LMFDB - Embedded newform 22.13.d.a.17.1

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			17.1
Character	$\chi$	$=$	22.17
Dual form			22.13.d.a.13.1

$q$-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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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	−0.999572	−	0.0292437i	$-0.990690\pi$
$3$	−974.141	−	707.755i	−1.33627	−	0.970857i	−0.336697	−	0.941613i	$-0.609310\pi$
$4$	1656.87	−	1203.78i	0.404508	−	0.293893i
$5$	1693.39	−	5211.73i	0.108377	−	0.333550i	−0.882131	−	0.471004i	$-0.843892\pi$
$5$	1693.39	−	5211.73i	0.108377	−	0.333550i	0.990508	+	0.137453i	$0.0438918\pi$
$6$	51824.5	+	16838.8i	1.11078	+	0.360914i
$7$	23282.7	+	32045.9i	0.197900	+	0.272386i	0.896421	−	0.443204i	$-0.146158\pi$
$7$	23282.7	+	32045.9i	0.197900	+	0.272386i	−0.698521	+	0.715590i	$0.746158\pi$
$8$	−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	−0.284475	−	0.958684i	$-0.591819\pi$
$13$	235938.	−	76660.8i	0.0488806	−	0.0158823i	0.333355	+	0.942801i	$0.391819\pi$
$14$	−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	0.352628	−	0.935764i	$-0.385288\pi$
$17$	2.12124e6	+	689234.i	0.0878814	+	0.0285544i	−0.264746	+	0.964318i	$0.585288\pi$
$18$	−2.44302e7	−	3.36253e7i	−0.718278	−	0.988625i
$19$	2.20372e7	−	3.03315e7i	0.468418	−	0.644723i	−0.507809	−	0.861469i	$-0.669545\pi$
$19$	2.20372e7	−	3.03315e7i	0.468418	−	0.644723i	0.976228	+	0.216747i	$0.0695446\pi$
$20$	−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	−0.999265	−	0.0383427i	$-0.987792\pi$
$29$	−4.32401e8	−	5.95150e8i	−0.726941	−	1.00055i	0.272324	−	0.962206i	$-0.412208\pi$
$30$	1.75519e8	−	2.41581e8i	0.240766	−	0.331386i
$31$	−4.11680e8	−	1.26702e9i	−0.463863	−	1.42762i	−0.860406	−	0.509609i	$-0.829790\pi$
$31$	−4.11680e8	−	1.26702e9i	−0.463863	−	1.42762i	0.396543	−	0.918016i	$-0.370210\pi$
$32$			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	−0.942971	−	0.332875i	$-0.891981\pi$
$37$	−2.35478e9	+	1.71085e9i	−0.917782	+	0.666808i	0.0251886	+	0.999683i	$0.491981\pi$
$38$	−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	−0.654454	−	0.756102i	$-0.727101\pi$
$41$	1.26771e9	−	1.74485e9i	0.266880	−	0.367328i	0.921333	+	0.388774i	$0.127101\pi$
$42$	6.67001e8	+	2.05282e9i	0.121515	+	0.373986i
$43$			9.05523e9i			1.43248i	0.697854	+	0.716240i	$0.254138\pi$
$43$			9.05523e9i			1.43248i	−0.697854	+	0.716240i	$0.745862\pi$
$44$	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	0.552663	−	0.833405i	$-0.313612\pi$
$47$	−7.45605e8	−	5.41714e8i	−0.0691707	−	0.0502554i	−0.621833	+	0.783150i	$0.713612\pi$
$48$	−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	0.992838	−	0.119469i	$-0.0381192\pi$
$53$	2.64627e9	+	8.14439e9i	0.119393	+	0.367454i	−0.873445	+	0.486923i	$0.838119\pi$
$54$			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	−0.193697	−	0.981061i	$-0.562048\pi$
$59$	2.86614e10	−	2.08237e10i	0.679493	−	0.493680i	0.873189	+	0.487381i	$0.162048\pi$
$60$	−4.17591e9	+	1.28521e10i	−0.0895043	+	0.275466i
$61$	−6.78713e10	−	2.20527e10i	−1.31737	−	0.428039i	−0.435778	−	0.900054i	$-0.643527\pi$
$61$	−6.78713e10	−	2.20527e10i	−1.31737	−	0.428039i	−0.881590	+	0.472016i	$0.843527\pi$
$62$	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	−0.553997	−	0.832519i	$-0.686898\pi$
$71$	4.91313e10	−	1.51211e11i	0.383538	−	1.18041i	0.937535	−	0.347890i	$-0.113102\pi$
$72$	−8.09553e10	−	2.63040e10i	−0.581099	−	0.188810i
$73$	−1.65141e11	−	2.27297e11i	−1.09123	−	1.50196i	−0.846518	−	0.532360i	$-0.821305\pi$
$73$	−1.65141e11	−	2.27297e11i	−1.09123	−	1.50196i	−0.244717	−	0.969595i	$-0.578695\pi$
