LMFDB - Embedded newform 22.13.d.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,13,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.1078639801$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	22.13
Dual form			22.13.d.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-43.0399 - 13.9845i) q^{2} +(-974.141 + 707.755i) q^{3} +(1656.87 + 1203.78i) q^{4} +(1693.39 + 5211.73i) q^{5} +(51824.5 - 16838.8i) q^{6} +(23282.7 - 32045.9i) q^{7} +(-54477.1 - 74981.2i) q^{8} +(283809. - 873474. i) q^{9} -247993. i q^{10} +(1.16794e6 - 1.33205e6i) q^{11} -2.46600e6 q^{12} +(235938. + 76660.8i) q^{13} +(-1.45023e6 + 1.05366e6i) q^{14} +(-5.33823e6 - 3.87845e6i) q^{15} +(1.29611e6 + 3.98902e6i) q^{16} +(2.12124e6 - 689234. i) q^{17} +(-2.44302e7 + 3.36253e7i) q^{18} +(2.20372e7 + 3.03315e7i) q^{19} +(-3.46807e6 + 1.06736e7i) q^{20} +4.76957e7i q^{21} +(-6.88959e7 + 4.09983e7i) q^{22} +1.00113e8 q^{23} +(1.06137e8 + 3.44859e7i) q^{24} +(1.73219e8 - 1.25851e8i) q^{25} +(-9.08267e6 - 6.59894e6i) q^{26} +(1.43992e8 + 4.43163e8i) q^{27} +(7.71528e7 - 2.50685e7i) q^{28} +(-4.32401e8 + 5.95150e8i) q^{29} +(1.75519e8 + 2.41581e8i) q^{30} +(-4.11680e8 + 1.26702e9i) q^{31} -1.89813e8i q^{32} +(-1.94969e8 + 2.12421e9i) q^{33} -1.00937e8 q^{34} +(2.06441e8 + 6.70769e7i) q^{35} +(1.52171e9 - 1.10559e9i) q^{36} +(-2.35478e9 - 1.71085e9i) q^{37} +(-5.24305e8 - 1.61365e9i) q^{38} +(-2.84093e8 + 9.23075e7i) q^{39} +(2.98531e8 - 4.10892e8i) q^{40} +(1.26771e9 + 1.74485e9i) q^{41} +(6.67001e8 - 2.05282e9i) q^{42} -9.05523e9i q^{43} +(3.53861e9 - 8.01086e8i) q^{44} +5.03291e9 q^{45} +(-4.30886e9 - 1.40003e9i) q^{46} +(-7.45605e8 + 5.41714e8i) q^{47} +(-4.08584e9 - 2.96854e9i) q^{48} +(3.79234e9 + 1.16716e10i) q^{49} +(-9.21532e9 + 2.99424e9i) q^{50} +(-1.57858e9 + 2.17273e9i) q^{51} +(2.98634e8 + 4.11035e8i) q^{52} +(2.64627e9 - 8.14439e9i) q^{53} -2.10874e10i q^{54} +(8.92005e9 + 3.83128e9i) q^{55} -3.67122e9 q^{56} +(-4.29346e10 - 1.39503e10i) q^{57} +(2.69334e10 - 1.95683e10i) q^{58} +(2.86614e10 + 2.08237e10i) q^{59} +(-4.17591e9 - 1.28521e10i) q^{60} +(-6.78713e10 + 2.20527e10i) q^{61} +(3.54374e10 - 4.87754e10i) q^{62} +(-2.13835e10 - 2.94318e10i) q^{63} +(-2.65444e9 + 8.16951e9i) q^{64} +1.35946e9i q^{65} +(3.80976e10 - 8.86995e10i) q^{66} +1.76414e11 q^{67} +(4.34431e9 + 1.41155e9i) q^{68} +(-9.75242e10 + 7.08555e10i) q^{69} +(-7.94718e9 - 5.77397e9i) q^{70} +(4.91313e10 + 1.51211e11i) q^{71} +(-8.09553e10 + 2.63040e10i) q^{72} +(-1.65141e11 + 2.27297e11i) q^{73} +(7.74241e10 + 1.06565e11i) q^{74} +(-7.96682e10 + 2.45194e11i) q^{75} +7.67833e10i q^{76} +(-1.54940e10 - 6.84413e10i) q^{77} +1.35182e10 q^{78} +(1.34835e11 + 4.38105e10i) q^{79} +(-1.85949e10 + 1.35100e10i) q^{80} +(-5.90474e10 - 4.29004e10i) q^{81} +(-3.01611e10 - 9.28263e10i) q^{82} +(4.31001e11 - 1.40041e11i) q^{83} +(-5.74153e10 + 7.90254e10i) q^{84} +(7.18419e9 + 9.88819e9i) q^{85} +(-1.26633e11 + 3.89736e11i) q^{86} -8.85793e11i q^{87} +(-1.63504e11 - 1.50071e10i) q^{88} +6.81851e11 q^{89} +(-2.16616e11 - 7.03828e10i) q^{90} +(7.94994e9 - 5.77597e9i) q^{91} +(1.65874e11 + 1.20515e11i) q^{92} +(-4.95706e11 - 1.52563e12i) q^{93} +(3.96664e10 - 1.28884e10i) q^{94} +(-1.20762e11 + 1.66215e11i) q^{95} +(1.34341e11 + 1.84904e11i) q^{96} +(-3.33707e11 + 1.02704e12i) q^{97} -5.55379e11i q^{98} +(-8.32040e11 - 1.39821e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 1240 q^{3} + 24576 q^{4} + 1440 q^{5} - 147200 q^{6} + 439200 q^{7} + 563348 q^{9} - 7317468 q^{11} + 737280 q^{12} + 13341600 q^{13} - 7524864 q^{14} - 29808888 q^{15} - 50331648 q^{16} + 29458800 q^{17}+ \cdots - 5181480396620 q^{99}+O(q^{100}) $ 48 * q + 1240 * q^3 + 24576 * q^4 + 1440 * q^5 - 147200 * q^6 + 439200 * q^7 + 563348 * q^9 - 7317468 * q^11 + 737280 * q^12 + 13341600 * q^13 - 7524864 * q^14 - 29808888 * q^15 - 50331648 * q^16 + 29458800 * q^17 - 96857600 * q^18 + 59195700 * q^19 - 2949120 * q^20 - 147874560 * q^22 + 297521280 * q^23 - 301465600 * q^24 - 349772268 * q^25 + 603191808 * q^26 - 434593340 * q^27 - 981811200 * q^28 + 121665600 * q^29 + 3275650560 * q^30 - 1117400544 * q^31 - 13803991820 * q^33 - 2568870912 * q^34 + 1026283680 * q^35 + 7058374656 * q^36 + 11737565760 * q^37 + 4500864000 * q^38 - 23697921920 * q^39 - 7817134080 * q^40 + 4863244680 * q^41 + 12992468480 * q^42 - 18701991936 * q^44 + 29640403232 * q^45 + 33202391040 * q^46 + 8084031480 * q^47 + 5200936960 * q^48 + 593931516 * q^49 - 13593646080 * q^50 - 30011589660 * q^51 + 55099392000 * q^52 + 40815862920 * q^53 + 29310331992 * q^55 - 7285506048 * q^56 - 98665594300 * q^57 + 81900510720 * q^58 - 156541010940 * q^59 - 30685659136 * q^60 + 255357655680 * q^61 + 67163788800 * q^62 - 429459850400 * q^63 + 103079215104 * q^64 + 460708043264 * q^66 + 76186270200 * q^67 + 60331622400 * q^68 - 1054414688600 * q^69 - 352820375040 * q^70 + 60925955544 * q^71 + 95420416000 * q^72 + 363471756600 * q^73 + 378662860800 * q^74 - 57777629724 * q^75 + 326539185480 * q^77 - 1234846474240 * q^78 + 137547461520 * q^79 - 120795955200 * q^80 - 1017431491848 * q^81 + 613199754240 * q^82 + 715268672100 * q^83 - 354644459520 * q^84 + 1202406730800 * q^85 - 80499776256 * q^86 - 270225899520 * q^88 + 724193830584 * q^89 - 1005067351040 * q^90 + 1925501559192 * q^91 - 608833290240 * q^92 - 2466072811400 * q^93 + 300785049600 * q^94 + 6877125644400 * q^95 + 1350178653780 * q^97 - 5181480396620 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−43.0399	−	13.9845i	−0.672499	−	0.218508i
$2$	−43.0399	−	13.9845i	−0.672499	−	0.218508i
$3$	−974.141	+	707.755i	−1.33627	+	0.970857i	−0.336697	+	0.941613i	$0.609310\pi$
$3$	−974.141	+	707.755i	−1.33627	+	0.970857i	−0.999572	+	0.0292437i	$0.990690\pi$
$4$	1656.87	+	1203.78i	0.404508	+	0.293893i
$5$	1693.39	+	5211.73i	0.108377	+	0.333550i	0.990508	−	0.137453i	$-0.0438918\pi$
$5$	1693.39	+	5211.73i	0.108377	+	0.333550i	−0.882131	+	0.471004i	$0.843892\pi$
$6$	51824.5	−	16838.8i	1.11078	−	0.360914i
$7$	23282.7	−	32045.9i	0.197900	−	0.272386i	−0.698521	−	0.715590i	$-0.746158\pi$
$7$	23282.7	−	32045.9i	0.197900	−	0.272386i	0.896421	+	0.443204i	$0.146158\pi$
$8$	−54477.1	−	74981.2i	−0.207813	−	0.286031i
$9$	283809.	−	873474.i	0.534037	−	1.64360i
$10$		−	247993.i		−	0.247993i
$11$	1.16794e6	−	1.33205e6i	0.659269	−	0.751907i
$11$	1.16794e6	−	1.33205e6i	0.659269	−	0.751907i
$12$	−2.46600e6			−0.825860
$13$	235938.	+	76660.8i	0.0488806	+	0.0158823i	0.333355	−	0.942801i	$-0.391819\pi$
$13$	235938.	+	76660.8i	0.0488806	+	0.0158823i	−0.284475	+	0.958684i	$0.591819\pi$
$14$	−1.45023e6	+	1.05366e6i	−0.192606	+	0.139936i
$15$	−5.33823e6	−	3.87845e6i	−0.468651	−	0.340495i
$16$	1.29611e6	+	3.98902e6i	0.0772542	+	0.237764i
$17$	2.12124e6	−	689234.i	0.0878814	−	0.0285544i	−0.264746	−	0.964318i	$-0.585288\pi$
$17$	2.12124e6	−	689234.i	0.0878814	−	0.0285544i	0.352628	+	0.935764i	$0.385288\pi$
$18$	−2.44302e7	+	3.36253e7i	−0.718278	+	0.988625i
$19$	2.20372e7	+	3.03315e7i	0.468418	+	0.644723i	0.976228	−	0.216747i	$-0.0695446\pi$
$19$	2.20372e7	+	3.03315e7i	0.468418	+	0.644723i	−0.507809	+	0.861469i	$0.669545\pi$
$20$	−3.46807e6	+	1.06736e7i	−0.0541886	+	0.166775i
$21$			4.76957e7i			0.556114i
$22$	−6.88959e7	+	4.09983e7i	−0.607655	+	0.361601i
$23$	1.00113e8			0.676276			0.338138	−	0.941097i	$-0.390203\pi$
$23$	1.00113e8			0.676276			0.338138	+	0.941097i	$0.390203\pi$
$24$	1.06137e8	+	3.44859e7i	0.555390	+	0.180457i
$25$	1.73219e8	−	1.25851e8i	0.709507	−	0.515487i
$26$	−9.08267e6	−	6.59894e6i	−0.0294018	−	0.0213616i
$27$	1.43992e8	+	4.43163e8i	0.371670	+	1.14388i
$28$	7.71528e7	−	2.50685e7i	0.160104	−	0.0520211i
$29$	−4.32401e8	+	5.95150e8i	−0.726941	+	1.00055i	0.272324	+	0.962206i	$0.412208\pi$
$29$	−4.32401e8	+	5.95150e8i	−0.726941	+	1.00055i	−0.999265	+	0.0383427i	$0.987792\pi$
$30$	1.75519e8	+	2.41581e8i	0.240766	+	0.331386i
$31$	−4.11680e8	+	1.26702e9i	−0.463863	+	1.42762i	0.396543	+	0.918016i	$0.370210\pi$
$31$	−4.11680e8	+	1.26702e9i	−0.463863	+	1.42762i	−0.860406	+	0.509609i	$0.829790\pi$
$32$		−	1.89813e8i		−	0.176777i
$33$	−1.94969e8	+	2.12421e9i	−0.150967	+	1.64481i
$34$	−1.00937e8			−0.0653395
$35$	2.06441e8	+	6.70769e7i	0.112302	+	0.0364892i
$36$	1.52171e9	−	1.10559e9i	0.699063	−	0.507899i
$37$	−2.35478e9	−	1.71085e9i	−0.917782	−	0.666808i	0.0251886	−	0.999683i	$-0.491981\pi$
$37$	−2.35478e9	−	1.71085e9i	−0.917782	−	0.666808i	−0.942971	+	0.332875i	$0.891981\pi$
$38$	−5.24305e8	−	1.61365e9i	−0.174134	−	0.535928i
$39$	−2.84093e8	+	9.23075e7i	−0.0807371	+	0.0262331i
$40$	2.98531e8	−	4.10892e8i	0.0728835	−	0.100315i
$41$	1.26771e9	+	1.74485e9i	0.266880	+	0.367328i	0.921333	−	0.388774i	$-0.127101\pi$
$41$	1.26771e9	+	1.74485e9i	0.266880	+	0.367328i	−0.654454	+	0.756102i	$0.727101\pi$
$42$	6.67001e8	−	2.05282e9i	0.121515	−	0.373986i
$43$		−	9.05523e9i		−	1.43248i	−0.697854	−	0.716240i	$-0.745862\pi$
$43$		−	9.05523e9i		−	1.43248i	0.697854	−	0.716240i	$-0.254138\pi$
$44$	3.53861e9	−	8.01086e8i	0.487660	−	0.110399i
$45$	5.03291e9			0.606100
$46$	−4.30886e9	−	1.40003e9i	−0.454794	−	0.147772i
$47$	−7.45605e8	+	5.41714e8i	−0.0691707	+	0.0502554i	−0.621833	−	0.783150i	$-0.713612\pi$
$47$	−7.45605e8	+	5.41714e8i	−0.0691707	+	0.0502554i	0.552663	+	0.833405i	$0.313612\pi$
$48$	−4.08584e9	−	2.96854e9i	−0.334067	−	0.242714i
$49$	3.79234e9	+	1.16716e10i	0.273987	+	0.843246i
$50$	−9.21532e9	+	2.99424e9i	−0.589780	+	0.191631i
$51$	−1.57858e9	+	2.17273e9i	−0.0897110	+	0.123477i
$52$	2.98634e8	+	4.11035e8i	0.0151050	+	0.0207902i
$53$	2.64627e9	−	8.14439e9i	0.119393	−	0.367454i	−0.873445	−	0.486923i	$-0.838119\pi$
$53$	2.64627e9	−	8.14439e9i	0.119393	−	0.367454i	0.992838	+	0.119469i	$0.0381192\pi$
$54$		−	2.10874e10i		−	0.850471i
$55$	8.92005e9	+	3.83128e9i	0.322249	+	0.138410i
$56$	−3.67122e9			−0.119037
$57$	−4.29346e10	−	1.39503e10i	−1.25187	−	0.406756i
$58$	2.69334e10	−	1.95683e10i	0.707495	−	0.514025i
$59$	2.86614e10	+	2.08237e10i	0.679493	+	0.493680i	0.873189	−	0.487381i	$-0.162048\pi$
$59$	2.86614e10	+	2.08237e10i	0.679493	+	0.493680i	−0.193697	+	0.981061i	$0.562048\pi$
$60$	−4.17591e9	−	1.28521e10i	−0.0895043	−	0.275466i
