LMFDB - Embedded newform 9.44.a.c.1.2

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			1.2
Root			$321562.$ 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)

$f(q)$	$=$	\(q-2.34437e6 q^{2} -3.30001e12 q^{4} +6.18875e14 q^{5} -6.01464e16 q^{7} +2.83578e19 q^{8} -1.45087e21 q^{10} +9.76031e21 q^{11} -7.58355e23 q^{13} +1.41006e23 q^{14} -3.74540e25 q^{16} -2.78579e26 q^{17} +4.05410e27 q^{19} -2.04230e27 q^{20} -2.28818e28 q^{22} -1.45822e29 q^{23} -7.53862e29 q^{25} +1.77787e30 q^{26} +1.98484e29 q^{28} +9.74099e30 q^{29} +1.20460e32 q^{31} -1.61632e32 q^{32} +6.53093e32 q^{34} -3.72231e31 q^{35} +9.29506e32 q^{37} -9.50433e33 q^{38} +1.75499e34 q^{40} -7.39680e34 q^{41} +1.90025e35 q^{43} -3.22092e34 q^{44} +3.41860e35 q^{46} +3.68345e35 q^{47} -2.18020e36 q^{49} +1.76733e36 q^{50} +2.50258e36 q^{52} +1.07634e37 q^{53} +6.04041e36 q^{55} -1.70562e36 q^{56} -2.28365e37 q^{58} +1.44976e38 q^{59} +4.49263e38 q^{61} -2.82402e38 q^{62} +7.08373e38 q^{64} -4.69327e38 q^{65} +5.03842e38 q^{67} +9.19315e38 q^{68} +8.72649e37 q^{70} +4.05279e39 q^{71} -1.07882e40 q^{73} -2.17911e39 q^{74} -1.33786e40 q^{76} -5.87048e38 q^{77} -8.21320e40 q^{79} -2.31793e40 q^{80} +1.73408e41 q^{82} -4.07702e40 q^{83} -1.72406e41 q^{85} -4.45489e41 q^{86} +2.76781e41 q^{88} -1.83342e41 q^{89} +4.56124e40 q^{91} +4.81213e41 q^{92} -8.63538e41 q^{94} +2.50898e42 q^{95} -2.07049e42 q^{97} +5.11119e42 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.34437e6	−0.790463	−0.395232	−	0.918582i	$-0.629336\pi$
$2$	−2.34437e6	−0.790463	−0.395232	+	0.918582i	$0.629336\pi$
$3$	0	0
$3$	0	0
$4$	−3.30001e12	−0.375168
$5$	6.18875e14	0.580427	0.290214	−	0.956962i	$-0.406274\pi$
$5$	6.18875e14	0.580427	0.290214	+	0.956962i	$0.406274\pi$
$6$	0	0
$7$	−6.01464e16	−0.0407007	−0.0203504	−	0.999793i	$-0.506478\pi$
$7$	−6.01464e16	−0.0407007	−0.0203504	+	0.999793i	$0.506478\pi$
$8$	2.83578e19	1.08702
$9$	0	0
$10$	−1.45087e21	−0.458806
$11$	9.76031e21	0.397668	0.198834	−	0.980033i	$-0.436284\pi$
$11$	9.76031e21	0.397668	0.198834	+	0.980033i	$0.436284\pi$
$12$	0	0
$13$	−7.58355e23	−0.851315	−0.425658	−	0.904884i	$-0.639957\pi$
$13$	−7.58355e23	−0.851315	−0.425658	+	0.904884i	$0.639957\pi$
$14$	1.41006e23	0.0321724
$15$	0	0
$16$	−3.74540e25	−0.484081
$17$	−2.78579e26	−0.977906	−0.488953	−	0.872310i	$-0.662621\pi$
$17$	−2.78579e26	−0.977906	−0.488953	+	0.872310i	$0.662621\pi$
$18$	0	0
$19$	4.05410e27	1.30224	0.651122	−	0.758973i	$-0.274298\pi$
$19$	4.05410e27	1.30224	0.651122	+	0.758973i	$0.274298\pi$
$20$	−2.04230e27	−0.217758
$21$	0	0
$22$	−2.28818e28	−0.314342
$23$	−1.45822e29	−0.770324	−0.385162	−	0.922849i	$-0.625854\pi$
$23$	−1.45822e29	−0.770324	−0.385162	+	0.922849i	$0.625854\pi$
$24$	0	0
$25$	−7.53862e29	−0.663104
$26$	1.77787e30	0.672933
$27$	0	0
$28$	1.98484e29	0.0152696
$29$	9.74099e30	0.352408	0.176204	−	0.984354i	$-0.443618\pi$
$29$	9.74099e30	0.352408	0.176204	+	0.984354i	$0.443618\pi$
$30$	0	0
$31$	1.20460e32	1.03888	0.519440	−	0.854507i	$-0.326141\pi$
$31$	1.20460e32	1.03888	0.519440	+	0.854507i	$0.326141\pi$
$32$	−1.61632e32	−0.704371
$33$	0	0
$34$	6.53093e32	0.772998
$35$	−3.72231e31	−0.0236238
$36$	0	0
$37$	9.29506e32	0.178614	0.0893069	−	0.996004i	$-0.471535\pi$
$37$	9.29506e32	0.178614	0.0893069	+	0.996004i	$0.471535\pi$
$38$	−9.50433e33	−1.02938
$39$	0	0
$40$	1.75499e34	0.630936
$41$	−7.39680e34	−1.56383	−0.781917	−	0.623382i	$-0.785758\pi$
$41$	−7.39680e34	−1.56383	−0.781917	+	0.623382i	$0.785758\pi$
$42$	0	0
$43$	1.90025e35	1.44291	0.721455	−	0.692462i	$-0.243474\pi$
$43$	1.90025e35	1.44291	0.721455	+	0.692462i	$0.243474\pi$
$44$	−3.22092e34	−0.149192
$45$	0	0
$46$	3.41860e35	0.608912
$47$	3.68345e35	0.413191	0.206595	−	0.978426i	$-0.433762\pi$
$47$	3.68345e35	0.413191	0.206595	+	0.978426i	$0.433762\pi$
$48$	0	0
$49$	−2.18020e36	−0.998343
$50$	1.76733e36	0.524159
$51$	0	0
$52$	2.50258e36	0.319386
$53$	1.07634e37	0.912047	0.456023	−	0.889968i	$-0.349273\pi$
$53$	1.07634e37	0.912047	0.456023	+	0.889968i	$0.349273\pi$
$54$	0	0
$55$	6.04041e36	0.230818
$56$	−1.70562e36	−0.0442425
$57$	0	0
$58$	−2.28365e37	−0.278566
$59$	1.44976e38	1.22455	0.612275	−	0.790645i	$-0.290255\pi$
$59$	1.44976e38	1.22455	0.612275	+	0.790645i	$0.290255\pi$
$60$	0	0
$61$	4.49263e38	1.85314	0.926572	−	0.376117i	$-0.122741\pi$
$61$	4.49263e38	1.85314	0.926572	+	0.376117i	$0.122741\pi$
$62$	−2.82402e38	−0.821196
$63$	0	0
$64$	7.08373e38	1.04086
$65$	−4.69327e38	−0.494127
$66$	0	0
$67$	5.03842e38	0.276494	0.138247	−	0.990398i	$-0.455853\pi$
$67$	5.03842e38	0.276494	0.138247	+	0.990398i	$0.455853\pi$
$68$	9.19315e38	0.366879
$69$	0	0
$70$	8.72649e37	0.0186738
$71$	4.05279e39	0.639293	0.319646	−	0.947537i	$-0.396436\pi$
$71$	4.05279e39	0.639293	0.319646	+	0.947537i	$0.396436\pi$
$72$	0	0
$73$	−1.07882e40	−0.936503	−0.468251	−	0.883595i	$-0.655116\pi$
$73$	−1.07882e40	−0.936503	−0.468251	+	0.883595i	$0.655116\pi$
$74$	−2.17911e39	−0.141188
$75$	0	0
$76$	−1.33786e40	−0.488560
$77$	−5.87048e38	−0.0161854
$78$	0	0
$79$	−8.21320e40	−1.30476	−0.652379	−	0.757893i	$-0.726229\pi$
$79$	−8.21320e40	−1.30476	−0.652379	+	0.757893i	$0.726229\pi$
$80$	−2.31793e40	−0.280974