$74$	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	−0.0182483	−	0.999833i	$-0.505809\pi$
$79$	1.34835e11	−	4.38105e10i	0.554676	−	0.180225i	0.572924	+	0.819608i	$0.305809\pi$
$80$	−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	0.881906	−	0.471425i	$-0.156260\pi$
$83$	4.31001e11	+	1.40041e11i	1.31829	+	0.428337i	0.436381	+	0.899762i	$0.356260\pi$
$84$	−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	−0.924496	−	0.381191i	$-0.875514\pi$
$97$	−3.33707e11	−	1.02704e12i	−0.400622	−	1.23299i	0.523874	−	0.851796i	$-0.324486\pi$
$98$			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	−0.650238	−	0.759731i	$-0.725331\pi$
$101$	−7.74626e11	+	2.51691e11i	−0.729733	+	0.237105i	−0.0794951	+	0.996835i	$0.525331\pi$
$102$	9.83265e10	+	7.14384e10i	0.0873111	+	0.0634353i
$103$	−2.81320e11	+	2.04391e11i	−0.235601	+	0.171174i	−0.699321	−	0.714808i	$-0.746514\pi$
$103$	−2.81320e11	+	2.04391e11i	−0.235601	+	0.171174i	0.463720	+	0.885982i	$0.346514\pi$
$104$	−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	−0.474527	−	0.880241i	$-0.657381\pi$
$107$	7.64275e11	−	1.05193e12i	0.509269	−	0.700948i	0.983796	+	0.179293i	$0.0573809\pi$
$108$	−2.94896e11	−	9.07598e11i	−0.185835	−	0.571941i
$109$			5.20080e11i			0.310106i	0.987906	+	0.155053i	$0.0495549\pi$
$109$			5.20080e11i			0.310106i	−0.987906	+	0.155053i	$0.950445\pi$
$110$	−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	0.538523	−	0.842611i	$-0.318982\pi$
$113$	−2.00771e11	−	1.45869e11i	−0.0964340	−	0.0700634i	−0.634957	+	0.772547i	$0.718982\pi$
$114$	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	−0.464473	−	0.885588i	$-0.653756\pi$
$127$	−5.70964e12	−	1.85517e12i	−1.36077	−	0.442142i	−0.896301	+	0.443445i	$0.853756\pi$
$128$	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	$0.0498688\pi$
$131$			1.57710e12i			0.312054i	−0.987753	+	0.156027i	$0.950131\pi$
$132$	−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	−0.738726	−	0.674006i	$-0.764572\pi$
$137$	1.68660e12	−	5.19081e12i	0.255087	−	0.785076i	0.993813	−	0.111070i	$-0.0354278\pi$
$138$	5.18831e12	+	1.68579e12i	0.751193	+	0.244077i
$139$	−1.51726e12	−	2.08832e12i	−0.210363	−	0.289540i	0.690777	−	0.723068i	$-0.257269\pi$
$139$	−1.51726e12	−	2.08832e12i	−0.210363	−	0.289540i	−0.901140	+	0.433528i	$0.857269\pi$
$140$	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	0.815172	−	0.579218i	$-0.196642\pi$
$149$	1.24111e13	+	4.03260e12i	1.13420	+	0.368525i	0.319032	+	0.947744i	$0.396642\pi$
$150$	6.85783e12	+	9.43899e12i	0.602059	+	0.828663i
$151$	3.90947e12	−	5.38093e12i	0.329804	−	0.453937i	−0.611625	−	0.791148i	$-0.709484\pi$
$151$	3.90947e12	−	5.38093e12i	0.329804	−	0.453937i	0.941429	+	0.337211i	$0.109484\pi$
$152$	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	−0.286260	−	0.958152i	$-0.592412\pi$
$157$	−1.92589e13	−	1.39924e13i	−1.28598	−	0.934316i	−0.999716	+	0.0238356i	$0.992412\pi$
$158$	−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	0.989755	+	0.142774i	$0.0456022\pi$
$163$	5.11922e12	+	1.57553e13i	0.272947	+	0.840044i	−0.716808	+	0.697270i	$0.754398\pi$
$164$		−	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	0.481720	−	0.876325i	$-0.340012\pi$
$167$	3.00766e13	−	9.77248e12i	1.38653	−	0.450511i	0.904811	+	0.425814i	$0.140012\pi$
$168$	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	−0.955505	−	0.294976i	$-0.904688\pi$
$173$	−1.01792e13	+	1.40105e13i	−0.379698	+	0.522610i	0.575806	+	0.817586i	$0.304688\pi$
$174$	−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	0.416896	−	0.908954i	$-0.363118\pi$
$179$	−1.04848e13	−	7.61762e12i	−0.318743	−	0.231580i	−0.735639	+	0.677374i	$0.763118\pi$
