LMFDB - Embedded newform 98.16.c.m.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,16,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$139.839634998$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 11041039 x^{8} + 10251836788 x^{7} + 100086056086567 x^{6} + \cdots + 12\!\cdots\!25 $ x^10 - 2x^9 + 11041039x^8 + 10251836788x^7 + 100086056086567x^6 + 67517626050179350x^5 + 266968630608932668831x^4 + 130403899669863282233290x^3 + 531639154391012701500584575x^2 + 238948900825518555440992768500*x + 120052637231856930389048520650625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{4}\cdot 5^{2}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$778.235 + 1347.94i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.16.c.m.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-64.0000 - 110.851i) q^{2} +(-1753.97 + 3037.97i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +449016. q^{6} +2.09715e6 q^{8} +(1.02163e6 + 1.76951e6i) q^{9} +O(q^{10})$	\(q+(-64.0000 - 110.851i) q^{2} +(-1753.97 + 3037.97i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +449016. q^{6} +2.09715e6 q^{8} +(1.02163e6 + 1.76951e6i) q^{9} +(4.62913e6 - 8.01788e6i) q^{10} +(-4.41234e7 + 7.64240e7i) q^{11} +(-2.87371e7 - 4.97740e7i) q^{12} +1.28410e8 q^{13} -2.53730e8 q^{15} +(-1.34218e8 - 2.32472e8i) q^{16} +(-8.93874e7 + 1.54823e8i) q^{17} +(1.30768e8 - 2.26498e8i) q^{18} +(-2.51228e9 - 4.35140e9i) q^{19} -1.18506e9 q^{20} +1.12956e10 q^{22} +(3.50108e9 + 6.06404e9i) q^{23} +(-3.67834e9 + 6.37108e9i) q^{24} +(1.26430e10 - 2.18983e10i) q^{25} +(-8.21822e9 - 1.42344e10i) q^{26} -5.75027e10 q^{27} +1.06127e11 q^{29} +(1.62387e10 + 2.81263e10i) q^{30} +(7.64697e10 - 1.32449e11i) q^{31} +(-1.71799e10 + 2.97564e10i) q^{32} +(-1.54782e11 - 2.68091e11i) q^{33} +2.28832e10 q^{34} -3.34767e10 q^{36} +(-2.00321e11 - 3.46966e11i) q^{37} +(-3.21572e11 + 5.56979e11i) q^{38} +(-2.25227e11 + 3.90104e11i) q^{39} +(7.58436e10 + 1.31365e11i) q^{40} -4.37251e10 q^{41} -2.44454e12 q^{43} +(-7.22918e11 - 1.25213e12i) q^{44} +(-7.38945e10 + 1.27989e11i) q^{45} +(4.48138e11 - 7.76198e11i) q^{46} +(-1.20549e12 - 2.08797e12i) q^{47} +9.41656e11 q^{48} -3.23660e12 q^{50} +(-3.13566e11 - 5.43112e11i) q^{51} +(-1.05193e12 + 1.82200e12i) q^{52} +(-5.08120e12 + 8.80091e12i) q^{53} +(3.68018e12 + 6.37425e12i) q^{54} -6.38290e12 q^{55} +1.76259e13 q^{57} +(-6.79212e12 - 1.17643e13i) q^{58} +(-1.13900e13 + 1.97280e13i) q^{59} +(2.07855e12 - 3.60016e12i) q^{60} +(-2.02342e13 - 3.50467e13i) q^{61} -1.95762e13 q^{62} +4.39805e12 q^{64} +(4.64394e12 + 8.04355e12i) q^{65} +(-1.98121e13 + 3.43156e13i) q^{66} +(-2.61618e13 + 4.53136e13i) q^{67} +(-1.46452e12 - 2.53663e12i) q^{68} -2.45631e13 q^{69} +4.87140e13 q^{71} +(2.14251e12 + 3.71094e12i) q^{72} +(2.90981e13 - 5.03994e13i) q^{73} +(-2.56411e13 + 4.44116e13i) q^{74} +(4.43508e13 + 7.68178e13i) q^{75} +8.23224e13 q^{76} +5.76581e13 q^{78} +(-8.16442e13 - 1.41412e14i) q^{79} +(9.70798e12 - 1.68147e13i) q^{80} +(8.61989e13 - 1.49301e14i) q^{81} +(2.79841e12 + 4.84699e12i) q^{82} +1.62502e14 q^{83} -1.29308e13 q^{85} +(1.56451e14 + 2.70980e14i) q^{86} +(-1.86143e14 + 3.22410e14i) q^{87} +(-9.25335e13 + 1.60273e14i) q^{88} +(-4.92355e13 - 8.52783e13i) q^{89} +1.89170e13 q^{90} -1.14723e14 q^{92} +(2.68251e14 + 4.64624e14i) q^{93} +(-1.54303e14 + 2.67260e14i) q^{94} +(1.81714e14 - 3.14737e14i) q^{95} +(-6.02660e13 - 1.04384e14i) q^{96} +6.71892e14 q^{97} -1.80311e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 640 q^{2} - 1979 q^{3} - 81920 q^{4} - 300953 q^{5} + 506624 q^{6} + 20971520 q^{8} - 17367046 q^{9}+O(q^{10}) $ 10 * q - 640 * q^2 - 1979 * q^3 - 81920 * q^4 - 300953 * q^5 + 506624 * q^6 + 20971520 * q^8 - 17367046 * q^9	\( 10 q - 640 q^{2} - 1979 q^{3} - 81920 q^{4} - 300953 q^{5} + 506624 q^{6} + 20971520 q^{8} - 17367046 q^{9} - 38521984 q^{10} + 14189887 q^{11} - 32423936 q^{12} + 772602348 q^{13} + 1426775646 q^{15} - 1342177280 q^{16} + 145564295 q^{17} - 2222981888 q^{18} - 3550131629 q^{19} + 9861627904 q^{20} - 3632611072 q^{22} + 9869524537 q^{23} - 4150263808 q^{24} - 51839554204 q^{25} - 49446550272 q^{26} + 342946209778 q^{27} - 165255956188 q^{29} - 91313641344 q^{30} + 106825666677 q^{31} - 171798691840 q^{32} + 139826141649 q^{33} - 37264459520 q^{34} + 569083363328 q^{36} - 596799401515 q^{37} - 454416848512 q^{38} - 2827795559666 q^{39} - 631144185856 q^{40} - 1756981189740 q^{41} - 5305116572344 q^{43} + 232487108608 q^{44} - 10836341974062 q^{45} + 1263299140736 q^{46} - 4284391851525 q^{47} + 1062467534848 q^{48} + 13270925876224 q^{50} - 8298359375823 q^{51} - 6329158434816 q^{52} - 4037801378823 q^{53} - 21948557425792 q^{54} + 47232884322970 q^{55} - 75972269020058 q^{57} + 10576381196032 q^{58} - 6081930248483 q^{59} - 11688146092032 q^{60} - 29484338931189 q^{61} - 27347370669312 q^{62} + 43980465111040 q^{64} + 78038741223618 q^{65} + 17897746131072 q^{66} - 2851190345117 q^{67} + 2384925409280 q^{68} + 41705305747074 q^{69} + 190169727933856 q^{71} - 36421335252992 q^{72} - 284202883487269 q^{73} - 76390323393920 q^{74} + 151851953188876 q^{75} + 116330713219072 q^{76} + 723915663274496 q^{78} + 536529323488905 q^{79} - 80786455789568 q^{80} + 23023662902123 q^{81} + 112446796143360 q^{82} + 949641950127416 q^{83} + 24\!\cdots\!86 q^{85}+ \cdots - 989855214604404 q^{99}+O(q^{100}) \) 10 * q - 640 * q^2 - 1979 * q^3 - 81920 * q^4 - 300953 * q^5 + 506624 * q^6 + 20971520 * q^8 - 17367046 * q^9 - 38521984 * q^10 + 14189887 * q^11 - 32423936 * q^12 + 772602348 * q^13 + 1426775646 * q^15 - 1342177280 * q^16 + 145564295 * q^17 - 2222981888 * q^18 - 3550131629 * q^19 + 9861627904 * q^20 - 3632611072 * q^22 + 9869524537 * q^23 - 4150263808 * q^24 - 51839554204 * q^25 - 49446550272 * q^26 + 342946209778 * q^27 - 165255956188 * q^29 - 91313641344 * q^30 + 106825666677 * q^31 - 171798691840 * q^32 + 139826141649 * q^33 - 37264459520 * q^34 + 569083363328 * q^36 - 596799401515 * q^37 - 454416848512 * q^38 - 2827795559666 * q^39 - 631144185856 * q^40 - 1756981189740 * q^41 - 5305116572344 * q^43 + 232487108608 * q^44 - 10836341974062 * q^45 + 1263299140736 * q^46 - 4284391851525 * q^47 + 1062467534848 * q^48 + 13270925876224 * q^50 - 8298359375823 * q^51 - 6329158434816 * q^52 - 4037801378823 * q^53 - 21948557425792 * q^54 + 47232884322970 * q^55 - 75972269020058 * q^57 + 10576381196032 * q^58 - 6081930248483 * q^59 - 11688146092032 * q^60 - 29484338931189 * q^61 - 27347370669312 * q^62 + 43980465111040 * q^64 + 78038741223618 * q^65 + 17897746131072 * q^66 - 2851190345117 * q^67 + 2384925409280 * q^68 + 41705305747074 * q^69 + 190169727933856 * q^71 - 36421335252992 * q^72 - 284202883487269 * q^73 - 76390323393920 * q^74 + 151851953188876 * q^75 + 116330713219072 * q^76 + 723915663274496 * q^78 + 536529323488905 * q^79 - 80786455789568 * q^80 + 23023662902123 * q^81 + 112446796143360 * q^82 + 949641950127416 * q^83 + 2471416802444186 * q^85 + 339527460630016 * q^86 - 1562035609957686 * q^87 + 29758349901824 * q^88 - 160148042721333 * q^89 + 2774103545359872 * q^90 - 323404580028416 * q^92 + 1714374265333339 * q^93 - 548402156995200 * q^94 - 739988010259049 * q^95 - 67997922230272 * q^96 + 4057131581852468 * q^97 - 989855214604404 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−64.0000	−	110.851i	−0.353553	−	0.612372i
$2$	−64.0000	−	110.851i	−0.353553	−	0.612372i
$3$	−1753.97	+	3037.97i	−0.463034	+	0.801998i	−0.999110	−	0.0421711i	$-0.986573\pi$
$3$	−1753.97	+	3037.97i	−0.463034	+	0.801998i	0.536076	+	0.844169i	$0.319906\pi$
$4$	−8192.00	+	14189.0i	−0.250000	+	0.433013i
$5$	36165.1	+	62639.7i	0.207021	+	0.358571i	0.950775	−	0.309883i	$-0.100290\pi$
$5$	36165.1	+	62639.7i	0.207021	+	0.358571i	−0.743754	+	0.668454i	$0.766957\pi$
$6$	449016.			0.654829
$7$		0			0
$7$		0			0
$8$	2.09715e6			0.353553
$9$	1.02163e6	+	1.76951e6i	0.0711991	+	0.123320i
$10$	4.62913e6	−	8.01788e6i	0.146386	−	0.253548i
$11$	−4.41234e7	+	7.64240e7i	−0.682691	+	1.18246i	0.291466	+	0.956581i	$0.405857\pi$
$11$	−4.41234e7	+	7.64240e7i	−0.682691	+	1.18246i	−0.974157	+	0.225874i	$0.927476\pi$
$12$	−2.87371e7	−	4.97740e7i	−0.231517	−	0.400999i
$13$	1.28410e8			0.567574			0.283787	−	0.958887i	$-0.408409\pi$
$13$	1.28410e8			0.567574			0.283787	+	0.958887i	$0.408409\pi$
$14$		0			0
$15$	−2.53730e8			−0.383431
$16$	−1.34218e8	−	2.32472e8i	−0.125000	−	0.216506i
$17$	−8.93874e7	+	1.54823e8i	−0.0528335	+	0.0915103i	−0.891233	−	0.453547i	$-0.850159\pi$
$17$	−8.93874e7	+	1.54823e8i	−0.0528335	+	0.0915103i	0.838399	+	0.545057i	$0.183492\pi$
$18$	1.30768e8	−	2.26498e8i	0.0503453	−	0.0872007i
$19$	−2.51228e9	−	4.35140e9i	−0.644787	−	1.11680i	−0.984351	−	0.176221i	$-0.943613\pi$
$19$	−2.51228e9	−	4.35140e9i	−0.644787	−	1.11680i	0.339564	−	0.940583i	$-0.389721\pi$
$20$	−1.18506e9			−0.207021
$21$		0			0
$22$	1.12956e10			0.965471
$23$	3.50108e9	+	6.06404e9i	0.214409	+	0.371367i	0.953090	−	0.302688i	$-0.0978841\pi$
$23$	3.50108e9	+	6.06404e9i	0.214409	+	0.371367i	−0.738681	+	0.674056i	$0.764551\pi$
$24$	−3.67834e9	+	6.37108e9i	−0.163707	+	0.283549i
$25$	1.26430e10	−	2.18983e10i	0.414285	−	0.717562i
$26$	−8.21822e9	−	1.42344e10i	−0.200668	−	0.347567i
$27$	−5.75027e10			−1.05794
$28$		0			0
$29$	1.06127e11			1.14246			0.571229	−	0.820791i	$-0.306467\pi$
$29$	1.06127e11			1.14246			0.571229	+	0.820791i	$0.306467\pi$
$30$	1.62387e10	+	2.81263e10i	0.135563	+	0.234802i
