LMFDB - Embedded newform 374.2.g.f.103.1

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)

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")

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);

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			103.1
Root			$-1.44028 - 1.04643i$ of defining polynomial
Character	$\chi$	$=$	374.103
Dual form			374.2.g.f.69.1

$q$ -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 $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$ .

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

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	0.319306	+	0.947652i	$0.396550\pi$
$3$	−0.859156	+	2.64421i	−0.496034	+	1.52664i	−0.815339	+	0.578983i	$0.803450\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.75895	+	2.00449i	−1.23384	+	0.896436i	−0.997172	−	0.0751552i	$-0.976055\pi$
$5$	−2.75895	+	2.00449i	−1.23384	+	0.896436i	−0.236666	+	0.971591i	$0.576055\pi$
$6$	2.24930	−	1.63421i	0.918273	−	0.667164i
$7$	1.14902	+	3.53632i	0.434289	+	1.33661i	0.893813	+	0.448440i	$0.148020\pi$
$7$	1.14902	+	3.53632i	0.434289	+	1.33661i	−0.459524	+	0.888165i	$0.651980\pi$
$8$	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	0.999959	−	0.00908644i	$-0.00289234\pi$
$13$	4.68837	+	3.40630i	1.30032	+	0.944739i	0.300363	+	0.953825i	$0.402892\pi$
$14$	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	−0.464225	−	0.885717i	$-0.653667\pi$
$19$	1.88284	−	5.79478i	0.431953	−	1.32941i	0.896177	−	0.443696i	$-0.146333\pi$
$20$	−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	0.976546	+	0.215307i	$0.0690754\pi$
$29$	1.68587	+	5.18858i	0.313058	+	0.963494i	−0.663488	+	0.748187i	$0.730925\pi$
$30$	−2.92993	+	9.01740i	−0.534930	+	1.64634i
$31$	−2.28455	−	1.65982i	−0.410317	−	0.298112i	0.363413	−	0.931628i	$-0.381611\pi$
$31$	−2.28455	−	1.65982i	−0.410317	−	0.298112i	−0.773730	+	0.633516i	$0.781611\pi$
$32$	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	1.00000		5.67107e-5i	$-1.80516e-5\pi$
$37$	1.16150	+	3.57473i	0.190950	+	0.587683i	−0.809050	+	0.587739i	$0.800018\pi$
$38$	−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	−0.615084	−	0.788462i	$-0.710878\pi$
$41$	2.21533	−	6.81807i	0.345976	−	1.06480i	0.961059	−	0.276342i	$-0.0891222\pi$
$42$	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	−0.976457	−	0.215714i	$-0.930792\pi$
$47$	−0.409236	+	1.25950i	−0.0596932	+	0.183717i	0.916763	+	0.399431i	$0.130792\pi$
$48$	−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	0.918338	−	0.395798i	$-0.129532\pi$
$53$	6.01114	+	4.36735i	0.825693	+	0.599901i	−0.0926446	+	0.995699i	$0.529532\pi$
$54$	−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	0.763328	+	0.646011i	$0.223564\pi$
$59$	4.03643	+	12.4229i	0.525498	+	1.61732i	−0.237830	+	0.971307i	$0.576436\pi$
$60$	7.67066	−	5.57306i	0.990278	−	0.719479i
$61$	−8.66153	+	6.29297i	−1.10899	+	0.805732i	−0.982505	−	0.186236i	$-0.940371\pi$
$61$	−8.66153	+	6.29297i	−1.10899	+	0.805732i	−0.126490	+	0.991968i	$0.540371\pi$
$62$	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	−0.329021	−	0.944323i	$-0.606719\pi$
$71$	3.93847	−	2.86146i	0.467410	−	0.339593i	0.796431	+	0.604729i	$0.206719\pi$
$72$	−3.82665	+	2.78022i	−0.450974	+	0.327652i
