LMFDB - Embedded newform 9.44.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,44,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 44, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 44);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	9.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:	$105.399355811$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 11258260111x - 264759545317170 $ x^3 - 11258260111*x - 264759545317170
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-24885.9$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.65343e6 q^{2} +1.28583e13 q^{4} -5.54482e14 q^{5} -5.57604e17 q^{7} +1.89031e19 q^{8} +O(q^{10})$	\(q+4.65343e6 q^{2} +1.28583e13 q^{4} -5.54482e14 q^{5} -5.57604e17 q^{7} +1.89031e19 q^{8} -2.58024e21 q^{10} +1.13059e22 q^{11} +5.07130e23 q^{13} -2.59477e24 q^{14} -2.51386e25 q^{16} -8.73610e25 q^{17} +5.55222e27 q^{19} -7.12968e27 q^{20} +5.26114e28 q^{22} -1.85137e29 q^{23} -8.29418e29 q^{25} +2.35989e30 q^{26} -7.16982e30 q^{28} -4.19782e31 q^{29} -9.30312e31 q^{31} -2.83254e32 q^{32} -4.06528e32 q^{34} +3.09181e32 q^{35} -3.20928e33 q^{37} +2.58368e34 q^{38} -1.04814e34 q^{40} -6.48857e33 q^{41} +3.51189e33 q^{43} +1.45375e35 q^{44} -8.61520e35 q^{46} -6.21410e35 q^{47} -1.87289e36 q^{49} -3.85963e36 q^{50} +6.52081e36 q^{52} -8.28552e36 q^{53} -6.26895e36 q^{55} -1.05404e37 q^{56} -1.95342e38 q^{58} +7.48073e36 q^{59} -2.24824e38 q^{61} -4.32914e38 q^{62} -1.09698e39 q^{64} -2.81194e38 q^{65} -1.89786e39 q^{67} -1.12331e39 q^{68} +1.43875e39 q^{70} +9.53945e39 q^{71} +2.48260e39 q^{73} -1.49341e40 q^{74} +7.13920e40 q^{76} -6.30424e39 q^{77} -3.50244e39 q^{79} +1.39389e40 q^{80} -3.01941e40 q^{82} +2.23114e41 q^{83} +4.84401e40 q^{85} +1.63423e40 q^{86} +2.13717e41 q^{88} +4.38099e41 q^{89} -2.82777e41 q^{91} -2.38054e42 q^{92} -2.89169e42 q^{94} -3.07861e42 q^{95} -6.11565e42 q^{97} -8.71537e42 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots + 15\!\cdots\!80 q^{8}+O(q^{10}) $ 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8	$ 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots - 24\!\cdots\!08 q^{98}+O(q^{100}) $ 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8 + 424411733447436982320 * q^10 - 26665053285822824598396 * q^11 + 2675160683143344673595682 * q^13 - 14021968617857741064904128 * q^14 - 79484355831457348071124992 * q^16 + 408654222932442443796841194 * q^17 + 1577331357975519701176464900 * q^19 - 14558304937461364568422335360 * q^20 + 139626647360508967807005852192 * q^22 + 1215339635928561142484811048 * q^23 - 2310484082897201607166539950475 * q^25 + 1738302877111230473099097494544 * q^26 + 16881555000174595924306194912768 * q^28 - 57118989018136587596191009705650 * q^29 - 255565972342397832812135282963424 * q^31 + 144698056390774688063435943542784 * q^32 + 460541119788760022406607937310288 * q^34 - 2398213530857285851552147980593520 * q^35 - 2320645576165979428293572256842694 * q^37 + 30659398199572233844432077267455520 * q^38 - 32703585947405178164040064943232000 * q^40 - 25742376604739002042016577514061166 * q^41 + 240714339689128182512406300123419292 * q^43 + 103743099769332204870397943787455232 * q^44 - 1897545066442972080018141849284700864 * q^46 - 308713553347399687962182796433367856 * q^47 + 3434980292250886821160584750829904379 * q^49 - 1991781591031845842073119994352349400 * q^50 - 1723278372049486147633277645433304704 * q^52 - 15000497558784669132889458695112796362 * q^53 + 3996571389110251928625895283213506440 * q^55 + 64188456562605926675684864956824883200 * q^56 - 103653602500512241322054964115851073680 * q^58 - 226996261182733939538282061249836505900 * q^59 - 9393429368478033721028929889113591854 * q^61 + 208603081649583360642384119938663534848 * q^62 - 1119010168436659689243622515721507700736 * q^64 + 270218921102297342477494789001032451460 * q^65 - 733015616887151283726086660162187354444 * q^67 - 5475599618745313926138424496016357744768 * q^68 + 5947953535225896394715748735968145697920 * q^70 + 18523878066158899993345833814569898287864 * q^71 - 20251106025908798058937016734369224029298 * q^73 - 16747422277652165725566811926177721225008 * q^74 + 77507609539490133886259513865936229344000 * q^76 - 59055613160181778232413942942559747685792 * q^77 + 15233568018599764739559826813006999294800 * q^79 + 100962488695267720109813470111835940986880 * q^80 - 320808727539069549327137360482471983405168 * q^82 + 89206610196719670053085531955706819434428 * q^83 + 438725373228516358990025164547060204838420 * q^85 - 251282426033382455934203370485070655838496 * q^86 - 25677613216166441601684725395949811087360 * q^88 - 203691422331055117225246388044508249665950 * q^89 - 1168954967602248602369466051364648836229584 * q^91 - 688199578839743838535125048241381149958656 * q^92 - 1324027207656692012199753325229034662658432 * q^94 - 3125746305909018830165692627580442029979000 * q^95 - 3881062021784775072625368160679539917597594 * q^97 - 24120041445786820251814869563279238673540008 * 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 $

$2$	4.65343e6	1.56902	0.784509	−	0.620118i	$-0.212915\pi$
$2$	4.65343e6	1.56902	0.784509	+	0.620118i	$0.212915\pi$
$3$	0	0
$3$	0	0
$4$	1.28583e13	1.46182
$5$	−5.54482e14	−0.520035	−0.260017	−	0.965604i	$-0.583728\pi$
$5$	−5.54482e14	−0.520035	−0.260017	+	0.965604i	$0.583728\pi$
$6$	0	0
$7$	−5.57604e17	−0.377327	−0.188663	−	0.982042i	$-0.560416\pi$
$7$	−5.57604e17	−0.377327	−0.188663	+	0.982042i	$0.560416\pi$
$8$	1.89031e19	0.724599
$9$	0	0
$10$	−2.58024e21	−0.815944
$11$	1.13059e22	0.460643	0.230321	−	0.973115i	$-0.426022\pi$
$11$	1.13059e22	0.460643	0.230321	+	0.973115i	$0.426022\pi$
$12$	0	0
$13$	5.07130e23	0.569294	0.284647	−	0.958632i	$-0.408124\pi$
$13$	5.07130e23	0.569294	0.284647	+	0.958632i	$0.408124\pi$
$14$	−2.59477e24	−0.592033
$15$	0	0
$16$	−2.51386e25	−0.324909
$17$	−8.73610e25	−0.306666	−0.153333	−	0.988175i	$-0.549001\pi$
$17$	−8.73610e25	−0.306666	−0.153333	+	0.988175i	$0.549001\pi$
