LMFDB - Embedded newform 43.2.e.b.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(4,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.e (of order $7$, degree $6$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			41.1
Root			$-0.623490 - 0.781831i$ of defining polynomial
Character	$\chi$	$=$	43.41
Dual form			43.2.e.b.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.240787i) q^{2} +(0.178448 + 0.0859360i) q^{3} +(-1.05496 + 1.32288i) q^{4} +(0.445042 - 1.94986i) q^{5} +0.109916 q^{6} -2.55496 q^{7} +(-0.455927 + 1.99755i) q^{8} +(-1.84601 - 2.31482i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.240787i) q^{2} +(0.178448 + 0.0859360i) q^{3} +(-1.05496 + 1.32288i) q^{4} +(0.445042 - 1.94986i) q^{5} +0.109916 q^{6} -2.55496 q^{7} +(-0.455927 + 1.99755i) q^{8} +(-1.84601 - 2.31482i) q^{9} +(-0.246980 - 1.08209i) q^{10} +(2.95593 + 3.70662i) q^{11} +(-0.301938 + 0.145406i) q^{12} +(-0.143104 + 0.626980i) q^{13} +(-1.27748 + 0.615201i) q^{14} +(0.246980 - 0.309703i) q^{15} +(-0.500000 - 2.19064i) q^{16} +(-0.246980 - 1.08209i) q^{17} +(-1.48039 - 0.712916i) q^{18} +(3.33997 - 4.18819i) q^{19} +(2.10992 + 2.64575i) q^{20} +(-0.455927 - 0.219563i) q^{21} +(2.37047 + 1.14156i) q^{22} +(3.27144 + 4.10225i) q^{23} +(-0.253020 + 0.317278i) q^{24} +(0.900969 + 0.433884i) q^{25} +(0.0794168 + 0.347948i) q^{26} +(-0.262709 - 1.15100i) q^{27} +(2.69537 - 3.37989i) q^{28} +(0.821552 - 0.395639i) q^{29} +(0.0489173 - 0.214321i) q^{30} +(-5.37047 + 2.58628i) q^{31} +(-3.33244 - 4.17874i) q^{32} +(0.208947 + 0.915458i) q^{33} +(-0.384043 - 0.481575i) q^{34} +(-1.13706 + 4.98180i) q^{35} +5.00969 q^{36} -11.3937 q^{37} +(0.661522 - 2.89832i) q^{38} +(-0.0794168 + 0.0995855i) q^{39} +(3.69202 + 1.77798i) q^{40} +(6.99396 - 3.36811i) q^{41} -0.280831 q^{42} +(-5.45593 + 3.63770i) q^{43} -8.02177 q^{44} +(-5.33513 + 2.56926i) q^{45} +(2.62349 + 1.26341i) q^{46} +(-0.623490 + 0.781831i) q^{47} +(0.0990311 - 0.433884i) q^{48} -0.472189 q^{49} +0.554958 q^{50} +(0.0489173 - 0.214321i) q^{51} +(-0.678448 - 0.850747i) q^{52} +(-1.72252 - 7.54686i) q^{53} +(-0.408502 - 0.512245i) q^{54} +(8.54288 - 4.11403i) q^{55} +(1.16487 - 5.10365i) q^{56} +(0.955927 - 0.460350i) q^{57} +(0.315511 - 0.395639i) q^{58} +(1.85474 + 8.12615i) q^{59} +(0.149145 + 0.653447i) q^{60} +(7.11745 + 3.42758i) q^{61} +(-2.06249 + 2.58628i) q^{62} +(4.71648 + 5.91428i) q^{63} +(1.37651 + 0.662892i) q^{64} +(1.15883 + 0.558065i) q^{65} +(0.324904 + 0.407417i) q^{66} +(0.291053 - 0.364968i) q^{67} +(1.69202 + 0.814835i) q^{68} +(0.231250 + 1.01317i) q^{69} +(0.631023 + 2.76469i) q^{70} +(5.91185 - 7.41323i) q^{71} +(5.46562 - 2.63210i) q^{72} +(2.82155 - 12.3620i) q^{73} +(-5.69687 + 2.74347i) q^{74} +(0.123490 + 0.154851i) q^{75} +(2.01693 + 8.83673i) q^{76} +(-7.55227 - 9.47025i) q^{77} +(-0.0157295 + 0.0689153i) q^{78} -5.09783 q^{79} -4.49396 q^{80} +(-1.92447 + 8.43165i) q^{81} +(2.68598 - 3.36811i) q^{82} +(-13.4438 - 6.47421i) q^{83} +(0.771438 - 0.371505i) q^{84} -2.21983 q^{85} +(-1.85205 + 3.13257i) q^{86} +0.180604 q^{87} +(-8.75182 + 4.21466i) q^{88} +(15.3300 + 7.38256i) q^{89} +(-2.04892 + 2.56926i) q^{90} +(0.365625 - 1.60191i) q^{91} -8.87800 q^{92} -1.18060 q^{93} +(-0.123490 + 0.541044i) q^{94} +(-6.67994 - 8.37638i) q^{95} +(-0.235562 - 1.03206i) q^{96} +(10.3218 + 12.9432i) q^{97} +(-0.236094 + 0.113697i) q^{98} +(3.12349 - 13.6849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9} + 8 q^{10} + 14 q^{11} + 7 q^{12} - 9 q^{13} - 8 q^{14} - 8 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 14 q^{20} + q^{21} + q^{23} - 11 q^{24} + q^{25} - 8 q^{26} + 33 q^{27} + 28 q^{28} + 9 q^{29} - 18 q^{30} - 18 q^{31} - 21 q^{32} + 7 q^{33} + 18 q^{34} + 4 q^{35} - 14 q^{36} - 4 q^{37} - 16 q^{38} + 8 q^{39} + 12 q^{40} + 23 q^{41} - 24 q^{42} - 29 q^{43} - 42 q^{44} - 30 q^{45} + 11 q^{46} + q^{47} + 5 q^{48} + 10 q^{49} + 4 q^{50} - 18 q^{51} - 10 q^{53} + 27 q^{54} + 14 q^{55} + 9 q^{56} + 2 q^{57} - 13 q^{58} + 22 q^{59} + 28 q^{60} + 19 q^{61} + 12 q^{62} + 9 q^{63} + 13 q^{64} - 10 q^{65} + 28 q^{66} - 4 q^{67} + 17 q^{69} - 26 q^{70} + 28 q^{71} - 15 q^{72} + 21 q^{73} - 2 q^{74} - 4 q^{75} + 28 q^{76} - 49 q^{77} + 25 q^{78} + 6 q^{79} - 8 q^{80} - 58 q^{81} - 13 q^{82} - 39 q^{83} - 14 q^{84} - 16 q^{85} - 25 q^{86} - 22 q^{87} - 21 q^{88} + 11 q^{89} + 6 q^{90} + 10 q^{91} - 14 q^{92} + 16 q^{93} + 4 q^{94} + 8 q^{95} + 21 q^{96} - 19 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9 + 8 * q^10 + 14 * q^11 + 7 * q^12 - 9 * q^13 - 8 * q^14 - 8 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 14 * q^20 + q^21 + q^23 - 11 * q^24 + q^25 - 8 * q^26 + 33 * q^27 + 28 * q^28 + 9 * q^29 - 18 * q^30 - 18 * q^31 - 21 * q^32 + 7 * q^33 + 18 * q^34 + 4 * q^35 - 14 * q^36 - 4 * q^37 - 16 * q^38 + 8 * q^39 + 12 * q^40 + 23 * q^41 - 24 * q^42 - 29 * q^43 - 42 * q^44 - 30 * q^45 + 11 * q^46 + q^47 + 5 * q^48 + 10 * q^49 + 4 * q^50 - 18 * q^51 - 10 * q^53 + 27 * q^54 + 14 * q^55 + 9 * q^56 + 2 * q^57 - 13 * q^58 + 22 * q^59 + 28 * q^60 + 19 * q^61 + 12 * q^62 + 9 * q^63 + 13 * q^64 - 10 * q^65 + 28 * q^66 - 4 * q^67 + 17 * q^69 - 26 * q^70 + 28 * q^71 - 15 * q^72 + 21 * q^73 - 2 * q^74 - 4 * q^75 + 28 * q^76 - 49 * q^77 + 25 * q^78 + 6 * q^79 - 8 * q^80 - 58 * q^81 - 13 * q^82 - 39 * q^83 - 14 * q^84 - 16 * q^85 - 25 * q^86 - 22 * q^87 - 21 * q^88 + 11 * q^89 + 6 * q^90 + 10 * q^91 - 14 * q^92 + 16 * q^93 + 4 * q^94 + 8 * q^95 + 21 * q^96 - 19 * q^97 + 5 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	0.500000	−	0.240787i	0.353553	−	0.170262i	−0.248673	−	0.968587i	$-0.579995\pi$
$2$	0.500000	−	0.240787i	0.353553	−	0.170262i	0.602227	+	0.798325i	$0.294280\pi$
$3$	0.178448	+	0.0859360i	0.103027	+	0.0496152i	0.484687	−	0.874687i	$-0.338933\pi$
$3$	0.178448	+	0.0859360i	0.103027	+	0.0496152i	−0.381660	+	0.924303i	$0.624648\pi$
$4$	−1.05496	+	1.32288i	−0.527479	+	0.661438i
$5$	0.445042	−	1.94986i	0.199029	−	0.872002i	−0.772488	−	0.635030i	$-0.780988\pi$
$5$	0.445042	−	1.94986i	0.199029	−	0.872002i	0.971516	−	0.236972i	$-0.0761550\pi$
$6$	0.109916			0.0448731
$7$	−2.55496			−0.965683			−0.482842	−	0.875708i	$-0.660395\pi$
$7$	−2.55496			−0.965683			−0.482842	+	0.875708i	$0.660395\pi$
$8$	−0.455927	+	1.99755i	−0.161195	+	0.706239i
$9$	−1.84601	−	2.31482i	−0.615337	−	0.771608i
$10$	−0.246980	−	1.08209i	−0.0781018	−	0.342186i
$11$	2.95593	+	3.70662i	0.891246	+	1.11759i	0.992441	+	0.122720i	$0.0391617\pi$
$11$	2.95593	+	3.70662i	0.891246	+	1.11759i	−0.101196	+	0.994867i	$0.532267\pi$
$12$	−0.301938	+	0.145406i	−0.0871619	+	0.0419750i
$13$	−0.143104	+	0.626980i	−0.0396899	+	0.173893i	−0.990888	−	0.134688i	$-0.956997\pi$
$13$	−0.143104	+	0.626980i	−0.0396899	+	0.173893i	0.951198	+	0.308581i	$0.0998540\pi$
$14$	−1.27748	+	0.615201i	−0.341421	+	0.164420i
$15$	0.246980	−	0.309703i	0.0637699	−	0.0799649i
$16$	−0.500000	−	2.19064i	−0.125000	−	0.547661i
$17$	−0.246980	−	1.08209i	−0.0599014	−	0.262445i	0.936106	−	0.351719i	$-0.114403\pi$
$17$	−0.246980	−	1.08209i	−0.0599014	−	0.262445i	−0.996007	+	0.0892736i	$0.971545\pi$
$18$	−1.48039	−	0.712916i	−0.348930	−	0.168036i
$19$	3.33997	−	4.18819i	0.766242	−	0.960837i	−0.233693	−	0.972311i	$-0.575081\pi$
$19$	3.33997	−	4.18819i	0.766242	−	0.960837i	0.999934	+	0.0114739i	$0.00365234\pi$
$20$	2.10992	+	2.64575i	0.471792	+	0.591608i
$21$	−0.455927	−	0.219563i	−0.0994914	−	0.0479125i
$22$	2.37047	+	1.14156i	0.505386	+	0.243381i
$23$	3.27144	+	4.10225i	0.682142	+	0.855379i	0.995550	−	0.0942397i	$-0.0300420\pi$
$23$	3.27144	+	4.10225i	0.682142	+	0.855379i	−0.313408	+	0.949619i	$0.601471\pi$
$24$	−0.253020	+	0.317278i	−0.0516476	+	0.0647640i
$25$	0.900969	+	0.433884i	0.180194	+	0.0867767i
$26$	0.0794168	+	0.347948i	0.0155749	+	0.0682382i
$27$	−0.262709	−	1.15100i	−0.0505584	−	0.221511i
$28$	2.69537	−	3.37989i	0.509378	−	0.638740i
$29$	0.821552	−	0.395639i	0.152558	−	0.0734682i	−0.356047	−	0.934468i	$-0.615876\pi$
$29$	0.821552	−	0.395639i	0.152558	−	0.0734682i	0.508605	+	0.861000i	$0.330161\pi$
$30$	0.0489173	−	0.214321i	0.00893104	−	0.0391295i
$31$	−5.37047	+	2.58628i	−0.964565	+	0.464510i	−0.848769	−	0.528763i	$-0.822656\pi$
$31$	−5.37047	+	2.58628i	−0.964565	+	0.464510i	−0.115795	+	0.993273i	$0.536942\pi$
$32$	−3.33244	−	4.17874i	−0.589097	−	0.738705i
$33$	0.208947	+	0.915458i	0.0363731	+	0.159361i
$34$	−0.384043	−	0.481575i	−0.0658628	−	0.0825894i
$35$	−1.13706	+	4.98180i	−0.192199	+	0.842078i
$36$	5.00969			0.834948
$37$	−11.3937			−1.87312			−0.936559	−	0.350510i	$-0.886008\pi$
$37$	−11.3937			−1.87312			−0.936559	+	0.350510i	$0.886008\pi$
$38$	0.661522	−	2.89832i	0.107313	−	0.470169i
$39$	−0.0794168	+	0.0995855i	−0.0127169	+	0.0159464i
$40$	3.69202	+	1.77798i	0.583760	+	0.281124i
$41$	6.99396	−	3.36811i	1.09227	−	0.526011i	0.201052	−	0.979581i	$-0.435564\pi$
$41$	6.99396	−	3.36811i	1.09227	−	0.526011i	0.891221	+	0.453570i	$0.149850\pi$
$42$	−0.280831			−0.0433332
$43$	−5.45593	+	3.63770i	−0.832021	+	0.554744i
$43$	−5.45593	+	3.63770i	−0.832021	+	0.554744i
$44$	−8.02177			−1.20933
$45$	−5.33513	+	2.56926i	−0.795314	+	0.383003i
$46$	2.62349	+	1.26341i	0.386812	+	0.186279i
$47$	−0.623490	+	0.781831i	−0.0909453	+	0.114042i	−0.825222	−	0.564808i	$-0.808950\pi$
$47$	−0.623490	+	0.781831i	−0.0909453	+	0.114042i	0.734277	+	0.678850i	$0.237521\pi$
$48$	0.0990311	−	0.433884i	0.0142939	−	0.0626257i
$49$	−0.472189			−0.0674556
$50$	0.554958			0.0784829
$51$	0.0489173	−	0.214321i	0.00684980	−	0.0300109i
$52$	−0.678448	−	0.850747i	−0.0940838	−	0.117977i
$53$	−1.72252	−	7.54686i	−0.236606	−	1.03664i	−0.944032	−	0.329853i	$-0.893001\pi$
