LMFDB - Embedded newform 18.8.c.b.13.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [18,8,Mod(7,18)] 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("18.7"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.62293045871$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1336x^{6} + 633664x^{4} + 125389995x^{2} + 8783438400 $ x^8 + 1336x^6 + 633664x^4 + 125389995*x^2 + 8783438400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.2
Root			$15.0676i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.8.c.b.7.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 + 6.92820i) q^{2} +(-11.3727 - 45.3615i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-247.107 + 428.002i) q^{5} +(268.783 - 260.238i) q^{6} +(648.241 + 1122.79i) q^{7} -512.000 q^{8} +(-1928.33 + 1031.76i) q^{9} -3953.72 q^{10} +(-1689.64 - 2926.54i) q^{11} +(2878.11 + 821.230i) q^{12} +(38.2139 - 66.1885i) q^{13} +(-5185.93 + 8982.29i) q^{14} +(22225.1 + 6341.62i) q^{15} +(-2048.00 - 3547.24i) q^{16} -9573.21 q^{17} +(-14861.6 - 9232.78i) q^{18} +37865.7 q^{19} +(-15814.9 - 27392.1i) q^{20} +(43559.0 - 42174.2i) q^{21} +(13517.1 - 23412.4i) q^{22} +(-28457.3 + 49289.6i) q^{23} +(5822.80 + 23225.1i) q^{24} +(-83061.4 - 143867. i) q^{25} +611.423 q^{26} +(68732.4 + 75737.8i) q^{27} -82974.9 q^{28} +(97744.5 + 169298. i) q^{29} +(44964.3 + 179346. i) q^{30} +(28786.4 - 49859.4i) q^{31} +(16384.0 - 28377.9i) q^{32} +(-113537. + 109927. i) q^{33} +(-38292.8 - 66325.1i) q^{34} -640740. q^{35} +(4520.39 - 139895. i) q^{36} +213026. q^{37} +(151463. + 262342. i) q^{38} +(-3437.00 - 980.701i) q^{39} +(126519. - 219137. i) q^{40} +(50636.7 - 87705.3i) q^{41} +(466428. + 133089. i) q^{42} +(66588.1 + 115334. i) q^{43} +216274. q^{44} +(34906.9 - 1.08028e6i) q^{45} -455317. q^{46} +(-148716. - 257584. i) q^{47} +(-137617. + 133242. i) q^{48} +(-428661. + 742463. i) q^{49} +(664491. - 1.15093e6i) q^{50} +(108873. + 434255. i) q^{51} +(2445.69 + 4236.06i) q^{52} +765684. q^{53} +(-249797. + 779143. i) q^{54} +1.67009e6 q^{55} +(-331899. - 574867. i) q^{56} +(-430634. - 1.71765e6i) q^{57} +(-781956. + 1.35439e6i) q^{58} +(-794098. + 1.37542e6i) q^{59} +(-1.06269e6 + 1.02891e6i) q^{60} +(739606. + 1.28103e6i) q^{61} +460582. q^{62} +(-2.40847e6 - 1.49627e6i) q^{63} +262144. q^{64} +(18885.9 + 32711.3i) q^{65} +(-1.21574e6 - 346896. i) q^{66} +(-1.33764e6 + 2.31686e6i) q^{67} +(306343. - 530601. i) q^{68} +(2.55948e6 + 730313. i) q^{69} +(-2.56296e6 - 4.43918e6i) q^{70} +2.09279e6 q^{71} +(987302. - 528262. i) q^{72} +3.26596e6 q^{73} +(852103. + 1.47589e6i) q^{74} +(-5.58137e6 + 5.40393e6i) q^{75} +(-1.21170e6 + 2.09873e6i) q^{76} +(2.19059e6 - 3.79421e6i) q^{77} +(-6953.51 - 27735.0i) q^{78} +(-1.14308e6 - 1.97987e6i) q^{79} +2.02430e6 q^{80} +(2.65391e6 - 3.97914e6i) q^{81} +810187. q^{82} +(247921. + 429412. i) q^{83} +(943645. + 3.76386e6i) q^{84} +(2.36561e6 - 4.09735e6i) q^{85} +(-532705. + 922672. i) q^{86} +(6.56801e6 - 6.35920e6i) q^{87} +(865096. + 1.49839e6i) q^{88} -1.01396e7 q^{89} +(7.62405e6 - 4.07929e6i) q^{90} +99087.4 q^{91} +(-1.82127e6 - 3.15453e6i) q^{92} +(-2.58907e6 - 738757. i) q^{93} +(1.18973e6 - 2.06067e6i) q^{94} +(-9.35690e6 + 1.62066e7i) q^{95} +(-1.47359e6 - 420470. i) q^{96} +(-7.16868e6 - 1.24165e7i) q^{97} -6.85858e6 q^{98} +(6.27767e6 + 3.90002e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{2} - 12 q^{3} - 256 q^{4} + 54 q^{5} + 480 q^{6} - 44 q^{7} - 4096 q^{8} - 2238 q^{9} + 864 q^{10} + 2172 q^{11} + 4608 q^{12} - 6398 q^{13} + 352 q^{14} + 17604 q^{15} - 16384 q^{16} - 51972 q^{17}+ \cdots + 26558784 q^{99}+O(q^{100}) $ 8 * q + 32 * q^2 - 12 * q^3 - 256 * q^4 + 54 * q^5 + 480 * q^6 - 44 * q^7 - 4096 * q^8 - 2238 * q^9 + 864 * q^10 + 2172 * q^11 + 4608 * q^12 - 6398 * q^13 + 352 * q^14 + 17604 * q^15 - 16384 * q^16 - 51972 * q^17 - 22416 * q^18 + 90712 * q^19 + 3456 * q^20 + 192390 * q^21 - 17376 * q^22 - 2028 * q^23 + 6144 * q^24 - 173446 * q^25 - 102368 * q^26 - 288360 * q^27 + 5632 * q^28 + 283098 * q^29 + 172800 * q^30 - 812 * q^31 + 131072 * q^32 + 342108 * q^33 - 207888 * q^34 - 1492992 * q^35 - 36096 * q^36 + 441688 * q^37 + 362848 * q^38 + 67428 * q^39 - 27648 * q^40 + 610704 * q^41 + 349200 * q^42 - 84380 * q^43 - 278016 * q^44 - 652698 * q^45 - 32448 * q^46 + 855708 * q^47 - 245760 * q^48 - 1273038 * q^49 + 1387568 * q^50 + 1748556 * q^51 - 409472 * q^52 - 1842600 * q^53 + 640800 * q^54 + 7016760 * q^55 + 22528 * q^56 - 4893306 * q^57 - 2264784 * q^58 + 380796 * q^59 + 255744 * q^60 - 3151130 * q^61 - 12992 * q^62 - 3149076 * q^63 + 2097152 * q^64 - 326538 * q^65 - 6234192 * q^66 - 9961580 * q^67 + 1663104 * q^68 + 15322554 * q^69 - 5971968 * q^70 + 8970384 * q^71 + 1145856 * q^72 + 29234932 * q^73 + 1766752 * q^74 - 26321244 * q^75 - 2902784 * q^76 - 5954826 * q^77 + 6127680 * q^78 - 17309396 * q^79 - 442368 * q^80 + 6907266 * q^81 + 9771264 * q^82 - 11520192 * q^83 - 9519360 * q^84 - 14675148 * q^85 + 675040 * q^86 + 37274652 * q^87 - 1112064 * q^88 + 26066064 * q^89 + 28333152 * q^90 + 26231936 * q^91 - 129792 * q^92 - 48684366 * q^93 - 6845664 * q^94 - 31016952 * q^95 - 2359296 * q^96 - 22003112 * q^97 - 20368608 * q^98 + 26558784 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	−11.3727	−	45.3615i	−0.243186	−	0.969980i
$3$	−11.3727	−	45.3615i	−0.243186	−	0.969980i
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−247.107	+	428.002i	−0.884078	+	1.53127i	−0.0373103	+	0.999304i	$0.511879\pi$
$5$	−247.107	+	428.002i	−0.884078	+	1.53127i	−0.846767	+	0.531964i	$0.821454\pi$
$6$	268.783	−	260.238i	0.508010	−	0.491860i
$7$	648.241	+	1122.79i	0.714321	+	1.23724i	0.963221	+	0.268711i	$0.0865977\pi$
$7$	648.241	+	1122.79i	0.714321	+	1.23724i	−0.248900	+	0.968529i	$0.580069\pi$
$8$	−512.000			−0.353553
$9$	−1928.33	+	1031.76i	−0.881722	+	0.471770i
$10$	−3953.72			−1.25027
$11$	−1689.64	−	2926.54i	−0.382754	−	0.662950i	0.608701	−	0.793400i	$-0.291691\pi$
$11$	−1689.64	−	2926.54i	−0.382754	−	0.662950i	−0.991455	+	0.130450i	$0.958358\pi$
$12$	2878.11	+	821.230i	0.480810	+	0.137193i
$13$	38.2139	−	66.1885i	0.00482414	−	0.00835566i	−0.863603	−	0.504172i	$-0.831798\pi$
$13$	38.2139	−	66.1885i	0.00482414	−	0.00835566i	0.868427	+	0.495816i	$0.165131\pi$
$14$	−5185.93	+	8982.29i	−0.505101	+	0.874861i
$15$	22225.1	+	6341.62i	1.70029	+	0.485155i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−9573.21			−0.472592			−0.236296	−	0.971681i	$-0.575933\pi$
$17$	−9573.21			−0.472592			−0.236296	+	0.971681i	$0.575933\pi$
$18$	−14861.6	−	9232.78i	−0.600635	−	0.373146i
$19$	37865.7			1.26651			0.633255	−	0.773943i	$-0.281718\pi$
$19$	37865.7			1.26651			0.633255	+	0.773943i	$0.281718\pi$
$20$	−15814.9	−	27392.1i	−0.442039	−	0.765634i
$21$	43559.0	−	42174.2i	1.02639	−	0.993756i
$22$	13517.1	−	23412.4i	0.270648	−	0.468776i
$23$	−28457.3	+	49289.6i	−0.487693	+	0.844710i	−0.999900	−	0.0141527i	$-0.995495\pi$
$23$	−28457.3	+	49289.6i	−0.487693	+	0.844710i	0.512207	+	0.858862i	$0.328828\pi$
$24$	5822.80	+	23225.1i	0.0859791	+	0.342940i
$25$	−83061.4	−	143867.i	−1.06319	−	1.84149i
$26$	611.423			0.00682237
$27$	68732.4	+	75737.8i	0.672029	+	0.740524i
$28$	−82974.9			−0.714321
$29$	97744.5	+	169298.i	0.744216	+	1.28902i	0.950560	+	0.310541i	$0.100510\pi$
$29$	97744.5	+	169298.i	0.744216	+	1.28902i	−0.206344	+	0.978480i	$0.566157\pi$
$30$	44964.3	+	179346.i	0.304049	+	1.21274i
$31$	28786.4	−	49859.4i	0.173548	−	0.300595i	−0.766110	−	0.642710i	$-0.777810\pi$
$31$	28786.4	−	49859.4i	0.173548	−	0.300595i	0.939658	+	0.342115i	$0.111143\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	−113537.	+	109927.i	−0.549968	+	0.532484i
$34$	−38292.8	−	66325.1i	−0.167086	−	0.289402i
$35$	−640740.			−2.52606
$36$	4520.39	−	139895.i	0.0161479	−	0.499739i
$37$	213026.			0.691395			0.345697	−	0.938346i	$-0.387642\pi$
$37$	213026.			0.691395			0.345697	+	0.938346i	$0.387642\pi$
$38$	151463.	+	262342.i	0.447779	+	0.775576i
$39$	−3437.00	−	980.701i	−0.00927798	−	0.00264734i
$40$	126519.	−	219137.i	0.312569	−	0.541385i
$41$	50636.7	−	87705.3i	0.114742	−	0.198739i	−0.802935	−	0.596067i	$-0.796729\pi$
$41$	50636.7	−	87705.3i	0.114742	−	0.198739i	0.917676	+	0.397328i	$0.130063\pi$
$42$	466428.	+	133089.i	0.971431	+	0.277184i
$43$	66588.1	+	115334.i	0.127719	+	0.221217i	0.922793	−	0.385297i	$-0.125901\pi$
$43$	66588.1	+	115334.i	0.127719	+	0.221217i	−0.795073	+	0.606513i	$0.792568\pi$
$44$	216274.			0.382754
$45$	34906.9	−	1.08028e6i	0.0571041	−	1.76723i
$46$	−455317.			−0.689703
$47$	−148716.	−	257584.i	−0.208937	−	0.361890i	0.742443	−	0.669910i	$-0.233667\pi$
$47$	−148716.	−	257584.i	−0.208937	−	0.361890i	−0.951380	+	0.308019i	$0.900334\pi$
$48$	−137617.	+	133242.i	−0.179609	+	0.173899i
$49$	−428661.	+	742463.i	−0.520509	+	0.901548i
$50$	664491.	−	1.15093e6i	0.751786	−	1.30213i
$51$	108873.	+	434255.i	0.114928	+	0.458405i
$52$	2445.69	+	4236.06i	0.00241207	+	0.00417783i
$53$	765684.			0.706454			0.353227	−	0.935538i	$-0.385084\pi$
$53$	765684.			0.706454			0.353227	+	0.935538i	$0.385084\pi$
$54$	−249797.	+	779143.i	−0.215878	+	0.673347i
$55$	1.67009e6			1.35354
$56$	−331899.	−	574867.i	−0.252551	−	0.437430i
$57$	−430634.	−	1.71765e6i	−0.307997	−	1.22849i
$58$	−781956.	+	1.35439e6i	−0.526240	+	0.911475i
$59$	−794098.	+	1.37542e6i	−0.503376	+	0.871872i	0.496617	+	0.867970i	$0.334575\pi$
$59$	−794098.	+	1.37542e6i	−0.503376	+	0.871872i	−0.999992	+	0.00390212i	$0.998758\pi$
$60$	−1.06269e6	+	1.02891e6i	−0.635152	+	0.614960i
$61$	739606.	+	1.28103e6i	0.417201	+	0.722614i	0.995657	−	0.0931000i	$-0.0296776\pi$
