LMFDB - Embedded newform 570.2.bi.a.557.22

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			557.22
Character	$\chi$	$=$	570.557
Dual form			570.2.bi.a.263.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 - 0.996195i) q^{2} +(-1.71062 + 0.271617i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.70877 + 1.44225i) q^{5} +(0.121493 + 1.72778i) q^{6} +(-3.51350 + 0.941441i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.85245 - 0.929267i) q^{9} +O(q^{10})$	\(q+(0.0871557 - 0.996195i) q^{2} +(-1.71062 + 0.271617i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.70877 + 1.44225i) q^{5} +(0.121493 + 1.72778i) q^{6} +(-3.51350 + 0.941441i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.85245 - 0.929267i) q^{9} +(1.28784 + 1.82797i) q^{10} +(1.29408 - 0.747136i) q^{11} +(1.73180 + 0.0295558i) q^{12} +(1.36985 - 2.93764i) q^{13} +(0.631636 + 3.58219i) q^{14} +(2.53132 - 2.93128i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.302375 + 3.45616i) q^{17} +(-0.677124 - 2.92259i) q^{18} +(2.58276 - 3.51132i) q^{19} +(1.93326 - 1.12362i) q^{20} +(5.75456 - 2.56478i) q^{21} +(-0.631507 - 1.35427i) q^{22} +(3.19035 - 2.23391i) q^{23} +(0.180380 - 1.72263i) q^{24} +(0.839814 - 4.92897i) q^{25} +(-2.80707 - 1.62067i) q^{26} +(-4.62705 + 2.36440i) q^{27} +(3.62361 - 0.317024i) q^{28} +(3.57713 + 3.00157i) q^{29} +(-2.69951 - 2.77717i) q^{30} +(4.43573 - 7.68290i) q^{31} +(0.422618 - 0.906308i) q^{32} +(-2.01074 + 1.62956i) q^{33} +(3.41666 + 0.602449i) q^{34} +(4.64599 - 6.67607i) q^{35} +(-2.97048 + 0.419827i) q^{36} +(5.15462 + 5.15462i) q^{37} +(-3.27285 - 2.87896i) q^{38} +(-1.54537 + 5.39727i) q^{39} +(-0.950846 - 2.02383i) q^{40} +(-1.28662 + 3.53495i) q^{41} +(-2.05347 - 5.95620i) q^{42} +(-2.95931 - 2.07213i) q^{43} +(-1.40416 + 0.511071i) q^{44} +(-3.53395 + 5.70186i) q^{45} +(-1.94735 - 3.37291i) q^{46} +(-5.46752 + 0.478346i) q^{47} +(-1.70036 - 0.329830i) q^{48} +(5.39623 - 3.11551i) q^{49} +(-4.83702 - 1.26621i) q^{50} +(-0.421503 - 5.99432i) q^{51} +(-1.85915 + 2.65514i) q^{52} +(8.38937 - 5.87430i) q^{53} +(1.95213 + 4.81552i) q^{54} +(-1.13373 + 3.14307i) q^{55} -3.63745i q^{56} +(-3.46439 + 6.70805i) q^{57} +(3.30191 - 3.30191i) q^{58} +(-7.15446 + 6.00331i) q^{59} +(-3.00188 + 2.44719i) q^{60} +(-0.00426072 + 0.0241638i) q^{61} +(-7.26707 - 5.08846i) q^{62} +(-9.14724 + 5.95039i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(1.89607 + 6.99543i) q^{65} +(1.44811 + 2.14512i) q^{66} +(-0.0962128 - 1.09972i) q^{67} +(0.897938 - 3.35115i) q^{68} +(-4.85071 + 4.68792i) q^{69} +(-6.24574 - 5.21017i) q^{70} +(5.99409 - 1.05692i) q^{71} +(0.159335 + 2.99577i) q^{72} +(6.61286 - 3.08363i) q^{73} +(5.58426 - 4.68575i) q^{74} +(-0.0978130 + 8.65970i) q^{75} +(-3.15326 + 3.00948i) q^{76} +(-3.84336 + 3.84336i) q^{77} +(5.24204 + 2.00990i) q^{78} +(5.00093 - 13.7399i) q^{79} +(-2.09900 + 0.770839i) q^{80} +(7.27293 - 5.30137i) q^{81} +(3.40937 + 1.58981i) q^{82} +(12.3490 - 3.30890i) q^{83} +(-6.11251 + 1.52654i) q^{84} +(-4.46797 - 6.34190i) q^{85} +(-2.32217 + 2.76745i) q^{86} +(-6.93439 - 4.16294i) q^{87} +(0.386746 + 1.44336i) q^{88} +(9.69825 - 3.52987i) q^{89} +(5.37216 + 4.01745i) q^{90} +(-2.04734 + 11.6111i) q^{91} +(-3.52979 + 1.64597i) q^{92} +(-5.50104 + 14.3474i) q^{93} +5.48841i q^{94} +(0.650852 + 9.72504i) q^{95} +(-0.476771 + 1.66514i) q^{96} +(-1.56748 - 0.137137i) q^{97} +(-2.63334 - 5.64723i) q^{98} +(2.99700 - 3.33371i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$	−1.71062	+	0.271617i	−0.987628	+	0.156818i
$3$	−1.71062	+	0.271617i	−0.987628	+	0.156818i
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	−1.70877	+	1.44225i	−0.764187	+	0.644995i
$5$	−1.70877	+	1.44225i	−0.764187	+	0.644995i
$6$	0.121493	+	1.72778i	0.0495992	+	0.705365i
$7$	−3.51350	+	0.941441i	−1.32798	+	0.355831i	−0.851962	−	0.523604i	$-0.824587\pi$
$7$	−3.51350	+	0.941441i	−1.32798	+	0.355831i	−0.476018	+	0.879435i	$0.657920\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	2.85245	−	0.929267i	0.950816	−	0.309756i
$10$	1.28784	+	1.82797i	0.407249	+	0.578055i
$11$	1.29408	−	0.747136i	0.390179	−	0.225270i	−0.292059	−	0.956400i	$-0.594340\pi$
$11$	1.29408	−	0.747136i	0.390179	−	0.225270i	0.682238	+	0.731130i	$0.261007\pi$
$12$	1.73180	+	0.0295558i	0.499927	+	0.00853204i
$13$	1.36985	−	2.93764i	0.379927	−	0.814756i	−0.619627	−	0.784896i	$-0.712716\pi$
$13$	1.36985	−	2.93764i	0.379927	−	0.814756i	0.999554	−	0.0298594i	$-0.00950597\pi$
$14$	0.631636	+	3.58219i	0.168812	+	0.957380i
$15$	2.53132	−	2.93128i	0.653585	−	0.756853i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.302375	+	3.45616i	−0.0733368	+	0.838243i	0.867069	+	0.498188i	$0.166001\pi$
$17$	−0.302375	+	3.45616i	−0.0733368	+	0.838243i	−0.940406	+	0.340055i	$0.889554\pi$
$18$	−0.677124	−	2.92259i	−0.159600	−	0.688860i
$19$	2.58276	−	3.51132i	0.592526	−	0.805551i
$19$	2.58276	−	3.51132i	0.592526	−	0.805551i
$20$	1.93326	−	1.12362i	0.432290	−	0.251248i
$21$	5.75456	−	2.56478i	1.25575	−	0.559680i
$22$	−0.631507	−	1.35427i	−0.134638	−	0.288731i
$23$	3.19035	−	2.23391i	0.665234	−	0.465802i	−0.191546	−	0.981484i	$-0.561350\pi$
$23$	3.19035	−	2.23391i	0.665234	−	0.465802i	0.856780	+	0.515682i	$0.172461\pi$
$24$	0.180380	−	1.72263i	0.0368198	−	0.351631i
$25$	0.839814	−	4.92897i	0.167963	−	0.985793i
$26$	−2.80707	−	1.62067i	−0.550513	−	0.317839i
$27$	−4.62705	+	2.36440i	−0.890477	+	0.455028i
$28$	3.62361	−	0.317024i	0.684797	−	0.0599120i
$29$	3.57713	+	3.00157i	0.664256	+	0.557377i	0.911359	−	0.411612i	$-0.135034\pi$
$29$	3.57713	+	3.00157i	0.664256	+	0.557377i	−0.247103	+	0.968989i	$0.579479\pi$
$30$	−2.69951	−	2.77717i	−0.492860	−	0.507039i
$31$	4.43573	−	7.68290i	0.796680	−	1.37989i	−0.125087	−	0.992146i	$-0.539921\pi$
$31$	4.43573	−	7.68290i	0.796680	−	1.37989i	0.921767	−	0.387744i	$-0.126746\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$	−2.01074	+	1.62956i	−0.350025	+	0.283670i
$34$	3.41666	+	0.602449i	0.585952	+	0.103319i
$35$	4.64599	−	6.67607i	0.785315	−	1.12846i
$36$	−2.97048	+	0.419827i	−0.495080	+	0.0699711i
$37$	5.15462	+	5.15462i	0.847415	+	0.847415i	0.989810	−	0.142395i	$-0.0454804\pi$
$37$	5.15462	+	5.15462i	0.847415	+	0.847415i	−0.142395	+	0.989810i	$0.545480\pi$
$38$	−3.27285	−	2.87896i	−0.530927	−	0.467030i
$39$	−1.54537	+	5.39727i	−0.247458	+	0.864254i
$40$	−0.950846	−	2.02383i	−0.150342	−	0.319996i
$41$	−1.28662	+	3.53495i	−0.200936	+	0.552067i	−0.998704	−	0.0508976i	$-0.983792\pi$
$41$	−1.28662	+	3.53495i	−0.200936	+	0.552067i	0.797768	+	0.602965i	$0.206014\pi$
$42$	−2.05347	−	5.95620i	−0.316858	−	0.919062i
$43$	−2.95931	−	2.07213i	−0.451290	−	0.315997i	0.325741	−	0.945459i	$-0.394386\pi$
$43$	−2.95931	−	2.07213i	−0.451290	−	0.315997i	−0.777031	+	0.629462i	$0.783275\pi$
$44$	−1.40416	+	0.511071i	−0.211685	+	0.0770469i
$45$	−3.53395	+	5.70186i	−0.526810	+	0.849983i
$46$	−1.94735	−	3.37291i	−0.287121	−	0.497308i
$47$	−5.46752	+	0.478346i	−0.797520	+	0.0697740i	−0.478629	−	0.878017i	$-0.658866\pi$
$47$	−5.46752	+	0.478346i	−0.797520	+	0.0697740i	−0.318891	+	0.947791i	$0.603311\pi$
$48$	−1.70036	−	0.329830i	−0.245425	−	0.0476069i
$49$	5.39623	−	3.11551i	0.770889	−	0.445073i
$50$	−4.83702	−	1.26621i	−0.684057	−	0.179069i
$51$	−0.421503	−	5.99432i	−0.0590222	−	0.839372i
$52$	−1.85915	+	2.65514i	−0.257818	+	0.368202i
$53$	8.38937	−	5.87430i	1.15237	−	0.806897i	0.168484	−	0.985704i	$-0.446113\pi$
$53$	8.38937	−	5.87430i	1.15237	−	0.806897i	0.983884	+	0.178807i	$0.0572239\pi$
$54$	1.95213	+	4.81552i	0.265651	+	0.655309i
$55$	−1.13373	+	3.14307i	−0.152872	+	0.423812i
$56$		−	3.63745i		−	0.486074i
$57$	−3.46439	+	6.70805i	−0.458870	+	0.888503i
$58$	3.30191	−	3.30191i	0.433563	−	0.433563i
$59$	−7.15446	+	6.00331i	−0.931432	+	0.781564i	−0.976074	−	0.217439i	$-0.930230\pi$
$59$	−7.15446	+	6.00331i	−0.931432	+	0.781564i	0.0446422	+	0.999003i	$0.485785\pi$
$60$	−3.00188	+	2.44719i	−0.387541	+	0.315930i
$61$	−0.00426072	+	0.0241638i	−0.000545530	+	0.00309385i	−0.985079	−	0.172101i	$-0.944944\pi$
$61$	−0.00426072	+	0.0241638i	−0.000545530	+	0.00309385i	0.984534	+	0.175195i	$0.0560556\pi$
$62$	−7.26707	−	5.08846i	−0.922919	−	0.646235i
$63$	−9.14724	+	5.95039i	−1.15244	+	0.749679i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	1.89607	+	6.99543i	0.235178	+	0.867676i
$66$	1.44811	+	2.14512i	0.178250	+	0.264045i
$67$	−0.0962128	−	1.09972i	−0.0117543	−	0.134352i	0.988050	−	0.154133i	$-0.0492585\pi$
$67$	−0.0962128	−	1.09972i	−0.0117543	−	0.134352i	−0.999804	+	0.0197815i	$0.993703\pi$
$68$	0.897938	−	3.35115i	0.108891	−	0.406387i
$69$	−4.85071	+	4.68792i	−0.583957	+	0.564359i
$70$	−6.24574	−	5.21017i	−0.746509	−	0.622734i
$71$	5.99409	−	1.05692i	0.711367	−	0.125433i	0.193757	−	0.981050i	$-0.437933\pi$
$71$	5.99409	−	1.05692i	0.711367	−	0.125433i	0.517611	+	0.855616i	$0.326822\pi$
$72$	0.159335	+	2.99577i	0.0187778	+	0.353054i
$73$	6.61286	−	3.08363i	0.773977	−	0.360911i	0.00483407	−	0.999988i	$-0.498461\pi$
$73$	6.61286	−	3.08363i	0.773977	−	0.360911i	0.769143	+	0.639077i	$0.220683\pi$
$74$	5.58426	−	4.68575i	0.649157	−	0.544708i
$75$	−0.0978130	+	8.65970i	−0.0112945	+	0.999936i
$76$	−3.15326	+	3.00948i	−0.361703	+	0.345211i
$77$	−3.84336	+	3.84336i	−0.437992	+	0.437992i
$78$	5.24204	+	2.00990i	0.593544	+	0.227576i
$79$	5.00093	−	13.7399i	0.562649	−	1.54586i	−0.253090	−	0.967443i	$-0.581447\pi$
