LMFDB - Embedded newform 126.16.g.e.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,16,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$179.793816426$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 11644556445 x^{8} + 11479653183988 x^{7} + \cdots + 46\!\cdots\!16 $ x^10 - x^9 - 11644556445x^8 + 11479653183988x^7 + 48023776184400520544x^6 - 203745902928198332791260x^5 - 82205873721347244692502758305x^4 + 878306814073876478096064537643597x^3 + 49092320356349199537919480463412520521x^2 - 967093764473364601221262551586766131681348x + 4687798913050036135019167674805317845969954416
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{7}\cdot 5^{2}\cdot 7^{7} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.4
Root			$33130.3 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.16.g.e.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(64.0000 + 110.851i) q^{2} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +(780333. + 2.03437e6i) q^{7} -2.09715e6 q^{8} +O(q^{10})$	\(q+(64.0000 + 110.851i) q^{2} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +(780333. + 2.03437e6i) q^{7} -2.09715e6 q^{8} +(-4.62913e6 + 8.01788e6i) q^{10} +(4.41234e7 - 7.64240e7i) q^{11} -1.28410e8 q^{13} +(-1.75571e8 + 2.16700e8i) q^{14} +(-1.34218e8 - 2.32472e8i) q^{16} +(-8.93874e7 + 1.54823e8i) q^{17} +(2.51228e9 + 4.35140e9i) q^{19} -1.18506e9 q^{20} +1.12956e10 q^{22} +(-3.50108e9 - 6.06404e9i) q^{23} +(1.26430e10 - 2.18983e10i) q^{25} +(-8.21822e9 - 1.42344e10i) q^{26} +(-3.52580e10 - 5.59341e9i) q^{28} -1.06127e11 q^{29} +(-7.64697e10 + 1.32449e11i) q^{31} +(1.71799e10 - 2.97564e10i) q^{32} -2.28832e10 q^{34} +(-9.92113e10 + 1.22453e11i) q^{35} +(-2.00321e11 - 3.46966e11i) q^{37} +(-3.21572e11 + 5.56979e11i) q^{38} +(-7.58436e10 - 1.31365e11i) q^{40} -4.37251e10 q^{41} -2.44454e12 q^{43} +(7.22918e11 + 1.25213e12i) q^{44} +(4.48138e11 - 7.76198e11i) q^{46} +(-1.20549e12 - 2.08797e12i) q^{47} +(-3.52972e12 + 3.17496e12i) q^{49} +3.23660e12 q^{50} +(1.05193e12 - 1.82200e12i) q^{52} +(5.08120e12 - 8.80091e12i) q^{53} +6.38290e12 q^{55} +(-1.63648e12 - 4.26637e12i) q^{56} +(-6.79212e12 - 1.17643e13i) q^{58} +(-1.13900e13 + 1.97280e13i) q^{59} +(2.02342e13 + 3.50467e13i) q^{61} -1.95762e13 q^{62} +4.39805e12 q^{64} +(-4.64394e12 - 8.04355e12i) q^{65} +(-2.61618e13 + 4.53136e13i) q^{67} +(-1.46452e12 - 2.53663e12i) q^{68} +(-1.99236e13 - 3.16072e12i) q^{70} -4.87140e13 q^{71} +(-2.90981e13 + 5.03994e13i) q^{73} +(2.56411e13 - 4.44116e13i) q^{74} -8.23224e13 q^{76} +(1.89905e14 + 3.01270e13i) q^{77} +(-8.16442e13 - 1.41412e14i) q^{79} +(9.70798e12 - 1.68147e13i) q^{80} +(-2.79841e12 - 4.84699e12i) q^{82} +1.62502e14 q^{83} -1.29308e13 q^{85} +(-1.56451e14 - 2.70980e14i) q^{86} +(-9.25335e13 + 1.60273e14i) q^{88} +(-4.92355e13 - 8.52783e13i) q^{89} +(-1.00202e14 - 2.61232e14i) q^{91} +1.14723e14 q^{92} +(1.54303e14 - 2.67260e14i) q^{94} +(-1.81714e14 + 3.14737e14i) q^{95} -6.71892e14 q^{97} +(-5.77851e14 - 1.88076e14i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 640 q^{2} - 81920 q^{4} - 300953 q^{5} + 4054316 q^{7} - 20971520 q^{8}+O(q^{10}) $ 10 * q + 640 * q^2 - 81920 * q^4 - 300953 * q^5 + 4054316 * q^7 - 20971520 * q^8	\( 10 q + 640 q^{2} - 81920 q^{4} - 300953 q^{5} + 4054316 q^{7} - 20971520 q^{8} + 38521984 q^{10} - 14189887 q^{11} - 772602348 q^{13} + 815024000 q^{14} - 1342177280 q^{16} + 145564295 q^{17} + 3550131629 q^{19} + 9861627904 q^{20} - 3632611072 q^{22} - 9869524537 q^{23} - 51839554204 q^{25} - 49446550272 q^{26} + 37897158656 q^{28} + 165255956188 q^{29} - 106825666677 q^{31} + 171798691840 q^{32} + 37264459520 q^{34} - 1475862848131 q^{35} - 596799401515 q^{37} - 454416848512 q^{38} + 631144185856 q^{40} - 1756981189740 q^{41} - 5305116572344 q^{43} - 232487108608 q^{44} + 1263299140736 q^{46} - 4284391851525 q^{47} + 1588100454346 q^{49} - 13270925876224 q^{50} + 6329158434816 q^{52} + 4037801378823 q^{53} - 47232884322970 q^{55} - 8502516908032 q^{56} + 10576381196032 q^{58} - 6081930248483 q^{59} + 29484338931189 q^{61} - 27347370669312 q^{62} + 43980465111040 q^{64} - 78038741223618 q^{65} - 2851190345117 q^{67} + 2384925409280 q^{68} - 190125208943488 q^{70} - 190169727933856 q^{71} + 284202883487269 q^{73} + 76390323393920 q^{74} - 116330713219072 q^{76} + 656655421831969 q^{77} + 536529323488905 q^{79} - 80786455789568 q^{80} - 112446796143360 q^{82} + 949641950127416 q^{83} + 24\!\cdots\!86 q^{85}+ \cdots + 939580168008832 q^{98}+O(q^{100}) \) 10 * q + 640 * q^2 - 81920 * q^4 - 300953 * q^5 + 4054316 * q^7 - 20971520 * q^8 + 38521984 * q^10 - 14189887 * q^11 - 772602348 * q^13 + 815024000 * q^14 - 1342177280 * q^16 + 145564295 * q^17 + 3550131629 * q^19 + 9861627904 * q^20 - 3632611072 * q^22 - 9869524537 * q^23 - 51839554204 * q^25 - 49446550272 * q^26 + 37897158656 * q^28 + 165255956188 * q^29 - 106825666677 * q^31 + 171798691840 * q^32 + 37264459520 * q^34 - 1475862848131 * q^35 - 596799401515 * q^37 - 454416848512 * q^38 + 631144185856 * q^40 - 1756981189740 * q^41 - 5305116572344 * q^43 - 232487108608 * q^44 + 1263299140736 * q^46 - 4284391851525 * q^47 + 1588100454346 * q^49 - 13270925876224 * q^50 + 6329158434816 * q^52 + 4037801378823 * q^53 - 47232884322970 * q^55 - 8502516908032 * q^56 + 10576381196032 * q^58 - 6081930248483 * q^59 + 29484338931189 * q^61 - 27347370669312 * q^62 + 43980465111040 * q^64 - 78038741223618 * q^65 - 2851190345117 * q^67 + 2384925409280 * q^68 - 190125208943488 * q^70 - 190169727933856 * q^71 + 284202883487269 * q^73 + 76390323393920 * q^74 - 116330713219072 * q^76 + 656655421831969 * q^77 + 536529323488905 * q^79 - 80786455789568 * q^80 - 112446796143360 * q^82 + 949641950127416 * q^83 + 2471416802444186 * q^85 - 339527460630016 * q^86 + 29758349901824 * q^88 - 160148042721333 * q^89 - 1307014889481672 * q^91 + 323404580028416 * q^92 + 548402156995200 * q^94 + 739988010259049 * q^95 - 4057131581852468 * q^97 + 939580168008832 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$		0			0
$3$		0			0
$4$	−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	$0.766957\pi$
$6$		0			0
$7$	780333.	+	2.03437e6i	0.358133	+	0.933670i
$7$	780333.	+	2.03437e6i	0.358133	+	0.933670i
$8$	−2.09715e6			−0.353553
$9$		0			0
