LMFDB - Embedded newform 81.12.c.e.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,12,Mod(28,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("81.28");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	81.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:	$62.2357976253$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			28.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	81.28
Dual form			81.12.c.e.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(39.0000 + 67.5500i) q^{2} +(-2018.00 + 3495.28i) q^{4} +(-2685.00 + 4650.56i) q^{5} +(13880.0 + 24040.9i) q^{7} -155064. q^{8} +O(q^{10})$	\(q+(39.0000 + 67.5500i) q^{2} +(-2018.00 + 3495.28i) q^{4} +(-2685.00 + 4650.56i) q^{5} +(13880.0 + 24040.9i) q^{7} -155064. q^{8} -418860. q^{10} +(318918. + 552382. i) q^{11} +(-383107. + 663561. i) q^{13} +(-1.08264e6 + 1.87519e6i) q^{14} +(-1.91463e6 - 3.31624e6i) q^{16} -3.08435e6 q^{17} -1.95114e7 q^{19} +(-1.08367e7 - 1.87696e7i) q^{20} +(-2.48756e7 + 4.30858e7i) q^{22} +(7.65618e6 - 1.32609e7i) q^{23} +(9.99561e6 + 1.73129e7i) q^{25} -5.97647e7 q^{26} -1.12039e8 q^{28} +(5.37563e6 + 9.31087e6i) q^{29} +(2.54687e7 - 4.41131e7i) q^{31} +(-9.44424e6 + 1.63579e7i) q^{32} +(-1.20290e8 - 2.08348e8i) q^{34} -1.49071e8 q^{35} +6.64741e8 q^{37} +(-7.60945e8 - 1.31799e9i) q^{38} +(4.16347e8 - 7.21134e8i) q^{40} +(4.49417e8 - 7.78413e8i) q^{41} +(4.78974e8 + 8.29607e8i) q^{43} -2.57431e9 q^{44} +1.19436e9 q^{46} +(-7.77871e8 - 1.34731e9i) q^{47} +(6.03355e8 - 1.04504e9i) q^{49} +(-7.79658e8 + 1.35041e9i) q^{50} +(-1.54622e9 - 2.67813e9i) q^{52} -3.79242e9 q^{53} -3.42518e9 q^{55} +(-2.15229e9 - 3.72787e9i) q^{56} +(-4.19299e8 + 7.26248e8i) q^{58} +(2.77653e8 - 4.80910e8i) q^{59} +(-2.47521e9 - 4.28719e9i) q^{61} +3.97312e9 q^{62} -9.31563e9 q^{64} +(-2.05728e9 - 3.56332e9i) q^{65} +(-2.64620e9 + 4.58335e9i) q^{67} +(6.22423e9 - 1.07807e10i) q^{68} +(-5.81378e9 - 1.00698e10i) q^{70} +1.48311e10 q^{71} +1.39710e10 q^{73} +(2.59249e10 + 4.49032e10i) q^{74} +(3.93740e10 - 6.81978e10i) q^{76} +(-8.85316e9 + 1.53341e10i) q^{77} +(-1.86027e9 - 3.22208e9i) q^{79} +2.05631e10 q^{80} +7.01090e10 q^{82} +(4.38423e9 + 7.59370e9i) q^{83} +(8.28149e9 - 1.43440e10i) q^{85} +(-3.73599e10 + 6.47093e10i) q^{86} +(-4.94527e10 - 8.56546e10i) q^{88} +2.54728e10 q^{89} -2.12701e10 q^{91} +(3.09003e10 + 5.35210e10i) q^{92} +(6.06739e10 - 1.05090e11i) q^{94} +(5.23881e10 - 9.07389e10i) q^{95} +(1.95462e10 + 3.38551e10i) q^{97} +9.41233e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 78 q^{2} - 4036 q^{4} - 5370 q^{5} + 27760 q^{7} - 310128 q^{8}+O(q^{10}) $ 2 * q + 78 * q^2 - 4036 * q^4 - 5370 * q^5 + 27760 * q^7 - 310128 * q^8	\( 2 q + 78 q^{2} - 4036 q^{4} - 5370 q^{5} + 27760 q^{7} - 310128 q^{8} - 837720 q^{10} + 637836 q^{11} - 766214 q^{13} - 2165280 q^{14} - 3829264 q^{16} - 6168708 q^{17} - 39022808 q^{19} - 21673320 q^{20} - 49751208 q^{22} + 15312360 q^{23} + 19991225 q^{25} - 119529384 q^{26} - 224078720 q^{28} + 10751262 q^{29} + 50937400 q^{31} - 18888480 q^{32} - 240579612 q^{34} - 298142400 q^{35} + 1329481660 q^{37} - 1521889512 q^{38} + 832693680 q^{40} + 898833450 q^{41} + 957947188 q^{43} - 5148612192 q^{44} + 2388728160 q^{46} - 1555741344 q^{47} + 1206709143 q^{49} - 1559315550 q^{50} - 3092439704 q^{52} - 7584834060 q^{53} - 6850358640 q^{55} - 4304576640 q^{56} - 838598436 q^{58} + 555306924 q^{59} - 4950420998 q^{61} + 7946234400 q^{62} - 18631268224 q^{64} - 4114569180 q^{65} - 5292399284 q^{67} + 12448452744 q^{68} - 11627553600 q^{70} + 29662172496 q^{71} + 27942010420 q^{73} + 51849784740 q^{74} + 78748026544 q^{76} - 17706327360 q^{77} - 3720542360 q^{79} + 41126295360 q^{80} + 140218018200 q^{82} + 8768454036 q^{83} + 16562980980 q^{85} - 74719880664 q^{86} - 98905401504 q^{88} + 50945538348 q^{89} - 42540201280 q^{91} + 61800684960 q^{92} + 121347824832 q^{94} + 104776239480 q^{95} + 39092494846 q^{97} + 188246626308 q^{98}+O(q^{100}) \) 2 * q + 78 * q^2 - 4036 * q^4 - 5370 * q^5 + 27760 * q^7 - 310128 * q^8 - 837720 * q^10 + 637836 * q^11 - 766214 * q^13 - 2165280 * q^14 - 3829264 * q^16 - 6168708 * q^17 - 39022808 * q^19 - 21673320 * q^20 - 49751208 * q^22 + 15312360 * q^23 + 19991225 * q^25 - 119529384 * q^26 - 224078720 * q^28 + 10751262 * q^29 + 50937400 * q^31 - 18888480 * q^32 - 240579612 * q^34 - 298142400 * q^35 + 1329481660 * q^37 - 1521889512 * q^38 + 832693680 * q^40 + 898833450 * q^41 + 957947188 * q^43 - 5148612192 * q^44 + 2388728160 * q^46 - 1555741344 * q^47 + 1206709143 * q^49 - 1559315550 * q^50 - 3092439704 * q^52 - 7584834060 * q^53 - 6850358640 * q^55 - 4304576640 * q^56 - 838598436 * q^58 + 555306924 * q^59 - 4950420998 * q^61 + 7946234400 * q^62 - 18631268224 * q^64 - 4114569180 * q^65 - 5292399284 * q^67 + 12448452744 * q^68 - 11627553600 * q^70 + 29662172496 * q^71 + 27942010420 * q^73 + 51849784740 * q^74 + 78748026544 * q^76 - 17706327360 * q^77 - 3720542360 * q^79 + 41126295360 * q^80 + 140218018200 * q^82 + 8768454036 * q^83 + 16562980980 * q^85 - 74719880664 * q^86 - 98905401504 * q^88 + 50945538348 * q^89 - 42540201280 * q^91 + 61800684960 * q^92 + 121347824832 * q^94 + 104776239480 * q^95 + 39092494846 * q^97 + 188246626308 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	39.0000	+	67.5500i	0.861786	+	1.49266i	0.870203	+	0.492693i	$0.163988\pi$
$2$	39.0000	+	67.5500i	0.861786	+	1.49266i	−0.00841668	+	0.999965i	$0.502679\pi$
$3$		0			0
$3$		0			0
$4$	−2018.00	+	3495.28i	−0.985352	+	1.70668i
$5$	−2685.00	+	4650.56i	−0.384246	+	0.665533i	−0.991664	−	0.128849i	$-0.958872\pi$
$5$	−2685.00	+	4650.56i	−0.384246	+	0.665533i	0.607418	+	0.794382i	$0.292205\pi$
$6$		0			0
$7$	13880.0	+	24040.9i	0.312141	+	0.540643i	0.978826	−	0.204696i	$-0.0656207\pi$
$7$	13880.0	+	24040.9i	0.312141	+	0.540643i	−0.666685	+	0.745340i	$0.732287\pi$
$8$	−155064.			−1.67308
$9$		0			0
$10$	−418860.			−1.32455
$11$	318918.	+	552382.i	0.597062	+	1.03414i	0.993252	+	0.115973i	$0.0369986\pi$
$11$	318918.	+	552382.i	0.597062	+	1.03414i	−0.396191	+	0.918168i	$0.629668\pi$
$12$		0			0
$13$	−383107.	+	663561.i	−0.286175	+	0.495670i	−0.972893	−	0.231254i	$-0.925717\pi$
$13$	−383107.	+	663561.i	−0.286175	+	0.495670i	0.686718	+	0.726923i	$0.259051\pi$
$14$	−1.08264e6	+	1.87519e6i	−0.537997	+	0.931838i
$15$		0			0
$16$	−1.91463e6	−	3.31624e6i	−0.456484	−	0.790653i
$17$	−3.08435e6			−0.526860			−0.263430	−	0.964679i	$-0.584854\pi$
$17$	−3.08435e6			−0.526860			−0.263430	+	0.964679i	$0.584854\pi$
$18$		0			0
$19$	−1.95114e7			−1.80777			−0.903886	−	0.427773i	$-0.859298\pi$
$19$	−1.95114e7			−1.80777			−0.903886	+	0.427773i	$0.859298\pi$
$20$	−1.08367e7	−	1.87696e7i	−0.757235	−	1.31157i
$21$		0			0
$22$	−2.48756e7	+	4.30858e7i	−1.02908	+	1.78242i
$23$	7.65618e6	−	1.32609e7i	0.248033	−	0.429605i	−0.714947	−	0.699178i	$-0.753549\pi$
$23$	7.65618e6	−	1.32609e7i	0.248033	−	0.429605i	0.962980	+	0.269573i	$0.0868826\pi$
$24$		0			0
$25$	9.99561e6	+	1.73129e7i	0.204710	+	0.354568i
$26$	−5.97647e7			−0.986487
$27$		0			0
$28$	−1.12039e8			−1.23027
$29$	5.37563e6	+	9.31087e6i	0.0486677	+	0.0842949i	0.889333	−	0.457260i	$-0.151169\pi$
$29$	5.37563e6	+	9.31087e6i	0.0486677	+	0.0842949i	−0.840665	+	0.541555i	$0.817836\pi$
$30$		0			0
$31$	2.54687e7	−	4.41131e7i	0.159778	−	0.276744i	−0.775010	−	0.631948i	$-0.782255\pi$
$31$	2.54687e7	−	4.41131e7i	0.159778	−	0.276744i	0.934789	+	0.355205i	$0.115589\pi$
$32$	−9.44424e6	+	1.63579e7i	−0.0497556	+	0.0861793i
$33$		0			0
$34$	−1.20290e8	−	2.08348e8i	−0.454041	−	0.786422i
$35$	−1.49071e8			−0.479755
$36$		0			0
$37$	6.64741e8			1.57595			0.787976	−	0.615706i	$-0.211129\pi$
$37$	6.64741e8			1.57595			0.787976	+	0.615706i	$0.211129\pi$
$38$	−7.60945e8	−	1.31799e9i	−1.55791	−	2.69839i
$39$		0			0
$40$	4.16347e8	−	7.21134e8i	0.642873	−	1.11349i
$41$	4.49417e8	−	7.78413e8i	0.605812	−	1.04930i	−0.386110	−	0.922453i	$-0.626182\pi$
$41$	4.49417e8	−	7.78413e8i	0.605812	−	1.04930i	0.991923	−	0.126845i	$-0.0404851\pi$
$42$		0			0
$43$	4.78974e8	+	8.29607e8i	0.496861	+	0.860589i	0.999993	−	0.00362061i	$-0.00115248\pi$
$43$	4.78974e8	+	8.29607e8i	0.496861	+	0.860589i	−0.503132	+	0.864209i	$0.667819\pi$
$44$	−2.57431e9			−2.35326
