LMFDB - Embedded newform 374.2.g.f.69.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [374,2,Mod(69,374)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("374.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(374, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$374 = 2 \cdot 11 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	374.g (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} + 68 x^{12} + 28 x^{11} + 306 x^{10} + 228 x^{9} + 1035 x^{8} + \cdots + 3481$ x^16 - 4x^15 + 10x^14 - 8x^13 + 68x^12 + 28x^11 + 306x^10 + 228x^9 + 1035x^8 + 264x^7 + 2972x^6 + 4642x^5 + 9487x^4 + 8098x^3 + 7793x^2 + 2124*x + 3481
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.1
Root			$-1.44028 + 1.04643i$ of defining polynomial
Character	$\chi$	$=$	374.69
Dual form			374.2.g.f.103.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.859156 - 2.64421i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.75895 - 2.00449i) q^{5} +(2.24930 + 1.63421i) q^{6} +(1.14902 - 3.53632i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.82665 + 2.78022i) q^{9} +3.41024 q^{10} +(-3.13492 + 1.08273i) q^{11} -2.78029 q^{12} +(4.68837 - 3.40630i) q^{13} +(1.14902 + 3.53632i) q^{14} +(-2.92993 + 9.01740i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.809017 + 0.587785i) q^{17} +(1.46165 - 4.49849i) q^{18} +(1.88284 + 5.79478i) q^{19} +(-2.75895 + 2.00449i) q^{20} -10.3380 q^{21} +(1.89979 - 2.71860i) q^{22} -2.76089 q^{23} +(2.24930 - 1.63421i) q^{24} +(2.04871 + 6.30528i) q^{25} +(-1.79080 + 5.51152i) q^{26} +(3.89127 + 2.82718i) q^{27} +(-3.00818 - 2.18557i) q^{28} +(1.68587 - 5.18858i) q^{29} +(-2.92993 - 9.01740i) q^{30} +(-2.28455 + 1.65982i) q^{31} +1.00000 q^{32} +(5.55634 + 7.35915i) q^{33} -1.00000 q^{34} +(-10.2586 + 7.45332i) q^{35} +(1.46165 + 4.49849i) q^{36} +(1.16150 - 3.57473i) q^{37} +(-4.92933 - 3.58137i) q^{38} +(-13.0350 - 9.47050i) q^{39} +(1.05382 - 3.24334i) q^{40} +(2.21533 + 6.81807i) q^{41} +(8.36360 - 6.07651i) q^{42} -5.51776 q^{43} +(0.0609919 + 3.31606i) q^{44} +16.1304 q^{45} +(2.23360 - 1.62281i) q^{46} +(-0.409236 - 1.25950i) q^{47} +(-0.859156 + 2.64421i) q^{48} +(-5.52222 - 4.01213i) q^{49} +(-5.36360 - 3.89688i) q^{50} +(0.859156 - 2.64421i) q^{51} +(-1.79080 - 5.51152i) q^{52} +(6.01114 - 4.36735i) q^{53} -4.80988 q^{54} +(10.8194 + 3.29673i) q^{55} +3.71831 q^{56} +(13.7050 - 9.95724i) q^{57} +(1.68587 + 5.18858i) q^{58} +(4.03643 - 12.4229i) q^{59} +(7.67066 + 5.57306i) q^{60} +(-8.66153 - 6.29297i) q^{61} +(0.872619 - 2.68564i) q^{62} +(5.43486 + 16.7268i) q^{63} +(-0.809017 + 0.587785i) q^{64} -19.7629 q^{65} +(-8.82077 - 2.68774i) q^{66} -6.57919 q^{67} +(0.809017 - 0.587785i) q^{68} +(2.37203 + 7.30036i) q^{69} +(3.91844 - 12.0597i) q^{70} +(3.93847 + 2.86146i) q^{71} +(-3.82665 - 2.78022i) q^{72} +(-0.842658 + 2.59343i) q^{73} +(1.16150 + 3.57473i) q^{74} +(14.9123 - 10.8344i) q^{75} +6.09299 q^{76} +(0.226787 + 12.3302i) q^{77} +16.1122 q^{78} +(-1.33410 + 0.969278i) q^{79} +(1.05382 + 3.24334i) q^{80} +(-0.252510 + 0.777147i) q^{81} +(-5.79980 - 4.21380i) q^{82} +(5.81718 + 4.22643i) q^{83} +(-3.19461 + 9.83200i) q^{84} +(-1.05382 - 3.24334i) q^{85} +(4.46396 - 3.24326i) q^{86} -15.1681 q^{87} +(-1.99848 - 2.64690i) q^{88} +4.21816 q^{89} +(-13.0498 + 9.48123i) q^{90} +(-6.65875 - 20.4935i) q^{91} +(-0.853161 + 2.62576i) q^{92} +(6.35169 + 4.61477i) q^{93} +(1.07139 + 0.778412i) q^{94} +(6.42094 - 19.7616i) q^{95} +(-0.859156 - 2.64421i) q^{96} +(4.88525 - 3.54934i) q^{97} +6.82584 q^{98} +(8.98599 - 12.8590i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} - q^{5} + 2 q^{7} - 4 q^{8} - 13 q^{9} + 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{13} + 2 q^{14} - 6 q^{15} - 4 q^{16} + 4 q^{17} + 2 q^{18} + 10 q^{19} - q^{20} + 6 q^{22}+ \cdots + 65 q^{99}+O(q^{100})$ 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 - q^5 + 2 * q^7 - 4 * q^8 - 13 * q^9 + 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^13 + 2 * q^14 - 6 * q^15 - 4 * q^16 + 4 * q^17 + 2 * q^18 + 10 * q^19 - q^20 + 6 * q^22 - 24 * q^23 - 37 * q^25 + 15 * q^26 - 4 * q^27 - 13 * q^28 - 16 * q^29 - 6 * q^30 + 11 * q^31 + 16 * q^32 + 36 * q^33 - 16 * q^34 + 2 * q^36 + 5 * q^37 - 25 * q^38 - 30 * q^39 - q^40 + 4 * q^41 + 35 * q^42 + 16 * q^43 + 6 * q^44 + 6 * q^45 - 14 * q^46 - 14 * q^47 + 5 * q^48 + 2 * q^49 + 13 * q^50 - 5 * q^51 + 15 * q^52 + 5 * q^53 - 34 * q^54 + 81 * q^55 + 22 * q^56 - 12 * q^57 - 16 * q^58 + 17 * q^59 + 4 * q^60 - 30 * q^61 - 4 * q^62 + 72 * q^63 - 4 * q^64 + 6 * q^65 + 11 * q^66 + 26 * q^67 + 4 * q^68 - 73 * q^69 - 10 * q^70 - q^71 - 13 * q^72 - 43 * q^73 + 5 * q^74 + 67 * q^75 + 30 * q^76 + 40 * q^77 + 70 * q^78 - 13 * q^79 - q^80 - 39 * q^81 - 21 * q^82 - 24 * q^83 - 35 * q^84 + q^85 + 26 * q^86 - 92 * q^87 - 4 * q^88 + 24 * q^89 - 29 * q^90 - 10 * q^91 + 26 * q^92 + 11 * q^93 - 4 * q^94 - 39 * q^95 + 5 * q^96 + 3 * q^97 + 2 * q^98 + 65 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$ .

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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

)

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.859156	−	2.64421i	−0.496034	−	1.52664i	−0.815339	−	0.578983i	$-0.803450\pi$
$3$	−0.859156	−	2.64421i	−0.496034	−	1.52664i	0.319306	−	0.947652i	$-0.396550\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.75895	−	2.00449i	−1.23384	−	0.896436i	−0.236666	−	0.971591i	$-0.576055\pi$
$5$	−2.75895	−	2.00449i	−1.23384	−	0.896436i	−0.997172	+	0.0751552i	$0.976055\pi$
$6$	2.24930	+	1.63421i	0.918273	+	0.667164i
$7$	1.14902	−	3.53632i	0.434289	−	1.33661i	−0.459524	−	0.888165i	$-0.651980\pi$
$7$	1.14902	−	3.53632i	0.434289	−	1.33661i	0.893813	−	0.448440i	$-0.148020\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−3.82665	+	2.78022i	−1.27555	+	0.926740i
$10$	3.41024			1.07841
$11$	−3.13492	+	1.08273i	−0.945213	+	0.326454i
$11$	−3.13492	+	1.08273i	−0.945213	+	0.326454i
$12$	−2.78029			−0.802600
$13$	4.68837	−	3.40630i	1.30032	−	0.944739i	0.300363	−	0.953825i	$-0.402892\pi$
$13$	4.68837	−	3.40630i	1.30032	−	0.944739i	0.999959	+	0.00908644i	$0.00289234\pi$
$14$	1.14902	+	3.53632i	0.307089	+	0.945122i
$15$	−2.92993	+	9.01740i	−0.756505	+	2.32828i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$18$	1.46165	−	4.49849i	0.344514	−	1.06030i
$19$	1.88284	+	5.79478i	0.431953	+	1.32941i	0.896177	+	0.443696i	$0.146333\pi$
$19$	1.88284	+	5.79478i	0.431953	+	1.32941i	−0.464225	+	0.885717i	$0.653667\pi$
$20$	−2.75895	+	2.00449i	−0.616919	+	0.448218i
$21$	−10.3380			−2.25593
$22$	1.89979	−	2.71860i	0.405037	−	0.579608i
$23$	−2.76089			−0.575685			−0.287842	−	0.957678i	$-0.592938\pi$
$23$	−2.76089			−0.575685			−0.287842	+	0.957678i	$0.592938\pi$
$24$	2.24930	−	1.63421i	0.459136	−	0.333582i
$25$	2.04871	+	6.30528i	0.409742	+	1.26106i
$26$	−1.79080	+	5.51152i	−0.351205	+	1.08090i
$27$	3.89127	+	2.82718i	0.748876	+	0.544090i
$28$	−3.00818	−	2.18557i	−0.568492	−	0.413034i
$29$	1.68587	−	5.18858i	0.313058	−	0.963494i	−0.663488	−	0.748187i	$-0.730925\pi$
$29$	1.68587	−	5.18858i	0.313058	−	0.963494i	0.976546	−	0.215307i	$-0.0690754\pi$
$30$	−2.92993	−	9.01740i	−0.534930	−	1.64634i
$31$	−2.28455	+	1.65982i	−0.410317	+	0.298112i	−0.773730	−	0.633516i	$-0.781611\pi$
$31$	−2.28455	+	1.65982i	−0.410317	+	0.298112i	0.363413	+	0.931628i	$0.381611\pi$
$32$	1.00000			0.176777
$33$	5.55634	+	7.35915i	0.967234	+	1.28106i
$34$	−1.00000			−0.171499
$35$	−10.2586	+	7.45332i	−1.73402	+	1.25984i
$36$	1.46165	+	4.49849i	0.243608	+	0.749749i
$37$	1.16150	−	3.57473i	0.190950	−	0.587683i	−0.809050	−	0.587739i	$-0.800018\pi$
$37$	1.16150	−	3.57473i	0.190950	−	0.587683i	1.00000		5.67107e-5i	$1.80516e-5\pi$
$38$	−4.92933	−	3.58137i	−0.799644	−	0.580975i
$39$	−13.0350	−	9.47050i	−2.08727	−	1.51649i
$40$	1.05382	−	3.24334i	0.166624	−	0.512816i
$41$	2.21533	+	6.81807i	0.345976	+	1.06480i	0.961059	+	0.276342i	$0.0891222\pi$
$41$	2.21533	+	6.81807i	0.345976	+	1.06480i	−0.615084	+	0.788462i	$0.710878\pi$
$42$	8.36360	−	6.07651i	1.29053	−	0.937625i
$43$	−5.51776			−0.841450			−0.420725	−	0.907188i	$-0.638224\pi$
$43$	−5.51776			−0.841450			−0.420725	+	0.907188i	$0.638224\pi$
$44$	0.0609919	+	3.31606i	0.00919487	+	0.499915i
$45$	16.1304			2.40458
$46$	2.23360	−	1.62281i	0.329327	−	0.239270i
$47$	−0.409236	−	1.25950i	−0.0596932	−	0.183717i	0.916763	−	0.399431i	$-0.130792\pi$
$47$	−0.409236	−	1.25950i	−0.0596932	−	0.183717i	−0.976457	+	0.215714i	$0.930792\pi$
$48$	−0.859156	+	2.64421i	−0.124008	+	0.381659i
$49$	−5.52222	−	4.01213i	−0.788889	−	0.573161i
