LMFDB - Embedded newform 13.9.f.a.2.4

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			2.4
Character	$\chi$	$=$	13.2
Dual form			13.9.f.a.7.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.97311 - 1.33254i) q^{2} +(73.7308 + 127.705i) q^{3} +(-198.746 - 114.746i) q^{4} +(-65.5592 + 65.5592i) q^{5} +(-196.499 - 733.343i) q^{6} +(-2444.94 + 655.120i) q^{7} +(1767.47 + 1767.47i) q^{8} +(-7591.95 + 13149.6i) q^{9} +(413.394 - 238.673i) q^{10} +(-3565.33 + 13306.0i) q^{11} -33841.3i q^{12} +(5082.27 - 28105.2i) q^{13} +13032.0 q^{14} +(-13206.0 - 3538.54i) q^{15} +(22940.4 + 39734.0i) q^{16} +(60886.5 + 35152.8i) q^{17} +(55278.1 - 55278.1i) q^{18} +(10134.6 + 37822.9i) q^{19} +(20552.3 - 5506.98i) q^{20} +(-263930. - 263930. i) q^{21} +(35461.6 - 61421.3i) q^{22} +(278141. - 160585. i) q^{23} +(-95398.6 + 356033. i) q^{24} +382029. i q^{25} +(-62726.0 + 132998. i) q^{26} -1.27155e6 q^{27} +(561096. + 150345. i) q^{28} +(348501. + 603621. i) q^{29} +(60959.7 + 35195.1i) q^{30} +(704939. - 704939. i) q^{31} +(-226755. - 846260. i) q^{32} +(-1.96212e6 + 525750. i) q^{33} +(-255953. - 255953. i) q^{34} +(117339. - 203238. i) q^{35} +(3.01775e6 - 1.74230e6i) q^{36} +(-646353. + 2.41222e6i) q^{37} -201603. i q^{38} +(3.96390e6 - 1.42318e6i) q^{39} -231748. q^{40} +(-3.75874e6 - 1.00715e6i) q^{41} +(960856. + 1.66425e6i) q^{42} +(1.88819e6 + 1.09015e6i) q^{43} +(2.23541e6 - 2.23541e6i) q^{44} +(-364358. - 1.35980e6i) q^{45} +(-1.59721e6 + 427972. i) q^{46} +(-5.30008e6 - 5.30008e6i) q^{47} +(-3.38283e6 + 5.85924e6i) q^{48} +(556099. - 321064. i) q^{49} +(509070. - 1.89987e6i) q^{50} +1.03674e7i q^{51} +(-4.23505e6 + 5.00263e6i) q^{52} +137263. q^{53} +(6.32355e6 + 1.69439e6i) q^{54} +(-638591. - 1.10607e6i) q^{55} +(-5.47927e6 - 3.16346e6i) q^{56} +(-4.08296e6 + 4.08296e6i) q^{57} +(-928784. - 3.46627e6i) q^{58} +(1.15724e7 - 3.10082e6i) q^{59} +(2.21861e6 + 2.21861e6i) q^{60} +(-2.44433e6 + 4.23371e6i) q^{61} +(-4.44510e6 + 2.56638e6i) q^{62} +(9.94729e6 - 3.71238e7i) q^{63} -7.23479e6i q^{64} +(1.50936e6 + 2.17574e6i) q^{65} +1.04585e7 q^{66} +(-9.87283e6 - 2.64542e6i) q^{67} +(-8.06731e6 - 1.39730e7i) q^{68} +(4.10151e7 + 2.36801e7i) q^{69} +(-854365. + 854365. i) q^{70} +(985912. + 3.67947e6i) q^{71} +(-3.66602e7 + 9.82306e6i) q^{72} +(3.80599e7 + 3.80599e7i) q^{73} +(6.42877e6 - 1.11350e7i) q^{74} +(-4.87872e7 + 2.81673e7i) q^{75} +(2.32582e6 - 8.68008e6i) q^{76} -3.48681e7i q^{77} +(-2.16094e7 + 1.79559e6i) q^{78} +1.02114e7 q^{79} +(-4.10889e6 - 1.10097e6i) q^{80} +(-4.39413e7 - 7.61086e7i) q^{81} +(1.73506e7 + 1.00174e7i) q^{82} +(2.14542e7 - 2.14542e7i) q^{83} +(2.21701e7 + 8.27401e7i) q^{84} +(-6.29626e6 + 1.68708e6i) q^{85} +(-7.93753e6 - 7.93753e6i) q^{86} +(-5.13905e7 + 8.90109e7i) q^{87} +(-2.98196e7 + 1.72164e7i) q^{88} +(2.07862e7 - 7.75752e7i) q^{89} +7.24798e6i q^{90} +(5.98643e6 + 7.20451e7i) q^{91} -7.37060e7 q^{92} +(1.42000e8 + 3.80488e7i) q^{93} +(1.92953e7 + 3.34205e7i) q^{94} +(-3.14406e6 - 1.81522e6i) q^{95} +(9.13532e7 - 9.13532e7i) q^{96} +(-1.54032e7 - 5.74855e7i) q^{97} +(-3.19337e6 + 855662. i) q^{98} +(-1.47901e8 - 1.47901e8i) 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 $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−4.97311	−	1.33254i	−0.310820	−	0.0832839i	0.100037	−	0.994984i	$-0.468104\pi$
$2$	−4.97311	−	1.33254i	−0.310820	−	0.0832839i	−0.410857	+	0.911700i	$0.634770\pi$
$3$	73.7308	+	127.705i	0.910256	+	1.57661i	0.813702	+	0.581283i	$0.197449\pi$
$3$	73.7308	+	127.705i	0.910256	+	1.57661i	0.0965548	+	0.995328i	$0.469218\pi$
$4$	−198.746	−	114.746i	−0.776353	−	0.448227i
$5$	−65.5592	+	65.5592i	−0.104895	+	0.104895i	−0.757606	−	0.652712i	$-0.773631\pi$
$5$	−65.5592	+	65.5592i	−0.104895	+	0.104895i	0.652712	+	0.757606i	$0.273631\pi$
$6$	−196.499	−	733.343i	−0.151619	−	0.565851i
$7$	−2444.94	+	655.120i	−1.01830	+	0.272853i	−0.729094	−	0.684413i	$-0.760058\pi$
$7$	−2444.94	+	655.120i	−1.01830	+	0.272853i	−0.289208	+	0.957266i	$0.593392\pi$
$8$	1767.47	+	1767.47i	0.431511	+	0.431511i
$9$	−7591.95	+	13149.6i	−1.15713	+	2.00421i
$10$	413.394	−	238.673i	0.0413394	−	0.0238673i
$11$	−3565.33	+	13306.0i	−0.243517	+	0.908818i	0.730606	+	0.682799i	$0.239238\pi$
$11$	−3565.33	+	13306.0i	−0.243517	+	0.908818i	−0.974123	+	0.226019i	$0.927429\pi$
$12$		−	33841.3i		−	1.63201i
$13$	5082.27	−	28105.2i	0.177944	−	0.984041i
$13$	5082.27	−	28105.2i	0.177944	−	0.984041i
$14$	13032.0			0.339233
$15$	−13206.0	−	3538.54i	−0.260859	−	0.0698970i
$16$	22940.4	+	39734.0i	0.350043	+	0.606293i
$17$	60886.5	+	35152.8i	0.728996	+	0.420886i	0.818055	−	0.575140i	$-0.195053\pi$
$17$	60886.5	+	35152.8i	0.728996	+	0.420886i	−0.0890589	+	0.996026i	$0.528386\pi$
$18$	55278.1	−	55278.1i	0.526579	−	0.526579i
$19$	10134.6	+	37822.9i	0.0777666	+	0.290229i	0.993846	−	0.110767i	$-0.0353308\pi$
$19$	10134.6	+	37822.9i	0.0777666	+	0.290229i	−0.916080	+	0.400996i	$0.868664\pi$
$20$	20552.3	−	5506.98i	0.128452	−	0.0344186i
$21$	−263930.	−	263930.i	−1.35710	−	1.35710i
$22$	35461.6	−	61421.3i	0.151380	−	0.262197i
$23$	278141.	−	160585.i	0.993925	−	0.573843i	0.0874799	−	0.996166i	$-0.472119\pi$
$23$	278141.	−	160585.i	0.993925	−	0.573843i	0.906445	+	0.422323i	$0.138785\pi$
$24$	−95398.6	+	356033.i	−0.287539	+	1.07311i
$25$			382029.i			0.977994i
$26$	−62726.0	+	132998.i	−0.137263	+	0.291039i
$27$	−1.27155e6			−2.39264
$28$	561096.	+	150345.i	0.912862	+	0.244601i
$29$	348501.	+	603621.i	0.492733	+	0.853439i	0.999965	−	0.00837065i	$-0.00266449\pi$
$29$	348501.	+	603621.i	0.492733	+	0.853439i	−0.507232	+	0.861810i	$0.669331\pi$
$30$	60959.7	+	35195.1i	0.0752589	+	0.0434507i
$31$	704939.	−	704939.i	0.763317	−	0.763317i	−0.213604	−	0.976920i	$-0.568520\pi$
$31$	704939.	−	704939.i	0.763317	−	0.763317i	0.976920	+	0.213604i	$0.0685201\pi$
$32$	−226755.	−	846260.i	−0.216250	−	0.807056i
$33$	−1.96212e6	+	525750.i	−1.65452	+	0.443326i
$34$	−255953.	−	255953.i	−0.191533	−	0.191533i
$35$	117339.	−	203238.i	0.0781937	−	0.135435i
$36$	3.01775e6	−	1.74230e6i	1.79669	−	1.03732i
$37$	−646353.	+	2.41222e6i	−0.344876	+	1.28709i	0.547881	+	0.836556i	$0.315434\pi$
$37$	−646353.	+	2.41222e6i	−0.344876	+	1.28709i	−0.892757	+	0.450538i	$0.851232\pi$
$38$		−	201603.i		−	0.0966856i
$39$	3.96390e6	−	1.42318e6i	1.71342	−	0.615180i
$40$	−231748.			−0.0905265
$41$	−3.75874e6	−	1.00715e6i	−1.33017	−	0.356418i	−0.477391	−	0.878691i	$-0.658417\pi$
$41$	−3.75874e6	−	1.00715e6i	−1.33017	−	0.356418i	−0.852778	+	0.522273i	$0.825084\pi$
$42$	960856.	+	1.66425e6i	0.308789	+	0.534838i
$43$	1.88819e6	+	1.09015e6i	0.552297	+	0.318869i	0.750048	−	0.661384i	$-0.230030\pi$
$43$	1.88819e6	+	1.09015e6i	0.552297	+	0.318869i	−0.197751	+	0.980252i	$0.563364\pi$
$44$	2.23541e6	−	2.23541e6i	0.596412	−	0.596412i
$45$	−364358.	−	1.35980e6i	−0.0888543	−	0.331609i
$46$	−1.59721e6	+	427972.i	−0.356723	+	0.0955837i
$47$	−5.30008e6	−	5.30008e6i	−1.08615	−	1.08615i	−0.995921	−	0.0902318i	$-0.971239\pi$
$47$	−5.30008e6	−	5.30008e6i	−1.08615	−	1.08615i	−0.0902318	−	0.995921i	$-0.528761\pi$
$48$	−3.38283e6	+	5.85924e6i	−0.637258	+	1.10376i
$49$	556099.	−	321064.i	0.0964645	−	0.0556938i
$50$	509070.	−	1.89987e6i	0.0814511	−	0.303980i
$51$			1.03674e7i			1.53246i
$52$	−4.23505e6	+	5.00263e6i	−0.579222	+	0.684203i
$53$	137263.			0.0173960			0.00869800	−	0.999962i	$-0.497231\pi$
$53$	137263.			0.0173960			0.00869800	+	0.999962i	$0.497231\pi$
$54$	6.32355e6	+	1.69439e6i	0.743680	+	0.199268i
$55$	−638591.	−	1.10607e6i	−0.0697866	−	0.120874i
$56$	−5.47927e6	−	3.16346e6i	−0.557148	−	0.321670i
$57$	−4.08296e6	+	4.08296e6i	−0.386790	+	0.386790i
$58$	−928784.	−	3.46627e6i	−0.0820735	−	0.306302i
$59$	1.15724e7	−	3.10082e6i	0.955027	−	0.255899i	0.252533	−	0.967588i	$-0.418736\pi$
$59$	1.15724e7	−	3.10082e6i	0.955027	−	0.255899i	0.702494	+	0.711690i	$0.252070\pi$
$60$	2.21861e6	+	2.21861e6i	0.171189	+	0.171189i
$61$	−2.44433e6	+	4.23371e6i	−0.176539	+	0.305775i	−0.940693	−	0.339259i	$-0.889824\pi$
$61$	−2.44433e6	+	4.23371e6i	−0.176539	+	0.305775i	0.764154	+	0.645034i	$0.223157\pi$
$62$	−4.44510e6	+	2.56638e6i	−0.300826	+	0.173682i
$63$	9.94729e6	−	3.71238e7i	0.631455	−	2.35662i
$64$		−	7.23479e6i		−	0.431227i
$65$	1.50936e6	+	2.17574e6i	0.0845553	+	0.121886i
$66$	1.04585e7			0.551178
$67$	−9.87283e6	−	2.64542e6i	−0.489940	−	0.131279i	0.00538740	−	0.999985i	$-0.498285\pi$
$67$	−9.87283e6	−	2.64542e6i	−0.489940	−	0.131279i	−0.495327	+	0.868707i	$0.664952\pi$
$68$	−8.06731e6	−	1.39730e7i	−0.377305	−	0.653512i
$69$	4.10151e7	+	2.36801e7i	1.80945	+	1.04469i
$70$	−854365.	+	854365.i	−0.0355837	+	0.0355837i
$71$	985912.	+	3.67947e6i	0.0387976	+	0.144795i	0.982608	−	0.185694i	$-0.0594532\pi$
$71$	985912.	+	3.67947e6i	0.0387976	+	0.144795i	−0.943810	+	0.330488i	$0.892787\pi$
$72$	−3.66602e7	+	9.82306e6i	−1.36416	+	0.365525i
$73$	3.80599e7	+	3.80599e7i	1.34022	+	1.34022i	0.895835	+	0.444386i	$0.146578\pi$
$73$	3.80599e7	+	3.80599e7i	1.34022	+	1.34022i	0.444386	+	0.895835i	$0.353422\pi$
$74$	6.42877e6	−	1.11350e7i	0.214388	−	0.371332i
$75$	−4.87872e7	+	2.81673e7i	−1.54192	+	0.890226i
$76$	2.32582e6	−	8.68008e6i	0.0697143	−	0.260177i
$77$		−	3.48681e7i		−	0.991896i
$78$	−2.16094e7	+	1.79559e6i	−0.583800	+	0.0485096i
$79$	1.02114e7			0.262166			0.131083	−	0.991371i	$-0.458155\pi$
$79$	1.02114e7			0.262166			0.131083	+	0.991371i	$0.458155\pi$
$80$	−4.10889e6	−	1.10097e6i	−0.100315	−	0.0268792i
$81$	−4.39413e7	−	7.61086e7i	−1.02078	−	1.76805i
$82$	1.73506e7	+	1.00174e7i	0.383759	+	0.221563i