$45$		0			0
$46$	1.19436e9			0.855005
$47$	−7.77871e8	−	1.34731e9i	−0.494731	−	0.856899i	0.505250	−	0.862973i	$-0.331400\pi$
$47$	−7.77871e8	−	1.34731e9i	−0.494731	−	0.856899i	−0.999982	+	0.00607340i	$0.998067\pi$
$48$		0			0
$49$	6.03355e8	−	1.04504e9i	0.305137	−	0.528512i
$50$	−7.79658e8	+	1.35041e9i	−0.352833	+	0.611124i
$51$		0			0
$52$	−1.54622e9	−	2.67813e9i	−0.563966	−	0.976818i
$53$	−3.79242e9			−1.24566			−0.622829	−	0.782358i	$-0.714017\pi$
$53$	−3.79242e9			−1.24566			−0.622829	+	0.782358i	$0.714017\pi$
$54$		0			0
$55$	−3.42518e9			−0.917674
$56$	−2.15229e9	−	3.72787e9i	−0.522235	−	0.904538i
$57$		0			0
$58$	−4.19299e8	+	7.26248e8i	−0.0838823	+	0.145288i
$59$	2.77653e8	−	4.80910e8i	0.0505612	−	0.0875745i	−0.839637	−	0.543148i	$-0.817232\pi$
$59$	2.77653e8	−	4.80910e8i	0.0505612	−	0.0875745i	0.890198	+	0.455573i	$0.150566\pi$
$60$		0			0
$61$	−2.47521e9	−	4.28719e9i	−0.375230	−	0.649918i	0.615131	−	0.788425i	$-0.289103\pi$
$61$	−2.47521e9	−	4.28719e9i	−0.375230	−	0.649918i	−0.990361	+	0.138507i	$0.955770\pi$
$62$	3.97312e9			0.550779
$63$		0			0
$64$	−9.31563e9			−1.08448
$65$	−2.05728e9	−	3.56332e9i	−0.219923	−	0.380918i
$66$		0			0
$67$	−2.64620e9	+	4.58335e9i	−0.239448	+	0.414736i	−0.960556	−	0.278087i	$-0.910300\pi$
$67$	−2.64620e9	+	4.58335e9i	−0.239448	+	0.414736i	0.721108	+	0.692823i	$0.243633\pi$
$68$	6.22423e9	−	1.07807e10i	0.519142	−	0.899181i
$69$		0			0
$70$	−5.81378e9	−	1.00698e10i	−0.413446	−	0.716110i
$71$	1.48311e10			0.975556			0.487778	−	0.872968i	$-0.337808\pi$
$71$	1.48311e10			0.975556			0.487778	+	0.872968i	$0.337808\pi$
$72$		0			0
$73$	1.39710e10			0.788773			0.394386	−	0.918945i	$-0.370957\pi$
$73$	1.39710e10			0.788773			0.394386	+	0.918945i	$0.370957\pi$
$74$	2.59249e10	+	4.49032e10i	1.35813	+	2.35236i
$75$		0			0
$76$	3.93740e10	−	6.81978e10i	1.78129	−	3.08529i
$77$	−8.85316e9	+	1.53341e10i	−0.372734	+	0.645595i
$78$		0			0
$79$	−1.86027e9	−	3.22208e9i	−0.0680185	−	0.117812i	0.830010	−	0.557748i	$-0.188334\pi$
$79$	−1.86027e9	−	3.22208e9i	−0.0680185	−	0.117812i	−0.898029	+	0.439936i	$0.855001\pi$
$80$	2.05631e10			0.701608
$81$		0			0
$82$	7.01090e10			2.08832
$83$	4.38423e9	+	7.59370e9i	0.122170	+	0.211604i	0.920623	−	0.390453i	$-0.127681\pi$
$83$	4.38423e9	+	7.59370e9i	0.122170	+	0.211604i	−0.798453	+	0.602057i	$0.794348\pi$
$84$		0			0
$85$	8.28149e9	−	1.43440e10i	0.202444	−	0.350643i
$86$	−3.73599e10	+	6.47093e10i	−0.856376	+	1.48329i
$87$		0			0
$88$	−4.94527e10	−	8.56546e10i	−0.998931	−	1.73020i
$89$	2.54728e10			0.483539			0.241769	−	0.970334i	$-0.422272\pi$
$89$	2.54728e10			0.483539			0.241769	+	0.970334i	$0.422272\pi$
$90$		0			0
$91$	−2.12701e10			−0.357307
$92$	3.09003e10	+	5.35210e10i	0.488799	+	0.846625i
$93$		0			0
$94$	6.06739e10	−	1.05090e11i	0.852705	−	1.47693i
$95$	5.23881e10	−	9.07389e10i	0.694629	−	1.20313i
$96$		0			0
$97$	1.95462e10	+	3.38551e10i	0.231110	+	0.400294i	0.958135	−	0.286317i	$-0.0924309\pi$
$97$	1.95462e10	+	3.38551e10i	0.231110	+	0.400294i	−0.727025	+	0.686611i	$0.759098\pi$
$98$	9.41233e10			1.05185
$99$		0			0
$100$	−8.06846e10			−0.806846
$101$	4.65539e9	+	8.06337e9i	0.0440746	+	0.0763395i	0.887221	−	0.461344i	$-0.152633\pi$
$101$	4.65539e9	+	8.06337e9i	0.0440746	+	0.0763395i	−0.843147	+	0.537684i	$0.819299\pi$
$102$		0			0
$103$	−2.42875e10	+	4.20672e10i	−0.206433	+	0.357552i	−0.950588	−	0.310454i	$-0.899519\pi$
$103$	−2.42875e10	+	4.20672e10i	−0.206433	+	0.357552i	0.744156	+	0.668006i	$0.232852\pi$
$104$	5.94061e10	−	1.02894e11i	0.478793	−	0.829294i
$105$		0			0
$106$	−1.47904e11	−	2.56178e11i	−1.07349	−	1.85934i
$107$	−2.25596e11			−1.55496			−0.777482	−	0.628906i	$-0.783503\pi$
$107$	−2.25596e11			−1.55496			−0.777482	+	0.628906i	$0.783503\pi$
$108$		0			0
$109$	−6.94512e10			−0.432348			−0.216174	−	0.976355i	$-0.569358\pi$
$109$	−6.94512e10			−0.432348			−0.216174	+	0.976355i	$0.569358\pi$
$110$	−1.33582e11	−	2.31371e11i	−0.790839	−	1.36977i
$111$		0			0
$112$	5.31502e10	−	9.20588e10i	0.284974	−	0.493590i
$113$	−1.79832e11	+	3.11479e11i	−0.918198	+	1.59037i	−0.116047	+	0.993244i	$0.537022\pi$
$113$	−1.79832e11	+	3.11479e11i	−0.918198	+	1.59037i	−0.802151	+	0.597121i	$0.796311\pi$
$114$		0			0
$115$	4.11137e10	+	7.12110e10i	0.190611	+	0.330148i
$116$	−4.33921e10			−0.191819
$117$		0			0
$118$	4.33139e10			0.174292
$119$	−4.28108e10	−	7.41505e10i	−0.164454	−	0.284843i
$120$		0			0
$121$	−6.07615e10	+	1.05242e11i	−0.212966	+	0.368867i
$122$	1.93066e11	−	3.34401e11i	0.646737	−	1.12018i
$123$		0			0
$124$	1.02792e11	+	1.78040e11i	0.314875	+	0.545380i
$125$	−3.69560e11			−1.08313
$126$		0			0
$127$	2.50273e11			0.672192			0.336096	−	0.941828i	$-0.390893\pi$
$127$	2.50273e11			0.672192			0.336096	+	0.941828i	$0.390893\pi$
$128$	−3.43968e11	−	5.95770e11i	−0.884837	−	1.53258i
$129$		0			0
$130$	1.60468e11	−	2.77939e11i	0.379054	−	0.656540i
$131$	−4.89459e10	+	8.47768e10i	−0.110847	+	0.191993i	−0.916112	−	0.400922i	$-0.868690\pi$
$131$	−4.89459e10	+	8.47768e10i	−0.110847	+	0.191993i	0.805265	+	0.592915i	$0.202023\pi$
$132$		0			0
$133$	−2.70818e11	−	4.69071e11i	−0.564279	−	0.977360i
$134$	−4.12807e11			−0.825412
$135$		0			0
$136$	4.78272e11			0.881477
$137$	−7.75074e10	−	1.34247e11i	−0.137208	−	0.237651i	0.789231	−	0.614097i	$-0.210480\pi$
$137$	−7.75074e10	−	1.34247e11i	−0.137208	−	0.237651i	−0.926439	+	0.376445i	$0.877146\pi$
$138$		0			0
$139$	5.63133e11	−	9.75374e11i	0.920512	−	1.59437i	0.121887	−	0.992544i	$-0.461105\pi$
$139$	5.63133e11	−	9.75374e11i	0.920512	−	1.59437i	0.798625	−	0.601829i	$-0.205561\pi$
$140$	3.00826e11	−	5.21045e11i	0.472727	−	0.818788i
$141$		0			0
$142$	5.78412e11	+	1.00184e12i	0.840721	+	1.45617i
$143$	−4.88719e11			−0.683457
$144$		0			0
$145$	−5.77343e10			−0.0748014
$146$	5.44869e11	+	9.43741e11i	0.679754	+	1.17737i
$147$		0			0
$148$	−1.34145e12	+	2.32345e12i	−1.55287	+	2.68964i
$149$	−6.92290e11	+	1.19908e12i	−0.772261	+	1.33759i	0.164061	+	0.986450i	$0.447541\pi$
$149$	−6.92290e11	+	1.19908e12i	−0.772261	+	1.33759i	−0.936321	+	0.351144i	$0.885793\pi$
$150$		0			0
$151$	3.49301e11	+	6.05007e11i	0.362098	+	0.627172i	0.988306	−	0.152484i	$-0.0487272\pi$
$151$	3.49301e11	+	6.05007e11i	0.362098	+	0.627172i	−0.626208	+	0.779656i	$0.715394\pi$
$152$	3.02552e12			3.02454
$153$		0			0
$154$	−1.38109e12			−1.28487
$155$	1.36767e11	+	2.36887e11i	0.122788	+	0.212675i
$156$		0			0
$157$	−1.06563e12	+	1.84573e12i	−0.891580	+	1.54426i	−0.0535991	+	0.998563i	$0.517069\pi$
$157$	−1.06563e12	+	1.84573e12i	−0.891580	+	1.54426i	−0.837981	+	0.545699i	$0.816264\pi$
$158$	1.45101e11	−	2.51323e11i	0.117235	−	0.203057i
$159$		0			0
$160$	−5.07156e10	−	8.78419e10i	−0.0382368	−	0.0662281i
$161$	4.25071e11			0.309684
$162$		0			0
$163$	−1.63564e11			−0.111342			−0.0556708	−	0.998449i	$-0.517730\pi$
$163$	−1.63564e11			−0.111342			−0.0556708	+	0.998449i	$0.517730\pi$
$164$	1.81385e12	+	3.14167e12i	1.19388	+	2.06785i
$165$		0			0
$166$	−3.41970e11	+	5.92309e11i	−0.210568	+	0.364715i
$167$	−4.40471e9	+	7.62919e9i	−0.00262408	+	0.00454504i	−0.867334	−	0.497726i	$-0.834169\pi$
$167$	−4.40471e9	+	7.62919e9i	−0.00262408	+	0.00454504i	0.864710	+	0.502271i	$0.167502\pi$
$168$		0			0
$169$	6.02538e11	+	1.04363e12i	0.336208	+	0.582329i
$170$	1.29191e12			0.697853
$171$		0			0
$172$	−3.86627e12			−1.95833
$173$	−3.65426e11	−	6.32936e11i	−0.179286	−	0.310532i	0.762350	−	0.647164i	$-0.224045\pi$
$173$	−3.65426e11	−	6.32936e11i	−0.179286	−	0.310532i	−0.941636	+	0.336633i	$0.890712\pi$
$174$		0			0
$175$	−2.77478e11	+	4.80606e11i	−0.127797	+	0.221350i
$176$	1.22122e12	−	2.11522e12i	0.545098	−	0.944138i
$177$		0			0
$178$	9.93438e11	+	1.72069e12i	0.416707	+	0.721758i
$179$	−3.92371e12			−1.59590			−0.797950	−	0.602724i	$-0.794082\pi$
$179$	−3.92371e12			−1.59590			−0.797950	+	0.602724i	$0.794082\pi$
$180$		0			0
$181$	2.27931e12			0.872110			0.436055	−	0.899920i	$-0.356375\pi$
$181$	2.27931e12			0.872110			0.436055	+	0.899920i	$0.356375\pi$
$182$	−8.29534e11	−	1.43679e12i	−0.307923	−	0.533338i
$183$		0			0
$184$	−1.18720e12	+	2.05629e12i	−0.414978	+	0.718763i
$185$	−1.78483e12	+	3.09141e12i	−0.605553	+	1.04885i
$186$		0			0
$187$	−9.83656e11	−	1.70374e12i	−0.314568	−	0.544848i