$73$	−0.842658	−	2.59343i	−0.0986256	−	0.303539i	0.889556	−	0.456826i	$-0.151014\pi$
$73$	−0.842658	−	2.59343i	−0.0986256	−	0.303539i	−0.988182	+	0.153288i	$0.951014\pi$
$74$	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	0.510202	−	0.860055i	$-0.329571\pi$
$79$	−1.33410	−	0.969278i	−0.150098	−	0.109052i	−0.660299	+	0.751002i	$0.729571\pi$
$80$	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	−0.220823	−	0.975314i	$-0.570874\pi$
$83$	5.81718	−	4.22643i	0.638518	−	0.463910i	0.859341	+	0.511403i	$0.170874\pi$
$84$	−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	0.807496	−	0.589874i	$-0.200822\pi$
$97$	4.88525	+	3.54934i	0.496022	+	0.360381i	−0.311473	+	0.950255i	$0.600822\pi$
$98$	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	0.154683	−	0.987964i	$-0.450564\pi$
$101$	−7.40803	−	5.38225i	−0.737127	−	0.535554i	−0.891810	+	0.452410i	$0.850564\pi$
$102$	0.859156	−	2.64421i	0.0850691	−	0.261816i
$103$	−2.58351	−	7.95122i	−0.254561	−	0.783457i	−0.993916	−	0.110142i	$-0.964870\pi$
$103$	−2.58351	−	7.95122i	−0.254561	−	0.783457i	0.739355	−	0.673315i	$-0.235130\pi$
$104$	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	0.537538	+	0.843239i	$0.319354\pi$
$107$	−4.06505	+	12.5109i	−0.392983	+	1.20948i	−0.930521	+	0.366238i	$0.880646\pi$
$108$	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	−0.783879	−	0.620914i	$-0.786762\pi$
$113$	2.28821	−	7.04238i	0.215257	−	0.662492i	0.999135	−	0.0415777i	$-0.0132384\pi$
$114$	−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	−0.617758	−	0.786368i	$-0.711959\pi$
$127$	−0.684912	+	0.497617i	−0.0607761	+	0.0441564i	0.556982	+	0.830524i	$0.311959\pi$
$128$	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	−0.602162	+	0.798374i	$0.705694\pi$
$137$	−18.1135	+	13.1602i	−1.54754	+	1.12435i	−0.945377	+	0.325979i	$0.894306\pi$
$138$	−6.21006	+	4.51187i	−0.528635	+	0.384076i
$139$	2.90956	+	8.95470i	0.246785	+	0.759528i	0.995338	+	0.0964517i	$0.0307493\pi$
$139$	2.90956	+	8.95470i	0.246785	+	0.759528i	−0.748552	+	0.663076i	$0.769251\pi$
$140$	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	−0.996524	−	0.0833021i	$-0.973453\pi$
$149$	−14.9560	+	10.8662i	−1.22524	+	0.890191i	−0.228718	+	0.973493i	$0.573453\pi$
$150$	−5.69600	−	17.5305i	−0.465077	−	1.43136i
$151$	−6.86950	+	21.1421i	−0.559032	+	1.72052i	0.126018	+	0.992028i	$0.459780\pi$
$151$	−6.86950	+	21.1421i	−0.559032	+	1.72052i	−0.685050	+	0.728496i	$0.740220\pi$
$152$	−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	−0.610832	−	0.791760i	$-0.709165\pi$
$157$	4.36953	−	13.4480i	0.348727	−	1.07327i	0.959558	−	0.281510i	$-0.0908352\pi$
$158$	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	0.0583817	−	0.998294i	$-0.481406\pi$
$163$	−11.1459	−	8.09795i	−0.873012	−	0.634280i	−0.931393	+	0.364014i	$0.881406\pi$
$164$	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	0.564733	−	0.825274i	$-0.308979\pi$
$167$	−0.589757	−	0.428484i	−0.0456368	−	0.0331571i	−0.610370	+	0.792117i	$0.708979\pi$
$168$	−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	0.676105	+	0.736805i	$0.263667\pi$
$173$	−3.99795	+	12.3044i	−0.303959	+	0.935489i	−0.980064	+	0.198684i	$0.936333\pi$
$174$	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	−0.936891	−	0.349623i	$-0.886310\pi$