$50$	−5.36360	−	3.89688i	−0.758527	−	0.551102i
$51$	0.859156	−	2.64421i	0.120306	−	0.370263i
$52$	−1.79080	−	5.51152i	−0.248339	−	0.764310i
$53$	6.01114	−	4.36735i	0.825693	−	0.599901i	−0.0926446	−	0.995699i	$-0.529532\pi$
$53$	6.01114	−	4.36735i	0.825693	−	0.599901i	0.918338	+	0.395798i	$0.129532\pi$
$54$	−4.80988			−0.654542
$55$	10.8194	+	3.29673i	1.45889	+	0.444531i
$56$	3.71831			0.496880
$57$	13.7050	−	9.95724i	1.81527	−	1.31887i
$58$	1.68587	+	5.18858i	0.221366	+	0.681293i
$59$	4.03643	−	12.4229i	0.525498	−	1.61732i	−0.237830	−	0.971307i	$-0.576436\pi$
$59$	4.03643	−	12.4229i	0.525498	−	1.61732i	0.763328	−	0.646011i	$-0.223564\pi$
$60$	7.67066	+	5.57306i	0.990278	+	0.719479i
$61$	−8.66153	−	6.29297i	−1.10899	−	0.805732i	−0.126490	−	0.991968i	$-0.540371\pi$
$61$	−8.66153	−	6.29297i	−1.10899	−	0.805732i	−0.982505	+	0.186236i	$0.940371\pi$
$62$	0.872619	−	2.68564i	0.110823	−	0.341077i
$63$	5.43486	+	16.7268i	0.684729	+	2.10738i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−19.7629			−2.45128
$66$	−8.82077	−	2.68774i	−1.08576	−	0.330838i
$67$	−6.57919			−0.803776			−0.401888	−	0.915689i	$-0.631646\pi$
$67$	−6.57919			−0.803776			−0.401888	+	0.915689i	$0.631646\pi$
$68$	0.809017	−	0.587785i	0.0981077	−	0.0712794i
$69$	2.37203	+	7.30036i	0.285559	+	0.878860i
$70$	3.91844	−	12.0597i	0.468344	−	1.44141i
$71$	3.93847	+	2.86146i	0.467410	+	0.339593i	0.796431	−	0.604729i	$-0.206719\pi$
$71$	3.93847	+	2.86146i	0.467410	+	0.339593i	−0.329021	+	0.944323i	$0.606719\pi$
$72$	−3.82665	−	2.78022i	−0.450974	−	0.327652i
$73$	−0.842658	+	2.59343i	−0.0986256	+	0.303539i	−0.988182	−	0.153288i	$-0.951014\pi$
$73$	−0.842658	+	2.59343i	−0.0986256	+	0.303539i	0.889556	+	0.456826i	$0.151014\pi$
$74$	1.16150	+	3.57473i	0.135022	+	0.415554i
$75$	14.9123	−	10.8344i	1.72193	−	1.25105i
$76$	6.09299			0.698914
$77$	0.226787	+	12.3302i	0.0258448	+	1.40515i
$78$	16.1122			1.82434
$79$	−1.33410	+	0.969278i	−0.150098	+	0.109052i	−0.660299	−	0.751002i	$-0.729571\pi$
$79$	−1.33410	+	0.969278i	−0.150098	+	0.109052i	0.510202	+	0.860055i	$0.329571\pi$
$80$	1.05382	+	3.24334i	0.117821	+	0.362616i
$81$	−0.252510	+	0.777147i	−0.0280567	+	0.0863497i
$82$	−5.79980	−	4.21380i	−0.640480	−	0.465336i
$83$	5.81718	+	4.22643i	0.638518	+	0.463910i	0.859341	−	0.511403i	$-0.170874\pi$
$83$	5.81718	+	4.22643i	0.638518	+	0.463910i	−0.220823	+	0.975314i	$0.570874\pi$
$84$	−3.19461	+	9.83200i	−0.348560	+	1.07276i
$85$	−1.05382	−	3.24334i	−0.114303	−	0.351789i
$86$	4.46396	−	3.24326i	0.481361	−	0.349729i
$87$	−15.1681			−1.62619
$88$	−1.99848	−	2.64690i	−0.213038	−	0.282161i
$89$	4.21816			0.447124			0.223562	−	0.974690i	$-0.428232\pi$
$89$	4.21816			0.447124			0.223562	+	0.974690i	$0.428232\pi$
$90$	−13.0498	+	9.48123i	−1.37557	+	0.999410i
$91$	−6.65875	−	20.4935i	−0.698027	−	2.14831i
$92$	−0.853161	+	2.62576i	−0.0889481	+	0.273754i
$93$	6.35169	+	4.61477i	0.658640	+	0.478530i
$94$	1.07139	+	0.778412i	0.110506	+	0.0802871i
$95$	6.42094	−	19.7616i	0.658774	−	2.02750i
$96$	−0.859156	−	2.64421i	−0.0876872	−	0.269874i
$97$	4.88525	−	3.54934i	0.496022	−	0.360381i	−0.311473	−	0.950255i	$-0.600822\pi$
$97$	4.88525	−	3.54934i	0.496022	−	0.360381i	0.807496	+	0.589874i	$0.200822\pi$
$98$	6.82584			0.689514
$99$	8.98599	−	12.8590i	0.903126	−	1.29238i
$100$	6.62977			0.662977
$101$	−7.40803	+	5.38225i	−0.737127	+	0.535554i	−0.891810	−	0.452410i	$-0.850564\pi$
$101$	−7.40803	+	5.38225i	−0.737127	+	0.535554i	0.154683	+	0.987964i	$0.450564\pi$
$102$	0.859156	+	2.64421i	0.0850691	+	0.261816i
$103$	−2.58351	+	7.95122i	−0.254561	+	0.783457i	0.739355	+	0.673315i	$0.235130\pi$
$103$	−2.58351	+	7.95122i	−0.254561	+	0.783457i	−0.993916	+	0.110142i	$0.964870\pi$
$104$	4.68837	+	3.40630i	0.459733	+	0.334016i
$105$	28.5219	+	20.7224i	2.78345	+	2.02230i
$106$	−2.29605	+	7.06651i	−0.223012	+	0.686360i
$107$	−4.06505	−	12.5109i	−0.392983	−	1.20948i	−0.930521	−	0.366238i	$-0.880646\pi$
$107$	−4.06505	−	12.5109i	−0.392983	−	1.20948i	0.537538	−	0.843239i	$-0.319354\pi$
$108$	3.89127	−	2.82718i	0.374438	−	0.272045i
$109$	13.7399			1.31605			0.658023	−	0.752998i	$-0.271393\pi$
$109$	13.7399			1.31605			0.658023	+	0.752998i	$0.271393\pi$
$110$	−10.6908	+	3.69236i	−1.01933	+	0.352053i
$111$	−10.4503			−0.991895
$112$	−3.00818	+	2.18557i	−0.284246	+	0.206517i
$113$	2.28821	+	7.04238i	0.215257	+	0.662492i	0.999135	+	0.0415777i	$0.0132384\pi$
$113$	2.28821	+	7.04238i	0.215257	+	0.662492i	−0.783879	+	0.620914i	$0.786762\pi$
$114$	−5.23483	+	16.1111i	−0.490287	+	1.50895i
$115$	7.61713	+	5.53417i	0.710301	+	0.516064i
$116$	−4.41367	−	3.20672i	−0.409799	−	0.297736i
$117$	−8.47047	+	26.0694i	−0.783095	+	2.41012i
$118$	4.03643	+	12.4229i	0.371584	+	1.14362i
$119$	3.00818	−	2.18557i	0.275759	−	0.200351i
$120$	−9.48146			−0.865535
$121$	8.65541	−	6.78852i	0.786855	−	0.617138i
$122$	10.7062			0.969297
$123$	16.1251	−	11.7156i	1.45395	−	1.05636i
$124$	0.872619	+	2.68564i	0.0783635	+	0.241178i
$125$	1.71749	−	5.28588i	0.153617	−	0.472784i
$126$	−14.2287	−	10.3377i	−1.26759	−	0.920958i
$127$	−0.684912	−	0.497617i	−0.0607761	−	0.0441564i	0.556982	−	0.830524i	$-0.311959\pi$
$127$	−0.684912	−	0.497617i	−0.0607761	−	0.0441564i	−0.617758	+	0.786368i	$0.711959\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.74061	+	14.5901i	0.417388	+	1.28459i
$130$	15.9885	−	11.6163i	1.40228	−	1.01882i
$131$	−14.1686			−1.23791			−0.618957	−	0.785425i	$-0.712444\pi$
$131$	−14.1686			−1.23791			−0.618957	+	0.785425i	$0.712444\pi$
$132$	8.71597	−	3.01029i	0.758628	−	0.262012i
$133$	22.6556			1.96449
$134$	5.32267	−	3.86715i	0.459809	−	0.334071i
$135$	−5.06876	−	15.6000i	−0.436250	−	1.34264i
$136$	−0.309017	+	0.951057i	−0.0264980	+	0.0815524i
$137$	−18.1135	−	13.1602i	−1.54754	−	1.12435i	−0.945377	−	0.325979i	$-0.894306\pi$
$137$	−18.1135	−	13.1602i	−1.54754	−	1.12435i	−0.602162	−	0.798374i	$-0.705694\pi$
$138$	−6.21006	−	4.51187i	−0.528635	−	0.384076i
$139$	2.90956	−	8.95470i	0.246785	−	0.759528i	−0.748552	−	0.663076i	$-0.769251\pi$
$139$	2.90956	−	8.95470i	0.246785	−	0.759528i	0.995338	−	0.0964517i	$-0.0307493\pi$
$140$	3.91844	+	12.0597i	0.331169	+	1.01923i
$141$	−2.97878	+	2.16421i	−0.250858	+	0.182259i
$142$	−4.86821			−0.408531
$143$	−11.0096	+	15.7547i	−0.920666	+	1.31747i
$144$	4.72999			0.394166
$145$	−15.0517	+	10.9357i	−1.24997	+	0.908159i
$146$	−0.842658	−	2.59343i	−0.0697389	−	0.214634i
$147$	−5.86446	+	18.0490i	−0.483693	+	1.48865i
$148$	−3.04085	−	2.20931i	−0.249956	−	0.181604i
$149$	−14.9560	−	10.8662i	−1.22524	−	0.890191i	−0.228718	−	0.973493i	$-0.573453\pi$
$149$	−14.9560	−	10.8662i	−1.22524	−	0.890191i	−0.996524	+	0.0833021i	$0.973453\pi$
$150$	−5.69600	+	17.5305i	−0.465077	+	1.43136i
$151$	−6.86950	−	21.1421i	−0.559032	−	1.72052i	−0.685050	−	0.728496i	$-0.740220\pi$
$151$	−6.86950	−	21.1421i	−0.559032	−	1.72052i	0.126018	−	0.992028i	$-0.459780\pi$
$152$	−4.92933	+	3.58137i	−0.399822	+	0.290488i
$153$	−4.72999			−0.382397
$154$	−7.43096	−	9.84201i	−0.598804	−	0.793091i
$155$	9.63003			0.773503
$156$	−13.0350	+	9.47050i	−1.04364	+	0.758247i
$157$	4.36953	+	13.4480i	0.348727	+	1.07327i	0.959558	+	0.281510i	$0.0908352\pi$
$157$	4.36953	+	13.4480i	0.348727	+	1.07327i	−0.610832	+	0.791760i	$0.709165\pi$
$158$	0.509579	−	1.56832i	0.0405400	−	0.124769i
$159$	−16.7127	−	12.1425i	−1.32540	−	0.962961i
$160$	−2.75895	−	2.00449i	−0.218114	−	0.158469i
$161$	−3.17232	+	9.76339i	−0.250014	+	0.769463i
$162$	−0.252510	−	0.777147i	−0.0198391	−	0.0610585i
$163$	−11.1459	+	8.09795i	−0.873012	+	0.634280i	−0.931393	−	0.364014i	$-0.881406\pi$
$163$	−11.1459	+	8.09795i	−0.873012	+	0.634280i	0.0583817	+	0.998294i	$0.481406\pi$
$164$	7.16894			0.559800
$165$	−0.578292	−	31.4411i	−0.0450200	−	2.44769i
$166$	−7.19042			−0.558085
$167$	−0.589757	+	0.428484i	−0.0456368	+	0.0331571i	−0.610370	−	0.792117i	$-0.708979\pi$
$167$	−0.589757	+	0.428484i	−0.0456368	+	0.0331571i	0.564733	+	0.825274i	$0.308979\pi$
$168$	−3.19461	−	9.83200i	−0.246469	−	0.758555i
$169$	6.36073	−	19.5763i	0.489287	−	1.50587i
$170$	2.75895	+	2.00449i	0.211601	+	0.153737i
$171$	−23.3157	−	16.9399i	−1.78300	−	1.29542i
$172$	−1.70508	+	5.24770i	−0.130011	+	0.400133i
$173$	−3.99795	−	12.3044i	−0.303959	−	0.935489i	−0.980064	−	0.198684i	$-0.936333\pi$
$173$	−3.99795	−	12.3044i	−0.303959	−	0.935489i	0.676105	−	0.736805i	$-0.263667\pi$
$174$	12.2713	−	8.91559i	0.930282	−	0.675889i
$175$	24.6515			1.86348
$176$	3.17261	+	0.966713i	0.239145	+	0.0728688i
$177$	−36.3166			−2.72972
$178$	−3.41256	+	2.47937i	−0.255782	+	0.185837i
$179$	0.355520	+	1.09418i	0.0265728	+	0.0817827i	0.963463	−	0.267840i	$-0.0863098\pi$
