LMFDB - Embedded newform 152.2.o.c.107.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] 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("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$152 = 2^{3} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	152.o (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.12
Character	$\chi$	$=$	152.107
Dual form			152.2.o.c.27.12

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14168 + 0.834605i) q^{2} +(-1.05104 + 0.606818i) q^{3} +(0.606869 + 1.90570i) q^{4} +(2.45005 - 1.41453i) q^{5} +(-1.70640 - 0.184411i) q^{6} +0.450769i q^{7} +(-0.897660 + 2.68220i) q^{8} +(-0.763544 + 1.32250i) q^{9} +(3.97775 + 0.429874i) q^{10} -2.15933 q^{11} +(-1.79426 - 1.63471i) q^{12} +(1.86406 - 3.22864i) q^{13} +(-0.376214 + 0.514634i) q^{14} +(-1.71673 + 2.97346i) q^{15} +(-3.26342 + 2.31303i) q^{16} +(-0.716566 - 1.24113i) q^{17} +(-1.97549 + 0.872612i) q^{18} +(-0.0305680 - 4.35879i) q^{19} +(4.18254 + 3.81063i) q^{20} +(-0.273535 - 0.473776i) q^{21} +(-2.46527 - 1.80219i) q^{22} +(1.12985 + 0.652319i) q^{23} +(-0.684132 - 3.36382i) q^{24} +(1.50182 - 2.60122i) q^{25} +(4.82280 - 2.13033i) q^{26} -5.49424i q^{27} +(-0.859032 + 0.273558i) q^{28} +(4.22992 - 7.32644i) q^{29} +(-4.44162 + 1.96195i) q^{30} +0.497284 q^{31} +(-5.65625 - 0.0829299i) q^{32} +(2.26955 - 1.31032i) q^{33} +(0.217763 - 2.01502i) q^{34} +(0.637628 + 1.10440i) q^{35} +(-2.98366 - 0.652507i) q^{36} -6.72997 q^{37} +(3.60297 - 5.00186i) q^{38} +4.52457i q^{39} +(1.59476 + 7.84129i) q^{40} +(-7.30919 + 4.21996i) q^{41} +(0.0831265 - 0.769194i) q^{42} +(2.90174 + 5.02595i) q^{43} +(-1.31043 - 4.11505i) q^{44} +4.32024i q^{45} +(0.745499 + 1.68772i) q^{46} +(0.567335 + 0.327551i) q^{47} +(2.02640 - 4.41138i) q^{48} +6.79681 q^{49} +(3.88559 - 1.71634i) q^{50} +(1.50628 + 0.869651i) q^{51} +(7.28408 + 1.59298i) q^{52} +(-3.86444 + 6.69340i) q^{53} +(4.58552 - 6.27266i) q^{54} +(-5.29047 + 3.05445i) q^{55} +(-1.20905 - 0.404637i) q^{56} +(2.67712 + 4.56271i) q^{57} +(10.9439 - 4.83414i) q^{58} +(-12.1090 + 6.99113i) q^{59} +(-6.70837 - 1.46708i) q^{60} +(2.13281 + 1.23138i) q^{61} +(0.567740 + 0.415036i) q^{62} +(-0.596141 - 0.344182i) q^{63} +(-6.38841 - 4.81541i) q^{64} -10.5471i q^{65} +(3.68470 + 0.398204i) q^{66} +(2.16651 + 1.25083i) q^{67} +(1.93036 - 2.11877i) q^{68} -1.58336 q^{69} +(-0.193774 + 1.79304i) q^{70} +(-8.35311 - 14.4680i) q^{71} +(-2.86180 - 3.23513i) q^{72} +(8.25523 + 14.2985i) q^{73} +(-7.68347 - 5.61686i) q^{74} +3.64532i q^{75} +(8.28802 - 2.70347i) q^{76} -0.973361i q^{77} +(-3.77623 + 5.16562i) q^{78} +(4.05535 + 7.02407i) q^{79} +(-4.72367 + 10.2832i) q^{80} +(1.04337 + 1.80717i) q^{81} +(-11.8668 - 1.28244i) q^{82} +11.8333 q^{83} +(0.736877 - 0.808796i) q^{84} +(-3.51124 - 2.02722i) q^{85} +(-0.881831 + 8.15984i) q^{86} +10.2672i q^{87} +(1.93835 - 5.79177i) q^{88} +(-6.95256 - 4.01406i) q^{89} +(-3.60569 + 4.93233i) q^{90} +(1.45537 + 0.840259i) q^{91} +(-0.557457 + 2.54903i) q^{92} +(-0.522665 + 0.301761i) q^{93} +(0.374340 + 0.847459i) q^{94} +(-6.24056 - 10.6360i) q^{95} +(5.99526 - 3.34515i) q^{96} +(-5.47310 + 3.15990i) q^{97} +(7.75978 + 5.67265i) q^{98} +(1.64875 - 2.85571i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100})$ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$ .

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.14168	+	0.834605i	0.807290	+	0.590155i
$2$	1.14168	+	0.834605i	0.807290	+	0.590155i
$3$	−1.05104	+	0.606818i	−0.606818	+	0.350346i	−0.771719	−	0.635964i	$-0.780603\pi$
$3$	−1.05104	+	0.606818i	−0.606818	+	0.350346i	0.164901	+	0.986310i	$0.447269\pi$
$4$	0.606869	+	1.90570i	0.303434	+	0.952852i
$5$	2.45005	−	1.41453i	1.09569	−	0.632599i	0.160607	−	0.987018i	$-0.448655\pi$
$5$	2.45005	−	1.41453i	1.09569	−	0.632599i	0.935087	+	0.354419i	$0.115321\pi$
$6$	−1.70640	−	0.184411i	−0.696637	−	0.0752853i
$7$			0.450769i			0.170375i	0.996365	+	0.0851873i	$0.0271489\pi$
$7$			0.450769i			0.170375i	−0.996365	+	0.0851873i	$0.972851\pi$
$8$	−0.897660	+	2.68220i	−0.317371	+	0.948302i
$9$	−0.763544	+	1.32250i	−0.254515	+	0.440832i
$10$	3.97775	+	0.429874i	1.25787	+	0.135938i
$11$	−2.15933			−0.651064			−0.325532	−	0.945531i	$-0.605543\pi$
$11$	−2.15933			−0.651064			−0.325532	+	0.945531i	$0.605543\pi$
$12$	−1.79426	−	1.63471i	−0.517958	−	0.471901i
$13$	1.86406	−	3.22864i	0.516996	−	0.895464i	−0.482809	−	0.875726i	$-0.660383\pi$
$13$	1.86406	−	3.22864i	0.516996	−	0.895464i	0.999805	−	0.0197382i	$-0.00628328\pi$
$14$	−0.376214	+	0.514634i	−0.100547	+	0.137542i
$15$	−1.71673	+	2.97346i	−0.443258	+	0.767745i
$16$	−3.26342	+	2.31303i	−0.815855	+	0.578257i
$17$	−0.716566	−	1.24113i	−0.173793	−	0.301018i	0.765950	−	0.642900i	$-0.222269\pi$
$17$	−0.716566	−	1.24113i	−0.173793	−	0.301018i	−0.939743	+	0.341882i	$0.888936\pi$
$18$	−1.97549	+	0.872612i	−0.465627	+	0.205677i
$19$	−0.0305680	−	4.35879i	−0.00701278	−	0.999975i
$19$	−0.0305680	−	4.35879i	−0.00701278	−	0.999975i
$20$	4.18254	+	3.81063i	0.935245	+	0.852082i
$21$	−0.273535	−	0.473776i	−0.0596901	−	0.103386i
$22$	−2.46527	−	1.80219i	−0.525597	−	0.384229i
$23$	1.12985	+	0.652319i	0.235590	+	0.136018i	0.613148	−	0.789968i	$-0.289903\pi$
$23$	1.12985	+	0.652319i	0.235590	+	0.136018i	−0.377558	+	0.925986i	$0.623236\pi$
$24$	−0.684132	−	3.36382i	−0.139648	−	0.686636i
$25$	1.50182	−	2.60122i	0.300363	−	0.520245i
$26$	4.82280	−	2.13033i	0.945828	−	0.417791i
$27$		−	5.49424i		−	1.05737i
$28$	−0.859032	+	0.273558i	−0.162342	+	0.0516975i
$29$	4.22992	−	7.32644i	0.785477	−	1.36049i	−0.143237	−	0.989688i	$-0.545751\pi$
$29$	4.22992	−	7.32644i	0.785477	−	1.36049i	0.928714	−	0.370797i	$-0.120915\pi$
$30$	−4.44162	+	1.96195i	−0.810926	+	0.358202i
$31$	0.497284			0.0893149			0.0446575	−	0.999002i	$-0.485780\pi$
$31$	0.497284			0.0893149			0.0446575	+	0.999002i	$0.485780\pi$
$32$	−5.65625	−	0.0829299i	−0.999893	−	0.0146601i
$33$	2.26955	−	1.31032i	0.395077	−	0.228098i
$34$	0.217763	−	2.01502i	0.0373460	−	0.345574i
$35$	0.637628	+	1.10440i	0.107779	+	0.186678i
$36$	−2.98366	−	0.652507i	−0.497277	−	0.108751i
$37$	−6.72997			−1.10640			−0.553200	−	0.833049i	$-0.686593\pi$
$37$	−6.72997			−1.10640			−0.553200	+	0.833049i	$0.686593\pi$
$38$	3.60297	−	5.00186i	0.584479	−	0.811409i
$39$			4.52457i			0.724511i
$40$	1.59476	+	7.84129i	0.252154	+	1.23982i
$41$	−7.30919	+	4.21996i	−1.14150	+	0.659047i	−0.946802	−	0.321815i	$-0.895707\pi$
$41$	−7.30919	+	4.21996i	−1.14150	+	0.659047i	−0.194701	+	0.980863i	$0.562374\pi$
$42$	0.0831265	−	0.769194i	0.0128267	−	0.118689i
$43$	2.90174	+	5.02595i	0.442511	+	0.766451i	0.997875	−	0.0651562i	$-0.0207546\pi$
$43$	2.90174	+	5.02595i	0.442511	+	0.766451i	−0.555364	+	0.831607i	$0.687421\pi$
$44$	−1.31043	−	4.11505i	−0.197555	−	0.620368i
$45$			4.32024i			0.644023i
$46$	0.745499	+	1.68772i	0.109918	+	0.248841i
$47$	0.567335	+	0.327551i	0.0827543	+	0.0477782i	0.540806	−	0.841147i	$-0.318119\pi$
$47$	0.567335	+	0.327551i	0.0827543	+	0.0477782i	−0.458052	+	0.888925i	$0.651453\pi$
$48$	2.02640	−	4.41138i	0.292485	−	0.636728i
$49$	6.79681			0.970972
$50$	3.88559	−	1.71634i	0.549505	−	0.242727i
$51$	1.50628	+	0.869651i	0.210921	+	0.121775i
$52$	7.28408	+	1.59298i	1.01012	+	0.220907i
$53$	−3.86444	+	6.69340i	−0.530821	+	0.919409i	0.468532	+	0.883446i	$0.344783\pi$
$53$	−3.86444	+	6.69340i	−0.530821	+	0.919409i	−0.999353	+	0.0359626i	$0.988550\pi$
$54$	4.58552	−	6.27266i	0.624010	−	0.853601i
$55$	−5.29047	+	3.05445i	−0.713367	+	0.411862i
$56$	−1.20905	−	0.404637i	−0.161567	−	0.0540719i
$57$	2.67712	+	4.56271i	0.354593	+	0.604346i
$58$	10.9439	−	4.83414i	1.43700	−	0.634753i
$59$	−12.1090	+	6.99113i	−1.57646	+	0.910168i	−0.581109	+	0.813826i	$0.697381\pi$
$59$	−12.1090	+	6.99113i	−1.57646	+	0.910168i	−0.995348	+	0.0963425i	$0.969286\pi$
$60$	−6.70837	−	1.46708i	−0.866047	−	0.189399i
$61$	2.13281	+	1.23138i	0.273078	+	0.157662i	0.630286	−	0.776363i	$-0.282938\pi$
$61$	2.13281	+	1.23138i	0.273078	+	0.157662i	−0.357208	+	0.934025i	$0.616271\pi$
$62$	0.567740	+	0.415036i	0.0721030	+	0.0527096i
$63$	−0.596141	−	0.344182i	−0.0751067	−	0.0433629i
$64$	−6.38841	−	4.81541i	−0.798552	−	0.601926i
$65$		−	10.5471i		−	1.30821i
$66$	3.68470	+	0.398204i	0.453555	+	0.0490155i
$67$	2.16651	+	1.25083i	0.264681	+	0.152814i	0.626468	−	0.779447i	$-0.284500\pi$
$67$	2.16651	+	1.25083i	0.264681	+	0.152814i	−0.361787	+	0.932261i	$0.617833\pi$
$68$	1.93036	−	2.11877i	0.234091	−	0.256938i
$69$	−1.58336			−0.190614
$70$	−0.193774	+	1.79304i	−0.0231604	+	0.214310i
$71$	−8.35311	−	14.4680i	−0.991332	−	1.71704i	−0.609444	−	0.792829i	$-0.708607\pi$
