LMFDB - Embedded newform 210.2.x.a.23.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.8
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.35576 + 1.07792i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.962923 + 2.01811i) q^{5} +(-1.58855 - 0.690295i) q^{6} +(1.50791 - 2.17399i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.676173 + 2.92281i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.35576 + 1.07792i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.962923 + 2.01811i) q^{5} +(-1.58855 - 0.690295i) q^{6} +(1.50791 - 2.17399i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.676173 + 2.92281i) q^{9} +(-1.45244 - 1.70012i) q^{10} +(-0.149681 + 0.0864181i) q^{11} +(1.71308 + 0.255627i) q^{12} +(-2.28029 - 2.28029i) q^{13} +(-0.893856 + 2.49019i) q^{14} +(-0.869874 + 3.77403i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.891651 + 3.32769i) q^{17} +(-1.40961 - 2.64821i) q^{18} +(2.38005 + 1.37412i) q^{19} +(1.84297 + 1.26628i) q^{20} +(4.38775 - 1.32200i) q^{21} +(0.122214 - 0.122214i) q^{22} +(-1.68559 - 6.29072i) q^{23} +(-1.72087 + 0.196462i) q^{24} +(-3.14556 + 3.88657i) q^{25} +(2.79277 + 1.61241i) q^{26} +(-2.23382 + 4.69148i) q^{27} +(0.218891 - 2.63668i) q^{28} +0.840779 q^{29} +(-0.136558 - 3.87058i) q^{30} +(4.06710 + 7.04442i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.296083 - 0.0441815i) q^{33} -3.44508i q^{34} +(5.83935 + 0.949743i) q^{35} +(2.04699 + 2.19314i) q^{36} +(-1.58924 - 5.93113i) q^{37} +(-2.65460 - 0.711298i) q^{38} +(-0.633554 - 5.54949i) q^{39} +(-2.10791 - 0.746132i) q^{40} -10.1114i q^{41} +(-3.89608 + 2.41259i) q^{42} +(-3.19626 - 3.19626i) q^{43} +(-0.0864181 + 0.149681i) q^{44} +(-5.24745 + 4.17903i) q^{45} +(3.25632 + 5.64011i) q^{46} +(1.52745 - 0.409280i) q^{47} +(1.61139 - 0.635163i) q^{48} +(-2.45244 - 6.55634i) q^{49} +(2.03246 - 4.56827i) q^{50} +(-4.79585 + 3.55042i) q^{51} +(-3.11493 - 0.834642i) q^{52} +(-10.2236 - 2.73940i) q^{53} +(0.943463 - 5.10978i) q^{54} +(-0.318532 - 0.218858i) q^{55} +(0.470991 + 2.60349i) q^{56} +(1.74558 + 4.42849i) q^{57} +(-0.812130 + 0.217610i) q^{58} +(-4.86826 - 8.43207i) q^{59} +(1.13368 + 3.70334i) q^{60} +(6.03552 - 10.4538i) q^{61} +(-5.75174 - 5.75174i) q^{62} +(7.37375 + 2.93732i) q^{63} -1.00000i q^{64} +(2.40614 - 6.79761i) q^{65} +(0.297429 - 0.0339558i) q^{66} +(1.24153 + 0.332666i) q^{67} +(0.891651 + 3.32769i) q^{68} +(4.49564 - 10.3457i) q^{69} +(-5.88619 + 0.593954i) q^{70} +9.00908i q^{71} +(-2.54486 - 1.58861i) q^{72} +(-0.0189461 + 0.0707076i) q^{73} +(3.07018 + 5.31771i) q^{74} +(-8.45404 + 1.87860i) q^{75} +2.74825 q^{76} +(-0.0378323 + 0.455714i) q^{77} +(2.04828 + 5.19642i) q^{78} +(12.0207 + 6.94014i) q^{79} +(2.22920 + 0.175141i) q^{80} +(-8.08558 + 3.95264i) q^{81} +(2.61703 + 9.76690i) q^{82} +(5.33300 - 5.33300i) q^{83} +(3.13890 - 3.33876i) q^{84} +(-7.57424 + 1.40485i) q^{85} +(3.91461 + 2.26010i) q^{86} +(1.13990 + 0.906293i) q^{87} +(0.0447333 - 0.166947i) q^{88} +(-7.02662 + 12.1705i) q^{89} +(3.98703 - 5.39477i) q^{90} +(-8.39577 + 1.51886i) q^{91} +(-4.60513 - 4.60513i) q^{92} +(-2.07932 + 13.9346i) q^{93} +(-1.36948 + 0.790668i) q^{94} +(-0.481331 + 6.12638i) q^{95} +(-1.39209 + 1.03058i) q^{96} +(-6.33765 + 6.33765i) q^{97} +(4.06578 + 5.69820i) q^{98} +(-0.353793 - 0.379054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	1.35576	+	1.07792i	0.782749	+	0.622338i
$3$	1.35576	+	1.07792i	0.782749	+	0.622338i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.962923	+	2.01811i	0.430632	+	0.902528i
$5$	0.962923	+	2.01811i	0.430632	+	0.902528i
$6$	−1.58855	−	0.690295i	−0.648523	−	0.281812i
$7$	1.50791	−	2.17399i	0.569935	−	0.821690i
$7$	1.50791	−	2.17399i	0.569935	−	0.821690i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.676173	+	2.92281i	0.225391	+	0.974268i
$10$	−1.45244	−	1.70012i	−0.459301	−	0.537627i
$11$	−0.149681	+	0.0864181i	−0.0451304	+	0.0260560i	−0.522395	−	0.852703i	$-0.674962\pi$
$11$	−0.149681	+	0.0864181i	−0.0451304	+	0.0260560i	0.477265	+	0.878759i	$0.341628\pi$
$12$	1.71308	+	0.255627i	0.494525	+	0.0737931i
$13$	−2.28029	−	2.28029i	−0.632437	−	0.632437i	0.316241	−	0.948679i	$-0.397579\pi$
$13$	−2.28029	−	2.28029i	−0.632437	−	0.632437i	−0.948679	+	0.316241i	$0.897579\pi$
$14$	−0.893856	+	2.49019i	−0.238893	+	0.665530i
$15$	−0.869874	+	3.77403i	−0.224600	+	0.974451i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.891651	+	3.32769i	−0.216257	+	0.807083i	0.769463	+	0.638691i	$0.220524\pi$
$17$	−0.891651	+	3.32769i	−0.216257	+	0.807083i	−0.985720	+	0.168391i	$0.946143\pi$
$18$	−1.40961	−	2.64821i	−0.332248	−	0.624188i
$19$	2.38005	+	1.37412i	0.546021	+	0.315245i	0.747516	−	0.664244i	$-0.231247\pi$
$19$	2.38005	+	1.37412i	0.546021	+	0.315245i	−0.201495	+	0.979490i	$0.564580\pi$
$20$	1.84297	+	1.26628i	0.412101	+	0.283148i
$21$	4.38775	−	1.32200i	0.957485	−	0.288485i
$22$	0.122214	−	0.122214i	0.0260560	−	0.0260560i
$23$	−1.68559	−	6.29072i	−0.351471	−	1.31171i	−0.884868	−	0.465842i	$-0.845752\pi$
$23$	−1.68559	−	6.29072i	−0.351471	−	1.31171i	0.533397	−	0.845865i	$-0.320915\pi$
$24$	−1.72087	+	0.196462i	−0.351272	+	0.0401027i
$25$	−3.14556	+	3.88657i	−0.629112	+	0.777315i
$26$	2.79277	+	1.61241i	0.547707	+	0.316219i
$27$	−2.23382	+	4.69148i	−0.429900	+	0.902877i
$28$	0.218891	−	2.63668i	0.0413665	−	0.498286i
$29$	0.840779			0.156129			0.0780644	−	0.996948i	$-0.475126\pi$
$29$	0.840779			0.156129			0.0780644	+	0.996948i	$0.475126\pi$
$30$	−0.136558	−	3.87058i	−0.0249319	−	0.706667i
$31$	4.06710	+	7.04442i	0.730472	+	1.26522i	0.956682	+	0.291136i	$0.0940333\pi$
$31$	4.06710	+	7.04442i	0.730472	+	1.26522i	−0.226209	+	0.974079i	$0.572633\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.296083	−	0.0441815i	−0.0515414	−	0.00769102i
$34$		−	3.44508i		−	0.590826i
$35$	5.83935	+	0.949743i	0.987030	+	0.160536i
$36$	2.04699	+	2.19314i	0.341164	+	0.365523i
$37$	−1.58924	−	5.93113i	−0.261270	−	0.975072i	−0.964494	−	0.264104i	$-0.914924\pi$
$37$	−1.58924	−	5.93113i	−0.261270	−	0.975072i	0.703224	−	0.710968i	$-0.251743\pi$
$38$	−2.65460	−	0.711298i	−0.430633	−	0.115388i
$39$	−0.633554	−	5.54949i	−0.101450	−	0.888629i
$40$	−2.10791	−	0.746132i	−0.333290	−	0.117974i
$41$		−	10.1114i		−	1.57914i	−0.613659	−	0.789571i	$-0.710303\pi$
$41$		−	10.1114i		−	1.57914i	0.613659	−	0.789571i	$-0.289697\pi$
$42$	−3.89608	+	2.41259i	−0.601178	+	0.372271i
$43$	−3.19626	−	3.19626i	−0.487426	−	0.487426i	0.420067	−	0.907493i	$-0.362006\pi$
$43$	−3.19626	−	3.19626i	−0.487426	−	0.487426i	−0.907493	+	0.420067i	$0.862006\pi$
$44$	−0.0864181	+	0.149681i	−0.0130280	+	0.0225652i
$45$	−5.24745	+	4.17903i	−0.782243	+	0.622973i
$46$	3.25632	+	5.64011i	0.480118	+	0.831589i
$47$	1.52745	−	0.409280i	0.222802	−	0.0596996i	−0.145691	−	0.989330i	$-0.546541\pi$
$47$	1.52745	−	0.409280i	0.222802	−	0.0596996i	0.368493	+	0.929631i	$0.379874\pi$
$48$	1.61139	−	0.635163i	0.232584	−	0.0916778i
$49$	−2.45244	−	6.55634i	−0.350349	−	0.936619i
$50$	2.03246	−	4.56827i	0.287433	−	0.646051i
$51$	−4.79585	+	3.55042i	−0.671553	+	0.497158i
$52$	−3.11493	−	0.834642i	−0.431963	−	0.115744i
$53$	−10.2236	−	2.73940i	−1.40431	−	0.376285i	−0.524422	−	0.851458i	$-0.675719\pi$
$53$	−10.2236	−	2.73940i	−1.40431	−	0.376285i	−0.879892	+	0.475174i	$0.842385\pi$
$54$	0.943463	−	5.10978i	0.128389	−	0.695353i
$55$	−0.318532	−	0.218858i	−0.0429509	−	0.0295109i
$56$	0.470991	+	2.60349i	0.0629388	+	0.347906i
$57$	1.74558	+	4.42849i	0.231208	+	0.586567i
$58$	−0.812130	+	0.217610i	−0.106638	+	0.0285736i
$59$	−4.86826	−	8.43207i	−0.633793	−	1.09776i	−0.986769	−	0.162130i	$-0.948164\pi$
$59$	−4.86826	−	8.43207i	−0.633793	−	1.09776i	0.352976	−	0.935632i	$-0.385170\pi$
$60$	1.13368	+	3.70334i	0.146358	+	0.478100i
$61$	6.03552	−	10.4538i	0.772769	−	1.33848i	−0.163270	−	0.986581i	$-0.552204\pi$
$61$	6.03552	−	10.4538i	0.772769	−	1.33848i	0.936040	−	0.351894i	$-0.114462\pi$
$62$	−5.75174	−	5.75174i	−0.730472	−	0.730472i
$63$	7.37375	+	2.93732i	0.929005	+	0.370068i
$64$		−	1.00000i		−	0.125000i
$65$	2.40614	−	6.79761i	0.298444	−	0.843140i
$66$	0.297429	−	0.0339558i	0.0366110	−	0.00417967i
$67$	1.24153	+	0.332666i	0.151677	+	0.0406416i	0.333858	−	0.942623i	$-0.391649\pi$
$67$	1.24153	+	0.332666i	0.151677	+	0.0406416i	−0.182182	+	0.983265i	$0.558316\pi$
$68$	0.891651	+	3.32769i	0.108129	+	0.403541i
$69$	4.49564	−	10.3457i	0.541211	−	1.24547i
$70$	−5.88619	+	0.593954i	−0.703534	+	0.0709910i
$71$			9.00908i			1.06918i	0.845111	+	0.534591i	$0.179534\pi$
$71$			9.00908i			1.06918i	−0.845111	+	0.534591i	$0.820466\pi$
$72$	−2.54486	−	1.58861i	−0.299915	−	0.187219i
$73$	−0.0189461	+	0.0707076i	−0.00221747	+	0.00827570i	−0.967026	−	0.254679i	$-0.918030\pi$
$73$	−0.0189461	+	0.0707076i	−0.00221747	+	0.00827570i	0.964808	+	0.262955i	$0.0846969\pi$
$74$	3.07018	+	5.31771i	0.356901	+	0.618171i
$75$	−8.45404	+	1.87860i	−0.976189	+	0.216922i
$76$	2.74825			0.315245
$77$	−0.0378323	+	0.455714i	−0.00431139	+	0.0519334i
$78$	2.04828	+	5.19642i	0.231922	+	0.588379i
$79$	12.0207	+	6.94014i	1.35243	+	0.780826i	0.988590	−	0.150634i	$-0.0481316\pi$
$79$	12.0207	+	6.94014i	1.35243	+	0.780826i	0.363842	+	0.931461i	$0.381465\pi$
$80$	2.22920	+	0.175141i	0.249232	+	0.0195814i
