LMFDB - Embedded newform 462.2.y.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	462.37
Dual form			462.2.y.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.269783 - 2.56681i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-0.146873 - 2.64167i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.269783 - 2.56681i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-0.146873 - 2.64167i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(1.29048 + 2.23517i) q^{10} +(1.41370 + 3.00024i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.71598 - 2.69982i) q^{13} +(1.20864 + 2.35355i) q^{14} +(-0.797558 - 2.45463i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(0.464721 + 0.206907i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-4.98865 - 5.54045i) q^{19} +(-2.08803 - 1.51705i) q^{20} +(-0.692898 - 2.55341i) q^{21} +(-2.51179 - 2.16585i) q^{22} +(-2.63753 + 4.56834i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-1.62501 + 0.345406i) q^{25} +(4.49283 + 0.954981i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.06142 - 1.65848i) q^{28} +(-1.41639 - 4.35919i) q^{29} +(1.72699 + 1.91802i) q^{30} +(0.326742 - 3.10874i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.00659 + 2.64075i) q^{33} -0.508700 q^{34} +(-6.74105 + 1.08967i) q^{35} +(0.309017 - 0.951057i) q^{36} +(9.20197 + 1.95594i) q^{37} +(6.81086 + 3.03239i) q^{38} +(-4.19610 - 1.86822i) q^{39} +(2.52455 + 0.536610i) q^{40} +(0.269143 - 0.828337i) q^{41} +(1.67156 + 2.05083i) q^{42} +9.54037 q^{43} +(3.17556 + 0.956968i) q^{44} +(-1.29048 - 2.23517i) q^{45} +(0.551395 - 5.24617i) q^{46} +(3.13726 + 3.48428i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-6.95686 + 0.775981i) q^{49} +(1.34403 - 0.976495i) q^{50} +(0.497584 + 0.105765i) q^{51} +(-4.49283 + 0.954981i) q^{52} +(0.540266 - 5.14029i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(7.31967 - 4.43812i) q^{55} +(2.55777 + 0.676637i) q^{56} +(-6.03156 - 4.38218i) q^{57} +(3.06698 + 3.40622i) q^{58} +(-3.52909 + 3.91945i) q^{59} +(-2.35782 - 1.04977i) q^{60} +(-1.12312 - 10.6858i) q^{61} +(0.965945 + 2.97287i) q^{62} +(-1.20864 - 2.35355i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-5.92742 + 10.2666i) q^{65} +(-2.90721 - 1.59629i) q^{66} +(2.02628 + 3.50961i) q^{67} +(0.464721 - 0.206907i) q^{68} +(-1.63009 + 5.01689i) q^{69} +(5.71505 - 3.73730i) q^{70} +(9.68258 - 7.03481i) q^{71} +(0.104528 + 0.994522i) q^{72} +(-5.85831 + 6.50631i) q^{73} +(-9.20197 + 1.95594i) q^{74} +(-1.51768 + 0.675717i) q^{75} -7.45541 q^{76} +(7.71802 - 4.17519i) q^{77} +4.59320 q^{78} +(7.51118 - 3.34419i) q^{79} +(-2.52455 + 0.536610i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.0910407 + 0.866194i) q^{82} +(4.44183 - 3.22718i) q^{83} +(-2.36119 - 1.19364i) q^{84} +(0.405718 - 1.24867i) q^{85} +(-8.71556 + 3.88042i) q^{86} +(-2.29176 - 3.96945i) q^{87} +(-3.29026 + 0.417385i) q^{88} +(2.45001 - 4.24355i) q^{89} +(2.08803 + 1.51705i) q^{90} +(-6.58625 + 10.2129i) q^{91} +(1.63009 + 5.01689i) q^{92} +(-0.326742 - 3.10874i) q^{93} +(-4.28322 - 1.90701i) q^{94} +(-12.8755 + 14.2996i) q^{95} +(0.669131 + 0.743145i) q^{96} +(12.1255 + 8.80966i) q^{97} +(6.03978 - 3.53850i) q^{98} +(2.51179 + 2.16585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−0.269783	−	2.56681i	−0.120651	−	1.14791i	−0.872512	−	0.488593i	$-0.837510\pi$
$5$	−0.269783	−	2.56681i	−0.120651	−	1.14791i	0.751861	−	0.659321i	$-0.229156\pi$
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−0.146873	−	2.64167i	−0.0555128	−	0.998458i
$7$	−0.146873	−	2.64167i	−0.0555128	−	0.998458i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	1.29048	+	2.23517i	0.408084	+	0.706823i
$11$	1.41370	+	3.00024i	0.426247	+	0.904607i
$11$	1.41370	+	3.00024i	0.426247	+	0.904607i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.71598	−	2.69982i	−1.03063	−	0.748795i	−0.0621932	−	0.998064i	$-0.519809\pi$
$13$	−3.71598	−	2.69982i	−1.03063	−	0.748795i	−0.968434	+	0.249270i	$0.919809\pi$
$14$	1.20864	+	2.35355i	0.323023	+	0.629012i
$15$	−0.797558	−	2.45463i	−0.205929	−	0.633783i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	0.464721	+	0.206907i	0.112711	+	0.0501823i	0.462318	−	0.886714i	$-0.347018\pi$
$17$	0.464721	+	0.206907i	0.112711	+	0.0501823i	−0.349606	+	0.936897i	$0.613685\pi$
$18$	−0.669131	+	0.743145i	−0.157716	+	0.175161i
$19$	−4.98865	−	5.54045i	−1.14447	−	1.27107i	−0.957414	−	0.288719i	$-0.906771\pi$
$19$	−4.98865	−	5.54045i	−1.14447	−	1.27107i	−0.187060	−	0.982349i	$-0.559896\pi$
$20$	−2.08803	−	1.51705i	−0.466899	−	0.339222i
$21$	−0.692898	−	2.55341i	−0.151203	−	0.557199i
$22$	−2.51179	−	2.16585i	−0.535515	−	0.461761i
$23$	−2.63753	+	4.56834i	−0.549964	+	0.952565i	0.448313	+	0.893877i	$0.352025\pi$
$23$	−2.63753	+	4.56834i	−0.549964	+	0.952565i	−0.998276	+	0.0586883i	$0.981308\pi$
$24$	−0.104528	+	0.994522i	−0.0213368	+	0.203006i
$25$	−1.62501	+	0.345406i	−0.325002	+	0.0690813i
$26$	4.49283	+	0.954981i	0.881117	+	0.187287i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−2.06142	−	1.65848i	−0.389572	−	0.313422i
$29$	−1.41639	−	4.35919i	−0.263016	−	0.809481i	−0.992144	−	0.125103i	$-0.960074\pi$
$29$	−1.41639	−	4.35919i	−0.263016	−	0.809481i	0.729127	−	0.684378i	$-0.239926\pi$
$30$	1.72699	+	1.91802i	0.315305	+	0.350181i
$31$	0.326742	−	3.10874i	0.0586846	−	0.558346i	−0.925192	−	0.379499i	$-0.876096\pi$
$31$	0.326742	−	3.10874i	0.0586846	−	0.558346i	0.983877	−	0.178848i	$-0.0572369\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.00659	+	2.64075i	0.349303	+	0.459696i
$34$	−0.508700			−0.0872414
$35$	−6.74105	+	1.08967i	−1.13945	+	0.184188i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	9.20197	+	1.95594i	1.51279	+	0.321554i	0.888223	−	0.459413i	$-0.151940\pi$
$37$	9.20197	+	1.95594i	1.51279	+	0.321554i	0.624571	+	0.780968i	$0.285274\pi$
$38$	6.81086	+	3.03239i	1.10487	+	0.491919i
$39$	−4.19610	−	1.86822i	−0.671914	−	0.299155i
$40$	2.52455	+	0.536610i	0.399167	+	0.0848455i
$41$	0.269143	−	0.828337i	0.0420331	−	0.129365i	−0.927838	−	0.372984i	$-0.878335\pi$
$41$	0.269143	−	0.828337i	0.0420331	−	0.129365i	0.969871	+	0.243619i	$0.0783347\pi$
$42$	1.67156	+	2.05083i	0.257927	+	0.316450i
$43$	9.54037			1.45489			0.727446	−	0.686165i	$-0.240707\pi$
$43$	9.54037			1.45489			0.727446	+	0.686165i	$0.240707\pi$
$44$	3.17556	+	0.956968i	0.478734	+	0.144268i
$45$	−1.29048	−	2.23517i	−0.192373	−	0.333199i
$46$	0.551395	−	5.24617i	0.0812987	−	0.773506i
$47$	3.13726	+	3.48428i	0.457617	+	0.508235i	0.927155	−	0.374677i	$-0.122246\pi$
$47$	3.13726	+	3.48428i	0.457617	+	0.508235i	−0.469539	+	0.882912i	$0.655580\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−6.95686	+	0.775981i	−0.993837	+	0.110854i
$50$	1.34403	−	0.976495i	0.190075	−	0.138097i
$51$	0.497584	+	0.105765i	0.0696757	+	0.0148100i
$52$	−4.49283	+	0.954981i	−0.623044	+	0.132432i
$53$	0.540266	−	5.14029i	0.0742113	−	0.706073i	−0.892646	−	0.450758i	$-0.851154\pi$
$53$	0.540266	−	5.14029i	0.0742113	−	0.706073i	0.966858	−	0.255316i	$-0.0821794\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	7.31967	−	4.43812i	0.986984	−	0.598436i
$56$	2.55777	+	0.676637i	0.341796	+	0.0904194i
$57$	−6.03156	−	4.38218i	−0.798899	−	0.580434i
$58$	3.06698	+	3.40622i	0.402714	+	0.447259i
$59$	−3.52909	+	3.91945i	−0.459448	+	0.510269i	−0.927700	−	0.373326i	$-0.878217\pi$
$59$	−3.52909	+	3.91945i	−0.459448	+	0.510269i	0.468252	+	0.883595i	$0.344884\pi$
$60$	−2.35782	−	1.04977i	−0.304393	−	0.135524i
$61$	−1.12312	−	10.6858i	−0.143801	−	1.36817i	−0.793772	−	0.608216i	$-0.791886\pi$
$61$	−1.12312	−	10.6858i	−0.143801	−	1.36817i	0.649971	−	0.759959i	$-0.274781\pi$
$62$	0.965945	+	2.97287i	0.122675	+	0.377555i
$63$	−1.20864	−	2.35355i	−0.152274	−	0.296519i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−5.92742	+	10.2666i	−0.735206	+	1.27341i
$66$	−2.90721	−	1.59629i	−0.357852	−	0.196490i
$67$	2.02628	+	3.50961i	0.247549	+	0.428767i	0.962845	−	0.270054i	$-0.0870416\pi$
$67$	2.02628	+	3.50961i	0.247549	+	0.428767i	−0.715296	+	0.698821i	$0.753708\pi$
$68$	0.464721	−	0.206907i	0.0563557	−	0.0250912i
$69$	−1.63009	+	5.01689i	−0.196239	+	0.603962i
$70$	5.71505	−	3.73730i	0.683079	−	0.446693i
$71$	9.68258	−	7.03481i	1.14911	−	0.834878i	0.160749	−	0.986995i	$-0.448609\pi$
$71$	9.68258	−	7.03481i	1.14911	−	0.834878i	0.988362	+	0.152117i	$0.0486091\pi$
$72$	0.104528	+	0.994522i	0.0123188	+	0.117206i
$73$	−5.85831	+	6.50631i	−0.685663	+	0.761506i	−0.981025	−	0.193879i	$-0.937893\pi$
$73$	−5.85831	+	6.50631i	−0.685663	+	0.761506i	0.295362	+	0.955385i	$0.404560\pi$
$74$	−9.20197	+	1.95594i	−1.06971	+	0.227373i
$75$	−1.51768	+	0.675717i	−0.175247	+	0.0780251i
$76$	−7.45541			−0.855195
$77$	7.71802	−	4.17519i	0.879550	−	0.475807i
$78$	4.59320			0.520078
$79$	7.51118	−	3.34419i	0.845074	−	0.376251i	0.0619216	−	0.998081i	$-0.480277\pi$
$79$	7.51118	−	3.34419i	0.845074	−	0.376251i	0.783152	+	0.621830i	$0.213610\pi$
$80$	−2.52455	+	0.536610i	−0.282253	+	0.0599948i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	0.0910407	+	0.866194i	0.0100538	+	0.0956551i
$83$	4.44183	−	3.22718i	0.487554	−	0.354229i	−0.316689	−	0.948529i	$-0.602571\pi$
