LMFDB - Embedded newform 539.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(1,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("539.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.53209$ of defining polynomial
Character	$\chi$	$=$	539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53209 q^{2} +2.87939 q^{3} +0.347296 q^{4} +2.34730 q^{5} -4.41147 q^{6} +2.53209 q^{8} +5.29086 q^{9} +O(q^{10})$	\(q-1.53209 q^{2} +2.87939 q^{3} +0.347296 q^{4} +2.34730 q^{5} -4.41147 q^{6} +2.53209 q^{8} +5.29086 q^{9} -3.59627 q^{10} +1.00000 q^{11} +1.00000 q^{12} -0.184793 q^{13} +6.75877 q^{15} -4.57398 q^{16} -3.92127 q^{17} -8.10607 q^{18} +0.773318 q^{19} +0.815207 q^{20} -1.53209 q^{22} +8.35504 q^{23} +7.29086 q^{24} +0.509800 q^{25} +0.283119 q^{26} +6.59627 q^{27} -8.17024 q^{29} -10.3550 q^{30} +2.65270 q^{31} +1.94356 q^{32} +2.87939 q^{33} +6.00774 q^{34} +1.83750 q^{36} -6.82295 q^{37} -1.18479 q^{38} -0.532089 q^{39} +5.94356 q^{40} +0.426022 q^{41} +1.18479 q^{43} +0.347296 q^{44} +12.4192 q^{45} -12.8007 q^{46} -7.68004 q^{47} -13.1702 q^{48} -0.781059 q^{50} -11.2909 q^{51} -0.0641778 q^{52} +6.55438 q^{53} -10.1061 q^{54} +2.34730 q^{55} +2.22668 q^{57} +12.5175 q^{58} +0.204393 q^{59} +2.34730 q^{60} +14.5817 q^{61} -4.06418 q^{62} +6.17024 q^{64} -0.433763 q^{65} -4.41147 q^{66} +3.75877 q^{67} -1.36184 q^{68} +24.0574 q^{69} -9.96585 q^{71} +13.3969 q^{72} +0.120615 q^{73} +10.4534 q^{74} +1.46791 q^{75} +0.268571 q^{76} +0.815207 q^{78} +0.327696 q^{79} -10.7365 q^{80} +3.12061 q^{81} -0.652704 q^{82} +3.35504 q^{83} -9.20439 q^{85} -1.81521 q^{86} -23.5253 q^{87} +2.53209 q^{88} -4.65270 q^{89} -19.0273 q^{90} +2.90167 q^{92} +7.63816 q^{93} +11.7665 q^{94} +1.81521 q^{95} +5.59627 q^{96} +13.1206 q^{97} +5.29086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 6 q^{5} - 3 q^{6} + 3 q^{8}+O(q^{10}) $ 3 * q + 3 * q^3 + 6 * q^5 - 3 * q^6 + 3 * q^8	$ 3 q + 3 q^{3} + 6 q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 3 q^{13} + 9 q^{15} - 6 q^{16} - 3 q^{17} - 12 q^{18} + 9 q^{19} + 6 q^{20} + 6 q^{24} + 3 q^{25} + 9 q^{26} + 6 q^{27} - 3 q^{29} - 6 q^{30} + 9 q^{31} - 9 q^{32} + 3 q^{33} - 6 q^{34} + 3 q^{36} + 3 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{45} - 24 q^{46} - 3 q^{47} - 18 q^{48} + 15 q^{50} - 18 q^{51} + 9 q^{52} + 9 q^{53} - 18 q^{54} + 6 q^{55} + 15 q^{58} + 6 q^{60} + 12 q^{61} - 3 q^{62} - 3 q^{64} + 15 q^{65} - 3 q^{66} - 21 q^{68} + 21 q^{69} - 9 q^{71} + 12 q^{72} + 6 q^{73} + 18 q^{74} + 9 q^{75} - 9 q^{76} + 6 q^{78} - 3 q^{79} - 27 q^{80} + 15 q^{81} - 3 q^{82} - 15 q^{83} - 27 q^{85} - 9 q^{86} - 24 q^{87} + 3 q^{88} - 15 q^{89} - 36 q^{90} - 3 q^{92} + 6 q^{93} + 9 q^{95} + 3 q^{96} + 45 q^{97}+O(q^{100}) $ 3 * q + 3 * q^3 + 6 * q^5 - 3 * q^6 + 3 * q^8 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 3 * q^13 + 9 * q^15 - 6 * q^16 - 3 * q^17 - 12 * q^18 + 9 * q^19 + 6 * q^20 + 6 * q^24 + 3 * q^25 + 9 * q^26 + 6 * q^27 - 3 * q^29 - 6 * q^30 + 9 * q^31 - 9 * q^32 + 3 * q^33 - 6 * q^34 + 3 * q^36 + 3 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^45 - 24 * q^46 - 3 * q^47 - 18 * q^48 + 15 * q^50 - 18 * q^51 + 9 * q^52 + 9 * q^53 - 18 * q^54 + 6 * q^55 + 15 * q^58 + 6 * q^60 + 12 * q^61 - 3 * q^62 - 3 * q^64 + 15 * q^65 - 3 * q^66 - 21 * q^68 + 21 * q^69 - 9 * q^71 + 12 * q^72 + 6 * q^73 + 18 * q^74 + 9 * q^75 - 9 * q^76 + 6 * q^78 - 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 - 15 * q^83 - 27 * q^85 - 9 * q^86 - 24 * q^87 + 3 * q^88 - 15 * q^89 - 36 * q^90 - 3 * q^92 + 6 * q^93 + 9 * q^95 + 3 * q^96 + 45 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.53209	−1.08335	−0.541675	−	0.840588i	$-0.682210\pi$
$2$	−1.53209	−1.08335	−0.541675	+	0.840588i	$0.682210\pi$
$3$	2.87939	1.66241	0.831207	−	0.555963i	$-0.187650\pi$
$3$	2.87939	1.66241	0.831207	+	0.555963i	$0.187650\pi$
$4$	0.347296	0.173648
$5$	2.34730	1.04974	0.524871	−	0.851182i	$-0.324113\pi$
$5$	2.34730	1.04974	0.524871	+	0.851182i	$0.324113\pi$
$6$	−4.41147	−1.80098
$7$	0	0
$7$	0	0
$8$	2.53209	0.895229
$9$	5.29086	1.76362
$10$	−3.59627	−1.13724
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−0.184793	−0.0512522	−0.0256261	−	0.999672i	$-0.508158\pi$
$13$	−0.184793	−0.0512522	−0.0256261	+	0.999672i	$0.508158\pi$
$14$	0	0
$15$	6.75877	1.74511
$16$	−4.57398	−1.14349
$17$	−3.92127	−0.951049	−0.475524	−	0.879703i	$-0.657742\pi$
$17$	−3.92127	−0.951049	−0.475524	+	0.879703i	$0.657742\pi$
$18$	−8.10607	−1.91062
$19$	0.773318	0.177411	0.0887057	−	0.996058i	$-0.471727\pi$
$19$	0.773318	0.177411	0.0887057	+	0.996058i	$0.471727\pi$
$20$	0.815207	0.182286
$21$	0	0
$22$	−1.53209	−0.326642
$23$	8.35504	1.74215	0.871073	−	0.491154i	$-0.163425\pi$
$23$	8.35504	1.74215	0.871073	+	0.491154i	$0.163425\pi$
$24$	7.29086	1.48824
$25$	0.509800	0.101960
$26$	0.283119	0.0555241
$27$	6.59627	1.26945
$28$	0	0
$29$	−8.17024	−1.51718	−0.758588	−	0.651570i	$-0.774111\pi$
$29$	−8.17024	−1.51718	−0.758588	+	0.651570i	$0.774111\pi$
$30$	−10.3550	−1.89056
$31$	2.65270	0.476440	0.238220	−	0.971211i	$-0.423436\pi$
$31$	2.65270	0.476440	0.238220	+	0.971211i	$0.423436\pi$
$32$	1.94356	0.343577
$33$	2.87939	0.501237
$34$	6.00774	1.03032
$35$	0	0
$36$	1.83750	0.306249
$37$	−6.82295	−1.12169	−0.560843	−	0.827922i	$-0.689523\pi$
$37$	−6.82295	−1.12169	−0.560843	+	0.827922i	$0.689523\pi$
$38$	−1.18479	−0.192199
$39$	−0.532089	−0.0852024
$40$	5.94356	0.939760
$41$	0.426022	0.0665335	0.0332667	−	0.999447i	$-0.489409\pi$
$41$	0.426022	0.0665335	0.0332667	+	0.999447i	$0.489409\pi$
$42$	0	0
$43$	1.18479	0.180679	0.0903396	−	0.995911i	$-0.471205\pi$
$43$	1.18479	0.180679	0.0903396	+	0.995911i	$0.471205\pi$
$44$	0.347296	0.0523569
$45$	12.4192	1.85135
$46$	−12.8007	−1.88735
