LMFDB - Embedded newform 930.2.bf.a.377.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.17
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.134174 - 1.72685i) q^{3} -1.00000i q^{4} +(2.18104 + 0.493020i) q^{5} +(1.31594 + 1.12619i) q^{6} +(-3.79793 + 1.01765i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.96399 + 0.463396i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.134174 - 1.72685i) q^{3} -1.00000i q^{4} +(2.18104 + 0.493020i) q^{5} +(1.31594 + 1.12619i) q^{6} +(-3.79793 + 1.01765i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.96399 + 0.463396i) q^{9} +(-1.89085 + 1.19361i) q^{10} +(0.225535 - 0.130213i) q^{11} +(-1.72685 + 0.134174i) q^{12} +(3.81277 + 1.02163i) q^{13} +(1.96595 - 3.40513i) q^{14} +(0.558731 - 3.83247i) q^{15} -1.00000 q^{16} +(1.09590 + 4.08994i) q^{17} +(1.76819 - 2.42353i) q^{18} +(3.85397 + 2.22509i) q^{19} +(0.493020 - 2.18104i) q^{20} +(2.26691 + 6.42189i) q^{21} +(-0.0674030 + 0.251552i) q^{22} +(-2.45373 - 2.45373i) q^{23} +(1.12619 - 1.31594i) q^{24} +(4.51386 + 2.15059i) q^{25} +(-3.41843 + 1.97363i) q^{26} +(1.19790 + 5.05619i) q^{27} +(1.01765 + 3.79793i) q^{28} +5.25460 q^{29} +(2.31488 + 3.10505i) q^{30} +(-1.71838 + 5.29596i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.255118 - 0.371993i) q^{33} +(-3.66694 - 2.11711i) q^{34} +(-8.78515 + 0.347083i) q^{35} +(0.463396 + 2.96399i) q^{36} +(0.196556 - 0.0526671i) q^{37} +(-4.29854 + 1.15179i) q^{38} +(1.25262 - 6.72114i) q^{39} +(1.19361 + 1.89085i) q^{40} +(9.80119 - 5.65872i) q^{41} +(-6.14391 - 2.93802i) q^{42} +(-0.797629 - 2.97679i) q^{43} +(-0.130213 - 0.225535i) q^{44} +(-6.69305 - 0.450625i) q^{45} +3.47009 q^{46} +(4.49966 - 4.49966i) q^{47} +(0.134174 + 1.72685i) q^{48} +(7.32645 - 4.22993i) q^{49} +(-4.71248 + 1.67108i) q^{50} +(6.91566 - 2.44121i) q^{51} +(1.02163 - 3.81277i) q^{52} +(-1.20308 + 4.48997i) q^{53} +(-4.42231 - 2.72822i) q^{54} +(0.556098 - 0.172806i) q^{55} +(-3.40513 - 1.96595i) q^{56} +(3.32528 - 6.95375i) q^{57} +(-3.71556 + 3.71556i) q^{58} +(4.15001 - 7.18804i) q^{59} +(-3.83247 - 0.558731i) q^{60} +2.18907 q^{61} +(-2.52973 - 4.95989i) q^{62} +(10.7855 - 4.77626i) q^{63} +1.00000i q^{64} +(7.81211 + 4.10798i) q^{65} +(0.443434 + 0.0826430i) q^{66} +(-3.84020 + 14.3318i) q^{67} +(4.08994 - 1.09590i) q^{68} +(-3.90798 + 4.56643i) q^{69} +(5.96661 - 6.45746i) q^{70} +(-1.34039 + 0.773872i) q^{71} +(-2.42353 - 1.76819i) q^{72} +(-13.1503 - 3.52362i) q^{73} +(-0.101745 + 0.176228i) q^{74} +(3.10810 - 8.08330i) q^{75} +(2.22509 - 3.85397i) q^{76} +(-0.724054 + 0.724054i) q^{77} +(3.86683 + 5.63830i) q^{78} +(5.52132 + 3.18774i) q^{79} +(-2.18104 - 0.493020i) q^{80} +(8.57053 - 2.74700i) q^{81} +(-2.92917 + 10.9318i) q^{82} +(-1.30341 + 4.86439i) q^{83} +(6.42189 - 2.26691i) q^{84} +(0.373770 + 9.46062i) q^{85} +(2.66892 + 1.54090i) q^{86} +(-0.705030 - 9.07388i) q^{87} +(0.251552 + 0.0674030i) q^{88} +16.1989 q^{89} +(5.05134 - 4.41406i) q^{90} -15.5203 q^{91} +(-2.45373 + 2.45373i) q^{92} +(9.37586 + 2.25681i) q^{93} +6.36348i q^{94} +(7.30864 + 6.75309i) q^{95} +(-1.31594 - 1.12619i) q^{96} +(1.09975 + 1.09975i) q^{97} +(-2.18957 + 8.17160i) q^{98} +(-0.608144 + 0.490461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.134174	−	1.72685i	−0.0774654	−	0.996995i
$3$	−0.134174	−	1.72685i	−0.0774654	−	0.996995i
$4$		−	1.00000i		−	0.500000i
$5$	2.18104	+	0.493020i	0.975390	+	0.220485i
$5$	2.18104	+	0.493020i	0.975390	+	0.220485i
$6$	1.31594	+	1.12619i	0.537230	+	0.459765i
$7$	−3.79793	+	1.01765i	−1.43548	+	0.384636i	−0.890949	−	0.454104i	$-0.849960\pi$
$7$	−3.79793	+	1.01765i	−1.43548	+	0.384636i	−0.544532	+	0.838740i	$0.683293\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.96399	+	0.463396i	−0.987998	+	0.154465i
$10$	−1.89085	+	1.19361i	−0.597938	+	0.377453i
$11$	0.225535	−	0.130213i	0.0680013	−	0.0392606i	−0.465614	−	0.884988i	$-0.654166\pi$
$11$	0.225535	−	0.130213i	0.0680013	−	0.0392606i	0.533615	+	0.845727i	$0.320833\pi$
$12$	−1.72685	+	0.134174i	−0.498498	+	0.0387327i
$13$	3.81277	+	1.02163i	1.05747	+	0.283349i	0.745336	−	0.666689i	$-0.232289\pi$
$13$	3.81277	+	1.02163i	1.05747	+	0.283349i	0.312135	+	0.950038i	$0.398956\pi$
$14$	1.96595	−	3.40513i	0.525423	−	0.910059i
$15$	0.558731	−	3.83247i	0.144264	−	0.989539i
$16$	−1.00000			−0.250000
$17$	1.09590	+	4.08994i	0.265794	+	0.991957i	0.961763	+	0.273885i	$0.0883086\pi$
$17$	1.09590	+	4.08994i	0.265794	+	0.991957i	−0.695969	+	0.718072i	$0.745025\pi$
$18$	1.76819	−	2.42353i	0.416767	−	0.571232i
$19$	3.85397	+	2.22509i	0.884160	+	0.510470i	0.872028	−	0.489456i	$-0.162805\pi$
$19$	3.85397	+	2.22509i	0.884160	+	0.510470i	0.0121324	+	0.999926i	$0.496138\pi$
$20$	0.493020	−	2.18104i	0.110243	−	0.487695i
$21$	2.26691	+	6.42189i	0.494680	+	1.40137i
$22$	−0.0674030	+	0.251552i	−0.0143704	+	0.0536310i
$23$	−2.45373	−	2.45373i	−0.511637	−	0.511637i	0.403391	−	0.915028i	$-0.367832\pi$
$23$	−2.45373	−	2.45373i	−0.511637	−	0.511637i	−0.915028	+	0.403391i	$0.867832\pi$
$24$	1.12619	−	1.31594i	0.229882	−	0.268615i
$25$	4.51386	+	2.15059i	0.902772	+	0.430118i
$26$	−3.41843	+	1.97363i	−0.670410	+	0.387061i
$27$	1.19790	+	5.05619i	0.230537	+	0.973064i
$28$	1.01765	+	3.79793i	0.192318	+	0.717741i
$29$	5.25460			0.975754			0.487877	−	0.872912i	$-0.337771\pi$
$29$	5.25460			0.975754			0.487877	+	0.872912i	$0.337771\pi$
$30$	2.31488	+	3.10505i	0.422638	+	0.566902i
$31$	−1.71838	+	5.29596i	−0.308631	+	0.951182i
$31$	−1.71838	+	5.29596i	−0.308631	+	0.951182i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.255118	−	0.371993i	−0.0444104	−	0.0647557i
$34$	−3.66694	−	2.11711i	−0.628875	−	0.363081i
$35$	−8.78515	+	0.347083i	−1.48496	+	0.0586678i
$36$	0.463396	+	2.96399i	0.0772326	+	0.493999i
$37$	0.196556	−	0.0526671i	0.0323137	−	0.00865842i	−0.242626	−	0.970120i	$-0.578009\pi$
$37$	0.196556	−	0.0526671i	0.0323137	−	0.00865842i	0.274940	+	0.961461i	$0.411342\pi$
$38$	−4.29854	+	1.15179i	−0.697315	+	0.186845i
$39$	1.25262	−	6.72114i	0.200580	−	1.07624i
$40$	1.19361	+	1.89085i	0.188726	+	0.298969i
$41$	9.80119	−	5.65872i	1.53069	−	0.883744i	0.531359	−	0.847147i	$-0.321682\pi$
$41$	9.80119	−	5.65872i	1.53069	−	0.883744i	0.999330	−	0.0365970i	$-0.0116518\pi$
$42$	−6.14391	−	2.93802i	−0.948026	−	0.453346i
$43$	−0.797629	−	2.97679i	−0.121637	−	0.453957i	0.878060	−	0.478550i	$-0.158838\pi$
$43$	−0.797629	−	2.97679i	−0.121637	−	0.453957i	−0.999698	+	0.0245935i	$0.992171\pi$
$44$	−0.130213	−	0.225535i	−0.0196303	−	0.0340007i
$45$	−6.69305	−	0.450625i	−0.997741	−	0.0671752i
$46$	3.47009			0.511637
$47$	4.49966	−	4.49966i	0.656342	−	0.656342i	−0.298170	−	0.954513i	$-0.596376\pi$
$47$	4.49966	−	4.49966i	0.656342	−	0.656342i	0.954513	+	0.298170i	$0.0963763\pi$
$48$	0.134174	+	1.72685i	0.0193663	+	0.249249i
$49$	7.32645	−	4.22993i	1.04664	−	0.604276i
$50$	−4.71248	+	1.67108i	−0.666445	+	0.236327i
$51$	6.91566	−	2.44121i	0.968386	−	0.341838i
$52$	1.02163	−	3.81277i	0.141674	−	0.528736i
$53$	−1.20308	+	4.48997i	−0.165256	+	0.616744i	0.832751	+	0.553647i	$0.186764\pi$
$53$	−1.20308	+	4.48997i	−0.165256	+	0.616744i	−0.998007	+	0.0630969i	$0.979902\pi$
$54$	−4.42231	−	2.72822i	−0.601800	−	0.371263i
$55$	0.556098	−	0.172806i	0.0749842	−	0.0233011i
$56$	−3.40513	−	1.96595i	−0.455029	−	0.262711i
$57$	3.32528	−	6.95375i	0.440444	−	0.921047i
$58$	−3.71556	+	3.71556i	−0.487877	+	0.487877i
$59$	4.15001	−	7.18804i	0.540286	−	0.935803i	−0.458601	−	0.888642i	$-0.651649\pi$
$59$	4.15001	−	7.18804i	0.540286	−	0.935803i	0.998887	−	0.0471605i	$-0.0150172\pi$
$60$	−3.83247	−	0.558731i	−0.494770	−	0.0721319i
$61$	2.18907			0.280281			0.140141	−	0.990132i	$-0.455245\pi$
$61$	2.18907			0.280281			0.140141	+	0.990132i	$0.455245\pi$
$62$	−2.52973	−	4.95989i	−0.321276	−	0.629906i
$63$	10.7855	−	4.77626i	1.35884	−	0.601752i
$64$			1.00000i			0.125000i
$65$	7.81211	+	4.10798i	0.968973	+	0.509532i
$66$	0.443434	+	0.0826430i	0.0545830	+	0.0101726i
$67$	−3.84020	+	14.3318i	−0.469155	+	1.75091i	0.173577	+	0.984820i	$0.444468\pi$
$67$	−3.84020	+	14.3318i	−0.469155	+	1.75091i	−0.642732	+	0.766091i	$0.722199\pi$
$68$	4.08994	−	1.09590i	0.495978	−	0.132897i
$69$	−3.90798	+	4.56643i	−0.470466	+	0.549734i
$70$	5.96661	−	6.45746i	0.713147	−	0.771814i
$71$	−1.34039	+	0.773872i	−0.159075	+	0.0918418i	−0.577424	−	0.816444i	$-0.695942\pi$
$71$	−1.34039	+	0.773872i	−0.159075	+	0.0918418i	0.418350	+	0.908286i	$0.362609\pi$
$72$	−2.42353	−	1.76819i	−0.285616	−	0.208383i
$73$	−13.1503	−	3.52362i	−1.53913	−	0.412409i	−0.613146	−	0.789969i	$-0.710096\pi$
$73$	−13.1503	−	3.52362i	−1.53913	−	0.412409i	−0.925985	+	0.377560i	$0.876763\pi$
$74$	−0.101745	+	0.176228i	−0.0118276	+	0.0204860i
$75$	3.10810	−	8.08330i	0.358892	−	0.933379i
$76$	2.22509	−	3.85397i	0.255235	−	0.442080i
$77$	−0.724054	+	0.724054i	−0.0825136	+	0.0825136i
$78$	3.86683	+	5.63830i	0.437832	+	0.638412i
$79$	5.52132	+	3.18774i	0.621197	+	0.358648i	0.777335	−	0.629087i	$-0.216571\pi$
$79$	5.52132	+	3.18774i	0.621197	+	0.358648i	−0.156138	+	0.987735i	$0.549904\pi$
$80$	−2.18104	−	0.493020i	−0.243848	−	0.0551213i
$81$	8.57053	−	2.74700i	0.952281	−	0.305223i
