LMFDB - Embedded newform 9.42.a.b.1.1

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			1.1
Root			$52412.2$ 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)

$f(q)$	$=$	$q-2.40087e6 q^{2} +3.56518e12 q^{4} +3.38080e14 q^{5} -9.19453e16 q^{7} -3.27996e18 q^{8} +O(q^{10})$	\(q-2.40087e6 q^{2} +3.56518e12 q^{4} +3.38080e14 q^{5} -9.19453e16 q^{7} -3.27996e18 q^{8} -8.11687e20 q^{10} -2.15850e21 q^{11} -8.71848e22 q^{13} +2.20749e23 q^{14} +3.48699e22 q^{16} -5.13467e24 q^{17} +4.11372e25 q^{19} +1.20531e27 q^{20} +5.18229e27 q^{22} -2.60656e27 q^{23} +6.88231e28 q^{25} +2.09320e29 q^{26} -3.27801e29 q^{28} +4.19842e29 q^{29} -2.68405e30 q^{31} +7.12899e30 q^{32} +1.23277e31 q^{34} -3.10848e31 q^{35} -1.06323e32 q^{37} -9.87652e31 q^{38} -1.10889e33 q^{40} +1.44220e33 q^{41} -7.60160e31 q^{43} -7.69544e33 q^{44} +6.25802e33 q^{46} +3.36927e34 q^{47} -3.61137e34 q^{49} -1.65236e35 q^{50} -3.10829e35 q^{52} -3.75996e35 q^{53} -7.29746e35 q^{55} +3.01577e35 q^{56} -1.00799e36 q^{58} +6.72854e34 q^{59} -2.74886e35 q^{61} +6.44406e36 q^{62} -1.71925e37 q^{64} -2.94754e37 q^{65} +2.47724e37 q^{67} -1.83060e37 q^{68} +7.46308e37 q^{70} +1.25628e38 q^{71} +2.44972e38 q^{73} +2.55268e38 q^{74} +1.46661e38 q^{76} +1.98464e38 q^{77} +6.92089e38 q^{79} +1.17888e37 q^{80} -3.46253e39 q^{82} -1.80861e39 q^{83} -1.73593e39 q^{85} +1.82505e38 q^{86} +7.07980e39 q^{88} +7.15901e39 q^{89} +8.01623e39 q^{91} -9.29284e39 q^{92} -8.08920e40 q^{94} +1.39076e40 q^{95} +7.50364e40 q^{97} +8.67045e40 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40087e6	−1.61903	−0.809514	−	0.587100i	$-0.800270\pi$
$2$	−2.40087e6	−1.61903	−0.809514	+	0.587100i	$0.800270\pi$
$3$	0	0
$3$	0	0
$4$	3.56518e12	1.62125
$5$	3.38080e14	1.58538	0.792691	−	0.609624i	$-0.208679\pi$
$5$	3.38080e14	1.58538	0.792691	+	0.609624i	$0.208679\pi$
$6$	0	0
$7$	−9.19453e16	−0.435532	−0.217766	−	0.976001i	$-0.569877\pi$
$7$	−9.19453e16	−0.435532	−0.217766	+	0.976001i	$0.569877\pi$
$8$	−3.27996e18	−1.00583
$9$	0	0
$10$	−8.11687e20	−2.56678
$11$	−2.15850e21	−0.967392	−0.483696	−	0.875236i	$-0.660706\pi$
$11$	−2.15850e21	−0.967392	−0.483696	+	0.875236i	$0.660706\pi$
$12$	0	0
$13$	−8.71848e22	−1.27234	−0.636169	−	0.771550i	$-0.719482\pi$
$13$	−8.71848e22	−1.27234	−0.636169	+	0.771550i	$0.719482\pi$
$14$	2.20749e23	0.705138
$15$	0	0
$16$	3.48699e22	0.00721093
$17$	−5.13467e24	−0.306415	−0.153207	−	0.988194i	$-0.548960\pi$
$17$	−5.13467e24	−0.306415	−0.153207	+	0.988194i	$0.548960\pi$
$18$	0	0
$19$	4.11372e25	0.251065	0.125532	−	0.992090i	$-0.459936\pi$
$19$	4.11372e25	0.251065	0.125532	+	0.992090i	$0.459936\pi$
$20$	1.20531e27	2.57031
$21$	0	0
$22$	5.18229e27	1.56624
$23$	−2.60656e27	−0.316699	−0.158350	−	0.987383i	$-0.550617\pi$
$23$	−2.60656e27	−0.316699	−0.158350	+	0.987383i	$0.550617\pi$
$24$	0	0
$25$	6.88231e28	1.51344
$26$	2.09320e29	2.05995
$27$	0	0
$28$	−3.27801e29	−0.706107
$29$	4.19842e29	0.440480	0.220240	−	0.975446i	$-0.429316\pi$
$29$	4.19842e29	0.440480	0.220240	+	0.975446i	$0.429316\pi$
$30$	0	0
$31$	−2.68405e30	−0.717589	−0.358794	−	0.933417i	$-0.616812\pi$
$31$	−2.68405e30	−0.717589	−0.358794	+	0.933417i	$0.616812\pi$
$32$	7.12899e30	0.994154
$33$	0	0
$34$	1.23277e31	0.496094
$35$	−3.10848e31	−0.690484
$36$	0	0
$37$	−1.06323e32	−0.755947	−0.377974	−	0.925816i	$-0.623379\pi$
$37$	−1.06323e32	−0.755947	−0.377974	+	0.925816i	$0.623379\pi$
$38$	−9.87652e31	−0.406481
$39$	0	0
$40$	−1.10889e33	−1.59462
$41$	1.44220e33	1.25013	0.625065	−	0.780573i	$-0.285072\pi$
$41$	1.44220e33	1.25013	0.625065	+	0.780573i	$0.285072\pi$
$42$	0	0
$43$	−7.60160e31	−0.0248200	−0.0124100	−	0.999923i	$-0.503950\pi$
$43$	−7.60160e31	−0.0248200	−0.0124100	+	0.999923i	$0.503950\pi$
$44$	−7.69544e33	−1.56839
$45$	0	0
$46$	6.25802e33	0.512745
$47$	3.36927e34	1.77636	0.888179	−	0.459499i	$-0.151971\pi$
$47$	3.36927e34	1.77636	0.888179	+	0.459499i	$0.151971\pi$
$48$	0	0
$49$	−3.61137e34	−0.810312
$50$	−1.65236e35	−2.45030
$51$	0	0
$52$	−3.10829e35	−2.06278
$53$	−3.75996e35	−1.68861	−0.844303	−	0.535866i	$-0.819985\pi$
$53$	−3.75996e35	−1.68861	−0.844303	+	0.535866i	$0.819985\pi$
$54$	0	0
$55$	−7.29746e35	−1.53369
$56$	3.01577e35	0.438070
$57$	0	0
$58$	−1.00799e36	−0.713150
$59$	6.72854e34	0.0335316	0.0167658	−	0.999859i	$-0.494663\pi$
$59$	6.72854e34	0.0335316	0.0167658	+	0.999859i	$0.494663\pi$
$60$	0	0
$61$	−2.74886e35	−0.0691657	−0.0345828	−	0.999402i	$-0.511010\pi$
$61$	−2.74886e35	−0.0691657	−0.0345828	+	0.999402i	$0.511010\pi$
$62$	6.44406e36	1.16180
$63$	0	0
$64$	−1.71925e37	−1.61677
$65$	−2.94754e37	−2.01714
$66$	0	0
$67$	2.47724e37	0.910824	0.455412	−	0.890281i	$-0.349492\pi$
$67$	2.47724e37	0.910824	0.455412	+	0.890281i	$0.349492\pi$
$68$	−1.83060e37	−0.496776
$69$	0	0
$70$	7.46308e37	1.11791
$71$	1.25628e38	1.40698	0.703491	−	0.710704i	$-0.251623\pi$
$71$	1.25628e38	1.40698	0.703491	+	0.710704i	$0.251623\pi$
$72$	0	0
$73$	2.44972e38	1.55238	0.776189	−	0.630500i	$-0.217150\pi$
$73$	2.44972e38	1.55238	0.776189	+	0.630500i	$0.217150\pi$
$74$	2.55268e38	1.22390
$75$	0	0
$76$	1.46661e38	0.407040
$77$	1.98464e38	0.421330
$78$	0	0
$79$	6.92089e38	0.868574	0.434287	−	0.900775i	$-0.357000\pi$
