LMFDB - Embedded newform 9.42.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$95.8245034108$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 196497525461x^{2} + 10360343667016365x + 6095744045744274504000 $ x^4 - x^3 - 196497525461x^2 + 10360343667016365x + 6095744045744274504000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{10}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-433547.$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58383e6 q^{2} +4.47715e12 q^{4} -2.55548e14 q^{5} +1.98945e17 q^{7} -5.88630e18 q^{8} +O(q^{10})$	\(q-2.58383e6 q^{2} +4.47715e12 q^{4} -2.55548e14 q^{5} +1.98945e17 q^{7} -5.88630e18 q^{8} +6.60294e20 q^{10} +2.76444e21 q^{11} -8.56075e22 q^{13} -5.14041e23 q^{14} +5.36384e24 q^{16} +3.38977e24 q^{17} +2.99407e26 q^{19} -1.14413e27 q^{20} -7.14285e27 q^{22} +1.40889e28 q^{23} +1.98303e28 q^{25} +2.21195e29 q^{26} +8.90709e29 q^{28} +4.94074e28 q^{29} +5.76050e30 q^{31} -9.15126e29 q^{32} -8.75860e30 q^{34} -5.08402e31 q^{35} -1.16818e32 q^{37} -7.73616e32 q^{38} +1.50424e33 q^{40} -1.48580e32 q^{41} +2.64197e32 q^{43} +1.23768e34 q^{44} -3.64032e34 q^{46} -2.16318e34 q^{47} -4.98839e33 q^{49} -5.12381e34 q^{50} -3.83278e35 q^{52} -5.57170e34 q^{53} -7.06449e35 q^{55} -1.17105e36 q^{56} -1.27660e35 q^{58} +2.05748e36 q^{59} +1.01936e36 q^{61} -1.48842e37 q^{62} -9.43067e36 q^{64} +2.18769e37 q^{65} -2.42878e37 q^{67} +1.51765e37 q^{68} +1.31362e38 q^{70} -5.77043e36 q^{71} -1.22382e38 q^{73} +3.01839e38 q^{74} +1.34049e39 q^{76} +5.49973e38 q^{77} -7.70707e38 q^{79} -1.37072e39 q^{80} +3.83906e38 q^{82} -1.70727e39 q^{83} -8.66251e38 q^{85} -6.82641e38 q^{86} -1.62723e40 q^{88} +4.08353e39 q^{89} -1.70312e40 q^{91} +6.30780e40 q^{92} +5.58928e40 q^{94} -7.65129e40 q^{95} +1.60920e40 q^{97} +1.28891e40 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots - 62\!\cdots\!84 q^{8}+O(q^{10}) $ 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8	$ 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots + 68\!\cdots\!22 q^{98}+O(q^{100}) $ 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8 + 725751018728422700940 * q^10 - 724810647231440683056 * q^11 - 8843977274373065537608 * q^13 - 493449664223337937919568 * q^14 - 5962194966280197033033200 * q^16 + 38231582029295844707285688 * q^17 + 261842746845948075837831248 * q^19 - 785441926018305471679038360 * q^20 - 6322149663566345845522943976 * q^22 + 15395573913207335266380880032 * q^23 + 117350921958371528604086683900 * q^25 + 62942545095927728709970694052 * q^26 + 684437536459146482218511575712 * q^28 + 1036098964520685524199931325064 * q^29 + 9280613209905247622577480610304 * q^31 - 19645397922916950127447685511456 * q^32 + 92420157643501864091330064020004 * q^34 - 207436667553525639419383641992640 * q^35 + 200754880510048713109452091192856 * q^37 - 1146938682238729575315585266559528 * q^38 + 2565083222429486590317315499815600 * q^40 - 2357905268481965433001096926030504 * q^41 + 3943358618915609696106480688157360 * q^43 + 18494278585991583572852191821764304 * q^44 - 44252120640849956767942988241684816 * q^46 + 8890000412230234893665157147040320 * q^47 - 33104900387055220681685954563991580 * q^49 + 216323679312314207800001999371642050 * q^50 - 596234086188669794371774262733483208 * q^52 - 95704753827317216756019399314791128 * q^53 + 1291057043675253444545805475556816160 * q^55 - 1940580325939766339139469085046208320 * q^56 + 3859053206955865617315425524661917116 * q^58 + 1809289331104083090977131835906657808 * q^59 + 5381027332088000515346282395501157240 * q^61 - 14109494547714507002913033009898657152 * q^62 - 389844533130084697385386794140537792 * q^64 + 9754648834359651370261564655441346480 * q^65 - 73273159367285254897696664016673247728 * q^67 + 89019363361032581039655795923994746424 * q^68 - 127374089191018487217525315519713602080 * q^70 + 84396091414708989106237239330896374752 * q^71 - 44706579271813174655854382994714255832 * q^73 + 299692406925616462116506150539738813812 * q^74 + 1128262001217587654782588548338718696272 * q^76 - 833312137190144115784050615522845895552 * q^77 + 1416534390331633014953369475707893311680 * q^79 - 1539903590051088861086709486592809053280 * q^80 + 613971248288365719286532695984150451412 * q^82 - 1526205590962076227407755639349783073104 * q^83 - 285377453319367852617718519171747770960 * q^85 + 12934468921257599734617599325958640634024 * q^86 - 13219976774504188013705589441700285953696 * q^88 + 39593715237961905051969833281675978558872 * q^89 - 8845052344004724172694600210873108791616 * q^91 + 65206363053810587386463980322833360400544 * q^92 + 98582759073905793403791649187553312740832 * q^94 - 7880313586718908134850457997267850706400 * q^95 + 36750128325858234547252025624989137001352 * q^97 + 68350119771260167200829379908744318383822 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.58383e6	−1.74240	−0.871202	−	0.490924i	$-0.836659\pi$
$2$	−2.58383e6	−1.74240	−0.871202	+	0.490924i	$0.836659\pi$
$3$	0	0
$3$	0	0
$4$	4.47715e12	2.03597
$5$	−2.55548e14	−1.19836	−0.599181	−	0.800613i	$-0.704507\pi$
$5$	−2.55548e14	−1.19836	−0.599181	+	0.800613i	$0.704507\pi$
$6$	0	0
$7$	1.98945e17	0.942375	0.471188	−	0.882033i	$-0.343825\pi$
$7$	1.98945e17	0.942375	0.471188	+	0.882033i	$0.343825\pi$
$8$	−5.88630e18	−1.80509
$9$	0	0
$10$	6.60294e20	2.08803
$11$	2.76444e21	1.23896	0.619480	−	0.785012i	$-0.287343\pi$
$11$	2.76444e21	1.23896	0.619480	+	0.785012i	$0.287343\pi$
$12$	0	0
$13$	−8.56075e22	−1.24932	−0.624659	−	0.780898i	$-0.714762\pi$
$13$	−8.56075e22	−1.24932	−0.624659	+	0.780898i	$0.714762\pi$
$14$	−5.14041e23	−1.64200
$15$	0	0
$16$	5.36384e24	1.10922
$17$	3.38977e24	0.202287	0.101143	−	0.994872i	$-0.467750\pi$
$17$	3.38977e24	0.202287	0.101143	+	0.994872i	$0.467750\pi$
$18$	0	0
$19$	2.99407e26	1.82731	0.913656	−	0.406488i	$-0.133247\pi$
$19$	2.99407e26	1.82731	0.913656	+	0.406488i	$0.133247\pi$