$53$	−1.72252	−	7.54686i	−0.236606	−	1.03664i	0.707426	−	0.706788i	$-0.249856\pi$
$54$	−0.408502	−	0.512245i	−0.0555900	−	0.0697077i
$55$	8.54288	−	4.11403i	1.15192	−	0.554736i
$56$	1.16487	−	5.10365i	0.155663	−	0.682004i
$57$	0.955927	−	0.460350i	0.126616	−	0.0609749i
$58$	0.315511	−	0.395639i	0.0414287	−	0.0519499i
$59$	1.85474	+	8.12615i	0.241467	+	1.05793i	0.939683	+	0.342047i	$0.111120\pi$
$59$	1.85474	+	8.12615i	0.241467	+	1.05793i	−0.698216	+	0.715887i	$0.746023\pi$
$60$	0.149145	+	0.653447i	0.0192545	+	0.0843596i
$61$	7.11745	+	3.42758i	0.911296	+	0.438857i	0.829956	−	0.557829i	$-0.188366\pi$
$61$	7.11745	+	3.42758i	0.911296	+	0.438857i	0.0813403	+	0.996686i	$0.474080\pi$
$62$	−2.06249	+	2.58628i	−0.261937	+	0.328458i
$63$	4.71648	+	5.91428i	0.594221	+	0.745129i
$64$	1.37651	+	0.662892i	0.172064	+	0.0828615i
$65$	1.15883	+	0.558065i	0.143736	+	0.0692194i
$66$	0.324904	+	0.407417i	0.0399930	+	0.0501496i
$67$	0.291053	−	0.364968i	0.0355577	−	0.0445880i	−0.763735	−	0.645530i	$-0.776636\pi$
$67$	0.291053	−	0.364968i	0.0355577	−	0.0445880i	0.799292	+	0.600942i	$0.205208\pi$
$68$	1.69202	+	0.814835i	0.205188	+	0.0988132i
$69$	0.231250	+	1.01317i	0.0278392	+	0.121972i
$70$	0.631023	+	2.76469i	0.0754216	+	0.330444i
$71$	5.91185	−	7.41323i	0.701608	−	0.879789i	−0.295535	−	0.955332i	$-0.595498\pi$
$71$	5.91185	−	7.41323i	0.701608	−	0.879789i	0.997143	+	0.0755435i	$0.0240692\pi$
$72$	5.46562	−	2.63210i	0.644129	−	0.310196i
$73$	2.82155	−	12.3620i	0.330238	−	1.44687i	−0.488432	−	0.872602i	$-0.662431\pi$
$73$	2.82155	−	12.3620i	0.330238	−	1.44687i	0.818670	−	0.574264i	$-0.194712\pi$
$74$	−5.69687	+	2.74347i	−0.662247	+	0.318921i
$75$	0.123490	+	0.154851i	0.0142594	+	0.0178807i
$76$	2.01693	+	8.83673i	0.231357	+	1.01364i
$77$	−7.55227	−	9.47025i	−0.860661	−	1.07923i
$78$	−0.0157295	+	0.0689153i	−0.00178101	+	0.00780312i
$79$	−5.09783			−0.573551			−0.286776	−	0.957998i	$-0.592583\pi$
$79$	−5.09783			−0.573551			−0.286776	+	0.957998i	$0.592583\pi$
$80$	−4.49396			−0.502440
$81$	−1.92447	+	8.43165i	−0.213830	+	0.936849i
$82$	2.68598	−	3.36811i	0.296617	−	0.371946i
$83$	−13.4438	−	6.47421i	−1.47565	−	0.710637i	−0.488821	−	0.872384i	$-0.662573\pi$
$83$	−13.4438	−	6.47421i	−1.47565	−	0.710637i	−0.986832	+	0.161746i	$0.948287\pi$
$84$	0.771438	−	0.371505i	0.0841708	−	0.0405345i
$85$	−2.21983			−0.240775
$86$	−1.85205	+	3.13257i	−0.199712	+	0.337793i
$87$	0.180604			0.0193628
$88$	−8.75182	+	4.21466i	−0.932948	+	0.449284i
$89$	15.3300	+	7.38256i	1.62498	+	0.782550i	0.999998	+	0.00191168i	$0.000608506\pi$
$89$	15.3300	+	7.38256i	1.62498	+	0.782550i	0.624983	+	0.780638i	$0.285106\pi$
$90$	−2.04892	+	2.56926i	−0.215975	+	0.270824i
$91$	0.365625	−	1.60191i	0.0383279	−	0.167926i
$92$	−8.87800			−0.925596
$93$	−1.18060			−0.122423
$94$	−0.123490	+	0.541044i	−0.0127370	+	0.0558044i
$95$	−6.67994	−	8.37638i	−0.685347	−	0.859398i
$96$	−0.235562	−	1.03206i	−0.0240419	−	0.105335i
$97$	10.3218	+	12.9432i	1.04802	+	1.31418i	0.947678	+	0.319229i	$0.103424\pi$
$97$	10.3218	+	12.9432i	1.04802	+	1.31418i	0.100347	+	0.994952i	$0.468005\pi$
$98$	−0.236094	+	0.113697i	−0.0238491	+	0.0114851i
$99$	3.12349	−	13.6849i	0.313923	−	1.37538i
$100$	−1.52446	+	0.734141i	−0.152446	+	0.0734141i
$101$	−2.36443	+	2.96490i	−0.235269	+	0.295019i	−0.885425	−	0.464783i	$-0.846132\pi$
$101$	−2.36443	+	2.96490i	−0.235269	+	0.295019i	0.650155	+	0.759801i	$0.274704\pi$
$102$	−0.0271471	−	0.118939i	−0.00268796	−	0.0117767i
$103$	1.31767	+	5.77308i	0.129834	+	0.568838i	0.997435	+	0.0715779i	$0.0228035\pi$
$103$	1.31767	+	5.77308i	0.129834	+	0.568838i	−0.867601	+	0.497260i	$0.834339\pi$
$104$	−1.18718	−	0.571714i	−0.116412	−	0.0560612i
$105$	−0.631023	+	0.791277i	−0.0615815	+	0.0772208i
$106$	−2.67845	−	3.35867i	−0.260154	−	0.326223i
$107$	−1.77144	−	0.853080i	−0.171251	−	0.0824703i	0.346294	−	0.938126i	$-0.387440\pi$
$107$	−1.77144	−	0.853080i	−0.171251	−	0.0824703i	−0.517546	+	0.855656i	$0.673154\pi$
$108$	1.79978	+	0.866729i	0.173184	+	0.0834011i
$109$	−5.18933	−	6.50722i	−0.497048	−	0.623278i	0.468513	−	0.883457i	$-0.344790\pi$
$109$	−5.18933	−	6.50722i	−0.497048	−	0.623278i	−0.965561	+	0.260178i	$0.916219\pi$
$110$	3.28083	−	4.11403i	0.312815	−	0.392258i
$111$	−2.03319	−	0.979132i	−0.192982	−	0.0929351i
$112$	1.27748	+	5.59700i	0.120710	+	0.528867i
$113$	0.407010	+	1.78323i	0.0382882	+	0.167752i	0.990457	−	0.137820i	$-0.0440095\pi$
$113$	0.407010	+	1.78323i	0.0382882	+	0.167752i	−0.952169	+	0.305572i	$0.901152\pi$
$114$	0.367117	−	0.460350i	0.0343837	−	0.0431157i
$115$	9.45473	−	4.55316i	0.881658	−	0.424584i
$116$	−0.343322	+	1.50419i	−0.0318767	+	0.139661i
$117$	1.71552	−	0.826151i	0.158600	−	0.0763777i
$118$	2.88404	+	3.61648i	0.265498	+	0.332924i
$119$	0.631023	+	2.76469i	0.0578457	+	0.253439i
$120$	0.506041	+	0.634555i	0.0461950	+	0.0579267i
$121$	−2.55376	+	11.1888i	−0.232160	+	1.01716i
$122$	4.38404			0.396913
$123$	1.53750			0.138632
$124$	2.24429	−	9.83288i	0.201543	−	0.883019i
$125$	7.48188	−	9.38198i	0.669199	−	0.839150i
$126$	3.78232	+	1.82147i	0.336956	+	0.162270i
$127$	−2.67241	+	1.28696i	−0.237138	+	0.114200i	−0.548679	−	0.836033i	$-0.684869\pi$
$127$	−2.67241	+	1.28696i	−0.237138	+	0.114200i	0.311541	+	0.950233i	$0.399155\pi$
$128$	11.5375			1.01978
$129$	−1.28621	+	0.180280i	−0.113244	+	0.0158727i
$130$	0.713792			0.0626037
$131$	6.40581	−	3.08488i	0.559678	−	0.269527i	−0.132585	−	0.991172i	$-0.542328\pi$
$131$	6.40581	−	3.08488i	0.559678	−	0.269527i	0.692264	+	0.721645i	$0.256614\pi$
$132$	−1.43147	−	0.689359i	−0.124593	−	0.0600010i
$133$	−8.53348	+	10.7006i	−0.739947	+	0.927864i
$134$	0.0576465	−	0.252566i	0.00497990	−	0.0218184i
$135$	−2.36121			−0.203220
$136$	2.27413			0.195005
$137$	−1.85205	+	8.11437i	−0.158231	+	0.693257i	0.832110	+	0.554610i	$0.187133\pi$
$137$	−1.85205	+	8.11437i	−0.158231	+	0.693257i	−0.990342	+	0.138647i	$0.955725\pi$
$138$	0.359584	+	0.450904i	0.0306098	+	0.0383835i
$139$	−1.34385	−	5.88781i	−0.113984	−	0.499398i	−0.999401	−	0.0346001i	$-0.988984\pi$
$139$	−1.34385	−	5.88781i	−0.113984	−	0.499398i	0.885417	−	0.464798i	$-0.153873\pi$
$140$	−5.39075	−	6.75978i	−0.455601	−	0.571306i
$141$	−0.178448	+	0.0859360i	−0.0150280	+	0.00723712i
$142$	1.17092	−	5.13011i	0.0982610	−	0.430510i
$143$	−2.74698	+	1.32288i	−0.229714	+	0.110624i
$144$	−4.14795	+	5.20136i	−0.345662	+	0.433447i
$145$	−0.405813	−	1.77798i	−0.0337010	−	0.147654i
$146$	−1.56584	−	6.86041i	−0.129590	−	0.567771i
$147$	−0.0842611	−	0.0405780i	−0.00694974	−	0.00334682i
$148$	12.0199	−	15.0725i	0.988031	−	1.23895i
$149$	1.38740	+	1.73974i	0.113660	+	0.142525i	0.835407	−	0.549632i	$-0.185232\pi$
$149$	1.38740	+	1.73974i	0.113660	+	0.142525i	−0.721747	+	0.692157i	$0.756661\pi$
$150$	0.0990311	+	0.0476909i	0.00808586	+	0.00389394i
$151$	−0.445042	−	0.214321i	−0.0362170	−	0.0174412i	0.415688	−	0.909507i	$-0.363541\pi$
$151$	−0.445042	−	0.214321i	−0.0362170	−	0.0174412i	−0.451905	+	0.892066i	$0.649255\pi$
$152$	6.84332	+	8.58125i	0.555067	+	0.696032i
$153$	−2.04892	+	2.56926i	−0.165645	+	0.207712i
$154$	−6.05645	−	2.91663i	−0.488043	−	0.235029i
$155$	2.65279	+	11.6226i	0.213077	+	0.933553i
$156$	−0.0479579	−	0.210117i	−0.00383970	−	0.0168228i
$157$	−4.80798	+	6.02901i	−0.383718	+	0.481168i	−0.935754	−	0.352653i	$-0.885280\pi$
$157$	−4.80798	+	6.02901i	−0.383718	+	0.481168i	0.552036	+	0.833820i	$0.313851\pi$
$158$	−2.54892	+	1.22749i	−0.202781	+	0.0976542i
$159$	0.341166	−	1.49475i	0.0270563	−	0.118541i
$160$	−9.63102	+	4.63806i	−0.761399	+	0.366671i
$161$	−8.35839	−	10.4811i	−0.658733	−	0.826025i
$162$	1.06800	+	4.67921i	0.0839099	+	0.367633i
$163$	0.608424	+	0.762940i	0.0476555	+	0.0597581i	0.805088	−	0.593155i	$-0.202118\pi$
$163$	0.608424	+	0.762940i	0.0476555	+	0.0597581i	−0.757433	+	0.652913i	$0.773547\pi$
$164$	−2.92274	+	12.8054i	−0.228228	+	0.999930i
$165$	1.87800			0.146202
$166$	−8.28083			−0.642717
$167$	1.25691	−	5.50686i	0.0972622	−	0.426134i	−0.902729	−	0.430209i	$-0.858440\pi$
$167$	1.25691	−	5.50686i	0.0972622	−	0.426134i	0.999992	+	0.00407497i	$0.00129711\pi$
$168$	0.646457	−	0.810631i	0.0498752	−	0.0625415i
$169$	11.3400	+	5.46104i	0.872305	+	0.420080i
$170$	−1.10992	+	0.534508i	−0.0851267	+	0.0409949i
$171$	−15.8605			−1.21289
$172$	0.943550	−	11.0551i	0.0719450	−	0.842946i
$173$	−8.65279			−0.657860			−0.328930	−	0.944354i	$-0.606688\pi$
$173$	−8.65279			−0.657860			−0.328930	+	0.944354i	$0.606688\pi$
$174$	0.0903019	−	0.0434871i	0.00684577	−	0.00329675i
$175$	−2.30194	−	1.10855i	−0.174010	−	0.0837989i
$176$	6.64191	−	8.32869i	0.500653	−	0.627799i
$177$	−0.367354	+	1.60948i	−0.0276120	+	0.120976i
$178$	9.44265			0.707756
$179$	−1.99462			−0.149085			−0.0745426	−	0.997218i	$-0.523750\pi$
$179$	−1.99462			−0.149085			−0.0745426	+	0.997218i	$0.523750\pi$
$180$	2.22952	−	9.76817i	0.166179	−	0.728076i
$181$	−5.52177	−	6.92408i	−0.410430	−	0.514663i	0.533054	−	0.846081i	$-0.321044\pi$
$181$	−5.52177	−	6.92408i	−0.410430	−	0.514663i	−0.943484	+	0.331418i	$0.892473\pi$
$182$	−0.202907	−	0.888992i	−0.0150404	−	0.0658965i
$183$	0.975541	+	1.22329i	0.0721141	+	0.0904282i
$184$	−9.68598	+	4.66452i	−0.714060	+	0.343873i
$185$	−5.07069	+	22.2161i	−0.372804	+	1.63336i
$186$	−0.590302	+	0.284274i	−0.0432830	+	0.0208440i
$187$	3.28083	−	4.11403i	0.239918	−	0.300848i
$188$	−0.376510	−	1.64960i	−0.0274598	−	0.120309i
$189$	0.671211	+	2.94077i	0.0488234	+	0.213909i
$190$	−5.35690	−	2.57975i	−0.388630	−	0.187154i
$191$	−4.70440	+	5.89913i	−0.340398	+	0.426846i	−0.922337	−	0.386387i	$-0.873723\pi$
$191$	−4.70440	+	5.89913i	−0.340398	+	0.426846i	0.581939	+	0.813233i	$0.302294\pi$
