LMFDB - Embedded newform 9.50.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,50,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, 50, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 50);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 50 $
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:	$136.859584589$
Analytic rank:	$0$
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} - x^{2} - 27962089502x + 71708842875120 $ x^3 - x^2 - 27962089502*x + 71708842875120
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{6}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$165922.$ 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)

$f(q)$	$=$	$q+2.25719e7 q^{2} -5.34581e13 q^{4} +1.06460e17 q^{5} +5.68014e20 q^{7} -1.39135e22 q^{8} +O(q^{10})$	\(q+2.25719e7 q^{2} -5.34581e13 q^{4} +1.06460e17 q^{5} +5.68014e20 q^{7} -1.39135e22 q^{8} +2.40300e24 q^{10} +4.66926e25 q^{11} +1.95401e27 q^{13} +1.28212e28 q^{14} -2.83961e29 q^{16} +1.59552e30 q^{17} -3.45099e31 q^{19} -5.69114e30 q^{20} +1.05394e33 q^{22} +2.46487e33 q^{23} -6.42986e33 q^{25} +4.41057e34 q^{26} -3.03649e34 q^{28} -4.27652e35 q^{29} +2.26555e36 q^{31} +1.42307e36 q^{32} +3.60138e37 q^{34} +6.04707e37 q^{35} -1.55810e38 q^{37} -7.78954e38 q^{38} -1.48123e39 q^{40} +1.49379e39 q^{41} +5.17800e39 q^{43} -2.49610e39 q^{44} +5.56368e40 q^{46} -5.79235e40 q^{47} +6.57162e40 q^{49} -1.45134e41 q^{50} -1.04457e41 q^{52} +5.51356e41 q^{53} +4.97089e42 q^{55} -7.90307e42 q^{56} -9.65293e42 q^{58} +1.93125e42 q^{59} +2.41153e43 q^{61} +5.11377e43 q^{62} +1.91977e44 q^{64} +2.08023e44 q^{65} -8.25642e44 q^{67} -8.52932e43 q^{68} +1.36494e45 q^{70} +1.77228e45 q^{71} +6.25517e45 q^{73} -3.51693e45 q^{74} +1.84483e45 q^{76} +2.65220e46 q^{77} +4.72997e46 q^{79} -3.02304e46 q^{80} +3.37178e46 q^{82} -4.29785e46 q^{83} +1.69858e47 q^{85} +1.16877e47 q^{86} -6.49658e47 q^{88} +7.42748e47 q^{89} +1.10990e48 q^{91} -1.31767e47 q^{92} -1.30744e48 q^{94} -3.67392e48 q^{95} -5.90631e48 q^{97} +1.48334e48 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 24225168 q^{2} + 31502767984896 q^{4} - 63\!\cdots\!50 q^{5}+ \cdots - 12\!\cdots\!00 q^{8}+O(q^{10}) $ 3 * q + 24225168 * q^2 + 31502767984896 * q^4 - 63884035717079250 * q^5 + 509391477498711192 * q^7 - 12774393005516465664000 * q^8	$ 3 q + 24225168 q^{2} + 31502767984896 q^{4} - 63\!\cdots\!50 q^{5}+ \cdots + 28\!\cdots\!76 q^{98}+O(q^{100}) $ 3 * q + 24225168 * q^2 + 31502767984896 * q^4 - 63884035717079250 * q^5 + 509391477498711192 * q^7 - 12774393005516465664000 * q^8 - 1782704508900495946524000 * q^10 + 20839986192711815613370524 * q^11 - 187524857197340618282341014 * q^13 + 9454369415029168241295938688 * q^14 - 958699697068386571735634214912 * q^16 + 3305035636247475259184114894538 * q^17 - 45882942802931464757155696518660 * q^19 - 19614616637279540996591887296000 * q^20 + 1789915191438262082177360193562944 * q^22 - 4533392548023086653463590407813576 * q^23 - 13921151905580403838435182832171875 * q^25 + 85826222237480824536590109710199264 * q^26 - 59263339345763305527729286468663296 * q^28 - 1118089919316361970349176934175494810 * q^29 + 934226816157578575389156342339525216 * q^31 - 731728685735702515419064521056059392 * q^32 - 44386547077569962679458968510685418528 * q^34 + 118496887985378726635932152589238374000 * q^35 + 242135148519373130928922851818564983602 * q^37 - 1156029602765443663092741329710471492800 * q^38 + 521466322563622592824981612412298240000 * q^40 + 6211739675976490815696297371880432723714 * q^41 - 7795173962887472637660666233812713782844 * q^43 - 2342252938597505040255206661879982328832 * q^44 + 26787138361451470082912377308943265940096 * q^46 - 72757717838871152990888073123214445891472 * q^47 - 280157966384090888246597869444400847657429 * q^49 + 537697283161263679965664107392030595750000 * q^50 - 123529799747407597799198092229890019578368 * q^52 + 155850890670432045962015052011776669693854 * q^53 + 4640026560861316230546160030865773419591000 * q^55 - 6722101775263505338291028050795018900439040 * q^56 - 16549417550295130349814323361508282251506400 * q^58 + 62596927936822013761436024025606581543386380 * q^59 - 24037263967789435219196348055077866809754374 * q^61 - 188825800588885099392385526941761279238024704 * q^62 + 514652981263254699809134733483815976080244736 * q^64 + 244975900670806240216695171564505814930314500 * q^65 - 1019040852324305100821779153549119164107459188 * q^67 - 147929481309005416179289053660840704965292544 * q^68 + 2807457123724968989995337407321309803024672000 * q^70 + 3208129335291950593367863544185773469328334504 * q^71 + 5668108076325412165814435883536677392865317726 * q^73 - 10012493148932275797653251806650724700277983392 * q^74 + 753841821393723585433963960120373529551508480 * q^76 + 32043339793247959180079389483660528277811891936 * q^77 - 7871365395380306420112251724245018715125364240 * q^79 + 30434832804539714147732706266001913558351872000 * q^80 + 118639125705754411670909153459409940471487282784 * q^82 - 94164681901361229355849854653903786480577085116 * q^83 + 297863286656785614551226799130947646752077538500 * q^85 + 347916436657924446515600473690440815675104929984 * q^86 - 1057522149818049090984983413770258669302102016000 * q^88 - 367807201561165354579457777200332871192114777230 * q^89 + 1613372397893666548508325640004129525440352221776 * q^91 - 467187868629171186038576611613065932844001728512 * q^92 + 904097685092930858948295844890436017323554129152 * q^94 - 1475636199748052355599968141572624301097796705000 * q^95 - 10431108583780665799950508389192126734793760399578 * q^97 + 2841886978251444216347516645227034756825518204176 * 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 $

$2$	2.25719e7	0.951336	0.475668	−	0.879625i	$-0.342206\pi$
$2$	2.25719e7	0.951336	0.475668	+	0.879625i	$0.342206\pi$
$3$	0	0
$3$	0	0
$4$	−5.34581e13	−0.0949606
$5$	1.06460e17	0.798768	0.399384	−	0.916784i	$-0.369224\pi$
$5$	1.06460e17	0.798768	0.399384	+	0.916784i	$0.369224\pi$
$6$	0	0
$7$	5.68014e20	1.12062	0.560308	−	0.828284i	$-0.310683\pi$
$7$	5.68014e20	1.12062	0.560308	+	0.828284i	$0.310683\pi$
