LMFDB - Embedded newform 462.2.p.a.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(241,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("462.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.2
Root			$0.500000 + 1.56688i$ of defining polynomial
Character	$\chi$	$=$	462.241
Dual form			462.2.p.a.439.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.606961 + 0.350429i) q^{5} -1.00000 q^{6} +(-1.82993 + 1.91085i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.606961 + 0.350429i) q^{5} -1.00000 q^{6} +(-1.82993 + 1.91085i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.350429 - 0.606961i) q^{10} +(2.78007 + 1.80865i) q^{11} +(0.866025 - 0.500000i) q^{12} -7.03562 q^{13} +(0.629345 - 2.56981i) q^{14} -0.700858 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.308893 + 0.535018i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.391696 + 0.678438i) q^{19} +0.700858i q^{20} +(-2.54019 + 0.739877i) q^{21} +(-3.31194 - 0.176300i) q^{22} +(2.63592 + 4.56555i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.25440 + 3.90473i) q^{25} +(6.09302 - 3.51781i) q^{26} +1.00000i q^{27} +(0.739877 + 2.54019i) q^{28} +2.09176i q^{29} +(0.606961 - 0.350429i) q^{30} +(-5.35024 - 3.08896i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.50329 + 2.95637i) q^{33} -0.617785i q^{34} +(0.441081 - 1.80107i) q^{35} +1.00000 q^{36} +(1.99709 + 3.45907i) q^{37} +(-0.678438 - 0.391696i) q^{38} +(-6.09302 - 3.51781i) q^{39} +(-0.350429 - 0.606961i) q^{40} +5.85343 q^{41} +(1.82993 - 1.91085i) q^{42} -3.62441i q^{43} +(2.95637 - 1.50329i) q^{44} +(-0.606961 - 0.350429i) q^{45} +(-4.56555 - 2.63592i) q^{46} +(-2.03495 + 1.17488i) q^{47} -1.00000i q^{48} +(-0.302687 - 6.99345i) q^{49} -4.50880i q^{50} +(-0.535018 + 0.308893i) q^{51} +(-3.51781 + 6.09302i) q^{52} +(-3.95068 + 6.84278i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.32120 - 0.123562i) q^{55} +(-1.91085 - 1.82993i) q^{56} +0.783393i q^{57} +(-1.04588 - 1.81152i) q^{58} +(-3.25961 - 1.88193i) q^{59} +(-0.350429 + 0.606961i) q^{60} +(4.18286 + 7.24493i) q^{61} +6.17793 q^{62} +(-2.56981 - 0.629345i) q^{63} -1.00000 q^{64} +(4.27034 - 2.46548i) q^{65} +(-2.78007 - 1.80865i) q^{66} +(-1.07040 + 1.85399i) q^{67} +(0.308893 + 0.535018i) q^{68} +5.27184i q^{69} +(0.518548 + 1.78031i) q^{70} -4.48503 q^{71} +(-0.866025 + 0.500000i) q^{72} +(2.64471 - 4.58078i) q^{73} +(-3.45907 - 1.99709i) q^{74} +(-3.90473 + 2.25440i) q^{75} +0.783393 q^{76} +(-8.54340 + 2.00259i) q^{77} +7.03562 q^{78} +(3.75818 - 2.16979i) q^{79} +(0.606961 + 0.350429i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.06922 + 2.92671i) q^{82} +4.03988 q^{83} +(-0.629345 + 2.56981i) q^{84} -0.432980i q^{85} +(1.81220 + 3.13883i) q^{86} +(-1.04588 + 1.81152i) q^{87} +(-1.80865 + 2.78007i) q^{88} +(14.0396 - 8.10574i) q^{89} +0.700858 q^{90} +(12.8747 - 13.4440i) q^{91} +5.27184 q^{92} +(-3.08896 - 5.35024i) q^{93} +(1.17488 - 2.03495i) q^{94} +(-0.475489 - 0.274523i) q^{95} +(0.500000 + 0.866025i) q^{96} +10.4926i q^{97} +(3.75886 + 5.90516i) q^{98} +(-0.176300 + 3.31194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.606961	+	0.350429i	−0.271441	+	0.156717i	−0.629542	−	0.776966i	$-0.716758\pi$
$5$	−0.606961	+	0.350429i	−0.271441	+	0.156717i	0.358101	+	0.933683i	$0.383424\pi$
$6$	−1.00000			−0.408248
$7$	−1.82993	+	1.91085i	−0.691650	+	0.722233i
$7$	−1.82993	+	1.91085i	−0.691650	+	0.722233i
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.350429	−	0.606961i	0.110815	−	0.191938i
$11$	2.78007	+	1.80865i	0.838223	+	0.545328i
$11$	2.78007	+	1.80865i	0.838223	+	0.545328i
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−7.03562			−1.95133			−0.975665	−	0.219267i	$-0.929633\pi$
$13$	−7.03562			−1.95133			−0.975665	+	0.219267i	$0.929633\pi$
$14$	0.629345	−	2.56981i	0.168199	−	0.686811i
$15$	−0.700858			−0.180961
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.308893	+	0.535018i	−0.0749175	+	0.129761i	−0.901050	−	0.433714i	$-0.857203\pi$
$17$	−0.308893	+	0.535018i	−0.0749175	+	0.129761i	0.826133	+	0.563475i	$0.190536\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	0.391696	+	0.678438i	0.0898613	+	0.155644i	0.907452	−	0.420155i	$-0.138024\pi$
$19$	0.391696	+	0.678438i	0.0898613	+	0.155644i	−0.817591	+	0.575799i	$0.804691\pi$
$20$			0.700858i			0.156717i
$21$	−2.54019	+	0.739877i	−0.554316	+	0.161454i
$22$	−3.31194	−	0.176300i	−0.706107	−	0.0375874i
$23$	2.63592	+	4.56555i	0.549627	+	0.951982i	0.998300	+	0.0582859i	$0.0185635\pi$
$23$	2.63592	+	4.56555i	0.549627	+	0.951982i	−0.448673	+	0.893696i	$0.648103\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−2.25440	+	3.90473i	−0.450880	+	0.780947i
$26$	6.09302	−	3.51781i	1.19494	−	0.689899i
$27$			1.00000i			0.192450i
$28$	0.739877	+	2.54019i	0.139824	+	0.480051i
$29$			2.09176i			0.388431i	0.980959	+	0.194215i	$0.0622161\pi$
$29$			2.09176i			0.388431i	−0.980959	+	0.194215i	$0.937784\pi$
$30$	0.606961	−	0.350429i	0.110815	−	0.0639793i
$31$	−5.35024	−	3.08896i	−0.960932	−	0.554794i	−0.0644719	−	0.997920i	$-0.520536\pi$
$31$	−5.35024	−	3.08896i	−0.960932	−	0.554794i	−0.896460	+	0.443125i	$0.853870\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.50329	+	2.95637i	0.261689	+	0.514638i
$34$		−	0.617785i		−	0.105949i
$35$	0.441081	−	1.80107i	0.0745563	−	0.304437i
$36$	1.00000			0.166667
$37$	1.99709	+	3.45907i	0.328320	+	0.568667i	0.982179	−	0.187950i	$-0.0601842\pi$
$37$	1.99709	+	3.45907i	0.328320	+	0.568667i	−0.653859	+	0.756617i	$0.726851\pi$
$38$	−0.678438	−	0.391696i	−0.110057	−	0.0635416i
$39$	−6.09302	−	3.51781i	−0.975665	−	0.563300i
$40$	−0.350429	−	0.606961i	−0.0554077	−	0.0959689i
$41$	5.85343			0.914152			0.457076	−	0.889428i	$-0.348897\pi$
$41$	5.85343			0.914152			0.457076	+	0.889428i	$0.348897\pi$
$42$	1.82993	−	1.91085i	0.282365	−	0.294850i
$43$		−	3.62441i		−	0.552717i	−0.961055	−	0.276359i	$-0.910872\pi$
$43$		−	3.62441i		−	0.552717i	0.961055	−	0.276359i	$-0.0891277\pi$
$44$	2.95637	−	1.50329i	0.445690	−	0.226629i
$45$	−0.606961	−	0.350429i	−0.0904803	−	0.0522389i
$46$	−4.56555	−	2.63592i	−0.673153	−	0.388645i
$47$	−2.03495	+	1.17488i	−0.296828	+	0.171374i	−0.641017	−	0.767527i	$-0.721487\pi$
$47$	−2.03495	+	1.17488i	−0.296828	+	0.171374i	0.344189	+	0.938900i	$0.388154\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−0.302687	−	6.99345i	−0.0432409	−	0.999065i
$50$		−	4.50880i		−	0.637640i
$51$	−0.535018	+	0.308893i	−0.0749175	+	0.0432536i
$52$	−3.51781	+	6.09302i	−0.487832	+	0.844951i
$53$	−3.95068	+	6.84278i	−0.542668	+	0.939928i	0.456082	+	0.889938i	$0.349252\pi$
$53$	−3.95068	+	6.84278i	−0.542668	+	0.939928i	−0.998750	+	0.0499906i	$0.984081\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−2.32120	−	0.123562i	−0.312990	−	0.0166610i
$56$	−1.91085	−	1.82993i	−0.255348	−	0.244535i
$57$			0.783393i			0.103763i
$58$	−1.04588	−	1.81152i	−0.137331	−	0.237864i
$59$	−3.25961	−	1.88193i	−0.424365	−	0.245007i	0.272578	−	0.962134i	$-0.412124\pi$
$59$	−3.25961	−	1.88193i	−0.424365	−	0.245007i	−0.696943	+	0.717127i	$0.745457\pi$
$60$	−0.350429	+	0.606961i	−0.0452402	+	0.0783583i
$61$	4.18286	+	7.24493i	0.535560	+	0.927618i	0.999136	+	0.0415604i	$0.0132329\pi$
$61$	4.18286	+	7.24493i	0.535560	+	0.927618i	−0.463576	+	0.886057i	$0.653434\pi$
$62$	6.17793			0.784597
$63$	−2.56981	−	0.629345i	−0.323766	−	0.0792900i
$64$	−1.00000			−0.125000
$65$	4.27034	−	2.46548i	0.529671	−	0.305806i
$66$	−2.78007	−	1.80865i	−0.342203	−	0.222629i
$67$	−1.07040	+	1.85399i	−0.130771	+	0.226501i	−0.923974	−	0.382456i	$-0.875078\pi$
$67$	−1.07040	+	1.85399i	−0.130771	+	0.226501i	0.793203	+	0.608957i	$0.208412\pi$
$68$	0.308893	+	0.535018i	0.0374587	+	0.0648804i
$69$			5.27184i			0.634655i
$70$	0.518548	+	1.78031i	0.0619784	+	0.212788i
$71$	−4.48503			−0.532275			−0.266138	−	0.963935i	$-0.585748\pi$
$71$	−4.48503			−0.532275			−0.266138	+	0.963935i	$0.585748\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	2.64471	−	4.58078i	0.309540	−	0.536139i	−0.668722	−	0.743513i	$-0.733158\pi$
$73$	2.64471	−	4.58078i	0.309540	−	0.536139i	0.978262	+	0.207373i	$0.0664915\pi$
$74$	−3.45907	−	1.99709i	−0.402108	−	0.232157i
$75$	−3.90473	+	2.25440i	−0.450880	+	0.260316i
$76$	0.783393			0.0898613
$77$	−8.54340	+	2.00259i	−0.973611	+	0.228216i
$78$	7.03562			0.796627
$79$	3.75818	−	2.16979i	0.422828	−	0.244120i	−0.273458	−	0.961884i	$-0.588168\pi$
$79$	3.75818	−	2.16979i	0.422828	−	0.244120i	0.696287	+	0.717764i	$0.254834\pi$
$80$	0.606961	+	0.350429i	0.0678603	+	0.0391791i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.06922	+	2.92671i	−0.559801	+	0.323202i