$83$	4.44183	−	3.22718i	0.487554	−	0.354229i	0.804243	+	0.594301i	$0.202571\pi$
$84$	−2.36119	−	1.19364i	−0.257627	−	0.130237i
$85$	0.405718	−	1.24867i	0.0440063	−	0.135437i
$86$	−8.71556	+	3.88042i	−0.939823	+	0.418436i
$87$	−2.29176	−	3.96945i	−0.245703	−	0.425570i
$88$	−3.29026	+	0.417385i	−0.350743	+	0.0444934i
$89$	2.45001	−	4.24355i	0.259701	−	0.449815i	−0.706461	−	0.707752i	$-0.749709\pi$
$89$	2.45001	−	4.24355i	0.259701	−	0.449815i	0.966162	+	0.257937i	$0.0830427\pi$
$90$	2.08803	+	1.51705i	0.220098	+	0.159911i
$91$	−6.58625	+	10.2129i	−0.690427	+	1.07061i
$92$	1.63009	+	5.01689i	0.169948	+	0.523047i
$93$	−0.326742	−	3.10874i	−0.0338815	−	0.322361i
$94$	−4.28322	−	1.90701i	−0.441780	−	0.196693i
$95$	−12.8755	+	14.2996i	−1.32099	+	1.46711i
$96$	0.669131	+	0.743145i	0.0682929	+	0.0758469i
$97$	12.1255	+	8.80966i	1.23115	+	0.894486i	0.996976	−	0.0777083i	$-0.0247603\pi$
$97$	12.1255	+	8.80966i	1.23115	+	0.894486i	0.234178	+	0.972194i	$0.424760\pi$
$98$	6.03978	−	3.53850i	0.610110	−	0.357443i
$99$	2.51179	+	2.16585i	0.252444	+	0.217676i
$100$	−0.830656	+	1.43874i	−0.0830656	+	0.143874i
$101$	−1.69792	+	16.1547i	−0.168950	+	1.60745i	0.501273	+	0.865289i	$0.332865\pi$
$101$	−1.69792	+	16.1547i	−0.168950	+	1.60745i	−0.670223	+	0.742160i	$0.733801\pi$
$102$	−0.497584	+	0.105765i	−0.0492682	+	0.0104723i
$103$	−7.18316	−	1.52683i	−0.707778	−	0.150443i	−0.160062	−	0.987107i	$-0.551169\pi$
$103$	−7.18316	−	1.52683i	−0.707778	−	0.150443i	−0.547716	+	0.836664i	$0.684503\pi$
$104$	3.71598	−	2.69982i	0.364382	−	0.264739i
$105$	−6.36719	+	2.46741i	−0.621374	+	0.240794i
$106$	1.59719	+	4.91564i	0.155133	+	0.477449i
$107$	10.8194	+	12.0161i	1.04595	+	1.16164i	0.986559	+	0.163408i	$0.0522488\pi$
$107$	10.8194	+	12.0161i	1.04595	+	1.16164i	0.0593896	+	0.998235i	$0.481085\pi$
$108$	0.104528	−	0.994522i	0.0100583	−	0.0956979i
$109$	−0.799681	−	1.38509i	−0.0765955	−	0.132667i	0.825183	−	0.564865i	$-0.191072\pi$
$109$	−0.799681	−	1.38509i	−0.0765955	−	0.132667i	−0.901779	+	0.432197i	$0.857738\pi$
$110$	−4.88170	+	7.03160i	−0.465452	+	0.670437i
$111$	9.40754			0.892925
$112$	−2.61185	+	0.422198i	−0.246796	+	0.0398940i
$113$	−1.65303	+	5.08749i	−0.155504	+	0.478591i	−0.998212	−	0.0597800i	$-0.980960\pi$
$113$	−1.65303	+	5.08749i	−0.155504	+	0.478591i	0.842708	+	0.538371i	$0.180960\pi$
$114$	7.29250	+	1.55007i	0.683005	+	0.145177i
$115$	12.4376	+	5.53760i	1.15982	+	0.516383i
$116$	−4.18726	−	1.86429i	−0.388777	−	0.173095i
$117$	−4.49283	−	0.954981i	−0.415362	−	0.0882880i
$118$	1.62980	−	5.01601i	0.150035	−	0.461761i
$119$	0.478326	−	1.25803i	0.0438480	−	0.115323i
$120$	2.58095			0.235608
$121$	−7.00290	+	8.48289i	−0.636627	+	0.771172i
$122$	5.37232	+	9.30514i	0.486387	+	0.842447i
$123$	0.0910407	−	0.866194i	0.00820886	−	0.0781021i
$124$	−2.09161	−	2.32297i	−0.187832	−	0.208609i
$125$	−2.66280	−	8.19525i	−0.238168	−	0.733005i
$126$	2.06142	+	1.65848i	0.183646	+	0.147749i
$127$	−15.0027	+	10.9001i	−1.33128	+	0.967229i	−0.331560	+	0.943434i	$0.607575\pi$
$127$	−15.0027	+	10.9001i	−1.33128	+	0.967229i	−0.999717	+	0.0237948i	$0.992425\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	9.33189	−	1.98355i	0.821627	−	0.174642i
$130$	1.23917	−	11.7899i	0.108682	−	1.03404i
$131$	−0.739255	+	1.28043i	−0.0645890	+	0.111871i	−0.896512	−	0.443020i	$-0.853907\pi$
$131$	−0.739255	+	1.28043i	−0.0645890	+	0.111871i	0.831923	+	0.554892i	$0.187240\pi$
$132$	3.30514	+	0.275819i	0.287675	+	0.0240070i
$133$	−13.9034	+	13.9921i	−1.20557	+	1.21327i
$134$	−3.27858	−	2.38203i	−0.283226	−	0.205776i
$135$	−1.72699	−	1.91802i	−0.148636	−	0.165077i
$136$	−0.340387	+	0.378038i	−0.0291879	+	0.0324165i
$137$	−9.15427	−	4.07574i	−0.782102	−	0.348214i	−0.0234625	−	0.999725i	$-0.507469\pi$
$137$	−9.15427	−	4.07574i	−0.782102	−	0.348214i	−0.758640	+	0.651510i	$0.774136\pi$
$138$	−0.551395	−	5.24617i	−0.0469378	−	0.446584i
$139$	2.61043	+	8.03409i	0.221414	+	0.681443i	0.998636	+	0.0522159i	$0.0166284\pi$
$139$	2.61043	+	8.03409i	0.221414	+	0.681443i	−0.777222	+	0.629227i	$0.783372\pi$
$140$	−3.70086	+	5.73871i	−0.312780	+	0.485010i
$141$	3.79313	+	2.75587i	0.319439	+	0.232086i
$142$	−5.98417	+	10.3649i	−0.502180	+	0.869801i
$143$	2.84682	−	14.9656i	0.238063	−	1.25148i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−10.8071	+	4.81164i	−0.897482	+	0.399585i
$146$	2.70548	−	8.32660i	0.223907	−	0.689114i
$147$	−6.64350	+	2.20544i	−0.547946	+	0.181901i
$148$	7.61086	−	5.52962i	0.625609	−	0.454532i
$149$	−0.919512	−	8.74857i	−0.0753294	−	0.716711i	−0.965380	−	0.260849i	$-0.915998\pi$
$149$	−0.919512	−	8.74857i	−0.0753294	−	0.716711i	0.890050	−	0.455862i	$-0.150669\pi$
$150$	1.11164	−	1.23460i	0.0907646	−	0.100804i
$151$	17.1103	−	3.63691i	1.39242	−	0.295968i	0.550168	−	0.835054i	$-0.314564\pi$
$151$	17.1103	−	3.63691i	1.39242	−	0.295968i	0.842250	+	0.539086i	$0.181230\pi$
$152$	6.81086	−	3.03239i	0.552434	−	0.245959i
$153$	0.508700			0.0411260
$154$	−5.35256	+	6.95343i	−0.431321	+	0.560323i
$155$	−8.06771			−0.648014
$156$	−4.19610	+	1.86822i	−0.335957	+	0.149578i
$157$	−6.83258	+	1.45231i	−0.545299	+	0.115907i	−0.472321	−	0.881427i	$-0.656584\pi$
$157$	−6.83258	+	1.45231i	−0.545299	+	0.115907i	−0.0729784	+	0.997334i	$0.523250\pi$
$158$	−5.50160	+	6.11015i	−0.437684	+	0.486097i
$159$	−0.540266	−	5.14029i	−0.0428459	−	0.407652i
$160$	2.08803	−	1.51705i	0.165074	−	0.119933i
$161$	12.4554	+	6.29653i	0.981626	+	0.496236i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	17.7844	−	7.91813i	1.39298	−	0.620196i	0.433292	−	0.901254i	$-0.357352\pi$
$163$	17.7844	−	7.91813i	1.39298	−	0.620196i	0.959691	+	0.281058i	$0.0906852\pi$
$164$	−0.435483	−	0.754278i	−0.0340055	−	0.0588992i
$165$	6.23698	−	5.86298i	0.485548	−	0.456433i
$166$	−2.74520	+	4.75482i	−0.213069	+	0.369046i
$167$	12.8184	+	9.31311i	0.991918	+	0.720670i	0.960340	−	0.278831i	$-0.0899469\pi$
$167$	12.8184	+	9.31311i	0.991918	+	0.720670i	0.0315775	+	0.999501i	$0.489947\pi$
$168$	2.64255	+	0.130061i	0.203877	+	0.0100345i
$169$	2.50227	+	7.70120i	0.192482	+	0.592400i
$170$	0.137239	+	1.30574i	0.0105257	+	0.100146i
$171$	−6.81086	−	3.03239i	−0.520840	−	0.231893i
$172$	6.38375	−	7.08987i	0.486757	−	0.540598i
$173$	3.39427	+	3.76972i	0.258062	+	0.286607i	0.858228	−	0.513269i	$-0.171566\pi$
$173$	3.39427	+	3.76972i	0.258062	+	0.286607i	−0.600166	+	0.799875i	$0.704899\pi$
$174$	3.70815	+	2.69413i	0.281114	+	0.204241i
$175$	1.15112	+	4.24201i	0.0870165	+	0.320666i
$176$	2.83603	−	1.71957i	0.213774	−	0.129617i
$177$	−2.63707	+	4.56754i	−0.198214	+	0.343317i
$178$	−0.512192	+	4.87318i	−0.0383904	+	0.365260i
$179$	1.61643	−	0.343582i	0.120817	−	0.0256805i	−0.147106	−	0.989121i	$-0.546996\pi$
$179$	1.61643	−	0.343582i	0.120817	−	0.0256805i	0.267924	+	0.963440i	$0.413663\pi$
$180$	−2.52455	−	0.536610i	−0.188169	−	0.0399966i
$181$	5.26806	−	3.82747i	0.391572	−	0.284493i	−0.374528	−	0.927216i	$-0.622195\pi$
$181$	5.26806	−	3.82747i	0.391572	−	0.284493i	0.766099	+	0.642722i	$0.222195\pi$
$182$	1.86287	−	12.0088i	0.138085	−	0.890155i
$183$	−3.32028	−	10.2188i	−0.245442	−	0.755393i
$184$	−3.52971	−	3.92014i	−0.260214	−	0.288996i
$185$	2.53799	−	24.1474i	0.186597	−	1.77535i
$186$	1.56293	+	2.70708i	0.114600	+	0.198493i
$187$	0.0362056	+	1.68678i	0.00264761	+	0.123350i
$188$	4.68857			0.341949
$189$	−1.67156	−	2.05083i	−0.121588	−	0.149176i
$190$	5.94613	−	18.3003i	0.431377	−	1.32764i
$191$	10.8712	+	2.31074i	0.786610	+	0.167199i	0.583669	−	0.811992i	$-0.301617\pi$
$191$	10.8712	+	2.31074i	0.786610	+	0.167199i	0.202941	+	0.979191i	$0.434950\pi$
$192$	−0.913545	−	0.406737i	−0.0659295	−	0.0293537i
$193$	−15.9179	−	7.08711i	−1.14580	−	0.510141i	−0.256080	−	0.966656i	$-0.582431\pi$
$193$	−15.9179	−	7.08711i	−1.14580	−	0.510141i	−0.889716	+	0.456514i	$0.849098\pi$
$194$	−14.6604	−	3.11616i	−1.05255	−	0.223727i
$195$	−3.66335	+	11.2746i	−0.262338	+	0.807392i
$196$	−4.07838	+	5.68918i	−0.291313	+	0.406370i
$197$	−12.0569			−0.859016			−0.429508	−	0.903063i	$-0.641313\pi$
$197$	−12.0569			−0.859016			−0.429508	+	0.903063i	$0.641313\pi$
$198$	−3.17556	−	0.956968i	−0.225678	−	0.0680088i
$199$	5.05611	+	8.75744i	0.358418	+	0.620798i	0.987697	−	0.156381i	$-0.0499829\pi$
$199$	5.05611	+	8.75744i	0.358418	+	0.620798i	−0.629279	+	0.777180i	$0.716650\pi$
$200$	0.173654	−	1.65221i	0.0122792	−	0.116829i
$201$	2.71169	+	3.01163i	0.191268	+	0.212424i
$202$	−5.01956	−	15.4486i	−0.353175	−	1.08696i
$203$	−11.3075	+	4.38188i	−0.793632	+	0.307547i
$204$	0.411547	−	0.299007i	0.0288141	−	0.0209346i
$205$	−2.19880	−	0.467369i	−0.153571	−	0.0326424i
$206$	7.18316	−	1.52683i	0.500475	−	0.106379i
$207$	−0.551395	+	5.24617i	−0.0383246	+	0.364634i
$208$	−2.29660	+	3.97783i	−0.159241	+	0.275813i
$209$	9.57024	−	22.7997i	0.661987	−	1.57709i
$210$	4.81313	−	4.84386i	0.332138	−	0.334258i
$211$	1.03651	+	0.753066i	0.0713561	+	0.0518432i	0.622891	−	0.782308i	$-0.285958\pi$
$211$	1.03651	+	0.753066i	0.0713561	+	0.0518432i	−0.551535	+	0.834152i	$0.685958\pi$
$212$	−3.45847	−	3.84102i	−0.237529	−	0.263803i
$213$	8.00838	−	8.89420i	0.548725	−	0.609421i
$214$	−14.7714	−	6.57665i	−1.00975	−	0.449570i
$215$	−2.57383	−	24.4883i	−0.175534	−	1.67009i