$180$	8.33886e12	−	6.05854e12i	0.245172	−	0.178128i
$181$	1.58445e13	−	4.87643e13i	0.450616	−	1.38685i	−0.425590	−	0.904916i	$-0.639934\pi$
$181$	1.58445e13	−	4.87643e13i	0.450616	−	1.38685i	0.876206	−	0.481937i	$-0.160066\pi$
$182$	−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	−0.0239799	−	0.999712i	$-0.507634\pi$
$191$	4.46377e13	−	3.24312e13i	0.919393	−	0.667978i	0.943373	+	0.331734i	$0.107634\pi$
$192$	−3.19622e12	+	9.83694e12i	−0.0638012	+	0.196360i
$193$	1.77814e13	+	5.77751e12i	0.344050	+	0.111789i	0.475945	−	0.879475i	$-0.342106\pi$
$193$	1.77814e13	+	5.77751e12i	0.344050	+	0.111789i	−0.131895	+	0.991264i	$0.542106\pi$
$194$	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	$-0.824124\pi$
$197$		−	6.13561e13i		−	1.04969i	0.851198	−	0.524844i	$-0.175876\pi$
$198$	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	0.254350	−	0.967112i	$-0.418139\pi$
$211$	9.07678e13	−	2.94922e13i	1.02858	−	0.334205i	0.774228	+	0.632907i	$0.218139\pi$
$212$	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	0.852255	−	0.523127i	$-0.175235\pi$
$223$	7.60121e13	+	5.52260e13i	0.618093	+	0.449071i	−0.234162	+	0.972198i	$0.575235\pi$
$224$	−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	0.872264	−	0.489036i	$-0.162651\pi$
$227$	1.88292e13	+	2.59162e13i	0.137619	+	0.189416i	−0.734645	+	0.678452i	$0.762651\pi$
$228$	−5.43437e13	+	7.47977e13i	−0.386848	+	0.532451i
$229$	3.59682e12	+	1.10699e13i	0.0249405	+	0.0767590i	0.962752	−	0.270386i	$-0.0871512\pi$
$229$	3.59682e12	+	1.10699e13i	0.0249405	+	0.0767590i	−0.937812	+	0.347145i	$0.887151\pi$
$230$			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	−0.102097	−	0.994774i	$-0.532555\pi$
$233$	6.40053e13	−	2.07966e13i	0.400019	−	0.129974i	0.502116	+	0.864800i	$0.332555\pi$
$234$	−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	0.228299	−	0.973591i	$-0.426683\pi$
$239$	2.01973e14	−	2.77992e14i	1.08369	−	1.49157i	0.855392	−	0.517982i	$-0.173317\pi$
$240$	8.55227e12	+	2.63212e13i	0.0447522	+	0.137733i
$241$		−	3.45260e13i		−	0.176215i	−0.996111	−	0.0881077i	$-0.971918\pi$
$241$		−	3.45260e13i		−	0.176215i	0.996111	−	0.0881077i	$-0.0280820\pi$
$242$	−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	0.868840	−	0.495093i	$-0.164866\pi$
$251$	−3.12760e13	−	9.62575e13i	−0.125074	−	0.384939i	−0.993915	+	0.110153i	$0.964866\pi$
$252$			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	0.303064	−	0.952970i	$-0.401990\pi$
$257$	3.75455e14	−	2.72784e14i	1.30304	−	0.946717i	0.999980	+	0.00625283i	$0.00199035\pi$
$258$	−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	$0.310147\pi$
$263$			5.47581e14i			1.65468i	−0.561702	+	0.827340i	$0.689853\pi$
$264$	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	−0.990891	−	0.134664i	$-0.957004\pi$
$269$	−4.17119e13	+	1.28376e14i	−0.110090	+	0.338821i	0.880802	+	0.473485i	$0.157004\pi$
$270$	1.09902e14	+	3.57092e13i	0.283675	+	0.0921716i
$271$	−1.60128e14	−	2.20397e14i	−0.404251	−	0.556403i	0.557554	−	0.830141i	$-0.311740\pi$
$271$	−1.60128e14	−	2.20397e14i	−0.404251	−	0.556403i	−0.961804	+	0.273738i	$0.911740\pi$
$272$	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	−0.892259	−	0.451523i	$-0.850881\pi$
$277$	−6.09254e14	+	1.97959e14i	−1.34871	+	0.438224i	−0.456454	+	0.889747i	$0.650881\pi$
$278$	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	0.636816	−	0.771015i	$-0.280251\pi$
$281$	3.44036e14	+	1.11784e14i	0.698820	+	0.227060i	0.0620039	+	0.998076i	$0.480251\pi$
$282$	−2.95188e13	−	4.06292e13i	−0.0586954	−	0.0807873i
$283$	−2.53813e14	+	3.49344e14i	−0.494078	+	0.680040i	−0.981134	−	0.193331i	$-0.938071\pi$
