LMFDB - Embedded newform 387.10.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,10,Mod(1,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, 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("387.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	387.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:	$199.318868595$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 6541 x^{15} + 10299 x^{14} + 17445509 x^{13} - 2347983 x^{12} + \cdots - 37\!\cdots\!40 $ x^17 - 3x^16 - 6541x^15 + 10299x^14 + 17445509x^13 - 2347983x^12 - 24275147889x^11 - 32817396993x^10 + 18668870018715x^9 + 54284997199479x^8 - 7688031373215127x^7 - 34414384567646799x^6 + 1472871456600457271x^5 + 8285298256630038219x^4 - 82173286944147552299x^3 - 301942019130667260459x^2 + 866271940633182378600x - 378136193010971707440
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{7} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-14.8584$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.8584 q^{2} -193.078 q^{4} -542.767 q^{5} -12329.9 q^{7} +12591.6 q^{8} +O(q^{10})$	\(q-17.8584 q^{2} -193.078 q^{4} -542.767 q^{5} -12329.9 q^{7} +12591.6 q^{8} +9692.93 q^{10} +62214.2 q^{11} -1612.70 q^{13} +220192. q^{14} -126009. q^{16} -299545. q^{17} +178333. q^{19} +104797. q^{20} -1.11104e6 q^{22} -2.13660e6 q^{23} -1.65853e6 q^{25} +28800.2 q^{26} +2.38064e6 q^{28} -353461. q^{29} -3.54498e6 q^{31} -4.19657e6 q^{32} +5.34939e6 q^{34} +6.69226e6 q^{35} -4.68076e6 q^{37} -3.18473e6 q^{38} -6.83428e6 q^{40} +3.19964e7 q^{41} +3.41880e6 q^{43} -1.20122e7 q^{44} +3.81561e7 q^{46} +3.67397e7 q^{47} +1.11673e8 q^{49} +2.96186e7 q^{50} +311377. q^{52} -2.84403e7 q^{53} -3.37678e7 q^{55} -1.55253e8 q^{56} +6.31223e6 q^{58} +3.96644e7 q^{59} +1.10955e8 q^{61} +6.33075e7 q^{62} +1.39460e8 q^{64} +875319. q^{65} +8.80180e7 q^{67} +5.78356e7 q^{68} -1.19513e8 q^{70} +2.56106e8 q^{71} +7.55335e7 q^{73} +8.35907e7 q^{74} -3.44322e7 q^{76} -7.67095e8 q^{77} +5.64490e7 q^{79} +6.83933e7 q^{80} -5.71404e8 q^{82} -2.06085e8 q^{83} +1.62583e8 q^{85} -6.10542e7 q^{86} +7.83374e8 q^{88} -3.67011e7 q^{89} +1.98844e7 q^{91} +4.12531e8 q^{92} -6.56111e8 q^{94} -9.67931e7 q^{95} +6.35358e8 q^{97} -1.99429e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 48 q^{2} + 4522 q^{4} - 4033 q^{5} - 76 q^{7} - 41046 q^{8}+O(q^{10}) $ 17 * q - 48 * q^2 + 4522 * q^4 - 4033 * q^5 - 76 * q^7 - 41046 * q^8	\( 17 q - 48 q^{2} + 4522 q^{4} - 4033 q^{5} - 76 q^{7} - 41046 q^{8} + 23763 q^{10} - 78370 q^{11} + 114452 q^{13} + 376208 q^{14} + 412586 q^{16} - 726937 q^{17} + 544263 q^{19} - 3642183 q^{20} + 5269148 q^{22} - 5575241 q^{23} + 10874708 q^{25} - 8009180 q^{26} + 12534764 q^{28} - 8223345 q^{29} + 13054147 q^{31} - 37111710 q^{32} + 27991291 q^{34} - 17826330 q^{35} + 46733879 q^{37} - 15733789 q^{38} + 52241669 q^{40} - 53667013 q^{41} + 58119617 q^{43} - 81727236 q^{44} + 146859355 q^{46} - 122945511 q^{47} + 111396073 q^{49} + 96642133 q^{50} - 54447944 q^{52} + 993146 q^{53} - 248155792 q^{55} + 141048116 q^{56} - 466599837 q^{58} + 95519644 q^{59} - 311752038 q^{61} + 212471691 q^{62} - 829842590 q^{64} + 107969830 q^{65} - 292438130 q^{67} + 88281129 q^{68} - 1650972530 q^{70} + 13576908 q^{71} - 501490738 q^{73} + 494831691 q^{74} - 1248630771 q^{76} - 787365348 q^{77} + 740350275 q^{79} + 27802861 q^{80} - 1600400057 q^{82} - 754109940 q^{83} + 1071609956 q^{85} - 164102448 q^{86} + 1863375104 q^{88} - 1470581868 q^{89} + 2895349644 q^{91} - 1041082071 q^{92} - 706582361 q^{94} - 3297255729 q^{95} + 1949310583 q^{97} - 6695989160 q^{98}+O(q^{100}) \) 17 * q - 48 * q^2 + 4522 * q^4 - 4033 * q^5 - 76 * q^7 - 41046 * q^8 + 23763 * q^10 - 78370 * q^11 + 114452 * q^13 + 376208 * q^14 + 412586 * q^16 - 726937 * q^17 + 544263 * q^19 - 3642183 * q^20 + 5269148 * q^22 - 5575241 * q^23 + 10874708 * q^25 - 8009180 * q^26 + 12534764 * q^28 - 8223345 * q^29 + 13054147 * q^31 - 37111710 * q^32 + 27991291 * q^34 - 17826330 * q^35 + 46733879 * q^37 - 15733789 * q^38 + 52241669 * q^40 - 53667013 * q^41 + 58119617 * q^43 - 81727236 * q^44 + 146859355 * q^46 - 122945511 * q^47 + 111396073 * q^49 + 96642133 * q^50 - 54447944 * q^52 + 993146 * q^53 - 248155792 * q^55 + 141048116 * q^56 - 466599837 * q^58 + 95519644 * q^59 - 311752038 * q^61 + 212471691 * q^62 - 829842590 * q^64 + 107969830 * q^65 - 292438130 * q^67 + 88281129 * q^68 - 1650972530 * q^70 + 13576908 * q^71 - 501490738 * q^73 + 494831691 * q^74 - 1248630771 * q^76 - 787365348 * q^77 + 740350275 * q^79 + 27802861 * q^80 - 1600400057 * q^82 - 754109940 * q^83 + 1071609956 * q^85 - 164102448 * q^86 + 1863375104 * q^88 - 1470581868 * q^89 + 2895349644 * q^91 - 1041082071 * q^92 - 706582361 * q^94 - 3297255729 * q^95 + 1949310583 * q^97 - 6695989160 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−17.8584	−0.789236	−0.394618	−	0.918845i	$-0.629123\pi$
$2$	−17.8584	−0.789236	−0.394618	+	0.918845i	$0.629123\pi$
$3$	0	0
$3$	0	0
$4$	−193.078	−0.377106
$5$	−542.767	−0.388372	−0.194186	−	0.980965i	$-0.562207\pi$
$5$	−542.767	−0.388372	−0.194186	+	0.980965i	$0.562207\pi$
$6$	0	0
$7$	−12329.9	−1.94097	−0.970484	−	0.241166i	$-0.922470\pi$
$7$	−12329.9	−1.94097	−0.970484	+	0.241166i	$0.922470\pi$
$8$	12591.6	1.08686
$9$	0	0
$10$	9692.93	0.306517
$11$	62214.2	1.28122	0.640608	−	0.767868i	$-0.278682\pi$
$11$	62214.2	1.28122	0.640608	+	0.767868i	$0.278682\pi$
$12$	0	0
$13$	−1612.70	−0.0156606	−0.00783029	−	0.999969i	$-0.502492\pi$
$13$	−1612.70	−0.0156606	−0.00783029	+	0.999969i	$0.502492\pi$
$14$	220192.	1.53188
$15$	0	0
$16$	−126009.	−0.480685
$17$	−299545.	−0.869845	−0.434922	−	0.900468i	$-0.643224\pi$
$17$	−299545.	−0.869845	−0.434922	+	0.900468i	$0.643224\pi$
$18$	0	0
$19$	178333.	0.313935	0.156968	−	0.987604i	$-0.449828\pi$
$19$	178333.	0.313935	0.156968	+	0.987604i	$0.449828\pi$
