LMFDB - Embedded newform 920.2.bb.a.251.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [920,2,Mod(11,920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(920, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 0, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("920.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [480,2,0,-4,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			251.2
Character	$\chi$	$=$	920.251
Dual form			920.2.bb.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41405 + 0.0214454i) q^{2} +(-0.417492 - 2.90372i) q^{3} +(1.99908 - 0.0606497i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.652627 + 4.09706i) q^{6} +(2.59694 - 2.99703i) q^{7} +(-2.82550 + 0.128633i) q^{8} +(-5.37883 + 1.57937i) q^{9} +(1.36281 + 0.377808i) q^{10} +(1.45984 + 2.27156i) q^{11} +(-1.01071 - 5.77946i) q^{12} +(1.80368 - 1.56290i) q^{13} +(-3.60793 + 4.29364i) q^{14} +(-0.417492 + 2.90372i) q^{15} +(3.99264 - 0.242487i) q^{16} +(-6.50839 - 2.97228i) q^{17} +(7.57208 - 2.34866i) q^{18} +(4.78524 - 2.18535i) q^{19} +(-1.93519 - 0.505013i) q^{20} +(-9.78674 - 6.28955i) q^{21} +(-2.11301 - 3.18079i) q^{22} +(-2.91434 - 3.80876i) q^{23} +(1.55314 + 8.15077i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-2.51698 + 2.24870i) q^{26} +(3.17571 + 6.95383i) q^{27} +(5.00972 - 6.14880i) q^{28} +(-3.38405 - 1.54544i) q^{29} +(0.528084 - 4.11497i) q^{30} +(-8.17242 - 1.17502i) q^{31} +(-5.64060 + 0.428513i) q^{32} +(5.98650 - 5.18734i) q^{33} +(9.26694 + 4.06338i) q^{34} +(-3.33610 + 2.14398i) q^{35} +(-10.6569 + 3.48351i) q^{36} +(-2.31872 + 0.680838i) q^{37} +(-6.71971 + 3.19281i) q^{38} +(-5.29125 - 4.58489i) q^{39} +(2.74729 + 0.672613i) q^{40} +(7.76984 + 2.28143i) q^{41} +(13.9738 + 8.68387i) q^{42} +(4.51454 - 0.649093i) q^{43} +(3.05611 + 4.45249i) q^{44} +5.60591 q^{45} +(4.20270 + 5.32328i) q^{46} +2.82882i q^{47} +(-2.37101 - 11.4923i) q^{48} +(-1.24187 - 8.63743i) q^{49} +(-1.20117 - 0.746453i) q^{50} +(-5.91348 + 20.1395i) q^{51} +(3.51091 - 3.23375i) q^{52} +(6.73907 - 7.77731i) q^{53} +(-4.63974 - 9.76497i) q^{54} +(-0.760736 - 2.59083i) q^{55} +(-6.95213 + 8.80215i) q^{56} +(-8.34345 - 12.9827i) q^{57} +(4.81836 + 2.11276i) q^{58} +(0.524253 + 0.605020i) q^{59} +(-0.658491 + 5.83010i) q^{60} +(-0.543398 + 3.77942i) q^{61} +(11.5814 + 1.48627i) q^{62} +(-9.23509 + 20.2220i) q^{63} +(7.96691 - 0.726904i) q^{64} +(-2.17094 + 0.991434i) q^{65} +(-8.35398 + 7.46354i) q^{66} +(-8.78544 + 13.6704i) q^{67} +(-13.1911 - 5.54710i) q^{68} +(-9.84286 + 10.0526i) q^{69} +(4.67144 - 3.10325i) q^{70} +(5.47514 - 8.51948i) q^{71} +(14.9947 - 5.15440i) q^{72} +(1.80492 + 3.95221i) q^{73} +(3.26419 - 1.01247i) q^{74} +(1.21865 - 2.66848i) q^{75} +(9.43354 - 4.65891i) q^{76} +(10.5990 + 1.52391i) q^{77} +(7.58042 + 6.36980i) q^{78} +(-5.70803 - 6.58742i) q^{79} +(-3.89923 - 0.892193i) q^{80} +(4.71819 - 3.03220i) q^{81} +(-11.0359 - 3.05943i) q^{82} +(3.96423 + 13.5009i) q^{83} +(-19.9459 - 11.9798i) q^{84} +(5.40737 + 4.68551i) q^{85} +(-6.36987 + 1.01467i) q^{86} +(-3.07472 + 10.4716i) q^{87} +(-4.41698 - 6.23051i) q^{88} +(-17.0823 + 2.45607i) q^{89} +(-7.92705 + 0.120221i) q^{90} -9.46443i q^{91} +(-6.05700 - 7.43726i) q^{92} +24.2210i q^{93} +(-0.0606650 - 4.00009i) q^{94} +(-5.20709 + 0.748667i) q^{95} +(3.59919 + 16.1998i) q^{96} +(-2.42670 + 8.26459i) q^{97} +(1.94131 + 12.1871i) q^{98} +(-11.4399 - 9.91271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41405	+	0.0214454i	−0.999885	+	0.0151642i
$2$	−1.41405	+	0.0214454i	−0.999885	+	0.0151642i
$3$	−0.417492	−	2.90372i	−0.241039	−	1.67647i	−0.646934	−	0.762546i	$-0.723949\pi$
$3$	−0.417492	−	2.90372i	−0.241039	−	1.67647i	0.405895	−	0.913920i	$-0.366960\pi$
$4$	1.99908	−	0.0606497i	0.999540	−	0.0303249i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$6$	0.652627	+	4.09706i	0.266434	+	1.67262i
$7$	2.59694	−	2.99703i	0.981550	−	1.13277i	−0.00959057	−	0.999954i	$-0.503053\pi$
$7$	2.59694	−	2.99703i	0.981550	−	1.13277i	0.991141	−	0.132815i	$-0.0424017\pi$
$8$	−2.82550	+	0.128633i	−0.998965	+	0.0454786i
$9$	−5.37883	+	1.57937i	−1.79294	+	0.526456i
$10$	1.36281	+	0.377808i	0.430960	+	0.119473i
$11$	1.45984	+	2.27156i	0.440159	+	0.684901i	0.988477	−	0.151369i	$-0.0483682\pi$
$11$	1.45984	+	2.27156i	0.440159	+	0.684901i	−0.548318	+	0.836270i	$0.684732\pi$
$12$	−1.01071	−	5.77946i	−0.291767	−	1.66839i
$13$	1.80368	−	1.56290i	0.500251	−	0.433470i	−0.367830	−	0.929893i	$-0.619899\pi$
$13$	1.80368	−	1.56290i	0.500251	−	0.433470i	0.868081	+	0.496423i	$0.165354\pi$
$14$	−3.60793	+	4.29364i	−0.964260	+	1.14752i
$15$	−0.417492	+	2.90372i	−0.107796	+	0.749738i
$16$	3.99264	−	0.242487i	0.998161	−	0.0606218i
$17$	−6.50839	−	2.97228i	−1.57852	−	0.720884i	−0.582737	−	0.812661i	$-0.698018\pi$
$17$	−6.50839	−	2.97228i	−1.57852	−	0.720884i	−0.995780	+	0.0917766i	$0.970745\pi$
$18$	7.57208	−	2.34866i	1.78476	−	0.553584i
$19$	4.78524	−	2.18535i	1.09781	−	0.501353i	0.217648	−	0.976027i	$-0.430161\pi$
$19$	4.78524	−	2.18535i	1.09781	−	0.501353i	0.880162	+	0.474674i	$0.157434\pi$
$20$	−1.93519	−	0.505013i	−0.432722	−	0.112924i
$21$	−9.78674	−	6.28955i	−2.13564	−	1.37249i
$22$	−2.11301	−	3.18079i	−0.450494	−	0.678147i
$23$	−2.91434	−	3.80876i	−0.607682	−	0.794181i
$23$	−2.91434	−	3.80876i	−0.607682	−	0.794181i
$24$	1.55314	+	8.15077i	0.317033	+	1.66377i
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−2.51698	+	2.24870i	−0.493620	+	0.441006i
$27$	3.17571	+	6.95383i	0.611165	+	1.33827i
$28$	5.00972	−	6.14880i	0.946748	−	1.16201i
$29$	−3.38405	−	1.54544i	−0.628402	−	0.286982i	0.0756452	−	0.997135i	$-0.475898\pi$
$29$	−3.38405	−	1.54544i	−0.628402	−	0.286982i	−0.704047	+	0.710153i	$0.748626\pi$
$30$	0.528084	−	4.11497i	0.0964145	−	0.751287i
$31$	−8.17242	−	1.17502i	−1.46781	−	0.211039i	−0.638411	−	0.769696i	$-0.720408\pi$
$31$	−8.17242	−	1.17502i	−1.46781	−	0.211039i	−0.829399	+	0.558656i	$0.811317\pi$
$32$	−5.64060	+	0.428513i	−0.997127	+	0.0757511i
$33$	5.98650	−	5.18734i	1.04212	−	0.902999i
$34$	9.26694	+	4.06338i	1.58927	+	0.696865i
$35$	−3.33610	+	2.14398i	−0.563904	+	0.362399i
$36$	−10.6569	+	3.48351i	−1.77616	+	0.580585i
$37$	−2.31872	+	0.680838i	−0.381195	+	0.111929i	−0.466716	−	0.884407i	$-0.654563\pi$
$37$	−2.31872	+	0.680838i	−0.381195	+	0.111929i	0.0855203	+	0.996336i	$0.472745\pi$
$38$	−6.71971	+	3.19281i	−1.09008	+	0.517943i
$39$	−5.29125	−	4.58489i	−0.847278	−	0.734170i
$40$	2.74729	+	0.672613i	0.434384	+	0.106349i
$41$	7.76984	+	2.28143i	1.21344	+	0.356299i	0.824979	−	0.565164i	$-0.191187\pi$
$41$	7.76984	+	2.28143i	1.21344	+	0.356299i	0.388466	+	0.921463i	$0.373005\pi$
$42$	13.9738	+	8.68387i	2.15621	+	1.33995i
$43$	4.51454	−	0.649093i	0.688461	−	0.0989858i	0.210799	−	0.977529i	$-0.432393\pi$
$43$	4.51454	−	0.649093i	0.688461	−	0.0989858i	0.477662	+	0.878544i	$0.341484\pi$
$44$	3.05611	+	4.45249i	0.460726	+	0.671238i
$45$	5.60591			0.835680
$46$	4.20270	+	5.32328i	0.619655	+	0.784874i
$47$			2.82882i			0.412625i	0.978486	+	0.206313i	$0.0661464\pi$
$47$			2.82882i			0.412625i	−0.978486	+	0.206313i	$0.933854\pi$
$48$	−2.37101	−	11.4923i	−0.342226	−	1.65877i
$49$	−1.24187	−	8.63743i	−0.177411	−	1.23392i
$50$	−1.20117	−	0.746453i	−0.169871	−	0.105564i
$51$	−5.91348	+	20.1395i	−0.828053	+	2.82009i
$52$	3.51091	−	3.23375i	0.486876	−	0.448441i
$53$	6.73907	−	7.77731i	0.925683	−	1.06830i	−0.0718021	−	0.997419i	$-0.522875\pi$
$53$	6.73907	−	7.77731i	0.925683	−	1.06830i	0.997485	−	0.0708763i	$-0.0225796\pi$
$54$	−4.63974	−	9.76497i	−0.631389	−	1.32884i
$55$	−0.760736	−	2.59083i	−0.102578	−	0.349347i
$56$	−6.95213	+	8.80215i	−0.929018	+	1.17624i
$57$	−8.34345	−	12.9827i	−1.10512	−	1.71960i
$58$	4.81836	+	2.11276i	0.632681	+	0.277419i
$59$	0.524253	+	0.605020i	0.0682519	+	0.0787669i	0.788849	−	0.614587i	$-0.210678\pi$
$59$	0.524253	+	0.605020i	0.0682519	+	0.0787669i	−0.720597	+	0.693354i	$0.756132\pi$
$60$	−0.658491	+	5.83010i	−0.0850108	+	0.752662i
$61$	−0.543398	+	3.77942i	−0.0695750	+	0.483905i	0.925007	+	0.379950i	$0.124059\pi$
$61$	−0.543398	+	3.77942i	−0.0695750	+	0.483905i	−0.994582	+	0.103955i	$0.966850\pi$
$62$	11.5814	+	1.48627i	1.47084	+	0.188757i
$63$	−9.23509	+	20.2220i	−1.16351	+	2.54774i
$64$	7.96691	−	0.726904i	0.995863	−	0.0908630i
$65$	−2.17094	+	0.991434i	−0.269272	+	0.122972i
$66$	−8.35398	+	7.46354i	−1.02830	+	0.918698i
$67$	−8.78544	+	13.6704i	−1.07331	+	1.67011i	−0.434705	+	0.900573i	$0.643148\pi$
$67$	−8.78544	+	13.6704i	−1.07331	+	1.67011i	−0.638607	+	0.769533i	$0.720489\pi$
$68$	−13.1911	−	5.54710i	−1.59965	−	0.672685i
$69$	−9.84286	+	10.0526i	−1.18494	+	1.21019i
$70$	4.67144	−	3.10325i	0.558344	−	0.370909i
$71$	5.47514	−	8.51948i	0.649779	−	1.01108i	−0.347523	−	0.937671i	$-0.612977\pi$
$71$	5.47514	−	8.51948i	0.649779	−	1.01108i	0.997302	−	0.0734047i	$-0.0233865\pi$
$72$	14.9947	−	5.15440i	1.76715	−	0.607452i
$73$	1.80492	+	3.95221i	0.211249	+	0.462572i	0.985362	−	0.170477i	$-0.0545308\pi$
$73$	1.80492	+	3.95221i	0.211249	+	0.462572i	−0.774112	+	0.633048i	$0.781803\pi$
$74$	3.26419	−	1.01247i	0.379454	−	0.117697i
$75$	1.21865	−	2.66848i	0.140718	−	0.308130i
$76$	9.43354	−	4.65891i	1.08210	−	0.534413i
