LMFDB - Embedded newform 13.9.f.a.6.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,9,Mod(2,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.2"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			6.2
Character	$\chi$	$=$	13.6
Dual form			13.9.f.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+(-4.98932 - 18.6204i) q^{2} +(51.4031 - 89.0328i) q^{3} +(-100.124 + 57.8065i) q^{4} +(663.519 - 663.519i) q^{5} +(-1914.29 - 512.934i) q^{6} +(-974.220 + 3635.84i) q^{7} +(-1913.63 - 1913.63i) q^{8} +(-2004.06 - 3471.13i) q^{9} +(-15665.5 - 9044.49i) q^{10} +(2951.13 - 790.754i) q^{11} +11885.7i q^{12} +(13335.2 + 25256.7i) q^{13} +72561.5 q^{14} +(-24968.0 - 93182.0i) q^{15} +(-40883.3 + 70811.9i) q^{16} +(76115.3 - 43945.2i) q^{17} +(-54635.0 + 54635.0i) q^{18} +(48100.1 + 12888.4i) q^{19} +(-28078.3 + 104790. i) q^{20} +(273631. + 273631. i) q^{21} +(-29448.3 - 51006.0i) q^{22} +(-398503. - 230076. i) q^{23} +(-268742. + 72009.2i) q^{24} -489891. i q^{25} +(403757. - 374321. i) q^{26} +262452. q^{27} +(-112632. - 420350. i) q^{28} +(-39516.7 + 68445.0i) q^{29} +(-1.61051e6 + 929830. i) q^{30} +(-247923. + 247923. i) q^{31} +(853326. + 228648. i) q^{32} +(81294.4 - 303395. i) q^{33} +(-1.19804e6 - 1.19804e6i) q^{34} +(1.76604e6 + 3.05886e6i) q^{35} +(401308. + 231695. i) q^{36} +(699301. - 187377. i) q^{37} -959948. i q^{38} +(2.93415e6 + 111006. i) q^{39} -2.53946e6 q^{40} +(290714. + 1.08496e6i) q^{41} +(3.72989e6 - 6.46035e6i) q^{42} +(1.61388e6 - 931776. i) q^{43} +(-249768. + 249768. i) q^{44} +(-3.63290e6 - 973432. i) q^{45} +(-2.29585e6 + 8.56821e6i) q^{46} +(1.25272e6 + 1.25272e6i) q^{47} +(4.20306e6 + 7.27991e6i) q^{48} +(-7.27775e6 - 4.20181e6i) q^{49} +(-9.12197e6 + 2.44423e6i) q^{50} -9.03568e6i q^{51} +(-2.79517e6 - 1.75794e6i) q^{52} -2.09430e6 q^{53} +(-1.30946e6 - 4.88696e6i) q^{54} +(1.43345e6 - 2.48282e6i) q^{55} +(8.82193e6 - 5.09335e6i) q^{56} +(3.61998e6 - 3.61998e6i) q^{57} +(1.47164e6 + 394324. i) q^{58} +(-5.48291e6 + 2.04625e7i) q^{59} +(7.88642e6 + 7.88642e6i) q^{60} +(-1.17743e7 - 2.03937e7i) q^{61} +(5.85339e6 + 3.37946e6i) q^{62} +(1.45729e7 - 3.90479e6i) q^{63} +3.90215e6i q^{64} +(2.56065e7 + 7.91018e6i) q^{65} -6.05494e6 q^{66} +(4.35129e6 + 1.62392e7i) q^{67} +(-5.08063e6 + 8.79991e6i) q^{68} +(-4.09686e7 + 2.36532e7i) q^{69} +(4.81460e7 - 4.81460e7i) q^{70} +(-3.29995e7 - 8.84219e6i) q^{71} +(-2.80743e6 + 1.04775e7i) q^{72} +(3.93076e7 + 3.93076e7i) q^{73} +(-6.97808e6 - 1.20864e7i) q^{74} +(-4.36164e7 - 2.51819e7i) q^{75} +(-5.56100e6 + 1.49006e6i) q^{76} +1.15002e7i q^{77} +(-1.25725e7 - 5.51889e7i) q^{78} +2.79609e6 q^{79} +(1.98582e7 + 7.41119e7i) q^{80} +(2.66395e7 - 4.61409e7i) q^{81} +(1.87519e7 - 1.08264e7i) q^{82} +(-3.81318e7 + 3.81318e7i) q^{83} +(-4.32146e7 - 1.15793e7i) q^{84} +(2.13455e7 - 7.96625e7i) q^{85} +(-2.54022e7 - 2.54022e7i) q^{86} +(4.06257e6 + 7.03657e6i) q^{87} +(-7.16058e6 - 4.13416e6i) q^{88} +(3.13321e6 - 839541. i) q^{89} +7.25028e7i q^{90} +(-1.04821e8 + 2.38790e7i) q^{91} +5.31995e7 q^{92} +(9.32926e6 + 3.48173e7i) q^{93} +(1.70759e7 - 2.95763e7i) q^{94} +(4.04671e7 - 2.33637e7i) q^{95} +(6.42208e7 - 6.42208e7i) q^{96} +(3.75627e7 + 1.00649e7i) q^{97} +(-4.19284e7 + 1.56479e8i) q^{98} +(-8.65906e6 - 8.65906e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) $ 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−4.98932	−	18.6204i	−0.311833	−	1.16378i	−0.926902	−	0.375303i	$-0.877539\pi$
$2$	−4.98932	−	18.6204i	−0.311833	−	1.16378i	0.615070	−	0.788473i	$-0.289128\pi$
$3$	51.4031	−	89.0328i	0.634606	−	1.09917i	−0.351992	−	0.936003i	$-0.614496\pi$
$3$	51.4031	−	89.0328i	0.634606	−	1.09917i	0.986598	−	0.163167i	$-0.0521711\pi$
$4$	−100.124	+	57.8065i	−0.391108	+	0.225807i
$5$	663.519	−	663.519i	1.06163	−	1.06163i	0.0636595	−	0.997972i	$-0.479723\pi$
$5$	663.519	−	663.519i	1.06163	−	1.06163i	0.997972	−	0.0636595i	$-0.0202771\pi$
$6$	−1914.29	−	512.934i	−1.47708	−	0.395782i
$7$	−974.220	+	3635.84i	−0.405756	+	1.51430i	0.396902	+	0.917861i	$0.370085\pi$
$7$	−974.220	+	3635.84i	−0.405756	+	1.51430i	−0.802657	+	0.596440i	$0.796581\pi$
$8$	−1913.63	−	1913.63i	−0.467194	−	0.467194i
$9$	−2004.06	−	3471.13i	−0.305450	−	0.529056i
$10$	−15665.5	−	9044.49i	−1.56655	−	0.904449i
$11$	2951.13	−	790.754i	0.201566	−	0.0540096i	−0.156623	−	0.987658i	$-0.550061\pi$
$11$	2951.13	−	790.754i	0.201566	−	0.0540096i	0.358190	+	0.933649i	$0.383394\pi$
$12$			11885.7i			0.573193i
$13$	13335.2	+	25256.7i	0.466902	+	0.884309i
$13$	13335.2	+	25256.7i	0.466902	+	0.884309i
$14$	72561.5			1.88883
$15$	−24968.0	−	93182.0i	−0.493196	−	1.84063i
$16$	−40883.3	+	70811.9i	−0.623829	+	1.08050i
$17$	76115.3	−	43945.2i	0.911331	−	0.526157i	0.0304719	−	0.999536i	$-0.490299\pi$
$17$	76115.3	−	43945.2i	0.911331	−	0.526157i	0.880859	+	0.473378i	$0.156966\pi$
$18$	−54635.0	+	54635.0i	−0.520453	+	0.520453i
$19$	48100.1	+	12888.4i	0.369089	+	0.0988972i	0.438596	−	0.898684i	$-0.355476\pi$
$19$	48100.1	+	12888.4i	0.369089	+	0.0988972i	−0.0695067	+	0.997581i	$0.522143\pi$
$20$	−28078.3	+	104790.i	−0.175490	+	0.654936i
$21$	273631.	+	273631.i	1.40698	+	1.40698i
$22$	−29448.3	−	51006.0i	−0.125710	−	0.217736i
$23$	−398503.	−	230076.i	−1.42403	−	0.822166i	−0.427394	−	0.904066i	$-0.640568\pi$
$23$	−398503.	−	230076.i	−1.42403	−	0.822166i	−0.996641	+	0.0818992i	$0.973901\pi$
$24$	−268742.	+	72009.2i	−0.810011	+	0.217042i
$25$		−	489891.i		−	1.25412i
$26$	403757.	−	374321.i	0.883542	−	0.819126i
$27$	262452.			0.493849
$28$	−112632.	−	420350.i	−0.183245	−	0.683878i
$29$	−39516.7	+	68445.0i	−0.0558713	+	0.0967720i	−0.892608	−	0.450833i	$-0.851127\pi$
$29$	−39516.7	+	68445.0i	−0.0558713	+	0.0967720i	0.836737	+	0.547605i	$0.184460\pi$
$30$	−1.61051e6	+	929830.i	−1.98829	+	1.14794i
$31$	−247923.	+	247923.i	−0.268454	+	0.268454i	−0.828477	−	0.560023i	$-0.810792\pi$
$31$	−247923.	+	247923.i	−0.268454	+	0.268454i	0.560023	+	0.828477i	$0.310792\pi$
$32$	853326.	+	228648.i	0.813795	+	0.218056i
$33$	81294.4	−	303395.i	0.0685496	−	0.255831i
$34$	−1.19804e6	−	1.19804e6i	−0.896512	−	0.896512i
$35$	1.76604e6	+	3.05886e6i	1.17687	+	2.03839i
$36$	401308.	+	231695.i	0.238929	+	0.137945i
$37$	699301.	−	187377.i	0.373128	−	0.0999792i	−0.0673818	−	0.997727i	$-0.521465\pi$
$37$	699301.	−	187377.i	0.373128	−	0.0999792i	0.440509	+	0.897748i	$0.354798\pi$
$38$		−	959948.i		−	0.460377i
$39$	2.93415e6	+	111006.i	1.26831	+	0.0479829i
$40$	−2.53946e6			−0.991976
$41$	290714.	+	1.08496e6i	0.102880	+	0.383953i	0.998096	−	0.0616790i	$-0.0196455\pi$
$41$	290714.	+	1.08496e6i	0.102880	+	0.383953i	−0.895216	+	0.445632i	$0.852979\pi$
$42$	3.72989e6	−	6.46035e6i	1.19867	−	2.07615i
$43$	1.61388e6	−	931776.i	0.472061	−	0.272545i	−0.245041	−	0.969513i	$-0.578801\pi$
$43$	1.61388e6	−	931776.i	0.472061	−	0.272545i	0.717102	+	0.696968i	$0.245468\pi$
$44$	−249768.	+	249768.i	−0.0666386	+	0.0666386i
$45$	−3.63290e6	−	973432.i	−0.885938	−	0.237386i
$46$	−2.29585e6	+	8.56821e6i	−0.512757	+	1.91363i
$47$	1.25272e6	+	1.25272e6i	0.256721	+	0.256721i	0.823719	−	0.566998i	$-0.191895\pi$
$47$	1.25272e6	+	1.25272e6i	0.256721	+	0.256721i	−0.566998	+	0.823719i	$0.691895\pi$
$48$	4.20306e6	+	7.27991e6i	0.791772	+	1.37139i
$49$	−7.27775e6	−	4.20181e6i	−1.26245	−	0.728873i
$50$	−9.12197e6	+	2.44423e6i	−1.45952	+	0.391076i
$51$		−	9.03568e6i		−	1.33561i
$52$	−2.79517e6	−	1.75794e6i	−0.382292	−	0.240431i
$53$	−2.09430e6			−0.265421			−0.132711	−	0.991155i	$-0.542368\pi$
$53$	−2.09430e6			−0.265421			−0.132711	+	0.991155i	$0.542368\pi$
$54$	−1.30946e6	−	4.88696e6i	−0.153998	−	0.574730i
$55$	1.43345e6	−	2.48282e6i	0.156651	−	0.271327i
$56$	8.82193e6	−	5.09335e6i	0.897040	−	0.517906i
$57$	3.61998e6	−	3.61998e6i	0.342931	−	0.342931i
$58$	1.47164e6	+	394324.i	0.130043	+	0.0348450i
$59$	−5.48291e6	+	2.04625e7i	−0.452484	+	1.68869i	0.242898	+	0.970052i	$0.421902\pi$
$59$	−5.48291e6	+	2.04625e7i	−0.452484	+	1.68869i	−0.695381	+	0.718641i	$0.744765\pi$
$60$	7.88642e6	+	7.88642e6i	0.608520	+	0.608520i
$61$	−1.17743e7	−	2.03937e7i	−0.850387	−	1.47291i	−0.880860	−	0.473378i	$-0.843035\pi$
$61$	−1.17743e7	−	2.03937e7i	−0.850387	−	1.47291i	0.0304726	−	0.999536i	$-0.490299\pi$
$62$	5.85339e6	+	3.37946e6i	0.396133	+	0.228707i
$63$	1.45729e7	−	3.90479e6i	0.925088	−	0.247877i
$64$			3.90215e6i			0.232586i
$65$	2.56065e7	+	7.91018e6i	1.43449	+	0.443132i
$66$	−6.05494e6			−0.319105
$67$	4.35129e6	+	1.62392e7i	0.215933	+	0.805872i	0.985836	+	0.167711i	$0.0536377\pi$
$67$	4.35129e6	+	1.62392e7i	0.215933	+	0.805872i	−0.769903	+	0.638160i	$0.779696\pi$
$68$	−5.08063e6	+	8.79991e6i	−0.237620	+	0.411569i
$69$	−4.09686e7	+	2.36532e7i	−1.80740	+	1.04350i
$70$	4.81460e7	−	4.81460e7i	2.00525	−	2.00525i
$71$	−3.29995e7	−	8.84219e6i	−1.29860	−	0.347958i	−0.457677	−	0.889119i	$-0.651318\pi$
$71$	−3.29995e7	−	8.84219e6i	−1.29860	−	0.347958i	−0.840919	+	0.541161i	$0.817985\pi$
$72$	−2.80743e6	+	1.04775e7i	−0.104467	+	0.389876i
$73$	3.93076e7	+	3.93076e7i	1.38415	+	1.38415i	0.837091	+	0.547064i	$0.184255\pi$
$73$	3.93076e7	+	3.93076e7i	1.38415	+	1.38415i	0.547064	+	0.837091i	$0.315745\pi$
$74$	−6.97808e6	−	1.20864e7i	−0.232707	−	0.403060i
$75$	−4.36164e7	−	2.51819e7i	−1.37849	−	0.795873i
$76$	−5.56100e6	+	1.49006e6i	−0.166686	+	0.0446633i
$77$			1.15002e7i			0.327147i
$78$	−1.25725e7	−	5.51889e7i	−0.339658	−	1.49099i
$79$	2.79609e6			0.0717864			0.0358932	−	0.999356i	$-0.488572\pi$
$79$	2.79609e6			0.0717864			0.0358932	+	0.999356i	$0.488572\pi$
$80$	1.98582e7	+	7.41119e7i	0.484820	+	1.80937i
$81$	2.66395e7	−	4.61409e7i	0.618850	−	1.07188i