$82$	−2.92917	+	10.9318i	−0.323473	+	1.20722i
$83$	−1.30341	+	4.86439i	−0.143068	+	0.533936i	0.856766	+	0.515705i	$0.172470\pi$
$83$	−1.30341	+	4.86439i	−0.143068	+	0.533936i	−0.999834	+	0.0182307i	$0.994197\pi$
$84$	6.42189	−	2.26691i	0.700686	−	0.247340i
$85$	0.373770	+	9.46062i	0.0405410	+	1.02615i
$86$	2.66892	+	1.54090i	0.287797	+	0.166160i
$87$	−0.705030	−	9.07388i	−0.0755871	−	0.972822i
$88$	0.251552	+	0.0674030i	0.0268155	+	0.00718519i
$89$	16.1989			1.71708			0.858541	−	0.512745i	$-0.171371\pi$
$89$	16.1989			1.71708			0.858541	+	0.512745i	$0.171371\pi$
$90$	5.05134	−	4.41406i	0.532458	−	0.465283i
$91$	−15.5203			−1.62697
$92$	−2.45373	+	2.45373i	−0.255819	+	0.255819i
$93$	9.37586	+	2.25681i	0.972232	+	0.234020i
$94$			6.36348i			0.656342i
$95$	7.30864	+	6.75309i	0.749850	+	0.692852i
$96$	−1.31594	−	1.12619i	−0.134308	−	0.114941i
$97$	1.09975	+	1.09975i	0.111663	+	0.111663i	0.760731	−	0.649068i	$-0.224841\pi$
$97$	1.09975	+	1.09975i	0.111663	+	0.111663i	−0.649068	+	0.760731i	$0.724841\pi$
$98$	−2.18957	+	8.17160i	−0.221180	+	0.825456i
$99$	−0.608144	+	0.490461i	−0.0611208	+	0.0492932i
$100$	2.15059	−	4.51386i	0.215059	−	0.451386i
$101$		−	13.7066i		−	1.36386i	−0.731417	−	0.681930i	$-0.761141\pi$
$101$		−	13.7066i		−	1.36386i	0.731417	−	0.681930i	$-0.238859\pi$
$102$	−3.16392	+	6.61631i	−0.313274	+	0.655112i
$103$	13.8135	+	3.70130i	1.36108	+	0.364700i	0.864213	−	0.503126i	$-0.167817\pi$
$103$	13.8135	+	3.70130i	1.36108	+	0.364700i	0.496867	+	0.867827i	$0.334484\pi$
$104$	1.97363	+	3.41843i	0.193531	+	0.335205i
$105$	1.77810	+	15.1240i	0.173525	+	1.47595i
$106$	−2.32418	−	4.02559i	−0.225744	−	0.391000i
$107$	−0.255089	−	0.952005i	−0.0246604	−	0.0920338i	0.952499	−	0.304542i	$-0.0985034\pi$
$107$	−0.255089	−	0.952005i	−0.0246604	−	0.0920338i	−0.977159	+	0.212508i	$0.931837\pi$
$108$	5.05619	−	1.19790i	0.486532	−	0.115268i
$109$			16.5426i			1.58449i	0.610202	+	0.792246i	$0.291088\pi$
$109$			16.5426i			1.58449i	−0.610202	+	0.792246i	$0.708912\pi$
$110$	−0.271029	+	0.515413i	−0.0258416	+	0.0491427i
$111$	−0.117321	−	0.332356i	−0.0111356	−	0.0315458i
$112$	3.79793	−	1.01765i	0.358870	−	0.0961590i
$113$	−4.49168	+	16.7632i	−0.422542	+	1.57695i	0.346692	+	0.937979i	$0.387305\pi$
$113$	−4.49168	+	16.7632i	−0.422542	+	1.57695i	−0.769234	+	0.638968i	$0.779362\pi$
$114$	2.56572	+	7.26838i	0.240301	+	0.680746i
$115$	−4.14194	−	6.56141i	−0.386238	−	0.611855i
$116$		−	5.25460i		−	0.487877i
$117$	−11.7744	−	1.26128i	−1.08855	−	0.116605i
$118$	2.14821	+	8.01721i	0.197758	+	0.738044i
$119$	−8.32427	−	14.4181i	−0.763085	−	1.32170i
$120$	3.10505	−	2.31488i	0.283451	−	0.211319i
$121$	−5.46609	+	9.46754i	−0.496917	+	0.860686i
$122$	−1.54790	+	1.54790i	−0.140141	+	0.140141i
$123$	−11.0868	−	16.1659i	−0.999664	−	1.45763i
$124$	5.29596	+	1.71838i	0.475591	+	0.154315i
$125$	8.78462	+	6.91595i	0.785721	+	0.618581i
$126$	−4.24915	+	11.0038i	−0.378544	+	0.980296i
$127$	3.78694	−	1.01471i	0.336037	−	0.0900408i	−0.0868550	−	0.996221i	$-0.527682\pi$
$127$	3.78694	−	1.01471i	0.336037	−	0.0900408i	0.422892	+	0.906180i	$0.361015\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−5.03344	+	1.77679i	−0.443170	+	0.156438i
$130$	−8.42878	+	2.61922i	−0.739253	+	0.229720i
$131$	−4.80305	−	2.77304i	−0.419644	−	0.242282i	0.275281	−	0.961364i	$-0.411229\pi$
$131$	−4.80305	−	2.77304i	−0.419644	−	0.242282i	−0.694925	+	0.719082i	$0.744562\pi$
$132$	−0.371993	+	0.255118i	−0.0323778	+	0.0222052i
$133$	−16.9014	−	4.52873i	−1.46554	−	0.392690i
$134$	−7.41870	−	12.8496i	−0.640878	−	1.11003i
$135$	0.119873	+	11.6183i	0.0103170	+	0.999947i
$136$	−2.11711	+	3.66694i	−0.181541	+	0.314438i
$137$	−2.04448	−	0.547817i	−0.174672	−	0.0468032i	0.170423	−	0.985371i	$-0.445487\pi$
$137$	−2.04448	−	0.547817i	−0.174672	−	0.0468032i	−0.345095	+	0.938568i	$0.612153\pi$
$138$	−0.465596	−	5.99232i	−0.0396342	−	0.510100i
$139$		−	8.98460i		−	0.762064i	−0.924562	−	0.381032i	$-0.875569\pi$
$139$		−	8.98460i		−	0.762064i	0.924562	−	0.381032i	$-0.124431\pi$
$140$	0.347083	+	8.78515i	0.0293339	+	0.742481i
$141$	−8.37395	−	7.16648i	−0.705214	−	0.603526i
$142$	0.400586	−	1.49501i	0.0336164	−	0.125458i
$143$	0.992941	−	0.266058i	0.0830339	−	0.0222489i
$144$	2.96399	−	0.463396i	0.247000	−	0.0386163i
$145$	11.4605	+	2.59062i	0.951741	+	0.215139i
$146$	11.7903	−	6.80712i	0.975770	−	0.563361i
$147$	−8.28746	−	12.0841i	−0.683538	−	0.996681i
$148$	−0.0526671	−	0.196556i	−0.00432921	−	0.0161568i
$149$	0.868246	−	1.50385i	0.0711295	−	0.123200i	−0.828267	−	0.560333i	$-0.810673\pi$
$149$	0.868246	−	1.50385i	0.0711295	−	0.123200i	0.899397	+	0.437134i	$0.144006\pi$
$150$	3.51800	+	7.91351i	0.287243	+	0.646136i
$151$	2.13775			0.173967			0.0869837	−	0.996210i	$-0.472277\pi$
$151$	2.13775			0.173967			0.0869837	+	0.996210i	$0.472277\pi$
$152$	1.15179	+	4.29854i	0.0934225	+	0.348658i
$153$	−5.14349	−	11.6147i	−0.415827	−	0.938996i
$154$		−	1.02397i		−	0.0825136i
$155$	−6.35888	+	10.7035i	−0.510757	+	0.859725i
$156$	−6.72114	−	1.25262i	−0.538122	−	0.100290i
$157$	−10.5251	−	10.5251i	−0.839995	−	0.839995i	0.148863	−	0.988858i	$-0.452439\pi$
$157$	−10.5251	−	10.5251i	−0.839995	−	0.839995i	−0.988858	+	0.148863i	$0.952439\pi$
$158$	−6.15823	+	1.65009i	−0.489923	+	0.131274i
$159$	7.91490	+	1.47510i	0.627693	+	0.116983i
$160$	1.89085	−	1.19361i	0.149484	−	0.0943631i
$161$	11.8161	+	6.82203i	0.931240	+	0.537652i
$162$	−4.11785	+	8.00270i	−0.323529	+	0.628752i
$163$	−6.55056	+	6.55056i	−0.513079	+	0.513079i	−0.915469	−	0.402389i	$-0.868180\pi$
$163$	−6.55056	+	6.55056i	−0.513079	+	0.513079i	0.402389	+	0.915469i	$0.368180\pi$
$164$	−5.65872	−	9.80119i	−0.441872	−	0.765345i
$165$	−0.373023	−	0.937109i	−0.0290398	−	0.0729539i
$166$	−2.51799	−	4.36129i	−0.195434	−	0.338502i
$167$	−2.31775	−	8.64995i	−0.179353	−	0.669353i	−0.995769	−	0.0918896i	$-0.970709\pi$
$167$	−2.31775	−	8.64995i	−0.179353	−	0.669353i	0.816417	−	0.577463i	$-0.195957\pi$
$168$	−2.93802	+	6.14391i	−0.226673	+	0.474013i
$169$	2.23514	+	1.29046i	0.171934	+	0.0992660i
$170$	−6.95397	−	6.42538i	−0.533345	−	0.492804i
$171$	−12.4542	−	4.80924i	−0.952399	−	0.367772i
$172$	−2.97679	+	0.797629i	−0.226978	+	0.0608187i
$173$	0.217580	−	0.812020i	0.0165423	−	0.0617367i	−0.957161	−	0.289555i	$-0.906493\pi$
$173$	0.217580	−	0.812020i	0.0165423	−	0.0617367i	0.973704	+	0.227818i	$0.0731593\pi$
$174$	6.91473	+	5.91767i	0.524204	+	0.448617i
$175$	−19.3319	−	3.57425i	−1.46135	−	0.270188i
$176$	−0.225535	+	0.130213i	−0.0170003	+	0.00981515i
$177$	−12.9695	−	6.20199i	−0.974844	−	0.466170i
$178$	−11.4544	+	11.4544i	−0.858541	+	0.858541i
$179$	−9.42040	+	16.3166i	−0.704114	+	1.21956i	0.262896	+	0.964824i	$0.415322\pi$
$179$	−9.42040	+	16.3166i	−0.704114	+	1.21956i	−0.967010	+	0.254737i	$0.918011\pi$
$180$	−0.450625	+	6.69305i	−0.0335876	+	0.498871i
$181$	1.43029	+	2.47733i	0.106313	+	0.184139i	0.914274	−	0.405097i	$-0.132762\pi$
$181$	1.43029	+	2.47733i	0.106313	+	0.184139i	−0.807961	+	0.589236i	$0.799429\pi$
$182$	10.9745	−	10.9745i	0.813483	−	0.813483i
$183$	−0.293716	−	3.78018i	−0.0217121	−	0.279439i
$184$		−	3.47009i		−	0.255819i
$185$	0.454663	−	0.0179628i	0.0334275	−	0.00132065i
$186$	−8.22554	+	5.03393i	−0.603126	+	0.369106i
$187$	0.779725	+	0.779725i	0.0570192	+	0.0570192i
$188$	−4.49966	−	4.49966i	−0.328171	−	0.328171i
$189$	−9.69499	−	17.9840i	−0.705206	−	1.30814i
$190$	−9.94314	+	0.392833i	−0.721351	+	0.0284991i
$191$	2.96477	−	1.71171i	0.214523	−	0.123855i	−0.388889	−	0.921285i	$-0.627141\pi$
$191$	2.96477	−	1.71171i	0.214523	−	0.123855i	0.603412	+	0.797430i	$0.293808\pi$
$192$	1.72685	−	0.134174i	0.124624	−	0.00968317i
$193$	−3.51371	−	13.1133i	−0.252922	−	0.943919i	−0.969235	−	0.246139i	$-0.920838\pi$
$193$	−3.51371	−	13.1133i	−0.252922	−	0.943919i	0.716312	−	0.697780i	$-0.245829\pi$
$194$	−1.55528			−0.111663
$195$	6.04567	−	14.0415i	0.432939	−	1.00553i
$196$	−4.22993	−	7.32645i	−0.302138	−	0.523318i
$197$	0.118824	+	0.0318387i	0.00846584	+	0.00226841i	0.263049	−	0.964782i	$-0.415272\pi$
$197$	0.118824	+	0.0318387i	0.00846584	+	0.00226841i	−0.254584	+	0.967051i	$0.581938\pi$
$198$	0.0832144	−	0.776832i	0.00591379	−	0.0552070i
$199$	−9.88901	+	5.70942i	−0.701013	+	0.404730i	−0.807725	−	0.589560i	$-0.799301\pi$
$199$	−9.88901	+	5.70942i	−0.701013	+	0.404730i	0.106712	+	0.994290i	$0.465968\pi$
$200$	1.67108	+	4.71248i	0.118164	+	0.333223i
$201$	25.2641	+	4.70848i	1.78199	+	0.332111i
$202$	9.69205	+	9.69205i	0.681930	+	0.681930i
$203$	−19.9566	+	5.34735i	−1.40068	+	0.375310i
$204$	−2.44121	−	6.91566i	−0.170919	−	0.484193i
$205$	24.1666	−	7.50971i	1.68787	−	0.524501i
$206$	−12.3848	+	7.15037i	−0.862890	+	0.498190i
$207$	8.40988	+	6.13579i	0.584527	+	0.426467i
$208$	−3.81277	−	1.02163i	−0.264368	−	0.0708371i
$209$	1.15894			0.0801654
$210$	−11.9516	−	9.43700i	−0.824739	−	0.651215i
$211$	−4.52765	+	7.84211i	−0.311696	+	0.539873i	−0.978730	−	0.205154i	$-0.934230\pi$
$211$	−4.52765	+	7.84211i	−0.311696	+	0.539873i	0.667034	+	0.745028i	$0.267564\pi$
$212$	4.48997	+	1.20308i	0.308372	+	0.0826281i
$213$	1.51620	+	2.21081i	0.103889	+	0.151482i
$214$	0.853544	+	0.492794i	0.0583471	+	0.0336867i
