LMFDB - Embedded newform 7.10.c.a.4.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,10,Mod(2,7)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7.2"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.60525085315$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + \cdots + 761760000 $ x^10 - x^9 + 430x^8 + 61x^7 + 146753x^6 + 23608x^5 + 16136944x^4 + 30575648x^3 + 1399072384x^2 + 1034227200x + 761760000
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.2
Root			$-5.11725 + 8.86334i$ of defining polynomial
Character	$\chi$	$=$	7.4
Dual form			7.10.c.a.2.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.2345 - 21.1908i) q^{2} +(-79.7348 + 138.105i) q^{3} +(-43.3662 + 75.1124i) q^{4} +(1014.15 + 1756.56i) q^{5} +3902.06 q^{6} +(-4235.51 + 4734.35i) q^{7} -10405.9 q^{8} +(-2873.78 - 4977.54i) q^{9} +(24815.2 - 42981.2i) q^{10} +(-4289.29 + 7429.26i) q^{11} +(-6915.59 - 11978.1i) q^{12} -38438.1 q^{13} +(152144. + 31831.3i) q^{14} -323452. q^{15} +(149514. + 258966. i) q^{16} +(150942. - 261439. i) q^{17} +(-70318.7 + 121795. i) q^{18} +(458143. + 793527. i) q^{19} -175919. q^{20} +(-316119. - 962436. i) q^{21} +209909. q^{22} +(-966607. - 1.67421e6i) q^{23} +(829711. - 1.43710e6i) q^{24} +(-1.08043e6 + 1.87136e6i) q^{25} +(470272. + 814534. i) q^{26} -2.22228e6 q^{27} +(-171931. - 523450. i) q^{28} +4.52529e6 q^{29} +(3.95727e6 + 6.85420e6i) q^{30} +(-147255. + 255054. i) q^{31} +(994560. - 1.72263e6i) q^{32} +(-684011. - 1.18474e6i) q^{33} -7.38680e6 q^{34} +(-1.26116e7 - 2.63858e6i) q^{35} +498500. q^{36} +(8.05632e6 + 1.39540e7i) q^{37} +(1.12103e7 - 1.94168e7i) q^{38} +(3.06486e6 - 5.30849e6i) q^{39} +(-1.05531e7 - 1.82785e7i) q^{40} +1.28783e7 q^{41} +(-1.65272e7 + 1.84737e7i) q^{42} +1.15410e7 q^{43} +(-372020. - 644357. i) q^{44} +(5.82889e6 - 1.00959e7i) q^{45} +(-2.36519e7 + 4.09663e7i) q^{46} +(1.39268e7 + 2.41219e7i) q^{47} -4.76860e7 q^{48} +(-4.47455e6 - 4.01048e7i) q^{49} +5.28742e7 q^{50} +(2.40707e7 + 4.16916e7i) q^{51} +(1.66692e6 - 2.88718e6i) q^{52} +(2.11827e7 - 3.66896e7i) q^{53} +(2.71885e7 + 4.70918e7i) q^{54} -1.73999e7 q^{55} +(4.40742e7 - 4.92651e7i) q^{56} -1.46120e8 q^{57} +(-5.53647e7 - 9.58945e7i) q^{58} +(-1.17321e6 + 2.03205e6i) q^{59} +(1.40269e7 - 2.42952e7i) q^{60} +(4.34201e6 + 7.52057e6i) q^{61} +7.20638e6 q^{62} +(3.57374e7 + 7.47691e6i) q^{63} +1.04431e8 q^{64} +(-3.89820e7 - 6.75188e7i) q^{65} +(-1.67371e7 + 2.89895e7i) q^{66} +(-1.26144e8 + 2.18488e8i) q^{67} +(1.30915e7 + 2.26752e7i) q^{68} +3.08289e8 q^{69} +(9.83831e7 + 2.99531e8i) q^{70} -2.50094e8 q^{71} +(2.99042e7 + 5.17957e7i) q^{72} +(-2.32270e7 + 4.02303e7i) q^{73} +(1.97130e8 - 3.41439e8i) q^{74} +(-1.72296e8 - 2.98426e8i) q^{75} -7.94716e7 q^{76} +(-1.70054e7 - 5.17737e7i) q^{77} -1.49988e8 q^{78} +(-5.53584e7 - 9.58836e7i) q^{79} +(-3.03259e8 + 5.25261e8i) q^{80} +(2.33758e8 - 4.04880e8i) q^{81} +(-1.57560e8 - 2.72902e8i) q^{82} +2.81805e8 q^{83} +(8.59998e7 + 1.79927e7i) q^{84} +6.12310e8 q^{85} +(-1.41198e8 - 2.44562e8i) q^{86} +(-3.60823e8 + 6.24964e8i) q^{87} +(4.46338e7 - 7.73080e7i) q^{88} +(1.45677e8 + 2.52321e8i) q^{89} -2.85254e8 q^{90} +(1.62805e8 - 1.81980e8i) q^{91} +1.67672e8 q^{92} +(-2.34827e7 - 4.06733e7i) q^{93} +(3.40774e8 - 5.90238e8i) q^{94} +(-9.29250e8 + 1.60951e9i) q^{95} +(1.58602e8 + 2.74707e8i) q^{96} +1.01107e8 q^{97} +(-7.95107e8 + 5.85481e8i) q^{98} +4.93059e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + 4298 q^{10} + 42213 q^{11} + 135604 q^{12} - 319676 q^{13} - 39522 q^{14} + 151394 q^{15} + 322064 q^{16}+ \cdots - 1900777180 q^{99}+O(q^{100}) $ 10 * q - 18 * q^2 + 161 * q^3 - 940 * q^4 + 1533 * q^5 - 8708 * q^6 - 1036 * q^7 + 34272 * q^8 - 35734 * q^9 + 4298 * q^10 + 42213 * q^11 + 135604 * q^12 - 319676 * q^13 - 39522 * q^14 + 151394 * q^15 + 322064 * q^16 + 324681 * q^17 - 1012868 * q^18 - 16121 * q^19 - 350616 * q^20 - 1557857 * q^21 - 62692 * q^22 + 2638863 * q^23 + 8449728 * q^24 - 1304092 * q^25 + 4179252 * q^26 - 18331558 * q^27 - 22156316 * q^28 + 15292500 * q^29 + 20557942 * q^30 + 19179237 * q^31 - 6263520 * q^32 + 1689359 * q^33 - 62909700 * q^34 - 43746759 * q^35 + 71476528 * q^36 + 39566985 * q^37 + 67365270 * q^38 - 44299486 * q^39 + 5721744 * q^40 - 53436852 * q^41 - 183129856 * q^42 + 101835992 * q^43 + 99704916 * q^44 + 85098230 * q^45 - 14489202 * q^46 + 32509659 * q^47 - 185141600 * q^48 - 49024598 * q^49 + 3328464 * q^50 + 44168403 * q^51 + 103893272 * q^52 - 25714707 * q^53 + 51200926 * q^54 - 144695222 * q^55 + 115352832 * q^56 - 121710346 * q^57 - 46645516 * q^58 + 46776513 * q^59 + 132391756 * q^60 - 113075039 * q^61 + 467465628 * q^62 + 318071530 * q^63 - 192008960 * q^64 - 338113566 * q^65 - 836682602 * q^66 - 126707879 * q^67 + 32262636 * q^68 + 1323616182 * q^69 + 697712470 * q^70 - 1188736032 * q^71 - 950557728 * q^72 - 859257651 * q^73 + 591757530 * q^74 - 169061732 * q^75 + 1101475592 * q^76 + 1911891891 * q^77 + 519432424 * q^78 - 527065417 * q^79 - 1257352656 * q^80 + 551662715 * q^81 - 1341703076 * q^82 - 144863208 * q^83 + 486452204 * q^84 - 1197360222 * q^85 - 678648216 * q^86 - 340781350 * q^87 + 903700608 * q^88 + 1661554797 * q^89 + 1967758744 * q^90 + 726641384 * q^91 - 1301840952 * q^92 - 423057489 * q^93 - 272580882 * q^94 - 1197123495 * q^95 - 1441922272 * q^96 + 869770188 * q^97 - 2404833858 * q^98 - 1900777180 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−12.2345	−	21.1908i	−0.540694	−	0.936509i	−0.998864	−	0.0476448i	$-0.984828\pi$
$2$	−12.2345	−	21.1908i	−0.540694	−	0.936509i	0.458171	−	0.888864i	$-0.348505\pi$
$3$	−79.7348	+	138.105i	−0.568332	+	0.984381i	0.428399	+	0.903590i	$0.359078\pi$
$3$	−79.7348	+	138.105i	−0.568332	+	0.984381i	−0.996731	+	0.0807907i	$0.974255\pi$
$4$	−43.3662	+	75.1124i	−0.0846995	+	0.146704i
$5$	1014.15	+	1756.56i	0.725666	+	1.25689i	0.958699	+	0.284421i	$0.0918014\pi$
$5$	1014.15	+	1756.56i	0.725666	+	1.25689i	−0.233034	+	0.972469i	$0.574865\pi$
$6$	3902.06			1.22918
$7$	−4235.51	+	4734.35i	−0.666752	+	0.745280i
$7$	−4235.51	+	4734.35i	−0.666752	+	0.745280i
$8$	−10405.9			−0.898201
$9$	−2873.78	−	4977.54i	−0.146003	−	0.252885i
$10$	24815.2	−	42981.2i	0.784726	−	1.35919i
$11$	−4289.29	+	7429.26i	−0.0883320	+	0.152996i	−0.906806	−	0.421548i	$-0.861487\pi$
$11$	−4289.29	+	7429.26i	−0.0883320	+	0.152996i	0.818474	+	0.574543i	$0.194820\pi$
$12$	−6915.59	−	11978.1i	−0.0962750	−	0.166753i
$13$	−38438.1			−0.373265			−0.186633	−	0.982430i	$-0.559757\pi$
$13$	−38438.1			−0.373265			−0.186633	+	0.982430i	$0.559757\pi$
$14$	152144.	+	31831.3i	1.05847	+	0.221451i
$15$	−323452.			−1.64968
$16$	149514.	+	258966.i	0.570352	+	0.987878i
$17$	150942.	−	261439.i	0.438318	−	0.759190i	−0.559242	−	0.829005i	$-0.688908\pi$
$17$	150942.	−	261439.i	0.438318	−	0.759190i	0.997560	+	0.0698150i	$0.0222409\pi$
$18$	−70318.7	+	121795.i	−0.157886	+	0.273467i
$19$	458143.	+	793527.i	0.806510	+	1.39692i	0.915267	+	0.402848i	$0.131980\pi$
$19$	458143.	+	793527.i	0.806510	+	1.39692i	−0.108757	+	0.994068i	$0.534687\pi$
$20$	−175919.			−0.245854
$21$	−316119.	−	962436.i	−0.354702	−	1.07990i
$22$	209909.			0.191042
$23$	−966607.	−	1.67421e6i	−0.720236	−	1.24749i	−0.960905	−	0.276878i	$-0.910700\pi$
$23$	−966607.	−	1.67421e6i	−0.720236	−	1.24749i	0.240669	−	0.970607i	$-0.422633\pi$
$24$	829711.	−	1.43710e6i	0.510477	−	0.884172i
$25$	−1.08043e6	+	1.87136e6i	−0.553182	+	0.958139i
$26$	470272.	+	814534.i	0.201822	+	0.349566i
$27$	−2.22228e6			−0.804751
$28$	−171931.	−	523450.i	−0.0528619	−	0.160940i
$29$	4.52529e6			1.18811			0.594054	−	0.804425i	$-0.297527\pi$
$29$	4.52529e6			1.18811			0.594054	+	0.804425i	$0.297527\pi$
$30$	3.95727e6	+	6.85420e6i	0.891970	+	1.54494i
$31$	−147255.	+	255054.i	−0.0286380	+	0.0496025i	−0.879989	−	0.474994i	$-0.842450\pi$
$31$	−147255.	+	255054.i	−0.0286380	+	0.0496025i	0.851351	+	0.524596i	$0.175784\pi$
$32$	994560.	−	1.72263e6i	0.167670	−	0.290413i
$33$	−684011.	−	1.18474e6i	−0.100404	−	0.173905i
$34$	−7.38680e6			−0.947984
$35$	−1.26116e7	−	2.63858e6i	−1.42057	−	0.297210i
$36$	498500.			0.0494657
$37$	8.05632e6	+	1.39540e7i	0.706690	+	1.22402i	0.966078	+	0.258250i	$0.0831458\pi$
$37$	8.05632e6	+	1.39540e7i	0.706690	+	1.22402i	−0.259388	+	0.965773i	$0.583521\pi$
$38$	1.12103e7	−	1.94168e7i	0.872150	−	1.51061i
$39$	3.06486e6	−	5.30849e6i	0.212139	−	0.367435i
$40$	−1.05531e7	−	1.82785e7i	−0.651794	−	1.12894i
$41$	1.28783e7			0.711757			0.355878	−	0.934532i	$-0.384182\pi$
$41$	1.28783e7			0.711757			0.355878	+	0.934532i	$0.384182\pi$
$42$	−1.65272e7	+	1.84737e7i	−0.819555	+	0.916079i
$43$	1.15410e7			0.514795			0.257398	−	0.966306i	$-0.417135\pi$
$43$	1.15410e7			0.514795			0.257398	+	0.966306i	$0.417135\pi$
$44$	−372020.	−	644357.i	−0.0149634	−	0.0259173i
$45$	5.82889e6	−	1.00959e7i	0.211899	−	0.367020i
$46$	−2.36519e7	+	4.09663e7i	−0.778854	+	1.34902i
$47$	1.39268e7	+	2.41219e7i	0.416304	+	0.721059i	0.995564	−	0.0940834i	$-0.0299920\pi$
$47$	1.39268e7	+	2.41219e7i	0.416304	+	0.721059i	−0.579261	+	0.815142i	$0.696659\pi$
$48$	−4.76860e7			−1.29660
$49$	−4.47455e6	−	4.01048e7i	−0.110884	−	0.993833i
$50$	5.28742e7			1.19641
$51$	2.40707e7	+	4.16916e7i	0.498221	+	0.862944i
$52$	1.66692e6	−	2.88718e6i	0.0316154	−	0.0547594i
$53$	2.11827e7	−	3.66896e7i	0.368757	−	0.638706i	−0.620614	−	0.784116i	$-0.713117\pi$
$53$	2.11827e7	−	3.66896e7i	0.368757	−	0.638706i	0.989372	+	0.145410i	$0.0464500\pi$
$54$	2.71885e7	+	4.70918e7i	0.435124	+	0.753657i
$55$	−1.73999e7			−0.256398
$56$	4.40742e7	−	4.92651e7i	0.598878	−	0.669411i
$57$	−1.46120e8			−1.83346
$58$	−5.53647e7	−	9.58945e7i	−0.642402	−	1.11267i