$83$	4.03988			0.443435			0.221717	−	0.975111i	$-0.428834\pi$
$83$	4.03988			0.443435			0.221717	+	0.975111i	$0.428834\pi$
$84$	−0.629345	+	2.56981i	−0.0686671	+	0.280389i
$85$		−	0.432980i		−	0.0469632i
$86$	1.81220	+	3.13883i	0.195415	+	0.338469i
$87$	−1.04588	+	1.81152i	−0.112130	+	0.194215i
$88$	−1.80865	+	2.78007i	−0.192803	+	0.296356i
$89$	14.0396	−	8.10574i	1.48819	−	0.859207i	0.488281	−	0.872687i	$-0.337624\pi$
$89$	14.0396	−	8.10574i	1.48819	−	0.859207i	0.999909	+	0.0134796i	$0.00429082\pi$
$90$	0.700858			0.0738769
$91$	12.8747	−	13.4440i	1.34964	−	1.40931i
$92$	5.27184			0.549627
$93$	−3.08896	−	5.35024i	−0.320311	−	0.554794i
$94$	1.17488	−	2.03495i	0.121179	−	0.209889i
$95$	−0.475489	−	0.274523i	−0.0487841	−	0.0281655i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$			10.4926i			1.06536i	0.846317	+	0.532680i	$0.178815\pi$
$97$			10.4926i			1.06536i	−0.846317	+	0.532680i	$0.821185\pi$
$98$	3.75886	+	5.90516i	0.379702	+	0.596512i
$99$	−0.176300	+	3.31194i	−0.0177189	+	0.332862i
$100$	2.25440	+	3.90473i	0.225440	+	0.390473i
$101$	7.49737	−	12.9858i	0.746016	−	1.29214i	−0.203702	−	0.979033i	$-0.565297\pi$
$101$	7.49737	−	12.9858i	0.746016	−	1.29214i	0.949718	−	0.313105i	$-0.101369\pi$
$102$	0.308893	−	0.535018i	0.0305849	−	0.0529746i
$103$	12.4289	−	7.17585i	1.22466	−	0.707057i	0.258752	−	0.965944i	$-0.416689\pi$
$103$	12.4289	−	7.17585i	1.22466	−	0.707057i	0.965908	+	0.258887i	$0.0833556\pi$
$104$		−	7.03562i		−	0.689899i
$105$	1.28252	−	1.33923i	0.125161	−	0.130696i
$106$		−	7.90136i		−	0.767448i
$107$	9.93081	−	5.73356i	0.960048	−	0.554284i	0.0638601	−	0.997959i	$-0.479659\pi$
$107$	9.93081	−	5.73356i	0.960048	−	0.554284i	0.896188	+	0.443675i	$0.146326\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−1.25820	−	0.726424i	−0.120514	−	0.0695788i	0.438531	−	0.898716i	$-0.355499\pi$
$109$	−1.25820	−	0.726424i	−0.120514	−	0.0695788i	−0.559045	+	0.829137i	$0.688832\pi$
$110$	2.07200	−	1.05359i	0.197557	−	0.100456i
$111$			3.99419i			0.379111i
$112$	2.56981	+	0.629345i	0.242824	+	0.0594675i
$113$	12.0074			1.12956			0.564781	−	0.825241i	$-0.308961\pi$
$113$	12.0074			1.12956			0.564781	+	0.825241i	$0.308961\pi$
$114$	−0.391696	−	0.678438i	−0.0366857	−	0.0635416i
$115$	−3.19980	−	1.84740i	−0.298383	−	0.172271i
$116$	1.81152	+	1.04588i	0.168195	+	0.0971077i
$117$	−3.51781	−	6.09302i	−0.325222	−	0.563300i
$118$	3.76387			0.346492
$119$	−0.457085	−	1.56929i	−0.0419009	−	0.143857i
$120$		−	0.700858i		−	0.0639793i
$121$	4.45758	+	10.0563i	0.405235	+	0.914213i
$122$	−7.24493	−	4.18286i	−0.655925	−	0.378698i
$123$	5.06922	+	2.92671i	0.457076	+	0.263893i
$124$	−5.35024	+	3.08896i	−0.480466	+	0.277397i
$125$		−	6.66432i		−	0.596074i
$126$	2.54019	−	0.739877i	0.226298	−	0.0659135i
$127$		−	3.43188i		−	0.304530i	−0.988340	−	0.152265i	$-0.951343\pi$
$127$		−	3.43188i		−	0.304530i	0.988340	−	0.152265i	$-0.0486568\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.81220	−	3.13883i	0.159556	−	0.276359i
$130$	−2.46548	+	4.27034i	−0.216237	+	0.374534i
$131$	7.30288	+	12.6490i	0.638056	+	1.10515i	0.985859	+	0.167578i	$0.0535945\pi$
$131$	7.30288	+	12.6490i	0.638056	+	1.10515i	−0.347803	+	0.937568i	$0.613072\pi$
$132$	3.31194	+	0.176300i	0.288267	+	0.0153450i
$133$	−2.01317	−	0.493024i	−0.174564	−	0.0427506i
$134$		−	2.14081i		−	0.184938i
$135$	−0.350429	−	0.606961i	−0.0301601	−	0.0522389i
$136$	−0.535018	−	0.308893i	−0.0458774	−	0.0264873i
$137$	−8.35804	+	14.4765i	−0.714075	+	1.23681i	0.249240	+	0.968442i	$0.419819\pi$
$137$	−8.35804	+	14.4765i	−0.714075	+	1.23681i	−0.963315	+	0.268373i	$0.913514\pi$
$138$	−2.63592	−	4.56555i	−0.224384	−	0.388645i
$139$	−12.9399			−1.09755			−0.548775	−	0.835970i	$-0.684906\pi$
$139$	−12.9399			−1.09755			−0.548775	+	0.835970i	$0.684906\pi$
$140$	−1.33923	−	1.28252i	−0.113186	−	0.108393i
$141$	−2.34976			−0.197885
$142$	3.88415	−	2.24252i	0.325951	−	0.188188i
$143$	−19.5595	−	12.7250i	−1.63565	−	1.06411i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−0.733014	−	1.26962i	−0.0608735	−	0.105436i
$146$			5.28943i			0.437756i
$147$	3.23459	−	6.20785i	0.266785	−	0.512015i
$148$	3.99419			0.328320
$149$	8.42523	−	4.86431i	0.690221	−	0.398500i	−0.113474	−	0.993541i	$-0.536198\pi$
$149$	8.42523	−	4.86431i	0.690221	−	0.398500i	0.803695	+	0.595041i	$0.202864\pi$
$150$	2.25440	−	3.90473i	0.184071	−	0.318820i
$151$	17.1367	+	9.89387i	1.39456	+	0.805151i	0.993816	−	0.111037i	$-0.0354173\pi$
$151$	17.1367	+	9.89387i	1.39456	+	0.805151i	0.400747	+	0.916189i	$0.368751\pi$
$152$	−0.678438	+	0.391696i	−0.0550286	+	0.0317708i
$153$	−0.617785			−0.0499450
$154$	6.39751	−	6.00599i	0.515526	−	0.483976i
$155$	4.32985			0.347782
$156$	−6.09302	+	3.51781i	−0.487832	+	0.281650i
$157$	10.4014	+	6.00523i	0.830119	+	0.479269i	0.853893	−	0.520448i	$-0.174235\pi$
$157$	10.4014	+	6.00523i	0.830119	+	0.479269i	−0.0237745	+	0.999717i	$0.507568\pi$
$158$	−2.16979	+	3.75818i	−0.172619	+	0.298985i
$159$	−6.84278	+	3.95068i	−0.542668	+	0.313309i
$160$	−0.700858			−0.0554077
$161$	−13.5476	−	3.31780i	−1.06770	−	0.261479i
$162$		−	1.00000i		−	0.0785674i
$163$	−11.1980	−	19.3955i	−0.877094	−	1.51917i	−0.854515	−	0.519426i	$-0.826146\pi$
$163$	−11.1980	−	19.3955i	−0.877094	−	1.51917i	−0.0225784	−	0.999745i	$-0.507188\pi$
$164$	2.92671	−	5.06922i	0.228538	−	0.395839i
$165$	−1.94843	−	1.26761i	−0.151685	−	0.0986829i
$166$	−3.49864	+	2.01994i	−0.271547	+	0.156778i
$167$	−17.9924			−1.39229			−0.696145	−	0.717901i	$-0.745103\pi$
$167$	−17.9924			−1.39229			−0.696145	+	0.717901i	$0.745103\pi$
$168$	−0.739877	−	2.54019i	−0.0570827	−	0.195980i
$169$	36.4999			2.80769
$170$	0.216490	+	0.374971i	0.0166040	+	0.0287590i
$171$	−0.391696	+	0.678438i	−0.0299538	+	0.0518815i
$172$	−3.13883	−	1.81220i	−0.239334	−	0.138179i
$173$	−0.189191	−	0.327689i	−0.0143839	−	0.0249137i	0.858744	−	0.512405i	$-0.171245\pi$
$173$	−0.189191	−	0.327689i	−0.0143839	−	0.0249137i	−0.873128	+	0.487491i	$0.837912\pi$
$174$		−	2.09176i		−	0.158576i
$175$	−3.33596	−	11.4532i	−0.252175	−	0.865782i
$176$	0.176300	−	3.31194i	0.0132891	−	0.249647i
$177$	−1.88193	−	3.25961i	−0.141455	−	0.245007i
$178$	−8.10574	+	14.0396i	−0.607551	+	1.05231i
$179$	2.15547	−	3.73338i	0.161107	−	0.279046i	−0.774159	−	0.632991i	$-0.781827\pi$
$179$	2.15547	−	3.73338i	0.161107	−	0.279046i	0.935266	+	0.353946i	$0.115160\pi$
$180$	−0.606961	+	0.350429i	−0.0452402	+	0.0261194i
$181$			6.96276i			0.517538i	0.965939	+	0.258769i	$0.0833169\pi$
$181$			6.96276i			0.517538i	−0.965939	+	0.258769i	$0.916683\pi$
$182$	−4.42783	+	18.0802i	−0.328212	+	1.34019i
$183$			8.36572i			0.618412i
$184$	−4.56555	+	2.63592i	−0.336576	+	0.194323i
$185$	−2.42431	−	1.39968i	−0.178239	−	0.102906i
$186$	5.35024	+	3.08896i	0.392299	+	0.226494i
$187$	−1.82640	+	0.928709i	−0.133560	+	0.0679139i
$188$			2.34976i			0.171374i
$189$	−1.91085	−	1.82993i	−0.138994	−	0.133108i
$190$	0.549047			0.0398321
$191$	9.27949	+	16.0725i	0.671440	+	1.16297i	0.977496	+	0.210955i	$0.0676574\pi$
$191$	9.27949	+	16.0725i	0.671440	+	1.16297i	−0.306055	+	0.952014i	$0.599009\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−15.1738	−	8.76059i	−1.09223	−	0.630601i	−0.158063	−	0.987429i	$-0.550525\pi$
$193$	−15.1738	−	8.76059i	−1.09223	−	0.630601i	−0.934170	+	0.356828i	$0.883858\pi$
$194$	−5.24629	−	9.08684i	−0.376662	−	0.652397i
$195$	4.93097			0.353114
$196$	−6.20785	−	3.23459i	−0.443418	−	0.231042i
$197$			18.8663i			1.34417i	0.740474	+	0.672086i	$0.234601\pi$
$197$			18.8663i			1.34417i	−0.740474	+	0.672086i	$0.765399\pi$
$198$	−1.50329	−	2.95637i	−0.106834	−	0.210100i
$199$	−11.7194	−	6.76618i	−0.830764	−	0.479642i	0.0233504	−	0.999727i	$-0.492567\pi$
$199$	−11.7194	−	6.76618i	−0.830764	−	0.479642i	−0.854114	+	0.520086i	$0.825900\pi$
$200$	−3.90473	−	2.25440i	−0.276106	−	0.159410i
$201$	−1.85399	+	1.07040i	−0.130771	+	0.0755004i
$202$			14.9947i			1.05503i
$203$	−3.99704	−	3.82779i	−0.280537	−	0.268658i
$204$			0.617785i			0.0432536i
$205$	−3.55280	+	2.05121i	−0.248138	+	0.143263i
$206$	−7.17585	+	12.4289i	−0.499965	+	0.865965i
$207$	−2.63592	+	4.56555i	−0.183209	+	0.317327i
$208$	3.51781	+	6.09302i	0.243916	+	0.422475i
$209$	−0.138113	+	2.59455i	−0.00955344	+	0.179469i
$210$	−0.441081	+	1.80107i	−0.0304375	+	0.124286i
$211$		−	4.94368i		−	0.340337i	−0.985415	−	0.170168i	$-0.945569\pi$
$211$		−	4.94368i		−	0.340337i	0.985415	−	0.170168i	$-0.0544312\pi$
$212$	3.95068	+	6.84278i	0.271334	+	0.469964i
$213$	−3.88415	−	2.24252i	−0.266138	−	0.153655i
$214$	−5.73356	+	9.93081i	−0.391938	+	0.678856i