$8$	−1.39135e22	−1.04167
$9$	0	0
$10$	2.40300e24	0.759897
$11$	4.66926e25	1.42931	0.714656	−	0.699476i	$-0.246583\pi$
$11$	4.66926e25	1.42931	0.714656	+	0.699476i	$0.246583\pi$
$12$	0	0
$13$	1.95401e27	0.998421	0.499211	−	0.866481i	$-0.333623\pi$
$13$	1.95401e27	0.998421	0.499211	+	0.866481i	$0.333623\pi$
$14$	1.28212e28	1.06608
$15$	0	0
$16$	−2.83961e29	−0.896022
$17$	1.59552e30	1.13999	0.569997	−	0.821647i	$-0.306944\pi$
$17$	1.59552e30	1.13999	0.569997	+	0.821647i	$0.306944\pi$
$18$	0	0
$19$	−3.45099e31	−1.61614	−0.808072	−	0.589084i	$-0.799489\pi$
$19$	−3.45099e31	−1.61614	−0.808072	+	0.589084i	$0.799489\pi$
$20$	−5.69114e30	−0.0758515
$21$	0	0
$22$	1.05394e33	1.35976
$23$	2.46487e33	1.07019	0.535096	−	0.844791i	$-0.320275\pi$
$23$	2.46487e33	1.07019	0.535096	+	0.844791i	$0.320275\pi$
$24$	0	0
$25$	−6.42986e33	−0.361969
$26$	4.41057e34	0.949834
$27$	0	0
$28$	−3.03649e34	−0.106414
$29$	−4.27652e35	−0.634365	−0.317183	−	0.948364i	$-0.602737\pi$
$29$	−4.27652e35	−0.634365	−0.317183	+	0.948364i	$0.602737\pi$
$30$	0	0
$31$	2.26555e36	0.655861	0.327930	−	0.944702i	$-0.393649\pi$
$31$	2.26555e36	0.655861	0.327930	+	0.944702i	$0.393649\pi$
$32$	1.42307e36	0.189258
$33$	0	0
$34$	3.60138e37	1.08452
$35$	6.04707e37	0.895113
$36$	0	0
$37$	−1.55810e38	−0.591088	−0.295544	−	0.955329i	$-0.595501\pi$
$37$	−1.55810e38	−0.591088	−0.295544	+	0.955329i	$0.595501\pi$
$38$	−7.78954e38	−1.53749
$39$	0	0
$40$	−1.48123e39	−0.832057
$41$	1.49379e39	0.458233	0.229117	−	0.973399i	$-0.426416\pi$
$41$	1.49379e39	0.458233	0.229117	+	0.973399i	$0.426416\pi$
$42$	0	0
$43$	5.17800e39	0.494521	0.247260	−	0.968949i	$-0.420470\pi$
$43$	5.17800e39	0.494521	0.247260	+	0.968949i	$0.420470\pi$
$44$	−2.49610e39	−0.135728
$45$	0	0
$46$	5.56368e40	1.01811
$47$	−5.79235e40	−0.625831	−0.312916	−	0.949781i	$-0.601306\pi$
$47$	−5.79235e40	−0.625831	−0.312916	+	0.949781i	$0.601306\pi$
$48$	0	0
$49$	6.57162e40	0.255781
$50$	−1.45134e41	−0.344354
$51$	0	0
$52$	−1.04457e41	−0.0948107
$53$	5.51356e41	0.313815	0.156907	−	0.987613i	$-0.449848\pi$
$53$	5.51356e41	0.313815	0.156907	+	0.987613i	$0.449848\pi$
$54$	0	0
$55$	4.97089e42	1.14169
$56$	−7.90307e42	−1.16732
$57$	0	0
$58$	−9.65293e42	−0.603494
$59$	1.93125e42	0.0794262	0.0397131	−	0.999211i	$-0.487356\pi$
$59$	1.93125e42	0.0794262	0.0397131	+	0.999211i	$0.487356\pi$
$60$	0	0
$61$	2.41153e43	0.438239	0.219120	−	0.975698i	$-0.429681\pi$
$61$	2.41153e43	0.438239	0.219120	+	0.975698i	$0.429681\pi$
$62$	5.11377e43	0.623943
$63$	0	0
$64$	1.91977e44	1.07607
$65$	2.08023e44	0.797507
$66$	0	0
$67$	−8.25642e44	−1.50646	−0.753232	−	0.657755i	$-0.771506\pi$
$67$	−8.25642e44	−1.50646	−0.753232	+	0.657755i	$0.771506\pi$
$68$	−8.52932e43	−0.108254
$69$	0	0
$70$	1.36494e45	0.851553
$71$	1.77228e45	0.781094	0.390547	−	0.920583i	$-0.372286\pi$
$71$	1.77228e45	0.781094	0.390547	+	0.920583i	$0.372286\pi$
$72$	0	0
$73$	6.25517e45	1.39582	0.697910	−	0.716186i	$-0.254114\pi$
$73$	6.25517e45	1.39582	0.697910	+	0.716186i	$0.254114\pi$
$74$	−3.51693e45	−0.562323
$75$	0	0
$76$	1.84483e45	0.153470
$77$	2.65220e46	1.60171
$78$	0	0
$79$	4.72997e46	1.52404	0.762018	−	0.647556i	$-0.224209\pi$
$79$	4.72997e46	1.52404	0.762018	+	0.647556i	$0.224209\pi$
$80$	−3.02304e46	−0.715714
$81$	0	0
$82$	3.37178e46	0.435933
$83$	−4.29785e46	−0.412893	−0.206447	−	0.978458i	$-0.566190\pi$
$83$	−4.29785e46	−0.412893	−0.206447	+	0.978458i	$0.566190\pi$
$84$	0	0
$85$	1.69858e47	0.910591
$86$	1.16877e47	0.470455
$87$	0	0
$88$	−6.49658e47	−1.48888
$89$	7.42748e47	1.29058	0.645292	−	0.763936i	$-0.276736\pi$
$89$	7.42748e47	1.29058	0.645292	+	0.763936i	$0.276736\pi$
$90$	0	0
$91$	1.10990e48	1.11885
$92$	−1.31767e47	−0.101626
$93$	0	0
$94$	−1.30744e48	−0.595375
$95$	−3.67392e48	−1.29092
$96$	0	0
$97$	−5.90631e48	−1.24569	−0.622843	−	0.782347i	$-0.714023\pi$
$97$	−5.90631e48	−1.24569	−0.622843	+	0.782347i	$0.714023\pi$
$98$	1.48334e48	0.243334
$99$	0	0
$100$	3.43728e47	0.0343728
$101$	1.67953e48	0.131618	0.0658090	−	0.997832i	$-0.479037\pi$
$101$	1.67953e48	0.131618	0.0658090	+	0.997832i	$0.479037\pi$
$102$	0	0
$103$	−9.66426e48	−0.468443	−0.234221	−	0.972183i	$-0.575254\pi$
$103$	−9.66426e48	−0.468443	−0.234221	+	0.972183i	$0.575254\pi$
$104$	−2.71871e49	−1.04003
$105$	0	0
$106$	1.24452e49	0.298543
$107$	−1.13270e49	−0.215879	−0.107940	−	0.994157i	$-0.534425\pi$
$107$	−1.13270e49	−0.215879	−0.107940	+	0.994157i	$0.534425\pi$
$108$	0	0
$109$	4.53029e49	0.548500	0.274250	−	0.961658i	$-0.411570\pi$
$109$	4.53029e49	0.548500	0.274250	+	0.961658i	$0.411570\pi$
$110$	1.12203e50	1.08613
$111$	0	0
$112$	−1.61294e50	−1.00410
$113$	−9.56756e48	−0.0479048	−0.0239524	−	0.999713i	$-0.507625\pi$
$113$	−9.56756e48	−0.0479048	−0.0239524	+	0.999713i	$0.507625\pi$
$114$	0	0
$115$	2.62410e50	0.854836
$116$	2.28614e49	0.0602397
$117$	0	0
$118$	4.35920e49	0.0755609
$119$	9.06275e50	1.27750
$120$	0	0
$121$	1.11301e51	1.04293
$122$	5.44328e50	0.416913
$123$	0	0
$124$	−1.21112e50	−0.0622809
$125$	−2.57563e51	−1.08790
$126$	0	0
$127$	3.33633e51	0.955164	0.477582	−	0.878587i	$-0.341513\pi$
$127$	3.33633e51	0.955164	0.477582	+	0.878587i	$0.341513\pi$
$128$	3.53218e51	0.834445
$129$	0	0
$130$	4.69549e51	0.758697
$131$	7.56140e51	1.01264	0.506320	−	0.862346i	$-0.331005\pi$
$131$	7.56140e51	1.01264	0.506320	+	0.862346i	$0.331005\pi$
$132$	0	0
$133$	−1.96021e52	−1.81108
$134$	−1.86363e52	−1.43315
$135$	0	0
$136$	−2.21992e52	−1.18750
$137$	3.63264e52	1.62393	0.811967	−	0.583704i	$-0.198397\pi$
$137$	3.63264e52	1.62393	0.811967	+	0.583704i	$0.198397\pi$
$138$	0	0
$139$	4.58875e52	1.43824	0.719121	−	0.694885i	$-0.244545\pi$
$139$	4.58875e52	1.43824	0.719121	+	0.694885i	$0.244545\pi$
$140$	−3.23265e51	−0.0850005
$141$	0	0
$142$	4.00038e52	0.743082
$143$	9.12376e52	1.42706
$144$	0	0
$145$	−4.55278e52	−0.506711
$146$	1.41191e53	1.32789
$147$	0	0
$148$	8.32929e51	0.0561301
$149$	−1.90143e53	−1.08647	−0.543233	−	0.839582i	$-0.682800\pi$
$149$	−1.90143e53	−1.08647	−0.543233	+	0.839582i	$0.682800\pi$
$150$	0	0
$151$	2.73658e53	1.12791	0.563953	−	0.825807i	$-0.309280\pi$
$151$	2.73658e53	1.12791	0.563953	+	0.825807i	$0.309280\pi$