$10$	−4.62913e6	+	8.01788e6i	−0.146386	+	0.253548i
$11$	4.41234e7	−	7.64240e7i	0.682691	−	1.18246i	−0.291466	−	0.956581i	$-0.594143\pi$
$11$	4.41234e7	−	7.64240e7i	0.682691	−	1.18246i	0.974157	−	0.225874i	$-0.0725238\pi$
$12$		0			0
$13$	−1.28410e8			−0.567574			−0.283787	−	0.958887i	$-0.591591\pi$
$13$	−1.28410e8			−0.567574			−0.283787	+	0.958887i	$0.591591\pi$
$14$	−1.75571e8	+	2.16700e8i	−0.445135	+	0.549413i
$15$		0			0
$16$	−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	$0.183492\pi$
$18$		0			0
$19$	2.51228e9	+	4.35140e9i	0.644787	+	1.11680i	0.984351	+	0.176221i	$0.0563873\pi$
$19$	2.51228e9	+	4.35140e9i	0.644787	+	1.11680i	−0.339564	+	0.940583i	$0.610279\pi$
$20$	−1.18506e9			−0.207021
$21$		0			0
$22$	1.12956e10			0.965471
$23$	−3.50108e9	−	6.06404e9i	−0.214409	−	0.371367i	0.738681	−	0.674056i	$-0.235449\pi$
$23$	−3.50108e9	−	6.06404e9i	−0.214409	−	0.371367i	−0.953090	+	0.302688i	$0.902116\pi$
$24$		0			0
$25$	1.26430e10	−	2.18983e10i	0.414285	−	0.717562i
$26$	−8.21822e9	−	1.42344e10i	−0.200668	−	0.347567i
$27$		0			0
$28$	−3.52580e10	−	5.59341e9i	−0.493824	−	0.0783414i
$29$	−1.06127e11			−1.14246			−0.571229	−	0.820791i	$-0.693533\pi$
$29$	−1.06127e11			−1.14246			−0.571229	+	0.820791i	$0.693533\pi$
$30$		0			0
$31$	−7.64697e10	+	1.32449e11i	−0.499202	+	0.864644i	−1.00000		0.000920959i	$-0.999707\pi$
$31$	−7.64697e10	+	1.32449e11i	−0.499202	+	0.864644i	0.500797	+	0.865565i	$0.333040\pi$
$32$	1.71799e10	−	2.97564e10i	0.0883883	−	0.153093i
$33$		0			0
$34$	−2.28832e10			−0.0747178
$35$	−9.92113e10	+	1.22453e11i	−0.260646	+	0.321705i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−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
$45$		0			0
$46$	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	$0.946160\pi$
$48$		0			0
$49$	−3.52972e12	+	3.17496e12i	−0.743481	+	0.668757i
$50$	3.23660e12			0.585887
$51$		0			0
$52$	1.05193e12	−	1.82200e12i	0.141894	−	0.245767i
$53$	5.08120e12	−	8.80091e12i	0.594152	−	1.02910i	−0.399514	−	0.916727i	$-0.630821\pi$
$53$	5.08120e12	−	8.80091e12i	0.594152	−	1.02910i	0.993666	−	0.112375i	$-0.0358456\pi$
$54$		0			0
$55$	6.38290e12			0.565325
$56$	−1.63648e12	−	4.26637e12i	−0.126619	−	0.330102i
$57$		0			0
$58$	−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	$0.963484\pi$
$60$		0			0
$61$	2.02342e13	+	3.50467e13i	0.824351	+	1.42782i	0.902414	+	0.430870i	$0.141793\pi$
$61$	2.02342e13	+	3.50467e13i	0.824351	+	1.42782i	−0.0780625	+	0.996948i	$0.524873\pi$
$62$	−1.95762e13			−0.705979
$63$		0			0
$64$	4.39805e12			0.125000
$65$	−4.64394e12	−	8.04355e12i	−0.117500	−	0.203515i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−1.99236e13	−	3.16072e12i	−0.289156	−	0.0458723i
$71$	−4.87140e13			−0.635647			−0.317824	−	0.948150i	$-0.602952\pi$
$71$	−4.87140e13			−0.635647			−0.317824	+	0.948150i	$0.602952\pi$
$72$		0			0
$73$	−2.90981e13	+	5.03994e13i	−0.308278	+	0.533954i	−0.977986	−	0.208671i	$-0.933086\pi$
$73$	−2.90981e13	+	5.03994e13i	−0.308278	+	0.533954i	0.669707	+	0.742625i	$0.266420\pi$
$74$	2.56411e13	−	4.44116e13i	0.245300	−	0.424873i
$75$		0			0
$76$	−8.23224e13			−0.644787
$77$	1.89905e14	+	3.01270e13i	1.34852	+	0.213932i
$78$		0			0
$79$	−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
$81$		0			0
$82$	−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
$87$		0			0
$88$	−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	$0.870979\pi$
$90$		0			0
$91$	−1.00202e14	−	2.61232e14i	−0.203267	−	0.529927i
$92$	1.14723e14			0.214409
$93$		0			0
$94$	1.54303e14	−	2.67260e14i	0.245422	−	0.425084i
$95$	−1.81714e14	+	3.14737e14i	−0.266969	+	0.462403i
$96$		0			0
$97$	−6.71892e14			−0.844329			−0.422164	−	0.906519i	$-0.638730\pi$
$97$	−6.71892e14			−0.844329			−0.422164	+	0.906519i	$0.638730\pi$
$98$	−5.77851e14	−	1.88076e14i	−0.672389	−	0.218846i
$99$		0			0
$100$	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	$0.277138\pi$
$102$		0			0
$103$	5.49597e14	+	9.51930e14i	0.440317	+	0.762651i	0.997713	−	0.0675959i	$-0.0215329\pi$
$103$	5.49597e14	+	9.51930e14i	0.440317	+	0.762651i	−0.557396	+	0.830247i	$0.688200\pi$
$104$	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	$-0.773961\pi$
$107$	−1.56756e15	−	2.71509e15i	−0.943726	−	1.63458i	−0.185444	−	0.982655i	$-0.559372\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	3.68198e14	−	4.54453e14i	0.157379	−	0.194247i
$113$	−1.37056e15			−0.548036			−0.274018	−	0.961725i	$-0.588353\pi$
$113$	−1.37056e15			−0.548036			−0.274018	+	0.961725i	$0.588353\pi$
$114$		0			0
$115$	2.53233e14	−	4.38613e14i	0.0887742	−	0.153762i
$116$	8.69391e14	−	1.50583e15i	0.285615	−	0.494699i
$117$		0			0
$118$	−2.91584e15			−0.842652
$119$	−3.84719e14	−	6.10327e13i	−0.104362	−	0.0165562i
$120$		0			0
$121$	−1.80513e15	−	3.12658e15i	−0.432134	−	0.748477i
$122$	−2.58998e15	+	4.48597e15i	−0.582904	+	1.00962i
$123$		0			0
$124$	−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
$129$		0			0
$130$	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	$-0.558062\pi$
$132$		0			0
$133$	−6.89192e15	+	8.50644e15i	−0.811807	+	1.00198i
$134$	−6.69743e15			−0.745799
$135$		0			0
$136$	1.87459e14	−	3.24688e14i	0.0186795	−	0.0323538i
$137$	−5.66307e15	+	9.80872e15i	−0.534130	+	0.925141i	0.465074	+	0.885272i	$0.346028\pi$
$137$	−5.66307e15	+	9.80872e15i	−0.534130	+	0.925141i	−0.999205	+	0.0398695i	$0.987306\pi$
$138$		0			0
$139$	1.40279e16			1.18681			0.593407	−	0.804903i	$-0.297783\pi$
$139$	1.40279e16			1.18681			0.593407	+	0.804903i	$0.297783\pi$
$140$	−9.24739e14	−	2.41084e15i	−0.0741410	−	0.193289i
$141$		0			0
$142$	−3.11770e15	−	5.40001e15i	−0.224735	−	0.389253i
$143$	−5.66588e15	+	9.81358e15i	−0.387478	+	0.671131i
$144$		0			0
$145$	−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	0.926537	−	0.376203i	$-0.122771\pi$
$149$	2.73587e15	+	4.73867e15i	0.137467	+	0.238100i	−0.789070	+	0.614303i	$0.789437\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	8.81433e15	+	2.29794e16i	0.345767	+	0.901431i
$155$	−1.10621e16			−0.413381
$156$		0			0
$157$	−3.68210e15	+	6.37759e15i	−0.124982	+	0.216476i	−0.921726	−	0.387842i	$-0.873221\pi$
$157$	−3.68210e15	+	6.37759e15i	−0.124982	+	0.216476i	0.796744	+	0.604317i	$0.206554\pi$
$158$	1.04505e16	−	1.81007e16i	0.338226	−	0.585825i
$159$		0			0
$160$	2.48524e15			0.0731929