$192$	0.188669	+	0.236584i	0.0136160	+	0.0170739i
$193$	7.24578	+	3.48939i	0.521563	+	0.251171i	0.676093	−	0.736817i	$-0.263672\pi$
$193$	7.24578	+	3.48939i	0.521563	+	0.251171i	−0.154530	+	0.987988i	$0.549386\pi$
$194$	8.27748	+	3.98622i	0.594288	+	0.286194i
$195$	0.158834	+	0.199171i	0.0113743	+	0.0142629i
$196$	0.498140	−	0.624647i	0.0355814	−	0.0446177i
$197$	17.4710	+	8.41359i	1.24476	+	0.599443i	0.936101	−	0.351731i	$-0.114407\pi$
$197$	17.4710	+	8.41359i	1.24476	+	0.599443i	0.308655	+	0.951174i	$0.400121\pi$
$198$	−1.73341	−	7.59455i	−0.123188	−	0.539721i
$199$	−5.04288	−	22.0943i	−0.357480	−	1.56622i	−0.759448	−	0.650568i	$-0.774531\pi$
$199$	−5.04288	−	22.0943i	−0.357480	−	1.56622i	0.401968	−	0.915654i	$-0.368326\pi$
$200$	−1.27748	+	1.60191i	−0.0903314	+	0.113272i
$201$	0.0833017	−	0.0401160i	0.00587565	−	0.00282956i
$202$	−0.468304	+	2.05177i	−0.0329498	+	0.144362i
$203$	−2.09903	+	1.01084i	−0.147323	+	0.0709471i
$204$	0.231914	+	0.290811i	0.0162372	+	0.0203608i
$205$	−3.45473	−	15.1362i	−0.241289	−	1.05716i
$206$	2.04892	+	2.56926i	0.142755	+	0.179009i
$207$	3.45689	−	15.1456i	0.240270	−	1.05269i
$208$	1.44504			0.100196
$209$	25.3967			1.75673
$210$	−0.124982	+	0.547581i	−0.00862456	+	0.0377867i
$211$	−10.2823	+	12.8936i	−0.707864	+	0.887634i	−0.997583	−	0.0694779i	$-0.977867\pi$
$211$	−10.2823	+	12.8936i	−0.707864	+	0.887634i	0.289719	+	0.957112i	$0.406438\pi$
$212$	11.8007	+	5.68294i	0.810478	+	0.390306i
$213$	1.69202	−	0.814835i	0.115935	−	0.0558315i
$214$	−1.09113			−0.0745881
$215$	4.66487	+	12.2572i	0.318142	+	0.835934i
$216$	2.41896			0.164589
$217$	13.7213	−	6.60784i	0.931464	−	0.448570i
$218$	−4.16152	−	2.00408i	−0.281854	−	0.135734i
$219$	1.56584	−	1.96351i	0.105810	−	0.132681i
$220$	−3.57002	+	15.6413i	−0.240691	+	1.05454i
$221$	0.713792			0.0480148
$222$	−1.25236			−0.0840527
$223$	0.335126	−	1.46828i	0.0224417	−	0.0983234i	−0.962467	−	0.271400i	$-0.912514\pi$
$223$	0.335126	−	1.46828i	0.0224417	−	0.0983234i	0.984908	+	0.173076i	$0.0553707\pi$
$224$	8.51424	+	10.6765i	0.568881	+	0.713355i
$225$	−0.658834	−	2.88654i	−0.0439222	−	0.192436i
$226$	0.632883	+	0.793610i	0.0420987	+	0.0527902i
$227$	16.5417	−	7.96605i	1.09791	−	0.528726i	0.204909	−	0.978781i	$-0.434310\pi$
$227$	16.5417	−	7.96605i	1.09791	−	0.528726i	0.893001	+	0.450055i	$0.148596\pi$
$228$	−0.399477	+	1.75022i	−0.0264560	+	0.115911i
$229$	−5.57122	+	2.68296i	−0.368157	+	0.177295i	−0.608810	−	0.793316i	$-0.708353\pi$
$229$	−5.57122	+	2.68296i	−0.368157	+	0.177295i	0.240653	+	0.970611i	$0.422638\pi$
$230$	3.63102	−	4.55316i	0.239423	−	0.300226i
$231$	−0.533852	−	2.33896i	−0.0351249	−	0.153892i
$232$	0.415739	+	1.82147i	0.0272946	+	0.119585i
$233$	−3.98307	−	1.91815i	−0.260940	−	0.125662i	0.298840	−	0.954303i	$-0.403400\pi$
$233$	−3.98307	−	1.91815i	−0.260940	−	0.125662i	−0.559780	+	0.828641i	$0.689114\pi$
$234$	0.658834	−	0.826151i	0.0430693	−	0.0540072i
$235$	1.24698	+	1.56366i	0.0813440	+	0.102002i
$236$	−12.7066	−	6.11915i	−0.827126	−	0.398323i
$237$	−0.909698	−	0.438087i	−0.0590912	−	0.0284568i
$238$	0.981214	+	1.23040i	0.0636026	+	0.0797552i
$239$	−6.51507	+	8.16963i	−0.421425	+	0.528450i	−0.946542	−	0.322580i	$-0.895450\pi$
$239$	−6.51507	+	8.16963i	−0.421425	+	0.528450i	0.525118	+	0.851030i	$0.324021\pi$
$240$	−0.801938	−	0.386193i	−0.0517649	−	0.0249286i
$241$	−5.40731	−	23.6910i	−0.348315	−	1.52607i	−0.781005	−	0.624525i	$-0.785292\pi$
$241$	−5.40731	−	23.6910i	−0.348315	−	1.52607i	0.432689	−	0.901543i	$-0.357565\pi$
$242$	1.41723	+	6.20929i	0.0911030	+	0.399149i
$243$	−3.27628	+	4.10833i	−0.210174	+	0.263549i
$244$	−12.0429	+	5.79954i	−0.770966	+	0.371278i
$245$	−0.210144	+	0.920700i	−0.0134256	+	0.0588214i
$246$	0.768750	−	0.370210i	0.0490137	−	0.0236038i
$247$	2.14795	+	2.69344i	0.136671	+	0.171380i
$248$	−2.71768	−	11.9069i	−0.172573	−	0.756090i
$249$	−1.84266	−	2.31062i	−0.116774	−	0.146430i
$250$	1.48188	−	6.49253i	0.0937222	−	0.410624i
$251$	−21.9269			−1.38401			−0.692007	−	0.721890i	$-0.743273\pi$
$251$	−21.9269			−1.38401			−0.692007	+	0.721890i	$0.743273\pi$
$252$	−12.7995			−0.806296
$253$	−5.53534	+	24.2519i	−0.348004	+	1.52471i
$254$	−1.02632	+	1.28696i	−0.0643970	+	0.0807513i
$255$	−0.396125	−	0.190764i	−0.0248063	−	0.0119461i
$256$	3.01573	−	1.45230i	0.188483	−	0.0907687i
$257$	−2.89546			−0.180614			−0.0903069	−	0.995914i	$-0.528785\pi$
$257$	−2.89546			−0.180614			−0.0903069	+	0.995914i	$0.528785\pi$
$258$	−0.599695	+	0.399842i	−0.0373354	+	0.0248931i
$259$	29.1105			1.80884
$260$	−1.96077	+	0.944258i	−0.121602	+	0.0585604i
$261$	−2.43243	−	1.17140i	−0.150564	−	0.0725076i
$262$	2.46011	−	3.08488i	0.151986	−	0.190584i
$263$	3.86616	−	16.9387i	0.238397	−	1.04449i	−0.704054	−	0.710146i	$-0.748629\pi$
$263$	3.86616	−	16.9387i	0.238397	−	1.04449i	0.942452	−	0.334342i	$-0.108514\pi$
$264$	−1.92394			−0.118410
$265$	−15.4819			−0.951044
$266$	−1.69016	+	7.40508i	−0.103630	+	0.454035i
$267$	2.10119	+	2.63481i	0.128591	+	0.161247i
$268$	0.175760	+	0.770053i	0.0107362	+	0.0470385i
$269$	−8.77293	−	11.0009i	−0.534895	−	0.670737i	0.438802	−	0.898584i	$-0.355403\pi$
$269$	−8.77293	−	11.0009i	−0.534895	−	0.670737i	−0.973697	+	0.227847i	$0.926832\pi$
$270$	−1.18060	+	0.568549i	−0.0718493	+	0.0346008i
$271$	0.477033	−	2.09002i	0.0289777	−	0.126960i	−0.958370	−	0.285529i	$-0.907831\pi$
$271$	0.477033	−	2.09002i	0.0289777	−	0.126960i	0.987348	+	0.158569i	$0.0506880\pi$
$272$	−2.24698	+	1.08209i	−0.136243	+	0.0656112i
$273$	0.202907	−	0.254437i	0.0122805	−	0.0153992i
$274$	1.02781	+	4.50313i	0.0620923	+	0.272044i
$275$	1.05496	+	4.62207i	0.0636164	+	0.278722i
$276$	−1.58426	−	0.762940i	−0.0953613	−	0.0459236i
$277$	−14.5022	+	18.1851i	−0.871350	+	1.09264i	0.123606	+	0.992331i	$0.460554\pi$
$277$	−14.5022	+	18.1851i	−0.871350	+	1.09264i	−0.994957	+	0.100307i	$0.968017\pi$
$278$	−2.08964	−	2.62032i	−0.125328	−	0.157157i
$279$	15.9007	+	7.65739i	0.951952	+	0.458436i
$280$	−9.43296	−	4.54267i	−0.563727	−	0.271477i
$281$	−11.0571	−	13.8652i	−0.659612	−	0.827127i	0.333689	−	0.942683i	$-0.391707\pi$
$281$	−11.0571	−	13.8652i	−0.659612	−	0.827127i	−0.993301	+	0.115556i	$0.963135\pi$
$282$	−0.0685317	+	0.0859360i	−0.00408100	+	0.00511741i
$283$	−3.52230	−	1.69625i	−0.209379	−	0.100832i	0.326255	−	0.945282i	$-0.394213\pi$
$283$	−3.52230	−	1.69625i	−0.209379	−	0.100832i	−0.535634	+	0.844450i	$0.679927\pi$
$284$	3.57002	+	15.6413i	0.211842	+	0.928140i
$285$	−0.472189	−	2.06879i	−0.0279701	−	0.122545i
$286$	−1.05496	+	1.32288i	−0.0623810	+	0.0782233i
$287$	−17.8693	+	8.60539i	−1.05479	+	0.507960i
$288$	−3.52134	+	15.4280i	−0.207497	+	0.909104i
$289$	14.2066	−	6.84152i	0.835680	−	0.402442i
$290$	−0.631023	−	0.791277i	−0.0370549	−	0.0464654i
$291$	0.729627	+	3.19670i	0.0427715	+	0.187394i
$292$	13.3768	+	16.7740i	0.782818	+	0.981623i
$293$	6.23772	−	27.3292i	0.364411	−	1.59659i	−0.377445	−	0.926032i	$-0.623197\pi$
$293$	6.23772	−	27.3292i	0.364411	−	1.59659i	0.741857	−	0.670559i	$-0.233946\pi$
$294$	−0.0519012			−0.00302694
$295$	16.6703			0.970580
$296$	5.19471	−	22.7595i	0.301936	−	1.32287i
$297$	3.48978	−	4.37604i	0.202498	−	0.253924i
$298$	1.11260	+	0.535802i	0.0644515	+	0.0310382i
$299$	−3.04019	+	1.46408i	−0.175819	+	0.0846698i
$300$	−0.335126			−0.0193485
$301$	13.9397	−	9.29417i	0.803469	−	0.535707i
$302$	−0.274127			−0.0157742
$303$	−0.676719	+	0.325891i	−0.0388765	+	0.0187219i
$304$	−10.8448	−	5.22259i	−0.621993	−	0.299536i
$305$	9.85086	−	12.3526i	0.564058	−	0.707307i
$306$	−0.405813	+	1.77798i	−0.0231988	+	0.101641i
$307$	−0.633415			−0.0361509			−0.0180755	−	0.999837i	$-0.505754\pi$
$307$	−0.633415			−0.0361509			−0.0180755	+	0.999837i	$0.505754\pi$
$308$	20.4953			1.16783
$309$	−0.260980	+	1.14343i	−0.0148466	+	0.0650474i
$310$	4.12498	+	5.17256i	0.234283	+	0.293782i
$311$	5.64460	+	24.7306i	0.320076	+	1.40234i	0.837417	+	0.546564i	$0.184065\pi$
$311$	5.64460	+	24.7306i	0.320076	+	1.40234i	−0.517342	+	0.855779i	$0.673078\pi$
$312$	−0.162718	−	0.204042i	−0.00921212	−	0.0115516i
$313$	−13.4661	+	6.48496i	−0.761152	+	0.366551i	−0.773851	−	0.633368i	$-0.781672\pi$
$313$	−13.4661	+	6.48496i	−0.761152	+	0.366551i	0.0126990	+	0.999919i	$0.495958\pi$
$314$	−0.952279	+	4.17221i	−0.0537402	+	0.235451i
$315$	13.6310	−	6.56435i	0.768021	−	0.369859i
$316$	5.37800	−	6.74380i	0.302536	−	0.379368i
$317$	1.07822	+	4.72399i	0.0605589	+	0.265326i	0.996139	−	0.0877883i	$-0.0279799\pi$
$317$	1.07822	+	4.72399i	0.0605589	+	0.265326i	−0.935580	+	0.353114i	$0.885123\pi$
$318$	−0.189333	−	0.829522i	−0.0106173	−	0.0465173i
$319$	3.89493	+	1.87570i	0.218074	+	0.105019i
$320$	1.90515	−	2.38898i	0.106501	−	0.133548i
$321$	−0.242799	−	0.304461i	−0.0135517	−	0.0169933i
$322$	−6.70291	−	3.22795i	−0.373538	−	0.179887i
$323$	−5.35690	−	2.57975i	−0.298066	−	0.143541i
$324$	−9.12379	−	11.4409i	−0.506877	−	0.635604i
$325$	−0.400969	+	0.502799i	−0.0222418	+	0.0278903i
$326$	0.487918	+	0.234969i	0.0270233	+	0.0130137i
$327$	−0.366822	−	1.60715i	−0.0202853	−	0.0888756i
$328$	3.53923	+	15.5064i	0.195421	+	0.856196i
$329$	1.59299	−	1.99755i	0.0878244	−	0.110128i
$330$	0.939001	−	0.452199i	0.0516903	−	0.0248927i
$331$	−2.74751	+	12.0376i	−0.151017	+	0.661648i	0.841574	+	0.540142i	$0.181630\pi$
$331$	−2.74751	+	12.0376i	−0.151017	+	0.661648i	−0.992591	+	0.121506i	$0.961228\pi$
$332$	22.7473	−	10.9545i	1.24842	−	0.601207i
$333$	21.0330	+	26.3745i	1.15260	+	1.44531i
$334$	−0.697530	−	3.05608i	−0.0381671	−	0.167221i
$335$	−0.582105	−	0.729937i	−0.0318038	−	0.0398807i
$336$	−0.253020	+	1.10855i	−0.0138034	+	0.0604766i
$337$	6.20344			0.337923			0.168961	−	0.985623i	$-0.445959\pi$