$31$	7.64697e10	−	1.32449e11i	0.499202	−	0.864644i	−0.500797	−	0.865565i	$-0.666960\pi$
$31$	7.64697e10	−	1.32449e11i	0.499202	−	0.864644i	1.00000		0.000920959i	$0.000293150\pi$
$32$	−1.71799e10	+	2.97564e10i	−0.0883883	+	0.153093i
$33$	−1.54782e11	−	2.68091e11i	−0.632218	−	1.09503i
$34$	2.28832e10			0.0747178
$35$		0			0
$36$	−3.34767e10			−0.0711991
$37$	−2.00321e11	−	3.46966e11i	−0.346907	−	0.600861i	0.638791	−	0.769380i	$-0.279435\pi$
$37$	−2.00321e11	−	3.46966e11i	−0.346907	−	0.600861i	−0.985698	+	0.168519i	$0.946101\pi$
$38$	−3.21572e11	+	5.56979e11i	−0.455933	+	0.789700i
$39$	−2.25227e11	+	3.90104e11i	−0.262806	+	0.455194i
$40$	7.58436e10	+	1.31365e11i	0.0731929	+	0.126774i
$41$	−4.37251e10			−0.0350633			−0.0175316	−	0.999846i	$-0.505581\pi$
$41$	−4.37251e10			−0.0350633			−0.0175316	+	0.999846i	$0.505581\pi$
$42$		0			0
$43$	−2.44454e12			−1.37146			−0.685731	−	0.727855i	$-0.740517\pi$
$43$	−2.44454e12			−1.37146			−0.685731	+	0.727855i	$0.740517\pi$
$44$	−7.22918e11	−	1.25213e12i	−0.341345	−	0.591228i
$45$	−7.38945e10	+	1.27989e11i	−0.0294794	+	0.0510598i
$46$	4.48138e11	−	7.76198e11i	0.151610	−	0.262596i
$47$	−1.20549e12	−	2.08797e12i	−0.347080	−	0.601160i	0.638650	−	0.769498i	$-0.279493\pi$
$47$	−1.20549e12	−	2.08797e12i	−0.347080	−	0.601160i	−0.985729	+	0.168338i	$0.946160\pi$
$48$	9.41656e11			0.231517
$49$		0			0
$50$	−3.23660e12			−0.585887
$51$	−3.13566e11	−	5.43112e11i	−0.0489274	−	0.0847447i
$52$	−1.05193e12	+	1.82200e12i	−0.141894	+	0.245767i
$53$	−5.08120e12	+	8.80091e12i	−0.594152	+	1.02910i	0.399514	+	0.916727i	$0.369179\pi$
$53$	−5.08120e12	+	8.80091e12i	−0.594152	+	1.02910i	−0.993666	+	0.112375i	$0.964154\pi$
$54$	3.68018e12	+	6.37425e12i	0.374038	+	0.647852i
$55$	−6.38290e12			−0.565325
$56$		0			0
$57$	1.76259e13			1.19423
$58$	−6.79212e12	−	1.17643e13i	−0.403920	−	0.699610i
$59$	−1.13900e13	+	1.97280e13i	−0.595845	+	1.03203i	0.397582	+	0.917567i	$0.369849\pi$
$59$	−1.13900e13	+	1.97280e13i	−0.595845	+	1.03203i	−0.993427	+	0.114467i	$0.963484\pi$
$60$	2.07855e12	−	3.60016e12i	0.0958577	−	0.166030i
$61$	−2.02342e13	−	3.50467e13i	−0.824351	−	1.42782i	−0.902414	−	0.430870i	$-0.858207\pi$
$61$	−2.02342e13	−	3.50467e13i	−0.824351	−	1.42782i	0.0780625	−	0.996948i	$-0.475127\pi$
$62$	−1.95762e13			−0.705979
$63$		0			0
$64$	4.39805e12			0.125000
$65$	4.64394e12	+	8.04355e12i	0.117500	+	0.203515i
$66$	−1.98121e13	+	3.43156e13i	−0.447046	+	0.774306i
$67$	−2.61618e13	+	4.53136e13i	−0.527360	+	0.913414i	0.472132	+	0.881528i	$0.343485\pi$
$67$	−2.61618e13	+	4.53136e13i	−0.527360	+	0.913414i	−0.999492	+	0.0318859i	$0.989849\pi$
$68$	−1.46452e12	−	2.53663e12i	−0.0264167	−	0.0457551i
$69$	−2.45631e13			−0.397114
$70$		0			0
$71$	4.87140e13			0.635647			0.317824	−	0.948150i	$-0.397048\pi$
$71$	4.87140e13			0.635647			0.317824	+	0.948150i	$0.397048\pi$
$72$	2.14251e12	+	3.71094e12i	0.0251727	+	0.0436003i
$73$	2.90981e13	−	5.03994e13i	0.308278	−	0.533954i	−0.669707	−	0.742625i	$-0.733580\pi$
$73$	2.90981e13	−	5.03994e13i	0.308278	−	0.533954i	0.977986	+	0.208671i	$0.0669138\pi$
$74$	−2.56411e13	+	4.44116e13i	−0.245300	+	0.424873i
$75$	4.43508e13	+	7.68178e13i	0.383656	+	0.664511i
$76$	8.23224e13			0.644787
$77$		0			0
$78$	5.76581e13			0.371664
$79$	−8.16442e13	−	1.41412e14i	−0.478324	−	0.828482i	0.521367	−	0.853333i	$-0.325422\pi$
$79$	−8.16442e13	−	1.41412e14i	−0.478324	−	0.828482i	−0.999691	+	0.0248508i	$0.992089\pi$
$80$	9.70798e12	−	1.68147e13i	0.0517552	−	0.0896427i
$81$	8.61989e13	−	1.49301e14i	0.418662	−	0.725144i
$82$	2.79841e12	+	4.84699e12i	0.0123967	+	0.0214718i
$83$	1.62502e14			0.657315			0.328658	−	0.944449i	$-0.393404\pi$
$83$	1.62502e14			0.657315			0.328658	+	0.944449i	$0.393404\pi$
$84$		0			0
$85$	−1.29308e13			−0.0437505
$86$	1.56451e14	+	2.70980e14i	0.484885	+	0.839846i
$87$	−1.86143e14	+	3.22410e14i	−0.528997	+	0.916250i
$88$	−9.25335e13	+	1.60273e14i	−0.241368	+	0.418061i
$89$	−4.92355e13	−	8.52783e13i	−0.117992	−	0.204368i	0.800980	−	0.598691i	$-0.204312\pi$
$89$	−4.92355e13	−	8.52783e13i	−0.117992	−	0.204368i	−0.918972	+	0.394323i	$0.870979\pi$
$90$	1.89170e13			0.0416901
$91$		0			0
$92$	−1.14723e14			−0.214409
$93$	2.68251e14	+	4.64624e14i	0.462295	+	0.800719i
$94$	−1.54303e14	+	2.67260e14i	−0.245422	+	0.425084i
$95$	1.81714e14	−	3.14737e14i	0.266969	−	0.462403i
$96$	−6.02660e13	−	1.04384e14i	−0.0818536	−	0.141775i
$97$	6.71892e14			0.844329			0.422164	−	0.906519i	$-0.361270\pi$
$97$	6.71892e14			0.844329			0.422164	+	0.906519i	$0.361270\pi$
$98$		0			0
$99$	−1.80311e14			−0.194428
$100$	2.07142e14	+	3.58781e14i	0.207142	+	0.358781i
$101$	−3.66484e14	+	6.34768e14i	−0.340130	+	0.589122i	−0.984457	−	0.175628i	$-0.943804\pi$
$101$	−3.66484e14	+	6.34768e14i	−0.340130	+	0.589122i	0.644327	+	0.764750i	$0.277138\pi$
$102$	−4.01364e13	+	6.95183e13i	−0.0345969	+	0.0599236i
$103$	−5.49597e14	−	9.51930e14i	−0.440317	−	0.762651i	0.557396	−	0.830247i	$-0.311800\pi$
$103$	−5.49597e14	−	9.51930e14i	−0.440317	−	0.762651i	−0.997713	+	0.0675959i	$0.978467\pi$
$104$	2.69295e14			0.200668
$105$		0			0
$106$	1.30079e15			0.840258
$107$	1.56756e15	+	2.71509e15i	0.943726	+	1.63458i	0.758282	+	0.651926i	$0.226039\pi$
$107$	1.56756e15	+	2.71509e15i	0.943726	+	1.63458i	0.185444	+	0.982655i	$0.440628\pi$
$108$	4.71062e14	−	8.15904e14i	0.264485	−	0.458101i
$109$	6.81694e14	−	1.18073e15i	0.357183	−	0.618659i	−0.630306	−	0.776347i	$-0.717071\pi$
$109$	6.81694e14	−	1.18073e15i	0.357183	−	0.618659i	0.987489	+	0.157688i	$0.0504040\pi$
$110$	4.08506e14	+	7.07553e14i	0.199873	+	0.346189i
$111$	1.40543e15			0.642519
$112$		0			0
$113$	1.37056e15			0.548036			0.274018	−	0.961725i	$-0.411647\pi$
$113$	1.37056e15			0.548036			0.274018	+	0.961725i	$0.411647\pi$
$114$	−1.12806e15	−	1.95385e15i	−0.422225	−	0.731315i
$115$	−2.53233e14	+	4.38613e14i	−0.0887742	+	0.153762i
$116$	−8.69391e14	+	1.50583e15i	−0.285615	+	0.494699i
$117$	1.31187e14	+	2.27223e14i	0.0404108	+	0.0699935i
$118$	2.91584e15			0.842652
$119$		0			0
$120$	−5.32110e14			−0.135563
$121$	−1.80513e15	−	3.12658e15i	−0.432134	−	0.748477i
$122$	−2.58998e15	+	4.48597e15i	−0.582904	+	1.00962i
$123$	7.66926e13	−	1.32835e14i	0.0162355	−	0.0281207i
$124$	1.25288e15	+	2.17005e15i	0.249601	+	0.432322i
$125$	4.03627e15			0.757104
$126$		0			0
$127$	−7.19653e15			−1.19838			−0.599191	−	0.800606i	$-0.704511\pi$
$127$	−7.19653e15			−1.19838			−0.599191	+	0.800606i	$0.704511\pi$
$128$	−2.81475e14	−	4.87529e14i	−0.0441942	−	0.0765466i
$129$	4.28765e15	−	7.42643e15i	0.635034	−	1.09991i
$130$	5.94425e14	−	1.02957e15i	0.0830848	−	0.143907i
$131$	−7.14085e15	−	1.23683e16i	−0.942357	−	1.63221i	−0.760958	−	0.648801i	$-0.775271\pi$
$131$	−7.14085e15	−	1.23683e16i	−0.942357	−	1.63221i	−0.181399	−	0.983410i	$-0.558062\pi$
$132$	5.07191e15			0.632218
$133$		0			0
$134$	6.69743e15			0.745799
$135$	−2.07959e15	−	3.60196e15i	−0.219015	−	0.379346i
$136$	−1.87459e14	+	3.24688e14i	−0.0186795	+	0.0323538i
$137$	5.66307e15	−	9.80872e15i	0.534130	−	0.925141i	−0.465074	−	0.885272i	$-0.653972\pi$
$137$	5.66307e15	−	9.80872e15i	0.534130	−	0.925141i	0.999205	−	0.0398695i	$-0.0126942\pi$
$138$	1.57204e15	+	2.72286e15i	0.140401	+	0.243182i
$139$	−1.40279e16			−1.18681			−0.593407	−	0.804903i	$-0.702217\pi$
$139$	−1.40279e16			−1.18681			−0.593407	+	0.804903i	$0.702217\pi$
$140$		0			0
$141$	8.45756e15			0.642839
$142$	−3.11770e15	−	5.40001e15i	−0.224735	−	0.389253i
$143$	−5.66588e15	+	9.81358e15i	−0.387478	+	0.671131i
$144$	2.74241e14	−	4.75000e14i	0.0177998	−	0.0308301i
$145$	3.83808e15	+	6.64776e15i	0.236513	+	0.409652i
$146$	−7.44911e15			−0.435972
$147$		0			0
$148$	6.56411e15			0.346907
$149$	−2.73587e15	−	4.73867e15i	−0.137467	−	0.238100i	0.789070	−	0.614303i	$-0.210563\pi$
$149$	−2.73587e15	−	4.73867e15i	−0.137467	−	0.238100i	−0.926537	+	0.376203i	$0.877229\pi$
$150$	5.67690e15	−	9.83268e15i	0.271286	−	0.469880i
$151$	1.44081e16	−	2.49556e16i	0.655059	−	1.13460i	−0.326820	−	0.945087i	$-0.605977\pi$
$151$	1.44081e16	−	2.49556e16i	0.655059	−	1.13460i	0.981879	−	0.189509i	$-0.0606897\pi$
$152$	−5.26864e15	−	9.12555e15i	−0.227967	−	0.394850i
$153$	−3.65283e14			−0.0150468
$154$		0			0
$155$	1.10621e16			0.413381
$156$	−3.69012e15	−	6.39147e15i	−0.131403	−	0.227597i
$157$	3.68210e15	−	6.37759e15i	0.124982	−	0.216476i	−0.796744	−	0.604317i	$-0.793446\pi$
$157$	3.68210e15	−	6.37759e15i	0.124982	−	0.216476i	0.921726	+	0.387842i	$0.126779\pi$
$158$	−1.04505e16	+	1.81007e16i	−0.338226	+	0.585825i
$159$	−1.78246e16	−	3.08731e16i	−0.550225	−	0.953018i
$160$	−2.48524e15			−0.0731929
$161$		0			0
$162$	−2.20669e16			−0.592078
$163$	−3.57987e16	−	6.20052e16i	−0.917193	−	1.58862i	−0.803659	−	0.595090i	$-0.797116\pi$
$163$	−3.57987e16	−	6.20052e16i	−0.917193	−	1.58862i	−0.113534	−	0.993534i	$-0.536217\pi$
$164$	3.58196e14	−	6.20414e14i	0.00876581	−	0.0151828i
$165$	1.11954e16	−	1.93910e16i	0.261765	−	0.453390i
$166$	−1.04001e16	−	1.80136e16i	−0.232396	−	0.402522i
$167$	9.04861e16			1.93290			0.966448	−	0.256862i	$-0.0826886\pi$
$167$	9.04861e16			1.93290			0.966448	+	0.256862i	$0.0826886\pi$
$168$		0			0
$169$	−3.46968e16			−0.677860
$170$	8.27571e14	+	1.43339e15i	0.0154681	+	0.0267916i
$171$	5.13324e15	−	8.89103e15i	0.0918165	−	0.159031i
$172$	2.00257e16	−	3.46855e16i	0.342866	−	0.593861i
$173$	−3.18743e14	−	5.52079e14i	−0.00522511	−	0.00905015i	0.863401	−	0.504518i	$-0.168330\pi$
