LMFDB - Embedded newform 9.44.a.c.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,44,Mod(1,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.1"); S:= CuspForms(chi, 44); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 44, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,-1660014] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$105.399355811$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 886516819907x^{2} - 42308083143723387x + 94580276745082867224894 $ x^4 - x^3 - 886516819907x^2 - 42308083143723387x + 94580276745082867224894
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 11 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-388484.$ 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)

$f(q)$	$=$	\(q+1.91590e6 q^{2} -5.12540e12 q^{4} -2.05854e15 q^{5} +1.37114e18 q^{7} -2.66723e19 q^{8} -3.94396e21 q^{10} +2.95641e22 q^{11} +4.85026e23 q^{13} +2.62698e24 q^{14} -6.01799e24 q^{16} -2.08153e26 q^{17} -1.07725e27 q^{19} +1.05508e28 q^{20} +5.66420e28 q^{22} +2.47106e29 q^{23} +3.10071e30 q^{25} +9.29263e29 q^{26} -7.02766e30 q^{28} -1.39089e31 q^{29} +1.48976e31 q^{31} +2.23082e32 q^{32} -3.98801e32 q^{34} -2.82255e33 q^{35} +9.02009e33 q^{37} -2.06390e33 q^{38} +5.49059e34 q^{40} -5.58080e34 q^{41} -2.06648e35 q^{43} -1.51528e35 q^{44} +4.73431e35 q^{46} -6.46223e35 q^{47} -3.03780e35 q^{49} +5.94067e36 q^{50} -2.48595e36 q^{52} +4.21095e36 q^{53} -6.08589e37 q^{55} -3.65715e37 q^{56} -2.66481e37 q^{58} -4.40127e37 q^{59} +4.53571e37 q^{61} +2.85424e37 q^{62} +4.80338e38 q^{64} -9.98445e38 q^{65} -1.64891e37 q^{67} +1.06687e39 q^{68} -5.40774e39 q^{70} -6.75118e39 q^{71} -5.28077e39 q^{73} +1.72816e40 q^{74} +5.52132e39 q^{76} +4.05366e40 q^{77} +1.01508e41 q^{79} +1.23883e40 q^{80} -1.06923e41 q^{82} -2.11545e41 q^{83} +4.28491e41 q^{85} -3.95917e41 q^{86} -7.88542e41 q^{88} +7.34681e41 q^{89} +6.65040e41 q^{91} -1.26652e42 q^{92} -1.23810e42 q^{94} +2.21755e42 q^{95} -6.37472e42 q^{97} -5.82013e41 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1660014 q^{2} + 29333750564548 q^{4} - 16\!\cdots\!20 q^{5} + 11\!\cdots\!28 q^{7} - 77\!\cdots\!48 q^{8} + 53\!\cdots\!60 q^{10} - 87\!\cdots\!96 q^{11} - 16\!\cdots\!96 q^{13} + 13\!\cdots\!08 q^{14}+ \cdots - 62\!\cdots\!46 q^{98}+O(q^{100}) $ 4 * q - 1660014 * q^2 + 29333750564548 * q^4 - 1650650807536920 * q^5 + 114481425784209728 * q^7 - 77966588660971173048 * q^8 + 5359044979781953498260 * q^10 - 8715200555107127298096 * q^11 - 1622373819341917660395496 * q^13 + 13467578670319198438149408 * q^14 + 265331272220473559715915280 * q^16 - 293411853143037894856883976 * q^17 - 2594414378517928782354874288 * q^19 - 8558701143076231384453792920 * q^20 + 74078936455805689993083157032 * q^22 + 165719576853043327961325838944 * q^23 + 2162829068891925341689803823900 * q^25 - 6101006421154528454709899598228 * q^26 - 41688560653908286820790912158656 * q^28 - 50103930548121691368807724902264 * q^29 + 153232269806257085529351412219424 * q^31 - 1375373155850513577371148105862368 * q^32 + 60331877005992911765859543576156 * q^34 - 794758271825314756362531708950400 * q^35 + 19599702088800583695304816898379128 * q^37 - 30934350335669500918957603769116056 * q^38 + 196041911393456394134889832442905680 * q^40 + 9038336825299507042215563101837656 * q^41 + 57884775638210824781567117092305200 * q^43 - 1103928490692495293822086256175019824 * q^44 + 718247490543964330689612210436911024 * q^46 - 489795556049192314087538359958202240 * q^47 - 4317642451006561098818513062358614620 * q^49 + 5579808201219996041105683525421159550 * q^50 - 13582094185786578557618520483683206504 * q^52 + 40271515633256644720413455555285829864 * q^53 - 47661104270181626262923295497298490080 * q^55 + 117390605534482290403396341738920952960 * q^56 + 166036404448317657164763132092855468772 * q^58 + 31284936358538459187079576876991825232 * q^59 - 246678251415393769778200255087667843560 * q^61 - 1447587501085892804433014348598690126576 * q^62 + 3779239307999191671459925914328934335552 * q^64 - 3201204112021109289173748012488728936080 * q^65 + 1029262961963280586877382927523715757776 * q^67 + 5728258265472538567897226405540492998008 * q^68 - 13998939704532003940217885479727831428800 * q^70 + 7158914166122718301934674138622261107872 * q^71 + 5436935716056938749789214886435330158696 * q^73 + 39560290302967463129010858736787279461788 * q^74 - 84965301579645016687884089536788004332208 * q^76 + 70649133554843036086189895413395482145024 * q^77 - 18459961314698254348045108075380001958560 * q^79 - 422317828506146509768424873205600266179680 * q^80 + 147229844429377279789779107991029019615756 * q^82 - 207863929126228047172838511060419328637008 * q^83 + 221112002042063917840135331898684555973680 * q^85 - 458138780643704418519204317947537057045416 * q^86 + 1517878779794169852250121294325123418262688 * q^88 + 442176536724138726190556195414134338798168 * q^89 - 241286657628373017846026300207834298513536 * q^91 + 501856507576284139621951265540431125198432 * q^92 - 12731451681111622228496468053131446537940672 * q^94 + 877953040109009235535219131018818763586080 * q^95 - 5068444705076967721898551548017617825231864 * q^97 - 6262356698119668842821753019159492533814046 * q^98

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 $

$2$	1.91590e6	0.645995	0.322997	−	0.946400i	$-0.395309\pi$
$2$	1.91590e6	0.645995	0.322997	+	0.946400i	$0.395309\pi$
$3$	0	0
$3$	0	0
$4$	−5.12540e12	−0.582691
$5$	−2.05854e15	−1.93065	−0.965326	−	0.261047i	$-0.915932\pi$
$5$	−2.05854e15	−1.93065	−0.965326	+	0.261047i	$0.915932\pi$
$6$	0	0
$7$	1.37114e18	0.927844	0.463922	−	0.885876i	$-0.346442\pi$
$7$	1.37114e18	0.927844	0.463922	+	0.885876i	$0.346442\pi$
$8$	−2.66723e19	−1.02241
$9$	0	0
$10$	−3.94396e21	−1.24719
$11$	2.95641e22	1.20454	0.602271	−	0.798292i	$-0.294263\pi$
$11$	2.95641e22	1.20454	0.602271	+	0.798292i	$0.294263\pi$
$12$	0	0
$13$	4.85026e23	0.544481	0.272241	−	0.962229i	$-0.412235\pi$
$13$	4.85026e23	0.544481	0.272241	+	0.962229i	$0.412235\pi$