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	−8.26026	−	0.406554i	−0.560743	−	0.0275987i
$218$	1.29391	+	0.940081i	0.0876347	+	0.0636703i
$219$	−4.37755	+	7.58215i	−0.295808	+	0.512354i
$220$	1.59965	−	8.40926i	0.107848	−	0.566952i
$221$	−1.16828	−	2.02352i	−0.0785872	−	0.136117i
$222$	−8.59422	+	3.82639i	−0.576806	+	0.256811i
$223$	3.33097	−	10.2517i	0.223058	−	0.686502i	−0.775425	−	0.631440i	$-0.782464\pi$
$223$	3.33097	−	10.2517i	0.223058	−	0.686502i	0.998483	−	0.0550623i	$-0.0175357\pi$
$224$	2.21432	−	1.44803i	0.147950	−	0.0967507i
$225$	−1.34403	+	0.976495i	−0.0896020	+	0.0650997i
$226$	−0.559155	−	5.32000i	−0.0371944	−	0.353881i
$227$	−0.144137	+	0.160080i	−0.00956670	+	0.0106249i	−0.747909	−	0.663801i	$-0.768942\pi$
$227$	−0.144137	+	0.160080i	−0.00956670	+	0.0106249i	0.738342	+	0.674426i	$0.235609\pi$
$228$	−7.29250	+	1.55007i	−0.482957	+	0.102656i
$229$	24.4229	−	10.8738i	1.61391	−	0.718559i	0.616291	−	0.787518i	$-0.288634\pi$
$229$	24.4229	−	10.8738i	1.61391	−	0.718559i	0.997620	+	0.0689588i	$0.0219677\pi$
$230$	−13.6147			−0.897726
$231$	6.68129	−	5.68862i	0.439597	−	0.374284i
$232$	4.58352			0.300923
$233$	−17.4631	+	7.77507i	−1.14405	+	0.509362i	−0.889154	−	0.457608i	$-0.848706\pi$
$233$	−17.4631	+	7.77507i	−1.14405	+	0.509362i	−0.254892	+	0.966970i	$0.582040\pi$
$234$	4.49283	−	0.954981i	0.293706	−	0.0624290i
$235$	8.09712	−	8.99277i	0.528198	−	0.586624i
$236$	0.551298	+	5.24525i	0.0358864	+	0.341437i
$237$	6.65175	−	4.83278i	0.432077	−	0.313923i
$238$	0.0747144	+	1.34382i	0.00484301	+	0.0871069i
$239$	5.96697	−	18.3645i	0.385971	−	1.18790i	−0.549802	−	0.835295i	$-0.685297\pi$
$239$	5.96697	−	18.3645i	0.385971	−	1.18790i	0.935773	−	0.352603i	$-0.114703\pi$
$240$	−2.35782	+	1.04977i	−0.152196	+	0.0677622i
$241$	3.38348	+	5.86035i	0.217949	+	0.377499i	0.954181	−	0.299231i	$-0.0967301\pi$
$241$	3.38348	+	5.86035i	0.217949	+	0.377499i	−0.736232	+	0.676729i	$0.763397\pi$
$242$	2.94716	−	10.5978i	0.189451	−	0.681255i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−8.69260	−	6.31554i	−0.556487	−	0.404311i
$245$	3.86864	+	17.6476i	0.247158	+	1.12746i
$246$	0.269143	+	0.828337i	0.0171599	+	0.0528128i
$247$	3.57950	+	34.0566i	0.227758	+	2.16697i
$248$	2.85562	+	1.27140i	0.181332	+	0.0807342i
$249$	3.67379	−	4.08016i	0.232817	−	0.258570i
$250$	5.76589	+	6.40367i	0.364667	+	0.405004i
$251$	−21.4165	−	15.5600i	−1.35180	−	0.982140i	−0.998920	−	0.0464710i	$-0.985202\pi$
$251$	−21.4165	−	15.5600i	−1.35180	−	0.982140i	−0.352880	−	0.935669i	$-0.614798\pi$
$252$	−2.55777	−	0.676637i	−0.161124	−	0.0426241i
$253$	−17.4348	−	1.45496i	−1.09612	−	0.0914728i
$254$	9.27219	−	16.0599i	0.581789	−	1.00769i
$255$	0.137239	−	1.30574i	0.00859422	−	0.0817685i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	13.1259	+	2.78999i	0.818770	+	0.174035i	0.598211	−	0.801339i	$-0.295879\pi$
$257$	13.1259	+	2.78999i	0.818770	+	0.174035i	0.220559	+	0.975374i	$0.429212\pi$
$258$	−7.71832	+	5.60769i	−0.480522	+	0.349119i
$259$	3.81543	−	24.5958i	0.237079	−	1.52831i
$260$	3.66335	+	11.2746i	0.227191	+	0.699222i
$261$	−3.06698	−	3.40622i	−0.189841	−	0.210840i
$262$	0.154546	−	1.47041i	0.00954791	−	0.0908423i
$263$	13.8015	+	23.9049i	0.851036	+	1.47404i	0.880274	+	0.474465i	$0.157359\pi$
$263$	13.8015	+	23.9049i	0.851036	+	1.47404i	−0.0292379	+	0.999572i	$0.509308\pi$
$264$	−3.13158	+	1.09235i	−0.192735	+	0.0672293i
$265$	−13.3399			−0.819465
$266$	7.01025	−	18.4374i	0.429826	−	1.13047i
$267$	1.51419	−	4.66020i	0.0926670	−	0.285200i
$268$	3.96399	+	0.842573i	0.242139	+	0.0514683i
$269$	−14.3943	−	6.40876i	−0.877637	−	0.390749i	−0.0820783	−	0.996626i	$-0.526156\pi$
$269$	−14.3943	−	6.40876i	−0.877637	−	0.390749i	−0.795558	+	0.605877i	$0.792822\pi$
$270$	2.35782	+	1.04977i	0.143492	+	0.0638868i
$271$	13.7288	+	2.91814i	0.833963	+	0.177264i	0.605055	−	0.796184i	$-0.293151\pi$
$271$	13.7288	+	2.91814i	0.833963	+	0.177264i	0.228908	+	0.973448i	$0.426484\pi$
$272$	0.157197	−	0.483803i	0.00953147	−	0.0293349i
$273$	−4.31894	+	11.3591i	−0.261394	+	0.687485i
$274$	10.0206			0.605366
$275$	−3.33358	−	4.38712i	−0.201022	−	0.264553i
$276$	2.63753	+	4.56834i	0.158761	+	0.274982i
$277$	−0.929611	+	8.84466i	−0.0558549	+	0.531424i	0.930441	+	0.366441i	$0.119424\pi$
$277$	−0.929611	+	8.84466i	−0.0558549	+	0.531424i	−0.986296	+	0.164983i	$0.947243\pi$
$278$	−5.65251	−	6.27775i	−0.339015	−	0.376514i
$279$	−0.965945	−	2.97287i	−0.0578296	−	0.177981i
$280$	1.04676	−	6.74785i	0.0625558	−	0.403261i
$281$	−14.0048	+	10.1751i	−0.835457	+	0.606995i	−0.921098	−	0.389331i	$-0.872706\pi$
$281$	−14.0048	+	10.1751i	−0.835457	+	0.606995i	0.0856411	+	0.996326i	$0.472706\pi$
$282$	−4.58611	−	0.974808i	−0.273099	−	0.0580490i
$283$	29.2815	−	6.22397i	1.74060	−	0.369976i	0.775398	−	0.631473i	$-0.217549\pi$
$283$	29.2815	−	6.22397i	1.74060	−	0.369976i	0.965204	+	0.261497i	$0.0842161\pi$
$284$	1.25103	−	11.9028i	0.0742351	−	0.706299i
$285$	−9.62103	+	16.6641i	−0.569901	+	0.987097i
$286$	3.48635	+	14.8296i	0.206152	+	0.876895i
$287$	−2.22772	−	0.589327i	−0.131498	−	0.0347869i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	−11.2021	−	12.4412i	−0.658945	−	0.731833i
$290$	7.91572	−	8.79130i	0.464827	−	0.516243i
$291$	13.6921	+	6.09612i	0.802646	+	0.357361i
$292$	0.915158	+	8.70715i	0.0535556	+	0.509547i
$293$	−5.75889	−	17.7240i	−0.336438	−	1.03545i	−0.966009	−	0.258507i	$-0.916769\pi$
$293$	−5.75889	−	17.7240i	−0.336438	−	1.03545i	0.629571	−	0.776943i	$-0.283231\pi$
$294$	5.17211	−	4.71692i	0.301643	−	0.275096i
$295$	11.0126	+	8.00111i	0.641178	+	0.465843i
$296$	−4.70377	+	8.14717i	−0.273401	+	0.473545i
$297$	2.90721	+	1.59629i	0.168693	+	0.0926263i
$298$	4.39838	+	7.61822i	0.254791	+	0.441312i
$299$	22.1347	−	9.85501i	1.28008	−	0.569930i
$300$	−0.513374	+	1.58000i	−0.0296397	+	0.0912215i
$301$	−1.40122	−	25.2025i	−0.0807651	−	1.45265i
$302$	−14.1518	+	10.2819i	−0.814344	+	0.591656i
$303$	1.69792	+	16.1547i	0.0975432	+	0.928061i
$304$	−4.98865	+	5.54045i	−0.286118	+	0.317767i
$305$	−27.1254	+	5.76569i	−1.55320	+	0.330142i
$306$	−0.464721	+	0.206907i	−0.0265663	+	0.0118281i
$307$	20.6429			1.17815			0.589076	−	0.808078i	$-0.299492\pi$
$307$	20.6429			1.17815			0.589076	+	0.808078i	$0.299492\pi$
$308$	2.06159	−	8.52935i	0.117470	−	0.486005i
$309$	−7.34364			−0.417765
$310$	7.37022	−	3.28143i	0.418600	−	0.186373i
$311$	−12.4520	+	2.64675i	−0.706088	+	0.150084i	−0.546941	−	0.837171i	$-0.684208\pi$
$311$	−12.4520	+	2.64675i	−0.706088	+	0.150084i	−0.159147	+	0.987255i	$0.550874\pi$
$312$	3.07345	−	3.41342i	0.174000	−	0.193247i
$313$	0.706765	+	6.72442i	0.0399487	+	0.380087i	0.996170	+	0.0874410i	$0.0278689\pi$
$313$	0.706765	+	6.72442i	0.0399487	+	0.380087i	−0.956221	+	0.292646i	$0.905464\pi$
$314$	5.65117	−	4.10581i	0.318914	−	0.231704i
$315$	−5.71505	+	3.73730i	−0.322007	+	0.210573i
$316$	2.54074	−	7.81960i	0.142928	−	0.439887i
$317$	−18.7347	+	8.34122i	−1.05224	+	0.468490i	−0.858634	−	0.512589i	$-0.828687\pi$
$317$	−18.7347	+	8.34122i	−1.05224	+	0.468490i	−0.193611	+	0.981078i	$0.562020\pi$
$318$	2.58430	+	4.47614i	0.144921	+	0.251010i
$319$	11.0763	−	10.4121i	0.620152	−	0.582966i
$320$	−1.29048	+	2.23517i	−0.0721398	+	0.124950i
$321$	13.0812	+	9.50407i	0.730123	+	0.530466i
$322$	−13.9396	−	0.686083i	−0.776826	−	0.0382339i
$323$	−1.17197	−	3.60695i	−0.0652101	−	0.200696i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	6.97103	+	3.10370i	0.386683	+	0.172163i
$326$	−13.0263	+	14.4671i	−0.721459	+	0.801261i
$327$	−1.07018	−	1.18856i	−0.0591812	−	0.0657274i
$328$	0.704626	+	0.511941i	0.0389064	+	0.0282672i
$329$	8.74355	−	8.79937i	0.482048	−	0.485125i
$330$	−3.31307	+	7.89291i	−0.182379	+	0.434490i
$331$	−6.04337	+	10.4674i	−0.332174	+	0.575342i	−0.982938	−	0.183938i	$-0.941115\pi$
$331$	−6.04337	+	10.4674i	−0.332174	+	0.575342i	0.650764	+	0.759280i	$0.274449\pi$
$332$	0.573903	−	5.46032i	0.0314970	−	0.299674i
$333$	9.20197	−	1.95594i	0.504265	−	0.107185i
$334$	−15.4982	−	3.29424i	−0.848023	−	0.180253i
$335$	8.46186	−	6.14790i	0.462321	−	0.335896i
$336$	−2.46699	+	0.956006i	−0.134585	+	0.0521544i
$337$	−3.94851	−	12.1523i	−0.215089	−	0.661977i	−0.999147	−	0.0412891i	$-0.986854\pi$
$337$	−3.94851	−	12.1523i	−0.215089	−	0.661977i	0.784058	−	0.620688i	$-0.213146\pi$
$338$	−5.41830	−	6.01763i	−0.294716	−	0.327316i
$339$	−0.559155	+	5.32000i	−0.0303691	+	0.288943i
$340$	−0.656466	−	1.13703i	−0.0356018	−	0.0616642i
$341$	9.78889	−	3.41453i	0.530098	−	0.184907i
$342$	7.45541			0.403143
$343$	3.07166	+	18.2638i	0.165854	+	0.986150i
$344$	−2.94814	+	9.07343i	−0.158953	+	0.489206i
$345$	13.3172	+	2.83065i	0.716973	+	0.152397i
$346$	−4.63410	−	2.06324i	−0.249131	−	0.110920i
$347$	−2.96984	−	1.32226i	−0.159429	−	0.0709825i	0.325471	−	0.945552i	$-0.394477\pi$
$347$	−2.96984	−	1.32226i	−0.159429	−	0.0709825i	−0.484900	+	0.874570i	$0.661144\pi$
$348$	−4.48336	−	0.952968i	−0.240333	−	0.0510845i
$349$	−8.06890	+	24.8335i	−0.431918	+	1.32931i	0.464294	+	0.885681i	$0.346308\pi$
$349$	−8.06890	+	24.8335i	−0.431918	+	1.32931i	−0.896212	+	0.443626i	$0.853692\pi$
$350$	−2.77698	−	3.40707i	−0.148436	−	0.182115i
$351$	−4.59320			−0.245167
