LMFDB - Embedded newform 121.8.a.d.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,8,Mod(1,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	121.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$37.7985880836$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 395x^{3} + 660x^{2} + 21600x - 76032 $ x^5 - 2x^4 - 395x^3 + 660x^2 + 21600x - 76032
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$5.55452$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.55452 q^{2} -81.6995 q^{3} -115.365 q^{4} -319.514 q^{5} -290.403 q^{6} +1172.95 q^{7} -865.048 q^{8} +4487.81 q^{9} -1135.72 q^{10} +9425.29 q^{12} -748.946 q^{13} +4169.27 q^{14} +26104.2 q^{15} +11691.9 q^{16} -19497.5 q^{17} +15952.0 q^{18} +57481.8 q^{19} +36860.9 q^{20} -95829.1 q^{21} +33810.1 q^{23} +70674.0 q^{24} +23964.3 q^{25} -2662.15 q^{26} -187975. q^{27} -135317. q^{28} -120078. q^{29} +92787.8 q^{30} -80005.9 q^{31} +152285. q^{32} -69304.4 q^{34} -374773. q^{35} -517738. q^{36} +255921. q^{37} +204320. q^{38} +61188.5 q^{39} +276395. q^{40} -400624. q^{41} -340627. q^{42} +392171. q^{43} -1.43392e6 q^{45} +120179. q^{46} -830888. q^{47} -955225. q^{48} +552260. q^{49} +85181.8 q^{50} +1.59294e6 q^{51} +86402.4 q^{52} +233588. q^{53} -668162. q^{54} -1.01465e6 q^{56} -4.69624e6 q^{57} -426821. q^{58} +2.54412e6 q^{59} -3.01152e6 q^{60} -402196. q^{61} -284383. q^{62} +5.26396e6 q^{63} -955265. q^{64} +239299. q^{65} +3.68081e6 q^{67} +2.24934e6 q^{68} -2.76227e6 q^{69} -1.33214e6 q^{70} -836212. q^{71} -3.88217e6 q^{72} +2.87284e6 q^{73} +909677. q^{74} -1.95787e6 q^{75} -6.63141e6 q^{76} +217496. q^{78} +2.44329e6 q^{79} -3.73574e6 q^{80} +5.54263e6 q^{81} -1.42403e6 q^{82} -5.36332e6 q^{83} +1.10554e7 q^{84} +6.22973e6 q^{85} +1.39398e6 q^{86} +9.81034e6 q^{87} -3.89069e6 q^{89} -5.09690e6 q^{90} -878473. q^{91} -3.90052e6 q^{92} +6.53644e6 q^{93} -2.95341e6 q^{94} -1.83663e7 q^{95} -1.24416e7 q^{96} -5.44653e6 q^{97} +1.96302e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{2} - 14 q^{3} + 166 q^{4} - 515 q^{5} - 692 q^{6} + 1286 q^{7} - 2334 q^{8} + 1133 q^{9} + 6836 q^{10} + 10496 q^{12} + 6533 q^{13} - 18668 q^{14} + 2074 q^{15} + 15010 q^{16} - 32705 q^{17}+ \cdots - 9136104 q^{98}+O(q^{100}) $ 5 * q - 8 * q^2 - 14 * q^3 + 166 * q^4 - 515 * q^5 - 692 * q^6 + 1286 * q^7 - 2334 * q^8 + 1133 * q^9 + 6836 * q^10 + 10496 * q^12 + 6533 * q^13 - 18668 * q^14 + 2074 * q^15 + 15010 * q^16 - 32705 * q^17 + 21848 * q^18 + 29910 * q^19 - 79078 * q^20 - 23132 * q^21 - 45214 * q^23 - 94992 * q^24 + 11764 * q^25 - 58196 * q^26 - 230348 * q^27 + 21856 * q^28 + 242061 * q^29 + 477220 * q^30 + 55310 * q^31 - 40750 * q^32 - 194608 * q^34 - 1092602 * q^35 - 1250618 * q^36 + 586689 * q^37 - 166692 * q^38 - 283790 * q^39 + 1951374 * q^40 + 565735 * q^41 - 1120208 * q^42 - 287040 * q^43 - 1566547 * q^45 - 1904780 * q^46 - 3182566 * q^47 + 949544 * q^48 - 765183 * q^49 - 4244056 * q^50 + 3141694 * q^51 + 4918498 * q^52 - 1220883 * q^53 + 913528 * q^54 - 5142192 * q^56 - 7377636 * q^57 - 10076868 * q^58 + 1304864 * q^59 - 7345528 * q^60 - 3437754 * q^61 + 4156516 * q^62 + 7075454 * q^63 - 4731286 * q^64 - 3342779 * q^65 - 5199446 * q^67 - 10501510 * q^68 - 11265124 * q^69 + 9858572 * q^70 - 3440220 * q^71 - 5576286 * q^72 + 9963974 * q^73 + 7512132 * q^74 - 241456 * q^75 - 7011480 * q^76 - 8493404 * q^78 - 7834562 * q^79 - 17690746 * q^80 + 4373321 * q^81 - 898480 * q^82 - 6230682 * q^83 + 19063160 * q^84 + 11708303 * q^85 + 6786552 * q^86 + 13109106 * q^87 - 13960869 * q^89 - 12112156 * q^90 + 573182 * q^91 - 3324824 * q^92 + 7120948 * q^93 - 9234428 * q^94 - 8171634 * q^95 - 4167472 * q^96 - 15733241 * q^97 - 9136104 * q^98

Coefficient data

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

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

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

$2$	3.55452	0.314178	0.157089	−	0.987584i	$-0.449789\pi$
$2$	3.55452	0.314178	0.157089	+	0.987584i	$0.449789\pi$
$3$	−81.6995	−1.74701	−0.873504	−	0.486816i	$-0.838158\pi$
$3$	−81.6995	−1.74701	−0.873504	+	0.486816i	$0.838158\pi$
$4$	−115.365	−0.901292
$5$	−319.514	−1.14313	−0.571564	−	0.820557i	$-0.693663\pi$
$5$	−319.514	−1.14313	−0.571564	+	0.820557i	$0.693663\pi$
$6$	−290.403	−0.548873
$7$	1172.95	1.29251	0.646257	−	0.763120i	$-0.276334\pi$
$7$	1172.95	1.29251	0.646257	+	0.763120i	$0.276334\pi$
$8$	−865.048	−0.597345
$9$	4487.81	2.05204
$10$	−1135.72	−0.359146
$11$	0	0
$11$	0	0
$12$	9425.29	1.57456
$13$	−748.946	−0.0945472	−0.0472736	−	0.998882i	$-0.515053\pi$
$13$	−748.946	−0.0945472	−0.0472736	+	0.998882i	$0.515053\pi$
$14$	4169.27	0.406080
$15$	26104.2	1.99706
$16$	11691.9	0.713619
$17$	−19497.5	−0.962516	−0.481258	−	0.876579i	$-0.659820\pi$
$17$	−19497.5	−0.962516	−0.481258	+	0.876579i	$0.659820\pi$
$18$	15952.0	0.644707
$19$	57481.8	1.92262	0.961308	−	0.275474i	$-0.0888349\pi$
$19$	57481.8	1.92262	0.961308	+	0.275474i	$0.0888349\pi$
$20$	36860.9	1.03029
$21$	−95829.1	−2.25803
$22$	0	0
$23$	33810.1	0.579428	0.289714	−	0.957113i	$-0.406440\pi$
$23$	33810.1	0.579428	0.289714	+	0.957113i	$0.406440\pi$
$24$	70674.0	1.04357
$25$	23964.3	0.306743
$26$	−2662.15	−0.0297047
$27$	−187975.	−1.83792
$28$	−135317.	−1.16493
$29$	−120078.	−0.914264	−0.457132	−	0.889399i	$-0.651123\pi$
$29$	−120078.	−0.914264	−0.457132	+	0.889399i	$0.651123\pi$
$30$	92787.8	0.627432
$31$	−80005.9	−0.482343	−0.241171	−	0.970483i	$-0.577532\pi$
$31$	−80005.9	−0.482343	−0.241171	+	0.970483i	$0.577532\pi$
$32$	152285.	0.821549
$33$	0	0
$34$	−69304.4	−0.302402
$35$	−374773.	−1.47751
$36$	−517738.	−1.84949
$37$	255921.	0.830615	0.415308	−	0.909681i	$-0.363674\pi$
$37$	255921.	0.830615	0.415308	+	0.909681i	$0.363674\pi$
$38$	204320.	0.604045
$39$	61188.5	0.165175
$40$	276395.	0.682842
$41$	−400624.	−0.907808	−0.453904	−	0.891051i	$-0.649969\pi$
$41$	−400624.	−0.907808	−0.453904	+	0.891051i	$0.649969\pi$
$42$	−340627.	−0.709425
$43$	392171.	0.752204	0.376102	−	0.926578i	$-0.377264\pi$
$43$	392171.	0.752204	0.376102	+	0.926578i	$0.377264\pi$