$283$	−2.53813e14	+	3.49344e14i	−0.494078	+	0.680040i	0.487056	+	0.873371i	$0.338071\pi$
$284$	−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	0.830912	−	0.556404i	$-0.187819\pi$
$293$	2.84557e13	+	3.91659e13i	0.0449742	+	0.0619017i	−0.785938	+	0.618306i	$0.787819\pi$
$294$	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	$0.274021\pi$
$307$			1.26988e15i			1.51681i	−0.651783	+	0.758405i	$0.725979\pi$
$308$	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	0.905343	−	0.424682i	$-0.139614\pi$
$311$	7.06857e14	+	5.13562e14i	0.781213	+	0.567584i	−0.124130	+	0.992266i	$0.539614\pi$
$312$	2.23979e13	−	1.62730e13i	0.0242817	−	0.0176417i
$313$	−3.63311e14	+	1.11816e15i	−0.386378	+	1.18915i	0.549098	+	0.835758i	$0.314971\pi$
$313$	−3.63311e14	+	1.11816e15i	−0.386378	+	1.18915i	−0.935476	+	0.353391i	$0.885029\pi$
$314$	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	0.999511	−	0.0312617i	$-0.00995253\pi$
$317$	1.75058e14	+	5.38772e14i	0.172514	+	0.530945i	−0.826997	+	0.562207i	$0.809953\pi$
$318$			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	0.974585	−	0.224020i	$-0.0719181\pi$
$337$	6.74345e14	+	9.28157e14i	0.460366	+	0.633639i	−0.514219	+	0.857659i	$0.671918\pi$
$338$	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	−0.278478	−	0.960443i	$-0.589830\pi$
$347$	−1.86497e15	−	6.05966e14i	−1.06831	−	0.347114i	−0.789828	+	0.613329i	$0.789830\pi$
$348$	1.06630e15	+	1.46764e15i	0.600351	+	0.826313i
$349$	1.07095e15	−	1.47404e15i	0.592677	−	0.815750i	−0.402336	−	0.915492i	$-0.631802\pi$
$349$	1.07095e15	−	1.47404e15i	0.592677	−	0.815750i	0.995013	+	0.0997420i	$0.0318018\pi$
$350$	−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	0.967848	+	0.251535i	$0.0809353\pi$
$359$	1.94378e15	+	2.67539e15i	0.907990	+	1.24974i	−0.0598578	+	0.998207i	$0.519065\pi$
$360$	−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	−0.0951734	−	0.995461i	$-0.530341\pi$
$367$	2.00886e15	−	1.45953e15i	0.822156	−	0.597331i	0.917329	+	0.398130i	$0.130341\pi$
$368$	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	$-0.913845\pi$
$373$		−	1.44012e15i		−	0.534745i	0.963593	−	0.267372i	$-0.0861554\pi$
$374$	−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	−0.786956	−	0.617009i	$-0.788344\pi$
$379$	6.29413e14	−	1.93713e15i	0.212374	−	0.653619i	0.999330	−	0.0366097i	$-0.0116558\pi$
$380$	−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	−0.942985	−	0.332836i	$-0.891994\pi$
$383$	−1.18596e15	−	3.65000e15i	−0.375730	−	1.15638i	0.567254	−	0.823543i	$-0.308006\pi$
$384$		−	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	−0.714334	−	0.699805i	$-0.753270\pi$
$389$	−9.33881e14	+	6.78504e14i	−0.269522	+	0.195819i	0.444812	+	0.895624i	$0.353270\pi$
$390$	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	0.682473	+	0.730911i	$0.260904\pi$
$401$	−1.24434e15	+	3.82970e15i	−0.299278	+	0.921082i	−0.981751	+	0.190171i	$0.939096\pi$
$402$	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	0.331406	−	0.943488i	$-0.392477\pi$
$409$	5.40230e15	−	1.75531e15i	1.15409	−	0.374986i	0.822682	+	0.568502i	$0.192477\pi$
$410$	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	0.999700	−	0.0245012i	$-0.00779975\pi$
$421$	7.15656e15	+	5.19955e15i	1.28532	+	0.933841i	0.285622	+	0.958342i	$0.407800\pi$
$422$	−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	−0.883714	−	0.468027i	$-0.844965\pi$
$431$	−8.48409e15	+	2.75665e15i	−1.32355	+	0.430049i	−0.439840	+	0.898076i	$0.644965\pi$
$432$	−1.58116e15	−	1.14878e15i	−0.243261	−	0.176739i
$433$	7.71807e15	−	5.60751e15i	1.17107	−	0.850829i	0.179930	−	0.983679i	$-0.442413\pi$
