LMFDB - Embedded newform 8041.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25118 q^{2} +2.59454 q^{3} +3.06780 q^{4} +2.27169 q^{5} -5.84076 q^{6} +2.89150 q^{7} -2.40380 q^{8} +3.73163 q^{9} +O(q^{10})$	\(q-2.25118 q^{2} +2.59454 q^{3} +3.06780 q^{4} +2.27169 q^{5} -5.84076 q^{6} +2.89150 q^{7} -2.40380 q^{8} +3.73163 q^{9} -5.11397 q^{10} -1.00000 q^{11} +7.95952 q^{12} -3.36805 q^{13} -6.50928 q^{14} +5.89398 q^{15} -0.724210 q^{16} +1.00000 q^{17} -8.40055 q^{18} +5.15910 q^{19} +6.96908 q^{20} +7.50211 q^{21} +2.25118 q^{22} -5.42604 q^{23} -6.23676 q^{24} +0.160565 q^{25} +7.58207 q^{26} +1.89823 q^{27} +8.87054 q^{28} +2.22608 q^{29} -13.2684 q^{30} +4.51212 q^{31} +6.43793 q^{32} -2.59454 q^{33} -2.25118 q^{34} +6.56859 q^{35} +11.4479 q^{36} +2.36272 q^{37} -11.6140 q^{38} -8.73852 q^{39} -5.46069 q^{40} +2.80583 q^{41} -16.8886 q^{42} -1.00000 q^{43} -3.06780 q^{44} +8.47709 q^{45} +12.2150 q^{46} +4.51414 q^{47} -1.87899 q^{48} +1.36078 q^{49} -0.361460 q^{50} +2.59454 q^{51} -10.3325 q^{52} +2.61713 q^{53} -4.27325 q^{54} -2.27169 q^{55} -6.95060 q^{56} +13.3855 q^{57} -5.01131 q^{58} +3.48199 q^{59} +18.0815 q^{60} +14.4022 q^{61} -10.1576 q^{62} +10.7900 q^{63} -13.0445 q^{64} -7.65115 q^{65} +5.84076 q^{66} -7.22410 q^{67} +3.06780 q^{68} -14.0781 q^{69} -14.7871 q^{70} -3.75188 q^{71} -8.97009 q^{72} -1.63157 q^{73} -5.31890 q^{74} +0.416591 q^{75} +15.8271 q^{76} -2.89150 q^{77} +19.6720 q^{78} +3.39098 q^{79} -1.64518 q^{80} -6.26985 q^{81} -6.31642 q^{82} +7.49008 q^{83} +23.0150 q^{84} +2.27169 q^{85} +2.25118 q^{86} +5.77565 q^{87} +2.40380 q^{88} +17.8605 q^{89} -19.0834 q^{90} -9.73871 q^{91} -16.6460 q^{92} +11.7069 q^{93} -10.1621 q^{94} +11.7199 q^{95} +16.7035 q^{96} -17.4916 q^{97} -3.06336 q^{98} -3.73163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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 $

$2$	−2.25118	−1.59182	−0.795911	−	0.605413i	$-0.793008\pi$
$2$	−2.25118	−1.59182	−0.795911	+	0.605413i	$0.793008\pi$
$3$	2.59454	1.49796	0.748979	−	0.662594i	$-0.230545\pi$
$3$	2.59454	1.49796	0.748979	+	0.662594i	$0.230545\pi$
$4$	3.06780	1.53390
$5$	2.27169	1.01593	0.507965	−	0.861378i	$-0.330398\pi$
$5$	2.27169	1.01593	0.507965	+	0.861378i	$0.330398\pi$
$6$	−5.84076	−2.38448
$7$	2.89150	1.09288	0.546442	−	0.837497i	$-0.315982\pi$
$7$	2.89150	1.09288	0.546442	+	0.837497i	$0.315982\pi$
$8$	−2.40380	−0.849873
$9$	3.73163	1.24388
$10$	−5.11397	−1.61718
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	7.95952	2.29772
$13$	−3.36805	−0.934128	−0.467064	−	0.884224i	$-0.654688\pi$
$13$	−3.36805	−0.934128	−0.467064	+	0.884224i	$0.654688\pi$
$14$	−6.50928	−1.73968
$15$	5.89398	1.52182
$16$	−0.724210	−0.181052
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−8.40055	−1.98003
$19$	5.15910	1.18358	0.591789	−	0.806093i	$-0.298422\pi$
$19$	5.15910	1.18358	0.591789	+	0.806093i	$0.298422\pi$
$20$	6.96908	1.55833
$21$	7.50211	1.63709
$22$	2.25118	0.479953
$23$	−5.42604	−1.13141	−0.565704	−	0.824609i	$-0.691395\pi$
$23$	−5.42604	−1.13141	−0.565704	+	0.824609i	$0.691395\pi$
$24$	−6.23676	−1.27307
$25$	0.160565	0.0321130
$26$	7.58207	1.48697
$27$	1.89823	0.365315
$28$	8.87054	1.67638
$29$	2.22608	0.413373	0.206687	−	0.978407i	$-0.433732\pi$
$29$	2.22608	0.413373	0.206687	+	0.978407i	$0.433732\pi$
$30$	−13.2684	−2.42247
$31$	4.51212	0.810401	0.405201	−	0.914228i	$-0.367202\pi$
$31$	4.51212	0.810401	0.405201	+	0.914228i	$0.367202\pi$
$32$	6.43793	1.13808
$33$	−2.59454	−0.451651
$34$	−2.25118	−0.386074
$35$	6.56859	1.11029
$36$	11.4479	1.90798
$37$	2.36272	0.388429	0.194214	−	0.980959i	$-0.437784\pi$
$37$	2.36272	0.388429	0.194214	+	0.980959i	$0.437784\pi$
$38$	−11.6140	−1.88405
$39$	−8.73852	−1.39928
$40$	−5.46069	−0.863411
$41$	2.80583	0.438197	0.219099	−	0.975703i	$-0.429688\pi$
$41$	2.80583	0.438197	0.219099	+	0.975703i	$0.429688\pi$
$42$	−16.8886	−2.60596
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−3.06780	−0.462488
$45$	8.47709	1.26369
$46$	12.2150	1.80100
$47$	4.51414	0.658456	0.329228	−	0.944251i	$-0.393212\pi$
$47$	4.51414	0.658456	0.329228	+	0.944251i	$0.393212\pi$
$48$	−1.87899	−0.271209
$49$	1.36078	0.194398
$50$	−0.361460	−0.0511181
$51$	2.59454	0.363308
$52$	−10.3325	−1.43286
$53$	2.61713	0.359491	0.179745	−	0.983713i	$-0.442473\pi$
$53$	2.61713	0.359491	0.179745	+	0.983713i	$0.442473\pi$
$54$	−4.27325	−0.581516
$55$	−2.27169	−0.306314
$56$	−6.95060	−0.928813
$57$	13.3855	1.77295
$58$	−5.01131	−0.658017
$59$	3.48199	0.453317	0.226658	−	0.973974i	$-0.427220\pi$
$59$	3.48199	0.453317	0.226658	+	0.973974i	$0.427220\pi$
$60$	18.0815	2.33432
$61$	14.4022	1.84402	0.922008	−	0.387170i	$-0.126548\pi$
$61$	14.4022	1.84402	0.922008	+	0.387170i	$0.126548\pi$
$62$	−10.1576	−1.29002
$63$	10.7900	1.35941
$64$	−13.0445	−1.63056
$65$	−7.65115	−0.949008
$66$	5.84076	0.718948
$67$	−7.22410	−0.882564	−0.441282	−	0.897368i	$-0.645476\pi$
$67$	−7.22410	−0.882564	−0.441282	+	0.897368i	$0.645476\pi$
$68$	3.06780	0.372025
$69$	−14.0781	−1.69480
$70$	−14.7871	−1.76739
$71$	−3.75188	−0.445267	−0.222633	−	0.974902i	$-0.571465\pi$
$71$	−3.75188	−0.445267	−0.222633	+	0.974902i	$0.571465\pi$
$72$	−8.97009	−1.05714
$73$	−1.63157	−0.190960	−0.0954801	−	0.995431i	$-0.530439\pi$
$73$	−1.63157	−0.190960	−0.0954801	+	0.995431i	$0.530439\pi$
$74$	−5.31890	−0.618310
$75$	0.416591	0.0481038
$76$	15.8271	1.81549
$77$	−2.89150	−0.329517
$78$	19.6720	2.22741
$79$	3.39098	0.381515	0.190757	−	0.981637i	$-0.438906\pi$