$71$	−8.35311	−	14.4680i	−0.991332	−	1.71704i	−0.381888	−	0.924209i	$-0.624726\pi$
$72$	−2.86180	−	3.23513i	−0.337267	−	0.381264i
$73$	8.25523	+	14.2985i	0.966202	+	1.67351i	0.706351	+	0.707862i	$0.250340\pi$
$73$	8.25523	+	14.2985i	0.966202	+	1.67351i	0.259851	+	0.965649i	$0.416327\pi$
$74$	−7.68347	−	5.61686i	−0.893186	−	0.652947i
$75$			3.64532i			0.420925i
$76$	8.28802	−	2.70347i	0.950701	−	0.310109i
$77$		−	0.973361i		−	0.110925i
$78$	−3.77623	+	5.16562i	−0.427574	+	0.584891i
$79$	4.05535	+	7.02407i	0.456262	+	0.790269i	0.998760	−	0.0497881i	$-0.0158546\pi$
$79$	4.05535	+	7.02407i	0.456262	+	0.790269i	−0.542498	+	0.840057i	$0.682521\pi$
$80$	−4.72367	+	10.2832i	−0.528123	+	1.14970i
$81$	1.04337	+	1.80717i	0.115930	+	0.200796i
$82$	−11.8668	−	1.28244i	−1.31046	−	0.141621i
$83$	11.8333			1.29887			0.649435	−	0.760417i	$-0.275006\pi$
$83$	11.8333			1.29887			0.649435	+	0.760417i	$0.275006\pi$
$84$	0.736877	−	0.808796i	0.0803999	−	0.0882469i
$85$	−3.51124	−	2.02722i	−0.380848	−	0.219882i
$86$	−0.881831	+	8.15984i	−0.0950903	+	0.879898i
$87$			10.2672i			1.10076i
$88$	1.93835	−	5.79177i	0.206629	−	0.617405i
$89$	−6.95256	−	4.01406i	−0.736970	−	0.425490i	0.0839965	−	0.996466i	$-0.473232\pi$
$89$	−6.95256	−	4.01406i	−0.736970	−	0.425490i	−0.820967	+	0.570976i	$0.806565\pi$
$90$	−3.60569	+	4.93233i	−0.380073	+	0.519914i
$91$	1.45537	+	0.840259i	0.152564	+	0.0880831i
$92$	−0.557457	+	2.54903i	−0.0581189	+	0.265755i
$93$	−0.522665	+	0.301761i	−0.0541979	+	0.0312912i
$94$	0.374340	+	0.847459i	0.0386102	+	0.0874088i
$95$	−6.24056	−	10.6360i	−0.640267	−	1.09123i
$96$	5.99526	−	3.34515i	0.611889	−	0.341413i
$97$	−5.47310	+	3.15990i	−0.555709	+	0.320839i	−0.751422	−	0.659822i	$-0.770632\pi$
$97$	−5.47310	+	3.15990i	−0.555709	+	0.320839i	0.195712	+	0.980661i	$0.437298\pi$
$98$	7.75978	+	5.67265i	0.783856	+	0.573024i
$99$	1.64875	−	2.85571i	0.165705	−	0.287010i
$100$	5.86857	+	1.28342i	0.586857	+	0.128342i
$101$	4.61075	+	2.66202i	0.458787	+	0.264881i	0.711534	−	0.702652i	$-0.248001\pi$
$101$	4.61075	+	2.66202i	0.458787	+	0.264881i	−0.252747	+	0.967532i	$0.581334\pi$
$102$	0.993875	+	2.25001i	0.0984083	+	0.222784i
$103$	17.9095			1.76468			0.882340	−	0.470613i	$-0.155967\pi$
$103$	17.9095			1.76468			0.882340	+	0.470613i	$0.155967\pi$
$104$	6.98658	+	7.89800i	0.685090	+	0.774463i
$105$	−1.34034	−	0.773848i	−0.130804	−	0.0755199i
$106$	−9.99830	+	4.41645i	−0.971120	+	0.428963i
$107$			0.909747i			0.0879485i	0.999033	+	0.0439743i	$0.0140020\pi$
$107$			0.909747i			0.0879485i	−0.999033	+	0.0439743i	$0.985998\pi$
$108$	10.4704	−	3.33428i	1.00751	−	0.320841i
$109$	0.935166	+	1.61976i	0.0895727	+	0.155144i	0.907331	−	0.420418i	$-0.138117\pi$
$109$	0.935166	+	1.61976i	0.0895727	+	0.155144i	−0.817758	+	0.575562i	$0.804783\pi$
$110$	−8.58929	−	0.928242i	−0.818957	−	0.0885044i
$111$	7.07346	−	4.08386i	0.671383	−	0.387623i
$112$	−1.04264	−	1.47105i	−0.0985202	−	0.139001i
$113$		−	2.34200i		−	0.220317i	−0.993914	−	0.110159i	$-0.964864\pi$
$113$		−	2.34200i		−	0.220317i	0.993914	−	0.110159i	$-0.0351359\pi$
$114$	−0.751646	+	7.44350i	−0.0703981	+	0.697148i
$115$	3.69091			0.344179
$116$	16.5290	+	3.61479i	1.53468	+	0.335625i
$117$	2.84658	+	4.93042i	0.263166	+	0.455818i
$118$	−19.6594	−	2.12459i	−1.80980	−	0.195584i
$119$	0.559462	−	0.323006i	0.0512858	−	0.0296099i
$120$	−6.43439	−	7.27378i	−0.587377	−	0.664002i
$121$	−6.33727			−0.576116
$122$	1.40727	+	3.18589i	0.127408	+	0.288437i
$123$	5.12150	−	8.87069i	0.461790	−	0.799843i
$124$	0.301786	+	0.947677i	0.0271012	+	0.0851039i
$125$			5.64786i			0.505160i
$126$	−0.393346	−	0.890488i	−0.0350421	−	0.0793310i
$127$	1.06604	−	1.84643i	0.0945955	−	0.163844i	−0.814844	−	0.579680i	$-0.803178\pi$
$127$	1.06604	−	1.84643i	0.0945955	−	0.163844i	0.909440	+	0.415836i	$0.136511\pi$
$128$	−3.27456	−	10.8295i	−0.289433	−	0.957198i
$129$	−6.09968	−	3.52165i	−0.537047	−	0.310064i
$130$	8.80266	−	12.0414i	0.772044	−	1.05610i
$131$	−8.72441	−	15.1111i	−0.762255	−	1.32026i	−0.941686	−	0.336494i	$-0.890759\pi$
$131$	−8.72441	−	15.1111i	−0.762255	−	1.32026i	0.179430	−	0.983771i	$-0.442575\pi$
$132$	3.87441	+	3.52989i	0.337224	+	0.307237i
$133$	1.96481	−	0.0137791i	0.170370	−	0.00119480i
$134$	1.42951	+	3.23623i	0.123491	+	0.279568i
$135$	−7.77179	−	13.4611i	−0.668889	−	1.15855i
$136$	3.97219	−	0.807863i	0.340613	−	0.0692737i
$137$	−4.28881	+	7.42843i	−0.366417	+	0.634654i	−0.989003	−	0.147898i	$-0.952749\pi$
$137$	−4.28881	+	7.42843i	−0.366417	+	0.634654i	0.622585	+	0.782552i	$0.286082\pi$
$138$	−1.80769	−	1.32148i	−0.153880	−	0.112492i
$139$	−2.38145	+	4.12479i	−0.201992	+	0.349860i	−0.949170	−	0.314763i	$-0.898075\pi$
$139$	−2.38145	+	4.12479i	−0.201992	+	0.349860i	0.747178	+	0.664624i	$0.231408\pi$
$140$	−1.71771	+	1.88536i	−0.145173	+	0.159342i
$141$	−0.795055			−0.0669557
$142$	2.53849	−	23.4894i	0.213026	−	1.97119i
$143$	−4.02512	+	6.97172i	−0.336598	+	0.583004i
$144$	−0.567205	−	6.08196i	−0.0472671	−	0.506830i
$145$		−	23.9335i		−	1.98757i
$146$	−2.50875	+	23.2142i	−0.207625	+	1.92122i
$147$	−7.14371	+	4.12442i	−0.589203	+	0.340177i
$148$	−4.08421	−	12.8253i	−0.335720	−	1.05424i
$149$	−9.33207	+	5.38787i	−0.764513	+	0.441392i	−0.830914	−	0.556401i	$-0.812182\pi$
$149$	−9.33207	+	5.38787i	−0.764513	+	0.441392i	0.0664008	+	0.997793i	$0.478848\pi$
$150$	−3.04240	+	4.16179i	−0.248411	+	0.339809i
$151$	5.40642			0.439968			0.219984	−	0.975503i	$-0.429399\pi$
$151$	5.40642			0.439968			0.219984	+	0.975503i	$0.429399\pi$
$152$	11.7186	+	3.83072i	0.950504	+	0.310713i
$153$	2.18852			0.176931
$154$	0.812372	−	1.11127i	0.0654628	−	0.0895485i
$155$	1.21837	−	0.703426i	0.0978618	−	0.0565005i
$156$	−8.62250	+	2.74582i	−0.690352	+	0.219842i
$157$	−13.3288	+	7.69539i	−1.06375	+	0.614159i	−0.926468	−	0.376373i	$-0.877171\pi$
$157$	−13.3288	+	7.69539i	−1.06375	+	0.614159i	−0.137286	+	0.990531i	$0.543838\pi$
$158$	−1.23241	+	11.4039i	−0.0980453	+	0.907242i
$159$		−	9.38003i		−	0.743885i
$160$	−13.9754	+	7.79777i	−1.10485	+	0.616468i
$161$	−0.294045	+	0.509301i	−0.0231740	+	0.0401386i
$162$	−0.317077	+	2.93401i	−0.0249119	+	0.230517i
$163$	0.534048			0.0418298			0.0209149	−	0.999781i	$-0.493342\pi$
$163$	0.534048			0.0418298			0.0209149	+	0.999781i	$0.493342\pi$
$164$	−12.4777	−	11.3682i	−0.974346	−	0.887706i
$165$	3.70699	−	6.42070i	0.288589	−	0.499851i
$166$	13.5098	+	9.87610i	1.04856	+	0.766534i
$167$	6.81811	−	11.8093i	0.527601	−	0.913832i	−0.471881	−	0.881662i	$-0.656425\pi$
$167$	6.81811	−	11.8093i	0.527601	−	0.913832i	0.999482	−	0.0321697i	$-0.0102417\pi$
$168$	1.51630	−	0.308385i	0.116985	−	0.0237924i
$169$	−0.449417	−	0.778413i	−0.0345705	−	0.0598779i
$170$	−2.31679	−	5.24493i	−0.177690	−	0.402268i
$171$	5.78783	+	3.28770i	0.442606	+	0.251417i
$172$	−7.81701	+	8.57995i	−0.596041	+	0.654215i
$173$	−0.822987	−	1.42546i	−0.0625706	−	0.108375i	0.833043	−	0.553208i	$-0.186597\pi$
$173$	−0.822987	−	1.42546i	−0.0625706	−	0.108375i	−0.895614	+	0.444833i	$0.853263\pi$
$174$	−8.56903	+	11.7218i	−0.649616	+	0.888629i
$175$	1.17255	+	0.676972i	0.0886365	+	0.0511743i
$176$	7.04682	−	4.99460i	0.531174	−	0.376482i
$177$	8.48469	−	14.6959i	0.637748	−	1.10461i
$178$	−4.58745	−	10.3854i	−0.343844	−	0.778420i
$179$		−	7.67159i		−	0.573402i	−0.958020	−	0.286701i	$-0.907441\pi$
$179$		−	7.67159i		−	0.573402i	0.958020	−	0.286701i	$-0.0925586\pi$
$180$	−8.23310	+	2.62182i	−0.613659	+	0.195419i
$181$	11.7649	−	20.3774i	0.874479	−	1.51464i	0.0171632	−	0.999853i	$-0.494537\pi$
$181$	11.7649	−	20.3774i	0.874479	−	1.51464i	0.857316	−	0.514790i	$-0.172130\pi$
$182$	0.960285	+	2.17397i	0.0711810	+	0.161145i
$183$	−2.98889			−0.220945
$184$	−2.76387	+	2.44492i	−0.203755	+	0.180242i
$185$	−16.4887	+	9.51977i	−1.21228	+	0.699908i
$186$	−0.848568	−	0.0917045i	−0.0622200	−	0.00672410i
$187$	1.54731	+	2.68001i	0.113150	+	0.195982i
$188$	−0.279918	+	1.27995i	−0.0204151	+	0.0933502i
$189$	2.47663			0.180148
$190$	1.75214	−	17.3513i	0.127114	−	1.25880i
$191$		−	23.8645i		−	1.72678i	−0.504540	−	0.863388i	$-0.668338\pi$
$191$		−	23.8645i		−	1.72678i	0.504540	−	0.863388i	$-0.331662\pi$
$192$	9.63655	+	1.18458i	0.695458	+	0.0854899i
$193$	16.5463	−	9.55301i	1.19103	−	0.687641i	0.232489	−	0.972599i	$-0.425313\pi$
$193$	16.5463	−	9.55301i	1.19103	−	0.687641i	0.958540	+	0.284958i	$0.0919798\pi$
$194$	−8.88580	−	0.960286i	−0.637963	−	0.0689445i
$195$	6.40016	+	11.0854i	0.458325	+	0.793843i
$196$	4.12477	+	12.9527i	0.294627	+	0.925193i
$197$			11.2480i			0.801385i	0.916213	+	0.400693i	$0.131230\pi$
