LMFDB - Embedded newform 7.7.d.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,7,Mod(3,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, degree $2$, 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:	$1.61037858534$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	7.3
Dual form			7.7.d.b.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.12132 - 7.13834i) q^{2} +(-23.0772 - 13.3236i) q^{3} +(-1.97056 + 3.41311i) q^{4} +(68.5660 - 39.5866i) q^{5} +219.643i q^{6} +(337.286 + 62.3451i) q^{7} -495.044 q^{8} +(-9.46299 - 16.3904i) q^{9} +O(q^{10})$	\(q+(-4.12132 - 7.13834i) q^{2} +(-23.0772 - 13.3236i) q^{3} +(-1.97056 + 3.41311i) q^{4} +(68.5660 - 39.5866i) q^{5} +219.643i q^{6} +(337.286 + 62.3451i) q^{7} -495.044 q^{8} +(-9.46299 - 16.3904i) q^{9} +(-565.165 - 326.298i) q^{10} +(854.459 - 1479.97i) q^{11} +(90.9500 - 52.5100i) q^{12} +3129.09i q^{13} +(-945.025 - 2664.61i) q^{14} -2109.75 q^{15} +(2166.35 + 3752.23i) q^{16} +(3529.96 + 2038.03i) q^{17} +(-78.0000 + 135.100i) q^{18} +(5085.89 - 2936.34i) q^{19} +312.032i q^{20} +(-6952.95 - 5932.62i) q^{21} -14086.0 q^{22} +(-6660.75 - 11536.8i) q^{23} +(11424.2 + 6595.77i) q^{24} +(-4678.30 + 8103.05i) q^{25} +(22336.5 - 12896.0i) q^{26} +19930.1i q^{27} +(-877.435 + 1028.34i) q^{28} +6510.23 q^{29} +(8694.94 + 15060.1i) q^{30} +(-10386.6 - 5996.69i) q^{31} +(2015.04 - 3490.16i) q^{32} +(-39437.0 + 22769.0i) q^{33} -33597.4i q^{34} +(25594.4 - 9077.27i) q^{35} +74.5896 q^{36} +(2320.45 + 4019.14i) q^{37} +(-41921.2 - 24203.2i) q^{38} +(41690.8 - 72210.6i) q^{39} +(-33943.2 + 19597.1i) q^{40} +19308.8i q^{41} +(-13693.7 + 74082.7i) q^{42} +91636.4 q^{43} +(3367.53 + 5832.73i) q^{44} +(-1297.68 - 749.215i) q^{45} +(-54902.2 + 95093.3i) q^{46} +(-55800.2 + 32216.2i) q^{47} -115454. i q^{48} +(109875. + 42056.3i) q^{49} +77123.1 q^{50} +(-54307.7 - 94063.7i) q^{51} +(-10680.0 - 6166.07i) q^{52} +(-74799.9 + 129557. i) q^{53} +(142268. - 82138.5i) q^{54} -135301. i q^{55} +(-166971. - 30863.5i) q^{56} -156491. q^{57} +(-26830.7 - 46472.2i) q^{58} +(52855.0 + 30515.9i) q^{59} +(4157.39 - 7200.80i) q^{60} +(-85403.4 + 49307.7i) q^{61} +98857.1i q^{62} +(-2169.88 - 6118.22i) q^{63} +244074. q^{64} +(123870. + 214549. i) q^{65} +(325065. + 187676. i) q^{66} +(155906. - 270038. i) q^{67} +(-13912.0 + 8032.11i) q^{68} +354981. i q^{69} +(-170279. - 145291. i) q^{70} -401209. q^{71} +(4684.59 + 8113.95i) q^{72} +(-582322. - 336204. i) q^{73} +(19126.6 - 33128.3i) q^{74} +(215924. - 124664. i) q^{75} +23145.0i q^{76} +(380466. - 445901. i) q^{77} -687285. q^{78} +(160076. + 277260. i) q^{79} +(297076. + 171517. i) q^{80} +(258643. - 447983. i) q^{81} +(137833. - 79577.6i) q^{82} +832356. i q^{83} +(33949.9 - 12040.6i) q^{84} +322714. q^{85} +(-377663. - 654131. i) q^{86} +(-150238. - 86739.7i) q^{87} +(-422995. + 732648. i) q^{88} +(328654. - 189748. i) q^{89} +12351.0i q^{90} +(-195084. + 1.05540e6i) q^{91} +52501.7 q^{92} +(159795. + 276773. i) q^{93} +(459941. + 265547. i) q^{94} +(232480. - 402666. i) q^{95} +(-93003.0 + 53695.3i) q^{96} -1.05514e6i q^{97} +(-152619. - 957653. i) q^{98} -32342.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9	\( 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9} - 1200 q^{10} + 1882 q^{11} + 4284 q^{12} - 1820 q^{14} - 16500 q^{15} + 248 q^{16} + 13458 q^{17} - 312 q^{18} + 18078 q^{19} - 16170 q^{21} - 28088 q^{22} + 2470 q^{23} + 24840 q^{24} + 2500 q^{25} + 43848 q^{26} - 45444 q^{28} - 34544 q^{29} + 15900 q^{30} - 17202 q^{31} + 7008 q^{32} - 67770 q^{33} + 154350 q^{35} + 82368 q^{36} - 43870 q^{37} - 81924 q^{38} + 10668 q^{39} - 76800 q^{40} - 22344 q^{42} + 320216 q^{43} - 4332 q^{44} - 187200 q^{45} - 113636 q^{46} - 354714 q^{47} + 140140 q^{49} + 160000 q^{50} + 28206 q^{51} + 196056 q^{52} + 104530 q^{53} + 285876 q^{54} - 346192 q^{56} + 25164 q^{57} - 59432 q^{58} - 62646 q^{59} - 384300 q^{60} - 140682 q^{61} + 181272 q^{63} - 33248 q^{64} - 77700 q^{65} + 652824 q^{66} + 432494 q^{67} + 381276 q^{68} - 338100 q^{70} - 1481528 q^{71} + 29328 q^{72} - 971778 q^{73} + 50024 q^{74} + 1192500 q^{75} + 642670 q^{77} - 1409856 q^{78} + 935990 q^{79} + 1767000 q^{80} + 1104066 q^{81} + 286776 q^{82} - 1405908 q^{84} - 579300 q^{85} - 738712 q^{86} - 1826208 q^{87} - 840616 q^{88} - 679290 q^{89} + 711480 q^{91} + 2124456 q^{92} + 395958 q^{93} + 860892 q^{94} - 291750 q^{95} + 5040 q^{96} - 361424 q^{98} + 157872 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9 - 1200 * q^10 + 1882 * q^11 + 4284 * q^12 - 1820 * q^14 - 16500 * q^15 + 248 * q^16 + 13458 * q^17 - 312 * q^18 + 18078 * q^19 - 16170 * q^21 - 28088 * q^22 + 2470 * q^23 + 24840 * q^24 + 2500 * q^25 + 43848 * q^26 - 45444 * q^28 - 34544 * q^29 + 15900 * q^30 - 17202 * q^31 + 7008 * q^32 - 67770 * q^33 + 154350 * q^35 + 82368 * q^36 - 43870 * q^37 - 81924 * q^38 + 10668 * q^39 - 76800 * q^40 - 22344 * q^42 + 320216 * q^43 - 4332 * q^44 - 187200 * q^45 - 113636 * q^46 - 354714 * q^47 + 140140 * q^49 + 160000 * q^50 + 28206 * q^51 + 196056 * q^52 + 104530 * q^53 + 285876 * q^54 - 346192 * q^56 + 25164 * q^57 - 59432 * q^58 - 62646 * q^59 - 384300 * q^60 - 140682 * q^61 + 181272 * q^63 - 33248 * q^64 - 77700 * q^65 + 652824 * q^66 + 432494 * q^67 + 381276 * q^68 - 338100 * q^70 - 1481528 * q^71 + 29328 * q^72 - 971778 * q^73 + 50024 * q^74 + 1192500 * q^75 + 642670 * q^77 - 1409856 * q^78 + 935990 * q^79 + 1767000 * q^80 + 1104066 * q^81 + 286776 * q^82 - 1405908 * q^84 - 579300 * q^85 - 738712 * q^86 - 1826208 * q^87 - 840616 * q^88 - 679290 * q^89 + 711480 * q^91 + 2124456 * q^92 + 395958 * q^93 + 860892 * q^94 - 291750 * q^95 + 5040 * q^96 - 361424 * q^98 + 157872 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−4.12132	−	7.13834i	−0.515165	−	0.892292i	−0.999845	−	0.0176005i	$-0.994397\pi$
$2$	−4.12132	−	7.13834i	−0.515165	−	0.892292i	0.484680	−	0.874692i	$-0.338936\pi$
$3$	−23.0772	−	13.3236i	−0.854710	−	0.493467i	0.00752738	−	0.999972i	$-0.497604\pi$
$3$	−23.0772	−	13.3236i	−0.854710	−	0.493467i	−0.862237	+	0.506505i	$0.830937\pi$
$4$	−1.97056	+	3.41311i	−0.0307900	+	0.0533299i
$5$	68.5660	−	39.5866i	0.548528	−	0.316693i	−0.200000	−	0.979796i	$-0.564094\pi$
$5$	68.5660	−	39.5866i	0.548528	−	0.316693i	0.748528	+	0.663103i	$0.230761\pi$
$6$			219.643i			1.01687i
$7$	337.286	+	62.3451i	0.983342	+	0.181764i
$7$	337.286	+	62.3451i	0.983342	+	0.181764i
$8$	−495.044			−0.966882
$9$	−9.46299	−	16.3904i	−0.0129808	−	0.0224834i
$10$	−565.165	−	326.298i	−0.565165	−	0.326298i
$11$	854.459	−	1479.97i	0.641968	−	1.11192i	−0.343025	−	0.939326i	$-0.611452\pi$
$11$	854.459	−	1479.97i	0.641968	−	1.11192i	0.984993	−	0.172594i	$-0.0552150\pi$
$12$	90.9500	−	52.5100i	0.0526331	−	0.0303877i
$13$			3129.09i			1.42426i	0.702049	+	0.712129i	$0.252269\pi$
$13$			3129.09i			1.42426i	−0.702049	+	0.712129i	$0.747731\pi$
$14$	−945.025	−	2664.61i	−0.344397	−	0.971067i
$15$	−2109.75			−0.625110
$16$	2166.35	+	3752.23i	0.528894	+	0.916071i
$17$	3529.96	+	2038.03i	0.718494	+	0.414823i	0.814198	−	0.580587i	$-0.197177\pi$
$17$	3529.96	+	2038.03i	0.718494	+	0.414823i	−0.0957039	+	0.995410i	$0.530510\pi$
$18$	−78.0000	+	135.100i	−0.0133745	+	0.0231653i
$19$	5085.89	−	2936.34i	0.741492	−	0.428101i	−0.0811196	−	0.996704i	$-0.525850\pi$
$19$	5085.89	−	2936.34i	0.741492	−	0.428101i	0.822611	+	0.568604i	$0.192516\pi$
$20$			312.032i			0.0390039i
$21$	−6952.95	−	5932.62i	−0.750778	−	0.640602i
$22$	−14086.0			−1.32288
$23$	−6660.75	−	11536.8i	−0.547444	−	0.948201i	−0.998449	−	0.0556791i	$-0.982268\pi$
$23$	−6660.75	−	11536.8i	−0.547444	−	0.948201i	0.451005	−	0.892522i	$-0.351066\pi$
$24$	11424.2	+	6595.77i	0.826404	+	0.477124i
$25$	−4678.30	+	8103.05i	−0.299411	+	0.518596i
$26$	22336.5	−	12896.0i	1.27085	−	0.733728i
$27$			19930.1i			1.01256i
$28$	−877.435	+	1028.34i	−0.0399706	+	0.0468450i
$29$	6510.23			0.266933			0.133466	−	0.991053i	$-0.457389\pi$
$29$	6510.23			0.266933			0.133466	+	0.991053i	$0.457389\pi$
$30$	8694.94	+	15060.1i	0.322035	+	0.557781i
$31$	−10386.6	−	5996.69i	−0.348648	−	0.201292i	0.315442	−	0.948945i	$-0.397847\pi$
$31$	−10386.6	−	5996.69i	−0.348648	−	0.201292i	−0.664090	+	0.747653i	$0.731181\pi$
$32$	2015.04	−	3490.16i	0.0614943	−	0.106511i
$33$	−39437.0	+	22769.0i	−1.09739	+	0.633580i
$34$		−	33597.4i		−	0.854809i
$35$	25594.4	−	9077.27i	0.596954	−	0.211715i
$36$	74.5896			0.00159871
$37$	2320.45	+	4019.14i	0.0458107	+	0.0793465i	0.888022	−	0.459802i	$-0.152080\pi$
$37$	2320.45	+	4019.14i	0.0458107	+	0.0793465i	−0.842211	+	0.539148i	$0.818746\pi$
$38$	−41921.2	−	24203.2i	−0.763981	−	0.441085i
$39$	41690.8	−	72210.6i	0.702824	−	1.21733i
$40$	−33943.2	+	19597.1i	−0.530362	+	0.306205i
$41$			19308.8i			0.280158i	0.990140	+	0.140079i	$0.0447357\pi$
$41$			19308.8i			0.280158i	−0.990140	+	0.140079i	$0.955264\pi$
$42$	−13693.7	+	74082.7i	−0.184830	+	0.999929i
$43$	91636.4			1.15256			0.576279	−	0.817253i	$-0.304504\pi$
$43$	91636.4			1.15256			0.576279	+	0.817253i	$0.304504\pi$
$44$	3367.53	+	5832.73i	0.0395324	+	0.0684722i
$45$	−1297.68	−	749.215i	−0.0142406	−	0.00822184i
$46$	−54902.2	+	95093.3i	−0.564048	+	0.976960i
$47$	−55800.2	+	32216.2i	−0.537455	+	0.310300i	−0.744047	−	0.668128i	$-0.767096\pi$
$47$	−55800.2	+	32216.2i	−0.537455	+	0.310300i	0.206592	+	0.978427i	$0.433763\pi$
$48$		−	115454.i		−	1.04397i
$49$	109875.	+	42056.3i	0.933924	+	0.357473i
$50$	77123.1			0.616985
$51$	−54307.7	−	94063.7i	−0.409403	−	0.709106i
$52$	−10680.0	−	6166.07i	−0.0759555	−	0.0438529i
$53$	−74799.9	+	129557.i	−0.502428	+	0.870230i	0.497568	+	0.867425i	$0.334226\pi$
