LMFDB - Embedded newform 9.42.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,42,Mod(1,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 42, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 42 $
Character orbit:	$[\chi]$	$=$	9.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$95.8245034108$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 14982256920x + 433388802120300 $ x^3 - x^2 - 14982256920*x + 433388802120300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5}\cdot 7 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$103995.$ 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)

$f(q)$	$=$	$q+1.34440e6 q^{2} -3.91623e11 q^{4} -1.06877e14 q^{5} -3.99469e17 q^{7} -3.48285e18 q^{8} +O(q^{10})$	\(q+1.34440e6 q^{2} -3.91623e11 q^{4} -1.06877e14 q^{5} -3.99469e17 q^{7} -3.48285e18 q^{8} -1.43685e20 q^{10} -2.59920e21 q^{11} -3.34490e22 q^{13} -5.37044e23 q^{14} -3.82115e24 q^{16} -2.78752e25 q^{17} +2.51816e26 q^{19} +4.18553e25 q^{20} -3.49435e27 q^{22} +2.03286e27 q^{23} -3.40521e28 q^{25} -4.49686e28 q^{26} +1.56441e29 q^{28} +6.39430e29 q^{29} -3.99382e29 q^{31} +2.52174e30 q^{32} -3.74753e31 q^{34} +4.26939e31 q^{35} -1.48588e32 q^{37} +3.38540e32 q^{38} +3.72236e32 q^{40} -5.94247e31 q^{41} -1.25575e33 q^{43} +1.01790e33 q^{44} +2.73297e33 q^{46} -3.54758e33 q^{47} +1.15008e35 q^{49} -4.57795e34 q^{50} +1.30994e34 q^{52} -1.54656e34 q^{53} +2.77793e35 q^{55} +1.39129e36 q^{56} +8.59647e35 q^{58} +1.46481e35 q^{59} -4.04266e36 q^{61} -5.36927e35 q^{62} +1.17930e37 q^{64} +3.57491e36 q^{65} -8.80253e36 q^{67} +1.09166e37 q^{68} +5.73975e37 q^{70} -1.53426e38 q^{71} -2.36946e38 q^{73} -1.99761e38 q^{74} -9.86167e37 q^{76} +1.03830e39 q^{77} -4.62673e38 q^{79} +4.08391e38 q^{80} -7.98903e37 q^{82} -1.09848e39 q^{83} +2.97921e39 q^{85} -1.68823e39 q^{86} +9.05262e39 q^{88} +1.60084e40 q^{89} +1.33618e40 q^{91} -7.96115e38 q^{92} -4.76936e39 q^{94} -2.69132e40 q^{95} +8.97977e38 q^{97} +1.54616e41 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 289380 q^{2} - 2254266178800 q^{4} - 38650546192026 q^{5} - 44\!\cdots\!68 q^{7}+ \cdots - 22\!\cdots\!96 q^{8}+O(q^{10}) $ 3 * q + 289380 * q^2 - 2254266178800 * q^4 - 38650546192026 * q^5 - 44602211301408768 * q^7 - 2268032948689999296 * q^8	$ 3 q + 289380 q^{2} - 2254266178800 q^{4} - 38650546192026 q^{5} - 44\!\cdots\!68 q^{7}+ \cdots + 26\!\cdots\!92 q^{98}+O(q^{100}) $ 3 * q + 289380 * q^2 - 2254266178800 * q^4 - 38650546192026 * q^5 - 44602211301408768 * q^7 - 2268032948689999296 * q^8 + 303684786396357841224 * q^10 - 2162403578017276790604 * q^11 + 44715417115247213223642 * q^13 - 320671470159767900457984 * q^14 - 5459234621059712438935296 * q^16 + 10989933423479049968718714 * q^17 + 196397070114735534584831028 * q^19 - 531636782784591447776761824 * q^20 - 4513503674461058254096349328 * q^22 + 4665149638066794122614978584 * q^23 - 4609009761244207114343812899 * q^25 - 122894273592250273312332501576 * q^26 - 599824891534617466777136050176 * q^28 + 941555486655490244273102003214 * q^29 - 6480085319036017864686465368808 * q^31 + 9194142460916956643740243289088 * q^32 - 50410977973081452147630100226760 * q^34 + 153374925211463555312750388019200 * q^35 - 442820255707228186224391784737998 * q^37 + 832008681100278182323288015176048 * q^38 - 830400317719830554628641188275072 * q^40 + 438132779830146983268076758934098 * q^41 - 1310999240696843410630649721463476 * q^43 + 1443247128257998435455229084014528 * q^44 + 7997471516728167525889026089716512 * q^46 - 64523854533555761088559286850643968 * q^47 + 171140726678012788361144930683431723 * q^49 - 28333303327284754376413888152266724 * q^50 - 20984793566307791589805690265685024 * q^52 - 34693992770270063328682081068689946 * q^53 + 100035221507232528994896069839569896 * q^55 + 568132015233041377672136741101977600 * q^56 - 2740694640626009342372591817401518296 * q^58 + 4582685445865314260503003260089664948 * q^59 - 8693740159306202291599355552752714662 * q^61 - 265004064722629998116825545352842464 * q^62 + 16981741764860889983034117450588819456 * q^64 - 2721360738989032295650621165564283148 * q^65 + 32867814173503669322418795877934200116 * q^67 - 33261671085355608094778443956314848800 * q^68 + 98543364272473044599951459881688524800 * q^70 - 149748844745311390685366673232301225496 * q^71 + 6619123649433674932122580558210670046 * q^73 - 14490759310413784046620539770501448744 * q^74 - 536779250932404614788199202699778310208 * q^76 + 954944421253262491346753072408971247616 * q^77 - 1112771209183156752666617542198723627800 * q^79 + 2423764999311265237507278994973679346176 * q^80 - 107939940778839787676218322470600048296 * q^82 + 1187635824307222104653182519688468749260 * q^83 + 6153092316082135211652182465439269196852 * q^85 - 2889811785377479896729751911427106623344 * q^86 + 11348012623814378178834124633898985613056 * q^88 + 2907470395792485617492963651915834875602 * q^89 + 19747616149564653802226421926044582182912 * q^91 - 10266693573432860781998326486887076136832 * q^92 + 34628213999509804914437049475497096849408 * q^94 + 84590150972982168777889232049326900017896 * q^95 - 52479807025249236413871256717456940920314 * q^97 + 268218382984038433881798894561914095373892 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.34440e6	0.906593	0.453296	−	0.891360i	$-0.350248\pi$
$2$	1.34440e6	0.906593	0.453296	+	0.891360i	$0.350248\pi$
$3$	0	0
$3$	0	0
$4$	−3.91623e11	−0.178089
$5$	−1.06877e14	−0.501185	−0.250592	−	0.968093i	$-0.580625\pi$
$5$	−1.06877e14	−0.501185	−0.250592	+	0.968093i	$0.580625\pi$
$6$	0	0
$7$	−3.99469e17	−1.89223	−0.946113	−	0.323835i	$-0.895028\pi$
$7$	−3.99469e17	−1.89223	−0.946113	+	0.323835i	$0.895028\pi$
$8$	−3.48285e18	−1.06805
$9$	0	0
$10$	−1.43685e20	−0.454370
$11$	−2.59920e21	−1.16490	−0.582450	−	0.812866i	$-0.697906\pi$
$11$	−2.59920e21	−1.16490	−0.582450	+	0.812866i	$0.697906\pi$
$12$	0	0
$13$	−3.34490e22	−0.488139	−0.244070	−	0.969758i	$-0.578483\pi$
$13$	−3.34490e22	−0.488139	−0.244070	+	0.969758i	$0.578483\pi$