$81$	0	0
$82$	1.73408e41	1.23615
$83$	−4.07702e40	−0.223956	−0.111978	−	0.993711i	$-0.535719\pi$
$83$	−4.07702e40	−0.223956	−0.111978	+	0.993711i	$0.535719\pi$
$84$	0	0
$85$	−1.72406e41	−0.567603
$86$	−4.45489e41	−1.14057
$87$	0	0
$88$	2.76781e41	0.432273
$89$	−1.83342e41	−0.224583	−0.112292	−	0.993675i	$-0.535819\pi$
$89$	−1.83342e41	−0.224583	−0.112292	+	0.993675i	$0.535819\pi$
$90$	0	0
$91$	4.56124e40	0.0346491
$92$	4.81213e41	0.289001
$93$	0	0
$94$	−8.63538e41	−0.326612
$95$	2.50898e42	0.755858
$96$	0	0
$97$	−2.07049e42	−0.398547	−0.199274	−	0.979944i	$-0.563858\pi$
$97$	−2.07049e42	−0.398547	−0.199274	+	0.979944i	$0.563858\pi$
$98$	5.11119e42	0.789154
$99$	0	0
$100$	2.48775e42	0.248775
$101$	−1.86748e43	−1.50781	−0.753904	−	0.656985i	$-0.771831\pi$
$101$	−1.86748e43	−1.50781	−0.753904	+	0.656985i	$0.771831\pi$
$102$	0	0
$103$	1.80725e43	0.957233	0.478617	−	0.878024i	$-0.341138\pi$
$103$	1.80725e43	0.957233	0.478617	+	0.878024i	$0.341138\pi$
$104$	−2.15053e43	−0.925396
$105$	0	0
$106$	−2.52333e43	−0.720939
$107$	−5.57930e43	−1.30265	−0.651326	−	0.758798i	$-0.725787\pi$
$107$	−5.57930e43	−1.30265	−0.651326	+	0.758798i	$0.725787\pi$
$108$	0	0
$109$	−9.67648e43	−1.51722	−0.758609	−	0.651546i	$-0.774121\pi$
$109$	−9.67648e43	−1.51722	−0.758609	+	0.651546i	$0.774121\pi$
$110$	−1.41610e43	−0.182453
$111$	0	0
$112$	2.25272e42	0.0197024
$113$	−1.75497e44	−1.26790	−0.633948	−	0.773375i	$-0.718567\pi$
$113$	−1.75497e44	−1.26790	−0.633948	+	0.773375i	$0.718567\pi$
$114$	0	0
$115$	−9.02453e43	−0.447117
$116$	−3.21454e43	−0.132212
$117$	0	0
$118$	−3.39877e44	−0.967961
$119$	1.67556e43	0.0398015
$120$	0	0
$121$	−5.07137e44	−0.841860
$122$	−1.05324e45	−1.46484
$123$	0	0
$124$	−3.97518e44	−0.389754
$125$	−1.17013e45	−0.965311
$126$	0	0
$127$	2.40153e45	1.40834	0.704170	−	0.710032i	$-0.251319\pi$
$127$	2.40153e45	1.40834	0.704170	+	0.710032i	$0.251319\pi$
$128$	−2.38964e44	−0.118391
$129$	0	0
$130$	1.10028e45	0.390589
$131$	−4.93252e45	−1.48503	−0.742516	−	0.669828i	$-0.766368\pi$
$131$	−4.93252e45	−1.48503	−0.742516	+	0.669828i	$0.766368\pi$
$132$	0	0
$133$	−2.43840e44	−0.0530023
$134$	−1.18119e45	−0.218558
$135$	0	0
$136$	−7.89989e45	−1.06300
$137$	4.38206e45	0.503716	0.251858	−	0.967764i	$-0.418958\pi$
$137$	4.38206e45	0.503716	0.251858	+	0.967764i	$0.418958\pi$
$138$	0	0
$139$	−1.27611e46	−1.07416	−0.537082	−	0.843530i	$-0.680473\pi$
$139$	−1.27611e46	−1.07416	−0.537082	+	0.843530i	$0.680473\pi$
$140$	1.22837e44	0.00886290
$141$	0	0
$142$	−9.50126e45	−0.505338
$143$	−7.40178e45	−0.338541
$144$	0	0
$145$	6.02846e45	0.204548
$146$	2.52916e46	0.740271
$147$	0	0
$148$	−3.06738e45	−0.0670102
$149$	−6.74357e46	−1.27463	−0.637316	−	0.770602i	$-0.719955\pi$
$149$	−6.74357e46	−1.27463	−0.637316	+	0.770602i	$0.719955\pi$
$150$	0	0
$151$	1.15191e47	1.63461	0.817303	−	0.576209i	$-0.195468\pi$
$151$	1.15191e47	1.63461	0.817303	+	0.576209i	$0.195468\pi$
$152$	1.14965e47	1.41557
$153$	0	0
$154$	1.37626e45	0.0127940
$155$	7.45494e46	0.602994
$156$	0	0
$157$	1.70621e47	1.04759	0.523795	−	0.851844i	$-0.324516\pi$
$157$	1.70621e47	1.04759	0.523795	+	0.851844i	$0.324516\pi$
$158$	1.92548e47	1.03136
$159$	0	0
$160$	−1.00030e47	−0.408836
$161$	8.77065e45	0.0313527
$162$	0	0
$163$	2.46516e47	0.675790	0.337895	−	0.941184i	$-0.390285\pi$
$163$	2.46516e47	0.675790	0.337895	+	0.941184i	$0.390285\pi$
$164$	2.44095e47	0.586701
$165$	0	0
$166$	9.55804e46	0.177029
$167$	1.01601e48	1.65384	0.826920	−	0.562319i	$-0.190091\pi$
$167$	1.01601e48	1.65384	0.826920	+	0.562319i	$0.190091\pi$
$168$	0	0
$169$	−2.18429e47	−0.275262
$170$	4.04183e47	0.448669
$171$	0	0
$172$	−6.27085e47	−0.541333
$173$	−1.53528e48	−1.17003	−0.585015	−	0.811023i	$-0.698911\pi$
$173$	−1.53528e48	−1.17003	−0.585015	+	0.811023i	$0.698911\pi$
$174$	0	0
$175$	4.53421e46	0.0269888
$176$	−3.65562e47	−0.192504
$177$	0	0
$178$	4.29822e47	0.177525
$179$	−4.05033e48	−1.48303	−0.741515	−	0.670936i	$-0.765892\pi$
$179$	−4.05033e48	−1.48303	−0.741515	+	0.670936i	$0.765892\pi$
$180$	0	0
$181$	2.03822e48	0.587708	0.293854	−	0.955850i	$-0.405062\pi$
$181$	2.03822e48	0.587708	0.293854	+	0.955850i	$0.405062\pi$
$182$	−1.06932e47	−0.0273889
$183$	0	0
$184$	−4.13517e48	−0.837357
$185$	5.75248e47	0.103672
$186$	0	0
$187$	−2.71902e48	−0.388882
$188$	−1.21554e48	−0.155016
$189$	0	0
$190$	−5.88199e48	−0.597478
$191$	−3.56591e48	−0.323559	−0.161779	−	0.986827i	$-0.551723\pi$
$191$	−3.56591e48	−0.323559	−0.161779	+	0.986827i	$0.551723\pi$
$192$	0	0
$193$	−2.12053e48	−0.153802	−0.0769012	−	0.997039i	$-0.524503\pi$
$193$	−2.12053e48	−0.153802	−0.0769012	+	0.997039i	$0.524503\pi$
$194$	4.85399e48	0.315037
$195$	0	0
$196$	7.19468e48	0.374546
$197$	−1.79197e49	−0.836192	−0.418096	−	0.908403i	$-0.637302\pi$
$197$	−1.79197e49	−0.836192	−0.418096	+	0.908403i	$0.637302\pi$
$198$	0	0
$199$	−7.04650e48	−0.264626	−0.132313	−	0.991208i	$-0.542240\pi$
$199$	−7.04650e48	−0.264626	−0.132313	+	0.991208i	$0.542240\pi$
$200$	−2.13778e49	−0.720807
$201$	0	0
$202$	4.37806e49	1.19187
$203$	−5.85886e47	−0.0143433
$204$	0	0
$205$	−4.57769e49	−0.907693
$206$	−4.23687e49	−0.756658
$207$	0	0
$208$	2.84034e49	0.412106