$44$	0	0
$45$	−1.43392e6	−2.34575
$46$	120179.	0.182044
$47$	−830888.	−1.16735	−0.583674	−	0.811988i	$-0.698385\pi$
$47$	−830888.	−1.16735	−0.583674	+	0.811988i	$0.698385\pi$
$48$	−955225.	−1.24670
$49$	552260.	0.670590
$50$	85181.8	0.0963722
$51$	1.59294e6	1.68152
$52$	86402.4	0.0852146
$53$	233588.	0.215518	0.107759	−	0.994177i	$-0.465632\pi$
$53$	233588.	0.215518	0.107759	+	0.994177i	$0.465632\pi$
$54$	−668162.	−0.577436
$55$	0	0
$56$	−1.01465e6	−0.772076
$57$	−4.69624e6	−3.35883
$58$	−426821.	−0.287242
$59$	2.54412e6	1.61271	0.806354	−	0.591434i	$-0.201438\pi$
$59$	2.54412e6	1.61271	0.806354	+	0.591434i	$0.201438\pi$
$60$	−3.01152e6	−1.79993
$61$	−402196.	−0.226873	−0.113437	−	0.993545i	$-0.536186\pi$
$61$	−402196.	−0.226873	−0.113437	+	0.993545i	$0.536186\pi$
$62$	−284383.	−0.151542
$63$	5.26396e6	2.65229
$64$	−955265.	−0.455506
$65$	239299.	0.108080
$66$	0	0
$67$	3.68081e6	1.49514	0.747570	−	0.664183i	$-0.231221\pi$
$67$	3.68081e6	1.49514	0.747570	+	0.664183i	$0.231221\pi$
$68$	2.24934e6	0.867508
$69$	−2.76227e6	−1.01227
$70$	−1.33214e6	−0.464202
$71$	−836212.	−0.277276	−0.138638	−	0.990343i	$-0.544272\pi$
$71$	−836212.	−0.277276	−0.138638	+	0.990343i	$0.544272\pi$
$72$	−3.88217e6	−1.22578
$73$	2.87284e6	0.864334	0.432167	−	0.901794i	$-0.357749\pi$
$73$	2.87284e6	0.864334	0.432167	+	0.901794i	$0.357749\pi$
$74$	909677.	0.260961
$75$	−1.95787e6	−0.535883
$76$	−6.63141e6	−1.73284
$77$	0	0
$78$	217496.	0.0518944
$79$	2.44329e6	0.557545	0.278772	−	0.960357i	$-0.410072\pi$
$79$	2.44329e6	0.557545	0.278772	+	0.960357i	$0.410072\pi$
$80$	−3.73574e6	−0.815758
$81$	5.54263e6	1.15883
$82$	−1.42403e6	−0.285214
$83$	−5.36332e6	−1.02958	−0.514791	−	0.857316i	$-0.672130\pi$
$83$	−5.36332e6	−1.02958	−0.514791	+	0.857316i	$0.672130\pi$
$84$	1.10554e7	2.03515
$85$	6.22973e6	1.10028
$86$	1.39398e6	0.236326
$87$	9.81034e6	1.59723
$88$	0	0
$89$	−3.89069e6	−0.585008	−0.292504	−	0.956264i	$-0.594488\pi$
$89$	−3.89069e6	−0.585008	−0.292504	+	0.956264i	$0.594488\pi$
$90$	−5.09690e6	−0.736983
$91$	−878473.	−0.122203
$92$	−3.90052e6	−0.522234
$93$	6.53644e6	0.842657
$94$	−2.95341e6	−0.366755
$95$	−1.83663e7	−2.19780
$96$	−1.24416e7	−1.43525
$97$	−5.44653e6	−0.605925	−0.302962	−	0.953003i	$-0.597976\pi$
$97$	−5.44653e6	−0.605925	−0.302962	+	0.953003i	$0.597976\pi$
$98$	1.96302e6	0.210685
$99$	0	0
$100$	−2.76465e6	−0.276465
$101$	−1.51556e7	−1.46369	−0.731845	−	0.681471i	$-0.761340\pi$
$101$	−1.51556e7	−1.46369	−0.731845	+	0.681471i	$0.761340\pi$
$102$	5.66213e6	0.528299
$103$	−2.45083e6	−0.220996	−0.110498	−	0.993876i	$-0.535245\pi$
$103$	−2.45083e6	−0.220996	−0.110498	+	0.993876i	$0.535245\pi$
$104$	647874.	0.0564773
$105$	3.06188e7	2.58122
$106$	830292.	0.0677112
$107$	−1.53861e7	−1.21419	−0.607093	−	0.794631i	$-0.707664\pi$
$107$	−1.53861e7	−1.21419	−0.607093	+	0.794631i	$0.707664\pi$
$108$	2.16858e7	1.65650
$109$	−1.29092e6	−0.0954785	−0.0477392	−	0.998860i	$-0.515202\pi$
$109$	−1.29092e6	−0.0954785	−0.0477392	+	0.998860i	$0.515202\pi$
$110$	0	0
$111$	−2.09086e7	−1.45109
$112$	1.37140e7	0.922362
$113$	−59376.6	−0.00387116	−0.00193558	−	0.999998i	$-0.500616\pi$
$113$	−59376.6	−0.00387116	−0.00193558	+	0.999998i	$0.500616\pi$
$114$	−1.66929e7	−1.05527
$115$	−1.08028e7	−0.662361
$116$	1.38529e7	0.824019
$117$	−3.36113e6	−0.194015
$118$	9.04314e6	0.506678
$119$	−2.28695e7	−1.24406
$120$	−2.25813e7	−1.19293
$121$	0	0
$122$	−1.42962e6	−0.0712787
$123$	3.27308e7	1.58595
$124$	9.22991e6	0.434732
$125$	1.73051e7	0.792482
$126$	1.87109e7	0.833292
$127$	−2.63135e7	−1.13990	−0.569948	−	0.821681i	$-0.693036\pi$
$127$	−2.63135e7	−1.13990	−0.569948	+	0.821681i	$0.693036\pi$
$128$	−2.28880e7	−0.964659
$129$	−3.20401e7	−1.31411
$130$	850593.	0.0339563
$131$	4.62778e7	1.79855	0.899277	−	0.437380i	$-0.144093\pi$
$131$	4.62778e7	1.79855	0.899277	+	0.437380i	$0.144093\pi$
$132$	0	0
$133$	6.74231e7	2.48501
$134$	1.30835e7	0.469741
$135$	6.00607e7	2.10098
$136$	1.68663e7	0.574954
$137$	3.07016e7	1.02009	0.510046	−	0.860147i	$-0.329628\pi$
$137$	3.07016e7	1.02009	0.510046	+	0.860147i	$0.329628\pi$
$138$	−9.81856e6	−0.318032
$139$	−1.42519e7	−0.450112	−0.225056	−	0.974346i	$-0.572256\pi$
$139$	−1.42519e7	−0.450112	−0.225056	+	0.974346i	$0.572256\pi$
$140$	4.32358e7	1.33167
$141$	6.78832e7	2.03937
$142$	−2.97233e6	−0.0871141
$143$	0	0
$144$	5.24712e7	1.46437
$145$	3.83667e7	1.04512
$146$	1.02116e7	0.271555
$147$	−4.51194e7	−1.17153
$148$	−2.95244e7	−0.748627
$149$	−1.88767e7	−0.467491	−0.233746	−	0.972298i	$-0.575098\pi$
$149$	−1.88767e7	−0.467491	−0.233746	+	0.972298i	$0.575098\pi$
$150$	−6.95931e6	−0.168363
$151$	−4.79916e7	−1.13435	−0.567174	−	0.823598i	$-0.691963\pi$
$151$	−4.79916e7	−1.13435	−0.567174	+	0.823598i	$0.691963\pi$
$152$	−4.97245e7	−1.14847
$153$	−8.75011e7	−1.97512
$154$	0	0
$155$	2.55630e7	0.551380
$156$	−7.05903e6	−0.148871
$157$	−3.63862e7	−0.750391	−0.375195	−	0.926946i	$-0.622424\pi$
$157$	−3.63862e7	−0.750391	−0.375195	+	0.926946i	$0.622424\pi$
$158$	8.68472e6	0.175169
$159$	−1.90840e7	−0.376512
$160$	−4.86573e7	−0.939136
$161$	3.96575e7	0.748918
$162$	1.97014e7	0.364078
$163$	−1.73647e6	−0.0314058	−0.0157029	−	0.999877i	$-0.504999\pi$
$163$	−1.73647e6	−0.0314058	−0.0157029	+	0.999877i	$0.504999\pi$
$164$	4.62182e7	0.818200
$165$	0	0
$166$	−1.90641e7	−0.323472
$167$	1.98374e7	0.329592	0.164796	−	0.986328i	$-0.447303\pi$
$167$	1.98374e7	0.329592	0.164796	+	0.986328i	$0.447303\pi$
$168$	8.28968e7	1.34882
$169$	−6.21876e7	−0.991061
$170$	2.21437e7	0.345684
$171$	2.57967e8	3.94529
$172$	−4.52429e7	−0.677955
$173$	8.23811e6	0.120967	0.0604834	−	0.998169i	$-0.480736\pi$
$173$	8.23811e6	0.120967	0.0604834	+	0.998169i	$0.480736\pi$
$174$	3.48711e7	0.501814
$175$	2.81089e7	0.396470
$176$	0	0
$177$	−2.07853e8	−2.81741
$178$	−1.38296e7	−0.183797
$179$	2.04852e6	0.0266965	0.0133483	−	0.999911i	$-0.495751\pi$
$179$	2.04852e6	0.0266965	0.0133483	+	0.999911i	$0.495751\pi$
$180$	1.65425e8	2.11420
$181$	1.49435e7	0.187317	0.0936587	−	0.995604i	$-0.470144\pi$
$181$	1.49435e7	0.187317	0.0936587	+	0.995604i	$0.470144\pi$