$79$	3.39098	0.381515	0.190757	+	0.981637i	$0.438906\pi$
$80$	−1.64518	−0.183937
$81$	−6.26985	−0.696650
$82$	−6.31642	−0.697532
$83$	7.49008	0.822143	0.411072	−	0.911603i	$-0.365155\pi$
$83$	7.49008	0.822143	0.411072	+	0.911603i	$0.365155\pi$
$84$	23.0150	2.51114
$85$	2.27169	0.246399
$86$	2.25118	0.242751
$87$	5.77565	0.619215
$88$	2.40380	0.256246
$89$	17.8605	1.89321	0.946607	−	0.322390i	$-0.104486\pi$
$89$	17.8605	1.89321	0.946607	+	0.322390i	$0.104486\pi$
$90$	−19.0834	−2.01157
$91$	−9.73871	−1.02089
$92$	−16.6460	−1.73546
$93$	11.7069	1.21395
$94$	−10.1621	−1.04814
$95$	11.7199	1.20243
$96$	16.7035	1.70479
$97$	−17.4916	−1.77601	−0.888003	−	0.459837i	$-0.847908\pi$
$97$	−17.4916	−1.77601	−0.888003	+	0.459837i	$0.847908\pi$
$98$	−3.06336	−0.309446
$99$	−3.73163	−0.375042
$100$	0.492580	0.0492580
$101$	2.19688	0.218598	0.109299	−	0.994009i	$-0.465139\pi$
$101$	2.19688	0.218598	0.109299	+	0.994009i	$0.465139\pi$
$102$	−5.84076	−0.578322
$103$	−8.92839	−0.879740	−0.439870	−	0.898061i	$-0.644975\pi$
$103$	−8.92839	−0.879740	−0.439870	+	0.898061i	$0.644975\pi$
$104$	8.09612	0.793890
$105$	17.0425	1.66317
$106$	−5.89163	−0.572246
$107$	9.79697	0.947109	0.473554	−	0.880765i	$-0.342971\pi$
$107$	9.79697	0.947109	0.473554	+	0.880765i	$0.342971\pi$
$108$	5.82339	0.560356
$109$	3.59095	0.343950	0.171975	−	0.985101i	$-0.444985\pi$
$109$	3.59095	0.343950	0.171975	+	0.985101i	$0.444985\pi$
$110$	5.11397	0.487598
$111$	6.13017	0.581850
$112$	−2.09405	−0.197870
$113$	14.5269	1.36657	0.683287	−	0.730150i	$-0.260550\pi$
$113$	14.5269	1.36657	0.683287	+	0.730150i	$0.260550\pi$
$114$	−30.1331	−2.82222
$115$	−12.3263	−1.14943
$116$	6.82917	0.634073
$117$	−12.5683	−1.16194
$118$	−7.83858	−0.721600
$119$	2.89150	0.265064
$120$	−14.1680	−1.29335
$121$	1.00000	0.0909091
$122$	−32.4220	−2.93535
$123$	7.27983	0.656400
$124$	13.8423	1.24307
$125$	−10.9937	−0.983305
$126$	−24.2902	−2.16394
$127$	−7.19978	−0.638877	−0.319438	−	0.947607i	$-0.603494\pi$
$127$	−7.19978	−0.638877	−0.319438	+	0.947607i	$0.603494\pi$
$128$	16.4896	1.45749
$129$	−2.59454	−0.228436
$130$	17.2241	1.51065
$131$	16.2363	1.41857	0.709285	−	0.704921i	$-0.249018\pi$
$131$	16.2363	1.41857	0.709285	+	0.704921i	$0.249018\pi$
$132$	−7.95952	−0.692787
$133$	14.9175	1.29352
$134$	16.2627	1.40489
$135$	4.31219	0.371134
$136$	−2.40380	−0.206124
$137$	−16.4239	−1.40318	−0.701592	−	0.712578i	$-0.747527\pi$
$137$	−16.4239	−1.40318	−0.701592	+	0.712578i	$0.747527\pi$
$138$	31.6922	2.69782
$139$	16.2689	1.37991	0.689957	−	0.723850i	$-0.257629\pi$
$139$	16.2689	1.37991	0.689957	+	0.723850i	$0.257629\pi$
$140$	20.1511	1.70308
$141$	11.7121	0.986338
$142$	8.44615	0.708785
$143$	3.36805	0.281650
$144$	−2.70248	−0.225207
$145$	5.05696	0.419958
$146$	3.67294	0.303975
$147$	3.53060	0.291199
$148$	7.24835	0.595811
$149$	0.335883	0.0275166	0.0137583	−	0.999905i	$-0.495620\pi$
$149$	0.335883	0.0275166	0.0137583	+	0.999905i	$0.495620\pi$
$150$	−0.937821	−0.0765728
$151$	7.80684	0.635312	0.317656	−	0.948206i	$-0.397104\pi$
$151$	7.80684	0.635312	0.317656	+	0.948206i	$0.397104\pi$
$152$	−12.4015	−1.00589
$153$	3.73163	0.301684
$154$	6.50928	0.524533
$155$	10.2501	0.823311
$156$	−26.8080	−2.14636
$157$	3.61687	0.288657	0.144329	−	0.989530i	$-0.453898\pi$
$157$	3.61687	0.288657	0.144329	+	0.989530i	$0.453898\pi$
$158$	−7.63369	−0.607303
$159$	6.79025	0.538502
$160$	14.6250	1.15621
$161$	−15.6894	−1.23650
$162$	14.1145	1.10894
$163$	21.0957	1.65235	0.826173	−	0.563416i	$-0.190513\pi$
$163$	21.0957	1.65235	0.826173	+	0.563416i	$0.190513\pi$
$164$	8.60772	0.672150
$165$	−5.89398	−0.458846
$166$	−16.8615	−1.30871
$167$	−20.1482	−1.55912	−0.779559	−	0.626329i	$-0.784557\pi$
$167$	−20.1482	−1.55912	−0.779559	+	0.626329i	$0.784557\pi$
$168$	−18.0336	−1.39132
$169$	−1.65626	−0.127405
$170$	−5.11397	−0.392224
$171$	19.2518	1.47222
$172$	−3.06780	−0.233917
$173$	10.5035	0.798568	0.399284	−	0.916827i	$-0.369259\pi$
$173$	10.5035	0.798568	0.399284	+	0.916827i	$0.369259\pi$
$174$	−13.0020	−0.985681
$175$	0.464273	0.0350958
$176$	0.724210	0.0545894
$177$	9.03416	0.679049
$178$	−40.2073	−3.01366
$179$	7.07499	0.528809	0.264405	−	0.964412i	$-0.414825\pi$
$179$	7.07499	0.528809	0.264405	+	0.964412i	$0.414825\pi$
$180$	26.0060	1.93837
$181$	4.29488	0.319236	0.159618	−	0.987179i	$-0.448974\pi$
$181$	4.29488	0.319236	0.159618	+	0.987179i	$0.448974\pi$
$182$	21.9236	1.62508
$183$	37.3671	2.76226
$184$	13.0431	0.961552
$185$	5.36736	0.394616
$186$	−26.3542	−1.93239
$187$	−1.00000	−0.0731272
$188$	13.8485	1.01000
$189$	5.48874	0.399247
$190$	−26.3835	−1.91406
$191$	17.6569	1.27761	0.638803	−	0.769370i	$-0.279430\pi$
$191$	17.6569	1.27761	0.638803	+	0.769370i	$0.279430\pi$
$192$	−33.8445	−2.44251
$193$	0.0213178	0.00153449	0.000767244	−	1.00000i	$-0.499756\pi$
$193$	0.0213178	0.00153449	0.000767244		1.00000i	$0.499756\pi$
$194$	39.3768	2.82709
$195$	−19.8512	−1.42157
$196$	4.17461	0.298186
$197$	5.18643	0.369518	0.184759	−	0.982784i	$-0.440850\pi$
$197$	5.18643	0.369518	0.184759	+	0.982784i	$0.440850\pi$
$198$	8.40055	0.597001
$199$	21.4477	1.52039	0.760193	−	0.649697i	$-0.225104\pi$
$199$	21.4477	1.52039	0.760193	+	0.649697i	$0.225104\pi$
$200$	−0.385966	−0.0272919
$201$	−18.7432	−1.32204
$202$	−4.94557	−0.347969
$203$	6.43672	0.451769
$204$	7.95952	0.557278
$205$	6.37397	0.445177
$206$	20.0994	1.40039
$207$	−20.2479	−1.40733
$208$	2.43917	0.169126
$209$	−5.15910	−0.356862