$18$	0	0
$19$	5.55222e27	1.78346	0.891732	−	0.452564i	$-0.149491\pi$
$19$	5.55222e27	1.78346	0.891732	+	0.452564i	$0.149491\pi$
$20$	−7.12968e27	−0.760196
$21$	0	0
$22$	5.26114e28	0.722757
$23$	−1.85137e29	−0.978012	−0.489006	−	0.872280i	$-0.662640\pi$
$23$	−1.85137e29	−0.978012	−0.489006	+	0.872280i	$0.662640\pi$
$24$	0	0
$25$	−8.29418e29	−0.729564
$26$	2.35989e30	0.893233
$27$	0	0
$28$	−7.16982e30	−0.551583
$29$	−4.19782e31	−1.51868	−0.759340	−	0.650694i	$-0.774478\pi$
$29$	−4.19782e31	−1.51868	−0.759340	+	0.650694i	$0.774478\pi$
$30$	0	0
$31$	−9.30312e31	−0.802329	−0.401164	−	0.916006i	$-0.631394\pi$
$31$	−9.30312e31	−0.802329	−0.401164	+	0.916006i	$0.631394\pi$
$32$	−2.83254e32	−1.23439
$33$	0	0
$34$	−4.06528e32	−0.481165
$35$	3.09181e32	0.196223
$36$	0	0
$37$	−3.20928e33	−0.616695	−0.308347	−	0.951274i	$-0.599776\pi$
$37$	−3.20928e33	−0.616695	−0.308347	+	0.951274i	$0.599776\pi$
$38$	2.58368e34	2.79829
$39$	0	0
$40$	−1.04814e34	−0.376817
$41$	−6.48857e33	−0.137182	−0.0685908	−	0.997645i	$-0.521850\pi$
$41$	−6.48857e33	−0.137182	−0.0685908	+	0.997645i	$0.521850\pi$
$42$	0	0
$43$	3.51189e33	0.0266667	0.0133333	−	0.999911i	$-0.495756\pi$
$43$	3.51189e33	0.0266667	0.0133333	+	0.999911i	$0.495756\pi$
$44$	1.45375e35	0.673375
$45$	0	0
$46$	−8.61520e35	−1.53452
$47$	−6.21410e35	−0.697067	−0.348533	−	0.937296i	$-0.613320\pi$
$47$	−6.21410e35	−0.697067	−0.348533	+	0.937296i	$0.613320\pi$
$48$	0	0
$49$	−1.87289e36	−0.857624
$50$	−3.85963e36	−1.14470
$51$	0	0
$52$	6.52081e36	0.832204
$53$	−8.28552e36	−0.702083	−0.351042	−	0.936360i	$-0.614172\pi$
$53$	−8.28552e36	−0.702083	−0.351042	+	0.936360i	$0.614172\pi$
$54$	0	0
$55$	−6.26895e36	−0.239550
$56$	−1.05404e37	−0.273411
$57$	0	0
$58$	−1.95342e38	−2.38284
$59$	7.48073e36	0.0631867	0.0315933	−	0.999501i	$-0.489942\pi$
$59$	7.48073e36	0.0631867	0.0315933	+	0.999501i	$0.489942\pi$
$60$	0	0
$61$	−2.24824e38	−0.927366	−0.463683	−	0.886001i	$-0.653472\pi$
$61$	−2.24824e38	−0.927366	−0.463683	+	0.886001i	$0.653472\pi$
$62$	−4.32914e38	−1.25887
$63$	0	0
$64$	−1.09698e39	−1.61186
$65$	−2.81194e38	−0.296053
$66$	0	0
$67$	−1.89786e39	−1.04149	−0.520745	−	0.853712i	$-0.674346\pi$
$67$	−1.89786e39	−1.04149	−0.520745	+	0.853712i	$0.674346\pi$
$68$	−1.12331e39	−0.448290
$69$	0	0
$70$	1.43875e39	0.307878
$71$	9.53945e39	1.50476	0.752382	−	0.658727i	$-0.228905\pi$
$71$	9.53945e39	1.50476	0.752382	+	0.658727i	$0.228905\pi$
$72$	0	0
$73$	2.48260e39	0.215509	0.107755	−	0.994178i	$-0.465634\pi$
$73$	2.48260e39	0.215509	0.107755	+	0.994178i	$0.465634\pi$
$74$	−1.49341e40	−0.967605
$75$	0	0
$76$	7.13920e40	2.60710
$77$	−6.30424e39	−0.173813
$78$	0	0
$79$	−3.50244e39	−0.0556402	−0.0278201	−	0.999613i	$-0.508857\pi$
$79$	−3.50244e39	−0.0556402	−0.0278201	+	0.999613i	$0.508857\pi$
$80$	1.39389e40	0.168964
$81$	0	0
$82$	−3.01941e40	−0.215240
$83$	2.23114e41	1.22560	0.612799	−	0.790239i	$-0.290043\pi$
$83$	2.23114e41	1.22560	0.612799	+	0.790239i	$0.290043\pi$
$84$	0	0
$85$	4.84401e40	0.159477
$86$	1.63423e40	0.0418405
$87$	0	0
$88$	2.13717e41	0.333781
$89$	4.38099e41	0.536645	0.268323	−	0.963329i	$-0.413531\pi$
$89$	4.38099e41	0.536645	0.268323	+	0.963329i	$0.413531\pi$
$90$	0	0
$91$	−2.82777e41	−0.214810
$92$	−2.38054e42	−1.42967
$93$	0	0
$94$	−2.89169e42	−1.09371
$95$	−3.07861e42	−0.927463
$96$	0	0
$97$	−6.11565e42	−1.17720	−0.588600	−	0.808424i	$-0.700321\pi$
$97$	−6.11565e42	−1.17720	−0.588600	+	0.808424i	$0.700321\pi$
$98$	−8.71537e42	−1.34563
$99$	0	0
$100$	−1.06649e43	−1.06649
$101$	−8.20815e42	−0.662728	−0.331364	−	0.943503i	$-0.607509\pi$
$101$	−8.20815e42	−0.662728	−0.331364	+	0.943503i	$0.607509\pi$
$102$	0	0
$103$	2.72199e43	1.44174	0.720868	−	0.693072i	$-0.243743\pi$
$103$	2.72199e43	1.44174	0.720868	+	0.693072i	$0.243743\pi$
$104$	9.58630e42	0.412510
$105$	0	0
$106$	−3.85561e43	−1.10158
$107$	4.26383e43	0.995517	0.497758	−	0.867316i	$-0.334157\pi$
$107$	4.26383e43	0.995517	0.497758	+	0.867316i	$0.334157\pi$
$108$	0	0
$109$	2.42680e43	0.380508	0.190254	−	0.981735i	$-0.439069\pi$
$109$	2.42680e43	0.380508	0.190254	+	0.981735i	$0.439069\pi$
$110$	−2.91721e43	−0.375859
$111$	0	0
$112$	1.40174e43	0.122597
$113$	−1.73831e44	−1.25586	−0.627931	−	0.778269i	$-0.716098\pi$
$113$	−1.73831e44	−1.25586	−0.627931	+	0.778269i	$0.716098\pi$
$114$	0	0
$115$	1.02655e44	0.508600
$116$	−5.39767e44	−2.22003
$117$	0	0
$118$	3.48110e43	0.0991410
$119$	4.87128e43	0.115713
$120$	0	0
$121$	−4.74576e44	−0.787808
$122$	−1.04620e45	−1.45505
$123$	0	0
$124$	−1.19622e45	−1.17286
$125$	1.09027e45	0.899433
$126$	0	0
$127$	−2.81930e45	−1.65334	−0.826669	−	0.562688i	$-0.809767\pi$
$127$	−2.81930e45	−1.65334	−0.826669	+	0.562688i	$0.809767\pi$
$128$	−2.61318e45	−1.29466
$129$	0	0
$130$	−1.30852e45	−0.464512
$131$	−5.22187e45	−1.57215	−0.786073	−	0.618133i	$-0.787889\pi$
$131$	−5.22187e45	−1.57215	−0.786073	+	0.618133i	$0.787889\pi$
$132$	0	0
$133$	−3.09594e45	−0.672949
$134$	−8.83154e45	−1.63412
$135$	0	0
$136$	−1.65139e45	−0.222210
$137$	1.17929e46	1.35559	0.677794	−	0.735252i	$-0.262936\pi$
$137$	1.17929e46	1.35559	0.677794	+	0.735252i	$0.262936\pi$
$138$	0	0
$139$	7.89914e45	0.664908	0.332454	−	0.943119i	$-0.392123\pi$
$139$	7.89914e45	0.664908	0.332454	+	0.943119i	$0.392123\pi$
$140$	3.97554e45	0.286842
$141$	0	0
$142$	4.43911e46	2.36100
$143$	5.73358e45	0.262241
$144$	0	0
$145$	2.32761e46	0.789767
$146$	1.15526e46	0.338138
$147$	0	0
$148$	−4.12658e46	−0.901495
$149$	−5.77438e45	−0.109144	−0.0545721	−	0.998510i	$-0.517379\pi$
$149$	−5.77438e45	−0.109144	−0.0545721	+	0.998510i	$0.517379\pi$
$150$	0	0
$151$	−1.97310e46	−0.279992	−0.139996	−	0.990152i	$-0.544709\pi$
$151$	−1.97310e46	−0.279992	−0.139996	+	0.990152i	$0.544709\pi$
$152$	1.04954e47	1.29230
$153$	0	0
$154$	−2.93363e46	−0.272715
$155$	5.15842e46	0.417239
$156$	0	0
$157$	−1.33604e47	−0.820306	−0.410153	−	0.912017i	$-0.634525\pi$
$157$	−1.33604e47	−0.820306	−0.410153	+	0.912017i	$0.634525\pi$
$158$	−1.62984e46	−0.0873005
$159$	0	0
$160$	1.57059e47	0.641924