$61$	739606.	+	1.28103e6i	0.417201	+	0.722614i	−0.578455	+	0.815714i	$0.696344\pi$
$62$	460582.			0.245435
$63$	−2.40847e6	−	1.49627e6i	−1.21353	−	0.753906i
$64$	262144.			0.125000
$65$	18885.9	+	32711.3i	0.00852983	+	0.0147741i
$66$	−1.21574e6	−	346896.i	−0.520521	−	0.148524i
$67$	−1.33764e6	+	2.31686e6i	−0.543346	+	0.941104i	0.455362	+	0.890306i	$0.349510\pi$
$67$	−1.33764e6	+	2.31686e6i	−0.543346	+	0.941104i	−0.998709	+	0.0507976i	$0.983824\pi$
$68$	306343.	−	530601.i	0.118148	−	0.204638i
$69$	2.55948e6	+	730313.i	0.937951	+	0.267632i
$70$	−2.56296e6	−	4.43918e6i	−0.893097	−	1.54689i
$71$	2.09279e6			0.693940			0.346970	−	0.937876i	$-0.387211\pi$
$71$	2.09279e6			0.693940			0.346970	+	0.937876i	$0.387211\pi$
$72$	987302.	−	528262.i	0.311736	−	0.166796i
$73$	3.26596e6			0.982608			0.491304	−	0.870988i	$-0.336520\pi$
$73$	3.26596e6			0.982608			0.491304	+	0.870988i	$0.336520\pi$
$74$	852103.	+	1.47589e6i	0.244445	+	0.423391i
$75$	−5.58137e6	+	5.40393e6i	−1.52766	+	1.47909i
$76$	−1.21170e6	+	2.09873e6i	−0.316628	+	0.548415i
$77$	2.19059e6	−	3.79421e6i	0.546819	−	0.947118i
$78$	−6953.51	−	27735.0i	−0.00165910	−	0.00661756i
$79$	−1.14308e6	−	1.97987e6i	−0.260845	−	0.451796i	0.705622	−	0.708589i	$-0.250668\pi$
$79$	−1.14308e6	−	1.97987e6i	−0.260845	−	0.451796i	−0.966467	+	0.256792i	$0.917334\pi$
$80$	2.02430e6			0.442039
$81$	2.65391e6	−	3.97914e6i	0.554866	−	0.831940i
$82$	810187.			0.162269
$83$	247921.	+	429412.i	0.0475927	+	0.0824330i	0.888840	−	0.458217i	$-0.151512\pi$
$83$	247921.	+	429412.i	0.0475927	+	0.0824330i	−0.841248	+	0.540650i	$0.818178\pi$
$84$	943645.	+	3.76386e6i	0.173713	+	0.692877i
$85$	2.36561e6	−	4.09735e6i	0.417808	−	0.723665i
$86$	−532705.	+	922672.i	−0.0903113	+	0.156424i
$87$	6.56801e6	−	6.35920e6i	1.06934	−	1.03535i
$88$	865096.	+	1.49839e6i	0.135324	+	0.234388i
$89$	−1.01396e7			−1.52459			−0.762296	−	0.647228i	$-0.775928\pi$
$89$	−1.01396e7			−1.52459			−0.762296	+	0.647228i	$0.775928\pi$
$90$	7.62405e6	−	4.07929e6i	1.10239	−	0.589842i
$91$	99087.4			0.0137839
$92$	−1.82127e6	−	3.15453e6i	−0.243847	−	0.422355i
$93$	−2.58907e6	−	738757.i	−0.333775	−	0.0952382i
$94$	1.18973e6	−	2.06067e6i	0.147741	−	0.255895i
$95$	−9.35690e6	+	1.62066e7i	−1.11969	+	1.93937i
$96$	−1.47359e6	−	420470.i	−0.169992	−	0.0485049i
$97$	−7.16868e6	−	1.24165e7i	−0.797514	−	1.38133i	−0.921231	−	0.389017i	$-0.872815\pi$
$97$	−7.16868e6	−	1.24165e7i	−0.797514	−	1.38133i	0.123717	−	0.992318i	$-0.460518\pi$
$98$	−6.85858e6			−0.736111
$99$	6.27767e6	+	3.90002e6i	0.650243	+	0.403965i
$100$	1.06319e7			1.06319
$101$	−4.56727e6	−	7.91074e6i	−0.441095	−	0.763998i	0.556676	−	0.830730i	$-0.312076\pi$
$101$	−4.56727e6	−	7.91074e6i	−0.441095	−	0.763998i	−0.997771	+	0.0667310i	$0.978743\pi$
$102$	−2.57311e6	+	2.49131e6i	−0.240081	+	0.232449i
$103$	−9.52814e6	+	1.65032e7i	−0.859168	+	1.48812i	0.0135560	+	0.999908i	$0.495685\pi$
$103$	−9.52814e6	+	1.65032e7i	−0.859168	+	1.48812i	−0.872724	+	0.488214i	$0.837648\pi$
$104$	−19565.5	+	33888.5i	−0.00170559	+	0.00295417i
$105$	7.28692e6	+	2.90649e7i	0.614301	+	2.45023i
$106$	3.06273e6	+	5.30481e6i	0.249769	+	0.432613i
$107$	1.52746e7			1.20539			0.602695	−	0.797972i	$-0.294094\pi$
$107$	1.52746e7			1.20539			0.602695	+	0.797972i	$0.294094\pi$
$108$	−6.39725e6	+	1.38593e6i	−0.488664	+	0.105866i
$109$	−3.46009e6			−0.255914			−0.127957	−	0.991780i	$-0.540842\pi$
$109$	−3.46009e6			−0.255914			−0.127957	+	0.991780i	$0.540842\pi$
$110$	6.68036e6	+	1.15707e7i	0.478548	+	0.828869i
$111$	−2.42267e6	−	9.66316e6i	−0.168137	−	0.670639i
$112$	2.65520e6	−	4.59893e6i	0.178580	−	0.309310i
$113$	636461.	−	1.10238e6i	0.0414951	−	0.0718717i	−0.844532	−	0.535505i	$-0.820121\pi$
$113$	636461.	−	1.10238e6i	0.0414951	−	0.0718717i	0.886027	+	0.463634i	$0.153455\pi$
$114$	1.01777e7	−	9.85410e6i	0.643400	−	0.622946i
$115$	−1.40640e7	−	2.43596e7i	−0.862318	−	1.49358i
$116$	−1.25113e7			−0.744216
$117$	−5398.18	+	167061.i	−0.000311600	+	0.00964325i
$118$	−1.27056e7			−0.711880
$119$	−6.20575e6	−	1.07487e7i	−0.337582	−	0.584710i
$120$	−1.13792e7	−	3.24691e6i	−0.601144	−	0.171528i
$121$	4.03381e6	−	6.98677e6i	0.206998	−	0.358532i
$122$	−5.91684e6	+	1.02483e7i	−0.295006	+	0.510965i
$123$	−4.55431e6	−	1.29951e6i	−0.220676	−	0.0629669i
$124$	1.84233e6	+	3.19100e6i	0.0867742	+	0.150297i
$125$	4.34898e7			1.99160
$126$	732575.	−	2.26714e7i	0.0326254	−	1.00968i
$127$	3.66855e7			1.58921			0.794606	−	0.607125i	$-0.207677\pi$
$127$	3.66855e7			1.58921			0.794606	+	0.607125i	$0.207677\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	4.47444e6	−	4.33219e6i	0.183516	−	0.177682i
$130$	−151087.	+	261690.i	−0.00603150	+	0.0104469i
$131$	1.44227e7	−	2.49808e7i	0.560526	−	0.970860i	−0.436924	−	0.899498i	$-0.643932\pi$
$131$	1.44227e7	−	2.49808e7i	0.560526	−	0.970860i	0.997450	−	0.0713618i	$-0.0227345\pi$
$132$	−2.45961e6	−	9.81051e6i	−0.0930803	−	0.371264i
$133$	2.45461e7	+	4.25151e7i	0.904695	+	1.56698i
$134$	−2.14022e7			−0.768408
$135$	−4.94002e7	+	1.07023e7i	−1.72807	+	0.374376i
$136$	4.90148e6			0.167086
$137$	2.78318e6	+	4.82062e6i	0.0924741	+	0.160170i	0.908552	−	0.417773i	$-0.137189\pi$
$137$	2.78318e6	+	4.82062e6i	0.0924741	+	0.160170i	−0.816078	+	0.577942i	$0.803856\pi$
$138$	5.17817e6	+	2.06539e7i	0.167726	+	0.668998i
$139$	3.66917e6	−	6.35518e6i	0.115882	−	0.200713i	−0.802250	−	0.596988i	$-0.796364\pi$
$139$	3.66917e6	−	6.35518e6i	0.115882	−	0.200713i	0.918132	+	0.396275i	$0.129697\pi$
$140$	2.05037e7	−	3.55134e7i	0.631515	−	1.09382i
$141$	−9.99310e6	+	9.67541e6i	−0.300216	+	0.290672i
$142$	8.37117e6	+	1.44993e7i	0.245345	+	0.424950i
$143$	−258271.			−0.00738584
$144$	7.60911e6	+	4.72718e6i	0.212356	+	0.131927i
$145$	−9.66134e7			−2.63178
$146$	1.30638e7	+	2.26272e7i	0.347404	+	0.601722i
$147$	3.85543e7	+	1.10009e7i	1.00106	+	0.285640i
$148$	−6.81683e6	+	1.18071e7i	−0.172849	+	0.299383i
$149$	1.35688e7	−	2.35019e7i	0.336039	−	0.582036i	−0.647645	−	0.761942i	$-0.724246\pi$
$149$	1.35688e7	−	2.35019e7i	0.336039	−	0.582036i	0.983684	+	0.179906i	$0.0575793\pi$
$150$	−5.97650e7	−	1.70531e7i	−1.44587	−	0.412558i
$151$	−1.85992e6	−	3.22147e6i	−0.0439617	−	0.0761439i	0.843207	−	0.537589i	$-0.180665\pi$
$151$	−1.85992e6	−	3.22147e6i	−0.0439617	−	0.0761439i	−0.887169	+	0.461445i	$0.847331\pi$
$152$	−1.93873e7			−0.447779
$153$	1.84603e7	−	9.87727e6i	0.416695	−	0.222955i
$154$	3.50494e7			0.773319
$155$	1.42266e7	+	2.46413e7i	0.306861	+	0.531498i
$156$	164340.	−	159115.i	0.00346583	−	0.00335565i
$157$	−4.37533e7	+	7.57829e7i	−0.902322	+	1.56287i	−0.0778508	+	0.996965i	$0.524806\pi$
$157$	−4.37533e7	+	7.57829e7i	−0.902322	+	1.56287i	−0.824472	+	0.565903i	$0.808528\pi$
$158$	9.14465e6	−	1.58390e7i	0.184445	−	0.319468i
$159$	−8.70786e6	−	3.47325e7i	−0.171799	−	0.685246i
$160$	8.09721e6	+	1.40248e7i	0.156284	+	0.270692i
$161$	−7.37889e7			−1.39348
$162$	3.81839e7	+	2.47023e6i	0.705632	+	0.0456494i
$163$	5.45422e7			0.986452			0.493226	−	0.869901i	$-0.335818\pi$
$163$	5.45422e7			0.986452			0.493226	+	0.869901i	$0.335818\pi$
$164$	3.24075e6	+	5.61314e6i	0.0573709	+	0.0993693i
$165$	−1.89934e7	−	7.57577e7i	−0.329161	−	1.31290i
$166$	−1.98337e6	+	3.43530e6i	−0.0336531	+	0.0582889i
$167$	−2.78552e7	+	4.82466e7i	−0.462805	+	0.801602i	−0.999099	−	0.0424288i	$-0.986490\pi$
$167$	−2.78552e7	+	4.82466e7i	−0.462805	+	0.801602i	0.536294	+	0.844031i	$0.319824\pi$
$168$	−2.23022e7	+	2.15932e7i	−0.362882	+	0.351346i
$169$	3.13713e7	+	5.43368e7i	0.499953	+	0.865945i
$170$	3.78497e7			0.590870
$171$	−7.30175e7	+	3.90684e7i	−1.11671	+	0.597502i
$172$	−8.52328e6			−0.127719
$173$	−3.94697e7	−	6.83635e7i	−0.579566	−	1.00384i	−0.995529	−	0.0944557i	$-0.969889\pi$
$173$	−3.94697e7	−	6.83635e7i	−0.579566	−	1.00384i	0.415964	−	0.909381i	$-0.363444\pi$
$174$	7.03299e7	+	2.00677e7i	1.01209	+	0.288785i
$175$	1.07688e8	−	1.86521e8i	1.51891	−	2.63083i
$176$	−6.92077e6	+	1.19871e7i	−0.0956886	+	0.165737i
$177$	7.14220e7	+	2.03793e7i	0.968112	+	0.276237i
$178$	−4.05582e7	−	7.02489e7i	−0.539025	−	0.933618i
$179$	4.56081e7			0.594369			0.297185	−	0.954820i	$-0.403952\pi$
$179$	4.56081e7			0.594369			0.297185	+	0.954820i	$0.403952\pi$
$180$	5.87583e7	+	3.65038e7i	0.750958	+	0.466535i
$181$	−9.15090e7			−1.14707			−0.573534	−	0.819182i	$-0.694428\pi$
$181$	−9.15090e7			−1.14707			−0.573534	+	0.819182i	$0.694428\pi$
$182$	396349.	+	686497.i	0.00487336	+	0.00844090i
$183$	4.96983e7	−	4.81184e7i	0.599464	−	0.580406i
$184$	1.45702e7	−	2.52363e7i	0.172426	−	0.298650i
$185$	−5.26402e7	+	9.11755e7i	−0.611247	+	1.05871i
$186$	−5.23804e6	−	2.08927e7i	−0.0596862	−	0.238067i
$187$	1.61753e7	+	2.80164e7i	0.180887	+	0.313305i
$188$	1.90357e7			0.208937
$189$	−4.04822e7	+	1.26268e8i	−0.436162	+	1.36043i
$190$	−1.49710e8			−1.58349
$191$	−1.06146e7	−	1.83851e7i	−0.110227	−	0.190919i	0.805635	−	0.592413i	$-0.201824\pi$
$191$	−1.06146e7	−	1.83851e7i	−0.110227	−	0.190919i	−0.915862	+	0.401494i	$0.868491\pi$
$192$	−2.98128e6	−	1.18912e7i	−0.0303982	−	0.121247i
$193$	8.36437e7	−	1.44875e8i	0.837495	−	1.45058i	−0.0544869	−	0.998514i	$-0.517352\pi$
$193$	8.36437e7	−	1.44875e8i	0.837495	−	1.45058i	0.891982	−	0.452070i	$-0.149314\pi$
$194$	5.73494e7	−	9.93321e7i	0.563927	−	0.976751i
$195$	1.26905e6	−	1.22871e6i	0.0122562	−	0.0118666i
$196$	−2.74343e7	−	4.75177e7i	−0.260254	−	0.450774i
$197$	9.03018e7			0.841521			0.420760	−	0.907172i	$-0.361763\pi$
$197$	9.03018e7			0.841521			0.420760	+	0.907172i	$0.361763\pi$
$198$	−1.90946e6	+	5.90931e7i	−0.0174816	+	0.541014i
$199$	−1.21600e7			−0.109382			−0.0546912	−	0.998503i	$-0.517417\pi$