$188$	6.27897e12			1.94994
$189$		0			0
$190$	8.17255e12			2.39449
$191$	1.69354e12	+	2.93330e12i	0.482073	+	0.834975i	0.999788	−	0.0205777i	$-0.00655056\pi$
$191$	1.69354e12	+	2.93330e12i	0.482073	+	0.834975i	−0.517715	+	0.855553i	$0.673217\pi$
$192$		0			0
$193$	2.46460e12	−	4.26882e12i	0.662494	−	1.14747i	−0.317464	−	0.948270i	$-0.602831\pi$
$193$	2.46460e12	−	4.26882e12i	0.662494	−	1.14747i	0.979958	−	0.199203i	$-0.0638353\pi$
$194$	−1.52461e12	+	2.64070e12i	−0.398335	+	0.689936i
$195$		0			0
$196$	2.43514e12	+	4.21778e12i	0.601333	+	1.04154i
$197$	−6.35785e12			−1.52667			−0.763337	−	0.646001i	$-0.776440\pi$
$197$	−6.35785e12			−1.52667			−0.763337	+	0.646001i	$0.776440\pi$
$198$		0			0
$199$	−3.78554e12			−0.859875			−0.429938	−	0.902859i	$-0.641464\pi$
$199$	−3.78554e12			−0.859875			−0.429938	+	0.902859i	$0.641464\pi$
$200$	−1.54996e12	−	2.68461e12i	−0.342496	−	0.593220i
$201$		0			0
$202$	−3.63120e11	+	6.28943e11i	−0.0759658	+	0.131577i
$203$	−1.49228e11	+	2.58470e11i	−0.0303823	+	0.0526237i
$204$		0			0
$205$	2.41337e12	+	4.18008e12i	0.465562	+	0.806377i
$206$	−3.78885e12			−0.711604
$207$		0			0
$208$	2.93404e12			0.522537
$209$	−6.22254e12	−	1.07778e13i	−1.07935	−	1.86949i
$210$		0			0
$211$	−8.97469e10	+	1.55446e11i	−0.0147729	+	0.0255874i	−0.873317	−	0.487152i	$-0.838036\pi$
$211$	−8.97469e10	+	1.55446e11i	−0.0147729	+	0.0255874i	0.858544	+	0.512739i	$0.171369\pi$
$212$	7.65310e12	−	1.32556e13i	1.22741	−	2.12594i
$213$		0			0
$214$	−8.79823e12	−	1.52390e13i	−1.34005	−	2.32103i
$215$	−5.14418e12			−0.763668
$216$		0			0
$217$	1.41402e12			0.199493
$218$	−2.70860e12	−	4.69143e12i	−0.372592	−	0.645348i
$219$		0			0
$220$	6.91201e12	−	1.19720e13i	0.904232	−	1.56618i
$221$	1.18164e12	−	2.04666e12i	0.150774	−	0.261148i
$222$		0			0
$223$	−1.11284e12	−	1.92750e12i	−0.135132	−	0.234055i	0.790516	−	0.612441i	$-0.209812\pi$
$223$	−1.11284e12	−	1.92750e12i	−0.135132	−	0.234055i	−0.925648	+	0.378386i	$0.876479\pi$
$224$	−5.24344e11			−0.0621230
$225$		0			0
$226$	−2.80538e13			−3.16516
$227$	−2.07924e11	−	3.60135e11i	−0.0228961	−	0.0396573i	0.854350	−	0.519698i	$-0.173955\pi$
$227$	−2.07924e11	−	3.60135e11i	−0.0228961	−	0.0396573i	−0.877246	+	0.480040i	$0.840622\pi$
$228$		0			0
$229$	−9.06239e12	+	1.56965e13i	−0.950928	+	1.64705i	−0.207504	+	0.978234i	$0.566534\pi$
$229$	−9.06239e12	+	1.56965e13i	−0.950928	+	1.64705i	−0.743424	+	0.668821i	$0.766799\pi$
$230$	−3.20687e12	+	5.55446e12i	−0.328532	+	0.569034i
$231$		0			0
$232$	−8.33567e11	−	1.44378e12i	−0.0814248	−	0.141032i
$233$	1.87641e10			0.00179007			0.000895033	−	1.00000i	$-0.499715\pi$
$233$	1.87641e10			0.00179007			0.000895033		1.00000i	$0.499715\pi$
$234$		0			0
$235$	8.35433e12			0.760394
$236$	1.12061e12	+	1.94095e12i	0.0996410	+	0.172583i
$237$		0			0
$238$	3.33925e12	−	5.78374e12i	0.283449	−	0.490948i
$239$	−8.81262e12	+	1.52639e13i	−0.730999	+	1.26613i	0.225458	+	0.974253i	$0.427612\pi$
$239$	−8.81262e12	+	1.52639e13i	−0.730999	+	1.26613i	−0.956457	+	0.291874i	$0.905721\pi$
$240$		0			0
$241$	4.45058e11	+	7.70864e11i	0.0352633	+	0.0610779i	0.883118	−	0.469150i	$-0.155440\pi$
$241$	4.45058e11	+	7.70864e11i	0.0352633	+	0.0610779i	−0.847855	+	0.530228i	$0.822106\pi$
$242$	−9.47880e12			−0.734123
$243$		0			0
$244$	1.99799e13			1.47894
$245$	3.24001e12	+	5.61187e12i	0.234495	+	0.406157i
$246$		0			0
$247$	7.47496e12	−	1.29470e13i	0.517339	−	0.896058i
$248$	−3.94928e12	+	6.84035e12i	−0.267321	+	0.463014i
$249$		0			0
$250$	−1.44128e13	−	2.49638e13i	−0.933425	−	1.61674i
$251$	2.42280e13			1.53502			0.767508	−	0.641040i	$-0.221497\pi$
$251$	2.42280e13			1.53502			0.767508	+	0.641040i	$0.221497\pi$
$252$		0			0
$253$	9.76677e12			0.592364
$254$	9.76065e12	+	1.69059e13i	0.579286	+	1.00335i
$255$		0			0
$256$	1.72903e13	−	2.99477e13i	0.982839	−	1.70233i
$257$	3.90246e12	−	6.75926e12i	0.217123	−	0.376068i	−0.736804	−	0.676106i	$-0.763666\pi$
$257$	3.90246e12	−	6.75926e12i	0.217123	−	0.376068i	0.953927	+	0.300038i	$0.0969993\pi$
$258$		0			0
$259$	9.22660e12	+	1.59809e13i	0.491918	+	0.852028i
$260$	1.66064e13			0.866806
$261$		0			0
$262$	−7.63556e12			−0.382106
$263$	8.29779e12	+	1.43722e13i	0.406636	+	0.704314i	0.994510	−	0.104638i	$-0.0333684\pi$
$263$	8.29779e12	+	1.43722e13i	0.406636	+	0.704314i	−0.587874	+	0.808952i	$0.700035\pi$
$264$		0			0
$265$	1.01826e13	−	1.76368e13i	0.478639	−	0.829027i
$266$	2.11238e13	−	3.65875e13i	0.972576	−	1.68455i
$267$		0			0
$268$	−1.06801e13	−	1.84984e13i	−0.471881	−	0.817322i
$269$	−2.85236e13			−1.23471			−0.617357	−	0.786683i	$-0.711797\pi$
$269$	−2.85236e13			−1.23471			−0.617357	+	0.786683i	$0.711797\pi$
$270$		0			0
$271$	2.33800e13			0.971658			0.485829	−	0.874054i	$-0.338518\pi$
$271$	2.33800e13			0.971658			0.485829	+	0.874054i	$0.338518\pi$
$272$	5.90540e12	+	1.02285e13i	0.240503	+	0.416563i
$273$		0			0
$274$	6.04557e12	−	1.04712e13i	0.236488	−	0.409610i
$275$	−6.37556e12	+	1.10428e13i	−0.244449	+	0.423398i
$276$		0			0
$277$	1.51821e13	+	2.62961e13i	0.559361	+	0.968841i	0.997550	+	0.0699584i	$0.0222867\pi$
$277$	1.51821e13	+	2.62961e13i	0.559361	+	0.968841i	−0.438189	+	0.898883i	$0.644380\pi$
$278$	8.78487e13			3.17314
$279$		0			0
$280$	2.31156e13			0.802667
$281$	7.98743e12	+	1.38346e13i	0.271971	+	0.471067i	0.969366	−	0.245619i	$-0.0789912\pi$
$281$	7.98743e12	+	1.38346e13i	0.271971	+	0.471067i	−0.697396	+	0.716686i	$0.745658\pi$
$282$		0			0
$283$	−1.43523e13	+	2.48588e13i	−0.469997	+	0.814058i	−0.999411	−	0.0343051i	$-0.989078\pi$
$283$	−1.43523e13	+	2.48588e13i	−0.469997	+	0.814058i	0.529415	+	0.848363i	$0.322412\pi$
$284$	−2.99291e13	+	5.18388e13i	−0.961265	+	1.66496i
$285$		0			0
$286$	−1.90600e13	−	3.30130e13i	−0.588994	−	1.02017i
$287$	2.49516e13			0.756394
$288$		0			0
$289$	−2.47587e13			−0.722419
$290$	−2.25164e12	−	3.89995e12i	−0.0644628	−	0.111653i
$291$		0			0
$292$	−2.81935e13	+	4.88326e13i	−0.777219	+	1.34618i
$293$	2.40877e13	−	4.17211e13i	0.651663	−	1.12871i	−0.331056	−	0.943611i	$-0.607405\pi$
$293$	2.40877e13	−	4.17211e13i	0.651663	−	1.12871i	0.982719	−	0.185103i	$-0.0592619\pi$
$294$		0			0
$295$	1.49100e12	+	2.58249e12i	0.0388558	+	0.0673003i
$296$	−1.03077e14			−2.63669
$297$		0			0
$298$	−1.07997e14			−2.66209
$299$	5.86627e12	+	1.01607e13i	0.141962	+	0.245885i
$300$		0			0
$301$	−1.32963e13	+	2.30299e13i	−0.310181	+	0.537249i
$302$	−2.72455e13	+	4.71905e13i	−0.624102	+	1.08098i
$303$		0			0
$304$	3.73572e13	+	6.47045e13i	0.825219	+	1.42932i
$305$	2.65838e13			0.576723
$306$		0			0
$307$	2.57350e13			0.538597			0.269298	−	0.963057i	$-0.413208\pi$
$307$	2.57350e13			0.538597			0.269298	+	0.963057i	$0.413208\pi$
$308$	−3.57314e13	−	6.18885e13i	−0.734549	−	1.27228i
$309$		0			0
$310$	−1.06678e13	+	1.84772e13i	−0.211634	+	0.366562i
$311$	1.73021e13	−	2.99682e13i	0.337223	−	0.584088i	−0.646686	−	0.762756i	$-0.723846\pi$
$311$	1.73021e13	−	2.99682e13i	0.337223	−	0.584088i	0.983909	+	0.178668i	$0.0571789\pi$
$312$		0			0
$313$	−6.30329e12	−	1.09176e13i	−0.118597	−	0.205416i	0.800615	−	0.599179i	$-0.204506\pi$
$313$	−6.30329e12	−	1.09176e13i	−0.118597	−	0.205416i	−0.919212	+	0.393763i	$0.871173\pi$
$314$	−1.66239e14			−3.07341
$315$		0			0
$316$	1.50161e13			0.268089
$317$	−4.09121e13	−	7.08619e13i	−0.717838	−	1.24333i	−0.961855	−	0.273561i	$-0.911799\pi$
$317$	−4.09121e13	−	7.08619e13i	−0.717838	−	1.24333i	0.244017	−	0.969771i	$-0.421535\pi$
$318$		0			0
$319$	−3.42877e12	+	5.93881e12i	−0.0581152	+	0.100658i
$320$	2.50125e13	−	4.33229e13i	0.416708	−	0.721759i
$321$		0			0
$322$	1.65778e13	+	2.87135e13i	0.266882	+	0.462253i
$323$	6.01801e13			0.952443
$324$		0			0
$325$	−1.53176e13			−0.234332
$326$	−6.37901e12	−	1.10488e13i	−0.0959526	−	0.166195i
$327$		0			0
$328$	−6.96884e13	+	1.20704e14i	−1.01357	+	1.75556i
$329$	2.15937e13	−	3.74014e13i	0.308851	−	0.534946i
$330$		0			0
$331$	1.70057e13	+	2.94548e13i	0.235256	+	0.407476i	0.959347	−	0.282229i	$-0.0910737\pi$
$331$	1.70057e13	+	2.94548e13i	0.235256	+	0.407476i	−0.724091	+	0.689705i	$0.757740\pi$
$332$	−3.53895e13			−0.481520
$333$		0			0
$334$	−6.87135e11			−0.00904558
$335$	−1.42101e13	−	2.46126e13i	−0.184014	−	0.318721i
$336$		0			0