$79$	5.00093	−	13.7399i	0.562649	−	1.54586i	0.815738	−	0.578421i	$-0.196331\pi$
$80$	−2.09900	+	0.770839i	−0.234675	+	0.0861825i
$81$	7.27293	−	5.30137i	0.808103	−	0.589041i
$82$	3.40937	+	1.58981i	0.376502	+	0.175566i
$83$	12.3490	−	3.30890i	1.35548	−	0.363199i	0.493323	−	0.869846i	$-0.335782\pi$
$83$	12.3490	−	3.30890i	1.35548	−	0.363199i	0.862153	+	0.506647i	$0.169115\pi$
$84$	−6.11251	+	1.52654i	−0.666929	+	0.166559i
$85$	−4.46797	−	6.34190i	−0.484620	−	0.687876i
$86$	−2.32217	+	2.76745i	−0.250406	+	0.298422i
$87$	−6.93439	−	4.16294i	−0.743445	−	0.446314i
$88$	0.386746	+	1.44336i	0.0412273	+	0.153862i
$89$	9.69825	−	3.52987i	1.02801	−	0.374166i	0.227689	−	0.973734i	$-0.426883\pi$
$89$	9.69825	−	3.52987i	1.02801	−	0.374166i	0.800324	+	0.599568i	$0.204661\pi$
$90$	5.37216	+	4.01745i	0.566275	+	0.423477i
$91$	−2.04734	+	11.6111i	−0.214620	+	1.21717i
$92$	−3.52979	+	1.64597i	−0.368007	+	0.171604i
$93$	−5.50104	+	14.3474i	−0.570431	+	1.48775i
$94$			5.48841i			0.566086i
$95$	0.650852	+	9.72504i	0.0667760	+	0.997768i
$96$	−0.476771	+	1.66514i	−0.0486603	+	0.169948i
$97$	−1.56748	−	0.137137i	−0.159154	−	0.0139242i	0.00730024	−	0.999973i	$-0.497676\pi$
$97$	−1.56748	−	0.137137i	−0.159154	−	0.0139242i	−0.166454	+	0.986049i	$0.553232\pi$
$98$	−2.63334	−	5.64723i	−0.266008	−	0.570456i
$99$	2.99700	−	3.33371i	0.301210	−	0.335051i
$100$	−1.68296	+	4.70825i	−0.168296	+	0.470825i
$101$	−2.13927	−	5.87758i	−0.212865	−	0.584841i	0.786603	−	0.617459i	$-0.211838\pi$
$101$	−2.13927	−	5.87758i	−0.212865	−	0.584841i	−0.999468	+	0.0326176i	$0.989616\pi$
$102$	−6.00824	−	0.102540i	−0.594905	−	0.0101530i
$103$	−16.9707	−	4.54728i	−1.67217	−	0.448057i	−0.706475	−	0.707738i	$-0.749716\pi$
$103$	−16.9707	−	4.54728i	−1.67217	−	0.448057i	−0.965694	+	0.259681i	$0.916383\pi$
$104$	2.48300	+	2.08349i	0.243478	+	0.204303i
$105$	−6.13419	+	12.6822i	−0.598636	+	1.23765i
$106$	−5.12076	−	8.86942i	−0.497373	−	0.861474i
$107$	4.75092	+	17.7307i	0.459289	+	1.71409i	0.675163	+	0.737669i	$0.264073\pi$
$107$	4.75092	+	17.7307i	0.459289	+	1.71409i	−0.215874	+	0.976421i	$0.569260\pi$
$108$	4.96733	−	1.52500i	0.477982	−	0.146743i
$109$	−1.32656	+	0.233909i	−0.127062	+	0.0224044i	−0.236817	−	0.971554i	$-0.576104\pi$
$109$	−1.32656	+	0.233909i	−0.127062	+	0.0224044i	0.109756	+	0.993959i	$0.464993\pi$
$110$	3.03230	+	1.40335i	0.289119	+	0.133804i
$111$	−10.2177	−	7.41752i	−0.969820	−	0.704040i
$112$	−3.62361	−	0.317024i	−0.342399	−	0.0299560i
$113$	8.48059	+	8.48059i	0.797787	+	0.797787i	0.982746	−	0.184959i	$-0.0592153\pi$
$113$	8.48059	+	8.48059i	0.797787	+	0.797787i	−0.184959	+	0.982746i	$0.559215\pi$
$114$	6.38059	+	4.03586i	0.597597	+	0.377992i
$115$	−2.22973	+	8.41853i	−0.207923	+	0.785032i
$116$	−3.00157	−	3.57713i	−0.278689	−	0.332128i
$117$	1.17756	−	9.65243i	0.108865	−	0.892367i
$118$	5.35691	+	7.65046i	0.493144	+	0.704282i
$119$	−2.19138	−	12.4279i	−0.200883	−	1.13927i
$120$	2.17624	+	3.20374i	0.198663	+	0.292460i
$121$	−4.38358	+	7.59258i	−0.398507	+	0.690234i
$122$	0.0237005	+	0.00635052i	0.00214574	+	0.000574949i
$123$	1.24076	−	6.39643i	0.111876	−	0.576747i
$124$	−5.70246	+	6.79593i	−0.512096	+	0.610292i
$125$	5.67376	+	9.63371i	0.507477	+	0.861665i
$126$	5.13052	+	9.63104i	0.457063	+	0.858002i
$127$	−5.36453	−	2.50152i	−0.476025	−	0.221974i	0.169772	−	0.985483i	$-0.445697\pi$
$127$	−5.36453	−	2.50152i	−0.476025	−	0.221974i	−0.645797	+	0.763509i	$0.723475\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$	5.62508	+	2.74083i	0.495261	+	0.241317i
$130$	7.13406	−	1.27916i	0.625699	−	0.112190i
$131$	5.34423	+	6.36900i	0.466927	+	0.556462i	0.947194	−	0.320660i	$-0.103905\pi$
$131$	5.34423	+	6.36900i	0.466927	+	0.556462i	−0.480267	+	0.877122i	$0.659460\pi$
$132$	2.26316	−	1.25564i	0.196983	−	0.109290i
$133$	−5.76885	+	14.7685i	−0.500222	+	1.28060i
$134$	−1.10392			−0.0953639
$135$	4.49653	−	10.7136i	0.387000	−	0.922080i
$136$	−3.26014	−	1.18659i	−0.279555	−	0.101750i
$137$	−10.1342	−	14.4731i	−0.865824	−	1.23652i	−0.970278	−	0.241995i	$-0.922198\pi$
$137$	−10.1342	−	14.4731i	−0.865824	−	1.23652i	0.104454	−	0.994530i	$-0.466691\pi$
$138$	4.24731	+	5.24083i	0.361555	+	0.446129i
$139$	−0.674859	−	1.85416i	−0.0572408	−	0.157268i	0.907776	−	0.419454i	$-0.137779\pi$
$139$	−0.674859	−	1.85416i	−0.0572408	−	0.157268i	−0.965017	+	0.262187i	$0.915556\pi$
$140$	−5.73469	+	5.76788i	−0.484670	+	0.487475i
$141$	9.22294	−	2.30334i	0.776711	−	0.193976i
$142$	−0.530478	−	6.06339i	−0.0445168	−	0.508829i
$143$	−0.422133	−	4.82500i	−0.0353005	−	0.403487i
$144$	2.99825	+	0.102370i	0.249854	+	0.00853080i
$145$	−10.4415	+	0.0301249i	−0.867122	+	0.00250173i
$146$	−2.49554	−	6.85645i	−0.206533	−	0.567444i
$147$	−8.38467	+	6.79517i	−0.691556	+	0.560456i
$148$	−4.18122	−	5.97140i	−0.343694	−	0.490846i
$149$	2.59564	+	0.944737i	0.212643	+	0.0773959i	0.446146	−	0.894960i	$-0.352796\pi$
$149$	2.59564	+	0.944737i	0.212643	+	0.0773959i	−0.233502	+	0.972356i	$0.575019\pi$
$150$	8.61822	+	0.852184i	0.703675	+	0.0695805i
$151$	12.4673			1.01457			0.507287	−	0.861777i	$-0.330649\pi$
$151$	12.4673			1.01457			0.507287	+	0.861777i	$0.330649\pi$
$152$	2.72320	+	3.40355i	0.220881	+	0.276064i
$153$	2.34919	+	10.1395i	0.189921	+	0.819732i
$154$	3.49377	+	4.16371i	0.281536	+	0.335521i
$155$	3.50104	+	19.5258i	0.281210	+	1.56835i
$156$	2.45912	−	5.04692i	0.196887	−	0.404077i
$157$	12.8685	−	18.3782i	1.02702	−	1.46674i	0.148573	−	0.988901i	$-0.452532\pi$
$157$	12.8685	−	18.3782i	1.02702	−	1.46674i	0.878449	−	0.477837i	$-0.158579\pi$
$158$	−13.2518	−	6.17941i	−1.05426	−	0.491608i
$159$	−12.7555	+	12.3274i	−1.01157	+	0.977626i
$160$	0.584966	+	2.15820i	0.0462456	+	0.170620i
$161$	−9.10622	+	10.8524i	−0.717670	+	0.855286i
$162$	−4.64732	−	7.70730i	−0.365128	−	0.605542i
$163$	5.66624	+	1.51826i	0.443814	+	0.118920i	0.473803	−	0.880631i	$-0.342881\pi$
$163$	5.66624	+	1.51826i	0.443814	+	0.118920i	−0.0299895	+	0.999550i	$0.509547\pi$
$164$	1.88091	−	3.25783i	0.146874	−	0.254394i
$165$	1.08566	−	5.68455i	0.0845189	−	0.442541i
$166$	−2.22002	−	12.5904i	−0.172307	−	0.977203i
$167$	−9.79103	−	13.9830i	−0.757653	−	1.08204i	−0.993893	−	0.110346i	$-0.964804\pi$
$167$	−9.79103	−	13.9830i	−0.757653	−	1.08204i	0.236240	−	0.971695i	$-0.424085\pi$
$168$	0.987992	+	6.22229i	0.0762252	+	0.480060i
$169$	1.60297	+	1.91034i	0.123305	+	0.146950i
$170$	−6.70718	+	3.89824i	−0.514417	+	0.298981i
$171$	4.10424	−	12.4159i	0.313859	−	0.949470i
$172$	2.55453	+	2.55453i	0.194781	+	0.194781i
$173$	−11.0016	−	0.962515i	−0.836436	−	0.0731787i	−0.339115	−	0.940745i	$-0.610127\pi$
$173$	−11.0016	−	0.962515i	−0.836436	−	0.0731787i	−0.497321	+	0.867566i	$0.665683\pi$
$174$	−4.75147	+	6.54518i	−0.360208	+	0.496189i
$175$	1.68964	+	18.1086i	0.127725	+	1.36888i
$176$	1.47157	−	0.259478i	0.110924	−	0.0195589i
$177$	10.6080	−	12.2127i	0.797344	−	0.917959i
$178$	−2.67118	−	9.96900i	−0.200214	−	0.747208i
$179$	1.95063	+	3.37858i	0.145797	+	0.252527i	0.929670	−	0.368394i	$-0.120092\pi$
$179$	1.95063	+	3.37858i	0.145797	+	0.252527i	−0.783873	+	0.620921i	$0.786759\pi$
$180$	4.47038	−	5.00157i	0.333202	−	0.372795i
$181$	7.17674	+	6.02200i	0.533443	+	0.447612i	0.869288	−	0.494305i	$-0.164577\pi$
$181$	7.17674	+	6.02200i	0.533443	+	0.447612i	−0.335845	+	0.941917i	$0.609022\pi$
$182$	11.3884	+	3.05152i	0.844167	+	0.226194i
$183$	0.000725198	−	0.0424923i	5.36082e−5	−	0.00314112i
$184$	1.33206	+	3.65982i	0.0982011	+	0.269805i
$185$	−16.2423	−	1.37381i	−1.19416	−	0.101005i
$186$	13.8133	+	6.73056i	1.01284	+	0.493509i
$187$	2.19093	+	4.69846i	0.160217	+	0.343585i
$188$	5.46752	+	0.478346i	0.398760	+	0.0348870i
$189$	14.0312	−	12.6634i	1.02062	−	0.921128i
$190$	9.74476	+	0.199218i	0.706959	+	0.0144528i
$191$		−	15.4503i		−	1.11794i	−0.829186	−	0.558972i	$-0.811196\pi$
$191$		−	15.4503i		−	1.11794i	0.829186	−	0.558972i	$-0.188804\pi$
$192$	1.61725	+	0.620083i	0.116715	+	0.0447507i
$193$	15.5477	−	7.25000i	1.11915	−	0.521866i	0.227127	−	0.973865i	$-0.427067\pi$
$193$	15.5477	−	7.25000i	1.11915	−	0.521866i	0.892019	+	0.451999i	$0.149289\pi$
$194$	−0.273231	+	1.54957i	−0.0196168	+	0.111252i
$195$	−5.14353	−	11.4515i	−0.368336	−	0.820061i
$196$	−5.85525	+	2.13114i	−0.418232	+	0.152224i
$197$	−2.85675	−	10.6615i	−0.203535	−	0.759602i	−0.989891	−	0.141829i	$-0.954702\pi$
$197$	−2.85675	−	10.6615i	−0.203535	−	0.759602i	0.786356	−	0.617773i	$-0.211965\pi$
$198$	−3.05982	−	3.27615i	−0.217452	−	0.232826i
$199$	−0.455930	+	0.543356i	−0.0323200	+	0.0385175i	−0.781962	−	0.623326i	$-0.785781\pi$
$199$	−0.455930	+	0.543356i	−0.0323200	+	0.0385175i	0.749642	+	0.661843i	$0.230226\pi$
$200$	4.54366	+	2.08691i	0.321285	+	0.147567i
$201$	0.463285	+	1.85507i	0.0326776	+	0.130846i
$202$	−6.04167	+	1.61886i	−0.425090	+	0.113903i
$203$	−15.3941	−	7.17837i	−1.08045	−	0.503823i
$204$	−0.625803	+	5.97644i	−0.0438150	+	0.418435i
$205$	−2.89976	−	7.89606i	−0.202528	−	0.551485i
$206$	−6.00906	+	16.5098i	−0.418671	+	1.15029i
$207$	7.02441	−	9.33679i	0.488230	−	0.648952i
$208$	2.29197	−	2.29197i	0.158919	−	0.158919i
$209$	0.718862	−	6.47359i	0.0497247	−	0.447788i
$210$	12.0993	+	7.21617i	0.834929	+	0.497963i
$211$	2.45548	−	2.06040i	0.169042	−	0.141843i	−0.554342	−	0.832289i	$-0.687030\pi$
$211$	2.45548	−	2.06040i	0.169042	−	0.141843i	0.723384	+	0.690446i	$0.242586\pi$
$212$	−9.28198	+	4.32826i	−0.637489	+	0.297266i