$152$	4.80153e53	1.68350
$153$	0	0
$154$	5.98654e53	1.52376
$155$	2.41190e53	0.523881
$156$	0	0
$157$	6.65092e53	1.05521	0.527607	−	0.849489i	$-0.323090\pi$
$157$	6.65092e53	1.05521	0.527607	+	0.849489i	$0.323090\pi$
$158$	1.06765e54	1.44987
$159$	0	0
$160$	1.51500e53	0.151173
$161$	1.40008e54	1.19928
$162$	0	0
$163$	−4.80475e53	−0.304141	−0.152070	−	0.988370i	$-0.548594\pi$
$163$	−4.80475e53	−0.304141	−0.152070	+	0.988370i	$0.548594\pi$
$164$	−7.98554e52	−0.0435141
$165$	0	0
$166$	−9.70107e53	−0.392800
$167$	5.81006e53	0.203061	0.101531	−	0.994832i	$-0.467626\pi$
$167$	5.81006e53	0.203061	0.101531	+	0.994832i	$0.467626\pi$
$168$	0	0
$169$	−1.20849e52	−0.00315515
$170$	3.83403e54	0.866277
$171$	0	0
$172$	−2.76806e53	−0.0469600
$173$	5.03434e54	0.740991	0.370496	−	0.928834i	$-0.379188\pi$
$173$	5.03434e54	0.740991	0.370496	+	0.928834i	$0.379188\pi$
$174$	0	0
$175$	−3.65225e54	−0.405628
$176$	−1.32589e55	−1.28070
$177$	0	0
$178$	1.67653e55	1.22778
$179$	−1.02146e55	−0.652114	−0.326057	−	0.945350i	$-0.605720\pi$
$179$	−1.02146e55	−0.652114	−0.326057	+	0.945350i	$0.605720\pi$
$180$	0	0
$181$	−4.89697e54	−0.238124	−0.119062	−	0.992887i	$-0.537989\pi$
$181$	−4.89697e54	−0.238124	−0.119062	+	0.992887i	$0.537989\pi$
$182$	2.50526e55	1.06440
$183$	0	0
$184$	−3.42950e55	−1.11479
$185$	−1.65875e55	−0.472143
$186$	0	0
$187$	7.44987e55	1.62941
$188$	3.09648e54	0.0594293
$189$	0	0
$190$	−8.29273e55	−1.22810
$191$	2.57335e55	0.335105	0.167553	−	0.985863i	$-0.446414\pi$
$191$	2.57335e55	0.335105	0.167553	+	0.985863i	$0.446414\pi$
$192$	0	0
$193$	6.57181e55	0.663026	0.331513	−	0.943451i	$-0.392441\pi$
$193$	6.57181e55	0.663026	0.331513	+	0.943451i	$0.392441\pi$
$194$	−1.33317e56	−1.18507
$195$	0	0
$196$	−3.51306e54	−0.0242891
$197$	−1.67063e56	−1.01967	−0.509833	−	0.860273i	$-0.670293\pi$
$197$	−1.67063e56	−1.01967	−0.509833	+	0.860273i	$0.670293\pi$
$198$	0	0
$199$	−2.81794e56	−1.34286	−0.671431	−	0.741067i	$-0.734320\pi$
$199$	−2.81794e56	−1.34286	−0.671431	+	0.741067i	$0.734320\pi$
$200$	8.94620e55	0.377054
$201$	0	0
$202$	3.79103e55	0.125213
$203$	−2.42912e56	−0.710880
$204$	0	0
$205$	1.59029e56	0.366022
$206$	−2.18141e56	−0.445646
$207$	0	0
$208$	−5.54861e56	−0.894607
$209$	−1.61135e57	−2.30997
$210$	0	0
$211$	−1.09882e57	−1.24741	−0.623703	−	0.781662i	$-0.714372\pi$
$211$	−1.09882e57	−1.24741	−0.623703	+	0.781662i	$0.714372\pi$
$212$	−2.94745e55	−0.0298001
$213$	0	0
$214$	−2.55671e56	−0.205373
$215$	5.51249e56	0.395008
$216$	0	0
$217$	1.28686e57	0.734968
$218$	1.02257e57	0.521808
$219$	0	0
$220$	−2.65734e56	−0.108416
$221$	3.11765e57	1.13819
$222$	0	0
$223$	1.62911e57	0.476958	0.238479	−	0.971148i	$-0.423351\pi$
$223$	1.62911e57	0.476958	0.238479	+	0.971148i	$0.423351\pi$
$224$	8.08326e56	0.212085
$225$	0	0
$226$	−2.15958e56	−0.0455736
$227$	−3.87678e57	−0.734239	−0.367120	−	0.930174i	$-0.619656\pi$
$227$	−3.87678e57	−0.734239	−0.367120	+	0.930174i	$0.619656\pi$
$228$	0	0
$229$	6.74432e57	1.03031	0.515156	−	0.857097i	$-0.327734\pi$
$229$	6.74432e57	1.03031	0.515156	+	0.857097i	$0.327734\pi$
$230$	5.92309e57	0.813236
$231$	0	0
$232$	5.95014e57	0.660802
$233$	1.07268e58	1.07214	0.536069	−	0.844174i	$-0.319909\pi$
$233$	1.07268e58	1.07214	0.536069	+	0.844174i	$0.319909\pi$
$234$	0	0
$235$	−6.16653e57	−0.499894
$236$	−1.03241e56	−0.00754236
$237$	0	0
$238$	2.04564e58	1.21533
$239$	6.84695e57	0.367070	0.183535	−	0.983013i	$-0.441246\pi$
$239$	6.84695e57	0.367070	0.183535	+	0.983013i	$0.441246\pi$
$240$	0	0
$241$	6.43851e57	0.281429	0.140714	−	0.990050i	$-0.455060\pi$
$241$	6.43851e57	0.281429	0.140714	+	0.990050i	$0.455060\pi$
$242$	2.51227e58	0.992180
$243$	0	0
$244$	−1.28916e57	−0.0416155
$245$	6.99614e57	0.204310
$246$	0	0
$247$	−6.74325e58	−1.61359
$248$	−3.15217e58	−0.683193
$249$	0	0
$250$	−5.81369e58	−1.03496
$251$	−4.88114e57	−0.0787980	−0.0393990	−	0.999224i	$-0.512544\pi$
$251$	−4.88114e57	−0.0787980	−0.0393990	+	0.999224i	$0.512544\pi$
$252$	0	0
$253$	1.15091e59	1.52964
$254$	7.53074e58	0.908682
$255$	0	0
$256$	−2.83455e58	−0.282232
$257$	−9.71196e58	−0.878912	−0.439456	−	0.898264i	$-0.644829\pi$
$257$	−9.71196e58	−0.878912	−0.439456	+	0.898264i	$0.644829\pi$
$258$	0	0
$259$	−8.85021e58	−0.662383
$260$	−1.11205e58	−0.0757318
$261$	0	0
$262$	1.70675e59	0.963361
$263$	1.69871e59	0.873381	0.436690	−	0.899612i	$-0.356151\pi$
$263$	1.69871e59	0.873381	0.436690	+	0.899612i	$0.356151\pi$
$264$	0	0
$265$	5.86973e58	0.250666
$266$	−4.42457e59	−1.72294
$267$	0	0
$268$	4.41372e58	0.143055
$269$	−3.89211e58	−0.115148	−0.0575738	−	0.998341i	$-0.518336\pi$
$269$	−3.89211e58	−0.115148	−0.0575738	+	0.998341i	$0.518336\pi$
$270$	0	0
$271$	−2.42138e59	−0.597468	−0.298734	−	0.954336i	$-0.596564\pi$
$271$	−2.42138e59	−0.597468	−0.298734	+	0.954336i	$0.596564\pi$
$272$	−4.53064e59	−1.02146
$273$	0	0
$274$	8.19956e59	1.54491
$275$	−3.00227e59	−0.517367
$276$	0	0
$277$	−1.36745e60	−1.97313	−0.986566	−	0.163363i	$-0.947766\pi$
$277$	−1.36745e60	−1.97313	−0.986566	+	0.163363i	$0.947766\pi$
$278$	1.03577e60	1.36825
$279$	0	0
$280$	−8.41360e59	−0.932417
$281$	−1.32527e60	−1.34585	−0.672927	−	0.739709i	$-0.734963\pi$
$281$	−1.32527e60	−1.34585	−0.672927	+	0.739709i	$0.734963\pi$
$282$	0	0
$283$	−1.55414e60	−1.32655	−0.663273	−	0.748378i	$-0.730833\pi$
$283$	−1.55414e60	−1.32655	−0.663273	+	0.748378i	$0.730833\pi$
$284$	−9.47427e58	−0.0741731
$285$	0	0
$286$	2.05941e60	1.35761
$287$	8.48496e59	0.513504
$288$	0	0
$289$	5.86836e59	0.299585
$290$	−1.02765e60	−0.482052
$291$	0	0
$292$	−3.34389e59	−0.132548
$293$	−3.60920e60	−1.31569	−0.657846	−	0.753152i	$-0.728532\pi$
$293$	−3.60920e60	−1.31569	−0.657846	+	0.753152i	$0.728532\pi$
$294$	0	0
$295$	2.05600e59	0.0634431
$296$	2.16786e60	0.615722
$297$	0	0
$298$	−4.29189e60	−1.03359
$299$	4.81637e60	1.06850
$300$	0	0
$301$	2.94117e60	0.554168
$302$	6.17699e60	1.07302
$303$	0	0
$304$	9.79944e60	1.44810
$305$	2.56731e60	0.350052
$306$	0	0
$307$	6.56165e60	0.762295	0.381147	−	0.924514i	$-0.375529\pi$
$307$	6.56165e60	0.762295	0.381147	+	0.924514i	$0.375529\pi$
$308$	−1.41782e60	−0.152099
$309$	0	0
$310$	5.44412e60	0.498386