$215$	−0.272042	−	6.88575i	−0.0185531	−	0.469604i
$216$	−2.72822	+	4.42231i	−0.185632	+	0.300900i
$217$	1.13686	−	21.8624i	0.0771750	−	1.48411i
$218$	−11.6974	−	11.6974i	−0.792246	−	0.792246i
$219$	−4.32032	+	23.1814i	−0.291940	+	1.56645i
$220$	−0.172806	−	0.556098i	−0.0116506	−	0.0374921i
$221$			16.7136i			1.12428i
$222$	0.317969	+	0.152053i	0.0213407	+	0.0102051i
$223$	−5.00992	−	18.6973i	−0.335489	−	1.25206i	−0.903338	−	0.428929i	$-0.858891\pi$
$223$	−5.00992	−	18.6973i	−0.335489	−	1.25206i	0.567850	−	0.823132i	$-0.307776\pi$
$224$	−1.96595	+	3.40513i	−0.131356	+	0.227515i
$225$	−14.3756	−	4.28264i	−0.958376	−	0.285509i
$226$	−8.67726	−	15.0294i	−0.577203	−	0.999744i
$227$	20.2537	+	5.42697i	1.34429	+	0.360201i	0.858023	−	0.513612i	$-0.171693\pi$
$227$	20.2537	+	5.42697i	1.34429	+	0.360201i	0.486264	+	0.873812i	$0.338359\pi$
$228$	−6.95375	−	3.32528i	−0.460524	−	0.220222i
$229$	−2.59523	−	1.49835i	−0.171497	−	0.0990141i	0.411794	−	0.911277i	$-0.364902\pi$
$229$	−2.59523	−	1.49835i	−0.171497	−	0.0990141i	−0.583292	+	0.812263i	$0.698236\pi$
$230$	7.56841	+	1.71083i	0.499046	+	0.112809i
$231$	1.34748	+	1.15318i	0.0886576	+	0.0758737i
$232$	3.71556	+	3.71556i	0.243938	+	0.243938i
$233$	15.6830	+	15.6830i	1.02743	+	1.02743i	0.999613	+	0.0278173i	$0.00885565\pi$
$233$	15.6830	+	15.6830i	1.02743	+	1.02743i	0.0278173	+	0.999613i	$0.491144\pi$
$234$	9.21765	−	7.43393i	0.602576	−	0.485971i
$235$	12.0323	−	7.59551i	0.784904	−	0.495476i
$236$	−7.18804	−	4.15001i	−0.467901	−	0.270143i
$237$	4.76391	−	9.96218i	0.309449	−	0.647113i
$238$	16.0813	+	4.30896i	1.04239	+	0.279308i
$239$	−14.4663	−	25.0564i	−0.935749	−	1.62077i	−0.773292	−	0.634050i	$-0.781391\pi$
$239$	−14.4663	−	25.0564i	−0.935749	−	1.62077i	−0.162457	−	0.986716i	$-0.551942\pi$
$240$	−0.558731	+	3.83247i	−0.0360659	+	0.247385i
$241$	7.28823	−	12.6236i	0.469476	−	0.813157i	−0.529915	−	0.848051i	$-0.677776\pi$
$241$	7.28823	−	12.6236i	0.469476	−	0.813157i	0.999391	+	0.0348943i	$0.0111094\pi$
$242$	−2.82946	−	10.5597i	−0.181884	−	0.678802i
$243$	−5.89359	−	14.4314i	−0.378074	−	0.925775i
$244$		−	2.18907i		−	0.140141i
$245$	18.0647	−	5.61355i	1.15411	−	0.358637i
$246$	19.2706	+	3.59146i	1.22865	+	0.228983i
$247$	12.4211	+	12.4211i	0.790333	+	0.790333i
$248$	−4.95989	+	2.52973i	−0.314953	+	0.160638i
$249$	8.57493	+	1.59811i	0.543414	+	0.101276i
$250$	−11.1020	+	1.32135i	−0.702151	+	0.0835697i
$251$	21.9482	+	12.6718i	1.38536	+	0.799837i	0.992788	−	0.119886i	$-0.0382528\pi$
$251$	21.9482	+	12.6718i	1.38536	+	0.799837i	0.392570	+	0.919722i	$0.371586\pi$
$252$	−4.77626	−	10.7855i	−0.300876	−	0.679420i
$253$	−0.872907	−	0.233895i	−0.0548792	−	0.0147048i
$254$	−1.96027	+	3.39528i	−0.122998	+	0.213039i
$255$	16.2869	−	1.91481i	1.01992	−	0.119910i
$256$	1.00000			0.0625000
$257$	−4.52881	−	1.21349i	−0.282500	−	0.0756955i	0.114787	−	0.993390i	$-0.463381\pi$
$257$	−4.52881	−	1.21349i	−0.282500	−	0.0756955i	−0.397287	+	0.917695i	$0.630048\pi$
$258$	2.30280	−	4.81556i	0.143366	−	0.299804i
$259$	−0.692910	+	0.400052i	−0.0430553	+	0.0248580i
$260$	4.10798	−	7.81211i	0.254766	−	0.484487i
$261$	−15.5746	+	2.43496i	−0.964043	+	0.150720i
$262$	5.35710	−	1.43543i	0.330963	−	0.0886812i
$263$	−5.43999	−	5.43999i	−0.335444	−	0.335444i	0.519205	−	0.854650i	$-0.326228\pi$
$263$	−5.43999	−	5.43999i	−0.335444	−	0.335444i	−0.854650	+	0.519205i	$0.826228\pi$
$264$	0.0826430	−	0.443434i	0.00508632	−	0.0272915i
$265$	−4.83761	+	9.19965i	−0.297172	+	0.565130i
$266$	15.1534	−	8.74883i	0.929116	−	0.536425i
$267$	−2.17347	−	27.9730i	−0.133014	−	1.71192i
$268$	14.3318	+	3.84020i	0.875456	+	0.234578i
$269$	−4.48837	−	7.77409i	−0.273661	−	0.473995i	0.696135	−	0.717911i	$-0.254901\pi$
$269$	−4.48837	−	7.77409i	−0.273661	−	0.473995i	−0.969796	+	0.243916i	$0.921568\pi$
$270$	−8.30016	−	8.13064i	−0.505132	−	0.494815i
$271$	−24.4726			−1.48660			−0.743301	−	0.668957i	$-0.766741\pi$
$271$	−24.4726			−1.48660			−0.743301	+	0.668957i	$0.766741\pi$
$272$	−1.09590	−	4.08994i	−0.0664485	−	0.247989i
$273$	2.08242	+	26.8011i	0.126034	+	1.62208i
$274$	1.83303	−	1.05830i	0.110738	−	0.0639344i
$275$	1.29807	−	0.102728i	0.0782764	−	0.00619475i
$276$	4.56643	+	3.90798i	0.274867	+	0.235233i
$277$	−22.6397	−	22.6397i	−1.36029	−	1.36029i	−0.873545	−	0.486744i	$-0.838185\pi$
$277$	−22.6397	−	22.6397i	−1.36029	−	1.36029i	−0.486744	−	0.873545i	$-0.661815\pi$
$278$	6.35307	+	6.35307i	0.381032	+	0.381032i
$279$	2.63916	−	16.4935i	0.158002	−	0.987439i
$280$	−6.45746	−	5.96661i	−0.385907	−	0.356573i
$281$		−	0.0358575i		−	0.00213908i	−0.999999	−	0.00106954i	$-0.999660\pi$
$281$		−	0.0358575i		−	0.00213908i	0.999999	−	0.00106954i	$-0.000340445\pi$
$282$	10.9887	−	0.853813i	0.654370	−	0.0508438i
$283$	−19.5773	+	19.5773i	−1.16375	+	1.16375i	−0.180103	+	0.983648i	$0.557643\pi$
$283$	−19.5773	+	19.5773i	−1.16375	+	1.16375i	−0.983648	+	0.180103i	$0.942357\pi$
$284$	0.773872	+	1.34039i	0.0459209	+	0.0795373i
$285$	10.6809	−	13.5270i	0.632683	−	0.801269i
$286$	−0.513984	+	0.890247i	−0.0303925	+	0.0526414i
$287$	−31.4656	+	31.4656i	−1.85736	+	1.85736i
$288$	−1.76819	+	2.42353i	−0.104192	+	0.142808i
$289$	−0.804211	+	0.464311i	−0.0473065	+	0.0273124i
$290$	−9.93563	+	6.27194i	−0.583440	+	0.368301i
$291$	1.75154	−	2.04666i	0.102677	−	0.119977i
$292$	−3.52362	+	13.1503i	−0.206204	+	0.769566i
$293$	−25.8796	+	6.93442i	−1.51190	+	0.405113i	−0.917067	−	0.398734i	$-0.869450\pi$
$293$	−25.8796	+	6.93442i	−1.51190	+	0.405113i	−0.594836	+	0.803847i	$0.702783\pi$
$294$	14.4049	+	2.68464i	0.840109	+	0.156571i
$295$	12.5952	−	13.6313i	0.733320	−	0.793648i
$296$	0.176228	+	0.101745i	0.0102430	+	0.00591381i
$297$	0.928549	+	0.984365i	0.0538799	+	0.0571186i
$298$	0.449437	+	1.67732i	0.0260352	+	0.0971647i
$299$	−6.84869	−	11.8623i	−0.396070	−	0.686013i
$300$	−8.08330	−	3.10810i	−0.466689	−	0.179446i
$301$	6.05868	+	10.4939i	0.349216	+	0.604860i
$302$	−1.51162	+	1.51162i	−0.0869837	+	0.0869837i
$303$	−23.6692	+	1.83907i	−1.35976	+	0.105652i
$304$	−3.85397	−	2.22509i	−0.221040	−	0.127618i
$305$	4.77444	+	1.07925i	0.273383	+	0.0617979i
$306$	11.8499	+	4.57586i	0.677411	+	0.261584i
$307$	10.1195	−	2.71151i	0.577550	−	0.154754i	0.0417928	−	0.999126i	$-0.486693\pi$
$307$	10.1195	−	2.71151i	0.577550	−	0.154754i	0.535757	+	0.844372i	$0.320026\pi$
$308$	0.724054	+	0.724054i	0.0412568	+	0.0412568i
$309$	4.53818	−	24.3503i	0.258168	−	1.38524i
$310$	−3.07211	−	12.0649i	−0.174484	−	0.685241i
$311$			19.8765i			1.12709i	0.826084	+	0.563547i	$0.190564\pi$
$311$			19.8765i			1.12709i	−0.826084	+	0.563547i	$0.809436\pi$
$312$	5.63830	−	3.86683i	0.319206	−	0.218916i
$313$	1.02635	+	3.83038i	0.0580126	+	0.216506i	0.988847	−	0.148936i	$-0.0475847\pi$
$313$	1.02635	+	3.83038i	0.0580126	+	0.216506i	−0.930834	+	0.365442i	$0.880918\pi$
$314$	14.8847			0.839995
$315$	25.8783	−	5.09975i	1.45808	−	0.287338i
$316$	3.18774	−	5.52132i	0.179324	−	0.310599i
$317$	−2.43934	−	9.10376i	−0.137007	−	0.511318i	−0.999982	−	0.00607024i	$-0.998068\pi$
$317$	−2.43934	−	9.10376i	−0.137007	−	0.511318i	0.862974	−	0.505248i	$-0.168599\pi$
$318$	−6.63974	+	4.55363i	−0.372338	+	0.255355i
$319$	1.18509	−	0.684215i	0.0663526	−	0.0383087i
$320$	−0.493020	+	2.18104i	−0.0275607	+	0.121924i
$321$	−1.60974	+	0.568234i	−0.0898469	+	0.0317157i
$322$	−13.1792	+	3.53134i	−0.734446	+	0.196794i
$323$	−4.87693	+	18.2010i	−0.271360	+	1.01273i
$324$	−2.74700	−	8.57053i	−0.152611	−	0.476141i
$325$	15.0132	+	12.8112i	0.832783	+	0.710637i
$326$		−	9.26389i		−	0.513079i
$327$	28.5665	−	2.21958i	1.57973	−	0.122743i
$328$	10.9318	+	2.92917i	0.603608	+	0.161736i
$329$	−12.5103	+	21.6684i	−0.689714	+	1.19462i
$330$	0.926403	+	0.398870i	0.0509968	+	0.0219571i
$331$	−0.625145	−	1.08278i	−0.0343611	−	0.0595152i	0.848333	−	0.529462i	$-0.177606\pi$
$331$	−0.625145	−	1.08278i	−0.0343611	−	0.0595152i	−0.882695	+	0.469947i	$0.844273\pi$
$332$	4.86439	+	1.30341i	0.266968	+	0.0715338i
$333$	−0.558186	+	0.247188i	−0.0305884	+	0.0135458i
$334$	7.75533	+	4.47754i	0.424353	+	0.245000i
$335$	−15.4415	+	29.3650i	−0.843660	+	1.60438i
$336$	−2.26691	−	6.42189i	−0.123670	−	0.350343i
$337$	21.6918	+	21.6918i	1.18163	+	1.18163i	0.979323	+	0.202304i	$0.0648429\pi$
$337$	21.6918	+	21.6918i	1.18163	+	1.18163i	0.202304	+	0.979323i	$0.435157\pi$
$338$	−2.49297	+	0.667990i	−0.135600	+	0.0363339i
$339$	29.5501	+	5.50726i	1.60494	+	0.299113i
$340$	9.46062	−	0.373770i	0.513074	−	0.0202705i
$341$	0.302045	+	1.41818i	0.0163566	+	0.0767987i
$342$	12.2071	−	5.40582i	0.660085	−	0.292313i
$343$	−4.05882	+	4.05882i	−0.219155	+	0.219155i
$344$	1.54090	−	2.66892i	0.0830799	−	0.143899i
$345$	−10.7748	+	8.03286i	−0.580096	+	0.432474i
$346$	0.420332	+	0.728037i	0.0225972	+	0.0391395i
$347$	−4.62501	−	17.2608i	−0.248283	−	0.926606i	−0.971705	−	0.236199i	$-0.924098\pi$
$347$	−4.62501	−	17.2608i	−0.248283	−	0.926606i	0.723421	−	0.690407i	$-0.242569\pi$
$348$	−9.07388	+	0.705030i	−0.486411	+	0.0377936i
$349$			5.52625i			0.295814i	0.989001	+	0.147907i	$0.0472536\pi$
$349$			5.52625i			0.295814i	−0.989001	+	0.147907i	$0.952746\pi$
$350$	16.1971	−	11.1423i	0.865770	−	0.595582i
$351$	−0.598214	+	20.5019i	−0.0319303	+	1.09431i