$161$	1.03233e47	0.369030
$162$	0	0
$163$	−1.04926e47	−0.287641	−0.143820	−	0.989604i	$-0.545939\pi$
$163$	−1.04926e47	−0.287641	−0.143820	+	0.989604i	$0.545939\pi$
$164$	−8.34318e46	−0.200534
$165$	0	0
$166$	1.03825e48	1.92299
$167$	6.74904e47	1.09860	0.549298	−	0.835627i	$-0.314895\pi$
$167$	6.74904e47	1.09860	0.549298	+	0.835627i	$0.314895\pi$
$168$	0	0
$169$	−5.36351e47	−0.675904
$170$	2.25412e47	0.250222
$171$	0	0
$172$	4.51569e46	0.0389818
$173$	4.15452e47	0.316614	0.158307	−	0.987390i	$-0.449397\pi$
$173$	4.15452e47	0.316614	0.158307	+	0.987390i	$0.449397\pi$
$174$	0	0
$175$	4.62486e47	0.275284
$176$	−2.84215e47	−0.149667
$177$	0	0
$178$	2.03866e48	0.842006
$179$	6.34938e47	0.232483	0.116241	−	0.993221i	$-0.462915\pi$
$179$	6.34938e47	0.232483	0.116241	+	0.993221i	$0.462915\pi$
$180$	0	0
$181$	5.38506e47	0.155275	0.0776375	−	0.996982i	$-0.475262\pi$
$181$	5.38506e47	0.155275	0.0776375	+	0.996982i	$0.475262\pi$
$182$	−1.31588e48	−0.337041
$183$	0	0
$184$	−3.49965e48	−0.708666
$185$	1.77949e48	0.320703
$186$	0	0
$187$	−9.87699e47	−0.141263
$188$	−7.99026e48	−1.01898
$189$	0	0
$190$	−1.43261e49	−1.45521
$191$	−1.22017e49	−1.10714	−0.553572	−	0.832802i	$-0.686735\pi$
$191$	−1.22017e49	−1.10714	−0.553572	+	0.832802i	$0.686735\pi$
$192$	0	0
$193$	8.36996e46	0.00607073	0.00303537	−	0.999995i	$-0.499034\pi$
$193$	8.36996e46	0.00607073	0.00303537	+	0.999995i	$0.499034\pi$
$194$	−2.84587e49	−1.84705
$195$	0	0
$196$	−2.40822e49	−1.25369
$197$	−1.24344e49	−0.580229	−0.290115	−	0.956992i	$-0.593693\pi$
$197$	−1.24344e49	−0.580229	−0.290115	+	0.956992i	$0.593693\pi$
$198$	0	0
$199$	2.54032e49	0.953997	0.476999	−	0.878904i	$-0.341725\pi$
$199$	2.54032e49	0.953997	0.476999	+	0.878904i	$0.341725\pi$
$200$	−1.56785e49	−0.528641
$201$	0	0
$202$	−3.81960e49	−1.03983
$203$	2.34072e49	0.573039
$204$	0	0
$205$	3.59779e48	0.0713392
$206$	1.26666e50	2.26211
$207$	0	0
$208$	−1.27485e49	−0.184969
$209$	6.27731e49	0.821540
$210$	0	0
$211$	1.72327e50	1.83772	0.918861	−	0.394582i	$-0.129110\pi$
$211$	1.72327e50	1.83772	0.918861	+	0.394582i	$0.129110\pi$
$212$	−1.06538e50	−1.02632
$213$	0	0
$214$	1.98414e50	1.56198
$215$	−1.94728e48	−0.0138676
$216$	0	0
$217$	5.18746e49	0.302740
$218$	1.12929e50	0.597024
$219$	0	0
$220$	−8.06078e49	−0.350179
$221$	−4.43033e49	−0.174583
$222$	0	0
$223$	−1.43740e50	−0.466683	−0.233342	−	0.972395i	$-0.574966\pi$
$223$	−1.43740e50	−0.466683	−0.233342	+	0.972395i	$0.574966\pi$
$224$	1.57943e50	0.465767
$225$	0	0
$226$	−8.08911e50	−1.97047
$227$	7.21848e48	0.0159915	0.00799576	−	0.999968i	$-0.497455\pi$
$227$	7.21848e48	0.0159915	0.00799576	+	0.999968i	$0.497455\pi$
$228$	0	0
$229$	8.60814e50	1.57923	0.789617	−	0.613600i	$-0.210279\pi$
$229$	8.60814e50	1.57923	0.789617	+	0.613600i	$0.210279\pi$
$230$	4.77698e50	0.798003
$231$	0	0
$232$	−7.93516e50	−1.10043
$233$	8.15789e50	1.03140	0.515698	−	0.856770i	$-0.327533\pi$
$233$	8.15789e50	1.03140	0.515698	+	0.856770i	$0.327533\pi$
$234$	0	0
$235$	3.44561e50	0.362499
$236$	9.61892e49	0.0923673
$237$	0	0
$238$	2.26681e50	0.181556
$239$	−1.19865e51	−0.877276	−0.438638	−	0.898664i	$-0.644539\pi$
$239$	−1.19865e51	−0.877276	−0.438638	+	0.898664i	$0.644539\pi$
$240$	0	0
$241$	1.15117e51	0.704326	0.352163	−	0.935939i	$-0.385446\pi$
$241$	1.15117e51	0.704326	0.352163	+	0.935939i	$0.385446\pi$
$242$	−2.20841e51	−1.23609
$243$	0	0
$244$	−2.89085e51	−1.35564
$245$	1.03849e51	0.445995
$246$	0	0
$247$	2.81570e51	1.01532
$248$	−1.75858e51	−0.581366
$249$	0	0
$250$	5.07349e51	1.41123
$251$	3.52535e51	0.899948	0.449974	−	0.893042i	$-0.351433\pi$
$251$	3.52535e51	0.899948	0.449974	+	0.893042i	$0.351433\pi$
$252$	0	0
$253$	−2.09315e51	−0.450514
$254$	−1.31194e52	−2.59412
$255$	0	0
$256$	−2.51112e51	−0.419478
$257$	9.00901e51	1.38393	0.691967	−	0.721930i	$-0.256745\pi$
$257$	9.00901e51	1.38393	0.691967	+	0.721930i	$0.256745\pi$
$258$	0	0
$259$	1.78951e51	0.232696
$260$	−3.61567e51	−0.432775
$261$	0	0
$262$	−2.42996e52	−2.46673
$263$	8.70831e51	0.814489	0.407245	−	0.913319i	$-0.366490\pi$
$263$	8.70831e51	0.814489	0.407245	+	0.913319i	$0.366490\pi$
$264$	0	0
$265$	4.59417e51	0.365108
$266$	−1.44067e52	−1.05587
$267$	0	0
$268$	−2.44032e52	−1.52247
$269$	−2.29589e52	−1.32214	−0.661071	−	0.750324i	$-0.729898\pi$
$269$	−2.29589e52	−1.32214	−0.661071	+	0.750324i	$0.729898\pi$
$270$	0	0
$271$	−2.04437e52	−1.00397	−0.501983	−	0.864877i	$-0.667396\pi$
$271$	−2.04437e52	−1.00397	−0.501983	+	0.864877i	$0.667396\pi$
$272$	2.19613e51	0.0996384
$273$	0	0
$274$	5.48773e52	2.12694
$275$	−9.37735e51	−0.336068
$276$	0	0
$277$	3.67190e52	1.12610	0.563049	−	0.826424i	$-0.309628\pi$
$277$	3.67190e52	1.12610	0.563049	+	0.826424i	$0.309628\pi$
$278$	3.67581e52	1.04325
$279$	0	0
$280$	5.84447e51	0.142183
$281$	3.21289e52	0.723952	0.361976	−	0.932187i	$-0.382102\pi$
$281$	3.21289e52	0.723952	0.361976	+	0.932187i	$0.382102\pi$
$282$	0	0
$283$	7.76513e52	1.50224	0.751121	−	0.660164i	$-0.229513\pi$
$283$	7.76513e52	1.50224	0.751121	+	0.660164i	$0.229513\pi$
$284$	1.22661e53	2.19969
$285$	0	0
$286$	2.66808e52	0.411461
$287$	3.61805e51	0.0517623
$288$	0	0
$289$	−7.35209e52	−0.905956
$290$	1.08314e53	1.23916
$291$	0	0
$292$	3.19220e52	0.315035
$293$	−7.07016e52	−0.648299	−0.324150	−	0.946006i	$-0.605078\pi$
$293$	−7.07016e52	−0.648299	−0.324150	+	0.946006i	$0.605078\pi$
$294$	0	0
$295$	−4.14793e51	−0.0328593
$296$	−6.06652e52	−0.446856
$297$	0	0
$298$	−2.68707e52	−0.171249
$299$	−9.38883e52	−0.556777
$300$	0	0
$301$	−1.95824e51	−0.0100621
$302$	−9.18168e52	−0.439312
$303$	0	0
$304$	−1.39575e53	−0.579463
$305$	1.24661e53	0.482263
$306$	0	0
$307$	−4.17987e53	−1.40504	−0.702518	−	0.711666i	$-0.747941\pi$
$307$	−4.17987e53	−1.40504	−0.702518	+	0.711666i	$0.747941\pi$
$308$	−8.10616e52	−0.254083
$309$	0	0
$310$	2.40043e53	0.654655
$311$	−1.08737e53	−0.276714	−0.138357	−	0.990382i	$-0.544182\pi$
$311$	−1.08737e53	−0.276714	−0.138357	+	0.990382i	$0.544182\pi$
$312$	0	0
$313$	5.09671e52	0.113002	0.0565011	−	0.998403i	$-0.482006\pi$