$83$	2.14542e7	−	2.14542e7i	0.452065	−	0.452065i	−0.443974	−	0.896039i	$-0.646432\pi$
$83$	2.14542e7	−	2.14542e7i	0.452065	−	0.452065i	0.896039	+	0.443974i	$0.146432\pi$
$84$	2.21701e7	+	8.27401e7i	0.445299	+	1.66188i
$85$	−6.29626e6	+	1.68708e6i	−0.120617	+	0.0323191i
$86$	−7.93753e6	−	7.93753e6i	−0.145108	−	0.145108i
$87$	−5.13905e7	+	8.90109e7i	−0.897027	+	1.55370i
$88$	−2.98196e7	+	1.72164e7i	−0.497246	+	0.287085i
$89$	2.07862e7	−	7.75752e7i	0.331295	−	1.23641i	−0.576535	−	0.817073i	$-0.695596\pi$
$89$	2.07862e7	−	7.75752e7i	0.331295	−	1.23641i	0.907830	−	0.419338i	$-0.137738\pi$
$90$			7.24798e6i			0.110471i
$91$	5.98643e6	+	7.20451e7i	0.0872976	+	1.05060i
$92$	−7.37060e7			−1.02885
$93$	1.42000e8	+	3.80488e7i	1.89827	+	0.508639i
$94$	1.92953e7	+	3.34205e7i	0.247139	+	0.428057i
$95$	−3.14406e6	−	1.81522e6i	−0.0386008	−	0.0222862i
$96$	9.13532e7	−	9.13532e7i	1.07557	−	1.07557i
$97$	−1.54032e7	−	5.74855e7i	−0.173990	−	0.649339i	−0.996721	−	0.0809092i	$-0.974218\pi$
$97$	−1.54032e7	−	5.74855e7i	−0.173990	−	0.649339i	0.822732	−	0.568430i	$-0.192449\pi$
$98$	−3.19337e6	+	855662.i	−0.0346215	+	0.00927679i
$99$	−1.47901e8	−	1.47901e8i	−1.53968	−	1.53968i
$100$	4.38364e7	−	7.59268e7i	0.438364	−	0.759268i
$101$	1.98072e7	−	1.14357e7i	0.190343	−	0.109895i	−0.401800	−	0.915727i	$-0.631615\pi$
$101$	1.98072e7	−	1.14357e7i	0.190343	−	0.109895i	0.592143	+	0.805833i	$0.298282\pi$
$102$	1.38150e7	−	5.15581e7i	0.127629	−	0.476318i
$103$			4.71823e7i			0.419208i	0.977786	+	0.209604i	$0.0672175\pi$
$103$			4.71823e7i			0.419208i	−0.977786	+	0.209604i	$0.932782\pi$
$104$	5.86578e7	−	4.06923e7i	0.501410	−	0.347840i
$105$	3.46061e7			0.284705
$106$	−682624.	−	182909.i	−0.00540702	−	0.00144881i
$107$	2.61920e7	+	4.53659e7i	0.199818	+	0.346094i	0.948469	−	0.316870i	$-0.102632\pi$
$107$	2.61920e7	+	4.53659e7i	0.199818	+	0.346094i	−0.748652	+	0.662964i	$0.769298\pi$
$108$	2.52715e8	+	1.45905e8i	1.85753	+	1.07245i
$109$	−1.65909e7	+	1.65909e7i	−0.117534	+	0.117534i	−0.763428	−	0.645893i	$-0.776485\pi$
$109$	−1.65909e7	+	1.65909e7i	−0.117534	+	0.117534i	0.645893	+	0.763428i	$0.276485\pi$
$110$	1.70190e6	+	6.35157e6i	0.0116242	+	0.0433821i
$111$	−3.55710e8	+	9.53122e7i	−2.34317	+	0.627851i
$112$	−8.21186e7	−	8.21186e7i	−0.521879	−	0.521879i
$113$	−1.19176e8	+	2.06418e8i	−0.730926	+	1.26600i	0.225562	+	0.974229i	$0.427578\pi$
$113$	−1.19176e8	+	2.06418e8i	−0.730926	+	1.26600i	−0.956488	+	0.291772i	$0.905755\pi$
$114$	2.57457e7	−	1.48643e7i	0.152435	−	0.0880087i
$115$	−7.70689e6	+	2.87625e7i	−0.0440644	+	0.164451i
$116$		−	1.59957e8i		−	0.883426i
$117$	3.30989e8	+	2.80203e8i	1.76632	+	1.49530i
$118$	−6.16829e7			−0.318153
$119$	−1.71893e8	−	4.60587e7i	−0.857178	−	0.229680i
$120$	−1.70870e7	−	2.95955e7i	−0.0824024	−	0.142725i
$121$	2.13020e7	+	1.22987e7i	0.0993756	+	0.0573745i
$122$	1.77976e7	−	1.77976e7i	0.0803380	−	0.0803380i
$123$	−1.48516e8	−	5.54270e8i	−0.648863	−	2.42159i
$124$	−2.20993e8	+	5.92149e7i	−0.934742	+	0.250463i
$125$	−5.06546e7	−	5.06546e7i	−0.207481	−	0.207481i
$126$	−9.89380e7	+	1.71366e8i	−0.392537	+	0.679895i
$127$	1.41025e8	−	8.14210e7i	0.542104	−	0.312984i	−0.203827	−	0.979007i	$-0.565338\pi$
$127$	1.41025e8	−	8.14210e7i	0.542104	−	0.312984i	0.745931	+	0.666023i	$0.232005\pi$
$128$	−6.76898e7	+	2.52622e8i	−0.252164	+	0.941090i
$129$			3.21510e8i			1.16101i
$130$	−4.60697e6	−	1.28315e7i	−0.0161303	−	0.0449267i
$131$	1.52273e8			0.517056			0.258528	−	0.966004i	$-0.416763\pi$
$131$	1.52273e8			0.517056			0.258528	+	0.966004i	$0.416763\pi$
$132$	4.50293e8	+	1.20656e8i	1.48320	+	0.397422i
$133$	−4.95572e7	−	8.58355e7i	−0.158380	−	0.274322i
$134$	4.55736e7	+	2.63119e7i	0.141349	+	0.0816082i
$135$	8.33616e7	−	8.33616e7i	0.250975	−	0.250975i
$136$	4.54835e7	+	1.69747e8i	0.132953	+	0.496187i
$137$	1.87802e8	−	5.03215e7i	0.533113	−	0.142847i	0.0177874	−	0.999842i	$-0.494338\pi$
$137$	1.87802e8	−	5.03215e7i	0.533113	−	0.142847i	0.515325	+	0.856995i	$0.327671\pi$
$138$	−1.72418e8	−	1.72418e8i	−0.475408	−	0.475408i
$139$	3.79750e7	−	6.57746e7i	0.101727	−	0.176197i	−0.810669	−	0.585505i	$-0.800896\pi$
$139$	3.79750e7	−	6.57746e7i	0.101727	−	0.176197i	0.912396	+	0.409308i	$0.134230\pi$
$140$	−4.66415e7	+	2.69285e7i	−0.121412	+	0.0700971i
$141$	2.86070e8	−	1.06763e9i	0.723762	−	2.70112i
$142$		−	1.96122e7i		−	0.0482362i
$143$	3.55848e8	+	1.67829e8i	0.850981	+	0.401350i
$144$	−6.96651e8			−1.62019
$145$	−6.24204e7	−	1.67255e7i	−0.141206	−	0.0378361i
$146$	−1.38560e8	−	2.39993e8i	−0.304948	−	0.528186i
$147$	8.20032e7	+	4.73446e7i	0.175615	+	0.101391i
$148$	4.05254e8	−	4.05254e8i	0.844656	−	0.844656i
$149$	1.99429e8	+	7.44281e8i	0.404617	+	1.51005i	0.804761	+	0.593599i	$0.202294\pi$
$149$	1.99429e8	+	7.44281e8i	0.404617	+	1.51005i	−0.400144	+	0.916452i	$0.631040\pi$
$150$	2.80158e8	−	7.50682e7i	0.553399	−	0.148283i
$151$	−3.90740e7	−	3.90740e7i	−0.0751588	−	0.0751588i	0.668528	−	0.743687i	$-0.266925\pi$
$151$	−3.90740e7	−	3.90740e7i	−0.0751588	−	0.0751588i	−0.743687	+	0.668528i	$0.766925\pi$
$152$	−4.89383e7	+	8.47636e7i	−0.0916799	+	0.158794i
$153$	−9.24494e8	+	5.33757e8i	−1.68709	+	0.974042i
$154$	−4.64633e7	+	1.73403e8i	−0.0826089	+	0.308301i
$155$			9.24305e7i			0.160136i
$156$	−9.51116e8	−	1.71991e8i	−1.60596	−	0.290406i
$157$	1.10291e9			1.81527			0.907637	−	0.419756i	$-0.137884\pi$
$157$	1.10291e9			1.81527			0.907637	+	0.419756i	$0.137884\pi$
$158$	−5.07823e7	−	1.36071e7i	−0.0814862	−	0.0218342i
$159$	1.01205e7	+	1.75292e7i	0.0158348	+	0.0274267i
$160$	7.03460e7	+	4.06143e7i	0.107339	+	0.0619725i
$161$	−5.74836e8	+	5.74836e8i	−0.855541	+	0.855541i
$162$	1.17107e8	+	4.37051e8i	0.170029	+	0.634559i
$163$	−4.28611e8	+	1.14846e8i	−0.607174	+	0.162692i	−0.549290	−	0.835632i	$-0.685102\pi$
$163$	−4.28611e8	+	1.14846e8i	−0.607174	+	0.162692i	−0.0578835	+	0.998323i	$0.518435\pi$
$164$	6.31469e8	+	6.31469e8i	0.872924	+	0.872924i
$165$	9.41676e7	−	1.63103e8i	0.127047	−	0.220053i
$166$	−1.35283e8	+	7.81057e7i	−0.178160	+	0.102861i
$167$	5.69393e7	−	2.12500e8i	0.0732059	−	0.273208i	−0.919615	−	0.392822i	$-0.871499\pi$
$167$	5.69393e7	−	2.12500e8i	0.0732059	−	0.273208i	0.992821	+	0.119614i	$0.0381656\pi$
$168$		−	9.32977e8i		−	1.17121i
$169$	−7.64072e8	−	2.85676e8i	−0.936672	−	0.350209i
$170$	3.35601e7			0.0401817
$171$	−5.74300e8	−	1.53883e8i	−0.671667	−	0.179973i
$172$	−2.50181e8	−	4.33326e8i	−0.285851	−	0.495109i
$173$	6.94146e8	+	4.00765e8i	0.774937	+	0.447410i	0.834633	−	0.550807i	$-0.185680\pi$
$173$	6.94146e8	+	4.00765e8i	0.774937	+	0.447410i	−0.0596961	+	0.998217i	$0.519013\pi$
$174$	3.74182e8	−	3.74182e8i	0.408212	−	0.408212i
$175$	−2.50275e8	−	9.34039e8i	−0.266849	−	0.995893i
$176$	−6.10491e8	+	1.63581e8i	−0.636251	+	0.170483i
$177$	1.24923e9	+	1.24923e9i	1.27277	+	1.27277i
$178$	−2.06744e8	+	3.58092e8i	−0.205946	+	0.356709i
$179$	5.17193e8	−	2.98602e8i	0.503780	−	0.290857i	−0.226493	−	0.974013i	$-0.572726\pi$
$179$	5.17193e8	−	2.98602e8i	0.503780	−	0.290857i	0.730273	+	0.683155i	$0.239393\pi$
$180$	−8.36175e7	+	3.12065e8i	−0.0796539	+	0.297272i
$181$		−	8.00726e8i		−	0.746053i	−0.927821	−	0.373027i	$-0.878320\pi$
$181$		−	8.00726e8i		−	0.746053i	0.927821	−	0.373027i	$-0.121680\pi$
$182$	6.62319e7	−	3.66266e8i	0.0603645	−	0.333819i
$183$	−7.20891e8			−0.642784
$184$	7.75435e8	+	2.07777e8i	0.676510	+	0.181270i
$185$	−1.15769e8	−	2.00518e8i	−0.0988337	−	0.171185i
$186$	−6.55482e8	−	3.78443e8i	−0.547657	−	0.316190i
$187$	−6.84824e8	+	6.84824e8i	−0.560032	+	0.560032i
$188$	4.45207e8	+	1.66153e9i	0.356394	+	1.33008i
$189$	3.10886e9	−	8.33017e8i	2.43643	−	0.652840i
$190$	1.32169e7	+	1.32169e7i	0.0101418	+	0.0101418i
$191$	5.10712e8	−	8.84579e8i	0.383745	−	0.664666i	−0.607849	−	0.794052i	$-0.707968\pi$
$191$	5.10712e8	−	8.84579e8i	0.383745	−	0.664666i	0.991594	+	0.129387i	$0.0413009\pi$
$192$	9.23923e8	−	5.33427e8i	0.679878	−	0.392528i
$193$	3.32350e7	−	1.24035e8i	0.0239534	−	0.0893952i	−0.952914	−	0.303239i	$-0.901932\pi$
$193$	3.32350e7	−	1.24035e8i	0.0239534	−	0.0893952i	0.976868	+	0.213844i	$0.0685985\pi$
$194$			3.06408e8i			0.216318i
$195$	−1.66568e8	+	3.53173e8i	−0.115200	+	0.244258i
$196$	−1.47363e8			−0.0998540
$197$	−1.59614e9	−	4.27684e8i	−1.05976	−	0.283961i	−0.313478	−	0.949596i	$-0.601494\pi$
$197$	−1.59614e9	−	4.27684e8i	−1.05976	−	0.283961i	−0.746277	+	0.665635i	$0.768161\pi$
$198$	5.38446e8	+	9.32616e8i	0.350333	+	0.606795i
$199$	−1.84891e9	−	1.06747e9i	−1.17897	−	0.680680i	−0.223195	−	0.974774i	$-0.571649\pi$
$199$	−1.84891e9	−	1.06747e9i	−1.17897	−	0.680680i	−0.955776	+	0.294094i	$0.904982\pi$
$200$	−6.75225e8	+	6.75225e8i	−0.422016	+	0.422016i
$201$	−3.90097e8	−	1.45586e9i	−0.238995	−	0.891942i
$202$	−1.13742e8	+	3.04771e7i	−0.0683149	+	0.0183049i
$203$	−1.24751e9	−	1.24751e9i	−0.734615	−	0.734615i
$204$	1.18962e9	−	2.06048e9i	0.686889	−	1.18973i
$205$	3.12448e8	−	1.80392e8i	0.176914	−	0.102141i
$206$	6.28723e7	−	2.34643e8i	0.0349133	−	0.130298i
$207$			4.87661e9i			2.65605i
$208$	1.23332e9	−	4.42806e8i	0.658905	−	0.236570i
$209$	−5.39405e8			−0.282703
$210$	−1.72100e8	−	4.61141e7i	−0.0884919	−	0.0237113i
$211$	9.21952e8	+	1.59687e9i	0.465135	+	0.805637i	0.999208	−	0.0398016i	$-0.0126726\pi$
$211$	9.21952e8	+	1.59687e9i	0.465135	+	0.805637i	−0.534073	+	0.845438i	$0.679339\pi$
$212$	−2.72805e7	−	1.57504e7i	−0.0135054	−	0.00779737i
$213$	−3.97197e8	+	3.97197e8i	−0.192969	+	0.192969i
$214$	−6.98039e7	−	2.60512e8i	−0.0332832	−	0.124214i
$215$	−1.95258e8	+	5.23191e7i	−0.0913807	+	0.0244854i
$216$	−2.24742e9	−	2.24742e9i	−1.03245	−	1.03245i
$217$	−1.26172e9	+	2.18536e9i	−0.569013	+	0.985560i