$337$	2.99720e13	−	5.19130e13i	0.375622	−	0.650596i	−0.614798	−	0.788685i	$-0.710762\pi$
$337$	2.99720e13	−	5.19130e13i	0.375622	−	0.650596i	0.990420	+	0.138088i	$0.0440958\pi$
$338$	−4.69980e13	+	8.14029e13i	−0.579479	+	1.00369i
$339$		0			0
$340$	3.34241e13	+	5.78922e13i	0.398957	+	0.691013i
$341$	3.24897e13			0.381590
$342$		0			0
$343$	8.83888e13			1.00526
$344$	−7.42716e13	−	1.28642e14i	−0.831287	−	1.43983i
$345$		0			0
$346$	2.85032e13	−	4.93690e13i	0.309012	−	0.535224i
$347$	4.89343e13	−	8.47566e13i	0.522157	−	0.904402i	−0.477511	−	0.878626i	$-0.658461\pi$
$347$	4.89343e13	−	8.47566e13i	0.522157	−	0.904402i	0.999668	−	0.0257762i	$-0.00820572\pi$
$348$		0			0
$349$	7.13948e13	+	1.23659e14i	0.738120	+	1.27846i	0.953341	+	0.301895i	$0.0976193\pi$
$349$	7.13948e13	+	1.23659e14i	0.738120	+	1.27846i	−0.215221	+	0.976565i	$0.569047\pi$
$350$	−4.32866e13			−0.440534
$351$		0			0
$352$	−1.20478e13			−0.118829
$353$	7.21230e13	+	1.24921e14i	0.700346	+	1.21303i	0.968345	+	0.249616i	$0.0803043\pi$
$353$	7.21230e13	+	1.24921e14i	0.700346	+	1.21303i	−0.267999	+	0.963419i	$0.586362\pi$
$354$		0			0
$355$	−3.98215e13	+	6.89728e13i	−0.374853	+	0.649265i
$356$	−5.14040e13	+	8.90344e13i	−0.476455	+	0.825245i
$357$		0			0
$358$	−1.53025e14	−	2.65047e14i	−1.37533	−	2.38213i
$359$	1.24349e14			1.10059			0.550293	−	0.834972i	$-0.314516\pi$
$359$	1.24349e14			1.10059			0.550293	+	0.834972i	$0.314516\pi$
$360$		0			0
$361$	2.64205e14			2.26804
$362$	8.88930e13	+	1.53967e14i	0.751572	+	1.30176i
$363$		0			0
$364$	4.29231e13	−	7.43449e13i	0.352073	−	0.609809i
$365$	−3.75121e13	+	6.49729e13i	−0.303083	+	0.524955i
$366$		0			0
$367$	8.00548e13	+	1.38659e14i	0.627659	+	1.08714i	0.988020	+	0.154325i	$0.0493202\pi$
$367$	8.00548e13	+	1.38659e14i	0.627659	+	1.08714i	−0.360361	+	0.932813i	$0.617347\pi$
$368$	−5.86351e13			−0.452892
$369$		0			0
$370$	−2.78433e14			−2.08743
$371$	−5.26387e13	−	9.11730e13i	−0.388820	−	0.673457i
$372$		0			0
$373$	1.73629e13	−	3.00734e13i	0.124516	−	0.215667i	−0.797028	−	0.603943i	$-0.793596\pi$
$373$	1.73629e13	−	3.00734e13i	0.124516	−	0.215667i	0.921544	+	0.388275i	$0.126929\pi$
$374$	7.67252e13	−	1.32892e14i	0.542181	−	0.939084i
$375$		0			0
$376$	1.20620e14	+	2.08920e14i	0.827723	+	1.43366i
$377$	−8.23777e12			−0.0557099
$378$		0			0
$379$	−1.46500e14			−0.962327			−0.481163	−	0.876631i	$-0.659786\pi$
$379$	−1.46500e14			−0.962327			−0.481163	+	0.876631i	$0.659786\pi$
$380$	2.11438e14	+	3.66222e14i	1.36891	+	2.37102i
$381$		0			0
$382$	−1.32096e14	+	2.28798e14i	−0.830888	+	1.43914i
$383$	3.21709e13	−	5.57217e13i	0.199467	−	0.345486i	−0.748889	−	0.662695i	$-0.769412\pi$
$383$	3.21709e13	−	5.57217e13i	0.199467	−	0.345486i	0.948356	+	0.317209i	$0.102746\pi$
$384$		0			0
$385$	−4.75415e13	−	8.23443e13i	−0.286443	−	0.496134i
$386$	3.84478e14			2.28371
$387$		0			0
$388$	−1.57777e14			−0.910899
$389$	−1.99450e13	−	3.45458e13i	−0.113530	−	0.196640i	0.803661	−	0.595087i	$-0.202883\pi$
$389$	−1.99450e13	−	3.45458e13i	−0.113530	−	0.196640i	−0.917191	+	0.398447i	$0.869549\pi$
$390$		0			0
$391$	−2.36144e13	+	4.09013e13i	−0.130679	+	0.226342i
$392$	−9.35586e13	+	1.62048e14i	−0.510517	+	0.884241i
$393$		0			0
$394$	−2.47956e14	−	4.29473e14i	−1.31567	−	2.27880i
$395$	1.99793e13			0.104543
$396$		0			0
$397$	1.06552e14			0.542268			0.271134	−	0.962542i	$-0.412601\pi$
$397$	1.06552e14			0.542268			0.271134	+	0.962542i	$0.412601\pi$
$398$	−1.47636e14	−	2.55713e14i	−0.741029	−	1.28350i
$399$		0			0
$400$	3.82758e13	−	6.62957e13i	0.186894	−	0.323709i
$401$	1.70722e13	−	2.95700e13i	0.0822236	−	0.142415i	−0.821981	−	0.569515i	$-0.807131\pi$
$401$	1.70722e13	−	2.95700e13i	0.0822236	−	0.142415i	0.904205	+	0.427099i	$0.140464\pi$
$402$		0			0
$403$	1.95145e13	+	3.38001e13i	0.0914490	+	0.158394i
$404$	−3.75783e13			−0.173716
$405$		0			0
$406$	−2.32795e13			−0.104732
$407$	2.11998e14	+	3.67191e14i	0.940940	+	1.62976i
$408$		0			0
$409$	−2.66675e13	+	4.61894e13i	−0.115213	+	0.199556i	−0.917865	−	0.396893i	$-0.870089\pi$
$409$	−2.66675e13	+	4.61894e13i	−0.115213	+	0.199556i	0.802652	+	0.596448i	$0.203422\pi$
$410$	−1.88243e14	+	3.26046e14i	−0.802430	+	1.38985i
$411$		0			0
$412$	−9.80245e13	−	1.69783e14i	−0.406818	−	0.704629i
$413$	1.54153e13			0.0631288
$414$		0			0
$415$	−4.70866e13			−0.187773
$416$	−7.23631e12	−	1.25337e13i	−0.0284776	−	0.0493247i
$417$		0			0
$418$	4.85358e14	−	8.40665e14i	1.86034	−	3.22221i
$419$	−5.06438e13	+	8.77177e13i	−0.191580	+	0.331826i	−0.945774	−	0.324826i	$-0.894694\pi$
$419$	−5.06438e13	+	8.77177e13i	−0.191580	+	0.331826i	0.754194	+	0.656651i	$0.228028\pi$
$420$		0			0
$421$	7.89642e13	+	1.36770e14i	0.290991	+	0.504010i	0.974044	−	0.226358i	$-0.0726818\pi$
$421$	7.89642e13	+	1.36770e14i	0.290991	+	0.504010i	−0.683054	+	0.730368i	$0.739349\pi$
$422$	−1.40005e13			−0.0509244
$423$		0			0
$424$	5.88067e14			2.08408
$425$	−3.08300e13	−	5.33991e13i	−0.107854	−	0.186808i
$426$		0			0
$427$	6.87118e13	−	1.19012e14i	0.234249	−	0.405732i
$428$	4.55252e14	−	7.88520e14i	1.53219	−	2.65382i
$429$		0			0
$430$	−2.00623e14	−	3.47489e14i	−0.658118	−	1.13989i
$431$	−5.13171e14			−1.66202			−0.831012	−	0.556254i	$-0.812238\pi$
$431$	−5.13171e14			−1.66202			−0.831012	+	0.556254i	$0.812238\pi$
$432$		0			0
$433$	−7.49248e13			−0.236560			−0.118280	−	0.992980i	$-0.537738\pi$
$433$	−7.49248e13			−0.236560			−0.118280	+	0.992980i	$0.537738\pi$
$434$	5.51469e13	+	9.55172e13i	0.171920	+	0.297775i
$435$		0			0
$436$	1.40152e14	−	2.42751e14i	0.426015	−	0.737880i
$437$	−1.49383e14	+	2.58739e14i	−0.448387	+	0.776629i
$438$		0			0
$439$	1.84168e14	+	3.18988e14i	0.539086	+	0.933725i	0.998954	+	0.0457373i	$0.0145637\pi$
$439$	1.84168e14	+	3.18988e14i	0.539086	+	0.933725i	−0.459867	+	0.887988i	$0.652103\pi$
$440$	5.31122e14			1.53534
$441$		0			0
$442$	1.84335e14			0.519740
$443$	−5.56239e13	−	9.63434e13i	−0.154896	−	0.268288i	0.778125	−	0.628110i	$-0.216171\pi$
$443$	−5.56239e13	−	9.63434e13i	−0.154896	−	0.268288i	−0.933021	+	0.359821i	$0.882838\pi$
$444$		0			0
$445$	−6.83944e13	+	1.18463e14i	−0.185798	+	0.321811i
$446$	8.68017e13	−	1.50345e14i	0.232909	−	0.403410i
$447$		0			0
$448$	−1.29301e14	−	2.23956e14i	−0.338511	−	0.586318i
$449$	8.83314e13			0.228434			0.114217	−	0.993456i	$-0.463564\pi$
$449$	8.83314e13			0.228434			0.114217	+	0.993456i	$0.463564\pi$
$450$		0			0
$451$	5.73308e14			1.44683
$452$	−7.25803e14	−	1.25713e15i	−1.80950	−	3.13414i
$453$		0			0
$454$	1.62181e13	−	2.80905e13i	0.0394632	−	0.0683522i
$455$	5.71102e13	−	9.89178e13i	0.137294	−	0.237800i
$456$		0			0
$457$	4.71047e12	+	8.15877e12i	0.0110541	+	0.0191463i	0.871500	−	0.490396i	$-0.163148\pi$
$457$	4.71047e12	+	8.15877e12i	0.0110541	+	0.0191463i	−0.860445	+	0.509543i	$0.829815\pi$
$458$	−1.41373e15			−3.27799
$459$		0			0
$460$	−3.31870e14			−0.751276
$461$	−3.48567e14	−	6.03735e14i	−0.779706	−	1.35049i	−0.932111	−	0.362172i	$-0.882035\pi$
$461$	−3.48567e14	−	6.03735e14i	−0.779706	−	1.35049i	0.152405	−	0.988318i	$-0.451298\pi$
$462$		0			0
$463$	9.39706e13	−	1.62762e14i	0.205256	−	0.355515i	−0.744958	−	0.667111i	$-0.767531\pi$
$463$	9.39706e13	−	1.62762e14i	0.205256	−	0.355515i	0.950214	+	0.311597i	$0.100864\pi$
$464$	2.05847e13	−	3.56538e13i	0.0444320	−	0.0769585i
$465$		0			0
$466$	7.31798e11	+	1.26751e12i	0.00154266	+	0.00267196i
$467$	−3.20007e14			−0.666678			−0.333339	−	0.942807i	$-0.608175\pi$
$467$	−3.20007e14			−0.666678			−0.333339	+	0.942807i	$0.608175\pi$
$468$		0			0
$469$	−1.46917e14			−0.298966
$470$	3.25819e14	+	5.64335e14i	0.655297	+	1.13501i
$471$		0			0
$472$	−4.30541e13	+	7.45718e13i	−0.0845927	+	0.146519i
$473$	−3.05507e14	+	5.29153e14i	−0.593314	+	1.02765i
$474$		0			0
$475$	−1.95028e14	−	3.37799e14i	−0.370069	−	0.640979i
$476$	3.45569e14			0.648181
$477$		0			0
$478$	−1.37477e15			−2.51986
$479$	−7.51912e13	−	1.30235e14i	−0.136245	−	0.235984i	0.789827	−	0.613329i	$-0.210170\pi$
$479$	−7.51912e13	−	1.30235e14i	−0.136245	−	0.235984i	−0.926072	+	0.377346i	$0.876837\pi$
$480$		0			0
$481$	−2.54667e14	+	4.41096e14i	−0.450998	+	0.781151i
$482$	−3.47146e13	+	6.01274e13i	−0.0607789	+	0.105272i
$483$		0			0
$484$	−2.45234e14	−	4.24757e14i	−0.419692	−	0.726928i
$485$	−2.09927e14			−0.355212
$486$		0			0
