LMFDB - Embedded newform 570.2.u.e.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.271
Dual form			570.2.u.e.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.439693 - 0.761570i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.439693 - 0.761570i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.939693 + 0.342020i) q^{10} +(-0.266044 + 0.460802i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.141559 + 0.802823i) q^{13} +(0.673648 + 0.565258i) q^{14} +(0.766044 - 0.642788i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-5.08512 + 1.85083i) q^{17} +1.00000 q^{18} +(-3.37939 - 2.75314i) q^{19} -1.00000 q^{20} +(0.826352 - 0.300767i) q^{21} +(0.0923963 - 0.524005i) q^{22} +(-4.02094 + 3.37397i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(0.173648 + 0.984808i) q^{25} +(-0.407604 - 0.705990i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.826352 - 0.300767i) q^{28} +(-5.14543 - 1.87278i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-1.29813 - 2.24843i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.407604 - 0.342020i) q^{33} +(4.14543 - 3.47843i) q^{34} +(-0.152704 + 0.866025i) q^{35} +(-0.939693 + 0.342020i) q^{36} +2.53209 q^{37} +(4.11721 + 1.43128i) q^{38} -0.815207 q^{39} +(0.939693 - 0.342020i) q^{40} +(0.354570 - 2.01087i) q^{41} +(-0.673648 + 0.565258i) q^{42} +(-1.31521 - 1.10359i) q^{43} +(0.0923963 + 0.524005i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.62449 - 4.54574i) q^{46} +(-8.69119 - 3.16333i) q^{47} +(0.939693 + 0.342020i) q^{48} +(3.11334 - 5.39246i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.939693 - 5.32926i) q^{51} +(0.624485 + 0.524005i) q^{52} +(-2.17365 + 1.82391i) q^{53} +(-0.173648 + 0.984808i) q^{54} +(0.500000 - 0.181985i) q^{55} +0.879385 q^{56} +(3.29813 - 2.84997i) q^{57} +5.47565 q^{58} +(-0.152704 + 0.0555796i) q^{59} +(0.173648 - 0.984808i) q^{60} +(1.08125 - 0.907278i) q^{61} +(1.98886 + 1.66885i) q^{62} +(0.152704 + 0.866025i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.407604 - 0.705990i) q^{65} +(0.500000 + 0.181985i) q^{66} +(-10.9966 - 4.00243i) q^{67} +(-2.70574 + 4.68647i) q^{68} +(-2.62449 - 4.54574i) q^{69} +(-0.152704 - 0.866025i) q^{70} +(-5.88326 - 4.93664i) q^{71} +(0.766044 - 0.642788i) q^{72} +(-1.87686 + 10.6442i) q^{73} +(-2.37939 + 0.866025i) q^{74} -1.00000 q^{75} +(-4.35844 + 0.0632028i) q^{76} +0.467911 q^{77} +(0.766044 - 0.278817i) q^{78} +(0.843426 - 4.78331i) q^{79} +(-0.766044 + 0.642788i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.354570 + 2.01087i) q^{82} +(7.02869 + 12.1740i) q^{83} +(0.439693 - 0.761570i) q^{84} +(5.08512 + 1.85083i) q^{85} +(1.61334 + 0.587208i) q^{86} +(2.73783 - 4.74205i) q^{87} +(-0.266044 - 0.460802i) q^{88} +(-0.699340 - 3.96616i) q^{89} +(-0.766044 - 0.642788i) q^{90} +(0.549163 - 0.460802i) q^{91} +(-0.911474 + 5.16923i) q^{92} +(2.43969 - 0.887975i) q^{93} +9.24897 q^{94} +(0.819078 + 4.28125i) q^{95} -1.00000 q^{96} +(6.88326 - 2.50530i) q^{97} +(-1.08125 + 6.13208i) q^{98} +(0.407604 - 0.342020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 - 3 * q^8	$ 6 q + 3 q^{7} - 3 q^{8} + 3 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 9 q^{17} + 6 q^{18} - 9 q^{19} - 6 q^{20} + 6 q^{21} - 3 q^{22} - 21 q^{23} - 6 q^{26} + 3 q^{27} - 6 q^{28} - 15 q^{29} - 3 q^{30} + 6 q^{31} - 6 q^{33} + 9 q^{34} - 3 q^{35} + 6 q^{37} - 6 q^{38} - 12 q^{39} + 18 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} + 3 q^{45} + 3 q^{46} - 6 q^{47} + 12 q^{49} - 3 q^{50} - 9 q^{52} - 12 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{57} - 6 q^{58} - 3 q^{59} + 9 q^{61} + 18 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} - 3 q^{70} - 15 q^{73} - 3 q^{74} - 6 q^{75} - 18 q^{76} + 12 q^{77} + 27 q^{79} + 18 q^{82} - 9 q^{83} - 3 q^{84} + 9 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 33 q^{89} + 15 q^{91} + 15 q^{92} + 9 q^{93} + 30 q^{94} - 12 q^{95} - 6 q^{96} + 6 q^{97} - 9 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^7 - 3 * q^8 + 3 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 9 * q^17 + 6 * q^18 - 9 * q^19 - 6 * q^20 + 6 * q^21 - 3 * q^22 - 21 * q^23 - 6 * q^26 + 3 * q^27 - 6 * q^28 - 15 * q^29 - 3 * q^30 + 6 * q^31 - 6 * q^33 + 9 * q^34 - 3 * q^35 + 6 * q^37 - 6 * q^38 - 12 * q^39 + 18 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 + 3 * q^46 - 6 * q^47 + 12 * q^49 - 3 * q^50 - 9 * q^52 - 12 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^57 - 6 * q^58 - 3 * q^59 + 9 * q^61 + 18 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 - 3 * q^70 - 15 * q^73 - 3 * q^74 - 6 * q^75 - 18 * q^76 + 12 * q^77 + 27 * q^79 + 18 * q^82 - 9 * q^83 - 3 * q^84 + 9 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 33 * q^89 + 15 * q^91 + 15 * q^92 + 9 * q^93 + 30 * q^94 - 12 * q^95 - 6 * q^96 + 6 * q^97 - 9 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	−0.439693	−	0.761570i	−0.166188	−	0.287846i	0.770888	−	0.636970i	$-0.219813\pi$
$7$	−0.439693	−	0.761570i	−0.166188	−	0.287846i	−0.937077	+	0.349124i	$0.886479\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	0.939693	+	0.342020i	0.297157	+	0.108156i
$11$	−0.266044	+	0.460802i	−0.0802154	+	0.138937i	−0.903342	−	0.428920i	$-0.858894\pi$
$11$	−0.266044	+	0.460802i	−0.0802154	+	0.138937i	0.823127	+	0.567857i	$0.192227\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.141559	+	0.802823i	0.0392615	+	0.222663i	0.998125	−	0.0612035i	$-0.0194939\pi$
$13$	0.141559	+	0.802823i	0.0392615	+	0.222663i	−0.958864	+	0.283866i	$0.908383\pi$
$14$	0.673648	+	0.565258i	0.180040	+	0.151072i
$15$	0.766044	−	0.642788i	0.197792	−	0.165967i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−5.08512	+	1.85083i	−1.23332	+	0.448893i	−0.874734	−	0.484603i	$-0.838964\pi$
$17$	−5.08512	+	1.85083i	−1.23332	+	0.448893i	−0.358589	+	0.933496i	$0.616742\pi$
$18$	1.00000			0.235702
$19$	−3.37939	−	2.75314i	−0.775284	−	0.631613i
$19$	−3.37939	−	2.75314i	−0.775284	−	0.631613i
$20$	−1.00000			−0.223607
$21$	0.826352	−	0.300767i	0.180325	−	0.0656328i
$22$	0.0923963	−	0.524005i	0.0196989	−	0.111718i
$23$	−4.02094	+	3.37397i	−0.838425	+	0.703522i	−0.957209	−	0.289398i	$-0.906545\pi$
$23$	−4.02094	+	3.37397i	−0.838425	+	0.703522i	0.118784	+	0.992920i	$0.462100\pi$
$24$	−0.766044	−	0.642788i	−0.156368	−	0.131208i
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	−0.407604	−	0.705990i	−0.0799377	−	0.138456i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.826352	−	0.300767i	−0.156166	−	0.0568397i
$29$	−5.14543	−	1.87278i	−0.955482	−	0.347767i	−0.183221	−	0.983072i	$-0.558652\pi$
$29$	−5.14543	−	1.87278i	−0.955482	−	0.347767i	−0.772262	+	0.635305i	$0.780875\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−1.29813	−	2.24843i	−0.233152	−	0.403830i	0.725582	−	0.688135i	$-0.241571\pi$
$31$	−1.29813	−	2.24843i	−0.233152	−	0.403830i	−0.958734	+	0.284305i	$0.908237\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.407604	−	0.342020i	−0.0709547	−	0.0595381i
$34$	4.14543	−	3.47843i	0.710935	−	0.596546i
$35$	−0.152704	+	0.866025i	−0.0258116	+	0.146385i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	2.53209			0.416273			0.208136	−	0.978100i	$-0.433260\pi$
$37$	2.53209			0.416273			0.208136	+	0.978100i	$0.433260\pi$
$38$	4.11721	+	1.43128i	0.667900	+	0.232185i
$39$	−0.815207			−0.130538
$40$	0.939693	−	0.342020i	0.148578	−	0.0540781i
$41$	0.354570	−	2.01087i	0.0553746	−	0.314045i	−0.944522	−	0.328449i	$-0.893474\pi$
$41$	0.354570	−	2.01087i	0.0553746	−	0.314045i	0.999896	+	0.0144042i	$0.00458517\pi$
$42$	−0.673648	+	0.565258i	−0.103946	+	0.0872212i
$43$	−1.31521	−	1.10359i	−0.200567	−	0.168296i	0.536972	−	0.843600i	$-0.319568\pi$
$43$	−1.31521	−	1.10359i	−0.200567	−	0.168296i	−0.737539	+	0.675304i	$0.764012\pi$
$44$	0.0923963	+	0.524005i	0.0139293	+	0.0789968i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	2.62449	−	4.54574i	0.386959	−	0.670233i
$47$	−8.69119	−	3.16333i	−1.26774	−	0.461420i	−0.381381	−	0.924418i	$-0.624551\pi$
$47$	−8.69119	−	3.16333i	−1.26774	−	0.461420i	−0.886359	+	0.462998i	$0.846774\pi$
$48$	0.939693	+	0.342020i	0.135633	+	0.0493664i
$49$	3.11334	−	5.39246i	0.444763	−	0.770352i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.939693	−	5.32926i	−0.131583	−	0.746246i
$52$	0.624485	+	0.524005i	0.0866005	+	0.0726665i
$53$	−2.17365	+	1.82391i	−0.298574	+	0.250533i	−0.779750	−	0.626091i	$-0.784654\pi$
$53$	−2.17365	+	1.82391i	−0.298574	+	0.250533i	0.481177	+	0.876624i	$0.340210\pi$
$54$	−0.173648	+	0.984808i	−0.0236305	+	0.134015i
$55$	0.500000	−	0.181985i	0.0674200	−	0.0245389i
$56$	0.879385			0.117513
$57$	3.29813	−	2.84997i	0.436848	−	0.377487i
$58$	5.47565			0.718988
$59$	−0.152704	+	0.0555796i	−0.0198803	+	0.00723585i	−0.351941	−	0.936022i	$-0.614478\pi$
$59$	−0.152704	+	0.0555796i	−0.0198803	+	0.00723585i	0.332061	+	0.943258i	$0.392256\pi$
$60$	0.173648	−	0.984808i	0.0224179	−	0.127138i
$61$	1.08125	−	0.907278i	0.138440	−	0.116165i	−0.570938	−	0.820993i	$-0.693420\pi$
$61$	1.08125	−	0.907278i	0.138440	−	0.116165i	0.709378	+	0.704828i	$0.248976\pi$
$62$	1.98886	+	1.66885i	0.252585	+	0.211944i
$63$	0.152704	+	0.866025i	0.0192389	+	0.109109i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.407604	−	0.705990i	0.0505570	−	0.0875673i
$66$	0.500000	+	0.181985i	0.0615457	+	0.0224008i
$67$	−10.9966	−	4.00243i	−1.34345	−	0.488975i	−0.432551	−	0.901609i	$-0.642387\pi$
$67$	−10.9966	−	4.00243i	−1.34345	−	0.488975i	−0.910897	+	0.412634i	$0.864609\pi$
