LMFDB - Embedded newform 16.11.f.a.3.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [16,11,Mod(3,16)] 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("16.3"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, 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:	$10.1657160428$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.15
Character	$\chi$	$=$	16.3
Dual form			16.11.f.a.11.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(26.0928 - 18.5248i) q^{2} +(164.886 - 164.886i) q^{3} +(337.664 - 966.726i) q^{4} +(897.573 - 897.573i) q^{5} +(1247.85 - 7356.80i) q^{6} +594.817 q^{7} +(-9097.83 - 31479.7i) q^{8} +4674.41i q^{9} +(6792.79 - 40047.5i) q^{10} +(2978.45 + 2978.45i) q^{11} +(-103723. - 215075. i) q^{12} +(-32786.7 - 32786.7i) q^{13} +(15520.4 - 11018.9i) q^{14} -295994. i q^{15} +(-820543. - 652856. i) q^{16} -591643. q^{17} +(86592.6 + 121968. i) q^{18} +(1.87986e6 - 1.87986e6i) q^{19} +(-564629. - 1.17079e6i) q^{20} +(98076.8 - 98076.8i) q^{21} +(132891. + 22540.7i) q^{22} +3.55022e6 q^{23} +(-6.69065e6 - 3.69045e6i) q^{24} +8.15435e6i q^{25} +(-1.46286e6 - 248129. i) q^{26} +(1.05071e7 + 1.05071e7i) q^{27} +(200848. - 575025. i) q^{28} +(1.92759e7 + 1.92759e7i) q^{29} +(-5.48323e6 - 7.72330e6i) q^{30} +5.18621e7i q^{31} +(-3.35042e7 - 1.83444e6i) q^{32} +982206. q^{33} +(-1.54376e7 + 1.09601e7i) q^{34} +(533892. - 533892. i) q^{35} +(4.51888e6 + 1.57838e6i) q^{36} +(6.64716e7 - 6.64716e7i) q^{37} +(1.42267e7 - 8.38750e7i) q^{38} -1.08121e7 q^{39} +(-3.64213e7 - 2.00894e7i) q^{40} -1.67178e8i q^{41} +(742241. - 4.37595e6i) q^{42} +(-3.64240e7 - 3.64240e7i) q^{43} +(3.88505e6 - 1.87363e6i) q^{44} +(4.19563e6 + 4.19563e6i) q^{45} +(9.26351e7 - 6.57672e7i) q^{46} +2.54335e8i q^{47} +(-2.42942e8 + 2.76490e7i) q^{48} -2.82121e8 q^{49} +(1.51058e8 + 2.12769e8i) q^{50} +(-9.75534e7 + 9.75534e7i) q^{51} +(-4.27667e7 + 2.06249e7i) q^{52} +(4.68378e7 - 4.68378e7i) q^{53} +(4.68800e8 + 7.95171e7i) q^{54} +5.34675e6 q^{55} +(-5.41154e6 - 1.87247e7i) q^{56} -6.19926e8i q^{57} +(8.60045e8 + 1.45879e8i) q^{58} +(1.66425e8 + 1.66425e8i) q^{59} +(-2.86145e8 - 9.99464e7i) q^{60} +(-5.92082e8 - 5.92082e8i) q^{61} +(9.60736e8 + 1.35323e9i) q^{62} +2.78042e6i q^{63} +(-9.08201e8 + 5.72794e8i) q^{64} -5.88570e7 q^{65} +(2.56285e7 - 1.81952e7i) q^{66} +(-1.32368e9 + 1.32368e9i) q^{67} +(-1.99776e8 + 5.71957e8i) q^{68} +(5.85381e8 - 5.85381e8i) q^{69} +(4.04047e6 - 2.38209e7i) q^{70} +2.48493e8 q^{71} +(1.47149e8 - 4.25270e7i) q^{72} -1.98224e9i q^{73} +(5.03054e8 - 2.96580e9i) q^{74} +(1.34454e9 + 1.34454e9i) q^{75} +(-1.18255e9 - 2.45208e9i) q^{76} +(1.77163e6 + 1.77163e6i) q^{77} +(-2.82118e8 + 2.00293e8i) q^{78} -7.20756e8i q^{79} +(-1.32248e9 + 1.50511e8i) q^{80} +3.18891e9 q^{81} +(-3.09695e9 - 4.36214e9i) q^{82} +(-3.72085e9 + 3.72085e9i) q^{83} +(-6.16964e7 - 1.27930e8i) q^{84} +(-5.31043e8 + 5.31043e8i) q^{85} +(-1.62515e9 - 2.75655e8i) q^{86} +6.35665e9 q^{87} +(6.66632e7 - 1.20858e8i) q^{88} -1.51157e9i q^{89} +(1.87199e8 + 3.17523e7i) q^{90} +(-1.95021e7 - 1.95021e7i) q^{91} +(1.19878e9 - 3.43209e9i) q^{92} +(8.55132e9 + 8.55132e9i) q^{93} +(4.71150e9 + 6.63630e9i) q^{94} -3.37463e9i q^{95} +(-5.82684e9 + 5.22190e9i) q^{96} -7.26855e9 q^{97} +(-7.36133e9 + 5.22624e9i) q^{98} +(-1.39225e7 + 1.39225e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 2 q^{13} + 757836 q^{14} - 469032 q^{16} - 4 q^{17} + 2066926 q^{18}+ \cdots - 25616384098 q^{99}+O(q^{100}) $ 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8 - 147364 * q^10 - 45906 * q^11 - 10988 * q^12 - 2 * q^13 + 757836 * q^14 - 469032 * q^16 - 4 * q^17 + 2066926 * q^18 - 5107042 * q^19 + 5301516 * q^20 - 118100 * q^21 - 20568924 * q^22 - 8279748 * q^23 + 58519728 * q^24 - 18451512 * q^26 - 25871552 * q^27 - 36459784 * q^28 - 29652306 * q^29 + 132781252 * q^30 - 52661752 * q^32 - 4 * q^33 + 68474900 * q^34 + 14674460 * q^35 - 15810676 * q^36 - 94618130 * q^37 + 156046000 * q^38 - 279841732 * q^39 - 125381720 * q^40 + 107395416 * q^42 + 172486862 * q^43 + 73663988 * q^44 + 19649346 * q^45 - 437620836 * q^46 + 625190376 * q^48 + 1049193778 * q^49 - 875760314 * q^50 - 72924900 * q^51 - 771392444 * q^52 + 607072398 * q^53 + 913650464 * q^54 - 1427102468 * q^55 - 1385623464 * q^56 + 37561720 * q^58 + 1543683854 * q^59 + 318869600 * q^60 + 1673280158 * q^61 - 983062992 * q^62 - 867678656 * q^64 + 1098715212 * q^65 + 768197860 * q^66 - 4830427746 * q^67 - 855827792 * q^68 + 1698121420 * q^69 - 5103882496 * q^70 + 7572888316 * q^71 + 6888513460 * q^72 + 2513658844 * q^74 - 11656678318 * q^75 - 2250244316 * q^76 - 1336459028 * q^77 + 14243324268 * q^78 - 13115458328 * q^80 - 8523250762 * q^81 + 2724305648 * q^82 + 16141605438 * q^83 - 1633924184 * q^84 + 4779968748 * q^85 - 4025865500 * q^86 - 31832612676 * q^87 + 1023457912 * q^88 + 18960485240 * q^90 + 19874217404 * q^91 + 28060187160 * q^92 - 15001617056 * q^93 - 14829002256 * q^94 + 23525947312 * q^96 - 4 * q^97 - 43134832310 * q^98 - 25616384098 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	26.0928	−	18.5248i	0.815399	−	0.578900i
$2$	26.0928	−	18.5248i	0.815399	−	0.578900i
$3$	164.886	−	164.886i	0.678542	−	0.678542i	−0.281128	−	0.959670i	$-0.590709\pi$
$3$	164.886	−	164.886i	0.678542	−	0.678542i	0.959670	+	0.281128i	$0.0907086\pi$
$4$	337.664	−	966.726i	0.329750	−	0.944068i
$5$	897.573	−	897.573i	0.287223	−	0.287223i	−0.548758	−	0.835981i	$-0.684899\pi$
$5$	897.573	−	897.573i	0.287223	−	0.287223i	0.835981	+	0.548758i	$0.184899\pi$
$6$	1247.85	−	7356.80i	0.160474	−	0.946090i
$7$	594.817			0.0353910			0.0176955	−	0.999843i	$-0.494367\pi$
$7$	594.817			0.0353910			0.0176955	+	0.999843i	$0.494367\pi$
$8$	−9097.83	−	31479.7i	−0.277644	−	0.960684i
$9$			4674.41i			0.0791616i
$10$	6792.79	−	40047.5i	0.0679279	−	0.400475i
$11$	2978.45	+	2978.45i	0.0184938	+	0.0184938i	0.716293	−	0.697799i	$-0.245837\pi$
$11$	2978.45	+	2978.45i	0.0184938	+	0.0184938i	−0.697799	+	0.716293i	$0.745837\pi$
$12$	−103723.	−	215075.i	−0.416841	−	0.864339i
$13$	−32786.7	−	32786.7i	−0.0883042	−	0.0883042i	0.661575	−	0.749879i	$-0.269888\pi$
$13$	−32786.7	−	32786.7i	−0.0883042	−	0.0883042i	−0.749879	+	0.661575i	$0.769888\pi$
$14$	15520.4	−	11018.9i	0.0288578	−	0.0204879i
$15$		−	295994.i		−	0.389786i
$16$	−820543.	−	652856.i	−0.782530	−	0.622612i
$17$	−591643.			−0.416692			−0.208346	−	0.978055i	$-0.566808\pi$
$17$	−591643.			−0.416692			−0.208346	+	0.978055i	$0.566808\pi$
$18$	86592.6	+	121968.i	0.0458266	+	0.0645482i
$19$	1.87986e6	−	1.87986e6i	0.759204	−	0.759204i	−0.216973	−	0.976178i	$-0.569618\pi$
$19$	1.87986e6	−	1.87986e6i	0.759204	−	0.759204i	0.976178	+	0.216973i	$0.0696184\pi$
$20$	−564629.	−	1.17079e6i	−0.176447	−	0.365870i
$21$	98076.8	−	98076.8i	0.0240143	−	0.0240143i
$22$	132891.	+	22540.7i	0.0257859	+	0.00437376i
$23$	3.55022e6			0.551590			0.275795	−	0.961216i	$-0.411059\pi$
$23$	3.55022e6			0.551590			0.275795	+	0.961216i	$0.411059\pi$
$24$	−6.69065e6	−	3.69045e6i	−0.840257	−	0.463471i
$25$			8.15435e6i			0.835005i
$26$	−1.46286e6	−	248129.i	−0.123122	−	0.0208838i
$27$	1.05071e7	+	1.05071e7i	0.732256	+	0.732256i
$28$	200848.	−	575025.i	0.0116702	−	0.0334115i
$29$	1.92759e7	+	1.92759e7i	0.939778	+	0.939778i	0.998287	−	0.0585086i	$-0.0186345\pi$
$29$	1.92759e7	+	1.92759e7i	0.939778	+	0.939778i	−0.0585086	+	0.998287i	$0.518635\pi$
$30$	−5.48323e6	−	7.72330e6i	−0.225647	−	0.317831i
$31$			5.18621e7i			1.81152i	0.423796	+	0.905758i	$0.360697\pi$
$31$			5.18621e7i			1.81152i	−0.423796	+	0.905758i	$0.639303\pi$
$32$	−3.35042e7	−	1.83444e6i	−0.998504	−	0.0546705i
$33$	982206.			0.0250976
$34$	−1.54376e7	+	1.09601e7i	−0.339770	+	0.241223i
$35$	533892.	−	533892.i	0.0101651	−	0.0101651i
$36$	4.51888e6	+	1.57838e6i	0.0747340	+	0.0261035i
$37$	6.64716e7	−	6.64716e7i	0.958579	−	0.958579i	−0.0405970	−	0.999176i	$-0.512926\pi$
$37$	6.64716e7	−	6.64716e7i	0.958579	−	0.958579i	0.999176	+	0.0405970i	$0.0129260\pi$
$38$	1.42267e7	−	8.38750e7i	0.179551	−	1.05856i
$39$	−1.08121e7			−0.119836
$40$	−3.64213e7	−	2.00894e7i	−0.355677	−	0.196185i
$41$		−	1.67178e8i		−	1.44298i	−0.692424	−	0.721491i	$-0.743457\pi$
$41$		−	1.67178e8i		−	1.44298i	0.692424	−	0.721491i	$-0.256543\pi$
$42$	742241.	−	4.37595e6i	0.00567935	−	0.0334831i
$43$	−3.64240e7	−	3.64240e7i	−0.247768	−	0.247768i	0.572286	−	0.820054i	$-0.306057\pi$
$43$	−3.64240e7	−	3.64240e7i	−0.247768	−	0.247768i	−0.820054	+	0.572286i	$0.806057\pi$
$44$	3.88505e6	−	1.87363e6i	0.0235577	−	0.0113611i
$45$	4.19563e6	+	4.19563e6i	0.0227371	+	0.0227371i
$46$	9.26351e7	−	6.57672e7i	0.449766	−	0.319316i
$47$			2.54335e8i			1.10896i	0.832196	+	0.554481i	$0.187083\pi$
$47$			2.54335e8i			1.10896i	−0.832196	+	0.554481i	$0.812917\pi$
$48$	−2.42942e8	+	2.76490e7i	−0.953448	+	0.108511i
$49$	−2.82121e8			−0.998747
$50$	1.51058e8	+	2.12769e8i	0.483385	+	0.680862i
$51$	−9.75534e7	+	9.75534e7i	−0.282743	+	0.282743i
$52$	−4.27667e7	+	2.06249e7i	−0.112484	+	0.0542470i
$53$	4.68378e7	−	4.68378e7i	0.112000	−	0.112000i	−0.648886	−	0.760886i	$-0.724765\pi$
$53$	4.68378e7	−	4.68378e7i	0.112000	−	0.112000i	0.760886	+	0.648886i	$0.224765\pi$
$54$	4.68800e8	+	7.95171e7i	1.02098	+	0.173178i
$55$	5.34675e6			0.0106237
$56$	−5.41154e6	−	1.87247e7i	−0.00982610	−	0.0339996i
$57$		−	6.19926e8i		−	1.03030i
$58$	8.60045e8	+	1.45879e8i	1.31033	+	0.222256i
$59$	1.66425e8	+	1.66425e8i	0.232787	+	0.232787i	0.813855	−	0.581068i	$-0.197365\pi$
$59$	1.66425e8	+	1.66425e8i	0.232787	+	0.232787i	−0.581068	+	0.813855i	$0.697365\pi$
$60$	−2.86145e8	−	9.99464e7i	−0.367985	−	0.128532i
$61$	−5.92082e8	−	5.92082e8i	−0.701024	−	0.701024i	0.263606	−	0.964630i	$-0.415088\pi$
$61$	−5.92082e8	−	5.92082e8i	−0.701024	−	0.701024i	−0.964630	+	0.263606i	$0.915088\pi$