$77$	10.5990	+	1.52391i	1.20787	+	0.173666i
$78$	7.58042	+	6.36980i	0.858313	+	0.721238i
$79$	−5.70803	−	6.58742i	−0.642204	−	0.741143i	0.337559	−	0.941304i	$-0.390399\pi$
$79$	−5.70803	−	6.58742i	−0.642204	−	0.741143i	−0.979763	+	0.200161i	$0.935853\pi$
$80$	−3.89923	−	0.892193i	−0.435947	−	0.0997502i
$81$	4.71819	−	3.03220i	0.524243	−	0.336911i
$82$	−11.0359	−	3.05943i	−1.21871	−	0.337858i
$83$	3.96423	+	13.5009i	0.435131	+	1.48192i	0.827160	+	0.561967i	$0.189955\pi$
$83$	3.96423	+	13.5009i	0.435131	+	1.48192i	−0.392029	+	0.919953i	$0.628227\pi$
$84$	−19.9459	−	11.9798i	−2.17628	−	1.30710i
$85$	5.40737	+	4.68551i	0.586511	+	0.508215i
$86$	−6.36987	+	1.01467i	−0.686881	+	0.109414i
$87$	−3.07472	+	10.4716i	−0.329645	+	1.12267i
$88$	−4.41698	−	6.23051i	−0.470852	−	0.664174i
$89$	−17.0823	+	2.45607i	−1.81072	+	0.260343i	−0.962885	−	0.269913i	$-0.913005\pi$
$89$	−17.0823	+	2.45607i	−1.81072	+	0.260343i	−0.847838	+	0.530256i	$0.822096\pi$
$90$	−7.92705	+	0.120221i	−0.835584	+	0.0126724i
$91$		−	9.46443i		−	0.992141i
$92$	−6.05700	−	7.43726i	−0.631486	−	0.775388i
$93$			24.2210i			2.51160i
$94$	−0.0606650	−	4.00009i	−0.00625712	−	0.412578i
$95$	−5.20709	+	0.748667i	−0.534236	+	0.0768116i
$96$	3.59919	+	16.1998i	0.367341	+	1.65339i
$97$	−2.42670	+	8.26459i	−0.246394	+	0.839142i	0.739697	+	0.672940i	$0.234969\pi$
$97$	−2.42670	+	8.26459i	−0.246394	+	0.839142i	−0.986092	+	0.166202i	$0.946850\pi$
$98$	1.94131	+	12.1871i	0.196102	+	1.23109i
$99$	−11.4399	−	9.91271i	−1.14975	−	0.996265i
$100$	1.71452	+	1.02976i	0.171452	+	0.102976i
$101$	0.816787	+	2.78172i	0.0812733	+	0.276792i	0.990096	−	0.140391i	$-0.0448359\pi$
$101$	0.816787	+	2.78172i	0.0812733	+	0.276792i	−0.908823	+	0.417182i	$0.863018\pi$
$102$	7.93007	−	28.6051i	0.785194	−	2.83232i
$103$	−9.50954	+	6.11141i	−0.937003	+	0.602175i	−0.917544	−	0.397635i	$-0.869831\pi$
$103$	−9.50954	+	6.11141i	−0.937003	+	0.602175i	−0.0194595	+	0.999811i	$0.506195\pi$
$104$	−4.89526	+	4.64798i	−0.480020	+	0.455772i
$105$	7.61833	+	8.79203i	0.743473	+	0.858014i
$106$	−9.36261	+	11.1420i	−0.909377	+	1.08221i
$107$	7.97864	+	1.14716i	0.771324	+	0.110900i	0.516730	−	0.856148i	$-0.327149\pi$
$107$	7.97864	+	1.14716i	0.771324	+	0.110900i	0.254594	+	0.967048i	$0.418058\pi$
$108$	6.77024	+	13.7087i	0.651467	+	1.31912i
$109$	0.538879	−	1.17998i	0.0516153	−	0.113022i	−0.882067	−	0.471123i	$-0.843849\pi$
$109$	0.538879	−	1.17998i	0.0516153	−	0.113022i	0.933683	+	0.358102i	$0.116576\pi$
$110$	1.13128	+	3.64725i	0.107863	+	0.347752i
$111$	2.94501	+	6.44868i	0.279528	+	0.612082i
$112$	9.64191	−	12.5958i	0.911074	−	1.19019i
$113$	9.28256	−	14.4440i	0.873230	−	1.35877i	−0.0595116	−	0.998228i	$-0.518954\pi$
$113$	9.28256	−	14.4440i	0.873230	−	1.35877i	0.932742	−	0.360545i	$-0.117409\pi$
$114$	12.0765	+	18.1792i	1.13107	+	1.70264i
$115$	1.72324	+	4.47554i	0.160693	+	0.417346i
$116$	−6.85871	−	2.88422i	−0.636816	−	0.267793i
$117$	−7.23331	+	11.2552i	−0.668719	+	1.04055i
$118$	−0.754295	−	0.844286i	−0.0694385	−	0.0777229i
$119$	−25.8099	+	11.7870i	−2.36599	+	1.08051i
$120$	0.806111	−	8.25818i	0.0735875	−	0.753865i
$121$	1.54073	−	3.37372i	0.140066	−	0.306702i
$122$	0.687341	−	5.35594i	0.0622290	−	0.484904i
$123$	3.38079	−	23.5139i	0.304836	−	2.12018i
$124$	−16.4086	−	1.85330i	−1.47353	−	0.166431i
$125$	−0.654861	−	0.755750i	−0.0585725	−	0.0675963i
$126$	12.6252	−	28.7930i	1.12474	−	2.56509i
$127$	−2.14629	−	3.33970i	−0.190453	−	0.296350i	0.732875	−	0.680363i	$-0.238178\pi$
$127$	−2.14629	−	3.33970i	−0.190453	−	0.296350i	−0.923328	+	0.384013i	$0.874542\pi$
$128$	−11.2500	+	1.19873i	−0.994371	+	0.105954i
$129$	−3.76957	−	12.8380i	−0.331893	−	1.13032i
$130$	3.04856	−	1.44850i	0.267376	−	0.127041i
$131$	−2.91737	+	3.36682i	−0.254892	+	0.294161i	−0.868745	−	0.495259i	$-0.835073\pi$
$131$	−2.91737	+	3.36682i	−0.254892	+	0.294161i	0.613854	+	0.789420i	$0.289619\pi$
$132$	11.6529	−	10.7330i	1.01425	−	0.934186i
$133$	5.87744	−	20.0167i	0.509638	−	1.73567i
$134$	12.1299	−	19.5191i	1.04786	−	1.68619i
$135$	−1.08795	−	7.56685i	−0.0936358	−	0.651251i
$136$	18.7718	+	7.56099i	1.60967	+	0.648350i
$137$		−	0.380632i		−	0.0325196i	−0.999868	−	0.0162598i	$-0.994824\pi$
$137$		−	0.380632i		−	0.0325196i	0.999868	−	0.0162598i	$-0.00517588\pi$
$138$	13.7027	−	14.4259i	1.16645	−	1.22802i
$139$	7.59377			0.644095			0.322048	−	0.946723i	$-0.395629\pi$
$139$	7.59377			0.644095			0.322048	+	0.946723i	$0.395629\pi$
$140$	−6.53911	+	4.48833i	−0.552655	+	0.379333i
$141$	8.21410	−	1.18101i	0.691752	−	0.0994590i
$142$	−7.55942	+	12.1644i	−0.634372	+	1.02081i
$143$	6.18330	+	1.81558i	0.517074	+	0.151827i
$144$	−21.0928	+	7.61015i	−1.75773	+	0.634179i
$145$	2.81157	+	2.43624i	0.233488	+	0.202319i
$146$	−2.63700	−	5.54992i	−0.218240	−	0.459315i
$147$	−24.5622	+	7.21212i	−2.02586	+	0.594846i
$148$	−4.59402	+	1.50168i	−0.377626	+	0.123437i
$149$	12.5592	−	8.07132i	1.02889	−	0.661228i	0.0866762	−	0.996237i	$-0.472375\pi$
$149$	12.5592	−	8.07132i	1.02889	−	0.661228i	0.942215	+	0.335008i	$0.108739\pi$
$150$	−1.66601	+	3.79950i	−0.136029	+	0.310228i
$151$	11.8155	−	10.2382i	0.961529	−	0.833169i	−0.0245076	−	0.999700i	$-0.507802\pi$
$151$	11.8155	−	10.2382i	0.961529	−	0.833169i	0.986036	+	0.166530i	$0.0532563\pi$
$152$	−13.2396	+	6.79024i	−1.07387	+	0.550761i
$153$	39.7019	+	5.70827i	3.20971	+	0.461486i
$154$	−15.0203	−	1.92759i	−1.21037	−	0.155329i
$155$	7.51034	+	3.42986i	0.603245	+	0.275493i
$156$	−10.8557	−	8.84465i	−0.869152	−	0.708139i
$157$	−8.62870	−	18.8942i	−0.688645	−	1.50792i	−0.853216	−	0.521557i	$-0.825351\pi$
$157$	−8.62870	−	18.8942i	−0.688645	−	1.50792i	0.164571	−	0.986365i	$-0.447376\pi$
$158$	8.21272	+	9.19254i	0.653369	+	0.731319i
$159$	−25.3967	−	16.3214i	−2.01409	−	1.29437i
$160$	5.53284	+	1.17799i	0.437410	+	0.0931279i
$161$	−18.9833	−	1.15676i	−1.49609	−	0.0911651i
$162$	−6.60673	+	4.38886i	−0.519074	+	0.344822i
$163$	−5.21835	−	3.35363i	−0.408733	−	0.262677i	0.320079	−	0.947391i	$-0.396291\pi$
$163$	−5.21835	−	3.35363i	−0.408733	−	0.262677i	−0.728812	+	0.684714i	$0.759927\pi$
$164$	15.6709	+	4.08952i	1.22369	+	0.319338i
$165$	−7.20545	+	3.29062i	−0.560944	+	0.256174i
$166$	−5.89516	−	19.0060i	−0.457553	−	1.47515i
$167$	0.149124	+	0.0681026i	0.0115396	+	0.00526994i	0.421176	−	0.906979i	$-0.361617\pi$
$167$	0.149124	+	0.0681026i	0.0115396	+	0.00526994i	−0.409637	+	0.912249i	$0.634345\pi$
$168$	28.4615	+	16.5122i	2.19585	+	1.27395i
$169$	−1.03948	+	7.22974i	−0.0799600	+	0.556134i
$170$	−7.74677	−	6.50959i	−0.594150	−	0.499262i
$171$	−22.2876	+	19.3123i	−1.70437	+	1.47685i
$172$	8.98556	−	1.57139i	0.685143	−	0.119818i
$173$	0.159051	+	0.247488i	0.0120924	+	0.0188161i	0.847247	−	0.531199i	$-0.178258\pi$
$173$	0.159051	+	0.247488i	0.0120924	+	0.0188161i	−0.835155	+	0.550015i	$0.814622\pi$
$174$	4.12325	−	14.8732i	0.312583	−	1.12754i
$175$	3.80500	−	1.11725i	0.287631	−	0.0844560i
$176$	6.37945	+	8.71553i	0.480869	+	0.656958i
$177$	1.53794	−	1.77488i	0.115599	−	0.133408i
$178$	24.1026	−	3.83934i	1.80657	−	0.287771i
$179$	15.1020	+	4.43435i	1.12878	+	0.331439i	0.792227	−	0.610227i	$-0.208922\pi$
$179$	15.1020	+	4.43435i	1.12878	+	0.331439i	0.336550	+	0.941666i	$0.390740\pi$
$180$	11.2067	−	0.339997i	0.835296	−	0.0253419i
$181$	1.10560	+	7.68959i	0.0821783	+	0.571562i	0.988758	+	0.149527i	$0.0477751\pi$
$181$	1.10560	+	7.68959i	0.0821783	+	0.571562i	−0.906579	+	0.422035i	$0.861316\pi$
$182$	0.202968	+	13.3832i	0.0150450	+	0.992027i
$183$	11.2012			0.828020
$184$	8.72440	+	10.3868i	0.643171	+	0.765723i
$185$	2.41661			0.177673
$186$	−0.519429	−	34.2498i	−0.0380864	−	2.51131i
$187$	−2.74951	−	19.1232i	−0.201064	−	1.39843i
$188$	0.171567	+	5.65503i	0.0125128	+	0.412436i
$189$	29.0879	+	8.54099i	2.11584	+	0.621265i
$190$	7.34704	−	1.17032i	0.533010	−	0.0849040i
$191$	−1.79097	+	2.06689i	−0.129590	+	0.149555i	−0.816836	−	0.576870i	$-0.804274\pi$
$191$	−1.79097	+	2.06689i	−0.129590	+	0.149555i	0.687246	+	0.726425i	$0.258819\pi$
$192$	−5.43685	−	22.8302i	−0.392371	−	1.64763i
$193$	1.96732	−	0.577657i	0.141611	−	0.0415806i	−0.210159	−	0.977667i	$-0.567398\pi$
$193$	1.96732	−	0.577657i	0.141611	−	0.0415806i	0.351770	+	0.936087i	$0.385580\pi$
$194$	3.25424	−	11.7386i	0.233641	−	0.842782i
$195$	3.78520	+	5.88989i	0.271064	+	0.421784i
$196$	−3.00647	−	17.1916i	−0.214748	−	1.22797i
$197$	−0.118757	+	0.102904i	−0.00846109	+	0.00733158i	−0.659081	−	0.752072i	$-0.729055\pi$
$197$	−0.118757	+	0.102904i	−0.00846109	+	0.00733158i	0.650620	+	0.759404i	$0.274509\pi$
$198$	16.3891	+	13.7717i	1.16473	+	0.978715i
$199$	2.62241	−	18.2392i	0.185898	−	1.29295i	−0.656597	−	0.754241i	$-0.728005\pi$
$199$	2.62241	−	18.2392i	0.185898	−	1.29295i	0.842495	−	0.538704i	$-0.181086\pi$
$200$	−2.44651	−	1.41937i	−0.172994	−	0.100364i
$201$	43.3629	+	19.8032i	3.05859	+	1.39681i
$202$	−1.21463	−	3.91598i	−0.0854613	−	0.275527i
$203$	−13.4199	+	6.12866i	−0.941892	+	0.430148i
$204$	−10.6001	+	40.6191i	−0.742154	+	2.84390i
$205$	−6.81235	−	4.37803i	−0.475795	−	0.305775i
$206$	13.3159	−	8.84578i	0.927764	−	0.616315i
$207$	21.6912	+	15.8839i	1.50764	+	1.10400i
$208$	6.82247	−	6.67746i	0.473053	−	0.462999i
$209$	11.9498	+	7.67970i	0.826588	+	0.531216i