$311$	4.77277e60	0.403776	0.201888	−	0.979409i	$-0.435292\pi$
$311$	4.77277e60	0.403776	0.201888	+	0.979409i	$0.435292\pi$
$312$	0	0
$313$	−9.64049e59	−0.0697048	−0.0348524	−	0.999392i	$-0.511096\pi$
$313$	−9.64049e59	−0.0697048	−0.0348524	+	0.999392i	$0.511096\pi$
$314$	1.50124e61	1.00386
$315$	0	0
$316$	−2.52855e60	−0.144723
$317$	1.84778e61	0.978809	0.489405	−	0.872057i	$-0.337214\pi$
$317$	1.84778e61	0.978809	0.489405	+	0.872057i	$0.337214\pi$
$318$	0	0
$319$	−1.99682e61	−0.906706
$320$	2.04379e61	0.859530
$321$	0	0
$322$	3.16025e61	1.14091
$323$	−5.50610e61	−1.84239
$324$	0	0
$325$	−1.25640e61	−0.361397
$326$	−1.08452e61	−0.289340
$327$	0	0
$328$	−2.07839e61	−0.477330
$329$	−3.29013e61	−0.701317
$330$	0	0
$331$	−6.60491e61	−1.21361	−0.606807	−	0.794849i	$-0.707550\pi$
$331$	−6.60491e61	−1.21361	−0.606807	+	0.794849i	$0.707550\pi$
$332$	2.29755e60	0.0392086
$333$	0	0
$334$	1.31144e61	0.193179
$335$	−8.78977e61	−1.20332
$336$	0	0
$337$	5.02594e61	0.594682	0.297341	−	0.954771i	$-0.403900\pi$
$337$	5.02594e61	0.594682	0.297341	+	0.954771i	$0.403900\pi$
$338$	−2.72780e59	−0.00300160
$339$	0	0
$340$	−9.08030e60	−0.0864703
$341$	1.05784e62	0.937430
$342$	0	0
$343$	−1.08608e62	−0.833984
$344$	−7.20441e61	−0.515130
$345$	0	0
$346$	1.13635e62	0.704931
$347$	−2.35153e62	−1.35919	−0.679594	−	0.733589i	$-0.737844\pi$
$347$	−2.35153e62	−1.35919	−0.679594	+	0.733589i	$0.737844\pi$
$348$	0	0
$349$	−2.73741e62	−1.37441	−0.687206	−	0.726463i	$-0.741163\pi$
$349$	−2.73741e62	−1.37441	−0.687206	+	0.726463i	$0.741163\pi$
$350$	−8.24383e61	−0.385889
$351$	0	0
$352$	6.64470e61	0.270508
$353$	3.98901e62	1.51490	0.757452	−	0.652891i	$-0.226444\pi$
$353$	3.98901e62	1.51490	0.757452	+	0.652891i	$0.226444\pi$
$354$	0	0
$355$	1.88677e62	0.623913
$356$	−3.97059e61	−0.122555
$357$	0	0
$358$	−2.30564e62	−0.620379
$359$	−3.99475e62	−1.00387	−0.501933	−	0.864906i	$-0.667378\pi$
$359$	−3.99475e62	−1.00387	−0.501933	+	0.864906i	$0.667378\pi$
$360$	0	0
$361$	7.34970e62	1.61192
$362$	−1.10534e62	−0.226536
$363$	0	0
$364$	−5.93333e61	−0.106246
$365$	6.65925e62	1.11494
$366$	0	0
$367$	4.47176e62	0.654878	0.327439	−	0.944872i	$-0.393814\pi$
$367$	4.47176e62	0.654878	0.327439	+	0.944872i	$0.393814\pi$
$368$	−6.99926e62	−0.958916
$369$	0	0
$370$	−3.74412e62	−0.449166
$371$	3.13178e62	0.351666
$372$	0	0
$373$	−1.90519e63	−1.87531	−0.937654	−	0.347569i	$-0.887007\pi$
$373$	−1.90519e63	−1.87531	−0.937654	+	0.347569i	$0.887007\pi$
$374$	1.68158e63	1.55011
$375$	0	0
$376$	8.05919e62	0.651913
$377$	−8.35634e62	−0.633364
$378$	0	0
$379$	−1.10306e63	−0.734408	−0.367204	−	0.930140i	$-0.619685\pi$
$379$	−1.10306e63	−0.734408	−0.367204	+	0.930140i	$0.619685\pi$
$380$	1.96400e62	0.122587
$381$	0	0
$382$	5.80855e62	0.318798
$383$	1.13569e63	0.584643	0.292321	−	0.956320i	$-0.405572\pi$
$383$	1.13569e63	0.584643	0.292321	+	0.956320i	$0.405572\pi$
$384$	0	0
$385$	2.82353e63	1.27940
$386$	1.48338e63	0.630760
$387$	0	0
$388$	3.15740e62	0.118291
$389$	2.42232e63	0.852053	0.426026	−	0.904711i	$-0.359913\pi$
$389$	2.42232e63	0.852053	0.426026	+	0.904711i	$0.359913\pi$
$390$	0	0
$391$	3.93273e63	1.22001
$392$	−9.14344e62	−0.266441
$393$	0	0
$394$	−3.77094e63	−0.970045
$395$	5.03552e63	1.21735
$396$	0	0
$397$	−2.38482e62	−0.0509434	−0.0254717	−	0.999676i	$-0.508109\pi$
$397$	−2.38482e62	−0.0509434	−0.0254717	+	0.999676i	$0.508109\pi$
$398$	−6.36064e63	−1.27751
$399$	0	0
$400$	1.82583e63	0.324332
$401$	−3.76821e63	−0.629649	−0.314824	−	0.949150i	$-0.601946\pi$
$401$	−3.76821e63	−0.629649	−0.314824	+	0.949150i	$0.601946\pi$
$402$	0	0
$403$	4.42689e63	0.654825
$404$	−8.97846e61	−0.0124985
$405$	0	0
$406$	−5.48300e63	−0.676286
$407$	−7.27516e63	−0.844850
$408$	0	0
$409$	4.86604e63	0.501135	0.250567	−	0.968099i	$-0.419383\pi$
$409$	4.86604e63	0.501135	0.250567	+	0.968099i	$0.419383\pi$
$410$	3.58960e63	0.348210
$411$	0	0
$412$	5.16633e62	0.0444836
$413$	1.09698e63	0.0890063
$414$	0	0
$415$	−4.57548e63	−0.329806
$416$	2.78070e63	0.188959
$417$	0	0
$418$	−3.63714e64	−2.19756
$419$	−2.47515e64	−1.41045	−0.705225	−	0.708983i	$-0.749154\pi$
$419$	−2.47515e64	−1.41045	−0.705225	+	0.708983i	$0.749154\pi$
$420$	0	0
$421$	−1.56805e64	−0.795149	−0.397575	−	0.917570i	$-0.630148\pi$
$421$	−1.56805e64	−0.795149	−0.397575	+	0.917570i	$0.630148\pi$
$422$	−2.48026e64	−1.18670
$423$	0	0
$424$	−7.67131e63	−0.326893
$425$	−1.02589e64	−0.412642
$426$	0	0
$427$	1.36978e64	0.491098
$428$	6.05517e62	0.0205000
$429$	0	0
$430$	1.24427e64	0.375785
$431$	5.26924e64	1.50333	0.751666	−	0.659544i	$-0.229251\pi$
$431$	5.26924e64	1.50333	0.751666	+	0.659544i	$0.229251\pi$
$432$	0	0
$433$	3.37012e64	0.858405	0.429202	−	0.903208i	$-0.358795\pi$
$433$	3.37012e64	0.858405	0.429202	+	0.903208i	$0.358795\pi$
$434$	2.90470e64	0.699201
$435$	0	0
$436$	−2.42181e63	−0.0520859
$437$	−8.50623e64	−1.72958
$438$	0	0
$439$	−7.18240e64	−1.30584	−0.652918	−	0.757428i	$-0.726456\pi$
$439$	−7.18240e64	−1.30584	−0.652918	+	0.757428i	$0.726456\pi$
$440$	−6.91625e64	−1.18927
$441$	0	0
$442$	7.03713e64	1.08280
$443$	1.13418e65	1.65116	0.825582	−	0.564282i	$-0.190847\pi$
$443$	1.13418e65	1.65116	0.825582	+	0.564282i	$0.190847\pi$
$444$	0	0
$445$	7.90729e64	1.03088
$446$	3.67720e64	0.453747
$447$	0	0
$448$	1.09046e65	1.20586
$449$	1.35648e65	1.42030	0.710148	−	0.704053i	$-0.248628\pi$
$449$	1.35648e65	1.42030	0.710148	+	0.704053i	$0.248628\pi$
$450$	0	0
$451$	6.97491e64	0.654958
$452$	5.11463e62	0.00454907
$453$	0	0
$454$	−8.75064e64	−0.698508
$455$	1.18160e65	0.893700
$456$	0	0
$457$	−2.05883e65	−1.39854	−0.699268	−	0.714859i	$-0.746491\pi$
$457$	−2.05883e65	−1.39854	−0.699268	+	0.714859i	$0.746491\pi$
$458$	1.52232e65	0.980172
$459$	0	0
$460$	−1.40279e64	−0.0811757
$461$	−2.18282e65	−1.19769	−0.598847	−	0.800863i	$-0.704374\pi$
$461$	−2.18282e65	−1.19769	−0.598847	+	0.800863i	$0.704374\pi$
$462$	0	0
$463$	9.59055e64	0.473270	0.236635	−	0.971599i	$-0.423955\pi$
$463$	9.59055e64	0.473270	0.236635	+	0.971599i	$0.423955\pi$
$464$	1.21436e65	0.568405
$465$	0	0
$466$	2.42125e65	1.01996
$467$	−1.86197e65	−0.744234	−0.372117	−	0.928186i	$-0.621368\pi$
$467$	−1.86197e65	−0.744234	−0.372117	+	0.928186i	$0.621368\pi$