$62$	9.60736e8	+	1.35323e9i	1.04869	+	1.47711i
$63$			2.78042e6i			0.00280161i
$64$	−9.08201e8	+	5.72794e8i	−0.845828	+	0.533456i
$65$	−5.88570e7			−0.0507261
$66$	2.56285e7	−	1.81952e7i	0.0204646	−	0.0145290i
$67$	−1.32368e9	+	1.32368e9i	−0.980414	+	0.980414i	−0.999812	−	0.0193975i	$-0.993825\pi$
$67$	−1.32368e9	+	1.32368e9i	−0.980414	+	0.980414i	0.0193975	+	0.999812i	$0.493825\pi$
$68$	−1.99776e8	+	5.71957e8i	−0.137404	+	0.393386i
$69$	5.85381e8	−	5.85381e8i	0.374277	−	0.374277i
$70$	4.04047e6	−	2.38209e7i	0.00240404	−	0.0141732i
$71$	2.48493e8			0.137728			0.0688642	−	0.997626i	$-0.478062\pi$
$71$	2.48493e8			0.137728			0.0688642	+	0.997626i	$0.478062\pi$
$72$	1.47149e8	−	4.25270e7i	0.0760493	−	0.0219787i
$73$		−	1.98224e9i		−	0.956184i	−0.878310	−	0.478092i	$-0.841329\pi$
$73$		−	1.98224e9i		−	0.956184i	0.878310	−	0.478092i	$-0.158671\pi$
$74$	5.03054e8	−	2.96580e9i	0.226702	−	1.33654i
$75$	1.34454e9	+	1.34454e9i	0.566586	+	0.566586i
$76$	−1.18255e9	−	2.45208e9i	−0.466393	−	0.967088i
$77$	1.77163e6	+	1.77163e6i	0.000654515	+	0.000654515i
$78$	−2.82118e8	+	2.00293e8i	−0.0977143	+	0.0693732i
$79$		−	7.20756e8i		−	0.234235i	−0.993118	−	0.117118i	$-0.962635\pi$
$79$		−	7.20756e8i		−	0.234235i	0.993118	−	0.117118i	$-0.0373655\pi$
$80$	−1.32248e9	+	1.50511e8i	−0.403590	+	0.0459322i
$81$	3.18891e9			0.914572
$82$	−3.09695e9	−	4.36214e9i	−0.835342	−	1.17661i
$83$	−3.72085e9	+	3.72085e9i	−0.944608	+	0.944608i	−0.998544	−	0.0539365i	$-0.982823\pi$
$83$	−3.72085e9	+	3.72085e9i	−0.944608	+	0.944608i	0.0539365	+	0.998544i	$0.482823\pi$
$84$	−6.16964e7	−	1.27930e8i	−0.0147524	−	0.0305898i
$85$	−5.31043e8	+	5.31043e8i	−0.119684	+	0.119684i
$86$	−1.62515e9	−	2.75655e8i	−0.345463	−	0.0585969i
$87$	6.35665e9			1.27536
$88$	6.66632e7	−	1.20858e8i	0.0126320	−	0.0229014i
$89$		−	1.51157e9i		−	0.270694i	−0.990798	−	0.135347i	$-0.956785\pi$
$89$		−	1.51157e9i		−	0.270694i	0.990798	−	0.135347i	$-0.0432150\pi$
$90$	1.87199e8	+	3.17523e7i	0.0317022	+	0.00537728i
$91$	−1.95021e7	−	1.95021e7i	−0.00312518	−	0.00312518i
$92$	1.19878e9	−	3.43209e9i	0.181887	−	0.520739i
$93$	8.55132e9	+	8.55132e9i	1.22919	+	1.22919i
$94$	4.71150e9	+	6.63630e9i	0.641978	+	0.904246i
$95$		−	3.37463e9i		−	0.436122i
$96$	−5.82684e9	+	5.22190e9i	−0.714623	+	0.640431i
$97$	−7.26855e9			−0.846427			−0.423213	−	0.906030i	$-0.639098\pi$
$97$	−7.26855e9			−0.846427			−0.423213	+	0.906030i	$0.639098\pi$
$98$	−7.36133e9	+	5.22624e9i	−0.814377	+	0.578175i
$99$	−1.39225e7	+	1.39225e7i	−0.00146400	+	0.00146400i
$100$	7.88302e9	+	2.75343e9i	0.788302	+	0.275343i
$101$	−8.20815e9	+	8.20815e9i	−0.780977	+	0.780977i	−0.979996	−	0.199019i	$-0.936225\pi$
$101$	−8.20815e9	+	8.20815e9i	−0.780977	+	0.780977i	0.199019	+	0.979996i	$0.436225\pi$
$102$	−7.38280e8	+	4.35260e9i	−0.0668683	+	0.394228i
$103$	1.02559e10			0.884679			0.442339	−	0.896848i	$-0.354149\pi$
$103$	1.02559e10			0.884679			0.442339	+	0.896848i	$0.354149\pi$
$104$	−7.33828e8	+	1.33041e9i	−0.0603154	+	0.109350i
$105$		−	1.76062e8i		−	0.0137949i
$106$	3.54467e8	−	2.08979e9i	0.0264878	−	0.156161i
$107$	−1.17081e10	−	1.17081e10i	−0.834771	−	0.834771i	0.153394	−	0.988165i	$-0.450980\pi$
$107$	−1.17081e10	−	1.17081e10i	−0.834771	−	0.834771i	−0.988165	+	0.153394i	$0.950980\pi$
$108$	1.37053e10	−	6.60961e9i	0.932761	−	0.449839i
$109$	1.41157e10	+	1.41157e10i	0.917424	+	0.917424i	0.996841	−	0.0794177i	$-0.0253061\pi$
$109$	1.41157e10	+	1.41157e10i	0.917424	+	0.917424i	−0.0794177	+	0.996841i	$0.525306\pi$
$110$	1.39511e8	−	9.90474e7i	0.00866256	−	0.00615006i
$111$		−	2.19204e10i		−	1.30087i
$112$	−4.88073e8	−	3.88330e8i	−0.0276945	−	0.0220349i
$113$	−3.09464e10			−1.67964			−0.839822	−	0.542862i	$-0.817341\pi$
$113$	−3.09464e10			−1.67964			−0.839822	+	0.542862i	$0.817341\pi$
$114$	−1.14840e10	−	1.61756e10i	−0.596443	−	0.840108i
$115$	3.18658e9	−	3.18658e9i	0.158430	−	0.158430i
$116$	2.51433e10	−	1.21258e10i	1.19711	−	0.577323i
$117$	1.53259e8	−	1.53259e8i	0.00699030	−	0.00699030i
$118$	7.42549e9	+	1.25950e9i	0.324575	+	0.0550539i
$119$	−3.51919e8			−0.0147471
$120$	−9.31780e9	+	2.69290e9i	−0.374461	+	0.108222i
$121$		−	2.59197e10i		−	0.999316i
$122$	−2.64173e10	−	4.48085e9i	−0.977437	−	0.165791i
$123$	−2.75653e10	−	2.75653e10i	−0.979124	−	0.979124i
$124$	5.01365e10	+	1.75120e10i	1.71019	+	0.597346i
$125$	1.60845e10	+	1.60845e10i	0.527056	+	0.527056i
$126$	5.15067e7	+	7.25488e7i	0.00162185	+	0.00228443i
$127$		−	2.04898e10i		−	0.620183i	−0.950707	−	0.310091i	$-0.899640\pi$
$127$		−	2.04898e10i		−	0.620183i	0.950707	−	0.310091i	$-0.100360\pi$
$128$	−1.30866e10	+	3.17700e10i	−0.380869	+	0.924629i
$129$	−1.20116e10			−0.336242
$130$	−1.53574e9	+	1.09031e9i	−0.0413620	+	0.0293653i
$131$	−3.06708e10	+	3.06708e10i	−0.795002	+	0.795002i	−0.982303	−	0.187300i	$-0.940026\pi$
$131$	−3.06708e10	+	3.06708e10i	−0.795002	+	0.795002i	0.187300	+	0.982303i	$0.440026\pi$
$132$	3.31655e8	−	9.49524e8i	0.00827594	−	0.0236939i
$133$	1.11818e9	−	1.11818e9i	0.0268690	−	0.0268690i
$134$	−1.00176e10	+	5.90595e10i	−0.231867	+	1.36699i
$135$	1.88617e10			0.420642
$136$	5.38267e9	+	1.86247e10i	0.115692	+	0.400309i
$137$		−	1.69311e10i		−	0.350818i	−0.984496	−	0.175409i	$-0.943875\pi$
$137$		−	1.69311e10i		−	0.350818i	0.984496	−	0.175409i	$-0.0561248\pi$
$138$	4.43014e9	−	2.61183e10i	0.0885160	−	0.521854i
$139$	2.77232e10	+	2.77232e10i	0.534281	+	0.534281i	0.921844	−	0.387562i	$-0.126683\pi$
$139$	2.77232e10	+	2.77232e10i	0.534281	+	0.534281i	−0.387562	+	0.921844i	$0.626683\pi$
$140$	−3.35851e8	−	6.96403e8i	−0.00624463	−	0.0129485i
$141$	4.19362e10	+	4.19362e10i	0.752477	+	0.752477i
$142$	6.48388e9	−	4.60329e9i	0.112303	−	0.0797309i
$143$		−	1.95307e8i		−	0.00326616i
$144$	3.05172e9	−	3.83555e9i	0.0492870	−	0.0619463i
$145$	3.46031e10			0.539853
$146$	−3.67206e10	−	5.17220e10i	−0.553535	−	0.779671i
$147$	−4.65178e10	+	4.65178e10i	−0.677692	+	0.677692i
$148$	−4.18148e10	−	8.67049e10i	−0.588873	−	1.22105i
$149$	−3.61541e10	+	3.61541e10i	−0.492296	+	0.492296i	−0.909029	−	0.416733i	$-0.863175\pi$
$149$	−3.61541e10	+	3.61541e10i	−0.492296	+	0.492296i	0.416733	+	0.909029i	$0.363175\pi$
$150$	5.99899e10	+	1.01754e10i	0.789990	+	0.133997i
$151$	1.31299e11			1.67255			0.836273	−	0.548314i	$-0.184730\pi$
$151$	1.31299e11			1.67255			0.836273	+	0.548314i	$0.184730\pi$
$152$	−7.62803e10	−	4.20749e10i	−0.940144	−	0.518567i
$153$		−	2.76558e9i		−	0.0329860i
$154$	7.90458e7	+	1.34076e7i	0.000912589	+	0.000154792i
$155$	4.65501e10	+	4.65501e10i	0.520309	+	0.520309i
$156$	−3.65086e9	+	1.04524e10i	−0.0395160	+	0.113134i
$157$	−5.17940e8	−	5.17940e8i	−0.00542976	−	0.00542976i	0.704387	−	0.709816i	$-0.251222\pi$
$157$	−5.17940e8	−	5.17940e8i	−0.00542976	−	0.00542976i	−0.709816	+	0.704387i	$0.751222\pi$
$158$	−1.33519e10	−	1.88065e10i	−0.135599	−	0.190995i
$159$		−	1.54458e10i		−	0.151993i
$160$	−3.17191e10	+	2.84260e10i	−0.302496	+	0.271091i
$161$	2.11173e9			0.0195213
$162$	8.32076e10	−	5.90740e10i	0.745741	−	0.529446i
$163$	−4.83970e10	+	4.83970e10i	−0.420611	+	0.420611i	−0.885414	−	0.464803i	$-0.846125\pi$
$163$	−4.83970e10	+	4.83970e10i	−0.420611	+	0.420611i	0.464803	+	0.885414i	$0.346125\pi$
$164$	−1.61616e11	−	5.64501e10i	−1.36227	−	0.475823i
$165$	8.81602e8	−	8.81602e8i	0.00720863	−	0.00720863i
$166$	−2.81592e10	+	1.66015e11i	−0.223398	+	1.31707i
$167$	−9.49901e9			−0.0731301			−0.0365651	−	0.999331i	$-0.511642\pi$
$167$	−9.49901e9			−0.0731301			−0.0365651	+	0.999331i	$0.511642\pi$
$168$	−3.97971e9	−	2.19514e9i	−0.0297376	−	0.0164027i
$169$		−	1.35709e11i		−	0.984405i
$170$	−4.01891e9	+	2.36938e10i	−0.0283050	+	0.166875i
$171$	8.78726e9	+	8.78726e9i	0.0600998	+	0.0600998i
$172$	−4.75111e10	+	2.29130e10i	−0.315612	+	0.152209i
$173$	−1.43674e11	−	1.43674e11i	−0.927145	−	0.927145i	0.0703756	−	0.997521i	$-0.477580\pi$
$173$	−1.43674e11	−	1.43674e11i	−0.927145	−	0.927145i	−0.997521	+	0.0703756i	$0.977580\pi$
$174$	1.65863e11	−	1.17756e11i	1.03993	−	0.738305i
$175$			4.85034e9i			0.0295517i
$176$	−4.99444e8	−	4.38844e9i	−0.00295749	−	0.0259864i
$177$	5.48823e10			0.315912
$178$	−2.80016e10	−	3.94411e10i	−0.156705	−	0.220724i
$179$	−8.07599e9	+	8.07599e9i	−0.0439472	+	0.0439472i	−0.728739	−	0.684792i	$-0.759893\pi$
$179$	−8.07599e9	+	8.07599e9i	−0.0439472	+	0.0439472i	0.684792	+	0.728739i	$0.259893\pi$
$180$	5.47273e9	−	2.63931e9i	0.0289629	−	0.0139678i
$181$	1.85974e11	−	1.85974e11i	0.957324	−	0.957324i	−0.0418019	−	0.999126i	$-0.513310\pi$
$181$	1.85974e11	−	1.85974e11i	0.957324	−	0.957324i	0.999126	+	0.0418019i	$0.0133098\pi$
$182$	−8.70136e8	−	1.47591e8i	−0.00435743	−	0.000739100i
$183$	−1.95252e11			−0.951348
$184$	−3.22993e10	−	1.11760e11i	−0.153146	−	0.529904i
$185$		−	1.19326e11i		−	0.550652i
$186$	3.81539e11	+	6.47160e10i	1.71386	+	0.290701i
$187$	−1.76218e9	−	1.76218e9i	−0.00770622	−	0.00770622i
$188$	2.45872e11	+	8.58797e10i	1.04694	+	0.365680i
$189$	6.24979e9	+	6.24979e9i	0.0259153	+	0.0259153i
$190$	−6.25144e10	−	8.80534e10i	−0.252471	−	0.355614i
$191$			3.87444e11i			1.52420i	0.647459	+	0.762101i	$0.275832\pi$
$191$			3.87444e11i			1.52420i	−0.647459	+	0.762101i	$0.724168\pi$
$192$	−5.53038e10	+	2.44195e11i	−0.211957	+	0.935902i
$193$	−1.33306e11			−0.497810			−0.248905	−	0.968528i	$-0.580071\pi$
$193$	−1.33306e11			−0.497810			−0.248905	+	0.968528i	$0.580071\pi$
$194$	−1.89657e11	+	1.34649e11i	−0.690175	+	0.489996i
$195$	−9.70468e9	+	9.70468e9i	−0.0344198	+	0.0344198i
$196$	−9.52621e10	+	2.72734e11i	−0.329337	+	0.942886i
$197$	−3.38045e10	+	3.38045e10i	−0.113932	+	0.113932i	−0.761774	−	0.647843i	$-0.775671\pi$
$197$	−3.38045e10	+	3.38045e10i	−0.113932	+	0.113932i	0.647843	+	0.761774i	$0.275671\pi$
$198$	−1.05365e8	+	6.21187e8i	−0.000346234	+	0.00204125i
$199$	−3.03439e11			−0.972313			−0.486157	−	0.873872i	$-0.661602\pi$