$82$	1.87519e7	−	1.08264e7i	0.414754	−	0.239458i
$83$	−3.81318e7	+	3.81318e7i	−0.803479	+	0.803479i	−0.983638	−	0.180159i	$-0.942339\pi$
$83$	−3.81318e7	+	3.81318e7i	−0.803479	+	0.803479i	0.180159	+	0.983638i	$0.442339\pi$
$84$	−4.32146e7	−	1.15793e7i	−0.867987	−	0.232576i
$85$	2.13455e7	−	7.96625e7i	0.408913	−	1.52608i
$86$	−2.54022e7	−	2.54022e7i	−0.464385	−	0.464385i
$87$	4.06257e6	+	7.03657e6i	0.0709126	+	0.122824i
$88$	−7.16058e6	−	4.13416e6i	−0.119404	−	0.0689377i
$89$	3.13321e6	−	839541.i	0.0499378	−	0.0133808i	−0.233764	−	0.972293i	$-0.575104\pi$
$89$	3.13321e6	−	839541.i	0.0499378	−	0.0133808i	0.283701	+	0.958913i	$0.408438\pi$
$90$			7.25028e7i			1.10506i
$91$	−1.04821e8	+	2.38790e7i	−1.52856	+	0.348217i
$92$	5.31995e7			0.742602
$93$	9.32926e6	+	3.48173e7i	0.124714	+	0.465439i
$94$	1.70759e7	−	2.95763e7i	0.218712	−	0.378820i
$95$	4.04671e7	−	2.33637e7i	0.496829	−	0.286844i
$96$	6.42208e7	−	6.42208e7i	0.756120	−	0.756120i
$97$	3.75627e7	+	1.00649e7i	0.424297	+	0.113690i	0.464648	−	0.885496i	$-0.346181\pi$
$97$	3.75627e7	+	1.00649e7i	0.424297	+	0.113690i	−0.0403511	+	0.999186i	$0.512848\pi$
$98$	−4.19284e7	+	1.56479e8i	−0.454573	+	1.69649i
$99$	−8.65906e6	−	8.65906e6i	−0.0901426	−	0.0901426i
$100$	2.83189e7	+	4.90497e7i	0.283189	+	0.490497i
$101$	3.74519e7	+	2.16229e7i	0.359906	+	0.207792i	0.669039	−	0.743227i	$-0.266706\pi$
$101$	3.74519e7	+	2.16229e7i	0.359906	+	0.207792i	−0.309134	+	0.951019i	$0.600039\pi$
$102$	−1.68248e8	+	4.50819e7i	−1.55435	+	0.416487i
$103$			3.26556e7i			0.290140i	0.989421	+	0.145070i	$0.0463408\pi$
$103$			3.26556e7i			0.290140i	−0.989421	+	0.145070i	$0.953659\pi$
$104$	2.28134e7	−	7.38506e7i	0.195010	−	0.631278i
$105$	3.63119e8			2.98739
$106$	1.04491e7	+	3.89967e7i	0.0827670	+	0.308891i
$107$	8.65955e7	−	1.49988e8i	0.660633	−	1.14425i	−0.319817	−	0.947479i	$-0.603621\pi$
$107$	8.65955e7	−	1.49988e8i	0.660633	−	1.14425i	0.980450	−	0.196770i	$-0.0630453\pi$
$108$	−2.62777e7	+	1.51714e7i	−0.193149	+	0.111514i
$109$	1.11165e7	−	1.11165e7i	0.0787518	−	0.0787518i	−0.666634	−	0.745385i	$-0.732265\pi$
$109$	1.11165e7	−	1.11165e7i	0.0787518	−	0.0787518i	0.745385	+	0.666634i	$0.232265\pi$
$110$	−5.33830e7	−	1.43039e7i	−0.364613	−	0.0976978i
$111$	1.92635e7	−	7.18925e7i	0.126895	−	0.473578i
$112$	−2.17631e8	−	2.17631e8i	−1.38309	−	1.38309i
$113$	−5.95709e7	−	1.03180e8i	−0.365359	−	0.632821i	0.623475	−	0.781844i	$-0.285721\pi$
$113$	−5.95709e7	−	1.03180e8i	−0.365359	−	0.632821i	−0.988834	+	0.149023i	$0.952387\pi$
$114$	−8.54669e7	−	4.93443e7i	−0.506032	−	0.292158i
$115$	−4.17074e8	+	1.11755e8i	−2.38464	+	0.638961i
$116$		−	9.13729e6i		−	0.0504645i
$117$	6.09450e7	−	9.69043e7i	0.325233	−	0.517130i
$118$	4.08376e8			2.10636
$119$	8.56245e7	+	3.19555e8i	0.426983	+	1.59352i
$120$	−1.30536e8	+	2.26095e8i	−0.629514	+	1.09035i
$121$	−1.77556e8	+	1.02512e8i	−0.828313	+	0.478227i
$122$	−3.20994e8	+	3.20994e8i	−1.44896	+	1.44896i
$123$	1.11541e8	+	2.98872e7i	0.487318	+	0.130577i
$124$	1.04914e7	−	3.91545e7i	0.0443760	−	0.165613i
$125$	−6.58650e7	−	6.58650e7i	−0.269783	−	0.269783i
$126$	−1.45418e8	−	2.51871e8i	−0.576946	−	0.999299i
$127$	6.23194e7	+	3.59801e7i	0.239557	+	0.138308i	0.614973	−	0.788548i	$-0.289167\pi$
$127$	6.23194e7	+	3.59801e7i	0.239557	+	0.138308i	−0.375416	+	0.926856i	$0.622500\pi$
$128$	2.91111e8	−	7.80030e7i	1.08447	−	0.290584i
$129$		−	1.91585e8i		−	0.691834i
$130$	1.95317e7	−	5.16270e8i	0.0683858	−	1.80760i
$131$	−7.03059e7			−0.238730			−0.119365	−	0.992850i	$-0.538086\pi$
$131$	−7.03059e7			−0.238730			−0.119365	+	0.992850i	$0.538086\pi$
$132$	9.39869e6	+	3.50764e7i	0.0309579	+	0.115536i
$133$	−9.37202e7	+	1.62328e8i	−0.299520	+	0.518785i
$134$	2.80671e8	−	1.62045e8i	0.870519	−	0.502594i
$135$	1.74142e8	−	1.74142e8i	0.524286	−	0.524286i
$136$	−2.29751e8	−	6.15616e7i	−0.671586	−	0.179951i
$137$	6.41675e7	−	2.39476e8i	0.182151	−	0.679798i	−0.813071	−	0.582165i	$-0.802206\pi$
$137$	6.41675e7	−	2.39476e8i	0.182151	−	0.679798i	0.995222	−	0.0976338i	$-0.0311274\pi$
$138$	6.44839e8	+	6.44839e8i	1.77801	+	1.77801i
$139$	2.70609e8	+	4.68709e8i	0.724909	+	1.25558i	0.959012	+	0.283367i	$0.0914513\pi$
$139$	2.70609e8	+	4.68709e8i	0.724909	+	1.25558i	−0.234103	+	0.972212i	$0.575215\pi$
$140$	−3.53644e8	−	2.04177e8i	−0.920565	−	0.531488i
$141$	1.75927e8	−	4.71394e7i	0.445097	−	0.119263i
$142$			6.58581e8i			1.61978i
$143$	5.93258e7	+	6.39912e7i	0.141873	+	0.153030i
$144$	3.27730e8			0.762196
$145$	1.91945e7	+	7.16347e7i	0.0434214	+	0.162051i
$146$	5.35805e8	−	9.28041e8i	1.17922	−	2.04247i
$147$	−7.48198e8	+	4.31972e8i	−1.60231	+	0.925095i
$148$	−5.91850e7	+	5.91850e7i	−0.123357	+	0.123357i
$149$	−3.00073e8	−	8.04043e7i	−0.608810	−	0.163130i	−0.0587743	−	0.998271i	$-0.518719\pi$
$149$	−3.00073e8	−	8.04043e7i	−0.608810	−	0.163130i	−0.550036	+	0.835141i	$0.685386\pi$
$150$	−2.51282e8	+	9.37796e8i	−0.496359	+	1.85244i
$151$	−4.09028e8	−	4.09028e8i	−0.786766	−	0.786766i	0.194197	−	0.980963i	$-0.437790\pi$
$151$	−4.09028e8	−	4.09028e8i	−0.786766	−	0.786766i	−0.980963	+	0.194197i	$0.937790\pi$
$152$	−6.73821e7	−	1.16709e8i	−0.126232	−	0.218641i
$153$	−3.05079e8	−	1.76138e8i	−0.556733	−	0.321430i
$154$	2.14139e8	−	5.73783e7i	0.380726	−	0.102015i
$155$			3.29003e8i			0.569998i
$156$	−3.00195e8	+	1.58499e8i	−0.506880	+	0.267625i
$157$	−2.01668e8			−0.331924			−0.165962	−	0.986132i	$-0.553073\pi$
$157$	−2.01668e8			−0.331924			−0.165962	+	0.986132i	$0.553073\pi$
$158$	−1.39506e7	−	5.20643e7i	−0.0223854	−	0.0835433i
$159$	−1.07654e8	+	1.86462e8i	−0.168438	+	0.291743i
$160$	7.17911e8	−	4.14486e8i	1.09545	−	0.632456i
$161$	1.22475e9	−	1.22475e9i	1.82282	−	1.82282i
$162$	−9.92076e8	−	2.65826e8i	−1.44041	−	0.385956i
$163$	6.96756e7	−	2.60033e8i	0.0987030	−	0.368365i	−0.898852	−	0.438253i	$-0.855598\pi$
$163$	6.96756e7	−	2.60033e8i	0.0987030	−	0.368365i	0.997555	+	0.0698880i	$0.0222642\pi$
$164$	−9.18252e7	−	9.18252e7i	−0.126936	−	0.126936i
$165$	−1.47368e8	−	2.55249e8i	−0.198823	−	0.344372i
$166$	9.00281e8	+	5.19777e8i	1.18562	+	0.684518i
$167$	−9.12665e8	+	2.44548e8i	−1.17340	+	0.314411i	−0.792305	−	0.610125i	$-0.791119\pi$
$167$	−9.12665e8	+	2.44548e8i	−1.17340	+	0.314411i	−0.381094	+	0.924536i	$0.624452\pi$
$168$		−	1.04726e9i		−	1.31467i
$169$	−4.60076e8	+	6.73607e8i	−0.564005	+	0.825772i
$170$	−1.58985e9			−1.90353
$171$	−5.16582e7	−	1.92791e8i	−0.0604164	−	0.225477i
$172$	−1.07725e8	+	1.86586e8i	−0.123085	+	0.213189i
$173$	1.69893e8	−	9.80878e7i	0.189667	−	0.109504i	−0.402160	−	0.915569i	$-0.631740\pi$
$173$	1.69893e8	−	9.80878e7i	0.189667	−	0.109504i	0.591827	+	0.806065i	$0.298407\pi$
$174$	1.10754e8	−	1.10754e8i	0.120827	−	0.120827i
$175$	1.78116e9	+	4.77262e8i	1.89912	+	0.508867i
$176$	−6.46572e7	+	2.41304e8i	−0.0673855	+	0.251486i
$177$	1.54000e9	+	1.54000e9i	1.56901	+	1.56901i
$178$	−3.12652e7	−	5.41529e7i	−0.0311445	−	0.0539439i
$179$	−9.30403e8	−	5.37169e8i	−0.906273	−	0.523237i	−0.0270430	−	0.999634i	$-0.508609\pi$
$179$	−9.30403e8	−	5.37169e8i	−0.906273	−	0.523237i	−0.879230	+	0.476397i	$0.841942\pi$
$180$	4.20010e8	−	1.12541e8i	0.400101	−	0.107207i
$181$		−	1.05276e9i		−	0.980882i	−0.871474	−	0.490441i	$-0.836836\pi$
$181$		−	1.05276e9i		−	0.980882i	0.871474	−	0.490441i	$-0.163164\pi$
$182$	9.67622e8	+	1.83267e9i	0.881901	+	1.67031i
$183$	−2.42095e9			−2.15864
$184$	3.22307e8	+	1.20287e9i	0.281189	+	1.04941i
$185$	3.39671e8	−	5.88328e8i	0.289983	−	0.502265i
$186$	6.01765e8	−	3.47429e8i	0.502777	−	0.290278i
$187$	1.89877e8	−	1.89877e8i	0.155276	−	0.155276i
$188$	−1.97842e8	−	5.30116e7i	−0.158375	−	0.0424365i
$189$	−2.55686e8	+	9.54232e8i	−0.200382	+	0.747837i
$190$	−6.36944e8	−	6.36944e8i	−0.488750	−	0.488750i
$191$	1.81605e7	+	3.14548e7i	0.0136456	+	0.0236349i	0.872768	−	0.488136i	$-0.162323\pi$
$191$	1.81605e7	+	3.14548e7i	0.0136456	+	0.0236349i	−0.859122	+	0.511771i	$0.828990\pi$
$192$	3.47420e8	+	2.00583e8i	0.255652	+	0.147601i
$193$	3.65182e8	−	9.78501e7i	0.263196	−	0.0705232i	−0.124808	−	0.992181i	$-0.539831\pi$
$193$	3.65182e8	−	9.78501e7i	0.263196	−	0.0705232i	0.388004	+	0.921658i	$0.373165\pi$
$194$		−	7.49649e8i		−	0.529238i
$195$	2.02052e9	−	1.87321e9i	1.39741	−	1.29553i
$196$	9.71567e8			0.658338
$197$	−8.58779e7	−	3.20501e8i	−0.0570186	−	0.212796i	0.931539	−	0.363642i	$-0.118467\pi$
$197$	−8.58779e7	−	3.20501e8i	−0.0570186	−	0.212796i	−0.988557	+	0.150846i	$0.951800\pi$
$198$	−1.18032e8	+	2.04438e8i	−0.0767964	+	0.133015i
$199$	−1.52214e9	+	8.78811e8i	−0.970608	+	0.560381i	−0.899421	−	0.437083i	$-0.856012\pi$
$199$	−1.52214e9	+	8.78811e8i	−0.970608	+	0.560381i	−0.0711861	+	0.997463i	$0.522678\pi$
$200$	−9.37469e8	+	9.37469e8i	−0.585918	+	0.585918i
$201$	1.66949e9	+	4.47339e8i	1.02282	+	0.274065i
$202$	2.15767e8	−	8.05254e8i	0.129592	−	0.483646i
$203$	−2.10357e8	−	2.10357e8i	−0.123872	−	0.123872i
$204$	5.22321e8	+	9.04686e8i	0.301590	+	0.522369i
$205$	9.12787e8	+	5.26998e8i	0.516837	+	0.298396i
$206$	6.08060e8	−	1.62929e8i	0.337658	−	0.0904753i
$207$			1.84434e9i			1.00452i
$208$	−2.33367e9	−	8.82879e7i	−1.24677	−	0.0471680i
$209$	1.52141e8			0.0797374
$210$	−1.81172e9	−	6.76142e9i	−0.931565	−	3.47665i
$211$	−1.08965e9	+	1.88733e9i	−0.549741	+	0.952180i	0.448551	+	0.893757i	$0.351940\pi$
$211$	−1.08965e9	+	1.88733e9i	−0.549741	+	0.952180i	−0.998292	+	0.0584224i	$0.981393\pi$
$212$	2.09689e8	−	1.21064e8i	0.103808	−	0.0599339i
$213$	−2.48352e9	+	2.48352e9i	−1.20656	+	1.20656i
$214$	−3.22489e9	−	8.64106e8i	−1.53766	−	0.412014i
$215$	4.52591e8	−	1.68909e9i	0.211813	−	0.790497i