$68$	−2.70574	+	4.68647i	−0.328119	+	0.568318i
$69$	−2.62449	−	4.54574i	−0.315951	−	0.547243i
$70$	−0.152704	−	0.866025i	−0.0182516	−	0.103510i
$71$	−5.88326	−	4.93664i	−0.698214	−	0.585871i	0.223051	−	0.974807i	$-0.428398\pi$
$71$	−5.88326	−	4.93664i	−0.698214	−	0.585871i	−0.921265	+	0.388936i	$0.872843\pi$
$72$	0.766044	−	0.642788i	0.0902792	−	0.0757532i
$73$	−1.87686	+	10.6442i	−0.219670	+	1.24581i	0.652947	+	0.757404i	$0.273532\pi$
$73$	−1.87686	+	10.6442i	−0.219670	+	1.24581i	−0.872617	+	0.488405i	$0.837579\pi$
$74$	−2.37939	+	0.866025i	−0.276598	+	0.100673i
$75$	−1.00000			−0.115470
$76$	−4.35844	+	0.0632028i	−0.499947	+	0.00724985i
$77$	0.467911			0.0533234
$78$	0.766044	−	0.278817i	0.0867375	−	0.0315699i
$79$	0.843426	−	4.78331i	0.0948928	−	0.538164i	−0.899887	−	0.436122i	$-0.856351\pi$
$79$	0.843426	−	4.78331i	0.0948928	−	0.538164i	0.994780	−	0.102042i	$-0.0325375\pi$
$80$	−0.766044	+	0.642788i	−0.0856464	+	0.0718658i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	0.354570	+	2.01087i	0.0391557	+	0.222063i
$83$	7.02869	+	12.1740i	0.771498	+	1.33627i	0.936742	+	0.350022i	$0.113826\pi$
$83$	7.02869	+	12.1740i	0.771498	+	1.33627i	−0.165243	+	0.986253i	$0.552841\pi$
$84$	0.439693	−	0.761570i	0.0479744	−	0.0830941i
$85$	5.08512	+	1.85083i	0.551559	+	0.200751i
$86$	1.61334	+	0.587208i	0.173971	+	0.0633203i
$87$	2.73783	−	4.74205i	0.293526	−	0.508402i
$88$	−0.266044	−	0.460802i	−0.0283604	−	0.0491217i
$89$	−0.699340	−	3.96616i	−0.0741299	−	0.420412i	−0.999177	−	0.0405596i	$-0.987086\pi$
$89$	−0.699340	−	3.96616i	−0.0741299	−	0.420412i	0.925047	−	0.379852i	$-0.124025\pi$
$90$	−0.766044	−	0.642788i	−0.0807482	−	0.0677558i
$91$	0.549163	−	0.460802i	0.0575679	−	0.0483052i
$92$	−0.911474	+	5.16923i	−0.0950277	+	0.538929i
$93$	2.43969	−	0.887975i	0.252984	−	0.0920788i
$94$	9.24897			0.953958
$95$	0.819078	+	4.28125i	0.0840356	+	0.439247i
$96$	−1.00000			−0.102062
$97$	6.88326	−	2.50530i	0.698889	−	0.254375i	0.0319524	−	0.999489i	$-0.489828\pi$
$97$	6.88326	−	2.50530i	0.698889	−	0.254375i	0.666936	+	0.745115i	$0.267605\pi$
$98$	−1.08125	+	6.13208i	−0.109223	+	0.619434i
$99$	0.407604	−	0.342020i	0.0409657	−	0.0343743i
$100$	0.766044	+	0.642788i	0.0766044	+	0.0642788i
$101$	0.975185	+	5.53055i	0.0970345	+	0.550310i	0.994105	+	0.108423i	$0.0345799\pi$
$101$	0.975185	+	5.53055i	0.0970345	+	0.550310i	−0.897070	+	0.441888i	$0.854309\pi$
$102$	2.70574	+	4.68647i	0.267908	+	0.464030i
$103$	−8.24763	+	14.2853i	−0.812663	+	1.40757i	0.0983313	+	0.995154i	$0.468650\pi$
$103$	−8.24763	+	14.2853i	−0.812663	+	1.40757i	−0.910994	+	0.412419i	$0.864684\pi$
$104$	−0.766044	−	0.278817i	−0.0751168	−	0.0273403i
$105$	−0.826352	−	0.300767i	−0.0806437	−	0.0293519i
$106$	1.41875	−	2.45734i	0.137801	−	0.238678i
$107$	−1.51114	−	2.61738i	−0.146088	−	0.253032i	0.783690	−	0.621152i	$-0.213335\pi$
$107$	−1.51114	−	2.61738i	−0.146088	−	0.253032i	−0.929778	+	0.368120i	$0.880002\pi$
$108$	−0.173648	−	0.984808i	−0.0167093	−	0.0947632i
$109$	−1.28106	−	1.07494i	−0.122703	−	0.102960i	0.579371	−	0.815064i	$-0.303298\pi$
$109$	−1.28106	−	1.07494i	−0.122703	−	0.102960i	−0.702074	+	0.712104i	$0.747743\pi$
$110$	−0.407604	+	0.342020i	−0.0388635	+	0.0326103i
$111$	−0.439693	+	2.49362i	−0.0417338	+	0.236684i
$112$	−0.826352	+	0.300767i	−0.0780829	+	0.0284199i
$113$	14.6655			1.37961			0.689807	−	0.723993i	$-0.257695\pi$
$113$	14.6655			1.37961			0.689807	+	0.723993i	$0.257695\pi$
$114$	−2.12449	+	3.80612i	−0.198976	+	0.356476i
$115$	5.24897			0.489469
$116$	−5.14543	+	1.87278i	−0.477741	+	0.173884i
$117$	0.141559	−	0.802823i	0.0130872	−	0.0742210i
$118$	0.124485	−	0.104455i	0.0114598	−	0.00961590i
$119$	3.64543	+	3.05888i	0.334176	+	0.280407i
$120$	0.173648	+	0.984808i	0.0158518	+	0.0899002i
$121$	5.35844	+	9.28109i	0.487131	+	0.843736i
$122$	−0.705737	+	1.22237i	−0.0638944	+	0.110668i
$123$	1.91875	+	0.698367i	0.173008	+	0.0629696i
$124$	−2.43969	−	0.887975i	−0.219091	−	0.0797426i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−0.439693	−	0.761570i	−0.0391709	−	0.0678460i
$127$	−0.407604	−	2.31164i	−0.0361690	−	0.205124i	0.961368	−	0.275266i	$-0.0887660\pi$
$127$	−0.407604	−	2.31164i	−0.0361690	−	0.205124i	−0.997537	+	0.0701417i	$0.977655\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	1.31521	−	1.10359i	0.115798	−	0.0971657i
$130$	−0.141559	+	0.802823i	−0.0124156	+	0.0704122i
$131$	−11.7442	+	4.27455i	−1.02610	+	0.373469i	−0.799594	−	0.600541i	$-0.794952\pi$
$131$	−11.7442	+	4.27455i	−1.02610	+	0.373469i	−0.226504	+	0.974010i	$0.572730\pi$
$132$	−0.532089			−0.0463124
$133$	−0.610815	+	3.78417i	−0.0529643	+	0.328129i
$134$	11.7023			1.01093
$135$	−0.939693	+	0.342020i	−0.0808759	+	0.0294364i
$136$	0.939693	−	5.32926i	0.0805780	−	0.456980i
$137$	7.77972	−	6.52796i	0.664666	−	0.557721i	−0.246815	−	0.969063i	$-0.579384\pi$
$137$	7.77972	−	6.52796i	0.664666	−	0.557721i	0.911481	+	0.411342i	$0.134940\pi$
$138$	4.02094	+	3.37397i	0.342286	+	0.287212i
$139$	2.86706	+	16.2599i	0.243181	+	1.37915i	0.824680	+	0.565600i	$0.191355\pi$
$139$	2.86706	+	16.2599i	0.243181	+	1.37915i	−0.581499	+	0.813547i	$0.697534\pi$
$140$	0.439693	+	0.761570i	0.0371608	+	0.0643644i
$141$	4.62449	−	8.00984i	0.389452	−	0.674550i
$142$	7.21688	+	2.62673i	0.605627	+	0.220430i
$143$	−0.407604	−	0.148356i	−0.0340855	−	0.0124061i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.73783	+	4.74205i	0.227364	+	0.393806i
$146$	−1.87686	−	10.6442i	−0.155330	−	0.880920i
$147$	4.76991	+	4.00243i	0.393416	+	0.330115i
$148$	1.93969	−	1.62760i	0.159442	−	0.133788i
$149$	−2.28833	+	12.9778i	−0.187468	+	1.06318i	0.735276	+	0.677768i	$0.237052\pi$
$149$	−2.28833	+	12.9778i	−0.187468	+	1.06318i	−0.922744	+	0.385414i	$0.874059\pi$
$150$	0.939693	−	0.342020i	0.0767256	−	0.0279258i
$151$	9.46791			0.770488			0.385244	−	0.922815i	$-0.374117\pi$
$151$	9.46791			0.770488			0.385244	+	0.922815i	$0.374117\pi$
$152$	4.07398	−	1.55007i	0.330443	−	0.125727i
$153$	5.41147			0.437492
$154$	−0.439693	+	0.160035i	−0.0354314	+	0.0128960i
$155$	−0.450837	+	2.55682i	−0.0362121	+	0.205369i
$156$	−0.624485	+	0.524005i	−0.0499988	+	0.0419540i
$157$	−4.42262	−	3.71102i	−0.352963	−	0.296171i	0.449015	−	0.893524i	$-0.351775\pi$
$157$	−4.42262	−	3.71102i	−0.352963	−	0.296171i	−0.801979	+	0.597353i	$0.796219\pi$
$158$	0.843426	+	4.78331i	0.0670994	+	0.380539i
$159$	−1.41875	−	2.45734i	−0.112514	−	0.194880i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	4.33750	+	1.57872i	0.341843	+	0.124421i
$162$	−0.939693	−	0.342020i	−0.0738292	−	0.0268716i
$163$	−0.946967	+	1.64019i	−0.0741721	+	0.128470i	−0.900726	−	0.434388i	$-0.856965\pi$
$163$	−0.946967	+	1.64019i	−0.0741721	+	0.128470i	0.826554	+	0.562858i	$0.190298\pi$
$164$	−1.02094	−	1.76833i	−0.0797224	−	0.138083i
$165$	0.0923963	+	0.524005i	0.00719304	+	0.0407938i
$166$	−10.7686	−	9.03590i	−0.835803	−	0.701322i
$167$	5.05097	−	4.23827i	0.390856	−	0.327967i	−0.426090	−	0.904681i	$-0.640109\pi$
$167$	5.05097	−	4.23827i	0.390856	−	0.327967i	0.816947	+	0.576713i	$0.195665\pi$
$168$	−0.152704	+	0.866025i	−0.0117813	+	0.0668153i
$169$	11.5915	−	4.21897i	0.891655	−	0.324536i
$170$	−5.41147			−0.415041
$171$	2.23396	+	3.74292i	0.170835	+	0.286228i
$172$	−1.71688			−0.130911
$173$	16.3478	−	5.95010i	1.24290	−	0.452378i	0.364902	−	0.931046i	$-0.381103\pi$
$173$	16.3478	−	5.95010i	1.24290	−	0.452378i	0.877996	+	0.478668i	$0.158880\pi$
$174$	−0.950837	+	5.39246i	−0.0720828	+	0.408802i
$175$	0.673648	−	0.565258i	0.0509230	−	0.0427295i
$176$	0.407604	+	0.342020i	0.0307243	+	0.0257807i
$177$	−0.0282185	−	0.160035i	−0.00212103	−	0.0120290i
$178$	2.01367	+	3.48778i	0.150931	+	0.261420i
$179$	−4.93582	+	8.54909i	−0.368921	+	0.638989i	−0.989397	−	0.145236i	$-0.953606\pi$
$179$	−4.93582	+	8.54909i	−0.368921	+	0.638989i	0.620476	+	0.784225i	$0.286939\pi$
$180$	0.939693	+	0.342020i	0.0700406	+	0.0254927i
$181$	−7.93629	−	2.88857i	−0.589900	−	0.214706i	0.0297856	−	0.999556i	$-0.490518\pi$
$181$	−7.93629	−	2.88857i	−0.589900	−	0.214706i	−0.619685	+	0.784850i	$0.712740\pi$
$182$	−0.358441	+	0.620838i	−0.0265694	+	0.0460195i
$183$	0.705737	+	1.22237i	0.0521696	+	0.0903604i
$184$	−0.911474	−	5.16923i	−0.0671948	−	0.381080i
$185$	−1.93969	−	1.62760i	−0.142609	−	0.119663i
$186$	−1.98886	+	1.66885i	−0.145830	+	0.122366i
$187$	0.500000	−	2.83564i	0.0365636	−	0.207363i
$188$	−8.69119	+	3.16333i	−0.633870	+	0.230710i
$189$	−0.879385			−0.0639659
$190$	−2.23396	−	3.74292i	−0.162068	−	0.271540i
$191$	19.8675			1.43756			0.718782	−	0.695236i	$-0.244700\pi$
$191$	19.8675			1.43756			0.718782	+	0.695236i	$0.244700\pi$
$192$	0.939693	−	0.342020i	0.0678165	−	0.0246832i
$193$	−2.34090	+	13.2759i	−0.168502	+	0.955620i	0.776879	+	0.629651i	$0.216802\pi$
$193$	−2.34090	+	13.2759i	−0.168502	+	0.955620i	−0.945380	+	0.325970i	$0.894309\pi$
$194$	−5.61128	+	4.70842i	−0.402867	+	0.338045i
$195$	0.624485	+	0.524005i	0.0447203	+	0.0375248i
$196$	−1.08125	−	6.13208i	−0.0772323	−	0.438006i
$197$	−6.01114	−	10.4116i	−0.428276	−	0.741796i	0.568444	−	0.822722i	$-0.307546\pi$
$197$	−6.01114	−	10.4116i	−0.428276	−	0.741796i	−0.996720	+	0.0809258i	$0.974212\pi$
$198$	−0.266044	+	0.460802i	−0.0189070	+	0.0327478i
$199$	−1.38191	−	0.502975i	−0.0979611	−	0.0356549i	0.292575	−	0.956243i	$-0.405488\pi$
$199$	−1.38191	−	0.502975i	−0.0979611	−	0.0356549i	−0.390536	+	0.920588i	$0.627710\pi$
$200$	−0.939693	−	0.342020i	−0.0664463	−	0.0241845i