$197$			11.2480i			0.801385i	−0.916213	+	0.400693i	$0.868770\pi$
$198$	4.26574	−	1.88426i	0.303153	−	0.133909i
$199$	9.91953	+	5.72704i	0.703177	+	0.405979i	0.808530	−	0.588456i	$-0.200264\pi$
$199$	9.91953	+	5.72704i	0.703177	+	0.405979i	−0.105353	+	0.994435i	$0.533597\pi$
$200$	5.62888	+	6.36319i	0.398022	+	0.449946i
$201$	−3.03611			−0.214151
$202$	3.04227	+	6.88733i	0.214053	+	0.484591i
$203$	3.30253	+	1.90672i	0.231792	+	0.133825i
$204$	−0.743183	+	3.39829i	−0.0520332	+	0.237928i
$205$	−11.9386	+	20.6782i	−0.833825	+	1.44423i
$206$	20.4470	+	14.9474i	1.42461	+	1.04143i
$207$	−1.72538	+	0.996149i	−0.119922	+	0.0692371i
$208$	1.38473	+	14.8480i	0.0960138	+	1.02953i
$209$	0.0660065	+	9.41209i	0.00456577	+	0.651048i
$210$	−0.884388	−	2.00215i	−0.0610286	−	0.138161i
$211$	−13.8288	+	7.98406i	−0.952013	+	0.549645i	−0.893706	−	0.448653i	$-0.851904\pi$
$211$	−13.8288	+	7.98406i	−0.952013	+	0.549645i	−0.0583076	+	0.998299i	$0.518570\pi$
$212$	−15.1008	−	3.30246i	−1.03713	−	0.226814i
$213$	17.5589	+	10.1376i	1.20312	+	0.694619i
$214$	−0.759279	+	1.03864i	−0.0519033	+	0.0710000i
$215$	14.2188	+	8.20921i	0.969712	+	0.559864i
$216$	14.7366	+	4.93196i	1.00270	+	0.335577i
$217$			0.224160i			0.0152170i
$218$	−0.284195	+	2.62974i	−0.0192481	+	0.178108i
$219$	−17.3531	−	10.0188i	−1.17262	−	0.677011i
$220$	−9.03151	−	8.22842i	−0.608904	−	0.554760i
$221$	−5.34288			−0.359401
$222$	11.4840	+	1.24108i	0.770759	+	0.0832956i
$223$	8.06323	+	13.9659i	0.539954	+	0.935227i	0.998906	+	0.0467660i	$0.0148915\pi$
$223$	8.06323	+	13.9659i	0.539954	+	0.935227i	−0.458952	+	0.888461i	$0.651775\pi$
$224$	0.0373822	−	2.54966i	0.00249770	−	0.170356i
$225$	2.29341	+	3.97230i	0.152894	+	0.264820i
$226$	1.95465	−	2.67382i	0.130021	−	0.177860i
$227$			13.0282i			0.864715i	0.901702	+	0.432357i	$0.142318\pi$
$227$			13.0282i			0.864715i	−0.901702	+	0.432357i	$0.857682\pi$
$228$	−7.07052	+	7.87077i	−0.468257	+	0.521254i
$229$		−	12.7253i		−	0.840914i	−0.907312	−	0.420457i	$-0.861870\pi$
$229$		−	12.7253i		−	0.840914i	0.907312	−	0.420457i	$-0.138130\pi$
$230$	4.21384	+	3.08045i	0.277853	+	0.203119i
$231$	0.590653	+	1.02304i	0.0388621	+	0.0673111i
$232$	15.8540	+	17.9222i	1.04086	+	1.17665i
$233$	5.77758	+	10.0071i	0.378502	+	0.655585i	0.990845	−	0.135008i	$-0.0431060\pi$
$233$	5.77758	+	10.0071i	0.378502	+	0.655585i	−0.612343	+	0.790593i	$0.709773\pi$
$234$	−0.865069	+	8.00474i	−0.0565513	+	0.523286i
$235$	1.85333			0.120898
$236$	−20.6716	−	18.8335i	−1.34561	−	1.22595i
$237$	−8.52466	−	4.92171i	−0.553736	−	0.319700i
$238$	0.908310	+	0.0981607i	0.0588770	+	0.00636282i
$239$			18.8301i			1.21802i	0.793163	+	0.609010i	$0.208433\pi$
$239$			18.8301i			1.21802i	−0.793163	+	0.609010i	$0.791567\pi$
$240$	−1.27529	−	13.6745i	−0.0823194	−	0.882685i
$241$	−8.47571	−	4.89346i	−0.545969	−	0.315215i	0.201526	−	0.979483i	$-0.435410\pi$
$241$	−8.47571	−	4.89346i	−0.545969	−	0.315215i	−0.747494	+	0.664268i	$0.768743\pi$
$242$	−7.23514	−	5.28912i	−0.465093	−	0.339998i
$243$	12.0812	+	6.97509i	0.775009	+	0.447452i
$244$	−1.05231	+	4.81179i	−0.0673670	+	0.308043i
$245$	16.6525	−	9.61432i	1.06389	−	0.614236i
$246$	13.2506	−	5.85307i	0.844830	−	0.373178i
$247$	−14.1300	−	8.02634i	−0.899068	−	0.510704i
$248$	−0.446392	+	1.33382i	−0.0283459	+	0.0846975i
$249$	−12.4372	+	7.18063i	−0.788177	+	0.455054i
$250$	−4.71373	+	6.44805i	−0.298123	+	0.407810i
$251$	8.19032	−	14.1861i	0.516969	−	0.895416i	−0.482837	−	0.875710i	$-0.660394\pi$
$251$	8.19032	−	14.1861i	0.516969	−	0.895416i	0.999806	−	0.0197059i	$-0.00627298\pi$
$252$	0.294130	−	1.34494i	0.0185284	−	0.0847233i
$253$	−2.43972	−	1.40858i	−0.153384	−	0.0885564i
$254$	2.75812	−	1.21831i	0.173060	−	0.0764438i
$255$	4.92060			0.308140
$256$	5.29982	−	15.0968i	0.331239	−	0.943547i
$257$	7.56834	+	4.36958i	0.472100	+	0.272567i	0.717118	−	0.696951i	$-0.245461\pi$
$257$	7.56834	+	4.36958i	0.472100	+	0.272567i	−0.245019	+	0.969518i	$0.578794\pi$
$258$	−4.02470	−	9.11142i	−0.250567	−	0.567252i
$259$		−	3.03366i		−	0.188502i
$260$	20.0996	−	6.40070i	1.24653	−	0.396955i
$261$	6.45946	+	11.1881i	0.399831	+	0.692527i
$262$	2.65133	−	24.5335i	0.163800	−	1.51569i
$263$	−24.1288	+	13.9308i	−1.48785	+	0.859008i	−0.999904	−	0.0138683i	$-0.995585\pi$
$263$	−24.1288	+	13.9308i	−1.48785	+	0.859008i	−0.487942	+	0.872876i	$0.662252\pi$
$264$	1.47727	+	7.26360i	0.0909197	+	0.447044i
$265$			21.8655i			1.34319i
$266$	2.25468	+	1.62411i	0.138243	+	0.0995804i
$267$	9.74322			0.596276
$268$	−1.06893	+	4.88782i	−0.0652955	+	0.298571i
$269$	−11.8357	−	20.5001i	−0.721638	−	1.24991i	−0.960343	−	0.278822i	$-0.910056\pi$
$269$	−11.8357	−	20.5001i	−0.721638	−	1.24991i	0.238704	−	0.971092i	$-0.423277\pi$
$270$	2.36183	−	21.8547i	0.143736	−	1.33003i
$271$	−15.9524	+	9.21013i	−0.969041	+	0.559476i	−0.898944	−	0.438064i	$-0.855664\pi$
$271$	−15.9524	+	9.21013i	−0.969041	+	0.559476i	−0.0700969	+	0.997540i	$0.522331\pi$
$272$	5.20922	+	2.39289i	0.315855	+	0.145090i
$273$	−2.03954			−0.123438
$274$	−11.0963	+	4.90144i	−0.670349	+	0.296107i
$275$	−3.24293	+	5.61691i	−0.195556	+	0.338713i
$276$	−0.960889	−	3.01741i	−0.0578387	−	0.181627i
$277$		−	26.0321i		−	1.56412i	−0.623203	−	0.782060i	$-0.714169\pi$
$277$		−	26.0321i		−	1.56412i	0.623203	−	0.782060i	$-0.285831\pi$
$278$	−6.16143	+	2.72163i	−0.369538	+	0.163232i
$279$	−0.379699	+	0.657657i	−0.0227320	+	0.0393729i
$280$	−3.53461	+	0.718868i	−0.211233	+	0.0429606i
$281$	18.1670	+	10.4887i	1.08375	+	0.625706i	0.931907	−	0.362698i	$-0.118144\pi$
$281$	18.1670	+	10.4887i	1.08375	+	0.625706i	0.151848	+	0.988404i	$0.451478\pi$
$282$	−0.907699	−	0.663557i	−0.0540527	−	0.0395143i
$283$	−5.72882	−	9.92260i	−0.340543	−	0.589837i	0.643991	−	0.765033i	$-0.277277\pi$
$283$	−5.72882	−	9.92260i	−0.340543	−	0.589837i	−0.984534	+	0.175196i	$0.943944\pi$
$284$	22.5025	−	24.6988i	1.33528	−	1.46560i
$285$	13.0132	+	7.39198i	0.770835	+	0.437863i
$286$	−10.4140	+	4.60009i	−0.615795	+	0.272009i
$287$	−1.90223	−	3.29475i	−0.112285	−	0.194483i
$288$	4.42847	−	7.41705i	0.260950	−	0.437054i
$289$	7.47307	−	12.9437i	0.439592	−	0.761396i
$290$	19.9750	−	27.3244i	1.17297	−	1.60454i
$291$	3.83496	−	6.64235i	0.224810	−	0.389382i
$292$	−22.2388	+	24.4093i	−1.30143	+	1.42845i
$293$	−10.4003			−0.607590			−0.303795	−	0.952737i	$-0.598254\pi$
$293$	−10.4003			−0.607590			−0.303795	+	0.952737i	$0.598254\pi$
$294$	−11.5981	−	1.25340i	−0.676415	−	0.0731000i
$295$	−19.7784	+	34.2572i	−1.15154	+	1.99453i
$296$	6.04122	−	18.0511i	0.351139	−	1.04920i
$297$			11.8639i			0.688413i
$298$	−15.1510	−	1.63736i	−0.877673	−	0.0948499i
$299$	4.21221	−	2.43192i	0.243598	−	0.140642i
$300$	−6.94690	+	2.21223i	−0.401079	+	0.127723i
$301$	−2.26554	+	1.30801i	−0.130584	+	0.0753926i
$302$	6.17241	+	4.51223i	0.355182	+	0.259649i
$303$	−6.46144			−0.371200
$304$	10.1818	+	14.1539i	0.583964	+	0.811780i
$305$	6.96731			0.398947
$306$	2.49859	+	1.82655i	0.142835	+	0.104417i
$307$	−2.39992	+	1.38560i	−0.136971	+	0.0790801i	−0.566920	−	0.823773i	$-0.691865\pi$
$307$	−2.39992	+	1.38560i	−0.136971	+	0.0790801i	0.429949	+	0.902853i	$0.358532\pi$
$308$	1.85494	−	0.590703i	0.105695	−	0.0336584i
$309$	−18.8236	+	10.8678i	−1.07084	+	0.618249i
$310$	1.97807	+	0.213770i	0.112347	+	0.0121413i
$311$		−	13.8001i		−	0.782530i	−0.920278	−	0.391265i	$-0.872038\pi$
$311$		−	13.8001i		−	0.782530i	0.920278	−	0.391265i	$-0.127962\pi$
$312$	−12.1358	−	4.06153i	−0.687055	−	0.229939i
$313$	5.89194	−	10.2051i	0.333032	−	0.576829i	−0.650073	−	0.759872i	$-0.725262\pi$
$313$	5.89194	−	10.2051i	0.333032	−	0.576829i	0.983105	+	0.183043i	$0.0585949\pi$
$314$	−21.6398	−	2.33861i	−1.22121	−	0.131975i
$315$	−1.94743			−0.109725
$316$	−10.9247	+	11.9910i	−0.614564	+	0.674545i
$317$	8.86581	−	15.3560i	0.497953	−	0.862480i	−0.502044	−	0.864842i	$-0.667418\pi$
$317$	8.86581	−	15.3560i	0.497953	−	0.862480i	0.999997	+	0.00236177i	$0.000751775\pi$
$318$	7.82862	−	10.7090i	0.439007	−	0.600531i
$319$	−9.13381	+	15.8202i	−0.511395	+	0.885763i
$320$	−22.4635	−	2.76135i	−1.25575	−	0.154364i
$321$	−0.552051	−	0.956180i	−0.0308125	−	0.0533687i
$322$	−0.760771	+	0.336048i	−0.0423961	+	0.0187272i
$323$	−5.38792	+	3.16130i	−0.299792	+	0.175900i
$324$	−2.81074	+	3.08506i	−0.156152	+	0.171392i
$325$	−5.59894	−	9.69766i	−0.310574	−	0.537929i
$326$	0.609712	+	0.445719i	0.0337688	+	0.0246861i
$327$	−1.96579	−	1.13495i	−0.108709	−	0.0627630i
$328$	−4.75762	−	23.3928i	−0.262696	−	1.29165i
$329$	−0.147650	+	0.255737i	−0.00814020	+	0.0140992i
$330$	9.59095	−	4.23652i	0.527965	−	0.233212i
$331$			27.3712i			1.50445i	0.658904	+	0.752227i	$0.271020\pi$