$352$	0.0674030	−	0.251552i	0.00359259	−	0.0134077i
$353$	−18.3117	+	4.90659i	−0.974631	+	0.261152i	−0.710782	−	0.703412i	$-0.751659\pi$
$353$	−18.3117	+	4.90659i	−0.974631	+	0.261152i	−0.263849	+	0.964564i	$0.584992\pi$
$354$	13.5563	−	4.78532i	0.720507	−	0.254337i
$355$	−3.30497	+	1.02701i	−0.175410	+	0.0545079i
$356$		−	16.1989i		−	0.858541i
$357$	−23.7809	+	16.3093i	−1.25862	+	0.863178i
$358$	−4.87636	−	18.1988i	−0.257724	−	0.961838i
$359$	−15.8626	−	27.4748i	−0.837196	−	1.45007i	−0.892230	−	0.451581i	$-0.850860\pi$
$359$	−15.8626	−	27.4748i	−0.837196	−	1.45007i	0.0550345	−	0.998484i	$-0.482473\pi$
$360$	−4.41406	−	5.05134i	−0.232641	−	0.266229i
$361$	0.402031	+	0.696339i	0.0211596	+	0.0366494i
$362$	−2.76311	−	0.740372i	−0.145226	−	0.0389131i
$363$	17.0824	+	8.16880i	0.896593	+	0.428751i
$364$			15.5203i			0.813483i
$365$	−26.9442	−	14.1685i	−1.41032	−	0.741615i
$366$	2.88068	+	2.46530i	0.150575	+	0.128863i
$367$	−3.12148	+	11.6495i	−0.162940	+	0.608099i	0.835354	+	0.549712i	$0.185262\pi$
$367$	−3.12148	+	11.6495i	−0.162940	+	0.608099i	−0.998294	+	0.0583873i	$0.981404\pi$
$368$	2.45373	+	2.45373i	0.127909	+	0.127909i
$369$	−26.4285	+	21.3142i	−1.37581	+	1.10958i
$370$	−0.308794	+	0.334197i	−0.0160534	+	0.0173741i
$371$		−	18.2769i		−	0.948888i
$372$	2.25681	−	9.37586i	0.117010	−	0.486116i
$373$	−5.72451	+	5.72451i	−0.296404	+	0.296404i	−0.839603	−	0.543200i	$-0.817213\pi$
$373$	−5.72451	+	5.72451i	−0.296404	+	0.296404i	0.543200	+	0.839603i	$0.317213\pi$
$374$	−1.10270			−0.0570192
$375$	10.7641	−	16.0976i	0.555856	−	0.831278i
$376$	6.36348			0.328171
$377$	20.0345	+	5.36824i	1.03183	+	0.276478i
$378$	19.5720	+	5.86120i	1.00667	+	0.301468i
$379$	−15.2650	−	8.81324i	−0.784109	−	0.452706i	0.0537753	−	0.998553i	$-0.482875\pi$
$379$	−15.2650	−	8.81324i	−0.784109	−	0.452706i	−0.837885	+	0.545847i	$0.816208\pi$
$380$	6.75309	−	7.30864i	0.346426	−	0.374925i
$381$	−2.26035	−	6.40332i	−0.115801	−	0.328052i
$382$	−0.886046	+	3.30677i	−0.0453340	+	0.169189i
$383$	9.86701	−	36.8242i	0.504180	−	1.88163i	0.0332689	−	0.999446i	$-0.489408\pi$
$383$	9.86701	−	36.8242i	0.504180	−	1.88163i	0.470911	−	0.882180i	$-0.343925\pi$
$384$	−1.12619	+	1.31594i	−0.0574706	+	0.0671538i
$385$	−1.93616	+	1.22222i	−0.0986760	+	0.0622899i
$386$	11.7571	+	6.78796i	0.598420	+	0.345498i
$387$	3.74360	+	8.45358i	0.190298	+	0.429720i
$388$	1.09975	−	1.09975i	0.0558314	−	0.0558314i
$389$	6.86018	−	11.8822i	0.347825	−	0.602450i	−0.638038	−	0.770005i	$-0.720254\pi$
$389$	6.86018	−	11.8822i	0.347825	−	0.602450i	0.985863	+	0.167555i	$0.0535871\pi$
$390$	5.65390	+	14.2038i	0.286297	+	0.719236i
$391$	7.34657	−	12.7246i	0.371532	−	0.643512i
$392$	8.17160	+	2.18957i	0.412728	+	0.110590i
$393$	−4.14417	+	8.66619i	−0.209046	+	0.437152i
$394$	−0.106534	+	0.0615077i	−0.00536713	+	0.00309871i
$395$	10.4706	+	9.67470i	0.526833	+	0.486787i
$396$	0.490461	+	0.608144i	0.0246466	+	0.0305604i
$397$	−28.5932	+	7.66153i	−1.43505	+	0.384521i	−0.890798	−	0.454399i	$-0.849854\pi$
$397$	−28.5932	+	7.66153i	−1.43505	+	0.384521i	−0.544255	+	0.838920i	$0.683187\pi$
$398$	2.95541	−	11.0298i	0.148141	−	0.552872i
$399$	−5.55268	+	29.7938i	−0.277982	+	1.49156i
$400$	−4.51386	−	2.15059i	−0.225693	−	0.107530i
$401$			23.4886i			1.17296i	0.809963	+	0.586481i	$0.199487\pi$
$401$			23.4886i			1.17296i	−0.809963	+	0.586481i	$0.800513\pi$
$402$	−21.1938	+	14.5350i	−1.05705	+	0.724941i
$403$	−11.9623	+	18.4367i	−0.595884	+	0.918397i
$404$	−13.7066			−0.681930
$405$	20.0470	−	1.76588i	0.996143	−	0.0877472i
$406$	10.3303	−	17.8926i	0.512683	−	0.887993i
$407$	0.0374724	−	0.0374724i	0.00185744	−	0.00185744i
$408$	6.61631	+	3.16392i	0.327556	+	0.156637i
$409$	−32.0543	−	18.5066i	−1.58499	−	0.915092i	−0.994116	−	0.108325i	$-0.965451\pi$
$409$	−32.0543	−	18.5066i	−1.58499	−	0.915092i	−0.590870	−	0.806767i	$-0.701215\pi$
$410$	−11.7782	+	22.3986i	−0.581686	+	1.10619i
$411$	−0.671680	+	3.60401i	−0.0331315	+	0.177773i
$412$	3.70130	−	13.8135i	0.182350	−	0.680540i
$413$	−8.44654	+	31.5229i	−0.415627	+	1.55114i
$414$	−10.2853	+	1.60803i	−0.505497	+	0.0790301i
$415$	−5.24103	+	9.96681i	−0.257272	+	0.489252i
$416$	3.41843	−	1.97363i	0.167602	−	0.0967653i
$417$	−15.5150	+	1.20550i	−0.759774	+	0.0590336i
$418$	−0.819493	+	0.819493i	−0.0400827	+	0.0400827i
$419$	24.7793			1.21055			0.605273	−	0.796018i	$-0.293064\pi$
$419$	24.7793			1.21055			0.605273	+	0.796018i	$0.293064\pi$
$420$	15.1240	−	1.77810i	0.737977	−	0.0867623i
$421$	11.8864	+	20.5878i	0.579305	+	1.00339i	0.995559	+	0.0941378i	$0.0300094\pi$
$421$	11.8864	+	20.5878i	0.579305	+	1.00339i	−0.416254	+	0.909248i	$0.636657\pi$
$422$	−2.34368	−	8.74674i	−0.114089	−	0.425785i
$423$	−11.2518	+	15.4221i	−0.547083	+	0.749847i
$424$	−4.02559	+	2.32418i	−0.195500	+	0.112872i
$425$	−3.84907	+	20.8183i	−0.186707	+	1.00983i
$426$	−2.63539	−	0.491159i	−0.127685	−	0.0237967i
$427$	−8.31391	+	2.22771i	−0.402338	+	0.107806i
$428$	−0.952005	+	0.255089i	−0.0460169	+	0.0123302i
$429$	−0.592668	−	1.67896i	−0.0286143	−	0.0810609i
$430$	5.06132	+	4.67660i	0.244079	+	0.225526i
$431$	6.73190	+	3.88667i	0.324264	+	0.187214i	0.653292	−	0.757106i	$-0.273388\pi$
$431$	6.73190	+	3.88667i	0.324264	+	0.187214i	−0.329027	+	0.944320i	$0.606721\pi$
$432$	−1.19790	−	5.05619i	−0.0576342	−	0.243266i
$433$	19.9432	−	19.9432i	0.958408	−	0.958408i	−0.0407605	−	0.999169i	$-0.512978\pi$
$433$	19.9432	−	19.9432i	0.958408	−	0.958408i	0.999169	+	0.0407605i	$0.0129781\pi$
$434$	14.6551	+	16.2629i	0.703470	+	0.780645i
$435$	2.93591	−	20.1381i	0.140766	−	0.965547i
$436$	16.5426			0.792246
$437$	−3.99682	−	14.9163i	−0.191194	−	0.713545i
$438$	−13.3368	−	19.4467i	−0.637257	−	0.929197i
$439$	19.1289	−	11.0441i	0.912974	−	0.527106i	0.0315873	−	0.999501i	$-0.489944\pi$
$439$	19.1289	−	11.0441i	0.912974	−	0.527106i	0.881387	+	0.472395i	$0.156610\pi$
$440$	0.515413	+	0.271029i	0.0245713	+	0.0129208i
$441$	−19.7554	+	15.9325i	−0.940735	+	0.758692i
$442$	−11.8183	−	11.8183i	−0.562139	−	0.562139i
$443$	6.52073	−	24.3357i	0.309809	−	1.15622i	−0.618916	−	0.785457i	$-0.712428\pi$
$443$	6.52073	−	24.3357i	0.309809	−	1.15622i	0.928726	−	0.370767i	$-0.120905\pi$
$444$	−0.332356	+	0.117321i	−0.0157729	+	0.00556779i
$445$	35.3305	+	7.98639i	1.67483	+	0.378591i
$446$	16.7635	+	9.67841i	0.793775	+	0.458286i
$447$	−2.71341	−	1.29755i	−0.128340	−	0.0613720i
$448$	−1.01765	−	3.79793i	−0.0480795	−	0.179435i
$449$	−11.5523			−0.545185			−0.272593	−	0.962130i	$-0.587881\pi$
$449$	−11.5523			−0.545185			−0.272593	+	0.962130i	$0.587881\pi$
$450$	13.1934	−	7.13683i	0.621943	−	0.336433i
$451$	1.47367	−	2.55248i	0.0693926	−	0.120192i
$452$	16.7632	+	4.49168i	0.788473	+	0.211271i
$453$	−0.286830	−	3.69156i	−0.0134765	−	0.173445i
$454$	−18.1590	+	10.4841i	−0.852244	+	0.492043i
$455$	−33.8503	−	7.65181i	−1.58693	−	0.358722i
$456$	7.26838	−	2.56572i	0.340373	−	0.120151i
$457$	16.3279	+	16.3279i	0.763789	+	0.763789i	0.977005	−	0.213216i	$-0.0683940\pi$
$457$	16.3279	+	16.3279i	0.763789	+	0.763789i	−0.213216	+	0.977005i	$0.568394\pi$
$458$	2.89460	−	0.775605i	0.135256	−	0.0362417i
$459$	−19.3667	+	10.4404i	−0.903962	+	0.487317i
$460$	−6.56141	+	4.14194i	−0.305927	+	0.193119i
$461$			5.11822i			0.238379i	0.992872	+	0.119190i	$0.0380296\pi$
$461$			5.11822i			0.238379i	−0.992872	+	0.119190i	$0.961970\pi$
$462$	−1.76823	+	0.137390i	−0.0822657	+	0.00639195i
$463$	13.0478	−	13.0478i	0.606381	−	0.606381i	−0.335618	−	0.941998i	$-0.608945\pi$
$463$	13.0478	−	13.0478i	0.606381	−	0.606381i	0.941998	+	0.335618i	$0.108945\pi$
$464$	−5.25460			−0.243938
$465$	19.3365	+	9.54467i	0.896708	+	0.442623i
$466$	−22.1792			−1.02743
$467$	−3.08661	+	3.08661i	−0.142831	+	0.142831i	−0.774907	−	0.632076i	$-0.782203\pi$
$467$	−3.08661	+	3.08661i	−0.142831	+	0.142831i	0.632076	+	0.774907i	$0.282203\pi$
$468$	−1.26128	+	11.7744i	−0.0583027	+	0.544274i
$469$		−	58.3392i		−	2.69385i
$470$	−3.13732	+	13.8790i	−0.144714	+	0.640190i
$471$	−16.7630	+	19.5874i	−0.772400	+	0.902541i
$472$	8.01721	−	2.14821i	0.369022	−	0.0988792i
$473$	−0.567509	−	0.567509i	−0.0260941	−	0.0260941i
$474$	3.67573	+	10.4129i	0.168832	+	0.478281i
$475$	12.6110	+	18.3320i	0.578633	+	0.841132i
$476$	−14.4181	+	8.32427i	−0.660851	+	0.381542i
$477$	1.48530	−	13.8657i	0.0680072	−	0.634868i
$478$	27.9468	+	7.48832i	1.27826	+	0.342508i
$479$	−9.26360	+	16.0450i	−0.423264	+	0.733116i	−0.996257	−	0.0864453i	$-0.972449\pi$
$479$	−9.26360	+	16.0450i	−0.423264	+	0.733116i	0.572992	+	0.819561i	$0.305783\pi$
$480$	−2.31488	−	3.10505i	−0.105659	−	0.141725i
$481$	0.803230			0.0366241
$482$	3.77267	+	14.0798i	0.171840	+	0.641316i
$483$	10.1952	−	21.3199i	0.463897	−	0.970091i
$484$	9.46754	+	5.46609i	0.430343	+	0.248459i
$485$	1.85640	+	2.94080i	0.0842949	+	0.133535i
$486$	14.3719	+	6.03715i	0.651925	+	0.273851i
$487$	−4.69626	+	17.5267i	−0.212808	+	0.794210i	0.774119	+	0.633041i	$0.218193\pi$
$487$	−4.69626	+	17.5267i	−0.212808	+	0.794210i	−0.986927	+	0.161170i	$0.948473\pi$
$488$	1.54790	+	1.54790i	0.0700703	+	0.0700703i
$489$	12.1907	+	10.4329i	0.551283	+	0.471792i
$490$	−8.80431	+	16.7431i	−0.397738	+	0.756375i