$79$	6.92089e38	0.868574	0.434287	+	0.900775i	$0.357000\pi$
$80$	1.17888e37	0.0114321
$81$	0	0
$82$	−3.46253e39	−2.02400
$83$	−1.80861e39	−0.824600	−0.412300	−	0.911048i	$-0.635274\pi$
$83$	−1.80861e39	−0.824600	−0.412300	+	0.911048i	$0.635274\pi$
$84$	0	0
$85$	−1.73593e39	−0.485784
$86$	1.82505e38	0.0401843
$87$	0	0
$88$	7.07980e39	0.973031
$89$	7.15901e39	0.780473	0.390237	−	0.920715i	$-0.372393\pi$
$89$	7.15901e39	0.780473	0.390237	+	0.920715i	$0.372393\pi$
$90$	0	0
$91$	8.01623e39	0.554143
$92$	−9.29284e39	−0.513450
$93$	0	0
$94$	−8.08920e40	−2.87597
$95$	1.39076e40	0.398034
$96$	0	0
$97$	7.50364e40	1.40104	0.700521	−	0.713632i	$-0.252951\pi$
$97$	7.50364e40	1.40104	0.700521	+	0.713632i	$0.252951\pi$
$98$	8.67045e40	1.31192
$99$	0	0
$100$	2.45366e41	2.45366
$101$	9.43857e40	0.769694	0.384847	−	0.922980i	$-0.374254\pi$
$101$	9.43857e40	0.769694	0.384847	+	0.922980i	$0.374254\pi$
$102$	0	0
$103$	−2.03470e41	−1.11003	−0.555017	−	0.831839i	$-0.687288\pi$
$103$	−2.03470e41	−1.11003	−0.555017	+	0.831839i	$0.687288\pi$
$104$	2.85963e41	1.27975
$105$	0	0
$106$	9.02720e41	2.73390
$107$	1.95974e41	0.489589	0.244794	−	0.969575i	$-0.421280\pi$
$107$	1.95974e41	0.489589	0.244794	+	0.969575i	$0.421280\pi$
$108$	0	0
$109$	1.27681e41	0.218214	0.109107	−	0.994030i	$-0.465201\pi$
$109$	1.27681e41	0.218214	0.109107	+	0.994030i	$0.465201\pi$
$110$	1.75203e42	2.48308
$111$	0	0
$112$	−3.20613e39	−0.00314059
$113$	−1.47167e42	−1.20144	−0.600720	−	0.799460i	$-0.705119\pi$
$113$	−1.47167e42	−1.20144	−0.600720	+	0.799460i	$0.705119\pi$
$114$	0	0
$115$	−8.81225e41	−0.502089
$116$	1.49681e42	0.714131
$117$	0	0
$118$	−1.61544e41	−0.0542886
$119$	4.72109e41	0.133453
$120$	0	0
$121$	−3.19384e41	−0.0641524
$122$	6.59966e41	0.111981
$123$	0	0
$124$	−9.56910e42	−1.16339
$125$	7.89360e42	0.813992
$126$	0	0
$127$	−3.99623e42	−0.297628	−0.148814	−	0.988865i	$-0.547546\pi$
$127$	−3.99623e42	−0.297628	−0.148814	+	0.988865i	$0.547546\pi$
$128$	2.56002e43	1.62345
$129$	0	0
$130$	7.07668e43	3.26581
$131$	−1.69219e43	−0.667404	−0.333702	−	0.942679i	$-0.608298\pi$
$131$	−1.69219e43	−0.667404	−0.333702	+	0.942679i	$0.608298\pi$
$132$	0	0
$133$	−3.78237e42	−0.109347
$134$	−5.94754e43	−1.47465
$135$	0	0
$136$	1.68415e43	0.308201
$137$	3.96792e43	0.624873	0.312436	−	0.949939i	$-0.398855\pi$
$137$	3.96792e43	0.624873	0.312436	+	0.949939i	$0.398855\pi$
$138$	0	0
$139$	−2.45873e43	−0.287679	−0.143839	−	0.989601i	$-0.545945\pi$
$139$	−2.45873e43	−0.287679	−0.143839	+	0.989601i	$0.545945\pi$
$140$	−1.10823e44	−1.11945
$141$	0	0
$142$	−3.01616e44	−2.27795
$143$	1.88189e44	1.23085
$144$	0	0
$145$	1.41940e44	0.698330
$146$	−5.88147e44	−2.51334
$147$	0	0
$148$	−3.79060e44	−1.22558
$149$	2.54122e42	0.00715687	0.00357844	−	0.999994i	$-0.498861\pi$
$149$	2.54122e42	0.00715687	0.00357844	+	0.999994i	$0.498861\pi$
$150$	0	0
$151$	7.23871e43	0.155108	0.0775539	−	0.996988i	$-0.475289\pi$
$151$	7.23871e43	0.155108	0.0775539	+	0.996988i	$0.475289\pi$
$152$	−1.34928e44	−0.252528
$153$	0	0
$154$	−4.76488e44	−0.682145
$155$	−9.07422e44	−1.13765
$156$	0	0
$157$	−1.76934e45	−1.70557	−0.852783	−	0.522266i	$-0.825087\pi$
$157$	−1.76934e45	−1.70557	−0.852783	+	0.522266i	$0.825087\pi$
$158$	−1.66162e45	−1.40625
$159$	0	0
$160$	2.41017e45	1.57611
$161$	2.39661e44	0.137933
$162$	0	0
$163$	1.55154e45	0.693295	0.346648	−	0.937995i	$-0.387320\pi$
$163$	1.55154e45	0.693295	0.346648	+	0.937995i	$0.387320\pi$
$164$	5.14168e45	2.02678
$165$	0	0
$166$	4.34224e45	1.33505
$167$	5.53546e45	1.50476	0.752378	−	0.658732i	$-0.228907\pi$
$167$	5.53546e45	1.50476	0.752378	+	0.658732i	$0.228907\pi$
$168$	0	0
$169$	2.90574e45	0.618842
$170$	4.16774e45	0.786499
$171$	0	0
$172$	−2.71010e44	−0.0402395
$173$	−6.50011e45	−0.856990	−0.428495	−	0.903544i	$-0.640956\pi$
$173$	−6.50011e45	−0.856990	−0.428495	+	0.903544i	$0.640956\pi$
$174$	0	0
$175$	−6.32796e45	−0.659149
$176$	−7.52669e43	−0.00697580
$177$	0	0
$178$	−1.71879e46	−1.26361
$179$	1.33774e46	0.876765	0.438383	−	0.898788i	$-0.355551\pi$
$179$	1.33774e46	0.876765	0.438383	+	0.898788i	$0.355551\pi$
$180$	0	0
$181$	1.31888e46	0.688328	0.344164	−	0.938910i	$-0.388162\pi$
$181$	1.31888e46	0.688328	0.344164	+	0.938910i	$0.388162\pi$
$182$	−1.92460e46	−0.897173
$183$	0	0
$184$	8.54941e45	0.318545
$185$	−3.59456e46	−1.19847
$186$	0	0
$187$	1.10832e46	0.296423
$188$	1.20121e47	2.87993
$189$	0	0
$190$	−3.33905e46	−0.644428
$191$	1.01788e47	1.76406	0.882031	−	0.471192i	$-0.156176\pi$
$191$	1.01788e47	1.76406	0.882031	+	0.471192i	$0.156176\pi$
$192$	0	0
$193$	8.24135e46	1.15365	0.576824	−	0.816868i	$-0.304292\pi$
$193$	8.24135e46	1.15365	0.576824	+	0.816868i	$0.304292\pi$
$194$	−1.80153e47	−2.26833
$195$	0	0
$196$	−1.28752e47	−1.31372
$197$	−2.27618e46	−0.209242	−0.104621	−	0.994512i	$-0.533363\pi$
$197$	−2.27618e46	−0.209242	−0.104621	+	0.994512i	$0.533363\pi$
$198$	0	0
$199$	1.53840e47	1.14969	0.574846	−	0.818262i	$-0.305062\pi$
$199$	1.53840e47	1.14969	0.574846	+	0.818262i	$0.305062\pi$
$200$	−2.25737e47	−1.52226
$201$	0	0
$202$	−2.26608e47	−1.24616
$203$	−3.86025e46	−0.191843
$204$	0	0
$205$	4.87577e47	1.98193
$206$	4.88505e47	1.79718
$207$	0	0
$208$	−3.04013e45	−0.00917474