$213$	−9.96654	+	3.43608i	−0.682896	+	0.235437i
$214$	18.0773	−	3.18751i	1.23574	−	0.217894i
$215$	8.04532	−	0.727270i	0.548686	−	0.0495994i
$216$	−1.08626	−	5.08134i	−0.0739108	−	0.345742i
$217$	−8.35195	+	31.1699i	−0.566967	+	2.11595i
$218$	0.117401	+	1.34190i	0.00795142	+	0.0908851i
$219$	−10.4745	+	7.07108i	−0.707803	+	0.477820i
$220$	1.66229	−	2.89845i	0.112072	−	0.195414i
$221$	9.73877	+	5.62268i	0.655101	+	0.378223i
$222$	−8.27983	+	9.53233i	−0.555706	+	0.639768i
$223$	−11.9161	−	8.34373i	−0.797959	−	0.558737i	0.101963	−	0.994788i	$-0.467488\pi$
$223$	−11.9161	−	8.34373i	−0.797959	−	0.558737i	−0.899922	+	0.436051i	$0.856377\pi$
$224$	−0.631636	+	3.58219i	−0.0422030	+	0.239345i
$225$	−2.18480	−	14.8400i	−0.145653	−	0.989336i
$226$	9.18745	−	7.70919i	0.611140	−	0.512808i
$227$	0.603767	−	0.603767i	0.0400734	−	0.0400734i	−0.686786	−	0.726860i	$-0.740979\pi$
$227$	0.603767	−	0.603767i	0.0400734	−	0.0400734i	0.726860	+	0.686786i	$0.240979\pi$
$228$	4.57660	−	6.00456i	0.303093	−	0.397662i
$229$			18.9512i			1.25233i	0.779689	+	0.626167i	$0.215377\pi$
$229$			18.9512i			1.25233i	−0.779689	+	0.626167i	$0.784623\pi$
$230$	8.19216	+	2.95496i	0.540175	+	0.194845i
$231$	5.53062	−	7.61846i	0.363888	−	0.501258i
$232$	−3.82512	+	2.67838i	−0.251132	+	0.175844i
$233$	7.48734	−	10.6930i	0.490512	−	0.700524i	−0.495235	−	0.868759i	$-0.664918\pi$
$233$	7.48734	−	10.6930i	0.490512	−	0.700524i	0.985747	+	0.168235i	$0.0538068\pi$
$234$	−9.51307	−	2.01434i	−0.621889	−	0.131682i
$235$	8.65286	−	8.70294i	0.564451	−	0.567717i
$236$	8.08823	−	4.66974i	0.526499	−	0.303974i
$237$	−4.82270	+	24.8622i	−0.313268	+	1.61497i
$238$	−12.5716	+	1.09987i	−0.814897	+	0.0712942i
$239$	−5.56236	−	9.63428i	−0.359799	−	0.623190i	0.628128	−	0.778110i	$-0.283821\pi$
$239$	−5.56236	−	9.63428i	−0.359799	−	0.623190i	−0.987927	+	0.154920i	$0.950488\pi$
$240$	3.38122	−	1.88874i	0.218257	−	0.121918i
$241$	−18.5334	+	6.74561i	−1.19384	+	0.434523i	−0.861071	−	0.508484i	$-0.830206\pi$
$241$	−18.5334	+	6.74561i	−1.19384	+	0.434523i	−0.332771	+	0.943008i	$0.607984\pi$
$242$	7.18163	+	5.02863i	0.461653	+	0.323253i
$243$	−11.0013	+	11.0441i	−0.705732	+	0.708479i
$244$	0.00839199	−	0.0230568i	0.000537242	−	0.00147606i
$245$	−4.72757	+	13.1064i	−0.302033	+	0.837339i
$246$	−6.26395	−	1.79353i	−0.399375	−	0.114351i
$247$	−6.77701	−	12.3972i	−0.431211	−	0.788814i
$248$	6.27306	+	6.27306i	0.398340	+	0.398340i
$249$	−20.2257	+	9.01446i	−1.28175	+	0.571268i
$250$	10.0916	−	4.81254i	0.638246	−	0.304372i
$251$	7.86219	+	1.38632i	0.496257	+	0.0875035i	0.416175	−	0.909285i	$-0.363370\pi$
$251$	7.86219	+	1.38632i	0.496257	+	0.0875035i	0.0800826	+	0.996788i	$0.474482\pi$
$252$	10.0415	−	4.27159i	0.632558	−	0.269085i
$253$	2.45953	−	5.27447i	0.154629	−	0.331603i
$254$	−2.95955	+	5.12609i	−0.185699	+	0.321640i
$255$	9.36558	+	9.63502i	0.586495	+	0.603368i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	25.6562	−	2.24463i	1.60039	−	0.140016i	0.748281	−	0.663382i	$-0.230879\pi$
$257$	25.6562	−	2.24463i	1.60039	−	0.140016i	0.852108	+	0.523366i	$0.175324\pi$
$258$	3.22066	−	5.36480i	0.200509	−	0.333998i
$259$	−22.9636	−	13.2580i	−1.42689	−	0.823813i
$260$	−0.652519	−	7.21840i	−0.0404675	−	0.447666i
$261$	12.9928	+	5.23771i	0.804237	+	0.324206i
$262$	6.81055	−	4.76880i	0.420757	−	0.294617i
$263$	−11.2736	−	24.1763i	−0.695161	−	1.49078i	−0.863128	−	0.504985i	$-0.831498\pi$
$263$	−11.2736	−	24.1763i	−0.695161	−	1.49078i	0.167967	−	0.985793i	$-0.446280\pi$
$264$	−1.05362	−	2.36399i	−0.0648456	−	0.145493i
$265$	−5.86331	+	22.1374i	−0.360180	+	1.35989i
$266$	14.2096	+	7.03406i	0.871244	+	0.431286i
$267$	−15.6313	+	8.67249i	−0.956618	+	0.530748i
$268$	−0.0962128	+	1.09972i	−0.00587713	+	0.0671759i
$269$	−29.8393	−	10.8606i	−1.81933	−	0.662183i	−0.995435	−	0.0954466i	$-0.969572\pi$
$269$	−29.8393	−	10.8606i	−1.81933	−	0.662183i	−0.823899	−	0.566737i	$-0.808206\pi$
$270$	−10.2809	−	5.41317i	−0.625678	−	0.329435i
$271$	0.100583	+	0.570433i	0.00610996	+	0.0346513i	0.987710	−	0.156296i	$-0.0499553\pi$
$271$	0.100583	+	0.570433i	0.00610996	+	0.0346513i	−0.981600	+	0.190947i	$0.938844\pi$
$272$	−1.46622	+	3.14431i	−0.0889025	+	0.190652i
$273$	0.348468	−	20.4182i	0.0210903	−	1.23577i
$274$	−15.3013	+	8.83423i	−0.924387	+	0.533695i
$275$	−2.59582	−	7.00592i	−0.156534	−	0.422473i
$276$	5.59107	−	3.77438i	0.336543	−	0.227191i
$277$	8.35751	−	31.1907i	0.502154	−	1.87407i	0.0165936	−	0.999862i	$-0.494718\pi$
$277$	8.35751	−	31.1907i	0.502154	−	1.87407i	0.485561	−	0.874203i	$-0.338615\pi$
$278$	−1.90592	+	0.510690i	−0.114310	+	0.0306292i
$279$	5.51321	−	26.0371i	0.330067	−	1.55880i
$280$	5.24612	+	6.21557i	0.313516	+	0.371452i
$281$	2.01999	+	0.356179i	0.120503	+	0.0212479i	0.233574	−	0.972339i	$-0.424958\pi$
$281$	2.01999	+	0.356179i	0.120503	+	0.0212479i	−0.113072	+	0.993587i	$0.536069\pi$
$282$	−1.49074	−	9.38859i	−0.0887725	−	0.559082i
$283$	0.362247	−	4.14050i	0.0215334	−	0.246127i	−0.977798	−	0.209552i	$-0.932799\pi$
$283$	0.362247	−	4.14050i	0.0215334	−	0.246127i	0.999331	−	0.0365756i	$-0.0116450\pi$
$284$	−6.08656			−0.361171
$285$	−3.75485	−	16.4591i	−0.222418	−	0.974951i
$286$	−4.84343			−0.286398
$287$	1.19259	−	13.6314i	0.0703963	−	0.804633i
$288$	0.363295	−	2.97792i	0.0214074	−	0.175476i
$289$	4.88809	+	0.861902i	0.287535	+	0.0507001i
$290$	−0.880029	+	10.4044i	−0.0516771	+	0.610969i
$291$	2.71862	−	0.191166i	0.159368	−	0.0112063i
$292$	−7.04786	+	1.88847i	−0.412445	+	0.110514i
$293$	−6.33646	+	23.6480i	−0.370180	+	1.38153i	0.490081	+	0.871677i	$0.336967\pi$
$293$	−6.33646	+	23.6480i	−0.370180	+	1.38153i	−0.860261	+	0.509853i	$0.829700\pi$
$294$	6.03854	+	8.94500i	0.352175	+	0.521683i
$295$	3.56707	−	20.5768i	0.207683	−	1.19803i
$296$	−6.31310	+	3.64487i	−0.366941	+	0.211854i
$297$	−4.22124	+	6.51675i	−0.244941	+	0.378140i
$298$	1.16737	−	2.50343i	0.0676238	−	0.145020i
$299$	−2.19213	−	12.4322i	−0.126774	−	0.718973i
$300$	1.60007	−	8.51116i	0.0923800	−	0.491392i
$301$	12.3483	+	4.49442i	0.711746	+	0.259054i
$302$	1.08660	−	12.4198i	0.0625266	−	0.714682i
$303$	5.25592	+	9.47326i	0.301945	+	0.544224i
$304$	3.62794	−	2.41620i	0.208077	−	0.138579i
$305$	−0.0275696	−	0.0474354i	−0.00157863	−	0.00271615i
$306$	10.3057	−	1.45653i	0.589137	−	0.0832645i
$307$	11.8162	+	25.3399i	0.674386	+	1.44623i	0.883546	+	0.468344i	$0.155149\pi$
$307$	11.8162	+	25.3399i	0.674386	+	1.44623i	−0.209160	+	0.977881i	$0.567073\pi$
$308$	4.45237	−	3.11758i	0.253697	−	0.177641i
$309$	30.2655	+	3.16915i	1.72174	+	0.180287i
$310$	19.7566	−	1.78593i	1.12210	−	0.101434i
$311$	−29.6444	−	17.1152i	−1.68098	−	0.970513i	−0.961014	−	0.276501i	$-0.910825\pi$
$311$	−29.6444	−	17.1152i	−1.68098	−	0.970513i	−0.719964	−	0.694012i	$-0.755842\pi$
$312$	−4.81339	−	2.88963i	−0.272504	−	0.163593i
$313$	1.10775	−	0.0969157i	0.0626138	−	0.00547800i	−0.0558058	−	0.998442i	$-0.517773\pi$
$313$	1.10775	−	0.0969157i	0.0626138	−	0.00547800i	0.118420	+	0.992964i	$0.462217\pi$
$314$	−17.1867	−	14.4213i	−0.969900	−	0.813843i
$315$	7.04859	−	23.3605i	0.397143	−	1.31622i
$316$	−7.31087	+	12.6628i	−0.411269	+	0.712338i
$317$	−14.3403	+	30.7528i	−0.805430	+	1.72725i	−0.127858	+	0.991792i	$0.540810\pi$
$317$	−14.3403	+	30.7528i	−0.805430	+	1.72725i	−0.677571	+	0.735457i	$0.736968\pi$
$318$	11.1688	+	13.7813i	0.626314	+	0.772819i
$319$	6.87166	+	1.21166i	0.384739	+	0.0678399i
$320$	2.20097	−	0.394641i	0.123038	−	0.0220611i
$321$	−12.9430	−	29.0401i	−0.722407	−	1.62086i
$322$	10.0174	+	10.0174i	0.558248	+	0.558248i
$323$	11.3547	+	9.98818i	0.631794	+	0.555757i
$324$	−8.08301	+	3.95790i	−0.449056	+	0.219883i
$325$	−13.3291	−	9.21900i	−0.739367	−	0.511378i
$326$	2.00633	−	5.51235i	0.111120	−	0.305301i
$327$	2.20572	−	0.760447i	0.121976	−	0.0420528i
$328$	−3.08150	−	2.15769i	−0.170147	−	0.119139i
$329$	18.7598	−	6.82802i	1.03426	−	0.376441i
$330$	−5.56829	−	1.57697i	−0.306524	−	0.0868096i
$331$	4.10578	+	7.11143i	0.225674	+	0.390879i	0.956522	−	0.291662i	$-0.0942082\pi$
$331$	4.10578	+	7.11143i	0.225674	+	0.390879i	−0.730847	+	0.682541i	$0.760875\pi$
$332$	−12.7360	+	1.11425i	−0.698976	+	0.0611525i
$333$	19.4933	+	9.91327i	1.06823	+	0.543244i
$334$	−14.7832	+	8.53507i	−0.808900	+	0.467018i
$335$	1.75048	+	1.74040i	0.0956387	+	0.0950884i
$336$	6.28473	−	0.441924i	0.342860	−	0.0241089i
$337$	5.75243	−	8.21532i	0.313355	−	0.447517i	−0.631322	−	0.775521i	$-0.717487\pi$
$337$	5.75243	−	8.21532i	0.313355	−	0.447517i	0.944676	+	0.328004i	$0.106376\pi$
$338$	2.04278	−	1.43037i	0.111113	−	0.0778020i
$339$	−16.8105	−	12.2036i	−0.913024	−	0.662809i
$340$	3.29883	+	7.02141i	0.178904	+	0.380790i
$341$		−	13.2564i		−	0.717872i
$342$	−12.0110	−	5.17074i	−0.649479	−	0.279602i
$343$	1.97785	−	1.97785i	0.106794	−	0.106794i
$344$	2.76745	−	2.32217i	0.149211	−	0.125203i
$345$	1.52760	−	15.0065i	0.0822433	−	0.807925i
$346$	−1.91771	+	10.8758i	−0.103096	+	0.584689i
$347$	6.27006	+	4.39035i	0.336595	+	0.235686i	0.729638	−	0.683834i	$-0.239689\pi$
$347$	6.27006	+	4.39035i	0.336595	+	0.235686i	−0.393043	+	0.919520i	$0.628578\pi$
$348$	6.10616	+	5.30384i	0.327324	+	0.284316i
$349$	−12.9502	−	7.47683i	−0.693211	−	0.400225i	0.111603	−	0.993753i	$-0.464401\pi$
$349$	−12.9502	−	7.47683i	−0.693211	−	0.400225i	−0.804814	+	0.593528i	$0.797735\pi$
$350$	18.1869	−	0.104943i	0.972133	−	0.00560945i
$351$	0.607405	+	16.8315i	0.0324209	+	0.898399i
