LMFDB - Embedded newform 9.42.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$95.8245034108$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 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			1.2
Root			$30895.0$ 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)

$f(q)$	$=$	$q+467196. q^{2} -1.98075e12 q^{4} +2.77079e14 q^{5} +3.80292e17 q^{7} -1.95278e18 q^{8} +O(q^{10})$	\(q+467196. q^{2} -1.98075e12 q^{4} +2.77079e14 q^{5} +3.80292e17 q^{7} -1.95278e18 q^{8} +1.29450e20 q^{10} -1.78075e20 q^{11} +2.06379e22 q^{13} +1.77671e23 q^{14} +3.44339e24 q^{16} +2.32357e25 q^{17} +2.05644e26 q^{19} -5.48825e26 q^{20} -8.31962e25 q^{22} +4.66038e27 q^{23} +3.12982e28 q^{25} +9.64193e27 q^{26} -7.53263e29 q^{28} -1.57858e30 q^{29} -4.51602e30 q^{31} +5.90294e30 q^{32} +1.08556e31 q^{34} +1.05371e32 q^{35} -1.32006e32 q^{37} +9.60760e31 q^{38} -5.41074e32 q^{40} +3.66611e32 q^{41} -6.46266e32 q^{43} +3.52723e32 q^{44} +2.17731e33 q^{46} -2.68528e34 q^{47} +1.00054e35 q^{49} +1.46224e34 q^{50} -4.08785e34 q^{52} +1.90002e35 q^{53} -4.93410e34 q^{55} -7.42624e35 q^{56} -7.37507e35 q^{58} +3.62437e36 q^{59} +2.16433e36 q^{61} -2.10987e36 q^{62} -4.81426e36 q^{64} +5.71832e36 q^{65} +3.15856e36 q^{67} -4.60242e37 q^{68} +4.92289e37 q^{70} +4.01004e37 q^{71} +7.75186e37 q^{73} -6.16729e37 q^{74} -4.07329e38 q^{76} -6.77206e37 q^{77} -8.36639e38 q^{79} +9.54091e38 q^{80} +1.71279e38 q^{82} +1.97827e39 q^{83} +6.43814e39 q^{85} -3.01933e38 q^{86} +3.47741e38 q^{88} -3.68899e39 q^{89} +7.84841e39 q^{91} -9.23105e39 q^{92} -1.25455e40 q^{94} +5.69796e40 q^{95} +4.15034e40 q^{97} +4.67449e40 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	467196.	0.315054	0.157527	−	0.987515i	$-0.449648\pi$
$2$	467196.	0.315054	0.157527	+	0.987515i	$0.449648\pi$
$3$	0	0
$3$	0	0
$4$	−1.98075e12	−0.900741
$5$	2.77079e14	1.29933	0.649664	−	0.760221i	$-0.274909\pi$
$5$	2.77079e14	1.29933	0.649664	+	0.760221i	$0.274909\pi$
$6$	0	0
$7$	3.80292e17	1.80139	0.900693	−	0.434455i	$-0.143059\pi$
$7$	3.80292e17	1.80139	0.900693	+	0.434455i	$0.143059\pi$
$8$	−1.95278e18	−0.598835
$9$	0	0
$10$	1.29450e20	0.409358
$11$	−1.78075e20	−0.0798094	−0.0399047	−	0.999203i	$-0.512705\pi$
$11$	−1.78075e20	−0.0798094	−0.0399047	+	0.999203i	$0.512705\pi$
$12$	0	0
$13$	2.06379e22	0.301180	0.150590	−	0.988596i	$-0.451883\pi$
$13$	2.06379e22	0.301180	0.150590	+	0.988596i	$0.451883\pi$
$14$	1.77671e23	0.567534
$15$	0	0
$16$	3.44339e24	0.712076
$17$	2.32357e25	1.38661	0.693303	−	0.720646i	$-0.256155\pi$
$17$	2.32357e25	1.38661	0.693303	+	0.720646i	$0.256155\pi$
$18$	0	0
$19$	2.05644e26	1.25507	0.627533	−	0.778590i	$-0.284065\pi$
$19$	2.05644e26	1.25507	0.627533	+	0.778590i	$0.284065\pi$
$20$	−5.48825e26	−1.17036
$21$	0	0
$22$	−8.31962e25	−0.0251442
$23$	4.66038e27	0.566240	0.283120	−	0.959085i	$-0.408631\pi$
$23$	4.66038e27	0.566240	0.283120	+	0.959085i	$0.408631\pi$
$24$	0	0
$25$	3.12982e28	0.688255
$26$	9.64193e27	0.0948878
$27$	0	0
$28$	−7.53263e29	−1.62258
$29$	−1.57858e30	−1.65618	−0.828090	−	0.560595i	$-0.810573\pi$
$29$	−1.57858e30	−1.65618	−0.828090	+	0.560595i	$0.810573\pi$
$30$	0	0
$31$	−4.51602e30	−1.20737	−0.603685	−	0.797223i	$-0.706302\pi$
$31$	−4.51602e30	−1.20737	−0.603685	+	0.797223i	$0.706302\pi$
$32$	5.90294e30	0.823178
$33$	0	0
$34$	1.08556e31	0.436856
$35$	1.05371e32	2.34059
$36$	0	0
$37$	−1.32006e32	−0.938555	−0.469277	−	0.883051i	$-0.655486\pi$
$37$	−1.32006e32	−0.938555	−0.469277	+	0.883051i	$0.655486\pi$
$38$	9.60760e31	0.395413
$39$	0	0
$40$	−5.41074e32	−0.778084
$41$	3.66611e32	0.317787	0.158893	−	0.987296i	$-0.449207\pi$
$41$	3.66611e32	0.317787	0.158893	+	0.987296i	$0.449207\pi$
$42$	0	0
$43$	−6.46266e32	−0.211012	−0.105506	−	0.994419i	$-0.533646\pi$
$43$	−6.46266e32	−0.211012	−0.105506	+	0.994419i	$0.533646\pi$
$44$	3.52723e32	0.0718876
$45$	0	0
$46$	2.17731e33	0.178396
$47$	−2.68528e34	−1.41574	−0.707871	−	0.706342i	$-0.750344\pi$
$47$	−2.68528e34	−1.41574	−0.707871	+	0.706342i	$0.750344\pi$
$48$	0	0
$49$	1.00054e35	2.24499
$50$	1.46224e34	0.216837
$51$	0	0
$52$	−4.08785e34	−0.271285
$53$	1.90002e35	0.853300	0.426650	−	0.904417i	$-0.359694\pi$
$53$	1.90002e35	0.853300	0.426650	+	0.904417i	$0.359694\pi$
$54$	0	0
$55$	−4.93410e34	−0.103699
$56$	−7.42624e35	−1.07873
$57$	0	0
$58$	−7.37507e35	−0.521786
$59$	3.62437e36	1.80620	0.903100	−	0.429430i	$-0.141286\pi$
$59$	3.62437e36	1.80620	0.903100	+	0.429430i	$0.141286\pi$
$60$	0	0
$61$	2.16433e36	0.544580	0.272290	−	0.962215i	$-0.412219\pi$
$61$	2.16433e36	0.544580	0.272290	+	0.962215i	$0.412219\pi$
$62$	−2.10987e36	−0.380387
$63$	0	0
$64$	−4.81426e36	−0.452731
$65$	5.71832e36	0.391332
$66$	0	0
$67$	3.15856e36	0.116133	0.0580664	−	0.998313i	$-0.481506\pi$
$67$	3.15856e36	0.116133	0.0580664	+	0.998313i	$0.481506\pi$
$68$	−4.60242e37	−1.24897
$69$	0	0
$70$	4.92289e37	0.737412
$71$	4.01004e37	0.449110	0.224555	−	0.974461i	$-0.427907\pi$
$71$	4.01004e37	0.449110	0.224555	+	0.974461i	$0.427907\pi$
$72$	0	0
$73$	7.75186e37	0.491232	0.245616	−	0.969367i	$-0.421010\pi$
$73$	7.75186e37	0.491232	0.245616	+	0.969367i	$0.421010\pi$
$74$	−6.16729e37	−0.295695
$75$	0	0
$76$	−4.07329e38	−1.13049
$77$	−6.77206e37	−0.143768