$487$	1.76546e14			0.292045			0.146022	−	0.989281i	$-0.453353\pi$
$487$	1.76546e14			0.292045			0.146022	+	0.989281i	$0.453353\pi$
$488$	3.83816e14	+	6.64789e14i	0.627790	+	1.08736i
$489$		0			0
$490$	−2.52721e14	+	4.37726e14i	−0.404169	+	0.700041i
$491$	−4.30479e14	+	7.45612e14i	−0.680775	+	1.17914i	0.293969	+	0.955815i	$0.405024\pi$
$491$	−4.30479e14	+	7.45612e14i	−0.680775	+	1.17914i	−0.974745	+	0.223323i	$0.928310\pi$
$492$		0			0
$493$	−1.65803e13	−	2.87180e13i	−0.0256410	−	0.0444116i
$494$	1.16609e15			1.78334
$495$		0			0
$496$	−1.95053e14			−0.291745
$497$	2.05855e14	+	3.56552e14i	0.304511	+	0.527428i
$498$		0			0
$499$	−3.00605e14	+	5.20663e14i	−0.434953	+	0.753362i	−0.997292	−	0.0735457i	$-0.976569\pi$
$499$	−3.00605e14	+	5.20663e14i	−0.434953	+	0.753362i	0.562338	+	0.826907i	$0.309902\pi$
$500$	7.45772e14	−	1.29171e15i	1.06726	−	1.84855i
$501$		0			0
$502$	9.44894e14	+	1.63660e15i	1.32286	+	2.29125i
$503$	−1.09203e15			−1.51221			−0.756103	−	0.654453i	$-0.772899\pi$
$503$	−1.09203e15			−1.51221			−0.756103	+	0.654453i	$0.772899\pi$
$504$		0			0
$505$	−4.99989e13			−0.0677420
$506$	3.80904e14	+	6.59745e14i	0.510491	+	0.884196i
$507$		0			0
$508$	−5.05051e14	+	8.74774e14i	−0.662346	+	1.14722i
$509$	4.38186e14	−	7.58960e14i	0.568474	−	0.984625i	−0.428244	−	0.903663i	$-0.640868\pi$
$509$	4.38186e14	−	7.58960e14i	0.568474	−	0.984625i	0.996717	−	0.0809617i	$-0.0257992\pi$
$510$		0			0
$511$	1.93918e14	+	3.35875e14i	0.246208	+	0.426445i
$512$	1.28839e15			1.61832
$513$		0			0
$514$	6.08784e14			0.748455
$515$	−1.30424e14	−	2.25901e14i	−0.158642	−	0.274776i
$516$		0			0
$517$	4.96154e14	−	8.59364e14i	0.590770	−	1.02324i
$518$	−7.19675e14	+	1.24651e15i	−0.847857	+	1.46853i
$519$		0			0
$520$	3.19011e14	+	5.52543e14i	0.367948	+	0.637305i
$521$	3.71989e14			0.424544			0.212272	−	0.977211i	$-0.431914\pi$
$521$	3.71989e14			0.424544			0.212272	+	0.977211i	$0.431914\pi$
$522$		0			0
$523$	−9.73507e14			−1.08788			−0.543939	−	0.839125i	$-0.683068\pi$
$523$	−9.73507e14			−1.08788			−0.543939	+	0.839125i	$0.683068\pi$
$524$	−1.97546e14	−	3.42159e14i	−0.218447	−	0.378361i
$525$		0			0
$526$	−6.47227e14	+	1.12103e15i	−0.700867	+	1.21394i
$527$	−7.85545e13	+	1.36060e14i	−0.0841807	+	0.145805i
$528$		0			0
$529$	3.59171e14	+	6.22102e14i	0.376960	+	0.652913i
$530$	1.58849e15			1.64994
$531$		0			0
$532$	2.18605e15			2.22405
$533$	3.44349e14	+	5.96431e14i	0.346737	+	0.600565i
$534$		0			0
$535$	6.05724e14	−	1.04915e15i	0.597488	−	1.03488i
$536$	4.10330e14	−	7.10713e14i	0.400615	−	0.693886i
$537$		0			0
$538$	−1.11242e15	−	1.92677e15i	−1.06406	−	1.84301i
$539$	7.69683e14			0.728741
$540$		0			0
$541$	1.74606e15			1.61985			0.809925	−	0.586533i	$-0.199508\pi$
$541$	1.74606e15			1.61985			0.809925	+	0.586533i	$0.199508\pi$
$542$	9.11820e14	+	1.57932e15i	0.837361	+	1.45035i
$543$		0			0
$544$	2.91294e13	−	5.04536e13i	0.0262142	−	0.0454044i
$545$	1.86476e14	−	3.22987e14i	0.166128	−	0.287742i
$546$		0			0
$547$	−8.73122e13	−	1.51229e14i	−0.0762333	−	0.132040i	0.825389	−	0.564565i	$-0.190956\pi$
$547$	−8.73122e13	−	1.51229e14i	−0.0762333	−	0.132040i	−0.901622	+	0.432525i	$0.857623\pi$
$548$	6.25639e14			0.540793
$549$		0			0
$550$	−9.94588e14			−0.842652
$551$	−1.04886e14	−	1.81668e14i	−0.0879800	−	0.152386i
$552$		0			0
$553$	5.16411e13	−	8.94451e13i	0.0424627	−	0.0735475i
$554$	−1.18420e15	+	2.05110e15i	−0.964099	+	1.66987i
$555$		0			0
$556$	2.27280e15	+	3.93661e15i	1.81406	+	3.14204i
$557$	−1.58365e15			−1.25157			−0.625785	−	0.779995i	$-0.715221\pi$
$557$	−1.58365e15			−1.25157			−0.625785	+	0.779995i	$0.715221\pi$
$558$		0			0
$559$	−7.33993e14			−0.568757
$560$	2.85416e14	+	4.94356e14i	0.219000	+	0.379320i
$561$		0			0
$562$	−6.23020e14	+	1.07910e15i	−0.468761	+	0.811919i
$563$	−4.87899e14	+	8.45066e14i	−0.363525	+	0.629643i	−0.988538	−	0.150971i	$-0.951760\pi$
$563$	−4.87899e14	+	8.45066e14i	−0.363525	+	0.629643i	0.625014	+	0.780614i	$0.285093\pi$
$564$		0			0
$565$	−9.65699e14	−	1.67264e15i	−0.705627	−	1.22218i
$566$	−2.23895e15			−1.62015
$567$		0			0
$568$	−2.29977e15			−1.63218
$569$	9.62137e14	+	1.66647e15i	0.676269	+	1.17133i	0.976096	+	0.217339i	$0.0697377\pi$
$569$	9.62137e14	+	1.66647e15i	0.676269	+	1.17133i	−0.299827	+	0.953994i	$0.596929\pi$
$570$		0			0
$571$	−8.05660e14	+	1.39544e15i	−0.555461	+	0.962086i	0.442407	+	0.896814i	$0.354125\pi$
$571$	−8.05660e14	+	1.39544e15i	−0.555461	+	0.962086i	−0.997868	+	0.0652716i	$0.979209\pi$
$572$	9.86235e14	−	1.70821e15i	0.673445	−	1.16644i
$573$		0			0
$574$	9.73113e14	+	1.68548e15i	0.651850	+	1.12904i
$575$	3.06113e14			0.203099
$576$		0			0
$577$	−2.53250e15			−1.64848			−0.824239	−	0.566242i	$-0.808397\pi$
$577$	−2.53250e15			−1.64848			−0.824239	+	0.566242i	$0.808397\pi$
$578$	−9.65588e14	−	1.67245e15i	−0.622571	−	1.07832i
$579$		0			0
$580$	1.16508e14	−	2.01797e14i	0.0737057	−	0.127662i
$581$	−1.21706e14	+	2.10801e14i	−0.0762682	+	0.132100i
$582$		0			0
$583$	−1.20947e15	−	2.09486e15i	−0.743735	−	1.28819i
$584$	−2.16640e15			−1.31968
$585$		0			0
$586$	3.75768e15			2.24638
$587$	−1.55754e15	−	2.69773e15i	−0.922421	−	1.59768i	−0.795658	−	0.605747i	$-0.792875\pi$
$587$	−1.55754e15	−	2.69773e15i	−0.922421	−	1.59768i	−0.126763	−	0.991933i	$-0.540459\pi$
$588$		0			0
$589$	−4.96930e14	+	8.60708e14i	−0.288843	+	0.500290i
$590$	−1.16298e14	+	2.01434e14i	−0.0669709	+	0.115997i
$591$		0			0
$592$	−1.27273e15	−	2.20444e15i	−0.719396	−	1.24603i
$593$	2.20723e15			1.23608			0.618040	−	0.786146i	$-0.287927\pi$
$593$	2.20723e15			1.23608			0.618040	+	0.786146i	$0.287927\pi$
$594$		0			0
$595$	4.59788e14			0.252764
$596$	−2.79408e15	−	4.83950e15i	−1.52190	−	2.63600i
$597$		0			0
$598$	−4.57569e14	+	7.92533e14i	−0.244681	+	0.423800i
$599$	1.70579e15	−	2.95452e15i	0.903813	−	1.56545i	0.0813112	−	0.996689i	$-0.474089\pi$
$599$	1.70579e15	−	2.95452e15i	0.903813	−	1.56545i	0.822502	−	0.568762i	$-0.192577\pi$
$600$		0			0
$601$	7.87726e14	+	1.36438e15i	0.409794	+	0.709784i	0.994866	−	0.101197i	$-0.0322672\pi$
$601$	7.87726e14	+	1.36438e15i	0.409794	+	0.709784i	−0.585072	+	0.810981i	$0.698934\pi$
$602$	−2.07422e15			−1.06924
$603$		0			0
$604$	−2.81956e15			−1.42718
$605$	−3.26290e14	−	5.65150e14i	−0.163662	−	0.283471i
$606$		0			0
$607$	2.52796e14	−	4.37856e14i	0.124518	−	0.215672i	−0.797026	−	0.603945i	$-0.793595\pi$
$607$	2.52796e14	−	4.37856e14i	0.124518	−	0.215672i	0.921544	+	0.388273i	$0.126928\pi$
$608$	1.84270e14	−	3.19166e14i	0.0899468	−	0.155792i
$609$		0			0
$610$	1.03677e15	+	1.79573e15i	0.497012	+	0.860850i
$611$	1.19203e15			0.566319
$612$		0			0
$613$	−1.98375e15			−0.925665			−0.462832	−	0.886446i	$-0.653167\pi$
$613$	−1.98375e15			−0.925665			−0.462832	+	0.886446i	$0.653167\pi$
$614$	1.00367e15	+	1.73840e15i	0.464155	+	0.803940i
$615$		0			0
$616$	1.37281e15	−	2.37777e15i	0.623614	−	1.08013i
$617$	−9.65493e14	+	1.67228e15i	−0.434691	+	0.752907i	−0.997270	−	0.0738362i	$-0.976476\pi$
$617$	−9.65493e14	+	1.67228e15i	−0.434691	+	0.752907i	0.562579	+	0.826743i	$0.309809\pi$
$618$		0			0
$619$	−4.73844e14	−	8.20722e14i	−0.209574	−	0.362993i	0.742006	−	0.670393i	$-0.233874\pi$
$619$	−4.73844e14	−	8.20722e14i	−0.209574	−	0.362993i	−0.951580	+	0.307400i	$0.900541\pi$
$620$	−1.10398e15			−0.483958
$621$		0			0
$622$	2.69913e15			1.16246
$623$	3.53562e14	+	6.12387e14i	0.150932	+	0.261422i
$624$		0			0
$625$	5.04201e14	−	8.73302e14i	0.211477	−	0.366290i
$626$	4.91657e14	−	8.51575e14i	0.204411	−	0.354050i
$627$		0			0
$628$	−4.30090e15	−	7.44938e15i	−1.75704	−	3.04328i
$629$	−2.05030e15			−0.830306
$630$		0			0
$631$	1.00593e15			0.400318			0.200159	−	0.979763i	$-0.435854\pi$
$631$	1.00593e15			0.400318			0.200159	+	0.979763i	$0.435854\pi$
$632$	2.88461e14	+	4.99629e14i	0.113800	+	0.197108i
$633$		0			0
$634$	3.19115e15	−	5.52723e15i	1.23725	−	2.14297i
$635$	−6.71983e14	+	1.16391e15i	−0.258287	+	0.447367i
$636$		0			0
$637$	4.62299e14	+	8.00725e14i	0.174645	+	0.302494i
$638$	−5.34888e14			−0.200332
$639$		0			0
$640$	3.69422e15			1.35998
$641$	5.65722e14	+	9.79859e14i	0.206483	+	0.357639i	0.950604	−	0.310406i	$-0.100465\pi$
$641$	5.65722e14	+	9.79859e14i	0.206483	+	0.357639i	−0.744121	+	0.668044i	$0.767132\pi$
$642$		0			0