$53$	−74799.9	+	129557.i	−0.502428	+	0.870230i	−0.999996	+	0.00280549i	$0.999107\pi$
$54$	142268.	−	82138.5i	0.903496	−	0.521634i
$55$		−	135301.i		−	0.813226i
$56$	−166971.	−	30863.5i	−0.950776	−	0.175744i
$57$	−156491.			−0.845014
$58$	−26830.7	−	46472.2i	−0.137515	−	0.238182i
$59$	52855.0	+	30515.9i	0.257354	+	0.148583i	0.623127	−	0.782121i	$-0.285862\pi$
$59$	52855.0	+	30515.9i	0.257354	+	0.148583i	−0.365773	+	0.930704i	$0.619195\pi$
$60$	4157.39	−	7200.80i	0.0192472	−	0.0333371i
$61$	−85403.4	+	49307.7i	−0.376258	+	0.217233i	−0.676189	−	0.736728i	$-0.736370\pi$
$61$	−85403.4	+	49307.7i	−0.376258	+	0.217233i	0.299931	+	0.953961i	$0.403036\pi$
$62$			98857.1i			0.414794i
$63$	−2169.88	−	6118.22i	−0.00867788	−	0.0244683i
$64$	244074.			0.931069
$65$	123870.	+	214549.i	0.451052	+	0.781245i
$66$	325065.	+	187676.i	1.13068	+	0.652796i
$67$	155906.	−	270038.i	0.518369	−	0.897842i	−0.481403	−	0.876499i	$-0.659873\pi$
$67$	155906.	−	270038.i	0.518369	−	0.897842i	0.999772	−	0.0213423i	$-0.00679398\pi$
$68$	−13912.0	+	8032.11i	−0.0442449	+	0.0255448i
$69$			354981.i			1.08058i
$70$	−170279.	−	145291.i	−0.496441	−	0.423589i
$71$	−401209.			−1.12097			−0.560487	−	0.828163i	$-0.689386\pi$
$71$	−401209.			−1.12097			−0.560487	+	0.828163i	$0.689386\pi$
$72$	4684.59	+	8113.95i	0.0125509	+	0.0217388i
$73$	−582322.	−	336204.i	−1.49691	−	0.864239i	−0.496912	−	0.867801i	$-0.665533\pi$
$73$	−582322.	−	336204.i	−1.49691	−	0.864239i	−0.999994	+	0.00356186i	$0.998866\pi$
$74$	19126.6	−	33128.3i	0.0472002	−	0.0817531i
$75$	215924.	−	124664.i	0.511819	−	0.295499i
$76$			23145.0i			0.0527249i
$77$	380466.	−	445901.i	0.833381	−	0.976712i
$78$	−687285.			−1.44828
$79$	160076.	+	277260.i	0.324672	+	0.562348i	0.981446	−	0.191739i	$-0.0614128\pi$
$79$	160076.	+	277260.i	0.324672	+	0.562348i	−0.656774	+	0.754087i	$0.728079\pi$
$80$	297076.	+	171517.i	0.580226	+	0.334994i
$81$	258643.	−	447983.i	0.486682	−	0.842958i
$82$	137833.	−	79577.6i	0.249983	−	0.144328i
$83$			832356.i			1.45571i	0.685731	+	0.727855i	$0.259483\pi$
$83$			832356.i			1.45571i	−0.685731	+	0.727855i	$0.740517\pi$
$84$	33949.9	−	12040.6i	0.0572797	−	0.0203147i
$85$	322714.			0.525486
$86$	−377663.	−	654131.i	−0.593757	−	1.02842i
$87$	−150238.	−	86739.7i	−0.228150	−	0.131723i
$88$	−422995.	+	732648.i	−0.620707	+	1.07510i
$89$	328654.	−	189748.i	0.466196	−	0.269158i	−0.248450	−	0.968645i	$-0.579921\pi$
$89$	328654.	−	189748.i	0.466196	−	0.269158i	0.714646	+	0.699486i	$0.246588\pi$
$90$			12351.0i			0.0169424i
$91$	−195084.	+	1.05540e6i	−0.258879	+	1.40053i
$92$	52501.7			0.0674233
$93$	159795.	+	276773.i	0.198662	+	0.344092i
$94$	459941.	+	265547.i	0.553756	+	0.319711i
$95$	232480.	−	402666.i	0.271153	−	0.469650i
$96$	−93003.0	+	53695.3i	−0.105119	+	0.0606908i
$97$		−	1.05514e6i		−	1.15610i	−0.816001	−	0.578050i	$-0.803814\pi$
$97$		−	1.05514e6i		−	1.15610i	0.816001	−	0.578050i	$-0.196186\pi$
$98$	−152619.	−	957653.i	−0.162155	−	1.01749i
$99$	−32342.9			−0.0333330
$100$	−18437.8	−	31935.2i	−0.0184378	−	0.0319352i
$101$	73886.6	+	42658.4i	0.0717136	+	0.0414039i	0.535428	−	0.844581i	$-0.320150\pi$
$101$	73886.6	+	42658.4i	0.0717136	+	0.0414039i	−0.463714	+	0.885985i	$0.653484\pi$
$102$	−447639.	+	775333.i	−0.421820	+	0.730614i
$103$	−710952.	+	410468.i	−0.650621	+	0.375636i	−0.788694	−	0.614786i	$-0.789243\pi$
$103$	−710952.	+	410468.i	−0.650621	+	0.375636i	0.138073	+	0.990422i	$0.455909\pi$
$104$		−	1.54904e6i		−	1.37709i
$105$	−711588.	−	131532.i	−0.614697	−	0.113623i
$106$	1.23310e6			1.03533
$107$	−155767.	−	269796.i	−0.127152	−	0.220234i	0.795420	−	0.606059i	$-0.207250\pi$
$107$	−155767.	−	269796.i	−0.127152	−	0.220234i	−0.922572	+	0.385825i	$0.873917\pi$
$108$	−68023.9	−	39273.6i	−0.0539995	−	0.0311766i
$109$	−159434.	+	276148.i	−0.123113	+	0.213237i	−0.920994	−	0.389578i	$-0.872621\pi$
$109$	−159434.	+	276148.i	−0.123113	+	0.213237i	0.797881	+	0.602815i	$0.205954\pi$
$110$	−965821.	+	557617.i	−0.725635	+	0.418946i
$111$		−	123667.i		−	0.0904243i
$112$	496747.	+	1.40064e6i	0.353575	+	0.996945i
$113$	1.29031e6			0.894253			0.447126	−	0.894471i	$-0.352447\pi$
$113$	1.29031e6			0.894253			0.447126	+	0.894471i	$0.352447\pi$
$114$	644948.	+	1.11708e6i	0.435322	+	0.753999i
$115$	−913402.	−	527353.i	−0.600577	−	0.346743i
$116$	−12828.8	+	22220.2i	−0.00821888	+	0.0142355i
$117$	51287.0	−	29610.6i	0.0320221	−	0.0184880i
$118$		−	503063.i		−	0.306179i
$119$	1.06355e6	+	907474.i	0.631126	+	0.538509i
$120$	1.04442e6			0.604408
$121$	−574420.	−	994924.i	−0.324245	−	0.561609i
$122$	703949.	+	406425.i	0.387670	+	0.223821i
$123$	257263.	−	445592.i	0.138249	−	0.239454i
$124$	40934.8	−	23633.7i	0.0214698	−	0.0123956i
$125$			1.97787e6i			1.01267i
$126$	−34731.2	+	40704.5i	−0.0173623	+	0.0203484i
$127$	−1.93791e6			−0.946068			−0.473034	−	0.881044i	$-0.656841\pi$
$127$	−1.93791e6			−0.946068			−0.473034	+	0.881044i	$0.656841\pi$
$128$	−1.13487e6	−	1.96565e6i	−0.541149	−	0.937297i
$129$	−2.11471e6	−	1.22093e6i	−0.985102	−	0.568749i
$130$	1.02102e6	−	1.76845e6i	0.464733	−	0.804940i
$131$	−867795.	+	501022.i	−0.386014	+	0.222865i	−0.680432	−	0.732811i	$-0.738208\pi$
$131$	−867795.	+	501022.i	−0.386014	+	0.222865i	0.294417	+	0.955677i	$0.404874\pi$
$132$		−	179471.i		−	0.0780318i
$133$	1.89847e6	−	673308.i	0.806953	−	0.286193i
$134$	−2.57016e6			−1.06818
$135$	788967.	+	1.36653e6i	0.320669	+	0.555416i
$136$	−1.74749e6	−	1.00891e6i	−0.694699	−	0.401085i
$137$	−905043.	+	1.56758e6i	−0.351971	+	0.609632i	−0.986595	−	0.163189i	$-0.947822\pi$
$137$	−905043.	+	1.56758e6i	−0.351971	+	0.609632i	0.634623	+	0.772822i	$0.281155\pi$
$138$	2.53397e6	−	1.46299e6i	0.964195	−	0.556678i
$139$		−	1.68964e6i		−	0.629145i	−0.949233	−	0.314573i	$-0.898139\pi$
$139$		−	1.68964e6i		−	0.629145i	0.949233	−	0.314573i	$-0.101861\pi$
$140$	−19453.6	+	105244.i	−0.00708952	+	0.0383542i
$141$	1.71695e6			0.612490
$142$	1.65351e6	+	2.86396e6i	0.577487	+	1.00024i
$143$	4.63095e6	+	2.67368e6i	1.58366	+	0.914327i
$144$	41000.3	−	71014.6i	0.0137309	−	0.0237826i
$145$	446380.	−	257718.i	0.146420	−	0.0845358i
$146$			5.54241e6i			1.78090i
$147$	−1.97527e6	−	2.43447e6i	−0.621833	−	0.766396i
$148$	−18290.4			−0.00564206
$149$	−884078.	−	1.53127e6i	−0.267259	−	0.462906i	0.700894	−	0.713265i	$-0.252784\pi$
$149$	−884078.	−	1.53127e6i	−0.267259	−	0.462906i	−0.968153	+	0.250360i	$0.919451\pi$
$150$	−1.77978e6	−	1.02756e6i	−0.527343	−	0.304462i
$151$	336812.	−	583376.i	0.0978267	−	0.169441i	−0.812958	−	0.582322i	$-0.802144\pi$
$151$	336812.	−	583376.i	0.0978267	−	0.169441i	0.910785	+	0.412881i	$0.135478\pi$
$152$	−2.51774e6	+	1.45362e6i	−0.716935	+	0.413923i
$153$		−	77143.2i		−	0.0215389i
$154$	−4.75101e6	−	878193.i	−1.30084	−	0.240452i
$155$	−949554.			−0.254991
$156$	164309.	+	284591.i	0.0432800	+	0.0749631i
$157$	5.53760e6	+	3.19714e6i	1.43094	+	0.826156i	0.997193	−	0.0748767i	$-0.0238563\pi$
$157$	5.53760e6	+	3.19714e6i	1.43094	+	0.826156i	0.433751	+	0.901033i	$0.357190\pi$
$158$	1.31945e6	−	2.28535e6i	0.334519	−	0.579404i
$159$	3.45234e6	−	1.99321e6i	0.858860	−	0.495863i
$160$		−	319075.i		−	0.0778992i
$161$	−1.52732e6	−	4.30646e6i	−0.365976	−	1.03191i
$162$	−4.26380e6			−1.00289
$163$	412138.	+	713844.i	0.0951655	+	0.164832i	0.909678	−	0.415315i	$-0.136329\pi$
$163$	412138.	+	713844.i	0.0951655	+	0.164832i	−0.814512	+	0.580147i	$0.802995\pi$
$164$	−65903.1	−	38049.2i	−0.0149408	−	0.00862608i
$165$	−1.80269e6	+	3.12235e6i	−0.401300	+	0.695073i
$166$	5.94164e6	−	3.43041e6i	1.29892	−	0.749931i
$167$		−	4.22248e6i		−	0.906605i	−0.891357	−	0.453303i	$-0.850246\pi$
$167$		−	4.22248e6i		−	0.906605i	0.891357	−	0.453303i	$-0.149754\pi$
$168$	3.44201e6	+	2.93691e6i	0.725914	+	0.619387i
$169$	−4.96442e6			−1.02851
$170$	−1.33001e6	−	2.30364e6i	−0.270712	−	0.468887i
$171$	−96255.5	−	55573.1i	−0.0192503	−	0.0111142i
$172$	−180575.	+	312766.i	−0.0354873	+	0.0614658i
$173$	−6.17496e6	+	3.56512e6i	−1.19260	+	0.688550i	−0.958896	−	0.283757i	$-0.908419\pi$
$173$	−6.17496e6	+	3.56512e6i	−1.19260	+	0.688550i	−0.233707	+	0.972307i	$0.575086\pi$
$174$			1.42993e6i			0.271435i
$175$	−2.08311e6	+	2.44138e6i	−0.388686	+	0.455535i
$176$	7.40423e6			1.35813
$177$	−813163.	−	1.40844e6i	−0.146642	−	0.253991i
$178$	−2.70898e6	−	1.56403e6i	−0.480336	−	0.277322i
$179$	−1.92765e6	+	3.33879e6i	−0.336101	+	0.582144i	−0.983696	−	0.179841i	$-0.942442\pi$
$179$	−1.92765e6	+	3.33879e6i	−0.336101	+	0.582144i	0.647595	+	0.761985i	$0.275775\pi$
$180$	5114.31	−	2952.75i	0.000876940	−	0.000506302i
$181$			6.61340e6i			1.11529i	0.830079	+	0.557646i	$0.188295\pi$
$181$			6.61340e6i			1.11529i	−0.830079	+	0.557646i	$0.811705\pi$
$182$	8.33781e6	−	2.95707e6i	1.38305	−	0.490510i
$183$	2.62782e6			0.428788
$184$	3.29736e6	+	5.71120e6i	0.529314	+	0.916798i
$185$	318208.	+	183718.i	0.0502569	+	0.0290159i
$186$	1.31713e6	−	2.28134e6i	0.204687	−	0.354529i
$187$	6.03242e6	−	3.48282e6i	0.922500	−	0.532606i
$188$		−	253936.i		−	0.0382166i
$189$	−1.24255e6	+	6.72217e6i	−0.184046	+	0.995689i
$190$	−3.83249e6			−0.558754
$191$	−3.48201e6	−	6.03102e6i	−0.499724	−	0.865547i	0.500276	−	0.865866i	$-0.333232\pi$
$191$	−3.48201e6	−	6.03102e6i	−0.499724	−	0.865547i	−1.00000		0.000318612i	$0.999899\pi$
$192$	−5.63254e6	−	3.25195e6i	−0.795794	−	0.459452i
$193$	2.20298e6	−	3.81567e6i	0.306435	−	0.530760i	−0.671145	−	0.741326i	$-0.734197\pi$
$193$	2.20298e6	−	3.81567e6i	0.306435	−	0.530760i	0.977580	+	0.210566i	$0.0675306\pi$
$194$	−7.53195e6	+	4.34858e6i	−1.03158	+	0.595582i
$195$		−	6.60159e6i		−	0.890317i
$196$	−360059.	+	292142.i	−0.0478195	+	0.0387995i