$179$	0.355520	+	1.09418i	0.0265728	+	0.0817827i	−0.936891	+	0.349623i	$0.886310\pi$
$180$	4.98458	−	15.3410i	0.371529	−	1.14345i
$181$	−1.87984	−	1.36578i	−0.139727	−	0.101518i	0.515726	−	0.856754i	$-0.327522\pi$
$181$	−1.87984	−	1.36578i	−0.139727	−	0.101518i	−0.655453	+	0.755236i	$0.727522\pi$
$182$	17.4328	+	12.6657i	1.29221	+	0.938844i
$183$	−9.19832	+	28.3095i	−0.679960	+	2.09270i
$184$	−0.853161	−	2.62576i	−0.0628958	−	0.193573i
$185$	−10.3700	+	7.53428i	−0.762421	+	0.553931i
$186$	−7.85112			−0.575672
$187$	−3.17261	−	0.966713i	−0.232004	−	0.0706931i
$188$	−1.32431			−0.0965855
$189$	14.4690	−	10.5123i	1.05246	−	0.764659i
$190$	6.42094	+	19.7616i	0.465824	+	1.43366i
$191$	−0.457712	+	1.40869i	−0.0331189	+	0.101929i	−0.966249	−	0.257608i	$-0.917066\pi$
$191$	−0.457712	+	1.40869i	−0.0331189	+	0.101929i	0.933131	+	0.359538i	$0.117066\pi$
$192$	2.24930	+	1.63421i	0.162329	+	0.117939i
$193$	6.53465	+	4.74770i	0.470374	+	0.341747i	0.797587	−	0.603204i	$-0.206109\pi$
$193$	6.53465	+	4.74770i	0.470374	+	0.341747i	−0.327213	+	0.944951i	$0.606109\pi$
$194$	−1.86600	+	5.74296i	−0.133971	+	0.412320i
$195$	16.9794	+	52.2572i	1.21592	+	3.74222i
$196$	−5.52222	+	4.01213i	−0.394444	+	0.286581i
$197$	18.6196			1.32659			0.663297	−	0.748356i	$-0.269157\pi$
$197$	18.6196			1.32659			0.663297	+	0.748356i	$0.269157\pi$
$198$	0.288491	+	15.6850i	0.0205022	+	1.11468i
$199$	−25.0238			−1.77389			−0.886945	−	0.461875i	$-0.847177\pi$
$199$	−25.0238			−1.77389			−0.886945	+	0.461875i	$0.847177\pi$
$200$	−5.36360	+	3.89688i	−0.379263	+	0.275551i
$201$	5.65255	+	17.3968i	0.398700	+	1.22707i
$202$	2.82962	−	8.70866i	0.199091	−	0.612739i
$203$	−16.4114	−	11.9236i	−1.15185	−	0.836871i
$204$	−2.24930	−	1.63421i	−0.157482	−	0.114418i
$205$	7.55480	−	23.2513i	0.527650	−	1.62394i
$206$	−2.58351	−	7.95122i	−0.180002	−	0.553988i
$207$	10.5649	−	7.67587i	0.734313	−	0.533510i
$208$	−5.79515			−0.401821
$209$	−12.1767	−	16.1276i	−0.842280	−	1.11557i
$210$	−35.2550			−2.43283
$211$	−5.10622	+	3.70989i	−0.351527	+	0.255399i	−0.749509	−	0.661994i	$-0.769711\pi$
$211$	−5.10622	+	3.70989i	−0.351527	+	0.255399i	0.397982	+	0.917393i	$0.369711\pi$
$212$	−2.29605	−	7.06651i	−0.157693	−	0.485330i
$213$	4.18255	−	12.8726i	0.286584	−	0.882015i
$214$	10.6424	+	7.73218i	0.727502	+	0.528561i
$215$	15.2232	+	11.0603i	1.03821	+	0.754306i
$216$	−1.48633	+	4.57447i	−0.101132	+	0.311253i
$217$	3.24467	+	9.98606i	0.220262	+	0.677898i
$218$	−11.1158	+	8.07613i	−0.752859	+	0.546984i
$219$	7.58156			0.512314
$220$	6.47875	−	9.27110i	0.436797	−	0.625057i
$221$	5.79515			0.389824
$222$	8.45444	−	6.14251i	0.567425	−	0.412258i
$223$	−5.33590	−	16.4222i	−0.357319	−	1.09971i	−0.954653	−	0.297721i	$-0.903773\pi$
$223$	−5.33590	−	16.4222i	−0.357319	−	1.09971i	0.597334	−	0.801992i	$-0.296227\pi$
$224$	1.14902	−	3.53632i	0.0767722	−	0.236281i
$225$	−25.3698	−	18.4322i	−1.69132	−	1.22881i
$226$	−5.99061	−	4.35243i	−0.398489	−	0.289519i
$227$	2.92073	−	8.98908i	0.193856	−	0.596626i	−0.806132	−	0.591735i	$-0.798443\pi$
$227$	2.92073	−	8.98908i	0.193856	−	0.596626i	0.999988	−	0.00489107i	$-0.00155688\pi$
$228$	−5.23483	−	16.1111i	−0.346685	−	1.06699i
$229$	8.36115	−	6.07473i	0.552521	−	0.401430i	−0.276193	−	0.961102i	$-0.589073\pi$
$229$	8.36115	−	6.07473i	0.552521	−	0.401430i	0.828714	+	0.559672i	$0.189073\pi$
$230$	−9.41530			−0.620826
$231$	32.4087	−	11.1932i	2.13233	−	0.736458i
$232$	5.45559			0.358177
$233$	1.51471	−	1.10050i	0.0992320	−	0.0720963i	−0.537063	−	0.843542i	$-0.680466\pi$
$233$	1.51471	−	1.10050i	0.0992320	−	0.0720963i	0.636295	+	0.771446i	$0.280466\pi$
$234$	−8.47047	−	26.0694i	−0.553732	−	1.70421i
$235$	−1.39559	+	4.29520i	−0.0910385	+	0.280188i
$236$	−10.5675	−	7.67775i	−0.687886	−	0.499779i
$237$	3.70917	+	2.69487i	0.240936	+	0.175051i
$238$	−1.14902	+	3.53632i	−0.0744800	+	0.229226i
$239$	6.15962	+	18.9574i	0.398432	+	1.22625i	0.926256	+	0.376895i	$0.123008\pi$
$239$	6.15962	+	18.9574i	0.398432	+	1.22625i	−0.527824	+	0.849354i	$0.676992\pi$
$240$	7.67066	−	5.57306i	0.495139	−	0.359740i
$241$	7.25414			0.467280			0.233640	−	0.972323i	$-0.424936\pi$
$241$	7.25414			0.467280			0.233640	+	0.972323i	$0.424936\pi$
$242$	−3.01218	+	10.5795i	−0.193630	+	0.680079i
$243$	16.7015			1.07140
$244$	−8.66153	+	6.29297i	−0.554497	+	0.402866i
$245$	7.19323	+	22.1385i	0.459559	+	1.41438i
$246$	−6.15924	+	18.9562i	−0.392699	+	1.20860i
$247$	28.5662	+	20.7546i	1.81763	+	1.32058i
$248$	−2.28455	−	1.65982i	−0.145069	−	0.105399i
$249$	6.17770	−	19.0130i	0.391496	−	1.20490i
$250$	1.71749	+	5.28588i	0.108623	+	0.334309i
$251$	22.2116	−	16.1377i	1.40198	−	1.01860i	0.407557	−	0.913180i	$-0.366381\pi$
$251$	22.2116	−	16.1377i	1.40198	−	1.01860i	0.994428	−	0.105422i	$-0.0336193\pi$
$252$	17.5876			1.10791
$253$	8.65515	−	2.98929i	0.544144	−	0.187935i
$254$	0.846597			0.0531202
$255$	−7.67066	+	5.57306i	−0.480355	+	0.348999i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.63218	+	14.2564i	−0.288948	+	0.889290i	0.696240	+	0.717809i	$0.254855\pi$
$257$	−4.63218	+	14.2564i	−0.288948	+	0.889290i	−0.985188	+	0.171480i	$0.945145\pi$
$258$	−12.4111	−	9.01718i	−0.772680	−	0.561385i
$259$	−11.3068	−	8.21489i	−0.702572	−	0.510449i
$260$	−6.10707	+	18.7956i	−0.378744	+	1.16565i
$261$	7.97416	+	24.5419i	0.493588	+	1.51911i
$262$	11.4626	−	8.32808i	0.708163	−	0.514510i
$263$	8.23668			0.507895			0.253948	−	0.967218i	$-0.418271\pi$
$263$	8.23668			0.507895			0.253948	+	0.967218i	$0.418271\pi$
$264$	−5.28196	+	7.55849i	−0.325082	+	0.465193i
$265$	−25.3387			−1.55654
$266$	−18.3288	+	13.3167i	−1.12381	+	0.816496i
$267$	−3.62406	−	11.1537i	−0.221789	−	0.682595i
$268$	−2.03308	+	6.25718i	−0.124190	+	0.382218i
$269$	24.5155	+	17.8116i	1.49474	+	1.08599i	0.972419	+	0.233241i	$0.0749332\pi$
$269$	24.5155	+	17.8116i	1.49474	+	1.08599i	0.522320	+	0.852750i	$0.325067\pi$
$270$	13.2702	+	9.64136i	0.807598	+	0.586754i
$271$	−0.836260	+	2.57374i	−0.0507992	+	0.156344i	−0.973238	−	0.229799i	$-0.926193\pi$
$271$	−0.836260	+	2.57374i	−0.0507992	+	0.156344i	0.922439	+	0.386143i	$0.126193\pi$
$272$	−0.309017	−	0.951057i	−0.0187369	−	0.0576663i
$273$	−48.4683	+	35.2143i	−2.93343	+	2.13126i
$274$	22.3895			1.35260
$275$	−13.2494	−	17.5483i	−0.798971	−	1.05821i
$276$	7.67605			0.462044
$277$	−7.51962	+	5.46333i	−0.451810	+	0.328259i	−0.790310	−	0.612707i	$-0.790081\pi$
$277$	−7.51962	+	5.46333i	−0.451810	+	0.328259i	0.338500	+	0.940966i	$0.390081\pi$
$278$	2.90956	+	8.95470i	0.174504	+	0.537067i
$279$	4.12748	−	12.7031i	0.247106	−	0.760514i
$280$	−10.2586	−	7.45332i	−0.613070	−	0.445421i
$281$	−10.6999	−	7.77390i	−0.638300	−	0.463752i	0.220966	−	0.975282i	$-0.429079\pi$
$281$	−10.6999	−	7.77390i	−0.638300	−	0.463752i	−0.859266	+	0.511530i	$0.829079\pi$
$282$	1.13779	−	3.50176i	0.0677545	−	0.208527i
$283$	6.78133	+	20.8708i	0.403108	+	1.24064i	0.922464	+	0.386082i	$0.126172\pi$
$283$	6.78133	+	20.8708i	0.403108	+	1.24064i	−0.519356	+	0.854558i	$0.673828\pi$
$284$	3.93847	−	2.86146i	0.233705	−	0.169797i
$285$	−57.7704			−3.42203
$286$	−0.353457	−	19.2171i	−0.0209004	−	1.13633i
$287$	26.6564			1.57348
$288$	−3.82665	+	2.78022i	−0.225487	+	0.163826i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	5.74923	−	17.6943i	0.337606	−	1.03905i
$291$	−13.5824	−	9.86819i	−0.796214	−	0.578484i
$292$	2.20611	+	1.60283i	0.129103	+	0.0937986i
$293$	4.24383	−	13.0612i	0.247927	−	0.763041i	−0.747214	−	0.664583i	$-0.768609\pi$
$293$	4.24383	−	13.0612i	0.247927	−	0.763041i	0.995141	−	0.0984579i	$-0.0313910\pi$
$294$	−5.86446	−	18.0490i	−0.342022	−	1.05264i
$295$	−36.0378	+	26.1830i	−2.09820	+	1.52443i
$296$	3.75870			0.218470
$297$	−15.2599	−	4.64977i	−0.885468	−	0.269807i
$298$	18.4866			1.07090
$299$	−12.9441	+	9.40442i	−0.748575	+	0.543871i
$300$	−5.69600	−	17.5305i	−0.328859	−	1.01212i
$301$	−6.34002	+	19.5126i	−0.365433	+	1.12469i
$302$	17.9846	+	13.0666i	1.03490	+	0.751896i
$303$	20.5964	+	14.9642i	1.18323	+	0.859671i
$304$	1.88284	−	5.79478i	0.107988	−	0.332353i
$305$	11.2825	+	34.7239i	0.646033	+	1.98829i
$306$	3.82665	−	2.78022i	0.218755	−	0.158935i
$307$	−7.04440			−0.402045			−0.201023	−	0.979587i	$-0.564427\pi$
$307$	−7.04440			−0.402045			−0.201023	+	0.979587i	$0.564427\pi$
$308$	11.7968	+	3.59454i	0.672183	+	0.204818i
$309$	23.2443			1.32232
$310$	−7.79086	+	5.66039i	−0.442491	+	0.321489i
$311$	5.51561	+	16.9753i	0.312761	+	0.962581i	0.976666	+	0.214763i	$0.0688981\pi$
$311$	5.51561	+	16.9753i	0.312761	+	0.962581i	−0.663905	+	0.747817i	$0.731102\pi$