$216$	−5.02235e8	−	5.02235e8i	−0.230724	−	0.230724i
$217$	−6.59876e8	−	1.14294e9i	−0.297593	−	0.515447i
$218$	−2.62457e8	−	1.51529e8i	−0.116207	−	0.0670920i
$219$	5.52019e9	−	1.47913e9i	2.39982	−	0.643029i
$220$			3.31452e8i			0.141491i
$221$	2.12492e9	+	1.33641e9i	0.890788	+	0.560234i
$222$	−1.43478e9			−0.590709
$223$	−2.61664e8	−	9.76542e8i	−0.105809	−	0.394886i	0.892626	−	0.450797i	$-0.148860\pi$
$223$	−2.61664e8	−	9.76542e8i	−0.105809	−	0.394886i	−0.998436	+	0.0559113i	$0.982194\pi$
$224$	−1.66265e9	+	2.87980e9i	−0.660405	+	1.14385i
$225$	−1.70048e9	+	9.81772e8i	−0.663500	+	0.383072i
$226$	−1.62403e9	+	1.62403e9i	−0.622530	+	0.622530i
$227$	1.19814e9	+	3.21040e8i	0.451236	+	0.120908i	0.477278	−	0.878752i	$-0.341624\pi$
$227$	1.19814e9	+	3.21040e8i	0.451236	+	0.120908i	−0.0260416	+	0.999661i	$0.508290\pi$
$228$	−1.53188e8	+	5.71705e8i	−0.0566872	+	0.211560i
$229$	−2.48667e9	−	2.48667e9i	−0.904224	−	0.904224i	0.0915738	−	0.995798i	$-0.470810\pi$
$229$	−2.48667e9	−	2.48667e9i	−0.904224	−	0.904224i	−0.995798	+	0.0915738i	$0.970810\pi$
$230$	4.16184e9	+	7.20852e9i	1.48722	+	2.57593i
$231$	1.02390e9	+	5.91147e8i	0.359590	+	0.207610i
$232$	2.06599e8	−	5.53579e7i	0.0713141	−	0.0191086i
$233$		−	2.11514e9i		−	0.717654i	−0.933404	−	0.358827i	$-0.883177\pi$
$233$		−	2.11514e9i		−	0.717654i	0.933404	−	0.358827i	$-0.116823\pi$
$234$	−2.10847e9	−	6.51334e8i	−0.703241	−	0.217240i
$235$	1.66240e9			0.545086
$236$	−6.33896e8	−	2.36573e9i	−0.204348	−	0.762636i
$237$	1.43728e8	−	2.48943e8i	0.0455561	−	0.0789055i
$238$	5.52304e9	−	3.18873e9i	1.72135	−	0.993824i
$239$	−5.77210e8	+	5.77210e8i	−0.176906	+	0.176906i	−0.790006	−	0.613100i	$-0.789922\pi$
$239$	−5.77210e8	+	5.77210e8i	−0.176906	+	0.176906i	0.613100	+	0.790006i	$0.289922\pi$
$240$	7.61917e9	+	2.04155e9i	2.29648	+	0.615340i
$241$	1.53986e9	−	5.74685e9i	0.456472	−	1.70358i	−0.227253	−	0.973836i	$-0.572974\pi$
$241$	1.53986e9	−	5.74685e9i	0.456472	−	1.70358i	0.683725	−	0.729740i	$-0.260359\pi$
$242$	2.79471e9	+	2.79471e9i	0.814844	+	0.814844i
$243$	−1.87773e9	−	3.25233e9i	−0.538528	−	0.932758i
$244$	2.35778e9	+	1.36126e9i	0.665187	+	0.384046i
$245$	−7.61691e9	+	2.04094e9i	−2.11405	+	0.566457i
$246$		−	2.22605e9i		−	0.607847i
$247$	3.15906e8	+	1.38672e9i	0.0848730	+	0.372564i
$248$	9.48864e8			0.250840
$249$	1.43489e9	+	5.35507e9i	0.373267	+	1.39305i
$250$	−8.97812e8	+	1.55506e9i	−0.229840	+	0.398094i
$251$	3.69338e8	−	2.13237e8i	0.0930526	−	0.0537240i	−0.452752	−	0.891637i	$-0.649558\pi$
$251$	3.69338e8	−	2.13237e8i	0.0930526	−	0.0537240i	0.545804	+	0.837913i	$0.316224\pi$
$252$	−1.23337e9	+	1.23337e9i	−0.305838	+	0.305838i
$253$	−1.35797e9	−	3.63867e8i	−0.331442	−	0.0888097i
$254$	3.59033e8	−	1.33993e9i	0.0862580	−	0.321919i
$255$	−5.99535e9	−	5.99535e9i	−1.41793	−	1.41793i
$256$	−2.40542e9	−	4.16631e9i	−0.560056	−	0.970045i
$257$	5.92653e9	+	3.42168e9i	1.35853	+	0.784345i	0.989425	−	0.145044i	$-0.0463324\pi$
$257$	5.92653e9	+	3.42168e9i	1.35853	+	0.784345i	0.369101	+	0.929389i	$0.379666\pi$
$258$	−3.56739e9	+	9.55878e8i	−0.805140	+	0.215737i
$259$			2.72509e9i			0.605595i
$260$	−3.02108e9	+	6.88225e8i	−0.661102	+	0.150604i
$261$	3.16776e8			0.0682637
$262$	3.50779e8	+	1.30912e9i	0.0744437	+	0.277828i
$263$	−1.31656e9	+	2.28035e9i	−0.275180	+	0.476626i	−0.970181	−	0.242383i	$-0.922071\pi$
$263$	−1.31656e9	+	2.28035e9i	−0.275180	+	0.476626i	0.695000	+	0.719009i	$0.255404\pi$
$264$	−7.36152e8	+	4.25018e8i	−0.151549	+	0.0874966i
$265$	−1.38961e9	+	1.38961e9i	−0.281779	+	0.281779i
$266$	3.49022e9	+	9.35200e8i	0.697149	+	0.186801i
$267$	8.63101e7	−	3.22114e8i	0.0169831	−	0.0633817i
$268$	−1.37440e9	−	1.37440e9i	−0.266424	−	0.266424i
$269$	−4.49130e9	−	7.77916e9i	−0.857754	−	1.48567i	−0.874066	−	0.485807i	$-0.838526\pi$
$269$	−4.49130e9	−	7.77916e9i	−0.857754	−	1.48567i	0.0163114	−	0.999867i	$-0.494808\pi$
$270$	−4.11144e9	−	2.37374e9i	−0.773641	−	0.446662i
$271$	6.99061e9	−	1.87313e9i	1.29610	−	0.347289i	0.456125	−	0.889916i	$-0.349237\pi$
$271$	6.99061e9	−	1.87313e9i	1.29610	−	0.347289i	0.839974	+	0.542627i	$0.182570\pi$
$272$			7.18649e9i			1.31293i
$273$	−3.26210e9	+	1.05599e10i	−0.587283	+	1.90113i
$274$	−4.77930e9			−0.847933
$275$	−3.87383e8	−	1.44573e9i	−0.0677345	−	0.252789i
$276$	2.73462e9	−	4.73650e9i	0.471260	−	0.816247i
$277$	−3.77235e9	+	2.17797e9i	−0.640756	+	0.369941i	−0.784906	−	0.619615i	$-0.787289\pi$
$277$	−3.77235e9	+	2.17797e9i	−0.640756	+	0.369941i	0.144149	+	0.989556i	$0.453955\pi$
$278$	7.37739e9	−	7.37739e9i	1.23516	−	1.23516i
$279$	1.35743e9	+	3.63721e8i	0.224027	+	0.0600277i
$280$	2.47399e9	−	9.23306e9i	0.402500	−	1.50215i
$281$	−9.73480e8	−	9.73480e8i	−0.156136	−	0.156136i	0.624716	−	0.780852i	$-0.285215\pi$
$281$	−9.73480e8	−	9.73480e8i	−0.156136	−	0.156136i	−0.780852	+	0.624716i	$0.785215\pi$
$282$	−1.75551e9	−	3.04063e9i	−0.277592	−	0.480803i
$283$	8.27573e8	+	4.77800e8i	0.129021	+	0.0744904i	0.563121	−	0.826374i	$-0.309600\pi$
$283$	8.27573e8	+	4.77800e8i	0.129021	+	0.0744904i	−0.434100	+	0.900865i	$0.642934\pi$
$284$	3.81517e9	−	1.02227e9i	0.586463	−	0.157142i
$285$		−	4.80386e9i		−	0.728133i
$286$	8.95546e8	−	1.42394e9i	0.133852	−	0.212828i
$287$	−4.22796e9			−0.623165
$288$	−9.16449e8	−	3.42024e9i	−0.133211	−	0.497148i
$289$	3.74479e8	−	6.48616e8i	0.0536829	−	0.0929815i
$290$	1.23810e9	−	7.14817e8i	0.175051	−	0.101066i
$291$	2.82694e9	−	2.82694e9i	0.394226	−	0.394226i
$292$	−6.20785e9	−	1.66339e9i	−0.853906	−	0.228803i
$293$	−3.20227e9	+	1.19510e10i	−0.434497	+	1.62157i	0.307769	+	0.951461i	$0.400418\pi$
$293$	−3.20227e9	+	1.19510e10i	−0.434497	+	1.62157i	−0.742266	+	0.670105i	$0.766249\pi$
$294$	1.17765e10	+	1.17765e10i	1.57626	+	1.57626i
$295$	9.93925e9	+	1.72153e10i	1.31240	+	2.27314i
$296$	−1.69677e9	−	9.79632e8i	−0.221033	−	0.127613i
$297$	7.74531e8	−	2.07535e8i	0.0995435	−	0.0266726i
$298$			5.98864e9i			0.759387i
$299$	4.96851e8	−	1.31330e10i	0.0621644	−	1.64316i
$300$	5.82272e9			0.718854
$301$	1.81551e9	+	6.77557e9i	0.221173	+	0.825429i
$302$	−5.57550e9	+	9.65705e9i	−0.670279	+	1.16096i
$303$	3.85029e9	−	2.22297e9i	0.456797	−	0.263732i
$304$	−2.87914e9	+	2.87914e9i	−0.337108	+	0.337108i
$305$	−2.13441e10	−	5.71914e9i	−2.46649	−	0.660893i
$306$	−1.75761e9	+	6.55951e9i	−0.200465	+	0.748145i
$307$	5.41804e9	+	5.41804e9i	0.609942	+	0.609942i	0.942931	−	0.332989i	$-0.108057\pi$
$307$	5.41804e9	+	5.41804e9i	0.609942	+	0.609942i	−0.332989	+	0.942931i	$0.608057\pi$
$308$	−6.64787e8	−	1.15144e9i	−0.0738719	−	0.127950i
$309$	2.90742e9	+	1.67860e9i	0.318914	+	0.184125i
$310$	6.12618e9	−	1.64150e9i	0.663350	−	0.177744i
$311$		−	1.42159e9i		−	0.151961i	−0.997109	−	0.0759807i	$-0.975791\pi$
$311$		−	1.42159e9i		−	0.151961i	0.997109	−	0.0759807i	$-0.0242087\pi$
$312$	−5.40245e9	−	5.82729e9i	−0.570128	−	0.614962i
$313$	8.31488e9			0.866320			0.433160	−	0.901317i	$-0.357398\pi$
$313$	8.31488e9			0.866320			0.433160	+	0.901317i	$0.357398\pi$
$314$	1.00619e9	+	3.75515e9i	0.103505	+	0.386286i
$315$	7.07848e9	−	1.22603e10i	0.718949	−	1.24526i
$316$	−2.79955e8	+	1.61632e8i	−0.0280763	+	0.0162098i
$317$	5.61866e9	−	5.61866e9i	0.556411	−	0.556411i	−0.371873	−	0.928284i	$-0.621284\pi$
$317$	5.61866e9	−	5.61866e9i	0.556411	−	0.556411i	0.928284	+	0.371873i	$0.121284\pi$
$318$	4.00911e9	+	1.07424e9i	0.392048	+	0.105049i
$319$	−6.24960e7	+	2.33238e8i	−0.00603517	+	0.0225236i
$320$	2.58915e9	+	2.58915e9i	0.246921	+	0.246921i
$321$	−8.90256e9	−	1.54197e10i	−0.838484	−	1.45230i
$322$	−2.89160e10	−	1.66946e10i	−2.68977	−	1.55294i
$323$	4.22754e9	−	1.13276e9i	0.388398	−	0.104071i
$324$			6.15974e9i			0.558962i
$325$	1.23731e10	−	6.53279e9i	1.10903	−	0.585552i
$326$	−5.18955e9			−0.459473
$327$	−4.18309e8	−	1.56115e9i	−0.0365853	−	0.136538i
$328$	1.51989e9	−	2.63253e9i	0.131316	−	0.227446i
$329$	−5.77510e9	+	3.33426e9i	−0.492919	+	0.284587i
$330$	−4.01757e9	+	4.01757e9i	−0.338772	+	0.338772i
$331$	3.67557e8	+	9.84867e7i	0.0306206	+	0.00820476i	0.274097	−	0.961702i	$-0.411621\pi$
$331$	3.67557e8	+	9.84867e7i	0.0306206	+	0.00820476i	−0.243476	+	0.969907i	$0.578288\pi$
$332$	1.61363e9	−	6.02216e9i	0.132817	−	0.495678i
$333$	−2.05185e9	−	2.05185e9i	−0.166867	−	0.166867i
$334$	9.10716e9	+	1.57741e10i	0.731808	+	1.26753i
$335$	1.36622e10	+	7.88788e9i	1.08478	+	0.626298i
$336$	−3.05633e10	+	8.18940e9i	−2.39796	+	0.642532i
$337$		−	1.40990e10i		−	1.09312i	−0.837419	−	0.546561i	$-0.815937\pi$
$337$		−	1.40990e10i		−	1.09312i	0.837419	−	0.546561i	$-0.184063\pi$
$338$	1.48383e10	+	5.20595e9i	1.13689	+	0.398872i
$339$	−1.22485e10			−0.927437
$340$	2.46782e9	+	9.21001e9i	0.184670	+	0.689199i
$341$	−5.35608e8	+	9.27700e8i	−0.0396122	+	0.0686104i
$342$	−3.33211e9	+	1.92379e9i	−0.243565	+	0.140622i
$343$	7.02353e9	−	7.02353e9i	0.507433	−	0.507433i
$344$	−4.87144e9	−	1.30530e9i	−0.347876	−	0.0932130i
$345$	−1.14891e10	+	4.28778e10i	−0.810978	+	3.02661i
$346$	−2.67409e9	−	2.67409e9i	−0.186583	−	0.186583i
$347$	−5.01283e9	−	8.68248e9i	−0.345752	−	0.598861i	0.639738	−	0.768593i	$-0.279043\pi$
$347$	−5.01283e9	−	8.68248e9i	−0.345752	−	0.598861i	−0.985490	+	0.169733i	$0.945710\pi$
$348$	−8.13519e8	−	4.69685e8i	−0.0554690	−	0.0320251i
$349$	3.81092e7	−	1.02113e7i	0.00256879	−	0.000688305i	−0.257534	−	0.966269i	$-0.582910\pi$
$349$	3.81092e7	−	1.02113e7i	0.00256879	−	0.000688305i	0.260103	+	0.965581i	$0.416243\pi$
$350$		−	3.55472e10i		−	2.36883i
$351$	3.49985e9	+	6.62868e9i	0.230579	+	0.436716i
$352$	2.69908e9			0.175811
$353$	−3.03153e9	−	1.13138e10i	−0.195237	−	0.728635i	−0.992205	−	0.124614i	$-0.960231\pi$