$61$	−6.78713e10	+	2.20527e10i	−1.31737	+	0.428039i	−0.881590	−	0.472016i	$-0.843527\pi$
$61$	−6.78713e10	+	2.20527e10i	−1.31737	+	0.428039i	−0.435778	+	0.900054i	$0.643527\pi$
$62$	3.54374e10	−	4.87754e10i	0.623895	−	0.858718i
$63$	−2.13835e10	−	2.94318e10i	−0.342007	−	0.470732i
$64$	−2.65444e9	+	8.16951e9i	−0.0386271	+	0.118882i
$65$			1.35946e9i			0.0180254i
$66$	3.80976e10	−	8.86995e10i	0.460928	−	1.07314i
$67$	1.76414e11			1.95022			0.975110	−	0.221722i	$-0.0711678\pi$
$67$	1.76414e11			1.95022			0.975110	+	0.221722i	$0.0711678\pi$
$68$	4.34431e9	+	1.41155e9i	0.0439407	+	0.0142772i
$69$	−9.75242e10	+	7.08555e10i	−0.903687	+	0.656567i
$70$	−7.94718e9	−	5.77397e9i	−0.0675499	−	0.0490779i
$71$	4.91313e10	+	1.51211e11i	0.383538	+	1.18041i	0.937535	+	0.347890i	$0.113102\pi$
$71$	4.91313e10	+	1.51211e11i	0.383538	+	1.18041i	−0.553997	+	0.832519i	$0.686898\pi$
$72$	−8.09553e10	+	2.63040e10i	−0.581099	+	0.188810i
$73$	−1.65141e11	+	2.27297e11i	−1.09123	+	1.50196i	−0.244717	+	0.969595i	$0.578695\pi$
$73$	−1.65141e11	+	2.27297e11i	−1.09123	+	1.50196i	−0.846518	+	0.532360i	$0.821305\pi$
$74$	7.74241e10	+	1.06565e11i	0.471504	+	0.648970i
$75$	−7.96682e10	+	2.45194e11i	−0.447628	+	1.37766i
$76$			7.67833e10i			0.398460i
$77$	−1.54940e10	−	6.84413e10i	−0.0743396	−	0.328378i
$78$	1.35182e10			0.0600277
$79$	1.34835e11	+	4.38105e10i	0.554676	+	0.180225i	0.572924	−	0.819608i	$-0.305809\pi$
$79$	1.34835e11	+	4.38105e10i	0.554676	+	0.180225i	−0.0182483	+	0.999833i	$0.505809\pi$
$80$	−1.85949e10	+	1.35100e10i	−0.0709337	+	0.0515364i
$81$	−5.90474e10	−	4.29004e10i	−0.209069	−	0.151898i
$82$	−3.01611e10	−	9.28263e10i	−0.0992120	−	0.305343i
$83$	4.31001e11	−	1.40041e11i	1.31829	−	0.428337i	0.436381	−	0.899762i	$-0.356260\pi$
$83$	4.31001e11	−	1.40041e11i	1.31829	−	0.428337i	0.881906	+	0.471425i	$0.156260\pi$
$84$	−5.74153e10	+	7.90254e10i	−0.163438	+	0.224953i
$85$	7.18419e9	+	9.88819e9i	0.0190487	+	0.0262182i
$86$	−1.26633e11	+	3.89736e11i	−0.313008	+	0.963341i
$87$		−	8.85793e11i		−	2.04276i
$88$	−1.63504e11	−	1.50071e10i	−0.352074	−	0.0323147i
$89$	6.81851e11			1.37199			0.685993	−	0.727608i	$-0.259368\pi$
$89$	6.81851e11			1.37199			0.685993	+	0.727608i	$0.259368\pi$
$90$	−2.16616e11	−	7.03828e10i	−0.407601	−	0.132438i
$91$	7.94994e9	−	5.77597e9i	0.0139996	−	0.0101713i
$92$	1.65874e11	+	1.20515e11i	0.273559	+	0.198752i
$93$	−4.95706e11	−	1.52563e12i	−0.766172	−	2.35804i
$94$	3.96664e10	−	1.28884e10i	0.0574984	−	0.0186824i
$95$	−1.20762e11	+	1.66215e11i	−0.164282	+	0.226114i
$96$	1.34341e11	+	1.84904e11i	0.171625	+	0.236221i
$97$	−3.33707e11	+	1.02704e12i	−0.400622	+	1.23299i	0.523874	+	0.851796i	$0.324486\pi$
$97$	−3.33707e11	+	1.02704e12i	−0.400622	+	1.23299i	−0.924496	+	0.381191i	$0.875514\pi$
$98$		−	5.55379e11i		−	0.626950i
$99$	−8.32040e11	−	1.39821e12i	−0.883758	−	1.48512i
$100$	4.38499e11			0.438499
$101$	−7.74626e11	−	2.51691e11i	−0.729733	−	0.237105i	−0.0794951	−	0.996835i	$-0.525331\pi$
$101$	−7.74626e11	−	2.51691e11i	−0.729733	−	0.237105i	−0.650238	+	0.759731i	$0.725331\pi$
$102$	9.83265e10	−	7.14384e10i	0.0873111	−	0.0634353i
$103$	−2.81320e11	−	2.04391e11i	−0.235601	−	0.171174i	0.463720	−	0.885982i	$-0.346514\pi$
$103$	−2.81320e11	−	2.04391e11i	−0.235601	−	0.171174i	−0.699321	+	0.714808i	$0.746514\pi$
$104$	−7.10506e9	−	2.18671e10i	−0.00561524	−	0.0172819i
$105$	−2.48577e11	+	8.07676e10i	−0.185492	+	0.0602700i
$106$	−2.27791e11	+	3.13527e11i	−0.160583	+	0.221024i
$107$	7.64275e11	+	1.05193e12i	0.509269	+	0.700948i	0.983796	−	0.179293i	$-0.0573809\pi$
$107$	7.64275e11	+	1.05193e12i	0.509269	+	0.700948i	−0.474527	+	0.880241i	$0.657381\pi$
$108$	−2.94896e11	+	9.07598e11i	−0.185835	+	0.571941i
$109$		−	5.20080e11i		−	0.310106i	−0.987906	−	0.155053i	$-0.950445\pi$
$109$		−	5.20080e11i		−	0.310106i	0.987906	−	0.155053i	$-0.0495549\pi$
$110$	−3.30340e11	−	2.89640e11i	−0.186468	−	0.163494i
$111$	3.50474e12			1.87378
$112$	1.58009e11	+	5.13402e10i	0.0800522	+	0.0260105i
$113$	−2.00771e11	+	1.45869e11i	−0.0964340	+	0.0700634i	−0.634957	−	0.772547i	$-0.718982\pi$
$113$	−2.00771e11	+	1.45869e11i	−0.0964340	+	0.0700634i	0.538523	+	0.842611i	$0.318982\pi$
$114$	1.65281e12	+	1.20084e12i	0.752999	+	0.547086i
$115$	1.69531e11	+	5.21762e11i	0.0732928	+	0.225572i
$116$	−1.43286e12	+	4.65565e11i	−0.588108	+	0.191088i
$117$	1.33922e11	−	1.84328e11i	0.0522081	−	0.0718583i
$118$	−9.42373e11	−	1.29706e12i	−0.349085	−	0.480474i
$119$	2.73012e10	−	8.40245e10i	0.00961391	−	0.0295886i
$120$			6.11553e11i			0.204808i
$121$	−4.10283e11	−	3.11149e12i	−0.130729	−	0.991418i
$122$	3.22957e12			0.979458
$123$	−2.46985e12	−	8.02502e11i	−0.713246	−	0.231748i
$124$	−2.20732e12	+	1.60371e12i	−0.607205	+	0.441160i
$125$	2.03159e12	+	1.47604e12i	0.532570	+	0.386935i
$126$	5.08752e11	+	1.56578e12i	0.127140	+	0.391298i
$127$	−5.70964e12	+	1.85517e12i	−1.36077	+	0.442142i	−0.896301	−	0.443445i	$-0.853756\pi$
$127$	−5.70964e12	+	1.85517e12i	−1.36077	+	0.442142i	−0.464473	+	0.885588i	$0.653756\pi$
$128$	2.28493e11	−	3.14494e11i	0.0519534	−	0.0715077i
$129$	6.40888e12	+	8.82106e12i	1.39073	+	1.91418i
$130$	1.90114e10	−	5.85110e10i	0.00393870	−	0.0121221i
$131$		−	1.57710e12i		−	0.312054i	−0.987753	−	0.156027i	$-0.950131\pi$
$131$		−	1.57710e12i		−	0.312054i	0.987753	−	0.156027i	$-0.0498688\pi$
$132$	−2.88013e12	+	3.28484e12i	−0.544464	+	0.620970i
$133$	1.48509e12			0.268313
$134$	−7.59283e12	−	2.46706e12i	−1.31152	−	0.426139i
$135$	−2.06581e12	+	1.50090e12i	−0.341262	+	0.247941i
$136$	−1.67239e11	−	1.21506e11i	−0.0264304	−	0.0192028i
$137$	1.68660e12	+	5.19081e12i	0.255087	+	0.785076i	0.993813	+	0.111070i	$0.0354278\pi$
$137$	1.68660e12	+	5.19081e12i	0.255087	+	0.785076i	−0.738726	+	0.674006i	$0.764572\pi$
$138$	5.18831e12	−	1.68579e12i	0.751193	−	0.244077i
$139$	−1.51726e12	+	2.08832e12i	−0.210363	+	0.289540i	−0.901140	−	0.433528i	$-0.857269\pi$
$139$	−1.51726e12	+	2.08832e12i	−0.210363	+	0.289540i	0.690777	+	0.723068i	$0.257269\pi$
$140$	2.61300e11	+	3.59648e11i	0.0347033	+	0.0477650i
$141$	3.42924e11	−	1.05541e12i	0.0436398	−	0.134310i
$142$		−	7.19517e12i		−	0.877629i
$143$	3.77676e11	−	2.24746e11i	0.0441675	−	0.0262830i
$144$	3.85215e12			0.432045
$145$	−3.83398e12	−	1.24574e12i	−0.412517	−	0.134035i
$146$	1.02863e13	−	7.47343e12i	1.06204	−	0.771619i
$147$	−1.19549e13	−	8.68575e12i	−1.18479	−	0.860802i
$148$	−1.84206e12	−	5.66929e12i	−0.175281	−	0.539459i
$149$	1.24111e13	−	4.03260e12i	1.13420	−	0.368525i	0.319032	−	0.947744i	$-0.396642\pi$
$149$	1.24111e13	−	4.03260e12i	1.13420	−	0.368525i	0.815172	+	0.579218i	$0.196642\pi$
$150$	6.85783e12	−	9.43899e12i	0.602059	−	0.828663i
$151$	3.90947e12	+	5.38093e12i	0.329804	+	0.453937i	0.941429	−	0.337211i	$-0.109484\pi$
$151$	3.90947e12	+	5.38093e12i	0.329804	+	0.453937i	−0.611625	+	0.791148i	$0.709484\pi$
$152$	1.07378e12	−	3.30475e12i	0.0870668	−	0.267964i
$153$		−	2.04846e12i		−	0.159691i
$154$	−2.90257e11	+	3.16239e12i	−0.0217599	+	0.237078i
$155$	−7.30051e12			−0.526457
$156$	−5.81823e11	−	1.89046e11i	−0.0403686	−	0.0131165i
$157$	−1.92589e13	+	1.39924e13i	−1.28598	+	0.934316i	−0.999716	−	0.0238356i	$-0.992412\pi$
$157$	−1.92589e13	+	1.39924e13i	−1.28598	+	0.934316i	−0.286260	+	0.958152i	$0.592412\pi$
$158$	−5.19061e12	−	3.77120e12i	−0.333638	−	0.242402i
$159$	3.18639e12	+	9.80669e12i	0.197204	+	0.606931i
$160$	9.89251e11	−	3.21427e11i	0.0589640	−	0.0191585i
$161$	2.33091e12	−	3.20822e12i	0.133835	−	0.184208i
$162$	1.94145e12	+	2.67218e12i	0.107408	+	0.147834i
$163$	5.11922e12	−	1.57553e13i	0.272947	−	0.840044i	−0.716808	−	0.697270i	$-0.754398\pi$
$163$	5.11922e12	−	1.57553e13i	0.272947	−	0.840044i	0.989755	−	0.142774i	$-0.0456022\pi$
$164$			4.41702e12i			0.227021i
$165$	−1.14010e13	+	2.58100e12i	−0.564987	+	0.127904i
$166$	−2.05087e13			−0.980141
$167$	3.00766e13	+	9.77248e12i	1.38653	+	0.450511i	0.904811	−	0.425814i	$-0.140012\pi$
$167$	3.00766e13	+	9.77248e12i	1.38653	+	0.450511i	0.481720	+	0.876325i	$0.340012\pi$
$168$	3.57628e12	−	2.59832e12i	0.159066	−	0.115568i
$169$	−1.87988e13	−	1.36581e13i	−0.806880	−	0.586233i
$170$	−1.70925e11	−	5.26054e11i	−0.00708130	−	0.0217940i
$171$	3.27482e13	−	1.06405e13i	1.30982	−	0.425585i
$172$	1.09005e13	−	1.50033e13i	0.420995	−	0.579450i
$173$	−1.01792e13	−	1.40105e13i	−0.379698	−	0.522610i	0.575806	−	0.817586i	$-0.304688\pi$
$173$	−1.01792e13	−	1.40105e13i	−0.379698	−	0.522610i	−0.955505	+	0.294976i	$0.904688\pi$
$174$	−1.23874e13	+	3.81245e13i	−0.446359	+	1.37375i
$175$		−	8.48114e12i		−	0.295275i
$176$	6.82735e12	+	2.93243e12i	0.229708	+	0.0986625i
$177$	−4.26583e13			−1.38728
$178$	−2.93468e13	−	9.53535e12i	−0.922658	−	0.299790i
$179$	−1.04848e13	+	7.61762e12i	−0.318743	+	0.231580i	−0.735639	−	0.677374i	$-0.763118\pi$
$179$	−1.04848e13	+	7.61762e12i	−0.318743	+	0.231580i	0.416896	+	0.908954i	$0.363118\pi$
$180$	8.33886e12	+	6.05854e12i	0.245172	+	0.178128i
$181$	1.58445e13	+	4.87643e13i	0.450616	+	1.38685i	0.876206	+	0.481937i	$0.160066\pi$
$181$	1.58445e13	+	4.87643e13i	0.450616	+	1.38685i	−0.425590	+	0.904916i	$0.639934\pi$
$182$	−4.22939e11	+	1.37421e11i	−0.0116372	+	0.00378116i
$183$	5.05083e13	−	6.95187e13i	1.34479	−	1.85095i
$184$	−5.45387e12	−	7.50660e12i	−0.140539	−	0.193436i
$185$	4.92890e12	−	1.51696e13i	0.122948	−	0.378393i
$186$			7.25950e13i			1.75319i
$187$	1.55938e12	−	3.63058e12i	0.0364672	−	0.0849037i
$188$	−1.88748e12			−0.0427498
$189$	1.75541e13	+	5.70368e12i	0.385131	+	0.125137i
$190$	7.52202e12	−	5.46507e12i	0.159887	−	0.116165i
$191$	4.46377e13	+	3.24312e13i	0.919393	+	0.667978i	0.943373	−	0.331734i	$-0.107634\pi$
$191$	4.46377e13	+	3.24312e13i	0.919393	+	0.667978i	−0.0239799	+	0.999712i	$0.507634\pi$
$192$	−3.19622e12	−	9.83694e12i	−0.0638012	−	0.196360i
$193$	1.77814e13	−	5.77751e12i	0.344050	−	0.111789i	−0.131895	−	0.991264i	$-0.542106\pi$
$193$	1.77814e13	−	5.77751e12i	0.344050	−	0.111789i	0.475945	+	0.879475i	$0.342106\pi$
$194$	2.87254e13	−	3.95371e13i	0.538835	−	0.741643i
$195$	−9.62163e11	−	1.32430e12i	−0.0175001	−	0.0240868i
$196$	−7.76671e12	+	2.39035e13i	−0.136994	+	0.421623i
$197$			6.13561e13i			1.04969i	0.851198	+	0.524844i	$0.175876\pi$
