LMFDB - Embedded newform 325.10.a.j.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.a (trivial)

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:	yes
Analytic conductor:	$167.386646753$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 7725 x^{17} + 25733 x^{16} + 24561606 x^{15} - 42570866 x^{14} + \cdots + 12\!\cdots\!08 $ x^19 - 5x^18 - 7725x^17 + 25733x^16 + 24561606x^15 - 42570866x^14 - 41459410756x^13 + 9996387424x^12 + 39961513875168x^11 + 43193073786240x^10 - 21995961932941568x^9 - 46602332877675008x^8 + 6510708601836890112x^7 + 17415084890884207104x^6 - 890933775068660526080x^5 - 2030469113646857670656x^4 + 40149910908665330221056x^3 - 21051832642683757953024x^2 - 213111133009343099633664x + 124215692984994590097408
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{6}\cdot 5^{10} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-40.2935$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+42.2935 q^{2} -17.8757 q^{3} +1276.74 q^{4} -756.026 q^{6} +10170.4 q^{7} +32343.7 q^{8} -19363.5 q^{9} +35856.7 q^{11} -22822.7 q^{12} +28561.0 q^{13} +430141. q^{14} +714238. q^{16} -303091. q^{17} -818949. q^{18} +123771. q^{19} -181802. q^{21} +1.51651e6 q^{22} +2.12421e6 q^{23} -578166. q^{24} +1.20795e6 q^{26} +697982. q^{27} +1.29849e7 q^{28} -3.35353e6 q^{29} +6.59212e6 q^{31} +1.36477e7 q^{32} -640963. q^{33} -1.28188e7 q^{34} -2.47222e7 q^{36} +1.47855e7 q^{37} +5.23470e6 q^{38} -510547. q^{39} -1.71561e7 q^{41} -7.68905e6 q^{42} -1.47264e7 q^{43} +4.57799e7 q^{44} +8.98402e7 q^{46} +4.96504e7 q^{47} -1.27675e7 q^{48} +6.30826e7 q^{49} +5.41795e6 q^{51} +3.64651e7 q^{52} -6.53569e7 q^{53} +2.95201e7 q^{54} +3.28947e8 q^{56} -2.21249e6 q^{57} -1.41833e8 q^{58} -4.08231e7 q^{59} -1.53242e8 q^{61} +2.78804e8 q^{62} -1.96933e8 q^{63} +2.11519e8 q^{64} -2.71086e7 q^{66} +2.35390e8 q^{67} -3.86969e8 q^{68} -3.79716e7 q^{69} -1.27603e6 q^{71} -6.26287e8 q^{72} +1.91725e8 q^{73} +6.25330e8 q^{74} +1.58024e8 q^{76} +3.64676e8 q^{77} -2.15928e7 q^{78} -4.06694e8 q^{79} +3.68654e8 q^{81} -7.25593e8 q^{82} -1.84283e8 q^{83} -2.32115e8 q^{84} -6.22830e8 q^{86} +5.99466e7 q^{87} +1.15974e9 q^{88} +5.16484e7 q^{89} +2.90476e8 q^{91} +2.71207e9 q^{92} -1.17839e8 q^{93} +2.09989e9 q^{94} -2.43961e8 q^{96} +1.54370e7 q^{97} +2.66799e9 q^{98} -6.94310e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 33 q^{2} - 73 q^{3} + 5803 q^{4} - 3549 q^{6} - 1066 q^{7} + 20349 q^{8} + 113200 q^{9} + 146427 q^{11} - 135219 q^{12} + 542659 q^{13} - 17870 q^{14} + 2549547 q^{16} - 605113 q^{17} + 1793704 q^{18}+ \cdots + 2637491156 q^{99}+O(q^{100}) $ 19 * q + 33 * q^2 - 73 * q^3 + 5803 * q^4 - 3549 * q^6 - 1066 * q^7 + 20349 * q^8 + 113200 * q^9 + 146427 * q^11 - 135219 * q^12 + 542659 * q^13 - 17870 * q^14 + 2549547 * q^16 - 605113 * q^17 + 1793704 * q^18 + 1053529 * q^19 + 3299072 * q^21 + 649675 * q^22 + 1123254 * q^23 + 1379083 * q^24 + 942513 * q^26 + 7258805 * q^27 - 17353598 * q^28 - 3588820 * q^29 + 7130168 * q^31 + 30008261 * q^32 - 37563217 * q^33 - 1511147 * q^34 + 70702660 * q^36 + 27070972 * q^37 + 20491605 * q^38 - 2084953 * q^39 + 20503041 * q^41 + 23549976 * q^42 - 8670194 * q^43 + 104623747 * q^44 + 15807622 * q^46 + 28326738 * q^47 - 293352359 * q^48 + 140788329 * q^49 + 212022459 * q^51 + 165739483 * q^52 + 49738834 * q^53 - 282194663 * q^54 + 246272386 * q^56 + 86542887 * q^57 + 221230676 * q^58 + 174278586 * q^59 + 73706348 * q^61 + 109597172 * q^62 - 389044938 * q^63 + 533531111 * q^64 + 910842685 * q^66 + 642771579 * q^67 - 1492314643 * q^68 + 672264794 * q^69 + 843585844 * q^71 + 875456724 * q^72 - 59348471 * q^73 - 252835516 * q^74 + 786885077 * q^76 - 82517582 * q^77 - 101362989 * q^78 + 521000922 * q^79 + 1182486371 * q^81 + 1010685747 * q^82 - 529236749 * q^83 + 4389156140 * q^84 + 2617322430 * q^86 - 752432206 * q^87 - 1484178139 * q^88 + 2211890531 * q^89 - 30446026 * q^91 + 439634668 * q^92 + 2323400966 * q^93 - 2064823418 * q^94 - 1372415809 * q^96 - 630790806 * q^97 + 1028814699 * q^98 + 2637491156 * q^99

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 $

$2$	42.2935	1.86913	0.934564	−	0.355795i	$-0.115790\pi$
$2$	42.2935	1.86913	0.934564	+	0.355795i	$0.115790\pi$
$3$	−17.8757	−0.127414	−0.0637069	−	0.997969i	$-0.520292\pi$
$3$	−17.8757	−0.127414	−0.0637069	+	0.997969i	$0.520292\pi$
$4$	1276.74	2.49364
$5$	0	0
$5$	0	0
$6$	−756.026	−0.238153
$7$	10170.4	1.60101	0.800507	−	0.599324i	$-0.204564\pi$
$7$	10170.4	1.60101	0.800507	+	0.599324i	$0.204564\pi$
$8$	32343.7	2.79181
$9$	−19363.5	−0.983766
$10$	0	0
$11$	35856.7	0.738420	0.369210	−	0.929346i	$-0.379628\pi$
$11$	35856.7	0.738420	0.369210	+	0.929346i	$0.379628\pi$
$12$	−22822.7	−0.317724
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	430141.	2.99250
$15$	0	0
$16$	714238.	2.72460
$17$	−303091.	−0.880141	−0.440070	−	0.897963i	$-0.645047\pi$
$17$	−303091.	−0.880141	−0.440070	+	0.897963i	$0.645047\pi$
$18$	−818949.	−1.83878
$19$	123771.	0.217885	0.108942	−	0.994048i	$-0.465254\pi$
$19$	123771.	0.217885	0.108942	+	0.994048i	$0.465254\pi$
$20$	0	0
$21$	−181802.	−0.203991
$22$	1.51651e6	1.38020
$23$	2.12421e6	1.58278	0.791392	−	0.611310i	$-0.209357\pi$
$23$	2.12421e6	1.58278	0.791392	+	0.611310i	$0.209357\pi$
$24$	−578166.	−0.355715
$25$	0	0
$26$	1.20795e6	0.518403
$27$	697982.	0.252759
$28$	1.29849e7	3.99235
$29$	−3.35353e6	−0.880463	−0.440231	−	0.897884i	$-0.645104\pi$
$29$	−3.35353e6	−0.880463	−0.440231	+	0.897884i	$0.645104\pi$
$30$	0	0
$31$	6.59212e6	1.28203	0.641014	−	0.767529i	$-0.278514\pi$
$31$	6.59212e6	1.28203	0.641014	+	0.767529i	$0.278514\pi$
$32$	1.36477e7	2.30083
$33$	−640963.	−0.0940850
$34$	−1.28188e7	−1.64510
$35$	0	0
$36$	−2.47222e7	−2.45316
$37$	1.47855e7	1.29696	0.648481	−	0.761231i	$-0.275405\pi$
$37$	1.47855e7	1.29696	0.648481	+	0.761231i	$0.275405\pi$
$38$	5.23470e6	0.407255
$39$	−510547.	−0.0353383
$40$	0	0