$20$	104797.	0.146458
$21$	0	0
$22$	−1.11104e6	−1.01118
$23$	−2.13660e6	−1.59202	−0.796008	−	0.605286i	$-0.793059\pi$
$23$	−2.13660e6	−1.59202	−0.796008	+	0.605286i	$0.793059\pi$
$24$	0	0
$25$	−1.65853e6	−0.849167
$26$	28800.2	0.0123599
$27$	0	0
$28$	2.38064e6	0.731951
$29$	−353461.	−0.0928004	−0.0464002	−	0.998923i	$-0.514775\pi$
$29$	−353461.	−0.0928004	−0.0464002	+	0.998923i	$0.514775\pi$
$30$	0	0
$31$	−3.54498e6	−0.689423	−0.344712	−	0.938709i	$-0.612023\pi$
$31$	−3.54498e6	−0.689423	−0.344712	+	0.938709i	$0.612023\pi$
$32$	−4.19657e6	−0.707488
$33$	0	0
$34$	5.34939e6	0.686513
$35$	6.69226e6	0.753818
$36$	0	0
$37$	−4.68076e6	−0.410590	−0.205295	−	0.978700i	$-0.565815\pi$
$37$	−4.68076e6	−0.410590	−0.205295	+	0.978700i	$0.565815\pi$
$38$	−3.18473e6	−0.247769
$39$	0	0
$40$	−6.83428e6	−0.422107
$41$	3.19964e7	1.76837	0.884186	−	0.467135i	$-0.154714\pi$
$41$	3.19964e7	1.76837	0.884186	+	0.467135i	$0.154714\pi$
$42$	0	0
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	−1.20122e7	−0.483155
$45$	0	0
$46$	3.81561e7	1.25648
$47$	3.67397e7	1.09823	0.549117	−	0.835746i	$-0.314964\pi$
$47$	3.67397e7	1.09823	0.549117	+	0.835746i	$0.314964\pi$
$48$	0	0
$49$	1.11673e8	2.76736
$50$	2.96186e7	0.670193
$51$	0	0
$52$	311377.	0.00590570
$53$	−2.84403e7	−0.495099	−0.247549	−	0.968875i	$-0.579625\pi$
$53$	−2.84403e7	−0.495099	−0.247549	+	0.968875i	$0.579625\pi$
$54$	0	0
$55$	−3.37678e7	−0.497589
$56$	−1.55253e8	−2.10956
$57$	0	0
$58$	6.31223e6	0.0732414
$59$	3.96644e7	0.426154	0.213077	−	0.977035i	$-0.431651\pi$
$59$	3.96644e7	0.426154	0.213077	+	0.977035i	$0.431651\pi$
$60$	0	0
$61$	1.10955e8	1.02603	0.513016	−	0.858379i	$-0.328528\pi$
$61$	1.10955e8	1.02603	0.513016	+	0.858379i	$0.328528\pi$
$62$	6.33075e7	0.544118
$63$	0	0
$64$	1.39460e8	1.03906
$65$	875319.	0.00608214
$66$	0	0
$67$	8.80180e7	0.533623	0.266812	−	0.963749i	$-0.414030\pi$
$67$	8.80180e7	0.533623	0.266812	+	0.963749i	$0.414030\pi$
$68$	5.78356e7	0.328024
$69$	0	0
$70$	−1.19513e8	−0.594941
$71$	2.56106e8	1.19607	0.598037	−	0.801469i	$-0.295948\pi$
$71$	2.56106e8	1.19607	0.598037	+	0.801469i	$0.295948\pi$
$72$	0	0
$73$	7.55335e7	0.311306	0.155653	−	0.987812i	$-0.450252\pi$
$73$	7.55335e7	0.311306	0.155653	+	0.987812i	$0.450252\pi$
$74$	8.35907e7	0.324053
$75$	0	0
$76$	−3.44322e7	−0.118387
$77$	−7.67095e8	−2.48680
$78$	0	0
$79$	5.64490e7	0.163055	0.0815275	−	0.996671i	$-0.474020\pi$
$79$	5.64490e7	0.163055	0.0815275	+	0.996671i	$0.474020\pi$
$80$	6.83933e7	0.186685
$81$	0	0
$82$	−5.71404e8	−1.39566
$83$	−2.06085e8	−0.476645	−0.238323	−	0.971186i	$-0.576598\pi$
$83$	−2.06085e8	−0.476645	−0.238323	+	0.971186i	$0.576598\pi$
$84$	0	0
$85$	1.62583e8	0.337824
$86$	−6.10542e7	−0.120357
$87$	0	0
$88$	7.83374e8	1.39251
$89$	−3.67011e7	−0.0620046	−0.0310023	−	0.999519i	$-0.509870\pi$
$89$	−3.67011e7	−0.0620046	−0.0310023	+	0.999519i	$0.509870\pi$
$90$	0	0
$91$	1.98844e7	0.0303967
$92$	4.12531e8	0.600359
$93$	0	0
$94$	−6.56111e8	−0.866766
$95$	−9.67931e7	−0.121924
$96$	0	0
$97$	6.35358e8	0.728695	0.364348	−	0.931263i	$-0.381292\pi$
$97$	6.35358e8	0.728695	0.364348	+	0.931263i	$0.381292\pi$
$98$	−1.99429e9	−2.18410
$99$	0	0
$100$	3.20226e8	0.320226
$101$	3.94028e8	0.376774	0.188387	−	0.982095i	$-0.439674\pi$
$101$	3.94028e8	0.376774	0.188387	+	0.982095i	$0.439674\pi$
$102$	0	0
$103$	1.21187e9	1.06093	0.530467	−	0.847706i	$-0.322017\pi$
$103$	1.21187e9	1.06093	0.530467	+	0.847706i	$0.322017\pi$
$104$	−2.03064e7	−0.0170209
$105$	0	0
$106$	5.07897e8	0.390750
$107$	−1.78380e9	−1.31558	−0.657792	−	0.753200i	$-0.728509\pi$
$107$	−1.78380e9	−1.31558	−0.657792	+	0.753200i	$0.728509\pi$
$108$	0	0
$109$	−2.01755e9	−1.36901	−0.684504	−	0.729010i	$-0.739981\pi$
$109$	−2.01755e9	−1.36901	−0.684504	+	0.729010i	$0.739981\pi$
$110$	6.03038e8	0.392715
$111$	0	0
$112$	1.55367e9	0.932993
$113$	1.34770e9	0.777571	0.388786	−	0.921328i	$-0.372895\pi$
$113$	1.34770e9	0.777571	0.388786	+	0.921328i	$0.372895\pi$
$114$	0	0
$115$	1.15967e9	0.618295
$116$	6.82456e7	0.0349956
$117$	0	0
$118$	−7.08341e8	−0.336336
$119$	3.69336e9	1.68834
$120$	0	0
$121$	1.51266e9	0.641516
$122$	−1.98147e9	−0.809782
$123$	0	0
$124$	6.84459e8	0.259986
$125$	1.96029e9	0.718165
$126$	0	0
$127$	2.05640e9	0.701441	0.350721	−	0.936480i	$-0.385937\pi$
$127$	2.05640e9	0.701441	0.350721	+	0.936480i	$0.385937\pi$
$128$	−3.41892e8	−0.112575
$129$	0	0
$130$	−1.56318e7	−0.00480024
$131$	2.96429e8	0.0879426	0.0439713	−	0.999033i	$-0.485999\pi$
$131$	2.96429e8	0.0879426	0.0439713	+	0.999033i	$0.485999\pi$
$132$	0	0
$133$	−2.19882e9	−0.609338
$134$	−1.57186e9	−0.421155
$135$	0	0
$136$	−3.77174e9	−0.945401
$137$	−3.88758e9	−0.942839	−0.471419	−	0.881909i	$-0.656258\pi$
$137$	−3.88758e9	−0.942839	−0.471419	+	0.881909i	$0.656258\pi$
$138$	0	0
$139$	4.47607e9	1.01702	0.508511	−	0.861056i	$-0.330196\pi$
$139$	4.47607e9	1.01702	0.508511	+	0.861056i	$0.330196\pi$
$140$	−1.29213e9	−0.284270
$141$	0	0
$142$	−4.57364e9	−0.943985
$143$	−1.00333e8	−0.0200646
$144$	0	0
$145$	1.91847e8	0.0360411
$146$	−1.34891e9	−0.245694
$147$	0	0
$148$	9.03753e8	0.154836
$149$	−5.77103e7	−0.00959213	−0.00479607	−	0.999988i	$-0.501527\pi$
$149$	−5.77103e7	−0.00959213	−0.00479607	+	0.999988i	$0.501527\pi$
$150$	0	0
$151$	9.70737e9	1.51952	0.759758	−	0.650206i	$-0.225317\pi$
$151$	9.70737e9	1.51952	0.759758	+	0.650206i	$0.225317\pi$
$152$	2.24549e9	0.341204
$153$	0	0
$154$	1.36991e10	1.96267
$155$	1.92410e9	0.267753
$156$	0	0
$157$	3.48104e9	0.457258	0.228629	−	0.973514i	$-0.426576\pi$
$157$	3.48104e9	0.457258	0.228629	+	0.973514i	$0.426576\pi$
$158$	−1.00809e9	−0.128689
$159$	0	0
$160$	2.27776e9	0.274769
$161$	2.63440e10	3.09005
$162$	0	0
$163$	−8.59453e9	−0.953626	−0.476813	−	0.879005i	$-0.658208\pi$
$163$	−8.59453e9	−0.953626	−0.476813	+	0.879005i	$0.658208\pi$
$164$	−6.17781e9	−0.666864
$165$	0	0
$166$	3.68035e9	0.376186