$209$	−8.87947e46	−0.242878
$210$	0	0
$211$	−7.00983e47	−1.57731	−0.788655	−	0.614836i	$-0.789222\pi$
$211$	−7.00983e47	−1.57731	−0.788655	+	0.614836i	$0.789222\pi$
$212$	−1.34049e48	−2.73766
$213$	0	0
$214$	−4.70509e47	−0.792658
$215$	−2.56994e46	−0.0393491
$216$	0	0
$217$	2.46786e47	0.312533
$218$	−3.06546e47	−0.353295
$219$	0	0
$220$	−2.60167e48	−2.48649
$221$	4.47665e47	0.389863
$222$	0	0
$223$	−2.18317e47	−0.158066	−0.0790330	−	0.996872i	$-0.525183\pi$
$223$	−2.18317e47	−0.158066	−0.0790330	+	0.996872i	$0.525183\pi$
$224$	−6.55477e47	−0.432985
$225$	0	0
$226$	3.53329e48	1.94516
$227$	1.64330e48	0.826391	0.413196	−	0.910642i	$-0.364413\pi$
$227$	1.64330e48	0.826391	0.413196	+	0.910642i	$0.364413\pi$
$228$	0	0
$229$	2.31385e48	0.972093	0.486047	−	0.873933i	$-0.338438\pi$
$229$	2.31385e48	0.972093	0.486047	+	0.873933i	$0.338438\pi$
$230$	2.11571e48	0.812897
$231$	0	0
$232$	−1.37706e48	−0.443048
$233$	5.25096e48	1.54683	0.773414	−	0.633901i	$-0.218547\pi$
$233$	5.25096e48	1.54683	0.773414	+	0.633901i	$0.218547\pi$
$234$	0	0
$235$	1.13908e49	2.81620
$236$	2.39884e47	0.0543633
$237$	0	0
$238$	−1.13347e48	−0.216065
$239$	4.02474e48	0.704013	0.352007	−	0.935998i	$-0.385499\pi$
$239$	4.02474e48	0.704013	0.352007	+	0.935998i	$0.385499\pi$
$240$	0	0
$241$	−2.82992e48	−0.417277	−0.208638	−	0.977993i	$-0.566903\pi$
$241$	−2.82992e48	−0.417277	−0.208638	+	0.977993i	$0.566903\pi$
$242$	7.66800e47	0.103865
$243$	0	0
$244$	−9.80016e47	−0.112135
$245$	−1.22093e49	−1.28465
$246$	0	0
$247$	−3.58654e48	−0.319439
$248$	8.80357e48	0.721771
$249$	0	0
$250$	−1.89516e49	−1.31788
$251$	−2.68976e48	−0.172346	−0.0861732	−	0.996280i	$-0.527464\pi$
$251$	−2.68976e48	−0.172346	−0.0861732	+	0.996280i	$0.527464\pi$
$252$	0	0
$253$	5.62627e48	0.306372
$254$	9.59444e48	0.481868
$255$	0	0
$256$	−2.36562e49	−1.01164
$257$	6.05982e48	0.239238	0.119619	−	0.992820i	$-0.461833\pi$
$257$	6.05982e48	0.239238	0.119619	+	0.992820i	$0.461833\pi$
$258$	0	0
$259$	9.77589e48	0.329239
$260$	−1.05085e50	−3.27030
$261$	0	0
$262$	4.06275e49	1.08055
$263$	4.72993e49	1.16349	0.581743	−	0.813372i	$-0.302371\pi$
$263$	4.72993e49	1.16349	0.581743	+	0.813372i	$0.302371\pi$
$264$	0	0
$265$	−1.27117e50	−2.67709
$266$	9.08100e48	0.177035
$267$	0	0
$268$	8.83179e49	1.47668
$269$	−3.21338e49	−0.497784	−0.248892	−	0.968531i	$-0.580066\pi$
$269$	−3.21338e49	−0.497784	−0.248892	+	0.968531i	$0.580066\pi$
$270$	0	0
$271$	1.33856e50	1.78142	0.890709	−	0.454574i	$-0.150208\pi$
$271$	1.33856e50	1.78142	0.890709	+	0.454574i	$0.150208\pi$
$272$	−1.79046e47	−0.00220954
$273$	0	0
$274$	−9.52648e49	−1.01169
$275$	−1.48555e50	−1.46409
$276$	0	0
$277$	5.53962e49	0.470592	0.235296	−	0.971924i	$-0.424394\pi$
$277$	5.53962e49	0.470592	0.235296	+	0.971924i	$0.424394\pi$
$278$	5.90310e49	0.465760
$279$	0	0
$280$	1.01957e50	0.694508
$281$	2.22399e49	0.140816	0.0704082	−	0.997518i	$-0.477570\pi$
$281$	2.22399e49	0.140816	0.0704082	+	0.997518i	$0.477570\pi$
$282$	0	0
$283$	−1.61973e50	−0.886790	−0.443395	−	0.896326i	$-0.646226\pi$
$283$	−1.61973e50	−0.886790	−0.443395	+	0.896326i	$0.646226\pi$
$284$	4.47884e50	2.28108
$285$	0	0
$286$	−4.51817e50	−1.99278
$287$	−1.32603e50	−0.544471
$288$	0	0
$289$	−2.54441e50	−0.906110
$290$	−3.40780e50	−1.13062
$291$	0	0
$292$	8.73367e50	2.51680
$293$	−4.58527e49	−0.123191	−0.0615955	−	0.998101i	$-0.519619\pi$
$293$	−4.58527e49	−0.123191	−0.0615955	+	0.998101i	$0.519619\pi$
$294$	0	0
$295$	2.27478e49	0.0531604
$296$	3.48735e50	0.760353
$297$	0	0
$298$	−6.10115e48	−0.0115872
$299$	2.27252e50	0.402948
$300$	0	0
$301$	6.98931e48	0.0108099
$302$	−1.73792e50	−0.251124
$303$	0	0
$304$	1.43445e48	0.00181041
$305$	−9.29333e49	−0.109654
$306$	0	0
$307$	−1.04806e51	−1.08156	−0.540779	−	0.841165i	$-0.681871\pi$
$307$	−1.04806e51	−1.08156	−0.540779	+	0.841165i	$0.681871\pi$
$308$	7.07560e50	0.683083
$309$	0	0
$310$	2.17861e51	1.84189
$311$	1.45879e51	1.15453	0.577265	−	0.816557i	$-0.304120\pi$
$311$	1.45879e51	1.15453	0.577265	+	0.816557i	$0.304120\pi$
$312$	0	0
$313$	5.50229e50	0.381843	0.190922	−	0.981605i	$-0.438852\pi$
$313$	5.50229e50	0.381843	0.190922	+	0.981605i	$0.438852\pi$
$314$	4.24796e51	2.76136
$315$	0	0
$316$	2.46742e51	1.40818
$317$	−2.01228e51	−1.07640	−0.538199	−	0.842818i	$-0.680895\pi$
$317$	−2.01228e51	−1.07640	−0.538199	+	0.842818i	$0.680895\pi$
$318$	0	0
$319$	−9.06229e50	−0.426117
$320$	−5.81243e51	−2.56320
$321$	0	0
$322$	−5.75396e50	−0.223317
$323$	−2.11226e50	−0.0769299
$324$	0	0
$325$	−6.00033e51	−1.92560
$326$	−3.72506e51	−1.12246
$327$	0	0
$328$	−4.73035e51	−1.25742
$329$	−3.09789e51	−0.773660
$330$	0	0
$331$	7.84661e51	1.73065	0.865323	−	0.501215i	$-0.167113\pi$
$331$	7.84661e51	1.73065	0.865323	+	0.501215i	$0.167113\pi$
$332$	−6.44800e51	−1.33689
$333$	0	0
$334$	−1.32899e52	−2.43624
$335$	8.37504e51	1.44400
$336$	0	0
$337$	1.59637e51	0.243624	0.121812	−	0.992553i	$-0.461129\pi$
$337$	1.59637e51	0.243624	0.121812	+	0.992553i	$0.461129\pi$
$338$	−6.97632e51	−1.00192
$339$	0	0
$340$	−6.18889e51	−0.787580
$341$	5.79352e51	0.694190
$342$	0	0
$343$	7.41827e51	0.788448
$344$	2.49329e50	0.0249646
$345$	0	0
$346$	1.56060e52	1.38749