$161$	9.60447e15	−	1.18544e16i	0.269948	−	0.333186i
$162$		0			0
$163$	−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
$165$		0			0
$166$	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
$171$		0			0
$172$	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	$0.834997\pi$
$174$		0			0
$175$	5.44148e16	+	8.63248e15i	0.818336	+	0.129823i
$176$	−2.36886e16			−0.341345
$177$		0			0
$178$	6.30214e15	−	1.09156e16i	0.0834330	−	0.144510i
$179$	−2.71119e16	+	4.69593e16i	−0.344162	+	0.596106i	−0.985201	−	0.171402i	$-0.945170\pi$
$179$	−2.71119e16	+	4.69593e16i	−0.344162	+	0.596106i	0.641039	+	0.767508i	$0.278504\pi$
$180$		0			0
$181$	−1.48558e17			−1.73503			−0.867514	−	0.497412i	$-0.834284\pi$
$181$	−1.48558e17			−1.73503			−0.867514	+	0.497412i	$0.834284\pi$
$182$	2.25450e16	−	2.78264e16i	0.252647	−	0.311833i
$183$		0			0
$184$	7.34229e15	+	1.27172e16i	0.0758050	+	0.131298i
$185$	1.44892e16	−	2.50961e16i	0.143634	−	0.248781i
$186$		0			0
$187$	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	$-0.904858\pi$
$191$	−9.39211e16	−	1.62676e17i	−0.732846	−	1.26933i	0.222815	−	0.974861i	$-0.428475\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	−1.61340e16	−	7.60924e16i	−0.103710	−	0.489126i
$197$	8.85598e16			0.547949			0.273974	−	0.961737i	$-0.411662\pi$
$197$	8.85598e16			0.547949			0.273974	+	0.961737i	$0.411662\pi$
$198$		0			0
$199$	4.61131e16	−	7.98703e16i	0.264501	−	0.458129i	−0.702932	−	0.711257i	$-0.748126\pi$
$199$	4.61131e16	−	7.98703e16i	0.264501	−	0.458129i	0.967433	+	0.253129i	$0.0814595\pi$
$200$	−2.65142e16	+	4.59240e16i	−0.146472	+	0.253697i
$201$		0			0
$202$	−9.38198e16			−0.481016
$203$	−8.28143e16	−	2.15901e17i	−0.409152	−	1.06668i
$204$		0			0
$205$	−1.58132e15	−	2.73893e15i	−0.00725882	−	0.0125727i
$206$	−7.03484e16	+	1.21847e17i	−0.311351	+	0.539275i
$207$		0			0
$208$	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
$213$		0			0
$214$	2.00648e17	−	3.47532e17i	0.667315	−	1.15582i
$215$	−8.84070e16	−	1.53125e17i	−0.283921	−	0.491766i
$216$		0			0
$217$	−3.29122e17	−	5.22127e16i	−0.986073	−	0.156433i
$218$	1.74514e17			0.505133
$219$		0			0
$220$	−5.22888e16	+	9.05668e16i	−0.141331	+	0.244793i
$221$	1.14782e16	−	1.98808e16i	0.0299869	−	0.0519389i
$222$		0			0
$223$	−3.23682e17			−0.790373			−0.395187	−	0.918601i	$-0.629320\pi$
$223$	−3.23682e17			−0.790373			−0.395187	+	0.918601i	$0.629320\pi$
$224$	7.39414e16	+	1.17302e16i	0.174593	+	0.0276979i
$225$		0			0
$226$	−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	$0.191542\pi$
$228$		0			0
$229$	−3.54581e17	−	6.14153e17i	−0.709495	−	1.22888i	−0.965045	−	0.262086i	$-0.915590\pi$
$229$	−3.54581e17	−	6.14153e17i	−0.709495	−	1.22888i	0.255549	−	0.966796i	$-0.417744\pi$
$230$	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	$0.0629466\pi$
$233$	3.75817e17	+	6.50934e17i	0.660400	+	1.14385i	−0.320111	+	0.947380i	$0.603720\pi$
$234$		0			0
$235$	8.71931e16	−	1.51023e17i	0.143705	−	0.248905i
$236$	−1.86614e17	−	3.23224e17i	−0.297922	−	0.516017i
$237$		0			0
$238$	−1.78565e16	−	4.65527e16i	−0.0267589	−	0.0697618i
$239$	−4.14880e17			−0.602474			−0.301237	−	0.953549i	$-0.597400\pi$
$239$	−4.14880e17			−0.602474			−0.301237	+	0.953549i	$0.597400\pi$
$240$		0			0
$241$	3.73589e17	−	6.47074e17i	0.509643	−	0.882727i	−0.490295	−	0.871557i	$-0.663111\pi$
$241$	3.73589e17	−	6.47074e17i	0.509643	−	0.882727i	0.999938	−	0.0111705i	$-0.00355575\pi$
$242$	2.31057e17	−	4.00202e17i	0.305565	−	0.529253i
$243$		0			0
$244$	−6.63034e17			−0.824351
$245$	−3.26531e17	−	1.06278e17i	−0.393713	−	0.128144i
$246$		0			0
$247$	−3.22601e17	−	5.58762e17i	−0.365964	−	0.633869i
$248$	1.60369e17	−	2.77766e17i	0.176495	−	0.305698i
$249$		0			0
$250$	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
$255$		0			0
$256$	−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	$0.961654\pi$
$258$		0			0
$259$	5.49538e17	−	6.78274e17i	0.436767	−	0.539085i
$260$	1.52173e17			0.117500
$261$		0			0
$262$	9.14029e17	−	1.58315e18i	0.666347	−	1.15415i
$263$	−5.22388e17	+	9.04802e17i	−0.370105	+	0.641040i	−0.989581	−	0.143975i	$-0.954012\pi$
$263$	−5.22388e17	+	9.04802e17i	−0.370105	+	0.641040i	0.619477	+	0.785015i	$0.287345\pi$
$264$		0			0
$265$	7.35048e17			0.492008
$266$	−1.38403e18	−	2.19566e17i	−0.900604	−	0.142874i
$267$		0			0
$268$	−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	$-0.126252\pi$
$270$		0			0
$271$	−1.29784e18	−	2.24793e18i	−0.734433	−	1.27208i	−0.954972	−	0.296697i	$-0.904115\pi$
$271$	−1.29784e18	−	2.24793e18i	−0.734433	−	1.27208i	0.220539	−	0.975378i	$-0.429218\pi$
$272$	4.79895e16			0.0264167
$273$		0			0
$274$	−1.44974e18			−0.755375
$275$	−1.11570e18	−	1.93245e18i	−0.565657	−	0.979746i
$276$		0			0
$277$	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
$279$		0			0
$280$	2.08061e17	−	2.56802e17i	0.0921522	−	0.113740i
$281$	1.24946e18			0.538797			0.269398	−	0.963029i	$-0.413175\pi$
$281$	1.24946e18			0.538797			0.269398	+	0.963029i	$0.413175\pi$
$282$		0			0
$283$	−8.65425e17	+	1.49896e18i	−0.353860	+	0.612903i	−0.986922	−	0.161198i	$-0.948464\pi$
$283$	−8.65425e17	+	1.49896e18i	−0.353860	+	0.612903i	0.633062	+	0.774101i	$0.281798\pi$
$284$	3.99065e17	−	6.91201e17i	0.158912	−	0.275243i
$285$		0			0
$286$	−1.45046e18			−0.547976
$287$	−3.41202e16	−	8.89529e16i	−0.0125573	−	0.0327375i
$288$		0			0
$289$	1.41523e18	+	2.45125e18i	0.494417	+	0.856356i
$290$	4.91275e17	−	8.50913e17i	0.167240	−	0.289668i
$291$		0			0
$292$	−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
$297$		0			0
$298$	−3.50191e17	+	6.06549e17i	−0.0972039	+	0.168362i
$299$	4.49572e17	+	7.78682e17i	0.121693	+	0.210778i
$300$		0			0
$301$	−1.90756e18	−	4.97309e18i	−0.491166	−	1.28049i
$302$	3.68848e18			0.926394
$303$		0			0
$304$	6.74385e17	−	1.16807e18i	0.161197	−	0.279201i
$305$	−1.46354e18	+	2.53493e18i	−0.341316	+	0.591176i
$306$		0			0
$307$	3.50631e18			0.778596			0.389298	−	0.921112i	$-0.372718\pi$
$307$	3.50631e18			0.778596			0.389298	+	0.921112i	$0.372718\pi$
$308$	−1.98318e18	+	2.44776e18i	−0.429765	+	0.530442i
$309$		0			0
$310$	−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	$0.131182\pi$
$312$		0			0
$313$	−2.42097e18	−	4.19325e18i	−0.464951	−	0.805319i	0.534248	−	0.845328i	$-0.320595\pi$
$313$	−2.42097e18	−	4.19325e18i	−0.464951	−	0.805319i	−0.999199	+	0.0400086i	$0.987261\pi$