$197$			6.13561e13i			1.04969i	−0.851198	+	0.524844i	$0.824124\pi$
$198$	1.62577e13	+	7.18145e13i	0.269816	+	1.19185i
$199$	−5.68662e13			−0.915664			−0.457832	−	0.889039i	$-0.651374\pi$
$199$	−5.68662e13			−0.915664			−0.457832	+	0.889039i	$0.651374\pi$
$200$	−1.88730e13	−	6.13220e12i	−0.294890	−	0.0958156i
$201$	−1.71852e14	+	1.24858e14i	−2.60602	+	1.89338i
$202$	2.98201e13	+	2.16655e13i	0.438935	+	0.318905i
$203$	9.00464e12	+	2.77134e13i	0.128674	+	0.396017i
$204$	−5.23100e12	+	1.69965e12i	−0.0725777	+	0.0235819i
$205$	−6.94694e12	+	9.56165e12i	−0.0935989	+	0.128828i
$206$	9.24967e12	+	1.27311e13i	0.121038	+	0.166595i
$207$	2.84130e13	−	8.74462e13i	0.361156	−	1.11152i
$208$			1.04052e12i			0.0128490i
$209$	6.61411e13	+	6.07070e12i	0.793585	+	0.0728385i
$210$	1.18282e13			0.137913
$211$	9.07678e13	+	2.94922e13i	1.02858	+	0.334205i	0.774228	−	0.632907i	$-0.218139\pi$
$211$	9.07678e13	+	2.94922e13i	1.02858	+	0.334205i	0.254350	+	0.967112i	$0.418139\pi$
$212$	1.41886e13	−	1.03086e13i	0.156288	−	0.113550i
$213$	−1.54881e14	−	1.12528e14i	−1.65852	−	1.20498i
$214$	−1.81835e13	−	5.59632e13i	−0.189320	−	0.582666i
$215$	4.71934e13	−	1.53341e13i	0.477805	−	0.155248i
$216$	2.53846e13	−	3.49389e13i	0.249947	−	0.344023i
$217$	3.10179e13	+	4.26924e13i	0.297066	+	0.408877i
$218$	−7.27306e12	+	2.23842e13i	−0.0677607	+	0.208546i
$219$		−	3.38299e14i		−	3.06645i
$220$	1.01673e13	+	1.70857e13i	0.0896747	+	0.150695i
$221$	5.53318e11			0.00474921
$222$	−1.50844e14	−	4.90121e13i	−1.26011	−	0.409436i
$223$	7.60121e13	−	5.52260e13i	0.618093	−	0.449071i	−0.234162	−	0.972198i	$-0.575235\pi$
$223$	7.60121e13	−	5.52260e13i	0.618093	−	0.449071i	0.852255	+	0.523127i	$0.175235\pi$
$224$	−6.08272e12	−	4.41936e12i	−0.0481515	−	0.0349841i
$225$	−6.07666e13	−	1.87020e14i	−0.468349	−	1.44143i
$226$	1.06811e13	−	3.47049e12i	0.0801612	−	0.0260459i
$227$	1.88292e13	−	2.59162e13i	0.137619	−	0.189416i	−0.734645	−	0.678452i	$-0.762651\pi$
$227$	1.88292e13	−	2.59162e13i	0.137619	−	0.189416i	0.872264	+	0.489036i	$0.162651\pi$
$228$	−5.43437e13	−	7.47977e13i	−0.386848	−	0.532451i
$229$	3.59682e12	−	1.10699e13i	0.0249405	−	0.0767590i	−0.937812	−	0.347145i	$-0.887151\pi$
$229$	3.59682e12	−	1.10699e13i	0.0249405	−	0.0767590i	0.962752	+	0.270386i	$0.0871512\pi$
$230$		−	2.48274e13i		−	0.167712i
$231$	6.35330e13	+	5.57055e13i	0.418146	+	0.366628i
$232$	6.81810e13			0.437256
$233$	6.40053e13	+	2.07966e13i	0.400019	+	0.129974i	0.502116	−	0.864800i	$-0.332555\pi$
$233$	6.40053e13	+	2.07966e13i	0.400019	+	0.129974i	−0.102097	+	0.994774i	$0.532555\pi$
$234$	−8.34175e12	+	6.06064e12i	−0.0508115	+	0.0369167i
$235$	−4.08587e12	−	2.96856e12i	−0.0242592	−	0.0176254i
$236$	2.24208e13	+	6.90042e13i	0.129772	+	0.399396i
$237$	−1.62355e14	+	5.27524e13i	−0.916169	+	0.297681i
$238$	−2.35008e12	+	3.23461e12i	−0.0129307	+	0.0177976i
$239$	2.01973e14	+	2.77992e14i	1.08369	+	1.49157i	0.855392	+	0.517982i	$0.173317\pi$
$239$	2.01973e14	+	2.77992e14i	1.08369	+	1.49157i	0.228299	+	0.973591i	$0.426683\pi$
$240$	8.55227e12	−	2.63212e13i	0.0447522	−	0.137733i
$241$			3.45260e13i			0.176215i	0.996111	+	0.0881077i	$0.0280820\pi$
$241$			3.45260e13i			0.176215i	−0.996111	+	0.0881077i	$0.971918\pi$
$242$	−2.58542e13	+	1.39656e14i	−0.128718	+	0.695293i
$243$	−1.59752e14			−0.775904
$244$	−1.39000e14	−	4.51640e13i	−0.658684	−	0.214019i
$245$	−5.44073e13	+	3.95292e13i	−0.251571	+	0.182777i
$246$	9.50794e13	+	6.90792e13i	0.429018	+	0.311700i
$247$	2.87415e12	+	8.84573e12i	0.0126569	+	0.0389540i
$248$	1.17430e14	−	3.81553e13i	0.504742	−	0.164000i
$249$	−3.20741e14	+	4.41463e14i	−1.34573	+	1.85224i
$250$	−6.67979e13	−	9.19394e13i	−0.273604	−	0.376584i
$251$	−3.12760e13	+	9.62575e13i	−0.125074	+	0.384939i	−0.993915	−	0.110153i	$-0.964866\pi$
$251$	−3.12760e13	+	9.62575e13i	−0.125074	+	0.384939i	0.868840	+	0.495093i	$0.164866\pi$
$252$		−	7.45056e13i		−	0.290928i
$253$	1.16926e14	−	1.33356e14i	0.445848	−	0.508497i
$254$	2.71686e14			1.01173
$255$	−1.39968e13	−	4.54785e12i	−0.0509083	−	0.0165411i
$256$	−1.42324e13	+	1.03404e13i	−0.0505636	+	0.0367366i
$257$	3.75455e14	+	2.72784e14i	1.30304	+	0.946717i	0.999980	−	0.00625283i	$-0.00199035\pi$
$257$	3.75455e14	+	2.72784e14i	1.30304	+	0.946717i	0.303064	+	0.952970i	$0.401990\pi$
$258$	−1.52479e14	−	4.69283e14i	−0.517002	−	1.59117i
$259$	−1.09651e14	+	3.56279e13i	−0.363258	+	0.118030i
$260$	−1.63649e12	+	2.25244e12i	−0.00529754	+	0.00729144i
$261$	3.97128e14	+	5.46600e14i	1.25628	+	1.72913i
$262$	−2.20549e13	+	6.78781e13i	−0.0681864	+	0.209856i
$263$		−	5.47581e14i		−	1.65468i	−0.561702	−	0.827340i	$-0.689853\pi$
$263$		−	5.47581e14i		−	1.65468i	0.561702	−	0.827340i	$-0.310147\pi$
$264$	1.69898e14	−	1.01102e14i	0.501838	−	0.298632i
$265$	4.69275e13			0.135504
$266$	−6.39180e13	−	2.07682e13i	−0.180440	−	0.0586286i
$267$	−6.64219e14	+	4.82583e14i	−1.83334	+	1.33200i
$268$	2.92294e14	+	2.12364e14i	0.788880	+	0.573155i
$269$	−4.17119e13	−	1.28376e14i	−0.110090	−	0.338821i	0.880802	−	0.473485i	$-0.157004\pi$
$269$	−4.17119e13	−	1.28376e14i	−0.110090	−	0.338821i	−0.990891	+	0.134664i	$0.957004\pi$
$270$	1.09902e14	−	3.57092e13i	0.283675	−	0.0921716i
$271$	−1.60128e14	+	2.20397e14i	−0.404251	+	0.556403i	−0.961804	−	0.273738i	$-0.911740\pi$
$271$	−1.60128e14	+	2.20397e14i	−0.404251	+	0.556403i	0.557554	+	0.830141i	$0.311740\pi$
$272$	5.49873e12	+	7.56836e12i	0.0135784	+	0.0186891i
$273$	−3.65639e12	+	1.12532e13i	−0.00883236	+	0.0271832i
$274$		−	2.46998e14i		−	0.583701i
$275$	3.46690e13	−	3.77723e14i	0.0801576	−	0.873328i
$276$	−2.46879e14			−0.558509
$277$	−6.09254e14	−	1.97959e14i	−1.34871	−	0.438224i	−0.456454	−	0.889747i	$-0.650881\pi$
$277$	−6.09254e14	−	1.97959e14i	−1.34871	−	0.438224i	−0.892259	+	0.451523i	$0.850881\pi$
$278$	9.45067e13	−	6.86631e13i	0.204736	−	0.148749i
$279$	9.89873e14	+	7.19185e14i	2.09872	+	1.52481i
$280$	−6.21681e12	−	1.91334e13i	−0.0129009	−	0.0397049i
$281$	3.44036e14	−	1.11784e14i	0.698820	−	0.227060i	0.0620039	−	0.998076i	$-0.480251\pi$
$281$	3.44036e14	−	1.11784e14i	0.698820	−	0.227060i	0.636816	+	0.771015i	$0.280251\pi$
$282$	−2.95188e13	+	4.06292e13i	−0.0586954	+	0.0807873i
$283$	−2.53813e14	−	3.49344e14i	−0.494078	−	0.680040i	0.487056	−	0.873371i	$-0.338071\pi$
$283$	−2.53813e14	−	3.49344e14i	−0.494078	−	0.680040i	−0.981134	+	0.193331i	$0.938071\pi$
$284$	−1.00621e14	+	3.09680e14i	−0.191769	+	0.590204i
$285$		−	2.47387e14i		−	0.461644i
$286$	−1.93981e13	+	4.39142e12i	−0.0354456	+	0.00802433i
$287$	8.54310e13			0.152871
$288$	−1.65796e14	−	5.38705e13i	−0.290549	−	0.0944052i
$289$	−4.67327e14	+	3.39533e14i	−0.802109	+	0.582766i
$290$	1.47593e14	+	1.07233e14i	0.248129	+	0.180277i
$291$	−4.01818e14	−	1.23667e15i	−0.661715	−	2.03655i
$292$	−5.47234e14	+	1.77807e14i	−0.882827	+	0.286848i
$293$	2.84557e13	−	3.91659e13i	0.0449742	−	0.0619017i	−0.785938	−	0.618306i	$-0.787819\pi$
$293$	2.84557e13	−	3.91659e13i	0.0449742	−	0.0619017i	0.830912	+	0.556404i	$0.187819\pi$
$294$	3.93072e14	+	5.41017e14i	0.608679	+	0.837774i
$295$	−5.99925e13	+	1.84638e14i	−0.0910258	+	0.280149i
$296$			2.69766e14i			0.401086i
$297$	7.58489e14	+	3.25781e14i	1.10512	+	0.474665i
$298$	−5.90565e14			−0.843277
$299$	2.36204e13	+	7.67475e12i	0.0330568	+	0.0107408i
$300$	−4.27160e14	+	3.10350e14i	−0.585953	+	0.425720i
$301$	−2.90183e14	−	2.10830e14i	−0.390188	−	0.283488i
$302$	−9.30137e13	−	2.86267e14i	−0.122604	−	0.377337i
$303$	9.32731e14	−	3.03063e14i	1.20531	−	0.391630i
$304$	−9.24305e13	+	1.27220e14i	−0.117105	+	0.161181i
$305$	−2.29865e14	−	3.16383e14i	−0.285545	−	0.393019i
$306$	−2.86467e13	+	8.81656e13i	−0.0348937	+	0.107392i
$307$		−	1.26988e15i		−	1.51681i	−0.651783	−	0.758405i	$-0.725979\pi$
$307$		−	1.26988e15i		−	1.51681i	0.651783	−	0.758405i	$-0.274021\pi$
$308$	5.67170e13	−	1.32050e14i	0.0664369	−	0.154680i
$309$	4.18704e14			0.481012
$310$	3.14213e14	+	1.02094e14i	0.354042	+	0.115035i
$311$	7.06857e14	−	5.13562e14i	0.781213	−	0.567584i	−0.124130	−	0.992266i	$-0.539614\pi$
$311$	7.06857e14	−	5.13562e14i	0.781213	−	0.567584i	0.905343	+	0.424682i	$0.139614\pi$
$312$	2.23979e13	+	1.62730e13i	0.0242817	+	0.0176417i
$313$	−3.63311e14	−	1.11816e15i	−0.386378	−	1.18915i	−0.935476	−	0.353391i	$-0.885029\pi$
$313$	−3.63311e14	−	1.11816e15i	−0.386378	−	1.18915i	0.549098	−	0.835758i	$-0.314971\pi$
$314$	1.02458e15	−	3.32905e14i	1.06897	−	0.347330i
$315$	1.17180e14	−	1.61284e14i	0.119947	−	0.165093i
$316$	1.70665e14	+	2.34900e14i	0.171404	+	0.235918i
$317$	1.75058e14	−	5.38772e14i	0.172514	−	0.530945i	−0.826997	−	0.562207i	$-0.809953\pi$
$317$	1.75058e14	−	5.38772e14i	0.172514	−	0.530945i	0.999511	+	0.0312617i	$0.00995253\pi$
$318$		−	4.66639e14i		−	0.451251i
$319$	2.87752e14	+	1.27108e15i	0.273070	+	1.20622i
$320$	−4.70723e13			−0.0438395
$321$	−1.48902e15	−	4.83813e14i	−1.36104	−	0.442229i
$322$	−1.45187e14	+	1.05485e14i	−0.130255	+	0.0946356i
$323$	6.76517e13	+	4.91518e13i	0.0595749	+	0.0432837i
$324$	−4.61908e13	−	1.42161e14i	−0.0399287	−	0.122888i
$325$	5.05168e13	−	1.64139e13i	0.0428683	−	0.0139287i
$326$	−4.40661e14	+	6.06518e14i	−0.367113	+	0.505287i
$327$	3.68089e14	+	5.06631e14i	0.301069	+	0.414386i
$328$	6.17699e13	−	1.90108e14i	0.0496060	−	0.152672i
$329$			3.65062e13i			0.0287867i
$330$	5.26791e14	+	4.83511e13i	0.407901	+	0.0374388i
$331$	−1.48833e15			−1.13170			−0.565849	−	0.824509i	$-0.691452\pi$
$331$	−1.48833e15			−1.13170			−0.565849	+	0.824509i	$0.691452\pi$
$332$	8.82691e14	+	2.86804e14i	0.659144	+	0.214169i
$333$	−2.16269e15	+	1.57128e15i	−1.58609	+	1.15236i
$334$	−1.15783e15	−	8.41213e14i	−0.834000	−	0.605936i
$335$	2.98738e14	+	9.19420e14i	0.211359	+	0.650497i
$336$	−1.90259e14	+	6.18189e13i	−0.132224	+	0.0429621i
$337$	6.74345e14	−	9.28157e14i	0.460366	−	0.633639i	−0.514219	−	0.857659i	$-0.671918\pi$
$337$	6.74345e14	−	9.28157e14i	0.460366	−	0.633639i	0.974585	+	0.224020i	$0.0719181\pi$
$338$	6.18095e14	+	8.50735e14i	0.414529	+	0.570550i
$339$	9.23400e13	−	2.84193e14i	0.0608403	−	0.187247i
$340$			2.50316e13i			0.0162038i
$341$	1.20692e15	+	2.02818e15i	0.767630	+	1.28997i
$342$	−1.55828e15			−0.973843