$433$	7.71807e15	−	5.60751e15i	1.17107	−	0.850829i	0.991136	+	0.132850i	$0.0424129\pi$
$434$	−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	$0.0630352\pi$
$439$			2.81649e15i			0.393478i	−0.980456	+	0.196739i	$0.936965\pi$
$440$	−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	0.122629	−	0.992453i	$-0.460867\pi$
$443$	−5.92081e15	−	4.30172e15i	−0.783355	−	0.569141i	−0.905984	+	0.423312i	$0.860867\pi$
$444$	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	−0.997165	−	0.0752518i	$-0.976024\pi$
$449$	−1.92283e15	−	5.91788e15i	−0.234673	−	0.722250i	0.762491	−	0.646999i	$-0.223976\pi$
$450$		−	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	−0.112385	−	0.993665i	$-0.535849\pi$
$457$	−7.17258e15	−	2.33051e15i	−0.787369	−	0.255832i	−0.674983	+	0.737833i	$0.735849\pi$
$458$	−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	$0.421095\pi$
$461$			1.86103e16i			1.93887i	−0.245358	+	0.969433i	$0.578905\pi$
$462$	−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	−0.981930	−	0.189247i	$-0.939395\pi$
$467$	−7.91408e14	+	2.43570e15i	−0.0762955	+	0.234813i	0.905634	+	0.424060i	$0.139395\pi$
$468$	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	−0.650482	−	0.759522i	$-0.725433\pi$
$479$	−1.96054e16	−	6.37020e15i	−1.62317	−	0.527399i	−0.972687	+	0.232122i	$0.925433\pi$
$480$	−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	0.532656	−	0.846332i	$-0.321194\pi$
$487$	−1.43615e15	−	1.04343e15i	−0.107653	−	0.0782146i	−0.640309	+	0.768117i	$0.721194\pi$
$488$	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	0.448838	−	0.893613i	$-0.351838\pi$
$491$	−7.56260e15	−	1.04090e16i	−0.539737	−	0.742884i	−0.988575	+	0.150729i	$0.951838\pi$
$492$	−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	−0.220273	−	0.975438i	$-0.570695\pi$
$499$	9.87065e15	−	7.17144e15i	0.639355	−	0.464519i	0.859629	+	0.510919i	$0.170695\pi$
$500$	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	−0.999940	−	0.0109539i	$-0.996513\pi$
$503$	−1.10218e16	+	1.51702e16i	−0.680524	+	0.936661i	0.319416	+	0.947615i	$0.396513\pi$
$504$	−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	0.705926	−	0.708286i	$-0.250531\pi$
$509$	4.35537e15	+	3.16436e15i	0.250449	+	0.181962i	−0.455477	+	0.890248i	$0.650531\pi$
$510$	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	−0.961786	−	0.273803i	$-0.911718\pi$
$521$	−1.99717e16	+	1.45103e16i	−0.998592	+	0.725519i	−0.0368058	+	0.999322i	$0.511718\pi$
$522$	−9.44843e15	+	2.90793e16i	−0.467021	+	1.43734i
$523$	2.98859e15	+	9.71051e14i	0.146035	+	0.0474495i	0.381122	−	0.924525i	$-0.375538\pi$
$523$	2.98859e15	+	9.71051e14i	0.146035	+	0.0474495i	−0.235088	+	0.971974i	$0.575538\pi$
$524$	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	0.426561	−	0.904459i	$-0.359725\pi$
$541$	3.26755e16	−	1.06169e16i	1.30328	−	0.423463i	0.876723	+	0.480996i	$0.159725\pi$
$542$	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	−0.898563	−	0.438844i	$-0.855388\pi$
$547$	−5.45185e15	+	7.50383e15i	−0.203526	+	0.280129i	0.695037	+	0.718974i	$0.255388\pi$
$548$	−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	0.494870	−	0.868967i	$-0.335216\pi$
$557$	−1.44683e16	−	1.99138e16i	−0.484490	−	0.666843i	−0.979360	+	0.202124i	$0.935216\pi$
$558$	−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	0.282008	−	0.959412i	$-0.409000\pi$
$563$	3.42050e16	−	1.11139e16i	1.07409	−	0.348991i	0.792077	+	0.610421i	$0.209000\pi$
$564$	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	−0.541220	−	0.840881i	$-0.682037\pi$
$569$	1.44488e16	−	1.98870e16i	0.425752	−	0.585997i	0.966972	+	0.254884i	$0.0820372\pi$