$215$	1.27010	+	2.19987i	0.0866199	+	0.150030i
$216$	−1.00000			−0.0680414
$217$	15.6931	−	4.57090i	1.06532	−	0.310293i
$218$	1.45285			0.0983993
$219$	4.58078	−	2.64471i	0.309540	−	0.178713i
$220$	−1.26761	+	1.94843i	−0.0854619	+	0.131363i
$221$	2.17325	−	3.76418i	0.146189	−	0.253206i
$222$	−1.99709	−	3.45907i	−0.134036	−	0.232157i
$223$		−	22.9194i		−	1.53480i	−0.641169	−	0.767400i	$-0.721550\pi$
$223$		−	22.9194i		−	1.53480i	0.641169	−	0.767400i	$-0.278450\pi$
$224$	−2.54019	+	0.739877i	−0.169724	+	0.0494351i
$225$	−4.50880			−0.300587
$226$	−10.3987	+	6.00371i	−0.691713	+	0.399361i
$227$	−12.1141	+	20.9823i	−0.804042	+	1.39264i	0.112894	+	0.993607i	$0.463988\pi$
$227$	−12.1141	+	20.9823i	−0.804042	+	1.39264i	−0.916936	+	0.399034i	$0.869345\pi$
$228$	0.678438	+	0.391696i	0.0449307	+	0.0259407i
$229$	−11.5855	+	6.68891i	−0.765594	+	0.442016i	−0.831300	−	0.555823i	$-0.812403\pi$
$229$	−11.5855	+	6.68891i	−0.765594	+	0.442016i	0.0657068	+	0.997839i	$0.479070\pi$
$230$	3.69481			0.243628
$231$	−8.40009	−	2.53741i	−0.552686	−	0.166949i
$232$	−2.09176			−0.137331
$233$	−24.1664	+	13.9525i	−1.58319	+	0.914057i	−0.588805	+	0.808275i	$0.700401\pi$
$233$	−24.1664	+	13.9525i	−1.58319	+	0.914057i	−0.994389	+	0.105782i	$0.966265\pi$
$234$	6.09302	+	3.51781i	0.398313	+	0.229966i
$235$	0.823423	−	1.42621i	0.0537142	−	0.0930357i
$236$	−3.25961	+	1.88193i	−0.212182	+	0.122503i
$237$	4.33957			0.281886
$238$	1.18049	+	1.13051i	0.0765201	+	0.0732798i
$239$		−	9.27514i		−	0.599959i	−0.953946	−	0.299979i	$-0.903020\pi$
$239$		−	9.27514i		−	0.599959i	0.953946	−	0.299979i	$-0.0969798\pi$
$240$	0.350429	+	0.606961i	0.0226201	+	0.0391791i
$241$	−9.54851	+	16.5385i	−0.615074	+	1.06534i	0.375298	+	0.926904i	$0.377540\pi$
$241$	−9.54851	+	16.5385i	−0.615074	+	1.06534i	−0.990372	+	0.138434i	$0.955793\pi$
$242$	−8.88855	−	6.48026i	−0.571378	−	0.416567i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	8.36572			0.535560
$245$	2.63443	+	4.13868i	0.168307	+	0.264411i
$246$	−5.85343			−0.373201
$247$	−2.75583	−	4.77323i	−0.175349	−	0.303713i
$248$	3.08896	−	5.35024i	0.196149	−	0.339741i
$249$	3.49864	+	2.01994i	0.221717	+	0.128009i
$250$	3.33216	+	5.77147i	0.210744	+	0.365020i
$251$		−	12.1328i		−	0.765818i	−0.923786	−	0.382909i	$-0.874922\pi$
$251$		−	12.1328i		−	0.765818i	0.923786	−	0.382909i	$-0.125078\pi$
$252$	−1.82993	+	1.91085i	−0.115275	+	0.120372i
$253$	−0.929428	+	17.4600i	−0.0584326	+	1.09770i
$254$	1.71594	+	2.97210i	0.107668	+	0.186486i
$255$	0.216490	−	0.374971i	0.0135571	−	0.0234816i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	17.2747	−	9.97355i	1.07757	−	0.622133i	0.147327	−	0.989088i	$-0.452933\pi$
$257$	17.2747	−	9.97355i	1.07757	−	0.622133i	0.930239	+	0.366955i	$0.119600\pi$
$258$			3.62441i			0.225646i
$259$	−10.2643	−	2.51372i	−0.637793	−	0.156195i
$260$		−	4.93097i		−	0.305806i
$261$	−1.81152	+	1.04588i	−0.112130	+	0.0647385i
$262$	−12.6490	−	7.30288i	−0.781456	−	0.451174i
$263$	−14.5377	−	8.39335i	−0.896433	−	0.517556i	−0.0203919	−	0.999792i	$-0.506491\pi$
$263$	−14.5377	−	8.39335i	−0.896433	−	0.517556i	−0.876041	+	0.482236i	$0.839825\pi$
$264$	−2.95637	+	1.50329i	−0.181952	+	0.0925209i
$265$		−	5.53773i		−	0.340180i
$266$	1.98997	−	0.579614i	0.122013	−	0.0355384i
$267$	16.2115			0.992127
$268$	1.07040	+	1.85399i	0.0653853	+	0.113251i
$269$	−16.8835	−	9.74767i	−1.02940	−	0.594326i	−0.112589	−	0.993642i	$-0.535914\pi$
$269$	−16.8835	−	9.74767i	−1.02940	−	0.594326i	−0.916813	+	0.399316i	$0.869248\pi$
$270$	0.606961	+	0.350429i	0.0369384	+	0.0213264i
$271$	5.34130	+	9.25140i	0.324461	+	0.561983i	0.981403	−	0.191958i	$-0.0614838\pi$
$271$	5.34130	+	9.25140i	0.324461	+	0.561983i	−0.656942	+	0.753941i	$0.728150\pi$
$272$	0.617785			0.0374587
$273$	17.8718	−	5.20549i	1.08165	−	0.315051i
$274$		−	16.7161i		−	1.00986i
$275$	−13.3297	+	6.77802i	−0.803810	+	0.408730i
$276$	4.56555	+	2.63592i	0.274814	+	0.158664i
$277$	26.6632	+	15.3940i	1.60203	+	0.924934i	0.991080	+	0.133268i	$0.0425471\pi$
$277$	26.6632	+	15.3940i	1.60203	+	0.924934i	0.610954	+	0.791666i	$0.290786\pi$
$278$	11.2063	−	6.46997i	0.672110	−	0.388043i
$279$		−	6.17793i		−	0.369863i
$280$	1.80107	+	0.441081i	0.107635	+	0.0263596i
$281$			21.3381i			1.27292i	0.771308	+	0.636462i	$0.219603\pi$
$281$			21.3381i			1.27292i	−0.771308	+	0.636462i	$0.780397\pi$
$282$	2.03495	−	1.17488i	0.121179	−	0.0699630i
$283$	1.26154	−	2.18504i	0.0749905	−	0.129887i	−0.826092	−	0.563536i	$-0.809441\pi$
$283$	1.26154	−	2.18504i	0.0749905	−	0.129887i	0.901082	+	0.433648i	$0.142774\pi$
$284$	−2.24252	+	3.88415i	−0.133069	+	0.230482i
$285$	−0.274523	−	0.475489i	−0.0162614	−	0.0281655i
$286$	23.3015	+	1.24038i	1.37785	+	0.0733454i
$287$	−10.7114	+	11.1850i	−0.632273	+	0.660231i
$288$			1.00000i			0.0589256i
$289$	8.30917	+	14.3919i	0.488775	+	0.846583i
$290$	1.26962	+	0.733014i	0.0745545	+	0.0430441i
$291$	−5.24629	+	9.08684i	−0.307543	+	0.532680i
$292$	−2.64471	−	4.58078i	−0.154770	−	0.268070i
$293$	−5.71831			−0.334067			−0.167034	−	0.985951i	$-0.553419\pi$
$293$	−5.71831			−0.334067			−0.167034	+	0.985951i	$0.553419\pi$
$294$	0.302687	+	6.99345i	0.0176530	+	0.407866i
$295$	2.63794			0.153587
$296$	−3.45907	+	1.99709i	−0.201054	+	0.116079i
$297$	−1.80865	+	2.78007i	−0.104948	+	0.161316i
$298$	−4.86431	+	8.42523i	−0.281782	+	0.488060i
$299$	−18.5453	−	32.1214i	−1.07250	−	1.85763i
$300$			4.50880i			0.260316i
$301$	6.92570	+	6.63243i	0.399191	+	0.382287i
$302$	−19.7877			−1.13866
$303$	12.9858	−	7.49737i	0.746016	−	0.430713i
$304$	0.391696	−	0.678438i	0.0224653	−	0.0389111i
$305$	−5.07766	−	2.93159i	−0.290746	−	0.167862i
$306$	0.535018	−	0.308893i	0.0305849	−	0.0176582i
$307$	−20.7839			−1.18620			−0.593099	−	0.805130i	$-0.702096\pi$
$307$	−20.7839			−1.18620			−0.593099	+	0.805130i	$0.702096\pi$
$308$	−2.53741	+	8.40009i	−0.144582	+	0.478640i
$309$	14.3517			0.816439
$310$	−3.74976	+	2.16492i	−0.212972	+	0.122959i
$311$	−6.38045	−	3.68376i	−0.361802	−	0.208887i	0.308069	−	0.951364i	$-0.400317\pi$
$311$	−6.38045	−	3.68376i	−0.361802	−	0.208887i	−0.669871	+	0.742477i	$0.733651\pi$
$312$	3.51781	−	6.09302i	0.199157	−	0.344950i
$313$	−6.36871	+	3.67697i	−0.359981	+	0.207835i	−0.669072	−	0.743197i	$-0.733308\pi$
$313$	−6.36871	+	3.67697i	−0.359981	+	0.207835i	0.309092	+	0.951032i	$0.399975\pi$
$314$	−12.0105			−0.677789
$315$	1.78031	−	0.518548i	0.100309	−	0.0292169i
$316$		−	4.33957i		−	0.244120i
$317$	7.39030	+	12.8004i	0.415080	+	0.718940i	0.995437	−	0.0954222i	$-0.0304201\pi$
$317$	7.39030	+	12.8004i	0.415080	+	0.718940i	−0.580356	+	0.814363i	$0.697087\pi$
$318$	3.95068	−	6.84278i	0.221543	−	0.383724i
$319$	−3.78327	+	5.81525i	−0.211822	+	0.325591i
$320$	0.606961	−	0.350429i	0.0339301	−	0.0195896i
$321$	11.4671			0.640032
$322$	13.3915	−	3.90051i	0.746278	−	0.217367i
$323$	−0.483969			−0.0269287
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	15.8611	−	27.4722i	0.879815	−	1.52388i
$326$	19.3955	+	11.1980i	1.07422	+	0.620199i
$327$	−0.726424	−	1.25820i	−0.0401714	−	0.0695788i
$328$			5.85343i			0.323202i
$329$	1.47881	−	6.03843i	0.0815292	−	0.332909i
$330$	2.32120	+	0.123562i	0.127778	+	0.00680184i
$331$	−13.6449	−	23.6336i	−0.749991	−	1.29902i	−0.947826	−	0.318787i	$-0.896725\pi$
$331$	−13.6449	−	23.6336i	−0.749991	−	1.29902i	0.197836	−	0.980235i	$-0.436609\pi$
$332$	2.01994	−	3.49864i	0.110859	−	0.192013i
$333$	−1.99709	+	3.45907i	−0.109440	+	0.189556i
$334$	15.5818	−	8.99618i	0.852600	−	0.492249i
$335$		−	1.50040i		−	0.0819757i
$336$	1.91085	+	1.82993i	0.104245	+	0.0998311i
$337$		−	13.0929i		−	0.713215i	−0.934254	−	0.356607i	$-0.883933\pi$
$337$		−	13.0929i		−	0.713215i	0.934254	−	0.356607i	$-0.116067\pi$
$338$	−31.6099	+	18.2500i	−1.71935	+	0.992667i
$339$	10.3987	+	6.00371i	0.564781	+	0.326077i
$340$	−0.374971	−	0.216490i	−0.0203357	−	0.0117408i
$341$	−9.28720	−	18.2642i	−0.502930	−	0.989064i
$342$		−	0.783393i		−	0.0423610i
$343$	13.9173	+	12.2192i	0.751465	+	0.659773i
$344$	3.62441			0.195415
$345$	−1.84740	−	3.19980i	−0.0994609	−	0.172271i
$346$	0.327689	+	0.189191i	0.0176167	+	0.0101710i
$347$	9.82708	+	5.67367i	0.527545	+	0.304578i	0.740016	−	0.672589i	$-0.234818\pi$
$347$	9.82708	+	5.67367i	0.527545	+	0.304578i	−0.212471	+	0.977167i	$0.568151\pi$
$348$	1.04588	+	1.81152i	0.0560651	+	0.0971077i
$349$	−12.4060			−0.664076			−0.332038	−	0.943266i	$-0.607736\pi$
$349$	−12.4060			−0.664076			−0.332038	+	0.943266i	$0.607736\pi$
$350$	8.61563	+	8.25080i	0.460525	+	0.441024i
$351$		−	7.03562i		−	0.375534i
$352$	1.50329	+	2.95637i	0.0801255	+	0.157575i