$81$	−8.08558	+	3.95264i	−0.898398	+	0.439183i
$82$	2.61703	+	9.76690i	0.289003	+	1.07857i
$83$	5.33300	−	5.33300i	0.585372	−	0.585372i	−0.351002	−	0.936375i	$-0.614159\pi$
$83$	5.33300	−	5.33300i	0.585372	−	0.585372i	0.936375	+	0.351002i	$0.114159\pi$
$84$	3.13890	−	3.33876i	0.342482	−	0.364289i
$85$	−7.57424	+	1.40485i	−0.821542	+	0.152378i
$86$	3.91461	+	2.26010i	0.422123	+	0.243713i
$87$	1.13990	+	0.906293i	0.122210	+	0.0971649i
$88$	0.0447333	−	0.166947i	0.00476859	−	0.0177966i
$89$	−7.02662	+	12.1705i	−0.744820	+	1.29007i	0.205458	+	0.978666i	$0.434132\pi$
$89$	−7.02662	+	12.1705i	−0.744820	+	1.29007i	−0.950279	+	0.311401i	$0.899202\pi$
$90$	3.98703	−	5.39477i	0.420270	−	0.568659i
$91$	−8.39577	+	1.51886i	−0.880116	+	0.159219i
$92$	−4.60513	−	4.60513i	−0.480118	−	0.480118i
$93$	−2.07932	+	13.9346i	−0.215615	+	1.44495i
$94$	−1.36948	+	0.790668i	−0.141251	+	0.0815512i
$95$	−0.481331	+	6.12638i	−0.0493835	+	0.628554i
$96$	−1.39209	+	1.03058i	−0.142079	+	0.105183i
$97$	−6.33765	+	6.33765i	−0.643491	+	0.643491i	−0.951412	−	0.307921i	$-0.900367\pi$
$97$	−6.33765	+	6.33765i	−0.643491	+	0.643491i	0.307921	+	0.951412i	$0.400367\pi$
$98$	4.06578	+	5.69820i	0.410706	+	0.575605i
$99$	−0.353793	−	0.379054i	−0.0355576	−	0.0380963i
$100$	−0.780849	+	4.93865i	−0.0780849	+	0.493865i
$101$	8.57430	−	4.95037i	0.853174	−	0.492580i	−0.00854630	−	0.999963i	$-0.502720\pi$
$101$	8.57430	−	4.95037i	0.853174	−	0.492580i	0.861721	+	0.507383i	$0.169387\pi$
$102$	3.71352	−	4.67070i	0.367693	−	0.462468i
$103$	8.70127	−	2.33150i	0.857362	−	0.229729i	0.196747	−	0.980454i	$-0.436962\pi$
$103$	8.70127	−	2.33150i	0.857362	−	0.229729i	0.660615	+	0.750725i	$0.270296\pi$
$104$	3.22481			0.316219
$105$	6.89301	+	7.58198i	0.672689	+	0.739925i
$106$	10.5842			1.02803
$107$	5.87171	−	1.57332i	0.567640	−	0.152099i	0.0364257	−	0.999336i	$-0.488403\pi$
$107$	5.87171	−	1.57332i	0.567640	−	0.152099i	0.531214	+	0.847238i	$0.321736\pi$
$108$	0.411194	+	5.17986i	0.0395672	+	0.498432i
$109$	−13.6018	+	7.85302i	−1.30282	+	0.752183i	−0.980887	−	0.194579i	$-0.937666\pi$
$109$	−13.6018	+	7.85302i	−1.30282	+	0.752183i	−0.321933	+	0.946763i	$0.604333\pi$
$110$	0.364323	+	0.128959i	0.0347369	+	0.0122957i
$111$	4.23866	−	9.75428i	0.402316	−	0.925835i
$112$	−1.12878	−	2.39288i	−0.106659	−	0.226106i
$113$	1.64994	−	1.64994i	0.155213	−	0.155213i	−0.625228	−	0.780442i	$-0.714994\pi$
$113$	1.64994	−	1.64994i	0.155213	−	0.155213i	0.780442	+	0.625228i	$0.214994\pi$
$114$	−2.83228	−	3.82580i	−0.265267	−	0.358319i
$115$	11.0723	−	9.45920i	1.03250	−	0.882075i
$116$	0.728136	−	0.420390i	0.0676057	−	0.0390322i
$117$	5.12296	−	8.20670i	0.473618	−	0.758710i
$118$	6.88476	+	6.88476i	0.633793	+	0.633793i
$119$	5.88982	+	6.95628i	0.539919	+	0.637681i
$120$	−2.05355	−	3.28374i	−0.187463	−	0.299763i
$121$	−5.48506	+	9.50041i	−0.498642	+	0.863674i
$122$	−3.12422	+	11.6597i	−0.282853	+	1.05562i
$123$	10.8993	−	13.7087i	0.982760	−	1.23607i
$124$	7.04442	+	4.06710i	0.632608	+	0.365236i
$125$	−10.8725	−	2.60563i	−0.972464	−	0.233054i
$126$	−7.88273	−	0.928770i	−0.702249	−	0.0827414i
$127$	2.13805	−	2.13805i	0.189721	−	0.189721i	−0.605854	−	0.795576i	$-0.707169\pi$
$127$	2.13805	−	2.13805i	0.189721	−	0.189721i	0.795576	+	0.605854i	$0.207169\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−0.888049	−	7.77869i	−0.0781883	−	0.684875i
$130$	−0.564797	+	7.18874i	−0.0495360	+	0.630494i
$131$	5.20685	+	3.00618i	0.454925	+	0.262651i	0.709908	−	0.704294i	$-0.248737\pi$
$131$	5.20685	+	3.00618i	0.454925	+	0.262651i	−0.254983	+	0.966946i	$0.582070\pi$
$132$	−0.278506	+	0.109779i	−0.0242408	+	0.00955505i
$133$	6.57622	−	3.10215i	0.570230	−	0.268991i
$134$	−1.28532			−0.111035
$135$	−11.6189	+	0.00942738i	−1.00000	+	0.000811380i
$136$	−1.72254	−	2.98352i	−0.147706	−	0.255835i
$137$	−2.50449	+	9.34687i	−0.213973	+	0.798557i	0.772553	+	0.634951i	$0.218980\pi$
$137$	−2.50449	+	9.34687i	−0.213973	+	0.798557i	−0.986526	+	0.163607i	$0.947687\pi$
$138$	−1.66480	+	11.1567i	−0.141717	+	0.949720i
$139$			10.1596i			0.861723i	0.902418	+	0.430861i	$0.141790\pi$
$139$			10.1596i			0.861723i	−0.902418	+	0.430861i	$0.858210\pi$
$140$	5.53190	−	2.09717i	0.467530	−	0.177243i
$141$	2.51203	+	1.09159i	0.211551	+	0.0919283i
$142$	−2.33172	−	8.70211i	−0.195674	−	0.730265i
$143$	0.538372	+	0.144256i	0.0450210	+	0.0120633i
$144$	2.86931	+	0.875819i	0.239109	+	0.0729850i
$145$	0.809605	+	1.69679i	0.0672341	+	0.140911i
$146$		−	0.0732019i		−	0.00605824i
$147$	3.74229	−	11.5324i	0.308659	−	0.951173i
$148$	−4.34189	−	4.34189i	−0.356901	−	0.356901i
$149$	−2.65975	+	4.60681i	−0.217895	+	0.377405i	−0.954164	−	0.299284i	$-0.903252\pi$
$149$	−2.65975	+	4.60681i	−0.217895	+	0.377405i	0.736269	+	0.676689i	$0.236586\pi$
$150$	7.67976	−	4.00265i	0.627050	−	0.326815i
$151$	−7.80296	−	13.5151i	−0.634996	−	1.09984i	−0.986516	−	0.163665i	$-0.947669\pi$
$151$	−7.80296	−	13.5151i	−0.634996	−	1.09984i	0.351520	−	0.936180i	$-0.385665\pi$
$152$	−2.65460	+	0.711298i	−0.215317	+	0.0576939i
$153$	−10.3291	−	0.356030i	−0.835058	−	0.0287833i
$154$	−0.0814043	−	0.449978i	−0.00655974	−	0.0362602i
$155$	−10.3001	+	14.9911i	−0.827327	+	1.20411i
$156$	−3.32342	−	4.48922i	−0.266086	−	0.359425i
$157$	8.75604	+	2.34617i	0.698808	+	0.187245i	0.590697	−	0.806894i	$-0.298853\pi$
$157$	8.75604	+	2.34617i	0.698808	+	0.187245i	0.108112	+	0.994139i	$0.465520\pi$
$158$	−13.4073	−	3.59248i	−1.06663	−	0.285802i
$159$	−10.9078	−	14.7342i	−0.865049	−	1.16849i
$160$	−2.19857	+	0.407786i	−0.173812	+	0.0322383i
$161$	−16.2177	−	5.82136i	−1.27813	−	0.458787i
$162$	6.78705	−	5.91066i	0.533241	−	0.464386i
$163$	−21.2648	+	5.69789i	−1.66559	+	0.446293i	−0.963916	−	0.266207i	$-0.914229\pi$
$163$	−21.2648	+	5.69789i	−1.66559	+	0.446293i	−0.701672	+	0.712500i	$0.747563\pi$
$164$	−5.05572	−	8.75677i	−0.394786	−	0.683789i
$165$	−0.195942	−	0.640072i	−0.0152540	−	0.0498295i
$166$	−3.77100	+	6.53156i	−0.292686	+	0.506947i
$167$	6.24746	+	6.24746i	0.483443	+	0.483443i	0.906229	−	0.422786i	$-0.138948\pi$
$167$	6.24746	+	6.24746i	0.483443	+	0.483443i	−0.422786	+	0.906229i	$0.638948\pi$
$168$	−2.16781	+	4.03740i	−0.167250	+	0.311492i
$169$		−	2.60059i		−	0.200046i
$170$	6.95255	−	3.31734i	0.533236	−	0.254428i
$171$	−2.40697	+	7.88557i	−0.184065	+	0.603024i
$172$	−4.36618	−	1.16991i	−0.332918	−	0.0892051i
$173$	−5.21669	−	19.4689i	−0.396617	−	1.48020i	−0.819008	−	0.573783i	$-0.805475\pi$
$173$	−5.21669	−	19.4689i	−0.396617	−	1.48020i	0.422390	−	0.906414i	$-0.361191\pi$
$174$	−1.33562	−	0.580386i	−0.101253	−	0.0439989i
$175$	3.70615	+	12.6990i	0.280159	+	0.959954i
$176$			0.172836i			0.0130280i
$177$	2.48891	−	16.6795i	0.187078	−	1.25371i
$178$	3.63725	−	13.5744i	0.272623	−	1.01744i
$179$	−0.0831851	−	0.144081i	−0.00621755	−	0.0107691i	0.862900	−	0.505375i	$-0.168646\pi$
$179$	−0.0831851	−	0.144081i	−0.00621755	−	0.0107691i	−0.869117	+	0.494606i	$0.835312\pi$
$180$	−2.45491	+	6.24287i	−0.182978	+	0.465316i
$181$	−0.628045			−0.0466822			−0.0233411	−	0.999728i	$-0.507430\pi$
$181$	−0.628045			−0.0466822			−0.0233411	+	0.999728i	$0.507430\pi$
$182$	7.71658	−	3.64009i	0.571991	−	0.269821i
$183$	19.4511	−	7.66707i	1.43787	−	0.566766i
$184$	5.64011	+	3.25632i	0.415794	+	0.240059i
$185$	10.4394	−	8.91849i	0.767519	−	0.655701i
$186$	−1.59806	−	13.9979i	−0.117176	−	1.02638i
$187$	−0.154110	−	0.575145i	−0.0112696	−	0.0420588i
$188$	1.11817	−	1.11817i	0.0815512	−	0.0815512i
$189$	6.83083	+	11.9306i	0.496870	+	0.867825i
$190$	−1.12069	−	6.04221i	−0.0813038	−	0.438348i
$191$	0.811340	+	0.468427i	0.0587065	+	0.0338942i	0.529066	−	0.848581i	$-0.322542\pi$
$191$	0.811340	+	0.468427i	0.0587065	+	0.0338942i	−0.470359	+	0.882475i	$0.655876\pi$
$192$	1.07792	−	1.35576i	0.0777922	−	0.0978436i
$193$	−6.34457	+	23.6783i	−0.456692	+	1.70440i	0.226373	+	0.974041i	$0.427313\pi$
$193$	−6.34457	+	23.6783i	−0.456692	+	1.70440i	−0.683065	+	0.730358i	$0.739353\pi$
$194$	4.48140	−	7.76201i	0.321746	−	0.557280i
$195$	10.5894	−	6.62231i	0.758325	−	0.474234i
$196$	−5.40204	−	4.45173i	−0.385860	−	0.317981i
$197$	−3.05486	−	3.05486i	−0.217650	−	0.217650i	0.589857	−	0.807507i	$-0.299184\pi$
$197$	−3.05486	−	3.05486i	−0.217650	−	0.217650i	−0.807507	+	0.589857i	$0.799184\pi$
$198$	0.439844	+	0.274569i	0.0312584	+	0.0195128i
$199$	−8.08620	+	4.66857i	−0.573216	+	0.330946i	−0.758433	−	0.651751i	$-0.774035\pi$
$199$	−8.08620	+	4.66857i	−0.573216	+	0.330946i	0.185217	+	0.982698i	$0.440701\pi$
$200$	−0.523975	−	4.97247i	−0.0370506	−	0.351607i
$201$	1.32463	+	1.78928i	0.0934319	+	0.126206i
$202$	−7.00088	+	7.00088i	−0.492580	+	0.492580i
$203$	1.26782	−	1.82784i	0.0889832	−	0.128289i
$204$	−2.37812	+	5.47268i	−0.166502	+	0.383164i
$205$	20.4060	−	9.73654i	1.42522	−	0.680029i
$206$	−7.80135	+	4.50411i	−0.543546	+	0.313816i
$207$	17.2468	−	9.18028i	1.19874	−	0.638074i
$208$	−3.11493	+	0.834642i	−0.215981	+	0.0578720i
$209$	−0.474996			−0.0328562
$210$	−8.62050	−	5.53959i	−0.594871	−	0.382268i
$211$	−17.7735			−1.22358			−0.611790	−	0.791020i	$-0.709550\pi$
$211$	−17.7735			−1.22358			−0.611790	+	0.791020i	$0.709550\pi$
$212$	−10.2236	+	2.73940i	−0.702157	+	0.188142i
$213$	−9.71108	+	12.2142i	−0.665392	+	0.836901i