$218$	1.04617e8	−	6.04004e7i	0.0463207	−	0.0267432i
$219$	−2.05427e9	+	7.66665e9i	−0.893062	+	3.33295i
$220$			2.93104e8i			0.125121i
$221$	1.29742e9	−	1.53257e9i	0.543889	−	0.642467i
$222$	1.89599e9			0.780594
$223$	−7.37820e7	−	1.97698e7i	−0.0298353	−	0.00799435i	0.243871	−	0.969808i	$-0.421583\pi$
$223$	−7.37820e7	−	1.97698e7i	−0.0298353	−	0.00799435i	−0.273706	+	0.961813i	$0.588249\pi$
$224$	1.10880e9	+	1.92050e9i	0.440416	+	0.762822i
$225$	−5.02355e9	−	2.90035e9i	−1.96011	−	1.13167i
$226$	8.67734e8	−	8.67734e8i	0.332624	−	0.332624i
$227$	−1.03762e9	−	3.87245e9i	−0.390783	−	1.45842i	−0.828846	−	0.559476i	$-0.811002\pi$
$227$	−1.03762e9	−	3.87245e9i	−0.390783	−	1.45842i	0.438064	−	0.898944i	$-0.355664\pi$
$228$	1.27998e9	−	3.42969e8i	0.473656	−	0.126916i
$229$	2.68019e9	+	2.68019e9i	0.974593	+	0.974593i	0.999685	−	0.0250926i	$-0.00798806\pi$
$229$	2.68019e9	+	2.68019e9i	0.974593	+	0.974593i	−0.0250926	+	0.999685i	$0.507988\pi$
$230$	7.66545e7	−	1.32770e8i	0.0273922	−	0.0474446i
$231$	4.45285e9	−	2.57086e9i	1.56383	−	0.902879i
$232$	−4.50918e8	+	1.68285e9i	−0.155649	+	0.580889i
$233$		−	5.24959e9i		−	1.78115i	−0.454833	−	0.890577i	$-0.650301\pi$
$233$		−	5.24959e9i		−	1.78115i	0.454833	−	0.890577i	$-0.349699\pi$
$234$	−1.27266e9	−	1.83454e9i	−0.424473	−	0.611876i
$235$	6.94938e8			0.227863
$236$	−2.65578e9	−	7.11614e8i	−0.856139	−	0.229402i
$237$	7.52892e8	+	1.30405e9i	0.238638	+	0.413333i
$238$	7.93470e8	+	4.58110e8i	0.247299	+	0.142778i
$239$	1.48148e9	−	1.48148e9i	0.454049	−	0.454049i	−0.442647	−	0.896696i	$-0.645960\pi$
$239$	1.48148e9	−	1.48148e9i	0.454049	−	0.454049i	0.896696	+	0.442647i	$0.145960\pi$
$240$	−1.62351e8	−	6.05903e8i	−0.0489340	−	0.182624i
$241$	−1.75278e9	+	4.69656e8i	−0.519588	+	0.139223i	−0.509076	−	0.860721i	$-0.670013\pi$
$241$	−1.75278e9	+	4.69656e8i	−0.519588	+	0.139223i	−0.0105122	+	0.999945i	$0.503346\pi$
$242$	−8.95489e7	−	8.95489e7i	−0.0261095	−	0.0261095i
$243$	2.30835e9	−	3.99818e9i	0.662028	−	1.14667i
$244$	9.71605e8	−	5.60956e8i	0.274113	−	0.158259i
$245$	−1.54087e7	+	5.75061e7i	−0.00427663	+	0.0159606i
$246$			2.95435e9i			0.806718i
$247$	1.11453e9	−	9.26092e7i	0.299435	−	0.0248809i
$248$	2.49192e9			0.658760
$249$	4.32166e9	+	1.15799e9i	1.12423	+	0.301235i
$250$	1.84412e8	+	3.19410e8i	0.0472094	+	0.0817691i
$251$	2.15605e9	+	1.24479e9i	0.543205	+	0.313619i	0.746377	−	0.665524i	$-0.231792\pi$
$251$	2.15605e9	+	1.24479e9i	0.543205	+	0.313619i	−0.203172	+	0.979143i	$0.565125\pi$
$252$	−6.23680e9	+	6.23680e9i	−1.54653	+	1.54653i
$253$	1.14508e9	+	4.27348e9i	0.279481	+	1.04304i
$254$	−8.09832e8	+	2.16994e8i	−0.194563	+	0.0521330i
$255$	−6.79677e8	−	6.79677e8i	−0.160747	−	0.160747i
$256$	−2.52795e8	+	4.37854e8i	−0.0588584	+	0.101946i
$257$	−3.67852e9	+	2.12379e9i	−0.843219	+	0.486833i	−0.858357	−	0.513053i	$-0.828514\pi$
$257$	−3.67852e9	+	2.12379e9i	−0.843219	+	0.486833i	0.0151383	+	0.999885i	$0.495181\pi$
$258$	4.28425e8	−	1.59891e9i	0.0966933	−	0.360864i
$259$		−	6.32118e9i		−	1.40475i
$260$	−5.03223e7	−	6.05615e8i	−0.0110120	−	0.132527i
$261$	−1.05832e10			−2.28063
$262$	−7.57271e8	−	2.02910e8i	−0.160711	−	0.0430624i
$263$	9.58547e8	+	1.66025e9i	0.200351	+	0.347017i	0.948641	−	0.316353i	$-0.102459\pi$
$263$	9.58547e8	+	1.66025e9i	0.200351	+	0.347017i	−0.748291	+	0.663371i	$0.769125\pi$
$264$	−4.39724e9	−	2.53875e9i	−0.905242	−	0.522642i
$265$	−8.99885e6	+	8.99885e6i	−0.00182475	+	0.00182475i
$266$	1.32074e8	+	4.92907e8i	0.0263810	+	0.0984551i
$267$	1.14394e10	−	3.06517e9i	2.25090	−	0.603127i
$268$	1.65864e9	+	1.65864e9i	0.321523	+	0.321523i
$269$	4.29984e9	−	7.44755e9i	0.821190	−	1.42234i	−0.0836066	−	0.996499i	$-0.526644\pi$
$269$	4.29984e9	−	7.44755e9i	0.821190	−	1.42234i	0.904797	−	0.425844i	$-0.140023\pi$
$270$	−5.25650e8	+	3.03484e8i	−0.0989103	+	0.0571059i
$271$	−7.32551e8	+	2.73392e9i	−0.135819	+	0.506884i	0.864174	+	0.503193i	$0.167841\pi$
$271$	−7.32551e8	+	2.73392e9i	−0.135819	+	0.506884i	−0.999993	+	0.00369072i	$0.998825\pi$
$272$			3.22568e9i			0.589313i
$273$	−8.75916e9	+	6.07644e9i	−1.57693	+	1.09395i
$274$	−1.00102e9			−0.177599
$275$	−5.08328e9	−	1.36206e9i	−0.888819	−	0.238158i
$276$	−5.43440e9	−	9.41266e9i	−0.936516	−	1.62209i
$277$	2.19884e9	+	1.26950e9i	0.373487	+	0.215633i	0.674981	−	0.737835i	$-0.264152\pi$
$277$	2.19884e9	+	1.26950e9i	0.373487	+	0.215633i	−0.301494	+	0.953468i	$0.597485\pi$
$278$	−2.76501e8	+	2.76501e8i	−0.0462933	+	0.0462933i
$279$	3.91784e9	+	1.46216e10i	0.646591	+	2.41311i
$280$	5.66611e8	−	1.51823e8i	0.0921834	−	0.0247005i
$281$	3.55542e9	+	3.55542e9i	0.570250	+	0.570250i	0.932198	−	0.361948i	$-0.117888\pi$
$281$	3.55542e9	+	3.55542e9i	0.570250	+	0.570250i	−0.361948	+	0.932198i	$0.617888\pi$
$282$	−2.84532e9	+	4.92823e9i	−0.449919	+	0.779282i
$283$	−4.06562e9	+	2.34729e9i	−0.633842	+	0.365949i	−0.782238	−	0.622979i	$-0.785922\pi$
$283$	−4.06562e9	+	2.34729e9i	−0.633842	+	0.365949i	0.148397	+	0.988928i	$0.452589\pi$
$284$	2.26259e8	−	8.44412e8i	0.0347803	−	0.129802i
$285$		−	5.35351e8i		−	0.0811446i
$286$	−1.54603e9	−	1.30881e9i	−0.231076	−	0.195620i
$287$	9.84971e9			1.45176
$288$	1.28495e10	+	3.44302e9i	1.86774	+	0.500460i
$289$	−1.01644e9	−	1.76052e9i	−0.145710	−	0.252377i
$290$	2.88136e8	+	1.66356e8i	0.0407386	+	0.0235204i
$291$	6.20553e9	−	6.20553e9i	0.865380	−	0.865380i
$292$	−3.19704e9	−	1.19315e10i	−0.439760	−	1.64121i
$293$	−1.04752e10	+	2.80681e9i	−1.42132	+	0.380841i	−0.885950	−	0.463780i	$-0.846493\pi$
$293$	−1.04752e10	+	2.80681e9i	−1.42132	+	0.380841i	−0.535366	+	0.844620i	$0.679826\pi$
$294$	−3.44723e8	−	3.44723e8i	−0.0461403	−	0.0461403i
$295$	−5.55391e8	+	9.61965e8i	−0.0733349	+	0.127020i
$296$	−5.40594e9	+	3.12112e9i	−0.704213	+	0.406578i
$297$	4.53349e9	−	1.69192e10i	0.582649	−	2.17447i
$298$		−	3.96714e9i		−	0.503052i
$299$	−3.09968e9	−	8.63334e9i	−0.387821	−	1.08017i
$300$	1.29284e10			1.59609
$301$	−5.33070e9	−	1.42836e9i	−0.649409	−	0.174009i
$302$	1.42252e8	+	2.46387e8i	0.0171013	+	0.0296204i
$303$	2.92080e9	+	1.68632e9i	0.346522	+	0.200065i
$304$	−1.27036e9	+	1.27036e9i	−0.148742	+	0.148742i
$305$	−1.17310e8	−	4.37807e8i	−0.0135561	−	0.0505922i
$306$	5.30887e9	−	1.42251e9i	0.605503	−	0.162244i
$307$	8.38319e9	+	8.38319e9i	0.943747	+	0.943747i	0.998500	−	0.0547530i	$-0.0174371\pi$
$307$	8.38319e9	+	8.38319e9i	0.943747	+	0.943747i	−0.0547530	+	0.998500i	$0.517437\pi$
$308$	−4.00099e9	+	6.92992e9i	−0.444595	+	0.770061i
$309$	−6.02543e9	+	3.47878e9i	−0.660928	+	0.381587i
$310$	1.23168e8	−	4.59667e8i	0.0133367	−	0.0497734i
$311$		−	8.63026e9i		−	0.922534i	−0.887261	−	0.461267i	$-0.847395\pi$
$311$		−	8.63026e9i		−	0.922534i	0.887261	−	0.461267i	$-0.152605\pi$
$312$	9.52152e9	+	4.49065e9i	1.00482	+	0.473904i
$313$	−3.68043e9			−0.383461			−0.191730	−	0.981448i	$-0.561410\pi$
$313$	−3.68043e9			−0.383461			−0.191730	+	0.981448i	$0.561410\pi$
$314$	−5.48491e9	−	1.46968e9i	−0.564223	−	0.151183i
$315$	1.78167e9	+	3.08594e9i	0.180961	+	0.313434i
$316$	−2.02947e9	−	1.17172e9i	−0.203533	−	0.117510i
$317$	−5.79623e8	+	5.79623e8i	−0.0573996	+	0.0573996i	−0.735224	−	0.677824i	$-0.762923\pi$
$317$	−5.79623e8	+	5.79623e8i	−0.0573996	+	0.0573996i	0.677824	+	0.735224i	$0.262923\pi$
$318$	−2.69720e7	−	1.00661e8i	−0.00263757	−	0.00984355i
$319$	−9.27431e9	+	2.48504e9i	−0.895610	+	0.239978i
$320$	4.74307e8	+	4.74307e8i	0.0452335	+	0.0452335i
$321$	−3.86231e9	+	6.68972e9i	−0.363770	+	0.630069i
$322$	3.62472e9	−	2.09273e9i	0.337172	−	0.194666i
$323$	−7.12521e8	+	2.65916e9i	−0.0654618	+	0.244307i
$324$			2.01684e10i			1.83017i
$325$	1.07370e10	+	1.94157e9i	0.962386	+	0.174028i
$326$	2.28457e9			0.202271
$327$	−3.34201e9	−	8.95489e8i	−0.292292	−	0.0783194i
$328$	−4.86335e9	−	8.42357e9i	−0.420185	−	0.727781i
$329$	1.64306e10	+	9.48620e9i	1.40239	+	0.809671i
$330$	−6.85648e8	+	6.85648e8i	−0.0578156	+	0.0578156i
$331$	−1.54711e9	−	5.77389e9i	−0.128887	−	0.481013i	0.871061	−	0.491174i	$-0.163432\pi$
$331$	−1.54711e9	−	5.77389e9i	−0.128887	−	0.481013i	−0.999948	+	0.0101612i	$0.996766\pi$
$332$	−6.72574e9	+	1.80216e9i	−0.553590	+	0.148334i
$333$	−2.68128e10	−	2.68128e10i	−2.18054	−	2.18054i
$334$	−5.66331e8	+	9.80914e8i	−0.0455077	+	0.0788216i
$335$	8.20687e8	−	4.73824e8i	0.0651626	−	0.0376216i
$336$	4.43232e9	−	1.65417e10i	0.347756	−	1.29784i
$337$			7.90055e9i			0.612545i	0.951944	+	0.306272i	$0.0990818\pi$
$337$			7.90055e9i			0.612545i	−0.951944	+	0.306272i	$0.900918\pi$
$338$	3.41914e9	+	2.43886e9i	0.261969	+	0.186861i
$339$	−3.51476e10			−2.66132
$340$	1.44494e9	+	3.87172e8i	0.108127	+	0.0289726i
$341$	6.86658e9	+	1.18933e10i	0.507835	+	0.879597i
$342$	2.65100e9	+	1.53056e9i	0.193779	+	0.111878i
$343$	9.16868e9	−	9.16868e9i	0.662415	−	0.662415i
$344$	1.41052e9	+	5.26413e9i	0.100727	+	0.375918i
$345$	−4.24137e9	+	1.13647e9i	−0.299385	+	0.0802198i
$346$	−2.91803e9	−	2.91803e9i	−0.203604	−	0.203604i
$347$	−2.02100e9	+	3.50048e9i	−0.139395	+	0.241440i	−0.927268	−	0.374398i	$-0.877849\pi$
$347$	−2.02100e9	+	3.50048e9i	−0.139395	+	0.241440i	0.787873	+	0.615838i	$0.211183\pi$
$348$	2.04273e10	−	1.17937e10i	1.39282	−	0.804145i
$349$	−1.92667e9	+	7.19044e9i	−0.129869	+	0.484679i	−0.999966	−	0.00820173i	$-0.997389\pi$
$349$	−1.92667e9	+	7.19044e9i	−0.129869	+	0.484679i	0.870097	+	0.492880i	$0.164056\pi$
$350$			4.97858e9i			0.331767i
$351$	−6.46234e9	+	3.57371e10i	−0.425757	+	2.35446i
$352$	1.20688e10			0.786128
$353$	1.36078e10	+	3.64619e9i	0.876371	+	0.234823i	0.668841	−	0.743406i	$-0.266791\pi$
$353$	1.36078e10	+	3.64619e9i	0.876371	+	0.234823i	0.207530	+	0.978229i	$0.433457\pi$