$78$	0	0
$79$	−8.36639e38	−1.04998	−0.524992	−	0.851107i	$-0.675932\pi$
$79$	−8.36639e38	−1.04998	−0.524992	+	0.851107i	$0.675932\pi$
$80$	9.54091e38	0.925221
$81$	0	0
$82$	1.71279e38	0.100120
$83$	1.97827e39	0.901954	0.450977	−	0.892536i	$-0.351076\pi$
$83$	1.97827e39	0.901954	0.450977	+	0.892536i	$0.351076\pi$
$84$	0	0
$85$	6.43814e39	1.80166
$86$	−3.01933e38	−0.0664802
$87$	0	0
$88$	3.47741e38	0.0477927
$89$	−3.68899e39	−0.402172	−0.201086	−	0.979574i	$-0.564447\pi$
$89$	−3.68899e39	−0.402172	−0.201086	+	0.979574i	$0.564447\pi$
$90$	0	0
$91$	7.84841e39	0.542541
$92$	−9.23105e39	−0.510036
$93$	0	0
$94$	−1.25455e40	−0.446035
$95$	5.69796e40	1.63074
$96$	0	0
$97$	4.15034e40	0.774932	0.387466	−	0.921884i	$-0.373350\pi$
$97$	4.15034e40	0.774932	0.387466	+	0.921884i	$0.373350\pi$
$98$	4.67449e40	0.707294
$99$	0	0
$100$	−6.19939e40	−0.619939
$101$	2.21812e41	1.80883	0.904413	−	0.426658i	$-0.140309\pi$
$101$	2.21812e41	1.80883	0.904413	+	0.426658i	$0.140309\pi$
$102$	0	0
$103$	1.19436e41	0.651584	0.325792	−	0.945441i	$-0.394369\pi$
$103$	1.19436e41	0.651584	0.325792	+	0.945441i	$0.394369\pi$
$104$	−4.03011e40	−0.180357
$105$	0	0
$106$	8.87680e40	0.268835
$107$	3.26711e41	0.816199	0.408100	−	0.912937i	$-0.366192\pi$
$107$	3.26711e41	0.816199	0.408100	+	0.912937i	$0.366192\pi$
$108$	0	0
$109$	−1.38640e40	−0.0236943	−0.0118472	−	0.999930i	$-0.503771\pi$
$109$	−1.38640e40	−0.0236943	−0.0118472	+	0.999930i	$0.503771\pi$
$110$	−2.30519e40	−0.0326706
$111$	0	0
$112$	1.30949e42	1.28272
$113$	1.13961e40	0.00930355	0.00465177	−	0.999989i	$-0.498519\pi$
$113$	1.13961e40	0.00930355	0.00465177	+	0.999989i	$0.498519\pi$
$114$	0	0
$115$	1.29129e42	0.735732
$116$	3.12677e42	1.49179
$117$	0	0
$118$	1.69329e42	0.569050
$119$	8.83635e42	2.49782
$120$	0	0
$121$	−4.94681e42	−0.993630
$122$	1.01117e42	0.171572
$123$	0	0
$124$	8.94510e42	1.08753
$125$	−3.92803e42	−0.405060
$126$	0	0
$127$	−1.88436e43	−1.40342	−0.701710	−	0.712463i	$-0.747580\pi$
$127$	−1.88436e43	−1.40342	−0.701710	+	0.712463i	$0.747580\pi$
$128$	−1.52299e43	−0.965812
$129$	0	0
$130$	2.67158e42	0.123290
$131$	9.29935e42	0.366767	0.183384	−	0.983041i	$-0.441295\pi$
$131$	9.29935e42	0.366767	0.183384	+	0.983041i	$0.441295\pi$
$132$	0	0
$133$	7.82046e43	2.26086
$134$	1.47567e42	0.0365881
$135$	0	0
$136$	−4.53741e43	−0.830349
$137$	1.16680e43	0.183749	0.0918746	−	0.995771i	$-0.470714\pi$
$137$	1.16680e43	0.183749	0.0918746	+	0.995771i	$0.470714\pi$
$138$	0	0
$139$	−1.12714e44	−1.31878	−0.659391	−	0.751800i	$-0.729186\pi$
$139$	−1.12714e44	−1.31878	−0.659391	+	0.751800i	$0.729186\pi$
$140$	−2.08714e44	−2.10827
$141$	0	0
$142$	1.87348e43	0.141494
$143$	−3.67510e42	−0.0240370
$144$	0	0
$145$	−4.37392e44	−2.15192
$146$	3.62164e43	0.154765
$147$	0	0
$148$	2.61472e44	0.845395
$149$	8.33811e42	0.0234827	0.0117414	−	0.999931i	$-0.496263\pi$
$149$	8.33811e42	0.0234827	0.0117414	+	0.999931i	$0.496263\pi$
$150$	0	0
$151$	4.48224e44	0.960434	0.480217	−	0.877150i	$-0.340558\pi$
$151$	4.48224e44	0.960434	0.480217	+	0.877150i	$0.340558\pi$
$152$	−4.01576e44	−0.751578
$153$	0	0
$154$	−3.16388e43	−0.0452945
$155$	−1.25129e45	−1.56877
$156$	0	0
$157$	−1.18993e45	−1.14704	−0.573521	−	0.819191i	$-0.694423\pi$
$157$	−1.18993e45	−1.14704	−0.573521	+	0.819191i	$0.694423\pi$
$158$	−3.90874e44	−0.330801
$159$	0	0
$160$	1.63558e45	1.06958
$161$	1.77230e45	1.02002
$162$	0	0
$163$	−1.65419e45	−0.739161	−0.369580	−	0.929199i	$-0.620499\pi$
$163$	−1.65419e45	−0.739161	−0.369580	+	0.929199i	$0.620499\pi$
$164$	−7.26164e44	−0.286244
$165$	0	0
$166$	9.24240e44	0.284164
$167$	1.65893e45	0.450962	0.225481	−	0.974248i	$-0.427605\pi$
$167$	1.65893e45	0.450962	0.225481	+	0.974248i	$0.427605\pi$
$168$	0	0
$169$	−4.26953e45	−0.909291
$170$	3.00787e45	0.567619
$171$	0	0
$172$	1.28009e45	0.190067
$173$	7.93101e45	1.04564	0.522821	−	0.852442i	$-0.324880\pi$
$173$	7.93101e45	1.04564	0.522821	+	0.852442i	$0.324880\pi$
$174$	0	0
$175$	1.19024e46	1.23981
$176$	−6.13183e44	−0.0568304
$177$	0	0
$178$	−1.72348e45	−0.126706
$179$	1.74304e46	1.14241	0.571204	−	0.820808i	$-0.306476\pi$
$179$	1.74304e46	1.14241	0.571204	+	0.820808i	$0.306476\pi$
$180$	0	0
$181$	2.91732e46	1.52255	0.761277	−	0.648427i	$-0.224573\pi$
$181$	2.91732e46	1.52255	0.761277	+	0.648427i	$0.224573\pi$
$182$	3.66675e45	0.170930
$183$	0	0
$184$	−9.10067e45	−0.339084
$185$	−3.65762e46	−1.21949
$186$	0	0
$187$	−4.13771e45	−0.110664
$188$	5.31888e46	1.27522
$189$	0	0
$190$	2.66207e46	0.513772
$191$	−3.24072e46	−0.561639	−0.280820	−	0.959761i	$-0.590606\pi$
$191$	−3.24072e46	−0.561639	−0.280820	+	0.959761i	$0.590606\pi$
$192$	0	0
$193$	5.78799e45	0.0810219	0.0405110	−	0.999179i	$-0.487101\pi$
$193$	5.78799e45	0.0810219	0.0405110	+	0.999179i	$0.487101\pi$
$194$	1.93903e46	0.244145
$195$	0	0
$196$	−1.98182e47	−2.02216
$197$	1.23332e47	1.13375	0.566875	−	0.823804i	$-0.308152\pi$
$197$	1.23332e47	1.13375	0.566875	+	0.823804i	$0.308152\pi$
$198$	0	0
$199$	−8.02314e46	−0.599592	−0.299796	−	0.954003i	$-0.596919\pi$
$199$	−8.02314e46	−0.599592	−0.299796	+	0.954003i	$0.596919\pi$
$200$	−6.11183e46	−0.412151
$201$	0	0
$202$	1.03630e47	0.569877
$203$	−6.00321e47	−2.98342
$204$	0	0
$205$	1.01580e47	0.412910