$210$	−38.3656	−2.64748
$211$	−15.8795	−1.09319	−0.546595	−	0.837397i	$-0.684076\pi$
$211$	−15.8795	−1.09319	−0.546595	+	0.837397i	$0.684076\pi$
$212$	8.02883	0.551423
$213$	−9.73440	−0.666990
$214$	−22.0547	−1.50763
$215$	−2.27169	−0.154928
$216$	−4.56297	−0.310471
$217$	13.0468	0.885675
$218$	−8.08386	−0.547508
$219$	−4.23316	−0.286050
$220$	−6.96908	−0.469855
$221$	−3.36805	−0.226559
$222$	−13.8001	−0.926201
$223$	−5.12283	−0.343050	−0.171525	−	0.985180i	$-0.554869\pi$
$223$	−5.12283	−0.343050	−0.171525	+	0.985180i	$0.554869\pi$
$224$	18.6153	1.24379
$225$	0.599168	0.0399445
$226$	−32.7026	−2.17534
$227$	7.84634	0.520780	0.260390	−	0.965504i	$-0.416149\pi$
$227$	7.84634	0.520780	0.260390	+	0.965504i	$0.416149\pi$
$228$	41.0640	2.71953
$229$	−11.0708	−0.731579	−0.365789	−	0.930698i	$-0.619201\pi$
$229$	−11.0708	−0.731579	−0.365789	+	0.930698i	$0.619201\pi$
$230$	27.7486	1.82969
$231$	−7.50211	−0.493603
$232$	−5.35106	−0.351315
$233$	−27.5745	−1.80647	−0.903233	−	0.429150i	$-0.858813\pi$
$233$	−27.5745	−1.80647	−0.903233	+	0.429150i	$0.858813\pi$
$234$	28.2934	1.84960
$235$	10.2547	0.668945
$236$	10.6820	0.695342
$237$	8.79801	0.571492
$238$	−6.50928	−0.421934
$239$	−23.0433	−1.49055	−0.745273	−	0.666760i	$-0.767681\pi$
$239$	−23.0433	−1.49055	−0.745273	+	0.666760i	$0.767681\pi$
$240$	−4.26848	−0.275529
$241$	22.9565	1.47876	0.739380	−	0.673288i	$-0.235119\pi$
$241$	22.9565	1.47876	0.739380	+	0.673288i	$0.235119\pi$
$242$	−2.25118	−0.144711
$243$	−21.9620	−1.40887
$244$	44.1831	2.82854
$245$	3.09127	0.197494
$246$	−16.3882	−1.04487
$247$	−17.3761	−1.10561
$248$	−10.8463	−0.688738
$249$	19.4333	1.23154
$250$	24.7487	1.56525
$251$	−8.31480	−0.524825	−0.262413	−	0.964956i	$-0.584518\pi$
$251$	−8.31480	−0.524825	−0.262413	+	0.964956i	$0.584518\pi$
$252$	33.1016	2.08520
$253$	5.42604	0.341132
$254$	16.2080	1.01698
$255$	5.89398	0.369095
$256$	−11.0321	−0.689504
$257$	2.82069	0.175950	0.0879748	−	0.996123i	$-0.471960\pi$
$257$	2.82069	0.175950	0.0879748	+	0.996123i	$0.471960\pi$
$258$	5.84076	0.363630
$259$	6.83181	0.424508
$260$	−23.4722	−1.45568
$261$	8.30691	0.514185
$262$	−36.5508	−2.25811
$263$	21.8621	1.34807	0.674037	−	0.738698i	$-0.264559\pi$
$263$	21.8621	1.34807	0.674037	+	0.738698i	$0.264559\pi$
$264$	6.23676	0.383846
$265$	5.94531	0.365217
$266$	−33.5820	−2.05905
$267$	46.3399	2.83595
$268$	−22.1621	−1.35376
$269$	14.0951	0.859395	0.429697	−	0.902973i	$-0.358620\pi$
$269$	14.0951	0.859395	0.429697	+	0.902973i	$0.358620\pi$
$270$	−9.70750	−0.590779
$271$	7.81861	0.474947	0.237473	−	0.971394i	$-0.423681\pi$
$271$	7.81861	0.474947	0.237473	+	0.971394i	$0.423681\pi$
$272$	−0.724210	−0.0439117
$273$	−25.2675	−1.52926
$274$	36.9730	2.23362
$275$	−0.160565	−0.00968242
$276$	−43.1886	−2.59965
$277$	18.1081	1.08801	0.544004	−	0.839083i	$-0.316908\pi$
$277$	18.1081	1.08801	0.544004	+	0.839083i	$0.316908\pi$
$278$	−36.6243	−2.19658
$279$	16.8376	1.00804
$280$	−15.7896	−0.943609
$281$	26.2321	1.56487	0.782437	−	0.622730i	$-0.213977\pi$
$281$	26.2321	1.56487	0.782437	+	0.622730i	$0.213977\pi$
$282$	−26.3660	−1.57008
$283$	13.9705	0.830462	0.415231	−	0.909716i	$-0.363701\pi$
$283$	13.9705	0.830462	0.415231	+	0.909716i	$0.363701\pi$
$284$	−11.5100	−0.682994
$285$	30.4076	1.80119
$286$	−7.58207	−0.448337
$287$	8.11306	0.478899
$288$	24.0240	1.41562
$289$	1.00000	0.0588235
$290$	−11.3841	−0.668499
$291$	−45.3827	−2.66038
$292$	−5.00531	−0.292914
$293$	−23.7255	−1.38606	−0.693029	−	0.720910i	$-0.743724\pi$
$293$	−23.7255	−1.38606	−0.693029	+	0.720910i	$0.743724\pi$
$294$	−7.94801	−0.463537
$295$	7.91000	0.460538
$296$	−5.67951	−0.330115
$297$	−1.89823	−0.110147
$298$	−0.756133	−0.0438016
$299$	18.2751	1.05688
$300$	1.27802	0.0737864
$301$	−2.89150	−0.166663
$302$	−17.5746	−1.01130
$303$	5.69990	0.327451
$304$	−3.73627	−0.214290
$305$	32.7174	1.87339
$306$	−8.40055	−0.480228
$307$	−23.6493	−1.34974	−0.674869	−	0.737937i	$-0.735800\pi$
$307$	−23.6493	−1.34974	−0.674869	+	0.737937i	$0.735800\pi$
$308$	−8.87054	−0.505446
$309$	−23.1650	−1.31781
$310$	−23.0749	−1.31056
$311$	−11.7354	−0.665452	−0.332726	−	0.943024i	$-0.607968\pi$
$311$	−11.7354	−0.665452	−0.332726	+	0.943024i	$0.607968\pi$
$312$	21.0057	1.18921
$313$	−4.64742	−0.262688	−0.131344	−	0.991337i	$-0.541929\pi$
$313$	−4.64742	−0.262688	−0.131344	+	0.991337i	$0.541929\pi$
$314$	−8.14221	−0.459491
$315$	24.5115	1.38107
$316$	10.4028	0.585205
$317$	6.74175	0.378654	0.189327	−	0.981914i	$-0.439369\pi$
$317$	6.74175	0.378654	0.189327	+	0.981914i	$0.439369\pi$
$318$	−15.2861	−0.857199
$319$	−2.22608	−0.124637
$320$	−29.6330	−1.65654
$321$	25.4186	1.41873
$322$	35.3196	1.96829
$323$	5.15910	0.287060
$324$	−19.2346	−1.06859
$325$	−0.540790	−0.0299976
$326$	−47.4903	−2.63024
$327$	9.31685	0.515223
$328$	−6.74466	−0.372412
$329$	13.0527	0.719616
$330$	13.2684	0.730401
$331$	−27.4292	−1.50765	−0.753823	−	0.657077i	$-0.771793\pi$
$331$	−27.4292	−1.50765	−0.753823	+	0.657077i	$0.771793\pi$
$332$	22.9781	1.26109
$333$	8.81679	0.483157
$334$	45.3572	2.48184
$335$	−16.4109	−0.896623
$336$	−5.43310	−0.296400
$337$	−17.3114	−0.943012	−0.471506	−	0.881863i	$-0.656289\pi$
$337$	−17.3114	−0.943012	−0.471506	+	0.881863i	$0.656289\pi$
$338$	3.72854	0.202806
$339$	37.6905	2.04707
$340$	6.96908	0.377951
$341$	−4.51212	−0.244345
$342$	−43.3393	−2.34352
$343$	−16.3058	−0.880431
$344$	2.40380	0.129604
$345$	−31.9810	−1.72180
$346$	−23.6453	−1.27118
$347$	24.8503	1.33403	0.667017	−	0.745042i	$-0.267571\pi$