$59$	−1.17321e6	+	2.03205e6i	−0.0126049	+	0.0218324i	−0.872259	−	0.489044i	$-0.837346\pi$
$59$	−1.17321e6	+	2.03205e6i	−0.0126049	+	0.0218324i	0.859654	+	0.510876i	$0.170679\pi$
$60$	1.40269e7	−	2.42952e7i	0.139727	−	0.242014i
$61$	4.34201e6	+	7.52057e6i	0.0401519	+	0.0695451i	0.885403	−	0.464824i	$-0.153882\pi$
$61$	4.34201e6	+	7.52057e6i	0.0401519	+	0.0695451i	−0.845251	+	0.534369i	$0.820549\pi$
$62$	7.20638e6			0.0619376
$63$	3.57374e7	+	7.47691e6i	0.285818	+	0.0597984i
$64$	1.04431e8			0.778070
$65$	−3.89820e7	−	6.75188e7i	−0.270866	−	0.469153i
$66$	−1.67371e7	+	2.89895e7i	−0.108575	+	0.188058i
$67$	−1.26144e8	+	2.18488e8i	−0.764771	+	1.32462i	0.175597	+	0.984462i	$0.443814\pi$
$67$	−1.26144e8	+	2.18488e8i	−0.764771	+	1.32462i	−0.940368	+	0.340159i	$0.889519\pi$
$68$	1.30915e7	+	2.26752e7i	0.0742507	+	0.128606i
$69$	3.08289e8			1.63733
$70$	9.83831e7	+	2.99531e8i	0.489755	+	1.49108i
$71$	−2.50094e8			−1.16799			−0.583997	−	0.811756i	$-0.698512\pi$
$71$	−2.50094e8			−1.16799			−0.583997	+	0.811756i	$0.698512\pi$
$72$	2.99042e7	+	5.17957e7i	0.131140	+	0.227142i
$73$	−2.32270e7	+	4.02303e7i	−0.0957282	+	0.165806i	−0.909912	−	0.414801i	$-0.863851\pi$
$73$	−2.32270e7	+	4.02303e7i	−0.0957282	+	0.165806i	0.814184	+	0.580607i	$0.197185\pi$
$74$	1.97130e8	−	3.41439e8i	0.764206	−	1.32364i
$75$	−1.72296e8	−	2.98426e8i	−0.628782	−	1.08908i
$76$	−7.94716e7			−0.273244
$77$	−1.70054e7	−	5.17737e7i	−0.0551289	−	0.167842i
$78$	−1.49988e8			−0.458808
$79$	−5.53584e7	−	9.58836e7i	−0.159905	−	0.276963i	0.774929	−	0.632048i	$-0.217785\pi$
$79$	−5.53584e7	−	9.58836e7i	−0.159905	−	0.276963i	−0.934834	+	0.355084i	$0.884452\pi$
$80$	−3.03259e8	+	5.25261e8i	−0.827769	+	1.43374i
$81$	2.33758e8	−	4.04880e8i	0.603369	−	1.04507i
$82$	−1.57560e8	−	2.72902e8i	−0.384843	−	0.666567i
$83$	2.81805e8			0.651774			0.325887	−	0.945409i	$-0.394337\pi$
$83$	2.81805e8			0.651774			0.325887	+	0.945409i	$0.394337\pi$
$84$	8.59998e7	+	1.79927e7i	0.188469	+	0.0394312i
$85$	6.12310e8			1.27229
$86$	−1.41198e8	−	2.44562e8i	−0.278347	−	0.482111i
$87$	−3.60823e8	+	6.24964e8i	−0.675240	+	1.16955i
$88$	4.46338e7	−	7.73080e7i	0.0793399	−	0.137421i
$89$	1.45677e8	+	2.52321e8i	0.246115	+	0.426283i	0.962444	−	0.271479i	$-0.0875127\pi$
$89$	1.45677e8	+	2.52321e8i	0.246115	+	0.426283i	−0.716330	+	0.697762i	$0.754179\pi$
$90$	−2.85254e8			−0.458291
$91$	1.62805e8	−	1.81980e8i	0.248875	−	0.278187i
$92$	1.67672e8			0.244015
$93$	−2.34827e7	−	4.06733e7i	−0.0325518	−	0.0563815i
$94$	3.40774e8	−	5.90238e8i	0.450185	−	0.779744i
$95$	−9.29250e8	+	1.60951e9i	−1.17051	+	2.02739i
$96$	1.58602e8	+	2.74707e8i	0.190585	+	0.330103i
$97$	1.01107e8			0.115960			0.0579798	−	0.998318i	$-0.481534\pi$
$97$	1.01107e8			0.115960			0.0579798	+	0.998318i	$0.481534\pi$
$98$	−7.95107e8	+	5.85481e8i	−0.870780	+	0.641203i
$99$	4.93059e7			0.0515871
$100$	−9.37085e7	−	1.62308e8i	−0.0937085	−	0.162308i
$101$	5.29724e8	−	9.17509e8i	0.506528	−	0.877332i	−0.493443	−	0.869778i	$-0.664262\pi$
$101$	5.29724e8	−	9.17509e8i	0.506528	−	0.877332i	0.999971	−	0.00755447i	$-0.00240468\pi$
$102$	5.88985e8	−	1.02015e9i	0.538770	−	0.933177i
$103$	2.52542e8	+	4.37415e8i	0.221088	+	0.382936i	0.955139	−	0.296159i	$-0.0957058\pi$
$103$	2.52542e8	+	4.37415e8i	0.221088	+	0.382936i	−0.734050	+	0.679095i	$0.762372\pi$
$104$	3.99983e8			0.335267
$105$	1.36998e9	−	1.53133e9i	1.09993	−	1.22947i
$106$	−1.03664e9			−0.797539
$107$	943656.	+	1.63446e6i	0.000695964	+	0.00120544i	0.866373	−	0.499397i	$-0.166445\pi$
$107$	943656.	+	1.63446e6i	0.000695964	+	0.00120544i	−0.865677	+	0.500603i	$0.833112\pi$
$108$	9.63717e7	−	1.66921e8i	0.0681620	−	0.118060i
$109$	5.32240e7	−	9.21867e7i	0.0361151	−	0.0625531i	−0.847403	−	0.530950i	$-0.821835\pi$
$109$	5.32240e7	−	9.21867e7i	0.0361151	−	0.0625531i	0.883518	+	0.468397i	$0.155168\pi$
$110$	2.12879e8	+	3.68717e8i	0.138633	+	0.240119i
$111$	−2.56948e9			−1.60654
$112$	−1.85931e9	−	3.89001e8i	−1.11653	−	0.233598i
$113$	−2.40785e9			−1.38924			−0.694620	−	0.719377i	$-0.744427\pi$
$113$	−2.40785e9			−1.38924			−0.694620	+	0.719377i	$0.744427\pi$
$114$	1.78770e9	+	3.09639e9i	0.991342	+	1.71705i
$115$	1.96057e9	−	3.39580e9i	1.04530	−	1.81051i
$116$	−1.96245e8	+	3.39906e8i	−0.100632	+	0.174300i
$117$	1.10463e8	+	1.91327e8i	0.0544980	+	0.0943932i
$118$	5.74144e7			0.0272616
$119$	5.98429e8	+	1.82194e9i	0.273559	+	0.832861i
$120$	3.36580e9			1.48174
$121$	1.14218e9	+	1.97831e9i	0.484395	+	0.838997i
$122$	1.06245e8	−	1.84021e8i	0.0434198	−	0.0752052i
$123$	−1.02685e9	+	1.77856e9i	−0.404515	+	0.700640i
$124$	−1.27718e7	−	2.21214e7i	−0.00485126	−	0.00840262i
$125$	−4.21360e8			−0.154368
$126$	−2.78787e8	−	8.48779e8i	−0.0985384	−	0.300004i
$127$	1.51077e9			0.515326			0.257663	−	0.966235i	$-0.417048\pi$
$127$	1.51077e9			0.515326			0.257663	+	0.966235i	$0.417048\pi$
$128$	−1.78687e9	−	3.09496e9i	−0.588368	−	1.01908i
$129$	−9.20218e8	+	1.59386e9i	−0.292575	+	0.506755i
$130$	−9.53851e8	+	1.65212e9i	−0.292911	+	0.507336i
$131$	1.02677e8	+	1.77843e8i	0.0304617	+	0.0527612i	0.880854	−	0.473387i	$-0.156969\pi$
$131$	1.02677e8	+	1.77843e8i	0.0304617	+	0.0527612i	−0.850393	+	0.526149i	$0.823636\pi$
$132$	1.18652e8			0.0340166
$133$	−5.69730e9	−	1.19198e9i	−1.57884	−	0.330321i
$134$	6.17325e9			1.65403
$135$	−2.25372e9	−	3.90356e9i	−0.583980	−	1.01148i
$136$	−1.57068e9	+	2.72050e9i	−0.393698	+	0.681905i
$137$	2.94515e9	−	5.10114e9i	0.714273	−	1.23716i	−0.248966	−	0.968512i	$-0.580091\pi$
$137$	2.94515e9	−	5.10114e9i	0.714273	−	1.23716i	0.963239	−	0.268645i	$-0.0865759\pi$
$138$	−3.77176e9	−	6.53289e9i	−0.885296	−	1.53338i
$139$	1.53632e9			0.349073			0.174537	−	0.984651i	$-0.444157\pi$
$139$	1.53632e9			0.349073			0.174537	+	0.984651i	$0.444157\pi$
$140$	7.45106e8	−	8.32862e8i	0.163924	−	0.183230i
$141$	−4.44179e9			−0.946395
$142$	3.05977e9	+	5.29968e9i	0.631527	+	1.09384i
$143$	1.64872e8	−	2.85567e8i	0.0329712	−	0.0571079i
$144$	8.59343e8	−	1.48843e9i	0.166546	−	0.288467i
$145$	4.58932e9	+	7.94893e9i	0.862169	+	1.49332i
$146$	1.13668e9			0.207038
$147$	5.89544e9	+	2.57979e9i	1.04133	+	0.455676i
$148$	−1.39749e9			−0.239425
$149$	3.06047e8	+	5.30089e8i	0.0508686	+	0.0881070i	0.890338	−	0.455299i	$-0.150468\pi$
$149$	3.06047e8	+	5.30089e8i	0.0508686	+	0.0881070i	−0.839470	+	0.543406i	$0.817134\pi$
$150$	−4.21592e9	+	7.30218e9i	−0.679957	+	1.17772i
$151$	−5.27233e8	+	9.13194e8i	−0.0825289	+	0.142944i	−0.904336	−	0.426822i	$-0.859633\pi$
$151$	−5.27233e8	+	9.13194e8i	−0.0825289	+	0.142944i	0.821807	+	0.569766i	$0.192966\pi$
$152$	−4.76738e9	−	8.25734e9i	−0.724408	−	1.25471i
$153$	−1.73510e9			−0.255984
$154$	−8.89072e8	+	9.93784e8i	−0.127378	+	0.142380i
$155$	−5.97355e8			−0.0831266
$156$	2.65822e8	+	4.60418e8i	0.0359361	+	0.0622431i
$157$	1.84813e9	−	3.20105e9i	0.242764	−	0.420479i	−0.718737	−	0.695282i	$-0.755279\pi$
$157$	1.84813e9	−	3.20105e9i	0.242764	−	0.420479i	0.961500	+	0.274803i	$0.0886128\pi$
$158$	−1.35457e9	+	2.34618e9i	−0.172919	+	0.299505i
$159$	3.37800e9	+	5.85087e9i	0.419153	+	0.725995i
$160$	4.03453e9			0.486690
$161$	1.20204e10	+	2.51488e9i	1.40994	+	0.294986i
$162$	−1.14396e10			−1.30495
$163$	−6.57764e9	−	1.13928e10i	−0.729837	−	1.26412i	−0.956952	−	0.290247i	$-0.906262\pi$
$163$	−6.57764e9	−	1.13928e10i	−0.729837	−	1.26412i	0.227114	−	0.973868i	$-0.427071\pi$
$164$	−5.58483e8	+	9.67321e8i	−0.0602855	+	0.104418i
$165$	1.38738e9	−	2.40301e9i	0.145719	−	0.252393i
$166$	−3.44774e9	−	5.97167e9i	−0.352410	−	0.610393i
$167$	6.15786e9			0.612641			0.306320	−	0.951928i	$-0.400902\pi$
$167$	6.15786e9			0.612641			0.306320	+	0.951928i	$0.400902\pi$
$168$	3.28950e9	+	1.00150e10i	0.318594	+	0.969972i
$169$	−9.12701e9			−0.860673
$170$	−7.49131e9	−	1.29753e10i	−0.687920	−	1.19151i
$171$	2.63321e9	−	4.56085e9i	0.235506	−	0.407909i
$172$	−5.00488e8	+	8.66871e8i	−0.0436029	+	0.0755225i
$173$	7.73798e9	+	1.34026e10i	0.656780	+	1.13758i	0.981444	+	0.191747i	$0.0614155\pi$
$173$	7.73798e9	+	1.34026e10i	0.656780	+	1.13758i	−0.324664	+	0.945829i	$0.605251\pi$
$174$	1.76580e10			1.46039
$175$	−4.28351e9	−	1.30413e10i	−0.345246	−	1.05112i
$176$	−2.56524e9			−0.201521
$177$	−1.87091e8	−	3.24051e8i	−0.0143276	−	0.0248161i
$178$	3.56458e9	−	6.17404e9i	0.266145	−	0.460977i
$179$	1.98868e9	−	3.44450e9i	0.144786	−	0.250777i	−0.784507	−	0.620120i	$-0.787084\pi$
$179$	1.98868e9	−	3.44450e9i	0.144786	−	0.250777i	0.929293	+	0.369343i	$0.120417\pi$
$180$	5.05553e8	+	8.75644e8i	0.0358955	+	0.0621729i
$181$	−2.68948e10			−1.86258			−0.931288	−	0.364283i	$-0.881314\pi$
$181$	−2.68948e10			−1.86258			−0.931288	+	0.364283i	$0.881314\pi$
$182$	−5.84813e9	−	1.22354e9i	−0.395090	−	0.0826600i
$183$	−1.38484e9			−0.0912785
$184$	1.00584e10	+	1.74217e10i	0.646917	+	1.12049i
$185$	−1.63406e10	+	2.83028e10i	−1.02564	+	1.77646i
$186$	−5.74600e8	+	9.95236e8i	−0.0352012	+	0.0609702i
$187$	1.29487e9	+	2.24277e9i	0.0774351	+	0.134121i
$188$	−2.41580e9			−0.141043
$189$	9.41248e9	−	1.05210e10i	0.536569	−	0.599765i
$190$	4.54756e10			2.53156
$191$	−8.68177e8	−	1.50373e9i	−0.0472018	−	0.0817559i	0.841459	−	0.540321i	$-0.181697\pi$
$191$	−8.68177e8	−	1.50373e9i	−0.0472018	−	0.0817559i	−0.888661	+	0.458565i	$0.848364\pi$
$192$	−8.32677e9	+	1.44224e10i	−0.442202	+	0.765917i
$193$	−7.30896e9	+	1.26595e10i	−0.379182	+	0.656763i	−0.990943	−	0.134280i	$-0.957128\pi$
$193$	−7.30896e9	+	1.26595e10i	−0.379182	+	0.656763i	0.611761	+	0.791042i	$0.290461\pi$
$194$	−1.23699e9	−	2.14253e9i	−0.0626986	−	0.108597i
$195$	1.24329e10			0.615767
$196$	3.20641e9	+	1.40310e9i	0.155191	+	0.0679102i
$197$	−4.40160e9			−0.208215			−0.104108	−	0.994566i	$-0.533199\pi$
$197$	−4.40160e9			−0.208215			−0.104108	+	0.994566i	$0.533199\pi$
