i	$0.861532\pi$
$810$	−11.7106	+	16.3665i	−0.411467	+	0.575061i
$811$	−10.3112	−	8.65213i	−0.362076	−	0.303817i	0.443542	−	0.896254i	$-0.353722\pi$
$811$	−10.3112	−	8.65213i	−0.362076	−	0.303817i	−0.805617	+	0.592436i	$0.798166\pi$
$812$	11.1838	−	5.21510i	0.392475	−	0.183014i
$813$	28.8285	+	33.8534i	1.01106	+	1.18729i
$814$	−20.1754	−	24.0441i	−0.707148	−	0.842746i
$815$	−3.26743	+	0.739263i	−0.114453	+	0.0258953i
$816$	−3.69275	−	1.68937i	−0.129272	−	0.0591398i
$817$	33.5353	+	5.60068i	1.17325	+	0.195943i
$818$	−3.26255	−	3.26255i	−0.114072	−	0.114072i
$819$	14.6482	+	11.9325i	0.511850	+	0.416957i
$820$	0.442632	−	11.2590i	0.0154574	−	0.393182i
$821$	−6.66053	−	18.2997i	−0.232454	−	0.638662i	0.767543	−	0.640997i	$-0.221479\pi$
$821$	−6.66053	−	18.2997i	−0.232454	−	0.638662i	−0.999997	+	0.00233490i	$0.999257\pi$
$822$	−2.22138	+	0.0161570i	−0.0774795	+	0.000563539i
$823$	1.97353	−	0.172661i	0.0687928	−	0.00601859i	−0.0527074	−	0.998610i	$-0.516785\pi$
$823$	1.97353	−	0.172661i	0.0687928	−	0.00601859i	0.121500	+	0.992591i	$0.461229\pi$
$824$	−0.0372941	+	0.0645953i	−0.00129920	+	0.00225028i
$825$	12.6220	−	18.6525i	0.439443	−	0.649398i
$826$	−0.657712	+	3.73007i	−0.0228847	+	0.129786i
$827$	20.2475	+	28.9164i	0.704075	+	1.00552i	0.998753	+	0.0499263i	$0.0158987\pi$
$827$	20.2475	+	28.9164i	0.704075	+	1.00552i	−0.294678	+	0.955597i	$0.595212\pi$
$828$	17.0970	−	8.27733i	0.594162	−	0.287657i
$829$	−24.3941	−	14.0840i	−0.847243	−	0.489156i	0.0124764	−	0.999922i	$-0.496029\pi$
$829$	−24.3941	−	14.0840i	−0.847243	−	0.489156i	−0.859720	+	0.510766i	$0.829362\pi$
$830$	15.9126	−	2.16523i	0.552333	−	0.0751561i
$831$	10.4198	−	10.5725i	0.361459	−	0.366756i
$832$	2.62768	+	1.22531i	0.0910983	+	0.0424798i
$833$	−5.32931	−	0.466255i	−0.184650	−	0.0161548i
$834$	−17.6009	−	4.57921i	−0.609471	−	0.158565i
$835$	1.97376	+	41.1114i	0.0683047	+	1.42272i
$836$	3.03290	+	10.9225i	0.104895	+	0.377762i
$837$	40.5972	+	22.2722i	1.40324	+	0.769840i
$838$	2.29556	+	1.60737i	0.0792990	+	0.0555257i
$839$	−31.8437	+	26.7200i	−1.09937	+	0.922478i	−0.997382	−	0.0723079i	$-0.976964\pi$
$839$	−31.8437	+	26.7200i	−1.09937	+	0.922478i	−0.101984	+	0.994786i	$0.532519\pi$
$840$	0.269329	−	8.40838i	0.00929273	−	0.290117i
$841$	−3.07631	−	1.11968i	−0.106080	−	0.0386098i
$842$	3.30477	−	0.289130i	0.113890	−	0.00996407i
$843$	−3.35728	+	19.8847i	−0.115631	+	0.684866i
$844$	11.3525	−	6.55436i	0.390769	−	0.225610i
$845$	−8.12239	+	6.28872i	−0.279419	+	0.216339i
$846$	−8.35904	+	4.98960i	−0.287390	+	0.171546i
$847$	2.38196	−	8.88958i	0.0818450	−	0.305450i
$848$	7.78987	−	2.08729i	0.267505	−	0.0716778i
$849$	7.72518	+	16.2569i	0.265127	+	0.557937i
$850$	11.3491	+	2.93564i	0.389271	+	0.100692i
$851$	26.1372	+	71.8113i	0.895971	+	2.46166i