$14$	−5.37044e23	−1.71548
$15$	0	0
$16$	−3.82115e24	−0.790195
$17$	−2.78752e25	−1.66347	−0.831736	−	0.555172i	$-0.812652\pi$
$17$	−2.78752e25	−1.66347	−0.831736	+	0.555172i	$0.812652\pi$
$18$	0	0
$19$	2.51816e26	1.53686	0.768430	−	0.639934i	$-0.221038\pi$
$19$	2.51816e26	1.53686	0.768430	+	0.639934i	$0.221038\pi$
$20$	4.18553e25	0.0892556
$21$	0	0
$22$	−3.49435e27	−1.05609
$23$	2.03286e27	0.246995	0.123497	−	0.992345i	$-0.460589\pi$
$23$	2.03286e27	0.246995	0.123497	+	0.992345i	$0.460589\pi$
$24$	0	0
$25$	−3.40521e28	−0.748814
$26$	−4.49686e28	−0.442544
$27$	0	0
$28$	1.56441e29	0.336985
$29$	6.39430e29	0.670863	0.335431	−	0.942065i	$-0.391118\pi$
$29$	6.39430e29	0.670863	0.335431	+	0.942065i	$0.391118\pi$
$30$	0	0
$31$	−3.99382e29	−0.106776	−0.0533880	−	0.998574i	$-0.517002\pi$
$31$	−3.99382e29	−0.106776	−0.0533880	+	0.998574i	$0.517002\pi$
$32$	2.52174e30	0.351662
$33$	0	0
$34$	−3.74753e31	−1.50809
$35$	4.26939e31	0.948355
$36$	0	0
$37$	−1.48588e32	−1.05645	−0.528223	−	0.849106i	$-0.677141\pi$
$37$	−1.48588e32	−1.05645	−0.528223	+	0.849106i	$0.677141\pi$
$38$	3.38540e32	1.39331
$39$	0	0
$40$	3.72236e32	0.535289
$41$	−5.94247e31	−0.0515107	−0.0257554	−	0.999668i	$-0.508199\pi$
$41$	−5.94247e31	−0.0515107	−0.0257554	+	0.999668i	$0.508199\pi$
$42$	0	0
$43$	−1.25575e33	−0.410015	−0.205008	−	0.978760i	$-0.565722\pi$
$43$	−1.25575e33	−0.410015	−0.205008	+	0.978760i	$0.565722\pi$
$44$	1.01790e33	0.207456
$45$	0	0
$46$	2.73297e33	0.223924
$47$	−3.54758e33	−0.187037	−0.0935183	−	0.995618i	$-0.529811\pi$
$47$	−3.54758e33	−0.187037	−0.0935183	+	0.995618i	$0.529811\pi$
$48$	0	0
$49$	1.15008e35	2.58052
$50$	−4.57795e34	−0.678869
$51$	0	0
$52$	1.30994e34	0.0869324
$53$	−1.54656e34	−0.0694564	−0.0347282	−	0.999397i	$-0.511057\pi$
$53$	−1.54656e34	−0.0694564	−0.0347282	+	0.999397i	$0.511057\pi$
$54$	0	0
$55$	2.77793e35	0.583830
$56$	1.39129e36	2.02099
$57$	0	0
$58$	8.59647e35	0.608200
$59$	1.46481e35	0.0729988	0.0364994	−	0.999334i	$-0.488379\pi$
$59$	1.46481e35	0.0729988	0.0364994	+	0.999334i	$0.488379\pi$
$60$	0	0
$61$	−4.04266e36	−1.01720	−0.508600	−	0.861003i	$-0.669837\pi$
$61$	−4.04266e36	−1.01720	−0.508600	+	0.861003i	$0.669837\pi$
$62$	−5.36927e35	−0.0968023
$63$	0	0
$64$	1.17930e37	1.10901
$65$	3.57491e36	0.244648
$66$	0	0
$67$	−8.80253e36	−0.323649	−0.161824	−	0.986820i	$-0.551738\pi$
$67$	−8.80253e36	−0.323649	−0.161824	+	0.986820i	$0.551738\pi$
$68$	1.09166e37	0.296246
$69$	0	0
$70$	5.73975e37	0.859772
$71$	−1.53426e38	−1.71832	−0.859160	−	0.511707i	$-0.829013\pi$
$71$	−1.53426e38	−1.71832	−0.859160	+	0.511707i	$0.829013\pi$
$72$	0	0
$73$	−2.36946e38	−1.50152	−0.750759	−	0.660577i	$-0.770312\pi$
$73$	−2.36946e38	−1.50152	−0.750759	+	0.660577i	$0.770312\pi$
$74$	−1.99761e38	−0.957766
$75$	0	0
$76$	−9.86167e37	−0.273698
$77$	1.03830e39	2.20426
$78$	0	0
$79$	−4.62673e38	−0.580656	−0.290328	−	0.956927i	$-0.593764\pi$
$79$	−4.62673e38	−0.580656	−0.290328	+	0.956927i	$0.593764\pi$
$80$	4.08391e38	0.396033
$81$	0	0
$82$	−7.98903e37	−0.0466992
$83$	−1.09848e39	−0.500830	−0.250415	−	0.968139i	$-0.580567\pi$
$83$	−1.09848e39	−0.500830	−0.250415	+	0.968139i	$0.580567\pi$
$84$	0	0
$85$	2.97921e39	0.833706
$86$	−1.68823e39	−0.371717
$87$	0	0
$88$	9.05262e39	1.24417
$89$	1.60084e40	1.74523	0.872617	−	0.488405i	$-0.162421\pi$
$89$	1.60084e40	1.74523	0.872617	+	0.488405i	$0.162421\pi$
$90$	0	0
$91$	1.33618e40	0.923670
$92$	−7.96115e38	−0.0439871
$93$	0	0
$94$	−4.76936e39	−0.169566
$95$	−2.69132e40	−0.770250
$96$	0	0
$97$	8.97977e38	0.0167666	0.00838329	−	0.999965i	$-0.497331\pi$
$97$	8.97977e38	0.0167666	0.00838329	+	0.999965i	$0.497331\pi$
$98$	1.54616e41	2.33948
$99$	0	0
$100$	1.33356e40	0.133356
$101$	9.88339e40	0.805968	0.402984	−	0.915207i	$-0.367973\pi$
$101$	9.88339e40	0.805968	0.402984	+	0.915207i	$0.367973\pi$
$102$	0	0
$103$	−2.00844e41	−1.09571	−0.547856	−	0.836573i	$-0.684556\pi$
$103$	−2.00844e41	−1.09571	−0.547856	+	0.836573i	$0.684556\pi$
$104$	1.16498e41	0.521356
$105$	0	0
$106$	−2.07919e40	−0.0629687
$107$	−1.39775e41	−0.349189	−0.174595	−	0.984640i	$-0.555862\pi$
$107$	−1.39775e41	−0.349189	−0.174595	+	0.984640i	$0.555862\pi$
$108$	0	0
$109$	9.35581e41	1.59896	0.799481	−	0.600691i	$-0.205108\pi$
$109$	9.35581e41	1.59896	0.799481	+	0.600691i	$0.205108\pi$
$110$	3.73464e41	0.529296
$111$	0	0
$112$	1.52643e42	1.49523
$113$	1.69777e42	1.38603	0.693013	−	0.720925i	$-0.256283\pi$
$113$	1.69777e42	1.38603	0.693013	+	0.720925i	$0.256283\pi$
$114$	0	0
$115$	−2.17266e41	−0.123790
$116$	−2.50415e41	−0.119474
$117$	0	0
$118$	1.96929e41	0.0661802
$119$	1.11353e43	3.14767
$120$	0	0
$121$	1.77730e42	0.356994
$122$	−5.43494e42	−0.922186
$123$	0	0
$124$	1.56407e41	0.0190156
$125$	8.49956e42	0.876479
$126$	0	0
$127$	1.24842e43	0.929793	0.464896	−	0.885365i	$-0.346092\pi$
$127$	1.24842e43	0.929793	0.464896	+	0.885365i	$0.346092\pi$
$128$	1.03091e43	0.653758
$129$	0	0
$130$	4.80610e42	0.221796
$131$	−4.74003e43	−1.86947	−0.934737	−	0.355339i	$-0.884365\pi$
$131$	−4.74003e43	−1.86947	−0.934737	+	0.355339i	$0.884365\pi$
$132$	0	0
$133$	−1.00593e44	−2.90809
$134$	−1.18341e43	−0.293418
$135$	0	0
$136$	9.70853e43	1.77667
$137$	−4.51190e43	−0.710539	−0.355269	−	0.934764i	$-0.615611\pi$
$137$	−4.51190e43	−0.710539	−0.355269	+	0.934764i	$0.615611\pi$
$138$	0	0
$139$	1.39477e43	0.163192	0.0815959	−	0.996665i	$-0.473998\pi$
$139$	1.39477e43	0.163192	0.0815959	+	0.996665i	$0.473998\pi$
$140$	−1.67199e43	−0.168892
$141$	0	0
$142$	−2.06266e44	−1.55782
$143$	8.69404e43	0.568634
$144$	0	0
$145$	−6.83401e43	−0.336226
$146$	−3.18549e44	−1.36126
$147$	0	0
$148$	5.81903e43	0.188142
$149$	2.52241e44	0.710391	0.355196	−	0.934792i	$-0.384414\pi$
$149$	2.52241e44	0.710391	0.355196	+	0.934792i	$0.384414\pi$
$150$	0	0
$151$	−3.68239e44	−0.789046	−0.394523	−	0.918886i	$-0.629090\pi$
$151$	−3.68239e44	−0.789046	−0.394523	+	0.918886i	$0.629090\pi$
$152$	−8.77037e44	−1.64144
$153$	0	0
$154$	1.39588e45	1.99836
$155$	4.26846e43	0.0535144
$156$	0	0
$157$	−4.32607e44	−0.417014	−0.208507	−	0.978021i	$-0.566860\pi$