$313$	5.09671e52	0.113002	0.0565011	+	0.998403i	$0.482006\pi$
$314$	−6.21715e53	−1.28707
$315$	0	0
$316$	−4.50354e52	−0.0813358
$317$	−5.92996e53	−1.00064	−0.500320	−	0.865841i	$-0.666784\pi$
$317$	−5.92996e53	−1.00064	−0.500320	+	0.865841i	$0.666784\pi$
$318$	0	0
$319$	−4.74603e53	−0.699569
$320$	6.08255e53	0.838226
$321$	0	0
$322$	4.80387e53	0.579015
$323$	−4.85047e53	−0.546928
$324$	0	0
$325$	−4.20622e53	−0.415336
$326$	−4.88266e53	−0.451313
$327$	0	0
$328$	−1.22654e53	−0.0994016
$329$	3.46501e53	0.263022
$330$	0	0
$331$	4.62094e53	0.307913	0.153957	−	0.988078i	$-0.450798\pi$
$331$	4.62094e53	0.307913	0.153957	+	0.988078i	$0.450798\pi$
$332$	2.86886e54	1.79160
$333$	0	0
$334$	3.14061e54	1.72372
$335$	1.05233e54	0.541611
$336$	0	0
$337$	−2.44988e54	−1.10943	−0.554717	−	0.832039i	$-0.687173\pi$
$337$	−2.44988e54	−1.10943	−0.554717	+	0.832039i	$0.687173\pi$
$338$	−2.49587e54	−1.06051
$339$	0	0
$340$	6.22856e53	0.233126
$341$	−1.05181e54	−0.369587
$342$	0	0
$343$	2.26203e54	0.700932
$344$	6.63855e52	0.0193227
$345$	0	0
$346$	1.93327e54	0.496772
$347$	−2.06865e54	−0.499579	−0.249789	−	0.968300i	$-0.580361\pi$
$347$	−2.06865e54	−0.499579	−0.249789	+	0.968300i	$0.580361\pi$
$348$	0	0
$349$	−9.24540e54	−1.97324	−0.986618	−	0.163050i	$-0.947867\pi$
$349$	−9.24540e54	−1.97324	−0.986618	+	0.163050i	$0.947867\pi$
$350$	2.15215e54	0.431926
$351$	0	0
$352$	−3.20245e54	−0.568611
$353$	3.55103e54	0.593196	0.296598	−	0.955002i	$-0.404148\pi$
$353$	3.55103e54	0.593196	0.296598	+	0.955002i	$0.404148\pi$
$354$	0	0
$355$	−5.28945e54	−0.782530
$356$	5.63320e54	0.784477
$357$	0	0
$358$	2.95463e54	0.364770
$359$	6.37557e54	0.741291	0.370645	−	0.928774i	$-0.379137\pi$
$359$	6.37557e54	0.741291	0.370645	+	0.928774i	$0.379137\pi$
$360$	0	0
$361$	2.11353e55	2.18074
$362$	2.50590e54	0.243629
$363$	0	0
$364$	−3.63603e54	−0.314013
$365$	−1.37656e54	−0.112072
$366$	0	0
$367$	1.19284e55	0.863502	0.431751	−	0.901993i	$-0.357896\pi$
$367$	1.19284e55	0.863502	0.431751	+	0.901993i	$0.357896\pi$
$368$	4.65408e54	0.317764
$369$	0	0
$370$	8.28071e54	0.503189
$371$	4.62004e54	0.264915
$372$	0	0
$373$	−6.58590e54	−0.336415	−0.168208	−	0.985752i	$-0.553798\pi$
$373$	−6.58590e54	−0.336415	−0.168208	+	0.985752i	$0.553798\pi$
$374$	−4.59618e54	−0.221645
$375$	0	0
$376$	−1.17466e55	−0.505094
$377$	−2.12884e55	−0.864576
$378$	0	0
$379$	4.25975e55	1.54398	0.771989	−	0.635636i	$-0.219262\pi$
$379$	4.25975e55	1.54398	0.771989	+	0.635636i	$0.219262\pi$
$380$	−3.95856e55	−1.35578
$381$	0	0
$382$	−5.67798e55	−1.73713
$383$	1.85965e53	0.00537846	0.00268923	−	0.999996i	$-0.499144\pi$
$383$	1.85965e53	0.00537846	0.00268923	+	0.999996i	$0.499144\pi$
$384$	0	0
$385$	3.49559e54	0.0903888
$386$	3.89490e53	0.00952509
$387$	0	0
$388$	−7.86367e55	−1.72085
$389$	−7.73460e55	−1.60148	−0.800740	−	0.599012i	$-0.795560\pi$
$389$	−7.73460e55	−1.60148	−0.800740	+	0.599012i	$0.795560\pi$
$390$	0	0
$391$	1.61737e55	0.299923
$392$	−3.54034e55	−0.621434
$393$	0	0
$394$	−5.78624e55	−0.910390
$395$	1.94204e54	0.0289349
$396$	0	0
$397$	−5.40998e55	−0.723102	−0.361551	−	0.932352i	$-0.617753\pi$
$397$	−5.40998e55	−0.723102	−0.361551	+	0.932352i	$0.617753\pi$
$398$	1.18212e56	1.49684
$399$	0	0
$400$	2.08504e55	0.237041
$401$	1.27603e56	1.37486	0.687429	−	0.726252i	$-0.258739\pi$
$401$	1.27603e56	1.37486	0.687429	+	0.726252i	$0.258739\pi$
$402$	0	0
$403$	−4.71789e55	−0.456761
$404$	−1.05543e56	−0.968787
$405$	0	0
$406$	1.08924e56	0.899108
$407$	−3.62839e55	−0.284076
$408$	0	0
$409$	1.15025e56	0.810481	0.405240	−	0.914210i	$-0.367188\pi$
$409$	1.15025e56	0.810481	0.405240	+	0.914210i	$0.367188\pi$
$410$	1.67421e55	0.111932
$411$	0	0
$412$	3.50001e56	2.10756
$413$	−4.17128e54	−0.0238420
$414$	0	0
$415$	−1.23713e56	−0.637354
$416$	−1.43646e56	−0.702729
$417$	0	0
$418$	2.92110e56	1.28901
$419$	3.32264e55	0.139278	0.0696389	−	0.997572i	$-0.477815\pi$
$419$	3.32264e55	0.139278	0.0696389	+	0.997572i	$0.477815\pi$
$420$	0	0
$421$	−3.83623e55	−0.145158	−0.0725788	−	0.997363i	$-0.523123\pi$
$421$	−3.83623e55	−0.145158	−0.0725788	+	0.997363i	$0.523123\pi$
$422$	8.01909e56	2.88342
$423$	0	0
$424$	−1.56622e56	−0.508729
$425$	7.24588e55	0.223732
$426$	0	0
$427$	1.25363e56	0.349920
$428$	5.48255e56	1.45526
$429$	0	0
$430$	−9.06153e54	−0.0217585
$431$	−2.91528e56	−0.665916	−0.332958	−	0.942942i	$-0.608047\pi$
$431$	−2.91528e56	−0.665916	−0.332958	+	0.942942i	$0.608047\pi$
$432$	0	0
$433$	−8.91932e56	−1.84434	−0.922172	−	0.386780i	$-0.873587\pi$
$433$	−8.91932e56	−1.84434	−0.922172	+	0.386780i	$0.873587\pi$
$434$	2.41394e56	0.475005
$435$	0	0
$436$	3.12044e56	0.556233
$437$	−1.02792e57	−1.74425
$438$	0	0
$439$	−4.59768e56	−0.707216	−0.353608	−	0.935394i	$-0.615045\pi$
$439$	−4.59768e56	−0.707216	−0.353608	+	0.935394i	$0.615045\pi$
$440$	−1.18502e56	−0.173578
$441$	0	0
$442$	−2.06162e56	−0.273924
$443$	−7.17753e56	−0.908437	−0.454219	−	0.890890i	$-0.650082\pi$
$443$	−7.17753e56	−0.908437	−0.454219	+	0.890890i	$0.650082\pi$
$444$	0	0
$445$	−2.42918e56	−0.279074
$446$	−6.68882e56	−0.732234
$447$	0	0
$448$	6.11679e56	0.608200
$449$	2.56945e56	0.243526	0.121763	−	0.992559i	$-0.461145\pi$
$449$	2.56945e56	0.243526	0.121763	+	0.992559i	$0.461145\pi$
$450$	0	0
$451$	−7.33594e55	−0.0631917
$452$	−2.23517e57	−1.83584
$453$	0	0
$454$	3.35907e55	0.0250910
$455$	1.56795e56	0.111709
$456$	0	0
$457$	−1.11475e57	−0.722733	−0.361367	−	0.932424i	$-0.617690\pi$
$457$	−1.11475e57	−0.722733	−0.361367	+	0.932424i	$0.617690\pi$
$458$	4.00574e57	2.47785
$459$	0	0
$460$	1.31997e57	0.743481
$461$	−2.02024e57	−1.08601	−0.543003	−	0.839731i	$-0.682713\pi$
$461$	−2.02024e57	−1.08601	−0.543003	+	0.839731i	$0.682713\pi$
$462$	0	0
$463$	−2.86426e56	−0.140288	−0.0701442	−	0.997537i	$-0.522346\pi$
$463$	−2.86426e56	−0.140288	−0.0701442	+	0.997537i	$0.522346\pi$
$464$	1.05527e57	0.493432
$465$	0	0
$466$	3.79621e57	1.61828
$467$	−1.63037e57	−0.663701	−0.331850	−	0.943332i	$-0.607673\pi$
$467$	−1.63037e57	−0.663701	−0.331850	+	0.943332i	$0.607673\pi$
$468$	0	0