$570$	−3.45958e15	−	1.06475e16i	−0.100873	−	0.310455i
$571$		−	3.11031e16i		−	0.897403i	−0.893682	−	0.448701i	$-0.851887\pi$
$571$		−	3.11031e16i		−	0.897403i	0.893682	−	0.448701i	$-0.148113\pi$
$572$	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	−0.611931	−	0.790911i	$-0.709607\pi$
$577$	1.28427e16	−	3.95257e16i	0.348018	−	1.07109i	0.959948	−	0.280177i	$-0.0903930\pi$
$578$	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	−0.352186	−	0.935930i	$-0.614562\pi$
$587$	1.75546e16	−	1.27542e16i	0.429105	−	0.311763i	0.781291	+	0.624167i	$0.214562\pi$
$588$	−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	$0.171561\pi$
$593$			4.46367e16i			1.02651i	−0.858236	+	0.513256i	$0.828439\pi$
$594$	−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	−0.784520	−	0.620104i	$-0.787090\pi$
$599$	9.91535e15	−	3.05163e16i	0.214658	−	0.660649i	0.999178	−	0.0405454i	$-0.0129095\pi$
$600$	2.27250e16	+	7.38380e15i	0.487076	+	0.158261i
$601$	3.70136e16	+	5.09449e16i	0.785443	+	1.08107i	0.994661	+	0.103200i	$0.0329082\pi$
$601$	3.70136e16	+	5.09449e16i	0.785443	+	1.08107i	−0.209218	+	0.977869i	$0.567092\pi$
$602$	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	−0.455504	−	0.890234i	$-0.650541\pi$
$607$	−1.50430e16	+	4.88778e15i	−0.300749	+	0.0977192i	0.154756	+	0.987953i	$0.450541\pi$
$608$	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	−0.988676	−	0.150068i	$-0.952051\pi$
$613$	−2.86752e16	+	3.94680e16i	−0.540435	+	0.743844i	0.448241	+	0.893913i	$0.352051\pi$
$614$	−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	0.608018	−	0.793923i	$-0.291965\pi$
$619$	2.29737e15	+	1.66914e15i	0.0408401	+	0.0296721i	−0.567178	+	0.823595i	$0.691965\pi$
$620$	−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	−0.768330	−	0.640055i	$-0.778912\pi$
$631$	−2.50610e16	+	1.82079e16i	−0.397028	+	0.288458i	0.371301	+	0.928513i	$0.378912\pi$
$632$	−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	0.726326	−	0.687350i	$-0.241226\pi$
$641$	2.06063e16	+	1.49713e16i	0.297065	+	0.215830i	−0.429262	+	0.903180i	$0.641226\pi$
$642$	5.73215e16	−	4.16465e16i	0.818667	−	0.594797i
$643$	1.57101e16	−	4.83508e16i	0.222287	−	0.684129i	−0.776269	−	0.630402i	$-0.782890\pi$
$643$	1.57101e16	−	4.83508e16i	0.222287	−	0.684129i	0.998556	−	0.0537268i	$-0.0171100\pi$
$644$	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	0.833415	−	0.552648i	$-0.186382\pi$
$647$	−1.21526e16	−	3.74019e16i	−0.165670	−	0.509880i	−0.999085	+	0.0427677i	$0.986382\pi$
$648$		−	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	−0.974817	−	0.223005i	$-0.928413\pi$
$653$	−8.24907e16	+	5.99330e16i	−1.06396	+	0.773014i	−0.0891447	+	0.996019i	$0.528413\pi$
$654$	−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	$0.249597\pi$
$659$			1.15685e17i			1.41242i	−0.708001	+	0.706211i	$0.750403\pi$
$660$	−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	−0.672680	−	0.739934i	$-0.734857\pi$
$673$	−7.26572e16	+	2.36078e16i	−0.781967	+	0.254076i	−0.109287	+	0.994010i	$0.534857\pi$
$674$	−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	0.236278	−	0.971685i	$-0.424072\pi$
$677$	−1.38363e16	−	4.49570e15i	−0.143711	−	0.0466944i	−0.379989	+	0.924991i	$0.624072\pi$
$678$	−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	−0.977791	−	0.209580i	$-0.932790\pi$
$691$	−3.37390e16	−	1.03838e17i	−0.309930	−	0.953866i	0.667862	−	0.744286i	$-0.267210\pi$
$692$			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	−0.891480	−	0.453061i	$-0.850332\pi$
$701$	−2.19654e16	+	3.02328e16i	−0.185111	+	0.254783i	0.706369	+	0.707844i	$0.250332\pi$