$331$			27.3712i			1.50445i	−0.658904	+	0.752227i	$0.728980\pi$
$332$	7.18124	+	22.5507i	0.394122	+	1.23763i
$333$	5.13863	−	8.90036i	0.281595	−	0.487737i
$334$	17.6402	−	7.79203i	0.965229	−	0.426361i
$335$	7.07739			0.386679
$336$	1.98851	+	0.913437i	0.108482	+	0.0498321i
$337$	10.7104	−	6.18363i	0.583430	−	0.336844i	−0.179065	−	0.983837i	$-0.557307\pi$
$337$	10.7104	−	6.18363i	0.583430	−	0.336844i	0.762495	+	0.646994i	$0.223974\pi$
$338$	0.136577	−	1.26378i	0.00742880	−	0.0687408i
$339$	1.42117	+	2.46154i	0.0771873	+	0.133692i
$340$	1.73241	−	7.92164i	0.0939532	−	0.429611i
$341$	−1.07380			−0.0581497
$342$	3.86392	+	8.58406i	0.208937	+	0.464173i
$343$			6.21917i			0.335804i
$344$	−16.0854	+	3.27144i	−0.867266	+	0.176384i
$345$	−3.87929	+	2.23971i	−0.208854	+	0.120582i
$346$	0.250104	−	2.31429i	0.0134457	−	0.124417i
$347$	−5.69195	−	9.85874i	−0.305560	−	0.529245i	0.671826	−	0.740709i	$-0.265510\pi$
$347$	−5.69195	−	9.85874i	−0.305560	−	0.529245i	−0.977386	+	0.211464i	$0.932177\pi$
$348$	−19.5662	+	6.23082i	−1.04886	+	0.334007i
$349$		−	2.93676i		−	0.157201i	−0.996906	−	0.0786007i	$-0.974955\pi$
$349$		−	2.93676i		−	0.157201i	0.996906	−	0.0786007i	$-0.0250452\pi$
$350$	0.773674	+	1.75150i	0.0413546	+	0.0936218i
$351$	−17.7389	−	10.2416i	−0.946833	−	0.546655i
$352$	12.2137	+	0.179073i	0.650994	+	0.00954464i
$353$	19.1919			1.02148			0.510740	−	0.859735i	$-0.329371\pi$
$353$	19.1919			1.02148			0.510740	+	0.859735i	$0.329371\pi$
$354$	21.9521	−	9.69667i	1.16674	−	0.515372i
$355$	−40.9310	−	23.6315i	−2.17239	−	1.25423i
$356$	3.43033	−	15.6855i	0.181807	−	0.831332i
$357$	−0.392011	+	0.678984i	−0.0207474	+	0.0359356i
$358$	6.40275	−	8.75851i	0.338396	−	0.462901i
$359$	3.85728	−	2.22700i	0.203579	−	0.117537i	−0.394745	−	0.918791i	$-0.629167\pi$
$359$	3.85728	−	2.22700i	0.203579	−	0.117537i	0.598324	+	0.801254i	$0.295834\pi$
$360$	−11.5878	−	3.87811i	−0.610728	−	0.204394i
$361$	−18.9981	+	0.266479i	−0.999902	+	0.0140252i
$362$	30.4389	−	13.4455i	1.59983	−	0.706678i
$363$	6.66072	−	3.84557i	0.349597	−	0.201840i
$364$	−0.718066	+	3.28343i	−0.0376369	+	0.172099i
$365$	40.4514	+	23.3546i	2.11732	+	1.22244i
$366$	−3.41235	−	2.49454i	−0.178367	−	0.130392i
$367$	16.5629	+	9.56259i	0.864576	+	0.499163i	0.865542	−	0.500837i	$-0.166974\pi$
$367$	16.5629	+	9.56259i	0.864576	+	0.499163i	−0.000966198		1.00000i	$0.500308\pi$
$368$	−5.19601	+	0.484581i	−0.270861	+	0.0252605i
$369$		−	12.8885i		−	0.670949i
$370$	−26.7701	−	2.89304i	−1.39171	−	0.150402i
$371$	−3.01718	−	1.74197i	−0.156644	−	0.0904384i
$372$	−0.892257	−	0.812917i	−0.0462614	−	0.0421478i
$373$	−20.6810			−1.07082			−0.535411	−	0.844592i	$-0.679843\pi$
$373$	−20.6810			−1.07082			−0.535411	+	0.844592i	$0.679843\pi$
$374$	−0.470223	+	4.35111i	−0.0243146	+	0.224991i
$375$	−3.42722	−	5.93612i	−0.176981	−	0.306540i
$376$	−1.38783	+	1.22768i	−0.0715720	+	0.0633126i
$377$	−15.7696	−	27.3138i	−0.812177	−	1.40673i
$378$	2.82752	+	2.06701i	0.145432	+	0.106315i
$379$		−	2.56021i		−	0.131509i	−0.997836	−	0.0657546i	$-0.979055\pi$
$379$		−	2.56021i		−	0.131509i	0.997836	−	0.0657546i	$-0.0209454\pi$
$380$	16.4819	−	18.3473i	0.845502	−	0.941197i
$381$			2.58756i			0.132565i
$382$	19.9175	−	27.2457i	1.01907	−	1.39401i
$383$	9.13650	+	15.8249i	0.466853	+	0.808613i	0.999283	−	0.0378608i	$-0.0120543\pi$
$383$	9.13650	+	15.8249i	0.466853	+	0.808613i	−0.532430	+	0.846474i	$0.678721\pi$
$384$	10.0132	+	9.39513i	0.510984	+	0.479443i
$385$	−1.37685	−	2.38478i	−0.0701709	−	0.121540i
$386$	26.8636	+	2.90314i	1.36732	+	0.147766i
$387$	−8.86241			−0.450502
$388$	−9.34329	−	8.51247i	−0.474334	−	0.432155i
$389$	12.4317	+	7.17743i	0.630311	+	0.363910i	0.780872	−	0.624690i	$-0.214775\pi$
$389$	12.4317	+	7.17743i	0.630311	+	0.363910i	−0.150562	+	0.988601i	$0.548108\pi$
$390$	−1.94500	+	17.9976i	−0.0984887	+	0.911344i
$391$		−	1.86972i		−	0.0945558i
$392$	−6.10122	+	18.2304i	−0.308158	+	0.920775i
$393$	18.3394	+	10.5883i	0.925100	+	0.534107i
$394$	−9.38762	+	12.8416i	−0.472941	+	0.646950i
$395$	19.8716	+	11.4729i	0.999847	+	0.577262i
$396$	6.44272	+	1.40898i	0.323759	+	0.0708040i
$397$	22.8960	−	13.2190i	1.14912	−	0.663444i	0.200447	−	0.979705i	$-0.435761\pi$
$397$	22.8960	−	13.2190i	1.14912	−	0.663444i	0.948673	+	0.316260i	$0.102427\pi$
$398$	6.54512	+	14.8173i	0.328077	+	0.742726i
$399$	−2.05673	+	1.20676i	−0.102965	+	0.0604137i
$400$	1.11564	+	11.9626i	0.0557819	+	0.598131i
$401$	−6.10144	+	3.52267i	−0.304691	+	0.175914i	−0.644549	−	0.764563i	$-0.722955\pi$
$401$	−6.10144	+	3.52267i	−0.304691	+	0.175914i	0.339857	+	0.940477i	$0.389621\pi$
$402$	−3.46627	−	2.53396i	−0.172882	−	0.126382i
$403$	0.926966	−	1.60555i	0.0461755	−	0.0799783i
$404$	−2.27490	+	10.4022i	−0.113180	+	0.517530i
$405$	5.11260	+	2.95176i	0.254047	+	0.146674i
$406$	2.17908	+	4.93317i	0.108146	+	0.244829i
$407$	14.5323			0.720337
$408$	−3.68470	+	3.25949i	−0.182420	+	0.161369i
$409$	17.6696	+	10.2015i	0.873705	+	0.504434i	0.868578	−	0.495553i	$-0.165035\pi$
$409$	17.6696	+	10.2015i	0.873705	+	0.504434i	0.00512749	+	0.999987i	$0.498368\pi$
$410$	−30.8882	+	13.6439i	−1.52546	+	0.673825i
$411$		−	10.4101i		−	0.513492i
$412$	10.8687	+	34.1303i	0.535465	+	1.68148i
$413$	−3.15139	−	5.45836i	−0.155070	−	0.268588i
$414$	−2.80122	−	0.302727i	−0.137673	−	0.0148782i
$415$	28.9920	−	16.7386i	1.42316	−	0.821664i
$416$	−10.8113	+	18.1074i	−0.530068	+	0.887789i
$417$		−	5.78043i		−	0.283069i
$418$	−7.78002	+	10.8007i	−0.380533	+	0.528279i
$419$	−7.69306			−0.375831			−0.187915	−	0.982185i	$-0.560173\pi$
$419$	−7.69306			−0.375831			−0.187915	+	0.982185i	$0.560173\pi$
$420$	0.661313	−	3.02393i	0.0322688	−	0.147552i
$421$	−3.05025	−	5.28319i	−0.148660	−	0.257487i	0.782072	−	0.623188i	$-0.214163\pi$
$421$	−3.05025	−	5.28319i	−0.148660	−	0.257487i	−0.930732	+	0.365701i	$0.880829\pi$
$422$	−22.4516	−	2.42634i	−1.09293	−	0.118112i
$423$	−0.866371	+	0.500199i	−0.0421244	+	0.0243205i
$424$	−14.4841	−	16.3736i	−0.703410	−	0.795172i
$425$	−4.30461			−0.208804
$426$	11.5857	+	26.2287i	0.561331	+	1.27078i
$427$	−0.555067	+	0.961404i	−0.0268616	+	0.0465256i
$428$	−1.73371	+	0.552097i	−0.0838020	+	0.0266866i
$429$		−	9.77007i		−	0.471703i
$430$	9.38185	+	21.2394i	0.452433	+	1.02425i
$431$	−4.72335	+	8.18108i	−0.227516	+	0.394069i	−0.957071	−	0.289853i	$-0.906394\pi$
$431$	−4.72335	+	8.18108i	−0.227516	+	0.394069i	0.729555	+	0.683922i	$0.239727\pi$
$432$	12.7083	+	17.9300i	0.611429	+	0.862658i
$433$	−14.9419	−	8.62669i	−0.718061	−	0.414572i	0.0959778	−	0.995383i	$-0.469402\pi$
$433$	−14.9419	−	8.62669i	−0.718061	−	0.414572i	−0.814038	+	0.580811i	$0.802736\pi$
$434$	−0.187085	+	0.255919i	−0.00898038	+	0.0122845i
$435$	14.5233	+	25.1550i	0.696337	+	1.20609i
$436$	−2.51925	+	2.76513i	−0.120650	+	0.132426i
$437$	2.80879	−	4.94472i	0.134362	−	0.236538i
$438$	−11.4500	−	25.9213i	−0.547101	−	1.23857i
$439$	−4.84656	−	8.39450i	−0.231314	−	0.400647i	0.726881	−	0.686763i	$-0.240969\pi$
$439$	−4.84656	−	8.39450i	−0.231314	−	0.400647i	−0.958195	+	0.286116i	$0.907636\pi$
$440$	−3.44362	−	16.9320i	−0.164168	−	0.807200i
$441$	−5.18966	+	8.98876i	−0.247127	+	0.428036i
$442$	−6.09986	−	4.45920i	−0.290141	−	0.212102i
$443$	8.03408	−	13.9154i	0.381711	−	0.661142i	−0.609596	−	0.792712i	$-0.708668\pi$
$443$	8.03408	−	13.9154i	0.381711	−	0.661142i	0.991307	+	0.131570i	$0.0420018\pi$
$444$	12.0753	+	11.0016i	0.573069	+	0.522111i
$445$	−22.7121			−1.07666
$446$	−2.45040	+	22.6742i	−0.116030	+	1.07366i
$447$	6.53892	−	11.3257i	0.309280	−	0.535689i
$448$	2.17064	−	2.87970i	0.102553	−	0.136053i
$449$			12.4409i			0.587123i	0.955940	+	0.293562i	$0.0948406\pi$
$449$			12.4409i			0.587123i	−0.955940	+	0.293562i	$0.905159\pi$
$450$	−0.696961	+	6.44918i	−0.0328551	+	0.304017i
$451$	15.7830	−	9.11231i	0.743192	−	0.429082i
$452$	4.46317	−	1.42129i	0.209930	−	0.0668518i
$453$	−5.68236	+	3.28071i	−0.266981	+	0.154141i
$454$	−10.8734	+	14.8741i	−0.510315	+	0.698075i
$455$	4.75430			0.222885
$456$	−14.6413	+	3.08481i	−0.685640	+	0.144460i
$457$	−23.5694			−1.10253			−0.551265	−	0.834330i	$-0.685855\pi$
$457$	−23.5694			−1.10253			−0.551265	+	0.834330i	$0.685855\pi$
$458$	10.6206	−	14.5283i	0.496270	−	0.678862i
$459$	−6.81906	+	3.93698i	−0.318286	+	0.183763i
$460$	2.23990	+	7.03379i	0.104436	+	0.327952i
$461$	−0.956655	+	0.552325i	−0.0445559	+	0.0257243i	−0.522112	−	0.852877i	$-0.674856\pi$
$461$	−0.956655	+	0.552325i	−0.0445559	+	0.0257243i	0.477557	+	0.878601i	$0.341523\pi$
$462$	−0.179498	+	1.66095i	−0.00835100	+	0.0772743i