$198$	−6.03234e8	−	1.04483e9i	−0.0278928	−	0.0483118i
$199$	1.76429e10	−	3.05585e10i	0.797502	−	1.38131i	−0.123736	−	0.992315i	$-0.539488\pi$
$199$	1.76429e10	−	3.05585e10i	0.797502	−	1.38131i	0.921238	−	0.388999i	$-0.127179\pi$
$200$	1.12429e10	−	1.94732e10i	0.496869	−	0.860602i
$201$	−2.01162e10	−	3.48423e10i	−0.869288	−	1.50565i
$202$	−2.59236e10			−1.09551
$203$	−1.91669e10	+	2.14243e10i	−0.792173	+	0.885472i
$204$	−4.17541e9			−0.168796
$205$	1.30605e10	+	2.26215e10i	0.516498	+	0.894600i
$206$	6.17945e9	−	1.07031e10i	0.239082	−	0.414102i
$207$	−5.55564e9	+	9.62266e9i	−0.210314	+	0.364274i
$208$	−5.74705e9	−	9.95418e9i	−0.212892	−	0.368740i
$209$	−7.86042e9			−0.284962
$210$	−4.92112e10	−	1.02959e10i	−1.74613	−	0.365323i
$211$	1.08123e10			0.375533			0.187766	−	0.982214i	$-0.439875\pi$
$211$	1.08123e10			0.375533			0.187766	+	0.982214i	$0.439875\pi$
$212$	1.83723e9	+	3.18217e9i	0.0624671	+	0.108196i
$213$	1.99412e10	−	3.45391e10i	0.663808	−	1.14975i
$214$	2.30903e7	−	3.99936e7i	0.000752607	−	0.00130355i
$215$	1.17043e10	+	2.02724e10i	0.373569	+	0.647041i
$216$	2.31248e10			0.722829
$217$	−5.83812e8	−	1.77744e9i	−0.0178733	−	0.0544159i
$218$	−2.60468e9			−0.0781088
$219$	−3.70400e9	−	6.41551e9i	−0.108811	−	0.188466i
$220$	7.54567e8	−	1.30695e9i	0.0217168	−	0.0376146i
$221$	−5.80193e9	+	1.00492e10i	−0.163609	+	0.283379i
$222$	3.14363e10	+	5.44492e10i	0.868646	+	1.50454i
$223$	3.21844e10			0.871512			0.435756	−	0.900065i	$-0.356481\pi$
$223$	3.21844e10			0.871512			0.435756	+	0.900065i	$0.356481\pi$
$224$	3.94306e9	+	1.20048e10i	0.104645	+	0.318595i
$225$	1.24197e10			0.323065
$226$	2.94589e10	+	5.10243e10i	0.751153	+	1.30104i
$227$	4.50385e9	−	7.80090e9i	0.112582	−	0.194997i	−0.804229	−	0.594320i	$-0.797421\pi$
$227$	4.50385e9	−	7.80090e9i	0.112582	−	0.194997i	0.916810	+	0.399323i	$0.130755\pi$
$228$	6.33665e9	−	1.09754e10i	0.155293	−	0.268976i
$229$	−2.31909e10	−	4.01679e10i	−0.557261	−	0.965204i	−0.997724	−	0.0674334i	$-0.978519\pi$
$229$	−2.31909e10	−	4.01679e10i	−0.557261	−	0.965204i	0.440463	−	0.897771i	$-0.354814\pi$
$230$	−9.59463e10			−2.26075
$231$	8.50612e9	+	1.77964e9i	0.196552	+	0.0411223i
$232$	−4.70896e10			−1.06716
$233$	2.17672e10	+	3.77018e10i	0.483838	+	0.838032i	0.999828	−	0.0185626i	$-0.00590900\pi$
$233$	2.17672e10	+	3.77018e10i	0.483838	+	0.838032i	−0.515990	+	0.856595i	$0.672576\pi$
$234$	2.70292e9	−	4.68159e9i	0.0589334	−	0.102076i
$235$	−2.82476e10	+	4.89263e10i	−0.604194	+	1.04650i
$236$	−1.01755e8	−	1.76245e8i	−0.00213526	−	0.00369838i
$237$	1.76560e10			0.363517
$238$	3.12868e10	−	3.49717e10i	0.632070	−	0.706513i
$239$	−2.74289e10			−0.543773			−0.271887	−	0.962329i	$-0.587648\pi$
$239$	−2.74289e10			−0.543773			−0.271887	+	0.962329i	$0.587648\pi$
$240$	−4.83607e10	−	8.37631e10i	−0.940896	−	1.62968i
$241$	5.75409e9	−	9.96638e9i	0.109875	−	0.190310i	−0.805844	−	0.592128i	$-0.798288\pi$
$241$	5.75409e9	−	9.96638e9i	0.109875	−	0.190310i	0.915720	+	0.401818i	$0.131622\pi$
$242$	2.79480e10	−	4.84073e10i	0.523819	−	0.907281i
$243$	1.54067e10	+	2.66852e10i	0.283453	+	0.490955i
$244$	−7.53185e8			−0.0136034
$245$	6.59084e10	−	4.85320e10i	1.16867	−	0.860559i
$246$	5.02520e10			0.874874
$247$	−1.76102e10	−	3.05017e10i	−0.301042	−	0.521420i
$248$	1.53232e9	−	2.65406e9i	0.0257227	−	0.0445531i
$249$	−2.24697e10	+	3.89186e10i	−0.370424	+	0.641594i
$250$	5.15513e9	+	8.92894e9i	0.0834659	+	0.144567i
$251$	−2.69146e10			−0.428012			−0.214006	−	0.976832i	$-0.568651\pi$
$251$	−2.69146e10			−0.428012			−0.214006	+	0.976832i	$0.568651\pi$
$252$	−2.11140e9	+	2.36007e9i	−0.0329813	+	0.0368658i
$253$	1.65842e10			0.254480
$254$	−1.84835e10	−	3.20144e10i	−0.278634	−	0.482607i
$255$	−4.88224e10	+	8.45630e10i	−0.723084	+	1.25242i
$256$	−1.69887e10	+	2.94254e10i	−0.247219	+	0.428195i
$257$	1.78979e10	+	3.10001e10i	0.255919	+	0.443265i	0.965145	−	0.261716i	$-0.0842885\pi$
$257$	1.78979e10	+	3.10001e10i	0.255919	+	0.443265i	−0.709225	+	0.704982i	$0.750955\pi$
$258$	4.50337e10			0.632774
$259$	−1.00186e11	−	2.09606e10i	−1.38343	−	0.289438i
$260$	6.76200e9			0.0917688
$261$	−1.30047e10	−	2.25248e10i	−0.173468	−	0.300455i
$262$	2.51242e9	−	4.35163e9i	0.0329409	−	0.0570554i
$263$	6.63817e10	−	1.14976e11i	0.855554	−	1.48186i	−0.0205759	−	0.999788i	$-0.506550\pi$
$263$	6.63817e10	−	1.14976e11i	0.855554	−	1.48186i	0.876130	−	0.482075i	$-0.160117\pi$
$264$	7.11774e9	+	1.23283e10i	0.0901829	+	0.156201i
$265$	8.59298e10			1.07038
$266$	4.44447e10	+	1.35314e11i	0.544318	+	1.65720i
$267$	−4.64623e10			−0.559499
$268$	−1.09408e10	−	1.89500e10i	−0.129551	−	0.224390i
$269$	−3.64397e10	+	6.31154e10i	−0.424316	+	0.734937i	−0.996356	−	0.0852884i	$-0.972819\pi$
$269$	−3.64397e10	+	6.31154e10i	−0.424316	+	0.734937i	0.572040	+	0.820226i	$0.306152\pi$
$270$	−5.51463e10	+	9.55162e10i	−0.631509	+	1.09381i
$271$	−2.06838e10	−	3.58253e10i	−0.232953	−	0.403486i	0.725723	−	0.687987i	$-0.241505\pi$
$271$	−2.06838e10	−	3.58253e10i	−0.232953	−	0.403486i	−0.958676	+	0.284501i	$0.908172\pi$
$272$	9.02719e10			0.999982
$273$	1.21510e10	+	3.69943e10i	0.132398	+	0.403091i
$274$	−1.44130e11			−1.54481
$275$	−9.26857e9	−	1.60536e10i	−0.0977273	−	0.169269i
$276$	−1.33693e10	+	2.31563e10i	−0.138681	+	0.240203i
$277$	8.09314e10	−	1.40177e11i	0.825958	−	1.43060i	−0.0752266	−	0.997166i	$-0.523968\pi$
$277$	8.09314e10	−	1.40177e11i	0.825958	−	1.43060i	0.901185	−	0.433435i	$-0.142699\pi$
$278$	−1.87962e10	−	3.25559e10i	−0.188742	−	0.326910i
$279$	1.69272e9			0.0167250
$280$	1.31235e11	+	2.74567e10i	1.27596	+	0.266954i
$281$	1.39939e11			1.33894			0.669471	−	0.742838i	$-0.266521\pi$
$281$	1.39939e11			1.33894			0.669471	+	0.742838i	$0.266521\pi$
$282$	5.43432e10	+	9.41251e10i	0.511710	+	0.886308i
$283$	−8.86550e10	+	1.53555e11i	−0.821607	+	1.42306i	0.0828783	+	0.996560i	$0.473589\pi$
$283$	−8.86550e10	+	1.53555e11i	−0.821607	+	1.42306i	−0.904485	+	0.426505i	$0.859745\pi$
$284$	1.08456e10	−	1.87851e10i	0.0989285	−	0.171349i
$285$	−1.48187e11	−	2.56668e11i	−1.33048	−	2.30446i
$286$	−8.06852e9			−0.0713094
$287$	−5.45462e10	+	6.09705e10i	−0.474565	+	0.530458i
$288$	−1.14326e10			−0.0979217
$289$	1.37270e10	+	2.37759e10i	0.115754	+	0.200492i
$290$	1.12296e11	−	1.94503e11i	0.932338	−	1.61486i
$291$	−8.06172e9	+	1.39633e10i	−0.0659036	+	0.114148i
$292$	−2.01453e9	−	3.48927e9i	−0.0162163	−	0.0280874i
$293$	−1.65710e11			−1.31355			−0.656773	−	0.754088i	$-0.728079\pi$
$293$	−1.65710e11			−1.31355			−0.656773	+	0.754088i	$0.728079\pi$
$294$	−1.74600e10	−	1.56491e11i	−0.136295	−	1.22160i
$295$	−4.75922e9			−0.0365879
$296$	−8.38331e10	−	1.45203e11i	−0.634750	−	1.09942i
$297$	9.53199e9	−	1.65099e10i	0.0710853	−	0.123123i
$298$	7.48866e9	−	1.29707e10i	0.0550087	−	0.0952778i
$299$	3.71546e10	+	6.43536e10i	0.268839	+	0.465643i
$300$	2.98873e10			0.213030
$301$	−4.88819e10	+	5.46391e10i	−0.343241	+	0.383667i
$302$	2.58017e10			0.178491
$303$	8.44749e10	+	1.46315e11i	0.575753	+	0.997233i
$304$	−1.36998e11	+	2.37287e11i	−0.919988	+	1.59347i
$305$	−8.80688e9	+	1.52540e10i	−0.0582737	+	0.100933i
$306$	2.12281e10	+	3.67681e10i	0.138409	+	0.239731i
$307$	2.12825e11			1.36741			0.683706	−	0.729757i	$-0.260367\pi$
$307$	2.12825e11			1.36741			0.683706	+	0.729757i	$0.260367\pi$
$308$	4.62631e9	+	9.67908e8i	0.0292925	+	0.00612852i
$309$	−8.05455e10			−0.502606
$310$	7.30834e9	+	1.26584e10i	0.0449460	+	0.0778488i
$311$	7.94338e10	−	1.37583e11i	0.481486	−	0.833959i	−0.518288	−	0.855206i	$-0.673430\pi$
$311$	7.94338e10	−	1.37583e11i	0.481486	−	0.833959i	0.999774	+	0.0212476i	$0.00676381\pi$
$312$	−3.18925e10	+	5.52395e10i	−0.190543	+	0.330031i
$313$	1.48658e11	+	2.57484e11i	0.875468	+	1.51635i	0.856264	+	0.516539i	$0.172780\pi$
$313$	1.48658e11	+	2.57484e11i	0.875468	+	1.51635i	0.0192038	+	0.999816i	$0.493887\pi$
$314$	−9.04437e10			−0.525043
$315$	2.31094e10	+	7.03574e10i	0.132249	+	0.402636i
$316$	9.60273e9			0.0541755
$317$	−7.66580e10	−	1.32776e11i	−0.426374	−	0.738502i	0.570174	−	0.821524i	$-0.306876\pi$
$317$	−7.66580e10	−	1.32776e11i	−0.426374	−	0.738502i	−0.996548	+	0.0830226i	$0.973543\pi$
$318$	8.26564e10	−	1.43165e11i	0.453267	−	0.785082i
$319$	−1.94103e10	+	3.36196e10i	−0.104948	+	0.181775i
$320$	1.05908e11	+	1.83439e11i	0.564619	+	0.977948i
$321$	−3.00969e8			−0.00158216
$322$	−9.37711e10	−	2.85490e11i	−0.486091	−	1.47992i
$323$	2.76612e11			1.41403
$324$	2.02743e10	+	3.51162e10i	0.102210	+	0.177033i
$325$	4.15298e10	−	7.19318e10i	0.206483	−	0.357640i
$326$	−1.60948e11	+	2.78771e11i	−0.789237	+	1.36700i
$327$	8.48762e9	+	1.47010e10i	0.0410507	+	0.0711019i
$328$	−1.34010e11			−0.639301
$329$	−1.73188e11	−	3.62342e10i	−0.814962	−	0.170505i
$330$	−6.78955e10			−0.315158
$331$	−1.22438e11	−	2.12070e11i	−0.560650	−	0.971074i	−0.997440	−	0.0715104i	$-0.977218\pi$
$331$	−1.22438e11	−	2.12070e11i	−0.560650	−	0.971074i	0.436790	−	0.899563i	$-0.356115\pi$
$332$	−1.22208e10	+	2.11671e10i	−0.0552050	+	0.0956179i
$333$	4.63043e10	−	8.02013e10i	0.206358	−	0.357423i
$334$	−7.53384e10	−	1.30490e11i	−0.331251	−	0.573744i
$335$	−5.11716e11			−2.21987
$336$	2.01974e11	−	2.25762e11i	0.864509	−	0.966327i
$337$	−4.96265e10			−0.209594			−0.104797	−	0.994494i	$-0.533419\pi$
$337$	−4.96265e10			−0.209594			−0.104797	+	0.994494i	$0.533419\pi$
$338$	1.11664e11	+	1.93408e11i	0.465361	+	0.806028i
$339$	1.91990e11	−	3.32536e11i	0.789550	−	1.36754i
$340$	−2.65535e10	+	4.59921e10i	−0.107762	+	0.186650i
$341$	−1.26324e9	−	2.18800e9i	−0.00505931	−	0.00876298i
$342$	−1.28864e11			−0.509347
$343$	2.08822e11	+	1.48680e11i	0.814616	+	0.580001i
$344$	−1.20094e11			−0.462390
$345$	3.12651e11	+	5.41527e11i	1.18816	+	2.05795i