$312$	4.97894	−	15.3236i	0.281877	−	0.867528i
$313$	5.60729	+	4.07393i	0.316943	+	0.230272i	0.734870	−	0.678208i	$-0.237243\pi$
$313$	5.60729	+	4.07393i	0.316943	+	0.230272i	−0.417927	+	0.908481i	$0.637243\pi$
$314$	−11.4396	−	8.31134i	−0.645573	−	0.469036i
$315$	18.5342	−	57.0425i	1.04428	−	3.21398i
$316$	0.509579	+	1.56832i	0.0286661	+	0.0882251i
$317$	18.7330	−	13.6103i	1.05215	−	0.764431i	0.0795294	−	0.996833i	$-0.474658\pi$
$317$	18.7330	−	13.6103i	1.05215	−	0.764431i	0.972620	+	0.232401i	$0.0746583\pi$
$318$	20.6580			1.15844
$319$	0.332747	+	18.0911i	0.0186302	+	1.01291i
$320$	3.41024			0.190638
$321$	−29.5890	+	21.4977i	−1.65150	+	1.19988i
$322$	−3.17232	−	9.76339i	−0.176786	−	0.544092i
$323$	−1.88284	+	5.79478i	−0.104764	+	0.322430i
$324$	0.661081	+	0.480303i	0.0367267	+	0.0266835i
$325$	31.0828	+	22.5830i	1.72417	+	1.25268i
$326$	4.25734	−	13.1028i	0.235792	−	0.725694i
$327$	−11.8047	−	36.3313i	−0.652804	−	2.00912i
$328$	−5.79980	+	4.21380i	−0.320240	+	0.232668i
$329$	−4.92421			−0.271481
$330$	18.9485	+	25.0965i	1.04308	+	1.38152i
$331$	20.9563			1.15186			0.575931	−	0.817498i	$-0.304640\pi$
$331$	20.9563			1.15186			0.575931	+	0.817498i	$0.304640\pi$
$332$	5.81718	−	4.22643i	0.319259	−	0.231955i
$333$	5.49389	+	16.9085i	0.301064	+	0.926578i
$334$	0.225267	−	0.693301i	0.0123261	−	0.0379357i
$335$	18.1516	+	13.1879i	0.991729	+	0.720533i
$336$	8.36360	+	6.07651i	0.456272	+	0.331501i
$337$	9.51475	−	29.2834i	0.518302	−	1.59517i	−0.258892	−	0.965906i	$-0.583357\pi$
$337$	9.51475	−	29.2834i	0.518302	−	1.59517i	0.777193	−	0.629262i	$-0.216643\pi$
$338$	6.36073	+	19.5763i	0.345978	+	1.06481i
$339$	16.6556	−	12.1010i	0.904609	−	0.657237i
$340$	−3.41024			−0.184946
$341$	5.36473	−	7.67694i	0.290516	−	0.415729i
$342$	28.8198			1.55840
$343$	0.523900	−	0.380636i	0.0282879	−	0.0205524i
$344$	−1.70508	−	5.24770i	−0.0919318	−	0.282937i
$345$	8.08921	−	24.8960i	0.435508	−	1.34036i
$346$	10.4668	+	7.60456i	0.562697	+	0.408824i
$347$	−10.9364	−	7.94576i	−0.587097	−	0.426551i	0.254179	−	0.967157i	$-0.418195\pi$
$347$	−10.9364	−	7.94576i	−0.587097	−	0.426551i	−0.841276	+	0.540607i	$0.818195\pi$
$348$	−4.68720	+	14.4257i	−0.251260	+	0.773300i
$349$	2.89049	+	8.89602i	0.154725	+	0.476193i	0.998133	−	0.0610799i	$-0.0194544\pi$
$349$	2.89049	+	8.89602i	0.154725	+	0.476193i	−0.843408	+	0.537273i	$0.819454\pi$
$350$	−19.9435	+	14.4898i	−1.06603	+	0.774513i
$351$	27.8740			1.48780
$352$	−3.13492	+	1.08273i	−0.167092	+	0.0577095i
$353$	9.44716			0.502822			0.251411	−	0.967880i	$-0.419105\pi$
$353$	9.44716			0.502822			0.251411	+	0.967880i	$0.419105\pi$
$354$	29.3807	−	21.3463i	1.56157	−	1.13454i
$355$	−5.13024	−	15.7893i	−0.272285	−	0.838006i
$356$	1.30348	−	4.01171i	0.0690844	−	0.212620i
$357$	−8.36360	−	6.07651i	−0.442648	−	0.321603i
$358$	−0.930764	−	0.676239i	−0.0491924	−	0.0357404i
$359$	−2.85209	+	8.77784i	−0.150528	+	0.463277i	−0.997680	−	0.0680729i	$-0.978315\pi$
$359$	−2.85209	+	8.77784i	−0.150528	+	0.463277i	0.847153	+	0.531350i	$0.178315\pi$
$360$	4.98458	+	15.3410i	0.262710	+	0.808539i
$361$	−14.6631	+	10.6533i	−0.771740	+	0.560702i
$362$	2.32361			0.122126
$363$	−25.3866	−	17.0543i	−1.33245	−	0.895119i
$364$	−21.5482			−1.12943
$365$	7.52336	−	5.46604i	0.393791	−	0.286106i
$366$	−9.19832	−	28.3095i	−0.480804	−	1.47976i
$367$	−3.86737	+	11.9025i	−0.201875	+	0.621307i	0.797952	+	0.602721i	$0.205917\pi$
$367$	−3.86737	+	11.9025i	−0.201875	+	0.621307i	−0.999827	+	0.0185867i	$0.994083\pi$
$368$	2.23360	+	1.62281i	0.116435	+	0.0845947i
$369$	−27.4330	−	19.9312i	−1.42810	−	1.03758i
$370$	3.96100	−	12.1907i	0.205923	−	0.633765i
$371$	−8.53743	−	26.2755i	−0.443241	−	1.36416i
$372$	6.35169	−	4.61477i	0.329320	−	0.239265i
$373$	3.73887			0.193591			0.0967956	−	0.995304i	$-0.469141\pi$
$373$	3.73887			0.193591			0.0967956	+	0.995304i	$0.469141\pi$
$374$	3.13492	−	1.08273i	0.162103	−	0.0559865i
$375$	−15.4526			−0.797968
$376$	1.07139	−	0.778412i	0.0552529	−	0.0401436i
$377$	−9.76987	−	30.0686i	−0.503174	−	1.54861i
$378$	−5.52665	+	17.0093i	−0.284260	+	0.874863i
$379$	−2.09865	−	1.52476i	−0.107800	−	0.0783215i	0.532579	−	0.846380i	$-0.321223\pi$
$379$	−2.09865	−	1.52476i	−0.107800	−	0.0783215i	−0.640379	+	0.768059i	$0.721223\pi$
$380$	−16.8102	−	12.2133i	−0.862347	−	0.626532i
$381$	−0.727359	+	2.23858i	−0.0372637	+	0.114686i
$382$	−0.457712	−	1.40869i	−0.0234186	−	0.0720750i
$383$	19.3992	−	14.0944i	0.991253	−	0.720188i	0.0310581	−	0.999518i	$-0.490112\pi$
$383$	19.3992	−	14.0944i	0.991253	−	0.720188i	0.960195	+	0.279330i	$0.0901123\pi$
$384$	−2.78029			−0.141881
$385$	24.0900	−	34.4728i	1.22774	−	1.75690i
$386$	−8.07727			−0.411122
$387$	21.1145	−	15.3406i	1.07331	−	0.779806i
$388$	−1.86600	−	5.74296i	−0.0947318	−	0.291555i
$389$	−0.353026	+	1.08650i	−0.0178991	+	0.0550879i	−0.959607	−	0.281343i	$-0.909220\pi$
$389$	−0.353026	+	1.08650i	−0.0178991	+	0.0550879i	0.941708	+	0.336431i	$0.109220\pi$
$390$	−44.4526	−	32.2967i	−2.25095	−	1.63541i
$391$	−2.23360	−	1.62281i	−0.112958	−	0.0820689i
$392$	2.10930	−	6.49176i	0.106536	−	0.327883i
$393$	12.1730	+	37.4647i	0.614047	+	1.88984i
$394$	−15.0636	+	10.9443i	−0.758893	+	0.551368i
$395$	5.62361			0.282954
$396$	−9.45278	−	12.5198i	−0.475020	−	0.629145i
$397$	−20.5651			−1.03213			−0.516066	−	0.856549i	$-0.672604\pi$
$397$	−20.5651			−1.03213			−0.516066	+	0.856549i	$0.672604\pi$
$398$	20.2447	−	14.7086i	1.01477	−	0.737276i
$399$	−19.4647	−	59.9063i	−0.974455	−	2.99906i
$400$	2.04871	−	6.30528i	0.102436	−	0.315264i
$401$	25.1311	+	18.2588i	1.25499	+	0.911802i	0.998500	−	0.0547461i	$-0.0174349\pi$
$401$	25.1311	+	18.2588i	1.25499	+	0.911802i	0.256487	+	0.966548i	$0.417435\pi$
$402$	−14.7986	−	10.7518i	−0.738085	−	0.536250i
$403$	−5.05696	+	15.5637i	−0.251905	+	0.775284i
$404$	2.82962	+	8.70866i	0.140779	+	0.433272i
$405$	2.25445	−	1.63795i	0.112024	−	0.0813905i
$406$	20.2856			1.00676
$407$	0.229250	+	12.4641i	0.0113635	+	0.617822i
$408$	2.78029			0.137645
$409$	28.7290	−	20.8728i	1.42056	−	1.03210i	0.428878	−	0.903363i	$-0.358909\pi$
$409$	28.7290	−	20.8728i	1.42056	−	1.03210i	0.991679	−	0.128733i	$-0.0410909\pi$
$410$	7.55480	+	23.2513i	0.373105	+	1.14830i
$411$	−19.2361	+	59.2025i	−0.948845	+	2.92024i
$412$	6.76371	+	4.91412i	0.333224	+	0.242102i
$413$	−39.2933	−	28.5483i	−1.93350	−	1.40477i
$414$	−4.03544	+	12.4198i	−0.198331	+	0.610401i
$415$	−7.57744	−	23.3210i	−0.371962	−	1.14478i
$416$	4.68837	−	3.40630i	0.229866	−	0.167008i
$417$	−26.1779			−1.28194
$418$	19.3307	+	5.89018i	0.945495	+	0.288098i
$419$	−20.2087			−0.987257			−0.493629	−	0.869673i	$-0.664330\pi$
$419$	−20.2087			−0.987257			−0.493629	+	0.869673i	$0.664330\pi$
$420$	28.5219	−	20.7224i	1.39173	−	1.01115i
$421$	−6.17973	−	19.0193i	−0.301182	−	0.926942i	−0.981075	−	0.193630i	$-0.937974\pi$
$421$	−6.17973	−	19.0193i	−0.301182	−	0.926942i	0.679893	−	0.733311i	$-0.262026\pi$
$422$	1.95040	−	6.00273i	0.0949442	−	0.292208i
$423$	5.06768	+	3.68189i	0.246399	+	0.179019i
$424$	6.01114	+	4.36735i	0.291927	+	0.212097i
$425$	−2.04871	+	6.30528i	−0.0993771	+	0.305851i
$426$	4.18255	+	12.8726i	0.202645	+	0.623678i
$427$	−32.2063	+	23.3992i	−1.55857	+	1.13237i
$428$	−13.1548			−0.635860
$429$	51.1177	+	15.5759i	2.46799	+	0.752010i
$430$	−18.8169			−0.907432
$431$	−0.0618243	+	0.0449180i	−0.00297797	+	0.00216362i	−0.589273	−	0.807934i	$-0.700586\pi$
$431$	−0.0618243	+	0.0449180i	−0.00297797	+	0.00216362i	0.586295	+	0.810097i	$0.300586\pi$
$432$	−1.48633	−	4.57447i	−0.0715113	−	0.220089i
$433$	9.49780	−	29.2312i	0.456435	−	1.40476i	−0.413007	−	0.910728i	$-0.635522\pi$
$433$	9.49780	−	29.2312i	0.456435	−	1.40476i	0.869442	−	0.494035i	$-0.164478\pi$
$434$	−8.49465	−	6.17173i	−0.407756	−	0.296252i
$435$	41.8480	+	30.4043i	2.00646	+	1.45778i
$436$	4.24587	−	13.0674i	0.203340	−	0.625817i
$437$	−5.19830	−	15.9987i	−0.248668	−	0.765323i
$438$	−6.13361	+	4.45633i	−0.293075	+	0.212932i
$439$	11.7279			0.559742			0.279871	−	0.960038i	$-0.409708\pi$
$439$	11.7279			0.559742			0.279871	+	0.960038i	$0.409708\pi$
$440$	0.207997	+	11.3086i	0.00991588	+	0.539116i
$441$	32.2862			1.53744
$442$	−4.68837	+	3.40630i	−0.223003	+	0.162021i
$443$	0.863723	+	2.65826i	0.0410367	+	0.126298i	0.969476	−	0.245186i	$-0.0788491\pi$
$443$	0.863723	+	2.65826i	0.0410367	+	0.126298i	−0.928439	+	0.371484i	$0.878849\pi$
$444$	−3.22931	+	9.93879i	−0.153256	+	0.471674i
$445$	−11.6377	−	8.45526i	−0.551678	−	0.400818i
$446$	13.9696	+	10.1495i	0.661479	+	0.480592i
$447$	−15.8829	+	48.8825i	−0.751235	+	2.31206i
$448$	1.14902	+	3.53632i	0.0542862	+	0.167076i