$491$	6.57336	−	3.79513i	0.296651	−	0.171272i	−0.344286	−	0.938865i	$-0.611879\pi$
$491$	6.57336	−	3.79513i	0.296651	−	0.171272i	0.640938	+	0.767593i	$0.278546\pi$
$492$	−16.1659	+	11.0868i	−0.728815	+	0.499832i
$493$	5.75849	+	21.4910i	0.259350	+	0.967906i
$494$	−17.5660			−0.790333
$495$	−1.56819	+	0.769888i	−0.0704851	+	0.0346039i
$496$	1.71838	−	5.29596i	0.0771577	−	0.237795i
$497$	4.30316	−	4.30316i	0.193023	−	0.193023i
$498$	−7.19343	+	4.93336i	−0.322345	+	0.221069i
$499$	22.7085	+	13.1108i	1.01657	+	0.586919i	0.913110	−	0.407714i	$-0.133674\pi$
$499$	22.7085	+	13.1108i	1.01657	+	0.586919i	0.103464	+	0.994633i	$0.467007\pi$
$500$	6.91595	−	8.78462i	0.309291	−	0.392860i
$501$	−14.6261	+	5.16299i	−0.653448	+	0.230665i
$502$	−24.4800	+	6.55940i	−1.09260	+	0.292760i
$503$	33.4545	−	8.96410i	1.49166	−	0.399690i	0.581364	−	0.813644i	$-0.302519\pi$
$503$	33.4545	−	8.96410i	1.49166	−	0.399690i	0.910298	+	0.413954i	$0.135853\pi$
$504$	11.0038	+	4.24915i	0.490148	+	0.189272i
$505$	6.75765	−	29.8947i	0.300711	−	1.33030i
$506$	0.782627	−	0.451850i	0.0347920	−	0.0200872i
$507$	1.92852	−	4.03289i	0.0856488	−	0.179107i
$508$	−1.01471	−	3.78694i	−0.0450204	−	0.168018i
$509$	8.15621	+	14.1270i	0.361518	+	0.626167i	0.988211	−	0.153099i	$-0.0489254\pi$
$509$	8.15621	+	14.1270i	0.361518	+	0.626167i	−0.626693	+	0.779266i	$0.715592\pi$
$510$	−10.1626	+	12.8705i	−0.450007	+	0.569917i
$511$	53.5299			2.36802
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−6.63378	+	22.1518i	−0.292889	+	0.978026i
$514$	4.06042	−	2.34429i	0.179098	−	0.103402i
$515$	28.3029	+	14.8830i	1.24717	+	0.655823i
$516$	1.77679	+	5.03344i	0.0782189	+	0.221585i
$517$	0.428917	−	1.60074i	0.0188638	−	0.0704005i
$518$	0.207082	−	0.772840i	0.00909866	−	0.0339567i
$519$	−1.43143	−	0.266775i	−0.0628327	−	0.0117101i
$520$	2.61922	+	8.42878i	0.114860	+	0.369626i
$521$	−6.84869	−	3.95409i	−0.300046	−	0.173232i	0.342417	−	0.939548i	$-0.388754\pi$
$521$	−6.84869	−	3.95409i	−0.300046	−	0.173232i	−0.642464	+	0.766316i	$0.722088\pi$
$522$	9.29113	−	12.7347i	0.406662	−	0.557382i
$523$	11.5676	−	11.5676i	0.505817	−	0.505817i	−0.407423	−	0.913240i	$-0.633572\pi$
$523$	11.5676	−	11.5676i	0.505817	−	0.505817i	0.913240	+	0.407423i	$0.133572\pi$
$524$	−2.77304	+	4.80305i	−0.121141	+	0.209822i
$525$	−3.57835	+	33.8627i	−0.156172	+	1.47789i
$526$	7.69331			0.335444
$527$	−23.5433	−	1.22427i	−1.02556	−	0.0533300i
$528$	0.255118	+	0.371993i	0.0111026	+	0.0161889i
$529$		−	10.9585i		−	0.476455i
$530$	−3.08442	−	9.92584i	−0.133979	−	0.431151i
$531$	−8.96972	+	23.2284i	−0.389253	+	1.00803i
$532$	−4.52873	+	16.9014i	−0.196345	+	0.732770i
$533$	43.1508	−	11.5622i	1.86907	−	0.500815i
$534$	21.3168	+	18.2431i	0.922468	+	0.789454i
$535$	−0.0870014	−	2.20212i	−0.00376140	−	0.0952061i
$536$	−12.8496	+	7.41870i	−0.555017	+	0.320439i
$537$	29.4403	+	14.0783i	1.27044	+	0.607524i
$538$	8.67087	+	2.32335i	0.373828	+	0.100167i
$539$	1.10158	−	1.90799i	0.0474484	−	0.0821831i
$540$	11.6183	−	0.119873i	0.499973	−	0.00515850i
$541$	12.3963	−	21.4710i	0.532958	−	0.923110i	−0.466302	−	0.884626i	$-0.654414\pi$
$541$	12.3963	−	21.4710i	0.532958	−	0.923110i	0.999259	−	0.0384839i	$-0.0122528\pi$
$542$	17.3047	−	17.3047i	0.743301	−	0.743301i
$543$	4.08607	−	2.80228i	0.175350	−	0.120258i
$544$	3.66694	+	2.11711i	0.157219	+	0.0907704i
$545$	−8.15583	+	36.0800i	−0.349357	+	1.54550i
$546$	−20.4237	−	17.4788i	−0.874056	−	0.748022i
$547$	4.86690	−	18.1635i	0.208094	−	0.776616i	−0.780391	−	0.625292i	$-0.784980\pi$
$547$	4.86690	−	18.1635i	0.208094	−	0.776616i	0.988484	−	0.151324i	$-0.0483536\pi$
$548$	−0.547817	+	2.04448i	−0.0234016	+	0.0873360i
$549$	−6.48838	+	1.01440i	−0.276917	+	0.0432937i
$550$	−0.845233	+	0.990512i	−0.0360408	+	0.0422356i
$551$	20.2510	+	11.6919i	0.862723	+	0.498093i
$552$	−5.99232	+	0.465596i	−0.255050	+	0.0198171i
$553$	−24.2136	−	6.48801i	−1.02967	−	0.275898i
$554$	32.0174			1.36029
$555$	−0.0920229	−	0.782723i	−0.00390615	−	0.0332247i
$556$	−8.98460			−0.381032
$557$	18.5856	−	18.5856i	0.787496	−	0.787496i	−0.193587	−	0.981083i	$-0.562012\pi$
$557$	18.5856	−	18.5856i	0.787496	−	0.787496i	0.981083	+	0.193587i	$0.0620122\pi$
$558$	9.79648	+	13.5288i	0.414718	+	0.572721i
$559$		−	12.1647i		−	0.514512i
$560$	8.78515	−	0.347083i	0.371240	−	0.0146669i
$561$	1.24185	−	1.45108i	0.0524308	−	0.0612648i
$562$	0.0253551	+	0.0253551i	0.00106954	+	0.00106954i
$563$	6.51191	−	24.3028i	0.274444	−	1.02424i	−0.681769	−	0.731568i	$-0.738789\pi$
$563$	6.51191	−	24.3028i	0.274444	−	1.02424i	0.956213	−	0.292672i	$-0.0945444\pi$
$564$	−7.16648	+	8.37395i	−0.301763	+	0.352607i
$565$	−18.0611	+	34.3466i	−0.759836	+	1.44497i
$566$		−	27.6865i		−	1.16375i
$567$	−29.7547	+	19.1547i	−1.24958	+	0.804423i
$568$	−1.49501	−	0.400586i	−0.0627291	−	0.0168082i
$569$	−18.5120	−	32.0637i	−0.776063	−	1.34418i	−0.934195	−	0.356763i	$-0.883880\pi$
$569$	−18.5120	−	32.0637i	−0.776063	−	1.34418i	0.158132	−	0.987418i	$-0.449453\pi$
$570$	2.01247	+	17.1176i	0.0842932	+	0.716976i
$571$	21.6539	+	37.5056i	0.906186	+	1.56956i	0.819317	+	0.573340i	$0.194353\pi$
$571$	21.6539	+	37.5056i	0.906186	+	1.56956i	0.0868683	+	0.996220i	$0.472314\pi$
$572$	−0.266058	−	0.992941i	−0.0111244	−	0.0415169i
$573$	−3.35365	−	4.89003i	−0.140101	−	0.204284i
$574$		−	44.4991i		−	1.85736i
$575$	−5.79882	−	16.3527i	−0.241827	−	0.681957i
$576$	−0.463396	−	2.96399i	−0.0193081	−	0.123500i
$577$	22.6716	−	6.07484i	0.943832	−	0.252899i	0.246089	−	0.969247i	$-0.420854\pi$
$577$	22.6716	−	6.07484i	0.943832	−	0.252899i	0.697743	+	0.716348i	$0.254188\pi$
$578$	0.240345	−	0.896980i	0.00999704	−	0.0373095i
$579$	−22.1733	+	7.82710i	−0.921489	+	0.325283i
$580$	2.59062	−	11.4605i	0.107570	−	0.475870i
$581$		−	19.8010i		−	0.821484i
$582$	0.208679	+	2.68574i	0.00865000	+	0.111327i
$583$	0.313313	+	1.16930i	0.0129761	+	0.0484275i
$584$	−6.80712	−	11.7903i	−0.281681	−	0.487885i
$585$	−25.0587	−	8.55594i	−1.03605	−	0.353744i
$586$	13.3963	−	23.2030i	0.553395	−	0.958508i
$587$	13.7989	−	13.7989i	0.569541	−	0.569541i	−0.362459	−	0.932000i	$-0.618063\pi$
$587$	13.7989	−	13.7989i	0.569541	−	0.569541i	0.932000	+	0.362459i	$0.118063\pi$
$588$	−12.0841	+	8.28746i	−0.498340	+	0.341769i
$589$	−18.4066	+	16.5869i	−0.758429	+	0.683450i
$590$	0.732673	+	18.5450i	0.0301637	+	0.763484i
$591$	0.0390375	−	0.209462i	0.00160579	−	0.00861612i
$592$	−0.196556	+	0.0526671i	−0.00807841	+	0.00216460i
$593$	11.9050	+	11.9050i	0.488880	+	0.488880i	0.907953	−	0.419072i	$-0.137645\pi$
$593$	11.9050	+	11.9050i	0.488880	+	0.488880i	−0.419072	+	0.907953i	$0.637645\pi$
$594$	−1.35263	−	0.0394678i	−0.0554992	−	0.00161938i
$595$	−11.0472	−	35.5504i	−0.452890	−	1.45742i
$596$	−1.50385	−	0.868246i	−0.0615999	−	0.0355647i
$597$	11.1861	+	16.3107i	0.457818	+	0.667554i
$598$	13.2307	+	3.54514i	0.541042	+	0.144972i
$599$	−14.1782	−	24.5573i	−0.579304	−	1.00338i	−0.995559	−	0.0941358i	$-0.969991\pi$
$599$	−14.1782	−	24.5573i	−0.579304	−	1.00338i	0.416256	−	0.909248i	$-0.363342\pi$
$600$	7.91351	−	3.51800i	0.323068	−	0.143622i
$601$	−11.6264	+	20.1374i	−0.474249	+	0.821423i	−0.999565	−	0.0294837i	$-0.990614\pi$
$601$	−11.6264	+	20.1374i	−0.474249	+	0.821423i	0.525316	+	0.850907i	$0.323947\pi$
$602$	−11.7045	−	3.13620i	−0.477038	−	0.127822i
$603$	4.74103	−	44.2590i	0.193070	−	1.80237i
$604$		−	2.13775i		−	0.0869837i
$605$	−16.5894	+	17.9542i	−0.674457	+	0.729942i
$606$	15.4363	−	18.0371i	0.627055	−	0.732707i
$607$	2.03110	−	7.58016i	0.0824397	−	0.307669i	−0.912377	−	0.409350i	$-0.865755\pi$
$607$	2.03110	−	7.58016i	0.0824397	−	0.307669i	0.994817	+	0.101681i	$0.0324221\pi$
$608$	4.29854	−	1.15179i	0.174329	−	0.0467113i
$609$	11.9117	+	33.7444i	0.482686	+	1.36739i
$610$	−4.13918	+	2.61289i	−0.167591	+	0.105793i
$611$	21.7531	−	12.5592i	0.880037	−	0.508090i
$612$	−11.6147	+	5.14349i	−0.469498	+	0.207913i
$613$	0.570360	+	2.12861i	0.0230366	+	0.0859739i	0.976487	−	0.215576i	$-0.0691628\pi$
$613$	0.570360	+	2.12861i	0.0230366	+	0.0859739i	−0.953451	+	0.301550i	$0.902496\pi$
$614$	−5.23823	+	9.07288i	−0.211398	+	0.366152i
$615$	−16.2106	−	40.7245i	−0.653676	−	1.64217i
$616$	−1.02397			−0.0412568
$617$	−12.5021	−	46.6586i	−0.503317	−	1.87840i	−0.477297	−	0.878742i	$-0.658384\pi$
$617$	−12.5021	−	46.6586i	−0.503317	−	1.87840i	−0.0260192	−	0.999661i	$-0.508283\pi$
$618$	14.0093	+	20.4273i	0.563537	+	0.821705i
$619$			19.7493i			0.793791i	0.917864	+	0.396895i	$0.129912\pi$
$619$			19.7493i			0.793791i	−0.917864	+	0.396895i	$0.870088\pi$
$620$	10.7035	+	6.35888i	0.429863	+	0.255379i
$621$	9.46717	−	15.3458i	0.379905	−	0.615807i
$622$	−14.0548	−	14.0548i	−0.563547	−	0.563547i
$623$	−61.5223	+	16.4849i	−2.46484	+	0.660452i
$624$	−1.25262	+	6.72114i	−0.0501449	+	0.269061i
$625$	15.7499	+	19.4150i	0.629996	+	0.776598i
$626$	−3.43423	−	1.98275i	−0.137259	−	0.0792467i
$627$	−0.155499	−	2.00131i	−0.00621005	−	0.0799245i
$628$	−10.5251	+	10.5251i	−0.419997	+	0.419997i
$629$	0.430811	+	0.746186i	0.0171776	+	0.0297524i
$630$	−14.6927	+	21.9048i	−0.585369	+	0.872708i
$631$	−3.73706	−	6.47277i	−0.148770	−	0.257677i	0.782003	−	0.623274i	$-0.214198\pi$
$631$	−3.73706	−	6.47277i	−0.148770	−	0.257677i	−0.930773	+	0.365597i	$0.880865\pi$