$20$	−1.14413e27	−2.43983
$21$	0	0
$22$	−7.14285e27	−2.15877
$23$	1.40889e28	1.71181	0.855904	−	0.517134i	$-0.173001\pi$
$23$	1.40889e28	1.71181	0.855904	+	0.517134i	$0.173001\pi$
$24$	0	0
$25$	1.98303e28	0.436072
$26$	2.21195e29	2.17682
$27$	0	0
$28$	8.90709e29	1.91865
$29$	4.94074e28	0.0518361	0.0259181	−	0.999664i	$-0.491749\pi$
$29$	4.94074e28	0.0518361	0.0259181	+	0.999664i	$0.491749\pi$
$30$	0	0
$31$	5.76050e30	1.54009	0.770044	−	0.637991i	$-0.220234\pi$
$31$	5.76050e30	1.54009	0.770044	+	0.637991i	$0.220234\pi$
$32$	−9.15126e29	−0.127616
$33$	0	0
$34$	−8.75860e30	−0.352466
$35$	−5.08402e31	−1.12931
$36$	0	0
$37$	−1.16818e32	−0.830569	−0.415284	−	0.909692i	$-0.636318\pi$
$37$	−1.16818e32	−0.830569	−0.415284	+	0.909692i	$0.636318\pi$
$38$	−7.73616e32	−3.18392
$39$	0	0
$40$	1.50424e33	2.16315
$41$	−1.48580e32	−0.128793	−0.0643964	−	0.997924i	$-0.520512\pi$
$41$	−1.48580e32	−0.128793	−0.0643964	+	0.997924i	$0.520512\pi$
$42$	0	0
$43$	2.64197e32	0.0862631	0.0431315	−	0.999069i	$-0.486267\pi$
$43$	2.64197e32	0.0862631	0.0431315	+	0.999069i	$0.486267\pi$
$44$	1.23768e34	2.52249
$45$	0	0
$46$	−3.64032e34	−2.98266
$47$	−2.16318e34	−1.14048	−0.570238	−	0.821480i	$-0.693149\pi$
$47$	−2.16318e34	−1.14048	−0.570238	+	0.821480i	$0.693149\pi$
$48$	0	0
$49$	−4.98839e33	−0.111928
$50$	−5.12381e34	−0.759814
$51$	0	0
$52$	−3.83278e35	−2.54358
$53$	−5.57170e34	−0.250226	−0.125113	−	0.992142i	$-0.539929\pi$
$53$	−5.57170e34	−0.250226	−0.125113	+	0.992142i	$0.539929\pi$
$54$	0	0
$55$	−7.06449e35	−1.48472
$56$	−1.17105e36	−1.70107
$57$	0	0
$58$	−1.27660e35	−0.0903195
$59$	2.05748e36	1.02534	0.512672	−	0.858584i	$-0.328656\pi$
$59$	2.05748e36	1.02534	0.512672	+	0.858584i	$0.328656\pi$
$60$	0	0
$61$	1.01936e36	0.256489	0.128244	−	0.991743i	$-0.459066\pi$
$61$	1.01936e36	0.256489	0.128244	+	0.991743i	$0.459066\pi$
$62$	−1.48842e37	−2.68346
$63$	0	0
$64$	−9.43067e36	−0.886856
$65$	2.18769e37	1.49714
$66$	0	0
$67$	−2.42878e37	−0.893006	−0.446503	−	0.894782i	$-0.647331\pi$
$67$	−2.42878e37	−0.893006	−0.446503	+	0.894782i	$0.647331\pi$
$68$	1.51765e37	0.411851
$69$	0	0
$70$	1.31362e38	1.96771
$71$	−5.77043e36	−0.0646268	−0.0323134	−	0.999478i	$-0.510287\pi$
$71$	−5.77043e36	−0.0646268	−0.0323134	+	0.999478i	$0.510287\pi$
$72$	0	0
$73$	−1.22382e38	−0.775532	−0.387766	−	0.921758i	$-0.626753\pi$
$73$	−1.22382e38	−0.775532	−0.387766	+	0.921758i	$0.626753\pi$
$74$	3.01839e38	1.44719
$75$	0	0
$76$	1.34049e39	3.72036
$77$	5.49973e38	1.16757
$78$	0	0
$79$	−7.70707e38	−0.967240	−0.483620	−	0.875278i	$-0.660678\pi$
$79$	−7.70707e38	−0.967240	−0.483620	+	0.875278i	$0.660678\pi$
$80$	−1.37072e39	−1.32924
$81$	0	0
$82$	3.83906e38	0.224409
$83$	−1.70727e39	−0.778397	−0.389198	−	0.921154i	$-0.627248\pi$
$83$	−1.70727e39	−0.778397	−0.389198	+	0.921154i	$0.627248\pi$
$84$	0	0
$85$	−8.66251e38	−0.242413
$86$	−6.82641e38	−0.150305
$87$	0	0
$88$	−1.62723e40	−2.23643
$89$	4.08353e39	0.445185	0.222592	−	0.974912i	$-0.428548\pi$
$89$	4.08353e39	0.445185	0.222592	+	0.974912i	$0.428548\pi$
$90$	0	0
$91$	−1.70312e40	−1.17733
$92$	6.30780e40	3.48520
$93$	0	0
$94$	5.58928e40	1.98717
$95$	−7.65129e40	−2.18978
$96$	0	0
$97$	1.60920e40	0.300462	0.150231	−	0.988651i	$-0.451998\pi$
$97$	1.60920e40	0.300462	0.150231	+	0.988651i	$0.451998\pi$
$98$	1.28891e40	0.195025
$99$	0	0
$100$	8.87832e40	0.887832
$101$	−8.47485e39	−0.0691105	−0.0345552	−	0.999403i	$-0.511001\pi$
$101$	−8.47485e39	−0.0691105	−0.0345552	+	0.999403i	$0.511001\pi$
$102$	0	0
$103$	2.25909e41	1.23246	0.616228	−	0.787568i	$-0.288660\pi$
$103$	2.25909e41	1.23246	0.616228	+	0.787568i	$0.288660\pi$
$104$	5.03911e41	2.25513
$105$	0	0
$106$	1.43963e41	0.435995
$107$	6.78077e41	1.69399	0.846996	−	0.531599i	$-0.178409\pi$
$107$	6.78077e41	1.69399	0.846996	+	0.531599i	$0.178409\pi$
$108$	0	0
$109$	7.17358e41	1.22601	0.613003	−	0.790080i	$-0.289961\pi$
$109$	7.17358e41	1.22601	0.613003	+	0.790080i	$0.289961\pi$
$110$	1.82534e42	2.58699
$111$	0	0
$112$	1.06711e42	1.04530
$113$	−1.60519e42	−1.31045	−0.655223	−	0.755435i	$-0.727425\pi$
$113$	−1.60519e42	−1.31045	−0.655223	+	0.755435i	$0.727425\pi$
$114$	0	0
$115$	−3.60039e42	−2.05137
$116$	2.21204e41	0.105537
$117$	0	0
$118$	−5.31619e42	−1.78657
$119$	6.74380e41	0.190630
$120$	0	0
$121$	2.66363e42	0.535024
$122$	−2.63386e42	−0.446907
$123$	0	0
$124$	2.57906e43	3.13558
$125$	6.55340e42	0.675790
$126$	0	0
$127$	2.84948e42	0.212222	0.106111	−	0.994354i	$-0.466160\pi$
$127$	2.84948e42	0.212222	0.106111	+	0.994354i	$0.466160\pi$
$128$	2.63796e43	1.67288
$129$	0	0
$130$	−5.65261e43	−2.60862
$131$	−2.19486e43	−0.865656	−0.432828	−	0.901477i	$-0.642484\pi$
$131$	−2.19486e43	−0.865656	−0.432828	+	0.901477i	$0.642484\pi$
$132$	0	0
$133$	5.95656e43	1.72201
$134$	6.27555e43	1.55598
$135$	0	0
$136$	−1.99532e43	−0.365145
$137$	−3.35892e43	−0.528966	−0.264483	−	0.964390i	$-0.585201\pi$
$137$	−3.35892e43	−0.528966	−0.264483	+	0.964390i	$0.585201\pi$
$138$	0	0
$139$	4.50230e43	0.526782	0.263391	−	0.964689i	$-0.415159\pi$
$139$	4.50230e43	0.526782	0.263391	+	0.964689i	$0.415159\pi$
$140$	−2.27619e44	−2.29924
$141$	0	0
$142$	1.49098e43	0.112606
$143$	−2.36657e44	−1.54786
$144$	0	0
$145$	−1.26260e43	−0.0621185
$146$	3.16215e44	1.35129
$147$	0	0
$148$	−5.23013e44	−1.69102
$149$	2.36545e44	0.666186	0.333093	−	0.942894i	$-0.391908\pi$
$149$	2.36545e44	0.666186	0.333093	+	0.942894i	$0.391908\pi$
$150$	0	0
$151$	−4.16293e44	−0.892015	−0.446007	−	0.895029i	$-0.647154\pi$
$151$	−4.16293e44	−0.892015	−0.446007	+	0.895029i	$0.647154\pi$
$152$	−1.76240e45	−3.29845
$153$	0	0
$154$	−1.42104e45	−2.03437
$155$	−1.47209e45	−1.84558
$156$	0	0
$157$	1.20032e45	1.15706	0.578528	−	0.815663i	$-0.303627\pi$
$157$	1.20032e45	1.15706	0.578528	+	0.815663i	$0.303627\pi$
$158$	1.99138e45	1.68532
$159$	0	0
$160$	2.33859e44	0.152931
$161$	2.80291e45	1.61317
$162$	0	0
$163$	2.08406e45	0.931246	0.465623	−	0.884983i	$-0.345830\pi$