$210$	−10.9613	−	12.2690i	−0.756399	−	0.846641i
$211$	−4.89813	−	10.7254i	−0.337201	−	0.738367i	0.662744	−	0.748846i	$-0.269392\pi$
$211$	−4.89813	−	10.7254i	−0.337201	−	0.738367i	−0.999945	+	0.0104787i	$0.996664\pi$
$212$	13.0003	−	15.9562i	0.892861	−	1.09588i
$213$	−27.0240	−	12.3415i	−1.85166	−	0.845623i
$214$	−11.3068	−	1.45103i	−0.772917	−	0.0991904i
$215$	−4.51454	−	0.649093i	−0.307889	−	0.0442678i
$216$	−9.86746	−	19.2396i	−0.671395	−	1.30909i
$217$	−24.7448	+	21.4415i	−1.67979	+	1.45554i
$218$	−0.736698	+	1.68011i	−0.0498955	+	0.113791i
$219$	10.7226	−	6.89099i	0.724566	−	0.465650i
$220$	−1.67791	−	5.13314i	−0.113124	−	0.346076i
$221$	−16.3844	+	4.81090i	−1.10214	+	0.323616i
$222$	−4.30270	−	9.05561i	−0.288778	−	0.607773i
$223$	11.8047	+	10.2288i	0.790500	+	0.684972i	0.953413	−	0.301668i	$-0.0975435\pi$
$223$	11.8047	+	10.2288i	0.790500	+	0.684972i	−0.162913	+	0.986640i	$0.552089\pi$
$224$	−13.3640	+	18.0178i	−0.892921	+	1.20387i
$225$	−5.37883	−	1.57937i	−0.358589	−	0.105291i
$226$	−12.8163	+	20.6236i	−0.852525	+	1.37186i
$227$	−6.86109	+	0.986475i	−0.455386	+	0.0654747i	−0.366191	−	0.930540i	$-0.619338\pi$
$227$	−6.86109	+	0.986475i	−0.455386	+	0.0654747i	−0.0891948	+	0.996014i	$0.528429\pi$
$228$	−17.4666	−	25.4473i	−1.15675	−	1.68529i
$229$	13.4293			0.887433			0.443717	−	0.896167i	$-0.353660\pi$
$229$	13.4293			0.887433			0.443717	+	0.896167i	$0.353660\pi$
$230$	−2.53272	−	6.29169i	−0.167003	−	0.414861i
$231$		−	31.4129i		−	2.06682i
$232$	9.76042	+	3.93135i	0.640803	+	0.258106i
$233$	−3.44109	−	23.9333i	−0.225433	−	1.56792i	−0.716993	−	0.697080i	$-0.754482\pi$
$233$	−3.44109	−	23.9333i	−0.225433	−	1.56792i	0.491560	−	0.870844i	$-0.336427\pi$
$234$	9.98689	−	16.0706i	0.652864	−	1.05057i
$235$	0.796970	−	2.71423i	0.0519886	−	0.177057i
$236$	1.08472	+	1.17769i	0.0706091	+	0.0766609i
$237$	−16.7450	+	19.3248i	−1.08770	+	1.25528i
$238$	36.2437	−	17.2209i	2.34933	−	1.11626i
$239$	3.66216	+	12.4722i	0.236886	+	0.806759i	0.989024	+	0.147754i	$0.0472043\pi$
$239$	3.66216	+	12.4722i	0.236886	+	0.806759i	−0.752138	+	0.659005i	$0.770978\pi$
$240$	−0.962783	+	11.6948i	−0.0621473	+	0.754894i
$241$	−7.57875	−	11.7928i	−0.488190	−	0.759639i	0.506534	−	0.862220i	$-0.330926\pi$
$241$	−7.57875	−	11.7928i	−0.488190	−	0.759639i	−0.994725	+	0.102581i	$0.967290\pi$
$242$	−2.10632	+	4.80366i	−0.135399	+	0.308791i
$243$	4.24410	+	4.89795i	0.272259	+	0.314204i
$244$	−0.857075	+	7.58831i	−0.0548686	+	0.485792i
$245$	−1.24187	+	8.63743i	−0.0793405	+	0.551825i
$246$	−4.27635	+	33.3224i	−0.272650	+	2.12456i
$247$	5.21557	−	11.4205i	0.331859	−	0.726670i
$248$	23.2423	+	2.26877i	1.47589	+	0.144067i
$249$	37.5479	−	17.1476i	2.37950	−	1.08668i
$250$	0.942214	+	1.05462i	0.0595908	+	0.0667003i
$251$	7.24186	−	11.2686i	0.457102	−	0.711265i	−0.533835	−	0.845588i	$-0.679250\pi$
$251$	7.24186	−	11.2686i	0.457102	−	0.711265i	0.990938	+	0.134324i	$0.0428862\pi$
$252$	−17.2352	+	40.9856i	−1.08572	+	2.58185i
$253$	4.39734	−	12.1803i	0.276458	−	0.765767i
$254$	3.10659	+	4.67647i	0.194925	+	0.293428i
$255$	11.3479	−	17.6577i	0.710633	−	1.10577i
$256$	15.8824	−	1.93633i	0.992650	−	0.121021i
$257$	−5.88964	−	12.8965i	−0.367386	−	0.804463i	−0.999561	−	0.0296371i	$-0.990565\pi$
$257$	−5.88964	−	12.8965i	−0.367386	−	0.804463i	0.632175	−	0.774826i	$-0.282162\pi$
$258$	5.60569	+	18.0727i	0.348995	+	1.12516i
$259$	−3.98109	+	8.71736i	−0.247373	+	0.541671i
$260$	−4.27975	+	2.11362i	−0.265419	+	0.131081i
$261$	20.6431	+	2.96802i	1.27777	+	0.183716i
$262$	4.05310	−	4.82342i	0.250402	−	0.297992i
$263$	−1.14086	−	1.31662i	−0.0703485	−	0.0811865i	0.719484	−	0.694509i	$-0.244378\pi$
$263$	−1.14086	−	1.31662i	−0.0703485	−	0.0811865i	−0.789833	+	0.613322i	$0.789833\pi$
$264$	−16.2476	+	15.4269i	−0.999971	+	0.949459i
$265$	−8.65721	+	5.56365i	−0.531808	+	0.341773i
$266$	−7.88173	+	28.4307i	−0.483260	+	1.74320i
$267$	14.2635	+	48.5770i	0.872911	+	2.97286i
$268$	−16.7337	+	27.8611i	−1.02217	+	1.70189i
$269$	−4.89624	−	4.24261i	−0.298529	−	0.258677i	0.492697	−	0.870201i	$-0.336011\pi$
$269$	−4.89624	−	4.24261i	−0.298529	−	0.258677i	−0.791226	+	0.611524i	$0.790557\pi$
$270$	1.70069	+	10.6766i	0.103501	+	0.649756i
$271$	−5.41170	+	18.4306i	−0.328737	+	1.11958i	0.614903	+	0.788603i	$0.289195\pi$
$271$	−5.41170	+	18.4306i	−0.328737	+	1.11958i	−0.943640	+	0.330974i	$0.892623\pi$
$272$	−26.7064	−	10.2891i	−1.61931	−	0.623866i
$273$	−27.4821	+	3.95133i	−1.66329	+	0.239145i
$274$	0.00816280	+	0.538233i	0.000493133	+	0.0325159i
$275$			2.70021i			0.162829i
$276$	−19.0670	+	20.6928i	−1.14770	+	1.24556i
$277$		−	24.1858i		−	1.45319i	−0.687068	−	0.726593i	$-0.741103\pi$
$277$		−	24.1858i		−	1.45319i	0.687068	−	0.726593i	$-0.258897\pi$
$278$	−10.7380	+	0.162851i	−0.644021	+	0.00976717i
$279$	45.8139	−	6.58704i	2.74281	−	0.394356i
$280$	9.15038	−	6.48696i	0.546840	−	0.387670i
$281$	1.99525	−	6.79520i	0.119027	−	0.405368i	−0.878328	−	0.478059i	$-0.841341\pi$
$281$	1.99525	−	6.79520i	0.119027	−	0.405368i	0.997354	+	0.0726912i	$0.0231587\pi$
$282$	−11.5898	+	1.84616i	−0.690164	+	0.109937i
$283$	9.33245	+	8.08661i	0.554756	+	0.480699i	0.886537	−	0.462657i	$-0.153104\pi$
$283$	9.33245	+	8.08661i	0.554756	+	0.480699i	−0.331781	+	0.943356i	$0.607649\pi$
$284$	10.4285	−	17.3632i	0.618820	−	1.03032i
$285$	4.34784	+	14.8074i	0.257544	+	0.877114i
$286$	−8.78244	−	2.43472i	−0.519317	−	0.143968i
$287$	27.0153	−	17.3617i	1.59466	−	1.02483i
$288$	29.6631	−	11.2135i	1.74791	−	0.660761i
$289$	22.3920	+	25.8418i	1.31718	+	1.52011i
$290$	−4.02795	−	3.38467i	−0.236529	−	0.198755i
$291$	25.0112	+	3.59607i	1.46618	+	0.210805i
$292$	3.84787	+	7.79132i	0.225180	+	0.455953i
$293$	−1.27492	+	2.79168i	−0.0744815	+	0.163092i	−0.943210	−	0.332197i	$-0.892210\pi$
$293$	−1.27492	+	2.79168i	−0.0744815	+	0.163092i	0.868729	+	0.495288i	$0.164938\pi$
$294$	34.5776	−	10.7251i	2.01661	−	0.625498i
$295$	−0.332563	−	0.728212i	−0.0193626	−	0.0423981i
$296$	6.46397	−	2.22197i	0.375711	−	0.129150i
$297$	−11.1600	+	17.3653i	−0.647569	+	1.00764i
$298$	−17.5863	+	11.6826i	−1.01875	+	0.676755i
$299$	−11.2092	−	2.31497i	−0.648247	−	0.133878i
$300$	2.27435	−	5.40842i	0.131309	−	0.312255i
$301$	9.77864	−	15.2159i	0.563631	−	0.877027i
$302$	−16.4881	+	14.7307i	−0.948784	+	0.847654i
$303$	7.73635	−	3.53307i	0.444442	−	0.202970i
$304$	18.5758	−	9.88567i	1.06540	−	0.566982i
$305$	1.58617	−	3.47323i	0.0908239	−	0.198877i
$306$	−56.2629	−	7.22036i	−3.21634	−	0.412761i
$307$	3.35843	−	23.3584i	0.191676	−	1.33313i	−0.635896	−	0.771775i	$-0.719369\pi$
$307$	3.35843	−	23.3584i	0.191676	−	1.33313i	0.827572	−	0.561360i	$-0.189722\pi$
$308$	21.2807	+	2.40359i	1.21258	+	0.136957i
$309$	21.7160	+	25.0616i	1.23538	+	1.42571i
$310$	−10.6936	−	4.68893i	−0.607353	−	0.266313i
$311$	−0.336387	−	0.523428i	−0.0190748	−	0.0296809i	0.831585	−	0.555397i	$-0.187434\pi$
$311$	−0.336387	−	0.523428i	−0.0190748	−	0.0296809i	−0.850660	+	0.525716i	$0.823797\pi$
$312$	15.5402	+	12.2740i	0.879790	+	0.694878i
$313$	−0.772329	−	2.63031i	−0.0436546	−	0.148674i	0.934782	−	0.355223i	$-0.115595\pi$
$313$	−0.772329	−	2.63031i	−0.0436546	−	0.148674i	−0.978436	+	0.206549i	$0.933777\pi$
$314$	12.6066	+	26.5323i	0.711432	+	1.49731i
$315$	14.5582	−	16.8011i	0.820262	−	0.946633i
$316$	−11.8103	−	12.8226i	−0.664384	−	0.721327i
$317$	−0.192504	+	0.655608i	−0.0108121	+	0.0368226i	−0.964722	−	0.263269i	$-0.915199\pi$
$317$	−0.192504	+	0.655608i	−0.0108121	+	0.0368226i	0.953910	+	0.300092i	$0.0970174\pi$
$318$	36.2622	+	22.5347i	2.03348	+	1.26368i
$319$	−1.42961	−	9.94316i	−0.0800428	−	0.556710i
$320$	−7.84898	−	1.54708i	−0.438772	−	0.0864843i
$321$		−	23.6467i		−	1.31983i
$322$	26.8682	+	1.22861i	1.49730	+	0.0684676i
$323$	−37.6397			−2.09433
$324$	9.24814	−	6.34776i	0.513785	−	0.352653i
$325$	2.36232	−	0.339650i	0.131038	−	0.0188404i
$326$	7.45094	+	4.63030i	0.412669	+	0.256448i
$327$	−3.65132	−	1.07212i	−0.201918	−	0.0592886i
$328$	−22.2471	−	5.44672i	−1.22839	−	0.300745i
$329$	8.47804	+	7.34626i	0.467409	+	0.405012i
$330$	10.1183	−	4.80763i	0.556994	−	0.264651i
$331$	1.28006	−	0.375858i	0.0703582	−	0.0206590i	−0.246364	−	0.969177i	$-0.579236\pi$
$331$	1.28006	−	0.375858i	0.0703582	−	0.0206590i	0.316722	+	0.948518i	$0.397418\pi$
$332$	8.74364	+	26.7490i	0.479870	+	1.46804i
$333$	11.3967	−	7.32423i	0.624537	−	0.401365i
$334$	−0.212329	−	0.0931026i	−0.0116181	−	0.00509435i
$335$	12.2810	−	10.6415i	0.670981	−	0.581408i
$336$	−40.6001	−	22.7388i	−2.21492	−	1.24050i
$337$	10.7118	+	1.54012i	0.583507	+	0.0838957i	0.427746	−	0.903899i	$-0.359308\pi$
$337$	10.7118	+	1.54012i	0.583507	+	0.0838957i	0.155761	+	0.987795i	$0.450217\pi$
$338$	1.31483	−	10.2455i	0.0715175	−	0.557283i
$339$	−45.8167	−	20.9238i	−2.48842	−	1.13642i
$340$	11.0939	+	9.03875i	0.601653	+	0.490195i
$341$	−9.26132	−	20.2795i	−0.501529	−	1.09819i
$342$	31.1016	−	27.7865i	1.68178	−	1.50252i
$343$	−5.75895	−	3.70105i	−0.310954	−	0.199838i
$344$	−12.6723	+	2.41473i	−0.683247	+	0.130194i
$345$	12.2763	−	6.87231i	0.660933	−	0.369993i
$346$	−0.230213	−	0.346549i	−0.0123763	−	0.0186306i
$347$	−27.1339	−	17.4379i	−1.45662	−	0.936116i	−0.998894	−	0.0470255i	$-0.985026\pi$