$463$		−	26.1205i		−	1.21392i	−0.794731	−	0.606962i	$-0.792388\pi$
$463$		−	26.1205i		−	1.21392i	0.794731	−	0.606962i	$-0.207612\pi$
$464$	3.14223	+	33.6932i	0.145874	+	1.56417i
$465$	−0.853703	+	1.47866i	−0.0395895	+	0.0685711i
$466$	−1.75579	+	16.2469i	−0.0813356	+	0.752622i
$467$	−18.4324			−0.852950			−0.426475	−	0.904499i	$-0.640245\pi$
$467$	−18.4324			−0.852950			−0.426475	+	0.904499i	$0.640245\pi$
$468$	−7.66842	+	8.41686i	−0.354473	+	0.389069i
$469$	−0.563837	+	0.976594i	−0.0260356	+	0.0450949i
$470$	2.11591	+	1.54680i	0.0975997	+	0.0713485i
$471$	9.33940	−	16.1763i	0.430337	−	0.745365i
$472$	−7.88187	−	38.7544i	−0.362792	−	1.78382i
$473$	−6.26582	−	10.8527i	−0.288103	−	0.499008i
$474$	−5.62475	−	12.7337i	−0.258353	−	0.584880i
$475$	−11.3841	−	6.46659i	−0.522338	−	0.296708i
$476$	0.955074	+	0.870148i	0.0437758	+	0.0398832i
$477$	−5.90133	−	10.2214i	−0.270204	−	0.468006i
$478$	−15.7157	+	21.4980i	−0.718820	+	0.983295i
$479$	−26.2671	−	15.1653i	−1.20018	−	0.692922i	−0.239581	−	0.970876i	$-0.577010\pi$
$479$	−26.2671	−	15.1653i	−1.20018	−	0.692922i	−0.960594	+	0.277955i	$0.910343\pi$
$480$	9.95684	−	16.6763i	0.454465	−	0.761164i
$481$	−12.5450	+	21.7287i	−0.572005	+	0.990741i
$482$	−5.59245	−	12.6606i	−0.254729	−	0.576676i
$483$		−	0.713727i		−	0.0324757i
$484$	−3.84589	−	12.0770i	−0.174813	−	0.548953i
$485$	−8.93957	+	15.4838i	−0.405925	+	0.703083i
$486$	7.97143	+	18.0464i	0.361592	+	0.818599i
$487$	41.6132			1.88568			0.942838	−	0.333253i	$-0.108146\pi$
$487$	41.6132			1.88568			0.942838	+	0.333253i	$0.108146\pi$
$488$	−5.21734	+	4.61526i	−0.236178	+	0.208923i
$489$	−0.561305	+	0.324070i	−0.0253831	+	0.0146549i
$490$	27.0360	+	2.92177i	1.22136	+	0.131992i
$491$	15.3752	+	26.6306i	0.693873	+	1.20182i	0.970559	+	0.240863i	$0.0774304\pi$
$491$	15.3752	+	26.6306i	0.693873	+	1.20182i	−0.276686	+	0.960960i	$0.589236\pi$
$492$	20.0130	+	4.37671i	0.902255	+	0.197317i
$493$	−12.1241			−0.546041
$494$	−9.43307	−	20.9565i	−0.424414	−	0.942875i
$495$		−	9.32884i		−	0.419300i
$496$	−1.62285	+	1.15023i	−0.0728680	+	0.0516469i
$497$	6.52173	−	3.76532i	0.292540	−	0.168898i
$498$	−20.1923	−	2.18218i	−0.904840	−	0.0977857i
$499$	12.0566	+	20.8826i	0.539728	+	0.934835i	0.998918	+	0.0464978i	$0.0148061\pi$
$499$	12.0566	+	20.8826i	0.539728	+	0.934835i	−0.459191	+	0.888338i	$0.651861\pi$
$500$	−10.7631	+	3.42751i	−0.481343	+	0.153283i
$501$			16.5494i			0.739373i
$502$	21.1905	−	9.36026i	0.945778	−	0.417769i
$503$	10.6337	+	6.13939i	0.474135	+	0.273742i	0.717969	−	0.696075i	$-0.245072\pi$
$503$	10.6337	+	6.13939i	0.474135	+	0.273742i	−0.243834	+	0.969817i	$0.578405\pi$
$504$	1.45830	−	1.29001i	0.0649577	−	0.0574617i
$505$	15.0621			0.670253
$506$	−1.60978	−	3.64435i	−0.0715635	−	0.162011i
$507$	0.944710	+	0.545429i	0.0419560	+	0.0242233i
$508$	4.16570	+	0.911011i	0.184823	+	0.0404196i
$509$	2.27630	−	3.94266i	0.100895	−	0.174755i	−0.811159	−	0.584826i	$-0.801163\pi$
$509$	2.27630	−	3.94266i	0.100895	−	0.174755i	0.912054	+	0.410071i	$0.134496\pi$
$510$	5.61776	+	4.10676i	0.248758	+	0.181850i
$511$	−6.44531	+	3.72120i	−0.285124	+	0.164616i
$512$	18.6505	−	12.8124i	0.824245	−	0.566234i
$513$	−23.9482	+	0.167948i	−1.05734	+	0.00741507i
$514$	4.99375	+	11.3052i	0.220265	+	0.498653i
$515$	43.8792	−	25.3337i	1.93355	−	1.11633i
$516$	3.00952	−	13.7614i	0.132487	−	0.605810i
$517$	−1.22507	−	0.707292i	−0.0538784	−	0.0311067i
$518$	2.53191	−	3.46347i	0.111246	−	0.152176i
$519$	1.72998	+	0.998807i	0.0759379	+	0.0438428i
$520$	28.2894	+	9.46770i	1.24057	+	0.415186i
$521$		−	14.0347i		−	0.614871i	−0.951569	−	0.307436i	$-0.900529\pi$
$521$		−	14.0347i		−	0.614871i	0.951569	−	0.307436i	$-0.0994709\pi$
$522$	−1.96302	+	18.1644i	−0.0859189	+	0.795032i
$523$	−5.94814	−	3.43416i	−0.260094	−	0.150165i	0.364283	−	0.931288i	$-0.381314\pi$
$523$	−5.94814	−	3.43416i	−0.260094	−	0.150165i	−0.624378	+	0.781123i	$0.714647\pi$
$524$	23.5028	−	25.7966i	1.02672	−	1.12693i
$525$	−1.64320			−0.0717149
$526$	−39.1741	−	4.23353i	−1.70807	−	0.184591i
$527$	−0.356337	−	0.617194i	−0.0155223	−	0.0268854i
$528$	−4.37567	+	9.52565i	−0.190427	+	0.414551i
$529$	−10.6490	−	18.4445i	−0.462998	−	0.801936i
$530$	−18.2491	+	24.9634i	−0.792689	+	1.08434i
$531$		−	21.3522i		−	0.926605i
$532$	1.21864	+	3.73598i	0.0528347	+	0.161975i
$533$			31.4650i			1.36290i
$534$	11.1236	+	8.13174i	0.481367	+	0.351895i
$535$	1.28687	+	2.22892i	0.0556362	+	0.0963647i
$536$	−5.29978	+	4.68819i	−0.228915	+	0.202499i
$537$	4.65526	+	8.06314i	0.200889	+	0.347950i
$538$	3.59686	−	33.2828i	0.155072	−	1.43492i
$539$	−14.6766			−0.632165
$540$	20.9365	−	22.9799i	0.900963	−	0.988896i
$541$	34.4443	+	19.8865i	1.48088	+	0.854985i	0.999765	−	0.0216733i	$-0.00689936\pi$
$541$	34.4443	+	19.8865i	1.48088	+	0.854985i	0.481113	+	0.876659i	$0.340233\pi$
$542$	−25.8994	−	2.79894i	−1.11247	−	0.120225i
$543$			28.5566i			1.22548i
$544$	3.95015	+	7.07956i	0.169361	+	0.303534i
$545$	4.58240	+	2.64565i	0.196289	+	0.113327i
$546$	−2.32850	−	1.70221i	−0.0996506	−	0.0728477i
$547$	−9.78439	−	5.64902i	−0.418350	−	0.241535i	0.276021	−	0.961152i	$-0.410984\pi$
$547$	−9.78439	−	5.64902i	−0.418350	−	0.241535i	−0.694371	+	0.719617i	$0.744317\pi$
$548$	−16.7591	−	3.66511i	−0.715915	−	0.156566i
$549$	−3.25699	+	1.88042i	−0.139005	+	0.0802545i
$550$	−8.39029	+	3.70616i	−0.357763	+	0.158031i
$551$	−32.0637	−	18.2134i	−1.36596	−	0.775916i
$552$	1.42132	−	4.24688i	0.0604952	−	0.180759i
$553$	−3.16623	+	1.82802i	−0.134642	+	0.0777355i
$554$	21.7266	−	29.7204i	0.923073	−	1.26270i
$555$	11.5535	−	20.0113i	0.490420	−	0.849433i
$556$	−9.30587	−	2.03513i	−0.394657	−	0.0863088i
$557$	−20.8369	−	12.0302i	−0.882888	−	0.509735i	−0.0112782	−	0.999936i	$-0.503590\pi$
$557$	−20.8369	−	12.0302i	−0.882888	−	0.509735i	−0.871609	+	0.490201i	$0.836923\pi$
$558$	−0.982379	+	0.433936i	−0.0415874	+	0.0183700i
$559$	21.6360			0.915106
$560$	−4.63537	−	2.12929i	−0.195880	−	0.0899787i
$561$	−3.25256	−	1.87787i	−0.137323	−	0.0792836i
$562$	11.9870	+	27.1371i	0.505641	+	1.14471i
$563$			30.2137i			1.27336i	0.771130	+	0.636678i	$0.219692\pi$
$563$			30.2137i			1.27336i	−0.771130	+	0.636678i	$0.780308\pi$
$564$	−0.482494	−	1.51514i	−0.0203167	−	0.0637989i
$565$	−3.31284	−	5.73801i	−0.139372	−	0.241400i
$566$	1.74097	−	16.1097i	0.0731786	−	0.677143i
$567$	−0.814614	+	0.470318i	−0.0342106	+	0.0197515i
$568$	46.3044	−	9.41737i	1.94289	−	0.395144i
$569$		−	31.3114i		−	1.31264i	−0.754482	−	0.656320i	$-0.772112\pi$
$569$		−	31.3114i		−	1.31264i	0.754482	−	0.656320i	$-0.227888\pi$
$570$	8.68752	+	19.3001i	0.363880	+	0.808394i
$571$	−36.8938			−1.54396			−0.771978	−	0.635649i	$-0.780733\pi$
$571$	−36.8938			−1.54396			−0.771978	+	0.635649i	$0.780733\pi$
$572$	−15.7288	−	3.43978i	−0.657652	−	0.143824i
$573$	14.4814	+	25.0826i	0.604970	+	1.04784i
$574$	0.578083	−	5.34917i	0.0241287	−	0.223270i
$575$	3.39366	−	1.95933i	0.141525	−	0.0817096i
$576$	11.2462	−	4.77188i	0.468592	−	0.198828i
$577$	−1.16074			−0.0483220			−0.0241610	−	0.999708i	$-0.507691\pi$
$577$	−1.16074			−0.0483220			−0.0241610	+	0.999708i	$0.507691\pi$
$578$	19.3348	−	8.54055i	0.804220	−	0.355240i
$579$	−11.5939	+	20.0812i	−0.481825	+	0.834545i
$580$	45.6101	−	14.5245i	1.89386	−	0.603096i
$581$			5.33407i			0.221294i
$582$	9.92205	−	4.38277i	0.411282	−	0.181671i
$583$	8.34461	−	14.4533i	0.345598	−	0.598594i
$584$	−45.7618	+	9.30702i	−1.89364	+	0.385127i
$585$	13.9485	+	8.05317i	0.576700	+	0.332958i
$586$	−11.8738	−	8.68011i	−0.490501	−	0.358572i
$587$	−0.751317	−	1.30132i	−0.0310102	−	0.0537112i	0.850104	−	0.526615i	$-0.176539\pi$
$587$	−0.751317	−	1.30132i	−0.0310102	−	0.0537112i	−0.881114	+	0.472904i	$0.843206\pi$
$588$	−12.1952	−	11.1108i	−0.502923	−	0.458202i
$589$	−0.0152010	−	2.16756i	−0.000626346	−	0.0893127i
$590$	−51.1718	+	22.6036i	−2.10671	+	0.930576i
$591$	−6.82547	−	11.8221i	−0.280763	−	0.486295i
$592$	21.9627	−	15.5666i	0.902662	−	0.639783i
$593$	9.24084	−	16.0056i	0.379476	−	0.657271i	−0.611510	−	0.791237i	$-0.709438\pi$
$593$	9.24084	−	16.0056i	0.379476	−	0.657271i	0.990986	+	0.133965i	$0.0427710\pi$
$594$	−9.90167	+	13.5448i	−0.406270	+	0.555749i
$595$	0.913806	−	1.58276i	0.0374624	−	0.0648868i
$596$	−15.9310	−	14.5144i	−0.652561	−	0.594534i
$597$	−13.9011			−0.568934
$598$	6.83869	+	0.739055i	0.279655	+	0.0302222i
$599$	−16.6212	+	28.7888i	−0.679124	+	1.17628i	0.296121	+	0.955150i	$0.404307\pi$
$599$	−16.6212	+	28.7888i	−0.679124	+	1.17628i	−0.975245	+	0.221127i	$0.929027\pi$
$600$	−9.77748	−	3.27226i	−0.399164	−	0.133589i
$601$			11.1345i			0.454186i	0.973873	+	0.227093i	$0.0729221\pi$
