LMFDB - Embedded newform 9.42.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,42,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, 42, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 42 $
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:	$95.8245034108$
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} - 2784108376x + 1945534874860 $ x^3 - x^2 - 2784108376*x + 1945534874860
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			1.2
Root			$698.922$ 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)

$f(q)$	$=$	$q+81363.7 q^{2} -2.19240e12 q^{4} -9.10518e13 q^{5} -1.69829e16 q^{7} -3.57303e17 q^{8} +O(q^{10})$	\(q+81363.7 q^{2} -2.19240e12 q^{4} -9.10518e13 q^{5} -1.69829e16 q^{7} -3.57303e17 q^{8} -7.40831e18 q^{10} +3.48555e21 q^{11} -1.03131e23 q^{13} -1.38179e21 q^{14} +4.79207e24 q^{16} -1.01608e25 q^{17} -1.72697e26 q^{19} +1.99622e26 q^{20} +2.83598e26 q^{22} -1.09881e28 q^{23} -3.71843e28 q^{25} -8.39114e27 q^{26} +3.72334e28 q^{28} -1.22079e30 q^{29} +5.57694e29 q^{31} +1.17562e30 q^{32} -8.26720e29 q^{34} +1.54633e30 q^{35} +1.14515e32 q^{37} -1.40513e31 q^{38} +3.25331e31 q^{40} +6.17804e32 q^{41} -1.51443e32 q^{43} -7.64174e33 q^{44} -8.94030e32 q^{46} +1.94739e34 q^{47} -4.42792e34 q^{49} -3.02545e33 q^{50} +2.26105e35 q^{52} +1.38685e35 q^{53} -3.17366e35 q^{55} +6.06805e33 q^{56} -9.93283e34 q^{58} -2.19974e36 q^{59} +2.83478e36 q^{61} +4.53761e34 q^{62} -1.04422e37 q^{64} +9.39028e36 q^{65} +2.71602e37 q^{67} +2.22766e37 q^{68} +1.25815e35 q^{70} -4.91576e37 q^{71} -2.29426e38 q^{73} +9.31739e36 q^{74} +3.78622e38 q^{76} -5.91949e37 q^{77} +1.69414e38 q^{79} -4.36327e38 q^{80} +5.02668e37 q^{82} +3.52307e39 q^{83} +9.25158e38 q^{85} -1.23220e37 q^{86} -1.24540e39 q^{88} -6.37675e39 q^{89} +1.75147e39 q^{91} +2.40903e40 q^{92} +1.58447e39 q^{94} +1.57244e40 q^{95} +3.79303e40 q^{97} -3.60272e39 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 344688 q^{2} + 6271704903936 q^{4} + 212302350281550 q^{5} + 57\!\cdots\!92 q^{7}+ \cdots + 35\!\cdots\!20 q^{8}+O(q^{10}) $ 3 * q + 344688 * q^2 + 6271704903936 * q^4 + 212302350281550 * q^5 + 57878416258239192 * q^7 + 3555831711183237120 * q^8	$ 3 q + 344688 q^{2} + 6271704903936 q^{4} + 212302350281550 q^{5} + 57\!\cdots\!92 q^{7}+ \cdots + 38\!\cdots\!16 q^{98}+O(q^{100}) $ 3 * q + 344688 * q^2 + 6271704903936 * q^4 + 212302350281550 * q^5 + 57878416258239192 * q^7 + 3555831711183237120 * q^8 - 911610678410074173600 * q^10 + 3064080929502798535164 * q^11 - 98515763053518962936694 * q^13 + 663773359066872932212608 * q^14 + 13217913642093764057038848 * q^16 - 35582277130790298867301302 * q^17 - 233456308095243376865478180 * q^19 + 1234817679506740618000857600 * q^20 + 10093688647003206881596695744 * q^22 - 2812708670812770779627026056 * q^23 - 12630087813294771903109831875 * q^25 + 445502868787427067716672131104 * q^26 + 526606706694181610802628184064 * q^28 + 12736322664295346653179017670 * q^29 - 55977552834365071134409017504 * q^31 + 14842037794660482009412112744448 * q^32 - 42547131667082319398961759011808 * q^34 - 35330944415319146254058128592400 * q^35 + 4945769903781582545269841455122 * q^37 - 384288369224763756133358504473920 * q^38 - 1326138456985596139721995183104000 * q^40 + 3123151500646359746292805811918274 * q^41 + 1491980858362212236675453498061156 * q^43 - 6827579920847638909574240093432832 * q^44 + 34089155258950859800971794327519616 * q^46 + 63038106682044077762675687404413168 * q^47 - 97136113131667199274890334287198229 * q^49 - 286202165340727366859498513545830000 * q^50 + 364999309722184195149034320029732352 * q^52 - 79896749344137562310547533743021506 * q^53 - 1107430856215374719020572615529578600 * q^55 + 1507500925934438536531619079138017280 * q^56 + 1060511497310363735425511566792954080 * q^58 - 192512048683375799719343226678403860 * q^59 + 8740556115036354715092732710435455386 * q^61 + 12005332293025961804297174175449366016 * q^62 - 28669651485797320669854651690478731264 * q^64 - 23272939413910136331858458170260680700 * q^65 + 11266872945514675454702655007279407852 * q^67 - 95413181576279049358373233907724317184 * q^68 + 59324379124057015483688060122385068800 * q^70 + 140970915469820223119231433051520161384 * q^71 + 45825493210252135256288871746499029406 * q^73 + 255935787825178849200244145003411599008 * q^74 + 26100578647791289060370838422069130240 * q^76 + 429017620126390531124795910645506217696 * q^77 - 520184835554750143118446358634240850320 * q^79 - 715918562852781559130521454428746547200 * q^80 - 579816777788457983576303882284492608096 * q^82 + 619777491338381742927488037142663372644 * q^83 - 106299433069331216483654652405294143100 * q^85 + 4751113477095326918262488958359640807744 * q^86 + 18329036816788093472347699011602935234560 * q^88 + 142389067128374093799211866144944441010 * q^89 + 25080596935320871627133801126628392473296 * q^91 + 67617289414955565381239604024555789723648 * q^92 - 53008068396962431152763933809330449227008 * q^94 + 33170437179755379504247502944935502503000 * q^95 + 116011691364103339137369463947331771078182 * q^97 + 38494567059701712876195969460820421029616 * 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 $

$2$	81363.7	0.0548676	0.0274338	−	0.999624i	$-0.491266\pi$
$2$	81363.7	0.0548676	0.0274338	+	0.999624i	$0.491266\pi$
$3$	0	0
$3$	0	0
$4$	−2.19240e12	−0.996990
$5$	−9.10518e13	−0.426976	−0.213488	−	0.976946i	$-0.568482\pi$
$5$	−9.10518e13	−0.426976	−0.213488	+	0.976946i	$0.568482\pi$
$6$	0	0
$7$	−1.69829e16	−0.0804457	−0.0402228	−	0.999191i	$-0.512807\pi$
$7$	−1.69829e16	−0.0804457	−0.0402228	+	0.999191i	$0.512807\pi$
$8$	−3.57303e17	−0.109570
$9$	0	0
$10$	−7.40831e18	−0.0234271
$11$	3.48555e21	1.56215	0.781073	−	0.624440i	$-0.214673\pi$
$11$	3.48555e21	1.56215	0.781073	+	0.624440i	$0.214673\pi$
$12$	0	0
$13$	−1.03131e23	−1.50505	−0.752526	−	0.658563i	$-0.771165\pi$
$13$	−1.03131e23	−1.50505	−0.752526	+	0.658563i	$0.771165\pi$
$14$	−1.38179e21	−0.00441386
$15$	0	0
$16$	4.79207e24	0.990978
$17$	−1.01608e25	−0.606352	−0.303176	−	0.952935i	$-0.598047\pi$