$179$	0.355520	−	1.09418i	0.0265728	−	0.0817827i	0.963463	+	0.267840i	$0.0863098\pi$
$180$	4.98458	+	15.3410i	0.371529	+	1.14345i
$181$	−1.87984	+	1.36578i	−0.139727	+	0.101518i	−0.655453	−	0.755236i	$-0.727522\pi$
$181$	−1.87984	+	1.36578i	−0.139727	+	0.101518i	0.515726	+	0.856754i	$0.327522\pi$
$182$	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	0.933131	−	0.359538i	$-0.117066\pi$
$191$	−0.457712	−	1.40869i	−0.0331189	−	0.101929i	−0.966249	+	0.257608i	$0.917066\pi$
$192$	2.24930	−	1.63421i	0.162329	−	0.117939i
$193$	6.53465	−	4.74770i	0.470374	−	0.341747i	−0.327213	−	0.944951i	$-0.606109\pi$
$193$	6.53465	−	4.74770i	0.470374	−	0.341747i	0.797587	+	0.603204i	$0.206109\pi$
$194$	−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	0.397982	−	0.917393i	$-0.369711\pi$
$211$	−5.10622	−	3.70989i	−0.351527	−	0.255399i	−0.749509	+	0.661994i	$0.769711\pi$
$212$	−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	0.597334	+	0.801992i	$0.296227\pi$
$223$	−5.33590	+	16.4222i	−0.357319	+	1.09971i	−0.954653	+	0.297721i	$0.903773\pi$
$224$	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	0.999988	+	0.00489107i	$0.00155688\pi$
$227$	2.92073	+	8.98908i	0.193856	+	0.596626i	−0.806132	+	0.591735i	$0.798443\pi$
$228$	−5.23483	+	16.1111i	−0.346685	+	1.06699i
$229$	8.36115	+	6.07473i	0.552521	+	0.401430i	0.828714	−	0.559672i	$-0.189073\pi$
$229$	8.36115	+	6.07473i	0.552521	+	0.401430i	−0.276193	+	0.961102i	$0.589073\pi$
$230$	−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	0.636295	−	0.771446i	$-0.280466\pi$
$233$	1.51471	+	1.10050i	0.0992320	+	0.0720963i	−0.537063	+	0.843542i	$0.680466\pi$
$234$	−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	−0.527824	−	0.849354i	$-0.676992\pi$
$239$	6.15962	−	18.9574i	0.398432	−	1.22625i	0.926256	−	0.376895i	$-0.123008\pi$
$240$	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	0.994428	+	0.105422i	$0.0336193\pi$
$251$	22.2116	+	16.1377i	1.40198	+	1.01860i	0.407557	+	0.913180i	$0.366381\pi$
$252$	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	−0.985188	−	0.171480i	$-0.945145\pi$
$257$	−4.63218	−	14.2564i	−0.288948	−	0.889290i	0.696240	−	0.717809i	$-0.254855\pi$
$258$	−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	0.522320	−	0.852750i	$-0.325067\pi$
$269$	24.5155	−	17.8116i	1.49474	−	1.08599i	0.972419	−	0.233241i	$-0.0749332\pi$
$270$	13.2702	−	9.64136i	0.807598	−	0.586754i
$271$	−0.836260	−	2.57374i	−0.0507992	−	0.156344i	0.922439	−	0.386143i	$-0.126193\pi$
$271$	−0.836260	−	2.57374i	−0.0507992	−	0.156344i	−0.973238	+	0.229799i	$0.926193\pi$
$272$	−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	0.338500	−	0.940966i	$-0.390081\pi$
$277$	−7.51962	−	5.46333i	−0.451810	−	0.328259i	−0.790310	+	0.612707i	$0.790081\pi$
$278$	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	−0.859266	−	0.511530i	$-0.829079\pi$
$281$	−10.6999	+	7.77390i	−0.638300	+	0.463752i	0.220966	+	0.975282i	$0.429079\pi$
$282$	1.13779	+	3.50176i	0.0677545	+	0.208527i
$283$	6.78133	−	20.8708i	0.403108	−	1.24064i	−0.519356	−	0.854558i	$-0.673828\pi$
$283$	6.78133	−	20.8708i	0.403108	−	1.24064i	0.922464	−	0.386082i	$-0.126172\pi$