$182$	−3.12255e6	−0.0383937
$183$	3.28592e7	0.396350
$184$	−2.92474e7	−0.346118
$185$	−8.17704e7	−0.949500
$186$	2.32339e7	0.264745
$187$	0	0
$188$	9.58557e7	1.05212
$189$	−2.20485e8	−2.37554
$190$	−6.52833e7	−0.690501
$191$	−1.48943e8	−1.54669	−0.773345	−	0.633986i	$-0.781418\pi$
$191$	−1.48943e8	−1.54669	−0.773345	+	0.633986i	$0.781418\pi$
$192$	7.80447e7	0.795773
$193$	−9.71258e7	−0.972487	−0.486244	−	0.873823i	$-0.661633\pi$
$193$	−9.71258e7	−0.972487	−0.486244	+	0.873823i	$0.661633\pi$
$194$	−1.93598e7	−0.190368
$195$	−1.95506e7	−0.188816
$196$	−6.37116e7	−0.604397
$197$	8.53356e7	0.795240	0.397620	−	0.917550i	$-0.369836\pi$
$197$	8.53356e7	0.795240	0.397620	+	0.917550i	$0.369836\pi$
$198$	0	0
$199$	−1.97389e8	−1.77557	−0.887784	−	0.460260i	$-0.847756\pi$
$199$	−1.97389e8	−1.77557	−0.887784	+	0.460260i	$0.847756\pi$
$200$	−2.07303e7	−0.183232
$201$	−3.00720e8	−2.61202
$202$	−5.38710e7	−0.459860
$203$	−1.40845e8	−1.18170
$204$	−1.83770e8	−1.51554
$205$	1.28005e8	1.03774
$206$	−8.71155e6	−0.0694321
$207$	1.51733e8	1.18901
$208$	−8.75662e6	−0.0674707
$209$	0	0
$210$	1.08835e8	0.810964
$211$	8.47260e7	0.620909	0.310455	−	0.950588i	$-0.399519\pi$
$211$	8.47260e7	0.620909	0.310455	+	0.950588i	$0.399519\pi$
$212$	−2.69479e7	−0.194245
$213$	6.83181e7	0.484403
$214$	−5.46902e7	−0.381471
$215$	−1.25304e8	−0.859865
$216$	1.62607e8	1.09787
$217$	−9.38426e7	−0.623435
$218$	−4.58859e6	−0.0299973
$219$	−2.34710e8	−1.51000
$220$	0	0
$221$	1.46026e7	0.0910032
$222$	−7.43202e7	−0.455902
$223$	3.38697e7	0.204524	0.102262	−	0.994757i	$-0.467392\pi$
$223$	3.38697e7	0.204524	0.102262	+	0.994757i	$0.467392\pi$
$224$	1.78623e8	1.06186
$225$	1.07547e8	0.629450
$226$	−211056.	−0.00121623
$227$	−1.79835e8	−1.02043	−0.510216	−	0.860046i	$-0.670434\pi$
$227$	−1.79835e8	−1.02043	−0.510216	+	0.860046i	$0.670434\pi$
$228$	5.41783e8	3.02728
$229$	−3.27884e8	−1.80425	−0.902124	−	0.431476i	$-0.857993\pi$
$229$	−3.27884e8	−1.80425	−0.902124	+	0.431476i	$0.857993\pi$
$230$	−3.83989e7	−0.208100
$231$	0	0
$232$	1.03874e8	0.546131
$233$	1.07847e8	0.558548	0.279274	−	0.960211i	$-0.409906\pi$
$233$	1.07847e8	0.558548	0.279274	+	0.960211i	$0.409906\pi$
$234$	−1.19472e7	−0.0609552
$235$	2.65481e8	1.33443
$236$	−2.93503e8	−1.45352
$237$	−1.99615e8	−0.974036
$238$	−8.12903e7	−0.390858
$239$	3.41087e8	1.61611	0.808057	−	0.589104i	$-0.200519\pi$
$239$	3.41087e8	1.61611	0.808057	+	0.589104i	$0.200519\pi$
$240$	3.05208e8	1.42514
$241$	3.54106e8	1.62957	0.814786	−	0.579761i	$-0.196854\pi$
$241$	3.54106e8	1.62957	0.814786	+	0.579761i	$0.196854\pi$
$242$	0	0
$243$	−4.17289e7	−0.186558
$244$	4.63995e7	0.204479
$245$	−1.76455e8	−0.766571
$246$	1.16342e8	0.498271
$247$	−4.30507e7	−0.181778
$248$	6.92089e7	0.288125
$249$	4.38181e8	1.79869
$250$	6.15114e7	0.248981
$251$	−1.05465e8	−0.420969	−0.210485	−	0.977597i	$-0.567504\pi$
$251$	−1.05465e8	−0.420969	−0.210485	+	0.977597i	$0.567504\pi$
$252$	−6.07279e8	−2.39049
$253$	0	0
$254$	−9.35318e7	−0.358131
$255$	−5.08966e8	−1.92220
$256$	4.09178e7	0.152431
$257$	−2.23825e8	−0.822514	−0.411257	−	0.911519i	$-0.634910\pi$
$257$	−2.23825e8	−0.822514	−0.411257	+	0.911519i	$0.634910\pi$
$258$	−1.13887e8	−0.412864
$259$	3.00182e8	1.07358
$260$	−2.76068e7	−0.0974113
$261$	−5.38889e8	−1.87611
$262$	1.64496e8	0.565067
$263$	−1.88630e8	−0.639389	−0.319694	−	0.947521i	$-0.603580\pi$
$263$	−1.88630e8	−0.639389	−0.319694	+	0.947521i	$0.603580\pi$
$264$	0	0
$265$	−7.46345e7	−0.246365
$266$	2.39657e8	0.780736
$267$	3.17868e8	1.02201
$268$	−4.24638e8	−1.34756
$269$	2.59669e8	0.813368	0.406684	−	0.913569i	$-0.366685\pi$
$269$	2.59669e8	0.813368	0.406684	+	0.913569i	$0.366685\pi$
$270$	2.13487e8	0.660083
$271$	−2.86150e8	−0.873377	−0.436688	−	0.899613i	$-0.643849\pi$
$271$	−2.86150e8	−0.873377	−0.436688	+	0.899613i	$0.643849\pi$
$272$	−2.27964e8	−0.686870
$273$	7.17708e7	0.213491
$274$	1.09130e8	0.320491
$275$	0	0
$276$	3.18670e8	0.912347
$277$	−4.34772e8	−1.22909	−0.614543	−	0.788884i	$-0.710659\pi$
$277$	−4.34772e8	−1.22909	−0.614543	+	0.788884i	$0.710659\pi$
$278$	−5.06586e7	−0.141415
$279$	−3.59051e8	−0.989787
$280$	3.24197e8	0.882583
$281$	−1.15733e8	−0.311161	−0.155580	−	0.987823i	$-0.549725\pi$
$281$	−1.15733e8	−0.311161	−0.155580	+	0.987823i	$0.549725\pi$
$282$	2.41292e8	0.640725
$283$	−4.38018e8	−1.14879	−0.574394	−	0.818579i	$-0.694762\pi$
$283$	−4.38018e8	−1.14879	−0.574394	+	0.818579i	$0.694762\pi$
$284$	9.64699e7	0.249906
$285$	1.50051e9	3.83957
$286$	0	0
$287$	−4.69911e8	−1.17335
$288$	6.83428e8	1.68585
$289$	−3.01858e7	−0.0735631
$290$	1.36375e8	0.328355
$291$	4.44979e8	1.05856
$292$	−3.31426e8	−0.779017
$293$	−4.69303e8	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$293$	−4.69303e8	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$294$	−1.60378e8	−0.368068
$295$	−8.12882e8	−1.84353
$296$	−2.21384e8	−0.496164
$297$	0	0
$298$	−6.70976e7	−0.146876
$299$	−2.53220e7	−0.0547833
$300$	2.25871e8	0.482987
$301$	4.59995e8	0.972233
$302$	−1.70587e8	−0.356387
$303$	1.23821e9	2.55708
$304$	6.72073e8	1.37202
$305$	1.28507e8	0.259345
$306$	−3.11025e8	−0.620540
$307$	−6.07426e7	−0.119814	−0.0599072	−	0.998204i	$-0.519080\pi$
$307$	−6.07426e7	−0.119814	−0.0599072	+	0.998204i	$0.519080\pi$
$308$	0	0
$309$	2.00232e8	0.386081
$310$	9.08643e7	0.173232
$311$	3.59605e8	0.677898	0.338949	−	0.940805i	$-0.389929\pi$
$311$	3.59605e8	0.677898	0.338949	+	0.940805i	$0.389929\pi$
$312$	−5.29310e7	−0.0986663
$313$	4.47128e8	0.824189	0.412094	−	0.911141i	$-0.364797\pi$
$313$	4.47128e8	0.824189	0.412094	+	0.911141i	$0.364797\pi$
$314$	−1.29335e8	−0.235757
$315$	−1.68191e9	−3.03191
$316$	−2.81871e8	−0.502511
$317$	8.38315e8	1.47809	0.739043	−	0.673658i	$-0.235278\pi$
$317$	8.38315e8	1.47809	0.739043	+	0.673658i	$0.235278\pi$
$318$	−6.78345e7	−0.118292
$319$	0	0
$320$	3.05221e8	0.520702
$321$	1.25704e9	2.12119
$322$	1.40963e8	0.235294
$323$	−1.12075e9	−1.85055
$324$	−6.39428e8	−1.04444
$325$	−1.79480e7	−0.0290017
$326$	−6.17232e6	−0.00986703
$327$	1.05467e8	0.166802
$328$	3.46559e8	0.542275
$329$	−9.74587e8	−1.50881
$330$	0	0