$352$	−0.130234	−	1.48859i	−0.00694152	−	0.0793419i
$353$	4.19379	−	15.6514i	0.223213	−	0.833042i	−0.759900	−	0.650040i	$-0.774752\pi$
$353$	4.19379	−	15.6514i	0.223213	−	0.833042i	0.983113	−	0.183002i	$-0.0585814\pi$
$354$	−11.2416	−	11.6320i	−0.597486	−	0.618234i
$355$	−8.71819	+	10.4510i	−0.462714	+	0.554683i
$356$	−10.1639	+	1.79216i	−0.538684	+	0.0949845i
$357$	7.12425	+	20.6642i	0.377055	+	1.09367i
$358$	3.53574	−	1.64874i	0.186869	−	0.0871387i
$359$	3.20464	−	2.68902i	0.169135	−	0.141921i	−0.554291	−	0.832323i	$-0.687011\pi$
$359$	3.20464	−	2.68902i	0.169135	−	0.141921i	0.723426	+	0.690402i	$0.242566\pi$
$360$	−4.59292	−	4.88928i	−0.242068	−	0.257688i
$361$	−5.65869	−	18.1378i	−0.297826	−	0.954620i
$362$	6.62458	−	6.62458i	0.348180	−	0.348180i
$363$	5.43637	−	14.1787i	0.285335	−	0.744187i
$364$	4.03248	−	11.0791i	0.211359	−	0.580704i
$365$	−6.85251	+	14.8066i	−0.358677	+	0.775015i
$366$	−0.0422674	−	0.00442589i	−0.00220935	−	0.000231345i
$367$	25.3501	+	11.8210i	1.32327	+	0.617049i	0.950456	−	0.310858i	$-0.100616\pi$
$367$	25.3501	+	11.8210i	1.32327	+	0.617049i	0.372810	+	0.927908i	$0.378394\pi$
$368$	3.76199	−	1.00802i	0.196107	−	0.0525468i
$369$	−0.385096	+	11.2789i	−0.0200473	+	0.587155i
$370$	−2.78420	+	16.0608i	−0.144744	+	0.834962i
$371$	−23.9458	+	28.5375i	−1.24320	+	1.48159i
$372$	7.90886	−	13.1741i	0.410055	−	0.683047i
$373$	3.61782	+	13.5019i	0.187324	+	0.699101i	0.994121	+	0.108273i	$0.0345321\pi$
$373$	3.61782	+	13.5019i	0.187324	+	0.699101i	−0.806798	+	0.590828i	$0.798801\pi$
$374$	4.87153	−	1.77309i	0.251901	−	0.0916845i
$375$	−12.3223	−	14.9385i	−0.636323	−	0.771423i
$376$	0.953052	−	5.40503i	0.0491499	−	0.278743i
$377$	13.7177	−	6.39665i	0.706495	−	0.329444i
$378$	−11.3923	−	15.0815i	−0.585958	−	0.775710i
$379$			18.1240i			0.930966i	0.885057	+	0.465483i	$0.154119\pi$
$379$			18.1240i			0.930966i	−0.885057	+	0.465483i	$0.845881\pi$
$380$	1.04777	−	9.69031i	0.0537495	−	0.497103i
$381$	9.85613	+	2.82206i	0.504945	+	0.144578i
$382$	−15.3915	−	1.34658i	−0.787498	−	0.0688972i
$383$	14.4178	+	30.9190i	0.736714	+	1.57989i	0.812634	+	0.582774i	$0.198033\pi$
$383$	14.4178	+	30.9190i	0.736714	+	1.57989i	−0.0759202	+	0.997114i	$0.524189\pi$
$384$	0.758676	−	1.55705i	0.0387160	−	0.0794580i
$385$	1.02434	−	12.1105i	0.0522050	−	0.617210i
$386$	−5.86734	−	16.1204i	−0.298640	−	0.820506i
$387$	−10.3668	−	3.16066i	−0.526976	−	0.160665i
$388$	1.51986	+	0.407245i	0.0771591	+	0.0206747i
$389$	20.3936	+	17.1123i	1.03400	+	0.867628i	0.991321	−	0.131461i	$-0.0419668\pi$
$389$	20.3936	+	17.1123i	1.03400	+	0.867628i	0.0426773	+	0.999089i	$0.486411\pi$
$390$	−11.8562	+	4.12589i	−0.600364	+	0.208923i
$391$	6.75607	+	11.7019i	0.341669	+	0.591788i
$392$	1.61271	+	6.01871i	0.0814540	+	0.303991i
$393$	−10.8719	−	9.44337i	−0.548414	−	0.476355i
$394$	−10.8699	+	1.91666i	−0.547620	+	0.0965601i
$395$	11.2710	+	30.6911i	0.567106	+	1.54423i
$396$	−3.53036	+	2.76264i	−0.177407	+	0.138828i
$397$	17.5329	+	1.53393i	0.879952	+	0.0769859i	0.518171	−	0.855277i	$-0.326613\pi$
$397$	17.5329	+	1.53393i	0.879952	+	0.0769859i	0.361781	+	0.932263i	$0.382169\pi$
$398$	0.501551	+	0.501551i	0.0251405	+	0.0251405i
$399$	5.85693	−	26.8303i	0.293213	−	1.34319i
$400$	2.47497	−	4.34448i	0.123749	−	0.217224i
$401$	−7.68434	−	9.15784i	−0.383738	−	0.457321i	0.539253	−	0.842144i	$-0.318707\pi$
$401$	−7.68434	−	9.15784i	−0.383738	−	0.457321i	−0.922990	+	0.384823i	$0.874262\pi$
$402$	1.88838	−	0.299843i	0.0941841	−	0.0149548i
$403$	−16.4934	−	23.5550i	−0.821593	−	1.17336i
$404$	1.08613	+	6.15977i	0.0540372	+	0.306460i
$405$	−4.78186	+	19.5482i	−0.237613	+	0.971360i
$406$	−8.49273	+	14.7098i	−0.421487	+	0.730038i
$407$	10.5217	+	2.81928i	0.521540	+	0.139746i
$408$	5.89916	+	1.14430i	0.292052	+	0.0566514i
$409$	3.37102	−	4.01742i	0.166686	−	0.198649i	−0.676235	−	0.736686i	$-0.736390\pi$
$409$	3.37102	−	4.01742i	0.166686	−	0.198649i	0.842921	+	0.538037i	$0.180834\pi$
$410$	−8.11875	+	2.20054i	−0.400956	+	0.108677i
$411$	21.2669	+	22.0054i	1.04902	+	1.08545i
$412$	15.9232	+	7.42512i	0.784481	+	0.365809i
$413$	19.4855	−	27.8281i	0.958818	−	1.36933i
$414$	−8.68904	−	7.81144i	−0.427043	−	0.383911i
$415$	−16.3293	+	23.4645i	−0.801576	+	1.15183i
$416$	−2.08349	−	2.48300i	−0.102151	−	0.121739i
$417$	1.65805	+	2.98846i	0.0811950	+	0.146346i
$418$	−6.38630	−	1.28034i	−0.312364	−	0.0626233i
$419$	11.0863			0.541602			0.270801	−	0.962635i	$-0.412711\pi$
$419$	11.0863			0.541602			0.270801	+	0.962635i	$0.412711\pi$
$420$	8.24323	−	11.4243i	0.402229	−	0.557448i
$421$	−7.25631	−	2.64108i	−0.353651	−	0.128718i	0.159085	−	0.987265i	$-0.449146\pi$
$421$	−7.25631	−	2.64108i	−0.353651	−	0.128718i	−0.512736	+	0.858547i	$0.671368\pi$
$422$	−1.83855	−	2.62572i	−0.0894990	−	0.127818i
$423$	−15.1513	+	6.44525i	−0.736682	+	0.313379i
$424$	3.50281	+	9.62389i	0.170111	+	0.467377i
$425$	16.7814	+	4.39293i	0.814017	+	0.213089i
$426$	2.55437	+	10.2281i	0.123760	+	0.495552i
$427$	−0.00777868	−	0.0889107i	−0.000376437	−	0.00430269i
$428$	−1.59984	−	18.2863i	−0.0773314	−	0.883902i
$429$	2.03266	+	8.13909i	0.0981377	+	0.392959i
$430$	−0.0233061	−	8.07809i	−0.00112392	−	0.389560i
$431$	−1.66515	−	4.57496i	−0.0802075	−	0.220368i	0.893107	−	0.449845i	$-0.148521\pi$
$431$	−1.66515	−	4.57496i	−0.0802075	−	0.220368i	−0.973314	+	0.229477i	$0.926299\pi$
$432$	−5.15668	+	0.639261i	−0.248101	+	0.0307564i
$433$	−7.41058	−	10.5834i	−0.356130	−	0.508606i	0.600613	−	0.799540i	$-0.294923\pi$
$433$	−7.41058	−	10.5834i	−0.356130	−	0.508606i	−0.956743	+	0.290933i	$0.906034\pi$
$434$	30.3234	+	11.0368i	1.45557	+	0.529783i
$435$	17.8533	−	2.88763i	0.856001	−	0.138451i
$436$	1.34703			0.0645110
$437$	0.395957	−	16.9720i	0.0189412	−	0.811880i
$438$	6.13126	+	11.0510i	0.292963	+	0.528035i
$439$	25.4106	+	30.2831i	1.21278	+	1.44533i	0.860508	+	0.509437i	$0.170146\pi$
$439$	25.4106	+	30.2831i	1.21278	+	1.44533i	0.352272	+	0.935898i	$0.385409\pi$
$440$	−2.74255	−	1.90858i	−0.130746	−	0.0909881i
$441$	12.4973	−	13.9014i	0.595110	−	0.661970i
$442$	6.45008	−	9.21166i	0.306799	−	0.438154i
$443$	−0.435266	−	0.202968i	−0.0206801	−	0.00964328i	0.412251	−	0.911070i	$-0.364743\pi$
$443$	−0.435266	−	0.202968i	−0.0206801	−	0.00964328i	−0.432931	+	0.901427i	$0.642521\pi$
$444$	8.77442	+	9.07912i	0.416415	+	0.430876i
$445$	−11.4811	+	20.0191i	−0.544258	+	0.948996i
$446$	−9.35053	+	11.1435i	−0.442760	+	0.527661i
$447$	−4.69677	−	0.911067i	−0.222150	−	0.0430920i
$448$	3.51350	+	0.941441i	0.165997	+	0.0444789i
$449$	−3.62660	+	6.28146i	−0.171150	+	0.296440i	−0.938822	−	0.344402i	$-0.888082\pi$
$449$	−3.62660	+	6.28146i	−0.171150	+	0.296440i	0.767672	+	0.640843i	$0.221415\pi$
$450$	−14.9740	+	0.883092i	−0.705880	+	0.0416293i
$451$	0.976108	+	5.53578i	0.0459631	+	0.260670i
$452$	−6.87911	−	9.82439i	−0.323566	−	0.462100i
$453$	−21.3268	+	3.38633i	−1.00202	+	0.159103i
$454$	−0.548848	−	0.654091i	−0.0257587	−	0.0306980i
$455$	−13.2476	−	22.7934i	−0.621058	−	1.06857i
$456$	−5.58283	−	5.08252i	−0.261440	−	0.238011i
$457$	−14.5973	−	14.5973i	−0.682833	−	0.682833i	0.277805	−	0.960638i	$-0.410393\pi$
$457$	−14.5973	−	14.5973i	−0.682833	−	0.682833i	−0.960638	+	0.277805i	$0.910393\pi$
$458$	18.8791	+	1.65171i	0.882164	+	0.0771793i
$459$	−6.77264	−	16.7068i	−0.316120	−	0.779806i
$460$	3.65771	−	7.90345i	0.170542	−	0.368500i
$461$	−9.58175	+	1.68952i	−0.446266	+	0.0786888i	−0.392265	−	0.919852i	$-0.628309\pi$
$461$	−9.58175	+	1.68952i	−0.446266	+	0.0786888i	−0.0540010	+	0.998541i	$0.517197\pi$
$462$	−7.10744	−	6.17356i	−0.330668	−	0.287220i
$463$	2.58882	+	9.66161i	0.120313	+	0.449013i	0.999629	−	0.0272246i	$-0.00866692\pi$
$463$	2.58882	+	9.66161i	0.120313	+	0.449013i	−0.879317	+	0.476238i	$0.842000\pi$
$464$	2.33481	+	4.04400i	0.108391	+	0.187738i
$465$	−11.2925	−	32.4503i	−0.523676	−	1.50485i
$466$	−9.99978	−	8.39081i	−0.463231	−	0.388697i
$467$	36.6306	+	9.81513i	1.69506	+	0.454190i	0.971688	−	0.236268i	$-0.0759245\pi$
$467$	36.6306	+	9.81513i	1.69506	+	0.454190i	0.723372	+	0.690458i	$0.242591\pi$
$468$	−2.83580	+	9.30130i	−0.131085	+	0.429953i
$469$	1.37336	+	3.77328i	0.0634160	+	0.174234i
$470$	−7.91567	−	9.37845i	−0.365123	−	0.432596i
$471$	−17.0214	+	34.9334i	−0.784303	+	1.60965i
$472$	−3.94704	−	8.46445i	−0.181677	−	0.389608i
$473$	−5.37774	−	0.470491i	−0.247269	−	0.0216332i
$474$	24.3472	+	6.97122i	1.11831	+	0.320199i
$475$	−15.1381	−	15.6792i	−0.694585	−	0.719411i
$476$			12.6196i			0.578420i
$477$	18.4714	−	24.5521i	0.845749	−	1.12416i
$478$	−10.0824	+	4.70151i	−0.461159	+	0.215042i
$479$	−4.64278	+	26.3305i	−0.212134	+	1.20307i	0.673677	+	0.739026i	$0.264714\pi$
$479$	−4.64278	+	26.3305i	−0.212134	+	1.20307i	−0.885811	+	0.464046i	$0.846397\pi$
$480$	−1.58686	−	3.53297i	−0.0724298	−	0.161257i
$481$	22.2035	−	8.08140i	1.01239	−	0.368480i
$482$	5.10465	+	19.0508i	0.232510	+	0.867741i
$483$	12.6296	−	21.0377i	0.574667	−	0.957248i
$484$	5.63542	−	6.71603i	0.256155	−	0.305274i
$485$	2.87626	−	2.02637i	0.130604	−	0.0920129i
$486$	10.0432	+	11.9220i	0.455571	+	0.540792i
$487$	−28.4601	+	7.62586i	−1.28965	+	0.345561i	−0.837528	−	0.546395i	$-0.816000\pi$
$487$	−28.4601	+	7.62586i	−1.28965	+	0.345561i	−0.452123	+	0.891956i	$0.649333\pi$
$488$	−0.0222376	−	0.0103696i	−0.00100665	−	0.000469409i
$489$	−10.1052	−	1.05813i	−0.456972	−	0.0478502i
$490$	12.6445	+	5.85188i	0.571221	+	0.264361i