$199$	−3.03439e11			−0.972313			−0.486157	+	0.873872i	$0.661602\pi$
$200$	2.56696e11	−	7.41869e10i	0.802176	−	0.231834i
$201$			4.36512e11i			1.33050i
$202$	−6.21189e10	+	3.66227e11i	−0.184700	+	1.08892i
$203$	1.14656e10	+	1.14656e10i	0.0332597	+	0.0332597i
$204$	6.13672e10	+	1.27248e11i	0.173694	+	0.360163i
$205$	−1.50055e11	−	1.50055e11i	−0.414458	−	0.414458i
$206$	2.67603e11	−	1.89988e11i	0.721366	−	0.512141i
$207$			1.65952e10i			0.0436648i
$208$	5.49788e9	+	4.83080e10i	0.0141214	+	0.124080i
$209$	1.11982e10			0.0280812
$210$	−3.26152e9	−	4.59395e9i	−0.00798589	−	0.0112484i
$211$	5.80393e11	−	5.80393e11i	1.38775	−	1.38775i	0.557713	−	0.830034i	$-0.311679\pi$
$211$	5.80393e11	−	5.80393e11i	1.38775	−	1.38775i	0.830034	−	0.557713i	$-0.188321\pi$
$212$	−2.94639e10	−	6.10948e10i	−0.0688036	−	0.142667i
$213$	4.09730e10	−	4.09730e10i	0.0934544	−	0.0934544i
$214$	−5.22387e11	−	8.86063e10i	−1.16392	−	0.197422i
$215$	−6.53865e10			−0.142330
$216$	2.35168e11	−	4.26351e11i	0.500161	−	0.906774i
$217$			3.08485e10i			0.0641114i
$218$	6.29808e11	+	1.06827e11i	1.27916	+	0.216969i
$219$	−3.26843e11	−	3.26843e11i	−0.648811	−	0.648811i
$220$	1.80540e9	−	5.16884e9i	0.00350316	−	0.0100295i
$221$	1.93980e10	+	1.93980e10i	0.0367957	+	0.0367957i
$222$	−4.06072e11	−	5.71965e11i	−0.753075	−	1.06073i
$223$		−	2.56973e11i		−	0.465975i	−0.972480	−	0.232987i	$-0.925150\pi$
$223$		−	2.56973e11i		−	0.465975i	0.972480	−	0.232987i	$-0.0748501\pi$
$224$	−1.99289e10	−	1.09115e9i	−0.0353381	−	0.00193484i
$225$	−3.81168e10			−0.0661004
$226$	−8.07476e11	+	5.73275e11i	−1.36958	+	0.972346i
$227$	5.97754e11	−	5.97754e11i	0.991729	−	0.991729i	−0.00823681	−	0.999966i	$-0.502622\pi$
$227$	5.97754e11	−	5.97754e11i	0.991729	−	0.991729i	0.999966	+	0.00823681i	$0.00262189\pi$
$228$	−5.99298e11	−	2.09326e11i	−0.972677	−	0.339742i
$229$	−2.29479e11	+	2.29479e11i	−0.364389	+	0.364389i	−0.865426	−	0.501037i	$-0.832952\pi$
$229$	−2.29479e11	+	2.29479e11i	−0.364389	+	0.364389i	0.501037	+	0.865426i	$0.332952\pi$
$230$	2.41159e10	−	1.42178e11i	0.0374684	−	0.220898i
$231$	5.84233e8			0.000888231
$232$	4.31431e11	−	7.82170e11i	0.641906	−	1.16375i
$233$			1.10233e12i			1.60521i	0.596511	+	0.802605i	$0.296553\pi$
$233$			1.10233e12i			1.60521i	−0.596511	+	0.802605i	$0.703447\pi$
$234$	1.15986e9	−	6.83803e9i	0.00165320	−	0.00974657i
$235$	2.28284e11	+	2.28284e11i	0.318520	+	0.318520i
$236$	2.17083e11	−	1.04692e11i	0.296529	−	0.143006i
$237$	−1.18842e11	−	1.18842e11i	−0.158939	−	0.158939i
$238$	−9.18254e9	+	6.51923e9i	−0.0120248	+	0.00853712i
$239$			5.03570e10i			0.0645759i	0.999479	+	0.0322879i	$0.0102794\pi$
$239$			5.03570e10i			0.0645759i	−0.999479	+	0.0322879i	$0.989721\pi$
$240$	−1.93242e11	+	2.42876e11i	−0.242686	+	0.305020i
$241$	1.21541e12			1.49499			0.747496	−	0.664266i	$-0.231256\pi$
$241$	1.21541e12			1.49499			0.747496	+	0.664266i	$0.231256\pi$
$242$	−4.80157e11	−	6.76316e11i	−0.578504	−	0.814841i
$243$	−9.46261e10	+	9.46261e10i	−0.111681	+	0.111681i
$244$	−7.72306e11	+	3.72457e11i	−0.892977	+	0.430652i
$245$	−2.53225e11	+	2.53225e11i	−0.286864	+	0.286864i
$246$	−1.22990e12	−	2.08613e11i	−1.36519	−	0.231561i
$247$	−1.23269e11			−0.134082
$248$	1.63260e12	−	4.71833e11i	1.74029	−	0.502956i
$249$			1.22703e12i			1.28191i
$250$	7.17650e11	+	1.21727e11i	0.734874	+	0.124648i
$251$	5.81126e11	+	5.81126e11i	0.583313	+	0.583313i	0.935812	−	0.352499i	$-0.114668\pi$
$251$	5.81126e11	+	5.81126e11i	0.583313	+	0.583313i	−0.352499	+	0.935812i	$0.614668\pi$
$252$	2.68790e9	+	9.38846e8i	0.00264491	+	0.000923830i
$253$	1.05741e10	+	1.05741e10i	0.0102010	+	0.0102010i
$254$	−3.79570e11	−	5.34636e11i	−0.359024	−	0.505696i
$255$			1.75123e11i			0.162421i
$256$	2.47069e11	+	1.07139e12i	0.224708	+	0.974426i
$257$	5.51092e11			0.491540			0.245770	−	0.969328i	$-0.420959\pi$
$257$	5.51092e11			0.491540			0.245770	+	0.969328i	$0.420959\pi$
$258$	−3.13416e11	+	2.22513e11i	−0.274172	+	0.194651i
$259$	3.95384e10	−	3.95384e10i	0.0339251	−	0.0339251i
$260$	−1.98739e10	+	5.68986e10i	−0.0167269	+	0.0478889i
$261$	−9.01037e10	+	9.01037e10i	−0.0743943	+	0.0743943i
$262$	−2.32115e11	+	1.36846e12i	−0.188017	+	1.10847i
$263$	−9.77100e11			−0.776534			−0.388267	−	0.921547i	$-0.626926\pi$
$263$	−9.77100e11			−0.776534			−0.388267	+	0.921547i	$0.626926\pi$
$264$	−8.93595e9	−	3.09196e10i	−0.00696821	−	0.0241109i
$265$		−	8.40808e10i		−	0.0643380i
$266$	8.46230e9	−	4.98902e10i	0.00635448	−	0.0374634i
$267$	−2.49237e11	−	2.49237e11i	−0.183677	−	0.183677i
$268$	8.32679e11	+	1.72660e12i	0.602287	+	1.24887i
$269$	−1.14482e12	−	1.14482e12i	−0.812783	−	0.812783i	0.172268	−	0.985050i	$-0.444891\pi$
$269$	−1.14482e12	−	1.14482e12i	−0.812783	−	0.812783i	−0.985050	+	0.172268i	$0.944891\pi$
$270$	4.92155e11	−	3.49410e11i	0.342991	−	0.243510i
$271$		−	9.42778e11i		−	0.645005i	−0.946569	−	0.322502i	$-0.895476\pi$
$271$		−	9.42778e11i		−	0.645005i	0.946569	−	0.322502i	$-0.104524\pi$
$272$	4.85468e11	+	3.86258e11i	0.326074	+	0.259438i
$273$	−6.43124e9			−0.00424113
$274$	−3.13645e11	−	4.41778e11i	−0.203088	−	0.286056i
$275$	−2.42873e10	+	2.42873e10i	−0.0154424	+	0.0154424i
$276$	−3.68241e11	−	7.63565e11i	−0.229925	−	0.476761i
$277$	1.26656e12	−	1.26656e12i	0.776654	−	0.776654i	−0.202607	−	0.979260i	$-0.564941\pi$
$277$	1.26656e12	−	1.26656e12i	0.776654	−	0.776654i	0.979260	+	0.202607i	$0.0649413\pi$
$278$	1.23694e12	+	2.09808e11i	0.744948	+	0.126357i
$279$	−2.42425e11			−0.143402
$280$	−2.16640e10	−	1.19495e10i	−0.0125878	−	0.00694319i
$281$		−	2.14730e12i		−	1.22563i	−0.790225	−	0.612817i	$-0.790036\pi$
$281$		−	2.14730e12i		−	1.22563i	0.790225	−	0.612817i	$-0.209964\pi$
$282$	1.87109e12	+	3.17371e11i	1.04918	+	0.177960i
$283$	−3.69965e11	−	3.69965e11i	−0.203811	−	0.203811i	0.597820	−	0.801631i	$-0.296034\pi$
$283$	−3.69965e11	−	3.69965e11i	−0.203811	−	0.203811i	−0.801631	+	0.597820i	$0.796034\pi$
$284$	8.39072e10	−	2.40225e11i	0.0454159	−	0.130025i
$285$	−5.56429e11	−	5.56429e11i	−0.295927	−	0.295927i
$286$	−3.61802e9	−	5.09610e9i	−0.00189078	−	0.00266322i
$287$		−	9.94405e10i		−	0.0510686i
$288$	8.57491e9	−	1.56613e11i	0.00432780	−	0.0790432i
$289$	−1.66595e12			−0.826368
$290$	9.02891e11	−	6.41016e11i	0.440195	−	0.312521i
$291$	−1.19848e12	+	1.19848e12i	−0.574336	+	0.574336i
$292$	−1.91628e12	−	6.69330e11i	−0.902703	−	0.315301i
$293$	−1.42404e12	+	1.42404e12i	−0.659455	+	0.659455i	−0.955251	−	0.295796i	$-0.904415\pi$
$293$	−1.42404e12	+	1.42404e12i	−0.659455	+	0.659455i	0.295796	+	0.955251i	$0.404415\pi$
$294$	−3.52045e11	+	2.07551e12i	−0.160273	+	0.944905i
$295$	2.98758e11			0.133724
$296$	−2.69725e12	−	1.48776e12i	−1.18703	−	0.654748i
$297$			6.25895e10i			0.0270844i
$298$	−2.73613e11	+	1.61311e12i	−0.116427	+	0.686407i
$299$	−1.16400e11	−	1.16400e11i	−0.0487077	−	0.0487077i
$300$	1.75380e12	−	8.45797e11i	0.721728	−	0.348065i
$301$	−2.16656e10	−	2.16656e10i	−0.00876877	−	0.00876877i
$302$	3.42596e12	−	2.43229e12i	1.36379	−	0.968237i
$303$			2.70681e12i			1.05985i
$304$	−2.76979e12	+	3.15227e11i	−1.06679	+	0.121410i
$305$	−1.06287e12			−0.402701
$306$	−5.12319e10	−	7.21617e10i	−0.0190956	−	0.0268967i
$307$	3.93970e11	−	3.93970e11i	0.144468	−	0.144468i	−0.631174	−	0.775642i	$-0.717426\pi$
$307$	3.93970e11	−	3.93970e11i	0.144468	−	0.144468i	0.775642	+	0.631174i	$0.217426\pi$
$308$	2.31090e9	−	1.11447e9i	0.000833733	−	0.000402081i
$309$	1.69104e12	−	1.69104e12i	0.600292	−	0.600292i
$310$	2.07695e12	+	3.52289e11i	0.725467	+	0.123052i
$311$	1.60514e12			0.551711			0.275856	−	0.961199i	$-0.411039\pi$
$311$	1.60514e12			0.551711			0.275856	+	0.961199i	$0.411039\pi$
$312$	9.83670e10	+	3.40363e11i	0.0332718	+	0.115125i
$313$		−	5.41434e12i		−	1.80229i	−0.433520	−	0.901144i	$-0.642729\pi$
$313$		−	5.41434e12i		−	1.80229i	0.433520	−	0.901144i	$-0.357271\pi$
$314$	−2.31092e10	−	3.91974e9i	−0.00757071	−	0.00128413i
$315$	2.49563e9	+	2.49563e9i	0.000804688	+	0.000804688i
$316$	−6.96773e11	−	2.43373e11i	−0.221134	−	0.0772391i
$317$	4.19055e12	+	4.19055e12i	1.30911	+	1.30911i	0.922061	+	0.387044i	$0.126504\pi$
$317$	4.19055e12	+	4.19055e12i	1.30911	+	1.30911i	0.387044	+	0.922061i	$0.373496\pi$
$318$	−2.86130e11	−	4.03023e11i	−0.0879889	−	0.123935i
$319$			1.14825e11i			0.0347602i
$320$	−3.01052e11	+	1.32930e12i	−0.0897205	+	0.396163i
$321$	−3.86100e12			−1.13285
$322$	5.51009e10	−	3.91194e10i	0.0159177	−	0.0113009i
$323$	−1.11221e12	+	1.11221e12i	−0.316354	+	0.316354i
$324$	1.07678e12	−	3.08281e12i	0.301580	−	0.863418i
$325$	2.67355e11	−	2.67355e11i	0.0737345	−	0.0737345i
$326$	−3.66267e11	+	2.15936e12i	−0.0994740	+	0.586458i
$327$	4.65495e12			1.24502
$328$	−5.26272e12	+	1.52096e12i	−1.38625	+	0.400635i
$329$			1.51283e11i			0.0392473i
$330$	6.67192e9	−	3.93349e10i	0.00170483	−	0.0100510i
$331$	8.37494e11	+	8.37494e11i	0.210786	+	0.210786i	0.804601	−	0.593815i	$-0.202379\pi$
$331$	8.37494e11	+	8.37494e11i	0.210786	+	0.210786i	−0.593815	+	0.804601i	$0.702379\pi$
$332$	2.34065e12	+	4.85344e12i	0.580290	+	1.20326i
$333$	3.10716e11	+	3.10716e11i	0.0758826	+	0.0758826i
$334$	−2.47855e11	+	1.75967e11i	−0.0596302	+	0.0423350i
$335$			2.37620e12i			0.563196i
$336$	−1.44506e11	+	1.64461e10i	−0.0337435	+	0.00384032i
$337$	5.67260e12			1.30507			0.652533	−	0.757760i	$-0.273706\pi$
$337$	5.67260e12			1.30507			0.652533	+	0.757760i	$0.273706\pi$
$338$	−2.51397e12	−	3.54101e12i	−0.569872	−	0.802682i
$339$	−5.10261e12	+	5.10261e12i	−1.13971	+	1.13971i
$340$	3.34059e11	+	6.92687e11i	0.0735239	+	0.152455i
$341$	−1.54469e11	+	1.54469e11i	−0.0335018	+	0.0335018i
$342$	3.92066e11	+	6.65016e10i	0.0837971	+	0.0142135i
$343$	−3.35832e11			−0.0707377
$344$	−8.15238e11	+	1.47800e12i	−0.169236	+	0.306818i
$345$		−	1.05084e12i		−	0.215002i
$346$	−6.41038e12	−	1.08732e12i	−1.29272	−	0.219268i