$643$	4.34153e14	−	7.51975e14i	0.155769	−	0.269801i	−0.777569	−	0.628797i	$-0.783548\pi$
$643$	4.34153e14	−	7.51975e14i	0.155769	−	0.269801i	0.933339	+	0.358996i	$0.116881\pi$
$644$	−8.57794e14	+	1.48574e15i	−0.305148	+	0.528532i
$645$		0			0
$646$	2.34702e15	+	4.06516e15i	0.820802	+	1.42167i
$647$	1.37636e15			0.477265			0.238633	−	0.971110i	$-0.423301\pi$
$647$	1.37636e15			0.477265			0.238633	+	0.971110i	$0.423301\pi$
$648$		0			0
$649$	3.54195e14			0.120753
$650$	−5.97385e14	−	1.03470e15i	−0.201944	−	0.349777i
$651$		0			0
$652$	3.30073e14	−	5.71703e14i	0.109711	−	0.190024i
$653$	1.27638e15	−	2.21075e15i	0.420685	−	0.728648i	−0.575321	−	0.817927i	$-0.695123\pi$
$653$	1.27638e15	−	2.21075e15i	0.420685	−	0.728648i	0.996007	+	0.0892793i	$0.0284564\pi$
$654$		0			0
$655$	−2.62839e14	−	4.55251e14i	−0.0851850	−	0.147545i
$656$	−3.44187e15			−1.10617
$657$		0			0
$658$	3.36862e15			1.06466
$659$	4.63396e14	+	8.02626e14i	0.145239	+	0.251561i	0.929462	−	0.368918i	$-0.120272\pi$
$659$	4.63396e14	+	8.02626e14i	0.145239	+	0.251561i	−0.784223	+	0.620479i	$0.786938\pi$
$660$		0			0
$661$	9.51659e14	−	1.64832e15i	0.293342	−	0.508082i	−0.681256	−	0.732045i	$-0.738566\pi$
$661$	9.51659e14	−	1.64832e15i	0.293342	−	0.508082i	0.974598	+	0.223963i	$0.0718994\pi$
$662$	−1.32645e15	+	2.29747e15i	−0.405482	+	0.702315i
$663$		0			0
$664$	−6.79836e14	−	1.17751e15i	−0.204399	−	0.354030i
$665$	2.90859e15			0.867288
$666$		0			0
$667$	1.64627e14			0.0482847
$668$	−1.77774e13	−	3.07914e13i	−0.00517128	−	0.00895692i
$669$		0			0
$670$	1.10839e15	−	1.91978e15i	0.317161	−	0.549339i
$671$	1.57878e15	−	2.73452e15i	0.448071	−	0.776083i
$672$		0			0
$673$	−2.46495e15	−	4.26942e15i	−0.688217	−	1.19203i	−0.972414	−	0.233261i	$-0.925060\pi$
$673$	−2.46495e15	−	4.26942e15i	−0.688217	−	1.19203i	0.284197	−	0.958766i	$-0.408273\pi$
$674$	4.67563e15			1.29482
$675$		0			0
$676$	−4.86369e15			−1.32513
$677$	2.15147e14	+	3.72645e14i	0.0581429	+	0.100707i	0.893632	−	0.448801i	$-0.148149\pi$
$677$	2.15147e14	+	3.72645e14i	0.0581429	+	0.100707i	−0.835489	+	0.549507i	$0.814815\pi$
$678$		0			0
$679$	−5.42604e14	+	9.39817e14i	−0.144278	+	0.249896i
$680$	−1.28416e15	+	2.22423e15i	−0.338704	+	0.586653i
$681$		0			0
$682$	1.26710e15	+	2.19468e15i	0.328849	+	0.569583i
$683$	3.81244e15			0.981498			0.490749	−	0.871301i	$-0.336723\pi$
$683$	3.81244e15			0.981498			0.490749	+	0.871301i	$0.336723\pi$
$684$		0			0
$685$	8.32429e14			0.210887
$686$	3.44716e15	+	5.97066e15i	0.866322	+	1.50051i
$687$		0			0
$688$	1.83412e15	−	3.17678e15i	0.453618	−	0.785690i
$689$	1.45290e15	−	2.51650e15i	0.356476	−	0.617435i
$690$		0			0
$691$	−2.01864e15	−	3.49639e15i	−0.487450	−	0.844289i	0.512445	−	0.858720i	$-0.328740\pi$
$691$	−2.01864e15	−	3.49639e15i	−0.487450	−	0.844289i	−0.999896	+	0.0144309i	$0.995406\pi$
$692$	2.94972e15			0.706638
$693$		0			0
$694$	7.63374e15			1.79995
$695$	3.02402e15	+	5.23776e15i	0.707406	+	1.22526i
$696$		0			0
$697$	−1.38616e15	+	2.40090e15i	−0.319178	+	0.552833i
$698$	−5.56879e15	+	9.64544e15i	−1.27220	+	2.20352i
$699$		0			0
$700$	−1.11990e15	−	1.93973e15i	−0.251849	−	0.436216i
$701$	4.71267e15			1.05152			0.525761	−	0.850632i	$-0.323781\pi$
$701$	4.71267e15			1.05152			0.525761	+	0.850632i	$0.323781\pi$
$702$		0			0
$703$	−1.29700e16			−2.84896
$704$	−2.97092e15	−	5.14579e15i	−0.647503	−	1.12151i
$705$		0			0
$706$	−5.62559e15	+	9.74381e15i	−1.20710	+	2.09075i
$707$	−1.29234e14	+	2.23839e14i	−0.0275150	+	0.0476573i
$708$		0			0
$709$	−4.33353e14	−	7.50589e14i	−0.0908422	−	0.157343i	0.817024	−	0.576604i	$-0.195623\pi$
$709$	−4.33353e14	−	7.50589e14i	−0.0908422	−	0.157343i	−0.907866	+	0.419261i	$0.862289\pi$
$710$	−6.21215e15			−1.29217
$711$		0			0
$712$	−3.94991e15			−0.808997
$713$	−3.89986e14	−	6.75475e14i	−0.0792604	−	0.137283i
$714$		0			0
$715$	1.31221e15	−	2.27281e15i	0.262615	−	0.454863i
$716$	7.91806e15	−	1.37145e16i	1.57252	−	2.72369i
$717$		0			0
$718$	4.84962e15	+	8.39979e15i	0.948470	+	1.64280i
$719$	−2.62666e13			−0.00509795			−0.00254897	−	0.999997i	$-0.500811\pi$
$719$	−2.62666e13			−0.00509795			−0.00254897	+	0.999997i	$0.500811\pi$
$720$		0			0
$721$	−1.34844e15			−0.257744
$722$	1.03040e16	+	1.78470e16i	1.95457	+	3.38541i
$723$		0			0
$724$	−4.59965e15	+	7.96682e15i	−0.859335	+	1.48841i
$725$	−1.07465e14	+	1.86136e14i	−0.0199255	+	0.0345120i
$726$		0			0
$727$	2.84009e15	+	4.91918e15i	0.518672	+	0.898367i	0.999765	+	0.0216967i	$0.00690683\pi$
$727$	2.84009e15	+	4.91918e15i	0.518672	+	0.898367i	−0.481092	+	0.876670i	$0.659760\pi$
$728$	3.29823e15			0.597803
$729$		0			0
$730$	−5.85190e15			−1.04477
$731$	−1.47732e15	−	2.55880e15i	−0.261776	−	0.453410i
$732$		0			0
$733$	8.11558e14	−	1.40566e15i	0.141660	−	0.245363i	−0.786462	−	0.617639i	$-0.788089\pi$
$733$	8.11558e14	−	1.40566e15i	0.141660	−	0.245363i	0.928122	+	0.372276i	$0.121423\pi$
$734$	−6.24427e15	+	1.08154e16i	−1.08182	+	1.87376i
$735$		0			0
$736$	1.44614e14	+	2.50478e14i	0.0246820	+	0.0427506i
$737$	−3.37568e15			−0.571861
$738$		0			0
$739$	3.64794e15			0.608840			0.304420	−	0.952538i	$-0.401537\pi$
$739$	3.64794e15			0.608840			0.304420	+	0.952538i	$0.401537\pi$
$740$	−7.20357e15	−	1.24769e16i	−1.19337	−	2.06697i
$741$		0			0
$742$	4.10582e15	−	7.11149e15i	0.670160	−	1.16075i
$743$	3.38022e15	−	5.85472e15i	0.547655	−	0.948566i	−0.450780	−	0.892635i	$-0.648854\pi$
$743$	3.38022e15	−	5.85472e15i	0.547655	−	0.948566i	0.998435	−	0.0559310i	$-0.0178127\pi$
$744$		0			0
$745$	−3.71760e15	−	6.43907e15i	−0.593476	−	1.02793i
$746$	2.70861e15			0.429224
$747$		0			0
$748$	7.94007e15			1.23984
$749$	−3.13127e15	−	5.42352e15i	−0.485367	−	0.840680i
$750$		0			0
$751$	−1.32417e13	+	2.29352e13i	−0.00202266	+	0.00350335i	−0.867035	−	0.498247i	$-0.833977\pi$
$751$	−1.32417e13	+	2.29352e13i	−0.00202266	+	0.00350335i	0.865012	+	0.501751i	$0.167311\pi$
$752$	−2.97867e15	+	5.15921e15i	−0.451673	+	0.782321i
$753$		0			0
$754$	−3.21273e14	−	5.56461e14i	−0.0480100	−	0.0831558i
$755$	−3.75149e15			−0.556539
$756$		0			0
$757$	7.37364e15			1.07809			0.539045	−	0.842277i	$-0.318785\pi$
$757$	7.37364e15			1.07809			0.539045	+	0.842277i	$0.318785\pi$
$758$	−5.71351e15	−	9.89609e15i	−0.829320	−	1.43642i
$759$		0			0
$760$	−8.12351e15	+	1.40703e16i	−1.16217	+	2.01293i
$761$	3.10492e15	−	5.37787e15i	0.440996	−	0.763827i	−0.556768	−	0.830668i	$-0.687959\pi$
$761$	3.10492e15	−	5.37787e15i	0.440996	−	0.763827i	0.997764	+	0.0668412i	$0.0212921\pi$
$762$		0			0
$763$	−9.63982e14	−	1.66967e15i	−0.134953	−	0.233746i
$764$	−1.36703e16			−1.90005
$765$		0			0
$766$	5.01866e15			0.687591
$767$	2.12742e14	+	3.68480e14i	0.0289387	+	0.0501233i
$768$		0			0
$769$	4.43098e15	−	7.67468e15i	0.594162	−	1.02912i	−0.399503	−	0.916732i	$-0.630817\pi$
$769$	4.43098e15	−	7.67468e15i	0.594162	−	1.02912i	0.993665	−	0.112386i	$-0.0358494\pi$
$770$	3.70824e15	−	6.42285e15i	0.493706	−	0.855124i
$771$		0			0
$772$	9.94714e15	+	1.72290e16i	1.30558	+	2.26133i
$773$	2.95047e15			0.384507			0.192254	−	0.981345i	$-0.438420\pi$
$773$	2.95047e15			0.384507			0.192254	+	0.981345i	$0.438420\pi$
$774$		0			0
$775$	1.01830e15			0.130833
$776$	−3.03092e15	−	5.24971e15i	−0.386665	−	0.669723i
$777$		0			0
$778$	1.55571e15	−	2.69457e15i	0.195678	−	0.338924i
$779$	−8.76875e15	+	1.51879e16i	−1.09517	+	1.89689i
$780$		0			0
$781$	4.72990e15	+	8.19243e15i	0.582467	+	1.00886i
$782$	−3.68384e15			−0.450468
$783$		0			0
$784$	−4.62081e15			−0.557160
$785$	−5.72246e15	−	9.91159e15i	−0.685172	−	1.18675i
$786$		0			0
$787$	−6.77726e15	+	1.17386e16i	−0.800190	+	1.38597i	0.119301	+	0.992858i	$0.461935\pi$
$787$	−6.77726e15	+	1.17386e16i	−0.800190	+	1.38597i	−0.919491	+	0.393112i	$0.871399\pi$
$788$	1.28301e16	−	2.22225e16i	1.50431	−	2.60554i
$789$		0			0
$790$	7.79193e14	+	1.34960e15i	0.0900941	+	0.156047i
$791$	−9.98429e15			−1.14643
$792$		0			0
$793$	3.79308e15			0.429526
$794$	4.15553e15	+	7.19758e15i	0.467319	+	0.809420i
$795$		0			0
$796$	7.63921e15	−	1.32315e16i	0.847279	−	1.46753i
$797$	−7.99612e15	+	1.38497e16i	−0.880762	+	1.52553i	−0.0302677	+	0.999542i	$0.509636\pi$
$797$	−7.99612e15	+	1.38497e16i	−0.880762	+	1.52553i	−0.850495	+	0.525983i	$0.823697\pi$
$798$		0			0