$201$	5.85117	−	10.1345i	0.412709	−	0.714834i
$202$	−2.80793	−	4.86348i	−0.197566	−	0.342194i
$203$	0.836152	+	4.74205i	0.0586864	+	0.332827i
$204$	−4.14543	−	3.47843i	−0.290238	−	0.243539i
$205$	−1.56418	+	1.31250i	−0.109247	+	0.0916690i
$206$	2.86437	−	16.2447i	0.199570	−	1.13182i
$207$	4.93242	−	1.79525i	0.342827	−	0.124779i
$208$	0.815207			0.0565245
$209$	2.16772	−	0.824773i	0.149944	−	0.0570507i
$210$	0.879385			0.0606833
$211$	−19.3148	+	7.03001i	−1.32969	+	0.483966i	−0.906549	−	0.422100i	$-0.861293\pi$
$211$	−19.3148	+	7.03001i	−1.32969	+	0.483966i	−0.423136	+	0.906066i	$0.639071\pi$
$212$	−0.492726	+	2.79439i	−0.0338406	+	0.191919i
$213$	5.88326	−	4.93664i	0.403114	−	0.338253i
$214$	2.31521	+	1.94269i	0.158264	+	0.132800i
$215$	0.298133	+	1.69080i	0.0203325	+	0.115311i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−1.14156	+	1.97724i	−0.0774941	+	0.134224i
$218$	1.57145	+	0.571962i	0.106432	+	0.0387381i
$219$	−10.1566	−	3.69669i	−0.686318	−	0.249799i
$220$	0.266044	−	0.460802i	0.0179367	−	0.0310673i
$221$	−2.20574	−	3.82045i	−0.148374	−	0.256991i
$222$	−0.439693	−	2.49362i	−0.0295102	−	0.167361i
$223$	−17.6630	−	14.8210i	−1.18280	−	0.992487i	−0.999956	−	0.00934504i	$-0.997025\pi$
$223$	−17.6630	−	14.8210i	−1.18280	−	0.992487i	−0.182844	−	0.983142i	$-0.558530\pi$
$224$	0.673648	−	0.565258i	0.0450100	−	0.0377679i
$225$	0.173648	−	0.984808i	0.0115765	−	0.0656539i
$226$	−13.7811	+	5.01590i	−0.916702	+	0.333652i
$227$	−5.54757			−0.368205			−0.184103	−	0.982907i	$-0.558938\pi$
$227$	−5.54757			−0.368205			−0.184103	+	0.982907i	$0.558938\pi$
$228$	0.694593	−	4.30320i	0.0460005	−	0.284986i
$229$	1.18748			0.0784709			0.0392355	−	0.999230i	$-0.487508\pi$
$229$	1.18748			0.0784709			0.0392355	+	0.999230i	$0.487508\pi$
$230$	−4.93242	+	1.79525i	−0.325234	+	0.118376i
$231$	−0.0812519	+	0.460802i	−0.00534598	+	0.0303186i
$232$	4.19459	−	3.51968i	0.275389	−	0.231078i
$233$	4.53983	+	3.80937i	0.297414	+	0.249560i	0.779267	−	0.626692i	$-0.215592\pi$
$233$	4.53983	+	3.80937i	0.297414	+	0.249560i	−0.481853	+	0.876252i	$0.660036\pi$
$234$	0.141559	+	0.802823i	0.00925402	+	0.0524822i
$235$	4.62449	+	8.00984i	0.301668	+	0.522505i
$236$	−0.0812519	+	0.140732i	−0.00528905	+	0.00916090i
$237$	4.56418	+	1.66122i	0.296475	+	0.107908i
$238$	−4.47178	−	1.62760i	−0.289863	−	0.105501i
$239$	8.55350	−	14.8151i	0.553280	−	0.958309i	−0.444755	−	0.895652i	$-0.646709\pi$
$239$	8.55350	−	14.8151i	0.553280	−	0.958309i	0.998035	−	0.0626568i	$-0.0199573\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	1.63294	+	9.26087i	0.105187	+	0.596545i	0.991145	+	0.132780i	$0.0423905\pi$
$241$	1.63294	+	9.26087i	0.105187	+	0.596545i	−0.885958	+	0.463765i	$0.846498\pi$
$242$	−8.20961	−	6.88868i	−0.527734	−	0.442821i
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$	0.245100	−	1.39003i	0.0156909	−	0.0889876i
$245$	−5.85117	+	2.12965i	−0.373817	+	0.136058i
$246$	−2.04189			−0.130186
$247$	1.73190	−	3.10278i	0.110198	−	0.197425i
$248$	2.59627			0.164863
$249$	−13.2096	+	4.80790i	−0.837125	+	0.304689i
$250$	−0.173648	+	0.984808i	−0.0109825	+	0.0622847i
$251$	−9.32888	+	7.82786i	−0.588834	+	0.494090i	−0.887835	−	0.460163i	$-0.847791\pi$
$251$	−9.32888	+	7.82786i	−0.588834	+	0.494090i	0.299001	+	0.954253i	$0.403347\pi$
$252$	0.673648	+	0.565258i	0.0424358	+	0.0356079i
$253$	−0.484985	−	2.75049i	−0.0304908	−	0.172922i
$254$	1.17365	+	2.03282i	0.0736412	+	0.127550i
$255$	−2.70574	+	4.68647i	−0.169440	+	0.293478i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−24.1386	−	8.78574i	−1.50573	−	0.548039i	−0.548190	−	0.836354i	$-0.684683\pi$
$257$	−24.1386	−	8.78574i	−1.50573	−	0.548039i	−0.957536	+	0.288314i	$0.906905\pi$
$258$	−0.858441	+	1.48686i	−0.0534442	+	0.0925680i
$259$	−1.11334	−	1.92836i	−0.0691796	−	0.119823i
$260$	−0.141559	−	0.802823i	−0.00877913	−	0.0497889i
$261$	4.19459	+	3.51968i	0.259639	+	0.217863i
$262$	9.57398	−	8.03352i	0.591482	−	0.496313i
$263$	0.619271	−	3.51206i	0.0381859	−	0.216563i	−0.959744	−	0.280877i	$-0.909375\pi$
$263$	0.619271	−	3.51206i	0.0381859	−	0.216563i	0.997930	+	0.0643139i	$0.0204859\pi$
$264$	0.500000	−	0.181985i	0.0307729	−	0.0112004i
$265$	2.83750			0.174306
$266$	−0.720285	−	3.76487i	−0.0441635	−	0.230839i
$267$	4.02734			0.246469
$268$	−10.9966	+	4.00243i	−0.671724	+	0.244488i
$269$	2.17617	−	12.3417i	0.132684	−	0.752487i	−0.843761	−	0.536719i	$-0.819664\pi$
$269$	2.17617	−	12.3417i	0.132684	−	0.752487i	0.976445	−	0.215768i	$-0.0692254\pi$
$270$	0.766044	−	0.642788i	0.0466200	−	0.0391188i
$271$	−12.2135	−	10.2483i	−0.741916	−	0.622541i	0.191436	−	0.981505i	$-0.438686\pi$
$271$	−12.2135	−	10.2483i	−0.741916	−	0.622541i	−0.933351	+	0.358964i	$0.883130\pi$
$272$	0.939693	+	5.32926i	0.0569772	+	0.323134i
$273$	0.358441	+	0.620838i	0.0216938	+	0.0375748i
$274$	−5.07785	+	8.79509i	−0.306764	+	0.531331i
$275$	−0.500000	−	0.181985i	−0.0301511	−	0.0109741i
$276$	−4.93242	−	1.79525i	−0.296897	−	0.108062i
$277$	4.52734	−	7.84158i	0.272022	−	0.471155i	−0.697358	−	0.716723i	$-0.745641\pi$
$277$	4.52734	−	7.84158i	0.272022	−	0.471155i	0.969379	+	0.245568i	$0.0789745\pi$
$278$	−8.25537	−	14.2987i	−0.495124	−	0.857580i
$279$	0.450837	+	2.55682i	0.0269909	+	0.153073i
$280$	−0.673648	−	0.565258i	−0.0402582	−	0.0337806i
$281$	17.9834	−	15.0899i	1.07280	−	0.900185i	0.0774961	−	0.996993i	$-0.475307\pi$
$281$	17.9834	−	15.0899i	1.07280	−	0.900185i	0.995303	+	0.0968072i	$0.0308630\pi$
$282$	−1.60607	+	9.10846i	−0.0956399	+	0.542401i
$283$	−24.9650	+	9.08651i	−1.48401	+	0.540137i	−0.951866	−	0.306515i	$-0.900837\pi$
$283$	−24.9650	+	9.08651i	−1.48401	+	0.540137i	−0.532148	+	0.846651i	$0.678615\pi$
$284$	−7.68004			−0.455727
$285$	−4.35844	+	0.0632028i	−0.258172	+	0.00374381i
$286$	0.433763			0.0256489
$287$	−1.68732	+	0.614134i	−0.0995993	+	0.0362512i
$288$	0.173648	−	0.984808i	0.0102323	−	0.0580304i
$289$	9.41013	−	7.89604i	0.553537	−	0.464473i
$290$	−4.19459	−	3.51968i	−0.246315	−	0.206683i
$291$	1.27197	+	7.21372i	0.0745644	+	0.422876i
$292$	5.40420	+	9.36035i	0.316257	+	0.547773i
$293$	9.40420	−	16.2886i	0.549399	−	0.951587i	−0.448917	−	0.893574i	$-0.648190\pi$
$293$	9.40420	−	16.2886i	0.549399	−	0.951587i	0.998316	−	0.0580137i	$-0.0184767\pi$
$294$	−5.85117	−	2.12965i	−0.341247	−	0.124204i
$295$	0.152704	+	0.0555796i	0.00889075	+	0.00323597i
$296$	−1.26604	+	2.19285i	−0.0735873	+	0.127457i
$297$	0.266044	+	0.460802i	0.0154375	+	0.0267385i
$298$	−2.28833	−	12.9778i	−0.132560	−	0.751783i
$299$	−3.27790	−	2.75049i	−0.189566	−	0.159065i
$300$	−0.766044	+	0.642788i	−0.0442276	+	0.0371114i
$301$	−0.262174	+	1.48686i	−0.0151115	+	0.0857014i
$302$	−8.89693	+	3.23822i	−0.511961	+	0.186338i
$303$	−5.61587			−0.322623
$304$	−3.29813	+	2.84997i	−0.189161	+	0.163457i
$305$	−1.41147			−0.0808208
$306$	−5.08512	+	1.85083i	−0.290697	+	0.105805i
$307$	−1.09761	+	6.22486i	−0.0626440	+	0.355272i	0.937333	+	0.348436i	$0.113287\pi$
$307$	−1.09761	+	6.22486i	−0.0626440	+	0.355272i	−0.999977	+	0.00683582i	$0.997824\pi$
$308$	0.358441	−	0.300767i	0.0204241	−	0.0171378i
$309$	−12.6361	−	10.6029i	−0.718842	−	0.603180i
$310$	−0.450837	−	2.55682i	−0.0256058	−	0.145218i
$311$	−5.41013	−	9.37062i	−0.306780	−	0.531359i	0.670876	−	0.741570i	$-0.265918\pi$
$311$	−5.41013	−	9.37062i	−0.306780	−	0.531359i	−0.977656	+	0.210211i	$0.932585\pi$
$312$	0.407604	−	0.705990i	0.0230760	−	0.0399688i
$313$	−4.77079	−	1.73643i	−0.269661	−	0.0981486i	0.203651	−	0.979044i	$-0.434719\pi$
$313$	−4.77079	−	1.73643i	−0.269661	−	0.0981486i	−0.473312	+	0.880895i	$0.656942\pi$
$314$	5.42514	+	1.97459i	0.306159	+	0.111433i
$315$	0.439693	−	0.761570i	0.0247739	−	0.0429096i
$316$	−2.42855	−	4.20637i	−0.136617	−	0.236627i
$317$	−0.500000	−	2.83564i	−0.0280828	−	0.159265i	0.967541	−	0.252712i	$-0.0813226\pi$
$317$	−0.500000	−	2.83564i	−0.0280828	−	0.159265i	−0.995624	+	0.0934468i	$0.970211\pi$
$318$	2.17365	+	1.82391i	0.121892	+	0.102280i
$319$	2.23190	−	1.87278i	0.124962	−	0.104856i
$320$	−0.173648	+	0.984808i	−0.00970723	+	0.0550524i
$321$	2.84002	−	1.03368i	0.158515	−	0.0576946i
$322$	−4.61587			−0.257232
$323$	22.2802	+	7.74535i	1.23970	+	0.430963i
$324$	1.00000			0.0555556
$325$	−0.766044	+	0.278817i	−0.0424925	+	0.0154660i
$326$	0.328878	−	1.86516i	0.0182149	−	0.103302i
$327$	1.28106	−	1.07494i	0.0708427	−	0.0594441i
$328$	1.56418	+	1.31250i	0.0863673	+	0.0724707i
$329$	1.41235	+	8.00984i	0.0778655	+	0.441597i
$330$	−0.266044	−	0.460802i	−0.0146453	−	0.0253663i
$331$	−0.599670	+	1.03866i	−0.0329609	+	0.0570899i	−0.882035	−	0.471183i	$-0.843827\pi$
$331$	−0.599670	+	1.03866i	−0.0329609	+	0.0570899i	0.849074	+	0.528273i	$0.177160\pi$
$332$	13.2096	+	4.80790i	0.724971	+	0.263868i
$333$	−2.37939	−	0.866025i	−0.130390	−	0.0474579i
$334$	−3.29679	+	5.71021i	−0.180392	+	0.312449i
$335$	5.85117	+	10.1345i	0.319683	+	0.553708i
$336$	−0.152704	−	0.866025i	−0.00833067	−	0.0472456i
$337$	11.6040	+	9.73692i	0.632111	+	0.530404i	0.901584	−	0.432604i	$-0.142405\pi$
$337$	11.6040	+	9.73692i	0.632111	+	0.530404i	−0.269473	+	0.963008i	$0.586850\pi$
$338$	−9.44949	+	7.92907i	−0.513985	+	0.431284i
$339$	−2.54664	+	14.4427i	−0.138314	+	0.784420i
$340$	5.08512	−	1.85083i	0.275779	−	0.100376i
$341$	1.38144			0.0748094
$342$	−3.37939	−	2.75314i	−0.182736	−	0.148873i
$343$	−11.6313			−0.628034
$344$	1.61334	−	0.587208i	0.0869855	−	0.0316601i
$345$	−0.911474	+	5.16923i	−0.0490721	+	0.278302i
$346$	−13.3268	+	11.1825i	−0.716454	+	0.601176i