$209$	3.95693e49	0.517861
$210$	0	0
$211$	−1.48444e50	−1.58303	−0.791516	−	0.611149i	$-0.790708\pi$
$211$	−1.48444e50	−1.58303	−0.791516	+	0.611149i	$0.790708\pi$
$212$	−3.55193e49	−0.342171
$213$	0	0
$214$	1.30799e50	1.02970
$215$	1.17602e50	0.837504
$216$	0	0
$217$	−7.24522e48	−0.0422831
$218$	2.26853e50	1.19930
$219$	0	0
$220$	−1.99334e49	−0.0865954
$221$	2.11262e50	0.832506
$222$	0	0
$223$	−8.53574e49	−0.277132	−0.138566	−	0.990353i	$-0.544249\pi$
$223$	−8.53574e49	−0.277132	−0.138566	+	0.990353i	$0.544249\pi$
$224$	9.72157e48	0.0286684
$225$	0	0
$226$	4.11431e50	1.00223
$227$	4.48691e50	0.994012	0.497006	−	0.867747i	$-0.334433\pi$
$227$	4.48691e50	0.994012	0.497006	+	0.867747i	$0.334433\pi$
$228$	0	0
$229$	7.28299e50	1.33612	0.668062	−	0.744106i	$-0.267124\pi$
$229$	7.28299e50	1.33612	0.668062	+	0.744106i	$0.267124\pi$
$230$	2.11569e50	0.353429
$231$	0	0
$232$	2.76233e50	0.383075
$233$	−9.17803e50	−1.16037	−0.580186	−	0.814484i	$-0.697020\pi$
$233$	−9.17803e50	−1.16037	−0.580186	+	0.814484i	$0.697020\pi$
$234$	0	0
$235$	2.27959e50	0.239827
$236$	−4.78421e50	−0.459412
$237$	0	0
$238$	−3.92813e49	−0.0314616
$239$	1.09851e50	0.0803990	0.0401995	−	0.999192i	$-0.487201\pi$
$239$	1.09851e50	0.0803990	0.0401995	+	0.999192i	$0.487201\pi$
$240$	0	0
$241$	−1.97410e51	−1.20782	−0.603910	−	0.797052i	$-0.706391\pi$
$241$	−1.97410e51	−1.20782	−0.603910	+	0.797052i	$0.706391\pi$
$242$	1.18892e51	0.665459
$243$	0	0
$244$	−1.48257e51	−0.695240
$245$	−1.34927e51	−0.579466
$246$	0	0
$247$	−3.07445e51	−1.10862
$248$	3.41597e51	1.12928
$249$	0	0
$250$	2.74321e51	0.763043
$251$	−6.49802e51	−1.65881	−0.829404	−	0.558650i	$-0.811320\pi$
$251$	−6.49802e51	−1.65881	−0.829404	+	0.558650i	$0.811320\pi$
$252$	0	0
$253$	−1.42326e51	−0.306333
$254$	−5.63007e51	−1.11324
$255$	0	0
$256$	−5.67070e51	−0.947277
$257$	−6.62733e51	−1.01807	−0.509033	−	0.860747i	$-0.669997\pi$
$257$	−6.62733e51	−1.01807	−0.509033	+	0.860747i	$0.669997\pi$
$258$	0	0
$259$	−5.59065e49	−0.00726971
$260$	1.54878e51	0.185380
$261$	0	0
$262$	1.15637e52	1.17386
$263$	−2.00645e51	−0.187663	−0.0938315	−	0.995588i	$-0.529912\pi$
$263$	−2.00645e51	−0.187663	−0.0938315	+	0.995588i	$0.529912\pi$
$264$	0	0
$265$	6.66118e51	0.529377
$266$	5.71652e50	0.0418964
$267$	0	0
$268$	−1.66268e51	−0.103732
$269$	1.18548e52	0.682686	0.341343	−	0.939939i	$-0.389118\pi$
$269$	1.18548e52	0.682686	0.341343	+	0.939939i	$0.389118\pi$
$270$	0	0
$271$	1.04772e52	0.514522	0.257261	−	0.966342i	$-0.417180\pi$
$271$	1.04772e52	0.514522	0.257261	+	0.966342i	$0.417180\pi$
$272$	1.04339e52	0.473386
$273$	0	0
$274$	−1.02732e52	−0.398169
$275$	−7.35793e51	−0.263695
$276$	0	0
$277$	−2.05756e52	−0.631012	−0.315506	−	0.948924i	$-0.602174\pi$
$277$	−2.05756e52	−0.631012	−0.315506	+	0.948924i	$0.602174\pi$
$278$	2.99168e52	0.849087
$279$	0	0
$280$	−1.05557e51	−0.0256795
$281$	4.36534e52	0.983631	0.491816	−	0.870699i	$-0.336333\pi$
$281$	4.36534e52	0.983631	0.491816	+	0.870699i	$0.336333\pi$
$282$	0	0
$283$	−5.12915e51	−0.0992286	−0.0496143	−	0.998768i	$-0.515799\pi$
$283$	−5.12915e51	−0.0992286	−0.0496143	+	0.998768i	$0.515799\pi$
$284$	−1.33743e52	−0.239842
$285$	0	0
$286$	1.73525e52	0.267604
$287$	4.44891e51	0.0636492
$288$	0	0
$289$	−3.54642e51	−0.0437005
$290$	−1.41330e52	−0.161687
$291$	0	0
$292$	3.56013e52	0.351346
$293$	1.29030e52	0.118314	0.0591571	−	0.998249i	$-0.481159\pi$
$293$	1.29030e52	0.118314	0.0591571	+	0.998249i	$0.481159\pi$
$294$	0	0
$295$	8.97217e52	0.710762
$296$	2.63587e52	0.194157
$297$	0	0
$298$	1.58094e53	1.00755
$299$	1.10584e53	0.655788
$300$	0	0
$301$	−1.14293e52	−0.0587275
$302$	−2.70050e53	−1.29210
$303$	0	0
$304$	−1.51842e53	−0.630392
$305$	2.78038e53	1.07562
$306$	0	0
$307$	−2.82932e53	−0.951058	−0.475529	−	0.879700i	$-0.657743\pi$
$307$	−2.82932e53	−0.951058	−0.475529	+	0.879700i	$0.657743\pi$
$308$	1.93727e51	0.00607224
$309$	0	0
$310$	−1.74772e53	−0.476644
$311$	2.02380e53	0.515014	0.257507	−	0.966276i	$-0.417099\pi$
$311$	2.02380e53	0.515014	0.257507	+	0.966276i	$0.417099\pi$
$312$	0	0
$313$	−4.97243e52	−0.110247	−0.0551234	−	0.998480i	$-0.517555\pi$
$313$	−4.97243e52	−0.110247	−0.0551234	+	0.998480i	$0.517555\pi$
$314$	−4.00000e53	−0.828081
$315$	0	0
$316$	2.71037e53	0.489504
$317$	−1.06498e54	−1.79708	−0.898540	−	0.438893i	$-0.855371\pi$
$317$	−1.06498e54	−1.79708	−0.898540	+	0.438893i	$0.855371\pi$
$318$	0	0
$319$	9.50751e52	0.140142
$320$	4.38394e53	0.604144
$321$	0	0
$322$	−2.05617e52	−0.0247832
$323$	−1.12939e54	−1.27347
$324$	0	0
$325$	5.71695e53	0.564511
$326$	−5.77925e53	−0.534187
$327$	0	0
$328$	−2.09757e54	−1.69992
$329$	−2.21546e52	−0.0168172
$330$	0	0
$331$	3.46154e51	0.00230657	0.00115329	−	0.999999i	$-0.499633\pi$
$331$	3.46154e51	0.00230657	0.00115329	+	0.999999i	$0.499633\pi$
$332$	1.34542e53	0.0840213
$333$	0	0
$334$	−2.38190e54	−1.30730
$335$	3.11815e53	0.160485
$336$	0	0
$337$	3.36356e54	1.52320	0.761599	−	0.648048i	$-0.224414\pi$
$337$	3.36356e54	1.52320	0.761599	+	0.648048i	$0.224414\pi$
$338$	5.12080e53	0.217585
$339$	0	0
$340$	5.68941e53	0.212947
$341$	1.17572e54	0.413129
$342$	0	0
$343$	2.62480e53	0.0813340
$344$	5.38869e54	1.56847
$345$	0	0