$206$	5.57998e46	0.205284
$207$	0	0
$208$	7.10641e46	0.214463
$209$	−3.66201e46	−0.100166
$210$	0	0
$211$	4.89315e46	0.110103	0.0550514	−	0.998484i	$-0.482468\pi$
$211$	4.89315e46	0.110103	0.0550514	+	0.998484i	$0.482468\pi$
$212$	−3.76346e47	−0.768602
$213$	0	0
$214$	1.52638e47	0.257147
$215$	−1.79067e47	−0.274174
$216$	0	0
$217$	−1.71740e48	−2.17494
$218$	−6.47720e45	−0.00746499
$219$	0	0
$220$	9.77323e46	0.0934056
$221$	4.79536e47	0.417618
$222$	0	0
$223$	1.26157e48	0.913402	0.456701	−	0.889620i	$-0.349031\pi$
$223$	1.26157e48	0.913402	0.456701	+	0.889620i	$0.349031\pi$
$224$	2.24484e48	1.48286
$225$	0	0
$226$	5.32422e45	0.00293112
$227$	7.98999e46	0.0401806	0.0200903	−	0.999798i	$-0.493605\pi$
$227$	7.98999e46	0.0401806	0.0200903	+	0.999798i	$0.493605\pi$
$228$	0	0
$229$	1.47316e48	0.618903	0.309452	−	0.950915i	$-0.399855\pi$
$229$	1.47316e48	0.618903	0.309452	+	0.950915i	$0.399855\pi$
$230$	6.03288e47	0.231795
$231$	0	0
$232$	3.08261e48	0.991780
$233$	1.22067e48	0.359585	0.179792	−	0.983705i	$-0.442457\pi$
$233$	1.22067e48	0.359585	0.179792	+	0.983705i	$0.442457\pi$
$234$	0	0
$235$	−7.44036e48	−1.83951
$236$	−7.17897e48	−1.62692
$237$	0	0
$238$	4.12831e48	0.786946
$239$	3.67173e48	0.642265	0.321132	−	0.947034i	$-0.395937\pi$
$239$	3.67173e48	0.642265	0.321132	+	0.947034i	$0.395937\pi$
$240$	0	0
$241$	7.53187e48	1.11059	0.555295	−	0.831654i	$-0.312605\pi$
$241$	7.53187e48	1.11059	0.555295	+	0.831654i	$0.312605\pi$
$242$	−2.31113e48	−0.313047
$243$	0	0
$244$	−4.28700e48	−0.490526
$245$	2.77229e49	2.91699
$246$	0	0
$247$	4.24405e48	0.378001
$248$	8.81876e48	0.723016
$249$	0	0
$250$	−1.83516e48	−0.127616
$251$	−1.42036e49	−0.910093	−0.455047	−	0.890468i	$-0.650377\pi$
$251$	−1.42036e49	−0.910093	−0.455047	+	0.890468i	$0.650377\pi$
$252$	0	0
$253$	−8.29899e47	−0.0451913
$254$	−8.80366e48	−0.442153
$255$	0	0
$256$	3.47132e48	0.148448
$257$	−1.04474e49	−0.412458	−0.206229	−	0.978504i	$-0.566119\pi$
$257$	−1.04474e49	−0.412458	−0.206229	+	0.978504i	$0.566119\pi$
$258$	0	0
$259$	−5.02009e49	−1.69070
$260$	−1.13266e49	−0.352488
$261$	0	0
$262$	4.34462e48	0.115551
$263$	−7.26469e49	−1.78700	−0.893499	−	0.449066i	$-0.851757\pi$
$263$	−7.26469e49	−1.78700	−0.893499	+	0.449066i	$0.851757\pi$
$264$	0	0
$265$	5.26455e49	1.10872
$266$	3.65369e49	0.712292
$267$	0	0
$268$	−6.25631e48	−0.104606
$269$	−1.15272e50	−1.78567	−0.892835	−	0.450384i	$-0.851287\pi$
$269$	−1.15272e50	−1.78567	−0.892835	+	0.450384i	$0.851287\pi$
$270$	0	0
$271$	−3.19469e48	−0.0425166	−0.0212583	−	0.999774i	$-0.506767\pi$
$271$	−3.19469e48	−0.0425166	−0.0212583	+	0.999774i	$0.506767\pi$
$272$	8.00096e49	0.987369
$273$	0	0
$274$	5.45126e48	0.0578909
$275$	−5.57344e48	−0.0549292
$276$	0	0
$277$	−1.21524e50	−1.03235	−0.516174	−	0.856484i	$-0.672644\pi$
$277$	−1.21524e50	−1.03235	−0.516174	+	0.856484i	$0.672644\pi$
$278$	−5.26594e49	−0.415487
$279$	0	0
$280$	−2.05766e50	−1.40163
$281$	1.33789e50	0.847110	0.423555	−	0.905871i	$-0.360782\pi$
$281$	1.33789e50	0.847110	0.423555	+	0.905871i	$0.360782\pi$
$282$	0	0
$283$	1.22161e50	0.668822	0.334411	−	0.942427i	$-0.391463\pi$
$283$	1.22161e50	0.668822	0.334411	+	0.942427i	$0.391463\pi$
$284$	−7.94289e49	−0.404532
$285$	0	0
$286$	−1.71699e48	−0.00757294
$287$	1.39419e50	0.572457
$288$	0	0
$289$	2.59093e50	0.922678
$290$	−2.04348e50	−0.677971
$291$	0	0
$292$	−1.53545e50	−0.442473
$293$	3.57046e50	0.959263	0.479631	−	0.877470i	$-0.340770\pi$
$293$	3.57046e50	0.959263	0.479631	+	0.877470i	$0.340770\pi$
$294$	0	0
$295$	1.00424e51	2.34685
$296$	2.57779e50	0.562040
$297$	0	0
$298$	3.89553e48	0.00739832
$299$	9.61802e49	0.170540
$300$	0	0
$301$	−2.45770e50	−0.380115
$302$	2.09409e50	0.302588
$303$	0	0
$304$	7.08111e50	0.893703
$305$	5.99691e50	0.707588
$306$	0	0
$307$	−1.10483e51	−1.14014	−0.570069	−	0.821597i	$-0.693083\pi$
$307$	−1.10483e51	−1.14014	−0.570069	+	0.821597i	$0.693083\pi$
$308$	1.34138e50	0.129497
$309$	0	0
$310$	−5.84600e50	−0.494247
$311$	−1.79220e50	−0.141840	−0.0709199	−	0.997482i	$-0.522593\pi$
$311$	−1.79220e50	−0.141840	−0.0709199	+	0.997482i	$0.522593\pi$
$312$	0	0
$313$	−2.12064e51	−1.47166	−0.735832	−	0.677164i	$-0.763209\pi$
$313$	−2.12064e51	−1.47166	−0.735832	+	0.677164i	$0.763209\pi$
$314$	−5.55932e50	−0.361380
$315$	0	0
$316$	1.65717e51	0.945764
$317$	−9.10910e50	−0.487260	−0.243630	−	0.969868i	$-0.578338\pi$
$317$	−9.10910e50	−0.487260	−0.243630	+	0.969868i	$0.578338\pi$
$318$	0	0
$319$	2.81106e50	0.132179
$320$	−1.33393e51	−0.588246
$321$	0	0
$322$	8.28013e50	0.321360
$323$	4.77828e51	1.74028
$324$	0	0
$325$	6.45928e50	0.207288
$326$	−7.72831e50	−0.232875
$327$	0	0
$328$	−7.15908e50	−0.190302
$329$	−1.02119e52	−2.55030
$330$	0	0
$331$	1.92970e51	0.425614	0.212807	−	0.977094i	$-0.431739\pi$
$331$	1.92970e51	0.425614	0.212807	+	0.977094i	$0.431739\pi$
$332$	−3.91846e51	−0.812427
$333$	0	0
$334$	7.75045e50	0.142077
$335$	8.75171e50	0.150895
$336$	0	0
$337$	−9.78943e51	−1.49398	−0.746990	−	0.664836i	$-0.768502\pi$
$337$	−9.78943e51	−1.49398	−0.746990	+	0.664836i	$0.768502\pi$
$338$	−1.99471e51	−0.286475
$339$	0	0
$340$	−1.27523e52	−1.62283
$341$	8.04192e50	0.0963595
$342$	0	0
$343$	2.11010e52	2.24272
$344$	1.26201e51	0.126362
