LMFDB - Embedded newform 572.2.bb.b.51.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(51,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7, 5]))

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

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

chi := DirichletCharacter("572.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bb (of order $10$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.6
Character	$\chi$	$=$	572.51
Dual form			572.2.bb.b.415.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38768 + 0.272646i) q^{2} +(-0.00197950 - 0.000643177i) q^{3} +(1.85133 - 0.756692i) q^{4} +(0.569619 + 0.784014i) q^{5} +(0.00292227 + 0.000352825i) q^{6} +(0.226728 - 0.0736686i) q^{7} +(-2.36275 + 1.55481i) q^{8} +(-2.42705 - 1.76335i) q^{9} +O(q^{10})$	\(q+(-1.38768 + 0.272646i) q^{2} +(-0.00197950 - 0.000643177i) q^{3} +(1.85133 - 0.756692i) q^{4} +(0.569619 + 0.784014i) q^{5} +(0.00292227 + 0.000352825i) q^{6} +(0.226728 - 0.0736686i) q^{7} +(-2.36275 + 1.55481i) q^{8} +(-2.42705 - 1.76335i) q^{9} +(-1.00421 - 0.932658i) q^{10} +(-3.19378 + 0.894308i) q^{11} +(-0.00415139 + 0.000307136i) q^{12} +(-1.01406 - 3.46001i) q^{13} +(-0.294542 + 0.164045i) q^{14} +(-0.000623299 - 0.00191832i) q^{15} +(2.85483 - 2.80177i) q^{16} +(-2.74649 - 3.78022i) q^{17} +(3.84874 + 1.78525i) q^{18} +(-2.19509 - 0.713228i) q^{19} +(1.64781 + 1.02044i) q^{20} -0.000496190 q^{21} +(4.18812 - 2.11179i) q^{22} +7.15402i q^{23} +(0.00567707 - 0.00155807i) q^{24} +(1.25487 - 3.86210i) q^{25} +(2.35055 + 4.52492i) q^{26} +(0.00734037 + 0.0101032i) q^{27} +(0.364005 - 0.307948i) q^{28} +(-2.71367 + 0.881726i) q^{29} +(0.00138796 + 0.00249208i) q^{30} +(-1.24040 - 0.901203i) q^{31} +(-3.19771 + 4.66633i) q^{32} +(0.00689727 + 0.000283886i) q^{33} +(4.84191 + 4.49692i) q^{34} +(0.186906 + 0.135795i) q^{35} +(-5.82758 - 1.42802i) q^{36} +(-0.841914 + 0.273554i) q^{37} +(3.24055 + 0.391252i) q^{38} +(-0.000218079 + 0.00750130i) q^{39} +(-2.56486 - 0.966780i) q^{40} +(2.69948 - 8.30815i) q^{41} +(0.000688555 - 0.000135284i) q^{42} -3.12010 q^{43} +(-5.23602 + 4.07236i) q^{44} -2.90728i q^{45} +(-1.95051 - 9.92752i) q^{46} +(2.27891 - 7.01376i) q^{47} +(-0.00745317 + 0.00370993i) q^{48} +(-5.61714 + 4.08109i) q^{49} +(-0.688380 + 5.70151i) q^{50} +(0.00300531 + 0.00924940i) q^{51} +(-4.49552 - 5.63829i) q^{52} +(1.35397 + 0.983720i) q^{53} +(-0.0129407 - 0.0120187i) q^{54} +(-2.52039 - 1.99455i) q^{55} +(-0.421162 + 0.526579i) q^{56} +(0.00388644 + 0.00282366i) q^{57} +(3.52532 - 1.96343i) q^{58} +(-1.84755 - 5.68617i) q^{59} +(-0.00260551 - 0.00307979i) q^{60} +(-3.30738 - 4.55221i) q^{61} +(1.96699 + 0.912394i) q^{62} +(-0.680185 - 0.221005i) q^{63} +(3.16516 - 7.34723i) q^{64} +(2.13507 - 2.76592i) q^{65} +(-0.00964863 + 0.00148657i) q^{66} +2.54705 q^{67} +(-7.94511 - 4.92018i) q^{68} +(0.00460131 - 0.0141614i) q^{69} +(-0.296390 - 0.137482i) q^{70} +(-8.03766 + 5.83970i) q^{71} +(8.47617 + 0.392773i) q^{72} +(-1.44811 - 4.45684i) q^{73} +(1.09373 - 0.609151i) q^{74} +(-0.00496804 + 0.00683792i) q^{75} +(-4.60353 + 0.340588i) q^{76} +(-0.658238 + 0.438046i) q^{77} +(-0.00174257 - 0.0104689i) q^{78} +(-3.52119 - 2.55829i) q^{79} +(3.82279 + 0.642287i) q^{80} +(2.78114 + 8.55947i) q^{81} +(-1.48084 + 12.2651i) q^{82} +(-3.64387 - 5.01536i) q^{83} +(-0.000918611 + 0.000375463i) q^{84} +(1.39929 - 4.30657i) q^{85} +(4.32970 - 0.850681i) q^{86} +0.00593882 q^{87} +(6.15562 - 7.07873i) q^{88} +10.0246i q^{89} +(0.792657 + 4.03438i) q^{90} +(-0.484810 - 0.709779i) q^{91} +(5.41339 + 13.2444i) q^{92} +(0.00187573 + 0.00258173i) q^{93} +(-1.25013 + 10.3542i) q^{94} +(-0.691185 - 2.12725i) q^{95} +(0.00933114 - 0.00718028i) q^{96} +(7.20693 - 9.91949i) q^{97} +(6.68212 - 7.19475i) q^{98} +(9.32843 + 3.46123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) $ 304 * q - 14 * q^4 + 72 * q^9	$ 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) $ 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.38768	+	0.272646i	−0.981240	+	0.192790i
$2$	−1.38768	+	0.272646i	−0.981240	+	0.192790i
$3$	−0.00197950		0.000643177i	−0.00114286		0.000371339i	0.308446	−	0.951242i	$-0.400191\pi$
$3$	−0.00197950		0.000643177i	−0.00114286		0.000371339i	−0.309588	+	0.950871i	$0.600191\pi$
$4$	1.85133	−	0.756692i	0.925664	−	0.378346i
$5$	0.569619	+	0.784014i	0.254741	+	0.350622i	0.917165	−	0.398508i	$-0.130472\pi$
$5$	0.569619	+	0.784014i	0.254741	+	0.350622i	−0.662423	+	0.749130i	$0.730472\pi$
$6$	0.00292227		0.000352825i	0.00119301		0.000144040i
$7$	0.226728	−	0.0736686i	0.0856953	−	0.0278441i	−0.265856	−	0.964013i	$-0.585654\pi$
$7$	0.226728	−	0.0736686i	0.0856953	−	0.0278441i	0.351551	+	0.936169i	$0.385654\pi$
$8$	−2.36275	+	1.55481i	−0.835358	+	0.549707i
$9$	−2.42705	−	1.76335i	−0.809016	−	0.587784i
$10$	−1.00421	−	0.932658i	−0.317559	−	0.294932i
$11$	−3.19378	+	0.894308i	−0.962960	+	0.269644i
$11$	−3.19378	+	0.894308i	−0.962960	+	0.269644i
$12$	−0.00415139		0.000307136i	−0.00119840		8.86627e-5i
$13$	−1.01406	−	3.46001i	−0.281249	−	0.959635i
$13$	−1.01406	−	3.46001i	−0.281249	−	0.959635i
$14$	−0.294542	+	0.164045i	−0.0787196	+	0.0438429i
$15$	−0.000623299	−	0.00191832i	−0.000160935	−	0.000495308i
$16$	2.85483	−	2.80177i	0.713709	−	0.700443i
$17$	−2.74649	−	3.78022i	−0.666121	−	0.916837i	0.333543	−	0.942735i	$-0.391756\pi$
$17$	−2.74649	−	3.78022i	−0.666121	−	0.916837i	−0.999665	+	0.0258976i	$0.991756\pi$
$18$	3.84874	+	1.78525i	0.907158	+	0.420788i
$19$	−2.19509	−	0.713228i	−0.503588	−	0.163626i	0.0461962	−	0.998932i	$-0.485290\pi$
$19$	−2.19509	−	0.713228i	−0.503588	−	0.163626i	−0.549784	+	0.835307i	$0.685290\pi$
$20$	1.64781	+	1.02044i	0.368461	+	0.228177i
$21$	−0.000496190	0		−0.000108278	0
$22$	4.18812	−	2.11179i	0.892910	−	0.450234i
$23$			7.15402i			1.49172i	0.666104	+	0.745859i	$0.267961\pi$
$23$			7.15402i			1.49172i	−0.666104	+	0.745859i	$0.732039\pi$
$24$	0.00567707	−	0.00155807i	0.00115883	−	0.000318039i
$25$	1.25487	−	3.86210i	0.250975	−	0.772421i
$26$	2.35055	+	4.52492i	0.460980	+	0.887410i
$27$	0.00734037	+	0.0101032i	0.00141266	+	0.00194435i
$28$	0.364005	−	0.307948i	0.0687904	−	0.0581968i
$29$	−2.71367	+	0.881726i	−0.503917	+	0.163732i	−0.549934	−	0.835208i	$-0.685347\pi$
$29$	−2.71367	+	0.881726i	−0.503917	+	0.163732i	0.0460172	+	0.998941i	$0.485347\pi$
$30$	0.00138796	+	0.00249208i	0.000253406	+	0.000454989i
$31$	−1.24040	−	0.901203i	−0.222782	−	0.161861i	0.470796	−	0.882242i	$-0.343967\pi$
$31$	−1.24040	−	0.901203i	−0.222782	−	0.161861i	−0.693578	+	0.720381i	$0.743967\pi$
$32$	−3.19771	+	4.66633i	−0.565281	+	0.824898i
$33$	0.00689727		0.000283886i	0.00120066		4.94182e-5i
$34$	4.84191	+	4.49692i	0.830382	+	0.771216i
$35$	0.186906	+	0.135795i	0.0315929	+	0.0229536i
$36$	−5.82758	−	1.42802i	−0.971263	−	0.238003i
$37$	−0.841914	+	0.273554i	−0.138410	+	0.0449721i	−0.377403	−	0.926049i	$-0.623183\pi$
$37$	−0.841914	+	0.273554i	−0.138410	+	0.0449721i	0.238993	+	0.971021i	$0.423183\pi$
$38$	3.24055	+	0.391252i	0.525686	+	0.0634695i
$39$	−0.000218079		0.00750130i	−3.49205e−5		0.00120117i
$40$	−2.56486	−	0.966780i	−0.405539	−	0.152861i
$41$	2.69948	−	8.30815i	0.421588	−	1.29752i	−0.484635	−	0.874716i	$-0.661048\pi$
$41$	2.69948	−	8.30815i	0.421588	−	1.29752i	0.906223	−	0.422799i	$-0.138952\pi$
$42$	0.000688555	0	0.000135284i	0.000106246	0	2.08748e-5i
$43$	−3.12010			−0.475810			−0.237905	−	0.971288i	$-0.576461\pi$
$43$	−3.12010			−0.475810			−0.237905	+	0.971288i	$0.576461\pi$
$44$	−5.23602	+	4.07236i	−0.789359	+	0.613932i
$45$		−	2.90728i		−	0.433391i
$46$	−1.95051	−	9.92752i	−0.287588	−	1.46373i
$47$	2.27891	−	7.01376i	0.332413	−	1.02306i	−0.635569	−	0.772044i	$-0.719235\pi$
$47$	2.27891	−	7.01376i	0.332413	−	1.02306i	0.967982	−	0.251018i	$-0.0807654\pi$
$48$	−0.00745317	+	0.00370993i	−0.00107577	+	0.000535482i
$49$	−5.61714	+	4.08109i	−0.802449	+	0.583013i
$50$	−0.688380	+	5.70151i	−0.0973517	+	0.806316i
$51$	0.00300531	+	0.00924940i	0.000420828	+	0.00129518i
$52$	−4.49552	−	5.63829i	−0.623416	−	0.781890i
$53$	1.35397	+	0.983720i	0.185983	+	0.135124i	0.676881	−	0.736093i	$-0.263331\pi$
$53$	1.35397	+	0.983720i	0.185983	+	0.135124i	−0.490898	+	0.871217i	$0.663331\pi$
$54$	−0.0129407	−	0.0120187i	−0.00176101	−	0.00163553i
$55$	−2.52039	−	1.99455i	−0.339849	−	0.268945i
$56$	−0.421162	+	0.526579i	−0.0562802	+	0.0703671i
$57$	0.00388644	+	0.00282366i	0.000514772	+	0.000374003i
$58$	3.52532	−	1.96343i	0.462897	−	0.257811i
$59$	−1.84755	−	5.68617i	−0.240530	−	0.740276i	−0.996340	−	0.0854843i	$-0.972756\pi$
$59$	−1.84755	−	5.68617i	−0.240530	−	0.740276i	0.755809	−	0.654792i	$-0.227244\pi$
$60$	−0.00260551	−	0.00307979i	−0.000336370	−	0.000397599i
$61$	−3.30738	−	4.55221i	−0.423466	−	0.582851i	0.542972	−	0.839751i	$-0.317299\pi$
$61$	−3.30738	−	4.55221i	−0.423466	−	0.582851i	−0.966438	+	0.256900i	$0.917299\pi$
$62$	1.96699	+	0.912394i	0.249808	+	0.115874i
$63$	−0.680185	−	0.221005i	−0.0856952	−	0.0278441i
$64$	3.16516	−	7.34723i	0.395645	−	0.918404i
$65$	2.13507	−	2.76592i	0.264823	−	0.343071i
$66$	−0.00964863	+	0.00148657i	−0.00118766	+	0.000182984i
$67$	2.54705			0.311171			0.155586	−	0.987822i	$-0.450274\pi$
$67$	2.54705			0.311171			0.155586	+	0.987822i	$0.450274\pi$
$68$	−7.94511	−	4.92018i	−0.963486	−	0.596659i
$69$	0.00460131	−	0.0141614i	0.000553932	−	0.00170483i
$70$	−0.296390	−	0.137482i	−0.0354254	−	0.0164322i
$71$	−8.03766	+	5.83970i	−0.953895	+	0.693045i	−0.951725	−	0.306953i	$-0.900691\pi$
$71$	−8.03766	+	5.83970i	−0.953895	+	0.693045i	−0.00216986	+	0.999998i	$0.500691\pi$