$491$	−3.37900	+	9.28372i	−0.152492	+	0.418969i	−0.992291	−	0.123929i	$-0.960451\pi$
$491$	−3.37900	+	9.28372i	−0.152492	+	0.418969i	0.839799	+	0.542897i	$0.182673\pi$
$492$	−2.33264	+	6.08380i	−0.105164	+	0.274279i
$493$	−11.4556	+	11.4556i	−0.515932	+	0.515932i
$494$	−12.9407	+	5.67074i	−0.582228	+	0.255138i
$495$	−0.313142	+	10.0190i	−0.0140747	+	0.450320i
$496$	6.79593	−	5.70246i	0.305146	−	0.256048i
$497$	−20.0652	+	9.35657i	−0.900048	+	0.419699i
$498$	7.21738	+	20.9344i	0.323418	+	0.938092i
$499$	27.5388	−	4.85583i	1.23281	−	0.217377i	0.480976	−	0.876734i	$-0.340283\pi$
$499$	27.5388	−	4.85583i	1.23281	−	0.217377i	0.751830	+	0.659357i	$0.229171\pi$
$500$	−3.91469	−	10.4726i	−0.175070	−	0.468349i
$501$	20.5468	+	21.2603i	0.917962	+	0.949839i
$502$	2.06628	−	7.71145i	0.0922224	−	0.344179i
$503$	−0.974289	−	11.1362i	−0.0434414	−	0.496537i	−0.986483	−	0.163863i	$-0.947605\pi$
$503$	−0.974289	−	11.1362i	−0.0434414	−	0.496537i	0.943042	−	0.332675i	$-0.107951\pi$
$504$	−3.38016	−	10.3756i	−0.150564	−	0.462167i
$505$	12.1325	+	6.95810i	0.539888	+	0.309631i
$506$	−5.04004	−	2.90987i	−0.224057	−	0.129359i
$507$	−3.26095	−	2.83248i	−0.144824	−	0.125795i
$508$	4.84865	+	3.39506i	0.215124	+	0.150631i
$509$	2.57318	−	14.5933i	0.114054	−	0.646835i	−0.873160	−	0.487434i	$-0.837933\pi$
$509$	2.57318	−	14.5933i	0.114054	−	0.646835i	0.987214	−	0.159400i	$-0.0509560\pi$
$510$	10.4146	−	8.49019i	0.461167	−	0.375952i
$511$	−20.3313	+	17.0600i	−0.899402	+	0.754688i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.64843	+	22.3537i	−0.161082	+	0.986941i
$514$		−	25.7542i		−	1.13597i
$515$	35.5574	−	16.7057i	1.56684	−	0.736142i
$516$	−5.06368	−	3.67598i	−0.222916	−	0.161826i
$517$	−6.71801	+	4.70400i	−0.295458	+	0.206882i
$518$	−15.2090	+	21.7207i	−0.668244	+	0.954351i
$519$	19.0810	−	1.34172i	0.837563	−	0.0588950i
$520$	−7.24781	+	0.0209107i	−0.317837	+	0.000916993i
$521$	−21.2065	+	12.2436i	−0.929076	+	0.536402i	−0.886519	−	0.462692i	$-0.846884\pi$
$521$	−21.2065	+	12.2436i	−0.929076	+	0.536402i	−0.0425565	+	0.999094i	$0.513550\pi$
$522$	6.35018	−	12.4869i	0.277940	−	0.546537i
$523$	5.97160	−	0.522447i	0.261120	−	0.0228450i	0.0441558	−	0.999025i	$-0.485940\pi$
$523$	5.97160	−	0.522447i	0.261120	−	0.0228450i	0.216964	+	0.976180i	$0.430385\pi$
$524$	−4.15707	−	7.20026i	−0.181602	−	0.314545i
$525$	−7.80893	−	30.5180i	−0.340810	−	1.33191i
$526$	−25.0669	+	9.12361i	−1.09297	+	0.397808i
$527$	25.2121	+	17.6537i	1.09826	+	0.769008i
$528$	−2.44682	+	0.843571i	−0.106484	+	0.0367117i
$529$	−2.67847	+	7.35905i	−0.116455	+	0.319959i
$530$	21.5422	+	7.77040i	0.935732	+	0.337525i
$531$	−14.8291	+	23.7725i	−0.643526	+	1.03164i
$532$	8.24574	−	13.5424i	0.357498	−	0.587139i
$533$	8.62196	+	8.62196i	0.373459	+	0.373459i
$534$	7.27713	+	16.3276i	0.314912	+	0.706566i
$535$	−33.6904	−	23.4457i	−1.45656	−	1.01365i
$536$	1.08715	+	0.191693i	0.0469576	+	0.00827989i
$537$	−4.25446	−	5.24966i	−0.183594	−	0.226539i
$538$	−13.4200	+	28.7792i	−0.578575	+	1.24076i
$539$	4.65542	−	8.06343i	0.200523	−	0.347316i
$540$	−6.28861	+	9.77002i	−0.270619	+	0.420435i
$541$	6.19727	+	5.20013i	0.266442	+	0.223571i	0.766214	−	0.642586i	$-0.222138\pi$
$541$	6.19727	+	5.20013i	0.266442	+	0.223571i	−0.499772	+	0.866157i	$0.666583\pi$
$542$	0.577028	−	0.0504834i	0.0247855	−	0.00216845i
$543$	−13.9124	−	8.35204i	−0.597037	−	0.358420i
$544$	3.00456	+	1.73468i	0.128819	+	0.0743739i
$545$	1.92944	−	2.31294i	0.0826482	−	0.0990754i
$546$	−20.3101	−	2.12671i	−0.869193	−	0.0910146i
$547$	18.4846	−	12.9431i	0.790346	−	0.553406i	−0.107246	−	0.994232i	$-0.534203\pi$
$547$	18.4846	−	12.9431i	0.790346	−	0.553406i	0.897592	+	0.440826i	$0.145314\pi$
$548$	7.46701	+	16.0131i	0.318975	+	0.684044i
$549$	0.0103011	+	0.0728853i	0.000439640	+	0.00311067i
$550$	−7.20550	+	1.97534i	−0.307244	+	0.0842288i
$551$	19.7783	−	4.80810i	0.842585	−	0.204832i
$552$	−3.27273	−	5.89875i	−0.139296	−	0.251068i
$553$	−4.63545	+	52.9834i	−0.197119	+	2.25308i
$554$	−30.3436	−	11.0442i	−1.28917	−	0.469221i
$555$	28.1577	−	2.06162i	1.19523	−	0.0875109i
$556$	0.342635	+	1.94318i	0.0145310	+	0.0824091i
$557$	−3.04569	+	6.53151i	−0.129050	+	0.276749i	−0.960207	−	0.279289i	$-0.909901\pi$
$557$	−3.04569	+	6.53151i	−0.129050	+	0.276749i	0.831157	+	0.556038i	$0.187679\pi$
$558$	−25.4575	−	7.76151i	−1.07770	−	0.328571i
$559$	−10.1410	+	5.85489i	−0.428917	+	0.247636i
$560$	6.64915	−	4.68443i	0.280978	−	0.197953i
$561$	−5.02403	−	7.44219i	−0.212115	−	0.314210i
$562$	0.530878	−	1.98126i	0.0223937	−	0.0835746i
$563$	−27.4965	+	7.36766i	−1.15884	+	0.310510i	−0.786502	−	0.617588i	$-0.788110\pi$
$563$	−27.4965	+	7.36766i	−1.15884	+	0.310510i	−0.372337	+	0.928098i	$0.621443\pi$
$564$	−9.48279	+	0.666802i	−0.399297	+	0.0280774i
$565$	−26.7226	−	2.26025i	−1.12423	−	0.0950896i
$566$	−4.09318	−	0.721738i	−0.172049	−	0.0303369i
$567$	−20.5625	+	25.4734i	−0.863545	+	1.06978i
$568$	−0.530478	+	6.06339i	−0.0222584	+	0.254414i
$569$	−26.5691			−1.11383			−0.556916	−	0.830568i	$-0.688016\pi$
$569$	−26.5691			−1.11383			−0.556916	+	0.830568i	$0.688016\pi$
$570$	−16.7237	+	2.30605i	−0.700479	+	0.0965900i
$571$	−25.0210			−1.04710			−0.523548	−	0.851996i	$-0.675392\pi$
$571$	−25.0210			−1.04710			−0.523548	+	0.851996i	$0.675392\pi$
$572$	−0.422133	+	4.82500i	−0.0176503	+	0.201743i
$573$	4.19656	+	26.4296i	0.175314	+	1.10411i
$574$	−13.4755	−	2.37610i	−0.562458	−	0.0991765i
$575$	−8.33155	−	17.6012i	−0.347450	−	0.734020i
$576$	−2.93493	−	0.621455i	−0.122289	−	0.0258940i
$577$	−41.5365	+	11.1297i	−1.72919	+	0.463334i	−0.979996	−	0.199018i	$-0.936225\pi$
$577$	−41.5365	+	11.1297i	−1.72919	+	0.463334i	−0.749192	+	0.662353i	$0.769558\pi$
$578$	1.28465	−	4.79437i	0.0534343	−	0.199419i
$579$	−24.6270	+	16.6250i	−1.02346	+	0.690912i
$580$	10.2881	+	1.78348i	0.427191	+	0.0740552i
$581$	−40.2731	+	23.2517i	−1.67081	+	0.964642i
$582$	0.0465053	−	2.72494i	0.00192771	−	0.112952i
$583$	6.46759	−	13.8698i	0.267860	−	0.574428i
$584$	1.26702	+	7.18563i	0.0524297	+	0.297344i
$585$	11.9091	+	18.1922i	0.492379	+	0.752153i
$586$	23.0057	+	8.37340i	0.950358	+	0.345902i
$587$	−1.41698	+	16.1961i	−0.0584848	+	0.668485i	0.909206	+	0.416346i	$0.136689\pi$
$587$	−1.41698	+	16.1961i	−0.0584848	+	0.668485i	−0.967691	+	0.252139i	$0.918866\pi$
$588$	9.43726	−	5.23595i	0.389186	−	0.215927i
$589$	−15.5207	−	35.4183i	−0.639519	−	1.45939i
$590$	−20.1876	−	5.34689i	−0.831112	−	0.220128i
$591$	7.78266	+	17.4619i	0.320136	+	0.718286i
$592$	3.08078	+	6.60674i	0.126619	+	0.271536i
$593$	−4.97308	+	3.48219i	−0.204220	+	0.142996i	−0.671213	−	0.741265i	$-0.734226\pi$
$593$	−4.97308	+	3.48219i	−0.204220	+	0.142996i	0.466993	+	0.884261i	$0.345337\pi$
$594$	6.12405	+	4.77315i	0.251273	+	0.195845i
$595$	21.6688	+	18.0760i	0.888333	+	0.741043i
$596$	−2.39216	−	1.38111i	−0.0979866	−	0.0565726i
$597$	0.632338	−	1.05331i	0.0258799	−	0.0431093i
$598$	−12.5760	+	1.10025i	−0.514269	+	0.0449927i
$599$	−1.29900	−	1.08999i	−0.0530757	−	0.0445358i	0.615864	−	0.787853i	$-0.288807\pi$
$599$	−1.29900	−	1.08999i	−0.0530757	−	0.0445358i	−0.668940	+	0.743317i	$0.733252\pi$
$600$	−8.33931	−	2.33578i	−0.340451	−	0.0953576i
$601$	9.51126	−	16.4740i	0.387973	−	0.671988i	−0.604204	−	0.796830i	$-0.706509\pi$
$601$	9.51126	−	16.4740i	0.387973	−	0.671988i	0.992177	+	0.124841i	$0.0398422\pi$
$602$	5.55355	−	11.9096i	0.226346	−	0.485400i
$603$	−1.29637	−	3.04748i	−0.0527924	−	0.124103i
$604$	−12.2779	−	2.16492i	−0.499580	−	0.0880894i
$605$	−3.45988	−	19.2962i	−0.140664	−	0.784503i
$606$	9.89529	−	4.41027i	0.401969	−	0.179155i
$607$	23.2357	+	23.2357i	0.943109	+	0.943109i	0.998467	−	0.0553574i	$-0.0176298\pi$
$607$	23.2357	+	23.2357i	0.943109	+	0.943109i	−0.0553574	+	0.998467i	$0.517630\pi$
$608$	−2.09081	−	3.82472i	−0.0847936	−	0.155113i
$609$	28.2832	+	8.09818i	1.14609	+	0.328155i
$610$	−0.0496578	+	0.0233305i	−0.00201059	+	0.000944623i
$611$	−6.08445	+	16.7169i	−0.246151	+	0.676293i
$612$	−0.552791	−	10.3934i	−0.0223453	−	0.420129i
$613$	32.1495	+	22.5113i	1.29851	+	0.909224i	0.998993	−	0.0448674i	$-0.0142865\pi$
$613$	32.1495	+	22.5113i	1.29851	+	0.909224i	0.299514	+	0.954092i	$0.403175\pi$
$614$	26.2733	−	9.56271i	1.06031	−	0.385920i
$615$	7.10509	+	12.7195i	0.286505	+	0.512902i
$616$	−2.71767	−	4.70714i	−0.109498	−	0.189656i
$617$	−3.46738	+	0.303356i	−0.139591	+	0.0122127i	−0.156737	−	0.987640i	$-0.550098\pi$
$617$	−3.46738	+	0.303356i	−0.139591	+	0.0122127i	0.0171459	+	0.999853i	$0.494542\pi$
$618$	5.79490	−	29.8741i	0.233105	−	1.20171i
$619$	3.17771	−	1.83465i	0.127723	−	0.0737409i	−0.434777	−	0.900538i	$-0.643173\pi$
$619$	3.17771	−	1.83465i	0.127723	−	0.0737409i	0.562500	+	0.826797i	$0.309840\pi$
$620$	−0.0572320	−	19.8371i	−0.00229849	−	0.796677i
$621$	−9.48008	+	17.8797i	−0.380422	+	0.717486i
$622$	−19.6337	+	28.0399i	−0.787241	+	1.12430i
$623$	−30.7517	+	21.5326i	−1.23204	+	0.862684i
$624$	−3.29815	+	4.54322i	−0.132032	+	0.181874i
$625$	−23.5894	−	8.27883i	−0.943577	−	0.331153i
$626$		−	1.11198i		−	0.0444438i
$627$	0.528635	+	11.2691i	0.0211117	+	0.450045i
$628$	−15.8644	+	15.8644i	−0.633058	+	0.633058i
$629$	−19.3739	+	16.2566i	−0.772486	+	0.648193i
$630$	−22.6573	−	9.05777i	−0.902688	−	0.360870i
$631$	−0.514163	+	2.91596i	−0.0204685	+	0.116083i	−0.993330	−	0.115305i	$-0.963215\pi$
$631$	−0.514163	+	2.91596i	−0.0204685	+	0.116083i	0.972862	+	0.231388i	$0.0743266\pi$