$314$	−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	$-0.936980\pi$
$317$	−3.78325e18	−	6.55279e18i	−0.660573	−	1.14415i	0.319892	−	0.947454i	$-0.396353\pi$
$318$		0			0
$319$	−4.68268e18	+	8.11064e18i	−0.779946	+	1.35091i
$320$	1.59056e17	+	2.75492e17i	0.0258776	+	0.0448213i
$321$		0			0
$322$	1.92877e18	+	3.05984e17i	0.299475	+	0.0475094i
$323$	−8.98265e17			−0.136265
$324$		0			0
$325$	−1.62348e18	+	2.81195e18i	−0.235137	+	0.407270i
$326$	4.58224e18	−	7.93667e18i	0.648553	−	1.12333i
$327$		0			0
$328$	9.16982e16			0.0123967
$329$	3.30701e18	−	4.08171e18i	0.436984	−	0.539353i
$330$		0			0
$331$	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
$333$		0			0
$334$	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
$339$		0			0
$340$	1.05929e17	−	1.83475e17i	0.0109376	−	0.0189445i
$341$	6.74821e18	+	1.16882e19i	0.681602	+	1.18057i
$342$		0			0
$343$	−9.21340e18	−	4.70322e18i	−0.890664	−	0.454662i
$344$	5.12657e18			0.484885
$345$		0			0
$346$	4.07991e16	−	7.06662e16i	0.00369471	−	0.00639942i
$347$	−1.36492e18	+	2.36411e18i	−0.120959	+	0.209506i	−0.920146	−	0.391576i	$-0.871930\pi$
$347$	−1.36492e18	+	2.36411e18i	−0.120959	+	0.209506i	0.799187	+	0.601082i	$0.205264\pi$
$348$		0			0
$349$	4.58227e18			0.388947			0.194473	−	0.980908i	$-0.437700\pi$
$349$	4.58227e18			0.388947			0.194473	+	0.980908i	$0.437700\pi$
$350$	2.52563e18	+	6.58443e18i	0.209826	+	0.547025i
$351$		0			0
$352$	−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	$0.859606\pi$
$354$		0			0
$355$	−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	0.991404	−	0.130840i	$-0.0417674\pi$
$359$	5.56822e18	+	9.64444e18i	0.382391	+	0.662321i	−0.609012	+	0.793161i	$0.708434\pi$
$360$		0			0
$361$	−5.03255e18	+	8.71664e18i	−0.331501	+	0.574176i
$362$	−9.50771e18	−	1.64678e19i	−0.613425	−	1.06248i
$363$		0			0
$364$	4.52747e18	+	7.18248e17i	0.280282	+	0.0444645i
$365$	−4.20934e18			−0.255280
$366$		0			0
$367$	−3.78163e18	+	6.54998e18i	−0.220132	+	0.381280i	−0.954848	−	0.297095i	$-0.903982\pi$
$367$	−3.78163e18	+	6.54998e18i	−0.220132	+	0.381280i	0.734716	+	0.678375i	$0.237316\pi$
$368$	−9.39813e17	+	1.62780e18i	−0.0536022	+	0.0928418i
$369$		0			0
$370$	3.70924e18			0.203129
$371$	2.18693e19	+	3.46939e18i	1.17363	+	0.186187i
$372$		0			0
$373$	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
$375$		0			0
$376$	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
$381$		0			0
$382$	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	$0.558986\pi$
$384$		0			0
$385$	4.98079e18	+	1.29852e19i	0.202462	+	0.527827i
$386$	1.84485e19			0.735454
$387$		0			0
$388$	5.50414e18	−	9.53345e18i	0.211082	−	0.365605i
$389$	−1.43129e19	+	2.47907e19i	−0.538402	+	0.932539i	0.460589	+	0.887614i	$0.347638\pi$
$389$	−1.43129e19	+	2.47907e19i	−0.538402	+	0.932539i	−0.998990	+	0.0449254i	$0.985695\pi$
$390$		0			0
$391$	1.25181e18			0.0453119
$392$	7.40236e18	−	6.65838e18i	0.262860	−	0.236441i
$393$		0			0
$394$	5.66783e18	+	9.81697e18i	0.193729	+	0.335549i
$395$	5.90534e18	−	1.02283e19i	0.198046	−	0.343026i
$396$		0			0
$397$	1.58957e19	+	2.75322e19i	0.513277	+	0.889023i	0.999881	+	0.0154000i	$0.00490216\pi$
$397$	1.58957e19	+	2.75322e19i	0.513277	+	0.889023i	−0.486604	+	0.873623i	$0.661765\pi$
$398$	1.18050e19			0.374060
$399$		0			0
$400$	−6.78764e18			−0.207142
$401$	−7.62440e18	−	1.32058e19i	−0.228361	−	0.395534i	0.728961	−	0.684555i	$-0.240003\pi$
$401$	−7.62440e18	−	1.32058e19i	−0.228361	−	0.395534i	−0.957323	+	0.289021i	$0.906670\pi$
$402$		0			0
$403$	9.81945e18	−	1.70078e19i	0.283334	−	0.490749i
$404$	−6.00447e18	−	1.04000e19i	−0.170065	−	0.294561i
$405$		0			0
$406$	1.86328e19	−	2.29977e19i	0.508548	−	0.627682i
$407$	−3.53554e19			−0.947321
$408$		0			0
$409$	−1.56830e19	+	2.71637e19i	−0.405046	+	0.701560i	−0.994327	−	0.106368i	$-0.966078\pi$
$409$	−1.56830e19	+	2.71637e19i	−0.405046	+	0.701560i	0.589281	+	0.807928i	$0.299411\pi$
$410$	2.02409e17	−	3.50583e17i	0.00513276	−	0.00889021i
$411$		0			0
$412$	−1.80092e19			−0.440317
$413$	−4.90220e19	−	7.77696e18i	−1.17697	−	0.186717i
$414$		0			0
$415$	5.87690e18	+	1.01791e19i	0.136078	+	0.235694i
$416$	−2.20606e18	+	3.82101e18i	−0.0501669	+	0.0868917i
$417$		0			0
$418$	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
$423$		0			0
$424$	−1.06561e19	+	1.84568e19i	−0.210065	+	0.363842i
$425$	2.26024e18	+	3.91486e18i	0.0437762	+	0.0758226i
$426$		0			0
$427$	−5.55083e19	+	6.85118e19i	−1.03788	+	1.28102i
$428$	5.13658e19			0.943726
$429$		0			0
$430$	1.13161e19	−	1.96000e19i	0.200763	−	0.347731i
$431$	−2.85381e19	+	4.94295e19i	−0.497560	+	0.861800i	−0.999996	−	0.00281486i	$-0.999104\pi$
$431$	−2.85381e19	+	4.94295e19i	−0.497560	+	0.861800i	0.502436	+	0.864615i	$0.332437\pi$
$432$		0			0
$433$	−9.74941e19			−1.64180			−0.820898	−	0.571075i	$-0.806526\pi$
$433$	−9.74941e19			−1.64180			−0.820898	+	0.571075i	$0.806526\pi$
$434$	−1.52760e19	−	3.98252e19i	−0.252834	−	0.659151i
$435$		0			0
$436$	1.11689e19	+	1.93451e19i	0.178591	+	0.309329i
$437$	1.75914e19	−	3.04692e19i	0.276496	−	0.478905i
$438$		0			0
$439$	2.76963e19	+	4.79714e19i	0.420667	+	0.728616i	0.996005	−	0.0892995i	$-0.0284628\pi$
$439$	2.76963e19	+	4.79714e19i	0.420667	+	0.728616i	−0.575338	+	0.817916i	$0.695130\pi$
$440$	−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	$0.141377\pi$
$443$	5.80429e19	+	1.00533e20i	0.823610	+	1.42653i	−0.0793678	+	0.996845i	$0.525290\pi$
$444$		0			0
$445$	3.56121e18	−	6.16819e18i	0.0488537	−	0.0846170i
$446$	−2.07157e19	−	3.58806e19i	−0.279439	−	0.484003i
$447$		0			0
$448$	3.43194e18	+	8.94723e18i	0.0447667	+	0.116709i
$449$	−1.86141e19			−0.238778			−0.119389	−	0.992848i	$-0.538094\pi$
$449$	−1.86141e19			−0.238778			−0.119389	+	0.992848i	$0.538094\pi$
$450$		0			0
$451$	−1.92930e18	+	3.34165e18i	−0.0239374	+	0.0414607i
$452$	1.12276e19	−	1.94468e19i	0.137009	−	0.237307i
$453$		0			0
$454$	−9.35220e18			−0.110407
$455$	1.27397e19	−	1.57241e19i	0.147936	−	0.182592i
$456$		0			0
$457$	−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
$459$		0			0
$460$	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
$465$		0			0
$466$	−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	$-0.549045\pi$
$468$		0			0
$469$	−1.12599e20	−	1.78630e19i	−1.04169	−	0.165256i