$163$	2.08406e45	0.931246	0.465623	+	0.884983i	$0.345830\pi$
$164$	−6.65216e44	−0.262219
$165$	0	0
$166$	4.41129e45	1.35628
$167$	3.55110e45	0.965328	0.482664	−	0.875806i	$-0.339669\pi$
$167$	3.55110e45	0.965328	0.482664	+	0.875806i	$0.339669\pi$
$168$	0	0
$169$	2.63319e45	0.560795
$170$	2.23825e45	0.422382
$171$	0	0
$172$	1.18285e45	0.175629
$173$	−1.13689e46	−1.49890	−0.749449	−	0.662062i	$-0.769681\pi$
$173$	−1.13689e46	−1.49890	−0.749449	+	0.662062i	$0.769681\pi$
$174$	0	0
$175$	3.94514e45	0.410944
$176$	1.48280e46	1.37427
$177$	0	0
$178$	−1.05511e46	−0.775692
$179$	−7.48686e45	−0.490696	−0.245348	−	0.969435i	$-0.578902\pi$
$179$	−7.48686e45	−0.490696	−0.245348	+	0.969435i	$0.578902\pi$
$180$	0	0
$181$	−5.11394e45	−0.266898	−0.133449	−	0.991056i	$-0.542605\pi$
$181$	−5.11394e45	−0.266898	−0.133449	+	0.991056i	$0.542605\pi$
$182$	4.40057e46	2.05138
$183$	0	0
$184$	−8.29313e46	−3.08996
$185$	2.98527e46	0.995322
$186$	0	0
$187$	9.37084e45	0.250626
$188$	−9.68487e46	−2.32198
$189$	0	0
$190$	1.97696e47	3.81549
$191$	6.00314e46	1.04039	0.520193	−	0.854049i	$-0.325860\pi$
$191$	6.00314e46	1.04039	0.520193	+	0.854049i	$0.325860\pi$
$192$	0	0
$193$	−9.10745e45	−0.127489	−0.0637444	−	0.997966i	$-0.520304\pi$
$193$	−9.10745e45	−0.127489	−0.0637444	+	0.997966i	$0.520304\pi$
$194$	−4.15790e46	−0.523526
$195$	0	0
$196$	−2.23338e46	−0.227883
$197$	3.20025e46	0.294189	0.147094	−	0.989122i	$-0.453008\pi$
$197$	3.20025e46	0.294189	0.147094	+	0.989122i	$0.453008\pi$
$198$	0	0
$199$	−4.23622e46	−0.316585	−0.158293	−	0.987392i	$-0.550599\pi$
$199$	−4.23622e46	−0.316585	−0.158293	+	0.987392i	$0.550599\pi$
$200$	−1.16727e47	−0.787148
$201$	0	0
$202$	2.18976e46	0.120418
$203$	9.82936e45	0.0488491
$204$	0	0
$205$	3.79694e46	0.154340
$206$	−5.83712e47	−2.14744
$207$	0	0
$208$	−4.59184e47	−1.38576
$209$	8.27693e47	2.26397
$210$	0	0
$211$	5.34998e47	1.20382	0.601911	−	0.798563i	$-0.294406\pi$
$211$	5.34998e47	1.20382	0.601911	+	0.798563i	$0.294406\pi$
$212$	−2.49454e47	−0.509454
$213$	0	0
$214$	−1.75204e48	−2.95162
$215$	−6.75152e46	−0.103374
$216$	0	0
$217$	1.14602e48	1.45134
$218$	−1.85353e48	−2.13620
$219$	0	0
$220$	−3.16288e48	−3.02286
$221$	−2.90190e47	−0.252721
$222$	0	0
$223$	2.57714e48	1.86590	0.932950	−	0.360006i	$-0.117225\pi$
$223$	2.57714e48	1.86590	0.932950	+	0.360006i	$0.117225\pi$
$224$	−1.82060e47	−0.120263
$225$	0	0
$226$	4.14755e48	2.28333
$227$	−2.96815e48	−1.49264	−0.746320	−	0.665587i	$-0.768181\pi$
$227$	−2.96815e48	−1.49264	−0.746320	+	0.665587i	$0.768181\pi$
$228$	0	0
$229$	−2.39386e48	−1.00571	−0.502854	−	0.864371i	$-0.667717\pi$
$229$	−2.39386e48	−1.00571	−0.502854	+	0.864371i	$0.667717\pi$
$230$	9.30279e48	3.57431
$231$	0	0
$232$	−2.90827e47	−0.0935686
$233$	2.35236e48	0.692960	0.346480	−	0.938057i	$-0.387377\pi$
$233$	2.35236e48	0.692960	0.346480	+	0.938057i	$0.387377\pi$
$234$	0	0
$235$	5.52796e48	1.36670
$236$	9.21167e48	2.08758
$237$	0	0
$238$	−1.74248e48	−0.332155
$239$	5.65009e48	0.988322	0.494161	−	0.869370i	$-0.335475\pi$
$239$	5.65009e48	0.988322	0.494161	+	0.869370i	$0.335475\pi$
$240$	0	0
$241$	1.15148e49	1.69788	0.848940	−	0.528490i	$-0.177241\pi$
$241$	1.15148e49	1.69788	0.848940	+	0.528490i	$0.177241\pi$
$242$	−6.88236e48	−0.932229
$243$	0	0
$244$	4.56385e48	0.522204
$245$	1.27477e48	0.134131
$246$	0	0
$247$	−2.56315e49	−2.28289
$248$	−3.39080e49	−2.77999
$249$	0	0
$250$	−1.69329e49	−1.17750
$251$	−1.49455e48	−0.0957634	−0.0478817	−	0.998853i	$-0.515247\pi$
$251$	−1.49455e48	−0.0957634	−0.0478817	+	0.998853i	$0.515247\pi$
$252$	0	0
$253$	3.89479e49	2.12086
$254$	−7.36258e48	−0.369776
$255$	0	0
$256$	−4.74222e49	−2.02797
$257$	5.98105e48	0.236129	0.118064	−	0.993006i	$-0.462331\pi$
$257$	5.98105e48	0.236129	0.118064	+	0.993006i	$0.462331\pi$
$258$	0	0
$259$	−2.32405e49	−0.782707
$260$	9.79460e49	3.04813
$261$	0	0
$262$	5.67115e49	1.50832
$263$	−3.57534e49	−0.879476	−0.439738	−	0.898126i	$-0.644929\pi$
$263$	−3.57534e49	−0.879476	−0.439738	+	0.898126i	$0.644929\pi$
$264$	0	0
$265$	1.42384e49	0.299861
$266$	−1.53907e50	−3.00045
$267$	0	0
$268$	−1.08740e50	−1.81814
$269$	−2.52785e48	−0.0391589	−0.0195794	−	0.999808i	$-0.506233\pi$
$269$	−2.52785e48	−0.0391589	−0.0195794	+	0.999808i	$0.506233\pi$
$270$	0	0
$271$	5.81899e49	0.774421	0.387211	−	0.921991i	$-0.373439\pi$
$271$	5.81899e49	0.774421	0.387211	+	0.921991i	$0.373439\pi$
$272$	1.81822e49	0.224380
$273$	0	0
$274$	8.67887e49	0.921673
$275$	5.48197e49	0.540277
$276$	0	0
$277$	−1.51629e50	−1.28810	−0.644048	−	0.764985i	$-0.722746\pi$
$277$	−1.51629e50	−1.28810	−0.644048	+	0.764985i	$0.722746\pi$
$278$	−1.16332e50	−0.917867
$279$	0	0
$280$	2.99261e50	2.03850
$281$	1.12012e50	0.709226	0.354613	−	0.935013i	$-0.384613\pi$
$281$	1.12012e50	0.709226	0.354613	+	0.935013i	$0.384613\pi$
$282$	0	0
$283$	−2.86308e50	−1.56752	−0.783758	−	0.621066i	$-0.786700\pi$
$283$	−2.86308e50	−1.56752	−0.783758	+	0.621066i	$0.786700\pi$
$284$	−2.58351e49	−0.131578
$285$	0	0
$286$	6.11481e50	2.69699
$287$	−2.95593e49	−0.121371
$288$	0	0
$289$	−2.69315e50	−0.959080
$290$	3.26234e49	0.108236
$291$	0	0
$292$	−5.47924e50	−1.57896
$293$	1.89439e50	0.508960	0.254480	−	0.967078i	$-0.418096\pi$
$293$	1.89439e50	0.508960	0.254480	+	0.967078i	$0.418096\pi$
$294$	0	0
$295$	−5.25787e50	−1.22873
$296$	6.87628e50	1.49925
$297$	0	0
$298$	−6.11193e50	−1.16077
$299$	−1.20611e51	−2.13859
$300$	0	0
$301$	5.25608e49	0.0812922
$302$	1.07563e51	1.55425
$303$	0	0
$304$	1.60597e51	2.02688
$305$	−2.60497e50	−0.307366
$306$	0	0
$307$	4.49477e50	0.463843	0.231921	−	0.972735i	$-0.425499\pi$
$307$	4.49477e50	0.463843	0.231921	+	0.972735i	$0.425499\pi$
$308$	2.46231e51	2.37713
$309$	0	0
$310$	3.80362e51	3.21575
$311$	4.89729e50	0.387586	0.193793	−	0.981042i	$-0.437921\pi$
$311$	4.89729e50	0.387586	0.193793	+	0.981042i	$0.437921\pi$
$312$	0	0
$313$	1.99055e51	1.38139	0.690693	−	0.723148i	$-0.257306\pi$
$313$	1.99055e51	1.38139	0.690693	+	0.723148i	$0.257306\pi$