$346$	3.59927e54	0.924865
$347$	1.72459e54	0.416487	0.208244	−	0.978077i	$-0.433225\pi$
$347$	1.72459e54	0.416487	0.208244	+	0.978077i	$0.433225\pi$
$348$	0	0
$349$	−9.94419e53	−0.212238	−0.106119	−	0.994353i	$-0.533842\pi$
$349$	−9.94419e53	−0.212238	−0.106119	+	0.994353i	$0.533842\pi$
$350$	−1.06299e53	−0.0213337
$351$	0	0
$352$	−1.57757e54	−0.280106
$353$	5.27615e54	0.881375	0.440687	−	0.897661i	$-0.354735\pi$
$353$	5.27615e54	0.881375	0.440687	+	0.897661i	$0.354735\pi$
$354$	0	0
$355$	2.50817e54	0.371063
$356$	6.05031e53	0.0842564
$357$	0	0
$358$	9.49547e54	1.17228
$359$	−3.67568e54	−0.427372	−0.213686	−	0.976902i	$-0.568547\pi$
$359$	−3.67568e54	−0.427372	−0.213686	+	0.976902i	$0.568547\pi$
$360$	0	0
$361$	6.74396e54	0.695841
$362$	−4.77835e54	−0.464562
$363$	0	0
$364$	−1.50521e53	−0.0129992
$365$	−6.67657e54	−0.543572
$366$	0	0
$367$	−1.91563e55	−1.38673	−0.693364	−	0.720587i	$-0.743872\pi$
$367$	−1.91563e55	−1.38673	−0.693364	+	0.720587i	$0.743872\pi$
$368$	5.46159e54	0.372899
$369$	0	0
$370$	−1.34860e54	−0.0819492
$371$	−6.47379e53	−0.0371210
$372$	0	0
$373$	−2.66201e55	−1.35978	−0.679891	−	0.733313i	$-0.737973\pi$
$373$	−2.66201e55	−1.35978	−0.679891	+	0.733313i	$0.737973\pi$
$374$	6.37440e54	0.307397
$375$	0	0
$376$	1.04454e55	0.449147
$377$	−7.38713e54	−0.300011
$378$	0	0
$379$	−2.91659e55	−1.05714	−0.528570	−	0.848890i	$-0.677271\pi$
$379$	−2.91659e55	−1.05714	−0.528570	+	0.848890i	$0.677271\pi$
$380$	−8.27968e54	−0.283574
$381$	0	0
$382$	8.35983e54	0.255761
$383$	−8.50754e54	−0.246054	−0.123027	−	0.992403i	$-0.539260\pi$
$383$	−8.50754e54	−0.246054	−0.123027	+	0.992403i	$0.539260\pi$
$384$	0	0
$385$	−3.63309e53	−0.00939444
$386$	4.97132e54	0.121575
$387$	0	0
$388$	6.83263e54	0.149522
$389$	−4.01341e55	−0.830993	−0.415497	−	0.909595i	$-0.636392\pi$
$389$	−4.01341e55	−0.830993	−0.415497	+	0.909595i	$0.636392\pi$
$390$	0	0
$391$	4.06229e55	0.753304
$392$	−6.18255e55	−1.08522
$393$	0	0
$394$	4.20103e55	0.660979
$395$	−5.08295e55	−0.757318
$396$	0	0
$397$	3.05288e54	0.0408051	0.0204026	−	0.999792i	$-0.493505\pi$
$397$	3.05288e54	0.0408051	0.0204026	+	0.999792i	$0.493505\pi$
$398$	1.65196e55	0.209177
$399$	0	0
$400$	2.82351e55	0.320996
$401$	6.81054e55	0.733800	0.366900	−	0.930260i	$-0.380419\pi$
$401$	6.81054e55	0.733800	0.366900	+	0.930260i	$0.380419\pi$
$402$	0	0
$403$	−9.13511e55	−0.884414
$404$	6.16270e55	0.565681
$405$	0	0
$406$	1.37354e54	0.0113378
$407$	9.07227e54	0.0710291
$408$	0	0
$409$	−7.81408e55	−0.550588	−0.275294	−	0.961360i	$-0.588775\pi$
$409$	−7.81408e55	−0.550588	−0.275294	+	0.961360i	$0.588775\pi$
$410$	1.07318e56	0.717498
$411$	0	0
$412$	−5.96395e55	−0.359123
$413$	−8.71976e54	−0.0498401
$414$	0	0
$415$	−2.52316e55	−0.129990
$416$	1.22574e56	0.599642
$417$	0	0
$418$	−9.27652e55	−0.409350
$419$	−2.00491e56	−0.840413	−0.420207	−	0.907428i	$-0.638042\pi$
$419$	−2.00491e56	−0.840413	−0.420207	+	0.907428i	$0.638042\pi$
$420$	0	0
$421$	2.87650e56	1.08843	0.544214	−	0.838946i	$-0.316828\pi$
$421$	2.87650e56	1.08843	0.544214	+	0.838946i	$0.316828\pi$
$422$	3.48008e56	1.25133
$423$	0	0
$424$	3.05225e56	0.991413
$425$	2.10010e56	0.648453
$426$	0	0
$427$	−2.70216e55	−0.0754243
$428$	1.84117e56	0.488713
$429$	0	0
$430$	−2.75702e56	−0.662016
$431$	−4.69093e56	−1.07151	−0.535757	−	0.844372i	$-0.679974\pi$
$431$	−4.69093e56	−1.07151	−0.535757	+	0.844372i	$0.679974\pi$
$432$	0	0
$433$	4.37174e56	0.903993	0.451996	−	0.892020i	$-0.350712\pi$
$433$	4.37174e56	0.903993	0.451996	+	0.892020i	$0.350712\pi$
$434$	1.69855e55	0.0334233
$435$	0	0
$436$	3.19325e56	0.569211
$437$	−5.91176e56	−1.00315
$438$	0	0
$439$	3.15508e56	0.485314	0.242657	−	0.970112i	$-0.421981\pi$
$439$	3.15508e56	0.485314	0.242657	+	0.970112i	$0.421981\pi$
$440$	1.71293e56	0.250903
$441$	0	0
$442$	−4.95277e56	−0.658065
$443$	8.23492e56	1.04227	0.521134	−	0.853475i	$-0.325509\pi$
$443$	8.23492e56	1.04227	0.521134	+	0.853475i	$0.325509\pi$
$444$	0	0
$445$	−1.13466e56	−0.130354
$446$	2.00110e56	0.219063
$447$	0	0
$448$	−4.26061e55	−0.0423638
$449$	−8.61086e56	−0.816113	−0.408057	−	0.912957i	$-0.633793\pi$
$449$	−8.61086e56	−0.816113	−0.408057	+	0.912957i	$0.633793\pi$
$450$	0	0
$451$	−7.21951e56	−0.621888
$452$	5.79143e56	0.475674
$453$	0	0
$454$	−1.05190e57	−0.785730
$455$	2.82283e55	0.0201113
$456$	0	0
$457$	−1.34211e57	−0.870141	−0.435070	−	0.900396i	$-0.643277\pi$
$457$	−1.34211e57	−0.870141	−0.435070	+	0.900396i	$0.643277\pi$
$458$	−1.70740e57	−1.05616
$459$	0	0
$460$	2.97811e56	0.167744
$461$	−2.56415e57	−1.37840	−0.689198	−	0.724573i	$-0.742037\pi$
$461$	−2.56415e57	−1.37840	−0.689198	+	0.724573i	$0.742037\pi$
$462$	0	0
$463$	−1.67394e57	−0.819875	−0.409937	−	0.912114i	$-0.634449\pi$
$463$	−1.67394e57	−0.819875	−0.409937	+	0.912114i	$0.634449\pi$
$464$	−3.64839e56	−0.170594
$465$	0	0
$466$	2.15167e57	0.917231
$467$	−2.78817e57	−1.13503	−0.567514	−	0.823364i	$-0.692095\pi$
$467$	−2.78817e57	−1.13503	−0.567514	+	0.823364i	$0.692095\pi$
$468$	0	0
$469$	−3.03043e55	−0.0112535
$470$	−5.34422e56	−0.189575
$471$	0	0
$472$	4.11118e57	1.33111
$473$	1.85470e57	0.573799
$474$	0	0
$475$	−3.05624e57	−0.863524
$476$	−5.52935e55	−0.0149322
$477$	0	0