$347$	3.39579e51	0.284568	0.142284	−	0.989826i	$-0.454555\pi$
$347$	3.39579e51	0.284568	0.142284	+	0.989826i	$0.454555\pi$
$348$	0	0
$349$	9.21738e51	0.686572	0.343286	−	0.939231i	$-0.388460\pi$
$349$	9.21738e51	0.686572	0.343286	+	0.939231i	$0.388460\pi$
$350$	1.51926e52	1.06718
$351$	0	0
$352$	−1.53879e52	−0.961737
$353$	−1.05771e52	−0.623715	−0.311857	−	0.950129i	$-0.600951\pi$
$353$	−1.05771e52	−0.623715	−0.311857	+	0.950129i	$0.600951\pi$
$354$	0	0
$355$	4.24721e52	2.23060
$356$	2.55231e52	1.26535
$357$	0	0
$358$	−3.21174e52	−1.41951
$359$	−1.47439e52	−0.615428	−0.307714	−	0.951479i	$-0.599564\pi$
$359$	−1.47439e52	−0.615428	−0.307714	+	0.951479i	$0.599564\pi$
$360$	0	0
$361$	−2.51548e52	−0.936966
$362$	−3.16647e52	−1.11442
$363$	0	0
$364$	2.85793e52	0.898407
$365$	8.28200e52	2.46111
$366$	0	0
$367$	5.60693e52	1.48960	0.744802	−	0.667285i	$-0.232544\pi$
$367$	5.60693e52	1.48960	0.744802	+	0.667285i	$0.232544\pi$
$368$	−9.08906e49	−0.00228370
$369$	0	0
$370$	8.63009e52	1.94035
$371$	3.45711e52	0.735442
$372$	0	0
$373$	−8.78610e52	−1.67404	−0.837018	−	0.547175i	$-0.815703\pi$
$373$	−8.78610e52	−1.67404	−0.837018	+	0.547175i	$0.815703\pi$
$374$	−2.66094e52	−0.479918
$375$	0	0
$376$	−1.10511e53	−1.78671
$377$	−3.66038e52	−0.560440
$378$	0	0
$379$	−2.73345e52	−0.375498	−0.187749	−	0.982217i	$-0.560119\pi$
$379$	−2.73345e52	−0.375498	−0.187749	+	0.982217i	$0.560119\pi$
$380$	4.95832e52	0.645314
$381$	0	0
$382$	−2.44381e53	−2.85607
$383$	−2.55810e52	−0.283362	−0.141681	−	0.989912i	$-0.545251\pi$
$383$	−2.55810e52	−0.283362	−0.141681	+	0.989912i	$0.545251\pi$
$384$	0	0
$385$	6.70967e52	0.667969
$386$	−1.97864e53	−1.86779
$387$	0	0
$388$	2.67518e53	2.27145
$389$	−1.34317e53	−1.08185	−0.540923	−	0.841072i	$-0.681925\pi$
$389$	−1.34317e53	−1.08185	−0.540923	+	0.841072i	$0.681925\pi$
$390$	0	0
$391$	1.33838e52	0.0970413
$392$	1.18452e53	0.815035
$393$	0	0
$394$	5.46483e52	0.338770
$395$	2.33981e53	1.37702
$396$	0	0
$397$	6.36376e52	0.337683	0.168841	−	0.985643i	$-0.445997\pi$
$397$	6.36376e52	0.337683	0.168841	+	0.985643i	$0.445997\pi$
$398$	−3.69351e53	−1.86138
$399$	0	0
$400$	2.39986e51	0.0109133
$401$	1.74531e53	0.754071	0.377036	−	0.926199i	$-0.376943\pi$
$401$	1.74531e53	0.754071	0.377036	+	0.926199i	$0.376943\pi$
$402$	0	0
$403$	2.34008e53	0.913015
$404$	3.36501e53	1.24787
$405$	0	0
$406$	9.26797e52	0.310600
$407$	2.29498e53	0.731298
$408$	0	0
$409$	−2.90188e53	−0.836279	−0.418140	−	0.908383i	$-0.637318\pi$
$409$	−2.90188e53	−0.836279	−0.418140	+	0.908383i	$0.637318\pi$
$410$	−1.17061e54	−3.20881
$411$	0	0
$412$	−7.25405e53	−1.79965
$413$	−6.18657e51	−0.0146041
$414$	0	0
$415$	−6.11453e53	−1.30731
$416$	−6.21540e53	−1.26490
$417$	0	0
$418$	2.13185e53	0.393227
$419$	1.59662e53	0.280424	0.140212	−	0.990121i	$-0.455222\pi$
$419$	1.59662e53	0.280424	0.140212	+	0.990121i	$0.455222\pi$
$420$	0	0
$421$	−4.06387e53	−0.647377	−0.323688	−	0.946164i	$-0.604923\pi$
$421$	−4.06387e53	−0.647377	−0.323688	+	0.946164i	$0.604923\pi$
$422$	1.68297e54	2.55371
$423$	0	0
$424$	1.23325e54	1.69845
$425$	−3.53384e53	−0.463739
$426$	0	0
$427$	2.52744e52	0.0301238
$428$	6.98682e53	0.793748
$429$	0	0
$430$	6.17011e52	0.0637074
$431$	9.52197e53	0.937438	0.468719	−	0.883347i	$-0.344716\pi$
$431$	9.52197e53	0.937438	0.468719	+	0.883347i	$0.344716\pi$
$432$	0	0
$433$	4.92132e53	0.440636	0.220318	−	0.975428i	$-0.429291\pi$
$433$	4.92132e53	0.440636	0.220318	+	0.975428i	$0.429291\pi$
$434$	−5.92501e53	−0.505999
$435$	0	0
$436$	4.55205e53	0.353780
$437$	−1.07227e53	−0.0795120
$438$	0	0
$439$	1.37566e54	0.928940	0.464470	−	0.885589i	$-0.346245\pi$
$439$	1.37566e54	0.928940	0.464470	+	0.885589i	$0.346245\pi$
$440$	2.39354e54	1.54263
$441$	0	0
$442$	−1.07479e54	−0.631199
$443$	−2.53462e54	−1.42114	−0.710570	−	0.703626i	$-0.751563\pi$
$443$	−2.53462e54	−1.42114	−0.710570	+	0.703626i	$0.751563\pi$
$444$	0	0
$445$	2.42032e54	1.23735
$446$	5.24152e53	0.255913
$447$	0	0
$448$	1.58077e54	0.704156
$449$	3.83879e54	1.63359	0.816797	−	0.576926i	$-0.195748\pi$
$449$	3.83879e54	1.63359	0.816797	+	0.576926i	$0.195748\pi$
$450$	0	0
$451$	−3.11298e54	−1.20937
$452$	−5.24676e54	−1.94784
$453$	0	0
$454$	−3.94535e54	−1.33795
$455$	2.71013e54	0.878528
$456$	0	0
$457$	5.46700e54	1.61982	0.809910	−	0.586554i	$-0.199516\pi$
$457$	5.46700e54	1.61982	0.809910	+	0.586554i	$0.199516\pi$
$458$	−5.55527e54	−1.57385
$459$	0	0
$460$	−3.14172e54	−0.814014
$461$	6.86605e54	1.70152	0.850762	−	0.525551i	$-0.176141\pi$
$461$	6.86605e54	1.70152	0.850762	+	0.525551i	$0.176141\pi$
$462$	0	0
$463$	2.69469e54	0.611082	0.305541	−	0.952179i	$-0.401163\pi$
$463$	2.69469e54	0.611082	0.305541	+	0.952179i	$0.401163\pi$
$464$	1.46399e52	0.00317628
$465$	0	0
$466$	−1.26069e55	−2.50436
$467$	1.01233e54	0.192453	0.0962267	−	0.995359i	$-0.469323\pi$
$467$	1.01233e54	0.192453	0.0962267	+	0.995359i	$0.469323\pi$
$468$	0	0
$469$	−2.27770e54	−0.396693
$470$	−2.73480e55	−4.55952
$471$	0	0
$472$	−2.20693e53	−0.0337271
$473$	1.64081e53	0.0240107
$474$	0	0
$475$	2.83119e54	0.379970
$476$	1.68315e54	0.216362
$477$	0	0
$478$	−9.66289e54	−1.13982
$479$	−8.03512e54	−0.908060	−0.454030	−	0.890986i	$-0.650014\pi$