$72$	8.47617	+	0.392773i	0.998927	+	0.0462887i
$73$	−1.44811	−	4.45684i	−0.169489	−	0.521633i	0.829850	−	0.557986i	$-0.188426\pi$
$73$	−1.44811	−	4.45684i	−0.169489	−	0.521633i	−0.999339	+	0.0363532i	$0.988426\pi$
$74$	1.09373	−	0.609151i	0.127143	−	0.0708124i
$75$	−0.00496804	+	0.00683792i	−0.000573660	+	0.000789575i
$76$	−4.60353	+	0.340588i	−0.528061	+	0.0390681i
$77$	−0.658238	+	0.438046i	−0.0750132	+	0.0499200i
$78$	−0.00174257	−	0.0104689i	−0.000197308	−	0.00118537i
$79$	−3.52119	−	2.55829i	−0.396165	−	0.287831i	0.371812	−	0.928308i	$-0.378737\pi$
$79$	−3.52119	−	2.55829i	−0.396165	−	0.287831i	−0.767977	+	0.640477i	$0.778737\pi$
$80$	3.82279	+	0.642287i	0.427401	+	0.0718098i
$81$	2.78114	+	8.55947i	0.309016	+	0.951052i
$82$	−1.48084	+	12.2651i	−0.163532	+	1.35445i
$83$	−3.64387	−	5.01536i	−0.399967	−	0.550507i	0.560769	−	0.827972i	$-0.310506\pi$
$83$	−3.64387	−	5.01536i	−0.399967	−	0.550507i	−0.960736	+	0.277465i	$0.910506\pi$
$84$	−0.000918611	0	0.000375463i	−0.000100229	0	4.09664e-5i
$85$	1.39929	−	4.30657i	0.151774	−	0.467113i
$86$	4.32970	−	0.850681i	0.466884	−	0.0917313i
$87$	0.00593882			0.000636708
$88$	6.15562	−	7.07873i	0.656191	−	0.754595i
$89$			10.0246i			1.06261i	0.847181	+	0.531304i	$0.178298\pi$
$89$			10.0246i			1.06261i	−0.847181	+	0.531304i	$0.821702\pi$
$90$	0.792657	+	4.03438i	0.0835534	+	0.425261i
$91$	−0.484810	−	0.709779i	−0.0508219	−	0.0744051i
$92$	5.41339	+	13.2444i	0.564385	+	1.38083i
$93$	0.00187573	+	0.00258173i	0.000194504	+	0.000267712i
$94$	−1.25013	+	10.3542i	−0.128941	+	1.06796i
$95$	−0.691185	−	2.12725i	−0.0709141	−	0.218251i
$96$	0.00933114	−	0.00718028i	0.000952356	−	0.000732835i
$97$	7.20693	−	9.91949i	0.731753	−	1.00717i	−0.267298	−	0.963614i	$-0.586131\pi$
$97$	7.20693	−	9.91949i	0.731753	−	1.00717i	0.999051	−	0.0435575i	$-0.0138692\pi$
$98$	6.68212	−	7.19475i	0.674996	−	0.726780i
$99$	9.32843	+	3.46123i	0.937542	+	0.347867i
$100$	−0.599240	−	8.09958i	−0.0599240	−	0.809958i
$101$	−2.74189	+	3.77388i	−0.272828	+	0.375515i	−0.923342	−	0.383979i	$-0.874554\pi$
$101$	−2.74189	+	3.77388i	−0.272828	+	0.375515i	0.650514	+	0.759494i	$0.274554\pi$
$102$	−0.00669223	−	0.0120159i	−0.000662630	−	0.00118975i
$103$	9.71191	−	3.15559i	0.956943	−	0.310930i	0.211409	−	0.977398i	$-0.432195\pi$
$103$	9.71191	−	3.15559i	0.956943	−	0.310930i	0.745534	+	0.666468i	$0.232195\pi$
$104$	7.77561	+	6.59848i	0.762461	+	0.647034i
$105$	−0.000282640	0	0.000389020i	−2.75828e−5	0	3.79645e-5i
$106$	−2.14709	−	0.995936i	−0.208544	−	0.0967338i
$107$	−3.71333	+	11.4285i	−0.358982	+	1.10483i	0.594683	+	0.803960i	$0.297278\pi$
$107$	−3.71333	+	11.4285i	−0.358982	+	1.10483i	−0.953665	+	0.300871i	$0.902722\pi$
$108$	0.0212344	+	0.0131499i	0.00204328	+	0.00126535i
$109$	−4.10495			−0.393182			−0.196591	−	0.980486i	$-0.562987\pi$
$109$	−4.10495			−0.393182			−0.196591	+	0.980486i	$0.562987\pi$
$110$	4.04130	+	2.08063i	0.385323	+	0.198380i
$111$	0.00184251			0.000174883
$112$	0.440870	−	0.845553i	0.0416583	−	0.0798972i
$113$	−0.921204	+	2.83517i	−0.0866596	+	0.266711i	−0.984990	−	0.172609i	$-0.944780\pi$
$113$	−0.921204	+	2.83517i	−0.0866596	+	0.266711i	0.898331	+	0.439319i	$0.144780\pi$
$114$	−0.00616301	−	0.00285873i	−0.000577219	−	0.000267745i
$115$	−5.60885	+	4.07507i	−0.523028	+	0.380002i
$116$	−4.35671	+	3.68578i	−0.404510	+	0.342216i
$117$	−3.64006	+	10.1858i	−0.336524	+	0.941674i
$118$	4.11412	+	7.38687i	0.378736	+	0.680017i
$119$	−0.901190	−	0.654753i	−0.0826120	−	0.0600211i
$120$	0.00445531	+	0.00356339i	0.000406712	+	0.000325292i
$121$	9.40043	−	5.71244i	0.854584	−	0.519313i
$122$	5.83073	+	5.41528i	0.527889	+	0.490277i
$123$	−0.0106872	+	0.0147097i	−0.000963635	+	0.00132633i
$124$	−2.97832	−	0.729822i	−0.267461	−	0.0655400i
$125$	8.35106	−	2.71342i	0.746941	−	0.242696i
$126$	1.00414	+	0.121236i	0.0894556	+	0.0108006i
$127$	7.65685	−	5.56303i	0.679436	−	0.493639i	−0.193735	−	0.981054i	$-0.562060\pi$
$127$	7.65685	−	5.56303i	0.679436	−	0.493639i	0.873170	+	0.487415i	$0.162060\pi$
$128$	−2.38905	+	11.0586i	−0.211164	+	0.977451i
$129$	0.00617622	+	0.00200678i	0.000543786	+	0.000176687i
$130$	−2.20868	+	4.42034i	−0.193714	+	0.387690i
$131$	−21.7416			−1.89958			−0.949788	−	0.312895i	$-0.898701\pi$
$131$	−21.7416			−1.89958			−0.949788	+	0.312895i	$0.898701\pi$
$132$	0.0129839	−	0.00469354i	0.00113011	−	0.000408520i
$133$	−0.550232			−0.0477111
$134$	−3.53450	+	0.694442i	−0.305334	+	0.0599907i
$135$	−0.00373979	+	0.0115099i	−0.000321870	+	0.000990615i
$136$	12.3668	+	4.66144i	1.06044	+	0.399716i
$137$	8.34690	+	11.4885i	0.713124	+	0.981531i	0.999724	+	0.0234805i	$0.00747476\pi$
$137$	8.34690	+	11.4885i	0.713124	+	0.981531i	−0.286601	+	0.958050i	$0.592525\pi$
$138$	−0.00252412	+	0.0209060i	−0.000214867	+	0.00177964i
$139$	6.19789	+	19.0751i	0.525698	+	1.61793i	0.762932	+	0.646479i	$0.223759\pi$
$139$	6.19789	+	19.0751i	0.525698	+	1.61793i	−0.237234	+	0.971452i	$0.576241\pi$
$140$	0.448780	+	0.109971i	0.0379288	+	0.00929426i
$141$	−0.00902218	+	0.0124180i	−0.000759805	+	0.00104578i
$142$	9.56155	−	10.2951i	0.802388	−	0.863945i
$143$	6.33299	+	10.1436i	0.529591	+	0.848253i
$144$	−11.8693	+	1.76595i	−0.989111	+	0.147162i
$145$	−2.23705	−	1.62531i	−0.185777	−	0.134975i
$146$	3.22466	+	5.78985i	0.266875	+	0.479172i
$147$	0.0137440	−	0.00446569i	0.00113358	−	0.000368324i
$148$	−1.35166	+	1.14351i	−0.111106	+	0.0939958i
$149$	7.91074	−	5.74749i	0.648073	−	0.470853i	−0.214541	−	0.976715i	$-0.568826\pi$
$149$	7.91074	−	5.74749i	0.648073	−	0.470853i	0.862614	+	0.505862i	$0.168826\pi$
$150$	0.00502973	−	0.0108434i	0.000410676	−	0.000885358i
$151$	−9.92907	−	3.22615i	−0.808016	−	0.262540i	−0.124259	−	0.992250i	$-0.539655\pi$
$151$	−9.92907	−	3.22615i	−0.808016	−	0.262540i	−0.683757	+	0.729710i	$0.739655\pi$
$152$	6.29537	−	1.72776i	0.510622	−	0.140140i
$153$			14.0178i			1.13327i
$154$	0.793994	−	0.787335i	0.0639819	−	0.0634453i
$155$		−	1.48583i		−	0.119345i
$156$	0.00527244	+	0.0140524i	0.000422133	+	0.00112509i
$157$	−0.841233	+	2.58905i	−0.0671377	+	0.206629i	−0.978997	−	0.203874i	$-0.934647\pi$
$157$	−0.841233	+	2.58905i	−0.0671377	+	0.206629i	0.911859	+	0.410503i	$0.134647\pi$
$158$	5.58380	+	2.59006i	0.444224	+	0.206054i
$159$	−0.00204748	−	0.00281812i	−0.000162376	−	0.000223491i
$160$	−5.47994	+	0.150979i	−0.433228	+	0.0119359i
$161$	0.527027	+	1.62202i	0.0415355	+	0.127833i
$162$	−6.19305	−	11.1196i	−0.486572	−	0.873636i
$163$	14.1621	+	10.2894i	1.10926	+	0.805926i	0.982547	−	0.186013i	$-0.0595566\pi$
$163$	14.1621	+	10.2894i	1.10926	+	0.805926i	0.126715	+	0.991939i	$0.459557\pi$
$164$	−1.28908	−	17.4238i	−0.100661	−	1.36057i
$165$	0.00370625	+	0.00556926i	0.000288531	+	0.000433566i
$166$	6.42395	+	5.96624i	0.498596	+	0.463070i
$167$	2.77095	−	3.81388i	0.214422	−	0.295127i	−0.688234	−	0.725488i	$-0.741614\pi$
$167$	2.77095	−	3.81388i	0.214422	−	0.295127i	0.902657	+	0.430362i	$0.141614\pi$
$168$	0.00117237		0.000771479i	9.04505e−5		5.95209e-5i
$169$	−10.9434	+	7.01730i	−0.841798	+	0.539793i
$170$	−0.767601	+	6.35766i	−0.0588723	+	0.487610i
$171$	4.06991	+	5.60176i	0.311234	+	0.428377i
$172$	−5.77632	+	2.36095i	−0.440440	+	0.180021i
$173$	17.3954	+	5.65212i	1.32255	+	0.429722i	0.883370	−	0.468677i	$-0.155269\pi$
$173$	17.3954	+	5.65212i	1.32255	+	0.429722i	0.439180	+	0.898399i	$0.355269\pi$
$174$	−0.00824119	+	0.00161919i	−0.000624763	+	0.000122751i
$175$		−	0.968094i		−	0.0731810i
$176$	−6.61206	+	11.5013i	−0.498403	+	0.866946i
$177$			0.0124441i			0.000935353i
$178$	−2.73317	−	13.9110i	−0.204860	−	1.04267i
$179$	−8.54496	−	2.77643i	−0.638681	−	0.207520i	−0.0282640	−	0.999600i	$-0.508998\pi$
$179$	−8.54496	−	2.77643i	−0.638681	−	0.207520i	−0.610417	+	0.792081i	$0.708998\pi$
$180$	−2.19991	−	5.38233i	−0.163972	−	0.401175i
$181$	7.80431	−	5.67016i	0.580090	−	0.421460i	−0.258667	−	0.965967i	$-0.583283\pi$
$181$	7.80431	−	5.67016i	0.580090	−	0.421460i	0.838757	+	0.544507i	$0.183283\pi$
$182$	0.866281	+	0.852767i	0.0642130	+	0.0632113i
$183$	0.00361906	+	0.0111383i	0.000267529	+	0.000823368i
$184$	−11.1231	−	16.9032i	−0.820007	−	1.24612i
$185$	−0.694041	−	0.504250i	−0.0510269	−	0.0370732i
$186$	−0.00330682	−	0.00307121i	−0.000242468	−	0.000225192i
$187$	12.1523	+	9.61696i	0.888668	+	0.703262i
$188$	−1.08825	−	14.7092i	−0.0793686	−	1.07278i
$189$	0.00240856	+	0.00174992i	0.000175197	+	0.000127288i
$190$	1.53913	+	2.76350i	0.111660	+	0.200485i
$191$	18.6047	−	6.04504i	1.34619	−	0.437404i	0.454781	−	0.890603i	$-0.349717\pi$
$191$	18.6047	−	6.04504i	1.34619	−	0.437404i	0.891409	+	0.453199i	$0.149717\pi$
$192$	−0.0109910	+	0.0125081i	−0.000793207	+	0.000902691i
$193$	−15.9398	+	11.5809i	−1.14737	+	0.833613i	−0.988129	−	0.153626i	$-0.950905\pi$
$193$	−15.9398	+	11.5809i	−1.14737	+	0.833613i	−0.159241	+	0.987240i	$0.550905\pi$
$194$	−7.29643	+	15.7300i	−0.523853	+	1.12935i
$195$	−0.00600534	+	0.00410191i	−0.000430052	+	0.000293744i
$196$	−7.31104	+	11.8059i	−0.522217	+	0.843278i
$197$	12.4262			0.885327			0.442664	−	0.896688i	$-0.354034\pi$
$197$	12.4262			0.885327			0.442664	+	0.896688i	$0.354034\pi$
$198$	−13.8886	−	2.25973i	−0.987019	−	0.160592i
$199$		−	16.0076i		−	1.13475i	−0.823460	−	0.567374i	$-0.807959\pi$
$199$		−	16.0076i		−	1.13475i	0.823460	−	0.567374i	$-0.192041\pi$
$200$	3.03987	+	11.0763i	0.214951	+	0.783210i
$201$	−0.00504187	−	0.00163820i	−0.000355626	−	0.000115550i
$202$	2.77594	−	5.98452i	0.195314	−	0.421069i
$203$	−0.550312	+	0.399825i	−0.0386243	+	0.0280622i
$204$	0.0125628	+	0.0148496i	0.000879570	+	0.00103968i
$205$	8.05138	−	2.61605i	0.562333	−	0.182713i