$284$	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	0.995141	+	0.0984579i	$0.0313910\pi$
$293$	4.24383	+	13.0612i	0.247927	+	0.763041i	−0.747214	+	0.664583i	$0.768609\pi$
$294$	−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	−0.663905	−	0.747817i	$-0.731102\pi$
$311$	5.51561	−	16.9753i	0.312761	−	0.962581i	0.976666	−	0.214763i	$-0.0688981\pi$
$312$	4.97894	+	15.3236i	0.281877	+	0.867528i
$313$	5.60729	−	4.07393i	0.316943	−	0.230272i	−0.417927	−	0.908481i	$-0.637243\pi$
$313$	5.60729	−	4.07393i	0.316943	−	0.230272i	0.734870	+	0.678208i	$0.237243\pi$
$314$	−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	0.972620	−	0.232401i	$-0.0746583\pi$
$317$	18.7330	+	13.6103i	1.05215	+	0.764431i	0.0795294	+	0.996833i	$0.474658\pi$
$318$	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	0.777193	+	0.629262i	$0.216643\pi$
$337$	9.51475	+	29.2834i	0.518302	+	1.59517i	−0.258892	+	0.965906i	$0.583357\pi$
$338$	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	−0.841276	−	0.540607i	$-0.818195\pi$
$347$	−10.9364	+	7.94576i	−0.587097	+	0.426551i	0.254179	+	0.967157i	$0.418195\pi$
$348$	−4.68720	−	14.4257i	−0.251260	−	0.773300i
$349$	2.89049	−	8.89602i	0.154725	−	0.476193i	−0.843408	−	0.537273i	$-0.819454\pi$
$349$	2.89049	−	8.89602i	0.154725	−	0.476193i	0.998133	+	0.0610799i	$0.0194544\pi$
$350$	−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	0.847153	−	0.531350i	$-0.178315\pi$
$359$	−2.85209	−	8.77784i	−0.150528	−	0.463277i	−0.997680	+	0.0680729i	$0.978315\pi$
$360$	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	−0.999827	−	0.0185867i	$-0.994083\pi$
$367$	−3.86737	−	11.9025i	−0.201875	−	0.621307i	0.797952	−	0.602721i	$-0.205917\pi$
$368$	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	−0.640379	−	0.768059i	$-0.721223\pi$
$379$	−2.09865	+	1.52476i	−0.107800	+	0.0783215i	0.532579	+	0.846380i	$0.321223\pi$
$380$	−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	0.960195	−	0.279330i	$-0.0901123\pi$
$383$	19.3992	+	14.0944i	0.991253	+	0.720188i	0.0310581	+	0.999518i	$0.490112\pi$
$384$	−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	0.941708	−	0.336431i	$-0.109220\pi$
$389$	−0.353026	−	1.08650i	−0.0178991	−	0.0550879i	−0.959607	+	0.281343i	$0.909220\pi$
$390$	−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	0.256487	−	0.966548i	$-0.417435\pi$
$401$	25.1311	−	18.2588i	1.25499	−	0.911802i	0.998500	+	0.0547461i	$0.0174349\pi$
$402$	−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	0.991679	+	0.128733i	$0.0410909\pi$
$409$	28.7290	+	20.8728i	1.42056	+	1.03210i	0.428878	+	0.903363i	$0.358909\pi$
$410$	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	0.679893	+	0.733311i	$0.262026\pi$
$421$	−6.17973	+	19.0193i	−0.301182	+	0.926942i	−0.981075	+	0.193630i	$0.937974\pi$
$422$	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	0.586295	−	0.810097i	$-0.300586\pi$
$431$	−0.0618243	−	0.0449180i	−0.00297797	−	0.00216362i	−0.589273	+	0.807934i	$0.700586\pi$
$432$	−1.48633	+	4.57447i	−0.0715113	+	0.220089i
$433$	9.49780	+	29.2312i	0.456435	+	1.40476i	0.869442	+	0.494035i	$0.164478\pi$
$433$	9.49780	+	29.2312i	0.456435	+	1.40476i	−0.413007	+	0.910728i	$0.635522\pi$
$434$	−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	−0.928439	−	0.371484i	$-0.878849\pi$