$17$	−1.01608e25	−0.606352	−0.303176	+	0.952935i	$0.598047\pi$
$18$	0	0
$19$	−1.72697e26	−1.05399	−0.526995	−	0.849868i	$-0.676681\pi$
$19$	−1.72697e26	−1.05399	−0.526995	+	0.849868i	$0.676681\pi$
$20$	1.99622e26	0.425691
$21$	0	0
$22$	2.83598e26	0.0857112
$23$	−1.09881e28	−1.33506	−0.667530	−	0.744583i	$-0.732648\pi$
$23$	−1.09881e28	−1.33506	−0.667530	+	0.744583i	$0.732648\pi$
$24$	0	0
$25$	−3.71843e28	−0.817692
$26$	−8.39114e27	−0.0825786
$27$	0	0
$28$	3.72334e28	0.0802035
$29$	−1.22079e30	−1.28081	−0.640403	−	0.768039i	$-0.721233\pi$
$29$	−1.22079e30	−1.28081	−0.640403	+	0.768039i	$0.721233\pi$
$30$	0	0
$31$	5.57694e29	0.149101	0.0745506	−	0.997217i	$-0.476248\pi$
$31$	5.57694e29	0.149101	0.0745506	+	0.997217i	$0.476248\pi$
$32$	1.17562e30	0.163943
$33$	0	0
$34$	−8.26720e29	−0.0332691
$35$	1.54633e30	0.0343484
$36$	0	0
$37$	1.14515e32	0.814194	0.407097	−	0.913385i	$-0.366541\pi$
$37$	1.14515e32	0.814194	0.407097	+	0.913385i	$0.366541\pi$
$38$	−1.40513e31	−0.0578299
$39$	0	0
$40$	3.25331e31	0.0467838
$41$	6.17804e32	0.535527	0.267764	−	0.963485i	$-0.413715\pi$
$41$	6.17804e32	0.535527	0.267764	+	0.963485i	$0.413715\pi$
$42$	0	0
$43$	−1.51443e32	−0.0494478	−0.0247239	−	0.999694i	$-0.507871\pi$
$43$	−1.51443e32	−0.0494478	−0.0247239	+	0.999694i	$0.507871\pi$
$44$	−7.64174e33	−1.55744
$45$	0	0
$46$	−8.94030e32	−0.0732515
$47$	1.94739e34	1.02671	0.513354	−	0.858177i	$-0.328403\pi$
$47$	1.94739e34	1.02671	0.513354	+	0.858177i	$0.328403\pi$
$48$	0	0
$49$	−4.42792e34	−0.993528
$50$	−3.02545e33	−0.0448648
$51$	0	0
$52$	2.26105e35	1.50052
$53$	1.38685e35	0.622837	0.311418	−	0.950273i	$-0.399196\pi$
$53$	1.38685e35	0.622837	0.311418	+	0.950273i	$0.399196\pi$
$54$	0	0
$55$	−3.17366e35	−0.666999
$56$	6.06805e33	0.00881443
$57$	0	0
$58$	−9.93283e34	−0.0702747
$59$	−2.19974e36	−1.09624	−0.548119	−	0.836400i	$-0.684656\pi$
$59$	−2.19974e36	−1.09624	−0.548119	+	0.836400i	$0.684656\pi$
$60$	0	0
$61$	2.83478e36	0.713277	0.356639	−	0.934242i	$-0.383923\pi$
$61$	2.83478e36	0.713277	0.356639	+	0.934242i	$0.383923\pi$
$62$	4.53761e34	0.00818083
$63$	0	0
$64$	−1.04422e37	−0.981983
$65$	9.39028e36	0.642621
$66$	0	0
$67$	2.71602e37	0.998617	0.499308	−	0.866424i	$-0.333587\pi$
$67$	2.71602e37	0.998617	0.499308	+	0.866424i	$0.333587\pi$
$68$	2.22766e37	0.604526
$69$	0	0
$70$	1.25815e35	0.00188461
$71$	−4.91576e37	−0.550548	−0.275274	−	0.961366i	$-0.588769\pi$
$71$	−4.91576e37	−0.550548	−0.275274	+	0.961366i	$0.588769\pi$
$72$	0	0
$73$	−2.29426e38	−1.45386	−0.726932	−	0.686709i	$-0.759055\pi$
$73$	−2.29426e38	−1.45386	−0.726932	+	0.686709i	$0.759055\pi$
$74$	9.31739e36	0.0446729
$75$	0	0
$76$	3.78622e38	1.05082
$77$	−5.91949e37	−0.125668
$78$	0	0
$79$	1.69414e38	0.212615	0.106307	−	0.994333i	$-0.466097\pi$
$79$	1.69414e38	0.212615	0.106307	+	0.994333i	$0.466097\pi$
$80$	−4.36327e38	−0.423124
$81$	0	0
$82$	5.02668e37	0.0293831
$83$	3.52307e39	1.60628	0.803138	−	0.595793i	$-0.203162\pi$
$83$	3.52307e39	1.60628	0.803138	+	0.595793i	$0.203162\pi$
$84$	0	0
$85$	9.25158e38	0.258898
$86$	−1.23220e37	−0.00271308
$87$	0	0
$88$	−1.24540e39	−0.171164
$89$	−6.37675e39	−0.695192	−0.347596	−	0.937644i	$-0.613002\pi$
$89$	−6.37675e39	−0.695192	−0.347596	+	0.937644i	$0.613002\pi$
$90$	0	0
$91$	1.75147e39	0.121075
$92$	2.40903e40	1.33104
$93$	0	0
$94$	1.58447e39	0.0563330
$95$	1.57244e40	0.450029
$96$	0	0
$97$	3.79303e40	0.708216	0.354108	−	0.935205i	$-0.384785\pi$
$97$	3.79303e40	0.708216	0.354108	+	0.935205i	$0.384785\pi$
$98$	−3.60272e39	−0.0545125
$99$	0	0
$100$	8.15230e40	0.815230
$101$	2.06559e41	1.68444	0.842222	−	0.539131i	$-0.181247\pi$
$101$	2.06559e41	1.68444	0.842222	+	0.539131i	$0.181247\pi$
$102$	0	0
$103$	−2.70863e40	−0.147770	−0.0738851	−	0.997267i	$-0.523540\pi$
$103$	−2.70863e40	−0.147770	−0.0738851	+	0.997267i	$0.523540\pi$
$104$	3.68491e40	0.164909
$105$	0	0
$106$	1.12839e40	0.0341736
$107$	3.86524e41	0.965626	0.482813	−	0.875723i	$-0.339615\pi$
$107$	3.86524e41	0.965626	0.482813	+	0.875723i	$0.339615\pi$
$108$	0	0
$109$	5.41460e41	0.925387	0.462693	−	0.886518i	$-0.346883\pi$
$109$	5.41460e41	0.925387	0.462693	+	0.886518i	$0.346883\pi$
$110$	−2.58221e40	−0.0365966
$111$	0	0
$112$	−8.13834e40	−0.0797198
$113$	1.99438e42	1.62817	0.814086	−	0.580744i	$-0.197238\pi$
$113$	1.99438e42	1.62817	0.814086	+	0.580744i	$0.197238\pi$
$114$	0	0
$115$	1.00048e42	0.570038
$116$	2.67647e42	1.27695
$117$	0	0
$118$	−1.78979e41	−0.0601479
$119$	1.72560e41	0.0487784
$120$	0	0
$121$	7.17056e42	1.44030
$122$	2.30649e41	0.0391358
$123$	0	0
$124$	−1.22269e42	−0.148652
$125$	7.52625e42	0.776111
$126$	0	0
$127$	−7.87891e42	−0.586800	−0.293400	−	0.955990i	$-0.594787\pi$
$127$	−7.87891e42	−0.586800	−0.293400	+	0.955990i	$0.594787\pi$
$128$	−3.43483e42	−0.217822
$129$	0	0
$130$	7.64028e41	0.0352591
$131$	−8.75549e42	−0.345318	−0.172659	−	0.984982i	$-0.555236\pi$
$131$	−8.75549e42	−0.345318	−0.172659	+	0.984982i	$0.555236\pi$
$132$	0	0
$133$	2.93290e42	0.0847889
$134$	2.20985e42	0.0547917
$135$	0	0
$136$	3.63048e42	0.0664380
$137$	1.30585e43	0.205647	0.102824	−	0.994700i	$-0.467212\pi$
$137$	1.30585e43	0.205647	0.102824	+	0.994700i	$0.467212\pi$
$138$	0	0
$139$	−7.47721e43	−0.874855	−0.437428	−	0.899254i	$-0.644110\pi$
$139$	−7.47721e43	−0.874855	−0.437428	+	0.899254i	$0.644110\pi$
$140$	−3.39017e42	−0.0342450
$141$	0	0
$142$	−3.99965e42	−0.0302072
$143$	−3.59469e44	−2.35111
$144$	0	0
$145$	1.11155e44	0.546873
$146$	−1.86670e43	−0.0797701
$147$	0	0
$148$	−2.51064e44	−0.811743
$149$	−3.41118e44	−0.960696	−0.480348	−	0.877078i	$-0.659490\pi$
$149$	−3.41118e44	−0.960696	−0.480348	+	0.877078i	$0.659490\pi$
$150$	0	0
$151$	−4.86675e44	−1.04282	−0.521412	−	0.853305i	$-0.674595\pi$
$151$	−4.86675e44	−1.04282	−0.521412	+	0.853305i	$0.674595\pi$
$152$	6.17052e43	0.115486
$153$	0	0
$154$	−4.81631e42	−0.00689509
$155$	−5.07791e43	−0.0636627
$156$	0	0
$157$	1.02260e45	0.985744	0.492872	−	0.870102i	$-0.335947\pi$
$157$	1.02260e45	0.985744	0.492872	+	0.870102i	$0.335947\pi$
$158$	1.37841e43	0.0116657
$159$	0	0
$160$	−1.07042e44	−0.0699995