$345$	0	0
$346$	3.70534e51	0.329433
$347$	1.94813e52	1.63254	0.816268	−	0.577673i	$-0.196039\pi$
$347$	1.94813e52	1.63254	0.816268	+	0.577673i	$0.196039\pi$
$348$	0	0
$349$	−1.88816e52	−1.40643	−0.703214	−	0.710978i	$-0.748252\pi$
$349$	−1.88816e52	−1.40643	−0.703214	+	0.710978i	$0.748252\pi$
$350$	5.56078e51	0.390608
$351$	0	0
$352$	−1.05117e51	−0.0656973
$353$	−5.89357e51	−0.347534	−0.173767	−	0.984787i	$-0.555594\pi$
$353$	−5.89357e51	−0.347534	−0.173767	+	0.984787i	$0.555594\pi$
$354$	0	0
$355$	1.11110e52	0.583541
$356$	7.30697e51	0.362253
$357$	0	0
$358$	8.14344e51	0.359920
$359$	−3.41142e52	−1.42396	−0.711981	−	0.702198i	$-0.752202\pi$
$359$	−3.41142e52	−1.42396	−0.711981	+	0.702198i	$0.752202\pi$
$360$	0	0
$361$	1.54423e52	0.575193
$362$	1.36296e52	0.479686
$363$	0	0
$364$	−1.55457e52	−0.488689
$365$	2.14788e52	0.638272
$366$	0	0
$367$	5.39142e52	1.43235	0.716174	−	0.697922i	$-0.245892\pi$
$367$	5.39142e52	1.43235	0.716174	+	0.697922i	$0.245892\pi$
$368$	1.60475e52	0.403206
$369$	0	0
$370$	−1.70883e52	−0.384205
$371$	7.22560e52	1.53712
$372$	0	0
$373$	1.69349e52	0.322665	0.161333	−	0.986900i	$-0.448421\pi$
$373$	1.69349e52	0.322665	0.161333	+	0.986900i	$0.448421\pi$
$374$	−1.93312e51	−0.0348652
$375$	0	0
$376$	5.24376e52	0.847796
$377$	−3.25785e52	−0.498808
$378$	0	0
$379$	−1.30321e53	−1.79024	−0.895119	−	0.445828i	$-0.852909\pi$
$379$	−1.30321e53	−1.79024	−0.895119	+	0.445828i	$0.852909\pi$
$380$	−1.12862e53	−1.46888
$381$	0	0
$382$	−1.51405e52	−0.176947
$383$	1.57363e53	1.74312	0.871561	−	0.490286i	$-0.163108\pi$
$383$	1.57363e53	1.74312	0.871561	+	0.490286i	$0.163108\pi$
$384$	0	0
$385$	−1.87640e52	−0.186801
$386$	2.70413e51	0.0255263
$387$	0	0
$388$	−8.22080e52	−0.698013
$389$	3.61986e52	0.291558	0.145779	−	0.989317i	$-0.453431\pi$
$389$	3.61986e52	0.291558	0.145779	+	0.989317i	$0.453431\pi$
$390$	0	0
$391$	1.08287e53	0.785152
$392$	−1.95383e53	−1.34438
$393$	0	0
$394$	5.76201e52	0.357192
$395$	−2.31815e53	−1.36427
$396$	0	0
$397$	−5.10834e52	−0.271065	−0.135533	−	0.990773i	$-0.543275\pi$
$397$	−5.10834e52	−0.271065	−0.135533	+	0.990773i	$0.543275\pi$
$398$	−3.74838e52	−0.188904
$399$	0	0
$400$	1.07772e53	0.490089
$401$	−1.32940e53	−0.574375	−0.287188	−	0.957874i	$-0.592720\pi$
$401$	−1.32940e53	−0.574375	−0.287188	+	0.957874i	$0.592720\pi$
$402$	0	0
$403$	−9.32009e52	−0.363636
$404$	−4.39354e53	−1.62928
$405$	0	0
$406$	−2.80468e53	−0.939938
$407$	2.35071e52	0.0749055
$408$	0	0
$409$	−1.41227e53	−0.406995	−0.203498	−	0.979075i	$-0.565231\pi$
$409$	−1.41227e53	−0.406995	−0.203498	+	0.979075i	$0.565231\pi$
$410$	4.74579e52	0.130089
$411$	0	0
$412$	−2.36572e53	−0.586909
$413$	1.37832e54	3.25367
$414$	0	0
$415$	5.48137e53	1.17193
$416$	1.21824e53	0.247924
$417$	0	0
$418$	−1.71088e52	−0.0315577
$419$	−5.25506e53	−0.922976	−0.461488	−	0.887147i	$-0.652684\pi$
$419$	−5.25506e53	−0.922976	−0.461488	+	0.887147i	$0.652684\pi$
$420$	0	0
$421$	1.41717e53	0.225755	0.112878	−	0.993609i	$-0.463993\pi$
$421$	1.41717e53	0.225755	0.112878	+	0.993609i	$0.463993\pi$
$422$	2.28606e52	0.0346883
$423$	0	0
$424$	−3.71030e53	−0.510986
$425$	7.27236e53	0.954338
$426$	0	0
$427$	8.23076e53	0.980999
$428$	−6.47133e53	−0.735184
$429$	0	0
$430$	−8.36594e52	−0.0863796
$431$	5.32701e53	0.524444	0.262222	−	0.965008i	$-0.415545\pi$
$431$	5.32701e53	0.524444	0.262222	+	0.965008i	$0.415545\pi$
$432$	0	0
$433$	1.65417e54	1.48108	0.740539	−	0.672014i	$-0.234570\pi$
$433$	1.65417e54	1.48108	0.740539	+	0.672014i	$0.234570\pi$
$434$	−8.02364e53	−0.685223
$435$	0	0
$436$	2.74611e52	0.0213425
$437$	9.58378e53	0.710669
$438$	0	0
$439$	−7.22284e53	−0.487736	−0.243868	−	0.969808i	$-0.578416\pi$
$439$	−7.22284e53	−0.487736	−0.243868	+	0.969808i	$0.578416\pi$
$440$	9.63519e52	0.0620984
$441$	0	0
$442$	2.24037e53	0.131572
$443$	1.23574e54	0.692866	0.346433	−	0.938075i	$-0.387393\pi$
$443$	1.23574e54	0.692866	0.346433	+	0.938075i	$0.387393\pi$
$444$	0	0
$445$	−1.02214e54	−0.522554
$446$	5.89401e53	0.287771
$447$	0	0
$448$	−1.83082e54	−0.815543
$449$	−1.61171e54	−0.685862	−0.342931	−	0.939361i	$-0.611420\pi$
$449$	−1.61171e54	−0.685862	−0.342931	+	0.939361i	$0.611420\pi$
$450$	0	0
$451$	−6.52844e52	−0.0253624
$452$	−2.25729e52	−0.00838009
$453$	0	0
$454$	3.73290e52	0.0126590
$455$	2.17463e54	0.704940
$456$	0	0
$457$	3.90797e54	1.15789	0.578947	−	0.815365i	$-0.303464\pi$
$457$	3.90797e54	1.15789	0.578947	+	0.815365i	$0.303464\pi$
$458$	6.88255e53	0.194988
$459$	0	0
$460$	−2.55773e54	−0.662704
$461$	−1.14081e54	−0.282711	−0.141356	−	0.989959i	$-0.545146\pi$
$461$	−1.14081e54	−0.282711	−0.141356	+	0.989959i	$0.545146\pi$
$462$	0	0
$463$	−3.28172e54	−0.744203	−0.372101	−	0.928192i	$-0.621363\pi$
$463$	−3.28172e54	−0.744203	−0.372101	+	0.928192i	$0.621363\pi$
$464$	−5.43566e54	−1.17933
$465$	0	0
$466$	5.70292e53	0.113289
$467$	−5.71824e54	−1.08709	−0.543546	−	0.839379i	$-0.682919\pi$
$467$	−5.71824e54	−1.08709	−0.543546	+	0.839379i	$0.682919\pi$
$468$	0	0
$469$	1.20117e54	0.209200
$470$	−3.47611e54	−0.579546
$471$	0	0
$472$	−7.07757e54	−1.08162
$473$	1.15084e53	0.0168408
$474$	0	0
$475$	6.43628e54	0.863805
$476$	−1.75026e55	−2.24989
$477$	0	0
$478$	1.71542e54	0.202348