$347$	24.8503	1.33403	0.667017	+	0.745042i	$0.267571\pi$
$348$	17.7185	0.949814
$349$	−27.8455	−1.49053	−0.745267	−	0.666766i	$-0.767678\pi$
$349$	−27.8455	−1.49053	−0.745267	+	0.666766i	$0.767678\pi$
$350$	−1.04516	−0.0558662
$351$	−6.39333	−0.341251
$352$	−6.43793	−0.343143
$353$	2.46230	0.131055	0.0655275	−	0.997851i	$-0.479127\pi$
$353$	2.46230	0.131055	0.0655275	+	0.997851i	$0.479127\pi$
$354$	−20.3375	−1.08093
$355$	−8.52311	−0.452360
$356$	54.7926	2.90400
$357$	7.50211	0.397054
$358$	−15.9270	−0.841771
$359$	−7.29823	−0.385186	−0.192593	−	0.981279i	$-0.561690\pi$
$359$	−7.29823	−0.385186	−0.192593	+	0.981279i	$0.561690\pi$
$360$	−20.3773	−1.07398
$361$	7.61632	0.400859
$362$	−9.66853	−0.508166
$363$	2.59454	0.136178
$364$	−29.8764	−1.56595
$365$	−3.70641	−0.194002
$366$	−84.1200	−4.39702
$367$	−14.5793	−0.761033	−0.380517	−	0.924774i	$-0.624254\pi$
$367$	−14.5793	−0.761033	−0.380517	+	0.924774i	$0.624254\pi$
$368$	3.92959	0.204844
$369$	10.4703	0.545062
$370$	−12.0829	−0.628159
$371$	7.56744	0.392882
$372$	35.9143	1.86207
$373$	19.1269	0.990352	0.495176	−	0.868793i	$-0.335104\pi$
$373$	19.1269	0.990352	0.495176	+	0.868793i	$0.335104\pi$
$374$	2.25118	0.116406
$375$	−28.5235	−1.47295
$376$	−10.8511	−0.559603
$377$	−7.49755	−0.386143
$378$	−12.3561	−0.635530
$379$	19.2061	0.986554	0.493277	−	0.869872i	$-0.335799\pi$
$379$	19.2061	0.986554	0.493277	+	0.869872i	$0.335799\pi$
$380$	35.9542	1.84441
$381$	−18.6801	−0.957010
$382$	−39.7488	−2.03372
$383$	−36.2466	−1.85212	−0.926058	−	0.377382i	$-0.876825\pi$
$383$	−36.2466	−1.85212	−0.926058	+	0.377382i	$0.876825\pi$
$384$	42.7830	2.18326
$385$	−6.56859	−0.334766
$386$	−0.0479901	−0.00244263
$387$	−3.73163	−0.189689
$388$	−53.6608	−2.72421
$389$	−19.0736	−0.967071	−0.483536	−	0.875325i	$-0.660648\pi$
$389$	−19.0736	−0.967071	−0.483536	+	0.875325i	$0.660648\pi$
$390$	44.6886	2.26289
$391$	−5.42604	−0.274407
$392$	−3.27105	−0.165213
$393$	42.1257	2.12496
$394$	−11.6756	−0.588207
$395$	7.70324	0.387592
$396$	−11.4479	−0.575277
$397$	34.8493	1.74904	0.874519	−	0.484992i	$-0.161177\pi$
$397$	34.8493	1.74904	0.874519	+	0.484992i	$0.161177\pi$
$398$	−48.2825	−2.42018
$399$	38.7041	1.93763
$400$	−0.116283	−0.00581413
$401$	11.0172	0.550175	0.275088	−	0.961419i	$-0.411293\pi$
$401$	11.0172	0.550175	0.275088	+	0.961419i	$0.411293\pi$
$402$	42.1943	2.10446
$403$	−15.1970	−0.757018
$404$	6.73960	0.335307
$405$	−14.2431	−0.707747
$406$	−14.4902	−0.719137
$407$	−2.36272	−0.117116
$408$	−6.23676	−0.308766
$409$	−18.7995	−0.929573	−0.464787	−	0.885423i	$-0.653869\pi$
$409$	−18.7995	−0.929573	−0.464787	+	0.885423i	$0.653869\pi$
$410$	−14.3489	−0.708643
$411$	−42.6123	−2.10191
$412$	−27.3905	−1.34943
$413$	10.0682	0.495423
$414$	45.5817	2.24022
$415$	17.0151	0.835240
$416$	−21.6833	−1.06311
$417$	42.2104	2.06705
$418$	11.6140	0.568062
$419$	0.252047	0.0123133	0.00615665	−	0.999981i	$-0.498040\pi$
$419$	0.252047	0.0123133	0.00615665	+	0.999981i	$0.498040\pi$
$420$	52.2828	2.55114
$421$	10.2925	0.501628	0.250814	−	0.968035i	$-0.419302\pi$
$421$	10.2925	0.501628	0.250814	+	0.968035i	$0.419302\pi$
$422$	35.7475	1.74016
$423$	16.8451	0.819037
$424$	−6.29107	−0.305521
$425$	0.160565	0.00778854
$426$	21.9139	1.06173
$427$	41.6441	2.01530
$428$	30.0551	1.45277
$429$	8.73852	0.421900
$430$	5.11397	0.246618
$431$	16.1480	0.777820	0.388910	−	0.921276i	$-0.372852\pi$
$431$	16.1480	0.777820	0.388910	+	0.921276i	$0.372852\pi$
$432$	−1.37472	−0.0661411
$433$	−28.1248	−1.35159	−0.675796	−	0.737089i	$-0.736200\pi$
$433$	−28.1248	−1.35159	−0.675796	+	0.737089i	$0.736200\pi$
$434$	−29.3707	−1.40984
$435$	13.1205	0.629079
$436$	11.0163	0.527585
$437$	−27.9935	−1.33911
$438$	9.52959	0.455341
$439$	6.42514	0.306655	0.153328	−	0.988175i	$-0.451001\pi$
$439$	6.42514	0.306655	0.153328	+	0.988175i	$0.451001\pi$
$440$	5.46069	0.260328
$441$	5.07793	0.241806
$442$	7.58207	0.360642
$443$	27.3868	1.30119	0.650593	−	0.759426i	$-0.274520\pi$
$443$	27.3868	1.30119	0.650593	+	0.759426i	$0.274520\pi$
$444$	18.8061	0.892499
$445$	40.5736	1.92337
$446$	11.5324	0.546074
$447$	0.871462	0.0412187
$448$	−37.7182	−1.78202
$449$	−15.3982	−0.726688	−0.363344	−	0.931655i	$-0.618365\pi$
$449$	−15.3982	−0.726688	−0.363344	+	0.931655i	$0.618365\pi$
$450$	−1.34883	−0.0635846
$451$	−2.80583	−0.132121
$452$	44.5655	2.09619
$453$	20.2551	0.951669
$454$	−17.6635	−0.828989
$455$	−22.1233	−1.03716
$456$	−32.1761	−1.50678
$457$	2.82124	0.131972	0.0659860	−	0.997821i	$-0.478981\pi$
$457$	2.82124	0.131972	0.0659860	+	0.997821i	$0.478981\pi$
$458$	24.9223	1.16454
$459$	1.89823	0.0886018
$460$	−37.8145	−1.76311
$461$	−4.15714	−0.193617	−0.0968086	−	0.995303i	$-0.530863\pi$
$461$	−4.15714	−0.193617	−0.0968086	+	0.995303i	$0.530863\pi$
$462$	16.8886	0.785728
$463$	−25.4616	−1.18330	−0.591650	−	0.806195i	$-0.701523\pi$
$463$	−25.4616	−1.18330	−0.591650	+	0.806195i	$0.701523\pi$
$464$	−1.61215	−0.0748422
$465$	26.5944	1.23328
$466$	62.0751	2.87557
$467$	25.4414	1.17729	0.588644	−	0.808393i	$-0.299662\pi$
$467$	25.4414	1.17729	0.588644	+	0.808393i	$0.299662\pi$
$468$	−38.5570	−1.78230
$469$	−20.8885	−0.964541
$470$	−23.0852	−1.06484
$471$	9.38410	0.432396
$472$	−8.37002	−0.385261
$473$	1.00000	0.0459800
$474$	−19.8059	−0.909714
$475$	0.828370	0.0380082
$476$	8.87054	0.406581
$477$	9.76616	0.447162
$478$	51.8745	2.37268
$479$	−5.87406	−0.268393	−0.134196	−	0.990955i	$-0.542845\pi$
$479$	−5.87406	−0.268393	−0.134196	+	0.990955i	$0.542845\pi$