$206$	−12.6167	+	7.02687i	−0.879046	+	0.489585i
$207$	12.6151	−	17.3632i	0.876808	−	1.20682i
$208$	−12.5891	−	7.03661i	−0.872899	−	0.487901i
$209$	7.64847	+	0.314805i	0.529056	+	0.0217755i
$210$	0.000498279	0	0.000462776i	3.43845e−5	0	3.19346e-5i
$211$	−13.2804	−	9.64877i	−0.914260	−	0.664248i	0.0278290	−	0.999613i	$-0.491141\pi$
$211$	−13.2804	−	9.64877i	−0.914260	−	0.664248i	−0.942089	+	0.335364i	$0.891141\pi$
$212$	3.25102	+	0.796647i	0.223281	+	0.0547139i
$213$	0.0196665	−	0.00639003i	0.00134753	−	0.000437838i
$214$	2.03701	−	16.8715i	0.139247	−	1.15331i
$215$	−1.77727	−	2.44620i	−0.121209	−	0.166829i
$216$	−0.0330519	−	0.0124584i	−0.00224890	−	0.000847684i
$217$	−0.347624	−	0.112950i	−0.0235983	−	0.00766754i
$218$	5.69636	−	1.11920i	0.385806	−	0.0758015i
$219$			0.00975368i			0.000659093i
$220$	−6.17532	−	1.78541i	−0.416340	−	0.120372i
$221$	−10.2945	+	13.3362i	−0.692483	+	0.897093i
$222$	−0.00255682		0.000502353i	−0.000171602		3.37157e-5i
$223$	4.41542	−	13.5893i	0.295679	−	0.910005i	−0.687314	−	0.726360i	$-0.741210\pi$
$223$	4.41542	−	13.5893i	0.295679	−	0.910005i	0.982993	−	0.183645i	$-0.0587896\pi$
$224$	−0.381251	+	1.29356i	−0.0254734	+	0.0864297i
$225$	−9.85589	+	7.16072i	−0.657059	+	0.477382i
$226$	0.505341	−	4.18548i	0.0336148	−	0.278414i
$227$	7.80404	−	2.53569i	0.517973	−	0.168299i	−0.0383525	−	0.999264i	$-0.512211\pi$
$227$	7.80404	−	2.53569i	0.517973	−	0.168299i	0.556325	+	0.830965i	$0.312211\pi$
$228$	0.00933172	+	0.00228669i	0.000618008	+	0.000151440i
$229$	−15.4931	+	21.3244i	−1.02381	+	1.40916i	−0.114319	+	0.993444i	$0.536469\pi$
$229$	−15.4931	+	21.3244i	−1.02381	+	1.40916i	−0.909495	+	0.415715i	$0.863531\pi$
$230$	6.67226	−	7.18414i	0.439956	−	0.473708i
$231$	0.00158472		0.000443747i	0.000104267		2.91964e-5i
$232$	5.04082	−	6.30253i	0.330946	−	0.413782i
$233$	6.74032	−	9.27725i	0.441573	−	0.607773i	−0.528988	−	0.848629i	$-0.677428\pi$
$233$	6.74032	−	9.27725i	0.441573	−	0.607773i	0.970561	+	0.240856i	$0.0774283\pi$
$234$	2.27414	−	15.1270i	0.148665	−	0.988886i
$235$	6.79699	−	2.20848i	0.443387	−	0.144065i
$236$	−7.72310	−	9.12894i	−0.502731	−	0.594244i
$237$	0.00532475	+	0.00732889i	0.000345880	+	0.000476062i
$238$	1.42908	+	0.662884i	0.0926336	+	0.0429684i
$239$	−12.8589	−	4.17810i	−0.831771	−	0.270259i	−0.137980	−	0.990435i	$-0.544061\pi$
$239$	−12.8589	−	4.17810i	−0.831771	−	0.270259i	−0.693791	+	0.720176i	$0.744061\pi$
$240$	−0.00715411	−	0.00373014i	−0.000461796	−	0.000240779i
$241$	−9.34843			−0.602185			−0.301093	−	0.953595i	$-0.597351\pi$
$241$	−9.34843			−0.602185			−0.301093	+	0.953595i	$0.597351\pi$
$242$	−11.4873	+	10.4900i	−0.738434	+	0.674326i
$243$		−	0.0561968i		−	0.00360502i
$244$	−9.56766	−	5.92497i	−0.612507	−	0.379308i
$245$	−6.39926	−	2.07925i	−0.408834	−	0.132838i
$246$	0.0108200	−	0.0233263i	0.000689855	−	0.00148723i
$247$	−0.241830	+	8.31829i	−0.0153873	+	0.529280i
$248$	4.33195	+	0.200736i	0.275079	+	0.0127467i
$249$	0.00398726	+	0.0122715i	0.000252683	+	0.000777677i
$250$	−10.8488	+	6.04225i	−0.686140	+	0.382146i
$251$	4.47103	−	6.15384i	0.282209	−	0.388427i	−0.644255	−	0.764811i	$-0.722833\pi$
$251$	4.47103	−	6.15384i	0.282209	−	0.388427i	0.926464	+	0.376384i	$0.122833\pi$
$252$	−1.42648	+	0.105537i	−0.0898597	+	0.00664818i
$253$	−6.39790	−	22.8484i	−0.402233	−	1.43646i
$254$	−9.10854	+	9.80733i	−0.571521	+	0.615366i
$255$	−0.00553977	+	0.00762485i	−0.000346914	+	0.000477486i
$256$	0.300160	−	15.9972i	0.0187600	−	0.999824i
$257$	−5.21833	−	16.0604i	−0.325510	−	1.00182i	−0.971210	−	0.238226i	$-0.923434\pi$
$257$	−5.21833	−	16.0604i	−0.325510	−	1.00182i	0.645700	−	0.763592i	$-0.276566\pi$
$258$	−0.00911777	−	0.00110085i	−0.000567648	−	6.85358e-5i
$259$	−0.170734	+	0.124045i	−0.0106089	+	0.00770779i
$260$	1.85976	−	6.73623i	0.115338	−	0.417763i
$261$	8.14101	+	2.64517i	0.503916	+	0.163732i
$262$	30.1705	−	5.92777i	1.86394	−	0.366219i
$263$	−5.18584			−0.319773			−0.159886	−	0.987135i	$-0.551113\pi$
$263$	−5.18584			−0.319773			−0.159886	+	0.987135i	$0.551113\pi$
$264$	−0.0167379	+	0.0100532i	−0.00103015	+	0.000618729i
$265$			1.62188i			0.0996313i
$266$	0.763547	−	0.150018i	0.0468161	−	0.00919822i
$267$	0.00644762	−	0.0198437i	0.000394588	−	0.00121442i
$268$	4.71542	−	1.92733i	0.288040	−	0.117730i
$269$	−17.2970	+	12.5670i	−1.05462	+	0.766225i	−0.973085	−	0.230446i	$-0.925982\pi$
$269$	−17.2970	+	12.5670i	−1.05462	+	0.766225i	−0.0815329	+	0.996671i	$0.525982\pi$
$270$	0.00205152	−	0.0169917i	0.000124852	−	0.00103408i
$271$	22.3208	−	7.25248i	1.35589	−	0.440557i	0.461224	−	0.887284i	$-0.347411\pi$
$271$	22.3208	−	7.25248i	1.35589	−	0.440557i	0.894670	+	0.446727i	$0.147411\pi$
$272$	−18.4321	−	3.09686i	−1.11761	−	0.187775i
$273$	0.000503165		0.00171682i	3.04530e−5		0.000103907i
$274$	−14.7151	−	13.6667i	−0.888975	−	0.825634i
$275$	−0.553877	+	13.4569i	−0.0334000	+	0.811484i
$276$	−0.00219726	−	0.0296991i	−0.000132260	−	0.00178768i
$277$	11.1829	−	15.3919i	0.671915	−	0.924812i	−0.327887	−	0.944717i	$-0.606336\pi$
$277$	11.1829	−	15.3919i	0.671915	−	0.924812i	0.999802	+	0.0199052i	$0.00633645\pi$
$278$	−13.8015	−	24.7804i	−0.827756	−	1.48623i
$279$	1.42137	+	4.37452i	0.0850951	+	0.261896i
$280$	−0.652747	−	0.0302473i	−0.0390091	−	0.00180762i
$281$	−2.71983	+	1.97607i	−0.162252	+	0.117883i	−0.665948	−	0.745998i	$-0.731973\pi$
$281$	−2.71983	+	1.97607i	−0.162252	+	0.117883i	0.503697	+	0.863881i	$0.331973\pi$
$282$	0.00913422	−	0.0196921i	0.000543935	−	0.00117265i
$283$	−5.33736	+	16.4267i	−0.317273	+	0.976467i	0.657535	+	0.753424i	$0.271599\pi$
$283$	−5.33736	+	16.4267i	−0.317273	+	0.976467i	−0.974809	+	0.223043i	$0.928401\pi$
$284$	−10.4615	+	16.8932i	−0.620775	+	1.00243i
$285$			0.00465544i			0.000275764i
$286$	−11.5538	−	12.3495i	−0.683191	−	0.730240i
$287$		−	2.08256i		−	0.122930i
$288$	15.9894	−	5.68670i	0.942184	−	0.335092i
$289$	−1.49355	+	4.59667i	−0.0878559	+	0.270393i
$290$	3.54744	+	1.64549i	0.208313	+	0.0966267i
$291$	−0.0206461	+	0.0150003i	−0.00121029	+	0.000879331i
$292$	−6.05339	−	7.15529i	−0.354248	−	0.418732i
$293$	−4.56654	−	14.0544i	−0.266780	−	0.821064i	−0.991278	−	0.131787i	$-0.957928\pi$
$293$	−4.56654	−	14.0544i	−0.266780	−	0.821064i	0.724498	−	0.689277i	$-0.242072\pi$
$294$	−0.0178547	+	0.00994420i	−0.00104131	+	0.000579957i
$295$	3.40563	−	4.68745i	0.198284	−	0.272914i
$296$	1.56391	−	1.95535i	0.0909002	−	0.113653i
$297$	−0.0324788	−	0.0257027i	−0.00188461	−	0.00149142i
$298$	−9.41057	+	10.1325i	−0.545140	+	0.586961i
$299$	24.7530	−	7.25459i	1.43150	−	0.419544i
$300$	−0.00402327	+	0.0164185i	−0.000232284	+	0.000947923i
$301$	−0.707415	+	0.229853i	−0.0407747	+	0.0132485i
$302$	14.6580	+	1.76975i	0.843473	+	0.101838i
$303$	0.00785483	−	0.00570687i	0.000451248	−	0.000327851i
$304$	−8.26492	+	4.11399i	−0.474026	+	0.235954i
$305$	1.68505	−	5.18605i	0.0964857	−	0.296953i
$306$	−3.82189	−	19.4523i	−0.218483	−	1.11201i
$307$			16.7556i			0.956291i	0.878281	+	0.478146i	$0.158691\pi$
$307$			16.7556i			0.956291i	−0.878281	+	0.478146i	$0.841309\pi$
$308$	−0.887149	+	1.30905i	−0.0505500	+	0.0745901i
$309$	−0.0212543			−0.00120911
$310$	0.405106	+	2.06186i	0.0230085	+	0.117106i
$311$	−28.1377	−	9.14250i	−1.59554	−	0.518423i	−0.629543	−	0.776966i	$-0.716758\pi$
$311$	−28.1377	−	9.14250i	−1.59554	−	0.518423i	−0.966000	+	0.258542i	$0.916758\pi$
$312$	−0.0111478	−	0.0180628i	−0.000631120	−	0.00102260i
$313$	−4.49216	+	3.26375i	−0.253912	+	0.184478i	−0.707459	−	0.706755i	$-0.750159\pi$
$313$	−4.49216	+	3.26375i	−0.253912	+	0.184478i	0.453547	+	0.891232i	$0.350159\pi$
$314$	0.461471	−	3.82214i	0.0260423	−	0.215696i
$315$	−0.214175	−	0.659163i	−0.0120674	−	0.0371396i
$316$	−8.45472	−	2.07179i	−0.475615	−	0.116547i
$317$	−13.8753	+	19.0977i	−0.779313	+	1.07263i	0.216044	+	0.976384i	$0.430685\pi$
$317$	−13.8753	+	19.0977i	−0.779313	+	1.07263i	−0.995357	+	0.0962492i	$0.969315\pi$
$318$	0.00360960	+	0.00335241i	0.000202416	+	0.000187994i
$319$	7.87834	−	5.24290i	0.441102	−	0.293546i
$320$	7.56326	−	1.70359i	0.422799	−	0.0952338i
$321$	0.0147011	−	0.0202343i	0.000820533	−	0.00112937i
$322$	−1.17358	−	2.10716i	−0.0654012	−	0.117427i
$323$	3.33263	+	10.2568i	0.185433	+	0.570703i
$324$	11.6257	+	13.7419i	0.645872	+	0.763440i
$325$	−14.6354	−	0.425483i	−0.811828	−	0.0236016i
$326$	−22.4579	−	10.4172i	−1.24383	−	0.576953i
$327$	0.00812573	+	0.00264021i	0.000449354	+	0.000146004i
$328$	6.53936	+	23.8272i	0.361076	+	1.31564i
$329$		−	1.75810i		−	0.0969274i
$330$	−0.00666153	−	0.00671788i	−0.000366705	−	0.000369807i
$331$	28.4836			1.56560			0.782799	−	0.622275i	$-0.213791\pi$
$331$	28.4836			1.56560			0.782799	+	0.622275i	$0.213791\pi$
$332$	−10.5411	−	6.52779i	−0.578517	−	0.358259i
$333$	2.52574	+	0.820662i	0.138410	+	0.0449720i
$334$	−2.80536	+	6.04794i	−0.153502	+	0.330929i
$335$	1.45085	+	1.99692i	0.0792683	+	0.109103i
$336$	−0.00141654	+	0.00139021i	−7.72787e−5	+	7.58423e-5i
$337$	32.2706	−	10.4854i	1.75789	−	0.571174i	0.760915	−	0.648852i	$-0.224751\pi$
$337$	32.2706	−	10.4854i	1.75789	−	0.571174i	0.996979	+	0.0776779i	$0.0247506\pi$
$338$	13.2727	−	12.7215i	0.721940	−	0.691956i
$339$	0.00364704	−	0.00501972i	0.000198080	−	0.000272634i
$340$	−0.668202	−	9.03170i	−0.0362383	−	0.489813i
$341$	4.76751	+	1.76894i	0.258175	+	0.0957936i
$342$	−7.17505	−	6.66382i	−0.387982	−	0.360338i
$343$	−1.95380	+	2.68917i	−0.105495	+	0.145202i
$344$	7.37200	−	4.85114i	0.397472	−	0.261556i
$345$	0.0137237	−	0.00445910i	0.000738859	−	0.000240070i
$346$	−25.6804	−	3.10056i	−1.38059	−	0.166687i
$347$	−2.79351	+	2.02960i	−0.149963	+	0.108955i	−0.660237	−	0.751057i	$-0.729544\pi$