$161$	1.86609e44	0.107400
$162$	0	0
$163$	−2.57464e45	−1.15046	−0.575228	−	0.817993i	$-0.695087\pi$
$163$	−2.57464e45	−1.15046	−0.575228	+	0.817993i	$0.695087\pi$
$164$	−1.35447e45	−0.533915
$165$	0	0
$166$	2.86650e44	0.0881325
$167$	1.90182e45	0.516991	0.258495	−	0.966013i	$-0.416773\pi$
$167$	1.90182e45	0.516991	0.258495	+	0.966013i	$0.416773\pi$
$168$	0	0
$169$	5.94059e45	1.26518
$170$	7.52743e43	0.0142051
$171$	0	0
$172$	3.32025e44	0.0492989
$173$	1.22944e45	0.162092	0.0810462	−	0.996710i	$-0.474174\pi$
$173$	1.22944e45	0.162092	0.0810462	+	0.996710i	$0.474174\pi$
$174$	0	0
$175$	6.31498e44	0.0657797
$176$	1.67030e46	1.54805
$177$	0	0
$178$	−5.18837e44	−0.0381435
$179$	2.04820e46	1.34241	0.671206	−	0.741271i	$-0.265777\pi$
$179$	2.04820e46	1.34241	0.671206	+	0.741271i	$0.265777\pi$
$180$	0	0
$181$	1.96476e46	1.02541	0.512706	−	0.858564i	$-0.328643\pi$
$181$	1.96476e46	1.02541	0.512706	+	0.858564i	$0.328643\pi$
$182$	1.42506e44	0.00664309
$183$	0	0
$184$	3.92607e45	0.146282
$185$	−1.04268e46	−0.347641
$186$	0	0
$187$	−3.54160e46	−0.947210
$188$	−4.26947e46	−1.02362
$189$	0	0
$190$	1.27940e45	0.0246920
$191$	8.46016e46	1.46620	0.733102	−	0.680118i	$-0.238072\pi$
$191$	8.46016e46	1.46620	0.733102	+	0.680118i	$0.238072\pi$
$192$	0	0
$193$	1.25564e46	0.175768	0.0878840	−	0.996131i	$-0.471990\pi$
$193$	1.25564e46	0.175768	0.0878840	+	0.996131i	$0.471990\pi$
$194$	3.08615e45	0.0388581
$195$	0	0
$196$	9.70779e46	0.990538
$197$	−1.78208e47	−1.63821	−0.819103	−	0.573647i	$-0.805528\pi$
$197$	−1.78208e47	−1.63821	−0.819103	+	0.573647i	$0.805528\pi$
$198$	0	0
$199$	−1.36946e47	−1.02343	−0.511717	−	0.859154i	$-0.670990\pi$
$199$	−1.36946e47	−1.02343	−0.511717	+	0.859154i	$0.670990\pi$
$200$	1.32861e46	0.0895945
$201$	0	0
$202$	1.68064e46	0.0924214
$203$	2.07326e46	0.103035
$204$	0	0
$205$	−5.62521e46	−0.228657
$206$	−2.20384e45	−0.00810780
$207$	0	0
$208$	−4.94212e47	−1.49147
$209$	−6.01945e47	−1.64649
$210$	0	0
$211$	1.52351e47	0.342812	0.171406	−	0.985200i	$-0.445169\pi$
$211$	1.52351e47	0.342812	0.171406	+	0.985200i	$0.445169\pi$
$212$	−3.04053e47	−0.620962
$213$	0	0
$214$	3.14490e46	0.0529816
$215$	1.37892e46	0.0211130
$216$	0	0
$217$	−9.47128e45	−0.0119946
$218$	4.40552e46	0.0507737
$219$	0	0
$220$	6.95794e47	0.664991
$221$	1.04789e48	0.912591
$222$	0	0
$223$	−5.14471e47	−0.372487	−0.186243	−	0.982504i	$-0.559631\pi$
$223$	−5.14471e47	−0.372487	−0.186243	+	0.982504i	$0.559631\pi$
$224$	−1.99654e46	−0.0131885
$225$	0	0
$226$	1.62270e47	0.0893339
$227$	−1.86061e47	−0.0935677	−0.0467838	−	0.998905i	$-0.514897\pi$
$227$	−1.86061e47	−0.0935677	−0.0467838	+	0.998905i	$0.514897\pi$
$228$	0	0
$229$	1.08478e48	0.455738	0.227869	−	0.973692i	$-0.426824\pi$
$229$	1.08478e48	0.455738	0.227869	+	0.973692i	$0.426824\pi$
$230$	8.14030e46	0.0312766
$231$	0	0
$232$	4.36193e47	0.140338
$233$	1.31896e48	0.388541	0.194270	−	0.980948i	$-0.437766\pi$
$233$	1.31896e48	0.388541	0.194270	+	0.980948i	$0.437766\pi$
$234$	0	0
$235$	−1.77313e48	−0.438380
$236$	4.82271e48	1.09294
$237$	0	0
$238$	1.40401e46	0.00267635
$239$	2.46866e48	0.431821	0.215911	−	0.976413i	$-0.430728\pi$
$239$	2.46866e48	0.431821	0.215911	+	0.976413i	$0.430728\pi$
$240$	0	0
$241$	7.05413e48	1.04015	0.520073	−	0.854122i	$-0.325905\pi$
$241$	7.05413e48	1.04015	0.520073	+	0.854122i	$0.325905\pi$
$242$	5.83423e47	0.0790258
$243$	0	0
$244$	−6.21499e48	−0.711130
$245$	4.03170e48	0.424213
$246$	0	0
$247$	1.78105e49	1.58631
$248$	−1.99266e47	−0.0163370
$249$	0	0
$250$	6.12364e47	0.0425833
$251$	1.10391e48	0.0707330	0.0353665	−	0.999374i	$-0.488740\pi$
$251$	1.10391e48	0.0707330	0.0353665	+	0.999374i	$0.488740\pi$
$252$	0	0
$253$	−3.82995e49	−2.08556
$254$	−6.41058e47	−0.0321963
$255$	0	0
$256$	2.26832e49	0.970031
$257$	−1.99173e49	−0.786324	−0.393162	−	0.919469i	$-0.628619\pi$
$257$	−1.99173e49	−0.786324	−0.393162	+	0.919469i	$0.628619\pi$
$258$	0	0
$259$	−1.94480e48	−0.0654984
$260$	−2.05873e49	−0.640686
$261$	0	0
$262$	−7.12379e47	−0.0189468
$263$	−3.95658e49	−0.973255	−0.486627	−	0.873610i	$-0.661773\pi$
$263$	−3.95658e49	−0.973255	−0.486627	+	0.873610i	$0.661773\pi$
$264$	0	0
$265$	−1.26275e49	−0.265936
$266$	2.38632e47	0.00465217
$267$	0	0
$268$	−5.95460e49	−0.995611
$269$	7.39690e49	1.14585	0.572926	−	0.819607i	$-0.305808\pi$
$269$	7.39690e49	1.14585	0.572926	+	0.819607i	$0.305808\pi$
$270$	0	0
$271$	−2.66721e49	−0.354966	−0.177483	−	0.984124i	$-0.556795\pi$
$271$	−2.66721e49	−0.354966	−0.177483	+	0.984124i	$0.556795\pi$
$272$	−4.86913e49	−0.600881
$273$	0	0
$274$	1.06249e48	0.0112834
$275$	−1.29608e50	−1.27735
$276$	0	0
$277$	1.32709e50	1.12737	0.563684	−	0.825991i	$-0.309384\pi$
$277$	1.32709e50	1.12737	0.563684	+	0.825991i	$0.309384\pi$
$278$	−6.08374e48	−0.0480012
$279$	0	0
$280$	−5.52506e47	−0.00376355
$281$	−1.25230e49	−0.0792918	−0.0396459	−	0.999214i	$-0.512623\pi$
$281$	−1.25230e49	−0.0792918	−0.0396459	+	0.999214i	$0.512623\pi$
$282$	0	0
$283$	−9.97157e49	−0.545936	−0.272968	−	0.962023i	$-0.588005\pi$
$283$	−9.97157e49	−0.545936	−0.272968	+	0.962023i	$0.588005\pi$
$284$	1.07773e50	0.548890
$285$	0	0
$286$	−2.92478e49	−0.129000
$287$	−1.04921e49	−0.0430808
$288$	0	0
$289$	−1.77564e50	−0.632337
$290$	9.04402e48	0.0300056
$291$	0	0
$292$	5.02994e50	1.44949
$293$	3.65149e50	0.981035	0.490517	−	0.871431i	$-0.336808\pi$
$293$	3.65149e50	0.981035	0.490517	+	0.871431i	$0.336808\pi$
$294$	0	0
$295$	2.00290e50	0.468067
$296$	−4.09166e49	−0.0892113
$297$	0	0
$298$	−2.77546e49	−0.0527111
$299$	1.13321e51	2.00933
$300$	0	0
$301$	2.57195e48	0.00397786
$302$	−3.95977e49	−0.0572173
$303$	0	0
$304$	−8.27578e50	−1.04448
$305$	−2.58112e50	−0.304552
$306$	0	0
$307$	1.30418e51	1.34586	0.672932	−	0.739705i	$-0.265035\pi$
$307$	1.30418e51	1.34586	0.672932	+	0.739705i	$0.265035\pi$
$308$	1.29779e50	0.125290
$309$	0	0
$310$	−4.13157e48	−0.00349302
$311$	−3.10188e50	−0.245492	−0.122746	−	0.992438i	$-0.539170\pi$
$311$	−3.10188e50	−0.245492	−0.122746	+	0.992438i	$0.539170\pi$
$312$	0	0
$313$	9.82549e50	0.681860	0.340930	−	0.940089i	$-0.389258\pi$