$353$	−3.03153e9	−	1.13138e10i	−0.195237	−	0.728635i	0.796968	−	0.604021i	$-0.206436\pi$
$354$	2.09918e10	−	3.63589e10i	1.33671	−	2.31525i
$355$	−2.77628e10	+	1.60288e10i	−1.74803	+	1.00923i
$356$	−2.65178e8	+	2.65178e8i	−0.0165096	+	0.0165096i
$357$	3.28523e10	+	8.80273e9i	2.02252	+	0.541932i
$358$	−5.36022e9	+	2.00046e10i	−0.326325	+	1.21786i
$359$	−1.40429e10	−	1.40429e10i	−0.845433	−	0.845433i	0.144126	−	0.989559i	$-0.453963\pi$
$359$	−1.40429e10	−	1.40429e10i	−0.845433	−	0.845433i	−0.989559	+	0.144126i	$0.953963\pi$
$360$	5.08923e9	+	8.81480e9i	0.303000	+	0.524811i
$361$	−1.25607e10	−	7.25192e9i	−0.739579	−	0.426996i
$362$	−1.96029e10	+	5.25258e9i	−1.14153	+	0.305871i
$363$			2.10778e10i			1.21394i
$364$	9.11470e9	−	8.45018e9i	0.519202	−	0.481349i
$365$	5.21627e10			2.93892
$366$	1.20789e10	+	4.50790e10i	0.673136	+	2.51218i
$367$	3.03888e9	−	5.26349e9i	0.167513	−	0.290141i	−0.770032	−	0.638006i	$-0.779760\pi$
$367$	3.03888e9	−	5.26349e9i	0.167513	−	0.290141i	0.937545	+	0.347864i	$0.113093\pi$
$368$	3.25842e10	−	1.88125e10i	1.77671	−	1.02578i
$369$	3.18343e9	−	3.18343e9i	0.171708	−	0.171708i
$370$	−1.26496e10	−	3.38946e9i	−0.674950	−	0.180852i
$371$	2.04031e9	−	7.61454e9i	0.107696	−	0.401928i
$372$	−2.94675e9	−	2.94675e9i	−0.153876	−	0.153876i
$373$	9.91178e9	+	1.71677e10i	0.512055	+	0.886905i	0.999902	+	0.0139760i	$0.00444884\pi$
$373$	9.91178e9	+	1.71677e10i	0.512055	+	0.886905i	−0.487848	+	0.872929i	$0.662218\pi$
$374$	−4.48293e9	−	2.58822e9i	−0.229127	−	0.132286i
$375$	−9.24982e9	+	2.47848e9i	−0.467744	+	0.125332i
$376$		−	4.79447e9i		−	0.239877i
$377$	−2.25566e9	−	8.53368e7i	−0.111663	−	0.00422446i
$378$	1.90439e10			0.932800
$379$	−3.28686e9	−	1.22667e10i	−0.159303	−	0.594527i	−0.998698	−	0.0510059i	$-0.983757\pi$
$379$	−3.28686e9	−	1.22667e10i	−0.159303	−	0.594527i	0.839395	−	0.543522i	$-0.182909\pi$
$380$	−2.70114e9	+	4.67852e9i	−0.129543	+	0.224375i
$381$	6.40682e9	−	3.69898e9i	0.304048	−	0.175542i
$382$	4.95093e8	−	4.95093e8i	0.0232506	−	0.0232506i
$383$	−2.41518e10	−	6.47144e9i	−1.12242	−	0.300750i	−0.350555	−	0.936542i	$-0.614007\pi$
$383$	−2.41518e10	−	6.47144e9i	−1.12242	−	0.300750i	−0.771860	+	0.635792i	$0.780674\pi$
$384$	8.01920e9	−	2.99281e10i	0.368813	−	1.37643i
$385$	7.63061e9	+	7.63061e9i	0.347309	+	0.347309i
$386$	−3.64402e9	−	6.31163e9i	−0.164146	−	0.284310i
$387$	−6.46864e9	−	3.73467e9i	−0.288383	−	0.166498i
$388$	−4.34273e9	+	1.16363e9i	−0.191618	+	0.0513439i
$389$			4.13431e10i			1.80553i	0.430135	+	0.902765i	$0.358466\pi$
$389$			4.13431e10i			1.80553i	−0.430135	+	0.902765i	$0.641534\pi$
$390$	−4.49610e10	−	2.82768e10i	−1.94347	−	1.22229i
$391$	−4.04429e10			−1.73036
$392$	5.88620e9	+	2.19676e10i	0.249282	+	0.930333i
$393$	−3.61394e9	+	6.25953e9i	−0.151499	+	0.262405i
$394$	−5.53938e9	+	3.19817e9i	−0.229867	+	0.132714i
$395$	1.85526e9	−	1.85526e9i	0.0762107	−	0.0762107i
$396$	1.36753e9	+	3.66428e8i	0.0556103	+	0.0149007i
$397$	2.78639e9	−	1.03989e10i	0.112171	−	0.418627i	−0.886889	−	0.461983i	$-0.847138\pi$
$397$	2.78639e9	−	1.03989e10i	0.112171	−	0.418627i	0.999060	+	0.0433557i	$0.0138049\pi$
$398$	2.39583e10	+	2.39583e10i	0.954824	+	0.954824i
$399$	9.63502e9	+	1.66883e10i	0.380155	+	0.658448i
$400$	3.46901e10	+	2.00284e10i	1.35508	+	0.782358i
$401$	−9.64623e9	+	2.58470e9i	−0.373061	+	0.0999615i	−0.440478	−	0.897763i	$-0.645191\pi$
$401$	−9.64623e9	+	2.58470e9i	−0.373061	+	0.0999615i	0.0674166	+	0.997725i	$0.478524\pi$
$402$		−	3.33186e10i		−	1.27580i
$403$	−9.56783e9	−	2.95563e9i	−0.362738	−	0.112054i
$404$	−4.99977e9			−0.187683
$405$	−1.29396e10	−	4.82912e10i	−0.480951	−	1.79493i
$406$	−2.86739e9	+	4.96647e9i	−0.105532	+	0.182786i
$407$	1.91556e9	−	1.10595e9i	0.0698101	−	0.0403049i
$408$	−1.72909e10	+	1.72909e10i	−0.623990	+	0.623990i
$409$	−4.28037e10	−	1.14692e10i	−1.52964	−	0.409865i	−0.606736	−	0.794903i	$-0.707522\pi$
$409$	−4.28037e10	−	1.14692e10i	−1.52964	−	0.409865i	−0.922901	+	0.385038i	$0.874188\pi$
$410$	5.25872e9	−	1.96258e10i	0.186099	−	0.694532i
$411$	−1.80228e10	−	1.80228e10i	−0.631620	−	0.631620i
$412$	−1.88770e9	−	3.26960e9i	−0.0655156	−	0.113476i
$413$	−6.90568e10	−	3.98699e10i	−2.37359	−	1.37039i
$414$	3.43424e10	−	9.20203e9i	1.16904	−	0.313244i
$415$			5.06023e10i			1.70600i
$416$	5.60437e9	+	2.46013e10i	0.187134	+	0.821457i
$417$	5.56406e10			1.84013
$418$	−7.59083e8	−	2.83293e9i	−0.0248647	−	0.0927965i
$419$	−1.28346e10	+	2.22302e10i	−0.416415	+	0.721251i	−0.995576	−	0.0939618i	$-0.970047\pi$
$419$	−1.28346e10	+	2.22302e10i	−0.416415	+	0.721251i	0.579161	+	0.815213i	$0.303380\pi$
$420$	−3.63568e10	+	2.09906e10i	−1.16839	+	0.674572i
$421$	2.72449e10	−	2.72449e10i	0.867274	−	0.867274i	−0.124896	−	0.992170i	$-0.539860\pi$
$421$	2.72449e10	−	2.72449e10i	0.867274	−	0.867274i	0.992170	+	0.124896i	$0.0398596\pi$
$422$	4.05796e10	+	1.08733e10i	1.27955	+	0.342855i
$423$	1.83783e9	−	6.85887e9i	0.0574042	−	0.214235i
$424$	4.00771e9	+	4.00771e9i	0.124003	+	0.124003i
$425$	−2.15284e10	−	3.72882e10i	−0.659865	−	1.14292i
$426$	5.86353e10	+	3.38531e10i	1.78041	+	1.02792i
$427$	8.56191e10	−	2.29416e10i	2.57548	−	0.690099i
$428$			2.00231e10i			0.596701i
$429$	8.74685e9	−	1.99260e9i	0.258239	−	0.0588289i
$430$	−3.37097e10			−0.986011
$431$	1.14964e10	+	4.29050e10i	0.333159	+	1.24337i	0.905851	+	0.423596i	$0.139232\pi$
$431$	1.14964e10	+	4.29050e10i	0.333159	+	1.24337i	−0.572692	+	0.819770i	$0.694101\pi$
$432$	−1.07299e10	+	1.85847e10i	−0.308078	+	0.533606i
$433$	2.35551e10	−	1.35995e10i	0.670089	−	0.386876i	−0.126021	−	0.992028i	$-0.540221\pi$
$433$	2.35551e10	−	1.35995e10i	0.670089	−	0.386876i	0.796110	+	0.605151i	$0.206887\pi$
$434$	−1.79897e10	+	1.79897e10i	−0.507065	+	0.507065i
$435$	7.36449e9	+	1.97331e9i	0.205677	+	0.0551110i
$436$	−4.70418e8	+	1.75562e9i	−0.0130178	+	0.0485832i
$437$	−1.62027e10	−	1.62027e10i	−0.444286	−	0.444286i
$438$	−5.50841e10	−	9.54084e10i	−1.49668	−	2.59233i
$439$	2.09497e10	+	1.20953e10i	0.564052	+	0.325656i	0.754770	−	0.655989i	$-0.227748\pi$
$439$	2.09497e10	+	1.20953e10i	0.564052	+	0.325656i	−0.190718	+	0.981645i	$0.561082\pi$
$440$	−7.49428e9	+	2.00809e9i	−0.199949	+	0.0535762i
$441$			3.36827e10i			0.890539i
$442$	1.42825e10	−	4.62347e10i	0.374210	−	1.21138i
$443$	5.32413e10			1.38240			0.691200	−	0.722663i	$-0.257082\pi$
$443$	5.32413e10			1.38240			0.691200	+	0.722663i	$0.257082\pi$
$444$	2.22711e9	+	8.31171e9i	0.0573074	+	0.213874i
$445$	1.52189e9	−	2.63600e9i	0.0388101	−	0.0672210i
$446$	−1.68781e10	+	9.74457e9i	−0.426564	+	0.246277i
$447$	−2.25833e10	+	2.25833e10i	−0.565663	+	0.565663i
$448$	−1.41876e10	−	3.80156e9i	−0.352206	−	0.0943733i
$449$	8.69341e9	−	3.24442e10i	0.213897	−	0.798274i	−0.772655	−	0.634826i	$-0.781072\pi$
$449$	8.69341e9	−	3.24442e10i	0.213897	−	0.798274i	0.986552	−	0.163448i	$-0.0522616\pi$
$450$	2.67652e10	+	2.67652e10i	0.652711	+	0.652711i
$451$	1.71587e9	+	2.97198e9i	0.0414743	+	0.0718356i
$452$	1.19289e10	+	6.88716e9i	0.285790	+	0.165001i
$453$	−5.74422e10	+	1.53916e10i	−1.36408	+	0.365503i
$454$		−	2.39116e10i		−	0.562841i
$455$	−5.37065e10	+	8.53948e10i	−1.25309	+	1.99244i
$456$	−1.38546e10			−0.320431
$457$	1.12702e10	+	4.20611e10i	0.258385	+	0.964307i	0.966176	+	0.257885i	$0.0830255\pi$
$457$	1.12702e10	+	4.20611e10i	0.258385	+	0.964307i	−0.707790	+	0.706423i	$0.750308\pi$
$458$	−3.38960e10	+	5.87096e10i	−0.770348	+	1.33428i
$459$	1.99766e10	−	1.15335e10i	0.450060	−	0.259842i
$460$	3.52989e10	−	3.52989e10i	0.788370	−	0.788370i
$461$	7.84469e10	+	2.10198e10i	1.73689	+	0.465398i	0.981751	−	0.190169i	$-0.0609036\pi$
$461$	7.84469e10	+	2.10198e10i	1.73689	+	0.465398i	0.755137	+	0.655567i	$0.227570\pi$
$462$	5.89884e9	−	2.20148e10i	0.129479	−	0.483222i
$463$	−2.02524e10	−	2.02524e10i	−0.440709	−	0.440709i	0.451541	−	0.892250i	$-0.350874\pi$
$463$	−2.02524e10	−	2.02524e10i	−0.440709	−	0.440709i	−0.892250	+	0.451541i	$0.850874\pi$
$464$	−3.23115e9	−	5.59651e9i	−0.0697084	−	0.120738i
$465$	2.92921e10	+	1.69118e10i	0.626525	+	0.361725i
$466$	−3.93847e10	+	1.05531e10i	−0.835188	+	0.223788i
$467$		−	3.72385e10i		−	0.782934i	−0.920192	−	0.391467i	$-0.871968\pi$
$467$		−	3.72385e10i		−	0.782934i	0.920192	−	0.391467i	$-0.128032\pi$
$468$	−5.00349e8	+	1.32254e10i	−0.0104301	+	0.275694i
$469$	−6.32823e10			−1.30795
$470$	−8.29427e9	−	3.09547e10i	−0.169976	−	0.634358i
$471$	−1.03664e10	+	1.79551e10i	−0.210641	+	0.364842i
$472$	4.96499e10	−	2.86654e10i	1.00035	−	0.577550i
$473$	4.02598e9	−	4.02598e9i	0.0804317	−	0.0804317i
$474$	−5.35253e9	−	1.43421e9i	−0.106034	−	0.0284118i
$475$	6.31391e9	−	2.35638e10i	0.124029	−	0.462883i
$476$	−2.70454e10	−	2.70454e10i	−0.526824	−	0.526824i
$477$	4.19711e9	+	7.26960e9i	0.0810730	+	0.140423i
$478$	1.36278e10	+	7.86800e9i	0.261044	+	0.150714i
$479$	3.12907e10	−	8.38433e9i	0.594393	−	0.159267i	0.0509330	−	0.998702i	$-0.483781\pi$
$479$	3.12907e10	−	8.38433e9i	0.594393	−	0.159267i	0.543460	+	0.839435i	$0.317114\pi$
$480$		−	8.52235e10i		−	1.60544i
$481$	1.40579e10	+	1.51634e10i	0.262627	+	0.283279i
$482$	−1.14692e11			−2.12492
$483$	−4.60869e10	−	1.71999e11i	−0.846816	−	3.16036i
$484$	1.18517e10	−	2.05278e10i	0.215974	−	0.374077i
$485$	3.16018e10	−	1.82453e10i	0.571143	−	0.329750i
$486$	−5.11910e10	+	5.11910e10i	−0.917590	+	0.917590i
$487$	−2.32994e10	−	6.24306e9i	−0.414218	−	0.110989i	0.0456904	−	0.998956i	$-0.485451\pi$
$487$	−2.32994e10	−	6.24306e9i	−0.414218	−	0.110989i	−0.459909	+	0.887966i	$0.652118\pi$
$488$	−1.64943e10	+	6.15577e10i	−0.290841	+	1.08543i
$489$	−1.95699e10	−	1.95699e10i	−0.342258	−	0.342258i
$490$	7.60065e10	+	1.31647e11i	1.31846	+	2.28364i