$354$	−4.54793e9	−	7.87724e9i	−0.289601	−	0.501604i
$355$	−3.05859e8	−	1.76588e8i	−0.0192579	−	0.0111185i
$356$	−1.30326e10	+	1.30326e10i	−0.811395	+	0.811395i
$357$	−6.79188e9	−	2.53476e10i	−0.418136	−	1.56050i
$358$	−2.96996e9	+	7.95799e8i	−0.180808	+	0.0484475i
$359$	6.56212e9	+	6.56212e9i	0.395063	+	0.395063i	0.876488	−	0.481424i	$-0.159880\pi$
$359$	6.56212e9	+	6.56212e9i	0.395063	+	0.395063i	−0.481424	+	0.876488i	$0.659880\pi$
$360$	1.75942e9	−	3.04740e9i	0.104751	−	0.181435i
$361$	1.33803e10	−	7.72514e9i	0.787840	−	0.454860i
$362$	−1.06700e9	+	3.98210e9i	−0.0621342	+	0.231888i
$363$			3.62718e9i			0.208902i
$364$	7.07712e9	−	1.50056e10i	0.403135	−	0.854768i
$365$	−4.99036e9			−0.281164
$366$	3.58507e9	+	9.60617e8i	0.199790	+	0.0535335i
$367$	−1.81267e9	−	3.13964e9i	−0.0999204	−	0.173067i	0.811731	−	0.584031i	$-0.198525\pi$
$367$	−1.81267e9	−	3.13964e9i	−0.0999204	−	0.173067i	−0.911652	+	0.410964i	$0.865192\pi$
$368$	1.27613e10	+	7.36777e9i	0.695833	+	0.401740i
$369$	4.17799e10	−	4.17799e10i	2.25352	−	2.25352i
$370$	3.08534e8	+	1.15146e9i	0.0164625	+	0.0614389i
$371$	−3.35600e8	+	8.99237e7i	−0.0177144	+	0.00474656i
$372$	−2.38561e10	−	2.38561e10i	−1.24574	−	1.24574i
$373$	−1.44196e10	+	2.49754e10i	−0.744933	+	1.29026i	0.205293	+	0.978701i	$0.434185\pi$
$373$	−1.44196e10	+	2.49754e10i	−0.744933	+	1.29026i	−0.950226	+	0.311562i	$0.899148\pi$
$374$	4.31827e9	−	2.49315e9i	0.220710	−	0.127427i
$375$	2.73406e9	−	1.02037e10i	0.138256	−	0.515978i
$376$		−	1.87355e10i		−	0.937374i
$377$	1.87361e10	−	6.72692e9i	0.927498	−	0.333005i
$378$	−1.65707e10			−0.811661
$379$	−2.59117e9	−	6.94303e8i	−0.125586	−	0.0336506i	0.195479	−	0.980708i	$-0.437374\pi$
$379$	−2.59117e9	−	6.94303e8i	−0.125586	−	0.0336506i	−0.321064	+	0.947057i	$0.604041\pi$
$380$	4.16580e8	+	7.21538e8i	0.0199786	+	0.0346039i
$381$	2.07958e10	+	1.20065e10i	0.986907	+	0.569791i
$382$	−3.71857e9	+	3.71857e9i	−0.174631	+	0.174631i
$383$	−8.07044e8	−	3.01193e9i	−0.0375061	−	0.139975i	0.944634	−	0.328126i	$-0.106417\pi$
$383$	−8.07044e8	−	3.01193e9i	−0.0375061	−	0.139975i	−0.982140	+	0.188151i	$0.939750\pi$
$384$	−3.72520e10	+	9.98165e9i	−1.71327	+	0.459068i
$385$	2.28593e9	+	2.28593e9i	0.104045	+	0.104045i
$386$	−3.30563e8	+	5.72552e8i	−0.0148904	+	0.0257909i
$387$	−2.86701e10	+	1.65527e10i	−1.27816	+	0.737947i
$388$	−3.53492e9	+	1.31925e10i	−0.155974	+	0.582103i
$389$		−	2.03044e10i		−	0.886731i	−0.896341	−	0.443366i	$-0.853784\pi$
$389$		−	2.03044e10i		−	0.886731i	0.896341	−	0.443366i	$-0.146216\pi$
$390$	1.29898e9	−	1.53441e9i	0.0561492	−	0.0663260i
$391$	2.25800e10			0.966090
$392$	1.55036e9	+	4.15417e8i	0.0656581	+	0.0175930i
$393$	1.12272e10	+	1.94461e10i	0.470654	+	0.815196i
$394$	7.36787e9	+	4.25384e9i	0.305743	+	0.176521i
$395$	−6.69450e8	+	6.69450e8i	−0.0274998	+	0.0274998i
$396$	1.24237e10	+	4.63660e10i	0.505209	+	1.88547i
$397$	−3.21153e10	+	8.60526e9i	−1.29285	+	0.346419i	−0.838744	−	0.544527i	$-0.816709\pi$
$397$	−3.21153e10	+	8.60526e9i	−1.29285	+	0.346419i	−0.454110	+	0.890946i	$0.650043\pi$
$398$	7.77239e9	+	7.77239e9i	0.309758	+	0.309758i
$399$	7.30777e9	−	1.26574e10i	0.288332	−	0.499406i
$400$	−1.51795e10	+	8.76391e9i	−0.592951	+	0.342340i
$401$	1.26223e9	−	4.71073e9i	0.0488161	−	0.182184i	−0.937213	−	0.348758i	$-0.886604\pi$
$401$	1.26223e9	−	4.71073e9i	0.0488161	−	0.182184i	0.986029	+	0.166574i	$0.0532703\pi$
$402$			7.76000e9i			0.297137i
$403$	−1.62298e10	−	2.33951e10i	−0.615307	−	0.886962i
$404$	−5.24881e9			−0.197031
$405$	7.87038e9	+	2.10886e9i	0.292534	+	0.0783842i
$406$	4.54165e9	+	7.86637e9i	0.167151	+	0.289514i
$407$	−2.97926e10	−	1.72007e10i	−1.08575	−	0.626859i
$408$	−1.83240e10	+	1.83240e10i	−0.661272	+	0.661272i
$409$	1.80178e9	+	6.72435e9i	0.0643887	+	0.240302i	0.990618	−	0.136658i	$-0.0436361\pi$
$409$	1.80178e9	+	6.72435e9i	0.0643887	+	0.240302i	−0.926230	+	0.376960i	$0.876969\pi$
$410$	−1.79422e9	+	4.80760e8i	−0.0634951	+	0.0170135i
$411$	2.02732e10	+	2.02732e10i	0.710484	+	0.710484i
$412$	5.41399e9	−	9.37730e9i	0.187901	−	0.325453i
$413$	−2.62625e10	+	1.51626e10i	−0.902683	+	0.521164i
$414$	6.49829e9	−	2.42519e10i	0.221206	−	0.825553i
$415$			2.81305e9i			0.0948385i
$416$	−2.49367e10	+	2.07206e9i	−0.832656	+	0.0691878i
$417$	1.11997e10			0.370392
$418$	2.68253e9	+	7.18780e8i	0.0878696	+	0.0235446i
$419$	−2.53610e10	−	4.39266e10i	−0.822832	−	1.42519i	−0.903565	−	0.428450i	$-0.859060\pi$
$419$	−2.53610e10	−	4.39266e10i	−0.822832	−	1.42519i	0.0807337	−	0.996736i	$-0.474274\pi$
$420$	−6.87783e9	−	3.97092e9i	−0.221032	−	0.127613i
$421$	1.31089e10	−	1.31089e10i	0.417291	−	0.417291i	−0.466978	−	0.884269i	$-0.654657\pi$
$421$	1.31089e10	−	1.31089e10i	0.417291	−	0.417291i	0.884269	+	0.466978i	$0.154657\pi$
$422$	−2.45708e9	−	9.16995e9i	−0.0774764	−	0.289146i
$423$	1.09932e11	−	2.94562e10i	3.43371	−	0.920059i
$424$	2.42608e8	+	2.42608e8i	0.00750657	+	0.00750657i
$425$	−1.34294e10	+	2.32604e10i	−0.411624	+	0.712954i
$426$	2.50459e9	−	1.44602e9i	0.0760497	−	0.0439073i
$427$	3.20267e9	−	1.19525e10i	0.0963386	−	0.359540i
$428$		−	1.20217e10i		−	0.358255i
$429$	4.80425e9	+	5.78179e10i	0.141839	+	1.70700i
$430$	1.04076e9			0.0304421
$431$	−1.98659e10	−	5.32304e9i	−0.575703	−	0.154259i	−0.0407919	−	0.999168i	$-0.512988\pi$
$431$	−1.98659e10	−	5.32304e9i	−0.575703	−	0.154259i	−0.534911	+	0.844909i	$0.679655\pi$
$432$	−2.91698e10	−	5.05236e10i	−0.837527	−	1.45064i
$433$	9.18138e9	+	5.30087e9i	0.261190	+	0.150798i	0.624877	−	0.780723i	$-0.285149\pi$
$433$	9.18138e9	+	5.30087e9i	0.261190	+	0.150798i	−0.363687	+	0.931521i	$0.618482\pi$
$434$	9.18673e9	−	9.18673e9i	0.258942	−	0.258942i
$435$	−2.46637e9	−	9.20461e9i	−0.0688812	−	0.257068i
$436$	5.20113e9	−	1.39364e9i	0.143930	−	0.0385660i
$437$	8.89264e9	+	8.89264e9i	0.243840	+	0.243840i
$438$	2.04323e10	−	3.53897e10i	0.555162	−	0.961569i
$439$	−3.20324e10	+	1.84939e10i	−0.862446	+	0.497934i	−0.864831	−	0.502064i	$-0.832574\pi$
$439$	−3.20324e10	+	1.84939e10i	−0.862446	+	0.497934i	0.00238450	+	0.999997i	$0.499241\pi$
$440$	8.26259e8	−	3.08364e9i	0.0220448	−	0.0822722i
$441$			9.75001e9i			0.257781i
$442$	−8.49442e9	+	5.89278e9i	−0.222559	+	0.154394i
$443$	3.40344e10			0.883696			0.441848	−	0.897090i	$-0.354323\pi$
$443$	3.40344e10			0.883696			0.441848	+	0.897090i	$0.354323\pi$
$444$	8.16327e10	+	2.18734e10i	2.10055	+	0.562840i
$445$	3.72304e9	+	6.44850e9i	0.0949419	+	0.164444i
$446$	3.40582e8	+	1.96635e8i	0.00860761	+	0.00496960i
$447$	−8.03446e10	+	8.03446e10i	−2.01246	+	2.01246i
$448$	4.73966e9	+	1.76887e10i	0.117662	+	0.439120i
$449$	3.37442e10	−	9.04172e9i	0.830258	−	0.222467i	0.181432	−	0.983403i	$-0.441927\pi$
$449$	3.37442e10	−	9.04172e9i	0.830258	−	0.222467i	0.648826	+	0.760936i	$0.275260\pi$
$450$	2.11178e10	+	2.11178e10i	0.514991	+	0.514991i
$451$	2.68023e10	−	4.64230e10i	0.647838	−	1.12209i
$452$	4.73714e10	−	2.73499e10i	1.13491	−	0.655242i
$453$	2.10901e9	−	7.87091e9i	0.0500824	−	0.186910i
$454$			2.06408e10i			0.485852i
$455$	−5.11568e9	−	4.33075e9i	−0.119360	−	0.101046i
$456$	−1.44330e10			−0.333809
$457$	−7.15743e10	−	1.91783e10i	−1.64094	−	0.439688i	−0.683882	−	0.729592i	$-0.739710\pi$
$457$	−7.15743e10	−	1.91783e10i	−1.64094	−	0.439688i	−0.957056	+	0.289904i	$0.906377\pi$
$458$	−9.75741e9	−	1.69003e10i	−0.221755	−	0.384090i
$459$	−7.74200e10	−	4.46985e10i	−1.74422	−	1.00703i
$460$	4.83211e9	−	4.83211e9i	0.107921	−	0.107921i
$461$	−7.68153e9	−	2.86679e10i	−0.170076	−	0.634734i	−0.997338	−	0.0729170i	$-0.976769\pi$
$461$	−7.68153e9	−	2.86679e10i	−0.170076	−	0.634734i	0.827262	−	0.561817i	$-0.189897\pi$
$462$	−2.55703e10	+	6.85155e9i	−0.561265	+	0.150391i
$463$	9.49299e9	+	9.49299e9i	0.206576	+	0.206576i	0.802810	−	0.596235i	$-0.203337\pi$
$463$	9.49299e9	+	9.49299e9i	0.206576	+	0.206576i	−0.596235	+	0.802810i	$0.703337\pi$
$464$	−1.59895e10	+	2.76947e10i	−0.344956	+	0.597481i
$465$	−1.18039e10	+	6.81497e9i	−0.252472	+	0.145765i
$466$	−6.99529e9	+	2.61068e10i	−0.148341	+	0.553617i
$467$		−	7.51331e10i		−	1.57966i	−0.613325	−	0.789831i	$-0.710168\pi$
$467$		−	7.51331e10i		−	1.57966i	0.613325	−	0.789831i	$-0.289832\pi$
$468$	−3.36306e10	−	9.36691e10i	−0.701053	−	1.95260i
$469$	2.58716e10			0.534726
$470$	−3.45601e9	−	9.26034e8i	−0.0708244	−	0.0189773i
$471$	8.13185e10	+	1.40848e11i	1.65236	+	2.86198i
$472$	2.59345e10	+	1.49733e10i	0.522528	+	0.301682i
$473$	−2.12376e10	+	2.12376e10i	−0.424287	+	0.424287i
$474$	−2.00652e9	−	7.48844e9i	−0.0397494	−	0.148347i
$475$	−1.44495e10	+	3.87172e9i	−0.283842	+	0.0760553i
$476$	2.88781e10	+	2.88781e10i	0.562523	+	0.562523i
$477$	−1.04209e9	+	1.80496e9i	−0.0201295	+	0.0348653i
$478$	−9.34167e9	+	5.39342e9i	−0.178942	+	0.103312i
$479$	−3.26509e9	+	1.21855e10i	−0.0620231	+	0.231473i	−0.989979	−	0.141218i	$-0.954898\pi$
$479$	−3.26509e9	+	1.21855e10i	−0.0620231	+	0.231473i	0.927955	+	0.372691i	$0.121565\pi$
$480$			1.19781e10i			0.225643i
$481$	6.45110e10	+	3.04254e10i	1.20518	+	0.568403i
$482$	9.34262e9			0.173093
$483$	−1.15793e11	−	3.10266e10i	−2.12762	−	0.570093i
$484$	−2.82247e9	−	4.88866e9i	−0.0514337	−	0.0890858i
$485$	4.77853e9	+	2.75889e9i	0.0863629	+	0.0498617i
$486$	−1.68074e10	+	1.68074e10i	−0.301270	+	0.301270i
$487$	2.05128e8	+	7.65548e8i	0.00364678	+	0.0136100i	0.967725	−	0.252008i	$-0.0810908\pi$
$487$	2.05128e8	+	7.65548e8i	0.00364678	+	0.0136100i	−0.964078	+	0.265618i	$0.914424\pi$
$488$	−1.18032e10	+	3.16267e9i	−0.208124	+	0.0557667i
$489$	−4.62683e10	−	4.62683e10i	−0.809185	−	0.809185i
$490$	1.53259e8	−	2.65452e8i	0.00265852	−	0.00460470i