$479$	−8.03512e54	−0.908060	−0.454030	+	0.890986i	$0.650014\pi$
$480$	0	0
$481$	9.26974e54	0.961820
$482$	6.79428e54	0.675583
$483$	0	0
$484$	−1.13866e54	−0.104007
$485$	2.53683e55	2.22119
$486$	0	0
$487$	3.58922e54	0.288839	0.144420	−	0.989517i	$-0.453868\pi$
$487$	3.58922e54	0.288839	0.144420	+	0.989517i	$0.453868\pi$
$488$	9.01614e53	0.0695688
$489$	0	0
$490$	2.93130e55	2.07989
$491$	−8.12128e53	−0.0552655	−0.0276327	−	0.999618i	$-0.508797\pi$
$491$	−8.12128e53	−0.0552655	−0.0276327	+	0.999618i	$0.508797\pi$
$492$	0	0
$493$	−2.15575e54	−0.134970
$494$	8.61083e54	0.517181
$495$	0	0
$496$	−9.35926e52	−0.00517448
$497$	−1.15509e55	−0.612785
$498$	0	0
$499$	−6.57141e54	−0.321068	−0.160534	−	0.987030i	$-0.551322\pi$
$499$	−6.57141e54	−0.321068	−0.160534	+	0.987030i	$0.551322\pi$
$500$	2.81421e55	1.31969
$501$	0	0
$502$	6.45777e54	0.279034
$503$	3.12409e55	1.29592	0.647962	−	0.761672i	$-0.275621\pi$
$503$	3.12409e55	1.29592	0.647962	+	0.761672i	$0.275621\pi$
$504$	0	0
$505$	3.19099e55	1.22026
$506$	−1.35080e55	−0.496026
$507$	0	0
$508$	−1.42472e55	−0.482530
$509$	2.10477e55	0.684684	0.342342	−	0.939575i	$-0.388780\pi$
$509$	2.10477e55	0.684684	0.342342	+	0.939575i	$0.388780\pi$
$510$	0	0
$511$	−2.25240e55	−0.676110
$512$	5.00094e53	0.0144217
$513$	0	0
$514$	−1.45489e55	−0.387334
$515$	−6.87889e55	−1.75983
$516$	0	0
$517$	−7.27259e55	−1.71843
$518$	−2.34707e55	−0.533047
$519$	0	0
$520$	9.66782e55	2.02890
$521$	−1.04403e55	−0.210639	−0.105320	−	0.994438i	$-0.533587\pi$
$521$	−1.04403e55	−0.210639	−0.105320	+	0.994438i	$0.533587\pi$
$522$	0	0
$523$	3.89473e55	0.726429	0.363215	−	0.931706i	$-0.381679\pi$
$523$	3.89473e55	0.726429	0.363215	+	0.931706i	$0.381679\pi$
$524$	−6.03297e55	−1.08203
$525$	0	0
$526$	−1.13560e56	−1.88372
$527$	1.37817e55	0.219880
$528$	0	0
$529$	−6.09452e55	−0.899702
$530$	3.05191e56	4.33428
$531$	0	0
$532$	−1.34848e55	−0.177279
$533$	−1.25738e56	−1.59059
$534$	0	0
$535$	6.62549e55	0.776185
$536$	−8.12524e55	−0.916132
$537$	0	0
$538$	7.71493e55	0.805926
$539$	7.79515e55	0.783890
$540$	0	0
$541$	7.83261e55	0.730067	0.365033	−	0.930994i	$-0.381058\pi$
$541$	7.83261e55	0.730067	0.365033	+	0.930994i	$0.381058\pi$
$542$	−3.21370e56	−2.88417
$543$	0	0
$544$	−3.66050e55	−0.304623
$545$	4.31663e55	0.345953
$546$	0	0
$547$	−1.75108e56	−1.30187	−0.650933	−	0.759135i	$-0.725622\pi$
$547$	−1.75108e56	−1.30187	−0.650933	+	0.759135i	$0.725622\pi$
$548$	1.41463e56	1.01308
$549$	0	0
$550$	3.56662e56	2.37040
$551$	1.72711e55	0.110589
$552$	0	0
$553$	−6.36343e55	−0.378291
$554$	−1.32999e56	−0.761902
$555$	0	0
$556$	−8.76581e55	−0.466400
$557$	−2.17848e56	−1.11718	−0.558588	−	0.829445i	$-0.688657\pi$
$557$	−2.17848e56	−1.11718	−0.558588	+	0.829445i	$0.688657\pi$
$558$	0	0
$559$	6.62744e54	0.0315794
$560$	−1.08393e54	−0.00497903
$561$	0	0
$562$	−5.33952e55	−0.227986
$563$	−3.30210e56	−1.35947	−0.679733	−	0.733459i	$-0.737905\pi$
$563$	−3.30210e56	−1.35947	−0.679733	+	0.733459i	$0.737905\pi$
$564$	0	0
$565$	−4.97541e56	−1.90474
$566$	3.88877e56	1.43574
$567$	0	0
$568$	−4.12053e56	−1.41518
$569$	8.68468e55	0.287708	0.143854	−	0.989599i	$-0.454050\pi$
$569$	8.68468e55	0.287708	0.143854	+	0.989599i	$0.454050\pi$
$570$	0	0
$571$	4.87083e56	1.50163	0.750815	−	0.660512i	$-0.229661\pi$
$571$	4.87083e56	1.50163	0.750815	+	0.660512i	$0.229661\pi$
$572$	6.70926e56	1.99552
$573$	0	0
$574$	3.18363e56	0.881514
$575$	−1.79391e56	−0.479304
$576$	0	0
$577$	−7.14972e56	−1.77904	−0.889518	−	0.456900i	$-0.848960\pi$
$577$	−7.14972e56	−1.77904	−0.889518	+	0.456900i	$0.848960\pi$
$578$	6.10880e56	1.46702
$579$	0	0
$580$	5.06041e56	1.13217
$581$	1.66293e56	0.359139
$582$	0	0
$583$	8.11589e56	1.63354
$584$	−8.03498e56	−1.56143
$585$	0	0
$586$	1.10087e56	0.199450
$587$	−4.35978e56	−0.762752	−0.381376	−	0.924420i	$-0.624550\pi$
$587$	−4.35978e56	−0.762752	−0.381376	+	0.924420i	$0.624550\pi$
$588$	0	0
$589$	−1.10414e56	−0.180161
$590$	−5.46147e55	−0.0860682
$591$	0	0
$592$	−3.70747e54	−0.00545109
$593$	8.14584e56	1.15695	0.578475	−	0.815700i	$-0.303648\pi$
$593$	8.14584e56	1.15695	0.578475	+	0.815700i	$0.303648\pi$
$594$	0	0
$595$	1.59610e56	0.211574
$596$	9.05989e54	0.0116031
$597$	0	0
$598$	−5.45605e56	−0.652385
$599$	1.46611e57	1.69401	0.847004	−	0.531587i	$-0.178404\pi$
$599$	1.46611e57	1.69401	0.847004	+	0.531587i	$0.178404\pi$
$600$	0	0
$601$	1.27455e57	1.37540	0.687700	−	0.725995i	$-0.258620\pi$
$601$	1.27455e57	1.37540	0.687700	+	0.725995i	$0.258620\pi$
$602$	−1.67805e55	−0.0175015
$603$	0	0
$604$	2.58073e56	0.251469
$605$	−1.07977e56	−0.101706
$606$	0	0
$607$	7.08566e56	0.623752	0.311876	−	0.950123i	$-0.399043\pi$
$607$	7.08566e56	0.623752	0.311876	+	0.950123i	$0.399043\pi$
$608$	2.93267e56	0.249597
$609$	0	0
$610$	2.23121e56	0.177533
$611$	−2.93750e57	−2.26012
$612$	0	0
$613$	−1.17754e57	−0.847298	−0.423649	−	0.905827i	$-0.639251\pi$
$613$	−1.17754e57	−0.847298	−0.423649	+	0.905827i	$0.639251\pi$
$614$	2.51626e57	1.75107
$615$	0	0
$616$	−6.50955e56	−0.423786
$617$	−1.61404e57	−1.01641	−0.508205	−	0.861236i	$-0.669691\pi$
$617$	−1.61404e57	−1.01641	−0.508205	+	0.861236i	$0.669691\pi$
$618$	0	0
$619$	−6.36804e56	−0.375273	−0.187637	−	0.982239i	$-0.560083\pi$