$443$	0.863723	−	2.65826i	0.0410367	−	0.126298i	0.969476	+	0.245186i	$0.0788491\pi$
$444$	−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	−0.0836201	−	0.996498i	$-0.526648\pi$
$449$	−22.4014	−	16.2755i	−1.05719	−	0.768090i	−0.973566	+	0.228407i	$0.926648\pi$
$450$	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	−0.715099	−	0.699023i	$-0.753618\pi$
$457$	−5.79901	+	4.21322i	−0.271266	+	0.197086i	0.443833	+	0.896110i	$0.353618\pi$
$458$	−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	−0.307417	−	0.951575i	$-0.599465\pi$
$467$	10.8610	−	7.89099i	0.502588	−	0.365151i	0.810005	+	0.586424i	$0.199465\pi$
$468$	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	−0.408006	−	0.912979i	$-0.633776\pi$
$479$	7.31452	−	5.31431i	0.334209	−	0.242817i	0.742214	+	0.670163i	$0.233776\pi$
$480$	−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	−0.931270	−	0.364330i	$-0.881298\pi$
$487$	0.800867	−	2.46482i	0.0362908	−	0.111691i	0.967561	+	0.252638i	$0.0812982\pi$
$488$	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	0.911865	+	0.410489i	$0.134642\pi$
$491$	9.20532	+	28.3311i	0.415430	+	1.27856i	−0.496435	+	0.868074i	$0.665358\pi$
$492$	−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	−0.998922	−	0.0464215i	$-0.985218\pi$
$499$	−4.87116	−	14.9919i	−0.218063	−	0.671129i	0.780859	−	0.624707i	$-0.214782\pi$
$500$	−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	0.501810	+	0.864978i	$0.332668\pi$
$503$	−9.25329	+	28.4787i	−0.412584	+	1.26980i	−0.914394	+	0.404825i	$0.867332\pi$
$504$	−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	0.770044	+	0.637991i	$0.220234\pi$
$509$	−5.14248	+	15.8269i	−0.227936	+	0.701516i	−0.997980	+	0.0635251i	$0.979766\pi$
$510$	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	−0.999292	−	0.0376216i	$-0.988022\pi$
$521$	−4.86093	−	14.9604i	−0.212961	−	0.655427i	0.786331	−	0.617806i	$-0.211978\pi$
$522$	−20.8766	+	15.1677i	−0.913745	+	0.663874i
$523$	−20.4507	+	14.8583i	−0.894246	+	0.649708i	−0.936982	−	0.349378i	$-0.886393\pi$
$523$	−20.4507	+	14.8583i	−0.894246	+	0.649708i	0.0427354	+	0.999086i	$0.486393\pi$
$524$	−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	0.603840	−	0.797106i	$-0.293637\pi$
$541$	0.752308	+	0.546584i	0.0323443	+	0.0234995i	−0.571496	+	0.820605i	$0.693637\pi$
$542$	−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	−0.996012	−	0.0892218i	$-0.971562\pi$
$547$	−3.22236	+	9.91740i	−0.137778	+	0.424037i	0.858234	+	0.513259i	$0.171562\pi$
$548$	−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	0.579058	+	0.815287i	$0.303421\pi$
$557$	13.9199	+	42.8409i	0.589804	+	1.81523i	0.0107460	+	0.999942i	$0.496579\pi$
$558$	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	0.288946	−	0.957345i	$-0.406695\pi$
$563$	−12.6291	−	9.17560i	−0.532254	−	0.386705i	−0.821200	+	0.570640i	$0.806695\pi$
$564$	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	−0.972368	−	0.233452i	$-0.924998\pi$
$569$	−1.15658	+	3.55959i	−0.0484864	+	0.149226i	0.923882	+	0.382677i	$0.124998\pi$
$570$	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	−0.386287	−	0.922379i	$-0.626243\pi$
$577$	8.92560	−	6.48483i	0.371578	−	0.269967i	0.757865	+	0.652412i	$0.226243\pi$