$478$	−2.57533e56	−0.0635525
$479$	3.93113e57	0.927478	0.463739	−	0.885972i	$-0.346507\pi$
$479$	3.93113e57	0.927478	0.463739	+	0.885972i	$0.346507\pi$
$480$	0	0
$481$	−7.04895e56	−0.152057
$482$	4.62802e57	0.954737
$483$	0	0
$484$	1.67356e57	0.315839
$485$	−1.28137e57	−0.231328
$486$	0	0
$487$	4.59837e57	0.759855	0.379928	−	0.925016i	$-0.375949\pi$
$487$	4.59837e57	0.759855	0.379928	+	0.925016i	$0.375949\pi$
$488$	1.27401e58	2.01440
$489$	0	0
$490$	3.16319e57	0.458046
$491$	−5.46081e57	−0.756842	−0.378421	−	0.925634i	$-0.623533\pi$
$491$	−5.46081e57	−0.756842	−0.378421	+	0.925634i	$0.623533\pi$
$492$	0	0
$493$	−2.71364e57	−0.344622
$494$	7.20766e57	0.876324
$495$	0	0
$496$	−4.51169e57	−0.502902
$497$	−2.43761e56	−0.0260197
$498$	0	0
$499$	4.19230e57	0.410478	0.205239	−	0.978712i	$-0.434203\pi$
$499$	4.19230e57	0.410478	0.205239	+	0.978712i	$0.434203\pi$
$500$	3.86143e57	0.362154
$501$	0	0
$502$	1.52338e58	1.31123
$503$	−8.78676e57	−0.724631	−0.362316	−	0.932056i	$-0.618014\pi$
$503$	−8.78676e57	−0.724631	−0.362316	+	0.932056i	$0.618014\pi$
$504$	0	0
$505$	−1.15574e58	−0.875173
$506$	3.33666e57	0.242145
$507$	0	0
$508$	−7.92507e57	−0.528364
$509$	−2.23159e58	−1.42620	−0.713102	−	0.701060i	$-0.752710\pi$
$509$	−2.23159e58	−1.42620	−0.713102	+	0.701060i	$0.752710\pi$
$510$	0	0
$511$	6.48874e56	0.0381163
$512$	1.53962e58	0.867178
$513$	0	0
$514$	1.55369e58	0.804744
$515$	1.11846e58	0.555604
$516$	0	0
$517$	3.59516e57	0.164313
$518$	1.31066e56	0.00574644
$519$	0	0
$520$	−1.33091e58	−0.537125
$521$	−4.83482e58	−1.87227	−0.936136	−	0.351638i	$-0.885625\pi$
$521$	−4.83482e58	−1.87227	−0.936136	+	0.351638i	$0.885625\pi$
$522$	0	0
$523$	−3.33314e58	−1.18869	−0.594343	−	0.804212i	$-0.702588\pi$
$523$	−3.33314e58	−1.18869	−0.594343	+	0.804212i	$0.702588\pi$
$524$	1.62774e58	0.557137
$525$	0	0
$526$	4.70386e57	0.148341
$527$	−3.35575e58	−1.01593
$528$	0	0
$529$	−1.45702e58	−0.406602
$530$	−1.56163e58	−0.418453
$531$	0	0
$532$	8.04675e56	0.0198848
$533$	5.60940e58	1.33132
$534$	0	0
$535$	−3.45289e58	−0.756095
$536$	1.42878e58	0.300554
$537$	0	0
$538$	−2.77921e58	−0.539638
$539$	−2.12794e58	−0.397010
$540$	0	0
$541$	6.69687e58	1.15380	0.576900	−	0.816815i	$-0.304262\pi$
$541$	6.69687e58	1.15380	0.576900	+	0.816815i	$0.304262\pi$
$542$	−2.45624e58	−0.406711
$543$	0	0
$544$	4.50272e58	0.688809
$545$	−5.98853e58	−0.880635
$546$	0	0
$547$	5.70829e58	0.775852	0.387926	−	0.921691i	$-0.373192\pi$
$547$	5.70829e58	0.775852	0.387926	+	0.921691i	$0.373192\pi$
$548$	−1.44608e58	−0.188978
$549$	0	0
$550$	1.72497e58	0.208442
$551$	3.94910e58	0.458922
$552$	0	0
$553$	4.93995e57	0.0531046
$554$	4.82369e58	0.498792
$555$	0	0
$556$	4.21118e58	0.402992
$557$	−1.85005e59	−1.70332	−0.851661	−	0.524093i	$-0.824404\pi$
$557$	−1.85005e59	−1.70332	−0.851661	+	0.524093i	$0.824404\pi$
$558$	0	0
$559$	−1.44106e59	−1.22837
$560$	1.39415e57	0.0114358
$561$	0	0
$562$	−1.02340e59	−0.777524
$563$	2.39144e59	1.74875	0.874377	−	0.485247i	$-0.161270\pi$
$563$	2.39144e59	1.74875	0.874377	+	0.485247i	$0.161270\pi$
$564$	0	0
$565$	−1.08611e59	−0.735922
$566$	1.20246e58	0.0784366
$567$	0	0
$568$	1.14928e59	0.694924
$569$	2.48333e59	1.44584	0.722921	−	0.690930i	$-0.242799\pi$
$569$	2.48333e59	1.44584	0.722921	+	0.690930i	$0.242799\pi$
$570$	0	0
$571$	5.26109e57	0.0284053	0.0142027	−	0.999899i	$-0.495479\pi$
$571$	5.26109e57	0.0284053	0.0142027	+	0.999899i	$0.495479\pi$
$572$	2.44260e58	0.127010
$573$	0	0
$574$	−1.04299e58	−0.0503124
$575$	1.09929e59	0.510805
$576$	0	0
$577$	1.90433e59	0.821224	0.410612	−	0.911810i	$-0.365315\pi$
$577$	1.90433e59	0.821224	0.410612	+	0.911810i	$0.365315\pi$
$578$	8.31412e57	0.0345436
$579$	0	0
$580$	−1.98940e58	−0.0767397
$581$	2.45218e57	0.00911519
$582$	0	0
$583$	1.05054e59	0.362692
$584$	−3.05930e59	−1.01800
$585$	0	0
$586$	−3.02494e58	−0.0935231
$587$	5.30546e59	1.58126	0.790630	−	0.612294i	$-0.209753\pi$
$587$	5.30546e59	1.58126	0.790630	+	0.612294i	$0.209753\pi$
$588$	0	0
$589$	4.88356e59	1.35287
$590$	−2.10341e59	−0.561831
$591$	0	0
$592$	−3.48137e58	−0.0864636
$593$	−3.29065e59	−0.788144	−0.394072	−	0.919080i	$-0.628934\pi$
$593$	−3.29065e59	−0.788144	−0.394072	+	0.919080i	$0.628934\pi$
$594$	0	0
$595$	1.03696e58	0.0231019
$596$	2.22539e59	0.478201
$597$	0	0
$598$	−2.59251e59	−0.518376
$599$	−4.73910e59	−0.914154	−0.457077	−	0.889427i	$-0.651104\pi$
$599$	−4.73910e59	−0.914154	−0.457077	+	0.889427i	$0.651104\pi$
$600$	0	0
$601$	6.03771e59	1.08410	0.542052	−	0.840345i	$-0.317648\pi$
$601$	6.03771e59	1.08410	0.542052	+	0.840345i	$0.317648\pi$
$602$	2.67946e58	0.0464219
$603$	0	0
$604$	−3.80131e59	−0.613252
$605$	−3.13854e59	−0.488639
$606$	0	0
$607$	−1.12859e60	−1.63674	−0.818370	−	0.574692i	$-0.805122\pi$
$607$	−1.12859e60	−1.63674	−0.818370	+	0.574692i	$0.805122\pi$
$608$	−6.55271e59	−0.917264
$609$	0	0
$610$	−6.51824e59	−0.850234
$611$	−2.79336e59	−0.351756
$612$	0	0
$613$	5.36469e59	0.629716	0.314858	−	0.949139i	$-0.398043\pi$
$613$	5.36469e59	0.629716	0.314858	+	0.949139i	$0.398043\pi$
$614$	6.63298e59	0.751776
$615$	0	0
$616$	−1.66474e58	−0.0175938
$617$	−5.39956e58	−0.0551096	−0.0275548	−	0.999620i	$-0.508772\pi$