$199$	−1.21600e7			−0.109382			−0.0546912	+	0.998503i	$0.517417\pi$
$200$	4.25275e7	+	7.36597e7i	0.375893	+	0.651066i
$201$	1.20309e8	+	3.43284e7i	1.04499	+	0.298172i
$202$	3.65382e7	−	6.32859e7i	0.311901	−	0.540229i
$203$	−1.26724e8	+	2.19492e8i	−1.06322	+	1.84155i
$204$	−2.75528e7	−	7.86181e6i	−0.227227	−	0.0648361i
$205$	2.50254e7	+	4.33452e7i	0.202881	+	0.351401i
$206$	−1.52450e8			−1.21505
$207$	4.01994e6	−	1.24407e8i	0.0315009	−	0.974878i
$208$	−313049.			−0.00241207
$209$	−6.39795e7	−	1.10816e8i	−0.484762	−	0.839633i
$210$	−1.72220e8	+	1.66745e8i	−1.28326	+	1.24247i
$211$	−6.08112e7	+	1.05328e8i	−0.445651	+	0.771890i	−0.998097	−	0.0616584i	$-0.980361\pi$
$211$	−6.08112e7	+	1.05328e8i	−0.445651	+	0.771890i	0.552446	+	0.833548i	$0.313694\pi$
$212$	−2.45019e7	+	4.24385e7i	−0.176613	+	0.305904i
$213$	−2.38006e7	−	9.49321e7i	−0.168756	−	0.673108i
$214$	6.10985e7	+	1.05826e8i	0.426170	+	0.738147i
$215$	−6.58176e7			−0.451656
$216$	−3.51910e7	−	3.87777e7i	−0.237598	−	0.261815i
$217$	7.46420e7			0.495877
$218$	−1.38404e7	−	2.39722e7i	−0.0904794	−	0.156715i
$219$	−3.71426e7	−	1.48149e8i	−0.238956	−	0.953110i
$220$	−5.34429e7	+	9.25658e7i	−0.338384	+	0.586099i
$221$	−365830.	+	633636.i	−0.00227985	+	0.00394882i
$222$	5.72577e7	−	5.54374e7i	0.351235	−	0.340069i
$223$	1.74885e7	+	3.02910e7i	0.105605	+	0.182914i	0.913985	−	0.405747i	$-0.132989\pi$
$223$	1.74885e7	+	3.02910e7i	0.105605	+	0.182914i	−0.808380	+	0.588661i	$0.799655\pi$
$224$	4.24831e7			0.252551
$225$	3.08605e8	+	1.91722e8i	1.80620	+	1.12210i
$226$	1.01834e7			0.0586830
$227$	1.18975e8	+	2.06070e8i	0.675094	+	1.16930i	0.976441	+	0.215783i	$0.0692304\pi$
$227$	1.18975e8	+	2.06070e8i	0.675094	+	1.16930i	−0.301347	+	0.953515i	$0.597436\pi$
$228$	1.08982e8	+	3.10965e7i	0.608951	+	0.173756i
$229$	−1.28628e8	+	2.22790e8i	−0.707800	+	1.22595i	0.257871	+	0.966179i	$0.416979\pi$
$229$	−1.28628e8	+	2.22790e8i	−0.707800	+	1.22595i	−0.965671	+	0.259767i	$0.916354\pi$
$230$	1.12512e8	−	1.94877e8i	0.609751	−	1.05612i
$231$	−1.97024e8	−	5.62181e7i	−1.05166	−	0.300078i
$232$	−5.00452e7	−	8.66808e7i	−0.263120	−	0.455738i
$233$	5.52588e7			0.286191			0.143095	−	0.989709i	$-0.454294\pi$
$233$	5.52588e7			0.286191			0.143095	+	0.989709i	$0.454294\pi$
$234$	−1.17902e6	+	630842.i	−0.00601543	+	0.00321859i
$235$	1.46996e8			0.738868
$236$	−5.08223e7	−	8.80268e7i	−0.251688	−	0.435936i
$237$	−7.68101e7	+	7.43683e7i	−0.374800	+	0.362884i
$238$	4.96460e7	−	8.59894e7i	0.238707	−	0.413452i
$239$	1.44017e8	−	2.49445e8i	0.682373	−	1.18190i	−0.291882	−	0.956454i	$-0.594282\pi$
$239$	1.44017e8	−	2.49445e8i	0.682373	−	1.18190i	0.974255	−	0.225450i	$-0.0723851\pi$
$240$	−2.30217e7	−	9.18253e7i	−0.107497	−	0.428769i
$241$	−1.22152e8	−	2.11573e8i	−0.562135	−	0.973647i	−0.997310	−	0.0733010i	$-0.976647\pi$
$241$	−1.22152e8	−	2.11573e8i	−0.562135	−	0.973647i	0.435174	−	0.900346i	$-0.356687\pi$
$242$	6.45410e7			0.292740
$243$	−2.10682e8	−	7.51316e7i	−0.941900	−	0.335893i
$244$	−9.46695e7			−0.417201
$245$	−2.11851e8	−	3.66936e8i	−0.920341	−	1.59408i
$246$	−9.21398e6	−	3.67513e7i	−0.0394616	−	0.157398i
$247$	1.44700e6	−	2.50628e6i	0.00610983	−	0.0105825i
$248$	−1.47386e7	+	2.55280e7i	−0.0613587	+	0.106276i
$249$	1.66592e7	−	1.61296e7i	0.0683845	−	0.0662105i
$250$	1.73959e8	+	3.01306e8i	0.704138	+	1.21960i
$251$	1.02372e8			0.408623			0.204312	−	0.978906i	$-0.434504\pi$
$251$	1.02372e8			0.408623			0.204312	+	0.978906i	$0.434504\pi$
$252$	1.60002e8	−	8.56102e7i	0.629832	−	0.336995i
$253$	1.92331e8			0.746667
$254$	1.46742e8	+	2.54165e8i	0.561871	+	0.973190i
$255$	−2.12765e8	−	6.07096e7i	−0.803545	−	0.229280i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	2.28864e8	−	3.96405e8i	0.841031	−	1.45671i	−0.0479922	−	0.998848i	$-0.515282\pi$
$257$	2.28864e8	−	3.96405e8i	0.841031	−	1.45671i	0.889024	−	0.457861i	$-0.151384\pi$
$258$	4.79120e7	+	1.36710e7i	0.173690	+	0.0495601i
$259$	1.38092e8	+	2.39182e8i	0.493878	+	0.855422i
$260$	−2.41739e6			−0.00852983
$261$	−3.63159e8	−	2.25613e8i	−1.26431	−	0.785458i
$262$	2.30763e8			0.792704
$263$	1.30943e8	+	2.26799e8i	0.443850	+	0.768771i	0.997971	−	0.0636651i	$-0.0202789\pi$
$263$	1.30943e8	+	2.26799e8i	0.443850	+	0.768771i	−0.554121	+	0.832436i	$0.686946\pi$
$264$	5.81307e7	−	5.62827e7i	0.194443	−	0.188261i
$265$	−1.89206e8	+	3.27714e8i	−0.624560	+	1.08177i
$266$	−1.96369e8	+	3.40121e8i	−0.639716	+	1.10802i
$267$	1.15314e8	+	4.59945e8i	0.370759	+	1.47882i
$268$	−8.56088e7	−	1.48279e8i	−0.271673	−	0.470552i
$269$	1.32207e8			0.414115			0.207058	−	0.978329i	$-0.433611\pi$
$269$	1.32207e8			0.414115			0.207058	+	0.978329i	$0.433611\pi$
$270$	−2.71748e8	−	2.99446e8i	−0.840221	−	0.925859i
$271$	−4.89979e8			−1.49550			−0.747748	−	0.663982i	$-0.768865\pi$
$271$	−4.89979e8			−1.49550			−0.747748	+	0.663982i	$0.768865\pi$
$272$	1.96059e7	+	3.39585e7i	0.0590740	+	0.102319i
$273$	−1.12689e6	−	4.49475e6i	−0.00335206	−	0.0133701i
$274$	−2.22655e7	+	3.85649e7i	−0.0653890	+	0.113257i
$275$	−2.80688e8	+	4.86166e8i	−0.813878	+	1.40968i
$276$	−1.22381e8	+	1.18491e8i	−0.350376	+	0.339237i
$277$	−1.54361e8	−	2.67362e8i	−0.436375	−	0.755823i	0.561032	−	0.827794i	$-0.310405\pi$
$277$	−1.54361e8	−	2.67362e8i	−0.436375	−	0.755823i	−0.997407	+	0.0719708i	$0.977071\pi$
$278$	5.87067e7			0.163882
$279$	−4.06642e6	+	1.25846e8i	−0.0112098	+	0.346916i
$280$	3.28059e8			0.893097
$281$	8.29464e7	+	1.43667e8i	0.223010	+	0.386265i	0.955721	−	0.294275i	$-0.0950783\pi$
$281$	8.29464e7	+	1.43667e8i	0.223010	+	0.386265i	−0.732710	+	0.680541i	$0.761745\pi$
$282$	−1.07006e8	−	3.05326e7i	−0.284142	−	0.0810759i
$283$	1.93742e8	−	3.35570e8i	0.508125	−	0.880098i	−0.491831	−	0.870691i	$-0.663672\pi$
$283$	1.93742e8	−	3.35570e8i	0.508125	−	0.880098i	0.999956	−	0.00940753i	$-0.00299456\pi$
$284$	−6.69694e7	+	1.15994e8i	−0.173485	+	0.300485i
$285$	8.41569e8	+	2.40130e8i	2.15344	+	0.614454i
$286$	−1.03309e6	−	1.78936e6i	−0.00261129	−	0.00452289i
$287$	1.31299e8			0.327850
$288$	−2.31444e6	+	7.16262e7i	−0.00570915	+	0.176684i
$289$	−3.18692e8			−0.776657
$290$	−3.86454e8	−	6.69357e8i	−0.930475	−	1.61163i
$291$	−4.81704e8	+	4.66391e8i	−1.14592	+	1.10949i
$292$	−1.04511e8	+	1.81018e8i	−0.245652	+	0.425482i
$293$	3.11159e8	−	5.38943e8i	0.722679	−	1.25172i	−0.237243	−	0.971450i	$-0.576244\pi$
$293$	3.11159e8	−	5.38943e8i	0.722679	−	1.25172i	0.959922	−	0.280267i	$-0.0904230\pi$
$294$	7.80004e7	+	3.11115e8i	0.179012	+	0.714013i
$295$	−3.92455e8	−	6.79751e8i	−0.890046	−	1.54160i
$296$	−1.09069e8			−0.244445
$297$	1.05517e8	−	3.29118e8i	0.233708	−	0.728961i
$298$	2.17101e8			0.475231
$299$	2.17493e6	+	3.76710e6i	0.00470540	+	0.00815000i
$300$	−1.20913e8	−	4.82277e8i	−0.258552	−	1.03127i
$301$	−8.63303e7	+	1.49528e8i	−0.182465	+	0.316039i
$302$	1.48793e7	−	2.57718e7i	0.0310856	−	0.0538419i
$303$	−3.06901e8	+	2.97144e8i	−0.633795	+	0.613646i
$304$	−7.75490e7	−	1.34319e8i	−0.158314	−	0.274208i
$305$	−7.31047e8			−1.47535
$306$	1.42273e8	+	8.83874e7i	0.283855	+	0.176346i
$307$	9.07649e8			1.79033			0.895166	−	0.445732i	$-0.147057\pi$
$307$	9.07649e8			1.79033			0.895166	+	0.445732i	$0.147057\pi$
$308$	1.40198e8	+	2.42830e8i	0.273409	+	0.473559i
$309$	8.56971e8	+	2.44525e8i	1.65239	+	0.471486i
$310$	−1.13813e8	+	1.97130e8i	−0.216983	+	0.375826i
$311$	−1.36555e8	+	2.36520e8i	−0.257422	+	0.445868i	−0.965551	−	0.260215i	$-0.916206\pi$
$311$	−1.36555e8	+	2.36520e8i	−0.257422	+	0.445868i	0.708128	+	0.706084i	$0.249540\pi$
$312$	1.75974e6	+	502119.i	0.00328026	+	0.000935977i
$313$	7.93428e7	+	1.37426e8i	0.146252	+	0.253316i	0.929839	−	0.367966i	$-0.119946\pi$
$313$	7.93428e7	+	1.37426e8i	0.146252	+	0.253316i	−0.783587	+	0.621282i	$0.786612\pi$
$314$	−7.00052e8			−1.27608
$315$	1.23556e9	−	6.61091e8i	2.22728	−	1.19172i
$316$	1.46314e8			0.260845
$317$	5.13517e8	+	8.89437e8i	0.905414	+	1.56822i	0.820361	+	0.571846i	$0.193772\pi$
$317$	5.13517e8	+	8.89437e8i	0.905414	+	1.56822i	0.0850524	+	0.996376i	$0.472894\pi$
$318$	2.05803e8	−	1.99260e8i	0.358886	−	0.347476i
$319$	3.30306e8	−	5.72107e8i	0.569704	−	0.986756i
$320$	−6.47777e7	+	1.12198e8i	−0.110510	+	0.191408i
$321$	−1.73713e8	−	6.92880e8i	−0.293133	−	1.16920i
$322$	−2.95155e8	−	5.11224e8i	−0.492669	−	0.853328i
$323$	−3.62497e8			−0.598543
$324$	1.35621e8	+	2.74427e8i	0.221524	+	0.448249i
$325$	−1.26964e7			−0.0205158
$326$	2.18169e8	+	3.77880e8i	0.348764	+	0.604076i
$327$	3.93504e7	+	1.56955e8i	0.0622347	+	0.248232i
$328$	−2.59260e7	+	4.49051e7i	−0.0405673	+	0.0702647i
$329$	1.92808e8	−	3.33953e8i	0.298497	−	0.517012i
$330$	4.48891e8	−	4.34621e8i	0.687611	−	0.665751i
$331$	1.60293e8	+	2.77636e8i	0.242950	+	0.420802i	0.961553	−	0.274618i	$-0.0885514\pi$
$331$	1.60293e8	+	2.77636e8i	0.242950	+	0.420802i	−0.718603	+	0.695421i	$0.755218\pi$
$332$	−3.17339e7			−0.0475927
$333$	−4.10783e8	+	2.19792e8i	−0.609618	+	0.326179i
$334$	−4.45683e8			−0.654506
$335$	−6.61080e8	−	1.14502e9i	−0.960721	−	1.66402i
$336$	−2.38811e8	−	6.81414e7i	−0.343453	−	0.0979995i
$337$	−3.91897e8	+	6.78786e8i	−0.557786	+	0.966114i	0.439895	+	0.898049i	$0.355016\pi$
$337$	−3.91897e8	+	6.78786e8i	−0.557786	+	0.966114i	−0.997681	+	0.0680647i	$0.978318\pi$
$338$	−2.50971e8	+	4.34694e8i	−0.353520	+	0.612315i
$339$	−5.72439e7	−	1.63338e7i	−0.0798051	−	0.0227713i
$340$	1.51399e8	+	2.62231e8i	0.208904	+	0.361832i
$341$	−1.94554e8			−0.265706
$342$	−5.62744e8	−	3.49606e8i	−0.760710	−	0.472593i
$343$	−4.37951e7			−0.0585998
$344$	−3.40931e7	−	5.90510e7i	−0.0451557	−	0.0782119i
$345$	−9.45042e8	+	9.14998e8i	−1.23904	+	1.19965i
$346$	3.15758e8	−	5.46908e8i	0.409815	−	0.709820i