$347$	2.18949e12	+	2.18949e12i	0.435207	+	0.435207i	0.890395	−	0.455188i	$-0.150428\pi$
$347$	2.18949e12	+	2.18949e12i	0.435207	+	0.435207i	−0.455188	+	0.890395i	$0.650428\pi$
$348$	2.14641e12	−	6.14514e12i	0.420549	−	1.20403i
$349$	5.47135e12	+	5.47135e12i	1.05674	+	1.05674i	0.998290	+	0.0584472i	$0.0186149\pi$
$349$	5.47135e12	+	5.47135e12i	1.05674	+	1.05674i	0.0584472	+	0.998290i	$0.481385\pi$
$350$	8.98517e10	+	1.26559e11i	0.0171075	+	0.0240964i
$351$		−	6.88986e11i		−	0.129323i
$352$	−9.43268e10	−	1.05254e11i	−0.0174551	−	0.0194772i
$353$	−4.25125e12			−0.775610			−0.387805	−	0.921741i	$-0.626767\pi$
$353$	−4.25125e12			−0.775610			−0.387805	+	0.921741i	$0.626767\pi$
$354$	1.43203e12	−	1.01668e12i	0.257594	−	0.182881i
$355$	2.23041e11	−	2.23041e11i	0.0395588	−	0.0395588i
$356$	−1.46128e12	−	5.10403e11i	−0.255554	−	0.0892613i
$357$	−5.80264e10	+	5.80264e10i	−0.0100066	+	0.0100066i
$358$	−6.11187e10	+	3.60331e11i	−0.0103934	+	0.0612755i
$359$	5.67158e11			0.0951113			0.0475556	−	0.998869i	$-0.484857\pi$
$359$	5.67158e11			0.0951113			0.0475556	+	0.998869i	$0.484857\pi$
$360$	9.39059e10	−	1.70248e11i	0.0155303	−	0.0281559i
$361$		−	9.36718e11i		−	0.152782i
$362$	1.40744e12	−	8.29770e12i	0.226406	−	1.33480i
$363$	−4.27378e12	−	4.27378e12i	−0.678078	−	0.678078i
$364$	−2.54383e10	+	1.22680e10i	−0.00398091	+	0.00191985i
$365$	−1.77920e12	−	1.77920e12i	−0.274638	−	0.274638i
$366$	−5.09466e12	+	3.61700e12i	−0.775728	+	0.550735i
$367$		−	1.10309e13i		−	1.65684i	−0.560105	−	0.828421i	$-0.689239\pi$
$367$		−	1.10309e13i		−	1.65684i	0.560105	−	0.828421i	$-0.310761\pi$
$368$	−2.91311e12	−	2.31779e12i	−0.431636	−	0.343427i
$369$	7.81461e11			0.114229
$370$	−2.21050e12	−	3.11355e12i	−0.318773	−	0.449001i
$371$	2.78599e10	−	2.78599e10i	0.00396379	−	0.00396379i
$372$	1.11543e13	−	5.37932e12i	1.56576	−	0.755114i
$373$	−1.31996e12	+	1.31996e12i	−0.182817	+	0.182817i	−0.792582	−	0.609765i	$-0.791264\pi$
$373$	−1.31996e12	+	1.31996e12i	−0.182817	+	0.182817i	0.609765	+	0.792582i	$0.291264\pi$
$374$	−7.86240e10	−	1.33361e10i	−0.0107448	−	0.00182251i
$375$	5.30420e12			0.715260
$376$	8.00639e12	−	2.31390e12i	1.06536	−	0.307896i
$377$		−	1.26399e12i		−	0.165973i
$378$	2.78850e11	+	4.72981e10i	0.0361337	+	0.00612893i
$379$	−2.27051e12	−	2.27051e12i	−0.290354	−	0.290354i	0.546866	−	0.837220i	$-0.315821\pi$
$379$	−2.27051e12	−	2.27051e12i	−0.290354	−	0.290354i	−0.837220	+	0.546866i	$0.815821\pi$
$380$	−3.26234e12	−	1.13949e12i	−0.411729	−	0.143811i
$381$	−3.37848e12	−	3.37848e12i	−0.420820	−	0.420820i
$382$	7.17733e12	+	1.01095e13i	0.882360	+	1.24283i
$383$		−	1.46929e13i		−	1.78284i	−0.453173	−	0.891422i	$-0.649708\pi$
$383$		−	1.46929e13i		−	1.78284i	0.453173	−	0.891422i	$-0.350292\pi$
$384$	3.08063e12	+	7.39621e12i	0.368964	+	0.885835i
$385$	3.18033e9			0.000375984
$386$	−3.47832e12	+	2.46947e12i	−0.405914	+	0.288182i
$387$	1.70261e11	−	1.70261e11i	0.0196137	−	0.0196137i
$388$	−2.45433e12	+	7.02670e12i	−0.279109	+	0.799085i
$389$	−1.23504e13	+	1.23504e13i	−1.38654	+	1.38654i	−0.554073	+	0.832468i	$0.686927\pi$
$389$	−1.23504e13	+	1.23504e13i	−1.38654	+	1.38654i	−0.832468	+	0.554073i	$0.813073\pi$
$390$	−7.34446e10	+	4.32999e11i	−0.00814023	+	0.0479914i
$391$	−2.10046e12			−0.229843
$392$	2.56669e12	+	8.88110e12i	0.277296	+	0.959481i
$393$			1.01143e13i			1.07889i
$394$	−2.55831e11	+	1.50828e12i	−0.0269446	+	0.158855i
$395$	−6.46931e11	−	6.46931e11i	−0.0672779	−	0.0672779i
$396$	8.75811e9	+	1.81603e10i	0.000899362	+	0.00186487i
$397$	2.95797e12	+	2.95797e12i	0.299945	+	0.299945i	0.840992	−	0.541047i	$-0.181972\pi$
$397$	2.95797e12	+	2.95797e12i	0.299945	+	0.299945i	−0.541047	+	0.840992i	$0.681972\pi$
$398$	−7.91756e12	+	5.62115e12i	−0.792823	+	0.562872i
$399$		−	3.68742e11i		−	0.0364635i
$400$	5.32362e12	−	6.69099e12i	0.519885	−	0.653417i
$401$	−8.73885e12			−0.842816			−0.421408	−	0.906871i	$-0.638464\pi$
$401$	−8.73885e12			−0.842816			−0.421408	+	0.906871i	$0.638464\pi$
$402$	8.08631e12	+	1.13898e13i	0.770229	+	1.08489i
$403$	1.70039e12	−	1.70039e12i	0.159964	−	0.159964i
$404$	5.16344e12	+	1.07066e13i	0.479769	+	0.994823i
$405$	2.86228e12	−	2.86228e12i	0.262686	−	0.262686i
$406$	5.11569e11	+	8.67715e10i	0.0463740	+	0.00786587i
$407$	3.95964e11			0.0354555
$408$	3.95848e12	+	2.18343e12i	0.350128	+	0.193125i
$409$			3.28505e12i			0.287029i	0.989648	+	0.143515i	$0.0458404\pi$
$409$			3.28505e12i			0.287029i	−0.989648	+	0.143515i	$0.954160\pi$
$410$	−6.69508e12	−	1.13561e12i	−0.577878	−	0.0980187i
$411$	−2.79169e12	−	2.79169e12i	−0.238045	−	0.238045i
$412$	3.46303e12	−	9.91460e12i	0.291723	−	0.835197i
$413$	9.89926e10	+	9.89926e10i	0.00823858	+	0.00823858i
$414$	3.07423e11	+	4.33015e11i	0.0252775	+	0.0356042i
$415$			6.67947e12i			0.542627i
$416$	1.03835e12	+	1.15864e12i	0.0833445	+	0.0929998i
$417$	9.14233e12			0.725065
$418$	2.92191e11	−	2.07444e11i	0.0228973	−	0.0162562i
$419$	1.76933e12	−	1.76933e12i	0.137006	−	0.137006i	−0.635278	−	0.772284i	$-0.719114\pi$
$419$	1.76933e12	−	1.76933e12i	0.137006	−	0.137006i	0.772284	+	0.635278i	$0.219114\pi$
$420$	−1.70204e11	−	5.94498e10i	−0.0130234	−	0.00454887i
$421$	1.38246e12	−	1.38246e12i	0.104530	−	0.104530i	−0.652908	−	0.757438i	$-0.726451\pi$
$421$	1.38246e12	−	1.38246e12i	0.104530	−	0.104530i	0.757438	+	0.652908i	$0.226451\pi$
$422$	4.39239e12	−	2.58957e13i	0.328200	−	1.93493i
$423$	−1.18887e12			−0.0877872
$424$	−1.90056e12	−	1.04832e12i	−0.138693	−	0.0765004i
$425$		−	4.82446e12i		−	0.347940i
$426$	3.10082e11	−	1.82812e12i	0.0221018	−	0.130303i
$427$	−3.52180e11	−	3.52180e11i	−0.0248099	−	0.0248099i
$428$	−1.52719e13	+	7.36512e12i	−1.06335	+	0.512816i
$429$	−3.22033e10	−	3.22033e10i	−0.00221623	−	0.00221623i
$430$	−1.70611e12	+	1.21127e12i	−0.116055	+	0.0823947i
$431$			1.56710e13i			1.05369i	0.849963	+	0.526843i	$0.176624\pi$
$431$			1.56710e13i			1.05369i	−0.849963	+	0.526843i	$0.823376\pi$
$432$	−1.76189e12	−	1.54811e13i	−0.117101	−	1.02892i
$433$	1.11898e13			0.735162			0.367581	−	0.929991i	$-0.380186\pi$
$433$	1.11898e13			0.735162			0.367581	+	0.929991i	$0.380186\pi$
$434$	5.71462e11	+	8.04922e11i	0.0371141	+	0.0522763i
$435$	5.70556e12	−	5.70556e12i	0.366313	−	0.366313i
$436$	1.84124e13	−	8.87966e12i	1.16863	−	0.563591i
$437$	6.67394e12	−	6.67394e12i	0.418770	−	0.418770i
$438$	−1.45829e13	−	2.47353e12i	−0.904636	−	0.153443i
$439$	−1.97275e13			−1.20990			−0.604950	−	0.796263i	$-0.706807\pi$
$439$	−1.97275e13			−1.20990			−0.604950	+	0.796263i	$0.706807\pi$
$440$	−4.86438e10	−	1.68314e11i	−0.00294961	−	0.0102060i
$441$		−	1.31875e12i		−	0.0790624i
$442$	8.65493e11	+	1.46804e11i	0.0513041	+	0.00870212i
$443$	1.18912e13	+	1.18912e13i	0.696957	+	0.696957i	0.963753	−	0.266796i	$-0.0859651\pi$
$443$	1.18912e13	+	1.18912e13i	0.696957	+	0.696957i	−0.266796	+	0.963753i	$0.585965\pi$
$444$	−2.11911e13	−	7.40174e12i	−1.22811	−	0.428962i
$445$	−1.35675e12	−	1.35675e12i	−0.0777497	−	0.0777497i
$446$	−4.76037e12	−	6.70512e12i	−0.269753	−	0.379955i
$447$			1.19226e13i			0.668087i
$448$	−5.40213e11	+	3.40708e11i	−0.0299347	+	0.0188796i
$449$	−1.18979e13			−0.651985			−0.325992	−	0.945372i	$-0.605698\pi$
$449$	−1.18979e13			−0.651985			−0.325992	+	0.945372i	$0.605698\pi$
$450$	−9.94572e11	+	7.06106e11i	−0.0538981	+	0.0382655i
$451$	4.97932e11	−	4.97932e11i	0.0266862	−	0.0266862i
$452$	−1.04495e13	+	2.99166e13i	−0.553862	+	1.58570i
$453$	2.16494e13	−	2.16494e13i	1.13489	−	1.13489i
$454$	4.52377e12	−	2.66703e13i	0.234543	−	1.38277i
$455$	−3.50091e10			−0.00179525
$456$	−1.95151e13	+	5.63998e12i	−0.989797	+	0.286058i
$457$			1.11981e13i			0.561775i	0.959741	+	0.280888i	$0.0906288\pi$
$457$			1.11981e13i			0.561775i	−0.959741	+	0.280888i	$0.909371\pi$
$458$	−1.73668e12	+	1.02388e13i	−0.0861774	+	0.508067i
$459$	−6.21644e12	−	6.21644e12i	−0.305125	−	0.305125i
$460$	−2.00456e12	−	4.15655e12i	−0.0973263	−	0.201810i
$461$	−1.84984e13	−	1.84984e13i	−0.888444	−	0.888444i	0.105930	−	0.994374i	$-0.466218\pi$
$461$	−1.84984e13	−	1.84984e13i	−0.888444	−	0.888444i	−0.994374	+	0.105930i	$0.966218\pi$
$462$	1.52442e10	−	1.08228e10i	0.000724263	−	0.000514197i
$463$			2.55828e13i			1.20238i	0.799105	+	0.601191i	$0.205307\pi$
$463$			2.55828e13i			1.20238i	−0.799105	+	0.601191i	$0.794693\pi$
$464$	−3.23231e12	−	2.84011e13i	−0.150287	−	1.32052i
$465$	1.53509e13			0.706104
$466$	2.04204e13	+	2.87628e13i	0.929256	+	1.30889i
$467$	2.52205e13	−	2.52205e13i	1.13545	−	1.13545i	0.146199	−	0.989255i	$-0.453296\pi$
$467$	2.52205e13	−	2.52205e13i	1.13545	−	1.13545i	0.989255	−	0.146199i	$-0.0467038\pi$
$468$	−9.64093e10	−	1.99909e11i	−0.00429428	−	0.00890438i
$469$	−7.87348e11	+	7.87348e11i	−0.0346979	+	0.0346979i
$470$	1.01855e13	+	1.72764e12i	0.444112	+	0.0753295i
$471$	−1.70802e11			−0.00736864
$472$	3.72491e12	−	6.75313e12i	0.159003	−	0.288267i
$473$		−	2.16974e11i		−	0.00916436i
$474$	−5.30245e12	−	8.99393e11i	−0.221608	−	0.0375888i
$475$	1.53291e13	+	1.53291e13i	0.633940	+	0.633940i
$476$	−1.18830e11	+	3.40209e11i	−0.00486287	+	0.0139223i
$477$	2.18939e11	+	2.18939e11i	0.00886609	+	0.00886609i
$478$	9.32854e11	+	1.31395e12i	0.0373830	+	0.0526551i
$479$			1.09655e13i			0.434862i	0.976076	+	0.217431i	$0.0697677\pi$
$479$			1.09655e13i			0.434862i	−0.976076	+	0.217431i	$0.930232\pi$
$480$	−5.42982e11	+	9.91705e12i	−0.0213098	+	0.389203i
$481$	−4.35878e12			−0.169293
$482$	3.17135e13	−	2.25153e13i	1.21901	−	0.865451i
$483$	3.48195e11	−	3.48195e11i	0.0132460	−	0.0132460i
$484$	−2.50572e13	−	8.75213e12i	−0.943423	−	0.329524i
$485$	−6.52406e12	+	6.52406e12i	−0.243114	+	0.243114i
$486$	−7.16126e11	+	4.22198e12i	−0.0264124	+	0.155717i
$487$	−3.50513e13			−1.27956			−0.639778	−	0.768560i	$-0.720974\pi$
$487$	−3.50513e13			−1.27956			−0.639778	+	0.768560i	$0.720974\pi$