$331$	8.41816e8	1.27591	0.637954	−	0.770075i	$-0.279781\pi$
$331$	8.41816e8	1.27591	0.637954	+	0.770075i	$0.279781\pi$
$332$	6.18742e8	0.927953
$333$	1.14853e9	1.70446
$334$	7.05125e7	0.103551
$335$	−1.17607e9	−1.70914
$336$	−1.12043e9	−1.61137
$337$	4.36327e8	0.621022	0.310511	−	0.950570i	$-0.399500\pi$
$337$	4.36327e8	0.621022	0.310511	+	0.950570i	$0.399500\pi$
$338$	−2.21047e8	−0.311370
$339$	4.85104e6	0.00676295
$340$	−7.18695e8	−0.991673
$341$	0	0
$342$	9.16951e8	1.23952
$343$	−3.18201e8	−0.425767
$344$	−3.39246e8	−0.449325
$345$	8.82585e8	1.15715
$346$	2.92826e7	0.0380052
$347$	7.57899e8	0.973774	0.486887	−	0.873465i	$-0.338132\pi$
$347$	7.57899e8	0.973774	0.486887	+	0.873465i	$0.338132\pi$
$348$	−1.13177e9	−1.43957
$349$	2.18017e8	0.274537	0.137269	−	0.990534i	$-0.456168\pi$
$349$	2.18017e8	0.274537	0.137269	+	0.990534i	$0.456168\pi$
$350$	9.99136e7	0.124562
$351$	1.40783e8	0.173770
$352$	0	0
$353$	−2.63455e8	−0.318783	−0.159392	−	0.987215i	$-0.550953\pi$
$353$	−2.63455e8	−0.318783	−0.159392	+	0.987215i	$0.550953\pi$
$354$	−7.38820e8	−0.885171
$355$	2.67182e8	0.316962
$356$	4.48851e8	0.527263
$357$	1.86843e9	2.17339
$358$	7.28151e6	0.00838747
$359$	6.63672e8	0.757047	0.378523	−	0.925592i	$-0.376432\pi$
$359$	6.63672e8	0.757047	0.378523	+	0.925592i	$0.376432\pi$
$360$	1.24041e9	1.40122
$361$	2.41029e9	2.69646
$362$	5.31171e7	0.0588511
$363$	0	0
$364$	1.01345e8	0.110141
$365$	−9.17914e8	−0.988045
$366$	1.16799e8	0.124525
$367$	1.22959e9	1.29846	0.649231	−	0.760591i	$-0.275091\pi$
$367$	1.22959e9	1.29846	0.649231	+	0.760591i	$0.275091\pi$
$368$	3.95306e8	0.413491
$369$	−1.79793e9	−1.86286
$370$	−2.90655e8	−0.298313
$371$	2.73986e8	0.278560
$372$	−7.54079e8	−0.759480
$373$	3.64020e7	0.0363198	0.0181599	−	0.999835i	$-0.494219\pi$
$373$	3.64020e7	0.0363198	0.0181599	+	0.999835i	$0.494219\pi$
$374$	0	0
$375$	−1.41382e9	−1.38447
$376$	7.18758e8	0.697309
$377$	8.99321e7	0.0864411
$378$	−7.83718e8	−0.746343
$379$	−5.73489e8	−0.541113	−0.270557	−	0.962704i	$-0.587208\pi$
$379$	−5.73489e8	−0.541113	−0.270557	+	0.962704i	$0.587208\pi$
$380$	2.11883e9	1.98086
$381$	2.14980e9	1.99141
$382$	−5.29421e8	−0.485937
$383$	−2.09853e9	−1.90862	−0.954309	−	0.298822i	$-0.903406\pi$
$383$	−2.09853e9	−1.90862	−0.954309	+	0.298822i	$0.903406\pi$
$384$	1.86994e9	1.68527
$385$	0	0
$386$	−3.45236e8	−0.305535
$387$	1.75999e9	1.54355
$388$	6.28340e8	0.546115
$389$	−7.10772e8	−0.612219	−0.306110	−	0.951996i	$-0.599027\pi$
$389$	−7.10772e8	−0.612219	−0.306110	+	0.951996i	$0.599027\pi$
$390$	−6.94931e7	−0.0593219
$391$	−6.59213e8	−0.557709
$392$	−4.77731e8	−0.400574
$393$	−3.78088e9	−3.14209
$394$	3.03327e8	0.249847
$395$	−7.80665e8	−0.637345
$396$	0	0
$397$	1.92902e8	0.154729	0.0773644	−	0.997003i	$-0.475350\pi$
$397$	1.92902e8	0.154729	0.0773644	+	0.997003i	$0.475350\pi$
$398$	−7.01624e8	−0.557845
$399$	−5.50843e9	−4.34133
$400$	2.80189e8	0.218898
$401$	−7.89590e7	−0.0611500	−0.0305750	−	0.999532i	$-0.509734\pi$
$401$	−7.89590e7	−0.0611500	−0.0305750	+	0.999532i	$0.509734\pi$
$402$	−1.06892e9	−0.820641
$403$	5.99201e7	0.0456042
$404$	1.74843e9	1.31921
$405$	−1.77095e9	−1.32469
$406$	−5.00638e8	−0.371264
$407$	0	0
$408$	−1.37797e9	−1.00445
$409$	−1.85156e9	−1.33815	−0.669076	−	0.743194i	$-0.733310\pi$
$409$	−1.85156e9	−1.33815	−0.669076	+	0.743194i	$0.733310\pi$
$410$	4.54998e8	0.326036
$411$	−2.50831e9	−1.78211
$412$	2.82741e8	0.199182
$413$	2.98412e9	2.08445
$414$	5.39340e8	0.373561
$415$	1.71366e9	1.17694
$416$	−1.14053e8	−0.0776751
$417$	1.16437e9	0.786349
$418$	0	0
$419$	−2.08403e9	−1.38406	−0.692029	−	0.721869i	$-0.743283\pi$
$419$	−2.08403e9	−1.38406	−0.692029	+	0.721869i	$0.743283\pi$
$420$	−3.53235e9	−2.32643
$421$	3.10519e8	0.202815	0.101408	−	0.994845i	$-0.467665\pi$
$421$	3.10519e8	0.202815	0.101408	+	0.994845i	$0.467665\pi$
$422$	3.01161e8	0.195076
$423$	−3.72887e9	−2.39544
$424$	−2.02064e8	−0.128739
$425$	−4.67245e8	−0.295245
$426$	2.42838e8	0.152189
$427$	−4.71754e8	−0.293237
$428$	1.77502e9	1.09434
$429$	0	0
$430$	−4.45396e8	−0.270151
$431$	−1.71710e9	−1.03306	−0.516530	−	0.856269i	$-0.672777\pi$
$431$	−1.71710e9	−1.03306	−0.516530	+	0.856269i	$0.672777\pi$
$432$	−2.19779e9	−1.31158
$433$	3.81261e8	0.225691	0.112846	−	0.993613i	$-0.464003\pi$
$433$	3.81261e8	0.225691	0.112846	+	0.993613i	$0.464003\pi$
$434$	−3.33566e8	−0.195870
$435$	−3.13454e9	−1.82584
$436$	1.48927e8	0.0860540
$437$	1.94347e9	1.11402
$438$	−8.34281e8	−0.474409
$439$	−1.04531e9	−0.589682	−0.294841	−	0.955546i	$-0.595267\pi$
$439$	−1.04531e9	−0.589682	−0.294841	+	0.955546i	$0.595267\pi$
$440$	0	0
$441$	2.47844e9	1.37608
$442$	5.19052e7	0.0285912
$443$	3.17253e9	1.73378	0.866889	−	0.498502i	$-0.166116\pi$
$443$	3.17253e9	1.73378	0.866889	+	0.498502i	$0.166116\pi$
$444$	2.41213e9	1.30786
$445$	1.24313e9	0.668739
$446$	1.20391e8	0.0642571
$447$	1.54222e9	0.816712
$448$	−1.12047e9	−0.588747
$449$	−3.26325e8	−0.170133	−0.0850665	−	0.996375i	$-0.527110\pi$
$449$	−3.26325e8	−0.170133	−0.0850665	+	0.996375i	$0.527110\pi$
$450$	3.82280e8	0.197760
$451$	0	0
$452$	6.85001e6	0.00348904
$453$	3.92089e9	1.98171
$454$	−6.39228e8	−0.320598
$455$	2.80685e8	0.139694
$456$	4.06247e9	2.00638
$457$	−6.45607e8	−0.316418	−0.158209	−	0.987406i	$-0.550572\pi$
$457$	−6.45607e8	−0.316418	−0.158209	+	0.987406i	$0.550572\pi$
$458$	−1.16547e9	−0.566856
$459$	3.66505e9	1.76903
$460$	1.24627e9	0.596980
$461$	−2.91854e9	−1.38744	−0.693718	−	0.720247i	$-0.744028\pi$
$461$	−2.91854e9	−1.38744	−0.693718	+	0.720247i	$0.744028\pi$
$462$	0	0
$463$	6.58609e8	0.308386	0.154193	−	0.988041i	$-0.450722\pi$
$463$	6.58609e8	0.308386	0.154193	+	0.988041i	$0.450722\pi$
$464$	−1.40395e9	−0.652436
$465$	−2.08849e9	−0.963266
$466$	3.83343e8	0.175484
$467$	−4.28948e9	−1.94893	−0.974463	−	0.224546i	$-0.927910\pi$
$467$	−4.28948e9	−1.94893	−0.974463	+	0.224546i	$0.927910\pi$
$468$	3.87758e8	0.174864
$469$	4.31739e9	1.93249
$470$	9.43657e8	0.419249
$471$	2.97273e9	1.31094
$472$	−2.20079e9	−0.963343
$473$	0	0
$474$	−7.09538e8	−0.306021
$475$	1.37751e9	0.589750
$476$	2.63835e9	1.12127