$314$	−3.10142e51	−2.01606
$315$	0	0
$316$	−3.45057e51	−1.96927
$317$	−8.77183e50	−0.469219	−0.234609	−	0.972090i	$-0.575381\pi$
$317$	−8.77183e50	−0.469219	−0.234609	+	0.972090i	$0.575381\pi$
$318$	0	0
$319$	1.36584e50	0.0642230
$320$	2.40999e51	1.06277
$321$	0	0
$322$	−7.24225e51	−2.81079
$323$	1.01492e51	0.369641
$324$	0	0
$325$	−1.69762e51	−0.544793
$326$	−5.38486e51	−1.62261
$327$	0	0
$328$	8.74587e50	0.232482
$329$	−4.30354e51	−1.07476
$330$	0	0
$331$	2.35505e51	0.519429	0.259715	−	0.965685i	$-0.416372\pi$
$331$	2.35505e51	0.519429	0.259715	+	0.965685i	$0.416372\pi$
$332$	−7.64370e51	−1.58479
$333$	0	0
$334$	−9.17543e51	−1.68199
$335$	6.20670e51	1.07014
$336$	0	0
$337$	2.75468e51	0.420396	0.210198	−	0.977659i	$-0.432589\pi$
$337$	2.75468e51	0.420396	0.210198	+	0.977659i	$0.432589\pi$
$338$	−6.80371e51	−0.977132
$339$	0	0
$340$	−3.87834e51	−0.493547
$341$	1.59246e52	1.90811
$342$	0	0
$343$	−9.85894e51	−1.04785
$344$	−1.55514e51	−0.155712
$345$	0	0
$346$	2.93752e52	2.61169
$347$	−8.25043e51	−0.691389	−0.345695	−	0.938347i	$-0.612357\pi$
$347$	−8.25043e51	−0.691389	−0.345695	+	0.938347i	$0.612357\pi$
$348$	0	0
$349$	8.65779e51	0.644891	0.322445	−	0.946588i	$-0.395495\pi$
$349$	8.65779e51	0.644891	0.322445	+	0.946588i	$0.395495\pi$
$350$	−1.01936e52	−0.716031
$351$	0	0
$352$	−2.52981e51	−0.158112
$353$	6.01269e51	0.354558	0.177279	−	0.984161i	$-0.443270\pi$
$353$	6.01269e51	0.354558	0.177279	+	0.984161i	$0.443270\pi$
$354$	0	0
$355$	1.47463e51	0.0774463
$356$	1.82826e52	0.906385
$357$	0	0
$358$	1.93448e52	0.854991
$359$	1.54293e52	0.644035	0.322017	−	0.946734i	$-0.395639\pi$
$359$	1.54293e52	0.644035	0.322017	+	0.946734i	$0.395639\pi$
$360$	0	0
$361$	6.27973e52	2.33907
$362$	1.32136e52	0.465044
$363$	0	0
$364$	−7.62513e52	−2.39701
$365$	3.12746e52	0.929369
$366$	0	0
$367$	−3.80556e52	−1.01103	−0.505515	−	0.862818i	$-0.668698\pi$
$367$	−3.80556e52	−1.01103	−0.505515	+	0.862818i	$0.668698\pi$
$368$	7.55703e52	1.89876
$369$	0	0
$370$	−7.71344e52	−1.73425
$371$	−1.10846e52	−0.235807
$372$	0	0
$373$	4.94905e52	0.942955	0.471478	−	0.881878i	$-0.343721\pi$
$373$	4.94905e52	0.942955	0.471478	+	0.881878i	$0.343721\pi$
$374$	−2.42126e52	−0.436691
$375$	0	0
$376$	1.27331e53	2.05865
$377$	−4.22964e51	−0.0647598
$378$	0	0
$379$	4.34671e52	0.597113	0.298557	−	0.954392i	$-0.403495\pi$
$379$	4.34671e52	0.597113	0.298557	+	0.954392i	$0.403495\pi$
$380$	−3.42560e53	−4.45834
$381$	0	0
$382$	−1.55111e53	−1.81277
$383$	2.09548e52	0.232118	0.116059	−	0.993242i	$-0.462974\pi$
$383$	2.09548e52	0.232118	0.116059	+	0.993242i	$0.462974\pi$
$384$	0	0
$385$	−1.40545e53	−1.39917
$386$	2.35321e52	0.222137
$387$	0	0
$388$	7.20463e52	0.611732
$389$	1.49021e53	1.20028	0.600139	−	0.799896i	$-0.295112\pi$
$389$	1.49021e53	1.20028	0.600139	+	0.799896i	$0.295112\pi$
$390$	0	0
$391$	4.77581e52	0.346277
$392$	2.93631e52	0.202040
$393$	0	0
$394$	−8.26890e52	−0.512596
$395$	1.96953e53	1.15910
$396$	0	0
$397$	3.46598e53	1.83916	0.919582	−	0.392898i	$-0.128528\pi$
$397$	3.46598e53	1.83916	0.919582	+	0.392898i	$0.128528\pi$
$398$	1.09457e53	0.551620
$399$	0	0
$400$	1.06366e53	0.483698
$401$	−3.81967e53	−1.65031	−0.825157	−	0.564904i	$-0.808913\pi$
$401$	−3.81967e53	−1.65031	−0.825157	+	0.564904i	$0.808913\pi$
$402$	0	0
$403$	−4.93142e53	−1.92406
$404$	−3.79432e52	−0.140707
$405$	0	0
$406$	−2.53974e52	−0.0851149
$407$	−3.22938e53	−1.02904
$408$	0	0
$409$	−1.49738e53	−0.431523	−0.215761	−	0.976446i	$-0.569223\pi$
$409$	−1.49738e53	−0.431523	−0.215761	+	0.976446i	$0.569223\pi$
$410$	−9.81065e52	−0.268923
$411$	0	0
$412$	1.01143e54	2.50925
$413$	4.09327e53	0.966260
$414$	0	0
$415$	4.36290e53	0.932801
$416$	7.83416e52	0.159433
$417$	0	0
$418$	−2.13862e54	−3.94475
$419$	−5.57082e53	−0.978434	−0.489217	−	0.872162i	$-0.662717\pi$
$419$	−5.57082e53	−0.978434	−0.489217	+	0.872162i	$0.662717\pi$
$420$	0	0
$421$	−4.02757e53	−0.641593	−0.320797	−	0.947148i	$-0.603951\pi$
$421$	−4.02757e53	−0.641593	−0.320797	+	0.947148i	$0.603951\pi$
$422$	−1.38234e54	−2.09754
$423$	0	0
$424$	3.27967e53	0.451679
$425$	6.72201e52	0.0882117
$426$	0	0
$427$	2.02798e53	0.241708
$428$	3.03585e54	3.44892
$429$	0	0
$430$	1.74448e53	0.180120
$431$	1.10307e54	1.08597	0.542986	−	0.839742i	$-0.317294\pi$
$431$	1.10307e54	1.08597	0.542986	+	0.839742i	$0.317294\pi$
$432$	0	0
$433$	2.59468e53	0.232317	0.116159	−	0.993231i	$-0.462942\pi$
$433$	2.59468e53	0.232317	0.116159	+	0.993231i	$0.462942\pi$
$434$	−2.96113e54	−2.52882
$435$	0	0
$436$	3.21172e54	2.49612
$437$	4.21830e54	3.12801
$438$	0	0
$439$	−6.51584e53	−0.439995	−0.219997	−	0.975500i	$-0.570605\pi$
$439$	−6.51584e53	−0.439995	−0.219997	+	0.975500i	$0.570605\pi$
$440$	4.15837e54	2.68005
$441$	0	0
$442$	7.49801e53	0.440342
$443$	8.31973e53	0.466480	0.233240	−	0.972419i	$-0.425067\pi$
$443$	8.31973e53	0.466480	0.233240	+	0.972419i	$0.425067\pi$
$444$	0	0
$445$	−1.04354e54	−0.533493
$446$	−6.65889e54	−3.25115
$447$	0	0
$448$	−1.87619e54	−0.835751
$449$	−1.75134e54	−0.745280	−0.372640	−	0.927976i	$-0.621547\pi$
$449$	−1.75134e54	−0.745280	−0.372640	+	0.927976i	$0.621547\pi$
$450$	0	0
$451$	−4.10741e53	−0.159569
$452$	−7.18670e54	−2.66803
$453$	0	0
$454$	7.66919e54	2.60078
$455$	4.35230e54	1.41086
$456$	0	0
$457$	5.74991e54	1.70364	0.851822	−	0.523831i	$-0.175498\pi$
$457$	5.74991e54	1.70364	0.851822	+	0.523831i	$0.175498\pi$
$458$	6.18534e54	1.75235
$459$	0	0
$460$	−1.61195e55	−4.17653
$461$	−7.61685e54	−1.88758	−0.943792	−	0.330540i	$-0.892769\pi$
$461$	−7.61685e54	−1.88758	−0.943792	+	0.330540i	$0.892769\pi$
$462$	0	0
$463$	4.82618e54	1.09444	0.547221	−	0.836988i	$-0.315686\pi$
$463$	4.82618e54	1.09444	0.547221	+	0.836988i	$0.315686\pi$
$464$	2.65013e53	0.0574974
$465$	0	0
$466$	−6.07811e54	−1.20742
$467$	8.48997e54	1.61402	0.807012	−	0.590535i	$-0.201083\pi$
$467$	8.48997e54	1.61402	0.807012	+	0.590535i	$0.201083\pi$
$468$	0	0
$469$	−4.83194e54	−0.841547