$347$	−10.3853	−	8.71431i	−0.557513	−	0.467809i	0.319963	−	0.947430i	$-0.396330\pi$
$347$	−10.3853	−	8.71431i	−0.557513	−	0.467809i	−0.877476	+	0.479621i	$0.840774\pi$
$348$	−0.950837	−	5.39246i	−0.0509702	−	0.289066i
$349$	12.2592	+	21.2336i	0.656222	+	1.13661i	0.981586	+	0.191021i	$0.0611798\pi$
$349$	12.2592	+	21.2336i	0.656222	+	1.13661i	−0.325364	+	0.945589i	$0.605487\pi$
$350$	−0.439693	+	0.761570i	−0.0235026	+	0.0407076i
$351$	0.766044	+	0.278817i	0.0408884	+	0.0148822i
$352$	−0.500000	−	0.181985i	−0.0266501	−	0.00969984i
$353$	15.8648	−	27.4787i	0.844400	−	1.46254i	−0.0417411	−	0.999128i	$-0.513290\pi$
$353$	15.8648	−	27.4787i	0.844400	−	1.46254i	0.886141	−	0.463415i	$-0.153376\pi$
$354$	0.0812519	+	0.140732i	0.00431849	+	0.00747984i
$355$	1.33363	+	7.56337i	0.0707815	+	0.401422i
$356$	−3.08512	−	2.58872i	−0.163511	−	0.137202i
$357$	−3.64543	+	3.05888i	−0.192937	+	0.161893i
$358$	1.71419	−	9.72167i	0.0905979	−	0.513806i
$359$	−19.5278	+	7.10754i	−1.03064	+	0.375122i	−0.801324	−	0.598231i	$-0.795871\pi$
$359$	−19.5278	+	7.10754i	−1.03064	+	0.375122i	−0.229314	+	0.973352i	$0.573648\pi$
$360$	−1.00000			−0.0527046
$361$	3.84049	+	18.6078i	0.202131	+	0.979358i
$362$	8.44562			0.443892
$363$	−10.0706	+	3.66539i	−0.528568	+	0.192383i
$364$	0.124485	−	0.705990i	0.00652479	−	0.0370040i
$365$	8.27972	−	6.94751i	0.433380	−	0.363649i
$366$	−1.08125	−	0.907278i	−0.0565179	−	0.0474242i
$367$	1.01367	+	5.74881i	0.0529132	+	0.300086i	0.999767	−	0.0215782i	$-0.00686907\pi$
$367$	1.01367	+	5.74881i	0.0529132	+	0.300086i	−0.946854	+	0.321664i	$0.895758\pi$
$368$	2.62449	+	4.54574i	0.136811	+	0.236963i
$369$	−1.02094	+	1.76833i	−0.0531482	+	0.0920555i
$370$	2.37939	+	0.866025i	0.123698	+	0.0450225i
$371$	2.34477	+	0.853427i	0.121734	+	0.0443077i
$372$	1.29813	−	2.24843i	0.0673051	−	0.116576i
$373$	−12.4855	−	21.6254i	−0.646472	−	1.11972i	−0.983959	−	0.178393i	$-0.942910\pi$
$373$	−12.4855	−	21.6254i	−0.646472	−	1.11972i	0.337487	−	0.941330i	$-0.390423\pi$
$374$	0.500000	+	2.83564i	0.0258544	+	0.146628i
$375$	0.766044	+	0.642788i	0.0395584	+	0.0331934i
$376$	7.08512	−	5.94512i	0.365387	−	0.306596i
$377$	0.775129	−	4.39598i	0.0399212	−	0.226404i
$378$	0.826352	−	0.300767i	0.0425030	−	0.0154698i
$379$	27.2267			1.39854			0.699270	−	0.714857i	$-0.253508\pi$
$379$	27.2267			1.39854			0.699270	+	0.714857i	$0.253508\pi$
$380$	3.37939	+	2.75314i	0.173359	+	0.141233i
$381$	2.34730			0.120256
$382$	−18.6694	+	6.79509i	−0.955208	+	0.347667i
$383$	5.34137	−	30.2924i	0.272931	−	1.54787i	−0.472527	−	0.881316i	$-0.656658\pi$
$383$	5.34137	−	30.2924i	0.272931	−	1.54787i	0.745458	−	0.666553i	$-0.232231\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$	−0.358441	−	0.300767i	−0.0182678	−	0.0153285i
$386$	−2.34090	−	13.2759i	−0.119149	−	0.675726i
$387$	0.858441	+	1.48686i	0.0436370	+	0.0755815i
$388$	3.66250	−	6.34364i	0.185935	−	0.322050i
$389$	−14.7087	−	5.35354i	−0.745762	−	0.271435i	−0.0589408	−	0.998261i	$-0.518772\pi$
$389$	−14.7087	−	5.35354i	−0.745762	−	0.271435i	−0.686821	+	0.726826i	$0.740995\pi$
$390$	−0.766044	−	0.278817i	−0.0387902	−	0.0141185i
$391$	14.2023	−	24.5992i	0.718243	−	1.24403i
$392$	3.11334	+	5.39246i	0.157247	+	0.272361i
$393$	−2.17024	−	12.3081i	−0.109474	−	0.620860i
$394$	9.20961	+	7.72778i	0.463973	+	0.389320i
$395$	−3.72075	+	3.12208i	−0.187211	+	0.157089i
$396$	0.0923963	−	0.524005i	0.00464309	−	0.0263323i
$397$	−27.1827	+	9.89371i	−1.36426	+	0.496551i	−0.917370	−	0.398037i	$-0.869692\pi$
$397$	−27.1827	+	9.89371i	−1.36426	+	0.496551i	−0.446893	+	0.894588i	$0.647469\pi$
$398$	1.47060			0.0737145
$399$	−3.62061	−	1.25865i	−0.181257	−	0.0630113i
$400$	1.00000			0.0500000
$401$	2.01589	−	0.733725i	0.100669	−	0.0366405i	−0.291195	−	0.956664i	$-0.594053\pi$
$401$	2.01589	−	0.733725i	0.100669	−	0.0366405i	0.391864	+	0.920023i	$0.371831\pi$
$402$	−2.03209	+	11.5245i	−0.101351	+	0.574792i
$403$	1.62133	−	1.36046i	0.0807642	−	0.0677692i
$404$	4.30200	+	3.60981i	0.214033	+	0.179595i
$405$	−0.173648	−	0.984808i	−0.00862865	−	0.0489355i
$406$	−2.40760	−	4.17009i	−0.119487	−	0.206958i
$407$	−0.673648	+	1.16679i	−0.0333915	+	0.0578358i
$408$	5.08512	+	1.85083i	0.251751	+	0.0916299i
$409$	−12.3712	−	4.50276i	−0.611718	−	0.222647i	0.0175367	−	0.999846i	$-0.494418\pi$
$409$	−12.3712	−	4.50276i	−0.611718	−	0.222647i	−0.629255	+	0.777199i	$0.716640\pi$
$410$	1.02094	−	1.76833i	0.0504209	−	0.0873315i
$411$	5.07785	+	8.79509i	0.250472	+	0.433830i
$412$	2.86437	+	16.2447i	0.141117	+	0.800317i
$413$	0.109470	+	0.0918566i	0.00538669	+	0.00451997i
$414$	−4.02094	+	3.37397i	−0.197619	+	0.165822i
$415$	2.44104	−	13.8438i	0.119826	−	0.679566i
$416$	−0.766044	+	0.278817i	−0.0375584	+	0.0136701i
$417$	−16.5107			−0.808534
$418$	−1.75490	+	1.51644i	−0.0858350	+	0.0741713i
$419$	34.2841			1.67489			0.837443	−	0.546525i	$-0.184050\pi$
$419$	34.2841			1.67489			0.837443	+	0.546525i	$0.184050\pi$
$420$	−0.826352	+	0.300767i	−0.0403218	+	0.0146759i
$421$	−1.70068	+	9.64506i	−0.0828863	+	0.470072i	0.914906	+	0.403666i	$0.132264\pi$
$421$	−1.70068	+	9.64506i	−0.0828863	+	0.470072i	−0.997793	+	0.0664055i	$0.978847\pi$
$422$	15.7456	−	13.2121i	0.766482	−	0.643155i
$423$	7.08512	+	5.94512i	0.344490	+	0.289062i
$424$	−0.492726	−	2.79439i	−0.0239289	−	0.135707i
$425$	−2.70574	−	4.68647i	−0.131248	−	0.227327i
$426$	−3.84002	+	6.65111i	−0.186050	+	0.322248i
$427$	−1.16637	−	0.424525i	−0.0564448	−	0.0205442i
$428$	−2.84002	−	1.03368i	−0.137278	−	0.0499650i
$429$	0.216881	−	0.375650i	0.0104711	−	0.0181365i
$430$	−0.858441	−	1.48686i	−0.0413977	−	0.0717029i
$431$	2.61318	+	14.8201i	0.125872	+	0.713858i	0.980786	+	0.195087i	$0.0624990\pi$
$431$	2.61318	+	14.8201i	0.125872	+	0.713858i	−0.854914	+	0.518771i	$0.826390\pi$
$432$	−0.766044	−	0.642788i	−0.0368563	−	0.0309261i
$433$	4.13950	−	3.47345i	0.198932	−	0.166923i	−0.537880	−	0.843021i	$-0.680775\pi$
$433$	4.13950	−	3.47345i	0.198932	−	0.166923i	0.736812	+	0.676098i	$0.236330\pi$
$434$	0.396459	−	2.24843i	0.0190307	−	0.107928i
$435$	−5.14543	+	1.87278i	−0.246704	+	0.0897931i
$436$	−1.67230			−0.0800888
$437$	22.8773	−	0.331749i	1.09437	−	0.0158697i
$438$	10.8084			0.516445
$439$	19.4564	−	7.08153i	0.928601	−	0.337983i	0.166946	−	0.985966i	$-0.446609\pi$
$439$	19.4564	−	7.08153i	0.928601	−	0.337983i	0.761655	+	0.647983i	$0.224387\pi$
$440$	−0.0923963	+	0.524005i	−0.00440482	+	0.0249810i
$441$	−4.76991	+	4.00243i	−0.227139	+	0.190592i
$442$	3.37939	+	2.83564i	0.160741	+	0.134878i
$443$	0.409825	+	2.32423i	0.0194714	+	0.110428i	0.992994	−	0.118161i	$-0.0377000\pi$
$443$	0.409825	+	2.32423i	0.0194714	+	0.110428i	−0.973523	+	0.228589i	$0.926589\pi$
$444$	1.26604	+	2.19285i	0.0600838	+	0.104068i
$445$	−2.01367	+	3.48778i	−0.0954571	+	0.165337i
$446$	21.6668	+	7.88609i	1.02595	+	0.373417i
$447$	−12.3833	−	4.50714i	−0.585708	−	0.213180i
$448$	−0.439693	+	0.761570i	−0.0207735	+	0.0359808i
$449$	−13.5018	−	23.3858i	−0.637190	−	1.10365i	−0.986047	−	0.166469i	$-0.946763\pi$
$449$	−13.5018	−	23.3858i	−0.637190	−	1.10365i	0.348857	−	0.937176i	$-0.386570\pi$
$450$	0.173648	+	0.984808i	0.00818585	+	0.0464243i
$451$	0.832282	+	0.698367i	0.0391906	+	0.0328848i
$452$	11.2344	−	9.42680i	0.528423	−	0.443399i
$453$	−1.64409	+	9.32407i	−0.0772459	+	0.438083i
$454$	5.21301	−	1.89738i	0.244659	−	0.0890485i
$455$	−0.716881			−0.0336079
$456$	0.819078	+	4.28125i	0.0383568	+	0.200488i
$457$	−6.31584			−0.295442			−0.147721	−	0.989029i	$-0.547194\pi$
$457$	−6.31584			−0.295442			−0.147721	+	0.989029i	$0.547194\pi$
$458$	−1.11587	+	0.406142i	−0.0521410	+	0.0189778i
$459$	−0.939693	+	5.32926i	−0.0438611	+	0.248749i
$460$	4.02094	−	3.37397i	0.187478	−	0.157312i
$461$	21.7460	+	18.2471i	1.01281	+	0.849852i	0.988708	−	0.149858i	$-0.0478816\pi$
$461$	21.7460	+	18.2471i	1.01281	+	0.849852i	0.0241062	+	0.999709i	$0.492326\pi$
$462$	−0.0812519	−	0.460802i	−0.00378018	−	0.0214385i
$463$	2.77450	+	4.80558i	0.128942	+	0.223334i	0.923267	−	0.384159i	$-0.125509\pi$
$463$	2.77450	+	4.80558i	0.128942	+	0.223334i	−0.794325	+	0.607493i	$0.792175\pi$
$464$	−2.73783	+	4.74205i	−0.127100	+	0.220144i
$465$	−2.43969	−	0.887975i	−0.113138	−	0.0411789i
$466$	−5.56893	−	2.02692i	−0.257975	−	0.0938954i
$467$	−13.9376	+	24.1407i	−0.644957	+	1.11710i	0.339355	+	0.940658i	$0.389791\pi$
$467$	−13.9376	+	24.1407i	−0.644957	+	1.11710i	−0.984312	+	0.176439i	$0.943542\pi$
$468$	−0.407604	−	0.705990i	−0.0188415	−	0.0326344i
$469$	1.78699	+	10.1345i	0.0825155	+	0.467969i
$470$	−7.08512	−	5.94512i	−0.326812	−	0.274228i
$471$	4.42262	−	3.71102i	0.203784	−	0.170995i
$472$	0.0282185	−	0.160035i	0.00129886	−	0.00736621i
$473$	0.858441	−	0.312447i	0.0394711	−	0.0143663i
$474$	−4.85710			−0.223094
$475$	2.12449	−	3.80612i	0.0974781	−	0.174637i
$476$	4.75877			0.218118
$477$	2.66637	−	0.970481i	0.122085	−	0.0444353i
$478$	−2.97060	+	16.8471i	−0.135872	+	0.770569i
$479$	7.61515	−	6.38987i	0.347945	−	0.291961i	−0.452019	−	0.892008i	$-0.649296\pi$
$479$	7.61515	−	6.38987i	0.347945	−	0.291961i	0.799964	+	0.600048i	$0.204852\pi$
$480$	0.766044	+	0.642788i	0.0349650	+	0.0293391i
$481$	0.358441	+	2.03282i	0.0163435	+	0.0926885i
$482$	−4.70187	−	8.14387i	−0.214164	−	0.370943i
$483$	−2.30793	+	3.99746i	−0.105015	+	0.181891i
$484$	10.0706	+	3.66539i	0.457753	+	0.166609i
$485$	−6.88326	−	2.50530i	−0.312553	−	0.113760i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−3.03549	−	5.25763i	−0.137551	−	0.238246i	0.789018	−	0.614370i	$-0.210590\pi$