$468$	0	0
$469$	−4.68976e65	−1.68817
$470$	−1.39190e65	−0.475567
$471$	0	0
$472$	−2.68704e64	−0.0827363
$473$	2.41774e65	0.706825
$474$	0	0
$475$	2.21894e65	0.584994
$476$	−4.84477e64	−0.121312
$477$	0	0
$478$	1.54549e65	0.349207
$479$	−9.86762e64	−0.211832	−0.105916	−	0.994375i	$-0.533778\pi$
$479$	−9.86762e64	−0.211832	−0.105916	+	0.994375i	$0.533778\pi$
$480$	0	0
$481$	−3.04453e65	−0.590155
$482$	1.45330e65	0.267733
$483$	0	0
$484$	−5.94993e64	−0.0990376
$485$	−6.28785e65	−0.995015
$486$	0	0
$487$	3.74023e65	0.535104	0.267552	−	0.963543i	$-0.413785\pi$
$487$	3.74023e65	0.535104	0.267552	+	0.963543i	$0.413785\pi$
$488$	−3.35528e65	−0.456503
$489$	0	0
$490$	1.57916e65	0.194367
$491$	−1.40013e65	−0.163935	−0.0819676	−	0.996635i	$-0.526120\pi$
$491$	−1.40013e65	−0.163935	−0.0819676	+	0.996635i	$0.526120\pi$
$492$	0	0
$493$	−6.82325e65	−0.723172
$494$	−1.52208e66	−1.53507
$495$	0	0
$496$	−6.43326e65	−0.587665
$497$	1.00668e66	0.875306
$498$	0	0
$499$	2.84241e65	0.223987	0.111994	−	0.993709i	$-0.464276\pi$
$499$	2.84241e65	0.223987	0.111994	+	0.993709i	$0.464276\pi$
$500$	1.37688e65	0.103307
$501$	0	0
$502$	−1.10177e65	−0.0749634
$503$	9.62685e65	0.623833	0.311917	−	0.950109i	$-0.399029\pi$
$503$	9.62685e65	0.623833	0.311917	+	0.950109i	$0.399029\pi$
$504$	0	0
$505$	1.78803e65	0.105132
$506$	2.59783e66	1.45520
$507$	0	0
$508$	−1.78354e65	−0.0907030
$509$	−3.05352e66	−1.47984	−0.739921	−	0.672694i	$-0.765137\pi$
$509$	−3.05352e66	−1.47984	−0.739921	+	0.672694i	$0.765137\pi$
$510$	0	0
$511$	3.55303e66	1.56418
$512$	−2.62825e66	−1.10294
$513$	0	0
$514$	−2.19218e66	−0.836140
$515$	−1.02886e66	−0.374177
$516$	0	0
$517$	−2.70460e66	−0.894508
$518$	−1.99766e66	−0.630149
$519$	0	0
$520$	−2.89434e66	−0.830743
$521$	4.02652e66	1.10257	0.551284	−	0.834318i	$-0.314138\pi$
$521$	4.02652e66	1.10257	0.551284	+	0.834318i	$0.314138\pi$
$522$	0	0
$523$	6.70243e65	0.167086	0.0835431	−	0.996504i	$-0.473376\pi$
$523$	6.70243e65	0.167086	0.0835431	+	0.996504i	$0.473376\pi$
$524$	−4.04218e65	−0.0961609
$525$	0	0
$526$	3.83432e66	0.830878
$527$	3.61471e66	0.747677
$528$	0	0
$529$	7.70839e65	0.145311
$530$	1.32491e66	0.238467
$531$	0	0
$532$	1.04789e66	0.171981
$533$	2.91888e66	0.457510
$534$	0	0
$535$	−1.20587e66	−0.172437
$536$	1.14876e67	1.56925
$537$	0	0
$538$	−8.78525e65	−0.109544
$539$	3.06846e66	0.365591
$540$	0	0
$541$	1.63687e67	1.78107	0.890536	−	0.454913i	$-0.150330\pi$
$541$	1.63687e67	1.78107	0.890536	+	0.454913i	$0.150330\pi$
$542$	−5.46552e66	−0.568393
$543$	0	0
$544$	2.27054e66	0.215752
$545$	4.82294e66	0.438125
$546$	0	0
$547$	−1.21163e67	−1.00619	−0.503095	−	0.864231i	$-0.667805\pi$
$547$	−1.21163e67	−1.00619	−0.503095	+	0.864231i	$0.667805\pi$
$548$	−1.94194e66	−0.154210
$549$	0	0
$550$	−6.77670e66	−0.492189
$551$	1.47582e67	1.02523
$552$	0	0
$553$	2.68669e67	1.70786
$554$	−3.08659e67	−1.87711
$555$	0	0
$556$	−2.45306e66	−0.136576
$557$	2.42193e67	1.29035	0.645177	−	0.764033i	$-0.276783\pi$
$557$	2.42193e67	1.29035	0.645177	+	0.764033i	$0.276783\pi$
$558$	0	0
$559$	1.01178e67	0.493740
$560$	−1.71713e67	−0.802041
$561$	0	0
$562$	−2.99138e67	−1.28036
$563$	−3.00539e66	−0.123153	−0.0615764	−	0.998102i	$-0.519613\pi$
$563$	−3.00539e66	−0.123153	−0.0615764	+	0.998102i	$0.519613\pi$
$564$	0	0
$565$	−1.01856e66	−0.0382649
$566$	−3.50799e67	−1.26199
$567$	0	0
$568$	−2.46587e67	−0.813646
$569$	−1.27892e67	−0.404197	−0.202099	−	0.979365i	$-0.564776\pi$
$569$	−1.27892e67	−0.404197	−0.202099	+	0.979365i	$0.564776\pi$
$570$	0	0
$571$	−1.78328e67	−0.517172	−0.258586	−	0.965988i	$-0.583257\pi$
$571$	−1.78328e67	−0.517172	−0.258586	+	0.965988i	$0.583257\pi$
$572$	−4.87739e66	−0.135514
$573$	0	0
$574$	1.91522e67	0.488514
$575$	−1.58488e67	−0.387376
$576$	0	0
$577$	−4.00078e67	−0.898127	−0.449064	−	0.893500i	$-0.648242\pi$
$577$	−4.00078e67	−0.898127	−0.449064	+	0.893500i	$0.648242\pi$
$578$	1.32460e67	0.285006
$579$	0	0
$580$	2.43383e66	0.0481176
$581$	−2.44124e67	−0.462695
$582$	0	0
$583$	2.57443e67	0.448540
$584$	−8.70315e67	−1.45399
$585$	0	0
$586$	−8.14666e67	−1.25167
$587$	9.20452e67	1.35634	0.678168	−	0.734907i	$-0.262774\pi$
$587$	9.20452e67	1.35634	0.678168	+	0.734907i	$0.262774\pi$
$588$	0	0
$589$	−7.81837e67	−1.05996
$590$	4.64080e66	0.0603557
$591$	0	0
$592$	4.42438e67	0.529628
$593$	3.70854e66	0.0425954	0.0212977	−	0.999773i	$-0.493220\pi$
$593$	3.70854e66	0.0425954	0.0212977	+	0.999773i	$0.493220\pi$
$594$	0	0
$595$	9.64819e67	1.02042
$596$	1.01647e67	0.103171
$597$	0	0
$598$	1.08715e68	1.01650
$599$	−1.91162e67	−0.171571	−0.0857857	−	0.996314i	$-0.527340\pi$
$599$	−1.91162e67	−0.171571	−0.0857857	+	0.996314i	$0.527340\pi$
$600$	0	0
$601$	3.78925e67	0.313421	0.156711	−	0.987645i	$-0.449911\pi$
$601$	3.78925e67	0.313421	0.156711	+	0.987645i	$0.449911\pi$
$602$	6.63879e67	0.527200
$603$	0	0
$604$	−1.46292e67	−0.107107
$605$	1.18491e68	0.833063
$606$	0	0
$607$	2.02918e68	1.31582	0.657910	−	0.753096i	$-0.271441\pi$
$607$	2.02918e68	1.31582	0.657910	+	0.753096i	$0.271441\pi$
$608$	−4.91101e67	−0.305867
$609$	0	0
$610$	5.79491e67	0.333017
$611$	−1.13183e68	−0.624843
$612$	0	0
$613$	2.45514e68	1.25111	0.625553	−	0.780182i	$-0.284874\pi$
$613$	2.45514e68	1.25111	0.625553	+	0.780182i	$0.284874\pi$
$614$	1.48109e68	0.725198
$615$	0	0
$616$	−3.69015e68	−1.66846
$617$	2.87337e68	1.24855	0.624274	−	0.781205i	$-0.285395\pi$
$617$	2.87337e68	1.24855	0.624274	+	0.781205i	$0.285395\pi$
$618$	0	0
$619$	−3.11706e68	−1.25119	−0.625596	−	0.780147i	$-0.715144\pi$
$619$	−3.11706e68	−1.25119	−0.625596	+	0.780147i	$0.715144\pi$
$620$	−1.28935e67	−0.0497480
$621$	0	0
$622$	1.07731e68	0.384127
$623$	4.21891e68	1.44625
$624$	0	0
$625$	−1.59984e68	−0.507010
$626$	−2.17604e67	−0.0663127
$627$	0	0
$628$	−3.55545e67	−0.100204
$629$	−2.48597e68	−0.673837
$630$	0	0
$631$	−2.97792e68	−0.746781	−0.373391	−	0.927674i	$-0.621805\pi$
$631$	−2.97792e68	−0.746781	−0.373391	+	0.927674i	$0.621805\pi$
$632$	−6.58106e68	−1.58755
$633$	0	0
$634$	4.17079e68	0.931176
$635$	3.55185e68	0.762955
$636$	0	0
$637$	1.28410e68	0.255377
$638$	−4.50720e68	−0.862582
$639$	0	0
$640$	3.76035e68	0.666529