$477$	1.04830e9	0.442252
$478$	1.21240e9	0.507748
$479$	−1.90987e9	−0.794015	−0.397008	−	0.917815i	$-0.629951\pi$
$479$	−1.90987e9	−0.794015	−0.397008	+	0.917815i	$0.629951\pi$
$480$	3.97528e9	1.64068
$481$	−1.91671e8	−0.0785323
$482$	1.25868e9	0.511977
$483$	−3.24000e9	−1.30837
$484$	0	0
$485$	1.74024e9	0.692650
$486$	−1.48326e8	−0.0586126
$487$	−2.36533e9	−0.927985	−0.463992	−	0.885839i	$-0.653584\pi$
$487$	−2.36533e9	−0.927985	−0.463992	+	0.885839i	$0.653584\pi$
$488$	3.47919e8	0.135522
$489$	1.41869e8	0.0548662
$490$	−6.27213e8	−0.240840
$491$	−2.03801e9	−0.777001	−0.388501	−	0.921448i	$-0.627007\pi$
$491$	−2.03801e9	−0.777001	−0.388501	+	0.921448i	$0.627007\pi$
$492$	−3.77600e9	−1.42940
$493$	2.34123e9	0.879994
$494$	−1.53025e8	−0.0571107
$495$	0	0
$496$	−9.35423e8	−0.344209
$497$	−9.80831e8	−0.358383
$498$	1.55752e9	0.565109
$499$	1.86875e9	0.673285	0.336643	−	0.941633i	$-0.390709\pi$
$499$	1.86875e9	0.673285	0.336643	+	0.941633i	$0.390709\pi$
$500$	−1.99641e9	−0.714257
$501$	−1.62070e9	−0.575800
$502$	−3.74878e8	−0.132259
$503$	2.39098e9	0.837698	0.418849	−	0.908056i	$-0.362434\pi$
$503$	2.39098e9	0.837698	0.418849	+	0.908056i	$0.362434\pi$
$504$	−4.55358e9	−1.58433
$505$	4.84244e9	1.67319
$506$	0	0
$507$	5.08070e9	1.73139
$508$	3.03566e9	1.02738
$509$	−2.85560e9	−0.959810	−0.479905	−	0.877320i	$-0.659329\pi$
$509$	−2.85560e9	−0.959810	−0.479905	+	0.877320i	$0.659329\pi$
$510$	−1.80913e9	−0.603913
$511$	3.36969e9	1.11716
$512$	3.07511e9	1.01255
$513$	−1.08051e10	−3.53362
$514$	−7.95592e8	−0.258416
$515$	7.83076e8	0.252626
$516$	3.69632e9	1.18439
$517$	0	0
$518$	1.06700e9	0.337296
$519$	−6.73050e8	−0.211330
$520$	−2.07005e8	−0.0645608
$521$	1.62591e9	0.503691	0.251845	−	0.967767i	$-0.418963\pi$
$521$	1.62591e9	0.503691	0.251845	+	0.967767i	$0.418963\pi$
$522$	−1.91549e9	−0.589432
$523$	2.57830e9	0.788092	0.394046	−	0.919091i	$-0.371075\pi$
$523$	2.57830e9	0.788092	0.394046	+	0.919091i	$0.371075\pi$
$524$	−5.33886e9	−1.62102
$525$	−2.29648e9	−0.692636
$526$	−6.70489e8	−0.200882
$527$	1.55992e9	0.464263
$528$	0	0
$529$	−2.26170e9	−0.664263
$530$	−2.65290e8	−0.0774026
$531$	1.14175e10	3.30934
$532$	−7.77829e9	−2.23972
$533$	3.00046e8	0.0858307
$534$	1.12987e9	0.321095
$535$	4.91607e9	1.38797
$536$	−3.18408e9	−0.893114
$537$	−1.67363e8	−0.0466390
$538$	9.23000e8	0.255543
$539$	0	0
$540$	−6.92893e9	−1.89360
$541$	4.71333e8	0.127979	0.0639893	−	0.997951i	$-0.479618\pi$
$541$	4.71333e8	0.127979	0.0639893	+	0.997951i	$0.479618\pi$
$542$	−1.01713e9	−0.274396
$543$	−1.22088e9	−0.327245
$544$	−2.96919e9	−0.790754
$545$	4.12466e8	0.109144
$546$	2.55111e8	0.0670741
$547$	−6.65818e9	−1.73940	−0.869700	−	0.493580i	$-0.835688\pi$
$547$	−6.65818e9	−1.73940	−0.869700	+	0.493580i	$0.835688\pi$
$548$	−3.54191e9	−0.919401
$549$	−1.80498e9	−0.465553
$550$	0	0
$551$	−6.90232e9	−1.75778
$552$	2.38950e9	0.604672
$553$	2.86584e9	0.720634
$554$	−1.54541e9	−0.386152
$555$	6.68060e9	1.65879
$556$	1.64417e9	0.405682
$557$	−4.60389e9	−1.12884	−0.564420	−	0.825488i	$-0.690900\pi$
$557$	−4.60389e9	−1.12884	−0.564420	+	0.825488i	$0.690900\pi$
$558$	−1.27626e9	−0.310970
$559$	−2.93714e8	−0.0711187
$560$	−4.38182e9	−1.05438
$561$	0	0
$562$	−4.11376e8	−0.0977601
$563$	6.42800e9	1.51809	0.759043	−	0.651040i	$-0.225667\pi$
$563$	6.42800e9	1.51809	0.759043	+	0.651040i	$0.225667\pi$
$564$	−7.83137e9	−1.83806
$565$	1.89717e7	0.00442523
$566$	−1.55695e9	−0.360924
$567$	6.50121e9	1.49780
$568$	7.23363e8	0.165629
$569$	5.62798e9	1.28074	0.640368	−	0.768068i	$-0.278782\pi$
$569$	5.62798e9	1.28074	0.640368	+	0.768068i	$0.278782\pi$
$570$	5.33361e9	1.20631
$571$	4.73895e9	1.06526	0.532631	−	0.846348i	$-0.321204\pi$
$571$	4.73895e9	1.06526	0.532631	+	0.846348i	$0.321204\pi$
$572$	0	0
$573$	1.21686e10	2.70208
$574$	−1.67031e9	−0.368642
$575$	8.10237e8	0.177736
$576$	−4.28705e9	−0.934716
$577$	7.10047e9	1.53876	0.769382	−	0.638789i	$-0.220564\pi$
$577$	7.10047e9	1.53876	0.769382	+	0.638789i	$0.220564\pi$
$578$	−1.07296e8	−0.0231119
$579$	7.93513e9	1.69894
$580$	−4.42619e9	−0.941959
$581$	−6.29089e9	−1.33075
$582$	1.58169e9	0.332575
$583$	0	0
$584$	−2.48515e9	−0.516306
$585$	1.07393e9	0.221784
$586$	−1.66815e9	−0.342447
$587$	5.86107e9	1.19603	0.598017	−	0.801483i	$-0.295956\pi$
$587$	5.86107e9	1.19603	0.598017	+	0.801483i	$0.295956\pi$
$588$	5.20521e9	1.05589
$589$	−4.59888e9	−0.927361
$590$	−2.88941e9	−0.579198
$591$	−6.97187e9	−1.38929
$592$	2.99221e9	0.592743
$593$	−3.00227e9	−0.591232	−0.295616	−	0.955307i	$-0.595525\pi$
$593$	−3.00227e9	−0.591232	−0.295616	+	0.955307i	$0.595525\pi$
$594$	0	0
$595$	7.30714e9	1.42213
$596$	2.17772e9	0.421346
$597$	1.61266e10	3.10193
$598$	−9.00075e7	−0.0172117
$599$	−6.20963e9	−1.18052	−0.590258	−	0.807215i	$-0.700974\pi$
$599$	−6.20963e9	−1.18052	−0.590258	+	0.807215i	$0.700974\pi$
$600$	1.69365e9	0.320107
$601$	−8.43380e9	−1.58476	−0.792379	−	0.610029i	$-0.791158\pi$
$601$	−8.43380e9	−1.58476	−0.792379	+	0.610029i	$0.791158\pi$
$602$	1.63506e9	0.305455
$603$	1.65188e10	3.06809
$604$	5.53657e9	1.02238
$605$	0	0
$606$	4.40124e9	0.803379
$607$	−7.72609e9	−1.40217	−0.701083	−	0.713080i	$-0.747300\pi$
$607$	−7.72609e9	−1.40217	−0.701083	+	0.713080i	$0.747300\pi$
$608$	8.75364e9	1.57952
$609$	1.15070e10	2.06444
$610$	4.56782e8	0.0814807
$611$	6.22290e8	0.110369
$612$	1.00946e10	1.78016
$613$	1.10992e10	1.94617	0.973087	−	0.230439i	$-0.0740162\pi$
$613$	1.10992e10	1.94617	0.973087	+	0.230439i	$0.0740162\pi$
$614$	−2.15911e8	−0.0376431
$615$	−1.04580e10	−1.81294
$616$	0	0
$617$	3.83189e9	0.656772	0.328386	−	0.944544i	$-0.393495\pi$
$617$	3.83189e9	0.656772	0.328386	+	0.944544i	$0.393495\pi$
$618$	7.11729e8	0.121298
$619$	−8.61390e9	−1.45976	−0.729882	−	0.683574i	$-0.760425\pi$
$619$	−8.61390e9	−1.45976	−0.729882	+	0.683574i	$0.760425\pi$
$620$	−2.94909e9	−0.496954
$621$	−6.35546e9	−1.06494
$622$	1.27822e9	0.212981
$623$	−4.56357e9	−0.756130
$624$	7.15412e8	0.117872
$625$	−7.40144e9	−1.21265
$626$	1.58933e9	0.258942
$627$	0	0
$628$	4.19770e9	0.676321
$629$	−4.98982e9	−0.799480
$630$	−5.97839e9	−0.952560