$347$	−27.1339	−	17.4379i	−1.45662	−	0.936116i	−0.457731	−	0.889091i	$-0.651338\pi$
$348$	−5.51153	+	21.1200i	−0.295449	+	1.13215i
$349$	−8.97024	+	4.09657i	−0.480166	+	0.219285i	−0.640768	−	0.767735i	$-0.721384\pi$
$349$	−8.97024	+	4.09657i	−0.480166	+	0.219285i	0.160602	+	0.987019i	$0.448657\pi$
$350$	−5.35650	+	1.66145i	−0.286317	+	0.0888080i
$351$	16.5961	+	7.57918i	0.885834	+	0.404547i
$352$	−9.20778	−	12.1874i	−0.490776	−	0.649590i
$353$	2.39019	−	16.6241i	0.127217	−	0.884813i	−0.821842	−	0.569715i	$-0.807054\pi$
$353$	2.39019	−	16.6241i	0.127217	−	0.884813i	0.949059	−	0.315098i	$-0.102037\pi$
$354$	−2.13666	+	2.54275i	−0.113562	+	0.135146i
$355$	−7.65357	+	6.63186i	−0.406209	+	0.351982i
$356$	−34.0000	+	5.94591i	−1.80199	+	0.315133i
$357$	45.0016	+	70.0238i	2.38174	+	3.70605i
$358$	−21.4501	−	5.94653i	−1.13367	−	0.314284i
$359$	13.0464	−	3.83076i	0.688561	−	0.202180i	0.0813088	−	0.996689i	$-0.474090\pi$
$359$	13.0464	−	3.83076i	0.688561	−	0.202180i	0.607252	+	0.794509i	$0.292272\pi$
$360$	−15.8395	+	0.721104i	−0.834816	+	0.0380055i
$361$	5.68045	−	6.55559i	0.298971	−	0.345031i
$362$	−1.72827	−	10.8498i	−0.0908361	−	0.570251i
$363$	−10.4396	−	3.06534i	−0.547937	−	0.160889i
$364$	−0.574015	−	18.9201i	−0.0300865	−	0.991685i
$365$	−0.618336	−	4.30062i	−0.0323652	−	0.225105i
$366$	−15.8391	+	0.240215i	−0.827924	+	0.0125562i
$367$	−28.7128			−1.49880			−0.749398	−	0.662119i	$-0.769657\pi$
$367$	−28.7128			−1.49880			−0.749398	+	0.662119i	$0.769657\pi$
$368$	−12.5595	−	14.5003i	−0.654709	−	0.755881i
$369$	−45.3959			−2.36321
$370$	−3.41721	+	0.0518251i	−0.177652	+	0.00269426i
$371$	−5.80783	−	40.3944i	−0.301528	−	2.09717i
$372$	1.46900	+	48.4198i	0.0761640	+	2.51045i
$373$	−16.5850	−	4.86979i	−0.858738	−	0.252148i	−0.177419	−	0.984135i	$-0.556775\pi$
$373$	−16.5850	−	4.86979i	−0.858738	−	0.252148i	−0.681318	+	0.731987i	$0.738593\pi$
$374$	4.29805	+	26.9823i	0.222247	+	1.39522i
$375$	−1.92109	+	2.21705i	−0.0992046	+	0.114488i
$376$	−0.363879	−	7.99282i	−0.0187656	−	0.412198i
$377$	−8.51911	+	2.50144i	−0.438757	+	0.128831i
$378$	−41.3150	−	11.4536i	−2.12501	−	0.589109i
$379$	2.38394	+	3.70949i	0.122455	+	0.190543i	0.897069	−	0.441891i	$-0.145692\pi$
$379$	2.38394	+	3.70949i	0.122455	+	0.190543i	−0.774614	+	0.632434i	$0.782056\pi$
$380$	−10.3640	+	1.81245i	−0.531661	+	0.0929769i
$381$	−8.80150	+	7.62654i	−0.450914	+	0.390719i
$382$	2.48820	−	2.96110i	0.127307	−	0.151503i
$383$	−0.634390	+	4.41228i	−0.0324158	+	0.225457i	−0.999589	−	0.0286605i	$-0.990876\pi$
$383$	−0.634390	+	4.41228i	−0.0324158	+	0.225457i	0.967173	+	0.254117i	$0.0817849\pi$
$384$	8.17759	+	32.1665i	0.417311	+	1.64149i
$385$	−9.74037	−	4.44828i	−0.496415	−	0.226705i
$386$	−2.76950	+	0.859026i	−0.140964	+	0.0437233i
$387$	−23.2578	+	10.6215i	−1.18226	+	0.539921i
$388$	−4.34993	+	16.6688i	−0.220834	+	0.846228i
$389$	−4.01908	−	2.58291i	−0.203775	−	0.130959i	0.434773	−	0.900540i	$-0.356829\pi$
$389$	−4.01908	−	2.58291i	−0.203775	−	0.130959i	−0.638549	+	0.769581i	$0.720465\pi$
$390$	−5.47878	−	8.24743i	−0.277429	−	0.417625i
$391$	7.64695	+	33.4511i	0.386723	+	1.69170i
$392$	4.61998	+	24.2453i	0.233344	+	1.22457i
$393$	10.9943	+	7.06561i	0.554589	+	0.356413i
$394$	0.165722	−	0.148058i	0.00834894	−	0.00745904i
$395$	3.62093	+	7.92872i	0.182189	+	0.398937i
$396$	−23.4704	−	19.1225i	−1.17943	−	0.960940i
$397$	−14.1911	−	6.48085i	−0.712230	−	0.325264i	0.0261421	−	0.999658i	$-0.491678\pi$
$397$	−14.1911	−	6.48085i	−0.712230	−	0.325264i	−0.738372	+	0.674394i	$0.764405\pi$
$398$	−3.31707	+	25.8475i	−0.166270	+	1.29562i
$399$	−60.5768	−	8.70963i	−3.03263	−	0.436027i
$400$	3.48992	+	1.95459i	0.174496	+	0.0977296i
$401$	11.5198	−	9.98198i	0.575272	−	0.498476i	−0.317940	−	0.948111i	$-0.602991\pi$
$401$	11.5198	−	9.98198i	0.575272	−	0.498476i	0.893213	+	0.449634i	$0.148446\pi$
$402$	−61.7421	−	27.0728i	−3.07942	−	1.35027i
$403$	−16.5769	+	10.6533i	−0.825753	+	0.530679i
$404$	1.80153	+	5.51134i	0.0896296	+	0.274200i
$405$	−5.38134	+	1.58010i	−0.267401	+	0.0785160i
$406$	18.8450	−	8.95403i	0.935261	−	0.444381i
$407$	−4.93153	−	4.27320i	−0.244447	−	0.211814i
$408$	14.1180	−	57.6648i	0.698943	−	2.85483i
$409$	−29.2118	−	8.57736i	−1.44443	−	0.424123i	−0.536735	−	0.843751i	$-0.680342\pi$
$409$	−29.2118	−	8.57736i	−1.44443	−	0.424123i	−0.907696	+	0.419628i	$0.862161\pi$
$410$	9.72690	+	6.04467i	0.480377	+	0.298525i
$411$	−1.10525	+	0.158911i	−0.0545180	+	0.00783850i
$412$	−18.6397	+	12.7940i	−0.918311	+	0.630313i
$413$	3.17471			0.156217
$414$	−31.0131	−	21.9954i	−1.52421	−	1.08102i
$415$		−	14.0709i		−	0.690713i
$416$	−9.50412	+	9.58858i	−0.465978	+	0.470119i
$417$	−3.17034	−	22.0502i	−0.155252	−	1.07980i
$418$	−17.0624	−	10.6032i	−0.834548	−	0.518620i
$419$	−3.44656	+	11.7379i	−0.168375	+	0.573434i	0.831465	+	0.555577i	$0.187503\pi$
$419$	−3.44656	+	11.7379i	−0.168375	+	0.573434i	−0.999841	+	0.0178571i	$0.994316\pi$
$420$	15.7629	+	17.1139i	0.769151	+	0.835074i
$421$	23.9730	−	27.6663i	1.16837	−	1.34837i	0.242676	−	0.970107i	$-0.421975\pi$
$421$	23.9730	−	27.6663i	1.16837	−	1.34837i	0.925697	−	0.378267i	$-0.123480\pi$
$422$	7.15621	+	15.0612i	0.348359	+	0.733169i
$423$	−4.46774	−	15.2157i	−0.217229	−	0.739814i
$424$	−18.0408	+	22.8416i	−0.876141	+	1.10929i
$425$	−3.86827	−	6.01914i	−0.187639	−	0.291971i
$426$	38.4780	+	16.8719i	1.86427	+	0.817447i
$427$	9.91583	+	11.4435i	0.479861	+	0.553789i
$428$	16.0195	+	1.80935i	0.774333	+	0.0874584i
$429$	2.69046	−	18.7126i	0.129897	−	0.903453i
$430$	6.39771	+	0.821035i	0.308525	+	0.0395938i
$431$	9.06396	−	19.8473i	0.436596	−	0.956011i	−0.555615	−	0.831440i	$-0.687517\pi$
$431$	9.06396	−	19.8473i	0.436596	−	0.956011i	0.992211	−	0.124571i	$-0.0397556\pi$
$432$	14.3657	+	26.9941i	0.691169	+	1.29875i
$433$	10.9007	−	4.97819i	0.523854	−	0.239236i	−0.135893	−	0.990723i	$-0.543390\pi$
$433$	10.9007	−	4.97819i	0.523854	−	0.239236i	0.659748	+	0.751487i	$0.270663\pi$
$434$	34.5306	−	30.8501i	1.65752	−	1.48085i
$435$	5.90035	−	9.18113i	0.282900	−	0.440201i
$436$	1.00570	−	2.39156i	0.0481642	−	0.114535i
$437$	−22.2693	−	11.8570i	−1.06528	−	0.567196i
$438$	−15.0145	+	9.97417i	−0.717421	+	0.476584i
$439$	−16.7995	+	26.1406i	−0.801799	+	1.24762i	0.163518	+	0.986540i	$0.447716\pi$
$439$	−16.7995	+	26.1406i	−0.801799	+	1.24762i	−0.965316	+	0.261083i	$0.915921\pi$
$440$	2.48273	+	7.22253i	0.118359	+	0.344321i
$441$	20.3215	+	44.4979i	0.967692	+	2.11895i
$442$	23.0652	−	7.15423i	1.09710	−	0.340292i
$443$	13.2235	−	28.9555i	0.628269	−	1.37572i	−0.281081	−	0.959684i	$-0.590693\pi$
$443$	13.2235	−	28.9555i	0.628269	−	1.37572i	0.909350	−	0.416033i	$-0.136580\pi$
$444$	6.27843	+	12.7128i	0.297961	+	0.603324i
$445$	17.0823	+	2.45607i	0.809780	+	0.116429i
$446$	−16.9118	−	14.2109i	−0.800796	−	0.672906i
$447$	−28.6803	−	33.0988i	−1.35653	−	1.56552i
$448$	18.5110	−	25.7648i	0.874563	−	1.21727i
$449$	−24.2593	+	15.5905i	−1.14487	+	0.735761i	−0.968611	−	0.248583i	$-0.920035\pi$
$449$	−24.2593	+	15.5905i	−1.14487	+	0.735761i	−0.176256	+	0.984344i	$0.556399\pi$
$450$	7.63982	+	2.11796i	0.360144	+	0.0998414i
$451$	6.16033	+	20.9802i	0.290079	+	0.987917i
$452$	17.6806	−	29.4376i	0.831624	−	1.38463i
$453$	−34.6617	−	30.0345i	−1.62855	−	1.41114i
$454$	9.68077	−	1.54206i	0.454341	−	0.0723727i
$455$	−2.66644	+	9.08105i	−0.125004	+	0.425726i
$456$	25.2444	+	35.6093i	1.18218	+	1.66756i
$457$	12.7643	−	1.83523i	0.597089	−	0.0858485i	0.162857	−	0.986650i	$-0.447929\pi$
$457$	12.7643	−	1.83523i	0.597089	−	0.0858485i	0.434232	+	0.900801i	$0.357020\pi$
$458$	−18.9897	+	0.287996i	−0.887331	+	0.0134572i
$459$		−	54.6973i		−	2.55305i
$460$	3.71633	+	8.84245i	0.173275	+	0.412281i
$461$		−	15.8262i		−	0.737100i	−0.929608	−	0.368550i	$-0.879854\pi$
$461$		−	15.8262i		−	0.737100i	0.929608	−	0.368550i	$-0.120146\pi$
$462$	0.673661	+	44.4194i	0.0313416	+	2.06658i
$463$	9.06780	−	1.30375i	0.421417	−	0.0605905i	0.0716554	−	0.997429i	$-0.477172\pi$
$463$	9.06780	−	1.30375i	0.421417	−	0.0605905i	0.349761	+	0.936839i	$0.386263\pi$
$464$	−13.8860	−	5.34981i	−0.644643	−	0.248359i
$465$	6.82385	−	23.2399i	0.316448	−	1.07772i
$466$	5.37914	+	33.7691i	0.249184	+	1.56433i
$467$	14.1975	+	12.3022i	0.656982	+	0.569278i	0.918256	−	0.395986i	$-0.129597\pi$
$467$	14.1975	+	12.3022i	0.656982	+	0.569278i	−0.261274	+	0.965265i	$0.584143\pi$
$468$	−13.7773	+	22.9388i	−0.636857	+	1.06035i
$469$	18.1553	+	61.8314i	0.838335	+	2.85511i
$470$	−1.06875	+	3.85515i	−0.0492977	+	0.177825i
$471$	−51.2612	+	32.9435i	−2.36199	+	1.51796i
$472$	−1.55910	−	1.64205i	−0.0717635	−	0.0755814i
$473$	8.06497	+	9.30747i	0.370828	+	0.427958i
$474$	23.2639	−	27.6853i	1.06854	−	1.27163i
$475$	5.20709	+	0.748667i	0.238918	+	0.0343512i
$476$	−50.8812	+	25.1285i	−2.33213	+	1.15176i
$477$	−23.9651	+	52.4763i	−1.09729	+	2.40273i
$478$	−5.44596	−	17.5578i	−0.249092	−	0.803074i
$479$	13.5771	+	29.7298i	0.620355	+	1.35839i	0.915261	+	0.402861i	$0.131984\pi$
$479$	13.5771	+	29.7298i	0.620355	+	1.35839i	−0.294906	+	0.955526i	$0.595288\pi$
$480$	1.11062	−	16.5576i	0.0506929	−	0.755750i
$481$	−3.11815	+	4.85194i	−0.142176	+	0.221229i
$482$	10.9696	+	16.5130i	0.499653	+	0.752148i
$483$	4.56648	+	55.6052i	0.207782	+	2.53012i