$337$	6.20344			0.337923			0.168961	+	0.985623i	$0.445959\pi$
$338$	6.98493			0.379930
$339$	−0.0806133	+	0.353190i	−0.00437831	+	0.0191826i
$340$	2.34183	−	2.93656i	0.127004	−	0.159257i
$341$	−25.4611	−	12.2614i	−1.37879	−	0.663992i
$342$	−7.93027	+	3.81902i	−0.428820	+	0.206509i
$343$	19.0911			1.03082
$344$	−4.77897	−	12.5570i	−0.257665	−	0.677028i
$345$	2.07846			0.111900
$346$	−4.32640	+	2.08348i	−0.232589	+	0.112009i
$347$	−16.2986	−	7.84899i	−0.874954	−	0.421356i	−0.0581750	−	0.998306i	$-0.518528\pi$
$347$	−16.2986	−	7.84899i	−0.874954	−	0.421356i	−0.816779	+	0.576951i	$0.804242\pi$
$348$	−0.190530	+	0.238916i	−0.0102135	+	0.0128073i
$349$	−1.61476	+	7.07473i	−0.0864362	+	0.378702i	−0.999581	−	0.0289329i	$-0.990789\pi$
$349$	−1.61476	+	7.07473i	−0.0864362	+	0.378702i	0.913145	+	0.407634i	$0.133646\pi$
$350$	−1.41789			−0.0757897
$351$	0.759251			0.0405258
$352$	5.63856	−	24.7041i	0.300536	−	1.31673i
$353$	6.50902	+	8.16206i	0.346440	+	0.434423i	0.924273	−	0.381733i	$-0.124673\pi$
$353$	6.50902	+	8.16206i	0.346440	+	0.434423i	−0.577832	+	0.816156i	$0.696101\pi$
$354$	0.203866	+	0.893196i	0.0108354	+	0.0474728i
$355$	−11.8237	−	14.8265i	−0.627537	−	0.786907i
$356$	−25.9388	+	12.4915i	−1.37475	+	0.662046i
$357$	−0.124982	+	0.547581i	−0.00661474	+	0.0289811i
$358$	−0.997312	+	0.480280i	−0.0527096	+	0.0253836i
$359$	−17.5417	+	21.9966i	−0.925814	+	1.16093i	0.0608467	+	0.998147i	$0.480620\pi$
$359$	−17.5417	+	21.9966i	−0.925814	+	1.16093i	−0.986661	+	0.162787i	$0.947952\pi$
$360$	−2.69979	−	11.8286i	−0.142291	−	0.623420i
$361$	−2.15764	−	9.45323i	−0.113560	−	0.497538i
$362$	−4.42812	−	2.13247i	−0.232737	−	0.112080i
$363$	−1.41723	+	1.77715i	−0.0743853	+	0.0932762i
$364$	1.73341	+	2.17362i	0.0908552	+	0.113929i
$365$	−22.8485	−	11.0032i	−1.19594	−	0.575936i
$366$	0.782323	+	0.376747i	0.0408927	+	0.0196929i
$367$	10.2552	+	12.8596i	0.535316	+	0.671265i	0.973782	−	0.227483i	$-0.0730496\pi$
$367$	10.2552	+	12.8596i	0.535316	+	0.671265i	−0.438466	+	0.898748i	$0.644478\pi$
$368$	7.35086	−	9.21768i	0.383190	−	0.480505i
$369$	−20.7075	−	9.97221i	−1.07799	−	0.519133i
$370$	2.81402	+	12.3290i	0.146294	+	0.640955i
$371$	4.40097	+	19.2819i	0.228487	+	1.00107i
$372$	1.24549	−	1.56179i	0.0645755	−	0.0809751i
$373$	9.73609	−	4.68866i	0.504116	−	0.242769i	−0.164500	−	0.986377i	$-0.552601\pi$
$373$	9.73609	−	4.68866i	0.504116	−	0.242769i	0.668616	+	0.743608i	$0.266887\pi$
$374$	0.649809	−	2.84700i	0.0336008	−	0.147215i
$375$	2.14138	−	1.03123i	0.110580	−	0.0532526i
$376$	−1.27748	−	1.60191i	−0.0658810	−	0.0826121i
$377$	0.130490	+	0.571714i	0.00672058	+	0.0294448i
$378$	1.04370	+	1.30876i	0.0536824	+	0.0673156i
$379$	2.16272	−	9.47549i	0.111091	−	0.486723i	−0.888520	−	0.458838i	$-0.848266\pi$
$379$	2.16272	−	9.47549i	0.111091	−	0.486723i	0.999611	−	0.0278848i	$-0.00887716\pi$
$380$	18.1280			0.929945
$381$	−0.587482			−0.0300976
$382$	−0.931764	+	4.08232i	−0.0476732	+	0.208870i
$383$	−14.7397	+	18.4831i	−0.753166	+	0.944440i	−0.999695	−	0.0246955i	$-0.992138\pi$
$383$	−14.7397	+	18.4831i	−0.753166	+	0.944440i	0.246529	+	0.969135i	$0.420710\pi$
$384$	2.05884	+	0.991487i	0.105065	+	0.0505966i
$385$	−21.8267	+	10.5112i	−1.11239	+	0.535699i
$386$	4.46309			0.227165
$387$	18.4923	+	5.91428i	0.940018	+	0.300640i
$388$	−28.0113			−1.42206
$389$	7.11141	−	3.42467i	0.360563	−	0.173638i	−0.244828	−	0.969567i	$-0.578731\pi$
$389$	7.11141	−	3.42467i	0.360563	−	0.173638i	0.605390	+	0.795929i	$0.293017\pi$
$390$	0.127375	+	0.0613404i	0.00644987	+	0.00310609i
$391$	3.63102	−	4.55316i	0.183629	−	0.230263i
$392$	0.215284	−	0.943219i	0.0108735	−	0.0476398i
$393$	1.40821			0.0710346
$394$	10.7614			0.542151
$395$	−2.26875	+	9.94004i	−0.114153	+	0.500138i
$396$	14.8083	+	18.5690i	0.744144	+	0.933127i
$397$	5.69418	+	24.9478i	0.285783	+	1.25210i	0.890253	+	0.455467i	$0.150528\pi$
$397$	5.69418	+	24.9478i	0.285783	+	1.25210i	−0.604470	+	0.796628i	$0.706615\pi$
$398$	−7.84146	−	9.83288i	−0.393057	−	0.492878i
$399$	−2.44235	+	1.17618i	−0.122271	+	0.0588824i
$400$	0.500000	−	2.19064i	0.0250000	−	0.109532i
$401$	7.84697	−	3.77890i	0.391859	−	0.188709i	−0.227571	−	0.973762i	$-0.573078\pi$
$401$	7.84697	−	3.77890i	0.391859	−	0.188709i	0.619430	+	0.785052i	$0.287364\pi$
$402$	0.0319914	−	0.0401160i	0.00159559	−	0.00200080i
$403$	−0.853011	−	3.73729i	−0.0424915	−	0.186167i
$404$	−1.42782	−	6.25569i	−0.0710367	−	0.311232i
$405$	15.5840	+	7.50487i	0.774376	+	0.372920i
$406$	−0.806118	+	1.01084i	−0.0400070	+	0.0501672i
$407$	−33.6790	−	42.2322i	−1.66941	−	2.09337i
$408$	0.405813	+	0.195429i	0.0200907	+	0.00967519i
$409$	−11.9438	−	5.75185i	−0.590585	−	0.284411i	0.114625	−	0.993409i	$-0.463433\pi$
$409$	−11.9438	−	5.75185i	−0.590585	−	0.284411i	−0.705211	+	0.708998i	$0.749148\pi$
$410$	−5.37196	−	6.73623i	−0.265302	−	0.332679i
$411$	−1.02781	+	1.28883i	−0.0506982	+	0.0635735i
$412$	−9.02715	−	4.34724i	−0.444736	−	0.214173i
$413$	−4.73878	−	20.7620i	−0.233180	−	1.02163i
$414$	−1.91843	−	8.40518i	−0.0942856	−	0.413092i
$415$	−18.6069	+	23.3323i	−0.913375	+	1.14534i
$416$	3.09688	−	1.49138i	0.151837	−	0.0731207i
$417$	0.266167	−	1.16615i	0.0130343	−	0.0571068i
$418$	12.6984	−	6.11521i	0.621097	−	0.299105i
$419$	0.711636	+	0.892363i	0.0347657	+	0.0435948i	0.798910	−	0.601450i	$-0.205410\pi$
$419$	0.711636	+	0.892363i	0.0347657	+	0.0435948i	−0.764145	+	0.645045i	$0.776839\pi$
$420$	−0.381059	−	1.66953i	−0.0185938	−	0.0814647i
$421$	2.07756	+	2.60517i	0.101254	+	0.126968i	0.829877	−	0.557947i	$-0.188411\pi$
$421$	2.07756	+	2.60517i	0.101254	+	0.126968i	−0.728623	+	0.684915i	$0.759839\pi$
$422$	−2.03654	+	8.92267i	−0.0991372	+	0.434349i
$423$	2.96077			0.143958
$424$	15.8605			0.770256
$425$	0.246980	−	1.08209i	0.0119803	−	0.0524890i
$426$	0.649809	−	0.814835i	0.0314833	−	0.0394789i
$427$	−18.1848	−	8.75733i	−0.880023	−	0.423797i
$428$	2.99731	−	1.44343i	0.144881	−	0.0697708i
$429$	−0.603875			−0.0291554
$430$	5.28382	+	5.00536i	0.254808	+	0.241380i
$431$	20.3515			0.980298			0.490149	−	0.871639i	$-0.336942\pi$
$431$	20.3515			0.980298			0.490149	+	0.871639i	$0.336942\pi$
$432$	−2.39008	+	1.15100i	−0.114993	+	0.0553777i
$433$	−8.97650	−	4.32285i	−0.431383	−	0.207743i	0.205575	−	0.978641i	$-0.434093\pi$
$433$	−8.97650	−	4.32285i	−0.431383	−	0.207743i	−0.636958	+	0.770898i	$0.719808\pi$
$434$	5.26958	−	6.60784i	0.252948	−	0.317187i
$435$	0.0803763	−	0.352152i	0.00385375	−	0.0168844i
$436$	14.0828			0.674442
$437$	28.1075			1.34457
$438$	0.310134	−	1.35879i	0.0148188	−	0.0649254i
$439$	5.10470	+	6.40110i	0.243634	+	0.305508i	0.888581	−	0.458720i	$-0.151692\pi$
$439$	5.10470	+	6.40110i	0.243634	+	0.305508i	−0.644947	+	0.764228i	$0.723120\pi$
$440$	4.32304	+	18.9405i	0.206093	+	0.902953i
$441$	0.871666	+	1.09303i	0.0415079	+	0.0520493i
$442$	0.356896	−	0.171872i	0.0169758	−	0.00817512i
$443$	−6.76636	+	29.6453i	−0.321479	+	1.40849i	0.513442	+	0.858124i	$0.328370\pi$
$443$	−6.76636	+	29.6453i	−0.321479	+	1.40849i	−0.834922	+	0.550369i	$0.814487\pi$
$444$	3.44020	−	1.65671i	0.163265	−	0.0786241i
$445$	21.2174	−	26.6058i	1.00580	−	1.26124i
$446$	−0.185981	−	0.814835i	−0.00880644	−	0.0385835i
$447$	0.0980717	+	0.429680i	0.00463863	+	0.0203232i
$448$	−3.51693	−	1.69366i	−0.166159	−	0.0800180i
$449$	−13.8415	+	17.3566i	−0.653219	+	0.819111i	−0.992586	−	0.121543i	$-0.961216\pi$
$449$	−13.8415	+	17.3566i	−0.653219	+	0.819111i	0.339367	+	0.940654i	$0.389787\pi$
$450$	−1.02446	−	1.28463i	−0.0482934	−	0.0605581i
$451$	33.1579	+	15.9680i	1.56135	+	0.751905i
$452$	−2.78836	−	1.34281i	−0.131154	−	0.0631603i
$453$	−0.0609989	−	0.0764902i	−0.00286598	−	0.00359382i
$454$	6.35272	−	7.96605i	0.298148	−	0.373865i
$455$	−2.96077	−	1.42583i	−0.138803	−	0.0668441i
$456$	0.483738	+	2.11939i	0.0226531	+	0.0992498i
$457$	−2.49635	−	10.9372i	−0.116774	−	0.511622i	−0.999156	−	0.0410869i	$-0.986918\pi$
$457$	−2.49635	−	10.9372i	−0.116774	−	0.511622i	0.882381	−	0.470535i	$-0.155939\pi$
$458$	−2.13959	+	2.68296i	−0.0999764	+	0.125366i
$459$	−1.18060	+	0.568549i	−0.0551059	+	0.0265376i
$460$	−3.95108	+	17.3108i	−0.184220	+	0.807121i
$461$	31.1247	−	14.9889i	1.44962	−	0.698102i	0.467094	−	0.884208i	$-0.345301\pi$
$461$	31.1247	−	14.9889i	1.44962	−	0.698102i	0.982530	+	0.186106i	$0.0595866\pi$
$462$	−0.830117	−	1.04093i	−0.0386206	−	0.0484286i
$463$	−2.26540	−	9.92535i	−0.105282	−	0.461270i	−0.999896	−	0.0144304i	$-0.995406\pi$
$463$	−2.26540	−	9.92535i	−0.105282	−	0.461270i	0.894614	−	0.446840i	$-0.147451\pi$
$464$	−1.27748	−	1.60191i	−0.0593055	−	0.0743667i
$465$	−0.525418	+	2.30201i	−0.0243657	+	0.106753i
$466$	−2.45340			−0.113652
$467$	14.9782			0.693110			0.346555	−	0.938030i	$-0.387351\pi$
$467$	14.9782			0.693110			0.346555	+	0.938030i	$0.387351\pi$
$468$	−0.716907	+	3.14098i	−0.0331390	+	0.145192i
$469$	−0.743627	+	0.932479i	−0.0343375	+	0.0430579i
$470$	1.00000	+	0.481575i	0.0461266	+	0.0222134i
$471$	−1.37608	+	0.662687i	−0.0634066	+	0.0305350i
$472$	−17.0780			−0.786078
$473$	−29.6109	−	9.47025i	−1.36151	−	0.435442i
$474$	−0.560335			−0.0257370
$475$	4.82640	−	2.32427i	0.221450	−	0.106645i
$476$	−4.32304	−	2.08187i	−0.198146	−	0.0954223i
$477$	−14.2899	+	17.9189i	−0.654288	+	0.820451i
$478$	−1.29039	+	5.65356i	−0.0590210	+	0.258588i
$479$	29.0573			1.32766			0.663830	−	0.747883i	$-0.268930\pi$
$479$	29.0573			1.32766			0.663830	+	0.747883i	$0.268930\pi$
$480$	−2.11721			−0.0966371
$481$	1.63049	−	7.14364i	0.0743439	−	0.325722i
$482$	−8.40813	−	10.5435i	−0.382980	−	0.480242i
$483$	−0.590834	−	2.58861i	−0.0268839	−	0.117786i
$484$	−12.1072	−	15.1820i	−0.550329	−	0.690090i
$485$	29.8310	−	14.3659i	1.35456	−	0.652320i
$486$	−0.648908	+	2.84305i	−0.0294351	+	0.128963i