$197$	8.03700e6			1.05122			0.525612	−	0.850724i	$-0.323836\pi$
$197$	8.03700e6			1.05122			0.525612	+	0.850724i	$0.323836\pi$
$198$	133296.	+	230875.i	0.0171720	+	0.0297427i
$199$	−1.02987e7	−	5.94597e6i	−1.30684	−	0.754507i	−0.325276	−	0.945619i	$-0.605457\pi$
$199$	−1.02987e7	−	5.94597e6i	−1.30684	−	0.754507i	−0.981568	+	0.191112i	$0.938791\pi$
$200$	2.31596e6	−	4.01137e6i	0.289495	−	0.501421i
$201$	−7.19575e6	+	4.15447e6i	−0.886110	+	0.511596i
$202$		−	703236.i		−	0.0853193i
$203$	2.19581e6	+	405881.i	0.262486	+	0.0485188i
$204$	428067.			0.0504221
$205$	764369.	+	1.32393e6i	0.0887241	+	0.153675i
$206$	5.86012e6	+	3.38334e6i	0.670355	+	0.387030i
$207$	−126061.	+	218344.i	−0.0142125	+	0.0246168i
$208$	−1.17411e7	+	6.77871e6i	−1.30472	+	0.753281i
$209$		−	1.00359e7i		−	1.09931i
$210$	1.99376e6	+	5.62164e6i	0.215286	+	0.607023i
$211$	6.94536e6			0.739345			0.369673	−	0.929162i	$-0.379470\pi$
$211$	6.94536e6			0.739345			0.369673	+	0.929162i	$0.379470\pi$
$212$	−294796.	−	510601.i	−0.0309395	−	0.0535889i
$213$	9.25877e6	+	5.34555e6i	0.958108	+	0.553164i
$214$	−1.28393e6	+	2.22383e6i	−0.131009	+	0.226914i
$215$	6.28314e6	−	3.62757e6i	0.632210	−	0.365007i
$216$		−	9.86629e6i		−	0.979023i
$217$	−3.12938e6	−	2.67015e6i	−0.306252	−	0.261310i
$218$	2.62832e6			0.253693
$219$	8.95889e6	+	1.55173e7i	0.852947	+	1.47735i
$220$	461796.	+	266618.i	0.0433693	+	0.0250393i
$221$	−6.37717e6	+	1.10456e7i	−0.590815	+	1.02332i
$222$	−882777.	+	509672.i	−0.0806849	+	0.0465834i
$223$			9.06445e6i			0.817386i	0.912672	+	0.408693i	$0.134015\pi$
$223$			9.06445e6i			0.817386i	−0.912672	+	0.408693i	$0.865985\pi$
$224$	897241.	−	1.05155e6i	0.0798298	−	0.0935595i
$225$	177083.			0.0155464
$226$	−5.31780e6	−	9.21070e6i	−0.460688	−	0.797934i
$227$	−5.43728e6	−	3.13922e6i	−0.464841	−	0.268376i	0.249237	−	0.968443i	$-0.419820\pi$
$227$	−5.43728e6	−	3.13922e6i	−0.464841	−	0.268376i	−0.714077	+	0.700067i	$0.753154\pi$
$228$	308375.	−	534121.i	0.0260180	−	0.0450645i
$229$	1.74716e7	−	1.00872e7i	1.45488	−	0.839974i	0.456126	−	0.889915i	$-0.349237\pi$
$229$	1.74716e7	−	1.00872e7i	1.45488	−	0.839974i	0.998752	+	0.0499415i	$0.0159035\pi$
$230$			8.69356e6i			0.714520i
$231$	−1.47211e7	+	5.22096e6i	−1.19427	+	0.423559i
$232$	−3.22285e6			−0.258093
$233$	−1.10365e7	−	1.91158e7i	−0.872496	−	1.51121i	−0.859407	−	0.511293i	$-0.829167\pi$
$233$	−1.10365e7	−	1.91158e7i	−0.872496	−	1.51121i	−0.0130889	−	0.999914i	$-0.504166\pi$
$234$	−422740.	−	244069.i	−0.0329933	−	0.0190487i
$235$	−2.55066e6	+	4.41788e6i	−0.196539	+	0.340416i
$236$	−208308.	+	120267.i	−0.0158479	+	0.00914976i
$237$		−	8.53115e6i		−	0.640859i
$238$	2.09463e6	−	1.13320e7i	0.155374	−	0.840570i
$239$	−5.36550e6			−0.393022			−0.196511	−	0.980502i	$-0.562961\pi$
$239$	−5.36550e6			−0.393022			−0.196511	+	0.980502i	$0.562961\pi$
$240$	−4.57045e6	−	7.91625e6i	−0.330617	−	0.572645i
$241$	9.98289e6	+	5.76362e6i	0.713190	+	0.411760i	0.812241	−	0.583322i	$-0.198247\pi$
$241$	9.98289e6	+	5.76362e6i	0.713190	+	0.411760i	−0.0990512	+	0.995082i	$0.531581\pi$
$242$	−4.73474e6	+	8.20080e6i	−0.334079	+	0.578642i
$243$	645059.	−	372425.i	0.0449553	−	0.0259549i
$244$		−	388655.i		−	0.0267544i
$245$	9.19857e6	−	1.46595e6i	0.625492	−	0.0996832i
$246$	−4.24105e6			−0.284884
$247$	9.18809e6	+	1.59142e7i	0.609725	+	1.05608i
$248$	5.14181e6	+	2.96862e6i	0.337101	+	0.194626i
$249$	1.10900e7	−	1.92084e7i	0.718345	−	1.24421i
$250$	1.41187e7	−	8.15145e6i	0.903599	−	0.521693i
$251$			8.22585e6i			0.520187i	0.965583	+	0.260094i	$0.0837535\pi$
$251$			8.22585e6i			0.520187i	−0.965583	+	0.260094i	$0.916247\pi$
$252$	25158.1	+	4650.30i	0.00157208	+	0.000290589i
$253$	−2.27654e7			−1.40577
$254$	7.98675e6	+	1.38335e7i	0.487381	+	0.844169i
$255$	−7.44732e6	−	4.29971e6i	−0.449138	−	0.259310i
$256$	−1.54396e6	+	2.67421e6i	−0.0920270	+	0.159396i
$257$	−2.03099e7	+	1.17260e7i	−1.19649	+	0.690794i	−0.959771	−	0.280784i	$-0.909406\pi$
$257$	−2.03099e7	+	1.17260e7i	−1.19649	+	0.690794i	−0.236720	+	0.971578i	$0.576072\pi$
$258$			2.01273e7i			1.17200i
$259$	532083.	+	1.50027e6i	0.0306253	+	0.0863515i
$260$	−976376.			−0.0555517
$261$	−61606.2	−	106705.i	−0.00346500	−	0.00600155i
$262$	7.15293e6	+	4.12974e6i	0.397722	+	0.229625i
$263$	6.27475e6	−	1.08682e7i	0.344929	−	0.597434i	−0.640412	−	0.768031i	$-0.721236\pi$
$263$	6.27475e6	−	1.08682e7i	0.344929	−	0.597434i	0.985341	+	0.170598i	$0.0545698\pi$
$264$	1.95230e7	−	1.12716e7i	1.06105	−	0.612597i
$265$			1.18443e7i			0.636461i
$266$	−1.26305e7	−	1.07770e7i	−0.671082	−	0.572602i
$267$	−1.01125e7			−0.531283
$268$	614446.	+	1.06425e6i	0.0319212	+	0.0552892i
$269$	−1.73800e6	−	1.00344e6i	−0.0892881	−	0.0515505i	0.454691	−	0.890649i	$-0.349750\pi$
$269$	−1.73800e6	−	1.00344e6i	−0.0892881	−	0.0515505i	−0.543979	+	0.839099i	$0.683083\pi$
$270$	6.50317e6	−	1.12638e7i	0.330395	−	0.572261i
$271$	−4.67469e6	+	2.69893e6i	−0.234879	+	0.135608i	−0.612821	−	0.790222i	$-0.709965\pi$
$271$	−4.67469e6	+	2.69893e6i	−0.234879	+	0.135608i	0.377942	+	0.925829i	$0.376632\pi$
$272$			1.76603e7i			0.877589i
$273$	1.85637e7	−	2.17564e7i	0.912383	−	1.06930i
$274$	1.49199e7			0.725293
$275$	7.99483e6	+	1.38475e7i	0.384425	+	0.665843i
$276$	−1.21159e6	−	699512.i	−0.0576273	−	0.0332712i
$277$	8.46055e6	−	1.46541e7i	0.398070	−	0.689477i	−0.595418	−	0.803416i	$-0.703013\pi$
$277$	8.46055e6	−	1.46541e7i	0.398070	−	0.689477i	0.993488	+	0.113939i	$0.0363468\pi$
$278$	−1.20612e7	+	6.96357e6i	−0.561381	+	0.324114i
$279$			226986.i			0.0104517i
$280$	−1.26704e7	+	4.49365e6i	−0.577184	+	0.204703i
$281$	2.07013e6			0.0932994			0.0466497	−	0.998911i	$-0.485146\pi$
$281$	2.07013e6			0.0932994			0.0466497	+	0.998911i	$0.485146\pi$
$282$	−7.07608e6	−	1.22561e7i	−0.315534	−	0.546520i
$283$	−3.23089e7	−	1.86536e7i	−1.42549	−	0.823005i	−0.428725	−	0.903435i	$-0.641037\pi$
$283$	−3.23089e7	−	1.86536e7i	−1.42549	−	0.823005i	−0.996760	+	0.0804303i	$0.974371\pi$
$284$	790608.	−	1.36937e6i	0.0345148	−	0.0597815i
$285$	−1.07299e7	+	6.19493e6i	−0.463514	+	0.267610i
$286$		−	4.40764e7i		−	1.88412i
$287$	−1.20381e6	+	6.51259e6i	−0.0509227	+	0.275491i
$288$	−76273.3			−0.00319297
$289$	−3.76169e6	−	6.51544e6i	−0.155844	−	0.269929i
$290$	−3.67935e6	−	2.12428e6i	−0.150861	−	0.0870997i
$291$	−1.40583e7	+	2.43497e7i	−0.570497	+	0.988130i
$292$	2.29500e6	−	1.32502e6i	0.0921796	−	0.0532199i
$293$			1.58491e7i			0.630089i	0.949077	+	0.315045i	$0.102019\pi$
$293$			1.58491e7i			0.630089i	−0.949077	+	0.315045i	$0.897981\pi$
$294$	−9.23739e6	+	2.41334e7i	−0.363502	+	0.949677i
$295$	4.83208e6			0.188221
$296$	−1.14872e6	−	1.98965e6i	−0.0442936	−	0.0767187i
$297$	2.94959e7	+	1.70295e7i	1.12588	+	0.650028i
$298$	−7.28714e6	+	1.26217e7i	−0.275365	+	0.476945i
$299$	3.60996e7	−	2.08421e7i	1.35048	−	0.779701i
$300$			982630.i			0.0363937i
$301$	3.09077e7	+	5.71308e6i	1.13336	+	0.209494i
$302$	−5.55245e6			−0.201588
$303$	−1.13673e6	−	1.96887e6i	−0.0408629	−	0.0707766i
$304$	2.20356e7	+	1.27223e7i	0.784341	+	0.452840i
$305$	−3.90385e6	+	6.76166e6i	−0.137592	+	0.238316i
$306$	−550674.	+	317932.i	−0.0192190	+	0.0110961i
$307$		−	1.77302e7i		−	0.612772i	−0.951907	−	0.306386i	$-0.900880\pi$
$307$		−	1.77302e7i		−	0.612772i	0.951907	−	0.306386i	$-0.0991198\pi$
$308$	772180.	+	2.17725e6i	0.0264281	+	0.0745171i
$309$	2.18757e7			0.741457
$310$	3.91342e6	+	6.77824e6i	0.131362	+	0.227526i
$311$	1.64992e7	+	9.52581e6i	0.548506	+	0.316680i	0.748519	−	0.663113i	$-0.230765\pi$
$311$	1.64992e7	+	9.52581e6i	0.548506	+	0.316680i	−0.200013	+	0.979793i	$0.564099\pi$
$312$	−2.06388e7	+	3.57474e7i	−0.679548	+	1.17701i
$313$	−5.01014e7	+	2.89261e7i	−1.63387	+	0.943314i	−0.650983	+	0.759092i	$0.725643\pi$
$313$	−5.01014e7	+	2.89261e7i	−1.63387	+	0.943314i	−0.982885	+	0.184222i	$0.941024\pi$
$314$		−	5.27057e7i		−	1.70243i
$315$	−390979.	−	333604.i	−0.0125090	−	0.0106733i
$316$	−1.26176e6			−0.0399866
$317$	−2.31329e7	−	4.00673e7i	−0.726193	−	1.25780i	−0.958481	−	0.285156i	$-0.907955\pi$
$317$	−2.31329e7	−	4.00673e7i	−0.726193	−	1.25780i	0.232288	−	0.972647i	$-0.425379\pi$
$318$	−2.84564e7	−	1.64293e7i	−0.884909	−	0.510902i
$319$	5.56272e6	−	9.63492e6i	0.171362	−	0.296808i
$320$	1.67352e7	−	9.66207e6i	0.510718	−	0.294863i
$321$			8.30151e6i			0.250982i
$322$	−2.44464e7	+	2.86508e7i	−0.732228	+	0.858162i
$323$	2.39373e7			0.710344
$324$	1.01934e6	+	1.76556e6i	0.0299699	+	0.0519094i
$325$	−2.53552e7	−	1.46388e7i	−0.738613	−	0.426439i
$326$	3.39710e6	−	5.88396e6i	0.0980519	−	0.169831i
$327$	7.35859e6	−	4.24848e6i	0.210451	−	0.121504i
$328$		−	9.55869e6i		−	0.270880i
$329$	−2.08292e7	+	7.38723e6i	−0.584903	+	0.207441i
$330$	2.97179e7			0.826944
$331$	−5.50862e6	−	9.54121e6i	−0.151900	−	0.263099i	0.780026	−	0.625747i	$-0.215206\pi$
$331$	−5.50862e6	−	9.54121e6i	−0.151900	−	0.263099i	−0.931926	+	0.362648i	$0.881873\pi$
$332$	−2.84093e6	−	1.64021e6i	−0.0776329	−	0.0448214i
$333$	43916.8	−	76066.1i	0.00118932	−	0.00205996i
$334$	−3.01415e7	+	1.74022e7i	−0.808956	+	0.467051i
$335$		−	2.46872e7i		−	0.656655i
$336$	7.19801e6	−	3.89412e7i	0.189756	−	1.02658i
$337$	5.44482e7			1.42264			0.711318	−	0.702871i	$-0.248099\pi$
$337$	5.44482e7			1.42264			0.711318	+	0.702871i	$0.248099\pi$
$338$	2.04599e7	+	3.54377e7i	0.529852	+	0.917730i
$339$	−2.97768e7	−	1.71916e7i	−0.764326	−	0.441284i
$340$	−635928.	+	1.10146e6i	−0.0161797	+	0.0280241i
$341$	−1.77498e7	+	1.02478e7i	−0.447641	+	0.258446i
$342$			916139.i			0.0229025i
$343$	3.44374e7	+	2.10352e7i	0.853391	+	0.521272i
$344$	−4.53640e7			−1.11439
$345$	1.40525e7	+	2.43396e7i	0.342213	+	0.592730i
$346$	5.08980e7	+	2.93860e7i	1.22878	+	0.709434i