$157$	−4.32607e44	−0.417014	−0.208507	+	0.978021i	$0.566860\pi$
$158$	−6.22016e44	−0.526418
$159$	0	0
$160$	−2.69515e44	−0.176248
$161$	−8.12066e44	−0.467370
$162$	0	0
$163$	−1.63490e45	−0.730541	−0.365270	−	0.930901i	$-0.619023\pi$
$163$	−1.63490e45	−0.730541	−0.365270	+	0.930901i	$0.619023\pi$
$164$	2.32720e43	0.00917351
$165$	0	0
$166$	−1.47679e45	−0.454049
$167$	4.35680e45	1.18435	0.592175	−	0.805810i	$-0.298270\pi$
$167$	4.35680e45	1.18435	0.592175	+	0.805810i	$0.298270\pi$
$168$	0	0
$169$	−3.57662e45	−0.761720
$170$	4.00524e45	0.755832
$171$	0	0
$172$	4.91780e44	0.0730193
$173$	2.11282e44	0.0278559	0.0139280	−	0.999903i	$-0.495566\pi$
$173$	2.11282e44	0.0278559	0.0139280	+	0.999903i	$0.495566\pi$
$174$	0	0
$175$	1.36028e46	1.41693
$176$	9.93191e45	0.920499
$177$	0	0
$178$	2.15217e46	1.58222
$179$	−4.71116e45	−0.308774	−0.154387	−	0.988010i	$-0.549340\pi$
$179$	−4.71116e45	−0.308774	−0.154387	+	0.988010i	$0.549340\pi$
$180$	0	0
$181$	−6.10024e45	−0.318373	−0.159186	−	0.987249i	$-0.550887\pi$
$181$	−6.10024e45	−0.318373	−0.159186	+	0.987249i	$0.550887\pi$
$182$	1.79636e46	0.837393
$183$	0	0
$184$	−7.08017e45	−0.263802
$185$	1.58805e46	0.529474
$186$	0	0
$187$	7.24531e46	1.93778
$188$	1.38931e45	0.0333092
$189$	0	0
$190$	−3.61820e46	−0.698303
$191$	−1.46963e46	−0.254697	−0.127348	−	0.991858i	$-0.540647\pi$
$191$	−1.46963e46	−0.254697	−0.127348	+	0.991858i	$0.540647\pi$
$192$	0	0
$193$	−8.24885e46	−1.15470	−0.577349	−	0.816497i	$-0.695913\pi$
$193$	−8.24885e46	−1.15470	−0.577349	+	0.816497i	$0.695913\pi$
$194$	1.20724e45	0.0152005
$195$	0	0
$196$	−4.50397e46	−0.459564
$197$	−6.11379e46	−0.562022	−0.281011	−	0.959705i	$-0.590670\pi$
$197$	−6.11379e46	−0.562022	−0.281011	+	0.959705i	$0.590670\pi$
$198$	0	0
$199$	−2.06724e47	−1.54491	−0.772453	−	0.635072i	$-0.780971\pi$
$199$	−2.06724e47	−1.54491	−0.772453	+	0.635072i	$0.780971\pi$
$200$	1.18599e47	0.799769
$201$	0	0
$202$	1.32872e47	0.730685
$203$	−2.55432e47	−1.26942
$204$	0	0
$205$	6.35111e45	0.0258164
$206$	−2.70014e47	−0.993365
$207$	0	0
$208$	1.27813e47	0.385725
$209$	−6.54518e47	−1.79029
$210$	0	0
$211$	3.08234e45	0.00693570	0.00346785	−	0.999994i	$-0.498896\pi$
$211$	3.08234e45	0.00693570	0.00346785	+	0.999994i	$0.498896\pi$
$212$	6.05669e45	0.0123694
$213$	0	0
$214$	−1.87913e47	−0.316573
$215$	1.34210e47	0.205493
$216$	0	0
$217$	1.59541e47	0.202044
$218$	1.25779e48	1.44961
$219$	0	0
$220$	−1.08790e47	−0.103974
$221$	9.32397e47	0.812006
$222$	0	0
$223$	−5.03674e47	−0.364670	−0.182335	−	0.983236i	$-0.558365\pi$
$223$	−5.03674e47	−0.364670	−0.182335	+	0.983236i	$0.558365\pi$
$224$	−1.00736e48	−0.665425
$225$	0	0
$226$	2.28248e48	1.25656
$227$	1.43782e47	0.0723058	0.0361529	−	0.999346i	$-0.488490\pi$
$227$	1.43782e47	0.0723058	0.0361529	+	0.999346i	$0.488490\pi$
$228$	0	0
$229$	−2.29667e48	−0.964874	−0.482437	−	0.875931i	$-0.660248\pi$
$229$	−2.29667e48	−0.964874	−0.482437	+	0.875931i	$0.660248\pi$
$230$	−2.92091e47	−0.112227
$231$	0	0
$232$	−2.22704e48	−0.716513
$233$	−2.20055e47	−0.0648239	−0.0324119	−	0.999475i	$-0.510319\pi$
$233$	−2.20055e47	−0.0648239	−0.0324119	+	0.999475i	$0.510319\pi$
$234$	0	0
$235$	3.79154e47	0.0937398
$236$	−5.73653e46	−0.0130003
$237$	0	0
$238$	1.49702e49	2.85365
$239$	1.04096e49	1.82087	0.910434	−	0.413655i	$-0.135748\pi$
$239$	1.04096e49	1.82087	0.910434	+	0.413655i	$0.135748\pi$
$240$	0	0
$241$	−8.83597e48	−1.30288	−0.651440	−	0.758700i	$-0.725835\pi$
$241$	−8.83597e48	−1.30288	−0.651440	+	0.758700i	$0.725835\pi$
$242$	2.38940e48	0.323648
$243$	0	0
$244$	1.58320e48	0.181152
$245$	−1.22916e49	−1.29332
$246$	0	0
$247$	−8.42297e48	−0.750201
$248$	1.39099e48	0.114042
$249$	0	0
$250$	1.14268e49	0.794609
$251$	2.56380e49	1.64275	0.821377	−	0.570386i	$-0.193206\pi$
$251$	2.56380e49	1.64275	0.821377	+	0.570386i	$0.193206\pi$
$252$	0	0
$253$	−5.28381e48	−0.287724
$254$	1.67838e49	0.842943
$255$	0	0
$256$	−1.20736e49	−0.516317
$257$	−3.19009e49	−1.25943	−0.629715	−	0.776827i	$-0.716828\pi$
$257$	−3.19009e49	−1.25943	−0.629715	+	0.776827i	$0.716828\pi$
$258$	0	0
$259$	5.93561e49	1.99904
$260$	−1.40002e48	−0.0435692
$261$	0	0
$262$	−6.37248e49	−1.69485
$263$	−2.05862e49	−0.506389	−0.253194	−	0.967415i	$-0.581481\pi$
$263$	−2.05862e49	−0.506389	−0.253194	+	0.967415i	$0.581481\pi$
$264$	0	0
$265$	1.65292e48	0.0348105
$266$	−1.35236e50	−2.63645
$267$	0	0
$268$	3.44727e48	0.0576384
$269$	−9.01933e49	−1.39718	−0.698590	−	0.715522i	$-0.746189\pi$
$269$	−9.01933e49	−1.39718	−0.698590	+	0.715522i	$0.746189\pi$
$270$	0	0
$271$	−2.40475e49	−0.320037	−0.160018	−	0.987114i	$-0.551155\pi$
$271$	−2.40475e49	−0.320037	−0.160018	+	0.987114i	$0.551155\pi$
$272$	1.06515e50	1.31447
$273$	0	0
$274$	−6.06578e49	−0.644169
$275$	8.85081e49	0.872294
$276$	0	0
$277$	−7.23233e49	−0.614388	−0.307194	−	0.951647i	$-0.599390\pi$
$277$	−7.23233e49	−0.614388	−0.307194	+	0.951647i	$0.599390\pi$
$278$	1.87512e49	0.147949
$279$	0	0
$280$	−1.48697e50	−1.01289
$281$	−1.01780e50	−0.644440	−0.322220	−	0.946665i	$-0.604429\pi$
$281$	−1.01780e50	−0.644440	−0.322220	+	0.946665i	$0.604429\pi$
$282$	0	0
$283$	6.28092e49	0.343875	0.171938	−	0.985108i	$-0.444997\pi$
$283$	6.28092e49	0.343875	0.171938	+	0.985108i	$0.444997\pi$
$284$	6.00852e49	0.306014
$285$	0	0
$286$	1.16882e50	0.515519
$287$	2.37383e49	0.0974700
$288$	0	0
$289$	4.96222e50	1.76714
$290$	−9.18762e49	−0.304820
$291$	0	0
$292$	9.27933e49	0.267404
$293$	5.08876e50	1.36718	0.683590	−	0.729866i	$-0.260418\pi$
$293$	5.08876e50	1.36718	0.683590	+	0.729866i	$0.260418\pi$
$294$	0	0
$295$	−1.56554e49	−0.0365859
$296$	5.17509e50	1.12833
$297$	0	0
$298$	3.39112e50	0.644036
$299$	−6.79972e49	−0.120568
$300$	0	0
$301$	5.01633e50	0.775842
$302$	−4.95059e50	−0.715344
$303$	0	0
$304$	−9.62225e50	−1.21442
$305$	4.32066e50	0.509805
$306$	0	0
$307$	−1.50028e50	−0.154823	−0.0774113	−	0.996999i	$-0.524665\pi$
$307$	−1.50028e50	−0.154823	−0.0774113	+	0.996999i	$0.524665\pi$
$308$	−4.06621e50	−0.392555
$309$	0	0
$310$	5.73849e49	0.0485158
$311$	1.32377e51	1.04767	0.523836	−	0.851819i	$-0.324500\pi$