$470$	−1.42833e55	−2.38135
$471$	0	0
$472$	−1.21110e55	−1.85084
$473$	7.30358e53	0.106877
$474$	0	0
$475$	5.93732e54	0.796840
$476$	3.01930e54	0.388118
$477$	0	0
$478$	−1.45989e55	−1.72206
$479$	7.54248e54	0.852385	0.426193	−	0.904632i	$-0.359855\pi$
$479$	7.54248e54	0.852385	0.426193	+	0.904632i	$0.359855\pi$
$480$	0	0
$481$	1.00005e55	1.03764
$482$	−2.97523e55	−2.95839
$483$	0	0
$484$	1.19255e55	1.08930
$485$	−4.11228e54	−0.360062
$486$	0	0
$487$	2.26646e55	1.82392	0.911958	−	0.410283i	$-0.134570\pi$
$487$	2.26646e55	1.82392	0.911958	+	0.410283i	$0.134570\pi$
$488$	−6.00029e54	−0.462984
$489$	0	0
$490$	−3.29380e54	−0.233710
$491$	9.02019e54	0.613826	0.306913	−	0.951738i	$-0.400704\pi$
$491$	9.02019e54	0.613826	0.306913	+	0.951738i	$0.400704\pi$
$492$	0	0
$493$	1.67480e53	0.0104858
$494$	6.62273e55	3.97772
$495$	0	0
$496$	3.08984e55	1.70829
$497$	−1.14800e54	−0.0609027
$498$	0	0
$499$	−4.11207e54	−0.200909	−0.100454	−	0.994942i	$-0.532030\pi$
$499$	−4.11207e54	−0.200909	−0.100454	+	0.994942i	$0.532030\pi$
$500$	2.93406e55	1.37589
$501$	0	0
$502$	3.86167e54	0.166859
$503$	3.08721e55	1.28063	0.640313	−	0.768114i	$-0.278805\pi$
$503$	3.08721e55	1.28063	0.640313	+	0.768114i	$0.278805\pi$
$504$	0	0
$505$	2.16573e54	0.0828194
$506$	−1.00635e56	−3.69540
$507$	0	0
$508$	1.27576e55	0.432078
$509$	−2.73650e54	−0.0890185	−0.0445092	−	0.999009i	$-0.514172\pi$
$509$	−2.73650e54	−0.0890185	−0.0445092	+	0.999009i	$0.514172\pi$
$510$	0	0
$511$	−2.43474e55	−0.730843
$512$	6.45215e55	1.86067
$513$	0	0
$514$	−1.54540e55	−0.411432
$515$	−5.77308e55	−1.47693
$516$	0	0
$517$	−5.97998e55	−1.41300
$518$	6.00494e55	1.36379
$519$	0	0
$520$	−1.28774e56	−2.70246
$521$	7.68480e54	0.155046	0.0775228	−	0.996991i	$-0.475299\pi$
$521$	7.68480e54	0.155046	0.0775228	+	0.996991i	$0.475299\pi$
$522$	0	0
$523$	−5.42535e55	−1.01191	−0.505957	−	0.862559i	$-0.668860\pi$
$523$	−5.42535e55	−1.01191	−0.505957	+	0.862559i	$0.668860\pi$
$524$	−9.82673e55	−1.76245
$525$	0	0
$526$	9.23806e55	1.53240
$527$	1.95268e55	0.311540
$528$	0	0
$529$	1.30757e56	1.93029
$530$	−3.67896e55	−0.522480
$531$	0	0
$532$	2.66684e56	3.50598
$533$	1.27196e55	0.160903
$534$	0	0
$535$	−1.73282e56	−2.03002
$536$	1.42965e56	1.61195
$537$	0	0
$538$	6.53154e54	0.0682306
$539$	−1.37901e55	−0.138675
$540$	0	0
$541$	1.06824e56	0.995687	0.497844	−	0.867267i	$-0.334125\pi$
$541$	1.06824e56	0.995687	0.497844	+	0.867267i	$0.334125\pi$
$542$	−1.50353e56	−1.34936
$543$	0	0
$544$	−3.10207e54	−0.0258151
$545$	−1.83320e56	−1.46920
$546$	0	0
$547$	−2.25958e56	−1.67991	−0.839956	−	0.542654i	$-0.817419\pi$
$547$	−2.25958e56	−1.67991	−0.839956	+	0.542654i	$0.817419\pi$
$548$	−1.50384e56	−1.07696
$549$	0	0
$550$	−1.41645e56	−0.941381
$551$	1.47929e55	0.0947208
$552$	0	0
$553$	−1.53329e56	−0.911503
$554$	3.91785e56	2.24438
$555$	0	0
$556$	2.01575e56	1.07251
$557$	9.26630e55	0.475198	0.237599	−	0.971363i	$-0.423640\pi$
$557$	9.26630e55	0.475198	0.237599	+	0.971363i	$0.423640\pi$
$558$	0	0
$559$	−2.26173e55	−0.107770
$560$	−2.72698e56	−1.25264
$561$	0	0
$562$	−2.89420e56	−1.23576
$563$	−1.20733e56	−0.497053	−0.248526	−	0.968625i	$-0.579946\pi$
$563$	−1.20733e56	−0.497053	−0.248526	+	0.968625i	$0.579946\pi$
$564$	0	0
$565$	4.10205e56	1.57039
$566$	7.39772e56	2.73125
$567$	0	0
$568$	3.39665e55	0.116657
$569$	−2.31976e56	−0.768495	−0.384248	−	0.923230i	$-0.625539\pi$
$569$	−2.31976e56	−0.768495	−0.384248	+	0.923230i	$0.625539\pi$
$570$	0	0
$571$	2.57033e55	0.0792409	0.0396204	−	0.999215i	$-0.487385\pi$
$571$	2.57033e55	0.0792409	0.0396204	+	0.999215i	$0.487385\pi$
$572$	−1.05955e57	−3.15139
$573$	0	0
$574$	7.63763e55	0.211478
$575$	2.79386e56	0.746472
$576$	0	0
$577$	−2.83608e56	−0.705690	−0.352845	−	0.935682i	$-0.614786\pi$
$577$	−2.83608e56	−0.705690	−0.352845	+	0.935682i	$0.614786\pi$
$578$	6.95864e56	1.67111
$579$	0	0
$580$	−5.65284e55	−0.126472
$581$	−3.39653e56	−0.733542
$582$	0	0
$583$	−1.54027e56	−0.310020
$584$	7.20379e56	1.39990
$585$	0	0
$586$	−4.89479e56	−0.886814
$587$	−3.96279e56	−0.693298	−0.346649	−	0.937995i	$-0.612681\pi$
$587$	−3.96279e56	−0.693298	−0.346649	+	0.937995i	$0.612681\pi$
$588$	0	0
$589$	1.72473e57	2.81422
$590$	1.35854e57	2.14095
$591$	0	0
$592$	−6.26594e56	−0.921279
$593$	−1.25467e57	−1.78200	−0.891001	−	0.454001i	$-0.849996\pi$
$593$	−1.25467e57	−1.78200	−0.891001	+	0.454001i	$0.849996\pi$
$594$	0	0
$595$	−1.72337e56	−0.228444
$596$	1.05905e57	1.35634
$597$	0	0
$598$	3.11639e57	3.72629
$599$	1.06361e57	1.22895	0.614475	−	0.788936i	$-0.289368\pi$
$599$	1.06361e57	1.22895	0.614475	+	0.788936i	$0.289368\pi$
$600$	0	0
$601$	−4.74011e56	−0.511519	−0.255759	−	0.966740i	$-0.582325\pi$
$601$	−4.74011e56	−0.511519	−0.255759	+	0.966740i	$0.582325\pi$
$602$	−1.35808e56	−0.141644
$603$	0	0
$604$	−1.86381e57	−1.81612
$605$	−6.80686e56	−0.641153
$606$	0	0
$607$	−3.75437e56	−0.330498	−0.165249	−	0.986252i	$-0.552843\pi$
$607$	−3.75437e56	−0.330498	−0.165249	+	0.986252i	$0.552843\pi$
$608$	−2.73995e56	−0.233195
$609$	0	0
$610$	6.73080e56	0.535556
$611$	1.85184e57	1.42482
$612$	0	0
$613$	1.97052e57	1.41788	0.708941	−	0.705267i	$-0.249173\pi$
$613$	1.97052e57	1.41788	0.708941	+	0.705267i	$0.249173\pi$
$614$	−1.16137e57	−0.808202
$615$	0	0
$616$	−3.23731e57	−2.10756
$617$	−1.04592e57	−0.658649	−0.329325	−	0.944217i	$-0.606821\pi$
$617$	−1.04592e57	−0.658649	−0.329325	+	0.944217i	$0.606821\pi$
$618$	0	0
$619$	−3.26806e57	−1.92589	−0.962947	−	0.269692i	$-0.913078\pi$
$619$	−3.26806e57	−1.92589	−0.962947	+	0.269692i	$0.913078\pi$
$620$	−6.59076e57	−3.75756
$621$	0	0
$622$	−1.26538e57	−0.675332
$623$	8.12399e56	0.419531
$624$	0	0
$625$	−2.57649e57	−1.24591
$626$	−5.14325e57	−2.40693
$627$	0	0
$628$	5.37402e57	2.35574
$629$	−3.95988e56	−0.168013
$630$	0	0
$631$	7.88492e54	0.00313470	0.00156735	−	0.999999i	$-0.499501\pi$
$631$	7.88492e54	0.00313470	0.00156735	+	0.999999i	$0.499501\pi$
$632$	4.53662e57	1.74595
$633$	0	0