$480$	37.9450	1.73195
$481$	−7.95775	−0.362842
$482$	−51.6792	−2.35393
$483$	−40.7067	−1.85222
$484$	3.06780	0.139445
$485$	−39.7355	−1.80430
$486$	49.4405	2.24266
$487$	−22.6644	−1.02702	−0.513510	−	0.858084i	$-0.671655\pi$
$487$	−22.6644	−1.02702	−0.513510	+	0.858084i	$0.671655\pi$
$488$	−34.6201	−1.56718
$489$	54.7337	2.47514
$490$	−6.95900	−0.314376
$491$	−29.5954	−1.33562	−0.667811	−	0.744331i	$-0.732769\pi$
$491$	−29.5954	−1.33562	−0.667811	+	0.744331i	$0.732769\pi$
$492$	22.3331	1.00685
$493$	2.22608	0.100258
$494$	39.1167	1.75994
$495$	−8.47709	−0.381017
$496$	−3.26772	−0.146725
$497$	−10.8486	−0.486625
$498$	−43.7478	−1.96039
$499$	−4.00671	−0.179365	−0.0896824	−	0.995970i	$-0.528585\pi$
$499$	−4.00671	−0.179365	−0.0896824	+	0.995970i	$0.528585\pi$
$500$	−33.7264	−1.50829
$501$	−52.2754	−2.33549
$502$	18.7181	0.835429
$503$	−40.3477	−1.79901	−0.899507	−	0.436906i	$-0.856074\pi$
$503$	−40.3477	−1.79901	−0.899507	+	0.436906i	$0.856074\pi$
$504$	−25.9370	−1.15533
$505$	4.99063	0.222080
$506$	−12.2150	−0.543022
$507$	−4.29724	−0.190847
$508$	−22.0875	−0.979973
$509$	19.6291	0.870046	0.435023	−	0.900419i	$-0.356740\pi$
$509$	19.6291	0.870046	0.435023	+	0.900419i	$0.356740\pi$
$510$	−13.2684	−0.587534
$511$	−4.71767	−0.208698
$512$	−8.14413	−0.359923
$513$	9.79316	0.432379
$514$	−6.34987	−0.280081
$515$	−20.2825	−0.893754
$516$	−7.95952	−0.350398
$517$	−4.51414	−0.198532
$518$	−15.3796	−0.675741
$519$	27.2518	1.19622
$520$	18.3919	0.806536
$521$	9.21567	0.403746	0.201873	−	0.979412i	$-0.435297\pi$
$521$	9.21567	0.403746	0.201873	+	0.979412i	$0.435297\pi$
$522$	−18.7003	−0.818491
$523$	−20.0541	−0.876904	−0.438452	−	0.898755i	$-0.644473\pi$
$523$	−20.0541	−0.876904	−0.438452	+	0.898755i	$0.644473\pi$
$524$	49.8097	2.17594
$525$	1.20457	0.0525720
$526$	−49.2154	−2.14589
$527$	4.51212	0.196551
$528$	1.87899	0.0817725
$529$	6.44189	0.280082
$530$	−13.3839	−0.581361
$531$	12.9935	0.563869
$532$	45.7640	1.98412
$533$	−9.45017	−0.409332
$534$	−104.319	−4.51433
$535$	22.2557	0.962196
$536$	17.3653	0.750067
$537$	18.3563	0.792134
$538$	−31.7306	−1.36800
$539$	−1.36078	−0.0586131
$540$	13.2289	0.569282
$541$	−40.3063	−1.73291	−0.866453	−	0.499259i	$-0.833606\pi$
$541$	−40.3063	−1.73291	−0.866453	+	0.499259i	$0.833606\pi$
$542$	−17.6011	−0.756031
$543$	11.1432	0.478201
$544$	6.43793	0.276024
$545$	8.15751	0.349429
$546$	56.8815	2.43430
$547$	−22.4987	−0.961974	−0.480987	−	0.876728i	$-0.659722\pi$
$547$	−22.4987	−0.961974	−0.480987	+	0.876728i	$0.659722\pi$
$548$	−50.3851	−2.15234
$549$	53.7437	2.29373
$550$	0.361460	0.0154127
$551$	11.4846	0.489260
$552$	33.8409	1.44036
$553$	9.80501	0.416951
$554$	−40.7645	−1.73192
$555$	13.9258	0.591118
$556$	49.9098	2.11665
$557$	22.5531	0.955606	0.477803	−	0.878467i	$-0.341433\pi$
$557$	22.5531	0.955606	0.477803	+	0.878467i	$0.341433\pi$
$558$	−37.9043	−1.60462
$559$	3.36805	0.142453
$560$	−4.75704	−0.201022
$561$	−2.59454	−0.109541
$562$	−59.0530	−2.49100
$563$	−27.0420	−1.13969	−0.569843	−	0.821754i	$-0.692996\pi$
$563$	−27.0420	−1.13969	−0.569843	+	0.821754i	$0.692996\pi$
$564$	35.9304	1.51294
$565$	33.0005	1.38834
$566$	−31.4501	−1.32195
$567$	−18.1293	−0.761358
$568$	9.01879	0.378420
$569$	−14.7218	−0.617169	−0.308584	−	0.951197i	$-0.599855\pi$
$569$	−14.7218	−0.617169	−0.308584	+	0.951197i	$0.599855\pi$
$570$	−68.4530	−2.86718
$571$	−31.8750	−1.33393	−0.666963	−	0.745091i	$-0.732406\pi$
$571$	−31.8750	−1.33393	−0.666963	+	0.745091i	$0.732406\pi$
$572$	10.3325	0.432023
$573$	45.8114	1.91380
$574$	−18.2639	−0.762322
$575$	−0.871231	−0.0363328
$576$	−48.6772	−2.02822
$577$	−25.0074	−1.04107	−0.520535	−	0.853840i	$-0.674268\pi$
$577$	−25.0074	−1.04107	−0.520535	+	0.853840i	$0.674268\pi$
$578$	−2.25118	−0.0936366
$579$	0.0553098	0.00229860
$580$	15.5137	0.644173
$581$	21.6576	0.898508
$582$	102.165	4.23485
$583$	−2.61713	−0.108391
$584$	3.92196	0.162292
$585$	−28.5512	−1.18045
$586$	53.4103	2.20636
$587$	−13.6654	−0.564032	−0.282016	−	0.959410i	$-0.591003\pi$
$587$	−13.6654	−0.564032	−0.282016	+	0.959410i	$0.591003\pi$
$588$	10.8312	0.446670
$589$	23.2785	0.959174
$590$	−17.8068	−0.733094
$591$	13.4564	0.553522
$592$	−1.71111	−0.0703260
$593$	31.7313	1.30305	0.651524	−	0.758628i	$-0.274130\pi$
$593$	31.7313	1.30305	0.651524	+	0.758628i	$0.274130\pi$
$594$	4.27325	0.175334
$595$	6.56859	0.269286
$596$	1.03042	0.0422077
$597$	55.6468	2.27747
$598$	−41.1406	−1.68236
$599$	−1.02166	−0.0417440	−0.0208720	−	0.999782i	$-0.506644\pi$
$599$	−1.02166	−0.0417440	−0.0208720	+	0.999782i	$0.506644\pi$
$600$	−1.00140	−0.0408821
$601$	−25.8237	−1.05337	−0.526685	−	0.850061i	$-0.676565\pi$
$601$	−25.8237	−1.05337	−0.526685	+	0.850061i	$0.676565\pi$
$602$	6.50928	0.265299
$603$	−26.9576	−1.09780
$604$	23.9498	0.974504
$605$	2.27169	0.0923572
$606$	−12.8315	−0.521243
$607$	−16.9880	−0.689524	−0.344762	−	0.938690i	$-0.612040\pi$
$607$	−16.9880	−0.689524	−0.344762	+	0.938690i	$0.612040\pi$
$608$	33.2139	1.34700
$609$	16.7003	0.676731
$610$	−73.6526	−2.98211
$611$	−15.2038	−0.615082
$612$	11.4479	0.462753
$613$	0.866915	0.0350144	0.0175072	−	0.999847i	$-0.494427\pi$
$613$	0.866915	0.0350144	0.0175072	+	0.999847i	$0.494427\pi$
$614$	53.2388	2.14854
$615$	16.5375	0.666857
$616$	6.95060	0.280048
$617$	−42.3379	−1.70446	−0.852229	−	0.523169i	$-0.824750\pi$
$617$	−42.3379	−1.70446	−0.852229	+	0.523169i	$0.824750\pi$
$618$	52.1486	2.09772
$619$	10.9199	0.438908	0.219454	−	0.975623i	$-0.429572\pi$