$631$	−4.54713e9	−0.720501	−0.360251	−	0.932856i	$-0.617309\pi$
$631$	−4.54713e9	−0.720501	−0.360251	+	0.932856i	$0.617309\pi$
$632$	−2.11356e9	−0.333047
$633$	−6.92207e9	−1.08473
$634$	2.97981e9	0.464383
$635$	8.40752e9	1.30305
$636$	2.20163e9	0.339347
$637$	−4.13613e8	−0.0634024
$638$	0	0
$639$	−3.75276e9	−0.568981
$640$	7.31306e9	1.10273
$641$	−4.89028e9	−0.733383	−0.366692	−	0.930343i	$-0.619510\pi$
$641$	−4.89028e9	−0.733383	−0.366692	+	0.930343i	$0.619510\pi$
$642$	4.46816e9	0.666433
$643$	−5.21443e8	−0.0773515	−0.0386758	−	0.999252i	$-0.512314\pi$
$643$	−5.21443e8	−0.0773515	−0.0386758	+	0.999252i	$0.512314\pi$
$644$	−4.57510e9	−0.674994
$645$	1.02373e10	1.50219
$646$	−3.98374e9	−0.581403
$647$	−9.73790e9	−1.41351	−0.706757	−	0.707456i	$-0.749843\pi$
$647$	−9.73790e9	−1.41351	−0.706757	+	0.707456i	$0.749843\pi$
$648$	−4.79464e9	−0.692219
$649$	0	0
$650$	−6.37965e7	−0.00911172
$651$	7.66689e9	1.08915
$652$	2.00328e8	0.0283058
$653$	−1.00912e10	−1.41823	−0.709115	−	0.705093i	$-0.750905\pi$
$653$	−1.00912e10	−1.41823	−0.709115	+	0.705093i	$0.750905\pi$
$654$	3.74886e8	0.0524055
$655$	−1.47864e10	−2.05598
$656$	−4.68407e9	−0.647829
$657$	1.28928e10	1.77365
$658$	−3.46419e9	−0.474036
$659$	−4.52574e9	−0.616014	−0.308007	−	0.951384i	$-0.599662\pi$
$659$	−4.52574e9	−0.616014	−0.308007	+	0.951384i	$0.599662\pi$
$660$	0	0
$661$	−8.94120e9	−1.20418	−0.602089	−	0.798429i	$-0.705665\pi$
$661$	−8.94120e9	−1.20418	−0.602089	+	0.798429i	$0.705665\pi$
$662$	2.99225e9	0.400863
$663$	−1.19302e9	−0.158983
$664$	4.63953e9	0.615015
$665$	−2.15426e10	−2.84068
$666$	4.08246e9	0.535503
$667$	−4.05986e9	−0.529750
$668$	−2.28855e9	−0.297059
$669$	−2.76714e9	−0.357305
$670$	−4.18037e9	−0.536974
$671$	0	0
$672$	−1.45934e10	−1.85508
$673$	2.02469e8	0.0256039	0.0128020	−	0.999918i	$-0.495925\pi$
$673$	2.02469e8	0.0256039	0.0128020	+	0.999918i	$0.495925\pi$
$674$	1.55093e9	0.195112
$675$	−4.50470e9	−0.563770
$676$	7.17429e9	0.893235
$677$	1.49069e10	1.84640	0.923202	−	0.384315i	$-0.125562\pi$
$677$	1.49069e10	1.84640	0.923202	+	0.384315i	$0.125562\pi$
$678$	1.72431e7	0.00212477
$679$	−6.38848e9	−0.783165
$680$	−5.38902e9	−0.657247
$681$	1.46924e10	1.78270
$682$	0	0
$683$	6.60107e9	0.792760	0.396380	−	0.918087i	$-0.370266\pi$
$683$	6.60107e9	0.792760	0.396380	+	0.918087i	$0.370266\pi$
$684$	−2.97605e10	−3.55585
$685$	−9.80961e9	−1.16610
$686$	−1.13105e9	−0.133767
$687$	2.67880e10	3.15204
$688$	4.58523e9	0.536787
$689$	−1.74944e8	−0.0203766
$690$	3.13717e9	0.363552
$691$	3.59633e9	0.414655	0.207327	−	0.978272i	$-0.433523\pi$
$691$	3.59633e9	0.414655	0.207327	+	0.978272i	$0.433523\pi$
$692$	−9.50393e8	−0.109026
$693$	0	0
$694$	2.69397e9	0.305939
$695$	4.55368e9	0.514535
$696$	−8.48641e9	−0.954096
$697$	7.81118e9	0.873780
$698$	7.74946e8	0.0862537
$699$	−8.81101e9	−0.975788
$700$	−3.24279e9	−0.357335
$701$	−3.23118e9	−0.354281	−0.177140	−	0.984186i	$-0.556685\pi$
$701$	−3.23118e9	−0.354281	−0.177140	+	0.984186i	$0.556685\pi$
$702$	5.00417e8	0.0545949
$703$	1.47108e10	1.59696
$704$	0	0
$705$	−2.16896e10	−2.33126
$706$	−9.36459e8	−0.100155
$707$	−1.77767e10	−1.89184
$708$	2.39791e10	2.53931
$709$	−4.34061e9	−0.457392	−0.228696	−	0.973498i	$-0.573446\pi$
$709$	−4.34061e9	−0.457392	−0.228696	+	0.973498i	$0.573446\pi$
$710$	9.49703e8	0.0995826
$711$	1.09650e10	1.14410
$712$	3.36563e9	0.349452
$713$	−2.70501e9	−0.279483
$714$	6.64138e9	0.682833
$715$	0	0
$716$	−2.36328e8	−0.0240614
$717$	−2.78666e10	−2.82337
$718$	2.35904e9	0.237848
$719$	−1.90019e10	−1.90654	−0.953269	−	0.302122i	$-0.902305\pi$
$719$	−1.90019e10	−1.90654	−0.953269	+	0.302122i	$0.902305\pi$
$720$	−1.67653e10	−1.67397
$721$	−2.87470e9	−0.285640
$722$	8.56742e9	0.847168
$723$	−2.89303e10	−2.84688
$724$	−1.72396e9	−0.168828
$725$	−2.87760e9	−0.280444
$726$	0	0
$727$	1.69617e9	0.163719	0.0818596	−	0.996644i	$-0.473914\pi$
$727$	1.69617e9	0.163719	0.0818596	+	0.996644i	$0.473914\pi$
$728$	7.59921e8	0.0729976
$729$	−8.71251e9	−0.832908
$730$	−3.26275e9	−0.310423
$731$	−7.64635e9	−0.724008
$732$	−3.79082e9	−0.357227
$733$	9.95818e9	0.933933	0.466967	−	0.884275i	$-0.345347\pi$
$733$	9.95818e9	0.933933	0.466967	+	0.884275i	$0.345347\pi$
$734$	4.37061e9	0.407949
$735$	1.44163e10	1.33921
$736$	5.14879e9	0.476028
$737$	0	0
$738$	−6.39077e9	−0.585270
$739$	1.41060e10	1.28573	0.642865	−	0.765980i	$-0.277746\pi$
$739$	1.41060e10	1.28573	0.642865	+	0.765980i	$0.277746\pi$
$740$	9.43347e9	0.855777
$741$	3.51723e9	0.317568
$742$	9.73888e8	0.0875176
$743$	−6.02795e9	−0.539149	−0.269575	−	0.962979i	$-0.586883\pi$
$743$	−6.02795e9	−0.539149	−0.269575	+	0.962979i	$0.586883\pi$
$744$	−5.65433e9	−0.503357
$745$	6.03137e9	0.534403
$746$	1.29392e8	0.0114109
$747$	−2.40696e10	−2.11274
$748$	0	0
$749$	−1.80471e10	−1.56935
$750$	−5.02545e9	−0.434971
$751$	−2.76640e9	−0.238328	−0.119164	−	0.992875i	$-0.538021\pi$
$751$	−2.76640e9	−0.238328	−0.119164	+	0.992875i	$0.538021\pi$
$752$	−9.71469e9	−0.833041
$753$	8.61644e9	0.735437
$754$	3.19666e8	0.0271579
$755$	1.53340e10	1.29670
$756$	2.54363e10	2.14105
$757$	1.70574e10	1.42915	0.714574	−	0.699560i	$-0.246621\pi$
$757$	1.70574e10	1.42915	0.714574	+	0.699560i	$0.246621\pi$
$758$	−2.03848e9	−0.170006
$759$	0	0
$760$	1.58877e10	1.31284
$761$	−2.32728e9	−0.191427	−0.0957134	−	0.995409i	$-0.530513\pi$
$761$	−2.32728e9	−0.191427	−0.0957134	+	0.995409i	$0.530513\pi$
$762$	7.64150e9	0.625657
$763$	−1.51418e9	−0.123407
$764$	1.71829e10	1.39402
$765$	2.79579e10	2.25782
$766$	−7.45927e9	−0.599647
$767$	−1.90541e9	−0.152477
$768$	−3.34297e9	−0.266298
$769$	−1.81837e10	−1.44191	−0.720957	−	0.692980i	$-0.756297\pi$
$769$	−1.81837e10	−1.44191	−0.720957	+	0.692980i	$0.756297\pi$
$770$	0	0
$771$	1.82864e10	1.43694
$772$	1.12050e10	0.876495
$773$	7.25197e9	0.564713	0.282357	−	0.959310i	$-0.408884\pi$
$773$	7.25197e9	0.564713	0.282357	+	0.959310i	$0.408884\pi$
$774$	6.25592e9	0.484951
$775$	−1.91729e9	−0.147955
$776$	4.71151e9	0.361946
$777$	−2.45247e10	−1.87556
$778$	−2.52646e9	−0.192346
$779$	−2.30286e10	−1.74537
$780$	2.25546e9	0.170178
$781$	0	0