$619$	−6.36804e56	−0.375273	−0.187637	+	0.982239i	$0.560083\pi$
$620$	−3.23512e57	−1.84442
$621$	0	0
$622$	−3.50238e57	−1.86922
$623$	−6.58238e56	−0.339921
$624$	0	0
$625$	−4.61045e56	−0.222948
$626$	−1.32103e57	−0.618215
$627$	0	0
$628$	−6.30801e57	−2.76516
$629$	5.45933e56	0.231633
$630$	0	0
$631$	−2.73724e57	−1.08820	−0.544102	−	0.839019i	$-0.683130\pi$
$631$	−2.73724e57	−1.08820	−0.544102	+	0.839019i	$0.683130\pi$
$632$	−2.27003e57	−0.873636
$633$	0	0
$634$	4.83123e57	1.74272
$635$	−1.35104e57	−0.471854
$636$	0	0
$637$	3.14857e57	1.03099
$638$	2.17574e57	0.689896
$639$	0	0
$640$	8.65491e57	2.57379
$641$	2.81100e57	0.809602	0.404801	−	0.914405i	$-0.367341\pi$
$641$	2.81100e57	0.809602	0.404801	+	0.914405i	$0.367341\pi$
$642$	0	0
$643$	1.13133e57	0.305679	0.152840	−	0.988251i	$-0.451158\pi$
$643$	1.13133e57	0.305679	0.152840	+	0.988251i	$0.451158\pi$
$644$	8.54433e56	0.223624
$645$	0	0
$646$	5.07127e56	0.124552
$647$	−2.99702e57	−0.713102	−0.356551	−	0.934276i	$-0.616047\pi$
$647$	−2.99702e57	−0.713102	−0.356551	+	0.934276i	$0.616047\pi$
$648$	0	0
$649$	−1.45236e56	−0.0324382
$650$	1.44060e58	3.11760
$651$	0	0
$652$	5.53153e57	1.12401
$653$	−1.36513e57	−0.268815	−0.134407	−	0.990926i	$-0.542913\pi$
$653$	−1.36513e57	−0.268815	−0.134407	+	0.990926i	$0.542913\pi$
$654$	0	0
$655$	−5.72096e57	−1.05809
$656$	5.02893e55	0.00901461
$657$	0	0
$658$	7.43764e57	1.25258
$659$	8.45274e57	1.37990	0.689949	−	0.723858i	$-0.257633\pi$
$659$	8.45274e57	1.37990	0.689949	+	0.723858i	$0.257633\pi$
$660$	0	0
$661$	−1.12370e58	−1.72393	−0.861964	−	0.506970i	$-0.830766\pi$
$661$	−1.12370e58	−1.72393	−0.861964	+	0.506970i	$0.830766\pi$
$662$	−1.88387e58	−2.80197
$663$	0	0
$664$	5.93216e57	0.829406
$665$	−1.27874e57	−0.173356
$666$	0	0
$667$	−1.09434e57	−0.139500
$668$	1.97349e58	2.43959
$669$	0	0
$670$	−2.01074e58	−2.33788
$671$	5.93342e56	0.0669103
$672$	0	0
$673$	1.32183e58	1.40239	0.701193	−	0.712971i	$-0.252651\pi$
$673$	1.32183e58	1.40239	0.701193	+	0.712971i	$0.252651\pi$
$674$	−3.83269e57	−0.394435
$675$	0	0
$676$	1.03595e58	1.00330
$677$	−4.87678e57	−0.458211	−0.229105	−	0.973402i	$-0.573580\pi$
$677$	−4.87678e57	−0.458211	−0.229105	+	0.973402i	$0.573580\pi$
$678$	0	0
$679$	−6.89924e57	−0.610198
$680$	5.69377e57	0.488616
$681$	0	0
$682$	−1.39095e58	−1.12391
$683$	−2.89510e57	−0.227007	−0.113504	−	0.993538i	$-0.536207\pi$
$683$	−2.89510e57	−0.227007	−0.113504	+	0.993538i	$0.536207\pi$
$684$	0	0
$685$	1.34147e58	0.990662
$686$	−1.78103e58	−1.27652
$687$	0	0
$688$	−2.65067e54	−0.000178975 0
$689$	3.27812e58	2.14848
$690$	0	0
$691$	6.99589e57	0.432059	0.216029	−	0.976387i	$-0.430689\pi$
$691$	6.99589e57	0.432059	0.216029	+	0.976387i	$0.430689\pi$
$692$	−2.31740e58	−1.38940
$693$	0	0
$694$	−8.15286e57	−0.460724
$695$	−8.31247e57	−0.456080
$696$	0	0
$697$	−7.40520e57	−0.383058
$698$	−2.21298e58	−1.11158
$699$	0	0
$700$	−2.25603e58	−1.06865
$701$	6.70824e56	0.0308595	0.0154298	−	0.999881i	$-0.495088\pi$
$701$	6.70824e56	0.0308595	0.0154298	+	0.999881i	$0.495088\pi$
$702$	0	0
$703$	−4.37383e57	−0.189792
$704$	3.71100e58	1.56405
$705$	0	0
$706$	2.53943e58	1.00981
$707$	−8.67832e57	−0.335226
$708$	0	0
$709$	−1.26212e58	−0.460102	−0.230051	−	0.973179i	$-0.573889\pi$
$709$	−1.26212e58	−0.460102	−0.230051	+	0.973179i	$0.573889\pi$
$710$	−1.01970e59	−3.61141
$711$	0	0
$712$	−2.34813e58	−0.785022
$713$	6.99613e57	0.227260
$714$	0	0
$715$	6.36228e58	1.95137
$716$	4.76926e58	1.42146
$717$	0	0
$718$	3.53983e58	0.996396
$719$	3.64927e58	0.998307	0.499153	−	0.866514i	$-0.333644\pi$
$719$	3.64927e58	0.998307	0.499153	+	0.866514i	$0.333644\pi$
$720$	0	0
$721$	1.87081e58	0.483455
$722$	6.03936e58	1.51698
$723$	0	0
$724$	4.70205e58	1.11595
$725$	2.88948e58	0.666639
$726$	0	0
$727$	−5.20217e58	−1.13430	−0.567152	−	0.823613i	$-0.691955\pi$
$727$	−5.20217e58	−1.13430	−0.567152	+	0.823613i	$0.691955\pi$
$728$	−2.62929e58	−0.557373
$729$	0	0
$730$	−1.98840e59	−3.98461
$731$	3.90317e56	0.00760521
$732$	0	0
$733$	2.57497e58	0.474396	0.237198	−	0.971461i	$-0.423771\pi$
$733$	2.57497e58	0.474396	0.237198	+	0.971461i	$0.423771\pi$
$734$	−1.34615e59	−2.41171
$735$	0	0
$736$	−1.85821e58	−0.314848
$737$	−5.34713e58	−0.881124
$738$	0	0
$739$	1.07870e59	1.68148	0.840738	−	0.541442i	$-0.182121\pi$
$739$	1.07870e59	1.68148	0.840738	+	0.541442i	$0.182121\pi$
$740$	−1.28152e59	−1.94302
$741$	0	0
$742$	−8.30009e58	−1.19070
$743$	1.21669e59	1.69788	0.848942	−	0.528487i	$-0.177240\pi$
$743$	1.21669e59	1.69788	0.848942	+	0.528487i	$0.177240\pi$
$744$	0	0
$745$	8.59134e56	0.0113464
$746$	2.10943e59	2.71031
$747$	0	0
$748$	3.95136e58	0.480577
$749$	−1.80189e58	−0.213231
$750$	0	0
$751$	6.80995e58	0.763001	0.381500	−	0.924369i	$-0.375408\pi$
$751$	6.80995e58	0.763001	0.381500	+	0.924369i	$0.375408\pi$
$752$	1.17486e57	0.0128092
$753$	0	0
$754$	8.78812e58	0.907368
$755$	2.44726e58	0.245905
$756$	0	0
$757$	−2.77019e58	−0.263660	−0.131830	−	0.991272i	$-0.542085\pi$
$757$	−2.77019e58	−0.263660	−0.131830	+	0.991272i	$0.542085\pi$
$758$	6.56267e58	0.607942
$759$	0	0
$760$	−4.56165e58	−0.400353
$761$	7.33770e57	0.0626866	0.0313433	−	0.999509i	$-0.490021\pi$
$761$	7.33770e57	0.0626866	0.0313433	+	0.999509i	$0.490021\pi$