$347$	−2.79351	+	2.02960i	−0.149963	+	0.108955i	0.510274	+	0.860012i	$0.329544\pi$
$348$	0.0109947	−	0.00449385i	0.000589378	−	0.000240896i
$349$	−7.64514	+	23.5293i	−0.409235	+	1.25950i	0.508071	+	0.861315i	$0.330359\pi$
$349$	−7.64514	+	23.5293i	−0.409235	+	1.25950i	−0.917307	+	0.398182i	$0.869641\pi$
$350$	0.263947	+	1.34341i	0.0141085	+	0.0718081i
$351$	0.0275135	−	0.0356430i	0.00146856	−	0.00190248i
$352$	6.03965	−	17.7630i	0.321915	−	0.946769i
$353$		−	16.1502i		−	0.859587i	−0.902927	−	0.429793i	$-0.858586\pi$
$353$		−	16.1502i		−	0.859587i	0.902927	−	0.429793i	$-0.141414\pi$
$354$	−0.00339282	−	0.0172684i	−0.000180326	−	0.000917805i
$355$	−9.15681	−	2.97523i	−0.485993	−	0.157909i
$356$	7.58556	+	18.5589i	0.402034	+	0.983619i
$357$	0.00136278	+	0.00187571i	7.21260e−5	+	9.92729e-5i
$358$	12.6147	+	1.52305i	0.666707	+	0.0804958i
$359$	−6.08251	+	1.97633i	−0.321023	+	0.104307i	−0.465095	−	0.885261i	$-0.653980\pi$
$359$	−6.08251	+	1.97633i	−0.321023	+	0.104307i	0.144073	+	0.989567i	$0.453980\pi$
$360$	4.52025	+	6.86917i	0.238238	+	0.362037i
$361$	−11.0616	−	8.03672i	−0.582189	−	0.422985i
$362$	−9.28396	+	9.99620i	−0.487954	+	0.525389i
$363$	−0.0222822	+	0.00526161i	−0.00116951	+	0.000276163i
$364$	−1.43463	−	0.947183i	−0.0751949	−	0.0496459i
$365$	2.66935	−	3.67404i	0.139720	−	0.192308i
$366$	−0.00805892	−	0.0144697i	−0.000421247	−	0.000756345i
$367$	4.71820	−	1.53304i	0.246288	−	0.0800238i	−0.183272	−	0.983062i	$-0.558669\pi$
$367$	4.71820	−	1.53304i	0.246288	−	0.0800238i	0.429560	+	0.903038i	$0.358669\pi$
$368$	20.0439	+	20.4236i	1.04486	+	1.06465i
$369$	−21.2020	+	15.4041i	−1.10373	+	0.801908i
$370$	1.10059	+	0.510512i	0.0572170	+	0.0265403i
$371$	0.379454	+	0.123292i	0.0197003	+	0.00640100i
$372$	0.00542617	+	0.00336027i	0.000281334	+	0.000174222i
$373$			10.9801i			0.568530i	0.958746	+	0.284265i	$0.0917495\pi$
$373$			10.9801i			0.568530i	−0.958746	+	0.284265i	$0.908250\pi$
$374$	−19.4856	−	10.0320i	−1.00758	−	0.518743i
$375$	−0.0182761			−0.000943774
$376$	5.52054	+	20.1150i	0.284700	+	1.03735i
$377$	5.80261	+	8.49523i	0.298849	+	0.437526i
$378$	−0.00381942	−	0.00177165i	−0.000196450	−	9.11238e-5i
$379$	−30.5233	+	22.1764i	−1.56787	+	1.13913i	−0.638718	+	0.769441i	$0.720535\pi$
$379$	−30.5233	+	22.1764i	−1.56787	+	1.13913i	−0.929157	+	0.369686i	$0.879465\pi$
$380$	−2.88928	−	3.41522i	−0.148217	−	0.175197i
$381$	−0.0187347	+	0.00608728i	−0.000959809	+	0.000311861i
$382$	−24.1693	+	13.4611i	−1.23661	+	0.688730i
$383$	−14.9562	−	10.8663i	−0.764226	−	0.555243i	0.135978	−	0.990712i	$-0.456582\pi$
$383$	−14.9562	−	10.8663i	−0.764226	−	0.555243i	−0.900204	+	0.435469i	$0.856582\pi$
$384$	0.0118417	−	0.0203539i	0.000604297	−	0.00103868i
$385$	−0.718379	−	0.266548i	−0.0366120	−	0.0135845i
$386$	18.9619	−	20.4166i	0.965134	−	1.03918i
$387$	7.57262	+	5.50183i	0.384938	+	0.279674i
$388$	5.83640	−	23.8177i	0.296298	−	1.20916i
$389$	−7.86175	−	24.1960i	−0.398606	−	1.22678i	−0.926117	−	0.377236i	$-0.876875\pi$
$389$	−7.86175	−	24.1960i	−0.398606	−	1.22678i	0.527511	−	0.849548i	$-0.323125\pi$
$390$	0.00721515	−	0.00732948i	0.000365353	−	0.000371143i
$391$	27.0438	−	19.6484i	1.36766	−	0.993664i
$392$	6.92658	−	18.3762i	0.349845	−	0.928136i
$393$	0.0430375	+	0.0139837i	0.00217095	+	0.000705386i
$394$	−17.2436	+	3.38794i	−0.868718	+	0.170682i
$395$		−	4.21791i		−	0.212226i
$396$	19.8891	−	0.650874i	0.999464	−	0.0327077i
$397$		−	18.6788i		−	0.937464i	−0.883340	−	0.468732i	$-0.844711\pi$
$397$		−	18.6788i		−	0.937464i	0.883340	−	0.468732i	$-0.155289\pi$
$398$	4.36440	+	22.2135i	0.218768	+	1.11346i
$399$	0.00108918		0.000353897i	5.45273e−5		1.77170e-5i
$400$	−7.23827	−	14.5415i	−0.361914	−	0.727077i
$401$	11.0731	+	15.2408i	0.552963	+	0.761088i	0.990410	−	0.138156i	$-0.0441175\pi$
$401$	11.0731	+	15.2408i	0.552963	+	0.761088i	−0.437448	+	0.899244i	$0.644118\pi$
$402$	0.00744317		0.000898662i	0.000371232		4.48212e-5i
$403$	−1.86034	+	5.20567i	−0.0926700	+	0.259313i
$404$	−2.22046	+	9.06146i	−0.110472	+	0.450824i
$405$	−5.12655	+	7.05609i	−0.254740	+	0.350620i
$406$	0.654648	−	0.704870i	0.0324896	−	0.0349821i
$407$	2.44424	−	1.62660i	0.121157	−	0.0806277i
$408$	−0.0214818	−	0.0171813i	−0.00106351	−	0.000850603i
$409$	5.48488	+	3.98500i	0.271210	+	0.197045i	0.715074	−	0.699048i	$-0.246393\pi$
$409$	5.48488	+	3.98500i	0.271210	+	0.197045i	−0.443864	+	0.896094i	$0.646393\pi$
$410$	−10.4595	+	5.82543i	−0.516558	+	0.287697i
$411$	−0.00913350	−	0.0281100i	−0.000450522	−	0.00138657i
$412$	15.5921	−	13.1910i	0.768169	−	0.649872i
$413$	−0.837784	−	1.15311i	−0.0412246	−	0.0567409i
$414$	−12.7717	+	27.5340i	−0.627696	+	1.35322i
$415$	1.85649	−	5.71369i	0.0911315	−	0.280474i
$416$	19.3882	+	6.33221i	0.950586	+	0.310462i
$417$		−	0.0417455i		−	0.00204429i
$418$	−10.6995	+	1.64847i	−0.523329	+	0.0806295i
$419$			11.7338i			0.573233i	0.958045	+	0.286616i	$0.0925305\pi$
$419$			11.7338i			0.573233i	−0.958045	+	0.286616i	$0.907469\pi$
$420$	−0.000817627	0	0.000506333i	−3.98961e−5	0	2.47065e-5i
$421$	13.4732	+	4.37772i	0.656646	+	0.213357i	0.618342	−	0.785909i	$-0.287805\pi$
$421$	13.4732	+	4.37772i	0.656646	+	0.213357i	0.0383037	+	0.999266i	$0.487805\pi$
$422$	21.0597	+	9.76859i	1.02517	+	0.475527i
$423$	−17.8988	+	13.0042i	−0.870267	+	0.632286i
$424$	−4.72859	−	0.219116i	−0.229641	−	0.0106412i
$425$	−18.0461	+	5.86353i	−0.875364	+	0.284423i
$426$	−0.0255486	+	0.0142293i	−0.00123784	+	0.000689413i
$427$	−1.08523	−	0.788466i	−0.0525180	−	0.0381566i
$428$	1.77323	+	23.9677i	0.0857122	+	1.15852i
$429$	−0.00601198	−	0.0241525i	−0.000290261	−	0.00116609i
$430$	3.13323	+	2.90998i	0.151098	+	0.140332i
$431$	21.0448	−	28.9657i	1.01369	−	1.39523i	0.0971626	−	0.995269i	$-0.469023\pi$
$431$	21.0448	−	28.9657i	1.01369	−	1.39523i	0.916532	−	0.399962i	$-0.130977\pi$
$432$	0.0492623	+	0.00827680i	0.00237013	+	0.000398218i
$433$	1.68132	+	5.17458i	0.0807993	+	0.248675i	0.983293	−	0.182027i	$-0.0582660\pi$
$433$	1.68132	+	5.17458i	0.0807993	+	0.248675i	−0.902494	+	0.430702i	$0.858266\pi$
$434$	0.513188	+	0.0619604i	0.0246338	+	0.00297420i
$435$	0.00338286	+	0.00465611i	0.000162196	+	0.000223243i
$436$	−7.59960	+	3.10618i	−0.363955	+	0.148759i
$437$	5.10245	−	15.7037i	0.244083	−	0.751211i
$438$	−0.00265930	−	0.0135350i	−0.000127066	−	0.000646728i
$439$	−6.16127			−0.294061			−0.147031	−	0.989132i	$-0.546972\pi$
$439$	−6.16127			−0.294061			−0.147031	+	0.989132i	$0.546972\pi$
$440$	9.05618	+	0.793908i	0.431736	+	0.0378481i
$441$	20.8295			0.991880
$442$	10.6494	−	21.3132i	0.506542	−	1.01377i
$443$	3.16204	+	1.02741i	0.150233	+	0.0488137i	0.383168	−	0.923679i	$-0.374833\pi$
$443$	3.16204	+	1.02741i	0.150233	+	0.0488137i	−0.232935	+	0.972492i	$0.574833\pi$
$444$	0.00341109	−	0.00139421i	0.000161883	−	6.61664e-5i
$445$	−7.85945	+	5.71022i	−0.372574	+	0.270691i
$446$	−2.42215	+	20.0615i	−0.114692	+	0.949937i
$447$	−0.0193559	+	0.00628912i	−0.000915504	+	0.000297465i
$448$	0.176372	−	1.89900i	0.00833280	−	0.0897193i
$449$	17.8065	−	24.5085i	0.840339	−	1.15663i	−0.145570	−	0.989348i	$-0.546502\pi$
$449$	17.8065	−	24.5085i	0.840339	−	1.15663i	0.985909	−	0.167280i	$-0.0534983\pi$
$450$	11.7245	−	12.6240i	0.552699	−	0.595100i
$451$	−1.19150	+	28.9486i	−0.0561055	+	1.36313i
$452$	0.439902	+	5.94591i	0.0206913	+	0.279672i
$453$	0.0175796	+	0.0127723i	0.000825960	+	0.000600095i
$454$	−10.1382	+	5.64647i	−0.475809	+	0.265002i
$455$	0.280320	−	0.784401i	0.0131416	−	0.0367733i
$456$	−0.0135729		0.000628949i	−0.000635611		2.94532e-5i
$457$	23.2308	−	16.8782i	1.08669	−	0.789527i	0.107853	−	0.994167i	$-0.465602\pi$
$457$	23.2308	−	16.8782i	1.08669	−	0.789527i	0.978837	+	0.204640i	$0.0656024\pi$
$458$	15.6855	−	33.8157i	0.732936	−	1.58010i
$459$	0.0180319	−	0.0554964i	0.000841656	−	0.00259035i
$460$	−7.30026	+	11.7885i	−0.340376	+	0.549640i
$461$	34.1002			1.58821			0.794103	−	0.607783i	$-0.207941\pi$
$461$	34.1002			1.58821			0.794103	+	0.607783i	$0.207941\pi$
$462$	−0.00207811	+	0.00104785i	−9.66822e−5	+	4.87503e-5i
$463$	−29.8899			−1.38910			−0.694550	−	0.719445i	$-0.744396\pi$
$463$	−29.8899			−1.38910			−0.694550	+	0.719445i	$0.744396\pi$
$464$	−5.27670	+	10.1203i	−0.244964	+	0.469822i
$465$	−0.000955654		0.00294120i	−4.43174e−5		0.000136395i
$466$	−6.82402	+	14.7116i	−0.316117	+	0.681502i
$467$	−23.7447	−	32.6817i	−1.09877	−	1.51233i	−0.837002	−	0.547200i	$-0.815694\pi$
$467$	−23.7447	−	32.6817i	−1.09877	−	1.51233i	−0.261771	−	0.965130i	$-0.584306\pi$
$468$	0.968536	+	21.6116i	0.0447706	+	0.998996i
$469$	0.577488	−	0.187637i	0.0266659	−	0.00866429i
$470$	−8.82994	+	4.91784i	−0.407295	+	0.226843i
$471$	0.00333043	−	0.00458395i	0.000153458	−	0.000211217i
$472$	13.2062	+	10.5624i	0.607864	+	0.486174i
$473$	9.96489	−	2.79033i	0.458186	−	0.128299i
$474$	−0.00938725	−	0.00871840i	−0.000431171	−	0.000400449i
$475$	−5.50912	+	7.58265i	−0.252776	+	0.347916i
$476$	−2.16385	−	0.530239i	−0.0991797	−	0.0243035i
$477$	−1.55151	−	4.77507i	−0.0710389	−	0.218635i
$478$	18.9832	+	2.29196i	0.868270	+	0.104832i
$479$	−22.7998	−	31.3812i	−1.04175	−	1.43385i	−0.895748	−	0.444561i	$-0.853360\pi$
$479$	−22.7998	−	31.3812i	−1.04175	−	1.43385i	−0.146001	−	0.989284i	$-0.546640\pi$
$480$	0.0109446	+	0.00322571i	0.000499552	+	0.000147233i
$481$	1.80025	+	2.63563i	0.0820844	+	0.120175i
$482$	12.9727	−	2.54881i	0.590888	−	0.116095i
$483$		−	0.00354976i		−	0.000161520i
$484$	13.0807	−	17.6888i	0.594578	−	0.804038i
$485$	11.8822			0.539544
$486$	0.0153218	+	0.0779833i	0.000695012	+	0.00353739i
$487$	0.951747	−	2.92917i	0.0431278	−	0.132734i	−0.927174	−	0.374630i	$-0.877770\pi$