$491$	1.62862e10	−	9.40287e9i	0.280217	−	0.161784i	−0.353304	−	0.935508i	$-0.614942\pi$
$491$	1.62862e10	−	9.40287e9i	0.280217	−	0.161784i	0.633522	+	0.773725i	$0.281609\pi$
$492$	−3.40833e10	+	1.27201e11i	−0.581677	+	2.17085i
$493$			4.90031e10i			0.829538i
$494$	−5.66608e9	−	1.02460e9i	−0.0951425	−	0.0172046i
$495$	1.93926e10			0.323010
$496$	4.41816e10	+	1.18384e10i	0.729987	+	0.195599i
$497$	−4.82100e9	−	8.35021e9i	−0.0790153	−	0.136859i
$498$	−1.99491e10	−	1.15176e10i	−0.324343	−	0.187260i
$499$	1.50353e10	−	1.50353e10i	0.242499	−	0.242499i	−0.575385	−	0.817883i	$-0.695148\pi$
$499$	1.50353e10	−	1.50353e10i	0.242499	−	0.242499i	0.817883	+	0.575385i	$0.195148\pi$
$500$	4.25499e9	+	1.58798e10i	0.0680798	+	0.254077i
$501$	3.13356e10	−	8.39636e9i	0.497379	−	0.133272i
$502$	−9.06353e9	−	9.06353e9i	−0.142719	−	0.142719i
$503$	−4.37597e9	+	7.57939e9i	−0.0683600	+	0.118403i	−0.898180	−	0.439629i	$-0.855110\pi$
$503$	−4.37597e9	+	7.57939e9i	−0.0683600	+	0.118403i	0.829820	+	0.558032i	$0.188443\pi$
$504$	8.31967e10	−	4.80337e10i	1.28939	−	0.744429i
$505$	−5.48829e8	+	2.04826e9i	−0.00843863	+	0.0314934i
$506$		−	2.27784e10i		−	0.347473i
$507$	−1.98532e10	−	1.18639e11i	−0.300469	−	1.79555i
$508$	−3.73710e10			−0.561152
$509$	2.51012e10	+	6.72584e9i	0.373958	+	0.100202i	0.440903	−	0.897555i	$-0.354658\pi$
$509$	2.51012e10	+	6.72584e9i	0.373958	+	0.100202i	−0.0669445	+	0.997757i	$0.521325\pi$
$510$	2.47441e9	+	4.28581e9i	0.0365756	+	0.0633508i
$511$	−1.17988e11	−	6.81205e10i	−1.73043	−	0.999066i
$512$	4.91833e10	−	4.91833e10i	0.715711	−	0.715711i
$513$	−1.28867e10	−	4.80936e10i	−0.186068	−	0.694414i
$514$	2.11237e10	−	5.66009e9i	0.302634	−	0.0810906i
$515$	−3.09323e9	−	3.09323e9i	−0.0439727	−	0.0439727i
$516$	3.68921e10	−	6.38989e10i	0.520396	−	0.901352i
$517$	8.94194e10	−	5.16263e10i	1.25161	−	0.722618i
$518$	−8.42324e9	+	3.14360e10i	−0.116993	+	0.436624i
$519$			1.18195e11i			1.62903i
$520$	−1.17780e9	+	6.51332e9i	−0.0161087	+	0.0890818i
$521$	−5.06096e10			−0.686882			−0.343441	−	0.939174i	$-0.611592\pi$
$521$	−5.06096e10			−0.686882			−0.343441	+	0.939174i	$0.611592\pi$
$522$	5.26315e10	+	1.41026e10i	0.708866	+	0.189940i
$523$	6.60774e10	+	1.14449e11i	0.883174	+	1.52970i	0.847792	+	0.530328i	$0.177931\pi$
$523$	6.60774e10	+	1.14449e11i	0.883174	+	1.52970i	0.0353814	+	0.999374i	$0.488735\pi$
$524$	−3.02637e10	−	1.74728e10i	−0.401418	−	0.231759i
$525$	1.00829e11	−	1.00829e11i	1.32723	−	1.32723i
$526$	−2.55461e9	−	9.53393e9i	−0.0333719	−	0.124546i
$527$	6.77018e10	−	1.81406e10i	0.877724	−	0.235185i
$528$	−6.59021e10	−	6.59021e10i	−0.847937	−	0.847937i
$529$	1.24195e10	−	2.15111e10i	0.158591	−	0.274688i
$530$	5.67436e7	−	3.27609e7i	0.000719140	−	0.000415196i
$531$	−4.70825e10	+	1.75714e11i	−0.592218	+	2.21019i
$532$			2.27460e10i			0.283961i
$533$	−4.74091e10	+	1.00521e11i	−0.587426	+	1.24552i
$534$	−6.09737e10			−0.749855
$535$	−4.69128e9	−	1.25702e9i	−0.0572633	−	0.0153436i
$536$	−1.27742e10	−	2.21256e10i	−0.154766	−	0.268063i
$537$	7.62661e10	+	4.40323e10i	0.917138	+	0.529510i
$538$	−3.13078e10	+	3.13078e10i	−0.373700	+	0.373700i
$539$	2.28940e9	+	8.54415e9i	0.0271248	+	0.101231i
$540$	−2.61333e10	+	7.00238e9i	−0.307340	+	0.0823514i
$541$	1.03283e10	+	1.03283e10i	0.120570	+	0.120570i	0.764817	−	0.644247i	$-0.222829\pi$
$541$	1.03283e10	+	1.03283e10i	0.120570	+	0.120570i	−0.644247	+	0.764817i	$0.722829\pi$
$542$	7.28612e9	−	1.26199e10i	0.0844305	−	0.146238i
$543$	1.02257e11	−	5.90382e10i	1.17624	−	0.679100i
$544$	1.59421e10	−	5.94968e10i	0.182033	−	0.679357i
$545$		−	2.17537e9i		−	0.0246574i
$546$	5.16574e10	−	1.85469e10i	0.581249	−	0.208689i
$547$	−1.42921e11			−1.59642			−0.798211	−	0.602378i	$-0.794220\pi$
$547$	−1.42921e11			−1.59642			−0.798211	+	0.602378i	$0.794220\pi$
$548$	−4.30993e10	−	1.15484e10i	−0.477912	−	0.128056i
$549$	−3.71145e10	−	6.42843e10i	−0.408559	−	0.707645i
$550$	2.34647e10	+	1.35474e10i	0.256428	+	0.148049i
$551$	−1.92988e10	+	1.92988e10i	−0.209375	+	0.209375i
$552$	3.06391e10	+	1.14347e11i	0.330005	+	1.23159i
$553$	−2.49662e10	+	6.68968e9i	−0.266964	+	0.0715327i
$554$	−9.24343e9	−	9.24343e9i	−0.0981283	−	0.0981283i
$555$	1.70715e10	−	2.95687e10i	0.179928	−	0.311645i
$556$	−1.50948e10	+	8.71497e9i	−0.157953	+	0.0911941i
$557$	1.70438e10	−	6.36085e10i	0.177071	−	0.660837i	−0.819119	−	0.573624i	$-0.805537\pi$
$557$	1.70438e10	−	6.36085e10i	0.177071	−	0.660837i	0.996190	−	0.0872130i	$-0.0277961\pi$
$558$		−	7.79354e10i		−	0.803892i
$559$	4.02351e10	−	4.75276e10i	0.412058	−	0.486741i
$560$	1.07673e10			0.109485
$561$	−1.37948e11	−	3.69632e10i	−1.39272	−	0.373179i
$562$	−1.29437e10	−	2.24192e10i	−0.129752	−	0.224737i
$563$	−7.62846e10	−	4.40429e10i	−0.759282	−	0.438372i	0.0697556	−	0.997564i	$-0.477778\pi$
$563$	−7.62846e10	−	4.40429e10i	−0.759282	−	0.438372i	−0.829038	+	0.559192i	$0.811111\pi$
$564$	−1.79362e11	+	1.79362e11i	−1.77261	+	1.77261i
$565$	−5.71955e9	−	2.13457e10i	−0.0561265	−	0.209467i
$566$	2.33466e10	−	6.25571e9i	0.227488	−	0.0609553i
$567$	1.57294e11	+	1.57294e11i	1.52188	+	1.52188i
$568$	−4.76079e9	+	8.24593e9i	−0.0457389	+	0.0792221i
$569$	−1.71490e11	+	9.90101e10i	−1.63603	+	0.944562i	−0.653848	+	0.756626i	$0.726846\pi$
$569$	−1.71490e11	+	9.90101e10i	−1.63603	+	0.944562i	−0.982181	+	0.187936i	$0.939820\pi$
$570$	−7.13378e8	+	2.66236e9i	−0.00675803	+	0.0252213i
$571$		−	5.00980e10i		−	0.471277i	−0.971841	−	0.235638i	$-0.924282\pi$
$571$		−	5.00980e10i		−	0.471277i	0.971841	−	0.235638i	$-0.0757181\pi$
$572$	−5.14657e10	−	7.41876e10i	−0.480766	−	0.693022i
$573$	1.50621e11			1.39723
$574$	−4.89837e10	−	1.31252e10i	−0.451237	−	0.120908i
$575$	6.13480e10	+	1.06258e11i	0.561215	+	0.972053i
$576$	9.51350e10	+	5.49262e10i	0.864272	+	0.498988i
$577$	5.78192e9	−	5.78192e9i	0.0521637	−	0.0521637i	−0.680544	−	0.732707i	$-0.738256\pi$
$577$	5.78192e9	−	5.78192e9i	0.0521637	−	0.0521637i	0.732707	+	0.680544i	$0.238256\pi$
$578$	2.70889e9	+	1.01097e10i	0.0242706	+	0.0905791i
$579$	1.82904e10	−	4.90089e9i	0.162745	−	0.0436074i
$580$	1.04866e10	+	1.04866e10i	0.0926668	+	0.0926668i
$581$	−3.83993e10	+	6.65095e10i	−0.336991	+	0.583686i
$582$	−3.91299e10	+	2.25917e10i	−0.341049	+	0.196905i
$583$	−4.89388e8	+	1.82642e9i	−0.00423622	+	0.0158098i
$584$			1.34540e11i			1.15664i
$585$	−4.00693e10	+	3.32947e9i	−0.342128	+	0.0284284i
$586$	5.58344e10			0.473491
$587$	2.21544e11	+	5.93624e10i	1.86598	+	0.499987i	1.00000		9.36499e-5i	$-2.98097e-5\pi$
$587$	2.21544e11	+	5.93624e10i	1.86598	+	0.499987i	0.865979	+	0.500081i	$0.166696\pi$
$588$	−1.08652e10	−	1.88191e10i	−0.0908927	−	0.157431i
$589$	3.38071e10	+	1.95186e10i	0.280897	+	0.162176i
$590$	4.04388e9	−	4.04388e9i	0.0333726	−	0.0333726i
$591$	−6.30669e10	−	2.35369e11i	−0.516954	−	1.92930i
$592$	−1.10675e11	+	2.96552e10i	−0.901077	+	0.241443i
$593$	5.91845e10	+	5.91845e10i	0.478618	+	0.478618i	0.904690	−	0.426071i	$-0.140103\pi$
$593$	5.91845e10	+	5.91845e10i	0.478618	+	0.478618i	−0.426071	+	0.904690i	$0.640103\pi$
$594$	−4.50911e10	+	7.81001e10i	−0.362197	+	0.627344i
$595$	1.42888e10	−	8.24962e9i	0.114006	−	0.0658212i
$596$	4.57676e10	−	1.70807e11i	0.362721	−	1.35369i
$597$		−	3.14821e11i		−	2.47837i
$598$	3.91077e9	+	4.70650e10i	0.0305814	+	0.368039i
$599$	1.44391e11			1.12159			0.560795	−	0.827955i	$-0.310496\pi$
$599$	1.44391e11			1.12159			0.560795	+	0.827955i	$0.310496\pi$
$600$	−1.36015e11	−	3.64450e10i	−1.04950	−	0.281212i
$601$	−1.00373e11	−	1.73851e11i	−0.769341	−	1.33254i	−0.937921	−	0.346850i	$-0.887251\pi$
$601$	−1.00373e11	−	1.73851e11i	−0.769341	−	1.33254i	0.168580	−	0.985688i	$-0.446082\pi$
$602$	2.46068e10	+	1.42068e10i	0.187357	+	0.108171i
$603$	1.09740e11	−	1.09740e11i	0.830037	−	0.830037i
$604$	3.28222e9	+	1.22494e10i	0.0246615	+	0.0920380i
$605$	−2.20284e9	+	5.90250e8i	−0.0164423	+	0.00440569i
$606$	−1.22784e10	−	1.22784e10i	−0.0910438	−	0.0910438i
$607$	3.35431e10	−	5.80984e10i	0.247086	−	0.427966i	−0.715630	−	0.698480i	$-0.753860\pi$
$607$	3.35431e10	−	5.80984e10i	0.247086	−	0.427966i	0.962716	+	0.270514i	$0.0871935\pi$
$608$	2.97099e10	−	1.71530e10i	0.217414	−	0.125524i
$609$	6.73339e10	−	2.51294e11i	0.489513	−	1.82689i
$610$			2.33359e9i			0.0168541i
$611$	−1.75896e11	+	1.22023e11i	−1.26209	+	0.875544i
$612$	2.44986e11			1.74637
$613$	1.79346e11	+	4.80555e10i	1.27013	+	0.340331i	0.830081	−	0.557642i	$-0.188294\pi$
$613$	1.79346e11	+	4.80555e10i	1.27013	+	0.340331i	0.440050	+	0.897973i	$0.354961\pi$
$614$	−3.05196e10	−	5.28615e10i	−0.214736	−	0.371934i
$615$	4.60741e10	+	2.66009e10i	0.322074	+	0.185950i
$616$	6.16284e10	−	6.16284e10i	0.428014	−	0.428014i
$617$	6.90475e10	+	2.57689e11i	0.476439	+	1.77809i	0.615853	+	0.787861i	$0.288811\pi$
$617$	6.90475e10	+	2.57689e11i	0.476439	+	1.77809i	−0.139414	+	0.990234i	$0.544522\pi$
$618$	3.46008e10	−	9.27125e9i	0.237209	−	0.0635601i
$619$	−1.29392e11	−	1.29392e11i	−0.881341	−	0.881341i	0.112330	−	0.993671i	$-0.464169\pi$
$619$	−1.29392e11	−	1.29392e11i	−0.881341	−	0.881341i	−0.993671	+	0.112330i	$0.964169\pi$
$620$	1.06061e10	−	1.83702e10i	0.0717773	−	0.124322i
$621$	−3.53669e11	+	2.04191e11i	−2.37811	+	1.37300i
$622$	−1.15002e10	+	4.29193e10i	−0.0768322	+	0.286742i
$623$			2.03284e11i			1.34943i
$624$	1.47482e11	+	1.24853e11i	0.972752	+	0.823496i
$625$	−1.42588e11			−0.934467
$626$	1.83032e10	+	4.90432e9i	0.119187	+	0.0319361i
$627$	−3.97708e10	−	6.88850e10i	−0.257332	−	0.445712i
$628$	−2.19200e11	−	1.26555e11i	−1.40929	−	0.813656i
$629$	−1.24150e11	+	1.24150e11i	−0.793133	+	0.793133i
$630$	−4.74830e9	−	1.77209e10i	−0.0301423	−	0.112492i