$449$	−22.4014	+	16.2755i	−1.05719	+	0.768090i	−0.973566	−	0.228407i	$-0.926648\pi$
$449$	−22.4014	+	16.2755i	−1.05719	+	0.768090i	−0.0836201	+	0.996498i	$0.526648\pi$
$450$	31.3588			1.47827
$451$	−14.3270	−	18.9755i	−0.674630	−	0.893521i
$452$	7.40480			0.348292
$453$	−50.0023	+	36.3288i	−2.34931	+	1.70688i
$454$	2.92073	+	8.98908i	0.137077	+	0.421878i
$455$	−22.7080	+	69.8880i	−1.06457	+	3.27640i
$456$	13.7050	+	9.95724i	0.641794	+	0.466290i
$457$	−5.79901	−	4.21322i	−0.271266	−	0.197086i	0.443833	−	0.896110i	$-0.353618\pi$
$457$	−5.79901	−	4.21322i	−0.271266	−	0.197086i	−0.715099	+	0.699023i	$0.753618\pi$
$458$	−3.19368	+	9.82913i	−0.149231	+	0.459285i
$459$	1.48633	+	4.57447i	0.0693761	+	0.213518i
$460$	7.61713	−	5.53417i	0.355151	−	0.258032i
$461$	−3.31539			−0.154413			−0.0772066	−	0.997015i	$-0.524600\pi$
$461$	−3.31539			−0.154413			−0.0772066	+	0.997015i	$0.524600\pi$
$462$	−19.6400	+	28.1048i	−0.913734	+	1.30756i
$463$	22.6136			1.05094			0.525472	−	0.850811i	$-0.323889\pi$
$463$	22.6136			1.05094			0.525472	+	0.850811i	$0.323889\pi$
$464$	−4.41367	+	3.20672i	−0.204899	+	0.148868i
$465$	−8.27370	−	25.4638i	−0.383684	−	1.18086i
$466$	−0.578568	+	1.78065i	−0.0268016	+	0.0824870i
$467$	10.8610	+	7.89099i	0.502588	+	0.365151i	0.810005	−	0.586424i	$-0.199465\pi$
$467$	10.8610	+	7.89099i	0.502588	+	0.365151i	−0.307417	+	0.951575i	$0.599465\pi$
$468$	22.1760	+	16.1118i	1.02509	+	0.744768i
$469$	−7.55963	+	23.2661i	−0.349071	+	1.07433i
$470$	−1.39559	−	4.29520i	−0.0643739	−	0.198123i
$471$	31.8053	−	23.1079i	1.46551	−	1.06476i
$472$	13.0622			0.601235
$473$	17.2977	−	5.97422i	0.795349	−	0.274695i
$474$	−4.58479			−0.210586
$475$	−32.6803	+	23.7437i	−1.49948	+	1.08943i
$476$	−1.14902	−	3.53632i	−0.0526653	−	0.162087i
$477$	−10.8603	+	33.4246i	−0.497259	+	1.53041i
$478$	−16.1261	−	11.7163i	−0.737590	−	0.535890i
$479$	7.31452	+	5.31431i	0.334209	+	0.242817i	0.742214	−	0.670163i	$-0.233776\pi$
$479$	7.31452	+	5.31431i	0.334209	+	0.242817i	−0.408006	+	0.912979i	$0.633776\pi$
$480$	−2.92993	+	9.01740i	−0.133732	+	0.411586i
$481$	−6.73108	−	20.7161i	−0.306911	−	0.944574i
$482$	−5.86873	+	4.26388i	−0.267313	+	0.194214i
$483$	28.5420			1.29870
$484$	−3.78160	−	10.3295i	−0.171891	−	0.469525i
$485$	−20.5928			−0.935070
$486$	−13.5118	+	9.81691i	−0.612908	+	0.445304i
$487$	0.800867	+	2.46482i	0.0362908	+	0.111691i	0.967561	−	0.252638i	$-0.0812982\pi$
$487$	0.800867	+	2.46482i	0.0362908	+	0.111691i	−0.931270	+	0.364330i	$0.881298\pi$
$488$	3.30841	−	10.1822i	0.149765	−	0.460928i
$489$	30.9887	+	22.5146i	1.40136	+	1.01815i
$490$	−18.8321	−	13.6823i	−0.850749	−	0.618105i
$491$	9.20532	−	28.3311i	0.415430	−	1.27856i	−0.496435	−	0.868074i	$-0.665358\pi$
$491$	9.20532	−	28.3311i	0.415430	−	1.27856i	0.911865	−	0.410489i	$-0.134642\pi$
$492$	−6.15924	−	18.9562i	−0.277680	−	0.854611i
$493$	4.41367	−	3.20672i	0.198782	−	0.144423i
$494$	−35.3098			−1.58866
$495$	−50.5676	+	17.4649i	−2.27284	+	0.784987i
$496$	2.82385			0.126795
$497$	14.6445	−	10.6398i	0.656893	−	0.477261i
$498$	6.17770	+	19.0130i	0.276829	+	0.851992i
$499$	−4.87116	+	14.9919i	−0.218063	+	0.671129i	0.780859	+	0.624707i	$0.214782\pi$
$499$	−4.87116	+	14.9919i	−0.218063	+	0.671129i	−0.998922	+	0.0464215i	$0.985218\pi$
$500$	−4.49644	−	3.26686i	−0.201087	−	0.146098i
$501$	1.63969	+	1.19131i	0.0732561	+	0.0532237i
$502$	−8.48408	+	26.1113i	−0.378663	+	1.16541i
$503$	−9.25329	−	28.4787i	−0.412584	−	1.26980i	−0.914394	−	0.404825i	$-0.867332\pi$
$503$	−9.25329	−	28.4787i	−0.412584	−	1.26980i	0.501810	−	0.864978i	$-0.332668\pi$
$504$	−14.2287	+	10.3377i	−0.633795	+	0.460479i
$505$	31.2270			1.38958
$506$	−5.24510	+	7.50575i	−0.233173	+	0.333671i
$507$	−57.2288			−2.54162
$508$	−0.684912	+	0.497617i	−0.0303880	+	0.0220782i
$509$	−5.14248	−	15.8269i	−0.227936	−	0.701516i	−0.997980	−	0.0635251i	$-0.979766\pi$
$509$	−5.14248	−	15.8269i	−0.227936	−	0.701516i	0.770044	−	0.637991i	$-0.220234\pi$
$510$	2.92993	−	9.01740i	0.129740	−	0.399297i
$511$	8.20299	+	5.95982i	0.362879	+	0.263647i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−9.05622	+	27.8722i	−0.399842	+	1.23059i
$514$	−4.63218	−	14.2564i	−0.204317	−	0.628823i
$515$	23.0659	−	16.7584i	1.01641	−	0.738462i
$516$	15.3409			0.675347
$517$	2.64661	+	3.50533i	0.116398	+	0.154164i
$518$	13.9760			0.614071
$519$	−29.1006	+	21.1429i	−1.27738	+	0.928068i
$520$	−6.10707	−	18.7956i	−0.267813	−	0.824242i
$521$	−4.86093	+	14.9604i	−0.212961	+	0.655427i	0.786331	+	0.617806i	$0.211978\pi$
$521$	−4.86093	+	14.9604i	−0.212961	+	0.655427i	−0.999292	+	0.0376216i	$0.988022\pi$
$522$	−20.8766	−	15.1677i	−0.913745	−	0.663874i
$523$	−20.4507	−	14.8583i	−0.894246	−	0.649708i	0.0427354	−	0.999086i	$-0.486393\pi$
$523$	−20.4507	−	14.8583i	−0.894246	−	0.649708i	−0.936982	+	0.349378i	$0.886393\pi$
$524$	−4.37833	+	13.4751i	−0.191268	+	0.588663i
$525$	−21.1795	−	65.1839i	−0.924350	−	2.84486i
$526$	−6.66361	+	4.84140i	−0.290547	+	0.211095i
$527$	−2.82385			−0.123009
$528$	−0.169575	−	9.21961i	−0.00737980	−	0.401232i
$529$	−15.3775			−0.668587
$530$	20.4994	−	14.8937i	0.890439	−	0.646942i
$531$	19.0923	+	58.7600i	0.828535	+	2.54997i
$532$	7.00098	−	21.5468i	0.303531	−	0.934172i
$533$	33.6107	+	24.4196i	1.45584	+	1.05773i
$534$	9.48790	+	6.89336i	0.410582	+	0.298305i
$535$	−13.8628	+	42.6653i	−0.599342	+	1.84458i
$536$	−2.03308	−	6.25718i	−0.0878157	−	0.270269i
$537$	2.58779	−	1.88014i	0.111671	−	0.0811340i
$538$	−30.3029			−1.30645
$539$	21.6557	+	6.59863i	0.932779	+	0.284223i
$540$	−16.4029			−0.705867
$541$	0.752308	−	0.546584i	0.0323443	−	0.0234995i	−0.571496	−	0.820605i	$-0.693637\pi$
$541$	0.752308	−	0.546584i	0.0323443	−	0.0234995i	0.603840	+	0.797106i	$0.293637\pi$
$542$	−0.836260	−	2.57374i	−0.0359205	−	0.110552i
$543$	−1.99634	+	6.14411i	−0.0856712	+	0.263669i
$544$	0.809017	+	0.587785i	0.0346863	+	0.0252011i
$545$	−37.9077	−	27.5416i	−1.62379	−	1.17975i
$546$	18.5132	−	56.9779i	0.792293	−	2.43843i
$547$	−3.22236	−	9.91740i	−0.137778	−	0.424037i	0.858234	−	0.513259i	$-0.171562\pi$
$547$	−3.22236	−	9.91740i	−0.137778	−	0.424037i	−0.996012	+	0.0892218i	$0.971562\pi$
$548$	−18.1135	+	13.1602i	−0.773770	+	0.562176i
$549$	50.6404			2.16128
$550$	21.0337	+	6.40909i	0.896879	+	0.273284i
$551$	33.2409			1.41611
$552$	−6.21006	+	4.51187i	−0.264318	+	0.192038i
$553$	1.89477	+	5.83152i	0.0805740	+	0.247981i
$554$	2.87224	−	8.83985i	0.122030	−	0.375569i
$555$	28.8317	+	20.9475i	1.22384	+	0.889170i
$556$	−7.61732	−	5.53431i	−0.323046	−	0.234707i
$557$	13.9199	−	42.8409i	0.589804	−	1.81523i	0.0107460	−	0.999942i	$-0.496579\pi$
$557$	13.9199	−	42.8409i	0.589804	−	1.81523i	0.579058	−	0.815287i	$-0.303421\pi$
$558$	4.12748	+	12.7031i	0.174730	+	0.537764i
$559$	−25.8693	+	18.7952i	−1.09416	+	0.794950i
$560$	12.6804			0.535843
$561$	0.169575	+	9.21961i	0.00715946	+	0.389252i
$562$	13.2257			0.557894
$563$	−12.6291	+	9.17560i	−0.532254	+	0.386705i	−0.821200	−	0.570640i	$-0.806695\pi$
$563$	−12.6291	+	9.17560i	−0.532254	+	0.386705i	0.288946	+	0.957345i	$0.406695\pi$
$564$	1.13779	+	3.50176i	0.0479097	+	0.147451i
$565$	7.80335	−	24.0162i	0.328289	−	1.01037i
$566$	−17.7538	−	12.8989i	−0.746246	−	0.542179i
$567$	2.45810	+	1.78592i	0.103231	+	0.0750015i
$568$	−1.50436	+	4.62995i	−0.0631216	+	0.194268i
$569$	−1.15658	−	3.55959i	−0.0484864	−	0.149226i	0.923882	−	0.382677i	$-0.124998\pi$
$569$	−1.15658	−	3.55959i	−0.0484864	−	0.149226i	−0.972368	+	0.233452i	$0.924998\pi$
$570$	46.7373	−	33.9566i	1.95761	−	1.42229i
$571$	−16.9510			−0.709376			−0.354688	−	0.934985i	$-0.615413\pi$
$571$	−16.9510			−0.709376			−0.354688	+	0.934985i	$0.615413\pi$
$572$	11.5815	+	15.3392i	0.484246	+	0.641364i
$573$	4.11812			0.172037
$574$	−21.5654	+	15.6682i	−0.900124	+	0.653979i
$575$	−5.65626	−	17.4082i	−0.235882	−	0.725971i
$576$	1.46165	−	4.49849i	0.0609020	−	0.187437i
$577$	8.92560	+	6.48483i	0.371578	+	0.269967i	0.757865	−	0.652412i	$-0.226243\pi$
$577$	8.92560	+	6.48483i	0.371578	+	0.269967i	−0.386287	+	0.922379i	$0.626243\pi$
$578$	−0.809017	−	0.587785i	−0.0336507	−	0.0244486i
$579$	6.93964	−	21.3580i	0.288401	−	0.887608i
$580$	5.74923	+	17.6943i	0.238724	+	0.734716i
$581$	21.6301	−	15.7152i	0.897367	−	0.651975i
$582$	16.7888			0.695917
$583$	−14.1158	+	20.1997i	−0.584615	+	0.836585i
$584$	−2.72690			−0.112840
$585$	75.6255	−	54.9452i	3.12673	−	2.27170i
$586$	4.24383	+	13.0612i	0.175311	+	0.539552i
$587$	10.8403	−	33.3631i	0.447428	−	1.37704i	−0.432371	−	0.901696i	$-0.642323\pi$
$587$	10.8403	−	33.3631i	0.447428	−	1.37704i	0.879799	−	0.475346i	$-0.157677\pi$
$588$	15.3534	+	11.1549i	0.633162	+	0.460019i