$852$	−20.3249	−	11.5383i	−0.696321	−	0.395296i
$853$	1.17065	+	0.819696i	0.0400822	+	0.0280659i	0.593446	−	0.804874i	$-0.297767\pi$
$853$	1.17065	+	0.819696i	0.0400822	+	0.0280659i	−0.553364	+	0.832940i	$0.686656\pi$
$854$	15.4626			0.529121
$855$	11.9401	+	26.6915i	0.408342	+	0.912829i
$856$	11.5917			0.396197
$857$	−11.8970	−	8.33035i	−0.406393	−	0.284559i	0.352453	−	0.935829i	$-0.385348\pi$
$857$	−11.8970	−	8.33035i	−0.406393	−	0.284559i	−0.758846	+	0.651270i	$0.774236\pi$
$858$	−11.3571	−	6.44737i	−0.387726	−	0.220110i
$859$	1.95250	+	5.36445i	0.0666185	+	0.183033i	0.968535	−	0.248878i	$-0.0800618\pi$
$859$	1.95250	+	5.36445i	0.0666185	+	0.183033i	−0.901916	+	0.431911i	$0.857840\pi$
$860$	16.6569	+	5.17253i	0.567995	+	0.176382i
$861$	8.13692	+	17.1234i	0.277305	+	0.583564i
$862$	35.9615	−	9.63586i	1.22485	−	0.328199i
$863$	−0.678133	+	2.53083i	−0.0230839	+	0.0861503i	−0.976507	−	0.215486i	$-0.930866\pi$
$863$	−0.678133	+	2.53083i	−0.0230839	+	0.0861503i	0.953423	+	0.301637i	$0.0975330\pi$
$864$	−0.565705	−	5.16527i	−0.0192457	−	0.175726i
$865$	−3.41786	+	26.8615i	−0.116211	+	0.913320i
$866$	31.6914	−	18.2970i	1.07692	−	0.621758i
$867$	3.31699	−	19.6461i	0.112651	−	0.667216i
$868$	−19.2834	+	1.68708i	−0.654520	+	0.0572631i
$869$	27.3630	+	9.95932i	0.928226	+	0.337847i
$870$	−16.0482	+	15.0520i	−0.544084	+	0.510310i
$871$	4.09740	−	3.43813i	0.138835	−	0.116497i
$872$	16.6743	+	11.6755i	0.564664	+	0.395382i
$873$	−9.09272	−	0.662390i	−0.307742	−	0.0224185i
$874$	2.15649	−	27.5152i	0.0729442	−	0.930714i
$875$	3.48308	+	24.0343i	0.117750	+	0.812507i
$876$	24.1407	+	6.28065i	0.815638	+	0.212204i
$877$	−0.964956	−	0.0844227i	−0.0325843	−	0.00285075i	0.0708520	−	0.997487i	$-0.477428\pi$
$877$	−0.964956	−	0.0844227i	−0.0325843	−	0.00285075i	−0.103436	+	0.994636i	$0.532984\pi$
$878$	−32.7934	−	15.2918i	−1.10672	−	0.516073i
$879$	−27.7083	+	28.1143i	−0.934577	+	0.948271i
$880$	0.784038	+	5.76201i	0.0264299	+	0.194237i
$881$	−47.3202	−	27.3203i	−1.59426	−	0.920445i	−0.992565	−	0.121717i	$-0.961160\pi$
$881$	−47.3202	−	27.3203i	−1.59426	−	0.920445i	−0.601693	−	0.798728i	$-0.705507\pi$
$882$	−2.98289	−	6.16122i	−0.100439	−	0.207459i
$883$	29.6339	+	42.3215i	0.997259	+	1.42423i	0.903475	+	0.428641i	$0.141007\pi$
$883$	29.6339	+	42.3215i	0.997259	+	1.42423i	0.0937841	+	0.995593i	$0.470104\pi$
$884$	1.18038	−	6.69426i	0.0397005	−	0.225152i
$885$	−0.959190	−	6.68492i	−0.0322428	−	0.224711i
$886$	3.21103	−	5.56167i	0.107877	−	0.186848i
$887$	14.1291	−	1.23614i	0.474409	−	0.0415054i	0.152555	−	0.988295i	$-0.451250\pi$
$887$	14.1291	−	1.23614i	0.474409	−	0.0415054i	0.321853	+	0.946790i	$0.395694\pi$
$888$	20.9041	−	0.152044i	0.701495	−	0.00510225i
$889$	−2.64361	−	7.26325i	−0.0886637	−	0.243602i