$167$	−1.56830e10	−1.56029	−0.780146	−	0.625597i	$-0.784855\pi$
$167$	−1.56830e10	−1.56029	−0.780146	+	0.625597i	$0.784855\pi$
$168$	0	0
$169$	−1.06019e10	−0.999755
$170$	−2.90347e9	−0.266623
$171$	0	0
$172$	−6.60097e8	−0.0575082
$173$	−1.41376e10	−1.19997	−0.599984	−	0.800012i	$-0.704826\pi$
$173$	−1.41376e10	−1.19997	−0.599984	+	0.800012i	$0.704826\pi$
$174$	0	0
$175$	2.04495e10	1.64821
$176$	−7.83953e9	−0.615861
$177$	0	0
$178$	6.55422e8	0.0489363
$179$	3.13844e9	0.228494	0.114247	−	0.993452i	$-0.463554\pi$
$179$	3.13844e9	0.228494	0.114247	+	0.993452i	$0.463554\pi$
$180$	0	0
$181$	9.58919e9	0.664092	0.332046	−	0.943263i	$-0.392261\pi$
$181$	9.58919e9	0.664092	0.332046	+	0.943263i	$0.392261\pi$
$182$	−3.55103e8	−0.0239902
$183$	0	0
$184$	−2.69031e10	−1.73030
$185$	2.54056e9	0.159462
$186$	0	0
$187$	−1.86360e10	−1.11446
$188$	−7.09363e9	−0.414151
$189$	0	0
$190$	1.72857e9	0.0962266
$191$	1.32511e10	0.720444	0.360222	−	0.932867i	$-0.382701\pi$
$191$	1.32511e10	0.720444	0.360222	+	0.932867i	$0.382701\pi$
$192$	0	0
$193$	2.54411e9	0.131986	0.0659930	−	0.997820i	$-0.478978\pi$
$193$	2.54411e9	0.131986	0.0659930	+	0.997820i	$0.478978\pi$
$194$	−1.13465e10	−0.575113
$195$	0	0
$196$	−2.15616e10	−1.04359
$197$	1.71149e10	0.809612	0.404806	−	0.914403i	$-0.367339\pi$
$197$	1.71149e10	0.809612	0.404806	+	0.914403i	$0.367339\pi$
$198$	0	0
$199$	−4.13350e10	−1.86844	−0.934221	−	0.356695i	$-0.883903\pi$
$199$	−4.13350e10	−1.86844	−0.934221	+	0.356695i	$0.883903\pi$
$200$	−2.08835e10	−0.922927
$201$	0	0
$202$	−7.03671e9	−0.297364
$203$	4.35813e9	0.180123
$204$	0	0
$205$	−1.73666e10	−0.686787
$206$	−2.16420e10	−0.837328
$207$	0	0
$208$	2.03214e8	0.00752780
$209$	1.10948e10	0.402219
$210$	0	0
$211$	1.63594e9	0.0568192	0.0284096	−	0.999596i	$-0.490956\pi$
$211$	1.63594e9	0.0568192	0.0284096	+	0.999596i	$0.490956\pi$
$212$	5.49120e9	0.186705
$213$	0	0
$214$	3.18557e10	1.03831
$215$	−1.85561e9	−0.0592262
$216$	0	0
$217$	4.37092e10	1.33815
$218$	3.60302e10	1.08047
$219$	0	0
$220$	6.51983e9	0.187644
$221$	4.83075e8	0.0136223
$222$	0	0
$223$	−1.03055e10	−0.279059	−0.139529	−	0.990218i	$-0.544559\pi$
$223$	−1.03055e10	−0.279059	−0.139529	+	0.990218i	$0.544559\pi$
$224$	5.17432e10	1.37321
$225$	0	0
$226$	−2.40677e10	−0.613687
$227$	−3.19747e10	−0.799263	−0.399632	−	0.916676i	$-0.630862\pi$
$227$	−3.19747e10	−0.799263	−0.399632	+	0.916676i	$0.630862\pi$
$228$	0	0
$229$	4.65306e10	1.11810	0.559048	−	0.829135i	$-0.311167\pi$
$229$	4.65306e10	1.11810	0.559048	+	0.829135i	$0.311167\pi$
$230$	−2.07099e10	−0.487981
$231$	0	0
$232$	−4.45062e9	−0.100861
$233$	7.78222e10	1.72982	0.864912	−	0.501924i	$-0.167374\pi$
$233$	7.78222e10	1.72982	0.864912	+	0.501924i	$0.167374\pi$
$234$	0	0
$235$	−1.99411e10	−0.426524
$236$	−7.65833e9	−0.160705
$237$	0	0
$238$	−6.59574e10	−1.33250
$239$	8.97205e10	1.77869	0.889347	−	0.457233i	$-0.151160\pi$
$239$	8.97205e10	1.77869	0.889347	+	0.457233i	$0.151160\pi$
$240$	0	0
$241$	3.18390e8	0.00607971	0.00303986	−	0.999995i	$-0.499032\pi$
$241$	3.18390e8	0.00607971	0.00303986	+	0.999995i	$0.499032\pi$
$242$	−2.70137e10	−0.506308
$243$	0	0
$244$	−2.14229e10	−0.386923
$245$	−6.06123e10	−1.07476
$246$	0	0
$247$	−2.87597e8	−0.00491641
$248$	−4.46368e10	−0.749308
$249$	0	0
$250$	−3.50075e10	−0.566802
$251$	−5.74998e10	−0.914396	−0.457198	−	0.889365i	$-0.651147\pi$
$251$	−5.74998e10	−0.914396	−0.457198	+	0.889365i	$0.651147\pi$
$252$	0	0
$253$	−1.32927e11	−2.03972
$254$	−3.67240e10	−0.553603
$255$	0	0
$256$	−6.52980e10	−0.950211
$257$	−2.98098e9	−0.0426246	−0.0213123	−	0.999773i	$-0.506784\pi$
$257$	−2.98098e9	−0.0426246	−0.0213123	+	0.999773i	$0.506784\pi$
$258$	0	0
$259$	5.77133e10	0.796942
$260$	−1.69005e8	−0.00229361
$261$	0	0
$262$	−5.29373e9	−0.0694075
$263$	−3.90444e10	−0.503220	−0.251610	−	0.967829i	$-0.580960\pi$
$263$	−3.90444e10	−0.503220	−0.251610	+	0.967829i	$0.580960\pi$
$264$	0	0
$265$	1.54364e10	0.192283
$266$	3.92674e10	0.480912
$267$	0	0
$268$	−1.69944e10	−0.201233
$269$	−8.79555e10	−1.02418	−0.512092	−	0.858931i	$-0.671129\pi$
$269$	−8.79555e10	−1.02418	−0.512092	+	0.858931i	$0.671129\pi$
$270$	0	0
$271$	1.39932e11	1.57600	0.787999	−	0.615677i	$-0.211117\pi$
$271$	1.39932e11	1.57600	0.787999	+	0.615677i	$0.211117\pi$
$272$	3.77452e10	0.418121
$273$	0	0
$274$	6.94260e10	0.744122
$275$	−1.03184e11	−1.08797
$276$	0	0
$277$	−1.30837e11	−1.33528	−0.667641	−	0.744483i	$-0.732696\pi$
$277$	−1.30837e11	−1.33528	−0.667641	+	0.744483i	$0.732696\pi$
$278$	−7.99353e10	−0.802670
$279$	0	0
$280$	8.42660e10	0.819296
$281$	−5.07202e10	−0.485292	−0.242646	−	0.970115i	$-0.578015\pi$
$281$	−5.07202e10	−0.485292	−0.242646	+	0.970115i	$0.578015\pi$
$282$	0	0
$283$	1.50237e11	1.39231	0.696156	−	0.717891i	$-0.254892\pi$
$283$	1.50237e11	1.39231	0.696156	+	0.717891i	$0.254892\pi$
$284$	−4.94486e10	−0.451047
$285$	0	0
$286$	1.79178e9	0.0158357
$287$	−3.94512e11	−3.43235
$288$	0	0
$289$	−2.88607e10	−0.243370
$290$	−3.42607e9	−0.0284449
$291$	0	0
$292$	−1.45839e10	−0.117395
$293$	−7.70103e9	−0.0610442	−0.0305221	−	0.999534i	$-0.509717\pi$
$293$	−7.70103e9	−0.0610442	−0.0305221	+	0.999534i	$0.509717\pi$
$294$	0	0
$295$	−2.15285e10	−0.165506
$296$	−5.89380e10	−0.446255
$297$	0	0
$298$	1.03061e9	0.00757046
$299$	3.44569e9	0.0249319
$300$	0	0
$301$	−4.21535e10	−0.295995
$302$	−1.73358e11	−1.19926
$303$	0	0
$304$	−2.24715e10	−0.150904
$305$	−6.02225e10	−0.398483
$306$	0	0
$307$	−1.58304e11	−1.01711	−0.508555	−	0.861030i	$-0.669820\pi$
$307$	−1.58304e11	−1.01711	−0.508555	+	0.861030i	$0.669820\pi$
$308$	1.48109e11	0.937788
$309$	0	0
$310$	−3.43612e10	−0.211320
$311$	1.37182e10	0.0831528	0.0415764	−	0.999135i	$-0.486762\pi$
$311$	1.37182e10	0.0831528	0.0415764	+	0.999135i	$0.486762\pi$
$312$	0	0
$313$	−6.35309e10	−0.374141	−0.187071	−	0.982346i	$-0.559899\pi$
$313$	−6.35309e10	−0.374141	−0.187071	+	0.982346i	$0.559899\pi$