$799$	2.39923e15	+	4.15559e15i	0.260654	+	0.451466i
$800$	−3.77604e14			−0.0407419
$801$		0			0
$802$	2.66327e15			0.283437
$803$	4.45561e15	+	7.71733e15i	0.470946	+	0.815703i
$804$		0			0
$805$	−1.14132e15	+	1.97682e15i	−0.118995	+	0.206105i
$806$	−1.52213e15	+	2.63640e15i	−0.157619	+	0.273004i
$807$		0			0
$808$	−7.21884e14	−	1.25034e15i	−0.0737403	−	0.127722i
$809$	−9.45859e15			−0.959643			−0.479821	−	0.877366i	$-0.659299\pi$
$809$	−9.45859e15			−0.959643			−0.479821	+	0.877366i	$0.659299\pi$
$810$		0			0
$811$	−1.07996e16			−1.08092			−0.540461	−	0.841369i	$-0.681750\pi$
$811$	−1.07996e16			−1.08092			−0.540461	+	0.841369i	$0.681750\pi$
$812$	−6.02282e14	−	1.04318e15i	−0.0598745	−	0.103706i
$813$		0			0
$814$	−1.65358e16	+	2.86409e16i	−1.62178	+	2.80900i
$815$	4.39171e14	−	7.60666e14i	0.0427825	−	0.0741015i
$816$		0			0
$817$	−9.34545e15	−	1.61868e16i	−0.898212	−	1.55575i
$818$	−4.16012e15			−0.397158
$819$		0			0
$820$	−1.94807e16			−1.83497
$821$	−5.52054e15	−	9.56186e15i	−0.516529	−	0.894654i	−0.999816	−	0.0191922i	$-0.993891\pi$
$821$	−5.52054e15	−	9.56186e15i	−0.516529	−	0.894654i	0.483287	−	0.875462i	$-0.339443\pi$
$822$		0			0
$823$	−6.30518e15	+	1.09209e16i	−0.582101	+	1.00823i	0.413129	+	0.910672i	$0.364436\pi$
$823$	−6.30518e15	+	1.09209e16i	−0.582101	+	1.00823i	−0.995230	+	0.0975557i	$0.968898\pi$
$824$	3.76612e15	−	6.52311e15i	0.345378	−	0.598212i
$825$		0			0
$826$	6.01197e14	+	1.04130e15i	0.0544035	+	0.0942296i
$827$	7.86172e14			0.0706704			0.0353352	−	0.999376i	$-0.488750\pi$
$827$	7.86172e14			0.0706704			0.0353352	+	0.999376i	$0.488750\pi$
$828$		0			0
$829$	−5.92589e15			−0.525659			−0.262829	−	0.964842i	$-0.584656\pi$
$829$	−5.92589e15			−0.525659			−0.262829	+	0.964842i	$0.584656\pi$
$830$	−1.83638e15	−	3.18070e15i	−0.161820	−	0.280281i
$831$		0			0
$832$	3.56888e15	−	6.18149e15i	0.310352	−	0.537545i
$833$	−1.86096e15	+	3.22328e15i	−0.160764	+	0.278452i
$834$		0			0
$835$	−2.36533e13	−	4.09687e13i	−0.00201658	−	0.00349283i
$836$	5.02283e16			4.25416
$837$		0			0
$838$	−7.90044e15			−0.660403
$839$	1.05104e16	+	1.82046e16i	0.872831	+	1.51179i	0.859055	+	0.511883i	$0.171052\pi$
$839$	1.05104e16	+	1.82046e16i	0.872831	+	1.51179i	0.0137758	+	0.999905i	$0.495615\pi$
$840$		0			0
$841$	6.04246e15	−	1.04658e16i	0.495263	−	0.857821i
$842$	−6.15921e15	+	1.06681e16i	−0.501543	+	0.868699i
$843$		0			0
$844$	−3.62219e14	−	6.27381e14i	−0.0291130	−	0.0504252i
$845$	−6.47126e15			−0.516746
$846$		0			0
$847$	−3.37348e15			−0.265901
$848$	7.26108e15	+	1.25766e16i	0.568623	+	0.984883i
$849$		0			0
$850$	2.40474e15	−	4.16513e15i	0.185893	−	0.321977i
$851$	5.08938e15	−	8.81506e15i	0.390888	−	0.677037i
$852$		0			0
$853$	9.91891e15	+	1.71801e16i	0.752046	+	1.30258i	0.946829	+	0.321736i	$0.104266\pi$
$853$	9.91891e15	+	1.71801e16i	0.752046	+	1.30258i	−0.194783	+	0.980846i	$0.562400\pi$
$854$	1.07190e16			0.807491
$855$		0			0
$856$	3.49818e16			2.60157
$857$	3.98319e15	+	6.89909e15i	0.294332	+	0.509797i	0.974829	−	0.222953i	$-0.0715696\pi$
$857$	3.98319e15	+	6.89909e15i	0.294332	+	0.509797i	−0.680498	+	0.732750i	$0.738236\pi$
$858$		0			0
$859$	7.98745e15	−	1.38347e16i	0.582701	−	1.00927i	−0.412457	−	0.910977i	$-0.635329\pi$
$859$	7.98745e15	−	1.38347e16i	0.582701	−	1.00927i	0.995158	−	0.0982902i	$-0.0313373\pi$
$860$	1.03809e16	−	1.79803e16i	0.752481	−	1.30334i
$861$		0			0
$862$	−2.00137e16	−	3.46647e16i	−1.43231	−	2.48083i
$863$	4.02926e15			0.286527			0.143264	−	0.989685i	$-0.454240\pi$
$863$	4.02926e15			0.286527			0.143264	+	0.989685i	$0.454240\pi$
$864$		0			0
$865$	3.92467e15			0.275559
$866$	−2.92207e15	−	5.06117e15i	−0.203865	−	0.353104i
$867$		0			0
$868$	−2.85350e15	+	4.94240e15i	−0.196571	+	0.340471i
$869$	1.18655e15	−	2.05516e15i	0.0812225	−	0.140682i
$870$		0			0
$871$	−2.02756e15	−	3.51183e15i	−0.137048	−	0.237374i
$872$	1.07694e16			0.723352
$873$		0			0
$874$	−2.33037e16			−1.54565
$875$	−5.12949e15	−	8.88454e15i	−0.338088	−	0.585586i
$876$		0			0
$877$	−4.88479e15	+	8.46070e15i	−0.317942	+	0.550692i	−0.980058	−	0.198709i	$-0.936325\pi$
$877$	−4.88479e15	+	8.46070e15i	−0.317942	+	0.550692i	0.662116	+	0.749401i	$0.269658\pi$
$878$	−1.43651e16	+	2.48810e16i	−0.929155	+	1.60934i
$879$		0			0
$880$	6.55796e15	+	1.13587e16i	0.418903	+	0.725562i
$881$	−1.62583e16			−1.03207			−0.516033	−	0.856569i	$-0.672592\pi$
$881$	−1.62583e16			−1.03207			−0.516033	+	0.856569i	$0.672592\pi$
$882$		0			0
$883$	1.66061e16			1.04108			0.520540	−	0.853837i	$-0.325731\pi$
$883$	1.66061e16			1.04108			0.520540	+	0.853837i	$0.325731\pi$
$884$	4.76909e15	+	8.26031e15i	0.297131	+	0.514646i
$885$		0			0
$886$	4.33867e15	−	7.51479e15i	0.266975	−	0.462414i
$887$	−9.56571e15	+	1.65683e16i	−0.584975	+	1.01321i	0.409904	+	0.912129i	$0.365562\pi$
$887$	−9.56571e15	+	1.65683e16i	−0.584975	+	1.01321i	−0.994879	+	0.101077i	$0.967771\pi$
$888$		0			0
$889$	3.47379e15	+	6.01678e15i	0.209819	+	0.363416i
$890$	−1.06695e16			−0.640472
$891$		0			0
$892$	8.98286e15			0.532608
$893$	1.51773e16	+	2.62879e16i	0.894361	+	1.54908i
$894$		0			0
$895$	1.05352e16	−	1.82475e16i	0.613218	−	1.06212i
$896$	9.54855e15	−	1.65386e16i	0.552387	−	0.956762i
$897$		0			0
$898$	3.44493e15	+	5.96679e15i	0.196861	+	0.340973i
$899$	5.47641e14			0.0311041
$900$		0			0
$901$	1.16972e16			0.656287
$902$	2.23590e16	+	3.87270e16i	1.24686	+	2.15962i
$903$		0			0
$904$	2.78855e16	−	4.82991e16i	1.53622	−	2.66080i
$905$	−6.11994e15	+	1.06001e16i	−0.335105	+	0.580418i
$906$		0			0
$907$	5.36258e15	+	9.28827e15i	0.290091	+	0.502452i	0.973831	−	0.227274i	$-0.0729812\pi$
$907$	5.36258e15	+	9.28827e15i	0.290091	+	0.502452i	−0.683740	+	0.729726i	$0.739648\pi$
$908$	1.67836e15			0.0902430
$909$		0			0
$910$	8.90919e15			0.473272
$911$	−1.41124e16	−	2.44435e16i	−0.745162	−	1.29066i	−0.950119	−	0.311888i	$-0.899039\pi$
$911$	−1.41124e16	−	2.44435e16i	−0.745162	−	1.29066i	0.204957	−	0.978771i	$-0.434295\pi$
$912$		0			0
$913$	−2.79642e15	+	4.84354e15i	−0.145886	+	0.252681i
$914$	−3.67417e14	+	6.36384e14i	−0.0190526	+	0.0330001i
$915$		0			0
$916$	−3.65758e16	−	6.33511e16i	−1.87400	−	3.24586i
$917$	−2.71748e15			−0.138399
$918$		0			0
$919$	1.83551e16			0.923679			0.461839	−	0.886964i	$-0.347190\pi$
$919$	1.83551e16			0.923679			0.461839	+	0.886964i	$0.347190\pi$
$920$	−6.37525e15	−	1.10423e16i	−0.318907	−	0.552364i
$921$		0			0
$922$	2.71882e16	−	4.70914e16i	1.34388	−	2.32767i
$923$	−5.68189e15	+	9.84133e15i	−0.279180	+	0.483553i
$924$		0			0
$925$	6.64449e15	+	1.15086e16i	0.322613	+	0.558783i
$926$	1.46594e16			0.707549
$927$		0			0
$928$	−2.03075e14			−0.00968596
$929$	−5.50625e15	−	9.53711e15i	−0.261078	−	0.452200i	0.705451	−	0.708759i	$-0.250745\pi$
$929$	−5.50625e15	−	9.53711e15i	−0.261078	−	0.452200i	−0.966529	+	0.256559i	$0.917411\pi$
$930$		0			0
$931$	−1.17723e16	+	2.03902e16i	−0.551617	+	0.955429i
$932$	−3.78659e13	+	6.55856e13i	−0.00176385	+	0.00305507i
$933$		0			0
$934$	−1.24803e16	−	2.16164e16i	−0.574534	−	0.995122i
$935$	1.05645e16			0.483486
$936$		0			0
$937$	8.36357e15			0.378289			0.189145	−	0.981949i	$-0.439429\pi$
$937$	8.36357e15			0.378289			0.189145	+	0.981949i	$0.439429\pi$
$938$	−5.72976e15	−	9.92424e15i	−0.257645	−	0.446254i
$939$		0			0
$940$	−1.68590e16	+	2.92007e16i	−0.749255	+	1.29775i
$941$	1.11471e16	−	1.93073e16i	0.492514	−	0.853059i	−0.507449	−	0.861682i	$-0.669411\pi$
$941$	1.11471e16	−	1.93073e16i	0.492514	−	0.853059i	0.999963	+	0.00862287i	$0.00274478\pi$
$942$		0			0
$943$	−6.88163e15	−	1.19193e16i	−0.300523	−	0.520520i
$944$	−2.12642e15			−0.0923214
$945$		0			0
$946$	−4.76590e16			−2.04524
$947$	−1.89019e16	−	3.27391e16i	−0.806457	−	1.39682i	−0.915303	−	0.402765i	$-0.868049\pi$
$947$	−1.89019e16	−	3.27391e16i	−0.806457	−	1.39682i	0.108847	−	0.994059i	$-0.465284\pi$
$948$		0			0
$949$	−5.35239e15	+	9.27061e15i	−0.225727	+	0.390971i
$950$	1.52122e16	−	2.63483e16i	0.637841	−	1.10477i
$951$		0			0
$952$	6.63842e15	+	1.14981e16i	0.275145	+	0.476565i
$953$	−4.79568e15			−0.197624			−0.0988119	−	0.995106i	$-0.531504\pi$
$953$	−4.79568e15			−0.197624			−0.0988119	+	0.995106i	$0.531504\pi$
$954$		0			0
$955$	−1.81887e16			−0.740939
$956$	−3.55677e16	−	6.16051e16i	−1.44058	−	2.49516i
$957$		0			0