$346$	1.89341e11	−	3.27948e11i	0.710234	−	1.23016i
$347$	1.52077e11	−	2.63405e11i	0.563094	−	0.975308i	−0.434130	−	0.900850i	$-0.642944\pi$
$347$	1.52077e11	−	2.63405e11i	0.563094	−	0.975308i	0.997224	−	0.0744576i	$-0.0237225\pi$
$348$	−3.12951e10	−	5.42046e10i	−0.114385	−	0.198121i
$349$	4.96999e11			1.79325			0.896626	−	0.442788i	$-0.146011\pi$
$349$	4.96999e11			1.79325			0.896626	+	0.442788i	$0.146011\pi$
$350$	−2.23949e11	+	2.50325e11i	−0.797707	+	0.891658i
$351$	8.54203e10			0.300385
$352$	8.53191e9	+	1.47777e10i	0.0296213	+	0.0513056i
$353$	−8.82246e10	+	1.52809e11i	−0.302415	+	0.523798i	−0.976682	−	0.214689i	$-0.931126\pi$
$353$	−8.82246e10	+	1.52809e11i	−0.302415	+	0.523798i	0.674267	+	0.738487i	$0.264460\pi$
$354$	−4.57793e9	+	7.92920e9i	−0.0154937	+	0.0268358i
$355$	−2.53632e11	−	4.39304e11i	−0.847573	−	1.46804i
$356$	−2.52699e10			−0.0833832
$357$	−2.99334e11	−	6.26262e10i	−0.975325	−	0.204056i
$358$	−9.73223e10			−0.313140
$359$	8.72570e10	+	1.51134e11i	0.277253	+	0.480215i	0.970701	−	0.240291i	$-0.0772428\pi$
$359$	8.72570e10	+	1.51134e11i	0.277253	+	0.480215i	−0.693448	+	0.720506i	$0.743909\pi$
$360$	−6.06547e10	+	1.05057e11i	−0.190328	+	0.329658i
$361$	−2.58446e11	+	4.47641e11i	−0.800916	+	1.38723i
$362$	3.29044e11	+	5.69921e11i	1.00708	+	1.74432i
$363$	−3.64285e11			−1.10119
$364$	6.60870e9	+	2.01204e10i	0.0197315	+	0.0600733i
$365$	−9.42224e10			−0.277867
$366$	1.69428e10	+	2.93458e10i	0.0493537	+	0.0854832i
$367$	−1.94008e11	+	3.36032e11i	−0.558243	+	0.966905i	0.439401	+	0.898291i	$0.355191\pi$
$367$	−1.94008e11	+	3.36032e11i	−0.558243	+	0.966905i	−0.997643	+	0.0686134i	$0.978143\pi$
$368$	2.89043e11	−	5.00637e11i	0.821575	−	1.42301i
$369$	−3.70095e10	−	6.41023e10i	−0.103919	−	0.179993i
$370$	7.99677e11			2.21823
$371$	8.39817e10	+	2.55685e11i	0.230145	+	0.700686i
$372$	4.07343e9			0.0110285
$373$	−3.02948e11	−	5.24721e11i	−0.810360	−	1.40359i	−0.912612	−	0.408827i	$-0.865938\pi$
$373$	−3.02948e11	−	5.24721e11i	−0.810360	−	1.40359i	0.102251	−	0.994759i	$-0.467395\pi$
$374$	3.16841e10	−	5.48785e10i	0.0837373	−	0.145037i
$375$	3.35970e10	−	5.81918e10i	0.0877324	−	0.151957i
$376$	−1.44920e11	−	2.51009e11i	−0.373924	−	0.647656i
$377$	−1.73944e11			−0.443479
$378$	−3.38106e11	−	7.07380e10i	−0.851805	−	0.178213i
$379$	5.34706e11			1.33119			0.665593	−	0.746315i	$-0.268179\pi$
$379$	5.34706e11			1.33119			0.665593	+	0.746315i	$0.268179\pi$
$380$	−8.05960e10	−	1.39596e11i	−0.198284	−	0.343438i
$381$	−1.20461e11	+	2.08645e11i	−0.292876	+	0.507277i
$382$	−2.12434e10	+	3.67947e10i	−0.0510434	+	0.0884098i
$383$	−1.26206e11	−	2.18595e11i	−0.299699	−	0.519094i	0.676368	−	0.736564i	$-0.263553\pi$
$383$	−1.26206e11	−	2.18595e11i	−0.299699	−	0.519094i	−0.976067	+	0.217470i	$0.930220\pi$
$384$	5.69904e11			1.33755
$385$	7.36974e10	−	8.23772e10i	0.170954	−	0.191088i
$386$	3.57686e11			0.820086
$387$	−3.31663e10	−	5.74457e10i	−0.0751619	−	0.130184i
$388$	−4.38461e9	+	7.59436e9i	−0.00982172	+	0.0170117i
$389$	−4.16836e10	+	7.21981e10i	−0.0922979	+	0.159865i	−0.908478	−	0.417933i	$-0.862755\pi$
$389$	−4.16836e10	+	7.21981e10i	−0.0922979	+	0.159865i	0.816180	+	0.577798i	$0.196088\pi$
$390$	−1.52110e11	−	2.63463e11i	−0.332941	−	0.576671i
$391$	−5.83606e11			−1.26277
$392$	4.65616e10	+	4.17325e11i	0.0995958	+	0.892663i
$393$	−3.27479e10			−0.0692495
$394$	5.38514e10	+	9.32733e10i	0.112581	+	0.194995i
$395$	1.12283e11	−	1.94480e11i	0.232075	−	0.401966i
$396$	−2.13821e9	+	3.70349e9i	−0.00436940	+	0.00756803i
$397$	−5.67001e10	−	9.82075e10i	−0.114558	−	0.198421i	0.803045	−	0.595919i	$-0.203212\pi$
$397$	−5.67001e10	−	9.82075e10i	−0.114558	−	0.198421i	−0.917603	+	0.397498i	$0.869879\pi$
$398$	−8.63410e11			−1.72482
$399$	6.18891e11	−	6.91782e11i	1.22246	−	1.36644i
$400$	−6.46160e11			−1.26203
$401$	−2.56734e11	−	4.44676e11i	−0.495831	−	0.858805i	0.504157	−	0.863612i	$-0.331803\pi$
$401$	−2.56734e11	−	4.44676e11i	−0.495831	−	0.858805i	−0.999988	+	0.00480724i	$0.998470\pi$
$402$	−4.92223e11	+	8.52556e11i	−0.940037	+	1.62819i
$403$	5.66022e9	−	9.80379e9i	0.0106896	−	0.0185149i
$404$	4.59442e10	+	7.95777e10i	0.0858054	+	0.148619i
$405$	9.48260e11			1.75138
$406$	6.88496e11	+	1.44046e11i	1.25758	+	0.263108i
$407$	−1.38223e11			−0.249693
$408$	−2.50476e11	−	4.33838e11i	−0.447503	−	0.775098i
$409$	−3.87550e11	+	6.71256e11i	−0.684814	+	1.18613i	0.288681	+	0.957425i	$0.406783\pi$
$409$	−3.87550e11	+	6.71256e11i	−0.684814	+	1.18613i	−0.973495	+	0.228708i	$0.926550\pi$
$410$	3.19578e11	−	5.53526e11i	0.558534	−	0.967409i
$411$	4.69662e11	+	8.13478e11i	0.811889	+	1.40623i
$412$	−4.38071e10			−0.0749043
$413$	−4.65133e9	−	1.41611e10i	−0.00786686	−	0.0239510i
$414$	2.71882e11			0.454861
$415$	2.85792e11	+	4.95007e11i	0.472970	+	0.819209i
$416$	−3.82290e10	+	6.62146e10i	−0.0625855	+	0.108401i
$417$	−1.22499e11	+	2.12174e11i	−0.198390	+	0.343621i
$418$	9.61684e10	+	1.66569e11i	0.154077	+	0.266870i
$419$	9.73463e11			1.54297			0.771483	−	0.636250i	$-0.219515\pi$
$419$	9.73463e11			1.54297			0.771483	+	0.636250i	$0.219515\pi$
$420$	5.56113e10	+	1.69311e11i	0.0872050	+	0.265499i
$421$	−8.24555e11			−1.27924			−0.639618	−	0.768693i	$-0.720907\pi$
$421$	−8.24555e11			−1.27924			−0.639618	+	0.768693i	$0.720907\pi$
$422$	−1.32283e11	−	2.29121e11i	−0.203048	−	0.351690i
$423$	8.00451e10	−	1.38642e11i	0.121563	−	0.210554i
$424$	−2.20425e11	+	3.81787e11i	−0.331218	+	0.573687i
$425$	3.26165e11	+	5.64935e11i	0.484939	+	0.839940i
$426$	−9.75882e11			−1.43567
$427$	−5.39956e10	−	1.12969e10i	−0.0786019	−	0.0164450i
$428$	−1.63691e8			−0.000235791
$429$	2.62921e10	+	4.55393e10i	0.0374773	+	0.0649125i
$430$	2.86392e11	−	4.96045e11i	0.403973	−	0.699702i
$431$	2.22097e11	−	3.84683e11i	0.310024	−	0.536977i	−0.668343	−	0.743853i	$-0.732996\pi$
$431$	2.22097e11	−	3.84683e11i	0.310024	−	0.536977i	0.978367	+	0.206876i	$0.0663296\pi$
$432$	−3.32262e11	−	5.75495e11i	−0.458991	−	0.794996i
$433$	7.57077e11			1.03501			0.517505	−	0.855680i	$-0.326861\pi$
$433$	7.57077e11			1.03501			0.517505	+	0.855680i	$0.326861\pi$
$434$	−3.05227e10	+	3.41175e10i	−0.0412970	+	0.0461609i
$435$	−1.46371e12			−1.95999
$436$	4.61624e9	+	7.99557e9i	0.00611786	+	0.0105964i
$437$	8.85688e11	−	1.53406e12i	1.16175	−	2.01222i
$438$	−9.06331e10	+	1.56981e11i	−0.117667	+	0.203805i
$439$	−5.04945e10	−	8.74591e10i	−0.0648865	−	0.112387i	0.831757	−	0.555140i	$-0.187335\pi$
$439$	−5.04945e10	−	8.74591e10i	−0.0648865	−	0.112387i	−0.896644	+	0.442753i	$0.854002\pi$
$440$	1.81061e11			0.230297
$441$	−1.86764e11	+	1.37525e11i	−0.235136	+	0.173144i
$442$	2.83935e11			0.353849
$443$	−3.63399e11	−	6.29425e11i	−0.448298	−	0.776475i	0.549977	−	0.835180i	$-0.314636\pi$
$443$	−3.63399e11	−	6.29425e11i	−0.448298	−	0.776475i	−0.998275	+	0.0587046i	$0.981303\pi$
$444$	1.11428e11	−	1.93000e11i	0.136073	−	0.235686i
$445$	−2.95477e11	+	5.11781e11i	−0.357194	+	0.618678i
$446$	−3.93760e11	−	6.82012e11i	−0.471221	−	0.816179i
$447$	−9.76103e10			−0.115641
$448$	−4.42317e11	+	4.94412e11i	−0.518780	+	0.579880i
$449$	−1.85410e11			−0.215291			−0.107645	−	0.994189i	$-0.534331\pi$
$449$	−1.85410e11			−0.215291			−0.107645	+	0.994189i	$0.534331\pi$
$450$	−1.51949e11	−	2.63184e11i	−0.174680	−	0.302554i
$451$	−5.52388e10	+	9.56764e10i	−0.0628709	+	0.108896i
$452$	1.04419e11	−	1.80860e11i	0.117668	−	0.203807i
$453$	−8.40776e10	−	1.45627e11i	−0.0938077	−	0.162480i
$454$	−2.20410e11			−0.243489
$455$	4.84766e11	+	1.01422e11i	0.530250	+	0.110938i
$456$	1.52050e12			1.64682
$457$	4.49165e11	+	7.77977e11i	0.481707	+	0.834341i	0.999780	−	0.0209954i	$-0.00668354\pi$
$457$	4.49165e11	+	7.77977e11i	0.481707	+	0.834341i	−0.518072	+	0.855337i	$0.673350\pi$
$458$	−5.67459e11	+	9.82868e11i	−0.602615	+	1.04376i
$459$	−3.35435e11	+	5.80990e11i	−0.352737	+	0.610959i
$460$	1.70045e11	+	2.94526e11i	0.177073	+	0.306700i
$461$	−6.56915e11			−0.677416			−0.338708	−	0.940892i	$-0.609990\pi$
$461$	−6.56915e11			−0.677416			−0.338708	+	0.940892i	$0.609990\pi$
$462$	−6.63563e10	−	2.02024e11i	−0.0677631	−	0.206307i
$463$	7.36860e11			0.745196			0.372598	−	0.927993i	$-0.378467\pi$
$463$	7.36860e11			0.745196			0.372598	+	0.927993i	$0.378467\pi$
$464$	6.76596e11	+	1.17190e12i	0.677639	+	1.17370i
$465$	4.76300e10	−	8.24976e10i	0.0472435	−	0.0818282i
$466$	5.32621e11	−	9.22526e11i	0.523217	−	0.906238i
$467$	3.97280e11	+	6.88109e11i	0.386519	+	0.669470i	0.991979	−	0.126406i	$-0.0403441\pi$
$467$	3.97280e11	+	6.88109e11i	0.386519	+	0.669470i	−0.605460	+	0.795876i	$0.707011\pi$
$468$	−1.91614e10			−0.0184638
$469$	−5.00115e11	−	1.52262e12i	−0.477301	−	1.45316i
$470$	1.38238e12			1.30674
$471$	2.94720e11	+	5.10470e11i	0.275941	+	0.477943i
$472$	1.22082e10	−	2.11453e10i	0.0113218	−	0.0196099i
$473$	−4.95026e10	+	8.57410e10i	−0.0454729	+	0.0787614i
$474$	−2.16012e11	−	3.74144e11i	−0.196551	−	0.340437i
$475$	−1.97997e12			−1.78459
$476$	−1.62802e11	−	3.40611e10i	−0.145354	−	0.0304108i
$477$	−2.43498e11			−0.215359
$478$	3.35579e11	+	5.81240e11i	0.294015	+	0.509248i
$479$	−5.76669e11	+	9.98820e11i	−0.500515	+	0.866917i	0.499485	+	0.866322i	$0.333522\pi$
$479$	−5.76669e11	+	9.98820e11i	−0.500515	+	0.866917i	−1.00000		0.000594242i	$0.999811\pi$
$480$	−3.21692e11	+	5.57187e11i	−0.276602	+	0.479089i
$481$	−3.09670e11	−	5.36364e11i	−0.263783	−	0.456885i
$482$	−2.81594e11			−0.237636
$483$	−1.30576e12	+	1.45955e12i	−1.09170	+	1.22027i
$484$	−1.98128e11			−0.164112
$485$	1.02537e11	+	1.77599e11i	0.0841479	+	0.145748i
$486$	3.76987e11	−	6.52960e11i	0.306523	−	0.530913i
$487$	9.72094e11	−	1.68372e12i	0.783120	−	1.35640i	−0.146996	−	0.989137i	$-0.546961\pi$
$487$	9.72094e11	−	1.68372e12i	0.783120	−	1.35640i	0.930116	−	0.367266i	$-0.119706\pi$