$41$	−1.71561e7	−0.948182	−0.474091	−	0.880476i	$-0.657223\pi$
$41$	−1.71561e7	−0.948182	−0.474091	+	0.880476i	$0.657223\pi$
$42$	−7.68905e6	−0.381286
$43$	−1.47264e7	−0.656882	−0.328441	−	0.944524i	$-0.606523\pi$
$43$	−1.47264e7	−0.656882	−0.328441	+	0.944524i	$0.606523\pi$
$44$	4.57799e7	1.84135
$45$	0	0
$46$	8.98402e7	2.95842
$47$	4.96504e7	1.48417	0.742084	−	0.670307i	$-0.233838\pi$
$47$	4.96504e7	1.48417	0.742084	+	0.670307i	$0.233838\pi$
$48$	−1.27675e7	−0.347152
$49$	6.30826e7	1.56325
$50$	0	0
$51$	5.41795e6	0.112142
$52$	3.64651e7	0.691612
$53$	−6.53569e7	−1.13776	−0.568879	−	0.822421i	$-0.692623\pi$
$53$	−6.53569e7	−1.13776	−0.568879	+	0.822421i	$0.692623\pi$
$54$	2.95201e7	0.472440
$55$	0	0
$56$	3.28947e8	4.46972
$57$	−2.21249e6	−0.0277615
$58$	−1.41833e8	−1.64570
$59$	−4.08231e7	−0.438603	−0.219302	−	0.975657i	$-0.570378\pi$
$59$	−4.08231e7	−0.438603	−0.219302	+	0.975657i	$0.570378\pi$
$60$	0	0
$61$	−1.53242e8	−1.41708	−0.708541	−	0.705670i	$-0.750646\pi$
$61$	−1.53242e8	−1.41708	−0.708541	+	0.705670i	$0.750646\pi$
$62$	2.78804e8	2.39628
$63$	−1.96933e8	−1.57502
$64$	2.11519e8	1.57594
$65$	0	0
$66$	−2.71086e7	−0.175857
$67$	2.35390e8	1.42709	0.713544	−	0.700611i	$-0.247089\pi$
$67$	2.35390e8	1.42709	0.713544	+	0.700611i	$0.247089\pi$
$68$	−3.86969e8	−2.19476
$69$	−3.79716e7	−0.201669
$70$	0	0
$71$	−1.27603e6	−0.00595932	−0.00297966	−	0.999996i	$-0.500948\pi$
$71$	−1.27603e6	−0.00595932	−0.00297966	+	0.999996i	$0.500948\pi$
$72$	−6.26287e8	−2.74648
$73$	1.91725e8	0.790181	0.395091	−	0.918642i	$-0.370713\pi$
$73$	1.91725e8	0.790181	0.395091	+	0.918642i	$0.370713\pi$
$74$	6.25330e8	2.42419
$75$	0	0
$76$	1.58024e8	0.543326
$77$	3.64676e8	1.18222
$78$	−2.15928e7	−0.0660517
$79$	−4.06694e8	−1.17475	−0.587375	−	0.809315i	$-0.699839\pi$
$79$	−4.06694e8	−1.17475	−0.587375	+	0.809315i	$0.699839\pi$
$80$	0	0
$81$	3.68654e8	0.951561
$82$	−7.25593e8	−1.77227
$83$	−1.84283e8	−0.426220	−0.213110	−	0.977028i	$-0.568359\pi$
$83$	−1.84283e8	−0.426220	−0.213110	+	0.977028i	$0.568359\pi$
$84$	−2.32115e8	−0.508681
$85$	0	0
$86$	−6.22830e8	−1.22780
$87$	5.99466e7	0.112183
$88$	1.15974e9	2.06153
$89$	5.16484e7	0.0872573	0.0436287	−	0.999048i	$-0.486108\pi$
$89$	5.16484e7	0.0872573	0.0436287	+	0.999048i	$0.486108\pi$
$90$	0	0
$91$	2.90476e8	0.444041
$92$	2.71207e9	3.94689
$93$	−1.17839e8	−0.163348
$94$	2.09989e9	2.77410
$95$	0	0
$96$	−2.43961e8	−0.293157
$97$	1.54370e7	0.0177047	0.00885237	−	0.999961i	$-0.497182\pi$
$97$	1.54370e7	0.0177047	0.00885237	+	0.999961i	$0.497182\pi$
$98$	2.66799e9	2.92191
$99$	−6.94310e8	−0.726433
$100$	0	0
$101$	1.28995e9	1.23347	0.616734	−	0.787172i	$-0.288455\pi$
$101$	1.28995e9	1.23347	0.616734	+	0.787172i	$0.288455\pi$
$102$	2.29144e8	0.209608
$103$	−3.76841e8	−0.329906	−0.164953	−	0.986301i	$-0.552747\pi$
$103$	−3.76841e8	−0.329906	−0.164953	+	0.986301i	$0.552747\pi$
$104$	9.23770e8	0.774308
$105$	0	0
$106$	−2.76418e9	−2.12662
$107$	2.53670e9	1.87086	0.935431	−	0.353509i	$-0.115012\pi$
$107$	2.53670e9	1.87086	0.935431	+	0.353509i	$0.115012\pi$
$108$	8.91144e8	0.630291
$109$	−8.27423e8	−0.561447	−0.280723	−	0.959789i	$-0.590574\pi$
$109$	−8.27423e8	−0.561447	−0.280723	+	0.959789i	$0.590574\pi$
$110$	0	0
$111$	−2.64300e8	−0.165251
$112$	7.26406e9	4.36213
$113$	2.48830e9	1.43565	0.717826	−	0.696222i	$-0.245137\pi$
$113$	2.48830e9	1.43565	0.717826	+	0.696222i	$0.245137\pi$
$114$	−9.35739e7	−0.0518899
$115$	0	0
$116$	−4.28160e9	−2.19556
$117$	−5.53040e8	−0.272848
$118$	−1.72655e9	−0.819806
$119$	−3.08254e9	−1.40912
$120$	0	0
$121$	−1.07224e9	−0.454735
$122$	−6.48117e9	−2.64871
$123$	3.06677e8	0.120812
$124$	8.41645e9	3.19692
$125$	0	0
$126$	−8.32901e9	−2.94392
$127$	−4.91507e9	−1.67654	−0.838268	−	0.545258i	$-0.816432\pi$
$127$	−4.91507e9	−1.67654	−0.838268	+	0.545258i	$0.816432\pi$
$128$	1.95827e9	0.644803
$129$	2.63244e8	0.0836959
$130$	0	0
$131$	−4.26467e9	−1.26522	−0.632608	−	0.774472i	$-0.718016\pi$
$131$	−4.26467e9	−1.26522	−0.632608	+	0.774472i	$0.718016\pi$
$132$	−8.18346e8	−0.234614
$133$	1.25879e9	0.348837
$134$	9.95546e9	2.66741
$135$	0	0
$136$	−9.80308e9	−2.45718
$137$	3.27883e9	0.795199	0.397599	−	0.917559i	$-0.369843\pi$
$137$	3.27883e9	0.795199	0.397599	+	0.917559i	$0.369843\pi$
$138$	−1.60595e9	−0.376944
$139$	6.78731e9	1.54216	0.771082	−	0.636735i	$-0.219716\pi$
$139$	6.78731e9	1.54216	0.771082	+	0.636735i	$0.219716\pi$
$140$	0	0
$141$	−8.87535e8	−0.189103
$142$	−5.39677e7	−0.0111387
$143$	1.02410e9	0.204801
$144$	−1.38301e10	−2.68037
$145$	0	0
$146$	8.10875e9	1.47695
$147$	−1.12764e9	−0.199179
$148$	1.88773e10	3.23416
$149$	2.68819e9	0.446809	0.223404	−	0.974726i	$-0.428283\pi$
$149$	2.68819e9	0.446809	0.223404	+	0.974726i	$0.428283\pi$
$150$	0	0
$151$	−4.88103e9	−0.764038	−0.382019	−	0.924154i	$-0.624771\pi$
$151$	−4.88103e9	−0.764038	−0.382019	+	0.924154i	$0.624771\pi$
$152$	4.00321e9	0.608292
$153$	5.86888e9	0.865852
$154$	1.54234e10	2.20972
$155$	0	0
$156$	−6.51838e8	−0.0881209
$157$	9.49953e8	0.124782	0.0623912	−	0.998052i	$-0.480127\pi$
$157$	9.49953e8	0.124782	0.0623912	+	0.998052i	$0.480127\pi$
$158$	−1.72005e10	−2.19576
$159$	1.16830e9	0.144966
$160$	0	0
$161$	2.16039e10	2.53406
$162$	1.55917e10	1.77859
$163$	7.76185e9	0.861234	0.430617	−	0.902535i	$-0.358296\pi$
$163$	7.76185e9	0.861234	0.430617	+	0.902535i	$0.358296\pi$
$164$	−2.19040e10	−2.36443
$165$	0	0
$166$	−7.79398e9	−0.796659
$167$	1.78166e10	1.77255	0.886277	−	0.463155i	$-0.153283\pi$
$167$	1.78166e10	1.77255	0.886277	+	0.463155i	$0.153283\pi$
$168$	−5.88016e9	−0.569504
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	−2.39663e9	−0.214348
$172$	−1.88018e10	−1.63803
$173$	−1.43386e10	−1.21702	−0.608512	−	0.793544i	$-0.708233\pi$
$173$	−1.43386e10	−1.21702	−0.608512	+	0.793544i	$0.708233\pi$
$174$	2.53535e9	0.209685
$175$	0	0
$176$	2.56103e10	2.01190
$177$	7.29740e8	0.0558841
$178$	2.18439e9	0.163095
$179$	−6.90523e9	−0.502735	−0.251368	−	0.967892i	$-0.580880\pi$