$702$	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	0.620479	+	0.784223i	$0.286938\pi$
$709$	−4.34990e16	+	1.33876e17i	−0.342454	+	1.05396i	−0.962933	+	0.269741i	$0.913062\pi$
$710$	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	0.0907628	−	0.995873i	$-0.471069\pi$
$719$	1.47267e17	−	1.06996e17i	1.06594	−	0.774452i	0.975178	+	0.221421i	$0.0710695\pi$
$720$	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	0.932430	+	0.361351i	$0.117684\pi$
$733$	1.53237e17	+	2.10912e17i	0.987958	+	1.35981i	0.0555283	+	0.998457i	$0.482316\pi$
$734$	−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	−0.160200	−	0.987085i	$-0.551214\pi$
$739$	4.72986e16	−	1.53682e16i	0.290390	−	0.0943534i	0.450590	+	0.892731i	$0.351214\pi$
$740$	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	0.193420	−	0.981116i	$-0.438042\pi$
$743$	−3.81547e16	−	1.23972e16i	−0.226785	−	0.0736870i	−0.420205	+	0.907429i	$0.638042\pi$
$744$	−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	−0.999982	−	0.00599447i	$-0.998092\pi$
$751$	−2.35866e17	−	1.71366e17i	−1.31469	−	0.955182i	−0.314713	−	0.949187i	$-0.601908\pi$
$752$	−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	0.869819	−	0.493371i	$-0.164236\pi$
$757$	−2.33111e16	−	7.17441e16i	−0.123876	−	0.381251i	−0.993695	+	0.112121i	$0.964236\pi$
$758$			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	0.144312	−	0.989532i	$-0.453903\pi$
$761$	1.63673e17	−	5.31807e16i	0.842695	−	0.273808i	0.698383	+	0.715724i	$0.253903\pi$
$762$	−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	$-0.919396\pi$
$769$		−	1.03619e17i		−	0.501052i	0.968110	−	0.250526i	$-0.0806036\pi$
$770$	−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	0.254818	−	0.966989i	$-0.417984\pi$
$773$	−1.25040e17	−	9.08467e16i	−0.586100	−	0.425826i	−0.840918	+	0.541163i	$0.817984\pi$
$774$	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	−0.0863473	−	0.996265i	$-0.527519\pi$
$787$	−1.76251e17	−	5.72674e16i	−0.741794	−	0.241023i	−0.655446	+	0.755242i	$0.727519\pi$
$788$	−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	0.688768	+	0.724981i	$0.258152\pi$
$797$	−7.55037e16	+	2.32377e17i	−0.294590	+	0.906656i	−0.983359	+	0.181674i	$0.941848\pi$
$798$	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	0.707495	−	0.706719i	$-0.249825\pi$
$809$	2.42349e17	+	7.87440e16i	0.864471	+	0.280884i	0.156976	+	0.987602i	$0.449825\pi$
$810$	−1.06390e16	−	1.46434e16i	−0.0376697	−	0.0518479i
$811$	−2.92446e17	+	4.02518e17i	−1.02783	+	1.41469i	−0.121264	+	0.992620i	$0.538695\pi$
$811$	−2.92446e17	+	4.02518e17i	−1.02783	+	1.41469i	−0.906565	+	0.422065i	$0.861305\pi$
$812$	−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	0.942090	−	0.335360i	$-0.108858\pi$
$821$	1.01678e17	+	1.39947e17i	0.332022	+	0.456989i	−0.610068	+	0.792349i	$0.708858\pi$
$822$	1.74814e17	−	2.40611e17i	0.566690	−	0.779982i
$823$	3.62093e16	+	1.11441e17i	0.116525	+	0.358628i	0.992262	−	0.124161i	$-0.0396238\pi$
$823$	3.62093e16	+	1.11441e17i	0.116525	+	0.358628i	−0.875737	+	0.482789i	$0.839624\pi$
$824$		−	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	−0.572108	−	0.820179i	$-0.693874\pi$
$827$	−1.76869e17	+	5.74681e16i	−0.552864	+	0.179636i	0.0192441	+	0.999815i	$0.493874\pi$
$828$	1.52343e17	+	1.10684e17i	0.472760	+	0.343480i
$829$	−1.62988e17	+	1.18418e17i	−0.502144	+	0.364829i	−0.809835	−	0.586657i	$-0.800444\pi$
$829$	−1.62988e17	+	1.18418e17i	−0.502144	+	0.364829i	0.307692	+	0.951486i	$0.400444\pi$
$830$	−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	−0.269739	−	0.962934i	$-0.586937\pi$
$839$	−4.42586e17	−	3.21558e17i	−1.26890	−	0.921907i	−0.999158	+	0.0410263i	$0.986937\pi$