$488$	−4.51824e10	−	7.82582e10i	−0.0360645	−	0.0624655i
$489$	2.09787e12			1.65916
$490$	−1.83479e12	−	8.02887e11i	−1.43782	−	0.629176i
$491$	−7.04431e9			−0.00546980			−0.00273490	−	0.999996i	$-0.500871\pi$
$491$	−7.04431e9			−0.00546980			−0.00273490	+	0.999996i	$0.500871\pi$
$492$	−8.90611e10	−	1.54258e11i	−0.0685244	−	0.118688i
$493$	6.83056e11	−	1.18309e12i	0.520769	−	0.901999i
$494$	−4.30903e11	+	7.46346e11i	−0.325543	+	0.563857i
$495$	5.00036e10	+	8.66087e10i	0.0374350	+	0.0648393i
$496$	−8.80670e10			−0.0653350
$497$	1.05927e12	−	1.18403e12i	0.778762	−	0.870481i
$498$	1.09962e12			0.801145
$499$	−3.49974e10	−	6.06172e10i	−0.0252687	−	0.0437667i	0.853115	−	0.521724i	$-0.174711\pi$
$499$	−3.49974e10	−	6.06172e10i	−0.0252687	−	0.0437667i	−0.878383	+	0.477957i	$0.841377\pi$
$500$	1.82727e10	−	3.16493e10i	0.0130749	−	0.0226464i
$501$	−4.90996e11	+	8.50430e11i	−0.348184	+	0.603072i
$502$	3.29286e11	+	5.70340e11i	0.231423	+	0.400837i
$503$	−2.76650e12			−1.92697			−0.963484	−	0.267766i	$-0.913714\pi$
$503$	−2.76650e12			−1.92697			−0.963484	+	0.267766i	$0.913714\pi$
$504$	−3.71879e11	−	7.78038e10i	−0.256722	−	0.0537110i
$505$	2.14888e12			1.47028
$506$	−2.02900e11	−	3.51433e11i	−0.137596	−	0.238322i
$507$	7.27740e11	−	1.26048e12i	0.489148	−	0.847230i
$508$	−6.55164e10	+	1.13478e11i	−0.0436479	+	0.0756003i
$509$	−4.88478e11	−	8.46068e11i	−0.322563	−	0.558696i	0.658453	−	0.752622i	$-0.271211\pi$
$509$	−4.88478e11	−	8.46068e11i	−0.322563	−	0.558696i	−0.981016	+	0.193926i	$0.937878\pi$
$510$	2.38927e12			1.56387
$511$	−9.20863e10	−	2.80360e11i	−0.0597449	−	0.181896i
$512$	−9.98363e11			−0.642057
$513$	−1.01812e12	−	1.76344e12i	−0.649040	−	1.12417i
$514$	4.37944e11	−	7.58541e11i	0.276748	−	0.479342i
$515$	−5.12230e11	+	8.87208e11i	−0.320872	+	0.555767i
$516$	−7.98127e10	−	1.38240e11i	−0.0495619	−	0.0858438i
$517$	−2.38944e11			−0.147092
$518$	7.81548e11	+	2.37945e12i	0.476949	+	1.45209i
$519$	−2.46795e12			−1.49308
$520$	4.05642e11	+	7.02592e11i	0.243292	+	0.421394i
$521$	−5.65660e11	+	9.79751e11i	−0.336345	+	0.582567i	−0.983742	−	0.179586i	$-0.942524\pi$
$521$	−5.65660e11	+	9.79751e11i	−0.336345	+	0.582567i	0.647397	+	0.762153i	$0.275858\pi$
$522$	−3.18212e11	+	5.51160e11i	−0.187586	+	0.324908i
$523$	1.54001e12	+	2.66738e12i	0.900050	+	1.55893i	0.827428	+	0.561572i	$0.189803\pi$
$523$	1.54001e12	+	2.66738e12i	0.900050	+	1.55893i	0.0726222	+	0.997360i	$0.476863\pi$
$524$	−1.78109e10			−0.0103204
$525$	2.14261e12	+	4.48274e11i	1.23091	+	0.257529i
$526$	−3.24859e12			−1.85037
$527$	4.44540e10	+	7.69966e10i	0.0251052	+	0.0434834i
$528$	2.04539e11	−	3.54272e11i	0.114531	−	0.198373i
$529$	−9.68084e11	+	1.67677e12i	−0.537480	+	0.930943i
$530$	−1.05131e12	−	1.82092e12i	−0.578747	−	1.00242i
$531$	1.34862e10			0.00736145
$532$	3.36603e11	−	3.76246e11i	0.182186	−	0.203643i
$533$	−4.95019e11			−0.265674
$534$	5.68443e11	+	9.84572e11i	0.302518	+	0.523976i
$535$	−1.91401e9	+	3.31517e9i	−0.00101007	+	0.00174950i
$536$	1.31264e12	−	2.27356e12i	0.686918	−	1.18978i
$537$	3.17135e11	+	5.49294e11i	0.164573	+	0.285049i
$538$	1.78329e12			0.917701
$539$	3.17141e11	+	1.38778e11i	0.161847	+	0.0708226i
$540$	3.90941e11			0.197851
$541$	1.39651e12	+	2.41883e12i	0.700901	+	1.21400i	0.968151	+	0.250369i	$0.0805518\pi$
$541$	1.39651e12	+	2.41883e12i	0.700901	+	1.21400i	−0.267250	+	0.963627i	$0.586115\pi$
$542$	−5.06111e11	+	8.76611e11i	−0.251912	+	0.436325i
$543$	2.14445e12	−	3.71429e12i	1.05856	−	1.83348i
$544$	−3.00242e11	−	5.20034e11i	−0.146986	−	0.254587i
$545$	2.15908e11			0.104830
$546$	6.35276e11	−	7.10096e11i	0.305911	−	0.341940i
$547$	1.47553e12			0.704700			0.352350	−	0.935868i	$-0.385383\pi$
$547$	1.47553e12			0.704700			0.352350	+	0.935868i	$0.385383\pi$
$548$	2.55439e11	+	4.42434e11i	0.120997	+	0.209573i
$549$	2.49560e10	−	4.32250e10i	0.0117246	−	0.0203076i
$550$	−2.26793e11	+	3.92817e11i	−0.105681	+	0.183045i
$551$	2.07323e12	+	3.59094e12i	0.958220	+	1.65969i
$552$	−3.20802e12			−1.47066
$553$	6.88418e11	+	1.44030e11i	0.313032	+	0.0654920i
$554$	−3.96062e12			−1.78636
$555$	−2.60583e12	−	4.51343e12i	−1.16581	−	2.01924i
$556$	−6.66245e10	+	1.15397e11i	−0.0295663	+	0.0512104i
$557$	−1.10846e12	+	1.91990e12i	−0.487944	+	0.845144i	−0.999904	−	0.0138652i	$-0.995586\pi$
$557$	−1.10846e12	+	1.91990e12i	−0.487944	+	0.845144i	0.511960	+	0.859010i	$0.328920\pi$
$558$	−2.07096e10	−	3.58701e10i	−0.00904310	−	0.0156631i
$559$	−4.43614e11			−0.192155
$560$	−1.20231e12	−	3.66048e12i	−0.516619	−	1.57287i
$561$	−4.12984e11			−0.176035
$562$	−1.71209e12	−	2.96543e12i	−0.723957	−	1.25393i
$563$	−3.26827e11	+	5.66082e11i	−0.137098	+	0.237460i	−0.926397	−	0.376549i	$-0.877111\pi$
$563$	−3.26827e11	+	5.66082e11i	−0.137098	+	0.237460i	0.789299	+	0.614009i	$0.210444\pi$
$564$	1.92624e11	−	3.33634e11i	0.0801592	−	0.138840i
$565$	−2.44192e12	−	4.22953e12i	−1.00812	−	1.74612i
$566$	4.33860e12			1.77695
$567$	9.26762e11	+	2.82156e12i	0.376569	+	1.14648i
$568$	2.60244e12			1.04909
$569$	−1.29888e12	−	2.24973e12i	−0.519474	−	0.899756i	−0.999744	−	0.0226349i	$-0.992794\pi$
$569$	−1.29888e12	−	2.24973e12i	−0.519474	−	0.899756i	0.480269	−	0.877121i	$-0.340539\pi$
$570$	−3.62599e12	+	6.28040e12i	−1.43877	+	2.49202i
$571$	5.19555e11	−	8.99896e11i	0.204536	−	0.354266i	−0.745449	−	0.666563i	$-0.767765\pi$
$571$	5.19555e11	−	8.99896e11i	0.204536	−	0.354266i	0.949985	+	0.312296i	$0.101098\pi$
$572$	1.42998e10	+	2.47679e10i	0.00558530	+	0.00967402i
$573$	2.76896e11			0.107305
$574$	1.95936e12	+	4.09933e11i	0.753373	+	0.157619i
$575$	4.17742e12			1.59369
$576$	−3.00112e11	−	5.19808e11i	−0.113601	−	0.196762i
$577$	−2.33010e11	+	4.03585e11i	−0.0875152	+	0.151581i	−0.906460	−	0.422291i	$-0.861226\pi$
$577$	−2.33010e11	+	4.03585e11i	−0.0875152	+	0.151581i	0.818945	+	0.573872i	$0.194559\pi$
$578$	3.35887e11	−	5.81773e11i	0.125175	−	0.216809i
$579$	−1.16556e12	−	2.01881e12i	−0.431003	−	0.746519i
$580$	−7.96085e11			−0.292101
$581$	−1.19359e12	+	1.33416e12i	−0.434572	+	0.485754i
$582$	3.94524e11			0.142535
$583$	1.81718e11	+	3.14744e11i	0.0651461	+	0.112836i
$584$	2.41697e11	−	4.18631e11i	0.0859832	−	0.148927i
$585$	−2.24052e11	+	3.88069e11i	−0.0790946	+	0.136996i
$586$	2.02738e12	+	3.51153e12i	0.710226	+	1.23015i
$587$	5.17776e12			1.79999			0.899996	−	0.435897i	$-0.143569\pi$
$587$	5.17776e12			1.79999			0.899996	+	0.435897i	$0.143569\pi$
$588$	−4.49437e11	+	3.30945e11i	−0.155050	+	0.114171i
$589$	−2.69856e11			−0.0923874
$590$	5.82267e10	+	1.00852e11i	0.0197828	+	0.0342649i
$591$	3.50961e11	−	6.07882e11i	0.118335	−	0.204963i
$592$	−2.40907e12	+	4.17263e12i	−0.806123	+	1.39625i
$593$	−1.94396e12	−	3.36705e12i	−0.645568	−	1.11816i	−0.984170	−	0.177227i	$-0.943287\pi$
$593$	−1.94396e12	−	3.36705e12i	−0.645568	−	1.11816i	0.338601	−	0.940930i	$-0.390046\pi$
$594$	−4.66477e11			−0.153741
$595$	−2.59344e12	+	2.89889e12i	−0.848302	+	0.948212i
$596$	−5.30883e10			−0.0172342
$597$	2.81351e12	+	4.87315e12i	0.906493	+	1.57009i
$598$	9.09136e11	−	1.57467e12i	0.290719	−	0.503540i
$599$	−3.53757e11	+	6.12726e11i	−0.112275	+	0.194467i	−0.916687	−	0.399605i	$-0.869147\pi$
$599$	−3.53757e11	+	6.12726e11i	−0.112275	+	0.194467i	0.804412	+	0.594072i	$0.202481\pi$
$600$	1.79289e12	+	3.10538e12i	0.564773	+	0.978215i
$601$	−3.16274e12			−0.988845			−0.494422	−	0.869222i	$-0.664620\pi$
$601$	−3.16274e12			−0.988845			−0.494422	+	0.869222i	$0.664620\pi$
$602$	1.75589e12	+	3.67364e11i	0.544895	+	0.114002i
$603$	1.45005e12			0.446636
$604$	−4.57281e10	−	7.92034e10i	−0.0139803	−	0.0242146i
$605$	−2.31668e12	+	4.01260e12i	−0.703018	+	1.21766i
$606$	2.06702e12	−	3.58018e12i	0.622612	−	1.07840i
$607$	−1.94652e12	−	3.37148e12i	−0.581983	−	1.00802i	−0.995244	−	0.0974119i	$-0.968944\pi$
$607$	−1.94652e12	−	3.37148e12i	−0.581983	−	1.00802i	0.413261	−	0.910613i	$-0.364390\pi$
$608$	1.82260e12			0.540911
$609$	−1.43053e12	−	4.35531e12i	−0.421424	−	1.28304i
$610$	4.30991e11			0.126033
$611$	−5.35319e11	−	9.27200e11i	−0.155392	−	0.269146i
$612$	7.52446e10	−	1.30327e11i	0.0216817	−	0.0375538i
$613$	3.04157e12	−	5.26815e12i	0.870012	−	1.50691i	0.00802931	−	0.999968i	$-0.497444\pi$
$613$	3.04157e12	−	5.26815e12i	0.870012	−	1.50691i	0.861983	−	0.506937i	$-0.169223\pi$
$614$	−2.60381e12	−	4.50992e12i	−0.739351	−	1.28059i
$615$	−4.16552e12			−1.17417
$616$	1.76956e11	+	5.38751e11i	0.0495169	+	0.150756i
$617$	−5.40996e12			−1.50283			−0.751416	−	0.659829i	$-0.770629\pi$
$617$	−5.40996e12			−1.50283			−0.751416	+	0.659829i	$0.770629\pi$
$618$	9.85434e11	+	1.70682e12i	0.271756	+	0.470696i
$619$	6.49701e11	−	1.12531e12i	0.177871	−	0.308082i	−0.763280	−	0.646068i	$-0.776412\pi$
$619$	6.49701e11	−	1.12531e12i	0.177871	−	0.308082i	0.941151	+	0.337986i	$0.109746\pi$
$620$	2.59050e10	−	4.48688e10i	0.00704078	−	0.0121950i
$621$	2.14807e12	+	3.72057e12i	0.579611	+	1.00392i
$622$	−3.88733e12			−1.04135
$623$	−1.81159e12	−	3.79018e11i	−0.481797	−	0.100801i
$624$	1.83296e12			0.483974
$625$	1.68290e12	+	2.91487e12i	0.441162	+	0.764115i
$626$	3.63752e12	−	6.30038e12i	0.946720	−	1.63977i
$627$	6.26750e11	−	1.08556e12i	0.161953	−	0.280512i
$628$	1.60292e11	+	2.77635e11i	0.0411239	+	0.0712287i
$629$	4.86415e12			1.23902
$630$	1.20820e12	−	1.35049e12i	0.305566	−	0.341555i
$631$	−3.33319e12			−0.837004			−0.418502	−	0.908216i	$-0.637445\pi$
$631$	−3.33319e12			−0.837004			−0.418502	+	0.908216i	$0.637445\pi$
$632$	5.76053e11	+	9.97753e11i	0.143627	+	0.248769i
$633$	−8.62118e11	+	1.49323e12i	−0.213427	+	0.369667i
$634$	−1.87575e12	+	3.24889e12i	−0.461076	+	0.798607i
$635$	1.53215e12	+	2.65376e12i	0.373954	+	0.647708i
$636$	−5.85964e11			−0.142008