$311$	1.32377e51	1.04767	0.523836	+	0.851819i	$0.324500\pi$
$312$	0	0
$313$	−1.00439e51	−0.697018	−0.348509	−	0.937305i	$-0.613312\pi$
$313$	−1.00439e51	−0.697018	−0.348509	+	0.937305i	$0.613312\pi$
$314$	−5.81595e50	−0.378062
$315$	0	0
$316$	1.81193e50	0.103409
$317$	2.46384e51	1.31794	0.658972	−	0.752167i	$-0.270991\pi$
$317$	2.46384e51	1.31794	0.658972	+	0.752167i	$0.270991\pi$
$318$	0	0
$319$	−1.66200e51	−0.781489
$320$	−1.26040e51	−0.555818
$321$	0	0
$322$	−1.09174e51	−0.423714
$323$	−7.01942e51	−2.55652
$324$	0	0
$325$	1.13901e51	0.365526
$326$	−2.19795e51	−0.662303
$327$	0	0
$328$	2.06967e50	0.0550159
$329$	1.41715e51	0.353916
$330$	0	0
$331$	7.34740e51	1.62054	0.810270	−	0.586057i	$-0.199320\pi$
$331$	7.34740e51	1.62054	0.810270	+	0.586057i	$0.199320\pi$
$332$	4.30189e50	0.0891925
$333$	0	0
$334$	5.85726e51	1.07372
$335$	9.40785e50	0.162208
$336$	0	0
$337$	−6.00807e51	−0.916900	−0.458450	−	0.888720i	$-0.651595\pi$
$337$	−6.00807e51	−0.916900	−0.458450	+	0.888720i	$0.651595\pi$
$338$	−4.80839e51	−0.690570
$339$	0	0
$340$	−1.16673e51	−0.148474
$341$	1.03807e51	0.124383
$342$	0	0
$343$	−2.81387e52	−2.99071
$344$	4.37359e51	0.437916
$345$	0	0
$346$	2.84047e50	0.0252540
$347$	−8.44413e51	−0.707621	−0.353811	−	0.935317i	$-0.615114\pi$
$347$	−8.44413e51	−0.707621	−0.353811	+	0.935317i	$0.615114\pi$
$348$	0	0
$349$	1.62504e52	1.21044	0.605219	−	0.796059i	$-0.293086\pi$
$349$	1.62504e52	1.21044	0.605219	+	0.796059i	$0.293086\pi$
$350$	1.82875e52	1.28458
$351$	0	0
$352$	−6.55450e51	−0.409652
$353$	3.57047e50	0.0210544	0.0105272	−	0.999945i	$-0.496649\pi$
$353$	3.57047e50	0.0210544	0.0105272	+	0.999945i	$0.496649\pi$
$354$	0	0
$355$	1.63977e52	0.861195
$356$	−6.26926e51	−0.310808
$357$	0	0
$358$	−6.33367e51	−0.279932
$359$	8.95225e51	0.373677	0.186838	−	0.982391i	$-0.440176\pi$
$359$	8.95225e51	0.373677	0.186838	+	0.982391i	$0.440176\pi$
$360$	0	0
$361$	3.65641e52	1.36194
$362$	−8.20113e51	−0.288634
$363$	0	0
$364$	−5.23279e51	−0.164496
$365$	2.53240e52	0.752537
$366$	0	0
$367$	−2.14287e52	−0.569301	−0.284651	−	0.958631i	$-0.591878\pi$
$367$	−2.14287e52	−0.569301	−0.284651	+	0.958631i	$0.591878\pi$
$368$	−7.76787e51	−0.195174
$369$	0	0
$370$	2.13497e52	0.480018
$371$	6.17804e51	0.131427
$372$	0	0
$373$	1.75320e52	0.334041	0.167020	−	0.985953i	$-0.446585\pi$
$373$	1.75320e52	0.334041	0.167020	+	0.985953i	$0.446585\pi$
$374$	9.74057e52	1.75678
$375$	0	0
$376$	1.23557e52	0.199764
$377$	−2.13883e52	−0.327475
$378$	0	0
$379$	5.01381e52	0.688754	0.344377	−	0.938831i	$-0.388090\pi$
$379$	5.01381e52	0.688754	0.344377	+	0.938831i	$0.388090\pi$
$380$	1.05398e52	0.137173
$381$	0	0
$382$	−1.97576e52	−0.230906
$383$	2.69866e52	0.298933	0.149466	−	0.988767i	$-0.452244\pi$
$383$	2.69866e52	0.298933	0.149466	+	0.988767i	$0.452244\pi$
$384$	0	0
$385$	−1.10970e53	−1.10474
$386$	−1.10897e53	−1.04684
$387$	0	0
$388$	−3.51668e50	−0.00298595
$389$	1.55739e53	1.25438	0.627190	−	0.778866i	$-0.284205\pi$
$389$	1.55739e53	1.25438	0.627190	+	0.778866i	$0.284205\pi$
$390$	0	0
$391$	−5.66665e52	−0.410869
$392$	−4.00555e53	−2.75612
$393$	0	0
$394$	−8.21936e52	−0.509525
$395$	4.94489e52	0.291016
$396$	0	0
$397$	−3.01135e52	−0.159792	−0.0798961	−	0.996803i	$-0.525459\pi$
$397$	−3.01135e52	−0.159792	−0.0798961	+	0.996803i	$0.525459\pi$
$398$	−2.77919e53	−1.40060
$399$	0	0
$400$	1.30118e53	0.591709
$401$	−2.30382e53	−0.995378	−0.497689	−	0.867355i	$-0.665818\pi$
$401$	−2.30382e53	−0.995378	−0.497689	+	0.867355i	$0.665818\pi$
$402$	0	0
$403$	1.33589e52	0.0521215
$404$	−3.87056e52	−0.143534
$405$	0	0
$406$	−3.43402e53	−1.15085
$407$	3.86208e53	1.23065
$408$	0	0
$409$	1.23126e53	0.354831	0.177415	−	0.984136i	$-0.443226\pi$
$409$	1.23126e53	0.354831	0.177415	+	0.984136i	$0.443226\pi$
$410$	8.53840e51	0.0234049
$411$	0	0
$412$	7.86552e52	0.195135
$413$	−5.85147e52	−0.138130
$414$	0	0
$415$	1.17402e53	0.251008
$416$	−8.43496e52	−0.171660
$417$	0	0
$418$	−8.79932e53	−1.62306
$419$	1.08562e54	1.90673	0.953367	−	0.301814i	$-0.0975923\pi$
$419$	1.08562e54	1.90673	0.953367	+	0.301814i	$0.0975923\pi$
$420$	0	0
$421$	9.36709e53	1.49218	0.746091	−	0.665844i	$-0.231928\pi$
$421$	9.36709e53	1.49218	0.746091	+	0.665844i	$0.231928\pi$
$422$	4.14388e51	0.00628785
$423$	0	0
$424$	5.38645e52	0.0741828
$425$	9.49210e53	1.24563
$426$	0	0
$427$	1.61492e54	1.92477
$428$	5.47389e52	0.0621869
$429$	0	0
$430$	1.80432e53	0.186299
$431$	−1.72107e54	−1.69440	−0.847198	−	0.531278i	$-0.821712\pi$
$431$	−1.72107e54	−1.69440	−0.847198	+	0.531278i	$0.821712\pi$
$432$	0	0
$433$	−1.20576e54	−1.07959	−0.539795	−	0.841796i	$-0.681498\pi$
$433$	−1.20576e54	−1.07959	−0.539795	+	0.841796i	$0.681498\pi$
$434$	2.14486e53	0.183172
$435$	0	0
$436$	−3.66395e53	−0.284758
$437$	5.11907e53	0.379596
$438$	0	0
$439$	1.69765e54	1.14637	0.573187	−	0.819424i	$-0.305707\pi$
$439$	1.69765e54	1.14637	0.573187	+	0.819424i	$0.305707\pi$
$440$	−9.67514e53	−0.623558
$441$	0	0
$442$	1.25351e54	0.736159
$443$	3.00986e54	1.68760	0.843800	−	0.536657i	$-0.180313\pi$
$443$	3.00986e54	1.68760	0.843800	+	0.536657i	$0.180313\pi$
$444$	0	0
$445$	−1.71093e54	−0.874685
$446$	−6.77137e53	−0.330607
$447$	0	0
$448$	−4.71094e54	−2.09850
$449$	1.71494e54	0.729793	0.364896	−	0.931048i	$-0.381104\pi$
$449$	1.71494e54	0.729793	0.364896	+	0.931048i	$0.381104\pi$
$450$	0	0
$451$	1.54456e53	0.0600049
$452$	−6.64886e53	−0.246837
$453$	0	0
$454$	1.93299e53	0.0655520
$455$	−1.42807e54	−0.462929
$456$	0	0
$457$	1.21867e54	0.361081	0.180541	−	0.983568i	$-0.442215\pi$
$457$	1.21867e54	0.361081	0.180541	+	0.983568i	$0.442215\pi$
$458$	−3.08763e54	−0.874748
$459$	0	0
$460$	8.50861e52	0.0220457
$461$	1.07257e54	0.265801	0.132901	−	0.991129i	$-0.457571\pi$
$461$	1.07257e54	0.265801	0.132901	+	0.991129i	$0.457571\pi$
$462$	0	0
$463$	7.33040e53	0.166233	0.0831165	−	0.996540i	$-0.473513\pi$
$463$	7.33040e53	0.166233	0.0831165	+	0.996540i	$0.473513\pi$
$464$	−2.44336e54	−0.530112
$465$	0	0
$466$	−2.95841e53	−0.0587688
$467$	−4.62154e54	−0.878598	−0.439299	−	0.898341i	$-0.644773\pi$