$484$	2.87542	−	6.83778i	0.130701	−	0.310808i
$485$	4.65681	−	7.24613i	0.211455	−	0.329030i
$486$	−6.10641	−	6.83494i	−0.276993	−	0.310039i
$487$	−10.9200	+	4.98701i	−0.494833	+	0.225983i	−0.647170	−	0.762346i	$-0.724048\pi$
$487$	−10.9200	+	4.98701i	−0.494833	+	0.225983i	0.152336	+	0.988329i	$0.451320\pi$
$488$	1.04921	−	10.7486i	0.0474957	−	0.486568i
$489$	−7.55940	+	16.5528i	−0.341848	+	0.748542i
$490$	1.57084	−	12.2404i	0.0709634	−	0.552965i
$491$	−1.19567	+	8.31607i	−0.0539598	+	0.375299i	0.944892	+	0.327383i	$0.106167\pi$
$491$	−1.19567	+	8.31607i	−0.0539598	+	0.375299i	−0.998851	+	0.0479154i	$0.984742\pi$
$492$	5.33236	−	47.2113i	0.240402	−	2.12845i
$493$	17.4312	+	20.1167i	0.785062	+	0.906010i
$494$	−7.13017	+	16.2610i	−0.320802	+	0.731619i
$495$	8.18375	+	12.7342i	0.367832	+	0.572358i
$496$	−32.9145	−	2.70972i	−1.47790	−	0.121670i
$497$	−11.3145	−	38.5337i	−0.507525	−	1.72847i
$498$	−52.7270	+	25.0528i	−2.36275	+	1.12264i
$499$	9.34048	−	10.7795i	0.418137	−	0.482556i	−0.507131	−	0.861869i	$-0.669294\pi$
$499$	9.34048	−	10.7795i	0.418137	−	0.482556i	0.925269	+	0.379313i	$0.123840\pi$
$500$	−1.35496	−	1.47109i	−0.0605954	−	0.0657890i
$501$	0.135493	−	0.461447i	0.00605339	−	0.0206159i
$502$	−9.99870	+	16.0896i	−0.446264	+	0.718115i
$503$	0.453070	+	3.15117i	0.0202014	+	0.140504i	0.997426	−	0.0717040i	$-0.0228437\pi$
$503$	0.453070	+	3.15117i	0.0202014	+	0.140504i	−0.977225	+	0.212208i	$0.931935\pi$
$504$	23.4925	−	58.3253i	1.04644	−	2.59801i
$505$		−	2.89916i		−	0.129011i
$506$	−5.95685	+	17.3178i	−0.264814	+	0.769871i
$507$	21.4271			0.951613
$508$	−4.49316	−	6.54615i	−0.199352	−	0.290438i
$509$	22.4461	−	3.22727i	0.994908	−	0.143046i	0.374418	−	0.927260i	$-0.377843\pi$
$509$	22.4461	−	3.22727i	0.994908	−	0.143046i	0.620490	+	0.784214i	$0.286934\pi$
$510$	−15.6678	+	25.2122i	−0.693783	+	1.11641i
$511$	16.5321	+	4.85427i	0.731339	+	0.214740i
$512$	−22.4170	+	3.07867i	−0.990701	+	0.136059i
$513$	30.3931	+	26.3357i	1.34189	+	1.16275i
$514$	8.60483	+	18.1100i	0.379543	+	0.798799i
$515$	10.8461	−	3.18471i	0.477937	−	0.140335i
$516$	−8.31430	−	25.4356i	−0.366017	−	1.11974i
$517$	−6.42582	+	4.12962i	−0.282607	+	0.181621i
$518$	5.44251	−	12.4122i	0.239130	−	0.545360i
$519$	0.652233	−	0.565163i	0.0286299	−	0.0248079i
$520$	6.00646	−	3.08055i	0.263401	−	0.135091i
$521$	18.1624	+	2.61136i	0.795710	+	0.114406i	0.528167	−	0.849140i	$-0.322879\pi$
$521$	18.1624	+	2.61136i	0.795710	+	0.114406i	0.267543	+	0.963546i	$0.413788\pi$
$522$	−29.2540	−	3.75424i	−1.28041	−	0.164319i
$523$	28.2381	+	12.8959i	1.23477	+	0.563899i	0.922464	−	0.386083i	$-0.126172\pi$
$523$	28.2381	+	12.8959i	1.23477	+	0.563899i	0.312304	+	0.949982i	$0.398899\pi$
$524$	−5.62786	+	6.90749i	−0.245854	+	0.301755i
$525$	−4.83274	−	10.5822i	−0.210918	−	0.461846i
$526$	1.64147	+	1.83731i	0.0715716	+	0.0801104i
$527$	49.6968	+	31.9382i	2.16483	+	1.39125i
$528$	22.6441	−	22.1628i	0.985459	−	0.964513i
$529$	−6.01326	+	22.2000i	−0.261446	+	0.965218i
$530$	12.1224	−	8.05295i	0.526565	−	0.349798i
$531$	−3.77542	−	2.42631i	−0.163839	−	0.105293i
$532$	10.5355	−	40.3715i	0.456770	−	1.75033i
$533$	17.5799	−	8.02849i	0.761472	−	0.347753i
$534$	−21.2110	−	68.3844i	−0.917892	−	2.95928i
$535$	−7.33226	−	3.34853i	−0.317001	−	0.144770i
$536$	23.0648	−	39.7558i	0.996247	−	1.71719i
$537$	6.57115	−	45.7034i	0.283566	−	1.97225i
$538$	7.01451	+	5.89427i	0.302417	+	0.254120i
$539$	17.8075	−	15.4303i	0.767023	−	0.664629i
$540$	−2.63382	−	15.0608i	−0.113342	−	0.648112i
$541$	−22.0135	−	34.2536i	−0.946433	−	1.47268i	−0.880048	−	0.474884i	$-0.842490\pi$
$541$	−22.0135	−	34.2536i	−0.946433	−	1.47268i	−0.0663844	−	0.997794i	$-0.521146\pi$
$542$	7.25717	−	26.1778i	0.311722	−	1.12443i
$543$	21.8669	−	6.42069i	0.938397	−	0.275538i
$544$	37.9849	+	13.9765i	1.62859	+	0.599239i
$545$	−0.849490	+	0.980364i	−0.0363881	+	0.0419942i
$546$	38.7763	−	6.17674i	1.65947	−	0.264340i
$547$	−21.8908	−	6.42773i	−0.935985	−	0.274830i	−0.222044	−	0.975037i	$-0.571273\pi$
$547$	−21.8908	−	6.42773i	−0.935985	−	0.274830i	−0.713940	+	0.700207i	$0.753091\pi$
$548$	−0.0230852	−	0.760914i	−0.000986152	−	0.0325046i
$549$	−3.04624	−	21.1871i	−0.130010	−	0.904242i
$550$	−0.0579069	−	3.81823i	−0.00246916	−	0.162810i
$551$	−19.5708			−0.833745
$552$	26.5179	−	29.6696i	1.12868	−	1.26282i
$553$	−34.5661			−1.46990
$554$	0.518674	+	34.2000i	0.0220364	+	1.45302i
$555$	−1.00892	−	7.01717i	−0.0428261	−	0.297862i
$556$	15.1806	−	0.460560i	0.643799	−	0.0195321i
$557$	35.3582	+	10.3821i	1.49818	+	0.439904i	0.925140	−	0.379626i	$-0.123947\pi$
$557$	35.3582	+	10.3821i	1.49818	+	0.439904i	0.573036	+	0.819530i	$0.305765\pi$
$558$	−64.6419	+	10.2969i	−2.73651	+	0.435903i
$559$	7.12832	−	8.22653i	0.301496	−	0.347945i
$560$	−12.8000	+	9.36912i	−0.540898	+	0.395918i
$561$	−54.3807	+	15.9676i	−2.29596	+	0.674154i
$562$	−2.67566	+	9.65155i	−0.112866	+	0.407126i
$563$	15.6775	+	24.3947i	0.660728	+	1.02811i	0.996287	+	0.0860933i	$0.0274383\pi$
$563$	15.6775	+	24.3947i	0.660728	+	1.02811i	−0.335559	+	0.942019i	$0.608925\pi$
$564$	16.3490	−	2.85912i	0.688418	−	0.120390i
$565$	−12.9759	+	11.2437i	−0.545900	+	0.473025i
$566$	−13.3700	−	11.2347i	−0.561982	−	0.472231i
$567$	3.16527	−	22.0150i	0.132929	−	0.924542i
$568$	−14.3741	+	24.7761i	−0.603125	+	1.03958i
$569$	−1.81120	−	0.827150i	−0.0759297	−	0.0346759i	0.377088	−	0.926177i	$-0.376925\pi$
$569$	−1.81120	−	0.827150i	−0.0759297	−	0.0346759i	−0.453018	+	0.891501i	$0.649653\pi$
$570$	−6.46562	−	20.8452i	−0.270815	−	0.873108i
$571$	33.2637	−	15.1910i	1.39204	−	0.635725i	0.428565	−	0.903511i	$-0.359019\pi$
$571$	33.2637	−	15.1910i	1.39204	−	0.635725i	0.963479	+	0.267786i	$0.0862919\pi$
$572$	12.4710	+	3.25448i	0.521440	+	0.136077i
$573$	6.74940	+	4.33758i	0.281960	+	0.181205i
$574$	−37.8287	+	25.1296i	−1.57894	+	1.04889i
$575$	−0.392528	−	4.77974i	−0.0163696	−	0.199329i
$576$	−41.7046	+	16.4926i	−1.73769	+	0.687191i
$577$	22.7831	+	14.6418i	0.948471	+	0.609545i	0.920785	−	0.390071i	$-0.127550\pi$
$577$	22.7831	+	14.6418i	0.948471	+	0.609545i	0.0276862	+	0.999617i	$0.491186\pi$
$578$	−32.2177	−	36.0614i	−1.34008	−	1.49996i
$579$	−2.49870	−	5.47138i	−0.103842	−	0.227383i
$580$	5.76831	+	4.69971i	0.239516	+	0.195145i
$581$	50.7575	+	23.1802i	2.10578	+	0.961676i
$582$	−35.4443	−	4.54865i	−1.46921	−	0.188548i
$583$	27.5046	+	3.95456i	1.13912	+	0.163781i
$584$	−5.60817	−	10.9348i	−0.232068	−	0.452486i
$585$	10.1113	−	8.76147i	0.418050	−	0.362242i
$586$	1.74293	−	3.97492i	0.0719998	−	0.164202i
$587$	9.32193	−	5.99084i	0.384757	−	0.247268i	−0.333936	−	0.942596i	$-0.608377\pi$
$587$	9.32193	−	5.99084i	0.384757	−	0.247268i	0.718693	+	0.695327i	$0.244741\pi$
$588$	−48.6645	+	15.9073i	−2.00689	+	0.656006i
$589$	−41.6748	+	12.2368i	−1.71718	+	0.504210i
$590$	0.485878	+	1.02260i	0.0200033	+	0.0420996i
$591$	0.348384	+	0.301876i	0.0143306	+	0.0124175i
$592$	−9.09273	+	3.28060i	−0.373709	+	0.134832i
$593$	−11.2692	−	3.30894i	−0.462772	−	0.135882i	0.0420319	−	0.999116i	$-0.486617\pi$
$593$	−11.2692	−	3.30894i	−0.462772	−	0.135882i	−0.504804	+	0.863234i	$0.668435\pi$
$594$	15.4084	−	24.7947i	0.632214	−	1.01734i
$595$	28.0852	−	4.03804i	1.15138	−	0.165544i
$596$	24.6174	−	16.8969i	1.00837	−	0.692125i
$597$	−54.0566			−2.21239
$598$	15.9001	+	3.03309i	0.650202	+	0.124032i
$599$			7.73638i			0.316100i	0.987431	+	0.158050i	$0.0505207\pi$
$599$			7.73638i			0.316100i	−0.987431	+	0.158050i	$0.949479\pi$
$600$	−3.10006	+	7.69656i	−0.126559	+	0.314211i
$601$	0.791496	+	5.50498i	0.0322858	+	0.224553i	0.999576	−	0.0291200i	$-0.00927048\pi$
$601$	0.791496	+	5.50498i	0.0322858	+	0.224553i	−0.967290	+	0.253673i	$0.918361\pi$
$602$	−13.5012	+	21.7257i	−0.550267	+	0.885473i
$603$	25.6648	−	87.4063i	1.04515	−	3.55946i
$604$	22.9991	−	21.1835i	0.935821	−	0.861944i
$605$	−2.42880	+	2.80299i	−0.0987449	+	0.113958i
$606$	−10.8638	+	5.16185i	−0.441313	+	0.209686i
$607$	4.00465	+	13.6386i	0.162544	+	0.553573i	0.999975	+	0.00703109i	$0.00223808\pi$
$607$	4.00465	+	13.6386i	0.162544	+	0.553573i	−0.837431	+	0.546542i	$0.815944\pi$
$608$	−26.0552	+	14.3772i	−1.05668	+	0.583073i
$609$	23.3986	+	36.4090i	0.948161	+	1.47537i
$610$	−2.16844	+	4.94534i	−0.0877976	+	0.200231i
$611$	4.42115	+	5.10228i	0.178861	+	0.206416i
$612$	79.7134	+	9.00338i	3.22223	+	0.363940i
$613$	4.44807	−	30.9370i	0.179656	−	1.24953i	−0.677905	−	0.735150i	$-0.737112\pi$
$613$	4.44807	−	30.9370i	0.179656	−	1.24953i	0.857560	−	0.514383i	$-0.171979\pi$
$614$	−4.24806	+	33.1020i	−0.171438	+	1.33589i
$615$	−9.86849	+	21.6090i	−0.397936	+	0.871358i
$616$	−30.1436	−	2.94243i	−1.21452	−	0.118554i
$617$	6.32033	−	2.88640i	0.254447	−	0.116202i	−0.284108	−	0.958792i	$-0.591698\pi$
$617$	6.32033	−	2.88640i	0.254447	−	0.116202i	0.538555	+	0.842590i	$0.318970\pi$
$618$	−31.2450	−	34.9727i	−1.25686	−	1.40681i
$619$	4.44057	−	6.90965i	0.178481	−	0.277722i	−0.740473	−	0.672086i	$-0.765399\pi$
$619$	4.44057	−	6.90965i	0.178481	−	0.277722i	0.918955	+	0.394363i	$0.129035\pi$
$620$	15.2218	+	6.40106i	0.611322	+	0.257073i
$621$	17.2304	−	32.3613i	0.691431	−	1.29862i
$622$	0.486893	+	0.732940i	0.0195226	+	0.0293882i
$623$	−37.0008	+	57.5744i	−1.48241	+	2.30667i