$314$	−6.21658e10	−0.360884
$315$	0	0
$316$	−1.08991e10	−0.0614890
$317$	−8.45007e10	−0.469995	−0.234998	−	0.971996i	$-0.575508\pi$
$317$	−8.45007e10	−0.469995	−0.234998	+	0.971996i	$0.575508\pi$
$318$	0	0
$319$	−2.19903e10	−0.118897
$320$	−7.56944e10	−0.403542
$321$	0	0
$322$	−4.70461e11	−2.43878
$323$	−5.34187e10	−0.273075
$324$	0	0
$325$	2.67471e9	0.0132985
$326$	1.53484e11	0.752636
$327$	0	0
$328$	4.02884e11	1.92198
$329$	−4.52996e11	−2.13164
$330$	0	0
$331$	−3.02866e11	−1.38683	−0.693417	−	0.720537i	$-0.743895\pi$
$331$	−3.02866e11	−1.38683	−0.693417	+	0.720537i	$0.743895\pi$
$332$	3.97906e10	0.179746
$333$	0	0
$334$	2.80074e11	1.23144
$335$	−4.77733e10	−0.207245
$336$	0	0
$337$	4.25162e11	1.79564	0.897821	−	0.440360i	$-0.145149\pi$
$337$	4.25162e11	1.79564	0.897821	+	0.440360i	$0.145149\pi$
$338$	1.89333e11	0.789043
$339$	0	0
$340$	−3.13913e10	−0.127395
$341$	−2.20548e11	−0.883300
$342$	0	0
$343$	−8.79358e11	−3.43038
$344$	4.30480e10	0.165745
$345$	0	0
$346$	2.52475e11	0.947058
$347$	−2.27802e11	−0.843481	−0.421740	−	0.906717i	$-0.638581\pi$
$347$	−2.27802e11	−0.843481	−0.421740	+	0.906717i	$0.638581\pi$
$348$	0	0
$349$	−1.66392e11	−0.600369	−0.300184	−	0.953881i	$-0.597048\pi$
$349$	−1.66392e11	−0.600369	−0.300184	+	0.953881i	$0.597048\pi$
$350$	−3.65195e11	−1.30082
$351$	0	0
$352$	−2.61086e11	−0.906446
$353$	1.16576e11	0.399597	0.199799	−	0.979837i	$-0.435971\pi$
$353$	1.16576e11	0.399597	0.199799	+	0.979837i	$0.435971\pi$
$354$	0	0
$355$	−1.39006e11	−0.464522
$356$	7.08618e9	0.0233823
$357$	0	0
$358$	−5.60474e10	−0.180336
$359$	−5.13617e11	−1.63198	−0.815989	−	0.578067i	$-0.803807\pi$
$359$	−5.13617e11	−1.63198	−0.815989	+	0.578067i	$0.803807\pi$
$360$	0	0
$361$	−2.90885e11	−0.901445
$362$	−1.71247e11	−0.524125
$363$	0	0
$364$	−3.83925e9	−0.0114628
$365$	−4.09971e10	−0.120902
$366$	0	0
$367$	1.13487e11	0.326550	0.163275	−	0.986581i	$-0.447794\pi$
$367$	1.13487e11	0.326550	0.163275	+	0.986581i	$0.447794\pi$
$368$	2.69230e11	0.765257
$369$	0	0
$370$	−4.53703e10	−0.125853
$371$	3.50665e11	0.960971
$372$	0	0
$373$	−3.83069e11	−1.02468	−0.512339	−	0.858783i	$-0.671221\pi$
$373$	−3.83069e11	−1.02468	−0.512339	+	0.858783i	$0.671221\pi$
$374$	3.32808e11	0.879572
$375$	0	0
$376$	4.62609e11	1.19363
$377$	5.70025e8	0.00145331
$378$	0	0
$379$	3.39826e11	0.846020	0.423010	−	0.906125i	$-0.360974\pi$
$379$	3.39826e11	0.846020	0.423010	+	0.906125i	$0.360974\pi$
$380$	1.86887e10	0.0459782
$381$	0	0
$382$	−2.36642e11	−0.568600
$383$	−2.56152e11	−0.608279	−0.304140	−	0.952627i	$-0.598369\pi$
$383$	−2.56152e11	−0.608279	−0.304140	+	0.952627i	$0.598369\pi$
$384$	0	0
$385$	4.16354e11	0.965804
$386$	−4.54337e10	−0.104168
$387$	0	0
$388$	−1.22674e11	−0.274796
$389$	1.09872e11	0.243284	0.121642	−	0.992574i	$-0.461184\pi$
$389$	1.09872e11	0.243284	0.121642	+	0.992574i	$0.461184\pi$
$390$	0	0
$391$	6.40007e11	1.38481
$392$	1.40613e12	3.00773
$393$	0	0
$394$	−3.05645e11	−0.638975
$395$	−3.06386e10	−0.0633260
$396$	0	0
$397$	1.29718e11	0.262085	0.131042	−	0.991377i	$-0.458168\pi$
$397$	1.29718e11	0.262085	0.131042	+	0.991377i	$0.458168\pi$
$398$	7.38177e11	1.47464
$399$	0	0
$400$	2.08989e11	0.408182
$401$	2.09370e11	0.404357	0.202179	−	0.979349i	$-0.435198\pi$
$401$	2.09370e11	0.404357	0.202179	+	0.979349i	$0.435198\pi$
$402$	0	0
$403$	5.71698e9	0.0107968
$404$	−7.60784e10	−0.142084
$405$	0	0
$406$	−7.78292e10	−0.142159
$407$	−2.91210e11	−0.526055
$408$	0	0
$409$	4.47429e11	0.790623	0.395311	−	0.918547i	$-0.370637\pi$
$409$	4.47429e11	0.790623	0.395311	+	0.918547i	$0.370637\pi$
$410$	3.10139e11	0.542037
$411$	0	0
$412$	−2.33986e11	−0.400085
$413$	−4.89058e11	−0.827151
$414$	0	0
$415$	1.11856e11	0.185116
$416$	6.76780e9	0.0110797
$417$	0	0
$418$	−1.98136e11	−0.317446
$419$	3.30875e10	0.0524447	0.0262223	−	0.999656i	$-0.491652\pi$
$419$	3.30875e10	0.0524447	0.0262223	+	0.999656i	$0.491652\pi$
$420$	0	0
$421$	6.72742e11	1.04371	0.521854	−	0.853035i	$-0.325241\pi$
$421$	6.72742e11	1.04371	0.521854	+	0.853035i	$0.325241\pi$
$422$	−2.92151e10	−0.0448438
$423$	0	0
$424$	−3.58107e11	−0.538104
$425$	4.96804e11	0.738643
$426$	0	0
$427$	−1.36806e12	−1.99150
$428$	3.44413e11	0.496115
$429$	0	0
$430$	3.31382e10	0.0467435
$431$	−3.03216e11	−0.423257	−0.211629	−	0.977350i	$-0.567877\pi$
$431$	−3.03216e11	−0.423257	−0.211629	+	0.977350i	$0.567877\pi$
$432$	0	0
$433$	9.04290e11	1.23627	0.618134	−	0.786073i	$-0.287889\pi$
$433$	9.04290e11	1.23627	0.618134	+	0.786073i	$0.287889\pi$
$434$	−7.80576e11	−1.05611
$435$	0	0
$436$	3.89546e11	0.516261
$437$	−3.81025e11	−0.499790
$438$	0	0
$439$	−5.18533e11	−0.666325	−0.333163	−	0.942869i	$-0.608116\pi$
$439$	−5.18533e11	−0.666325	−0.333163	+	0.942869i	$0.608116\pi$
$440$	−4.25189e11	−0.540811
$441$	0	0
$442$	−8.62694e9	−0.0107512
$443$	−5.83805e10	−0.0720196	−0.0360098	−	0.999351i	$-0.511465\pi$
$443$	−5.83805e10	−0.0720196	−0.0360098	+	0.999351i	$0.511465\pi$
$444$	0	0
$445$	1.99201e10	0.0240809
$446$	1.84039e11	0.220243
$447$	0	0
$448$	−1.71953e12	−2.01678
$449$	−5.60165e10	−0.0650440	−0.0325220	−	0.999471i	$-0.510354\pi$
$449$	−5.60165e10	−0.0650440	−0.0325220	+	0.999471i	$0.510354\pi$
$450$	0	0
$451$	1.99063e12	2.26567
$452$	−2.60212e11	−0.293227
$453$	0	0
$454$	5.71016e11	0.630807
$455$	−1.07926e10	−0.0118052
$456$	0	0
$457$	4.66456e11	0.500251	0.250125	−	0.968213i	$-0.419528\pi$
$457$	4.66456e11	0.500251	0.250125	+	0.968213i	$0.419528\pi$
$458$	−8.30962e11	−0.882442
$459$	0	0
$460$	−2.23908e11	−0.233163
$461$	−5.12024e11	−0.528003	−0.264002	−	0.964522i	$-0.585042\pi$
$461$	−5.12024e11	−0.528003	−0.264002	+	0.964522i	$0.585042\pi$
$462$	0	0
$463$	7.61896e11	0.770515	0.385257	−	0.922809i	$-0.374113\pi$
$463$	7.61896e11	0.770515	0.385257	+	0.922809i	$0.374113\pi$
$464$	4.45391e10	0.0446077
$465$	0	0
$466$	−1.38978e12	−1.36524