$619$	10.9199	0.438908	0.219454	+	0.975623i	$0.429572\pi$
$620$	31.4453	1.26288
$621$	−10.2999	−0.413320
$622$	26.4184	1.05928
$623$	51.6438	2.06907
$624$	6.32852	0.253344
$625$	−25.7770	−1.03108
$626$	10.4622	0.418152
$627$	−13.3855	−0.534565
$628$	11.0958	0.442771
$629$	2.36272	0.0942078
$630$	−55.1798	−2.19841
$631$	−42.8332	−1.70516	−0.852580	−	0.522596i	$-0.824964\pi$
$631$	−42.8332	−1.70516	−0.852580	+	0.522596i	$0.824964\pi$
$632$	−8.15124	−0.324239
$633$	−41.1999	−1.63755
$634$	−15.1769	−0.602751
$635$	−16.3556	−0.649054
$636$	20.8311	0.826007
$637$	−4.58318	−0.181592
$638$	5.01131	0.198399
$639$	−14.0006	−0.553856
$640$	37.4593	1.48071
$641$	−39.1734	−1.54726	−0.773628	−	0.633641i	$-0.781560\pi$
$641$	−39.1734	−1.54726	−0.773628	+	0.633641i	$0.781560\pi$
$642$	−57.2218	−2.25836
$643$	11.9365	0.470731	0.235365	−	0.971907i	$-0.424371\pi$
$643$	11.9365	0.470731	0.235365	+	0.971907i	$0.424371\pi$
$644$	−48.1319	−1.89666
$645$	−5.89398	−0.232075
$646$	−11.6140	−0.456949
$647$	−0.0408462	−0.00160583	−0.000802915	−	1.00000i	$-0.500256\pi$
$647$	−0.0408462	−0.00160583	−0.000802915		1.00000i	$0.500256\pi$
$648$	15.0715	0.592064
$649$	−3.48199	−0.136680
$650$	1.21741	0.0477509
$651$	33.8504	1.32670
$652$	64.7175	2.53453
$653$	−18.5808	−0.727121	−0.363561	−	0.931571i	$-0.618439\pi$
$653$	−18.5808	−0.727121	−0.363561	+	0.931571i	$0.618439\pi$
$654$	−20.9739	−0.820143
$655$	36.8838	1.44117
$656$	−2.03201	−0.0793367
$657$	−6.08839	−0.237531
$658$	−29.3838	−1.14550
$659$	35.5844	1.38617	0.693086	−	0.720855i	$-0.256251\pi$
$659$	35.5844	1.38617	0.693086	+	0.720855i	$0.256251\pi$
$660$	−18.0815	−0.703823
$661$	−41.8997	−1.62971	−0.814855	−	0.579666i	$-0.803183\pi$
$661$	−41.8997	−1.62971	−0.814855	+	0.579666i	$0.803183\pi$
$662$	61.7481	2.39991
$663$	−8.73852	−0.339376
$664$	−18.0047	−0.698717
$665$	33.8880	1.31412
$666$	−19.8481	−0.769100
$667$	−12.0788	−0.467693
$668$	−61.8107	−2.39153
$669$	−13.2914	−0.513874
$670$	36.9438	1.42726
$671$	−14.4022	−0.555992
$672$	48.2981	1.86314
$673$	−31.4460	−1.21215	−0.606077	−	0.795406i	$-0.707257\pi$
$673$	−31.4460	−1.21215	−0.606077	+	0.795406i	$0.707257\pi$
$674$	38.9710	1.50111
$675$	0.304789	0.0117313
$676$	−5.08108	−0.195426
$677$	−35.1826	−1.35218	−0.676089	−	0.736820i	$-0.736327\pi$
$677$	−35.1826	−1.35218	−0.676089	+	0.736820i	$0.736327\pi$
$678$	−84.8480	−3.25857
$679$	−50.5771	−1.94097
$680$	−5.46069	−0.209408
$681$	20.3576	0.780106
$682$	10.1576	0.388954
$683$	30.7428	1.17634	0.588170	−	0.808737i	$-0.299849\pi$
$683$	30.7428	1.17634	0.588170	+	0.808737i	$0.299849\pi$
$684$	59.0607	2.25824
$685$	−37.3099	−1.42554
$686$	36.7073	1.40149
$687$	−28.7236	−1.09587
$688$	0.724210	0.0276102
$689$	−8.81462	−0.335810
$690$	71.9948	2.74079
$691$	−18.1745	−0.691391	−0.345695	−	0.938347i	$-0.612357\pi$
$691$	−18.1745	−0.691391	−0.345695	+	0.938347i	$0.612357\pi$
$692$	32.2227	1.22492
$693$	−10.7900	−0.409878
$694$	−55.9424	−2.12355
$695$	36.9580	1.40190
$696$	−13.8835	−0.526254
$697$	2.80583	0.106278
$698$	62.6851	2.37267
$699$	−71.5431	−2.70601
$700$	1.42430	0.0538334
$701$	23.6444	0.893035	0.446518	−	0.894775i	$-0.352664\pi$
$701$	23.6444	0.893035	0.446518	+	0.894775i	$0.352664\pi$
$702$	14.3925	0.543210
$703$	12.1895	0.459736
$704$	13.0445	0.491633
$705$	26.6063	1.00205
$706$	−5.54307	−0.208616
$707$	6.35229	0.238903
$708$	27.7150	1.04159
$709$	−24.3556	−0.914695	−0.457348	−	0.889288i	$-0.651201\pi$
$709$	−24.3556	−0.914695	−0.457348	+	0.889288i	$0.651201\pi$
$710$	19.1870	0.720076
$711$	12.6538	0.474556
$712$	−42.9332	−1.60899
$713$	−24.4830	−0.916894
$714$	−16.8886	−0.632039
$715$	7.65115	0.286137
$716$	21.7046	0.811140
$717$	−59.7867	−2.23277
$718$	16.4296	0.613148
$719$	−4.24272	−0.158227	−0.0791134	−	0.996866i	$-0.525209\pi$
$719$	−4.24272	−0.158227	−0.0791134	+	0.996866i	$0.525209\pi$
$720$	−6.13919	−0.228794
$721$	−25.8164	−0.961455
$722$	−17.1457	−0.638096
$723$	59.5616	2.21512
$724$	13.1758	0.489675
$725$	0.357430	0.0132746
$726$	−5.84076	−0.216771
$727$	−32.7954	−1.21631	−0.608157	−	0.793817i	$-0.708091\pi$
$727$	−32.7954	−1.21631	−0.608157	+	0.793817i	$0.708091\pi$
$728$	23.4099	0.867630
$729$	−38.1718	−1.41377
$730$	8.34378	0.308817
$731$	−1.00000	−0.0369863
$732$	114.635	4.23702
$733$	30.3450	1.12082	0.560409	−	0.828216i	$-0.310644\pi$
$733$	30.3450	1.12082	0.560409	+	0.828216i	$0.310644\pi$
$734$	32.8206	1.21143
$735$	8.02042	0.295838
$736$	−34.9325	−1.28763
$737$	7.22410	0.266103
$738$	−23.5705	−0.867643
$739$	−34.8569	−1.28223	−0.641115	−	0.767445i	$-0.721528\pi$
$739$	−34.8569	−1.28223	−0.641115	+	0.767445i	$0.721528\pi$
$740$	16.4660	0.605302
$741$	−45.0829	−1.65616
$742$	−17.0357	−0.625399
$743$	44.7376	1.64126	0.820631	−	0.571458i	$-0.193622\pi$
$743$	44.7376	1.64126	0.820631	+	0.571458i	$0.193622\pi$
$744$	−28.1410	−1.03170
$745$	0.763022	0.0279550
$746$	−43.0580	−1.57646
$747$	27.9502	1.02264
$748$	−3.06780	−0.112170
$749$	28.3280	1.03508
$750$	64.2115	2.34467
$751$	52.8444	1.92832	0.964159	−	0.265323i	$-0.0854787\pi$
$751$	52.8444	1.92832	0.964159	+	0.265323i	$0.0854787\pi$
$752$	−3.26919	−0.119215
$753$	−21.5731	−0.786166
$754$	16.8783	0.614672
$755$	17.7347	0.645432
$756$	16.8383	0.612404
$757$	3.01771	0.109680	0.0548402	−	0.998495i	$-0.482535\pi$
$757$	3.01771	0.109680	0.0548402	+	0.998495i	$0.482535\pi$
$758$	−43.2364	−1.57042
$759$	14.0781	0.511001
$760$	−28.1723	−1.02191
$761$	10.9133	0.395608	0.197804	−	0.980242i	$-0.436619\pi$