$624$	−22.2378	−	17.0228i	−0.890226	−	0.681457i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	1.14852	+	3.70283i	0.0459041	+	0.147995i
$627$	17.3107	−	37.9053i	0.691325	−	1.51379i
$628$	−18.3954	−	37.2477i	−0.734056	−	1.48635i
$629$	17.1148	+	2.46074i	0.682411	+	0.0981159i
$630$	−20.2257	+	24.0698i	−0.805813	+	0.958963i
$631$	−1.95427	−	2.25535i	−0.0777983	−	0.0897840i	0.715516	−	0.698596i	$-0.246192\pi$
$631$	−1.95427	−	2.25535i	−0.0777983	−	0.0897840i	−0.793314	+	0.608812i	$0.791646\pi$
$632$	16.9754	+	17.8785i	0.675246	+	0.711170i
$633$	−29.0987	+	18.7006i	−1.15657	+	0.743282i
$634$	0.258151	−	0.931192i	0.0102525	−	0.0369823i
$635$	1.11845	+	3.80910i	0.0443844	+	0.151159i
$636$	−51.7599	−	31.0876i	−2.05241	−	1.23270i
$637$	−15.7394	−	13.6382i	−0.623616	−	0.540367i
$638$	2.23478	+	14.0295i	0.0884757	+	0.555432i
$639$	−15.9945	+	54.4721i	−0.632731	+	2.15488i
$640$	11.1320	+	2.01932i	0.440033	+	0.0798207i
$641$	−21.3177	+	3.06502i	−0.841998	+	0.121061i	−0.549799	−	0.835297i	$-0.685296\pi$
$641$	−21.3177	+	3.06502i	−0.841998	+	0.121061i	−0.292198	+	0.956358i	$0.594387\pi$
$642$	0.507112	+	33.4376i	0.0200141	+	1.31968i
$643$		−	13.8501i		−	0.546194i	−0.961987	−	0.273097i	$-0.911952\pi$
$643$		−	13.8501i		−	0.546194i	0.961987	−	0.273097i	$-0.0880480\pi$
$644$	−38.0193	−	1.16112i	−1.49817	−	0.0457544i
$645$			13.3800i			0.526836i
$646$	53.2244	−	0.807197i	2.09409	−	0.0317588i
$647$	36.7399	−	5.28240i	1.44439	−	0.207673i	0.624875	−	0.780725i	$-0.285150\pi$
$647$	36.7399	−	5.28240i	1.44439	−	0.207673i	0.819519	+	0.573052i	$0.194241\pi$
$648$	−12.9412	+	9.17439i	−0.508379	+	0.360404i
$649$	−0.609012	+	2.07410i	−0.0239058	+	0.0814157i
$650$	−3.33316	+	0.530944i	−0.130737	+	0.0208253i
$651$	72.5910	+	62.9005i	2.84507	+	2.46526i
$652$	−10.6353	−	6.38769i	−0.416511	−	0.250161i
$653$	6.47854	+	22.0639i	0.253525	+	0.863426i	0.983647	+	0.180109i	$0.0576450\pi$
$653$	6.47854	+	22.0639i	0.253525	+	0.863426i	−0.730122	+	0.683317i	$0.760537\pi$
$654$	5.18614	+	1.43773i	0.202794	+	0.0562198i
$655$	3.74774	−	2.40852i	0.146436	−	0.0941089i
$656$	31.5754	+	7.22485i	1.23281	+	0.282083i
$657$	−15.9503	−	18.4077i	−0.622282	−	0.718152i
$658$	−12.1459	−	10.2062i	−0.473497	−	0.397878i
$659$	−3.08735	−	0.443894i	−0.120266	−	0.0172917i	0.0819189	−	0.996639i	$-0.473895\pi$
$659$	−3.08735	−	0.443894i	−0.120266	−	0.0172917i	−0.202185	+	0.979347i	$0.564804\pi$
$660$	−14.2047	+	7.01522i	−0.552917	+	0.273067i
$661$	8.05791	−	17.6444i	0.313416	−	0.686286i	−0.685719	−	0.727867i	$-0.740512\pi$
$661$	8.05791	−	17.6444i	0.313416	−	0.686286i	0.999135	+	0.0415805i	$0.0132393\pi$
$662$	−1.80200	+	0.558934i	−0.0700368	+	0.0217236i
$663$	20.8099	+	45.5673i	0.808190	+	1.76969i
$664$	−12.9376	−	37.6370i	−0.502076	−	1.46060i
$665$	−11.2787	+	17.5500i	−0.437370	+	0.680561i
$666$	−15.9585	+	10.6012i	−0.618379	+	0.410790i
$667$	3.97605	+	17.3930i	0.153953	+	0.673458i
$668$	0.302241	+	0.127098i	0.0116941	+	0.00491758i
$669$	24.7733	−	38.5480i	0.957791	−	1.49035i
$670$	−17.1377	+	15.3110i	−0.662087	+	0.591516i
$671$	−9.37844	+	4.28299i	−0.362050	+	0.165343i
$672$	57.8982	+	31.2831i	2.23347	+	1.20677i
$673$	−2.15050	+	4.70894i	−0.0828958	+	0.181516i	−0.946541	−	0.322584i	$-0.895449\pi$
$673$	−2.15050	+	4.70894i	−0.0828958	+	0.181516i	0.863645	+	0.504100i	$0.168176\pi$
$674$	−15.1800	−	1.94809i	−0.584712	−	0.0750376i
$675$	−1.08795	+	7.56685i	−0.0418752	+	0.291248i
$676$	−1.63952	+	14.5159i	−0.0630585	+	0.558303i
$677$	−23.8746	−	27.5527i	−0.917575	−	1.05894i	−0.998065	−	0.0621825i	$-0.980194\pi$
$677$	−23.8746	−	27.5527i	−0.917575	−	1.05894i	0.0804899	−	0.996755i	$-0.474352\pi$
$678$	65.2358	+	28.6047i	2.50537	+	1.09856i
$679$	18.4672	+	28.7355i	0.708706	+	1.10277i
$680$	−15.8812	−	12.5433i	−0.609017	−	0.481015i
$681$	5.72890	+	19.5109i	0.219532	+	0.747657i
$682$	13.5309	+	28.4776i	0.518124	+	1.09046i
$683$	−28.1117	+	32.4426i	−1.07566	+	1.24138i	−0.106670	+	0.994294i	$0.534019\pi$
$683$	−28.1117	+	32.4426i	−1.07566	+	1.24138i	−0.968993	+	0.247087i	$0.920527\pi$
$684$	−43.3833	+	39.9585i	−1.65880	+	1.52785i
$685$	−0.107236	+	0.365214i	−0.00409729	+	0.0139541i
$686$	8.22282	+	5.10997i	0.313949	+	0.195100i
$687$	−5.60663	−	38.9950i	−0.213906	−	1.48775i
$688$	17.8676	−	3.68632i	0.681194	−	0.140539i
$689$		−	24.5603i		−	0.935671i
$690$	−17.2119	+	9.98106i	−0.655247	+	0.379973i
$691$	41.1915			1.56700			0.783499	−	0.621394i	$-0.213433\pi$
$691$	41.1915			1.56700			0.783499	+	0.621394i	$0.213433\pi$
$692$	0.332965	+	0.485101i	0.0126574	+	0.0184408i
$693$	−59.4173	+	8.54292i	−2.25708	+	0.324519i
$694$	38.7427	+	24.0762i	1.47065	+	0.913920i
$695$	−7.28617	−	2.13941i	−0.276380	−	0.0811526i
$696$	7.34065	−	29.9829i	0.278247	−	1.13650i
$697$	−43.7881	−	37.9426i	−1.65859	−	1.43718i
$698$	12.5965	−	5.98513i	0.476786	−	0.226541i
$699$	−68.0591	+	19.9840i	−2.57423	+	0.755863i
$700$	7.53873	−	2.46424i	0.284937	−	0.0931395i
$701$	−33.5137	+	21.5380i	−1.26580	+	0.813477i	−0.989066	−	0.147471i	$-0.952887\pi$
$701$	−33.5137	+	21.5380i	−1.26580	+	0.813477i	−0.276729	+	0.960948i	$0.589250\pi$
$702$	−23.6303	−	10.3614i	−0.891867	−	0.391067i
$703$	−9.60778	+	8.32519i	−0.362364	+	0.313990i
$704$	13.2816	+	17.0361i	0.500570	+	0.642073i
$705$	−8.21410	−	1.18101i	−0.309361	−	0.0444794i
$706$	−3.02334	+	23.5586i	−0.113785	+	0.886640i
$707$	10.4580	+	4.77602i	0.393315	+	0.179621i
$708$	2.96682	−	3.64140i	0.111500	−	0.136852i
$709$	−2.59606	−	5.68457i	−0.0974969	−	0.213488i	0.854599	−	0.519289i	$-0.173803\pi$
$709$	−2.59606	−	5.68457i	−0.0974969	−	0.213488i	−0.952096	+	0.305801i	$0.901076\pi$
$710$	10.6803	−	9.54192i	0.400825	−	0.358102i
$711$	41.1065	+	26.4176i	1.54162	+	0.990736i
$712$	47.9502	−	9.13697i	1.79701	−	0.342422i
$713$	19.3419	+	34.5512i	0.724358	+	1.29395i
$714$	−65.1362	−	98.0522i	−2.43766	−	3.66951i
$715$	−5.42133	−	3.48407i	−0.202746	−	0.130297i
$716$	30.4591	+	7.94869i	1.13831	+	0.297056i
$717$	34.6869	−	15.8410i	1.29540	−	0.591591i
$718$	−18.3661	+	5.69667i	−0.685416	+	0.212598i
$719$	−20.9320	−	9.55935i	−0.780634	−	0.356503i	−0.0150889	−	0.999886i	$-0.504803\pi$
$719$	−20.9320	−	9.55935i	−0.780634	−	0.356503i	−0.765545	+	0.643383i	$0.777530\pi$
$720$	22.3824	−	1.35936i	0.834143	−	0.0506604i
$721$	−6.37963	+	44.3713i	−0.237590	+	1.65247i
$722$	−7.89186	+	9.39176i	−0.293705	+	0.349525i
$723$	−31.0789	+	26.9300i	−1.15584	+	1.00154i
$724$	2.67655	+	15.3050i	0.0994730	+	0.568808i
$725$	−2.01131	−	3.12966i	−0.0746983	−	0.116233i
$726$	14.8279	+	4.11067i	0.550314	+	0.152561i
$727$	39.0875	−	11.4771i	1.44968	−	0.425663i	0.540242	−	0.841510i	$-0.318333\pi$
$727$	39.0875	−	11.4771i	1.44968	−	0.425663i	0.909435	+	0.415847i	$0.136515\pi$
$728$	1.21744	+	26.7417i	0.0451212	+	0.991115i
$729$	23.4688	−	27.0845i	0.869216	−	1.00313i
$730$	0.966588	+	6.06804i	0.0357750	+	0.224588i
$731$	−31.3117	−	9.19394i	−1.15810	−	0.340050i
$732$	22.3922	−	0.679352i	0.827639	−	0.0251096i
$733$	5.37159	+	37.3602i	0.198404	+	1.37993i	0.808916	+	0.587924i	$0.200055\pi$
$733$	5.37159	+	37.3602i	0.198404	+	1.37993i	−0.610512	+	0.792007i	$0.709036\pi$
$734$	40.6014	−	0.615757i	1.49862	−	0.0227280i
$735$	25.5992			0.944240
$736$	18.0707	+	20.2348i	0.666096	+	0.745866i
$737$	−43.8785			−1.61628
$738$	64.1921	−	0.973531i	2.36294	−	0.0358362i
$739$	3.49281	+	24.2930i	0.128485	+	0.893633i	0.947476	+	0.319827i	$0.103625\pi$
$739$	3.49281	+	24.2930i	0.128485	+	0.893633i	−0.818991	+	0.573806i	$0.805466\pi$
$740$	4.83100	−	0.146567i	0.177591	−	0.00538790i
$741$	−35.3395	−	10.3766i	−1.29823	−	0.381194i
$742$	9.07884	+	56.9951i	0.333295	+	2.09236i
$743$	−4.37107	+	5.04448i	−0.160359	+	0.185064i	−0.830243	−	0.557402i	$-0.811798\pi$
$743$	−4.37107	+	5.04448i	−0.160359	+	0.185064i	0.669884	+	0.742466i	$0.266344\pi$
$744$	−3.11562	−	68.4365i	−0.114224	−	2.50900i
$745$	−14.3244	+	4.20603i	−0.524807	+	0.154097i
$746$	23.5564	+	6.53046i	0.862463	+	0.239097i
$747$	−42.6459	−	66.3583i	−1.56033	−	2.42792i
$748$	−6.65631	−	38.0621i	−0.243379	−	1.39169i
$749$	24.1581	−	20.9331i	0.882717	−	0.764879i
$750$	2.66897	−	3.17623i	0.0974571	−	0.115979i
$751$	3.13224	−	21.7852i	0.114297	−	0.794954i	−0.849360	−	0.527813i	$-0.823012\pi$
$751$	3.13224	−	21.7852i	0.114297	−	0.794954i	0.963658	−	0.267141i	$-0.0860789\pi$
$752$	0.685952	+	11.2945i	0.0250141	+	0.411866i
$753$	−35.7442	−	16.3238i	−1.30259	−	0.594873i
$754$	11.9928	−	3.71985i	0.436752	−	0.135469i
$755$	−14.2213	+	6.49464i	−0.517565	+	0.236364i
$756$	58.6671	+	15.3099i	2.13370	+	0.556817i
$757$	6.11457	+	3.92959i	0.222238	+	0.142823i	0.647023	−	0.762471i	$-0.276014\pi$
$757$	6.11457	+	3.92959i	0.222238	+	0.142823i	−0.424785	+	0.905294i	$0.639650\pi$
$758$	−3.45057	−	5.19428i	−0.125330	−	0.188665i
$759$	−37.2040	−	7.68349i	−1.35042	−	0.278893i
$760$	14.6163	−	2.78516i	0.530190	−	0.101028i
$761$	−25.1922	−	16.1901i	−0.913218	−	0.586890i	−0.00253575	−	0.999997i	$-0.500807\pi$
$761$	−25.1922	−	16.1901i	−0.913218	−	0.586890i	−0.910682	+	0.413107i	$0.864444\pi$
$762$	12.2822	−	10.9731i	0.444938	−	0.397512i
$763$	−2.13700	−	4.67937i	−0.0773645	−	0.169405i
$764$	−3.45494	+	4.24051i	−0.124995	+	0.153416i
$765$	−36.4855	−	16.6624i	−1.31913	−	0.602429i