$782$	−2.34319e9	−0.175220
$783$	2.25717e10	1.68035
$784$	6.45698e9	0.478546
$785$	1.16259e10	0.857793
$786$	−1.34392e10	−0.987177
$787$	−2.46484e10	−1.80251	−0.901255	−	0.433289i	$-0.857353\pi$
$787$	−2.46484e10	−1.80251	−0.901255	+	0.433289i	$0.857353\pi$
$788$	−9.84477e9	−0.716743
$789$	1.54110e10	1.11702
$790$	−2.77489e9	−0.200240
$791$	−6.96456e7	−0.00500352
$792$	0	0
$793$	3.01223e8	0.0214502
$794$	6.85676e8	0.0486124
$795$	6.09760e9	0.430402
$796$	2.27719e10	1.60031
$797$	−1.79632e10	−1.25684	−0.628419	−	0.777875i	$-0.716297\pi$
$797$	−1.79632e10	−1.25684	−0.628419	+	0.777875i	$0.716297\pi$
$798$	−1.95798e10	−1.36395
$799$	1.62003e10	1.12359
$800$	3.64942e9	0.252005
$801$	−1.74607e10	−1.20046
$802$	−2.80662e8	−0.0192120
$803$	0	0
$804$	3.46927e10	2.35419
$805$	−1.26711e10	−0.856110
$806$	2.12987e8	0.0143278
$807$	−2.12148e10	−1.42096
$808$	1.31103e10	0.874328
$809$	−2.28371e9	−0.151643	−0.0758213	−	0.997121i	$-0.524158\pi$
$809$	−2.28371e9	−0.151643	−0.0758213	+	0.997121i	$0.524158\pi$
$810$	−6.29488e9	−0.416189
$811$	1.63818e10	1.07842	0.539212	−	0.842170i	$-0.318722\pi$
$811$	1.63818e10	1.07842	0.539212	+	0.842170i	$0.318722\pi$
$812$	1.62487e10	1.06505
$813$	2.33783e10	1.52580
$814$	0	0
$815$	5.54826e8	0.0359009
$816$	1.86245e10	1.19997
$817$	2.25427e10	1.44620
$818$	−6.58140e9	−0.420419
$819$	−3.94242e9	−0.250766
$820$	−1.47674e10	−0.935308
$821$	−1.67011e10	−1.05328	−0.526639	−	0.850089i	$-0.676548\pi$
$821$	−1.67011e10	−1.05328	−0.526639	+	0.850089i	$0.676548\pi$
$822$	−8.91584e9	−0.559901
$823$	−6.83158e7	−0.00427190	−0.00213595	−	0.999998i	$-0.500680\pi$
$823$	−6.83158e7	−0.00427190	−0.00213595	+	0.999998i	$0.500680\pi$
$824$	2.12009e9	0.132011
$825$	0	0
$826$	1.06071e10	0.654888
$827$	−3.81992e9	−0.234847	−0.117423	−	0.993082i	$-0.537463\pi$
$827$	−3.81992e9	−0.234847	−0.117423	+	0.993082i	$0.537463\pi$
$828$	−1.75048e10	−1.07164
$829$	3.11968e9	0.190182	0.0950909	−	0.995469i	$-0.469686\pi$
$829$	3.11968e9	0.190182	0.0950909	+	0.995469i	$0.469686\pi$
$830$	6.09124e9	0.369770
$831$	3.55206e10	2.14722
$832$	7.15442e8	0.0430668
$833$	−1.07677e10	−0.645454
$834$	4.13879e9	0.247054
$835$	−6.33833e9	−0.376766
$836$	0	0
$837$	1.50391e10	0.886509
$838$	−7.40773e9	−0.434842
$839$	8.26757e9	0.483293	0.241647	−	0.970364i	$-0.422312\pi$
$839$	8.26757e9	0.483293	0.241647	+	0.970364i	$0.422312\pi$
$840$	−2.64867e10	−1.54188
$841$	−2.83108e9	−0.164122
$842$	1.10375e9	0.0637201
$843$	9.45533e9	0.543601
$844$	−9.77445e9	−0.559620
$845$	1.98698e10	1.13291
$846$	−1.32544e10	−0.752597
$847$	0	0
$848$	2.73109e9	0.153798
$849$	3.57859e10	2.00694
$850$	−1.66083e9	−0.0927597
$851$	8.65272e9	0.481282
$852$	−7.88154e9	−0.436589
$853$	3.31978e10	1.83142	0.915709	−	0.401842i	$-0.131630\pi$
$853$	3.31978e10	1.83142	0.915709	+	0.401842i	$0.131630\pi$
$854$	−1.67686e9	−0.0921286
$855$	−8.24243e10	−4.50997
$856$	1.33097e10	0.725288
$857$	8.65934e9	0.469950	0.234975	−	0.972001i	$-0.424499\pi$
$857$	8.65934e9	0.469950	0.234975	+	0.972001i	$0.424499\pi$
$858$	0	0
$859$	−1.89906e10	−1.02227	−0.511133	−	0.859502i	$-0.670774\pi$
$859$	−1.89906e10	−1.02227	−0.511133	+	0.859502i	$0.670774\pi$
$860$	1.44557e10	0.774990
$861$	3.83915e10	2.04986
$862$	−6.10348e9	−0.324565
$863$	1.78163e10	0.943582	0.471791	−	0.881710i	$-0.343608\pi$
$863$	1.78163e10	0.943582	0.471791	+	0.881710i	$0.343608\pi$
$864$	−2.86259e10	−1.50994
$865$	−2.63219e9	−0.138281
$866$	1.35520e9	0.0709073
$867$	2.46616e9	0.128515
$868$	1.08262e10	0.561896
$869$	0	0
$870$	−1.11418e10	−0.573638
$871$	−2.75673e9	−0.141361
$872$	1.11670e9	0.0570336
$873$	−2.44430e10	−1.24338
$874$	6.90810e9	0.350000
$875$	2.02980e10	1.02429
$876$	2.70774e10	1.36095
$877$	−2.25228e9	−0.112752	−0.0563760	−	0.998410i	$-0.517955\pi$
$877$	−2.25228e9	−0.112752	−0.0563760	+	0.998410i	$0.517955\pi$
$878$	−3.71557e9	−0.185266
$879$	3.83419e10	1.90420
$880$	0	0
$881$	−7.42229e9	−0.365698	−0.182849	−	0.983141i	$-0.558532\pi$
$881$	−7.42229e9	−0.365698	−0.182849	+	0.983141i	$0.558532\pi$
$882$	8.80966e9	0.432334
$883$	−2.43666e10	−1.19106	−0.595529	−	0.803334i	$-0.703057\pi$
$883$	−2.43666e10	−1.19106	−0.595529	+	0.803334i	$0.703057\pi$
$884$	−1.68463e9	−0.0820204
$885$	6.64121e10	3.22067
$886$	1.12768e10	0.544716
$887$	−2.93749e10	−1.41333	−0.706666	−	0.707547i	$-0.749802\pi$
$887$	−2.93749e10	−1.41333	−0.706666	+	0.707547i	$0.749802\pi$
$888$	1.80870e10	0.866803
$889$	−3.08643e10	−1.47333
$890$	4.41874e9	0.210104
$891$	0	0
$892$	−3.90739e9	−0.184336
$893$	−4.77610e10	−2.24436
$894$	5.48184e9	0.256593
$895$	−6.54531e8	−0.0305176
$896$	−2.68464e10	−1.24683
$897$	2.06879e9	0.0957069
$898$	−1.15993e9	−0.0534521
$899$	9.60697e9	0.440989
$900$	−1.24072e10	−0.567318
$901$	−4.55437e9	−0.207440
$902$	0	0
$903$	−3.75814e10	−1.69850
$904$	5.13636e7	0.00231242
$905$	−4.77467e9	−0.214128
$906$	1.39369e10	0.622612
$907$	−1.28310e9	−0.0570998	−0.0285499	−	0.999592i	$-0.509089\pi$
$907$	−1.28310e9	−0.0570998	−0.0285499	+	0.999592i	$0.509089\pi$
$908$	2.07467e10	0.919707
$909$	−6.80156e10	−3.00355
$910$	9.97700e8	0.0438889
$911$	3.24621e10	1.42253	0.711266	−	0.702923i	$-0.248122\pi$
$911$	3.24621e10	1.42253	0.711266	+	0.702923i	$0.248122\pi$
$912$	−5.49081e10	−2.39692
$913$	0	0
$914$	−2.29483e9	−0.0994119
$915$	−1.04990e10	−0.453079
$916$	3.78265e10	1.62615
$917$	5.42814e10	2.32465
$918$	1.30275e10	0.555791
$919$	3.54581e10	1.50699	0.753495	−	0.657453i	$-0.228366\pi$
$919$	3.54581e10	1.50699	0.753495	+	0.657453i	$0.228366\pi$
$920$	9.34496e9	0.395658
$921$	4.96264e9	0.209317
$922$	−1.03740e10	−0.435902
$923$	6.26277e8	0.0262156
$924$	0	0
$925$	6.13297e9	0.254786
$926$	2.34104e9	0.0968881
$927$	−1.09989e10	−0.453492
$928$	−1.82862e10	−0.751112
$929$	9.06137e9	0.370799	0.185400	−	0.982663i	$-0.440642\pi$
$929$	9.06137e9	0.370799	0.185400	+	0.982663i	$0.440642\pi$
$930$	−7.42357e9	−0.302637
$931$	3.17449e10	1.28929
$932$	−1.24418e10	−0.503415
$933$	−2.93796e10	−1.18429
$934$	−1.52471e10	−0.612311
$935$	0	0
$936$	2.90754e9	0.115894
$937$	−6.77993e9	−0.269238	−0.134619	−	0.990897i	$-0.542981\pi$