$761$	10.9133	0.395608	0.197804	+	0.980242i	$0.436619\pi$
$762$	42.0522	1.52339
$763$	10.3832	0.375898
$764$	54.1677	1.95972
$765$	8.47709	0.306490
$766$	81.5976	2.94824
$767$	−11.7275	−0.423456
$768$	−28.6231	−1.03285
$769$	13.9900	0.504493	0.252246	−	0.967663i	$-0.418831\pi$
$769$	13.9900	0.504493	0.252246	+	0.967663i	$0.418831\pi$
$770$	14.7871	0.532889
$771$	7.31838	0.263565
$772$	0.0653986	0.00235375
$773$	44.1771	1.58894	0.794471	−	0.607302i	$-0.207748\pi$
$773$	44.1771	1.58894	0.794471	+	0.607302i	$0.207748\pi$
$774$	8.40055	0.301952
$775$	0.724488	0.0260244
$776$	42.0464	1.50938
$777$	17.7254	0.635895
$778$	42.9381	1.53941
$779$	14.4756	0.518641
$780$	−60.8995	−2.18055
$781$	3.75188	0.134253
$782$	12.2150	0.436807
$783$	4.22562	0.151011
$784$	−0.985492	−0.0351962
$785$	8.21639	0.293256
$786$	−94.8323	−3.38256
$787$	−33.6564	−1.19972	−0.599861	−	0.800105i	$-0.704777\pi$
$787$	−33.6564	−1.19972	−0.599861	+	0.800105i	$0.704777\pi$
$788$	15.9109	0.566803
$789$	56.7220	2.01936
$790$	−17.3413	−0.616978
$791$	42.0045	1.49351
$792$	8.97009	0.318738
$793$	−48.5074	−1.72255
$794$	−78.4520	−2.78416
$795$	15.4253	0.547080
$796$	65.7972	2.33212
$797$	47.1585	1.67044	0.835220	−	0.549916i	$-0.185340\pi$
$797$	47.1585	1.67044	0.835220	+	0.549916i	$0.185340\pi$
$798$	−87.1299	−3.08436
$799$	4.51414	0.159699
$800$	1.03371	0.0365470
$801$	66.6489	2.35492
$802$	−24.8018	−0.875781
$803$	1.63157	0.0575767
$804$	−57.5004	−2.02788
$805$	−35.6414	−1.25619
$806$	34.2112	1.20504
$807$	36.5703	1.28734
$808$	−5.28088	−0.185781
$809$	54.1095	1.90239	0.951194	−	0.308592i	$-0.0998578\pi$
$809$	54.1095	1.90239	0.951194	+	0.308592i	$0.0998578\pi$
$810$	32.0638	1.12661
$811$	−28.4218	−0.998026	−0.499013	−	0.866595i	$-0.666304\pi$
$811$	−28.4218	−0.998026	−0.499013	+	0.866595i	$0.666304\pi$
$812$	19.7466	0.692968
$813$	20.2857	0.711449
$814$	5.31890	0.186427
$815$	47.9230	1.67867
$816$	−1.87899	−0.0657778
$817$	−5.15910	−0.180494
$818$	42.3209	1.47972
$819$	−36.3412	−1.26987
$820$	19.5541	0.682857
$821$	−3.44759	−0.120322	−0.0601609	−	0.998189i	$-0.519161\pi$
$821$	−3.44759	−0.120322	−0.0601609	+	0.998189i	$0.519161\pi$
$822$	95.9279	3.34587
$823$	−39.0127	−1.35990	−0.679948	−	0.733260i	$-0.737998\pi$
$823$	−39.0127	−1.35990	−0.679948	+	0.733260i	$0.737998\pi$
$824$	21.4621	0.747667
$825$	−0.416591	−0.0145039
$826$	−22.6653	−0.788625
$827$	−17.7155	−0.616027	−0.308014	−	0.951382i	$-0.599664\pi$
$827$	−17.7155	−0.616027	−0.308014	+	0.951382i	$0.599664\pi$
$828$	−62.1166	−2.15870
$829$	−5.53398	−0.192203	−0.0961015	−	0.995372i	$-0.530637\pi$
$829$	−5.53398	−0.192203	−0.0961015	+	0.995372i	$0.530637\pi$
$830$	−38.3041	−1.32955
$831$	46.9821	1.62979
$832$	43.9345	1.52315
$833$	1.36078	0.0471483
$834$	−95.0231	−3.29038
$835$	−45.7705	−1.58395
$836$	−15.8271	−0.547391
$837$	8.56505	0.296051
$838$	−0.567402	−0.0196006
$839$	19.7442	0.681645	0.340823	−	0.940128i	$-0.389294\pi$
$839$	19.7442	0.681645	0.340823	+	0.940128i	$0.389294\pi$
$840$	−40.9667	−1.41349
$841$	−24.0446	−0.829123
$842$	−23.1703	−0.798503
$843$	68.0601	2.34411
$844$	−48.7151	−1.67684
$845$	−3.76252	−0.129434
$846$	−37.9213	−1.30376
$847$	2.89150	0.0993532
$848$	−1.89535	−0.0650867
$849$	36.2471	1.24400
$850$	−0.361460	−0.0123980
$851$	−12.8202	−0.439471
$852$	−29.8632	−1.02310
$853$	9.13392	0.312739	0.156370	−	0.987699i	$-0.450021\pi$
$853$	9.13392	0.312739	0.156370	+	0.987699i	$0.450021\pi$
$854$	−93.7482	−3.20800
$855$	43.7342	1.49568
$856$	−23.5500	−0.804922
$857$	15.3110	0.523014	0.261507	−	0.965202i	$-0.415781\pi$
$857$	15.3110	0.523014	0.261507	+	0.965202i	$0.415781\pi$
$858$	−19.6720	−0.671590
$859$	13.8439	0.472347	0.236174	−	0.971711i	$-0.424107\pi$
$859$	13.8439	0.472347	0.236174	+	0.971711i	$0.424107\pi$
$860$	−6.96908	−0.237644
$861$	21.0496	0.717370
$862$	−36.3519	−1.23815
$863$	−38.7304	−1.31840	−0.659199	−	0.751969i	$-0.729104\pi$
$863$	−38.7304	−1.31840	−0.659199	+	0.751969i	$0.729104\pi$
$864$	12.2207	0.415756
$865$	23.8607	0.811289
$866$	63.3139	2.15149
$867$	2.59454	0.0881151
$868$	40.0250	1.35854
$869$	−3.39098	−0.115031
$870$	−29.5365	−1.00138
$871$	24.3311	0.824428
$872$	−8.63193	−0.292314
$873$	−65.2722	−2.20913
$874$	63.0183	2.13162
$875$	−31.7883	−1.07464
$876$	−12.9865	−0.438772
$877$	−0.994549	−0.0335835	−0.0167918	−	0.999859i	$-0.505345\pi$
$877$	−0.994549	−0.0335835	−0.0167918	+	0.999859i	$0.505345\pi$
$878$	−14.4641	−0.488141
$879$	−61.5567	−2.07625
$880$	1.64518	0.0554590
$881$	26.6999	0.899542	0.449771	−	0.893144i	$-0.351506\pi$
$881$	26.6999	0.899542	0.449771	+	0.893144i	$0.351506\pi$
$882$	−11.4313	−0.384913
$883$	−8.76900	−0.295100	−0.147550	−	0.989055i	$-0.547139\pi$
$883$	−8.76900	−0.295100	−0.147550	+	0.989055i	$0.547139\pi$
$884$	−10.3325	−0.347519
$885$	20.5228	0.689866
$886$	−61.6526	−2.07126
$887$	9.29693	0.312160	0.156080	−	0.987744i	$-0.450114\pi$
$887$	9.29693	0.312160	0.156080	+	0.987744i	$0.450114\pi$
$888$	−14.7357	−0.494498
$889$	−20.8182	−0.698219
$890$	−91.3383	−3.06167
$891$	6.26985	0.210048
$892$	−15.7158	−0.526204
$893$	23.2889	0.779334
$894$	−1.96181	−0.0656129
$895$	16.0722	0.537233
$896$	47.6798	1.59287
$897$	47.4156	1.58316
$898$	34.6642	1.15676
$899$	10.0444	0.334998
$900$	1.83813	0.0612709
$901$	2.61713	0.0871893
$902$	6.31642	0.210314
$903$	−7.50211	−0.249655
$904$	−34.9197	−1.16141
$905$	9.75662	0.324321
$906$	−45.5979	−1.51489
$907$	24.1274	0.801137	0.400568	−	0.916267i	$-0.368813\pi$
$907$	24.1274	0.801137	0.400568	+	0.916267i	$0.368813\pi$