$347$	1.67123e8	−	2.89465e8i	0.214725	−	0.371914i	−0.738463	−	0.674294i	$-0.764448\pi$
$347$	1.67123e8	−	2.89465e8i	0.214725	−	0.371914i	0.953187	+	0.302380i	$0.0977813\pi$
$348$	1.42287e8	+	5.67530e8i	0.180983	+	0.721875i
$349$	−5.83996e8	−	1.01151e9i	−0.735395	−	1.27374i	−0.954550	−	0.298052i	$-0.903663\pi$
$349$	−5.83996e8	−	1.01151e9i	−0.735395	−	1.27374i	0.219155	−	0.975690i	$-0.429670\pi$
$350$	1.72300e9			2.14807
$351$	7.63950e6	−	1.65505e6i	0.00942953	−	0.00204285i
$352$	−1.10732e8			−0.135324
$353$	1.81523e8	+	3.14408e8i	0.219645	+	0.380436i	0.954699	−	0.297572i	$-0.0961768\pi$
$353$	1.81523e8	+	3.14408e8i	0.219645	+	0.380436i	−0.735055	+	0.678008i	$0.762843\pi$
$354$	1.44496e8	+	5.76343e8i	0.173119	+	0.690510i
$355$	−5.17144e8	+	8.95720e8i	−0.613497	+	1.06261i
$356$	3.24466e8	−	5.61991e8i	0.381148	−	0.660168i
$357$	−4.17000e8	+	4.03743e8i	−0.485062	+	0.469641i
$358$	1.82432e8	+	3.15982e8i	0.210141	+	0.363975i
$359$	3.61722e8			0.412615			0.206307	−	0.978487i	$-0.433855\pi$
$359$	3.61722e8			0.412615			0.206307	+	0.978487i	$0.433855\pi$
$360$	−1.78723e7	+	5.53105e8i	−0.0201893	+	0.624811i
$361$	5.39942e8			0.604049
$362$	−3.66036e8	−	6.33993e8i	−0.405550	−	0.702432i
$363$	−3.62805e8	−	1.03521e8i	−0.398107	−	0.113594i
$364$	−3.17080e6	+	5.49198e6i	−0.00344598	+	0.00596862i
$365$	−8.07041e8	+	1.39784e9i	−0.868702	+	1.50464i
$366$	5.32167e8	+	1.51847e8i	0.567367	+	0.161890i
$367$	3.91996e8	+	6.78956e8i	0.413952	+	0.716986i	0.995318	−	0.0966565i	$-0.0308148\pi$
$367$	3.91996e8	+	6.78956e8i	0.413952	+	0.716986i	−0.581366	+	0.813642i	$0.697481\pi$
$368$	2.33123e8			0.243847
$369$	−7.15304e6	+	2.21369e8i	−0.00741137	+	0.229364i
$370$	−8.42243e8			−0.864433
$371$	4.96348e8	+	8.59699e8i	0.504635	+	0.874053i
$372$	1.23796e8	−	1.19861e8i	0.124683	−	0.120719i
$373$	4.38448e8	−	7.59414e8i	0.437459	−	0.757700i	−0.560034	−	0.828469i	$-0.689212\pi$
$373$	4.38448e8	−	7.59414e8i	0.437459	−	0.757700i	0.997493	+	0.0707691i	$0.0225453\pi$
$374$	−1.29402e8	+	2.24131e8i	−0.127906	+	0.221540i
$375$	−4.94595e8	−	1.97276e9i	−0.484329	−	1.93181i
$376$	7.61428e7	+	1.31883e8i	0.0738705	+	0.127948i
$377$	1.49408e7			0.0143608
$378$	−1.03674e9	+	2.24604e8i	−0.987299	+	0.213893i
$379$	−7.60110e8			−0.717198			−0.358599	−	0.933492i	$-0.616746\pi$
$379$	−7.60110e8			−0.717198			−0.358599	+	0.933492i	$0.616746\pi$
$380$	−5.98841e8	−	1.03722e9i	−0.559847	−	0.969683i
$381$	−4.17212e8	−	1.66411e9i	−0.386473	−	1.54150i
$382$	8.49171e7	−	1.47081e8i	0.0779423	−	0.135000i
$383$	1.00563e8	−	1.74180e8i	0.0914624	−	0.158418i	−0.816664	−	0.577113i	$-0.804179\pi$
$383$	1.00563e8	−	1.74180e8i	0.0914624	−	0.158418i	0.908127	+	0.418695i	$0.137513\pi$
$384$	7.04598e7	−	6.82198e7i	0.0635012	−	0.0614825i
$385$	1.08262e9	+	1.87515e9i	0.966861	+	1.67465i
$386$	1.33830e9			1.18440
$387$	−2.47401e8	−	1.53698e8i	−0.216976	−	0.134797i
$388$	9.17591e8			0.797514
$389$	−2.91728e8	−	5.05288e8i	−0.251278	−	0.435227i	0.712600	−	0.701571i	$-0.247518\pi$
$389$	−2.91728e8	−	5.05288e8i	−0.251278	−	0.435227i	−0.963878	+	0.266344i	$0.914184\pi$
$390$	1.35889e7	+	3.87741e6i	0.0116000	+	0.00330991i
$391$	2.72428e8	−	4.71859e8i	0.230480	−	0.399203i
$392$	2.19475e8	−	3.80141e8i	0.184028	−	0.318745i
$393$	−1.29719e9	−	3.70135e8i	−1.07803	−	0.307600i
$394$	3.61207e8	+	6.25629e8i	0.297522	+	0.515324i
$395$	1.12985e9			0.922428
$396$	−4.17047e8	+	2.23143e8i	−0.337483	+	0.180572i
$397$	8.20175e8			0.657869			0.328935	−	0.944353i	$-0.393310\pi$
$397$	8.20175e8			0.657869			0.328935	+	0.944353i	$0.393310\pi$
$398$	−4.86400e7	−	8.42469e7i	−0.0386725	−	0.0669828i
$399$	1.64939e9	−	1.59696e9i	1.29993	−	1.25860i
$400$	−3.40220e8	+	5.89278e8i	−0.265797	+	0.460373i
$401$	9.81617e8	−	1.70021e9i	0.760215	−	1.31673i	−0.182524	−	0.983201i	$-0.558427\pi$
$401$	9.81617e8	−	1.70021e9i	0.760215	−	1.31673i	0.942739	−	0.333530i	$-0.108240\pi$
$402$	2.43400e8	+	9.70836e8i	0.186866	+	0.745340i
$403$	−2.20008e6	−	3.81065e6i	−0.00167444	−	0.00290022i
$404$	5.84611e8			0.441095
$405$	1.04728e9	+	2.11915e9i	0.783378	+	1.58515i
$406$	−2.02758e9			−1.50362
$407$	−3.59937e8	−	6.23429e8i	−0.264634	−	0.458360i
$408$	−5.57429e7	−	2.22338e8i	−0.0406330	−	0.162071i
$409$	8.35315e7	−	1.44681e8i	0.0603696	−	0.104563i	−0.834261	−	0.551370i	$-0.814105\pi$
$409$	8.35315e7	−	1.44681e8i	0.0603696	−	0.104563i	0.894631	+	0.446806i	$0.147439\pi$
$410$	−2.00203e8	+	3.46762e8i	−0.143459	+	0.248478i
$411$	1.87018e8	−	1.81073e8i	0.132873	−	0.128649i
$412$	−6.09801e8	−	1.05621e9i	−0.429584	−	0.744061i
$413$	−2.05907e9			−1.43829
$414$	8.78000e8	−	4.69779e8i	0.608126	−	0.325381i
$415$	−2.45053e8			−0.168303
$416$	−1.25219e6	−	2.16886e6i	−0.000852796	−	0.00147709i
$417$	−3.30009e8	−	9.41634e7i	−0.222869	−	0.0635925i
$418$	5.11836e8	−	8.86526e8i	0.342779	−	0.593710i
$419$	5.02347e8	−	8.70091e8i	0.333622	−	0.577851i	−0.649597	−	0.760279i	$-0.725062\pi$
$419$	5.02347e8	−	8.70091e8i	0.333622	−	0.577851i	0.983219	+	0.182428i	$0.0583957\pi$
$420$	−1.84412e9	−	5.26195e8i	−1.21456	−	0.346557i
$421$	5.12781e8	+	8.88163e8i	0.334923	+	0.580103i	0.983470	−	0.181071i	$-0.0579565\pi$
$421$	5.12781e8	+	8.88163e8i	0.334923	+	0.580103i	−0.648547	+	0.761174i	$0.724623\pi$
$422$	−9.72979e8			−0.630246
$423$	5.52539e8	+	3.43266e8i	0.354954	+	0.220516i
$424$	−3.92030e8			−0.249769
$425$	7.95164e8	+	1.37727e9i	0.502453	+	0.870275i
$426$	5.62507e8	−	5.44624e8i	0.352528	−	0.341321i
$427$	−9.58885e8	+	1.66084e9i	−0.596031	+	1.03236i
$428$	−4.88788e8	+	8.46606e8i	−0.301347	+	0.521949i
$429$	2.93723e6	+	1.17156e7i	0.00179613	+	0.00716412i
$430$	−2.63270e8	−	4.55998e8i	−0.159684	−	0.276582i
$431$	−1.94903e8			−0.117260			−0.0586299	−	0.998280i	$-0.518673\pi$
$431$	−1.94903e8			−0.117260			−0.0586299	+	0.998280i	$0.518673\pi$
$432$	1.27896e8	−	3.98921e8i	0.0763246	−	0.238064i
$433$	−1.00973e9			−0.597721			−0.298861	−	0.954297i	$-0.596607\pi$
$433$	−1.00973e9			−0.597721			−0.298861	+	0.954297i	$0.596607\pi$
$434$	2.98568e8	+	5.17135e8i	0.175319	+	0.303662i
$435$	1.09875e9	+	4.38253e9i	0.640011	+	2.55277i
$436$	1.10723e8	−	1.91778e8i	0.0639786	−	0.110814i
$437$	−1.07756e9	+	1.86639e9i	−0.617669	+	1.06983i
$438$	8.77833e8	−	8.49926e8i	0.499174	−	0.483305i
$439$	7.79334e8	+	1.34985e9i	0.439641	+	0.761480i	0.997662	−	0.0683467i	$-0.0217724\pi$
$439$	7.79334e8	+	1.34985e9i	0.439641	+	0.761480i	−0.558021	+	0.829827i	$0.688439\pi$
$440$	−8.55086e8			−0.478548
$441$	6.05536e7	−	1.87399e9i	0.0336206	−	1.04047i
$442$	−5.85328e6			−0.00322419
$443$	2.01909e8	+	3.49717e8i	0.110343	+	0.191119i	0.915908	−	0.401387i	$-0.131472\pi$
$443$	2.01909e8	+	3.49717e8i	0.110343	+	0.191119i	−0.805566	+	0.592506i	$0.798139\pi$
$444$	6.13112e8	+	1.74943e8i	0.332430	+	0.0948542i
$445$	2.50556e9	−	4.33975e9i	1.34786	−	2.33456i
$446$	−1.39908e8	+	2.42328e8i	−0.0746743	+	0.129340i
$447$	−1.22039e9	−	3.48222e8i	−0.646283	−	0.184408i
$448$	1.69933e8	+	2.94332e8i	0.0892901	+	0.154655i
$449$	−3.14101e9			−1.63760			−0.818799	−	0.574080i	$-0.805360\pi$
$449$	−3.14101e9			−1.63760			−0.818799	+	0.574080i	$0.805360\pi$
$450$	−9.38674e7	+	2.90497e9i	−0.0485592	+	1.50279i
$451$	−3.42231e8			−0.175672
$452$	4.07335e7	+	7.05525e7i	0.0207476	+	0.0359358i
$453$	−1.24979e8	+	1.21005e8i	−0.0631672	+	0.0611591i
$454$	−9.51798e8	+	1.64856e9i	−0.477364	+	0.826818i
$455$	−2.44852e7	+	4.24096e7i	−0.0121861	+	0.0211069i
$456$	2.20485e8	+	8.79434e8i	0.108893	+	0.434337i
$457$	1.02471e8	+	1.77485e8i	0.0502221	+	0.0869871i	0.890044	−	0.455875i	$-0.150674\pi$
$457$	1.02471e8	+	1.77485e8i	0.0502221	+	0.0869871i	−0.839822	+	0.542863i	$0.817340\pi$
$458$	−2.05805e9			−1.00098
$459$	−6.57990e8	−	7.25054e8i	−0.317596	−	0.349966i
$460$	1.80020e9			0.862318
$461$	9.33580e8	+	1.61701e9i	0.443811	+	0.768704i	0.997969	−	0.0637082i	$-0.0202927\pi$
$461$	9.33580e8	+	1.61701e9i	0.443811	+	0.768704i	−0.554157	+	0.832412i	$0.686959\pi$
$462$	−3.98605e8	−	1.58989e9i	−0.188060	−	0.750103i
$463$	1.42398e9	−	2.46641e9i	0.666764	−	1.15487i	−0.312040	−	0.950069i	$-0.601012\pi$
$463$	1.42398e9	−	2.46641e9i	0.666764	−	1.15487i	0.978804	−	0.204800i	$-0.0656543\pi$
$464$	4.00361e8	−	6.93446e8i	0.186054	−	0.322255i
$465$	9.55969e8	−	9.25578e8i	0.440918	−	0.426901i
$466$	2.21035e8	+	3.82844e8i	0.101184	+	0.175255i
$467$	1.34709e8			0.0612051			0.0306025	−	0.999532i	$-0.490257\pi$
$467$	1.34709e8			0.0612051			0.0306025	+	0.999532i	$0.490257\pi$
$468$	−9.08669e6	−	5.64513e6i	−0.00409775	−	0.00254574i
$469$	−3.46845e9			−1.55250
$470$	5.87982e8	+	1.01841e9i	0.261229	+	0.452462i
$471$	3.93521e9	+	1.12286e9i	1.73538	+	0.495168i
$472$	4.06578e8	−	7.04214e8i	0.177970	−	0.308253i
$473$	2.25020e8	−	3.89746e8i	0.0977704	−	0.169343i
$474$	−8.22479e8	−	2.34683e8i	−0.354732	−	0.101218i
$475$	−3.14518e9	−	5.44762e9i	−1.34654	−	2.33227i
$476$	7.94336e8			0.337582
$477$	−1.47649e9	+	7.90003e8i	−0.622896	+	0.333284i
$478$	2.30427e9			0.965021
$479$	−1.06776e9	−	1.84942e9i	−0.443916	−	0.768884i	0.554060	−	0.832477i	$-0.313078\pi$
$479$	−1.06776e9	−	1.84942e9i	−0.443916	−	0.768884i	−0.997976	+	0.0635921i	$0.979744\pi$
$480$	5.44098e8	−	5.26800e8i	0.224560	−	0.217421i
$481$	8.14055e6	−	1.40999e7i	0.00333539	−	0.00577706i
$482$	9.77216e8	−	1.69259e9i	0.397490	−	0.688472i
$483$	8.39176e8	+	3.34717e9i	0.338874	+	1.35165i
$484$	2.58164e8	+	4.47153e8i	0.103499	+	0.179266i
$485$	7.08573e9			2.82026
$486$	−3.22200e8	−	1.76017e9i	−0.127320	−	0.695550i
$487$	−3.97659e9			−1.56013			−0.780064	−	0.625700i	$-0.784813\pi$
$487$	−3.97659e9			−1.56013			−0.780064	+	0.625700i	$0.784813\pi$
$488$	−3.78678e8	−	6.55890e8i	−0.147503	−	0.255483i
$489$	−6.20290e8	−	2.47411e9i	−0.239891	−	0.956839i