$352$	−1.89143	+	2.72442i	−0.100814	+	0.145212i
$353$	4.55999	+	7.89813i	0.242704	+	0.420375i	0.961483	−	0.274863i	$-0.0886324\pi$
$353$	4.55999	+	7.89813i	0.242704	+	0.420375i	−0.718780	+	0.695238i	$0.755299\pi$
$354$	0.551298	−	5.24525i	0.0293012	−	0.278782i
$355$	−20.6692	−	22.9555i	−1.09701	−	1.21835i
$356$	−1.51419	−	4.66020i	−0.0802520	−	0.246990i
$357$	0.206314	−	1.32999i	0.0109193	−	0.0703904i
$358$	−1.33693	+	0.971338i	−0.0706591	+	0.0513368i
$359$	−14.3773	−	3.05599i	−0.758806	−	0.161289i	−0.187769	−	0.982213i	$-0.560126\pi$
$359$	−14.3773	−	3.05599i	−0.758806	−	0.161289i	−0.571037	+	0.820924i	$0.693459\pi$
$360$	2.52455	−	0.536610i	0.133056	−	0.0282818i
$361$	−3.82399	+	36.3828i	−0.201262	+	1.91488i
$362$	−3.25584	+	5.63928i	−0.171123	+	0.296394i
$363$	−5.08617	+	9.75350i	−0.266955	+	0.511926i
$364$	3.18262	+	11.7283i	0.166815	+	0.614731i
$365$	18.2810	+	13.2819i	0.956869	+	0.695206i
$366$	7.18957	+	7.98483i	0.375805	+	0.417374i
$367$	−21.4499	+	23.8226i	−1.11968	+	1.24353i	−0.152808	+	0.988256i	$0.548832\pi$
$367$	−21.4499	+	23.8226i	−1.11968	+	1.24353i	−0.966869	+	0.255271i	$0.917835\pi$
$368$	4.81901	+	2.14556i	0.251208	+	0.111845i
$369$	−0.0910407	−	0.866194i	−0.00473939	−	0.0450923i
$370$	7.50306	+	23.0921i	0.390066	+	1.20050i
$371$	−13.6583	−	0.672236i	−0.709104	−	0.0349008i
$372$	−2.52888	−	1.83734i	−0.131116	−	0.0952615i
$373$	8.00339	−	13.8623i	0.414400	−	0.717761i	−0.580966	−	0.813928i	$-0.697325\pi$
$373$	8.00339	−	13.8623i	0.414400	−	0.717761i	0.995365	+	0.0961669i	$0.0306583\pi$
$374$	−0.719151	−	1.52622i	−0.0371864	−	0.0789192i
$375$	−4.30850	−	7.46253i	−0.222490	−	0.385364i
$376$	−4.28322	+	1.90701i	−0.220890	+	0.0983466i
$377$	−6.50575	+	20.0226i	−0.335063	+	1.03122i
$378$	2.36119	+	1.19364i	0.121447	+	0.0613942i
$379$	−7.75602	+	5.63508i	−0.398400	+	0.289455i	−0.768889	−	0.639382i	$-0.779190\pi$
$379$	−7.75602	+	5.63508i	−0.398400	+	0.289455i	0.370489	+	0.928837i	$0.379190\pi$
$380$	2.01134	+	19.1367i	0.103180	+	0.981690i
$381$	−12.4086	+	13.7812i	−0.635713	+	0.706031i
$382$	−10.8712	+	2.31074i	−0.556217	+	0.118228i
$383$	21.7236	−	9.67197i	1.11002	−	0.494215i	0.231944	−	0.972729i	$-0.425491\pi$
$383$	21.7236	−	9.67197i	1.11002	−	0.494215i	0.878080	+	0.478515i	$0.158825\pi$
$384$	1.00000			0.0510310
$385$	−12.7991	−	18.6843i	−0.652304	−	0.952241i
$386$	17.4243			0.886875
$387$	8.71556	−	3.88042i	0.443037	−	0.197253i
$388$	14.6604	−	3.11616i	0.744267	−	0.158199i
$389$	18.5298	−	20.5794i	0.939496	−	1.04342i	−0.0594824	−	0.998229i	$-0.518945\pi$
$389$	18.5298	−	20.5794i	0.939496	−	1.04342i	0.998979	−	0.0451869i	$-0.0143883\pi$
$390$	−1.23917	−	11.7899i	−0.0627477	−	0.597005i
$391$	−2.17094	+	1.57728i	−0.109789	+	0.0797665i
$392$	1.41179	−	6.85616i	0.0713059	−	0.346288i
$393$	−0.456885	+	1.40615i	−0.0230468	+	0.0709307i
$394$	11.0145	−	4.90397i	0.554902	−	0.247058i
$395$	−10.6103	−	18.3776i	−0.533863	−	0.924677i
$396$	3.29026	−	0.417385i	0.165342	−	0.0209744i
$397$	6.15590	−	10.6623i	0.308956	−	0.535127i	−0.669178	−	0.743102i	$-0.733354\pi$
$397$	6.15590	−	10.6623i	0.308956	−	0.535127i	0.978134	+	0.207975i	$0.0666871\pi$
$398$	−8.18096	−	5.94381i	−0.410074	−	0.297936i
$399$	−10.6904	+	16.5770i	−0.535190	+	0.829889i
$400$	0.513374	+	1.58000i	0.0256687	+	0.0790001i
$401$	−0.372063	−	3.53994i	−0.0185799	−	0.176776i	0.981296	−	0.192503i	$-0.0616605\pi$
$401$	−0.372063	−	3.53994i	−0.0185799	−	0.176776i	−0.999876	+	0.0157266i	$0.994994\pi$
$402$	−3.70219	−	1.64832i	−0.184648	−	0.0822108i
$403$	−9.60720	+	10.6699i	−0.478569	+	0.531504i
$404$	10.8691	+	12.0714i	0.540759	+	0.600574i
$405$	−2.08803	−	1.51705i	−0.103755	−	0.0753826i
$406$	8.54766	−	8.60223i	0.424213	−	0.426921i
$407$	7.14055	+	30.3732i	0.353944	+	1.50555i
$408$	−0.254350	+	0.440547i	−0.0125922	+	0.0218104i
$409$	2.13313	−	20.2954i	0.105476	−	1.00354i	−0.805923	−	0.592020i	$-0.798331\pi$
$409$	2.13313	−	20.2954i	0.105476	−	1.00354i	0.911400	−	0.411522i	$-0.135003\pi$
$410$	2.19880	−	0.467369i	0.108591	−	0.0230817i
$411$	−9.80162	−	2.08340i	−0.483478	−	0.102767i
$412$	−5.94113	+	4.31648i	−0.292698	+	0.212658i
$413$	10.8722	+	8.74703i	0.534988	+	0.430413i
$414$	−1.63009	−	5.01689i	−0.0801143	−	0.246567i
$415$	−9.48189	−	10.5307i	−0.465447	−	0.516932i
$416$	0.480120	−	4.56804i	0.0235398	−	0.223967i
$417$	4.22377	+	7.31579i	0.206839	+	0.358256i
$418$	0.530622	+	24.7211i	0.0259536	+	1.20915i
$419$	−25.0877			−1.22562			−0.612808	−	0.790232i	$-0.709960\pi$
$419$	−25.0877			−1.22562			−0.612808	+	0.790232i	$0.709960\pi$
$420$	−2.42684	+	6.38276i	−0.118418	+	0.311447i
$421$	0.137571	−	0.423401i	0.00670482	−	0.0206353i	−0.947648	−	0.319316i	$-0.896547\pi$
$421$	0.137571	−	0.423401i	0.00670482	−	0.0206353i	0.954353	+	0.298681i	$0.0965467\pi$
$422$	−1.25320	−	0.266375i	−0.0610046	−	0.0129669i
$423$	4.28322	+	1.90701i	0.208257	+	0.0927221i
$424$	4.72176	+	2.10226i	0.229309	+	0.102095i
$425$	−0.826643	−	0.175708i	−0.0400981	−	0.00852311i
$426$	−3.69842	+	11.3826i	−0.179189	+	0.551487i
$427$	−28.0634	+	4.53637i	−1.35808	+	0.219530i
$428$	16.1693			0.781573
$429$	−0.326911	−	15.2304i	−0.0157834	−	0.735332i
$430$	12.3116	+	21.3243i	0.593719	+	1.02835i
$431$	−3.13439	+	29.8218i	−0.150978	+	1.43646i	0.612418	+	0.790534i	$0.290197\pi$
$431$	−3.13439	+	29.8218i	−0.150978	+	1.43646i	−0.763397	+	0.645930i	$0.776470\pi$
$432$	−0.669131	−	0.743145i	−0.0321936	−	0.0357546i
$433$	−2.10253	−	6.47091i	−0.101041	−	0.310972i	0.887740	−	0.460345i	$-0.152274\pi$
$433$	−2.10253	−	6.47091i	−0.101041	−	0.310972i	−0.988781	+	0.149373i	$0.952274\pi$
$434$	7.71148	−	2.98835i	0.370163	−	0.143445i
$435$	−9.57055	+	6.95341i	−0.458873	+	0.333391i
$436$	−1.56441	−	0.332526i	−0.0749217	−	0.0159251i
$437$	38.4684	−	8.17671i	1.84019	−	0.391145i
$438$	0.915158	−	8.70715i	0.0437279	−	0.416044i
$439$	−6.58209	+	11.4005i	−0.314146	+	0.544117i	−0.979256	−	0.202629i	$-0.935051\pi$
$439$	−6.58209	+	11.4005i	−0.314146	+	0.544117i	0.665110	+	0.746746i	$0.268385\pi$
$440$	1.95900	+	8.33287i	0.0933918	+	0.397254i
$441$	−6.03978	+	3.53850i	−0.287609	+	0.168500i
$442$	1.89032	+	1.37340i	0.0899134	+	0.0653259i
$443$	−16.4623	−	18.2833i	−0.782149	−	0.868665i	0.211934	−	0.977284i	$-0.432024\pi$
$443$	−16.4623	−	18.2833i	−0.782149	−	0.868665i	−0.994083	+	0.108619i	$0.965357\pi$
$444$	6.29488	−	6.99117i	0.298742	−	0.331786i
$445$	−11.5534	−	5.14389i	−0.547682	−	0.243844i
$446$	1.12674	+	10.7202i	0.0533525	+	0.507616i
$447$	−2.71835	−	8.36622i	−0.128574	−	0.395709i
$448$	−1.43391	+	2.22349i	−0.0677460	+	0.105050i
$449$	9.46220	+	6.87469i	0.446549	+	0.324437i	0.788232	−	0.615379i	$-0.210997\pi$
$449$	9.46220	+	6.87469i	0.446549	+	0.324437i	−0.341683	+	0.939815i	$0.610997\pi$
$450$	0.830656	−	1.43874i	0.0391575	−	0.0678228i
$451$	2.86570	−	0.363528i	0.134941	−	0.0171178i
$452$	2.67465	+	4.63264i	0.125805	+	0.217901i
$453$	15.9803	−	7.11487i	0.750818	−	0.334286i
$454$	0.0665651	−	0.204866i	0.00312406	−	0.00961485i
$455$	27.9915	+	14.1504i	1.31226	+	0.663381i
$456$	6.03156	−	4.38218i	0.282454	−	0.205215i
$457$	−3.89550	−	37.0632i	−0.182224	−	1.73374i	−0.578562	−	0.815638i	$-0.696386\pi$
$457$	−3.89550	−	37.0632i	−0.182224	−	1.73374i	0.396338	−	0.918105i	$-0.370281\pi$
$458$	−17.8887	+	19.8674i	−0.835883	+	0.928342i
$459$	0.497584	−	0.105765i	0.0232252	−	0.00493668i
$460$	12.4376	−	5.53760i	0.579908	−	0.258192i
$461$	−1.68668			−0.0785564			−0.0392782	−	0.999228i	$-0.512506\pi$
$461$	−1.68668			−0.0785564			−0.0392782	+	0.999228i	$0.512506\pi$
$462$	−3.78989	+	7.91434i	−0.176322	+	0.368208i
$463$	−28.2274			−1.31184			−0.655920	−	0.754831i	$-0.727719\pi$
$463$	−28.2274			−1.31184			−0.655920	+	0.754831i	$0.727719\pi$
$464$	−4.18726	+	1.86429i	−0.194389	+	0.0865474i
$465$	−7.89141	+	1.67737i	−0.365955	+	0.0777862i
$466$	12.7909	−	14.2058i	0.592528	−	0.658069i
$467$	−0.807119	−	7.67922i	−0.0373490	−	0.355352i	−0.997196	−	0.0748293i	$-0.976159\pi$
$467$	−0.807119	−	7.67922i	−0.0373490	−	0.355352i	0.959847	−	0.280523i	$-0.0905078\pi$
$468$	−3.71598	+	2.69982i	−0.171771	+	0.124799i
$469$	8.97364	−	5.86822i	0.414364	−	0.270969i
$470$	−3.73940	+	11.5087i	−0.172486	+	0.530857i
$471$	−6.38132	+	2.84115i	−0.294036	+	0.130913i
$472$	−2.63707	−	4.56754i	−0.121381	−	0.210238i
$473$	13.4872	+	28.6234i	0.620144	+	1.31611i
$474$	−4.11101	+	7.12047i	−0.188825	+	0.327054i
$475$	10.0203	+	7.28018i	0.459763	+	0.334037i
$476$	−0.614836	−	1.19725i	−0.0281809	−	0.0548759i
$477$	−1.59719	−	4.91564i	−0.0731302	−	0.225072i
$478$	2.01840	+	19.2038i	0.0923193	+	0.878359i
$479$	−15.9375	−	7.09582i	−0.728202	−	0.324216i	0.00893498	−	0.999960i	$-0.497156\pi$
$479$	−15.9375	−	7.09582i	−0.728202	−	0.324216i	−0.737136	+	0.675744i	$0.763823\pi$
$480$	1.72699	−	1.91802i	0.0788261	−	0.0875453i
$481$	−28.9136	−	32.1119i	−1.31835	−	1.46417i
$482$	−5.47458	−	3.97752i	−0.249360	−	0.181171i
$483$	13.4924	+	3.56930i	0.613925	+	0.162409i
$484$	1.61817	+	10.8803i	0.0735530	+	0.494560i
$485$	19.3415	−	33.5005i	0.878253	−	1.52118i
$486$	−0.104528	+	0.994522i	−0.00474151	+	0.0451124i
$487$	3.31006	−	0.703575i	0.149993	−	0.0318820i	−0.132303	−	0.991209i	$-0.542237\pi$
$487$	3.31006	−	0.703575i	0.149993	−	0.0318820i	0.282296	+	0.959327i	$0.408904\pi$