$632$	11.9774	+	8.38669i	0.476436	+	0.333604i
$633$	−3.64076	+	4.19151i	−0.144707	+	0.166597i
$634$	29.3859	+	16.9660i	1.16706	+	0.673805i
$635$	12.7746	−	3.46247i	0.506944	−	0.137404i
$636$	14.7023	−	9.92515i	0.582985	−	0.393558i
$637$	−1.76027	−	20.1200i	−0.0697444	−	0.797182i
$638$	1.80595	−	6.73991i	0.0714984	−	0.266836i
$639$	16.1157	−	8.58492i	0.637526	−	0.339614i
$640$	−0.201312	−	2.22699i	−0.00795756	−	0.0880294i
$641$	10.5022	−	1.85183i	0.414813	−	0.0731427i	0.0376530	−	0.999291i	$-0.488012\pi$
$641$	10.5022	−	1.85183i	0.414813	−	0.0731427i	0.377160	+	0.926148i	$0.376901\pi$
$642$	−30.0576	+	10.3627i	−1.18628	+	0.408984i
$643$	11.7263	−	5.46807i	0.462441	−	0.215640i	−0.177413	−	0.984137i	$-0.556773\pi$
$643$	11.7263	−	5.46807i	0.462441	−	0.215640i	0.639854	+	0.768497i	$0.278995\pi$
$644$	10.8524	−	9.10622i	0.427643	−	0.358835i
$645$	−13.5650	+	3.42933i	−0.534120	+	0.135030i
$646$	10.9398	−	10.4410i	0.430421	−	0.410795i
$647$	25.9675	−	25.9675i	1.02089	−	1.02089i	0.0211120	−	0.999777i	$-0.493279\pi$
$647$	25.9675	−	25.9675i	1.02089	−	1.02089i	0.999777	−	0.0211120i	$-0.00672066\pi$
$648$	3.23836	+	8.39720i	0.127215	+	0.329873i
$649$	−4.77314	+	13.1141i	−0.187362	+	0.514774i
$650$	−10.3456	+	12.4749i	−0.405789	+	0.489307i
$651$	5.82075	−	55.5884i	0.228133	−	2.17868i
$652$	−5.31651	−	2.47913i	−0.208211	−	0.0970902i
$653$	36.1629	−	9.68983i	1.41517	−	0.379192i	0.531399	−	0.847122i	$-0.321666\pi$
$653$	36.1629	−	9.68983i	1.41517	−	0.379192i	0.883766	+	0.467929i	$0.155000\pi$
$654$	−0.565313	−	2.26360i	−0.0221055	−	0.0885137i
$655$	−18.3178	−	3.17546i	−0.715735	−	0.124075i
$656$	−2.41805	+	2.88172i	−0.0944090	+	0.112512i
$657$	15.9973	−	14.9410i	0.624115	−	0.582904i
$658$	−5.16701	−	19.2836i	−0.201431	−	0.751751i
$659$	−11.4918	+	4.18266i	−0.447655	+	0.162933i	−0.556004	−	0.831180i	$-0.687666\pi$
$659$	−11.4918	+	4.18266i	−0.447655	+	0.162933i	0.108349	+	0.994113i	$0.465444\pi$
$660$	−2.05628	+	5.40966i	−0.0800407	+	0.210571i
$661$	8.02889	−	45.5341i	0.312287	−	1.77107i	−0.274755	−	0.961514i	$-0.588597\pi$
$661$	8.02889	−	45.5341i	0.312287	−	1.77107i	0.587043	−	0.809556i	$-0.300292\pi$
$662$	7.44221	−	3.47036i	0.289250	−	0.134879i
$663$	−18.1866	−	6.97306i	−0.706308	−	0.270811i
$664$			12.7846i			0.496139i
$665$	−11.4423	−	33.5562i	−0.443714	−	1.30125i
$666$	11.5745	−	18.5551i	0.448503	−	0.718997i
$667$	18.1175	+	1.58508i	0.701513	+	0.0613744i
$668$	7.21416	+	15.4708i	0.279124	+	0.598583i
$669$	22.6502	+	11.0363i	0.875707	+	0.426690i
$670$	1.88635	−	1.59213i	0.0728759	−	0.0615093i
$671$	0.0125399	+	0.0344531i	0.000484098	+	0.00133005i
$672$	0.107508	−	6.29933i	0.00414720	−	0.243002i
$673$	15.7990	+	4.23333i	0.609007	+	0.163183i	0.550125	−	0.835082i	$-0.314580\pi$
$673$	15.7990	+	4.23333i	0.609007	+	0.163183i	0.0588815	+	0.998265i	$0.481247\pi$
$674$	−7.68270	−	6.44655i	−0.295926	−	0.248312i
$675$	7.76817	+	24.7922i	0.298997	+	0.954254i
$676$	−1.24689	−	2.15967i	−0.0479572	−	0.0830644i
$677$	2.88761	+	10.7767i	0.110980	+	0.414183i	0.998955	−	0.0457090i	$-0.0145547\pi$
$677$	2.88761	+	10.7767i	0.110980	+	0.414183i	−0.887975	+	0.459892i	$0.847888\pi$
$678$	−13.6223	+	15.6830i	−0.523161	+	0.602301i
$679$	5.63647	−	0.993862i	0.216308	−	0.0381409i
$680$	7.28221	−	2.67432i	0.279260	−	0.102556i
$681$	−0.868823	+	1.19681i	−0.0332934	+	0.0458619i
$682$	−13.2059	−	1.15537i	−0.505681	−	0.0442413i
$683$	12.7588	+	12.7588i	0.488200	+	0.488200i	0.907738	−	0.419538i	$-0.137808\pi$
$683$	12.7588	+	12.7588i	0.488200	+	0.488200i	−0.419538	+	0.907738i	$0.637808\pi$
$684$	−6.19789	+	11.5146i	−0.236982	+	0.440272i
$685$	38.1910	+	10.1152i	1.45920	+	0.386484i
$686$	−1.79795	−	2.14271i	−0.0686459	−	0.0818090i
$687$	−5.14748	−	32.4184i	−0.196388	−	1.23684i
$688$	−2.07213	−	2.95931i	−0.0789992	−	0.112823i
$689$	−5.76445	−	32.6918i	−0.219608	−	1.24546i
$690$	−14.8163	−	2.82970i	−0.564047	−	0.107725i
$691$	−16.0099	+	27.7300i	−0.609047	+	1.05490i	0.382351	+	0.924017i	$0.375114\pi$
$691$	−16.0099	+	27.7300i	−0.609047	+	1.05490i	−0.991398	+	0.130883i	$0.958219\pi$
$692$	10.6673	+	2.85830i	0.405511	+	0.108656i
$693$	−7.39148	+	14.5345i	−0.280779	+	0.552120i
$694$	4.92011	−	5.86356i	0.186765	−	0.222578i
$695$	3.82735	+	2.19502i	0.145180	+	0.0832619i
$696$	5.81584	−	5.62066i	0.220449	−	0.213051i
$697$	−11.8283	−	5.51565i	−0.448030	−	0.208920i
$698$	−8.57706	+	12.2493i	−0.324647	+	0.463643i
$699$	−9.90360	+	20.3254i	−0.374588	+	0.768778i
$700$	1.48055	−	18.1269i	0.0559596	−	0.685131i
$701$	−3.77595	−	4.50000i	−0.142616	−	0.169963i	0.690008	−	0.723801i	$-0.257607\pi$
$701$	−3.77595	−	4.50000i	−0.142616	−	0.169963i	−0.832624	+	0.553839i	$0.813162\pi$
$702$	16.8204	+	0.861868i	0.634844	+	0.0325291i
$703$	31.4127	−	4.78635i	1.18475	−	0.180521i
$704$	−1.49427			−0.0563175
$705$	−12.4379	+	17.2377i	−0.468439	+	0.649209i
$706$	−15.2264	−	5.54195i	−0.573052	−	0.208574i
$707$	13.0497	+	18.6369i	0.490785	+	0.700914i
$708$	−12.5675	+	10.1851i	−0.472316	+	0.382778i
$709$	0.738072	+	2.02784i	0.0277189	+	0.0761570i	0.952780	−	0.303661i	$-0.0982089\pi$
$709$	0.738072	+	2.02784i	0.0277189	+	0.0761570i	−0.925061	+	0.379818i	$0.875987\pi$
$710$	9.65142	+	9.59589i	0.362211	+	0.360127i
$711$	1.49682	−	43.8397i	0.0561352	−	1.64412i
$712$	0.899505	+	10.2814i	0.0337104	+	0.385311i
$713$	−3.01137	−	34.4201i	−0.112777	−	1.28904i
$714$	21.2065	−	5.29613i	0.793634	−	0.198203i
$715$	7.68020	+	7.63601i	0.287223	+	0.285570i
$716$	−1.33431	−	3.66598i	−0.0498654	−	0.137004i
$717$	12.1319	+	14.9698i	0.453075	+	0.559057i
$718$	−2.39948	−	3.42681i	−0.0895478	−	0.127888i
$719$	−39.0482	−	14.2124i	−1.45625	−	0.530033i	−0.511923	−	0.859031i	$-0.671067\pi$
$719$	−39.0482	−	14.2124i	−1.45625	−	0.530033i	−0.944331	+	0.328998i	$0.893289\pi$
$720$	−5.27098	+	4.14931i	−0.196438	+	0.154636i
$721$	63.9075			2.38004
$722$	−18.5620	+	4.05634i	−0.690804	+	0.150961i
$723$	29.8714	−	16.5732i	1.11093	−	0.616363i
$724$	−6.02200	−	7.17674i	−0.223806	−	0.266722i
$725$	17.7988	−	15.1108i	0.661029	−	0.561201i
$726$	−13.6509	−	6.65143i	−0.506633	−	0.246858i
$727$	−18.8063	+	26.8582i	−0.697487	+	0.996115i	0.301601	+	0.953434i	$0.402479\pi$
$727$	−18.8063	+	26.8582i	−0.697487	+	0.996115i	−0.999089	+	0.0426811i	$0.986410\pi$
$728$	−10.6855	−	4.98274i	−0.396032	−	0.184673i
$729$	15.8193	−	21.8804i	0.585898	−	0.810385i
$730$	14.1531	+	8.11692i	0.523828	+	0.300421i
$731$	8.05644	−	9.60130i	0.297978	−	0.355117i
$732$	−0.00809290	+	0.0417208i	−0.000299122	+	0.00154205i
$733$	−8.79037	−	2.35537i	−0.324680	−	0.0869976i	0.0927977	−	0.995685i	$-0.470419\pi$
$733$	−8.79037	−	2.35537i	−0.324680	−	0.0869976i	−0.417477	+	0.908687i	$0.637086\pi$
$734$	13.9854	−	24.2234i	0.516210	−	0.894103i
$735$	4.52716	−	23.7042i	0.166987	−	0.874343i
$736$	−0.676307	−	3.83553i	−0.0249290	−	0.141379i
$737$	−0.946145	−	1.35123i	−0.0348517	−	0.0497734i
$738$	11.2024	+	1.36665i	0.412366	+	0.0503071i
$739$	−19.4734	−	23.2075i	−0.716339	−	0.853700i	0.277930	−	0.960601i	$-0.410352\pi$
$739$	−19.4734	−	23.2075i	−0.716339	−	0.853700i	−0.994270	+	0.106901i	$0.965907\pi$
$740$	15.7570	+	4.17340i	0.579240	+	0.153417i
$741$	14.9602	+	19.3661i	0.549576	+	0.711433i
$742$	26.3419	+	26.3419i	0.967040	+	0.967040i
$743$	1.32557	+	0.115972i	0.0486304	+	0.00425461i	0.111445	−	0.993771i	$-0.464452\pi$
$743$	1.32557	+	0.115972i	0.0486304	+	0.00425461i	−0.0628146	+	0.998025i	$0.520008\pi$
$744$	−12.4347	−	9.02696i	−0.455878	−	0.330945i
$745$	−5.79792	+	2.12923i	−0.212419	+	0.0780091i
$746$	13.7658	−	2.42728i	0.504002	−	0.0888692i
$747$	32.1500	−	20.9140i	1.17631	−	0.765202i
$748$	−1.34176	−	5.00753i	−0.0490597	−	0.183093i
$749$	−33.3848	−	57.8241i	−1.21985	−	2.11285i
$750$	−15.9557	+	10.9735i	−0.582618	+	0.400694i
$751$	12.9584	+	10.8734i	0.472859	+	0.396776i	0.847836	−	0.530258i	$-0.177905\pi$
$751$	12.9584	+	10.8734i	0.472859	+	0.396776i	−0.374977	+	0.927034i	$0.622350\pi$
$752$	−5.30140	−	1.42050i	−0.193322	−	0.0518005i
$753$	−13.8258	−	0.235959i	−0.503839	−	0.00859881i
$754$	−5.17673	−	14.2230i	−0.188526	−	0.517970i
$755$	−21.3038	+	17.9810i	−0.775324	+	0.654395i
$756$	−16.0170	+	10.0345i	−0.582534	+	0.364952i
$757$	−11.8569	−	25.4272i	−0.430946	−	0.924167i	−0.995135	−	0.0985214i	$-0.968589\pi$
$757$	−11.8569	−	25.4272i	−0.430946	−	0.924167i	0.564189	−	0.825646i	$-0.309189\pi$
$758$	18.0550	+	1.57961i	0.655788	+	0.0573740i
$759$	−2.77468	+	9.69067i	−0.100715	+	0.351749i
$760$	−9.56212	−	1.88835i	−0.346855	−	0.0684977i
$761$		−	8.72796i		−	0.316388i	−0.987408	−	0.158194i	$-0.949433\pi$
$761$		−	8.72796i		−	0.316388i	0.987408	−	0.158194i	$-0.0505672\pi$
$762$	3.67034	−	9.57267i	0.132962	−	0.346781i
$763$	4.44068	−	2.07072i	0.160763	−	0.0749652i
$764$	−2.68292	+	15.2156i	−0.0970645	+	0.550480i
$765$	−18.6380	−	13.9380i	−0.673858	−	0.503930i
$766$	32.0580	−	11.6681i	1.15830	−	0.421587i
$767$	7.83507	+	29.2409i	0.282908	+	1.05583i
$768$	−1.48500	−	0.891495i	−0.0535855	−	0.0321691i
$769$	−9.75727	+	11.6283i	−0.351856	+	0.419326i	−0.912722	−	0.408581i	$-0.866024\pi$
$769$	−9.75727	+	11.6283i	−0.351856	+	0.419326i	0.560866	+	0.827907i	$0.310468\pi$
$770$	−11.9752	−	2.07594i	−0.431555	−	0.0748117i
$771$	−43.2783	+	10.8084i	−1.55863	+	0.389254i
$772$	−16.5704	+	4.44003i	−0.596382	+	0.159800i
$773$	−6.95175	−	3.24165i	−0.250037	−	0.116594i	0.293560	−	0.955941i	$-0.405160\pi$