$487$	21.5160	−	10.3616i	0.974984	−	0.469528i	0.122607	−	0.992455i	$-0.460875\pi$
$487$	21.5160	−	10.3616i	0.974984	−	0.469528i	0.852377	+	0.522928i	$0.175160\pi$
$488$	−10.0918	+	12.6547i	−0.456834	+	0.572852i
$489$	0.0430081	+	0.188431i	0.00194489	+	0.00852113i
$490$	0.116621	+	0.510950i	0.00526840	+	0.0230824i
$491$	0.608720	+	0.293144i	0.0274711	+	0.0132294i	0.447569	−	0.894249i	$-0.352290\pi$
$491$	0.608720	+	0.293144i	0.0274711	+	0.0132294i	−0.420098	+	0.907479i	$0.638004\pi$
$492$	−1.62200	+	2.03392i	−0.0731253	+	0.0916962i
$493$	−0.631023	−	0.791277i	−0.0284198	−	0.0356373i
$494$	1.72252	+	0.829522i	0.0774999	+	0.0373220i
$495$	−25.2935	−	12.1807i	−1.13686	−	0.547482i
$496$	8.35086	+	10.4716i	0.374964	+	0.470191i
$497$	−15.1045	+	18.9405i	−0.677531	+	0.849597i
$498$	−1.47770	−	0.711621i	−0.0662172	−	0.0318885i
$499$	−7.16391	−	31.3872i	−0.320701	−	1.40508i	−0.836309	−	0.548258i	$-0.815291\pi$
$499$	−7.16391	−	31.3872i	−0.320701	−	1.40508i	0.515608	−	0.856824i	$-0.327566\pi$
$500$	4.51812	+	19.7952i	0.202057	+	0.885268i
$501$	0.697530	−	0.874675i	0.0311633	−	0.0390776i
$502$	−10.9635	+	5.27972i	−0.489323	+	0.235646i
$503$	5.15117	−	22.5687i	0.229679	−	1.00629i	−0.720223	−	0.693743i	$-0.755960\pi$
$503$	5.15117	−	22.5687i	0.229679	−	1.00629i	0.949902	−	0.312548i	$-0.101182\pi$
$504$	−13.9644	+	6.72491i	−0.622025	+	0.299551i
$505$	4.72886	+	5.92980i	0.210431	+	0.263873i
$506$	3.07188	+	13.4588i	0.136562	+	0.598317i
$507$	1.55429	+	1.94902i	0.0690286	+	0.0865592i
$508$	1.11679	−	4.89295i	0.0495493	−	0.217090i
$509$	−29.2010			−1.29431			−0.647157	−	0.762357i	$-0.724042\pi$
$509$	−29.2010			−1.29431			−0.647157	+	0.762357i	$0.724042\pi$
$510$	−0.243996			−0.0108043
$511$	−7.20895	+	31.5845i	−0.318905	+	1.39721i
$512$	−13.2289	+	16.5885i	−0.584638	+	0.733113i
$513$	−5.69806	−	2.74404i	−0.251576	−	0.121152i
$514$	−1.44773	+	0.697190i	−0.0638566	+	0.0307517i
$515$	11.8431			0.521869
$516$	1.11841	−	1.89168i	0.0492352	−	0.0832766i
$517$	−4.74094			−0.208506
$518$	14.5553	−	7.00944i	0.639521	−	0.307977i
$519$	−1.54407	−	0.743586i	−0.0677773	−	0.0326398i
$520$	−1.64310	+	2.06039i	−0.0720549	+	0.0903540i
$521$	−0.211103	+	0.924904i	−0.00924860	+	0.0405208i	−0.979342	−	0.202212i	$-0.935187\pi$
$521$	−0.211103	+	0.924904i	−0.00924860	+	0.0405208i	0.970093	+	0.242733i	$0.0780440\pi$
$522$	−1.49827			−0.0655775
$523$	−36.8853			−1.61288			−0.806441	−	0.591315i	$-0.798609\pi$
$523$	−36.8853			−1.61288			−0.806441	+	0.591315i	$0.798609\pi$
$524$	−2.67696	+	11.7285i	−0.116943	+	0.512362i
$525$	−0.315511	−	0.395639i	−0.0137700	−	0.0172671i
$526$	−2.14556	−	9.40029i	−0.0935507	−	0.409872i
$527$	4.12498	+	5.17256i	0.179687	+	0.225320i
$528$	1.90097	−	0.915458i	0.0827291	−	0.0398402i
$529$	−1.00820	+	4.41720i	−0.0438346	+	0.192052i
$530$	−7.74094	+	3.72784i	−0.336245	+	0.161927i
$531$	15.3867	−	19.2944i	0.667727	−	0.837304i
$532$	−5.15316	−	22.5775i	−0.223418	−	0.978858i
$533$	1.11088	+	4.86706i	0.0481174	+	0.210816i
$534$	1.68502	+	0.811463i	0.0729180	+	0.0351155i
$535$	−2.45175	+	3.07439i	−0.105998	+	0.132918i
$536$	0.596343	+	0.747790i	0.0257581	+	0.0322996i
$537$	−0.355936	−	0.171410i	−0.0153598	−	0.00739688i
$538$	−7.03534	−	3.38804i	−0.303315	−	0.146069i
$539$	−1.39576	−	1.75022i	−0.0601195	−	0.0753874i
$540$	2.49098	−	3.12358i	0.107195	−	0.134418i
$541$	15.7811	+	7.59979i	0.678484	+	0.326741i	0.741194	−	0.671291i	$-0.234260\pi$
$541$	15.7811	+	7.59979i	0.678484	+	0.326741i	−0.0627100	+	0.998032i	$0.519974\pi$
$542$	−0.264733	−	1.15987i	−0.0113713	−	0.0498208i
$543$	−0.390321	−	1.71011i	−0.0167503	−	0.0733877i
$544$	−3.69873	+	4.63806i	−0.158582	+	0.198855i
$545$	−14.9976	+	7.22247i	−0.642427	+	0.309376i
$546$	0.0401881	−	0.176076i	0.00171989	−	0.00753535i
$547$	−14.5085	+	6.98692i	−0.620338	+	0.298739i	−0.717531	−	0.696526i	$-0.754728\pi$
$547$	−14.5085	+	6.98692i	−0.620338	+	0.298739i	0.0971929	+	0.995266i	$0.469014\pi$
$548$	−8.78046	−	11.0104i	−0.375083	−	0.470339i
$549$	−5.20464	−	22.8030i	−0.222128	−	0.973208i
$550$	1.64042	+	2.05702i	0.0699476	+	0.0877115i
$551$	1.08695	−	4.76224i	0.0463056	−	0.202878i
$552$	−2.12929			−0.0906288
$553$	13.0248			0.553869
$554$	−2.87233	+	12.5845i	−0.122034	+	0.534664i
$555$	−2.81402	+	3.52867i	−0.119448	+	0.149784i
$556$	9.20655	+	4.43364i	0.390445	+	0.188028i
$557$	−4.92639	+	2.37242i	−0.208738	+	0.100523i	−0.535332	−	0.844642i	$-0.679813\pi$
$557$	−4.92639	+	2.37242i	−0.208738	+	0.100523i	0.326594	+	0.945165i	$0.394099\pi$
$558$	9.79417			0.414620
$559$	−1.50000	−	3.94133i	−0.0634432	−	0.166700i
$560$	11.4819			0.485198
$561$	0.939001	−	0.452199i	0.0396447	−	0.0190919i
$562$	−8.86712	−	4.27018i	−0.374037	−	0.180127i
$563$	21.8143	−	27.3543i	0.919364	−	1.15285i	−0.0685200	−	0.997650i	$-0.521828\pi$
$563$	21.8143	−	27.3543i	0.919364	−	1.15285i	0.987884	−	0.155196i	$-0.0496009\pi$
$564$	0.0745725	−	0.326723i	0.00314007	−	0.0137575i
$565$	3.65817			0.153900
$566$	−2.16959			−0.0911946
$567$	4.91694	−	21.5425i	0.206492	−	0.904700i
$568$	12.1129	+	15.1891i	0.508246	+	0.637320i
$569$	1.40688	+	6.16394i	0.0589794	+	0.258406i	0.995818	−	0.0913554i	$-0.0291199\pi$
$569$	1.40688	+	6.16394i	0.0589794	+	0.258406i	−0.936839	+	0.349761i	$0.886263\pi$
$570$	−0.734234	−	0.920700i	−0.0307537	−	0.0385639i
$571$	−17.7136	+	8.53040i	−0.741289	+	0.356986i	−0.766113	−	0.642706i	$-0.777812\pi$
$571$	−17.7136	+	8.53040i	−0.741289	+	0.356986i	0.0248239	+	0.999692i	$0.492097\pi$
$572$	1.14795	−	5.02949i	0.0479981	−	0.210294i
$573$	−1.34644	+	0.648410i	−0.0562482	+	0.0270877i
$574$	−6.86257	+	8.60539i	−0.286438	+	0.359182i
$575$	1.16756	+	5.11543i	0.0486907	+	0.213328i
$576$	−1.00657	−	4.41009i	−0.0419406	−	0.183754i
$577$	−13.6386	−	6.56798i	−0.567780	−	0.273429i	0.127892	−	0.991788i	$-0.459179\pi$
$577$	−13.6386	−	6.56798i	−0.567780	−	0.273429i	−0.695672	+	0.718359i	$0.744893\pi$
$578$	5.45593	−	6.84152i	0.226937	−	0.284570i
$579$	0.993131	+	1.24535i	0.0412731	+	0.0517549i
$580$	2.78017	+	1.33886i	0.115440	+	0.0555931i
$581$	34.3485	+	16.5413i	1.42501	+	0.686251i
$582$	1.13454	+	1.42267i	0.0470282	+	0.0589714i
$583$	22.8817	−	28.6927i	0.947661	−	1.18833i
$584$	23.4073	+	11.2724i	0.968601	+	0.466454i
$585$	−0.847397	−	3.71269i	−0.0350356	−	0.153501i
$586$	−3.46167	−	15.1666i	−0.143000	−	0.626526i
$587$	−3.75600	+	4.70988i	−0.155027	+	0.194398i	−0.853279	−	0.521454i	$-0.825390\pi$
$587$	−3.75600	+	4.70988i	−0.155027	+	0.194398i	0.698253	+	0.715852i	$0.253961\pi$
$588$	0.142572	−	0.0686589i	0.00587956	−	0.00283145i
$589$	−7.10537	+	31.1306i	−0.292772	+	1.28272i
$590$	8.33513	−	4.01398i	0.343152	−	0.165253i
$591$	2.39463	+	3.00277i	0.0985020	+	0.123518i
$592$	5.69687	+	24.9596i	0.234140	+	1.02583i
$593$	25.4318	+	31.8904i	1.04436	+	1.30958i	0.949389	+	0.314102i	$0.101704\pi$
$593$	25.4318	+	31.8904i	1.04436	+	1.30958i	0.0949683	+	0.995480i	$0.469725\pi$
$594$	0.691194	−	3.02832i	0.0283600	−	0.124253i
$595$	5.67158			0.232512
$596$	−3.76510			−0.154225
$597$	0.998804	−	4.37604i	0.0408783	−	0.179100i
$598$	−1.16756	+	1.46408i	−0.0477452	+	0.0598706i
$599$	20.6586	+	9.94866i	0.844087	+	0.406491i	0.805380	−	0.592760i	$-0.201962\pi$
$599$	20.6586	+	9.94866i	0.844087	+	0.406491i	0.0387079	+	0.999251i	$0.487676\pi$
$600$	−0.365625	+	0.176076i	−0.0149266	+	0.00718826i
$601$	−11.6974			−0.477147			−0.238573	−	0.971124i	$-0.576680\pi$
$601$	−11.6974			−0.477147			−0.238573	+	0.971124i	$0.576680\pi$
$602$	4.73191	−	8.00358i	0.192858	−	0.326202i
$603$	−1.38212			−0.0562844
$604$	0.753020	−	0.362636i	0.0306400	−	0.0147554i
$605$	20.6799	+	9.95893i	0.840759	+	0.404888i
$606$	−0.259889	+	0.325891i	−0.0105573	+	0.0132384i
$607$	3.53050	−	15.4681i	0.143299	−	0.627832i	−0.851357	−	0.524586i	$-0.824220\pi$
$607$	3.53050	−	15.4681i	0.143299	−	0.627832i	0.994656	−	0.103246i	$-0.0329228\pi$
$608$	−28.6316			−1.16117
$609$	−0.461435			−0.0186983
$610$	1.95108	−	8.54825i	0.0789970	−	0.346109i
$611$	−0.400969	−	0.502799i	−0.0162215	−	0.0203411i
$612$	−1.23729	−	5.42093i	−0.0500145	−	0.219128i
$613$	20.3545	+	25.5237i	0.822111	+	1.03089i	0.998911	+	0.0466475i	$0.0148537\pi$
$613$	20.3545	+	25.5237i	0.822111	+	1.03089i	−0.176801	+	0.984247i	$0.556575\pi$
$614$	−0.316708	+	0.152518i	−0.0127813	+	0.00615514i
$615$	0.684252	−	2.99790i	0.0275917	−	0.120887i
$616$	22.3605	−	10.7683i	0.900932	−	0.433866i
$617$	22.4815	−	28.1909i	0.905071	−	1.13492i	−0.0852816	−	0.996357i	$-0.527179\pi$
$617$	22.4815	−	28.1909i	0.905071	−	1.13492i	0.990353	−	0.138567i	$-0.0442496\pi$
$618$	0.144833	+	0.634555i	0.00582604	+	0.0255255i
$619$	−2.01065	−	8.80923i	−0.0808148	−	0.354073i	0.918312	−	0.395858i	$-0.129553\pi$
$619$	−2.01065	−	8.80923i	−0.0808148	−	0.354073i	−0.999127	+	0.0417851i	$0.986696\pi$
$620$	−18.1739	−	8.75209i	−0.729881	−	0.351492i
$621$	3.86227	−	4.84314i	0.154988	−	0.194348i
$622$	8.77711	+	11.0061i	0.351930	+	0.441306i
$623$	−39.1676	−	18.8621i	−1.56922	−	0.755695i
$624$	0.257865	+	0.124181i	0.0103229	+	0.00497122i
$625$	−11.8463	−	14.8548i	−0.473852	−	0.594192i
$626$	−5.17158	+	6.48496i	−0.206698	+	0.259191i
$627$	4.53199	+	2.18249i	0.180990	+	0.0871603i
$628$	−2.90342	−	12.7207i	−0.115859	−	0.507612i
$629$	2.81402	+	12.3290i	0.112202	+	0.491590i
$630$	5.23490	−	6.56435i	0.208563	−	0.261530i
$631$	−15.3366	+	7.38573i	−0.610541	+	0.294021i	−0.713490	−	0.700666i	$-0.752887\pi$
$631$	−15.3366	+	7.38573i	−0.610541	+	0.294021i	0.102949	+	0.994687i	$0.467172\pi$
$632$	2.32424	−	10.1832i	0.0924533	−	0.405064i
$633$	−2.94289	+	1.41722i	−0.116969	+	0.0563294i
$634$	1.67659	+	2.10237i	0.0665858	+	0.0834959i
$635$	1.32006	+	5.78356i	0.0523850	+	0.229514i