$467$	−4.62154e54	−0.878598	−0.439299	+	0.898341i	$0.644773\pi$
$468$	0	0
$469$	3.51634e54	0.612417
$470$	5.09733e53	0.0849839
$471$	0	0
$472$	−5.10173e53	−0.0779662
$473$	3.26394e54	0.477627
$474$	0	0
$475$	−8.57486e54	−1.15082
$476$	−4.36083e54	−0.560566
$477$	0	0
$478$	1.39947e55	1.65079
$479$	−1.06254e54	−0.120079	−0.0600394	−	0.998196i	$-0.519123\pi$
$479$	−1.06254e54	−0.120079	−0.0600394	+	0.998196i	$0.519123\pi$
$480$	0	0
$481$	4.97010e54	0.515693
$482$	−1.18790e55	−1.18118
$483$	0	0
$484$	−6.96031e53	−0.0635768
$485$	−9.59727e52	−0.00840315
$486$	0	0
$487$	−1.81852e55	−1.46344	−0.731720	−	0.681605i	$-0.761282\pi$
$487$	−1.81852e55	−1.46344	−0.731720	+	0.681605i	$0.761282\pi$
$488$	1.40800e55	1.08642
$489$	0	0
$490$	−1.65248e55	−1.17251
$491$	−3.62159e54	−0.246450	−0.123225	−	0.992379i	$-0.539324\pi$
$491$	−3.62159e54	−0.246450	−0.123225	+	0.992379i	$0.539324\pi$
$492$	0	0
$493$	−1.78242e55	−1.11596
$494$	−1.13238e55	−0.680127
$495$	0	0
$496$	1.52610e54	0.0843738
$497$	6.12891e55	3.25145
$498$	0	0
$499$	2.06983e55	1.01128	0.505642	−	0.862744i	$-0.331256\pi$
$499$	2.06983e55	1.01128	0.505642	+	0.862744i	$0.331256\pi$
$500$	−3.32862e54	−0.156091
$501$	0	0
$502$	3.44676e55	1.48931
$503$	1.21024e55	0.502026	0.251013	−	0.967984i	$-0.419236\pi$
$503$	1.21024e55	0.502026	0.251013	+	0.967984i	$0.419236\pi$
$504$	0	0
$505$	−1.05630e55	−0.403939
$506$	−7.10354e54	−0.260849
$507$	0	0
$508$	−4.88911e54	−0.165586
$509$	−2.83445e55	−0.922051	−0.461025	−	0.887387i	$-0.652518\pi$
$509$	−2.83445e55	−0.922051	−0.461025	+	0.887387i	$0.652518\pi$
$510$	0	0
$511$	9.46525e55	2.84121
$512$	−3.89016e55	−1.12185
$513$	0	0
$514$	−4.28874e55	−1.14179
$515$	2.14656e55	0.549154
$516$	0	0
$517$	9.22086e54	0.217879
$518$	7.97982e55	1.81231
$519$	0	0
$520$	−1.24509e55	−0.261296
$521$	−2.07621e55	−0.418889	−0.209444	−	0.977821i	$-0.567165\pi$
$521$	−2.07621e55	−0.418889	−0.209444	+	0.977821i	$0.567165\pi$
$522$	0	0
$523$	3.43281e55	0.640273	0.320136	−	0.947371i	$-0.396271\pi$
$523$	3.43281e55	0.640273	0.320136	+	0.947371i	$0.396271\pi$
$524$	1.85630e55	0.332934
$525$	0	0
$526$	−2.76761e55	−0.459088
$527$	1.11328e55	0.177619
$528$	0	0
$529$	−6.36069e55	−0.938994
$530$	2.22217e54	0.0315589
$531$	0	0
$532$	3.93943e55	0.517899
$533$	1.98769e54	0.0251444
$534$	0	0
$535$	1.49386e55	0.175008
$536$	3.06579e55	0.345672
$537$	0	0
$538$	−1.21255e56	−1.26667
$539$	−2.98928e56	−3.00605
$540$	0	0
$541$	−1.41875e56	−1.32240	−0.661200	−	0.750209i	$-0.729953\pi$
$541$	−1.41875e56	−1.32240	−0.661200	+	0.750209i	$0.729953\pi$
$542$	−3.23294e55	−0.290143
$543$	0	0
$544$	−7.02941e55	−0.584980
$545$	−9.99917e55	−0.801375
$546$	0	0
$547$	−6.85690e54	−0.0509785	−0.0254893	−	0.999675i	$-0.508114\pi$
$547$	−6.85690e54	−0.0509785	−0.0254893	+	0.999675i	$0.508114\pi$
$548$	1.76696e55	0.126539
$549$	0	0
$550$	1.18990e56	0.790816
$551$	1.61018e56	1.03102
$552$	0	0
$553$	1.84823e56	1.09873
$554$	−9.72312e55	−0.557000
$555$	0	0
$556$	−5.46222e54	−0.0290627
$557$	4.86641e55	0.249562	0.124781	−	0.992184i	$-0.460177\pi$
$557$	4.86641e55	0.249562	0.124781	+	0.992184i	$0.460177\pi$
$558$	0	0
$559$	4.20035e55	0.200145
$560$	−1.63140e56	−0.749385
$561$	0	0
$562$	−1.36832e56	−0.584245
$563$	−1.31993e56	−0.543412	−0.271706	−	0.962380i	$-0.587588\pi$
$563$	−1.31993e56	−0.543412	−0.271706	+	0.962380i	$0.587588\pi$
$564$	0	0
$565$	−1.81452e56	−0.694655
$566$	8.44404e55	0.311755
$567$	0	0
$568$	5.34362e56	1.83525
$569$	5.17929e56	1.71581	0.857903	−	0.513811i	$-0.171767\pi$
$569$	5.17929e56	1.71581	0.857903	+	0.513811i	$0.171767\pi$
$570$	0	0
$571$	1.79414e56	0.553115	0.276558	−	0.960997i	$-0.410806\pi$
$571$	1.79414e56	0.553115	0.276558	+	0.960997i	$0.410806\pi$
$572$	−3.40478e55	−0.101268
$573$	0	0
$574$	3.19137e55	0.0883656
$575$	−6.92233e55	−0.184953
$576$	0	0
$577$	−6.52560e56	−1.62374	−0.811870	−	0.583838i	$-0.801550\pi$
$577$	−6.52560e56	−1.62374	−0.811870	+	0.583838i	$0.801550\pi$
$578$	6.67119e56	1.60207
$579$	0	0
$580$	2.67635e55	0.0598783
$581$	4.38808e56	0.947685
$582$	0	0
$583$	4.01982e55	0.0809098
$584$	8.25247e56	1.60369
$585$	0	0
$586$	6.84131e56	1.23948
$587$	−7.86168e56	−1.37542	−0.687708	−	0.725987i	$-0.741383\pi$
$587$	−7.86168e56	−1.37542	−0.687708	+	0.725987i	$0.741383\pi$
$588$	0	0
$589$	−1.00571e56	−0.164100
$590$	−2.10471e55	−0.0331685
$591$	0	0
$592$	5.67775e56	0.834798
$593$	−1.07653e57	−1.52898	−0.764492	−	0.644633i	$-0.777010\pi$
$593$	−1.07653e57	−1.52898	−0.764492	+	0.644633i	$0.777010\pi$
$594$	0	0
$595$	−1.19010e57	−1.57756
$596$	−9.87834e55	−0.126513
$597$	0	0
$598$	−9.14151e55	−0.109306
$599$	−8.88910e56	−1.02709	−0.513544	−	0.858063i	$-0.671668\pi$
$599$	−8.88910e56	−1.02709	−0.513544	+	0.858063i	$0.671668\pi$
$600$	0	0
$601$	5.98671e56	0.646043	0.323021	−	0.946392i	$-0.395301\pi$
$601$	5.98671e56	0.646043	0.323021	+	0.946392i	$0.395301\pi$
$602$	6.74394e56	0.703373
$603$	0	0
$604$	1.44211e56	0.140521
$605$	−1.89952e56	−0.178920
$606$	0	0
$607$	6.99287e56	0.615584	0.307792	−	0.951454i	$-0.400410\pi$
$607$	6.99287e56	0.615584	0.307792	+	0.951454i	$0.400410\pi$
$608$	6.35014e56	0.540455
$609$	0	0
$610$	5.80868e56	0.462185
$611$	1.18663e56	0.0912999
$612$	0	0
$613$	−1.99522e57	−1.43566	−0.717829	−	0.696219i	$-0.754864\pi$
$613$	−1.99522e57	−1.43566	−0.717829	+	0.696219i	$0.754864\pi$
$614$	−2.01697e56	−0.140361
$615$	0	0
$616$	−3.61624e57	−2.35425
$617$	2.01107e57	1.26643	0.633216	−	0.773975i	$-0.281735\pi$
$617$	2.01107e57	1.26643	0.633216	+	0.773975i	$0.281735\pi$
$618$	0	0
$619$	1.27917e56	0.0753823	0.0376911	−	0.999289i	$-0.488000\pi$
$619$	1.27917e56	0.0753823	0.0376911	+	0.999289i	$0.488000\pi$
$620$	−1.67162e55	−0.00953035
$621$	0	0
$622$	1.77968e57	0.949813
$623$	−6.39487e57	−3.30238
$624$	0	0
$625$	6.40106e56	0.309536
$626$	−1.35030e57	−0.631911
$627$	0	0
$628$	1.69419e56	0.0742658
$629$	4.14191e57	1.75737
$630$	0	0
$631$	2.77600e57	1.10361	0.551807	−	0.833972i	$-0.313939\pi$
$631$	2.77600e57	1.10361	0.551807	+	0.833972i	$0.313939\pi$
$632$	1.61142e57	0.620168
$633$	0	0