$479$	1.67327e55	1.89099	0.945494	−	0.325638i	$-0.105579\pi$
$479$	1.67327e55	1.89099	0.945494	+	0.325638i	$0.105579\pi$
$480$	0	0
$481$	−2.72433e54	−0.282674
$482$	3.51886e54	0.349895
$483$	0	0
$484$	9.79839e54	0.895004
$485$	1.14997e55	1.00689
$486$	0	0
$487$	4.35887e53	0.0350777	0.0175388	−	0.999846i	$-0.494417\pi$
$487$	4.35887e53	0.0350777	0.0175388	+	0.999846i	$0.494417\pi$
$488$	−4.22645e54	−0.326114
$489$	0	0
$490$	1.29520e55	0.919007
$491$	3.19181e54	0.217203	0.108602	−	0.994085i	$-0.465363\pi$
$491$	3.19181e54	0.217203	0.108602	+	0.994085i	$0.465363\pi$
$492$	0	0
$493$	−3.66795e55	−2.29647
$494$	1.98280e54	0.119091
$495$	0	0
$496$	−1.55504e55	−0.859740
$497$	1.52498e55	0.809021
$498$	0	0
$499$	−1.24829e55	−0.609895	−0.304948	−	0.952369i	$-0.598639\pi$
$499$	−1.24829e55	−0.609895	−0.304948	+	0.952369i	$0.598639\pi$
$500$	7.78044e54	0.364854
$501$	0	0
$502$	−6.63585e54	−0.286728
$503$	−3.88562e55	−1.61182	−0.805910	−	0.592038i	$-0.798324\pi$
$503$	−3.88562e55	−1.61182	−0.805910	+	0.592038i	$0.798324\pi$
$504$	0	0
$505$	6.14595e55	2.35026
$506$	−3.87726e53	−0.0142377
$507$	0	0
$508$	3.73245e55	1.26412
$509$	3.56393e55	1.15935	0.579675	−	0.814848i	$-0.303179\pi$
$509$	3.56393e55	1.15935	0.579675	+	0.814848i	$0.303179\pi$
$510$	0	0
$511$	2.94797e55	0.884900
$512$	3.51127e55	1.01258
$513$	0	0
$514$	−4.88099e54	−0.129946
$515$	3.30931e55	0.846622
$516$	0	0
$517$	4.78183e54	0.112990
$518$	−2.34537e55	−0.532661
$519$	0	0
$520$	−1.11666e55	−0.234343
$521$	1.50481e55	0.303605	0.151802	−	0.988411i	$-0.451492\pi$
$521$	1.50481e55	0.303605	0.151802	+	0.988411i	$0.451492\pi$
$522$	0	0
$523$	1.25388e55	0.233869	0.116934	−	0.993140i	$-0.462693\pi$
$523$	1.25388e55	0.233869	0.116934	+	0.993140i	$0.462693\pi$
$524$	−1.84197e55	−0.330363
$525$	0	0
$526$	−3.39403e55	−0.563000
$527$	−1.04933e56	−1.67415
$528$	0	0
$529$	−4.60203e55	−0.679372
$530$	2.45958e55	0.349305
$531$	0	0
$532$	−1.54904e56	−2.03645
$533$	7.56606e54	0.0957110
$534$	0	0
$535$	9.05248e55	1.06051
$536$	−6.16795e54	−0.0695445
$537$	0	0
$538$	−5.38545e55	−0.562582
$539$	−1.78172e55	−0.179172
$540$	0	0
$541$	−9.58874e55	−0.893753	−0.446876	−	0.894596i	$-0.647464\pi$
$541$	−9.58874e55	−0.893753	−0.446876	+	0.894596i	$0.647464\pi$
$542$	−1.49255e54	−0.0133950
$543$	0	0
$544$	1.37159e56	1.14142
$545$	−3.84142e54	−0.0307867
$546$	0	0
$547$	1.58424e56	1.17783	0.588913	−	0.808196i	$-0.299556\pi$
$547$	1.58424e56	1.17783	0.588913	+	0.808196i	$0.299556\pi$
$548$	−2.31114e55	−0.165511
$549$	0	0
$550$	−2.60389e54	−0.0173056
$551$	−3.24625e56	−2.07862
$552$	0	0
$553$	−3.18167e56	−1.89143
$554$	−5.67754e55	−0.325245
$555$	0	0
$556$	2.23258e56	1.18788
$557$	−4.01202e55	−0.205746	−0.102873	−	0.994694i	$-0.532804\pi$
$557$	−4.01202e55	−0.205746	−0.102873	+	0.994694i	$0.532804\pi$
$558$	0	0
$559$	−1.33375e55	−0.0635527
$560$	3.62833e56	1.66668
$561$	0	0
$562$	6.25055e55	0.266885
$563$	−1.77020e56	−0.728785	−0.364393	−	0.931245i	$-0.618723\pi$
$563$	−1.77020e56	−0.728785	−0.364393	+	0.931245i	$0.618723\pi$
$564$	0	0
$565$	3.15763e54	0.0120884
$566$	5.70732e55	0.210715
$567$	0	0
$568$	−7.83071e55	−0.268943
$569$	2.37062e56	0.785346	0.392673	−	0.919678i	$-0.371550\pi$
$569$	2.37062e56	0.785346	0.392673	+	0.919678i	$0.371550\pi$
$570$	0	0
$571$	−2.39316e56	−0.737788	−0.368894	−	0.929471i	$-0.620263\pi$
$571$	−2.39316e56	−0.737788	−0.368894	+	0.929471i	$0.620263\pi$
$572$	7.27945e54	0.0216511
$573$	0	0
$574$	6.51360e55	0.180355
$575$	1.45861e56	0.389717
$576$	0	0
$577$	−6.12915e55	−0.152509	−0.0762546	−	0.997088i	$-0.524296\pi$
$577$	−6.12915e55	−0.152509	−0.0762546	+	0.997088i	$0.524296\pi$
$578$	1.21047e56	0.290693
$579$	0	0
$580$	8.66364e56	1.93833
$581$	7.52319e56	1.62477
$582$	0	0
$583$	−3.38346e55	−0.0681014
$584$	−1.51376e56	−0.294167
$585$	0	0
$586$	1.66810e56	0.302219
$587$	3.83130e56	0.670294	0.335147	−	0.942166i	$-0.391214\pi$
$587$	3.83130e56	0.670294	0.335147	+	0.942166i	$0.391214\pi$
$588$	0	0
$589$	−9.28691e56	−1.51533
$590$	4.69176e56	0.739383
$591$	0	0
$592$	−4.54549e56	−0.668322
$593$	−8.56740e56	−1.21682	−0.608412	−	0.793621i	$-0.708193\pi$
$593$	−8.56740e56	−1.21682	−0.608412	+	0.793621i	$0.708193\pi$
$594$	0	0
$595$	2.44837e57	3.24548
$596$	−1.65157e55	−0.0211519
$597$	0	0
$598$	4.49350e55	0.0537293
$599$	−8.04501e56	−0.929558	−0.464779	−	0.885427i	$-0.653866\pi$
$599$	−8.04501e56	−0.929558	−0.464779	+	0.885427i	$0.653866\pi$
$600$	0	0
$601$	−1.48001e57	−1.59713	−0.798563	−	0.601911i	$-0.794406\pi$
$601$	−1.48001e57	−1.59713	−0.798563	+	0.601911i	$0.794406\pi$
$602$	−1.14823e56	−0.119757
$603$	0	0
$604$	−8.87820e56	−0.865103
$605$	−1.37066e57	−1.29105
$606$	0	0
$607$	2.38634e56	0.210070	0.105035	−	0.994469i	$-0.466504\pi$
$607$	2.38634e56	0.210070	0.105035	+	0.994469i	$0.466504\pi$
$608$	1.21390e57	1.03314
$609$	0	0
$610$	2.80173e56	0.222928
$611$	−5.54185e56	−0.426393
$612$	0	0
$613$	3.94981e56	0.284208	0.142104	−	0.989852i	$-0.454613\pi$
$613$	3.94981e56	0.284208	0.142104	+	0.989852i	$0.454613\pi$
$614$	−5.16171e56	−0.359204
$615$	0	0
$616$	1.32243e56	0.0860932
$617$	1.22003e57	0.768286	0.384143	−	0.923274i	$-0.374497\pi$
$617$	1.22003e57	0.768286	0.384143	+	0.923274i	$0.374497\pi$
$618$	0	0