$632$	1.65009	+	6.15823i	0.0656372	+	0.244961i
$633$	14.1496	+	6.76634i	0.562397	+	0.268938i
$634$	8.16221	+	4.71245i	0.324163	+	0.187155i
$635$	8.75974	−	0.346079i	0.347620	−	0.0137337i
$636$	1.47510	−	7.91490i	0.0584916	−	0.313846i
$637$	32.2555	−	8.64283i	1.27801	−	0.342441i
$638$	−0.354176	+	1.32180i	−0.0140219	+	0.0523306i
$639$	3.61429	−	2.91488i	0.142979	−	0.115311i
$640$	−1.19361	−	1.89085i	−0.0471816	−	0.0747422i
$641$	1.54921	−	0.894440i	0.0611903	−	0.0353282i	−0.469093	−	0.883149i	$-0.655419\pi$
$641$	1.54921	−	0.894440i	0.0611903	−	0.0353282i	0.530283	+	0.847821i	$0.322086\pi$
$642$	0.736456	−	1.54006i	0.0290656	−	0.0607813i
$643$	14.7320	−	14.7320i	0.580974	−	0.580974i	−0.354197	−	0.935171i	$-0.615246\pi$
$643$	14.7320	−	14.7320i	0.580974	−	0.580974i	0.935171	+	0.354197i	$0.115246\pi$
$644$	6.82203	−	11.8161i	0.268826	−	0.465620i
$645$	−11.8541	+	1.39366i	−0.466756	+	0.0548754i
$646$	−9.42151	−	16.3185i	−0.370684	−	0.642044i
$647$	12.7257	−	12.7257i	0.500298	−	0.500298i	−0.411233	−	0.911530i	$-0.634902\pi$
$647$	12.7257	−	12.7257i	0.500298	−	0.500298i	0.911530	+	0.411233i	$0.134902\pi$
$648$	8.00270	+	4.11785i	0.314376	+	0.161765i
$649$		−	2.16154i		−	0.0848478i
$650$	−19.6748	+	1.55705i	−0.771710	+	0.0610727i
$651$	−37.9055	+	0.970180i	−1.48563	+	0.0380244i
$652$	6.55056	+	6.55056i	0.256540	+	0.256540i
$653$	14.0607	+	14.0607i	0.550237	+	0.550237i	0.926509	−	0.376272i	$-0.122794\pi$
$653$	14.0607	+	14.0607i	0.550237	+	0.550237i	−0.376272	+	0.926509i	$0.622794\pi$
$654$	−18.6301	+	21.7690i	−0.728494	+	0.851237i
$655$	−9.10847	−	8.41611i	−0.355897	−	0.328845i
$656$	−9.80119	+	5.65872i	−0.382672	+	0.220936i
$657$	40.6104	+	4.35019i	1.58436	+	0.169717i
$658$	−6.47580	−	24.1680i	−0.252453	−	0.942167i
$659$	−11.6213			−0.452703			−0.226352	−	0.974046i	$-0.572680\pi$
$659$	−11.6213			−0.452703			−0.226352	+	0.974046i	$0.572680\pi$
$660$	−0.937109	+	0.373023i	−0.0364769	+	0.0145199i
$661$	−2.90630	−	5.03386i	−0.113042	−	0.195794i	0.803953	−	0.594692i	$-0.202726\pi$
$661$	−2.90630	−	5.03386i	−0.113042	−	0.195794i	−0.916995	+	0.398898i	$0.869393\pi$
$662$	1.20769	+	0.323599i	0.0469381	+	0.0125770i
$663$	28.8618	−	2.24253i	1.12090	−	0.0870926i
$664$	−4.36129	+	2.51799i	−0.169251	+	0.0977170i
$665$	−34.6299	−	18.2101i	−1.34289	−	0.706157i
$666$	0.219909	−	0.569486i	0.00852129	−	0.0220671i
$667$	−12.8933	−	12.8933i	−0.499232	−	0.499232i
$668$	−8.64995	+	2.31775i	−0.334676	+	0.0896763i
$669$	−31.6151	+	11.1600i	−1.22231	+	0.431472i
$670$	−9.84538	−	31.6830i	−0.380360	−	1.22402i
$671$	0.493711	−	0.285044i	0.0190595	−	0.0110040i
$672$	6.14391	+	2.93802i	0.237007	+	0.113336i
$673$	23.7356	+	6.35992i	0.914939	+	0.245157i	0.685421	−	0.728147i	$-0.259618\pi$
$673$	23.7356	+	6.35992i	0.914939	+	0.245157i	0.229518	+	0.973304i	$0.426285\pi$
$674$	−30.6768			−1.18163
$675$	−5.46662	+	25.3991i	−0.210410	+	0.977613i
$676$	1.29046	−	2.23514i	0.0496330	−	0.0859669i
$677$	−4.51088	−	1.20869i	−0.173367	−	0.0464536i	0.171091	−	0.985255i	$-0.445271\pi$
$677$	−4.51088	−	1.20869i	−0.173367	−	0.0464536i	−0.344458	+	0.938802i	$0.611937\pi$
$678$	−24.7893	+	17.0008i	−0.952027	+	0.652914i
$679$	−5.29594	−	3.05761i	−0.203240	−	0.117340i
$680$	−6.42538	+	6.95397i	−0.246402	+	0.266672i
$681$	6.65402	−	35.7032i	0.254982	−	1.36815i
$682$	−1.21638	−	0.789226i	−0.0465777	−	0.0302210i
$683$	18.5960	+	18.5960i	0.711554	+	0.711554i	0.966860	−	0.255306i	$-0.0821762\pi$
$683$	18.5960	+	18.5960i	0.711554	+	0.711554i	−0.255306	+	0.966860i	$0.582176\pi$
$684$	−4.80924	+	12.4542i	−0.183886	+	0.476199i
$685$	−4.18901	−	2.20278i	−0.160054	−	0.0841640i
$686$		−	5.74003i		−	0.219155i
$687$	−2.23922	+	4.68260i	−0.0854314	+	0.178652i
$688$	0.797629	+	2.97679i	0.0304093	+	0.113489i
$689$	−9.17415	+	15.8901i	−0.349507	+	0.605364i
$690$	1.93885	−	13.2990i	0.0738107	−	0.506285i
$691$	−19.5164	−	33.8034i	−0.742439	−	1.28594i	−0.951382	−	0.308014i	$-0.900336\pi$
$691$	−19.5164	−	33.8034i	−0.742439	−	1.28594i	0.208943	−	0.977928i	$-0.432998\pi$
$692$	−0.812020	−	0.217580i	−0.0308684	−	0.00827115i
$693$	1.81057	−	2.48162i	0.0687778	−	0.0942688i
$694$	15.4756	+	8.93483i	0.587445	+	0.339161i
$695$	4.42959	−	19.5958i	0.168024	−	0.743310i
$696$	5.91767	−	6.91473i	0.224309	−	0.262102i
$697$	33.8849	+	33.8849i	1.28348	+	1.28348i
$698$	−3.90765	−	3.90765i	−0.147907	−	0.147907i
$699$	24.9779	−	29.1865i	0.944753	−	1.10393i
$700$	−3.57425	+	19.3319i	−0.135094	+	0.730676i
$701$	−30.4055	−	17.5547i	−1.14840	−	0.663030i	−0.199904	−	0.979815i	$-0.564063\pi$
$701$	−30.4055	−	17.5547i	−1.14840	−	0.663030i	−0.948497	+	0.316785i	$0.897396\pi$
$702$	−14.0740	−	14.9200i	−0.531189	−	0.563120i
$703$	0.874710	+	0.234378i	0.0329903	+	0.00883973i
$704$	0.130213	+	0.225535i	0.00490757	+	0.00850017i
$705$	−14.7307	−	19.7589i	−0.554790	−	0.744163i
$706$	9.47881	−	16.4178i	0.356740	−	0.617891i
$707$	13.9486	+	52.0568i	0.524590	+	1.95780i
$708$	−6.20199	+	12.9695i	−0.233085	+	0.487422i
$709$		−	26.4736i		−	0.994236i	−0.867683	−	0.497118i	$-0.834392\pi$
$709$		−	26.4736i		−	0.994236i	0.867683	−	0.497118i	$-0.165608\pi$
$710$	1.61076	−	3.06317i	0.0604508	−	0.114959i
$711$	−17.8423	−	6.88988i	−0.669140	−	0.258391i
$712$	11.4544	+	11.4544i	0.429271	+	0.429271i
$713$	17.2113	−	8.77838i	0.644567	−	0.328753i
$714$	5.28323	−	28.3480i	0.197720	−	1.06090i
$715$	2.29681	−	0.0907424i	0.0858960	−	0.00339357i
$716$	16.3166	+	9.42040i	0.609781	+	0.352057i
$717$	−41.3276	+	28.3430i	−1.54341	+	1.05849i
$718$	30.6442	+	8.21108i	1.14363	+	0.306435i
$719$	−17.1054	+	29.6274i	−0.637923	+	1.10492i	0.347964	+	0.937508i	$0.386873\pi$
$719$	−17.1054	+	29.6274i	−0.637923	+	1.10492i	−0.985888	+	0.167408i	$0.946460\pi$
$720$	6.69305	+	0.450625i	0.249435	+	0.0167938i
$721$	−56.2291			−2.09408
$722$	−0.776665	−	0.208107i	−0.0289045	−	0.00774493i
$723$	−22.7769	−	10.8919i	−0.847081	−	0.405074i
$724$	2.47733	−	1.43029i	0.0920694	−	0.0531563i
$725$	23.7185	+	11.3005i	0.880884	+	0.419690i
$726$	−17.8553	+	6.30287i	−0.662672	+	0.233921i
$727$	19.4715	−	5.21737i	0.722157	−	0.193501i	0.121023	−	0.992650i	$-0.461382\pi$
$727$	19.4715	−	5.21737i	0.722157	−	0.193501i	0.601134	+	0.799148i	$0.294716\pi$
$728$	−10.9745	−	10.9745i	−0.406742	−	0.406742i
$729$	−24.1301	+	12.1136i	−0.893706	+	0.448654i
$730$	29.0711	−	9.03375i	1.07597	−	0.334354i
$731$	11.3008	−	6.52452i	0.417975	−	0.241318i
$732$	−3.78018	+	0.293716i	−0.139719	+	0.0108560i
$733$	−33.8859	−	9.07969i	−1.25160	−	0.335366i	−0.428648	−	0.903472i	$-0.641010\pi$
$733$	−33.8859	−	9.07969i	−1.25160	−	0.335366i	−0.822956	+	0.568105i	$0.807677\pi$
$734$	−6.03023	−	10.4447i	−0.222580	−	0.385519i
$735$	−12.1176	−	30.4418i	−0.446963	−	1.12286i
$736$	−3.47009			−0.127909
$737$	1.00009	+	3.73237i	0.0368386	+	0.137484i
$738$	3.61629	−	33.7592i	0.133118	−	1.24269i
$739$	−2.62763	+	1.51706i	−0.0966590	+	0.0558061i	−0.547550	−	0.836773i	$-0.684440\pi$
$739$	−2.62763	+	1.51706i	−0.0966590	+	0.0558061i	0.450891	+	0.892579i	$0.351106\pi$
$740$	−0.0179628	−	0.454663i	−0.000660325	−	0.0167137i
$741$	19.7827	−	23.1158i	0.726735	−	0.849182i
$742$	12.9237	+	12.9237i	0.474444	+	0.474444i
$743$	6.64399	+	6.64399i	0.243744	+	0.243744i	0.818397	−	0.574653i	$-0.194863\pi$
$743$	6.64399	+	6.64399i	0.243744	+	0.243744i	−0.574653	+	0.818397i	$0.694863\pi$
$744$	5.03393	+	8.22554i	0.184553	+	0.301563i
$745$	2.63510	−	2.85188i	0.0965428	−	0.104485i
$746$		−	8.09567i		−	0.296404i
$747$	1.60916	−	15.0220i	0.0588761	−	0.549627i
$748$	0.779725	−	0.779725i	0.0285096	−	0.0285096i
$749$	1.93762	+	3.35605i	0.0707990	+	0.122628i
$750$	3.77137	+	18.9941i	0.137711	+	0.693567i
$751$	−16.7324	+	28.9814i	−0.610576	+	1.05755i	0.380568	+	0.924753i	$0.375729\pi$
$751$	−16.7324	+	28.9814i	−0.610576	+	1.05755i	−0.991144	+	0.132795i	$0.957605\pi$
$752$	−4.49966	+	4.49966i	−0.164086	+	0.164086i
$753$	18.9374	−	39.6014i	0.690116	−	1.44315i
$754$	−17.9625	+	10.3706i	−0.654155	+	0.377677i
$755$	4.66251	+	1.05395i	0.169686	+	0.0383573i
$756$	−17.9840	+	9.69499i	−0.654071	+	0.352603i
$757$	6.22167	−	23.2196i	0.226131	−	0.843931i	−0.755818	−	0.654782i	$-0.772761\pi$
$757$	6.22167	−	23.2196i	0.226131	−	0.843931i	0.981948	−	0.189149i	$-0.0605728\pi$
$758$	17.0259	−	4.56207i	0.618408	−	0.165702i
$759$	−0.286779	+	1.53876i	−0.0104094	+	0.0558534i
$760$	0.392833	+	9.94314i	0.0142495	+	0.360676i
$761$	−2.83289	−	1.63557i	−0.102692	−	0.0592893i	0.447774	−	0.894147i	$-0.352217\pi$
$761$	−2.83289	−	1.63557i	−0.102692	−	0.0592893i	−0.550466	+	0.834857i	$0.685550\pi$
$762$	6.12614	+	2.92952i	0.221927	+	0.106125i
$763$	−16.8346	−	62.8275i	−0.609453	−	2.27451i
$764$	−1.71171	−	2.96477i	−0.0619275	−	0.107262i
$765$	−5.49186	−	27.8680i	−0.198559	−	1.00757i
$766$	19.0616	+	33.0156i	0.688723	+	1.19290i
$767$	23.1665	−	23.1665i	0.836495	−	0.836495i
$768$	−0.134174	−	1.72685i	−0.00484159	−	0.0623122i
$769$	−16.4357	−	9.48913i	−0.592685	−	0.342187i	0.173473	−	0.984839i	$-0.444501\pi$
$769$	−16.4357	−	9.48913i	−0.592685	−	0.342187i	−0.766159	+	0.642652i	$0.777834\pi$
$770$	0.504836	−	2.23331i	0.0181930	−	0.0804830i
$771$	−1.48786	+	7.98338i	−0.0535841	+	0.287515i