$488$	−1.32519e13	+	2.40252e13i	−0.478828	+	0.868097i
$489$			1.59600e13i			0.570805i
$490$	−1.91639e12	+	1.12983e13i	−0.0678428	+	0.399974i
$491$	2.45513e13	+	2.45513e13i	0.860334	+	0.860334i	0.991377	−	0.131043i	$-0.0418325\pi$
$491$	2.45513e13	+	2.45513e13i	0.860334	+	0.860334i	−0.131043	+	0.991377i	$0.541833\pi$
$492$	−3.59559e13	+	1.73403e13i	−1.24723	+	0.601494i
$493$	−1.14045e13	−	1.14045e13i	−0.391598	−	0.391598i
$494$	−3.21644e12	+	2.28354e12i	−0.109330	+	0.0776200i
$495$			2.49929e10i			0.000840990i
$496$	3.38585e13	−	4.25551e13i	1.12787	−	1.41757i
$497$	1.47808e11			0.00487435
$498$	2.27305e13	+	3.20166e13i	0.742099	+	1.04527i
$499$	−2.07304e13	+	2.07304e13i	−0.670046	+	0.670046i	−0.957727	−	0.287680i	$-0.907116\pi$
$499$	−2.07304e13	+	2.07304e13i	−0.670046	+	0.670046i	0.287680	+	0.957727i	$0.407116\pi$
$500$	2.09804e13	−	1.01181e13i	0.671374	−	0.323781i
$501$	−1.56625e12	+	1.56625e12i	−0.0496218	+	0.0496218i
$502$	2.59284e13	+	4.39793e12i	0.813312	+	0.137953i
$503$	3.69233e13			1.14673			0.573365	−	0.819300i	$-0.305638\pi$
$503$	3.69233e13			1.14673			0.573365	+	0.819300i	$0.305638\pi$
$504$	8.75268e10	−	2.52958e10i	0.00269146	−	0.000777849i
$505$			1.47348e13i			0.448630i
$506$	4.71793e11	+	8.00247e10i	0.0142232	+	0.00241252i
$507$	−2.23764e13	−	2.23764e13i	−0.667960	−	0.667960i
$508$	−1.98080e13	−	6.91867e12i	−0.585495	−	0.204505i
$509$	−3.67055e13	−	3.67055e13i	−1.07434	−	1.07434i	−0.997005	−	0.0773354i	$-0.975359\pi$
$509$	−3.67055e13	−	3.67055e13i	−1.07434	−	1.07434i	−0.0773354	−	0.997005i	$-0.524641\pi$
$510$	3.24411e12	+	4.56943e12i	0.0940254	+	0.132438i
$511$		−	1.17907e12i		−	0.0338403i
$512$	2.62940e13	+	2.33787e13i	0.747322	+	0.664463i
$513$	3.95038e13			1.11186
$514$	1.43795e13	−	1.02089e13i	0.400801	−	0.284552i
$515$	9.20538e12	−	9.20538e12i	0.254100	−	0.254100i
$516$	−4.05588e12	+	1.16119e13i	−0.110876	+	0.317436i
$517$	−7.57523e11	+	7.57523e11i	−0.0205089	+	0.0205089i
$518$	2.99225e11	−	1.76411e12i	0.00802323	−	0.0473017i
$519$	−4.73796e13			−1.25821
$520$	5.35471e11	+	1.85280e12i	0.0140838	+	0.0487317i
$521$		−	4.40960e13i		−	1.14871i	−0.818607	−	0.574355i	$-0.805253\pi$
$521$		−	4.40960e13i		−	1.14871i	0.818607	−	0.574355i	$-0.194747\pi$
$522$	−6.81900e11	+	4.02021e12i	−0.0175942	+	0.103728i
$523$	−1.60652e13	−	1.60652e13i	−0.410562	−	0.410562i	0.471373	−	0.881934i	$-0.343759\pi$
$523$	−1.60652e13	−	1.60652e13i	−0.410562	−	0.410562i	−0.881934	+	0.471373i	$0.843759\pi$
$524$	1.92938e13	+	4.00067e13i	0.488385	+	1.01269i
$525$	7.99752e11	+	7.99752e11i	0.0200521	+	0.0200521i
$526$	−2.54952e13	+	1.81006e13i	−0.633185	+	0.449535i
$527$		−	3.06839e13i		−	0.754844i
$528$	−8.05942e11	−	6.41240e11i	−0.0196397	−	0.0156261i
$529$	−2.88224e13			−0.695748
$530$	−1.55758e12	−	2.19390e12i	−0.0372452	−	0.0524611i
$531$	−7.77940e11	+	7.77940e11i	−0.0184278	+	0.0184278i
$532$	−7.03402e11	−	1.45854e12i	−0.0165061	−	0.0342262i
$533$	−5.48123e12	+	5.48123e12i	−0.127421	+	0.127421i
$534$	−1.11203e13	−	1.88621e12i	−0.256101	−	0.0434394i
$535$	−2.10177e13			−0.479532
$536$	5.37117e13	+	2.96265e13i	1.21407	+	0.669662i
$537$			2.66323e12i			0.0596400i
$538$	−5.10789e13	−	8.66392e12i	−1.13326	−	0.192222i
$539$	−8.40283e11	−	8.40283e11i	−0.0184706	−	0.0184706i
$540$	6.36892e12	−	1.82341e13i	0.138707	−	0.397115i
$541$	−1.19223e13	−	1.19223e13i	−0.257261	−	0.257261i	0.566678	−	0.823939i	$-0.308228\pi$
$541$	−1.19223e13	−	1.19223e13i	−0.257261	−	0.257261i	−0.823939	+	0.566678i	$0.808228\pi$
$542$	−1.74648e13	−	2.45997e13i	−0.373393	−	0.525936i
$543$		−	6.13288e13i		−	1.29917i
$544$	1.98225e13	+	1.08533e12i	0.416069	+	0.0227807i
$545$	2.53397e13			0.527011
$546$	−1.67809e11	+	1.19137e11i	−0.00345821	+	0.00245519i
$547$	−3.64662e13	+	3.64662e13i	−0.744653	+	0.744653i	−0.973469	−	0.228817i	$-0.926514\pi$
$547$	−3.64662e13	+	3.64662e13i	−0.744653	+	0.744653i	0.228817	+	0.973469i	$0.426514\pi$
$548$	−1.63677e13	−	5.71701e12i	−0.331196	−	0.115682i
$549$	2.76764e12	−	2.76764e12i	0.0554942	−	0.0554942i
$550$	−1.83805e11	+	1.08364e12i	−0.00365211	+	0.0215314i
$551$	7.24723e13			1.42697
$552$	−2.37533e13	−	1.31019e13i	−0.463478	−	0.255646i
$553$		−	4.28718e11i		−	0.00828983i
$554$	9.58528e12	−	5.65109e13i	0.183677	−	1.08289i
$555$	−1.96752e13	−	1.96752e13i	−0.373641	−	0.373641i
$556$	3.61619e13	−	1.74397e13i	0.680577	−	0.328219i
$557$	3.76130e13	+	3.76130e13i	0.701556	+	0.701556i	0.964745	−	0.263188i	$-0.0847740\pi$
$557$	3.76130e13	+	3.76130e13i	0.701556	+	0.701556i	−0.263188	+	0.964745i	$0.584774\pi$
$558$	−6.32554e12	+	4.49088e12i	−0.116930	+	0.0830157i
$559$			2.38845e12i			0.0437580i
$560$	−7.86635e11	+	8.95262e10i	−0.0142835	+	0.00162559i
$561$	−5.81115e11			−0.0104580
$562$	−3.97782e13	−	5.60289e13i	−0.709519	−	0.999379i
$563$	5.34683e13	−	5.34683e13i	0.945267	−	0.945267i	−0.0533114	−	0.998578i	$-0.516978\pi$
$563$	5.34683e13	−	5.34683e13i	0.945267	−	0.945267i	0.998578	+	0.0533114i	$0.0169776\pi$
$564$	5.47011e13	−	2.63805e13i	0.958519	−	0.462261i
$565$	−2.77766e13	+	2.77766e13i	−0.482433	+	0.482433i
$566$	−1.65069e13	−	2.79988e12i	−0.284174	−	0.0482011i
$567$	1.89682e12			0.0323676
$568$	−2.26075e12	−	7.82250e12i	−0.0382394	−	0.132313i
$569$			7.68283e13i			1.28813i	0.764970	+	0.644066i	$0.222754\pi$
$569$			7.68283e13i			1.28813i	−0.764970	+	0.644066i	$0.777246\pi$
$570$	−2.48265e13	−	4.21103e12i	−0.412611	−	0.0699864i
$571$	2.60133e13	+	2.60133e13i	0.428562	+	0.428562i	0.888138	−	0.459576i	$-0.151999\pi$
$571$	2.60133e13	+	2.60133e13i	0.428562	+	0.428562i	−0.459576	+	0.888138i	$0.651999\pi$
$572$	−1.88808e11	−	6.59481e10i	−0.00308348	−	0.00107702i
$573$	6.38840e13	+	6.38840e13i	1.03423	+	1.03423i
$574$	−1.84212e12	−	2.59468e12i	−0.0295636	−	0.0416413i
$575$			2.89498e13i			0.460581i
$576$	−2.67748e12	−	4.24530e12i	−0.0422292	−	0.0669571i
$577$	−1.68301e13			−0.263153			−0.131576	−	0.991306i	$-0.542004\pi$
$577$	−1.68301e13			−0.263153			−0.131576	+	0.991306i	$0.542004\pi$
$578$	−4.34693e13	+	3.08614e13i	−0.673819	+	0.478384i
$579$	−2.19803e13	+	2.19803e13i	−0.337785	+	0.337785i
$580$	1.16842e13	−	3.34517e13i	0.178016	−	0.509658i
$581$	−2.21322e12	+	2.21322e12i	−0.0334306	+	0.0334306i
$582$	−9.07005e12	+	5.34733e13i	−0.135830	+	0.800796i
$583$	2.79008e11			0.00414261
$584$	−6.24003e13	+	1.80341e13i	−0.918591	+	0.265479i
$585$		−	2.75122e11i		−	0.00401556i
$586$	−1.07771e13	+	6.35373e13i	−0.155960	+	0.919477i
$587$	2.16627e12	+	2.16627e12i	0.0310829	+	0.0310829i	0.722477	−	0.691395i	$-0.243003\pi$
$587$	2.16627e12	+	2.16627e12i	0.0310829	+	0.0310829i	−0.691395	+	0.722477i	$0.743003\pi$
$588$	2.92626e13	+	6.06773e13i	0.416319	+	0.863256i
$589$	9.74938e13	+	9.74938e13i	1.37531	+	1.37531i
$590$	7.79541e12	−	5.53443e12i	0.109038	−	0.0774128i
$591$			1.11478e13i			0.154615i
$592$	−9.79392e13	+	1.11464e13i	−1.34694	+	0.153294i
$593$	−9.10057e13			−1.24107			−0.620533	−	0.784180i	$-0.713084\pi$
$593$	−9.10057e13			−1.24107			−0.620533	+	0.784180i	$0.713084\pi$
$594$	1.15946e12	+	1.63313e12i	0.0156792	+	0.0220846i
$595$	−3.15873e11	+	3.15873e11i	−0.00423573	+	0.00423573i
$596$	2.27432e13	+	4.71590e13i	0.302427	+	0.627095i
$597$	−5.00328e13	+	5.00328e13i	−0.659755	+	0.659755i
$598$	−5.19350e12	−	8.80912e11i	−0.0679131	−	0.0115193i
$599$	1.35695e14			1.75967			0.879835	−	0.475280i	$-0.157653\pi$
$599$	1.35695e14			1.75967			0.879835	+	0.475280i	$0.157653\pi$
$600$	3.00932e13	−	5.45579e13i	0.387001	−	0.701620i
$601$			2.65917e13i			0.339135i	0.985519	+	0.169568i	$0.0542372\pi$
$601$			2.65917e13i			0.339135i	−0.985519	+	0.169568i	$0.945763\pi$
$602$	−9.66667e11	−	1.63964e11i	−0.0122263	−	0.00207380i
$603$	−6.18744e12	−	6.18744e12i	−0.0776112	−	0.0776112i
$604$	4.43350e13	−	1.26931e14i	0.551521	−	1.57900i
$605$	−2.32648e13	−	2.32648e13i	−0.287027	−	0.287027i
$606$	5.01431e13	+	7.06282e13i	0.613548	+	0.864201i
$607$		−	8.29244e13i		−	1.00633i	−0.864191	−	0.503163i	$-0.832169\pi$
$607$		−	8.29244e13i		−	1.00633i	0.864191	−	0.503163i	$-0.167831\pi$
$608$	−6.64320e13	+	5.95350e13i	−0.799575	+	0.716563i
$609$	3.78104e12			0.0451362
$610$	−2.77333e13	+	1.96895e13i	−0.328362	+	0.233124i
$611$	8.33881e12	−	8.33881e12i	0.0979261	−	0.0979261i
$612$	−2.67356e12	−	9.33837e11i	−0.0311410	−	0.0108771i
$613$	7.96191e13	−	7.96191e13i	0.919846	−	0.919846i	−0.0771719	−	0.997018i	$-0.524589\pi$
$613$	7.96191e13	−	7.96191e13i	0.919846	−	0.919846i	0.997018	+	0.0771719i	$0.0245890\pi$
$614$	2.98155e12	−	1.75780e13i	0.0341664	−	0.201431i
$615$	−4.94838e13			−0.562454
$616$	3.96524e10	−	7.18884e10i	0.000447060	−	0.000810504i
$617$		−	1.15397e14i		−	1.29054i	−0.763956	−	0.645269i	$-0.776745\pi$
$617$		−	1.15397e14i		−	1.29054i	0.763956	−	0.645269i	$-0.223255\pi$
$618$	1.27977e13	−	7.54502e13i	0.141968	−	0.836986i
$619$	−6.59266e13	−	6.59266e13i	−0.725450	−	0.725450i	0.244260	−	0.969710i	$-0.421455\pi$
$619$	−6.59266e13	−	6.59266e13i	−0.725450	−	0.725450i	−0.969710	+	0.244260i	$0.921455\pi$
$620$	6.07194e13	−	2.92829e13i	0.662780	−	0.319636i
$621$	3.73025e13	+	3.73025e13i	0.403905	+	0.403905i
$622$	4.18826e13	−	2.97350e13i	0.449865	−	0.319386i
$623$		−	8.99109e11i		−	0.00958014i
$624$	8.87181e12	+	7.05877e12i	0.0937755	+	0.0746115i
$625$	−5.07583e13			−0.532240
$626$	−1.00300e14	−	1.41275e14i	−1.04334	−	1.46958i
$627$	1.84642e12	−	1.84642e12i	0.0190542	−	0.0190542i
$628$	−6.75595e11	+	3.25816e11i	−0.00691653	+	0.00333561i
$629$	−3.93275e13	+	3.93275e13i	−0.399432	+	0.399432i
$630$	1.11349e11	+	1.88868e10i	0.00112197	+	0.000190307i
$631$	6.56864e13			0.656642			0.328321	−	0.944566i	$-0.393517\pi$
$631$	6.56864e13			0.656642			0.328321	+	0.944566i	$0.393517\pi$
$632$	−2.26892e13	+	6.55732e12i	−0.225026	+	0.0650340i
$633$		−	1.91397e14i		−	1.88329i
$634$	1.86972e14	+	3.17139e13i	1.82528	+	0.309602i
$635$	−1.83911e13	−	1.83911e13i	−0.178131	−	0.178131i