$631$	2.81131e11	−	7.53287e10i	1.77334	−	0.475164i	0.783993	−	0.620770i	$-0.213180\pi$
$631$	2.81131e11	−	7.53287e10i	1.77334	−	0.475164i	0.989343	+	0.145606i	$0.0465133\pi$
$632$	1.80483e10	+	1.80483e10i	0.113127	+	0.113127i
$633$	−1.35953e11	+	2.35477e11i	−0.846783	+	1.46667i
$634$	3.65490e9	−	2.11016e9i	0.0226214	−	0.0130605i
$635$	−3.90761e9	+	1.45834e10i	−0.0240335	+	0.0896942i
$636$		−	4.64516e9i		−	0.0283904i
$637$	−6.19731e9	−	1.72610e10i	−0.0376397	−	0.104835i
$638$	4.94336e10			0.298359
$639$	−5.58688e10	−	1.49700e10i	−0.335093	−	0.0897880i
$640$	−1.21240e10	−	2.09994e10i	−0.0722647	−	0.125166i
$641$	1.72098e11	+	9.93611e10i	1.01940	+	0.588551i	0.913930	−	0.405871i	$-0.133032\pi$
$641$	1.72098e11	+	9.93611e10i	1.01940	+	0.588551i	0.105470	+	0.994422i	$0.466365\pi$
$642$	2.81221e10	−	2.81221e10i	0.165542	−	0.165542i
$643$	5.78709e10	+	2.15977e11i	0.338545	+	1.26347i	0.899975	+	0.435942i	$0.143585\pi$
$643$	5.78709e10	+	2.15977e11i	0.338545	+	1.26347i	−0.561430	+	0.827524i	$0.689749\pi$
$644$	1.80207e11	−	4.82863e10i	1.04768	−	0.280725i
$645$	−2.10779e10	−	2.10779e10i	−0.121784	−	0.121784i
$646$	7.08690e9	−	1.22749e10i	0.0406936	−	0.0704834i
$647$	−6.94870e9	+	4.01183e9i	−0.0396539	+	0.0228942i	−0.519696	−	0.854351i	$-0.673955\pi$
$647$	−6.94870e9	+	4.01183e9i	−0.0396539	+	0.0228942i	0.480042	+	0.877246i	$0.340621\pi$
$648$	5.68548e10	−	2.12185e11i	0.322453	−	1.20341i
$649$			1.65038e11i			0.930262i
$650$	−5.08091e10	−	2.39632e10i	−0.284635	−	0.134243i
$651$	−3.72109e11			−2.07179
$652$	9.83630e10	+	2.63563e10i	0.544304	+	0.145846i
$653$	−9.18242e10	−	1.59044e11i	−0.505015	−	0.874712i	−0.999983	−	0.00580078i	$-0.998154\pi$
$653$	−9.18242e10	−	1.59044e11i	−0.505015	−	0.874712i	0.494968	−	0.868911i	$-0.335180\pi$
$654$	1.54269e10	+	8.90674e9i	0.0843273	+	0.0486864i
$655$	−9.98290e9	+	9.98290e9i	−0.0542365	+	0.0542365i
$656$	−4.62090e10	−	1.72454e11i	−0.249523	−	0.931233i
$657$	−7.89424e11	+	2.11525e11i	−4.23691	+	1.13528i
$658$	−6.90704e10	−	6.90704e10i	−0.368458	−	0.368458i
$659$	1.67578e11	−	2.90254e11i	0.888537	−	1.53899i	0.0469322	−	0.998898i	$-0.485056\pi$
$659$	1.67578e11	−	2.90254e11i	0.888537	−	1.53899i	0.841605	−	0.540093i	$-0.181611\pi$
$660$	−3.74309e10	+	2.16108e10i	−0.197267	+	0.113892i
$661$	3.05863e10	−	1.14150e11i	0.160222	−	0.597955i	−0.838380	−	0.545086i	$-0.816497\pi$
$661$	3.05863e10	−	1.14150e11i	0.160222	−	0.597955i	0.998601	−	0.0528688i	$-0.0168365\pi$
$662$			3.07758e10i			0.160243i
$663$	2.91377e11	+	5.26898e10i	1.50800	+	0.272692i
$664$	7.58395e10			0.390142
$665$	8.87624e9	+	2.37838e9i	0.0453881	+	0.0121617i
$666$	9.76139e10	+	1.69072e11i	0.496152	+	0.859360i
$667$	1.93865e11	+	1.11928e11i	0.979480	+	0.565503i
$668$	−3.57001e10	+	3.57001e10i	−0.179293	+	0.179293i
$669$	−2.91529e9	−	1.08800e10i	−0.0145538	−	0.0543156i
$670$	−4.71276e9	+	1.26278e9i	−0.0233871	+	0.00626655i
$671$	−4.76189e10	−	4.76189e10i	−0.234903	−	0.234903i
$672$	−1.63506e11	+	2.83201e11i	−0.801782	+	1.38873i
$673$	1.52595e10	−	8.81009e9i	0.0743842	−	0.0429457i	−0.462347	−	0.886699i	$-0.652992\pi$
$673$	1.52595e10	−	8.81009e9i	0.0743842	−	0.0429457i	0.536731	+	0.843754i	$0.319659\pi$
$674$	1.05278e10	−	3.92903e10i	0.0510151	−	0.190391i
$675$		−	4.85768e11i		−	2.33999i
$676$	1.19076e11	+	1.44451e11i	0.570214	+	0.691728i
$677$	−1.43484e11			−0.683045			−0.341523	−	0.939874i	$-0.610943\pi$
$677$	−1.43484e11			−0.683045			−0.341523	+	0.939874i	$0.610943\pi$
$678$	1.74793e11	+	4.68357e10i	0.827190	+	0.221645i
$679$	7.53199e10	+	1.30458e11i	0.354349	+	0.613750i
$680$	−1.41103e10	−	8.14659e9i	−0.0659935	−	0.0381013i
$681$	4.18029e11	−	4.18029e11i	1.94365	−	1.94365i
$682$	−1.83000e10	−	6.82966e10i	−0.0845890	−	0.315690i
$683$	−1.25375e11	+	3.35941e10i	−0.576140	+	0.154376i	−0.535111	−	0.844782i	$-0.679730\pi$
$683$	−1.25375e11	+	3.35941e10i	−0.576140	+	0.154376i	−0.0410288	+	0.999158i	$0.513064\pi$
$684$	9.64825e10	+	9.64825e10i	0.440782	+	0.440782i
$685$	−9.01314e9	+	1.56112e10i	−0.0409368	+	0.0709046i
$686$	−5.78145e10	+	3.33792e10i	−0.261060	+	0.150723i
$687$	−1.44662e11	+	5.39887e11i	−0.649424	+	2.42368i
$688$			1.00034e11i			0.446471i
$689$	6.97606e8	−	3.85780e9i	0.00309552	−	0.0171184i
$690$	2.26072e10			0.0997356
$691$	−2.10122e11	−	5.63021e10i	−0.921637	−	0.246952i	−0.233352	−	0.972392i	$-0.574970\pi$
$691$	−2.10122e11	−	5.63021e10i	−0.921637	−	0.246952i	−0.688285	+	0.725440i	$0.741636\pi$
$692$	−9.19726e10	−	1.59301e11i	−0.401083	−	0.694696i
$693$	4.58504e11	+	2.64717e11i	1.98797	+	1.14776i
$694$	1.47152e10	−	1.47152e10i	0.0634349	−	0.0634349i
$695$	1.82252e9	+	6.80174e9i	0.00781148	+	0.0291528i
$696$	−2.48155e11	+	6.64930e10i	−1.05752	+	0.283360i
$697$	−1.93452e11	−	1.93452e11i	−0.819676	−	0.819676i
$698$	1.91631e10	−	3.31915e10i	0.0807318	−	0.139832i
$699$	6.70401e11	−	3.87056e11i	2.80818	−	1.62131i
$700$	−5.74362e10	+	2.14355e11i	−0.239218	+	0.892774i
$701$		−	2.77036e11i		−	1.14727i	−0.819112	−	0.573634i	$-0.805533\pi$
$701$		−	2.77036e11i		−	1.14727i	0.819112	−	0.573634i	$-0.194467\pi$
$702$	7.97591e10	−	1.69113e11i	0.328422	−	0.696352i
$703$	−9.77878e10			−0.400372
$704$	9.62662e10	+	2.57945e10i	0.391907	+	0.105011i
$705$	5.12383e10	+	8.87474e10i	0.207414	+	0.359252i
$706$	−6.28143e10	−	3.62658e10i	−0.252836	−	0.145975i
$707$	−4.09357e10	+	4.09357e10i	−0.163842	+	0.163842i
$708$	−1.04936e11	−	3.91625e11i	−0.417629	−	1.55861i
$709$	−3.26663e10	+	8.75291e9i	−0.129275	+	0.0346392i	−0.322876	−	0.946441i	$-0.604650\pi$
$709$	−3.26663e10	+	8.75291e9i	−0.129275	+	0.0346392i	0.193601	+	0.981080i	$0.437983\pi$
$710$	1.28576e9	+	1.28576e9i	0.00505973	+	0.00505973i
$711$	−7.75243e10	+	1.34276e11i	−0.303361	+	0.525436i
$712$	1.73851e11	−	1.00373e11i	0.676483	−	0.390568i
$713$	8.28700e10	−	3.09275e11i	0.320656	−	1.19670i
$714$			1.35107e11i			0.519859i
$715$	−3.43318e10	+	1.23264e10i	−0.131363	+	0.0471640i
$716$	−1.37054e11			−0.521481
$717$	2.98423e11	+	7.99621e10i	1.12916	+	0.302557i
$718$	−2.38899e10	−	4.13785e10i	−0.0898910	−	0.155696i
$719$	−1.19093e11	−	6.87583e10i	−0.445626	−	0.257282i	0.260355	−	0.965513i	$-0.416160\pi$
$719$	−1.19093e11	−	6.87583e10i	−0.445626	−	0.257282i	−0.705981	+	0.708231i	$0.749494\pi$
$720$	4.56719e10	−	4.56719e10i	0.169949	−	0.169949i
$721$	−3.09101e10	−	1.15358e11i	−0.114382	−	0.426881i
$722$	−7.68360e10	+	2.05881e10i	−0.282759	+	0.0757650i
$723$	−1.89212e11	−	1.89212e11i	−0.692460	−	0.692460i
$724$	−9.18803e10	+	1.59141e11i	−0.334402	+	0.579201i
$725$	−2.30601e11	+	1.33137e11i	−0.834658	+	0.481890i
$726$	4.83337e9	−	1.80384e10i	0.0173982	−	0.0649309i
$727$			4.42320e11i			1.58343i	0.610891	+	0.791715i	$0.290811\pi$
$727$			4.42320e11i			1.58343i	−0.610891	+	0.791715i	$0.709189\pi$
$728$	−1.16757e11	+	1.37918e11i	−0.415677	+	0.491017i
$729$	1.04187e11			0.368895
$730$	2.48176e10	+	6.64986e9i	0.0873914	+	0.0234165i
$731$	7.66436e10	+	1.32751e11i	0.268415	+	0.464908i
$732$	1.43274e11	+	8.27195e10i	0.499027	+	0.288113i
$733$	1.14099e11	−	1.14099e11i	0.395246	−	0.395246i	−0.481307	−	0.876552i	$-0.659838\pi$
$733$	1.14099e11	−	1.14099e11i	0.395246	−	0.395246i	0.876552	+	0.481307i	$0.159838\pi$
$734$	4.83092e9	+	1.80292e10i	0.0166435	+	0.0621145i
$735$	−8.47994e9	+	2.27219e9i	−0.0290565	+	0.00778567i
$736$	−1.98966e11	−	1.98966e11i	−0.678060	−	0.678060i
$737$	7.03999e10	−	1.21936e11i	0.238617	−	0.413297i
$738$	−2.63449e11	+	1.52103e11i	−0.888121	+	0.512757i
$739$	−3.64040e10	+	1.35862e11i	−0.122059	+	0.455532i	−0.999718	−	0.0237546i	$-0.992438\pi$
$739$	−3.64040e10	+	1.35862e11i	−0.122059	+	0.455532i	0.877658	+	0.479287i	$0.159105\pi$
$740$			5.31362e10i			0.177200i
$741$	9.40017e10	+	1.35503e11i	0.311790	+	0.449445i
$742$	1.78880e9			0.00590129
$743$	−1.15586e11	−	3.09713e10i	−0.379272	−	0.101626i	0.0641459	−	0.997941i	$-0.479568\pi$
$743$	−1.15586e11	−	3.09713e10i	−0.379272	−	0.101626i	−0.443418	+	0.896315i	$0.646234\pi$
$744$	1.83731e11	+	3.18231e11i	0.599640	+	1.03861i
$745$	−6.18689e10	−	3.57200e10i	−0.200839	−	0.115954i
$746$	1.04991e11	−	1.04991e11i	0.338998	−	0.338998i
$747$	1.19236e11	+	4.44995e11i	0.382935	+	1.42913i
$748$	2.14687e11	−	5.75253e10i	0.685804	−	0.183761i
$749$	−9.37581e10	−	9.37581e10i	−0.297907	−	0.297907i
$750$	−2.71936e10	+	4.71008e10i	−0.0859453	+	0.148862i
$751$	−1.64983e11	+	9.52531e10i	−0.518657	+	0.299447i	−0.736385	−	0.676563i	$-0.763469\pi$
$751$	−1.64983e11	+	9.52531e10i	−0.518657	+	0.299447i	0.217728	+	0.976009i	$0.430135\pi$
$752$	8.90072e10	−	3.32179e11i	0.278326	−	1.03873i
$753$			3.67119e11i			1.14190i
$754$	−1.02140e11	+	8.48714e9i	−0.316018	+	0.0262589i
$755$	5.12332e9			0.0157675
$756$	−7.13460e11	−	1.91171e11i	−2.18415	−	0.585241i
$757$	−2.70239e10	−	4.68067e10i	−0.0822932	−	0.142536i	0.821941	−	0.569572i	$-0.192891\pi$
$757$	−2.70239e10	−	4.68067e10i	−0.0822932	−	0.142536i	−0.904235	+	0.427036i	$0.859558\pi$
$758$	1.19610e10	+	6.90570e9i	0.0362319	+	0.0209185i
$759$	−4.61320e11	+	4.61320e11i	−1.39006	+	1.39006i
$760$	−2.34868e9	−	8.76539e9i	−0.00703994	−	0.0262734i
$761$	4.93966e11	−	1.32358e11i	1.47285	−	0.394649i	0.568942	−	0.822378i	$-0.307353\pi$
$761$	4.93966e11	−	1.32358e11i	1.47285	−	0.394649i	0.903907	+	0.427729i	$0.140686\pi$
$762$	−8.74208e10	−	8.74208e10i	−0.259296	−	0.259296i
$763$	2.96948e10	−	5.14329e10i	0.0876157	−	0.151755i
$764$	−2.03004e11	+	1.17205e11i	−0.595843	+	0.344010i
$765$	2.56164e10	−	9.56018e10i	0.0747950	−	0.279139i
$766$			1.60541e10i			0.0466306i
$767$	−2.83350e10	−	3.41004e11i	−0.0818731	−	0.985321i
$768$	−7.45551e10			−0.214305