$467$	4.59638e11	0.447188	0.223594	−	0.974682i	$-0.428221\pi$
$467$	4.59638e11	0.447188	0.223594	+	0.974682i	$0.428221\pi$
$468$	0	0
$469$	−1.08525e12	−1.03575
$470$	3.56115e11	0.336628
$471$	0	0
$472$	4.99436e11	0.463171
$473$	2.12698e11	0.195384
$474$	0	0
$475$	−2.95770e11	−0.266583
$476$	−7.13108e11	−0.636684
$477$	0	0
$478$	−1.60226e12	−1.40381
$479$	1.47088e12	1.27663	0.638317	−	0.769773i	$-0.279631\pi$
$479$	1.47088e12	1.27663	0.638317	+	0.769773i	$0.279631\pi$
$480$	0	0
$481$	7.54865e9	0.00643008
$482$	−5.68593e9	−0.00479833
$483$	0	0
$484$	−2.92062e11	−0.241920
$485$	−3.44851e11	−0.283005
$486$	0	0
$487$	−2.00769e12	−1.61740	−0.808699	−	0.588223i	$-0.799828\pi$
$487$	−2.00769e12	−1.61740	−0.808699	+	0.588223i	$0.799828\pi$
$488$	1.39709e12	1.11516
$489$	0	0
$490$	1.08244e12	0.848243
$491$	6.70747e10	0.0520826	0.0260413	−	0.999661i	$-0.491710\pi$
$491$	6.70747e10	0.0520826	0.0260413	+	0.999661i	$0.491710\pi$
$492$	0	0
$493$	1.05877e11	0.0807220
$494$	5.13601e9	0.00388021
$495$	0	0
$496$	4.46698e11	0.331395
$497$	−3.15777e12	−2.32154
$498$	0	0
$499$	6.22530e11	0.449477	0.224739	−	0.974419i	$-0.427847\pi$
$499$	6.22530e11	0.449477	0.224739	+	0.974419i	$0.427847\pi$
$500$	−3.78489e11	−0.270825
$501$	0	0
$502$	1.02685e12	0.721674
$503$	7.04840e11	0.490947	0.245473	−	0.969403i	$-0.421057\pi$
$503$	7.04840e11	0.490947	0.245473	+	0.969403i	$0.421057\pi$
$504$	0	0
$505$	−2.13865e11	−0.146329
$506$	2.37385e12	1.60982
$507$	0	0
$508$	−3.97047e11	−0.264518
$509$	−3.83439e11	−0.253201	−0.126601	−	0.991954i	$-0.540407\pi$
$509$	−3.83439e11	−0.253201	−0.126601	+	0.991954i	$0.540407\pi$
$510$	0	0
$511$	−9.31321e11	−0.604234
$512$	1.34117e12	0.862517
$513$	0	0
$514$	5.32355e10	0.0336409
$515$	−6.57763e11	−0.412037
$516$	0	0
$517$	2.28573e12	1.40708
$518$	−1.03067e12	−0.628975
$519$	0	0
$520$	1.10216e10	0.00661044
$521$	2.71418e12	1.61387	0.806937	−	0.590638i	$-0.201124\pi$
$521$	2.71418e12	1.61387	0.806937	+	0.590638i	$0.201124\pi$
$522$	0	0
$523$	2.13908e12	1.25017	0.625086	−	0.780556i	$-0.285064\pi$
$523$	2.13908e12	1.25017	0.625086	+	0.780556i	$0.285064\pi$
$524$	−5.72339e10	−0.0331637
$525$	0	0
$526$	6.97270e11	0.397160
$527$	1.06188e12	0.599691
$528$	0	0
$529$	2.76389e12	1.53451
$530$	−2.75669e11	−0.151756
$531$	0	0
$532$	4.24546e11	0.229785
$533$	−5.16005e10	−0.0276937
$534$	0	0
$535$	9.68186e11	0.510936
$536$	1.10828e12	0.579975
$537$	0	0
$538$	1.57074e12	0.808323
$539$	6.94763e12	3.54558
$540$	0	0
$541$	9.70124e11	0.486900	0.243450	−	0.969913i	$-0.421721\pi$
$541$	9.70124e11	0.486900	0.243450	+	0.969913i	$0.421721\pi$
$542$	−2.49896e12	−1.24383
$543$	0	0
$544$	1.25706e12	0.615405
$545$	1.09506e12	0.531684
$546$	0	0
$547$	−3.62322e12	−1.73042	−0.865211	−	0.501408i	$-0.832816\pi$
$547$	−3.62322e12	−1.73042	−0.865211	+	0.501408i	$0.832816\pi$
$548$	7.50609e11	0.355550
$549$	0	0
$550$	1.84270e12	0.858663
$551$	−6.30336e10	−0.0291333
$552$	0	0
$553$	−6.96010e11	−0.316484
$554$	2.33654e12	1.05385
$555$	0	0
$556$	−8.64232e11	−0.383525
$557$	−2.48740e12	−1.09496	−0.547478	−	0.836820i	$-0.684412\pi$
$557$	−2.48740e12	−1.09496	−0.547478	+	0.836820i	$0.684412\pi$
$558$	0	0
$559$	−5.51349e9	−0.00238822
$560$	−8.43282e11	−0.362349
$561$	0	0
$562$	9.05781e11	0.383010
$563$	3.90454e11	0.163788	0.0818940	−	0.996641i	$-0.473903\pi$
$563$	3.90454e11	0.163788	0.0818940	+	0.996641i	$0.473903\pi$
$564$	0	0
$565$	−7.31487e11	−0.301987
$566$	−2.68298e12	−1.09886
$567$	0	0
$568$	3.22478e12	1.29997
$569$	−1.28781e12	−0.515046	−0.257523	−	0.966272i	$-0.582906\pi$
$569$	−1.28781e12	−0.515046	−0.257523	+	0.966272i	$0.582906\pi$
$570$	0	0
$571$	2.12561e12	0.836797	0.418399	−	0.908264i	$-0.362592\pi$
$571$	2.12561e12	0.836797	0.418399	+	0.908264i	$0.362592\pi$
$572$	1.93721e10	0.00756649
$573$	0	0
$574$	7.04535e12	2.70894
$575$	3.54361e12	1.35189
$576$	0	0
$577$	−1.77876e12	−0.668077	−0.334038	−	0.942560i	$-0.608411\pi$
$577$	−1.77876e12	−0.668077	−0.334038	+	0.942560i	$0.608411\pi$
$578$	5.15406e11	0.192076
$579$	0	0
$580$	−3.70414e10	−0.0135913
$581$	2.54101e12	0.925154
$582$	0	0
$583$	−1.76939e12	−0.634329
$584$	9.51085e11	0.338346
$585$	0	0
$586$	1.37528e11	0.0481783
$587$	−4.15189e12	−1.44336	−0.721680	−	0.692227i	$-0.756630\pi$
$587$	−4.15189e12	−1.44336	−0.721680	+	0.692227i	$0.756630\pi$
$588$	0	0
$589$	−6.32186e11	−0.216434
$590$	3.84464e11	0.130624
$591$	0	0
$592$	5.89816e11	0.197364
$593$	−2.72790e12	−0.905904	−0.452952	−	0.891535i	$-0.649629\pi$
$593$	−2.72790e12	−0.905904	−0.452952	+	0.891535i	$0.649629\pi$
$594$	0	0
$595$	−2.00463e12	−0.655705
$596$	1.11426e10	0.00361725
$597$	0	0
$598$	−6.15343e10	−0.0196772
$599$	−2.46904e12	−0.783623	−0.391812	−	0.920045i	$-0.628152\pi$
$599$	−2.46904e12	−0.783623	−0.391812	+	0.920045i	$0.628152\pi$
$600$	0	0
$601$	−1.80063e12	−0.562976	−0.281488	−	0.959565i	$-0.590828\pi$
$601$	−1.80063e12	−0.562976	−0.281488	+	0.959565i	$0.590828\pi$
$602$	7.52793e11	0.233610
$603$	0	0
$604$	−1.87428e12	−0.573019
$605$	−8.21022e11	−0.249147
$606$	0	0
$607$	−3.83396e12	−1.14630	−0.573150	−	0.819451i	$-0.694279\pi$
$607$	−3.83396e12	−1.14630	−0.573150	+	0.819451i	$0.694279\pi$
$608$	−7.48385e11	−0.222105
$609$	0	0
$610$	1.07548e12	0.314497
$611$	−5.92500e10	−0.0171990
$612$	0	0
$613$	−6.16914e12	−1.76463	−0.882313	−	0.470664i	$-0.844014\pi$
$613$	−6.16914e12	−1.76463	−0.882313	+	0.470664i	$0.844014\pi$
$614$	2.82704e12	0.802740
$615$	0	0
$616$	−9.65892e12	−2.70281
$617$	−3.63257e11	−0.100909	−0.0504546	−	0.998726i	$-0.516067\pi$
$617$	−3.63257e11	−0.100909	−0.0504546	+	0.998726i	$0.516067\pi$
$618$	0	0
$619$	4.53686e12	1.24208	0.621038	−	0.783781i	$-0.286711\pi$
$619$	4.53686e12	1.24208	0.621038	+	0.783781i	$0.286711\pi$
$620$	−3.71501e11	−0.100971
$621$	0	0
$622$	−2.44986e11	−0.0656272
$623$	4.52521e11	0.120349
$624$	0	0
$625$	2.17534e12	0.570251
$626$	1.13456e12	0.295286
$627$	0	0