$636$	1.61745	+	2.02822i	0.0641360	+	0.0804240i
$637$	0.0675722	−	0.296053i	0.00267731	−	0.0117301i
$638$	2.39911			0.0949816
$639$	−28.0737			−1.11058
$640$	5.13467	−	22.4965i	0.202966	−	0.889251i
$641$	−3.33662	+	4.18399i	−0.131788	+	0.165258i	−0.843347	−	0.537369i	$-0.819418\pi$
$641$	−3.33662	+	4.18399i	−0.131788	+	0.165258i	0.711559	+	0.702627i	$0.247990\pi$
$642$	−0.194710	−	0.0937673i	−0.00768459	−	0.00370070i
$643$	16.6896	−	8.03730i	0.658175	−	0.316960i	−0.0748175	−	0.997197i	$-0.523837\pi$
$643$	16.6896	−	8.03730i	0.658175	−	0.316960i	0.732992	+	0.680237i	$0.238123\pi$
$644$	22.6829			0.893832
$645$	−0.220897	+	2.58815i	−0.00869783	+	0.101908i
$646$	−3.29962			−0.129822
$647$	−19.2228	+	9.25722i	−0.755727	+	0.363939i	−0.771744	−	0.635933i	$-0.780616\pi$
$647$	−19.2228	+	9.25722i	−0.755727	+	0.363939i	0.0160175	+	0.999872i	$0.494901\pi$
$648$	−15.9652	−	7.68843i	−0.627172	−	0.302030i
$649$	−24.6380	+	30.8951i	−0.967127	+	1.21274i
$650$	−0.0794168	+	0.347948i	−0.00311498	+	0.0136476i
$651$	3.01639			0.118222
$652$	−1.65114			−0.0646635
$653$	−7.71475	+	33.8005i	−0.301902	+	1.32272i	0.565352	+	0.824850i	$0.308740\pi$
$653$	−7.71475	+	33.8005i	−0.301902	+	1.32272i	−0.867253	+	0.497867i	$0.834117\pi$
$654$	−0.570392	−	0.715249i	−0.0223041	−	0.0279685i
$655$	−3.16421	−	13.8633i	−0.123636	−	0.541684i
$656$	−10.8753	−	13.6372i	−0.424610	−	0.532444i
$657$	−33.8245	+	16.2890i	−1.31962	+	0.635496i
$658$	0.315511	−	1.38235i	0.0122999	−	0.0538894i
$659$	−42.2667	+	20.3545i	−1.64648	+	0.792901i	−0.646936	+	0.762544i	$0.723950\pi$
$659$	−42.2667	+	20.3545i	−1.64648	+	0.792901i	−0.999539	+	0.0303562i	$0.990336\pi$
$660$	−1.98121	+	2.48436i	−0.0771186	+	0.0967037i
$661$	−3.13892	−	13.7525i	−0.122090	−	0.534911i	−0.998569	−	0.0534718i	$-0.982971\pi$
$661$	−3.13892	−	13.7525i	−0.122090	−	0.534911i	0.876479	−	0.481439i	$-0.159886\pi$
$662$	1.52475	+	6.68038i	0.0592613	+	0.259641i
$663$	0.127375	+	0.0613404i	0.00494682	+	0.00238226i
$664$	19.0620	−	23.9029i	0.739747	−	0.927614i
$665$	17.0670	+	21.4013i	0.661829	+	0.829907i
$666$	16.8671	+	8.12278i	0.653588	+	0.314751i
$667$	4.31067	+	2.07591i	0.166910	+	0.0803795i
$668$	5.95891	+	7.47224i	0.230557	+	0.289110i
$669$	0.185981	−	0.233212i	0.00719043	−	0.00901651i
$670$	−0.466812	−	0.224805i	−0.0180345	−	0.00868497i
$671$	8.33393	+	36.5133i	0.321728	+	1.40958i
$672$	0.601851	+	2.63688i	0.0232169	+	0.101720i
$673$	15.1637	−	19.0147i	0.584517	−	0.732961i	−0.398359	−	0.917230i	$-0.630420\pi$
$673$	15.1637	−	19.0147i	0.584517	−	0.732961i	0.982876	+	0.184269i	$0.0589916\pi$
$674$	3.10172	−	1.49371i	0.119474	−	0.0575355i
$675$	0.262709	−	1.15100i	0.0101117	−	0.0443022i
$676$	−19.1875	+	9.24020i	−0.737980	+	0.355392i
$677$	−21.6084	−	27.0960i	−0.830476	−	1.04138i	−0.998453	−	0.0555936i	$-0.982295\pi$
$677$	−21.6084	−	27.0960i	−0.830476	−	1.04138i	0.167977	−	0.985791i	$-0.446277\pi$
$678$	0.0447370	+	0.196006i	0.00171811	+	0.00752755i
$679$	−26.3719	−	33.0693i	−1.01206	−	1.26908i
$680$	1.01208	−	4.43422i	0.0388116	−	0.170045i
$681$	3.63640			0.139347
$682$	−15.6829			−0.600530
$683$	6.51520	−	28.5449i	0.249297	−	1.09224i	−0.682963	−	0.730453i	$-0.739309\pi$
$683$	6.51520	−	28.5449i	0.249297	−	1.09224i	0.932260	−	0.361789i	$-0.117834\pi$
$684$	16.7322	−	20.9815i	0.639772	−	0.802249i
$685$	14.9976	+	7.22247i	0.573029	+	0.275956i
$686$	9.54556	−	4.59690i	0.364451	−	0.175511i
$687$	−1.22474			−0.0467266
$688$	10.6969	+	10.1331i	0.407814	+	0.386322i
$689$	4.97823			0.189655
$690$	1.03923	−	0.500466i	0.0395628	−	0.0190524i
$691$	−4.14406	−	1.99568i	−0.157648	−	0.0759191i	0.353396	−	0.935474i	$-0.385027\pi$
$691$	−4.14406	−	1.99568i	−0.157648	−	0.0759191i	−0.511044	+	0.859555i	$0.670741\pi$
$692$	9.12833	−	11.4466i	0.347007	−	0.435133i
$693$	−7.98039	+	34.9644i	−0.303150	+	1.32819i
$694$	−10.0392			−0.381084
$695$	−12.0785			−0.458162
$696$	−0.0823422	+	0.360765i	−0.00312117	+	0.0136747i
$697$	−5.37196	−	6.73623i	−0.203478	−	0.255153i
$698$	0.896125	+	3.92618i	0.0339188	+	0.148608i
$699$	−0.545933	−	0.684579i	−0.0206491	−	0.0258932i
$700$	3.89493	−	1.87570i	0.147214	−	0.0708947i
$701$	−0.839733	+	3.67911i	−0.0317163	+	0.138958i	−0.988307	−	0.152476i	$-0.951275\pi$
$701$	−0.839733	+	3.67911i	−0.0317163	+	0.138958i	0.956591	+	0.291434i	$0.0941324\pi$
$702$	0.379626	−	0.182818i	0.0143280	−	0.00690002i
$703$	−38.0547	+	47.7191i	−1.43526	+	1.79976i
$704$	1.61178	+	7.06166i	0.0607461	+	0.266146i
$705$	0.0881460	+	0.386193i	0.00331977	+	0.0145449i
$706$	5.21983	+	2.51374i	0.196451	+	0.0946058i
$707$	6.04102	−	7.57519i	0.227196	−	0.284895i
$708$	−1.74160	−	2.18390i	−0.0654534	−	0.0820760i
$709$	−4.38189	−	2.11021i	−0.164565	−	0.0792504i	0.349788	−	0.936829i	$-0.386254\pi$
$709$	−4.38189	−	2.11021i	−0.164565	−	0.0792504i	−0.514353	+	0.857578i	$0.671968\pi$
$710$	−9.48188	−	4.56623i	−0.355849	−	0.171368i
$711$	9.41066	+	11.8006i	0.352927	+	0.442557i
$712$	−21.7364	+	27.2566i	−0.814606	+	1.02148i
$713$	−28.1787	−	13.5702i	−1.05530	−	0.508207i
$714$	0.0693596	+	0.303884i	0.00259572	+	0.0113726i
$715$	1.35690	+	5.94495i	0.0507450	+	0.222328i
$716$	2.10424	−	2.63864i	0.0786393	−	0.0986105i
$717$	−1.86467	+	0.897976i	−0.0696372	+	0.0335355i
$718$	−3.47434	+	15.2221i	−0.129661	+	0.568084i
$719$	11.0739	−	5.33291i	0.412987	−	0.198884i	−0.215841	−	0.976429i	$-0.569249\pi$
$719$	11.0739	−	5.33291i	0.412987	−	0.198884i	0.628828	+	0.777544i	$0.283535\pi$
$720$	8.29590	+	10.4027i	0.309170	+	0.387687i
$721$	−3.36658	−	14.7500i	−0.125378	−	0.549318i
$722$	−3.35504	−	4.20708i	−0.124861	−	0.156571i
$723$	1.07098	−	4.69228i	0.0398303	−	0.174508i
$724$	14.9849			0.556911
$725$	0.911854			0.0338654
$726$	−0.280700	+	1.22983i	−0.0104178	+	0.0456432i
$727$	26.9426	−	33.7850i	0.999248	−	1.25302i	0.0319191	−	0.999490i	$-0.489838\pi$
$727$	26.9426	−	33.7850i	0.999248	−	1.25302i	0.967328	−	0.253526i	$-0.0815904\pi$
$728$	3.03319	+	1.46071i	0.112417	+	0.0541374i
$729$	22.4383	−	10.8057i	0.831050	−	0.400212i
$730$	−14.0737			−0.520890
$731$	5.28382	+	5.00536i	0.195429	+	0.185130i
$732$	−2.64742			−0.0978513
$733$	24.1090	−	11.6103i	0.890487	−	0.428836i	0.0680431	−	0.997682i	$-0.478324\pi$
$733$	24.1090	−	11.6103i	0.890487	−	0.428836i	0.822444	+	0.568847i	$0.192610\pi$
$734$	8.22401	+	3.96048i	0.303554	+	0.146184i
$735$	−0.116621	+	0.146238i	−0.00430163	+	0.00539408i
$736$	6.24041	−	27.3410i	0.230024	−	1.00780i
$737$	2.21313			0.0815216
$738$	−12.7549			−0.469516
$739$	−2.43738	+	10.6788i	−0.0896604	+	0.392828i	−0.999768	−	0.0215444i	$-0.993142\pi$
$739$	−2.43738	+	10.6788i	−0.0896604	+	0.392828i	0.910108	+	0.414372i	$0.135999\pi$
$740$	−24.0398	−	30.1450i	−0.883721	−	1.10815i
$741$	0.151833	+	0.665225i	0.00557774	+	0.0244377i
$742$	6.84332	+	8.58125i	0.251226	+	0.315028i
$743$	35.2875	−	16.9935i	1.29457	−	0.623433i	0.345478	−	0.938427i	$-0.387717\pi$
$743$	35.2875	−	16.9935i	1.29457	−	0.623433i	0.949094	+	0.314994i	$0.102003\pi$
$744$	0.538269	−	2.35831i	0.0197339	−	0.0864599i
$745$	4.00969	−	1.93096i	0.146904	−	0.0707451i
$746$	3.73908	−	4.68866i	0.136897	−	0.171664i
$747$	9.83081	+	43.0716i	0.359691	+	1.57591i
$748$	1.98121	+	8.68026i	0.0724403	+	0.317382i
$749$	4.52595	+	2.17958i	0.165375	+	0.0796402i
$750$	0.822380	−	1.03123i	0.0300291	−	0.0376553i
$751$	7.11596	+	8.92313i	0.259665	+	0.325610i	0.894525	−	0.447017i	$-0.147514\pi$
$751$	7.11596	+	8.92313i	0.259665	+	0.325610i	−0.634860	+	0.772627i	$0.718942\pi$
$752$	2.02446	+	0.974928i	0.0738244	+	0.0355520i
$753$	−3.91281	−	1.88431i	−0.142591	−	0.0686681i
$754$	0.202907	+	0.254437i	0.00738942	+	0.00926604i
$755$	−0.615957	+	0.772386i	−0.0224170	+	0.0281100i
$756$	−4.59837	−	2.21446i	−0.167241	−	0.0805390i
$757$	6.23048	+	27.2975i	0.226451	+	0.992145i	0.952509	+	0.304512i	$0.0984933\pi$
$757$	6.23048	+	27.2975i	0.226451	+	0.992145i	−0.726058	+	0.687634i	$0.758650\pi$
$758$	−1.20022	−	5.25850i	−0.0435939	−	0.190997i
$759$	−3.07188	+	3.85202i	−0.111502	+	0.139819i
$760$	19.7778	−	9.52447i	0.717415	−	0.345489i
$761$	6.91281	−	30.2870i	0.250589	−	1.09790i	−0.680395	−	0.732845i	$-0.738192\pi$
$761$	6.91281	−	30.2870i	0.250589	−	1.09790i	0.930985	−	0.365058i	$-0.118951\pi$
$762$	−0.293741	+	0.141458i	−0.0106411	+	0.00512449i
$763$	13.2585	+	16.6257i	0.479991	+	0.601890i
$764$	−2.84087	−	12.4467i	−0.102779	−	0.450305i
$765$	4.09783	+	5.13852i	0.148158	+	0.185784i
$766$	−2.91939	+	12.7907i	−0.105482	+	0.462146i
$767$	−5.36035			−0.193551
$768$	0.662955			0.0239223
$769$	2.36467	−	10.3603i	0.0852720	−	0.373601i	−0.914229	−	0.405199i	$-0.867202\pi$
$769$	2.36467	−	10.3603i	0.0852720	−	0.373601i	0.999501	+	0.0315975i	$0.0100595\pi$
$770$	−8.38239	+	10.5112i	−0.302080	+	0.378797i
$771$	−0.516689	−	0.248824i	−0.0186081	−	0.00896119i
$772$	−12.2600	+	5.90411i	−0.441248	+	0.212494i
$773$	−26.4359			−0.950835			−0.475417	−	0.879760i	$-0.657703\pi$
$773$	−26.4359			−0.950835			−0.475417	+	0.879760i	$0.657703\pi$
$774$	10.6703	−	1.49558i	0.383534	−	0.0537575i
$775$	−5.96077			−0.214117
$776$	−30.5606	+	14.7172i	−1.09706	+	0.528318i
$777$	5.19471	+	2.50164i	0.186359	+	0.0897459i
$778$	2.73109	−	3.42467i	0.0979142	−	0.122781i
$779$	9.25332	−	40.5414i	0.331534	−	1.45255i
$780$	−0.431041			−0.0154338
$781$	44.9530			1.60854
$782$	0.719169	−	3.15088i	0.0257174	−	0.112675i
$783$	−0.671211	−	0.841672i	−0.0239871	−	0.0300789i
$784$	0.236094	+	1.03440i	0.00843195	+	0.0369428i
$785$	9.61596	+	12.0580i	0.343208	+	0.430370i
$786$	0.704103	−	0.339078i	0.0251145	−	0.0120945i
$787$	3.70536	−	16.2342i	0.132082	−	0.578688i	−0.864961	−	0.501839i	$-0.832657\pi$
$787$	3.70536	−	16.2342i	0.132082	−	0.578688i	0.997043	−	0.0768489i	$-0.0244859\pi$