$173$	−3.18743e14	−	5.52079e14i	−0.00522511	−	0.00905015i	−0.868626	+	0.495468i	$0.834997\pi$
$174$	4.76527e16			0.748115
$175$		0			0
$176$	2.36886e16			0.341345
$177$	−3.99554e16	−	6.92048e16i	−0.551793	−	0.955733i
$178$	−6.30214e15	+	1.09156e16i	−0.0834330	+	0.144510i
$179$	2.71119e16	−	4.69593e16i	0.344162	−	0.596106i	−0.641039	−	0.767508i	$-0.721496\pi$
$179$	2.71119e16	−	4.69593e16i	0.344162	−	0.596106i	0.985201	+	0.171402i	$0.0548297\pi$
$180$	−1.21069e15	−	2.09697e15i	−0.0147397	−	0.0255299i
$181$	1.48558e17			1.73503			0.867514	−	0.497412i	$-0.165716\pi$
$181$	1.48558e17			1.73503			0.867514	+	0.497412i	$0.165716\pi$
$182$		0			0
$183$	1.41961e17			1.52681
$184$	7.34229e15	+	1.27172e16i	0.0758050	+	0.131298i
$185$	1.44892e16	−	2.50961e16i	0.143634	−	0.248781i
$186$	3.43361e16	−	5.94719e16i	0.326892	−	0.566194i
$187$	−7.88815e15	−	1.36627e16i	−0.0721379	−	0.124946i
$188$	3.95014e16			0.347080
$189$		0			0
$190$	−4.65187e16			−0.377551
$191$	9.39211e16	+	1.62676e17i	0.732846	+	1.26933i	0.955662	+	0.294467i	$0.0951420\pi$
$191$	9.39211e16	+	1.62676e17i	0.732846	+	1.26933i	−0.222815	+	0.974861i	$0.571525\pi$
$192$	−7.71404e15	+	1.33611e16i	−0.0578792	+	0.100250i
$193$	7.20643e16	−	1.24819e17i	0.520044	−	0.900743i	−0.479684	−	0.877441i	$-0.659249\pi$
$193$	7.20643e16	−	1.24819e17i	0.520044	−	0.900743i	0.999728	−	0.0233020i	$-0.00741792\pi$
$194$	−4.30011e16	−	7.44801e16i	−0.298515	−	0.517044i
$195$	−3.25814e16			−0.217625
$196$		0			0
$197$	−8.85598e16			−0.547949			−0.273974	−	0.961737i	$-0.588338\pi$
$197$	−8.85598e16			−0.547949			−0.273974	+	0.961737i	$0.588338\pi$
$198$	1.15399e16	+	1.99877e16i	0.0687406	+	0.119062i
$199$	−4.61131e16	+	7.98703e16i	−0.264501	+	0.458129i	−0.967433	−	0.253129i	$-0.918540\pi$
$199$	−4.61131e16	+	7.98703e16i	−0.264501	+	0.458129i	0.702932	+	0.711257i	$0.251874\pi$
$200$	2.65142e16	−	4.59240e16i	0.146472	−	0.253697i
$201$	−9.17741e16	−	1.58957e17i	−0.488371	−	0.845883i
$202$	9.38198e16			0.481016
$203$		0			0
$204$	1.02749e16			0.0489274
$205$	−1.58132e15	−	2.73893e15i	−0.00725882	−	0.0125727i
$206$	−7.03484e16	+	1.21847e17i	−0.311351	+	0.539275i
$207$	−7.15360e15	+	1.23904e16i	−0.0305314	+	0.0528820i
$208$	−1.72349e16	−	2.98516e16i	−0.0709468	−	0.122883i
$209$	4.43402e17			1.76076
$210$		0			0
$211$	5.05813e17			1.87013			0.935065	−	0.354476i	$-0.115341\pi$
$211$	5.05813e17			1.87013			0.935065	+	0.354476i	$0.115341\pi$
$212$	−8.32505e16	−	1.44194e17i	−0.297076	−	0.514551i
$213$	−8.54429e16	+	1.47992e17i	−0.294326	+	0.509788i
$214$	2.00648e17	−	3.47532e17i	0.667315	−	1.15582i
$215$	−8.84070e16	−	1.53125e17i	−0.283921	−	0.491766i
$216$	−1.20592e17			−0.374038
$217$		0			0
$218$	−1.74514e17			−0.505133
$219$	1.02074e17	+	1.76798e17i	0.285487	+	0.494478i
$220$	5.22888e16	−	9.05668e16i	0.141331	−	0.244793i
$221$	−1.14782e16	+	1.98808e16i	−0.0299869	+	0.0519389i
$222$	−8.99473e16	−	1.55793e17i	−0.227165	−	0.393461i
$223$	3.23682e17			0.790373			0.395187	−	0.918601i	$-0.370680\pi$
$223$	3.23682e17			0.790373			0.395187	+	0.918601i	$0.370680\pi$
$224$		0			0
$225$	5.16657e16			0.117987
$226$	−8.77157e16	−	1.51928e17i	−0.193760	−	0.335602i
$227$	−3.65320e16	+	6.32753e16i	−0.0780692	+	0.135220i	−0.902417	−	0.430864i	$-0.858209\pi$
$227$	−3.65320e16	+	6.32753e16i	−0.0780692	+	0.135220i	0.824348	+	0.566084i	$0.191542\pi$
$228$	−1.44391e17	+	2.50093e17i	−0.298558	+	0.517118i
$229$	3.54581e17	+	6.14153e17i	0.709495	+	1.22888i	0.965045	+	0.262086i	$0.0844104\pi$
$229$	3.54581e17	+	6.14153e17i	0.709495	+	1.22888i	−0.255549	+	0.966796i	$0.582256\pi$
$230$	6.48277e16			0.125546
$231$		0			0
$232$	2.22564e17			0.403920
$233$	−3.75817e17	−	6.50934e17i	−0.660400	−	1.14385i	−0.980511	−	0.196466i	$-0.937053\pi$
$233$	−3.75817e17	−	6.50934e17i	−0.660400	−	1.14385i	0.320111	−	0.947380i	$-0.396280\pi$
$234$	1.67919e16	−	2.90845e16i	0.0285747	−	0.0494929i
$235$	8.71931e16	−	1.51023e17i	0.143705	−	0.248905i
$236$	−1.86614e17	−	3.23224e17i	−0.297922	−	0.516017i
$237$	5.72806e17			0.885921
$238$		0			0
$239$	4.14880e17			0.602474			0.301237	−	0.953549i	$-0.402600\pi$
$239$	4.14880e17			0.602474			0.301237	+	0.953549i	$0.402600\pi$
$240$	3.40550e16	+	5.89850e16i	0.0479288	+	0.0830152i
$241$	−3.73589e17	+	6.47074e17i	−0.509643	+	0.882727i	0.490295	+	0.871557i	$0.336889\pi$
$241$	−3.73589e17	+	6.47074e17i	−0.509643	+	0.882727i	−0.999938	+	0.0111705i	$0.996444\pi$
$242$	−2.31057e17	+	4.00202e17i	−0.305565	+	0.529253i
$243$	−1.10170e17	−	1.90820e17i	−0.141259	−	0.244668i
$244$	6.63034e17			0.824351
$245$		0			0
$246$	−1.96333e16			−0.0229604
$247$	−3.22601e17	−	5.58762e17i	−0.365964	−	0.633869i
$248$	1.60369e17	−	2.77766e17i	0.176495	−	0.305698i
$249$	−2.85024e17	+	4.93676e17i	−0.304359	+	0.527166i
$250$	−2.58322e17	−	4.47426e17i	−0.267677	−	0.463630i
$251$	−1.85024e18			−1.86070			−0.930350	−	0.366674i	$-0.880497\pi$
$251$	−1.85024e18			−1.86070			−0.930350	+	0.366674i	$0.880497\pi$
$252$		0			0
$253$	−6.17918e17			−0.585500
$254$	4.60578e17	+	7.97744e17i	0.423692	+	0.733856i
$255$	2.26802e16	−	3.92833e16i	0.0202580	−	0.0350879i
$256$	−3.60288e16	+	6.24037e16i	−0.0312500	+	0.0541266i
$257$	−4.65713e17	−	8.06638e17i	−0.392301	−	0.679485i	0.600452	−	0.799661i	$-0.294988\pi$
$257$	−4.65713e17	−	8.06638e17i	−0.392301	−	0.679485i	−0.992753	+	0.120176i	$0.961654\pi$
$258$	−1.09764e18			−0.898073
$259$		0			0
$260$	−1.52173e17			−0.117500
$261$	1.08422e17	+	1.87793e17i	0.0813420	+	0.140888i
$262$	−9.14029e17	+	1.58315e18i	−0.666347	+	1.15415i
$263$	5.22388e17	−	9.04802e17i	0.370105	−	0.641040i	−0.619477	−	0.785015i	$-0.712655\pi$
$263$	5.22388e17	−	9.04802e17i	0.370105	−	0.641040i	0.989581	+	0.143975i	$0.0459884\pi$
$264$	−3.24602e17	−	5.62227e17i	−0.223523	−	0.387153i
$265$	−7.35048e17			−0.492008
$266$		0			0
$267$	3.45430e17			0.218537
$268$	−4.28635e17	−	7.42418e17i	−0.263680	−	0.456707i
$269$	1.33019e18	−	2.30396e18i	0.795741	−	1.37826i	−0.126627	−	0.991950i	$-0.540415\pi$
$269$	1.33019e18	−	2.30396e18i	0.795741	−	1.37826i	0.922368	−	0.386313i	$-0.126252\pi$
$270$	−2.66188e17	+	4.61050e17i	−0.154867	+	0.268238i
$271$	1.29784e18	+	2.24793e18i	0.734433	+	1.27208i	0.954972	+	0.296697i	$0.0958851\pi$
$271$	1.29784e18	+	2.24793e18i	0.734433	+	1.27208i	−0.220539	+	0.975378i	$0.570782\pi$
$272$	4.79895e16			0.0264167
$273$		0			0
$274$	−1.44974e18			−0.755375
$275$	1.11570e18	+	1.93245e18i	0.565657	+	0.979746i
$276$	2.01221e17	−	3.48525e17i	0.0992786	−	0.171956i
$277$	8.20822e17	−	1.42171e18i	0.394140	−	0.682671i	−0.598851	−	0.800861i	$-0.704376\pi$
$277$	8.20822e17	−	1.42171e18i	0.394140	−	0.682671i	0.992991	+	0.118190i	$0.0377091\pi$
$278$	8.97787e17	+	1.55501e18i	0.419602	+	0.726772i
$279$	3.12494e17			0.142171
$280$		0			0
$281$	−1.24946e18			−0.538797			−0.269398	−	0.963029i	$-0.586825\pi$
$281$	−1.24946e18			−0.538797			−0.269398	+	0.963029i	$0.586825\pi$
$282$	−5.41284e17	−	9.37532e17i	−0.227278	−	0.393657i
$283$	8.65425e17	−	1.49896e18i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$283$	8.65425e17	−	1.49896e18i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515356\pi$
$284$	−3.99065e17	+	6.91201e17i	−0.158912	+	0.275243i
$285$	6.37441e17	+	1.10408e18i	0.247231	+	0.428217i
$286$	1.45046e18			0.547976
$287$		0			0
$288$	−7.02058e16			−0.0251727
$289$	1.41523e18	+	2.45125e18i	0.494417	+	0.856356i
$290$	4.91275e17	−	8.50913e17i	0.167240	−	0.289668i
$291$	−1.17848e18	+	2.04119e18i	−0.390953	+	0.677150i
$292$	4.76743e17	+	8.25744e17i	0.154139	+	0.266977i
$293$	−2.19771e18			−0.692568			−0.346284	−	0.938130i	$-0.612557\pi$
$293$	−2.19771e18			−0.692568			−0.346284	+	0.938130i	$0.612557\pi$
$294$		0			0
$295$	−1.64768e18			−0.493409
$296$	−4.20103e17	−	7.27640e17i	−0.122650	−	0.212436i
$297$	2.53722e18	−	4.39459e18i	0.722245	−	1.25096i
$298$	−3.50191e17	+	6.06549e17i	−0.0972039	+	0.168362i
$299$	4.49572e17	+	7.78682e17i	0.121693	+	0.210778i
$300$	−1.45329e18			−0.383656
$301$		0			0
$302$	−3.68848e18			−0.926394
$303$	−1.28560e18	−	2.22673e18i	−0.314983	−	0.545567i
$304$	−6.74385e17	+	1.16807e18i	−0.161197	+	0.279201i
$305$	1.46354e18	−	2.53493e18i	0.341316	−	0.591176i
$306$	2.33781e16	+	4.04921e16i	0.00531984	+	0.00921423i
$307$	−3.50631e18			−0.778596			−0.389298	−	0.921112i	$-0.627282\pi$
$307$	−3.50631e18			−0.778596			−0.389298	+	0.921112i	$0.627282\pi$
$308$		0			0
$309$	3.85591e18			0.815526
$310$	−7.07976e17	−	1.22625e18i	−0.146152	−	0.253143i
$311$	5.52066e17	−	9.56206e17i	0.111247	−	0.192685i	−0.805026	−	0.593239i	$-0.797849\pi$
$311$	5.52066e17	−	9.56206e17i	0.111247	−	0.192685i	0.916273	+	0.400554i	$0.131182\pi$
$312$	−4.72335e17	+	8.18108e17i	−0.0929160	+	0.160935i
$313$	2.42097e18	+	4.19325e18i	0.464951	+	0.805319i	0.999199	−	0.0400086i	$-0.0127385\pi$
$313$	2.42097e18	+	4.19325e18i	0.464951	+	0.805319i	−0.534248	+	0.845328i	$0.679405\pi$
$314$	−9.42618e17			−0.176752
$315$		0			0
$316$	2.67532e18			0.478324
$317$	3.78325e18	+	6.55279e18i	0.660573	+	1.14415i	0.980465	+	0.196693i	$0.0630201\pi$
$317$	3.78325e18	+	6.55279e18i	0.660573	+	1.14415i	−0.319892	+	0.947454i	$0.603647\pi$
$318$	−2.28154e18	+	3.95175e18i	−0.389068	+	0.673886i
$319$	−4.68268e18	+	8.11064e18i	−0.779946	+	1.35091i
$320$	1.59056e17	+	2.75492e17i	0.0258776	+	0.0448213i
$321$	−1.09978e19			−1.74791
$322$		0			0
$323$	8.98265e17			0.136265
$324$	1.41228e18	+	2.44614e18i	0.209331	+	0.362572i
$325$	1.62348e18	−	2.81195e18i	0.235137	−	0.407270i
$326$	−4.58224e18	+	7.93667e18i	−0.648553	+	1.12333i