$628$	−6.72114e11	−0.172435
$629$	1.40210e12	0.357150
$630$	0	0
$631$	−1.55409e12	−0.390251	−0.195125	−	0.980778i	$-0.562511\pi$
$631$	−1.55409e12	−0.390251	−0.195125	+	0.980778i	$0.562511\pi$
$632$	7.10780e11	0.177218
$633$	0	0
$634$	1.50905e12	0.370937
$635$	−1.11615e12	−0.272420
$636$	0	0
$637$	−1.80094e11	−0.0433384
$638$	3.92710e11	0.0938381
$639$	0	0
$640$	1.85567e11	0.0437212
$641$	−5.21346e12	−1.21973	−0.609866	−	0.792504i	$-0.708777\pi$
$641$	−5.21346e12	−1.21973	−0.609866	+	0.792504i	$0.708777\pi$
$642$	0	0
$643$	5.32568e12	1.22864	0.614321	−	0.789056i	$-0.289430\pi$
$643$	5.32568e12	1.22864	0.614321	+	0.789056i	$0.289430\pi$
$644$	−5.08646e12	−1.16528
$645$	0	0
$646$	9.53971e11	0.215521
$647$	5.93392e11	0.133129	0.0665644	−	0.997782i	$-0.478796\pi$
$647$	5.93392e11	0.133129	0.0665644	+	0.997782i	$0.478796\pi$
$648$	0	0
$649$	2.46769e12	0.545995
$650$	−4.77659e10	−0.0104956
$651$	0	0
$652$	1.65942e12	0.359618
$653$	−5.02049e12	−1.08053	−0.540265	−	0.841495i	$-0.681676\pi$
$653$	−5.02049e12	−1.08053	−0.540265	+	0.841495i	$0.681676\pi$
$654$	0	0
$655$	−1.60892e11	−0.0341545
$656$	−4.03182e12	−0.850029
$657$	0	0
$658$	8.08978e12	1.68236
$659$	−7.32459e11	−0.151286	−0.0756430	−	0.997135i	$-0.524101\pi$
$659$	−7.32459e11	−0.151286	−0.0756430	+	0.997135i	$0.524101\pi$
$660$	0	0
$661$	−8.14141e12	−1.65880	−0.829398	−	0.558657i	$-0.811317\pi$
$661$	−8.14141e12	−1.65880	−0.829398	+	0.558657i	$0.811317\pi$
$662$	5.40869e12	1.09454
$663$	0	0
$664$	−2.59493e12	−0.518048
$665$	1.19345e12	0.236650
$666$	0	0
$667$	7.55203e11	0.147740
$668$	3.02805e12	0.588396
$669$	0	0
$670$	8.53153e11	0.163565
$671$	6.90295e12	1.31457
$672$	0	0
$673$	−7.58901e12	−1.42599	−0.712997	−	0.701167i	$-0.752663\pi$
$673$	−7.58901e12	−1.42599	−0.712997	+	0.701167i	$0.752663\pi$
$674$	−7.59270e12	−1.41719
$675$	0	0
$676$	2.04700e12	0.377014
$677$	−2.34458e12	−0.428960	−0.214480	−	0.976728i	$-0.568806\pi$
$677$	−2.34458e12	−0.428960	−0.214480	+	0.976728i	$0.568806\pi$
$678$	0	0
$679$	−7.83391e12	−1.41437
$680$	2.04717e12	0.367168
$681$	0	0
$682$	3.93863e12	0.697133
$683$	7.68157e12	1.35069	0.675347	−	0.737500i	$-0.263994\pi$
$683$	7.68157e12	1.35069	0.675347	+	0.737500i	$0.263994\pi$
$684$	0	0
$685$	2.11005e12	0.366172
$686$	1.57039e13	2.70738
$687$	0	0
$688$	−4.30798e11	−0.0733037
$689$	4.58655e10	0.00775354
$690$	0	0
$691$	1.02677e13	1.71325	0.856627	−	0.515937i	$-0.172556\pi$
$691$	1.02677e13	1.71325	0.856627	+	0.515937i	$0.172556\pi$
$692$	2.72967e12	0.452515
$693$	0	0
$694$	4.06818e12	0.665706
$695$	−2.42946e12	−0.394983
$696$	0	0
$697$	−9.58436e12	−1.53821
$698$	2.97149e12	0.473833
$699$	0	0
$700$	−3.94836e12	−0.621549
$701$	−9.20972e12	−1.44051	−0.720253	−	0.693711i	$-0.755974\pi$
$701$	−9.20972e12	−1.44051	−0.720253	+	0.693711i	$0.755974\pi$
$702$	0	0
$703$	−8.34732e11	−0.128899
$704$	8.67641e12	1.33126
$705$	0	0
$706$	−2.08185e12	−0.315376
$707$	−4.85833e12	−0.731307
$708$	0	0
$709$	−2.94952e12	−0.438372	−0.219186	−	0.975683i	$-0.570340\pi$
$709$	−2.94952e12	−0.438372	−0.219186	+	0.975683i	$0.570340\pi$
$710$	2.48242e12	0.366617
$711$	0	0
$712$	−4.62124e11	−0.0673904
$713$	7.57419e12	1.09757
$714$	0	0
$715$	5.44573e10	0.00779254
$716$	−6.05965e11	−0.0861666
$717$	0	0
$718$	9.17236e12	1.28802
$719$	1.00384e13	1.40083	0.700414	−	0.713737i	$-0.252999\pi$
$719$	1.00384e13	1.40083	0.700414	+	0.713737i	$0.252999\pi$
$720$	0	0
$721$	−1.49422e13	−2.05924
$722$	5.19474e12	0.711453
$723$	0	0
$724$	−1.85147e12	−0.250433
$725$	5.86225e11	0.0788030
$726$	0	0
$727$	4.11260e11	0.0546024	0.0273012	−	0.999627i	$-0.491309\pi$
$727$	4.11260e11	0.0546024	0.0273012	+	0.999627i	$0.491309\pi$
$728$	2.50376e11	0.0330370
$729$	0	0
$730$	7.32142e11	0.0954206
$731$	−1.02408e12	−0.132650
$732$	0	0
$733$	9.13015e12	1.16818	0.584090	−	0.811689i	$-0.301451\pi$
$733$	9.13015e12	1.16818	0.584090	+	0.811689i	$0.301451\pi$
$734$	−2.02669e12	−0.257725
$735$	0	0
$736$	8.96637e12	1.12633
$737$	5.47597e12	0.683687
$738$	0	0
$739$	−1.12794e13	−1.39119	−0.695596	−	0.718433i	$-0.744859\pi$
$739$	−1.12794e13	−1.39119	−0.695596	+	0.718433i	$0.744859\pi$
$740$	−4.90527e11	−0.0601340
$741$	0	0
$742$	−6.26231e12	−0.758433
$743$	−6.58448e12	−0.792633	−0.396316	−	0.918114i	$-0.629712\pi$
$743$	−6.58448e12	−0.792633	−0.396316	+	0.918114i	$0.629712\pi$
$744$	0	0
$745$	3.13232e10	0.00372532
$746$	6.84099e12	0.808713
$747$	0	0
$748$	3.59820e12	0.420270
$749$	2.19940e13	2.55351
$750$	0	0
$751$	−3.88685e12	−0.445880	−0.222940	−	0.974832i	$-0.571565\pi$
$751$	−3.88685e12	−0.445880	−0.222940	+	0.974832i	$0.571565\pi$
$752$	−4.62951e12	−0.527904
$753$	0	0
$754$	−1.01797e10	−0.00114700
$755$	−5.26884e12	−0.590138
$756$	0	0
$757$	−1.39930e10	−0.00154875	−0.000774374	−	1.00000i	$-0.500246\pi$
$757$	−1.39930e10	−0.00154875	−0.000774374		1.00000i	$0.500246\pi$
$758$	−6.06874e12	−0.667709
$759$	0	0
$760$	−1.21878e12	−0.132514
$761$	7.78034e11	0.0840945	0.0420472	−	0.999116i	$-0.486612\pi$
$761$	7.78034e11	0.0840945	0.0420472	+	0.999116i	$0.486612\pi$
$762$	0	0
$763$	2.48762e13	2.65720
$764$	−2.55849e12	−0.271684
$765$	0	0
$766$	4.57446e12	0.480076
$767$	−6.39667e10	−0.00667382
$768$	0	0
$769$	−1.51538e13	−1.56262	−0.781310	−	0.624144i	$-0.785448\pi$
$769$	−1.51538e13	−1.56262	−0.781310	+	0.624144i	$0.785448\pi$
$770$	−7.43540e12	−0.762248
$771$	0	0
$772$	−4.91213e11	−0.0497728
$773$	7.36906e12	0.742343	0.371171	−	0.928564i	$-0.378956\pi$
$773$	7.36906e12	0.742343	0.371171	+	0.928564i	$0.378956\pi$
$774$	0	0
$775$	5.87945e12	0.585435
$776$	8.00015e12	0.791991
$777$	0	0
$778$	−1.96213e12	−0.192009
$779$	5.70601e12	0.555154
$780$	0	0
$781$	1.59335e13	1.53243
$782$	−1.14295e13	−1.09294
$783$	0	0
$784$	−1.40717e13	−1.33023
$785$	−1.88939e12	−0.177586
$786$	0	0
$787$	2.97932e12	0.276842	0.138421	−	0.990374i	$-0.455797\pi$
$787$	2.97932e12	0.276842	0.138421	+	0.990374i	$0.455797\pi$