$14$	2.62698e24	0.599383
$15$	0	0
$16$	−6.01799e24	−0.0777807
$17$	−2.08153e26	−0.730686	−0.365343	−	0.930873i	$-0.619048\pi$
$17$	−2.08153e26	−0.730686	−0.365343	+	0.930873i	$0.619048\pi$
$18$	0	0
$19$	−1.07725e27	−0.346029	−0.173015	−	0.984919i	$-0.555351\pi$
$19$	−1.07725e27	−0.346029	−0.173015	+	0.984919i	$0.555351\pi$
$20$	1.05508e28	1.12497
$21$	0	0
$22$	5.66420e28	0.778128
$23$	2.47106e29	1.30537	0.652686	−	0.757628i	$-0.273642\pi$
$23$	2.47106e29	1.30537	0.652686	+	0.757628i	$0.273642\pi$
$24$	0	0
$25$	3.10071e30	2.72742
$26$	9.29263e29	0.351732
$27$	0	0
$28$	−7.02766e30	−0.540646
$29$	−1.39089e31	−0.503195	−0.251597	−	0.967832i	$-0.580956\pi$
$29$	−1.39089e31	−0.503195	−0.251597	+	0.967832i	$0.580956\pi$
$30$	0	0
$31$	1.48976e31	0.128481	0.0642406	−	0.997934i	$-0.479537\pi$
$31$	1.48976e31	0.128481	0.0642406	+	0.997934i	$0.479537\pi$
$32$	2.23082e32	0.972164
$33$	0	0
$34$	−3.98801e32	−0.472020
$35$	−2.82255e33	−1.79134
$36$	0	0
$37$	9.02009e33	1.73330	0.866651	−	0.498916i	$-0.166268\pi$
$37$	9.02009e33	1.73330	0.866651	+	0.498916i	$0.166268\pi$
$38$	−2.06390e33	−0.223533
$39$	0	0
$40$	5.49059e34	1.97392
$41$	−5.58080e34	−1.17989	−0.589947	−	0.807442i	$-0.700852\pi$
$41$	−5.58080e34	−1.17989	−0.589947	+	0.807442i	$0.700852\pi$
$42$	0	0
$43$	−2.06648e35	−1.56913	−0.784565	−	0.620047i	$-0.787113\pi$
$43$	−2.06648e35	−1.56913	−0.784565	+	0.620047i	$0.787113\pi$
$44$	−1.51528e35	−0.701876
$45$	0	0
$46$	4.73431e35	0.843264
$47$	−6.46223e35	−0.724901	−0.362450	−	0.932003i	$-0.618060\pi$
$47$	−6.46223e35	−0.724901	−0.362450	+	0.932003i	$0.618060\pi$
$48$	0	0
$49$	−3.03780e35	−0.139105
$50$	5.94067e36	1.76190
$51$	0	0
$52$	−2.48595e36	−0.317264
$53$	4.21095e36	0.356820	0.178410	−	0.983956i	$-0.442905\pi$
$53$	4.21095e36	0.356820	0.178410	+	0.983956i	$0.442905\pi$
$54$	0	0
$55$	−6.08589e37	−2.32555
$56$	−3.65715e37	−0.948637
$57$	0	0
$58$	−2.66481e37	−0.325061
$59$	−4.40127e37	−0.371757	−0.185879	−	0.982573i	$-0.559513\pi$
$59$	−4.40127e37	−0.371757	−0.185879	+	0.982573i	$0.559513\pi$
$60$	0	0
$61$	4.53571e37	0.187091	0.0935457	−	0.995615i	$-0.470180\pi$
$61$	4.53571e37	0.187091	0.0935457	+	0.995615i	$0.470180\pi$
$62$	2.85424e37	0.0829982
$63$	0	0
$64$	4.80338e38	0.705794
$65$	−9.98445e38	−1.05120
$66$	0	0
$67$	−1.64891e37	−0.00904878	−0.00452439	−	0.999990i	$-0.501440\pi$
$67$	−1.64891e37	−0.00904878	−0.00452439	+	0.999990i	$0.501440\pi$
$68$	1.06687e39	0.425764
$69$	0	0
$70$	−5.40774e39	−1.15720
$71$	−6.75118e39	−1.06494	−0.532470	−	0.846449i	$-0.678736\pi$
$71$	−6.75118e39	−1.06494	−0.532470	+	0.846449i	$0.678736\pi$
$72$	0	0
$73$	−5.28077e39	−0.458412	−0.229206	−	0.973378i	$-0.573613\pi$
$73$	−5.28077e39	−0.458412	−0.229206	+	0.973378i	$0.573613\pi$
$74$	1.72816e40	1.11970
$75$	0	0
$76$	5.52132e39	0.201628
$77$	4.05366e40	1.11763
$78$	0	0
$79$	1.01508e41	1.61257	0.806286	−	0.591526i	$-0.201474\pi$
$79$	1.01508e41	1.61257	0.806286	+	0.591526i	$0.201474\pi$
$80$	1.23883e40	0.150167
$81$	0	0
$82$	−1.06923e41	−0.762206
$83$	−2.11545e41	−1.16205	−0.581024	−	0.813886i	$-0.697348\pi$
$83$	−2.11545e41	−1.16205	−0.581024	+	0.813886i	$0.697348\pi$
$84$	0	0
$85$	4.28491e41	1.41070
$86$	−3.95917e41	−1.01365
$87$	0	0
$88$	−7.88542e41	−1.23154
$89$	7.34681e41	0.899940	0.449970	−	0.893044i	$-0.351435\pi$
$89$	7.34681e41	0.899940	0.449970	+	0.893044i	$0.351435\pi$
$90$	0	0
$91$	6.65040e41	0.505194
$92$	−1.26652e42	−0.760629
$93$	0	0
$94$	−1.23810e42	−0.468282
$95$	2.21755e42	0.668062
$96$	0	0
$97$	−6.37472e42	−1.22707	−0.613534	−	0.789668i	$-0.710253\pi$
$97$	−6.37472e42	−1.22707	−0.613534	+	0.789668i	$0.710253\pi$
$98$	−5.82013e41	−0.0898611
$99$	0	0
$100$	−1.58924e43	−1.58924
$101$	−1.97674e43	−1.59602	−0.798012	−	0.602642i	$-0.794115\pi$
$101$	−1.97674e43	−1.59602	−0.798012	+	0.602642i	$0.794115\pi$
$102$	0	0
$103$	2.37782e43	1.25944	0.629721	−	0.776821i	$-0.283169\pi$
$103$	2.37782e43	1.25944	0.629721	+	0.776821i	$0.283169\pi$
$104$	−1.29367e43	−0.556683
$105$	0	0
$106$	8.06778e42	0.230504
$107$	−1.70071e41	−0.00397081	−0.00198541	−	0.999998i	$-0.500632\pi$
$107$	−1.70071e41	−0.00397081	−0.00198541	+	0.999998i	$0.500632\pi$
$108$	0	0
$109$	5.49545e43	0.861656	0.430828	−	0.902434i	$-0.358222\pi$
$109$	5.49545e43	0.861656	0.430828	+	0.902434i	$0.358222\pi$
$110$	−1.16600e44	−1.50229
$111$	0	0
$112$	−8.25153e42	−0.0721683
$113$	−5.69482e43	−0.411427	−0.205714	−	0.978612i	$-0.565952\pi$
$113$	−5.69482e43	−0.411427	−0.205714	+	0.978612i	$0.565952\pi$
$114$	0	0
$115$	−5.08677e44	−2.52022
$116$	7.12888e43	0.293207
$117$	0	0
$118$	−8.43241e43	−0.240153
$119$	−2.85408e44	−0.677963
$120$	0	0
$121$	2.71636e44	0.450922
$122$	8.68999e43	0.120860
$123$	0	0
$124$	−7.63561e43	−0.0748648
$125$	−4.04265e45	−3.33504
$126$	0	0
$127$	−1.89728e45	−1.11263	−0.556316	−	0.830971i	$-0.687786\pi$
$127$	−1.89728e45	−1.11263	−0.556316	+	0.830971i	$0.687786\pi$
$128$	−1.04197e45	−0.516225
$129$	0	0
$130$	−1.91292e45	−0.679072
$131$	−1.03358e45	−0.311179	−0.155590	−	0.987822i	$-0.549728\pi$
$131$	−1.03358e45	−0.311179	−0.155590	+	0.987822i	$0.549728\pi$
$132$	0	0
$133$	−1.47706e45	−0.321061
$134$	−3.15916e43	−0.00584546
$135$	0	0
$136$	5.55191e45	0.747061
$137$	−7.28740e45	−0.837684	−0.418842	−	0.908059i	$-0.637564\pi$
$137$	−7.28740e45	−0.837684	−0.418842	+	0.908059i	$0.637564\pi$
$138$	0	0
$139$	−6.85030e44	−0.0576622	−0.0288311	−	0.999584i	$-0.509178\pi$
$139$	−6.85030e44	−0.0576622	−0.0288311	+	0.999584i	$0.509178\pi$
$140$	1.44667e46	1.04380
$141$	0	0
$142$	−1.29346e46	−0.687945
$143$	1.43394e46	0.655851
$144$	0	0
$145$	2.86320e46	0.971494
$146$	−1.01175e46	−0.296132
$147$	0	0
$148$	−4.62316e46	−1.00998
$149$	8.50711e45	0.160797	0.0803984	−	0.996763i	$-0.474381\pi$
$149$	8.50711e45	0.160797	0.0803984	+	0.996763i	$0.474381\pi$
$150$	0	0
$151$	8.58237e46	1.21788	0.608938	−	0.793218i	$-0.291596\pi$
$151$	8.58237e46	1.21788	0.608938	+	0.793218i	$0.291596\pi$
$152$	2.87326e46	0.353784
$153$	0	0
$154$	7.76643e46	0.721982
$155$	−3.06673e46	−0.248053
$156$	0	0