$179$	−6.90523e9	−0.502735	−0.251368	+	0.967892i	$0.580880\pi$
$180$	0	0
$181$	−2.82582e9	−0.195700	−0.0978499	−	0.995201i	$-0.531197\pi$
$181$	−2.82582e9	−0.195700	−0.0978499	+	0.995201i	$0.531197\pi$
$182$	1.22852e10	0.829970
$183$	2.73931e9	0.180556
$184$	6.87048e10	4.41882
$185$	0	0
$186$	−4.98381e9	−0.305319
$187$	−1.08678e10	−0.649914
$188$	6.33909e10	3.70098
$189$	7.09872e9	0.404671
$190$	0	0
$191$	1.72412e10	0.937382	0.468691	−	0.883362i	$-0.344726\pi$
$191$	1.72412e10	0.937382	0.468691	+	0.883362i	$0.344726\pi$
$192$	−3.78104e9	−0.200796
$193$	3.21481e10	1.66781	0.833907	−	0.551905i	$-0.186099\pi$
$193$	3.21481e10	1.66781	0.833907	+	0.551905i	$0.186099\pi$
$194$	6.52885e8	0.0330924
$195$	0	0
$196$	8.05403e10	3.89817
$197$	1.00080e10	0.473422	0.236711	−	0.971580i	$-0.423931\pi$
$197$	1.00080e10	0.473422	0.236711	+	0.971580i	$0.423931\pi$
$198$	−2.93649e10	−1.35780
$199$	−3.12646e10	−1.41324	−0.706618	−	0.707596i	$-0.749780\pi$
$199$	−3.12646e10	−1.41324	−0.706618	+	0.707596i	$0.749780\pi$
$200$	0	0
$201$	−4.20775e9	−0.181831
$202$	5.45567e10	2.30551
$203$	−3.41066e10	−1.40963
$204$	6.91733e9	0.279642
$205$	0	0
$206$	−1.59379e10	−0.616637
$207$	−4.11320e10	−1.55709
$208$	2.03994e10	0.755669
$209$	4.43802e9	0.160891
$210$	0	0
$211$	−9.88825e9	−0.343438	−0.171719	−	0.985146i	$-0.554932\pi$
$211$	−9.88825e9	−0.343438	−0.171719	+	0.985146i	$0.554932\pi$
$212$	−8.34441e10	−2.83716
$213$	2.28098e7	0.000759301 0
$214$	1.07286e11	3.49688
$215$	0	0
$216$	2.25753e10	0.705655
$217$	6.70442e10	2.05254
$218$	−3.49947e10	−1.04942
$219$	−3.42722e9	−0.100680
$220$	0	0
$221$	−8.65657e9	−0.244107
$222$	−1.11782e10	−0.308875
$223$	−5.89227e10	−1.59555	−0.797776	−	0.602954i	$-0.793990\pi$
$223$	−5.89227e10	−1.59555	−0.797776	+	0.602954i	$0.793990\pi$
$224$	1.38802e11	3.68366
$225$	0	0
$226$	1.05239e11	2.68342
$227$	−3.17692e10	−0.794128	−0.397064	−	0.917791i	$-0.629971\pi$
$227$	−3.17692e10	−0.794128	−0.397064	+	0.917791i	$0.629971\pi$
$228$	−2.82478e9	−0.0692273
$229$	−3.69817e10	−0.888642	−0.444321	−	0.895868i	$-0.646555\pi$
$229$	−3.69817e10	−0.888642	−0.444321	+	0.895868i	$0.646555\pi$
$230$	0	0
$231$	−6.51883e9	−0.150631
$232$	−1.08466e11	−2.45808
$233$	−6.74223e10	−1.49866	−0.749328	−	0.662199i	$-0.769623\pi$
$233$	−6.74223e10	−1.49866	−0.749328	+	0.662199i	$0.769623\pi$
$234$	−2.33900e10	−0.509987
$235$	0	0
$236$	−5.21206e10	−1.09372
$237$	7.26992e9	0.149679
$238$	−1.30372e11	−2.63382
$239$	−4.01567e10	−0.796099	−0.398050	−	0.917364i	$-0.630313\pi$
$239$	−4.01567e10	−0.796099	−0.398050	+	0.917364i	$0.630313\pi$
$240$	0	0
$241$	−6.18884e10	−1.18177	−0.590884	−	0.806756i	$-0.701221\pi$
$241$	−6.18884e10	−1.18177	−0.590884	+	0.806756i	$0.701221\pi$
$242$	−4.53489e10	−0.849959
$243$	−2.03283e10	−0.374001
$244$	−1.95651e11	−3.53369
$245$	0	0
$246$	1.29705e10	0.225812
$247$	3.53502e9	0.0604304
$248$	2.13214e11	3.57917
$249$	3.29418e9	0.0543063
$250$	0	0
$251$	2.92543e10	0.465219	0.232609	−	0.972570i	$-0.425274\pi$
$251$	2.92543e10	0.465219	0.232609	+	0.972570i	$0.425274\pi$
$252$	−2.51433e11	−3.92754
$253$	7.61671e10	1.16876
$254$	−2.07876e11	−3.13366
$255$	0	0
$256$	−2.54756e10	−0.370718
$257$	−8.76039e10	−1.25263	−0.626317	−	0.779568i	$-0.715438\pi$
$257$	−8.76039e10	−1.25263	−0.626317	+	0.779568i	$0.715438\pi$
$258$	1.11335e10	0.156438
$259$	1.50374e11	2.07645
$260$	0	0
$261$	6.49359e10	0.866169
$262$	−1.80368e11	−2.36485
$263$	4.82761e10	0.622202	0.311101	−	0.950377i	$-0.399302\pi$
$263$	4.82761e10	0.622202	0.311101	+	0.950377i	$0.399302\pi$
$264$	−2.07311e10	−0.262667
$265$	0	0
$266$	5.32388e10	0.652020
$267$	−9.23250e8	−0.0111178
$268$	3.00532e11	3.55864
$269$	9.63805e10	1.12229	0.561144	−	0.827718i	$-0.310362\pi$
$269$	9.63805e10	1.12229	0.561144	+	0.827718i	$0.310362\pi$
$270$	0	0
$271$	−1.73796e10	−0.195739	−0.0978697	−	0.995199i	$-0.531203\pi$
$271$	−1.73796e10	−0.195739	−0.0978697	+	0.995199i	$0.531203\pi$
$272$	−2.16479e11	−2.39803
$273$	−5.19245e9	−0.0565770
$274$	1.38673e11	1.48633
$275$	0	0
$276$	−4.84800e10	−0.502889
$277$	−4.25024e10	−0.433764	−0.216882	−	0.976198i	$-0.569589\pi$
$277$	−4.25024e10	−0.433764	−0.216882	+	0.976198i	$0.569589\pi$
$278$	2.87059e11	2.88250
$279$	−1.27646e11	−1.26122
$280$	0	0
$281$	−8.07754e10	−0.772859	−0.386430	−	0.922319i	$-0.626292\pi$
$281$	−8.07754e10	−0.772859	−0.386430	+	0.922319i	$0.626292\pi$
$282$	−3.75370e10	−0.353459
$283$	−8.54297e10	−0.791717	−0.395859	−	0.918311i	$-0.629553\pi$
$283$	−8.54297e10	−0.791717	−0.395859	+	0.918311i	$0.629553\pi$
$284$	−1.62916e9	−0.0148604
$285$	0	0
$286$	4.33130e10	0.382799
$287$	−1.74484e11	−1.51805
$288$	−2.64266e11	−2.26347
$289$	−2.67240e10	−0.225352
$290$	0	0
$291$	−2.75947e8	−0.00225583
$292$	2.44784e11	1.97043
$293$	−5.02198e10	−0.398080	−0.199040	−	0.979991i	$-0.563782\pi$
$293$	−5.02198e10	−0.398080	−0.199040	+	0.979991i	$0.563782\pi$
$294$	−4.76920e10	−0.372291
$295$	0	0
$296$	4.78217e11	3.62087
$297$	2.50273e10	0.186643
$298$	1.13693e11	0.835143
$299$	6.06695e10	0.438985
$300$	0	0
$301$	−1.49772e11	−1.05168
$302$	−2.06436e11	−1.42809
$303$	−2.30588e10	−0.157161
$304$	8.84018e10	0.593650
$305$	0	0
$306$	2.48216e11	1.61839
$307$	1.90032e11	1.22097	0.610483	−	0.792030i	$-0.290976\pi$
$307$	1.90032e11	1.22097	0.610483	+	0.792030i	$0.290976\pi$
$308$	4.65598e11	2.94803
$309$	6.73628e9	0.0420346
$310$	0	0
$311$	−4.45118e10	−0.269807	−0.134904	−	0.990859i	$-0.543072\pi$
$311$	−4.45118e10	−0.269807	−0.134904	+	0.990859i	$0.543072\pi$
$312$	−1.65130e10	−0.0986576
$313$	−2.86916e11	−1.68968	−0.844840	−	0.535019i	$-0.820304\pi$
$313$	−2.86916e11	−1.68968	−0.844840	+	0.535019i	$0.820304\pi$
$314$	4.01769e10	0.233234
$315$	0	0
$316$	−5.19244e11	−2.92940
$317$	6.81403e10	0.378998	0.189499	−	0.981881i	$-0.439314\pi$
$317$	6.81403e10	0.378998	0.189499	+	0.981881i	$0.439314\pi$
$318$	4.94115e10	0.270961
$319$	−1.20247e11	−0.650151
$320$	0	0
$321$	−4.53452e10	−0.238374
$322$	9.13707e11	4.73648