$788$	−3.30452e12	−0.305310
$789$	0	0
$790$	5.47156e11	0.0499792
$791$	−1.66170e13	−1.50924
$792$	0	0
$793$	−1.78936e11	−0.0160683
$794$	−2.31655e12	−0.206847
$795$	0	0
$796$	7.98090e12	0.704601
$797$	−5.65430e12	−0.496382	−0.248191	−	0.968711i	$-0.579836\pi$
$797$	−5.65430e12	−0.496382	−0.248191	+	0.968711i	$0.579836\pi$
$798$	0	0
$799$	−1.10052e13	−0.955293
$800$	6.96013e12	0.600776
$801$	0	0
$802$	−3.73901e12	−0.319133
$803$	4.69926e12	0.398850
$804$	0	0
$805$	−1.42987e13	−1.20009
$806$	−1.02096e11	−0.00852120
$807$	0	0
$808$	4.96143e12	0.409502
$809$	3.58080e12	0.293908	0.146954	−	0.989143i	$-0.453053\pi$
$809$	3.58080e12	0.293908	0.146954	+	0.989143i	$0.453053\pi$
$810$	0	0
$811$	−9.34503e12	−0.758554	−0.379277	−	0.925283i	$-0.623827\pi$
$811$	−9.34503e12	−0.758554	−0.379277	+	0.925283i	$0.623827\pi$
$812$	−8.41461e11	−0.0679254
$813$	0	0
$814$	5.20053e12	0.415181
$815$	4.66483e12	0.370362
$816$	0	0
$817$	6.09684e11	0.0478747
$818$	−7.99035e12	−0.623988
$819$	0	0
$820$	3.35311e12	0.258992
$821$	−2.46186e13	−1.89112	−0.945560	−	0.325449i	$-0.894485\pi$
$821$	−2.46186e13	−1.89112	−0.945560	+	0.325449i	$0.894485\pi$
$822$	0	0
$823$	−3.14911e12	−0.239270	−0.119635	−	0.992818i	$-0.538172\pi$
$823$	−3.14911e12	−0.239270	−0.119635	+	0.992818i	$0.538172\pi$
$824$	1.52593e13	1.15309
$825$	0	0
$826$	8.73378e12	0.652818
$827$	2.95396e12	0.219598	0.109799	−	0.993954i	$-0.464979\pi$
$827$	2.95396e12	0.219598	0.109799	+	0.993954i	$0.464979\pi$
$828$	0	0
$829$	1.06626e13	0.784092	0.392046	−	0.919946i	$-0.371767\pi$
$829$	1.06626e13	0.784092	0.392046	+	0.919946i	$0.371767\pi$
$830$	−1.99757e12	−0.146100
$831$	0	0
$832$	−2.24907e11	−0.0162723
$833$	−3.34510e13	−2.40717
$834$	0	0
$835$	8.51223e12	0.605974
$836$	−2.14217e12	−0.151679
$837$	0	0
$838$	−5.90889e11	−0.0413912
$839$	−2.20297e13	−1.53490	−0.767450	−	0.641108i	$-0.778475\pi$
$839$	−2.20297e13	−1.53490	−0.767450	+	0.641108i	$0.778475\pi$
$840$	0	0
$841$	−1.43822e13	−0.991388
$842$	−1.20141e13	−0.823732
$843$	0	0
$844$	−3.15864e11	−0.0214269
$845$	5.75436e12	0.388277
$846$	0	0
$847$	−1.86510e13	−1.24516
$848$	3.58372e12	0.237986
$849$	0	0
$850$	−8.87211e12	−0.582964
$851$	1.00009e13	0.653666
$852$	0	0
$853$	1.55188e13	1.00367	0.501833	−	0.864965i	$-0.332659\pi$
$853$	1.55188e13	1.00367	0.501833	+	0.864965i	$0.332659\pi$
$854$	2.44313e13	1.57176
$855$	0	0
$856$	−2.24608e13	−1.42986
$857$	−3.00703e13	−1.90425	−0.952124	−	0.305711i	$-0.901106\pi$
$857$	−3.00703e13	−1.90425	−0.952124	+	0.305711i	$0.901106\pi$
$858$	0	0
$859$	2.46295e13	1.54343	0.771714	−	0.635970i	$-0.219400\pi$
$859$	2.46295e13	1.54343	0.771714	+	0.635970i	$0.219400\pi$
$860$	3.58279e11	0.0223346
$861$	0	0
$862$	5.41495e12	0.334050
$863$	−3.46510e12	−0.212651	−0.106326	−	0.994331i	$-0.533909\pi$
$863$	−3.46510e12	−0.212651	−0.106326	+	0.994331i	$0.533909\pi$
$864$	0	0
$865$	7.67344e12	0.466034
$866$	−1.61492e13	−0.975707
$867$	0	0
$868$	−8.43930e12	−0.504624
$869$	3.51193e12	0.208909
$870$	0	0
$871$	−1.41946e11	−0.00835686
$872$	−2.54041e13	−1.48792
$873$	0	0
$874$	6.80449e12	0.394452
$875$	−2.41701e13	−1.39394
$876$	0	0
$877$	1.30687e13	0.745992	0.372996	−	0.927833i	$-0.378331\pi$
$877$	1.30687e13	0.745992	0.372996	+	0.927833i	$0.378331\pi$
$878$	9.26016e12	0.525888
$879$	0	0
$880$	4.25503e12	0.239183
$881$	−1.41012e13	−0.788615	−0.394307	−	0.918979i	$-0.629015\pi$
$881$	−1.41012e13	−0.788615	−0.394307	+	0.918979i	$0.629015\pi$
$882$	0	0
$883$	3.48937e13	1.93163	0.965815	−	0.259232i	$-0.0834693\pi$
$883$	3.48937e13	1.93163	0.965815	+	0.259232i	$0.0834693\pi$
$884$	−9.32714e10	−0.00513705
$885$	0	0
$886$	1.04258e12	0.0568405
$887$	8.10987e12	0.439903	0.219952	−	0.975511i	$-0.429410\pi$
$887$	8.10987e12	0.439903	0.219952	+	0.975511i	$0.429410\pi$
$888$	0	0
$889$	−2.53552e13	−1.36147
$890$	−3.55741e11	−0.0190055
$891$	0	0
$892$	1.98976e12	0.105235
$893$	6.55189e12	0.344774
$894$	0	0
$895$	−1.70344e12	−0.0887408
$896$	4.21549e12	0.218505
$897$	0	0
$898$	1.00036e12	0.0513351
$899$	1.25301e12	0.0639788
$900$	0	0
$901$	8.51913e12	0.430659
$902$	−3.55494e13	−1.78815
$903$	0	0
$904$	1.69696e13	0.845113
$905$	−5.20469e12	−0.257915
$906$	0	0
$907$	−3.06563e13	−1.50413	−0.752067	−	0.659087i	$-0.770943\pi$
$907$	−3.06563e13	−1.50413	−0.752067	+	0.659087i	$0.770943\pi$
$908$	6.17362e12	0.301407
$909$	0	0
$910$	1.92738e11	0.00931712
$911$	−1.17678e13	−0.566060	−0.283030	−	0.959111i	$-0.591340\pi$
$911$	−1.17678e13	−0.566060	−0.283030	+	0.959111i	$0.591340\pi$
$912$	0	0
$913$	−1.28214e13	−0.610686
$914$	−8.33015e12	−0.394816
$915$	0	0
$916$	−8.98406e12	−0.421641
$917$	−3.65493e12	−0.170694
$918$	0	0
$919$	2.31130e13	1.06890	0.534449	−	0.845201i	$-0.320519\pi$
$919$	2.31130e13	1.06890	0.534449	+	0.845201i	$0.320519\pi$
$920$	1.46021e13	0.672001
$921$	0	0
$922$	9.14392e12	0.416719
$923$	−4.13022e11	−0.0187312
$924$	0	0
$925$	7.76317e12	0.348659
$926$	−1.36062e13	−0.608118
$927$	0	0
$928$	1.48332e12	0.0656552
$929$	2.42929e13	1.07006	0.535030	−	0.844833i	$-0.320300\pi$
$929$	2.42929e13	1.07006	0.535030	+	0.844833i	$0.320300\pi$
$930$	0	0
$931$	1.99149e13	0.868770
$932$	−1.50258e13	−0.652327
$933$	0	0
$934$	−8.20840e12	−0.352937
$935$	1.01150e13	0.432825
$936$	0	0
$937$	2.26661e13	0.960615	0.480308	−	0.877100i	$-0.340525\pi$
$937$	2.26661e13	0.960615	0.480308	+	0.877100i	$0.340525\pi$
$938$	1.93809e13	0.817448
$939$	0	0
$940$	3.85019e12	0.160845
$941$	6.91129e12	0.287346	0.143673	−	0.989625i	$-0.454109\pi$
$941$	6.91129e12	0.287346	0.143673	+	0.989625i	$0.454109\pi$
$942$	0	0
$943$	−6.83634e13	−2.81528
$944$	−4.99805e12	−0.204846
$945$	0	0
$946$	−3.79844e12	−0.154204
$947$	2.55740e13	1.03329	0.516647	−	0.856198i	$-0.327180\pi$
$947$	2.55740e13	1.03329	0.516647	+	0.856198i	$0.327180\pi$
$948$	0	0
$949$	−1.21813e11	−0.00487523
$950$	5.28197e12	0.210397
$951$	0	0
$952$	4.65051e13	1.83499