$637$	1.71993e11	+	1.54155e12i	0.0413890	+	0.370963i
$638$	9.49900e11			0.226979
$639$	7.18715e11	+	1.24485e12i	0.170531	+	0.295368i
$640$	3.62431e12	−	6.27749e12i	0.853917	−	1.47903i
$641$	−9.73337e11	+	1.68587e12i	−0.227721	+	0.394424i	−0.957132	−	0.289651i	$-0.906461\pi$
$641$	−9.73337e11	+	1.68587e12i	−0.227721	+	0.394424i	0.729412	+	0.684075i	$0.239794\pi$
$642$	3.68221e9	+	6.37777e9i	0.000855461	+	0.00148170i
$643$	−1.31531e12			−0.303443			−0.151722	−	0.988423i	$-0.548482\pi$
$643$	−1.31531e12			−0.303443			−0.151722	+	0.988423i	$0.548482\pi$
$644$	−7.10177e11	+	7.93819e11i	−0.162697	+	0.181859i
$645$	−3.73295e12			−0.849246
$646$	−3.38421e12	−	5.86162e12i	−0.764558	−	1.32425i
$647$	3.35402e12	−	5.80933e12i	0.752483	−	1.30334i	−0.194134	−	0.980975i	$-0.562190\pi$
$647$	3.35402e12	−	5.80933e12i	0.752483	−	1.30334i	0.946616	−	0.322363i	$-0.104477\pi$
$648$	−2.43245e12	+	4.21313e12i	−0.541947	+	0.938680i
$649$	−1.00644e10	−	1.74321e10i	−0.00222684	−	0.00385699i
$650$	−2.03239e12			−0.446577
$651$	2.92023e11	+	6.10966e10i	0.0637240	+	0.0133322i
$652$	1.14099e12			0.247268
$653$	3.93686e12	+	6.81883e12i	0.847306	+	1.46758i	0.883604	+	0.468236i	$0.155110\pi$
$653$	3.93686e12	+	6.81883e12i	0.847306	+	1.46758i	−0.0362978	+	0.999341i	$0.511556\pi$
$654$	2.07684e11	−	3.59718e11i	0.0443917	−	0.0768888i
$655$	−2.08261e11	+	3.60718e11i	−0.0442101	+	0.0765741i
$656$	1.92549e12	+	3.33505e12i	0.405952	+	0.703129i
$657$	2.66997e11			0.0559065
$658$	1.35104e12	+	4.11330e12i	0.280965	+	0.855410i
$659$	8.22995e12			1.69986			0.849929	−	0.526897i	$-0.176644\pi$
$659$	8.22995e12			1.69986			0.849929	+	0.526897i	$0.176644\pi$
$660$	1.20331e11	+	2.08419e11i	0.0246847	+	0.0427552i
$661$	−2.84912e12	+	4.93481e12i	−0.580502	+	1.00546i	0.414918	+	0.909859i	$0.363810\pi$
$661$	−2.84912e12	+	4.93481e12i	−0.580502	+	1.00546i	−0.995420	+	0.0955999i	$0.969523\pi$
$662$	−2.99595e12	+	5.18913e12i	−0.606280	+	1.05011i
$663$	−9.25231e11	−	1.60255e12i	−0.185969	−	0.322107i
$664$	−2.93243e12			−0.585425
$665$	−3.68413e12	−	1.12165e13i	−0.730529	−	2.22412i
$666$	−2.26604e12			−0.446307
$667$	−4.37418e12	−	7.57630e12i	−0.855718	−	1.48215i
$668$	−2.67043e11	+	4.62532e11i	−0.0518904	+	0.0898768i
$669$	−2.56622e12	+	4.44482e12i	−0.495308	+	0.857899i
$670$	6.26060e12	+	1.08437e13i	1.20027	+	2.07893i
$671$	−7.44964e10			−0.0141868
$672$	−1.97232e12	−	4.12645e11i	−0.373092	−	0.0780576i
$673$	9.28143e12			1.74400			0.872002	−	0.489503i	$-0.162822\pi$
$673$	9.28143e12			1.74400			0.872002	+	0.489503i	$0.162822\pi$
$674$	6.07156e11	+	1.05162e12i	0.113326	+	0.196287i
$675$	2.40102e12	−	4.15869e12i	0.445173	−	0.771063i
$676$	3.95803e11	−	6.85552e11i	0.0728986	−	0.126264i
$677$	−6.45102e11	−	1.11735e12i	−0.118026	−	0.204428i	0.800959	−	0.598719i	$-0.204323\pi$
$677$	−6.45102e11	−	1.11735e12i	−0.118026	−	0.204428i	−0.918986	+	0.394291i	$0.870990\pi$
$678$	−9.39560e12			−1.70762
$679$	−4.28238e11	+	4.78674e11i	−0.0773163	+	0.0864223i
$680$	−6.37162e12			−1.14277
$681$	7.18228e11	+	1.24401e12i	0.127968	+	0.221646i
$682$	−3.09102e10	+	5.35381e10i	−0.00547107	+	0.00947618i
$683$	−1.27194e11	+	2.20307e11i	−0.0223653	+	0.0387379i	−0.876991	−	0.480506i	$-0.840453\pi$
$683$	−1.27194e11	+	2.20307e11i	−0.0223653	+	0.0387379i	0.854626	+	0.519244i	$0.173786\pi$
$684$	2.28384e11	+	3.95573e11i	0.0398946	+	0.0690994i
$685$	1.19473e13			2.07329
$686$	5.95811e11	−	6.24413e12i	0.102719	−	1.07650i
$687$	7.39650e12			1.26684
$688$	1.72554e12	+	2.98872e12i	0.293614	+	0.508555i
$689$	−8.14225e11	+	1.41028e12i	−0.137644	+	0.238407i
$690$	7.65026e12	−	1.32506e13i	1.28486	−	2.22544i
$691$	7.84952e11	+	1.35958e12i	0.130976	+	0.226857i	0.924053	−	0.382264i	$-0.124856\pi$
$691$	7.84952e11	+	1.35958e12i	0.130976	+	0.226857i	−0.793077	+	0.609121i	$0.791522\pi$
$692$	−1.34227e12			−0.222516
$693$	−2.08836e11	+	2.33432e11i	−0.0343958	+	0.0384468i
$694$	−7.44235e12			−1.21785
$695$	1.55806e12	+	2.69864e12i	0.253310	+	0.438746i
$696$	3.75468e12	−	6.50330e12i	0.606501	−	1.05049i
$697$	1.94388e12	−	3.36689e12i	0.311976	−	0.540359i
$698$	−6.08054e12	−	1.05318e13i	−0.969600	−	1.67940i
$699$	−6.94240e12			−1.09992
$700$	1.16533e12	+	2.43807e11i	0.183445	+	0.0383800i
$701$	−8.33084e12			−1.30304			−0.651520	−	0.758632i	$-0.725868\pi$
$701$	−8.33084e12			−1.30304			−0.651520	+	0.758632i	$0.725868\pi$
$702$	−1.04507e12	−	1.81012e12i	−0.162417	−	0.281314i
$703$	−7.38189e12	+	1.27858e13i	−1.13990	+	1.97437i
$704$	−4.47934e11	+	7.75844e11i	−0.0687285	+	0.119041i
$705$	−4.50464e12	−	7.80227e12i	−0.686767	−	1.18951i
$706$	4.31753e12			0.654056
$707$	2.10016e12	+	6.39402e12i	0.316129	+	0.962468i
$708$	3.24536e10			0.00485416
$709$	−1.16510e12	−	2.01801e12i	−0.173163	−	0.299926i	0.766361	−	0.642410i	$-0.222065\pi$
$709$	−1.16510e12	−	2.01801e12i	−0.173163	−	0.299926i	−0.939524	+	0.342483i	$0.888732\pi$
$710$	−6.20613e12	+	1.07493e13i	−0.916554	+	1.58752i
$711$	−3.18176e11	+	5.51098e11i	−0.0466933	+	0.0808752i
$712$	−1.51590e12	−	2.62562e12i	−0.221060	−	0.382888i
$713$	5.69352e11			0.0825046
$714$	2.33511e12	+	7.10932e12i	0.336252	+	1.02373i
$715$	6.68820e11			0.0957044
$716$	1.72483e11	+	2.98750e11i	0.0245267	+	0.0424814i
$717$	2.18704e12	−	3.78806e12i	0.309044	−	0.535280i
$718$	2.13509e12	−	3.69809e12i	0.299817	−	0.519299i
$719$	7.83347e11	+	1.35680e12i	0.109314	+	0.189337i	0.915492	−	0.402335i	$-0.131801\pi$
$719$	7.83347e11	+	1.35680e12i	0.109314	+	0.189337i	−0.806179	+	0.591672i	$0.798468\pi$
$720$	3.48601e12			0.483428
$721$	−3.14052e12	−	6.57054e11i	−0.432806	−	0.0905508i
$722$	1.26478e13			1.73220
$723$	9.17603e11	+	1.58934e12i	0.124891	+	0.216318i
$724$	1.16632e12	−	2.02013e12i	0.157759	−	0.273247i
$725$	−4.88927e12	+	8.46847e12i	−0.657239	+	1.13837i
$726$	4.45685e12	+	7.71949e12i	0.595406	+	1.03127i
$727$	2.09663e11			0.0278367			0.0139183	−	0.999903i	$-0.495570\pi$
$727$	2.09663e11			0.0278367			0.0139183	+	0.999903i	$0.495570\pi$
$728$	−1.69413e12	+	1.89366e12i	−0.223540	+	0.249868i
$729$	4.28830e12			0.562356
$730$	1.15276e12	+	1.99665e12i	0.150241	+	0.260225i
$731$	1.74202e12	−	3.01726e12i	0.225644	−	0.390827i
$732$	6.00550e10	−	1.04018e11i	0.00773125	−	0.0133909i
$733$	−4.07588e12	−	7.05962e12i	−0.521498	−	0.903262i	−0.999687	−	0.0250047i	$-0.992040\pi$
$733$	−4.07588e12	−	7.05962e12i	−0.521498	−	0.903262i	0.478189	−	0.878257i	$-0.341293\pi$
$734$	9.49438e12			1.20735
$735$	1.44730e12	+	1.29720e13i	0.182922	+	1.63950i
$736$	−3.84540e12			−0.483049
$737$	−1.08214e12	−	1.87432e12i	−0.135107	−	0.234013i
$738$	−9.05586e11	+	1.56852e12i	−0.112377	+	0.194642i
$739$	3.82789e12	−	6.63011e12i	0.472128	−	0.817750i	−0.527363	−	0.849640i	$-0.676819\pi$
$739$	3.82789e12	−	6.63011e12i	0.472128	−	0.817750i	0.999491	+	0.0318898i	$0.0101526\pi$
$740$	−1.41726e12	−	2.45477e12i	−0.173743	−	0.300931i
$741$	5.61657e12			0.684367
$742$	4.39070e12	−	4.90782e12i	0.531761	−	0.594390i
$743$	−7.82269e12			−0.941686			−0.470843	−	0.882217i	$-0.656050\pi$
$743$	−7.82269e12			−0.941686			−0.470843	+	0.882217i	$0.656050\pi$
$744$	2.44359e11	+	4.23242e11i	0.0292381	+	0.0506419i
$745$	−6.20754e11	+	1.07518e12i	−0.0738272	+	0.127872i
$746$	−7.41284e12	+	1.28394e13i	−0.876314	+	1.51782i
$747$	−8.09847e11	−	1.40270e12i	−0.0951613	−	0.164824i
$748$	−2.24614e11			−0.0262349
$749$	−1.17350e10	−	2.45517e9i	−0.00136243	−	0.000285045i
$750$	−1.64417e12			−0.189746
$751$	−5.68288e12	−	9.84304e12i	−0.651912	−	1.12914i	−0.982658	−	0.185425i	$-0.940634\pi$
$751$	−5.68288e12	−	9.84304e12i	−0.651912	−	1.12914i	0.330747	−	0.943720i	$-0.392699\pi$
$752$	−4.16450e12	+	7.21313e12i	−0.474879	+	0.822514i
$753$	2.14603e12	−	3.71703e12i	0.243253	−	0.421326i
$754$	2.12812e12	+	3.68601e12i	0.239786	+	0.415322i
$755$	−2.13877e12			−0.239554
$756$	3.82078e11	+	1.16325e12i	0.0425406	+	0.129517i
$757$	−1.15682e13			−1.28037			−0.640184	−	0.768222i	$-0.721142\pi$
$757$	−1.15682e13			−1.28037			−0.640184	+	0.768222i	$0.721142\pi$
$758$	−6.54187e12	−	1.13308e13i	−0.719764	−	1.24667i
$759$	−1.32234e12	+	2.29036e12i	−0.144629	+	0.250505i
$760$	9.66966e12	−	1.67483e13i	1.05136	−	1.82100i
$761$	−1.05812e12	−	1.83272e12i	−0.114368	−	0.198091i	0.803159	−	0.595765i	$-0.203151\pi$
$761$	−1.05812e12	−	1.83272e12i	−0.114368	−	0.198091i	−0.917527	+	0.397674i	$0.869818\pi$
$762$	5.89513e12			0.633426
$763$	2.11013e11	+	6.42439e11i	0.0225398	+	0.0686233i
$764$	1.50598e11			0.0159919
$765$	−1.75965e12	−	3.04780e12i	−0.185759	−	0.321744i
$766$	−3.08813e12	+	5.34880e12i	−0.324091	+	0.561342i
$767$	4.50959e10	−	7.81083e10i	0.00470498	−	0.00814926i
$768$	−2.70919e12	−	4.69245e12i	−0.281005	−	0.486715i
$769$	2.61186e12			0.269328			0.134664	−	0.990891i	$-0.457005\pi$
$769$	2.61186e12			0.269328			0.134664	+	0.990891i	$0.457005\pi$
$770$	−2.64729e12	−	5.53861e11i	−0.271390	−	0.0567797i
$771$	−5.70835e12			−0.581789
$772$	−6.33923e11	−	1.09799e12i	−0.0642331	−	0.111255i
$773$	4.15174e12	−	7.19102e12i	0.418237	−	0.724407i	−0.577525	−	0.816373i	$-0.695982\pi$
$773$	4.15174e12	−	7.19102e12i	0.418237	−	0.724407i	0.995762	+	0.0919653i	$0.0293149\pi$
$774$	−8.11546e11	+	1.40564e12i	−0.0812791	+	0.140780i
$775$	−3.18199e11	−	5.51137e11i	−0.0316841	−	0.0548784i
$776$	−1.05210e12			−0.104155
$777$	1.08830e13	−	1.21648e13i	1.07116	−	1.19732i
$778$	2.03991e12			0.199620
$779$	5.90011e12	+	1.02193e13i	0.574039	+	0.994265i
$780$	−5.39167e11	+	9.33864e11i	−0.0521552	+	0.0903354i
$781$	1.07272e12	−	1.85801e12i	0.103171	−	0.178698i
$782$	7.14013e12	+	1.23671e13i	0.682772	+	1.18260i
$783$	−1.00565e13			−0.956130
$784$	9.71677e12	−	7.15499e12i	0.918543	−	0.676374i
$785$	7.49710e12			0.704661
$786$	4.00654e11	+	6.93953e11i	0.0374428	+	0.0648528i