$323$	−3.75137e10	−0.191769
$324$	4.70677e11	2.37285
$325$	0	0
$326$	3.28276e11	1.60976
$327$	1.47907e10	0.0715361
$328$	−5.54893e11	−2.64714
$329$	5.04963e11	2.37617
$330$	0	0
$331$	1.38162e11	0.632648	0.316324	−	0.948651i	$-0.397551\pi$
$331$	1.38162e11	0.632648	0.316324	+	0.948651i	$0.397551\pi$
$332$	−2.35282e11	−1.06284
$333$	−2.86298e11	−1.27591
$334$	7.53525e11	3.31313
$335$	0	0
$336$	−1.29850e11	−0.555796
$337$	−1.49223e11	−0.630232	−0.315116	−	0.949053i	$-0.602043\pi$
$337$	−1.49223e11	−0.630232	−0.315116	+	0.949053i	$0.602043\pi$
$338$	3.45001e10	0.143779
$339$	−4.44800e10	−0.182922
$340$	0	0
$341$	2.36372e11	0.946676
$342$	−1.01362e11	−0.400643
$343$	2.31162e11	0.901763
$344$	−4.76306e11	−1.83389
$345$	0	0
$346$	−6.06431e11	−2.27478
$347$	−4.69450e11	−1.73823	−0.869114	−	0.494612i	$-0.835310\pi$
$347$	−4.69450e11	−1.73823	−0.869114	+	0.494612i	$0.835310\pi$
$348$	7.65364e10	0.279744
$349$	1.76945e11	0.638446	0.319223	−	0.947680i	$-0.396578\pi$
$349$	1.76945e11	0.638446	0.319223	+	0.947680i	$0.396578\pi$
$350$	0	0
$351$	1.99351e10	0.0701028
$352$	4.89361e11	1.69898
$353$	−2.07921e11	−0.712710	−0.356355	−	0.934351i	$-0.615981\pi$
$353$	−2.07921e11	−0.712710	−0.356355	+	0.934351i	$0.615981\pi$
$354$	3.08633e10	0.104455
$355$	0	0
$356$	6.59418e10	0.217588
$357$	5.51025e10	0.179541
$358$	−2.92047e11	−0.939677
$359$	−2.60546e11	−0.827866	−0.413933	−	0.910307i	$-0.635845\pi$
$359$	−2.60546e11	−0.827866	−0.413933	+	0.910307i	$0.635845\pi$
$360$	0	0
$361$	−3.07368e11	−0.952526
$362$	−1.19514e11	−0.365788
$363$	1.91671e10	0.0579396
$364$	3.70863e11	1.10728
$365$	0	0
$366$	1.15855e11	0.337482
$367$	4.03039e11	1.15971	0.579856	−	0.814719i	$-0.303109\pi$
$367$	4.03039e11	1.15971	0.579856	+	0.814719i	$0.303109\pi$
$368$	1.51719e12	4.31246
$369$	3.32202e11	0.932789
$370$	0	0
$371$	−6.64703e11	−1.82157
$372$	−1.50450e11	−0.407332
$373$	5.77536e10	0.154486	0.0772430	−	0.997012i	$-0.475388\pi$
$373$	5.77536e10	0.154486	0.0772430	+	0.997012i	$0.475388\pi$
$374$	−4.59639e11	−1.21477
$375$	0	0
$376$	1.60588e12	4.14351
$377$	−9.57801e10	−0.244196
$378$	3.00230e11	0.756382
$379$	−4.67395e11	−1.16361	−0.581805	−	0.813329i	$-0.697653\pi$
$379$	−4.67395e11	−1.16361	−0.581805	+	0.813329i	$0.697653\pi$
$380$	0	0
$381$	8.78602e10	0.213614
$382$	7.29190e11	1.75209
$383$	−5.86328e11	−1.39234	−0.696171	−	0.717876i	$-0.745115\pi$
$383$	−5.86328e11	−1.39234	−0.696171	+	0.717876i	$0.745115\pi$
$384$	−3.50053e10	−0.0821568
$385$	0	0
$386$	1.35966e12	3.11736
$387$	2.85153e11	0.646218
$388$	1.97091e10	0.0441493
$389$	3.66240e11	0.810947	0.405473	−	0.914107i	$-0.367107\pi$
$389$	3.66240e11	0.810947	0.405473	+	0.914107i	$0.367107\pi$
$390$	0	0
$391$	−6.43827e11	−1.39307
$392$	2.04033e12	4.36428
$393$	7.62339e10	0.161206
$394$	4.23273e11	0.884886
$395$	0	0
$396$	−8.86457e11	−1.81146
$397$	5.28128e11	1.06704	0.533521	−	0.845787i	$-0.320868\pi$
$397$	5.28128e11	1.06704	0.533521	+	0.845787i	$0.320868\pi$
$398$	−1.32229e12	−2.64152
$399$	−2.25018e10	−0.0444466
$400$	0	0
$401$	7.52669e11	1.45363	0.726815	−	0.686833i	$-0.241000\pi$
$401$	7.52669e11	1.45363	0.726815	+	0.686833i	$0.241000\pi$
$402$	−1.77961e11	−0.339865
$403$	1.88278e11	0.355571
$404$	1.64694e12	3.07583
$405$	0	0
$406$	−1.44249e12	−2.63478
$407$	5.30159e11	0.957703
$408$	1.75237e11	0.313079
$409$	−9.37938e11	−1.65737	−0.828684	−	0.559716i	$-0.810910\pi$
$409$	−9.37938e11	−1.65737	−0.828684	+	0.559716i	$0.810910\pi$
$410$	0	0
$411$	−5.86112e10	−0.101319
$412$	−4.81129e11	−0.822667
$413$	−4.15185e11	−0.702210
$414$	−1.73962e12	−2.91040
$415$	0	0
$416$	3.89791e11	0.638135
$417$	−1.21328e11	−0.196493
$418$	1.87699e11	0.300725
$419$	7.29788e11	1.15673	0.578367	−	0.815777i	$-0.303690\pi$
$419$	7.29788e11	1.15673	0.578367	+	0.815777i	$0.303690\pi$
$420$	0	0
$421$	−2.02779e11	−0.314596	−0.157298	−	0.987551i	$-0.550278\pi$
$421$	−2.02779e11	−0.314596	−0.157298	+	0.987551i	$0.550278\pi$
$422$	−4.18209e11	−0.641930
$423$	−9.61404e11	−1.46007
$424$	−2.11389e12	−3.17640
$425$	0	0
$426$	9.64708e8	0.00141923
$427$	−1.55853e12	−2.26877
$428$	3.23871e12	4.66526
$429$	−1.83066e10	−0.0260945
$430$	0	0
$431$	1.02524e12	1.43113	0.715565	−	0.698546i	$-0.246169\pi$
$431$	1.02524e12	1.43113	0.715565	+	0.698546i	$0.246169\pi$
$432$	4.98525e11	0.688669
$433$	3.63091e11	0.496386	0.248193	−	0.968711i	$-0.420163\pi$
$433$	3.63091e11	0.496386	0.248193	+	0.968711i	$0.420163\pi$
$434$	2.83554e12	3.83647
$435$	0	0
$436$	−1.05641e12	−1.40005
$437$	2.62915e11	0.344864
$438$	−1.44949e11	−0.188184
$439$	−9.87803e11	−1.26935	−0.634673	−	0.772781i	$-0.718865\pi$
$439$	−9.87803e11	−1.26935	−0.634673	+	0.772781i	$0.718865\pi$
$440$	0	0
$441$	−1.22150e12	−1.53787
$442$	−3.66117e11	−0.456268
$443$	5.18736e11	0.639926	0.319963	−	0.947430i	$-0.396330\pi$
$443$	5.18736e11	0.639926	0.319963	+	0.947430i	$0.396330\pi$
$444$	−3.37444e11	−0.412077
$445$	0	0
$446$	−2.49205e12	−2.98229
$447$	−4.80532e10	−0.0569296
$448$	2.15122e12	2.52310
$449$	4.17040e11	0.484249	0.242124	−	0.970245i	$-0.422156\pi$
$449$	4.17040e11	0.484249	0.242124	+	0.970245i	$0.422156\pi$
$450$	0	0
$451$	−6.15162e11	−0.700157
$452$	3.17692e12	3.58000
$453$	8.72517e10	0.0973491
$454$	−1.34363e12	−1.48433
$455$	0	0
$456$	−7.15601e10	−0.0775049
$457$	−6.20773e11	−0.665748	−0.332874	−	0.942971i	$-0.608018\pi$
$457$	−6.20773e11	−0.665748	−0.332874	+	0.942971i	$0.608018\pi$
$458$	−1.56409e12	−1.66099
$459$	−2.11552e11	−0.222464
$460$	0	0
$461$	−1.48991e10	−0.0153640	−0.00768202	−	0.999970i	$-0.502445\pi$
$461$	−1.48991e10	−0.0153640	−0.00768202	+	0.999970i	$0.502445\pi$
$462$	−2.75704e11	−0.281549
$463$	−4.48193e11	−0.453263	−0.226632	−	0.973981i	$-0.572771\pi$
$463$	−4.48193e11	−0.453263	−0.226632	+	0.973981i	$0.572771\pi$
$464$	−2.39522e12	−2.39891
$465$	0	0
$466$	−2.85153e12	−2.80118
$467$	−1.03476e12	−1.00673	−0.503364	−	0.864074i	$-0.667905\pi$
$467$	−1.03476e12	−1.00673	−0.503364	+	0.864074i	$0.667905\pi$