$634$	2.26649e57	0.817569
$635$	−7.28181e56	−0.254318
$636$	0	0
$637$	4.27043e56	0.139834
$638$	−3.52909e56	−0.111902
$639$	0	0
$640$	−6.74127e57	−2.00471
$641$	5.60781e57	1.61511	0.807557	−	0.589789i	$-0.200789\pi$
$641$	5.60781e57	1.61511	0.807557	+	0.589789i	$0.200789\pi$
$642$	0	0
$643$	−2.39387e57	−0.646810	−0.323405	−	0.946261i	$-0.604828\pi$
$643$	−2.39387e57	−0.646810	−0.323405	+	0.946261i	$0.604828\pi$
$644$	1.25491e58	3.28436
$645$	0	0
$646$	−2.62238e57	−0.644065
$647$	−5.56725e57	−1.32466	−0.662328	−	0.749214i	$-0.730431\pi$
$647$	−5.56725e57	−1.32466	−0.662328	+	0.749214i	$0.730431\pi$
$648$	0	0
$649$	5.68779e57	1.27036
$650$	4.38636e57	0.949250
$651$	0	0
$652$	9.33066e57	1.89599
$653$	−6.52017e57	−1.28392	−0.641961	−	0.766737i	$-0.721879\pi$
$653$	−6.52017e57	−1.28392	−0.641961	+	0.766737i	$0.721879\pi$
$654$	0	0
$655$	5.60893e57	1.03737
$656$	−7.96959e56	−0.142859
$657$	0	0
$658$	1.11196e58	1.87266
$659$	7.55343e57	1.23309	0.616543	−	0.787321i	$-0.288533\pi$
$659$	7.55343e57	1.23309	0.616543	+	0.787321i	$0.288533\pi$
$660$	0	0
$661$	−7.41557e57	−1.13767	−0.568833	−	0.822453i	$-0.692605\pi$
$661$	−7.41557e57	−1.13767	−0.568833	+	0.822453i	$0.692605\pi$
$662$	−6.08505e57	−0.905056
$663$	0	0
$664$	1.00495e58	1.40507
$665$	−1.52219e58	−2.06360
$666$	0	0
$667$	6.96093e56	0.0887336
$668$	1.58988e58	1.96538
$669$	0	0
$670$	−1.60371e58	−1.86463
$671$	2.81798e57	0.317779
$672$	0	0
$673$	−1.69942e58	−1.80298	−0.901490	−	0.432800i	$-0.857526\pi$
$673$	−1.69942e58	−1.80298	−0.901490	+	0.432800i	$0.857526\pi$
$674$	−7.11763e57	−0.732500
$675$	0	0
$676$	1.17892e58	1.14176
$677$	1.85953e57	0.174717	0.0873585	−	0.996177i	$-0.472157\pi$
$677$	1.85953e57	0.174717	0.0873585	+	0.996177i	$0.472157\pi$
$678$	0	0
$679$	3.20143e57	0.283148
$680$	5.09902e57	0.437576
$681$	0	0
$682$	−4.11464e58	−3.32470
$683$	1.28888e58	1.01062	0.505312	−	0.862937i	$-0.331377\pi$
$683$	1.28888e58	1.01062	0.505312	+	0.862937i	$0.331377\pi$
$684$	0	0
$685$	8.58366e57	0.633893
$686$	2.54738e58	1.82579
$687$	0	0
$688$	1.41711e57	0.0956843
$689$	4.76979e57	0.312612
$690$	0	0
$691$	5.69871e57	0.351947	0.175973	−	0.984395i	$-0.443693\pi$
$691$	5.69871e57	0.351947	0.175973	+	0.984395i	$0.443693\pi$
$692$	−5.09001e58	−3.05172
$693$	0	0
$694$	2.13177e58	1.20468
$695$	−1.15056e58	−0.631276
$696$	0	0
$697$	−5.03653e56	−0.0260531
$698$	−2.23703e58	−1.12366
$699$	0	0
$700$	1.76630e58	0.836671
$701$	8.78499e57	0.404131	0.202065	−	0.979372i	$-0.435235\pi$
$701$	8.78499e57	0.404131	0.202065	+	0.979372i	$0.435235\pi$
$702$	0	0
$703$	−3.49762e58	−1.51771
$704$	−2.60706e58	−1.09878
$705$	0	0
$706$	−1.55358e58	−0.617784
$707$	−1.68603e57	−0.0651280
$708$	0	0
$709$	4.95487e58	1.80628	0.903139	−	0.429347i	$-0.141256\pi$
$709$	4.95487e58	1.80628	0.903139	+	0.429347i	$0.141256\pi$
$710$	−3.81018e57	−0.134943
$711$	0	0
$712$	−2.40369e58	−0.803597
$713$	8.11589e58	2.63634
$714$	0	0
$715$	6.04773e58	1.85489
$716$	−3.35198e58	−0.999044
$717$	0	0
$718$	−3.98666e58	−1.12217
$719$	4.51451e58	1.23500	0.617501	−	0.786570i	$-0.288145\pi$
$719$	4.51451e58	1.23500	0.617501	+	0.786570i	$0.288145\pi$
$720$	0	0
$721$	4.49436e58	1.16144
$722$	−1.62258e59	−4.07561
$723$	0	0
$724$	−2.28959e58	−0.543397
$725$	9.79761e56	0.0226043
$726$	0	0
$727$	1.85132e58	0.403669	0.201834	−	0.979420i	$-0.435310\pi$
$727$	1.85132e58	0.403669	0.201834	+	0.979420i	$0.435310\pi$
$728$	1.00251e59	2.12517
$729$	0	0
$730$	−8.08083e58	−1.61934
$731$	8.95569e56	0.0174499
$732$	0	0
$733$	−7.75891e57	−0.142945	−0.0714725	−	0.997443i	$-0.522770\pi$
$733$	−7.75891e57	−0.142945	−0.0714725	+	0.997443i	$0.522770\pi$
$734$	9.83292e58	1.76162
$735$	0	0
$736$	−1.28931e58	−0.218455
$737$	−6.71422e58	−1.10640
$738$	0	0
$739$	−1.13939e59	−1.77608	−0.888041	−	0.459764i	$-0.847934\pi$
$739$	−1.13939e59	−1.77608	−0.888041	+	0.459764i	$0.847934\pi$
$740$	1.33655e59	2.02645
$741$	0	0
$742$	2.86408e58	0.410871
$743$	−9.08942e58	−1.26843	−0.634213	−	0.773158i	$-0.718676\pi$
$743$	−9.08942e58	−1.26843	−0.634213	+	0.773158i	$0.718676\pi$
$744$	0	0
$745$	−6.04488e58	−0.798333
$746$	−1.27875e59	−1.64301
$747$	0	0
$748$	4.19547e58	0.510267
$749$	1.34900e59	1.59638
$750$	0	0
$751$	1.09322e59	1.22487	0.612433	−	0.790522i	$-0.290191\pi$
$751$	1.09322e59	1.22487	0.612433	+	0.790522i	$0.290191\pi$
$752$	−1.16029e59	−1.26503
$753$	0	0
$754$	1.09287e58	0.112838
$755$	1.06383e59	1.06896
$756$	0	0
$757$	−1.50195e59	−1.42951	−0.714757	−	0.699372i	$-0.753463\pi$
$757$	−1.50195e59	−1.42951	−0.714757	+	0.699372i	$0.753463\pi$
$758$	−1.12312e59	−1.04041
$759$	0	0
$760$	4.50378e59	3.95274
$761$	1.91836e58	0.163887	0.0819436	−	0.996637i	$-0.473887\pi$
$761$	1.91836e58	0.163887	0.0819436	+	0.996637i	$0.473887\pi$
$762$	0	0
$763$	1.42715e59	1.15536
$764$	2.68770e59	2.11820
$765$	0	0
$766$	−5.41438e58	−0.404444
$767$	−1.76136e59	−1.28098
$768$	0	0
$769$	8.09865e58	0.558371	0.279185	−	0.960237i	$-0.409936\pi$
$769$	8.09865e58	0.558371	0.279185	+	0.960237i	$0.409936\pi$
$770$	3.63144e59	2.43792
$771$	0	0
$772$	−4.07755e58	−0.259564
$773$	1.75935e59	1.09062	0.545310	−	0.838234i	$-0.316412\pi$
$773$	1.75935e59	1.09062	0.545310	+	0.838234i	$0.316412\pi$
$774$	0	0
$775$	1.14232e59	0.671590
$776$	−9.47223e58	−0.542359
$777$	0	0
$778$	−3.85046e59	−2.09137
$779$	−4.44859e58	−0.235345
$780$	0	0
$781$	−1.59520e58	−0.0800700
$782$	−1.23399e59	−0.603354
$783$	0	0
$784$	−2.67569e58	−0.124153
$785$	−3.06740e59	−1.38657
$786$	0	0
$787$	−1.42029e59	−0.609390	−0.304695	−	0.952450i	$-0.598555\pi$
$787$	−1.42029e59	−0.609390	−0.304695	+	0.952450i	$0.598555\pi$
$788$	1.43280e59	0.598961
$789$	0	0
$790$	−5.08893e59	−2.01963
$791$	−3.19346e59	−1.23493
$792$	0	0
$793$	−8.72652e58	−0.320436
$794$	−8.95550e59	−3.20457
$795$	0	0
$796$	−1.89662e59	−0.644559
$797$	−1.77809e59	−0.588922	−0.294461	−	0.955664i	$-0.595140\pi$
$797$	−1.77809e59	−0.588922	−0.294461	+	0.955664i	$0.595140\pi$
$798$	0	0