$619$	−1.86279e57	−1.09775	−0.548876	−	0.835903i	$-0.684944\pi$
$619$	−1.86279e57	−1.09775	−0.548876	+	0.835903i	$0.684944\pi$
$620$	2.47850e57	1.41306
$621$	0	0
$622$	−8.37309e55	−0.0446872
$623$	−1.40289e57	−0.724468
$624$	0	0
$625$	−2.51165e57	−1.21456
$626$	−9.90757e56	−0.463653
$627$	0	0
$628$	2.35696e57	1.03319
$629$	−3.06726e57	−1.30141
$630$	0	0
$631$	6.46073e56	0.256850	0.128425	−	0.991719i	$-0.459008\pi$
$631$	6.46073e56	0.256850	0.128425	+	0.991719i	$0.459008\pi$
$632$	1.63377e57	0.628767
$633$	0	0
$634$	−4.25574e56	−0.153513
$635$	−5.22117e57	−1.82350
$636$	0	0
$637$	2.06490e57	0.676147
$638$	1.31332e56	0.0416434
$639$	0	0
$640$	−4.21989e57	−1.25491
$641$	4.46188e56	0.128507	0.0642537	−	0.997934i	$-0.479533\pi$
$641$	4.46188e56	0.128507	0.0642537	+	0.997934i	$0.479533\pi$
$642$	0	0
$643$	2.22872e57	0.602186	0.301093	−	0.953595i	$-0.402649\pi$
$643$	2.22872e57	0.602186	0.301093	+	0.953595i	$0.402649\pi$
$644$	−3.51049e57	−0.918771
$645$	0	0
$646$	2.23240e57	0.548283
$647$	5.44697e57	1.29604	0.648018	−	0.761625i	$-0.275598\pi$
$647$	5.44697e57	1.29604	0.648018	+	0.761625i	$0.275598\pi$
$648$	0	0
$649$	−6.45411e56	−0.144152
$650$	3.01775e56	0.0653070
$651$	0	0
$652$	3.27653e57	0.665793
$653$	7.53963e57	1.48467	0.742335	−	0.670029i	$-0.233719\pi$
$653$	7.53963e57	1.48467	0.742335	+	0.670029i	$0.233719\pi$
$654$	0	0
$655$	2.57666e57	0.476551
$656$	1.26238e57	0.226288
$657$	0	0
$658$	−4.77097e57	−0.803481
$659$	−5.72637e57	−0.934821	−0.467410	−	0.884040i	$-0.654813\pi$
$659$	−5.72637e57	−0.934821	−0.467410	+	0.884040i	$0.654813\pi$
$660$	0	0
$661$	−1.76604e56	−0.0270939	−0.0135469	−	0.999908i	$-0.504312\pi$
$661$	−1.76604e56	−0.0270939	−0.0135469	+	0.999908i	$0.504312\pi$
$662$	9.01549e56	0.134091
$663$	0	0
$664$	−3.86311e57	−0.540122
$665$	2.16689e58	2.93760
$666$	0	0
$667$	−7.35678e57	−0.937796
$668$	−3.28592e57	−0.406200
$669$	0	0
$670$	4.08876e56	0.0475399
$671$	−3.85414e56	−0.0434626
$672$	0	0
$673$	6.90741e57	0.732836	0.366418	−	0.930450i	$-0.380584\pi$
$673$	6.90741e57	0.732836	0.366418	+	0.930450i	$0.380584\pi$
$674$	−4.57359e57	−0.470684
$675$	0	0
$676$	8.45688e57	0.819036
$677$	9.79667e57	0.920473	0.460236	−	0.887796i	$-0.347765\pi$
$677$	9.79667e57	0.920473	0.460236	+	0.887796i	$0.347765\pi$
$678$	0	0
$679$	1.57834e58	1.39595
$680$	−1.25722e58	−1.07890
$681$	0	0
$682$	3.75715e56	0.0303584
$683$	−5.61812e57	−0.440521	−0.220261	−	0.975441i	$-0.570691\pi$
$683$	−5.61812e57	−0.440521	−0.220261	+	0.975441i	$0.570691\pi$
$684$	0	0
$685$	3.23297e57	0.238751
$686$	9.85833e57	0.706576
$687$	0	0
$688$	−2.22534e57	−0.150257
$689$	3.92122e57	0.256997
$690$	0	0
$691$	−2.14965e58	−1.32760	−0.663800	−	0.747910i	$-0.731057\pi$
$691$	−2.14965e58	−1.32760	−0.663800	+	0.747910i	$0.731057\pi$
$692$	−1.57093e58	−0.941853
$693$	0	0
$694$	9.10157e57	0.514336
$695$	−3.12306e58	−1.71353
$696$	0	0
$697$	8.51846e57	0.440645
$698$	−8.82141e57	−0.443100
$699$	0	0
$700$	−2.35758e58	−1.11675
$701$	−2.04727e58	−0.941793	−0.470897	−	0.882188i	$-0.656070\pi$
$701$	−2.04727e58	−0.941793	−0.470897	+	0.882188i	$0.656070\pi$
$702$	0	0
$703$	−2.71463e58	−1.17795
$704$	8.57302e56	0.0361322
$705$	0	0
$706$	−2.75346e57	−0.109492
$707$	8.43532e58	3.25839
$708$	0	0
$709$	−8.36202e57	−0.304834	−0.152417	−	0.988316i	$-0.548706\pi$
$709$	−8.36202e57	−0.304834	−0.152417	+	0.988316i	$0.548706\pi$
$710$	5.19101e57	0.183847
$711$	0	0
$712$	7.20377e57	0.240835
$713$	−2.10463e58	−0.683661
$714$	0	0
$715$	−1.01829e57	−0.0312319
$716$	−3.45254e58	−1.02901
$717$	0	0
$718$	−1.59380e58	−0.448625
$719$	−1.73291e58	−0.474061	−0.237030	−	0.971502i	$-0.576174\pi$
$719$	−1.73291e58	−0.474061	−0.237030	+	0.971502i	$0.576174\pi$
$720$	0	0
$721$	4.54203e58	1.17375
$722$	7.21457e57	0.181217
$723$	0	0
$724$	−5.77848e58	−1.37143
$725$	−4.94067e58	−1.13987
$726$	0	0
$727$	4.93894e58	1.07691	0.538454	−	0.842655i	$-0.319009\pi$
$727$	4.93894e58	1.07691	0.538454	+	0.842655i	$0.319009\pi$
$728$	−1.53262e58	−0.324893
$729$	0	0
$730$	1.00348e58	0.201090
$731$	−1.50165e58	−0.292591
$732$	0	0
$733$	−2.27310e57	−0.0418781	−0.0209391	−	0.999781i	$-0.506666\pi$
$733$	−2.27310e57	−0.0418781	−0.0209391	+	0.999781i	$0.506666\pi$
$734$	2.51885e58	0.451266
$735$	0	0
$736$	2.75099e58	0.466116
$737$	−5.62461e56	−0.00926850
$738$	0	0
$739$	−3.92889e56	−0.00612433	−0.00306217	−	0.999995i	$-0.500975\pi$
$739$	−3.92889e56	−0.00612433	−0.00306217	+	0.999995i	$0.500975\pi$
$740$	7.24484e58	1.09845
$741$	0	0
$742$	3.37577e58	0.484276
$743$	1.05436e59	1.47135	0.735675	−	0.677334i	$-0.236865\pi$
$743$	1.05436e59	1.47135	0.735675	+	0.677334i	$0.236865\pi$
$744$	0	0
$745$	2.31032e57	0.0305118
$746$	7.91193e57	0.101657
$747$	0	0
$748$	8.19578e57	0.0996799
$749$	1.24245e59	1.47029
$750$	0	0
$751$	1.36881e59	1.53364	0.766822	−	0.641860i	$-0.221837\pi$
$751$	1.36881e59	1.53364	0.766822	+	0.641860i	$0.221837\pi$
$752$	−9.24647e58	−1.00812
$753$	0	0
$754$	−1.52206e58	−0.157151
$755$	1.24194e59	1.24792
$756$	0	0
$757$	−1.35209e59	−1.28688	−0.643442	−	0.765495i	$-0.722494\pi$
$757$	−1.35209e59	−1.28688	−0.643442	+	0.765495i	$0.722494\pi$
$758$	−6.08855e58	−0.564021
$759$	0	0
$760$	−1.11268e59	−0.976547
$761$	−1.00172e59	−0.855776	−0.427888	−	0.903832i	$-0.640742\pi$