$487$	0.951747	−	2.92917i	0.0431278	−	0.132734i	0.970302	+	0.241897i	$0.0777696\pi$
$488$	14.8923	+	5.61340i	0.674143	+	0.254107i
$489$	−0.0214160	−	0.0294765i	−0.000968463	−	0.00133298i
$490$	9.44704	+	1.14060i	0.426774	+	0.0515272i
$491$	5.51663	+	16.9784i	0.248962	+	0.766226i	0.994960	+	0.100278i	$0.0319731\pi$
$491$	5.51663	+	16.9784i	0.248962	+	0.766226i	−0.745998	+	0.665949i	$0.768027\pi$
$492$	−0.00865486	+	0.0353195i	−0.000390191	+	0.00159232i
$493$	10.7862	+	7.83662i	0.485785	+	0.352944i
$494$	−1.93236	−	11.6091i	−0.0869412	−	0.522317i
$495$	2.60000	+	9.28520i	0.116861	+	0.417339i
$496$	−6.06610	+	0.902530i	−0.272376	+	0.0405248i
$497$	−1.39216	+	1.91615i	−0.0624471	+	0.0859510i
$498$	−0.00887884	−	0.0159419i	−0.000397871	−	0.000714373i
$499$	4.41112	+	13.5760i	0.197469	+	0.607747i	0.999939	+	0.0110542i	$0.00351874\pi$
$499$	4.41112	+	13.5760i	0.197469	+	0.607747i	−0.802470	+	0.596692i	$0.796481\pi$
$500$	13.4073	−	11.3426i	0.599594	−	0.507257i
$501$	−0.00793808	+	0.00576735i	−0.000354647	+	0.000257666i
$502$	−4.52655	+	9.75859i	−0.202030	+	0.435547i
$503$	−8.63904	+	26.5882i	−0.385196	+	1.18551i	0.551143	+	0.834411i	$0.314192\pi$
$503$	−8.63904	+	26.5882i	−0.385196	+	1.18551i	−0.936338	+	0.351099i	$0.885808\pi$
$504$	1.95073	−	0.535375i	0.0868922	−	0.0238475i
$505$	−4.52061			−0.201164
$506$	15.1078	+	29.9619i	0.671622	+	1.33197i
$507$	0.0261757	−	0.00685220i	0.00116251	−	0.000304317i
$508$	9.96585	−	16.0929i	0.442163	−	0.714006i
$509$	−1.21280	−	0.394061i	−0.0537563	−	0.0174665i	0.282015	−	0.959410i	$-0.408997\pi$
$509$	−1.21280	−	0.394061i	−0.0537563	−	0.0174665i	−0.335772	+	0.941943i	$0.608997\pi$
$510$	0.00560857	−	0.0120913i	0.000248352	−	0.000535410i
$511$	−0.656657	−	0.903811i	−0.0290488	−	0.0399822i
$512$	3.94504	+	22.2809i	0.174348	+	0.984684i
$513$	−0.00890692	−	0.0274127i	−0.000393250	−	0.00121030i
$514$	11.6202	+	20.8639i	0.512544	+	0.920268i
$515$	8.00611	+	5.81678i	0.352792	+	0.256318i
$516$	0.0129527		0.000958295i	0.000570212		4.21866e-5i
$517$	−1.00587	+	24.4384i	−0.0442380	+	1.07480i
$518$	0.203104	−	0.218685i	0.00892386	−	0.00960847i
$519$	−0.0307989	−	0.0223767i	−0.00135192	−	0.000982228i
$520$	−0.744159	+	9.85480i	−0.0326335	+	0.432162i
$521$	4.06892	+	12.5229i	0.178263	+	0.548636i	0.999767	−	0.0215655i	$-0.00686504\pi$
$521$	4.06892	+	12.5229i	0.178263	+	0.548636i	−0.821505	+	0.570202i	$0.806865\pi$
$522$	−12.0183	−	1.45105i	−0.526028	−	0.0635108i
$523$	13.8605	−	10.0702i	0.606076	−	0.440340i	−0.241954	−	0.970288i	$-0.577788\pi$
$523$	13.8605	−	10.0702i	0.606076	−	0.440340i	0.848030	+	0.529948i	$0.177788\pi$
$524$	−40.2509	+	16.4517i	−1.75837	+	0.718697i
$525$	−0.000622656		0.00191634i	−2.71749e−5		8.36359e-5i
$526$	7.19631	−	1.41390i	0.313774	−	0.0616489i
$527$			7.16412i			0.312074i
$528$	0.0204860	−	0.0185141i	0.000891537	−	0.000805724i
$529$	−28.1801			−1.22522
$530$	−0.442199	−	2.25065i	−0.0192079	−	0.0977622i
$531$	−5.54264	+	17.0585i	−0.240530	+	0.740275i
$532$	−1.01866	+	0.416356i	−0.0441645	+	0.0180513i
$533$	−31.4837	−	0.915299i	−1.36371	−	0.0396460i
$534$	−0.00353694	+	0.0292947i	−0.000153058	+	0.00126771i
$535$	−11.0753	+	3.59857i	−0.478825	+	0.155580i
$536$	−6.01803	+	3.96016i	−0.259939	+	0.171053i
$537$	0.0151290	+	0.0109919i	0.000652864	+	0.000474334i
$538$	20.5764	−	22.1550i	0.887113	−	0.955170i
$539$	14.2901	−	18.0575i	0.615520	−	0.777794i
$540$	0.00178586	+	0.0241385i	7.68513e−5	+	0.00103875i
$541$	0.301163	+	0.218808i	0.0129480	+	0.00940727i	0.594240	−	0.804287i	$-0.297453\pi$
$541$	0.301163	+	0.218808i	0.0129480	+	0.00940727i	−0.581292	+	0.813695i	$0.697453\pi$
$542$	−28.9969	+	16.1498i	−1.24552	+	0.693694i
$543$	−0.0190955	+	0.00620451i	−0.000819468	+	0.000266261i
$544$	26.4222	−	0.727963i	1.13284	−	0.0312112i
$545$	−2.33826	−	3.21833i	−0.100160	−	0.137858i
$546$	−0.00116632	−	0.00224522i	−4.99139e−5	−	9.60867e-5i
$547$	−11.0152	+	33.9012i	−0.470975	+	1.44951i	0.380336	+	0.924849i	$0.375808\pi$
$547$	−11.0152	+	33.9012i	−0.470975	+	1.44951i	−0.851310	+	0.524662i	$0.824192\pi$
$548$	24.1461	+	14.9530i	1.03147	+	0.638760i
$549$			16.8805i			0.720442i
$550$	−2.90037	−	18.8250i	−0.123672	−	0.802700i
$551$	6.58563			0.280557
$552$	0.0111464	+	0.0406139i	0.000474424	+	0.00172864i
$553$	−0.986820	−	0.320637i	−0.0419639	−	0.0136349i
$554$	−11.3218	+	24.4081i	−0.481016	+	1.03700i
$555$	0.00104953	+	0.00144455i	4.45500e−5	+	6.13178e-5i
$556$	25.9083	+	30.6244i	1.09876	+	1.29877i
$557$	−5.60748	−	17.2581i	−0.237597	−	0.731248i	−0.996766	−	0.0803547i	$-0.974395\pi$
$557$	−5.60748	−	17.2581i	−0.237597	−	0.731248i	0.759170	−	0.650893i	$-0.225605\pi$
$558$	−3.16511	−	5.68292i	−0.133990	−	0.240577i
$559$	3.16396	+	10.7956i	0.133821	+	0.456604i
$560$	0.914053	−	0.135995i	0.0386258	−	0.00574684i
$561$	−0.0178701	−	0.0268529i	−0.000754477	−	0.00113373i
$562$	3.23550	−	3.48371i	0.136481	−	0.146952i
$563$	−17.3961	−	12.6390i	−0.733157	−	0.532670i	0.157404	−	0.987534i	$-0.449688\pi$
$563$	−17.3961	−	12.6390i	−0.733157	−	0.532670i	−0.890561	+	0.454865i	$0.849688\pi$
$564$	−0.00730645	+	0.0298168i	−0.000307657	+	0.00125551i
$565$	−2.74755	+	0.892733i	−0.115590	+	0.0375576i
$566$	2.92789	−	24.2503i	0.123069	−	1.01932i
$567$	1.26113	+	1.73579i	0.0529624	+	0.0728965i
$568$	9.91137	−	26.2947i	0.415872	−	1.10330i
$569$	−38.6957	−	12.5730i	−1.62221	−	0.527088i	−0.649748	−	0.760150i	$-0.725125\pi$
$569$	−38.6957	−	12.5730i	−1.62221	−	0.527088i	−0.972462	+	0.233062i	$0.925125\pi$
$570$	−0.00126928	−	0.00646027i	−5.31645e−5	−	0.000270591i
$571$	−22.8169			−0.954857			−0.477429	−	0.878670i	$-0.658431\pi$
$571$	−22.8169			−0.954857			−0.477429	+	0.878670i	$0.658431\pi$
$572$	19.4000	+	13.9871i	0.811157	+	0.584829i
$573$	−0.0407160			−0.00170094
$574$	0.567802	+	2.88994i	0.0236996	+	0.120624i
$575$	27.6296	+	8.97740i	1.15223	+	0.374383i
$576$	−20.6378	+	12.2508i	−0.859906	+	0.510449i
$577$	1.00712	+	1.38618i	0.0419269	+	0.0577074i	0.829466	−	0.558558i	$-0.188645\pi$
$577$	1.00712	+	1.38618i	0.0419269	+	0.0577074i	−0.787539	+	0.616265i	$0.788645\pi$
$578$	0.819310	−	6.78594i	0.0340788	−	0.282258i
$579$	0.0390013	−	0.0126723i	0.00162084	−	0.000526643i
$580$	−5.37137	−	1.31623i	−0.223034	−	0.0546533i
$581$	−1.19564	−	0.868686i	−0.0496036	−	0.0360392i
$582$	0.0245605	−	0.0264447i	0.00101806	−	0.00109617i
$583$	−5.20404	−	1.93091i	−0.215529	−	0.0799702i
$584$	10.3510	+	8.27884i	0.428329	+	0.342581i
$585$	−10.0592	+	2.94815i	−0.415897	+	0.121891i
$586$	10.1688	+	18.2579i	0.420068	+	0.754229i
$587$	−1.72174	−	5.29899i	−0.0710640	−	0.218713i	0.909216	−	0.416324i	$-0.136682\pi$
$587$	−1.72174	−	5.29899i	−0.0710640	−	0.218713i	−0.980280	+	0.197611i	$0.936682\pi$
$588$	0.0220655	−	0.0186674i	0.000909964	−	0.000769831i
$589$	2.08002	+	2.86291i	0.0857059	+	0.117964i
$590$	−3.44793	+	7.43323i	−0.141949	+	0.306021i
$591$	−0.0245975	−	0.00799222i	−0.00101181	−	0.000328756i
$592$	−1.63709	+	3.13980i	−0.0672839	+	0.129045i
$593$	22.4536			0.922059			0.461030	−	0.887385i	$-0.347480\pi$
$593$	22.4536			0.922059			0.461030	+	0.887385i	$0.347480\pi$
$594$	0.0520781	+	0.0268119i	0.00213679	+	0.00110011i
$595$		−	1.07951i		−	0.0442554i
$596$	10.2963	−	16.6265i	0.421753	−	0.681047i
$597$	−0.0102957	+	0.0316870i	−0.000421376	+	0.00129686i
$598$	−32.3714	+	16.8159i	−1.32377	+	0.687653i
$599$	−25.9146	−	35.6683i	−1.05884	−	1.45737i	−0.880885	−	0.473331i	$-0.843052\pi$
$599$	−25.9146	−	35.6683i	−1.05884	−	1.45737i	−0.177956	−	0.984038i	$-0.556948\pi$
$600$	0.00110659	−	0.0238806i	4.51764e−5	−	0.000974922i
$601$	25.0246	−	8.13098i	1.02077	−	0.331670i	0.249637	−	0.968339i	$-0.419689\pi$
$601$	25.0246	−	8.13098i	1.02077	−	0.331670i	0.771136	+	0.636670i	$0.219689\pi$
$602$	0.918999	−	0.511837i	0.0374556	−	0.0208609i
$603$	−6.18181	−	4.49135i	−0.251743	−	0.182902i
$604$	−20.8232	+	1.54058i	−0.847282	+	0.0626854i
$605$	9.83329	+	4.11615i	0.399780	+	0.167345i
$606$	−0.00934406	+	0.0100609i	−0.000379576	+	0.000408697i
$607$	21.4860	+	15.6105i	0.872091	+	0.633611i	0.931147	−	0.364643i	$-0.118809\pi$
$607$	21.4860	+	15.6105i	0.872091	+	0.633611i	−0.0590562	+	0.998255i	$0.518809\pi$
$608$	10.3474	−	7.96231i	0.419643	−	0.322914i
$609$	0.00134650		0.000437504i	5.45629e−5		1.77286e-5i
$610$	−0.924361	+	7.65602i	−0.0374263	+	0.309983i
$611$	−26.5786	−	0.772697i	−1.07526	−	0.0312600i
$612$	10.6072	+	25.9515i	0.428769	+	1.04903i
$613$	14.0555	−	43.2584i	0.567697	−	1.74719i	−0.0921034	−	0.995749i	$-0.529359\pi$
$613$	14.0555	−	43.2584i	0.567697	−	1.74719i	0.659800	−	0.751441i	$-0.270641\pi$
$614$	−4.56834	−	23.2514i	−0.184363	−	0.938351i
$615$	−0.0176203			−0.000710518
$616$	0.874174	−	2.05842i	0.0352215	−	0.0829363i
$617$		−	26.2476i		−	1.05669i	−0.849030	−	0.528345i	$-0.822813\pi$
$617$		−	26.2476i		−	1.05669i	0.849030	−	0.528345i	$-0.177187\pi$
$618$	0.0294942	−	0.00579489i	0.00118643	−	0.000233105i
$619$	8.66203	−	26.6590i	0.348156	−	1.07152i	−0.611716	−	0.791078i	$-0.709520\pi$
$619$	8.66203	−	26.6590i	0.348156	−	1.07152i	0.959872	−	0.280438i	$-0.0904796\pi$
$620$	−1.12432	−	2.75076i	−0.0451537	−	0.110473i
$621$	−0.0722782	+	0.0525132i	−0.00290043	+	0.00210728i
$622$	41.5389	+	5.01526i	1.66556	+	0.201094i
$623$	0.738500	+	2.27287i	0.0295874	+	0.0910606i
$624$	0.0203944	+	0.0220260i	0.000816428	+	0.000881745i
$625$	−9.54223	−	6.93283i	−0.381689	−	0.277313i
$626$	5.34385	−	5.75382i	0.213583	−	0.229969i
$627$	−0.0149377	−	0.00554248i	−0.000596552	−	0.000221345i
$628$	0.401714	+	5.42973i	0.0160301	+	0.216670i
$629$	3.34640	+	2.43130i	0.133430	+	0.0969424i