$157$	2.17438e47	1.33504	0.667519	−	0.744593i	$-0.267356\pi$
$157$	2.17438e47	1.33504	0.667519	+	0.744593i	$0.267356\pi$
$158$	1.94480e47	1.04171
$159$	0	0
$160$	−4.59223e47	−1.87691
$161$	3.38818e47	1.21118
$162$	0	0
$163$	2.10328e47	0.576584	0.288292	−	0.957543i	$-0.406913\pi$
$163$	2.10328e47	0.576584	0.288292	+	0.957543i	$0.406913\pi$
$164$	2.86038e47	0.687514
$165$	0	0
$166$	−4.05300e47	−0.750677
$167$	−4.19368e47	−0.682639	−0.341320	−	0.939947i	$-0.610874\pi$
$167$	−4.19368e47	−0.682639	−0.341320	+	0.939947i	$0.610874\pi$
$168$	0	0
$169$	−5.58281e47	−0.703540
$170$	8.20948e47	0.911305
$171$	0	0
$172$	1.05915e48	0.914317
$173$	2.43273e47	0.185397	0.0926983	−	0.995694i	$-0.470451\pi$
$173$	2.43273e47	0.185397	0.0926983	+	0.995694i	$0.470451\pi$
$174$	0	0
$175$	4.25153e48	2.53062
$176$	−1.77916e47	−0.0936901
$177$	0	0
$178$	1.40758e48	0.581357
$179$	−3.65334e47	−0.133767	−0.0668836	−	0.997761i	$-0.521306\pi$
$179$	−3.65334e47	−0.133767	−0.0668836	+	0.997761i	$0.521306\pi$
$180$	0	0
$181$	−4.64912e48	−1.34054	−0.670272	−	0.742115i	$-0.733823\pi$
$181$	−4.64912e48	−1.34054	−0.670272	+	0.742115i	$0.733823\pi$
$182$	1.27415e48	0.326352
$183$	0	0
$184$	−6.59087e48	−1.33463
$185$	−1.85682e49	−3.34640
$186$	0	0
$187$	−6.15386e48	−0.880143
$188$	3.31215e48	0.422393
$189$	0	0
$190$	4.24862e48	0.431565
$191$	1.11668e49	1.01324	0.506621	−	0.862169i	$-0.330894\pi$
$191$	1.11668e49	1.01324	0.506621	+	0.862169i	$0.330894\pi$
$192$	0	0
$193$	−8.49609e48	−0.616222	−0.308111	−	0.951350i	$-0.599697\pi$
$193$	−8.49609e48	−0.616222	−0.308111	+	0.951350i	$0.599697\pi$
$194$	−1.22134e49	−0.792680
$195$	0	0
$196$	1.55699e48	0.0810552
$197$	2.47958e49	1.15706	0.578529	−	0.815662i	$-0.303627\pi$
$197$	2.47958e49	1.15706	0.578529	+	0.815662i	$0.303627\pi$
$198$	0	0
$199$	−1.43615e49	−0.539336	−0.269668	−	0.962953i	$-0.586914\pi$
$199$	−1.43615e49	−0.539336	−0.269668	+	0.962953i	$0.586914\pi$
$200$	−8.27031e49	−2.78854
$201$	0	0
$202$	−3.78724e49	−1.03102
$203$	−1.90711e49	−0.466886
$204$	0	0
$205$	1.14883e50	2.27797
$206$	4.55567e49	0.813593
$207$	0	0
$208$	−2.91888e48	−0.0423501
$209$	−3.18478e49	−0.416807
$210$	0	0
$211$	−1.63599e49	−0.174464	−0.0872322	−	0.996188i	$-0.527802\pi$
$211$	−1.63599e49	−0.174464	−0.0872322	+	0.996188i	$0.527802\pi$
$212$	−2.15828e49	−0.207916
$213$	0	0
$214$	−3.25840e47	−0.00256512
$215$	4.25392e50	3.02944
$216$	0	0
$217$	2.04267e49	0.119211
$218$	1.05288e50	0.556625
$219$	0	0
$220$	3.11926e50	1.35508
$221$	−1.00960e50	−0.397845
$222$	0	0
$223$	−3.73988e50	−1.21424	−0.607118	−	0.794612i	$-0.707674\pi$
$223$	−3.73988e50	−1.21424	−0.607118	+	0.794612i	$0.707674\pi$
$224$	3.05877e50	0.902017
$225$	0	0
$226$	−1.09107e50	−0.265780
$227$	−8.48595e49	−0.187994	−0.0939972	−	0.995572i	$-0.529964\pi$
$227$	−8.48595e49	−0.187994	−0.0939972	+	0.995572i	$0.529964\pi$
$228$	0	0
$229$	−7.41729e49	−0.136076	−0.0680381	−	0.997683i	$-0.521674\pi$
$229$	−7.41729e49	−0.136076	−0.0680381	+	0.997683i	$0.521674\pi$
$230$	−9.74577e50	−1.62805
$231$	0	0
$232$	3.70982e50	0.514471
$233$	1.00178e51	1.26654	0.633269	−	0.773932i	$-0.281713\pi$
$233$	1.00178e51	1.26654	0.633269	+	0.773932i	$0.281713\pi$
$234$	0	0
$235$	1.33028e51	1.39953
$236$	2.25583e50	0.216620
$237$	0	0
$238$	−5.46814e50	−0.437961
$239$	−8.73908e50	−0.639604	−0.319802	−	0.947484i	$-0.603616\pi$
$239$	−8.73908e50	−0.639604	−0.319802	+	0.947484i	$0.603616\pi$
$240$	0	0
$241$	−3.95900e50	−0.242225	−0.121112	−	0.992639i	$-0.538646\pi$
$241$	−3.95900e50	−0.242225	−0.121112	+	0.992639i	$0.538646\pi$
$242$	5.20428e50	0.291293
$243$	0	0
$244$	−2.32473e50	−0.109016
$245$	6.25342e50	0.268563
$246$	0	0
$247$	−5.22493e50	−0.188406
$248$	−3.97352e50	−0.131360
$249$	0	0
$250$	−7.74534e51	−2.15442
$251$	−1.46542e51	−0.374090	−0.187045	−	0.982351i	$-0.559891\pi$
$251$	−1.46542e51	−0.374090	−0.187045	+	0.982351i	$0.559891\pi$
$252$	0	0
$253$	7.30546e51	1.57238
$254$	−3.63501e51	−0.718755
$255$	0	0
$256$	−6.22141e51	−1.03927
$257$	−1.09888e52	−1.68806	−0.844030	−	0.536296i	$-0.819823\pi$
$257$	−1.09888e52	−1.68806	−0.844030	+	0.536296i	$0.819823\pi$
$258$	0	0
$259$	1.23678e52	1.60823
$260$	5.11743e51	0.612527
$261$	0	0
$262$	−1.98024e51	−0.201020
$263$	−1.90424e51	−0.178104	−0.0890519	−	0.996027i	$-0.528384\pi$
$263$	−1.90424e51	−0.178104	−0.0890519	+	0.996027i	$0.528384\pi$
$264$	0	0
$265$	−8.66841e51	−0.688895
$266$	−2.82991e51	−0.207404
$267$	0	0
$268$	8.45135e49	0.00527264
$269$	−2.81599e52	−1.62165	−0.810826	−	0.585287i	$-0.800982\pi$
$269$	−2.81599e52	−1.62165	−0.810826	+	0.585287i	$0.800982\pi$
$270$	0	0
$271$	−1.50188e52	−0.737558	−0.368779	−	0.929517i	$-0.620224\pi$
$271$	−1.50188e52	−0.737558	−0.368779	+	0.929517i	$0.620224\pi$
$272$	1.25266e51	0.0568333
$273$	0	0
$274$	−1.39620e52	−0.541140
$275$	9.16699e52	3.28529
$276$	0	0
$277$	−2.09522e52	−0.642561	−0.321280	−	0.946984i	$-0.604113\pi$
$277$	−2.09522e52	−0.642561	−0.321280	+	0.946984i	$0.604113\pi$
$278$	−1.31245e51	−0.0372495
$279$	0	0
$280$	7.52839e52	1.83149
$281$	1.94351e52	0.437926	0.218963	−	0.975733i	$-0.429733\pi$
$281$	1.94351e52	0.437926	0.218963	+	0.975733i	$0.429733\pi$
$282$	0	0
$283$	5.63973e52	1.09106	0.545532	−	0.838090i	$-0.316328\pi$
$283$	5.63973e52	1.09106	0.545532	+	0.838090i	$0.316328\pi$
$284$	3.46025e52	0.620531
$285$	0	0
$286$	2.74728e52	0.423676
$287$	−7.65207e52	−1.09476
$288$	0	0
$289$	−3.78251e52	−0.466098
$290$	5.48562e52	0.627580
$291$	0	0
$292$	2.70661e52	0.267112
$293$	1.38284e53	1.26800	0.633998	−	0.773334i	$-0.281413\pi$
$293$	1.38284e53	1.26800	0.633998	+	0.773334i	$0.281413\pi$
$294$	0	0
$295$	9.06018e52	0.717734
$296$	−2.40586e53	−1.77214
$297$	0	0
$298$	1.62988e52	0.103874
$299$	1.19853e53	0.710751
$300$	0	0
$301$	−2.83344e53	−1.45591
$302$	1.64430e53	0.786742
$303$	0	0
$304$	6.48286e51	0.0269144
$305$	−9.33693e52	−0.361208
$306$	0	0
$307$	1.55833e53	0.523822	0.261911	−	0.965092i	$-0.415647\pi$
$307$	1.55833e53	0.523822	0.261911	+	0.965092i	$0.415647\pi$
$308$	−2.07767e53	−0.651231
$309$	0	0
$310$	−5.87556e52	−0.160241