$491$	8.47055e9	+	4.89048e9i	0.145742	+	0.0841444i	0.571098	−	0.820882i	$-0.306518\pi$
$491$	8.47055e9	+	4.89048e9i	0.145742	+	0.0841444i	−0.425356	+	0.905026i	$0.639851\pi$
$492$	−1.28956e10	+	3.45535e9i	−0.220079	+	0.0589701i
$493$			6.94628e9i			0.117588i
$494$	2.42452e10	−	1.28011e10i	0.407115	−	0.214951i
$495$	−1.14909e10			−0.191396
$496$	−7.41999e9	−	2.76918e10i	−0.122596	−	0.457535i
$497$	6.42975e10	−	1.11367e11i	1.05383	−	1.82528i
$498$	9.25545e10	−	5.34363e10i	1.50480	−	0.868799i
$499$	−5.58956e10	+	5.58956e10i	−0.901521	+	0.901521i	−0.995568	−	0.0940470i	$-0.970020\pi$
$499$	−5.58956e10	+	5.58956e10i	−0.901521	+	0.901521i	0.0940470	+	0.995568i	$0.470020\pi$
$500$	1.04021e10	+	2.78723e9i	0.166433	+	0.0445957i
$501$	−2.51410e10	+	9.38277e10i	−0.399055	+	1.48929i
$502$	−5.81331e9	−	5.81331e9i	−0.0915395	−	0.0915395i
$503$	4.13652e10	+	7.16466e10i	0.646194	+	1.11924i	0.984024	+	0.178034i	$0.0569736\pi$
$503$	4.13652e10	+	7.16466e10i	0.646194	+	1.11924i	−0.337831	+	0.941207i	$0.609693\pi$
$504$	−3.53594e10	−	2.04147e10i	−0.548002	−	0.316389i
$505$	3.91973e10	−	1.05029e10i	0.602685	−	0.161489i
$506$			2.71014e10i			0.413418i
$507$	3.63238e10	+	7.55874e10i	0.549743	+	1.14398i
$508$	−8.31953e9			−0.124923
$509$	8.93261e9	+	3.33370e10i	0.133078	+	0.496655i	0.999998	−	0.00179213i	$-0.000570453\pi$
$509$	8.93261e9	+	3.33370e10i	0.133078	+	0.496655i	−0.866920	+	0.498447i	$0.833904\pi$
$510$	−8.17231e10	+	1.41549e11i	−1.20799	+	2.09230i
$511$	−1.81210e11	+	1.04622e11i	−2.65766	+	1.53440i
$512$	−1.10213e10	+	1.10213e10i	−0.160381	+	0.160381i
$513$	1.26240e10	+	3.38258e9i	0.182275	+	0.0488403i
$514$	3.41438e10	−	1.27426e11i	0.489169	−	1.82560i
$515$	2.16676e10	+	2.16676e10i	0.308022	+	0.308022i
$516$	1.10748e10	+	1.91822e10i	0.156221	+	0.270582i
$517$	4.68753e9	+	2.70635e9i	0.0656118	+	0.0378810i
$518$	5.07423e10	−	1.35964e10i	0.704776	−	0.188844i
$519$		−	2.01681e10i		−	0.277968i
$520$	−3.38642e10	−	6.41385e10i	−0.463156	−	0.877213i
$521$	5.63602e10			0.764930			0.382465	−	0.923970i	$-0.375075\pi$
$521$	5.63602e10			0.764930			0.382465	+	0.923970i	$0.375075\pi$
$522$	−1.58050e9	−	5.89849e9i	−0.0212869	−	0.0794436i
$523$	6.79419e10	−	1.17679e11i	0.908094	−	1.57286i	0.0913840	−	0.995816i	$-0.470871\pi$
$523$	6.79419e10	−	1.17679e11i	0.908094	−	1.57286i	0.816710	−	0.577049i	$-0.195796\pi$
$524$	7.03929e9	−	4.06414e9i	0.0933692	−	0.0539067i
$525$	1.34049e11	−	1.34049e11i	1.76452	−	1.76452i
$526$	4.90297e10	+	1.31375e10i	0.640496	+	0.171620i
$527$	−7.97571e9	+	2.97657e10i	−0.103401	+	0.385899i
$528$	1.81604e10	+	1.81604e10i	0.233663	+	0.233663i
$529$	6.67143e10	+	1.15553e11i	0.851915	+	1.47556i
$530$	3.28083e10	+	1.89419e10i	0.415796	+	0.240060i
$531$	8.20162e10	−	2.19762e10i	1.03162	−	0.276423i
$532$		−	2.16705e10i		−	0.270535i
$533$	−2.35258e10	+	2.18107e10i	−0.291498	+	0.270246i
$534$	−6.42852e9			−0.0790580
$535$	−4.20620e10	−	1.56978e11i	−0.513423	−	1.91612i
$536$	2.27491e10	−	3.94026e10i	0.275616	−	0.477381i
$537$	−9.56513e10	+	5.52243e10i	−1.15025	+	0.664099i
$538$	−1.22443e11	+	1.22443e11i	−1.46152	+	1.46152i
$539$	−2.48002e10	−	6.64520e9i	−0.293833	−	0.0787323i
$540$	−7.36921e9	+	2.75023e10i	−0.0866655	+	0.323440i
$541$	−4.10963e10	−	4.10963e10i	−0.479748	−	0.479748i	0.425303	−	0.905051i	$-0.360168\pi$
$541$	−4.10963e10	−	4.10963e10i	−0.479748	−	0.479748i	−0.905051	+	0.425303i	$0.860168\pi$
$542$	−6.97568e10	−	1.20822e11i	−0.808332	−	1.40007i
$543$	−9.37306e10	−	5.41154e10i	−1.07816	−	0.622474i
$544$	7.49992e10	−	2.00960e10i	0.856369	−	0.229463i
$545$		−	1.47520e10i		−	0.167211i
$546$	2.12906e11	+	8.05473e9i	2.39562	+	0.0906317i
$547$	−9.33641e10			−1.04287			−0.521436	−	0.853291i	$-0.674603\pi$
$547$	−9.33641e10			−1.04287			−0.521436	+	0.853291i	$0.674603\pi$
$548$	7.41859e9	+	2.76866e10i	0.0822620	+	0.307006i
$549$	−4.71929e10	+	8.17405e10i	−0.519502	+	0.899804i
$550$	−2.49874e10	+	1.44265e10i	−0.273068	+	0.157656i
$551$	−2.78290e9	+	2.78290e9i	−0.0301920	+	0.0301920i
$552$	1.23662e11	+	3.31352e10i	1.33193	+	0.356889i
$553$	−2.72400e9	+	1.01661e10i	−0.0291278	+	0.108706i
$554$	5.93761e10	+	5.93761e10i	0.630337	+	0.630337i
$555$	−3.49203e10	−	6.04838e10i	−0.368050	−	0.637481i
$556$	−5.41888e10	−	3.12859e10i	−0.567036	−	0.327378i
$557$	−9.90728e10	+	2.65465e10i	−1.02928	+	0.275795i	−0.733664	−	0.679512i	$-0.762192\pi$
$557$	−9.90728e10	+	2.65465e10i	−1.02928	+	0.275795i	−0.295616	+	0.955307i	$0.595525\pi$
$558$		−	2.70906e10i		−	0.279435i
$559$	4.50551e10	+	2.83360e10i	0.461420	+	0.290196i
$560$	−2.88805e11			−2.93666
$561$	−7.14500e9	−	2.66655e10i	−0.0721358	−	0.269214i
$562$	−1.32696e10	+	2.29836e10i	−0.133019	+	0.230395i
$563$	1.04955e11	−	6.05959e10i	1.04465	−	0.603129i	0.123503	−	0.992344i	$-0.460587\pi$
$563$	1.04955e11	−	6.05959e10i	1.04465	−	0.603129i	0.921147	+	0.389216i	$0.127254\pi$
$564$	−1.48895e10	+	1.48895e10i	−0.147151	+	0.147151i
$565$	−1.07988e11	−	2.89354e10i	−1.05970	−	0.283945i
$566$	4.76779e9	−	1.77936e10i	0.0464571	−	0.173380i
$567$	1.41808e11	+	1.41808e11i	1.37205	+	1.37205i
$568$	4.62281e10	+	8.00694e10i	0.444133	+	0.769260i
$569$	6.05752e9	+	3.49731e9i	0.0577891	+	0.0333645i	0.528616	−	0.848861i	$-0.322711\pi$
$569$	6.05752e9	+	3.49731e9i	0.0577891	+	0.0333645i	−0.470827	+	0.882226i	$0.656044\pi$
$570$	−8.94498e10	+	2.39680e10i	−0.847384	+	0.227056i
$571$		−	1.25793e11i		−	1.18335i	−0.806177	−	0.591674i	$-0.798467\pi$
$571$		−	1.25793e11i		−	1.18335i	0.806177	−	0.591674i	$-0.201533\pi$
$572$	−9.63903e9	−	2.97762e9i	−0.0900428	−	0.0278154i
$573$	3.73402e9			0.0346384
$574$	2.10947e10	+	7.87263e10i	0.194323	+	0.725225i
$575$	−1.12712e11	+	1.95223e11i	−1.03110	+	1.78591i
$576$	1.35449e10	−	7.82015e9i	0.123051	−	0.0710437i
$577$	−6.91773e10	+	6.91773e10i	−0.624109	+	0.624109i	−0.946579	−	0.322471i	$-0.895487\pi$
$577$	−6.91773e10	+	6.91773e10i	−0.624109	+	0.624109i	0.322471	+	0.946579i	$0.395487\pi$
$578$	−1.39459e10	−	3.73679e9i	−0.124950	−	0.0334802i
$579$	1.00596e10	−	3.75429e10i	0.0895090	−	0.334052i
$580$	−6.06277e9	−	6.06277e9i	−0.0535746	−	0.0535746i
$581$	−1.01492e11	−	1.75790e11i	−0.890693	−	1.54273i
$582$	−6.67434e10	−	3.85343e10i	−0.581723	−	0.335858i
$583$	−6.18056e9	+	1.65608e9i	−0.0535000	+	0.0143353i
$584$		−	1.50440e11i		−	1.29334i
$585$	−2.38597e10	−	1.04736e11i	−0.203724	−	0.894279i
$586$	2.38510e11			2.02263
$587$	−6.28177e9	−	2.34439e10i	−0.0529090	−	0.197459i	0.934412	−	0.356193i	$-0.115925\pi$
$587$	−6.28177e9	−	2.34439e10i	−0.0529090	−	0.197459i	−0.987321	+	0.158734i	$0.949259\pi$
$588$	4.99416e10	−	8.65014e10i	0.417785	−	0.723625i
$589$	−1.51204e10	+	8.72979e9i	−0.125633	+	0.0725342i
$590$	2.70965e11	−	2.70965e11i	2.23618	−	2.23618i
$591$	−3.29495e10	−	8.82879e9i	−0.270084	−	0.0723688i
$592$	−1.53212e10	+	5.71794e10i	−0.124740	+	0.465536i
$593$	−1.10882e10	−	1.10882e10i	−0.0896687	−	0.0896687i	0.660850	−	0.750518i	$-0.270196\pi$
$593$	−1.10882e10	−	1.10882e10i	−0.0896687	−	0.0896687i	−0.750518	+	0.660850i	$0.770196\pi$
$594$	−7.72877e9	−	1.33866e10i	−0.0620818	−	0.107529i
$595$	2.68845e11	+	1.55217e11i	2.14503	+	1.23843i
$596$	3.46923e10	−	9.29578e9i	0.274947	−	0.0736717i
$597$			1.80694e11i			1.42248i
$598$	−2.47021e11	+	5.62732e10i	−1.93165	+	0.440045i
$599$	1.62836e11			1.26487			0.632433	−	0.774615i	$-0.282056\pi$
$599$	1.62836e11			1.26487			0.632433	+	0.774615i	$0.282056\pi$
$600$	3.52767e10	+	1.31654e11i	0.272197	+	1.01585i
$601$	1.68197e10	−	2.91326e10i	0.128920	−	0.223296i	−0.794338	−	0.607475i	$-0.792182\pi$
$601$	1.68197e10	−	2.91326e10i	0.128920	−	0.223296i	0.923258	+	0.384180i	$0.125516\pi$
$602$	1.17106e11	−	6.76110e10i	0.891646	−	0.514792i
$603$	4.76483e10	−	4.76483e10i	0.360394	−	0.360394i
$604$	6.45979e10	+	1.73090e10i	0.485368	+	0.130054i
$605$	−4.97932e10	+	1.85831e11i	−0.371663	+	1.38706i
$606$	−6.06029e10	−	6.06029e10i	−0.449369	−	0.449369i
$607$	−5.96809e10	−	1.03370e11i	−0.439623	−	0.761450i	0.558037	−	0.829816i	$-0.311555\pi$
$607$	−5.96809e10	−	1.03370e11i	−0.439623	−	0.761450i	−0.997660	+	0.0683664i	$0.978221\pi$
$608$	3.80982e10	+	2.19960e10i	0.278798	+	0.160964i
$609$	−2.95417e10	+	7.91567e9i	−0.214766	+	0.0575464i
$610$			4.25971e11i			3.07653i
$611$	−1.49343e10	+	4.83448e10i	−0.107157	+	0.346885i
$612$	4.07276e10			0.290324
$613$	6.62936e10	+	2.47411e11i	0.469493	+	1.75217i	0.641545	+	0.767085i	$0.278294\pi$
$613$	6.62936e10	+	2.47411e11i	0.469493	+	1.75217i	−0.172052	+	0.985088i	$0.555040\pi$
$614$	7.38537e10	−	1.27918e11i	0.519635	−	0.900035i
$615$	9.38402e10	−	5.41787e10i	0.655977	−	0.378728i
$616$	2.20071e10	−	2.20071e10i	0.152841	−	0.152841i
$617$	−1.60712e11	−	4.30626e10i	−1.10894	−	0.297139i	−0.342539	−	0.939504i	$-0.611287\pi$
$617$	−1.60712e11	−	4.30626e10i	−1.10894	−	0.297139i	−0.766399	+	0.642364i	$0.777954\pi$
$618$	1.67501e10	−	6.25123e10i	0.114832	−	0.428560i
$619$	−1.16062e11	−	1.16062e11i	−0.790543	−	0.790543i	0.191039	−	0.981582i	$-0.438814\pi$
$619$	−1.16062e11	−	1.16062e11i	−0.790543	−	0.790543i	−0.981582	+	0.191039i	$0.938814\pi$
$620$	−1.90185e10	−	3.29411e10i	−0.128709	−	0.222931i
$621$	−1.04588e11	−	6.03838e10i	−0.703259	−	0.406026i
$622$	−2.64706e10	+	7.09278e9i	−0.176849	+	0.0473865i
$623$			1.22097e10i			0.0810503i
$624$	−1.27818e11	+	2.03235e11i	−0.843052	+	1.34048i
$625$	1.03958e11			0.681301
$626$	−4.14856e10	−	1.54826e11i	−0.270147	−	1.00820i
$627$	7.82054e9	−	1.35456e10i	0.0506019	−	0.0876450i
$628$	2.01918e10	−	1.16577e10i	0.129818	−	0.0749507i
$629$	4.49932e10	−	4.49932e10i	0.287438	−	0.287438i