$487$	−3.03549	−	5.25763i	−0.137551	−	0.238246i	−0.926569	+	0.376124i	$0.877257\pi$
$488$	0.245100	+	1.39003i	0.0110952	+	0.0629237i
$489$	−1.45084	−	1.21740i	−0.0656091	−	0.0550526i
$490$	4.76991	−	4.00243i	0.215483	−	0.180812i
$491$	−2.83110	+	16.0560i	−0.127766	+	0.724595i	0.851861	+	0.523768i	$0.175474\pi$
$491$	−2.83110	+	16.0560i	−0.127766	+	0.724595i	−0.979627	+	0.200827i	$0.935637\pi$
$492$	1.91875	−	0.698367i	0.0865038	−	0.0314848i
$493$	29.6313			1.33453
$494$	−0.566237	+	3.50800i	−0.0254762	+	0.157832i
$495$	−0.532089			−0.0239156
$496$	−2.43969	+	0.887975i	−0.109545	+	0.0398713i
$497$	−1.17277	+	6.65111i	−0.0526060	+	0.298343i
$498$	10.7686	−	9.03590i	0.482551	−	0.404909i
$499$	−0.190722	−	0.160035i	−0.00853790	−	0.00716415i	0.638509	−	0.769615i	$-0.279552\pi$
$499$	−0.190722	−	0.160035i	−0.00853790	−	0.00716415i	−0.647047	+	0.762450i	$0.723996\pi$
$500$	−0.173648	−	0.984808i	−0.00776578	−	0.0440419i
$501$	3.29679	+	5.71021i	0.147290	+	0.255113i
$502$	6.08899	−	10.5464i	0.271765	−	0.470711i
$503$	−4.74675	−	1.72768i	−0.211647	−	0.0770332i	0.234021	−	0.972232i	$-0.424812\pi$
$503$	−4.74675	−	1.72768i	−0.211647	−	0.0770332i	−0.445668	+	0.895198i	$0.647034\pi$
$504$	−0.826352	−	0.300767i	−0.0368086	−	0.0133972i
$505$	2.80793	−	4.86348i	0.124951	−	0.216422i
$506$	1.39646	+	2.41874i	0.0620802	+	0.107526i
$507$	2.14203	+	12.1480i	0.0951307	+	0.539513i
$508$	−1.79813	−	1.50881i	−0.0797793	−	0.0669428i
$509$	−17.3628	+	14.5691i	−0.769592	+	0.645764i	−0.940604	−	0.339505i	$-0.889741\pi$
$509$	−17.3628	+	14.5691i	−0.769592	+	0.645764i	0.171013	+	0.985269i	$0.445296\pi$
$510$	0.939693	−	5.32926i	0.0416103	−	0.235984i
$511$	8.93154	−	3.25082i	0.395108	−	0.143808i
$512$	1.00000			0.0441942
$513$	−4.07398	+	1.55007i	−0.179871	+	0.0684371i
$514$	25.6878			1.13304
$515$	15.5005	−	5.64171i	0.683032	−	0.248603i
$516$	0.298133	−	1.69080i	0.0131246	−	0.0744332i
$517$	3.76991	−	3.16333i	0.165801	−	0.139123i
$518$	1.70574	+	1.43128i	0.0749458	+	0.0628870i
$519$	3.02094	+	17.1326i	0.132605	+	0.752039i
$520$	0.407604	+	0.705990i	0.0178746	+	0.0309597i
$521$	−17.3922	+	30.1241i	−0.761965	+	1.31976i	0.179871	+	0.983690i	$0.442432\pi$
$521$	−17.3922	+	30.1241i	−0.761965	+	1.31976i	−0.941836	+	0.336072i	$0.890901\pi$
$522$	−5.14543	−	1.87278i	−0.225209	−	0.0819695i
$523$	−28.9063	−	10.5210i	−1.26398	−	0.460053i	−0.378881	−	0.925446i	$-0.623691\pi$
$523$	−28.9063	−	10.5210i	−1.26398	−	0.460053i	−0.885104	+	0.465393i	$0.845913\pi$
$524$	−6.24897	+	10.8235i	−0.272988	+	0.472828i
$525$	0.439693	+	0.761570i	0.0191898	+	0.0332376i
$526$	0.619271	+	3.51206i	0.0270015	+	0.153133i
$527$	10.7626	+	9.03093i	0.468828	+	0.393393i
$528$	−0.407604	+	0.342020i	−0.0177387	+	0.0148845i
$529$	0.790393	−	4.48254i	0.0343649	−	0.194893i
$530$	−2.66637	+	0.970481i	−0.115820	+	0.0421550i
$531$	0.162504			0.00705207
$532$	1.96451	+	3.29147i	0.0851722	+	0.142703i
$533$	1.66456			0.0721002
$534$	−3.78446	+	1.37743i	−0.163770	+	0.0596073i
$535$	−0.524815	+	2.97637i	−0.0226897	+	0.128680i
$536$	8.96451	−	7.52211i	0.387208	−	0.324906i
$537$	−7.56212	−	6.34537i	−0.326329	−	0.273823i
$538$	2.17617	+	12.3417i	0.0938215	+	0.532088i
$539$	1.65657	+	2.86927i	0.0713537	+	0.123588i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	28.8965	+	10.5175i	1.24236	+	0.452181i	0.877813	−	0.479004i	$-0.159002\pi$
$541$	28.8965	+	10.5175i	1.24236	+	0.452181i	0.364546	+	0.931186i	$0.381224\pi$
$542$	14.9820	+	5.45302i	0.643534	+	0.234227i
$543$	4.22281	−	7.31412i	0.181218	−	0.313879i
$544$	−2.70574	−	4.68647i	−0.116008	−	0.200931i
$545$	0.290393	+	1.64690i	0.0124390	+	0.0705454i
$546$	−0.549163	−	0.460802i	−0.0235020	−	0.0197205i
$547$	21.1826	−	17.7743i	0.905701	−	0.759974i	−0.0655950	−	0.997846i	$-0.520895\pi$
$547$	21.1826	−	17.7743i	0.905701	−	0.759974i	0.971296	+	0.237873i	$0.0764501\pi$
$548$	1.76352	−	10.0014i	0.0753338	−	0.427239i
$549$	−1.32635	+	0.482753i	−0.0566073	+	0.0206034i
$550$	0.532089			0.0226883
$551$	12.2324	+	20.4949i	0.521116	+	0.873113i
$552$	5.24897			0.223411
$553$	−4.01367	+	1.46086i	−0.170679	+	0.0621219i
$554$	−1.57233	+	8.91712i	−0.0668019	+	0.378852i
$555$	1.93969	−	1.62760i	0.0823354	−	0.0690876i
$556$	12.6480	+	10.6129i	0.536393	+	0.450087i
$557$	4.38032	+	24.8420i	0.185600	+	1.05259i	0.925182	+	0.379524i	$0.123912\pi$
$557$	4.38032	+	24.8420i	0.185600	+	1.05259i	−0.739582	+	0.673067i	$0.764977\pi$
$558$	−1.29813	−	2.24843i	−0.0549544	−	0.0951838i
$559$	0.699807	−	1.21210i	0.0295987	−	0.0512664i
$560$	0.826352	+	0.300767i	0.0349197	+	0.0127097i
$561$	2.70574	+	0.984808i	0.114236	+	0.0415786i
$562$	−11.7378	+	20.3305i	−0.495130	+	0.857591i
$563$	−15.4206	−	26.7092i	−0.649899	−	1.12566i	−0.983147	−	0.182819i	$-0.941478\pi$
$563$	−15.4206	−	26.7092i	−0.649899	−	1.12566i	0.333248	−	0.942839i	$-0.391856\pi$
$564$	−1.60607	−	9.10846i	−0.0676276	−	0.383535i
$565$	−11.2344	−	9.42680i	−0.472636	−	0.396588i
$566$	20.3516	−	17.0770i	0.855443	−	0.717802i
$567$	0.152704	−	0.866025i	0.00641295	−	0.0363696i
$568$	7.21688	−	2.62673i	0.302814	−	0.110215i
$569$	−18.4074			−0.771676			−0.385838	−	0.922566i	$-0.626088\pi$
$569$	−18.4074			−0.771676			−0.385838	+	0.922566i	$0.626088\pi$
$570$	4.07398	−	1.55007i	0.170640	−	0.0649251i
$571$	−33.3901			−1.39733			−0.698666	−	0.715448i	$-0.746223\pi$
$571$	−33.3901			−1.39733			−0.698666	+	0.715448i	$0.746223\pi$
$572$	−0.407604	+	0.148356i	−0.0170428	+	0.00620306i
$573$	−3.44996	+	19.5657i	−0.144124	+	0.817369i
$574$	1.37551	−	1.15419i	0.0574129	−	0.0481751i
$575$	−4.02094	−	3.37397i	−0.167685	−	0.140704i
$576$	0.173648	+	0.984808i	0.00723534	+	0.0410337i
$577$	23.0822	+	39.9795i	0.960924	+	1.66437i	0.720189	+	0.693778i	$0.244055\pi$
$577$	23.0822	+	39.9795i	0.960924	+	1.66437i	0.240735	+	0.970591i	$0.422611\pi$
$578$	−6.14203	+	10.6383i	−0.255475	+	0.442495i
$579$	−12.6677	−	4.61067i	−0.526452	−	0.191613i
$580$	5.14543	+	1.87278i	0.213652	+	0.0777631i
$581$	6.18092	−	10.7057i	0.256428	−	0.444146i
$582$	−3.66250	−	6.34364i	−0.151816	−	0.262952i
$583$	−0.262174	−	1.48686i	−0.0108581	−	0.0615796i
$584$	−8.27972	−	6.94751i	−0.342617	−	0.287490i
$585$	−0.624485	+	0.524005i	−0.0258193	+	0.0216650i
$586$	−3.26604	+	18.5227i	−0.134919	+	0.765164i
$587$	−40.3264	+	14.6776i	−1.66445	+	0.605810i	−0.991053	−	0.133472i	$-0.957387\pi$
$587$	−40.3264	+	14.6776i	−1.66445	+	0.605810i	−0.673396	+	0.739282i	$0.735165\pi$
$588$	6.22668			0.256784
$589$	−1.80335	+	11.1723i	−0.0743057	+	0.460345i
$590$	−0.162504			−0.00669018
$591$	11.2973	−	4.11186i	0.464707	−	0.169140i
$592$	0.439693	−	2.49362i	0.0180713	−	0.102487i
$593$	4.33821	−	3.64019i	0.178149	−	0.149485i	−0.549353	−	0.835590i	$-0.685126\pi$
$593$	4.33821	−	3.64019i	0.178149	−	0.149485i	0.727502	+	0.686106i	$0.240681\pi$
$594$	−0.407604	−	0.342020i	−0.0167242	−	0.0140333i
$595$	−0.826352	−	4.68647i	−0.0338771	−	0.192127i
$596$	6.58899	+	11.4125i	0.269896	+	0.467473i
$597$	0.735300	−	1.27358i	0.0300938	−	0.0521240i
$598$	4.02094	+	1.46350i	0.164429	+	0.0598471i
$599$	−7.69119	−	2.79936i	−0.314253	−	0.114379i	0.180078	−	0.983652i	$-0.442365\pi$
$599$	−7.69119	−	2.79936i	−0.314253	−	0.114379i	−0.494332	+	0.869273i	$0.664587\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−1.76945	−	3.06477i	−0.0721773	−	0.125015i	0.827678	−	0.561203i	$-0.189661\pi$
$601$	−1.76945	−	3.06477i	−0.0721773	−	0.125015i	−0.899855	+	0.436189i	$0.856328\pi$
$602$	−0.262174	−	1.48686i	−0.0106854	−	0.0606000i
$603$	8.96451	+	7.52211i	0.365063	+	0.306324i
$604$	7.25284	−	6.08586i	0.295114	−	0.247630i
$605$	1.86097	−	10.5541i	0.0756591	−	0.429084i
$606$	5.27719	−	1.92074i	0.214371	−	0.0780247i
$607$	−35.2077			−1.42904			−0.714518	−	0.699617i	$-0.753354\pi$
$607$	−35.2077			−1.42904			−0.714518	+	0.699617i	$0.753354\pi$
$608$	2.12449	−	3.80612i	0.0861593	−	0.154359i
$609$	−4.81521			−0.195122
$610$	1.32635	−	0.482753i	0.0537024	−	0.0195461i
$611$	1.30928	−	7.42528i	0.0529677	−	0.300395i
$612$	4.14543	−	3.47843i	0.167569	−	0.140607i
$613$	−27.9127	−	23.4215i	−1.12738	−	0.945985i	−0.128428	−	0.991719i	$-0.540993\pi$
$613$	−27.9127	−	23.4215i	−1.12738	−	0.945985i	−0.998954	+	0.0457334i	$0.985438\pi$
$614$	−1.09761	−	6.22486i	−0.0442960	−	0.251215i
$615$	−1.02094	−	1.76833i	−0.0411685	−	0.0713059i
$616$	−0.233956	+	0.405223i	−0.00942634	+	0.0163269i
$617$	37.6600	+	13.7071i	1.51614	+	0.551828i	0.960180	−	0.279383i	$-0.0901300\pi$
$617$	37.6600	+	13.7071i	1.51614	+	0.551828i	0.555956	+	0.831212i	$0.312352\pi$
$618$	15.5005	+	5.64171i	0.623520	+	0.226943i
$619$	16.2716	−	28.1832i	0.654009	−	1.13278i	−0.328132	−	0.944632i	$-0.606419\pi$
$619$	16.2716	−	28.1832i	0.654009	−	1.13278i	0.982141	−	0.188145i	$-0.0602477\pi$
$620$	1.29813	+	2.24843i	0.0521343	+	0.0902992i
$621$	0.911474	+	5.16923i	0.0365762	+	0.207434i
$622$	8.28880	+	6.95513i	0.332351	+	0.278875i
$623$	−2.71301	+	2.27649i	−0.108694	+	0.0912055i
$624$	−0.141559	+	0.802823i	−0.00566691	+	0.0321386i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	5.07697			0.202917
$627$	0.435822	+	2.27801i	0.0174051	+	0.0909748i
$628$	−5.77332			−0.230380
$629$	−12.8760	+	4.68647i	−0.513399	+	0.186862i
$630$	−0.152704	+	0.866025i	−0.00608386	+	0.0345033i
$631$	19.3412	−	16.2292i	0.769961	−	0.646074i	−0.170738	−	0.985316i	$-0.554615\pi$
$631$	19.3412	−	16.2292i	0.769961	−	0.646074i	0.940699	+	0.339242i	$0.110171\pi$
$632$	3.72075	+	3.12208i	0.148004	+	0.124190i
$633$	−3.56923	−	20.2421i	−0.141864	−	0.804552i
$634$	1.43969	+	2.49362i	0.0571775	+	0.0990343i