$490$	1.69481e9	−	2.93549e9i	0.650779	−	1.12718i
$491$	−2.42354e8	+	4.19770e8i	−0.0923986	+	0.160039i	−0.908520	−	0.417842i	$-0.862787\pi$
$491$	−2.42354e8	+	4.19770e8i	−0.0923986	+	0.160039i	0.816121	+	0.577881i	$0.196120\pi$
$492$	2.17764e8	−	2.10841e8i	0.0824344	−	0.0798138i
$493$	−9.35728e8	−	1.62073e9i	−0.351711	−	0.609181i
$494$	2.31520e7			0.00864060
$495$	−3.22048e9	+	1.72313e9i	−1.19344	+	0.638559i
$496$	−2.35818e8			−0.0867742
$497$	1.35663e9	+	2.34976e9i	0.495696	+	0.858571i
$498$	1.78386e8	+	5.09001e7i	0.0647230	+	0.0184678i
$499$	−2.12637e9	+	3.68298e9i	−0.766102	+	1.32693i	0.173560	+	0.984823i	$0.444473\pi$
$499$	−2.12637e9	+	3.68298e9i	−0.766102	+	1.32693i	−0.939662	+	0.342105i	$0.888860\pi$
$500$	−1.39167e9	+	2.41045e9i	−0.497900	+	0.862389i
$501$	2.50532e9	+	7.14860e8i	0.890086	+	0.253974i
$502$	4.09488e8	+	7.09254e8i	0.144470	+	0.250230i
$503$	−4.06410e9			−1.42389			−0.711944	−	0.702236i	$-0.752185\pi$
$503$	−4.06410e9			−1.42389			−0.711944	+	0.702236i	$0.752185\pi$
$504$	1.23314e9	+	7.66089e8i	0.429046	+	0.266546i
$505$	4.51442e9			1.55985
$506$	7.69323e8	+	1.33251e9i	0.263987	+	0.457238i
$507$	2.10802e9	−	2.04100e9i	0.718367	−	0.695530i
$508$	−1.17394e9	+	2.03332e9i	−0.397303	+	0.688149i
$509$	7.61421e8	−	1.31882e9i	0.255925	−	0.443275i	−0.709222	−	0.704986i	$-0.750953\pi$
$509$	7.61421e8	−	1.31882e9i	0.255925	−	0.443275i	0.965146	+	0.261711i	$0.0842867\pi$
$510$	−4.30452e8	−	1.71692e9i	−0.143691	−	0.573132i
$511$	2.11713e9	+	3.66697e9i	0.701897	+	1.21572i
$512$	−1.34218e8			−0.0441942
$513$	2.60260e9	+	2.86787e9i	0.851132	+	0.937882i
$514$	3.66183e9			1.18940
$515$	−4.70895e9	−	8.15613e9i	−1.51914	−	2.63123i
$516$	9.69324e7	+	3.86628e8i	0.0310595	+	0.123885i
$517$	−5.02555e8	+	8.70450e8i	−0.159943	+	0.277030i
$518$	−1.10474e9	+	1.91346e9i	−0.349224	+	0.604874i
$519$	−2.65219e9	+	2.56788e9i	−0.832760	+	0.806285i
$520$	−9.66957e6	−	1.67482e7i	−0.00301575	−	0.00522343i
$521$	2.24999e9			0.697025			0.348513	−	0.937304i	$-0.386687\pi$
$521$	2.24999e9			0.697025			0.348513	+	0.937304i	$0.386687\pi$
$522$	1.10461e8	−	3.41849e9i	0.0339908	−	1.05193i
$523$	4.11869e9			1.25893			0.629467	−	0.777027i	$-0.283273\pi$
$523$	4.11869e9			1.25893			0.629467	+	0.777027i	$0.283273\pi$
$524$	9.23051e8	+	1.59877e9i	0.280263	+	0.485430i
$525$	−9.68554e9	−	2.76364e9i	−2.92123	−	0.833534i
$526$	−1.04754e9	+	1.81440e9i	−0.313849	+	0.543603i
$527$	−2.75578e8	+	4.77315e8i	−0.0820176	+	0.142059i
$528$	6.22461e8	+	1.77611e8i	0.184032	+	0.0525110i
$529$	8.27727e7	+	1.43366e8i	0.0243104	+	0.0421069i
$530$	−3.02730e9			−0.883261
$531$	1.12176e8	−	3.47157e9i	0.0325139	−	1.00623i
$532$	−3.14190e9			−0.904695
$533$	−3.87005e6	−	6.70313e6i	−0.00110706	−	0.00191749i
$534$	−2.72534e9	+	2.63870e9i	−0.774508	+	0.749886i
$535$	−3.77447e9	+	6.53758e9i	−1.06566	+	1.84577i
$536$	6.84871e8	−	1.18623e9i	0.192102	−	0.332730i
$537$	−5.18686e8	−	2.06885e9i	−0.144542	−	0.576526i
$538$	5.28828e8	+	9.15957e8i	0.146412	+	0.253593i
$539$	2.89714e9			0.796908
$540$	9.87627e8	−	3.08051e9i	0.269907	−	0.841869i
$541$	5.52377e8			0.149984			0.0749920	−	0.997184i	$-0.476107\pi$
$541$	5.52377e8			0.149984			0.0749920	+	0.997184i	$0.476107\pi$
$542$	−1.95992e9	−	3.39468e9i	−0.528738	−	0.915801i
$543$	1.04070e9	+	4.15098e9i	0.278950	+	1.11263i
$544$	−1.56847e8	+	2.71668e8i	−0.0417716	+	0.0723506i
$545$	8.55013e8	−	1.48093e9i	0.226248	−	0.391873i
$546$	2.66330e7	−	2.57863e7i	0.00700238	−	0.00677977i
$547$	−1.01496e8	−	1.75797e8i	−0.0265152	−	0.0459257i	0.852463	−	0.522787i	$-0.175108\pi$
$547$	−1.01496e8	−	1.75797e8i	−0.0265152	−	0.0459257i	−0.878979	+	0.476861i	$0.841774\pi$
$548$	−3.56248e8			−0.0924741
$549$	−2.74792e9	−	1.70715e9i	−0.708763	−	0.440321i
$550$	−4.49101e9			−1.15100
$551$	3.70117e9	+	6.41061e9i	0.942558	+	1.63256i
$552$	−1.31045e9	−	3.73920e8i	−0.331616	−	0.0946220i
$553$	1.48198e9	−	2.56687e9i	0.372654	−	0.645455i
$554$	1.23489e9	−	2.13890e9i	0.308564	−	0.534448i
$555$	4.73451e9	+	1.35093e9i	1.17557	+	0.335434i
$556$	2.34827e8	+	4.06732e8i	0.0579410	+	0.100357i
$557$	−5.98849e8			−0.146833			−0.0734166	−	0.997301i	$-0.523390\pi$
$557$	−5.98849e8			−0.146833			−0.0734166	+	0.997301i	$0.523390\pi$
$558$	−8.88151e8	+	4.75210e8i	−0.216405	+	0.115789i
$559$	1.01784e7			0.00246455
$560$	1.31224e9	+	2.27286e9i	0.315758	+	0.546908i
$561$	1.08691e9	−	1.05236e9i	0.259910	−	0.251648i
$562$	−6.63571e8	+	1.14934e9i	−0.157692	+	0.273131i
$563$	1.24248e9	−	2.15204e9i	0.293434	−	0.508243i	−0.681185	−	0.732111i	$-0.738535\pi$
$563$	1.24248e9	−	2.15204e9i	0.293434	−	0.508243i	0.974619	+	0.223868i	$0.0718684\pi$
$564$	−2.16487e8	−	8.63487e8i	−0.0508106	−	0.202665i
$565$	3.14548e8	+	5.44813e8i	0.0733698	+	0.127080i
$566$	3.09987e9			0.718597
$567$	6.18810e9	+	4.00326e8i	1.42566	+	0.0922303i
$568$	−1.07151e9			−0.245345
$569$	−1.04396e9	−	1.80820e9i	−0.237570	−	0.411484i	0.722446	−	0.691427i	$-0.243018\pi$
$569$	−1.04396e9	−	1.80820e9i	−0.237570	−	0.411484i	−0.960017	+	0.279943i	$0.909684\pi$
$570$	1.70261e9	+	6.79108e9i	0.385081	+	1.53595i
$571$	−1.81719e9	+	3.14747e9i	−0.408484	+	0.707515i	−0.994720	−	0.102625i	$-0.967276\pi$
$571$	−1.81719e9	+	3.14747e9i	−0.408484	+	0.707515i	0.586236	+	0.810140i	$0.300609\pi$
$572$	8.26468e6	−	1.43148e7i	0.00184646	−	0.00319816i
$573$	−7.13258e8	+	6.90583e8i	−0.158382	+	0.153347i
$574$	5.25196e8	+	9.09667e8i	0.115912	+	0.200766i
$575$	9.45483e9			2.07404
$576$	−5.05499e8	+	2.70470e8i	−0.110215	+	0.0589713i
$577$	−2.40625e7			−0.00521466			−0.00260733	−	0.999997i	$-0.500830\pi$
$577$	−2.40625e7			−0.00521466			−0.00260733	+	0.999997i	$0.500830\pi$
$578$	−1.27477e9	−	2.20797e9i	−0.274590	−	0.475603i
$579$	−7.52300e9	−	2.14658e9i	−1.61070	−	0.459592i
$580$	3.09163e9	−	5.35486e9i	0.657945	−	1.13959i
$581$	−3.21426e8	+	5.56725e8i	−0.0679930	+	0.117767i
$582$	−5.15807e9	−	1.47178e9i	−1.08457	−	0.309466i
$583$	−1.29373e9	−	2.24081e9i	−0.270398	−	0.468344i
$584$	−1.67217e9			−0.347404
$585$	−7.01684e7	−	4.35923e7i	−0.0144909	−	0.00900252i
$586$	4.97854e9			1.02202
$587$	−1.36098e9	−	2.35728e9i	−0.277726	−	0.481036i	0.693093	−	0.720848i	$-0.256247\pi$
$587$	−1.36098e9	−	2.35728e9i	−0.277726	−	0.481036i	−0.970819	+	0.239812i	$0.922914\pi$
$588$	−1.84347e9	+	1.78486e9i	−0.373951	+	0.362063i
$589$	1.09002e9	−	1.88796e9i	0.219801	−	0.380706i
$590$	3.13964e9	−	5.43801e9i	0.629358	−	1.09008i
$591$	−1.02697e9	−	4.09622e9i	−0.204646	−	0.816258i
$592$	−4.36277e8	−	7.55654e8i	−0.0864244	−	0.149691i
$593$	−8.74434e9			−1.72201			−0.861005	−	0.508597i	$-0.830164\pi$
$593$	−8.74434e9			−1.72201			−0.861005	+	0.508597i	$0.830164\pi$
$594$	2.70226e9	−	5.85430e8i	0.529024	−	0.114610i
$595$	6.13394e9			1.19380
$596$	8.68403e8	+	1.50412e9i	0.168019	+	0.291018i
$597$	1.38291e8	+	5.51595e8i	0.0266002	+	0.106099i
$598$	−1.73995e7	+	3.01368e7i	−0.00332722	+	0.00576292i
$599$	−3.35946e9	+	5.81875e9i	−0.638668	+	1.10621i	0.347057	+	0.937844i	$0.387181\pi$
$599$	−3.35946e9	+	5.81875e9i	−0.638668	+	1.10621i	−0.985725	+	0.168362i	$0.946152\pi$
$600$	2.85766e9	−	2.76681e9i	0.540109	−	0.522939i
$601$	−2.15181e9	−	3.72704e9i	−0.404337	−	0.700331i	0.589907	−	0.807471i	$-0.299164\pi$
$601$	−2.15181e9	−	3.72704e9i	−0.404337	−	0.700331i	−0.994244	+	0.107139i	$0.965831\pi$
$602$	−1.38129e9			−0.258045
$603$	1.88958e8	−	5.84778e9i	0.0350957	−	1.08613i
$604$	2.38070e8			0.0439617
$605$	1.99357e9	+	3.45296e9i	0.366005	+	0.633939i
$606$	−3.28628e9	−	9.37695e8i	−0.599861	−	0.171162i
$607$	1.35564e9	−	2.34804e9i	0.246028	−	0.426134i	−0.716392	−	0.697698i	$-0.754208\pi$
$607$	1.35564e9	−	2.34804e9i	0.246028	−	0.426134i	0.962420	+	0.271564i	$0.0875410\pi$
$608$	6.20392e8	−	1.07455e9i	0.111945	−	0.193894i
$609$	1.13977e10	+	3.25217e9i	2.04482	+	0.583462i
$610$	−2.92419e9	−	5.06485e9i	−0.521616	−	0.903466i
$611$	−2.27321e7			−0.00403177
$612$	−4.32746e7	+	1.33924e9i	−0.00763138	+	0.236173i
$613$	7.94951e9			1.39389			0.696945	−	0.717124i	$-0.254542\pi$
$613$	7.94951e9			1.39389			0.696945	+	0.717124i	$0.254542\pi$
$614$	3.63060e9	+	6.28838e9i	0.632978	+	1.09635i
$615$	1.68160e9	−	1.62814e9i	0.291514	−	0.282246i
$616$	−1.12158e9	+	1.94264e9i	−0.193330	+	0.334857i
$617$	−4.82641e9	+	8.35958e9i	−0.827229	+	1.43280i	0.0729740	+	0.997334i	$0.476751\pi$
$617$	−4.82641e9	+	8.35958e9i	−0.827229	+	1.43280i	−0.900203	+	0.435470i	$0.856582\pi$
$618$	1.73377e9	+	6.91537e9i	0.295482	+	1.17857i
$619$	−3.97665e9	−	6.88776e9i	−0.673907	−	1.16724i	−0.976787	−	0.214212i	$-0.931282\pi$
$619$	−3.97665e9	−	6.88776e9i	−0.673907	−	1.16724i	0.302880	−	0.953029i	$-0.402052\pi$
$620$	−1.82101e9			−0.306861
$621$	−5.68902e9	+	1.23249e9i	−0.953272	+	0.206521i
$622$	−2.18488e9			−0.364050
$623$	−6.57287e9	−	1.13846e10i	−1.08905	−	1.88629i
$624$	3.56020e6	+	1.42003e7i	0.000586581	+	0.00233966i
$625$	−4.25747e9	+	7.37416e9i	−0.697544	+	1.20818i
$626$	−6.34743e8	+	1.09941e9i	−0.103416	+	0.179122i
$627$	−4.29915e9	+	4.16247e9i	−0.696540	+	0.674396i
$628$	−2.80021e9	−	4.85011e9i	−0.451161	−	0.781434i
$629$	−2.03934e9			−0.326748
$630$	9.52239e9	+	5.91581e9i	1.51724	+	0.942590i
$631$	−8.15927e9			−1.29285			−0.646425	−	0.762977i	$-0.723737\pi$
$631$	−8.15927e9			−1.29285			−0.646425	+	0.762977i	$0.723737\pi$
$632$	5.85257e8	+	1.01370e9i	0.0922225	+	0.159734i
$633$	5.46942e9	+	1.56062e9i	0.857094	+	0.244560i
$634$	−4.10813e9	+	7.11549e9i	−0.640224	+	1.10890i
$635$	−9.06526e9	+	1.57015e10i	−1.40499	+	2.43351i
$636$	2.20372e9	+	6.28802e8i	0.339670	+	0.0969202i
$637$	3.27617e7	+	5.67449e7i	0.00502202	+	0.00869839i
$638$	5.28490e9			0.805683