$488$	10.5098	+	2.23394i	0.475759	+	0.101126i
$489$	15.7495	−	11.4427i	0.712218	−	0.517456i
$490$	−10.7121	−	14.5484i	−0.483924	−	0.657228i
$491$	−3.83059	−	11.7893i	−0.172872	−	0.532045i	0.826658	−	0.562705i	$-0.190239\pi$
$491$	−3.83059	−	11.7893i	−0.172872	−	0.532045i	−0.999530	+	0.0306595i	$0.990239\pi$
$492$	−0.582789	−	0.647253i	−0.0262742	−	0.0291804i
$493$	0.243723	−	2.31887i	0.0109767	−	0.104437i
$494$	−17.1221	−	29.6564i	−0.770361	−	1.33430i
$495$	4.88170	−	7.03160i	0.219416	−	0.316047i
$496$	−3.12586			−0.140355
$497$	−20.0058	−	24.5450i	−0.897381	−	1.10099i
$498$	−1.69663	+	5.22168i	−0.0760277	+	0.233989i
$499$	40.1022	+	8.52399i	1.79522	+	0.381586i	0.980226	−	0.197879i	$-0.0634055\pi$
$499$	40.1022	+	8.52399i	1.79522	+	0.381586i	0.814997	+	0.579466i	$0.196739\pi$
$500$	−7.87201	−	3.50485i	−0.352047	−	0.156741i
$501$	14.4746	+	6.44450i	0.646677	+	0.287919i
$502$	25.8938	+	5.50390i	1.15570	+	0.245651i
$503$	10.1115	−	31.1201i	0.450851	−	1.38758i	−0.425087	−	0.905152i	$-0.639757\pi$
$503$	10.1115	−	31.1201i	0.450851	−	1.38758i	0.875938	−	0.482424i	$-0.160243\pi$
$504$	2.61185	−	0.422198i	0.116341	−	0.0188062i
$505$	41.9241			1.86560
$506$	16.5193	−	5.76220i	0.734372	−	0.256161i
$507$	4.04876	+	7.01266i	0.179812	+	0.311443i
$508$	−1.93842	+	18.4428i	−0.0860033	+	0.818267i
$509$	20.7430	+	23.0374i	0.919417	+	1.02112i	0.999704	+	0.0243447i	$0.00774991\pi$
$509$	20.7430	+	23.0374i	0.919417	+	1.02112i	−0.0802862	+	0.996772i	$0.525583\pi$
$510$	0.405718	+	1.24867i	0.0179655	+	0.0552921i
$511$	18.0480	+	14.5201i	0.798395	+	0.642333i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−7.29250	−	1.55007i	−0.321972	−	0.0684372i
$514$	−13.1259	+	2.78999i	−0.578958	+	0.123061i
$515$	−1.98119	+	18.8497i	−0.0873016	+	0.830619i
$516$	4.77018	−	8.26220i	0.209996	−	0.363723i
$517$	−6.01854	+	14.3383i	−0.264695	+	0.630597i
$518$	6.51847	+	24.0213i	0.286405	+	1.05544i
$519$	4.10387	+	2.98163i	0.180140	+	0.130879i
$520$	−7.93243	−	8.80986i	−0.347860	−	0.386338i
$521$	−28.2739	+	31.4014i	−1.23870	+	1.37572i	−0.338079	+	0.941118i	$0.609777\pi$
$521$	−28.2739	+	31.4014i	−1.23870	+	1.37572i	−0.900623	+	0.434601i	$0.856889\pi$
$522$	4.18726	+	1.86429i	0.183271	+	0.0815976i
$523$	2.83283	+	26.9525i	0.123871	+	1.17855i	0.863077	+	0.505073i	$0.168534\pi$
$523$	2.83283	+	26.9525i	0.123871	+	1.17855i	−0.739206	+	0.673479i	$0.764799\pi$
$524$	0.456885	+	1.40615i	0.0199591	+	0.0614278i
$525$	2.00793	+	3.90998i	0.0876332	+	0.170646i
$526$	−22.3313	−	16.2246i	−0.973690	−	0.707427i
$527$	0.795064	−	1.37709i	0.0346335	−	0.0599871i
$528$	2.41654	−	2.27164i	0.105166	−	0.0988603i
$529$	−2.41317	−	4.17973i	−0.104920	−	0.181727i
$530$	12.1866	−	5.42584i	0.529353	−	0.235683i
$531$	−1.62980	+	5.01601i	−0.0707273	+	0.217676i
$532$	1.09500	+	19.6948i	0.0474742	+	0.853876i
$533$	−3.23649	+	2.35145i	−0.140188	+	0.101852i
$534$	0.512192	+	4.87318i	0.0221647	+	0.210883i
$535$	27.9243	−	31.0131i	1.20727	−	1.34081i
$536$	−3.96399	+	0.842573i	−0.171218	+	0.0363936i
$537$	1.50967	−	0.672148i	0.0651471	−	0.0290053i
$538$	15.7565			0.679313
$539$	−12.1630	−	19.7752i	−0.523900	−	0.851780i
$540$	−2.58095			−0.111066
$541$	2.59000	−	1.15314i	0.111353	−	0.0495774i	−0.350304	−	0.936636i	$-0.613922\pi$
$541$	2.59000	−	1.15314i	0.111353	−	0.0495774i	0.461657	+	0.887059i	$0.347255\pi$
$542$	−13.7288	+	2.91814i	−0.589701	+	0.125345i
$543$	4.35716	−	4.83912i	0.186984	−	0.207666i
$544$	0.0531737	+	0.505914i	0.00227980	+	0.0216909i
$545$	−3.33952	+	2.42630i	−0.143049	+	0.103931i
$546$	−0.674618	−	12.1337i	−0.0288710	−	0.519276i
$547$	−3.02609	+	9.31336i	−0.129386	+	0.398210i	−0.994675	−	0.103064i	$-0.967135\pi$
$547$	−3.02609	+	9.31336i	−0.129386	+	0.398210i	0.865288	+	0.501274i	$0.167135\pi$
$548$	−9.15427	+	4.07574i	−0.391051	+	0.174107i
$549$	−5.37232	−	9.30514i	−0.229285	−	0.397134i
$550$	4.82978	+	2.65194i	0.205942	+	0.113079i
$551$	−17.0860	+	29.5939i	−0.727890	+	1.26074i
$552$	−4.26762	−	3.10061i	−0.181642	−	0.131971i
$553$	−9.93745	−	19.3509i	−0.422583	−	0.822884i
$554$	−2.74821	−	8.45811i	−0.116760	−	0.359350i
$555$	−2.53799	−	24.1474i	−0.107732	−	1.02500i
$556$	7.71722	+	3.43593i	0.327283	+	0.145716i
$557$	5.58312	−	6.20069i	0.236565	−	0.262732i	−0.613160	−	0.789959i	$-0.710102\pi$
$557$	5.58312	−	6.20069i	0.236565	−	0.262732i	0.849724	+	0.527227i	$0.176768\pi$
$558$	2.09161	+	2.32297i	0.0885450	+	0.0983392i
$559$	−35.4518	−	25.7572i	−1.49945	−	1.08942i
$560$	1.78834	+	6.59022i	0.0755710	+	0.278488i
$561$	0.386116	+	1.64239i	0.0163018	+	0.0693418i
$562$	8.65545	−	14.9917i	0.365108	−	0.632386i
$563$	−1.30204	+	12.3881i	−0.0548746	+	0.522097i	0.932212	+	0.361912i	$0.117876\pi$
$563$	−1.30204	+	12.3881i	−0.0548746	+	0.522097i	−0.987087	+	0.160185i	$0.948791\pi$
$564$	4.58611	−	0.974808i	0.193110	−	0.0410468i
$565$	13.5046	+	2.87049i	0.568143	+	0.120763i
$566$	−24.2184	+	17.5957i	−1.01798	+	0.739603i
$567$	−2.06142	−	1.65848i	−0.0865716	−	0.0696494i
$568$	3.69842	+	11.3826i	0.155182	+	0.477602i
$569$	−26.5169	−	29.4500i	−1.11165	−	1.23461i	−0.969586	−	0.244750i	$-0.921294\pi$
$569$	−26.5169	−	29.4500i	−1.11165	−	1.23461i	−0.142060	−	0.989858i	$-0.545373\pi$
$570$	2.01134	−	19.1367i	0.0842459	−	0.801546i
$571$	−20.1798	−	34.9524i	−0.844496	−	1.46271i	−0.886058	−	0.463575i	$-0.846567\pi$
$571$	−20.1798	−	34.9524i	−0.844496	−	1.46271i	0.0415614	−	0.999136i	$-0.486767\pi$
$572$	−9.21669	−	12.1295i	−0.385369	−	0.507161i
$573$	11.1140			0.464295
$574$	2.27483	−	0.367720i	0.0949495	−	0.0153483i
$575$	2.70808	−	8.33462i	0.112935	−	0.347578i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	−7.40131	−	3.29527i	−0.308120	−	0.137184i	0.246851	−	0.969053i	$-0.420604\pi$
$577$	−7.40131	−	3.29527i	−0.308120	−	0.137184i	−0.554971	+	0.831869i	$0.687271\pi$
$578$	15.2939	+	6.80927i	0.636141	+	0.283228i
$579$	−17.0436	−	3.62272i	−0.708306	−	0.150555i
$580$	−3.65563	+	11.2509i	−0.151792	+	0.467167i
$581$	−9.17752	−	11.2599i	−0.380748	−	0.467138i
$582$	−14.9879			−0.621268
$583$	16.1859	−	5.64591i	0.670351	−	0.233830i
$584$	−4.37755	−	7.58215i	−0.181144	−	0.313751i
$585$	−1.23917	+	11.7899i	−0.0512333	+	0.487452i
$586$	12.4700	+	13.8494i	0.515132	+	0.572112i
$587$	1.23645	+	3.80539i	0.0510337	+	0.157065i	0.973325	−	0.229429i	$-0.0736859\pi$
$587$	1.23645	+	3.80539i	0.0510337	+	0.157065i	−0.922292	+	0.386494i	$0.873686\pi$
$588$	−2.80641	+	6.41280i	−0.115734	+	0.264460i
$589$	−18.8538	+	13.6981i	−0.776859	+	0.564421i
$590$	−13.3148	−	2.83016i	−0.548163	−	0.116516i
$591$	−11.7934	+	2.50676i	−0.485116	+	0.103114i
$592$	0.983356	−	9.35601i	0.0404157	−	0.384530i
$593$	−14.0678	+	24.3661i	−0.577695	+	1.00060i	0.418048	+	0.908425i	$0.362714\pi$
$593$	−14.0678	+	24.3661i	−0.577695	+	1.00060i	−0.995743	+	0.0921723i	$0.970619\pi$
$594$	−3.30514	−	0.275819i	−0.135611	−	0.0113170i
$595$	−3.35817	−	0.888378i	−0.137672	−	0.0364199i
$596$	−7.11673	−	5.17061i	−0.291513	−	0.211796i
$597$	6.76639	+	7.51484i	0.276930	+	0.307562i
$598$	−16.2127	+	18.0060i	−0.662985	+	0.736320i
$599$	−37.7202	−	16.7941i	−1.54121	−	0.686189i	−0.552152	−	0.833743i	$-0.686193\pi$
$599$	−37.7202	−	16.7941i	−1.54121	−	0.686189i	−0.989054	+	0.147554i	$0.952860\pi$
$600$	−0.173654	−	1.65221i	−0.00708941	−	0.0674513i
$601$	7.31450	+	22.5117i	0.298365	+	0.918272i	0.982070	+	0.188514i	$0.0603671\pi$
$601$	7.31450	+	22.5117i	0.298365	+	0.918272i	−0.683706	+	0.729758i	$0.739633\pi$
$602$	11.5309	+	22.4537i	0.469963	+	0.915145i
$603$	3.27858	+	2.38203i	0.133514	+	0.0970037i
$604$	8.74629	−	15.1490i	0.355881	−	0.616405i
$605$	23.6633	+	15.6866i	0.962048	+	0.637750i
$606$	−8.12182	−	14.0674i	−0.329927	−	0.571450i
$607$	−27.2903	+	12.1504i	−1.10768	+	0.493171i	−0.877306	−	0.479932i	$-0.840661\pi$
$607$	−27.2903	+	12.1504i	−1.10768	+	0.493171i	−0.230373	+	0.973102i	$0.573995\pi$
$608$	2.30385	−	7.09052i	0.0934334	−	0.287559i
$609$	−10.1494	+	6.63709i	−0.411274	+	0.268948i
$610$	22.4352	−	16.3001i	0.908374	−	0.659972i
$611$	−2.25108	−	21.4176i	−0.0910688	−	0.866462i
$612$	0.340387	−	0.378038i	0.0137593	−	0.0152813i
$613$	11.8583	−	2.52055i	0.478951	−	0.101804i	0.0378913	−	0.999282i	$-0.487936\pi$
$613$	11.8583	−	2.52055i	0.478951	−	0.101804i	0.441060	+	0.897478i	$0.354603\pi$
$614$	−18.8582	+	8.39622i	−0.761056	+	0.338844i
$615$	−2.24792			−0.0906449
$616$	1.58584	+	8.63048i	0.0638954	+	0.347732i
$617$	16.1100			0.648565			0.324282	−	0.945960i	$-0.394877\pi$
$617$	16.1100			0.648565			0.324282	+	0.945960i	$0.394877\pi$
$618$	6.70875	−	2.98693i	0.269865	−	0.120152i
$619$	−0.264648	+	0.0562528i	−0.0106371	+	0.00226099i	−0.213227	−	0.977003i	$-0.568397\pi$
$619$	−0.264648	+	0.0562528i	−0.0106371	+	0.00226099i	0.202590	+	0.979264i	$0.435064\pi$
$620$	−5.39835	+	5.99547i	−0.216803	+	0.240784i
$621$	0.551395	+	5.24617i	0.0221267	+	0.210522i
$622$	10.2989	−	7.48261i	0.412949	−	0.300025i
$623$	−11.5699	−	5.84887i	−0.463538	−	0.234330i
$624$	−1.41938	+	4.36840i	−0.0568206	+	0.174876i
$625$	−27.9057	+	12.4244i	−1.11623	+	0.496977i
$626$	−3.38073	−	5.85559i	−0.135121	−	0.234037i
$627$	4.62078	−	24.2912i	0.184536	−	0.970098i
$628$	−3.49261	+	6.04938i	−0.139370	+	0.241397i