$469$	1.05825e57	0.392982
$470$	1.60339e57	0.568767
$471$	0	0
$472$	1.41409e56	0.0457850
$473$	3.97052e55	0.0122838
$474$	0	0
$475$	−4.60511e57	−1.30115
$476$	6.26363e56	0.169152
$477$	0	0
$478$	−5.57781e57	−1.37646
$479$	−7.76358e57	−1.83168	−0.915838	−	0.401548i	$-0.868472\pi$
$479$	−7.76358e57	−1.83168	−0.915838	+	0.401548i	$0.868472\pi$
$480$	0	0
$481$	−1.62752e57	−0.351081
$482$	5.35690e57	1.10510
$483$	0	0
$484$	−6.10223e57	−1.15163
$485$	3.39102e57	0.612185
$486$	0	0
$487$	1.02143e58	1.68786	0.843932	−	0.536451i	$-0.180235\pi$
$487$	1.02143e58	1.68786	0.843932	+	0.536451i	$0.180235\pi$
$488$	−4.24986e57	−0.671968
$489$	0	0
$490$	4.83251e57	0.699773
$491$	−4.75337e57	−0.658794	−0.329397	−	0.944192i	$-0.606845\pi$
$491$	−4.75337e57	−0.658794	−0.329397	+	0.944192i	$0.606845\pi$
$492$	0	0
$493$	3.66725e57	0.465728
$494$	1.31026e58	1.59305
$495$	0	0
$496$	2.33867e57	0.260683
$497$	−5.31923e57	−0.567788
$498$	0	0
$499$	−6.28971e57	−0.615841	−0.307921	−	0.951412i	$-0.599633\pi$
$499$	−6.28971e57	−0.615841	−0.307921	+	0.951412i	$0.599633\pi$
$500$	1.40190e58	1.31481
$501$	0	0
$502$	1.64050e58	1.41203
$503$	2.08189e58	1.71690	0.858451	−	0.512896i	$-0.171427\pi$
$503$	2.08189e58	1.71690	0.858451	+	0.512896i	$0.171427\pi$
$504$	0	0
$505$	4.55127e57	0.344642
$506$	−9.74030e57	−0.706865
$507$	0	0
$508$	−3.62514e58	−2.41688
$509$	−4.65765e57	−0.297669	−0.148835	−	0.988862i	$-0.547552\pi$
$509$	−4.65765e57	−0.297669	−0.148835	+	0.988862i	$0.547552\pi$
$510$	0	0
$511$	−1.38431e57	−0.0813174
$512$	1.13005e58	0.636491
$513$	0	0
$514$	4.19228e58	2.17142
$515$	−1.50929e58	−0.749754
$516$	0	0
$517$	−7.02563e57	−0.321099
$518$	8.32733e57	0.365104
$519$	0	0
$520$	−5.31543e57	−0.214520
$521$	−4.15022e57	−0.160716	−0.0803582	−	0.996766i	$-0.525606\pi$
$521$	−4.15022e57	−0.160716	−0.0803582	+	0.996766i	$0.525606\pi$
$522$	0	0
$523$	−3.61441e57	−0.128899	−0.0644497	−	0.997921i	$-0.520529\pi$
$523$	−3.61441e57	−0.128899	−0.0644497	+	0.997921i	$0.520529\pi$
$524$	−6.71442e58	−2.29819
$525$	0	0
$526$	4.05235e58	1.27795
$527$	8.12730e57	0.246047
$528$	0	0
$529$	−1.55852e57	−0.0434925
$530$	2.13787e58	0.572861
$531$	0	0
$532$	−3.98084e58	−0.983728
$533$	−3.29054e57	−0.0780967
$534$	0	0
$535$	−2.36422e58	−0.517703
$536$	−3.58753e58	−0.754662
$537$	0	0
$538$	−1.06838e59	−2.07446
$539$	−2.11748e58	−0.395058
$540$	0	0
$541$	−4.79722e58	−0.826511	−0.413256	−	0.910615i	$-0.635608\pi$
$541$	−4.79722e58	−0.826511	−0.413256	+	0.910615i	$0.635608\pi$
$542$	−9.51331e58	−1.57524
$543$	0	0
$544$	2.47453e58	0.378544
$545$	−1.34562e58	−0.197877
$546$	0	0
$547$	3.67046e58	0.498877	0.249439	−	0.968391i	$-0.419754\pi$
$547$	3.67046e58	0.498877	0.249439	+	0.968391i	$0.419754\pi$
$548$	1.51636e59	1.98162
$549$	0	0
$550$	−4.36368e58	−0.527297
$551$	−2.33072e59	−2.70851
$552$	0	0
$553$	1.95298e57	0.0209946
$554$	1.70869e59	1.76687
$555$	0	0
$556$	1.01569e59	0.971974
$557$	1.44377e59	1.32926	0.664632	−	0.747171i	$-0.268588\pi$
$557$	1.44377e59	1.32926	0.664632	+	0.747171i	$0.268588\pi$
$558$	0	0
$559$	1.78098e57	0.0151812
$560$	−7.77238e57	−0.0637546
$561$	0	0
$562$	1.49509e59	1.13589
$563$	1.85030e58	0.135304	0.0676521	−	0.997709i	$-0.478449\pi$
$563$	1.85030e58	0.135304	0.0676521	+	0.997709i	$0.478449\pi$
$564$	0	0
$565$	9.63864e58	0.653092
$566$	3.61344e59	2.35705
$567$	0	0
$568$	1.80325e59	1.09035
$569$	−7.55839e58	−0.440064	−0.220032	−	0.975493i	$-0.570616\pi$
$569$	−7.55839e58	−0.440064	−0.220032	+	0.975493i	$0.570616\pi$
$570$	0	0
$571$	1.65354e59	0.892767	0.446384	−	0.894842i	$-0.352712\pi$
$571$	1.65354e59	0.892767	0.446384	+	0.894842i	$0.352712\pi$
$572$	7.37239e58	0.383349
$573$	0	0
$574$	1.68363e58	0.0812160
$575$	1.53556e59	0.713522
$576$	0	0
$577$	−4.04625e59	−1.74491	−0.872453	−	0.488697i	$-0.837472\pi$
$577$	−4.04625e59	−1.74491	−0.872453	+	0.488697i	$0.837472\pi$
$578$	−3.42124e59	−1.42146
$579$	0	0
$580$	2.99291e59	1.15449
$581$	−1.24409e59	−0.462451
$582$	0	0
$583$	−9.36757e58	−0.323410
$584$	4.69288e58	0.156158
$585$	0	0
$586$	−3.29005e59	−1.01719
$587$	−3.79894e59	−1.13225	−0.566126	−	0.824319i	$-0.691558\pi$
$587$	−3.79894e59	−1.13225	−0.566126	+	0.824319i	$0.691558\pi$
$588$	0	0
$589$	−5.16530e59	−1.43092
$590$	−1.93021e58	−0.0515568
$591$	0	0
$592$	8.06767e58	0.200369
$593$	4.79450e59	1.14833	0.574166	−	0.818739i	$-0.305326\pi$
$593$	4.79450e59	1.14833	0.574166	+	0.818739i	$0.305326\pi$
$594$	0	0
$595$	−2.70104e58	−0.0601750
$596$	−7.42486e58	−0.159549
$597$	0	0
$598$	−4.36902e59	−0.873592
$599$	4.48279e59	0.864713	0.432356	−	0.901703i	$-0.357682\pi$
$599$	4.48279e59	0.864713	0.432356	+	0.901703i	$0.357682\pi$
$600$	0	0
$601$	−1.41250e59	−0.253621	−0.126811	−	0.991927i	$-0.540474\pi$
$601$	−1.41250e59	−0.253621	−0.126811	+	0.991927i	$0.540474\pi$
$602$	−9.11254e57	−0.0157876
$603$	0	0
$604$	−2.53707e59	−0.409296
$605$	2.63144e59	0.409688
$606$	0	0
$607$	7.01925e59	1.01797	0.508984	−	0.860776i	$-0.330021\pi$
$607$	7.01925e59	1.01797	0.508984	+	0.860776i	$0.330021\pi$
$608$	−1.57269e60	−2.20148
$609$	0	0
$610$	5.80100e59	0.756679
$611$	−3.15135e59	−0.396836
$612$	0	0
$613$	1.03814e60	1.21858	0.609292	−	0.792946i	$-0.291454\pi$
$613$	1.03814e60	1.21858	0.609292	+	0.792946i	$0.291454\pi$
$614$	−1.94507e60	−2.20453
$615$	0	0
$616$	−1.19169e59	−0.125945
$617$	1.00931e60	1.03014	0.515069	−	0.857149i	$-0.327766\pi$
$617$	1.00931e60	1.03014	0.515069	+	0.857149i	$0.327766\pi$
$618$	0	0
$619$	1.22876e59	0.116981	0.0584907	−	0.998288i	$-0.481371\pi$
$619$	1.22876e59	0.116981	0.0584907	+	0.998288i	$0.481371\pi$
$620$	6.63283e59	0.609927
$621$	0	0
$622$	−5.06001e59	−0.434169
$623$	−2.44286e59	−0.202491
$624$	0	0
$625$	3.38403e59	0.261827
$626$	2.37172e59	0.177302
$627$	0	0
$628$	−1.71791e60	−1.19914
$629$	2.80366e59	0.189119
$630$	0	0
$631$	2.36287e60	1.48870	0.744352	−	0.667787i	$-0.232758\pi$
$631$	2.36287e60	1.48870	0.744352	+	0.667787i	$0.232758\pi$
$632$	−6.62069e58	−0.0403168
$633$	0	0
$634$	−2.75946e60	−1.57002
$635$	1.56325e60	0.859794
$636$	0	0