$639$	−4.03558e9	+	2.15926e9i	−0.611862	+	0.327380i
$640$	−1.03644e9			−0.156284
$641$	−2.13189e9	−	3.69254e9i	−0.319714	−	0.553761i	0.660714	−	0.750637i	$-0.270253\pi$
$641$	−2.13189e9	−	3.69254e9i	−0.319714	−	0.553761i	−0.980428	+	0.196877i	$0.936920\pi$
$642$	4.10556e9	−	3.97504e9i	0.612350	−	0.592883i
$643$	5.32498e9	−	9.22314e9i	0.789914	−	1.36817i	−0.136106	−	0.990694i	$-0.543459\pi$
$643$	5.32498e9	−	9.22314e9i	0.789914	−	1.36817i	0.926019	−	0.377476i	$-0.123208\pi$
$644$	2.36124e9	−	4.08979e9i	0.348370	−	0.603394i
$645$	7.48522e8	+	2.98558e9i	0.109836	+	0.438097i
$646$	−1.44999e9	−	2.51145e9i	−0.211617	−	0.366531i
$647$	1.15267e10			1.67316			0.836581	−	0.547843i	$-0.184551\pi$
$647$	1.15267e10			1.67316			0.836581	+	0.547843i	$0.184551\pi$
$648$	−1.35880e9	+	2.03732e9i	−0.196175	+	0.294135i
$649$	5.36696e9			0.770677
$650$	−5.07857e7	−	8.79633e7i	−0.00725345	−	0.0125633i
$651$	−8.48878e8	−	3.38587e9i	−0.120590	−	0.480991i
$652$	−1.74535e9	+	3.02304e9i	−0.246613	+	0.427146i
$653$	4.68970e9	−	8.12279e9i	0.659096	−	1.14159i	−0.321754	−	0.946823i	$-0.604272\pi$
$653$	4.68970e9	−	8.12279e9i	0.659096	−	1.14159i	0.980850	−	0.194764i	$-0.0623942\pi$
$654$	−9.30012e8	+	9.00447e8i	−0.130007	+	0.125874i
$655$	7.12789e9	+	1.23459e10i	0.991098	+	1.71663i
$656$	−4.14816e8			−0.0573709
$657$	−6.29782e9	+	3.36969e9i	−0.866387	+	0.463565i
$658$	3.08493e9			0.422138
$659$	3.00912e8	+	5.21195e8i	0.0409582	+	0.0709417i	0.885778	−	0.464110i	$-0.153626\pi$
$659$	3.00912e8	+	5.21195e8i	0.0409582	+	0.0709417i	−0.844820	+	0.535051i	$0.820292\pi$
$660$	4.80671e9	+	1.37153e9i	0.650795	+	0.185695i
$661$	−3.52584e9	+	6.10694e9i	−0.474852	+	0.822467i	−0.999585	−	0.0287993i	$-0.990832\pi$
$661$	−3.52584e9	+	6.10694e9i	−0.474852	+	0.822467i	0.524734	+	0.851267i	$0.324165\pi$
$662$	−1.28235e9	+	2.22109e9i	−0.171792	+	0.297552i
$663$	3.29031e7	+	9.38845e6i	0.00438470	+	0.00125111i
$664$	−1.26936e8	−	2.19859e8i	−0.0168266	−	0.0291445i
$665$	−2.42621e10			−3.19928
$666$	−3.16589e9	−	1.96682e9i	−0.415276	−	0.257991i
$667$	−1.11262e10			−1.45180
$668$	−1.78273e9	−	3.08778e9i	−0.231403	−	0.400801i
$669$	1.17515e9	−	1.13779e9i	0.151741	−	0.146917i
$670$	5.28864e9	−	9.16019e9i	0.679332	−	1.17664i
$671$	2.49934e9	−	4.32898e9i	0.319371	−	0.553167i
$672$	−4.83146e8	−	1.92710e9i	−0.0614167	−	0.244969i
$673$	1.78637e9	+	3.09408e9i	0.225901	+	0.391271i	0.956589	−	0.291439i	$-0.0941342\pi$
$673$	1.78637e9	+	3.09408e9i	0.225901	+	0.391271i	−0.730689	+	0.682711i	$0.760801\pi$
$674$	−6.27036e9			−0.788829
$675$	5.18713e9	−	1.61792e10i	0.649178	−	2.02485i
$676$	−4.01553e9			−0.499953
$677$	5.97730e9	+	1.03530e10i	0.740363	+	1.28235i	0.952330	+	0.305070i	$0.0986798\pi$
$677$	5.97730e9	+	1.03530e10i	0.740363	+	1.28235i	−0.211967	+	0.977277i	$0.567987\pi$
$678$	−1.15812e8	−	4.61933e8i	−0.0142709	−	0.0569213i
$679$	9.29407e9	−	1.60978e10i	1.13936	−	1.97343i
$680$	−1.21119e9	+	2.09785e9i	−0.147717	+	0.255854i
$681$	7.99459e9	−	7.74044e9i	0.970022	−	0.939184i
$682$	−7.78218e8	−	1.34791e9i	−0.0939412	−	0.162711i
$683$	−3.34845e9			−0.402135			−0.201067	−	0.979577i	$-0.564441\pi$
$683$	−3.34845e9			−0.402135			−0.201067	+	0.979577i	$0.564441\pi$
$684$	1.71168e8	−	5.29723e9i	0.0204515	−	0.632925i
$685$	−2.75098e9			−0.327017
$686$	−1.75181e8	−	3.03422e8i	−0.0207182	−	0.0358849i
$687$	1.15689e10	+	3.30103e9i	1.36127	+	0.388420i
$688$	2.72745e8	−	4.72408e8i	0.0319299	−	0.0553042i
$689$	2.92598e7	−	5.06794e7i	0.00340803	−	0.00590289i
$690$	−1.01195e10	−	2.88745e9i	−1.17270	−	0.334613i
$691$	5.00574e9	+	8.67020e9i	0.577159	+	0.999668i	0.995803	+	0.0915180i	$0.0291719\pi$
$691$	5.00574e9	+	8.67020e9i	0.577159	+	0.999668i	−0.418645	+	0.908150i	$0.637495\pi$
$692$	5.05212e9			0.579566
$693$	−3.09447e8	+	9.57664e9i	−0.0353200	+	1.09307i
$694$	2.67396e9			0.303666
$695$	1.81336e9	+	3.14082e9i	0.204897	+	0.354892i
$696$	−3.36282e9	+	3.25591e9i	−0.378069	+	0.366050i
$697$	−4.84755e8	+	8.39621e8i	−0.0542260	+	0.0939223i
$698$	4.67197e9	−	8.09208e9i	0.520003	−	0.900671i
$699$	−6.28440e8	−	2.50662e9i	−0.0695975	−	0.277599i
$700$	6.89201e9	+	1.19373e10i	0.759456	+	1.31542i
$701$	1.74691e10			1.91539			0.957695	−	0.287786i	$-0.0929192\pi$
$701$	1.74691e10			1.91539			0.957695	+	0.287786i	$0.0929192\pi$
$702$	4.20246e7	+	4.63078e7i	0.00458483	+	0.00505213i
$703$	8.06638e9			0.875659
$704$	−4.42929e8	−	7.67176e8i	−0.0478443	−	0.0828687i
$705$	−1.67173e9	−	6.66793e9i	−0.179682	−	0.716687i
$706$	−1.45219e9	+	2.51526e9i	−0.155312	+	0.269009i
$707$	5.92138e9	−	1.02561e10i	0.630166	−	1.09148i
$708$	−3.41504e9	+	3.30647e9i	−0.361642	+	0.350145i
$709$	−5.25200e9	−	9.09673e9i	−0.553430	−	0.958569i	−0.998024	−	0.0628366i	$-0.979985\pi$
$709$	−5.25200e9	−	9.09673e9i	−0.553430	−	0.958569i	0.444594	−	0.895732i	$-0.353348\pi$
$710$	−8.27431e9			−0.867616
$711$	4.24699e9	+	2.63845e9i	0.443136	+	0.275300i
$712$	5.19145e9			0.539025
$713$	1.63837e9	+	2.83773e9i	0.169277	+	0.293196i
$714$	−4.46521e9	−	1.27409e9i	−0.459090	−	0.130995i
$715$	6.38207e7	−	1.10541e8i	0.00652966	−	0.0113097i
$716$	−1.45946e9	+	2.52786e9i	−0.148592	+	0.257369i
$717$	−1.29531e10	−	3.69597e9i	−1.31237	−	0.374466i
$718$	1.44689e9	+	2.50609e9i	0.145881	+	0.252674i
$719$	1.05208e9			0.105560			0.0527798	−	0.998606i	$-0.483192\pi$
$719$	1.05208e9			0.105560			0.0527798	+	0.998606i	$0.483192\pi$
$720$	−3.90351e9	+	2.08860e9i	−0.389755	+	0.208541i
$721$	−2.47061e10			−2.45489
$722$	2.15977e9	+	3.74083e9i	0.213564	+	0.369903i
$723$	−8.20809e9	+	7.94715e9i	−0.807715	+	0.782037i
$724$	2.92829e9	−	5.07195e9i	0.286767	−	0.496695i
$725$	1.62376e10	−	2.81243e10i	1.58248	−	2.74094i
$726$	−7.34003e8	−	2.92767e9i	−0.0711901	−	0.283952i
$727$	−8.91075e7	−	1.54339e8i	−0.00860090	−	0.0148972i	0.861693	−	0.507430i	$-0.169404\pi$
$727$	−8.91075e7	−	1.54339e8i	−0.00860090	−	0.0148972i	−0.870294	+	0.492533i	$0.836071\pi$
$728$	−5.07327e7			−0.00487336
$729$	−1.01207e9	+	1.04113e10i	−0.0967528	+	0.995308i
$730$	−1.29127e10			−1.22853
$731$	−6.37462e8	−	1.10412e9i	−0.0603592	−	0.104545i
$732$	1.07664e9	+	4.29435e9i	0.101457	+	0.404677i
$733$	−4.40710e9	+	7.63332e9i	−0.413322	+	0.715895i	−0.995251	−	0.0973448i	$-0.968965\pi$
$733$	−4.40710e9	+	7.63332e9i	−0.413322	+	0.715895i	0.581928	+	0.813240i	$0.302298\pi$
$734$	−3.13596e9	+	5.43165e9i	−0.292708	+	0.506986i
$735$	−1.42355e10	+	1.37829e10i	−1.32241	+	1.28037i
$736$	9.32490e8	+	1.61512e9i	0.0862128	+	0.149325i
$737$	9.04051e9			0.831873
$738$	−1.56230e9	+	8.35919e8i	−0.143076	+	0.0765538i
$739$	1.74796e10			1.59322			0.796612	−	0.604491i	$-0.206623\pi$
$739$	1.74796e10			1.59322			0.796612	+	0.604491i	$0.206623\pi$
$740$	−3.36897e9	−	5.83523e9i	−0.305623	−	0.529355i
$741$	−1.30145e8	−	3.71350e7i	−0.0117507	−	0.00335289i
$742$	−3.97078e9	+	6.87759e9i	−0.356831	+	0.618049i
$743$	−9.06212e9	+	1.56960e10i	−0.810529	+	1.40388i	0.101965	+	0.994788i	$0.467487\pi$
$743$	−9.06212e9	+	1.56960e10i	−0.810529	+	1.40388i	−0.912494	+	0.409090i	$0.865846\pi$
$744$	1.32561e9	+	3.78244e8i	0.118007	+	0.0336718i
$745$	6.70590e9	+	1.16150e10i	0.594169	+	1.02913i
$746$	7.01516e9			0.618660
$747$	−9.21124e8	−	5.72251e8i	−0.0808530	−	0.0502301i
$748$	−2.07044e9			−0.180887
$749$	9.90164e9	+	1.71501e10i	0.861035	+	1.49136i
$750$	1.16893e10	−	1.13177e10i	1.01175	−	0.979589i
$751$	−8.87091e8	+	1.53649e9i	−0.0764238	+	0.132370i	−0.901705	−	0.432353i	$-0.857684\pi$
$751$	−8.87091e8	+	1.53649e9i	−0.0764238	+	0.132370i	0.825281	+	0.564723i	$0.191017\pi$
$752$	−6.09142e8	+	1.05507e9i	−0.0522344	+	0.0904726i
$753$	−1.16424e9	−	4.64375e9i	−0.0993713	−	0.396356i
$754$	5.97632e7	+	1.03513e8i	0.00507732	+	0.00879417i
$755$	1.83840e9			0.155462
$756$	−5.70306e9	−	6.28433e9i	−0.480045	−	0.528972i
$757$	−2.57471e9			−0.215721			−0.107861	−	0.994166i	$-0.534400\pi$
$757$	−2.57471e9			−0.215721			−0.107861	+	0.994166i	$0.534400\pi$
$758$	−3.04044e9	−	5.26620e9i	−0.253568	−	0.439193i
$759$	−2.18731e9	−	8.72440e9i	−0.181579	−	0.724252i
$760$	4.79073e9	−	8.29779e9i	0.395871	−	0.685669i
$761$	2.58003e9	−	4.46874e9i	0.212216	−	0.367569i	−0.740192	−	0.672396i	$-0.765265\pi$
$761$	2.58003e9	−	4.46874e9i	0.212216	−	0.367569i	0.952408	+	0.304827i	$0.0985986\pi$
$762$	9.86044e9	−	9.54697e9i	0.807335	−	0.781670i
$763$	−2.24297e9	−	3.88494e9i	−0.182805	−	0.316627i
$764$	1.35867e9			0.110227
$765$	−3.34171e8	+	1.03418e10i	−0.0269869	+	0.835180i
$766$	1.60901e9			0.129347
$767$	6.06912e7	+	1.05120e8i	0.00485671	+	0.00841207i
$768$	7.54480e8	+	2.15280e8i	0.0601012	+	0.0171491i
$769$	−7.26584e9	+	1.25848e10i	−0.576161	+	0.997940i	0.419754	+	0.907638i	$0.362116\pi$
$769$	−7.26584e9	+	1.25848e10i	−0.576161	+	0.997940i	−0.995914	+	0.0903018i	$0.971217\pi$
$770$	−8.66097e9	+	1.50012e10i	−0.683674	+	1.18416i
$771$	−2.05843e10	−	5.87345e9i	−1.61751	−	0.461533i
$772$	5.35319e9	+	9.27200e9i	0.418748	+	0.725292i
$773$	−1.64129e10			−1.27807			−0.639037	−	0.769176i	$-0.720667\pi$
$773$	−1.64129e10			−1.27807			−0.639037	+	0.769176i	$0.720667\pi$
$774$	7.52510e7	−	2.32884e9i	0.00583336	−	0.180528i
$775$	−9.56415e9			−0.738057
$776$	3.67036e9	+	6.35726e9i	0.281964	+	0.488375i
$777$	9.27919e9	−	8.98420e9i	0.709638	−	0.687078i
$778$	2.33383e9	−	4.04231e9i	0.177681	−	0.307752i
$779$	1.91739e9	−	3.32102e9i	0.145322	−	0.251705i
$780$	2.74922e7	+	1.09656e8i	0.00207433	+	0.00827376i
$781$	−3.53607e9	−	6.12465e9i	−0.265609	−	0.460047i
$782$	4.35885e9			0.325948
$783$	−6.10407e9	+	1.90392e10i	−0.454416	+	1.41737i
$784$	3.51159e9			0.260254
$785$	−2.16235e10	−	3.74530e10i	−1.59545	−	2.76339i
$786$	−2.62439e9	−	1.04677e10i	−0.192774	−	0.768907i