$347$	2.97763e7	−	5.15740e7i	0.712659	−	1.23436i	−0.251197	−	0.967936i	$-0.580824\pi$
$347$	2.97763e7	−	5.15740e7i	0.712659	−	1.23436i	0.963856	−	0.266425i	$-0.0858426\pi$
$348$	592105.	−	341852.i	0.0140495	−	0.00811149i
$349$			6.05869e7i			1.42529i	0.701526	+	0.712644i	$0.252502\pi$
$349$			6.05869e7i			1.42529i	−0.701526	+	0.712644i	$0.747498\pi$
$350$	2.60126e7	+	4.80825e6i	0.606707	+	0.112146i
$351$	−6.23633e7			−1.44214
$352$	−3.44354e6	−	5.96439e6i	−0.0789546	−	0.136753i
$353$	−1.04579e7	−	6.03788e6i	−0.237750	−	0.137265i	0.376392	−	0.926461i	$-0.377165\pi$
$353$	−1.04579e7	−	6.03788e6i	−0.237750	−	0.137265i	−0.614142	+	0.789195i	$0.710498\pi$
$354$	−6.70261e6	+	1.16093e7i	−0.151089	+	0.261695i
$355$	−2.75093e7	+	1.58825e7i	−0.614886	+	0.355005i
$356$			1.49564e6i			0.0331496i
$357$	−1.24528e7	−	3.51122e7i	−0.273693	−	0.771709i
$358$	3.17779e7			0.692590
$359$	2.97916e7	+	5.16005e7i	0.643888	+	1.11525i	0.984557	+	0.175063i	$0.0560130\pi$
$359$	2.97916e7	+	5.16005e7i	0.643888	+	1.11525i	−0.340669	+	0.940183i	$0.610654\pi$
$360$	642408.	+	370894.i	0.0137690	+	0.00794955i
$361$	−6.27874e6	+	1.08751e7i	−0.133460	+	0.231159i
$362$	4.72087e7	−	2.72559e7i	0.995167	−	0.574560i
$363$			3.06134e7i			0.640017i
$364$	−3.21778e6	−	2.74558e6i	−0.0667194	−	0.0569284i
$365$	−5.32366e7			−1.09479
$366$	−1.08301e7	−	1.87583e7i	−0.220897	−	0.382604i
$367$	−8.96105e6	−	5.17366e6i	−0.181285	−	0.104665i	0.406612	−	0.913601i	$-0.366710\pi$
$367$	−8.96105e6	−	5.17366e6i	−0.181285	−	0.104665i	−0.587896	+	0.808936i	$0.700044\pi$
$368$	2.88590e7	−	4.99853e7i	0.579080	−	1.00300i
$369$	316478.	−	182719.i	0.00629890	−	0.00363667i
$370$		−	3.02864e6i		−	0.0597918i
$371$	−3.33063e7	+	3.90345e7i	−0.652235	+	0.764411i
$372$	−1.25954e6			−0.0244672
$373$	−4.13816e7	−	7.16750e7i	−0.797408	−	1.38115i	−0.921299	−	0.388856i	$-0.872870\pi$
$373$	−4.13816e7	−	7.16750e7i	−0.797408	−	1.38115i	0.123890	−	0.992296i	$-0.460463\pi$
$374$	−4.97230e7	−	2.87076e7i	−0.950480	−	0.548760i
$375$	2.63524e7	−	4.56437e7i	0.499720	−	0.865540i
$376$	2.76235e7	−	1.59484e7i	0.519655	−	0.300023i
$377$			2.03711e7i			0.380181i
$378$	5.31060e7	−	1.88345e7i	0.983260	−	0.348721i
$379$	−2.44479e7			−0.449079			−0.224540	−	0.974465i	$-0.572088\pi$
$379$	−2.44479e7			−0.449079			−0.224540	+	0.974465i	$0.572088\pi$
$380$	916231.	+	1.58696e6i	0.0166976	+	0.0289211i
$381$	4.47215e7	+	2.58200e7i	0.808614	+	0.466853i
$382$	−2.87010e7	+	4.97116e7i	−0.514881	+	0.891800i
$383$	7.59138e7	−	4.38289e7i	1.35122	−	0.780125i	0.362796	−	0.931869i	$-0.381822\pi$
$383$	7.59138e7	−	4.38289e7i	1.35122	−	0.780125i	0.988420	+	0.151744i	$0.0484889\pi$
$384$			6.04823e7i			1.06816i
$385$	8.43532e6	−	4.56350e7i	0.147815	−	0.799680i
$386$	−3.63167e7			−0.631458
$387$	−867154.	−	1.50196e6i	−0.0149611	−	0.0259134i
$388$	3.60132e6	+	2.07922e6i	0.0616547	+	0.0355964i
$389$	−5.10227e7	+	8.83740e7i	−0.866792	+	1.50133i	−0.00153550	+	0.999999i	$0.500489\pi$
$389$	−5.10227e7	+	8.83740e7i	−0.866792	+	1.50133i	−0.865257	+	0.501329i	$0.832845\pi$
$390$	−4.71244e7	+	2.72073e7i	−0.794423	+	0.458660i
$391$		−	5.42991e7i		−	0.908369i
$392$	−5.43930e7	−	2.08197e7i	−0.902994	−	0.345634i
$393$	2.67017e7			0.439907
$394$	−3.31231e7	−	5.73708e7i	−0.541554	−	0.937999i
$395$	2.19515e7	+	1.26737e7i	0.356183	+	0.205642i
$396$	63733.8	−	110390.i	0.00102632	−	0.00177764i
$397$	5.76513e7	−	3.32850e7i	0.921378	−	0.531958i	0.0373033	−	0.999304i	$-0.488123\pi$
$397$	5.76513e7	−	3.32850e7i	0.921378	−	0.531958i	0.884074	+	0.467346i	$0.154790\pi$
$398$			9.80209e7i			1.55478i
$399$	−5.27822e7	−	9.75642e6i	−0.830938	−	0.153593i
$400$	−4.05393e7			−0.633427
$401$	5.27910e7	+	9.14368e7i	0.818704	+	1.41804i	0.906637	+	0.421911i	$0.138641\pi$
$401$	5.27910e7	+	9.14368e7i	0.818704	+	1.41804i	−0.0879328	+	0.996126i	$0.528026\pi$
$402$	5.93120e7	+	3.42438e7i	0.912986	+	0.527113i
$403$	1.87642e7	−	3.25005e7i	0.286691	−	0.496564i
$404$	−291196.	+	168122.i	−0.00441613	+	0.00254965i
$405$		−	4.09552e7i		−	0.616515i
$406$	−6.15233e6	−	1.73472e7i	−0.0919309	−	0.259210i
$407$	7.93092e6			0.117636
$408$	2.68847e7	+	4.65656e7i	0.395844	+	0.685622i
$409$	3.06502e7	+	1.76959e7i	0.447986	+	0.258645i	0.706979	−	0.707234i	$-0.250057\pi$
$409$	3.06502e7	+	1.76959e7i	0.447986	+	0.258645i	−0.258993	+	0.965879i	$0.583391\pi$
$410$	6.30042e6	−	1.09126e7i	0.0914151	−	0.158336i
$411$	4.17716e7	−	2.41169e7i	0.601667	−	0.347372i
$412$		−	3.23541e6i		−	0.0462634i
$413$	1.59248e7	+	1.35878e7i	0.226060	+	0.192886i
$414$	2.07815e6			0.0292871
$415$	3.29502e7	+	5.70713e7i	0.461013	+	0.798498i
$416$	1.09210e7	+	6.30526e6i	0.151699	+	0.0875836i
$417$	−2.25122e7	+	3.89922e7i	−0.310462	+	0.537737i
$418$	−7.16399e7	+	4.13613e7i	−0.980903	+	0.566324i
$419$		−	1.04532e8i		−	1.42105i	−0.703673	−	0.710524i	$-0.748458\pi$
$419$		−	1.04532e8i		−	1.42105i	0.703673	−	0.710524i	$-0.251542\pi$
$420$	1.85116e6	−	2.16954e6i	0.0249860	−	0.0292833i
$421$	2.80706e7			0.376189			0.188094	−	0.982151i	$-0.439769\pi$
$421$	2.80706e7			0.376189			0.188094	+	0.982151i	$0.439769\pi$
$422$	−2.86240e7	−	4.95783e7i	−0.380885	−	0.659712i
$423$	1.05607e6	+	609724.i	0.0139532	+	0.00805586i
$424$	3.70292e7	−	6.41365e7i	0.485788	−	0.841410i
$425$	−3.30285e7	+	1.90690e7i	−0.430251	+	0.248405i
$426$		−	8.81229e7i		−	1.13988i
$427$	−3.18795e7	+	1.13063e7i	−0.409475	+	0.145224i
$428$	1.22779e6			0.0156601
$429$	−7.12462e7	−	1.23402e8i	−0.902380	−	1.56297i
$430$	−5.17897e7	−	2.99008e7i	−0.651385	−	0.376078i
$431$	−5.79149e7	+	1.00312e8i	−0.723366	+	1.25291i	0.236276	+	0.971686i	$0.424073\pi$
$431$	−5.79149e7	+	1.00312e8i	−0.723366	+	1.25291i	−0.959643	+	0.281222i	$0.909260\pi$
$432$	−7.47824e7	+	4.31757e7i	−0.927574	+	0.535535i
$433$			2.47052e7i			0.304315i	0.988356	+	0.152158i	$0.0486222\pi$
$433$			2.47052e7i			0.304315i	−0.988356	+	0.152158i	$0.951378\pi$
$434$	−6.16325e6	+	3.33431e7i	−0.0753947	+	0.407885i
$435$	−1.37349e7			−0.166862
$436$	−628351.	−	1.08834e6i	−0.00758128	−	0.0131312i
$437$	−6.77517e7	−	3.91165e7i	−0.811850	−	0.468722i
$438$	7.38449e7	−	1.27903e8i	0.878817	−	1.52216i
$439$	−2.00244e7	+	1.15611e7i	−0.236682	+	0.136648i	−0.613651	−	0.789578i	$-0.710300\pi$
$439$	−2.00244e7	+	1.15611e7i	−0.236682	+	0.136648i	0.376969	+	0.926226i	$0.376966\pi$
$440$			6.69797e7i			0.786294i
$441$	−350429.	−	2.19887e6i	−0.00408587	−	0.0256380i
$442$	1.05129e8			1.21747
$443$	3.30373e7	+	5.72222e7i	0.380008	+	0.658194i	0.991063	−	0.133395i	$-0.0425878\pi$
$443$	3.30373e7	+	5.72222e7i	0.380008	+	0.658194i	−0.611055	+	0.791588i	$0.709254\pi$
$444$	422090.	+	243694.i	0.00482232	+	0.00278417i
$445$	1.50230e7	−	2.60206e7i	0.170481	−	0.295282i
$446$	6.47051e7	−	3.73575e7i	0.729347	−	0.421088i
$447$			4.71164e7i			0.527533i
$448$	8.23229e7	+	1.52168e7i	0.915560	+	0.169235i
$449$	5.93142e7			0.655269			0.327635	−	0.944805i	$-0.393749\pi$
$449$	5.93142e7			0.655269			0.327635	+	0.944805i	$0.393749\pi$
$450$	−729815.	−	1.26408e6i	−0.00800894	−	0.0138719i
$451$	2.85763e7	+	1.64986e7i	0.311514	+	0.179852i
$452$	−2.54265e6	+	4.40399e6i	−0.0275341	+	0.0476904i
$453$	−1.55454e7	+	8.97511e6i	−0.167227	+	0.0965484i
$454$			5.17508e7i			0.553032i
$455$	2.84036e7	+	8.00873e7i	0.301536	+	0.850216i
$456$	7.74697e7			0.817029
$457$	3.59605e7	+	6.22853e7i	0.376770	+	0.652585i	0.990590	−	0.136861i	$-0.0437013\pi$
$457$	3.59605e7	+	6.22853e7i	0.376770	+	0.652585i	−0.613820	+	0.789446i	$0.710368\pi$
$458$	−1.44012e8	−	8.31455e7i	−1.49900	−	0.865450i
$459$	−4.06181e7	+	7.03527e7i	−0.420032	+	0.727516i
$460$	3.59983e6	−	2.07836e6i	0.0369836	−	0.0213525i
$461$		−	1.69505e8i		−	1.73014i	−0.501652	−	0.865069i	$-0.667274\pi$
$461$		−	1.69505e8i		−	1.73014i	0.501652	−	0.865069i	$-0.332726\pi$
$462$	9.79393e7	+	8.35668e7i	0.993187	+	0.847438i
$463$	−1.48412e8			−1.49529			−0.747644	−	0.664100i	$-0.768815\pi$
$463$	−1.48412e8			−1.49529			−0.747644	+	0.664100i	$0.768815\pi$
$464$	1.41034e7	+	2.44279e7i	0.141179	+	0.244530i
$465$	2.19130e7	+	1.26515e7i	0.217943	+	0.125830i
$466$	−9.09698e7	+	1.57564e8i	−0.898959	+	1.55704i
$467$	−4.75089e7	+	2.74293e7i	−0.466470	+	0.269317i	−0.714761	−	0.699369i	$-0.753465\pi$
$467$	−4.75089e7	+	2.74293e7i	−0.466470	+	0.269317i	0.248291	+	0.968686i	$0.420131\pi$
$468$			233398.i			0.00227698i
$469$	6.94206e7	−	8.13600e7i	0.672930	−	0.788665i
$470$	4.20484e7			0.405001
$471$	−8.51947e7	−	1.47562e8i	−0.815361	−	1.41225i
$472$	−2.61655e7	−	1.51067e7i	−0.248831	−	0.143662i
$473$	7.82996e7	−	1.35619e8i	0.739905	−	1.28155i
$474$	−6.08982e7	+	3.51596e7i	−0.571834	+	0.330148i
$475$			5.49484e7i			0.512712i
$476$	−5.19310e6	+	1.84178e6i	−0.0481511	+	0.0170772i
$477$	2.83132e6			0.0260876
$478$	2.21129e7	+	3.83008e7i	0.202471	+	0.350690i
$479$	4.74847e6	+	2.74153e6i	0.0432063	+	0.0249452i	0.521448	−	0.853283i	$-0.325392\pi$
$479$	4.74847e6	+	2.74153e6i	0.0432063	+	0.0249452i	−0.478241	+	0.878229i	$0.658726\pi$
$480$	−4.25123e6	+	7.36335e6i	−0.0384407	+	0.0665812i
$481$	−1.25763e7	+	7.26091e6i	−0.113010	+	0.0652463i
$482$		−	9.50150e7i		−	0.848498i
$483$	−2.21313e7	+	1.19730e8i	−0.196411	+	1.06258i
$484$	4.52772e6			0.0399341
$485$	−4.17695e7	−	7.23468e7i	−0.366129	−	0.634153i
$486$	−5.31699e6	−	3.06977e6i	−0.0463188	−	0.0267422i
$487$	−3.23529e6	+	5.60369e6i	−0.0280109	+	0.0485163i	−0.879691	−	0.475546i	$-0.842251\pi$
$487$	−3.23529e6	+	5.60369e6i	−0.0280109	+	0.0485163i	0.851680	+	0.524062i	$0.175584\pi$
$488$	4.22784e7	−	2.44094e7i	0.363797	−	0.210038i
$489$		−	2.19647e7i		−	0.187844i
$490$	−4.83747e7	−	5.96208e7i	−0.411178	−	0.506769i
$491$	1.88572e8			1.59306			0.796531	−	0.604597i	$-0.206666\pi$