$890$	0.692020	+	0.748658i	0.0231965	+	0.0250951i
$891$	0.680838	+	23.3955i	0.0228089	+	0.783778i
$892$	4.94303	+	4.94303i	0.165505	+	0.165505i
$893$	0.128034	+	14.1440i	0.00428449	+	0.473311i
$894$	18.3242	+	8.38302i	0.612854	+	0.280370i
$895$	25.5650	+	16.1312i	0.854544	+	0.539205i
$896$	1.39623	+	1.66396i	0.0466448	+	0.0555891i
$897$	20.6151	+	24.2084i	0.688320	+	0.808294i
$898$	4.00016	−	1.86531i	0.133487	−	0.0622461i
$899$	38.7818	+	32.5418i	1.29344	+	1.08533i
$900$	4.21773	+	14.3948i	0.140591	+	0.479827i
$901$	−9.45390	−	16.3746i	−0.314955	−	0.545518i
$902$	−7.51650	−	10.7347i	−0.250272	−	0.357425i
$903$	−28.8624	+	5.30595i	−0.960480	+	0.176571i
$904$	3.47451	−	2.00601i	0.115561	−	0.0667189i
$905$	−10.4466	−	32.6378i	−0.347256	−	1.08492i
$906$	6.43363	+	13.5390i	0.213743	+	0.449803i
$907$	2.72049	+	5.83412i	0.0903325	+	0.193719i	0.946283	−	0.323338i	$-0.104805\pi$
$907$	2.72049	+	5.83412i	0.0903325	+	0.193719i	−0.855951	+	0.517057i	$0.827027\pi$
$908$	−1.97879	−	0.922725i	−0.0656685	−	0.0306217i
$909$	−8.06344	−	1.30116i	−0.267447	−	0.0431568i
$910$	13.7350	−	3.10759i	0.455312	−	0.103015i
$911$			31.9485i			1.05850i	0.848466	+	0.529250i	$0.177527\pi$
$911$			31.9485i			1.05850i	−0.848466	+	0.529250i	$0.822473\pi$
$912$	−6.89365	−	3.07857i	−0.228272	−	0.101942i
$913$	13.2068	−	13.2068i	0.437080	−	0.437080i
$914$	−0.864251	−	4.90141i	−0.0285869	−	0.162124i
$915$	−26.1961	+	8.59531i	−0.866017	+	0.284152i
$916$	−12.8754	+	4.68627i	−0.425415	+	0.154839i
$917$	−18.7266	+	8.73235i	−0.618406	+	0.288368i
$918$	−11.3542	+	4.41544i	−0.374744	+	0.145731i
$919$	−23.4413	−	13.5339i	−0.773258	−	0.446441i	0.0607774	−	0.998151i	$-0.480642\pi$
$919$	−23.4413	−	13.5339i	−0.773258	−	0.446441i	−0.834036	+	0.551710i	$0.813975\pi$
$920$	3.00439	−	13.8358i	0.0990519	−	0.456154i
$921$	−11.9194	−	8.21753i	−0.392759	−	0.270777i
$922$	32.6510	−	22.8625i	1.07530	−	0.752936i
$923$	10.1256	−	37.7893i	0.333289	−	1.24385i
$924$	−5.67010	−	7.97368i	−0.186533	−	0.262315i
$925$	−59.3365	+	10.9945i	−1.95097	+	0.361497i
$926$	9.90004	−	27.2001i	0.325336	−	0.893852i
$927$	0.0610524	+	0.215275i	0.00200522	+	0.00707055i
$928$	0.495132	−	5.65938i	0.0162535	−	0.185778i
$929$	−4.47775	−	25.3946i	−0.146910	−	0.833170i	−0.965813	−	0.259238i	$-0.916529\pi$
$929$	−4.47775	−	25.3946i	−0.146910	−	0.833170i	0.818903	−	0.573932i	$-0.194582\pi$
$930$	31.7312	−	13.5773i	1.04051	−	0.445218i
$931$	−9.91560	−	0.777129i	−0.324971	−	0.0254694i
$932$	−15.5854	+	15.5854i	−0.510517	+	0.510517i
$933$	24.0591	+	40.9803i	0.787658	+	1.34163i
$934$	−18.5857	−	22.1496i	−0.608142	−	0.724756i
$935$	12.5731	−	5.27200i	0.411185	−	0.172413i
$936$	8.12927	−	3.09345i	0.265714	−	0.101113i