$313$	9.82549e50	0.681860	0.340930	+	0.940089i	$0.389258\pi$
$314$	8.32028e49	0.0540854
$315$	0	0
$316$	−3.71423e50	−0.211975
$317$	−2.98911e51	−1.59892	−0.799462	−	0.600717i	$-0.794882\pi$
$317$	−2.98911e51	−1.59892	−0.799462	+	0.600717i	$0.794882\pi$
$318$	0	0
$319$	−4.25514e51	−2.00081
$320$	9.50784e50	0.419283
$321$	0	0
$322$	1.51832e49	0.00589276
$323$	1.75474e51	0.639089
$324$	0	0
$325$	3.83486e51	1.23067
$326$	−2.09482e50	−0.0631227
$327$	0	0
$328$	−2.20743e50	−0.0586777
$329$	−3.30724e50	−0.0825942
$330$	0	0
$331$	−3.54686e51	−0.782294	−0.391147	−	0.920328i	$-0.627922\pi$
$331$	−3.54686e51	−0.782294	−0.391147	+	0.920328i	$0.627922\pi$
$332$	−7.72398e51	−1.60144
$333$	0	0
$334$	1.54739e50	0.0283660
$335$	−2.47298e51	−0.426385
$336$	0	0
$337$	−3.30444e51	−0.504295	−0.252147	−	0.967689i	$-0.581137\pi$
$337$	−3.30444e51	−0.504295	−0.252147	+	0.967689i	$0.581137\pi$
$338$	4.83349e50	0.0694174
$339$	0	0
$340$	−2.02832e51	−0.258118
$341$	1.94387e51	0.232918
$342$	0	0
$343$	1.50888e51	0.160371
$344$	5.41112e49	0.00541800
$345$	0	0
$346$	1.00032e50	0.00889362
$347$	−1.33458e52	−1.11838	−0.559189	−	0.829040i	$-0.688887\pi$
$347$	−1.33458e52	−1.11838	−0.559189	+	0.829040i	$0.688887\pi$
$348$	0	0
$349$	5.90464e51	0.439817	0.219908	−	0.975521i	$-0.429424\pi$
$349$	5.90464e51	0.439817	0.219908	+	0.975521i	$0.429424\pi$
$350$	5.13810e49	0.00360918
$351$	0	0
$352$	4.09768e51	0.256102
$353$	2.48492e52	1.46531	0.732657	−	0.680598i	$-0.238280\pi$
$353$	2.48492e52	1.46531	0.732657	+	0.680598i	$0.238280\pi$
$354$	0	0
$355$	4.47589e51	0.235071
$356$	1.39804e52	0.693099
$357$	0	0
$358$	1.66649e51	0.0736549
$359$	2.54547e52	1.06251	0.531254	−	0.847213i	$-0.321721\pi$
$359$	2.54547e52	1.06251	0.531254	+	0.847213i	$0.321721\pi$
$360$	0	0
$361$	2.97723e51	0.110896
$362$	1.59860e51	0.0562619
$363$	0	0
$364$	−3.83993e51	−0.120710
$365$	2.08897e52	0.620765
$366$	0	0
$367$	8.12057e51	0.215741	0.107870	−	0.994165i	$-0.465597\pi$
$367$	8.12057e51	0.215741	0.107870	+	0.994165i	$0.465597\pi$
$368$	−5.26556e52	−1.32301
$369$	0	0
$370$	−8.48365e50	−0.0190742
$371$	−2.35528e51	−0.0501045
$372$	0	0
$373$	9.33073e51	0.177781	0.0888903	−	0.996041i	$-0.471668\pi$
$373$	9.33073e51	0.177781	0.0888903	+	0.996041i	$0.471668\pi$
$374$	−2.88158e51	−0.0519711
$375$	0	0
$376$	−6.95808e51	−0.112496
$377$	1.25902e53	1.92768
$378$	0	0
$379$	2.43584e52	0.334614	0.167307	−	0.985905i	$-0.446493\pi$
$379$	2.43584e52	0.334614	0.167307	+	0.985905i	$0.446493\pi$
$380$	−3.44742e52	−0.448674
$381$	0	0
$382$	6.88350e51	0.0804471
$383$	−5.83695e52	−0.646564	−0.323282	−	0.946303i	$-0.604786\pi$
$383$	−5.83695e52	−0.646564	−0.323282	+	0.946303i	$0.604786\pi$
$384$	0	0
$385$	5.38980e51	0.0536571
$386$	1.02163e51	0.00964397
$387$	0	0
$388$	−8.31585e52	−0.706084
$389$	−1.42025e53	−1.14393	−0.571964	−	0.820279i	$-0.693818\pi$
$389$	−1.42025e53	−1.14393	−0.571964	+	0.820279i	$0.693818\pi$
$390$	0	0
$391$	1.11647e53	0.809516
$392$	1.58211e52	0.108861
$393$	0	0
$394$	−1.44996e52	−0.0898844
$395$	−1.54254e52	−0.0907814
$396$	0	0
$397$	−2.90471e53	−1.54133	−0.770667	−	0.637238i	$-0.780077\pi$
$397$	−2.90471e53	−1.54133	−0.770667	+	0.637238i	$0.780077\pi$
$398$	−1.11424e52	−0.0561534
$399$	0	0
$400$	−1.78190e53	−0.810314
$401$	−2.01288e53	−0.869677	−0.434839	−	0.900508i	$-0.643195\pi$
$401$	−2.01288e53	−0.869677	−0.434839	+	0.900508i	$0.643195\pi$
$402$	0	0
$403$	−5.75157e52	−0.224405
$404$	−4.52861e53	−1.67937
$405$	0	0
$406$	1.68688e51	0.00565330
$407$	3.99149e53	1.27189
$408$	0	0
$409$	6.23107e53	1.79570	0.897852	−	0.440298i	$-0.145127\pi$
$409$	6.23107e53	1.79570	0.897852	+	0.440298i	$0.145127\pi$
$410$	−4.57688e51	−0.0125459
$411$	0	0
$412$	5.93841e52	0.147325
$413$	3.73580e52	0.0881876
$414$	0	0
$415$	−3.20782e53	−0.685841
$416$	−1.21243e53	−0.246742
$417$	0	0
$418$	−4.89765e52	−0.0903388
$419$	7.69430e53	1.35139	0.675696	−	0.737180i	$-0.263843\pi$
$419$	7.69430e53	1.35139	0.675696	+	0.737180i	$0.263843\pi$
$420$	0	0
$421$	3.14569e53	0.501110	0.250555	−	0.968102i	$-0.419387\pi$
$421$	3.14569e53	0.501110	0.250555	+	0.968102i	$0.419387\pi$
$422$	1.23959e52	0.0188093
$423$	0	0
$424$	−4.95525e52	−0.0682442
$425$	3.77822e53	0.495809
$426$	0	0
$427$	−4.81429e52	−0.0573800
$428$	−8.47417e53	−0.962719
$429$	0	0
$430$	1.12194e51	0.00115842
$431$	5.35565e53	0.527264	0.263632	−	0.964623i	$-0.415079\pi$
$431$	5.35565e53	0.527264	0.263632	+	0.964623i	$0.415079\pi$
$432$	0	0
$433$	1.35139e54	1.20999	0.604993	−	0.796231i	$-0.293176\pi$
$433$	1.35139e54	1.20999	0.604993	+	0.796231i	$0.293176\pi$
$434$	−7.70618e50	−0.000658112 0
$435$	0	0
$436$	−1.18710e54	−0.922601
$437$	1.89761e54	1.40714
$438$	0	0
$439$	2.63178e52	0.0177716	0.00888582	−	0.999961i	$-0.497172\pi$
$439$	2.63178e52	0.0177716	0.00888582	+	0.999961i	$0.497172\pi$
$440$	1.13396e53	0.0730831
$441$	0	0
$442$	8.52606e52	0.0500717
$443$	9.66050e53	0.541656	0.270828	−	0.962628i	$-0.412703\pi$
$443$	9.66050e53	0.541656	0.270828	+	0.962628i	$0.412703\pi$
$444$	0	0
$445$	5.80615e53	0.296830
$446$	−4.18593e52	−0.0204375
$447$	0	0
$448$	1.77340e53	0.0789962
$449$	5.56332e53	0.236747	0.118373	−	0.992969i	$-0.462232\pi$
$449$	5.56332e53	0.236747	0.118373	+	0.992969i	$0.462232\pi$
$450$	0	0
$451$	2.15339e54	0.836571
$452$	−4.37249e54	−1.62327
$453$	0	0
$454$	−1.51386e52	−0.00513383
$455$	−1.59474e53	−0.0516961
$456$	0	0
$457$	−2.92141e54	−0.865587	−0.432794	−	0.901493i	$-0.642472\pi$
$457$	−2.92141e54	−0.865587	−0.432794	+	0.901493i	$0.642472\pi$
$458$	8.82619e52	0.0250052
$459$	0	0
$460$	−2.19346e54	−0.568322
$461$	1.66774e54	0.413295	0.206648	−	0.978415i	$-0.433745\pi$
$461$	1.66774e54	0.413295	0.206648	+	0.978415i	$0.433745\pi$
$462$	0	0
$463$	−2.72429e54	−0.617793	−0.308896	−	0.951096i	$-0.599960\pi$
$463$	−2.72429e54	−0.617793	−0.308896	+	0.951096i	$0.599960\pi$
$464$	−5.85013e54	−1.26925
$465$	0	0
$466$	1.07316e53	0.0213183
$467$	−4.71337e54	−0.896057	−0.448028	−	0.894019i	$-0.647874\pi$
$467$	−4.71337e54	−0.896057	−0.448028	+	0.894019i	$0.647874\pi$
$468$	0	0
$469$	−4.61259e53	−0.0803344
$470$	−1.44269e53	−0.0240528