$578$	−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	0.879799	+	0.475346i	$0.157677\pi$
$587$	10.8403	+	33.3631i	0.447428	+	1.37704i	−0.432371	+	0.901696i	$0.642323\pi$
$588$	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	−0.331188	−	0.943565i	$-0.607449\pi$
$599$	11.3526	−	8.24811i	0.463853	−	0.337009i	0.795041	+	0.606556i	$0.207449\pi$
$600$	14.9123	−	10.8344i	0.608793	−	0.442314i
$601$	−10.0404	−	30.9012i	−0.409557	−	1.26049i	−0.917030	−	0.398819i	$-0.869420\pi$
$601$	−10.0404	−	30.9012i	−0.409557	−	1.26049i	0.507473	−	0.861668i	$-0.330580\pi$
$602$	−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	0.505872	−	0.862608i	$-0.331171\pi$
$607$	−3.89748	−	2.83168i	−0.158194	−	0.114934i	−0.664066	+	0.747674i	$0.731171\pi$
$608$	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	−0.977441	−	0.211209i	$-0.932260\pi$
$613$	−1.54815	+	4.76471i	−0.0625292	+	0.192445i	0.914912	+	0.403654i	$0.132260\pi$
$614$	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	−0.527046	−	0.849837i	$-0.676700\pi$
$619$	9.92364	−	30.5418i	0.398865	−	1.22758i	0.925911	−	0.377743i	$-0.123300\pi$
$620$	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	0.900965	+	0.433891i	$0.142860\pi$
$631$	10.7287	+	33.0196i	0.427104	+	1.31449i	−0.473861	+	0.880600i	$0.657140\pi$
$632$	−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	0.790968	+	0.611857i	$0.209577\pi$
$641$	−5.28081	+	16.2527i	−0.208579	+	0.641941i	−0.999547	+	0.0300838i	$0.990423\pi$
$642$	11.3020	+	34.7840i	0.446054	+	1.37281i
$643$	7.40107	−	5.37719i	0.291870	−	0.212056i	−0.432208	−	0.901774i	$-0.642266\pi$
$643$	7.40107	−	5.37719i	0.291870	−	0.212056i	0.724078	+	0.689718i	$0.242266\pi$
$644$	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	0.948109	−	0.317946i	$-0.102993\pi$
$647$	23.8771	+	17.3477i	0.938706	+	0.682010i	−0.00940298	+	0.999956i	$0.502993\pi$
$648$	−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	0.996337	−	0.0855185i	$-0.0272547\pi$
$653$	3.57797	+	11.0119i	0.140017	+	0.430928i	−0.856320	+	0.516446i	$0.827255\pi$
$654$	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	0.994518	−	0.104563i	$-0.0333444\pi$
$673$	31.1929	+	22.6629i	1.20240	+	0.873592i	0.207878	+	0.978155i	$0.433344\pi$
$674$	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	−0.625227	−	0.780443i	$-0.714994\pi$
$677$	−1.98236	+	1.44027i	−0.0761882	+	0.0553540i	0.549039	+	0.835797i	$0.314994\pi$
$678$	−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	0.991961	+	0.126542i	$0.0403879\pi$
$691$	37.2969	+	27.0978i	1.41884	+	1.03085i	0.426882	+	0.904308i	$0.359612\pi$
$692$	−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	−0.878225	−	0.478249i	$-0.841272\pi$
$701$	3.00193	−	9.23901i	0.113382	−	0.348952i	0.991606	+	0.129296i	$0.0412718\pi$
$702$	−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	−0.305955	−	0.952046i	$-0.598976\pi$
$709$	13.4453	−	9.76860i	0.504950	−	0.366867i	0.810904	+	0.585179i	$0.198976\pi$
$710$	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	−0.999789	−	0.0205265i	$-0.993466\pi$
$719$	−5.44349	−	16.7533i	−0.203008	−	0.624794i	0.796781	−	0.604268i	$-0.206534\pi$
$720$	−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	−0.932193	−	0.361962i	$-0.882107\pi$