$761$	−1.00172e59	−0.855776	−0.427888	+	0.903832i	$0.640742\pi$
$762$	0	0
$763$	−5.27235e57	−0.0426827
$764$	6.41906e58	0.505892
$765$	0	0
$766$	7.35195e58	0.549177
$767$	7.47992e58	0.543991
$768$	0	0
$769$	6.49599e57	0.0447874	0.0223937	−	0.999749i	$-0.492871\pi$
$769$	6.49599e57	0.0447874	0.0223937	+	0.999749i	$0.492871\pi$
$770$	−8.76646e57	−0.0588525
$771$	0	0
$772$	−1.14646e58	−0.0729798
$773$	−1.39210e59	−0.862959	−0.431480	−	0.902123i	$-0.642008\pi$
$773$	−1.39210e59	−0.862959	−0.431480	+	0.902123i	$0.642008\pi$
$774$	0	0
$775$	−1.41343e59	−0.830978
$776$	−8.10469e58	−0.464057
$777$	0	0
$778$	1.69118e58	0.0918563
$779$	7.53912e58	0.398844
$780$	0	0
$781$	−7.14090e57	−0.0358432
$782$	5.05914e58	0.247365
$783$	0	0
$784$	3.44525e59	1.59861
$785$	−3.29706e59	−1.49038
$786$	0	0
$787$	1.95672e58	0.0839550	0.0419775	−	0.999119i	$-0.486634\pi$
$787$	1.95672e58	0.0839550	0.0419775	+	0.999119i	$0.486634\pi$
$788$	−2.44290e59	−1.02122
$789$	0	0
$790$	−1.08303e59	−0.429819
$791$	4.33385e57	0.0167593
$792$	0	0
$793$	4.46671e58	0.164017
$794$	−2.38660e58	−0.0854002
$795$	0	0
$796$	1.58918e59	0.540078
$797$	7.27616e58	0.240994	0.120497	−	0.992714i	$-0.461551\pi$
$797$	7.27616e58	0.240994	0.120497	+	0.992714i	$0.461551\pi$
$798$	0	0
$799$	−6.23945e59	−1.96308
$800$	1.84751e59	0.566556
$801$	0	0
$802$	−6.21091e58	−0.180959
$803$	−1.38042e58	−0.0392050
$804$	0	0
$805$	4.91068e59	1.32534
$806$	−4.35431e58	−0.114565
$807$	0	0
$808$	−4.33149e59	−1.08319
$809$	−5.83880e59	−1.42357	−0.711785	−	0.702397i	$-0.752113\pi$
$809$	−5.83880e59	−1.42357	−0.711785	+	0.702397i	$0.752113\pi$
$810$	0	0
$811$	−5.49280e59	−1.27311	−0.636556	−	0.771231i	$-0.719641\pi$
$811$	−5.49280e59	−1.27311	−0.636556	+	0.771231i	$0.719641\pi$
$812$	1.18909e60	2.68729
$813$	0	0
$814$	1.09824e58	0.0235993
$815$	−4.58341e59	−0.960413
$816$	0	0
$817$	−1.32901e59	−0.264835
$818$	−6.59806e58	−0.128225
$819$	0	0
$820$	−2.01205e59	−0.371925
$821$	−6.58660e59	−1.18748	−0.593741	−	0.804657i	$-0.702349\pi$
$821$	−6.58660e59	−1.18748	−0.593741	+	0.804657i	$0.702349\pi$
$822$	0	0
$823$	7.46037e59	1.27957	0.639785	−	0.768554i	$-0.279023\pi$
$823$	7.46037e59	1.27957	0.639785	+	0.768554i	$0.279023\pi$
$824$	−2.33231e59	−0.390192
$825$	0	0
$826$	6.43944e59	1.02508
$827$	6.94575e58	0.107859	0.0539295	−	0.998545i	$-0.482825\pi$
$827$	6.94575e58	0.107859	0.0539295	+	0.998545i	$0.482825\pi$
$828$	0	0
$829$	4.42746e59	0.654315	0.327157	−	0.944970i	$-0.393909\pi$
$829$	4.42746e59	0.654315	0.327157	+	0.944970i	$0.393909\pi$
$830$	2.56088e59	0.369222
$831$	0	0
$832$	−9.93560e58	−0.136353
$833$	2.32483e60	3.11293
$834$	0	0
$835$	4.59655e59	0.585948
$836$	7.25353e58	0.0902238
$837$	0	0
$838$	−2.45515e59	−0.290787
$839$	−3.15752e59	−0.364943	−0.182472	−	0.983211i	$-0.558410\pi$
$839$	−3.15752e59	−0.364943	−0.182472	+	0.983211i	$0.558410\pi$
$840$	0	0
$841$	1.58343e60	1.74294
$842$	6.62094e58	0.0711250
$843$	0	0
$844$	−9.69211e58	−0.0991741
$845$	−1.18300e60	−1.18147
$846$	0	0
$847$	−1.88123e60	−1.78991
$848$	6.54249e59	0.607614
$849$	0	0
$850$	3.39762e59	0.300668
$851$	−6.15200e59	−0.531447
$852$	0	0
$853$	−1.17009e60	−0.963307	−0.481654	−	0.876362i	$-0.659964\pi$
$853$	−1.17009e60	−0.963307	−0.481654	+	0.876362i	$0.659964\pi$
$854$	3.84538e59	0.309067
$855$	0	0
$856$	−6.37993e59	−0.488769
$857$	9.58112e59	0.716654	0.358327	−	0.933596i	$-0.383347\pi$
$857$	9.58112e59	0.716654	0.358327	+	0.933596i	$0.383347\pi$
$858$	0	0
$859$	−1.69896e60	−1.21150	−0.605750	−	0.795655i	$-0.707127\pi$
$859$	−1.69896e60	−1.21150	−0.605750	+	0.795655i	$0.707127\pi$
$860$	3.54687e59	0.246960
$861$	0	0
$862$	2.48876e59	0.165228
$863$	2.10049e59	0.136175	0.0680877	−	0.997679i	$-0.478310\pi$
$863$	2.10049e59	0.136175	0.0680877	+	0.997679i	$0.478310\pi$
$864$	0	0
$865$	2.19752e60	1.35863
$866$	7.72821e59	0.466619
$867$	0	0
$868$	3.40175e60	1.95906
$869$	1.48985e59	0.0837986
$870$	0	0
$871$	6.51858e58	0.0349769
$872$	2.70732e58	0.0141890
$873$	0	0
$874$	4.47751e59	0.223899
$875$	−1.49380e60	−0.729669
$876$	0	0
$877$	−2.03764e60	−0.949810	−0.474905	−	0.880037i	$-0.657518\pi$
$877$	−2.03764e60	−0.949810	−0.474905	+	0.880037i	$0.657518\pi$
$878$	−3.37448e59	−0.153663
$879$	0	0
$880$	−1.69900e59	−0.0738413
$881$	−1.81214e60	−0.769457	−0.384729	−	0.923030i	$-0.625705\pi$
$881$	−1.81214e60	−0.769457	−0.384729	+	0.923030i	$0.625705\pi$
$882$	0	0
$883$	−2.81878e59	−0.114253	−0.0571263	−	0.998367i	$-0.518194\pi$
$883$	−2.81878e59	−0.114253	−0.0571263	+	0.998367i	$0.518194\pi$
$884$	−9.49840e59	−0.376166
$885$	0	0
$886$	5.77331e59	0.218290
$887$	−3.17942e60	−1.17466	−0.587332	−	0.809346i	$-0.699822\pi$
$887$	−3.17942e60	−1.17466	−0.587332	+	0.809346i	$0.699822\pi$
$888$	0	0
$889$	−7.16606e60	−2.52810
$890$	−4.77541e59	−0.164633
$891$	0	0
$892$	−2.49886e60	−0.822739
$893$	−5.52212e60	−1.77685
$894$	0	0
$895$	4.82961e60	1.48436
$896$	−5.79180e60	−1.73980
$897$	0	0
$898$	−7.52984e59	−0.216083
$899$	7.12889e60	1.99962
$900$	0	0
$901$	4.41482e60	1.18319
$902$	−3.05006e58	−0.00799051
$903$	0	0
$904$	−2.22540e58	−0.00557129
$905$	8.08328e60	1.97830
$906$	0	0
$907$	−6.08024e60	−1.42223	−0.711117	−	0.703073i	$-0.751811\pi$