$471$	0	0
$472$	7.85973e53	0.120115
$473$	−5.27864e53	−0.0772447
$474$	0	0
$475$	6.42163e54	0.861839
$476$	−3.78321e53	−0.0486315
$477$	0	0
$478$	2.00859e53	0.0236930
$479$	6.42979e54	0.726639	0.363320	−	0.931665i	$-0.381643\pi$
$479$	6.42979e54	0.726639	0.363320	+	0.931665i	$0.381643\pi$
$480$	0	0
$481$	−1.18101e55	−1.22540
$482$	5.73950e53	0.0570703
$483$	0	0
$484$	−1.57208e55	−1.43596
$485$	−3.45362e54	−0.302391
$486$	0	0
$487$	2.20621e55	1.77543	0.887714	−	0.460396i	$-0.152292\pi$
$487$	2.20621e55	1.77543	0.887714	+	0.460396i	$0.152292\pi$
$488$	−1.01288e54	−0.0781538
$489$	0	0
$490$	3.28034e53	0.0232755
$491$	2.26714e54	0.154279	0.0771395	−	0.997020i	$-0.475421\pi$
$491$	2.26714e54	0.154279	0.0771395	+	0.997020i	$0.475421\pi$
$492$	0	0
$493$	1.24042e55	0.776619
$494$	1.44913e54	0.0870370
$495$	0	0
$496$	2.67251e54	0.147756
$497$	8.34840e53	0.0442892
$498$	0	0
$499$	−2.08851e54	−0.102041	−0.0510205	−	0.998698i	$-0.516247\pi$
$499$	−2.08851e54	−0.102041	−0.0510205	+	0.998698i	$0.516247\pi$
$500$	−1.65006e55	−0.773774
$501$	0	0
$502$	8.98182e52	0.00388095
$503$	4.18071e55	1.73423	0.867115	−	0.498107i	$-0.165971\pi$
$503$	4.18071e55	1.73423	0.867115	+	0.498107i	$0.165971\pi$
$504$	0	0
$505$	−1.88076e55	−0.719217
$506$	−3.11619e54	−0.114429
$507$	0	0
$508$	1.72738e55	0.585033
$509$	4.54501e55	1.47850	0.739248	−	0.673433i	$-0.235181\pi$
$509$	4.54501e55	1.47850	0.739248	+	0.673433i	$0.235181\pi$
$510$	0	0
$511$	3.89632e54	0.116957
$512$	9.39886e54	0.271045
$513$	0	0
$514$	−1.62055e54	−0.0431437
$515$	2.46626e54	0.0630943
$516$	0	0
$517$	6.78774e55	1.60387
$518$	−1.58236e53	−0.00359374
$519$	0	0
$520$	−3.35517e54	−0.0704120
$521$	−4.52665e55	−0.913278	−0.456639	−	0.889652i	$-0.650947\pi$
$521$	−4.52665e55	−0.913278	−0.456639	+	0.889652i	$0.650947\pi$
$522$	0	0
$523$	−1.00124e56	−1.86748	−0.933738	−	0.357957i	$-0.883473\pi$
$523$	−1.00124e56	−1.86748	−0.933738	+	0.357957i	$0.883473\pi$
$524$	1.91956e55	0.344278
$525$	0	0
$526$	−3.21922e54	−0.0534002
$527$	−5.66662e54	−0.0904078
$528$	0	0
$529$	5.29981e55	0.782383
$530$	−1.02742e54	−0.0145913
$531$	0	0
$532$	−6.43011e54	−0.0845337
$533$	−6.37148e55	−0.805996
$534$	0	0
$535$	−3.51937e55	−0.412299
$536$	−9.70440e54	−0.109418
$537$	0	0
$538$	6.01840e54	0.0628701
$539$	−1.54338e56	−1.55204
$540$	0	0
$541$	1.94080e55	0.180899	0.0904495	−	0.995901i	$-0.471170\pi$
$541$	1.94080e55	0.180899	0.0904495	+	0.995901i	$0.471170\pi$
$542$	−2.17014e54	−0.0194761
$543$	0	0
$544$	−1.19452e55	−0.0994069
$545$	−4.93009e55	−0.395118
$546$	0	0
$547$	−1.89248e56	−1.40699	−0.703495	−	0.710700i	$-0.748378\pi$
$547$	−1.89248e56	−1.40699	−0.703495	+	0.710700i	$0.748378\pi$
$548$	−2.86296e55	−0.205028
$549$	0	0
$550$	−1.05454e55	−0.0700853
$551$	2.10828e56	1.34996
$552$	0	0
$553$	−2.87714e54	−0.0171039
$554$	1.07977e55	0.0618560
$555$	0	0
$556$	1.63931e56	0.872222
$557$	4.31584e55	0.221327	0.110663	−	0.993858i	$-0.464702\pi$
$557$	4.31584e55	0.221327	0.110663	+	0.993858i	$0.464702\pi$
$558$	0	0
$559$	1.56185e55	0.0744215
$560$	7.41011e54	0.0340385
$561$	0	0
$562$	−1.01892e54	−0.00435055
$563$	−3.50637e56	−1.44356	−0.721781	−	0.692121i	$-0.756676\pi$
$563$	−3.50637e56	−1.44356	−0.721781	+	0.692121i	$0.756676\pi$
$564$	0	0
$565$	−1.81592e56	−0.695191
$566$	−8.11324e54	−0.0299542
$567$	0	0
$568$	1.75642e55	0.0603235
$569$	−3.92278e56	−1.29955	−0.649775	−	0.760127i	$-0.725137\pi$
$569$	−3.92278e56	−1.29955	−0.649775	+	0.760127i	$0.725137\pi$
$570$	0	0
$571$	3.12164e56	0.962370	0.481185	−	0.876619i	$-0.340206\pi$
$571$	3.12164e56	0.962370	0.481185	+	0.876619i	$0.340206\pi$
$572$	7.88102e56	2.34403
$573$	0	0
$574$	−8.53677e53	−0.00236374
$575$	4.08584e56	1.09167
$576$	0	0
$577$	5.15710e55	0.128322	0.0641611	−	0.997940i	$-0.479563\pi$
$577$	5.15710e55	0.128322	0.0641611	+	0.997940i	$0.479563\pi$
$578$	−1.44473e55	−0.0346948
$579$	0	0
$580$	−2.43698e56	−0.545227
$581$	−5.98320e55	−0.129218
$582$	0	0
$583$	4.83394e56	0.972962
$584$	8.19746e55	0.159300
$585$	0	0
$586$	2.97099e55	0.0538270
$587$	1.62999e56	0.285170	0.142585	−	0.989783i	$-0.454459\pi$
$587$	1.62999e56	0.285170	0.142585	+	0.989783i	$0.454459\pi$
$588$	0	0
$589$	−9.63123e55	−0.157151
$590$	1.62963e55	0.0256817
$591$	0	0
$592$	5.48766e56	0.806848
$593$	6.76525e56	0.960866	0.480433	−	0.877031i	$-0.340480\pi$
$593$	6.76525e56	0.960866	0.480433	+	0.877031i	$0.340480\pi$
$594$	0	0
$595$	−1.57119e55	−0.0208272
$596$	7.47868e56	0.957804
$597$	0	0
$598$	9.22024e55	0.110247
$599$	−8.22842e56	−0.950751	−0.475376	−	0.879783i	$-0.657688\pi$
$599$	−8.22842e56	−0.950751	−0.475376	+	0.879783i	$0.657688\pi$
$600$	0	0
$601$	−1.40310e57	−1.51412	−0.757062	−	0.653343i	$-0.773366\pi$
$601$	−1.40310e57	−1.51412	−0.757062	+	0.653343i	$0.773366\pi$
$602$	2.09264e53	0.000218256 0
$603$	0	0
$604$	1.06699e57	1.03969
$605$	−6.52892e56	−0.614973
$606$	0	0
$607$	−1.85452e57	−1.63254	−0.816271	−	0.577669i	$-0.803962\pi$
$607$	−1.85452e57	−1.63254	−0.816271	+	0.577669i	$0.803962\pi$
$608$	−2.03026e56	−0.172794
$609$	0	0
$610$	−2.10010e55	−0.0167100
$611$	−2.00837e57	−1.54525
$612$	0	0
$613$	1.52593e57	1.09798	0.548992	−	0.835828i	$-0.315012\pi$
$613$	1.52593e57	1.09798	0.548992	+	0.835828i	$0.315012\pi$
$614$	1.06113e56	0.0738443
$615$	0	0
$616$	2.11505e55	0.0137694
$617$	−2.09012e56	−0.131621	−0.0658105	−	0.997832i	$-0.520963\pi$
$617$	−2.09012e56	−0.131621	−0.0658105	+	0.997832i	$0.520963\pi$
$618$	0	0
$619$	−5.03746e56	−0.296861	−0.148431	−	0.988923i	$-0.547422\pi$
$619$	−5.03746e56	−0.296861	−0.148431	+	0.988923i	$0.547422\pi$
$620$	1.11328e56	0.0634710
$621$	0	0
$622$	−2.52381e55	−0.0134696
$623$	1.08296e56	0.0559251
$624$	0	0
$625$	1.00567e57	0.486311
$626$	7.99438e55	0.0374120
$627$	0	0
$628$	−2.24196e57	−0.982776
$629$	−1.16357e57	−0.493688
$630$	0	0
$631$	−2.05980e57	−0.818887	−0.409444	−	0.912335i	$-0.634277\pi$
$631$	−2.05980e57	−0.818887	−0.409444	+	0.912335i	$0.634277\pi$
$632$	−6.05320e55	−0.0232962
$633$	0	0
$634$	−2.43205e56	−0.0877291
$635$	7.17389e56	0.250549
$636$	0	0
$637$	4.56657e57	1.49531
$638$	−3.46214e56	−0.109779