$762$	0	0
$763$	−1.17397e58	−0.0950391
$764$	3.62893e59	2.85999
$765$	0	0
$766$	6.14167e58	0.458772
$767$	−5.86626e57	−0.0426635
$768$	0	0
$769$	7.07782e58	0.487988	0.243994	−	0.969777i	$-0.421542\pi$
$769$	7.07782e58	0.487988	0.243994	+	0.969777i	$0.421542\pi$
$770$	−1.61091e59	−1.08146
$771$	0	0
$772$	2.93819e59	1.87036
$773$	6.55116e57	0.0406105	0.0203053	−	0.999794i	$-0.493536\pi$
$773$	6.55116e57	0.0406105	0.0203053	+	0.999794i	$0.493536\pi$
$774$	0	0
$775$	−1.84724e59	−1.08602
$776$	−2.46116e59	−1.40921
$777$	0	0
$778$	3.22479e59	1.75154
$779$	5.93279e58	0.313864
$780$	0	0
$781$	−2.71167e59	−1.36110
$782$	−3.21329e58	−0.157113
$783$	0	0
$784$	−1.25928e57	−0.00584311
$785$	−5.98178e59	−2.70397
$786$	0	0
$787$	−3.33588e59	−1.43129	−0.715647	−	0.698462i	$-0.753868\pi$
$787$	−3.33588e59	−1.43129	−0.715647	+	0.698462i	$0.753868\pi$
$788$	−8.11500e58	−0.339235
$789$	0	0
$790$	−5.61760e59	−2.22944
$791$	1.35313e59	0.523265
$792$	0	0
$793$	2.39659e58	0.0880020
$794$	−1.52786e59	−0.546718
$795$	0	0
$796$	5.48467e59	1.86394
$797$	1.53090e59	0.507050	0.253525	−	0.967329i	$-0.418410\pi$
$797$	1.53090e59	0.507050	0.253525	+	0.967329i	$0.418410\pi$
$798$	0	0
$799$	−1.73001e59	−0.544302
$800$	4.90639e59	1.50459
$801$	0	0
$802$	−4.19027e59	−1.22086
$803$	−5.28772e59	−1.50176
$804$	0	0
$805$	8.10245e58	0.218676
$806$	−5.61824e59	−1.47820
$807$	0	0
$808$	−3.09581e59	−0.774180
$809$	1.38621e59	0.337974	0.168987	−	0.985618i	$-0.445950\pi$
$809$	1.38621e59	0.337974	0.168987	+	0.985618i	$0.445950\pi$
$810$	0	0
$811$	8.92972e58	0.206971	0.103486	−	0.994631i	$-0.467000\pi$
$811$	8.92972e58	0.206971	0.103486	+	0.994631i	$0.467000\pi$
$812$	−1.37625e59	−0.311026
$813$	0	0
$814$	−5.50997e59	−1.18399
$815$	5.24545e59	1.09914
$816$	0	0
$817$	−3.12708e57	−0.00623142
$818$	6.96705e59	1.35396
$819$	0	0
$820$	1.73830e60	3.21322
$821$	−5.66077e59	−1.02057	−0.510283	−	0.860007i	$-0.670459\pi$
$821$	−5.66077e59	−1.02057	−0.510283	+	0.860007i	$0.670459\pi$
$822$	0	0
$823$	−9.70422e59	−1.66442	−0.832212	−	0.554458i	$-0.812926\pi$
$823$	−9.70422e59	−1.66442	−0.832212	+	0.554458i	$0.812926\pi$
$824$	6.67372e59	1.11650
$825$	0	0
$826$	1.48532e58	0.0236444
$827$	−1.07249e60	−1.66545	−0.832725	−	0.553687i	$-0.813220\pi$
$827$	−1.07249e60	−1.66545	−0.832725	+	0.553687i	$0.813220\pi$
$828$	0	0
$829$	6.30712e59	0.932101	0.466051	−	0.884758i	$-0.345676\pi$
$829$	6.30712e59	0.932101	0.466051	+	0.884758i	$0.345676\pi$
$830$	1.46802e60	2.11657
$831$	0	0
$832$	1.49892e60	2.05708
$833$	1.85432e59	0.248292
$834$	0	0
$835$	1.87143e60	2.38561
$836$	−3.16569e59	−0.393767
$837$	0	0
$838$	−3.83330e59	−0.454015
$839$	−6.10677e59	−0.705815	−0.352908	−	0.935658i	$-0.614807\pi$
$839$	−6.10677e59	−0.705815	−0.352908	+	0.935658i	$0.614807\pi$
$840$	0	0
$841$	−7.32218e59	−0.805977
$842$	9.75685e59	1.04812
$843$	0	0
$844$	−2.49913e60	−2.55722
$845$	9.82372e59	0.981100
$846$	0	0
$847$	2.93658e58	0.0279404
$848$	−1.31110e58	−0.0121764
$849$	0	0
$850$	8.48430e59	0.750807
$851$	2.77137e59	0.239408
$852$	0	0
$853$	1.07715e60	0.886788	0.443394	−	0.896327i	$-0.353774\pi$
$853$	1.07715e60	0.886788	0.443394	+	0.896327i	$0.353774\pi$
$854$	−6.06808e58	−0.0487714
$855$	0	0
$856$	−6.42788e59	−0.492442
$857$	2.94243e59	0.220090	0.110045	−	0.993927i	$-0.464901\pi$
$857$	2.94243e59	0.220090	0.110045	+	0.993927i	$0.464901\pi$
$858$	0	0
$859$	1.39886e59	0.0997504	0.0498752	−	0.998755i	$-0.484118\pi$
$859$	1.39886e59	0.0997504	0.0498752	+	0.998755i	$0.484118\pi$
$860$	−9.16230e58	−0.0637950
$861$	0	0
$862$	−2.28610e60	−1.51774
$863$	3.64782e59	0.236490	0.118245	−	0.992984i	$-0.462273\pi$
$863$	3.64782e59	0.236490	0.118245	+	0.992984i	$0.462273\pi$
$864$	0	0
$865$	−2.19756e60	−1.35866
$866$	−1.18155e60	−0.713402
$867$	0	0
$868$	8.79834e59	0.506695
$869$	−1.49388e60	−0.840251
$870$	0	0
$871$	−2.15978e60	−1.15887
$872$	−4.18788e59	−0.219486
$873$	0	0
$874$	2.57437e59	0.128732
$875$	−7.25780e59	−0.354519
$876$	0	0
$877$	3.99235e60	1.86096	0.930480	−	0.366341i	$-0.119390\pi$
$877$	3.99235e60	1.86096	0.930480	+	0.366341i	$0.119390\pi$
$878$	−3.30278e60	−1.50398
$879$	0	0
$880$	−2.54462e58	−0.0110593
$881$	−1.50864e60	−0.640589	−0.320295	−	0.947318i	$-0.603782\pi$
$881$	−1.50864e60	−0.640589	−0.320295	+	0.947318i	$0.603782\pi$
$882$	0	0
$883$	−4.31876e60	−1.75051	−0.875254	−	0.483663i	$-0.839306\pi$
$883$	−4.31876e60	−1.75051	−0.875254	+	0.483663i	$0.839306\pi$
$884$	1.59601e60	0.632067
$885$	0	0
$886$	6.08531e60	2.30087
$887$	4.39179e60	1.62259	0.811293	−	0.584640i	$-0.198764\pi$
$887$	4.39179e60	1.62259	0.811293	+	0.584640i	$0.198764\pi$
$888$	0	0
$889$	3.67434e59	0.129626
$890$	−5.81088e60	−2.00330
$891$	0	0
$892$	−7.78340e59	−0.256265
$893$	1.38602e60	0.445981
$894$	0	0
$895$	4.52261e60	1.39001
$896$	−2.35382e60	−0.707064
$897$	0	0
$898$	−9.21644e60	−2.64483
$899$	−1.12688e60	−0.316084
$900$	0	0
$901$	1.93062e60	0.517414
$902$	7.47388e60	1.95800
$903$	0	0
$904$	4.82701e60	1.20844
$905$	4.45887e60	1.09126
$906$	0	0
$907$	1.38889e60	0.324875	0.162438	−	0.986719i	$-0.448064\pi$
$907$	1.38889e60	0.324875	0.162438	+	0.986719i	$0.448064\pi$
$908$	5.85864e60	1.33979
$909$	0	0
$910$	−6.50667e60	−1.42236