$787$	1.55736e9	−	2.69743e9i	0.113888	−	0.197260i	−0.803447	−	0.595377i	$-0.797003\pi$
$787$	1.55736e9	−	2.69743e9i	0.113888	−	0.197260i	0.917335	+	0.398117i	$0.130336\pi$
$788$	−2.88966e9	+	5.00503e9i	−0.210380	+	0.364389i
$789$	8.79879e9	−	8.51907e9i	0.637754	−	0.617480i
$790$	4.51942e9	+	7.82786e9i	0.326128	+	0.564869i
$791$	1.65032e9			0.118563
$792$	−3.21417e9	−	1.99681e9i	−0.229896	−	0.142823i
$793$	1.13053e8			0.00805055
$794$	3.28070e9	+	5.68234e9i	0.232592	+	0.402861i
$795$	1.70174e10	+	4.85567e9i	1.20118	+	0.342740i
$796$	3.89120e8	−	6.73975e8i	0.0273456	−	0.0473640i
$797$	−2.43716e9	+	4.22128e9i	−0.170522	+	0.295352i	−0.938602	−	0.345001i	$-0.887879\pi$
$797$	−2.43716e9	+	4.22128e9i	−0.170522	+	0.295352i	0.768081	+	0.640353i	$0.221212\pi$
$798$	1.76616e10	+	5.03950e9i	1.23033	+	0.351057i
$799$	1.42369e9	+	2.46591e9i	0.0987421	+	0.171026i
$800$	−5.44351e9			−0.375893
$801$	1.95524e10	−	1.04616e10i	1.34427	−	0.719257i
$802$	1.57059e10			1.07511
$803$	−5.51829e9	−	9.55796e9i	−0.376097	−	0.651420i
$804$	−5.75255e9	+	5.56967e9i	−0.390359	+	0.377949i
$805$	1.82338e10	−	3.15818e10i	1.23194	−	2.13379i
$806$	1.76006e7	−	3.04852e7i	0.00118401	−	0.00205077i
$807$	−1.50354e9	−	5.99710e9i	−0.100707	−	0.401683i
$808$	2.33844e9	+	4.05030e9i	0.155951	+	0.270114i
$809$	2.02049e10			1.34165			0.670823	−	0.741618i	$-0.265941\pi$
$809$	2.02049e10			1.34165			0.670823	+	0.741618i	$0.265941\pi$
$810$	−1.04928e10	+	1.57324e10i	−0.693735	+	1.04015i
$811$	−1.18619e10			−0.780871			−0.390436	−	0.920630i	$-0.627676\pi$
$811$	−1.18619e10			−0.780871			−0.390436	+	0.920630i	$0.627676\pi$
$812$	−8.11033e9	−	1.40475e10i	−0.531609	−	0.920774i
$813$	5.57237e9	+	2.22262e10i	0.363683	+	1.45060i
$814$	2.87950e9	−	4.98744e9i	0.187125	−	0.324110i
$815$	−1.34778e10	+	2.33442e10i	−0.872100	+	1.51052i
$816$	1.31743e9	−	1.27555e9i	0.0848816	−	0.0821831i
$817$	2.52141e9	+	4.36721e9i	0.161758	+	0.280173i
$818$	1.33650e9			0.0853756
$819$	−1.91073e8	+	1.02235e8i	−0.0121536	+	0.00650285i
$820$	−3.20325e9			−0.202881
$821$	1.94203e9	+	3.36370e9i	0.122477	+	0.212137i	0.920744	−	0.390167i	$-0.127583\pi$
$821$	1.94203e9	+	3.36370e9i	0.122477	+	0.212137i	−0.798267	+	0.602304i	$0.794249\pi$
$822$	2.00258e9	+	5.71408e8i	0.125759	+	0.0358835i
$823$	1.79920e9	−	3.11630e9i	0.112507	−	0.194868i	−0.804273	−	0.594259i	$-0.797445\pi$
$823$	1.79920e9	−	3.11630e9i	0.112507	−	0.194868i	0.916780	+	0.399392i	$0.130779\pi$
$824$	4.87841e9	−	8.44965e9i	0.303762	−	0.526131i
$825$	2.52454e10	+	7.20342e9i	1.56528	+	0.446632i
$826$	−8.23627e9	−	1.42656e10i	−0.508511	−	0.880767i
$827$	7.39042e9			0.454360			0.227180	−	0.973853i	$-0.427049\pi$
$827$	7.39042e9			0.454360			0.227180	+	0.973853i	$0.427049\pi$
$828$	6.76672e9	+	4.20385e9i	0.414259	+	0.257360i
$829$	−2.29211e10			−1.39731			−0.698657	−	0.715457i	$-0.746219\pi$
$829$	−2.29211e10			−1.39731			−0.698657	+	0.715457i	$0.746219\pi$
$830$	−9.80210e8	−	1.69777e9i	−0.0595040	−	0.103064i
$831$	−1.03724e10	+	1.00427e10i	−0.627013	+	0.607080i
$832$	1.00176e7	−	1.73509e7i	0.000603018	−	0.00104446i
$833$	4.10367e9	−	7.10776e9i	0.245988	−	0.426064i
$834$	−6.67651e8	−	2.66302e9i	−0.0398537	−	0.158962i
$835$	−1.37664e10	−	2.38442e10i	−0.818312	−	1.41736i
$836$	8.18938e9			0.484762
$837$	5.75480e9	−	1.24674e9i	0.339227	−	0.0734917i
$838$	8.03756e9			0.471813
$839$	1.19718e10	+	2.07358e10i	0.699830	+	1.21214i	0.968525	+	0.248916i	$0.0800744\pi$
$839$	1.19718e10	+	2.07358e10i	0.699830	+	1.21214i	−0.268695	+	0.963225i	$0.586592\pi$
$840$	−3.73090e9	−	1.48812e10i	−0.217188	−	0.866286i
$841$	−1.04830e10	+	1.81571e10i	−0.607716	+	1.05259i
$842$	−4.10225e9	+	7.10530e9i	−0.236826	+	0.410195i
$843$	5.57364e9	−	5.39645e9i	0.320437	−	0.310250i
$844$	−3.89191e9	−	6.74099e9i	−0.222825	−	0.385945i
$845$	−3.10083e10			−1.76799
$846$	−1.68064e8	+	5.20117e9i	−0.00954285	+	0.295328i
$847$	1.04595e10			0.591453
$848$	−1.56812e9	−	2.71606e9i	−0.0883067	−	0.152952i
$849$	−1.74253e10	−	4.97208e9i	−0.977246	−	0.278844i
$850$	−6.36132e9	+	1.10181e10i	−0.355288	+	0.615377i
$851$	−6.06215e9	+	1.04999e10i	−0.337189	+	0.584028i
$852$	6.02329e9	+	1.71866e9i	0.333653	+	0.0952034i
$853$	−5.92425e9	−	1.02611e10i	−0.326823	−	0.566073i	0.655057	−	0.755579i	$-0.272645\pi$
$853$	−5.92425e9	−	1.02611e10i	−0.326823	−	0.566073i	−0.981880	+	0.189506i	$0.939311\pi$
$854$	−1.53422e10			−0.842916
$855$	1.32177e9	−	4.09057e10i	0.0723229	−	2.23822i
$856$	−7.82061e9			−0.426170
$857$	3.91716e9	+	6.78473e9i	0.212588	+	0.368213i	0.952524	−	0.304464i	$-0.0984774\pi$
$857$	3.91716e9	+	6.78473e9i	0.212588	+	0.368213i	−0.739936	+	0.672678i	$0.765144\pi$
$858$	−6.94189e7	+	6.72120e7i	−0.00375208	+	0.00363280i
$859$	2.51447e9	−	4.35518e9i	0.135354	−	0.234439i	−0.790379	−	0.612618i	$-0.790116\pi$
$859$	2.51447e9	−	4.35518e9i	0.135354	−	0.234439i	0.925732	+	0.378179i	$0.123450\pi$
$860$	2.10616e9	−	3.64798e9i	0.112914	−	0.195573i
$861$	−1.49322e9	−	5.95592e9i	−0.0797283	−	0.318008i
$862$	−7.79614e8	−	1.35033e9i	−0.0414576	−	0.0718067i
$863$	−1.56414e10			−0.828395			−0.414197	−	0.910187i	$-0.635938\pi$
$863$	−1.56414e10			−0.828395			−0.414197	+	0.910187i	$0.635938\pi$
$864$	3.27539e9	−	7.09595e8i	0.172769	−	0.0374293i
$865$	3.90130e10			2.04952
$866$	−4.03893e9	−	6.99563e9i	−0.211326	−	0.366028i
$867$	3.62438e9	+	1.44564e10i	0.188872	+	0.753341i
$868$	−2.38854e9	+	4.13708e9i	−0.123969	+	0.214721i
$869$	−3.86279e9	+	6.69055e9i	−0.199679	+	0.345854i
$870$	−2.59680e10	+	2.51425e10i	−1.33697	+	1.29447i
$871$	1.02233e8	+	1.77072e8i	0.00524236	+	0.00908003i
$872$	1.77157e9			0.0904794
$873$	2.66344e10	+	1.65467e10i	1.35486	+	0.841709i
$874$	−1.72409e10			−0.873516
$875$	2.81919e10	+	4.88298e10i	1.42264	+	2.46409i
$876$	9.39979e9	+	2.68210e9i	0.472448	+	0.134806i
$877$	1.23053e10	−	2.13134e10i	0.616019	−	1.06698i	−0.374185	−	0.927354i	$-0.622078\pi$
$877$	1.23053e10	−	2.13134e10i	0.616019	−	1.06698i	0.990205	−	0.139623i	$-0.0445891\pi$
$878$	−6.23468e9	+	1.07988e10i	−0.310873	+	0.538448i
$879$	−2.79860e10	−	7.98541e9i	−1.38989	−	0.396585i
$880$	−3.42034e9	−	5.92421e9i	−0.169192	−	0.293050i
$881$	−3.74741e10			−1.84636			−0.923179	−	0.384370i	$-0.874419\pi$
$881$	−3.74741e10			−1.84636			−0.923179	+	0.384370i	$0.874419\pi$
$882$	1.32256e10	−	7.07642e9i	0.649045	−	0.347275i
$883$	6.80840e9			0.332799			0.166400	−	0.986058i	$-0.446786\pi$
$883$	6.80840e9			0.332799			0.166400	+	0.986058i	$0.446786\pi$
$884$	−2.34131e7	−	4.05527e7i	−0.00113993	−	0.00197441i
$885$	−2.63713e10	+	2.55329e10i	−1.27888	+	1.23822i
$886$	−1.61527e9	+	2.79774e9i	−0.0780240	+	0.135141i
$887$	1.35712e10	−	2.35059e10i	0.652956	−	1.13095i	−0.329446	−	0.944175i	$-0.606862\pi$
$887$	1.35712e10	−	2.35059e10i	0.652956	−	1.13095i	0.982402	−	0.186779i	$-0.0598048\pi$
$888$	1.24041e9	+	4.94754e9i	0.0594455	+	0.237107i
$889$	2.37811e10	+	4.11900e10i	1.13521	+	1.96624i
$890$	4.00889e10			1.90616
$891$	−1.61293e10	−	1.04345e9i	−0.763912	−	0.0494197i
$892$	−2.23853e9			−0.105605
$893$	−5.63125e9	−	9.75362e9i	−0.264621	−	0.458338i
$894$	−2.46901e9	−	9.84801e9i	−0.115569	−	0.460964i
$895$	−1.12701e10	+	1.95204e10i	−0.525469	+	0.910138i
$896$	−1.35946e9	+	2.35465e9i	−0.0631377	+	0.109358i
$897$	1.46146e8	−	1.41500e8i	0.00676105	−	0.00654611i
$898$	−1.25640e10	−	2.17616e10i	−0.578978	−	1.00282i
$899$	1.12548e10			0.516630
$900$	−2.05017e10	+	1.09695e10i	−0.937434	+	0.501580i
$901$	−7.33005e9			−0.333864
$902$	−1.36892e9	−	2.37105e9i	−0.0621093	−	0.107576i
$903$	7.76464e9	+	2.21553e9i	0.350925	+	0.100132i
$904$	−3.25868e8	+	5.64420e8i	−0.0146707	+	0.0254105i
$905$	2.26125e10	−	3.91661e10i	1.01410	−	1.75647i
$906$	−1.33826e9	−	3.81855e8i	−0.0597851	−	0.0170589i
$907$	3.76207e9	+	6.51610e9i	0.167418	+	0.289976i	0.937511	−	0.347955i	$-0.113124\pi$
$907$	3.76207e9	+	6.51610e9i	0.167418	+	0.289976i	−0.770093	+	0.637931i	$0.779790\pi$
$908$	−1.52288e10			−0.675094
$909$	1.69692e10	+	1.05422e10i	0.749354	+	0.465539i
$910$	−3.91763e8			−0.0172337
$911$	−6.96199e9	−	1.20585e10i	−0.305084	−	0.528421i	0.672196	−	0.740373i	$-0.265351\pi$
$911$	−6.96199e9	−	1.20585e10i	−0.305084	−	0.528421i	−0.977280	+	0.211952i	$0.932018\pi$
$912$	−5.21096e9	+	5.04530e9i	−0.227476	+	0.220245i
$913$	8.37796e8	−	1.45111e9i	0.0364326	−	0.0631032i
$914$	−8.19768e8	+	1.41988e9i	−0.0355124	+	0.0615092i
$915$	8.31396e9	+	3.31614e10i	0.358785	+	1.43106i
$916$	−8.23218e9	−	1.42586e10i	−0.353900	−	0.612973i
$917$	3.73975e10			1.60158
$918$	2.39136e9	−	7.45890e9i	0.102022	−	0.318218i
$919$	2.62089e10			1.11390			0.556948	−	0.830547i	$-0.311972\pi$
$919$	2.62089e10			1.11390			0.556948	+	0.830547i	$0.311972\pi$
$920$	7.20078e9	+	1.24721e10i	0.304875	+	0.528059i
$921$	−1.03224e10	−	4.11723e10i	−0.435383	−	1.73659i
$922$	−7.46864e9	+	1.29361e10i	−0.313822	+	0.543556i
$923$	7.99738e7	−	1.38519e8i	0.00334766	−	0.00579832i
$924$	9.42068e9	−	9.12119e9i	0.392853	−	0.380364i
$925$	−1.76942e10	−	3.06473e10i	−0.735082	−	1.27320i
$926$	2.27838e10			0.942946
$927$	1.34597e9	−	4.16544e10i	0.0554951	−	1.71744i
$928$	6.40578e9			0.263120
$929$	−7.39898e9	−	1.28154e10i	−0.302773	−	0.524418i	0.673990	−	0.738740i	$-0.264579\pi$
$929$	−7.39898e9	−	1.28154e10i	−0.302773	−	0.524418i	−0.976763	+	0.214322i	$0.931246\pi$
$930$	1.02365e10	+	2.92083e9i	0.417311	+	0.119074i
$931$	−1.62316e10	+	2.81139e10i	−0.659230	+	1.14182i
$932$	−1.76828e9	+	3.06275e9i	−0.0715477	+	0.123924i
$933$	1.22819e10	+	3.50447e9i	0.495085	+	0.141266i
$934$	5.38836e8	+	9.33291e8i	0.0216393	+	0.0374803i
$935$	−1.59881e10			−0.639671
$936$	2.76387e6	−	8.55350e7i	0.000110167	−	0.00340940i
$937$	−1.80752e9			−0.0717785			−0.0358892	−	0.999356i	$-0.511426\pi$