$639$	0	0
$640$	3.12747e56	0.0930046
$641$	−4.32782e57	−1.24646	−0.623232	−	0.782037i	$-0.714181\pi$
$641$	−4.32782e57	−1.24646	−0.623232	+	0.782037i	$0.714181\pi$
$642$	0	0
$643$	−2.48467e57	−0.671341	−0.335670	−	0.941980i	$-0.608963\pi$
$643$	−2.48467e57	−0.671341	−0.335670	+	0.941980i	$0.608963\pi$
$644$	−4.09123e56	−0.107076
$645$	0	0
$646$	1.42772e56	0.0350653
$647$	4.23499e57	1.00766	0.503831	−	0.863802i	$-0.331923\pi$
$647$	4.23499e57	1.00766	0.503831	+	0.863802i	$0.331923\pi$
$648$	0	0
$649$	−7.66730e57	−1.71248
$650$	3.12019e56	0.0675238
$651$	0	0
$652$	5.64464e57	1.14699
$653$	1.80067e57	0.354580	0.177290	−	0.984159i	$-0.443267\pi$
$653$	1.80067e57	0.354580	0.177290	+	0.984159i	$0.443267\pi$
$654$	0	0
$655$	7.97203e56	0.147442
$656$	2.96056e57	0.530695
$657$	0	0
$658$	−2.69089e55	−0.00453175
$659$	6.74103e57	1.10046	0.550231	−	0.835012i	$-0.314540\pi$
$659$	6.74103e57	1.10046	0.550231	+	0.835012i	$0.314540\pi$
$660$	0	0
$661$	9.42263e57	1.44558	0.722790	−	0.691068i	$-0.242859\pi$
$661$	9.42263e57	1.44558	0.722790	+	0.691068i	$0.242859\pi$
$662$	−2.88586e56	−0.0429226
$663$	0	0
$664$	−1.25880e57	−0.176000
$665$	−2.67046e56	−0.0362028
$666$	0	0
$667$	1.34142e58	1.70995
$668$	−4.16957e57	−0.515434
$669$	0	0
$670$	−2.01211e56	−0.0233947
$671$	9.88079e57	1.11424
$672$	0	0
$673$	−7.22539e57	−0.766571	−0.383285	−	0.923630i	$-0.625207\pi$
$673$	−7.22539e57	−0.766571	−0.383285	+	0.923630i	$0.625207\pi$
$674$	−2.68861e56	−0.0276694
$675$	0	0
$676$	−1.30242e58	−1.26137
$677$	9.31845e57	0.875540	0.437770	−	0.899087i	$-0.355768\pi$
$677$	9.31845e57	0.875540	0.437770	+	0.899087i	$0.355768\pi$
$678$	0	0
$679$	−6.44167e56	−0.0569729
$680$	−3.30562e56	−0.0283674
$681$	0	0
$682$	1.58161e56	0.0127796
$683$	−1.54469e58	−1.21121	−0.605603	−	0.795767i	$-0.707068\pi$
$683$	−1.54469e58	−1.21121	−0.605603	+	0.795767i	$0.707068\pi$
$684$	0	0
$685$	−1.18900e57	−0.0878064
$686$	1.22768e56	0.00879915
$687$	0	0
$688$	−7.25728e56	−0.0490017
$689$	−1.43028e58	−0.937401
$690$	0	0
$691$	1.40721e58	0.869078	0.434539	−	0.900653i	$-0.356911\pi$
$691$	1.40721e58	0.869078	0.434539	+	0.900653i	$0.356911\pi$
$692$	−2.69543e57	−0.161604
$693$	0	0
$694$	−1.08586e57	−0.0613627
$695$	6.80814e57	0.373542
$696$	0	0
$697$	−6.27738e57	−0.324718
$698$	4.80423e56	0.0241317
$699$	0	0
$700$	−1.38450e57	−0.0655817
$701$	2.16291e58	0.994991	0.497495	−	0.867467i	$-0.334253\pi$
$701$	2.16291e58	0.994991	0.497495	+	0.867467i	$0.334253\pi$
$702$	0	0
$703$	−1.97765e58	−0.858153
$704$	−3.63969e58	−1.53400
$705$	0	0
$706$	2.02182e57	0.0803982
$707$	−3.50798e57	−0.135506
$708$	0	0
$709$	−1.27581e58	−0.465090	−0.232545	−	0.972586i	$-0.574705\pi$
$709$	−1.27581e58	−0.465090	−0.232545	+	0.972586i	$0.574705\pi$
$710$	3.64175e56	0.0128978
$711$	0	0
$712$	2.27843e57	0.0761722
$713$	−6.12798e57	−0.199059
$714$	0	0
$715$	3.27303e58	1.00387
$716$	−4.49049e58	−1.33837
$717$	0	0
$718$	2.07109e57	0.0582973
$719$	−2.41677e58	−0.661138	−0.330569	−	0.943782i	$-0.607241\pi$
$719$	−2.41677e58	−0.661138	−0.330569	+	0.943782i	$0.607241\pi$
$720$	0	0
$721$	4.60005e56	0.0118875
$722$	2.42238e56	0.00608458
$723$	0	0
$724$	−4.30754e58	−1.02232
$725$	4.53944e58	1.04730
$726$	0	0
$727$	−4.92924e58	−1.07479	−0.537396	−	0.843330i	$-0.680592\pi$
$727$	−4.92924e58	−1.07479	−0.537396	+	0.843330i	$0.680592\pi$
$728$	−6.25805e56	−0.0132662
$729$	0	0
$730$	1.69966e57	0.0340599
$731$	1.53878e57	0.0299828
$732$	0	0
$733$	4.81159e58	0.886456	0.443228	−	0.896409i	$-0.353833\pi$
$733$	4.81159e58	0.886456	0.443228	+	0.896409i	$0.353833\pi$
$734$	6.60720e56	0.0118372
$735$	0	0
$736$	−1.29178e58	−0.218873
$737$	9.46682e58	1.55999
$738$	0	0
$739$	9.13074e58	1.42330	0.711648	−	0.702537i	$-0.247949\pi$
$739$	9.13074e58	1.42330	0.711648	+	0.702537i	$0.247949\pi$
$740$	2.28598e58	0.346595
$741$	0	0
$742$	−1.91634e56	−0.00274911
$743$	−1.50391e57	−0.0209870	−0.0104935	−	0.999945i	$-0.503340\pi$
$743$	−1.50391e57	−0.0209870	−0.0104935	+	0.999945i	$0.503340\pi$
$744$	0	0
$745$	3.10594e58	0.410194
$746$	7.59183e56	0.00975439
$747$	0	0
$748$	7.76461e58	0.944358
$749$	−6.56431e57	−0.0776804
$750$	0	0
$751$	−1.25195e59	−1.40272	−0.701358	−	0.712809i	$-0.747423\pi$
$751$	−1.25195e59	−1.40272	−0.701358	+	0.712809i	$0.747423\pi$
$752$	9.33204e58	1.01745
$753$	0	0
$754$	1.02438e58	0.105767
$755$	4.43126e58	0.445261
$756$	0	0
$757$	1.29607e58	0.123357	0.0616784	−	0.998096i	$-0.480355\pi$
$757$	1.29607e58	0.123357	0.0616784	+	0.998096i	$0.480355\pi$
$758$	1.98189e57	0.0183595
$759$	0	0
$760$	−5.61837e57	−0.0493096
$761$	−6.14300e58	−0.524801	−0.262401	−	0.964959i	$-0.584514\pi$
$761$	−6.14300e58	−0.524801	−0.262401	+	0.964959i	$0.584514\pi$
$762$	0	0
$763$	−9.19557e57	−0.0744433
$764$	−1.85481e59	−1.46179
$765$	0	0
$766$	−4.74916e57	−0.0354754
$767$	2.26862e59	1.64989
$768$	0	0
$769$	1.38280e59	0.953388	0.476694	−	0.879069i	$-0.341835\pi$
$769$	1.38280e59	0.953388	0.476694	+	0.879069i	$0.341835\pi$
$770$	4.38534e56	0.00294404
$771$	0	0
$772$	−2.75287e58	−0.175239
$773$	−1.19232e59	−0.739119	−0.369560	−	0.929207i	$-0.620491\pi$
$773$	−1.19232e59	−0.739119	−0.369560	+	0.929207i	$0.620491\pi$
$774$	0	0
$775$	−2.07375e58	−0.121919
$776$	−1.35526e58	−0.0775992
$777$	0	0
$778$	−1.15557e58	−0.0627646
$779$	−1.06693e59	−0.564440
$780$	0	0
$781$	−1.71342e59	−0.860036
$782$	9.08405e57	0.0444162
$783$	0	0
$784$	−2.12189e59	−0.984565
$785$	−9.31098e58	−0.420889
$786$	0	0
$787$	2.56981e59	1.10260	0.551301	−	0.834307i	$-0.314132\pi$
$787$	2.56981e59	1.10260	0.551301	+	0.834307i	$0.314132\pi$
$788$	3.90703e59	1.63327
$789$	0	0
$790$	−1.25507e57	−0.00498096
$791$	−3.38704e58	−0.130979
$792$	0	0
$793$	−2.92355e59	−1.07352
$794$	−2.36338e58	−0.0845693
$795$	0	0
$796$	3.00240e59	1.02035
$797$	−5.39123e59	−1.78563	−0.892816	−	0.450421i	$-0.851274\pi$
$797$	−5.39123e59	−1.78563	−0.892816	+	0.450421i	$0.851274\pi$
$798$	0	0
$799$	−1.97870e59	−0.622547
$800$	−4.37145e58	−0.134054
$801$	0	0
$802$	−1.63775e58	−0.0477171
$803$	−7.99677e59	−2.27115
$804$	0	0
$805$	−1.69911e58	−0.0458571
$806$	−4.67969e57	−0.0123126