$788$	−29.5613	+	14.2360i	−1.05308	+	0.507135i
$789$	2.14556	−	2.69044i	0.0763838	−	0.0957823i
$790$	1.25906	+	5.51631i	0.0447954	+	0.196261i
$791$	−1.03989	−	4.55607i	−0.0369743	−	0.161995i
$792$	25.9121	+	12.4786i	0.920748	+	0.443409i
$793$	−3.16756	+	3.97200i	−0.112483	+	0.141050i
$794$	8.85421	+	11.1028i	0.314224	+	0.394025i
$795$	−2.76271	−	1.33045i	−0.0979832	−	0.0471862i
$796$	34.5480	+	16.6374i	1.22452	+	0.589699i
$797$	−4.61141	−	5.78252i	−0.163344	−	0.204827i	0.693423	−	0.720531i	$-0.256102\pi$
$797$	−4.61141	−	5.78252i	−0.163344	−	0.204827i	−0.856767	+	0.515704i	$0.827531\pi$
$798$	−0.937969	+	1.17618i	−0.0332037	+	0.0416362i
$799$	1.00000	+	0.481575i	0.0353775	+	0.0170369i
$800$	−1.18933	−	5.21081i	−0.0420493	−	0.184230i
$801$	−11.2101	−	49.1146i	−0.396089	−	1.73538i
$802$	3.01357	−	3.77890i	0.106413	−	0.133438i
$803$	54.1616	−	26.0828i	1.91132	−	0.920444i
$804$	−0.0348113	+	0.152518i	−0.00122770	+	0.00537891i
$805$	−24.1564	+	11.6331i	−0.851403	+	0.410014i
$806$	−1.32640	−	1.66325i	−0.0467203	−	0.0585854i
$807$	−0.620137	−	2.71700i	−0.0218299	−	0.0956429i
$808$	−4.84452	−	6.07483i	−0.170430	−	0.213712i
$809$	−5.68957	+	24.9276i	−0.200035	+	0.876409i	0.770879	+	0.636981i	$0.219817\pi$
$809$	−5.68957	+	24.9276i	−0.200035	+	0.876409i	−0.970914	+	0.239428i	$0.923040\pi$
$810$	9.59909			0.337278
$811$	−23.1166			−0.811734			−0.405867	−	0.913932i	$-0.633030\pi$
$811$	−23.1166			−0.811734			−0.405867	+	0.913932i	$0.633030\pi$
$812$	0.877174	−	3.84315i	0.0307828	−	0.134868i
$813$	0.264733	−	0.331965i	0.00928461	−	0.0116425i
$814$	−27.0085	−	13.0066i	−0.946647	−	0.455881i
$815$	1.75840	−	0.846799i	0.0615940	−	0.0296621i
$816$	−0.493959			−0.0172920
$817$	−2.98725	+	35.0003i	−0.104511	+	1.22450i
$818$	−7.35690			−0.257228
$819$	−4.38308	+	2.11078i	−0.153157	+	0.0737567i
$820$	23.6679	+	11.3978i	0.826517	+	0.398030i
$821$	−9.88972	+	12.4013i	−0.345153	+	0.432809i	−0.923862	−	0.382726i	$-0.874985\pi$
$821$	−9.88972	+	12.4013i	−0.345153	+	0.432809i	0.578709	+	0.815534i	$0.303557\pi$
$822$	−0.203571	+	0.891901i	−0.00710034	+	0.0311086i
$823$	−17.6209			−0.614225			−0.307112	−	0.951673i	$-0.599363\pi$
$823$	−17.6209			−0.614225			−0.307112	+	0.951673i	$0.599363\pi$
$824$	−12.1328			−0.422664
$825$	−0.208947	+	0.915458i	−0.00727461	+	0.0318722i
$826$	−7.36861	−	9.23994i	−0.256387	−	0.321499i
$827$	−6.37638	−	27.9367i	−0.221728	−	0.971456i	−0.956177	−	0.292791i	$-0.905416\pi$
$827$	−6.37638	−	27.9367i	−0.221728	−	0.971456i	0.734448	−	0.678665i	$-0.237441\pi$
$828$	16.3889	+	20.5510i	0.569553	+	0.714197i
$829$	12.5245	−	6.03146i	0.434992	−	0.209481i	−0.203555	−	0.979063i	$-0.565250\pi$
$829$	12.5245	−	6.03146i	0.434992	−	0.209481i	0.638548	+	0.769582i	$0.279535\pi$
$830$	−3.68532	+	16.1464i	−0.127919	+	0.560451i
$831$	−4.15064	+	1.99884i	−0.143984	+	0.0693390i
$832$	−0.612605	+	0.768182i	−0.0212382	+	0.0266319i
$833$	0.116621	+	0.510950i	0.00404068	+	0.0177034i
$834$	−0.147711	−	0.647166i	−0.00511483	−	0.0224095i
$835$	−10.1782	−	4.90157i	−0.352232	−	0.169626i
$836$	−26.7925	+	33.5967i	−0.926637	+	1.16197i
$837$	4.38769	+	5.50199i	0.151661	+	0.190177i
$838$	0.570688	+	0.274829i	0.0197141	+	0.00949380i
$839$	22.7162	+	10.9396i	0.784252	+	0.377676i	0.782760	−	0.622323i	$-0.213811\pi$
$839$	22.7162	+	10.9396i	0.784252	+	0.377676i	0.00149135	+	0.999999i	$0.499525\pi$
$840$	−1.29291	−	1.62126i	−0.0446097	−	0.0559388i
$841$	−17.5628	+	22.0230i	−0.605613	+	0.759415i
$842$	1.66607	+	0.802337i	0.0574166	+	0.0276504i
$843$	−0.781601	−	3.42442i	−0.0269198	−	0.117943i
$844$	−6.20924	−	27.2045i	−0.213731	−	0.936416i
$845$	15.6950	−	19.6809i	0.539925	−	0.677044i
$846$	1.48039	−	0.712916i	0.0508967	−	0.0245106i
$847$	6.52475	−	28.5868i	0.224193	−	0.982255i
$848$	−15.6712	+	7.54686i	−0.538152	+	0.259160i
$849$	−0.482779	−	0.605385i	−0.0165689	−	0.0207768i
$850$	−0.137063	−	0.600514i	−0.00470123	−	0.0205975i
$851$	−37.2739	−	46.7400i	−1.27773	−	1.60223i
$852$	−0.707087	+	3.09795i	−0.0242244	+	0.106134i
$853$	21.9135			0.750304			0.375152	−	0.926963i	$-0.377590\pi$
$853$	21.9135			0.750304			0.375152	+	0.926963i	$0.377590\pi$
$854$	−11.2010			−0.383292
$855$	−7.05861	+	30.9258i	−0.241399	+	1.05764i
$856$	2.51171	−	3.14959i	0.0858486	−	0.107651i
$857$	−12.5058	−	6.02248i	−0.427190	−	0.205724i	0.207919	−	0.978146i	$-0.433331\pi$
$857$	−12.5058	−	6.02248i	−0.427190	−	0.205724i	−0.635110	+	0.772422i	$0.719045\pi$
$858$	−0.301938	+	0.145406i	−0.0103080	+	0.00496406i
$859$	−31.4959			−1.07463			−0.537313	−	0.843383i	$-0.680561\pi$
$859$	−31.4959			−1.07463			−0.537313	+	0.843383i	$0.680561\pi$
$860$	−21.1360	−	6.75978i	−0.720732	−	0.230507i
$861$	−3.92825			−0.133874
$862$	10.1758	−	4.90039i	0.346588	−	0.166908i
$863$	43.9635	+	21.1717i	1.49654	+	0.720694i	0.989940	−	0.141490i	$-0.0451893\pi$
$863$	43.9635	+	21.1717i	1.49654	+	0.720694i	0.506596	+	0.862184i	$0.330904\pi$
$864$	−3.93429	+	4.93344i	−0.133847	+	0.167839i
$865$	−3.85086	+	16.8717i	−0.130933	+	0.573655i
$866$	−5.52914			−0.187888
$867$	3.12306			0.106065
$868$	−5.73407	+	25.1226i	−0.194627	+	0.852717i
$869$	−15.0688	−	18.8957i	−0.511175	−	0.640993i
$870$	−0.0446055	−	0.195429i	−0.00151227	−	0.00662568i
$871$	0.187177	+	0.234713i	0.00634226	+	0.00795294i
$872$	15.3644	−	7.39912i	0.520305	−	0.250566i
$873$	10.9070	−	47.7865i	0.369145	−	1.61733i
$874$	14.0538	−	6.76793i	0.475376	−	0.228929i
$875$	−19.1159	+	23.9706i	−0.646235	+	0.810353i
$876$	0.945574	+	4.14283i	0.0319480	+	0.139973i
$877$	−0.0886785	−	0.388526i	−0.00299446	−	0.0131196i	0.973409	−	0.229076i	$-0.0735703\pi$
$877$	−0.0886785	−	0.388526i	−0.00299446	−	0.0131196i	−0.976403	+	0.215956i	$0.930713\pi$
$878$	4.09365	+	1.97140i	0.138154	+	0.0665315i
$879$	3.46167	−	4.34080i	0.116759	−	0.146412i
$880$	−13.2838	−	16.6574i	−0.447797	−	0.561520i
$881$	−18.7087	−	9.00964i	−0.630312	−	0.303542i	0.0913171	−	0.995822i	$-0.470892\pi$
$881$	−18.7087	−	9.00964i	−0.630312	−	0.303542i	−0.721630	+	0.692279i	$0.756607\pi$
$882$	0.699022	+	0.336631i	0.0235373	+	0.0113350i
$883$	13.3327	+	16.7187i	0.448682	+	0.562630i	0.953808	−	0.300416i	$-0.0971255\pi$
$883$	13.3327	+	16.7187i	0.448682	+	0.562630i	−0.505126	+	0.863046i	$0.668554\pi$
$884$	−0.753020	+	0.944258i	−0.0253268	+	0.0317588i
$885$	2.97477	+	1.43257i	0.0999959	+	0.0481555i
$886$	3.75504	+	16.4519i	0.126153	+	0.552713i
$887$	8.87100	+	38.8664i	0.297859	+	1.30501i	0.873308	+	0.487168i	$0.161970\pi$
$887$	8.87100	+	38.8664i	0.297859	+	1.30501i	−0.575449	+	0.817838i	$0.695173\pi$
$888$	2.88285	−	3.61498i	0.0967420	−	0.121311i
$889$	6.82789	−	3.28814i	0.229000	−	0.110281i
$890$	4.20237	−	18.4118i	0.140864	−	0.617165i
$891$	−36.9415	+	17.7901i	−1.23759	+	0.595990i
$892$	1.58881	+	1.99230i	0.0531973	+	0.0667073i
$893$	1.19202	+	5.22259i	0.0398895	+	0.174767i
$894$	0.152497	+	0.191226i	0.00510027	+	0.00639554i
$895$	−0.887691	+	3.88923i	−0.0296722	+	0.130003i
$896$	−29.4778			−0.984785
$897$	−0.668332			−0.0223150
$898$	−2.74147	+	12.0112i	−0.0914841	+	0.400818i
$899$	−3.38889	+	4.24953i	−0.113026	+	0.141730i
$900$	4.51357	+	2.17362i	0.150452	+	0.0724541i
$901$	−7.74094	+	3.72784i	−0.257888	+	0.124192i
$902$	20.4239			0.680040
$903$	3.28621	−	0.460607i	0.109358	−	0.0153280i
$904$	−3.74764			−0.124645
$905$	−15.9584	+	7.68515i	−0.530474	+	0.255463i
$906$	−0.0489173	−	0.0235573i	−0.00162517	−	0.000782641i
$907$	2.43296	−	3.05084i	0.0807851	−	0.101301i	−0.739797	−	0.672831i	$-0.765078\pi$
$907$	2.43296	−	3.05084i	0.0807851	−	0.101301i	0.820582	+	0.571529i	$0.193650\pi$
$908$	−6.91268	+	30.2864i	−0.229405	+	1.00509i
$909$	11.2280			0.372409
$910$	−1.82371			−0.0604553
$911$	10.4956	−	45.9842i	0.347734	−	1.52352i	−0.434577	−	0.900635i	$-0.643102\pi$
$911$	10.4956	−	45.9842i	0.347734	−	1.52352i	0.782311	−	0.622888i	$-0.214041\pi$
$912$	−1.48643	−	1.86392i	−0.0492205	−	0.0617206i
$913$	−15.7416	−	68.9685i	−0.520971	−	2.28252i
$914$	−3.88172	−	4.86753i	−0.128396	−	0.161003i
$915$	2.81940	−	1.35775i	0.0932064	−	0.0448858i
$916$	2.32818	−	10.2004i	0.0769254	−	0.337032i
$917$	−16.3666	+	7.88173i	−0.540472	+	0.260278i
$918$	−0.453403	+	0.568549i	−0.0149645	+	0.0187649i
$919$	1.23168	+	5.39633i	0.0406293	+	0.178009i	0.991171	−	0.132587i	$-0.0423285\pi$
$919$	1.23168	+	5.39633i	0.0406293	+	0.178009i	−0.950542	+	0.310596i	$0.899471\pi$
$920$	4.78448	+	20.9622i	0.157740	+	0.691102i
$921$	−0.113032	−	0.0544332i	−0.00372452	−	0.00179363i
$922$	11.9532	−	14.9889i	0.393659	−	0.493633i
$923$	3.80194	+	4.76748i	0.125142	+	0.156923i
$924$	3.65734	+	1.76128i	0.120318	+	0.0579420i
$925$	−10.2654	−	4.94355i	−0.337524	−	0.162543i
$926$	−3.52260	−	4.41720i	−0.115760	−	0.145158i
$927$	10.9312	−	13.7073i	0.359029	−	0.450208i
$928$	−4.39104	−	2.11461i	−0.144143	−	0.0694156i
$929$	7.55549	+	33.1028i	0.247888	+	1.08607i	0.933635	+	0.358227i	$0.116618\pi$
$929$	7.55549	+	33.1028i	0.247888	+	1.08607i	−0.685747	+	0.727840i	$0.740524\pi$
$930$	0.291585	+	1.27752i	0.00956145	+	0.0418915i
$931$	−1.57710	+	1.97762i	−0.0516873	+	0.0648138i
$932$	6.73945	−	3.24555i	0.220758	−	0.106311i
$933$	−1.11798	+	4.89820i	−0.0366011	+	0.160360i
$934$	7.48911	−	3.60657i	0.245051	−	0.118010i
$935$	−6.56166	−	8.22807i	−0.214589	−	0.269087i
$936$	0.868123	+	3.80350i	0.0283755	+	0.124321i
$937$	5.74094	+	7.19891i	0.187548	+	0.235178i	0.866712	−	0.498808i	$-0.166229\pi$
$937$	5.74094	+	7.19891i	0.187548	+	0.235178i	−0.679164	+	0.733987i	$0.737657\pi$
$938$	−0.147284	+	0.645296i	−0.00480901	+	0.0210696i
$939$	−2.96030			−0.0966057
$940$	−3.38404			−0.110375
$941$	8.68515	−	38.0521i	0.283128	−	1.24046i	−0.610631	−	0.791916i	$-0.709084\pi$