$635$	−1.17365	+	2.03282i	−0.0465748	+	0.0806699i
$636$	−2.66637	−	0.970481i	−0.105729	−	0.0384821i
$637$	4.76991	+	1.73611i	0.188991	+	0.0687871i
$638$	−1.45677	+	2.52319i	−0.0576739	+	0.0998942i
$639$	3.84002	+	6.65111i	0.151909	+	0.263114i
$640$	−0.173648	−	0.984808i	−0.00686405	−	0.0389279i
$641$	6.77972	+	5.68886i	0.267783	+	0.224696i	0.766785	−	0.641905i	$-0.221855\pi$
$641$	6.77972	+	5.68886i	0.267783	+	0.224696i	−0.499002	+	0.866601i	$0.666300\pi$
$642$	−2.31521	+	1.94269i	−0.0913740	+	0.0766718i
$643$	−2.11293	+	11.9830i	−0.0833258	+	0.472564i	0.914379	+	0.404858i	$0.132679\pi$
$643$	−2.11293	+	11.9830i	−0.0833258	+	0.472564i	−0.997705	+	0.0677061i	$0.978432\pi$
$644$	4.33750	−	1.57872i	0.170921	−	0.0622103i
$645$	−1.71688			−0.0676021
$646$	−23.5856	+	0.342020i	−0.927963	+	0.0134566i
$647$	0.238541			0.00937802			0.00468901	−	0.999989i	$-0.498507\pi$
$647$	0.238541			0.00937802			0.00468901	+	0.999989i	$0.498507\pi$
$648$	−0.939693	+	0.342020i	−0.0369146	+	0.0134358i
$649$	0.0150147	−	0.0851529i	0.000589380	−	0.00334254i
$650$	0.624485	−	0.524005i	0.0244943	−	0.0205532i
$651$	−1.74897	−	1.46756i	−0.0685476	−	0.0575182i
$652$	0.328878	+	1.86516i	0.0128799	+	0.0730453i
$653$	−4.84524	−	8.39220i	−0.189609	−	0.328412i	0.755511	−	0.655136i	$-0.227389\pi$
$653$	−4.84524	−	8.39220i	−0.189609	−	0.328412i	−0.945120	+	0.326724i	$0.894055\pi$
$654$	−0.836152	+	1.44826i	−0.0326961	+	0.0566314i
$655$	11.7442	+	4.27455i	0.458885	+	0.167020i
$656$	−1.91875	−	0.698367i	−0.0749145	−	0.0272667i
$657$	5.40420	−	9.36035i	0.210838	−	0.365182i
$658$	−4.06670	−	7.04374i	−0.158537	−	0.274593i
$659$	0.795912	+	4.51384i	0.0310043	+	0.175834i	0.996378	−	0.0850377i	$-0.0271011\pi$
$659$	0.795912	+	4.51384i	0.0310043	+	0.175834i	−0.965373	+	0.260872i	$0.915990\pi$
$660$	0.407604	+	0.342020i	0.0158660	+	0.0133131i
$661$	−14.2784	+	11.9810i	−0.555364	+	0.466006i	−0.876753	−	0.480942i	$-0.840295\pi$
$661$	−14.2784	+	11.9810i	−0.555364	+	0.466006i	0.321388	+	0.946947i	$0.395850\pi$
$662$	0.208263	−	1.18112i	0.00809438	−	0.0459055i
$663$	4.14543	−	1.50881i	0.160995	−	0.0585974i
$664$	−14.0574			−0.545532
$665$	2.90033	−	2.50622i	0.112470	−	0.0971870i
$666$	2.53209			0.0981165
$667$	27.0082	−	9.83018i	1.04576	−	0.380626i
$668$	1.14496	−	6.49341i	0.0442999	−	0.251237i
$669$	17.6630	−	14.8210i	0.682890	−	0.573013i
$670$	−8.96451	−	7.52211i	−0.346329	−	0.290605i
$671$	0.130415	+	0.739620i	0.00503461	+	0.0285527i
$672$	0.439693	+	0.761570i	0.0169615	+	0.0293782i
$673$	6.96720	−	12.0675i	0.268566	−	0.465169i	−0.699926	−	0.714215i	$-0.746784\pi$
$673$	6.96720	−	12.0675i	0.268566	−	0.465169i	0.968492	+	0.249046i	$0.0801170\pi$
$674$	−14.2344	−	5.18091i	−0.548289	−	0.199561i
$675$	0.939693	+	0.342020i	0.0361688	+	0.0131644i
$676$	6.16772	−	10.6828i	0.237220	−	0.410877i
$677$	−18.2208	−	31.5593i	−0.700280	−	1.21292i	−0.968368	−	0.249527i	$-0.919725\pi$
$677$	−18.2208	−	31.5593i	−0.700280	−	1.21292i	0.268088	−	0.963395i	$-0.413608\pi$
$678$	−2.54664	−	14.4427i	−0.0978030	−	0.554668i
$679$	−4.93448	−	4.14052i	−0.189368	−	0.158899i
$680$	−4.14543	+	3.47843i	−0.158970	+	0.133392i
$681$	0.963326	−	5.46329i	0.0369147	−	0.209354i
$682$	−1.29813	+	0.472482i	−0.0497081	+	0.0180923i
$683$	−28.5503			−1.09245			−0.546223	−	0.837640i	$-0.683935\pi$
$683$	−28.5503			−1.09245			−0.546223	+	0.837640i	$0.683935\pi$
$684$	4.11721	+	1.43128i	0.157426	+	0.0547265i
$685$	−10.1557			−0.388029
$686$	10.9299	−	3.97816i	0.417305	−	0.151887i
$687$	−0.206204	+	1.16944i	−0.00786717	+	0.0446169i
$688$	−1.31521	+	1.10359i	−0.0501418	+	0.0420740i
$689$	−1.77197	−	1.48686i	−0.0675068	−	0.0566450i
$690$	−0.911474	−	5.16923i	−0.0346992	−	0.196789i
$691$	0.0170741	+	0.0295733i	0.000649531	+	0.00112502i	0.866350	−	0.499437i	$-0.166460\pi$
$691$	0.0170741	+	0.0295733i	0.000649531	+	0.00112502i	−0.865700	+	0.500562i	$0.833127\pi$
$692$	8.69846	−	15.0662i	0.330666	−	0.572730i
$693$	−0.439693	−	0.160035i	−0.0167025	−	0.00607923i
$694$	12.7395	+	4.63679i	0.483584	+	0.176010i
$695$	8.25537	−	14.2987i	0.313144	−	0.542381i
$696$	2.73783	+	4.74205i	0.103777	+	0.179747i
$697$	1.91875	+	10.8818i	0.0726778	+	0.412176i
$698$	−18.7822	−	15.7602i	−0.710918	−	0.596531i
$699$	−4.53983	+	3.80937i	−0.171712	+	0.144084i
$700$	0.152704	−	0.866025i	0.00577166	−	0.0327327i
$701$	−43.8448	+	15.9582i	−1.65600	+	0.602733i	−0.989726	−	0.142977i	$-0.954332\pi$
$701$	−43.8448	+	15.9582i	−1.65600	+	0.602733i	−0.666270	+	0.745710i	$0.732110\pi$
$702$	−0.815207			−0.0307680
$703$	−8.55690	−	6.97118i	−0.322730	−	0.262923i
$704$	0.532089			0.0200539
$705$	−8.69119	+	3.16333i	−0.327329	+	0.119138i
$706$	−5.50980	+	31.2476i	−0.207364	+	1.17602i
$707$	3.78312	−	3.17441i	0.142279	−	0.119386i
$708$	−0.124485	−	0.104455i	−0.00467844	−	0.00392568i
$709$	0.132170	+	0.749571i	0.00496373	+	0.0281507i	0.987189	−	0.159555i	$-0.0510060\pi$
$709$	0.132170	+	0.749571i	0.00496373	+	0.0281507i	−0.982225	+	0.187706i	$0.939895\pi$
$710$	−3.84002	−	6.65111i	−0.144113	−	0.249612i
$711$	−2.42855	+	4.20637i	−0.0910777	+	0.157751i
$712$	3.78446	+	1.37743i	0.141829	+	0.0516214i
$713$	12.8059	+	4.66096i	0.479584	+	0.174554i
$714$	2.37939	−	4.12122i	0.0890463	−	0.154233i
$715$	0.216881	+	0.375650i	0.00811091	+	0.0140485i
$716$	1.71419	+	9.72167i	0.0640624	+	0.363316i
$717$	13.1047	+	10.9962i	0.489405	+	0.410659i
$718$	15.9192	−	13.3578i	0.594100	−	0.498509i
$719$	−3.77760	+	21.4238i	−0.140881	+	0.798974i	0.829702	+	0.558206i	$0.188510\pi$
$719$	−3.77760	+	21.4238i	−0.140881	+	0.798974i	−0.970583	+	0.240768i	$0.922601\pi$
$720$	0.939693	−	0.342020i	0.0350203	−	0.0127463i
$721$	14.5057			0.540220
$722$	−9.97313	−	16.1721i	−0.371161	−	0.601863i
$723$	−9.40373			−0.349729
$724$	−7.93629	+	2.88857i	−0.294950	+	0.107353i
$725$	0.950837	−	5.39246i	0.0353132	−	0.200271i
$726$	8.20961	−	6.88868i	0.304687	−	0.255663i
$727$	−37.7144	−	31.6461i	−1.39875	−	1.17369i	−0.961651	−	0.274278i	$-0.911561\pi$
$727$	−37.7144	−	31.6461i	−1.39875	−	1.17369i	−0.437100	−	0.899413i	$-0.643994\pi$
$728$	0.124485	+	0.705990i	0.00461373	+	0.0261657i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−5.40420	+	9.36035i	−0.200018	+	0.346442i
$731$	8.73055	+	3.17766i	0.322911	+	0.117530i
$732$	1.32635	+	0.482753i	0.0490234	+	0.0178430i
$733$	−22.2049	+	38.4599i	−0.820155	+	1.42055i	0.0854111	+	0.996346i	$0.472780\pi$
$733$	−22.2049	+	38.4599i	−0.820155	+	1.42055i	−0.905566	+	0.424205i	$0.860554\pi$
$734$	−2.91875	−	5.05542i	−0.107733	−	0.186599i
$735$	−1.08125	−	6.13208i	−0.0398826	−	0.226185i
$736$	−4.02094	−	3.37397i	−0.148214	−	0.124366i
$737$	4.76991	−	4.00243i	0.175702	−	0.147432i
$738$	0.354570	−	2.01087i	0.0130519	−	0.0740211i
$739$	35.0035	−	12.7402i	1.28762	−	0.468656i	0.394677	−	0.918820i	$-0.370857\pi$
$739$	35.0035	−	12.7402i	1.28762	−	0.468656i	0.892946	+	0.450163i	$0.148634\pi$
$740$	−2.53209			−0.0930814
$741$	2.75490	+	2.24438i	0.101204	+	0.0824492i
$742$	−2.49525			−0.0916036
$743$	24.0488	−	8.75303i	0.882263	−	0.321118i	0.139140	−	0.990273i	$-0.455566\pi$
$743$	24.0488	−	8.75303i	0.882263	−	0.321118i	0.743123	+	0.669155i	$0.233344\pi$
$744$	−0.450837	+	2.55682i	−0.0165285	+	0.0937377i
$745$	10.0949	−	8.47065i	0.369849	−	0.310340i
$746$	19.1288	+	16.0510i	0.700356	+	0.587668i
$747$	−2.44104	−	13.8438i	−0.0893129	−	0.506518i
$748$	−1.43969	−	2.49362i	−0.0526404	−	0.0911758i
$749$	−1.32888	+	2.30168i	−0.0485561	+	0.0841017i
$750$	−0.939693	−	0.342020i	−0.0343127	−	0.0124888i
$751$	−22.7481	−	8.27963i	−0.830090	−	0.302128i	−0.108194	−	0.994130i	$-0.534507\pi$
$751$	−22.7481	−	8.27963i	−0.830090	−	0.302128i	−0.721896	+	0.692002i	$0.756729\pi$
$752$	−4.62449	+	8.00984i	−0.168638	+	0.292089i
$753$	−6.08899	−	10.5464i	−0.221895	−	0.384334i
$754$	0.775129	+	4.39598i	0.0282285	+	0.160092i
$755$	−7.25284	−	6.08586i	−0.263958	−	0.221487i
$756$	−0.673648	+	0.565258i	−0.0245003	+	0.0205582i
$757$	6.75759	−	38.3242i	0.245609	−	1.39292i	−0.573466	−	0.819229i	$-0.694402\pi$
$757$	6.75759	−	38.3242i	0.245609	−	1.39292i	0.819075	−	0.573687i	$-0.194487\pi$
$758$	−25.5847	+	9.31207i	−0.929279	+	0.338230i
$759$	2.79292			0.101377
$760$	−4.11721	−	1.43128i	−0.149347	−	0.0519181i
$761$	−48.9050			−1.77280			−0.886402	−	0.462916i	$-0.846803\pi$
$761$	−48.9050			−1.77280			−0.886402	+	0.462916i	$0.846803\pi$
$762$	−2.20574	+	0.802823i	−0.0799054	+	0.0290832i
$763$	−0.255367	+	1.44826i	−0.00924490	+	0.0524305i
$764$	15.2194	−	12.7706i	0.550619	−	0.462024i
$765$	−4.14543	−	3.47843i	−0.149878	−	0.125763i
$766$	5.34137	+	30.2924i	0.192991	+	1.09451i
$767$	−0.0662372	−	0.114726i	−0.00239169	−	0.00414252i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−41.2622	−	15.0182i	−1.48795	−	0.541571i	−0.535044	−	0.844824i	$-0.679705\pi$
$769$	−41.2622	−	15.0182i	−1.48795	−	0.541571i	−0.952910	+	0.303253i	$0.901927\pi$
$770$	0.439693	+	0.160035i	0.0158454	+	0.00576726i
$771$	12.8439	−	22.2463i	0.462562	−	0.801180i
$772$	6.74035	+	11.6746i	0.242591	+	0.420179i
$773$	3.86437	+	21.9159i	0.138992	+	0.788261i	0.971996	+	0.234995i	$0.0755075\pi$
$773$	3.86437	+	21.9159i	0.138992	+	0.788261i	−0.833005	+	0.553266i	$0.813381\pi$
$774$	−1.31521	−	1.10359i	−0.0472742	−	0.0396677i
$775$	1.98886	−	1.66885i	0.0714418	−	0.0599468i
$776$	−1.27197	+	7.21372i	−0.0456612	+	0.258958i
$777$	2.09240	−	0.761570i	0.0750643	−	0.0273212i
$778$	15.6527			0.561177
$779$	−6.73442	+	5.81932i	−0.241286	+	0.208499i
$780$	0.815207			0.0291891
$781$	3.84002	−	1.39765i	0.137407	−	0.0500120i