$634$	3.31237e57	1.19484
$635$	−1.33427e57	−0.465998
$636$	0	0
$637$	−3.84689e57	−1.25965
$638$	−2.23439e57	−0.708492
$639$	0	0
$640$	−1.10180e57	−0.327653
$641$	−1.50182e57	−0.432541	−0.216271	−	0.976333i	$-0.569389\pi$
$641$	−1.50182e57	−0.432541	−0.216271	+	0.976333i	$0.569389\pi$
$642$	0	0
$643$	3.44585e57	0.931046	0.465523	−	0.885036i	$-0.345866\pi$
$643$	3.44585e57	0.931046	0.465523	+	0.885036i	$0.345866\pi$
$644$	3.18023e56	0.0832336
$645$	0	0
$646$	−9.43688e57	−2.31772
$647$	−6.27028e56	−0.149193	−0.0745966	−	0.997214i	$-0.523767\pi$
$647$	−6.27028e56	−0.149193	−0.0745966	+	0.997214i	$0.523767\pi$
$648$	0	0
$649$	−3.80733e56	−0.0850363
$650$	1.53128e57	0.331383
$651$	0	0
$652$	6.40263e56	0.130102
$653$	−4.27681e57	−0.842170	−0.421085	−	0.907021i	$-0.638351\pi$
$653$	−4.27681e57	−0.842170	−0.421085	+	0.907021i	$0.638351\pi$
$654$	0	0
$655$	5.06599e57	0.936952
$656$	2.27070e56	0.0407035
$657$	0	0
$658$	1.90521e57	0.320857
$659$	7.18638e57	1.17317	0.586583	−	0.809889i	$-0.300473\pi$
$659$	7.18638e57	1.17317	0.586583	+	0.809889i	$0.300473\pi$
$660$	0	0
$661$	−4.82359e57	−0.740014	−0.370007	−	0.929029i	$-0.620645\pi$
$661$	−4.82359e57	−0.740014	−0.370007	+	0.929029i	$0.620645\pi$
$662$	9.87782e57	1.46917
$663$	0	0
$664$	3.82584e57	0.534911
$665$	1.07510e58	1.45749
$666$	0	0
$667$	1.29987e57	0.165700
$668$	−1.70622e57	−0.210920
$669$	0	0
$670$	1.26479e57	0.147056
$671$	1.05077e58	1.18494
$672$	0	0
$673$	2.10611e57	0.223446	0.111723	−	0.993739i	$-0.464363\pi$
$673$	2.10611e57	0.223446	0.111723	+	0.993739i	$0.464363\pi$
$674$	−8.07722e57	−0.831255
$675$	0	0
$676$	1.40069e57	0.135654
$677$	−5.40673e57	−0.508004	−0.254002	−	0.967204i	$-0.581747\pi$
$677$	−5.40673e57	−0.508004	−0.254002	+	0.967204i	$0.581747\pi$
$678$	0	0
$679$	−3.58714e56	−0.0317262
$680$	−1.03761e58	−0.890438
$681$	0	0
$682$	1.39558e57	0.112765
$683$	2.46559e58	1.93329	0.966644	−	0.256125i	$-0.0824459\pi$
$683$	2.46559e58	1.93329	0.966644	+	0.256125i	$0.0824459\pi$
$684$	0	0
$685$	4.82217e57	0.356111
$686$	−3.78295e58	−2.71135
$687$	0	0
$688$	4.79841e57	0.323992
$689$	5.17309e56	0.0339044
$690$	0	0
$691$	2.01787e58	1.24621	0.623107	−	0.782136i	$-0.285870\pi$
$691$	2.01787e58	1.24621	0.623107	+	0.782136i	$0.285870\pi$
$692$	−8.27428e55	−0.00496084
$693$	0	0
$694$	−1.13523e58	−0.641524
$695$	−1.49068e57	−0.0817892
$696$	0	0
$697$	1.65647e57	0.0856866
$698$	2.18470e58	1.09737
$699$	0	0
$700$	−5.32715e57	−0.252339
$701$	−1.63846e57	−0.0753729	−0.0376864	−	0.999290i	$-0.511999\pi$
$701$	−1.63846e57	−0.0753729	−0.0376864	+	0.999290i	$0.511999\pi$
$702$	0	0
$703$	−3.74167e58	−1.62361
$704$	−3.06523e58	−1.29189
$705$	0	0
$706$	4.80012e56	0.0190878
$707$	−3.94811e58	−1.52507
$708$	0	0
$709$	−3.78678e58	−1.38046	−0.690228	−	0.723592i	$-0.742490\pi$
$709$	−3.78678e58	−1.38046	−0.690228	+	0.723592i	$0.742490\pi$
$710$	2.20450e58	0.780754
$711$	0	0
$712$	−5.57550e58	−1.86399
$713$	−8.11888e56	−0.0263731
$714$	0	0
$715$	−9.29189e57	−0.284991
$716$	1.84500e57	0.0549894
$717$	0	0
$718$	1.20354e58	0.338773
$719$	−2.43656e58	−0.666553	−0.333277	−	0.942829i	$-0.608154\pi$
$719$	−2.43656e58	−0.666553	−0.333277	+	0.942829i	$0.608154\pi$
$720$	0	0
$721$	8.02311e58	2.07334
$722$	4.91566e58	1.23472
$723$	0	0
$724$	2.38899e57	0.0566988
$725$	−2.17739e58	−0.502352
$726$	0	0
$727$	8.38626e57	0.182858	0.0914288	−	0.995812i	$-0.470857\pi$
$727$	8.38626e57	0.182858	0.0914288	+	0.995812i	$0.470857\pi$
$728$	−4.65373e58	−0.986524
$729$	0	0
$730$	3.40454e58	0.682245
$731$	3.50043e58	0.682048
$732$	0	0
$733$	2.90666e58	0.535505	0.267752	−	0.963488i	$-0.413719\pi$
$733$	2.90666e58	0.535505	0.267752	+	0.963488i	$0.413719\pi$
$734$	−2.88087e58	−0.516125
$735$	0	0
$736$	5.12636e57	0.0868587
$737$	2.28795e58	0.377019
$738$	0	0
$739$	3.92079e58	0.611170	0.305585	−	0.952165i	$-0.401148\pi$
$739$	3.92079e58	0.611170	0.305585	+	0.952165i	$0.401148\pi$
$740$	−6.21918e57	−0.0942937
$741$	0	0
$742$	8.30573e57	0.119151
$743$	1.22168e59	1.70485	0.852426	−	0.522848i	$-0.175130\pi$
$743$	1.22168e59	1.70485	0.852426	+	0.522848i	$0.175130\pi$
$744$	0	0
$745$	−2.69587e58	−0.356037
$746$	2.35699e58	0.302839
$747$	0	0
$748$	−2.83743e58	−0.345098
$749$	5.58356e58	0.660746
$750$	0	0
$751$	3.73440e58	0.418410	0.209205	−	0.977872i	$-0.432912\pi$
$751$	3.73440e58	0.418410	0.209205	+	0.977872i	$0.432912\pi$
$752$	1.35558e58	0.147795
$753$	0	0
$754$	−2.87543e58	−0.296886
$755$	3.93562e58	0.395458
$756$	0	0
$757$	1.05552e59	1.00461	0.502307	−	0.864690i	$-0.332485\pi$
$757$	1.05552e59	1.00461	0.502307	+	0.864690i	$0.332485\pi$
$758$	6.74055e58	0.624419
$759$	0	0
$760$	9.37348e58	0.822664
$761$	−4.90222e58	−0.418800	−0.209400	−	0.977830i	$-0.567151\pi$
$761$	−4.90222e58	−0.418800	−0.209400	+	0.977830i	$0.567151\pi$
$762$	0	0
$763$	−3.73736e59	−3.02560
$764$	5.75540e57	0.0453588
$765$	0	0
$766$	3.62807e58	0.271010
$767$	−4.89964e57	−0.0356336
$768$	0	0
$769$	−1.48791e59	−1.02586	−0.512930	−	0.858431i	$-0.671440\pi$
$769$	−1.48791e59	−1.02586	−0.512930	+	0.858431i	$0.671440\pi$
$770$	−1.49187e59	−1.00155
$771$	0	0
$772$	3.23044e58	0.205639
$773$	−4.35850e58	−0.270183	−0.135091	−	0.990833i	$-0.543133\pi$
$773$	−4.35850e58	−0.270183	−0.135091	+	0.990833i	$0.543133\pi$
$774$	0	0
$775$	1.35998e58	0.0799553
$776$	−3.12752e57	−0.0179075
$777$	0	0
$778$	2.09374e59	1.13721
$779$	−1.49641e58	−0.0791647
$780$	0	0
$781$	3.98785e59	2.00167
$782$	−7.61822e58	−0.372491
$783$	0	0
$784$	−4.39462e59	−2.03912
$785$	4.62356e58	0.209001
$786$	0	0
$787$	−1.24674e59	−0.534924	−0.267462	−	0.963568i	$-0.586185\pi$
$787$	−1.24674e59	−0.534924	−0.267462	+	0.963568i	$0.586185\pi$
$788$	2.39430e58	0.100090
$789$	0	0
$790$	6.64789e58	0.263833
$791$	−6.78208e59	−2.62268
$792$	0	0
$793$	1.35223e59	0.496535
$794$	−4.04845e58	−0.144867
$795$	0	0
$796$	8.09577e58	0.275131
$797$	2.54215e59	0.841988	0.420994	−	0.907063i	$-0.361681\pi$
$797$	2.54215e59	0.841988	0.420994	+	0.907063i	$0.361681\pi$
$798$	0	0
$799$	9.88896e58	0.311130
$800$	−8.58706e58	−0.263330
$801$	0	0
$802$	−3.09724e59	−0.902403