$733$	−10.5802	−	32.5625i	−0.390789	−	1.20272i	0.541404	−	0.840763i	$-0.317893\pi$
$734$	−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	0.383767	−	0.923430i	$-0.374627\pi$
$739$	−10.2180	−	7.42384i	−0.375876	−	0.273090i	−0.759643	+	0.650340i	$0.774627\pi$
$740$	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	−0.866888	−	0.498504i	$-0.833883\pi$
$743$	−18.0084	+	13.0839i	−0.660665	+	0.480001i	0.206222	+	0.978505i	$0.433883\pi$
$744$	−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	0.389687	+	0.920947i	$0.372583\pi$
$751$	−12.7950	+	39.3789i	−0.466896	+	1.43696i	−0.856583	+	0.516010i	$0.827417\pi$
$752$	−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	−0.251534	−	0.967848i	$-0.580935\pi$
$757$	−34.3849	−	24.9821i	−1.24974	−	0.907990i	−0.998207	+	0.0598586i	$0.980935\pi$
$758$	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	0.870460	−	0.492239i	$-0.163822\pi$
$761$	18.5186	+	13.4546i	0.671299	+	0.487728i	−0.199161	+	0.979967i	$0.563822\pi$
$762$	−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	−0.633281	−	0.773922i	$-0.718292\pi$
$773$	9.28488	−	28.5759i	0.333954	−	1.02780i	0.967235	−	0.253883i	$-0.0817077\pi$
$774$	−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	−0.112184	−	0.993687i	$-0.535785\pi$
$787$	22.3924	−	16.2690i	0.798202	−	0.579928i	0.910386	+	0.413760i	$0.135785\pi$
$788$	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	−0.820920	−	0.571044i	$-0.806539\pi$
$797$	−15.0050	+	10.9017i	−0.531503	+	0.386159i	0.289417	+	0.957203i	$0.406539\pi$
$798$	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	−0.659490	−	0.751714i	$-0.729228\pi$
$809$	−4.21983	+	3.06588i	−0.148361	+	0.107791i	0.511129	+	0.859504i	$0.329228\pi$
$810$	−0.861122	−	2.65026i	−0.0302568	−	0.0931207i
$811$	8.01578	−	24.6700i	0.281472	−	0.866282i	−0.705962	−	0.708250i	$-0.749485\pi$
$811$	8.01578	−	24.6700i	0.281472	−	0.866282i	0.987434	−	0.158032i	$-0.0505150\pi$
$812$	−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	0.993817	−	0.111031i	$-0.0354154\pi$
$821$	3.56844	+	10.9825i	0.124540	+	0.383293i	−0.869277	+	0.494325i	$0.835415\pi$
$822$	−19.2361	+	59.2025i	−0.670935	+	2.06492i
$823$	36.8461	+	26.7703i	1.28438	+	0.933154i	0.999676	−	0.0254628i	$-0.00810594\pi$
$823$	36.8461	+	26.7703i	1.28438	+	0.933154i	0.284700	+	0.958617i	$0.408106\pi$
$824$	−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	0.581864	−	0.813286i	$-0.302324\pi$
$827$	−0.339680	−	0.246792i	−0.0118118	−	0.00858180i	−0.593676	+	0.804705i	$0.702324\pi$
$828$	−4.03544	+	12.4198i	−0.140241	+	0.431619i
$829$	−6.44724	−	19.8426i	−0.223922	−	0.689161i	−0.998399	−	0.0565592i	$-0.981987\pi$
$829$	−6.44724	−	19.8426i	−0.223922	−	0.689161i	0.774477	−	0.632602i	$-0.218013\pi$
$830$	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	−0.988073	−	0.153983i	$-0.950790\pi$
$839$	−2.84430	+	8.75387i	−0.0981963	+	0.302217i	0.889877	+	0.456200i	$0.150790\pi$
$840$	−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	−0.251805	−	0.967778i	$-0.581024\pi$
$853$	17.2548	−	12.5364i	0.590795	−	0.429238i	0.842600	+	0.538541i	$0.181024\pi$
$854$	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	0.0944184	−	0.995533i	$-0.469901\pi$