$470$	2.23214e19			0.203230
$471$		0			0
$472$	2.38865e19	−	4.13727e19i	0.210663	−	0.364879i
$473$	−1.07862e20	+	1.86822e20i	−0.936285	+	1.62169i
$474$		0			0
$475$	1.27051e20			1.06850
$476$	4.01761e18	−	4.95879e18i	0.0332595	−	0.0410510i
$477$		0			0
$478$	−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	$0.317227\pi$
$480$		0			0
$481$	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
$486$		0			0
$487$	−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
$489$		0			0
$490$	−9.11696e18	−	4.29982e19i	−0.0607267	−	0.286405i
$491$	1.91764e19			0.125793			0.0628963	−	0.998020i	$-0.479966\pi$
$491$	1.91764e19			0.125793			0.0628963	+	0.998020i	$0.479966\pi$
$492$		0			0
$493$	9.48640e18	−	1.64309e19i	0.0603600	−	0.104547i
$494$	4.12930e19	−	7.15215e19i	0.258776	−	0.448213i
$495$		0			0
$496$	4.10543e19			0.249601
$497$	−3.80132e19	−	9.91021e19i	−0.227646	−	0.593485i
$498$		0			0
$499$	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
$501$		0			0
$502$	−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
$507$		0			0
$508$	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	$0.598545\pi$
$510$		0			0
$511$	−1.25237e20	−	1.98679e19i	−0.608942	−	0.0966038i
$512$	−9.22337e18			−0.0441942
$513$		0			0
$514$	5.96112e19	−	1.03250e20i	0.277399	−	0.480469i
$515$	−3.97524e19	+	6.88532e19i	−0.182309	+	0.315769i
$516$		0			0
$517$	−2.12761e20			−0.947792
$518$	1.10358e20	+	1.75074e19i	0.484541	+	0.0768687i
$519$		0			0
$520$	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	$0.0380867\pi$
$522$		0			0
$523$	−8.72709e18	−	1.51158e19i	−0.0356539	−	0.0617543i	0.847648	−	0.530559i	$-0.178018\pi$
$523$	−8.72709e18	−	1.51158e19i	−0.0356539	−	0.0617543i	−0.883302	+	0.468805i	$0.844685\pi$
$524$	2.33992e20			0.942357
$525$		0			0
$526$	−1.33731e20			−0.523407
$527$	−1.36708e19	−	2.36786e19i	−0.0527492	−	0.0913643i
$528$		0			0
$529$	1.08803e20	−	1.88452e20i	0.408058	−	0.706777i
$530$	4.70431e19	+	8.14810e19i	0.173951	+	0.301292i
$531$		0			0
$532$	−6.42389e19	−	1.67474e20i	−0.230920	−	0.602019i
$533$	5.61473e18			0.0199010
$534$		0			0
$535$	1.13382e20	−	1.96383e20i	0.390742	−	0.676785i
$536$	5.48653e19	−	9.50295e19i	0.186450	−	0.322941i
$537$		0			0
$538$	3.40529e20			1.12535
$539$	8.69001e19	+	4.09846e20i	0.283207	+	1.33569i
$540$		0			0
$541$	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
$543$		0			0
$544$	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
$549$		0			0
$550$	1.42810e20	−	2.47354e20i	0.399980	−	0.692785i
$551$	−2.66621e20	−	4.61800e20i	−0.736642	−	1.27590i
$552$		0			0
$553$	2.23974e20	−	2.76443e20i	0.602225	−	0.743304i
$554$	2.10130e20			0.557398
$555$		0			0
$556$	−1.14917e20	+	1.99042e20i	−0.296703	+	0.513905i
$557$	2.06737e20	−	3.58079e20i	0.526628	−	0.912146i	−0.472891	−	0.881121i	$-0.656789\pi$
$557$	2.06737e20	−	3.58079e20i	0.526628	−	0.912146i	0.999519	−	0.0310252i	$-0.00987722\pi$
$558$		0			0
$559$	3.13903e20			0.778407
$560$	4.17827e19	+	6.62850e18i	0.102232	+	0.0162183i
$561$		0			0
$562$	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	$0.324231\pi$
$564$		0			0
$565$	−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	0.889022	−	0.457864i	$-0.151385\pi$
$569$	2.21048e19	+	3.82867e19i	0.0479894	+	0.0831200i	−0.841033	+	0.540984i	$0.818052\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	7.67685e18	−	9.47525e18i	0.0156079	−	0.0192642i
$575$	−1.77056e20			−0.355305
$576$		0			0
$577$	7.74354e19	−	1.34122e20i	0.151398	−	0.262230i	−0.780343	−	0.625351i	$-0.784956\pi$
$577$	7.74354e19	−	1.34122e20i	0.151398	−	0.262230i	0.931742	+	0.363122i	$0.118289\pi$
$578$	−1.81150e20	+	3.13760e20i	−0.349606	+	0.605535i
$579$		0			0
$580$	1.25766e20			0.236513
$581$	1.26806e20	+	3.30589e20i	0.235406	+	0.613716i
$582$		0			0
$583$	−4.48400e20	−	7.76652e20i	−0.811245	−	1.40512i
$584$	6.10231e19	−	1.05695e20i	0.108993	−	0.188781i
$585$		0			0
$586$	−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
$591$		0			0
$592$	−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	$0.877440\pi$
$594$		0			0
$595$	−1.00903e19	−	2.63060e19i	−0.0156685	−	0.0408486i
$596$	−8.96490e19			−0.137467
$597$		0			0
$598$	−5.75452e19	+	9.96713e19i	−0.0860499	+	0.149043i
$599$	1.33101e20	−	2.30537e20i	0.196553	−	0.340439i	−0.750856	−	0.660466i	$-0.770359\pi$
$599$	1.33101e20	−	2.30537e20i	0.196553	−	0.340439i	0.947408	+	0.320027i	$0.103692\pi$
$600$		0			0
$601$	1.46615e20			0.211165			0.105582	−	0.994411i	$-0.466329\pi$
$601$	1.46615e20			0.211165			0.105582	+	0.994411i	$0.466329\pi$
$602$	4.29190e20	−	5.29733e20i	0.610486	−	0.753500i
$603$		0			0
$604$	2.36063e20	+	4.08873e20i	0.327530	+	0.567298i
$605$	1.30565e20	−	2.26146e20i	0.178921	−	0.309901i
$606$		0			0
$607$	−3.88783e20	−	6.73392e20i	−0.519747	−	0.900229i	−0.999737	−	0.0229544i	$-0.992693\pi$
$607$	−3.88783e20	−	6.73392e20i	−0.519747	−	0.900229i	0.479989	−	0.877274i	$-0.340641\pi$
$608$	1.72643e20			0.227967
$609$		0			0
$610$	−3.74667e20			−0.482694
$611$	1.54796e20	+	2.68115e20i	0.196993	+	0.341203i
$612$		0			0
$613$	−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
$615$		0			0
$616$	−3.98260e20	−	6.31809e19i	−0.476773	−	0.0756363i
$617$	5.23730e20			0.619396			0.309698	−	0.950835i	$-0.399772\pi$
$617$	5.23730e20			0.619396			0.309698	+	0.950835i	$0.399772\pi$
$618$		0			0
$619$	−1.24614e20	+	2.15838e20i	−0.143842	+	0.249142i	−0.928940	−	0.370229i	$-0.879279\pi$
$619$	−1.24614e20	+	2.15838e20i	−0.143842	+	0.249142i	0.785098	+	0.619372i	$0.212613\pi$
$620$	9.06209e19	−	1.56960e20i	0.103345	−	0.178999i
$621$		0			0
$622$	1.41329e20			0.157327
$623$	1.35067e20	−	1.66708e20i	0.148556	−	0.183357i
$624$		0			0
$625$	−2.39861e20	−	4.15451e20i	−0.257548	−	0.446087i
$626$	3.09885e20	−	5.36736e20i	0.328770	−	0.569447i
$627$		0			0
$628$	−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
$633$		0			0
$634$	4.84257e20	−	8.38757e20i	0.467096	−	0.809034i
$635$	−2.60263e20	−	4.50788e20i	−0.248090	−	0.429704i
$636$		0			0
$637$	4.53251e20	−	4.07696e20i	0.421981	−	0.379569i
$638$	−1.19877e21			−1.10301
$639$		0			0
$640$	−2.03591e19	+	3.52630e19i	−0.0182982	+	0.0316935i
$641$	−7.33100e20	+	1.26977e21i	−0.651221	+	1.12795i	0.331606	+	0.943418i	$0.392409\pi$
$641$	−7.33100e20	+	1.26977e21i	−0.651221	+	1.12795i	−0.982827	+	0.184529i	$0.940924\pi$