$908$	24.0710	0.798823
$909$	8.19795	0.271909
$910$	49.8035	1.65097
$911$	−36.7390	−1.21722	−0.608609	−	0.793470i	$-0.708272\pi$
$911$	−36.7390	−1.21722	−0.608609	+	0.793470i	$0.708272\pi$
$912$	−9.69390	−0.320997
$913$	−7.49008	−0.247886
$914$	−6.35110	−0.210076
$915$	84.8864	2.80626
$916$	−33.9630	−1.12217
$917$	46.9473	1.55033
$918$	−4.27325	−0.141038
$919$	−29.5533	−0.974872	−0.487436	−	0.873159i	$-0.662068\pi$
$919$	−29.5533	−0.974872	−0.487436	+	0.873159i	$0.662068\pi$
$920$	29.6299	0.976869
$921$	−61.3591	−2.02185
$922$	9.35845	0.308204
$923$	12.6365	0.415936
$924$	−23.0150	−0.757137
$925$	0.379370	0.0124736
$926$	57.3185	1.88360
$927$	−33.3174	−1.09429
$928$	14.3314	0.470450
$929$	−40.6271	−1.33293	−0.666466	−	0.745535i	$-0.732194\pi$
$929$	−40.6271	−1.33293	−0.666466	+	0.745535i	$0.732194\pi$
$930$	−59.8686	−1.96317
$931$	7.02041	0.230085
$932$	−84.5930	−2.77094
$933$	−30.4479	−0.996818
$934$	−57.2731	−1.87403
$935$	−2.27169	−0.0742921
$936$	30.2117	0.987500
$937$	9.42677	0.307959	0.153980	−	0.988074i	$-0.450791\pi$
$937$	9.42677	0.307959	0.153980	+	0.988074i	$0.450791\pi$
$938$	47.0237	1.53538
$939$	−12.0579	−0.393495
$940$	31.4594	1.02609
$941$	48.0386	1.56601	0.783007	−	0.622013i	$-0.213685\pi$
$941$	48.0386	1.56601	0.783007	+	0.622013i	$0.213685\pi$
$942$	−21.1253	−0.688298
$943$	−15.2245	−0.495779
$944$	−2.52169	−0.0820741
$945$	12.4687	0.405607
$946$	−2.25118	−0.0731921
$947$	55.5904	1.80644	0.903222	−	0.429174i	$-0.141195\pi$
$947$	55.5904	1.80644	0.903222	+	0.429174i	$0.141195\pi$
$948$	26.9905	0.876612
$949$	5.49519	0.178381
$950$	−1.86481	−0.0605023
$951$	17.4917	0.567208
$952$	−6.95060	−0.225270
$953$	20.0257	0.648695	0.324347	−	0.945938i	$-0.394855\pi$
$953$	20.0257	0.648695	0.324347	+	0.945938i	$0.394855\pi$
$954$	−21.9854	−0.711802
$955$	40.1109	1.29796
$956$	−70.6921	−2.28635
$957$	−5.77565	−0.186700
$958$	13.2236	0.427234
$959$	−47.4896	−1.53352
$960$	−76.8840	−2.48142
$961$	−10.6407	−0.343250
$962$	17.9143	0.577580
$963$	36.5586	1.17809
$964$	70.4260	2.26827
$965$	0.0484273	0.00155893
$966$	91.6381	2.94841
$967$	26.2198	0.843173	0.421586	−	0.906788i	$-0.361473\pi$
$967$	26.2198	0.843173	0.421586	+	0.906788i	$0.361473\pi$
$968$	−2.40380	−0.0772612
$969$	13.3855	0.430004
$970$	89.4517	2.87212
$971$	−54.9853	−1.76456	−0.882280	−	0.470724i	$-0.843993\pi$
$971$	−54.9853	−1.76456	−0.882280	+	0.470724i	$0.843993\pi$
$972$	−67.3751	−2.16106
$973$	47.0417	1.50809
$974$	51.0215	1.63483
$975$	−1.40310	−0.0449351
$976$	−10.4302	−0.333864
$977$	−25.5538	−0.817539	−0.408769	−	0.912638i	$-0.634042\pi$
$977$	−25.5538	−0.817539	−0.408769	+	0.912638i	$0.634042\pi$
$978$	−123.215	−3.93999
$979$	−17.8605	−0.570826
$980$	9.48340	0.302936
$981$	13.4001	0.427831
$982$	66.6245	2.12607
$983$	0.588734	0.0187777	0.00938885	−	0.999956i	$-0.497011\pi$
$983$	0.588734	0.0187777	0.00938885	+	0.999956i	$0.497011\pi$
$984$	−17.4993	−0.557857
$985$	11.7820	0.375404
$986$	−5.01131	−0.159592
$987$	33.8656	1.07795
$988$	−53.3063	−1.69590
$989$	5.42604	0.172538
$990$	19.0834	0.606511
$991$	−32.9635	−1.04712	−0.523560	−	0.851989i	$-0.675396\pi$
$991$	−32.9635	−1.04712	−0.523560	+	0.851989i	$0.675396\pi$
$992$	29.0487	0.922298
$993$	−71.1662	−2.25839
$994$	24.4221	0.774621
$995$	48.7224	1.54460
$996$	59.6175	1.88905
$997$	48.5585	1.53786	0.768932	−	0.639331i	$-0.220789\pi$
$997$	48.5585	1.53786	0.768932	+	0.639331i	$0.220789\pi$
$998$	9.01981	0.285517
$999$	4.48499	0.141899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.6	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.6	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25118 q^{2} +2.59454 q^{3} +3.06780 q^{4} +2.27169 q^{5} -5.84076 q^{6} +2.89150 q^{7} -2.40380 q^{8} +3.73163 q^{9} +O(q^{10})\)	\(q-2.25118 q^{2} +2.59454 q^{3} +3.06780 q^{4} +2.27169 q^{5} -5.84076 q^{6} +2.89150 q^{7} -2.40380 q^{8} +3.73163 q^{9} -5.11397 q^{10} -1.00000 q^{11} +7.95952 q^{12} -3.36805 q^{13} -6.50928 q^{14} +5.89398 q^{15} -0.724210 q^{16} +1.00000 q^{17} -8.40055 q^{18} +5.15910 q^{19} +6.96908 q^{20} +7.50211 q^{21} +2.25118 q^{22} -5.42604 q^{23} -6.23676 q^{24} +0.160565 q^{25} +7.58207 q^{26} +1.89823 q^{27} +8.87054 q^{28} +2.22608 q^{29} -13.2684 q^{30} +4.51212 q^{31} +6.43793 q^{32} -2.59454 q^{33} -2.25118 q^{34} +6.56859 q^{35} +11.4479 q^{36} +2.36272 q^{37} -11.6140 q^{38} -8.73852 q^{39} -5.46069 q^{40} +2.80583 q^{41} -16.8886 q^{42} -1.00000 q^{43} -3.06780 q^{44} +8.47709 q^{45} +12.2150 q^{46} +4.51414 q^{47} -1.87899 q^{48} +1.36078 q^{49} -0.361460 q^{50} +2.59454 q^{51} -10.3325 q^{52} +2.61713 q^{53} -4.27325 q^{54} -2.27169 q^{55} -6.95060 q^{56} +13.3855 q^{57} -5.01131 q^{58} +3.48199 q^{59} +18.0815 q^{60} +14.4022 q^{61} -10.1576 q^{62} +10.7900 q^{63} -13.0445 q^{64} -7.65115 q^{65} +5.84076 q^{66} -7.22410 q^{67} +3.06780 q^{68} -14.0781 q^{69} -14.7871 q^{70} -3.75188 q^{71} -8.97009 q^{72} -1.63157 q^{73} -5.31890 q^{74} +0.416591 q^{75} +15.8271 q^{76} -2.89150 q^{77} +19.6720 q^{78} +3.39098 q^{79} -1.64518 q^{80} -6.26985 q^{81} -6.31642 q^{82} +7.49008 q^{83} +23.0150 q^{84} +2.27169 q^{85} +2.25118 q^{86} +5.77565 q^{87} +2.40380 q^{88} +17.8605 q^{89} -19.0834 q^{90} -9.73871 q^{91} -16.6460 q^{92} +11.7069 q^{93} -10.1621 q^{94} +11.7199 q^{95} +16.7035 q^{96} -17.4916 q^{97} -3.06336 q^{98} -3.73163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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