$937$	−2.48715	−	28.4283i	−0.0812517	−	0.928712i	−0.921976	−	0.387248i	$-0.873426\pi$
$937$	−2.48715	−	28.4283i	−0.0812517	−	0.928712i	0.840724	−	0.541464i	$-0.182130\pi$
$938$	3.87072	−	1.03716i	0.126383	−	0.0338643i
$939$	2.35369	+	24.8221i	0.0768097	+	0.810037i
$940$	−0.915870	+	7.19798i	−0.0298724	+	0.234772i
$941$	24.8784	+	4.38673i	0.811012	+	0.143003i	0.563750	−	0.825945i	$-0.309358\pi$
$941$	24.8784	+	4.38673i	0.811012	+	0.143003i	0.247262	+	0.968949i	$0.420469\pi$
$942$	−11.0467	+	13.3610i	−0.359919	+	0.435326i
$943$	8.25795	+	30.8191i	0.268916	+	1.00361i
$944$	1.33576	+	1.12084i	0.0434754	+	0.0364802i
$945$	−17.5315	−	18.1551i	−0.570299	−	0.590586i
$946$	19.0616	−	6.93784i	0.619745	−	0.225569i
$947$	−2.27490	+	26.0022i	−0.0739243	+	0.844959i	0.865210	+	0.501409i	$0.167185\pi$
$947$	−2.27490	+	26.0022i	−0.0739243	+	0.844959i	−0.939135	+	0.343549i	$0.888371\pi$
$948$	−16.7247	+	9.81886i	−0.543192	+	0.318902i
$949$			41.7549i			1.35542i
$950$	21.1486	+	5.26668i	0.686150	+	0.170874i
$951$	−43.8952	−	20.0813i	−1.42340	−	0.651180i
$952$	2.92103	−	4.17166i	0.0946711	−	0.135204i
$953$	48.7398	+	4.26418i	1.57884	+	0.138130i	0.842580	−	0.538571i	$-0.181036\pi$
$953$	48.7398	+	4.26418i	1.57884	+	0.138130i	0.736258	+	0.676701i	$0.236591\pi$
$954$	11.7909	−	21.1264i	0.381746	−	0.683991i
$955$	−1.24668	−	2.36969i	−0.0403417	−	0.0766814i
$956$	−13.9453	+	16.6193i	−0.451023	+	0.537508i
$957$	−4.26013	+	25.2322i	−0.137710	+	0.815641i
$958$	−26.7207	−	7.15980i	−0.863308	−	0.231323i
$959$	0.483763	−	2.74356i	0.0156215	−	0.0885941i
$960$	−3.29039	−	2.04288i	−0.106197	−	0.0659336i
$961$	−24.2071	−	41.9279i	−0.780874	−	1.35251i
$962$	9.05680	+	33.8004i	0.292003	+	1.08977i
$963$	24.2295	−	24.9448i	0.780784	−	0.803836i
$964$	7.08251	−	19.4590i	0.228112	−	0.626734i
$965$	−5.67594	−	13.5365i	−0.182715	−	0.435754i
$966$	6.33274	+	22.9647i	0.203753	+	0.738876i
$967$	−1.71151	+	2.44428i	−0.0550383	+	0.0786029i	−0.845728	−	0.533614i	$-0.820833\pi$
$967$	−1.71151	+	2.44428i	−0.0550383	+	0.0786029i	0.790690	+	0.612217i	$0.209722\pi$
$968$	−2.99594	−	2.99594i	−0.0962931	−	0.0962931i
$969$	−2.78873	+	17.4797i	−0.0895870	+	0.561530i
$970$	−4.56903	+	5.02988i	−0.146703	+	0.161500i
$971$	3.21877	−	0.567557i	0.103295	−	0.0182138i	−0.121762	−	0.992559i	$-0.538854\pi$
$971$	3.21877	−	0.567557i	0.103295	−	0.0182138i	0.225057	+	0.974346i	$0.427743\pi$
$972$	−12.2979	−	9.57927i	−0.394454	−	0.307255i
$973$	9.63907	−	20.6711i	0.309014	−	0.662683i
$974$	−5.89709	−	2.14636i	−0.188955	−	0.0687739i
$975$	−21.5419	+	12.8997i	−0.689892	+	0.413122i
$976$	3.55930	−	6.16488i	0.113930	−	0.197333i
$977$	46.2751	+	12.3994i	1.48047	+	0.396691i	0.906508	−	0.422190i	$-0.138738\pi$
$977$	46.2751	+	12.3994i	1.48047	+	0.396691i	0.573964	+	0.818881i	$0.305405\pi$