$642$		0			0
$643$	9.96832e20			0.865047			0.432523	−	0.901623i	$-0.357623\pi$
$643$	9.96832e20			0.865047			0.432523	+	0.901623i	$0.357623\pi$
$644$	8.95224e19	+	2.33389e20i	0.0767870	+	0.200187i
$645$		0			0
$646$	−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	$0.117246\pi$
$648$		0			0
$649$	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	$-0.929184\pi$
$653$	−8.78143e20	−	1.52099e21i	−0.678760	−	1.17565i	0.296594	−	0.955004i	$-0.404149\pi$
$654$		0			0
$655$	5.16499e20	−	8.94602e20i	0.390175	−	0.675803i
$656$	5.86869e18	+	1.01649e19i	0.00438291	+	0.00759142i
$657$		0			0
$658$	6.64111e20	+	1.05356e20i	0.484782	+	0.0769069i
$659$	−1.29884e21			−0.937379			−0.468690	−	0.883363i	$-0.655274\pi$
$659$	−1.29884e21			−0.937379			−0.468690	+	0.883363i	$0.655274\pi$
$660$		0			0
$661$	−9.44597e20	+	1.63609e21i	−0.666401	+	1.15424i	0.312503	+	0.949917i	$0.398833\pi$
$661$	−9.44597e20	+	1.63609e21i	−0.666401	+	1.15424i	−0.978904	+	0.204323i	$0.934501\pi$
$662$	−8.56455e19	+	1.48342e20i	−0.0597406	+	0.103474i
$663$		0			0
$664$	−3.40792e20			−0.232396
$665$	−7.82087e20	−	1.24072e20i	−0.527343	−	0.0836588i
$666$		0			0
$667$	3.71558e20	+	6.43558e20i	0.244953	+	0.424271i
$668$	−7.41262e20	+	1.28390e21i	−0.483224	+	0.836969i
$669$		0			0
$670$	−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
$675$		0			0
$676$	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	$-0.408845\pi$
$678$		0			0
$679$	−5.24300e20	−	1.36687e21i	−0.302382	−	0.788325i
$680$	2.71178e19			0.0154681
$681$		0			0
$682$	−8.63771e20	+	1.49609e21i	−0.481965	+	0.834788i
$683$	−1.75583e21	+	3.04119e21i	−0.969010	+	1.67837i	−0.270577	+	0.962698i	$0.587214\pi$
$683$	−1.75583e21	+	3.04119e21i	−0.969010	+	1.67837i	−0.698433	+	0.715675i	$0.746119\pi$
$684$		0			0
$685$	−8.19220e20			−0.442305
$686$	−6.83000e19	−	1.32232e21i	−0.0364745	−	0.706165i
$687$		0			0
$688$	3.28101e20	+	5.68287e20i	0.171433	+	0.296930i
$689$	−6.52476e20	+	1.13012e21i	−0.337225	+	0.584092i
$690$		0			0
$691$	1.04240e21	+	1.80548e21i	0.527167	+	0.913079i	0.999499	+	0.0316586i	$0.0100789\pi$
$691$	1.04240e21	+	1.80548e21i	0.527167	+	0.913079i	−0.472332	+	0.881421i	$0.656588\pi$
$692$	1.04446e19			0.00522511
$693$		0			0
$694$	−3.49420e20			−0.171061
$695$	5.07321e20	+	8.78705e20i	0.245695	+	0.425556i
$696$		0			0
$697$	3.90847e18	−	6.76968e18i	0.00185251	−	0.00320865i
$698$	2.93265e20	+	5.07951e20i	0.137513	+	0.238180i
$699$		0			0
$700$	−5.68252e20	+	7.01372e20i	−0.260799	+	0.321894i
$701$	3.59508e21			1.63239			0.816194	−	0.577778i	$-0.196080\pi$
$701$	3.59508e21			1.63239			0.816194	+	0.577778i	$0.196080\pi$
$702$		0			0
$703$	1.00652e21	−	1.74335e21i	0.447362	−	0.774854i
$704$	1.94057e20	−	3.36116e20i	0.0853364	−	0.147807i
$705$		0			0
$706$	−2.69989e21			−1.16228
$707$	−1.57733e21	−	2.50231e20i	−0.671857	−	0.106585i
$708$		0			0
$709$	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
$711$		0			0
$712$	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
$717$		0			0
$718$	−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	$0.818498\pi$
$720$		0			0
$721$	−1.50770e21	+	1.86090e21i	−0.554372	+	0.684241i
$722$	−1.28833e21			−0.468813
$723$		0			0
$724$	1.21699e21	−	2.10788e21i	0.433757	−	0.751289i
$725$	−1.34176e21	+	2.32399e21i	−0.473303	+	0.819785i
$726$		0			0
$727$	6.16365e20			0.212976			0.106488	−	0.994314i	$-0.466039\pi$
$727$	6.16365e20			0.212976			0.106488	+	0.994314i	$0.466039\pi$
$728$	2.10139e20	+	5.47844e20i	0.0718658	+	0.187358i
$729$		0			0
$730$	−2.69398e20	−	4.66610e20i	−0.0902552	−	0.156327i
$731$	2.18511e20	−	3.78472e20i	0.0724591	−	0.125503i
$732$		0			0
$733$	−1.55870e20	−	2.69976e20i	−0.0506389	−	0.0877091i	0.839595	−	0.543213i	$-0.182792\pi$
$733$	−1.55870e20	−	2.69976e20i	−0.0506389	−	0.0877091i	−0.890234	+	0.455504i	$0.849459\pi$
$734$	−9.68098e20			−0.311314
$735$		0			0
$736$	−2.40592e20			−0.0758050
$737$	2.30870e21	+	3.99878e21i	0.720047	+	1.24716i
$738$		0			0
$739$	−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
$741$		0			0
$742$	1.01505e21	+	2.64628e21i	0.300924	+	0.784524i
$743$	−3.96804e21			−1.16456			−0.582278	−	0.812990i	$-0.697838\pi$
$743$	−3.96804e21			−1.16456			−0.582278	+	0.812990i	$0.697838\pi$
$744$		0			0
$745$	−1.97886e20	+	3.42748e20i	−0.0569171	+	0.0985833i
$746$	−2.18918e21	+	3.79178e21i	−0.623363	+	1.07970i
$747$		0			0
$748$	−2.58479e20			−0.0721379
$749$	4.30027e21	−	5.30767e21i	1.18818	−	1.46653i
$750$		0			0
$751$	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
$753$		0			0
$754$	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
$759$		0			0
$760$	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	$0.922209\pi$
$762$		0			0
$763$	2.93398e21	+	4.65453e20i	0.705543	+	0.111929i
$764$	3.07761e21			0.732846
$765$		0			0
$766$	−2.29871e21	+	3.98148e21i	−0.536746	+	0.929671i
$767$	1.46258e21	−	2.53327e21i	0.338186	−	0.585756i
$768$		0			0
$769$	7.98944e21			1.81163			0.905813	−	0.423677i	$-0.139261\pi$
$769$	7.98944e21			1.81163			0.905813	+	0.423677i	$0.139261\pi$
$770$	−1.12065e21	+	1.38318e21i	−0.251646	+	0.310597i
$771$		0			0
$772$	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	$0.171471\pi$
$774$		0			0
$775$	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
$780$		0			0
$781$	−2.14943e21	+	3.72292e21i	−0.433951	+	0.751625i
$782$	8.01157e19	+	1.38765e20i	0.0160202	+	0.0277477i
$783$		0			0
$784$	1.21184e21	+	3.94425e20i	0.237725	+	0.0773738i
$785$	−5.32654e20			−0.103496
$786$		0			0
$787$	−4.81188e20	+	8.33442e20i	−0.0917285	+	0.158878i	−0.908239	−	0.418453i	$-0.862573\pi$
$787$	−4.81188e20	+	8.33442e20i	−0.0917285	+	0.158878i	0.816510	+	0.577331i	$0.195906\pi$
$788$	−7.25482e20	+	1.25657e21i	−0.136987	+	0.237269i
$789$		0			0
$790$	1.51177e21			0.280080
$791$	−1.06949e21	−	2.78822e21i	−0.196270	−	0.511685i
$792$		0			0
$793$	−2.59827e21	−	4.50033e21i	−0.467881	−	0.810393i
$794$	−2.03466e21	+	3.52413e21i	−0.362942	+	0.628634i
$795$		0			0
$796$	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
$801$		0			0
$802$	9.75923e20	−	1.69035e21i	0.161476	−	0.279684i
$803$	2.56782e21	+	4.44759e21i	0.420918	+	0.729051i
$804$		0			0
$805$	1.08991e21	+	1.72905e20i	0.175356	+	0.0278188i
$806$	2.51378e21			0.400695
$807$		0			0