$214$	−5.26443	+	3.03942i	−0.359869	+	0.207770i
$215$	3.37267	−	9.52818i	0.230014	−	0.649816i
$216$	−1.73783	−	4.89693i	−0.118244	−	0.333194i
$217$	21.4473	+	1.78050i	1.45594	+	0.120868i
$218$	11.1059	−	11.1059i	0.752183	−	0.752183i
$219$	−0.101904	+	0.0754403i	−0.00688600	+	0.00509778i
$220$	−0.385286	−	0.0302707i	−0.0259760	−	0.00204085i
$221$	9.62130	−	5.55486i	0.647199	−	0.373660i
$222$	−1.56964	+	10.5190i	−0.105347	+	0.705986i
$223$	20.7814	+	20.7814i	1.39162	+	1.39162i	0.821694	+	0.569929i	$0.193029\pi$
$223$	20.7814	+	20.7814i	1.39162	+	1.39162i	0.569929	+	0.821694i	$0.306971\pi$
$224$	1.70964	+	2.01919i	0.114230	+	0.134913i
$225$	−13.4866	−	6.56586i	−0.899109	−	0.437724i
$226$	−1.16668	+	2.02076i	−0.0776067	+	0.134419i
$227$	−1.63340	+	6.09593i	−0.108413	+	0.404601i	−0.998710	−	0.0507784i	$-0.983830\pi$
$227$	−1.63340	+	6.09593i	−0.108413	+	0.404601i	0.890297	+	0.455380i	$0.150496\pi$
$228$	3.72596	+	2.96239i	0.246758	+	0.196189i
$229$	0.820517	+	0.473726i	0.0542213	+	0.0313047i	0.526866	−	0.849949i	$-0.323367\pi$
$229$	0.820517	+	0.473726i	0.0542213	+	0.0313047i	−0.472644	+	0.881253i	$0.656700\pi$
$230$	−8.24679	+	12.0026i	−0.543777	+	0.791428i
$231$	−0.542515	+	0.577059i	−0.0356949	+	0.0379677i
$232$	−0.594521	+	0.594521i	−0.0390322	+	0.0390322i
$233$	2.22516	+	8.30443i	0.145775	+	0.544041i	0.999720	+	0.0236767i	$0.00753723\pi$
$233$	2.22516	+	8.30443i	0.145775	+	0.544041i	−0.853944	+	0.520364i	$0.825796\pi$
$234$	−2.82435	+	9.25298i	−0.184634	+	0.604886i
$235$	2.29679	+	2.68847i	0.149826	+	0.175376i
$236$	−8.43207	−	4.86826i	−0.548881	−	0.316897i
$237$	8.81623	+	22.3665i	0.572676	+	1.45286i
$238$	−7.48955	−	5.19485i	−0.485476	−	0.336732i
$239$	−1.10308			−0.0713521			−0.0356760	−	0.999363i	$-0.511358\pi$
$239$	−1.10308			−0.0713521			−0.0356760	+	0.999363i	$0.511358\pi$
$240$	2.83347	+	2.64035i	0.182900	+	0.170434i
$241$	−7.44133	−	12.8888i	−0.479338	−	0.830238i	0.520381	−	0.853934i	$-0.325790\pi$
$241$	−7.44133	−	12.8888i	−0.479338	−	0.830238i	−0.999719	+	0.0236964i	$0.992456\pi$
$242$	2.83928	−	10.5963i	0.182516	−	0.681158i
$243$	−15.2227	−	3.35678i	−0.976540	−	0.215337i
$244$		−	12.0710i		−	0.772769i
$245$	10.8699	−	11.2625i	0.694453	−	0.719538i
$246$	−6.97988	+	16.0625i	−0.445021	+	1.02411i
$247$	−2.29380	−	8.56059i	−0.145951	−	0.544697i
$248$	−7.85703	−	2.10528i	−0.498922	−	0.133686i
$249$	12.9788	−	1.48172i	0.822499	−	0.0939000i
$250$	11.1764	−	0.297161i	0.706857	−	0.0187941i
$251$			21.0507i			1.32871i	0.747419	+	0.664353i	$0.231293\pi$
$251$			21.0507i			1.32871i	−0.747419	+	0.664353i	$0.768707\pi$
$252$	7.85451	−	1.14308i	0.494788	−	0.0720071i
$253$	0.795933	+	0.795933i	0.0500399	+	0.0500399i
$254$	−1.51183	+	2.61856i	−0.0948606	+	0.164303i
$255$	−11.7832	−	6.25979i	−0.737891	−	0.392003i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.77969	+	0.476866i	−0.111014	+	0.0297461i	−0.313898	−	0.949457i	$-0.601635\pi$
$257$	−1.77969	+	0.476866i	−0.111014	+	0.0297461i	0.202884	+	0.979203i	$0.434968\pi$
$258$	2.87106	+	7.28379i	0.178744	+	0.453469i
$259$	−15.2906	−	5.48860i	−0.950114	−	0.341045i
$260$	−1.31503	−	7.08997i	−0.0815548	−	0.439701i
$261$	0.568512	+	2.45743i	0.0351900	+	0.152111i
$262$	−5.80749	−	1.55611i	−0.358788	−	0.0961370i
$263$	18.6556	+	4.99875i	1.15035	+	0.308236i	0.783106	−	0.621888i	$-0.213634\pi$
$263$	18.6556	+	4.99875i	1.15035	+	0.308236i	0.367246	+	0.930124i	$0.380301\pi$
$264$	0.240603	−	0.178121i	0.0148081	−	0.0109626i
$265$	−4.31609	−	23.2701i	−0.265135	−	1.42947i
$266$	−5.54924	+	4.69850i	−0.340246	+	0.288083i
$267$	−22.6452	+	8.92609i	−1.38586	+	0.546268i
$268$	1.24153	−	0.332666i	0.0758383	−	0.0203208i
$269$	10.7688	+	18.6522i	0.656588	+	1.13724i	0.981493	+	0.191497i	$0.0613343\pi$
$269$	10.7688	+	18.6522i	0.656588	+	1.13724i	−0.324905	+	0.945747i	$0.605332\pi$
$270$	11.2206	−	3.01631i	0.682864	−	0.183567i
$271$	7.65045	−	13.2510i	0.464732	−	0.804939i	−0.534458	−	0.845195i	$-0.679484\pi$
$271$	7.65045	−	13.2510i	0.464732	−	0.804939i	0.999189	+	0.0402561i	$0.0128174\pi$
$272$	2.43604	+	2.43604i	0.147706	+	0.147706i
$273$	−13.0199	−	6.99077i	−0.787998	−	0.423101i
$274$		−	9.67660i		−	0.584585i
$275$	0.134959	−	0.853578i	0.00813833	−	0.0514727i
$276$	−1.27949	−	11.2074i	−0.0770161	−	0.674607i
$277$	17.6004	+	4.71602i	1.05751	+	0.283358i	0.745351	−	0.666673i	$-0.232282\pi$
$277$	17.6004	+	4.71602i	1.05751	+	0.283358i	0.312156	+	0.950031i	$0.398949\pi$
$278$	−2.62949	−	9.81338i	−0.157706	−	0.588567i
$279$	−17.8394	+	16.6506i	−1.06802	+	0.996844i
$280$	−4.80061	+	3.45747i	−0.286891	+	0.206624i
$281$			0.120405i			0.00718275i	0.999994	+	0.00359138i	$0.00114317\pi$
$281$			0.120405i			0.00718275i	−0.999994	+	0.00359138i	$0.998857\pi$
$282$	−2.70896	−	0.404232i	−0.161316	−	0.0240716i
$283$	−1.24800	+	4.65758i	−0.0741857	+	0.276865i	−0.993047	−	0.117715i	$-0.962443\pi$
$283$	−1.24800	+	4.65758i	−0.0741857	+	0.276865i	0.918862	+	0.394580i	$0.129110\pi$
$284$	4.50454	+	7.80210i	0.267295	+	0.462969i
$285$	−7.25633	+	7.78707i	−0.429828	+	0.461266i
$286$	−0.557364			−0.0329576
$287$	−21.9821	−	15.2471i	−1.29757	−	0.900008i
$288$	−2.99822	−	0.103345i	−0.176672	−	0.00608964i
$289$	4.44397	+	2.56573i	0.261410	+	0.150925i
$290$	−1.22118	−	1.42943i	−0.0717101	−	0.0839390i
$291$	−15.4238	+	1.76085i	−0.904161	+	0.103223i
$292$	0.0189461	+	0.0707076i	0.00110873	+	0.00413785i
$293$	−6.50068	+	6.50068i	−0.379774	+	0.379774i	−0.871020	−	0.491247i	$-0.836541\pi$
$293$	−6.50068	+	6.50068i	−0.379774	+	0.379774i	0.491247	+	0.871020i	$0.336541\pi$
$294$	−0.629979	+	12.1080i	−0.0367411	+	0.706152i
$295$	12.3291	−	17.9441i	0.717829	−	1.04475i
$296$	5.31771	+	3.07018i	0.309086	+	0.178451i
$297$	−0.0710692	−	0.895267i	−0.00412386	−	0.0519487i
$298$	1.37679	−	5.13823i	0.0797550	−	0.297650i
$299$	−10.5010	+	18.1883i	−0.607289	+	1.05186i
$300$	−6.38212	+	5.85394i	−0.368472	+	0.337977i
$301$	−11.7683	+	2.12897i	−0.678314	+	0.122712i
$302$	11.0350	+	11.0350i	0.634996	+	0.634996i
$303$	16.9608	+	2.53089i	0.974373	+	0.145396i
$304$	2.38005	−	1.37412i	0.136505	−	0.0788113i
$305$	26.9087	+	2.11414i	1.54079	+	0.121055i
$306$	10.0693	−	2.32947i	0.575623	−	0.133167i
$307$	−3.46539	+	3.46539i	−0.197780	+	0.197780i	−0.799048	−	0.601268i	$-0.794663\pi$
$307$	−3.46539	+	3.46539i	−0.197780	+	0.197780i	0.601268	+	0.799048i	$0.294663\pi$
$308$	0.195093	+	0.413576i	0.0111165	+	0.0235657i
$309$	14.3100	+	6.21833i	0.814068	+	0.353748i
$310$	6.06919	−	17.1462i	0.344707	−	0.973836i
$311$	17.5784	−	10.1489i	0.996778	−	0.575490i	0.0894849	−	0.995988i	$-0.471478\pi$
$311$	17.5784	−	10.1489i	0.996778	−	0.575490i	0.907294	+	0.420498i	$0.138145\pi$
$312$	4.37207	+	3.47609i	0.247520	+	0.196795i
$313$	11.8085	−	3.16408i	0.667455	−	0.178844i	0.0908470	−	0.995865i	$-0.471043\pi$
$313$	11.8085	−	3.16408i	0.667455	−	0.178844i	0.576608	+	0.817021i	$0.304376\pi$
$314$	−9.06492			−0.511563
$315$	1.17250	+	17.7095i	0.0660627	+	0.997815i
$316$	13.8803			0.780826
$317$	−26.1124	+	6.99681i	−1.46662	+	0.392980i	−0.901771	−	0.432214i	$-0.857732\pi$
$317$	−26.1124	+	6.99681i	−1.46662	+	0.392980i	−0.564850	+	0.825194i	$0.691066\pi$
$318$	14.3497	+	11.4089i	0.804689	+	0.639782i
$319$	−0.125848	+	0.0726586i	−0.00704615	+	0.00406810i
$320$	2.01811	−	0.962923i	0.112816	−	0.0538290i
$321$	9.65655	+	4.19619i	0.538976	+	0.234209i
$322$	17.1717	+	1.42556i	0.956944	+	0.0794432i
$323$	−6.69483	+	6.69483i	−0.372510	+	0.372510i
$324$	−5.02600	+	7.46588i	−0.279222	+	0.414771i
$325$	16.0353	−	1.68972i	0.889477	−	0.0937288i
$326$	19.0655	−	11.0075i	1.05594	−	0.609647i
$327$	−26.9058	−	4.01488i	−1.48789	−	0.222024i
$328$	7.14987	+	7.14987i	0.394786	+	0.394786i
$329$	1.41349	−	3.93782i	0.0779280	−	0.217099i
$330$	0.354928	+	0.567549i	0.0195381	+	0.0312425i
$331$	2.95741	−	5.12239i	0.162554	−	0.281552i	−0.773230	−	0.634126i	$-0.781360\pi$
$331$	2.95741	−	5.12239i	0.162554	−	0.281552i	0.935784	+	0.352574i	$0.114693\pi$
$332$	1.95201	−	7.28501i	0.107131	−	0.399817i
$333$	16.2609	−	8.65552i	0.891094	−	0.474320i
$334$	−7.65154	−	4.41762i	−0.418674	−	0.241721i
$335$	0.524137	+	2.82587i	0.0286366	+	0.154394i
$336$	1.04898	−	4.46090i	0.0572268	−	0.243362i
$337$	−8.82126	+	8.82126i	−0.480524	+	0.480524i	−0.905299	−	0.424775i	$-0.860353\pi$
$337$	−8.82126	+	8.82126i	−0.480524	+	0.480524i	0.424775	+	0.905299i	$0.360353\pi$
$338$	0.673083	+	2.51198i	0.0366109	+	0.136634i
$339$	4.01543	−	0.458419i	0.218088	−	0.0248979i
$340$	−5.85706	+	5.00376i	−0.317644	+	0.271367i
$341$	−1.21753	−	0.702942i	−0.0659330	−	0.0380664i
$342$	0.284016	−	8.23984i	0.0153578	−	0.445560i
$343$	−17.9514	−	4.55476i	−0.969287	−	0.245934i
$344$	4.52020			0.243713
$345$	25.2076	−	0.889351i	1.35713	−	0.0478811i
$346$	10.0779	+	17.4554i	0.541790	+	0.938407i
$347$	2.37362	−	8.85847i	0.127423	−	0.475547i	−0.872492	−	0.488629i	$-0.837497\pi$
$347$	2.37362	−	8.85847i	0.127423	−	0.475547i	0.999914	+	0.0130812i	$0.00416399\pi$
$348$	1.44032	+	0.214926i	0.0772095	+	0.0115212i
$349$		−	17.5265i		−	0.938173i	−0.883152	−	0.469086i	$-0.844583\pi$
$349$		−	17.5265i		−	0.938173i	0.883152	−	0.469086i	$-0.155417\pi$
$350$	−6.86661	−	11.3071i	−0.367036	−	0.604388i
$351$	15.7917	−	5.60417i	0.842898	−	0.299128i