$468$	−7.06090e11	−0.680384
$469$	2.39400e12	2.28479
$470$	0	0
$471$	−1.69810e10	−0.0158990
$472$	−1.32037e12	−1.22450
$473$	−5.28039e11	−0.485055
$474$	3.07471e11	0.279770
$475$	0	0
$476$	−3.93561e12	−3.51383
$477$	1.26554e12	1.11929
$478$	−1.69837e12	−1.48801
$479$	1.04148e12	0.903944	0.451972	−	0.892032i	$-0.350721\pi$
$479$	1.04148e12	0.903944	0.451972	+	0.892032i	$0.350721\pi$
$480$	0	0
$481$	4.22288e11	0.359713
$482$	−2.61748e12	−2.20888
$483$	−3.86185e11	−0.322874
$484$	−1.36898e12	−1.13395
$485$	0	0
$486$	−8.59757e11	−0.699056
$487$	−1.70613e12	−1.37446	−0.687230	−	0.726440i	$-0.741173\pi$
$487$	−1.70613e12	−1.37446	−0.687230	+	0.726440i	$0.741173\pi$
$488$	−4.95644e12	−3.95622
$489$	−1.38748e11	−0.109733
$490$	0	0
$491$	−1.18015e12	−0.916371	−0.458185	−	0.888857i	$-0.651500\pi$
$491$	−1.18015e12	−0.916371	−0.458185	+	0.888857i	$0.651500\pi$
$492$	3.91548e11	0.301261
$493$	1.01642e12	0.774931
$494$	1.49508e11	0.112952
$495$	0	0
$496$	4.70835e12	3.49302
$497$	−1.29776e10	−0.00954096
$498$	1.39323e11	0.101505
$499$	7.31237e11	0.527966	0.263983	−	0.964527i	$-0.414964\pi$
$499$	7.31237e11	0.527966	0.263983	+	0.964527i	$0.414964\pi$
$500$	0	0
$501$	−3.18483e11	−0.225848
$502$	1.23727e12	0.869554
$503$	7.77902e11	0.541837	0.270919	−	0.962602i	$-0.412673\pi$
$503$	7.77902e11	0.541837	0.270919	+	0.962602i	$0.412673\pi$
$504$	−6.36956e12	−4.39716
$505$	0	0
$506$	3.22138e12	2.18456
$507$	−1.45817e10	−0.00980107
$508$	−6.27529e12	−4.18068
$509$	4.16231e11	0.274855	0.137428	−	0.990512i	$-0.456117\pi$
$509$	4.16231e11	0.274855	0.137428	+	0.990512i	$0.456117\pi$
$510$	0	0
$511$	1.94992e12	1.26509
$512$	−2.08009e12	−1.33772
$513$	8.63897e10	0.0550724
$514$	−3.70508e12	−2.34133
$515$	0	0
$516$	3.36095e11	0.208707
$517$	1.78030e12	1.09594
$518$	6.35983e12	3.88116
$519$	2.56312e11	0.155066
$520$	0	0
$521$	1.04282e12	0.620070	0.310035	−	0.950725i	$-0.399659\pi$
$521$	1.04282e12	0.620070	0.310035	+	0.950725i	$0.399659\pi$
$522$	2.74637e12	1.61898
$523$	−2.17118e12	−1.26893	−0.634466	−	0.772951i	$-0.718780\pi$
$523$	−2.17118e12	−1.26893	−0.634466	+	0.772951i	$0.718780\pi$
$524$	−5.44490e12	−3.15500
$525$	0	0
$526$	2.04177e12	1.16298
$527$	−1.99801e12	−1.12837
$528$	−4.57801e11	−0.256344
$529$	2.71110e12	1.50520
$530$	0	0
$531$	7.90476e11	0.431483
$532$	1.60716e12	0.869873
$533$	−4.89996e11	−0.262978
$534$	−3.90475e10	−0.0207806
$535$	0	0
$536$	7.61338e12	3.98415
$537$	1.23436e11	0.0640555
$538$	4.07627e12	2.09770
$539$	2.26194e12	1.15433
$540$	0	0
$541$	1.38440e12	0.694825	0.347412	−	0.937712i	$-0.387060\pi$
$541$	1.38440e12	0.694825	0.347412	+	0.937712i	$0.387060\pi$
$542$	−7.35045e11	−0.365862
$543$	5.05134e10	0.0249349
$544$	−4.13648e12	−2.02505
$545$	0	0
$546$	−2.19607e11	−0.105750
$547$	−3.33424e12	−1.59240	−0.796202	−	0.605030i	$-0.793161\pi$
$547$	−3.33424e12	−1.59240	−0.796202	+	0.605030i	$0.793161\pi$
$548$	4.18622e12	1.98294
$549$	2.96731e12	1.39408
$550$	0	0
$551$	−4.15069e11	−0.191839
$552$	−1.22814e12	−0.563019
$553$	−4.13622e12	−1.88079
$554$	−1.79758e12	−0.810761
$555$	0	0
$556$	8.66565e12	3.84561
$557$	1.71526e12	0.755062	0.377531	−	0.925997i	$-0.376773\pi$
$557$	1.71526e12	0.755062	0.377531	+	0.925997i	$0.376773\pi$
$558$	−5.39861e12	−2.35737
$559$	−4.20600e11	−0.182186
$560$	0	0
$561$	1.94270e11	0.0828081
$562$	−3.41628e12	−1.44457
$563$	−3.47052e12	−1.45582	−0.727909	−	0.685674i	$-0.759508\pi$
$563$	−3.47052e12	−1.45582	−0.727909	+	0.685674i	$0.759508\pi$
$564$	−1.13316e12	−0.471556
$565$	0	0
$566$	−3.61313e12	−1.47982
$567$	3.74934e12	1.52346
$568$	−4.12715e10	−0.0166373
$569$	−5.47669e11	−0.219035	−0.109517	−	0.993985i	$-0.534931\pi$
$569$	−5.47669e11	−0.219035	−0.109517	+	0.993985i	$0.534931\pi$
$570$	0	0
$571$	−1.29752e12	−0.510802	−0.255401	−	0.966835i	$-0.582207\pi$
$571$	−1.29752e12	−0.510802	−0.255401	+	0.966835i	$0.582207\pi$
$572$	1.30752e12	0.510700
$573$	−3.08198e11	−0.119436
$574$	−7.37954e12	−2.83744
$575$	0	0
$576$	−4.09574e12	−1.55035
$577$	−3.94524e12	−1.48177	−0.740887	−	0.671629i	$-0.765595\pi$
$577$	−3.94524e12	−1.48177	−0.740887	+	0.671629i	$0.765595\pi$
$578$	−1.13025e12	−0.421212
$579$	−5.74669e11	−0.212503
$580$	0	0
$581$	−1.87422e12	−0.682384
$582$	−1.16708e10	−0.00421644
$583$	−2.34349e12	−0.840144
$584$	6.20112e12	2.20603
$585$	0	0
$586$	−2.12397e12	−0.744063
$587$	−1.69635e12	−0.589717	−0.294859	−	0.955541i	$-0.595273\pi$
$587$	−1.69635e12	−0.589717	−0.294859	+	0.955541i	$0.595273\pi$
$588$	−1.43971e12	−0.496681
$589$	8.15912e11	0.279334
$590$	0	0
$591$	−1.78899e11	−0.0603205
$592$	1.05603e13	3.53371
$593$	−3.51053e12	−1.16581	−0.582904	−	0.812541i	$-0.698084\pi$
$593$	−3.51053e12	−1.16581	−0.582904	+	0.812541i	$0.698084\pi$
$594$	1.05850e12	0.348859
$595$	0	0
$596$	3.43213e12	1.11418
$597$	5.58876e11	0.180066
$598$	2.56593e12	0.820519
$599$	4.59342e11	0.145786	0.0728929	−	0.997340i	$-0.476777\pi$
$599$	4.59342e11	0.145786	0.0728929	+	0.997340i	$0.476777\pi$
$600$	0	0
$601$	−3.63058e12	−1.13512	−0.567559	−	0.823333i	$-0.692112\pi$
$601$	−3.63058e12	−1.13512	−0.567559	+	0.823333i	$0.692112\pi$
$602$	−6.33440e12	−1.96572
$603$	−4.55796e12	−1.40392
$604$	−6.23183e12	−1.90524
$605$	0	0
$606$	−9.75238e11	−0.293754
$607$	2.08854e12	0.624444	0.312222	−	0.950009i	$-0.398927\pi$
$607$	2.08854e12	0.624444	0.312222	+	0.950009i	$0.398927\pi$
$608$	1.68918e12	0.501315
$609$	6.09678e11	0.179607
$610$	0	0
$611$	1.41807e12	0.411634
$612$	7.49306e12	2.15912
$613$	−1.12371e11	−0.0321428	−0.0160714	−	0.999871i	$-0.505116\pi$
$613$	−1.12371e11	−0.0321428	−0.0160714	+	0.999871i	$0.505116\pi$
$614$	8.03711e12	2.28214
$615$	0	0
$616$	1.17950e13	3.30053
$617$	2.51656e12	0.699075	0.349537	−	0.936922i	$-0.386339\pi$
$617$	2.51656e12	0.699075	0.349537	+	0.936922i	$0.386339\pi$
$618$	2.84901e11	0.0785681
$619$	−5.12708e12	−1.40366	−0.701830	−	0.712344i	$-0.747633\pi$
$619$	−5.12708e12	−1.40366	−0.701830	+	0.712344i	$0.747633\pi$