$311$	−3.09503e53	−0.787620	−0.393810	−	0.919192i	$-0.628843\pi$
$311$	−3.09503e53	−0.787620	−0.393810	+	0.919192i	$0.628843\pi$
$312$	0	0
$313$	−6.06624e53	−1.34498	−0.672490	−	0.740106i	$-0.734775\pi$
$313$	−6.06624e53	−1.34498	−0.672490	+	0.740106i	$0.734775\pi$
$314$	4.16591e53	0.862428
$315$	0	0
$316$	−5.20271e53	−0.939631
$317$	−7.12220e53	−1.20182	−0.600911	−	0.799316i	$-0.705195\pi$
$317$	−7.12220e53	−1.20182	−0.600911	+	0.799316i	$0.705195\pi$
$318$	0	0
$319$	−4.11204e53	−0.606119
$320$	−9.88795e53	−1.36264
$321$	0	0
$322$	6.49142e53	0.782418
$323$	2.24232e53	0.252839
$324$	0	0
$325$	1.50393e54	1.48503
$326$	4.02968e53	0.372470
$327$	0	0
$328$	1.48852e54	1.20634
$329$	−8.86065e53	−0.672595
$330$	0	0
$331$	−2.21005e53	−0.147265	−0.0736325	−	0.997285i	$-0.523459\pi$
$331$	−2.21005e53	−0.147265	−0.0736325	+	0.997285i	$0.523459\pi$
$332$	1.08425e54	0.677115
$333$	0	0
$334$	−8.03469e53	−0.440981
$335$	3.39435e52	0.0174700
$336$	0	0
$337$	−9.92988e53	−0.449678	−0.224839	−	0.974396i	$-0.572186\pi$
$337$	−9.92988e53	−0.449678	−0.224839	+	0.974396i	$0.572186\pi$
$338$	−1.06961e54	−0.454483
$339$	0	0
$340$	−2.19619e54	−0.822002
$341$	4.40434e53	0.154761
$342$	0	0
$343$	−3.41085e54	−1.05691
$344$	5.51176e54	1.60429
$345$	0	0
$346$	4.66087e53	0.119765
$347$	2.14712e53	0.0518530	0.0259265	−	0.999664i	$-0.491746\pi$
$347$	2.14712e53	0.0518530	0.0259265	+	0.999664i	$0.491746\pi$
$348$	0	0
$349$	2.01754e53	0.0430601	0.0215300	−	0.999768i	$-0.493146\pi$
$349$	2.01754e53	0.0430601	0.0215300	+	0.999768i	$0.493146\pi$
$350$	8.14552e54	1.63477
$351$	0	0
$352$	6.59521e54	1.17101
$353$	−7.42627e54	−1.24055	−0.620275	−	0.784384i	$-0.712979\pi$
$353$	−7.42627e54	−1.24055	−0.620275	+	0.784384i	$0.712979\pi$
$354$	0	0
$355$	1.38976e55	2.05603
$356$	−3.76554e54	−0.524387
$357$	0	0
$358$	−6.99945e53	−0.0864129
$359$	8.85340e54	1.02939	0.514694	−	0.857374i	$-0.327905\pi$
$359$	8.85340e54	1.02939	0.514694	+	0.857374i	$0.327905\pi$
$360$	0	0
$361$	−8.53135e54	−0.880264
$362$	−8.90727e54	−0.865985
$363$	0	0
$364$	−3.40860e54	−0.294372
$365$	1.08707e55	0.885034
$366$	0	0
$367$	2.72584e55	1.97324	0.986620	−	0.163035i	$-0.0521283\pi$
$367$	2.72584e55	1.97324	0.986620	+	0.163035i	$0.0521283\pi$
$368$	−1.48708e54	−0.101533
$369$	0	0
$370$	−3.55749e55	−2.16176
$371$	5.77382e54	0.331073
$372$	0	0
$373$	−2.12458e55	−1.08526	−0.542628	−	0.839973i	$-0.682571\pi$
$373$	−2.12458e55	−1.08526	−0.542628	+	0.839973i	$0.682571\pi$
$374$	−1.17902e55	−0.568567
$375$	0	0
$376$	1.72362e55	0.741146
$377$	−6.74618e54	−0.273980
$378$	0	0
$379$	2.08438e55	0.755499	0.377750	−	0.925908i	$-0.376698\pi$
$379$	2.08438e55	0.755499	0.377750	+	0.925908i	$0.376698\pi$
$380$	−1.13659e55	−0.389274
$381$	0	0
$382$	2.13946e55	0.654549
$383$	1.15099e55	0.332889	0.166444	−	0.986051i	$-0.446771\pi$
$383$	1.15099e55	0.332889	0.166444	+	0.986051i	$0.446771\pi$
$384$	0	0
$385$	−8.34463e55	−2.15775
$386$	−1.62777e55	−0.398076
$387$	0	0
$388$	3.26730e55	0.715001
$389$	−2.58934e54	−0.0536132	−0.0268066	−	0.999641i	$-0.508534\pi$
$389$	−2.58934e54	−0.0536132	−0.0268066	+	0.999641i	$0.508534\pi$
$390$	0	0
$391$	−5.14358e55	−0.953818
$392$	8.10249e54	0.142222
$393$	0	0
$394$	4.75065e55	0.747453
$395$	−2.08959e56	−3.11331
$396$	0	0
$397$	−4.99618e55	−0.667793	−0.333897	−	0.942610i	$-0.608364\pi$
$397$	−4.99618e55	−0.667793	−0.333897	+	0.942610i	$0.608364\pi$
$398$	−2.75153e55	−0.348408
$399$	0	0
$400$	−1.86601e55	−0.212140
$401$	−5.05004e55	−0.544115	−0.272058	−	0.962281i	$-0.587704\pi$
$401$	−5.05004e55	−0.544115	−0.272058	+	0.962281i	$0.587704\pi$
$402$	0	0
$403$	7.22572e54	0.0699556
$404$	1.01316e56	0.929988
$405$	0	0
$406$	−3.65384e55	−0.301606
$407$	2.66671e56	2.08783
$408$	0	0
$409$	2.15446e56	1.51806	0.759028	−	0.651058i	$-0.225674\pi$
$409$	2.15446e56	1.51806	0.759028	+	0.651058i	$0.225674\pi$
$410$	2.20105e56	1.47155
$411$	0	0
$412$	−1.21873e56	−0.733866
$413$	−6.03477e55	−0.344933
$414$	0	0
$415$	4.35474e56	2.24351
$416$	1.08200e56	0.529325
$417$	0	0
$418$	−6.10174e55	−0.269255
$419$	3.43101e56	1.43820	0.719102	−	0.694904i	$-0.244553\pi$
$419$	3.43101e56	1.43820	0.719102	+	0.694904i	$0.244553\pi$
$420$	0	0
$421$	−4.45367e56	−1.68521	−0.842603	−	0.538536i	$-0.818978\pi$
$421$	−4.45367e56	−1.68521	−0.842603	+	0.538536i	$0.818978\pi$
$422$	−3.13439e55	−0.112703
$423$	0	0
$424$	−1.12316e56	−0.364816
$425$	−6.45423e56	−1.99289
$426$	0	0
$427$	6.21911e55	0.173592
$428$	8.71683e53	0.00231376
$429$	0	0
$430$	8.15011e56	1.95700
$431$	1.15170e56	0.263074	0.131537	−	0.991311i	$-0.458009\pi$
$431$	1.15170e56	0.263074	0.131537	+	0.991311i	$0.458009\pi$
$432$	0	0
$433$	2.47297e56	0.511362	0.255681	−	0.966761i	$-0.417700\pi$
$433$	2.47297e56	0.511362	0.255681	+	0.966761i	$0.417700\pi$
$434$	3.91357e55	0.0770094
$435$	0	0
$436$	−2.81664e56	−0.502079
$437$	−2.66194e56	−0.451697
$438$	0	0
$439$	4.99561e55	0.0768424	0.0384212	−	0.999262i	$-0.487767\pi$
$439$	4.99561e55	0.0768424	0.0384212	+	0.999262i	$0.487767\pi$
$440$	1.62324e57	2.37767
$441$	0	0
$442$	−1.93429e56	−0.257006
$443$	−1.10930e57	−1.40401	−0.702003	−	0.712174i	$-0.747711\pi$
$443$	−1.10930e57	−1.40401	−0.702003	+	0.712174i	$0.747711\pi$
$444$	0	0
$445$	−1.51237e57	−1.73747
$446$	−7.16525e56	−0.784389
$447$	0	0
$448$	6.58613e56	0.654866
$449$	4.08332e55	0.0387005	0.0193503	−	0.999813i	$-0.493840\pi$
$449$	4.08332e55	0.0387005	0.0193503	+	0.999813i	$0.493840\pi$
$450$	0	0
$451$	−1.64991e57	−1.42123
$452$	2.91882e56	0.239735
$453$	0	0
$454$	−1.62583e56	−0.121443
$455$	−1.36901e57	−0.975353
$456$	0	0
$457$	−1.23487e57	−0.800611	−0.400305	−	0.916382i	$-0.631096\pi$
$457$	−1.23487e57	−0.800611	−0.400305	+	0.916382i	$0.631096\pi$
$458$	−1.42108e56	−0.0879045
$459$	0	0
$460$	2.60717e57	1.46851
$461$	−1.83528e57	−0.986580	−0.493290	−	0.869865i	$-0.664206\pi$
$461$	−1.83528e57	−0.986580	−0.493290	+	0.869865i	$0.664206\pi$
$462$	0	0
$463$	8.87478e56	0.434677	0.217338	−	0.976096i	$-0.430262\pi$
$463$	8.87478e56	0.434677	0.217338	+	0.976096i	$0.430262\pi$
$464$	8.37036e55	0.0391388
$465$	0	0