$353$	5.90974	+	3.41199i	0.314544	+	0.181602i	0.648958	−	0.760824i	$-0.275205\pi$
$353$	5.90974	+	3.41199i	0.314544	+	0.181602i	−0.334414	+	0.942426i	$0.608538\pi$
$354$	3.25961	+	1.88193i	0.173246	+	0.100024i
$355$	2.72224	−	1.57168i	0.144481	−	0.0834163i
$356$		−	16.2115i		−	0.859207i
$357$	0.388800	−	1.58759i	0.0205775	−	0.0840242i
$358$			4.31093i			0.227840i
$359$	17.6942	−	10.2157i	0.933862	−	0.539166i	0.0458314	−	0.998949i	$-0.485406\pi$
$359$	17.6942	−	10.2157i	0.933862	−	0.539166i	0.888031	+	0.459783i	$0.152073\pi$
$360$	0.350429	−	0.606961i	0.0184692	−	0.0319896i
$361$	9.19315	−	15.9230i	0.483850	−	0.838053i
$362$	−3.48138	−	6.02993i	−0.182977	−	0.316926i
$363$	−1.16779	+	10.9378i	−0.0612932	+	0.574088i
$364$	−5.20549	−	17.8718i	−0.272842	−	0.936739i
$365$			3.70714i			0.194040i
$366$	−4.18286	−	7.24493i	−0.218642	−	0.378698i
$367$	17.4563	+	10.0784i	0.911212	+	0.526088i	0.880821	−	0.473450i	$-0.156991\pi$
$367$	17.4563	+	10.0784i	0.911212	+	0.526088i	0.0303908	+	0.999538i	$0.490325\pi$
$368$	2.63592	−	4.56555i	0.137407	−	0.237995i
$369$	2.92671	+	5.06922i	0.152359	+	0.263893i
$370$	2.79936			0.145532
$371$	−5.84604	−	20.0710i	−0.303511	−	1.04203i
$372$	−6.17793			−0.320311
$373$	7.22139	−	4.16927i	0.373909	−	0.215877i	−0.301256	−	0.953543i	$-0.597406\pi$
$373$	7.22139	−	4.16927i	0.373909	−	0.215877i	0.675165	+	0.737667i	$0.264072\pi$
$374$	1.11736	−	1.71749i	0.0577771	−	0.0888091i
$375$	3.33216	−	5.77147i	0.172072	−	0.298037i
$376$	−1.17488	−	2.03495i	−0.0605897	−	0.104944i
$377$		−	14.7169i		−	0.757956i
$378$	2.56981	+	0.629345i	0.132177	+	0.0323700i
$379$	−12.2093			−0.627151			−0.313575	−	0.949563i	$-0.601527\pi$
$379$	−12.2093			−0.627151			−0.313575	+	0.949563i	$0.601527\pi$
$380$	−0.475489	+	0.274523i	−0.0243921	+	0.0140828i
$381$	1.71594	−	2.97210i	0.0879103	−	0.152265i
$382$	−16.0725	−	9.27949i	−0.822343	−	0.474780i
$383$	16.1528	−	9.32585i	0.825372	−	0.476529i	−0.0268936	−	0.999638i	$-0.508562\pi$
$383$	16.1528	−	9.32585i	0.825372	−	0.476529i	0.852265	+	0.523110i	$0.175228\pi$
$384$	1.00000			0.0510310
$385$	4.48374	−	4.20934i	0.228513	−	0.214528i
$386$	17.5212			0.891805
$387$	3.13883	−	1.81220i	0.159556	−	0.0921195i
$388$	9.08684	+	5.24629i	0.461314	+	0.266340i
$389$	4.75722	−	8.23974i	0.241201	−	0.417772i	−0.719856	−	0.694123i	$-0.755792\pi$
$389$	4.75722	−	8.23974i	0.241201	−	0.417772i	0.961057	+	0.276352i	$0.0891255\pi$
$390$	−4.27034	+	2.46548i	−0.216237	+	0.124845i
$391$	−3.25686			−0.164707
$392$	6.99345	−	0.302687i	0.353223	−	0.0152880i
$393$			14.6058i			0.736764i
$394$	−9.43317	−	16.3387i	−0.475236	−	0.823133i
$395$	−1.52071	+	2.63395i	−0.0765153	+	0.132528i
$396$	2.78007	+	1.80865i	0.139704	+	0.0908880i
$397$	−29.5051	+	17.0348i	−1.48082	+	0.854952i	−0.999764	−	0.0217370i	$-0.993080\pi$
$397$	−29.5051	+	17.0348i	−1.48082	+	0.854952i	−0.481057	+	0.876689i	$0.659747\pi$
$398$	13.5324			0.678316
$399$	−1.49695	−	1.43356i	−0.0749410	−	0.0717676i
$400$	4.50880			0.225440
$401$	14.8179	+	25.6653i	0.739969	+	1.28166i	0.952508	+	0.304512i	$0.0984934\pi$
$401$	14.8179	+	25.6653i	0.739969	+	1.28166i	−0.212539	+	0.977153i	$0.568173\pi$
$402$	1.07040	−	1.85399i	0.0533869	−	0.0924688i
$403$	37.6423	+	21.7328i	1.87509	+	1.08259i
$404$	−7.49737	−	12.9858i	−0.373008	−	0.646069i
$405$		−	0.700858i		−	0.0348259i
$406$	5.37544	+	1.31644i	0.266778	+	0.0653338i
$407$	−0.704177	+	13.2285i	−0.0349048	+	0.655712i
$408$	−0.308893	−	0.535018i	−0.0152925	−	0.0264873i
$409$	13.6644	−	23.6675i	0.675662	−	1.17028i	−0.300613	−	0.953746i	$-0.597191\pi$
$409$	13.6644	−	23.6675i	0.675662	−	1.17028i	0.976275	−	0.216534i	$-0.0694753\pi$
$410$	2.05121	−	3.55280i	0.101302	−	0.175460i
$411$	−14.4765	+	8.35804i	−0.714075	+	0.412272i
$412$		−	14.3517i		−	0.707057i
$413$	9.56095	−	2.78480i	0.470464	−	0.137031i
$414$		−	5.27184i		−	0.259097i
$415$	−2.45205	+	1.41569i	−0.120366	+	0.0694936i
$416$	−6.09302	−	3.51781i	−0.298735	−	0.172475i
$417$	−11.2063	−	6.46997i	−0.548775	−	0.316836i
$418$	−1.17766	−	2.31600i	−0.0576014	−	0.113279i
$419$			25.6972i			1.25539i	0.778459	+	0.627696i	$0.216002\pi$
$419$			25.6972i			1.25539i	−0.778459	+	0.627696i	$0.783998\pi$
$420$	−0.518548	−	1.78031i	−0.0253026	−	0.0868704i
$421$	−36.9246			−1.79959			−0.899797	−	0.436309i	$-0.856285\pi$
$421$	−36.9246			−1.79959			−0.899797	+	0.436309i	$0.856285\pi$
$422$	2.47184	+	4.28135i	0.120327	+	0.208413i
$423$	−2.03495	−	1.17488i	−0.0989426	−	0.0571245i
$424$	−6.84278	−	3.95068i	−0.332315	−	0.191862i
$425$	−1.39273	−	2.41229i	−0.0675575	−	0.117013i
$426$	4.48503			0.217300
$427$	−21.4983	−	5.26492i	−1.04038	−	0.254787i
$428$		−	11.4671i		−	0.554284i
$429$	−10.5766	−	20.7999i	−0.510641	−	1.00423i
$430$	−2.19987	−	1.27010i	−0.106087	−	0.0612495i
$431$	17.4320	+	10.0644i	0.839668	+	0.484783i	0.857152	−	0.515064i	$-0.172232\pi$
$431$	17.4320	+	10.0644i	0.839668	+	0.484783i	−0.0174831	+	0.999847i	$0.505565\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$			38.1992i			1.83574i	0.396884	+	0.917869i	$0.370092\pi$
$433$			38.1992i			1.83574i	−0.396884	+	0.917869i	$0.629908\pi$
$434$	−11.3052	+	11.8051i	−0.542667	+	0.566662i
$435$		−	1.46603i		−	0.0702907i
$436$	−1.25820	+	0.726424i	−0.0602570	+	0.0347894i
$437$	−2.06496	+	3.57662i	−0.0987804	+	0.171093i
$438$	−2.64471	+	4.58078i	−0.126369	+	0.218878i
$439$	3.66099	+	6.34102i	0.174729	+	0.302640i	0.940068	−	0.340988i	$-0.110762\pi$
$439$	3.66099	+	6.34102i	0.174729	+	0.302640i	−0.765338	+	0.643628i	$0.777428\pi$
$440$	0.123562	−	2.32120i	0.00589057	−	0.110659i
$441$	5.90516	−	3.75886i	0.281198	−	0.178993i
$442$			4.34650i			0.206742i
$443$	16.5124	+	28.6003i	0.784527	+	1.35884i	0.929281	+	0.369373i	$0.120428\pi$
$443$	16.5124	+	28.6003i	0.784527	+	1.35884i	−0.144754	+	0.989468i	$0.546239\pi$
$444$	3.45907	+	1.99709i	0.164160	+	0.0947778i
$445$	−5.68097	+	9.83973i	−0.269304	+	0.466448i
$446$	11.4597	+	19.8488i	0.542633	+	0.939869i
$447$	9.72861			0.460148
$448$	1.82993	−	1.91085i	0.0864562	−	0.0902791i
$449$	−22.5285			−1.06319			−0.531594	−	0.846999i	$-0.678407\pi$
$449$	−22.5285			−1.06319			−0.531594	+	0.846999i	$0.678407\pi$
$450$	3.90473	−	2.25440i	0.184071	−	0.106273i
$451$	16.2729	+	10.5868i	0.766263	+	0.498513i
$452$	6.00371	−	10.3987i	0.282391	−	0.489115i
$453$	9.89387	+	17.1367i	0.464854	+	0.805151i
$454$		−	24.2282i		−	1.13709i
$455$	−3.10328	+	12.6717i	−0.145484	+	0.594056i
$456$	−0.783393			−0.0366857
$457$	28.7305	−	16.5876i	1.34396	−	0.775934i	0.356572	−	0.934268i	$-0.383946\pi$
$457$	28.7305	−	16.5876i	1.34396	−	0.775934i	0.987386	+	0.158334i	$0.0506122\pi$
$458$	6.68891	−	11.5855i	0.312552	−	0.541356i
$459$	−0.535018	−	0.308893i	−0.0249725	−	0.0144179i
$460$	−3.19980	+	1.84740i	−0.149191	+	0.0861357i
$461$	−7.42955			−0.346029			−0.173014	−	0.984919i	$-0.555351\pi$
$461$	−7.42955			−0.346029			−0.173014	+	0.984919i	$0.555351\pi$
$462$	8.54340	−	2.00259i	0.397475	−	0.0931688i
$463$	−15.7504			−0.731984			−0.365992	−	0.930618i	$-0.619270\pi$
$463$	−15.7504			−0.731984			−0.365992	+	0.930618i	$0.619270\pi$
$464$	1.81152	−	1.04588i	0.0840977	−	0.0485538i
$465$	3.74976	+	2.16492i	0.173891	+	0.100396i
$466$	13.9525	−	24.1664i	0.646336	−	1.11949i
$467$	11.5815	−	6.68657i	0.535927	−	0.309418i	−0.207500	−	0.978235i	$-0.566533\pi$
$467$	11.5815	−	6.68657i	0.535927	−	0.309418i	0.743427	+	0.668817i	$0.233199\pi$
$468$	−7.03562			−0.325222
$469$	−1.58393	−	5.43806i	−0.0731392	−	0.251106i
$470$			1.64685i			0.0759633i
$471$	6.00523	+	10.4014i	0.276706	+	0.479269i
$472$	1.88193	−	3.25961i	0.0866231	−	0.150036i
$473$	6.55528	−	10.0761i	0.301412	−	0.463300i
$474$	−3.75818	+	2.16979i	−0.172619	+	0.0996616i
$475$	−3.53216			−0.162067
$476$	−1.58759	−	0.388800i	−0.0727671	−	0.0178206i
$477$	−7.90136			−0.361779
$478$	4.63757	+	8.03251i	0.212117	+	0.367398i
$479$	−5.63050	+	9.75230i	−0.257264	+	0.445594i	−0.965508	−	0.260374i	$-0.916154\pi$
$479$	−5.63050	+	9.75230i	−0.257264	+	0.445594i	0.708244	+	0.705968i	$0.249488\pi$
$480$	−0.606961	−	0.350429i	−0.0277038	−	0.0159948i
$481$	−14.0508	−	24.3367i	−0.640661	−	1.10966i
$482$		−	19.0970i		−	0.869845i
$483$	−10.0737	−	9.64711i	−0.458369	−	0.438959i
$484$	10.9378	+	1.16779i	0.497174	+	0.0530814i
$485$	−3.67690	−	6.36858i	−0.166960	−	0.289182i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−1.33482	+	2.31197i	−0.0604862	+	0.104765i	−0.894683	−	0.446702i	$-0.852598\pi$
$487$	−1.33482	+	2.31197i	−0.0604862	+	0.104765i	0.834197	+	0.551467i	$0.185932\pi$
$488$	−7.24493	+	4.18286i	−0.327962	+	0.189349i
$489$		−	22.3960i		−	1.01278i
$490$	−4.35082	−	2.26699i	−0.196550	−	0.102412i