$620$	0	0
$621$	1.48266e12	0.400063
$622$	−1.88256e12	−0.504304
$623$	5.25283e11	0.139700
$624$	−3.64652e11	−0.0962827
$625$	0	0
$626$	−1.21347e13	−3.15823
$627$	−7.93325e10	−0.0204997
$628$	1.21285e12	0.311163
$629$	−4.48134e12	−1.14151
$630$	0	0
$631$	−5.35545e12	−1.34482	−0.672410	−	0.740179i	$-0.734741\pi$
$631$	−5.35545e12	−1.34482	−0.672410	+	0.740179i	$0.734741\pi$
$632$	−1.31540e13	−3.27967
$633$	1.76759e11	0.0437588
$634$	2.88189e12	0.708396
$635$	0	0
$636$	1.49162e12	0.361494
$637$	1.80170e12	0.433566
$638$	−5.08565e12	−1.21522
$639$	2.47083e10	0.00586258
$640$	0	0
$641$	3.36716e12	0.787776	0.393888	−	0.919158i	$-0.371130\pi$
$641$	3.36716e12	0.787776	0.393888	+	0.919158i	$0.371130\pi$
$642$	−1.91781e12	−0.445551
$643$	−2.48176e12	−0.572545	−0.286272	−	0.958148i	$-0.592416\pi$
$643$	−2.48176e12	−0.572545	−0.286272	+	0.958148i	$0.592416\pi$
$644$	2.75827e13	6.31903
$645$	0	0
$646$	−1.58659e12	−0.358441
$647$	−7.11628e12	−1.59656	−0.798278	−	0.602289i	$-0.794255\pi$
$647$	−7.11628e12	−1.59656	−0.798278	+	0.602289i	$0.794255\pi$
$648$	1.19237e13	2.65657
$649$	−1.46378e12	−0.323874
$650$	0	0
$651$	−1.19846e12	−0.261523
$652$	9.90990e12	2.14761
$653$	−8.18428e12	−1.76145	−0.880727	−	0.473624i	$-0.842945\pi$
$653$	−8.18428e12	−1.76145	−0.880727	+	0.473624i	$0.842945\pi$
$654$	6.25553e11	0.133710
$655$	0	0
$656$	−1.22536e13	−2.58342
$657$	−3.71247e12	−0.777353
$658$	2.13567e13	4.44137
$659$	7.93218e12	1.63835	0.819177	−	0.573540i	$-0.194430\pi$
$659$	7.93218e12	1.63835	0.819177	+	0.573540i	$0.194430\pi$
$660$	0	0
$661$	−6.95667e12	−1.41741	−0.708704	−	0.705506i	$-0.750720\pi$
$661$	−6.95667e12	−1.41741	−0.708704	+	0.705506i	$0.750720\pi$
$662$	5.84336e12	1.18250
$663$	1.54742e11	0.0311026
$664$	−5.96040e12	−1.18992
$665$	0	0
$666$	−1.21086e13	−2.38483
$667$	−7.12358e12	−1.39358
$668$	2.27472e13	4.42011
$669$	1.05328e12	0.203295
$670$	0	0
$671$	−5.49478e12	−1.04640
$672$	−2.48118e12	−0.469349
$673$	8.76776e12	1.64748	0.823741	−	0.566966i	$-0.191883\pi$
$673$	8.76776e12	1.64748	0.823741	+	0.566966i	$0.191883\pi$
$674$	−6.31116e12	−1.17798
$675$	0	0
$676$	1.04148e12	0.191819
$677$	8.27870e12	1.51465	0.757327	−	0.653036i	$-0.226505\pi$
$677$	8.27870e12	1.51465	0.757327	+	0.653036i	$0.226505\pi$
$678$	−1.88122e12	−0.341905
$679$	1.57000e11	0.0283455
$680$	0	0
$681$	5.67896e11	0.101183
$682$	9.99701e12	1.76946
$683$	−2.14169e12	−0.376585	−0.188292	−	0.982113i	$-0.560295\pi$
$683$	−2.14169e12	−0.376585	−0.188292	+	0.982113i	$0.560295\pi$
$684$	−3.05988e12	−0.534506
$685$	0	0
$686$	9.77665e12	1.68551
$687$	6.61072e11	0.113225
$688$	−1.05181e13	−1.78974
$689$	−1.86666e12	−0.315558
$690$	0	0
$691$	6.38018e12	1.06459	0.532294	−	0.846559i	$-0.321330\pi$
$691$	6.38018e12	1.06459	0.532294	+	0.846559i	$0.321330\pi$
$692$	−1.83067e13	−3.03482
$693$	−7.06139e12	−1.16303
$694$	−1.98547e13	−3.24897
$695$	0	0
$696$	1.93890e12	0.313194
$697$	5.19986e12	0.834534
$698$	7.48364e12	1.19334
$699$	1.20522e12	0.190950
$700$	0	0
$701$	−1.01425e13	−1.58640	−0.793199	−	0.608963i	$-0.791586\pi$
$701$	−1.01425e13	−1.58640	−0.793199	+	0.608963i	$0.791586\pi$
$702$	8.43124e11	0.131031
$703$	1.83001e12	0.282588
$704$	7.58437e12	1.16370
$705$	0	0
$706$	−8.79373e12	−1.33215
$707$	1.31193e13	1.97480
$708$	9.31691e11	0.139355
$709$	2.51804e12	0.374244	0.187122	−	0.982337i	$-0.440084\pi$
$709$	2.51804e12	0.374244	0.187122	+	0.982337i	$0.440084\pi$
$710$	0	0
$711$	7.87500e12	1.15568
$712$	1.67050e12	0.243606
$713$	1.40030e13	2.02917
$714$	2.33048e12	0.335585
$715$	0	0
$716$	−8.81621e12	−1.25364
$717$	7.17827e11	0.101434
$718$	−1.10194e13	−1.54739
$719$	4.71730e12	0.658284	0.329142	−	0.944280i	$-0.393241\pi$
$719$	4.71730e12	0.658284	0.329142	+	0.944280i	$0.393241\pi$
$720$	0	0
$721$	−3.83261e12	−0.528184
$722$	−1.29997e13	−1.78039
$723$	1.10630e12	0.150574
$724$	−3.60784e12	−0.488005
$725$	0	0
$726$	8.10643e11	0.108297
$727$	−5.95951e12	−0.791235	−0.395617	−	0.918415i	$-0.629469\pi$
$727$	−5.95951e12	−0.791235	−0.395617	+	0.918415i	$0.629469\pi$
$728$	9.39507e12	1.23968
$729$	−6.89284e12	−0.903908
$730$	0	0
$731$	4.46342e12	0.578149
$732$	3.49740e12	0.450242
$733$	−7.46488e11	−0.0955113	−0.0477556	−	0.998859i	$-0.515207\pi$
$733$	−7.46488e11	−0.0955113	−0.0477556	+	0.998859i	$0.515207\pi$
$734$	1.70460e13	2.16765
$735$	0	0
$736$	2.89905e13	3.64171
$737$	8.44030e12	1.05379
$738$	1.40500e13	1.74350
$739$	−7.26086e12	−0.895547	−0.447773	−	0.894147i	$-0.647783\pi$
$739$	−7.26086e12	−0.895547	−0.447773	+	0.894147i	$0.647783\pi$
$740$	0	0
$741$	−6.31908e10	−0.00769967
$742$	−2.81127e13	−3.40474
$743$	4.75048e12	0.571857	0.285929	−	0.958251i	$-0.407698\pi$
$743$	4.75048e12	0.571857	0.285929	+	0.958251i	$0.407698\pi$
$744$	−3.81134e12	−0.456037
$745$	0	0
$746$	2.44260e12	0.288754
$747$	3.56835e12	0.419300
$748$	−1.38754e13	−1.62065
$749$	2.57991e13	2.99528
$750$	0	0
$751$	4.92391e12	0.564847	0.282423	−	0.959290i	$-0.408862\pi$
$751$	4.92391e12	0.564847	0.282423	+	0.959290i	$0.408862\pi$
$752$	3.54623e13	4.04377
$753$	−5.22939e11	−0.0592753
$754$	−4.05088e12	−0.456434
$755$	0	0
$756$	9.06325e12	1.00910
$757$	1.68932e13	1.86974	0.934870	−	0.354990i	$-0.115516\pi$
$757$	1.68932e13	1.86974	0.934870	+	0.354990i	$0.115516\pi$
$758$	−1.97678e13	−2.17494
$759$	−1.36154e12	−0.148916
$760$	0	0
$761$	4.94344e12	0.534317	0.267158	−	0.963653i	$-0.413915\pi$
$761$	4.94344e12	0.534317	0.267158	+	0.963653i	$0.413915\pi$
$762$	3.71592e12	0.399272
$763$	−8.41519e12	−0.898884
$764$	2.20126e13	2.33749
$765$	0	0
$766$	−2.47979e13	−2.60247
$767$	−1.16595e12	−0.121647
$768$	4.55393e11	0.0472347
$769$	1.27886e13	1.31873	0.659363	−	0.751824i	$-0.270826\pi$
$769$	1.27886e13	1.31873	0.659363	+	0.751824i	$0.270826\pi$
$770$	0	0
$771$	1.56598e12	0.159603
$772$	4.10449e13	4.15893
$773$	−6.68503e12	−0.673435	−0.336718	−	0.941606i	$-0.609317\pi$
$773$	−6.68503e12	−0.673435	−0.336718	+	0.941606i	$0.609317\pi$