$799$	−7.33268e58	−0.230703
$800$	−1.81472e58	−0.0556500
$801$	0	0
$802$	9.86938e59	2.87551
$803$	−3.38319e59	−0.960854
$804$	0	0
$805$	−7.16280e59	−1.93316
$806$	1.27419e60	3.35249
$807$	0	0
$808$	4.98855e58	0.124750
$809$	4.67029e59	1.13867	0.569336	−	0.822105i	$-0.307200\pi$
$809$	4.67029e59	1.13867	0.569336	+	0.822105i	$0.307200\pi$
$810$	0	0
$811$	−1.45390e59	−0.336983	−0.168492	−	0.985703i	$-0.553890\pi$
$811$	−1.45390e59	−0.336983	−0.168492	+	0.985703i	$0.553890\pi$
$812$	4.40076e58	0.0994555
$813$	0	0
$814$	8.34416e59	1.79301
$815$	−5.32578e59	−1.11597
$816$	0	0
$817$	7.91024e58	0.157630
$818$	3.86897e59	0.751887
$819$	0	0
$820$	1.69995e59	0.314233
$821$	1.07845e59	0.194432	0.0972158	−	0.995263i	$-0.469006\pi$
$821$	1.07845e59	0.194432	0.0972158	+	0.995263i	$0.469006\pi$
$822$	0	0
$823$	2.28591e59	0.392069	0.196035	−	0.980597i	$-0.437193\pi$
$823$	2.28591e59	0.392069	0.196035	+	0.980597i	$0.437193\pi$
$824$	−1.32977e60	−2.22469
$825$	0	0
$826$	−1.05763e60	−1.68362
$827$	5.76088e59	0.894594	0.447297	−	0.894385i	$-0.352387\pi$
$827$	5.76088e59	0.894594	0.447297	+	0.894385i	$0.352387\pi$
$828$	0	0
$829$	2.25613e59	0.333424	0.166712	−	0.986006i	$-0.446685\pi$
$829$	2.25613e59	0.333424	0.166712	+	0.986006i	$0.446685\pi$
$830$	−1.12730e60	−1.62532
$831$	0	0
$832$	8.07336e59	1.10796
$833$	−1.69095e58	−0.0226417
$834$	0	0
$835$	−9.07477e59	−1.15681
$836$	3.70571e60	4.60938
$837$	0	0
$838$	1.43940e60	1.70483
$839$	1.01240e60	1.17012	0.585060	−	0.810990i	$-0.301071\pi$
$839$	1.01240e60	1.17012	0.585060	+	0.810990i	$0.301071\pi$
$840$	0	0
$841$	−9.06044e59	−0.997313
$842$	1.04065e60	1.11791
$843$	0	0
$844$	2.39527e60	2.45095
$845$	−6.72907e59	−0.672036
$846$	0	0
$847$	5.29916e59	0.504194
$848$	−2.98857e59	−0.277555
$849$	0	0
$850$	−1.73685e59	−0.153701
$851$	−1.64584e60	−1.42177
$852$	0	0
$853$	−1.19199e60	−0.981337	−0.490669	−	0.871346i	$-0.663247\pi$
$853$	−1.19199e60	−0.981337	−0.490669	+	0.871346i	$0.663247\pi$
$854$	−5.23995e59	−0.421154
$855$	0	0
$856$	−3.99136e60	−3.05780
$857$	1.98782e60	1.48686	0.743431	−	0.668813i	$-0.233197\pi$
$857$	1.98782e60	1.48686	0.743431	+	0.668813i	$0.233197\pi$
$858$	0	0
$859$	1.93547e60	1.38015	0.690076	−	0.723737i	$-0.257577\pi$
$859$	1.93547e60	1.38015	0.690076	+	0.723737i	$0.257577\pi$
$860$	−3.02276e59	−0.210468
$861$	0	0
$862$	−2.85014e60	−1.89220
$863$	−1.93131e60	−1.25208	−0.626038	−	0.779793i	$-0.715325\pi$
$863$	−1.93131e60	−1.25208	−0.626038	+	0.779793i	$0.715325\pi$
$864$	0	0
$865$	2.90530e60	1.79622
$866$	−6.70421e59	−0.404791
$867$	0	0
$868$	5.13093e60	2.95489
$869$	−2.13058e60	−1.19837
$870$	0	0
$871$	2.07922e60	1.11565
$872$	−4.22258e60	−2.21305
$873$	0	0
$874$	−1.08994e61	−5.45026
$875$	1.30377e60	0.636848
$876$	0	0
$877$	4.31437e59	0.201106	0.100553	−	0.994932i	$-0.467939\pi$
$877$	4.31437e59	0.201106	0.100553	+	0.994932i	$0.467939\pi$
$878$	1.68358e60	0.766649
$879$	0	0
$880$	−3.78928e60	−1.64688
$881$	1.33549e60	0.567066	0.283533	−	0.958962i	$-0.408493\pi$
$881$	1.33549e60	0.567066	0.283533	+	0.958962i	$0.408493\pi$
$882$	0	0
$883$	−9.62321e59	−0.390055	−0.195027	−	0.980798i	$-0.562480\pi$
$883$	−9.62321e59	−0.390055	−0.195027	+	0.980798i	$0.562480\pi$
$884$	−1.29922e60	−0.514533
$885$	0	0
$886$	−2.14968e60	−0.812796
$887$	3.90527e60	1.44283	0.721417	−	0.692500i	$-0.243491\pi$
$887$	3.90527e60	1.44283	0.721417	+	0.692500i	$0.243491\pi$
$888$	0	0
$889$	5.66891e59	0.199993
$890$	2.69633e60	0.929560
$891$	0	0
$892$	1.15383e61	3.79892
$893$	−6.47670e60	−2.08400
$894$	0	0
$895$	1.91325e60	0.588031
$896$	5.24810e60	1.57648
$897$	0	0
$898$	4.52515e60	1.29858
$899$	2.84611e59	0.0798322
$900$	0	0
$901$	−1.88868e59	−0.0506175
$902$	1.06129e60	0.278034
$903$	0	0
$904$	9.44865e60	2.36547
$905$	1.30686e60	0.319840
$906$	0	0
$907$	−2.96464e60	−0.693462	−0.346731	−	0.937965i	$-0.612708\pi$
$907$	−2.96464e60	−0.693462	−0.346731	+	0.937965i	$0.612708\pi$
$908$	−1.32888e61	−3.03898
$909$	0	0
$910$	−1.12456e61	−2.45830
$911$	7.01681e60	1.49973	0.749865	−	0.661591i	$-0.230118\pi$
$911$	7.01681e60	1.49973	0.749865	+	0.661591i	$0.230118\pi$
$912$	0	0
$913$	−4.71965e60	−0.964403
$914$	−1.48568e61	−2.96844
$915$	0	0
$916$	−1.07177e61	−2.04760
$917$	−4.36657e60	−0.815773
$918$	0	0
$919$	−6.52121e60	−1.16509	−0.582546	−	0.812798i	$-0.697943\pi$
$919$	−6.52121e60	−1.16509	−0.582546	+	0.812798i	$0.697943\pi$
$920$	2.11930e61	3.70289
$921$	0	0
$922$	1.96806e61	3.28893
$923$	4.93992e59	0.0807394
$924$	0	0
$925$	−2.31654e60	−0.362188
$926$	−1.24700e61	−1.90696
$927$	0	0
$928$	−4.52140e58	−0.00661514
$929$	4.97882e60	0.712532	0.356266	−	0.934385i	$-0.384050\pi$
$929$	4.97882e60	0.712532	0.356266	+	0.934385i	$0.384050\pi$
$930$	0	0
$931$	−1.49356e60	−0.204528
$932$	1.05319e61	1.41085
$933$	0	0
$934$	−2.19366e61	−2.81228
$935$	−2.39470e60	−0.300340
$936$	0	0
$937$	9.62681e60	1.15564	0.577818	−	0.816166i	$-0.303904\pi$
$937$	9.62681e60	1.15564	0.577818	+	0.816166i	$0.303904\pi$
$938$	1.24849e61	1.46632
$939$	0	0
$940$	2.47495e61	2.78257
$941$	3.82719e60	0.421010	0.210505	−	0.977593i	$-0.432489\pi$
$941$	3.82719e60	0.421010	0.210505	+	0.977593i	$0.432489\pi$
$942$	0	0
$943$	−2.09332e60	−0.220469
$944$	1.10360e61	1.13733
$945$	0	0
$946$	−1.88712e60	−0.186222
$947$	−8.12706e59	−0.0784800	−0.0392400	−	0.999230i	$-0.512494\pi$
$947$	−8.12706e59	−0.0784800	−0.0392400	+	0.999230i	$0.512494\pi$
$948$	0	0
$949$	1.04768e61	0.968886
$950$	−1.53410e61	−1.38842
$951$	0	0
$952$	−3.96960e60	−0.344104
$953$	3.41043e60	0.289337	0.144669	−	0.989480i	$-0.453788\pi$
$953$	3.41043e60	0.289337	0.144669	+	0.989480i	$0.453788\pi$
$954$	0	0
$955$	−1.53409e61	−1.24676
$956$	2.52963e61	2.01220
$957$	0	0
$958$	−1.94885e61	−1.48520
$959$	−6.68241e60	−0.498485
$960$	0	0
$961$	1.91930e61	1.37187
$962$	−2.58396e61	−1.80800
$963$	0	0
$964$	5.15535e61	3.45684
$965$	2.32740e60	0.152778
$966$	0	0
$967$	−2.57180e61	−1.61806	−0.809030	−	0.587767i	$-0.800007\pi$