$782$	−4.93242	+	27.9731i	−0.176383	+	1.00032i
$783$	−4.19459	+	3.51968i	−0.149903	+	0.125783i
$784$	−4.76991	−	4.00243i	−0.170354	−	0.142944i
$785$	1.00253	+	5.68561i	0.0357817	+	0.202928i
$786$	6.24897	+	10.8235i	0.222893	+	0.386063i
$787$	7.90033	−	13.6838i	0.281616	−	0.487774i	−0.690167	−	0.723650i	$-0.742463\pi$
$787$	7.90033	−	13.6838i	0.281616	−	0.487774i	0.971783	+	0.235877i	$0.0757961\pi$
$788$	−11.2973	−	4.11186i	−0.402448	−	0.146479i
$789$	3.35117	+	1.21972i	0.119305	+	0.0434234i
$790$	2.42855	−	4.20637i	0.0864039	−	0.149656i
$791$	−6.44831	−	11.1688i	−0.229276	−	0.397117i
$792$	0.0923963	+	0.524005i	0.00328316	+	0.0186197i
$793$	0.881445	+	0.739620i	0.0313010	+	0.0262647i
$794$	22.1596	−	18.5941i	0.786414	−	0.659879i
$795$	−0.492726	+	2.79439i	−0.0174752	+	0.0991067i
$796$	−1.38191	+	0.502975i	−0.0489806	+	0.0178275i
$797$	−29.1898			−1.03396			−0.516979	−	0.855998i	$-0.672943\pi$
$797$	−29.1898			−1.03396			−0.516979	+	0.855998i	$0.672943\pi$
$798$	3.83275	−	0.0555796i	0.135678	−	0.00196750i
$799$	50.0506			1.77066
$800$	−0.939693	+	0.342020i	−0.0332232	+	0.0120922i
$801$	−0.699340	+	3.96616i	−0.0247100	+	0.140137i
$802$	−1.64337	+	1.37895i	−0.0580294	+	0.0486925i
$803$	−4.40554	−	3.69669i	−0.155468	−	0.130453i
$804$	−2.03209	−	11.5245i	−0.0716662	−	0.406439i
$805$	−2.30793	−	3.99746i	−0.0813440	−	0.140892i
$806$	−1.05825	+	1.83294i	−0.0372752	+	0.0645625i
$807$	11.7763	+	4.28623i	0.414546	+	0.150882i
$808$	−5.27719	−	1.92074i	−0.185651	−	0.0675714i
$809$	−11.9440	+	20.6877i	−0.419930	+	0.727340i	−0.995932	−	0.0901085i	$-0.971279\pi$
$809$	−11.9440	+	20.6877i	−0.419930	+	0.727340i	0.576002	+	0.817448i	$0.304612\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	8.90049	+	50.4772i	0.312539	+	1.77249i	0.585702	+	0.810527i	$0.300819\pi$
$811$	8.90049	+	50.4772i	0.312539	+	1.77249i	−0.273163	+	0.961968i	$0.588070\pi$
$812$	3.68866	+	3.09516i	0.129447	+	0.108619i
$813$	12.2135	−	10.2483i	0.428345	−	0.359424i
$814$	0.233956	−	1.32683i	0.00820014	−	0.0465053i
$815$	1.77972	−	0.647763i	0.0623407	−	0.0226902i
$816$	−5.41147			−0.189439
$817$	1.40626	+	7.35040i	0.0491988	+	0.257158i
$818$	13.1652			0.460310
$819$	−0.673648	+	0.245188i	−0.0235392	+	0.00856756i
$820$	−0.354570	+	2.01087i	−0.0123821	+	0.0702226i
$821$	−30.4152	+	25.5214i	−1.06150	+	0.890702i	−0.994255	−	0.107035i	$-0.965864\pi$
$821$	−30.4152	+	25.5214i	−1.06150	+	0.890702i	−0.0672419	+	0.997737i	$0.521420\pi$
$822$	−7.77972	−	6.52796i	−0.271349	−	0.227689i
$823$	−9.00552	−	51.0728i	−0.313913	−	1.78029i	−0.578253	−	0.815858i	$-0.696265\pi$
$823$	−9.00552	−	51.0728i	−0.313913	−	1.78029i	0.264340	−	0.964430i	$-0.414846\pi$
$824$	−8.24763	−	14.2853i	−0.287320	−	0.497652i
$825$	0.266044	−	0.460802i	0.00926248	−	0.0160431i
$826$	−0.134285	−	0.0488759i	−0.00467238	−	0.00170061i
$827$	27.8323	+	10.1301i	0.967825	+	0.352260i	0.777095	−	0.629383i	$-0.216692\pi$
$827$	27.8323	+	10.1301i	0.967825	+	0.352260i	0.190730	+	0.981643i	$0.438915\pi$
$828$	2.62449	−	4.54574i	0.0912072	−	0.157975i
$829$	−18.3105	−	31.7146i	−0.635949	−	1.10150i	−0.986313	−	0.164882i	$-0.947276\pi$
$829$	−18.3105	−	31.7146i	−0.635949	−	1.10150i	0.350365	−	0.936613i	$-0.386058\pi$
$830$	2.44104	+	13.8438i	0.0847296	+	0.480526i
$831$	6.93629	+	5.82024i	0.240617	+	0.201902i
$832$	0.624485	−	0.524005i	0.0216501	−	0.0181666i
$833$	−5.85117	+	33.1836i	−0.202731	+	1.14974i
$834$	15.5150	−	5.64700i	0.537241	−	0.195540i
$835$	−6.59358			−0.228180
$836$	1.13041	−	2.02520i	0.0390962	−	0.0700428i
$837$	−2.59627			−0.0897401
$838$	−32.2165	+	11.7258i	−1.11290	+	0.405062i
$839$	8.68257	−	49.2413i	0.299756	−	1.70000i	−0.347463	−	0.937694i	$-0.612957\pi$
$839$	8.68257	−	49.2413i	0.299756	−	1.70000i	0.647218	−	0.762305i	$-0.275932\pi$
$840$	0.673648	−	0.565258i	0.0232431	−	0.0195033i
$841$	0.752841	+	0.631708i	0.0259600	+	0.0217830i
$842$	−1.70068	−	9.64506i	−0.0586095	−	0.332391i
$843$	11.7378	+	20.3305i	0.404272	+	0.700220i
$844$	−10.2772	+	17.8006i	−0.353755	+	0.612722i
$845$	−11.5915	−	4.21897i	−0.398760	−	0.145137i
$846$	−8.69119	−	3.16333i	−0.298809	−	0.108758i
$847$	4.71213	−	8.16165i	0.161911	−	0.280438i
$848$	1.41875	+	2.45734i	0.0487200	+	0.0843855i
$849$	−4.61334	−	26.1636i	−0.158329	−	0.897931i
$850$	4.14543	+	3.47843i	0.142187	+	0.119309i
$851$	−10.1814	+	8.54320i	−0.349014	+	0.292857i
$852$	1.33363	−	7.56337i	0.0456893	−	0.259117i
$853$	18.2995	−	6.66047i	0.626562	−	0.228050i	−0.00917213	−	0.999958i	$-0.502920\pi$
$853$	18.2995	−	6.66047i	0.626562	−	0.228050i	0.635734	+	0.771908i	$0.280697\pi$
$854$	1.24123			0.0424740
$855$	0.694593	−	4.30320i	0.0237546	−	0.147166i
$856$	3.02229			0.103300
$857$	28.0976	−	10.2267i	0.959796	−	0.349337i	0.185843	−	0.982580i	$-0.440499\pi$
$857$	28.0976	−	10.2267i	0.959796	−	0.349337i	0.773954	+	0.633242i	$0.218276\pi$
$858$	−0.0753221	+	0.427173i	−0.00257145	+	0.0145834i
$859$	−2.35117	+	1.97286i	−0.0802208	+	0.0673132i	−0.682016	−	0.731337i	$-0.738897\pi$
$859$	−2.35117	+	1.97286i	−0.0802208	+	0.0673132i	0.601795	+	0.798650i	$0.294452\pi$
$860$	1.31521	+	1.10359i	0.0448482	+	0.0376321i
$861$	−0.311804	−	1.76833i	−0.0106262	−	0.0602645i
$862$	−7.52435	−	13.0326i	−0.256280	−	0.443891i
$863$	9.59627	−	16.6212i	0.326661	−	0.565793i	−0.655186	−	0.755467i	$-0.727410\pi$
$863$	9.59627	−	16.6212i	0.326661	−	0.565793i	0.981847	+	0.189674i	$0.0607432\pi$
$864$	0.939693	+	0.342020i	0.0319690	+	0.0116358i
$865$	−16.3478	−	5.95010i	−0.555841	−	0.202309i
$866$	−2.70187	+	4.67977i	−0.0918132	+	0.159025i
$867$	6.14203	+	10.6383i	0.208594	+	0.361296i
$868$	0.396459	+	2.24843i	0.0134567	+	0.0763168i
$869$	1.97977	+	1.66122i	0.0671591	+	0.0563532i
$870$	4.19459	−	3.51968i	0.142210	−	0.119328i
$871$	1.65657	−	9.39490i	0.0561309	−	0.318334i
$872$	1.57145	−	0.571962i	0.0532161	−	0.0193691i
$873$	−7.32501			−0.247914
$874$	−21.3842	+	8.13625i	−0.723331	+	0.275213i
$875$	−0.879385			−0.0297286
$876$	−10.1566	+	3.69669i	−0.343159	+	0.124900i
$877$	−8.87060	+	50.3077i	−0.299539	+	1.69877i	0.348619	+	0.937265i	$0.386651\pi$
$877$	−8.87060	+	50.3077i	−0.299539	+	1.69877i	−0.648158	+	0.761506i	$0.724460\pi$
$878$	−15.8610	+	13.3089i	−0.535282	+	0.449155i
$879$	14.4081	+	12.0898i	0.485972	+	0.407779i
$880$	−0.0923963	−	0.524005i	−0.00311468	−	0.0176642i
$881$	−14.1040	−	24.4289i	−0.475176	−	0.823029i	0.524420	−	0.851460i	$-0.324282\pi$
$881$	−14.1040	−	24.4289i	−0.475176	−	0.823029i	−0.999596	+	0.0284308i	$0.990949\pi$
$882$	3.11334	−	5.39246i	0.104832	−	0.181574i
$883$	−39.7863	−	14.4810i	−1.33891	−	0.487325i	−0.429444	−	0.903093i	$-0.641290\pi$
$883$	−39.7863	−	14.4810i	−1.33891	−	0.487325i	−0.909471	+	0.415768i	$0.863513\pi$
$884$	−4.14543	−	1.50881i	−0.139426	−	0.0507469i
$885$	−0.0812519	+	0.140732i	−0.00273125	+	0.00473067i
$886$	−1.18004	−	2.04390i	−0.0396444	−	0.0686661i
$887$	7.28968	+	41.3418i	0.244763	+	1.38812i	0.821041	+	0.570869i	$0.193393\pi$
$887$	7.28968	+	41.3418i	0.244763	+	1.38812i	−0.576278	+	0.817254i	$0.695495\pi$
$888$	−1.93969	−	1.62760i	−0.0650918	−	0.0546185i
$889$	−1.58125	+	1.32683i	−0.0530335	+	0.0445004i
$890$	0.699340	−	3.96616i	0.0234419	−	0.132946i
$891$	−0.500000	+	0.181985i	−0.0167506	+	0.00609673i
$892$	−23.0574			−0.772018
$893$	20.6618	+	34.6181i	0.691420	+	1.15845i
$894$	13.1780			0.440738
$895$	9.27631	−	3.37630i	0.310073	−	0.112857i
$896$	0.152704	−	0.866025i	0.00510147	−	0.0289319i
$897$	3.27790	−	2.75049i	0.109446	−	0.0918361i
$898$	20.6860	+	17.3576i	0.690300	+	0.579230i
$899$	2.46863	+	14.0003i	0.0823333	+	0.466935i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	7.67752	−	13.2979i	0.255775	−	0.443016i
$902$	−1.02094	−	0.371593i	−0.0339937	−	0.0123727i
$903$	−1.41875	−	0.516382i	−0.0472130	−	0.0171841i
$904$	−7.33275	+	12.7007i	−0.243884	+	0.422419i
$905$	4.22281	+	7.31412i	0.140371	+	0.243130i
$906$	−1.64409	−	9.32407i	−0.0546211	−	0.309772i
$907$	3.23648	+	2.71573i	0.107466	+	0.0901744i	0.694937	−	0.719070i	$-0.255432\pi$
$907$	3.23648	+	2.71573i	0.107466	+	0.0901744i	−0.587472	+	0.809245i	$0.699877\pi$
$908$	−4.24969	+	3.56591i	−0.141031	+	0.118339i
$909$	0.975185	−	5.53055i	0.0323448	−	0.183437i
$910$	0.673648	−	0.245188i	0.0223312	−	0.00812790i
$911$	17.0401			0.564565			0.282282	−	0.959331i	$-0.408908\pi$
$911$	17.0401			0.564565			0.282282	+	0.959331i	$0.408908\pi$
$912$	−2.23396	−	3.74292i	−0.0739737	−	0.123940i
$913$	−7.47977			−0.247544
$914$	5.93494	−	2.16014i	0.196311	−	0.0714512i
$915$	0.245100	−	1.39003i	0.00810275	−	0.0459530i
$916$	0.909663	−	0.763298i	0.0300561	−	0.0252201i
$917$	8.41921	+	7.06456i	0.278027	+	0.233292i
$918$	−0.939693	−	5.32926i	−0.0310145	−	0.175892i
$919$	11.2208	+	19.4349i	0.370138	+	0.641099i	0.989587	−	0.143939i	$-0.0459769\pi$
$919$	11.2208	+	19.4349i	0.370138	+	0.641099i	−0.619448	+	0.785038i	$0.712644\pi$
$920$	−2.62449	+	4.54574i	−0.0865267	+	0.149869i
$921$	−5.93969	−	2.16187i	−0.195720	−	0.0712361i
$922$	−26.6755	−	9.70907i	−0.878509	−	0.319751i
$923$	3.13041	−	5.42204i	0.103039	−	0.178469i
$924$	0.233956	+	0.405223i	0.00769657	+	0.0133309i
$925$	0.439693	+	2.49362i	0.0144570	+	0.0819897i
$926$	−4.25078	−	3.56683i	−0.139689	−	0.117213i
$927$	12.6361	−	10.6029i	0.415024	−	0.348246i
$928$	0.950837	−	5.39246i	0.0312128	−	0.177016i
$929$	−40.7614	+	14.8359i	−1.33734	+	0.486751i	−0.908973	−	0.416856i	$-0.863132\pi$
$929$	−40.7614	+	14.8359i	−1.33734	+	0.486751i	−0.428364	+	0.903606i	$0.640910\pi$
$930$	2.59627			0.0851349