$769$	4.45710e11	+	1.19428e11i	1.27452	+	0.341507i	0.831761	−	0.555134i	$-0.187333\pi$
$769$	4.45710e11	+	1.19428e11i	1.27452	+	0.341507i	0.442759	+	0.896641i	$0.354000\pi$
$770$	−8.32209e9	−	1.44143e10i	−0.0236739	−	0.0410044i
$771$	−5.42440e11	−	3.13178e11i	−1.53509	−	0.886285i
$772$	−2.08379e10	+	2.08379e10i	−0.0586657	+	0.0586657i
$773$	9.67821e10	+	3.61196e11i	0.271067	+	1.01164i	0.958431	+	0.285324i	$0.0921011\pi$
$773$	9.67821e10	+	3.61196e11i	0.271067	+	1.01164i	−0.687364	+	0.726313i	$0.741232\pi$
$774$	1.64637e11	−	4.41144e10i	0.458737	−	0.122918i
$775$	2.69307e11	+	2.69307e11i	0.746519	+	0.746519i
$776$	7.43793e10	−	1.28829e11i	0.205119	−	0.355276i
$777$	8.07249e11	−	4.66066e11i	2.21474	−	1.27868i
$778$	−2.70565e10	+	1.00976e11i	−0.0738504	+	0.275613i
$779$		−	1.52374e11i		−	0.413771i
$780$	7.36300e10	−	5.10789e10i	0.198919	−	0.137995i
$781$	−5.24742e10			−0.141040
$782$	−1.12293e11	−	3.00888e10i	−0.300280	−	0.0804597i
$783$	−4.43135e11	−	7.67533e11i	−1.17893	−	2.04197i
$784$	2.55143e10	+	1.47307e10i	0.0675335	+	0.0389905i
$785$	−7.23060e10	+	7.23060e10i	−0.190413	+	0.190413i
$786$	−2.99214e10	−	1.11668e11i	−0.0783957	−	0.292577i
$787$	−1.44016e11	+	3.85890e10i	−0.375415	+	0.100592i	−0.441593	−	0.897216i	$-0.645586\pi$
$787$	−1.44016e11	+	3.85890e10i	−0.375415	+	0.100592i	0.0661773	+	0.997808i	$0.478920\pi$
$788$	2.68151e11	+	2.68151e11i	0.695465	+	0.695465i
$789$	−1.41349e11	+	2.44823e11i	−0.364741	+	0.631750i
$790$	4.22132e9	−	2.43718e9i	0.0108378	−	0.00625719i
$791$	1.56149e11	−	5.82755e11i	0.398871	−	1.48861i
$792$		−	5.22823e11i		−	1.32878i
$793$	1.06566e11	+	9.02153e10i	0.269481	+	0.228133i
$794$	1.71180e11			0.430695
$795$	−1.81269e9	−	4.85710e8i	−0.00453791	−	0.00121593i
$796$	2.44976e11	+	4.24311e11i	0.610199	+	1.05690i
$797$	−3.90229e10	−	2.25299e10i	−0.0967132	−	0.0558374i	0.450863	−	0.892593i	$-0.351116\pi$
$797$	−3.90229e10	−	2.25299e10i	−0.0967132	−	0.0558374i	−0.547577	+	0.836756i	$0.684450\pi$
$798$	−5.32090e10	+	5.32090e10i	−0.131212	+	0.131212i
$799$	−1.36390e11	−	5.09016e11i	−0.334654	−	1.24895i
$800$	3.23296e11	−	8.66268e10i	0.789296	−	0.211491i
$801$	8.62278e11	+	8.62278e11i	2.09468	+	2.09468i
$802$	−1.25545e10	+	2.17450e10i	−0.0303460	+	0.0525608i
$803$	−6.42122e11	+	3.70729e11i	−1.54438	+	0.891651i
$804$	−8.95244e10	+	3.34110e11i	−0.214248	+	0.799585i
$805$		−	7.53717e10i		−	0.179484i
$806$	4.95374e10	+	1.37973e11i	0.117380	+	0.326930i
$807$	1.26812e12			2.98997
$808$	5.52209e10	+	1.47964e10i	0.129556	+	0.0347145i
$809$	−2.04766e11	−	3.54665e11i	−0.478040	−	0.827989i	0.521643	−	0.853164i	$-0.325319\pi$
$809$	−2.04766e11	−	3.54665e11i	−0.478040	−	0.827989i	−0.999683	+	0.0251745i	$0.991986\pi$
$810$	−3.63302e10	−	2.09752e10i	−0.0843971	−	0.0487267i
$811$	2.09616e11	−	2.09616e11i	0.484553	−	0.484553i	−0.422029	−	0.906582i	$-0.638682\pi$
$811$	2.09616e11	−	2.09616e11i	0.484553	−	0.484553i	0.906582	+	0.422029i	$0.138682\pi$
$812$	1.04791e11	+	3.91085e11i	0.241046	+	0.899595i
$813$	−4.03148e11	+	1.08023e11i	−0.922788	+	0.247260i
$814$	1.25241e11	+	1.25241e11i	0.285266	+	0.285266i
$815$	2.05702e10	−	3.56286e10i	0.0466238	−	0.0807549i
$816$	−4.11937e11	+	2.37832e11i	−0.929117	+	0.536426i
$817$	−2.20965e10	+	8.24652e10i	−0.0495947	+	0.185090i
$818$		−	3.58419e10i		−	0.0800531i
$819$	−9.92816e11	−	4.68243e11i	−2.20665	−	1.04072i
$820$	−8.27972e10			−0.183130
$821$	−6.82299e11	−	1.82821e11i	−1.50177	−	0.402397i	−0.588074	−	0.808807i	$-0.700114\pi$
$821$	−6.82299e11	−	1.82821e11i	−1.50177	−	0.402397i	−0.913691	+	0.406410i	$0.866780\pi$
$822$	−7.38059e10	−	1.27836e11i	−0.161660	−	0.280004i
$823$	−1.36007e11	−	7.85238e10i	−0.296458	−	0.171160i	0.344393	−	0.938826i	$-0.388085\pi$
$823$	−1.36007e11	−	7.85238e10i	−0.296458	−	0.171160i	−0.640850	+	0.767666i	$0.721418\pi$
$824$	−8.33932e10	+	8.33932e10i	−0.180893	+	0.180893i
$825$	−2.00852e11	−	7.49588e11i	−0.433570	−	1.61811i
$826$	1.50811e11	−	4.04097e10i	0.323976	−	0.0868092i
$827$	4.53870e11	+	4.53870e11i	0.970308	+	0.970308i	0.999572	−	0.0292635i	$-0.00931618\pi$
$827$	4.53870e11	+	4.53870e11i	0.970308	+	0.970308i	−0.0292635	+	0.999572i	$0.509316\pi$
$828$	5.59572e11	−	9.69208e11i	1.19052	−	2.06203i
$829$	3.02014e11	−	1.74368e11i	0.639454	−	0.369189i	−0.144950	−	0.989439i	$-0.546302\pi$
$829$	3.02014e11	−	1.74368e11i	0.639454	−	0.369189i	0.784404	+	0.620250i	$0.212969\pi$
$830$	3.74850e9	−	1.39896e10i	0.00789852	−	0.0294777i
$831$			3.74406e11i			0.785124i
$832$	−2.03335e11	−	3.67692e10i	−0.424345	−	0.0767344i
$833$	4.51452e10			0.0937630
$834$	−5.56974e10	−	1.49241e10i	−0.115125	−	0.0308477i
$835$	1.01985e10	+	1.76643e10i	0.0209792	+	0.0363370i
$836$	1.07205e11	+	6.18947e10i	0.219477	+	0.126715i
$837$	−8.96363e11	+	8.96363e11i	−1.82634	+	1.82634i
$838$	6.75893e10	+	2.52247e11i	0.137057	+	0.511504i
$839$	6.76103e11	−	1.81161e11i	1.36447	−	0.365609i	0.499016	−	0.866593i	$-0.333695\pi$
$839$	6.76103e11	−	1.81161e11i	1.36447	−	0.365609i	0.865457	+	0.500983i	$0.167028\pi$
$840$	6.11652e10	+	6.11652e10i	0.122853	+	0.122853i
$841$	7.21746e9	−	1.25010e10i	0.0144278	−	0.0249897i
$842$	−8.26604e10	+	4.77240e10i	−0.164456	+	0.0949486i
$843$	−1.91902e11	+	7.16189e11i	−0.379988	+	1.41814i
$844$		−	4.23162e11i		−	0.833944i
$845$	6.88207e10	−	3.13633e10i	0.134987	−	0.0615169i
$846$	−5.85957e11			−1.14389
$847$	−6.01394e10	−	1.61143e10i	−0.116849	−	0.0313096i
$848$	3.14887e9	+	5.45400e9i	0.00608935	+	0.0105471i
$849$	−5.99522e11	−	3.46134e11i	−1.15392	−	0.666214i
$850$	9.77814e10	−	9.77814e10i	0.187318	−	0.187318i
$851$	2.07589e11	+	7.74732e11i	0.395809	+	1.47718i
$852$	1.24518e11	−	3.33646e10i	0.236306	−	0.0633180i
$853$	−4.64755e11	−	4.64755e11i	−0.877865	−	0.877865i	0.115448	−	0.993313i	$-0.463170\pi$
$853$	−4.64755e11	−	4.64755e11i	−0.877865	−	0.877865i	−0.993313	+	0.115448i	$0.963170\pi$
$854$	−3.18545e10	+	5.51735e10i	−0.0598878	+	0.103729i
$855$	4.77391e10	−	2.75622e10i	0.0893326	−	0.0515762i
$856$	−3.38893e10	+	1.26476e11i	−0.0631200	+	0.235567i
$857$			1.96873e11i			0.364975i	0.983208	+	0.182488i	$0.0584149\pi$
$857$			1.96873e11i			0.364975i	−0.983208	+	0.182488i	$0.941585\pi$
$858$	5.31526e10	−	2.93937e11i	0.0980789	−	0.542381i
$859$	−6.78556e11			−1.24627			−0.623137	−	0.782113i	$-0.714142\pi$
$859$	−6.78556e11			−1.24627			−0.623137	+	0.782113i	$0.714142\pi$
$860$	4.48102e10	+	1.20068e10i	0.0819186	+	0.0219500i
$861$	7.26227e11	+	1.25786e12i	1.32148	+	2.28887i
$862$	9.17020e10	+	5.29442e10i	0.166092	+	0.0958935i
$863$	−4.94407e11	+	4.94407e11i	−0.891337	+	0.891337i	−0.994649	−	0.103312i	$-0.967056\pi$
$863$	−4.94407e11	+	4.94407e11i	−0.891337	+	0.891337i	0.103312	+	0.994649i	$0.467056\pi$
$864$	2.88329e11	+	1.07606e12i	0.517409	+	1.93099i
$865$	−7.17815e10	+	1.92338e10i	−0.128218	+	0.0343558i
$866$	−3.85964e10	−	3.85964e10i	−0.0686239	−	0.0686239i
$867$	1.49886e11	−	2.59609e11i	0.265267	−	0.459456i
$868$	5.01523e11	−	2.89554e11i	0.883510	−	0.510095i
$869$	−3.64069e10	+	1.35873e11i	−0.0638418	+	0.238261i
$870$			4.90621e10i			0.0856385i
$871$	−1.24526e11	+	2.64033e11i	−0.216366	+	0.458760i
$872$	−5.86479e10			−0.101435
$873$	8.72855e11	+	2.33881e11i	1.50274	+	0.402659i
$874$	−3.23743e10	−	5.60739e10i	−0.0554823	−	0.0960982i
$875$	1.57032e11	+	9.06627e10i	0.267890	+	0.154667i
$876$	1.28800e12	−	1.28800e12i	2.18725	−	2.18725i
$877$	−1.57814e11	−	5.88969e11i	−0.266776	−	0.995622i	−0.961154	−	0.276012i	$-0.910987\pi$
$877$	−1.57814e11	−	5.88969e11i	−0.266776	−	0.995622i	0.694378	−	0.719610i	$-0.255679\pi$
$878$	1.83945e11	−	4.92879e10i	0.309535	−	0.0829397i
$879$	−1.13079e12	−	1.13079e12i	−1.89420	−	1.89420i
$880$	2.92991e10	−	5.07475e10i	0.0488566	−	0.0846222i
$881$	−4.17616e11	+	2.41111e11i	−0.693223	+	0.400233i	−0.804818	−	0.593521i	$-0.797737\pi$
$881$	−4.17616e11	+	2.41111e11i	−0.693223	+	0.400233i	0.111595	+	0.993754i	$0.464404\pi$
$882$	1.29923e10	−	4.84879e10i	0.0214690	−	0.0801233i
$883$			1.96318e11i			0.322937i	0.986878	+	0.161469i	$0.0516231\pi$
$883$			1.96318e11i			0.322937i	−0.986878	+	0.161469i	$0.948377\pi$
$884$	−4.33713e11	+	1.55719e11i	−0.710222	+	0.254995i
$885$	−1.63798e11			−0.267014
$886$	−1.69257e11	−	4.53523e10i	−0.274670	−	0.0735977i
$887$	−4.16906e11	−	7.22102e11i	−0.673509	−	1.16655i	−0.976902	−	0.213686i	$-0.931453\pi$
$887$	−4.16906e11	−	7.22102e11i	−0.673509	−	1.16655i	0.303394	−	0.952865i	$-0.401880\pi$
$888$	−7.97168e11	−	4.60245e11i	−1.28203	−	0.740180i
$889$	−2.91458e11	+	2.91458e11i	−0.466627	+	0.466627i
$890$	−9.92222e9	−	3.70302e10i	−0.0158143	−	0.0590196i
$891$	1.16937e12	−	3.13331e11i	1.85541	−	0.497156i
$892$	1.23954e10	+	1.23954e10i	0.0195795	+	0.0195795i
$893$	1.46750e11	−	2.54179e11i	0.230767	−	0.399699i
$894$	5.06626e11	−	2.92500e11i	0.793117	−	0.457906i
$895$	−1.43307e10	+	5.34829e10i	−0.0223344	+	0.0833533i
$896$		−	6.61991e11i		−	1.02712i
$897$	8.73983e11	−	1.03239e12i	1.35000	−	1.59468i
$898$	−1.79862e11			−0.276589
$899$	6.71188e11	+	1.79844e11i	1.02756	+	0.275333i
$900$	6.65608e11	+	1.15287e12i	1.01449	+	1.75715i
$901$	8.35745e9	+	4.82518e9i	0.0126816	+	0.00732173i
$902$	−1.95152e11	+	1.95152e11i	−0.294813	+	0.294813i
$903$	−2.10628e11	−	7.86073e11i	−0.316785	−	1.18226i
$904$	−5.75477e11	+	1.54199e11i	−0.861696	+	0.230891i
$905$	5.24950e10	+	5.24950e10i	0.0782571	+	0.0782571i
$906$	−2.09766e10	+	3.63326e10i	−0.0311332	+	0.0539242i
$907$	5.68703e11	−	3.28341e11i	0.840343	−	0.485172i	−0.0170381	−	0.999855i	$-0.505424\pi$
$907$	5.68703e11	−	3.28341e11i	0.840343	−	0.485172i	0.857381	+	0.514683i	$0.172090\pi$