$491$	1.88572e8			1.59306			0.796531	+	0.604597i	$0.206666\pi$
$492$	1.01390e6	+	1.75613e6i	0.00851337	+	0.0147456i
$493$	2.29809e7	+	1.32680e7i	0.191790	+	0.110730i
$494$	7.57341e7	−	1.31175e8i	0.628218	−	1.08811i
$495$	−2.21763e6	+	1.28035e6i	−0.0182841	+	0.0105563i
$496$		−	5.19637e7i		−	0.425848i
$497$	−1.35322e8	−	2.50134e7i	−1.10230	−	0.203753i
$498$	−1.82822e8			−1.48026
$499$	−9.34328e6	−	1.61830e7i	−0.0751965	−	0.130244i	0.825975	−	0.563706i	$-0.190625\pi$
$499$	−9.34328e6	−	1.61830e7i	−0.0751965	−	0.130244i	−0.901172	+	0.433462i	$0.857292\pi$
$500$	−6.75071e6	−	3.89752e6i	−0.0540057	−	0.0311802i
$501$	−5.62587e7	+	9.74429e7i	−0.447380	+	0.774884i
$502$	5.87189e7	−	3.39014e7i	0.464159	−	0.267982i
$503$			2.76123e7i			0.216970i	0.994098	+	0.108485i	$0.0345999\pi$
$503$			2.76123e7i			0.216970i	−0.994098	+	0.108485i	$0.965400\pi$
$504$	1.07418e6	+	3.02879e6i	0.00839049	+	0.0236579i
$505$	6.75481e6			0.0524492
$506$	9.38233e7	+	1.62507e8i	0.724201	+	1.25435i
$507$	1.14565e8	+	6.61439e7i	0.879077	+	0.507535i
$508$	3.81877e6	−	6.61431e6i	0.0291295	−	0.0504537i
$509$	−2.42224e7	+	1.39848e7i	−0.183681	+	0.106048i	−0.589021	−	0.808118i	$-0.700486\pi$
$509$	−2.42224e7	+	1.39848e7i	−0.183681	+	0.106048i	0.405340	+	0.914166i	$0.367153\pi$
$510$			7.08820e7i			0.534350i
$511$	−1.75449e8	−	1.49702e8i	−1.31488	−	1.12193i
$512$	−1.19811e8			−0.892661
$513$	5.85217e7	+	1.01363e8i	0.433476	+	0.750802i
$514$	1.67408e8	+	9.66528e7i	1.23278	+	0.711746i
$515$	−3.24981e7	+	5.62883e7i	−0.237923	+	0.412094i
$516$	8.33433e6	−	4.81183e6i	0.0606627	−	0.0350236i
$517$			1.10110e8i			0.796809i
$518$	8.51654e6	−	9.98128e6i	0.0612737	−	0.0718120i
$519$	1.90001e8			1.35911
$520$	−6.13212e7	−	1.06211e8i	−0.436114	−	0.755372i
$521$	1.04605e8	+	6.03937e7i	0.739672	+	0.427050i	0.821950	−	0.569560i	$-0.192886\pi$
$521$	1.04605e8	+	6.03937e7i	0.739672	+	0.427050i	−0.0822780	+	0.996609i	$0.526220\pi$
$522$	−507798.	+	879531.i	−0.00357009	+	0.00618358i
$523$	2.02241e7	−	1.16764e7i	0.141372	−	0.0816212i	−0.427646	−	0.903946i	$-0.640657\pi$
$523$	2.02241e7	−	1.16764e7i	0.141372	−	0.0816212i	0.569018	+	0.822325i	$0.307324\pi$
$524$		−	3.94918e6i		−	0.0274482i
$525$	8.06003e7	−	2.85856e7i	0.557005	−	0.197546i
$526$	−1.03441e8			−0.710781
$527$	−2.44428e7	−	4.23362e7i	−0.167001	−	0.289254i
$528$	−1.70869e8	−	9.86510e7i	−1.16081	−	0.670193i
$529$	−1.47132e7	+	2.54841e7i	−0.0993897	+	0.172148i
$530$	8.45486e7	−	4.88142e7i	0.567909	−	0.327882i
$531$		−	1.15508e6i		−	0.00771490i
$532$	−1.44298e6	+	7.80649e6i	−0.00958350	+	0.0518466i
$533$	−6.04190e7			−0.399017
$534$	4.16770e7	+	7.21867e7i	0.273699	+	0.474060i
$535$	−2.13606e7	−	1.23326e7i	−0.139493	−	0.0805364i
$536$	−7.71804e7	+	1.33680e8i	−0.501202	+	0.868107i
$537$	8.89695e7	−	5.13666e7i	0.574537	−	0.331709i
$538$			1.65419e7i			0.106228i
$539$	1.56126e8	−	1.26676e8i	0.997030	−	0.808963i
$540$	−6.21883e6			−0.0394937
$541$	−2.77236e7	−	4.80187e7i	−0.175089	−	0.303263i	0.765103	−	0.643908i	$-0.222688\pi$
$541$	−2.77236e7	−	4.80187e7i	−0.175089	−	0.303263i	−0.940192	+	0.340645i	$0.889355\pi$
$542$	3.85318e7	+	2.22463e7i	0.242003	+	0.139721i
$543$	8.81143e7	−	1.52618e8i	0.550360	−	0.953252i
$544$	1.42261e7	−	8.21342e6i	0.0883666	−	0.0510185i
$545$			2.52459e7i			0.155956i
$546$	−2.31812e8	−	4.28488e7i	−1.42416	−	0.263245i
$547$	−2.34141e8			−1.43059			−0.715295	−	0.698822i	$-0.753708\pi$
$547$	−2.34141e8			−1.43059			−0.715295	+	0.698822i	$0.753708\pi$
$548$	−3.56689e6	−	6.17803e6i	−0.0216744	−	0.0375412i
$549$	1.61634e6	+	933195.i	0.00976824	+	0.00563969i
$550$	6.58985e7	−	1.14140e8i	0.396084	−	0.686038i
$551$	3.31103e7	−	1.91162e7i	0.197929	−	0.114274i
$552$		−	1.75731e8i		−	1.04480i
$553$	3.67056e7	+	1.03496e8i	0.217049	+	0.611994i
$554$	−1.39475e8			−0.820287
$555$	−4.89556e6	−	8.47936e6i	−0.0286367	−	0.0496003i
$556$	5.76695e6	+	3.32955e6i	0.0335523	+	0.0193714i
$557$	−1.04920e7	+	1.81727e7i	−0.0607146	+	0.105161i	−0.894785	−	0.446497i	$-0.852671\pi$
$557$	−1.04920e7	+	1.81727e7i	−0.0607146	+	0.105161i	0.834070	+	0.551658i	$0.186005\pi$
$558$	1.62030e6	−	935483.i	0.00932597	−	0.00538435i
$559$			2.86739e8i			1.64154i
$560$	8.95064e7	+	7.63715e7i	0.509671	+	0.434878i
$561$	−1.85615e8			−1.05129
$562$	−8.53167e6	−	1.47773e7i	−0.0480646	−	0.0832503i
$563$	−2.48295e8	−	1.43353e8i	−1.39137	−	0.803309i	−0.397904	−	0.917427i	$-0.630262\pi$
$563$	−2.48295e8	−	1.43353e8i	−1.39137	−	0.803309i	−0.993467	+	0.114118i	$0.963596\pi$
$564$	−3.38335e6	+	5.86013e6i	−0.0188586	+	0.0326641i
$565$	8.84717e7	−	5.10792e7i	0.490523	−	0.283203i
$566$			3.07509e8i			1.69593i
$567$	1.15166e8	−	1.34973e8i	0.631795	−	0.740455i
$568$	1.98616e8			1.08385
$569$	−8.68401e7	−	1.50411e8i	−0.471393	−	0.816477i	0.528071	−	0.849200i	$-0.322915\pi$
$569$	−8.68401e7	−	1.50411e8i	−0.471393	−	0.816477i	−0.999464	+	0.0327230i	$0.989582\pi$
$570$	8.84430e7	+	5.10626e7i	0.477572	+	0.275726i
$571$	1.16086e8	−	2.01068e8i	0.623553	−	1.08002i	−0.365266	−	0.930903i	$-0.619022\pi$
$571$	1.16086e8	−	2.01068e8i	0.623553	−	1.08002i	0.988819	−	0.149122i	$-0.0476446\pi$
$572$	−1.82512e7	+	1.05373e7i	−0.0975220	+	0.0563043i
$573$			1.85572e8i			0.986389i
$574$	5.14503e7	−	1.82473e7i	0.272052	−	0.0964856i
$575$	1.24644e8			0.655643
$576$	−2.30967e6	−	4.00047e6i	−0.0120860	−	0.0209336i
$577$	−5.17376e6	−	2.98707e6i	−0.0269326	−	0.0155496i	0.486473	−	0.873695i	$-0.338283\pi$
$577$	−5.17376e6	−	2.98707e6i	−0.0269326	−	0.0155496i	−0.513406	+	0.858146i	$0.671616\pi$
$578$	−3.10063e7	+	5.37044e7i	−0.160571	+	0.278116i
$579$	−1.01677e8	+	5.87032e7i	−0.523825	+	0.302431i
$580$			2.03140e6i			0.0104114i
$581$	−5.18933e7	+	2.80742e8i	−0.264596	+	1.43146i
$582$	2.31755e8			1.17560
$583$	1.27827e8	+	2.21403e8i	0.645085	+	1.11732i
$584$	2.88275e8	+	1.66436e8i	1.44733	+	0.835617i
$585$	2.34436e6	−	4.06056e6i	0.0117100	−	0.0202823i
$586$	1.13136e8	−	6.53193e7i	0.562224	−	0.324600i
$587$		−	2.60660e8i		−	1.28872i	−0.764721	−	0.644362i	$-0.777123\pi$
$587$		−	2.60660e8i		−	1.28872i	0.764721	−	0.644362i	$-0.222877\pi$
$588$	1.22015e7	−	1.94453e6i	0.0600181	−	0.00956493i
$589$	−7.04333e7			−0.344693
$590$	−1.99145e7	−	3.44930e7i	−0.0969648	−	0.167948i
$591$	−1.85471e8	−	1.07082e8i	−0.898492	−	0.518744i
$592$	−1.00538e7	+	1.74137e7i	−0.0484580	+	0.0839318i
$593$	−3.49494e8	+	2.01781e8i	−1.67601	+	0.967643i	−0.711843	+	0.702339i	$0.752139\pi$
$593$	−3.49494e8	+	2.01781e8i	−1.67601	+	0.967643i	−0.964165	+	0.265305i	$0.914527\pi$
$594$		−	2.80736e8i		−	1.33949i
$595$	1.08847e8	+	2.01196e7i	0.516732	+	0.0955145i
$596$	6.96852e6			0.0329156
$597$	1.58443e8	+	2.74432e8i	0.744648	+	1.28977i
$598$	−2.97556e8	−	1.71794e8i	−1.39144	−	0.803349i
$599$	−7.70989e7	+	1.33539e8i	−0.358730	+	0.621339i	−0.987749	−	0.156051i	$-0.950123\pi$
$599$	−7.70989e7	+	1.33539e8i	−0.358730	+	0.621339i	0.629019	+	0.777390i	$0.283457\pi$
$600$	−1.06892e8	+	6.17140e7i	−0.494869	+	0.285713i
$601$		−	2.75787e8i		−	1.27043i	−0.772335	−	0.635215i	$-0.780911\pi$
$601$		−	2.75787e8i		−	1.27043i	0.772335	−	0.635215i	$-0.219089\pi$
$602$	−8.65987e7	−	2.44175e8i	−0.396937	−	1.11921i
$603$	−5.90135e6			−0.0269153
$604$	1.32742e6	+	2.29916e6i	0.00602417	+	0.0104342i
$605$	−7.87714e7	−	4.54787e7i	−0.355715	−	0.205372i
$606$	−9.36964e6	+	1.62287e7i	−0.0421022	+	0.0729232i
$607$	−3.11136e7	+	1.79635e7i	−0.139118	+	0.0803201i	−0.567944	−	0.823067i	$-0.692261\pi$
$607$	−3.11136e7	+	1.79635e7i	−0.139118	+	0.0803201i	0.428825	+	0.903387i	$0.358928\pi$
$608$		−	2.36674e7i		−	0.105303i
$609$	−4.52653e7	−	3.86227e7i	−0.200407	−	0.170998i
$610$	6.43560e7			0.283530
$611$	−1.00808e8	−	1.74604e8i	−0.441946	−	0.765474i
$612$	263299.	+	152016.i	0.00114867	+	0.000663184i
$613$	7.66869e7	−	1.32826e8i	0.332920	−	0.576634i	−0.650163	−	0.759795i	$-0.725299\pi$
$613$	7.66869e7	−	1.32826e8i	0.332920	−	0.576634i	0.983083	+	0.183160i	$0.0586327\pi$
$614$	−1.26564e8	+	7.30719e7i	−0.546771	+	0.315679i
$615$		−	4.07366e7i		−	0.175130i
$616$	−1.88347e8	+	2.20741e8i	−0.805781	+	0.944365i
$617$	4.69361e7			0.199826			0.0999130	−	0.994996i	$-0.468144\pi$
$617$	4.69361e7			0.199826			0.0999130	+	0.994996i	$0.468144\pi$
$618$	−9.01566e7	−	1.56156e8i	−0.381973	−	0.661596i
$619$	1.82591e8	+	1.05419e8i	0.769853	+	0.444475i	0.832822	−	0.553541i	$-0.186724\pi$
$619$	1.82591e8	+	1.05419e8i	0.769853	+	0.444475i	−0.0629694	+	0.998015i	$0.520057\pi$
$620$	1.87116e6	−	3.24094e6i	0.00785118	−	0.0135986i
$621$	2.29929e8	−	1.32750e8i	0.960106	−	0.554318i
$622$		−	1.57036e8i		−	0.652570i
$623$	1.22680e8	−	4.35096e7i	0.507354	−	0.179937i
$624$	3.61268e8			1.48688
$625$	5.19886e6	+	9.00470e6i	0.0212945	+	0.0368832i
$626$	4.12968e8	+	2.38427e8i	1.68342	+	0.971925i
$627$	−1.33715e8	+	2.31601e8i	−0.542472	+	0.939588i
$628$	−2.18244e7	+	1.26003e7i	−0.0881177	+	0.0508748i
$629$			1.89165e7i			0.0760134i
$630$	−770025.	+	4.16583e6i	−0.00307952	+	0.0166602i
$631$	2.29695e8			0.914247			0.457124	−	0.889403i	$-0.348880\pi$
$631$	2.29695e8			0.914247			0.457124	+	0.889403i	$0.348880\pi$
$632$	−7.92445e7	−	1.37256e8i	−0.313919	−	0.543724i
$633$	−1.60279e8	−	9.25372e7i	−0.631926	−	0.364842i
$634$	−1.90676e8	+	3.30261e8i	−0.748218	+	1.29595i
$635$	−1.32875e8	+	7.67153e7i	−0.518945	+	0.299613i
$636$			1.57110e7i			0.0610706i
$637$	−1.31598e8	+	3.43810e8i	−0.509133	+	1.33015i
$638$	−9.17030e7			−0.353119
$639$	3.79664e6	+	6.57597e6i	0.0145511	+	0.0252033i
$640$	−1.55627e8	−	8.98514e7i	−0.593670	−	0.342756i
$641$	1.72569e8	−	2.98898e8i	0.655223	−	1.13488i	−0.326615	−	0.945157i	$-0.605908\pi$
$641$	1.72569e8	−	2.98898e8i	0.655223	−	1.13488i	0.981838	−	0.189722i	$-0.0607585\pi$