$327$	2.39134e18	+	4.14192e18i	0.330776	+	0.572920i
$328$	−9.16982e16			−0.0123967
$329$		0			0
$330$	−2.86603e18			−0.370191
$331$	6.69106e17	+	1.15893e18i	0.0844860	+	0.146334i	0.905172	−	0.425045i	$-0.139742\pi$
$331$	6.69106e17	+	1.15893e18i	0.0844860	+	0.146334i	−0.820686	+	0.571379i	$0.806409\pi$
$332$	−1.33122e18	+	2.30574e18i	−0.164329	+	0.284626i
$333$	4.09307e17	−	7.08940e17i	0.0493989	−	0.0855614i
$334$	−5.79111e18	−	1.00305e19i	−0.683382	−	1.18365i
$335$	−3.78457e18			−0.436698
$336$		0			0
$337$	4.59109e18			0.506631			0.253315	−	0.967384i	$-0.418479\pi$
$337$	4.59109e18			0.506631			0.253315	+	0.967384i	$0.418479\pi$
$338$	2.22060e18	+	3.84619e18i	0.239660	+	0.415103i
$339$	−2.40392e18	+	4.16371e18i	−0.253759	+	0.439524i
$340$	1.05929e17	−	1.83475e17i	0.0109376	−	0.0189445i
$341$	6.74821e18	+	1.16882e19i	0.681602	+	1.18057i
$342$	−1.31411e18			−0.129848
$343$		0			0
$344$	−5.12657e18			−0.484885
$345$	−8.88327e17	−	1.53863e18i	−0.0822110	−	0.142394i
$346$	−4.07991e16	+	7.06662e16i	−0.00369471	+	0.00639942i
$347$	1.36492e18	−	2.36411e18i	0.120959	−	0.209506i	−0.799187	−	0.601082i	$-0.794736\pi$
$347$	1.36492e18	−	2.36411e18i	0.120959	−	0.209506i	0.920146	+	0.391576i	$0.128070\pi$
$348$	−3.04977e18	−	5.28236e18i	−0.264498	−	0.458125i
$349$	−4.58227e18			−0.388947			−0.194473	−	0.980908i	$-0.562300\pi$
$349$	−4.58227e18			−0.388947			−0.194473	+	0.980908i	$0.562300\pi$
$350$		0			0
$351$	−7.38391e18			−0.600458
$352$	−1.51607e18	−	2.62591e18i	−0.120684	−	0.209031i
$353$	−1.05464e19	+	1.82670e19i	−0.821856	+	1.42350i	0.0824430	+	0.996596i	$0.473728\pi$
$353$	−1.05464e19	+	1.82670e19i	−0.821856	+	1.42350i	−0.904299	+	0.426900i	$0.859606\pi$
$354$	−5.11429e18	+	8.85821e18i	−0.390176	+	0.675806i
$355$	1.76175e18	+	3.05143e18i	0.131592	+	0.227925i
$356$	1.61335e18			0.117992
$357$		0			0
$358$	−6.94066e18			−0.486719
$359$	−5.56822e18	−	9.64444e18i	−0.382391	−	0.662321i	0.609012	−	0.793161i	$-0.291566\pi$
$359$	−5.56822e18	−	9.64444e18i	−0.382391	−	0.662321i	−0.991404	+	0.130840i	$0.958233\pi$
$360$	−1.54968e17	+	2.68413e17i	−0.0104225	+	0.0180524i
$361$	−5.03255e18	+	8.71664e18i	−0.331501	+	0.574176i
$362$	−9.50771e18	−	1.64678e19i	−0.613425	−	1.06248i
$363$	1.26646e19			0.800370
$364$		0			0
$365$	4.20934e18			0.255280
$366$	−9.08549e18	−	1.57365e19i	−0.539809	−	0.934977i
$367$	3.78163e18	−	6.54998e18i	0.220132	−	0.381280i	−0.734716	−	0.678375i	$-0.762684\pi$
$367$	3.78163e18	−	6.54998e18i	0.220132	−	0.381280i	0.954848	+	0.297095i	$0.0960177\pi$
$368$	9.39813e17	−	1.62780e18i	0.0536022	−	0.0928418i
$369$	−4.46709e16	−	7.73722e16i	−0.00249647	−	0.00432401i
$370$	−3.70924e18			−0.203129
$371$		0			0
$372$	−8.79005e18			−0.462295
$373$	1.71030e19	+	2.96233e19i	0.881569	+	1.52692i	0.849597	+	0.527433i	$0.176845\pi$
$373$	1.71030e19	+	2.96233e19i	0.881569	+	1.52692i	0.0319720	+	0.999489i	$0.489821\pi$
$374$	−1.00968e18	+	1.74882e18i	−0.0510092	+	0.0883505i
$375$	−7.07951e18	+	1.22621e19i	−0.350565	+	0.607196i
$376$	−2.52809e18	−	4.37878e18i	−0.122711	−	0.212542i
$377$	1.36277e19			0.648430
$378$		0			0
$379$	2.47705e19			1.13277			0.566383	−	0.824142i	$-0.308342\pi$
$379$	2.47705e19			1.13277			0.566383	+	0.824142i	$0.308342\pi$
$380$	2.97720e18	+	5.15665e18i	0.133484	+	0.231202i
$381$	1.26225e19	−	2.18628e19i	0.554891	−	0.961100i
$382$	1.20219e19	−	2.08225e19i	0.518201	−	0.897550i
$383$	1.79587e19	+	3.11053e19i	0.759073	+	1.31475i	0.943324	+	0.331874i	$0.107681\pi$
$383$	1.79587e19	+	3.11053e19i	0.759073	+	1.31475i	−0.184251	+	0.982879i	$0.558986\pi$
$384$	1.97480e18			0.0818536
$385$		0			0
$386$	−1.84485e19			−0.735454
$387$	−2.49741e18	−	4.32565e18i	−0.0976468	−	0.169129i
$388$	−5.50414e18	+	9.53345e18i	−0.211082	+	0.365605i
$389$	1.43129e19	−	2.47907e19i	0.538402	−	0.932539i	−0.460589	−	0.887614i	$-0.652362\pi$
$389$	1.43129e19	−	2.47907e19i	0.538402	−	0.932539i	0.998990	−	0.0449254i	$-0.0143050\pi$
$390$	2.08521e18	+	3.61168e18i	0.0769422	+	0.133268i
$391$	−1.25181e18			−0.0453119
$392$		0			0
$393$	5.00994e19			1.74537
$394$	5.66783e18	+	9.81697e18i	0.193729	+	0.335549i
$395$	5.90534e18	−	1.02283e19i	0.198046	−	0.343026i
$396$	1.47711e18	−	2.55843e18i	0.0486070	−	0.0841897i
$397$	−1.58957e19	−	2.75322e19i	−0.513277	−	0.889023i	−0.999881	−	0.0154000i	$-0.995098\pi$
$397$	−1.58957e19	−	2.75322e19i	−0.513277	−	0.889023i	0.486604	−	0.873623i	$-0.338235\pi$
$398$	1.18050e19			0.374060
$399$		0			0
$400$	−6.78764e18			−0.207142
$401$	7.62440e18	+	1.32058e19i	0.228361	+	0.395534i	0.957323	−	0.289021i	$-0.0933299\pi$
$401$	7.62440e18	+	1.32058e19i	0.228361	+	0.395534i	−0.728961	+	0.684555i	$0.759997\pi$
$402$	−1.17471e19	+	2.03466e19i	−0.345330	+	0.598130i
$403$	9.81945e18	−	1.70078e19i	0.283334	−	0.490749i
$404$	−6.00447e18	−	1.04000e19i	−0.170065	−	0.294561i
$405$	1.24695e19			0.346687
$406$		0			0
$407$	3.53554e19			0.947321
$408$	−6.57595e17	−	1.13899e18i	−0.0172984	−	0.0299618i
$409$	1.56830e19	−	2.71637e19i	0.405046	−	0.701560i	−0.589281	−	0.807928i	$-0.700589\pi$
$409$	1.56830e19	−	2.71637e19i	0.405046	−	0.701560i	0.994327	+	0.106368i	$0.0339222\pi$
$410$	−2.02409e17	+	3.50583e17i	−0.00513276	+	0.00889021i
$411$	1.98657e19	+	3.44084e19i	0.494641	+	0.856743i
$412$	1.80092e19			0.440317
$413$		0			0
$414$	1.83132e18			0.0431780
$415$	5.87690e18	+	1.01791e19i	0.136078	+	0.235694i
$416$	−2.20606e18	+	3.82101e18i	−0.0501669	+	0.0868917i
$417$	2.46046e19	−	4.26164e19i	0.549535	−	0.951822i
$418$	−2.83777e19	−	4.91517e19i	−0.622523	−	1.07824i
$419$	−2.28320e18			−0.0491970			−0.0245985	−	0.999697i	$-0.507831\pi$
$419$	−2.28320e18			−0.0491970			−0.0245985	+	0.999697i	$0.507831\pi$
$420$		0			0
$421$	−4.61315e19			−0.959140			−0.479570	−	0.877504i	$-0.659207\pi$
$421$	−4.61315e19			−0.959140			−0.479570	+	0.877504i	$0.659207\pi$
$422$	−3.23720e19	−	5.60700e19i	−0.661191	−	1.14522i
$423$	2.46312e18	−	4.26625e18i	0.0494235	−	0.0856040i
$424$	−1.06561e19	+	1.84568e19i	−0.210065	+	0.363842i
$425$	2.26024e18	+	3.91486e18i	0.0437762	+	0.0758226i
$426$	2.18734e19			0.416240
$427$		0			0
$428$	−5.13658e19			−0.943726
$429$	−1.98756e19	−	3.44255e19i	−0.358831	−	0.621513i
$430$	−1.13161e19	+	1.96000e19i	−0.200763	+	0.347731i
$431$	2.85381e19	−	4.94295e19i	0.497560	−	0.861800i	−0.502436	−	0.864615i	$-0.667563\pi$
$431$	2.85381e19	−	4.94295e19i	0.497560	−	0.861800i	0.999996	+	0.00281486i	$0.000895998\pi$
$432$	7.71789e18	+	1.33678e19i	0.132242	+	0.229050i
$433$	9.74941e19			1.64180			0.820898	−	0.571075i	$-0.193474\pi$
$433$	9.74941e19			1.64180			0.820898	+	0.571075i	$0.193474\pi$
$434$		0			0
$435$	−2.69275e19			−0.438054
$436$	1.11689e19	+	1.93451e19i	0.178591	+	0.309329i
$437$	1.75914e19	−	3.04692e19i	0.276496	−	0.478905i
$438$	1.30655e19	−	2.26302e19i	0.201870	−	0.349648i
$439$	−2.76963e19	−	4.79714e19i	−0.420667	−	0.728616i	0.575338	−	0.817916i	$-0.304870\pi$
$439$	−2.76963e19	−	4.79714e19i	−0.420667	−	0.728616i	−0.996005	+	0.0892995i	$0.971537\pi$
$440$	−1.33859e19			−0.199873
$441$		0			0
$442$	2.93842e18			0.0424079
$443$	−5.80429e19	−	1.00533e20i	−0.823610	−	1.42653i	−0.902977	−	0.429688i	$-0.858623\pi$
$443$	−5.80429e19	−	1.00533e20i	−0.823610	−	1.42653i	0.0793678	−	0.996845i	$-0.474710\pi$
$444$	−1.15133e19	+	1.99415e19i	−0.160630	+	0.278219i
$445$	3.56121e18	−	6.16819e18i	0.0488537	−	0.0846170i
$446$	−2.07157e19	−	3.58806e19i	−0.279439	−	0.484003i
$447$	1.91945e19			0.254608
$448$		0			0
$449$	1.86141e19			0.238778			0.119389	−	0.992848i	$-0.461906\pi$
$449$	1.86141e19			0.238778			0.119389	+	0.992848i	$0.461906\pi$
$450$	−3.30660e18	−	5.72720e18i	−0.0417146	−	0.0722518i
$451$	1.92930e18	−	3.34165e18i	0.0239374	−	0.0414607i
$452$	−1.12276e19	+	1.94468e19i	−0.137009	+	0.237307i
$453$	5.05429e19	+	8.75428e19i	0.606629	+	1.05071i
$454$	9.35220e18			0.110407
$455$		0			0
$456$	3.69641e19			0.422225
$457$	−2.24394e19	−	3.88662e19i	−0.252139	−	0.436717i	0.711976	−	0.702204i	$-0.247801\pi$
$457$	−2.24394e19	−	3.88662e19i	−0.252139	−	0.436717i	−0.964114	+	0.265487i	$0.914467\pi$
$458$	4.53864e19	−	7.86115e19i	0.501689	−	0.868951i
$459$	5.14002e18	−	8.90277e18i	0.0558946	−	0.0968122i
$460$	−4.14897e18	−	7.18623e18i	−0.0443871	−	0.0768808i
$461$	−7.40406e19			−0.779315			−0.389657	−	0.920960i	$-0.627407\pi$
$461$	−7.40406e19			−0.779315			−0.389657	+	0.920960i	$0.627407\pi$
$462$		0			0
$463$	1.23960e20			1.26306			0.631528	−	0.775353i	$-0.282428\pi$
$463$	1.23960e20			1.26306			0.631528	+	0.775353i	$0.282428\pi$
$464$	−1.42441e19	−	2.46715e19i	−0.142807	−	0.247349i
$465$	−1.94026e19	+	3.36063e19i	−0.191409	+	0.331531i
$466$	−4.81046e19	+	8.33196e19i	−0.466973	+	0.808821i
$467$	−9.76171e19	−	1.69078e20i	−0.932501	−	1.61514i	−0.779030	−	0.626987i	$-0.784288\pi$
$467$	−9.76171e19	−	1.69078e20i	−0.932501	−	1.61514i	−0.153471	−	0.988153i	$-0.549045\pi$
$468$	−4.29874e18			−0.0404108
$469$		0			0
$470$	−2.23214e19			−0.203230
$471$	1.29166e19	+	2.23722e19i	0.115742	+	0.200471i
$472$	−2.38865e19	+	4.13727e19i	−0.210663	+	0.364879i
$473$	1.07862e20	−	1.86822e20i	0.936285	−	1.62169i
$474$	−3.66596e19	−	6.34963e19i	−0.313220	−	0.542514i
$475$	−1.27051e20			−1.06850
$476$		0			0
$477$	−2.07644e19			−0.169212
$478$	−2.65523e19	−	4.59900e19i	−0.213007	−	0.368939i
$479$	−5.76848e19	+	9.99130e19i	−0.455559	+	0.789052i	−0.998720	−	0.0505766i	$-0.983894\pi$
$479$	−5.76848e19	+	9.99130e19i	−0.455559	+	0.789052i	0.543161	+	0.839629i	$0.317227\pi$