$953$	1.19246e13	0.468304	0.234152	−	0.972200i	$-0.424769\pi$
$953$	1.19246e13	0.468304	0.234152	+	0.972200i	$0.424769\pi$
$954$	0	0
$955$	−7.19223e12	−0.279800
$956$	−1.73231e13	−0.670756
$957$	0	0
$958$	−2.62675e13	−1.00757
$959$	4.79335e13	1.83002
$960$	0	0
$961$	−1.38728e13	−0.524696
$962$	−1.34807e11	−0.00507485
$963$	0	0
$964$	−6.14743e10	−0.00229270
$965$	−1.38086e12	−0.0512597
$966$	0	0
$967$	1.25487e13	0.461508	0.230754	−	0.973012i	$-0.425881\pi$
$967$	1.25487e13	0.461508	0.230754	+	0.973012i	$0.425881\pi$
$968$	1.90468e13	0.697239
$969$	0	0
$970$	6.15849e12	0.223358
$971$	−4.66392e13	−1.68370	−0.841850	−	0.539712i	$-0.818533\pi$
$971$	−4.66392e13	−1.68370	−0.841850	+	0.539712i	$0.818533\pi$
$972$	0	0
$973$	−5.51895e13	−1.97401
$974$	3.58541e13	1.27651
$975$	0	0
$976$	−1.39812e13	−0.493198
$977$	−4.30950e13	−1.51322	−0.756608	−	0.653869i	$-0.773145\pi$
$977$	−4.30950e13	−1.51322	−0.756608	+	0.653869i	$0.773145\pi$
$978$	0	0
$979$	−2.28333e12	−0.0794413
$980$	1.17029e13	0.405300
$981$	0	0
$982$	−1.19785e12	−0.0411054
$983$	−3.37522e13	−1.15295	−0.576476	−	0.817114i	$-0.695572\pi$
$983$	−3.37522e13	−1.15295	−0.576476	+	0.817114i	$0.695572\pi$
$984$	0	0
$985$	−9.28942e12	−0.314431
$986$	−1.89080e12	−0.0637087
$987$	0	0
$988$	5.55288e10	0.00185401
$989$	−7.30460e12	−0.242780
$990$	0	0
$991$	−2.60751e13	−0.858805	−0.429403	−	0.903113i	$-0.641276\pi$
$991$	−2.60751e13	−0.858805	−0.429403	+	0.903113i	$0.641276\pi$
$992$	1.48767e13	0.487759
$993$	0	0
$994$	5.63926e13	1.83224
$995$	2.24353e13	0.725651
$996$	0	0
$997$	4.12660e13	1.32271	0.661354	−	0.750074i	$-0.269982\pi$
$997$	4.12660e13	1.32271	0.661354	+	0.750074i	$0.269982\pi$
$998$	−1.11174e13	−0.354744
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.10.a.e.1.7		17
3.2	odd	2		43.10.a.b.1.11	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.11	✓	17	3.2	odd	2
387.10.a.e.1.7		17	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	387.a (trivial)

\(f(q)\)	\(=\)	\(q-17.8584 q^{2} -193.078 q^{4} -542.767 q^{5} -12329.9 q^{7} +12591.6 q^{8} +O(q^{10})\)	\(q-17.8584 q^{2} -193.078 q^{4} -542.767 q^{5} -12329.9 q^{7} +12591.6 q^{8} +9692.93 q^{10} +62214.2 q^{11} -1612.70 q^{13} +220192. q^{14} -126009. q^{16} -299545. q^{17} +178333. q^{19} +104797. q^{20} -1.11104e6 q^{22} -2.13660e6 q^{23} -1.65853e6 q^{25} +28800.2 q^{26} +2.38064e6 q^{28} -353461. q^{29} -3.54498e6 q^{31} -4.19657e6 q^{32} +5.34939e6 q^{34} +6.69226e6 q^{35} -4.68076e6 q^{37} -3.18473e6 q^{38} -6.83428e6 q^{40} +3.19964e7 q^{41} +3.41880e6 q^{43} -1.20122e7 q^{44} +3.81561e7 q^{46} +3.67397e7 q^{47} +1.11673e8 q^{49} +2.96186e7 q^{50} +311377. q^{52} -2.84403e7 q^{53} -3.37678e7 q^{55} -1.55253e8 q^{56} +6.31223e6 q^{58} +3.96644e7 q^{59} +1.10955e8 q^{61} +6.33075e7 q^{62} +1.39460e8 q^{64} +875319. q^{65} +8.80180e7 q^{67} +5.78356e7 q^{68} -1.19513e8 q^{70} +2.56106e8 q^{71} +7.55335e7 q^{73} +8.35907e7 q^{74} -3.44322e7 q^{76} -7.67095e8 q^{77} +5.64490e7 q^{79} +6.83933e7 q^{80} -5.71404e8 q^{82} -2.06085e8 q^{83} +1.62583e8 q^{85} -6.10542e7 q^{86} +7.83374e8 q^{88} -3.67011e7 q^{89} +1.98844e7 q^{91} +4.12531e8 q^{92} -6.56111e8 q^{94} -9.67931e7 q^{95} +6.35358e8 q^{97} -1.99429e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 48 q^{2} + 4522 q^{4} - 4033 q^{5} - 76 q^{7} - 41046 q^{8}+O(q^{10}) \) 17 * q - 48 * q^2 + 4522 * q^4 - 4033 * q^5 - 76 * q^7 - 41046 * q^8	\( 17 q - 48 q^{2} + 4522 q^{4} - 4033 q^{5} - 76 q^{7} - 41046 q^{8} + 23763 q^{10} - 78370 q^{11} + 114452 q^{13} + 376208 q^{14} + 412586 q^{16} - 726937 q^{17} + 544263 q^{19} - 3642183 q^{20} + 5269148 q^{22} - 5575241 q^{23} + 10874708 q^{25} - 8009180 q^{26} + 12534764 q^{28} - 8223345 q^{29} + 13054147 q^{31} - 37111710 q^{32} + 27991291 q^{34} - 17826330 q^{35} + 46733879 q^{37} - 15733789 q^{38} + 52241669 q^{40} - 53667013 q^{41} + 58119617 q^{43} - 81727236 q^{44} + 146859355 q^{46} - 122945511 q^{47} + 111396073 q^{49} + 96642133 q^{50} - 54447944 q^{52} + 993146 q^{53} - 248155792 q^{55} + 141048116 q^{56} - 466599837 q^{58} + 95519644 q^{59} - 311752038 q^{61} + 212471691 q^{62} - 829842590 q^{64} + 107969830 q^{65} - 292438130 q^{67} + 88281129 q^{68} - 1650972530 q^{70} + 13576908 q^{71} - 501490738 q^{73} + 494831691 q^{74} - 1248630771 q^{76} - 787365348 q^{77} + 740350275 q^{79} + 27802861 q^{80} - 1600400057 q^{82} - 754109940 q^{83} + 1071609956 q^{85} - 164102448 q^{86} + 1863375104 q^{88} - 1470581868 q^{89} + 2895349644 q^{91} - 1041082071 q^{92} - 706582361 q^{94} - 3297255729 q^{95} + 1949310583 q^{97} - 6695989160 q^{98}+O(q^{100}) \) 17 * q - 48 * q^2 + 4522 * q^4 - 4033 * q^5 - 76 * q^7 - 41046 * q^8 + 23763 * q^10 - 78370 * q^11 + 114452 * q^13 + 376208 * q^14 + 412586 * q^16 - 726937 * q^17 + 544263 * q^19 - 3642183 * q^20 + 5269148 * q^22 - 5575241 * q^23 + 10874708 * q^25 - 8009180 * q^26 + 12534764 * q^28 - 8223345 * q^29 + 13054147 * q^31 - 37111710 * q^32 + 27991291 * q^34 - 17826330 * q^35 + 46733879 * q^37 - 15733789 * q^38 + 52241669 * q^40 - 53667013 * q^41 + 58119617 * q^43 - 81727236 * q^44 + 146859355 * q^46 - 122945511 * q^47 + 111396073 * q^49 + 96642133 * q^50 - 54447944 * q^52 + 993146 * q^53 - 248155792 * q^55 + 141048116 * q^56 - 466599837 * q^58 + 95519644 * q^59 - 311752038 * q^61 + 212471691 * q^62 - 829842590 * q^64 + 107969830 * q^65 - 292438130 * q^67 + 88281129 * q^68 - 1650972530 * q^70 + 13576908 * q^71 - 501490738 * q^73 + 494831691 * q^74 - 1248630771 * q^76 - 787365348 * q^77 + 740350275 * q^79 + 27802861 * q^80 - 1600400057 * q^82 - 754109940 * q^83 + 1071609956 * q^85 - 164102448 * q^86 + 1863375104 * q^88 - 1470581868 * q^89 + 2895349644 * q^91 - 1041082071 * q^92 - 706582361 * q^94 - 3297255729 * q^95 + 1949310583 * q^97 - 6695989160 * q^98

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