$642$	5.92590e7	−	3.42132e7i	0.223949	−	0.129297i
$643$		−	2.22892e8i		−	0.838421i	−0.907889	−	0.419210i	$-0.862307\pi$
$643$		−	2.22892e8i		−	0.838421i	0.907889	−	0.419210i	$-0.137693\pi$
$644$	1.77081e7	+	3.27322e6i	0.0663002	+	0.0122551i
$645$	−1.93330e8			−0.720475
$646$	−9.86535e7	−	1.70873e8i	−0.365944	−	0.633834i
$647$	1.98029e8	+	1.14332e8i	0.731165	+	0.422138i	0.818848	−	0.574010i	$-0.194613\pi$
$647$	1.98029e8	+	1.14332e8i	0.731165	+	0.422138i	−0.0876831	+	0.996148i	$0.527946\pi$
$648$	−1.28040e8	+	2.21771e8i	−0.470564	+	0.815041i
$649$	9.03249e7	−	5.21491e7i	0.330425	−	0.190771i
$650$			2.41325e8i			0.878745i
$651$	3.66412e7	+	1.03314e8i	0.132809	+	0.374470i
$652$	−3.24857e6			−0.0117206
$653$	1.75264e8	+	3.03566e8i	0.629438	+	1.09022i	0.987665	+	0.156584i	$0.0500480\pi$
$653$	1.75264e8	+	3.03566e8i	0.629438	+	1.09022i	−0.358227	+	0.933635i	$0.616619\pi$
$654$	−6.06542e7	−	3.50187e7i	−0.216834	−	0.125189i
$655$	−3.96675e7	+	6.87062e7i	−0.141160	+	0.244496i
$656$	−7.24509e7	+	4.18296e7i	−0.256645	+	0.148174i
$657$			1.27260e7i			0.0448740i
$658$	1.38576e8	+	1.18240e8i	0.486419	+	0.415038i
$659$	7.89313e7			0.275799			0.137900	−	0.990446i	$-0.455965\pi$
$659$	7.89313e7			0.275799			0.137900	+	0.990446i	$0.455965\pi$
$660$	−7.10463e6	−	1.23056e7i	−0.0247121	−	0.0428026i
$661$	−1.00944e8	−	5.82803e7i	−0.349525	−	0.201798i	0.314951	−	0.949108i	$-0.398012\pi$
$661$	−1.00944e8	−	5.82803e7i	−0.349525	−	0.201798i	−0.664476	+	0.747310i	$0.731345\pi$
$662$	−4.54056e7	+	7.86447e7i	−0.156507	+	0.271079i
$663$	2.94334e8	−	1.69934e8i	1.00995	−	0.583095i
$664$		−	4.12053e8i		−	1.40750i
$665$	1.03516e8	−	1.21320e8i	0.352002	−	0.412541i
$666$	−723981.			−0.00245078
$667$	−4.33630e7	−	7.51069e7i	−0.146131	−	0.253106i
$668$	1.44118e7	+	8.32066e6i	0.0483492	+	0.0279144i
$669$	1.20771e8	−	2.09182e8i	0.403353	−	0.698627i
$670$	−1.76226e8	+	1.01744e8i	−0.585928	+	0.338286i
$671$			1.68525e8i			0.557825i
$672$	−3.47163e7	+	1.23124e7i	−0.114400	+	0.0405728i
$673$	9.78970e7			0.321162			0.160581	−	0.987023i	$-0.448663\pi$
$673$	9.78970e7			0.321162			0.160581	+	0.987023i	$0.448663\pi$
$674$	−2.24398e8	−	3.88669e8i	−0.732892	−	1.26941i
$675$	−1.61495e8	−	9.32392e7i	−0.525107	−	0.303171i
$676$	9.78269e6	−	1.69441e7i	0.0316678	−	0.0548503i
$677$	9.08049e7	−	5.24263e7i	0.292647	−	0.168960i	−0.346488	−	0.938054i	$-0.612626\pi$
$677$	9.08049e7	−	5.24263e7i	0.292647	−	0.168960i	0.639135	+	0.769095i	$0.279293\pi$
$678$			2.83409e8i			0.909337i
$679$	6.57829e7	−	3.55885e8i	0.210137	−	1.13684i
$680$	−1.59758e8			−0.508083
$681$	8.36513e7	+	1.44888e8i	0.264869	+	0.458767i
$682$	1.46305e8	+	8.44693e7i	0.461218	+	0.266285i
$683$	6.68328e7	−	1.15758e8i	0.209762	−	0.363319i	−0.741877	−	0.670536i	$-0.766064\pi$
$683$	6.68328e7	−	1.15758e8i	0.209762	−	0.363319i	0.951640	+	0.307217i	$0.0993976\pi$
$684$	379355.	−	219021.i	0.00118543	−	0.000684411i
$685$			1.43310e8i			0.445867i
$686$	8.22872e6	−	3.32518e8i	0.0254894	−	1.03001i
$687$	−5.37594e8			−1.65800
$688$	1.98517e8	+	3.43841e8i	0.609581	+	1.05583i
$689$	−4.05397e8	−	2.34056e8i	−1.23943	−	0.715586i
$690$	1.15830e8	−	2.00623e8i	0.352592	−	0.610707i
$691$	−3.39782e8	+	1.96173e8i	−1.02983	+	0.594573i	−0.916936	−	0.399034i	$-0.869346\pi$
$691$	−3.39782e8	+	1.96173e8i	−1.02983	+	0.594573i	−0.112895	+	0.993607i	$0.536012\pi$
$692$		−	2.81011e7i		−	0.0848019i
$693$	−1.09088e7	−	2.01642e6i	−0.0327777	−	0.00605873i
$694$	−4.90870e8			−1.46855
$695$	−6.68873e7	−	1.15852e8i	−0.199246	−	0.345104i
$696$	7.43742e7	+	4.29399e7i	0.220594	+	0.127360i
$697$	−3.93518e7	+	6.81593e7i	−0.116216	+	0.201292i
$698$	4.32490e8	−	2.49698e8i	1.27177	−	0.734259i
$699$			5.88184e8i			1.72219i
$700$	−4.22781e6	−	1.19208e7i	−0.0123260	−	0.0347545i
$701$	3.23223e8			0.938313			0.469156	−	0.883115i	$-0.344558\pi$
$701$	3.23223e8			0.938313			0.469156	+	0.883115i	$0.344558\pi$
$702$	2.57019e8	+	4.45170e8i	0.742940	+	1.28681i
$703$	2.36031e7	+	1.36273e7i	0.0679366	+	0.0392232i
$704$	2.08551e8	−	3.61222e8i	0.597716	−	1.03528i
$705$	1.17724e8	−	6.79681e7i	0.335968	−	0.193971i
$706$			9.95362e7i			0.282857i
$707$	2.22614e7	+	1.89946e7i	0.0629932	+	0.0537491i
$708$	6.40955e6			0.0180604
$709$	9.62589e7	+	1.66725e8i	0.270086	+	0.467803i	0.968884	−	0.247517i	$-0.0796145\pi$
$709$	9.62589e7	+	1.66725e8i	0.270086	+	0.467803i	−0.698798	+	0.715319i	$0.746281\pi$
$710$	2.26749e8	+	1.30914e8i	0.633535	+	0.365772i
$711$	3.02959e6	−	5.24741e6i	0.00842898	−	0.0145994i
$712$	−1.62698e8	+	9.39337e7i	−0.450757	+	0.260245i
$713$			1.59770e8i			0.440784i
$714$	−1.99321e8	+	2.33601e8i	−0.547593	+	0.641772i
$715$	4.23368e8			1.15824
$716$	−7.59712e6	−	1.31586e7i	−0.0206971	−	0.0358485i
$717$	1.23821e8	+	7.14878e7i	0.335920	+	0.193943i
$718$	2.45561e8	−	4.25325e8i	0.663417	−	1.14907i
$719$	−4.36923e8	+	2.52258e8i	−1.17549	+	0.678668i	−0.954966	−	0.296714i	$-0.904109\pi$
$719$	−4.36923e8	+	2.52258e8i	−1.17549	+	0.678668i	−0.220521	+	0.975382i	$0.570776\pi$
$720$		−	6.49225e6i		−	0.0173939i
$721$	−2.65385e8	+	9.41209e7i	−0.708061	+	0.251120i
$722$	1.03507e8			0.275016
$723$	−1.53585e8	−	2.66016e8i	−0.406380	−	0.703871i
$724$	−2.25723e7	−	1.30321e7i	−0.0594785	−	0.0343399i
$725$	−3.04568e7	+	5.27527e7i	−0.0799227	+	0.138430i
$726$	2.18529e8	−	1.26168e8i	0.571082	−	0.329714i
$727$			1.93623e8i			0.503912i	0.967739	+	0.251956i	$0.0810738\pi$
$727$			1.93623e8i			0.503912i	−0.967739	+	0.251956i	$0.918926\pi$
$728$	9.65749e7	−	5.22469e8i	0.250305	−	1.35415i
$729$	−3.96950e8			−1.02460
$730$	2.19405e8	+	3.80021e8i	0.563999	+	0.976875i
$731$	3.23473e8	+	1.86757e8i	0.828106	+	0.478107i
$732$	−5.17829e6	+	8.96906e6i	−0.0132024	+	0.0228672i
$733$	3.80177e8	−	2.19495e8i	0.965326	−	0.557331i	0.0675175	−	0.997718i	$-0.478492\pi$
$733$	3.80177e8	−	2.19495e8i	0.965326	−	0.557331i	0.897808	+	0.440387i	$0.145159\pi$
$734$			8.52893e7i			0.215678i
$735$	−2.31809e8	−	8.87281e7i	−0.583805	−	0.223460i
$736$	−5.36868e7			−0.134659
$737$	−2.66431e8	−	4.61472e8i	−0.665552	−	1.15277i
$738$	−2.60861e6	−	1.50608e6i	−0.00648994	−	0.00374697i
$739$	−1.45040e8	+	2.51216e8i	−0.359379	+	0.622463i	−0.987857	−	0.155364i	$-0.950345\pi$
$739$	−1.45040e8	+	2.51216e8i	−0.359379	+	0.622463i	0.628478	+	0.777827i	$0.283678\pi$
$740$	−1.25410e6	+	724054.i	−0.00309483	+	0.00178680i
$741$		−	4.89674e8i		−	1.20352i
$742$	4.15907e8	+	7.68776e7i	1.01809	+	0.188186i
$743$	−4.99948e8			−1.21887			−0.609437	−	0.792835i	$-0.708604\pi$
$743$	−4.99948e8			−1.21887			−0.609437	+	0.792835i	$0.708604\pi$
$744$	−7.91055e7	−	1.37015e8i	−0.192083	−	0.332697i
$745$	−1.21235e8	−	6.99953e7i	−0.293198	−	0.169278i
$746$	−3.41094e8	+	5.90791e8i	−0.821594	+	1.42304i
$747$	1.36426e7	−	7.87657e6i	0.0327293	−	0.0188962i
$748$			2.74524e7i			0.0655958i
$749$	−3.57176e7	−	1.00710e8i	−0.0850035	−	0.239677i
$750$	−4.34427e8			−1.02975
$751$	−1.39218e8	−	2.41133e8i	−0.328682	−	0.569294i	0.653568	−	0.756867i	$-0.273271\pi$
$751$	−1.39218e8	−	2.41133e8i	−0.328682	−	0.569294i	−0.982251	+	0.187573i	$0.939938\pi$
$752$	−2.41765e8	−	1.39583e8i	−0.568513	−	0.328231i
$753$	1.09598e8	−	1.89829e8i	0.256695	−	0.444609i
$754$	1.45416e8	−	8.39559e7i	0.339233	−	0.195856i
$755$		−	5.33330e7i		−	0.123924i
$756$	−2.04950e7	−	1.74874e7i	−0.0474332	−	0.0404725i
$757$	−6.70960e7			−0.154671			−0.0773356	−	0.997005i	$-0.524641\pi$
$757$	−6.70960e7			−0.154671			−0.0773356	+	0.997005i	$0.524641\pi$
$758$	1.00757e8	+	1.74517e8i	0.231350	+	0.400710i
$759$	5.25360e8	+	3.03317e8i	1.20152	+	0.693699i
$760$	−1.15088e8	+	1.99338e8i	−0.262173	+	0.454097i
$761$	4.30143e8	−	2.48343e8i	0.976020	−	0.563505i	0.0749539	−	0.997187i	$-0.476119\pi$
$761$	4.30143e8	−	2.48343e8i	0.976020	−	0.563505i	0.901066	+	0.433682i	$0.142786\pi$
$762$		−	4.25649e8i		−	0.962026i
$763$	−7.09915e7	+	8.32012e7i	−0.159821	+	0.187308i
$764$	2.74461e7			0.0615461
$765$	−3.05384e6	−	5.28940e6i	−0.00682122	−	0.0118147i
$766$	−6.25731e8	−	3.61266e8i	−1.39220	−	0.803786i
$767$	−9.54870e7	+	1.65388e8i	−0.211621	+	0.366538i
$768$	7.12603e7	−	4.11422e7i	0.157313	−	0.0908246i
$769$		−	4.13153e8i		−	0.908515i	−0.890870	−	0.454258i	$-0.849905\pi$
$769$		−	4.13153e8i		−	0.908515i	0.890870	−	0.454258i	$-0.150095\pi$
$770$	−3.60523e8	+	1.27862e8i	−0.789697	+	0.280073i
$771$	6.24928e8			1.36354
$772$	8.68220e6	+	1.50380e7i	0.0188703	+	0.0326843i
$773$	5.56860e8	+	3.21503e8i	1.20561	+	0.696060i	0.961798	−	0.273762i	$-0.0882680\pi$
$773$	5.56860e8	+	3.21503e8i	1.20561	+	0.696060i	0.243814	+	0.969822i	$0.421601\pi$
$774$	−7.14764e6	+	1.23801e7i	−0.0154149	+	0.0266993i
$775$	9.71830e7	−	5.61086e7i	0.208778	−	0.120538i
$776$			5.22341e8i			1.11781i
$777$	7.71003e6	−	4.17112e7i	0.0164359	−	0.0889180i
$778$	8.41124e8			1.78616
$779$	5.66972e7	+	9.82024e7i	0.119936	+	0.207735i
$780$	2.25320e7	+	1.30088e7i	0.0474805	+	0.0274129i
$781$	−3.42817e8	+	5.93776e8i	−0.719629	+	1.24643i
$782$	−3.87605e8	+	2.23784e8i	−0.810531	+	0.467960i
$783$			1.29750e8i			0.270285i
$784$	8.02233e7	+	5.03385e8i	0.166476	+	1.04461i
$785$	5.06255e8			1.04655
$786$	−1.10046e8	−	1.90606e8i	−0.226625	−	0.392525i
$787$	1.61147e8	+	9.30380e7i	0.330595	+	0.190869i	0.656105	−	0.754669i	$-0.272203\pi$
$787$	1.61147e8	+	9.30380e7i	0.330595	+	0.190869i	−0.325510	+	0.945539i	$0.605536\pi$
$788$	−1.58374e7	+	2.74312e7i	−0.0323672	+	0.0560617i
$789$	−2.89607e8	+	1.67205e8i	−0.589628	+	0.340422i
$790$		−	2.08930e8i		−	0.423759i
$791$	4.35205e8	+	8.04448e7i	0.879356	+	0.162543i
$792$	1.60112e7			0.0322290
$793$	−1.54288e8	−	2.67235e8i	−0.309395	−	0.535888i
$794$	−4.75199e8	−	2.74356e8i	−0.949323	−	0.548092i
$795$	1.57809e8	−	2.73333e8i	0.314072	−	0.543989i