$630$	−2.63609e11	−	7.06337e10i	−1.67339	−	0.448384i
$631$	4.58738e10	−	1.71203e11i	0.289366	−	1.07993i	−0.656224	−	0.754566i	$-0.727847\pi$
$631$	4.58738e10	−	1.71203e11i	0.289366	−	1.07993i	0.945590	−	0.325361i	$-0.105486\pi$
$632$	−5.35067e9	−	5.35067e9i	−0.0335382	−	0.0335382i
$633$	1.12023e11	+	1.94030e11i	0.697739	+	1.20852i
$634$	−1.32655e11	−	7.65884e10i	−0.821044	−	0.474030i
$635$	6.52236e10	−	1.74766e10i	0.401153	−	0.107489i
$636$		−	2.48923e10i		−	0.152138i
$637$	9.07385e9	−	2.39844e11i	0.0551104	−	1.45670i
$638$	4.65481e9			0.0280943
$639$	3.54406e10	+	1.32266e11i	0.212568	+	0.793313i
$640$	1.41401e11	−	2.44915e11i	0.842818	−	1.45980i
$641$	−1.69796e11	+	9.80317e10i	−1.00576	+	0.580677i	−0.909948	−	0.414723i	$-0.863879\pi$
$641$	−1.69796e11	+	9.80317e10i	−1.00576	+	0.580677i	−0.0958137	+	0.995399i	$0.530545\pi$
$642$	−2.42703e11	+	2.42703e11i	−1.42868	+	1.42868i
$643$	2.57564e11	+	6.90140e10i	1.50675	+	0.403732i	0.915354	−	0.402650i	$-0.131911\pi$
$643$	2.57564e11	+	6.90140e10i	1.50675	+	0.403732i	0.591395	+	0.806382i	$0.298578\pi$
$644$	−5.18280e10	+	1.93425e11i	−0.301315	+	1.12452i
$645$	−1.27120e11	−	1.27120e11i	−0.734473	−	0.734473i
$646$	−4.21851e10	−	7.30667e10i	−0.242231	−	0.419556i
$647$	2.15834e11	+	1.24612e11i	1.23169	+	0.711119i	0.967383	−	0.253319i	$-0.0815221\pi$
$647$	2.15834e11	+	1.24612e11i	1.23169	+	0.711119i	0.264311	+	0.964437i	$0.414855\pi$
$648$	−1.39275e11	+	3.73185e10i	−0.789900	+	0.211653i
$649$			6.47232e10i			0.364822i
$650$	−1.83376e11	−	1.97797e11i	−1.02728	−	1.10807i
$651$	−1.35679e11			−0.755419
$652$	8.05540e9	+	3.00632e10i	0.0445756	+	0.166358i
$653$	−3.14491e10	+	5.44714e10i	−0.172964	+	0.299582i	−0.939455	−	0.342673i	$-0.888668\pi$
$653$	−3.14491e10	+	5.44714e10i	−0.172964	+	0.299582i	0.766491	+	0.642255i	$0.222001\pi$
$654$	−2.69822e10	+	1.55782e10i	−0.147491	+	0.0851540i
$655$	−4.66493e10	+	4.66493e10i	−0.253443	+	0.253443i
$656$	−8.87135e10	−	2.37707e10i	−0.479043	−	0.128359i
$657$	5.76671e10	−	2.15217e11i	0.309504	−	1.15509i
$658$	9.08990e10	+	9.08990e10i	0.484904	+	0.484904i
$659$	−1.03418e11	−	1.79125e11i	−0.548344	−	0.949759i	−0.998388	−	0.0567531i	$-0.981925\pi$
$659$	−1.03418e11	−	1.79125e11i	−0.548344	−	0.949759i	0.450044	−	0.893006i	$-0.351408\pi$
$660$	2.95101e10	+	1.70377e10i	0.155523	+	0.0897913i
$661$	2.13632e11	−	5.72425e10i	1.11908	−	0.299856i	0.348567	−	0.937284i	$-0.386668\pi$
$661$	2.13632e11	−	5.72425e10i	1.11908	−	0.299856i	0.770510	+	0.637428i	$0.220002\pi$
$662$		−	7.33545e9i		−	0.0381940i
$663$	2.28212e11	−	1.20493e11i	1.18109	−	0.623600i
$664$	1.45940e11			0.750761
$665$	4.55227e10	+	1.69893e11i	0.232778	+	0.868738i
$666$	−2.79690e10	+	4.84437e10i	−0.142161	+	0.246230i
$667$	3.14951e10	−	1.81837e10i	0.159125	−	0.0918711i
$668$	7.72430e10	−	7.72430e10i	0.387930	−	0.387930i
$669$	−1.00395e11	−	2.69007e10i	−0.501194	−	0.134295i
$670$	7.87103e10	−	2.93751e11i	0.390600	−	1.45774i
$671$	−5.08740e10	−	5.08740e10i	−0.250961	−	0.250961i
$672$	1.70931e11	+	2.96062e11i	0.838194	+	1.45179i
$673$	−1.52808e11	−	8.82238e10i	−0.744879	−	0.430056i	0.0789614	−	0.996878i	$-0.474840\pi$
$673$	−1.52808e11	−	8.82238e10i	−0.744879	−	0.430056i	−0.823841	+	0.566821i	$0.808173\pi$
$674$	−2.62529e11	+	7.03445e10i	−1.27215	+	0.340871i
$675$		−	1.28573e11i		−	0.619347i
$676$	7.12565e9	−	9.40395e10i	0.0341223	−	0.450322i
$677$	9.15822e10			0.435970			0.217985	−	0.975952i	$-0.430052\pi$
$677$	9.15822e10			0.435970			0.217985	+	0.975952i	$0.430052\pi$
$678$	6.11118e10	+	2.28072e11i	0.289205	+	1.07933i
$679$	−7.31886e10	+	1.26766e11i	−0.344322	+	0.596383i
$680$	−1.93292e11	+	1.11597e11i	−0.904018	+	0.521935i
$681$	9.01712e10	−	9.01712e10i	0.419256	−	0.419256i
$682$	1.99465e10	+	5.34464e9i	0.0921995	+	0.0247048i
$683$	2.94515e9	−	1.09914e10i	0.0135339	−	0.0505094i	−0.958829	−	0.283985i	$-0.908343\pi$
$683$	2.94515e9	−	1.09914e10i	0.0135339	−	0.0505094i	0.972363	+	0.233476i	$0.0750100\pi$
$684$	1.63168e10	+	1.63168e10i	0.0745436	+	0.0745436i
$685$	−1.16321e11	−	2.01473e11i	−0.528317	−	0.915073i
$686$	−1.65824e11	−	9.57383e10i	−0.748773	−	0.432304i
$687$	−3.49218e11	+	9.35726e10i	−1.56772	+	0.420070i
$688$			1.52376e11i			0.680085i
$689$	−2.79279e10	−	5.28952e10i	−0.123926	−	0.234714i
$690$	8.55726e11			3.77519
$691$	4.14322e10	+	1.54627e11i	0.181730	+	0.678224i	0.995307	+	0.0967673i	$0.0308503\pi$
$691$	4.14322e10	+	1.54627e11i	0.181730	+	0.678224i	−0.813578	+	0.581456i	$0.802483\pi$
$692$	−1.13402e10	+	1.96418e10i	−0.0494535	+	0.0856560i
$693$	3.99188e10	−	2.30471e10i	0.173079	−	0.0999272i
$694$	−1.36661e11	+	1.36661e11i	−0.589123	+	0.589123i
$695$	4.90552e11	+	1.31443e11i	2.10255	+	0.563376i
$696$	5.69114e9	−	2.12396e10i	0.0242528	−	0.0905127i
$697$	6.98066e10	+	6.98066e10i	0.295778	+	0.295778i
$698$	−3.80278e8	−	6.58662e8i	−0.00160206	−	0.00277486i
$699$	−1.88317e11	−	1.08725e11i	−0.788824	−	0.455428i
$700$	−2.05926e11	+	5.51776e10i	−0.857667	+	0.229811i
$701$			3.03778e11i			1.25801i	0.777401	+	0.629005i	$0.216538\pi$
$701$			3.03778e11i			1.25801i	−0.777401	+	0.629005i	$0.783462\pi$
$702$	1.05967e11	−	9.82412e10i	0.436337	−	0.404525i
$703$	3.60514e10			0.147605
$704$	3.08564e9	+	1.15158e10i	0.0125619	+	0.0468816i
$705$	8.54528e10	−	1.48009e11i	0.345915	−	0.599143i
$706$	−1.95543e11	+	1.12897e11i	−0.787087	+	0.454425i
$707$	−1.15104e11	+	1.15104e11i	−0.460693	+	0.460693i
$708$	−2.43212e11	−	6.51684e10i	−0.967947	−	0.259361i
$709$	−4.40900e10	+	1.64546e11i	−0.174484	+	0.651183i	0.822155	+	0.569264i	$0.192772\pi$
$709$	−4.40900e10	+	1.64546e11i	−0.174484	+	0.651183i	−0.996639	+	0.0819191i	$0.973895\pi$
$710$	4.36981e11	+	4.36981e11i	1.71961	+	1.71961i
$711$	−5.60353e9	−	9.70559e9i	−0.0219272	−	0.0379790i
$712$	−7.60237e9	−	4.38923e9i	−0.0295821	−	0.0170792i
$713$	1.55839e11	−	4.17570e10i	0.603002	−	0.161574i
$714$		−	6.55642e11i		−	2.52275i
$715$	8.18232e10	+	3.09556e9i	0.313078	+	0.0118444i
$716$	1.24207e11			0.472601
$717$	2.17202e10	+	8.10610e10i	0.0821841	+	0.306715i
$718$	−1.91420e11	+	3.31549e11i	−0.720261	+	1.24753i
$719$	1.05020e10	−	6.06334e9i	0.0392968	−	0.0226880i	−0.480223	−	0.877146i	$-0.659444\pi$
$719$	1.05020e10	−	6.06334e9i	0.0392968	−	0.0226880i	0.519520	+	0.854458i	$0.326111\pi$
$720$	2.17455e11	−	2.17455e11i	0.809171	−	0.809171i
$721$	−1.18730e11	−	3.18137e10i	−0.439360	−	0.117726i
$722$	−7.23643e10	+	2.70067e11i	−0.266303	+	0.993855i
$723$	−4.32504e11	−	4.32504e11i	−1.58284	−	1.58284i
$724$	6.08566e10	+	1.05407e11i	0.221490	+	0.383631i
$725$	3.35306e10	+	1.93589e10i	0.121364	+	0.0700694i
$726$	3.92477e11	−	1.05164e11i	1.41276	−	0.378547i
$727$		−	2.10599e11i		−	0.753909i	−0.926232	−	0.376955i	$-0.876971\pi$
$727$		−	2.10599e11i		−	0.753909i	0.926232	−	0.376955i	$-0.123029\pi$
$728$	2.46284e11	+	1.54893e11i	0.876819	+	0.551449i
$729$	−3.65217e10			−0.129313
$730$	−2.60256e11	−	9.71290e11i	−0.916453	−	3.42025i
$731$	8.18941e10	−	1.41845e11i	0.286803	−	0.496757i
$732$	2.42394e11	−	1.39946e11i	0.844264	−	0.487436i
$733$	−1.21496e11	+	1.21496e11i	−0.420867	+	0.420867i	−0.885502	−	0.464635i	$-0.846185\pi$
$733$	−1.21496e11	+	1.21496e11i	−0.420867	+	0.420867i	0.464635	+	0.885502i	$0.346185\pi$
$734$	−1.13170e11	−	3.03239e10i	−0.389895	−	0.104472i
$735$	−2.09822e11	+	7.83066e11i	−0.718954	+	2.68317i
$736$	−2.87447e11	−	2.87447e11i	−0.979594	−	0.979594i
$737$	2.56825e10	+	4.44833e10i	0.0870496	+	0.150774i
$738$	−7.51600e10	−	4.33937e10i	−0.253374	−	0.146285i
$739$	−3.20792e11	+	8.59559e10i	−1.07559	+	0.288203i	−0.752787	−	0.658265i	$-0.771291\pi$
$739$	−3.20792e11	+	8.59559e10i	−1.07559	+	0.288203i	−0.322800	+	0.946467i	$0.604624\pi$
$740$			7.85409e10i			0.261920i
$741$	1.39702e11	+	4.31558e10i	0.463373	+	0.143142i
$742$	−1.51966e11			−0.501337
$743$	−9.37438e10	−	3.49857e11i	−0.307601	−	1.14798i	−0.930683	−	0.365825i	$-0.880787\pi$
$743$	−9.37438e10	−	3.49857e11i	−0.307601	−	1.14798i	0.623083	−	0.782156i	$-0.285880\pi$
$744$	4.87746e10	−	8.44800e10i	0.159185	−	0.275716i
$745$	−2.52454e11	+	1.45754e11i	−0.819516	+	0.473148i
$746$	2.70217e11	−	2.70217e11i	0.872483	−	0.872483i
$747$	2.08779e11	+	5.59421e10i	0.670508	+	0.179662i
$748$	−8.03506e9	+	2.99873e10i	−0.0256675	+	0.0957922i
$749$	4.60968e11	+	4.60968e11i	1.46468	+	1.46468i
$750$	9.23007e10	+	1.59869e11i	0.291716	+	0.505266i
$751$	−1.36043e11	−	7.85446e10i	−0.427678	−	0.246920i	0.270679	−	0.962670i	$-0.412752\pi$
$751$	−1.36043e11	−	7.85446e10i	−0.427678	−	0.246920i	−0.698357	+	0.715750i	$0.746085\pi$
$752$	−1.39923e11	+	3.74921e10i	−0.437538	+	0.117238i
$753$		−	4.38442e10i		−	0.136374i
$754$	9.66522e9	+	4.24271e10i	0.0299038	+	0.131268i
$755$	−5.42796e11			−1.67051
$756$	−2.95606e10	−	1.10322e11i	−0.0904953	−	0.337733i
$757$	2.61788e11	−	4.53431e11i	0.797199	−	1.38079i	−0.124234	−	0.992253i	$-0.539647\pi$
$757$	2.61788e11	−	4.53431e11i	0.797199	−	1.38079i	0.921433	−	0.388536i	$-0.127019\pi$
$758$	−2.12012e11	+	1.22405e11i	−0.642221	+	0.370786i
$759$	−1.02200e11	+	1.02200e11i	−0.307952	+	0.307952i
$760$	−1.22148e11	−	3.27295e10i	−0.366128	−	0.0981037i
$761$	9.91064e10	−	3.69870e11i	0.295504	−	1.10283i	−0.645313	−	0.763919i	$-0.723273\pi$
$761$	9.91064e10	−	3.69870e11i	0.295504	−	1.10283i	0.940816	−	0.338916i	$-0.110060\pi$
$762$	−1.00842e11	−	1.00842e11i	−0.299104	−	0.299104i
$763$	2.95878e10	+	5.12475e10i	0.0872999	+	0.151208i
$764$	−3.63659e9	−	2.09958e9i	−0.0106738	−	0.00616254i
$765$	−3.19297e11	+	8.55553e10i	−0.932285	+	0.249805i
$766$			4.82004e11i			1.40002i
$767$	−5.89932e11	+	1.34391e11i	−1.70459	+	0.388319i
$768$	−4.94584e11			−1.42166