$863$	31.4451	−	22.8462i	1.07040	−	0.777693i	0.975985	+	0.217839i	$0.0699008\pi$
$864$	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	−0.988659	−	0.150180i	$-0.952015\pi$
$877$	−2.97751	+	9.16382i	−0.100543	+	0.309440i	0.888115	+	0.459621i	$0.152015\pi$
$878$	−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	−0.386819	−	0.922155i	$-0.626426\pi$
$883$	13.9113	−	42.8147i	0.468153	−	1.44083i	0.854973	−	0.518673i	$-0.173574\pi$
$884$	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	0.990018	−	0.140938i	$-0.0450119\pi$
$887$	3.16396	+	9.73766i	0.106235	+	0.326958i	−0.883783	+	0.467897i	$0.845012\pi$
$888$	−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	−0.392491	−	0.919756i	$-0.628387\pi$
$907$	10.8709	−	7.89817i	0.360962	−	0.262255i	0.753453	+	0.657501i	$0.228387\pi$
$908$	−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	0.913750	−	0.406277i	$-0.133173\pi$
$911$	24.4396	+	17.7564i	0.809721	+	0.588297i	−0.104029	+	0.994574i	$0.533173\pi$
$912$	−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	−0.977997	−	0.208618i	$-0.933103\pi$
$919$	−32.7950	+	23.8270i	−1.08181	+	0.785979i	−0.103810	+	0.994597i	$0.533103\pi$
$920$	−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	−0.957037	−	0.289967i	$-0.906356\pi$
$929$	−29.7785	+	21.6354i	−0.977002	+	0.709833i	−0.0199652	+	0.999801i	$0.506356\pi$
$930$	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	0.812118	−	0.583494i	$-0.198315\pi$
$937$	15.5544	+	11.3009i	0.508140	+	0.369185i	−0.303978	+	0.952679i	$0.598315\pi$
$938$	−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	−0.399411	−	0.916772i	$-0.630785\pi$
$941$	10.7079	−	7.77972i	0.349067	−	0.253612i	0.748477	+	0.663160i	$0.230785\pi$
$942$	−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	−0.969440	−	0.245327i	$-0.921105\pi$
$953$	−10.1672	−	31.2913i	−0.329346	−	1.01362i	0.640094	−	0.768297i	$-0.278895\pi$
$954$	−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	−0.844743	−	0.535172i	$-0.820247\pi$
$971$	4.77493	−	14.6957i	0.153235	−	0.471608i	0.997978	+	0.0635643i	$0.0202468\pi$
$972$	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	−8.36410e−5	−	1.00000i	$-0.500027\pi$
$977$	−29.7306	−	21.6005i	−0.951166	−	0.691063i	−0.951082	+	0.308937i	$0.900027\pi$
$978$	−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	−0.890240	−	0.455491i	$-0.849464\pi$
$983$	−13.7248	−	42.2404i	−0.437752	−	1.34726i	0.452489	−	0.891770i	$-0.350536\pi$
$984$	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	0.854975	−	0.518670i	$-0.173573\pi$
$997$	−4.47046	−	13.7587i	−0.141581	−	0.435741i	−0.996555	+	0.0829288i	$0.973573\pi$
$998$	−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.103.1	yes	16
11.3	even	5	inner	374.2.g.f.69.1	✓	16
11.5	even	5		4114.2.a.bi.1.2		8
11.6	odd	10		4114.2.a.bg.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.f.69.1	✓	16	11.3	even	5	inner
374.2.g.f.103.1	yes	16	1.1	even	1	trivial
4114.2.a.bg.1.2		8	11.6	odd	10
4114.2.a.bi.1.2		8	11.5	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

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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.103.1

Level	$374$
Weight	$2$
Character	374.103
Analytic conductor	$2.986$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$