$343$	9.83756e14	+	3.19642e14i	0.604119	+	0.196290i
$344$	−6.78972e14	+	4.93302e14i	−0.409733	+	0.297689i
$345$	−5.34426e14	−	3.88283e14i	−0.316937	−	0.230268i
$346$	2.42183e14	+	7.45363e14i	0.141152	+	0.434421i
$347$	−1.86497e15	+	6.05966e14i	−1.06831	+	0.347114i	−0.789828	−	0.613329i	$-0.789830\pi$
$347$	−1.86497e15	+	6.05966e14i	−1.06831	+	0.347114i	−0.278478	+	0.960443i	$0.589830\pi$
$348$	1.06630e15	−	1.46764e15i	0.600351	−	0.826313i
$349$	1.07095e15	+	1.47404e15i	0.592677	+	0.815750i	0.995013	−	0.0997420i	$-0.0318018\pi$
$349$	1.07095e15	+	1.47404e15i	0.592677	+	0.815750i	−0.402336	+	0.915492i	$0.631802\pi$
$350$	−1.18605e14	+	3.65027e14i	−0.0645198	+	0.198572i
$351$			1.15597e14i			0.0618166i
$352$	−2.52840e14	−	2.21689e14i	−0.132920	−	0.116543i
$353$	−5.19563e14			−0.268528			−0.134264	−	0.990946i	$-0.542867\pi$
$353$	−5.19563e14			−0.268528			−0.134264	+	0.990946i	$0.542867\pi$
$354$	1.83601e15	+	5.96555e14i	0.932942	+	0.303131i
$355$	−7.04870e14	+	5.12118e14i	−0.352159	+	0.255859i
$356$	1.12974e15	+	8.20802e14i	0.554980	+	0.403216i
$357$	3.28735e13	+	1.01174e14i	0.0158795	+	0.0488720i
$358$	5.57792e14	−	1.81237e14i	0.264956	−	0.0860894i
$359$	1.94378e15	−	2.67539e15i	0.907990	−	1.24974i	−0.0598578	−	0.998207i	$-0.519065\pi$
$359$	1.94378e15	−	2.67539e15i	0.907990	−	1.24974i	0.967848	−	0.251535i	$-0.0809353\pi$
$360$	−2.74178e14	−	3.77374e14i	−0.125956	−	0.173363i
$361$	2.49586e14	−	7.68146e14i	0.112766	−	0.347057i
$362$		−	2.32039e15i		−	1.03112i
$363$	2.60185e15	+	2.74065e15i	1.13721	+	1.19788i
$364$	2.01250e13			0.00865222
$365$	−1.46426e15	−	4.75767e14i	−0.619243	−	0.201204i
$366$	−3.14606e15	+	2.28574e15i	−1.30882	+	0.950913i
$367$	2.00886e15	+	1.45953e15i	0.822156	+	0.597331i	0.917329	−	0.398130i	$-0.130341\pi$
$367$	2.00886e15	+	1.45953e15i	0.822156	+	0.597331i	−0.0951734	+	0.995461i	$0.530341\pi$
$368$	1.29758e14	+	3.99353e14i	0.0522452	+	0.160794i
$369$	1.88387e15	−	6.12105e14i	0.746263	−	0.242476i
$370$	−4.24279e14	+	5.83970e14i	−0.165364	+	0.227604i
$371$	−1.99382e14	−	2.74426e14i	−0.0764615	−	0.105240i
$372$	1.01521e15	−	3.12448e15i	0.383086	−	1.17902i
$373$			1.44012e15i			0.534745i	0.963593	+	0.267372i	$0.0861554\pi$
$373$			1.44012e15i			0.534745i	−0.963593	+	0.267372i	$0.913845\pi$
$374$	−1.17888e14	+	1.34453e14i	−0.0430763	+	0.0491292i
$375$	−3.02373e15			−1.08732
$376$	8.12368e13	+	2.63954e13i	0.0287492	+	0.00934118i
$377$	−1.47644e14	+	1.07270e14i	−0.0514243	+	0.0373620i
$378$	−6.75764e14	−	4.90972e14i	−0.231656	−	0.168308i
$379$	6.29413e14	+	1.93713e15i	0.212374	+	0.653619i	0.999330	+	0.0366097i	$0.0116558\pi$
$379$	6.29413e14	+	1.93713e15i	0.212374	+	0.653619i	−0.786956	+	0.617009i	$0.788344\pi$
$380$	−4.00174e14	+	1.30024e14i	−0.132907	+	0.0431840i
$381$	4.24898e15	−	5.84822e15i	1.38910	−	1.91194i
$382$	−1.46767e15	−	2.02007e15i	−0.472332	−	0.650109i
$383$	−1.18596e15	+	3.65000e15i	−0.375730	+	1.15638i	0.567254	+	0.823543i	$0.308006\pi$
$383$	−1.18596e15	+	3.65000e15i	−0.375730	+	1.15638i	−0.942985	+	0.332836i	$0.891994\pi$
$384$			4.68079e14i			0.145993i
$385$	3.30460e14	−	1.96649e14i	0.101474	−	0.0603847i
$386$	−8.46104e14			−0.255800
$387$	−7.90951e15	−	2.56996e15i	−2.35442	−	0.764997i
$388$	−1.78925e15	+	1.29996e15i	−0.524421	+	0.381014i
$389$	−9.33881e14	−	6.78504e14i	−0.269522	−	0.195819i	0.444812	−	0.895624i	$-0.353270\pi$
$389$	−9.33881e14	−	6.78504e14i	−0.269522	−	0.195819i	−0.714334	+	0.699805i	$0.753270\pi$
$390$	2.28917e13	+	7.04533e13i	0.00650563	+	0.0200223i
$391$	2.12364e14	−	6.90013e13i	0.0594321	−	0.0193106i
$392$	6.68557e14	−	9.20189e14i	0.184256	−	0.253607i
$393$	1.11620e15	+	1.53631e15i	0.302960	+	0.416989i
$394$	8.58035e14	−	2.64076e15i	0.229365	−	0.705914i
$395$			7.76910e14i			0.204545i
$396$	3.04562e14	−	3.31824e15i	0.0789777	−	0.860473i
$397$	−1.23343e15			−0.315045			−0.157523	−	0.987515i	$-0.550351\pi$
$397$	−1.23343e15			−0.315045			−0.157523	+	0.987515i	$0.550351\pi$
$398$	2.44752e15	+	7.95247e14i	0.615783	+	0.200080i
$399$	−1.44668e15	+	1.05108e15i	−0.358539	+	0.260494i
$400$	7.26535e14	+	5.27858e14i	0.177377	+	0.128872i
$401$	−1.24434e15	−	3.82970e15i	−0.299278	−	0.921082i	−0.981751	−	0.190171i	$-0.939096\pi$
$401$	−1.24434e15	−	3.82970e15i	−0.299278	−	0.921082i	0.682473	−	0.730911i	$-0.260904\pi$
$402$	9.14256e15	−	2.97060e15i	2.16626	−	0.703862i
$403$	−1.94262e14	+	2.67378e14i	−0.0453479	+	0.0624160i
$404$	−9.80471e14	−	1.34950e15i	−0.225500	−	0.310374i
$405$	1.23595e14	−	3.80386e14i	0.0280073	−	0.0861975i
$406$		−	1.31871e15i		−	0.294437i
$407$	−5.02916e15	+	1.13852e15i	−1.10644	+	0.250481i
$408$	2.48910e14			0.0539613
$409$	5.40230e15	+	1.75531e15i	1.15409	+	0.374986i	0.822682	−	0.568502i	$-0.192477\pi$
$409$	5.40230e15	+	1.75531e15i	1.15409	+	0.374986i	0.331406	+	0.943488i	$0.392477\pi$
$410$	4.32711e14	−	3.14383e14i	0.0910950	−	0.0661844i
$411$	−5.31680e15	−	3.86288e15i	−1.10306	−	0.801420i
$412$	−2.20067e14	−	6.77297e14i	−0.0449958	−	0.138483i
$413$	1.33463e15	−	4.33647e14i	0.268943	−	0.0873849i
$414$	−2.44579e15	+	3.36633e15i	−0.485754	+	0.668583i
$415$	1.45971e15	+	2.00912e15i	0.285744	+	0.393293i
$416$	1.45512e13	−	4.47839e13i	0.00280762	−	0.00864096i
$417$		−	3.10816e15i		−	0.591136i
$418$	−2.76181e15	−	1.18623e15i	−0.517769	−	0.222389i
$419$	1.99139e15			0.368021			0.184010	−	0.982924i	$-0.441092\pi$
$419$	1.99139e15			0.368021			0.184010	+	0.982924i	$0.441092\pi$
$420$	−5.09086e14	−	1.65412e14i	−0.0927460	−	0.0301350i
$421$	7.15656e15	−	5.19955e15i	1.28532	−	0.933841i	0.285622	−	0.958342i	$-0.407800\pi$
$421$	7.15656e15	−	5.19955e15i	1.28532	−	0.933841i	0.999700	+	0.0245012i	$0.00779975\pi$
$422$	−3.49420e15	−	2.53869e15i	−0.618690	−	0.449505i
$423$	2.61564e14	+	8.05010e14i	0.0456599	+	0.140527i
$424$	−7.54837e14	+	2.45261e14i	−0.129915	+	0.0422118i
$425$	2.80700e14	−	3.86350e14i	0.0476330	−	0.0655612i
$426$	5.09242e15	+	7.00911e15i	0.852052	+	1.17275i
$427$	−8.73529e14	+	2.68845e15i	−0.144115	+	0.443541i
$428$			2.66294e15i			0.433210i
$429$	−2.08844e14	+	4.86236e14i	−0.0335027	+	0.0780015i
$430$	−2.24564e15			−0.355246
$431$	−8.48409e15	−	2.75665e15i	−1.32355	−	0.430049i	−0.439840	−	0.898076i	$-0.644965\pi$
$431$	−8.48409e15	−	2.75665e15i	−1.32355	−	0.430049i	−0.883714	+	0.468027i	$0.844965\pi$
$432$	−1.58116e15	+	1.14878e15i	−0.243261	+	0.176739i
$433$	7.71807e15	+	5.60751e15i	1.17107	+	0.850829i	0.991136	−	0.132850i	$-0.0424129\pi$
$433$	7.71807e15	+	5.60751e15i	1.17107	+	0.850829i	0.179930	+	0.983679i	$0.442413\pi$
$434$	−7.37973e14	−	2.27125e15i	−0.110434	−	0.339880i
$435$	4.61651e15	−	1.50000e15i	0.681363	−	0.221388i
$436$	6.26064e14	−	8.61703e14i	0.0911380	−	0.125441i
$437$	2.20621e15	+	3.03658e15i	0.316780	+	0.436010i
$438$	−4.73094e15	+	1.45603e16i	−0.670044	+	2.06218i
$439$		−	2.81649e15i		−	0.393478i	−0.980456	−	0.196739i	$-0.936965\pi$
$439$		−	2.81649e15i		−	0.393478i	0.980456	−	0.196739i	$-0.0630352\pi$
$440$	−1.98664e14	−	8.77553e14i	−0.0273781	−	0.120936i
$441$	1.12712e16			1.53228
$442$	−2.38148e13	−	7.73788e12i	−0.00319384	−	0.00103774i
$443$	−5.92081e15	+	4.30172e15i	−0.783355	+	0.569141i	−0.905984	−	0.423312i	$-0.860867\pi$
$443$	−5.92081e15	+	4.30172e15i	−0.783355	+	0.569141i	0.122629	+	0.992453i	$0.460867\pi$
$444$	5.80690e15	+	4.21896e15i	0.757960	+	0.550690i
$445$	1.15464e15	+	3.55362e15i	0.148692	+	0.457626i
$446$	−4.04386e15	+	1.31393e15i	−0.513792	+	0.166941i
$447$	−9.23603e15	+	1.27123e16i	−1.15782	+	1.59360i
$448$	1.99997e14	+	2.75273e14i	0.0247375	+	0.0340482i
$449$	−1.92283e15	+	5.91788e15i	−0.234673	+	0.722250i	0.762491	+	0.646999i	$0.223976\pi$
$449$	−1.92283e15	+	5.91788e15i	−0.234673	+	0.722250i	−0.997165	+	0.0752518i	$0.976024\pi$
$450$			8.89913e15i			1.07170i
$451$	3.80482e15	+	3.49222e14i	0.452142	+	0.0414995i
$452$	−5.08245e14			−0.0595995
$453$	−7.61675e15	−	2.47483e15i	−0.881415	−	0.286389i
$454$	−1.17283e15	+	8.52114e14i	−0.133937	+	0.0973112i
$455$	4.35651e13	+	3.16519e13i	0.00490988	+	0.00356723i
$456$	1.29294e15	+	3.97926e15i	0.143810	+	0.442602i
$457$	−7.17258e15	+	2.33051e15i	−0.787369	+	0.255832i	−0.674983	−	0.737833i	$-0.735849\pi$
$457$	−7.17258e15	+	2.33051e15i	−0.787369	+	0.255832i	−0.112385	+	0.993665i	$0.535849\pi$
$458$	−3.09613e14	+	4.26146e14i	−0.0335449	+	0.0461706i
$459$	6.10886e14	+	8.40812e14i	0.0653257	+	0.0899131i
$460$	−3.47199e14	+	1.06857e15i	−0.0366464	+	0.112786i
$461$		−	1.86103e16i		−	1.93887i	−0.245358	−	0.969433i	$-0.578905\pi$
$461$		−	1.86103e16i		−	1.93887i	0.245358	−	0.969433i	$-0.421095\pi$
$462$	−1.95544e15	−	3.28604e15i	−0.201091	−	0.337925i
$463$	1.69597e16			1.72160			0.860800	−	0.508943i	$-0.169964\pi$
$463$	1.69597e16			1.72160			0.860800	+	0.508943i	$0.169964\pi$
$464$	−2.93450e15	−	9.53478e14i	−0.294054	−	0.0955439i
$465$	7.11172e15	−	5.16697e15i	0.703489	−	0.511114i
$466$	−2.46395e15	−	1.79017e15i	−0.240612	−	0.174815i
$467$	−7.91408e14	−	2.43570e15i	−0.0762955	−	0.234813i	0.905634	−	0.424060i	$-0.139395\pi$
$467$	−7.91408e14	−	2.43570e15i	−0.0762955	−	0.234813i	−0.981930	+	0.189247i	$0.939395\pi$
$468$	4.43783e14	−	1.44194e14i	0.0422373	−	0.0137237i
$469$	4.10739e15	−	5.65334e15i	0.385948	−	0.531213i
$470$	1.34342e14	+	1.84905e14i	0.0124630	+	0.0171539i
$471$	8.85767e15	−	2.72611e16i	0.811324	−	2.49700i
$472$		−	3.28348e15i		−	0.296949i
$473$	−1.20620e16	−	1.05759e16i	−1.07709	−	0.944390i
$474$	7.72546e15			0.681168
$475$	7.63453e15	+	2.48061e15i	0.664692	+	0.215971i
$476$	1.46382e14	−	1.06353e14i	0.0125848	−	0.00914337i
$477$	−6.36288e15	−	4.62290e15i	−0.540186	−	0.392468i
$478$	−4.80531e15	−	1.47892e16i	−0.402860	−	1.23988i
$479$	−1.96054e16	+	6.37020e15i	−1.62317	+	0.527399i	−0.972687	−	0.232122i	$-0.925433\pi$
$479$	−1.96054e16	+	6.37020e15i	−1.62317	+	0.527399i	−0.650482	+	0.759522i	$0.725433\pi$
$480$	−7.36178e14	+	1.01326e15i	−0.0601915	+	0.0828465i
$481$	−4.24426e14	−	5.84172e14i	−0.0342714	−	0.0471705i
$482$	4.82829e14	−	1.48600e15i	0.0385045	−	0.118505i
$483$			4.77497e15i			0.376086i
$484$	3.06578e15	−	5.64922e15i	0.238490	−	0.439457i
$485$	−5.91777e15			−0.454682
$486$	6.87570e15	+	2.23405e15i	0.521794	+	0.169541i