$796$	4.05885e7	−	2.34338e7i	0.0804756	−	0.0464626i
$797$		−	7.92223e7i		−	0.156485i	−0.996934	−	0.0782425i	$-0.975069\pi$
$797$		−	7.92223e7i		−	0.156485i	0.996934	−	0.0782425i	$-0.0249308\pi$
$798$	1.47888e8	+	4.16986e8i	0.291020	+	0.820565i
$799$	−2.62630e8			−0.514878
$800$	1.88540e7	+	3.26560e7i	0.0368241	+	0.0637813i
$801$	−6.22009e6	−	3.59117e6i	−0.0121032	−	0.00698777i
$802$	4.35138e8	−	7.53680e8i	0.843536	−	1.46105i
$803$	−9.95140e8	+	5.74544e8i	−1.92193	+	1.10963i
$804$		−	3.27466e7i		−	0.0630083i
$805$	−2.75200e8	−	2.34815e8i	−0.527547	−	0.450130i
$806$	−3.09333e8			−0.590774
$807$	2.67388e7	+	4.63129e7i	0.0508769	+	0.0881214i
$808$	−3.65771e7	−	2.11178e7i	−0.0693386	−	0.0400326i
$809$	−3.30935e8	+	5.73197e8i	−0.625025	+	1.08258i	0.363511	+	0.931590i	$0.381578\pi$
$809$	−3.30935e8	+	5.73197e8i	−0.625025	+	1.08258i	−0.988536	+	0.150986i	$0.951755\pi$
$810$	−2.92352e8	+	1.68789e8i	−0.550112	+	0.317607i
$811$		−	6.10402e8i		−	1.14434i	−0.820136	−	0.572168i	$-0.806102\pi$
$811$		−	6.10402e8i		−	1.14434i	0.820136	−	0.572168i	$-0.193898\pi$
$812$	−5.71230e6	+	6.69474e6i	−0.0106695	+	0.0125045i
$813$	1.43838e8			0.267672
$814$	−3.26859e7	−	5.66136e7i	−0.0606020	−	0.104966i
$815$	5.65173e7	+	3.26303e7i	0.104402	+	0.0602765i
$816$	2.35299e8	−	4.07550e8i	0.433061	−	0.750084i
$817$	4.66053e8	−	2.69076e8i	0.854612	−	0.493411i
$818$		−	2.91722e8i		−	0.532979i
$819$	1.91445e7	−	6.78975e6i	0.0348491	−	0.0123595i
$820$	−6.02495e6			−0.0109273
$821$	4.30331e8	+	7.45355e8i	0.777630	+	1.34690i	0.933304	+	0.359087i	$0.116912\pi$
$821$	4.30331e8	+	7.45355e8i	0.777630	+	1.34690i	−0.155674	+	0.987808i	$0.549755\pi$
$822$	−3.44309e8	−	1.98787e8i	−0.619915	−	0.357908i
$823$	1.03312e8	−	1.78941e8i	0.185332	−	0.321005i	−0.758356	−	0.651840i	$-0.773997\pi$
$823$	1.03312e8	−	1.78941e8i	0.185332	−	0.321005i	0.943688	+	0.330836i	$0.107331\pi$
$824$	3.51952e8	−	2.03200e8i	0.629074	−	0.363196i
$825$		−	4.26080e8i		−	0.758804i
$826$	3.13635e7	−	1.69676e8i	0.0556524	−	0.301079i
$827$	6.56220e8			1.16020			0.580100	−	0.814545i	$-0.303013\pi$
$827$	6.56220e8			1.16020			0.580100	+	0.814545i	$0.303013\pi$
$828$	−496823.	−	860523.i	−0.000875207	−	0.00151590i
$829$	−6.14177e8	−	3.54595e8i	−1.07803	−	0.622399i	−0.147664	−	0.989038i	$-0.547175\pi$
$829$	−6.14177e8	−	3.54595e8i	−1.07803	−	0.622399i	−0.930364	+	0.366638i	$0.880509\pi$
$830$	2.71596e8	−	4.70419e8i	0.474996	−	0.822716i
$831$	−3.90491e8	+	2.25450e8i	−0.680468	+	0.392869i
$832$			7.63731e8i			1.32608i
$833$	3.02144e8	+	3.72386e8i	0.522731	+	0.644255i
$834$	3.71119e8			0.639757
$835$	−1.67154e8	−	2.89519e8i	−0.287115	−	0.497298i
$836$	3.42538e7	+	1.97764e7i	0.0586259	+	0.0338477i
$837$	1.19515e8	−	2.07006e8i	0.203819	−	0.353026i
$838$	−7.46188e8	+	4.30812e8i	−1.26799	+	0.732075i
$839$		−	1.92379e8i		−	0.325741i	−0.986647	−	0.162870i	$-0.947925\pi$
$839$		−	1.92379e8i		−	0.325741i	0.986647	−	0.162870i	$-0.0520753\pi$
$840$	3.52267e8	+	6.51142e7i	0.594339	+	0.109860i
$841$	−5.52440e8			−0.928747
$842$	−1.15688e8	−	2.00377e8i	−0.193799	−	0.335670i
$843$	−4.77727e7	−	2.75816e7i	−0.0797439	−	0.0460402i
$844$	−1.36863e7	+	2.37053e7i	−0.0227645	+	0.0394292i
$845$	−3.40390e8	+	1.96524e8i	−0.564166	+	0.325721i
$846$		−	1.00515e7i		−	0.0166004i
$847$	−1.31715e8	−	3.71387e8i	−0.216763	−	0.611190i
$848$	−6.48171e8			−1.06292
$849$	4.97065e8	+	8.60942e8i	0.812251	+	1.40686i
$850$	2.72242e8	+	1.57179e8i	0.443300	+	0.255939i
$851$	3.09119e7	−	5.35410e7i	0.0501576	−	0.0868755i
$852$	−3.64900e7	+	2.10675e7i	−0.0590004	+	0.0340639i
$853$			2.71158e8i			0.436893i	0.975849	+	0.218446i	$0.0700989\pi$
$853$			2.71158e8i			0.436893i	−0.975849	+	0.218446i	$0.929901\pi$
$854$	2.12094e8	+	1.80969e8i	0.340529	+	0.290557i
$855$	−8.79981e6			−0.0140791
$856$	7.71114e7	+	1.33561e8i	0.122941	+	0.212940i
$857$	−6.34807e8	−	3.66506e8i	−1.00855	−	0.582289i	−0.0977865	−	0.995207i	$-0.531176\pi$
$857$	−6.34807e8	−	3.66506e8i	−1.00855	−	0.582289i	−0.910768	+	0.412918i	$0.864510\pi$
$858$	−5.87257e8	+	1.01716e9i	−0.929750	+	1.61037i
$859$	7.89632e8	−	4.55894e8i	1.24579	−	0.719258i	0.275524	−	0.961294i	$-0.411149\pi$
$859$	7.89632e8	−	4.55894e8i	1.24579	−	0.719258i	0.970267	+	0.242036i	$0.0778152\pi$
$860$			2.85935e7i			0.0449543i
$861$	1.14552e8	−	1.34253e8i	0.179470	−	0.210336i
$862$	9.54743e8			1.49061
$863$	−6.37469e8	−	1.10413e9i	−0.991806	−	1.71786i	−0.606538	−	0.795055i	$-0.707442\pi$
$863$	−6.37469e8	−	1.10413e9i	−0.991806	−	1.71786i	−0.385269	−	0.922804i	$-0.625891\pi$
$864$	6.95594e7	+	4.01601e7i	0.107849	+	0.0622664i
$865$	−2.82262e8	+	4.88892e8i	−0.436118	+	0.755378i
$866$	1.76354e8	−	1.01818e8i	0.271538	−	0.156773i
$867$			2.00477e8i			0.307615i
$868$	1.52802e7	−	5.41924e6i	0.0233652	−	0.00828666i
$869$	5.47113e8			0.833715
$870$	5.66060e7	+	9.80445e7i	0.0859617	+	0.148890i
$871$	8.44973e8	+	4.87845e8i	1.27876	+	0.738291i
$872$	7.89270e7	−	1.36706e8i	0.119035	−	0.206175i
$873$	−1.72942e7	+	9.98479e6i	−0.0259930	+	0.0150071i
$874$			6.44846e8i			0.965877i
$875$	−1.23311e8	+	6.67110e8i	−0.184067	+	0.995802i
$876$	−7.06162e7			−0.105049
$877$	1.85280e8	+	3.20914e8i	0.274682	+	0.475762i	0.970055	−	0.242886i	$-0.0780942\pi$
$877$	1.85280e8	+	3.20914e8i	0.274682	+	0.475762i	−0.695373	+	0.718649i	$0.744761\pi$
$878$	1.65054e8	+	9.52938e7i	0.243861	+	0.140793i
$879$	2.11167e8	−	3.65753e8i	0.310928	−	0.538543i
$880$	5.07678e8	−	2.93108e8i	0.744973	−	0.430111i
$881$		−	1.08555e8i		−	0.158753i	−0.996845	−	0.0793766i	$-0.974707\pi$
$881$		−	1.08555e8i		−	0.158753i	0.996845	−	0.0793766i	$-0.0252930\pi$
$882$	−1.42521e7	+	1.15637e7i	−0.0207717	+	0.0168536i
$883$	−9.05336e8			−1.31501			−0.657503	−	0.753452i	$-0.728387\pi$
$883$	−9.05336e8			−1.31501			−0.657503	+	0.753452i	$0.728387\pi$
$884$	−2.51332e7	−	4.35320e7i	−0.0363824	−	0.0630162i
$885$	−1.11511e8	−	6.43807e7i	−0.160874	−	0.0928808i
$886$	2.72314e8	−	4.71662e8i	0.391534	−	0.678157i
$887$	1.14198e9	−	6.59323e8i	1.63639	−	0.944772i	0.654333	−	0.756206i	$-0.272949\pi$
$887$	1.14198e9	−	6.59323e8i	1.63639	−	0.944772i	0.982061	−	0.188566i	$-0.0603839\pi$
$888$			6.12206e7i			0.0874297i
$889$	−6.53631e8	−	1.20819e8i	−0.930309	−	0.171961i
$890$	−2.47658e8			−0.351304
$891$	−4.41999e8	−	7.65566e8i	−0.624869	−	1.08230i
$892$	−3.09380e7	−	1.78621e7i	−0.0435911	−	0.0251673i
$893$	−1.89196e8	+	3.27697e8i	−0.265679	+	0.460169i
$894$	3.36333e8	−	1.94182e8i	0.470714	−	0.271767i
$895$			3.05237e8i			0.425763i
$896$	−2.60228e8	−	7.33742e8i	−0.361767	−	1.02004i
$897$	−1.11077e9			−1.53903
$898$	−2.44453e8	−	4.23405e8i	−0.337572	−	0.584692i
$899$	−6.76189e7	−	3.90398e7i	−0.0930656	−	0.0537314i
$900$	−348953.	+	604404.i	−0.000478673	+	0.000829086i
$901$	−5.28082e8	+	3.04888e8i	−0.721983	+	0.416837i
$902$		−	2.71983e8i		−	0.370615i
$903$	−6.37144e8	−	5.43644e8i	−0.865315	−	0.738331i
$904$	−6.38762e8			−0.864637
$905$	2.61802e8	+	4.53454e8i	0.353205	+	0.611770i
$906$	1.28135e8	+	7.39786e7i	0.172299	+	0.0994768i
$907$	−3.35264e8	+	5.80695e8i	−0.449330	+	0.778262i	−0.998343	−	0.0575518i	$-0.981671\pi$
$907$	−3.35264e8	+	5.80695e8i	−0.449330	+	0.778262i	0.549013	+	0.835814i	$0.315004\pi$
$908$	2.14290e7	−	1.23720e7i	0.0286249	−	0.0165266i
$909$		−	1.61470e6i		−	0.00214982i
$910$	4.54630e8	−	5.32820e8i	0.603300	−	0.707060i
$911$	−6.70095e8			−0.886301			−0.443151	−	0.896447i	$-0.646139\pi$
$911$	−6.70095e8			−0.886301			−0.443151	+	0.896447i	$0.646139\pi$
$912$	−3.39013e8	−	5.87189e8i	−0.446923	−	0.774093i
$913$	1.23186e9	+	7.11214e8i	1.61863	+	0.934519i
$914$	2.96409e8	−	5.13396e8i	0.388198	−	0.672378i
$915$	1.80179e8	−	1.04027e8i	0.235202	−	0.135794i
$916$			7.95101e7i			0.103451i
$917$	−3.23932e8	+	1.14885e8i	−0.420093	+	0.148989i
$918$	6.69601e8			0.865542
$919$	5.08201e8	+	8.80230e8i	0.654770	+	1.13410i	0.981951	+	0.189134i	$0.0605681\pi$
$919$	5.08201e8	+	8.80230e8i	0.654770	+	1.13410i	−0.327181	+	0.944962i	$0.606099\pi$
$920$	4.52174e8	+	2.61063e8i	0.580687	+	0.335260i
$921$	−2.36230e8	+	4.09163e8i	−0.302383	+	0.523742i
$922$	−1.20999e9	+	6.98586e8i	−1.54379	+	0.891307i
$923$		−	1.25542e9i		−	1.59656i
$924$	1.11891e7	−	6.05330e7i	0.0141834	−	0.0767319i
$925$	−4.34231e7			−0.0548650
$926$	6.11652e8	+	1.05941e9i	0.770320	+	1.33423i
$927$	1.34554e7	+	7.76851e6i	0.0168911	+	0.00975211i
$928$	1.31184e7	−	2.27217e7i	0.0164148	−	0.0284313i
$929$	9.93494e8	−	5.73594e8i	1.23913	−	0.715414i	0.270216	−	0.962800i	$-0.412905\pi$
$929$	9.93494e8	−	5.73594e8i	1.23913	−	0.715414i	0.968917	+	0.247386i	$0.0795716\pi$
$930$		−	2.08563e8i		−	0.259292i
$931$	6.82305e8	−	1.08737e8i	0.845531	−	0.134750i
$932$	8.69924e7			0.107457
$933$	−2.53836e8	−	4.39657e8i	−0.312542	−	0.541339i
$934$	3.91599e8	+	2.26090e8i	0.480618	+	0.277485i
$935$	2.75746e8	−	4.77606e8i	0.337345	−	0.584299i
$936$	−2.53893e7	+	1.46585e7i	−0.0309616	+	0.0178757i
$937$			1.59643e9i			1.94058i	0.241951	+	0.970288i	$0.422213\pi$
$937$			1.59643e9i			1.94058i	−0.241951	+	0.970288i	$0.577787\pi$
$938$	−8.66879e8	−	1.60237e8i	−1.05039	−	0.194157i
$939$	1.54160e9			1.86198
$940$	−1.00525e7	−	1.74114e7i	−0.0121029	−	0.0209629i
$941$	−9.21671e8	−	5.32127e8i	−1.10613	−	0.638626i	−0.168307	−	0.985735i	$-0.553830\pi$
$941$	−9.21671e8	−	5.32127e8i	−1.10613	−	0.638626i	−0.937825	+	0.347109i	$0.887163\pi$
$942$	−7.02230e8	+	1.21630e9i	−0.840091	+	1.45508i
$943$	2.22761e8	−	1.28611e8i	0.265646	−	0.153371i
$944$			2.64432e8i			0.314339i
$945$	1.80911e8	+	5.10100e8i	0.214373	+	0.604450i
$946$	−1.29079e9			−1.52469
$947$	4.50298e8	+	7.79940e8i	0.530213	+	0.918356i	0.999379	+	0.0352459i	$0.0112214\pi$