$352$	−0.0447333	−	0.166947i	−0.00238429	−	0.00889830i
$353$	−1.24625	−	0.333932i	−0.0663312	−	0.0177734i	0.225501	−	0.974243i	$-0.427598\pi$
$353$	−1.24625	−	0.333932i	−0.0663312	−	0.0177734i	−0.291832	+	0.956470i	$0.594265\pi$
$354$	1.91286	+	16.7553i	0.101667	+	0.890534i
$355$	−18.1814	+	8.67505i	−0.964966	+	0.460424i
$356$			14.0532i			0.744820i
$357$	0.486875	+	15.7798i	0.0257681	+	0.835156i
$358$	0.117642	+	0.117642i	0.00621755	+	0.00621755i
$359$	8.44776	−	14.6320i	0.445856	−	0.772245i	−0.552255	−	0.833675i	$-0.686233\pi$
$359$	8.44776	−	14.6320i	0.445856	−	0.772245i	0.998111	+	0.0614298i	$0.0195660\pi$
$360$	0.755487	−	6.66553i	0.0398177	−	0.351304i
$361$	−5.72357	−	9.91352i	−0.301241	−	0.521764i
$362$	0.606645	−	0.162550i	0.0318846	−	0.00854344i
$363$	−17.6771	+	6.96781i	−0.927808	+	0.365715i
$364$	−6.51152	+	5.51325i	−0.341296	+	0.288973i
$365$	−0.160940	+	0.0298507i	−0.00842396	+	0.00156246i
$366$	−16.8040	+	12.4401i	−0.878357	+	0.650257i
$367$	−31.9548	−	8.56227i	−1.66803	−	0.446947i	−0.703451	−	0.710744i	$-0.748358\pi$
$367$	−31.9548	−	8.56227i	−1.66803	−	0.446947i	−0.964578	+	0.263797i	$0.915025\pi$
$368$	−6.29072	−	1.68559i	−0.327927	−	0.0878677i
$369$	29.5538	−	6.83709i	1.53851	−	0.355924i
$370$	−7.77539	+	11.3165i	−0.404223	+	0.588318i
$371$	−21.3716	+	18.0951i	−1.10956	+	0.939453i
$372$	5.16654	+	13.1073i	0.267872	+	0.679584i
$373$	−6.44654	+	1.72735i	−0.333789	+	0.0894386i	−0.421821	−	0.906679i	$-0.638609\pi$
$373$	−6.44654	+	1.72735i	−0.333789	+	0.0894386i	0.0880318	+	0.996118i	$0.471942\pi$
$374$	0.297717	+	0.515661i	0.0153946	+	0.0266642i
$375$	−11.9318	−	15.2523i	−0.616156	−	0.787624i
$376$	−0.790668	+	1.36948i	−0.0407756	+	0.0706254i
$377$	−1.91722	−	1.91722i	−0.0987417	−	0.0987417i
$378$	−9.68595	−	9.75615i	−0.498191	−	0.501802i
$379$		−	16.1481i		−	0.829472i	−0.909942	−	0.414736i	$-0.863874\pi$
$379$		−	16.1481i		−	0.829472i	0.909942	−	0.414736i	$-0.136126\pi$
$380$	2.64635	+	5.54627i	0.135755	+	0.284518i
$381$	5.20333	−	0.594035i	0.266575	−	0.0304333i
$382$	−0.904932	−	0.242476i	−0.0463004	−	0.0124061i
$383$	4.19914	+	15.6714i	0.214566	+	0.800771i	0.986319	+	0.164849i	$0.0527135\pi$
$383$	4.19914	+	15.6714i	0.214566	+	0.800771i	−0.771753	+	0.635922i	$0.780620\pi$
$384$	−0.690295	+	1.58855i	−0.0352265	+	0.0810654i
$385$	−0.956112	+	0.362467i	−0.0487280	+	0.0184731i
$386$		−	24.5135i		−	1.24771i
$387$	7.18083	−	11.5033i	0.365022	−	0.584745i
$388$	−2.31974	+	8.65739i	−0.117767	+	0.439513i
$389$	−11.9713	−	20.7349i	−0.606970	−	1.05130i	−0.991737	−	0.128290i	$-0.959051\pi$
$389$	−11.9713	−	20.7349i	−0.606970	−	1.05130i	0.384766	−	0.923014i	$-0.374282\pi$
$390$	−8.51463	+	9.13741i	−0.431155	+	0.462691i
$391$	22.4365			1.13466
$392$	6.37017	+	2.90189i	0.321742	+	0.146568i
$393$	3.81882	+	9.68824i	0.192634	+	0.488707i
$394$	3.74143	+	2.16011i	0.188490	+	0.108825i
$395$	−2.43101	+	30.9419i	−0.122317	+	1.55686i
$396$	−0.495921	−	0.151373i	−0.0249210	−	0.00760680i
$397$	6.04487	+	22.5598i	0.303383	+	1.13224i	0.934328	+	0.356414i	$0.116001\pi$
$397$	6.04487	+	22.5598i	0.303383	+	1.13224i	−0.630945	+	0.775828i	$0.717333\pi$
$398$	6.60236	−	6.60236i	0.330946	−	0.330946i
$399$	12.2596	+	2.88287i	0.613750	+	0.144324i
$400$	1.79309	+	4.66742i	0.0896545	+	0.233371i
$401$	15.6286	+	9.02316i	0.780454	+	0.450595i	0.836591	−	0.547828i	$-0.184545\pi$
$401$	15.6286	+	9.02316i	0.780454	+	0.450595i	−0.0561374	+	0.998423i	$0.517878\pi$
$402$	−1.74259	−	1.38548i	−0.0869125	−	0.0691013i
$403$	6.78914	−	25.3374i	0.338191	−	1.26215i
$404$	4.95037	−	8.57430i	0.246290	−	0.426587i
$405$	−15.7627	−	12.5115i	−0.783253	−	0.621703i
$406$	−0.751535	+	2.09370i	−0.0372981	+	0.103908i
$407$	0.750436	+	0.750436i	0.0371977	+	0.0371977i
$408$	0.880653	−	5.90170i	0.0435988	−	0.292178i
$409$	8.76716	−	5.06172i	0.433508	−	0.250286i	−0.267332	−	0.963605i	$-0.586142\pi$
$409$	8.76716	−	5.06172i	0.433508	−	0.250286i	0.700840	+	0.713318i	$0.252809\pi$
$410$	−17.1907	+	14.6862i	−0.848989	+	0.725302i
$411$	−13.4707	+	9.97248i	−0.664459	+	0.491906i
$412$	6.36977	−	6.36977i	0.313816	−	0.313816i
$413$	−25.6721	−	2.13124i	−1.26324	−	0.104871i
$414$	−14.2831	+	13.3313i	−0.701976	+	0.655196i
$415$	15.8978	+	5.62733i	0.780395	+	0.276235i
$416$	2.79277	−	1.61241i	0.136927	−	0.0790547i
$417$	−10.9512	+	13.7739i	−0.536283	+	0.674512i
$418$	0.458811	−	0.122938i	0.0224412	−	0.00601310i
$419$	6.63936			0.324354			0.162177	−	0.986762i	$-0.448148\pi$
$419$	6.63936			0.324354			0.162177	+	0.986762i	$0.448148\pi$
$420$	9.76051	+	3.11968i	0.476264	+	0.152225i
$421$	8.33324			0.406137			0.203069	−	0.979165i	$-0.434909\pi$
$421$	8.33324			0.406137			0.203069	+	0.979165i	$0.434909\pi$
$422$	17.1679	−	4.60012i	0.835720	−	0.223931i
$423$	2.22907	+	4.18770i	0.108381	+	0.203613i
$424$	9.16619	−	5.29210i	0.445150	−	0.257007i
$425$	−10.1286	−	13.9329i	−0.491307	−	0.675845i
$426$	6.21893	−	14.3114i	0.301308	−	0.693389i
$427$	−13.6255	−	28.8845i	−0.659384	−	1.39782i
$428$	4.29839	−	4.29839i	0.207770	−	0.207770i
$429$	0.574407	+	0.775900i	0.0277326	+	0.0374608i
$430$	−0.791673	+	10.0764i	−0.0381779	+	0.485928i
$431$	−19.2198	+	11.0966i	−0.925787	+	0.534503i	−0.885477	−	0.464684i	$-0.846168\pi$
$431$	−19.2198	+	11.0966i	−0.925787	+	0.534503i	−0.0403101	+	0.999187i	$0.512835\pi$
$432$	2.94603	+	4.28029i	0.141741	+	0.205936i
$433$	8.46111	+	8.46111i	0.406615	+	0.406615i	0.880556	−	0.473941i	$-0.157169\pi$
$433$	8.46111	+	8.46111i	0.406615	+	0.406615i	−0.473941	+	0.880556i	$0.657169\pi$
$434$	−21.1773	+	3.83113i	−1.01654	+	0.183900i
$435$	−0.731372	+	3.17313i	−0.0350666	+	0.152140i
$436$	−7.85302	+	13.6018i	−0.376092	+	0.651410i
$437$	4.63243	−	17.2884i	0.221599	−	0.827019i
$438$	0.0789059	−	0.0992443i	0.00377027	−	0.00474208i
$439$	−6.47188	−	3.73654i	−0.308886	−	0.178335i	0.337542	−	0.941311i	$-0.390405\pi$
$439$	−6.47188	−	3.73654i	−0.308886	−	0.178335i	−0.646428	+	0.762975i	$0.723738\pi$
$440$	0.379993	−	0.0704801i	0.0181154	−	0.00336001i
$441$	17.5046	−	11.6012i	0.833553	−	0.552439i
$442$	−7.85576	+	7.85576i	−0.373660	+	0.373660i
$443$	0.830863	+	3.10082i	0.0394755	+	0.147325i	0.982851	−	0.184403i	$-0.0590352\pi$
$443$	0.830863	+	3.10082i	0.0394755	+	0.147325i	−0.943375	+	0.331728i	$0.892369\pi$
$444$	−1.20635	−	10.5668i	−0.0572508	−	0.501477i
$445$	−31.3275	−	2.46130i	−1.48506	−	0.116677i
$446$	−25.4519	−	14.6946i	−1.20518	−	0.695811i
$447$	−8.57176	+	3.37874i	−0.405430	+	0.159809i
$448$	−2.17399	−	1.50791i	−0.102711	−	0.0712418i
$449$	28.3899			1.33980			0.669901	−	0.742451i	$-0.266337\pi$
$449$	28.3899			1.33980			0.669901	+	0.742451i	$0.266337\pi$
$450$	14.7265	+	2.85154i	0.694212	+	0.134423i
$451$	0.873812	+	1.51349i	0.0411462	+	0.0712673i
$452$	0.603920	−	2.25386i	0.0284060	−	0.106013i
$453$	3.98929	−	26.7342i	0.187433	−	1.25608i
$454$		−	6.31097i		−	0.296189i
$455$	−11.1497	−	15.4811i	−0.522706	−	0.725764i
$456$	−4.36573	−	1.89710i	−0.204444	−	0.0888398i
$457$	0.586692	+	2.18957i	0.0274443	+	0.102424i	0.978289	−	0.207243i	$-0.0664492\pi$
$457$	0.586692	+	2.18957i	0.0274443	+	0.102424i	−0.950845	+	0.309667i	$0.899782\pi$
$458$	−0.915168	−	0.245219i	−0.0427630	−	0.0114583i
$459$	−13.6200	−	11.6166i	−0.635727	−	0.542218i
$460$	4.85929	−	13.7281i	0.226565	−	0.640074i
$461$			12.6234i			0.587928i	0.955816	+	0.293964i	$0.0949746\pi$
$461$			12.6234i			0.587928i	−0.955816	+	0.293964i	$0.905025\pi$
$462$	0.374676	−	0.697809i	0.0174315	−	0.0324650i
$463$	−8.56001	−	8.56001i	−0.397817	−	0.397817i	0.479645	−	0.877463i	$-0.340765\pi$
$463$	−8.56001	−	8.56001i	−0.397817	−	0.397817i	−0.877463	+	0.479645i	$0.840765\pi$
$464$	0.420390	−	0.728136i	0.0195161	−	0.0338029i
$465$	−30.1237	+	9.22160i	−1.39695	+	0.427641i
$466$	−4.29869	−	7.44555i	−0.199133	−	0.344908i
$467$	37.4312	−	10.0297i	1.73211	−	0.464118i	0.751443	−	0.659797i	$-0.229358\pi$
$467$	37.4312	−	10.0297i	1.73211	−	0.464118i	0.980668	+	0.195680i	$0.0626913\pi$
$468$	0.333267	−	9.66869i	0.0154053	−	0.446935i
$469$	2.59532	−	2.19743i	0.119841	−	0.101468i
$470$	−2.91436	−	2.00241i	−0.134429	−	0.0923642i
$471$	9.34211	+	12.6192i	0.430461	+	0.581461i
$472$	9.40475	+	2.52000i	0.432889	+	0.115992i
$473$	0.754634	+	0.202203i	0.0346981	+	0.00929733i
$474$	−14.3047	−	19.3226i	−0.657037	−	0.887515i
$475$	−12.8272	+	4.92785i	−0.588553	+	0.226105i
$476$	8.57888	+	3.07940i	0.393212	+	0.141144i
$477$	1.09382	−	31.7338i	0.0500826	−	1.45299i
$478$	1.06549	−	0.285497i	0.0487344	−	0.0130583i
$479$	−10.0175	−	17.3509i	−0.457713	−	0.792783i	0.541126	−	0.840941i	$-0.317998\pi$
$479$	−10.0175	−	17.3509i	−0.457713	−	0.792783i	−0.998840	+	0.0481586i	$0.984665\pi$
$480$	−3.42030	−	1.81703i	−0.156114	−	0.0829355i
$481$	−9.90075	+	17.1486i	−0.451435	+	0.781909i
$482$	10.5236	+	10.5236i	0.479338	+	0.479338i
$483$	−15.7123	−	25.3737i	−0.714935	−	1.15454i
$484$			10.9701i			0.498642i
$485$	−18.8928	−	6.68743i	−0.857876	−	0.303661i
$486$	15.5728	−	0.697540i	0.706399	−	0.0316411i
$487$	21.2750	+	5.70061i	0.964060	+	0.258319i	0.706318	−	0.707895i	$-0.250355\pi$
$487$	21.2750	+	5.70061i	0.964060	+	0.258319i	0.257742	+	0.966214i	$0.417021\pi$
$488$	3.12422	+	11.6597i	0.141427	+	0.527811i
$489$	−34.9718	−	15.1968i	−1.58148	−	0.687223i
$490$	−7.58457	+	13.6921i	−0.342636	+	0.618547i