$466$	1.91931e57	0.818177
$467$	9.54635e56	0.388620	0.194310	−	0.980940i	$-0.437753\pi$
$467$	9.54635e56	0.388620	0.194310	+	0.980940i	$0.437753\pi$
$468$	0	0
$469$	−2.26090e55	−0.00839586
$470$	2.54868e57	0.904090
$471$	0	0
$472$	1.17392e57	0.380089
$473$	−6.10935e57	−1.89008
$474$	0	0
$475$	−3.34024e57	−0.943766
$476$	1.46283e57	0.395043
$477$	0	0
$478$	−1.67432e57	−0.413181
$479$	−1.34733e57	−0.317877	−0.158939	−	0.987288i	$-0.550807\pi$
$479$	−1.34733e57	−0.317877	−0.158939	+	0.987288i	$0.550807\pi$
$480$	0	0
$481$	4.37498e57	0.943750
$482$	−7.58506e56	−0.156476
$483$	0	0
$484$	−1.39224e57	−0.262748
$485$	1.31226e58	2.36904
$486$	0	0
$487$	−9.08466e57	−1.50119	−0.750596	−	0.660762i	$-0.770233\pi$
$487$	−9.08466e57	−1.50119	−0.750596	+	0.660762i	$0.770233\pi$
$488$	−1.20978e57	−0.191284
$489$	0	0
$490$	1.19810e57	0.173491
$491$	8.89699e57	1.23308	0.616540	−	0.787324i	$-0.288534\pi$
$491$	8.89699e57	1.23308	0.616540	+	0.787324i	$0.288534\pi$
$492$	0	0
$493$	2.89518e57	0.367677
$494$	−1.00105e57	−0.121710
$495$	0	0
$496$	−8.96535e55	−0.00999335
$497$	−9.25683e57	−0.988098
$498$	0	0
$499$	−7.85254e56	−0.0768862	−0.0384431	−	0.999261i	$-0.512240\pi$
$499$	−7.85254e56	−0.0768862	−0.0384431	+	0.999261i	$0.512240\pi$
$500$	2.07202e58	1.94330
$501$	0	0
$502$	−2.80760e57	−0.241660
$503$	−2.18276e58	−1.80009	−0.900044	−	0.435800i	$-0.856466\pi$
$503$	−2.18276e58	−1.80009	−0.900044	+	0.435800i	$0.856466\pi$
$504$	0	0
$505$	4.06919e58	3.08137
$506$	1.39966e58	1.01575
$507$	0	0
$508$	9.72433e57	0.648321
$509$	9.01858e57	0.576376	0.288188	−	0.957574i	$-0.406947\pi$
$509$	9.01858e57	0.576376	0.288188	+	0.957574i	$0.406947\pi$
$510$	0	0
$511$	−7.24069e57	−0.425335
$512$	−2.75439e57	−0.155139
$513$	0	0
$514$	−2.10535e58	−1.09048
$515$	−4.89483e58	−2.43155
$516$	0	0
$517$	−1.91050e58	−0.873174
$518$	2.36956e58	1.03891
$519$	0	0
$520$	2.66308e58	1.07476
$521$	4.86422e57	0.188366	0.0941829	−	0.995555i	$-0.469976\pi$
$521$	4.86422e57	0.188366	0.0941829	+	0.995555i	$0.469976\pi$
$522$	0	0
$523$	−4.83195e58	−1.72320	−0.861601	−	0.507586i	$-0.830538\pi$
$523$	−4.83195e58	−1.72320	−0.861601	+	0.507586i	$0.830538\pi$
$524$	5.29750e57	0.181321
$525$	0	0
$526$	−3.64834e57	−0.115054
$527$	−3.10098e57	−0.0938795
$528$	0	0
$529$	2.52272e58	0.703998
$530$	−1.66078e58	−0.445023
$531$	0	0
$532$	7.57053e57	0.187079
$533$	−2.70683e58	−0.642430
$534$	0	0
$535$	3.50098e56	0.00766626
$536$	4.39803e56	0.00925156
$537$	0	0
$538$	−5.39517e58	−1.04758
$539$	−8.98097e57	−0.167558
$540$	0	0
$541$	−8.31551e58	−1.43267	−0.716337	−	0.697754i	$-0.754183\pi$
$541$	−8.31551e58	−1.43267	−0.716337	+	0.697754i	$0.754183\pi$
$542$	−2.87746e58	−0.476458
$543$	0	0
$544$	−4.64351e58	−0.710347
$545$	−1.13126e59	−1.66356
$546$	0	0
$547$	−1.45905e58	−0.198310	−0.0991548	−	0.995072i	$-0.531614\pi$
$547$	−1.45905e58	−0.198310	−0.0991548	+	0.995072i	$0.531614\pi$
$548$	3.73508e58	0.488111
$549$	0	0
$550$	1.75631e59	2.12228
$551$	1.49833e58	0.174120
$552$	0	0
$553$	1.39182e59	1.49622
$554$	−4.01424e58	−0.415091
$555$	0	0
$556$	3.51105e57	0.0335992
$557$	1.75662e59	1.61730	0.808650	−	0.588290i	$-0.200199\pi$
$557$	1.75662e59	1.61730	0.808650	+	0.588290i	$0.200199\pi$
$558$	0	0
$559$	−1.00229e59	−0.854361
$560$	1.69861e58	0.139332
$561$	0	0
$562$	3.72358e58	0.282898
$563$	1.51361e59	1.10684	0.553418	−	0.832903i	$-0.313323\pi$
$563$	1.51361e59	1.10684	0.553418	+	0.832903i	$0.313323\pi$
$564$	0	0
$565$	1.17230e59	0.794323
$566$	1.08052e59	0.704821
$567$	0	0
$568$	1.80069e59	1.08880
$569$	−2.44840e59	−1.42550	−0.712752	−	0.701417i	$-0.752551\pi$
$569$	−2.44840e59	−1.42550	−0.712752	+	0.701417i	$0.752551\pi$
$570$	0	0
$571$	−2.27586e59	−1.22877	−0.614384	−	0.789007i	$-0.710595\pi$
$571$	−2.27586e59	−1.22877	−0.614384	+	0.789007i	$0.710595\pi$
$572$	−7.34950e58	−0.382158
$573$	0	0
$574$	−1.46606e59	−0.707208
$575$	7.66205e59	3.56030
$576$	0	0
$577$	−5.18881e58	−0.223763	−0.111881	−	0.993722i	$-0.535688\pi$
$577$	−5.18881e58	−0.223763	−0.111881	+	0.993722i	$0.535688\pi$
$578$	−7.24693e58	−0.301097
$579$	0	0
$580$	−1.46751e59	−0.566081
$581$	−2.90059e59	−1.07820
$582$	0	0
$583$	1.24493e59	0.429805
$584$	1.40850e59	0.468685
$585$	0	0
$586$	2.64939e59	0.819119
$587$	−2.57601e59	−0.767764	−0.383882	−	0.923382i	$-0.625413\pi$
$587$	−2.57601e59	−0.767764	−0.383882	+	0.923382i	$0.625413\pi$
$588$	0	0
$589$	−1.60484e58	−0.0444583
$590$	1.73585e59	0.463653
$591$	0	0
$592$	−5.42828e58	−0.134817
$593$	−3.64832e59	−0.873810	−0.436905	−	0.899508i	$-0.643925\pi$
$593$	−3.64832e59	−0.873810	−0.436905	+	0.899508i	$0.643925\pi$
$594$	0	0
$595$	5.87523e59	1.30891
$596$	−4.36023e58	−0.0936948
$597$	0	0
$598$	2.29626e59	0.459141
$599$	3.13536e58	0.0604798	0.0302399	−	0.999543i	$-0.490373\pi$
$599$	3.13536e58	0.0604798	0.0302399	+	0.999543i	$0.490373\pi$
$600$	0	0
$601$	−5.61238e59	−1.00773	−0.503867	−	0.863781i	$-0.668090\pi$
$601$	−5.61238e59	−1.00773	−0.503867	+	0.863781i	$0.668090\pi$
$602$	−5.42859e59	−0.940509
$603$	0	0
$604$	−4.39881e59	−0.709645
$605$	−5.59173e59	−0.870574
$606$	0	0
$607$	−4.58204e59	−0.664511	−0.332255	−	0.943189i	$-0.607810\pi$
$607$	−4.58204e59	−0.664511	−0.332255	+	0.943189i	$0.607810\pi$
$608$	−2.40314e59	−0.336397
$609$	0	0
$610$	−1.78887e59	−0.233339
$611$	−3.13435e59	−0.394695
$612$	0	0
$613$	−1.17245e60	−1.37624	−0.688118	−	0.725599i	$-0.741563\pi$
$613$	−1.17245e60	−1.37624	−0.688118	+	0.725599i	$0.741563\pi$
$614$	2.98561e59	0.338387
$615$	0	0
$616$	−1.08120e60	−1.14267
$617$	1.43564e60	1.46526	0.732628	−	0.680629i	$-0.238293\pi$
$617$	1.43564e60	1.46526	0.732628	+	0.680629i	$0.238293\pi$
$618$	0	0
$619$	1.66096e60	1.58129	0.790644	−	0.612276i	$-0.209746\pi$
$619$	1.66096e60	1.58129	0.790644	+	0.612276i	$0.209746\pi$
$620$	1.57182e59	0.144538
$621$	0	0
$622$	−5.92978e59	−0.508798
$623$	1.00735e60	0.835005
$624$	0	0
$625$	4.79686e60	3.71139
$626$	−1.16223e60	−0.868850
$627$	0	0
$628$	−1.11446e60	−0.777914
$629$	−1.87756e60	−1.26650
$630$	0	0
$631$	−5.47413e59	−0.344892	−0.172446	−	0.985019i	$-0.555167\pi$