$947$	4.50298e8	+	7.79940e8i	0.530213	+	0.918356i	−0.469165	+	0.883110i	$0.655445\pi$
$948$	2.91178e7	+	1.68112e7i	0.0341770	+	0.0197321i
$949$	1.05201e9	−	1.82214e9i	1.23090	−	2.13198i
$950$	3.92240e8	−	2.26460e8i	0.457489	−	0.264132i
$951$			1.23285e9i			1.43341i
$952$	−5.26503e8	−	4.49239e8i	−0.610224	−	0.520675i
$953$	8.78154e8			1.01459			0.507297	−	0.861771i	$-0.330645\pi$
$953$	8.78154e8			1.01459			0.507297	+	0.861771i	$0.330645\pi$
$954$	−1.16688e7	−	2.02109e7i	−0.0134394	−	0.0232778i
$955$	−4.77495e8	−	2.75682e8i	−0.548225	−	0.316518i
$956$	1.05731e7	−	1.83131e7i	0.0121012	−	0.0209598i
$957$	−2.56744e8	+	1.48231e8i	−0.292930	+	0.169123i
$958$		−	4.51949e7i		−	0.0514036i
$959$	−4.02989e8	+	4.72298e8i	−0.456918	+	0.535501i
$960$	−5.14935e8			−0.582021
$961$	−3.71831e8	−	6.44031e8i	−0.418963	−	0.725665i
$962$	1.03662e8	+	5.98490e7i	0.116437	+	0.0672252i
$963$	−2.94804e6	+	5.10616e6i	−0.00330107	+	0.00571762i
$964$	−3.93438e7	+	2.27152e7i	−0.0439183	+	0.0253562i
$965$		−	3.48833e8i		−	0.388183i
$966$	9.45885e8	−	3.35466e8i	1.04932	−	0.372149i
$967$	−1.26782e8			−0.140210			−0.0701048	−	0.997540i	$-0.522333\pi$
$967$	−1.26782e8			−0.140210			−0.0701048	+	0.997540i	$0.522333\pi$
$968$	2.84363e8	+	4.92531e8i	0.313507	+	0.543010i
$969$	−5.52406e8	−	3.18932e8i	−0.607138	−	0.350531i
$970$	−3.44291e8	+	5.96329e8i	−0.377233	+	0.653387i
$971$	−1.31547e9	+	7.59488e8i	−1.43689	+	0.829589i	−0.997632	−	0.0687716i	$-0.978092\pi$
$971$	−1.31547e9	+	7.59488e8i	−1.43689	+	0.829589i	−0.439258	+	0.898361i	$0.644759\pi$
$972$			2.93555e6i			0.00319661i
$973$	1.05341e8	−	5.69894e8i	0.114356	−	0.618665i
$974$	5.33347e7			0.0577209
$975$	3.90084e8	+	6.75646e8i	0.420867	+	0.728963i
$976$	−3.70027e8	−	2.13635e8i	−0.398001	−	0.229786i
$977$	7.24987e8	−	1.25571e9i	0.777403	−	1.34650i	−0.156031	−	0.987752i	$-0.549870\pi$
$977$	7.24987e8	−	1.25571e9i	0.777403	−	1.34650i	0.933434	−	0.358750i	$-0.116797\pi$
$978$	−1.56791e8	+	9.05234e7i	−0.167612	+	0.0967708i
$979$		−	6.48529e8i		−	0.691164i
$980$	−1.31229e7	+	3.42845e7i	−0.0139428	+	0.0364267i
$981$	6.03490e6			0.00639239
$982$	−7.77166e8	−	1.34609e9i	−0.820690	−	1.42148i
$983$	−3.37363e8	−	1.94776e8i	−0.355170	−	0.205058i	0.311790	−	0.950151i	$-0.399072\pi$
$983$	−3.37363e8	−	1.94776e8i	−0.355170	−	0.205058i	−0.666960	+	0.745093i	$0.732405\pi$
$984$	−1.27356e8	+	2.20587e8i	−0.133670	+	0.231524i
$985$	5.51065e8	−	3.18158e8i	0.576626	−	0.332915i
$986$		−	2.18727e8i		−	0.228177i
$987$	5.79102e8	+	1.07043e8i	0.602288	+	0.111329i
$988$	−7.24228e7			−0.0750939
$989$	−6.10367e8	−	1.05719e9i	−0.630961	−	1.09286i
$990$	1.82791e7	+	1.05534e7i	0.0188386	+	0.0108765i
$991$	1.72641e8	−	2.99022e8i	0.177387	−	0.307244i	−0.763598	−	0.645692i	$-0.776569\pi$
$991$	1.72641e8	−	2.99022e8i	0.177387	−	0.307244i	0.940985	+	0.338449i	$0.109902\pi$
$992$	−4.18588e7	+	2.41672e7i	−0.0428797	+	0.0247566i
$993$			2.93579e8i			0.299831i
$994$	3.79153e8	+	1.06906e9i	0.386060	+	1.08854i
$995$	−9.41523e8			−0.955788
$996$	4.37070e7	+	7.57028e7i	0.0442357	+	0.0766185i
$997$	3.48025e8	+	2.00932e8i	0.351176	+	0.202752i	0.665203	−	0.746662i	$-0.268345\pi$
$997$	3.48025e8	+	2.00932e8i	0.351176	+	0.202752i	−0.314027	+	0.949414i	$0.601678\pi$
$998$	−7.70133e7	+	1.33391e8i	−0.0774773	+	0.134195i
$999$	−8.01020e7	+	4.62469e7i	−0.0803428	+	0.0463859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.7.d.b.3.1	✓	4
3.2	odd	2		63.7.m.b.10.2		4
4.3	odd	2		112.7.s.b.17.2		4
7.2	even	3		49.7.d.c.19.1		4
7.3	odd	6		49.7.b.b.48.3		4
7.4	even	3		49.7.b.b.48.4		4
7.5	odd	6	inner	7.7.d.b.5.1	yes	4
7.6	odd	2		49.7.d.c.31.1		4
21.5	even	6		63.7.m.b.19.2		4
21.11	odd	6		441.7.d.b.244.1		4
21.17	even	6		441.7.d.b.244.2		4
28.19	even	6		112.7.s.b.33.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.7.d.b.3.1	✓	4	1.1	even	1	trivial
7.7.d.b.5.1	yes	4	7.5	odd	6	inner
49.7.b.b.48.3		4	7.3	odd	6
49.7.b.b.48.4		4	7.4	even	3
49.7.d.c.19.1		4	7.2	even	3
49.7.d.c.31.1		4	7.6	odd	2
63.7.m.b.10.2		4	3.2	odd	2
63.7.m.b.19.2		4	21.5	even	6
112.7.s.b.17.2		4	4.3	odd	2
112.7.s.b.33.2		4	28.19	even	6
441.7.d.b.244.1		4	21.11	odd	6
441.7.d.b.244.2		4	21.17	even	6

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.12132 - 7.13834i) q^{2} +(-23.0772 - 13.3236i) q^{3} +(-1.97056 + 3.41311i) q^{4} +(68.5660 - 39.5866i) q^{5} +219.643i q^{6} +(337.286 + 62.3451i) q^{7} -495.044 q^{8} +(-9.46299 - 16.3904i) q^{9} +O(q^{10})\)	\(q+(-4.12132 - 7.13834i) q^{2} +(-23.0772 - 13.3236i) q^{3} +(-1.97056 + 3.41311i) q^{4} +(68.5660 - 39.5866i) q^{5} +219.643i q^{6} +(337.286 + 62.3451i) q^{7} -495.044 q^{8} +(-9.46299 - 16.3904i) q^{9} +(-565.165 - 326.298i) q^{10} +(854.459 - 1479.97i) q^{11} +(90.9500 - 52.5100i) q^{12} +3129.09i q^{13} +(-945.025 - 2664.61i) q^{14} -2109.75 q^{15} +(2166.35 + 3752.23i) q^{16} +(3529.96 + 2038.03i) q^{17} +(-78.0000 + 135.100i) q^{18} +(5085.89 - 2936.34i) q^{19} +312.032i q^{20} +(-6952.95 - 5932.62i) q^{21} -14086.0 q^{22} +(-6660.75 - 11536.8i) q^{23} +(11424.2 + 6595.77i) q^{24} +(-4678.30 + 8103.05i) q^{25} +(22336.5 - 12896.0i) q^{26} +19930.1i q^{27} +(-877.435 + 1028.34i) q^{28} +6510.23 q^{29} +(8694.94 + 15060.1i) q^{30} +(-10386.6 - 5996.69i) q^{31} +(2015.04 - 3490.16i) q^{32} +(-39437.0 + 22769.0i) q^{33} -33597.4i q^{34} +(25594.4 - 9077.27i) q^{35} +74.5896 q^{36} +(2320.45 + 4019.14i) q^{37} +(-41921.2 - 24203.2i) q^{38} +(41690.8 - 72210.6i) q^{39} +(-33943.2 + 19597.1i) q^{40} +19308.8i q^{41} +(-13693.7 + 74082.7i) q^{42} +91636.4 q^{43} +(3367.53 + 5832.73i) q^{44} +(-1297.68 - 749.215i) q^{45} +(-54902.2 + 95093.3i) q^{46} +(-55800.2 + 32216.2i) q^{47} -115454. i q^{48} +(109875. + 42056.3i) q^{49} +77123.1 q^{50} +(-54307.7 - 94063.7i) q^{51} +(-10680.0 - 6166.07i) q^{52} +(-74799.9 + 129557. i) q^{53} +(142268. - 82138.5i) q^{54} -135301. i q^{55} +(-166971. - 30863.5i) q^{56} -156491. q^{57} +(-26830.7 - 46472.2i) q^{58} +(52855.0 + 30515.9i) q^{59} +(4157.39 - 7200.80i) q^{60} +(-85403.4 + 49307.7i) q^{61} +98857.1i q^{62} +(-2169.88 - 6118.22i) q^{63} +244074. q^{64} +(123870. + 214549. i) q^{65} +(325065. + 187676. i) q^{66} +(155906. - 270038. i) q^{67} +(-13912.0 + 8032.11i) q^{68} +354981. i q^{69} +(-170279. - 145291. i) q^{70} -401209. q^{71} +(4684.59 + 8113.95i) q^{72} +(-582322. - 336204. i) q^{73} +(19126.6 - 33128.3i) q^{74} +(215924. - 124664. i) q^{75} +23145.0i q^{76} +(380466. - 445901. i) q^{77} -687285. q^{78} +(160076. + 277260. i) q^{79} +(297076. + 171517. i) q^{80} +(258643. - 447983. i) q^{81} +(137833. - 79577.6i) q^{82} +832356. i q^{83} +(33949.9 - 12040.6i) q^{84} +322714. q^{85} +(-377663. - 654131. i) q^{86} +(-150238. - 86739.7i) q^{87} +(-422995. + 732648. i) q^{88} +(328654. - 189748. i) q^{89} +12351.0i q^{90} +(-195084. + 1.05540e6i) q^{91} +52501.7 q^{92} +(159795. + 276773. i) q^{93} +(459941. + 265547. i) q^{94} +(232480. - 402666. i) q^{95} +(-93003.0 + 53695.3i) q^{96} -1.05514e6i q^{97} +(-152619. - 957653. i) q^{98} -32342.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9	\( 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9} - 1200 q^{10} + 1882 q^{11} + 4284 q^{12} - 1820 q^{14} - 16500 q^{15} + 248 q^{16} + 13458 q^{17} - 312 q^{18} + 18078 q^{19} - 16170 q^{21} - 28088 q^{22} + 2470 q^{23} + 24840 q^{24} + 2500 q^{25} + 43848 q^{26} - 45444 q^{28} - 34544 q^{29} + 15900 q^{30} - 17202 q^{31} + 7008 q^{32} - 67770 q^{33} + 154350 q^{35} + 82368 q^{36} - 43870 q^{37} - 81924 q^{38} + 10668 q^{39} - 76800 q^{40} - 22344 q^{42} + 320216 q^{43} - 4332 q^{44} - 187200 q^{45} - 113636 q^{46} - 354714 q^{47} + 140140 q^{49} + 160000 q^{50} + 28206 q^{51} + 196056 q^{52} + 104530 q^{53} + 285876 q^{54} - 346192 q^{56} + 25164 q^{57} - 59432 q^{58} - 62646 q^{59} - 384300 q^{60} - 140682 q^{61} + 181272 q^{63} - 33248 q^{64} - 77700 q^{65} + 652824 q^{66} + 432494 q^{67} + 381276 q^{68} - 338100 q^{70} - 1481528 q^{71} + 29328 q^{72} - 971778 q^{73} + 50024 q^{74} + 1192500 q^{75} + 642670 q^{77} - 1409856 q^{78} + 935990 q^{79} + 1767000 q^{80} + 1104066 q^{81} + 286776 q^{82} - 1405908 q^{84} - 579300 q^{85} - 738712 q^{86} - 1826208 q^{87} - 840616 q^{88} - 679290 q^{89} + 711480 q^{91} + 2124456 q^{92} + 395958 q^{93} + 860892 q^{94} - 291750 q^{95} + 5040 q^{96} - 361424 q^{98} + 157872 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9 - 1200 * q^10 + 1882 * q^11 + 4284 * q^12 - 1820 * q^14 - 16500 * q^15 + 248 * q^16 + 13458 * q^17 - 312 * q^18 + 18078 * q^19 - 16170 * q^21 - 28088 * q^22 + 2470 * q^23 + 24840 * q^24 + 2500 * q^25 + 43848 * q^26 - 45444 * q^28 - 34544 * q^29 + 15900 * q^30 - 17202 * q^31 + 7008 * q^32 - 67770 * q^33 + 154350 * q^35 + 82368 * q^36 - 43870 * q^37 - 81924 * q^38 + 10668 * q^39 - 76800 * q^40 - 22344 * q^42 + 320216 * q^43 - 4332 * q^44 - 187200 * q^45 - 113636 * q^46 - 354714 * q^47 + 140140 * q^49 + 160000 * q^50 + 28206 * q^51 + 196056 * q^52 + 104530 * q^53 + 285876 * q^54 - 346192 * q^56 + 25164 * q^57 - 59432 * q^58 - 62646 * q^59 - 384300 * q^60 - 140682 * q^61 + 181272 * q^63 - 33248 * q^64 - 77700 * q^65 + 652824 * q^66 + 432494 * q^67 + 381276 * q^68 - 338100 * q^70 - 1481528 * q^71 + 29328 * q^72 - 971778 * q^73 + 50024 * q^74 + 1192500 * q^75 + 642670 * q^77 - 1409856 * q^78 + 935990 * q^79 + 1767000 * q^80 + 1104066 * q^81 + 286776 * q^82 - 1405908 * q^84 - 579300 * q^85 - 738712 * q^86 - 1826208 * q^87 - 840616 * q^88 - 679290 * q^89 + 711480 * q^91 + 2124456 * q^92 + 395958 * q^93 + 860892 * q^94 - 291750 * q^95 + 5040 * q^96 - 361424 * q^98 + 157872 * q^99

Introduction

L-functions

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