$636$	−1.49318e13	−	5.21548e12i	−0.143492	−	0.0501197i
$637$	9.24984e12	+	9.24984e12i	0.0881936	+	0.0881936i
$638$	2.12710e12	+	2.99609e12i	0.0201227	+	0.0283434i
$639$			1.16156e12i			0.0109028i
$640$	1.67698e13	+	4.02621e13i	0.156181	+	0.374970i
$641$	−5.95259e13			−0.550068			−0.275034	−	0.961435i	$-0.588689\pi$
$641$	−5.95259e13			−0.550068			−0.275034	+	0.961435i	$0.588689\pi$
$642$	−1.00744e14	+	7.15242e13i	−0.923728	+	0.655809i
$643$	−1.10092e14	+	1.10092e14i	−1.00162	+	1.00162i	−0.00161693	+	0.999999i	$0.500515\pi$
$643$	−1.10092e14	+	1.10092e14i	−1.00162	+	1.00162i	−0.999999	+	0.00161693i	$0.999485\pi$
$644$	7.13055e11	−	2.04147e12i	0.00643715	−	0.0184295i
$645$	−1.07813e13	+	1.07813e13i	−0.0965767	+	0.0965767i
$646$	−8.41714e12	+	4.96240e13i	−0.0748173	+	0.441092i
$647$	−6.37697e13			−0.562462			−0.281231	−	0.959640i	$-0.590743\pi$
$647$	−6.37697e13			−0.562462			−0.281231	+	0.959640i	$0.590743\pi$
$648$	−2.90122e13	−	1.00386e14i	−0.253925	−	0.878615i
$649$			9.91377e11i			0.00861025i
$650$	2.02333e12	−	1.19287e13i	0.0174381	−	0.102808i
$651$	5.08647e12	+	5.08647e12i	0.0435023	+	0.0435023i
$652$	3.04448e13	+	6.31286e13i	0.258389	+	0.535782i
$653$	−6.65967e13	−	6.65967e13i	−0.560902	−	0.560902i	0.368662	−	0.929564i	$-0.379816\pi$
$653$	−6.65967e13	−	6.65967e13i	−0.560902	−	0.560902i	−0.929564	+	0.368662i	$0.879816\pi$
$654$	1.21461e14	−	8.62321e13i	1.01519	−	0.720743i
$655$			5.50585e13i			0.456687i
$656$	−1.09143e14	+	1.37177e14i	−0.898418	+	1.12918i
$657$	9.26580e12			0.0756931
$658$	2.80248e12	+	3.94738e12i	0.0227203	+	0.0320022i
$659$	−1.10357e14	+	1.10357e14i	−0.887914	+	0.887914i	−0.994323	−	0.106408i	$-0.966065\pi$
$659$	−1.10357e14	+	1.10357e14i	−0.887914	+	0.887914i	0.106408	+	0.994323i	$0.466065\pi$
$660$	−5.54583e11	−	1.14995e12i	−0.00442840	−	0.00918248i
$661$	1.06204e14	−	1.06204e14i	0.841656	−	0.841656i	−0.147418	−	0.989074i	$-0.547096\pi$
$661$	1.06204e14	−	1.06204e14i	0.841656	−	0.841656i	0.989074	+	0.147418i	$0.0470963\pi$
$662$	3.73669e13	+	6.33812e12i	0.293899	+	0.0498506i
$663$	6.39692e12			0.0499348
$664$	1.50983e14	+	8.32795e13i	1.16973	+	0.645205i
$665$		−	2.00729e12i		−	0.0154348i
$666$	1.38634e13	+	2.35148e12i	0.105803	+	0.0179461i
$667$	6.84339e13	+	6.84339e13i	0.518372	+	0.518372i
$668$	−3.20747e12	+	9.18294e12i	−0.0241146	+	0.0690398i
$669$	−4.23711e13	−	4.23711e13i	−0.316183	−	0.316183i
$670$	4.40187e13	+	6.20017e13i	0.326034	+	0.459229i
$671$		−	3.52697e12i		−	0.0259292i
$672$	−3.46590e12	+	3.10607e12i	−0.0252912	+	0.0226655i
$673$	1.33624e14			0.967854			0.483927	−	0.875108i	$-0.339210\pi$
$673$	1.33624e14			0.967854			0.483927	+	0.875108i	$0.339210\pi$
$674$	1.48014e14	−	1.05084e14i	1.06415	−	0.755503i
$675$	−8.56784e13	+	8.56784e13i	−0.611438	+	0.611438i
$676$	−1.31193e14	−	4.58238e13i	−0.929345	−	0.324607i
$677$	−7.38643e13	+	7.38643e13i	−0.519387	+	0.519387i	−0.917386	−	0.397999i	$-0.869705\pi$
$677$	−7.38643e13	+	7.38643e13i	−0.519387	+	0.519387i	0.397999	+	0.917386i	$0.369705\pi$
$678$	−3.86163e13	+	2.27666e14i	−0.269540	+	1.58909i
$679$	−4.32346e12			−0.0299559
$680$	2.15484e13	+	1.18857e13i	0.148208	+	0.0817487i
$681$		−	1.97122e14i		−	1.34586i
$682$	−1.16901e12	+	6.89201e12i	−0.00792313	+	0.0467115i
$683$	−4.47373e13	−	4.47373e13i	−0.301000	−	0.301000i	0.540405	−	0.841405i	$-0.318271\pi$
$683$	−4.47373e13	−	4.47373e13i	−0.301000	−	0.301000i	−0.841405	+	0.540405i	$0.818271\pi$
$684$	1.14620e13	−	5.52774e12i	0.0765562	−	0.0369204i
$685$	−1.51969e13	−	1.51969e13i	−0.100763	−	0.100763i
$686$	−8.76277e12	+	6.22121e12i	−0.0576794	+	0.0409501i
$687$			7.56755e13i			0.494506i
$688$	6.10780e12	+	5.36671e13i	0.0396226	+	0.348150i
$689$	−3.07132e12			−0.0197801
$690$	−1.94667e13	−	2.74194e13i	−0.124465	−	0.175313i
$691$	5.07819e13	−	5.07819e13i	0.322343	−	0.322343i	−0.527322	−	0.849666i	$-0.676804\pi$
$691$	5.07819e13	−	5.07819e13i	0.322343	−	0.322343i	0.849666	+	0.527322i	$0.176804\pi$
$692$	−1.87407e14	+	9.03799e13i	−1.18101	+	0.569563i
$693$	−8.28133e9	+	8.28133e9i	−5.18124e−5	+	5.18124e-5i
$694$	9.76898e13	+	1.65700e13i	0.606809	+	0.102926i
$695$	4.97673e13			0.306916
$696$	−5.78317e13	−	2.00105e14i	−0.354095	−	1.22522i
$697$			9.89099e13i			0.601279i
$698$	2.44118e14	+	4.14069e13i	1.47341	+	0.249917i
$699$	1.81758e14	+	1.81758e14i	1.08920	+	1.08920i
$700$	4.68895e12	+	1.63778e12i	0.0278988	+	0.00974466i
$701$	−9.71213e13	−	9.71213e13i	−0.573752	−	0.573752i	0.359423	−	0.933175i	$-0.382974\pi$
$701$	−9.71213e13	−	9.71213e13i	−0.573752	−	0.573752i	−0.933175	+	0.359423i	$0.882974\pi$
$702$	−1.27633e13	−	1.79775e13i	−0.0748649	−	0.105450i
$703$		−	2.49915e14i		−	1.45551i
$704$	−4.41106e12	−	9.98991e11i	−0.0255082	−	0.00577694i
$705$	7.52816e13			0.432258
$706$	−1.10927e14	+	7.87536e13i	−0.632431	+	0.449001i
$707$	−4.88234e12	+	4.88234e12i	−0.0276396	+	0.0276396i
$708$	1.85318e13	−	5.30561e13i	0.104172	−	0.298242i
$709$	1.14965e14	−	1.14965e14i	0.641702	−	0.641702i	−0.309271	−	0.950974i	$-0.600085\pi$
$709$	1.14965e14	−	1.14965e14i	0.641702	−	0.641702i	0.950974	+	0.309271i	$0.100085\pi$
$710$	1.68796e12	−	9.95155e12i	0.00935560	−	0.0551568i
$711$	3.36911e12			0.0185425
$712$	−4.75838e13	+	1.37520e13i	−0.260052	+	0.0751566i
$713$			1.84122e14i			0.999214i
$714$	−4.39141e11	+	2.58900e12i	−0.00236654	+	0.0139521i
$715$	−1.75302e11	−	1.75302e11i	−0.000938118	−	0.000938118i
$716$	5.08030e12	+	1.05342e13i	0.0269976	+	0.0559807i
$717$	8.30315e12	+	8.30315e12i	0.0438175	+	0.0438175i
$718$	1.47987e13	−	1.05065e13i	0.0775536	−	0.0550599i
$719$			2.79287e14i			1.45347i	0.686918	+	0.726735i	$0.258963\pi$
$719$			2.79287e14i			1.45347i	−0.686918	+	0.726735i	$0.741037\pi$
$720$	−7.03548e11	−	6.18183e12i	−0.00363606	−	0.0319488i
$721$	6.10035e12			0.0313097
$722$	−1.73525e13	−	2.44416e13i	−0.0884457	−	0.124578i
$723$	2.00404e14	−	2.00404e14i	1.01441	−	1.01441i
$724$	−1.16989e14	−	2.42582e14i	−0.588102	−	1.21946i
$725$	−1.57183e14	+	1.57183e14i	−0.784720	+	0.784720i
$726$	−1.90686e14	−	3.23438e13i	−0.945443	−	0.160364i
$727$	−8.92090e13			−0.439275			−0.219638	−	0.975582i	$-0.570487\pi$
$727$	−8.92090e13			−0.439275			−0.219638	+	0.975582i	$0.570487\pi$
$728$	−4.36494e11	+	7.91347e11i	−0.00213462	+	0.00386999i
$729$			2.19507e14i			1.06613i
$730$	−7.93837e13	−	1.34649e13i	−0.382928	−	0.0649516i
$731$	2.15500e13	+	2.15500e13i	0.103243	+	0.103243i
$732$	−6.59294e13	+	1.88755e14i	−0.313707	+	0.898138i
$733$	6.50793e12	+	6.50793e12i	0.0307555	+	0.0307555i	0.722317	−	0.691562i	$-0.243077\pi$
$733$	6.50793e12	+	6.50793e12i	0.0307555	+	0.0307555i	−0.691562	+	0.722317i	$0.743077\pi$
$734$	−2.04346e14	−	2.87827e14i	−0.959146	−	1.35099i
$735$			8.35062e13i			0.389298i
$736$	−1.18948e14	−	6.51266e12i	−0.550765	−	0.0301557i
$737$	−7.88503e12			−0.0362632
$738$	2.03905e13	−	1.44764e13i	0.0931419	−	0.0661270i
$739$	6.56349e13	−	6.56349e13i	0.297792	−	0.297792i	−0.542357	−	0.840148i	$-0.682468\pi$
$739$	6.56349e13	−	6.56349e13i	0.297792	−	0.297792i	0.840148	+	0.542357i	$0.182468\pi$
$740$	−1.15356e14	−	4.02921e13i	−0.519854	−	0.181577i
$741$	−2.03253e13	+	2.03253e13i	−0.0909802	+	0.0909802i
$742$	2.10843e11	−	1.24304e12i	0.000937431	−	0.00552671i
$743$	−1.73051e13			−0.0764239			−0.0382119	−	0.999270i	$-0.512166\pi$
$743$	−1.73051e13			−0.0764239			−0.0382119	+	0.999270i	$0.512166\pi$
$744$	1.91395e14	−	3.46992e14i	0.839586	−	1.52214i
$745$			6.49019e13i			0.282798i
$746$	−9.98939e12	+	5.88933e13i	−0.0432359	+	0.254901i
$747$	−1.73928e13	−	1.73928e13i	−0.0747767	−	0.0747767i
$748$	−2.29856e12	+	1.10852e12i	−0.00981632	+	0.00473407i
$749$	−6.96417e12	−	6.96417e12i	−0.0295434	−	0.0295434i
$750$	1.38401e14	−	9.82593e13i	0.583222	−	0.414064i
$751$		−	1.42024e14i		−	0.594514i	−0.954798	−	0.297257i	$-0.903928\pi$
$751$		−	1.42024e14i		−	0.594514i	0.954798	−	0.297257i	$-0.0960717\pi$
$752$	1.66044e14	−	2.08693e14i	0.690454	−	0.867797i
$753$	1.91639e14			0.791605
$754$	−2.34152e13	−	3.29810e13i	−0.0960817	−	0.135334i
$755$	1.17851e14	−	1.17851e14i	0.480394	−	0.480394i
$756$	8.15216e12	−	3.93151e12i	0.0330114	−	0.0159203i
$757$	1.39129e14	−	1.39129e14i	0.559679	−	0.559679i	−0.369537	−	0.929216i	$-0.620484\pi$
$757$	1.39129e14	−	1.39129e14i	0.559679	−	0.559679i	0.929216	+	0.369537i	$0.120484\pi$
$758$	−1.01305e14	−	1.71831e13i	−0.404840	−	0.0686683i
$759$	3.48705e12			0.0138436
$760$	−1.06232e14	+	3.07018e13i	−0.418976	+	0.121087i
$761$			1.12246e14i			0.439791i	0.975523	+	0.219895i	$0.0705716\pi$
$761$			1.12246e14i			0.439791i	−0.975523	+	0.219895i	$0.929428\pi$
$762$	−1.50739e14	−	2.55682e13i	−0.586749	−	0.0995233i
$763$	8.39626e12	+	8.39626e12i	0.0324686	+	0.0324686i
$764$	3.74552e14	+	1.30826e14i	1.43895	+	0.502605i
$765$	−2.48231e12	−	2.48231e12i	−0.00947435	−	0.00947435i
$766$	−2.72183e14	−	3.83378e14i	−1.03209	−	1.45373i
$767$		−	1.09131e13i		−	0.0411122i
$768$	2.17395e14	+	1.35919e14i	0.813663	+	0.508716i
$769$	−1.21311e14			−0.451094			−0.225547	−	0.974232i	$-0.572417\pi$
$769$	−1.21311e14			−0.451094			−0.225547	+	0.974232i	$0.572417\pi$
$770$	8.29837e10	−	5.89151e10i	0.000306577	−	0.000217657i
$771$	9.08672e13	−	9.08672e13i	0.333530	−	0.333530i
$772$	−4.50126e13	+	1.28871e14i	−0.164153	+	0.469967i
$773$	1.22232e14	−	1.22232e14i	0.442882	−	0.442882i	−0.450098	−	0.892979i	$-0.648611\pi$
$773$	1.22232e14	−	1.22232e14i	0.442882	−	0.442882i	0.892979	+	0.450098i	$0.148611\pi$
$774$	1.28853e12	−	7.59663e12i	0.00463862	−	0.0273474i
$775$	−4.22902e14			−1.51262
$776$	6.61281e13	+	2.28812e14i	0.235005	+	0.813149i
$777$		−	1.30386e13i		−	0.0460392i
$778$	−9.34672e13	+	5.51044e14i	−0.327915	+	1.93325i
$779$	−3.14273e14	−	3.14273e14i	−1.09552	−	1.09552i
$780$	6.10485e12	+	1.26587e13i	0.0211447	+	0.0438445i
$781$	7.40124e11	+	7.40124e11i	0.00254712	+	0.00254712i