$601$			11.1345i			0.454186i	−0.973873	+	0.227093i	$0.927078\pi$
$602$	−3.67820	−	0.397502i	−0.149912	−	0.0162010i
$603$	−3.30845	+	1.91013i	−0.134730	+	0.0777867i
$604$	3.28099	+	10.3030i	0.133502	+	0.419225i
$605$	−15.5266	+	8.96429i	−0.631247	+	0.364450i
$606$	−7.37690	−	5.39275i	−0.299666	−	0.219065i
$607$	−11.2378			−0.456127			−0.228064	−	0.973646i	$-0.573239\pi$
$607$	−11.2378			−0.456127			−0.228064	+	0.973646i	$0.573239\pi$
$608$	−0.188574	+	24.6569i	−0.00764769	+	0.999971i
$609$	−4.62812			−0.187541
$610$	7.95444	+	5.81495i	0.322066	+	0.235440i
$611$	2.11509	−	1.22115i	0.0855674	−	0.0494024i
$612$	1.32815	+	4.17067i	0.0536871	+	0.168589i
$613$	20.5664	−	11.8740i	0.830669	−	0.479587i	−0.0234126	−	0.999726i	$-0.507453\pi$
$613$	20.5664	−	11.8740i	0.830669	−	0.479587i	0.854082	+	0.520139i	$0.174120\pi$
$614$	−3.89637	−	0.421079i	−0.157245	−	0.0169934i
$615$		−	28.9781i		−	1.16851i
$616$	2.61075	+	0.873747i	0.105190	+	0.0352043i
$617$	−2.53920	+	4.39802i	−0.102224	+	0.177058i	−0.912601	−	0.408852i	$-0.865929\pi$
$617$	−2.53920	+	4.39802i	−0.102224	+	0.177058i	0.810376	+	0.585910i	$0.199263\pi$
$618$	−30.5609	−	3.30271i	−1.22934	−	0.132854i
$619$	45.0160			1.80935			0.904674	−	0.426105i	$-0.140115\pi$
$619$	45.0160			1.80935			0.904674	+	0.426105i	$0.140115\pi$
$620$	2.07991	+	1.89497i	0.0835313	+	0.0761036i
$621$	3.58400	−	6.20766i	0.143821	−	0.249105i
$622$	11.5176	−	15.7553i	0.461814	−	0.631728i
$623$	1.80941	−	3.13400i	0.0724927	−	0.125561i
$624$	−10.4655	−	14.7656i	−0.418953	−	0.591096i
$625$	15.4982	+	26.8436i	0.619927	+	1.07375i
$626$	15.2440	−	6.73357i	0.609272	−	0.269127i
$627$	−5.78080	−	9.85242i	−0.230863	−	0.393468i
$628$	−22.7540	−	20.7307i	−0.907982	−	0.827244i
$629$	4.82247	+	8.35276i	0.192284	+	0.333046i
$630$	−2.22334	−	1.62533i	−0.0885801	−	0.0647549i
$631$	−20.6719	−	11.9349i	−0.822936	−	0.475122i	0.0284918	−	0.999594i	$-0.490930\pi$
$631$	−20.6719	−	11.9349i	−0.822936	−	0.475122i	−0.851428	+	0.524472i	$0.824263\pi$
$632$	−22.4803	+	4.57203i	−0.894218	+	0.181866i
$633$	9.68974	−	16.7831i	0.385132	−	0.667069i
$634$	22.9381	−	10.1322i	0.910990	−	0.402402i
$635$		−	6.03179i		−	0.239364i
$636$	17.8756	−	5.69245i	0.708813	−	0.225720i
$637$	12.6696	−	21.9445i	0.501989	−	0.869471i
$638$	−23.6315	+	10.4385i	−0.935582	+	0.413265i
$639$	25.5119			1.00923
$640$	−23.3415	−	21.9007i	−0.922653	−	0.865701i
$641$	−0.303877	+	0.175444i	−0.0120024	+	0.00692960i	−0.505989	−	0.862540i	$-0.668872\pi$
$641$	−0.303877	+	0.175444i	−0.0120024	+	0.00692960i	0.493987	+	0.869469i	$0.335539\pi$
$642$	0.167767	−	1.55240i	0.00662123	−	0.0612682i
$643$	7.67194	+	13.2882i	0.302552	+	0.524035i	0.976713	−	0.214549i	$-0.0688281\pi$
$643$	7.67194	+	13.2882i	0.302552	+	0.524035i	−0.674161	+	0.738584i	$0.735495\pi$
$644$	−1.14902	−	0.251284i	−0.0452779	−	0.00990198i
$645$	−19.9260			−0.784585
$646$	−8.78972	−	0.887588i	−0.345827	−	0.0349217i
$647$			12.4035i			0.487632i	0.969821	+	0.243816i	$0.0783994\pi$
$647$			12.4035i			0.487632i	−0.969821	+	0.243816i	$0.921601\pi$
$648$	−5.78378	+	1.17630i	−0.227208	+	0.0462095i
$649$	26.1474	−	15.0962i	1.02637	−	0.592578i
$650$	1.70151	−	15.7445i	0.0667386	−	0.617551i
$651$	−0.136024	−	0.235601i	−0.00533122	−	0.00923394i
$652$	0.324097	+	1.01774i	0.0126926	+	0.0398577i
$653$			38.6270i			1.51159i	0.654808	+	0.755795i	$0.272750\pi$
$653$			38.6270i			1.51159i	−0.654808	+	0.755795i	$0.727250\pi$
$654$	−1.29707	−	2.93641i	−0.0507195	−	0.114823i
$655$	−42.7504	−	24.6820i	−1.67040	−	0.964404i
$656$	14.0921	−	30.6778i	0.550203	−	1.19777i
$657$	−25.2129			−0.983650
$658$	−0.382008	+	0.168741i	−0.0148922	+	0.00657820i
$659$	0.427803	+	0.246992i	0.0166648	+	0.00962144i	0.508309	−	0.861175i	$-0.330271\pi$
$659$	0.427803	+	0.246992i	0.0166648	+	0.00962144i	−0.491644	+	0.870796i	$0.663604\pi$
$660$	14.4856	+	3.16791i	0.563852	+	0.123311i
$661$	−12.5398	+	21.7195i	−0.487740	+	0.844791i	−0.999901	−	0.0140991i	$-0.995512\pi$
$661$	−12.5398	+	21.7195i	−0.487740	+	0.844791i	0.512160	+	0.858890i	$0.328845\pi$
$662$	−22.8441	+	31.2491i	−0.887861	+	1.21453i
$663$	5.61558	−	3.24216i	0.218091	−	0.125915i
$664$	−10.6222	+	31.7392i	−0.412223	+	1.23172i
$665$	4.79438	−	2.81305i	0.185918	−	0.109085i
$666$	13.2950	−	5.87265i	0.515169	−	0.227560i
$667$	9.55835	−	5.51852i	0.370101	−	0.213678i
$668$	26.6428	+	5.82660i	1.03084	+	0.225438i
$669$	−16.9495	−	9.78582i	−0.655307	−	0.378342i
$670$	8.08012	+	5.90683i	0.312162	+	0.228201i
$671$	−4.60545	−	2.65896i	−0.177791	−	0.102648i
$672$	1.50789	+	2.70248i	0.0581681	+	0.104250i
$673$			12.2784i			0.473296i	0.971595	+	0.236648i	$0.0760489\pi$
$673$			12.2784i			0.473296i	−0.971595	+	0.236648i	$0.923951\pi$
$674$	17.3887	+	1.87919i	0.669787	+	0.0723837i
$675$	−14.2917	−	8.25134i	−0.550089	−	0.317594i
$676$	1.21069	−	1.32885i	0.0465649	−	0.0511096i
$677$	−6.28293			−0.241473			−0.120736	−	0.992685i	$-0.538526\pi$
$677$	−6.28293			−0.241473			−0.120736	+	0.992685i	$0.538526\pi$
$678$	−0.431890	+	3.99640i	−0.0165866	+	0.153481i
$679$	−1.42438	−	2.46710i	−0.0546628	−	0.0946788i
$680$	8.58930	−	7.59811i	0.329385	−	0.291374i
$681$	−7.90577	−	13.6932i	−0.302950	−	0.524724i
$682$	−1.22594	−	0.896202i	−0.0469437	−	0.0343173i
$683$			28.9958i			1.10949i	0.832020	+	0.554746i	$0.187185\pi$
$683$			28.9958i			1.10949i	−0.832020	+	0.554746i	$0.812815\pi$
$684$	−2.75294	+	13.0251i	−0.105261	+	0.498027i
$685$			24.2667i			0.927181i
$686$	−5.19055	+	7.10031i	−0.198176	+	0.271091i
$687$	7.72197	+	13.3748i	0.294611	+	0.510282i
$688$	−21.0947	−	9.69001i	−0.804230	−	0.369428i
$689$	14.4071	+	24.9538i	0.548865	+	0.950662i
$690$	−6.29819	−	0.680643i	−0.239768	−	0.0259116i
$691$	29.0538			1.10526			0.552629	−	0.833427i	$-0.313625\pi$
$691$	29.0538			1.10526			0.552629	+	0.833427i	$0.313625\pi$
$692$	2.21705	−	2.43344i	0.0842797	−	0.0925054i
$693$	1.28727	+	0.743204i	0.0488992	+	0.0282320i
$694$	1.72977	−	16.0061i	0.0656612	−	0.607582i
$695$			13.4746i			0.511120i
$696$	−27.5386	−	9.21642i	−1.04385	−	0.349348i
$697$	10.4750	+	6.04776i	0.396770	+	0.229075i
$698$	2.45104	−	3.35285i	0.0927731	−	0.126907i
$699$	−12.1449	−	7.01188i	−0.459363	−	0.265214i
$700$	−0.578525	+	2.64537i	−0.0218662	+	0.0999855i
$701$	−21.1436	+	12.2073i	−0.798584	+	0.461063i	−0.842976	−	0.537952i	$-0.819198\pi$
$701$	−21.1436	+	12.2073i	−0.798584	+	0.461063i	0.0443920	+	0.999014i	$0.485865\pi$
$702$	−11.7045	−	26.4976i	−0.441758	−	1.00009i
$703$	0.205722	+	29.3345i	0.00775894	+	1.10637i
$704$	13.7947	+	10.3981i	0.519908	+	0.391893i
$705$	−1.94792	+	1.12463i	−0.0733630	+	0.0423561i
$706$	21.9110	+	16.0176i	0.824631	+	0.602832i
$707$	−1.19995	+	2.07838i	−0.0451289	+	0.0781656i
$708$	33.1552	+	7.25082i	1.24605	+	0.272502i
$709$	−3.14824	−	1.81764i	−0.118235	−	0.0682627i	0.439716	−	0.898137i	$-0.355079\pi$
$709$	−3.14824	−	1.81764i	−0.118235	−	0.0682627i	−0.557951	+	0.829874i	$0.688412\pi$
$710$	−27.0072	−	61.1409i	−1.01356	−	2.29458i
$711$	−12.3857			−0.464502
$712$	17.0076	−	15.0449i	0.637385	−	0.563832i
$713$	0.561857	+	0.324388i	0.0210417	+	0.0121484i
$714$	−1.01423	+	0.448008i	−0.0379568	+	0.0167663i
$715$			22.7747i			0.851726i
$716$	14.6198	−	4.65565i	0.546367	−	0.173990i
$717$	−11.4265	−	19.7912i	−0.426729	−	0.739116i
$718$	6.26244	+	0.676780i	0.233712	+	0.0252572i
$719$	34.9775	−	20.1943i	1.30444	−	0.753120i	0.323279	−	0.946304i	$-0.395215\pi$
$719$	34.9775	−	20.1943i	1.30444	−	0.753120i	0.981163	+	0.193184i	$0.0618813\pi$
$720$	−9.99283	−	14.0988i	−0.372411	−	0.525430i
$721$			8.07306i			0.300657i
$722$	−21.9122	−	15.5517i	−0.815488	−	0.578774i
$723$	11.8777			0.441738
$724$	45.9731	+	10.0540i	1.70858	+	0.373655i
$725$	−12.7051	−	22.0059i	−0.471857	−	0.817280i
$726$	10.8140	+	1.16866i	0.401343	+	0.0433730i
$727$	−4.07642	+	2.35352i	−0.151186	+	0.0872873i	−0.573685	−	0.819076i	$-0.694486\pi$
$727$	−4.07642	+	2.35352i	−0.151186	+	0.0872873i	0.422499	+	0.906364i	$0.361153\pi$
$728$	−3.56017	+	3.14933i	−0.131949	+	0.116722i
$729$	−23.1906			−0.858912
$730$	26.6907	+	60.4245i	0.987867	+	2.23641i
$731$	4.15857	−	7.20286i	0.153810	−	0.266407i
$732$	−1.81386	−	5.69594i	−0.0670423	−	0.210528i
$733$		−	23.9315i		−	0.883930i	−0.897032	−	0.441965i	$-0.854282\pi$
$733$		−	23.9315i		−	0.883930i	0.897032	−	0.441965i	$-0.145718\pi$
$734$	10.9285	+	24.7409i	0.403380	+	0.913203i
$735$	−11.6683	+	20.2101i	−0.430391	+	0.745459i
$736$	−6.33661	−	3.78338i	−0.233571	−	0.139457i
$737$	−4.67821	−	2.70097i	−0.172324	−	0.0994915i
$738$	10.7568	−	14.7146i	0.395964	−	0.541650i
$739$	1.44053	+	2.49507i	0.0529906	+	0.0917825i	0.891304	−	0.453406i	$-0.149791\pi$