$908$	−2.38126e11	+	8.88699e11i	−0.350319	+	1.30741i
$909$			3.47277e11i			0.508652i
$910$	1.96700e10	+	2.83542e10i	0.0286839	+	0.0413477i
$911$	1.01721e12			1.47686			0.738430	−	0.674330i	$-0.235568\pi$
$911$	1.01721e12			1.47686			0.738430	+	0.674330i	$0.235568\pi$
$912$	−2.55897e11	−	6.85674e10i	−0.369902	−	0.0991148i
$913$	2.08979e11	+	3.61962e11i	0.300759	+	0.520930i
$914$	3.30391e11	+	1.90751e11i	0.473417	+	0.273327i
$915$	4.72610e10	−	4.72610e10i	0.0674247	−	0.0674247i
$916$	−2.25136e11	−	8.40218e11i	−0.319788	−	1.19347i
$917$	−3.72299e11	+	9.97572e10i	−0.526519	+	0.141080i
$918$	3.25456e11	+	3.25456e11i	0.458270	+	0.458270i
$919$	1.28727e11	−	2.22962e11i	0.180472	−	0.312586i	−0.761570	−	0.648083i	$-0.775571\pi$
$919$	1.28727e11	−	2.22962e11i	0.180472	−	0.312586i	0.942041	+	0.335497i	$0.108904\pi$
$920$	−6.44586e10	+	3.72152e10i	−0.0899766	+	0.0519480i
$921$	−4.52480e11	+	1.68868e12i	−0.628870	+	2.34697i
$922$			1.52805e11i			0.211452i
$923$	1.08423e11	−	9.00917e9i	0.149388	−	0.0124130i
$924$	−1.17998e12			−1.61878
$925$	−9.21538e11	−	2.46925e11i	−1.25877	−	0.337287i
$926$	−3.45599e10	−	5.98596e10i	−0.0470034	−	0.0814122i
$927$	−6.20430e11	−	3.58206e11i	−0.840183	−	0.485080i
$928$	4.31796e11	−	4.31796e11i	0.582220	−	0.582220i
$929$	2.02480e11	+	7.55664e11i	0.271843	+	1.01453i	0.957927	+	0.287011i	$0.0926615\pi$
$929$	2.02480e11	+	7.55664e11i	0.271843	+	1.01453i	−0.686084	+	0.727522i	$0.740672\pi$
$930$	6.77833e10	−	1.81625e10i	0.0906130	−	0.0242797i
$931$	1.77794e10	+	1.77794e10i	0.0236657	+	0.0236657i
$932$	−6.02370e11	+	1.04334e12i	−0.798362	+	1.38280i
$933$	1.10213e12	−	6.36316e11i	1.45448	−	0.839742i
$934$	−1.00118e11	+	3.73646e11i	−0.131560	+	0.490990i
$935$		−	8.97931e10i		−	0.117489i
$936$	8.97622e10	+	1.08026e12i	0.116947	+	1.40743i
$937$	1.16924e12			1.51686			0.758430	−	0.651754i	$-0.225967\pi$
$937$	1.16924e12			1.51686			0.758430	+	0.651754i	$0.225967\pi$
$938$	−1.28662e11	−	3.44750e10i	−0.166203	−	0.0445341i
$939$	−2.71361e11	−	4.70011e11i	−0.349048	−	0.604568i
$940$	−1.38116e11	−	7.97415e10i	−0.176902	−	0.102135i
$941$	5.66327e10	−	5.66327e10i	0.0722286	−	0.0722286i	−0.670070	−	0.742298i	$-0.733736\pi$
$941$	5.66327e10	−	5.66327e10i	0.0722286	−	0.0722286i	0.742298	+	0.670070i	$0.233736\pi$
$942$	−2.16721e11	−	8.08813e11i	−0.275231	−	1.02717i
$943$	−1.20719e12	+	3.23466e11i	−1.52662	+	0.409056i
$944$	3.88684e11	+	3.88684e11i	0.489450	+	0.489450i
$945$	−1.49203e11	+	2.58426e11i	−0.187089	+	0.324048i
$946$	1.33917e11	−	7.73169e10i	0.167213	−	0.0965405i
$947$	2.35486e11	−	8.78847e11i	0.292797	−	1.09273i	−0.650155	−	0.759802i	$-0.725296\pi$
$947$	2.35486e11	−	8.78847e11i	0.292797	−	1.09273i	0.942952	−	0.332930i	$-0.108037\pi$
$948$		−	3.45566e11i		−	0.427856i
$949$	1.26311e12	−	8.76251e11i	1.55732	−	1.08035i
$950$	7.70180e10			0.0945579
$951$	−1.16757e11	−	3.12850e10i	−0.142745	−	0.0382484i
$952$	−2.22409e11	−	3.85224e11i	−0.270772	−	0.468992i
$953$	−5.61810e10	−	3.24361e10i	−0.0681112	−	0.0393240i	0.465558	−	0.885018i	$-0.345854\pi$
$953$	−5.61810e10	−	3.24361e10i	−0.0681112	−	0.0393240i	−0.533669	+	0.845694i	$0.679187\pi$
$954$	7.58763e9	−	7.58763e9i	0.00916036	−	0.00916036i
$955$	2.45104e10	+	9.14742e10i	0.0294671	+	0.109973i
$956$	−4.64431e11	+	1.24444e11i	−0.556020	+	0.148985i
$957$	−1.00116e12	−	1.00116e12i	−1.19359	−	1.19359i
$958$	3.24753e10	−	5.62489e10i	0.0385560	−	0.0667809i
$959$	−4.26200e11	+	2.46066e11i	−0.503893	+	0.290923i
$960$	−2.56006e10	+	9.55427e10i	−0.0301415	+	0.112490i
$961$		−	1.40987e11i		−	0.165305i
$962$	−2.80277e11	−	2.37273e11i	−0.327256	−	0.277043i
$963$	−7.95394e11			−0.924862
$964$	4.02250e11	+	1.07783e11i	0.465788	+	0.124807i
$965$	5.95276e9	+	1.03105e10i	0.00686451	+	0.0118897i
$966$	5.34507e11	+	3.08598e11i	0.613825	+	0.354392i
$967$	−1.20920e12	+	1.20920e12i	−1.38291	+	1.38291i	−0.543496	+	0.839411i	$0.682900\pi$
$967$	−1.20920e12	+	1.20920e12i	−1.38291	+	1.38291i	−0.839411	+	0.543496i	$0.817100\pi$
$968$	1.59131e10	+	5.93884e10i	0.0181239	+	0.0676395i
$969$	−3.92125e11	+	1.05069e11i	−0.444763	+	0.119174i
$970$	−2.00878e10	−	2.00878e10i	−0.0226906	−	0.0226906i
$971$	4.30654e11	−	7.45914e11i	0.484453	−	0.839097i	−0.515388	−	0.856957i	$-0.672352\pi$
$971$	4.30654e11	−	7.45914e11i	0.484453	−	0.839097i	0.999840	+	0.0178605i	$0.00568546\pi$
$972$	−9.17551e11	+	5.29749e11i	−1.02793	+	0.593478i
$973$	−4.97564e10	+	1.85693e11i	−0.0555133	+	0.207179i
$974$		−	4.08050e9i		−	0.00453396i
$975$	5.43697e11	+	1.51433e12i	0.601643	+	1.67572i
$976$	−2.24296e11			−0.247185
$977$	−7.25635e11	−	1.94433e11i	−0.796416	−	0.213399i	−0.162406	−	0.986724i	$-0.551925\pi$
$977$	−7.25635e11	−	1.94433e11i	−0.796416	−	0.213399i	−0.634010	+	0.773325i	$0.718592\pi$
$978$	1.68443e11	+	2.91752e11i	0.184119	+	0.318903i
$979$	9.58106e11	+	5.53163e11i	1.04300	+	0.602174i
$980$	9.66103e9	−	9.66103e9i	0.0104742	−	0.0104742i
$981$	−9.22073e10	−	3.44122e11i	−0.0995610	−	0.371567i
$982$	−9.35231e10	+	2.50594e10i	−0.100571	+	0.0269479i
$983$	1.09373e12	+	1.09373e12i	1.17137	+	1.17137i	0.981883	+	0.189489i	$0.0606832\pi$
$983$	1.09373e12	+	1.09373e12i	1.17137	+	1.17137i	0.189489	+	0.981883i	$0.439317\pi$
$984$	7.17157e11	−	1.24215e12i	0.764952	−	1.32494i
$985$	1.32680e11	−	7.66029e10i	0.140949	−	0.0813768i
$986$	6.52987e10	−	2.43698e11i	0.0690871	−	0.257837i
$987$			2.79770e12i			2.94803i
$988$	−2.32135e11	−	1.09482e11i	−0.243620	−	0.114899i
$989$	7.00245e11			0.731922
$990$	−9.64417e10	−	2.58415e10i	−0.100398	−	0.0269015i
$991$	9.37766e11	+	1.62426e12i	0.972299	+	1.68407i	0.688574	+	0.725166i	$0.258237\pi$
$991$	9.37766e11	+	1.62426e12i	0.972299	+	1.68407i	0.283725	+	0.958906i	$0.408430\pi$
$992$	−7.56410e11	−	4.36713e11i	−0.781107	−	0.450972i
$993$	6.23288e11	−	6.23288e11i	0.641050	−	0.641050i
$994$	1.28484e10	+	4.79507e10i	0.0131614	+	0.0491190i
$995$	1.91195e11	−	5.12307e10i	0.195068	−	0.0522682i
$996$	−7.26040e11	−	7.26040e11i	−0.737773	−	0.737773i
$997$	−3.34641e11	+	5.79615e11i	−0.338687	+	0.586623i	−0.984186	−	0.177138i	$-0.943316\pi$
$997$	−3.34641e11	+	5.79615e11i	−0.338687	+	0.586623i	0.645499	+	0.763761i	$0.276649\pi$
$998$	−9.48073e10	+	5.47370e10i	−0.0955695	+	0.0551771i
$999$	8.21868e11	−	3.06725e12i	0.825164	−	3.07955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.f.a.2.4	✓	32
13.7	odd	12	inner	13.9.f.a.7.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.f.a.2.4	✓	32	1.1	even	1	trivial
13.9.f.a.7.4	yes	32	13.7	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+(-4.97311 - 1.33254i) q^{2} +(73.7308 + 127.705i) q^{3} +(-198.746 - 114.746i) q^{4} +(-65.5592 + 65.5592i) q^{5} +(-196.499 - 733.343i) q^{6} +(-2444.94 + 655.120i) q^{7} +(1767.47 + 1767.47i) q^{8} +(-7591.95 + 13149.6i) q^{9} +(413.394 - 238.673i) q^{10} +(-3565.33 + 13306.0i) q^{11} -33841.3i q^{12} +(5082.27 - 28105.2i) q^{13} +13032.0 q^{14} +(-13206.0 - 3538.54i) q^{15} +(22940.4 + 39734.0i) q^{16} +(60886.5 + 35152.8i) q^{17} +(55278.1 - 55278.1i) q^{18} +(10134.6 + 37822.9i) q^{19} +(20552.3 - 5506.98i) q^{20} +(-263930. - 263930. i) q^{21} +(35461.6 - 61421.3i) q^{22} +(278141. - 160585. i) q^{23} +(-95398.6 + 356033. i) q^{24} +382029. i q^{25} +(-62726.0 + 132998. i) q^{26} -1.27155e6 q^{27} +(561096. + 150345. i) q^{28} +(348501. + 603621. i) q^{29} +(60959.7 + 35195.1i) q^{30} +(704939. - 704939. i) q^{31} +(-226755. - 846260. i) q^{32} +(-1.96212e6 + 525750. i) q^{33} +(-255953. - 255953. i) q^{34} +(117339. - 203238. i) q^{35} +(3.01775e6 - 1.74230e6i) q^{36} +(-646353. + 2.41222e6i) q^{37} -201603. i q^{38} +(3.96390e6 - 1.42318e6i) q^{39} -231748. q^{40} +(-3.75874e6 - 1.00715e6i) q^{41} +(960856. + 1.66425e6i) q^{42} +(1.88819e6 + 1.09015e6i) q^{43} +(2.23541e6 - 2.23541e6i) q^{44} +(-364358. - 1.35980e6i) q^{45} +(-1.59721e6 + 427972. i) q^{46} +(-5.30008e6 - 5.30008e6i) q^{47} +(-3.38283e6 + 5.85924e6i) q^{48} +(556099. - 321064. i) q^{49} +(509070. - 1.89987e6i) q^{50} +1.03674e7i q^{51} +(-4.23505e6 + 5.00263e6i) q^{52} +137263. q^{53} +(6.32355e6 + 1.69439e6i) q^{54} +(-638591. - 1.10607e6i) q^{55} +(-5.47927e6 - 3.16346e6i) q^{56} +(-4.08296e6 + 4.08296e6i) q^{57} +(-928784. - 3.46627e6i) q^{58} +(1.15724e7 - 3.10082e6i) q^{59} +(2.21861e6 + 2.21861e6i) q^{60} +(-2.44433e6 + 4.23371e6i) q^{61} +(-4.44510e6 + 2.56638e6i) q^{62} +(9.94729e6 - 3.71238e7i) q^{63} -7.23479e6i q^{64} +(1.50936e6 + 2.17574e6i) q^{65} +1.04585e7 q^{66} +(-9.87283e6 - 2.64542e6i) q^{67} +(-8.06731e6 - 1.39730e7i) q^{68} +(4.10151e7 + 2.36801e7i) q^{69} +(-854365. + 854365. i) q^{70} +(985912. + 3.67947e6i) q^{71} +(-3.66602e7 + 9.82306e6i) q^{72} +(3.80599e7 + 3.80599e7i) q^{73} +(6.42877e6 - 1.11350e7i) q^{74} +(-4.87872e7 + 2.81673e7i) q^{75} +(2.32582e6 - 8.68008e6i) q^{76} -3.48681e7i q^{77} +(-2.16094e7 + 1.79559e6i) q^{78} +1.02114e7 q^{79} +(-4.10889e6 - 1.10097e6i) q^{80} +(-4.39413e7 - 7.61086e7i) q^{81} +(1.73506e7 + 1.00174e7i) q^{82} +(2.14542e7 - 2.14542e7i) q^{83} +(2.21701e7 + 8.27401e7i) q^{84} +(-6.29626e6 + 1.68708e6i) q^{85} +(-7.93753e6 - 7.93753e6i) q^{86} +(-5.13905e7 + 8.90109e7i) q^{87} +(-2.98196e7 + 1.72164e7i) q^{88} +(2.07862e7 - 7.75752e7i) q^{89} +7.24798e6i q^{90} +(5.98643e6 + 7.20451e7i) q^{91} -7.37060e7 q^{92} +(1.42000e8 + 3.80488e7i) q^{93} +(1.92953e7 + 3.34205e7i) q^{94} +(-3.14406e6 - 1.81522e6i) q^{95} +(9.13532e7 - 9.13532e7i) q^{96} +(-1.54032e7 - 5.74855e7i) q^{97} +(-3.19337e6 + 855662. i) q^{98} +(-1.47901e8 - 1.47901e8i) 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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