$787$	−4.23933e12	+	7.34274e12i	−0.393923	+	0.682295i	−0.992963	−	0.118424i	$-0.962216\pi$
$787$	−4.23933e12	+	7.34274e12i	−0.393923	+	0.682295i	0.599040	+	0.800719i	$0.295549\pi$
$788$	1.90881e11	−	3.30615e11i	0.0176357	−	0.0305460i
$789$	1.05859e13	+	1.83353e13i	0.972478	+	1.68438i
$790$	−5.49492e12			−0.501926
$791$	1.01985e13	−	1.13996e13i	0.926278	−	1.03537i
$792$	−5.13072e11			−0.0463356
$793$	−1.66899e11	−	2.89077e11i	−0.0149873	−	0.0259588i
$794$	−1.38740e12	+	2.40304e12i	−0.123882	+	0.214570i
$795$	−6.85159e12	+	1.18673e13i	−0.608331	+	1.05366i
$796$	1.53021e12	+	2.65041e12i	0.135096	+	0.233993i
$797$	−8.15126e12			−0.715587			−0.357794	−	0.933801i	$-0.616471\pi$
$797$	−8.15126e12			−0.715587			−0.357794	+	0.933801i	$0.616471\pi$
$798$	−2.22312e13	−	4.65118e12i	−1.94066	−	0.406023i
$799$	8.40853e12			0.729894
$800$	2.14911e12	+	3.72237e12i	0.185504	+	0.321303i
$801$	8.37291e11	−	1.45023e12i	0.0718671	−	0.124477i
$802$	−6.28203e12	+	1.08808e13i	−0.536186	+	0.928701i
$803$	−1.99254e11	−	3.45119e11i	−0.0169117	−	0.0292920i
$804$	3.48945e12			0.294513
$805$	7.77292e12	+	2.36650e13i	0.652383	+	1.98621i
$806$	−2.77000e11			−0.0231192
$807$	−5.81103e12	−	1.00650e13i	−0.482305	−	0.835377i
$808$	−5.51224e12	+	9.54749e12i	−0.454964	+	0.788021i
$809$	1.95100e12	−	3.37922e12i	0.160136	−	0.277363i	−0.774782	−	0.632229i	$-0.782140\pi$
$809$	1.95100e12	−	3.37922e12i	0.160136	−	0.277363i	0.934917	+	0.354866i	$0.115474\pi$
$810$	−1.16015e13	−	2.00944e13i	−0.946959	−	1.64018i
$811$	−1.54921e13			−1.25752			−0.628761	−	0.777598i	$-0.716438\pi$
$811$	−1.54921e13			−1.25752			−0.628761	+	0.777598i	$0.716438\pi$
$812$	−7.78037e11	−	2.36876e12i	−0.0628055	−	0.191214i
$813$	6.59687e12			0.529579
$814$	1.69110e12	+	2.92906e12i	0.135008	+	0.233840i
$815$	1.33414e13	−	2.31080e13i	1.05924	−	1.83465i
$816$	−7.19781e12	+	1.24670e13i	−0.568322	+	0.984363i
$817$	5.28742e12	+	9.15808e12i	0.415188	+	0.719126i
$818$	1.89659e13			1.48110
$819$	−1.37368e12	−	2.87398e11i	−0.106686	−	0.0223207i
$820$	−2.26554e12			−0.174988
$821$	3.37626e12	+	5.84785e12i	0.259353	+	0.449213i	0.966069	−	0.258285i	$-0.0831573\pi$
$821$	3.37626e12	+	5.84785e12i	0.259353	+	0.449213i	−0.706716	+	0.707498i	$0.749824\pi$
$822$	1.14922e13	−	1.99050e13i	0.877967	−	1.52068i
$823$	−9.11164e11	+	1.57818e12i	−0.0692305	+	0.119911i	−0.898563	−	0.438845i	$-0.855388\pi$
$823$	−9.11164e11	+	1.57818e12i	−0.0692305	+	0.119911i	0.829332	+	0.558756i	$0.188721\pi$
$824$	−2.62792e12	−	4.55169e12i	−0.198582	−	0.343954i
$825$	2.95611e12			0.222166
$826$	−2.43179e11	+	2.71820e11i	−0.0181767	+	0.0203175i
$827$	−2.37120e13			−1.76276			−0.881382	−	0.472404i	$-0.843386\pi$
$827$	−2.37120e13			−1.76276			−0.881382	+	0.472404i	$0.843386\pi$
$828$	−4.81854e11	−	8.34595e11i	−0.0356270	−	0.0617077i
$829$	9.38126e12	−	1.62488e13i	0.689868	−	1.19489i	−0.282013	−	0.959411i	$-0.591002\pi$
$829$	9.38126e12	−	1.62488e13i	0.689868	−	1.19489i	0.971880	−	0.235475i	$-0.0756646\pi$
$830$	6.99305e12	−	1.21123e13i	0.511464	−	0.885882i
$831$	1.29061e13	+	2.23540e13i	0.938838	+	1.62611i
$832$	−4.01412e12			−0.290426
$833$	−1.11603e13	−	4.88367e12i	−0.803110	−	0.351434i
$834$	5.99484e12			0.429072
$835$	6.24499e12	+	1.08166e13i	0.444573	+	0.770022i
$836$	3.40876e11	−	5.90415e11i	0.0241362	−	0.0418051i
$837$	3.27242e11	−	5.66800e11i	0.0230465	−	0.0399177i
$838$	−1.19098e13	−	2.06284e13i	−0.834272	−	1.44500i
$839$	−5.63044e12			−0.392296			−0.196148	−	0.980574i	$-0.562843\pi$
$839$	−5.63044e12			−0.392296			−0.196148	+	0.980574i	$0.562843\pi$
$840$	−1.42559e13	+	1.59349e13i	−0.987955	+	1.10431i
$841$	5.97112e12			0.411599
$842$	1.00880e13	+	1.74730e13i	0.691675	+	1.19802i
$843$	−1.11580e13	+	1.93263e13i	−0.760964	+	1.31803i
$844$	−4.68889e11	+	8.12139e11i	−0.0318074	+	0.0550921i
$845$	−9.25614e12	−	1.60321e13i	−0.624561	−	1.08177i
$846$	−3.91725e12			−0.262914
$847$	−1.42037e13	−	2.97168e12i	−0.948258	−	0.198393i
$848$	1.26685e13			0.841285
$849$	−1.41378e13	−	2.44873e13i	−0.933892	−	1.61755i
$850$	7.98094e12	−	1.38234e13i	0.524407	−	0.908300i
$851$	1.55746e13	−	2.69760e13i	1.01797	−	1.76317i
$852$	1.72955e12	+	2.99566e12i	0.112449	+	0.194767i
$853$	2.09580e13			1.35544			0.677719	−	0.735321i	$-0.262968\pi$
$853$	2.09580e13			1.35544			0.677719	+	0.735321i	$0.262968\pi$
$854$	4.21220e11	+	1.28242e12i	0.0270987	+	0.0825031i
$855$	1.06819e13			0.683595
$856$	−9.81957e9	−	1.70080e10i	−0.000625116	−	0.00108273i
$857$	−5.40299e12	+	9.35825e12i	−0.342153	+	0.592626i	−0.984832	−	0.173509i	$-0.944489\pi$
$857$	−5.40299e12	+	9.35825e12i	−0.342153	+	0.592626i	0.642679	+	0.766135i	$0.277823\pi$
$858$	6.43342e11	−	1.11430e12i	0.0405274	−	0.0701956i
$859$	4.86016e12	+	8.41804e12i	0.304566	+	0.527524i	0.977165	−	0.212484i	$-0.0681553\pi$
$859$	4.86016e12	+	8.41804e12i	0.304566	+	0.527524i	−0.672599	+	0.740007i	$0.734822\pi$
$860$	−2.03028e12			−0.126565
$861$	−4.07108e12	−	1.23946e13i	−0.252462	−	0.768629i
$862$	−1.08690e13			−0.670512
$863$	8.16020e12	+	1.41339e13i	0.500786	+	0.867387i	1.00000		0.000907842i	$0.000288975\pi$
$863$	8.16020e12	+	1.41339e13i	0.500786	+	0.867387i	−0.499214	+	0.866479i	$0.666378\pi$
$864$	−2.21019e12	+	3.82816e12i	−0.134933	+	0.233711i
$865$	−1.56949e13	+	2.71844e13i	−0.953206	+	1.65100i
$866$	−9.26246e12	−	1.60431e13i	−0.559623	−	0.969296i
$867$	−4.37809e12			−0.263147
$868$	1.58826e11	+	3.32292e10i	0.00949689	+	0.00198692i
$869$	9.49793e11			0.0564989
$870$	1.79078e13	+	3.10172e13i	1.05976	+	1.83555i
$871$	4.84875e12	−	8.39829e12i	0.285462	−	0.494435i
$872$	−5.53843e11	+	9.59284e11i	−0.0324386	+	0.0561853i
$873$	−2.90559e11	−	5.03262e11i	−0.0169305	−	0.0293245i
$874$	−4.33438e13			−2.51261
$875$	1.78467e12	−	1.99486e12i	0.102925	−	0.115047i
$876$	6.42513e11			0.0368649
$877$	1.01234e13	+	1.75342e13i	0.577867	+	1.00089i	0.995724	+	0.0923817i	$0.0294480\pi$
$877$	1.01234e13	+	1.75342e13i	0.577867	+	1.00089i	−0.417857	+	0.908513i	$0.637219\pi$
$878$	−1.23555e12	+	2.14004e12i	−0.0701674	+	0.121534i
$879$	1.32129e13	−	2.28854e13i	0.746531	−	1.29303i
$880$	−2.60153e12	−	4.50599e12i	−0.146237	−	0.253290i
$881$	−1.15345e13			−0.645072			−0.322536	−	0.946557i	$-0.604535\pi$
$881$	−1.15345e13			−0.645072			−0.322536	+	0.946557i	$0.604535\pi$
$882$	5.19922e12	+	2.27513e12i	0.289288	+	0.126590i
$883$	1.65115e13			0.914035			0.457017	−	0.889458i	$-0.348918\pi$
$883$	1.65115e13			0.914035			0.457017	+	0.889458i	$0.348918\pi$
$884$	−5.03215e11	−	8.71593e11i	−0.0277152	−	0.0480041i
$885$	3.79476e11	−	6.57271e11i	0.0207941	−	0.0360164i
$886$	−8.89201e12	+	1.54014e13i	−0.484784	+	0.839670i
$887$	9.41136e12	+	1.63010e13i	0.510500	+	0.884213i	0.999926	+	0.0121677i	$0.00387319\pi$
$887$	9.41136e12	+	1.63010e13i	0.510500	+	0.884213i	−0.489425	+	0.872045i	$0.662793\pi$
$888$	2.67377e13			1.44300
$889$	−6.39888e12	+	7.15252e12i	−0.343595	+	0.384062i
$890$	1.44601e13			0.772530
$891$	2.00531e12	+	3.47329e12i	0.106594	+	0.184626i
$892$	−1.39571e12	+	2.41745e12i	−0.0738167	+	0.127854i
$893$	−1.27609e13	+	2.21025e13i	−0.671506	+	1.16308i
$894$	1.19421e12	+	2.06844e12i	0.0625264	+	0.108299i
$895$	8.06729e12			0.420266
$896$	2.22209e13	+	4.64902e12i	1.15180	+	0.240977i
$897$	−1.18501e13			−0.611160
$898$	2.26840e12	+	3.92899e12i	0.116406	+	0.201622i
$899$	−6.66373e11	+	1.15419e12i	−0.0340251	+	0.0589331i
$900$	−5.38596e11	+	9.32875e11i	−0.0273635	+	0.0473950i
$901$	−6.39472e12	−	1.10760e13i	−0.323266	−	0.559913i
$902$	2.70328e12			0.135976
$903$	−3.64832e12	−	1.11075e13i	−0.182599	−	0.555930i
$904$	2.50558e13			1.24782
$905$	−2.72753e13	−	4.72422e13i	−1.35161	−	2.34105i
$906$	−2.05730e12	+	3.56334e12i	−0.101442	+	0.175704i
$907$	1.05352e13	−	1.82476e13i	0.516906	−	0.895308i	−0.482901	−	0.875675i	$-0.660417\pi$
$907$	1.05352e13	−	1.82476e13i	0.516906	−	0.895308i	0.999807	−	0.0196327i	$-0.00624968\pi$
$908$	3.90630e11	+	6.76590e11i	0.0190712	+	0.0330323i
$909$	−6.08925e12			−0.295819
$910$	−3.78166e12	−	1.15134e13i	−0.182809	−	0.556568i
$911$	−1.97328e13			−0.949198			−0.474599	−	0.880202i	$-0.657407\pi$
$911$	−1.97328e13			−0.949198			−0.474599	+	0.880202i	$0.657407\pi$
$912$	−2.18470e13	−	3.78401e13i	−1.04572	−	1.81124i
$913$	−1.20874e12	+	2.09360e12i	−0.0575725	+	0.0997186i
$914$	1.09906e13	−	1.90363e13i	0.520912	−	0.902246i
$915$	−1.40443e12	−	2.43254e12i	−0.0662377	−	0.114727i
$916$	4.02281e12			0.188799
$917$	−1.27686e12	−	2.67143e11i	−0.0596323	−	0.0124762i
$918$	1.64155e13			0.762891
$919$	−1.24173e13	−	2.15074e13i	−0.574259	−	0.994645i	−0.996122	−	0.0879858i	$-0.971957\pi$
$919$	−1.24173e13	−	2.15074e13i	−0.574259	−	0.994645i	0.421863	−	0.906660i	$-0.361376\pi$
$920$	−2.04014e13	+	3.53363e13i	−0.938891	+	1.62621i
$921$	−1.69695e13	+	2.93921e13i	−0.777145	+	1.34605i
$922$	8.03703e12	+	1.39205e13i	0.366274	+	0.634406i
$923$	9.61314e12			0.435971
$924$	−5.02550e11	+	5.61739e11i	−0.0226807	+	0.0253519i
$925$	−3.48172e13			−1.56371
$926$	−9.01512e12	−	1.56146e13i	−0.402923	−	0.697883i
$927$	1.45150e12	−	2.51407e12i	0.0645593	−	0.111820i
$928$	4.50067e12	−	7.79540e12i	0.199210	−	0.345042i
$929$	1.81790e13	+	3.14869e13i	0.800754	+	1.38695i	0.919121	+	0.393976i	$0.128901\pi$
$929$	1.81790e13	+	3.14869e13i	0.800754	+	1.38695i	−0.118367	+	0.992970i	$0.537766\pi$
$930$	−2.33092e12			−0.102177
$931$	2.97742e13	−	2.19244e13i	1.29887	−	0.956431i
$932$	−3.77583e12			−0.163923
$933$	1.26673e13	+	2.19404e13i	0.547288	+	0.947931i
$934$	9.72105e12	−	1.68373e13i	0.417977	−	0.723957i
$935$	−2.62637e12	+	4.54901e12i	−0.112384	+	0.194655i
$936$	−1.14946e12	−	1.99093e12i	−0.0489501	−	0.0847841i
$937$	9.42112e12			0.399277			0.199639	−	0.979870i	$-0.436023\pi$