$491$			11.3063i			0.510245i	0.966909	+	0.255123i	$0.0821158\pi$
$491$			11.3063i			0.510245i	−0.966909	+	0.255123i	$0.917884\pi$
$492$	5.06922	−	2.92671i	0.228538	−	0.131946i
$493$	−1.11913	−	0.646130i	−0.0504031	−	0.0291002i
$494$	4.77323	+	2.75583i	0.214758	+	0.123991i
$495$	−1.05359	−	2.07200i	−0.0473554	−	0.0931293i
$496$			6.17793i			0.277397i
$497$	8.20731	−	8.57022i	0.368148	−	0.384427i
$498$	−4.03988			−0.181032
$499$	−10.7200	−	18.5676i	−0.479894	−	0.831200i	0.519840	−	0.854263i	$-0.325991\pi$
$499$	−10.7200	−	18.5676i	−0.479894	−	0.831200i	−0.999734	+	0.0230633i	$0.992658\pi$
$500$	−5.77147	−	3.33216i	−0.258108	−	0.149019i
$501$	−15.5818	−	8.99618i	−0.696145	−	0.401920i
$502$	6.06642	+	10.5073i	0.270757	+	0.468966i
$503$	30.0822			1.34130			0.670649	−	0.741775i	$-0.266016\pi$
$503$	30.0822			1.34130			0.670649	+	0.741775i	$0.266016\pi$
$504$	0.629345	−	2.56981i	0.0280332	−	0.114468i
$505$			10.5092i			0.467652i
$506$	−7.92509	−	15.5855i	−0.352313	−	0.692860i
$507$	31.6099	+	18.2500i	1.40384	+	0.810509i
$508$	−2.97210	−	1.71594i	−0.131866	−	0.0761326i
$509$	11.6751	−	6.74064i	0.517491	−	0.298774i	−0.218416	−	0.975856i	$-0.570089\pi$
$509$	11.6751	−	6.74064i	0.517491	−	0.298774i	0.735908	+	0.677082i	$0.236756\pi$
$510$			0.432980i			0.0191727i
$511$	3.91352	+	13.4362i	0.173124	+	0.594381i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.678438	+	0.391696i	−0.0299538	+	0.0172938i
$514$	−9.97355	+	17.2747i	−0.439914	+	0.761954i
$515$	−5.02925	+	8.71091i	−0.221615	+	0.383849i
$516$	−1.81220	−	3.13883i	−0.0797779	−	0.138179i
$517$	−7.78224	−	0.414263i	−0.342263	−	0.0182193i
$518$	10.1460	−	2.95521i	0.445790	−	0.129844i
$519$		−	0.378382i		−	0.0166091i
$520$	2.46548	+	4.27034i	0.108119	+	0.187267i
$521$	−9.63608	−	5.56339i	−0.422164	−	0.243737i	0.273839	−	0.961776i	$-0.411707\pi$
$521$	−9.63608	−	5.56339i	−0.422164	−	0.243737i	−0.696003	+	0.718039i	$0.745040\pi$
$522$	1.04588	−	1.81152i	0.0457770	−	0.0792881i
$523$	7.45440	+	12.9114i	0.325958	+	0.564576i	0.981706	−	0.190404i	$-0.0609798\pi$
$523$	7.45440	+	12.9114i	0.325958	+	0.564576i	−0.655748	+	0.754980i	$0.727646\pi$
$524$	14.6058			0.638056
$525$	2.83759	−	11.5868i	0.123842	−	0.505688i
$526$	16.7867			0.731935
$527$	3.30530	−	1.90832i	0.143981	−	0.0831275i
$528$	1.80865	−	2.78007i	0.0787113	−	0.120987i
$529$	−2.39614	+	4.15023i	−0.104180	+	0.180445i
$530$	2.76887	+	4.79582i	0.120272	+	0.208317i
$531$		−	3.76387i		−	0.163338i
$532$	−1.43356	+	1.49695i	−0.0621526	+	0.0649008i
$533$	−41.1825			−1.78381
$534$	−14.0396	+	8.10574i	−0.607551	+	0.350770i
$535$	−4.01841	+	6.96009i	−0.173731	+	0.300911i
$536$	−1.85399	−	1.07040i	−0.0800803	−	0.0462344i
$537$	3.73338	−	2.15547i	0.161107	−	0.0930152i
$538$	19.4953			0.840504
$539$	11.8072	−	19.9897i	0.508572	−	0.861019i
$540$	−0.700858			−0.0301601
$541$	−23.0202	+	13.2907i	−0.989717	+	0.571413i	−0.905190	−	0.425008i	$-0.860271\pi$
$541$	−23.0202	+	13.2907i	−0.989717	+	0.571413i	−0.0845270	+	0.996421i	$0.526938\pi$
$542$	−9.25140	−	5.34130i	−0.397382	−	0.229428i
$543$	−3.48138	+	6.02993i	−0.149400	+	0.258769i
$544$	−0.535018	+	0.308893i	−0.0229387	+	0.0132437i
$545$	1.01824			0.0436166
$546$	−12.8747	+	13.4440i	−0.550987	+	0.575350i
$547$		−	18.2285i		−	0.779393i	−0.920943	−	0.389696i	$-0.872580\pi$
$547$		−	18.2285i		−	0.779393i	0.920943	−	0.389696i	$-0.127420\pi$
$548$	8.35804	+	14.4765i	0.357038	+	0.618407i
$549$	−4.18286	+	7.24493i	−0.178520	+	0.309206i
$550$	8.15483	−	12.5348i	0.347723	−	0.534485i
$551$	−1.41913	+	0.819336i	−0.0604571	+	0.0349049i
$552$	−5.27184			−0.224384
$553$	−2.73109	+	11.1519i	−0.116138	+	0.474226i
$554$	−30.7880			−1.30805
$555$	−1.39968	−	2.42431i	−0.0594130	−	0.102906i
$556$	−6.46997	+	11.2063i	−0.274388	+	0.475253i
$557$	−27.2666	−	15.7424i	−1.15532	−	0.667025i	−0.205143	−	0.978732i	$-0.565766\pi$
$557$	−27.2666	−	15.7424i	−1.15532	−	0.667025i	−0.950178	+	0.311707i	$0.899099\pi$
$558$	3.08896	+	5.35024i	0.130766	+	0.226494i
$559$			25.5000i			1.07853i
$560$	−1.78031	+	0.518548i	−0.0752320	+	0.0219127i
$561$	−2.04606	−	0.108916i	−0.0863849	−	0.00459843i
$562$	−10.6691	−	18.4793i	−0.450047	−	0.779504i
$563$	−10.9701	+	19.0008i	−0.462335	+	0.800787i	−0.999077	−	0.0429591i	$-0.986321\pi$
$563$	−10.9701	+	19.0008i	−0.462335	+	0.800787i	0.536742	+	0.843746i	$0.319655\pi$
$564$	−1.17488	+	2.03495i	−0.0494713	+	0.0856868i
$565$	−7.28803	+	4.20774i	−0.306610	+	0.177021i
$566$			2.52307i			0.106053i
$567$	−0.739877	−	2.54019i	−0.0310719	−	0.106678i
$568$		−	4.48503i		−	0.188188i
$569$	26.8999	−	15.5307i	1.12770	−	0.651080i	0.184347	−	0.982861i	$-0.440983\pi$
$569$	26.8999	−	15.5307i	1.12770	−	0.651080i	0.943356	+	0.331781i	$0.107650\pi$
$570$	0.475489	+	0.274523i	0.0199160	+	0.0114985i
$571$	−8.45951	−	4.88410i	−0.354020	−	0.204393i	0.312435	−	0.949939i	$-0.398855\pi$
$571$	−8.45951	−	4.88410i	−0.354020	−	0.204393i	−0.666454	+	0.745546i	$0.732189\pi$
$572$	−20.7999	+	10.5766i	−0.869687	+	0.442228i
$573$			18.5590i			0.775313i
$574$	3.68382	−	15.0422i	0.153760	−	0.627849i
$575$	−23.7697			−0.991263
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	16.7912	+	9.69442i	0.699028	+	0.403584i	0.806985	−	0.590571i	$-0.201098\pi$
$577$	16.7912	+	9.69442i	0.699028	+	0.403584i	−0.107957	+	0.994156i	$0.534431\pi$
$578$	−14.3919	−	8.30917i	−0.598624	−	0.345616i
$579$	−8.76059	−	15.1738i	−0.364078	−	0.630601i
$580$	−1.46603			−0.0608735
$581$	−7.39272	+	7.71961i	−0.306702	+	0.320263i
$582$		−	10.4926i		−	0.434931i
$583$	−23.3594	+	11.8780i	−0.967446	+	0.491937i
$584$	4.58078	+	2.64471i	0.189554	+	0.109439i
$585$	4.27034	+	2.46548i	0.176557	+	0.101935i
$586$	4.95220	−	2.85916i	0.204574	−	0.118111i
$587$		−	14.0625i		−	0.580421i	−0.956963	−	0.290210i	$-0.906275\pi$
$587$		−	14.0625i		−	0.580421i	0.956963	−	0.290210i	$-0.0937253\pi$
$588$	−3.75886	−	5.90516i	−0.155013	−	0.243525i
$589$		−	4.83974i		−	0.199418i
$590$	−2.28452	+	1.31897i	−0.0940522	+	0.0543011i
$591$	−9.43317	+	16.3387i	−0.388029	+	0.672086i
$592$	1.99709	−	3.45907i	0.0820800	−	0.142167i
$593$	19.0546	+	33.0036i	0.782480	+	1.35530i	0.930493	+	0.366310i	$0.119379\pi$
$593$	19.0546	+	33.0036i	0.782480	+	1.35530i	−0.148013	+	0.988985i	$0.547288\pi$
$594$	0.176300	−	3.31194i	0.00723370	−	0.135890i
$595$	0.827358	+	0.792324i	0.0339184	+	0.0324821i
$596$		−	9.72861i		−	0.398500i
$597$	−6.76618	−	11.7194i	−0.276921	−	0.479642i
$598$	32.1214	+	18.5453i	1.31354	+	0.758375i
$599$	12.2662	−	21.2456i	0.501183	−	0.868074i	−0.498817	−	0.866708i	$-0.666232\pi$
$599$	12.2662	−	21.2456i	0.501183	−	0.868074i	0.999999	−	0.00136605i	$-0.000434826\pi$
$600$	−2.25440	−	3.90473i	−0.0920355	−	0.159410i
$601$	−3.08091			−0.125673			−0.0628365	−	0.998024i	$-0.520015\pi$
$601$	−3.08091			−0.125673			−0.0628365	+	0.998024i	$0.520015\pi$
$602$	−9.31404	−	2.28100i	−0.379612	−	0.0929667i
$603$	−2.14081			−0.0871804
$604$	17.1367	−	9.89387i	0.697282	−	0.402576i
$605$	−6.22961	−	4.54174i	−0.253270	−	0.184648i
$606$	−7.49737	+	12.9858i	−0.304560	+	0.527513i
$607$	−20.3839	−	35.3059i	−0.827356	−	1.43302i	−0.900105	−	0.435673i	$-0.856510\pi$
$607$	−20.3839	−	35.3059i	−0.827356	−	1.43302i	0.0727485	−	0.997350i	$-0.476823\pi$
$608$			0.783393i			0.0317708i
$609$	−1.54765	−	5.31348i	−0.0627138	−	0.215313i
$610$	5.86318			0.237393
$611$	14.3171	−	8.26600i	0.579209	−	0.334406i
$612$	−0.308893	+	0.535018i	−0.0124862	+	0.0216268i
$613$	−7.75535	−	4.47755i	−0.313236	−	0.180847i	0.335138	−	0.942169i	$-0.391217\pi$
$613$	−7.75535	−	4.47755i	−0.313236	−	0.180847i	−0.648373	+	0.761322i	$0.724550\pi$
$614$	17.9993	−	10.3919i	0.726394	−	0.419384i
$615$	−4.10242			−0.165426
$616$	−2.00259	−	8.54340i	−0.0806865	−	0.344223i
$617$	19.1914			0.772618			0.386309	−	0.922369i	$-0.373750\pi$
$617$	19.1914			0.772618			0.386309	+	0.922369i	$0.373750\pi$
$618$	−12.4289	+	7.17585i	−0.499965	+	0.288655i
$619$	2.91921	+	1.68541i	0.117333	+	0.0677422i	0.557518	−	0.830165i	$-0.311754\pi$
$619$	2.91921	+	1.68541i	0.117333	+	0.0677422i	−0.440185	+	0.897907i	$0.645087\pi$
$620$	2.16492	−	3.74976i	0.0869454	−	0.150594i
$621$	−4.56555	+	2.63592i	−0.183209	+	0.105776i
$622$	7.36751			0.295410
$623$	−10.2026	+	41.6604i	−0.408759	+	1.66909i
$624$			7.03562i			0.281650i
$625$	−8.93663	−	15.4787i	−0.357465	−	0.619148i
$626$	3.67697	−	6.36871i	0.146961	−	0.254545i
$627$	−1.41688	+	2.17789i	−0.0565848	+	0.0869764i
$628$	10.4014	−	6.00523i	0.415059	−	0.239635i
$629$	−2.46755			−0.0983876
$630$	−1.28252	+	1.33923i	−0.0510969	+	0.0533563i
$631$	33.1910			1.32131			0.660657	−	0.750688i	$-0.270278\pi$
$631$	33.1910			1.32131			0.660657	+	0.750688i	$0.270278\pi$