$589$	−13.9197	−	10.1133i	−0.573552	−	0.416710i
$590$	13.7652	−	42.3650i	0.566705	−	1.74414i
$591$	−15.9972	−	49.2342i	−0.658036	−	2.02523i
$592$	−3.04085	+	2.20931i	−0.124978	+	0.0908020i
$593$	34.6528			1.42302			0.711509	−	0.702677i	$-0.248012\pi$
$593$	34.6528			1.42302			0.711509	+	0.702677i	$0.248012\pi$
$594$	15.0786	−	5.20778i	0.618681	−	0.213678i
$595$	−12.6804			−0.519844
$596$	−14.9560	+	10.8662i	−0.612621	+	0.445095i
$597$	21.4993	+	66.1682i	0.879909	+	2.70808i
$598$	4.94419	−	15.2167i	0.202183	−	0.622256i
$599$	11.3526	+	8.24811i	0.463853	+	0.337009i	0.795041	−	0.606556i	$-0.207449\pi$
$599$	11.3526	+	8.24811i	0.463853	+	0.337009i	−0.331188	+	0.943565i	$0.607449\pi$
$600$	14.9123	+	10.8344i	0.608793	+	0.442314i
$601$	−10.0404	+	30.9012i	−0.409557	+	1.26049i	0.507473	+	0.861668i	$0.330580\pi$
$601$	−10.0404	+	30.9012i	−0.409557	+	1.26049i	−0.917030	+	0.398819i	$0.869420\pi$
$602$	−6.34002	−	19.5126i	−0.258400	−	0.795273i
$603$	25.1762	−	18.2916i	1.02525	−	0.744891i
$604$	−22.2302			−0.904533
$605$	−37.4873	+	1.37946i	−1.52408	+	0.0560832i
$606$	−25.4586			−1.03419
$607$	−3.89748	+	2.83168i	−0.158194	+	0.114934i	−0.664066	−	0.747674i	$-0.731171\pi$
$607$	−3.89748	+	2.83168i	−0.158194	+	0.114934i	0.505872	+	0.862608i	$0.331171\pi$
$608$	1.88284	+	5.79478i	0.0763592	+	0.235009i
$609$	−17.4285	+	53.6394i	−0.706238	+	2.17358i
$610$	−29.5379	−	21.4606i	−1.19596	−	0.868913i
$611$	−6.20888	−	4.51102i	−0.251184	−	0.182496i
$612$	−1.46165	+	4.49849i	−0.0590836	+	0.181841i
$613$	−1.54815	−	4.76471i	−0.0625292	−	0.192445i	0.914912	−	0.403654i	$-0.132260\pi$
$613$	−1.54815	−	4.76471i	−0.0625292	−	0.192445i	−0.977441	+	0.211209i	$0.932260\pi$
$614$	5.69904	−	4.14060i	0.229995	−	0.167101i
$615$	−67.9720			−2.74090
$616$	−11.6566	+	4.02592i	−0.469658	+	0.162209i
$617$	−17.4473			−0.702401			−0.351200	−	0.936300i	$-0.614226\pi$
$617$	−17.4473			−0.702401			−0.351200	+	0.936300i	$0.614226\pi$
$618$	−18.8051	+	13.6627i	−0.756450	+	0.549593i
$619$	9.92364	+	30.5418i	0.398865	+	1.22758i	0.925911	+	0.377743i	$0.123300\pi$
$619$	9.92364	+	30.5418i	0.398865	+	1.22758i	−0.527046	+	0.849837i	$0.676700\pi$
$620$	2.97584	−	9.15871i	0.119513	−	0.367822i
$621$	−10.7434	−	7.80551i	−0.431116	−	0.313224i
$622$	−14.4400	−	10.4913i	−0.578993	−	0.420663i
$623$	4.84675	−	14.9168i	0.194181	−	0.597628i
$624$	4.97894	+	15.3236i	0.199317	+	0.613435i
$625$	11.4840	−	8.34362i	0.459360	−	0.333745i
$626$	−6.93099			−0.277018
$627$	−32.1829	+	46.0538i	−1.28526	+	1.83921i
$628$	14.1401			0.564252
$629$	3.04085	−	2.20931i	0.121247	−	0.0880908i
$630$	18.5342	+	57.0425i	0.738421	+	2.27263i
$631$	10.7287	−	33.0196i	0.427104	−	1.31449i	−0.473861	−	0.880600i	$-0.657140\pi$
$631$	10.7287	−	33.0196i	0.427104	−	1.31449i	0.900965	−	0.433891i	$-0.142860\pi$
$632$	−1.33410	−	0.969278i	−0.0530675	−	0.0385558i
$633$	14.1968	+	10.3146i	0.564271	+	0.409967i
$634$	−7.15536	+	22.0219i	−0.284176	+	0.874603i
$635$	0.892164	+	2.74580i	0.0354045	+	0.108964i
$636$	−16.7127	+	12.1425i	−0.662701	+	0.481480i
$637$	−39.5568			−1.56730
$638$	−10.9029	−	14.4404i	−0.431649	−	0.571702i
$639$	−23.0266			−0.910919
$640$	−2.75895	+	2.00449i	−0.109057	+	0.0792345i
$641$	−5.28081	−	16.2527i	−0.208579	−	0.641941i	−0.999547	−	0.0300838i	$-0.990423\pi$
$641$	−5.28081	−	16.2527i	−0.208579	−	0.641941i	0.790968	−	0.611857i	$-0.209577\pi$
$642$	11.3020	−	34.7840i	0.446054	−	1.37281i
$643$	7.40107	+	5.37719i	0.291870	+	0.212056i	0.724078	−	0.689718i	$-0.242266\pi$
$643$	7.40107	+	5.37719i	0.291870	+	0.212056i	−0.432208	+	0.901774i	$0.642266\pi$
$644$	8.30523	+	6.03411i	0.327272	+	0.237777i
$645$	16.1666	−	49.7558i	0.636561	−	1.95913i
$646$	−1.88284	−	5.79478i	−0.0740793	−	0.227993i
$647$	23.8771	−	17.3477i	0.938706	−	0.682010i	−0.00940298	−	0.999956i	$-0.502993\pi$
$647$	23.8771	−	17.3477i	0.938706	−	0.682010i	0.948109	+	0.317946i	$0.102993\pi$
$648$	−0.817141			−0.0321003
$649$	0.796686	+	43.3150i	0.0312727	+	1.70026i
$650$	−38.4205			−1.50698
$651$	23.6176	−	17.1592i	0.925646	−	0.672521i
$652$	4.25734	+	13.1028i	0.166730	+	0.513143i
$653$	3.57797	−	11.0119i	0.140017	−	0.430928i	−0.856320	−	0.516446i	$-0.827255\pi$
$653$	3.57797	−	11.0119i	0.140017	−	0.430928i	0.996337	+	0.0855185i	$0.0272547\pi$
$654$	30.9052	+	22.4539i	1.20849	+	0.878019i
$655$	39.0903	+	28.4008i	1.52738	+	1.10971i
$656$	2.21533	−	6.81807i	0.0864939	−	0.266201i
$657$	−3.98577	−	12.2669i	−0.155500	−	0.478578i
$658$	3.98377	−	2.89438i	0.155304	−	0.112835i
$659$	−39.7485			−1.54838			−0.774191	−	0.632952i	$-0.781843\pi$
$659$	−39.7485			−1.54838			−0.774191	+	0.632952i	$0.781843\pi$
$660$	−30.0810	−	9.16585i	−1.17090	−	0.356780i
$661$	−0.315928			−0.0122882			−0.00614408	−	0.999981i	$-0.501956\pi$
$661$	−0.315928			−0.0122882			−0.00614408	+	0.999981i	$0.501956\pi$
$662$	−16.9540	+	12.3178i	−0.658936	+	0.478745i
$663$	−4.97894	−	15.3236i	−0.193366	−	0.595119i
$664$	−2.22196	+	6.83850i	−0.0862289	+	0.265385i
$665$	−62.5057	−	45.4130i	−2.42387	−	1.76104i
$666$	−14.3832	−	10.4500i	−0.557338	−	0.404930i
$667$	−4.65450	+	14.3251i	−0.180223	+	0.554669i
$668$	0.225267	+	0.693301i	0.00871585	+	0.0268246i
$669$	−38.8394	+	28.2185i	−1.50162	+	1.09099i
$670$	−22.4366			−0.866803
$671$	33.9667	+	10.3499i	1.31127	+	0.399552i
$672$	−10.3380			−0.398796
$673$	31.1929	−	22.6629i	1.20240	−	0.873592i	0.207878	−	0.978155i	$-0.433344\pi$
$673$	31.1929	−	22.6629i	1.20240	−	0.873592i	0.994518	+	0.104563i	$0.0333444\pi$
$674$	9.51475	+	29.2834i	0.366495	+	1.12795i
$675$	−9.85405	+	30.3276i	−0.379283	+	1.16731i
$676$	−16.6526	−	12.0988i	−0.640485	−	0.465340i
$677$	−1.98236	−	1.44027i	−0.0761882	−	0.0553540i	0.549039	−	0.835797i	$-0.314994\pi$
$677$	−1.98236	−	1.44027i	−0.0761882	−	0.0553540i	−0.625227	+	0.780443i	$0.714994\pi$
$678$	−6.36188	+	19.5798i	−0.244326	+	0.751959i
$679$	−6.93837	−	21.3541i	−0.266270	−	0.819495i
$680$	2.75895	−	2.00449i	0.105801	−	0.0768687i
$681$	−26.2784			−1.00699
$682$	0.172232	+	9.36408i	0.00659511	+	0.358569i
$683$	13.2420			0.506690			0.253345	−	0.967376i	$-0.418469\pi$
$683$	13.2420			0.506690			0.253345	+	0.967376i	$0.418469\pi$
$684$	−23.3157	+	16.9399i	−0.891499	+	0.647712i
$685$	23.5946	+	72.6166i	0.901502	+	2.77454i
$686$	−0.200112	+	0.615881i	−0.00764031	+	0.0235145i
$687$	−23.2464	−	16.8895i	−0.886906	−	0.644375i
$688$	4.46396	+	3.24326i	0.170187	+	0.123648i
$689$	13.3060	−	40.9515i	0.506916	−	1.56013i
$690$	8.08921	+	24.8960i	0.307951	+	0.947775i
$691$	37.2969	−	27.0978i	1.41884	−	1.03085i	0.426882	−	0.904308i	$-0.359612\pi$
$691$	37.2969	−	27.0978i	1.41884	−	1.03085i	0.991961	−	0.126542i	$-0.0403879\pi$
$692$	−12.9376			−0.491816
$693$	−35.1484	−	46.5526i	−1.33518	−	1.76839i
$694$	13.5181			0.513141
$695$	−25.9769	+	18.8733i	−0.985361	+	0.715907i
$696$	−4.68720	−	14.4257i	−0.177668	−	0.546806i
$697$	−2.21533	+	6.81807i	−0.0839114	+	0.258253i
$698$	−7.56741	−	5.49804i	−0.286431	−	0.208104i
$699$	−4.21133	−	3.05971i	−0.159287	−	0.115729i
$700$	7.61775	−	23.4450i	0.287924	−	0.886138i
$701$	3.00193	+	9.23901i	0.113382	+	0.348952i	0.991606	−	0.129296i	$-0.0412718\pi$
$701$	3.00193	+	9.23901i	0.113382	+	0.348952i	−0.878225	+	0.478249i	$0.841272\pi$
$702$	−22.5505	+	16.3839i	−0.851114	+	0.618371i
$703$	22.9017			0.863754
$704$	1.89979	−	2.71860i	0.0716010	−	0.102461i
$705$	12.5564			0.472903
$706$	−7.64291	+	5.55290i	−0.287645	+	0.208986i
$707$	10.5214	+	32.3815i	0.395698	+	1.21783i
$708$	−11.2224	+	34.5391i	−0.421765	+	1.29806i
$709$	13.4453	+	9.76860i	0.504950	+	0.366867i	0.810904	−	0.585179i	$-0.198976\pi$
$709$	13.4453	+	9.76860i	0.504950	+	0.366867i	−0.305955	+	0.952046i	$0.598976\pi$
$710$	13.4311	+	9.75829i	0.504062	+	0.366222i
$711$	2.41031	−	7.41816i	0.0903936	−	0.278203i
$712$	1.30348	+	4.01171i	0.0488501	+	0.150345i
$713$	6.30737	−	4.58257i	0.236213	−	0.171619i
$714$	10.3380			0.386889
$715$	61.9550	−	21.3978i	2.31698	−	0.800232i
$716$	1.15049			0.0429957
$717$	44.8351	−	32.5746i	1.67440	−	1.21652i
$718$	−2.85209	−	8.77784i	−0.106439	−	0.327586i
$719$	−5.44349	+	16.7533i	−0.203008	+	0.624794i	0.796781	+	0.604268i	$0.206534\pi$
$719$	−5.44349	+	16.7533i	−0.203008	+	0.624794i	−0.999789	+	0.0205265i	$0.993466\pi$
$720$	−13.0498	−	9.48123i	−0.486337	−	0.353345i
$721$	25.1496	+	18.2722i	0.936620	+	0.680494i
$722$	5.60079	−	17.2375i	0.208440	−	0.641512i
$723$	−6.23244	−	19.1815i	−0.231787	−	0.713367i
$724$	−1.87984	+	1.36578i	−0.0698636	+	0.0507589i
$725$	36.1693			1.34329
$726$	30.5625	−	1.12464i	1.13428	−	0.0417394i
$727$	−14.4755			−0.536865			−0.268433	−	0.963298i	$-0.586506\pi$