$978$	−0.469176	−	2.55214i	−0.0150026	−	0.0816085i
$979$	1.16769	+	0.205895i	0.0373194	+	0.00658042i
$980$	−4.98600	−	1.08269i	−0.159272	−	0.0345852i
$981$	59.9784	−	11.4778i	1.91496	−	0.366458i
$982$	1.14600	+	13.0989i	0.0365704	+	0.418002i
$983$	25.9425	+	55.6339i	0.827438	+	1.77445i	0.598729	+	0.800951i	$0.295673\pi$
$983$	25.9425	+	55.6339i	0.827438	+	1.77445i	0.228709	+	0.973495i	$0.426550\pi$
$984$	8.70003	+	0.697432i	0.277347	+	0.0222333i
$985$	32.0664	+	34.6909i	1.02172	+	1.10534i
$986$	−13.1169	+	2.31286i	−0.417727	+	0.0736566i
$987$	−4.25889	−	11.4416i	−0.135562	−	0.364190i
$988$	2.08179	−	12.4652i	0.0662306	−	0.396571i
$989$	−49.3884			−1.57046
$990$	14.0384	+	10.3568i	0.446170	+	0.329160i
$991$	0.247060	−	0.207308i	0.00784813	−	0.00658536i	−0.638855	−	0.769327i	$-0.720592\pi$
$991$	0.247060	−	0.207308i	0.00784813	−	0.00658536i	0.646703	+	0.762742i	$0.276147\pi$
$992$	−3.76615	+	8.07653i	−0.119575	+	0.256430i
$993$	0.307012	+	42.2103i	0.00974273	+	1.33950i
$994$	18.8402	−	22.4529i	0.597576	−	0.712163i
$995$	−11.9302	+	3.81857i	−0.378212	+	0.121057i
$996$	1.17427	+	12.3839i	0.0372081	+	0.392397i
$997$	30.0003	−	21.0064i	0.950118	−	0.665280i	0.00778985	−	0.999970i	$-0.497520\pi$
$997$	30.0003	−	21.0064i	0.950118	−	0.665280i	0.942328	+	0.334690i	$0.108631\pi$
$998$	14.7084	−	10.2990i	0.465587	−	0.326008i
$999$	43.3674	−	45.3024i	1.37208	−	1.43331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.47.38	yes	480
3.2	odd	2	inner	570.2.bi.a.47.2	yes	480
5.3	odd	4	inner	570.2.bi.a.503.28	yes	480
15.8	even	4	inner	570.2.bi.a.503.9	yes	480
19.17	even	9	inner	570.2.bi.a.17.9	✓	480
57.17	odd	18	inner	570.2.bi.a.17.28	yes	480
95.93	odd	36	inner	570.2.bi.a.473.2	yes	480
285.188	even	36	inner	570.2.bi.a.473.38	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.9	✓	480	19.17	even	9	inner
570.2.bi.a.17.28	yes	480	57.17	odd	18	inner
570.2.bi.a.47.2	yes	480	3.2	odd	2	inner
570.2.bi.a.47.38	yes	480	1.1	even	1	trivial
570.2.bi.a.473.2	yes	480	95.93	odd	36	inner
570.2.bi.a.473.38	yes	480	285.188	even	36	inner
570.2.bi.a.503.9	yes	480	15.8	even	4	inner
570.2.bi.a.503.28	yes	480	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(1.50626 + 0.855093i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.97892 - 1.04110i) q^{5} +(0.743394 + 1.56441i) q^{6} +(-2.09813 + 0.562193i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(1.53763 + 2.57598i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(1.50626 + 0.855093i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.97892 - 1.04110i) q^{5} +(0.743394 + 1.56441i) q^{6} +(-2.09813 + 0.562193i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(1.53763 + 2.57598i) q^{9} +(2.21818 + 0.282241i) q^{10} +(2.25218 - 1.30030i) q^{11} +(-0.288353 + 1.70788i) q^{12} +(-2.88829 + 0.252692i) q^{13} +(-2.04115 - 0.742919i) q^{14} +(3.87100 + 0.123992i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(1.92052 + 1.34476i) q^{17} +(-0.217968 + 2.99207i) q^{18} +(3.59309 + 2.46774i) q^{19} +(1.65514 + 1.50350i) q^{20} +(-3.64106 - 0.947290i) q^{21} +(2.59070 + 0.226657i) q^{22} +(-5.73853 - 2.67592i) q^{23} +(-1.21580 + 1.23362i) q^{24} +(2.83222 - 4.12050i) q^{25} +(-2.51089 - 1.44966i) q^{26} +(0.113370 + 5.19492i) q^{27} +(-1.24589 - 1.77932i) q^{28} +(-0.986495 + 5.59469i) q^{29} +(3.09982 + 2.32188i) q^{30} +(4.45573 - 7.71755i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(4.50425 - 0.0327612i) q^{33} +(0.801875 + 2.20313i) q^{34} +(-3.56673 + 3.29690i) q^{35} +(-1.89473 + 2.32594i) q^{36} +(-8.53429 - 8.53429i) q^{37} +(1.52785 + 4.08236i) q^{38} +(-4.56659 - 2.08913i) q^{39} +(0.493443 + 2.18094i) q^{40} +(-3.23906 - 3.86016i) q^{41} +(-2.43924 - 2.86440i) q^{42} +(7.06928 - 3.29646i) q^{43} +(1.99217 + 1.67163i) q^{44} +(5.72470 + 3.49683i) q^{45} +(-3.16588 - 5.48347i) q^{46} +(1.86125 + 2.65814i) q^{47} +(-1.70350 + 0.313166i) q^{48} +(-1.97607 + 1.14089i) q^{49} +(4.68344 - 1.75082i) q^{50} +(1.74291 + 3.66779i) q^{51} +(-1.22531 - 2.62768i) q^{52} +(-7.30907 - 3.40827i) q^{53} +(-2.88681 + 4.32045i) q^{54} +(3.10314 - 4.91793i) q^{55} -2.17215i q^{56} +(3.30197 + 6.78948i) q^{57} +(-4.01707 + 4.01707i) q^{58} +(-0.302793 - 1.71723i) q^{59} +(1.20745 + 3.67996i) q^{60} +(-6.68929 + 2.43470i) q^{61} +(8.07653 - 3.76615i) q^{62} +(-4.67436 - 4.54031i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-5.45260 + 3.50705i) q^{65} +(3.70845 + 2.55669i) q^{66} +(-1.51120 + 1.05816i) q^{67} +(-0.606808 + 2.26464i) q^{68} +(-6.35555 - 8.93761i) q^{69} +(-4.81272 + 0.654868i) q^{70} +(-4.61510 + 12.6799i) q^{71} +(-2.88618 + 0.818526i) q^{72} +(1.25518 - 14.3468i) q^{73} +(-2.09581 - 11.8859i) q^{74} +(7.78947 - 3.78472i) q^{75} +(-1.09001 + 4.22041i) q^{76} +(-3.99436 + 3.99436i) q^{77} +(-2.54245 - 4.33060i) q^{78} +(7.19735 + 8.57747i) q^{79} +(-0.846732 + 2.06955i) q^{80} +(-4.27137 + 7.92183i) q^{81} +(-0.439185 - 5.01990i) q^{82} +(6.93717 - 1.85881i) q^{83} +(-0.355155 - 3.74547i) q^{84} +(5.20059 + 0.661722i) q^{85} +(7.68159 + 1.35447i) q^{86} +(-6.26990 + 7.58351i) q^{87} +(0.673084 + 2.51198i) q^{88} +(0.349266 + 0.293069i) q^{89} +(2.68370 + 6.14799i) q^{90} +(5.91796 - 2.15396i) q^{91} +(0.551850 - 6.30767i) q^{92} +(13.3107 - 7.81457i) q^{93} +3.24499i q^{94} +(9.67958 + 1.14269i) q^{95} +(-1.57505 - 0.720560i) q^{96} +(-1.74306 + 2.48935i) q^{97} +(-2.27309 - 0.198869i) q^{98} +(6.81258 + 3.80220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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