$773$	−6.95175	−	3.24165i	−0.250037	−	0.116594i	−0.543597	+	0.839347i	$0.682938\pi$
$774$	−4.05216	+	10.0519i	−0.145652	+	0.361309i
$775$	−34.1436	−	28.3158i	−1.22647	−	1.01713i
$776$	0.538159	−	1.47858i	0.0193188	−	0.0530779i
$777$	42.8830	+	16.4422i	1.53842	+	0.589859i
$778$	18.8246	−	18.8246i	0.674895	−	0.674895i
$779$	9.08932	+	13.6477i	0.325659	+	0.488978i
$780$	3.07685	+	12.1707i	0.110169	+	0.435782i
$781$	6.96715	−	5.84613i	0.249304	−	0.209191i
$782$	12.2462	−	5.71047i	0.437921	−	0.204206i
$783$	−23.6485	−	5.43067i	−0.845128	−	0.194076i
$784$	6.13636	−	1.08201i	0.219156	−	0.0386431i
$785$	4.51656	+	49.9638i	0.161203	+	1.78329i
$786$	−10.3550	+	10.0075i	−0.369350	+	0.356954i
$787$	10.4875	−	39.1397i	0.373837	−	1.39518i	−0.481199	−	0.876612i	$-0.659798\pi$
$787$	10.4875	−	39.1397i	0.373837	−	1.39518i	0.855036	−	0.518569i	$-0.173535\pi$
$788$	0.961993	+	10.9956i	0.0342696	+	0.391703i
$789$	25.8516	+	38.2945i	0.920341	+	1.36332i
$790$	31.5566	−	8.55322i	1.12273	−	0.304310i
$791$	−37.7806	−	21.8126i	−1.34332	−	0.775568i
$792$	2.44444	+	3.75771i	0.0868593	+	0.133524i
$793$	0.0651480	+	0.0456171i	0.00231347	+	0.00161991i
$794$	3.05619	−	17.3325i	0.108460	−	0.615108i
$795$	4.01699	−	39.4613i	0.142468	−	1.39955i
$796$	0.543356	−	0.455930i	0.0192587	−	0.0161600i
$797$	17.2179	−	17.2179i	0.609889	−	0.609889i	−0.333028	−	0.942917i	$-0.608070\pi$
$797$	17.2179	−	17.2179i	0.609889	−	0.609889i	0.942917	+	0.333028i	$0.108070\pi$
$798$	−26.2177	−	8.17305i	−0.928098	−	0.289323i
$799$		−	19.0413i		−	0.673633i
$800$	−4.11224	−	2.84420i	−0.145390	−	0.100558i
$801$	24.3836	−	19.0811i	0.861551	−	0.674196i
$802$	−9.79273	+	6.85694i	−0.345793	+	0.242127i
$803$	6.25367	−	8.93116i	0.220687	−	0.315174i
$804$	−0.134118	−	1.90733i	−0.00472998	−	0.0672664i
$805$	−0.0913934	−	31.6777i	−0.00322119	−	1.11649i
$806$	−24.9028	+	14.3777i	−0.877165	+	0.506431i
$807$	53.9936	+	10.4735i	1.90067	+	0.368686i
$808$	6.23099	−	0.545141i	0.219206	−	0.0191780i
$809$	6.34640	+	10.9923i	0.223128	+	0.386468i	0.955756	−	0.294160i	$-0.0950400\pi$
$809$	6.34640	+	10.9923i	0.223128	+	0.386468i	−0.732628	+	0.680629i	$0.761707\pi$
$810$	19.0571	+	6.46741i	0.669598	+	0.227242i
$811$	11.8101	−	4.29852i	0.414708	−	0.150941i	−0.126235	−	0.992000i	$-0.540289\pi$
$811$	11.8101	−	4.29852i	0.414708	−	0.150941i	0.540944	+	0.841059i	$0.318067\pi$
$812$	13.9137	+	9.74247i	0.488275	+	0.341894i
$813$	−0.326998	−	0.948474i	−0.0114683	−	0.0332644i
$814$	3.72557	−	10.2359i	0.130581	−	0.358769i
$815$	−11.8720	+	5.57778i	−0.415859	+	0.195381i
$816$	1.65409	−	5.77698i	0.0579049	−	0.202235i
$817$	−14.9191	+	5.03925i	−0.521953	+	0.176301i
$818$	−3.70833	−	3.70833i	−0.129659	−	0.129659i
$819$	4.94983	+	35.0225i	0.172961	+	1.22378i
$820$	1.48457	+	8.27964i	0.0518433	+	0.289138i
$821$	−46.3083	−	8.16541i	−1.61617	−	0.284975i	−0.708834	−	0.705376i	$-0.750778\pi$
$821$	−46.3083	−	8.16541i	−1.61617	−	0.284975i	−0.907339	+	0.420401i	$0.861889\pi$
$822$	23.7752	−	19.2681i	0.829257	−	0.672053i
$823$	11.0484	−	23.6933i	0.385122	−	0.825898i	−0.614202	−	0.789149i	$-0.710522\pi$
$823$	11.0484	−	23.6933i	0.385122	−	0.825898i	0.999325	−	0.0367489i	$-0.0117002\pi$
$824$	8.78466	−	15.2155i	0.306028	−	0.530057i
$825$	6.34340	+	11.2794i	0.220849	+	0.392698i
$826$	−26.0240	−	21.8367i	−0.905490	−	0.759796i
$827$	6.74600	−	0.590198i	0.234581	−	0.0205232i	0.0307411	−	0.999527i	$-0.490213\pi$
$827$	6.74600	−	0.590198i	0.234581	−	0.0205232i	0.203840	+	0.979004i	$0.434658\pi$
$828$	−8.53901	+	7.97517i	−0.296751	+	0.277156i
$829$	18.3426	+	10.5901i	0.637065	+	0.367809i	0.783483	−	0.621413i	$-0.213441\pi$
$829$	18.3426	+	10.5901i	0.637065	+	0.367809i	−0.146418	+	0.989223i	$0.546775\pi$
$830$	21.9520	+	18.3123i	0.761966	+	0.635628i
$831$	−5.82463	+	55.6254i	−0.202054	+	1.92963i
$832$	−2.65514	+	1.85915i	−0.0920505	+	0.0644545i
$833$	9.13604	+	19.5923i	0.316545	+	0.678833i
$834$	3.12160	−	1.39128i	0.108092	−	0.0481760i
$835$	36.8977	+	9.77271i	1.27690	+	0.338199i
$836$	−1.83207	+	6.25041i	−0.0633634	+	0.216175i
$837$	−2.35891	+	46.0370i	−0.0815360	+	1.59127i
$838$	0.966237	−	11.0441i	0.0333781	−	0.381513i
$839$	34.6238	+	12.6020i	1.19535	+	0.435071i	0.861598	−	0.507591i	$-0.169464\pi$
$839$	34.6238	+	12.6020i	1.19535	+	0.435071i	0.333749	+	0.942662i	$0.391686\pi$
$840$	−10.6624	−	9.20756i	−0.367887	−	0.317691i
$841$	−1.24935	−	7.08542i	−0.0430810	−	0.244325i
$842$	−3.26346	+	6.99851i	−0.112466	+	0.241185i
$843$	−3.55219	−	0.0606236i	−0.122344	−	0.00208799i
$844$	−2.77596	+	1.60270i	−0.0955526	+	0.0551673i
$845$	−5.49431	−	0.952459i	−0.189010	−	0.0327656i
$846$	5.10020	+	15.6554i	0.175348	+	0.538244i
$847$	8.25375	−	30.8034i	0.283602	−	1.05842i
$848$	9.89256	−	2.65070i	0.339712	−	0.0910255i
$849$	0.504963	+	7.18123i	0.0173303	+	0.246459i
$850$	5.83881	−	16.3347i	0.200270	−	0.560274i
$851$	27.9600	+	4.93010i	0.958456	+	0.169002i
$852$	10.4118	−	1.65321i	0.356702	−	0.0566381i
$853$	−3.49514	+	39.9496i	−0.119671	+	1.36785i	0.664492	+	0.747295i	$0.268648\pi$
$853$	−3.49514	+	39.9496i	−0.119671	+	1.36785i	−0.784164	+	0.620554i	$0.786908\pi$
$854$	−0.0892503			−0.00305408
$855$	10.8937	+	27.1354i	0.372556	+	0.928010i
$856$	−18.3562			−0.627401
$857$	−0.0861037	+	0.984170i	−0.00294125	+	0.0336186i	−0.997523	−	0.0703340i	$-0.977593\pi$
$857$	−0.0861037	+	0.984170i	−0.00294125	+	0.0336186i	0.994582	+	0.103953i	$0.0331490\pi$
$858$	8.28527	−	1.31556i	0.282855	−	0.0449124i
$859$	−50.0294	−	8.82154i	−1.70698	−	0.300987i	−0.766858	−	0.641817i	$-0.778181\pi$
$859$	−50.0294	−	8.82154i	−1.70698	−	0.300987i	−0.940125	+	0.340830i	$0.889292\pi$
$860$	−8.04938	−	0.680835i	−0.274482	−	0.0232163i
$861$	1.66244	+	23.6420i	0.0566557	+	0.805717i
$862$	−4.70268	+	1.26008i	−0.160174	+	0.0429185i
$863$	−12.5118	+	46.6948i	−0.425908	+	1.58951i	0.336023	+	0.941854i	$0.390918\pi$
$863$	−12.5118	+	46.6948i	−0.425908	+	1.58951i	−0.761932	+	0.647657i	$0.775749\pi$
$864$	0.187394	+	5.19277i	0.00637526	+	0.176662i
$865$	20.1874	−	14.2224i	0.686393	−	0.483575i
$866$	−11.1890	+	6.45998i	−0.380218	+	0.219519i
$867$	−8.59577	−	0.146700i	−0.291928	−	0.00498220i
$868$	13.6377	−	29.2460i	0.462892	−	0.992675i
$869$	−3.79401	−	21.5169i	−0.128703	−	0.729912i
$870$	−1.32062	−	18.0370i	−0.0447732	−	0.611513i
$871$	−3.36237	−	1.22380i	−0.113930	−	0.0414670i
$872$	0.117401	−	1.34190i	0.00397571	−	0.0454426i
$873$	−4.59861	+	1.06544i	−0.155639	+	0.0360595i
$874$	−16.8729	−	1.87366i	−0.570734	−	0.0633773i
$875$	−29.0044	−	28.5066i	−0.980526	−	0.963698i
$876$	11.5433	−	5.14477i	0.390011	−	0.173826i
$877$	−15.5021	−	33.2444i	−0.523470	−	1.12258i	−0.973314	−	0.229477i	$-0.926298\pi$
$877$	−15.5021	−	33.2444i	−0.523470	−	1.12258i	0.449845	−	0.893107i	$-0.351479\pi$
$878$	32.3826	−	22.6745i	1.09286	−	0.765228i
$879$	4.41609	−	42.1738i	0.148951	−	1.42249i
$880$	−2.14035	+	2.56577i	−0.0721511	+	0.0864919i
$881$	−5.58351	−	3.22364i	−0.188113	−	0.108607i	0.402986	−	0.915206i	$-0.367972\pi$
$881$	−5.58351	−	3.22364i	−0.188113	−	0.108607i	−0.591099	+	0.806599i	$0.701306\pi$
$882$	−12.7593	−	13.6613i	−0.429627	−	0.460001i
$883$	30.6494	−	2.68147i	1.03143	−	0.0902387i	0.441149	−	0.897434i	$-0.354571\pi$
$883$	30.6494	−	2.68147i	1.03143	−	0.0902387i	0.590284	+	0.807195i	$0.299016\pi$
$884$	−8.61445	−	7.22838i	−0.289735	−	0.243117i
$885$	−0.512890	+	36.1680i	−0.0172406	+	1.21578i
$886$	−0.240131	+	0.415919i	−0.00806736	+	0.0139731i
$887$	1.18999	−	2.55195i	0.0399561	−	0.0856861i	−0.885317	−	0.464989i	$-0.846058\pi$
$887$	1.18999	−	2.55195i	0.0399561	−	0.0856861i	0.925273	+	0.379303i	$0.123836\pi$
$888$	9.80931	−	7.94973i	0.329179	−	0.266776i
$889$	21.2033	+	3.73872i	0.711137	+	0.125393i
$890$	18.9423	+	13.1822i	0.634946	+	0.441869i
$891$	5.45088	−	12.2943i	0.182611	−	0.411873i
$892$	10.2862	+	10.2862i	0.344406	+	0.344406i
$893$	−12.4417	+	20.4337i	−0.416345	+	0.683787i
$894$	−1.31695	+	4.59949i	−0.0440454	+	0.153830i
$895$	−8.20595	−	2.95994i	−0.274295	−	0.0989399i
$896$	1.24408	−	3.41808i	0.0415618	−	0.114190i
$897$	7.12671	+	20.6714i	0.237954	+	0.690197i
$898$	5.94148	+	4.16027i	0.198270	+	0.138830i
$899$	38.9279	−	14.1686i	1.29832	−	0.472550i
$900$	−0.425337	+	14.9940i	−0.0141779	+	0.499799i
$901$	17.7658	+	30.7713i	0.591865	+	1.02514i
$902$	5.59979	−	0.489918i	0.186453	−	0.0163125i
$903$	−22.3441	−	4.33424i	−0.743564	−	0.144235i
$904$	−10.3866	+	5.99668i	−0.345452	+	0.199447i
$905$	−20.9487	+	0.0604391i	−0.696358	+	0.00200906i
$906$	1.51469	+	21.5408i	0.0503221	+	0.715645i
$907$	27.2763	−	38.9545i	0.905693	−	1.29346i	−0.0498938	−	0.998755i	$-0.515888\pi$
$907$	27.2763	−	38.9545i	0.905693	−	1.29346i	0.955587	−	0.294709i	$-0.0952228\pi$
$908$	−0.699438	+	0.489751i	−0.0232117	+	0.0162530i
$909$	−11.5640	−	14.7776i	−0.383553	−	0.490141i
$910$	−23.8613	+	11.2106i	−0.790995	+	0.371629i
$911$		−	37.9378i		−	1.25693i	−0.777836	−	0.628467i	$-0.783683\pi$
$911$		−	37.9378i		−	1.25693i	0.777836	−	0.628467i	$-0.216317\pi$
$912$	−5.54975	+	5.11862i	−0.183771	+	0.169494i
$913$	13.5083	−	13.5083i	0.447061	−	0.447061i
$914$	−15.8140	+	13.2695i	−0.523080	+	0.438916i
$915$	0.0600455	+	0.0736557i	0.00198504	+	0.00243498i
$916$	3.29085	−	18.6633i	0.108733	−	0.616654i
$917$	−24.7730	−	17.3462i	−0.818077	−	0.572824i
$918$	−17.2335	+	5.29077i	−0.568790	+	0.174622i
$919$	−22.1029	−	12.7611i	−0.729107	−	0.420950i	0.0889886	−	0.996033i	$-0.471637\pi$