$480$	4.35904e18	−	7.55009e18i	0.0338908	−	0.0587006i
$481$	−2.57231e19	−	4.45538e19i	−0.196895	−	0.341033i
$482$	9.56387e19			0.720744
$483$		0			0
$484$	5.91505e19			0.432134
$485$	2.42990e19	+	4.20871e19i	0.174794	+	0.302752i
$486$	−1.41018e19	+	2.44250e19i	−0.0998855	+	0.173007i
$487$	−8.32998e18	+	1.44279e19i	−0.0581001	+	0.100632i	−0.893613	−	0.448839i	$-0.851838\pi$
$487$	−8.32998e18	+	1.44279e19i	−0.0581001	+	0.100632i	0.835512	+	0.549472i	$0.185171\pi$
$488$	−4.24342e19	−	7.34982e19i	−0.291452	−	0.504810i
$489$	2.51160e20			1.69877
$490$		0			0
$491$	−1.91764e19			−0.125793			−0.0628963	−	0.998020i	$-0.520034\pi$
$491$	−1.91764e19			−0.125793			−0.0628963	+	0.998020i	$0.520034\pi$
$492$	1.25653e18	+	2.17638e18i	0.00811774	+	0.0140603i
$493$	−9.48640e18	+	1.64309e19i	−0.0603600	+	0.104547i
$494$	−4.12930e19	+	7.15215e19i	−0.258776	+	0.448213i
$495$	−6.52096e18	−	1.12946e19i	−0.0402506	−	0.0697161i
$496$	−4.10543e19			−0.249601
$497$		0			0
$498$	7.29662e19			0.430429
$499$	7.96084e18	+	1.37886e19i	0.0462599	+	0.0801246i	0.888228	−	0.459402i	$-0.151936\pi$
$499$	7.96084e18	+	1.37886e19i	0.0462599	+	0.0801246i	−0.841968	+	0.539527i	$0.818603\pi$
$500$	−3.30652e19	+	5.72705e19i	−0.189276	+	0.327836i
$501$	−1.58710e20	+	2.74894e20i	−0.894997	+	1.55018i
$502$	1.18416e20	+	2.05102e20i	0.657857	+	1.13944i
$503$	−2.23533e20			−1.22344			−0.611718	−	0.791076i	$-0.709521\pi$
$503$	−2.23533e20			−1.22344			−0.611718	+	0.791076i	$0.709521\pi$
$504$		0			0
$505$	−5.30156e19			−0.281656
$506$	3.95468e19	+	6.84970e19i	0.207006	+	0.358544i
$507$	6.08572e19	−	1.05408e20i	0.313872	−	0.543642i
$508$	5.89539e19	−	1.02111e20i	0.299595	−	0.518914i
$509$	1.34304e20	+	2.32621e20i	0.672521	+	1.16484i	0.977187	+	0.212381i	$0.0681217\pi$
$509$	1.34304e20	+	2.32621e20i	0.672521	+	1.16484i	−0.304666	+	0.952459i	$0.598545\pi$
$510$	−5.80614e18			−0.0286491
$511$		0			0
$512$	9.22337e18			0.0441942
$513$	1.44463e20	+	2.50217e20i	0.682145	+	1.18151i
$514$	−5.96112e19	+	1.03250e20i	−0.277399	+	0.480469i
$515$	3.97524e19	−	6.88532e19i	0.182309	−	0.315769i
$516$	7.02489e19	+	1.21675e20i	0.317517	+	0.549955i
$517$	2.12761e20			0.947792
$518$		0			0
$519$	2.23626e18			0.00967761
$520$	9.73905e18	+	1.68685e19i	0.0415424	+	0.0719536i
$521$	9.34825e19	−	1.61916e20i	0.393050	−	0.680782i	−0.599801	−	0.800150i	$-0.704753\pi$
$521$	9.34825e19	−	1.61916e20i	0.393050	−	0.680782i	0.992850	+	0.119368i	$0.0380867\pi$
$522$	1.38780e19	−	2.40375e19i	0.0575174	−	0.0996231i
$523$	8.72709e18	+	1.51158e19i	0.0356539	+	0.0617543i	0.883302	−	0.468805i	$-0.155315\pi$
$523$	8.72709e18	+	1.51158e19i	0.0356539	+	0.0617543i	−0.847648	+	0.530559i	$0.821982\pi$
$524$	2.33992e20			0.942357
$525$		0			0
$526$	−1.33731e20			−0.523407
$527$	1.36708e19	+	2.36786e19i	0.0527492	+	0.0913643i
$528$	−4.15491e19	+	7.19651e19i	−0.158055	+	0.273758i
$529$	1.08803e20	−	1.88452e20i	0.408058	−	0.706777i
$530$	4.70431e19	+	8.14810e19i	0.173951	+	0.301292i
$531$	−4.65454e19			−0.169694
$532$		0			0
$533$	−5.61473e18			−0.0199010
$534$	−2.21075e19	−	3.82914e19i	−0.0772646	−	0.133826i
$535$	−1.13382e20	+	1.96383e20i	−0.390742	+	0.676785i
$536$	−5.48653e19	+	9.50295e19i	−0.186450	+	0.322941i
$537$	9.51071e19	+	1.64730e20i	0.318717	+	0.552035i
$538$	−3.40529e20			−1.12535
$539$		0			0
$540$	6.81440e19			0.219015
$541$	1.34892e20	+	2.33640e20i	0.427570	+	0.740573i	0.996657	−	0.0817047i	$-0.0260364\pi$
$541$	1.34892e20	+	2.33640e20i	0.427570	+	0.740573i	−0.569087	+	0.822278i	$0.692703\pi$
$542$	1.66124e20	−	2.87735e20i	0.519323	−	0.899493i
$543$	−2.60566e20	+	4.51314e20i	−0.803377	+	1.39149i
$544$	−3.07133e18	−	5.31969e18i	−0.00933973	−	0.0161769i
$545$	9.86140e19			0.295777
$546$		0			0
$547$	−2.48513e20			−0.725177			−0.362588	−	0.931949i	$-0.618107\pi$
$547$	−2.48513e20			−0.725177			−0.362588	+	0.931949i	$0.618107\pi$
$548$	9.27837e19	+	1.60706e20i	0.267065	+	0.462571i
$549$	4.13437e19	−	7.16094e19i	0.117386	−	0.203319i
$550$	1.42810e20	−	2.47354e20i	0.399980	−	0.692785i
$551$	−2.66621e20	−	4.61800e20i	−0.736642	−	1.27590i
$552$	−5.15126e19			−0.140401
$553$		0			0
$554$	−2.10130e20			−0.557398
$555$	5.08273e19	+	8.80355e19i	0.133015	+	0.230388i
$556$	1.14917e20	−	1.99042e20i	0.296703	−	0.513905i
$557$	−2.06737e20	+	3.58079e20i	−0.526628	+	0.912146i	0.472891	+	0.881121i	$0.343211\pi$
$557$	−2.06737e20	+	3.58079e20i	−0.526628	+	0.912146i	−0.999519	+	0.0310252i	$0.990123\pi$
$558$	−1.99996e19	−	3.46404e19i	−0.0502650	−	0.0870616i
$559$	−3.13903e20			−0.778407
$560$		0			0
$561$	5.53424e19			0.133609
$562$	7.99654e19	+	1.38504e20i	0.190493	+	0.329944i
$563$	−2.02086e20	+	3.50024e20i	−0.475033	+	0.822782i	−0.999591	−	0.0285928i	$-0.990897\pi$
$563$	−2.02086e20	+	3.50024e20i	−0.475033	+	0.822782i	0.524558	+	0.851375i	$0.324231\pi$
$564$	−6.92844e19	+	1.20004e20i	−0.160710	+	0.278357i
$565$	4.95663e19	+	8.58514e19i	0.113455	+	0.196510i
$566$	−2.21549e20			−0.500433
$567$		0			0
$568$	1.02161e20			0.224735
$569$	−2.21048e19	−	3.82867e19i	−0.0479894	−	0.0831200i	0.841033	−	0.540984i	$-0.181948\pi$
$569$	−2.21048e19	−	3.82867e19i	−0.0479894	−	0.0831200i	−0.889022	+	0.457864i	$0.848615\pi$
$570$	8.15924e19	−	1.41322e20i	0.174819	−	0.302795i
$571$	−1.47868e20	+	2.56116e20i	−0.312683	+	0.541583i	−0.978942	−	0.204137i	$-0.934561\pi$
$571$	−1.47868e20	+	2.56116e20i	−0.312683	+	0.541583i	0.666259	+	0.745720i	$0.267894\pi$
$572$	−9.28297e19	−	1.60786e20i	−0.193739	−	0.335566i
$573$	−6.58939e20			−1.35733
$574$		0			0
$575$	1.77056e20			0.355305
$576$	4.49317e18	+	7.78240e18i	0.00889988	+	0.0154151i
$577$	−7.74354e19	+	1.34122e20i	−0.151398	+	0.262230i	−0.931742	−	0.363122i	$-0.881711\pi$
$577$	−7.74354e19	+	1.34122e20i	−0.151398	+	0.262230i	0.780343	+	0.625351i	$0.215044\pi$
$578$	1.81150e20	−	3.13760e20i	0.349606	−	0.605535i
$579$	2.52797e20	+	4.37858e20i	0.481596	+	0.834149i
$580$	−1.25766e20			−0.236513
$581$		0			0
$582$	3.01691e20			0.552891
$583$	−4.48400e20	−	7.76652e20i	−0.811245	−	1.40512i
$584$	6.10231e19	−	1.05695e20i	0.108993	−	0.188781i
$585$	−9.48877e18	+	1.64350e19i	−0.0167317	+	0.0289802i
$586$	1.40653e20	+	2.43619e20i	0.244860	+	0.424110i
$587$	−2.59838e20			−0.446599			−0.223299	−	0.974750i	$-0.571683\pi$
$587$	−2.59838e20			−0.446599			−0.223299	+	0.974750i	$0.571683\pi$
$588$		0			0
$589$	−7.68453e20			−1.28752
$590$	1.05451e20	+	1.82647e20i	0.174447	+	0.302150i
$591$	1.55331e20	−	2.69042e20i	0.253719	−	0.439454i
$592$	−5.37732e19	+	9.31379e19i	−0.0867267	+	0.150215i
$593$	−8.67311e19	−	1.50223e20i	−0.138123	−	0.239235i	0.788663	−	0.614825i	$-0.210773\pi$
$593$	−8.67311e19	−	1.50223e20i	−0.138123	−	0.239235i	−0.926786	+	0.375590i	$0.877440\pi$
$594$	−6.49528e20			−1.02141
$595$		0			0
$596$	8.96490e19			0.137467
$597$	−1.61762e20	−	2.80180e20i	−0.244946	−	0.424258i
$598$	5.75452e19	−	9.96713e19i	0.0860499	−	0.149043i
$599$	−1.33101e20	+	2.30537e20i	−0.196553	+	0.340439i	−0.947408	−	0.320027i	$-0.896308\pi$
$599$	−1.33101e20	+	2.30537e20i	−0.196553	+	0.340439i	0.750856	+	0.660466i	$0.229641\pi$
$600$	9.30103e19	+	1.61099e20i	0.135643	+	0.234940i
$601$	−1.46615e20			−0.211165			−0.105582	−	0.994411i	$-0.533671\pi$
$601$	−1.46615e20			−0.211165			−0.105582	+	0.994411i	$0.533671\pi$
$602$		0			0
$603$	−1.06911e20			−0.150190
$604$	2.36063e20	+	4.08873e20i	0.327530	+	0.567298i
$605$	1.30565e20	−	2.26146e20i	0.178921	−	0.309901i
$606$	−1.64557e20	+	2.85021e20i	−0.222727	+	0.385774i
$607$	3.88783e20	+	6.73392e20i	0.519747	+	0.900229i	0.999737	+	0.0229544i	$0.00730725\pi$
$607$	3.88783e20	+	6.73392e20i	0.519747	+	0.900229i	−0.479989	+	0.877274i	$0.659359\pi$
$608$	1.72643e20			0.227967
$609$		0			0
$610$	−3.74667e20			−0.482694
$611$	−1.54796e20	−	2.68115e20i	−0.196993	−	0.341203i
$612$	2.99240e18	−	5.18298e18i	0.00376169	−	0.00651545i
$613$	−1.58828e20	+	2.75099e20i	−0.197231	+	0.341614i	−0.947629	−	0.319372i	$-0.896528\pi$
$613$	−1.58828e20	+	2.75099e20i	−0.197231	+	0.341614i	0.750399	+	0.660985i	$0.229861\pi$
$614$	2.24404e20	+	3.88679e20i	0.275275	+	0.476791i
$615$	1.10944e19			0.0134443
$616$		0			0
$617$	−5.23730e20			−0.619396			−0.309698	−	0.950835i	$-0.600228\pi$
$617$	−5.23730e20			−0.619396			−0.309698	+	0.950835i	$0.600228\pi$
$618$	−2.46778e20	−	4.27432e20i	−0.288332	−	0.499406i
$619$	1.24614e20	−	2.15838e20i	0.143842	−	0.249142i	−0.785098	−	0.619372i	$-0.787387\pi$
$619$	1.24614e20	−	2.15838e20i	0.143842	−	0.249142i	0.928940	+	0.370229i	$0.120721\pi$
$620$	−9.06209e19	+	1.56960e20i	−0.103345	+	0.178999i
$621$	−2.01322e20	−	3.48699e20i	−0.226831	−	0.392884i
$622$	−1.41329e20			−0.157327
$623$		0			0
$624$	1.20918e20			0.131403
$625$	−2.39861e20	−	4.15451e20i	−0.257548	−	0.446087i
$626$	3.09885e20	−	5.36736e20i	0.328770	−	0.569447i
$627$	−7.77714e20	+	1.34704e21i	−0.815292	+	1.41213i
$628$	6.03276e19	+	1.04490e20i	0.0624912	+	0.108238i
$629$	7.16246e19			0.0733132
$630$		0			0
$631$	−1.47167e21			−1.47092			−0.735460	−	0.677568i	$-0.763034\pi$
$631$	−1.47167e21			−1.47092			−0.735460	+	0.677568i	$0.763034\pi$
$632$	−1.71220e20	−	2.96562e20i	−0.169113	−	0.292913i
$633$	−8.87181e20	+	1.53664e21i	−0.865934	+	1.49984i
$634$	4.84257e20	−	8.38757e20i	0.467096	−	0.809034i
$635$	−2.60263e20	−	4.50788e20i	−0.248090	−	0.429704i
$636$	5.84075e20			0.550225
$637$		0			0
$638$	1.19877e21			1.10301
$639$	4.97676e19	+	8.62001e19i	0.0452575	+	0.0783883i
$640$	2.03591e19	−	3.52630e19i	0.0182982	−	0.0316935i