$803$	6.15868e59	1.74912
$804$	0	0
$805$	8.67909e58	0.234239
$806$	1.79596e58	0.0472530
$807$	0	0
$808$	−3.44224e59	−0.860812
$809$	−5.56333e59	−1.35641	−0.678203	−	0.734874i	$-0.737241\pi$
$809$	−5.56333e59	−1.35641	−0.678203	+	0.734874i	$0.737241\pi$
$810$	0	0
$811$	−4.60895e59	−1.06825	−0.534127	−	0.845404i	$-0.679360\pi$
$811$	−4.60895e59	−1.06825	−0.534127	+	0.845404i	$0.679360\pi$
$812$	1.00033e59	0.226071
$813$	0	0
$814$	5.19217e59	1.11570
$815$	1.74732e59	0.366136
$816$	0	0
$817$	−3.16218e59	−0.630136
$818$	1.65530e59	0.321687
$819$	0	0
$820$	−2.48724e57	−0.00459762
$821$	−4.31375e59	−0.777715	−0.388857	−	0.921298i	$-0.627130\pi$
$821$	−4.31375e59	−0.777715	−0.388857	+	0.921298i	$0.627130\pi$
$822$	0	0
$823$	6.85688e59	1.17606	0.588030	−	0.808839i	$-0.299904\pi$
$823$	6.85688e59	1.17606	0.588030	+	0.808839i	$0.299904\pi$
$824$	6.99511e59	1.17027
$825$	0	0
$826$	−7.86669e58	−0.125228
$827$	6.48288e59	1.00671	0.503356	−	0.864079i	$-0.332098\pi$
$827$	6.48288e59	1.00671	0.503356	+	0.864079i	$0.332098\pi$
$828$	0	0
$829$	3.30221e59	0.488018	0.244009	−	0.969773i	$-0.421537\pi$
$829$	3.30221e59	0.488018	0.244009	+	0.969773i	$0.421537\pi$
$830$	1.57834e59	0.227562
$831$	0	0
$832$	−3.94464e59	−0.541351
$833$	−3.20587e60	−4.29263
$834$	0	0
$835$	−4.65640e59	−0.593578
$836$	2.56324e59	0.318831
$837$	0	0
$838$	1.45950e60	1.72863
$839$	1.34134e60	1.55031	0.775153	−	0.631773i	$-0.217673\pi$
$839$	1.34134e60	1.55031	0.775153	+	0.631773i	$0.217673\pi$
$840$	0	0
$841$	−4.99615e59	−0.549943
$842$	1.25931e60	1.35280
$843$	0	0
$844$	−1.20711e57	−0.00123517
$845$	3.82257e59	0.381762
$846$	0	0
$847$	−7.09976e59	−0.675513
$848$	5.90965e58	0.0548841
$849$	0	0
$850$	1.27611e60	1.12928
$851$	−3.02058e59	−0.260937
$852$	0	0
$853$	−1.01106e60	−0.832382	−0.416191	−	0.909277i	$-0.636635\pi$
$853$	−1.01106e60	−0.832382	−0.416191	+	0.909277i	$0.636635\pi$
$854$	2.17109e60	1.74498
$855$	0	0
$856$	4.86815e59	0.372951
$857$	1.59400e60	1.19229	0.596143	−	0.802878i	$-0.296699\pi$
$857$	1.59400e60	1.19229	0.596143	+	0.802878i	$0.296699\pi$
$858$	0	0
$859$	2.28498e60	1.62938	0.814692	−	0.579894i	$-0.196906\pi$
$859$	2.28498e60	1.62938	0.814692	+	0.579894i	$0.196906\pi$
$860$	−5.25598e58	−0.0365962
$861$	0	0
$862$	−2.31380e60	−1.53613
$863$	−1.07116e60	−0.694439	−0.347220	−	0.937784i	$-0.612874\pi$
$863$	−1.07116e60	−0.694439	−0.347220	+	0.937784i	$0.612874\pi$
$864$	0	0
$865$	−2.25811e58	−0.0139609
$866$	−1.62102e60	−0.978749
$867$	0	0
$868$	−6.24797e58	−0.0359819
$869$	1.20258e60	0.676406
$870$	0	0
$871$	2.94435e59	0.157986
$872$	−3.25849e60	−1.70777
$873$	0	0
$874$	6.88206e59	0.344139
$875$	−3.39531e60	−1.65850
$876$	0	0
$877$	1.15644e60	0.539054	0.269527	−	0.962993i	$-0.413133\pi$
$877$	1.15644e60	0.539054	0.269527	+	0.962993i	$0.413133\pi$
$878$	2.28232e60	1.03930
$879$	0	0
$880$	−1.06149e60	−0.461340
$881$	3.12498e59	0.132691	0.0663454	−	0.997797i	$-0.478866\pi$
$881$	3.12498e59	0.132691	0.0663454	+	0.997797i	$0.478866\pi$
$882$	0	0
$883$	−3.90070e60	−1.58106	−0.790530	−	0.612424i	$-0.790195\pi$
$883$	−3.90070e60	−1.58106	−0.790530	+	0.612424i	$0.790195\pi$
$884$	−3.65148e59	−0.144610
$885$	0	0
$886$	4.04644e60	1.52997
$887$	−7.42130e58	−0.0274186	−0.0137093	−	0.999906i	$-0.504364\pi$
$887$	−7.42130e58	−0.0274186	−0.0137093	+	0.999906i	$0.504364\pi$
$888$	0	0
$889$	−4.98707e60	−1.75938
$890$	−2.30016e60	−0.792983
$891$	0	0
$892$	1.97250e59	0.0649438
$893$	−8.93337e59	−0.287449
$894$	0	0
$895$	5.03513e59	0.154753
$896$	−4.11817e60	−1.23706
$897$	0	0
$898$	2.30556e60	0.661625
$899$	−2.55376e59	−0.0716320
$900$	0	0
$901$	4.31108e59	0.115539
$902$	2.07650e59	0.0544000
$903$	0	0
$904$	−5.91310e60	−1.48034
$905$	6.51973e59	0.159564
$906$	0	0
$907$	−1.27830e60	−0.299009	−0.149505	−	0.988761i	$-0.547768\pi$
$907$	−1.27830e60	−0.299009	−0.149505	+	0.988761i	$0.547768\pi$
$908$	−5.63081e58	−0.0128769
$909$	0	0
$910$	−1.91989e60	−0.419688
$911$	−3.74088e60	−0.799552	−0.399776	−	0.916613i	$-0.630912\pi$
$911$	−3.74088e60	−0.799552	−0.399776	+	0.916613i	$0.630912\pi$
$912$	0	0
$913$	2.85516e60	0.583418
$914$	1.63838e60	0.327354
$915$	0	0
$916$	8.99426e59	0.171834
$917$	1.89350e61	3.53747
$918$	0	0
$919$	−4.88524e60	−0.872806	−0.436403	−	0.899751i	$-0.643748\pi$
$919$	−4.88524e60	−0.872806	−0.436403	+	0.899751i	$0.643748\pi$
$920$	7.56705e59	0.132214
$921$	0	0
$922$	1.44196e60	0.240973
$923$	5.13195e60	0.838780
$924$	0	0
$925$	5.05972e60	0.791081
$926$	9.85496e59	0.150706
$927$	0	0
$928$	1.61248e60	0.235917
$929$	−7.45596e60	−1.06704	−0.533521	−	0.845787i	$-0.679132\pi$
$929$	−7.45596e60	−1.06704	−0.533521	+	0.845787i	$0.679132\pi$
$930$	0	0
$931$	2.89608e61	3.96590
$932$	8.61785e58	0.0115444
$933$	0	0
$934$	−6.21318e60	−0.796531
$935$	−7.74355e60	−0.971185
$936$	0	0
$937$	−1.56022e60	−0.187294	−0.0936469	−	0.995605i	$-0.529852\pi$
$937$	−1.56022e60	−0.187294	−0.0936469	+	0.995605i	$0.529852\pi$
$938$	4.72735e60	0.555213
$939$	0	0
$940$	−1.48485e59	−0.0166941
$941$	5.75717e60	0.633318	0.316659	−	0.948539i	$-0.397439\pi$
$941$	5.75717e60	0.633318	0.316659	+	0.948539i	$0.397439\pi$
$942$	0	0
$943$	−1.20802e59	−0.0127229
$944$	−5.59726e59	−0.0576833
$945$	0	0
$946$	4.38803e60	0.433013
$947$	−4.40342e60	−0.425222	−0.212611	−	0.977137i	$-0.568197\pi$
$947$	−4.40342e60	−0.425222	−0.212611	+	0.977137i	$0.568197\pi$
$948$	0	0
$949$	7.92559e60	0.732950
$950$	−1.15280e61	−1.04333
$951$	0	0
$952$	−3.87826e61	−3.36186
$953$	1.39562e61	1.18403	0.592013	−	0.805928i	$-0.298333\pi$
$953$	1.39562e61	1.18403	0.592013	+	0.805928i	$0.298333\pi$
$954$	0	0
$955$	1.57069e60	0.127650
$956$	−4.07665e60	−0.324277
$957$	0	0
$958$	−1.42847e60	−0.108863
$959$	1.80236e61	1.34450
$960$	0	0
$961$	−1.38309e61	−0.988599
$962$	6.68178e60	0.467523
$963$	0	0
$964$	3.46036e60	0.232029
$965$	8.81610e60	0.578717
$966$	0	0
$967$	1.12963e61	0.710713	0.355356	−	0.934731i	$-0.384360\pi$
$967$	1.12963e61	0.710713	0.355356	+	0.934731i	$0.384360\pi$
$968$	−6.19008e60	−0.381286
$969$	0	0
$970$	−1.29025e59	−0.00761824