$967$	−2.57180e61	−1.61806	−0.809030	+	0.587767i	$0.800007\pi$
$968$	−1.56789e61	−0.965765
$969$	0	0
$970$	1.06254e61	0.627374
$971$	1.55166e61	0.897019	0.448509	−	0.893778i	$-0.351955\pi$
$971$	1.55166e61	0.897019	0.448509	+	0.893778i	$0.351955\pi$
$972$	0	0
$973$	8.95711e60	0.496426
$974$	−5.85616e61	−3.17800
$975$	0	0
$976$	5.46770e60	0.284501
$977$	−4.45394e60	−0.226937	−0.113469	−	0.993542i	$-0.536196\pi$
$977$	−4.45394e60	−0.226937	−0.113469	+	0.993542i	$0.536196\pi$
$978$	0	0
$979$	1.12887e61	0.551567
$980$	5.70736e60	0.273087
$981$	0	0
$982$	−2.33066e61	−1.06953
$983$	3.36188e61	1.51090	0.755450	−	0.655207i	$-0.227418\pi$
$983$	3.36188e61	1.51090	0.755450	+	0.655207i	$0.227418\pi$
$984$	0	0
$985$	−8.17819e60	−0.352545
$986$	−4.32739e59	−0.0182705
$987$	0	0
$988$	−1.14756e62	−4.64791
$989$	3.72224e60	0.147666
$990$	0	0
$991$	5.79150e60	0.220435	0.110218	−	0.993907i	$-0.464845\pi$
$991$	5.79150e60	0.220435	0.110218	+	0.993907i	$0.464845\pi$
$992$	−5.27158e60	−0.196540
$993$	0	0
$994$	2.96624e60	0.106117
$995$	1.08256e61	0.379384
$996$	0	0
$997$	1.75910e61	0.591615	0.295808	−	0.955248i	$-0.404411\pi$
$997$	1.75910e61	0.591615	0.295808	+	0.955248i	$0.404411\pi$
$998$	1.06249e61	0.350065
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.42.a.c.1.1		4
3.2	odd	2		3.42.a.b.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.b.1.4	✓	4	3.2	odd	2
9.42.a.c.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.58383e6 q^{2} +4.47715e12 q^{4} -2.55548e14 q^{5} +1.98945e17 q^{7} -5.88630e18 q^{8} +O(q^{10})\)	\(q-2.58383e6 q^{2} +4.47715e12 q^{4} -2.55548e14 q^{5} +1.98945e17 q^{7} -5.88630e18 q^{8} +6.60294e20 q^{10} +2.76444e21 q^{11} -8.56075e22 q^{13} -5.14041e23 q^{14} +5.36384e24 q^{16} +3.38977e24 q^{17} +2.99407e26 q^{19} -1.14413e27 q^{20} -7.14285e27 q^{22} +1.40889e28 q^{23} +1.98303e28 q^{25} +2.21195e29 q^{26} +8.90709e29 q^{28} +4.94074e28 q^{29} +5.76050e30 q^{31} -9.15126e29 q^{32} -8.75860e30 q^{34} -5.08402e31 q^{35} -1.16818e32 q^{37} -7.73616e32 q^{38} +1.50424e33 q^{40} -1.48580e32 q^{41} +2.64197e32 q^{43} +1.23768e34 q^{44} -3.64032e34 q^{46} -2.16318e34 q^{47} -4.98839e33 q^{49} -5.12381e34 q^{50} -3.83278e35 q^{52} -5.57170e34 q^{53} -7.06449e35 q^{55} -1.17105e36 q^{56} -1.27660e35 q^{58} +2.05748e36 q^{59} +1.01936e36 q^{61} -1.48842e37 q^{62} -9.43067e36 q^{64} +2.18769e37 q^{65} -2.42878e37 q^{67} +1.51765e37 q^{68} +1.31362e38 q^{70} -5.77043e36 q^{71} -1.22382e38 q^{73} +3.01839e38 q^{74} +1.34049e39 q^{76} +5.49973e38 q^{77} -7.70707e38 q^{79} -1.37072e39 q^{80} +3.83906e38 q^{82} -1.70727e39 q^{83} -8.66251e38 q^{85} -6.82641e38 q^{86} -1.62723e40 q^{88} +4.08353e39 q^{89} -1.70312e40 q^{91} +6.30780e40 q^{92} +5.58928e40 q^{94} -7.65129e40 q^{95} +1.60920e40 q^{97} +1.28891e40 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots - 62\!\cdots\!84 q^{8}+O(q^{10}) \) 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8	\( 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots + 68\!\cdots\!22 q^{98}+O(q^{100}) \) 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8 + 725751018728422700940 * q^10 - 724810647231440683056 * q^11 - 8843977274373065537608 * q^13 - 493449664223337937919568 * q^14 - 5962194966280197033033200 * q^16 + 38231582029295844707285688 * q^17 + 261842746845948075837831248 * q^19 - 785441926018305471679038360 * q^20 - 6322149663566345845522943976 * q^22 + 15395573913207335266380880032 * q^23 + 117350921958371528604086683900 * q^25 + 62942545095927728709970694052 * q^26 + 684437536459146482218511575712 * q^28 + 1036098964520685524199931325064 * q^29 + 9280613209905247622577480610304 * q^31 - 19645397922916950127447685511456 * q^32 + 92420157643501864091330064020004 * q^34 - 207436667553525639419383641992640 * q^35 + 200754880510048713109452091192856 * q^37 - 1146938682238729575315585266559528 * q^38 + 2565083222429486590317315499815600 * q^40 - 2357905268481965433001096926030504 * q^41 + 3943358618915609696106480688157360 * q^43 + 18494278585991583572852191821764304 * q^44 - 44252120640849956767942988241684816 * q^46 + 8890000412230234893665157147040320 * q^47 - 33104900387055220681685954563991580 * q^49 + 216323679312314207800001999371642050 * q^50 - 596234086188669794371774262733483208 * q^52 - 95704753827317216756019399314791128 * q^53 + 1291057043675253444545805475556816160 * q^55 - 1940580325939766339139469085046208320 * q^56 + 3859053206955865617315425524661917116 * q^58 + 1809289331104083090977131835906657808 * q^59 + 5381027332088000515346282395501157240 * q^61 - 14109494547714507002913033009898657152 * q^62 - 389844533130084697385386794140537792 * q^64 + 9754648834359651370261564655441346480 * q^65 - 73273159367285254897696664016673247728 * q^67 + 89019363361032581039655795923994746424 * q^68 - 127374089191018487217525315519713602080 * q^70 + 84396091414708989106237239330896374752 * q^71 - 44706579271813174655854382994714255832 * q^73 + 299692406925616462116506150539738813812 * q^74 + 1128262001217587654782588548338718696272 * q^76 - 833312137190144115784050615522845895552 * q^77 + 1416534390331633014953369475707893311680 * q^79 - 1539903590051088861086709486592809053280 * q^80 + 613971248288365719286532695984150451412 * q^82 - 1526205590962076227407755639349783073104 * q^83 - 285377453319367852617718519171747770960 * q^85 + 12934468921257599734617599325958640634024 * q^86 - 13219976774504188013705589441700285953696 * q^88 + 39593715237961905051969833281675978558872 * q^89 - 8845052344004724172694600210873108791616 * q^91 + 65206363053810587386463980322833360400544 * q^92 + 98582759073905793403791649187553312740832 * q^94 - 7880313586718908134850457997267850706400 * q^95 + 36750128325858234547252025624989137001352 * q^97 + 68350119771260167200829379908744318383822 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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