$807$	0	0
$808$	−7.38042e58	−0.184565
$809$	4.68209e59	1.14155	0.570775	−	0.821106i	$-0.306643\pi$
$809$	4.68209e59	1.14155	0.570775	+	0.821106i	$0.306643\pi$
$810$	0	0
$811$	5.03719e58	0.116751	0.0583756	−	0.998295i	$-0.481408\pi$
$811$	5.03719e58	0.116751	0.0583756	+	0.998295i	$0.481408\pi$
$812$	−4.54543e58	−0.102725
$813$	0	0
$814$	3.24763e58	0.0697856
$815$	2.34425e59	0.491217
$816$	0	0
$817$	2.61539e58	0.0521175
$818$	5.06983e58	0.0985259
$819$	0	0
$820$	1.23327e59	0.227969
$821$	7.92919e59	1.42953	0.714766	−	0.699363i	$-0.246533\pi$
$821$	7.92919e59	1.42953	0.714766	+	0.699363i	$0.246533\pi$
$822$	0	0
$823$	5.91534e58	0.101457	0.0507287	−	0.998712i	$-0.483846\pi$
$823$	5.91534e58	0.101457	0.0507287	+	0.998712i	$0.483846\pi$
$824$	9.67802e57	0.0161912
$825$	0	0
$826$	3.03958e57	0.00483864
$827$	−9.18303e59	−1.42601	−0.713006	−	0.701158i	$-0.752667\pi$
$827$	−9.18303e59	−1.42601	−0.713006	+	0.701158i	$0.752667\pi$
$828$	0	0
$829$	−6.10924e59	−0.902858	−0.451429	−	0.892307i	$-0.649086\pi$
$829$	−6.10924e59	−0.902858	−0.451429	+	0.892307i	$0.649086\pi$
$830$	−2.61000e58	−0.0376304
$831$	0	0
$832$	1.07692e60	1.47793
$833$	4.49912e59	0.602428
$834$	0	0
$835$	−1.73164e59	−0.220743
$836$	1.31971e60	1.64153
$837$	0	0
$838$	6.26037e58	0.0741476
$839$	1.07495e60	1.24242	0.621210	−	0.783644i	$-0.286641\pi$
$839$	1.07495e60	1.24242	0.621210	+	0.783644i	$0.286641\pi$
$840$	0	0
$841$	5.81851e59	0.640463
$842$	2.55945e58	0.0274947
$843$	0	0
$844$	−3.34016e59	−0.341780
$845$	−5.40902e59	−0.540202
$846$	0	0
$847$	−1.21777e59	−0.115866
$848$	6.64589e59	0.617217
$849$	0	0
$850$	3.07410e58	0.0272038
$851$	−1.25830e60	−1.08700
$852$	0	0
$853$	−7.04560e59	−0.580047	−0.290023	−	0.957020i	$-0.593663\pi$
$853$	−7.04560e59	−0.580047	−0.290023	+	0.957020i	$0.593663\pi$
$854$	−3.91709e57	−0.00314830
$855$	0	0
$856$	−1.38106e59	−0.105804
$857$	−1.18884e60	−0.889234	−0.444617	−	0.895721i	$-0.646660\pi$
$857$	−1.18884e60	−0.889234	−0.444617	+	0.895721i	$0.646660\pi$
$858$	0	0
$859$	2.54870e60	1.81744	0.908718	−	0.417410i	$-0.137062\pi$
$859$	2.54870e60	1.81744	0.908718	+	0.417410i	$0.137062\pi$
$860$	−3.02315e58	−0.0210495
$861$	0	0
$862$	4.35756e58	0.0289297
$863$	1.01594e60	0.658640	0.329320	−	0.944218i	$-0.393181\pi$
$863$	1.01594e60	0.658640	0.329320	+	0.944218i	$0.393181\pi$
$864$	0	0
$865$	−1.11943e59	−0.0692095
$866$	1.09954e59	0.0663890
$867$	0	0
$868$	2.07649e58	0.0119584
$869$	5.90501e59	0.332135
$870$	0	0
$871$	−2.80106e60	−1.50297
$872$	−1.93465e59	−0.101395
$873$	0	0
$874$	1.54396e59	0.0772064
$875$	−1.27818e59	−0.0624347
$876$	0	0
$877$	−3.07649e59	−0.143405	−0.0717023	−	0.997426i	$-0.522843\pi$
$877$	−3.07649e59	−0.143405	−0.0717023	+	0.997426i	$0.522843\pi$
$878$	2.14132e57	0.000975087 0
$879$	0	0
$880$	−1.52084e60	−0.660981
$881$	−1.76559e60	−0.749694	−0.374847	−	0.927087i	$-0.622305\pi$
$881$	−1.76559e60	−0.749694	−0.374847	+	0.927087i	$0.622305\pi$
$882$	0	0
$883$	1.02366e60	0.414918	0.207459	−	0.978244i	$-0.433481\pi$
$883$	1.02366e60	0.414918	0.207459	+	0.978244i	$0.433481\pi$
$884$	−2.29741e60	−0.909843
$885$	0	0
$886$	7.86015e58	0.0297193
$887$	4.52674e59	0.167244	0.0836221	−	0.996498i	$-0.473351\pi$
$887$	4.52674e59	0.167244	0.0836221	+	0.996498i	$0.473351\pi$
$888$	0	0
$889$	1.33807e59	0.0472055
$890$	4.72410e58	0.0162864
$891$	0	0
$892$	1.12793e60	0.371366
$893$	−3.36309e60	−1.08214
$894$	0	0
$895$	−1.86493e60	−0.573178
$896$	5.83335e58	0.0175228
$897$	0	0
$898$	4.52652e58	0.0129897
$899$	−6.80829e59	−0.190970
$900$	0	0
$901$	−1.40915e60	−0.377658
$902$	1.75208e59	0.0459007
$903$	0	0
$904$	−7.12599e59	−0.178399
$905$	−1.78895e60	−0.437826
$906$	0	0
$907$	−6.39985e60	−1.49699	−0.748497	−	0.663138i	$-0.769224\pi$
$907$	−6.39985e60	−1.49699	−0.748497	+	0.663138i	$0.769224\pi$
$908$	4.07921e59	0.0932860
$909$	0	0
$910$	−1.29754e58	−0.00283644
$911$	3.60826e60	0.771208	0.385604	−	0.922664i	$-0.373993\pi$
$911$	3.60826e60	0.771208	0.385604	+	0.922664i	$0.373993\pi$
$912$	0	0
$913$	1.22798e61	2.50924
$914$	−2.37697e59	−0.0474927
$915$	0	0
$916$	−2.37828e60	−0.454366
$917$	1.48694e59	0.0277793
$918$	0	0
$919$	6.99835e60	1.25034	0.625170	−	0.780489i	$-0.285030\pi$
$919$	6.99835e60	1.25034	0.625170	+	0.780489i	$0.285030\pi$
$920$	−3.57475e59	−0.0624591
$921$	0	0
$922$	1.35694e59	0.0226765
$923$	5.06969e60	0.828603
$924$	0	0
$925$	−4.25817e60	−0.665760
$926$	−2.21658e59	−0.0338968
$927$	0	0
$928$	−1.43519e60	−0.209979
$929$	1.28627e61	1.84081	0.920406	−	0.390963i	$-0.127858\pi$
$929$	1.28627e61	1.84081	0.920406	+	0.390963i	$0.127858\pi$
$930$	0	0
$931$	7.64690e60	1.04717
$932$	−2.89170e60	−0.387371
$933$	0	0
$934$	−3.83497e59	−0.0491645
$935$	3.22469e60	0.404436
$936$	0	0
$937$	−1.05021e61	−1.26071	−0.630354	−	0.776308i	$-0.717090\pi$
$937$	−1.05021e61	−1.26071	−0.630354	+	0.776308i	$0.717090\pi$
$938$	−3.75297e58	−0.00440775
$939$	0	0
$940$	3.88743e60	0.437060
$941$	7.41023e60	0.815163	0.407581	−	0.913169i	$-0.366372\pi$
$941$	7.41023e60	0.815163	0.407581	+	0.913169i	$0.366372\pi$
$942$	0	0
$943$	−6.78847e60	−0.714960
$944$	−1.05413e61	−1.08635
$945$	0	0
$946$	−4.29490e58	−0.00423823
$947$	−5.73646e60	−0.553949	−0.276974	−	0.960877i	$-0.589332\pi$
$947$	−5.73646e60	−0.553949	−0.276974	+	0.960877i	$0.589332\pi$
$948$	0	0
$949$	2.36610e61	2.18814
$950$	5.22488e59	0.0472870
$951$	0	0
$952$	−6.16562e58	−0.00534465
$953$	1.08849e61	0.923467	0.461733	−	0.887019i	$-0.347228\pi$
$953$	1.08849e61	0.923467	0.461733	+	0.887019i	$0.347228\pi$
$954$	0	0
$955$	−7.70313e60	−0.626034
$956$	−5.41230e60	−0.430521
$957$	0	0
$958$	5.23152e59	0.0398690
$959$	−2.21772e59	−0.0165434
$960$	0	0
$961$	−1.36794e61	−0.977769
$962$	−9.60914e59	−0.0672350
$963$	0	0
$964$	−1.54655e61	−1.03701
$965$	−1.14328e60	−0.0750487
$966$	0	0
$967$	2.37432e61	1.49381	0.746906	−	0.664930i	$-0.231539\pi$
$967$	2.37432e61	1.49381	0.746906	+	0.664930i	$0.231539\pi$
$968$	−2.56206e60	−0.157814
$969$	0	0
$970$	−2.80999e59	−0.0165915
$971$	1.71671e61	0.992436	0.496218	−	0.868198i	$-0.334722\pi$
$971$	1.71671e61	0.992436	0.496218	+	0.868198i	$0.334722\pi$