$487$	−1.43615e15	+	1.04343e15i	−0.107653	+	0.0782146i	−0.640309	−	0.768117i	$-0.721194\pi$
$487$	−1.43615e15	+	1.04343e15i	−0.107653	+	0.0782146i	0.532656	+	0.846332i	$0.321194\pi$
$488$	5.35097e15	+	3.88771e15i	0.396199	+	0.287855i
$489$	6.16407e15	+	1.89711e16i	0.450832	+	1.38752i
$490$	2.89448e15	−	9.40475e14i	0.209120	−	0.0679471i
$491$	−7.56260e15	+	1.04090e16i	−0.539737	+	0.742884i	−0.988575	−	0.150729i	$-0.951838\pi$
$491$	−7.56260e15	+	1.04090e16i	−0.539737	+	0.742884i	0.448838	+	0.893613i	$0.351838\pi$
$492$	−3.12617e15	−	4.30280e15i	−0.220405	−	0.303362i
$493$	−5.07031e14	+	1.56048e15i	−0.0353145	+	0.108687i
$494$		−	4.20913e14i		−	0.0289622i
$495$	5.87811e15	−	6.70408e15i	0.399583	−	0.455731i
$496$	−5.58776e15			−0.375273
$497$	5.98960e15	+	1.94614e15i	0.397429	+	0.129133i
$498$	1.99783e16	−	1.45151e16i	1.30973	−	0.951577i
$499$	9.87065e15	+	7.17144e15i	0.639355	+	0.464519i	0.859629	−	0.510919i	$-0.170695\pi$
$499$	9.87065e15	+	7.17144e15i	0.639355	+	0.464519i	−0.220273	+	0.975438i	$0.570695\pi$
$500$	1.58925e15	+	4.89120e15i	0.101712	+	0.313037i
$501$	−3.62153e16	+	1.17671e16i	−2.29016	+	0.744119i
$502$	2.69223e15	−	3.70553e15i	0.168225	−	0.231541i
$503$	−1.10218e16	−	1.51702e16i	−0.680524	−	0.936661i	0.319416	−	0.947615i	$-0.396513\pi$
$503$	−1.10218e16	−	1.51702e16i	−0.680524	−	0.936661i	−0.999940	+	0.0109539i	$0.996513\pi$
$504$	−1.04193e15	+	3.20672e15i	−0.0635702	+	0.195649i
$505$		−	4.46335e15i		−	0.269100i
$506$	−6.89738e15	+	4.10446e15i	−0.410943	+	0.244542i
$507$	2.79792e16			1.64736
$508$	−1.16933e16	−	3.79939e15i	−0.680387	−	0.221071i
$509$	4.35537e15	−	3.16436e15i	0.250449	−	0.181962i	−0.455477	−	0.890248i	$-0.650531\pi$
$509$	4.35537e15	−	3.16436e15i	0.250449	−	0.181962i	0.705926	+	0.708286i	$0.250531\pi$
$510$	5.38823e14	+	3.91478e14i	0.0306214	+	0.0222477i
$511$	3.43902e15	+	1.05842e16i	0.193156	+	0.594474i
$512$	7.57166e14	−	2.46018e14i	0.0420312	−	0.0136568i
$513$	−1.02686e16	+	1.41336e16i	−0.563389	+	0.775439i
$514$	−1.23448e16	−	1.69912e16i	−0.669430	−	0.921392i
$515$	5.88844e14	−	1.81228e15i	0.0315614	−	0.0971362i
$516$			2.23302e16i			1.18303i
$517$	−1.49229e14	+	1.62587e15i	−0.00781466	+	0.0851418i
$518$	5.21762e15			0.270081
$519$	1.98320e16	+	6.44381e15i	1.01476	+	0.329715i
$520$	1.01934e14	−	7.40593e13i	0.00515583	−	0.00374593i
$521$	−1.99717e16	−	1.45103e16i	−0.998592	−	0.725519i	−0.0368058	−	0.999322i	$-0.511718\pi$
$521$	−1.99717e16	−	1.45103e16i	−0.998592	−	0.725519i	−0.961786	+	0.273803i	$0.911718\pi$
$522$	−9.44843e15	−	2.90793e16i	−0.467021	−	1.43734i
$523$	2.98859e15	−	9.71051e14i	0.146035	−	0.0474495i	−0.235088	−	0.971974i	$-0.575538\pi$
$523$	2.98859e15	−	9.71051e14i	0.146035	−	0.0474495i	0.381122	+	0.924525i	$0.375538\pi$
$524$	1.89848e15	−	2.61304e15i	0.0917105	−	0.126229i
$525$	6.00257e15	+	8.26182e15i	0.286669	+	0.394566i
$526$	−7.65765e15	+	2.35678e16i	−0.361561	+	1.11277i
$527$			2.97141e15i			0.138707i
$528$	−8.72624e15	+	1.97548e15i	−0.402739	+	0.0911737i
$529$	−1.18920e16			−0.542651
$530$	−2.01975e15	−	6.56258e14i	−0.0911262	−	0.0296087i
$531$	2.63233e16	−	1.91250e16i	1.17428	−	0.853168i
$532$	2.46059e15	+	1.78773e15i	0.108535	+	0.0788553i
$533$	1.65338e14	+	5.08858e14i	0.00721124	+	0.0221939i
$534$	3.53366e16	−	1.14816e16i	1.52397	−	0.495169i
$535$	−4.18818e15	+	5.76453e15i	−0.178609	+	0.245834i
$536$	−9.61050e15	−	1.32277e16i	−0.405282	−	0.557823i
$537$	4.82222e15	−	1.48413e16i	0.201095	−	0.618907i
$538$			6.10862e15i			0.251912i
$539$	1.99764e16	+	8.58011e15i	0.814674	+	0.349913i
$540$	−5.22953e15			−0.210911
$541$	3.26755e16	+	1.06169e16i	1.30328	+	0.423463i	0.876723	−	0.480996i	$-0.159725\pi$
$541$	3.26755e16	+	1.06169e16i	1.30328	+	0.423463i	0.426561	+	0.904459i	$0.359725\pi$
$542$	9.97402e15	−	7.24655e15i	0.393436	−	0.285848i
$543$	−4.99479e16	−	3.62893e16i	−1.94858	−	1.41573i
$544$	−1.30825e14	−	4.02638e14i	−0.00504775	−	0.0155354i
$545$	2.71051e15	−	8.80699e14i	0.103436	−	0.0336084i
$546$	3.14741e14	−	4.33204e14i	0.0118795	−	0.0163507i
$547$	−5.45185e15	−	7.50383e15i	−0.203526	−	0.280129i	0.695037	−	0.718974i	$-0.255388\pi$
$547$	−5.45185e15	−	7.50383e15i	−0.203526	−	0.280129i	−0.898563	+	0.438844i	$0.855388\pi$
$548$	−3.45415e15	+	1.06308e16i	−0.127543	+	0.392538i
$549$			6.55426e16i			2.39381i
$550$	−6.77442e15	+	1.57723e16i	−0.244735	+	0.569796i
$551$	−2.75807e16			−0.985589
$552$	1.06257e16	+	3.45249e15i	0.375597	+	0.122039i
$553$	4.54327e15	−	3.30088e15i	0.158861	−	0.115419i
$554$	2.34539e16	+	1.70402e16i	0.811253	+	0.589410i
$555$	5.93491e15	+	1.82658e16i	0.203075	+	0.625000i
$556$	−5.02778e15	+	1.63362e15i	−0.170187	+	0.0552972i
$557$	−1.44683e16	+	1.99138e16i	−0.484490	+	0.666843i	−0.979360	−	0.202124i	$-0.935216\pi$
$557$	−1.44683e16	+	1.99138e16i	−0.484490	+	0.666843i	0.494870	+	0.868967i	$0.335216\pi$
$558$	−3.25466e16	−	4.47965e16i	−1.07820	−	1.48402i
$559$	6.94181e14	−	2.13647e15i	0.0227511	−	0.0700206i
$560$			9.10438e14i			0.0295204i
$561$	1.05050e15	+	4.64035e15i	0.0336993	+	0.148859i
$562$	−1.63705e16			−0.519570
$563$	3.42050e16	+	1.11139e16i	1.07409	+	0.348991i	0.792077	−	0.610421i	$-0.209000\pi$
$563$	3.42050e16	+	1.11139e16i	1.07409	+	0.348991i	0.282008	+	0.959412i	$0.409000\pi$
$564$	1.83867e15	−	1.33587e15i	0.0571253	−	0.0415039i
$565$	−1.10021e15	−	7.99351e14i	−0.0338209	−	0.0245723i
$566$	6.03869e15	+	1.85852e16i	0.183673	+	0.565286i
$567$	−2.74957e15	+	8.93389e14i	−0.0827497	+	0.0268870i
$568$	8.66144e15	−	1.19214e16i	0.257929	−	0.355009i
$569$	1.44488e16	+	1.98870e16i	0.425752	+	0.585997i	0.966972	−	0.254884i	$-0.0820372\pi$
$569$	1.44488e16	+	1.98870e16i	0.425752	+	0.585997i	−0.541220	+	0.840881i	$0.682037\pi$
$570$	−3.45958e15	+	1.06475e16i	−0.100873	+	0.310455i
$571$			3.11031e16i			0.897403i	0.893682	+	0.448701i	$0.148113\pi$
$571$			3.11031e16i			0.897403i	−0.893682	+	0.448701i	$0.851887\pi$
$572$	8.96304e14	+	8.22664e13i	0.0255905	+	0.00234880i
$573$	−6.64366e16			−1.87707
$574$	−3.67694e15	−	1.19471e15i	−0.102805	−	0.0334034i
$575$	1.73415e16	−	1.25994e16i	0.479822	−	0.348611i
$576$	6.38251e15	+	4.63716e15i	0.174766	+	0.126975i
$577$	1.28427e16	+	3.95257e16i	0.348018	+	1.07109i	0.959948	+	0.280177i	$0.0903930\pi$
$577$	1.28427e16	+	3.95257e16i	0.348018	+	1.07109i	−0.611931	+	0.790911i	$0.709607\pi$
$578$	2.48619e16	−	8.07812e15i	0.666756	−	0.216642i
$579$	−1.32325e16	+	1.82130e16i	−0.351213	+	0.483403i
$580$	−4.85280e15	−	6.67931e15i	−0.127475	−	0.175454i
$581$	5.54715e15	−	1.70724e16i	0.144216	−	0.443851i
$582$			5.88453e16i			1.51417i
$583$	−7.75805e15	−	1.30371e16i	−0.197579	−	0.332024i
$584$	2.60394e16			0.656378
$585$	1.18745e15	+	3.85827e14i	0.0296265	+	0.00962625i
$586$	−1.77245e15	+	1.28776e15i	−0.0437711	+	0.0318016i
$587$	1.75546e16	+	1.27542e16i	0.429105	+	0.311763i	0.781291	−	0.624167i	$-0.214562\pi$
$587$	1.75546e16	+	1.27542e16i	0.429105	+	0.311763i	−0.352186	+	0.935930i	$0.614562\pi$
$588$	−9.35192e15	−	2.87823e16i	−0.226275	−	0.696403i
$589$	−4.75030e16	+	1.54347e16i	−1.13770	+	0.369662i
$590$	5.16414e15	−	7.10783e15i	0.122429	−	0.168510i
$591$	−4.34250e16	−	5.97694e16i	−1.01910	−	1.40267i
$592$	3.77255e15	−	1.16107e16i	0.0876404	−	0.269729i
$593$		−	4.46367e16i		−	1.02651i	−0.858236	−	0.513256i	$-0.828439\pi$
$593$		−	4.46367e16i		−	1.02651i	0.858236	−	0.513256i	$-0.171561\pi$
$594$	−2.80894e16	−	2.46287e16i	−0.639475	−	0.560689i
$595$	4.84144e14			0.0109112
$596$	2.54179e16	+	8.25876e15i	0.567102	+	0.184263i
$597$	5.53957e16	−	4.02473e16i	1.22357	−	0.888978i
$598$	−9.09294e14	−	6.60641e14i	−0.0198837	−	0.0144464i
$599$	9.91535e15	+	3.05163e16i	0.214658	+	0.660649i	0.999178	+	0.0405454i	$0.0129095\pi$
$599$	9.91535e15	+	3.05163e16i	0.214658	+	0.660649i	−0.784520	+	0.620104i	$0.787090\pi$
$600$	2.27250e16	−	7.38380e15i	0.487076	−	0.158261i
$601$	3.70136e16	−	5.09449e16i	0.785443	−	1.08107i	−0.209218	−	0.977869i	$-0.567092\pi$
$601$	3.70136e16	−	5.09449e16i	0.785443	−	1.08107i	0.994661	−	0.103200i	$-0.0329082\pi$
$602$	9.54110e15	+	1.31322e16i	0.200456	+	0.275904i
$603$	5.00678e16	−	1.54093e17i	1.04149	−	3.20537i
$604$			1.36216e16i			0.280548i
$605$	1.55215e16	−	7.40726e15i	0.316520	−	0.151052i
$606$	−4.43828e16			−0.896147
$607$	−1.50430e16	−	4.88778e15i	−0.300749	−	0.0977192i	0.154756	−	0.987953i	$-0.450541\pi$
$607$	−1.50430e16	−	4.88778e15i	−0.300749	−	0.0977192i	−0.455504	+	0.890234i	$0.650541\pi$
$608$	5.75731e15	−	4.18293e15i	0.113972	−	0.0828055i
$609$	−2.83861e16	−	2.06237e16i	−0.556419	−	0.404262i
$610$	5.46893e15	+	1.68316e16i	0.106151	+	0.326699i
$611$	−2.17445e14	+	7.06520e13i	−0.00417928	+	0.00135793i
$612$	2.46591e15	−	3.39403e15i	0.0469319	−	0.0645962i
$613$	−2.86752e16	−	3.94680e16i	−0.540435	−	0.743844i	0.448241	−	0.893913i	$-0.352051\pi$
$613$	−2.86752e16	−	3.94680e16i	−0.540435	−	0.743844i	−0.988676	+	0.150068i	$0.952051\pi$
$614$	−1.77586e16	+	5.46554e16i	−0.331435	+	1.02005i
$615$		−	1.42311e16i		−	0.263020i
$616$	−4.28775e15	+	4.89024e15i	−0.0784774	+	0.0895048i
$617$	6.47599e16			1.17380			0.586902	−	0.809658i	$-0.300347\pi$
$617$	6.47599e16			1.17380			0.586902	+	0.809658i	$0.300347\pi$
$618$	−1.80210e16	−	5.85536e15i	−0.323480	−	0.105105i
$619$	2.29737e15	−	1.66914e15i	0.0408401	−	0.0296721i	−0.567178	−	0.823595i	$-0.691965\pi$
$619$	2.29737e15	−	1.66914e15i	0.0408401	−	0.0296721i	0.608018	+	0.793923i	$0.291965\pi$
$620$	−1.20960e16	−	8.78824e15i	−0.212956	−	0.154722i
$621$	1.44155e16	+	4.43664e16i	0.251351	+	0.773579i
$622$	−3.76050e16	+	1.22186e16i	−0.649386	+	0.210998i
$623$	1.58754e16	−	2.18506e16i	0.271516	−	0.373710i
$624$	−7.36433e14	−	1.01361e15i	−0.0124746	−	0.0171698i
$625$	1.19009e16	−	3.66271e16i	0.199664	−	0.614501i
$626$			5.32061e16i			0.884128i
$627$	−6.87273e16	+	4.08979e16i	−1.13116	+	0.673126i
$628$	−4.87532e16			−0.794777
$629$	−6.17423e15	−	2.00613e15i	−0.0996963	−	0.0323933i
$630$	−7.29889e15	+	5.30296e15i	−0.116738	+	0.0848154i
$631$	−2.50610e16	−	1.82079e16i	−0.397028	−	0.288458i	0.371301	−	0.928513i	$-0.378912\pi$
$631$	−2.50610e16	−	1.82079e16i	−0.397028	−	0.288458i	−0.768330	+	0.640055i	$0.778912\pi$
$632$	−4.06044e15	−	1.24967e16i	−0.0637192	−	0.196108i