$808$	7.68572e20	−	1.33121e21i	0.120254	−	0.208286i
$809$	3.61656e21	−	6.26406e21i	0.560636	−	0.971051i	−0.436805	−	0.899556i	$-0.643890\pi$
$809$	3.61656e21	−	6.26406e21i	0.560636	−	0.971051i	0.997441	−	0.0714944i	$-0.0227768\pi$
$810$		0			0
$811$	3.62138e21			0.551084			0.275542	−	0.961289i	$-0.411143\pi$
$811$	3.62138e21			0.551084			0.275542	+	0.961289i	$0.411143\pi$
$812$	3.74182e21	+	5.93611e20i	0.564174	+	0.0895018i
$813$		0			0
$814$	−2.26274e21	−	3.91919e21i	−0.334929	−	0.580113i
$815$	2.58933e21	−	4.48484e21i	0.379756	−	0.657757i
$816$		0			0
$817$	−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	0.927199	−	0.374568i	$-0.122209\pi$
$821$	1.00290e21	+	1.73708e21i	0.139214	+	0.241126i	−0.787985	+	0.615694i	$0.788876\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	−2.27532e21	−	5.93188e21i	−0.301782	−	0.786759i
$827$	5.67524e21			0.745921			0.372961	−	0.927847i	$-0.378343\pi$
$827$	5.67524e21			0.745921			0.372961	+	0.927847i	$0.378343\pi$
$828$		0			0
$829$	−5.62506e21	+	9.74289e21i	−0.726053	+	1.25756i	0.232486	+	0.972600i	$0.425314\pi$
$829$	−5.62506e21	+	9.74289e21i	−0.726053	+	1.25756i	−0.958539	+	0.284961i	$0.908019\pi$
$830$	−7.52244e20	+	1.30292e21i	−0.0962216	+	0.166661i
$831$		0			0
$832$	−5.64752e20			−0.0709468
$833$	−1.76046e20	−	8.30286e20i	−0.0219174	−	0.103369i
$834$		0			0
$835$	3.27244e21	+	5.66803e21i	0.400150	+	0.693080i
$836$	−3.63235e21	+	6.29141e21i	−0.440190	+	0.762432i
$837$		0			0
$838$	−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
$843$		0			0
$844$	−4.14362e21	+	7.17696e21i	−0.467532	+	0.809790i
$845$	−1.25481e21	−	2.17340e21i	−0.140331	−	0.243061i
$846$		0			0
$847$	4.95200e21	−	6.11206e21i	0.544070	−	0.671525i
$848$	−2.72795e21			−0.297076
$849$		0			0
$850$	−2.89311e20	+	5.01102e20i	−0.0309545	+	0.0536147i
$851$	−1.40268e21	+	2.42951e21i	−0.148760	+	0.257660i
$852$		0			0
$853$	−2.31226e21			−0.240946			−0.120473	−	0.992717i	$-0.538441\pi$
$853$	−2.31226e21			−0.240946			−0.120473	+	0.992717i	$0.538441\pi$
$854$	−1.11472e22	−	1.76841e21i	−1.15141	−	0.182662i
$855$		0			0
$856$	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	$0.952070\pi$
$858$		0			0
$859$	−7.50563e21	−	1.30001e22i	−0.742059	−	1.28528i	−0.951556	−	0.307475i	$-0.900516\pi$
$859$	−7.50563e21	−	1.30001e22i	−0.742059	−	1.28528i	0.209497	−	0.977809i	$-0.432817\pi$
$860$	2.89692e21			0.283921
$861$		0			0
$862$	−7.30576e21			−0.703656
$863$	−4.02642e21	−	6.97396e21i	−0.384448	−	0.665884i	0.607244	−	0.794515i	$-0.292275\pi$
$863$	−4.02642e21	−	6.97396e21i	−0.384448	−	0.665884i	−0.991692	+	0.128631i	$0.958942\pi$
$864$		0			0
$865$	2.30547e19	−	3.99320e19i	0.00216341	−	0.00374714i
$866$	−6.23962e21	−	1.08073e22i	−0.580462	−	1.00539i
$867$		0			0
$868$	3.43701e21	−	4.24218e21i	0.314256	−	0.387874i
$869$	−1.44097e22			−1.30619
$870$		0			0
$871$	3.35943e21	−	5.81871e21i	0.299316	−	0.518430i
$872$	−1.42962e21	+	2.47617e21i	−0.126283	+	0.218729i
$873$		0			0
$874$	4.50339e21			0.391025
$875$	3.14964e21	+	8.21126e21i	0.271144	+	0.706886i
$876$		0			0
$877$	−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
$879$		0			0
$880$	−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
$885$		0			0
$886$	−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	$0.797051\pi$
$888$		0			0
$889$	−5.61569e21	−	1.46404e22i	−0.429180	−	1.11889i
$890$	9.11669e20			0.0690895
$891$		0			0
$892$	2.65160e21	−	4.59271e21i	0.197593	−	0.342242i
$893$	6.05705e21	−	1.04911e22i	0.447585	−	0.775240i
$894$		0			0
$895$	−3.92202e21			−0.284995
$896$	−7.72168e20	+	9.53058e20i	−0.0556419	+	0.0686767i
$897$		0			0
$898$	−1.19130e21	−	2.06340e21i	−0.0844208	−	0.146221i
$899$	8.11549e21	−	1.40564e22i	0.570318	−	0.987819i
$900$		0			0
$901$	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
$906$		0			0
$907$	−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
$909$		0			0
$910$	2.55838e21	+	4.05867e20i	0.164117	+	0.0260359i
$911$	−3.71366e21			−0.236273			−0.118137	−	0.992997i	$-0.537692\pi$
$911$	−3.71366e21			−0.236273			−0.118137	+	0.992997i	$0.537692\pi$
$912$		0			0
$913$	7.17016e21	−	1.24191e22i	0.448743	−	0.777246i
$914$	2.87224e21	−	4.97487e21i	0.178289	−	0.308806i
$915$		0			0
$916$	1.16189e22			0.709495
$917$	1.95894e22	−	2.41785e22i	1.18646	−	1.46440i
$918$		0			0
$919$	−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
$921$		0			0
$922$	−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
$927$		0			0
$928$	−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	$0.757627\pi$
$930$		0			0
$931$	−2.26832e22	−	7.38283e21i	−1.22626	−	0.399117i
$932$	−1.23148e22			−0.660400
$933$		0			0
$934$	1.24950e22	−	2.16420e22i	0.659378	−	1.14208i
$935$	−5.70551e20	+	9.88223e20i	−0.0298681	+	0.0517330i
$936$		0			0
$937$	3.98160e21			0.205121			0.102561	−	0.994727i	$-0.467296\pi$
$937$	3.98160e21			0.205121			0.102561	+	0.994727i	$0.467296\pi$
$938$	−5.22622e21	−	1.36250e22i	−0.267096	−	0.696331i
$939$		0			0
$940$	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	$0.0719245\pi$
$942$		0			0
$943$	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	0.982099	−	0.188363i	$-0.0603182\pi$
$947$	6.89281e21	+	1.19387e22i	0.327922	+	0.567978i	−0.654177	+	0.756342i	$0.726985\pi$
$948$		0			0
$949$	3.73648e21	−	6.47177e21i	0.174971	−	0.303058i
$950$	8.13125e21	+	1.40837e22i	0.377772	+	0.654321i
$951$		0			0
$952$	8.06815e20	+	1.27995e20i	0.0368975	+	0.00585350i
$953$	−2.93636e22			−1.33233			−0.666165	−	0.745804i	$-0.732065\pi$
$953$	−2.93636e22			−1.33233			−0.666165	+	0.745804i	$0.732065\pi$
$954$		0			0
$955$	6.79332e21	−	1.17664e22i	0.303429	−	0.525554i
$956$	3.39870e21	−	5.88672e21i	0.150619	−	0.260879i
$957$		0			0
$958$	−1.47673e22			−0.644258
$959$	−2.43736e22	−	3.86668e21i	−1.05507	−	0.167378i
$960$		0			0
$961$	3.74106e19	+	6.47971e19i	0.00159430	+	0.00276141i
$962$	−3.29256e21	+	5.70288e21i	−0.139226	+	0.241147i
$963$		0			0
$964$	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
$969$		0			0
$970$	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	$0.979823\pi$
$972$		0			0
$973$	1.09464e22	+	2.85379e22i	0.425037	+	1.10809i
$974$	−2.13247e21			−0.0821659
$975$		0			0
$976$	5.43158e21	−	9.40777e21i	0.206088	−	0.356955i
$977$	−1.60354e22	+	2.77741e22i	−0.603769	+	1.04576i	0.388476	+	0.921459i	$0.373002\pi$