$782$	−5.48069e13	+	3.89107e13i	−0.187414	+	0.133056i
$783$			4.05068e14i			1.37632i
$784$	2.31493e14	+	1.84185e14i	0.781550	+	0.621833i
$785$	−9.29777e11			−0.00311911
$786$	1.87366e14	+	2.63911e14i	0.624567	+	0.879721i
$787$	2.76742e14	−	2.76742e14i	0.916647	−	0.916647i	−0.0801372	−	0.996784i	$-0.525536\pi$
$787$	2.76742e14	−	2.76742e14i	0.916647	−	0.916647i	0.996784	+	0.0801372i	$0.0255359\pi$
$788$	2.12652e13	+	4.40943e13i	0.0699903	+	0.145128i
$789$	−1.61110e14	+	1.61110e14i	−0.526911	+	0.526911i
$790$	−2.88645e13	−	4.89594e12i	−0.0938055	−	0.0159111i
$791$	−1.84074e13			−0.0594443
$792$	5.64940e11	+	3.11611e11i	0.00181291	+	0.000999970i
$793$			3.88249e13i			0.123807i
$794$	1.31978e14	+	2.23858e13i	0.418213	+	0.0709366i
$795$	−1.38637e13	−	1.38637e13i	−0.0436560	−	0.0436560i
$796$	−1.02460e14	+	2.93343e14i	−0.320620	+	0.917930i
$797$	7.42897e13	+	7.42897e13i	0.231013	+	0.231013i	0.813116	−	0.582102i	$-0.197770\pi$
$797$	7.42897e13	+	7.42897e13i	0.231013	+	0.231013i	−0.582102	+	0.813116i	$0.697770\pi$
$798$	−6.83088e12	−	9.62150e12i	−0.0211087	−	0.0297323i
$799$		−	1.50475e14i		−	0.462095i
$800$	1.49586e13	−	2.73205e14i	0.0456501	−	0.833757i
$801$	7.06571e12			0.0214286
$802$	−2.28021e14	+	1.61886e14i	−0.687231	+	0.487906i
$803$	5.90399e12	−	5.90399e12i	0.0176835	−	0.0176835i
$804$	4.21988e14	+	1.47394e14i	1.25609	+	0.438733i
$805$	1.89543e12	−	1.89543e12i	0.00560698	−	0.00560698i
$806$	1.28685e13	−	7.58673e13i	0.0378314	−	0.223038i
$807$	−3.77528e14			−1.10301
$808$	3.33066e14	+	1.83714e14i	0.967106	+	0.533439i
$809$			4.20914e14i			1.21465i	0.794454	+	0.607324i	$0.207757\pi$
$809$			4.20914e14i			1.21465i	−0.794454	+	0.607324i	$0.792243\pi$
$810$	2.16616e13	−	1.27708e14i	0.0621250	−	0.366263i
$811$	−7.48191e13	−	7.48191e13i	−0.213259	−	0.213259i	0.592391	−	0.805651i	$-0.298184\pi$
$811$	−7.48191e13	−	7.48191e13i	−0.213259	−	0.213259i	−0.805651	+	0.592391i	$0.798184\pi$
$812$	1.49557e13	−	7.21261e12i	0.0423668	−	0.0204321i
$813$	−1.55451e14	−	1.55451e14i	−0.437663	−	0.437663i
$814$	1.03318e13	−	7.33516e12i	0.0289104	−	0.0205252i
$815$			8.68798e13i			0.241619i
$816$	1.43735e14	−	1.63584e13i	0.397294	−	0.0452157i
$817$	−1.36945e14			−0.376214
$818$	6.08550e13	+	8.57161e13i	0.166161	+	0.234043i
$819$	9.11609e10	−	9.11609e10i	0.000247394	−	0.000247394i
$820$	−1.95730e14	+	9.43938e13i	−0.527944	+	0.254609i
$821$	1.20747e13	−	1.20747e13i	0.0323714	−	0.0323714i	−0.690736	−	0.723107i	$-0.742713\pi$
$821$	1.20747e13	−	1.20747e13i	0.0323714	−	0.0323714i	0.723107	+	0.690736i	$0.242713\pi$
$822$	−1.24558e14	−	2.11274e13i	−0.331905	−	0.0562972i
$823$	4.14339e14			1.09738			0.548690	−	0.836026i	$-0.315127\pi$
$823$	4.14339e14			1.09738			0.548690	+	0.836026i	$0.315127\pi$
$824$	−9.33060e13	−	3.22851e14i	−0.245626	−	0.849897i
$825$			8.00925e12i			0.0209567i
$826$	4.41681e12	+	7.49171e11i	0.0114870	+	0.00194841i
$827$	2.26977e14	+	2.26977e14i	0.586752	+	0.586752i	0.936750	−	0.349998i	$-0.113818\pi$
$827$	2.26977e14	+	2.26977e14i	0.586752	+	0.586752i	−0.349998	+	0.936750i	$0.613818\pi$
$828$	1.60430e13	+	5.60360e12i	0.0412225	+	0.0143984i
$829$	−1.60618e14	−	1.60618e14i	−0.410225	−	0.410225i	0.471592	−	0.881817i	$-0.343680\pi$
$829$	−1.60618e14	−	1.60618e14i	−0.410225	−	0.410225i	−0.881817	+	0.471592i	$0.843680\pi$
$830$	1.23736e14	+	1.74286e14i	0.314127	+	0.442457i
$831$		−	4.17676e14i		−	1.05398i
$832$	4.85570e13	+	1.09969e13i	0.121797	+	0.0275838i
$833$	1.66915e14			0.416170
$834$	2.38549e14	−	1.69360e14i	0.591217	−	0.419740i
$835$	−8.52606e12	+	8.52606e12i	−0.0210047	+	0.0210047i
$836$	3.78121e12	−	1.08255e13i	0.00925975	−	0.0265105i
$837$	−5.44920e14	+	5.44920e14i	−1.32649	+	1.32649i
$838$	1.33902e13	−	7.89434e13i	0.0324017	−	0.191027i
$839$	−1.89822e14			−0.456601			−0.228300	−	0.973591i	$-0.573317\pi$
$839$	−1.89822e14			−0.456601			−0.228300	+	0.973591i	$0.573317\pi$
$840$	−5.54238e12	+	1.60178e12i	−0.0132526	+	0.00383008i
$841$			3.22416e14i			0.766366i
$842$	1.04624e13	−	6.16818e13i	0.0247212	−	0.145746i
$843$	−3.54059e14	−	3.54059e14i	−0.831644	−	0.831644i
$844$	−3.65104e14	−	7.57059e14i	−0.852519	−	1.76774i
$845$	−1.21808e14	−	1.21808e14i	−0.282744	−	0.282744i
$846$	−3.10208e13	+	2.20235e13i	−0.0715816	+	0.0508200i
$847$		−	1.54175e13i		−	0.0353668i
$848$	−6.90108e13	+	7.85406e12i	−0.157376	+	0.0179108i
$849$	−1.22004e14			−0.276589
$850$	−8.93722e13	−	1.25884e14i	−0.201422	−	0.283710i
$851$	2.35989e14	−	2.35989e14i	0.528743	−	0.528743i
$852$	−2.57746e13	−	5.34448e13i	−0.0574108	−	0.119044i
$853$	5.70510e14	−	5.70510e14i	1.26333	−	1.26333i	0.313866	−	0.949467i	$-0.398376\pi$
$853$	5.70510e14	−	5.70510e14i	1.26333	−	1.26333i	0.949467	−	0.313866i	$-0.101624\pi$
$854$	−1.57134e13	−	2.66529e12i	−0.0345925	−	0.00586752i
$855$	1.57744e13			0.0345241
$856$	−2.62049e14	+	4.75086e14i	−0.570182	+	1.03372i
$857$		−	7.51978e14i		−	1.62668i	−0.581791	−	0.813338i	$-0.697648\pi$
$857$		−	7.51978e14i		−	1.62668i	0.581791	−	0.813338i	$-0.302352\pi$
$858$	−1.43683e12	−	2.43713e11i	−0.00309008	−	0.000524135i
$859$	5.07016e14	+	5.07016e14i	1.08407	+	1.08407i	0.996126	+	0.0879414i	$0.0280288\pi$
$859$	5.07016e14	+	5.07016e14i	1.08407	+	1.08407i	0.0879414	+	0.996126i	$0.471971\pi$
$860$	−2.20786e13	+	6.32108e13i	−0.0469332	+	0.134369i
$861$	−1.63963e13	−	1.63963e13i	−0.0346522	−	0.0346522i
$862$	2.90302e14	+	4.08900e14i	0.609978	+	0.859173i
$863$		−	4.84204e14i		−	1.01152i	−0.862674	−	0.505760i	$-0.831212\pi$
$863$		−	4.84204e14i		−	1.01152i	0.862674	−	0.505760i	$-0.168788\pi$
$864$	−3.32757e14	−	3.71306e14i	−0.691129	−	0.771194i
$865$	−2.57916e14			−0.532595
$866$	2.91973e14	−	2.07289e14i	0.599450	−	0.425585i
$867$	−2.74692e14	+	2.74692e14i	−0.560725	+	0.560725i
$868$	2.98220e13	+	1.04164e13i	0.0605255	+	0.0211407i
$869$	2.14673e12	−	2.14673e12i	0.00433191	−	0.00433191i
$870$	4.31794e13	−	2.54568e14i	0.0866324	−	0.510749i
$871$	8.67985e13			0.173149
$872$	3.15936e14	−	5.72780e14i	0.626637	−	1.13607i
$873$		−	3.39762e13i		−	0.0670045i
$874$	5.05081e13	−	2.97775e14i	0.0990384	−	0.583890i
$875$	9.56732e12	+	9.56732e12i	0.0186531	+	0.0186531i
$876$	−4.26330e14	+	2.05604e14i	−0.826467	+	0.398577i
$877$	−2.45981e14	−	2.45981e14i	−0.474136	−	0.474136i	0.429114	−	0.903250i	$-0.358826\pi$
$877$	−2.45981e14	−	2.45981e14i	−0.474136	−	0.474136i	−0.903250	+	0.429114i	$0.858826\pi$
$878$	−5.14745e14	+	3.65448e14i	−0.986551	+	0.700412i
$879$			4.69609e14i			0.894936i
$880$	−4.38723e12	−	3.49066e12i	−0.00831337	−	0.00661445i
$881$	9.78154e14			1.84301			0.921505	−	0.388366i	$-0.126960\pi$
$881$	9.78154e14			1.84301			0.921505	+	0.388366i	$0.126960\pi$
$882$	−2.44296e13	−	3.44099e13i	−0.0457692	−	0.0644674i
$883$	−1.31811e14	+	1.31811e14i	−0.245555	+	0.245555i	−0.819144	−	0.573588i	$-0.805551\pi$
$883$	−1.31811e14	+	1.31811e14i	−0.245555	+	0.245555i	0.573588	+	0.819144i	$0.305551\pi$
$884$	2.53026e13	−	1.22026e13i	0.0468710	−	0.0226043i
$885$	4.92609e13	−	4.92609e13i	0.0907373	−	0.0907373i
$886$	5.30555e14	+	8.99918e13i	0.971766	+	0.164829i
$887$	5.38836e14			0.981383			0.490692	−	0.871333i	$-0.336744\pi$
$887$	5.38836e14			0.981383			0.490692	+	0.871333i	$0.336744\pi$
$888$	−6.90049e14	+	1.99429e14i	−1.24973	+	0.361179i
$889$		−	1.21877e13i		−	0.0219489i
$890$	−6.05347e13	−	1.02678e13i	−0.108406	−	0.0183877i
$891$	9.49801e12	+	9.49801e12i	0.0169139	+	0.0169139i
$892$	−2.48422e14	−	8.67703e13i	−0.439912	−	0.153655i
$893$	4.78115e14	+	4.78115e14i	0.841929	+	0.841929i
$894$	2.20864e14	+	3.11093e14i	0.386755	+	0.544757i
$895$			1.44976e13i			0.0252453i
$896$	−7.78411e12	+	1.88973e13i	−0.0134793	+	0.0327236i
$897$	−3.83855e13			−0.0661005
$898$	−3.10448e14	+	2.20406e14i	−0.531627	+	0.377434i
$899$	−9.99691e14	+	9.99691e14i	−1.70242	+	1.70242i
$900$	−1.28707e13	+	3.68485e13i	−0.0217966	+	0.0624033i
$901$	−2.77113e13	+	2.77113e13i	−0.0466694	+	0.0466694i
$902$	3.76832e12	−	2.22165e13i	0.00631125	−	0.0372086i
$903$	−7.14470e12			−0.0119000
$904$	2.81545e14	+	9.74182e14i	0.466343	+	1.61361i
$905$		−	3.33850e14i		−	0.549932i
$906$	1.63842e14	−	9.65943e14i	0.268400	−	1.58238i
$907$	7.95684e14	+	7.95684e14i	1.29630	+	1.29630i	0.930821	+	0.365475i	$0.119093\pi$
$907$	7.95684e14	+	7.95684e14i	1.29630	+	1.29630i	0.365475	+	0.930821i	$0.380907\pi$
$908$	−3.76025e14	−	7.79704e14i	−0.609238	−	1.26328i
$909$	−3.83683e13	−	3.83683e13i	−0.0618234	−	0.0618234i
$910$	−9.13485e11	+	6.48537e11i	−0.00146384	+	0.00103927i
$911$			9.45697e14i			1.50716i	0.657355	+	0.753581i	$0.271675\pi$
$911$			9.45697e14i			1.50716i	−0.657355	+	0.753581i	$0.728325\pi$
$912$	−4.04722e14	+	5.08675e14i	−0.641480	+	0.806244i
$913$	−2.21647e13			−0.0349388
$914$	2.07442e14	+	2.92189e14i	0.325212	+	0.458071i
$915$	−1.75253e14	+	1.75253e14i	−0.273249	+	0.273249i
$916$	1.44356e14	+	2.99330e14i	0.223851	+	0.464165i
$917$	−1.82435e13	+	1.82435e13i	−0.0281359	+	0.0281359i
$918$	−2.77362e14	−	4.70457e13i	−0.425436	−	0.0721617i
$919$	3.86563e14			0.589716			0.294858	−	0.955541i	$-0.404728\pi$
$919$	3.86563e14			0.589716			0.294858	+	0.955541i	$0.404728\pi$
$920$	−1.29304e14	−	7.13217e13i	−0.196188	−	0.108214i
$921$		−	1.29920e14i		−	0.196055i
$922$	−8.25354e14	−	1.39995e14i	−1.23876	−	0.210116i
$923$	−8.14729e12	−	8.14729e12i	−0.0121620	−	0.0121620i
$924$	1.97274e11	−	5.64793e11i	0.000292894	−	0.000838551i
$925$	5.42033e14	+	5.42033e14i	0.800418	+	0.800418i
$926$	4.73916e14	+	6.67525e14i	0.696059	+	0.980421i
$927$			4.79401e13i			0.0700326i
$928$	−6.10465e14	−	6.81186e14i	−0.886995	−	0.989751i
$929$	−2.30584e14			−0.333235			−0.166617	−	0.986022i	$-0.553284\pi$
$929$	−2.30584e14			−0.333235			−0.166617	+	0.986022i	$0.553284\pi$
$930$	4.00547e14	−	2.84372e14i	0.575756	−	0.408763i
$931$	−5.30350e14	+	5.30350e14i	−0.758253	+	0.758253i