$727$	−14.4755			−0.536865			−0.268433	+	0.963298i	$0.586506\pi$
$728$	17.4328	−	12.6657i	0.646104	−	0.469422i
$729$	−13.5917	−	41.8309i	−0.503395	−	1.54929i
$730$	−2.87367	+	8.84424i	−0.106359	+	0.327340i
$731$	−4.46396	−	3.24326i	−0.165105	−	0.119956i
$732$	24.0815	+	17.4963i	0.890079	+	0.646680i
$733$	−10.5802	+	32.5625i	−0.390789	+	1.20272i	0.541404	+	0.840763i	$0.317893\pi$
$733$	−10.5802	+	32.5625i	−0.390789	+	1.20272i	−0.932193	+	0.361962i	$0.882107\pi$
$734$	−3.86737	−	11.9025i	−0.142747	−	0.439331i
$735$	52.3587	−	38.0408i	1.93128	−	1.40316i
$736$	−2.76089			−0.101768
$737$	20.6252	−	7.12346i	0.759739	−	0.262396i
$738$	33.9091			1.24821
$739$	−10.2180	+	7.42384i	−0.375876	+	0.273090i	−0.759643	−	0.650340i	$-0.774627\pi$
$739$	−10.2180	+	7.42384i	−0.375876	+	0.273090i	0.383767	+	0.923430i	$0.374627\pi$
$740$	3.96100	+	12.1907i	0.145609	+	0.448140i
$741$	30.3366	−	93.3665i	1.11444	−	3.42990i
$742$	22.3513	+	16.2392i	0.820541	+	0.596158i
$743$	−18.0084	−	13.0839i	−0.660665	−	0.480001i	0.206222	−	0.978505i	$-0.433883\pi$
$743$	−18.0084	−	13.0839i	−0.660665	−	0.480001i	−0.866888	+	0.498504i	$0.833883\pi$
$744$	−2.42613	+	7.46686i	−0.0889463	+	0.273748i
$745$	19.4816	+	59.9583i	0.713752	+	2.19670i
$746$	−3.02481	+	2.19765i	−0.110746	+	0.0804617i
$747$	−34.0107			−1.24439
$748$	−1.89979	+	2.71860i	−0.0694632	+	0.0994019i
$749$	−48.9135			−1.78726
$750$	12.5014	−	9.08280i	0.456486	−	0.331657i
$751$	−12.7950	−	39.3789i	−0.466896	−	1.43696i	−0.856583	−	0.516010i	$-0.827417\pi$
$751$	−12.7950	−	39.3789i	−0.466896	−	1.43696i	0.389687	−	0.920947i	$-0.372583\pi$
$752$	−0.409236	+	1.25950i	−0.0149233	+	0.0459292i
$753$	−61.7547	−	44.8674i	−2.25046	−	1.63506i
$754$	25.5779	+	18.5834i	0.931491	+	0.676768i
$755$	−23.4267	+	72.0999i	−0.852584	+	2.62398i
$756$	−5.52665	−	17.0093i	−0.201002	−	0.618622i
$757$	−34.3849	+	24.9821i	−1.24974	+	0.907990i	−0.998207	−	0.0598586i	$-0.980935\pi$
$757$	−34.3849	+	24.9821i	−1.24974	+	0.907990i	−0.251534	+	0.967848i	$0.580935\pi$
$758$	2.59407			0.0942210
$759$	−15.3404	−	20.3178i	−0.556822	−	0.737488i
$760$	20.7786			0.753719
$761$	18.5186	−	13.4546i	0.671299	−	0.487728i	−0.199161	−	0.979967i	$-0.563822\pi$
$761$	18.5186	−	13.4546i	0.671299	−	0.487728i	0.870460	+	0.492239i	$0.163822\pi$
$762$	−0.727359	−	2.23858i	−0.0263494	−	0.0810952i
$763$	15.7875	−	48.5888i	0.571545	−	1.75903i
$764$	1.19831	+	0.870620i	0.0433532	+	0.0314979i
$765$	13.0498	+	9.48123i	0.471816	+	0.342795i
$766$	−7.40984	+	22.8051i	−0.267728	+	0.823983i
$767$	−23.3917	−	71.9923i	−0.844626	−	2.59949i
$768$	2.24930	−	1.63421i	0.0811646	−	0.0589695i
$769$	−27.4280			−0.989078			−0.494539	−	0.869156i	$-0.664663\pi$
$769$	−27.4280			−0.989078			−0.494539	+	0.869156i	$0.664663\pi$
$770$	0.773398	+	42.0489i	0.0278713	+	1.51534i
$771$	41.6767			1.50095
$772$	6.53465	−	4.74770i	0.235187	−	0.170874i
$773$	9.28488	+	28.5759i	0.333954	+	1.02780i	0.967235	+	0.253883i	$0.0817077\pi$
$773$	9.28488	+	28.5759i	0.333954	+	1.02780i	−0.633281	+	0.773922i	$0.718292\pi$
$774$	−8.06502	+	24.8216i	−0.289891	+	0.892193i
$775$	−15.1460	−	11.0042i	−0.544061	−	0.395283i
$776$	4.88525	+	3.54934i	0.175370	+	0.127414i
$777$	−12.0076	+	36.9555i	−0.430769	+	1.32577i
$778$	−0.353026	−	1.08650i	−0.0126566	−	0.0389530i
$779$	−35.3381	+	25.6746i	−1.26612	+	0.919889i
$780$	54.9465			1.96740
$781$	−15.4450	−	4.70617i	−0.552664	−	0.168400i
$782$	2.76089			0.0987291
$783$	21.2292	−	15.4239i	0.758670	−	0.551206i
$784$	2.10930	+	6.49176i	0.0753322	+	0.231849i
$785$	14.9012	−	45.8611i	0.531846	−	1.63685i
$786$	−31.8693	−	23.1544i	−1.13674	−	0.825891i
$787$	22.3924	+	16.2690i	0.798202	+	0.579928i	0.910386	−	0.413760i	$-0.135785\pi$
$787$	22.3924	+	16.2690i	0.798202	+	0.579928i	−0.112184	+	0.993687i	$0.535785\pi$
$788$	5.75378	−	17.7083i	0.204970	−	0.630833i
$789$	−7.07659	−	21.7795i	−0.251933	−	0.775371i
$790$	−4.54959	+	3.30547i	−0.161867	+	0.117603i
$791$	27.5334			0.978973
$792$	15.0064	+	4.57255i	0.533230	+	0.162478i
$793$	−62.0442			−2.20326
$794$	16.6375	−	12.0879i	0.590443	−	0.428982i
$795$	21.7699	+	67.0008i	0.772099	+	2.37628i
$796$	−7.73278	+	23.7990i	−0.274081	+	0.843535i
$797$	−15.0050	−	10.9017i	−0.531503	−	0.386159i	0.289417	−	0.957203i	$-0.406539\pi$
$797$	−15.0050	−	10.9017i	−0.531503	−	0.386159i	−0.820920	+	0.571044i	$0.806539\pi$
$798$	50.9593	+	37.0241i	1.80394	+	1.31064i
$799$	0.409236	−	1.25950i	0.0144777	−	0.0445578i
$800$	2.04871	+	6.30528i	0.0724329	+	0.222925i
$801$	−16.1414	+	11.7274i	−0.570328	+	0.414368i
$802$	−31.0637			−1.09690
$803$	−0.166319	−	9.04257i	−0.00586926	−	0.319105i
$804$	18.2920			0.645110
$805$	28.3229	−	20.5778i	0.998250	−	0.725271i
$806$	−5.05696	−	15.5637i	−0.178124	−	0.548209i
$807$	26.0349	−	80.1271i	0.916471	−	2.82061i
$808$	−7.40803	−	5.38225i	−0.260614	−	0.189347i
$809$	−4.21983	−	3.06588i	−0.148361	−	0.107791i	0.511129	−	0.859504i	$-0.329228\pi$
$809$	−4.21983	−	3.06588i	−0.148361	−	0.107791i	−0.659490	+	0.751714i	$0.729228\pi$
$810$	−0.861122	+	2.65026i	−0.0302568	+	0.0931207i
$811$	8.01578	+	24.6700i	0.281472	+	0.866282i	0.987434	+	0.158032i	$0.0505150\pi$
$811$	8.01578	+	24.6700i	0.281472	+	0.866282i	−0.705962	+	0.708250i	$0.749485\pi$
$812$	−16.4114	+	11.9236i	−0.575927	+	0.418435i
$813$	7.52400			0.263878
$814$	−7.51167	−	9.94890i	−0.263284	−	0.348709i
$815$	46.9831			1.64575
$816$	−2.24930	+	1.63421i	−0.0787412	+	0.0572088i
$817$	−10.3890	−	31.9742i	−0.363467	−	1.11864i
$818$	−10.9735	+	33.7730i	−0.383679	+	1.18084i
$819$	82.4572	+	59.9087i	2.88129	+	2.09338i
$820$	−19.7787	−	14.3701i	−0.690703	−	0.501825i
$821$	3.56844	−	10.9825i	0.124540	−	0.383293i	−0.869277	−	0.494325i	$-0.835415\pi$
$821$	3.56844	−	10.9825i	0.124540	−	0.383293i	0.993817	+	0.111031i	$0.0354154\pi$
$822$	−19.2361	−	59.2025i	−0.670935	−	2.06492i
$823$	36.8461	−	26.7703i	1.28438	−	0.933154i	0.284700	−	0.958617i	$-0.408106\pi$
$823$	36.8461	−	26.7703i	1.28438	−	0.933154i	0.999676	+	0.0254628i	$0.00810594\pi$
$824$	−8.36041			−0.291249
$825$	−35.0182	+	50.1111i	−1.21918	+	1.74464i
$826$	48.5692			1.68994
$827$	−0.339680	+	0.246792i	−0.0118118	+	0.00858180i	−0.593676	−	0.804705i	$-0.702324\pi$
$827$	−0.339680	+	0.246792i	−0.0118118	+	0.00858180i	0.581864	+	0.813286i	$0.302324\pi$
$828$	−4.03544	−	12.4198i	−0.140241	−	0.431619i
$829$	−6.44724	+	19.8426i	−0.223922	+	0.689161i	0.774477	+	0.632602i	$0.218013\pi$
$829$	−6.44724	+	19.8426i	−0.223922	+	0.689161i	−0.998399	+	0.0565592i	$0.981987\pi$
$830$	19.8380	+	14.4131i	0.688587	+	0.500288i
$831$	20.9067	+	15.1896i	0.725246	+	0.526922i
$832$	−1.79080	+	5.51152i	−0.0620848	+	0.191077i
$833$	−2.10930	−	6.49176i	−0.0730829	−	0.224926i
$834$	21.1783	−	15.3870i	0.733346	−	0.532807i
$835$	2.48600			0.0860316
$836$	−19.1010	+	6.59705i	−0.660623	+	0.228164i
$837$	−13.5824			−0.469476
$838$	16.3491	−	11.8784i	0.564772	−	0.410331i
$839$	−2.84430	−	8.75387i	−0.0981963	−	0.302217i	0.889877	−	0.456200i	$-0.150790\pi$
$839$	−2.84430	−	8.75387i	−0.0981963	−	0.302217i	−0.988073	+	0.153983i	$0.950790\pi$
$840$	−10.8944	+	33.5295i	−0.375892	+	1.15688i
$841$	−0.617667	−	0.448762i	−0.0212989	−	0.0154745i
$842$	16.1787	+	11.7545i	0.557556	+	0.405088i
$843$	−11.3630	+	34.9716i	−0.391362	+	1.20449i
$844$	1.95040	+	6.00273i	0.0671357	+	0.206622i
$845$	−56.7895	+	41.2600i	−1.95362	+	1.41939i
$846$	−6.26400			−0.215361
$847$	−14.0612	−	38.4085i	−0.483147	−	1.31973i
$848$	−7.43017			−0.255153
$849$	49.3605	−	35.8625i	1.69405	−	1.23080i
$850$	−2.04871	−	6.30528i	−0.0702702	−	0.216269i
$851$	−3.20677	+	9.86943i	−0.109927	+	0.338320i
$852$	−10.9501	−	7.95569i	−0.375143	−	0.272557i
$853$	17.2548	+	12.5364i	0.590795	+	0.429238i	0.842600	−	0.538541i	$-0.181024\pi$
$853$	17.2548	+	12.5364i	0.590795	+	0.429238i	−0.251805	+	0.967778i	$0.581024\pi$
$854$	12.3017	−	37.8607i	0.420955	−	1.29557i
$855$	30.3710	+	93.4723i	1.03867	+	3.19669i
$856$	10.6424	−	7.73218i	0.363751	−	0.264281i
$857$	−9.36009			−0.319735			−0.159867	−	0.987139i	$-0.551107\pi$
$857$	−9.36009			−0.319735			−0.159867	+	0.987139i	$0.551107\pi$
$858$	−50.5103	+	17.4451i	−1.72439	+	0.595565i
$859$	−36.1312			−1.23278			−0.616391	−	0.787441i	$-0.711406\pi$
$859$	−36.1312			−1.23278			−0.616391	+	0.787441i	$0.711406\pi$
$860$	15.2232	−	11.0603i	0.519107	−	0.377153i
$861$	−22.9020	−	70.4850i	−0.780497	−	2.40212i
$862$	0.0236148	−	0.0726788i	0.000804322	−	0.00247545i
$863$	31.4451	+	22.8462i	1.07040	+	0.777693i	0.975985	−	0.217839i	$-0.0699008\pi$
$863$	31.4451	+	22.8462i	1.07040	+	0.777693i	0.0944184	+	0.995533i	$0.469901\pi$
$864$	3.89127	+	2.82718i	0.132384	+	0.0961825i