$941$	8.68515	−	38.0521i	0.283128	−	1.24046i	0.893758	−	0.448549i	$-0.148059\pi$
$942$	−0.528475	+	0.662687i	−0.0172186	+	0.0215915i
$943$	36.6972	+	17.6724i	1.19502	+	0.575493i
$944$	16.8741	−	8.12615i	0.549206	−	0.264484i
$945$	6.03279			0.196247
$946$	−17.0858	+	2.39480i	−0.555506	+	0.0778617i
$947$	18.4166			0.598458			0.299229	−	0.954181i	$-0.403271\pi$
$947$	18.4166			0.598458			0.299229	+	0.954181i	$0.403271\pi$
$948$	1.53923	−	0.741253i	0.0499918	−	0.0240748i
$949$	7.34697	+	3.53811i	0.238493	+	0.114852i
$950$	1.85354	−	2.32427i	0.0601369	−	0.0754093i
$951$	−0.213555	+	0.935645i	−0.00692499	+	0.0303404i
$952$	−5.81030			−0.188313
$953$	9.60819			0.311240			0.155620	−	0.987817i	$-0.450263\pi$
$953$	9.60819			0.311240			0.155620	+	0.987817i	$0.450263\pi$
$954$	−2.83028	+	12.4003i	−0.0916337	+	0.401474i
$955$	9.40880	+	11.7983i	0.304462	+	0.381783i
$956$	−3.93429	−	17.2372i	−0.127244	−	0.557492i
$957$	0.533852	+	0.669429i	0.0172570	+	0.0216396i
$958$	14.5286	−	6.99662i	0.469399	−	0.226051i
$959$	4.73191	−	20.7319i	0.152801	−	0.669467i
$960$	0.545269	−	0.262588i	0.0175985	−	0.00847499i
$961$	2.82490	−	3.54232i	0.0911260	−	0.114268i
$962$	−0.904854	−	3.96442i	−0.0291737	−	0.127818i
$963$	1.29536	+	5.67536i	0.0417425	+	0.182886i
$964$	37.0447	+	17.8398i	1.19313	+	0.574580i
$965$	10.0285	−	12.5753i	0.322828	−	0.404814i
$966$	−0.918723	−	1.15204i	−0.0295594	−	0.0370663i
$967$	52.9080	+	25.4792i	1.70141	+	0.819355i	0.993601	+	0.112948i	$0.0360295\pi$
$967$	52.9080	+	25.4792i	1.70141	+	0.819355i	0.707807	+	0.706406i	$0.249685\pi$
$968$	−21.1857	−	10.2025i	−0.680936	−	0.327921i
$969$	−0.734234	−	0.920700i	−0.0235870	−	0.0295772i
$970$	11.4564	−	14.3659i	0.367842	−	0.461260i
$971$	41.5245	+	19.9972i	1.33259	+	0.641739i	0.958350	−	0.285595i	$-0.0921912\pi$
$971$	41.5245	+	19.9972i	1.33259	+	0.641739i	0.374235	+	0.927334i	$0.377905\pi$
$972$	−1.97847	−	8.66823i	−0.0634593	−	0.278034i
$973$	3.43349	+	15.0431i	0.110073	+	0.482260i
$974$	8.26308	−	10.3616i	0.264766	−	0.332006i
$975$	−0.114761	+	0.0552658i	−0.00367528	+	0.00176992i
$976$	3.94989	−	17.3056i	0.126433	−	0.553938i
$977$	−10.6281	+	5.11822i	−0.340023	+	0.163746i	−0.596101	−	0.802910i	$-0.703284\pi$
$977$	−10.6281	+	5.11822i	−0.340023	+	0.163746i	0.256078	+	0.966656i	$0.417570\pi$
$978$	0.0668757	+	0.0838595i	0.00213845	+	0.00268153i
$979$	17.9502	+	78.6449i	0.573690	+	2.51350i
$980$	−0.996279	−	1.24929i	−0.0318250	−	0.0399072i
$981$	−5.48350	+	24.0248i	−0.175075	+	0.767052i
$982$	0.374945			0.0119650
$983$	−1.78581			−0.0569584			−0.0284792	−	0.999594i	$-0.509066\pi$
$983$	−1.78581			−0.0569584			−0.0284792	+	0.999594i	$0.509066\pi$
$984$	−0.700988	+	3.07123i	−0.0223467	+	0.0979072i
$985$	24.1806	−	30.3215i	0.770458	−	0.966124i
$986$	−0.506041	−	0.243696i	−0.0161156	−	0.00776087i
$987$	0.455927	−	0.219563i	0.0145123	−	0.00698876i
$988$	−5.82908			−0.185448
$989$	−32.7715	−	10.4811i	−1.04207	−	0.333279i
$990$	−15.5797			−0.495156
$991$	−43.2766	+	20.8409i	−1.37473	+	0.662033i	−0.967868	−	0.251458i	$-0.919090\pi$
$991$	−43.2766	+	20.8409i	−1.37473	+	0.662033i	−0.406858	+	0.913492i	$0.633376\pi$
$992$	28.7042	+	13.8232i	0.911358	+	0.438887i
$993$	−1.52475	+	1.91198i	−0.0483866	+	0.0606749i
$994$	−2.99164	+	13.1072i	−0.0948890	+	0.415736i
$995$	−45.3250			−1.43690
$996$	5.00059			0.158450
$997$	−2.03093	+	8.89807i	−0.0643201	+	0.281805i	−0.996852	−	0.0792823i	$-0.974737\pi$
$997$	−2.03093	+	8.89807i	−0.0643201	+	0.281805i	0.932532	+	0.361087i	$0.117594\pi$
$998$	−11.1396	−	13.9686i	−0.352617	−	0.442168i
$999$	2.99324	+	13.1142i	0.0947018	+	0.414916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.e.b.41.1	yes	6
3.2	odd	2		387.2.u.a.127.1		6
4.3	odd	2		688.2.u.c.385.1		6
43.8	odd	14		1849.2.a.l.1.2		3
43.21	even	7	inner	43.2.e.b.21.1	✓	6
43.35	even	7		1849.2.a.i.1.2		3
129.107	odd	14		387.2.u.a.64.1		6
172.107	odd	14		688.2.u.c.193.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.e.b.21.1	✓	6	43.21	even	7	inner
43.2.e.b.41.1	yes	6	1.1	even	1	trivial
387.2.u.a.64.1		6	129.107	odd	14
387.2.u.a.127.1		6	3.2	odd	2
688.2.u.c.193.1		6	172.107	odd	14
688.2.u.c.385.1		6	4.3	odd	2
1849.2.a.i.1.2		3	43.35	even	7
1849.2.a.l.1.2		3	43.8	odd	14

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.240787i) q^{2} +(0.178448 + 0.0859360i) q^{3} +(-1.05496 + 1.32288i) q^{4} +(0.445042 - 1.94986i) q^{5} +0.109916 q^{6} -2.55496 q^{7} +(-0.455927 + 1.99755i) q^{8} +(-1.84601 - 2.31482i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.240787i) q^{2} +(0.178448 + 0.0859360i) q^{3} +(-1.05496 + 1.32288i) q^{4} +(0.445042 - 1.94986i) q^{5} +0.109916 q^{6} -2.55496 q^{7} +(-0.455927 + 1.99755i) q^{8} +(-1.84601 - 2.31482i) q^{9} +(-0.246980 - 1.08209i) q^{10} +(2.95593 + 3.70662i) q^{11} +(-0.301938 + 0.145406i) q^{12} +(-0.143104 + 0.626980i) q^{13} +(-1.27748 + 0.615201i) q^{14} +(0.246980 - 0.309703i) q^{15} +(-0.500000 - 2.19064i) q^{16} +(-0.246980 - 1.08209i) q^{17} +(-1.48039 - 0.712916i) q^{18} +(3.33997 - 4.18819i) q^{19} +(2.10992 + 2.64575i) q^{20} +(-0.455927 - 0.219563i) q^{21} +(2.37047 + 1.14156i) q^{22} +(3.27144 + 4.10225i) q^{23} +(-0.253020 + 0.317278i) q^{24} +(0.900969 + 0.433884i) q^{25} +(0.0794168 + 0.347948i) q^{26} +(-0.262709 - 1.15100i) q^{27} +(2.69537 - 3.37989i) q^{28} +(0.821552 - 0.395639i) q^{29} +(0.0489173 - 0.214321i) q^{30} +(-5.37047 + 2.58628i) q^{31} +(-3.33244 - 4.17874i) q^{32} +(0.208947 + 0.915458i) q^{33} +(-0.384043 - 0.481575i) q^{34} +(-1.13706 + 4.98180i) q^{35} +5.00969 q^{36} -11.3937 q^{37} +(0.661522 - 2.89832i) q^{38} +(-0.0794168 + 0.0995855i) q^{39} +(3.69202 + 1.77798i) q^{40} +(6.99396 - 3.36811i) q^{41} -0.280831 q^{42} +(-5.45593 + 3.63770i) q^{43} -8.02177 q^{44} +(-5.33513 + 2.56926i) q^{45} +(2.62349 + 1.26341i) q^{46} +(-0.623490 + 0.781831i) q^{47} +(0.0990311 - 0.433884i) q^{48} -0.472189 q^{49} +0.554958 q^{50} +(0.0489173 - 0.214321i) q^{51} +(-0.678448 - 0.850747i) q^{52} +(-1.72252 - 7.54686i) q^{53} +(-0.408502 - 0.512245i) q^{54} +(8.54288 - 4.11403i) q^{55} +(1.16487 - 5.10365i) q^{56} +(0.955927 - 0.460350i) q^{57} +(0.315511 - 0.395639i) q^{58} +(1.85474 + 8.12615i) q^{59} +(0.149145 + 0.653447i) q^{60} +(7.11745 + 3.42758i) q^{61} +(-2.06249 + 2.58628i) q^{62} +(4.71648 + 5.91428i) q^{63} +(1.37651 + 0.662892i) q^{64} +(1.15883 + 0.558065i) q^{65} +(0.324904 + 0.407417i) q^{66} +(0.291053 - 0.364968i) q^{67} +(1.69202 + 0.814835i) q^{68} +(0.231250 + 1.01317i) q^{69} +(0.631023 + 2.76469i) q^{70} +(5.91185 - 7.41323i) q^{71} +(5.46562 - 2.63210i) q^{72} +(2.82155 - 12.3620i) q^{73} +(-5.69687 + 2.74347i) q^{74} +(0.123490 + 0.154851i) q^{75} +(2.01693 + 8.83673i) q^{76} +(-7.55227 - 9.47025i) q^{77} +(-0.0157295 + 0.0689153i) q^{78} -5.09783 q^{79} -4.49396 q^{80} +(-1.92447 + 8.43165i) q^{81} +(2.68598 - 3.36811i) q^{82} +(-13.4438 - 6.47421i) q^{83} +(0.771438 - 0.371505i) q^{84} -2.21983 q^{85} +(-1.85205 + 3.13257i) q^{86} +0.180604 q^{87} +(-8.75182 + 4.21466i) q^{88} +(15.3300 + 7.38256i) q^{89} +(-2.04892 + 2.56926i) q^{90} +(0.365625 - 1.60191i) q^{91} -8.87800 q^{92} -1.18060 q^{93} +(-0.123490 + 0.541044i) q^{94} +(-6.67994 - 8.37638i) q^{95} +(-0.235562 - 1.03206i) q^{96} +(10.3218 + 12.9432i) q^{97} +(-0.236094 + 0.113697i) q^{98} +(3.12349 - 13.6849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} - 7 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{7} + q^{8} - 6 q^{9} + 8 q^{10} + 14 q^{11} + 7 q^{12} - 9 q^{13} - 8 q^{14} - 8 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 14 q^{20} + q^{21} + q^{23} - 11 q^{24} + q^{25} - 8 q^{26} + 33 q^{27} + 28 q^{28} + 9 q^{29} - 18 q^{30} - 18 q^{31} - 21 q^{32} + 7 q^{33} + 18 q^{34} + 4 q^{35} - 14 q^{36} - 4 q^{37} - 16 q^{38} + 8 q^{39} + 12 q^{40} + 23 q^{41} - 24 q^{42} - 29 q^{43} - 42 q^{44} - 30 q^{45} + 11 q^{46} + q^{47} + 5 q^{48} + 10 q^{49} + 4 q^{50} - 18 q^{51} - 10 q^{53} + 27 q^{54} + 14 q^{55} + 9 q^{56} + 2 q^{57} - 13 q^{58} + 22 q^{59} + 28 q^{60} + 19 q^{61} + 12 q^{62} + 9 q^{63} + 13 q^{64} - 10 q^{65} + 28 q^{66} - 4 q^{67} + 17 q^{69} - 26 q^{70} + 28 q^{71} - 15 q^{72} + 21 q^{73} - 2 q^{74} - 4 q^{75} + 28 q^{76} - 49 q^{77} + 25 q^{78} + 6 q^{79} - 8 q^{80} - 58 q^{81} - 13 q^{82} - 39 q^{83} - 14 q^{84} - 16 q^{85} - 25 q^{86} - 22 q^{87} - 21 q^{88} + 11 q^{89} + 6 q^{90} + 10 q^{91} - 14 q^{92} + 16 q^{93} + 4 q^{94} + 8 q^{95} + 21 q^{96} - 19 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 7 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^7 + q^8 - 6 * q^9 + 8 * q^10 + 14 * q^11 + 7 * q^12 - 9 * q^13 - 8 * q^14 - 8 * q^15 - 3 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 14 * q^20 + q^21 + q^23 - 11 * q^24 + q^25 - 8 * q^26 + 33 * q^27 + 28 * q^28 + 9 * q^29 - 18 * q^30 - 18 * q^31 - 21 * q^32 + 7 * q^33 + 18 * q^34 + 4 * q^35 - 14 * q^36 - 4 * q^37 - 16 * q^38 + 8 * q^39 + 12 * q^40 + 23 * q^41 - 24 * q^42 - 29 * q^43 - 42 * q^44 - 30 * q^45 + 11 * q^46 + q^47 + 5 * q^48 + 10 * q^49 + 4 * q^50 - 18 * q^51 - 10 * q^53 + 27 * q^54 + 14 * q^55 + 9 * q^56 + 2 * q^57 - 13 * q^58 + 22 * q^59 + 28 * q^60 + 19 * q^61 + 12 * q^62 + 9 * q^63 + 13 * q^64 - 10 * q^65 + 28 * q^66 - 4 * q^67 + 17 * q^69 - 26 * q^70 + 28 * q^71 - 15 * q^72 + 21 * q^73 - 2 * q^74 - 4 * q^75 + 28 * q^76 - 49 * q^77 + 25 * q^78 + 6 * q^79 - 8 * q^80 - 58 * q^81 - 13 * q^82 - 39 * q^83 - 14 * q^84 - 16 * q^85 - 25 * q^86 - 22 * q^87 - 21 * q^88 + 11 * q^89 + 6 * q^90 + 10 * q^91 - 14 * q^92 + 16 * q^93 + 4 * q^94 + 8 * q^95 + 21 * q^96 - 19 * q^97 + 5 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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