$772$	−13.1133	+	3.51371i	−0.471959	+	0.126461i
$773$	−11.5049	−	11.5049i	−0.413801	−	0.413801i	0.469260	−	0.883060i	$-0.344521\pi$
$773$	−11.5049	−	11.5049i	−0.413801	−	0.413801i	−0.883060	+	0.469260i	$0.844521\pi$
$774$	−8.62471	−	3.33046i	−0.310009	−	0.119711i
$775$	−19.1460	+	20.2097i	−0.687744	+	0.725953i
$776$			1.55528i			0.0558314i
$777$	0.783798	+	1.14287i	0.0281186	+	0.0410003i
$778$	3.55109	+	13.2528i	0.127313	+	0.475138i
$779$	50.3646			1.80450
$780$	−14.0415	−	6.04567i	−0.502766	−	0.216470i
$781$	−0.201536	+	0.349070i	−0.00721152	+	0.0124907i
$782$	3.80286	+	14.1925i	0.135990	+	0.507522i
$783$	6.29450	+	26.5682i	0.224947	+	0.949471i
$784$	−7.32645	+	4.22993i	−0.261659	+	0.151069i
$785$	−17.7666	−	28.1447i	−0.634116	−	1.00453i
$786$	−3.19755	−	9.05829i	−0.114053	−	0.323099i
$787$	−15.7808	+	4.22846i	−0.562526	+	0.150728i	−0.528867	−	0.848705i	$-0.677383\pi$
$787$	−15.7808	+	4.22846i	−0.562526	+	0.150728i	−0.0336594	+	0.999433i	$0.510716\pi$
$788$	0.0318387	−	0.118824i	0.00113421	−	0.00423292i
$789$	−8.66412	+	10.1239i	−0.308451	+	0.360422i
$790$	−14.2449	+	0.562786i	−0.506810	+	0.0200230i
$791$		−	68.2363i		−	2.42620i
$792$	−0.776832	−	0.0832144i	−0.0276035	−	0.00295689i
$793$	8.34639	+	2.23641i	0.296389	+	0.0794172i
$794$	14.8009	−	25.6360i	0.525266	−	0.909787i
$795$	16.5355	+	7.11946i	0.586452	+	0.252501i
$796$	5.70942	+	9.88901i	0.202365	+	0.350507i
$797$	18.0930	+	4.84801i	0.640887	+	0.171725i	0.564605	−	0.825361i	$-0.309028\pi$
$797$	18.0930	+	4.84801i	0.640887	+	0.171725i	0.0762819	+	0.997086i	$0.475695\pi$
$798$	−17.1411	−	24.9938i	−0.606787	−	0.884769i
$799$	23.3345	+	13.4722i	0.825515	+	0.476611i
$800$	4.71248	−	1.67108i	0.166611	−	0.0590818i
$801$	−48.0135	+	7.50651i	−1.69647	+	0.265229i
$802$	−16.6089	−	16.6089i	−0.586481	−	0.586481i
$803$	−3.42468	+	0.917641i	−0.120854	+	0.0323828i
$804$	4.70848	−	25.2641i	0.166055	−	0.890997i
$805$	22.4080	+	20.7047i	0.789778	+	0.729745i
$806$	−4.57810	−	21.4953i	−0.161257	−	0.757141i
$807$	−12.8224	+	8.79381i	−0.451371	+	0.309557i
$808$	9.69205	−	9.69205i	0.340965	−	0.340965i
$809$	−7.07834	+	12.2601i	−0.248861	+	0.431040i	−0.963210	−	0.268749i	$-0.913390\pi$
$809$	−7.07834	+	12.2601i	−0.248861	+	0.431040i	0.714349	+	0.699790i	$0.246723\pi$
$810$	−12.9267	+	15.4240i	−0.454198	+	0.541945i
$811$	−16.6227	−	28.7914i	−0.583703	−	1.01100i	−0.995036	−	0.0995175i	$-0.968270\pi$
$811$	−16.6227	−	28.7914i	−0.583703	−	1.01100i	0.411333	−	0.911485i	$-0.365063\pi$
$812$	5.34735	+	19.9566i	0.187655	+	0.700338i
$813$	3.28358	+	42.2604i	0.115160	+	1.48214i
$814$			0.0529940i			0.00185744i
$815$	−17.5166	+	11.0575i	−0.613579	+	0.387326i
$816$	−6.91566	+	2.44121i	−0.242097	+	0.0854594i
$817$	3.54959	−	13.2473i	0.124184	−	0.463463i
$818$	35.7520	−	9.57971i	1.25004	−	0.334947i
$819$	46.0020	−	7.19202i	1.60744	−	0.251310i
$820$	−7.50971	−	24.1666i	−0.262250	−	0.843936i
$821$			15.7116i			0.548339i	0.961681	+	0.274169i	$0.0884029\pi$
$821$			15.7116i			0.548339i	−0.961681	+	0.274169i	$0.911597\pi$
$822$	−2.07347	−	3.02337i	−0.0723206	−	0.105452i
$823$	−11.6952	−	43.6471i	−0.407669	−	1.52144i	−0.799079	−	0.601226i	$-0.794679\pi$
$823$	−11.6952	−	43.6471i	−0.407669	−	1.52144i	0.391409	−	0.920217i	$-0.371988\pi$
$824$	7.15037	+	12.3848i	0.249095	+	0.431445i
$825$	−0.351563	−	2.22778i	−0.0122398	−	0.0775613i
$826$	−16.3175	−	28.2627i	−0.567757	−	0.983384i
$827$	36.4686	+	9.77174i	1.26814	+	0.339797i	0.829317	−	0.558778i	$-0.188730\pi$
$827$	36.4686	+	9.77174i	1.26814	+	0.339797i	0.438821	+	0.898575i	$0.355396\pi$
$828$	6.13579	−	8.40988i	0.213233	−	0.292263i
$829$			47.2497i			1.64105i	0.571611	+	0.820525i	$0.306319\pi$
$829$			47.2497i			1.64105i	−0.571611	+	0.820525i	$0.693681\pi$
$830$	−3.34164	−	10.7536i	−0.115990	−	0.373262i
$831$	−36.0576	+	42.1330i	−1.25083	+	1.46158i
$832$	−1.02163	+	3.81277i	−0.0354186	+	0.132184i
$833$	25.3292	+	25.3292i	0.877605	+	0.877605i
$834$	10.1184	−	11.8232i	0.350370	−	0.409404i
$835$	−0.790497	−	20.0086i	−0.0273563	−	0.692425i
$836$		−	1.15894i		−	0.0400827i
$837$	−28.8358	−	2.34443i	−0.996711	−	0.0810352i
$838$	−17.5216	+	17.5216i	−0.605273	+	0.605273i
$839$	−28.9385			−0.999066			−0.499533	−	0.866295i	$-0.666495\pi$
$839$	−28.9385			−0.999066			−0.499533	+	0.866295i	$0.666495\pi$
$840$	−9.43700	+	11.9516i	−0.325607	+	0.412370i
$841$	−1.38923			−0.0479043
$842$	−22.9627	−	6.15283i	−0.791346	−	0.212040i
$843$	−0.0619204	+	0.00481115i	−0.00213265	+	0.000165705i
$844$	7.84211	+	4.52765i	0.269937	+	0.155848i
$845$	4.23870	+	3.91651i	0.145816	+	0.134732i
$846$	−2.94881	−	18.8613i	−0.101382	−	0.648465i
$847$	11.1251	−	41.5196i	0.382265	−	1.42663i
$848$	1.20308	−	4.48997i	0.0413140	−	0.154186i
$849$	36.4338	+	31.1803i	1.25040	+	1.07010i
$850$	−11.9990	−	17.4424i	−0.411563	−	0.598271i
$851$	−0.611526	−	0.353065i	−0.0209628	−	0.0121029i
$852$	2.21081	−	1.51620i	0.0757410	−	0.0519443i
$853$	−3.29501	+	3.29501i	−0.112819	+	0.112819i	−0.761263	−	0.648444i	$-0.775420\pi$
$853$	−3.29501	+	3.29501i	−0.112819	+	0.112819i	0.648444	+	0.761263i	$0.275420\pi$
$854$	4.30360	−	7.45405i	0.147266	−	0.255072i
$855$	−24.7921	−	16.6293i	−0.847872	−	0.568711i
$856$	0.492794	−	0.853544i	0.0168434	−	0.0291735i
$857$	38.2009	+	10.2359i	1.30492	+	0.349651i	0.843307	−	0.537432i	$-0.180606\pi$
$857$	38.2009	+	10.2359i	1.30492	+	0.349651i	0.461609	+	0.887083i	$0.347272\pi$
$858$	1.60628	+	0.768123i	0.0548376	+	0.0262233i
$859$	13.5146	−	7.80266i	0.461113	−	0.266223i	−0.251399	−	0.967883i	$-0.580891\pi$
$859$	13.5146	−	7.80266i	0.461113	−	0.266223i	0.712512	+	0.701660i	$0.247557\pi$
$860$	−6.88575	+	0.272042i	−0.234802	+	0.00927655i
$861$	58.5581	+	50.1144i	1.99566	+	1.70789i
$862$	−7.50846	+	2.01189i	−0.255739	+	0.0685251i
$863$	−11.2748	+	42.0783i	−0.383800	+	1.43236i	0.456249	+	0.889852i	$0.349193\pi$
$863$	−11.2748	+	42.0783i	−0.383800	+	1.43236i	−0.840049	+	0.542510i	$0.817474\pi$
$864$	4.42231	+	2.72822i	0.150450	+	0.0928159i
$865$	0.874893	−	1.66378i	0.0297472	−	0.0565701i
$866$			28.2039i			0.958408i
$867$	0.909698	+	1.32645i	0.0308950	+	0.0450486i
$868$	−21.8624	−	1.13686i	−0.742057	−	0.0385875i
$869$	1.66033			0.0563230
$870$	12.1638	+	16.3158i	0.412390	+	0.553156i
$871$	−29.2836	+	50.7207i	−0.992237	+	1.71860i
$872$	−11.6974	+	11.6974i	−0.396123	+	0.396123i
$873$	−3.76928	−	2.75004i	−0.127571	−	0.0930747i
$874$	13.3736	+	7.72126i	0.452369	+	0.261176i
$875$	−40.4014	−	17.3266i	−1.36582	−	0.585746i
$876$	23.1814	+	4.32032i	0.783227	+	0.145970i
$877$	5.42960	−	20.2635i	0.183344	−	0.684251i	−0.811634	−	0.584166i	$-0.801422\pi$
$877$	5.42960	−	20.2635i	0.183344	−	0.684251i	0.994979	−	0.100085i	$-0.0319115\pi$
$878$	−5.71684	+	21.3356i	−0.192934	+	0.720040i
$879$	15.4470	+	43.7597i	0.521016	+	1.47598i
$880$	−0.556098	+	0.172806i	−0.0187461	+	0.00582528i
$881$	−26.6525	+	15.3878i	−0.897944	+	0.518428i	−0.876533	−	0.481343i	$-0.840149\pi$
$881$	−26.6525	+	15.3878i	−0.897944	+	0.518428i	−0.0214113	+	0.999771i	$0.506816\pi$
$882$	2.70320	−	25.2352i	0.0910215	−	0.849714i
$883$	−7.40694	+	7.40694i	−0.249263	+	0.249263i	−0.820668	−	0.571405i	$-0.806399\pi$
$883$	−7.40694	+	7.40694i	−0.249263	+	0.249263i	0.571405	+	0.820668i	$0.306399\pi$
$884$	16.7136			0.562139
$885$	−25.2292	−	19.9210i	−0.848070	−	0.669637i
$886$	12.5971	+	21.8188i	0.423207	+	0.733017i
$887$	12.7797	+	47.6943i	0.429099	+	1.60142i	0.754806	+	0.655948i	$0.227731\pi$
$887$	12.7797	+	47.6943i	0.429099	+	1.60142i	−0.325707	+	0.945471i	$0.605602\pi$
$888$	0.152053	−	0.317969i	0.00510256	−	0.0106704i
$889$	−13.3499	+	7.70757i	−0.447742	+	0.258504i
$890$	−30.6297	+	19.3352i	−1.02671	+	0.648117i
$891$	1.57526	−	1.73554i	0.0527732	−	0.0581427i
$892$	−18.6973	+	5.00992i	−0.626031	+	0.167744i
$893$	27.3536	−	7.32939i	0.915355	−	0.245269i
$894$	2.83617	−	1.00116i	0.0948559	−	0.0334839i
$895$	−28.5907	+	30.9427i	−0.955681	+	1.03430i
$896$	3.40513	+	1.96595i	0.113757	+	0.0656778i
$897$	−19.5654	+	13.4182i	−0.653270	+	0.448022i
$898$	8.16869	−	8.16869i	0.272593	−	0.272593i
$899$	−9.02941	+	27.8281i	−0.301148	+	0.928119i
$900$	−4.28264	+	14.3756i	−0.142755	+	0.479188i
$901$	−19.6822			−0.655708
$902$	0.762830	+	2.84692i	0.0253995	+	0.0947921i
$903$	17.3085	−	11.8704i	0.575991	−	0.395023i
$904$	−15.0294	+	8.67726i	−0.499872	+	0.288601i
$905$	1.89814	+	6.10832i	0.0630964	+	0.203048i
$906$	2.81315	+	2.40751i	0.0934606	+	0.0799841i
$907$	−6.40291	−	6.40291i	−0.212605	−	0.212605i	0.592768	−	0.805373i	$-0.298035\pi$
$907$	−6.40291	−	6.40291i	−0.212605	−	0.212605i	−0.805373	+	0.592768i	$0.798035\pi$
$908$	5.42697	−	20.2537i	0.180100	−	0.672143i
$909$	6.35159	+	40.6264i	0.210669	+	1.34749i
$910$	29.3464	−	18.5251i	0.972825	−	0.614103i
$911$	−44.4529	−	25.6649i	−1.47279	−	0.850317i	−0.473260	−	0.880923i	$-0.656923\pi$
$911$	−44.4529	−	25.6649i	−1.47279	−	0.850317i	−0.999532	+	0.0306061i	$0.990256\pi$
$912$	−3.32528	+	6.95375i	−0.110111	+	0.230262i
$913$	0.339441	+	1.26681i	0.0112338	+	0.0419253i
$914$	−23.0912			−0.763789
$915$	1.22310	−	8.38952i	0.0404344	−	0.277349i
$916$	−1.49835	+	2.59523i	−0.0495070	+	0.0857487i
$917$	21.0636	+	5.64398i	0.695582	+	0.186381i