$865$	−13.6340	+	41.9611i	−0.463570	+	1.42672i
$866$	9.49780	+	29.2312i	0.322748	+	0.993317i
$867$	2.24930	−	1.63421i	0.0763902	−	0.0555007i
$868$	10.5000			0.356392
$869$	3.13282	−	4.48307i	0.106274	−	0.152078i
$870$	−51.7270			−1.75371
$871$	−30.8457	+	22.4107i	−1.04517	+	0.759358i
$872$	4.24587	+	13.0674i	0.143783	+	0.442520i
$873$	−8.82617	+	27.1642i	−0.298721	+	0.919367i
$874$	13.6093	+	9.88776i	0.460342	+	0.334458i
$875$	−16.7192	−	12.1472i	−0.565211	−	0.410650i
$876$	2.34283	−	7.21049i	0.0791569	−	0.243620i
$877$	−2.97751	−	9.16382i	−0.100543	−	0.309440i	0.888115	−	0.459621i	$-0.152015\pi$
$877$	−2.97751	−	9.16382i	−0.100543	−	0.309440i	−0.988659	+	0.150180i	$0.952015\pi$
$878$	−9.48807	+	6.89349i	−0.320207	+	0.232644i
$879$	−38.1826			−1.28787
$880$	−6.81530	−	9.02658i	−0.229744	−	0.304286i
$881$	−0.587649			−0.0197984			−0.00989920	−	0.999951i	$-0.503151\pi$
$881$	−0.587649			−0.0197984			−0.00989920	+	0.999951i	$0.503151\pi$
$882$	−26.1201	+	18.9773i	−0.879509	+	0.639000i
$883$	13.9113	+	42.8147i	0.468153	+	1.44083i	0.854973	+	0.518673i	$0.173574\pi$
$883$	13.9113	+	42.8147i	0.468153	+	1.44083i	−0.386819	+	0.922155i	$0.626426\pi$
$884$	1.79080	−	5.51152i	0.0602311	−	0.185372i
$885$	100.195	+	72.7962i	3.36803	+	2.44702i
$886$	−2.26126	−	1.64290i	−0.0759684	−	0.0551942i
$887$	3.16396	−	9.73766i	0.106235	−	0.326958i	−0.883783	−	0.467897i	$-0.845012\pi$
$887$	3.16396	−	9.73766i	0.106235	−	0.326958i	0.990018	+	0.140938i	$0.0450119\pi$
$888$	−3.22931	−	9.93879i	−0.108368	−	0.333524i
$889$	−2.54671	+	1.85030i	−0.0854141	+	0.0620570i
$890$	14.3850			0.482185
$891$	−0.0498390	−	2.70969i	−0.00166967	−	0.0907781i
$892$	−17.2673			−0.578154
$893$	6.52799	−	4.74286i	0.218451	−	0.158714i
$894$	−15.8829	−	48.8825i	−0.531203	−	1.63488i
$895$	1.21241	−	3.73142i	0.0405264	−	0.124727i
$896$	−3.00818	−	2.18557i	−0.100496	−	0.0730147i
$897$	35.9882	+	26.1470i	1.20161	+	0.873022i
$898$	8.55656	−	26.3344i	0.285536	−	0.878790i
$899$	4.76065	+	14.6518i	0.158777	+	0.488664i
$900$	−25.3698	+	18.4322i	−0.845659	+	0.614407i
$901$	7.43017			0.247535
$902$	22.7443	+	6.93031i	0.757301	+	0.230754i
$903$	57.0424			1.89825
$904$	−5.99061	+	4.35243i	−0.199245	+	0.144760i
$905$	2.44867	+	7.53624i	0.0813966	+	0.250513i
$906$	19.0992	−	58.7812i	0.634528	−	1.95288i
$907$	10.8709	+	7.89817i	0.360962	+	0.262255i	0.753453	−	0.657501i	$-0.228387\pi$
$907$	10.8709	+	7.89817i	0.360962	+	0.262255i	−0.392491	+	0.919756i	$0.628387\pi$
$908$	−7.64657	−	5.55556i	−0.253760	−	0.184368i
$909$	13.3841	−	41.1919i	0.443921	−	1.36625i
$910$	−22.7080	−	69.8880i	−0.752762	−	2.31676i
$911$	24.4396	−	17.7564i	0.809721	−	0.588297i	−0.104029	−	0.994574i	$-0.533173\pi$
$911$	24.4396	−	17.7564i	0.809721	−	0.588297i	0.913750	+	0.406277i	$0.133173\pi$
$912$	−16.9403			−0.560948
$913$	−22.8124	−	6.95108i	−0.754981	−	0.230047i
$914$	7.16797			0.237095
$915$	82.1239	−	59.6665i	2.71493	−	1.97251i
$916$	−3.19368	−	9.82913i	−0.105522	−	0.324763i
$917$	−16.2800	+	50.1047i	−0.537613	+	1.65460i
$918$	−3.89127	−	2.82718i	−0.128431	−	0.0933107i
$919$	−32.7950	−	23.8270i	−1.08181	−	0.785979i	−0.103810	−	0.994597i	$-0.533103\pi$
$919$	−32.7950	−	23.8270i	−1.08181	−	0.785979i	−0.977997	+	0.208618i	$0.933103\pi$
$920$	−2.90949	+	8.95448i	−0.0959229	+	0.295220i
$921$	6.05224	+	18.6269i	0.199428	+	0.613777i
$922$	2.68221	−	1.94874i	0.0883338	−	0.0641783i
$923$	28.2120			0.928610
$924$	−0.630532	−	34.2814i	−0.0207430	−	1.12777i
$925$	24.9193			0.819341
$926$	−18.2948	+	13.2920i	−0.601205	+	0.436801i
$927$	−12.2200	−	37.6092i	−0.401357	−	1.23525i
$928$	1.68587	−	5.18858i	0.0553414	−	0.170323i
$929$	−29.7785	−	21.6354i	−0.977002	−	0.709833i	−0.0199652	−	0.999801i	$-0.506356\pi$
$929$	−29.7785	−	21.6354i	−0.977002	−	0.709833i	−0.957037	+	0.289967i	$0.906356\pi$
$930$	21.6608	+	15.7375i	0.710286	+	0.516053i
$931$	12.8520	−	39.5542i	0.421206	−	1.29634i
$932$	−0.578568	−	1.78065i	−0.0189516	−	0.0583271i
$933$	40.1475	−	29.1688i	1.31437	−	0.954945i
$934$	−13.4249			−0.439278
$935$	6.81530	+	9.02658i	0.222884	+	0.295201i
$936$	−27.4110			−0.895957
$937$	15.5544	−	11.3009i	0.508140	−	0.369185i	−0.303978	−	0.952679i	$-0.598315\pi$
$937$	15.5544	−	11.3009i	0.508140	−	0.369185i	0.812118	+	0.583494i	$0.198315\pi$
$938$	−7.55963	−	23.2661i	−0.246831	−	0.759666i
$939$	5.95480	−	18.3270i	0.194328	−	0.598079i
$940$	3.65371	+	2.65458i	0.119171	+	0.0865827i
$941$	10.7079	+	7.77972i	0.349067	+	0.253612i	0.748477	−	0.663160i	$-0.230785\pi$
$941$	10.7079	+	7.77972i	0.349067	+	0.253612i	−0.399411	+	0.916772i	$0.630785\pi$
$942$	−12.1486	+	37.3894i	−0.395821	+	1.21821i
$943$	−6.11626	−	18.8239i	−0.199173	−	0.612991i
$944$	−10.5675	+	7.67775i	−0.343943	+	0.249889i
$945$	−60.9909			−1.98404
$946$	−10.4826	+	15.0006i	−0.340818	+	0.487711i
$947$	−11.5737			−0.376095			−0.188048	−	0.982160i	$-0.560216\pi$
$947$	−11.5737			−0.376095			−0.188048	+	0.982160i	$0.560216\pi$
$948$	3.70917	−	2.69487i	0.120468	−	0.0875253i
$949$	4.88333	+	15.0293i	0.158520	+	0.487873i
$950$	12.4828	−	38.4180i	0.404995	−	1.24645i
$951$	−52.0831	−	37.8406i	−1.68891	−	1.22706i
$952$	3.00818	+	2.18557i	0.0974956	+	0.0708347i
$953$	−10.1672	+	31.2913i	−0.329346	+	1.01362i	0.640094	+	0.768297i	$0.278895\pi$
$953$	−10.1672	+	31.2913i	−0.329346	+	1.01362i	−0.969440	+	0.245327i	$0.921105\pi$
$954$	−10.8603	−	33.4246i	−0.351615	−	1.08216i
$955$	4.08651	−	2.96903i	0.132236	−	0.0960754i
$956$	19.9329			0.644677
$957$	47.5508	−	16.4229i	1.53710	−	0.530878i
$958$	−9.04124			−0.292109
$959$	−67.3516	+	48.9338i	−2.17490	+	1.58015i
$960$	−2.92993	−	9.01740i	−0.0945631	−	0.291035i
$961$	−7.11538	+	21.8989i	−0.229528	+	0.706416i
$962$	17.6222	+	12.8033i	0.568162	+	0.412794i
$963$	50.3386	+	36.5732i	1.62214	+	1.17855i
$964$	2.24165	−	6.89910i	0.0721988	−	0.222205i
$965$	−8.51202	−	26.1973i	−0.274012	−	0.843321i
$966$	−23.0909	+	16.7765i	−0.742939	+	0.539776i
$967$	27.4729			0.883470			0.441735	−	0.897146i	$-0.354363\pi$
$967$	27.4729			0.883470			0.441735	+	0.897146i	$0.354363\pi$
$968$	9.13093	+	6.13401i	0.293479	+	0.197155i
$969$	16.9403			0.544200
$970$	16.6599	−	12.1041i	0.534917	−	0.388640i
$971$	4.77493	+	14.6957i	0.153235	+	0.471608i	0.997978	−	0.0635643i	$-0.0202468\pi$
$971$	4.77493	+	14.6957i	0.153235	+	0.471608i	−0.844743	+	0.535172i	$0.820247\pi$
$972$	5.16105	−	15.8841i	0.165541	−	0.509482i
$973$	−28.3236	−	20.5783i	−0.908012	−	0.659709i
$974$	−2.09670	−	1.52334i	−0.0671825	−	0.0488110i
$975$	33.0092	−	101.592i	1.05714	−	3.25354i
$976$	3.30841	+	10.1822i	0.105900	+	0.325925i
$977$	−29.7306	+	21.6005i	−0.951166	+	0.691063i	−0.951082	−	0.308937i	$-0.900027\pi$
$977$	−29.7306	+	21.6005i	−0.951166	+	0.691063i	−8.36410e−5		1.00000i	$0.500027\pi$
$978$	−38.3041			−1.22483
$979$	−13.2236	+	4.56711i	−0.422627	+	0.145966i
$980$	23.2778			0.743582
$981$	−52.5778	+	38.2000i	−1.67868	+	1.21963i
$982$	9.20532	+	28.3311i	0.293754	+	0.904081i
$983$	−13.7248	+	42.2404i	−0.437752	+	1.34726i	0.452489	+	0.891770i	$0.350536\pi$
$983$	−13.7248	+	42.2404i	−0.437752	+	1.34726i	−0.890240	+	0.455491i	$0.849464\pi$
$984$	16.1251	+	11.7156i	0.514049	+	0.373479i
$985$	−51.3706	−	37.3229i	−1.63680	−	1.18921i
$986$	−1.68587	+	5.18858i	−0.0536891	+	0.165238i
$987$	4.23067	+	13.0207i	0.134664	+	0.414452i
$988$	28.5662	−	20.7546i	0.908813	−	0.660291i
$989$	15.2339			0.484410
$990$	30.6444	−	43.8522i	0.973944	−	1.39372i
$991$	−19.0390			−0.604794			−0.302397	−	0.953182i	$-0.597787\pi$
$991$	−19.0390			−0.604794			−0.302397	+	0.953182i	$0.597787\pi$
$992$	−2.28455	+	1.65982i	−0.0725344	+	0.0526993i
$993$	−18.0047	−	55.4128i	−0.571362	−	1.75847i
$994$	−5.59368	+	17.2156i	−0.177421	+	0.546045i
$995$	69.0393	+	50.1600i	2.18869	+	1.59018i
$996$	−16.1734	−	11.7507i	−0.512474	−	0.372334i
$997$	−4.47046	+	13.7587i	−0.141581	+	0.435741i	−0.996555	−	0.0829288i	$-0.973573\pi$
$997$	−4.47046	+	13.7587i	−0.141581	+	0.435741i	0.854975	+	0.518670i	$0.173573\pi$
$998$	−4.87116	−	14.9919i	−0.154194	−	0.474560i
$999$	14.6261	−	10.6265i	0.462750	−	0.336208i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.f.69.1	✓	16
11.2	odd	10		4114.2.a.bg.1.2		8
11.4	even	5	inner	374.2.g.f.103.1	yes	16
11.9	even	5		4114.2.a.bi.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.f.69.1	✓	16	1.1	even	1	trivial
374.2.g.f.103.1	yes	16	11.4	even	5	inner
4114.2.a.bg.1.2		8	11.2	odd	10
4114.2.a.bi.1.2		8	11.9	even	5

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	374.2.g.f.69.1

Level	$374$
Weight	$2$
Character	374.69
Analytic conductor	$2.986$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$