$972$	0	0
$973$	1.26985e60	0.0703783
$974$	1.79505e60	0.0974134
$975$	0	0
$976$	1.35845e61	0.706842
$977$	−3.29474e61	−1.67873	−0.839367	−	0.543565i	$-0.817074\pi$
$977$	−3.29474e61	−1.67873	−0.839367	+	0.543565i	$0.817074\pi$
$978$	0	0
$979$	−2.22265e61	−1.08599
$980$	−8.83912e60	−0.422936
$981$	0	0
$982$	1.84463e59	0.00846492
$983$	−3.50912e61	−1.57707	−0.788535	−	0.614990i	$-0.789160\pi$
$983$	−3.50912e61	−1.57707	−0.788535	+	0.614990i	$0.789160\pi$
$984$	0	0
$985$	1.62261e61	0.699474
$986$	1.00925e60	0.0426112
$987$	0	0
$988$	−3.90477e61	−1.58153
$989$	1.66407e60	0.0660157
$990$	0	0
$991$	−1.41075e61	−0.536959	−0.268480	−	0.963285i	$-0.586521\pi$
$991$	−1.41075e61	−0.536959	−0.268480	+	0.963285i	$0.586521\pi$
$992$	6.55635e59	0.0244441
$993$	0	0
$994$	6.79257e58	0.00243004
$995$	1.24691e61	0.436982
$996$	0	0
$997$	−1.88767e61	−0.634857	−0.317429	−	0.948282i	$-0.602819\pi$
$997$	−1.88767e61	−0.634857	−0.317429	+	0.948282i	$0.602819\pi$
$998$	−1.69929e59	−0.00559874
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.42.a.b.1.2		3
3.2	odd	2		1.42.a.a.1.2	✓	3
12.11	even	2		16.42.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.42.a.a.1.2	✓	3	3.2	odd	2
9.42.a.b.1.2		3	1.1	even	1	trivial
16.42.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:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+81363.7 q^{2} -2.19240e12 q^{4} -9.10518e13 q^{5} -1.69829e16 q^{7} -3.57303e17 q^{8} +O(q^{10})\)	\(q+81363.7 q^{2} -2.19240e12 q^{4} -9.10518e13 q^{5} -1.69829e16 q^{7} -3.57303e17 q^{8} -7.40831e18 q^{10} +3.48555e21 q^{11} -1.03131e23 q^{13} -1.38179e21 q^{14} +4.79207e24 q^{16} -1.01608e25 q^{17} -1.72697e26 q^{19} +1.99622e26 q^{20} +2.83598e26 q^{22} -1.09881e28 q^{23} -3.71843e28 q^{25} -8.39114e27 q^{26} +3.72334e28 q^{28} -1.22079e30 q^{29} +5.57694e29 q^{31} +1.17562e30 q^{32} -8.26720e29 q^{34} +1.54633e30 q^{35} +1.14515e32 q^{37} -1.40513e31 q^{38} +3.25331e31 q^{40} +6.17804e32 q^{41} -1.51443e32 q^{43} -7.64174e33 q^{44} -8.94030e32 q^{46} +1.94739e34 q^{47} -4.42792e34 q^{49} -3.02545e33 q^{50} +2.26105e35 q^{52} +1.38685e35 q^{53} -3.17366e35 q^{55} +6.06805e33 q^{56} -9.93283e34 q^{58} -2.19974e36 q^{59} +2.83478e36 q^{61} +4.53761e34 q^{62} -1.04422e37 q^{64} +9.39028e36 q^{65} +2.71602e37 q^{67} +2.22766e37 q^{68} +1.25815e35 q^{70} -4.91576e37 q^{71} -2.29426e38 q^{73} +9.31739e36 q^{74} +3.78622e38 q^{76} -5.91949e37 q^{77} +1.69414e38 q^{79} -4.36327e38 q^{80} +5.02668e37 q^{82} +3.52307e39 q^{83} +9.25158e38 q^{85} -1.23220e37 q^{86} -1.24540e39 q^{88} -6.37675e39 q^{89} +1.75147e39 q^{91} +2.40903e40 q^{92} +1.58447e39 q^{94} +1.57244e40 q^{95} +3.79303e40 q^{97} -3.60272e39 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 344688 q^{2} + 6271704903936 q^{4} + 212302350281550 q^{5} + 57\!\cdots\!92 q^{7}+ \cdots + 35\!\cdots\!20 q^{8}+O(q^{10}) \) 3 * q + 344688 * q^2 + 6271704903936 * q^4 + 212302350281550 * q^5 + 57878416258239192 * q^7 + 3555831711183237120 * q^8	\( 3 q + 344688 q^{2} + 6271704903936 q^{4} + 212302350281550 q^{5} + 57\!\cdots\!92 q^{7}+ \cdots + 38\!\cdots\!16 q^{98}+O(q^{100}) \) 3 * q + 344688 * q^2 + 6271704903936 * q^4 + 212302350281550 * q^5 + 57878416258239192 * q^7 + 3555831711183237120 * q^8 - 911610678410074173600 * q^10 + 3064080929502798535164 * q^11 - 98515763053518962936694 * q^13 + 663773359066872932212608 * q^14 + 13217913642093764057038848 * q^16 - 35582277130790298867301302 * q^17 - 233456308095243376865478180 * q^19 + 1234817679506740618000857600 * q^20 + 10093688647003206881596695744 * q^22 - 2812708670812770779627026056 * q^23 - 12630087813294771903109831875 * q^25 + 445502868787427067716672131104 * q^26 + 526606706694181610802628184064 * q^28 + 12736322664295346653179017670 * q^29 - 55977552834365071134409017504 * q^31 + 14842037794660482009412112744448 * q^32 - 42547131667082319398961759011808 * q^34 - 35330944415319146254058128592400 * q^35 + 4945769903781582545269841455122 * q^37 - 384288369224763756133358504473920 * q^38 - 1326138456985596139721995183104000 * q^40 + 3123151500646359746292805811918274 * q^41 + 1491980858362212236675453498061156 * q^43 - 6827579920847638909574240093432832 * q^44 + 34089155258950859800971794327519616 * q^46 + 63038106682044077762675687404413168 * q^47 - 97136113131667199274890334287198229 * q^49 - 286202165340727366859498513545830000 * q^50 + 364999309722184195149034320029732352 * q^52 - 79896749344137562310547533743021506 * q^53 - 1107430856215374719020572615529578600 * q^55 + 1507500925934438536531619079138017280 * q^56 + 1060511497310363735425511566792954080 * q^58 - 192512048683375799719343226678403860 * q^59 + 8740556115036354715092732710435455386 * q^61 + 12005332293025961804297174175449366016 * q^62 - 28669651485797320669854651690478731264 * q^64 - 23272939413910136331858458170260680700 * q^65 + 11266872945514675454702655007279407852 * q^67 - 95413181576279049358373233907724317184 * q^68 + 59324379124057015483688060122385068800 * q^70 + 140970915469820223119231433051520161384 * q^71 + 45825493210252135256288871746499029406 * q^73 + 255935787825178849200244145003411599008 * q^74 + 26100578647791289060370838422069130240 * q^76 + 429017620126390531124795910645506217696 * q^77 - 520184835554750143118446358634240850320 * q^79 - 715918562852781559130521454428746547200 * q^80 - 579816777788457983576303882284492608096 * q^82 + 619777491338381742927488037142663372644 * q^83 - 106299433069331216483654652405294143100 * q^85 + 4751113477095326918262488958359640807744 * q^86 + 18329036816788093472347699011602935234560 * q^88 + 142389067128374093799211866144944441010 * q^89 + 25080596935320871627133801126628392473296 * q^91 + 67617289414955565381239604024555789723648 * q^92 - 53008068396962431152763933809330449227008 * q^94 + 33170437179755379504247502944935502503000 * q^95 + 116011691364103339137369463947331771078182 * q^97 + 38494567059701712876195969460820421029616 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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