$641$	9.83451e68	1.67776	0.838882	−	0.544314i	$-0.183210\pi$
$641$	9.83451e68	1.67776	0.838882	+	0.544314i	$0.183210\pi$
$642$	0	0
$643$	2.53725e68	0.401046	0.200523	−	0.979689i	$-0.435736\pi$
$643$	2.53725e68	0.401046	0.200523	+	0.979689i	$0.435736\pi$
$644$	−7.48456e67	−0.113884
$645$	0	0
$646$	−1.24283e69	−1.75273
$647$	−8.46297e68	−1.14913	−0.574563	−	0.818460i	$-0.694828\pi$
$647$	−8.46297e68	−1.14913	−0.574563	+	0.818460i	$0.694828\pi$
$648$	0	0
$649$	9.01749e67	0.113525
$650$	−2.83593e68	−0.343810
$651$	0	0
$652$	2.56853e67	0.0288814
$653$	−5.94791e68	−0.644157	−0.322079	−	0.946713i	$-0.604382\pi$
$653$	−5.94791e68	−0.644157	−0.322079	+	0.946713i	$0.604382\pi$
$654$	0	0
$655$	8.04985e68	0.808865
$656$	−4.24179e68	−0.410587
$657$	0	0
$658$	−7.42647e68	−0.667187
$659$	1.75187e69	1.51638	0.758190	−	0.652034i	$-0.226084\pi$
$659$	1.75187e69	1.51638	0.758190	+	0.652034i	$0.226084\pi$
$660$	0	0
$661$	1.24865e69	1.00347	0.501736	−	0.865021i	$-0.332695\pi$
$661$	1.24865e69	1.00347	0.501736	+	0.865021i	$0.332695\pi$
$662$	−1.49085e69	−1.15455
$663$	0	0
$664$	5.97982e68	0.430101
$665$	−2.08683e69	−1.44663
$666$	0	0
$667$	−1.05411e69	−0.678893
$668$	−3.10595e67	−0.0192828
$669$	0	0
$670$	−1.98402e69	−1.14476
$671$	1.12600e69	0.626381
$672$	0	0
$673$	2.09516e68	0.108355	0.0541773	−	0.998531i	$-0.482746\pi$
$673$	2.09516e68	0.108355	0.0541773	+	0.998531i	$0.482746\pi$
$674$	1.13445e69	0.565742
$675$	0	0
$676$	6.46037e65	0.000299615 0
$677$	2.83899e69	1.26982	0.634910	−	0.772586i	$-0.281037\pi$
$677$	2.83899e69	1.26982	0.634910	+	0.772586i	$0.281037\pi$
$678$	0	0
$679$	−3.35487e69	−1.39594
$680$	−2.36333e69	−0.948540
$681$	0	0
$682$	2.38775e69	0.891810
$683$	−1.06976e69	−0.385460	−0.192730	−	0.981252i	$-0.561734\pi$
$683$	−1.06976e69	−0.385460	−0.192730	+	0.981252i	$0.561734\pi$
$684$	0	0
$685$	3.86730e69	1.29715
$686$	−2.45150e69	−0.793398
$687$	0	0
$688$	−1.47035e69	−0.443101
$689$	1.07735e69	0.313320
$690$	0	0
$691$	−2.08108e69	−0.563738	−0.281869	−	0.959453i	$-0.590954\pi$
$691$	−2.08108e69	−0.563738	−0.281869	+	0.959453i	$0.590954\pi$
$692$	−2.69126e68	−0.0703650
$693$	0	0
$694$	−5.30787e69	−1.29304
$695$	4.88518e69	1.14882
$696$	0	0
$697$	2.38337e69	0.522383
$698$	−6.17886e69	−1.30753
$699$	0	0
$700$	1.95242e68	0.0385187
$701$	4.28863e69	0.817010	0.408505	−	0.912756i	$-0.366050\pi$
$701$	4.28863e69	0.817010	0.408505	+	0.912756i	$0.366050\pi$
$702$	0	0
$703$	5.37697e69	0.955283
$704$	8.96391e69	1.53804
$705$	0	0
$706$	9.00397e69	1.44118
$707$	9.53998e68	0.147493
$708$	0	0
$709$	1.06701e70	1.53935	0.769673	−	0.638438i	$-0.220419\pi$
$709$	1.06701e70	1.53935	0.769673	+	0.638438i	$0.220419\pi$
$710$	4.25880e69	0.593551
$711$	0	0
$712$	−1.03342e70	−1.34437
$713$	5.58427e69	0.701897
$714$	0	0
$715$	9.71314e69	1.13989
$716$	5.46055e68	0.0619251
$717$	0	0
$718$	−9.01693e69	−0.955014
$719$	−1.57271e70	−1.60987	−0.804936	−	0.593362i	$-0.797800\pi$
$719$	−1.57271e70	−1.60987	−0.804936	+	0.593362i	$0.797800\pi$
$720$	0	0
$721$	−5.48943e69	−0.524945
$722$	1.65897e70	1.53348
$723$	0	0
$724$	2.61783e68	0.0226124
$725$	2.74974e69	0.229621
$726$	0	0
$727$	−1.05830e70	−0.826067	−0.413033	−	0.910716i	$-0.635531\pi$
$727$	−1.05830e70	−0.826067	−0.413033	+	0.910716i	$0.635531\pi$
$728$	−1.54426e70	−1.16548
$729$	0	0
$730$	1.50312e70	1.06068
$731$	8.26157e69	0.563750
$732$	0	0
$733$	−2.28917e70	−1.46093	−0.730466	−	0.682949i	$-0.760697\pi$
$733$	−2.28917e70	−1.46093	−0.730466	+	0.682949i	$0.760697\pi$
$734$	1.00936e70	0.623008
$735$	0	0
$736$	3.50769e69	0.202542
$737$	−3.85513e70	−2.15321
$738$	0	0
$739$	2.74741e70	1.43594	0.717968	−	0.696076i	$-0.245072\pi$
$739$	2.74741e70	1.43594	0.717968	+	0.696076i	$0.245072\pi$
$740$	8.86735e68	0.0448350
$741$	0	0
$742$	7.06903e69	0.334553
$743$	−1.03737e70	−0.475017	−0.237508	−	0.971386i	$-0.576331\pi$
$743$	−1.03737e70	−0.475017	−0.237508	+	0.971386i	$0.576331\pi$
$744$	0	0
$745$	−2.02426e70	−0.867834
$746$	−4.30039e70	−1.78405
$747$	0	0
$748$	−3.98256e69	−0.154729
$749$	−6.43387e69	−0.241918
$750$	0	0
$751$	−5.36589e70	−1.89001	−0.945003	−	0.327062i	$-0.893941\pi$
$751$	−5.36589e70	−1.89001	−0.945003	+	0.327062i	$0.893941\pi$
$752$	1.64480e70	0.560758
$753$	0	0
$754$	−1.88619e70	−0.602541
$755$	2.91336e70	0.900936
$756$	0	0
$757$	−3.78086e70	−1.09583	−0.547913	−	0.836535i	$-0.684578\pi$
$757$	−3.78086e70	−1.09583	−0.547913	+	0.836535i	$0.684578\pi$
$758$	−2.48981e70	−0.698668
$759$	0	0
$760$	5.11171e70	1.34472
$761$	−3.04475e70	−0.775581	−0.387791	−	0.921748i	$-0.626762\pi$
$761$	−3.04475e70	−0.775581	−0.387791	+	0.921748i	$0.626762\pi$
$762$	0	0
$763$	2.57327e70	0.614658
$764$	−1.37566e69	−0.0318218
$765$	0	0
$766$	2.56348e70	0.556192
$767$	3.77367e69	0.0793008
$768$	0	0
$769$	−1.49566e70	−0.294874	−0.147437	−	0.989071i	$-0.547102\pi$
$769$	−1.49566e70	−0.294874	−0.147437	+	0.989071i	$0.547102\pi$
$770$	6.37326e70	1.21714
$771$	0	0
$772$	−3.51316e69	−0.0629614
$773$	−3.62206e70	−0.628866	−0.314433	−	0.949280i	$-0.601814\pi$
$773$	−3.62206e70	−0.628866	−0.314433	+	0.949280i	$0.601814\pi$
$774$	0	0
$775$	−1.45671e70	−0.237401
$776$	8.21776e70	1.29760
$777$	0	0
$778$	5.46765e70	0.810588
$779$	−5.15506e70	−0.740570
$780$	0	0
$781$	8.27524e70	1.11643
$782$	8.87694e70	1.16064
$783$	0	0
$784$	−1.86608e70	−0.229186
$785$	7.08056e70	0.842871
$786$	0	0
$787$	−5.90448e70	−0.660391	−0.330195	−	0.943913i	$-0.607115\pi$
$787$	−5.90448e70	−0.660391	−0.330195	+	0.943913i	$0.607115\pi$
$788$	8.93087e69	0.0968282
$789$	0	0
$790$	1.13662e71	1.15811
$791$	−5.43451e69	−0.0536829
$792$	0	0
$793$	4.71214e70	0.437547
$794$	−5.38299e69	−0.0484642
$795$	0	0
$796$	1.50642e70	0.127519
$797$	−1.73928e71	−1.42771	−0.713856	−	0.700292i	$-0.753053\pi$
$797$	−1.73928e71	−1.42771	−0.713856	+	0.700292i	$0.753053\pi$
$798$	0	0
$799$	−9.24178e70	−0.713443
$800$	−9.15017e69	−0.0685053
$801$	0	0
$802$	−8.50558e70	−0.599007
$803$	2.92070e71	1.99506
$804$	0	0
$805$	1.49052e71	0.957943
$806$	9.99235e70	0.622958
$807$	0	0
$808$	−2.33682e70	−0.137103
$809$	−1.56081e71	−0.888403	−0.444202	−	0.895927i	$-0.646513\pi$
$809$	−1.56081e71	−0.888403	−0.444202	+	0.895927i	$0.646513\pi$