$840$	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	−0.518804	−	0.854893i	$-0.673623\pi$
$853$	−5.55091e17	−	1.80360e17i	−1.44102	−	0.468216i	−0.922215	+	0.386677i	$0.873623\pi$
$854$	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	$0.0513701\pi$
$857$			1.27318e17i			0.321369i	−0.987006	+	0.160684i	$0.948630\pi$
$858$	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	−0.802668	−	0.596426i	$-0.796587\pi$
$863$	8.14957e16	−	2.50818e17i	0.197274	−	0.607147i	0.999943	−	0.0107217i	$-0.00341290\pi$
$864$	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	−0.876090	−	0.482147i	$-0.839857\pi$
$877$	−6.67984e16	+	9.19401e16i	−0.146814	+	0.202073i	0.729276	+	0.684220i	$0.239857\pi$
$878$	−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	−0.193954	−	0.981011i	$-0.562131\pi$
$883$	−5.62566e17	−	4.08728e17i	−1.18689	−	0.862323i	−0.992932	+	0.118688i	$0.962131\pi$
$884$	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	0.817215	−	0.576333i	$-0.195517\pi$
$887$	8.06316e15	+	1.10980e16i	0.0165563	+	0.0227878i	−0.800659	+	0.599121i	$0.795517\pi$
$888$	−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	0.720167	+	0.693801i	$0.244065\pi$
$907$	−1.50465e17	+	4.63084e17i	−0.270266	+	0.831794i	−0.990433	+	0.137993i	$0.955935\pi$
$908$	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	0.890933	−	0.454135i	$-0.150052\pi$
$911$	−5.53223e16	−	1.70265e17i	−0.0967810	−	0.297861i	−0.987714	+	0.156274i	$0.950052\pi$
$912$			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	0.600615	−	0.799538i	$-0.294923\pi$
$919$	3.71426e17	+	1.20684e17i	0.616566	+	0.200334i	0.0159507	+	0.999873i	$0.494923\pi$
$920$	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	0.806865	+	0.590737i	$0.201163\pi$
$929$	−1.24148e17	+	3.82090e17i	−0.193129	+	0.594389i	−0.999993	+	0.00365286i	$0.998837\pi$
$930$	−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	0.210448	−	0.977605i	$-0.432508\pi$
$937$	6.46530e17	−	2.10070e17i	0.955325	−	0.310404i	0.744878	+	0.667201i	$0.232508\pi$
$938$	−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	−0.539324	−	0.842098i	$-0.681320\pi$
$941$	−1.02103e18	−	3.31752e17i	−1.47062	−	0.477833i	−0.931295	+	0.364265i	$0.881320\pi$
$942$	−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	0.924771	−	0.380523i	$-0.124256\pi$
$953$	2.07585e17	+	2.85717e17i	0.277102	+	0.381398i	−0.647669	+	0.761922i	$0.724256\pi$
$954$	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	$0.408901\pi$
$967$			1.56875e18i			1.91865i	−0.282304	+	0.959325i	$0.591099\pi$
$968$	−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	0.825815	−	0.563942i	$-0.190716\pi$
$971$	4.56504e17	+	3.31670e17i	0.544665	+	0.395722i	−0.281150	+	0.959664i	$0.590716\pi$
$972$	−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	−0.905723	−	0.423869i	$-0.860672\pi$
$977$	−3.67118e17	−	1.12987e18i	−0.422122	−	1.29916i	0.483602	−	0.875288i	$-0.339328\pi$
$978$			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	−0.429811	+	0.902919i	$0.641420\pi$
$983$	−1.28240e18	+	9.31719e17i	−1.42136	+	1.03268i	−0.991546	+	0.129757i	$0.958580\pi$
$984$	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	0.651820	−	0.758374i	$-0.274006\pi$
$997$	−2.66021e17	−	3.66146e17i	−0.270860	−	0.372806i	−0.922680	+	0.385567i	$0.874006\pi$
$998$	−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.17.1	yes	48
11.2	odd	10	inner	22.13.d.a.13.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.13.d.a.13.1	✓	48	11.2	odd	10	inner
22.13.d.a.17.1	yes	48	1.1	even	1	trivial

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

Related objects

Downloads

Learn more