$774$	1.20601e13	1.20786
$775$	0	0
$776$	4.99290e11	0.0494282
$777$	−2.68803e12	−0.264569
$778$	1.54896e13	1.51576
$779$	−2.12343e12	−0.206594
$780$	0	0
$781$	−4.57541e10	−0.00440049
$782$	−2.72297e13	−2.60383
$783$	−2.34070e12	−0.222545
$784$	4.50560e13	4.25922
$785$	0	0
$786$	3.22420e12	0.301315
$787$	−2.01354e13	−1.87100	−0.935502	−	0.353320i	$-0.885053\pi$
$787$	−2.01354e13	−1.87100	−0.935502	+	0.353320i	$0.885053\pi$
$788$	1.27776e13	1.18054
$789$	−8.62968e11	−0.0792772
$790$	0	0
$791$	2.53069e13	2.29850
$792$	−2.24566e13	−2.02806
$793$	−4.37676e12	−0.393028
$794$	2.23364e13	1.99444
$795$	0	0
$796$	−3.99169e13	−3.52410
$797$	−9.69728e12	−0.851309	−0.425655	−	0.904886i	$-0.639956\pi$
$797$	−9.69728e12	−0.851309	−0.425655	+	0.904886i	$0.639956\pi$
$798$	−9.51680e11	−0.0830764
$799$	−1.50486e13	−1.30628
$800$	0	0
$801$	−1.00009e12	−0.0858408
$802$	3.18330e13	2.71702
$803$	6.87465e12	0.583486
$804$	−5.37222e12	−0.453421
$805$	0	0
$806$	7.96293e12	0.664607
$807$	−1.72287e12	−0.142995
$808$	4.17219e13	3.44360
$809$	1.58607e13	1.30183	0.650915	−	0.759150i	$-0.274385\pi$
$809$	1.58607e13	1.30183	0.650915	+	0.759150i	$0.274385\pi$
$810$	0	0
$811$	5.88758e12	0.477906	0.238953	−	0.971031i	$-0.423196\pi$
$811$	5.88758e12	0.477906	0.238953	+	0.971031i	$0.423196\pi$
$812$	−4.35454e13	−3.51512
$813$	3.10672e11	0.0249399
$814$	2.24223e13	1.79007
$815$	0	0
$816$	3.86971e12	0.305543
$817$	−1.82269e12	−0.143125
$818$	−3.96687e13	−3.09783
$819$	−5.62461e12	−0.436833
$820$	0	0
$821$	5.94820e12	0.456921	0.228461	−	0.973553i	$-0.426631\pi$
$821$	5.94820e12	0.456921	0.228461	+	0.973553i	$0.426631\pi$
$822$	−2.47888e12	−0.189379
$823$	−7.68915e12	−0.584223	−0.292112	−	0.956384i	$-0.594358\pi$
$823$	−7.68915e12	−0.584223	−0.292112	+	0.956384i	$0.594358\pi$
$824$	−1.21884e13	−0.921034
$825$	0	0
$826$	−1.75597e13	−1.31252
$827$	1.51025e13	1.12273	0.561363	−	0.827570i	$-0.310277\pi$
$827$	1.51025e13	1.12273	0.561363	+	0.827570i	$0.310277\pi$
$828$	−5.25150e13	−3.88282
$829$	−7.23186e12	−0.531808	−0.265904	−	0.964000i	$-0.585670\pi$
$829$	−7.23186e12	−0.531808	−0.265904	+	0.964000i	$0.585670\pi$
$830$	0	0
$831$	7.59758e11	0.0552676
$832$	6.04119e12	0.437087
$833$	−1.91197e13	−1.37588
$834$	−5.13138e12	−0.367271
$835$	0	0
$836$	5.66621e12	0.401203
$837$	4.60118e12	0.324045
$838$	3.08653e13	2.16208
$839$	−1.30902e13	−0.912050	−0.456025	−	0.889967i	$-0.650727\pi$
$839$	−1.30902e13	−0.912050	−0.456025	+	0.889967i	$0.650727\pi$
$840$	0	0
$841$	−3.26100e12	−0.224786
$842$	−8.57624e12	−0.588021
$843$	1.44391e12	0.0984730
$844$	−1.26248e13	−0.856411
$845$	0	0
$846$	−4.06612e13	−2.72906
$847$	−1.09051e13	−0.728038
$848$	−4.66804e13	−3.09994
$849$	1.52711e12	0.100876
$850$	0	0
$851$	3.14074e13	2.05281
$852$	2.91223e10	0.00189342
$853$	2.60628e13	1.68559	0.842793	−	0.538238i	$-0.180910\pi$
$853$	2.60628e13	1.68559	0.842793	+	0.538238i	$0.180910\pi$
$854$	−6.59158e13	−4.24062
$855$	0	0
$856$	8.20463e13	5.22308
$857$	2.77627e13	1.75812	0.879060	−	0.476711i	$-0.158171\pi$
$857$	2.77627e13	1.75812	0.879060	+	0.476711i	$0.158171\pi$
$858$	−7.74249e11	−0.0487739
$859$	2.87614e13	1.80236	0.901180	−	0.433446i	$-0.142703\pi$
$859$	2.87614e13	1.80236	0.901180	+	0.433446i	$0.142703\pi$
$860$	0	0
$861$	3.11902e12	0.193421
$862$	4.33612e13	2.67497
$863$	2.86159e13	1.75614	0.878068	−	0.478536i	$-0.158832\pi$
$863$	2.86159e13	1.75614	0.878068	+	0.478536i	$0.158832\pi$
$864$	9.52583e12	0.581555
$865$	0	0
$866$	1.53564e13	0.927810
$867$	4.77710e11	0.0287130
$868$	8.55983e13	5.11831
$869$	−1.45827e13	−0.867459
$870$	0	0
$871$	6.72296e12	0.395803
$872$	−2.67620e13	−1.56745
$873$	−2.98913e11	−0.0174173
$874$	1.11196e13	0.644596
$875$	0	0
$876$	−4.37568e12	−0.251060
$877$	−1.76665e13	−1.00845	−0.504224	−	0.863573i	$-0.668221\pi$
$877$	−1.76665e13	−1.00845	−0.504224	+	0.863573i	$0.668221\pi$
$878$	−4.17777e13	−2.37257
$879$	8.97713e11	0.0507210
$880$	0	0
$881$	3.19102e13	1.78459	0.892294	−	0.451455i	$-0.149095\pi$
$881$	3.19102e13	1.78459	0.892294	+	0.451455i	$0.149095\pi$
$882$	−5.16614e13	−2.87447
$883$	1.95092e13	1.07998	0.539990	−	0.841671i	$-0.318428\pi$
$883$	1.95092e13	1.07998	0.539990	+	0.841671i	$0.318428\pi$
$884$	−1.10522e13	−0.608716
$885$	0	0
$886$	2.19392e13	1.19610
$887$	2.56301e13	1.39025	0.695126	−	0.718888i	$-0.255349\pi$
$887$	2.56301e13	1.39025	0.695126	+	0.718888i	$0.255349\pi$
$888$	−8.54846e12	−0.461349
$889$	−4.99880e13	−2.68416
$890$	0	0
$891$	1.32187e13	0.702652
$892$	−7.52292e13	−3.97873
$893$	6.14527e12	0.323377
$894$	−2.03234e12	−0.106409
$895$	0	0
$896$	1.99163e13	1.03234
$897$	−1.08451e12	−0.0559328
$898$	1.76381e13	0.905124
$899$	−2.21069e13	−1.12878
$900$	0	0
$901$	1.98091e13	1.00139
$902$	−2.60174e13	−1.30868
$903$	2.67728e12	0.133998
$904$	8.04808e13	4.00806
$905$	0	0
$906$	3.69018e12	0.181958
$907$	3.55084e13	1.74220	0.871101	−	0.491104i	$-0.163406\pi$
$907$	3.55084e13	1.74220	0.871101	+	0.491104i	$0.163406\pi$
$908$	−4.05612e13	−1.98027
$909$	−2.49780e13	−1.21344
$910$	0	0
$911$	−3.11189e13	−1.49689	−0.748447	−	0.663195i	$-0.769200\pi$
$911$	−3.11189e13	−1.49689	−0.748447	+	0.663195i	$0.769200\pi$
$912$	−1.58024e12	−0.0756392
$913$	−6.60778e12	−0.314729
$914$	−2.62547e13	−1.24437
$915$	0	0
$916$	−4.72161e13	−2.21595
$917$	−4.33732e13	−2.02563
$918$	−8.94727e12	−0.415813
$919$	1.24776e13	0.577047	0.288524	−	0.957473i	$-0.406836\pi$
$919$	1.24776e13	0.577047	0.288524	+	0.957473i	$0.406836\pi$
$920$	0	0
$921$	−3.39694e12	−0.155568
$922$	−6.30135e11	−0.0287174
$923$	−3.64446e10	−0.00165282
$924$	−8.32287e12	−0.375621
$925$	0	0
$926$	−1.89557e13	−0.847208
$927$	7.29694e12	0.324550
$928$	−4.57679e13	−2.02579
$929$	−2.91792e13	−1.28529	−0.642647	−	0.766162i	$-0.722164\pi$
$929$	−2.91792e13	−1.28529	−0.642647	+	0.766162i	$0.722164\pi$
$930$	0	0
$931$	7.80778e12	0.340607
$932$	−8.60810e13	−3.73711
$933$	7.95679e11	0.0343772
$934$	−4.37635e13	−1.88170
$935$	0	0
$936$	−1.78874e13	−0.761737