$617$	−5.39956e58	−0.0551096	−0.0275548	+	0.999620i	$0.508772\pi$
$618$	0	0
$619$	−8.54808e59	−0.813803	−0.406902	−	0.913472i	$-0.633391\pi$
$619$	−8.54808e59	−0.813803	−0.406902	+	0.913472i	$0.633391\pi$
$620$	−2.46014e59	−0.226224
$621$	0	0
$622$	−4.74454e59	−0.407100
$623$	1.10274e58	0.00914069
$624$	0	0
$625$	1.32880e59	0.102811
$626$	1.16572e59	0.0871460
$627$	0	0
$628$	−5.63053e59	−0.393022
$629$	−2.58941e59	−0.174667
$630$	0	0
$631$	−1.08863e60	−0.685883	−0.342942	−	0.939357i	$-0.611423\pi$
$631$	−1.08863e60	−0.685883	−0.342942	+	0.939357i	$0.611423\pi$
$632$	−2.32908e60	−1.41830
$633$	0	0
$634$	2.49671e60	1.42052
$635$	1.48624e60	0.817439
$636$	0	0
$637$	1.65336e60	0.849905
$638$	−2.22892e59	−0.110777
$639$	0	0
$640$	−1.47889e59	−0.0687172
$641$	5.75414e59	0.258543	0.129271	−	0.991609i	$-0.458736\pi$
$641$	5.75414e59	0.258543	0.129271	+	0.991609i	$0.458736\pi$
$642$	0	0
$643$	2.44929e60	1.02921	0.514605	−	0.857427i	$-0.327939\pi$
$643$	2.44929e60	1.02921	0.514605	+	0.857427i	$0.327939\pi$
$644$	−2.89432e58	−0.0117625
$645$	0	0
$646$	2.64771e60	1.00663
$647$	4.54713e60	1.67223	0.836113	−	0.548557i	$-0.184823\pi$
$647$	4.54713e60	1.67223	0.836113	+	0.548557i	$0.184823\pi$
$648$	0	0
$649$	1.41501e60	0.486965
$650$	−1.34027e60	−0.446225
$651$	0	0
$652$	−8.13506e59	−0.253535
$653$	9.46384e59	0.285387	0.142693	−	0.989767i	$-0.454424\pi$
$653$	9.46384e59	0.285387	0.142693	+	0.989767i	$0.454424\pi$
$654$	0	0
$655$	−3.05261e60	−0.861954
$656$	2.77039e60	0.757023
$657$	0	0
$658$	5.19387e58	0.0132934
$659$	7.05783e60	1.74837	0.874187	−	0.485589i	$-0.161395\pi$
$659$	7.05783e60	1.74837	0.874187	+	0.485589i	$0.161395\pi$
$660$	0	0
$661$	−4.92212e60	−1.14241	−0.571204	−	0.820808i	$-0.693523\pi$
$661$	−4.92212e60	−1.14241	−0.571204	+	0.820808i	$0.693523\pi$
$662$	−8.11513e57	−0.00182326
$663$	0	0
$664$	−1.15615e60	−0.243445
$665$	−1.50906e59	−0.0307640
$666$	0	0
$667$	−1.42045e60	−0.271469
$668$	−3.35284e60	−0.620468
$669$	0	0
$670$	−7.31011e59	−0.126857
$671$	4.38495e60	0.736937
$672$	0	0
$673$	9.64075e60	1.51980	0.759901	−	0.650039i	$-0.225248\pi$
$673$	9.64075e60	1.51980	0.759901	+	0.650039i	$0.225248\pi$
$674$	−7.88544e60	−1.20403
$675$	0	0
$676$	7.20820e59	0.103270
$677$	−9.30646e60	−1.29160	−0.645800	−	0.763506i	$-0.723476\pi$
$677$	−9.30646e60	−1.29160	−0.645800	+	0.763506i	$0.723476\pi$
$678$	0	0
$679$	1.24532e59	0.0162212
$680$	−4.88904e60	−0.616996
$681$	0	0
$682$	−2.75633e60	−0.326563
$683$	1.08277e60	0.124306	0.0621530	−	0.998067i	$-0.480203\pi$
$683$	1.08277e60	0.124306	0.0621530	+	0.998067i	$0.480203\pi$
$684$	0	0
$685$	2.71195e60	0.292371
$686$	−6.15350e59	−0.0642916
$687$	0	0
$688$	−7.11719e60	−0.698485
$689$	−8.16246e60	−0.776439
$690$	0	0
$691$	−1.51050e61	−1.35003	−0.675014	−	0.737804i	$-0.735863\pi$
$691$	−1.51050e61	−1.35003	−0.675014	+	0.737804i	$0.735863\pi$
$692$	5.06645e60	0.438958
$693$	0	0
$694$	−4.04308e60	−0.329218
$695$	−7.89754e60	−0.623474
$696$	0	0
$697$	2.06059e61	1.52928
$698$	2.33129e60	0.167766
$699$	0	0
$700$	−1.49630e59	−0.0101253
$701$	2.93153e60	0.192379	0.0961893	−	0.995363i	$-0.469335\pi$
$701$	2.93153e60	0.192379	0.0961893	+	0.995363i	$0.469335\pi$
$702$	0	0
$703$	3.76831e60	0.232599
$704$	6.91394e60	0.413917
$705$	0	0
$706$	−1.23693e61	−0.696694
$707$	1.12322e60	0.0613688
$708$	0	0
$709$	2.90358e60	0.149293	0.0746465	−	0.997210i	$-0.476217\pi$
$709$	2.90358e60	0.149293	0.0746465	+	0.997210i	$0.476217\pi$
$710$	−5.88009e60	−0.293312
$711$	0	0
$712$	−5.19917e60	−0.244126
$713$	−1.75656e61	−0.800273
$714$	0	0
$715$	−4.58078e60	−0.196499
$716$	1.33661e61	0.556385
$717$	0	0
$718$	8.61715e60	0.337822
$719$	3.54815e61	1.34999	0.674995	−	0.737822i	$-0.264146\pi$
$719$	3.54815e61	1.34999	0.674995	+	0.737822i	$0.264146\pi$
$720$	0	0
$721$	−1.08700e60	−0.0389601
$722$	−1.58103e61	−0.550037
$723$	0	0
$724$	−6.72615e60	−0.220489
$725$	−7.34337e60	−0.233684
$726$	0	0
$727$	1.03918e61	0.311674	0.155837	−	0.987783i	$-0.450193\pi$
$727$	1.03918e61	0.311674	0.155837	+	0.987783i	$0.450193\pi$
$728$	1.29346e60	0.0376643
$729$	0	0
$730$	1.56524e61	0.429673
$731$	−5.29370e61	−1.41103
$732$	0	0
$733$	−1.42956e61	−0.359308	−0.179654	−	0.983730i	$-0.557498\pi$
$733$	−1.42956e61	−0.359308	−0.179654	+	0.983730i	$0.557498\pi$
$734$	4.49095e61	1.09616
$735$	0	0
$736$	2.35694e61	0.542594
$737$	4.91765e60	0.109953
$738$	0	0
$739$	3.23314e61	0.681975	0.340988	−	0.940068i	$-0.389239\pi$
$739$	3.23314e61	0.681975	0.340988	+	0.940068i	$0.389239\pi$
$740$	−1.89833e60	−0.0388945
$741$	0	0
$742$	1.51770e60	0.0293428
$743$	4.05119e61	0.760893	0.380446	−	0.924803i	$-0.375770\pi$
$743$	4.05119e61	0.760893	0.380446	+	0.924803i	$0.375770\pi$
$744$	0	0
$745$	−4.17343e61	−0.739832
$746$	6.24073e61	1.07486
$747$	0	0
$748$	8.97280e60	0.145896
$749$	3.35575e60	0.0530189
$750$	0	0
$751$	−3.19198e61	−0.476214	−0.238107	−	0.971239i	$-0.576527\pi$
$751$	−3.19198e61	−0.476214	−0.238107	+	0.971239i	$0.576527\pi$
$752$	−1.37960e61	−0.200018
$753$	0	0
$754$	1.73182e61	0.237147
$755$	7.12886e61	0.948770
$756$	0	0
$757$	−2.67158e61	−0.335898	−0.167949	−	0.985796i	$-0.553714\pi$
$757$	−2.67158e61	−0.335898	−0.167949	+	0.985796i	$0.553714\pi$