$919$	−22.1029	−	12.7611i	−0.729107	−	0.420950i	−0.818095	+	0.575083i	$0.804970\pi$
$920$	−7.55458	−	4.33263i	−0.249067	−	0.142842i
$921$	−27.0958	−	40.1375i	−0.892836	−	1.32258i
$922$	0.847987	+	9.69254i	0.0279270	+	0.319207i
$923$	5.10612	−	19.0563i	0.168070	−	0.627246i
$924$	−6.76952	+	6.54234i	−0.222701	+	0.215227i
$925$	29.7359	−	21.0780i	0.977710	−	0.693042i
$926$	9.85047	−	1.73690i	0.323707	−	0.0570782i
$927$	−52.6336	+	2.79941i	−1.72871	+	0.0919446i
$928$	4.23211	−	1.97346i	0.138926	−	0.0647821i
$929$	−29.7420	+	24.9565i	−0.975803	+	0.818796i	−0.983451	−	0.181175i	$-0.942010\pi$
$929$	−29.7420	+	24.9565i	−0.975803	+	0.818796i	0.00764775	+	0.999971i	$0.497566\pi$
$930$	−33.3110	+	8.42128i	−1.09231	+	0.276145i
$931$	2.99761	−	26.9945i	0.0982428	−	0.884708i
$932$	−9.23042	+	9.23042i	−0.302352	+	0.302352i
$933$	55.3590	+	21.2257i	1.81237	+	0.694897i
$934$	12.9703	−	35.6357i	0.424403	−	1.16604i
$935$	−10.5202	−	4.86873i	−0.344046	−	0.159225i
$936$	9.01875	+	3.63567i	0.294787	+	0.118835i
$937$	13.6803	+	6.37923i	0.446916	+	0.208400i	0.633029	−	0.774128i	$-0.281811\pi$
$937$	13.6803	+	6.37923i	0.446916	+	0.208400i	−0.186113	+	0.982528i	$0.559589\pi$
$938$	3.87862	−	1.03927i	0.126641	−	0.0339335i
$939$	−1.86862	+	0.466670i	−0.0609801	+	0.0152292i
$940$	−10.0327	+	7.06817i	−0.327229	+	0.230538i
$941$	2.01753	−	2.40440i	0.0657695	−	0.0783811i	−0.732157	−	0.681136i	$-0.761486\pi$
$941$	2.01753	−	2.40440i	0.0657695	−	0.0783811i	0.797926	+	0.602755i	$0.205931\pi$
$942$	33.3170	+	20.0012i	1.08553	+	0.651676i
$943$	3.79200	+	14.1519i	0.123484	+	0.460850i
$944$	−8.77625	+	3.19429i	−0.285643	+	0.103965i
$945$	−5.71236	+	41.8755i	−0.185823	+	1.36221i
$946$	−0.937401	+	5.31627i	−0.0304775	+	0.172847i
$947$	−44.4069	+	20.7073i	−1.44303	+	0.672895i	−0.977267	−	0.212014i	$-0.931998\pi$
$947$	−44.4069	+	20.7073i	−1.44303	+	0.672895i	−0.465762	+	0.884910i	$0.654220\pi$
$948$	9.06670	−	23.6470i	0.294473	−	0.768019i
$949$		−	23.6503i		−	0.767722i
$950$	−16.9389	+	13.7140i	−0.549571	+	0.444940i
$951$	16.1778	−	56.5014i	0.524601	−	1.83219i
$952$	12.5716	+	1.09987i	0.407448	+	0.0356471i
$953$	−2.95657	−	6.34037i	−0.0957725	−	0.205385i	0.852585	−	0.522589i	$-0.175034\pi$
$953$	−2.95657	−	6.34037i	−0.0957725	−	0.205385i	−0.948357	+	0.317204i	$0.897256\pi$
$954$	−22.8488	−	20.5410i	−0.739756	−	0.665040i
$955$	22.2832	+	26.4011i	0.721069	+	0.854319i
$956$	3.80488	+	10.4538i	0.123058	+	0.338100i
$957$	−12.0839	−	0.206231i	−0.390618	−	0.00666650i
$958$	25.8257	+	6.91997i	0.834389	+	0.223574i
$959$	49.2322	+	41.3107i	1.58979	+	1.33399i
$960$	−3.65783	+	1.27290i	−0.118056	+	0.0410827i
$961$	−23.8513	−	41.3117i	−0.769398	−	1.33264i
$962$	−6.11549	−	22.8233i	−0.197171	−	0.735853i
$963$	30.0283	+	46.1610i	0.967649	+	1.48752i
$964$	19.4232	−	3.42484i	0.625580	−	0.110307i
$965$	−16.1111	+	34.8123i	−0.518635	+	1.12065i
$966$	−19.8569	−	14.4151i	−0.638885	−	0.463798i
$967$	−40.4674	−	3.54044i	−1.30134	−	0.113853i	−0.584676	−	0.811267i	$-0.698778\pi$
$967$	−40.4674	−	3.54044i	−1.30134	−	0.113853i	−0.716669	+	0.697414i	$0.754334\pi$
$968$	−6.19931	−	6.19931i	−0.199253	−	0.199253i
$969$	−22.1366	−	14.0019i	−0.711130	−	0.449805i
$970$	−1.76798	−	3.04193i	−0.0567664	−	0.0976704i
$971$	20.7326	+	24.7081i	0.665340	+	0.792921i	0.988142	−	0.153545i	$-0.0490691\pi$
$971$	20.7326	+	24.7081i	0.665340	+	0.792921i	−0.322802	+	0.946467i	$0.604625\pi$
$972$	12.7519	−	8.96595i	0.409018	−	0.287583i
$973$	4.11670	+	5.87926i	0.131975	+	0.188480i
$974$	5.11638	+	29.0164i	0.163939	+	0.929747i
$975$	25.3051	+	12.1498i	0.810413	+	0.389105i
$976$	−0.0122683	+	0.0212493i	−0.000392698	+	0.000680172i
$977$	−3.18510	−	0.853445i	−0.101900	−	0.0273041i	0.207509	−	0.978233i	$-0.433465\pi$
$977$	−3.18510	−	0.853445i	−0.101900	−	0.0273041i	−0.309409	+	0.950929i	$0.600131\pi$
$978$	−1.93483	+	9.97450i	−0.0618689	+	0.318949i
$979$	9.91299	−	11.8138i	0.316821	−	0.377572i
$980$	6.93166	−	12.0864i	0.221424	−	0.386085i
$981$	−3.56659	+	1.89995i	−0.113873	+	0.0606606i
$982$	8.95390	+	4.17527i	0.285730	+	0.133238i
$983$	18.5218	−	26.4518i	0.590753	−	0.843683i	−0.406806	−	0.913515i	$-0.633357\pi$
$983$	18.5218	−	26.4518i	0.590753	−	0.843683i	0.997559	+	0.0698321i	$0.0222463\pi$
$984$	5.85735	+	2.85400i	0.186725	+	0.0909823i
$985$	20.2582	+	14.0980i	0.645478	+	0.449199i
$986$	10.4135	+	12.4104i	0.331635	+	0.395227i
$987$	−30.2364	+	16.7756i	−0.962434	+	0.533975i
$988$	4.52130	+	13.3857i	0.143842	+	0.425855i
$989$	−14.0702			−0.447405
$990$	9.95357	+	1.18516i	0.316345	+	0.0376670i
$991$	38.6641	+	14.0726i	1.22821	+	0.447030i	0.872983	−	0.487751i	$-0.162183\pi$
$991$	38.6641	+	14.0726i	1.22821	+	0.447030i	0.355223	+	0.934782i	$0.384405\pi$
$992$	−5.08846	−	7.26707i	−0.161559	−	0.230730i
$993$	−8.95502	−	11.0498i	−0.284179	−	0.350653i
$994$	7.57216	+	20.8044i	0.240174	+	0.659874i
$995$	−0.00457588	−	1.58604i	−0.000145065	−	0.0502808i
$996$	21.4837	−	5.36536i	0.680739	−	0.170008i
$997$	−3.56687	−	40.7695i	−0.112964	−	1.29118i	−0.815175	−	0.579215i	$-0.803359\pi$
$997$	−3.56687	−	40.7695i	−0.112964	−	1.29118i	0.702211	−	0.711969i	$-0.252196\pi$
$998$	−2.43719	−	27.8572i	−0.0771479	−	0.881804i
$999$	−36.0383	−	11.6631i	−1.14020	−	0.369005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.557.22	yes	480
3.2	odd	2	inner	570.2.bi.a.557.4	yes	480
5.3	odd	4	inner	570.2.bi.a.443.9	yes	480
15.8	even	4	inner	570.2.bi.a.443.26	yes	480
19.16	even	9	inner	570.2.bi.a.377.26	yes	480
57.35	odd	18	inner	570.2.bi.a.377.9	yes	480
95.73	odd	36	inner	570.2.bi.a.263.4	✓	480
285.263	even	36	inner	570.2.bi.a.263.22	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.263.4	✓	480	95.73	odd	36	inner
570.2.bi.a.263.22	yes	480	285.263	even	36	inner
570.2.bi.a.377.9	yes	480	57.35	odd	18	inner
570.2.bi.a.377.26	yes	480	19.16	even	9	inner
570.2.bi.a.443.9	yes	480	5.3	odd	4	inner
570.2.bi.a.443.26	yes	480	15.8	even	4	inner
570.2.bi.a.557.4	yes	480	3.2	odd	2	inner
570.2.bi.a.557.22	yes	480	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-1.71062 + 0.271617i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.70877 + 1.44225i) q^{5} +(0.121493 + 1.72778i) q^{6} +(-3.51350 + 0.941441i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.85245 - 0.929267i) q^{9} +O(q^{10})\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-1.71062 + 0.271617i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-1.70877 + 1.44225i) q^{5} +(0.121493 + 1.72778i) q^{6} +(-3.51350 + 0.941441i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.85245 - 0.929267i) q^{9} +(1.28784 + 1.82797i) q^{10} +(1.29408 - 0.747136i) q^{11} +(1.73180 + 0.0295558i) q^{12} +(1.36985 - 2.93764i) q^{13} +(0.631636 + 3.58219i) q^{14} +(2.53132 - 2.93128i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.302375 + 3.45616i) q^{17} +(-0.677124 - 2.92259i) q^{18} +(2.58276 - 3.51132i) q^{19} +(1.93326 - 1.12362i) q^{20} +(5.75456 - 2.56478i) q^{21} +(-0.631507 - 1.35427i) q^{22} +(3.19035 - 2.23391i) q^{23} +(0.180380 - 1.72263i) q^{24} +(0.839814 - 4.92897i) q^{25} +(-2.80707 - 1.62067i) q^{26} +(-4.62705 + 2.36440i) q^{27} +(3.62361 - 0.317024i) q^{28} +(3.57713 + 3.00157i) q^{29} +(-2.69951 - 2.77717i) q^{30} +(4.43573 - 7.68290i) q^{31} +(0.422618 - 0.906308i) q^{32} +(-2.01074 + 1.62956i) q^{33} +(3.41666 + 0.602449i) q^{34} +(4.64599 - 6.67607i) q^{35} +(-2.97048 + 0.419827i) q^{36} +(5.15462 + 5.15462i) q^{37} +(-3.27285 - 2.87896i) q^{38} +(-1.54537 + 5.39727i) q^{39} +(-0.950846 - 2.02383i) q^{40} +(-1.28662 + 3.53495i) q^{41} +(-2.05347 - 5.95620i) q^{42} +(-2.95931 - 2.07213i) q^{43} +(-1.40416 + 0.511071i) q^{44} +(-3.53395 + 5.70186i) q^{45} +(-1.94735 - 3.37291i) q^{46} +(-5.46752 + 0.478346i) q^{47} +(-1.70036 - 0.329830i) q^{48} +(5.39623 - 3.11551i) q^{49} +(-4.83702 - 1.26621i) q^{50} +(-0.421503 - 5.99432i) q^{51} +(-1.85915 + 2.65514i) q^{52} +(8.38937 - 5.87430i) q^{53} +(1.95213 + 4.81552i) q^{54} +(-1.13373 + 3.14307i) q^{55} -3.63745i q^{56} +(-3.46439 + 6.70805i) q^{57} +(3.30191 - 3.30191i) q^{58} +(-7.15446 + 6.00331i) q^{59} +(-3.00188 + 2.44719i) q^{60} +(-0.00426072 + 0.0241638i) q^{61} +(-7.26707 - 5.08846i) q^{62} +(-9.14724 + 5.95039i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(1.89607 + 6.99543i) q^{65} +(1.44811 + 2.14512i) q^{66} +(-0.0962128 - 1.09972i) q^{67} +(0.897938 - 3.35115i) q^{68} +(-4.85071 + 4.68792i) q^{69} +(-6.24574 - 5.21017i) q^{70} +(5.99409 - 1.05692i) q^{71} +(0.159335 + 2.99577i) q^{72} +(6.61286 - 3.08363i) q^{73} +(5.58426 - 4.68575i) q^{74} +(-0.0978130 + 8.65970i) q^{75} +(-3.15326 + 3.00948i) q^{76} +(-3.84336 + 3.84336i) q^{77} +(5.24204 + 2.00990i) q^{78} +(5.00093 - 13.7399i) q^{79} +(-2.09900 + 0.770839i) q^{80} +(7.27293 - 5.30137i) q^{81} +(3.40937 + 1.58981i) q^{82} +(12.3490 - 3.30890i) q^{83} +(-6.11251 + 1.52654i) q^{84} +(-4.46797 - 6.34190i) q^{85} +(-2.32217 + 2.76745i) q^{86} +(-6.93439 - 4.16294i) q^{87} +(0.386746 + 1.44336i) q^{88} +(9.69825 - 3.52987i) q^{89} +(5.37216 + 4.01745i) q^{90} +(-2.04734 + 11.6111i) q^{91} +(-3.52979 + 1.64597i) q^{92} +(-5.50104 + 14.3474i) q^{93} +5.48841i q^{94} +(0.650852 + 9.72504i) q^{95} +(-0.476771 + 1.66514i) q^{96} +(-1.56748 - 0.137137i) q^{97} +(-2.63334 - 5.64723i) q^{98} +(2.99700 - 3.33371i) 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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