$769$	1.79536e11	+	6.70038e11i	0.513389	+	1.91599i	0.380205	+	0.924902i	$0.375853\pi$
$769$	1.79536e11	+	6.70038e11i	0.513389	+	1.91599i	0.133184	+	0.991091i	$0.457480\pi$
$770$	1.04014e11	−	1.80157e11i	0.295888	−	0.512493i
$771$	6.09284e11	−	3.51770e11i	1.72426	−	0.995501i
$772$	−3.09070e10	+	3.09070e10i	−0.0870137	+	0.0870137i
$773$	−4.28170e11	−	1.14728e11i	−1.19922	−	0.321329i	−0.396694	−	0.917951i	$-0.629843\pi$
$773$	−4.28170e11	−	1.14728e11i	−1.19922	−	0.321329i	−0.802523	+	0.596622i	$0.796509\pi$
$774$	−3.72670e10	+	1.39082e11i	−0.103839	+	0.387532i
$775$	1.21455e11	+	1.21455e11i	0.336674	+	0.336674i
$776$	−5.26205e10	−	9.11414e10i	−0.145114	−	0.251344i
$777$	2.42623e11	+	1.40078e11i	0.665652	+	0.384314i
$778$	7.69825e11	−	2.06274e11i	2.10123	−	0.563023i
$779$			5.59336e10i			0.151888i
$780$	−9.40183e10	+	3.04352e11i	−0.254000	+	0.822239i
$781$	−1.04378e11			−0.280546
$782$	2.01783e11	+	7.53063e11i	0.539581	+	2.01375i
$783$	−1.03712e10	+	1.79635e10i	−0.0275920	+	0.0477908i
$784$	5.95076e11	−	3.43568e11i	1.57510	−	0.909385i
$785$	−1.33811e11	+	1.33811e11i	−0.352381	+	0.352381i
$786$	1.34586e11	+	3.60622e10i	0.352623	+	0.0944849i
$787$	−2.66506e10	+	9.94613e10i	−0.0694716	+	0.259272i	−0.991923	−	0.126842i	$-0.959516\pi$
$787$	−2.66506e10	+	9.94613e10i	−0.0694716	+	0.259272i	0.922451	+	0.386113i	$0.126183\pi$
$788$	2.71255e10	+	2.71255e10i	0.0703513	+	0.0703513i
$789$	1.35350e11	+	2.34434e11i	0.349262	+	0.604940i
$790$	−4.38021e10	−	2.52892e10i	−0.112457	−	0.0649272i
$791$	4.33180e11	−	1.16070e11i	1.10653	−	0.296493i
$792$			3.31404e10i			0.0842282i
$793$	3.58066e11	−	5.69335e11i	0.905463	−	1.43971i
$794$	−2.07535e11			−0.522166
$795$	5.22906e10	+	1.95151e11i	0.130905	+	0.488543i
$796$	1.01602e11	−	1.75980e11i	0.253075	−	0.438339i
$797$	2.18908e11	−	1.26387e11i	0.542536	−	0.313233i	−0.203570	−	0.979060i	$-0.565254\pi$
$797$	2.18908e11	−	1.26387e11i	0.542536	−	0.313233i	0.746106	+	0.665827i	$0.231921\pi$
$798$	2.62671e11	−	2.62671e11i	0.647741	−	0.647741i
$799$	1.50402e11	+	4.03000e10i	0.369034	+	0.0988823i
$800$	1.12013e11	−	4.18037e11i	0.273468	−	1.02060i
$801$	−9.19331e9	−	9.19331e9i	−0.0223327	−	0.0223327i
$802$	9.62563e10	+	1.66721e11i	0.232665	+	0.402988i
$803$	1.47084e11	+	8.49193e10i	0.353757	+	0.204242i
$804$	−1.93015e11	+	5.17182e10i	−0.461920	+	0.123771i
$805$		−	1.62529e12i		−	3.87032i
$806$	−7.29797e9	+	1.92903e11i	−0.0172927	+	0.457088i
$807$	−9.23467e11			−2.17735
$808$	−3.02909e10	−	1.13047e11i	−0.0710668	−	0.265225i
$809$	−4.92127e10	+	8.52388e10i	−0.114890	+	0.198996i	−0.917736	−	0.397191i	$-0.869985\pi$
$809$	−4.92127e10	+	8.52388e10i	−0.114890	+	0.198996i	0.802846	+	0.596187i	$0.203318\pi$
$810$	−8.34643e11	+	4.81881e11i	−1.93892	+	1.11944i
$811$	4.28406e11	−	4.28406e11i	0.990312	−	0.990312i	−0.00964170	−	0.999954i	$-0.503069\pi$
$811$	4.28406e11	−	4.28406e11i	0.990312	−	0.990312i	0.999954	+	0.00964170i	$0.00306910\pi$
$812$	3.32217e10	+	8.90173e9i	0.0764184	+	0.0204763i
$813$	1.92569e11	−	7.18678e11i	0.440783	−	1.64502i
$814$	−3.01506e10	−	3.01506e10i	−0.0686749	−	0.0686749i
$815$	−1.26306e11	−	2.18768e11i	−0.286281	−	0.495854i
$816$	6.39834e11	+	3.69408e11i	1.44313	+	0.833193i
$817$	8.96370e10	−	2.40182e10i	0.201187	−	0.0539078i
$818$			8.54247e11i			1.90796i
$819$	2.92955e11	+	3.15992e11i	0.651125	+	0.702330i
$820$	−1.21856e11			−0.269519
$821$	−4.84546e10	−	1.80835e11i	−0.106650	−	0.398024i	0.891877	−	0.452278i	$-0.149389\pi$
$821$	−4.84546e10	−	1.80835e11i	−0.106650	−	0.398024i	−0.998527	+	0.0542539i	$0.982722\pi$
$822$	−2.45671e11	+	4.25514e11i	−0.538104	+	0.932023i
$823$	−6.94773e11	+	4.01128e11i	−1.51441	+	0.874346i	−0.514554	+	0.857458i	$0.672042\pi$
$823$	−6.94773e11	+	4.01128e11i	−1.51441	+	0.874346i	−0.999857	+	0.0168874i	$0.994624\pi$
$824$	6.24906e10	−	6.24906e10i	0.135552	−	0.135552i
$825$	−1.48630e11	−	3.98254e10i	−0.320843	−	0.0859695i
$826$	−3.97848e11	+	1.48479e12i	−0.854667	+	3.18966i
$827$	5.13633e11	+	5.13633e11i	1.09807	+	1.09807i	0.994636	+	0.103437i	$0.0329840\pi$
$827$	5.13633e11	+	5.13633e11i	1.09807	+	1.09807i	0.103437	+	0.994636i	$0.467016\pi$
$828$	−1.06615e11	−	1.84663e11i	−0.226828	−	0.392878i
$829$	3.93503e11	+	2.27189e11i	0.833163	+	0.481027i	0.854934	−	0.518736i	$-0.173597\pi$
$829$	3.93503e11	+	2.27189e11i	0.833163	+	0.481027i	−0.0217716	+	0.999763i	$0.506931\pi$
$830$	9.42236e11	−	2.52471e11i	1.98540	−	0.531986i
$831$			4.47817e11i			0.939067i
$832$	−9.85557e10	+	5.20360e10i	−0.205678	+	0.108595i
$833$	−7.38597e11			−1.53401
$834$	−2.77609e11	−	1.03605e12i	−0.573812	−	2.14149i
$835$	−4.43309e11	+	7.67833e11i	−0.911928	+	1.57951i
$836$	−1.52330e10	+	8.79476e9i	−0.0311860	+	0.0180052i
$837$	−6.50678e10	+	6.50678e10i	−0.132576	+	0.132576i
$838$	4.77971e11	+	1.28072e11i	0.969226	+	0.259703i
$839$	2.28581e11	−	8.53074e11i	0.461309	−	1.72163i	−0.207538	−	0.978227i	$-0.566545\pi$
$839$	2.28581e11	−	8.53074e11i	0.461309	−	1.72163i	0.668847	−	0.743400i	$-0.266788\pi$
$840$	−6.94874e11	−	6.94874e11i	−1.39569	−	1.39569i
$841$	2.47000e11	+	4.27817e11i	0.493757	+	0.855212i
$842$	−6.43244e11	−	3.71377e11i	−1.27976	−	0.738868i
$843$	−1.36712e11	+	3.66317e10i	−0.270704	+	0.0725350i
$844$		−	2.51956e11i		−	0.496541i
$845$	1.41682e11	+	7.52221e11i	0.277900	+	1.47543i
$846$	−1.36885e11			−0.267222
$847$	−1.99739e11	−	7.45435e11i	−0.388087	−	1.44836i
$848$	8.56219e10	−	1.48301e11i	0.165578	−	0.286789i
$849$	8.50797e10	−	4.91208e10i	0.163755	−	0.0945441i
$850$	−5.86910e11	+	5.86910e11i	−1.12433	+	1.12433i
$851$	−3.21785e11	−	8.62219e10i	−0.613546	−	0.164399i
$852$	1.05096e11	−	3.92223e11i	0.199447	−	0.744346i
$853$	2.44286e11	+	2.44286e11i	0.461427	+	0.461427i	0.899123	−	0.437696i	$-0.144205\pi$
$853$	2.44286e11	+	2.44286e11i	0.461427	+	0.461427i	−0.437696	+	0.899123i	$0.644205\pi$
$854$	−8.54362e11	−	1.47980e12i	−1.60624	−	2.78209i
$855$	−1.62197e11	−	9.36444e10i	−0.303513	−	0.175234i
$856$	−4.52732e11	+	1.21309e11i	−0.843231	+	0.225943i
$857$		−	3.32436e10i		−	0.0616290i	−0.999525	−	0.0308145i	$-0.990190\pi$
$857$		−	3.32436e10i		−	0.0616290i	0.999525	−	0.0308145i	$-0.00981011\pi$
$858$	−8.07438e10	−	1.52928e11i	−0.148991	−	0.282188i
$859$	9.65892e11			1.77401			0.887005	−	0.461760i	$-0.152782\pi$
$859$	9.65892e11			1.77401			0.887005	+	0.461760i	$0.152782\pi$
$860$	5.23254e10	+	1.95281e11i	0.0956575	+	0.356999i
$861$	−2.17330e11	+	3.76427e11i	−0.395465	+	0.684965i
$862$	7.41550e11	−	4.28134e11i	1.34311	−	0.775445i
$863$	3.29161e11	−	3.29161e11i	0.593425	−	0.593425i	−0.345130	−	0.938555i	$-0.612165\pi$
$863$	3.29161e11	−	3.29161e11i	0.593425	−	0.593425i	0.938555	+	0.345130i	$0.112165\pi$
$864$	2.23957e11	+	6.00091e10i	0.401892	+	0.107687i
$865$	4.76442e10	−	1.77810e11i	0.0851031	−	0.317609i
$866$	−3.70752e11	−	3.70752e11i	−0.659193	−	0.659193i
$867$	−3.84987e10	−	6.66818e10i	−0.0681350	−	0.118013i
$868$	1.32139e11	+	7.62902e10i	0.232783	+	0.134397i
$869$	8.25163e9	−	2.21102e9i	0.0144697	−	0.00387715i
$870$		−	1.46975e11i		−	0.256547i
$871$	−3.52125e11	+	3.26453e11i	−0.611820	+	0.567215i
$872$	−4.25455e10			−0.0735848
$873$	−4.03413e10	−	1.50556e11i	−0.0694533	−	0.259203i
$874$	−2.20861e11	+	3.82542e11i	−0.378506	+	0.655592i
$875$	3.03642e11	−	1.75308e11i	0.517999	−	0.299067i
$876$	−4.67199e11	+	4.67199e11i	−0.793388	+	0.793388i
$877$	8.01098e11	+	2.14654e11i	1.35421	+	0.362860i	0.861688	−	0.507438i	$-0.169407\pi$
$877$	8.01098e11	+	2.14654e11i	1.35421	+	0.362860i	0.492525	+	0.870298i	$0.336074\pi$
$878$	1.20695e11	−	4.50439e11i	0.203100	−	0.757980i
$879$	8.99427e11	+	8.99427e11i	1.50664	+	1.50664i
$880$	1.17209e11	+	2.03011e11i	0.195447	+	0.338524i
$881$	−1.93470e11	−	1.11700e11i	−0.321152	−	0.185417i	0.330754	−	0.943717i	$-0.392697\pi$
$881$	−1.93470e11	−	1.11700e11i	−0.321152	−	0.185417i	−0.651906	+	0.758300i	$0.726030\pi$
$882$	6.27186e11	−	1.68054e11i	1.03639	−	0.277699i
$883$			3.02031e11i			0.496831i	0.968654	+	0.248416i	$0.0799099\pi$
$883$			3.02031e11i			0.496831i	−0.968654	+	0.248416i	$0.920090\pi$
$884$	−2.90008e11	−	1.09717e10i	−0.474899	−	0.0179665i
$885$	2.04363e12			3.33142
$886$	−2.65638e11	−	9.91375e11i	−0.431078	−	1.60880i
$887$	−2.45556e11	+	4.25316e11i	−0.396695	+	0.687096i	−0.993316	−	0.115427i	$-0.963176\pi$
$887$	−2.45556e11	+	4.25316e11i	−0.396695	+	0.687096i	0.596621	+	0.802523i	$0.296510\pi$
$888$	−1.74439e11	+	1.00712e11i	−0.280538	+	0.161968i
$889$	−1.91531e11	+	1.91531e11i	−0.306642	+	0.306642i
$890$	−5.66766e10	−	1.51864e10i	−0.0903324	−	0.0242045i
$891$	4.21306e10	−	1.57233e11i	0.0668477	−	0.249479i
$892$	8.26492e10	+	8.26492e10i	0.130551	+	0.130551i
$893$	4.41103e10	+	7.64013e10i	0.0693641	+	0.120142i
$894$	5.33186e11	+	3.07835e11i	0.834696	+	0.481912i
$895$	−9.73762e11	+	2.60919e11i	−1.51761	+	0.406643i
$896$			1.13443e12i			1.76013i
$897$	−1.14373e12	−	7.19313e11i	−1.76666	−	1.11109i
$898$	−6.47499e11			−0.995712
$899$	−7.17198e9	−	2.67662e10i	−0.0109799	−	0.0409777i
$900$	1.13506e11	−	1.96597e11i	0.173000	−	0.299645i
$901$	−1.59408e11	+	9.20344e10i	−0.241887	+	0.139653i
$902$	4.67784e10	−	4.67784e10i	0.0706675	−	0.0706675i
$903$	6.96571e11	+	1.86646e11i	1.04765	+	0.280716i
$904$	−8.34512e10	+	3.11444e11i	−0.124956	+	0.466344i
$905$	−6.98530e11	−	6.98530e11i	−1.04134	−	1.04134i
$906$	5.73196e11	+	9.92804e11i	0.850727	+	1.47350i
$907$	−6.87314e11	−	3.96821e11i	−1.01561	−	0.586361i	−0.102779	−	0.994704i	$-0.532773\pi$
$907$	−6.87314e11	−	3.96821e11i	−1.01561	−	0.586361i	−0.912829	+	0.408343i	$0.866107\pi$
$908$	−1.38520e11	+	3.71164e10i	−0.203784	+	0.0546038i
$909$		−	1.73334e11i		−	0.253880i