$937$	9.42112e12			0.399277			0.199639	+	0.979870i	$0.436023\pi$
$938$	−2.61469e13	+	2.92263e13i	−1.10283	+	1.23271i
$939$	−4.74130e13			−1.99023
$940$	−2.44998e12	−	4.24350e12i	−0.102350	−	0.177275i
$941$	1.16425e13	−	2.01654e13i	0.484054	−	0.838406i	−0.515778	−	0.856722i	$-0.672497\pi$
$941$	1.16425e13	−	2.01654e13i	0.484054	−	0.838406i	0.999832	+	0.0183158i	$0.00583043\pi$
$942$	7.21151e12	−	1.24907e13i	0.298399	−	0.516842i
$943$	−1.24483e13	−	2.15610e13i	−0.512633	−	0.887906i
$944$	−7.01644e11			−0.0287570
$945$	2.80265e13	+	5.86365e12i	1.14321	+	0.239180i
$946$	2.42256e12			0.0983477
$947$	1.01843e13	+	1.76397e13i	0.411488	+	0.712717i	0.995053	−	0.0993491i	$-0.0316760\pi$
$947$	1.01843e13	+	1.76397e13i	0.411488	+	0.712717i	−0.583565	+	0.812066i	$0.698343\pi$
$948$	−7.65672e11	+	1.32618e12i	−0.0307897	+	0.0533293i
$949$	8.92802e11	−	1.54638e12i	0.0357320	−	0.0618896i
$950$	2.42239e13	+	4.19571e13i	0.964914	+	1.67128i
$951$	2.44493e13			0.969289
$952$	−6.22717e12	−	1.89589e13i	−0.245711	−	0.748077i
$953$	2.26713e13			0.890344			0.445172	−	0.895445i	$-0.353143\pi$
$953$	2.26713e13			0.890344			0.445172	+	0.895445i	$0.353143\pi$
$954$	2.97908e12	+	5.15992e12i	0.116443	+	0.201686i
$955$	1.76092e12	−	3.05001e12i	0.0685054	−	0.118655i
$956$	1.18949e12	−	2.06025e12i	0.0460573	−	0.0797736i
$957$	−3.09535e12	−	5.36130e12i	−0.119291	−	0.206617i
$958$	2.82210e13			1.08250
$959$	1.16764e13	+	3.55493e13i	0.445785	+	1.35721i
$960$	−3.37783e13			−1.28356
$961$	1.31764e13	+	2.28223e13i	0.498360	+	0.863184i
$962$	−7.57732e12	+	1.31243e13i	−0.285251	+	0.494070i
$963$	5.42373e9	−	9.39417e9i	0.000203226	−	0.000351998i
$964$	4.99066e11	+	8.64408e11i	0.0186128	+	0.0322383i
$965$	−2.96495e13			−1.10064
$966$	4.69043e13	+	9.81324e12i	1.73307	+	0.362590i
$967$	4.32858e12			0.159194			0.0795969	−	0.996827i	$-0.474637\pi$
$967$	4.32858e12			0.159194			0.0795969	+	0.996827i	$0.474637\pi$
$968$	−1.18854e13	−	2.05861e13i	−0.435084	−	0.753588i
$969$	−2.20556e13	+	3.82014e13i	−0.803640	+	1.39195i
$970$	2.50898e12	−	4.34568e12i	0.0909965	−	0.157611i
$971$	−1.63561e13	−	2.83297e13i	−0.590465	−	1.02272i	−0.994170	−	0.107826i	$-0.965611\pi$
$971$	−1.63561e13	−	2.83297e13i	−0.590465	−	1.02272i	0.403705	−	0.914889i	$-0.367722\pi$
$972$	−2.67252e12			−0.0960334
$973$	−6.50712e12	+	7.27350e12i	−0.232745	+	0.260157i
$974$	−4.75724e13			−1.69371
$975$	6.62275e12	+	1.14709e13i	0.234702	+	0.406516i
$976$	−1.29838e12	+	2.24887e12i	−0.0458014	+	0.0793304i
$977$	3.14481e12	−	5.44698e12i	0.110426	−	0.191263i	−0.805516	−	0.592573i	$-0.798112\pi$
$977$	3.14481e12	−	5.44698e12i	0.110426	−	0.191263i	0.915942	+	0.401311i	$0.131445\pi$
$978$	−2.56664e13	−	4.44555e13i	−0.897098	−	1.55382i
$979$	−2.49941e12			−0.0869591
$980$	7.87158e11	+	7.05519e12i	0.0272612	+	0.244338i
$981$	−6.11817e11			−0.0210917
$982$	8.61836e10	+	1.49274e11i	0.00295749	+	0.00512252i
$983$	−5.33975e12	+	9.24871e12i	−0.182402	+	0.315930i	−0.942698	−	0.333647i	$-0.891721\pi$
$983$	−5.33975e12	+	9.24871e12i	−0.182402	+	0.315930i	0.760296	+	0.649577i	$0.225054\pi$
$984$	1.06853e13	−	1.85074e13i	0.363336	−	0.629316i
$985$	−4.46388e12	−	7.73166e12i	−0.151095	−	0.261704i
$986$	−3.34274e13			−1.12631
$987$	1.88133e13	−	2.10290e13i	0.631011	−	0.705329i
$988$	3.05474e12			0.101992
$989$	−1.11556e13	−	1.93221e13i	−0.370774	−	0.642200i
$990$	1.22354e12	−	2.11923e12i	0.0404817	−	0.0701164i
$991$	−2.84247e13	+	4.92330e13i	−0.936191	+	1.62153i	−0.163695	+	0.986511i	$0.552341\pi$
$991$	−2.84247e13	+	4.92330e13i	−0.936191	+	1.62153i	−0.772496	+	0.635019i	$0.780992\pi$
$992$	2.92908e11	+	5.07332e11i	0.00960350	+	0.0166337i
$993$	3.90504e13			1.27454
$994$	−3.80502e13	−	7.96081e12i	−1.23629	−	0.258653i
$995$	7.15702e13			2.31488
$996$	−1.94885e12	−	3.37550e12i	−0.0627496	−	0.108685i
$997$	8.88145e12	−	1.53831e13i	0.284679	−	0.493079i	−0.687852	−	0.725851i	$-0.741446\pi$
$997$	8.88145e12	−	1.53831e13i	0.284679	−	0.493079i	0.972531	+	0.232772i	$0.0747796\pi$
$998$	−8.56351e11	+	1.48324e12i	−0.0273253	+	0.0473288i
$999$	−1.79034e13	−	3.10096e13i	−0.568709	−	0.985034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.10.c.a.4.2	yes	10
3.2	odd	2		63.10.e.b.46.4		10
4.3	odd	2		112.10.i.c.81.5		10
7.2	even	3	inner	7.10.c.a.2.2	✓	10
7.3	odd	6		49.10.a.f.1.4		5
7.4	even	3		49.10.a.e.1.4		5
7.5	odd	6		49.10.c.g.30.2		10
7.6	odd	2		49.10.c.g.18.2		10
21.2	odd	6		63.10.e.b.37.4		10
28.23	odd	6		112.10.i.c.65.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.c.a.2.2	✓	10	7.2	even	3	inner
7.10.c.a.4.2	yes	10	1.1	even	1	trivial
49.10.a.e.1.4		5	7.4	even	3
49.10.a.f.1.4		5	7.3	odd	6
49.10.c.g.18.2		10	7.6	odd	2
49.10.c.g.30.2		10	7.5	odd	6
63.10.e.b.37.4		10	21.2	odd	6
63.10.e.b.46.4		10	3.2	odd	2
112.10.i.c.65.5		10	28.23	odd	6
112.10.i.c.81.5		10	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.2345 - 21.1908i) q^{2} +(-79.7348 + 138.105i) q^{3} +(-43.3662 + 75.1124i) q^{4} +(1014.15 + 1756.56i) q^{5} +3902.06 q^{6} +(-4235.51 + 4734.35i) q^{7} -10405.9 q^{8} +(-2873.78 - 4977.54i) q^{9} +(24815.2 - 42981.2i) q^{10} +(-4289.29 + 7429.26i) q^{11} +(-6915.59 - 11978.1i) q^{12} -38438.1 q^{13} +(152144. + 31831.3i) q^{14} -323452. q^{15} +(149514. + 258966. i) q^{16} +(150942. - 261439. i) q^{17} +(-70318.7 + 121795. i) q^{18} +(458143. + 793527. i) q^{19} -175919. q^{20} +(-316119. - 962436. i) q^{21} +209909. q^{22} +(-966607. - 1.67421e6i) q^{23} +(829711. - 1.43710e6i) q^{24} +(-1.08043e6 + 1.87136e6i) q^{25} +(470272. + 814534. i) q^{26} -2.22228e6 q^{27} +(-171931. - 523450. i) q^{28} +4.52529e6 q^{29} +(3.95727e6 + 6.85420e6i) q^{30} +(-147255. + 255054. i) q^{31} +(994560. - 1.72263e6i) q^{32} +(-684011. - 1.18474e6i) q^{33} -7.38680e6 q^{34} +(-1.26116e7 - 2.63858e6i) q^{35} +498500. q^{36} +(8.05632e6 + 1.39540e7i) q^{37} +(1.12103e7 - 1.94168e7i) q^{38} +(3.06486e6 - 5.30849e6i) q^{39} +(-1.05531e7 - 1.82785e7i) q^{40} +1.28783e7 q^{41} +(-1.65272e7 + 1.84737e7i) q^{42} +1.15410e7 q^{43} +(-372020. - 644357. i) q^{44} +(5.82889e6 - 1.00959e7i) q^{45} +(-2.36519e7 + 4.09663e7i) q^{46} +(1.39268e7 + 2.41219e7i) q^{47} -4.76860e7 q^{48} +(-4.47455e6 - 4.01048e7i) q^{49} +5.28742e7 q^{50} +(2.40707e7 + 4.16916e7i) q^{51} +(1.66692e6 - 2.88718e6i) q^{52} +(2.11827e7 - 3.66896e7i) q^{53} +(2.71885e7 + 4.70918e7i) q^{54} -1.73999e7 q^{55} +(4.40742e7 - 4.92651e7i) q^{56} -1.46120e8 q^{57} +(-5.53647e7 - 9.58945e7i) q^{58} +(-1.17321e6 + 2.03205e6i) q^{59} +(1.40269e7 - 2.42952e7i) q^{60} +(4.34201e6 + 7.52057e6i) q^{61} +7.20638e6 q^{62} +(3.57374e7 + 7.47691e6i) q^{63} +1.04431e8 q^{64} +(-3.89820e7 - 6.75188e7i) q^{65} +(-1.67371e7 + 2.89895e7i) q^{66} +(-1.26144e8 + 2.18488e8i) q^{67} +(1.30915e7 + 2.26752e7i) q^{68} +3.08289e8 q^{69} +(9.83831e7 + 2.99531e8i) q^{70} -2.50094e8 q^{71} +(2.99042e7 + 5.17957e7i) q^{72} +(-2.32270e7 + 4.02303e7i) q^{73} +(1.97130e8 - 3.41439e8i) q^{74} +(-1.72296e8 - 2.98426e8i) q^{75} -7.94716e7 q^{76} +(-1.70054e7 - 5.17737e7i) q^{77} -1.49988e8 q^{78} +(-5.53584e7 - 9.58836e7i) q^{79} +(-3.03259e8 + 5.25261e8i) q^{80} +(2.33758e8 - 4.04880e8i) q^{81} +(-1.57560e8 - 2.72902e8i) q^{82} +2.81805e8 q^{83} +(8.59998e7 + 1.79927e7i) q^{84} +6.12310e8 q^{85} +(-1.41198e8 - 2.44562e8i) q^{86} +(-3.60823e8 + 6.24964e8i) q^{87} +(4.46338e7 - 7.73080e7i) q^{88} +(1.45677e8 + 2.52321e8i) q^{89} -2.85254e8 q^{90} +(1.62805e8 - 1.81980e8i) q^{91} +1.67672e8 q^{92} +(-2.34827e7 - 4.06733e7i) q^{93} +(3.40774e8 - 5.90238e8i) q^{94} +(-9.29250e8 + 1.60951e9i) q^{95} +(1.58602e8 + 2.74707e8i) q^{96} +1.01107e8 q^{97} +(-7.95107e8 + 5.85481e8i) q^{98} +4.93059e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + 4298 q^{10} + 42213 q^{11} + 135604 q^{12} - 319676 q^{13} - 39522 q^{14} + 151394 q^{15} + 322064 q^{16}+ \cdots - 1900777180 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 + 161 * q^3 - 940 * q^4 + 1533 * q^5 - 8708 * q^6 - 1036 * q^7 + 34272 * q^8 - 35734 * q^9 + 4298 * q^10 + 42213 * q^11 + 135604 * q^12 - 319676 * q^13 - 39522 * q^14 + 151394 * q^15 + 322064 * q^16 + 324681 * q^17 - 1012868 * q^18 - 16121 * q^19 - 350616 * q^20 - 1557857 * q^21 - 62692 * q^22 + 2638863 * q^23 + 8449728 * q^24 - 1304092 * q^25 + 4179252 * q^26 - 18331558 * q^27 - 22156316 * q^28 + 15292500 * q^29 + 20557942 * q^30 + 19179237 * q^31 - 6263520 * q^32 + 1689359 * q^33 - 62909700 * q^34 - 43746759 * q^35 + 71476528 * q^36 + 39566985 * q^37 + 67365270 * q^38 - 44299486 * q^39 + 5721744 * q^40 - 53436852 * q^41 - 183129856 * q^42 + 101835992 * q^43 + 99704916 * q^44 + 85098230 * q^45 - 14489202 * q^46 + 32509659 * q^47 - 185141600 * q^48 - 49024598 * q^49 + 3328464 * q^50 + 44168403 * q^51 + 103893272 * q^52 - 25714707 * q^53 + 51200926 * q^54 - 144695222 * q^55 + 115352832 * q^56 - 121710346 * q^57 - 46645516 * q^58 + 46776513 * q^59 + 132391756 * q^60 - 113075039 * q^61 + 467465628 * q^62 + 318071530 * q^63 - 192008960 * q^64 - 338113566 * q^65 - 836682602 * q^66 - 126707879 * q^67 + 32262636 * q^68 + 1323616182 * q^69 + 697712470 * q^70 - 1188736032 * q^71 - 950557728 * q^72 - 859257651 * q^73 + 591757530 * q^74 - 169061732 * q^75 + 1101475592 * q^76 + 1911891891 * q^77 + 519432424 * q^78 - 527065417 * q^79 - 1257352656 * q^80 + 551662715 * q^81 - 1341703076 * q^82 - 144863208 * q^83 + 486452204 * q^84 - 1197360222 * q^85 - 678648216 * q^86 - 340781350 * q^87 + 903700608 * q^88 + 1661554797 * q^89 + 1967758744 * q^90 + 726641384 * q^91 - 1301840952 * q^92 - 423057489 * q^93 - 272580882 * q^94 - 1197123495 * q^95 - 1441922272 * q^96 + 869770188 * q^97 - 2404833858 * q^98 - 1900777180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more