$637$	−9.49799e59	−0.488241
$638$	−2.20853e60	−1.09764
$639$	0	0
$640$	1.44896e60	0.673268
$641$	3.06701e60	1.37806	0.689029	−	0.724734i	$-0.258037\pi$
$641$	3.06701e60	1.37806	0.689029	+	0.724734i	$0.258037\pi$
$642$	0	0
$643$	8.63761e59	0.362959	0.181479	−	0.983395i	$-0.441911\pi$
$643$	8.63761e59	0.362959	0.181479	+	0.983395i	$0.441911\pi$
$644$	1.32740e60	0.539455
$645$	0	0
$646$	−2.25713e60	−0.858139
$647$	1.57232e60	0.578228	0.289114	−	0.957295i	$-0.406639\pi$
$647$	1.57232e60	0.578228	0.289114	+	0.957295i	$0.406639\pi$
$648$	0	0
$649$	8.45767e58	0.0291065
$650$	−1.95733e60	−0.651670
$651$	0	0
$652$	−1.34917e60	−0.420478
$653$	−1.42220e60	−0.428870	−0.214435	−	0.976738i	$-0.568791\pi$
$653$	−1.42220e60	−0.428870	−0.214435	+	0.976738i	$0.568791\pi$
$654$	0	0
$655$	2.89543e60	0.817571
$656$	1.63113e59	0.0445715
$657$	0	0
$658$	1.61241e60	0.412686
$659$	−2.37773e60	−0.589015	−0.294507	−	0.955649i	$-0.595156\pi$
$659$	−2.37773e60	−0.589015	−0.294507	+	0.955649i	$0.595156\pi$
$660$	0	0
$661$	−7.09142e60	−1.64589	−0.822947	−	0.568119i	$-0.807671\pi$
$661$	−7.09142e60	−1.64589	−0.822947	+	0.568119i	$0.807671\pi$
$662$	2.15032e60	0.483121
$663$	0	0
$664$	4.21754e60	0.888067
$665$	1.71664e60	0.349957
$666$	0	0
$667$	7.77170e60	1.48529
$668$	8.67810e60	1.60595
$669$	0	0
$670$	4.89693e60	0.849798
$671$	−2.54185e60	−0.427184
$672$	0	0
$673$	7.62590e60	1.20217	0.601086	−	0.799184i	$-0.294735\pi$
$673$	7.62590e60	1.20217	0.601086	+	0.799184i	$0.294735\pi$
$674$	−1.14003e61	−1.74072
$675$	0	0
$676$	−6.89655e60	−0.988048
$677$	1.33549e61	1.85347	0.926735	−	0.375717i	$-0.122603\pi$
$677$	1.33549e61	1.85347	0.926735	+	0.375717i	$0.122603\pi$
$678$	0	0
$679$	3.41011e60	0.444189
$680$	9.15667e59	0.115557
$681$	0	0
$682$	−4.89450e60	−0.579888
$683$	−7.17925e60	−0.824202	−0.412101	−	0.911138i	$-0.635205\pi$
$683$	−7.17925e60	−0.824202	−0.412101	+	0.911138i	$0.635205\pi$
$684$	0	0
$685$	−6.53894e60	−0.704953
$686$	1.05262e61	1.09977
$687$	0	0
$688$	−8.82839e58	−0.00866424
$689$	−4.20183e60	−0.399692
$690$	0	0
$691$	−1.17437e61	−1.04961	−0.524803	−	0.851224i	$-0.675861\pi$
$691$	−1.17437e61	−1.04961	−0.524803	+	0.851224i	$0.675861\pi$
$692$	5.34200e60	0.462831
$693$	0	0
$694$	−9.62632e60	−0.783848
$695$	−4.37993e60	−0.345776
$696$	0	0
$697$	5.66848e59	0.0420689
$698$	−4.30228e61	−3.09604
$699$	0	0
$700$	5.94678e60	0.402415
$701$	−1.27675e61	−0.837854	−0.418927	−	0.908020i	$-0.637594\pi$
$701$	−1.27675e61	−0.837854	−0.418927	+	0.908020i	$0.637594\pi$
$702$	0	0
$703$	−1.78186e61	−1.09985
$704$	−1.24024e61	−0.742494
$705$	0	0
$706$	1.65245e61	0.930735
$707$	4.57689e60	0.250065
$708$	0	0
$709$	−2.73809e61	−1.40784	−0.703921	−	0.710278i	$-0.748569\pi$
$709$	−2.73809e61	−1.40784	−0.703921	+	0.710278i	$0.748569\pi$
$710$	−2.46141e61	−1.22780
$711$	0	0
$712$	8.28142e60	0.388852
$713$	1.72235e61	0.784687
$714$	0	0
$715$	−3.17917e60	−0.136375
$716$	8.16420e60	0.339847
$717$	0	0
$718$	2.96683e61	1.16310
$719$	−2.16831e61	−0.824993	−0.412496	−	0.910959i	$-0.635343\pi$
$719$	−2.16831e61	−0.824993	−0.412496	+	0.910959i	$0.635343\pi$
$720$	0	0
$721$	−1.51779e61	−0.544006
$722$	9.83518e61	3.42162
$723$	0	0
$724$	6.92426e60	0.226984
$725$	3.48174e61	1.10797
$726$	0	0
$727$	1.57652e61	0.472835	0.236418	−	0.971652i	$-0.424027\pi$
$727$	1.57652e61	0.472835	0.236418	+	0.971652i	$0.424027\pi$
$728$	−5.34536e60	−0.155651
$729$	0	0
$730$	−6.40571e60	−0.175843
$731$	−3.06802e59	−0.00817777
$732$	0	0
$733$	2.88722e61	0.725679	0.362840	−	0.931852i	$-0.381807\pi$
$733$	2.88722e61	0.725679	0.362840	+	0.931852i	$0.381807\pi$
$734$	5.55081e61	1.35485
$735$	0	0
$736$	5.24407e61	1.20724
$737$	−2.14571e61	−0.479755
$738$	0	0
$739$	7.66659e60	0.161714	0.0808568	−	0.996726i	$-0.474234\pi$
$739$	7.66659e60	0.161714	0.0808568	+	0.996726i	$0.474234\pi$
$740$	2.28811e61	0.468809
$741$	0	0
$742$	2.14990e61	0.415656
$743$	−5.63267e61	−1.05792	−0.528962	−	0.848645i	$-0.677419\pi$
$743$	−5.63267e61	−1.05792	−0.528962	+	0.848645i	$0.677419\pi$
$744$	0	0
$745$	3.20179e60	0.0567588
$746$	−3.06470e61	−0.527841
$747$	0	0
$748$	−1.27001e61	−0.206501
$749$	−2.37753e61	−0.375635
$750$	0	0
$751$	−5.65647e60	−0.0843892	−0.0421946	−	0.999109i	$-0.513435\pi$
$751$	−5.65647e60	−0.0843892	−0.0421946	+	0.999109i	$0.513435\pi$
$752$	1.56214e61	0.226483
$753$	0	0
$754$	−9.90638e61	−1.35654
$755$	1.09405e61	0.145605
$756$	0	0
$757$	4.86809e61	0.612065	0.306032	−	0.952021i	$-0.400998\pi$
$757$	4.86809e61	0.612065	0.306032	+	0.952021i	$0.400998\pi$
$758$	1.98224e62	2.42253
$759$	0	0
$760$	−5.81951e61	−0.672039
$761$	−5.98651e61	−0.672053	−0.336026	−	0.941853i	$-0.609083\pi$
$761$	−5.98651e61	−0.672053	−0.336026	+	0.941853i	$0.609083\pi$
$762$	0	0
$763$	−1.35319e61	−0.143576
$764$	−1.56893e62	−1.61844
$765$	0	0
$766$	8.65375e59	0.00843890
$767$	3.79370e60	0.0359718
$768$	0	0
$769$	−2.53056e61	−0.226882	−0.113441	−	0.993545i	$-0.536187\pi$
$769$	−2.53056e61	−0.226882	−0.113441	+	0.993545i	$0.536187\pi$
$770$	1.62665e61	0.141822
$771$	0	0
$772$	1.07623e60	0.00887430
$773$	−1.22577e62	−0.982992	−0.491496	−	0.870880i	$-0.663550\pi$
$773$	−1.22577e62	−0.982992	−0.491496	+	0.870880i	$0.663550\pi$
$774$	0	0
$775$	7.71618e61	0.585350
$776$	−1.15605e62	−0.852998
$777$	0	0
$778$	−3.59924e62	−2.51275
$779$	−3.60260e61	−0.244658
$780$	0	0
$781$	1.07852e62	0.693159
$782$	7.52633e61	0.470585
$783$	0	0
$784$	4.70819e61	0.278649
$785$	7.40809e61	0.426588
$786$	0	0
$787$	−5.88188e61	−0.320671	−0.160335	−	0.987063i	$-0.551258\pi$
$787$	−5.88188e61	−0.320671	−0.160335	+	0.987063i	$0.551258\pi$
$788$	−1.59884e62	−0.848189
$789$	0	0
$790$	9.03715e60	0.0453993
$791$	9.69290e61	0.473870
$792$	0	0
$793$	−1.14015e62	−0.527944
$794$	−2.51749e62	−1.13456
$795$	0	0
$796$	3.26641e62	1.39457
$797$	1.91183e62	0.794504	0.397252	−	0.917710i	$-0.369964\pi$
$797$	1.91183e62	0.794504	0.397252	+	0.917710i	$0.369964\pi$
$798$	0	0
$799$	5.42870e61	0.213767
$800$	2.34936e62	0.900563
$801$	0	0
$802$	5.93792e62	2.15718
$803$	2.80682e61	0.0992727
$804$	0	0