$630$	0.476925	+	0.856315i	0.0190011	+	0.0341164i
$631$	−11.3061	−	34.7965i	−0.450087	−	1.38523i	−0.876807	−	0.480843i	$-0.840331\pi$
$631$	−11.3061	−	34.7965i	−0.450087	−	1.38523i	0.426719	−	0.904384i	$-0.359669\pi$
$632$	12.2973	+	0.569840i	0.489162	+	0.0226670i
$633$	0.0200826	+	0.0276413i	0.000798212	+	0.00109864i
$634$	14.0476	−	30.2846i	0.557901	−	1.20275i
$635$	8.72298	+	2.83427i	0.346161	+	0.112474i
$636$	−0.00592300	−	0.00366795i	−0.000234862	−	0.000145443i
$637$	19.8167	+	15.2969i	0.785167	+	0.606086i
$638$	−9.50318	+	9.42347i	−0.376234	+	0.373079i
$639$	29.8052			1.17908
$640$	−10.0309	+	4.42614i	−0.396507	+	0.174959i
$641$	9.09359	−	27.9872i	0.359175	−	1.10543i	−0.594374	−	0.804189i	$-0.702600\pi$
$641$	9.09359	−	27.9872i	0.359175	−	1.10543i	0.953549	−	0.301238i	$-0.0974000\pi$
$642$	−0.0148836	+	0.0320870i	−0.000587410	+	0.00126637i
$643$	−2.63236	+	1.91252i	−0.103810	+	0.0754224i	−0.638479	−	0.769639i	$-0.720436\pi$
$643$	−2.63236	+	1.91252i	−0.103810	+	0.0754224i	0.534669	+	0.845061i	$0.320436\pi$
$644$	2.20307	+	2.60410i	0.0868131	+	0.102616i
$645$	0.00194475	+	0.00598534i	7.65746e−5	+	0.000235672i
$646$	−7.42110	−	13.3245i	−0.291979	−	0.524247i
$647$	4.41259	−	6.07341i	0.173477	−	0.238770i	−0.713421	−	0.700735i	$-0.752855\pi$
$647$	4.41259	−	6.07341i	0.173477	−	0.238770i	0.886898	+	0.461965i	$0.152855\pi$
$648$	−19.8795	−	15.8997i	−0.780939	−	0.624601i
$649$	10.9858	+	16.5081i	0.431232	+	0.647999i
$650$	20.4254	−	3.39986i	0.801149	−	0.133353i
$651$	0.000615474	0	0.000447168i	2.41223e−5	0	1.75259e-5i
$652$	34.0046	+	8.33266i	1.33172	+	0.326332i
$653$	−12.8109	−	39.4280i	−0.501330	−	1.54294i	−0.806853	−	0.590752i	$-0.798831\pi$
$653$	−12.8109	−	39.4280i	−0.501330	−	1.54294i	0.305523	−	0.952185i	$-0.401169\pi$
$654$	−0.0119958	−	0.00144833i	−0.000469072	−	5.66341e-5i
$655$	−12.3845	−	17.0457i	−0.483901	−	0.666032i
$656$	−15.5710	−	31.2817i	−0.607944	−	1.22135i
$657$	−4.34433	+	13.3705i	−0.169489	+	0.521632i
$658$	0.479339	+	2.43969i	0.0186866	+	0.0951090i
$659$	−20.4794			−0.797763			−0.398882	−	0.917002i	$-0.630602\pi$
$659$	−20.4794			−0.797763			−0.398882	+	0.917002i	$0.630602\pi$
$660$	0.0110757	+	0.00750604i	0.000431121	+	0.000292172i
$661$			13.3131i			0.517820i	0.965901	+	0.258910i	$0.0833633\pi$
$661$			13.3131i			0.517820i	−0.965901	+	0.258910i	$0.916637\pi$
$662$	−39.5262	+	7.76592i	−1.53623	+	0.301831i
$663$	0.0289555	−	0.0197779i	0.00112454	−	0.000768108i
$664$	16.4075	+	6.18452i	0.636733	+	0.240006i
$665$	−0.313423	−	0.431389i	−0.0121540	−	0.0167286i
$666$	−3.72867	−	0.450187i	−0.144483	−	0.0174444i
$667$	−6.30789	−	19.4137i	−0.244243	−	0.751701i
$668$	2.24400	−	9.15750i	0.0868229	−	0.354314i
$669$	−0.0174806	+	0.0240600i	−0.000675840	+	0.000930214i
$670$	−2.55777	−	2.37552i	−0.0988152	−	0.0917745i
$671$	14.6341	+	11.5809i	0.564943	+	0.447077i
$672$	0.00158667	−	0.00231539i	6.12073e−5	−	8.93180e-5i
$673$	−21.3306	+	29.3590i	−0.822233	+	1.13171i	0.167087	+	0.985942i	$0.446564\pi$
$673$	−21.3306	+	29.3590i	−0.822233	+	1.13171i	−0.989319	+	0.145764i	$0.953436\pi$
$674$	−41.9226	+	23.3488i	−1.61480	+	0.899363i
$675$	0.0482307	−	0.0156711i	0.00185640	−	0.000603181i
$676$	−14.9498	+	21.2721i	−0.574994	+	0.818158i
$677$	−15.7611	−	21.6933i	−0.605749	−	0.833743i	0.390470	−	0.920616i	$-0.372313\pi$
$677$	−15.7611	−	21.6933i	−0.605749	−	0.833743i	−0.996219	+	0.0868731i	$0.972313\pi$
$678$	−0.00369233	+	0.00796013i	−0.000141803	+	0.000305707i
$679$	0.903262	−	2.77995i	0.0346640	−	0.106685i
$680$	3.38971	+	12.3510i	0.129989	+	0.473638i
$681$	−0.0170790			−0.000654468
$682$	−7.09809	−	1.15489i	−0.271800	−	0.0442230i
$683$	−30.2945			−1.15919			−0.579593	−	0.814906i	$-0.696789\pi$
$683$	−30.2945			−1.15919			−0.579593	+	0.814906i	$0.696789\pi$
$684$	11.7736	+	7.29102i	0.450173	+	0.278779i
$685$	−4.25260	+	13.0882i	−0.162484	+	0.500073i
$686$	1.97806	−	4.26442i	0.0755228	−	0.162816i
$687$	0.0443840	−	0.0322468i	0.00169335	−	0.00123029i
$688$	−8.90736	+	8.74179i	−0.339590	+	0.333278i
$689$	2.03067	−	5.68232i	0.0773626	−	0.216479i
$690$	−0.0178284	+	0.00992953i	−0.000678715	+	0.000378011i
$691$	−18.4003	−	13.3686i	−0.699980	−	0.508566i	0.179945	−	0.983677i	$-0.442408\pi$
$691$	−18.4003	−	13.3686i	−0.699980	−	0.508566i	−0.879926	+	0.475111i	$0.842408\pi$
$692$	36.4816	−	2.69905i	1.38682	−	0.102603i
$693$	2.37000	+	0.0975475i	0.0900290	+	0.00370552i
$694$	3.32314	−	3.57808i	0.126145	−	0.135822i
$695$	−11.4247	+	15.7248i	−0.433365	+	0.596475i
$696$	−0.0140319	+	0.00923370i	−0.000531879	+	0.000350003i
$697$	−38.8207	+	12.6136i	−1.47044	+	0.477775i
$698$	4.19386	−	34.7357i	0.158740	−	1.31476i
$699$	−0.0193094	+	0.0140291i	−0.000730347	+	0.000530628i
$700$	−0.732549	−	1.79226i	−0.0276877	−	0.0677410i
$701$	12.9918	+	4.22128i	0.490692	+	0.159435i	0.543903	−	0.839148i	$-0.316946\pi$
$701$	12.9918	+	4.22128i	0.490692	+	0.159435i	−0.0532116	+	0.998583i	$0.516946\pi$
$702$	−0.0284621	+	0.0569626i	−0.00107423	+	0.00214991i
$703$	2.04318			0.0770601
$704$	−3.53813	+	26.2960i	−0.133348	+	0.991069i
$705$	−0.0148751			−0.000560227
$706$	4.40328	+	22.4113i	0.165719	+	0.843461i
$707$	−0.343647	+	1.05764i	−0.0129242	+	0.0397765i
$708$	0.00941632	+	0.0230380i	0.000353887	+	0.000865822i
$709$	20.5021	+	28.2188i	0.769974	+	1.05978i	0.996318	+	0.0857308i	$0.0273225\pi$
$709$	20.5021	+	28.2188i	0.769974	+	1.05978i	−0.226344	+	0.974047i	$0.572677\pi$
$710$	13.5179	+	1.63211i	0.507319	+	0.0612519i
$711$	4.03492	+	12.4182i	0.151321	+	0.465719i
$712$	−15.5864	−	23.6857i	−0.584123	−	0.887658i
$713$	6.44723	−	8.87385i	0.241451	−	0.332328i
$714$	−0.00240251	−	0.00223133i	−8.99117e−5	−	8.35054e-5i
$715$	−4.34535	+	10.7432i	−0.162507	+	0.401771i
$716$	−17.9204	+	1.32583i	−0.669718	+	0.0495485i
$717$	0.0227668	+	0.0165411i	0.000850243	+	0.000617738i
$718$	7.90176	−	4.40089i	0.294891	−	0.164240i
$719$	−4.06051	+	1.31934i	−0.151432	+	0.0492031i	−0.383752	−	0.923436i	$-0.625368\pi$
$719$	−4.06051	+	1.31934i	−0.151432	+	0.0492031i	0.232320	+	0.972639i	$0.425368\pi$
$720$	−8.14553	−	8.29980i	−0.303566	−	0.309315i
$721$	1.96950	−	1.43092i	0.0733480	−	0.0532904i
$722$	17.5412	+	8.13652i	0.652815	+	0.302810i
$723$	0.0185052	+	0.00601270i	0.000688215	+	0.000223615i
$724$	10.1578	−	16.4028i	0.377511	−	0.609605i
$725$			11.5869i			0.430328i
$726$	0.0294861	−	0.0133766i	0.00109433	−	0.000496453i
$727$		−	40.6711i		−	1.50841i	−0.656641	−	0.754204i	$-0.728023\pi$
$727$		−	40.6711i		−	1.50841i	0.656641	−	0.754204i	$-0.271977\pi$
$728$	2.24905	+	0.923245i	0.0833554	+	0.0342177i
$729$	8.34339	−	25.6783i	0.309014	−	0.951048i
$730$	−2.70249	+	5.82619i	−0.100024	+	0.215637i
$731$	8.56930	+	11.7946i	0.316947	+	0.436240i
$732$	0.0151283	+	0.0178822i	0.000559160	+	0.000660944i
$733$	−7.28864	−	22.4321i	−0.269212	−	0.828549i	−0.990693	−	0.136115i	$-0.956538\pi$
$733$	−7.28864	−	22.4321i	−0.269212	−	0.828549i	0.721481	−	0.692434i	$-0.243462\pi$
$734$	−6.12939	+	3.41376i	−0.226240	+	0.126004i
$735$	0.0113300	+	0.00823172i	0.000417913	+	0.000303632i
$736$	−33.3830	−	22.8765i	−1.23051	−	0.843240i
$737$	−8.13470	+	2.27784i	−0.299646	+	0.0839055i
$738$	25.2218	−	27.1567i	0.928426	−	0.999652i
$739$	−4.25303	+	5.85379i	−0.156450	+	0.215335i	−0.880046	−	0.474889i	$-0.842488\pi$
$739$	−4.25303	+	5.85379i	−0.156450	+	0.215335i	0.723596	+	0.690224i	$0.242488\pi$
$740$	−1.66646	−	0.408357i	−0.0612603	−	0.0150115i
$741$	0.00582884	−	0.0163105i	0.000214128	−	0.000599181i
$742$	−0.560176	−	0.0676337i	−0.0205647	−	0.00248291i
$743$	7.64593	+	10.5237i	0.280502	+	0.386078i	0.925900	−	0.377769i	$-0.123309\pi$
$743$	7.64593	+	10.5237i	0.280502	+	0.386078i	−0.645398	+	0.763846i	$0.723309\pi$
$744$	−0.00844597	−	0.00318357i	−0.000309644	−	0.000116715i
$745$	9.01222	+	2.92825i	0.330182	+	0.107283i
$746$	−2.99369	−	15.2369i	−0.109607	−	0.557864i
$747$			18.5979i			0.680463i
$748$	29.7751	+	8.60857i	1.08868	+	0.314761i
$749$			2.86472i			0.104674i
$750$	0.0253614	−	0.00498290i	0.000926069	−	0.000181950i
$751$	38.1097	+	12.3826i	1.39064	+	0.451848i	0.906153	−	0.422949i	$-0.139005\pi$
$751$	38.1097	+	12.3826i	1.39064	+	0.451848i	0.484490	+	0.874797i	$0.339005\pi$
$752$	−13.1450	−	26.4081i	−0.479350	−	0.963004i
$753$	−0.0128084	+	0.00930584i	−0.000466764	+	0.000339124i
$754$	−10.3684	−	10.2066i	−0.377594	−	0.371703i
$755$	−3.12644	−	9.62220i	−0.113783	−	0.350188i
$756$	0.00578318	+	0.00141714i	0.000210332	+	5.15409e-5i
$757$	−20.5499	−	14.9304i	−0.746898	−	0.542653i	0.147966	−	0.988992i	$-0.452727\pi$
$757$	−20.5499	−	14.9304i	−0.746898	−	0.542653i	−0.894864	+	0.446339i	$0.852727\pi$
$758$	36.3103	−	39.0959i	1.31885	−	1.42003i
$759$	−0.00203093	+	0.0493432i	−7.37180e−5	+	0.00179105i
$760$	4.94055	+	3.95149i	0.179213	+	0.143336i
$761$	−22.2733	−	16.1825i	−0.807405	−	0.586614i	0.105672	−	0.994401i	$-0.466301\pi$
$761$	−22.2733	−	16.1825i	−0.807405	−	0.586614i	−0.913077	+	0.407787i	$0.866301\pi$
$762$	0.0243382	−	0.0135552i	0.000881679	−	0.000491052i
$763$	−0.930708	+	0.302405i	−0.0336939	+	0.0109478i
$764$	29.8692	−	25.2694i	1.08063	−	0.914215i
$765$	−10.9901	+	7.98480i	−0.397349	+	0.288691i
$766$	23.7171	+	11.0013i	0.856934	+	0.397492i
$767$	−17.8007	+	12.1586i	−0.642746	+	0.439023i
$768$	−0.0108832	+	0.0314733i	−0.000392713	+	0.00113570i
$769$	0.955971			0.0344732			0.0172366	−	0.999851i	$-0.494513\pi$
$769$	0.955971			0.0344732			0.0172366	+	0.999851i	$0.494513\pi$
$770$	1.06956	+	0.174021i	0.0385441	+	0.00627129i
$771$			0.0351477i			0.00126581i
$772$	−20.7466	+	33.5016i	−0.746685	+	1.20575i
$773$	−31.9614	−	10.3849i	−1.14957	−	0.373519i	−0.328590	−	0.944473i	$-0.606574\pi$