$758$	6.83757e61	0.835630
$759$	0	0
$760$	7.11492e61	0.821633
$761$	−4.67073e61	−0.524342	−0.262171	−	0.965021i	$-0.584438\pi$
$761$	−4.67073e61	−0.524342	−0.262171	+	0.965021i	$0.584438\pi$
$762$	0	0
$763$	5.82006e60	0.0617519
$764$	1.17676e61	0.121389
$765$	0	0
$766$	1.99448e61	0.194497
$767$	−1.09943e62	−1.04248
$768$	0	0
$769$	−3.41657e61	−0.306319	−0.153159	−	0.988202i	$-0.548945\pi$
$769$	−3.41657e61	−0.306319	−0.153159	+	0.988202i	$0.548945\pi$
$770$	8.51733e59	0.00742596
$771$	0	0
$772$	6.99779e60	0.0577017
$773$	−6.37216e61	−0.511008	−0.255504	−	0.966808i	$-0.582241\pi$
$773$	−6.37216e61	−0.511008	−0.255504	+	0.966808i	$0.582241\pi$
$774$	0	0
$775$	−9.08099e61	−0.688885
$776$	−5.87144e61	−0.433229
$777$	0	0
$778$	9.40894e61	0.656870
$779$	−2.99874e62	−2.03650
$780$	0	0
$781$	3.95565e61	0.254227
$782$	−9.52351e61	−0.595459
$783$	0	0
$784$	8.16570e61	0.483279
$785$	1.05593e62	0.608050
$786$	0	0
$787$	−2.17767e62	−1.18723	−0.593614	−	0.804750i	$-0.702300\pi$
$787$	−2.17767e62	−1.18723	−0.593614	+	0.804750i	$0.702300\pi$
$788$	5.91351e61	0.313712
$789$	0	0
$790$	1.19163e62	0.598632
$791$	1.05555e61	0.0516043
$792$	0	0
$793$	−3.40701e62	−1.57761
$794$	−7.15710e60	−0.0322549
$795$	0	0
$796$	2.32535e61	0.0992791
$797$	−7.92440e61	−0.329316	−0.164658	−	0.986351i	$-0.552652\pi$
$797$	−7.92440e61	−0.329316	−0.164658	+	0.986351i	$0.552652\pi$
$798$	0	0
$799$	−1.02613e62	−0.404062
$800$	1.21848e62	0.467072
$801$	0	0
$802$	−1.59664e62	−0.580042
$803$	−1.05297e62	−0.372417
$804$	0	0
$805$	5.42794e60	0.0181980
$806$	2.14161e62	0.699096
$807$	0	0
$808$	−5.29575e62	−1.63902
$809$	−3.01193e62	−0.907719	−0.453860	−	0.891073i	$-0.649953\pi$
$809$	−3.01193e62	−0.907719	−0.453860	+	0.891073i	$0.649953\pi$
$810$	0	0
$811$	4.60520e62	1.31613	0.658067	−	0.752959i	$-0.271374\pi$
$811$	4.60520e62	1.31613	0.658067	+	0.752959i	$0.271374\pi$
$812$	1.93343e60	0.00538114
$813$	0	0
$814$	−2.12688e61	−0.0561459
$815$	1.52563e62	0.392247
$816$	0	0
$817$	7.70381e62	1.87902
$818$	1.83191e62	0.435220
$819$	0	0
$820$	1.51064e62	0.340537
$821$	6.21732e62	1.36529	0.682646	−	0.730749i	$-0.260829\pi$
$821$	6.21732e62	1.36529	0.682646	+	0.730749i	$0.260829\pi$
$822$	0	0
$823$	4.56107e62	0.950539	0.475270	−	0.879840i	$-0.342350\pi$
$823$	4.56107e62	0.950539	0.475270	+	0.879840i	$0.342350\pi$
$824$	5.12496e62	1.04053
$825$	0	0
$826$	2.04424e61	0.0393967
$827$	−6.18607e62	−1.16157	−0.580786	−	0.814056i	$-0.697255\pi$
$827$	−6.18607e62	−1.16157	−0.580786	+	0.814056i	$0.697255\pi$
$828$	0	0
$829$	2.44434e62	0.435751	0.217876	−	0.975977i	$-0.430087\pi$
$829$	2.44434e62	0.435751	0.217876	+	0.975977i	$0.430087\pi$
$830$	5.91524e61	0.102753
$831$	0	0
$832$	−5.37198e62	−0.886101
$833$	6.07358e62	0.976286
$834$	0	0
$835$	6.28783e62	0.959934
$836$	−1.30579e62	−0.194285
$837$	0	0
$838$	4.70025e62	0.664316
$839$	4.81900e62	0.663858	0.331929	−	0.943304i	$-0.392301\pi$
$839$	4.81900e62	0.663858	0.331929	+	0.943304i	$0.392301\pi$
$840$	0	0
$841$	−6.69149e62	−0.875808
$842$	−6.74359e62	−0.860362
$843$	0	0
$844$	4.89867e62	0.593903
$845$	−1.35180e62	−0.159770
$846$	0	0
$847$	3.05025e61	0.0342643
$848$	−4.03131e62	−0.441505
$849$	0	0
$850$	−4.92342e62	−0.512578
$851$	−1.35542e62	−0.137590
$852$	0	0
$853$	−1.38529e63	−1.33702	−0.668510	−	0.743703i	$-0.733068\pi$
$853$	−1.38529e63	−1.33702	−0.668510	+	0.743703i	$0.733068\pi$
$854$	6.33486e61	0.0596201
$855$	0	0
$856$	−1.58216e63	−1.41601
$857$	2.18315e63	1.90545	0.952723	−	0.303840i	$-0.0982688\pi$
$857$	2.18315e63	1.90545	0.952723	+	0.303840i	$0.0982688\pi$
$858$	0	0
$859$	−3.10254e62	−0.257552	−0.128776	−	0.991674i	$-0.541105\pi$
$859$	−3.10254e62	−0.257552	−0.128776	+	0.991674i	$0.541105\pi$
$860$	−3.88087e62	−0.314205
$861$	0	0
$862$	1.09973e63	0.846993
$863$	−3.22226e62	−0.242063	−0.121032	−	0.992649i	$-0.538620\pi$
$863$	−3.22226e62	−0.242063	−0.121032	+	0.992649i	$0.538620\pi$
$864$	0	0
$865$	−9.50148e62	−0.679117
$866$	−1.02490e63	−0.714573
$867$	0	0
$868$	2.39093e61	0.0158633
$869$	−8.01634e62	−0.518861
$870$	0	0
$871$	−3.82091e62	−0.235384
$872$	−2.74404e63	−1.64925
$873$	0	0
$874$	1.38594e63	0.792953
$875$	7.03789e61	0.0392889
$876$	0	0
$877$	9.37907e62	0.498504	0.249252	−	0.968439i	$-0.419815\pi$
$877$	9.37907e62	0.498504	0.249252	+	0.968439i	$0.419815\pi$
$878$	−7.39667e62	−0.383623
$879$	0	0
$880$	−2.26237e62	−0.111734
$881$	1.19604e63	0.576452	0.288226	−	0.957562i	$-0.406935\pi$
$881$	1.19604e63	0.576452	0.288226	+	0.957562i	$0.406935\pi$
$882$	0	0
$883$	3.71532e63	1.70546	0.852728	−	0.522355i	$-0.174946\pi$
$883$	3.71532e63	1.70546	0.852728	+	0.522355i	$0.174946\pi$
$884$	−6.97167e62	−0.312330
$885$	0	0
$886$	−1.93057e63	−0.823875
$887$	−3.17967e63	−1.32442	−0.662208	−	0.749320i	$-0.730380\pi$
$887$	−3.17967e63	−1.32442	−0.662208	+	0.749320i	$0.730380\pi$
$888$	0	0
$889$	−1.44443e62	−0.0573204
$890$	2.66006e62	0.103040
$891$	0	0
$892$	2.81681e62	0.103971
$893$	1.49331e63	0.538076
$894$	0	0
$895$	−2.50665e63	−0.860791
$896$	1.43728e61	0.00481859
$897$	0	0
$898$	2.01871e63	0.645107
$899$	1.17340e63	0.366110
$900$	0	0
$901$	−2.99845e63	−0.891896
$902$	1.69252e63	0.491579
$903$	0	0