$766$	0.802436	−	6.25279i	0.0289932	−	0.225922i
$767$	1.89117	+	0.271909i	0.0682862	+	0.00981807i
$768$	−12.2534	−	45.3097i	−0.442155	−	1.63497i
$769$	−11.8041	+	10.2283i	−0.425665	+	0.368841i	−0.841189	−	0.540741i	$-0.818144\pi$
$769$	−11.8041	+	10.2283i	−0.425665	+	0.368841i	0.415524	+	0.909582i	$0.363598\pi$
$770$	13.8688	+	6.08120i	0.499796	+	0.219151i
$771$	−34.9891	+	22.4861i	−1.26010	+	0.809817i
$772$	3.89779	−	1.27410i	0.140285	−	0.0458558i
$773$	5.77655	−	1.69615i	0.207768	−	0.0610062i	−0.176192	−	0.984356i	$-0.556378\pi$
$773$	5.77655	−	1.69615i	0.207768	−	0.0610062i	0.383960	+	0.923350i	$0.374560\pi$
$774$	32.6600	−	15.5181i	1.17394	−	0.557787i
$775$	−6.23982	−	5.40683i	−0.224141	−	0.194219i
$776$	5.79355	−	23.6638i	0.207976	−	0.849479i
$777$	26.9749	+	7.92054i	0.967719	+	0.284148i
$778$	5.73858	+	3.56617i	0.205738	+	0.127853i
$779$	42.1663	−	6.06259i	1.51076	−	0.217215i
$780$	7.92414	+	11.5448i	0.283730	+	0.413370i
$781$	27.3453			0.978493
$782$	−11.5306	−	47.1376i	−0.412332	−	1.68564i
$783$		−	28.4400i		−	1.01636i
$784$	−7.05283	−	34.1850i	−0.251887	−	1.22089i
$785$	2.95606	+	20.5598i	0.105506	+	0.733812i
$786$	−15.6980	−	9.75535i	−0.559930	−	0.347962i
$787$	−3.50001	+	11.9200i	−0.124762	+	0.424900i	−0.998058	−	0.0622894i	$-0.980160\pi$
$787$	−3.50001	+	11.9200i	−0.124762	+	0.424900i	0.873296	+	0.487190i	$0.161978\pi$
$788$	−0.231164	+	0.212915i	−0.00823487	+	0.00758479i
$789$	−3.34681	+	3.86243i	−0.119150	+	0.137506i
$790$	−5.29021	−	11.1340i	−0.188217	−	0.396129i
$791$	−19.1827	−	65.3301i	−0.682057	−	2.32287i
$792$	33.5985	+	26.5368i	1.19387	+	0.942945i
$793$	4.92672	+	7.66613i	0.174953	+	0.272232i
$794$	20.2059	+	8.85992i	0.717080	+	0.314427i
$795$	19.7696	+	22.8154i	0.701157	+	0.809178i
$796$	4.13620	−	36.6208i	0.146604	−	1.29799i
$797$	−4.27810	+	29.7548i	−0.151538	+	1.05397i	0.762105	+	0.647453i	$0.224166\pi$
$797$	−4.27810	+	29.7548i	−0.151538	+	1.05397i	−0.913643	+	0.406517i	$0.866743\pi$
$798$	85.8454	+	11.0168i	3.03890	+	0.389989i
$799$	8.40804	−	18.4110i	0.297455	−	0.651336i
$800$	−4.97685	−	2.68905i	−0.175958	−	0.0950723i
$801$	88.0039	−	40.1901i	3.10947	−	1.42005i
$802$	−16.0755	+	14.3621i	−0.567647	+	0.507143i
$803$	−6.34279	+	9.86957i	−0.223832	+	0.348290i
$804$	87.8871	+	36.9582i	3.09954	+	1.30342i
$805$	17.8884	+	6.45811i	0.630485	+	0.227619i
$806$	23.2121	−	15.4198i	0.817610	−	0.543140i
$807$	−10.2752	+	15.9886i	−0.361705	+	0.562825i
$808$	−2.66565	−	7.75469i	−0.0937773	−	0.272809i
$809$	−12.6170	−	27.6274i	−0.443591	−	0.971328i	−0.990925	−	0.134414i	$-0.957085\pi$
$809$	−12.6170	−	27.6274i	−0.443591	−	0.971328i	0.547334	−	0.836914i	$-0.315643\pi$
$810$	7.57560	−	2.34975i	0.266179	−	0.0825619i
$811$	14.7235	−	32.2401i	0.517014	−	1.13210i	−0.453544	−	0.891234i	$-0.649841\pi$
$811$	14.7235	−	32.2401i	0.517014	−	1.13210i	0.970558	−	0.240868i	$-0.0774322\pi$
$812$	−26.4557	+	13.0656i	−0.928415	+	0.458513i
$813$	55.7766	+	8.01947i	1.95617	+	0.281255i
$814$	7.06508	+	5.93676i	0.247631	+	0.208083i
$815$	4.06214	+	4.68797i	0.142291	+	0.164212i
$816$	−18.7269	+	81.8437i	−0.655571	+	2.86510i
$817$	20.1847	−	12.9719i	0.706173	−	0.453830i
$818$	41.4909	+	11.5024i	1.45070	+	0.402171i
$819$	14.9478	+	50.9076i	0.522319	+	1.77885i
$820$	−13.8840	−	8.33887i	−0.484849	−	0.291206i
$821$	31.6509	+	27.4257i	1.10463	+	0.957163i	0.999305	−	0.0372753i	$-0.0118678\pi$
$821$	31.6509	+	27.4257i	1.10463	+	0.957163i	0.105320	+	0.994438i	$0.466413\pi$
$822$	1.55947	−	0.248411i	0.0543929	−	0.00866432i
$823$	−3.29630	+	11.2262i	−0.114902	+	0.391320i	−0.996783	−	0.0801528i	$-0.974459\pi$
$823$	−3.29630	+	11.2262i	−0.114902	+	0.391320i	0.881881	+	0.471473i	$0.156277\pi$
$824$	26.0831	−	18.4910i	0.908647	−	0.644166i
$825$	7.84065	−	1.12732i	0.272977	−	0.0392481i
$826$	−4.48921	+	0.0680829i	−0.156199	+	0.00236891i
$827$			8.57638i			0.298230i	0.988820	+	0.149115i	$0.0476425\pi$
$827$			8.57638i			0.298230i	−0.988820	+	0.149115i	$0.952358\pi$
$828$	44.3257	+	30.4375i	1.54043	+	1.05778i
$829$		−	33.8755i		−	1.17654i	−0.808663	−	0.588272i	$-0.799808\pi$
$829$		−	33.8755i		−	1.17654i	0.808663	−	0.588272i	$-0.200192\pi$
$830$	0.301756	+	19.8970i	0.0104741	+	0.690634i
$831$	−70.2290	+	10.0974i	−2.43622	+	0.350275i
$832$	13.2337	−	13.7626i	0.458795	−	0.477131i
$833$	−17.5903	+	59.9070i	−0.609467	+	2.07565i
$834$	4.95590	+	31.1121i	0.171609	+	1.07733i
$835$	−0.123897	−	0.107357i	−0.00428762	−	0.00371525i
$836$	24.3545	+	14.6276i	0.842317	+	0.505905i
$837$	−17.7824	−	60.5612i	−0.614648	−	2.09330i
$838$	4.62189	−	16.6719i	0.159660	−	0.575921i
$839$	24.5724	−	15.7917i	0.848334	−	0.545191i	−0.0427205	−	0.999087i	$-0.513603\pi$
$839$	24.5724	−	15.7917i	0.848334	−	0.545191i	0.891055	+	0.453896i	$0.149966\pi$
$840$	−22.6566	−	23.8619i	−0.781725	−	0.823314i
$841$	−9.92758	−	11.4570i	−0.342330	−	0.395070i
$842$	−33.3057	+	39.6357i	−1.14779	+	1.36594i
$843$	−20.5644	−	2.95671i	−0.708275	−	0.101835i
$844$	−10.4422	−	21.1439i	−0.359437	−	0.727802i
$845$	3.03423	−	6.64403i	0.104381	−	0.228562i
$846$	6.64392	+	21.4200i	0.228423	+	0.736435i
$847$	−6.10996	−	13.3789i	−0.209941	−	0.459706i
$848$	25.0208	−	32.6861i	0.859219	−	1.12245i
$849$	19.5851	−	30.4749i	0.672157	−	1.04590i
$850$	5.59901	+	8.42842i	0.192045	+	0.289092i
$851$	9.35069	+	6.84725i	0.320537	+	0.234721i
$852$	−54.7717	−	23.0326i	−1.87645	−	0.789083i
$853$	−0.546803	+	0.850842i	−0.0187222	+	0.0291323i	−0.850489	−	0.525994i	$-0.823694\pi$
$853$	−0.546803	+	0.850842i	−0.0187222	+	0.0291323i	0.831766	+	0.555126i	$0.187330\pi$
$854$	−14.2669	−	15.9690i	−0.488203	−	0.546449i
$855$	26.8257	−	12.2509i	0.917418	−	0.418971i
$856$	−22.6912	−	2.21497i	−0.775570	−	0.0757062i
$857$	0.0750635	−	0.164366i	0.00256412	−	0.00561464i	−0.908346	−	0.418220i	$-0.862654\pi$
$857$	0.0750635	−	0.164366i	0.00256412	−	0.00561464i	0.910910	+	0.412606i	$0.135381\pi$
$858$	−3.40316	+	26.5183i	−0.116182	+	0.905318i
$859$	−6.23836	+	43.3888i	−0.212850	+	1.48041i	0.550725	+	0.834687i	$0.314351\pi$
$859$	−6.23836	+	43.3888i	−0.212850	+	1.48041i	−0.763575	+	0.645719i	$0.776558\pi$
$860$	−9.06430	−	1.02378i	−0.309090	−	0.0349107i
$861$	−61.6922	−	71.1966i	−2.10246	−	2.42637i
$862$	−12.3913	+	28.2595i	−0.422048	+	0.962522i
$863$	−24.1786	−	37.6227i	−0.823050	−	1.28069i	−0.957112	−	0.289718i	$-0.906439\pi$
$863$	−24.1786	−	37.6227i	−0.823050	−	1.28069i	0.134062	−	0.990973i	$-0.457198\pi$
$864$	−20.8927	−	37.8630i	−0.710784	−	1.28812i
$865$	−0.0828827	−	0.282272i	−0.00281809	−	0.00959755i
$866$	−15.3074	+	7.27318i	−0.520166	+	0.247153i
$867$	65.6889	−	75.8091i	2.23091	−	2.57461i
$868$	−48.1665	+	44.3641i	−1.63488	+	1.50581i
$869$	6.63089	−	22.5827i	0.224937	−	0.766067i
$870$	−8.14651	+	13.1091i	−0.276192	+	0.444441i
$871$	5.51933	+	38.3878i	0.187015	+	1.30072i
$872$	−1.37082	+	3.40335i	−0.0464218	+	0.115252i
$873$		−	48.2865i		−	1.63425i
$874$	31.7442	+	16.2888i	1.07376	+	0.550977i
$875$	−3.96563			−0.134063
$876$	21.0174	−	14.4260i	0.710112	−	0.487408i
$877$	−47.1899	+	6.78489i	−1.59349	+	0.229109i	−0.881189	−	0.472764i	$-0.843256\pi$
$877$	−47.1899	+	6.78489i	−1.59349	+	0.229109i	−0.712302	+	0.701873i	$0.752347\pi$
$878$	23.1948	−	37.3244i	0.782787	−	1.25964i
$879$	8.63854	+	2.53650i	0.291371	+	0.0855542i
$880$	−3.66559	−	10.1598i	−0.123567	−	0.342486i
$881$	11.3449	+	9.83038i	0.382218	+	0.331194i	0.824686	−	0.565590i	$-0.191352\pi$
$881$	11.3449	+	9.83038i	0.382218	+	0.331194i	−0.442468	+	0.896784i	$0.645897\pi$
$882$	−29.6899	−	62.4865i	−0.999712	−	2.10403i
$883$	7.36183	−	2.16163i	0.247745	−	0.0727446i	−0.155502	−	0.987836i	$-0.549700\pi$
$883$	7.36183	−	2.16163i	0.247745	−	0.0727446i	0.403248	+	0.915091i	$0.367881\pi$
$884$	−32.4620	+	10.6111i	−1.09182	+	0.356890i
$885$	−1.97568	+	1.26969i	−0.0664118	+	0.0426803i
$886$	−18.0778	+	41.2281i	−0.607335	+	1.38509i
$887$	−36.4077	+	31.5475i	−1.22245	+	1.05926i	−0.226084	+	0.974108i	$0.572592\pi$
$887$	−36.4077	+	31.5475i	−1.22245	+	1.05926i	−0.996368	+	0.0851529i	$0.972862\pi$
$888$	−9.15065	−	17.8419i	−0.307076	−	0.598736i
$889$	−15.5829	−	2.24049i	−0.522635	−	0.0751436i
$890$	−24.2079	−	3.10667i	−0.811452	−	0.104136i
$891$	13.7756	+	6.29111i	0.461501	+	0.210760i
$892$	24.2189	+	19.7323i	0.810908	+	0.660685i
$893$	6.18195	+	13.5366i	0.206871	+	0.452984i
$894$	41.2652	+	46.1883i	1.38011	+	1.54477i
$895$	−13.2410	−	8.50945i	−0.442597	−	0.284440i
$896$	−25.6230	+	36.8296i	−0.856004	+	1.23039i
$897$	−2.04225	+	33.5150i	−0.0681888	+	1.11903i
$898$	33.9695	−	22.5660i	1.13358	−	0.753038i
$899$	25.8399	+	16.6063i	0.861810	+	0.553852i
$900$	−10.8485	−	2.83106i	−0.361617	−	0.0943686i
$901$	−66.9769	+	30.5873i	−2.23132	+	1.01901i
$902$	−9.16095	−	29.5349i	−0.305026	−	0.983405i
$903$	−48.2651	−	22.0420i	−1.60616	−	0.733510i
$904$	−24.3699	+	42.0054i	−0.810532	+	1.39708i
$905$	1.10560	−	7.68959i	0.0367512	−	0.255610i
$906$	49.6574	+	41.7270i	1.64976	+	1.38629i
$907$	21.8716	−	18.9518i	0.726234	−	0.629286i	−0.211202	−	0.977442i	$-0.567738\pi$
$907$	21.8716	−	18.9518i	0.726234	−	0.629286i	0.937436	+	0.348157i	$0.113192\pi$
$908$	−13.6560	+	2.38817i	−0.453191	+	0.0792541i
$909$	−8.78672	−	13.6724i	−0.291437	−	0.453485i
$910$	3.57573	−	12.8983i	0.118534	−	0.427573i