$932$	1.06565e15	+	3.72217e14i	1.51543	+	0.529317i
$933$	2.64665e14	−	2.64665e14i	0.374359	−	0.374359i
$934$	1.90868e14	−	1.12528e15i	0.268533	−	1.58316i
$935$	−3.16336e12			−0.00442681
$936$	−6.21886e12	−	3.43022e12i	−0.00865629	−	0.00477466i
$937$		−	8.79029e14i		−	1.21704i	−0.793538	−	0.608521i	$-0.791763\pi$
$937$		−	8.79029e14i		−	1.21704i	0.793538	−	0.608521i	$-0.208237\pi$
$938$	−5.95862e12	+	3.51296e13i	−0.00820599	+	0.0483792i
$939$	−8.92748e14	−	8.92748e14i	−1.22293	−	1.22293i
$940$	2.97772e14	−	1.43605e14i	0.405736	−	0.195673i
$941$	3.07810e14	+	3.07810e14i	0.417191	+	0.417191i	0.884235	−	0.467043i	$-0.154681\pi$
$941$	3.07810e14	+	3.07810e14i	0.417191	+	0.417191i	−0.467043	+	0.884235i	$0.654681\pi$
$942$	−4.45669e12	+	3.16407e12i	−0.00600838	+	0.00426571i
$943$		−	5.93521e14i		−	0.795934i
$944$	−2.79072e13	−	2.45211e14i	−0.0372269	−	0.327099i
$945$	1.12193e13			0.0148870
$946$	−4.01940e12	−	5.66145e12i	−0.00530525	−	0.00747260i
$947$	5.62830e14	−	5.62830e14i	0.738971	−	0.738971i	−0.233408	−	0.972379i	$-0.574988\pi$
$947$	5.62830e14	−	5.62830e14i	0.738971	−	0.738971i	0.972379	+	0.233408i	$0.0749878\pi$
$948$	−1.55017e14	+	7.47592e13i	−0.202459	+	0.0976390i
$949$	−6.49911e13	+	6.49911e13i	−0.0844351	+	0.0844351i
$950$	6.83946e14	+	1.16010e14i	0.883901	+	0.149926i
$951$	1.38192e15			1.77657
$952$	3.20170e12	+	1.10783e13i	0.00409445	+	0.0141674i
$953$		−	1.09871e15i		−	1.39772i	−0.715260	−	0.698859i	$-0.753692\pi$
$953$		−	1.09871e15i		−	1.39772i	0.715260	−	0.698859i	$-0.246308\pi$
$954$	9.76854e12	+	1.65692e12i	0.0123620	+	0.00209682i
$955$	3.47759e14	+	3.47759e14i	0.437786	+	0.437786i
$956$	4.86814e13	+	1.70037e13i	0.0609641	+	0.0212939i
$957$	1.89329e13	+	1.89329e13i	0.0235862	+	0.0235862i
$958$	2.03134e14	+	2.86121e14i	0.251742	+	0.354586i
$959$		−	1.00709e13i		−	0.0124158i
$960$	1.69544e14	+	2.68822e14i	0.207934	+	0.329692i
$961$	−1.87005e15			−2.28159
$962$	−1.13733e14	+	8.07455e13i	−0.138041	+	0.0980038i
$963$	5.47285e13	−	5.47285e13i	0.0660818	−	0.0660818i
$964$	4.10401e14	−	1.17497e15i	0.492973	−	1.41137i
$965$	−1.19652e14	+	1.19652e14i	−0.142983	+	0.142983i
$966$	2.63512e12	−	1.55356e13i	0.00313267	−	0.0184689i
$967$	−1.49027e15			−1.76251			−0.881255	−	0.472641i	$-0.843301\pi$
$967$	−1.49027e15			−1.76251			−0.881255	+	0.472641i	$0.843301\pi$
$968$	−8.15944e14	+	2.35813e14i	−0.960027	+	0.277454i
$969$			3.66775e14i			0.429319i
$970$	−4.93738e13	+	2.91088e14i	−0.0574960	+	0.338973i
$971$	−1.12747e15	−	1.12747e15i	−1.30620	−	1.30620i	−0.924136	−	0.382064i	$-0.875213\pi$
$971$	−1.12747e15	−	1.12747e15i	−1.30620	−	1.30620i	−0.382064	−	0.924136i	$-0.624787\pi$
$972$	5.95257e13	+	1.23429e14i	0.0686078	+	0.142261i
$973$	1.64903e13	+	1.64903e13i	0.0189088	+	0.0189088i
$974$	−9.14585e14	+	6.49318e14i	−1.04335	+	0.740735i
$975$		−	8.81659e13i		−	0.100064i
$976$	9.92840e13	+	8.72373e14i	0.112106	+	0.985039i
$977$	−2.27522e14			−0.255594			−0.127797	−	0.991800i	$-0.540791\pi$
$977$	−2.27522e14			−0.255594			−0.127797	+	0.991800i	$0.540791\pi$
$978$	2.95655e14	+	4.16439e14i	0.330439	+	0.465433i
$979$	4.50214e12	−	4.50214e12i	0.00500617	−	0.00500617i
$980$	1.59294e14	+	3.30304e14i	0.176226	+	0.365412i
$981$	−6.59826e13	+	6.59826e13i	−0.0726247	+	0.0726247i
$982$	1.09542e15	+	1.85803e14i	1.19956	+	0.203468i
$983$	−2.11621e14			−0.230563			−0.115282	−	0.993333i	$-0.536777\pi$
$983$	−2.11621e14			−0.230563			−0.115282	+	0.993333i	$0.536777\pi$
$984$	−6.16963e14	+	1.11853e15i	−0.668781	+	1.21248i
$985$			6.06841e13i			0.0654476i
$986$	−5.08839e14	−	8.63085e13i	−0.546004	−	0.0926124i
$987$	2.49444e13	+	2.49444e13i	0.0266309	+	0.0266309i
$988$	−4.16236e13	+	1.19168e14i	−0.0442135	+	0.126583i
$989$	−1.29313e14	−	1.29313e14i	−0.136667	−	0.136667i
$990$	4.62988e11	+	6.52133e11i	0.000486849	+	0.000685742i
$991$		−	1.57448e15i		−	1.64728i	−0.567111	−	0.823642i	$-0.691939\pi$
$991$		−	1.57448e15i		−	1.64728i	0.567111	−	0.823642i	$-0.308061\pi$
$992$	9.51378e13	−	1.73760e15i	0.0990364	−	1.80881i
$993$	2.76182e14			0.286054
$994$	3.85672e12	−	2.73812e12i	0.00397453	−	0.00282176i
$995$	−2.72359e14	+	2.72359e14i	−0.279271	+	0.279271i
$996$	1.18620e15	+	4.14323e14i	1.21021	+	0.422710i
$997$	−3.85504e14	+	3.85504e14i	−0.391339	+	0.391339i	−0.875164	−	0.483826i	$-0.839247\pi$
$997$	−3.85504e14	+	3.85504e14i	−0.391339	+	0.391339i	0.483826	+	0.875164i	$0.339247\pi$
$998$	−1.56887e14	+	9.24939e14i	−0.158465	+	0.934245i
$999$	1.39685e15			1.40385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.11.f.a.3.15	✓	38
4.3	odd	2		64.11.f.a.47.6		38
8.3	odd	2		128.11.f.a.95.14		38
8.5	even	2		128.11.f.b.95.6		38
16.3	odd	4		128.11.f.b.31.6		38
16.5	even	4		64.11.f.a.15.6		38
16.11	odd	4	inner	16.11.f.a.11.15	yes	38
16.13	even	4		128.11.f.a.31.14		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.11.f.a.3.15	✓	38	1.1	even	1	trivial
16.11.f.a.11.15	yes	38	16.11	odd	4	inner
64.11.f.a.15.6		38	16.5	even	4
64.11.f.a.47.6		38	4.3	odd	2
128.11.f.a.31.14		38	16.13	even	4
128.11.f.a.95.14		38	8.3	odd	2
128.11.f.b.31.6		38	16.3	odd	4
128.11.f.b.95.6		38	8.5	even	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(26.0928 - 18.5248i) q^{2} +(164.886 - 164.886i) q^{3} +(337.664 - 966.726i) q^{4} +(897.573 - 897.573i) q^{5} +(1247.85 - 7356.80i) q^{6} +594.817 q^{7} +(-9097.83 - 31479.7i) q^{8} +4674.41i q^{9} +(6792.79 - 40047.5i) q^{10} +(2978.45 + 2978.45i) q^{11} +(-103723. - 215075. i) q^{12} +(-32786.7 - 32786.7i) q^{13} +(15520.4 - 11018.9i) q^{14} -295994. i q^{15} +(-820543. - 652856. i) q^{16} -591643. q^{17} +(86592.6 + 121968. i) q^{18} +(1.87986e6 - 1.87986e6i) q^{19} +(-564629. - 1.17079e6i) q^{20} +(98076.8 - 98076.8i) q^{21} +(132891. + 22540.7i) q^{22} +3.55022e6 q^{23} +(-6.69065e6 - 3.69045e6i) q^{24} +8.15435e6i q^{25} +(-1.46286e6 - 248129. i) q^{26} +(1.05071e7 + 1.05071e7i) q^{27} +(200848. - 575025. i) q^{28} +(1.92759e7 + 1.92759e7i) q^{29} +(-5.48323e6 - 7.72330e6i) q^{30} +5.18621e7i q^{31} +(-3.35042e7 - 1.83444e6i) q^{32} +982206. q^{33} +(-1.54376e7 + 1.09601e7i) q^{34} +(533892. - 533892. i) q^{35} +(4.51888e6 + 1.57838e6i) q^{36} +(6.64716e7 - 6.64716e7i) q^{37} +(1.42267e7 - 8.38750e7i) q^{38} -1.08121e7 q^{39} +(-3.64213e7 - 2.00894e7i) q^{40} -1.67178e8i q^{41} +(742241. - 4.37595e6i) q^{42} +(-3.64240e7 - 3.64240e7i) q^{43} +(3.88505e6 - 1.87363e6i) q^{44} +(4.19563e6 + 4.19563e6i) q^{45} +(9.26351e7 - 6.57672e7i) q^{46} +2.54335e8i q^{47} +(-2.42942e8 + 2.76490e7i) q^{48} -2.82121e8 q^{49} +(1.51058e8 + 2.12769e8i) q^{50} +(-9.75534e7 + 9.75534e7i) q^{51} +(-4.27667e7 + 2.06249e7i) q^{52} +(4.68378e7 - 4.68378e7i) q^{53} +(4.68800e8 + 7.95171e7i) q^{54} +5.34675e6 q^{55} +(-5.41154e6 - 1.87247e7i) q^{56} -6.19926e8i q^{57} +(8.60045e8 + 1.45879e8i) q^{58} +(1.66425e8 + 1.66425e8i) q^{59} +(-2.86145e8 - 9.99464e7i) q^{60} +(-5.92082e8 - 5.92082e8i) q^{61} +(9.60736e8 + 1.35323e9i) q^{62} +2.78042e6i q^{63} +(-9.08201e8 + 5.72794e8i) q^{64} -5.88570e7 q^{65} +(2.56285e7 - 1.81952e7i) q^{66} +(-1.32368e9 + 1.32368e9i) q^{67} +(-1.99776e8 + 5.71957e8i) q^{68} +(5.85381e8 - 5.85381e8i) q^{69} +(4.04047e6 - 2.38209e7i) q^{70} +2.48493e8 q^{71} +(1.47149e8 - 4.25270e7i) q^{72} -1.98224e9i q^{73} +(5.03054e8 - 2.96580e9i) q^{74} +(1.34454e9 + 1.34454e9i) q^{75} +(-1.18255e9 - 2.45208e9i) q^{76} +(1.77163e6 + 1.77163e6i) q^{77} +(-2.82118e8 + 2.00293e8i) q^{78} -7.20756e8i q^{79} +(-1.32248e9 + 1.50511e8i) q^{80} +3.18891e9 q^{81} +(-3.09695e9 - 4.36214e9i) q^{82} +(-3.72085e9 + 3.72085e9i) q^{83} +(-6.16964e7 - 1.27930e8i) q^{84} +(-5.31043e8 + 5.31043e8i) q^{85} +(-1.62515e9 - 2.75655e8i) q^{86} +6.35665e9 q^{87} +(6.66632e7 - 1.20858e8i) q^{88} -1.51157e9i q^{89} +(1.87199e8 + 3.17523e7i) q^{90} +(-1.95021e7 - 1.95021e7i) q^{91} +(1.19878e9 - 3.43209e9i) q^{92} +(8.55132e9 + 8.55132e9i) q^{93} +(4.71150e9 + 6.63630e9i) q^{94} -3.37463e9i q^{95} +(-5.82684e9 + 5.22190e9i) q^{96} -7.26855e9 q^{97} +(-7.36133e9 + 5.22624e9i) q^{98} +(-1.39225e7 + 1.39225e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 2 q^{13} + 757836 q^{14} - 469032 q^{16} - 4 q^{17} + 2066926 q^{18}+ \cdots - 25616384098 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8 - 147364 * q^10 - 45906 * q^11 - 10988 * q^12 - 2 * q^13 + 757836 * q^14 - 469032 * q^16 - 4 * q^17 + 2066926 * q^18 - 5107042 * q^19 + 5301516 * q^20 - 118100 * q^21 - 20568924 * q^22 - 8279748 * q^23 + 58519728 * q^24 - 18451512 * q^26 - 25871552 * q^27 - 36459784 * q^28 - 29652306 * q^29 + 132781252 * q^30 - 52661752 * q^32 - 4 * q^33 + 68474900 * q^34 + 14674460 * q^35 - 15810676 * q^36 - 94618130 * q^37 + 156046000 * q^38 - 279841732 * q^39 - 125381720 * q^40 + 107395416 * q^42 + 172486862 * q^43 + 73663988 * q^44 + 19649346 * q^45 - 437620836 * q^46 + 625190376 * q^48 + 1049193778 * q^49 - 875760314 * q^50 - 72924900 * q^51 - 771392444 * q^52 + 607072398 * q^53 + 913650464 * q^54 - 1427102468 * q^55 - 1385623464 * q^56 + 37561720 * q^58 + 1543683854 * q^59 + 318869600 * q^60 + 1673280158 * q^61 - 983062992 * q^62 - 867678656 * q^64 + 1098715212 * q^65 + 768197860 * q^66 - 4830427746 * q^67 - 855827792 * q^68 + 1698121420 * q^69 - 5103882496 * q^70 + 7572888316 * q^71 + 6888513460 * q^72 + 2513658844 * q^74 - 11656678318 * q^75 - 2250244316 * q^76 - 1336459028 * q^77 + 14243324268 * q^78 - 13115458328 * q^80 - 8523250762 * q^81 + 2724305648 * q^82 + 16141605438 * q^83 - 1633924184 * q^84 + 4779968748 * q^85 - 4025865500 * q^86 - 31832612676 * q^87 + 1023457912 * q^88 + 18960485240 * q^90 + 19874217404 * q^91 + 28060187160 * q^92 - 15001617056 * q^93 - 14829002256 * q^94 + 23525947312 * q^96 - 4 * q^97 - 43134832310 * q^98 - 25616384098 * q^99

Introduction

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