$491$		−	34.1772i		−	1.54240i	−0.636595	−	0.771198i	$-0.719658\pi$
$491$		−	34.1772i		−	1.54240i	0.636595	−	0.771198i	$-0.280342\pi$
$492$	2.58475	−	17.3217i	0.116530	−	0.780925i
$493$	−0.749682	+	2.79785i	−0.0337640	+	0.126009i
$494$	4.43129	+	7.67521i	0.199373	+	0.345324i
$495$	0.424297	−	1.07899i	0.0190707	−	0.0484972i
$496$	8.13419			0.365236
$497$	19.5856	+	13.5848i	0.878536	+	0.609364i
$498$	−12.1531	+	4.79039i	−0.544592	+	0.214663i
$499$	5.61952	+	3.24443i	0.251564	+	0.145241i	0.620480	−	0.784222i	$-0.286938\pi$
$499$	5.61952	+	3.24443i	0.251564	+	0.145241i	−0.368916	+	0.929463i	$0.620271\pi$
$500$	−10.7187	+	3.17970i	−0.479353	+	0.142200i
$501$	1.73579	+	15.2043i	0.0775495	+	0.679279i
$502$	−5.44831	−	20.3334i	−0.243170	−	0.907523i
$503$	15.7838	−	15.7838i	0.703766	−	0.703766i	−0.261451	−	0.965217i	$-0.584201\pi$
$503$	15.7838	−	15.7838i	0.703766	−	0.703766i	0.965217	+	0.261451i	$0.0842010\pi$
$504$	−7.29103	+	3.13703i	−0.324768	+	0.139734i
$505$	18.2468	+	12.5371i	0.811972	+	0.557892i
$506$	−0.974815	−	0.562810i	−0.0433358	−	0.0250199i
$507$	2.80324	−	3.52578i	0.124496	−	0.156586i
$508$	0.782580	−	2.92063i	0.0347214	−	0.129582i
$509$	−1.27596	+	2.21004i	−0.0565561	+	0.0979581i	−0.892917	−	0.450221i	$-0.851345\pi$
$509$	−1.27596	+	2.21004i	−0.0565561	+	0.0979581i	0.836361	+	0.548179i	$0.184679\pi$
$510$	13.0018	+	2.99678i	0.575731	+	0.132700i
$511$	0.125149	+	0.147809i	0.00553625	+	0.00653868i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−11.7633	+	8.09642i	−0.519362	+	0.357466i
$514$	1.59563	−	0.921235i	0.0703801	−	0.0406339i
$515$	13.0839	+	15.3151i	0.576545	+	0.674864i
$516$	−4.65842	−	6.29252i	−0.205075	−	0.277013i
$517$	−0.193261	+	0.193261i	−0.00849960	+	0.00849960i
$518$	16.1902	+	1.34407i	0.711355	+	0.0590550i
$519$	13.9134	−	32.0184i	0.610731	−	1.40545i
$520$	3.10524	+	6.50803i	0.136174	+	0.285396i
$521$	−11.9593	+	6.90469i	−0.523945	+	0.302500i	−0.738547	−	0.674202i	$-0.764488\pi$
$521$	−11.9593	+	6.90469i	−0.523945	+	0.302500i	0.214602	+	0.976702i	$0.431155\pi$
$522$	−1.18517	−	2.22656i	−0.0518735	−	0.0974538i
$523$	0.896548	−	0.240229i	0.0392033	−	0.0105045i	−0.239164	−	0.970979i	$-0.576873\pi$
$523$	0.896548	−	0.240229i	0.0392033	−	0.0105045i	0.278367	+	0.960475i	$0.410207\pi$
$524$	6.01236			0.262651
$525$	−8.66386	+	21.2117i	−0.378122	+	0.925756i
$526$	−19.3137			−0.842116
$527$	−27.0681	+	7.25287i	−1.17910	+	0.315940i
$528$	−0.186304	+	0.234325i	−0.00810783	+	0.0101977i
$529$	−16.8134	+	9.70721i	−0.731017	+	0.422053i
$530$	10.1918	+	21.3601i	0.442702	+	0.927825i
$531$	21.3535	−	19.9305i	0.926663	−	0.864910i
$532$	4.14409	−	5.97465i	0.179669	−	0.259034i
$533$	−23.0570	+	23.0570i	−0.998709	+	0.998709i
$534$	19.5634	−	14.4830i	0.846589	−	0.626739i
$535$	8.82914	+	10.3348i	0.381717	+	0.446812i
$536$	−1.11312	+	0.642662i	−0.0480796	+	0.0277588i
$537$	0.0425287	−	0.285006i	0.00183525	−	0.0122989i
$538$	−15.2294	−	15.2294i	−0.656588	−	0.656588i
$539$	0.933669	+	0.769421i	0.0402160	+	0.0331413i
$540$	−10.0576	+	5.81764i	−0.432810	+	0.250351i
$541$	−14.3269	+	24.8148i	−0.615960	+	1.06687i	0.374256	+	0.927326i	$0.377898\pi$
$541$	−14.3269	+	24.8148i	−0.615960	+	1.06687i	−0.990215	+	0.139548i	$0.955435\pi$
$542$	−3.96017	+	14.7795i	−0.170104	+	0.634836i
$543$	−0.851479	−	0.676983i	−0.0365405	−	0.0290521i
$544$	−2.98352	−	1.72254i	−0.127918	−	0.0738532i
$545$	−28.9458	−	19.8882i	−1.23990	−	0.851916i
$546$	14.3856	+	3.38278i	0.615645	+	0.144769i
$547$	−5.24672	+	5.24672i	−0.224333	+	0.224333i	−0.810320	−	0.585987i	$-0.800707\pi$
$547$	−5.24672	+	5.24672i	−0.224333	+	0.224333i	0.585987	+	0.810320i	$0.300707\pi$
$548$	2.50449	+	9.34687i	0.106986	+	0.399279i
$549$	34.6356	+	10.5721i	1.47821	+	0.451204i
$550$	0.0905619	+	0.859423i	0.00386157	+	0.0366459i
$551$	2.00110	+	1.15533i	0.0852496	+	0.0492189i
$552$	4.13658	+	10.4944i	0.176065	+	0.446670i
$553$	33.2138	−	15.6677i	1.41239	−	0.666259i
$554$	−18.2213			−0.774149
$555$	23.7667	−	0.838515i	1.00884	−	0.0355930i
$556$	5.07978	+	8.79844i	0.215431	+	0.373137i
$557$	2.57858	−	9.62338i	0.109258	−	0.407756i	−0.889536	−	0.456866i	$-0.848972\pi$
$557$	2.57858	−	9.62338i	0.109258	−	0.407756i	0.998793	+	0.0491102i	$0.0156385\pi$
$558$	12.9221	−	20.7004i	0.547034	−	0.876318i
$559$			14.5768i			0.616532i
$560$	3.74218	−	4.58215i	0.158136	−	0.193631i
$561$	0.411025	−	0.945877i	0.0173535	−	0.0399350i
$562$	−0.0311631	−	0.116302i	−0.00131453	−	0.00490591i
$563$	23.4051	+	6.27139i	0.986409	+	0.264307i	0.715741	−	0.698366i	$-0.246089\pi$
$563$	23.4051	+	6.27139i	0.986409	+	0.264307i	0.270667	+	0.962673i	$0.412756\pi$
$564$	2.72128	−	0.310673i	0.114586	−	0.0130817i
$565$	4.91853	+	1.74100i	0.206924	+	0.0732445i
$566$		−	4.82189i		−	0.202679i
$567$	−3.59929	+	23.5382i	−0.151156	+	0.988510i
$568$	−6.37038	−	6.37038i	−0.267295	−	0.267295i
$569$	8.36329	−	14.4856i	0.350607	−	0.607270i	−0.635749	−	0.771896i	$-0.719309\pi$
$569$	8.36329	−	14.4856i	0.350607	−	0.607270i	0.986356	+	0.164627i	$0.0526419\pi$
$570$	4.99363	−	9.39981i	0.209160	−	0.393715i
$571$	11.2493	+	19.4844i	0.470770	+	0.815397i	0.999441	−	0.0334297i	$-0.0106430\pi$
$571$	11.2493	+	19.4844i	0.470770	+	0.815397i	−0.528671	+	0.848827i	$0.677310\pi$
$572$	0.538372	−	0.144256i	0.0225105	−	0.00603167i
$573$	0.595055	+	1.50964i	0.0248588	+	0.0630659i
$574$	25.1794	+	9.03817i	1.05097	+	0.377246i
$575$	29.7515	+	13.2367i	1.24072	+	0.552007i
$576$	2.92281	−	0.676173i	0.121784	−	0.0281739i
$577$	−42.9101	−	11.4977i	−1.78637	−	0.478656i	−0.794649	−	0.607069i	$-0.792345\pi$
$577$	−42.9101	−	11.4977i	−1.78637	−	0.478656i	−0.991721	+	0.128413i	$0.959012\pi$
$578$	−4.95660	−	1.32812i	−0.206167	−	0.0552424i
$579$	−34.1250	+	25.2631i	−1.41819	+	1.04990i
$580$	1.54953	+	1.06466i	0.0643408	+	0.0442075i
$581$	−3.55221	−	19.6355i	−0.147370	−	0.814619i
$582$	14.4425	−	5.69283i	0.598662	−	0.235975i
$583$	1.76700	−	0.473467i	0.0731817	−	0.0196090i
$584$	−0.0366010	−	0.0633947i	−0.00151456	−	0.00262329i
$585$	21.4951	+	2.43630i	0.888711	+	0.100729i
$586$	4.59667	−	7.96167i	0.189887	−	0.328894i
$587$	0.955230	+	0.955230i	0.0394266	+	0.0394266i	0.726545	−	0.687119i	$-0.241125\pi$
$587$	0.955230	+	0.955230i	0.0394266	+	0.0394266i	−0.687119	+	0.726545i	$0.741125\pi$
$588$	−2.52526	−	11.8585i	−0.104140	−	0.489035i
$589$			22.3548i			0.921112i
$590$	−7.26473	+	20.5237i	−0.299084	+	0.844947i
$591$	−0.848762	−	7.43456i	−0.0349134	−	0.305817i
$592$	−5.93113	−	1.58924i	−0.243768	−	0.0653175i
$593$	6.65439	+	24.8345i	0.273263	+	1.01983i	0.956996	+	0.290100i	$0.0936884\pi$
$593$	6.65439	+	24.8345i	0.273263	+	1.01983i	−0.683733	+	0.729732i	$0.739645\pi$
$594$	0.300360	+	0.846367i	0.0123239	+	0.0347269i
$595$	−8.36711	+	18.5847i	−0.343018	+	0.761898i
$596$			5.31949i			0.217895i
$597$	−15.9953	−	2.38682i	−0.654644	−	0.0976861i
$598$	5.43572	−	20.2864i	0.222283	−	0.829572i
$599$	−20.7500	−	35.9400i	−0.847821	−	1.46847i	−0.883149	−	0.469093i	$-0.844581\pi$
$599$	−20.7500	−	35.9400i	−0.847821	−	1.46847i	0.0353276	−	0.999376i	$-0.488753\pi$
$600$	4.64954	−	7.30628i	0.189817	−	0.298278i
$601$	6.20524			0.253117			0.126559	−	0.991959i	$-0.459607\pi$
$601$	6.20524			0.253117			0.126559	+	0.991959i	$0.459607\pi$
$602$	10.8163	−	5.10229i	0.440839	−	0.207954i
$603$	−0.132831	+	3.85368i	−0.00540931	+	0.156934i
$604$	−13.5151	−	7.80296i	−0.549922	−	0.317498i
$605$	−24.4546	−	1.92132i	−0.994221	−	0.0781128i
$606$	−17.0379	+	1.94512i	−0.692118	+	0.0790152i
$607$	7.92700	+	29.5840i	0.321747	+	1.20078i	0.917542	+	0.397640i	$0.130171\pi$
$607$	7.92700	+	29.5840i	0.321747	+	1.20078i	−0.595795	+	0.803137i	$0.703163\pi$
$608$	−1.94330	+	1.94330i	−0.0788113	+	0.0788113i
$609$	3.68912	−	1.11151i	0.149491	−	0.0450408i
$610$	−26.5390	+	4.92240i	−1.07453	+	0.199302i
$611$	−4.41630	−	2.54975i	−0.178665	−	0.103152i
$612$	−9.12327	+	4.85622i	−0.368786	+	0.196301i
$613$	−1.32432	+	4.94242i	−0.0534887	+	0.199623i	−0.987499	−	0.157622i	$-0.949617\pi$
$613$	−1.32432	+	4.94242i	−0.0534887	+	0.199623i	0.934011	+	0.357245i	$0.116284\pi$
$614$	2.45040	−	4.24422i	0.0988900	−	0.171283i
$615$	38.1609	+	8.79568i	1.53880	+	0.354676i
$616$	−0.295487	−	0.348990i	−0.0119055	−	0.0140612i
$617$	1.50283	+	1.50283i	0.0605015	+	0.0605015i	0.736710	−	0.676209i	$-0.236378\pi$
$617$	1.50283	+	1.50283i	0.0605015	+	0.0605015i	−0.676209	+	0.736710i	$0.736378\pi$
$618$	−15.4318	−	2.30274i	−0.620759	−	0.0926298i
$619$	26.6491	−	15.3858i	1.07112	−	0.618409i	0.142630	−	0.989776i	$-0.454444\pi$
$619$	26.6491	−	15.3858i	1.07112	−	0.618409i	0.928486	+	0.371367i	$0.121111\pi$
$620$	−1.42463	+	18.1327i	−0.0572146	+	0.728228i
$621$	33.2782	+	6.14443i	1.33541	+	0.246567i
$622$	−14.3527	+	14.3527i	−0.575490	+	0.575490i
$623$	15.8630	+	33.6277i	0.635536	+	1.34727i
$624$	−5.12278	−	2.22607i	−0.205075	−	0.0891142i
$625$	−5.21090	−	24.4509i	−0.208436	−	0.978036i
$626$	−10.5872	+	6.11252i	−0.423150	+	0.244306i
$627$	−0.643981	−	0.512008i	−0.0257181	−	0.0204476i
$628$	8.75604	−	2.34617i	0.349404	−	0.0936225i
$629$	21.1540			0.843466
$630$	−5.71609	−	16.8026i	−0.227735	−	0.669430i
$631$	15.9868			0.636424			0.318212	−	0.948020i	$-0.396918\pi$
$631$	15.9868			0.636424			0.318212	+	0.948020i	$0.396918\pi$