$633$	−1.09294e17	+	3.55117e16i	−1.69892	+	0.552013i
$634$	−1.50689e16	+	2.07406e16i	−0.232031	+	0.319364i
$635$	−1.93373e16	−	2.66155e16i	−0.294954	−	0.405969i
$636$	−6.52572e15	+	2.00841e16i	−0.0986020	+	0.303466i
$637$			3.04449e15i			0.0455700i
$638$	5.39058e15	−	5.87311e16i	0.0799302	−	0.870851i
$639$	1.46023e17			2.14494
$640$	2.02599e15	+	6.58283e14i	0.0294820	+	0.00957927i
$641$	2.06063e16	−	1.49713e16i	0.297065	−	0.215830i	−0.429262	−	0.903180i	$-0.641226\pi$
$641$	2.06063e16	−	1.49713e16i	0.297065	−	0.215830i	0.726326	+	0.687350i	$0.241226\pi$
$642$	5.73215e16	+	4.16465e16i	0.818667	+	0.594797i
$643$	1.57101e16	+	4.83508e16i	0.222287	+	0.684129i	0.998556	+	0.0537268i	$0.0171100\pi$
$643$	1.57101e16	+	4.83508e16i	0.222287	+	0.684129i	−0.776269	+	0.630402i	$0.782890\pi$
$644$	7.72400e15	−	2.50968e15i	0.108275	−	0.0351806i
$645$	−3.51202e16	+	4.83388e16i	−0.487752	+	0.671333i
$646$	−2.22436e15	−	3.06157e15i	−0.0306062	−	0.0421258i
$647$	−1.21526e16	+	3.74019e16i	−0.165670	+	0.509880i	−0.999085	−	0.0427677i	$-0.986382\pi$
$647$	−1.21526e16	+	3.74019e16i	−0.165670	+	0.509880i	0.833415	+	0.552648i	$0.186382\pi$
$648$			6.76454e15i			0.0913667i
$649$	6.12128e16	−	1.38576e16i	0.819170	−	0.185447i
$650$	−2.40378e15			−0.0318724
$651$	−6.04315e16	−	1.96354e16i	−0.793922	−	0.257961i
$652$	2.74479e16	−	1.99421e16i	0.357292	−	0.259588i
$653$	−8.24907e16	−	5.99330e16i	−1.06396	−	0.773014i	−0.0891447	−	0.996019i	$-0.528413\pi$
$653$	−8.24907e16	−	5.99330e16i	−1.06396	−	0.773014i	−0.974817	+	0.223005i	$0.928413\pi$
$654$	−8.75752e15	−	2.69529e16i	−0.111922	−	0.344460i
$655$	8.21939e15	−	2.67064e15i	0.104086	−	0.0338196i
$656$	−5.31714e15	+	7.31842e15i	−0.0667199	+	0.0918321i
$657$	1.51670e17	+	2.08756e17i	1.88585	+	2.59565i
$658$	5.10522e14	−	1.57122e15i	0.00629012	−	0.0193590i
$659$		−	1.15685e17i		−	1.41242i	−0.708001	−	0.706211i	$-0.750403\pi$
$659$		−	1.15685e17i		−	1.41242i	0.708001	−	0.706211i	$-0.249597\pi$
$660$	−2.19969e16	−	9.44795e15i	−0.266132	−	0.114307i
$661$	−7.83616e15			−0.0939495			−0.0469747	−	0.998896i	$-0.514958\pi$
$661$	−7.83616e15			−0.0939495			−0.0469747	+	0.998896i	$0.514958\pi$
$662$	6.40575e16	+	2.08135e16i	0.761066	+	0.247285i
$663$	−5.39010e14	+	3.91613e14i	−0.00634622	+	0.00461080i
$664$	−3.39801e16	−	2.46880e16i	−0.396475	−	0.288056i
$665$	2.51484e15	+	7.73987e15i	0.0290790	+	0.0894961i
$666$	1.15056e17	−	3.73838e16i	1.31845	−	0.428389i
$667$	−4.32890e16	+	5.95823e16i	−0.491613	+	0.676647i
$668$	3.80689e16	+	5.23974e16i	0.428462	+	0.589727i
$669$	−3.49600e16	+	1.07596e17i	−0.389955	+	1.20016i
$670$		−	4.37495e16i		−	0.483642i
$671$	−4.98940e16	+	1.16164e17i	−0.546654	+	1.27273i
$672$	9.05324e15			0.0983079
$673$	−7.26572e16	−	2.36078e16i	−0.781967	−	0.254076i	−0.109287	−	0.994010i	$-0.534857\pi$
$673$	−7.26572e16	−	2.36078e16i	−0.781967	−	0.254076i	−0.672680	+	0.739934i	$0.734857\pi$
$674$	−4.20036e16	+	3.05174e16i	−0.448051	+	0.325528i
$675$	8.07149e16	+	5.86428e16i	0.853358	+	0.620001i
$676$	−1.47056e16	−	4.52593e16i	−0.154100	−	0.474272i
$677$	−1.38363e16	+	4.49570e15i	−0.143711	+	0.0466944i	−0.379989	−	0.924991i	$-0.624072\pi$
$677$	−1.38363e16	+	4.49570e15i	−0.143711	+	0.0466944i	0.236278	+	0.971685i	$0.424072\pi$
$678$	−7.94861e15	+	1.09403e16i	−0.0818301	+	0.112629i
$679$	2.51430e16	+	3.46063e16i	0.256565	+	0.353132i
$680$	3.50055e14	−	1.07736e15i	0.00354065	−	0.0108970i
$681$			3.85725e16i			0.386719i
$682$	−2.35826e16	−	1.04171e17i	−0.234361	−	1.03524i
$683$	1.56197e17			1.53868			0.769339	−	0.638841i	$-0.220586\pi$
$683$	1.56197e17			1.53868			0.769339	+	0.638841i	$0.220586\pi$
$684$	6.70682e16	+	2.17918e16i	0.654908	+	0.212793i
$685$	−2.41970e16	+	1.75802e16i	−0.234217	+	0.170169i
$686$	−3.78707e16	−	2.75147e16i	−0.363378	−	0.264010i
$687$	4.33094e15	+	1.33293e16i	0.0411947	+	0.126784i
$688$	3.61215e16	−	1.17366e16i	0.340592	−	0.110665i
$689$	1.24871e15	−	1.71870e15i	0.0116720	−	0.0160652i
$690$	1.75717e16	+	2.41854e16i	0.162824	+	0.224108i
$691$	−3.37390e16	+	1.03838e17i	−0.309930	+	0.953866i	0.667862	+	0.744286i	$0.267210\pi$
$691$	−3.37390e16	+	1.03838e17i	−0.309930	+	0.953866i	−0.977791	+	0.209580i	$0.932790\pi$
$692$		−	3.54672e16i		−	0.322991i
$693$	−6.41791e16	−	5.89062e15i	−0.579421	−	0.0531816i
$694$	8.87424e16			0.794281
$695$	−1.34531e16	−	4.37117e15i	−0.119375	−	0.0387872i
$696$	−6.64179e16	+	4.82554e16i	−0.584291	+	0.424513i
$697$	3.89172e15	+	2.82750e15i	0.0339426	+	0.0246607i
$698$	−2.54800e16	−	7.84193e16i	−0.220327	−	0.678095i
$699$	−7.70690e16	+	2.50413e16i	−0.660719	+	0.214681i
$700$	1.02095e16	−	1.40521e16i	0.0867790	−	0.119441i
$701$	−2.19654e16	−	3.02328e16i	−0.185111	−	0.254783i	0.706369	−	0.707844i	$-0.250332\pi$
$701$	−2.19654e16	−	3.02328e16i	−0.185111	−	0.254783i	−0.891480	+	0.453061i	$0.850332\pi$
$702$	1.61657e15	−	4.97530e15i	0.0135074	−	0.0415716i
$703$		−	1.09126e17i		−	0.904060i
$704$	7.78199e15	+	1.30773e16i	0.0639226	+	0.107419i
$705$	6.08122e15			0.0495286
$706$	2.23619e16	+	7.26583e15i	0.180585	+	0.0586755i
$707$	−2.61011e16	+	1.89636e16i	−0.208998	+	0.151846i
$708$	−7.06790e16	−	5.13513e16i	−0.561166	−	0.407711i
$709$	−4.34990e16	−	1.33876e17i	−0.342454	−	1.05396i	−0.962933	−	0.269741i	$-0.913062\pi$
$709$	−4.34990e16	−	1.33876e17i	−0.342454	−	1.05396i	0.620479	−	0.784223i	$-0.286938\pi$
$710$	3.74993e16	−	1.21843e16i	0.292734	−	0.0951149i
$711$	7.65346e16	−	1.05341e17i	0.592435	−	0.815416i
$712$	−3.71452e16	−	5.11260e16i	−0.285117	−	0.392430i
$713$	−4.12146e16	+	1.26846e17i	−0.313700	+	0.965468i
$714$		−	4.81425e15i		−	0.0363362i
$715$	1.81087e15	+	1.58776e15i	0.0135535	+	0.0118836i
$716$	−2.65418e16			−0.196994
$717$	−3.93500e17	−	1.27856e17i	−2.89621	−	0.941035i
$718$	−1.21074e17	+	8.79656e16i	−0.883701	+	0.642046i
$719$	1.47267e17	+	1.06996e17i	1.06594	+	0.774452i	0.975178	−	0.221421i	$-0.0710695\pi$
$719$	1.47267e17	+	1.06996e17i	1.06594	+	0.774452i	0.0907628	+	0.995873i	$0.471069\pi$
$720$	6.52321e15	+	2.00764e16i	0.0468238	+	0.144109i
$721$	−1.30998e16	+	4.25638e15i	−0.0932508	+	0.0302990i
$722$	−2.14843e16	+	2.95706e16i	−0.151669	+	0.208755i
$723$	−2.44359e16	−	3.36332e16i	−0.171080	−	0.235471i
$724$	−3.24495e16	+	9.98692e16i	−0.225308	+	0.693426i
$725$			1.57510e17i			1.08462i
$726$	−7.36566e16	−	1.54343e17i	−0.503028	−	1.05406i
$727$	1.55067e17			1.05030			0.525148	−	0.851011i	$-0.324010\pi$
$727$	1.55067e17			1.05030			0.525148	+	0.851011i	$0.324010\pi$
$728$	−8.66178e14	−	2.81438e14i	−0.00581861	−	0.00189058i
$729$	1.87001e17	−	1.35864e17i	1.24589	−	0.905189i
$730$	5.63682e16	+	4.09539e16i	0.372475	+	0.270619i
$731$	−6.24117e15	−	1.92083e16i	−0.0409036	−	0.125888i
$732$	1.67371e17	−	5.43821e16i	1.08796	−	0.353500i
$733$	1.53237e17	−	2.10912e17i	0.987958	−	1.35981i	0.0555283	−	0.998457i	$-0.482316\pi$
$733$	1.53237e17	−	2.10912e17i	0.987958	−	1.35981i	0.932430	−	0.361351i	$-0.117684\pi$
$734$	−6.60506e16	−	9.09108e16i	−0.422377	−	0.581352i
$735$	2.50234e16	−	7.70141e16i	0.158717	−	0.488479i
$736$		−	1.90027e16i		−	0.119550i
$737$	2.06040e17	−	2.34992e17i	1.28572	−	1.46638i
$738$	−8.96414e16			−0.554844
$739$	4.72986e16	+	1.53682e16i	0.290390	+	0.0943534i	0.450590	−	0.892731i	$-0.351214\pi$
$739$	4.72986e16	+	1.53682e16i	0.290390	+	0.0943534i	−0.160200	+	0.987085i	$0.551214\pi$
$740$	2.64275e16	−	1.92007e16i	0.160940	−	0.116930i
$741$	−9.06044e15	−	6.58279e15i	−0.0547318	−	0.0397650i
$742$	4.74367e15	+	1.45995e16i	0.0284244	+	0.0874813i
$743$	−3.81547e16	+	1.23972e16i	−0.226785	+	0.0736870i	−0.420205	−	0.907429i	$-0.638042\pi$
$743$	−3.81547e16	+	1.23972e16i	−0.226785	+	0.0736870i	0.193420	+	0.981116i	$0.438042\pi$
$744$	−8.73887e16	+	1.20280e17i	−0.515250	+	0.709181i
$745$	4.20336e16	+	5.78543e16i	0.245844	+	0.338375i
$746$	2.01394e16	−	6.19828e16i	0.116846	−	0.359615i
$747$		−	4.16213e17i		−	2.39548i
$748$	6.95412e15	−	4.13823e15i	0.0397039	−	0.0236268i
$749$	5.15046e16			0.291713
$750$	1.30141e17	+	4.22854e16i	0.731218	+	0.237587i
$751$	−2.35866e17	+	1.71366e17i	−1.31469	+	0.955182i	−0.314713	+	0.949187i	$0.601908\pi$
$751$	−2.35866e17	+	1.71366e17i	−1.31469	+	0.955182i	−0.999982	+	0.00599447i	$0.998092\pi$
$752$	−3.12730e15	−	2.27211e15i	−0.0172927	−	0.0125639i
$753$	−3.76595e16	−	1.15904e17i	−0.206588	−	0.635812i
$754$	7.85472e15	−	2.55215e15i	0.0427467	−	0.0138892i
$755$	−2.14236e16	+	2.94871e16i	−0.115668	+	0.159203i
$756$	2.22188e16	+	3.05816e16i	0.119012	+	0.163806i
$757$	−2.33111e16	+	7.17441e16i	−0.123876	+	0.381251i	−0.993695	−	0.112121i	$-0.964236\pi$
$757$	−2.33111e16	+	7.17441e16i	−0.123876	+	0.381251i	0.869819	+	0.493371i	$0.164236\pi$
$758$		−	9.21761e16i		−	0.485963i
$759$	−1.95190e16	+	2.12662e17i	−0.102095	+	1.11234i
$760$	1.90418e16			0.0988156
$761$	1.63673e17	+	5.31807e16i	0.842695	+	0.273808i	0.698383	−	0.715724i	$-0.253903\pi$
$761$	1.63673e17	+	5.31807e16i	0.842695	+	0.273808i	0.144312	+	0.989532i	$0.453903\pi$
$762$	−2.64660e17	+	1.92287e17i	−1.35194	+	0.982245i
$763$	−1.66664e16	−	1.21089e16i	−0.0844687	−	0.0613701i
$764$	3.49185e16	+	1.07468e17i	0.175588	+	0.540406i
$765$	1.06760e16	−	3.46885e15i	0.0532649	−	0.0173068i
$766$	1.02087e17	−	1.40511e17i	0.505356	−	0.695563i
$767$	5.16593e15	+	7.11029e15i	0.0253733	+	0.0349233i
$768$	6.54585e15	−	2.01461e16i	0.0319006	−	0.0981799i
$769$			1.03619e17i			0.501052i	0.968110	+	0.250526i	$0.0806036\pi$
$769$			1.03619e17i			0.501052i	−0.968110	+	0.250526i	$0.919396\pi$
$770$	−1.69730e16	+	3.84242e15i	−0.0814356	+	0.0184357i
$771$	−5.58810e17			−2.66035
$772$	3.64162e16	+	1.18324e16i	0.172025	+	0.0558943i
$773$	−1.25040e17	+	9.08467e16i	−0.586100	+	0.425826i	−0.840918	−	0.541163i	$-0.817984\pi$
$773$	−1.25040e17	+	9.08467e16i	−0.586100	+	0.425826i	0.254818	+	0.966989i	$0.417984\pi$
$774$	3.04485e17	+	2.21221e17i	1.41619	+	1.02892i
$775$	8.81453e16	+	2.71283e17i	0.406807	+	1.25202i
$776$	9.51884e16	−	3.09286e16i	0.435927	−	0.141641i
$777$	8.16001e16	−	1.12313e17i	0.370821	−	0.510391i
$778$	3.07056e16	+	4.22626e16i	0.138465	+	0.190581i
$779$	−2.49873e16	+	7.69030e16i	−0.111814	+	0.344127i
$780$		−	3.35243e15i		−	0.0148865i
$781$	2.58802e17	+	1.11159e17i	1.14041	+	0.489822i