$907$	−6.08024e60	−1.42223	−0.711117	+	0.703073i	$0.751811\pi$
$908$	−1.58262e59	−0.0361923
$909$	0	0
$910$	1.01598e60	0.222094
$911$	1.17767e60	0.251707	0.125854	−	0.992049i	$-0.459833\pi$
$911$	1.17767e60	0.251707	0.125854	+	0.992049i	$0.459833\pi$
$912$	0	0
$913$	−3.52281e59	−0.0719844
$914$	1.82579e60	0.364799
$915$	0	0
$916$	−2.91796e60	−0.557471
$917$	3.53646e60	0.660690
$918$	0	0
$919$	1.05431e61	1.88365	0.941824	−	0.336106i	$-0.109110\pi$
$919$	1.05431e61	1.88365	0.941824	+	0.336106i	$0.109110\pi$
$920$	−2.52161e60	−0.440582
$921$	0	0
$922$	−5.32981e59	−0.0890692
$923$	8.27586e59	0.135263
$924$	0	0
$925$	−4.13156e60	−0.645965
$926$	−1.53321e60	−0.234464
$927$	0	0
$928$	−9.31826e60	−1.36333
$929$	8.77778e60	1.25621	0.628105	−	0.778128i	$-0.283831\pi$
$929$	8.77778e60	1.25621	0.628105	+	0.778128i	$0.283831\pi$
$930$	0	0
$931$	2.05755e61	2.81762
$932$	−2.41784e60	−0.323893
$933$	0	0
$934$	−2.67154e60	−0.342492
$935$	−1.14647e60	−0.143789
$936$	0	0
$937$	−2.70984e60	−0.325299	−0.162649	−	0.986684i	$-0.552004\pi$
$937$	−2.70984e60	−0.325299	−0.162649	+	0.986684i	$0.552004\pi$
$938$	5.61184e59	0.0659093
$939$	0	0
$940$	1.47375e61	1.65693
$941$	−1.22601e61	−1.34867	−0.674336	−	0.738425i	$-0.735570\pi$
$941$	−1.22601e61	−1.34867	−0.674336	+	0.738425i	$0.735570\pi$
$942$	0	0
$943$	1.70854e60	0.179944
$944$	1.24801e61	1.28615
$945$	0	0
$946$	5.37669e58	0.00530575
$947$	−9.52407e59	−0.0919704	−0.0459852	−	0.998942i	$-0.514643\pi$
$947$	−9.52407e59	−0.0919704	−0.0459852	+	0.998942i	$0.514643\pi$
$948$	0	0
$949$	1.59982e60	0.147949
$950$	3.00701e60	0.272145
$951$	0	0
$952$	−1.72554e61	−1.49578
$953$	7.74450e60	0.657036	0.328518	−	0.944498i	$-0.393451\pi$
$953$	7.74450e60	0.657036	0.328518	+	0.944498i	$0.393451\pi$
$954$	0	0
$955$	−8.97937e60	−0.729754
$956$	−7.27279e60	−0.578514
$957$	0	0
$958$	7.81747e60	0.595763
$959$	4.43725e60	0.331004
$960$	0	0
$961$	6.40401e60	0.457744
$962$	−1.27280e60	−0.0890574
$963$	0	0
$964$	−1.49188e61	−1.00035
$965$	1.60373e60	0.105274
$966$	0	0
$967$	4.02534e60	0.253256	0.126628	−	0.991950i	$-0.459585\pi$
$967$	4.02534e60	0.253256	0.126628	+	0.991950i	$0.459585\pi$
$968$	9.66000e60	0.595021
$969$	0	0
$970$	5.37264e60	0.317225
$971$	−1.95124e61	−1.12802	−0.564010	−	0.825768i	$-0.690742\pi$
$971$	−1.95124e61	−1.12802	−0.564010	+	0.825768i	$0.690742\pi$
$972$	0	0
$973$	−4.28640e61	−2.37564
$974$	2.03645e59	0.0110513
$975$	0	0
$976$	7.45263e60	0.387782
$977$	3.24028e61	1.65099	0.825493	−	0.564412i	$-0.190897\pi$
$977$	3.24028e61	1.65099	0.825493	+	0.564412i	$0.190897\pi$
$978$	0	0
$979$	6.56918e59	0.0320971
$980$	−5.49122e61	−2.62745
$981$	0	0
$982$	1.49120e60	0.0684307
$983$	−3.28427e60	−0.147602	−0.0738008	−	0.997273i	$-0.523513\pi$
$983$	−3.28427e60	−0.147602	−0.0738008	+	0.997273i	$0.523513\pi$
$984$	0	0
$985$	3.41727e61	1.47311
$986$	−1.71365e61	−0.723512
$987$	0	0
$988$	−8.40640e60	−0.340481
$989$	−3.01184e60	−0.119484
$990$	0	0
$991$	3.77304e60	0.143609	0.0718046	−	0.997419i	$-0.477124\pi$
$991$	3.77304e60	0.143609	0.0718046	+	0.997419i	$0.477124\pi$
$992$	−2.66577e61	−0.993881
$993$	0	0
$994$	7.12467e60	0.254885
$995$	−2.22304e61	−0.779067
$996$	0	0
$997$	−4.67033e61	−1.57071	−0.785356	−	0.619044i	$-0.787520\pi$
$997$	−4.67033e61	−1.57071	−0.785356	+	0.619044i	$0.787520\pi$
$998$	−5.83198e60	−0.192150
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.42.a.a.1.2		3
3.2	odd	2		3.42.a.a.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.a.1.2	✓	3	3.2	odd	2
9.42.a.a.1.2		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)

\(f(q)\)	\(=\)	\(q+467196. q^{2} -1.98075e12 q^{4} +2.77079e14 q^{5} +3.80292e17 q^{7} -1.95278e18 q^{8} +O(q^{10})\)	\(q+467196. q^{2} -1.98075e12 q^{4} +2.77079e14 q^{5} +3.80292e17 q^{7} -1.95278e18 q^{8} +1.29450e20 q^{10} -1.78075e20 q^{11} +2.06379e22 q^{13} +1.77671e23 q^{14} +3.44339e24 q^{16} +2.32357e25 q^{17} +2.05644e26 q^{19} -5.48825e26 q^{20} -8.31962e25 q^{22} +4.66038e27 q^{23} +3.12982e28 q^{25} +9.64193e27 q^{26} -7.53263e29 q^{28} -1.57858e30 q^{29} -4.51602e30 q^{31} +5.90294e30 q^{32} +1.08556e31 q^{34} +1.05371e32 q^{35} -1.32006e32 q^{37} +9.60760e31 q^{38} -5.41074e32 q^{40} +3.66611e32 q^{41} -6.46266e32 q^{43} +3.52723e32 q^{44} +2.17731e33 q^{46} -2.68528e34 q^{47} +1.00054e35 q^{49} +1.46224e34 q^{50} -4.08785e34 q^{52} +1.90002e35 q^{53} -4.93410e34 q^{55} -7.42624e35 q^{56} -7.37507e35 q^{58} +3.62437e36 q^{59} +2.16433e36 q^{61} -2.10987e36 q^{62} -4.81426e36 q^{64} +5.71832e36 q^{65} +3.15856e36 q^{67} -4.60242e37 q^{68} +4.92289e37 q^{70} +4.01004e37 q^{71} +7.75186e37 q^{73} -6.16729e37 q^{74} -4.07329e38 q^{76} -6.77206e37 q^{77} -8.36639e38 q^{79} +9.54091e38 q^{80} +1.71279e38 q^{82} +1.97827e39 q^{83} +6.43814e39 q^{85} -3.01933e38 q^{86} +3.47741e38 q^{88} -3.68899e39 q^{89} +7.84841e39 q^{91} -9.23105e39 q^{92} -1.25455e40 q^{94} +5.69796e40 q^{95} +4.15034e40 q^{97} +4.67449e40 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 289380 q^{2} - 2254266178800 q^{4} - 38650546192026 q^{5} - 44\!\cdots\!68 q^{7}+ \cdots - 22\!\cdots\!96 q^{8}+O(q^{10}) \) 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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