$632$	−13.4073	+	3.59248i	−0.533314	+	0.142901i
$633$	−24.0966	−	19.1584i	−0.957755	−	0.761480i
$634$	23.4118	−	13.5168i	0.929800	−	0.536820i
$635$	6.37360	+	2.25605i	0.252929	+	0.0895286i
$636$	−16.8136	−	7.30623i	−0.666701	−	0.289711i
$637$	−9.35805	+	20.5426i	−0.370780	+	0.813927i
$638$	0.102755	−	0.102755i	0.00406810	−	0.00406810i
$639$	−26.3318	+	6.09170i	−1.04167	+	0.240984i
$640$	−1.70012	+	1.45244i	−0.0672033	+	0.0574126i
$641$	29.7998	−	17.2049i	1.17702	−	0.679553i	0.221697	−	0.975116i	$-0.428841\pi$
$641$	29.7998	−	17.2049i	1.17702	−	0.679553i	0.955323	+	0.295563i	$0.0955072\pi$
$642$	−10.4136	−	1.55391i	−0.410990	−	0.0613281i
$643$	−4.05504	−	4.05504i	−0.159915	−	0.159915i	0.622614	−	0.782529i	$-0.286071\pi$
$643$	−4.05504	−	4.05504i	−0.159915	−	0.159915i	−0.782529	+	0.622614i	$0.786071\pi$
$644$	−16.9556	+	3.06739i	−0.668144	+	0.120872i
$645$	14.8431	−	9.28246i	0.584448	−	0.365496i
$646$	4.73396	−	8.19945i	0.186255	−	0.322603i
$647$	1.51377	−	5.64948i	0.0595126	−	0.222104i	−0.929765	−	0.368155i	$-0.879990\pi$
$647$	1.51377	−	5.64948i	0.0595126	−	0.222104i	0.989277	+	0.146051i	$0.0466563\pi$
$648$	2.92243	−	8.51231i	0.114804	−	0.334395i
$649$	1.45737	+	0.841411i	0.0572067	+	0.0330283i
$650$	−15.0516	+	5.78238i	−0.590370	+	0.226804i
$651$	27.1581	+	25.5324i	1.06441	+	1.00069i
$652$	−15.5669	+	15.5669i	−0.609647	+	0.609647i
$653$	−1.69456	−	6.32418i	−0.0663132	−	0.247484i	0.924810	−	0.380429i	$-0.124223\pi$
$653$	−1.69456	−	6.32418i	−0.0663132	−	0.247484i	−0.991123	+	0.132944i	$0.957557\pi$
$654$	27.0281	−	3.08565i	1.05688	−	0.120658i
$655$	−1.05301	+	13.4027i	−0.0411445	+	0.523688i
$656$	−8.75677	−	5.05572i	−0.341894	−	0.197393i
$657$	−0.219475	−	0.00756502i	−0.00856255	−	0.000295140i
$658$	−0.346140	+	4.16948i	−0.0134939	+	0.162543i
$659$	−32.3314			−1.25945			−0.629727	−	0.776817i	$-0.716833\pi$
$659$	−32.3314			−1.25945			−0.629727	+	0.776817i	$0.716833\pi$
$660$	−0.489726	−	0.456348i	−0.0190626	−	0.0177633i
$661$	16.4102	+	28.4234i	0.638285	+	1.10554i	0.985809	+	0.167871i	$0.0536891\pi$
$661$	16.4102	+	28.4234i	0.638285	+	1.10554i	−0.347524	+	0.937671i	$0.612978\pi$
$662$	−1.53087	+	5.71328i	−0.0594989	+	0.222053i
$663$	19.0319	+	2.83994i	0.739137	+	0.110294i
$664$			7.54199i			0.292686i
$665$	12.5929	+	10.2844i	0.488331	+	0.398813i
$666$	−13.4667	+	12.5692i	−0.521822	+	0.487048i
$667$	−1.41721	−	5.28911i	−0.0548747	−	0.204795i
$668$	8.53419	+	2.28673i	0.330198	+	0.0884762i
$669$	5.77389	+	50.5752i	0.223231	+	1.95535i
$670$	−1.23767	−	2.59393i	−0.0478152	−	0.100212i
$671$			2.08631i			0.0805412i
$672$	0.141325	+	4.58040i	0.00545172	+	0.176693i
$673$	6.60249	+	6.60249i	0.254507	+	0.254507i	0.822816	−	0.568308i	$-0.192402\pi$
$673$	6.60249	+	6.60249i	0.254507	+	0.254507i	−0.568308	+	0.822816i	$0.692402\pi$
$674$	6.23757	−	10.8038i	0.240262	−	0.416146i
$675$	−11.2072	−	23.4393i	−0.431364	−	0.902178i
$676$	−1.30030	−	2.25218i	−0.0500114	−	0.0866224i
$677$	8.50593	−	2.27916i	0.326909	−	0.0875951i	−0.0916318	−	0.995793i	$-0.529208\pi$
$677$	8.50593	−	2.27916i	0.326909	−	0.0875951i	0.418541	+	0.908198i	$0.362542\pi$
$678$	−3.75996	+	1.48207i	−0.144400	+	0.0569185i
$679$	4.22139	+	23.3346i	0.162002	+	0.895498i
$680$	4.36242	−	6.34918i	0.167291	−	0.243480i
$681$	−8.78543	+	6.50395i	−0.336658	+	0.249232i
$682$	1.35798	+	0.363869i	0.0519997	+	0.0139333i
$683$	−34.4132	−	9.22099i	−1.31678	−	0.352831i	−0.469012	−	0.883192i	$-0.655390\pi$
$683$	−34.4132	−	9.22099i	−1.31678	−	0.352831i	−0.847772	+	0.530361i	$0.822057\pi$
$684$	1.85829	+	8.03258i	0.0710535	+	0.307134i
$685$	−21.2747	+	3.94598i	−0.812864	+	0.150768i
$686$	18.5186	−	0.246614i	0.707044	−	0.00941576i
$687$	0.601786	+	1.52671i	0.0229596	+	0.0582477i
$688$	−4.36618	+	1.16991i	−0.166459	+	0.0446025i
$689$	17.0660	+	29.5592i	0.650164	+	1.12612i
$690$	−24.1185	+	7.38327i	−0.918177	+	0.281076i
$691$	−0.329316	+	0.570391i	−0.0125278	+	0.0216987i	−0.872221	−	0.489111i	$-0.837321\pi$
$691$	−0.329316	+	0.570391i	−0.0125278	+	0.0216987i	0.859694	+	0.510810i	$0.170654\pi$
$692$	−14.2523	−	14.2523i	−0.541790	−	0.541790i
$693$	−1.35754	+	0.197565i	−0.0515688	+	0.00750488i
$694$			9.17096i			0.348125i
$695$	−20.5031	+	9.78287i	−0.777728	+	0.371085i
$696$	−1.44687	+	0.165181i	−0.0548436	+	0.00626118i
$697$	33.6477	+	9.01588i	1.27450	+	0.341501i
$698$	4.53620	+	16.9293i	0.171698	+	0.640784i
$699$	−5.93473	+	13.6574i	−0.224472	+	0.516569i
$700$	9.55912	+	9.14458i	0.361301	+	0.345632i
$701$			11.3501i			0.428686i	0.976758	+	0.214343i	$0.0687610\pi$
$701$			11.3501i			0.428686i	−0.976758	+	0.214343i	$0.931239\pi$
$702$	−13.8031	+	9.50040i	−0.520965	+	0.358569i
$703$	4.36763	−	16.3002i	0.164728	−	0.614774i
$704$	0.0864181	+	0.149681i	0.00325701	+	0.00564130i
$705$	0.215944	+	6.12068i	0.00813291	+	0.230518i
$706$	1.29021			0.0485578
$707$	2.16718	−	26.1051i	0.0815053	−	0.981783i
$708$	−6.18427	−	15.6893i	−0.232419	−	0.589640i
$709$	−12.1585	−	7.01970i	−0.456621	−	0.263630i	0.254001	−	0.967204i	$-0.418253\pi$
$709$	−12.1585	−	7.01970i	−0.456621	−	0.263630i	−0.710622	+	0.703574i	$0.751587\pi$
$710$	15.3166	−	13.0851i	0.574821	−	0.491076i
$711$	−12.1566	+	39.8268i	−0.455909	+	1.49362i
$712$	−3.63725	−	13.5744i	−0.136312	−	0.508722i
$713$	37.4590	−	37.4590i	1.40285	−	1.40285i
$714$	−4.55440	−	15.1161i	−0.170444	−	0.565706i
$715$	0.227285	+	1.22540i	0.00849998	+	0.0458275i
$716$	−0.144081	−	0.0831851i	−0.00538456	−	0.00310877i
$717$	−1.49551	−	1.18903i	−0.0558507	−	0.0444051i
$718$	−4.37288	+	16.3198i	−0.163195	+	0.609051i
$719$	1.85130	−	3.20654i	0.0690418	−	0.119584i	−0.829438	−	0.558599i	$-0.811339\pi$
$719$	1.85130	−	3.20654i	0.0690418	−	0.119584i	0.898480	+	0.439015i	$0.144672\pi$
$720$	0.995421	+	6.63394i	0.0370971	+	0.247232i
$721$	8.05205	−	22.4321i	0.299874	−	0.835416i
$722$	8.09436	+	8.09436i	0.301241	+	0.301241i
$723$	3.80440	−	25.4952i	0.141487	−	0.948178i
$724$	−0.543903	+	0.314023i	−0.0202140	+	0.0116706i
$725$	−2.64472	+	3.26775i	−0.0982225	+	0.121361i
$726$	15.2714	−	11.3056i	0.566774	−	0.419589i
$727$	−1.93909	+	1.93909i	−0.0719167	+	0.0719167i	−0.742150	−	0.670234i	$-0.766194\pi$
$727$	−1.93909	+	1.93909i	−0.0719167	+	0.0719167i	0.670234	+	0.742150i	$0.266194\pi$
$728$	4.86271	−	7.01070i	0.180224	−	0.259834i
$729$	−17.0201	−	20.9599i	−0.630373	−	0.776293i
$730$	0.147730	−	0.0704878i	0.00546772	−	0.00260887i
$731$	13.4861	−	7.78622i	0.498802	−	0.287984i
$732$	13.0116	−	16.3654i	0.480924	−	0.604884i
$733$	−11.5739	+	3.10122i	−0.427492	+	0.114546i	−0.466149	−	0.884706i	$-0.654359\pi$
$733$	−11.5739	+	3.10122i	−0.427492	+	0.114546i	0.0386564	+	0.999253i	$0.487692\pi$
$734$	33.0821			1.22108
$735$	26.8771	−	3.55241i	0.991378	−	0.131032i
$736$	6.51264			0.240059
$737$	−0.214581	+	0.0574968i	−0.00790419	+	0.00211792i
$738$	−26.7772	+	14.2532i	−0.985682	+	0.524667i
$739$	10.6023	−	6.12123i	0.390011	−	0.225173i	−0.292154	−	0.956371i	$-0.594372\pi$
$739$	10.6023	−	6.12123i	0.390011	−	0.225173i	0.682165	+	0.731198i	$0.261039\pi$
$740$	4.58152	−	12.9433i	0.168420	−	0.475806i
$741$	6.11779	−	14.0786i	0.224743	−	0.517192i
$742$	15.9600	−	23.0099i	0.585910	−	0.844721i
$743$	−15.5281	+	15.5281i	−0.569671	+	0.569671i	−0.932036	−	0.362365i	$-0.881969\pi$
$743$	−15.5281	+	15.5281i	−0.569671	+	0.569671i	0.362365	+	0.932036i	$0.381969\pi$
$744$	−8.38292	−	11.3235i	−0.307333	−	0.415140i
$745$	−11.8582	−	0.931662i	−0.434451	−	0.0341334i
$746$	5.77981	−	3.33698i	0.211614	−	0.122175i
$747$	19.1933	+	11.9813i	0.702247	+	0.438372i
$748$	−0.421035	−	0.421035i	−0.0153946	−	0.0153946i
$749$	5.43361	−	15.1374i	0.198540	−	0.553110i
$750$	15.4728	+	11.6444i	0.564988	+	0.425193i
$751$	21.0530	−	36.4649i	0.768235	−	1.33062i	−0.170284	−	0.985395i	$-0.554468\pi$
$751$	21.0530	−	36.4649i	0.768235	−	1.33062i	0.938519	−	0.345228i	$-0.112198\pi$
$752$	0.409280	−	1.52745i	0.0149249	−	0.0557005i
$753$	−22.6910	+	28.5397i	−0.826904	+	1.04004i
$754$	2.34810	+	1.35568i	0.0855128	+	0.0493708i
$755$	19.7614	−	28.7613i	0.719191	−	1.04673i
$756$	11.8810	+	6.91681i	0.432107	+	0.251562i
$757$	23.9201	−	23.9201i	0.869389	−	0.869389i	−0.123015	−	0.992405i	$-0.539256\pi$
$757$	23.9201	−	23.9201i	0.869389	−	0.869389i	0.992405	+	0.123015i	$0.0392565\pi$
$758$	4.17944	+	15.5979i	0.151804	+	0.566540i
$759$	0.221142	+	1.93705i	0.00802694	+	0.0703104i
$760$	−3.99166	−	4.67236i	−0.144793	−	0.169484i
$761$	0.160794	+	0.0928347i	0.00582879	+	0.00336526i	0.502912	−	0.864338i	$-0.332262\pi$
$761$	0.160794	+	0.0928347i	0.00582879	+	0.00336526i	−0.497083	+	0.867703i	$0.665595\pi$
$762$	−4.87228	+	1.92051i	−0.176504	+	0.0695729i
$763$	−3.43791	+	41.4118i	−0.124461	+	1.49921i
$764$	0.936855			0.0338942
$765$	−9.22761	−	21.1881i	−0.333625	−	0.766058i
$766$	−8.11211	−	14.0506i	−0.293103	−	0.507668i
$767$	−8.12651	+	30.3285i	−0.293431	+	1.09510i
$768$	0.255627	−	1.71308i	0.00922413	−	0.0618156i
$769$		−	29.4164i		−	1.06078i	−0.847753	−	0.530392i	$-0.822045\pi$
$769$		−	29.4164i		−	1.06078i	0.847753	−	0.530392i	$-0.177955\pi$
$770$	0.829720	−	0.597577i	0.0299010	−	0.0215352i
$771$	−2.92686	−	1.27185i	−0.105408	−	0.0458045i
$772$	6.34457	+	23.6783i	0.228346	+	0.852199i
$773$	−17.1007	−	4.58211i	−0.615068	−	0.164807i	−0.0621831	−	0.998065i	$-0.519806\pi$