$937$	−6.77993e9	−0.269238	−0.134619	+	0.990897i	$0.542981\pi$
$938$	1.53463e10	0.607146
$939$	−3.65301e10	−1.43986
$940$	−3.06273e10	−1.20271
$941$	−3.67320e10	−1.43708	−0.718539	−	0.695486i	$-0.755189\pi$
$941$	−3.67320e10	−1.43708	−0.718539	+	0.695486i	$0.755189\pi$
$942$	1.05666e10	0.411869
$943$	−1.35452e10	−0.526009
$944$	2.97457e10	1.15086
$945$	7.04480e10	2.71555
$946$	0	0
$947$	−1.16838e10	−0.447052	−0.223526	−	0.974698i	$-0.571757\pi$
$947$	−1.16838e10	−0.447052	−0.223526	+	0.974698i	$0.571757\pi$
$948$	2.30287e10	0.877890
$949$	−2.15160e9	−0.0817204
$950$	4.89640e9	0.185287
$951$	−6.84899e10	−2.58223
$952$	1.97832e10	0.743136
$953$	1.37495e10	0.514589	0.257294	−	0.966333i	$-0.417169\pi$
$953$	1.37495e10	0.514589	0.257294	+	0.966333i	$0.417169\pi$
$954$	3.72620e9	0.138946
$955$	4.75894e10	1.76807
$956$	−3.93496e10	−1.45659
$957$	0	0
$958$	−6.78867e9	−0.249463
$959$	3.60114e10	1.31848
$960$	−2.49364e10	−0.909671
$961$	−2.11117e10	−0.767345
$962$	−6.81299e8	−0.0246732
$963$	−6.90499e10	−2.49156
$964$	−4.08516e10	−1.46872
$965$	3.10331e10	1.11168
$966$	−1.15166e10	−0.411061
$967$	−1.76579e10	−0.627981	−0.313991	−	0.949426i	$-0.601666\pi$
$967$	−1.76579e10	−0.627981	−0.313991	+	0.949426i	$0.601666\pi$
$968$	0	0
$969$	9.15649e10	3.23293
$970$	6.18573e9	0.217616
$971$	−3.02926e10	−1.06186	−0.530932	−	0.847414i	$-0.678158\pi$
$971$	−3.02926e10	−1.06186	−0.530932	+	0.847414i	$0.678158\pi$
$972$	4.81407e9	0.168143
$973$	−1.67167e10	−0.581775
$974$	−8.40763e9	−0.291553
$975$	1.46634e9	0.0506663
$976$	−4.70245e9	−0.161901
$977$	−1.50568e10	−0.516538	−0.258269	−	0.966073i	$-0.583152\pi$
$977$	−1.50568e10	−0.516538	−0.258269	+	0.966073i	$0.583152\pi$
$978$	5.04275e8	0.0172378
$979$	0	0
$980$	2.03568e10	0.690904
$981$	−5.79339e9	−0.195926
$982$	−7.24417e9	−0.244117
$983$	2.15787e10	0.724583	0.362291	−	0.932065i	$-0.381995\pi$
$983$	2.15787e10	0.724583	0.362291	+	0.932065i	$0.381995\pi$
$984$	−2.83137e10	−0.947358
$985$	−2.72659e10	−0.909062
$986$	8.32195e9	0.276475
$987$	7.96233e10	2.63591
$988$	4.96656e9	0.163835
$989$	1.32593e10	0.435848
$990$	0	0
$991$	−3.75301e10	−1.22496	−0.612481	−	0.790486i	$-0.709828\pi$
$991$	−3.75301e10	−1.22496	−0.612481	+	0.790486i	$0.709828\pi$
$992$	−1.21837e10	−0.396268
$993$	−6.87760e10	−2.22902
$994$	−3.48639e9	−0.112596
$995$	6.30686e10	2.02970
$996$	−5.05509e10	−1.62114
$997$	3.01118e10	0.962286	0.481143	−	0.876642i	$-0.340222\pi$
$997$	3.01118e10	0.962286	0.481143	+	0.876642i	$0.340222\pi$
$998$	6.64251e9	0.211532
$999$	−4.81068e10	−1.52661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.8.a.d.1.4	✓	5
11.10	odd	2		121.8.a.e.1.2	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.8.a.d.1.4	✓	5	1.1	even	1	trivial
121.8.a.e.1.2	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q+3.55452 q^{2} -81.6995 q^{3} -115.365 q^{4} -319.514 q^{5} -290.403 q^{6} +1172.95 q^{7} -865.048 q^{8} +4487.81 q^{9} -1135.72 q^{10} +9425.29 q^{12} -748.946 q^{13} +4169.27 q^{14} +26104.2 q^{15} +11691.9 q^{16} -19497.5 q^{17} +15952.0 q^{18} +57481.8 q^{19} +36860.9 q^{20} -95829.1 q^{21} +33810.1 q^{23} +70674.0 q^{24} +23964.3 q^{25} -2662.15 q^{26} -187975. q^{27} -135317. q^{28} -120078. q^{29} +92787.8 q^{30} -80005.9 q^{31} +152285. q^{32} -69304.4 q^{34} -374773. q^{35} -517738. q^{36} +255921. q^{37} +204320. q^{38} +61188.5 q^{39} +276395. q^{40} -400624. q^{41} -340627. q^{42} +392171. q^{43} -1.43392e6 q^{45} +120179. q^{46} -830888. q^{47} -955225. q^{48} +552260. q^{49} +85181.8 q^{50} +1.59294e6 q^{51} +86402.4 q^{52} +233588. q^{53} -668162. q^{54} -1.01465e6 q^{56} -4.69624e6 q^{57} -426821. q^{58} +2.54412e6 q^{59} -3.01152e6 q^{60} -402196. q^{61} -284383. q^{62} +5.26396e6 q^{63} -955265. q^{64} +239299. q^{65} +3.68081e6 q^{67} +2.24934e6 q^{68} -2.76227e6 q^{69} -1.33214e6 q^{70} -836212. q^{71} -3.88217e6 q^{72} +2.87284e6 q^{73} +909677. q^{74} -1.95787e6 q^{75} -6.63141e6 q^{76} +217496. q^{78} +2.44329e6 q^{79} -3.73574e6 q^{80} +5.54263e6 q^{81} -1.42403e6 q^{82} -5.36332e6 q^{83} +1.10554e7 q^{84} +6.22973e6 q^{85} +1.39398e6 q^{86} +9.81034e6 q^{87} -3.89069e6 q^{89} -5.09690e6 q^{90} -878473. q^{91} -3.90052e6 q^{92} +6.53644e6 q^{93} -2.95341e6 q^{94} -1.83663e7 q^{95} -1.24416e7 q^{96} -5.44653e6 q^{97} +1.96302e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{2} - 14 q^{3} + 166 q^{4} - 515 q^{5} - 692 q^{6} + 1286 q^{7} - 2334 q^{8} + 1133 q^{9} + 6836 q^{10} + 10496 q^{12} + 6533 q^{13} - 18668 q^{14} + 2074 q^{15} + 15010 q^{16} - 32705 q^{17}+ \cdots - 9136104 q^{98}+O(q^{100}) \) 5 * q - 8 * q^2 - 14 * q^3 + 166 * q^4 - 515 * q^5 - 692 * q^6 + 1286 * q^7 - 2334 * q^8 + 1133 * q^9 + 6836 * q^10 + 10496 * q^12 + 6533 * q^13 - 18668 * q^14 + 2074 * q^15 + 15010 * q^16 - 32705 * q^17 + 21848 * q^18 + 29910 * q^19 - 79078 * q^20 - 23132 * q^21 - 45214 * q^23 - 94992 * q^24 + 11764 * q^25 - 58196 * q^26 - 230348 * q^27 + 21856 * q^28 + 242061 * q^29 + 477220 * q^30 + 55310 * q^31 - 40750 * q^32 - 194608 * q^34 - 1092602 * q^35 - 1250618 * q^36 + 586689 * q^37 - 166692 * q^38 - 283790 * q^39 + 1951374 * q^40 + 565735 * q^41 - 1120208 * q^42 - 287040 * q^43 - 1566547 * q^45 - 1904780 * q^46 - 3182566 * q^47 + 949544 * q^48 - 765183 * q^49 - 4244056 * q^50 + 3141694 * q^51 + 4918498 * q^52 - 1220883 * q^53 + 913528 * q^54 - 5142192 * q^56 - 7377636 * q^57 - 10076868 * q^58 + 1304864 * q^59 - 7345528 * q^60 - 3437754 * q^61 + 4156516 * q^62 + 7075454 * q^63 - 4731286 * q^64 - 3342779 * q^65 - 5199446 * q^67 - 10501510 * q^68 - 11265124 * q^69 + 9858572 * q^70 - 3440220 * q^71 - 5576286 * q^72 + 9963974 * q^73 + 7512132 * q^74 - 241456 * q^75 - 7011480 * q^76 - 8493404 * q^78 - 7834562 * q^79 - 17690746 * q^80 + 4373321 * q^81 - 898480 * q^82 - 6230682 * q^83 + 19063160 * q^84 + 11708303 * q^85 + 6786552 * q^86 + 13109106 * q^87 - 13960869 * q^89 - 12112156 * q^90 + 573182 * q^91 - 3324824 * q^92 + 7120948 * q^93 - 9234428 * q^94 - 8171634 * q^95 - 4167472 * q^96 - 15733241 * q^97 - 9136104 * q^98

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