$629$	3.87165	+	2.81292i	0.154373	+	0.112158i
$630$	3.70086	−	5.73871i	0.147446	−	0.228636i
$631$	−7.60865	−	23.4170i	−0.302895	−	0.932216i	−0.980454	−	0.196748i	$-0.936962\pi$
$631$	−7.60865	−	23.4170i	−0.302895	−	0.932216i	0.677559	−	0.735469i	$-0.263038\pi$
$632$	0.859434	+	8.17697i	0.0341865	+	0.325262i
$633$	1.17043	+	0.521108i	0.0465203	+	0.0207122i
$634$	13.7223	−	15.2402i	0.544983	−	0.605264i
$635$	32.0260	+	35.5685i	1.27091	+	1.41149i
$636$	−4.18149	−	3.03803i	−0.165807	−	0.120466i
$637$	27.9465	+	15.8987i	1.10728	+	0.629930i
$638$	−5.88370	+	14.0171i	−0.232938	+	0.554940i
$639$	5.98417	−	10.3649i	0.236730	−	0.410028i
$640$	0.269783	−	2.56681i	0.0106641	−	0.101462i
$641$	36.2828	−	7.71214i	1.43308	−	0.304611i	0.575014	−	0.818144i	$-0.304997\pi$
$641$	36.2828	−	7.71214i	1.43308	−	0.304611i	0.858070	+	0.513532i	$0.171663\pi$
$642$	−15.8160	−	3.36179i	−0.624206	−	0.132679i
$643$	−1.97110	+	1.43209i	−0.0777325	+	0.0564760i	−0.625973	−	0.779845i	$-0.715298\pi$
$643$	−1.97110	+	1.43209i	−0.0777325	+	0.0564760i	0.548240	+	0.836321i	$0.315298\pi$
$644$	13.0136	−	5.04300i	0.512806	−	0.198722i
$645$	−7.60900	−	23.4181i	−0.299604	−	0.922086i
$646$	2.53773	+	2.81843i	0.0998455	+	0.110890i
$647$	−1.35929	+	12.9328i	−0.0534393	+	0.508441i	0.934761	+	0.355276i	$0.115613\pi$
$647$	−1.35929	+	12.9328i	−0.0534393	+	0.508441i	−0.988201	+	0.153165i	$0.951054\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−16.7484	−	5.04719i	−0.657431	−	0.198119i
$650$	−7.63075			−0.299303
$651$	−8.16428	+	1.31973i	−0.319983	+	0.0517245i
$652$	6.01578	−	18.5147i	0.235596	−	0.725090i
$653$	−7.19485	−	1.52931i	−0.281556	−	0.0598466i	0.0649690	−	0.997887i	$-0.479305\pi$
$653$	−7.19485	−	1.52931i	−0.281556	−	0.0598466i	−0.346525	+	0.938041i	$0.612638\pi$
$654$	1.46109	+	0.650519i	0.0571331	+	0.0254373i
$655$	3.48606	+	1.55209i	0.136212	+	0.0606453i
$656$	−0.851933	−	0.181084i	−0.0332624	−	0.00707014i
$657$	−2.70548	+	8.32660i	−0.105551	+	0.324852i
$658$	−4.40861	+	11.5949i	−0.171865	+	0.452018i
$659$	−12.4588			−0.485325			−0.242663	−	0.970111i	$-0.578021\pi$
$659$	−12.4588			−0.485325			−0.242663	+	0.970111i	$0.578021\pi$
$660$	−0.183693	−	8.55808i	−0.00715025	−	0.333123i
$661$	−7.54475	−	13.0679i	−0.293457	−	0.508282i	0.681168	−	0.732127i	$-0.261472\pi$
$661$	−7.54475	−	13.0679i	−0.293457	−	0.508282i	−0.974625	+	0.223845i	$0.928139\pi$
$662$	1.26341	−	12.0205i	0.0491038	−	0.467191i
$663$	−1.56347	−	1.73641i	−0.0607200	−	0.0674364i
$664$	1.69663	+	5.22168i	0.0658419	+	0.202640i
$665$	39.6660	+	31.9125i	1.53818	+	1.23751i
$666$	−7.61086	+	5.52962i	−0.294915	+	0.214268i
$667$	23.6500	+	5.02697i	0.915733	+	0.194645i
$668$	15.4982	−	3.29424i	0.599643	−	0.127458i
$669$	1.12674	−	10.7202i	0.0435622	−	0.414466i
$670$	−5.22972	+	9.05814i	−0.202042	+	0.349946i
$671$	30.4722	−	18.4761i	1.17637	−	0.713264i
$672$	1.86487	−	1.87677i	0.0719388	−	0.0723980i
$673$	10.1666	+	7.38648i	0.391894	+	0.284728i	0.766231	−	0.642565i	$-0.222130\pi$
$673$	10.1666	+	7.38648i	0.391894	+	0.284728i	−0.374337	+	0.927293i	$0.622130\pi$
$674$	8.54992	+	9.49565i	0.329331	+	0.365759i
$675$	−1.11164	+	1.23460i	−0.0427869	+	0.0475196i
$676$	7.39745	+	3.29356i	0.284517	+	0.126675i
$677$	2.56143	+	24.3704i	0.0984439	+	0.936631i	0.926578	+	0.376102i	$0.122736\pi$
$677$	2.56143	+	24.3704i	0.0984439	+	0.936631i	−0.828135	+	0.560529i	$0.810598\pi$
$678$	−1.65303	−	5.08749i	−0.0634841	−	0.195384i
$679$	21.4913	−	33.3254i	0.824761	−	1.27891i
$680$	1.06218	+	0.771722i	0.0407329	+	0.0295942i
$681$	−0.107705	+	0.186550i	−0.00412725	+	0.00714861i
$682$	−7.55378	+	7.10083i	−0.289249	+	0.271905i
$683$	23.1899	+	40.1662i	0.887339	+	1.53692i	0.843010	+	0.537898i	$0.180782\pi$
$683$	23.1899	+	40.1662i	0.887339	+	1.53692i	0.0443289	+	0.999017i	$0.485885\pi$
$684$	−6.81086	+	3.03239i	−0.260420	+	0.115946i
$685$	−7.99201	+	24.5969i	−0.305359	+	0.939798i
$686$	−10.2346	−	15.4354i	−0.390760	−	0.589327i
$687$	21.6284	−	15.7140i	0.825176	−	0.599525i
$688$	−0.997240	−	9.48810i	−0.0380194	−	0.361731i
$689$	−15.8855	+	17.6426i	−0.605188	+	0.672129i
$690$	−13.3172	+	2.83065i	−0.506976	+	0.107761i
$691$	17.8651	−	7.95404i	0.679619	−	0.302586i	−0.0377418	−	0.999288i	$-0.512016\pi$
$691$	17.8651	−	7.95404i	0.679619	−	0.302586i	0.717361	+	0.696701i	$0.245350\pi$
$692$	5.07266			0.192834
$693$	5.35256	−	6.95343i	0.203327	−	0.264139i
$694$	3.25089			0.123402
$695$	19.9178	−	8.86796i	0.755524	−	0.336381i
$696$	4.48336	−	0.952968i	0.169941	−	0.0361222i
$697$	0.296465	−	0.329258i	0.0112294	−	0.0124715i
$698$	−2.72940	−	25.9685i	−0.103309	−	0.982921i
$699$	−15.4650	+	11.2360i	−0.584939	+	0.424983i
$700$	3.92268	+	1.98301i	0.148263	+	0.0749507i
$701$	8.62894	−	26.5571i	0.325911	−	1.00305i	−0.645117	−	0.764083i	$-0.723192\pi$
$701$	8.62894	−	26.5571i	0.325911	−	1.00305i	0.971028	−	0.238966i	$-0.0768084\pi$
$702$	4.19610	−	1.86822i	0.158372	−	0.0705116i
$703$	−35.0686	−	60.7405i	−1.32264	−	2.29087i
$704$	0.619789	−	3.25820i	0.0233592	−	0.122798i
$705$	6.05048	−	10.4797i	0.227874	−	0.394690i
$706$	−7.37821	−	5.36059i	−0.277683	−	0.201748i
$707$	42.9247	+	2.11267i	1.61435	+	0.0794552i
$708$	1.62980	+	5.01601i	0.0612516	+	0.188513i
$709$	2.06222	+	19.6207i	0.0774482	+	0.736871i	0.962482	+	0.271344i	$0.0874682\pi$
$709$	2.06222	+	19.6207i	0.0774482	+	0.736871i	−0.885034	+	0.465526i	$0.845865\pi$
$710$	28.2191	+	12.5640i	1.05905	+	0.471517i
$711$	5.50160	−	6.11015i	0.206326	−	0.229148i
$712$	3.27876	+	3.64143i	0.122877	+	0.136468i
$713$	13.3400	+	9.69208i	0.499587	+	0.362971i
$714$	0.352477	+	1.29892i	0.0131911	+	0.0486108i
$715$	−39.1818	−	3.26979i	−1.46532	−	0.122283i
$716$	0.826270	−	1.43114i	0.0308791	−	0.0534842i
$717$	2.01840	−	19.2038i	0.0753784	−	0.717177i
$718$	14.3773	−	3.05599i	0.536557	−	0.114049i
$719$	−47.3320	−	10.0607i	−1.76519	−	0.375202i	−0.792965	−	0.609268i	$-0.791464\pi$
$719$	−47.3320	−	10.0607i	−1.76519	−	0.375202i	−0.972221	+	0.234066i	$0.924797\pi$
$720$	−2.08803	+	1.51705i	−0.0778164	+	0.0565369i
$721$	−2.97837	+	19.1998i	−0.110920	+	0.715038i
$722$	−11.3048	−	34.7927i	−0.420722	−	1.29485i
$723$	4.52798	+	5.02883i	0.168397	+	0.187024i
$724$	0.680656	−	6.47601i	0.0252964	−	0.240679i
$725$	3.80733	+	6.59450i	0.141401	+	0.244913i
$726$	0.679342	−	10.9790i	0.0252128	−	0.407469i
$727$	−31.9377			−1.18450			−0.592252	−	0.805753i	$-0.701761\pi$
$727$	−31.9377			−1.18450			−0.592252	+	0.805753i	$0.701761\pi$
$728$	−7.67781	−	9.41987i	−0.284558	−	0.349123i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−22.1027	−	4.69808i	−0.818058	−	0.173884i
$731$	4.43361	+	1.97397i	0.163983	+	0.0730099i
$732$	−9.81572	−	4.37024i	−0.362800	−	0.161529i
$733$	3.19979	+	0.680137i	0.118187	+	0.0251214i	0.266625	−	0.963800i	$-0.414091\pi$
$733$	3.19979	+	0.680137i	0.118187	+	0.0251214i	−0.148438	+	0.988922i	$0.547425\pi$
$734$	9.90598	−	30.4875i	0.365636	−	1.12531i
$735$	7.45324	+	16.4576i	0.274917	+	0.607049i
$736$	−5.27507			−0.194442
$737$	−7.66513	+	11.0409i	−0.282349	+	0.406695i
$738$	0.435483	+	0.754278i	0.0160303	+	0.0277654i
$739$	1.24254	−	11.8220i	0.0457076	−	0.434879i	−0.947607	−	0.319439i	$-0.896506\pi$
$739$	1.24254	−	11.8220i	0.0457076	−	0.434879i	0.993314	−	0.115440i	$-0.0368278\pi$
$740$	−16.2468	−	18.0439i	−0.597243	−	0.663306i
$741$	10.5821	+	32.5682i	0.388741	+	1.19642i
$742$	12.7509	−	4.94122i	0.468101	−	0.181398i
$743$	−37.6046	+	27.3213i	−1.37958	+	1.00232i	−0.382660	+	0.923889i	$0.624992\pi$
$743$	−37.6046	+	27.3213i	−1.37958	+	1.00232i	−0.996919	+	0.0784338i	$0.975008\pi$
$744$	3.05756	+	0.649904i	0.112095	+	0.0238266i
$745$	−22.2079	+	4.72043i	−0.813634	+	0.172943i
$746$	−1.67316	+	15.9191i	−0.0612589	+	0.582839i
$747$	2.74520	−	4.75482i	0.100442	−	0.173970i
$748$	1.27775	+	1.10177i	0.0467191	+	0.0402847i
$749$	30.1536	−	30.3461i	1.10179	−	1.10882i
$750$	6.97129	+	5.06494i	0.254556	+	0.184945i
$751$	−8.99197	−	9.98659i	−0.328122	−	0.364416i	0.556401	−	0.830914i	$-0.312182\pi$
$751$	−8.99197	−	9.98659i	−0.328122	−	0.364416i	−0.884522	+	0.466498i	$0.845515\pi$
$752$	3.13726	−	3.48428i	0.114404	−	0.127059i
$753$	−24.1836	−	10.7672i	−0.881301	−	0.392380i
$754$	−2.20064	−	20.9377i	−0.0801427	−	0.762507i
$755$	−13.9513	−	42.9378i	−0.507741	−	1.56267i
$756$	−2.64255	−	0.130061i	−0.0961087	−	0.00473029i
$757$	6.06972	+	4.40991i	0.220608	+	0.160281i	0.692600	−	0.721322i	$-0.256465\pi$
$757$	6.06972	+	4.40991i	0.220608	+	0.160281i	−0.471992	+	0.881603i	$0.656465\pi$
$758$	4.79348	−	8.30256i	0.174107	−	0.301562i
$759$	−17.3563	+	2.20173i	−0.629995	+	0.0799178i
$760$	−9.62103	−	16.6641i	−0.348992	−	0.604471i
$761$	−4.62280	+	2.05820i	−0.167576	+	0.0746098i	−0.488810	−	0.872390i	$-0.662569\pi$
$761$	−4.62280	+	2.05820i	−0.167576	+	0.0746098i	0.321234	+	0.947000i	$0.395902\pi$
$762$	5.73053	−	17.6368i	0.207595	−	0.638912i
$763$	−3.54149	+	2.31593i	−0.128211	+	0.0838421i
$764$	8.99144	−	6.53266i	0.325299	−	0.236344i
$765$	−0.137239	−	1.30574i	−0.00496188	−	0.0472091i
$766$	−15.9116	+	17.6716i	−0.574908	+	0.638500i
$767$	23.6958	−	5.03670i	0.855607	−	0.181865i
$768$	−0.913545	+	0.406737i	−0.0329647	+	0.0146768i
$769$	−35.6313			−1.28490			−0.642449	−	0.766329i	$-0.722081\pi$