$641$	7.33100e20	−	1.26977e21i	0.651221	−	1.12795i	−0.331606	−	0.943418i	$-0.607591\pi$
$641$	7.33100e20	−	1.26977e21i	0.651221	−	1.12795i	0.982827	−	0.184529i	$-0.0590760\pi$
$642$	7.03860e20	+	1.21912e21i	0.617979	+	1.07037i
$643$	−9.96832e20			−0.865047			−0.432523	−	0.901623i	$-0.642377\pi$
$643$	−9.96832e20			−0.865047			−0.432523	+	0.901623i	$0.642377\pi$
$644$		0			0
$645$	6.20253e20			0.525861
$646$	−5.74890e19	−	9.95738e19i	−0.0481771	−	0.0834452i
$647$	1.86678e20	−	3.23336e20i	0.154636	−	0.267838i	−0.778290	−	0.627905i	$-0.783913\pi$
$647$	1.86678e20	−	3.23336e20i	0.154636	−	0.267838i	0.932927	+	0.360067i	$0.117246\pi$
$648$	1.80772e20	−	3.13106e20i	0.148019	−	0.256377i
$649$	−1.00513e21	−	1.74094e21i	−0.813556	−	1.40912i
$650$	−4.15611e20			−0.332534
$651$		0			0
$652$	1.17305e21			0.917193
$653$	8.78143e20	+	1.52099e21i	0.678760	+	1.17565i	0.975354	+	0.220644i	$0.0708158\pi$
$653$	8.78143e20	+	1.52099e21i	0.678760	+	1.17565i	−0.296594	+	0.955004i	$0.595851\pi$
$654$	3.06092e20	−	5.30166e20i	0.233894	−	0.405116i
$655$	5.16499e20	−	8.94602e20i	0.390175	−	0.675803i
$656$	5.86869e18	+	1.01649e19i	0.00438291	+	0.00759142i
$657$	1.18910e20			0.0877966
$658$		0			0
$659$	1.29884e21			0.937379			0.468690	−	0.883363i	$-0.344726\pi$
$659$	1.29884e21			0.937379			0.468690	+	0.883363i	$0.344726\pi$
$660$	1.83426e20	+	3.17703e20i	0.130882	+	0.226695i
$661$	9.44597e20	−	1.63609e21i	0.666401	−	1.15424i	−0.312503	−	0.949917i	$-0.601167\pi$
$661$	9.44597e20	−	1.63609e21i	0.666401	−	1.15424i	0.978904	−	0.204323i	$-0.0654993\pi$
$662$	8.56455e19	−	1.48342e20i	0.0597406	−	0.103474i
$663$	−4.02649e19	−	6.97408e19i	−0.0277699	−	0.0480989i
$664$	3.40792e20			0.232396
$665$		0			0
$666$	−1.04783e20			−0.0698606
$667$	3.71558e20	+	6.43558e20i	0.244953	+	0.424271i
$668$	−7.41262e20	+	1.28390e21i	−0.483224	+	0.836969i
$669$	−5.67729e20	+	9.83335e20i	−0.365970	+	0.633878i
$670$	2.42213e20	+	4.19525e20i	0.154396	+	0.267422i
$671$	3.57121e21			2.25111
$672$		0			0
$673$	2.00920e21			1.23854			0.619270	−	0.785178i	$-0.287429\pi$
$673$	2.00920e21			1.23854			0.619270	+	0.785178i	$0.287429\pi$
$674$	−2.93830e20	−	5.08928e20i	−0.179121	−	0.310247i
$675$	−7.27005e20	+	1.25921e21i	−0.438288	+	0.759137i
$676$	2.84237e20	−	4.92312e20i	0.169465	−	0.293522i
$677$	−1.16940e21	−	2.02545e21i	−0.689520	−	1.19428i	−0.971993	−	0.235008i	$-0.924488\pi$
$677$	−1.16940e21	−	2.02545e21i	−0.689520	−	1.19428i	0.282474	−	0.959275i	$-0.408845\pi$
$678$	6.15403e20			0.358870
$679$		0			0
$680$	−2.71178e19			−0.0154681
$681$	−1.28152e20	−	2.21966e20i	−0.0722974	−	0.125223i
$682$	8.63771e20	−	1.49609e21i	0.481965	−	0.834788i
$683$	1.75583e21	−	3.04119e21i	0.969010	−	1.67837i	0.270577	−	0.962698i	$-0.412786\pi$
$683$	1.75583e21	−	3.04119e21i	0.969010	−	1.67837i	0.698433	−	0.715675i	$-0.253881\pi$
$684$	8.41030e19	+	1.45671e20i	0.0459082	+	0.0795154i
$685$	8.19220e20			0.442305
$686$		0			0
$687$	−2.48770e21			−1.31408
$688$	3.28101e20	+	5.68287e20i	0.171433	+	0.296930i
$689$	−6.52476e20	+	1.13012e21i	−0.337225	+	0.584092i
$690$	−1.13706e20	+	1.96944e20i	−0.0581319	+	0.100687i
$691$	−1.04240e21	−	1.80548e21i	−0.527167	−	0.913079i	−0.999499	−	0.0316586i	$-0.989921\pi$
$691$	−1.04240e21	−	1.80548e21i	−0.527167	−	0.913079i	0.472332	−	0.881421i	$-0.343412\pi$
$692$	1.04446e19			0.00522511
$693$		0			0
$694$	−3.49420e20			−0.171061
$695$	−5.07321e20	−	8.78705e20i	−0.245695	−	0.425556i
$696$	−3.90371e20	+	6.76142e20i	−0.187029	+	0.323943i
$697$	3.90847e18	−	6.76968e18i	0.00185251	−	0.00320865i
$698$	2.93265e20	+	5.07951e20i	0.137513	+	0.238180i
$699$	2.63669e21			1.22315
$700$		0			0
$701$	−3.59508e21			−1.63239			−0.816194	−	0.577778i	$-0.803920\pi$
$701$	−3.59508e21			−1.63239			−0.816194	+	0.577778i	$0.803920\pi$
$702$	4.72570e20	+	8.18516e20i	0.212294	+	0.367704i
$703$	−1.00652e21	+	1.74335e21i	−0.447362	+	0.774854i
$704$	−1.94057e20	+	3.36116e20i	−0.0853364	+	0.147807i
$705$	3.05868e20	+	5.29779e20i	0.133081	+	0.230503i
$706$	2.69989e21			1.16228
$707$		0			0
$708$	1.30926e21			0.551793
$709$	3.12666e20	+	5.41553e20i	0.130387	+	0.225836i	0.923826	−	0.382813i	$-0.125045\pi$
$709$	3.12666e20	+	5.41553e20i	0.130387	+	0.225836i	−0.793439	+	0.608650i	$0.791711\pi$
$710$	2.25503e20	−	3.90583e20i	0.0930498	−	0.161167i
$711$	1.66820e20	−	2.88941e20i	0.0681125	−	0.117974i
$712$	−1.03254e20	−	1.78842e20i	−0.0417165	−	0.0722551i
$713$	1.07090e21			0.428134
$714$		0			0
$715$	−8.19627e20			−0.320864
$716$	4.44202e20	+	7.69381e20i	0.172081	+	0.298053i
$717$	−7.27688e20	+	1.26039e21i	−0.278966	+	0.483183i
$718$	−7.12732e20	+	1.23449e21i	−0.270391	+	0.468332i
$719$	1.24093e20	+	2.14936e20i	0.0465889	+	0.0806943i	0.888379	−	0.459110i	$-0.151832\pi$
$719$	1.24093e20	+	2.14936e20i	0.0465889	+	0.0806943i	−0.841791	+	0.539804i	$0.818498\pi$
$720$	3.96718e19			0.0147397
$721$		0			0
$722$	1.28833e21			0.468813
$723$	−1.31053e21	−	2.26990e21i	−0.471964	−	0.817465i
$724$	−1.21699e21	+	2.10788e21i	−0.433757	+	0.751289i
$725$	1.34176e21	−	2.32399e21i	0.473303	−	0.819785i
$726$	−8.10533e20	−	1.40388e21i	−0.282974	−	0.490125i
$727$	−6.16365e20			−0.212976			−0.106488	−	0.994314i	$-0.533961\pi$
$727$	−6.16365e20			−0.212976			−0.106488	+	0.994314i	$0.533961\pi$
$728$		0			0
$729$	3.24666e21			1.09896
$730$	−2.69398e20	−	4.66610e20i	−0.0902552	−	0.156327i
$731$	2.18511e20	−	3.78472e20i	0.0724591	−	0.125503i
$732$	−1.16294e21	+	2.01428e21i	−0.381703	+	0.661129i
$733$	1.55870e20	+	2.69976e20i	0.0506389	+	0.0877091i	0.890234	−	0.455504i	$-0.150541\pi$
$733$	1.55870e20	+	2.69976e20i	0.0506389	+	0.0877091i	−0.839595	+	0.543213i	$0.817208\pi$
$734$	−9.68098e20			−0.311314
$735$		0			0
$736$	−2.40592e20			−0.0758050
$737$	−2.30870e21	−	3.99878e21i	−0.720047	−	1.24716i
$738$	−5.71787e18	+	9.90364e18i	−0.00176527	+	0.00305754i
$739$	−2.06784e21	+	3.58160e21i	−0.631950	+	1.09457i	0.355202	+	0.934789i	$0.384412\pi$
$739$	−2.06784e21	+	3.58160e21i	−0.631950	+	1.09457i	−0.987153	+	0.159781i	$0.948921\pi$
$740$	2.37391e20	+	4.11174e20i	0.0718170	+	0.124391i
$741$	2.26333e21			0.677816
$742$		0			0
$743$	3.96804e21			1.16456			0.582278	−	0.812990i	$-0.302162\pi$
$743$	3.96804e21			1.16456			0.582278	+	0.812990i	$0.302162\pi$
$744$	5.62563e20	+	9.74388e20i	0.163446	+	0.283097i
$745$	1.97886e20	−	3.42748e20i	0.0569171	−	0.0985833i
$746$	2.18918e21	−	3.79178e21i	0.623363	−	1.07970i
$747$	1.66017e20	+	2.87550e20i	0.0468002	+	0.0810604i
$748$	2.58479e20			0.0721379
$749$		0			0
$750$	1.81235e21			0.495774
$751$	1.09838e21	+	1.90245e21i	0.297476	+	0.515244i	0.975558	−	0.219743i	$-0.0705217\pi$
$751$	1.09838e21	+	1.90245e21i	0.297476	+	0.515244i	−0.678082	+	0.734987i	$0.737188\pi$
$752$	−3.23596e20	+	5.60484e20i	−0.0867699	+	0.150290i
$753$	3.24527e21	−	5.62098e21i	0.861567	−	1.49228i
$754$	−8.72174e20	−	1.51065e21i	−0.229255	−	0.397080i
$755$	2.08428e21			0.542444
$756$		0			0
$757$	1.22748e21			0.313181			0.156590	−	0.987664i	$-0.449950\pi$
$757$	1.22748e21			0.313181			0.156590	+	0.987664i	$0.449950\pi$
$758$	−1.58531e21	−	2.74584e21i	−0.400494	−	0.693675i
$759$	1.08381e21	−	1.87721e21i	0.271106	−	0.469570i
$760$	3.81081e20	−	6.60052e20i	0.0943877	−	0.163484i
$761$	−1.12372e21	−	1.94634e21i	−0.275597	−	0.477347i	0.694689	−	0.719310i	$-0.255542\pi$
$761$	−1.12372e21	−	1.94634e21i	−0.275597	−	0.477347i	−0.970285	+	0.241963i	$0.922209\pi$
$762$	−3.23136e21			−0.784735
$763$		0			0
$764$	−3.07761e21			−0.732846
$765$	−1.32105e19	−	2.28812e19i	−0.00311500	−	0.00539533i
$766$	2.29871e21	−	3.98148e21i	0.536746	−	0.929671i
$767$	−1.46258e21	+	2.53327e21i	−0.338186	+	0.585756i
$768$	−1.26387e20	−	2.18909e20i	−0.0289396	−	0.0501249i
$769$	−7.98944e21			−1.81163			−0.905813	−	0.423677i	$-0.860739\pi$
$769$	−7.98944e21			−1.81163			−0.905813	+	0.423677i	$0.860739\pi$
$770$		0			0
$771$	3.26738e21			0.726595
$772$	1.18070e21	+	2.04504e21i	0.260022	+	0.450372i
$773$	−6.92027e19	+	1.19863e20i	−0.0150930	+	0.0261419i	−0.873473	−	0.486872i	$-0.838138\pi$
$773$	−6.92027e19	+	1.19863e20i	−0.0150930	+	0.0261419i	0.858380	+	0.513014i	$0.171471\pi$
$774$	−3.19669e20	+	5.53683e20i	−0.0690467	+	0.119592i
$775$	−1.93361e21	−	3.34911e21i	−0.413624	−	0.716417i
$776$	1.40906e21			0.298515
$777$		0			0
$778$	−3.66411e21			−0.761415
$779$	1.09850e20	+	1.90265e20i	0.0226083	+	0.0391588i
$780$	2.66906e20	−	4.62296e20i	0.0544063	−	0.0942346i
$781$	−2.14943e21	+	3.72292e21i	−0.433951	+	0.751625i
$782$	8.01157e19	+	1.38765e20i	0.0160202	+	0.0277477i
$783$	−6.10259e21			−1.20865
$784$		0			0
$785$	5.32654e20			0.103496
$786$	−3.20636e21	−	5.55358e21i	−0.617083	−	1.06882i
$787$	4.81188e20	−	8.33442e20i	0.0917285	−	0.158878i	−0.816510	−	0.577331i	$-0.804094\pi$
$787$	4.81188e20	−	8.33442e20i	0.0917285	−	0.158878i	0.908239	+	0.418453i	$0.137427\pi$
$788$	7.25482e20	−	1.25657e21i	0.136987	−	0.237269i
$789$	1.83250e21	+	3.17399e21i	0.342742	+	0.593647i
$790$	−1.51177e21			−0.280080
$791$		0			0
$792$	−3.78140e20			−0.0687406
$793$	−2.59827e21	−	4.50033e21i	−0.467881	−	0.810393i
$794$	−2.03466e21	+	3.52413e21i	−0.362942	+	0.628634i
$795$	1.28925e21	−	2.23305e21i	0.227816	−	0.394589i
$796$	−7.55518e20	−	1.30860e21i	−0.132250	−	0.229064i
$797$	1.00646e22			1.74525			0.872626	−	0.488388i	$-0.162415\pi$
$797$	1.00646e22			1.74525			0.872626	+	0.488388i	$0.162415\pi$
$798$		0			0
$799$	4.31022e20			0.0733497
$800$	4.34409e20	+	7.52419e20i	0.0732359	+	0.126848i
$801$	1.00601e20	−	1.74246e20i	0.0168019	−	0.0291017i