$910$	1.85805e12	+	5.73974e11i	2.70951	+	0.837003i
$911$	3.76734e11			0.546967			0.273484	−	0.961877i	$-0.411824\pi$
$911$	3.76734e11			0.546967			0.273484	+	0.961877i	$0.411824\pi$
$912$	1.08341e11	+	4.04335e11i	0.156608	+	0.584470i
$913$	−8.23791e10	+	1.42685e11i	−0.118559	+	0.205350i
$914$	7.26963e11	−	4.19713e11i	1.04166	−	0.601405i
$915$	−1.60635e12	+	1.60635e12i	−2.29168	+	2.29168i
$916$	3.92720e11	+	1.05229e11i	0.557830	+	0.149470i
$917$	6.84934e10	−	2.55621e11i	0.0968660	−	0.361509i
$918$	−3.14428e11	−	3.14428e11i	−0.442742	−	0.442742i
$919$	1.45086e11	+	2.51297e11i	0.203406	+	0.352310i	0.949624	−	0.313392i	$-0.101465\pi$
$919$	1.45086e11	+	2.51297e11i	0.203406	+	0.352310i	−0.746217	+	0.665702i	$0.768132\pi$
$920$	1.01198e12	+	5.84268e11i	1.41261	+	0.815569i
$921$	7.60887e11	−	2.03879e11i	1.05750	−	0.283357i
$922$		−	1.56559e12i		−	2.16647i
$923$	−2.16730e11	−	9.51372e11i	−0.298615	−	1.31082i
$924$	−1.36688e11			−0.187518
$925$	−9.17944e10	−	3.42581e11i	−0.125386	−	0.467947i
$926$	−2.76062e11	+	4.78153e11i	−0.375459	+	0.650314i
$927$	1.13352e11	−	6.54437e10i	0.153500	−	0.0886235i
$928$	−4.93705e10	+	4.93705e10i	−0.0665695	+	0.0665695i
$929$	−9.98697e11	−	2.67600e11i	−1.34082	−	0.359272i	−0.484083	−	0.875022i	$-0.660847\pi$
$929$	−9.98697e11	−	2.67600e11i	−1.34082	−	0.359272i	−0.856739	+	0.515750i	$0.827513\pi$
$930$	1.68757e11	−	6.29809e11i	0.225595	−	0.841932i
$931$	−2.95906e11	−	2.95906e11i	−0.393872	−	0.393872i
$932$	1.22269e11	+	2.11776e11i	0.162051	+	0.280680i
$933$	−1.26568e11	−	7.30742e10i	−0.167031	−	0.0964356i
$934$	−6.93397e11	+	1.85795e11i	−0.911159	+	0.244144i
$935$		−	2.51974e11i		−	0.329692i
$936$	−3.02065e11	+	6.88127e10i	−0.393547	+	0.0896530i
$937$	−7.06150e11			−0.916091			−0.458045	−	0.888929i	$-0.651450\pi$
$937$	−7.06150e11			−0.916091			−0.458045	+	0.888929i	$0.651450\pi$
$938$	3.15736e11	+	1.17834e12i	0.407861	+	1.52216i
$939$	4.27411e11	−	7.40297e11i	0.549772	−	0.952234i
$940$	−1.66446e11	+	9.60978e10i	−0.213188	+	0.123084i
$941$	−5.15590e10	+	5.15590e10i	−0.0657577	+	0.0657577i	−0.739221	−	0.673463i	$-0.764806\pi$
$941$	−5.15590e10	+	5.15590e10i	−0.0657577	+	0.0657577i	0.673463	+	0.739221i	$0.264806\pi$
$942$	3.86053e11	+	1.03442e11i	0.490279	+	0.131370i
$943$	1.33773e11	−	4.99246e11i	0.169169	−	0.631347i
$944$	−1.22483e12	−	1.22483e12i	−1.54237	−	1.54237i
$945$	4.63499e11	+	8.02804e11i	0.581195	+	1.00666i
$946$	−9.50523e10	−	5.48785e10i	−0.118686	−	0.0685232i
$947$	8.11595e11	−	2.17466e11i	1.00911	−	0.270391i	0.283854	−	0.958867i	$-0.408387\pi$
$947$	8.11595e11	−	2.17466e11i	1.00911	−	0.270391i	0.725259	+	0.688477i	$0.241720\pi$
$948$			3.32335e10i			0.0411475i
$949$	−4.68607e11	+	1.51696e12i	−0.577755	+	1.87029i
$950$	−4.70270e11			−0.577368
$951$	−2.11428e11	−	7.89061e11i	−0.258488	−	0.964692i
$952$	4.47656e11	−	7.75363e11i	0.545000	−	0.943968i
$953$	7.41106e11	−	4.27878e11i	0.898481	−	0.518738i	0.0217737	−	0.999763i	$-0.493069\pi$
$953$	7.41106e11	−	4.27878e11i	0.898481	−	0.518738i	0.876707	+	0.481025i	$0.159735\pi$
$954$	1.14422e11	−	1.14422e11i	0.138139	−	0.138139i
$955$	3.29207e10	+	8.82108e9i	0.0395782	+	0.0106049i
$956$	2.44260e10	−	9.11589e10i	0.0292429	−	0.109136i
$957$	1.75534e10	+	1.75534e10i	0.0209273	+	0.0209273i
$958$	−3.12239e11	−	5.40814e11i	−0.370703	−	0.642076i
$959$	8.08183e11	+	4.66605e11i	0.955511	+	0.551664i
$960$	3.63610e11	−	9.74291e10i	0.428106	−	0.114711i
$961$			7.29960e11i			0.855865i
$962$	2.12209e11	−	3.37418e11i	0.247778	−	0.393974i
$963$	−6.94170e11			−0.807162
$964$	1.78028e11	+	6.64410e11i	0.206149	+	0.769357i
$965$	1.77380e11	−	3.07231e11i	0.204548	−	0.354287i
$966$	−2.97274e12	+	1.71631e12i	−3.41388	+	1.97101i
$967$	5.45340e11	−	5.45340e11i	0.623680	−	0.623680i	−0.322791	−	0.946470i	$-0.604621\pi$
$967$	5.45340e11	−	5.45340e11i	0.623680	−	0.623680i	0.946470	+	0.322791i	$0.104621\pi$
$968$	5.35947e11	+	1.43607e11i	0.610408	+	0.163558i
$969$	1.16455e11	−	4.34617e11i	0.132088	−	0.492960i
$970$	−4.97407e11	−	4.97407e11i	−0.561856	−	0.561856i
$971$	−1.53855e11	−	2.66485e11i	−0.173076	−	0.299776i	0.766418	−	0.642342i	$-0.222037\pi$
$971$	−1.53855e11	−	2.66485e11i	−0.173076	−	0.299776i	−0.939494	+	0.342566i	$0.888704\pi$
$972$	3.76011e11	+	2.17090e11i	0.421246	+	0.243206i
$973$	−1.96778e12	+	5.27266e11i	−2.19546	+	0.588272i
$974$			4.64993e11i			0.516667i
$975$	5.43806e10	−	1.43741e12i	0.0601763	−	1.59061i
$976$	1.92549e12			2.12199
$977$	8.58331e10	+	3.20333e11i	0.0942056	+	0.351580i	0.996898	−	0.0787069i	$-0.0250791\pi$
$977$	8.58331e10	+	3.20333e11i	0.0942056	+	0.351580i	−0.902692	+	0.430287i	$0.858412\pi$
$978$	−2.66759e11	+	4.62041e11i	−0.291584	+	0.505039i
$979$	8.58266e9	−	4.95520e9i	0.00934310	−	0.00539424i
$980$	6.44654e11	−	6.44654e11i	0.698912	−	0.698912i
$981$	−6.08648e10	−	1.63087e10i	−0.0657189	−	0.0176093i
$982$	4.88003e10	−	1.82125e11i	0.0524779	−	0.195850i
$983$	6.32118e10	+	6.32118e10i	0.0676993	+	0.0676993i	0.740146	−	0.672446i	$-0.234756\pi$
$983$	6.32118e10	+	6.32118e10i	0.0676993	+	0.0676993i	−0.672446	+	0.740146i	$0.734756\pi$
$984$	−1.56254e11	−	2.70640e11i	−0.166668	−	0.288677i
$985$	−2.69640e11	−	1.55677e11i	−0.286444	−	0.165379i
$986$	1.29343e11	−	3.46572e10i	0.136847	−	0.0366679i
$987$			6.85564e11i			0.722403i
$988$	−1.11791e11	−	1.20582e11i	−0.117322	−	0.126548i
$989$	−8.57517e11			−0.896308
$990$	5.73319e10	+	2.13966e11i	0.0596837	+	0.222742i
$991$	3.11940e11	−	5.40295e11i	0.323427	−	0.560191i	−0.657766	−	0.753222i	$-0.728498\pi$
$991$	3.11940e11	−	5.40295e11i	0.323427	−	0.560191i	0.981193	+	0.193031i	$0.0618318\pi$
$992$	−2.68246e11	+	1.54872e11i	−0.277005	+	0.159929i
$993$	2.76621e10	−	2.76621e10i	0.0284504	−	0.0284504i
$994$	−2.39449e12	−	6.41602e11i	−2.45283	−	0.657234i
$995$	−4.26865e11	+	1.59308e12i	−0.435510	+	1.62534i
$996$	−4.53224e11	−	4.53224e11i	−0.460549	−	0.460549i
$997$	−2.01149e11	−	3.48400e11i	−0.203581	−	0.352613i	0.746099	−	0.665835i	$-0.231925\pi$
$997$	−2.01149e11	−	3.48400e11i	−0.203581	−	0.352613i	−0.949680	+	0.313223i	$0.898591\pi$
$998$	1.31968e12	+	7.61918e11i	1.33029	+	0.768044i
$999$	1.83533e11	−	4.91775e10i	0.184269	−	0.0493747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.f.a.6.2	✓	32
13.11	odd	12	inner	13.9.f.a.11.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.f.a.6.2	✓	32	1.1	even	1	trivial
13.9.f.a.11.2	yes	32	13.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.98932 - 18.6204i) q^{2} +(51.4031 - 89.0328i) q^{3} +(-100.124 + 57.8065i) q^{4} +(663.519 - 663.519i) q^{5} +(-1914.29 - 512.934i) q^{6} +(-974.220 + 3635.84i) q^{7} +(-1913.63 - 1913.63i) q^{8} +(-2004.06 - 3471.13i) q^{9} +(-15665.5 - 9044.49i) q^{10} +(2951.13 - 790.754i) q^{11} +11885.7i q^{12} +(13335.2 + 25256.7i) q^{13} +72561.5 q^{14} +(-24968.0 - 93182.0i) q^{15} +(-40883.3 + 70811.9i) q^{16} +(76115.3 - 43945.2i) q^{17} +(-54635.0 + 54635.0i) q^{18} +(48100.1 + 12888.4i) q^{19} +(-28078.3 + 104790. i) q^{20} +(273631. + 273631. i) q^{21} +(-29448.3 - 51006.0i) q^{22} +(-398503. - 230076. i) q^{23} +(-268742. + 72009.2i) q^{24} -489891. i q^{25} +(403757. - 374321. i) q^{26} +262452. q^{27} +(-112632. - 420350. i) q^{28} +(-39516.7 + 68445.0i) q^{29} +(-1.61051e6 + 929830. i) q^{30} +(-247923. + 247923. i) q^{31} +(853326. + 228648. i) q^{32} +(81294.4 - 303395. i) q^{33} +(-1.19804e6 - 1.19804e6i) q^{34} +(1.76604e6 + 3.05886e6i) q^{35} +(401308. + 231695. i) q^{36} +(699301. - 187377. i) q^{37} -959948. i q^{38} +(2.93415e6 + 111006. i) q^{39} -2.53946e6 q^{40} +(290714. + 1.08496e6i) q^{41} +(3.72989e6 - 6.46035e6i) q^{42} +(1.61388e6 - 931776. i) q^{43} +(-249768. + 249768. i) q^{44} +(-3.63290e6 - 973432. i) q^{45} +(-2.29585e6 + 8.56821e6i) q^{46} +(1.25272e6 + 1.25272e6i) q^{47} +(4.20306e6 + 7.27991e6i) q^{48} +(-7.27775e6 - 4.20181e6i) q^{49} +(-9.12197e6 + 2.44423e6i) q^{50} -9.03568e6i q^{51} +(-2.79517e6 - 1.75794e6i) q^{52} -2.09430e6 q^{53} +(-1.30946e6 - 4.88696e6i) q^{54} +(1.43345e6 - 2.48282e6i) q^{55} +(8.82193e6 - 5.09335e6i) q^{56} +(3.61998e6 - 3.61998e6i) q^{57} +(1.47164e6 + 394324. i) q^{58} +(-5.48291e6 + 2.04625e7i) q^{59} +(7.88642e6 + 7.88642e6i) q^{60} +(-1.17743e7 - 2.03937e7i) q^{61} +(5.85339e6 + 3.37946e6i) q^{62} +(1.45729e7 - 3.90479e6i) q^{63} +3.90215e6i q^{64} +(2.56065e7 + 7.91018e6i) q^{65} -6.05494e6 q^{66} +(4.35129e6 + 1.62392e7i) q^{67} +(-5.08063e6 + 8.79991e6i) q^{68} +(-4.09686e7 + 2.36532e7i) q^{69} +(4.81460e7 - 4.81460e7i) q^{70} +(-3.29995e7 - 8.84219e6i) q^{71} +(-2.80743e6 + 1.04775e7i) q^{72} +(3.93076e7 + 3.93076e7i) q^{73} +(-6.97808e6 - 1.20864e7i) q^{74} +(-4.36164e7 - 2.51819e7i) q^{75} +(-5.56100e6 + 1.49006e6i) q^{76} +1.15002e7i q^{77} +(-1.25725e7 - 5.51889e7i) q^{78} +2.79609e6 q^{79} +(1.98582e7 + 7.41119e7i) q^{80} +(2.66395e7 - 4.61409e7i) q^{81} +(1.87519e7 - 1.08264e7i) q^{82} +(-3.81318e7 + 3.81318e7i) q^{83} +(-4.32146e7 - 1.15793e7i) q^{84} +(2.13455e7 - 7.96625e7i) q^{85} +(-2.54022e7 - 2.54022e7i) q^{86} +(4.06257e6 + 7.03657e6i) q^{87} +(-7.16058e6 - 4.13416e6i) q^{88} +(3.13321e6 - 839541. i) q^{89} +7.25028e7i q^{90} +(-1.04821e8 + 2.38790e7i) q^{91} +5.31995e7 q^{92} +(9.32926e6 + 3.48173e7i) q^{93} +(1.70759e7 - 2.95763e7i) q^{94} +(4.04671e7 - 2.33637e7i) q^{95} +(6.42208e7 - 6.42208e7i) q^{96} +(3.75627e7 + 1.00649e7i) q^{97} +(-4.19284e7 + 1.56479e8i) q^{98} +(-8.65906e6 - 8.65906e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) \) 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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