$958$	5.86491e15	−	1.01583e16i	0.234829	−	0.406735i
$959$	2.15160e15	−	3.72669e15i	0.0856564	−	0.148361i
$960$		0			0
$961$	1.14069e16	+	1.97574e16i	0.448942	+	0.777590i
$962$	−3.97280e16			−1.55466
$963$		0			0
$964$	−3.59251e15			−0.138987
$965$	1.32349e16	+	2.29236e16i	0.509121	+	0.881824i
$966$		0			0
$967$	−1.68710e16	+	2.92214e16i	−0.641645	+	1.11136i	0.343421	+	0.939182i	$0.388414\pi$
$967$	−1.68710e16	+	2.92214e16i	−0.641645	+	1.11136i	−0.985066	+	0.172180i	$0.944919\pi$
$968$	9.42193e15	−	1.63193e16i	0.356308	−	0.617143i
$969$		0			0
$970$	−8.18714e15	−	1.41805e16i	−0.306117	−	0.530211i
$971$	−3.58587e16			−1.33318			−0.666590	−	0.745425i	$-0.732247\pi$
$971$	−3.58587e16			−1.33318			−0.666590	+	0.745425i	$0.732247\pi$
$972$		0			0
$973$	3.12651e16			1.14932
$974$	6.88530e15	+	1.19257e16i	0.251680	+	0.435923i
$975$		0			0
$976$	−9.47823e15	+	1.64168e16i	−0.342573	+	0.593354i
$977$	−6.00117e15	+	1.03943e16i	−0.215683	+	0.373574i	−0.953484	−	0.301445i	$-0.902531\pi$
$977$	−6.00117e15	+	1.03943e16i	−0.215683	+	0.373574i	0.737801	+	0.675019i	$0.235864\pi$
$978$		0			0
$979$	8.12372e15	+	1.40707e16i	0.288702	+	0.500047i
$980$	−2.61534e16			−0.924240
$981$		0			0
$982$	−6.71547e16			−2.34673
$983$	−2.21343e15	−	3.83378e15i	−0.0769170	−	0.133224i	0.825001	−	0.565131i	$-0.191174\pi$
$983$	−2.21343e15	−	3.83378e15i	−0.0769170	−	0.133224i	−0.901918	+	0.431907i	$0.857841\pi$
$984$		0			0
$985$	1.70708e16	−	2.95675e16i	0.586618	−	1.01605i
$986$	1.29327e15	−	2.24000e15i	0.0441942	−	0.0765466i
$987$		0			0
$988$	3.01689e16	+	5.22541e16i	1.01952	+	1.76586i
$989$	1.46684e16			0.492951
$990$		0			0
$991$	−3.79167e16			−1.26016			−0.630080	−	0.776530i	$-0.716978\pi$
$991$	−3.79167e16			−1.26016			−0.630080	+	0.776530i	$0.716978\pi$
$992$	4.81065e14	+	8.33229e14i	0.0158997	+	0.0275391i
$993$		0			0
$994$	−1.60567e16	+	2.78111e16i	−0.524846	+	0.909060i
$995$	1.01642e16	−	1.76048e16i	0.330404	−	0.572276i
$996$		0			0
$997$	−2.88001e13	−	4.98833e13i	−0.000925915	−	0.00160373i	0.865562	−	0.500802i	$-0.166961\pi$
$997$	−2.88001e13	−	4.98833e13i	−0.000925915	−	0.00160373i	−0.866488	+	0.499198i	$0.833628\pi$
$998$	−4.68943e16			−1.49935
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.12.c.e.28.1		2
3.2	odd	2		81.12.c.a.28.1		2
9.2	odd	6		81.12.c.a.55.1		2
9.4	even	3		9.12.a.a.1.1		1
9.5	odd	6		3.12.a.a.1.1	✓	1
9.7	even	3	inner	81.12.c.e.55.1		2
36.23	even	6		48.12.a.f.1.1		1
36.31	odd	6		144.12.a.l.1.1		1
45.4	even	6		225.12.a.f.1.1		1
45.13	odd	12		225.12.b.a.199.2		2
45.14	odd	6		75.12.a.a.1.1		1
45.22	odd	12		225.12.b.a.199.1		2
45.23	even	12		75.12.b.a.49.1		2
45.32	even	12		75.12.b.a.49.2		2
63.41	even	6		147.12.a.c.1.1		1
72.5	odd	6		192.12.a.q.1.1		1
72.59	even	6		192.12.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.12.a.a.1.1	✓	1	9.5	odd	6
9.12.a.a.1.1		1	9.4	even	3
48.12.a.f.1.1		1	36.23	even	6
75.12.a.a.1.1		1	45.14	odd	6
75.12.b.a.49.1		2	45.23	even	12
75.12.b.a.49.2		2	45.32	even	12
81.12.c.a.28.1		2	3.2	odd	2
81.12.c.a.55.1		2	9.2	odd	6
81.12.c.e.28.1		2	1.1	even	1	trivial
81.12.c.e.55.1		2	9.7	even	3	inner
144.12.a.l.1.1		1	36.31	odd	6
147.12.a.c.1.1		1	63.41	even	6
192.12.a.g.1.1		1	72.59	even	6
192.12.a.q.1.1		1	72.5	odd	6
225.12.a.f.1.1		1	45.4	even	6
225.12.b.a.199.1		2	45.22	odd	12
225.12.b.a.199.2		2	45.13	odd	12

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(39.0000 + 67.5500i) q^{2} +(-2018.00 + 3495.28i) q^{4} +(-2685.00 + 4650.56i) q^{5} +(13880.0 + 24040.9i) q^{7} -155064. q^{8} +O(q^{10})\)	\(q+(39.0000 + 67.5500i) q^{2} +(-2018.00 + 3495.28i) q^{4} +(-2685.00 + 4650.56i) q^{5} +(13880.0 + 24040.9i) q^{7} -155064. q^{8} -418860. q^{10} +(318918. + 552382. i) q^{11} +(-383107. + 663561. i) q^{13} +(-1.08264e6 + 1.87519e6i) q^{14} +(-1.91463e6 - 3.31624e6i) q^{16} -3.08435e6 q^{17} -1.95114e7 q^{19} +(-1.08367e7 - 1.87696e7i) q^{20} +(-2.48756e7 + 4.30858e7i) q^{22} +(7.65618e6 - 1.32609e7i) q^{23} +(9.99561e6 + 1.73129e7i) q^{25} -5.97647e7 q^{26} -1.12039e8 q^{28} +(5.37563e6 + 9.31087e6i) q^{29} +(2.54687e7 - 4.41131e7i) q^{31} +(-9.44424e6 + 1.63579e7i) q^{32} +(-1.20290e8 - 2.08348e8i) q^{34} -1.49071e8 q^{35} +6.64741e8 q^{37} +(-7.60945e8 - 1.31799e9i) q^{38} +(4.16347e8 - 7.21134e8i) q^{40} +(4.49417e8 - 7.78413e8i) q^{41} +(4.78974e8 + 8.29607e8i) q^{43} -2.57431e9 q^{44} +1.19436e9 q^{46} +(-7.77871e8 - 1.34731e9i) q^{47} +(6.03355e8 - 1.04504e9i) q^{49} +(-7.79658e8 + 1.35041e9i) q^{50} +(-1.54622e9 - 2.67813e9i) q^{52} -3.79242e9 q^{53} -3.42518e9 q^{55} +(-2.15229e9 - 3.72787e9i) q^{56} +(-4.19299e8 + 7.26248e8i) q^{58} +(2.77653e8 - 4.80910e8i) q^{59} +(-2.47521e9 - 4.28719e9i) q^{61} +3.97312e9 q^{62} -9.31563e9 q^{64} +(-2.05728e9 - 3.56332e9i) q^{65} +(-2.64620e9 + 4.58335e9i) q^{67} +(6.22423e9 - 1.07807e10i) q^{68} +(-5.81378e9 - 1.00698e10i) q^{70} +1.48311e10 q^{71} +1.39710e10 q^{73} +(2.59249e10 + 4.49032e10i) q^{74} +(3.93740e10 - 6.81978e10i) q^{76} +(-8.85316e9 + 1.53341e10i) q^{77} +(-1.86027e9 - 3.22208e9i) q^{79} +2.05631e10 q^{80} +7.01090e10 q^{82} +(4.38423e9 + 7.59370e9i) q^{83} +(8.28149e9 - 1.43440e10i) q^{85} +(-3.73599e10 + 6.47093e10i) q^{86} +(-4.94527e10 - 8.56546e10i) q^{88} +2.54728e10 q^{89} -2.12701e10 q^{91} +(3.09003e10 + 5.35210e10i) q^{92} +(6.06739e10 - 1.05090e11i) q^{94} +(5.23881e10 - 9.07389e10i) q^{95} +(1.95462e10 + 3.38551e10i) q^{97} +9.41233e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 78 q^{2} - 4036 q^{4} - 5370 q^{5} + 27760 q^{7} - 310128 q^{8}+O(q^{10}) \) 2 * q + 78 * q^2 - 4036 * q^4 - 5370 * q^5 + 27760 * q^7 - 310128 * q^8	\( 2 q + 78 q^{2} - 4036 q^{4} - 5370 q^{5} + 27760 q^{7} - 310128 q^{8} - 837720 q^{10} + 637836 q^{11} - 766214 q^{13} - 2165280 q^{14} - 3829264 q^{16} - 6168708 q^{17} - 39022808 q^{19} - 21673320 q^{20} - 49751208 q^{22} + 15312360 q^{23} + 19991225 q^{25} - 119529384 q^{26} - 224078720 q^{28} + 10751262 q^{29} + 50937400 q^{31} - 18888480 q^{32} - 240579612 q^{34} - 298142400 q^{35} + 1329481660 q^{37} - 1521889512 q^{38} + 832693680 q^{40} + 898833450 q^{41} + 957947188 q^{43} - 5148612192 q^{44} + 2388728160 q^{46} - 1555741344 q^{47} + 1206709143 q^{49} - 1559315550 q^{50} - 3092439704 q^{52} - 7584834060 q^{53} - 6850358640 q^{55} - 4304576640 q^{56} - 838598436 q^{58} + 555306924 q^{59} - 4950420998 q^{61} + 7946234400 q^{62} - 18631268224 q^{64} - 4114569180 q^{65} - 5292399284 q^{67} + 12448452744 q^{68} - 11627553600 q^{70} + 29662172496 q^{71} + 27942010420 q^{73} + 51849784740 q^{74} + 78748026544 q^{76} - 17706327360 q^{77} - 3720542360 q^{79} + 41126295360 q^{80} + 140218018200 q^{82} + 8768454036 q^{83} + 16562980980 q^{85} - 74719880664 q^{86} - 98905401504 q^{88} + 50945538348 q^{89} - 42540201280 q^{91} + 61800684960 q^{92} + 121347824832 q^{94} + 104776239480 q^{95} + 39092494846 q^{97} + 188246626308 q^{98}+O(q^{100}) \) 2 * q + 78 * q^2 - 4036 * q^4 - 5370 * q^5 + 27760 * q^7 - 310128 * q^8 - 837720 * q^10 + 637836 * q^11 - 766214 * q^13 - 2165280 * q^14 - 3829264 * q^16 - 6168708 * q^17 - 39022808 * q^19 - 21673320 * q^20 - 49751208 * q^22 + 15312360 * q^23 + 19991225 * q^25 - 119529384 * q^26 - 224078720 * q^28 + 10751262 * q^29 + 50937400 * q^31 - 18888480 * q^32 - 240579612 * q^34 - 298142400 * q^35 + 1329481660 * q^37 - 1521889512 * q^38 + 832693680 * q^40 + 898833450 * q^41 + 957947188 * q^43 - 5148612192 * q^44 + 2388728160 * q^46 - 1555741344 * q^47 + 1206709143 * q^49 - 1559315550 * q^50 - 3092439704 * q^52 - 7584834060 * q^53 - 6850358640 * q^55 - 4304576640 * q^56 - 838598436 * q^58 + 555306924 * q^59 - 4950420998 * q^61 + 7946234400 * q^62 - 18631268224 * q^64 - 4114569180 * q^65 - 5292399284 * q^67 + 12448452744 * q^68 - 11627553600 * q^70 + 29662172496 * q^71 + 27942010420 * q^73 + 51849784740 * q^74 + 78748026544 * q^76 - 17706327360 * q^77 - 3720542360 * q^79 + 41126295360 * q^80 + 140218018200 * q^82 + 8768454036 * q^83 + 16562980980 * q^85 - 74719880664 * q^86 - 98905401504 * q^88 + 50945538348 * q^89 - 42540201280 * q^91 + 61800684960 * q^92 + 121347824832 * q^94 + 104776239480 * q^95 + 39092494846 * q^97 + 188246626308 * q^98

Introduction

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