$769$	−35.6313			−1.28490			−0.642449	+	0.766329i	$0.722081\pi$
$770$	19.2922	+	11.8631i	0.695242	+	0.427516i
$771$	13.4191			0.483278
$772$	−15.9179	+	7.08711i	−0.572898	+	0.255071i
$773$	−37.7133	+	8.01621i	−1.35645	+	0.288323i	−0.828042	−	0.560666i	$-0.810545\pi$
$773$	−37.7133	+	8.01621i	−1.35645	+	0.288323i	−0.528411	+	0.848989i	$0.677212\pi$
$774$	−6.38375	+	7.08987i	−0.229459	+	0.254840i
$775$	0.542820	+	5.16459i	0.0194987	+	0.185518i
$776$	−12.1255	+	8.80966i	−0.435279	+	0.316248i
$777$	−1.38171	−	24.8516i	−0.0495687	−	0.891548i
$778$	−8.55739	+	26.3369i	−0.306797	+	0.944225i
$779$	−5.93202	+	2.64111i	−0.212537	+	0.0946275i
$780$	5.92742	+	10.2666i	0.212236	+	0.367603i
$781$	34.7944	+	19.1050i	1.24504	+	0.683629i
$782$	1.34171	−	2.32392i	0.0479796	−	0.0831031i
$783$	−3.70815	−	2.69413i	−0.132518	−	0.0962803i
$784$	1.49892	+	6.83763i	0.0535328	+	0.244201i
$785$	5.57112	+	17.1462i	0.198842	+	0.611973i
$786$	−0.154546	−	1.47041i	−0.00551249	−	0.0524478i
$787$	31.9847	+	14.2405i	1.14013	+	0.507619i	0.887895	−	0.460047i	$-0.152167\pi$
$787$	31.9847	+	14.2405i	1.14013	+	0.507619i	0.252236	+	0.967666i	$0.418834\pi$
$788$	−8.06762	+	8.96000i	−0.287397	+	0.319187i
$789$	18.4700	+	20.5130i	0.657549	+	0.730282i
$790$	17.1678	+	12.4732i	0.610804	+	0.443775i
$791$	13.6823	+	3.61954i	0.486486	+	0.128696i
$792$	−2.83603	+	1.71957i	−0.100774	+	0.0611022i
$793$	−24.6762	+	42.7404i	−0.876277	+	1.51776i
$794$	−1.28693	+	12.2444i	−0.0456716	+	0.434536i
$795$	−13.0484	+	2.77353i	−0.462780	+	0.0983668i
$796$	9.89124	+	2.10245i	0.350586	+	0.0745193i
$797$	−16.7370	+	12.1602i	−0.592856	+	0.430735i	−0.843336	−	0.537387i	$-0.819411\pi$
$797$	−16.7370	+	12.1602i	−0.592856	+	0.430735i	0.250480	+	0.968122i	$0.419411\pi$
$798$	3.02370	−	19.4920i	0.107038	−	0.690011i
$799$	0.737029	+	2.26834i	0.0260742	+	0.0802482i
$800$	−1.11164	−	1.23460i	−0.0393022	−	0.0436496i
$801$	0.512192	−	4.87318i	0.0180974	−	0.172185i
$802$	1.77972	+	3.08257i	0.0628442	+	0.108849i
$803$	−27.8024	−	8.37836i	−0.981126	−	0.295666i
$804$	4.05255			0.142922
$805$	12.8018	−	33.6695i	0.451203	−	1.18669i
$806$	4.43678	−	13.6550i	0.156279	−	0.480977i
$807$	−15.4122	−	3.27597i	−0.542536	−	0.115320i
$808$	−14.8393	−	6.60689i	−0.522045	−	0.232429i
$809$	17.0258	+	7.58039i	0.598597	+	0.266512i	0.683587	−	0.729869i	$-0.260419\pi$
$809$	17.0258	+	7.58039i	0.598597	+	0.266512i	−0.0849899	+	0.996382i	$0.527086\pi$
$810$	2.52455	+	0.536610i	0.0887037	+	0.0188546i
$811$	0.654156	−	2.01328i	0.0229705	−	0.0706960i	−0.938914	−	0.344151i	$-0.888167\pi$
$811$	0.654156	−	2.01328i	0.0229705	−	0.0706960i	0.961885	+	0.273456i	$0.0881666\pi$
$812$	−4.30984	+	11.3352i	−0.151246	+	0.397787i
$813$	14.0355			0.492246
$814$	−18.8771	−	24.8430i	−0.661643	−	0.870747i
$815$	−25.1223	−	43.5131i	−0.879996	−	1.52420i
$816$	0.0531737	−	0.505914i	0.00186145	−	0.0177105i
$817$	−47.5935	−	52.8580i	−1.66509	−	1.84927i
$818$	6.30616	+	19.4084i	0.220490	+	0.678598i
$819$	−1.86287	+	12.0088i	−0.0650939	+	0.419623i
$820$	−1.81860	+	1.32129i	−0.0635084	+	0.0461416i
$821$	40.0431	+	8.51142i	1.39751	+	0.297050i	0.844247	−	0.535954i	$-0.180048\pi$
$821$	40.0431	+	8.51142i	1.39751	+	0.297050i	0.553266	+	0.833005i	$0.313381\pi$
$822$	9.80162	−	2.08340i	0.341871	−	0.0726669i
$823$	−1.13718	+	10.8196i	−0.0396398	+	0.377147i	0.956660	+	0.291206i	$0.0940565\pi$
$823$	−1.13718	+	10.8196i	−0.0396398	+	0.377147i	−0.996300	+	0.0859414i	$0.972610\pi$
$824$	3.67182	−	6.35978i	0.127914	−	0.221553i
$825$	−4.17287	−	3.59816i	−0.145281	−	0.125272i
$826$	−13.4900	−	3.56868i	−0.469378	−	0.124170i
$827$	−8.93989	−	6.49521i	−0.310870	−	0.225861i	0.421399	−	0.906875i	$-0.361539\pi$
$827$	−8.93989	−	6.49521i	−0.310870	−	0.225861i	−0.732270	+	0.681015i	$0.761539\pi$
$828$	3.52971	+	3.92014i	0.122666	+	0.136234i
$829$	−10.3153	+	11.4563i	−0.358264	+	0.397892i	−0.895152	−	0.445761i	$-0.852933\pi$
$829$	−10.3153	+	11.4563i	−0.358264	+	0.397892i	0.536888	+	0.843654i	$0.319600\pi$
$830$	12.9454	+	5.76364i	0.449340	+	0.200059i
$831$	0.929611	+	8.84466i	0.0322479	+	0.306818i
$832$	1.41938	+	4.36840i	0.0492081	+	0.151447i
$833$	−3.39355	−	1.07881i	−0.117580	−	0.0373785i
$834$	−6.83421	−	4.96534i	−0.236649	−	0.171936i
$835$	20.4468	−	35.4150i	0.707592	−	1.22559i
$836$	−10.5397	−	22.3680i	−0.364524	−	0.773615i
$837$	−1.56293	−	2.70708i	−0.0540228	−	0.0935703i
$838$	22.9188	−	10.2041i	0.791717	−	0.352495i
$839$	−4.39758	+	13.5344i	−0.151821	+	0.467258i	−0.997825	−	0.0659191i	$-0.979002\pi$
$839$	−4.39758	+	13.5344i	−0.151821	+	0.467258i	0.846004	+	0.533177i	$0.179002\pi$
$840$	−0.379072	−	6.81803i	−0.0130792	−	0.235244i
$841$	6.46510	−	4.69717i	0.222935	−	0.161971i
$842$	0.0465351	+	0.442752i	0.00160370	+	0.0152582i
$843$	−11.5832	+	12.8645i	−0.398948	+	0.443077i
$844$	1.25320	−	0.266375i	0.0431368	−	0.00916900i
$845$	19.0925	−	8.50051i	0.656801	−	0.292427i
$846$	−4.68857			−0.161196
$847$	23.4376	+	17.2534i	0.805324	+	0.592835i
$848$	−5.16861			−0.177491
$849$	27.3476	−	12.1759i	0.938566	−	0.417876i
$850$	0.826643	−	0.175708i	0.0283536	−	0.00602675i
$851$	−33.2059	+	36.8789i	−1.13828	+	1.26419i
$852$	−1.25103	−	11.9028i	−0.0428596	−	0.407782i
$853$	4.48302	−	3.25711i	0.153496	−	0.111521i	−0.508387	−	0.861129i	$-0.669758\pi$
$853$	4.48302	−	3.25711i	0.153496	−	0.111521i	0.661882	+	0.749608i	$0.269758\pi$
$854$	23.7921	−	15.5586i	0.814148	−	0.532404i
$855$	−5.94613	+	18.3003i	−0.203353	+	0.625857i
$856$	−14.7714	+	6.57665i	−0.504876	+	0.224785i
$857$	18.5811	+	32.1834i	0.634718	+	1.09936i	0.986575	+	0.163310i	$0.0522170\pi$
$857$	18.5811	+	32.1834i	0.634718	+	1.09936i	−0.351857	+	0.936054i	$0.614450\pi$
$858$	6.49342	+	13.7807i	0.221682	+	0.470466i
$859$	9.85311	−	17.0661i	0.336184	−	0.582288i	−0.647528	−	0.762042i	$-0.724197\pi$
$859$	9.85311	−	17.0661i	0.336184	−	0.582288i	0.983712	+	0.179754i	$0.0575303\pi$
$860$	−19.9206	−	14.4732i	−0.679287	−	0.493531i
$861$	−2.30157	−	0.113279i	−0.0784373	−	0.00386054i
$862$	−9.26620	−	28.5184i	−0.315608	−	0.971341i
$863$	2.99469	+	28.4926i	0.101941	+	0.969900i	0.919243	+	0.393691i	$0.128802\pi$
$863$	2.99469	+	28.4926i	0.101941	+	0.969900i	−0.817302	+	0.576209i	$0.804531\pi$
$864$	0.913545	+	0.406737i	0.0310794	+	0.0138375i
$865$	8.76045	−	9.72947i	0.297864	−	0.330812i
$866$	4.55271	+	5.05630i	0.154707	+	0.171820i
$867$	−13.5439	−	9.84024i	−0.459976	−	0.334192i
$868$	−5.82932	+	5.86653i	−0.197860	+	0.199123i
$869$	20.6520	+	17.8077i	0.700570	+	0.604084i
$870$	5.91493	−	10.2450i	0.200535	−	0.347337i
$871$	1.94571	−	18.5122i	0.0659280	−	0.627263i
$872$	1.56441	−	0.332526i	0.0529777	−	0.0112607i
$873$	14.6604	+	3.11616i	0.496178	+	0.105466i
$874$	−31.8169	+	23.1163i	−1.07622	+	0.781921i
$875$	−21.2581	+	8.23789i	−0.718653	+	0.278492i
$876$	2.70548	+	8.32660i	0.0914096	+	0.281330i
$877$	−25.7136	−	28.5578i	−0.868286	−	0.964330i	0.131349	−	0.991336i	$-0.458069\pi$
$877$	−25.7136	−	28.5578i	−0.868286	−	0.964330i	−0.999635	+	0.0270065i	$0.991403\pi$
$878$	1.37603	−	13.0921i	0.0464388	−	0.441836i
$879$	−9.31808	−	16.1394i	−0.314291	−	0.544368i
$880$	−5.17892	−	6.81566i	−0.174581	−	0.229756i
$881$	6.20381			0.209012			0.104506	−	0.994524i	$-0.466674\pi$
$881$	6.20381			0.209012			0.104506	+	0.994524i	$0.466674\pi$
$882$	4.07838	−	5.68918i	0.137326	−	0.191565i
$883$	4.97604	−	15.3147i	0.167457	−	0.515380i	−0.831752	−	0.555148i	$-0.812662\pi$
$883$	4.97604	−	15.3147i	0.167457	−	0.515380i	0.999209	+	0.0397676i	$0.0126617\pi$
$884$	−2.28550	−	0.485799i	−0.0768698	−	0.0163392i
$885$	12.4355	+	5.53662i	0.418013	+	0.186112i
$886$	22.4756	+	10.0068i	0.755082	+	0.336184i
$887$	30.4079	+	6.46340i	1.02100	+	0.217020i	0.687848	−	0.725855i	$-0.258555\pi$
$887$	30.4079	+	6.46340i	1.02100	+	0.217020i	0.333149	+	0.942874i	$0.391889\pi$
$888$	−2.90709	+	8.94711i	−0.0975556	+	0.300245i
$889$	30.9980	+	38.0313i	1.03964	+	1.27553i
$890$	12.6467			0.423919
$891$	3.17556	+	0.956968i	0.106385	+	0.0320596i
$892$	−5.38962	−	9.33509i	−0.180458	−	0.312562i
$893$	3.65381	−	34.7637i	0.122270	−	1.16332i
$894$	5.88618	+	6.53727i	0.196863	+	0.218639i
$895$	−1.31800	−	4.05637i	−0.0440557	−	0.135590i
$896$	0.405571	−	2.61448i	0.0135492	−	0.0873437i
$897$	19.6020	−	14.2417i	0.654493	−	0.475517i
$898$	−11.4403	−	2.43172i	−0.381769	−	0.0811475i
$899$	−14.0144	+	2.97885i	−0.467406	+	0.0993502i
$900$	−0.173654	+	1.65221i	−0.00578848	+	0.0550737i
$901$	1.31464	−	2.27702i	0.0437969	−	0.0758584i
$902$	−2.47009	+	1.49768i	−0.0822449	+	0.0498674i
$903$	−6.61050	−	24.3605i	−0.219984	−	0.810665i
$904$	−4.32768	−	3.14424i	−0.143936	−	0.104576i
$905$	−11.2456	−	12.4895i	−0.373817	−	0.415166i
$906$	−11.7048	+	12.9995i	−0.388867	+	0.431880i
$907$	1.27370	+	0.567088i	0.0422925	+	0.0188298i	0.427774	−	0.903886i	$-0.359298\pi$
$907$	1.27370	+	0.567088i	0.0422925	+	0.0188298i	−0.385481	+	0.922716i	$0.625965\pi$
$908$	0.0225164	+	0.214229i	0.000747233	+	0.00710945i
$909$	5.01956	+	15.4486i	0.166488	+	0.512399i
$910$	−31.3270	−	1.54186i	−1.03848	−	0.0511121i
$911$	26.4978	+	19.2518i	0.877911	+	0.637840i	0.932698	−	0.360658i	$-0.117448\pi$
$911$	26.4978	+	19.2518i	0.877911	+	0.637840i	−0.0547868	+	0.998498i	$0.517448\pi$