$773$	−17.1007	−	4.58211i	−0.615068	−	0.164807i	−0.552885	+	0.833258i	$0.686473\pi$
$774$	−3.95888	+	12.9699i	−0.142299	+	0.466192i
$775$	−40.1720	−	6.35157i	−1.44302	−	0.228155i
$776$		−	8.96279i		−	0.321746i
$777$	−14.8142	−	23.9233i	−0.531455	−	0.858244i
$778$	16.9300	+	16.9300i	0.606970	+	0.606970i
$779$	13.8944	−	24.0657i	0.497817	−	0.862245i
$780$	5.85956	−	11.0298i	0.209806	−	0.394930i
$781$	−0.778548	−	1.34848i	−0.0278586	−	0.0482526i
$782$	−21.6720	+	5.80700i	−0.774990	+	0.207658i
$783$	−1.87815	+	3.94450i	−0.0671197	+	0.140965i
$784$	−6.90417	−	1.15429i	−0.246578	−	0.0412247i
$785$	3.69655	+	19.9299i	0.131935	+	0.711327i
$786$	−6.19620	−	8.36973i	−0.221011	−	0.298538i
$787$	−9.72104	−	2.60475i	−0.346518	−	0.0928491i	0.0813625	−	0.996685i	$-0.474073\pi$
$787$	−9.72104	−	2.60475i	−0.346518	−	0.0928491i	−0.427880	+	0.903835i	$0.640740\pi$
$788$	−4.17302	−	1.11816i	−0.148658	−	0.0398327i
$789$	19.9042	+	26.8863i	0.708610	+	0.957179i
$790$	−5.66018	−	30.5168i	−0.201380	−	1.08574i
$791$	−1.09900	−	6.07491i	−0.0390758	−	0.215999i
$792$	0.518201	+	0.0178617i	0.0184135	+	0.000634687i
$793$	−37.6004	+	10.0750i	−1.33523	+	0.357774i
$794$	−11.6778	−	20.2265i	−0.414429	−	0.717813i
$795$	19.2318	−	36.2011i	0.682081	−	1.28392i
$796$	−4.66857	+	8.08620i	−0.165473	+	0.286608i
$797$	−1.48738	−	1.48738i	−0.0526858	−	0.0526858i	0.680273	−	0.732959i	$-0.261861\pi$
$797$	−1.48738	−	1.48738i	−0.0526858	−	0.0526858i	−0.732959	+	0.680273i	$0.761861\pi$
$798$	−12.5881	+	0.388395i	−0.445612	+	0.0137490i
$799$			5.44782i			0.192730i
$800$	−2.94001	−	4.04430i	−0.103945	−	0.142987i
$801$	−40.3231	−	12.3081i	−1.42475	−	0.434886i
$802$	−17.4314	−	4.67073i	−0.615524	−	0.164929i
$803$	−0.00327456	−	0.0122208i	−0.000115557	−	0.000431264i
$804$	2.04180	+	0.887252i	0.0720088	+	0.0312910i
$805$	−3.86820	−	38.3346i	−0.136336	−	1.35112i
$806$			26.2312i			0.923956i
$807$	−5.50561	+	36.8959i	−0.193807	+	1.29880i
$808$	−2.56250	+	9.56338i	−0.0901485	+	0.336439i
$809$	−12.1034	−	20.9637i	−0.425534	−	0.737046i	0.570936	−	0.820994i	$-0.306580\pi$
$809$	−12.1034	−	20.9637i	−0.425534	−	0.737046i	−0.996470	+	0.0839482i	$0.973247\pi$
$810$	18.4638	+	8.00552i	0.648751	+	0.281285i
$811$	−28.4058			−0.997462			−0.498731	−	0.866757i	$-0.666201\pi$
$811$	−28.4058			−0.997462			−0.498731	+	0.866757i	$0.666201\pi$
$812$	0.184039	−	2.21687i	0.00645850	−	0.0777968i
$813$	24.6557	−	9.71856i	0.864712	−	0.340845i
$814$	−0.919093	−	0.530639i	−0.0322142	−	0.0185989i
$815$	−31.9753	−	37.4281i	−1.12005	−	1.31105i
$816$	0.676827	+	5.92854i	0.0236937	+	0.207540i
$817$	−3.21521	−	11.9993i	−0.112486	−	0.419803i
$818$	−7.15836	+	7.15836i	−0.250286	+	0.250286i
$819$	−10.1163	−	23.5122i	−0.353493	−	0.821582i
$820$	12.8039	−	18.6351i	0.447131	−	0.650766i
$821$	−20.2229	−	11.6757i	−0.705783	−	0.407484i	0.103715	−	0.994607i	$-0.466927\pi$
$821$	−20.2229	−	11.6757i	−0.705783	−	0.407484i	−0.809498	+	0.587123i	$0.800260\pi$
$822$	10.4306	−	13.1191i	0.363809	−	0.457583i
$823$	9.58542	−	35.7733i	0.334127	−	1.24698i	−0.570686	−	0.821168i	$-0.693323\pi$
$823$	9.58542	−	35.7733i	0.334127	−	1.24698i	0.904813	−	0.425810i	$-0.140011\pi$
$824$	−4.50411	+	7.80135i	−0.156908	+	0.271773i
$825$	1.10306	−	1.01177i	0.0384037	−	0.0352254i
$826$	25.3489	−	4.58581i	0.882002	−	0.159561i
$827$	−13.5105	−	13.5105i	−0.469805	−	0.469805i	0.432047	−	0.901851i	$-0.357792\pi$
$827$	−13.5105	−	13.5105i	−0.469805	−	0.469805i	−0.901851	+	0.432047i	$0.857792\pi$
$828$	10.3460	−	16.5738i	0.359549	−	0.575978i
$829$	−34.5823	+	19.9661i	−1.20109	+	0.693452i	−0.960799	−	0.277247i	$-0.910578\pi$
$829$	−34.5823	+	19.9661i	−1.20109	+	0.693452i	−0.240296	+	0.970700i	$0.577245\pi$
$830$	−16.8126	−	1.32091i	−0.583574	−	0.0458496i
$831$	18.7785	+	25.3656i	0.651417	+	0.879925i
$832$	−2.28029	+	2.28029i	−0.0790547	+	0.0790547i
$833$	24.0042	−	2.31499i	0.831695	−	0.0802098i
$834$	7.01309	−	16.1390i	0.242844	−	0.558847i
$835$	−6.59226	+	18.6239i	−0.228135	+	0.644507i
$836$	−0.411359	+	0.237498i	−0.0142271	+	0.00821405i
$837$	−42.1340	+	3.34473i	−1.45636	+	0.115611i
$838$	−6.41313	+	1.71839i	−0.221538	+	0.0593609i
$839$	3.82196			0.131949			0.0659743	−	0.997821i	$-0.478984\pi$
$839$	3.82196			0.131949			0.0659743	+	0.997821i	$0.478984\pi$
$840$	−10.2354	−	0.487175i	−0.353154	−	0.0168091i
$841$	−28.2931			−0.975624
$842$	−8.04929	+	2.15680i	−0.277397	+	0.0743282i
$843$	−0.129787	+	0.163240i	−0.00447010	+	0.00562229i
$844$	−15.3923	+	8.88676i	−0.529825	+	0.305895i
$845$	5.24829	−	2.50417i	0.180547	−	0.0861461i
$846$	−3.23697	−	3.46809i	−0.111289	−	0.119235i
$847$	12.3828	+	26.2502i	0.425478	+	0.901967i
$848$	−7.48417	+	7.48417i	−0.257007	+	0.257007i
$849$	−6.71249	+	4.96933i	−0.230372	+	0.170547i
$850$	13.3895	+	10.8367i	0.459257	+	0.371696i
$851$	−34.6323	+	19.9950i	−1.18718	+	0.685419i
$852$	−2.30296	+	15.4333i	−0.0788982	+	0.528737i
$853$	−22.9546	−	22.9546i	−0.785949	−	0.785949i	0.194878	−	0.980827i	$-0.437569\pi$
$853$	−22.9546	−	22.9546i	−0.785949	−	0.785949i	−0.980827	+	0.194878i	$0.937569\pi$
$854$	20.6371	+	24.3738i	0.706186	+	0.834054i
$855$	−18.2317	+	2.73566i	−0.623511	+	0.0935576i
$856$	−3.03942	+	5.26443i	−0.103885	+	0.179935i
$857$	−2.42738	+	9.05910i	−0.0829176	+	0.309453i	−0.994912	−	0.100751i	$-0.967876\pi$
$857$	−2.42738	+	9.05910i	−0.0829176	+	0.309453i	0.911994	+	0.410203i	$0.134542\pi$
$858$	−0.755652	−	0.600794i	−0.0257975	−	0.0205108i
$859$	22.9758	+	13.2651i	0.783923	+	0.452598i	0.837819	−	0.545949i	$-0.183831\pi$
$859$	22.9758	+	13.2651i	0.783923	+	0.452598i	−0.0538960	+	0.998547i	$0.517164\pi$
$860$	−1.84327	−	9.93798i	−0.0628551	−	0.338882i
$861$	−13.3674	−	44.3664i	−0.455558	−	1.51200i
$862$	15.6929	−	15.6929i	0.534503	−	0.534503i
$863$	−7.52307	−	28.0765i	−0.256088	−	0.955735i	−0.967482	−	0.252941i	$-0.918602\pi$
$863$	−7.52307	−	28.0765i	−0.256088	−	0.955735i	0.711393	−	0.702794i	$-0.248064\pi$
$864$	−3.95347	−	3.37195i	−0.134500	−	0.114716i
$865$	34.2673	−	29.2750i	1.16512	−	0.995378i
$866$	−10.3627	−	5.98291i	−0.352139	−	0.203308i
$867$	3.25931	+	8.26875i	0.110692	+	0.280822i
$868$	19.4641	−	9.18168i	0.660656	−	0.311646i
$869$	−2.39901			−0.0813810
$870$	−0.114815	−	3.25430i	−0.00389259	−	0.110331i
$871$	−2.07246	−	3.58961i	−0.0702227	−	0.121629i
$872$	4.06502	−	15.1709i	0.137659	−	0.513751i
$873$	−22.8091	−	14.2384i	−0.771970	−	0.481896i
$874$			17.8983i			0.605420i
$875$	−22.0593	+	19.7076i	−0.745739	+	0.666238i
$876$	−0.0505309	+	0.116285i	−0.00170728	+	0.00392891i
$877$	−13.9767	−	52.1619i	−0.471961	−	1.76138i	−0.632712	−	0.774387i	$-0.718059\pi$
$877$	−13.9767	−	52.1619i	−0.471961	−	1.76138i	0.160752	−	0.986995i	$-0.448608\pi$
$878$	7.21845	+	1.93418i	0.243611	+	0.0652753i
$879$	−15.8206	+	1.80615i	−0.533615	+	0.0609198i
$880$	−0.348803	+	0.166428i	−0.0117581	+	0.00561028i
$881$			54.1575i			1.82461i	0.409509	+	0.912306i	$0.365700\pi$
$881$			54.1575i			1.82461i	−0.409509	+	0.912306i	$0.634300\pi$
$882$	−13.9055	+	15.7365i	−0.468224	+	0.529874i
$883$	19.2945	+	19.2945i	0.649313	+	0.649313i	0.952827	−	0.303514i	$-0.0981599\pi$
$883$	19.2945	+	19.2945i	0.649313	+	0.649313i	−0.303514	+	0.952827i	$0.598160\pi$
$884$	5.55486	−	9.62130i	0.186830	−	0.323599i
$885$	36.0577	−	11.0381i	1.21207	−	0.371042i
$886$	−1.60510	−	2.78012i	−0.0539245	−	0.0934001i
$887$	31.6212	−	8.47287i	1.06174	−	0.284491i	0.314642	−	0.949210i	$-0.398116\pi$
$887$	31.6212	−	8.47287i	1.06174	−	0.284491i	0.747093	+	0.664719i	$0.231449\pi$
$888$	3.90013	+	9.89450i	0.130880	+	0.332038i
$889$	−1.42411	−	7.87207i	−0.0477633	−	0.264021i
$890$	30.8970	−	5.73071i	1.03567	−	0.192094i
$891$	0.868674	−	1.29037i	0.0291017	−	0.0432292i
$892$	28.3879	+	7.60651i	0.950496	+	0.254685i
$893$	4.19782	+	1.12480i	0.140475	+	0.0376400i
$894$	7.40520	−	5.48215i	0.247667	−	0.183350i
$895$	0.210671	−	0.306616i	0.00704194	−	0.0102490i
$896$	2.49019	+	0.893856i	0.0831912	+	0.0298616i
$897$	−33.8424	+	13.3397i	−1.12996	+	0.445399i
$898$	−27.4225	+	7.34784i	−0.915102	+	0.245201i
$899$	3.41953	+	5.92280i	0.114048	+	0.197536i
$900$	−14.9627	+	1.05711i	−0.498757	+	0.0352372i
$901$	18.2317	−	31.5782i	0.607386	−	1.05202i
$902$	−1.23576	−	1.23576i	−0.0411462	−	0.0411462i
$903$	−18.2499	−	9.79892i	−0.607317	−	0.326088i
$904$			2.33337i			0.0776067i
$905$	−0.604759	−	1.26747i	−0.0201029	−	0.0421320i
$906$	3.06597	+	26.8558i	0.101860	+	0.892224i
$907$	10.4202	+	2.79208i	0.345997	+	0.0927095i	0.427632	−	0.903953i	$-0.359348\pi$
$907$	10.4202	+	2.79208i	0.345997	+	0.0927095i	−0.0816359	+	0.996662i	$0.526014\pi$
$908$	1.63340	+	6.09593i	0.0542063	+	0.202301i
$909$	20.2667	+	21.7137i	0.672203	+	0.720198i
$910$	14.7766	+	12.0678i	0.489839	+	0.400044i
$911$		−	25.0692i		−	0.830579i	−0.909689	−	0.415290i	$-0.863680\pi$
$911$		−	25.0692i		−	0.830579i	0.909689	−	0.415290i	$-0.136320\pi$
$912$	4.70797	+	0.702525i	0.155897	+	0.0232629i
$913$	−0.337378	+	1.25911i	−0.0111656	+	0.0416706i
$914$	−1.13340	−	1.96311i	−0.0374896	−	0.0649340i
$915$	34.2029	+	31.8718i	1.13071	+	1.05365i
$916$	0.947452			0.0313047
$917$	14.3868	−	6.78660i	0.475095	−	0.224113i
$918$	16.1625	+	7.69569i	0.533443	+	0.253996i
$919$	8.61762	+	4.97538i	0.284269	+	0.164123i	0.635354	−	0.772221i	$-0.280854\pi$