$782$	−1.01051e16			−0.0441875
$783$	−3.26011e17	−	1.05927e17i	−1.41469	−	0.459661i
$784$	−4.16430e16	+	3.02554e16i	−0.179327	+	0.130289i
$785$	−1.05537e17	−	7.66774e16i	−0.451012	−	0.327679i
$786$	−2.65564e16	−	8.17322e16i	−0.112625	−	0.346624i
$787$	−1.76251e17	+	5.72674e16i	−0.741794	+	0.241023i	−0.655446	−	0.755242i	$-0.727519\pi$
$787$	−1.76251e17	+	5.72674e16i	−0.741794	+	0.241023i	−0.0863473	+	0.996265i	$0.527519\pi$
$788$	−7.38595e16	+	1.01659e17i	−0.308496	+	0.424608i
$789$	3.87553e17	+	5.33421e17i	1.60646	+	2.21110i
$790$	1.08647e16	−	3.34381e16i	0.0446947	−	0.137556i
$791$			9.83012e15i			0.0401328i
$792$	−5.95123e16	+	1.38558e17i	−0.241133	+	0.561409i
$793$	−1.77040e16			−0.0711920
$794$	5.30869e16	+	1.72490e16i	0.211867	+	0.0688399i
$795$	−4.57140e16	+	3.32131e16i	−0.181070	+	0.131555i
$796$	−9.42198e16	−	6.84547e16i	−0.370394	−	0.269107i
$797$	−7.55037e16	−	2.32377e17i	−0.294590	−	0.906656i	−0.983359	−	0.181674i	$-0.941848\pi$
$797$	−7.55037e16	−	2.32377e17i	−0.294590	−	0.906656i	0.688768	−	0.724981i	$-0.258152\pi$
$798$	7.69640e16	−	2.50071e16i	0.298037	−	0.0968381i
$799$	−1.20824e15	+	1.66300e15i	−0.00464380	+	0.00639164i
$800$	−2.38881e16	−	3.28792e16i	−0.0911260	−	0.125424i
$801$	1.93515e17	−	5.95579e17i	0.732691	−	2.25499i
$802$			1.82231e17i			0.684821i
$803$	1.09897e17	+	4.85445e17i	0.409914	+	1.81070i
$804$	−4.35037e17			−1.61061
$805$	2.06675e16	+	6.71528e15i	0.0759473	+	0.0246768i
$806$	1.21002e16	−	8.79128e15i	0.0441348	−	0.0320658i
$807$	1.31492e17	+	9.55346e16i	0.476056	+	0.345875i
$808$	2.33272e16	+	7.17938e16i	0.0838292	+	0.258000i
$809$	2.42349e17	−	7.87440e16i	0.864471	−	0.280884i	0.156976	−	0.987602i	$-0.449825\pi$
$809$	2.42349e17	−	7.87440e16i	0.864471	−	0.280884i	0.707495	+	0.706719i	$0.249825\pi$
$810$	−1.06390e16	+	1.46434e16i	−0.0376697	+	0.0518479i
$811$	−2.92446e17	−	4.02518e17i	−1.02783	−	1.41469i	−0.906565	−	0.422065i	$-0.861305\pi$
$811$	−2.92446e17	−	4.02518e17i	−1.02783	−	1.41469i	−0.121264	−	0.992620i	$-0.538695\pi$
$812$	−1.84415e16	+	5.67571e16i	−0.0643369	+	0.198009i
$813$		−	3.28029e17i		−	1.13597i
$814$	2.32376e17	+	2.13284e16i	0.798814	+	0.0733184i
$815$	9.07814e16			0.309778
$816$	−1.07131e16	−	3.48089e15i	−0.0362889	−	0.0117910i
$817$	2.74659e17	−	1.99551e17i	0.923552	−	0.671000i
$818$	−2.07967e17	−	1.51097e17i	−0.694185	−	0.504355i
$819$	−2.78890e15	−	8.58334e15i	−0.00924121	−	0.0284415i
$820$	−2.30203e16	+	7.47976e15i	−0.0757231	+	0.0246039i
$821$	1.01678e17	−	1.39947e17i	0.332022	−	0.456989i	−0.610068	−	0.792349i	$-0.708858\pi$
$821$	1.01678e17	−	1.39947e17i	0.332022	−	0.456989i	0.942090	+	0.335360i	$0.108858\pi$
$822$	1.74814e17	+	2.40611e17i	0.566690	+	0.779982i
$823$	3.62093e16	−	1.11441e17i	0.116525	−	0.358628i	−0.875737	−	0.482789i	$-0.839624\pi$
$823$	3.62093e16	−	1.11441e17i	0.116525	−	0.358628i	0.992262	+	0.124161i	$0.0396238\pi$
$824$			3.22283e16i			0.102961i
$825$	2.33563e17	+	3.92492e17i	0.740764	+	1.24482i
$826$	−6.35067e16			−0.199958
$827$	−1.76869e17	−	5.74681e16i	−0.552864	−	0.179636i	0.0192441	−	0.999815i	$-0.493874\pi$
$827$	−1.76869e17	−	5.74681e16i	−0.552864	−	0.179636i	−0.572108	+	0.820179i	$0.693874\pi$
$828$	1.52343e17	−	1.10684e17i	0.472760	−	0.343480i
$829$	−1.62988e17	−	1.18418e17i	−0.502144	−	0.364829i	0.307692	−	0.951486i	$-0.400444\pi$
$829$	−1.62988e17	−	1.18418e17i	−0.502144	−	0.364829i	−0.809835	+	0.586657i	$0.800444\pi$
$830$	−3.47292e16	−	1.06886e17i	−0.106225	−	0.326927i
$831$	7.33605e17	−	2.38363e17i	2.22770	−	0.723823i
$832$	−1.25256e15	+	1.72400e15i	−0.00377624	+	0.00519755i
$833$	1.60889e16	+	2.21445e16i	0.0481568	+	0.0662821i
$834$	−4.34662e16	+	1.33775e17i	−0.129168	+	0.397538i
$835$			1.73300e17i			0.511303i
$836$	1.02279e17	+	8.96779e16i	0.299605	+	0.262693i
$837$	−6.20776e17			−1.80544
$838$	−8.57093e16	−	2.78486e16i	−0.247493	−	0.0804155i
$839$	−4.42586e17	+	3.21558e17i	−1.26890	+	0.921907i	−0.999158	−	0.0410263i	$-0.986937\pi$
$839$	−4.42586e17	+	3.21558e17i	−1.26890	+	0.921907i	−0.269739	+	0.962934i	$0.586937\pi$
$840$	1.95978e16	+	1.42386e16i	0.0557868	+	0.0405315i
$841$	−5.78972e16	−	1.78189e17i	−0.163637	−	0.503623i
$842$	−3.80731e17	+	1.23707e17i	−1.06843	+	0.347154i
$843$	−2.56023e17	+	3.52386e17i	−0.713369	+	0.981868i
$844$	1.14888e17	+	1.58129e17i	0.317848	+	0.437480i
$845$	3.93486e16	−	1.21102e17i	0.108091	−	0.332669i
$846$		−	3.83054e16i		−	0.104481i
$847$	−1.09263e17	−	5.92962e16i	−0.295920	−	0.160593i
$848$	3.59180e16			0.0965910
$849$	4.94499e17	+	1.60673e17i	1.32044	+	0.429038i
$850$	−1.74842e16	+	1.27030e16i	−0.0463588	+	0.0336816i
$851$	−2.35744e17	−	1.71278e17i	−0.620674	−	0.450946i
$852$	−1.21158e17	−	3.72886e17i	−0.316749	−	0.974853i
$853$	−5.55091e17	+	1.80360e17i	−1.44102	+	0.468216i	−0.922215	−	0.386677i	$-0.873623\pi$
$853$	−5.55091e17	+	1.80360e17i	−1.44102	+	0.468216i	−0.518804	+	0.854893i	$0.673623\pi$
$854$	7.51932e16	−	1.03495e17i	0.193835	−	0.266791i
$855$	1.10911e17	+	1.52656e17i	0.283908	+	0.390766i
$856$	3.72399e16	−	1.14613e17i	0.0946598	−	0.291333i
$857$		−	1.27318e17i		−	0.321369i	−0.987006	−	0.160684i	$-0.948630\pi$
$857$		−	1.27318e17i		−	0.321369i	0.987006	−	0.160684i	$-0.0513701\pi$
$858$	1.57884e16	−	1.80069e16i	0.0395744	−	0.0451353i
$859$	2.87699e17			0.716109			0.358055	−	0.933701i	$-0.383440\pi$
$859$	2.87699e17			0.716109			0.358055	+	0.933701i	$0.383440\pi$
$860$	9.66520e16	+	3.14041e16i	0.238902	+	0.0776240i
$861$	−8.32218e16	+	6.04641e16i	−0.204276	+	0.148415i
$862$	3.26604e17	+	2.37292e17i	0.796119	+	0.578415i
$863$	8.14957e16	+	2.50818e17i	0.197274	+	0.607147i	0.999943	+	0.0107217i	$0.00341290\pi$
$863$	8.14957e16	+	2.50818e17i	0.197274	+	0.607147i	−0.802668	+	0.596426i	$0.796587\pi$
$864$	8.41179e16	−	2.73316e16i	0.202212	−	0.0657025i
$865$	5.57815e16	−	7.67767e16i	0.133166	−	0.183287i
$866$	−2.53767e17	−	3.49280e17i	−0.601627	−	0.828069i
$867$	2.14936e17	−	6.61505e17i	0.506051	−	1.55747i
$868$			1.08074e17i			0.252700i
$869$	2.15836e17	−	1.28439e17i	0.501193	−	0.298248i
$870$	−2.19671e17			−0.506591
$871$	4.16226e16	+	1.35240e16i	0.0953280	+	0.0309739i
$872$	−3.89962e16	+	2.83324e16i	−0.0887000	+	0.0644443i
$873$	8.02387e17	+	5.82968e17i	1.81259	+	1.31692i
$874$	−5.24898e16	−	1.61547e17i	−0.117762	−	0.362435i
$875$	9.46021e16	−	3.07381e16i	0.210791	−	0.0684902i
$876$	4.07239e17	−	5.60516e17i	0.901207	−	1.24040i
$877$	−6.67984e16	−	9.19401e16i	−0.146814	−	0.202073i	0.729276	−	0.684220i	$-0.239857\pi$
$877$	−6.67984e16	−	9.19401e16i	−0.146814	−	0.202073i	−0.876090	+	0.482147i	$0.839857\pi$
$878$	−3.93872e16	+	1.21221e17i	−0.0859781	+	0.264613i
$879$			5.82928e16i			0.126381i
$880$	−3.72166e15	+	4.05480e16i	−0.00801385	+	0.0873119i
$881$	−7.71080e17			−1.64909			−0.824544	−	0.565798i	$-0.808568\pi$
$881$	−7.71080e17			−1.64909			−0.824544	+	0.565798i	$0.808568\pi$
$882$	−4.85109e17	−	1.57622e17i	−1.03045	−	0.334814i
$883$	−5.62566e17	+	4.08728e17i	−1.18689	+	0.862323i	−0.992932	−	0.118688i	$-0.962131\pi$
$883$	−5.62566e17	+	4.08728e17i	−1.18689	+	0.862323i	−0.193954	+	0.981011i	$0.562131\pi$
$884$	9.16774e14	+	6.66075e14i	0.00192109	+	0.00139576i
$885$	−7.22372e16	−	2.22323e17i	−0.150349	−	0.462727i
$886$	3.14988e17	−	1.02346e17i	0.651167	−	0.211577i
$887$	8.06316e15	−	1.10980e16i	0.0165563	−	0.0227878i	−0.800659	−	0.599121i	$-0.795517\pi$
$887$	8.06316e15	−	1.10980e16i	0.0165563	−	0.0227878i	0.817215	+	0.576333i	$0.195517\pi$
$888$	−1.90928e17	−	2.62790e17i	−0.389397	−	0.535959i
$889$	−7.34852e16	+	2.26164e17i	−0.148864	+	0.458156i
$890$		−	1.69095e17i		−	0.340243i
$891$	−1.26109e17	+	2.85491e16i	−0.252046	+	0.0570593i
$892$	1.92422e17			0.382002
$893$	−3.28620e16	−	1.06775e16i	−0.0648016	−	0.0210553i
$894$	5.75293e17	−	4.17975e17i	1.12684	−	0.818701i
$895$	−5.74558e16	−	4.17441e16i	−0.111788	−	0.0812188i
$896$	−4.75831e15	−	1.46446e16i	−0.00919612	−	0.0283027i
$897$	−2.84415e16	+	9.24119e15i	−0.0546006	+	0.0177408i
$898$	1.65517e17	−	2.27815e17i	0.315635	−	0.434434i
$899$	−5.76056e17	−	7.92874e17i	−1.09121	−	1.50192i
$900$	1.24450e17	−	3.83018e17i	0.234175	−	0.720716i
$901$		−	1.91001e16i		−	0.0357016i
$902$	−1.58875e17	−	6.82391e16i	−0.294997	−	0.126705i
$903$	4.31896e17			0.796622
$904$	2.18748e16	+	7.10756e15i	0.0400806	+	0.0130230i
$905$	−2.27315e17	+	1.65154e17i	−0.413749	+	0.300606i
$906$	2.93215e17	+	2.13033e17i	0.530172	+	0.385192i
$907$	−1.50465e17	−	4.63084e17i	−0.270266	−	0.831794i	−0.990433	−	0.137993i	$-0.955935\pi$
$907$	−1.50465e17	−	4.63084e17i	−0.270266	−	0.831794i	0.720167	−	0.693801i	$-0.244065\pi$
$908$	6.23951e16	−	2.02734e16i	0.111336	−	0.0361752i
$909$	−4.39692e17	+	6.05184e17i	−0.779409	+	1.07276i
$910$	−1.43240e15	−	1.97153e15i	−0.00252242	−	0.00347181i
$911$	−5.53223e16	+	1.70265e17i	−0.0967810	+	0.297861i	−0.987714	−	0.156274i	$-0.950052\pi$
$911$	−5.53223e16	+	1.70265e17i	−0.0967810	+	0.297861i	0.890933	+	0.454135i	$0.150052\pi$
$912$		−	1.89348e17i		−	0.329073i
$913$	3.16840e17	−	7.37674e17i	0.547036	−	1.27362i
$914$	3.41298e17			0.585405
$915$	4.47843e17	+	1.45513e17i	0.763130	+	0.247956i
$916$	1.92852e16	−	1.40115e16i	0.0326476	−	0.0237198i
$917$	−5.05395e16	−	3.67191e16i	−0.0849993	−	0.0617556i
$918$	−1.45341e16	−	4.47314e16i	−0.0242847	−	0.0747406i
$919$	3.71426e17	−	1.20684e17i	0.616566	−	0.200334i	0.0159507	−	0.999873i	$-0.494923\pi$
$919$	3.71426e17	−	1.20684e17i	0.616566	−	0.200334i	0.600615	+	0.799538i	$0.294923\pi$
$920$	2.98868e16	−	4.11357e16i	0.0492893	−	0.0678409i
$921$	8.98761e17	+	1.23704e18i	1.47261	+	2.02687i
$922$	−2.60256e17	+	8.00985e17i	−0.423658	+	1.30388i
$923$			3.94427e16i			0.0637906i
$924$	3.82084e16	+	1.68777e17i	0.0613941	+	0.271194i
$925$	−6.23206e17			−0.994903
$926$	−7.29944e17	−	2.37173e17i	−1.15777	−	0.376183i
$927$	−2.58371e17	+	1.87718e17i	−0.407161	+	0.295819i
$928$	1.12967e17	+	8.20752e16i	0.176874	+	0.128506i
$929$	−1.24148e17	−	3.82090e17i	−0.193129	−	0.594389i	−0.999993	−	0.00365286i	$-0.998837\pi$
$929$	−1.24148e17	−	3.82090e17i	−0.193129	−	0.594389i	0.806865	−	0.590737i	$-0.201163\pi$
$930$	−3.78345e17	+	1.22932e17i	−0.584778	+	0.190006i
$931$	−2.70446e17	+	3.72237e17i	−0.415319	+	0.571638i