$739$	1.44053	+	2.49507i	0.0529906	+	0.0917825i	−0.838313	+	0.545189i	$0.816458\pi$
$740$	−28.1484	−	25.6454i	−1.03475	−	0.942743i
$741$	19.7217	−	0.138307i	0.724494	−	0.00508084i
$742$	−1.99080	−	4.50692i	−0.0730844	−	0.165454i
$743$	17.8747	+	30.9598i	0.655758	+	1.13581i	0.981703	+	0.190418i	$0.0609843\pi$
$743$	17.8747	+	30.9598i	0.655758	+	1.13581i	−0.325945	+	0.945389i	$0.605682\pi$
$744$	−0.340208	−	1.67277i	−0.0124726	−	0.0613268i
$745$	−15.2427	+	26.4011i	−0.558448	+	0.967261i
$746$	−23.6111	−	17.2605i	−0.864463	−	0.631950i
$747$	−9.03522	+	15.6495i	−0.330581	+	0.572584i
$748$	−4.16830	+	4.57513i	−0.152408	+	0.167283i
$749$	−0.410086			−0.0149842
$750$	1.04152	−	9.63753i	0.0380311	−	0.351913i
$751$	24.3250	−	42.1322i	0.887632	−	1.53742i	0.0449656	−	0.998989i	$-0.485682\pi$
$751$	24.3250	−	42.1322i	0.887632	−	1.53742i	0.842667	−	0.538436i	$-0.180985\pi$
$752$	−2.60909	+	0.243324i	−0.0951436	+	0.00887312i
$753$			19.8801i			0.724473i
$754$	4.79235	−	44.3450i	0.174527	−	1.61495i
$755$	13.2460	−	7.64757i	0.482071	−	0.278324i
$756$	1.50299	+	4.71973i	0.0546632	+	0.171655i
$757$	−29.4372	+	16.9956i	−1.06991	+	0.617716i	−0.928158	−	0.372186i	$-0.878608\pi$
$757$	−29.4372	+	16.9956i	−1.06991	+	0.617716i	−0.141757	+	0.989902i	$0.545275\pi$
$758$	2.13676	−	2.92294i	0.0776108	−	0.106166i
$759$	3.41899			0.124102
$760$	34.1298	−	7.19092i	1.23802	−	0.260842i
$761$	−34.2969			−1.24326			−0.621631	−	0.783310i	$-0.713530\pi$
$761$	−34.2969			−1.24326			−0.621631	+	0.783310i	$0.713530\pi$
$762$	−2.15959	+	2.95417i	−0.0782338	+	0.107018i
$763$	−0.730135	+	0.421544i	−0.0264327	+	0.0152609i
$764$	45.4787	−	14.4826i	1.64536	−	0.523964i
$765$	5.36198	−	3.09574i	0.193863	−	0.111927i
$766$	−2.77656	+	25.6923i	−0.100321	+	0.928301i
$767$			52.1275i			1.88221i
$768$	3.59066	+	19.0833i	0.129567	+	0.688609i
$769$	−5.78344	+	10.0172i	−0.208556	+	0.361230i	−0.951260	−	0.308390i	$-0.900210\pi$
$769$	−5.78344	+	10.0172i	−0.208556	+	0.361230i	0.742704	+	0.669620i	$0.233543\pi$
$770$	0.418422	−	3.87178i	0.0150789	−	0.139529i
$771$	−10.6062			−0.381971
$772$	28.2467	+	25.7349i	1.01662	+	0.926220i
$773$	11.6089	−	20.1073i	0.417545	−	0.723209i	−0.578147	−	0.815933i	$-0.696224\pi$
$773$	11.6089	−	20.1073i	0.417545	−	0.723209i	0.995692	+	0.0927238i	$0.0295574\pi$
$774$	−10.1180	−	7.39662i	−0.363686	−	0.265866i
$775$	0.746830	−	1.29355i	0.0268269	−	0.0464656i
$776$	−3.56250	−	17.5165i	−0.127886	−	0.628805i
$777$	1.84088	+	3.18850i	0.0660412	+	0.114387i
$778$	8.20268	+	18.5699i	0.294080	+	0.665762i
$779$	18.6174	+	31.7302i	0.667036	+	1.13685i
$780$	−17.2415	+	18.9242i	−0.617343	+	0.677596i
$781$	18.0372	+	31.2413i	0.645421	+	1.11790i
$782$	1.56048	−	2.13462i	0.0558026	−	0.0763340i
$783$	−40.2532	−	23.2402i	−1.43853	−	0.830536i
$784$	−22.1808	+	15.7212i	−0.792173	+	0.561471i
$785$	−21.7708	+	37.7081i	−0.777033	+	1.34586i
$786$	12.1007	+	27.3946i	0.431618	+	0.977132i
$787$			33.9207i			1.20914i	0.796552	+	0.604571i	$0.206655\pi$
$787$			33.9207i			1.20914i	−0.796552	+	0.604571i	$0.793345\pi$
$788$	−21.4353	+	6.82605i	−0.763602	+	0.243168i
$789$	16.9069	−	29.2836i	0.601901	−	1.04252i
$790$	13.1117	+	29.6833i	0.466493	+	1.05608i
$791$	1.05570			0.0375364
$792$	6.17959	+	6.98573i	0.219582	+	0.248227i
$793$	7.95135	−	4.59072i	0.282361	−	0.163021i
$794$	37.1726	+	4.01723i	1.31921	+	0.142566i
$795$	−13.2684	−	22.9815i	−0.470581	−	0.815070i
$796$	−4.89420	+	22.3793i	−0.173470	+	0.793212i
$797$	12.2630			0.434378			0.217189	−	0.976130i	$-0.430311\pi$
$797$	12.2630			0.434378			0.217189	+	0.976130i	$0.430311\pi$
$798$	−3.35530	−	0.338819i	−0.118776	−	0.0119940i
$799$		−	0.938848i		−	0.0332141i
$800$	−8.71037	+	14.5886i	−0.307958	+	0.515785i
$801$	10.6172	−	6.12983i	0.375139	−	0.216587i
$802$	−9.90594	−	1.07053i	−0.349791	−	0.0378018i
$803$	−17.8258	−	30.8752i	−0.629059	−	1.08956i
$804$	−1.84252	−	5.78593i	−0.0649808	−	0.204054i
$805$			1.66375i			0.0586394i
$806$	2.39830	−	1.05938i	0.0844766	−	0.0373150i
$807$	24.8797	+	14.3643i	0.875806	+	0.505647i
$808$	−11.2790	+	9.97737i	−0.396792	+	0.351003i
$809$	35.6199			1.25233			0.626164	−	0.779691i	$-0.284624\pi$
$809$	35.6199			1.25233			0.626164	+	0.779691i	$0.284624\pi$
$810$	3.37340	+	7.63697i	0.118529	+	0.268336i
$811$	16.4875	+	9.51908i	0.578956	+	0.334260i	0.760718	−	0.649082i	$-0.224847\pi$
$811$	16.4875	+	9.51908i	0.578956	+	0.334260i	−0.181763	+	0.983342i	$0.558180\pi$
$812$	−1.62944	+	7.45077i	−0.0571820	+	0.261471i
$813$	11.1777	−	19.3604i	0.392021	−	0.679000i
$814$	16.5912	+	12.1287i	0.581521	+	0.425110i
$815$	1.30844	−	0.755429i	0.0458327	−	0.0264615i
$816$	−6.92715	+	0.646027i	−0.242499	+	0.0226155i
$817$	21.8184	−	12.8017i	0.763329	−	0.447875i
$818$	11.6588	+	26.3940i	0.407639	+	0.922846i
$819$	−2.22248	+	1.28315i	−0.0776597	+	0.0448369i
$820$	−46.6517	−	10.2024i	−1.62915	−	0.356284i
$821$	34.7173	+	20.0441i	1.21164	+	0.699543i	0.963117	−	0.269082i	$-0.0867204\pi$
$821$	34.7173	+	20.0441i	1.21164	+	0.699543i	0.248526	+	0.968625i	$0.420054\pi$
$822$	8.68832	−	11.8850i	0.303040	−	0.414537i
$823$	−27.7423	−	16.0170i	−0.967037	−	0.558319i	−0.0687052	−	0.997637i	$-0.521887\pi$
$823$	−27.7423	−	16.0170i	−0.967037	−	0.558319i	−0.898332	+	0.439318i	$0.855220\pi$
$824$	−16.0767	+	48.0370i	−0.560058	+	1.67345i
$825$		−	7.87146i		−	0.274049i
$826$	0.957699	−	8.86187i	0.0333226	−	0.308344i
$827$	−13.4637	−	7.77329i	−0.468180	−	0.270304i	0.247298	−	0.968940i	$-0.420457\pi$
$827$	−13.4637	−	7.77329i	−0.468180	−	0.270304i	−0.715477	+	0.698636i	$0.753791\pi$
$828$	−2.94545	−	2.68353i	−0.102361	−	0.0932592i
$829$	−5.94617			−0.206519			−0.103260	−	0.994654i	$-0.532927\pi$
$829$	−5.94617			−0.206519			−0.103260	+	0.994654i	$0.532927\pi$
$830$	47.0697	+	5.08681i	1.63381	+	0.176566i
$831$	15.7968	+	27.3608i	0.547984	+	0.949136i
$832$	−27.4556	+	11.6497i	−0.951852	+	0.403880i
$833$	−4.87036	−	8.43572i	−0.168748	−	0.292280i
$834$	4.82437	−	6.59940i	0.167054	−	0.228519i
$835$		−	38.5778i		−	1.33504i
$836$	−17.8966	+	5.83769i	−0.618967	+	0.201901i
$837$		−	2.73220i		−	0.0944386i
$838$	−8.78302	−	6.42067i	−0.303404	−	0.221798i
$839$	−6.06590	−	10.5064i	−0.209418	−	0.362723i	0.742113	−	0.670274i	$-0.233824\pi$
$839$	−6.06590	−	10.5064i	−0.209418	−	0.362723i	−0.951531	+	0.307552i	$0.900490\pi$
$840$	3.27879	−	2.90042i	0.113129	−	0.100074i
$841$	−21.2845	−	36.8658i	−0.733947	−	1.27123i
$842$	0.926964	−	8.57746i	0.0319453	−	0.295599i
$843$	−25.4590			−0.876855
$844$	−23.6075	−	21.5083i	−0.812604	−	0.740347i
$845$	−2.20218	−	1.27143i	−0.0757575	−	0.0437386i
$846$	−1.40659	−	0.152009i	−0.0483595	−	0.00522619i
$847$		−	2.85665i		−	0.0981555i
$848$	−2.87073	−	30.7819i	−0.0985812	−	1.05706i
$849$	12.0424	+	6.95270i	0.413295	+	0.238616i
$850$	−4.91449	−	3.59265i	−0.168565	−	0.123227i
$851$	−7.60385	−	4.39009i	−0.260657	−	0.150490i
$852$	−8.66339	+	39.6143i	−0.296803	+	1.35716i
$853$	13.8144	−	7.97575i	0.472996	−	0.273085i	−0.244497	−	0.969650i	$-0.578623\pi$
$853$	13.8144	−	7.97575i	0.472996	−	0.273085i	0.717493	+	0.696565i	$0.245289\pi$
$854$	−1.43610	+	0.634354i	−0.0491424	+	0.0217072i
$855$	18.8310	−	0.132061i	0.644007	−	0.00451639i
$856$	−2.44012	−	0.816643i	−0.0834017	−	0.0279123i
$857$	46.8936	−	27.0741i	1.60186	−	0.924832i	0.610740	−	0.791831i	$-0.290872\pi$
$857$	46.8936	−	27.0741i	1.60186	−	0.924832i	0.991116	−	0.133001i	$-0.0424614\pi$
$858$	8.15415	−	11.1543i	0.278378	−	0.380801i
$859$	10.3529	−	17.9317i	0.353236	−	0.611823i	−0.633578	−	0.773678i	$-0.718415\pi$
$859$	10.3529	−	17.9317i	0.353236	−	0.611823i	0.986814	+	0.161856i	$0.0517479\pi$
$860$	−7.01540	+	32.0787i	−0.239223	+	1.09387i
$861$	3.99863	+	2.30861i	0.136273	+	0.0786773i
$862$	−12.2205	+	5.39805i	−0.416233	+	0.183858i
$863$	24.9184			0.848231			0.424115	−	0.905608i	$-0.360585\pi$
$863$	24.9184			0.848231			0.424115	+	0.905608i	$0.360585\pi$
$864$	−0.455636	+	31.0768i	−0.0155011	+	1.05725i
$865$	−4.03271	−	2.32829i	−0.137116	−	0.0791642i
$866$	−9.85896	−	22.3195i	−0.335021	−	0.758447i
$867$			18.1392i			0.616038i
$868$	−0.427183	+	0.136036i	−0.0144995	+	0.00461736i
$869$	−8.75685	−	15.1673i	−0.297056	−	0.514516i
$870$	−4.41359	+	40.8402i	−0.149635	+	1.38461i
$871$	8.07699	−	4.66325i	0.273678	−	0.158008i
$872$	−5.18397	+	1.05431i	−0.175551	+	0.0357036i
$873$		−	9.65089i		−	0.326633i
$874$	7.33362	−	3.30106i	0.248064	−	0.111660i
$875$	−2.54588			−0.0860664
$876$	8.56187	−	39.1501i	0.289279	−	1.32276i
$877$	−19.0653	−	33.0221i	−0.643790	−	1.11508i	−0.984580	−	0.174937i	$-0.944028\pi$