$632$	2.16979	+	3.75818i	0.0863095	+	0.149492i
$633$	2.47184	−	4.28135i	0.0982468	−	0.170168i
$634$	−12.8004	−	7.39030i	−0.508368	−	0.293506i
$635$	1.20263	+	2.08302i	0.0477250	+	0.0826620i
$636$			7.90136i			0.313309i
$637$	2.12959	+	49.2033i	0.0843773	+	1.94950i
$638$	0.368779	−	6.92779i	0.0146001	−	0.274274i
$639$	−2.24252	−	3.88415i	−0.0887125	−	0.153655i
$640$	−0.350429	+	0.606961i	−0.0138519	+	0.0239922i
$641$	17.2306	−	29.8442i	0.680566	−	1.17878i	−0.294242	−	0.955731i	$-0.595067\pi$
$641$	17.2306	−	29.8442i	0.680566	−	1.17878i	0.974808	−	0.223045i	$-0.0715995\pi$
$642$	−9.93081	+	5.73356i	−0.391938	+	0.226285i
$643$		−	2.69205i		−	0.106164i	−0.998590	−	0.0530821i	$-0.983095\pi$
$643$		−	2.69205i		−	0.106164i	0.998590	−	0.0530821i	$-0.0169045\pi$
$644$	−9.64711	+	10.0737i	−0.380149	+	0.396959i
$645$			2.54020i			0.100020i
$646$	0.419129	−	0.241984i	0.0164904	−	0.00952074i
$647$	40.4270	+	23.3405i	1.58935	+	0.917611i	0.993414	+	0.114577i	$0.0365514\pi$
$647$	40.4270	+	23.3405i	1.58935	+	0.917611i	0.595934	+	0.803033i	$0.296782\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−5.65818	−	11.1274i	−0.222103	−	0.436788i
$650$			31.7222i			1.24425i
$651$	15.8761	+	3.88804i	0.622233	+	0.152384i
$652$	−22.3960			−0.877094
$653$	−19.9929	−	34.6287i	−0.782383	−	1.35513i	−0.930550	−	0.366165i	$-0.880671\pi$
$653$	−19.9929	−	34.6287i	−0.782383	−	1.35513i	0.148167	−	0.988962i	$-0.452663\pi$
$654$	1.25820	+	0.726424i	0.0491997	+	0.0284054i
$655$	−8.86513	−	5.11828i	−0.346389	−	0.199988i
$656$	−2.92671	−	5.06922i	−0.114269	−	0.197920i
$657$	5.28943			0.206360
$658$	1.73853	+	5.96884i	0.0677750	+	0.232689i
$659$		−	24.9930i		−	0.973590i	−0.873516	−	0.486795i	$-0.838166\pi$
$659$		−	24.9930i		−	0.973590i	0.873516	−	0.486795i	$-0.161834\pi$
$660$	−2.07200	+	1.05359i	−0.0806523	+	0.0410110i
$661$	12.7267	+	7.34774i	0.495010	+	0.285794i	0.726650	−	0.687007i	$-0.241076\pi$
$661$	12.7267	+	7.34774i	0.495010	+	0.285794i	−0.231641	+	0.972801i	$0.574409\pi$
$662$	23.6336	+	13.6449i	0.918547	+	0.530323i
$663$	3.76418	−	2.17325i	0.146189	−	0.0844021i
$664$			4.03988i			0.156778i
$665$	1.39469	−	0.406227i	0.0540836	−	0.0157528i
$666$		−	3.99419i		−	0.154772i
$667$	−9.55004	+	5.51372i	−0.369779	+	0.213492i
$668$	−8.99618	+	15.5818i	−0.348073	+	0.602879i
$669$	11.4597	−	19.8488i	0.443058	−	0.767400i
$670$	0.750200	+	1.29939i	0.0289828	+	0.0501996i
$671$	−1.47488	+	27.7067i	−0.0569371	+	1.06961i
$672$	−2.56981	−	0.629345i	−0.0991326	−	0.0242775i
$673$			51.7415i			1.99449i	0.0741830	+	0.997245i	$0.476365\pi$
$673$			51.7415i			1.99449i	−0.0741830	+	0.997245i	$0.523635\pi$
$674$	6.54644	+	11.3388i	0.252159	+	0.436753i
$675$	−3.90473	−	2.25440i	−0.150293	−	0.0867719i
$676$	18.2500	−	31.6099i	0.701922	−	1.21576i
$677$	18.7265	+	32.4353i	0.719718	+	1.24659i	0.961111	+	0.276161i	$0.0890624\pi$
$677$	18.7265	+	32.4353i	0.719718	+	1.24659i	−0.241393	+	0.970427i	$0.577604\pi$
$678$	−12.0074			−0.461142
$679$	−20.0497	−	19.2007i	−0.769438	−	0.736856i
$680$	0.432980			0.0166040
$681$	−20.9823	+	12.1141i	−0.804042	+	0.464214i
$682$	17.1751	+	11.1737i	0.657667	+	0.427863i
$683$	21.0079	−	36.3868i	0.803845	−	1.39230i	−0.113223	−	0.993570i	$-0.536117\pi$
$683$	21.0079	−	36.3868i	0.803845	−	1.39230i	0.917068	−	0.398731i	$-0.130549\pi$
$684$	0.391696	+	0.678438i	0.0149769	+	0.0259407i
$685$		−	11.7156i		−	0.447630i
$686$	−18.1623	−	3.62344i	−0.693441	−	0.138344i
$687$	−13.3778			−0.510396
$688$	−3.13883	+	1.81220i	−0.119667	+	0.0690896i
$689$	27.7955	−	48.1432i	1.05892	−	1.83411i
$690$	3.19980	+	1.84740i	0.121814	+	0.0703295i
$691$	−23.9459	+	13.8252i	−0.910945	+	0.525934i	−0.880735	−	0.473610i	$-0.842951\pi$
$691$	−23.9459	+	13.8252i	−0.910945	+	0.525934i	−0.0302096	+	0.999544i	$0.509617\pi$
$692$	−0.378382			−0.0143839
$693$	−6.00599	−	6.39751i	−0.228149	−	0.243021i
$694$	−11.3473			−0.430739
$695$	7.85403	−	4.53453i	0.297920	−	0.172004i
$696$	−1.81152	−	1.04588i	−0.0686655	−	0.0396440i
$697$	−1.80808	+	3.13169i	−0.0684859	+	0.118621i
$698$	10.7439	−	6.20298i	0.406662	−	0.234786i
$699$	−27.9050			−1.05546
$700$	−11.5868	−	2.83759i	−0.437938	−	0.107251i
$701$			8.73779i			0.330022i	0.986292	+	0.165011i	$0.0527659\pi$
$701$			8.73779i			0.330022i	−0.986292	+	0.165011i	$0.947234\pi$
$702$	3.51781	+	6.09302i	0.132771	+	0.229966i
$703$	−1.56451	+	2.70981i	−0.0590065	+	0.102202i
$704$	−2.78007	−	1.80865i	−0.104778	−	0.0681660i
$705$	1.42621	−	0.823423i	0.0537142	−	0.0310119i
$706$	−6.82398			−0.256824
$707$	11.0943	+	38.0895i	0.417243	+	1.43250i
$708$	−3.76387			−0.141455
$709$	16.6683	+	28.8703i	0.625990	+	1.08425i	0.988349	+	0.152208i	$0.0486382\pi$
$709$	16.6683	+	28.8703i	0.625990	+	1.08425i	−0.362359	+	0.932039i	$0.618028\pi$
$710$	−1.57168	+	2.72224i	−0.0589843	+	0.102164i
$711$	3.75818	+	2.16979i	0.140943	+	0.0813734i
$712$	8.10574	+	14.0396i	0.303776	+	0.526155i
$713$		−	32.5690i		−	1.21972i
$714$	0.457085	+	1.56929i	0.0171060	+	0.0587293i
$715$	16.3310	+	0.869332i	0.610747	+	0.0325112i
$716$	−2.15547	−	3.73338i	−0.0805536	−	0.139523i
$717$	4.63757	−	8.03251i	0.173193	−	0.299979i
$718$	−10.2157	+	17.6942i	−0.381248	+	0.660340i
$719$	−9.08278	+	5.24394i	−0.338730	+	0.195566i	−0.659711	−	0.751520i	$-0.729321\pi$
$719$	−9.08278	+	5.24394i	−0.338730	+	0.195566i	0.320980	+	0.947086i	$0.395988\pi$
$720$			0.700858i			0.0261194i
$721$	−9.03216	+	36.8811i	−0.336375	+	1.37353i
$722$			18.3863i			0.684267i
$723$	−16.5385	+	9.54851i	−0.615074	+	0.355113i
$724$	6.02993	+	3.48138i	0.224101	+	0.129385i
$725$	−8.16778	−	4.71567i	−0.303344	−	0.175136i
$726$	−4.45758	−	10.0563i	−0.165436	−	0.373226i
$727$		−	9.73041i		−	0.360881i	−0.983586	−	0.180440i	$-0.942248\pi$
$727$		−	9.73041i		−	0.360881i	0.983586	−	0.180440i	$-0.0577523\pi$
$728$	13.4440	+	12.8747i	0.498268	+	0.477169i
$729$	−1.00000			−0.0370370
$730$	−1.85357	−	3.21047i	−0.0686036	−	0.118825i
$731$	1.93912	+	1.11955i	0.0717210	+	0.0414082i
$732$	7.24493	+	4.18286i	0.267780	+	0.154603i
$733$	−0.800499	−	1.38650i	−0.0295671	−	0.0512117i	0.850863	−	0.525387i	$-0.176080\pi$
$733$	−0.800499	−	1.38650i	−0.0295671	−	0.0512117i	−0.880430	+	0.474176i	$0.842746\pi$
$734$	−20.1568			−0.744001
$735$	0.212140	+	4.90142i	0.00782491	+	0.180791i
$736$			5.27184i			0.194323i
$737$	−6.32902	+	3.21825i	−0.233132	+	0.118546i
$738$	−5.06922	−	2.92671i	−0.186600	−	0.107734i
$739$	23.6755	+	13.6691i	0.870918	+	0.502825i	0.867653	−	0.497170i	$-0.165627\pi$
$739$	23.6755	+	13.6691i	0.870918	+	0.502825i	0.00326478	+	0.999995i	$0.498961\pi$
$740$	−2.42431	+	1.39968i	−0.0891195	+	0.0514532i
$741$		−	5.51165i		−	0.202476i
$742$	15.0983	+	14.4590i	0.554277	+	0.530806i
$743$		−	49.7705i		−	1.82590i	−0.408067	−	0.912952i	$-0.633797\pi$
$743$		−	49.7705i		−	1.82590i	0.408067	−	0.912952i	$-0.366203\pi$
$744$	5.35024	−	3.08896i	0.196149	−	0.113247i
$745$	−3.40919	+	5.90489i	−0.124903	+	0.216338i
$746$	−4.16927	+	7.22139i	−0.152648	+	0.264394i
$747$	2.01994	+	3.49864i	0.0739058	+	0.128009i
$748$	−0.108916	+	2.04606i	−0.00398236	+	0.0748115i
$749$	−7.21677	+	29.4683i	−0.263695	+	1.07675i
$750$			6.66432i			0.243346i
$751$	11.5318	+	19.9737i	0.420803	+	0.728852i	0.996018	−	0.0891499i	$-0.0284150\pi$
$751$	11.5318	+	19.9737i	0.420803	+	0.728852i	−0.575215	+	0.818002i	$0.695082\pi$
$752$	2.03495	+	1.17488i	0.0742070	+	0.0428434i
$753$	6.06642	−	10.5073i	0.221073	−	0.382909i
$754$	7.35843	+	12.7452i	0.267978	+	0.464152i
$755$	−13.8684			−0.504722
$756$	−2.54019	+	0.739877i	−0.0923859	+	0.0269091i
$757$	−35.4691			−1.28915			−0.644574	−	0.764542i	$-0.722965\pi$
$757$	−35.4691			−1.28915			−0.644574	+	0.764542i	$0.722965\pi$
$758$	10.5736	−	6.10466i	0.384050	−	0.221731i
$759$	−9.53490	+	14.6561i	−0.346095	+	0.531982i
$760$	0.274523	−	0.475489i	0.00995801	−	0.0172478i
$761$	8.13485	+	14.0900i	0.294888	+	0.510761i	0.974959	−	0.222385i	$-0.0713843\pi$
$761$	8.13485	+	14.0900i	0.294888	+	0.510761i	−0.680071	+	0.733146i	$0.738051\pi$
$762$			3.43188i			0.124324i
$763$	3.69052	−	1.07493i	0.133606	−	0.0389151i
$764$	18.5590			0.671440
$765$	0.374971	−	0.216490i	0.0135571	−	0.00782720i
$766$	−9.32585	+	16.1528i	−0.336957	+	0.583626i
$767$	22.9333	+	13.2406i	0.828075	+	0.478089i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−31.2492			−1.12687			−0.563437	−	0.826159i	$-0.690521\pi$
$769$	−31.2492			−1.12687			−0.563437	+	0.826159i	$0.690521\pi$
$770$	−1.77836	+	5.88727i	−0.0640877	+	0.212163i
$771$	19.9471			0.718377
$772$	−15.1738	+	8.76059i	−0.546117	+	0.315301i
$773$	−14.3081	−	8.26079i	−0.514627	−	0.297120i	0.220107	−	0.975476i	$-0.429359\pi$