$932$	8.10137e16	+	1.11506e17i	0.123613	+	0.170138i
$933$	−3.25102e17	+	1.00056e18i	−0.492868	+	1.51689i
$934$			1.15900e17i			0.174583i
$935$	2.15622e16	+	1.97907e15i	0.0322719	+	0.00296204i
$936$	−2.11169e16			−0.0314032
$937$	6.46530e17	+	2.10070e17i	0.955325	+	0.310404i	0.744878	−	0.667201i	$-0.232508\pi$
$937$	6.46530e17	+	2.10070e17i	0.955325	+	0.310404i	0.210448	+	0.977605i	$0.432508\pi$
$938$	−2.55841e17	+	1.85879e17i	−0.375624	+	0.272907i
$939$	1.14530e18	+	8.32106e17i	1.67080	+	1.21391i
$940$	−3.19624e15	−	9.83701e15i	−0.00463310	−	0.0142592i
$941$	−1.02103e18	+	3.31752e17i	−1.47062	+	0.477833i	−0.931295	−	0.364265i	$-0.881320\pi$
$941$	−1.02103e18	+	3.31752e17i	−1.47062	+	0.477833i	−0.539324	+	0.842098i	$0.681320\pi$
$942$	−7.62467e17	+	1.04945e18i	−1.09123	+	1.50195i
$943$	1.26914e17	+	1.74682e17i	0.180484	+	0.248415i
$944$	−4.59178e16	+	1.41321e17i	−0.0648858	+	0.199698i
$945$			1.01146e17i			0.142022i
$946$	3.71249e17	+	6.23868e17i	0.517986	+	0.870454i
$947$	1.39804e18			1.93830			0.969151	−	0.246470i	$-0.0792705\pi$
$947$	1.39804e18			1.93830			0.969151	+	0.246470i	$0.0792705\pi$
$948$	−3.32503e17	−	1.08037e17i	−0.458085	−	0.148841i
$949$	−5.63878e16	+	4.09681e16i	−0.0771947	+	0.0560852i
$950$	−2.93899e17	−	2.13530e17i	−0.399813	−	0.290481i
$951$	2.10788e17	+	6.48738e17i	0.284946	+	0.876973i
$952$	−7.78755e15	+	2.53033e15i	−0.0104611	+	0.00339903i
$953$	2.07585e17	−	2.85717e17i	0.277102	−	0.381398i	−0.647669	−	0.761922i	$-0.724256\pi$
$953$	2.07585e17	−	2.85717e17i	0.277102	−	0.381398i	0.924771	+	0.380523i	$0.124256\pi$
$954$	2.09209e17	+	2.87951e17i	0.277517	+	0.381969i
$955$	−9.34332e16	+	2.87558e17i	−0.123163	+	0.379058i
$956$			7.03727e17i			0.921843i
$957$	−1.17992e18	−	1.03455e18i	−1.53596	−	1.34673i
$958$	9.32901e17			1.20682
$959$	2.05613e17	+	6.68077e16i	0.264325	+	0.0858845i
$960$	4.58550e16	−	3.33156e16i	0.0585813	−	0.0425618i
$961$	−7.98632e17	−	5.80240e17i	−1.01393	−	0.736660i
$962$	1.00979e16	+	3.10781e16i	0.0127403	+	0.0392106i
$963$	1.13575e18	−	3.69026e17i	1.42404	−	0.462700i
$964$	−4.15619e16	+	5.72050e16i	−0.0517884	+	0.0712807i
$965$	6.02217e16	+	8.28880e16i	0.0745742	+	0.102643i
$966$	6.67756e16	−	2.05514e17i	0.0821779	−	0.252917i
$967$		−	1.56875e18i		−	1.91865i	−0.282304	−	0.959325i	$-0.591099\pi$
$967$		−	1.56875e18i		−	1.91865i	0.282304	−	0.959325i	$-0.408901\pi$
$968$	−2.10953e17	+	2.00269e17i	−0.256409	+	0.243422i
$969$	−1.00690e17			−0.121630
$970$	2.54700e17	+	8.27571e16i	0.305773	+	0.0993516i
$971$	4.56504e17	−	3.31670e17i	0.544665	−	0.395722i	−0.281150	−	0.959664i	$-0.590716\pi$
$971$	4.56504e17	−	3.31670e17i	0.544665	−	0.395722i	0.825815	+	0.563942i	$0.190716\pi$
$972$	−2.64687e17	−	1.92307e17i	−0.313860	−	0.228032i
$973$	3.15964e16	+	9.72437e16i	0.0372358	+	0.114600i
$974$	7.64036e16	−	2.48250e16i	0.0894871	−	0.0290761i
$975$	−3.75935e16	+	5.17430e16i	−0.0437607	+	0.0602315i
$976$	−1.75937e17	−	2.42157e17i	−0.203545	−	0.280155i
$977$	−3.67118e17	+	1.12987e18i	−0.422122	+	1.29916i	0.483602	+	0.875288i	$0.339328\pi$
$977$	−3.67118e17	+	1.12987e18i	−0.422122	+	1.29916i	−0.905723	+	0.423869i	$0.860672\pi$
$978$		−	9.02714e17i		−	1.03161i
$979$	7.96358e17	−	9.08259e17i	0.904507	−	1.03161i
$980$	−1.37730e17			−0.155480
$981$	−4.54276e17	−	1.47603e17i	−0.509690	−	0.165608i
$982$	4.71059e17	−	3.42244e17i	0.525298	−	0.381652i
$983$	−1.28240e18	−	9.31719e17i	−1.42136	−	1.03268i	−0.991546	−	0.129757i	$-0.958580\pi$
$983$	−1.28240e18	−	9.31719e17i	−1.42136	−	1.03268i	−0.429811	−	0.902919i	$-0.641420\pi$
$984$	7.43774e16	+	2.28910e17i	0.0819352	+	0.252171i
$985$	−3.19771e17	+	1.03900e17i	−0.350124	+	0.113762i
$986$	4.36452e16	−	6.00724e16i	0.0474979	−	0.0653753i
$987$	−2.58374e16	−	3.55622e16i	−0.0279477	−	0.0384667i
$988$	−5.88627e15	+	1.81161e16i	−0.00632846	+	0.0194770i
$989$		−	9.06547e17i		−	0.968752i
$990$	−3.46747e17	+	2.06341e17i	−0.368300	+	0.219166i
$991$	1.95954e17			0.206877			0.103439	−	0.994636i	$-0.467015\pi$
$991$	1.95954e17			0.206877			0.103439	+	0.994636i	$0.467015\pi$
$992$	2.40497e17	+	7.81421e16i	0.252371	+	0.0820002i
$993$	1.44984e18	−	1.05337e18i	1.51225	−	1.09872i
$994$	−2.30576e17	−	1.67523e17i	−0.239054	−	0.173683i
$995$	−9.62969e16	−	2.96371e17i	−0.0992370	−	0.305420i
$996$	−1.06285e18	+	3.45341e17i	−1.08872	+	0.353747i
$997$	−2.66021e17	+	3.66146e17i	−0.270860	+	0.372806i	−0.922680	−	0.385567i	$-0.874006\pi$
$997$	−2.66021e17	+	3.66146e17i	−0.270860	+	0.372806i	0.651820	+	0.758374i	$0.274006\pi$
$998$	−3.24543e17	−	4.46694e17i	−0.328464	−	0.452093i
$999$	4.19114e17	−	1.28990e18i	0.421637	−	1.29767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.13.d.a.13.1	✓	48
11.6	odd	10	inner	22.13.d.a.17.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.13.d.a.13.1	✓	48	1.1	even	1	trivial
22.13.d.a.17.1	yes	48	11.6	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-43.0399 - 13.9845i) q^{2} +(-974.141 + 707.755i) q^{3} +(1656.87 + 1203.78i) q^{4} +(1693.39 + 5211.73i) q^{5} +(51824.5 - 16838.8i) q^{6} +(23282.7 - 32045.9i) q^{7} +(-54477.1 - 74981.2i) q^{8} +(283809. - 873474. i) q^{9} -247993. i q^{10} +(1.16794e6 - 1.33205e6i) q^{11} -2.46600e6 q^{12} +(235938. + 76660.8i) q^{13} +(-1.45023e6 + 1.05366e6i) q^{14} +(-5.33823e6 - 3.87845e6i) q^{15} +(1.29611e6 + 3.98902e6i) q^{16} +(2.12124e6 - 689234. i) q^{17} +(-2.44302e7 + 3.36253e7i) q^{18} +(2.20372e7 + 3.03315e7i) q^{19} +(-3.46807e6 + 1.06736e7i) q^{20} +4.76957e7i q^{21} +(-6.88959e7 + 4.09983e7i) q^{22} +1.00113e8 q^{23} +(1.06137e8 + 3.44859e7i) q^{24} +(1.73219e8 - 1.25851e8i) q^{25} +(-9.08267e6 - 6.59894e6i) q^{26} +(1.43992e8 + 4.43163e8i) q^{27} +(7.71528e7 - 2.50685e7i) q^{28} +(-4.32401e8 + 5.95150e8i) q^{29} +(1.75519e8 + 2.41581e8i) q^{30} +(-4.11680e8 + 1.26702e9i) q^{31} -1.89813e8i q^{32} +(-1.94969e8 + 2.12421e9i) q^{33} -1.00937e8 q^{34} +(2.06441e8 + 6.70769e7i) q^{35} +(1.52171e9 - 1.10559e9i) q^{36} +(-2.35478e9 - 1.71085e9i) q^{37} +(-5.24305e8 - 1.61365e9i) q^{38} +(-2.84093e8 + 9.23075e7i) q^{39} +(2.98531e8 - 4.10892e8i) q^{40} +(1.26771e9 + 1.74485e9i) q^{41} +(6.67001e8 - 2.05282e9i) q^{42} -9.05523e9i q^{43} +(3.53861e9 - 8.01086e8i) q^{44} +5.03291e9 q^{45} +(-4.30886e9 - 1.40003e9i) q^{46} +(-7.45605e8 + 5.41714e8i) q^{47} +(-4.08584e9 - 2.96854e9i) q^{48} +(3.79234e9 + 1.16716e10i) q^{49} +(-9.21532e9 + 2.99424e9i) q^{50} +(-1.57858e9 + 2.17273e9i) q^{51} +(2.98634e8 + 4.11035e8i) q^{52} +(2.64627e9 - 8.14439e9i) q^{53} -2.10874e10i q^{54} +(8.92005e9 + 3.83128e9i) q^{55} -3.67122e9 q^{56} +(-4.29346e10 - 1.39503e10i) q^{57} +(2.69334e10 - 1.95683e10i) q^{58} +(2.86614e10 + 2.08237e10i) q^{59} +(-4.17591e9 - 1.28521e10i) q^{60} +(-6.78713e10 + 2.20527e10i) q^{61} +(3.54374e10 - 4.87754e10i) q^{62} +(-2.13835e10 - 2.94318e10i) q^{63} +(-2.65444e9 + 8.16951e9i) q^{64} +1.35946e9i q^{65} +(3.80976e10 - 8.86995e10i) q^{66} +1.76414e11 q^{67} +(4.34431e9 + 1.41155e9i) q^{68} +(-9.75242e10 + 7.08555e10i) q^{69} +(-7.94718e9 - 5.77397e9i) q^{70} +(4.91313e10 + 1.51211e11i) q^{71} +(-8.09553e10 + 2.63040e10i) q^{72} +(-1.65141e11 + 2.27297e11i) q^{73} +(7.74241e10 + 1.06565e11i) q^{74} +(-7.96682e10 + 2.45194e11i) q^{75} +7.67833e10i q^{76} +(-1.54940e10 - 6.84413e10i) q^{77} +1.35182e10 q^{78} +(1.34835e11 + 4.38105e10i) q^{79} +(-1.85949e10 + 1.35100e10i) q^{80} +(-5.90474e10 - 4.29004e10i) q^{81} +(-3.01611e10 - 9.28263e10i) q^{82} +(4.31001e11 - 1.40041e11i) q^{83} +(-5.74153e10 + 7.90254e10i) q^{84} +(7.18419e9 + 9.88819e9i) q^{85} +(-1.26633e11 + 3.89736e11i) q^{86} -8.85793e11i q^{87} +(-1.63504e11 - 1.50071e10i) q^{88} +6.81851e11 q^{89} +(-2.16616e11 - 7.03828e10i) q^{90} +(7.94994e9 - 5.77597e9i) q^{91} +(1.65874e11 + 1.20515e11i) q^{92} +(-4.95706e11 - 1.52563e12i) q^{93} +(3.96664e10 - 1.28884e10i) q^{94} +(-1.20762e11 + 1.66215e11i) q^{95} +(1.34341e11 + 1.84904e11i) q^{96} +(-3.33707e11 + 1.02704e12i) q^{97} -5.55379e11i q^{98} +(-8.32040e11 - 1.39821e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 1240 q^{3} + 24576 q^{4} + 1440 q^{5} - 147200 q^{6} + 439200 q^{7} + 563348 q^{9} - 7317468 q^{11} + 737280 q^{12} + 13341600 q^{13} - 7524864 q^{14} - 29808888 q^{15} - 50331648 q^{16} + 29458800 q^{17}+ \cdots - 5181480396620 q^{99}+O(q^{100}) \) 48 * q + 1240 * q^3 + 24576 * q^4 + 1440 * q^5 - 147200 * q^6 + 439200 * q^7 + 563348 * q^9 - 7317468 * q^11 + 737280 * q^12 + 13341600 * q^13 - 7524864 * q^14 - 29808888 * q^15 - 50331648 * q^16 + 29458800 * q^17 - 96857600 * q^18 + 59195700 * q^19 - 2949120 * q^20 - 147874560 * q^22 + 297521280 * q^23 - 301465600 * q^24 - 349772268 * q^25 + 603191808 * q^26 - 434593340 * q^27 - 981811200 * q^28 + 121665600 * q^29 + 3275650560 * q^30 - 1117400544 * q^31 - 13803991820 * q^33 - 2568870912 * q^34 + 1026283680 * q^35 + 7058374656 * q^36 + 11737565760 * q^37 + 4500864000 * q^38 - 23697921920 * q^39 - 7817134080 * q^40 + 4863244680 * q^41 + 12992468480 * q^42 - 18701991936 * q^44 + 29640403232 * q^45 + 33202391040 * q^46 + 8084031480 * q^47 + 5200936960 * q^48 + 593931516 * q^49 - 13593646080 * q^50 - 30011589660 * q^51 + 55099392000 * q^52 + 40815862920 * q^53 + 29310331992 * q^55 - 7285506048 * q^56 - 98665594300 * q^57 + 81900510720 * q^58 - 156541010940 * q^59 - 30685659136 * q^60 + 255357655680 * q^61 + 67163788800 * q^62 - 429459850400 * q^63 + 103079215104 * q^64 + 460708043264 * q^66 + 76186270200 * q^67 + 60331622400 * q^68 - 1054414688600 * q^69 - 352820375040 * q^70 + 60925955544 * q^71 + 95420416000 * q^72 + 363471756600 * q^73 + 378662860800 * q^74 - 57777629724 * q^75 + 326539185480 * q^77 - 1234846474240 * q^78 + 137547461520 * q^79 - 120795955200 * q^80 - 1017431491848 * q^81 + 613199754240 * q^82 + 715268672100 * q^83 - 354644459520 * q^84 + 1202406730800 * q^85 - 80499776256 * q^86 - 270225899520 * q^88 + 724193830584 * q^89 - 1005067351040 * q^90 + 1925501559192 * q^91 - 608833290240 * q^92 - 2466072811400 * q^93 + 300785049600 * q^94 + 6877125644400 * q^95 + 1350178653780 * q^97 - 5181480396620 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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