$810$	0	0
$811$	−9.44857e70	−0.506238	−0.253119	−	0.967435i	$-0.581456\pi$
$811$	−9.44857e70	−0.506238	−0.253119	+	0.967435i	$0.581456\pi$
$812$	1.29856e70	0.0675056
$813$	0	0
$814$	−1.64214e71	−0.803736
$815$	−5.11513e70	−0.242938
$816$	0	0
$817$	−1.78692e71	−0.799216
$818$	1.09836e71	0.476747
$819$	0	0
$820$	−8.50140e69	−0.0347577
$821$	−4.10899e71	−1.63053	−0.815263	−	0.579091i	$-0.803408\pi$
$821$	−4.10899e71	−1.63053	−0.815263	+	0.579091i	$0.803408\pi$
$822$	0	0
$823$	−7.73454e70	−0.289160	−0.144580	−	0.989493i	$-0.546183\pi$
$823$	−7.73454e70	−0.289160	−0.144580	+	0.989493i	$0.546183\pi$
$824$	1.34464e71	0.487965
$825$	0	0
$826$	2.47608e70	0.0846748
$827$	2.26640e71	0.752404	0.376202	−	0.926538i	$-0.377230\pi$
$827$	2.26640e71	0.752404	0.376202	+	0.926538i	$0.377230\pi$
$828$	0	0
$829$	4.51215e71	1.41188	0.705939	−	0.708273i	$-0.250525\pi$
$829$	4.51215e71	1.41188	0.705939	+	0.708273i	$0.250525\pi$
$830$	−1.03277e71	−0.313756
$831$	0	0
$832$	3.75125e71	1.07437
$833$	1.04851e71	0.291589
$834$	0	0
$835$	6.18538e70	0.162199
$836$	8.61399e70	0.219357
$837$	0	0
$838$	−5.58689e71	−1.34181
$839$	−7.26480e71	−1.69456	−0.847278	−	0.531150i	$-0.821760\pi$
$839$	−7.26480e71	−1.69456	−0.847278	+	0.531150i	$0.821760\pi$
$840$	0	0
$841$	−2.71580e71	−0.597581
$842$	−3.53939e71	−0.756454
$843$	0	0
$844$	5.87410e70	0.118454
$845$	−1.28656e69	−0.00252023
$846$	0	0
$847$	6.32204e71	1.16873
$848$	−1.56564e71	−0.281185
$849$	0	0
$850$	−2.31564e71	−0.392561
$851$	−3.84050e71	−0.632578
$852$	0	0
$853$	−5.90172e71	−0.917757	−0.458878	−	0.888499i	$-0.651749\pi$
$853$	−5.90172e71	−0.917757	−0.458878	+	0.888499i	$0.651749\pi$
$854$	3.09186e71	0.467199
$855$	0	0
$856$	1.57598e71	0.224876
$857$	−7.99787e71	−1.10903	−0.554516	−	0.832173i	$-0.687097\pi$
$857$	−7.99787e71	−1.10903	−0.554516	+	0.832173i	$0.687097\pi$
$858$	0	0
$859$	−6.56838e71	−0.860252	−0.430126	−	0.902769i	$-0.641531\pi$
$859$	−6.56838e71	−0.860252	−0.430126	+	0.902769i	$0.641531\pi$
$860$	−2.94687e70	−0.0375102
$861$	0	0
$862$	1.18937e72	1.43017
$863$	1.10305e72	1.28924	0.644618	−	0.764505i	$-0.277016\pi$
$863$	1.10305e72	1.28924	0.644618	+	0.764505i	$0.277016\pi$
$864$	0	0
$865$	5.35955e71	0.591880
$866$	7.60701e71	0.816631
$867$	0	0
$868$	−6.87932e70	−0.0697930
$869$	2.20855e72	2.17832
$870$	0	0
$871$	−1.61331e72	−1.50409
$872$	−6.30323e71	−0.571359
$873$	0	0
$874$	−1.92002e72	−1.64541
$875$	−1.46299e72	−1.21912
$876$	0	0
$877$	1.55281e72	1.22357	0.611783	−	0.791026i	$-0.290453\pi$
$877$	1.55281e72	1.22357	0.611783	+	0.791026i	$0.290453\pi$
$878$	−1.62121e72	−1.24229
$879$	0	0
$880$	−1.41154e72	−1.02298
$881$	−6.02597e71	−0.424734	−0.212367	−	0.977190i	$-0.568117\pi$
$881$	−6.02597e71	−0.424734	−0.212367	+	0.977190i	$0.568117\pi$
$882$	0	0
$883$	−3.02172e71	−0.201473	−0.100737	−	0.994913i	$-0.532120\pi$
$883$	−3.02172e71	−0.201473	−0.100737	+	0.994913i	$0.532120\pi$
$884$	−1.66663e71	−0.108084
$885$	0	0
$886$	2.56006e72	1.57081
$887$	1.92132e72	1.14675	0.573377	−	0.819291i	$-0.305633\pi$
$887$	1.92132e72	1.14675	0.573377	+	0.819291i	$0.305633\pi$
$888$	0	0
$889$	1.89508e72	1.07037
$890$	1.78483e72	0.980711
$891$	0	0
$892$	−8.70888e70	−0.0452922
$893$	1.99893e72	1.01143
$894$	0	0
$895$	−1.08745e72	−0.520888
$896$	2.00632e72	0.935093
$897$	0	0
$898$	3.06184e72	1.35118
$899$	−9.68865e71	−0.416055
$900$	0	0
$901$	8.79698e71	0.357747
$902$	1.57437e72	0.623085
$903$	0	0
$904$	1.33118e71	0.0499013
$905$	−5.21331e71	−0.190206
$906$	0	0
$907$	5.55555e71	0.192021	0.0960105	−	0.995380i	$-0.469392\pi$
$907$	5.55555e71	0.192021	0.0960105	+	0.995380i	$0.469392\pi$
$908$	2.07245e71	0.0697238
$909$	0	0
$910$	2.66710e72	0.850208
$911$	−2.02494e72	−0.628365	−0.314182	−	0.949363i	$-0.601730\pi$
$911$	−2.02494e72	−0.628365	−0.314182	+	0.949363i	$0.601730\pi$
$912$	0	0
$913$	−2.00678e72	−0.590153
$914$	−4.64718e72	−1.33048
$915$	0	0
$916$	−3.60538e71	−0.0978390
$917$	4.29498e72	1.13478
$918$	0	0
$919$	−1.46950e72	−0.368077	−0.184038	−	0.982919i	$-0.558917\pi$
$919$	−1.46950e72	−0.368077	−0.184038	+	0.982919i	$0.558917\pi$
$920$	−3.65104e72	−0.890461
$921$	0	0
$922$	−4.92706e72	−1.13941
$923$	3.46305e72	0.779861
$924$	0	0
$925$	1.00183e72	0.213956
$926$	2.16477e72	0.450239
$927$	0	0
$928$	−6.08580e71	−0.120058
$929$	−7.04427e72	−1.35348	−0.676739	−	0.736223i	$-0.736607\pi$
$929$	−7.04427e72	−1.35348	−0.676739	+	0.736223i	$0.736607\pi$
$930$	0	0
$931$	−2.26786e72	−0.413379
$932$	−5.73435e71	−0.101811
$933$	0	0
$934$	−4.20283e72	−0.708016
$935$	7.93113e72	1.30152
$936$	0	0
$937$	−9.24309e72	−1.43945	−0.719726	−	0.694258i	$-0.755733\pi$
$937$	−9.24309e72	−1.43945	−0.719726	+	0.694258i	$0.755733\pi$
$938$	−1.05857e73	−1.60602
$939$	0	0
$940$	3.29651e71	0.0474702
$941$	−8.82463e72	−1.23809	−0.619043	−	0.785357i	$-0.712479\pi$
$941$	−8.82463e72	−1.23809	−0.619043	+	0.785357i	$0.712479\pi$
$942$	0	0
$943$	3.68201e72	0.490397
$944$	−5.48398e71	−0.0711676
$945$	0	0
$946$	5.45730e72	0.672427
$947$	−1.12021e73	−1.34501	−0.672504	−	0.740093i	$-0.734781\pi$
$947$	−1.12021e73	−1.34501	−0.672504	+	0.740093i	$0.734781\pi$
$948$	0	0
$949$	1.22226e73	1.39362
$950$	5.00856e72	0.556525
$951$	0	0
$952$	−1.26095e73	−1.33073
$953$	−8.31437e72	−0.855172	−0.427586	−	0.903975i	$-0.640636\pi$
$953$	−8.31437e72	−0.855172	−0.427586	+	0.903975i	$0.640636\pi$
$954$	0	0
$955$	2.73959e72	0.267672
$956$	−3.66025e71	−0.0348572
$957$	0	0
$958$	−2.22731e72	−0.201524
$959$	2.06339e73	1.81981
$960$	0	0
$961$	−6.79957e72	−0.569847
$962$	−6.87209e72	−0.561435
$963$	0	0
$964$	−3.44191e71	−0.0267246
$965$	6.99634e72	0.529604
$966$	0	0
$967$	1.19977e73	0.863277	0.431639	−	0.902047i	$-0.357936\pi$
$967$	1.19977e73	0.863277	0.431639	+	0.902047i	$0.357936\pi$
$968$	−1.54859e73	−1.08640
$969$	0	0
$970$	−1.41929e73	−0.946593
$971$	2.62188e73	1.70507	0.852535	−	0.522671i	$-0.175064\pi$
$971$	2.62188e73	1.70507	0.852535	+	0.522671i	$0.175064\pi$
$972$	0	0
$973$	2.60648e73	1.61172
$974$	8.44242e72	0.509064
$975$	0	0
$976$	−6.84779e72	−0.392672
$977$	1.17201e73	0.655413	0.327706	−	0.944780i	$-0.393724\pi$
$977$	1.17201e73	0.655413	0.327706	+	0.944780i	$0.393724\pi$
$978$	0	0