$918$	6.31186	−	21.0768i	0.208322	−	0.695639i
$919$	15.5763	−	8.99301i	0.513816	−	0.296652i	−0.220585	−	0.975368i	$-0.570797\pi$
$919$	15.5763	−	8.99301i	0.513816	−	0.296652i	0.734401	+	0.678716i	$0.237463\pi$
$920$	1.71083	−	7.56841i	0.0564043	−	0.249523i
$921$	−6.04013	−	17.1110i	−0.199029	−	0.563826i
$922$	−3.61913	−	3.61913i	−0.119190	−	0.119190i
$923$	−5.90119	+	1.58122i	−0.194240	+	0.0520465i
$924$	1.15318	−	1.34748i	0.0379369	−	0.0443288i
$925$	1.00049	+	0.184980i	0.0328960	+	0.00608212i
$926$			18.4523i			0.606381i
$927$	−42.6582	−	4.56955i	−1.40108	−	0.150084i
$928$	3.71556	−	3.71556i	0.121969	−	0.121969i
$929$	59.3125			1.94598			0.972991	−	0.230844i	$-0.0741487\pi$
$929$	59.3125			1.94598			0.972991	+	0.230844i	$0.0741487\pi$
$930$	−20.4221	+	6.92385i	−0.669666	+	0.227042i
$931$	37.6479			1.23386
$932$	15.6830	−	15.6830i	0.513715	−	0.513715i
$933$	34.3237	−	2.66691i	1.12371	−	0.0873108i
$934$		−	4.36513i		−	0.142831i
$935$	1.31619	+	2.08503i	0.0430440	+	0.0681878i
$936$	−7.43393	−	9.21765i	−0.242985	−	0.301288i
$937$	6.05658	−	1.62286i	0.197860	−	0.0530164i	−0.158528	−	0.987354i	$-0.550675\pi$
$937$	6.05658	−	1.62286i	0.197860	−	0.0530164i	0.356388	+	0.934338i	$0.384008\pi$
$938$	41.2521	+	41.2521i	1.34693	+	1.34693i
$939$	6.47677	−	2.28628i	0.211361	−	0.0746100i
$940$	−7.59551	−	12.0323i	−0.247738	−	0.392452i
$941$	24.7350	−	14.2807i	0.806336	−	0.465539i	−0.0393456	−	0.999226i	$-0.512527\pi$
$941$	24.7350	−	14.2807i	0.806336	−	0.465539i	0.845682	+	0.533687i	$0.179194\pi$
$942$	−1.99714	−	25.7037i	−0.0650705	−	0.837470i
$943$	−37.9344	−	10.1645i	−1.23531	−	0.331001i
$944$	−4.15001	+	7.18804i	−0.135071	+	0.233951i
$945$	−12.2787	−	44.0036i	−0.399425	−	1.43144i
$946$	0.802580			0.0260941
$947$	11.0586	+	41.2713i	0.359356	+	1.34114i	0.874913	+	0.484280i	$0.160919\pi$
$947$	11.0586	+	41.2713i	0.359356	+	1.34114i	−0.515556	+	0.856856i	$0.672415\pi$
$948$	−9.96218	−	4.76391i	−0.323557	−	0.154725i
$949$	−46.5394	−	26.8695i	−1.51073	−	0.872221i
$950$	−21.8800	−	4.04538i	−0.709882	−	0.131250i
$951$	−15.3935	+	5.43386i	−0.499168	+	0.176205i
$952$	4.30896	−	16.0813i	0.139654	−	0.521197i
$953$	−5.51805	−	5.51805i	−0.178747	−	0.178747i	0.612062	−	0.790810i	$-0.290340\pi$
$953$	−5.51805	−	5.51805i	−0.178747	−	0.178747i	−0.790810	+	0.612062i	$0.790340\pi$
$954$	8.75429	+	10.8548i	0.283431	+	0.351438i
$955$	7.31018	−	2.27161i	0.236552	−	0.0735077i
$956$	−25.0564	+	14.4663i	−0.810383	+	0.467875i
$957$	−1.34054	−	1.95467i	−0.0433336	−	0.0631856i
$958$	−4.79519	−	17.8959i	−0.154926	−	0.578190i
$959$	8.32228			0.268741
$960$	3.83247	+	0.558731i	0.123692	+	0.0180330i
$961$	−25.0943	−	18.2010i	−0.809494	−	0.587128i
$962$	−0.567969	+	0.567969i	−0.0183121	+	0.0183121i
$963$	1.19724	+	2.70353i	0.0385804	+	0.0871201i
$964$	−12.6236	−	7.28823i	−0.406578	−	0.234738i
$965$	−1.19840	−	30.3330i	−0.0385777	−	0.976455i
$966$	7.86639	+	22.2846i	0.253097	+	0.716994i
$967$	−17.5987	+	4.71555i	−0.565935	+	0.151642i	−0.530432	−	0.847728i	$-0.677970\pi$
$967$	−17.5987	+	4.71555i	−0.565935	+	0.151642i	−0.0355034	+	0.999370i	$0.511303\pi$
$968$	−10.5597	+	2.82946i	−0.339401	+	0.0909422i
$969$	32.0846	+	5.97962i	1.03071	+	0.192093i
$970$	−3.39213	−	0.766786i	−0.108915	−	0.0246200i
$971$	−15.4636	+	8.92793i	−0.496251	+	0.286511i	−0.727164	−	0.686464i	$-0.759162\pi$
$971$	−15.4636	+	8.92793i	−0.496251	+	0.286511i	0.230913	+	0.972974i	$0.425829\pi$
$972$	−14.4314	+	5.89359i	−0.462888	+	0.189037i
$973$	9.14319	+	34.1229i	0.293117	+	1.09393i
$974$	−9.07248	−	15.7140i	−0.290701	−	0.503509i
$975$	20.1086	−	27.6444i	0.643990	−	0.885330i
$976$	−2.18907			−0.0700703
$977$	−33.0354	+	33.0354i	−1.05690	+	1.05690i	−0.0586159	+	0.998281i	$0.518669\pi$
$977$	−33.0354	+	33.0354i	−1.05690	+	1.05690i	−0.998281	+	0.0586159i	$0.981331\pi$
$978$	−15.9973	+	1.24297i	−0.511537	+	0.0397459i
$979$	3.65342	−	2.10930i	0.116764	−	0.0674137i
$980$	−5.61355	−	18.0647i	−0.179318	−	0.577056i
$981$	−7.66576	−	49.0321i	−0.244749	−	1.56548i
$982$	−1.96450	+	7.33163i	−0.0626898	+	0.233962i
$983$	13.0795	−	48.8132i	0.417170	−	1.55690i	−0.363278	−	0.931681i	$-0.618343\pi$
$983$	13.0795	−	48.8132i	0.417170	−	1.55690i	0.780449	−	0.625220i	$-0.214991\pi$
$984$	3.59146	−	19.2706i	0.114492	−	0.614323i
$985$	0.243462	+	0.128024i	0.00775734	+	0.00407918i
$986$	−19.2683	−	11.1246i	−0.613628	−	0.354278i
$987$	39.0966	+	18.6960i	1.24446	+	0.595100i
$988$	12.4211	−	12.4211i	0.395167	−	0.395167i
$989$	−5.34707	+	9.26140i	−0.170027	+	0.294495i
$990$	0.564487	−	1.65327i	0.0179406	−	0.0525445i
$991$	25.2465			0.801981			0.400991	−	0.916082i	$-0.368666\pi$
$991$	25.2465			0.801981			0.400991	+	0.916082i	$0.368666\pi$
$992$	2.52973	+	4.95989i	0.0803189	+	0.157477i
$993$	−1.78592	+	1.22481i	−0.0566745	+	0.0388682i
$994$			6.08558i			0.193023i
$995$	−24.3832	+	7.57699i	−0.772998	+	0.240207i
$996$	1.59811	−	8.57493i	0.0506381	−	0.271707i
$997$	−3.66137	+	13.6644i	−0.115957	+	0.432757i	−0.999357	−	0.0358632i	$-0.988582\pi$
$997$	−3.66137	+	13.6644i	−0.115957	+	0.432757i	0.883400	+	0.468620i	$0.155249\pi$
$998$	−25.3281	+	6.78664i	−0.801747	+	0.214827i
$999$	0.501750	+	0.930735i	0.0158747	+	0.0294472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.17	✓	256
3.2	odd	2	inner	930.2.bf.a.377.44	yes	256
5.3	odd	4	inner	930.2.bf.a.563.64	yes	256
15.8	even	4	inner	930.2.bf.a.563.28	yes	256
31.25	even	3	inner	930.2.bf.a.707.28	yes	256
93.56	odd	6	inner	930.2.bf.a.707.64	yes	256
155.118	odd	12	inner	930.2.bf.a.893.44	yes	256
465.428	even	12	inner	930.2.bf.a.893.17	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.17	✓	256	1.1	even	1	trivial
930.2.bf.a.377.44	yes	256	3.2	odd	2	inner
930.2.bf.a.563.28	yes	256	15.8	even	4	inner
930.2.bf.a.563.64	yes	256	5.3	odd	4	inner
930.2.bf.a.707.28	yes	256	31.25	even	3	inner
930.2.bf.a.707.64	yes	256	93.56	odd	6	inner
930.2.bf.a.893.17	yes	256	465.428	even	12	inner
930.2.bf.a.893.44	yes	256	155.118	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.134174 - 1.72685i) q^{3} -1.00000i q^{4} +(2.18104 + 0.493020i) q^{5} +(1.31594 + 1.12619i) q^{6} +(-3.79793 + 1.01765i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.96399 + 0.463396i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.134174 - 1.72685i) q^{3} -1.00000i q^{4} +(2.18104 + 0.493020i) q^{5} +(1.31594 + 1.12619i) q^{6} +(-3.79793 + 1.01765i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.96399 + 0.463396i) q^{9} +(-1.89085 + 1.19361i) q^{10} +(0.225535 - 0.130213i) q^{11} +(-1.72685 + 0.134174i) q^{12} +(3.81277 + 1.02163i) q^{13} +(1.96595 - 3.40513i) q^{14} +(0.558731 - 3.83247i) q^{15} -1.00000 q^{16} +(1.09590 + 4.08994i) q^{17} +(1.76819 - 2.42353i) q^{18} +(3.85397 + 2.22509i) q^{19} +(0.493020 - 2.18104i) q^{20} +(2.26691 + 6.42189i) q^{21} +(-0.0674030 + 0.251552i) q^{22} +(-2.45373 - 2.45373i) q^{23} +(1.12619 - 1.31594i) q^{24} +(4.51386 + 2.15059i) q^{25} +(-3.41843 + 1.97363i) q^{26} +(1.19790 + 5.05619i) q^{27} +(1.01765 + 3.79793i) q^{28} +5.25460 q^{29} +(2.31488 + 3.10505i) q^{30} +(-1.71838 + 5.29596i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.255118 - 0.371993i) q^{33} +(-3.66694 - 2.11711i) q^{34} +(-8.78515 + 0.347083i) q^{35} +(0.463396 + 2.96399i) q^{36} +(0.196556 - 0.0526671i) q^{37} +(-4.29854 + 1.15179i) q^{38} +(1.25262 - 6.72114i) q^{39} +(1.19361 + 1.89085i) q^{40} +(9.80119 - 5.65872i) q^{41} +(-6.14391 - 2.93802i) q^{42} +(-0.797629 - 2.97679i) q^{43} +(-0.130213 - 0.225535i) q^{44} +(-6.69305 - 0.450625i) q^{45} +3.47009 q^{46} +(4.49966 - 4.49966i) q^{47} +(0.134174 + 1.72685i) q^{48} +(7.32645 - 4.22993i) q^{49} +(-4.71248 + 1.67108i) q^{50} +(6.91566 - 2.44121i) q^{51} +(1.02163 - 3.81277i) q^{52} +(-1.20308 + 4.48997i) q^{53} +(-4.42231 - 2.72822i) q^{54} +(0.556098 - 0.172806i) q^{55} +(-3.40513 - 1.96595i) q^{56} +(3.32528 - 6.95375i) q^{57} +(-3.71556 + 3.71556i) q^{58} +(4.15001 - 7.18804i) q^{59} +(-3.83247 - 0.558731i) q^{60} +2.18907 q^{61} +(-2.52973 - 4.95989i) q^{62} +(10.7855 - 4.77626i) q^{63} +1.00000i q^{64} +(7.81211 + 4.10798i) q^{65} +(0.443434 + 0.0826430i) q^{66} +(-3.84020 + 14.3318i) q^{67} +(4.08994 - 1.09590i) q^{68} +(-3.90798 + 4.56643i) q^{69} +(5.96661 - 6.45746i) q^{70} +(-1.34039 + 0.773872i) q^{71} +(-2.42353 - 1.76819i) q^{72} +(-13.1503 - 3.52362i) q^{73} +(-0.101745 + 0.176228i) q^{74} +(3.10810 - 8.08330i) q^{75} +(2.22509 - 3.85397i) q^{76} +(-0.724054 + 0.724054i) q^{77} +(3.86683 + 5.63830i) q^{78} +(5.52132 + 3.18774i) q^{79} +(-2.18104 - 0.493020i) q^{80} +(8.57053 - 2.74700i) q^{81} +(-2.92917 + 10.9318i) q^{82} +(-1.30341 + 4.86439i) q^{83} +(6.42189 - 2.26691i) q^{84} +(0.373770 + 9.46062i) q^{85} +(2.66892 + 1.54090i) q^{86} +(-0.705030 - 9.07388i) q^{87} +(0.251552 + 0.0674030i) q^{88} +16.1989 q^{89} +(5.05134 - 4.41406i) q^{90} -15.5203 q^{91} +(-2.45373 + 2.45373i) q^{92} +(9.37586 + 2.25681i) q^{93} +6.36348i q^{94} +(7.30864 + 6.75309i) q^{95} +(-1.31594 - 1.12619i) q^{96} +(1.09975 + 1.09975i) q^{97} +(-2.18957 + 8.17160i) q^{98} +(-0.608144 + 0.490461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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