$802$	9.75923e20	−	1.69035e21i	0.161476	−	0.279684i
$803$	2.56782e21	+	4.44759e21i	0.420918	+	0.729051i
$804$	3.00725e21			0.488371
$805$		0			0
$806$	−2.51378e21			−0.400695
$807$	4.66623e21	+	8.08215e21i	0.736910	+	1.27637i
$808$	−7.68572e20	+	1.33121e21i	−0.120254	+	0.208286i
$809$	−3.61656e21	+	6.26406e21i	−0.560636	+	0.971051i	0.436805	+	0.899556i	$0.356110\pi$
$809$	−3.61656e21	+	6.26406e21i	−0.560636	+	0.971051i	−0.997441	+	0.0714944i	$0.977223\pi$
$810$	−7.98051e20	−	1.38226e21i	−0.122572	−	0.212302i
$811$	−3.62138e21			−0.551084			−0.275542	−	0.961289i	$-0.588857\pi$
$811$	−3.62138e21			−0.551084			−0.275542	+	0.961289i	$0.588857\pi$
$812$		0			0
$813$	−9.10551e21			−1.36027
$814$	−2.26274e21	−	3.91919e21i	−0.334929	−	0.580113i
$815$	2.58933e21	−	4.48484e21i	0.379756	−	0.657757i
$816$	−8.41721e19	+	1.45790e20i	−0.0122318	+	0.0211862i
$817$	6.14137e21	+	1.06372e22i	0.884301	+	1.53165i
$818$	−4.01485e21			−0.572821
$819$		0			0
$820$	5.18168e19			0.00725882
$821$	−1.00290e21	−	1.73708e21i	−0.139214	−	0.241126i	0.787985	−	0.615694i	$-0.211124\pi$
$821$	−1.00290e21	−	1.73708e21i	−0.139214	−	0.241126i	−0.927199	+	0.374568i	$0.877791\pi$
$822$	2.54281e21	−	4.40428e21i	0.349764	−	0.605809i
$823$	3.22285e21	−	5.58214e21i	0.439280	−	0.760856i	−0.558354	−	0.829603i	$-0.688567\pi$
$823$	3.22285e21	−	5.58214e21i	0.439280	−	0.760856i	0.997634	+	0.0687472i	$0.0219002\pi$
$824$	−1.15259e21	−	1.99634e21i	−0.155675	−	0.269638i
$825$	−7.82763e21			−1.04767
$826$		0			0
$827$	−5.67524e21			−0.745921			−0.372961	−	0.927847i	$-0.621657\pi$
$827$	−5.67524e21			−0.745921			−0.372961	+	0.927847i	$0.621657\pi$
$828$	−1.17205e20	−	2.03004e20i	−0.0152657	−	0.0264410i
$829$	5.62506e21	−	9.74289e21i	0.726053	−	1.25756i	−0.232486	−	0.972600i	$-0.574686\pi$
$829$	5.62506e21	−	9.74289e21i	0.726053	−	1.25756i	0.958539	−	0.284961i	$-0.0919806\pi$
$830$	7.52244e20	−	1.30292e21i	0.0962216	−	0.166661i
$831$	2.87940e21	+	4.98726e21i	0.365001	+	0.632200i
$832$	5.64752e20			0.0709468
$833$		0			0
$834$	−6.29877e21			−0.777160
$835$	3.27244e21	+	5.66803e21i	0.400150	+	0.693080i
$836$	−3.63235e21	+	6.29141e21i	−0.440190	+	0.762432i
$837$	−4.39722e21	+	7.61620e21i	−0.528125	+	0.914740i
$838$	1.46125e20	+	2.53095e20i	0.0173938	+	0.0301269i
$839$	−3.23304e20			−0.0381413			−0.0190707	−	0.999818i	$-0.506071\pi$
$839$	−3.23304e20			−0.0381413			−0.0190707	+	0.999818i	$0.506071\pi$
$840$		0			0
$841$	2.63372e21			0.305211
$842$	2.95242e21	+	5.11374e21i	0.339107	+	0.587351i
$843$	2.19152e21	−	3.79582e21i	0.249481	−	0.432114i
$844$	−4.14362e21	+	7.17696e21i	−0.467532	+	0.809790i
$845$	−1.25481e21	−	2.17340e21i	−0.140331	−	0.243061i
$846$	−6.30560e20			−0.0698954
$847$		0			0
$848$	2.72795e21			0.297076
$849$	3.03586e21	+	5.25827e21i	0.327698	+	0.567590i
$850$	2.89311e20	−	5.01102e20i	0.0309545	−	0.0536147i
$851$	1.40268e21	−	2.42951e21i	0.148760	−	0.257660i
$852$	−1.39990e21	−	2.42469e21i	−0.147163	−	0.254894i
$853$	2.31226e21			0.240946			0.120473	−	0.992717i	$-0.461559\pi$
$853$	2.31226e21			0.240946			0.120473	+	0.992717i	$0.461559\pi$
$854$		0			0
$855$	7.42575e20			0.0760317
$856$	3.28741e21	+	5.69396e21i	0.333657	+	0.577912i
$857$	−6.20465e21	+	1.07468e22i	−0.624253	+	1.08124i	0.364431	+	0.931230i	$0.381263\pi$
$857$	−6.20465e21	+	1.07468e22i	−0.624253	+	1.08124i	−0.988685	+	0.150008i	$0.952070\pi$
$858$	−2.54407e21	+	4.40646e21i	−0.253732	+	0.439476i
$859$	7.50563e21	+	1.30001e22i	0.742059	+	1.28528i	0.951556	+	0.307475i	$0.0994839\pi$
$859$	7.50563e21	+	1.30001e22i	0.742059	+	1.28528i	−0.209497	+	0.977809i	$0.567183\pi$
$860$	2.89692e21			0.283921
$861$		0			0
$862$	−7.30576e21			−0.703656
$863$	4.02642e21	+	6.97396e21i	0.384448	+	0.665884i	0.991692	−	0.128631i	$-0.0410584\pi$
$863$	4.02642e21	+	6.97396e21i	0.384448	+	0.665884i	−0.607244	+	0.794515i	$0.707725\pi$
$864$	9.87890e20	−	1.71108e21i	0.0935094	−	0.161963i
$865$	2.30547e19	−	3.99320e19i	0.00216341	−	0.00374714i
$866$	−6.23962e21	−	1.08073e22i	−0.580462	−	1.00539i
$867$	−9.92910e21			−0.915728
$868$		0			0
$869$	1.44097e22			1.30619
$870$	1.72336e21	+	2.98495e21i	0.154875	+	0.268252i
$871$	−3.35943e21	+	5.81871e21i	−0.299316	+	0.518430i
$872$	1.42962e21	−	2.47617e21i	0.126283	−	0.218729i
$873$	6.86424e20	+	1.18892e21i	0.0601154	+	0.104123i
$874$	−4.50339e21			−0.391025
$875$		0			0
$876$	−3.34477e21			−0.285487
$877$	−8.39079e21	−	1.45333e22i	−0.710078	−	1.22989i	−0.964828	−	0.262884i	$-0.915326\pi$
$877$	−8.39079e21	−	1.45333e22i	−0.710078	−	1.22989i	0.254750	−	0.967007i	$-0.418007\pi$
$878$	−3.54513e21	+	6.14034e21i	−0.297456	+	0.515209i
$879$	3.85471e21	−	6.67656e21i	0.320683	−	0.555439i
$880$	8.56699e20	+	1.48385e21i	0.0706656	+	0.122396i
$881$	−1.27876e22			−1.04585			−0.522923	−	0.852380i	$-0.675159\pi$
$881$	−1.27876e22			−1.04585			−0.522923	+	0.852380i	$0.675159\pi$
$882$		0			0
$883$	1.05362e22			0.847190			0.423595	−	0.905852i	$-0.360768\pi$
$883$	1.05362e22			0.847190			0.423595	+	0.905852i	$0.360768\pi$
$884$	−1.88059e20	−	3.25728e20i	−0.0149935	−	0.0259694i
$885$	2.88998e21	−	5.00559e21i	0.228465	−	0.395713i
$886$	−7.42949e21	+	1.28683e22i	−0.582380	+	1.00871i
$887$	1.46329e21	+	2.53449e21i	0.113737	+	0.196999i	0.917274	−	0.398256i	$-0.130384\pi$
$887$	1.46329e21	+	2.53449e21i	0.113737	+	0.196999i	−0.803537	+	0.595255i	$0.797051\pi$
$888$	2.94739e21			0.227165
$889$		0			0
$890$	−9.11669e20			−0.0690895
$891$	7.60678e21	+	1.31753e22i	0.571634	+	0.990099i
$892$	−2.65160e21	+	4.59271e21i	−0.197593	+	0.342242i
$893$	−6.05705e21	+	1.04911e22i	−0.447585	+	0.775240i
$894$	−1.22845e21	−	2.12774e21i	−0.0900174	−	0.155915i
$895$	3.92202e21			0.284995
$896$		0			0
$897$	−3.15415e21			−0.225392
$898$	−1.19130e21	−	2.06340e21i	−0.0844208	−	0.146221i
$899$	8.11549e21	−	1.40564e22i	0.570318	−	0.987819i
$900$	−4.23245e20	+	7.33082e20i	−0.0294967	+	0.0510898i
$901$	−9.08391e20	−	1.57338e21i	−0.0627823	−	0.108742i
$902$	−4.93901e20			−0.0338525
$903$		0			0
$904$	2.87427e21			0.193760
$905$	5.37261e21	+	9.30563e21i	0.359187	+	0.622130i
$906$	6.46949e21	−	1.12055e22i	0.428952	−	0.742966i
$907$	−6.61058e21	+	1.14499e22i	−0.434695	+	0.752914i	−0.997271	−	0.0738316i	$-0.976477\pi$
$907$	−6.61058e21	+	1.14499e22i	−0.434695	+	0.752914i	0.562575	+	0.826746i	$0.309811\pi$
$908$	−5.98541e20	−	1.03670e21i	−0.0390346	−	0.0676099i
$909$	−1.49764e21			−0.0968676
$910$		0			0
$911$	3.71366e21			0.236273			0.118137	−	0.992997i	$-0.462308\pi$
$911$	3.71366e21			0.236273			0.118137	+	0.992997i	$0.462308\pi$
$912$	−2.36570e21	−	4.09752e21i	−0.149279	−	0.258559i
$913$	−7.17016e21	+	1.24191e22i	−0.448743	+	0.777246i
$914$	−2.87224e21	+	4.97487e21i	−0.178289	+	0.308806i
$915$	5.13402e21	+	8.89238e21i	0.316082	+	0.547470i
$916$	−1.16189e22			−0.709495
$917$		0			0
$918$	−1.31584e21			−0.0790469
$919$	−8.40486e20	−	1.45576e21i	−0.0500800	−	0.0867410i	0.839899	−	0.542743i	$-0.182614\pi$
$919$	−8.40486e20	−	1.45576e21i	−0.0500800	−	0.0867410i	−0.889979	+	0.456002i	$0.849281\pi$
$920$	−5.31069e20	+	9.19838e20i	−0.0313864	+	0.0543629i
$921$	6.14996e21	−	1.06520e22i	0.360516	−	0.624433i
$922$	4.73860e21	+	8.20749e21i	0.275529	+	0.477231i
$923$	6.25535e21			0.360777
$924$		0			0
$925$	−1.01306e22			−0.574873
$926$	−7.93342e21	−	1.37411e22i	−0.446558	−	0.773461i
$927$	1.12297e21	−	1.94504e21i	0.0627003	−	0.108600i
$928$	−1.82325e21	+	3.15795e21i	−0.100980	+	0.174902i
$929$	4.28845e21	+	7.42781e21i	0.235604	+	0.408078i	0.959448	−	0.281886i	$-0.0909599\pi$
$929$	4.28845e21	+	7.42781e21i	0.235604	+	0.408078i	−0.723844	+	0.689963i	$0.757627\pi$
$930$	4.96707e21			0.270694
$931$		0			0
$932$	1.23148e22			0.660400
$933$	1.93661e21	+	3.35431e21i	0.103022	+	0.178440i
$934$	−1.24950e22	+	2.16420e22i	−0.659378	+	1.14208i
$935$	5.70551e20	−	9.88223e20i	0.0298681	−	0.0517330i
$936$	2.75119e20	+	4.76520e20i	0.0142874	+	0.0247464i
$937$	−3.98160e21			−0.205121			−0.102561	−	0.994727i	$-0.532704\pi$
$937$	−3.98160e21			−0.205121			−0.102561	+	0.994727i	$0.532704\pi$
$938$		0			0
$939$	−1.69853e22			−0.861153
$940$	1.42857e21	+	2.47436e21i	0.0718527	+	0.124453i
$941$	5.87738e21	−	1.01799e22i	0.293266	−	0.507952i	−0.681314	−	0.731991i	$-0.738591\pi$
$941$	5.87738e21	−	1.01799e22i	0.293266	−	0.507952i	0.974580	+	0.224039i	$0.0719245\pi$
$942$	1.65332e21	−	2.86364e21i	0.0818420	−	0.141755i
$943$	−1.53085e20	−	2.65151e20i	−0.00751787	−	0.0130213i
$944$	6.11495e21			0.297922
$945$		0			0
$946$	−2.76125e22			−1.32411
$947$	−6.89281e21	−	1.19387e22i	−0.327922	−	0.567978i	0.654177	−	0.756342i	$-0.273015\pi$
$947$	−6.89281e21	−	1.19387e22i	−0.327922	−	0.567978i	−0.982099	+	0.188363i	$0.939682\pi$
$948$	−4.69243e21	+	8.12753e21i	−0.221480	+	0.383615i
$949$	3.73648e21	−	6.47177e21i	0.174971	−	0.303058i
$950$	8.13125e21	+	1.40837e22i	0.377772	+	0.654321i
$951$	−2.65429e22			−1.22347
$952$		0			0
$953$	2.93636e22			1.33233			0.666165	−	0.745804i	$-0.267935\pi$
$953$	2.93636e22			1.33233			0.666165	+	0.745804i	$0.267935\pi$
$954$	1.32892e21	+	2.30176e21i	0.0598256	+	0.103621i
$955$	−6.79332e21	+	1.17664e22i	−0.303429	+	0.525554i
$956$	−3.39870e21	+	5.88672e21i	−0.150619	+	0.260879i
$957$	−1.64266e22	−	2.84516e22i	−0.722283	−	1.25103i
$958$	1.47673e22			0.644258
$959$		0			0
$960$	−1.11592e21			−0.0479288
$961$	3.74106e19	+	6.47971e19i	0.00159430	+	0.00276141i
$962$	−3.29256e21	+	5.70288e21i	−0.139226	+	0.241147i
$963$	−3.20293e21	+	5.54764e21i	−0.134385	+	0.232761i