$631$	−5.47413e59	−0.344892	−0.172446	+	0.985019i	$0.555167\pi$
$632$	−2.70745e60	−1.64871
$633$	0	0
$634$	−1.36455e60	−0.776371
$635$	3.90563e60	2.14811
$636$	0	0
$637$	−1.47341e59	−0.0757401
$638$	−7.87829e59	−0.391550
$639$	0	0
$640$	2.14493e60	0.996651
$641$	3.66398e59	0.164628	0.0823142	−	0.996606i	$-0.473769\pi$
$641$	3.66398e59	0.164628	0.0823142	+	0.996606i	$0.473769\pi$
$642$	0	0
$643$	−2.84143e60	−1.19399	−0.596995	−	0.802245i	$-0.703639\pi$
$643$	−2.84143e60	−1.19399	−0.596995	+	0.802245i	$0.703639\pi$
$644$	−1.73658e60	−0.705745
$645$	0	0
$646$	4.29608e59	0.163333
$647$	1.01042e60	0.371585	0.185793	−	0.982589i	$-0.440515\pi$
$647$	1.01042e60	0.371585	0.185793	+	0.982589i	$0.440515\pi$
$648$	0	0
$649$	−1.30120e60	−0.447798
$650$	2.88138e60	0.959320
$651$	0	0
$652$	−1.07801e60	−0.335970
$653$	4.87378e59	0.146971	0.0734857	−	0.997296i	$-0.476588\pi$
$653$	4.87378e59	0.146971	0.0734857	+	0.997296i	$0.476588\pi$
$654$	0	0
$655$	2.12766e60	0.600779
$656$	3.35852e59	0.0917730
$657$	0	0
$658$	−1.69762e60	−0.434493
$659$	7.34783e60	1.82022	0.910108	−	0.414371i	$-0.135998\pi$
$659$	7.34783e60	1.82022	0.910108	+	0.414371i	$0.135998\pi$
$660$	0	0
$661$	6.39610e60	1.48451	0.742256	−	0.670116i	$-0.233756\pi$
$661$	6.39610e60	1.48451	0.742256	+	0.670116i	$0.233756\pi$
$662$	−4.23424e59	−0.0951324
$663$	0	0
$664$	5.64239e60	1.18809
$665$	3.04059e60	0.619858
$666$	0	0
$667$	−3.43697e60	−0.656857
$668$	2.14943e60	0.397768
$669$	0	0
$670$	6.50326e58	0.0112856
$671$	1.34094e60	0.225359
$672$	0	0
$673$	−5.66196e60	−0.892571	−0.446285	−	0.894891i	$-0.647253\pi$
$673$	−5.66196e60	−0.892571	−0.446285	+	0.894891i	$0.647253\pi$
$674$	−1.90247e60	−0.290489
$675$	0	0
$676$	2.86142e60	0.409946
$677$	−8.79026e60	−1.21996	−0.609980	−	0.792417i	$-0.708823\pi$
$677$	−8.79026e60	−1.21996	−0.609980	+	0.792417i	$0.708823\pi$
$678$	0	0
$679$	−8.74065e60	−1.13853
$680$	−1.14288e61	−1.44231
$681$	0	0
$682$	8.43830e59	0.0999748
$683$	−1.82024e60	−0.208969	−0.104485	−	0.994526i	$-0.533319\pi$
$683$	−1.82024e60	−0.208969	−0.104485	+	0.994526i	$0.533319\pi$
$684$	0	0
$685$	1.50014e61	1.61728
$686$	−6.53486e60	−0.682760
$687$	0	0
$688$	1.24360e60	0.122048
$689$	2.04242e60	0.194282
$690$	0	0
$691$	−9.14476e60	−0.817324	−0.408662	−	0.912686i	$-0.634005\pi$
$691$	−9.14476e60	−0.817324	−0.408662	+	0.912686i	$0.634005\pi$
$692$	−1.24687e60	−0.108029
$693$	0	0
$694$	4.11369e59	0.0334967
$695$	1.41016e60	0.111326
$696$	0	0
$697$	1.16166e61	0.862133
$698$	3.86541e59	0.0278166
$699$	0	0
$700$	−2.17908e61	−1.47457
$701$	−1.07211e61	−0.703560	−0.351780	−	0.936083i	$-0.614423\pi$
$701$	−1.07211e61	−0.703560	−0.351780	+	0.936083i	$0.614423\pi$
$702$	0	0
$703$	−9.71687e60	−0.599773
$704$	1.42008e61	0.850158
$705$	0	0
$706$	−1.42280e61	−0.801389
$707$	−2.71039e61	−1.48086
$708$	0	0
$709$	6.45364e60	0.331826	0.165913	−	0.986140i	$-0.446943\pi$
$709$	6.45364e60	0.331826	0.165913	+	0.986140i	$0.446943\pi$
$710$	2.66264e61	1.32818
$711$	0	0
$712$	−1.95956e61	−0.920108
$713$	3.68128e60	0.167716
$714$	0	0
$715$	−2.95181e61	−1.26622
$716$	1.87248e60	0.0779449
$717$	0	0
$718$	1.69623e61	0.664980
$719$	4.63987e60	0.176537	0.0882683	−	0.996097i	$-0.471867\pi$
$719$	4.63987e60	0.176537	0.0882683	+	0.996097i	$0.471867\pi$
$720$	0	0
$721$	3.26033e61	1.16857
$722$	−1.63452e61	−0.568646
$723$	0	0
$724$	2.38286e61	0.781123
$725$	−4.31276e61	−1.37242
$726$	0	0
$727$	1.44955e61	0.434753	0.217376	−	0.976088i	$-0.430250\pi$
$727$	1.44955e61	0.434753	0.217376	+	0.976088i	$0.430250\pi$
$728$	−1.77381e61	−0.516515
$729$	0	0
$730$	2.08272e61	0.571727
$731$	4.30143e61	1.14654
$732$	0	0
$733$	2.28885e61	0.575282	0.287641	−	0.957738i	$-0.407129\pi$
$733$	2.28885e61	0.575282	0.287641	+	0.957738i	$0.407129\pi$
$734$	5.22245e61	1.27470
$735$	0	0
$736$	5.51248e61	1.26904
$737$	−4.87487e59	−0.0108996
$738$	0	0
$739$	−1.52004e61	−0.320628	−0.160314	−	0.987066i	$-0.551251\pi$
$739$	−1.52004e61	−0.320628	−0.160314	+	0.987066i	$0.551251\pi$
$740$	9.51696e61	1.94992
$741$	0	0
$742$	1.10621e61	0.213872
$743$	7.23666e61	1.35919	0.679593	−	0.733589i	$-0.262156\pi$
$743$	7.23666e61	1.35919	0.679593	+	0.733589i	$0.262156\pi$
$744$	0	0
$745$	−1.75122e61	−0.310443
$746$	−4.07049e61	−0.701070
$747$	0	0
$748$	3.15410e61	0.512851
$749$	−2.33192e59	−0.00368430
$750$	0	0
$751$	−1.13301e62	−1.69034	−0.845171	−	0.534496i	$-0.820502\pi$
$751$	−1.13301e62	−1.69034	−0.845171	+	0.534496i	$0.820502\pi$
$752$	3.88896e60	0.0563833
$753$	0	0
$754$	−1.29250e61	−0.176990
$755$	−1.76672e62	−2.35129
$756$	0	0
$757$	−1.15154e62	−1.44783	−0.723916	−	0.689888i	$-0.757660\pi$
$757$	−1.15154e62	−1.44783	−0.723916	+	0.689888i	$0.757660\pi$
$758$	3.99348e61	0.488049
$759$	0	0
$760$	−5.91472e61	−0.683033
$761$	1.34334e62	1.50805	0.754025	−	0.656845i	$-0.228110\pi$
$761$	1.34334e62	1.50805	0.754025	+	0.656845i	$0.228110\pi$
$762$	0	0
$763$	7.53505e61	0.799482
$764$	−5.72346e61	−0.590407
$765$	0	0
$766$	2.20519e61	0.215044
$767$	−2.13473e61	−0.202415
$768$	0	0
$769$	9.50818e61	0.852474	0.426237	−	0.904612i	$-0.359839\pi$
$769$	9.50818e61	0.852474	0.426237	+	0.904612i	$0.359839\pi$
$770$	−1.59875e62	−1.39390
$771$	0	0
$772$	4.35459e61	0.359067
$773$	−2.61737e61	−0.209897	−0.104949	−	0.994478i	$-0.533468\pi$
$773$	−2.61737e61	−0.209897	−0.104949	+	0.994478i	$0.533468\pi$
$774$	0	0
$775$	4.61932e61	0.350422
$776$	1.70028e62	1.25457
$777$	0	0
$778$	−4.96092e60	−0.0346339
$779$	6.01190e61	0.408278
$780$	0	0
$781$	−1.99593e62	−1.28276
$782$	−9.85461e61	−0.616161
$783$	0	0
$784$	1.82814e60	0.0108197
$785$	−4.47605e62	−2.57749
$786$	0	0
$787$	3.01082e62	1.64145	0.820726	−	0.571322i	$-0.193569\pi$
$787$	3.01082e62	1.64145	0.820726	+	0.571322i	$0.193569\pi$
$788$	−1.27089e62	−0.674207
$789$	0	0
$790$	−4.00345e62	−2.01118
$791$	−7.80841e61	−0.381741
$792$	0	0
$793$	2.19994e61	0.101868
$794$	−9.57220e61	−0.431391
$795$	0	0
$796$	7.36086e61	0.314266
$797$	2.40878e62	1.00102	0.500511	−	0.865730i	$-0.333145\pi$
$797$	2.40878e62	1.00102	0.500511	+	0.865730i	$0.333145\pi$