$773$	−31.9614	−	10.3849i	−1.14957	−	0.373519i	−0.820982	+	0.570954i	$0.806574\pi$
$774$	−12.0084	−	5.57015i	−0.431635	−	0.200215i
$775$	−5.03708	+	3.65966i	−0.180937	+	0.131459i
$776$	−1.60529	+	34.6426i	−0.0576264	+	1.24360i
$777$	0.000417749	0	0.000135735i	1.49867e−5	0	4.86947e-6i
$778$	17.5065	+	31.4329i	0.627640	+	1.12692i
$779$	−11.8512	+	16.3118i	−0.424614	+	0.584431i
$780$	−0.00801398	+	0.0121382i	−0.000286947	+	0.000434616i
$781$	20.4480	−	25.8388i	0.731687	−	0.924587i
$782$	−32.1711	+	34.6392i	−1.15044	+	1.23869i
$783$	−0.0288276	−	0.0209445i	−0.00103021	−	0.000748494i
$784$	−4.60172	+	27.3888i	−0.164347	+	0.978171i
$785$	−2.50903	+	0.815234i	−0.0895511	+	0.0290969i
$786$	−0.0635350	−	0.00767099i	−0.00226622	−	0.000273615i
$787$	6.07735	+	8.36476i	0.216634	+	0.298171i	0.903479	−	0.428633i	$-0.141005\pi$
$787$	6.07735	+	8.36476i	0.216634	+	0.298171i	−0.686845	+	0.726804i	$0.741005\pi$
$788$	23.0049	−	9.40277i	0.819516	−	0.334960i
$789$	0.0102654	+	0.00333542i	0.000365457	+	0.000118744i
$790$	1.15000	+	5.85313i	0.0409151	+	0.208245i
$791$			0.710678i			0.0252688i
$792$	−27.4223	+	6.32588i	−0.974408	+	0.224780i
$793$	−12.3968	+	16.0598i	−0.440225	+	0.570299i
$794$	5.09271	+	25.9203i	0.180734	+	0.919878i
$795$	0.00104316	−	0.00321051i	3.69969e−5	−	0.000113865i
$796$	−12.1128	−	29.6353i	−0.429327	−	1.05040i
$797$	24.8725	−	18.0709i	0.881028	−	0.640105i	−0.0524950	−	0.998621i	$-0.516717\pi$
$797$	24.8725	−	18.0709i	0.881028	−	0.640105i	0.933523	+	0.358517i	$0.116717\pi$
$798$	−0.00160793		0.000194136i	−5.69200e−5		6.87232e-6i
$799$	−32.7725	+	10.6484i	−1.15941	+	0.376715i
$800$	14.0091	+	18.2056i	0.495297	+	0.643664i
$801$	17.6770	−	24.3303i	0.624585	−	0.859667i
$802$	−19.5212	−	18.1303i	−0.689319	−	0.640204i
$803$	8.61073	+	12.9391i	0.303866	+	0.456610i
$804$	−0.0105738		0.000782291i	−0.000372908		2.75893e-5i
$805$	−0.971482	+	1.33713i	−0.0342402	+	0.0471277i
$806$	1.16225	−	7.73103i	0.0409387	−	0.272314i
$807$	0.0423222	−	0.0137513i	0.00148981	−	0.000484070i
$808$	0.610733	−	13.1798i	0.0214855	−	0.463665i
$809$	−26.7277	−	36.7875i	−0.939695	−	1.29338i	−0.955956	−	0.293511i	$-0.905176\pi$
$809$	−26.7277	−	36.7875i	−0.939695	−	1.29338i	0.0162608	−	0.999868i	$-0.494824\pi$
$810$	5.19021	−	11.1894i	0.182366	−	0.393154i
$811$	34.0957	+	11.0784i	1.19726	+	0.389014i	0.838753	−	0.544513i	$-0.183285\pi$
$811$	34.0957	+	11.0784i	1.19726	+	0.389014i	0.358509	+	0.933526i	$0.383285\pi$
$812$	−0.716264	+	1.15662i	−0.0251359	+	0.0405895i
$813$	−0.0488486			−0.00171320
$814$	−2.94835	+	2.92362i	−0.103340	+	0.102473i
$815$			16.9643i			0.594234i
$816$	0.0344944	+	0.0179853i	0.00120755	+	0.000629612i
$817$	6.84889	+	2.22534i	0.239612	+	0.0778547i
$818$	−8.69777	−	4.03449i	−0.304110	−	0.141062i
$819$	−0.0749351	+	2.57756i	−0.00261844	+	0.0900672i
$820$	12.9262	−	10.9356i	0.451403	−	0.381887i
$821$	−1.54943	−	4.76864i	−0.0540753	−	0.166427i	0.920371	−	0.391045i	$-0.127886\pi$
$821$	−1.54943	−	4.76864i	−0.0540753	−	0.166427i	−0.974447	+	0.224619i	$0.927886\pi$
$822$	0.0203385	+	0.0365176i	0.000709386	+	0.00127370i
$823$	−6.99447	+	9.62706i	−0.243812	+	0.335578i	−0.913332	−	0.407216i	$-0.866500\pi$
$823$	−6.99447	+	9.62706i	−0.243812	+	0.335578i	0.669520	+	0.742794i	$0.266500\pi$
$824$	−18.0405	+	22.5560i	−0.628469	+	0.785775i
$825$	0.00975160	−	0.0262817i	0.000339507	−	0.000915013i
$826$	1.47697	+	1.37173i	0.0513903	+	0.0477287i
$827$	14.9779	−	20.6153i	0.520833	−	0.716865i	−0.464866	−	0.885381i	$-0.653898\pi$
$827$	14.9779	−	20.6153i	0.520833	−	0.716865i	0.985699	+	0.168516i	$0.0538975\pi$
$828$	10.2161	−	41.6906i	0.355033	−	1.44885i
$829$	−10.7152	−	32.9780i	−0.372154	−	1.14537i	−0.945379	−	0.325974i	$-0.894308\pi$
$829$	−10.7152	−	32.9780i	−0.372154	−	1.14537i	0.573225	−	0.819398i	$-0.305692\pi$
$830$	−1.01841	+	8.43495i	−0.0353494	+	0.292781i
$831$	−0.0320363	+	0.0232757i	−0.00111133	+	0.000807425i
$832$	−28.6312	−	3.50098i	−0.992607	−	0.121375i
$833$	30.8548	+	10.0253i	1.06906	+	0.347357i
$834$	0.0113817	+	0.0579295i	0.000394117	+	0.00200594i
$835$	4.56852			0.158100
$836$	14.3980	−	5.20473i	0.497967	−	0.180009i
$837$		−	0.0191471i		−	0.000661821i
$838$	−3.19917	−	16.2828i	−0.110513	−	0.562479i
$839$	−3.55620	+	10.9449i	−0.122774	+	0.377858i	−0.993489	−	0.113929i	$-0.963656\pi$
$839$	−3.55620	+	10.9449i	−0.122774	+	0.377858i	0.870715	+	0.491787i	$0.163656\pi$
$840$	0.00127266		0.000479707i	4.39108e−5		1.65515e-5i
$841$	−16.8749	+	12.2603i	−0.581893	+	0.422770i
$842$	−19.8902	−	2.40147i	−0.685460	−	0.0827601i
$843$	0.00665486	−	0.00216230i	0.000229206	−	7.44734e-5i
$844$	−31.8875	−	7.81387i	−1.09761	−	0.268965i
$845$	−11.7352	−	4.58256i	−0.403704	−	0.157645i
$846$	21.2923	−	22.9257i	0.732043	−	0.788203i
$847$	1.71052	−	1.98769i	0.0587741	−	0.0682978i
$848$	6.62153	−	0.985168i	0.227384	−	0.0338308i
$849$	0.0211306	−	0.0290837i	0.000725200	−	0.000998152i
$850$	23.4436	−	13.0569i	0.804108	−	0.447848i
$851$	−1.95701	−	6.02307i	−0.0670856	−	0.206468i
$852$	0.0315738	−	0.0267115i	0.00108170	−	0.000915121i
$853$	−7.27469	+	5.28537i	−0.249081	+	0.180968i	−0.705319	−	0.708890i	$-0.749196\pi$
$853$	−7.27469	+	5.28537i	−0.249081	+	0.180968i	0.456239	+	0.889857i	$0.349196\pi$
$854$	1.72093	+	0.798258i	0.0588890	+	0.0273158i
$855$	−2.07355	+	6.38174i	−0.0709140	+	0.218251i
$856$	−8.99537	−	32.7761i	−0.307455	−	1.12026i
$857$			38.2695i			1.30726i	0.756814	+	0.653630i	$0.226755\pi$
$857$			38.2695i			1.30726i	−0.756814	+	0.653630i	$0.773245\pi$
$858$	0.0149278	+	0.0318769i	0.000509627	+	0.00108826i
$859$		−	1.70590i		−	0.0582047i	−0.999576	−	0.0291023i	$-0.990735\pi$
$859$		−	1.70590i		−	0.0582047i	0.999576	−	0.0291023i	$-0.00926487\pi$
$860$	−5.14132	−	3.18387i	−0.175318	−	0.108569i
$861$	−0.00133946	+	0.00412242i	−4.56486e−5	+	0.000140492i
$862$	−21.3062	+	45.9331i	−0.725691	+	1.56449i
$863$	−4.03054	+	2.92836i	−0.137201	+	0.0996825i	−0.654269	−	0.756262i	$-0.727024\pi$
$863$	−4.03054	+	2.92836i	−0.137201	+	0.0996825i	0.517068	+	0.855945i	$0.327024\pi$
$864$	−0.0706171	+	0.00194558i	−0.00240244	+	6.61901e-5i
$865$	5.47743	+	16.8578i	0.186238	+	0.573183i
$866$	−3.74397	−	6.72227i	−0.127225	−	0.228432i
$867$	0.00591295	−	0.00813848i	0.000200814	−	0.000276397i
$868$	−0.729035	+	0.0539370i	−0.0247451	+	0.00183074i
$869$	13.5338	+	5.02160i	0.459103	+	0.170346i
$870$	−0.00596381	−	0.00553888i	−0.000202192	−	0.000187786i
$871$	−2.58285	−	8.81282i	−0.0875166	−	0.298611i
$872$	9.69895	−	6.38239i	0.328448	−	0.216135i
$873$	−34.9831	+	11.3667i	−1.18400	+	0.384705i
$874$	−2.79903	+	23.1830i	−0.0946785	+	0.784175i
$875$	1.69353	−	1.23042i	0.0572517	−	0.0415958i
$876$	0.00738053	+	0.0180573i	0.000249365	+	0.000610099i
$877$	−9.51924	+	29.2972i	−0.321442	+	0.989297i	0.651579	+	0.758581i	$0.274107\pi$
$877$	−9.51924	+	29.2972i	−0.321442	+	0.989297i	−0.973021	+	0.230716i	$0.925893\pi$
$878$	8.54989	−	1.67984i	0.288545	−	0.0566920i
$879$			0.0307577i			0.00103743i
$880$	−12.7836	+	1.36744i	−0.430934	+	0.0460962i
$881$	42.1571			1.42031			0.710154	−	0.704047i	$-0.248625\pi$
$881$	42.1571			1.42031			0.710154	+	0.704047i	$0.248625\pi$
$882$	−28.9047	+	5.67907i	−0.973272	+	0.191224i
$883$	9.43064	+	3.06420i	0.317366	+	0.103119i	0.463369	−	0.886166i	$-0.346641\pi$
$883$	9.43064	+	3.06420i	0.317366	+	0.103119i	−0.146002	+	0.989284i	$0.546641\pi$
$884$	−8.96707	+	32.4795i	−0.301595	+	1.09240i
$885$	−0.00975631	+	0.00708837i	−0.000327955	+	0.000238273i
$886$	−4.66803	−	0.563602i	−0.156826	−	0.0189346i
$887$	−1.33860	−	4.11979i	−0.0449458	−	0.138329i	0.926065	−	0.377363i	$-0.123169\pi$
$887$	−1.33860	−	4.11979i	−0.0449458	−	0.138329i	−0.971011	+	0.239034i	$0.923169\pi$
$888$	−0.00435339	+	0.00286474i	−0.000146090	+	9.61345e-5i
$889$	1.32621	−	1.82537i	0.0444795	−	0.0612208i
$890$	9.34955	−	10.0668i	0.313398	−	0.337441i
$891$	−16.5371	−	24.8498i	−0.554015	−	0.832501i
$892$	−2.10850	−	28.4993i	−0.0705977	−	0.954228i
$893$	−10.0048	+	13.7704i	−0.334798	+	0.460810i
$894$	0.0251452	−	0.0140046i	0.000840981	−	0.000468385i
$895$	−2.69062	−	8.28087i	−0.0899375	−	0.276799i
$896$	0.273006	+	2.68330i	0.00912048	+	0.0896426i
$897$	−0.0536645	−	0.00156014i	−0.00179181	−	5.20916e-5i
$898$	−18.0276	+	38.8649i	−0.601589	+	1.29694i
$899$	4.16065	+	1.35188i	0.138766	+	0.0450877i
$900$	−12.8280	+	20.7147i	−0.427601	+	0.690491i
$901$		−	7.82009i		−	0.260525i
$902$	−6.23928	−	40.4963i	−0.207745	−	1.34838i
$903$	0.00154816			5.15196e−5
$904$	−2.23157	−	8.13109i	−0.0742210	−	0.270436i
$905$	8.89097	+	2.88885i	0.295546	+	0.0960287i
$906$	−0.0278772	−	0.0129309i	−0.000926157	−	0.000429601i
$907$	7.81479	+	10.7561i	0.259486	+	0.357152i	0.918805	−	0.394712i	$-0.129155\pi$
$907$	7.81479	+	10.7561i	0.259486	+	0.357152i	−0.659319	+	0.751863i	$0.729155\pi$
$908$	12.5291	−	10.5996i	0.415793	−	0.351762i
$909$	13.3094	−	4.32448i	0.441444	−	0.143434i
$910$	−0.175131	+	1.16493i	−0.00580554	+	0.0386170i
$911$	25.5297	−	35.1386i	0.845837	−	1.16420i	−0.138927	−	0.990303i	$-0.544365\pi$
$911$	25.5297	−	35.1386i	0.845837	−	1.16420i	0.984765	−	0.173893i	$-0.0556346\pi$
$912$	0.0190064	−	0.00282782i	0.000629365	−	9.36385e-5i
$913$	16.1230	+	12.7592i	0.533593	+	0.422268i
$914$	−27.6352	+	29.7553i	−0.914092	+	0.984218i
$915$	−0.00667111	+	0.00918199i	−0.000220540	+	0.000303547i
$916$	−12.5468	+	51.2021i	−0.414558	+	1.69176i
$917$	−4.92945	+	1.60167i	−0.162785	+	0.0528920i
$918$	−0.00989166	+	0.0819277i	−0.000326473	+	0.00270402i
$919$	28.1146	−	20.4265i	0.927416	−	0.673807i	−0.0179426	−	0.999839i	$-0.505712\pi$
$919$	28.1146	−	20.4265i	0.927416	−	0.673807i	0.945359	+	0.326032i	$0.105712\pi$