$805$	−5.72408e61	−0.191909
$806$	−2.19543e62	−0.716667
$807$	0	0
$808$	−1.55159e62	−0.480212
$809$	−3.32609e62	−1.00240	−0.501200	−	0.865332i	$-0.667108\pi$
$809$	−3.32609e62	−1.00240	−0.501200	+	0.865332i	$0.667108\pi$
$810$	0	0
$811$	2.53671e61	0.0724974	0.0362487	−	0.999343i	$-0.488459\pi$
$811$	2.53671e61	0.0724974	0.0362487	+	0.999343i	$0.488459\pi$
$812$	3.00976e62	0.837678
$813$	0	0
$814$	−1.68845e62	−0.445720
$815$	5.81797e61	0.149583
$816$	0	0
$817$	1.94988e61	0.0475591
$818$	5.35262e62	1.27166
$819$	0	0
$820$	4.62614e61	0.104285
$821$	−8.50693e62	−1.86808	−0.934039	−	0.357170i	$-0.883742\pi$
$821$	−8.50693e62	−1.86808	−0.934039	+	0.357170i	$0.883742\pi$
$822$	0	0
$823$	−5.42465e62	−1.13051	−0.565256	−	0.824915i	$-0.691223\pi$
$823$	−5.42465e62	−1.13051	−0.565256	+	0.824915i	$0.691223\pi$
$824$	5.14539e62	1.04468
$825$	0	0
$826$	−1.94107e61	−0.0374086
$827$	7.20567e62	1.35303	0.676513	−	0.736431i	$-0.263490\pi$
$827$	7.20567e62	1.35303	0.676513	+	0.736431i	$0.263490\pi$
$828$	0	0
$829$	−8.50026e62	−1.51534	−0.757669	−	0.652639i	$-0.773662\pi$
$829$	−8.50026e62	−1.51534	−0.757669	+	0.652639i	$0.773662\pi$
$830$	−5.75689e62	−1.00002
$831$	0	0
$832$	−5.56310e62	−0.917626
$833$	1.63618e62	0.263004
$834$	0	0
$835$	−3.74222e62	−0.571308
$836$	8.07154e62	1.20094
$837$	0	0
$838$	1.54617e62	0.218529
$839$	−5.84952e62	−0.805820	−0.402910	−	0.915240i	$-0.632001\pi$
$839$	−5.84952e62	−0.805820	−0.402910	+	0.915240i	$0.632001\pi$
$840$	0	0
$841$	9.98130e62	1.30639
$842$	−1.78516e62	−0.227755
$843$	0	0
$844$	2.21582e63	2.68641
$845$	2.97397e62	0.351494
$846$	0	0
$847$	2.64625e62	0.297261
$848$	2.08286e62	0.228113
$849$	0	0
$850$	3.37181e62	0.351040
$851$	5.94155e62	0.603135
$852$	0	0
$853$	6.11541e62	0.590230	0.295115	−	0.955462i	$-0.404642\pi$
$853$	6.11541e62	0.590230	0.295115	+	0.955462i	$0.404642\pi$
$854$	5.83366e62	0.549031
$855$	0	0
$856$	8.05994e62	0.721350
$857$	3.04840e62	0.266063	0.133032	−	0.991112i	$-0.457529\pi$
$857$	3.04840e62	0.266063	0.133032	+	0.991112i	$0.457529\pi$
$858$	0	0
$859$	−4.98228e62	−0.413595	−0.206798	−	0.978384i	$-0.566304\pi$
$859$	−4.98228e62	−0.413595	−0.206798	+	0.978384i	$0.566304\pi$
$860$	−2.50387e61	−0.0202719
$861$	0	0
$862$	−1.35661e63	−1.04483
$863$	−2.55705e61	−0.0192091	−0.00960454	−	0.999954i	$-0.503057\pi$
$863$	−2.55705e61	−0.0192091	−0.00960454	+	0.999954i	$0.503057\pi$
$864$	0	0
$865$	−2.30361e62	−0.164650
$866$	−4.15054e63	−2.89381
$867$	0	0
$868$	6.67017e62	0.442551
$869$	−3.95985e61	−0.0256303
$870$	0	0
$871$	−9.62459e62	−0.592914
$872$	4.58739e62	0.275715
$873$	0	0
$874$	−4.78335e63	−2.73676
$875$	−6.07939e62	−0.339380
$876$	0	0
$877$	2.16419e63	1.15028	0.575141	−	0.818054i	$-0.304947\pi$
$877$	2.16419e63	1.15028	0.575141	+	0.818054i	$0.304947\pi$
$878$	−2.13950e63	−1.10963
$879$	0	0
$880$	1.57592e62	0.0778319
$881$	8.01449e62	0.386273	0.193136	−	0.981172i	$-0.438134\pi$
$881$	8.01449e62	0.386273	0.193136	+	0.981172i	$0.438134\pi$
$882$	0	0
$883$	−1.13427e62	−0.0520667	−0.0260334	−	0.999661i	$-0.508288\pi$
$883$	−1.13427e62	−0.0520667	−0.0260334	+	0.999661i	$0.508288\pi$
$884$	−5.69665e62	−0.255209
$885$	0	0
$886$	−3.34001e63	−1.42535
$887$	2.15665e63	0.898299	0.449150	−	0.893457i	$-0.351727\pi$
$887$	2.15665e63	0.898299	0.449150	+	0.893457i	$0.351727\pi$
$888$	0	0
$889$	1.57205e63	0.623849
$890$	−1.13040e63	−0.437872
$891$	0	0
$892$	−1.84825e63	−0.682205
$893$	−3.45021e63	−1.24319
$894$	0	0
$895$	−3.52062e62	−0.120899
$896$	1.45712e63	0.488510
$897$	0	0
$898$	1.19568e63	0.382096
$899$	3.90528e63	1.21848
$900$	0	0
$901$	7.23832e62	0.215305
$902$	−3.41372e62	−0.0991489
$903$	0	0
$904$	−3.28595e63	−0.909995
$905$	−2.98592e62	−0.0807484
$906$	0	0
$907$	7.76445e62	0.200241	0.100121	−	0.994975i	$-0.468077\pi$
$907$	7.76445e62	0.200241	0.100121	+	0.994975i	$0.468077\pi$
$908$	9.28172e61	0.0233767
$909$	0	0
$910$	7.29634e62	0.175273
$911$	2.02334e62	0.0474704	0.0237352	−	0.999718i	$-0.492444\pi$
$911$	2.02334e62	0.0474704	0.0237352	+	0.999718i	$0.492444\pi$
$912$	0	0
$913$	2.52252e63	0.564563
$914$	−5.18739e63	−1.13398
$915$	0	0
$916$	1.10686e64	2.30855
$917$	2.91173e63	0.593213
$918$	0	0
$919$	9.59396e63	1.86515	0.932577	−	0.360972i	$-0.117555\pi$
$919$	9.59396e63	1.86515	0.932577	+	0.360972i	$0.117555\pi$
$920$	1.94049e63	0.368531
$921$	0	0
$922$	−9.40102e63	−1.70396
$923$	4.83773e63	0.856654
$924$	0	0
$925$	2.66183e63	0.449918
$926$	−1.33286e63	−0.220115
$927$	0	0
$928$	1.18905e64	1.87464
$929$	7.48220e63	1.15263	0.576317	−	0.817226i	$-0.304489\pi$
$929$	7.48220e63	1.15263	0.576317	+	0.817226i	$0.304489\pi$
$930$	0	0
$931$	−1.03987e64	−1.52954
$932$	1.04896e64	1.50771
$933$	0	0
$934$	−7.58679e63	−1.04136
$935$	5.47661e62	0.0734619
$936$	0	0
$937$	−5.90450e63	−0.756453	−0.378227	−	0.925713i	$-0.623466\pi$
$937$	−5.90450e63	−0.756453	−0.378227	+	0.925713i	$0.623466\pi$
$938$	4.92450e63	0.616596
$939$	0	0
$940$	4.43046e63	0.529907
$941$	1.10650e64	1.29352	0.646759	−	0.762694i	$-0.276124\pi$
$941$	1.10650e64	1.29352	0.646759	+	0.762694i	$0.276124\pi$
$942$	0	0
$943$	1.20127e63	0.134165
$944$	−1.88055e62	−0.0205299
$945$	0	0
$946$	1.84765e62	0.0192735
$947$	−7.68969e63	−0.784123	−0.392062	−	0.919939i	$-0.628238\pi$
$947$	−7.68969e63	−0.784123	−0.392062	+	0.919939i	$0.628238\pi$
$948$	0	0
$949$	1.25900e63	0.122688
$950$	−2.14295e64	−2.04153
$951$	0	0
$952$	9.20821e62	0.0838457
$953$	−5.87345e63	−0.522873	−0.261436	−	0.965221i	$-0.584196\pi$
$953$	−5.87345e63	−0.522873	−0.261436	+	0.965221i	$0.584196\pi$
$954$	0	0
$955$	6.76564e63	0.575753
$956$	−1.54125e64	−1.28242
$957$	0	0
$958$	−3.61273e64	−2.87393
$959$	−6.57576e63	−0.511500
$960$	0	0
$961$	−4.78994e63	−0.356268
$962$	−7.57354e63	−0.550852
$963$	0	0
$964$	1.48021e64	1.02960
$965$	−4.64099e61	−0.00315699
$966$	0	0
$967$	−1.95511e64	−1.27205	−0.636023	−	0.771670i	$-0.719422\pi$
$967$	−1.95511e64	−1.27205	−0.636023	+	0.771670i	$0.719422\pi$
$968$	−8.97095e63	−0.570845
$969$	0	0
$970$	1.57799e64	0.960529