$773$	−14.3081	−	8.26079i	−0.514627	−	0.297120i	−0.734733	+	0.678356i	$0.762693\pi$
$774$	−1.81220	+	3.13883i	−0.0651383	+	0.112823i
$775$	24.1232	−	13.9275i	0.866529	−	0.500291i
$776$	−10.4926			−0.376662
$777$	−7.63228	−	7.30909i	−0.273807	−	0.262212i
$778$			9.51444i			0.341109i
$779$	2.29277	+	3.97119i	0.0821469	+	0.142283i
$780$	2.46548	−	4.27034i	0.0882785	−	0.152903i
$781$	−12.4687	−	8.11184i	−0.446165	−	0.290265i
$782$	2.82053	−	1.62843i	0.100862	−	0.0582326i
$783$	−2.09176			−0.0747535
$784$	−5.90516	+	3.75886i	−0.210899	+	0.134245i
$785$	−8.41762			−0.300438
$786$	−7.30288	−	12.6490i	−0.260485	−	0.451174i
$787$	11.0415	−	19.1245i	0.393589	−	0.681715i	−0.599331	−	0.800501i	$-0.704567\pi$
$787$	11.0415	−	19.1245i	0.393589	−	0.681715i	0.992920	+	0.118786i	$0.0379001\pi$
$788$	16.3387	+	9.43317i	0.582043	+	0.336043i
$789$	−8.39335	−	14.5377i	−0.298811	−	0.517556i
$790$		−	3.04142i		−	0.108209i
$791$	−21.9728	+	22.9443i	−0.781262	+	0.815807i
$792$	−3.31194	−	0.176300i	−0.117685	−	0.00626457i
$793$	−29.4290	−	50.9725i	−1.04505	−	1.81009i
$794$	17.0348	−	29.5051i	0.604543	−	1.04710i
$795$	2.76887	−	4.79582i	0.0982016	−	0.170090i
$796$	−11.7194	+	6.76618i	−0.415382	+	0.239821i
$797$		−	25.7347i		−	0.911571i	−0.890090	−	0.455785i	$-0.849358\pi$
$797$		−	25.7347i		−	0.911571i	0.890090	−	0.455785i	$-0.150642\pi$
$798$	2.01317	+	0.493024i	0.0712655	+	0.0174529i
$799$		−	1.45165i		−	0.0513555i
$800$	−3.90473	+	2.25440i	−0.138053	+	0.0797050i
$801$	14.0396	+	8.10574i	0.496063	+	0.286402i
$802$	−25.6653	−	14.8179i	−0.906274	−	0.523237i
$803$	15.6375	−	7.95153i	0.551836	−	0.280603i
$804$			2.14081i			0.0755004i
$805$	9.38553	−	2.73370i	0.330796	−	0.0963504i
$806$	−43.4655			−1.53101
$807$	−9.74767	−	16.8835i	−0.343134	−	0.594326i
$808$	12.9858	+	7.49737i	0.456840	+	0.263757i
$809$	−25.0947	−	14.4884i	−0.882281	−	0.509385i	−0.0108712	−	0.999941i	$-0.503460\pi$
$809$	−25.0947	−	14.4884i	−0.882281	−	0.509385i	−0.871410	+	0.490556i	$0.836794\pi$
$810$	0.350429	+	0.606961i	0.0123128	+	0.0213264i
$811$	1.48290			0.0520715			0.0260358	−	0.999661i	$-0.491712\pi$
$811$	1.48290			0.0520715			0.0260358	+	0.999661i	$0.491712\pi$
$812$	−5.31348	+	1.54765i	−0.186467	+	0.0543118i
$813$			10.6826i			0.374655i
$814$	−6.00441	−	11.8083i	−0.210454	−	0.413880i
$815$	13.5935	+	7.84819i	0.476159	+	0.274910i
$816$	0.535018	+	0.308893i	0.0187294	+	0.0108134i
$817$	2.45894	−	1.41967i	0.0860273	−	0.0496679i
$818$			27.3288i			0.955530i
$819$	18.0802	+	4.42783i	0.631774	+	0.154721i
$820$			4.10242i			0.143263i
$821$	4.78490	−	2.76257i	0.166994	−	0.0964142i	−0.414173	−	0.910198i	$-0.635929\pi$
$821$	4.78490	−	2.76257i	0.166994	−	0.0964142i	0.581168	+	0.813784i	$0.302596\pi$
$822$	8.35804	−	14.4765i	0.291520	−	0.504928i
$823$	8.11088	−	14.0485i	0.282728	−	0.489699i	−0.689328	−	0.724449i	$-0.742094\pi$
$823$	8.11088	−	14.0485i	0.282728	−	0.489699i	0.972056	+	0.234751i	$0.0754274\pi$
$824$	7.17585	+	12.4289i	0.249983	+	0.432982i
$825$	−14.9329	−	0.794903i	−0.519895	−	0.0276750i
$826$	−6.88763	+	7.19218i	−0.239651	+	0.250248i
$827$			5.86195i			0.203840i	0.994793	+	0.101920i	$0.0324986\pi$
$827$			5.86195i			0.203840i	−0.994793	+	0.101920i	$0.967501\pi$
$828$	2.63592	+	4.56555i	0.0916045	+	0.158664i
$829$	−16.8080	−	9.70409i	−0.583765	−	0.337037i	0.178863	−	0.983874i	$-0.442758\pi$
$829$	−16.8080	−	9.70409i	−0.583765	−	0.337037i	−0.762628	+	0.646837i	$0.776091\pi$
$830$	1.41569	−	2.45205i	0.0491394	−	0.0851119i
$831$	15.3940	+	26.6632i	0.534011	+	0.924934i
$832$	7.03562			0.243916
$833$	3.83512	+	1.99828i	0.132879	+	0.0692364i
$834$	12.9399			0.448073
$835$	10.9207	−	6.30504i	0.377925	−	0.218195i
$836$	2.17789	+	1.41688i	0.0753238	+	0.0490039i
$837$	3.08896	−	5.35024i	0.106770	−	0.184931i
$838$	−12.8486	−	22.2545i	−0.443848	−	0.768767i
$839$		−	17.8302i		−	0.615565i	−0.951457	−	0.307783i	$-0.900413\pi$
$839$		−	17.8302i		−	0.615565i	0.951457	−	0.307783i	$-0.0995870\pi$
$840$	1.33923	+	1.28252i	0.0462079	+	0.0442513i
$841$	24.6245			0.849122
$842$	31.9776	−	18.4623i	1.10202	−	0.636252i
$843$	−10.6691	+	18.4793i	−0.367462	+	0.636462i
$844$	−4.28135	−	2.47184i	−0.147370	−	0.0850842i
$845$	−22.1540	+	12.7906i	−0.762122	+	0.440011i
$846$	2.34976			0.0807863
$847$	−27.3732	−	9.88467i	−0.940555	−	0.339641i
$848$	7.90136			0.271334
$849$	2.18504	−	1.26154i	0.0749905	−	0.0432958i
$850$	2.41229	+	1.39273i	0.0827408	+	0.0477704i
$851$	−10.5283	+	18.2356i	−0.360907	+	0.625109i
$852$	−3.88415	+	2.24252i	−0.133069	+	0.0768273i
$853$	−2.57158			−0.0880491			−0.0440246	−	0.999030i	$-0.514018\pi$
$853$	−2.57158			−0.0880491			−0.0440246	+	0.999030i	$0.514018\pi$
$854$	21.2505	−	6.18960i	0.727179	−	0.211804i
$855$		−	0.549047i		−	0.0187770i
$856$	5.73356	+	9.93081i	0.195969	+	0.339428i
$857$	−8.16413	+	14.1407i	−0.278881	+	0.483037i	−0.971107	−	0.238644i	$-0.923297\pi$
$857$	−8.16413	+	14.1407i	−0.278881	+	0.483037i	0.692226	+	0.721681i	$0.256630\pi$
$858$	19.5595	+	12.7250i	0.667751	+	0.434423i
$859$	−22.3768	+	12.9193i	−0.763487	+	0.440799i	−0.830546	−	0.556950i	$-0.811972\pi$
$859$	−22.3768	+	12.9193i	−0.763487	+	0.440799i	0.0670596	+	0.997749i	$0.478638\pi$
$860$	2.54020			0.0866199
$861$	−14.8688	+	4.33082i	−0.506729	+	0.147594i
$862$	−20.1287			−0.685586
$863$	−8.89726	−	15.4105i	−0.302866	−	0.524580i	0.673918	−	0.738806i	$-0.264610\pi$
$863$	−8.89726	−	15.4105i	−0.302866	−	0.524580i	−0.976784	+	0.214227i	$0.931277\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	0.229663	+	0.132596i	0.00780878	+	0.00450840i
$866$	−19.0996	−	33.0815i	−0.649031	−	1.12416i
$867$			16.6183i			0.564388i
$868$	3.88804	−	15.8761i	0.131969	−	0.538870i
$869$	14.3724	+	0.765069i	0.487550	+	0.0259532i
$870$	0.733014	+	1.26962i	0.0248515	+	0.0430441i
$871$	7.53095	−	13.0440i	0.255176	−	0.441979i
$872$	0.726424	−	1.25820i	0.0245998	−	0.0426082i
$873$	−9.08684	+	5.24629i	−0.307543	+	0.177560i
$874$		−	4.12992i		−	0.139697i
$875$	12.7345	+	12.1953i	0.430505	+	0.412275i
$876$		−	5.28943i		−	0.178713i
$877$	1.31624	−	0.759931i	0.0444463	−	0.0256611i	−0.477612	−	0.878571i	$-0.658498\pi$
$877$	1.31624	−	0.759931i	0.0444463	−	0.0256611i	0.522058	+	0.852910i	$0.325164\pi$
$878$	−6.34102	−	3.66099i	−0.213999	−	0.123552i
$879$	−4.95220	−	2.85916i	−0.167034	−	0.0964370i
$880$	1.05359	+	2.07200i	0.0355165	+	0.0698470i
$881$		−	2.61558i		−	0.0881210i	−0.999029	−	0.0440605i	$-0.985971\pi$
$881$		−	2.61558i		−	0.0881210i	0.999029	−	0.0440605i	$-0.0140294\pi$
$882$	−3.23459	+	6.20785i	−0.108914	+	0.209029i
$883$	−32.7433			−1.10190			−0.550950	−	0.834538i	$-0.685735\pi$
$883$	−32.7433			−1.10190			−0.550950	+	0.834538i	$0.685735\pi$
$884$	−2.17325	−	3.76418i	−0.0730943	−	0.126603i
$885$	2.28452	+	1.31897i	0.0767933	+	0.0443366i
$886$	−28.6003	−	16.5124i	−0.960846	−	0.554745i
$887$	11.6100	+	20.1091i	0.389825	+	0.675197i	0.992426	−	0.122846i	$-0.0392022\pi$
$887$	11.6100	+	20.1091i	0.389825	+	0.675197i	−0.602601	+	0.798043i	$0.705869\pi$
$888$	−3.99419			−0.134036
$889$	6.55781	+	6.28012i	0.219942	+	0.210628i
$890$		−	11.3619i		−	0.380853i
$891$	−2.95637	+	1.50329i	−0.0990421	+	0.0503620i
$892$	−19.8488	−	11.4597i	−0.664588	−	0.383700i
$893$	−1.59416	−	0.920391i	−0.0533467	−	0.0307997i
$894$	−8.42523	+	4.86431i	−0.281782	+	0.162687i
$895$			3.02135i			0.100993i
$896$	−0.629345	+	2.56981i	−0.0210249	+	0.0858513i
$897$		−	37.0906i		−	1.23842i
$898$	19.5103	−	11.2643i	0.651067	−	0.375894i
$899$	6.46138	−	11.1914i	0.215499	−	0.373255i
$900$	−2.25440	+	3.90473i	−0.0751466	+	0.130158i
$901$	−2.44067	−	4.22737i	−0.0813106	−	0.140834i
$902$	−19.3862	−	1.03196i	−0.645489	−	0.0343606i
$903$	2.68162	+	9.20670i	0.0892386	+	0.306380i
$904$			12.0074i			0.399361i
$905$	−2.43995	−	4.22612i	−0.0811068	−	0.140481i
$906$	−17.1367	−	9.89387i	−0.569328	−	0.328702i
$907$	7.46536	−	12.9304i	0.247883	−	0.429346i	−0.715055	−	0.699068i	$-0.753598\pi$
$907$	7.46536	−	12.9304i	0.247883	−	0.429346i	0.962938	+	0.269722i	$0.0869317\pi$
$908$	12.1141	+	20.9823i	0.402021	+	0.696321i
$909$	14.9947			0.497344
$910$	−3.64831	−	12.5256i	−0.120940	−	0.415220i
$911$	33.6372			1.11445			0.557225	−	0.830362i	$-0.311866\pi$
$911$	33.6372			1.11445			0.557225	+	0.830362i	$0.311866\pi$
$912$	0.678438	−	0.391696i	0.0224653	−	0.0129704i
$913$	11.2312	+	7.30673i	0.371697	+	0.241817i
$914$	−16.5876	+	28.7305i	−0.548668	+	0.950321i
$915$	−2.93159	−	5.07766i	−0.0969154	−	0.167862i
$916$			13.3778i			0.442016i
$917$	−37.5341	−	9.19206i	−1.23948	−	0.303549i
$918$	0.617785			0.0203899
$919$	23.3845	−	13.5011i	0.771385	−	0.445359i	−0.0619837	−	0.998077i	$-0.519743\pi$