$904$	−4.97671e63	−1.37823
$905$	1.26140e63	0.341122
$906$	0	0
$907$	6.50266e63	1.67700	0.838502	−	0.544899i	$-0.183432\pi$
$907$	6.50266e63	1.67700	0.838502	+	0.544899i	$0.183432\pi$
$908$	−1.48069e63	−0.372921
$909$	0	0
$910$	−6.61777e61	−0.0158973
$911$	7.52857e63	1.76631	0.883156	−	0.469079i	$-0.155414\pi$
$911$	7.52857e63	1.76631	0.883156	+	0.469079i	$0.155414\pi$
$912$	0	0
$913$	−3.97930e62	−0.0890604
$914$	3.14640e63	0.687814
$915$	0	0
$916$	−2.40340e63	−0.501271
$917$	2.96674e62	0.0604419
$918$	0	0
$919$	2.17512e63	0.422864	0.211432	−	0.977393i	$-0.432187\pi$
$919$	2.17512e63	0.422864	0.211432	+	0.977393i	$0.432187\pi$
$920$	−2.55916e63	−0.486025
$921$	0	0
$922$	6.01133e63	1.08957
$923$	−3.07346e63	−0.544240
$924$	0	0
$925$	−7.00719e62	−0.118440
$926$	3.92433e63	0.648081
$927$	0	0
$928$	−1.57445e63	−0.248226
$929$	−7.86465e63	−1.21155	−0.605775	−	0.795636i	$-0.707137\pi$
$929$	−7.86465e63	−1.21155	−0.605775	+	0.795636i	$0.707137\pi$
$930$	0	0
$931$	−8.83875e63	−1.30009
$932$	3.02876e63	0.435334
$933$	0	0
$934$	6.53651e63	0.897198
$935$	−1.68273e63	−0.225718
$936$	0	0
$937$	1.79538e63	0.230015	0.115007	−	0.993365i	$-0.463311\pi$
$937$	1.79538e63	0.230015	0.115007	+	0.993365i	$0.463311\pi$
$938$	7.10445e61	0.00889548
$939$	0	0
$940$	−7.52269e62	−0.0899755
$941$	1.29813e64	1.51754	0.758771	−	0.651358i	$-0.225800\pi$
$941$	1.29813e64	1.51754	0.758771	+	0.651358i	$0.225800\pi$
$942$	0	0
$943$	1.07861e64	1.20466
$944$	−5.42991e63	−0.592781
$945$	0	0
$946$	−4.34812e63	−0.453567
$947$	−3.48486e63	−0.355353	−0.177677	−	0.984089i	$-0.556858\pi$
$947$	−3.48486e63	−0.355353	−0.177677	+	0.984089i	$0.556858\pi$
$948$	0	0
$949$	8.18131e63	0.797259
$950$	7.16495e63	0.682584
$951$	0	0
$952$	4.75150e62	0.0432650
$953$	−3.62975e63	−0.323131	−0.161566	−	0.986862i	$-0.551654\pi$
$953$	−3.62975e63	−0.323131	−0.161566	+	0.986862i	$0.551654\pi$
$954$	0	0
$955$	−2.20685e63	−0.187802
$956$	−3.62511e62	−0.0301631
$957$	0	0
$958$	−9.21603e63	−0.733137
$959$	−2.63565e62	−0.0205016
$960$	0	0
$961$	1.06576e63	0.0792697
$962$	1.65254e63	0.120195
$963$	0	0
$964$	6.51455e63	0.453135
$965$	−1.31235e63	−0.0892711
$966$	0	0
$967$	−2.78438e64	−1.81159	−0.905794	−	0.423719i	$-0.860724\pi$
$967$	−2.78438e64	−1.81159	−0.905794	+	0.423719i	$0.860724\pi$
$968$	−1.43813e64	−0.915118
$969$	0	0
$970$	3.00401e63	0.182856
$971$	2.13572e64	1.27154	0.635770	−	0.771878i	$-0.280683\pi$
$971$	2.13572e64	1.27154	0.635770	+	0.771878i	$0.280683\pi$
$972$	0	0
$973$	7.67536e62	0.0437192
$974$	−1.07803e64	−0.600638
$975$	0	0
$976$	−1.68267e64	−0.897072
$977$	−3.39336e64	−1.76969	−0.884843	−	0.465889i	$-0.845734\pi$
$977$	−3.39336e64	−1.76969	−0.884843	+	0.465889i	$0.845734\pi$
$978$	0	0
$979$	−1.78948e63	−0.0893096
$980$	4.45261e63	0.217397
$981$	0	0
$982$	1.28022e64	0.598255
$983$	−8.51968e63	−0.389514	−0.194757	−	0.980852i	$-0.562392\pi$
$983$	−8.51968e63	−0.389514	−0.194757	+	0.980852i	$0.562392\pi$
$984$	0	0
$985$	−1.10900e64	−0.485348
$986$	6.36178e63	0.272411
$987$	0	0
$988$	1.01457e64	0.415919
$989$	−2.77097e64	−1.11151
$990$	0	0
$991$	4.90354e63	0.188333	0.0941664	−	0.995556i	$-0.469981\pi$
$991$	4.90354e63	0.188333	0.0941664	+	0.995556i	$0.469981\pi$
$992$	−1.94701e64	−0.731757
$993$	0	0
$994$	5.71467e62	0.0205676
$995$	−4.36090e63	−0.153596
$996$	0	0
$997$	4.69596e64	1.58409	0.792043	−	0.610465i	$-0.209017\pi$
$997$	4.69596e64	1.58409	0.792043	+	0.610465i	$0.209017\pi$
$998$	−9.82831e63	−0.324468
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.34437e6 q^{2} -3.30001e12 q^{4} +6.18875e14 q^{5} -6.01464e16 q^{7} +2.83578e19 q^{8} -1.45087e21 q^{10} +9.76031e21 q^{11} -7.58355e23 q^{13} +1.41006e23 q^{14} -3.74540e25 q^{16} -2.78579e26 q^{17} +4.05410e27 q^{19} -2.04230e27 q^{20} -2.28818e28 q^{22} -1.45822e29 q^{23} -7.53862e29 q^{25} +1.77787e30 q^{26} +1.98484e29 q^{28} +9.74099e30 q^{29} +1.20460e32 q^{31} -1.61632e32 q^{32} +6.53093e32 q^{34} -3.72231e31 q^{35} +9.29506e32 q^{37} -9.50433e33 q^{38} +1.75499e34 q^{40} -7.39680e34 q^{41} +1.90025e35 q^{43} -3.22092e34 q^{44} +3.41860e35 q^{46} +3.68345e35 q^{47} -2.18020e36 q^{49} +1.76733e36 q^{50} +2.50258e36 q^{52} +1.07634e37 q^{53} +6.04041e36 q^{55} -1.70562e36 q^{56} -2.28365e37 q^{58} +1.44976e38 q^{59} +4.49263e38 q^{61} -2.82402e38 q^{62} +7.08373e38 q^{64} -4.69327e38 q^{65} +5.03842e38 q^{67} +9.19315e38 q^{68} +8.72649e37 q^{70} +4.05279e39 q^{71} -1.07882e40 q^{73} -2.17911e39 q^{74} -1.33786e40 q^{76} -5.87048e38 q^{77} -8.21320e40 q^{79} -2.31793e40 q^{80} +1.73408e41 q^{82} -4.07702e40 q^{83} -1.72406e41 q^{85} -4.45489e41 q^{86} +2.76781e41 q^{88} -1.83342e41 q^{89} +4.56124e40 q^{91} +4.81213e41 q^{92} -8.63538e41 q^{94} +2.50898e42 q^{95} -2.07049e42 q^{97} +5.11119e42 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1660014 q^{2} + 29333750564548 q^{4} - 16\!\cdots\!20 q^{5} + 11\!\cdots\!28 q^{7} - 77\!\cdots\!48 q^{8} + 53\!\cdots\!60 q^{10} - 87\!\cdots\!96 q^{11} - 16\!\cdots\!96 q^{13} + 13\!\cdots\!08 q^{14}+ \cdots - 62\!\cdots\!46 q^{98}+O(q^{100}) \) 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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