$964$	−6.12088e21	−	1.06017e22i	−0.254821	−	0.441364i
$965$	1.04248e22			0.430640
$966$		0			0
$967$	−1.59444e21			−0.0648498			−0.0324249	−	0.999474i	$-0.510323\pi$
$967$	−1.59444e21			−0.0648498			−0.0324249	+	0.999474i	$0.510323\pi$
$968$	−3.78563e21	−	6.55691e21i	−0.152782	−	0.264627i
$969$	−1.57553e21	+	2.72890e21i	−0.0630955	+	0.109285i
$970$	3.11027e21	−	5.38715e21i	0.123598	−	0.214078i
$971$	−1.12632e22	−	1.95084e22i	−0.444136	−	0.769266i	0.553855	−	0.832613i	$-0.313156\pi$
$971$	−1.12632e22	−	1.95084e22i	−0.444136	−	0.769266i	−0.997992	+	0.0633464i	$0.979823\pi$
$972$	3.61006e21			0.141259
$973$		0			0
$974$	2.13247e21			0.0821659
$975$	5.69507e21	+	9.86415e21i	0.217753	+	0.377159i
$976$	−5.43158e21	+	9.40777e21i	−0.206088	+	0.356955i
$977$	1.60354e22	−	2.77741e22i	0.603769	−	1.04576i	−0.388476	−	0.921459i	$-0.626998\pi$
$977$	1.60354e22	−	2.77741e22i	0.603769	−	1.04576i	0.992245	−	0.124299i	$-0.0396682\pi$
$978$	−1.60742e22	−	2.78414e22i	−0.600604	−	1.04028i
$979$	8.68975e21			0.322209
$980$		0			0
$981$	2.78575e21			0.101724
$982$	1.22729e21	+	2.12572e21i	0.0444744	+	0.0770319i
$983$	2.20571e22	−	3.82040e22i	0.793226	−	1.37391i	−0.130734	−	0.991418i	$-0.541733\pi$
$983$	2.20571e22	−	3.82040e22i	0.793226	−	1.37391i	0.923960	−	0.382490i	$-0.124933\pi$
$984$	1.60836e20	−	2.78576e20i	0.00574011	−	0.00994216i
$985$	−3.20277e21	−	5.54736e21i	−0.113437	−	0.196478i
$986$	2.42852e21			0.0853620
$987$		0			0
$988$	1.05710e22			0.365964
$989$	−8.55853e21	−	1.48238e22i	−0.294054	−	0.509316i
$990$	−8.34683e20	+	1.44571e21i	−0.0284615	+	0.0492967i
$991$	−6.13751e21	+	1.06305e22i	−0.207702	+	0.359750i	−0.950990	−	0.309221i	$-0.899932\pi$
$991$	−6.13751e21	+	1.06305e22i	−0.207702	+	0.359750i	0.743289	+	0.668971i	$0.233265\pi$
$992$	2.62748e21	+	4.55093e21i	0.0882473	+	0.152849i
$993$	−4.69437e21			−0.156480
$994$		0			0
$995$	−6.67074e21			−0.219029
$996$	−4.66984e21	−	8.08839e21i	−0.152180	−	0.263583i
$997$	−5.56992e21	+	9.64739e21i	−0.180151	+	0.312030i	−0.941932	−	0.335805i	$-0.890992\pi$
$997$	−5.56992e21	+	9.64739e21i	−0.180151	+	0.312030i	0.761781	+	0.647834i	$0.224325\pi$
$998$	1.01899e21	−	1.76494e21i	0.0327107	−	0.0566566i
$999$	1.15190e22	+	1.99515e22i	0.367006	+	0.635673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.16.c.m.67.2		10
7.2	even	3	inner	98.16.c.m.79.2		10
7.3	odd	6		98.16.a.j.1.2		5
7.4	even	3		98.16.a.k.1.4		5
7.5	odd	6		14.16.c.a.9.4	✓	10
7.6	odd	2		14.16.c.a.11.4	yes	10
21.5	even	6		126.16.g.e.37.4		10
21.20	even	2		126.16.g.e.109.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.16.c.a.9.4	✓	10	7.5	odd	6
14.16.c.a.11.4	yes	10	7.6	odd	2
98.16.a.j.1.2		5	7.3	odd	6
98.16.a.k.1.4		5	7.4	even	3
98.16.c.m.67.2		10	1.1	even	1	trivial
98.16.c.m.79.2		10	7.2	even	3	inner
126.16.g.e.37.4		10	21.5	even	6
126.16.g.e.109.4		10	21.20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-64.0000 - 110.851i) q^{2} +(-1753.97 + 3037.97i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +449016. q^{6} +2.09715e6 q^{8} +(1.02163e6 + 1.76951e6i) q^{9} +O(q^{10})\)	\(q+(-64.0000 - 110.851i) q^{2} +(-1753.97 + 3037.97i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +449016. q^{6} +2.09715e6 q^{8} +(1.02163e6 + 1.76951e6i) q^{9} +(4.62913e6 - 8.01788e6i) q^{10} +(-4.41234e7 + 7.64240e7i) q^{11} +(-2.87371e7 - 4.97740e7i) q^{12} +1.28410e8 q^{13} -2.53730e8 q^{15} +(-1.34218e8 - 2.32472e8i) q^{16} +(-8.93874e7 + 1.54823e8i) q^{17} +(1.30768e8 - 2.26498e8i) q^{18} +(-2.51228e9 - 4.35140e9i) q^{19} -1.18506e9 q^{20} +1.12956e10 q^{22} +(3.50108e9 + 6.06404e9i) q^{23} +(-3.67834e9 + 6.37108e9i) q^{24} +(1.26430e10 - 2.18983e10i) q^{25} +(-8.21822e9 - 1.42344e10i) q^{26} -5.75027e10 q^{27} +1.06127e11 q^{29} +(1.62387e10 + 2.81263e10i) q^{30} +(7.64697e10 - 1.32449e11i) q^{31} +(-1.71799e10 + 2.97564e10i) q^{32} +(-1.54782e11 - 2.68091e11i) q^{33} +2.28832e10 q^{34} -3.34767e10 q^{36} +(-2.00321e11 - 3.46966e11i) q^{37} +(-3.21572e11 + 5.56979e11i) q^{38} +(-2.25227e11 + 3.90104e11i) q^{39} +(7.58436e10 + 1.31365e11i) q^{40} -4.37251e10 q^{41} -2.44454e12 q^{43} +(-7.22918e11 - 1.25213e12i) q^{44} +(-7.38945e10 + 1.27989e11i) q^{45} +(4.48138e11 - 7.76198e11i) q^{46} +(-1.20549e12 - 2.08797e12i) q^{47} +9.41656e11 q^{48} -3.23660e12 q^{50} +(-3.13566e11 - 5.43112e11i) q^{51} +(-1.05193e12 + 1.82200e12i) q^{52} +(-5.08120e12 + 8.80091e12i) q^{53} +(3.68018e12 + 6.37425e12i) q^{54} -6.38290e12 q^{55} +1.76259e13 q^{57} +(-6.79212e12 - 1.17643e13i) q^{58} +(-1.13900e13 + 1.97280e13i) q^{59} +(2.07855e12 - 3.60016e12i) q^{60} +(-2.02342e13 - 3.50467e13i) q^{61} -1.95762e13 q^{62} +4.39805e12 q^{64} +(4.64394e12 + 8.04355e12i) q^{65} +(-1.98121e13 + 3.43156e13i) q^{66} +(-2.61618e13 + 4.53136e13i) q^{67} +(-1.46452e12 - 2.53663e12i) q^{68} -2.45631e13 q^{69} +4.87140e13 q^{71} +(2.14251e12 + 3.71094e12i) q^{72} +(2.90981e13 - 5.03994e13i) q^{73} +(-2.56411e13 + 4.44116e13i) q^{74} +(4.43508e13 + 7.68178e13i) q^{75} +8.23224e13 q^{76} +5.76581e13 q^{78} +(-8.16442e13 - 1.41412e14i) q^{79} +(9.70798e12 - 1.68147e13i) q^{80} +(8.61989e13 - 1.49301e14i) q^{81} +(2.79841e12 + 4.84699e12i) q^{82} +1.62502e14 q^{83} -1.29308e13 q^{85} +(1.56451e14 + 2.70980e14i) q^{86} +(-1.86143e14 + 3.22410e14i) q^{87} +(-9.25335e13 + 1.60273e14i) q^{88} +(-4.92355e13 - 8.52783e13i) q^{89} +1.89170e13 q^{90} -1.14723e14 q^{92} +(2.68251e14 + 4.64624e14i) q^{93} +(-1.54303e14 + 2.67260e14i) q^{94} +(1.81714e14 - 3.14737e14i) q^{95} +(-6.02660e13 - 1.04384e14i) q^{96} +6.71892e14 q^{97} -1.80311e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 640 q^{2} - 1979 q^{3} - 81920 q^{4} - 300953 q^{5} + 506624 q^{6} + 20971520 q^{8} - 17367046 q^{9}+O(q^{10}) \) 10 * q - 640 * q^2 - 1979 * q^3 - 81920 * q^4 - 300953 * q^5 + 506624 * q^6 + 20971520 * q^8 - 17367046 * q^9	\( 10 q - 640 q^{2} - 1979 q^{3} - 81920 q^{4} - 300953 q^{5} + 506624 q^{6} + 20971520 q^{8} - 17367046 q^{9} - 38521984 q^{10} + 14189887 q^{11} - 32423936 q^{12} + 772602348 q^{13} + 1426775646 q^{15} - 1342177280 q^{16} + 145564295 q^{17} - 2222981888 q^{18} - 3550131629 q^{19} + 9861627904 q^{20} - 3632611072 q^{22} + 9869524537 q^{23} - 4150263808 q^{24} - 51839554204 q^{25} - 49446550272 q^{26} + 342946209778 q^{27} - 165255956188 q^{29} - 91313641344 q^{30} + 106825666677 q^{31} - 171798691840 q^{32} + 139826141649 q^{33} - 37264459520 q^{34} + 569083363328 q^{36} - 596799401515 q^{37} - 454416848512 q^{38} - 2827795559666 q^{39} - 631144185856 q^{40} - 1756981189740 q^{41} - 5305116572344 q^{43} + 232487108608 q^{44} - 10836341974062 q^{45} + 1263299140736 q^{46} - 4284391851525 q^{47} + 1062467534848 q^{48} + 13270925876224 q^{50} - 8298359375823 q^{51} - 6329158434816 q^{52} - 4037801378823 q^{53} - 21948557425792 q^{54} + 47232884322970 q^{55} - 75972269020058 q^{57} + 10576381196032 q^{58} - 6081930248483 q^{59} - 11688146092032 q^{60} - 29484338931189 q^{61} - 27347370669312 q^{62} + 43980465111040 q^{64} + 78038741223618 q^{65} + 17897746131072 q^{66} - 2851190345117 q^{67} + 2384925409280 q^{68} + 41705305747074 q^{69} + 190169727933856 q^{71} - 36421335252992 q^{72} - 284202883487269 q^{73} - 76390323393920 q^{74} + 151851953188876 q^{75} + 116330713219072 q^{76} + 723915663274496 q^{78} + 536529323488905 q^{79} - 80786455789568 q^{80} + 23023662902123 q^{81} + 112446796143360 q^{82} + 949641950127416 q^{83} + 24\!\cdots\!86 q^{85}+ \cdots - 989855214604404 q^{99}+O(q^{100}) \) 10 * q - 640 * q^2 - 1979 * q^3 - 81920 * q^4 - 300953 * q^5 + 506624 * q^6 + 20971520 * q^8 - 17367046 * q^9 - 38521984 * q^10 + 14189887 * q^11 - 32423936 * q^12 + 772602348 * q^13 + 1426775646 * q^15 - 1342177280 * q^16 + 145564295 * q^17 - 2222981888 * q^18 - 3550131629 * q^19 + 9861627904 * q^20 - 3632611072 * q^22 + 9869524537 * q^23 - 4150263808 * q^24 - 51839554204 * q^25 - 49446550272 * q^26 + 342946209778 * q^27 - 165255956188 * q^29 - 91313641344 * q^30 + 106825666677 * q^31 - 171798691840 * q^32 + 139826141649 * q^33 - 37264459520 * q^34 + 569083363328 * q^36 - 596799401515 * q^37 - 454416848512 * q^38 - 2827795559666 * q^39 - 631144185856 * q^40 - 1756981189740 * q^41 - 5305116572344 * q^43 + 232487108608 * q^44 - 10836341974062 * q^45 + 1263299140736 * q^46 - 4284391851525 * q^47 + 1062467534848 * q^48 + 13270925876224 * q^50 - 8298359375823 * q^51 - 6329158434816 * q^52 - 4037801378823 * q^53 - 21948557425792 * q^54 + 47232884322970 * q^55 - 75972269020058 * q^57 + 10576381196032 * q^58 - 6081930248483 * q^59 - 11688146092032 * q^60 - 29484338931189 * q^61 - 27347370669312 * q^62 + 43980465111040 * q^64 + 78038741223618 * q^65 + 17897746131072 * q^66 - 2851190345117 * q^67 + 2384925409280 * q^68 + 41705305747074 * q^69 + 190169727933856 * q^71 - 36421335252992 * q^72 - 284202883487269 * q^73 - 76390323393920 * q^74 + 151851953188876 * q^75 + 116330713219072 * q^76 + 723915663274496 * q^78 + 536529323488905 * q^79 - 80786455789568 * q^80 + 23023662902123 * q^81 + 112446796143360 * q^82 + 949641950127416 * q^83 + 2471416802444186 * q^85 + 339527460630016 * q^86 - 1562035609957686 * q^87 + 29758349901824 * q^88 - 160148042721333 * q^89 + 2774103545359872 * q^90 - 323404580028416 * q^92 + 1714374265333339 * q^93 - 548402156995200 * q^94 - 739988010259049 * q^95 - 67997922230272 * q^96 + 4057131581852468 * q^97 - 989855214604404 * q^99

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