$971$	−2.50785e64	−1.49310	−0.746549	−	0.665330i	$-0.768291\pi$
$971$	−2.50785e64	−1.49310	−0.746549	+	0.665330i	$0.768291\pi$
$972$	0	0
$973$	−4.40459e63	−0.250888
$974$	4.75316e64	2.64829
$975$	0	0
$976$	5.65175e63	0.301309
$977$	−3.39735e64	−1.77177	−0.885884	−	0.463906i	$-0.846447\pi$
$977$	−3.39735e64	−1.77177	−0.885884	+	0.463906i	$0.846447\pi$
$978$	0	0
$979$	4.95312e63	0.247202
$980$	1.33531e64	0.651962
$981$	0	0
$982$	−2.21195e64	−1.03366
$983$	2.21328e64	1.01189	0.505947	−	0.862565i	$-0.331143\pi$
$983$	2.21328e64	1.01189	0.505947	+	0.862565i	$0.331143\pi$
$984$	0	0
$985$	6.89463e63	0.301739
$986$	1.70653e64	0.730735
$987$	0	0
$988$	3.62050e64	1.48421
$989$	−6.50180e62	−0.0260803
$990$	0	0
$991$	2.88177e64	1.10682	0.553408	−	0.832910i	$-0.313327\pi$
$991$	2.88177e64	1.10682	0.553408	+	0.832910i	$0.313327\pi$
$992$	2.63514e64	0.990383
$993$	0	0
$994$	−2.47526e64	−0.890870
$995$	−1.40856e64	−0.496112
$996$	0	0
$997$	−2.97127e64	−1.00230	−0.501148	−	0.865361i	$-0.667089\pi$
$997$	−2.97127e64	−1.00230	−0.501148	+	0.865361i	$0.667089\pi$
$998$	−2.92687e64	−0.966266
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.44.a.b.1.3		3
3.2	odd	2		1.44.a.a.1.1	✓	3
12.11	even	2		16.44.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.44.a.a.1.1	✓	3	3.2	odd	2
9.44.a.b.1.3		3	1.1	even	1	trivial
16.44.a.c.1.1		3	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+4.65343e6 q^{2} +1.28583e13 q^{4} -5.54482e14 q^{5} -5.57604e17 q^{7} +1.89031e19 q^{8} +O(q^{10})\)	\(q+4.65343e6 q^{2} +1.28583e13 q^{4} -5.54482e14 q^{5} -5.57604e17 q^{7} +1.89031e19 q^{8} -2.58024e21 q^{10} +1.13059e22 q^{11} +5.07130e23 q^{13} -2.59477e24 q^{14} -2.51386e25 q^{16} -8.73610e25 q^{17} +5.55222e27 q^{19} -7.12968e27 q^{20} +5.26114e28 q^{22} -1.85137e29 q^{23} -8.29418e29 q^{25} +2.35989e30 q^{26} -7.16982e30 q^{28} -4.19782e31 q^{29} -9.30312e31 q^{31} -2.83254e32 q^{32} -4.06528e32 q^{34} +3.09181e32 q^{35} -3.20928e33 q^{37} +2.58368e34 q^{38} -1.04814e34 q^{40} -6.48857e33 q^{41} +3.51189e33 q^{43} +1.45375e35 q^{44} -8.61520e35 q^{46} -6.21410e35 q^{47} -1.87289e36 q^{49} -3.85963e36 q^{50} +6.52081e36 q^{52} -8.28552e36 q^{53} -6.26895e36 q^{55} -1.05404e37 q^{56} -1.95342e38 q^{58} +7.48073e36 q^{59} -2.24824e38 q^{61} -4.32914e38 q^{62} -1.09698e39 q^{64} -2.81194e38 q^{65} -1.89786e39 q^{67} -1.12331e39 q^{68} +1.43875e39 q^{70} +9.53945e39 q^{71} +2.48260e39 q^{73} -1.49341e40 q^{74} +7.13920e40 q^{76} -6.30424e39 q^{77} -3.50244e39 q^{79} +1.39389e40 q^{80} -3.01941e40 q^{82} +2.23114e41 q^{83} +4.84401e40 q^{85} +1.63423e40 q^{86} +2.13717e41 q^{88} +4.38099e41 q^{89} -2.82777e41 q^{91} -2.38054e42 q^{92} -2.89169e42 q^{94} -3.07861e42 q^{95} -6.11565e42 q^{97} -8.71537e42 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots + 15\!\cdots\!80 q^{8}+O(q^{10}) \) 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8	\( 3 q + 2209944 q^{2} + 9822618421824 q^{4} - 535205380774170 q^{5} + 30\!\cdots\!56 q^{7}+ \cdots - 24\!\cdots\!08 q^{98}+O(q^{100}) \) 3 * q + 2209944 * q^2 + 9822618421824 * q^4 - 535205380774170 * q^5 + 301971425665478856 * q^7 + 15830863913787348480 * q^8 + 424411733447436982320 * q^10 - 26665053285822824598396 * q^11 + 2675160683143344673595682 * q^13 - 14021968617857741064904128 * q^14 - 79484355831457348071124992 * q^16 + 408654222932442443796841194 * q^17 + 1577331357975519701176464900 * q^19 - 14558304937461364568422335360 * q^20 + 139626647360508967807005852192 * q^22 + 1215339635928561142484811048 * q^23 - 2310484082897201607166539950475 * q^25 + 1738302877111230473099097494544 * q^26 + 16881555000174595924306194912768 * q^28 - 57118989018136587596191009705650 * q^29 - 255565972342397832812135282963424 * q^31 + 144698056390774688063435943542784 * q^32 + 460541119788760022406607937310288 * q^34 - 2398213530857285851552147980593520 * q^35 - 2320645576165979428293572256842694 * q^37 + 30659398199572233844432077267455520 * q^38 - 32703585947405178164040064943232000 * q^40 - 25742376604739002042016577514061166 * q^41 + 240714339689128182512406300123419292 * q^43 + 103743099769332204870397943787455232 * q^44 - 1897545066442972080018141849284700864 * q^46 - 308713553347399687962182796433367856 * q^47 + 3434980292250886821160584750829904379 * q^49 - 1991781591031845842073119994352349400 * q^50 - 1723278372049486147633277645433304704 * q^52 - 15000497558784669132889458695112796362 * q^53 + 3996571389110251928625895283213506440 * q^55 + 64188456562605926675684864956824883200 * q^56 - 103653602500512241322054964115851073680 * q^58 - 226996261182733939538282061249836505900 * q^59 - 9393429368478033721028929889113591854 * q^61 + 208603081649583360642384119938663534848 * q^62 - 1119010168436659689243622515721507700736 * q^64 + 270218921102297342477494789001032451460 * q^65 - 733015616887151283726086660162187354444 * q^67 - 5475599618745313926138424496016357744768 * q^68 + 5947953535225896394715748735968145697920 * q^70 + 18523878066158899993345833814569898287864 * q^71 - 20251106025908798058937016734369224029298 * q^73 - 16747422277652165725566811926177721225008 * q^74 + 77507609539490133886259513865936229344000 * q^76 - 59055613160181778232413942942559747685792 * q^77 + 15233568018599764739559826813006999294800 * q^79 + 100962488695267720109813470111835940986880 * q^80 - 320808727539069549327137360482471983405168 * q^82 + 89206610196719670053085531955706819434428 * q^83 + 438725373228516358990025164547060204838420 * q^85 - 251282426033382455934203370485070655838496 * q^86 - 25677613216166441601684725395949811087360 * q^88 - 203691422331055117225246388044508249665950 * q^89 - 1168954967602248602369466051364648836229584 * q^91 - 688199578839743838535125048241381149958656 * q^92 - 1324027207656692012199753325229034662658432 * q^94 - 3125746305909018830165692627580442029979000 * q^95 - 3881062021784775072625368160679539917597594 * q^97 - 24120041445786820251814869563279238673540008 * q^98

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