$912$	−3.72771	+	6.45658i	−0.123437	+	0.213799i
$913$	15.9617	+	8.76429i	0.528256	+	0.290056i
$914$	18.6337	+	32.2745i	0.616347	+	1.06754i
$915$	−25.3339	+	11.2794i	−0.837513	+	0.372885i
$916$	8.26132	−	25.4257i	0.272962	−	0.840090i
$917$	3.49105	+	1.76481i	0.115284	+	0.0582791i
$918$	−0.411547	+	0.299007i	−0.0135831	+	0.00986869i
$919$	2.01119	+	19.1352i	0.0663429	+	0.631210i	0.976287	+	0.216480i	$0.0694575\pi$
$919$	2.01119	+	19.1352i	0.0663429	+	0.631210i	−0.909944	+	0.414731i	$0.863876\pi$
$920$	−9.11001	+	10.1177i	−0.300348	+	0.333570i
$921$	20.1918	−	4.29190i	0.665342	−	0.141423i
$922$	1.54086	−	0.686034i	0.0507454	−	0.0225933i
$923$	−54.9730			−1.80946
$924$	0.243188	−	8.77159i	0.00800030	−	0.288564i
$925$	−15.6289			−0.513874
$926$	25.7870	−	11.4811i	0.847414	−	0.377293i
$927$	−7.18316	+	1.52683i	−0.235926	+	0.0501476i
$928$	3.06698	−	3.40622i	0.100678	−	0.111815i
$929$	−2.48168	−	23.6116i	−0.0814214	−	0.774673i	−0.956704	−	0.291062i	$-0.905992\pi$
$929$	−2.48168	−	23.6116i	−0.0814214	−	0.774673i	0.875283	−	0.483611i	$-0.160675\pi$
$930$	6.52691	−	4.74208i	0.214026	−	0.155499i
$931$	39.0046	+	34.6730i	1.27832	+	1.13636i
$932$	−5.90709	+	18.1802i	−0.193493	+	0.595511i
$933$	−11.6296	+	5.17783i	−0.380736	+	0.169515i
$934$	3.86076	+	6.68704i	0.126328	+	0.218806i
$935$	4.31988	−	0.547997i	0.141275	−	0.0179214i
$936$	2.29660	−	3.97783i	0.0750668	−	0.130019i
$937$	32.8897	+	23.8958i	1.07446	+	0.780641i	0.976709	−	0.214570i	$-0.0688351\pi$
$937$	32.8897	+	23.8958i	1.07446	+	0.780641i	0.0977512	+	0.995211i	$0.468835\pi$
$938$	−5.81100	+	9.01079i	−0.189736	+	0.294213i
$939$	2.08941	+	6.43053i	0.0681852	+	0.209852i
$940$	−1.26490	−	12.0347i	−0.0412563	−	0.392528i
$941$	36.5123	+	16.2563i	1.19027	+	0.529942i	0.903720	−	0.428124i	$-0.140825\pi$
$941$	36.5123	+	16.2563i	1.19027	+	0.529942i	0.286548	+	0.958066i	$0.407492\pi$
$942$	4.67403	−	5.19104i	0.152288	−	0.169133i
$943$	3.07425	+	3.41430i	0.100111	+	0.111185i
$944$	4.26687	+	3.10006i	0.138875	+	0.100898i
$945$	−4.81313	+	4.84386i	−0.156571	+	0.157571i
$946$	−23.9634	−	20.6630i	−0.779117	−	0.671813i
$947$	15.6774	−	27.1541i	0.509447	−	0.882388i	−0.490493	−	0.871445i	$-0.663183\pi$
$947$	15.6774	−	27.1541i	0.509447	−	0.882388i	0.999940	−	0.0109430i	$-0.00348335\pi$
$948$	0.859434	−	8.17697i	0.0279131	−	0.265576i
$949$	39.3352	−	8.36096i	1.27688	−	0.271408i
$950$	−12.1151	−	2.57515i	−0.393066	−	0.0835488i
$951$	−16.5911	+	12.0541i	−0.538002	+	0.390881i
$952$	1.04865	+	0.843667i	0.0339868	+	0.0273434i
$953$	−7.71526	−	23.7451i	−0.249922	−	0.769180i	−0.994788	−	0.101966i	$-0.967487\pi$
$953$	−7.71526	−	23.7451i	−0.249922	−	0.769180i	0.744866	−	0.667214i	$-0.232513\pi$
$954$	3.45847	+	3.84102i	0.111972	+	0.124358i
$955$	2.99838	−	28.5276i	0.0970252	−	0.923133i
$956$	−9.65477	−	16.7225i	−0.312257	−	0.540846i
$957$	8.66943	−	12.4875i	0.280243	−	0.403662i
$958$	17.4457			0.563646
$959$	−9.42226	+	24.7812i	−0.304261	+	0.800227i
$960$	−0.797558	+	2.45463i	−0.0257411	+	0.0792229i
$961$	20.7651	+	4.41375i	0.669841	+	0.142379i
$962$	39.4750	+	17.5754i	1.27272	+	0.566654i
$963$	14.7714	+	6.57665i	0.476001	+	0.211929i
$964$	6.61908	+	1.40693i	0.213186	+	0.0453141i
$965$	−13.8969	+	42.7703i	−0.447357	+	1.37682i
$966$	−13.7777	+	2.22712i	−0.443289	+	0.0716566i
$967$	4.99917			0.160762			0.0803812	−	0.996764i	$-0.474386\pi$
$967$	4.99917			0.160762			0.0803812	+	0.996764i	$0.474386\pi$
$968$	−5.90370	−	9.28151i	−0.189752	−	0.298319i
$969$	−1.89629	−	3.28446i	−0.0609175	−	0.105512i
$970$	−4.04348	+	38.4711i	−0.129828	+	1.23523i
$971$	39.2213	+	43.5596i	1.25867	+	1.39790i	0.881796	+	0.471631i	$0.156335\pi$
$971$	39.2213	+	43.5596i	1.25867	+	1.39790i	0.376875	+	0.926264i	$0.376999\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	20.8400	−	8.07590i	0.668101	−	0.258902i
$974$	−2.73772	+	1.98907i	−0.0877222	+	0.0637339i
$975$	7.46400	+	1.58652i	0.239039	+	0.0508094i
$976$	−10.5098	+	2.23394i	−0.336412	+	0.0715066i
$977$	−2.01430	+	19.1648i	−0.0644433	+	0.613137i	0.913870	+	0.406007i	$0.133079\pi$
$977$	−2.01430	+	19.1648i	−0.0644433	+	0.613137i	−0.978313	+	0.207130i	$0.933588\pi$
$978$	−9.73373	+	16.8593i	−0.311250	+	0.539102i
$979$	16.1953	+	1.35152i	0.517602	+	0.0431948i
$980$	15.7034	+	8.93359i	0.501625	+	0.285373i
$981$	−1.29391	−	0.940081i	−0.0413114	−	0.0300145i
$982$	8.29457	+	9.21205i	0.264690	+	0.293968i
$983$	4.70548	−	5.22596i	0.150081	−	0.166682i	−0.663416	−	0.748251i	$-0.730894\pi$
$983$	4.70548	−	5.22596i	0.150081	−	0.166682i	0.813498	+	0.581568i	$0.197561\pi$
$984$	0.795666	+	0.354253i	0.0253649	+	0.0112932i
$985$	3.25274	+	30.9477i	0.103641	+	0.986077i
$986$	0.720517	+	2.21752i	0.0229459	+	0.0706203i
$987$	6.72299	−	10.4250i	0.213995	−	0.331830i
$988$	27.7042	+	20.1283i	0.881387	+	0.640365i
$989$	−25.1630	+	43.5837i	−0.800138	+	1.38588i
$990$	−1.59965	+	8.40926i	−0.0508401	+	0.267264i
$991$	−8.64239	−	14.9691i	−0.274534	−	0.475508i	0.695483	−	0.718542i	$-0.255190\pi$
$991$	−8.64239	−	14.9691i	−0.274534	−	0.475508i	−0.970018	+	0.243035i	$0.921857\pi$
$992$	2.85562	−	1.27140i	0.0906660	−	0.0403671i
$993$	−3.73501	+	11.4952i	−0.118527	+	0.364789i
$994$	28.2595	+	14.2859i	0.896338	+	0.453121i
$995$	21.1147	−	15.3407i	0.669380	−	0.486333i
$996$	−0.573903	−	5.46032i	−0.0181848	−	0.173017i
$997$	4.07307	−	4.52361i	0.128996	−	0.143264i	−0.675187	−	0.737647i	$-0.735937\pi$
$997$	4.07307	−	4.52361i	0.128996	−	0.143264i	0.804182	+	0.594383i	$0.202604\pi$
$998$	−40.1022	+	8.52399i	−1.26941	+	0.269822i
$999$	8.59422	−	3.82639i	0.271909	−	0.121062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.a.37.1	yes	24
7.4	even	3	inner	462.2.y.a.235.3	yes	24
11.3	even	5	inner	462.2.y.a.289.3	yes	24
77.25	even	15	inner	462.2.y.a.25.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.a.25.1	✓	24	77.25	even	15	inner
462.2.y.a.37.1	yes	24	1.1	even	1	trivial
462.2.y.a.235.3	yes	24	7.4	even	3	inner
462.2.y.a.289.3	yes	24	11.3	even	5	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.269783 - 2.56681i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-0.146873 - 2.64167i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.269783 - 2.56681i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-0.146873 - 2.64167i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(1.29048 + 2.23517i) q^{10} +(1.41370 + 3.00024i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.71598 - 2.69982i) q^{13} +(1.20864 + 2.35355i) q^{14} +(-0.797558 - 2.45463i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(0.464721 + 0.206907i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-4.98865 - 5.54045i) q^{19} +(-2.08803 - 1.51705i) q^{20} +(-0.692898 - 2.55341i) q^{21} +(-2.51179 - 2.16585i) q^{22} +(-2.63753 + 4.56834i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-1.62501 + 0.345406i) q^{25} +(4.49283 + 0.954981i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.06142 - 1.65848i) q^{28} +(-1.41639 - 4.35919i) q^{29} +(1.72699 + 1.91802i) q^{30} +(0.326742 - 3.10874i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.00659 + 2.64075i) q^{33} -0.508700 q^{34} +(-6.74105 + 1.08967i) q^{35} +(0.309017 - 0.951057i) q^{36} +(9.20197 + 1.95594i) q^{37} +(6.81086 + 3.03239i) q^{38} +(-4.19610 - 1.86822i) q^{39} +(2.52455 + 0.536610i) q^{40} +(0.269143 - 0.828337i) q^{41} +(1.67156 + 2.05083i) q^{42} +9.54037 q^{43} +(3.17556 + 0.956968i) q^{44} +(-1.29048 - 2.23517i) q^{45} +(0.551395 - 5.24617i) q^{46} +(3.13726 + 3.48428i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-6.95686 + 0.775981i) q^{49} +(1.34403 - 0.976495i) q^{50} +(0.497584 + 0.105765i) q^{51} +(-4.49283 + 0.954981i) q^{52} +(0.540266 - 5.14029i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(7.31967 - 4.43812i) q^{55} +(2.55777 + 0.676637i) q^{56} +(-6.03156 - 4.38218i) q^{57} +(3.06698 + 3.40622i) q^{58} +(-3.52909 + 3.91945i) q^{59} +(-2.35782 - 1.04977i) q^{60} +(-1.12312 - 10.6858i) q^{61} +(0.965945 + 2.97287i) q^{62} +(-1.20864 - 2.35355i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-5.92742 + 10.2666i) q^{65} +(-2.90721 - 1.59629i) q^{66} +(2.02628 + 3.50961i) q^{67} +(0.464721 - 0.206907i) q^{68} +(-1.63009 + 5.01689i) q^{69} +(5.71505 - 3.73730i) q^{70} +(9.68258 - 7.03481i) q^{71} +(0.104528 + 0.994522i) q^{72} +(-5.85831 + 6.50631i) q^{73} +(-9.20197 + 1.95594i) q^{74} +(-1.51768 + 0.675717i) q^{75} -7.45541 q^{76} +(7.71802 - 4.17519i) q^{77} +4.59320 q^{78} +(7.51118 - 3.34419i) q^{79} +(-2.52455 + 0.536610i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.0910407 + 0.866194i) q^{82} +(4.44183 - 3.22718i) q^{83} +(-2.36119 - 1.19364i) q^{84} +(0.405718 - 1.24867i) q^{85} +(-8.71556 + 3.88042i) q^{86} +(-2.29176 - 3.96945i) q^{87} +(-3.29026 + 0.417385i) q^{88} +(2.45001 - 4.24355i) q^{89} +(2.08803 + 1.51705i) q^{90} +(-6.58625 + 10.2129i) q^{91} +(1.63009 + 5.01689i) q^{92} +(-0.326742 - 3.10874i) q^{93} +(-4.28322 - 1.90701i) q^{94} +(-12.8755 + 14.2996i) q^{95} +(0.669131 + 0.743145i) q^{96} +(12.1255 + 8.80966i) q^{97} +(6.03978 - 3.53850i) q^{98} +(2.51179 + 2.16585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Introduction

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