$920$	6.91636	−	18.3490i	0.228026	−	0.604950i
$921$	0.0107768	−	0.0331676i	0.000355108	−	0.00109291i
$922$	−47.3203	+	9.29728i	−1.55841	+	0.306190i
$923$	28.3561	+	21.8886i	0.933352	+	0.720472i
$924$	0.00259806	−	0.00202067i	8.54699e−5	−	6.64751e-5i
$925$			3.59484i			0.118197i
$926$	41.4776	−	8.14934i	1.36304	−	0.267804i
$927$	−29.1357	−	9.46676i	−0.956941	−	0.310929i
$928$	4.56313	−	15.4824i	0.149792	−	0.508235i
$929$	22.8251	+	31.4160i	0.748866	+	1.03073i	0.998059	+	0.0622719i	$0.0198346\pi$
$929$	22.8251	+	31.4160i	0.748866	+	1.03073i	−0.249193	+	0.968454i	$0.580165\pi$
$930$	0.000524239	−	0.00434201i	1.71905e−5	−	0.000142380i
$931$	15.2409	−	4.95206i	0.499499	−	0.162297i
$932$	5.45852	−	22.2756i	0.178800	−	0.729661i
$933$	0.0498183	+	0.0361951i	0.00163098	+	0.00118497i
$934$	41.8606	+	38.8780i	1.36972	+	1.27213i
$935$	−0.617619	+	15.0056i	−0.0201983	+	0.490736i
$936$	−7.23633	−	29.7260i	−0.236527	−	0.971623i
$937$	17.6167	−	24.2474i	0.575514	−	0.792127i	−0.417681	−	0.908594i	$-0.637157\pi$
$937$	17.6167	−	24.2474i	0.575514	−	0.792127i	0.993195	+	0.116467i	$0.0371569\pi$
$938$	−0.750212	+	0.417831i	−0.0244953	+	0.0136427i
$939$	0.0109914	−	0.00357132i	0.000358691	−	0.000116546i
$940$	10.9123	−	9.23185i	0.355921	−	0.301110i
$941$	−8.47963	+	6.16081i	−0.276428	+	0.200837i	−0.717358	−	0.696705i	$-0.754649\pi$
$941$	−8.47963	+	6.16081i	−0.276428	+	0.200837i	0.440930	+	0.897542i	$0.354649\pi$
$942$	−0.00337179	+	0.00726910i	−0.000109859	+	0.000236840i
$943$	59.4367	+	19.3122i	1.93553	+	0.628891i
$944$	−21.2058	−	11.0567i	−0.690190	−	0.359864i
$945$			0.00288513i			9.38532e-5i
$946$	−13.0673	+	6.58897i	−0.424856	+	0.214226i
$947$	−20.1255			−0.653990			−0.326995	−	0.945026i	$-0.606036\pi$
$947$	−20.1255			−0.653990			−0.326995	+	0.945026i	$0.606036\pi$
$948$	0.0154036	+	0.00953898i	0.000500285	+	0.000309812i
$949$	−13.9522	+	9.52998i	−0.452909	+	0.309356i
$950$	5.57753	−	12.0244i	0.180959	−	0.390122i
$951$	0.0397493	−	0.0288795i	0.00128896	−	0.000936483i
$952$	3.14730	+	0.145841i	0.102005	+	0.00472673i
$953$	23.3059	−	7.57255i	0.754953	−	0.245299i	0.0938417	−	0.995587i	$-0.470085\pi$
$953$	23.3059	−	7.57255i	0.754953	−	0.245299i	0.661111	+	0.750288i	$0.270085\pi$
$954$	3.45491	+	6.20327i	0.111857	+	0.200838i
$955$	15.3370	+	11.1430i	0.496294	+	0.360579i
$956$	−26.9675	+	1.99517i	−0.872192	+	0.0645283i
$957$	−0.0189673	+	0.00531113i	−0.000613124	+	0.000171684i
$958$	40.1949	+	37.3309i	1.29864	+	1.20611i
$959$	2.73882	+	1.98987i	0.0884412	+	0.0642563i
$960$	−0.0160672	−	0.00149226i	−0.000518566	−	4.81625e-5i
$961$	−8.85310	−	27.2470i	−0.285584	−	0.878937i
$962$	−3.21677	−	3.16659i	−0.103713	−	0.102095i
$963$	29.1649	−	21.1895i	0.939825	−	0.682823i
$964$	−17.3070	+	7.07388i	−0.557421	+	0.227834i
$965$	−18.1592	−	5.90028i	−0.584566	−	0.189937i
$966$	0.000967827		0.00492594i	3.11393e−5		0.000158489i
$967$		−	2.83455i		−	0.0911529i	−0.998961	−	0.0455765i	$-0.985488\pi$
$967$		−	2.83455i		−	0.0911529i	0.998961	−	0.0455765i	$-0.0145125\pi$
$968$	−13.3291	+	28.1129i	−0.428414	+	0.903583i
$969$		−	0.0224467i		−	0.000721093i
$970$	−16.4888	+	3.23964i	−0.529422	+	0.104018i
$971$	−18.6703	−	6.06635i	−0.599159	−	0.194679i	−0.00629371	−	0.999980i	$-0.502003\pi$
$971$	−18.6703	−	6.06635i	−0.599159	−	0.194679i	−0.592865	+	0.805302i	$0.702003\pi$
$972$	−0.0425236	−	0.104039i	−0.00136395	−	0.00333704i
$973$	2.81047	+	3.86829i	0.0900997	+	0.124012i
$974$	−0.522095	+	4.32426i	−0.0167290	+	0.138558i
$975$	0.0286972	+	0.0102554i	0.000919044	+	0.000328437i
$976$	−22.1963	−	3.72930i	−0.710485	−	0.119372i
$977$	−32.8782	+	45.2530i	−1.05187	+	1.44777i	−0.164688	+	0.986346i	$0.552662\pi$
$977$	−32.8782	+	45.2530i	−1.05187	+	1.44777i	−0.887179	+	0.461425i	$0.847338\pi$
$978$	0.0377552	+	0.0350651i	0.00120728	+	0.00112126i
$979$	−8.96511	−	32.0164i	−0.286526	−	1.02325i
$980$	−13.4205	+	0.992902i	−0.428702	+	0.0317171i
$981$	9.96290	+	7.23847i	0.318091	+	0.231107i
$982$	−12.2844	−	22.0566i	−0.392012	−	0.703855i
$983$	1.14198	+	3.51465i	0.0364234	+	0.112100i	0.967615	−	0.252430i	$-0.0812297\pi$
$983$	1.14198	+	3.51465i	0.0364234	+	0.112100i	−0.931192	+	0.364530i	$0.881230\pi$
$984$	0.00238050	−	0.0513719i	7.58874e−5	−	0.00163768i
$985$	7.07818	+	9.74228i	0.225529	+	0.310415i
$986$	−17.1044	−	7.93394i	−0.544716	−	0.252668i
$987$	−0.00113077	+	0.00348016i	−3.59929e−5	+	0.000110775i
$988$	5.84668	+	15.5829i	0.186008	+	0.495757i
$989$		−	22.3212i		−	0.709774i
$990$	−6.13955	−	12.1760i	−0.195128	−	0.386980i
$991$			10.6441i			0.338122i	0.985606	+	0.169061i	$0.0540735\pi$
$991$			10.6441i			0.338122i	−0.985606	+	0.169061i	$0.945927\pi$
$992$	8.17175	−	2.90632i	0.259453	−	0.0922758i
$993$	−0.0563831	−	0.0183200i	−0.00178926	−	0.000581367i
$994$	1.40945	−	3.03858i	0.0447051	−	0.0963778i
$995$	12.5502	−	9.11823i	0.397867	−	0.289067i
$996$	0.0166675	+	0.0197015i	0.000528130	+	0.000624267i
$997$	−9.52253	+	3.09406i	−0.301582	+	0.0979898i	−0.455899	−	0.890032i	$-0.650682\pi$
$997$	−9.52253	+	3.09406i	−0.301582	+	0.0979898i	0.154317	+	0.988021i	$0.450682\pi$
$998$	−9.82268	−	17.6366i	−0.310932	−	0.558275i
$999$	−0.00894372	−	0.00649800i	−0.000282967	−	0.000205587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bb.b.51.6	✓	304
4.3	odd	2	inner	572.2.bb.b.51.37	yes	304
11.8	odd	10	inner	572.2.bb.b.415.40	yes	304
13.12	even	2	inner	572.2.bb.b.51.71	yes	304
44.19	even	10	inner	572.2.bb.b.415.71	yes	304
52.51	odd	2	inner	572.2.bb.b.51.40	yes	304
143.129	odd	10	inner	572.2.bb.b.415.37	yes	304
572.415	even	10	inner	572.2.bb.b.415.6	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bb.b.51.6	✓	304	1.1	even	1	trivial
572.2.bb.b.51.37	yes	304	4.3	odd	2	inner
572.2.bb.b.51.40	yes	304	52.51	odd	2	inner
572.2.bb.b.51.71	yes	304	13.12	even	2	inner
572.2.bb.b.415.6	yes	304	572.415	even	10	inner
572.2.bb.b.415.37	yes	304	143.129	odd	10	inner
572.2.bb.b.415.40	yes	304	11.8	odd	10	inner
572.2.bb.b.415.71	yes	304	44.19	even	10	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38768 + 0.272646i) q^{2} +(-0.00197950 - 0.000643177i) q^{3} +(1.85133 - 0.756692i) q^{4} +(0.569619 + 0.784014i) q^{5} +(0.00292227 + 0.000352825i) q^{6} +(0.226728 - 0.0736686i) q^{7} +(-2.36275 + 1.55481i) q^{8} +(-2.42705 - 1.76335i) q^{9} +O(q^{10})\)	\(q+(-1.38768 + 0.272646i) q^{2} +(-0.00197950 - 0.000643177i) q^{3} +(1.85133 - 0.756692i) q^{4} +(0.569619 + 0.784014i) q^{5} +(0.00292227 + 0.000352825i) q^{6} +(0.226728 - 0.0736686i) q^{7} +(-2.36275 + 1.55481i) q^{8} +(-2.42705 - 1.76335i) q^{9} +(-1.00421 - 0.932658i) q^{10} +(-3.19378 + 0.894308i) q^{11} +(-0.00415139 + 0.000307136i) q^{12} +(-1.01406 - 3.46001i) q^{13} +(-0.294542 + 0.164045i) q^{14} +(-0.000623299 - 0.00191832i) q^{15} +(2.85483 - 2.80177i) q^{16} +(-2.74649 - 3.78022i) q^{17} +(3.84874 + 1.78525i) q^{18} +(-2.19509 - 0.713228i) q^{19} +(1.64781 + 1.02044i) q^{20} -0.000496190 q^{21} +(4.18812 - 2.11179i) q^{22} +7.15402i q^{23} +(0.00567707 - 0.00155807i) q^{24} +(1.25487 - 3.86210i) q^{25} +(2.35055 + 4.52492i) q^{26} +(0.00734037 + 0.0101032i) q^{27} +(0.364005 - 0.307948i) q^{28} +(-2.71367 + 0.881726i) q^{29} +(0.00138796 + 0.00249208i) q^{30} +(-1.24040 - 0.901203i) q^{31} +(-3.19771 + 4.66633i) q^{32} +(0.00689727 + 0.000283886i) q^{33} +(4.84191 + 4.49692i) q^{34} +(0.186906 + 0.135795i) q^{35} +(-5.82758 - 1.42802i) q^{36} +(-0.841914 + 0.273554i) q^{37} +(3.24055 + 0.391252i) q^{38} +(-0.000218079 + 0.00750130i) q^{39} +(-2.56486 - 0.966780i) q^{40} +(2.69948 - 8.30815i) q^{41} +(0.000688555 - 0.000135284i) q^{42} -3.12010 q^{43} +(-5.23602 + 4.07236i) q^{44} -2.90728i q^{45} +(-1.95051 - 9.92752i) q^{46} +(2.27891 - 7.01376i) q^{47} +(-0.00745317 + 0.00370993i) q^{48} +(-5.61714 + 4.08109i) q^{49} +(-0.688380 + 5.70151i) q^{50} +(0.00300531 + 0.00924940i) q^{51} +(-4.49552 - 5.63829i) q^{52} +(1.35397 + 0.983720i) q^{53} +(-0.0129407 - 0.0120187i) q^{54} +(-2.52039 - 1.99455i) q^{55} +(-0.421162 + 0.526579i) q^{56} +(0.00388644 + 0.00282366i) q^{57} +(3.52532 - 1.96343i) q^{58} +(-1.84755 - 5.68617i) q^{59} +(-0.00260551 - 0.00307979i) q^{60} +(-3.30738 - 4.55221i) q^{61} +(1.96699 + 0.912394i) q^{62} +(-0.680185 - 0.221005i) q^{63} +(3.16516 - 7.34723i) q^{64} +(2.13507 - 2.76592i) q^{65} +(-0.00964863 + 0.00148657i) q^{66} +2.54705 q^{67} +(-7.94511 - 4.92018i) q^{68} +(0.00460131 - 0.0141614i) q^{69} +(-0.296390 - 0.137482i) q^{70} +(-8.03766 + 5.83970i) q^{71} +(8.47617 + 0.392773i) q^{72} +(-1.44811 - 4.45684i) q^{73} +(1.09373 - 0.609151i) q^{74} +(-0.00496804 + 0.00683792i) q^{75} +(-4.60353 + 0.340588i) q^{76} +(-0.658238 + 0.438046i) q^{77} +(-0.00174257 - 0.0104689i) q^{78} +(-3.52119 - 2.55829i) q^{79} +(3.82279 + 0.642287i) q^{80} +(2.78114 + 8.55947i) q^{81} +(-1.48084 + 12.2651i) q^{82} +(-3.64387 - 5.01536i) q^{83} +(-0.000918611 + 0.000375463i) q^{84} +(1.39929 - 4.30657i) q^{85} +(4.32970 - 0.850681i) q^{86} +0.00593882 q^{87} +(6.15562 - 7.07873i) q^{88} +10.0246i q^{89} +(0.792657 + 4.03438i) q^{90} +(-0.484810 - 0.709779i) q^{91} +(5.41339 + 13.2444i) q^{92} +(0.00187573 + 0.00258173i) q^{93} +(-1.25013 + 10.3542i) q^{94} +(-0.691185 - 2.12725i) q^{95} +(0.00933114 - 0.00718028i) q^{96} +(7.20693 - 9.91949i) q^{97} +(6.68212 - 7.19475i) q^{98} +(9.32843 + 3.46123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) \) 304 * q - 14 * q^4 + 72 * q^9	\( 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) \) 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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