$798$	0	0
$799$	1.34513e62	0.529675
$800$	6.91713e62	2.65150
$801$	0	0
$802$	−9.67540e61	−0.351496
$803$	−1.56121e62	−0.552176
$804$	0	0
$805$	−6.97469e62	−2.33837
$806$	1.38438e61	0.0451909
$807$	0	0
$808$	5.27240e62	1.63179
$809$	1.56406e62	0.471369	0.235685	−	0.971830i	$-0.424267\pi$
$809$	1.56406e62	0.471369	0.235685	+	0.971830i	$0.424267\pi$
$810$	0	0
$811$	1.12549e62	0.321656	0.160828	−	0.986982i	$-0.448584\pi$
$811$	1.12549e62	0.321656	0.160828	+	0.986982i	$0.448584\pi$
$812$	9.77471e61	0.272050
$813$	0	0
$814$	5.10916e62	1.34873
$815$	−4.32967e62	−1.11318
$816$	0	0
$817$	2.22611e62	0.542965
$818$	4.12775e62	0.980657
$819$	0	0
$820$	−5.88821e62	−1.32735
$821$	−5.96819e61	−0.131058	−0.0655291	−	0.997851i	$-0.520874\pi$
$821$	−5.96819e61	−0.131058	−0.0655291	+	0.997851i	$0.520874\pi$
$822$	0	0
$823$	−4.06781e62	−0.847743	−0.423872	−	0.905722i	$-0.639329\pi$
$823$	−4.06781e62	−0.847743	−0.423872	+	0.905722i	$0.639329\pi$
$824$	−6.34218e62	−1.28767
$825$	0	0
$826$	−1.15620e62	−0.222825
$827$	4.41980e61	0.0829915	0.0414958	−	0.999139i	$-0.486788\pi$
$827$	4.41980e61	0.0829915	0.0414958	+	0.999139i	$0.486788\pi$
$828$	0	0
$829$	1.49177e62	0.265937	0.132969	−	0.991120i	$-0.457549\pi$
$829$	1.49177e62	0.265937	0.132969	+	0.991120i	$0.457549\pi$
$830$	8.34327e62	1.44930
$831$	0	0
$832$	2.32976e62	0.384291
$833$	6.32326e61	0.101642
$834$	0	0
$835$	8.63286e62	1.31794
$836$	1.63233e62	0.242870
$837$	0	0
$838$	6.57349e62	0.929072
$839$	−1.09602e62	−0.150986	−0.0754930	−	0.997146i	$-0.524053\pi$
$839$	−1.09602e62	−0.150986	−0.0754930	+	0.997146i	$0.524053\pi$
$840$	0	0
$841$	−5.70578e62	−0.746795
$842$	−8.53281e62	−1.08863
$843$	0	0
$844$	8.38508e61	0.101659
$845$	1.14924e63	1.35829
$846$	0	0
$847$	3.72452e62	0.418386
$848$	−2.53415e61	−0.0277537
$849$	0	0
$850$	−1.23657e63	−1.28739
$851$	2.22892e63	2.26260
$852$	0	0
$853$	−5.00803e61	−0.0483351	−0.0241675	−	0.999708i	$-0.507694\pi$
$853$	−5.00803e61	−0.0483351	−0.0241675	+	0.999708i	$0.507694\pi$
$854$	1.19152e62	0.112139
$855$	0	0
$856$	4.53618e60	0.00405980
$857$	−1.37674e63	−1.20161	−0.600805	−	0.799396i	$-0.705153\pi$
$857$	−1.37674e63	−1.20161	−0.600805	+	0.799396i	$0.705153\pi$
$858$	0	0
$859$	1.75498e62	0.145687	0.0728434	−	0.997343i	$-0.476793\pi$
$859$	1.75498e62	0.145687	0.0728434	+	0.997343i	$0.476793\pi$
$860$	−2.18031e63	−1.76523
$861$	0	0
$862$	2.20655e62	0.169944
$863$	−2.82644e62	−0.212328	−0.106164	−	0.994349i	$-0.533857\pi$
$863$	−2.82644e62	−0.212328	−0.106164	+	0.994349i	$0.533857\pi$
$864$	0	0
$865$	−5.00786e62	−0.357936
$866$	4.73797e62	0.330337
$867$	0	0
$868$	−1.04695e62	−0.0694629
$869$	3.00100e63	1.94241
$870$	0	0
$871$	−7.99766e60	−0.00492689
$872$	−1.46576e63	−0.880965
$873$	0	0
$874$	−5.10002e62	−0.291794
$875$	−5.54306e63	−3.09440
$876$	0	0
$877$	−6.64060e62	−0.352952	−0.176476	−	0.984305i	$-0.556470\pi$
$877$	−6.64060e62	−0.352952	−0.176476	+	0.984305i	$0.556470\pi$
$878$	9.57111e61	0.0496398
$879$	0	0
$880$	3.66248e62	0.180883
$881$	−3.34334e62	−0.161138	−0.0805690	−	0.996749i	$-0.525674\pi$
$881$	−3.34334e62	−0.161138	−0.0805690	+	0.996749i	$0.525674\pi$
$882$	0	0
$883$	2.18835e63	1.00453	0.502263	−	0.864715i	$-0.332501\pi$
$883$	2.18835e63	1.00453	0.502263	+	0.864715i	$0.332501\pi$
$884$	5.17459e62	0.231821
$885$	0	0
$886$	−2.12531e63	−0.906980
$887$	1.17168e63	0.488034	0.244017	−	0.969771i	$-0.421535\pi$
$887$	1.17168e63	0.488034	0.244017	+	0.969771i	$0.421535\pi$
$888$	0	0
$889$	−2.60144e63	−1.03235
$890$	−2.89756e63	−1.12240
$891$	0	0
$892$	1.91684e63	0.707524
$893$	6.96142e62	0.250837
$894$	0	0
$895$	7.52054e62	0.258258
$896$	−1.42868e63	−0.478977
$897$	0	0
$898$	7.82325e61	0.0250003
$899$	−2.07209e62	−0.0646511
$900$	0	0
$901$	−8.76523e62	−0.260723
$902$	−3.16108e63	−0.918109
$903$	0	0
$904$	1.51894e63	0.420647
$905$	9.57039e63	2.58813
$906$	0	0
$907$	−1.34194e63	−0.346081	−0.173041	−	0.984915i	$-0.555359\pi$
$907$	−1.34194e63	−0.346081	−0.173041	+	0.984915i	$0.555359\pi$
$908$	4.34939e62	0.109543
$909$	0	0
$910$	−2.62289e63	−0.630073
$911$	4.78106e63	1.12171	0.560853	−	0.827915i	$-0.310473\pi$
$911$	4.78106e63	1.12171	0.560853	+	0.827915i	$0.310473\pi$
$912$	0	0
$913$	−6.25414e63	−1.39974
$914$	−2.36588e63	−0.517190
$915$	0	0
$916$	3.80166e62	0.0792904
$917$	−1.41718e63	−0.288726
$918$	0	0
$919$	3.81921e63	0.742489	0.371245	−	0.928535i	$-0.378931\pi$
$919$	3.81921e63	0.742489	0.371245	+	0.928535i	$0.378931\pi$
$920$	1.35676e64	2.57670
$921$	0	0
$922$	−3.51622e63	−0.637326
$923$	−3.27450e63	−0.579840
$924$	0	0
$925$	2.79687e64	4.72744
$926$	1.70032e63	0.280799
$927$	0	0
$928$	−3.10282e63	−0.489188
$929$	−6.39575e63	−0.985266	−0.492633	−	0.870237i	$-0.663965\pi$
$929$	−6.39575e63	−0.985266	−0.492633	+	0.870237i	$0.663965\pi$
$930$	0	0
$931$	3.27246e62	0.0481344
$932$	−5.13450e63	−0.738000
$933$	0	0
$934$	1.82899e63	0.251046
$935$	1.26680e64	1.69925
$936$	0	0
$937$	1.49402e64	1.91405	0.957027	−	0.290000i	$-0.0936554\pi$
$937$	1.49402e64	1.91405	0.957027	+	0.290000i	$0.0936554\pi$
$938$	−4.33167e61	−0.00542368
$939$	0	0
$940$	−6.81820e63	−0.815494
$941$	−3.85740e63	−0.450939	−0.225469	−	0.974250i	$-0.572392\pi$
$941$	−3.85740e63	−0.450939	−0.225469	+	0.974250i	$0.572392\pi$
$942$	0	0
$943$	−1.37905e64	−1.54020
$944$	2.64868e62	0.0289155
$945$	0	0
$946$	−1.17049e64	−1.22098
$947$	−1.02507e64	−1.04527	−0.522633	−	0.852558i	$-0.675050\pi$
$947$	−1.02507e64	−1.04527	−0.522633	+	0.852558i	$0.675050\pi$
$948$	0	0
$949$	−2.56131e63	−0.249597
$950$	−6.39957e63	−0.609668
$951$	0	0
$952$	7.61247e63	0.693156
$953$	1.69549e63	0.150938	0.0754689	−	0.997148i	$-0.475955\pi$
$953$	1.69549e63	0.150938	0.0754689	+	0.997148i	$0.475955\pi$
$954$	0	0
$955$	−2.29874e64	−1.95622
$956$	4.47913e63	0.372691
$957$	0	0
$958$	−2.58135e63	−0.205347
$959$	−9.99207e63	−0.777240
$960$	0	0
$961$	−1.32228e64	−0.983493
$962$	8.38204e63	0.609657
$963$	0	0
$964$	2.02915e63	0.141142
$965$	1.74895e64	1.18971
$966$	0	0
$967$	4.59701e63	0.299093	0.149546	−	0.988755i	$-0.452219\pi$
$967$	4.59701e63	0.299093	0.149546	+	0.988755i	$0.452219\pi$