$919$	23.3845	−	13.5011i	0.771385	−	0.445359i	0.833368	+	0.552718i	$0.186409\pi$
$920$	1.84740	−	3.19980i	0.0609071	−	0.105494i
$921$	−17.9993	−	10.3919i	−0.593099	−	0.342426i
$922$	6.43418	−	3.71478i	0.211899	−	0.122340i
$923$	31.5550			1.03864
$924$	−6.39751	+	6.00599i	−0.210462	+	0.197583i
$925$	−18.0090			−0.592131
$926$	13.6403	−	7.87521i	0.448247	−	0.258795i
$927$	12.4289	+	7.17585i	0.408220	+	0.235686i
$928$	−1.04588	+	1.81152i	−0.0343328	+	0.0594661i
$929$	32.7038	−	18.8815i	1.07298	−	0.619483i	0.143983	−	0.989580i	$-0.454009\pi$
$929$	32.7038	−	18.8815i	1.07298	−	0.619483i	0.928993	+	0.370097i	$0.120676\pi$
$930$	−4.32985			−0.141981
$931$	4.62606	−	2.94466i	0.151613	−	0.0965075i
$932$			27.9050i			0.914057i
$933$	−3.68376	−	6.38045i	−0.120601	−	0.208887i
$934$	−6.68657	+	11.5815i	−0.218791	+	0.378958i
$935$	0.783108	−	1.20371i	0.0256104	−	0.0393656i
$936$	6.09302	−	3.51781i	0.199157	−	0.114983i
$937$	33.9310			1.10848			0.554239	−	0.832357i	$-0.313009\pi$
$937$	33.9310			1.10848			0.554239	+	0.832357i	$0.313009\pi$
$938$	4.09076	+	3.91753i	0.133568	+	0.127912i
$939$	−7.35395			−0.239987
$940$	−0.823423	−	1.42621i	−0.0268571	−	0.0465178i
$941$	13.4471	−	23.2911i	0.438364	−	0.759269i	−0.559199	−	0.829033i	$-0.688891\pi$
$941$	13.4471	−	23.2911i	0.438364	−	0.759269i	0.997564	+	0.0697641i	$0.0222247\pi$
$942$	−10.4014	−	6.00523i	−0.338895	−	0.195661i
$943$	15.4292	+	26.7241i	0.502443	+	0.870256i
$944$			3.76387i			0.122503i
$945$	1.80107	+	0.441081i	0.0585889	+	0.0143484i
$946$	−0.638985	+	12.0038i	−0.0207752	+	0.390278i
$947$	11.3627	+	19.6808i	0.369239	+	0.639540i	0.989447	−	0.144897i	$-0.0462852\pi$
$947$	11.3627	+	19.6808i	0.369239	+	0.639540i	−0.620208	+	0.784437i	$0.712952\pi$
$948$	2.16979	−	3.75818i	0.0704714	−	0.122060i
$949$	−18.6072	+	32.2286i	−0.604015	+	1.04618i
$950$	3.05894	−	1.76608i	0.0992451	−	0.0572992i
$951$			14.7806i			0.479294i
$952$	1.56929	−	0.457085i	0.0508611	−	0.0148142i
$953$		−	15.8105i		−	0.512152i	−0.966657	−	0.256076i	$-0.917570\pi$
$953$		−	15.8105i		−	0.512152i	0.966657	−	0.256076i	$-0.0824298\pi$
$954$	6.84278	−	3.95068i	0.221543	−	0.127908i
$955$	−11.2646	−	6.50360i	−0.364513	−	0.210452i
$956$	−8.03251	−	4.63757i	−0.259790	−	0.149990i
$957$	−6.18403	+	3.14452i	−0.199901	+	0.101648i
$958$		−	11.2610i		−	0.363826i
$959$	−12.3678	−	42.4621i	−0.399378	−	1.37117i
$960$	0.700858			0.0226201
$961$	3.58338	+	6.20660i	0.115593	+	0.200213i
$962$	24.3367	+	14.0508i	0.784646	+	0.453015i
$963$	9.93081	+	5.73356i	0.320016	+	0.184761i
$964$	9.54851	+	16.5385i	0.307537	+	0.532669i
$965$	12.2799			0.395303
$966$	13.5476	+	3.31780i	0.435888	+	0.106749i
$967$		−	50.1237i		−	1.61187i	−0.592005	−	0.805934i	$-0.701663\pi$
$967$		−	50.1237i		−	1.61187i	0.592005	−	0.805934i	$-0.298337\pi$
$968$	−10.0563	+	4.45758i	−0.323223	+	0.143272i
$969$	−0.419129	−	0.241984i	−0.0134644	−	0.00777365i
$970$	6.36858	+	3.67690i	0.204483	+	0.118058i
$971$	−28.9076	+	16.6898i	−0.927690	+	0.535602i	−0.886080	−	0.463532i	$-0.846582\pi$
$971$	−28.9076	+	16.6898i	−0.927690	+	0.535602i	−0.0416095	+	0.999134i	$0.513249\pi$
$972$			1.00000i			0.0320750i
$973$	23.6792	−	24.7263i	0.759121	−	0.792687i
$974$		−	2.66963i		−	0.0855405i
$975$	27.4722	−	15.8611i	0.879815	−	0.507962i
$976$	4.18286	−	7.24493i	0.133890	−	0.231904i
$977$	15.4092	−	26.6894i	0.492983	−	0.853871i	−0.506985	−	0.861955i	$-0.669240\pi$
$977$	15.4092	−	26.6894i	0.492983	−	0.853871i	0.999967	+	0.00808403i	$0.00257325\pi$
$978$	11.1980	+	19.3955i	0.358072	+	0.620199i
$979$	53.6914	+	2.85809i	1.71598	+	0.0913450i
$980$	4.90142	−	0.212140i	0.156570	−	0.00677657i
$981$		−	1.45285i		−	0.0463859i
$982$	−5.65314	−	9.79152i	−0.180399	−	0.312460i
$983$	−28.8714	−	16.6689i	−0.920855	−	0.531656i	−0.0369470	−	0.999317i	$-0.511763\pi$
$983$	−28.8714	−	16.6689i	−0.920855	−	0.531656i	−0.883908	+	0.467662i	$0.845097\pi$
$984$	−2.92671	+	5.06922i	−0.0933002	+	0.161601i
$985$	−6.61131	−	11.4511i	−0.210654	−	0.364863i
$986$	1.29226			0.0411540
$987$	4.29990	−	4.49003i	0.136867	−	0.142919i
$988$	−5.51165			−0.175349
$989$	16.5474	−	9.55365i	0.526177	−	0.303788i
$990$	1.94843	+	1.26761i	0.0619253	+	0.0402871i
$991$	29.0342	−	50.2888i	0.922303	−	1.59748i	0.126461	−	0.991972i	$-0.459638\pi$
$991$	29.0342	−	50.2888i	0.922303	−	1.59748i	0.795842	−	0.605504i	$-0.207029\pi$
$992$	−3.08896	−	5.35024i	−0.0980747	−	0.169870i
$993$		−	27.2898i		−	0.866015i
$994$	−2.82263	+	11.5257i	−0.0895284	+	0.365572i
$995$	9.48426			0.300671
$996$	3.49864	−	2.01994i	0.110859	−	0.0640043i
$997$	18.3242	−	31.7385i	0.580334	−	1.00517i	−0.415106	−	0.909773i	$-0.636255\pi$
$997$	18.3242	−	31.7385i	0.580334	−	1.00517i	0.995440	−	0.0953943i	$-0.0304112\pi$
$998$	18.5676	+	10.7200i	0.587747	+	0.339336i
$999$	−3.45907	+	1.99709i	−0.109440	+	0.0631852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.a.241.2	✓	16
3.2	odd	2		1386.2.bk.a.703.7		16
7.3	odd	6		3234.2.e.b.2155.4		16
7.4	even	3		3234.2.e.a.2155.5		16
7.5	odd	6		462.2.p.b.439.6	yes	16
11.10	odd	2		462.2.p.b.241.6	yes	16
21.5	even	6		1386.2.bk.b.901.3		16
33.32	even	2		1386.2.bk.b.703.3		16
77.10	even	6		3234.2.e.a.2155.12		16
77.32	odd	6		3234.2.e.b.2155.13		16
77.54	even	6	inner	462.2.p.a.439.2	yes	16
231.131	odd	6		1386.2.bk.a.901.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.2	✓	16	1.1	even	1	trivial
462.2.p.a.439.2	yes	16	77.54	even	6	inner
462.2.p.b.241.6	yes	16	11.10	odd	2
462.2.p.b.439.6	yes	16	7.5	odd	6
1386.2.bk.a.703.7		16	3.2	odd	2
1386.2.bk.a.901.7		16	231.131	odd	6
1386.2.bk.b.703.3		16	33.32	even	2
1386.2.bk.b.901.3		16	21.5	even	6
3234.2.e.a.2155.5		16	7.4	even	3
3234.2.e.a.2155.12		16	77.10	even	6
3234.2.e.b.2155.4		16	7.3	odd	6
3234.2.e.b.2155.13		16	77.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.606961 + 0.350429i) q^{5} -1.00000 q^{6} +(-1.82993 + 1.91085i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.606961 + 0.350429i) q^{5} -1.00000 q^{6} +(-1.82993 + 1.91085i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.350429 - 0.606961i) q^{10} +(2.78007 + 1.80865i) q^{11} +(0.866025 - 0.500000i) q^{12} -7.03562 q^{13} +(0.629345 - 2.56981i) q^{14} -0.700858 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.308893 + 0.535018i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.391696 + 0.678438i) q^{19} +0.700858i q^{20} +(-2.54019 + 0.739877i) q^{21} +(-3.31194 - 0.176300i) q^{22} +(2.63592 + 4.56555i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.25440 + 3.90473i) q^{25} +(6.09302 - 3.51781i) q^{26} +1.00000i q^{27} +(0.739877 + 2.54019i) q^{28} +2.09176i q^{29} +(0.606961 - 0.350429i) q^{30} +(-5.35024 - 3.08896i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.50329 + 2.95637i) q^{33} -0.617785i q^{34} +(0.441081 - 1.80107i) q^{35} +1.00000 q^{36} +(1.99709 + 3.45907i) q^{37} +(-0.678438 - 0.391696i) q^{38} +(-6.09302 - 3.51781i) q^{39} +(-0.350429 - 0.606961i) q^{40} +5.85343 q^{41} +(1.82993 - 1.91085i) q^{42} -3.62441i q^{43} +(2.95637 - 1.50329i) q^{44} +(-0.606961 - 0.350429i) q^{45} +(-4.56555 - 2.63592i) q^{46} +(-2.03495 + 1.17488i) q^{47} -1.00000i q^{48} +(-0.302687 - 6.99345i) q^{49} -4.50880i q^{50} +(-0.535018 + 0.308893i) q^{51} +(-3.51781 + 6.09302i) q^{52} +(-3.95068 + 6.84278i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.32120 - 0.123562i) q^{55} +(-1.91085 - 1.82993i) q^{56} +0.783393i q^{57} +(-1.04588 - 1.81152i) q^{58} +(-3.25961 - 1.88193i) q^{59} +(-0.350429 + 0.606961i) q^{60} +(4.18286 + 7.24493i) q^{61} +6.17793 q^{62} +(-2.56981 - 0.629345i) q^{63} -1.00000 q^{64} +(4.27034 - 2.46548i) q^{65} +(-2.78007 - 1.80865i) q^{66} +(-1.07040 + 1.85399i) q^{67} +(0.308893 + 0.535018i) q^{68} +5.27184i q^{69} +(0.518548 + 1.78031i) q^{70} -4.48503 q^{71} +(-0.866025 + 0.500000i) q^{72} +(2.64471 - 4.58078i) q^{73} +(-3.45907 - 1.99709i) q^{74} +(-3.90473 + 2.25440i) q^{75} +0.783393 q^{76} +(-8.54340 + 2.00259i) q^{77} +7.03562 q^{78} +(3.75818 - 2.16979i) q^{79} +(0.606961 + 0.350429i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.06922 + 2.92671i) q^{82} +4.03988 q^{83} +(-0.629345 + 2.56981i) q^{84} -0.432980i q^{85} +(1.81220 + 3.13883i) q^{86} +(-1.04588 + 1.81152i) q^{87} +(-1.80865 + 2.78007i) q^{88} +(14.0396 - 8.10574i) q^{89} +0.700858 q^{90} +(12.8747 - 13.4440i) q^{91} +5.27184 q^{92} +(-3.08896 - 5.35024i) q^{93} +(1.17488 - 2.03495i) q^{94} +(-0.475489 - 0.274523i) q^{95} +(0.500000 + 0.866025i) q^{96} +10.4926i q^{97} +(3.75886 + 5.90516i) q^{98} +(-0.176300 + 3.31194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more