$911$	−1.25104e60	−0.267389	−0.133694	−	0.991023i	$-0.542684\pi$
$911$	−1.25104e60	−0.267389	−0.133694	+	0.991023i	$0.542684\pi$
$912$	0	0
$913$	3.90388e60	0.797711
$914$	−1.31256e61	−2.62254
$915$	0	0
$916$	8.24929e60	1.57601
$917$	1.55589e60	0.290675
$918$	0	0
$919$	−1.70510e60	−0.304637	−0.152319	−	0.988331i	$-0.548674\pi$
$919$	−1.70510e60	−0.304637	−0.152319	+	0.988331i	$0.548674\pi$
$920$	2.89038e60	0.505016
$921$	0	0
$922$	−1.64845e61	−2.75482
$923$	−1.09528e61	−1.79016
$924$	0	0
$925$	−7.31747e60	−1.14408
$926$	−6.46962e60	−0.989359
$927$	0	0
$928$	2.99305e60	0.437905
$929$	1.11160e60	0.159084	0.0795422	−	0.996832i	$-0.474654\pi$
$929$	1.11160e60	0.159084	0.0795422	+	0.996832i	$0.474654\pi$
$930$	0	0
$931$	−1.48562e60	−0.203441
$932$	1.87206e61	2.50780
$933$	0	0
$934$	−2.43048e60	−0.311588
$935$	3.74700e60	0.469944
$936$	0	0
$937$	−6.31851e60	−0.758495	−0.379248	−	0.925295i	$-0.623817\pi$
$937$	−6.31851e60	−0.758495	−0.379248	+	0.925295i	$0.623817\pi$
$938$	5.46848e60	0.642257
$939$	0	0
$940$	4.06103e61	4.56578
$941$	6.22380e59	0.0684650	0.0342325	−	0.999414i	$-0.489101\pi$
$941$	6.22380e59	0.0684650	0.0342325	+	0.999414i	$0.489101\pi$
$942$	0	0
$943$	−3.75917e60	−0.395915
$944$	2.34624e57	0.000241794 0
$945$	0	0
$946$	−3.93937e59	−0.0388739
$947$	1.79375e61	1.73216	0.866079	−	0.499907i	$-0.166632\pi$
$947$	1.79375e61	1.73216	0.866079	+	0.499907i	$0.166632\pi$
$948$	0	0
$949$	−2.13578e61	−1.97515
$950$	−6.79733e60	−0.615183
$951$	0	0
$952$	−1.54850e60	−0.134231
$953$	−1.46295e61	−1.24116	−0.620578	−	0.784145i	$-0.713102\pi$
$953$	−1.46295e61	−1.24116	−0.620578	+	0.784145i	$0.713102\pi$
$954$	0	0
$955$	3.44125e61	2.79671
$956$	1.43489e61	1.14138
$957$	0	0
$958$	1.92913e61	1.47018
$959$	−3.64832e60	−0.272152
$960$	0	0
$961$	−6.78626e60	−0.485067
$962$	−2.22555e61	−1.55721
$963$	0	0
$964$	−1.00892e61	−0.676512
$965$	2.78623e61	1.82897
$966$	0	0
$967$	2.19658e61	1.38199	0.690993	−	0.722861i	$-0.257173\pi$
$967$	2.19658e61	1.38199	0.690993	+	0.722861i	$0.257173\pi$
$968$	1.04757e60	0.0645263
$969$	0	0
$970$	−6.09060e61	−3.59617
$971$	−8.01229e60	−0.463193	−0.231597	−	0.972812i	$-0.574395\pi$
$971$	−8.01229e60	−0.463193	−0.231597	+	0.972812i	$0.574395\pi$
$972$	0	0
$973$	2.26069e60	0.125293
$974$	−8.61726e60	−0.467639
$975$	0	0
$976$	−9.58525e57	−0.000498749 0
$977$	1.53487e60	0.0782047	0.0391024	−	0.999235i	$-0.487550\pi$
$977$	1.53487e60	0.0782047	0.0391024	+	0.999235i	$0.487550\pi$
$978$	0	0
$979$	−1.54528e61	−0.755024
$980$	−4.35283e61	−2.08275
$981$	0	0
$982$	1.94982e60	0.0894764
$983$	−2.13980e61	−0.961670	−0.480835	−	0.876811i	$-0.659666\pi$
$983$	−2.13980e61	−0.961670	−0.480835	+	0.876811i	$0.659666\pi$
$984$	0	0
$985$	−7.69531e60	−0.331729
$986$	5.17568e60	0.218520
$987$	0	0
$988$	−1.27866e61	−0.517892
$989$	1.98140e59	0.00786047
$990$	0	0
$991$	2.19295e61	0.834678	0.417339	−	0.908751i	$-0.362963\pi$
$991$	2.19295e61	0.834678	0.417339	+	0.908751i	$0.362963\pi$
$992$	−1.91346e61	−0.713393
$993$	0	0
$994$	2.77322e61	0.992117
$995$	5.20102e61	1.82270
$996$	0	0
$997$	1.15402e61	0.388116	0.194058	−	0.980990i	$-0.437835\pi$
$997$	1.15402e61	0.388116	0.194058	+	0.980990i	$0.437835\pi$
$998$	1.57771e61	0.519819
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.42.a.b.1.1		3
3.2	odd	2		1.42.a.a.1.3	✓	3
12.11	even	2		16.42.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.42.a.a.1.3	✓	3	3.2	odd	2
9.42.a.b.1.1		3	1.1	even	1	trivial
16.42.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q-2.40087e6 q^{2} +3.56518e12 q^{4} +3.38080e14 q^{5} -9.19453e16 q^{7} -3.27996e18 q^{8} +O(q^{10})\)	\(q-2.40087e6 q^{2} +3.56518e12 q^{4} +3.38080e14 q^{5} -9.19453e16 q^{7} -3.27996e18 q^{8} -8.11687e20 q^{10} -2.15850e21 q^{11} -8.71848e22 q^{13} +2.20749e23 q^{14} +3.48699e22 q^{16} -5.13467e24 q^{17} +4.11372e25 q^{19} +1.20531e27 q^{20} +5.18229e27 q^{22} -2.60656e27 q^{23} +6.88231e28 q^{25} +2.09320e29 q^{26} -3.27801e29 q^{28} +4.19842e29 q^{29} -2.68405e30 q^{31} +7.12899e30 q^{32} +1.23277e31 q^{34} -3.10848e31 q^{35} -1.06323e32 q^{37} -9.87652e31 q^{38} -1.10889e33 q^{40} +1.44220e33 q^{41} -7.60160e31 q^{43} -7.69544e33 q^{44} +6.25802e33 q^{46} +3.36927e34 q^{47} -3.61137e34 q^{49} -1.65236e35 q^{50} -3.10829e35 q^{52} -3.75996e35 q^{53} -7.29746e35 q^{55} +3.01577e35 q^{56} -1.00799e36 q^{58} +6.72854e34 q^{59} -2.74886e35 q^{61} +6.44406e36 q^{62} -1.71925e37 q^{64} -2.94754e37 q^{65} +2.47724e37 q^{67} -1.83060e37 q^{68} +7.46308e37 q^{70} +1.25628e38 q^{71} +2.44972e38 q^{73} +2.55268e38 q^{74} +1.46661e38 q^{76} +1.98464e38 q^{77} +6.92089e38 q^{79} +1.17888e37 q^{80} -3.46253e39 q^{82} -1.80861e39 q^{83} -1.73593e39 q^{85} +1.82505e38 q^{86} +7.07980e39 q^{88} +7.15901e39 q^{89} +8.01623e39 q^{91} -9.29284e39 q^{92} -8.08920e40 q^{94} +1.39076e40 q^{95} +7.50364e40 q^{97} +8.67045e40 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 344688 q^{2} + 6271704903936 q^{4} + 212302350281550 q^{5} + 57\!\cdots\!92 q^{7}+ \cdots + 35\!\cdots\!20 q^{8}+O(q^{10}) \) 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

Groups

Database

Properties

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