$977$	−1.60354e22	+	2.77741e22i	−0.603769	+	1.04576i	−0.992245	+	0.124299i	$0.960332\pi$
$978$		0			0
$979$	−8.68975e21			−0.322209
$980$	4.18292e21	−	3.76251e21i	0.153916	−	0.138447i
$981$		0			0
$982$	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	$-0.124933\pi$
$984$		0			0
$985$	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
$990$		0			0
$991$	−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
$993$		0			0
$994$	8.55275e21	−	1.05563e22i	0.282949	−	0.349233i
$995$	6.67074e21			0.219029
$996$		0			0
$997$	5.56992e21	−	9.64739e21i	0.180151	−	0.312030i	−0.761781	−	0.647834i	$-0.775675\pi$
$997$	5.56992e21	−	9.64739e21i	0.180151	−	0.312030i	0.941932	+	0.335805i	$0.109008\pi$
$998$	−1.01899e21	+	1.76494e21i	−0.0327107	+	0.0566566i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.16.c.a.9.4	✓	10	21.2	odd	6
14.16.c.a.11.4	yes	10	3.2	odd	2
98.16.a.j.1.2		5	21.11	odd	6
98.16.a.k.1.4		5	21.17	even	6
98.16.c.m.67.2		10	21.20	even	2
98.16.c.m.79.2		10	21.5	even	6
126.16.g.e.37.4		10	7.2	even	3	inner
126.16.g.e.109.4		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(64.0000 + 110.851i) q^{2} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +(780333. + 2.03437e6i) q^{7} -2.09715e6 q^{8} +O(q^{10})\)	\(q+(64.0000 + 110.851i) q^{2} +(-8192.00 + 14189.0i) q^{4} +(36165.1 + 62639.7i) q^{5} +(780333. + 2.03437e6i) q^{7} -2.09715e6 q^{8} +(-4.62913e6 + 8.01788e6i) q^{10} +(4.41234e7 - 7.64240e7i) q^{11} -1.28410e8 q^{13} +(-1.75571e8 + 2.16700e8i) q^{14} +(-1.34218e8 - 2.32472e8i) q^{16} +(-8.93874e7 + 1.54823e8i) q^{17} +(2.51228e9 + 4.35140e9i) q^{19} -1.18506e9 q^{20} +1.12956e10 q^{22} +(-3.50108e9 - 6.06404e9i) q^{23} +(1.26430e10 - 2.18983e10i) q^{25} +(-8.21822e9 - 1.42344e10i) q^{26} +(-3.52580e10 - 5.59341e9i) q^{28} -1.06127e11 q^{29} +(-7.64697e10 + 1.32449e11i) q^{31} +(1.71799e10 - 2.97564e10i) q^{32} -2.28832e10 q^{34} +(-9.92113e10 + 1.22453e11i) q^{35} +(-2.00321e11 - 3.46966e11i) q^{37} +(-3.21572e11 + 5.56979e11i) q^{38} +(-7.58436e10 - 1.31365e11i) q^{40} -4.37251e10 q^{41} -2.44454e12 q^{43} +(7.22918e11 + 1.25213e12i) q^{44} +(4.48138e11 - 7.76198e11i) q^{46} +(-1.20549e12 - 2.08797e12i) q^{47} +(-3.52972e12 + 3.17496e12i) q^{49} +3.23660e12 q^{50} +(1.05193e12 - 1.82200e12i) q^{52} +(5.08120e12 - 8.80091e12i) q^{53} +6.38290e12 q^{55} +(-1.63648e12 - 4.26637e12i) q^{56} +(-6.79212e12 - 1.17643e13i) q^{58} +(-1.13900e13 + 1.97280e13i) q^{59} +(2.02342e13 + 3.50467e13i) q^{61} -1.95762e13 q^{62} +4.39805e12 q^{64} +(-4.64394e12 - 8.04355e12i) q^{65} +(-2.61618e13 + 4.53136e13i) q^{67} +(-1.46452e12 - 2.53663e12i) q^{68} +(-1.99236e13 - 3.16072e12i) q^{70} -4.87140e13 q^{71} +(-2.90981e13 + 5.03994e13i) q^{73} +(2.56411e13 - 4.44116e13i) q^{74} -8.23224e13 q^{76} +(1.89905e14 + 3.01270e13i) q^{77} +(-8.16442e13 - 1.41412e14i) q^{79} +(9.70798e12 - 1.68147e13i) q^{80} +(-2.79841e12 - 4.84699e12i) q^{82} +1.62502e14 q^{83} -1.29308e13 q^{85} +(-1.56451e14 - 2.70980e14i) q^{86} +(-9.25335e13 + 1.60273e14i) q^{88} +(-4.92355e13 - 8.52783e13i) q^{89} +(-1.00202e14 - 2.61232e14i) q^{91} +1.14723e14 q^{92} +(1.54303e14 - 2.67260e14i) q^{94} +(-1.81714e14 + 3.14737e14i) q^{95} -6.71892e14 q^{97} +(-5.77851e14 - 1.88076e14i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 640 q^{2} - 81920 q^{4} - 300953 q^{5} + 4054316 q^{7} - 20971520 q^{8}+O(q^{10}) \) 10 * q + 640 * q^2 - 81920 * q^4 - 300953 * q^5 + 4054316 * q^7 - 20971520 * q^8	\( 10 q + 640 q^{2} - 81920 q^{4} - 300953 q^{5} + 4054316 q^{7} - 20971520 q^{8} + 38521984 q^{10} - 14189887 q^{11} - 772602348 q^{13} + 815024000 q^{14} - 1342177280 q^{16} + 145564295 q^{17} + 3550131629 q^{19} + 9861627904 q^{20} - 3632611072 q^{22} - 9869524537 q^{23} - 51839554204 q^{25} - 49446550272 q^{26} + 37897158656 q^{28} + 165255956188 q^{29} - 106825666677 q^{31} + 171798691840 q^{32} + 37264459520 q^{34} - 1475862848131 q^{35} - 596799401515 q^{37} - 454416848512 q^{38} + 631144185856 q^{40} - 1756981189740 q^{41} - 5305116572344 q^{43} - 232487108608 q^{44} + 1263299140736 q^{46} - 4284391851525 q^{47} + 1588100454346 q^{49} - 13270925876224 q^{50} + 6329158434816 q^{52} + 4037801378823 q^{53} - 47232884322970 q^{55} - 8502516908032 q^{56} + 10576381196032 q^{58} - 6081930248483 q^{59} + 29484338931189 q^{61} - 27347370669312 q^{62} + 43980465111040 q^{64} - 78038741223618 q^{65} - 2851190345117 q^{67} + 2384925409280 q^{68} - 190125208943488 q^{70} - 190169727933856 q^{71} + 284202883487269 q^{73} + 76390323393920 q^{74} - 116330713219072 q^{76} + 656655421831969 q^{77} + 536529323488905 q^{79} - 80786455789568 q^{80} - 112446796143360 q^{82} + 949641950127416 q^{83} + 24\!\cdots\!86 q^{85}+ \cdots + 939580168008832 q^{98}+O(q^{100}) \) 10 * q + 640 * q^2 - 81920 * q^4 - 300953 * q^5 + 4054316 * q^7 - 20971520 * q^8 + 38521984 * q^10 - 14189887 * q^11 - 772602348 * q^13 + 815024000 * q^14 - 1342177280 * q^16 + 145564295 * q^17 + 3550131629 * q^19 + 9861627904 * q^20 - 3632611072 * q^22 - 9869524537 * q^23 - 51839554204 * q^25 - 49446550272 * q^26 + 37897158656 * q^28 + 165255956188 * q^29 - 106825666677 * q^31 + 171798691840 * q^32 + 37264459520 * q^34 - 1475862848131 * q^35 - 596799401515 * q^37 - 454416848512 * q^38 + 631144185856 * q^40 - 1756981189740 * q^41 - 5305116572344 * q^43 - 232487108608 * q^44 + 1263299140736 * q^46 - 4284391851525 * q^47 + 1588100454346 * q^49 - 13270925876224 * q^50 + 6329158434816 * q^52 + 4037801378823 * q^53 - 47232884322970 * q^55 - 8502516908032 * q^56 + 10576381196032 * q^58 - 6081930248483 * q^59 + 29484338931189 * q^61 - 27347370669312 * q^62 + 43980465111040 * q^64 - 78038741223618 * q^65 - 2851190345117 * q^67 + 2384925409280 * q^68 - 190125208943488 * q^70 - 190169727933856 * q^71 + 284202883487269 * q^73 + 76390323393920 * q^74 - 116330713219072 * q^76 + 656655421831969 * q^77 + 536529323488905 * q^79 - 80786455789568 * q^80 - 112446796143360 * q^82 + 949641950127416 * q^83 + 2471416802444186 * q^85 - 339527460630016 * q^86 + 29758349901824 * q^88 - 160148042721333 * q^89 - 1307014889481672 * q^91 + 323404580028416 * q^92 + 548402156995200 * q^94 + 739988010259049 * q^95 - 4057131581852468 * q^97 + 939580168008832 * q^98

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