$937$	7.53729e12	0.319438	0.159719	−	0.987163i	$-0.448941\pi$
$937$	7.53729e12	0.319438	0.159719	+	0.987163i	$0.448941\pi$
$938$	1.01251e14	4.27056
$939$	5.12881e12	0.215289
$940$	0	0
$941$	−3.07136e13	−1.27696	−0.638480	−	0.769638i	$-0.720437\pi$
$941$	−3.07136e13	−1.27696	−0.638480	+	0.769638i	$0.720437\pi$
$942$	−7.18188e11	−0.0297173
$943$	−3.64431e13	−1.50077
$944$	−2.91574e13	−1.19502
$945$	0	0
$946$	−2.23326e13	−0.906630
$947$	3.53276e13	1.42738	0.713690	−	0.700461i	$-0.247022\pi$
$947$	3.53276e13	1.42738	0.713690	+	0.700461i	$0.247022\pi$
$948$	9.28183e12	0.373247
$949$	5.47587e12	0.219157
$950$	0	0
$951$	−1.21805e12	−0.0482896
$952$	−9.97008e13	−3.93398
$953$	−1.78624e13	−0.701491	−0.350745	−	0.936471i	$-0.614072\pi$
$953$	−1.78624e13	−0.701491	−0.350745	+	0.936471i	$0.614072\pi$
$954$	5.35240e13	2.09209
$955$	0	0
$956$	−5.12698e13	−1.98519
$957$	2.14949e12	0.0828383
$958$	4.40479e13	1.68959
$959$	3.33468e13	1.27312
$960$	0	0
$961$	1.70164e13	0.643596
$962$	1.78600e13	0.672349
$963$	−4.91193e13	−1.84049
$964$	−7.90156e13	−2.94691
$965$	0	0
$966$	−1.63331e13	−0.603493
$967$	3.15343e13	1.15975	0.579875	−	0.814706i	$-0.303101\pi$
$967$	3.15343e13	1.15975	0.579875	+	0.814706i	$0.303101\pi$
$968$	−3.46803e13	−1.26953
$969$	6.70583e11	0.0244341
$970$	0	0
$971$	−2.38079e13	−0.859476	−0.429738	−	0.902954i	$-0.641394\pi$
$971$	−2.38079e13	−0.859476	−0.429738	+	0.902954i	$0.641394\pi$
$972$	−2.59541e13	−0.932625
$973$	6.90293e13	2.46903
$974$	−7.21583e13	−2.56904
$975$	0	0
$976$	−1.09452e14	−3.86099
$977$	−6.31083e12	−0.221595	−0.110798	−	0.993843i	$-0.535341\pi$
$977$	−6.31083e12	−0.221595	−0.110798	+	0.993843i	$0.535341\pi$
$978$	−5.86816e12	−0.205105
$979$	1.85194e12	0.0644326
$980$	0	0
$981$	1.60218e13	0.552332
$982$	−4.99128e13	−1.71281
$983$	4.48363e12	0.153158	0.0765789	−	0.997064i	$-0.475600\pi$
$983$	4.48363e12	0.153158	0.0765789	+	0.997064i	$0.475600\pi$
$984$	9.91909e12	0.337282
$985$	0	0
$986$	4.29881e13	1.44845
$987$	−9.02655e12	−0.302757
$988$	4.51331e12	0.150692
$989$	−3.12818e13	−1.03970
$990$	0	0
$991$	−6.89574e12	−0.227117	−0.113559	−	0.993531i	$-0.536225\pi$
$991$	−6.89574e12	−0.227117	−0.113559	+	0.993531i	$0.536225\pi$
$992$	8.99672e13	2.94973
$993$	−2.46974e12	−0.0806082
$994$	−5.48871e11	−0.0178333
$995$	0	0
$996$	4.20583e12	0.135420
$997$	5.61756e13	1.80061	0.900305	−	0.435260i	$-0.143344\pi$
$997$	5.61756e13	1.80061	0.900305	+	0.435260i	$0.143344\pi$
$998$	3.09266e13	0.986835
$999$	1.03200e13	0.327819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.j.1.18	yes	19
5.4	even	2		325.10.a.i.1.2	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.10.a.i.1.2	✓	19	5.4	even	2
325.10.a.j.1.18	yes	19	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q+42.2935 q^{2} -17.8757 q^{3} +1276.74 q^{4} -756.026 q^{6} +10170.4 q^{7} +32343.7 q^{8} -19363.5 q^{9} +35856.7 q^{11} -22822.7 q^{12} +28561.0 q^{13} +430141. q^{14} +714238. q^{16} -303091. q^{17} -818949. q^{18} +123771. q^{19} -181802. q^{21} +1.51651e6 q^{22} +2.12421e6 q^{23} -578166. q^{24} +1.20795e6 q^{26} +697982. q^{27} +1.29849e7 q^{28} -3.35353e6 q^{29} +6.59212e6 q^{31} +1.36477e7 q^{32} -640963. q^{33} -1.28188e7 q^{34} -2.47222e7 q^{36} +1.47855e7 q^{37} +5.23470e6 q^{38} -510547. q^{39} -1.71561e7 q^{41} -7.68905e6 q^{42} -1.47264e7 q^{43} +4.57799e7 q^{44} +8.98402e7 q^{46} +4.96504e7 q^{47} -1.27675e7 q^{48} +6.30826e7 q^{49} +5.41795e6 q^{51} +3.64651e7 q^{52} -6.53569e7 q^{53} +2.95201e7 q^{54} +3.28947e8 q^{56} -2.21249e6 q^{57} -1.41833e8 q^{58} -4.08231e7 q^{59} -1.53242e8 q^{61} +2.78804e8 q^{62} -1.96933e8 q^{63} +2.11519e8 q^{64} -2.71086e7 q^{66} +2.35390e8 q^{67} -3.86969e8 q^{68} -3.79716e7 q^{69} -1.27603e6 q^{71} -6.26287e8 q^{72} +1.91725e8 q^{73} +6.25330e8 q^{74} +1.58024e8 q^{76} +3.64676e8 q^{77} -2.15928e7 q^{78} -4.06694e8 q^{79} +3.68654e8 q^{81} -7.25593e8 q^{82} -1.84283e8 q^{83} -2.32115e8 q^{84} -6.22830e8 q^{86} +5.99466e7 q^{87} +1.15974e9 q^{88} +5.16484e7 q^{89} +2.90476e8 q^{91} +2.71207e9 q^{92} -1.17839e8 q^{93} +2.09989e9 q^{94} -2.43961e8 q^{96} +1.54370e7 q^{97} +2.66799e9 q^{98} -6.94310e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 33 q^{2} - 73 q^{3} + 5803 q^{4} - 3549 q^{6} - 1066 q^{7} + 20349 q^{8} + 113200 q^{9} + 146427 q^{11} - 135219 q^{12} + 542659 q^{13} - 17870 q^{14} + 2549547 q^{16} - 605113 q^{17} + 1793704 q^{18}+ \cdots + 2637491156 q^{99}+O(q^{100}) \) 19 * q + 33 * q^2 - 73 * q^3 + 5803 * q^4 - 3549 * q^6 - 1066 * q^7 + 20349 * q^8 + 113200 * q^9 + 146427 * q^11 - 135219 * q^12 + 542659 * q^13 - 17870 * q^14 + 2549547 * q^16 - 605113 * q^17 + 1793704 * q^18 + 1053529 * q^19 + 3299072 * q^21 + 649675 * q^22 + 1123254 * q^23 + 1379083 * q^24 + 942513 * q^26 + 7258805 * q^27 - 17353598 * q^28 - 3588820 * q^29 + 7130168 * q^31 + 30008261 * q^32 - 37563217 * q^33 - 1511147 * q^34 + 70702660 * q^36 + 27070972 * q^37 + 20491605 * q^38 - 2084953 * q^39 + 20503041 * q^41 + 23549976 * q^42 - 8670194 * q^43 + 104623747 * q^44 + 15807622 * q^46 + 28326738 * q^47 - 293352359 * q^48 + 140788329 * q^49 + 212022459 * q^51 + 165739483 * q^52 + 49738834 * q^53 - 282194663 * q^54 + 246272386 * q^56 + 86542887 * q^57 + 221230676 * q^58 + 174278586 * q^59 + 73706348 * q^61 + 109597172 * q^62 - 389044938 * q^63 + 533531111 * q^64 + 910842685 * q^66 + 642771579 * q^67 - 1492314643 * q^68 + 672264794 * q^69 + 843585844 * q^71 + 875456724 * q^72 - 59348471 * q^73 - 252835516 * q^74 + 786885077 * q^76 - 82517582 * q^77 - 101362989 * q^78 + 521000922 * q^79 + 1182486371 * q^81 + 1010685747 * q^82 - 529236749 * q^83 + 4389156140 * q^84 + 2617322430 * q^86 - 752432206 * q^87 - 1484178139 * q^88 + 2211890531 * q^89 - 30446026 * q^91 + 439634668 * q^92 + 2323400966 * q^93 - 2064823418 * q^94 - 1372415809 * q^96 - 630790806 * q^97 + 1028814699 * q^98 + 2637491156 * q^99

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