$911$	53.3662	−	15.6697i	1.76810	−	0.519161i	0.774546	−	0.632517i	$-0.217978\pi$
$911$	53.3662	−	15.6697i	1.76810	−	0.519161i	0.993554	+	0.113356i	$0.0361600\pi$
$912$	−36.4605	−	49.8119i	−1.20733	−	1.64944i
$913$	−24.8810	+	28.7142i	−0.823441	+	0.950301i
$914$	−18.0100	+	2.86884i	−0.595719	+	0.0948930i
$915$	−10.7475	−	3.15575i	−0.355302	−	0.104326i
$916$	26.8463	−	0.814483i	0.887025	−	0.0269113i
$917$	2.51423	+	17.4869i	0.0830272	+	0.577467i
$918$	1.17301	+	77.3448i	0.0387149	+	2.55276i
$919$	43.0788			1.42104			0.710519	−	0.703678i	$-0.248460\pi$
$919$	43.0788			1.42104			0.710519	+	0.703678i	$0.248460\pi$
$920$	−5.44471	−	12.4240i	−0.179507	−	0.409606i
$921$	−69.2285			−2.28116
$922$	0.339399	+	22.3791i	0.0111775	+	0.737016i
$923$	−3.43968	−	23.9235i	−0.113218	−	0.787452i
$924$	−1.90518	−	62.7969i	−0.0626759	−	2.06587i
$925$	−2.31872	−	0.680838i	−0.0762391	−	0.0223858i
$926$	−12.7944	+	2.03804i	−0.420449	+	0.0669740i
$927$	41.4981	−	47.8913i	1.36298	−	1.57296i
$928$	19.7503	+	7.26712i	0.648335	+	0.238555i
$929$	29.9973	−	8.80800i	0.984179	−	0.288981i	0.250231	−	0.968186i	$-0.419494\pi$
$929$	29.9973	−	8.80800i	0.984179	−	0.288981i	0.733948	+	0.679205i	$0.237675\pi$
$930$	−9.15088	+	33.0087i	−0.300069	+	1.08240i
$931$	−24.8185	−	38.6183i	−0.813392	−	1.26566i
$932$	−8.33057	−	47.6359i	−0.272877	−	1.56037i
$933$	−1.37945	+	1.19530i	−0.0451612	+	0.0391324i
$934$	−20.3398	−	17.0915i	−0.665539	−	0.559250i
$935$	−2.74951	+	19.1232i	−0.0899185	+	0.625397i
$936$	18.9899	−	32.7321i	0.620705	−	1.06988i
$937$	19.8820	+	9.07979i	0.649515	+	0.296624i	0.712795	−	0.701372i	$-0.247429\pi$
$937$	19.8820	+	9.07979i	0.649515	+	0.296624i	−0.0632799	+	0.997996i	$0.520156\pi$
$938$	−26.9986	−	87.0434i	−0.881534	−	2.84207i
$939$	−7.31525	+	3.34076i	−0.238724	+	0.109022i
$940$	1.42859	−	5.47430i	0.0465954	−	0.178552i
$941$	24.7214	+	15.8875i	0.805894	+	0.517916i	0.877534	−	0.479514i	$-0.159187\pi$
$941$	24.7214	+	15.8875i	0.805894	+	0.517916i	−0.0716404	+	0.997431i	$0.522823\pi$
$942$	71.7794	−	47.6832i	2.33870	−	1.55360i
$943$	−13.9545	−	36.2423i	−0.454422	−	1.18021i
$944$	2.23986	+	2.28850i	0.0729014	+	0.0744845i
$945$	−25.5034	−	16.3900i	−0.829625	−	0.533168i
$946$	−11.6039	−	12.9883i	−0.377275	−	0.422285i
$947$	10.5359	+	23.0703i	0.342369	+	0.749685i	0.999993	−	0.00366193i	$-0.00116563\pi$
$947$	10.5359	+	23.0703i	0.342369	+	0.749685i	−0.657624	+	0.753346i	$0.728438\pi$
$948$	−32.3025	+	39.6473i	−1.04914	+	1.28768i
$949$	9.43240	+	4.30763i	0.306189	+	0.139832i
$950$	−7.37915	−	0.946985i	−0.239411	−	0.0307242i
$951$	1.98407	+	0.285267i	0.0643380	+	0.00925041i
$952$	71.4097	−	36.6241i	2.31440	−	1.18699i
$953$	42.1276	−	36.5038i	1.36465	−	1.18247i	0.400752	−	0.916187i	$-0.368749\pi$
$953$	42.1276	−	36.5038i	1.36465	−	1.18247i	0.963894	−	0.266286i	$-0.0857965\pi$
$954$	32.7625	−	74.7181i	1.06073	−	2.41909i
$955$	2.30074	−	1.47859i	0.0744501	−	0.0478462i
$956$	8.07740	+	24.7108i	0.261242	+	0.799204i
$957$	−28.2753	+	8.30239i	−0.914012	+	0.268378i
$958$	−19.8363	−	41.7482i	−0.640882	−	1.34882i
$959$	−1.14076	−	0.988478i	−0.0368372	−	0.0319196i
$960$	−1.21540	+	23.4372i	−0.0392267	+	0.756432i
$961$	35.6635	+	10.4718i	1.15044	+	0.337799i
$962$	4.30517	−	6.92776i	0.138804	−	0.223360i
$963$	−44.7276	+	6.43085i	−1.44133	+	0.207231i
$964$	−15.8658	−	23.1150i	−0.511002	−	0.744485i
$965$	−2.05037			−0.0660038
$966$	−7.64972	−	78.5307i	−0.246126	−	2.52668i
$967$			10.2475i			0.329537i	0.986332	+	0.164768i	$0.0526877\pi$
$967$			10.2475i			0.329537i	−0.986332	+	0.164768i	$0.947312\pi$
$968$	−3.91935	+	9.73064i	−0.125973	+	0.312755i
$969$	15.7143	+	109.295i	0.504816	+	3.51107i
$970$	−6.42957	+	10.3463i	−0.206441	+	0.332199i
$971$	−12.4872	+	42.5275i	−0.400734	+	1.36477i	0.474151	+	0.880443i	$0.342755\pi$
$971$	−12.4872	+	42.5275i	−0.400734	+	1.36477i	−0.874885	+	0.484330i	$0.839063\pi$
$972$	8.78136	+	9.53400i	0.281662	+	0.305803i
$973$	19.7206	−	22.7587i	0.632212	−	0.729611i
$974$	15.3345	−	7.28607i	0.491350	−	0.233461i
$975$	−1.97250	−	6.71772i	−0.0631706	−	0.215139i
$976$	−1.25313	+	15.2216i	−0.0401118	+	0.487232i
$977$	−10.8231	−	16.8411i	−0.346262	−	0.538794i	0.623821	−	0.781567i	$-0.285579\pi$
$977$	−10.8231	−	16.8411i	−0.346262	−	0.538794i	−0.970083	+	0.242773i	$0.921943\pi$
$978$	10.3344	−	23.5686i	0.330457	−	0.753640i
$979$	−30.5166	−	35.2180i	−0.975314	−	1.12557i
$980$	−1.95875	+	17.3422i	−0.0625700	+	0.553977i
$981$	−1.03492	+	7.19801i	−0.0330424	+	0.229815i
$982$	1.51240	−	11.7850i	0.0482625	−	0.376074i
$983$	23.9740	−	52.4956i	0.764650	−	1.67435i	0.0265612	−	0.999647i	$-0.491544\pi$
$983$	23.9740	−	52.4956i	0.764650	−	1.67435i	0.738089	−	0.674703i	$-0.235728\pi$
$984$	−6.52777	+	66.8735i	−0.208098	+	2.13185i
$985$	0.142938	−	0.0652776i	0.00455438	−	0.00207992i
$986$	−25.0800	−	28.0722i	−0.798711	−	0.894001i
$987$	17.7920	−	27.6849i	0.566325	−	0.881220i
$988$	9.73370	−	23.1468i	0.309670	−	0.736399i
$989$	−15.6291	−	15.3031i	−0.496978	−	0.486611i
$990$	−11.8453	−	17.8312i	−0.376469	−	0.566714i
$991$	−2.19995	+	3.42319i	−0.0698837	+	0.108741i	−0.874437	−	0.485140i	$-0.838769\pi$
$991$	−2.19995	+	3.42319i	−0.0698837	+	0.108741i	0.804553	+	0.593881i	$0.202405\pi$
$992$	46.6009	+	3.12581i	1.47958	+	0.0992446i
$993$	−1.62580	−	3.56001i	−0.0515933	−	0.112973i
$994$	16.8257	+	54.2459i	0.533678	+	1.72058i
$995$	−7.65477	+	16.7616i	−0.242673	+	0.531379i
$996$	74.0213	−	36.5566i	2.34546	−	1.15834i
$997$	−31.8879	−	4.58478i	−1.00990	−	0.145202i	−0.382546	−	0.923936i	$-0.624953\pi$
$997$	−31.8879	−	4.58478i	−1.00990	−	0.145202i	−0.627353	+	0.778735i	$0.715862\pi$
$998$	−12.9767	+	15.4431i	−0.410772	+	0.488841i
$999$	−12.0980	−	13.9619i	−0.382764	−	0.441734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.251.2	yes	480
8.3	odd	2		920.2.bb.b.251.20	yes	480
23.11	odd	22		920.2.bb.b.11.20	yes	480
184.11	even	22	inner	920.2.bb.a.11.2	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.2	✓	480	184.11	even	22	inner
920.2.bb.a.251.2	yes	480	1.1	even	1	trivial
920.2.bb.b.11.20	yes	480	23.11	odd	22
920.2.bb.b.251.20	yes	480	8.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41405 + 0.0214454i) q^{2} +(-0.417492 - 2.90372i) q^{3} +(1.99908 - 0.0606497i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.652627 + 4.09706i) q^{6} +(2.59694 - 2.99703i) q^{7} +(-2.82550 + 0.128633i) q^{8} +(-5.37883 + 1.57937i) q^{9} +(1.36281 + 0.377808i) q^{10} +(1.45984 + 2.27156i) q^{11} +(-1.01071 - 5.77946i) q^{12} +(1.80368 - 1.56290i) q^{13} +(-3.60793 + 4.29364i) q^{14} +(-0.417492 + 2.90372i) q^{15} +(3.99264 - 0.242487i) q^{16} +(-6.50839 - 2.97228i) q^{17} +(7.57208 - 2.34866i) q^{18} +(4.78524 - 2.18535i) q^{19} +(-1.93519 - 0.505013i) q^{20} +(-9.78674 - 6.28955i) q^{21} +(-2.11301 - 3.18079i) q^{22} +(-2.91434 - 3.80876i) q^{23} +(1.55314 + 8.15077i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-2.51698 + 2.24870i) q^{26} +(3.17571 + 6.95383i) q^{27} +(5.00972 - 6.14880i) q^{28} +(-3.38405 - 1.54544i) q^{29} +(0.528084 - 4.11497i) q^{30} +(-8.17242 - 1.17502i) q^{31} +(-5.64060 + 0.428513i) q^{32} +(5.98650 - 5.18734i) q^{33} +(9.26694 + 4.06338i) q^{34} +(-3.33610 + 2.14398i) q^{35} +(-10.6569 + 3.48351i) q^{36} +(-2.31872 + 0.680838i) q^{37} +(-6.71971 + 3.19281i) q^{38} +(-5.29125 - 4.58489i) q^{39} +(2.74729 + 0.672613i) q^{40} +(7.76984 + 2.28143i) q^{41} +(13.9738 + 8.68387i) q^{42} +(4.51454 - 0.649093i) q^{43} +(3.05611 + 4.45249i) q^{44} +5.60591 q^{45} +(4.20270 + 5.32328i) q^{46} +2.82882i q^{47} +(-2.37101 - 11.4923i) q^{48} +(-1.24187 - 8.63743i) q^{49} +(-1.20117 - 0.746453i) q^{50} +(-5.91348 + 20.1395i) q^{51} +(3.51091 - 3.23375i) q^{52} +(6.73907 - 7.77731i) q^{53} +(-4.63974 - 9.76497i) q^{54} +(-0.760736 - 2.59083i) q^{55} +(-6.95213 + 8.80215i) q^{56} +(-8.34345 - 12.9827i) q^{57} +(4.81836 + 2.11276i) q^{58} +(0.524253 + 0.605020i) q^{59} +(-0.658491 + 5.83010i) q^{60} +(-0.543398 + 3.77942i) q^{61} +(11.5814 + 1.48627i) q^{62} +(-9.23509 + 20.2220i) q^{63} +(7.96691 - 0.726904i) q^{64} +(-2.17094 + 0.991434i) q^{65} +(-8.35398 + 7.46354i) q^{66} +(-8.78544 + 13.6704i) q^{67} +(-13.1911 - 5.54710i) q^{68} +(-9.84286 + 10.0526i) q^{69} +(4.67144 - 3.10325i) q^{70} +(5.47514 - 8.51948i) q^{71} +(14.9947 - 5.15440i) q^{72} +(1.80492 + 3.95221i) q^{73} +(3.26419 - 1.01247i) q^{74} +(1.21865 - 2.66848i) q^{75} +(9.43354 - 4.65891i) q^{76} +(10.5990 + 1.52391i) q^{77} +(7.58042 + 6.36980i) q^{78} +(-5.70803 - 6.58742i) q^{79} +(-3.89923 - 0.892193i) q^{80} +(4.71819 - 3.03220i) q^{81} +(-11.0359 - 3.05943i) q^{82} +(3.96423 + 13.5009i) q^{83} +(-19.9459 - 11.9798i) q^{84} +(5.40737 + 4.68551i) q^{85} +(-6.36987 + 1.01467i) q^{86} +(-3.07472 + 10.4716i) q^{87} +(-4.41698 - 6.23051i) q^{88} +(-17.0823 + 2.45607i) q^{89} +(-7.92705 + 0.120221i) q^{90} -9.46443i q^{91} +(-6.05700 - 7.43726i) q^{92} +24.2210i q^{93} +(-0.0606650 - 4.00009i) q^{94} +(-5.20709 + 0.748667i) q^{95} +(3.59919 + 16.1998i) q^{96} +(-2.42670 + 8.26459i) q^{97} +(1.94131 + 12.1871i) q^{98} +(-11.4399 - 9.91271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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