$919$	8.61762	+	4.97538i	0.284269	+	0.164123i	−0.351086	+	0.936343i	$0.614187\pi$
$920$	−1.14063	+	14.5180i	−0.0376055	+	0.478643i
$921$	−8.43365	+	0.962822i	−0.277898	+	0.0317261i
$922$	−3.26716	−	12.1932i	−0.107598	−	0.401562i
$923$	20.5433	−	20.5433i	0.676191	−	0.676191i
$924$	−0.181303	+	0.771005i	−0.00596442	+	0.0253642i
$925$	28.0508	+	12.4800i	0.922306	+	0.410341i
$926$	10.4838	+	6.05284i	0.344520	+	0.198909i
$927$	12.6981	+	23.8556i	0.417060	+	0.783521i
$928$	−0.217610	+	0.812130i	−0.00714339	+	0.0266595i
$929$	−5.51726	+	9.55617i	−0.181015	+	0.313528i	−0.942227	−	0.334976i	$-0.891272\pi$
$929$	−5.51726	+	9.55617i	−0.181015	+	0.313528i	0.761211	+	0.648504i	$0.224605\pi$
$930$	26.7106	−	16.7040i	0.875874	−	0.547745i
$931$	3.17228	−	18.9744i	0.103967	−	0.621860i
$932$	6.07926	+	6.07926i	0.199133	+	0.199133i
$933$	34.7718	+	5.18865i	1.13838	+	0.169869i
$934$	−33.5599	+	19.3758i	−1.09811	+	0.633997i
$935$	1.01231	−	0.864831i	0.0331061	−	0.0282830i
$936$	2.18053	+	9.42549i	0.0712729	+	0.308082i
$937$	24.3351	−	24.3351i	0.794993	−	0.794993i	−0.187308	−	0.982301i	$-0.559976\pi$
$937$	24.3351	−	24.3351i	0.794993	−	0.794993i	0.982301	+	0.187308i	$0.0599763\pi$
$938$	−1.93815	+	2.79428i	−0.0632827	+	0.0912364i
$939$	19.4201	+	8.43889i	0.633751	+	0.275393i
$940$	3.33331	+	1.17989i	0.108721	+	0.0384836i
$941$	−15.8705	+	9.16283i	−0.517363	+	0.298700i	−0.735855	−	0.677139i	$-0.763220\pi$
$941$	−15.8705	+	9.16283i	−0.517363	+	0.298700i	0.218492	+	0.975839i	$0.429886\pi$
$942$	−12.2899	−	9.77127i	−0.400425	−	0.318365i
$943$	−63.6083	+	17.0438i	−2.07137	+	0.555022i
$944$	−9.73652			−0.316897
$945$	−17.4998	+	25.2737i	−0.569268	+	0.822152i
$946$	−0.781254			−0.0254008
$947$	50.6300	−	13.5663i	1.64525	−	0.440844i	0.686975	−	0.726681i	$-0.258938\pi$
$947$	50.6300	−	13.5663i	1.64525	−	0.440844i	0.958278	+	0.285837i	$0.0922715\pi$
$948$	18.8183	+	14.9618i	0.611191	+	0.485938i
$949$	0.204436	−	0.118031i	0.00663627	−	0.00383145i
$950$	11.1147	−	8.07987i	0.360609	−	0.262146i
$951$	−42.9442	−	18.6611i	−1.39256	−	0.605129i
$952$	−9.08357	−	0.754096i	−0.294400	−	0.0244404i
$953$	−9.37397	+	9.37397i	−0.303653	+	0.303653i	−0.842441	−	0.538788i	$-0.818882\pi$
$953$	−9.37397	+	9.37397i	−0.303653	+	0.303653i	0.538788	+	0.842441i	$0.318882\pi$
$954$	7.15676	+	30.9356i	0.231709	+	1.00158i
$955$	−0.164082	+	2.08843i	−0.00530956	+	0.0675802i
$956$	−0.955292	+	0.551538i	−0.0308963	+	0.0178380i
$957$	−0.248940	−	0.0371469i	−0.00804710	−	0.00120079i
$958$	14.1669	+	14.1669i	0.457713	+	0.457713i
$959$	16.5435	+	19.5389i	0.534216	+	0.630945i
$960$	3.77403	+	0.869874i	0.121806	+	0.0280751i
$961$	−17.5826	+	30.4539i	−0.567179	+	0.982384i
$962$	5.12501	−	19.1268i	0.165237	−	0.616672i
$963$	8.56880	+	16.0980i	0.276126	+	0.518752i
$964$	−12.8888	−	7.44133i	−0.415119	−	0.239669i
$965$	−53.8947	+	9.99627i	−1.73493	+	0.321791i
$966$	21.7441	+	20.4425i	0.699606	+	0.657726i
$967$	8.40858	−	8.40858i	0.270402	−	0.270402i	−0.558860	−	0.829262i	$-0.688761\pi$
$967$	8.40858	−	8.40858i	0.270402	−	0.270402i	0.829262	+	0.558860i	$0.188761\pi$
$968$	−2.83928	−	10.5963i	−0.0912578	−	0.340579i
$969$	−16.2931	+	1.86009i	−0.523409	+	0.0597546i
$970$	19.9798	+	1.56975i	0.641514	+	0.0504018i
$971$	−41.1227	−	23.7422i	−1.31969	−	0.761924i	−0.336013	−	0.941857i	$-0.609078\pi$
$971$	−41.1227	−	23.7422i	−1.31969	−	0.761924i	−0.983679	+	0.179933i	$0.942412\pi$
$972$	−14.8617	+	4.70432i	−0.476688	+	0.150891i
$973$	22.0868	+	15.3197i	0.708069	+	0.491126i
$974$	−22.0255			−0.705741
$975$	23.5614	+	14.9939i	0.754568	+	0.480189i
$976$	−6.03552	−	10.4538i	−0.193192	−	0.334619i
$977$	−14.0296	+	52.3593i	−0.448848	+	1.67512i	0.256723	+	0.966485i	$0.417357\pi$
$977$	−14.0296	+	52.3593i	−0.448848	+	1.67512i	−0.705571	+	0.708639i	$0.749310\pi$
$978$	37.7134	+	5.62761i	1.20594	+	0.179951i
$979$		−	2.42891i		−	0.0776283i
$980$	3.78235	−	15.1886i	0.120823	−	0.485182i
$981$	−32.1501	−	34.4455i	−1.02647	−	1.09976i
$982$	8.84572	+	33.0127i	0.282278	+	1.05348i
$983$	10.1451	+	2.71838i	0.323579	+	0.0867028i	0.416952	−	0.908928i	$-0.363098\pi$
$983$	10.1451	+	2.71838i	0.323579	+	0.0867028i	−0.0933730	+	0.995631i	$0.529765\pi$
$984$	1.98652	+	17.4005i	0.0633279	+	0.554708i
$985$	3.22346	−	9.10666i	0.102708	−	0.290162i
$986$		−	2.89655i		−	0.0922449i
$987$	6.16101	−	3.81511i	0.196107	−	0.121436i
$988$	−6.26678	−	6.26678i	−0.199373	−	0.199373i
$989$	−14.7192	+	25.4944i	−0.468044	+	0.810675i
$990$	−0.130576	+	1.15204i	−0.00414996	+	0.0366144i
$991$	−12.3659	−	21.4183i	−0.392815	−	0.680375i	0.600005	−	0.799996i	$-0.295165\pi$
$991$	−12.3659	−	21.4183i	−0.392815	−	0.680375i	−0.992820	+	0.119621i	$0.961832\pi$
$992$	−7.85703	+	2.10528i	−0.249461	+	0.0668428i
$993$	9.53107	−	3.75687i	0.302459	−	0.119221i
$994$	−22.4343	−	8.05282i	−0.711572	−	0.255420i
$995$	−17.2081	−	11.8234i	−0.545533	−	0.374827i
$996$	10.4991	−	7.77261i	0.332677	−	0.246285i
$997$	51.1086	+	13.6945i	1.61862	+	0.433709i	0.950597	−	0.310427i	$-0.100472\pi$
$997$	51.1086	+	13.6945i	1.61862	+	0.433709i	0.668028	+	0.744137i	$0.267139\pi$
$998$	−6.26776	−	1.67944i	−0.198403	−	0.0531618i
$999$	31.3759	+	5.79320i	0.992690	+	0.183289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.23.8	✓	64
3.2	odd	2	inner	210.2.x.a.23.9	yes	64
5.2	odd	4	inner	210.2.x.a.107.6	yes	64
7.4	even	3	inner	210.2.x.a.53.12	yes	64
15.2	even	4	inner	210.2.x.a.107.12	yes	64
21.11	odd	6	inner	210.2.x.a.53.6	yes	64
35.32	odd	12	inner	210.2.x.a.137.9	yes	64
105.32	even	12	inner	210.2.x.a.137.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.8	✓	64	1.1	even	1	trivial
210.2.x.a.23.9	yes	64	3.2	odd	2	inner
210.2.x.a.53.6	yes	64	21.11	odd	6	inner
210.2.x.a.53.12	yes	64	7.4	even	3	inner
210.2.x.a.107.6	yes	64	5.2	odd	4	inner
210.2.x.a.107.12	yes	64	15.2	even	4	inner
210.2.x.a.137.8	yes	64	105.32	even	12	inner
210.2.x.a.137.9	yes	64	35.32	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.35576 + 1.07792i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.962923 + 2.01811i) q^{5} +(-1.58855 - 0.690295i) q^{6} +(1.50791 - 2.17399i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.676173 + 2.92281i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.35576 + 1.07792i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.962923 + 2.01811i) q^{5} +(-1.58855 - 0.690295i) q^{6} +(1.50791 - 2.17399i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.676173 + 2.92281i) q^{9} +(-1.45244 - 1.70012i) q^{10} +(-0.149681 + 0.0864181i) q^{11} +(1.71308 + 0.255627i) q^{12} +(-2.28029 - 2.28029i) q^{13} +(-0.893856 + 2.49019i) q^{14} +(-0.869874 + 3.77403i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.891651 + 3.32769i) q^{17} +(-1.40961 - 2.64821i) q^{18} +(2.38005 + 1.37412i) q^{19} +(1.84297 + 1.26628i) q^{20} +(4.38775 - 1.32200i) q^{21} +(0.122214 - 0.122214i) q^{22} +(-1.68559 - 6.29072i) q^{23} +(-1.72087 + 0.196462i) q^{24} +(-3.14556 + 3.88657i) q^{25} +(2.79277 + 1.61241i) q^{26} +(-2.23382 + 4.69148i) q^{27} +(0.218891 - 2.63668i) q^{28} +0.840779 q^{29} +(-0.136558 - 3.87058i) q^{30} +(4.06710 + 7.04442i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.296083 - 0.0441815i) q^{33} -3.44508i q^{34} +(5.83935 + 0.949743i) q^{35} +(2.04699 + 2.19314i) q^{36} +(-1.58924 - 5.93113i) q^{37} +(-2.65460 - 0.711298i) q^{38} +(-0.633554 - 5.54949i) q^{39} +(-2.10791 - 0.746132i) q^{40} -10.1114i q^{41} +(-3.89608 + 2.41259i) q^{42} +(-3.19626 - 3.19626i) q^{43} +(-0.0864181 + 0.149681i) q^{44} +(-5.24745 + 4.17903i) q^{45} +(3.25632 + 5.64011i) q^{46} +(1.52745 - 0.409280i) q^{47} +(1.61139 - 0.635163i) q^{48} +(-2.45244 - 6.55634i) q^{49} +(2.03246 - 4.56827i) q^{50} +(-4.79585 + 3.55042i) q^{51} +(-3.11493 - 0.834642i) q^{52} +(-10.2236 - 2.73940i) q^{53} +(0.943463 - 5.10978i) q^{54} +(-0.318532 - 0.218858i) q^{55} +(0.470991 + 2.60349i) q^{56} +(1.74558 + 4.42849i) q^{57} +(-0.812130 + 0.217610i) q^{58} +(-4.86826 - 8.43207i) q^{59} +(1.13368 + 3.70334i) q^{60} +(6.03552 - 10.4538i) q^{61} +(-5.75174 - 5.75174i) q^{62} +(7.37375 + 2.93732i) q^{63} -1.00000i q^{64} +(2.40614 - 6.79761i) q^{65} +(0.297429 - 0.0339558i) q^{66} +(1.24153 + 0.332666i) q^{67} +(0.891651 + 3.32769i) q^{68} +(4.49564 - 10.3457i) q^{69} +(-5.88619 + 0.593954i) q^{70} +9.00908i q^{71} +(-2.54486 - 1.58861i) q^{72} +(-0.0189461 + 0.0707076i) q^{73} +(3.07018 + 5.31771i) q^{74} +(-8.45404 + 1.87860i) q^{75} +2.74825 q^{76} +(-0.0378323 + 0.455714i) q^{77} +(2.04828 + 5.19642i) q^{78} +(12.0207 + 6.94014i) q^{79} +(2.22920 + 0.175141i) q^{80} +(-8.08558 + 3.95264i) q^{81} +(2.61703 + 9.76690i) q^{82} +(5.33300 - 5.33300i) q^{83} +(3.13890 - 3.33876i) q^{84} +(-7.57424 + 1.40485i) q^{85} +(3.91461 + 2.26010i) q^{86} +(1.13990 + 0.906293i) q^{87} +(0.0447333 - 0.166947i) q^{88} +(-7.02662 + 12.1705i) q^{89} +(3.98703 - 5.39477i) q^{90} +(-8.39577 + 1.51886i) q^{91} +(-4.60513 - 4.60513i) q^{92} +(-2.07932 + 13.9346i) q^{93} +(-1.36948 + 0.790668i) q^{94} +(-0.481331 + 6.12638i) q^{95} +(-1.39209 + 1.03058i) q^{96} +(-6.33765 + 6.33765i) q^{97} +(4.06578 + 5.69820i) q^{98} +(-0.353793 - 0.379054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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