$931$	−25.3674	+	9.65177i	−0.831382	+	0.316324i
$932$	5.92633			0.194123
$933$	10.1677	−	3.70075i	0.332876	−	0.121157i
$934$	4.84049	−	27.4518i	0.158386	−	0.898250i
$935$	−2.20574	+	1.85083i	−0.0721353	+	0.0605287i
$936$	0.624485	+	0.524005i	0.0204119	+	0.0171276i
$937$	6.71823	+	38.1010i	0.219475	+	1.24470i	0.872970	+	0.487773i	$0.162191\pi$
$937$	6.71823	+	38.1010i	0.219475	+	1.24470i	−0.653495	+	0.756930i	$0.726698\pi$
$938$	−5.14543	−	8.91215i	−0.168004	−	0.290992i
$939$	2.53849	−	4.39679i	0.0828403	−	0.143484i
$940$	8.69119	+	3.16333i	0.283475	+	0.103177i
$941$	33.4231	+	12.1650i	1.08956	+	0.396568i	0.823458	−	0.567377i	$-0.192042\pi$
$941$	33.4231	+	12.1650i	1.08956	+	0.396568i	0.266103	+	0.963945i	$0.414264\pi$
$942$	−2.88666	+	4.99984i	−0.0940524	+	0.162904i
$943$	5.35891	+	9.28190i	0.174510	+	0.302260i
$944$	0.0282185	+	0.160035i	0.000918434	+	0.00520870i
$945$	0.673648	+	0.565258i	0.0219138	+	0.0183878i
$946$	−0.699807	+	0.587208i	−0.0227527	+	0.0190918i
$947$	−4.04798	+	22.9572i	−0.131542	+	0.746010i	0.845664	+	0.533716i	$0.179205\pi$
$947$	−4.04798	+	22.9572i	−0.131542	+	0.746010i	−0.977206	+	0.212294i	$0.931906\pi$
$948$	4.56418	−	1.66122i	0.148238	−	0.0539541i
$949$	−8.81109			−0.286020
$950$	−0.694593	+	4.30320i	−0.0225356	+	0.139614i
$951$	2.87939			0.0933705
$952$	−4.47178	+	1.62760i	−0.144931	+	0.0527507i
$953$	−3.21136	+	18.2125i	−0.104026	+	0.589962i	0.887579	+	0.460656i	$0.152386\pi$
$953$	−3.21136	+	18.2125i	−0.104026	+	0.589962i	−0.991605	+	0.129306i	$0.958725\pi$
$954$	−2.17365	+	1.82391i	−0.0703745	+	0.0590512i
$955$	−15.2194	−	12.7706i	−0.492488	−	0.413247i
$956$	−2.97060	−	16.8471i	−0.0960761	−	0.544874i
$957$	1.45677	+	2.52319i	0.0470906	+	0.0815633i
$958$	−4.97044	+	8.60905i	−0.160588	+	0.278146i
$959$	−8.39218	−	3.05450i	−0.270998	−	0.0986351i
$960$	−0.939693	−	0.342020i	−0.0303284	−	0.0110387i
$961$	12.1297	−	21.0093i	0.391281	−	0.677718i
$962$	−1.03209	−	1.78763i	−0.0332759	−	0.0576355i
$963$	0.524815	+	2.97637i	0.0169119	+	0.0959123i
$964$	7.20368	+	6.04460i	0.232015	+	0.194684i
$965$	10.3268	−	8.66523i	0.332432	−	0.278944i
$966$	0.801537	−	4.54574i	0.0257890	−	0.146257i
$967$	14.4500	−	5.25936i	0.464679	−	0.169129i	−0.0990613	−	0.995081i	$-0.531584\pi$
$967$	14.4500	−	5.25936i	0.464679	−	0.169129i	0.563741	+	0.825952i	$0.309362\pi$
$968$	−10.7169			−0.344454
$969$	−11.4966	+	20.5967i	−0.369324	+	0.661662i
$970$	7.32501			0.235192
$971$	−38.1318	+	13.8788i	−1.22371	+	0.445393i	−0.871438	−	0.490505i	$-0.836812\pi$
$971$	−38.1318	+	13.8788i	−1.22371	+	0.445393i	−0.352270	+	0.935898i	$0.614590\pi$
$972$	−0.173648	+	0.984808i	−0.00556977	+	0.0315877i
$973$	11.1224	−	9.33282i	0.356569	−	0.299197i
$974$	4.65064	+	3.90235i	0.149016	+	0.125039i
$975$	−0.141559	−	0.802823i	−0.00453353	−	0.0257109i
$976$	−0.705737	−	1.22237i	−0.0225901	−	0.0391272i
$977$	18.3721	−	31.8214i	0.587776	−	1.01806i	−0.406747	−	0.913541i	$-0.633337\pi$
$977$	18.3721	−	31.8214i	0.587776	−	1.01806i	0.994523	−	0.104517i	$-0.0333297\pi$
$978$	1.77972	+	0.647763i	0.0569090	+	0.0207132i
$979$	2.01367	+	0.732916i	0.0643572	+	0.0234241i
$980$	−3.11334	+	5.39246i	−0.0994520	+	0.172256i
$981$	0.836152	+	1.44826i	0.0266963	+	0.0462393i
$982$	−2.83110	−	16.0560i	−0.0903440	−	0.512366i
$983$	−16.4099	−	13.7695i	−0.523394	−	0.439180i	0.342419	−	0.939547i	$-0.388754\pi$
$983$	−16.4099	−	13.7695i	−0.523394	−	0.439180i	−0.865813	+	0.500368i	$0.833198\pi$
$984$	−1.56418	+	1.31250i	−0.0498642	+	0.0418410i
$985$	−2.08765	+	11.8396i	−0.0665180	+	0.377242i
$986$	−27.8444	+	10.1345i	−0.886745	+	0.322749i
$987$	−8.13341			−0.258889
$988$	−0.667718	−	3.49011i	−0.0212430	−	0.111035i
$989$	9.01186			0.286560
$990$	0.500000	−	0.181985i	0.0158910	−	0.00578387i
$991$	3.60250	−	20.4308i	0.114437	−	0.649006i	−0.872590	−	0.488453i	$-0.837561\pi$
$991$	3.60250	−	20.4308i	0.114437	−	0.649006i	0.987027	−	0.160553i	$-0.0513276\pi$
$992$	1.98886	−	1.66885i	0.0631462	−	0.0529860i
$993$	−0.918748	−	0.770921i	−0.0291556	−	0.0244644i
$994$	−1.17277	−	6.65111i	−0.0371980	−	0.210961i
$995$	0.735300	+	1.27358i	0.0233106	+	0.0403751i
$996$	−7.02869	+	12.1740i	−0.222712	+	0.385749i
$997$	−42.3432	−	15.4117i	−1.34102	−	0.488092i	−0.430888	−	0.902406i	$-0.641799\pi$
$997$	−42.3432	−	15.4117i	−1.34102	−	0.488092i	−0.910134	+	0.414314i	$0.864022\pi$
$998$	0.233956	+	0.0851529i	0.00740573	+	0.00269547i
$999$	1.26604	−	2.19285i	0.0400559	−	0.0693788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.e.271.1	yes	6
19.4	even	9	inner	570.2.u.e.61.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.e.61.1	✓	6	19.4	even	9	inner
570.2.u.e.271.1	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.439693 - 0.761570i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.439693 - 0.761570i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.939693 + 0.342020i) q^{10} +(-0.266044 + 0.460802i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.141559 + 0.802823i) q^{13} +(0.673648 + 0.565258i) q^{14} +(0.766044 - 0.642788i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-5.08512 + 1.85083i) q^{17} +1.00000 q^{18} +(-3.37939 - 2.75314i) q^{19} -1.00000 q^{20} +(0.826352 - 0.300767i) q^{21} +(0.0923963 - 0.524005i) q^{22} +(-4.02094 + 3.37397i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(0.173648 + 0.984808i) q^{25} +(-0.407604 - 0.705990i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.826352 - 0.300767i) q^{28} +(-5.14543 - 1.87278i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-1.29813 - 2.24843i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.407604 - 0.342020i) q^{33} +(4.14543 - 3.47843i) q^{34} +(-0.152704 + 0.866025i) q^{35} +(-0.939693 + 0.342020i) q^{36} +2.53209 q^{37} +(4.11721 + 1.43128i) q^{38} -0.815207 q^{39} +(0.939693 - 0.342020i) q^{40} +(0.354570 - 2.01087i) q^{41} +(-0.673648 + 0.565258i) q^{42} +(-1.31521 - 1.10359i) q^{43} +(0.0923963 + 0.524005i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.62449 - 4.54574i) q^{46} +(-8.69119 - 3.16333i) q^{47} +(0.939693 + 0.342020i) q^{48} +(3.11334 - 5.39246i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.939693 - 5.32926i) q^{51} +(0.624485 + 0.524005i) q^{52} +(-2.17365 + 1.82391i) q^{53} +(-0.173648 + 0.984808i) q^{54} +(0.500000 - 0.181985i) q^{55} +0.879385 q^{56} +(3.29813 - 2.84997i) q^{57} +5.47565 q^{58} +(-0.152704 + 0.0555796i) q^{59} +(0.173648 - 0.984808i) q^{60} +(1.08125 - 0.907278i) q^{61} +(1.98886 + 1.66885i) q^{62} +(0.152704 + 0.866025i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.407604 - 0.705990i) q^{65} +(0.500000 + 0.181985i) q^{66} +(-10.9966 - 4.00243i) q^{67} +(-2.70574 + 4.68647i) q^{68} +(-2.62449 - 4.54574i) q^{69} +(-0.152704 - 0.866025i) q^{70} +(-5.88326 - 4.93664i) q^{71} +(0.766044 - 0.642788i) q^{72} +(-1.87686 + 10.6442i) q^{73} +(-2.37939 + 0.866025i) q^{74} -1.00000 q^{75} +(-4.35844 + 0.0632028i) q^{76} +0.467911 q^{77} +(0.766044 - 0.278817i) q^{78} +(0.843426 - 4.78331i) q^{79} +(-0.766044 + 0.642788i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.354570 + 2.01087i) q^{82} +(7.02869 + 12.1740i) q^{83} +(0.439693 - 0.761570i) q^{84} +(5.08512 + 1.85083i) q^{85} +(1.61334 + 0.587208i) q^{86} +(2.73783 - 4.74205i) q^{87} +(-0.266044 - 0.460802i) q^{88} +(-0.699340 - 3.96616i) q^{89} +(-0.766044 - 0.642788i) q^{90} +(0.549163 - 0.460802i) q^{91} +(-0.911474 + 5.16923i) q^{92} +(2.43969 - 0.887975i) q^{93} +9.24897 q^{94} +(0.819078 + 4.28125i) q^{95} -1.00000 q^{96} +(6.88326 - 2.50530i) q^{97} +(-1.08125 + 6.13208i) q^{98} +(0.407604 - 0.342020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 - 3 * q^8	\( 6 q + 3 q^{7} - 3 q^{8} + 3 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 9 q^{17} + 6 q^{18} - 9 q^{19} - 6 q^{20} + 6 q^{21} - 3 q^{22} - 21 q^{23} - 6 q^{26} + 3 q^{27} - 6 q^{28} - 15 q^{29} - 3 q^{30} + 6 q^{31} - 6 q^{33} + 9 q^{34} - 3 q^{35} + 6 q^{37} - 6 q^{38} - 12 q^{39} + 18 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} + 3 q^{45} + 3 q^{46} - 6 q^{47} + 12 q^{49} - 3 q^{50} - 9 q^{52} - 12 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{57} - 6 q^{58} - 3 q^{59} + 9 q^{61} + 18 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} - 3 q^{70} - 15 q^{73} - 3 q^{74} - 6 q^{75} - 18 q^{76} + 12 q^{77} + 27 q^{79} + 18 q^{82} - 9 q^{83} - 3 q^{84} + 9 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 33 q^{89} + 15 q^{91} + 15 q^{92} + 9 q^{93} + 30 q^{94} - 12 q^{95} - 6 q^{96} + 6 q^{97} - 9 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^7 - 3 * q^8 + 3 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 9 * q^17 + 6 * q^18 - 9 * q^19 - 6 * q^20 + 6 * q^21 - 3 * q^22 - 21 * q^23 - 6 * q^26 + 3 * q^27 - 6 * q^28 - 15 * q^29 - 3 * q^30 + 6 * q^31 - 6 * q^33 + 9 * q^34 - 3 * q^35 + 6 * q^37 - 6 * q^38 - 12 * q^39 + 18 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 + 3 * q^46 - 6 * q^47 + 12 * q^49 - 3 * q^50 - 9 * q^52 - 12 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^57 - 6 * q^58 - 3 * q^59 + 9 * q^61 + 18 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 - 3 * q^70 - 15 * q^73 - 3 * q^74 - 6 * q^75 - 18 * q^76 + 12 * q^77 + 27 * q^79 + 18 * q^82 - 9 * q^83 - 3 * q^84 + 9 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 33 * q^89 + 15 * q^91 + 15 * q^92 + 9 * q^93 + 30 * q^94 - 12 * q^95 - 6 * q^96 + 6 * q^97 - 9 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

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