$968$	−7.24514e63	−0.461027
$969$	0	0
$970$	2.51417e64	1.53039
$971$	3.19574e63	0.190265	0.0951324	−	0.995465i	$-0.469673\pi$
$971$	3.19574e63	0.190265	0.0951324	+	0.995465i	$0.469673\pi$
$972$	0	0
$973$	−9.39274e62	−0.0535016
$974$	−1.74053e64	−0.969762
$975$	0	0
$976$	−2.72958e62	−0.0145521
$977$	−5.68464e63	−0.296462	−0.148231	−	0.988953i	$-0.547358\pi$
$977$	−5.68464e63	−0.296462	−0.148231	+	0.988953i	$0.547358\pi$
$978$	0	0
$979$	2.17202e64	1.08402
$980$	−3.20513e63	−0.156489
$981$	0	0
$982$	1.70458e64	0.796563
$983$	−2.85765e64	−1.30650	−0.653249	−	0.757143i	$-0.726594\pi$
$983$	−2.85765e64	−1.30650	−0.653249	+	0.757143i	$0.726594\pi$
$984$	0	0
$985$	−5.10432e64	−2.23388
$986$	5.54689e63	0.237518
$987$	0	0
$988$	2.67798e63	0.109783
$989$	−5.10638e64	−2.04830
$990$	0	0
$991$	−3.67835e64	−1.41276	−0.706381	−	0.707832i	$-0.749674\pi$
$991$	−3.67835e64	−1.41276	−0.706381	+	0.707832i	$0.749674\pi$
$992$	3.32338e63	0.124905
$993$	0	0
$994$	−1.77352e64	−0.638306
$995$	2.95638e64	1.04127
$996$	0	0
$997$	2.35927e64	0.795850	0.397925	−	0.917418i	$-0.369730\pi$
$997$	2.35927e64	0.795850	0.397925	+	0.917418i	$0.369730\pi$
$998$	−1.50447e63	−0.0496681
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.44.a.c.1.3		4
3.2	odd	2		3.44.a.b.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.44.a.b.1.2	✓	4	3.2	odd	2
9.44.a.c.1.3		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.91590e6 q^{2} -5.12540e12 q^{4} -2.05854e15 q^{5} +1.37114e18 q^{7} -2.66723e19 q^{8} -3.94396e21 q^{10} +2.95641e22 q^{11} +4.85026e23 q^{13} +2.62698e24 q^{14} -6.01799e24 q^{16} -2.08153e26 q^{17} -1.07725e27 q^{19} +1.05508e28 q^{20} +5.66420e28 q^{22} +2.47106e29 q^{23} +3.10071e30 q^{25} +9.29263e29 q^{26} -7.02766e30 q^{28} -1.39089e31 q^{29} +1.48976e31 q^{31} +2.23082e32 q^{32} -3.98801e32 q^{34} -2.82255e33 q^{35} +9.02009e33 q^{37} -2.06390e33 q^{38} +5.49059e34 q^{40} -5.58080e34 q^{41} -2.06648e35 q^{43} -1.51528e35 q^{44} +4.73431e35 q^{46} -6.46223e35 q^{47} -3.03780e35 q^{49} +5.94067e36 q^{50} -2.48595e36 q^{52} +4.21095e36 q^{53} -6.08589e37 q^{55} -3.65715e37 q^{56} -2.66481e37 q^{58} -4.40127e37 q^{59} +4.53571e37 q^{61} +2.85424e37 q^{62} +4.80338e38 q^{64} -9.98445e38 q^{65} -1.64891e37 q^{67} +1.06687e39 q^{68} -5.40774e39 q^{70} -6.75118e39 q^{71} -5.28077e39 q^{73} +1.72816e40 q^{74} +5.52132e39 q^{76} +4.05366e40 q^{77} +1.01508e41 q^{79} +1.23883e40 q^{80} -1.06923e41 q^{82} -2.11545e41 q^{83} +4.28491e41 q^{85} -3.95917e41 q^{86} -7.88542e41 q^{88} +7.34681e41 q^{89} +6.65040e41 q^{91} -1.26652e42 q^{92} -1.23810e42 q^{94} +2.21755e42 q^{95} -6.37472e42 q^{97} -5.82013e41 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1660014 q^{2} + 29333750564548 q^{4} - 16\!\cdots\!20 q^{5} + 11\!\cdots\!28 q^{7} - 77\!\cdots\!48 q^{8} + 53\!\cdots\!60 q^{10} - 87\!\cdots\!96 q^{11} - 16\!\cdots\!96 q^{13} + 13\!\cdots\!08 q^{14}+ \cdots - 62\!\cdots\!46 q^{98}+O(q^{100}) \) 4 * q - 1660014 * q^2 + 29333750564548 * q^4 - 1650650807536920 * q^5 + 114481425784209728 * q^7 - 77966588660971173048 * q^8 + 5359044979781953498260 * q^10 - 8715200555107127298096 * q^11 - 1622373819341917660395496 * q^13 + 13467578670319198438149408 * q^14 + 265331272220473559715915280 * q^16 - 293411853143037894856883976 * q^17 - 2594414378517928782354874288 * q^19 - 8558701143076231384453792920 * q^20 + 74078936455805689993083157032 * q^22 + 165719576853043327961325838944 * q^23 + 2162829068891925341689803823900 * q^25 - 6101006421154528454709899598228 * q^26 - 41688560653908286820790912158656 * q^28 - 50103930548121691368807724902264 * q^29 + 153232269806257085529351412219424 * q^31 - 1375373155850513577371148105862368 * q^32 + 60331877005992911765859543576156 * q^34 - 794758271825314756362531708950400 * q^35 + 19599702088800583695304816898379128 * q^37 - 30934350335669500918957603769116056 * q^38 + 196041911393456394134889832442905680 * q^40 + 9038336825299507042215563101837656 * q^41 + 57884775638210824781567117092305200 * q^43 - 1103928490692495293822086256175019824 * q^44 + 718247490543964330689612210436911024 * q^46 - 489795556049192314087538359958202240 * q^47 - 4317642451006561098818513062358614620 * q^49 + 5579808201219996041105683525421159550 * q^50 - 13582094185786578557618520483683206504 * q^52 + 40271515633256644720413455555285829864 * q^53 - 47661104270181626262923295497298490080 * q^55 + 117390605534482290403396341738920952960 * q^56 + 166036404448317657164763132092855468772 * q^58 + 31284936358538459187079576876991825232 * q^59 - 246678251415393769778200255087667843560 * q^61 - 1447587501085892804433014348598690126576 * q^62 + 3779239307999191671459925914328934335552 * q^64 - 3201204112021109289173748012488728936080 * q^65 + 1029262961963280586877382927523715757776 * q^67 + 5728258265472538567897226405540492998008 * q^68 - 13998939704532003940217885479727831428800 * q^70 + 7158914166122718301934674138622261107872 * q^71 + 5436935716056938749789214886435330158696 * q^73 + 39560290302967463129010858736787279461788 * q^74 - 84965301579645016687884089536788004332208 * q^76 + 70649133554843036086189895413395482145024 * q^77 - 18459961314698254348045108075380001958560 * q^79 - 422317828506146509768424873205600266179680 * q^80 + 147229844429377279789779107991029019615756 * q^82 - 207863929126228047172838511060419328637008 * q^83 + 221112002042063917840135331898684555973680 * q^85 - 458138780643704418519204317947537057045416 * q^86 + 1517878779794169852250121294325123418262688 * q^88 + 442176536724138726190556195414134338798168 * q^89 - 241286657628373017846026300207834298513536 * q^91 + 501856507576284139621951265540431125198432 * q^92 - 12731451681111622228496468053131446537940672 * q^94 + 877953040109009235535219131018818763586080 * q^95 - 5068444705076967721898551548017617825231864 * q^97 - 6262356698119668842821753019159492533814046 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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