$979$	3.46808e73	1.84465
$980$	−3.74000e71	−0.0194014
$981$	0	0
$982$	−3.16037e72	−0.155957
$983$	2.13585e73	1.02804	0.514019	−	0.857779i	$-0.328156\pi$
$983$	2.13585e73	1.02804	0.514019	+	0.857779i	$0.328156\pi$
$984$	0	0
$985$	−1.77855e73	−0.814477
$986$	−1.54014e73	−0.687979
$987$	0	0
$988$	3.60481e72	0.153228
$989$	1.27631e73	0.529232
$990$	0	0
$991$	−2.03182e73	−0.801827	−0.400913	−	0.916116i	$-0.631307\pi$
$991$	−2.03182e73	−0.801827	−0.400913	+	0.916116i	$0.631307\pi$
$992$	3.22404e72	0.124127
$993$	0	0
$994$	2.27227e73	0.832710
$995$	−2.99998e73	−1.07264
$996$	0	0
$997$	−1.66206e73	−0.565739	−0.282869	−	0.959158i	$-0.591286\pi$
$997$	−1.66206e73	−0.565739	−0.282869	+	0.959158i	$0.591286\pi$
$998$	6.41587e72	0.213087
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.50.a.a.1.2		3
3.2	odd	2		1.50.a.a.1.2	✓	3
12.11	even	2		16.50.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.50.a.a.1.2	✓	3	3.2	odd	2
9.50.a.a.1.2		3	1.1	even	1	trivial
16.50.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:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+2.25719e7 q^{2} -5.34581e13 q^{4} +1.06460e17 q^{5} +5.68014e20 q^{7} -1.39135e22 q^{8} +O(q^{10})\)	\(q+2.25719e7 q^{2} -5.34581e13 q^{4} +1.06460e17 q^{5} +5.68014e20 q^{7} -1.39135e22 q^{8} +2.40300e24 q^{10} +4.66926e25 q^{11} +1.95401e27 q^{13} +1.28212e28 q^{14} -2.83961e29 q^{16} +1.59552e30 q^{17} -3.45099e31 q^{19} -5.69114e30 q^{20} +1.05394e33 q^{22} +2.46487e33 q^{23} -6.42986e33 q^{25} +4.41057e34 q^{26} -3.03649e34 q^{28} -4.27652e35 q^{29} +2.26555e36 q^{31} +1.42307e36 q^{32} +3.60138e37 q^{34} +6.04707e37 q^{35} -1.55810e38 q^{37} -7.78954e38 q^{38} -1.48123e39 q^{40} +1.49379e39 q^{41} +5.17800e39 q^{43} -2.49610e39 q^{44} +5.56368e40 q^{46} -5.79235e40 q^{47} +6.57162e40 q^{49} -1.45134e41 q^{50} -1.04457e41 q^{52} +5.51356e41 q^{53} +4.97089e42 q^{55} -7.90307e42 q^{56} -9.65293e42 q^{58} +1.93125e42 q^{59} +2.41153e43 q^{61} +5.11377e43 q^{62} +1.91977e44 q^{64} +2.08023e44 q^{65} -8.25642e44 q^{67} -8.52932e43 q^{68} +1.36494e45 q^{70} +1.77228e45 q^{71} +6.25517e45 q^{73} -3.51693e45 q^{74} +1.84483e45 q^{76} +2.65220e46 q^{77} +4.72997e46 q^{79} -3.02304e46 q^{80} +3.37178e46 q^{82} -4.29785e46 q^{83} +1.69858e47 q^{85} +1.16877e47 q^{86} -6.49658e47 q^{88} +7.42748e47 q^{89} +1.10990e48 q^{91} -1.31767e47 q^{92} -1.30744e48 q^{94} -3.67392e48 q^{95} -5.90631e48 q^{97} +1.48334e48 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 24225168 q^{2} + 31502767984896 q^{4} - 63\!\cdots\!50 q^{5}+ \cdots - 12\!\cdots\!00 q^{8}+O(q^{10}) \) 3 * q + 24225168 * q^2 + 31502767984896 * q^4 - 63884035717079250 * q^5 + 509391477498711192 * q^7 - 12774393005516465664000 * q^8	\( 3 q + 24225168 q^{2} + 31502767984896 q^{4} - 63\!\cdots\!50 q^{5}+ \cdots + 28\!\cdots\!76 q^{98}+O(q^{100}) \) 3 * q + 24225168 * q^2 + 31502767984896 * q^4 - 63884035717079250 * q^5 + 509391477498711192 * q^7 - 12774393005516465664000 * q^8 - 1782704508900495946524000 * q^10 + 20839986192711815613370524 * q^11 - 187524857197340618282341014 * q^13 + 9454369415029168241295938688 * q^14 - 958699697068386571735634214912 * q^16 + 3305035636247475259184114894538 * q^17 - 45882942802931464757155696518660 * q^19 - 19614616637279540996591887296000 * q^20 + 1789915191438262082177360193562944 * q^22 - 4533392548023086653463590407813576 * q^23 - 13921151905580403838435182832171875 * q^25 + 85826222237480824536590109710199264 * q^26 - 59263339345763305527729286468663296 * q^28 - 1118089919316361970349176934175494810 * q^29 + 934226816157578575389156342339525216 * q^31 - 731728685735702515419064521056059392 * q^32 - 44386547077569962679458968510685418528 * q^34 + 118496887985378726635932152589238374000 * q^35 + 242135148519373130928922851818564983602 * q^37 - 1156029602765443663092741329710471492800 * q^38 + 521466322563622592824981612412298240000 * q^40 + 6211739675976490815696297371880432723714 * q^41 - 7795173962887472637660666233812713782844 * q^43 - 2342252938597505040255206661879982328832 * q^44 + 26787138361451470082912377308943265940096 * q^46 - 72757717838871152990888073123214445891472 * q^47 - 280157966384090888246597869444400847657429 * q^49 + 537697283161263679965664107392030595750000 * q^50 - 123529799747407597799198092229890019578368 * q^52 + 155850890670432045962015052011776669693854 * q^53 + 4640026560861316230546160030865773419591000 * q^55 - 6722101775263505338291028050795018900439040 * q^56 - 16549417550295130349814323361508282251506400 * q^58 + 62596927936822013761436024025606581543386380 * q^59 - 24037263967789435219196348055077866809754374 * q^61 - 188825800588885099392385526941761279238024704 * q^62 + 514652981263254699809134733483815976080244736 * q^64 + 244975900670806240216695171564505814930314500 * q^65 - 1019040852324305100821779153549119164107459188 * q^67 - 147929481309005416179289053660840704965292544 * q^68 + 2807457123724968989995337407321309803024672000 * q^70 + 3208129335291950593367863544185773469328334504 * q^71 + 5668108076325412165814435883536677392865317726 * q^73 - 10012493148932275797653251806650724700277983392 * q^74 + 753841821393723585433963960120373529551508480 * q^76 + 32043339793247959180079389483660528277811891936 * q^77 - 7871365395380306420112251724245018715125364240 * q^79 + 30434832804539714147732706266001913558351872000 * q^80 + 118639125705754411670909153459409940471487282784 * q^82 - 94164681901361229355849854653903786480577085116 * q^83 + 297863286656785614551226799130947646752077538500 * q^85 + 347916436657924446515600473690440815675104929984 * q^86 - 1057522149818049090984983413770258669302102016000 * q^88 - 367807201561165354579457777200332871192114777230 * q^89 + 1613372397893666548508325640004129525440352221776 * q^91 - 467187868629171186038576611613065932844001728512 * q^92 + 904097685092930858948295844890436017323554129152 * q^94 - 1475636199748052355599968141572624301097796705000 * q^95 - 10431108583780665799950508389192126734793760399578 * q^97 + 2841886978251444216347516645227034756825518204176 * q^98

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