$877$	−19.0653	−	33.0221i	−0.643790	−	1.11508i	0.340790	−	0.940140i	$-0.389306\pi$
$878$	1.47286	−	13.6288i	0.0497066	−	0.459950i
$879$	10.9311	−	6.31106i	0.368696	−	0.212867i
$880$	10.2000	−	22.2050i	0.343842	−	0.748529i
$881$	16.6723			0.561702			0.280851	−	0.959751i	$-0.409383\pi$
$881$	16.6723			0.561702			0.280851	+	0.959751i	$0.409383\pi$
$882$	−13.4270	+	5.93097i	−0.452111	+	0.199706i
$883$	16.1610	−	27.9917i	0.543861	−	0.941994i	−0.454817	−	0.890585i	$-0.650295\pi$
$883$	16.1610	−	27.9917i	0.543861	−	0.941994i	0.998678	−	0.0514093i	$-0.0163713\pi$
$884$	−3.24243	−	10.1820i	−0.109055	−	0.342456i
$885$		−	48.0076i		−	1.61376i
$886$	20.7862	−	9.18170i	0.698327	−	0.308465i
$887$	−5.27663	+	9.13939i	−0.177172	+	0.306871i	−0.940911	−	0.338655i	$-0.890028\pi$
$887$	−5.27663	+	9.13939i	−0.177172	+	0.306871i	0.763739	+	0.645525i	$0.223361\pi$
$888$	4.60419	+	22.6384i	0.154506	+	0.759694i
$889$	0.832314	+	0.480537i	0.0279149	+	0.0161167i
$890$	−25.9300	−	18.9557i	−0.869175	−	0.635395i
$891$	−2.25298	−	3.90228i	−0.0754777	−	0.130731i
$892$	−21.7216	+	23.8416i	−0.727293	+	0.798276i
$893$	1.41038	−	2.48291i	0.0471967	−	0.0830874i
$894$	16.9179	−	7.47296i	0.565818	−	0.249933i
$895$	−10.8517	−	18.7958i	−0.362733	−	0.628273i
$896$	4.88158	−	1.47607i	0.163082	−	0.0493120i
$897$	−2.95147	+	5.11209i	−0.0985465	+	0.170688i
$898$	−10.3833	+	14.2036i	−0.346494	+	0.473979i
$899$	2.10347	−	3.64332i	0.0701548	−	0.121512i
$900$	−6.17823	+	6.78122i	−0.205941	+	0.226041i
$901$	11.0765			0.369012
$902$	25.6243	+	2.76921i	0.853196	+	0.0922046i
$903$	1.58745	−	2.74954i	0.0528270	−	0.0914991i
$904$	6.28172	+	2.10232i	0.208927	+	0.0699222i
$905$		−	66.5675i		−	2.21278i
$906$	−9.22554	−	0.997001i	−0.306498	−	0.0331231i
$907$	−32.3892	+	18.6999i	−1.07546	+	0.620920i	−0.929669	−	0.368395i	$-0.879907\pi$
$907$	−32.3892	+	18.6999i	−1.07546	+	0.620920i	−0.145795	+	0.989315i	$0.546574\pi$
$908$	−24.8280	+	7.90643i	−0.823945	+	0.262384i
$909$	−7.04102	+	4.06513i	−0.233536	+	0.134832i
$910$	5.42789	+	3.96796i	0.179933	+	0.131537i
$911$	−40.7900			−1.35143			−0.675717	−	0.737162i	$-0.736166\pi$
$911$	−40.7900			−1.35143			−0.675717	+	0.737162i	$0.736166\pi$
$912$	−19.2902	−	8.69780i	−0.638764	−	0.288013i
$913$	−25.5520			−0.845647
$914$	−26.9087	−	19.6711i	−0.890062	−	0.650664i
$915$	−7.32291	+	4.22789i	−0.242088	+	0.139770i
$916$	24.2507	−	7.72262i	0.801267	−	0.255162i
$917$	6.81162	−	3.93269i	0.224940	−	0.129869i
$918$	−11.0710	−	1.19644i	−0.365398	−	0.0394884i
$919$		−	10.9991i		−	0.362826i	−0.983407	−	0.181413i	$-0.941933\pi$
$919$		−	10.9991i		−	0.362826i	0.983407	−	0.181413i	$-0.0580670\pi$
$920$	−3.31318	+	9.89977i	−0.109232	+	0.326386i
$921$	1.68161	−	2.91263i	0.0554109	−	0.0959744i
$922$	−1.55317	−	0.167850i	−0.0511509	−	0.00552786i
$923$	−62.2827			−2.05006
$924$	−1.59116	+	1.74646i	−0.0523455	+	0.0574544i
$925$	−10.1072	+	17.5061i	−0.332322	+	0.575599i
$926$	21.8003	−	29.8213i	0.716403	−	0.979988i
$927$	−13.6747	+	23.6853i	−0.449137	+	0.777928i
$928$	−24.5331	+	41.0893i	−0.805337	+	1.34882i
$929$	15.0117	+	26.0011i	0.492519	+	0.853067i	0.999963	−	0.00861738i	$-0.00274303\pi$
$929$	15.0117	+	26.0011i	0.492519	+	0.853067i	−0.507444	+	0.861685i	$0.669410\pi$
$930$	−2.20875	+	0.975649i	−0.0724278	+	0.0319928i
$931$	−0.207765	−	29.6259i	−0.00680921	−	0.970949i
$932$	−15.5643	+	17.0833i	−0.509825	+	0.559583i
$933$	8.37412	+	14.5044i	0.274156	+	0.474853i
$934$	−21.0439	−	15.3838i	−0.688578	−	0.503373i
$935$	7.58194	+	4.37744i	0.247956	+	0.143158i
$936$	−15.7796	+	3.20926i	−0.515774	+	0.104898i
$937$	20.0689	−	34.7604i	0.655623	−	1.13557i	−0.326115	−	0.945330i	$-0.605740\pi$
$937$	20.0689	−	34.7604i	0.655623	−	1.13557i	0.981737	−	0.190241i	$-0.0609271\pi$
$938$	−1.45879	+	0.644377i	−0.0476312	+	0.0210397i
$939$			14.3013i			0.466706i
$940$	1.12473	+	3.53190i	0.0366846	+	0.115198i
$941$	−0.433456	+	0.750768i	−0.0141303	+	0.0244743i	−0.873004	−	0.487713i	$-0.837831\pi$
$941$	−0.433456	+	0.750768i	−0.0141303	+	0.0244743i	0.858874	+	0.512187i	$0.171165\pi$
$942$	24.1634	−	10.6735i	0.787287	−	0.347761i
$943$	−11.0110			−0.358569
$944$	23.3461	−	50.8234i	0.759850	−	1.65416i
$945$	6.06786	−	3.50328i	0.197387	−	0.113962i
$946$	1.90417	−	17.6198i	0.0619098	−	0.572870i
$947$	−12.4598	−	21.5809i	−0.404888	−	0.701286i	0.589421	−	0.807826i	$-0.299356\pi$
$947$	−12.4598	−	21.5809i	−0.404888	−	0.701286i	−0.994308	+	0.106540i	$0.966023\pi$
$948$	4.20598	−	19.2323i	0.136604	−	0.624637i
$949$	61.5529			1.99809
$950$	−7.59995	−	16.8840i	−0.246575	−	0.547790i
$951$			21.5197i			0.697825i
$952$	0.364160	+	1.79054i	0.0118025	+	0.0580318i
$953$	−25.5317	+	14.7407i	−0.827053	+	0.477499i	−0.852843	−	0.522168i	$-0.825123\pi$
$953$	−25.5317	+	14.7407i	−0.827053	+	0.477499i	0.0257895	+	0.999667i	$0.491790\pi$
$954$	1.79340	−	16.5949i	0.0580635	−	0.537279i
$955$	−33.7572	−	58.4692i	−1.09236	−	1.89202i
$956$	−35.8846	+	11.4274i	−1.16059	+	0.369589i
$957$		−	22.1702i		−	0.716662i
$958$	−17.3316	−	39.2366i	−0.559959	−	1.26768i
$959$	−3.34851	−	1.93326i	−0.108129	−	0.0624282i
$960$	25.2856	−	10.7290i	0.816090	−	0.346275i
$961$	−30.7527			−0.992023
$962$	−32.4573	+	14.3370i	−1.04646	+	0.462244i
$963$	−1.20314	−	0.694632i	−0.0387706	−	0.0223842i
$964$	4.18183	−	19.1219i	0.134688	−	0.615875i
$965$	27.0261	−	46.8106i	0.870002	−	1.50689i
$966$	0.595680	−	0.814849i	0.0191657	−	0.0262173i
$967$	−50.5276	+	29.1722i	−1.62486	+	0.938113i	−0.639265	+	0.768986i	$0.720761\pi$
$967$	−50.5276	+	29.1722i	−1.62486	+	0.938113i	−0.985594	+	0.169127i	$0.945905\pi$
$968$	5.68872	−	16.9978i	0.182842	−	0.546331i
$969$	3.74458	−	6.59214i	0.120293	−	0.211770i
$970$	−23.1290	+	10.2165i	−0.742627	+	0.328033i
$971$	−0.791582	+	0.457020i	−0.0254031	+	0.0146665i	−0.512648	−	0.858599i	$-0.671335\pi$
$971$	−0.791582	+	0.457020i	−0.0254031	+	0.0146665i	0.487245	+	0.873265i	$0.338002\pi$
$972$	−5.96075	+	27.2562i	−0.191191	+	0.874242i
$973$	−1.85933	−	1.07348i	−0.0596073	−	0.0344143i
$974$	47.5090	+	34.7306i	1.52229	+	1.11284i
$975$	11.7694	+	6.79508i	0.376923	+	0.217617i
$976$	−9.80846	+	0.914739i	−0.313961	+	0.0292801i
$977$			19.2494i			0.615841i	0.951412	+	0.307921i	$0.0996331\pi$
$977$			19.2494i			0.615841i	−0.951412	+	0.307921i	$0.900367\pi$
$978$	−0.911301	−	0.0984840i	−0.0291402	−	0.00314917i
$979$	15.0129	+	8.66771i	0.479815	+	0.277021i
$980$	28.4279	+	25.9001i	0.908097	+	0.827348i
$981$	−2.85616			−0.0911903
$982$	−4.67249	+	43.2359i	−0.149105	+	1.37971i
$983$	−10.4028	−	18.0182i	−0.331799	−	0.574693i	0.651066	−	0.759021i	$-0.274322\pi$
$983$	−10.4028	−	18.0182i	−0.331799	−	0.574693i	−0.982865	+	0.184329i	$0.940989\pi$
$984$	19.1956	+	21.6998i	0.611934	+	0.691763i
$985$	15.9107	+	27.5581i	0.506956	+	0.878073i
$986$	−13.8418	−	10.1188i	−0.440813	−	0.322249i
$987$		−	0.358386i		−	0.0114076i
$988$	6.72081	−	31.7985i	0.213817	−	1.01164i
$989$			7.57143i			0.240758i
$990$	7.78590	−	10.6506i	0.247452	−	0.338497i
$991$	−2.09378	−	3.62654i	−0.0665113	−	0.115201i	0.830852	−	0.556493i	$-0.187853\pi$
$991$	−2.09378	−	3.62654i	−0.0665113	−	0.115201i	−0.897363	+	0.441292i	$0.854520\pi$
$992$	−2.81276	−	0.0412397i	−0.0893053	−	0.00130936i
$993$	−16.6093	−	28.7682i	−0.527080	−	0.912930i
$994$	10.5883	+	1.14427i	0.335840	+	0.0362941i
$995$	32.4044			1.02729
$996$	−21.2319	−	19.3440i	−0.672760	−	0.612937i
$997$	−4.65708	−	2.68877i	−0.147491	−	0.0851542i	0.424438	−	0.905457i	$-0.360472\pi$
$997$	−4.65708	−	2.68877i	−0.147491	−	0.0851542i	−0.571930	+	0.820303i	$0.693805\pi$
$998$	−3.66397	+	33.9038i	−0.115981	+	1.07321i
$999$			36.9760i			1.16987i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.107.12	yes	28
4.3	odd	2		608.2.s.c.335.10		28
8.3	odd	2	inner	152.2.o.c.107.8	yes	28
8.5	even	2		608.2.s.c.335.9		28
19.8	odd	6	inner	152.2.o.c.27.8	✓	28
76.27	even	6		608.2.s.c.559.9		28
152.27	even	6	inner	152.2.o.c.27.12	yes	28
152.141	odd	6		608.2.s.c.559.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.8	✓	28	19.8	odd	6	inner
152.2.o.c.27.12	yes	28	152.27	even	6	inner
152.2.o.c.107.8	yes	28	8.3	odd	2	inner
152.2.o.c.107.12	yes	28	1.1	even	1	trivial
608.2.s.c.335.9		28	8.5	even	2
608.2.s.c.335.10		28	4.3	odd	2
608.2.s.c.559.9		28	76.27	even	6
608.2.s.c.559.10		28	152.141	odd	6

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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

L-functions

Modular forms

Varieties

Fields

Representations

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	152.2.o.c.107.12

Level	$152$
Weight	$2$
Character	152.107
Analytic conductor	$1.214$
Analytic rank	$0$
Dimension	$28$
Inner twists	$4$