$971$	−1.69719e61	−0.981152	−0.490576	−	0.871398i	$-0.663214\pi$
$971$	−1.69719e61	−0.981152	−0.490576	+	0.871398i	$0.663214\pi$
$972$	0	0
$973$	−5.57166e60	−0.308796
$974$	−2.44481e61	−1.32674
$975$	0	0
$976$	1.54476e61	0.803786
$977$	−3.22632e61	−1.64388	−0.821938	−	0.569577i	$-0.807107\pi$
$977$	−3.22632e61	−1.64388	−0.821938	+	0.569577i	$0.807107\pi$
$978$	0	0
$979$	−4.16091e61	−2.03302
$980$	4.81369e60	0.230326
$981$	0	0
$982$	−4.86885e60	−0.223430
$983$	1.33938e61	0.601947	0.300973	−	0.953633i	$-0.402688\pi$
$983$	1.33938e61	0.601947	0.300973	+	0.953633i	$0.402688\pi$
$984$	0	0
$985$	6.53422e60	0.281677
$986$	−2.39628e61	−1.01172
$987$	0	0
$988$	3.29863e60	0.133603
$989$	−2.55277e60	−0.101272
$990$	0	0
$991$	2.73292e61	1.04020	0.520101	−	0.854105i	$-0.325894\pi$
$991$	2.73292e61	1.04020	0.520101	+	0.854105i	$0.325894\pi$
$992$	−1.00714e60	−0.0375491
$993$	0	0
$994$	8.23968e61	2.94774
$995$	2.20939e61	0.774283
$996$	0	0
$997$	−2.91866e61	−0.981595	−0.490798	−	0.871274i	$-0.663295\pi$
$997$	−2.91866e61	−0.981595	−0.490798	+	0.871274i	$0.663295\pi$
$998$	2.78267e61	0.916822
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.42.a.a.1.3		3
3.2	odd	2		3.42.a.a.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.a.1.1	✓	3	3.2	odd	2
9.42.a.a.1.3		3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+1.34440e6 q^{2} -3.91623e11 q^{4} -1.06877e14 q^{5} -3.99469e17 q^{7} -3.48285e18 q^{8} +O(q^{10})\)	\(q+1.34440e6 q^{2} -3.91623e11 q^{4} -1.06877e14 q^{5} -3.99469e17 q^{7} -3.48285e18 q^{8} -1.43685e20 q^{10} -2.59920e21 q^{11} -3.34490e22 q^{13} -5.37044e23 q^{14} -3.82115e24 q^{16} -2.78752e25 q^{17} +2.51816e26 q^{19} +4.18553e25 q^{20} -3.49435e27 q^{22} +2.03286e27 q^{23} -3.40521e28 q^{25} -4.49686e28 q^{26} +1.56441e29 q^{28} +6.39430e29 q^{29} -3.99382e29 q^{31} +2.52174e30 q^{32} -3.74753e31 q^{34} +4.26939e31 q^{35} -1.48588e32 q^{37} +3.38540e32 q^{38} +3.72236e32 q^{40} -5.94247e31 q^{41} -1.25575e33 q^{43} +1.01790e33 q^{44} +2.73297e33 q^{46} -3.54758e33 q^{47} +1.15008e35 q^{49} -4.57795e34 q^{50} +1.30994e34 q^{52} -1.54656e34 q^{53} +2.77793e35 q^{55} +1.39129e36 q^{56} +8.59647e35 q^{58} +1.46481e35 q^{59} -4.04266e36 q^{61} -5.36927e35 q^{62} +1.17930e37 q^{64} +3.57491e36 q^{65} -8.80253e36 q^{67} +1.09166e37 q^{68} +5.73975e37 q^{70} -1.53426e38 q^{71} -2.36946e38 q^{73} -1.99761e38 q^{74} -9.86167e37 q^{76} +1.03830e39 q^{77} -4.62673e38 q^{79} +4.08391e38 q^{80} -7.98903e37 q^{82} -1.09848e39 q^{83} +2.97921e39 q^{85} -1.68823e39 q^{86} +9.05262e39 q^{88} +1.60084e40 q^{89} +1.33618e40 q^{91} -7.96115e38 q^{92} -4.76936e39 q^{94} -2.69132e40 q^{95} +8.97977e38 q^{97} +1.54616e41 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 289380 q^{2} - 2254266178800 q^{4} - 38650546192026 q^{5} - 44\!\cdots\!68 q^{7}+ \cdots - 22\!\cdots\!96 q^{8}+O(q^{10}) \) 3 * q + 289380 * q^2 - 2254266178800 * q^4 - 38650546192026 * q^5 - 44602211301408768 * q^7 - 2268032948689999296 * q^8	\( 3 q + 289380 q^{2} - 2254266178800 q^{4} - 38650546192026 q^{5} - 44\!\cdots\!68 q^{7}+ \cdots + 26\!\cdots\!92 q^{98}+O(q^{100}) \) 3 * q + 289380 * q^2 - 2254266178800 * q^4 - 38650546192026 * q^5 - 44602211301408768 * q^7 - 2268032948689999296 * q^8 + 303684786396357841224 * q^10 - 2162403578017276790604 * q^11 + 44715417115247213223642 * q^13 - 320671470159767900457984 * q^14 - 5459234621059712438935296 * q^16 + 10989933423479049968718714 * q^17 + 196397070114735534584831028 * q^19 - 531636782784591447776761824 * q^20 - 4513503674461058254096349328 * q^22 + 4665149638066794122614978584 * q^23 - 4609009761244207114343812899 * q^25 - 122894273592250273312332501576 * q^26 - 599824891534617466777136050176 * q^28 + 941555486655490244273102003214 * q^29 - 6480085319036017864686465368808 * q^31 + 9194142460916956643740243289088 * q^32 - 50410977973081452147630100226760 * q^34 + 153374925211463555312750388019200 * q^35 - 442820255707228186224391784737998 * q^37 + 832008681100278182323288015176048 * q^38 - 830400317719830554628641188275072 * q^40 + 438132779830146983268076758934098 * q^41 - 1310999240696843410630649721463476 * q^43 + 1443247128257998435455229084014528 * q^44 + 7997471516728167525889026089716512 * q^46 - 64523854533555761088559286850643968 * q^47 + 171140726678012788361144930683431723 * q^49 - 28333303327284754376413888152266724 * q^50 - 20984793566307791589805690265685024 * q^52 - 34693992770270063328682081068689946 * q^53 + 100035221507232528994896069839569896 * q^55 + 568132015233041377672136741101977600 * q^56 - 2740694640626009342372591817401518296 * q^58 + 4582685445865314260503003260089664948 * q^59 - 8693740159306202291599355552752714662 * q^61 - 265004064722629998116825545352842464 * q^62 + 16981741764860889983034117450588819456 * q^64 - 2721360738989032295650621165564283148 * q^65 + 32867814173503669322418795877934200116 * q^67 - 33261671085355608094778443956314848800 * q^68 + 98543364272473044599951459881688524800 * q^70 - 149748844745311390685366673232301225496 * q^71 + 6619123649433674932122580558210670046 * q^73 - 14490759310413784046620539770501448744 * q^74 - 536779250932404614788199202699778310208 * q^76 + 954944421253262491346753072408971247616 * q^77 - 1112771209183156752666617542198723627800 * q^79 + 2423764999311265237507278994973679346176 * q^80 - 107939940778839787676218322470600048296 * q^82 + 1187635824307222104653182519688468749260 * q^83 + 6153092316082135211652182465439269196852 * q^85 - 2889811785377479896729751911427106623344 * q^86 + 11348012623814378178834124633898985613056 * q^88 + 2907470395792485617492963651915834875602 * q^89 + 19747616149564653802226421926044582182912 * q^91 - 10266693573432860781998326486887076136832 * q^92 + 34628213999509804914437049475497096849408 * q^94 + 84590150972982168777889232049326900017896 * q^95 - 52479807025249236413871256717456940920314 * q^97 + 268218382984038433881798894561914095373892 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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