$937$	−1.80752e9			−0.0717785			−0.0358892	+	0.999356i	$0.511426\pi$
$938$	−1.38738e10	−	2.40301e10i	−0.548890	−	0.950705i
$939$	5.33150e9	−	5.16200e9i	0.210145	−	0.203465i
$940$	−4.70386e9	+	8.14732e9i	−0.184717	+	0.319939i
$941$	−4.94359e9	+	8.56255e9i	−0.193410	+	0.334996i	−0.946378	−	0.323061i	$-0.895288\pi$
$941$	−4.94359e9	+	8.56255e9i	−0.193410	+	0.334996i	0.752968	+	0.658057i	$0.228621\pi$
$942$	7.96146e9	+	3.17554e10i	0.310323	+	1.23777i
$943$	2.88197e9	+	4.99172e9i	0.111918	+	0.193847i
$944$	6.50525e9			0.251688
$945$	−4.40396e10	−	4.85282e10i	−1.69759	−	1.87061i
$946$	3.60032e9			0.138268
$947$	−2.39570e10	−	4.14947e10i	−0.916658	−	1.58770i	−0.804455	−	0.594013i	$-0.797543\pi$
$947$	−2.39570e10	−	4.14947e10i	−0.916658	−	1.58770i	−0.112203	−	0.993685i	$-0.535791\pi$
$948$	−1.66398e9	−	6.63703e9i	−0.0634337	−	0.253014i
$949$	1.24805e8	−	2.16169e8i	0.00474024	−	0.00821034i
$950$	2.51615e10	−	4.35809e10i	0.952145	−	1.64916i
$951$	3.45061e10	−	3.34091e10i	1.30096	−	1.25960i
$952$	3.17734e9	+	5.50332e9i	0.119353	+	0.206726i
$953$	−3.94924e9			−0.147805			−0.0739024	−	0.997265i	$-0.523545\pi$
$953$	−3.94924e9			−0.147805			−0.0739024	+	0.997265i	$0.523545\pi$
$954$	−1.13792e10	−	7.06939e9i	−0.424321	−	0.263611i
$955$	1.04918e10			0.389797
$956$	9.21710e9	+	1.59645e10i	0.341186	+	0.590952i
$957$	−2.97081e10	−	8.47679e9i	−1.09568	−	0.312636i
$958$	8.54210e9	−	1.47954e10i	0.313896	−	0.543683i
$959$	−3.60835e9	+	6.24984e9i	−0.132112	+	0.228825i
$960$	5.82617e9	+	1.66242e9i	0.212537	+	0.0606444i
$961$	1.20990e10	+	2.09561e10i	0.439762	+	0.761690i
$962$	1.30249e8			0.00471695
$963$	−2.94545e10	+	1.57598e10i	−1.06282	+	0.568667i
$964$	1.56355e10			0.562135
$965$	4.13379e10	+	7.15993e10i	1.48082	+	2.56486i
$966$	−1.98332e10	+	1.92027e10i	−0.707901	+	0.685396i
$967$	−1.46470e10	+	2.53694e10i	−0.520903	+	0.902231i	0.478801	+	0.877923i	$0.341071\pi$
$967$	−1.46470e10	+	2.53694e10i	−0.520903	+	0.902231i	−0.999705	+	0.0243074i	$0.992262\pi$
$968$	−2.06531e9	+	3.57722e9i	−0.0731849	+	0.126760i
$969$	4.12255e9	+	1.64434e10i	0.145557	+	0.580574i
$970$	2.83429e10	+	4.90914e10i	0.997111	+	1.72705i
$971$	−1.82848e10			−0.640947			−0.320474	−	0.947257i	$-0.603842\pi$
$971$	−1.82848e10			−0.640947			−0.320474	+	0.947257i	$0.603842\pi$
$972$	1.09060e10	−	9.27295e9i	0.380921	−	0.323882i
$973$	9.51402e9			0.331108
$974$	−1.59064e10	−	2.75507e10i	−0.551588	−	0.955379i
$975$	1.44392e8	+	5.75928e8i	0.00498916	+	0.0199000i
$976$	3.02942e9	−	5.24712e9i	0.104300	−	0.180653i
$977$	−1.96584e10	+	3.40493e10i	−0.674399	+	1.16809i	0.302245	+	0.953230i	$0.402264\pi$
$977$	−1.96584e10	+	3.40493e10i	−0.674399	+	1.16809i	−0.976644	+	0.214863i	$0.931069\pi$
$978$	1.46600e10	−	1.41940e10i	0.501127	−	0.485196i
$979$	1.71322e10	+	2.96739e10i	0.583544	+	1.01073i
$980$	2.71169e10			0.920341
$981$	6.67218e9	−	3.56999e9i	0.225645	−	0.120733i
$982$	−3.87767e9			−0.130671
$983$	−1.07113e10	−	1.85526e10i	−0.359671	−	0.622969i	0.628234	−	0.778024i	$-0.283778\pi$
$983$	−1.07113e10	−	1.85526e10i	−0.359671	−	0.622969i	−0.987906	+	0.155055i	$0.950445\pi$
$984$	2.33181e9	+	6.65349e8i	0.0780207	+	0.0222621i
$985$	−2.23142e10	+	3.86494e10i	−0.743969	+	1.28859i
$986$	7.48582e9	−	1.29658e10i	0.248697	−	0.430756i
$987$	−1.73414e10	−	4.94812e9i	−0.574081	−	0.163806i
$988$	9.26079e7	+	1.60402e8i	0.00305491	+	0.00529126i
$989$	−7.57968e9			−0.249152
$990$	−2.48201e10	−	1.54196e10i	−0.812982	−	0.505067i
$991$	3.76297e10			1.22821			0.614105	−	0.789225i	$-0.289517\pi$
$991$	3.76297e10			1.22821			0.614105	+	0.789225i	$0.289517\pi$
$992$	−9.43271e8	−	1.63379e9i	−0.0306793	−	0.0531382i
$993$	1.07710e10	−	1.04286e10i	0.349088	−	0.337990i
$994$	−1.08531e10	+	1.87981e10i	−0.350510	+	0.607101i
$995$	3.00482e9	−	5.20450e9i	0.0967026	−	0.167494i
$996$	3.60899e8	+	1.43950e9i	0.0115739	+	0.0461640i
$997$	−1.98488e10	−	3.43792e10i	−0.634310	−	1.09866i	−0.986661	−	0.162789i	$-0.947951\pi$
$997$	−1.98488e10	−	3.43792e10i	−0.634310	−	1.09866i	0.352351	−	0.935868i	$-0.385382\pi$
$998$	−3.40219e10			−1.08343
$999$	1.46418e10	+	1.61341e10i	0.464638	+	0.511995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.8.c.b.13.2	yes	8
3.2	odd	2		54.8.c.b.37.4		8
4.3	odd	2		144.8.i.b.49.3		8
9.2	odd	6		54.8.c.b.19.4		8
9.4	even	3		162.8.a.h.1.4		4
9.5	odd	6		162.8.a.i.1.1		4
9.7	even	3	inner	18.8.c.b.7.2	✓	8
12.11	even	2		432.8.i.b.145.4		8
36.7	odd	6		144.8.i.b.97.3		8
36.11	even	6		432.8.i.b.289.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.8.c.b.7.2	✓	8	9.7	even	3	inner
18.8.c.b.13.2	yes	8	1.1	even	1	trivial
54.8.c.b.19.4		8	9.2	odd	6
54.8.c.b.37.4		8	3.2	odd	2
144.8.i.b.49.3		8	4.3	odd	2
144.8.i.b.97.3		8	36.7	odd	6
162.8.a.h.1.4		4	9.4	even	3
162.8.a.i.1.1		4	9.5	odd	6
432.8.i.b.145.4		8	12.11	even	2
432.8.i.b.289.4		8	36.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 6.92820i) q^{2} +(-11.3727 - 45.3615i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-247.107 + 428.002i) q^{5} +(268.783 - 260.238i) q^{6} +(648.241 + 1122.79i) q^{7} -512.000 q^{8} +(-1928.33 + 1031.76i) q^{9} -3953.72 q^{10} +(-1689.64 - 2926.54i) q^{11} +(2878.11 + 821.230i) q^{12} +(38.2139 - 66.1885i) q^{13} +(-5185.93 + 8982.29i) q^{14} +(22225.1 + 6341.62i) q^{15} +(-2048.00 - 3547.24i) q^{16} -9573.21 q^{17} +(-14861.6 - 9232.78i) q^{18} +37865.7 q^{19} +(-15814.9 - 27392.1i) q^{20} +(43559.0 - 42174.2i) q^{21} +(13517.1 - 23412.4i) q^{22} +(-28457.3 + 49289.6i) q^{23} +(5822.80 + 23225.1i) q^{24} +(-83061.4 - 143867. i) q^{25} +611.423 q^{26} +(68732.4 + 75737.8i) q^{27} -82974.9 q^{28} +(97744.5 + 169298. i) q^{29} +(44964.3 + 179346. i) q^{30} +(28786.4 - 49859.4i) q^{31} +(16384.0 - 28377.9i) q^{32} +(-113537. + 109927. i) q^{33} +(-38292.8 - 66325.1i) q^{34} -640740. q^{35} +(4520.39 - 139895. i) q^{36} +213026. q^{37} +(151463. + 262342. i) q^{38} +(-3437.00 - 980.701i) q^{39} +(126519. - 219137. i) q^{40} +(50636.7 - 87705.3i) q^{41} +(466428. + 133089. i) q^{42} +(66588.1 + 115334. i) q^{43} +216274. q^{44} +(34906.9 - 1.08028e6i) q^{45} -455317. q^{46} +(-148716. - 257584. i) q^{47} +(-137617. + 133242. i) q^{48} +(-428661. + 742463. i) q^{49} +(664491. - 1.15093e6i) q^{50} +(108873. + 434255. i) q^{51} +(2445.69 + 4236.06i) q^{52} +765684. q^{53} +(-249797. + 779143. i) q^{54} +1.67009e6 q^{55} +(-331899. - 574867. i) q^{56} +(-430634. - 1.71765e6i) q^{57} +(-781956. + 1.35439e6i) q^{58} +(-794098. + 1.37542e6i) q^{59} +(-1.06269e6 + 1.02891e6i) q^{60} +(739606. + 1.28103e6i) q^{61} +460582. q^{62} +(-2.40847e6 - 1.49627e6i) q^{63} +262144. q^{64} +(18885.9 + 32711.3i) q^{65} +(-1.21574e6 - 346896. i) q^{66} +(-1.33764e6 + 2.31686e6i) q^{67} +(306343. - 530601. i) q^{68} +(2.55948e6 + 730313. i) q^{69} +(-2.56296e6 - 4.43918e6i) q^{70} +2.09279e6 q^{71} +(987302. - 528262. i) q^{72} +3.26596e6 q^{73} +(852103. + 1.47589e6i) q^{74} +(-5.58137e6 + 5.40393e6i) q^{75} +(-1.21170e6 + 2.09873e6i) q^{76} +(2.19059e6 - 3.79421e6i) q^{77} +(-6953.51 - 27735.0i) q^{78} +(-1.14308e6 - 1.97987e6i) q^{79} +2.02430e6 q^{80} +(2.65391e6 - 3.97914e6i) q^{81} +810187. q^{82} +(247921. + 429412. i) q^{83} +(943645. + 3.76386e6i) q^{84} +(2.36561e6 - 4.09735e6i) q^{85} +(-532705. + 922672. i) q^{86} +(6.56801e6 - 6.35920e6i) q^{87} +(865096. + 1.49839e6i) q^{88} -1.01396e7 q^{89} +(7.62405e6 - 4.07929e6i) q^{90} +99087.4 q^{91} +(-1.82127e6 - 3.15453e6i) q^{92} +(-2.58907e6 - 738757. i) q^{93} +(1.18973e6 - 2.06067e6i) q^{94} +(-9.35690e6 + 1.62066e7i) q^{95} +(-1.47359e6 - 420470. i) q^{96} +(-7.16868e6 - 1.24165e7i) q^{97} -6.85858e6 q^{98} +(6.27767e6 + 3.90002e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{2} - 12 q^{3} - 256 q^{4} + 54 q^{5} + 480 q^{6} - 44 q^{7} - 4096 q^{8} - 2238 q^{9} + 864 q^{10} + 2172 q^{11} + 4608 q^{12} - 6398 q^{13} + 352 q^{14} + 17604 q^{15} - 16384 q^{16} - 51972 q^{17}+ \cdots + 26558784 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 - 12 * q^3 - 256 * q^4 + 54 * q^5 + 480 * q^6 - 44 * q^7 - 4096 * q^8 - 2238 * q^9 + 864 * q^10 + 2172 * q^11 + 4608 * q^12 - 6398 * q^13 + 352 * q^14 + 17604 * q^15 - 16384 * q^16 - 51972 * q^17 - 22416 * q^18 + 90712 * q^19 + 3456 * q^20 + 192390 * q^21 - 17376 * q^22 - 2028 * q^23 + 6144 * q^24 - 173446 * q^25 - 102368 * q^26 - 288360 * q^27 + 5632 * q^28 + 283098 * q^29 + 172800 * q^30 - 812 * q^31 + 131072 * q^32 + 342108 * q^33 - 207888 * q^34 - 1492992 * q^35 - 36096 * q^36 + 441688 * q^37 + 362848 * q^38 + 67428 * q^39 - 27648 * q^40 + 610704 * q^41 + 349200 * q^42 - 84380 * q^43 - 278016 * q^44 - 652698 * q^45 - 32448 * q^46 + 855708 * q^47 - 245760 * q^48 - 1273038 * q^49 + 1387568 * q^50 + 1748556 * q^51 - 409472 * q^52 - 1842600 * q^53 + 640800 * q^54 + 7016760 * q^55 + 22528 * q^56 - 4893306 * q^57 - 2264784 * q^58 + 380796 * q^59 + 255744 * q^60 - 3151130 * q^61 - 12992 * q^62 - 3149076 * q^63 + 2097152 * q^64 - 326538 * q^65 - 6234192 * q^66 - 9961580 * q^67 + 1663104 * q^68 + 15322554 * q^69 - 5971968 * q^70 + 8970384 * q^71 + 1145856 * q^72 + 29234932 * q^73 + 1766752 * q^74 - 26321244 * q^75 - 2902784 * q^76 - 5954826 * q^77 + 6127680 * q^78 - 17309396 * q^79 - 442368 * q^80 + 6907266 * q^81 + 9771264 * q^82 - 11520192 * q^83 - 9519360 * q^84 - 14675148 * q^85 + 675040 * q^86 + 37274652 * q^87 - 1112064 * q^88 + 26066064 * q^89 + 28333152 * q^90 + 26231936 * q^91 - 129792 * q^92 - 48684366 * q^93 - 6845664 * q^94 - 31016952 * q^95 - 2359296 * q^96 - 22003112 * q^97 - 20368608 * q^98 + 26558784 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more