$47$	−7.68004	−1.12025	−0.560125	−	0.828408i	$-0.689247\pi$
$47$	−7.68004	−1.12025	−0.560125	+	0.828408i	$0.689247\pi$
$48$	−13.1702	−1.90096
$49$	0	0
$50$	−0.781059	−0.110458
$51$	−11.2909	−1.58104
$52$	−0.0641778	−0.00889986
$53$	6.55438	0.900313	0.450157	−	0.892950i	$-0.351368\pi$
$53$	6.55438	0.900313	0.450157	+	0.892950i	$0.351368\pi$
$54$	−10.1061	−1.37526
$55$	2.34730	0.316509
$56$	0	0
$57$	2.22668	0.294931
$58$	12.5175	1.64363
$59$	0.204393	0.0266097	0.0133048	−	0.999911i	$-0.495765\pi$
$59$	0.204393	0.0266097	0.0133048	+	0.999911i	$0.495765\pi$
$60$	2.34730	0.303035
$61$	14.5817	1.86700	0.933499	−	0.358580i	$-0.116739\pi$
$61$	14.5817	1.86700	0.933499	+	0.358580i	$0.116739\pi$
$62$	−4.06418	−0.516151
$63$	0	0
$64$	6.17024	0.771281
$65$	−0.433763	−0.0538017
$66$	−4.41147	−0.543015
$67$	3.75877	0.459207	0.229603	−	0.973284i	$-0.426257\pi$
$67$	3.75877	0.459207	0.229603	+	0.973284i	$0.426257\pi$
$68$	−1.36184	−0.165148
$69$	24.0574	2.89617
$70$	0	0
$71$	−9.96585	−1.18273	−0.591365	−	0.806404i	$-0.701411\pi$
$71$	−9.96585	−1.18273	−0.591365	+	0.806404i	$0.701411\pi$
$72$	13.3969	1.57884
$73$	0.120615	0.0141169	0.00705844	−	0.999975i	$-0.497753\pi$
$73$	0.120615	0.0141169	0.00705844	+	0.999975i	$0.497753\pi$
$74$	10.4534	1.21518
$75$	1.46791	0.169500
$76$	0.268571	0.0308072
$77$	0	0
$78$	0.815207	0.0923041
$79$	0.327696	0.0368687	0.0184343	−	0.999830i	$-0.494132\pi$
$79$	0.327696	0.0368687	0.0184343	+	0.999830i	$0.494132\pi$
$80$	−10.7365	−1.20038
$81$	3.12061	0.346735
$82$	−0.652704	−0.0720791
$83$	3.35504	0.368263	0.184132	−	0.982902i	$-0.441053\pi$
$83$	3.35504	0.368263	0.184132	+	0.982902i	$0.441053\pi$
$84$	0	0
$85$	−9.20439	−0.998357
$86$	−1.81521	−0.195739
$87$	−23.5253	−2.52217
$88$	2.53209	0.269922
$89$	−4.65270	−0.493186	−0.246593	−	0.969119i	$-0.579311\pi$
$89$	−4.65270	−0.493186	−0.246593	+	0.969119i	$0.579311\pi$
$90$	−19.0273	−2.00566
$91$	0	0
$92$	2.90167	0.302520
$93$	7.63816	0.792040
$94$	11.7665	1.21362
$95$	1.81521	0.186236
$96$	5.59627	0.571167
$97$	13.1206	1.33220	0.666098	−	0.745864i	$-0.267963\pi$
$97$	13.1206	1.33220	0.666098	+	0.745864i	$0.267963\pi$
$98$	0	0
$99$	5.29086	0.531751
$100$	0.177052	0.0177052
$101$	−5.90167	−0.587239	−0.293619	−	0.955922i	$-0.594860\pi$
$101$	−5.90167	−0.587239	−0.293619	+	0.955922i	$0.594860\pi$
$102$	17.2986	1.71282
$103$	0.921274	0.0907759	0.0453879	−	0.998969i	$-0.485548\pi$
$103$	0.921274	0.0907759	0.0453879	+	0.998969i	$0.485548\pi$
$104$	−0.467911	−0.0458825
$105$	0	0
$106$	−10.0419	−0.975354
$107$	−10.3473	−1.00031	−0.500155	−	0.865936i	$-0.666724\pi$
$107$	−10.3473	−1.00031	−0.500155	+	0.865936i	$0.666724\pi$
$108$	2.29086	0.220438
$109$	0.475652	0.0455592	0.0227796	−	0.999741i	$-0.492748\pi$
$109$	0.475652	0.0455592	0.0227796	+	0.999741i	$0.492748\pi$
$110$	−3.59627	−0.342891
$111$	−19.6459	−1.86471
$112$	0	0
$113$	−3.14290	−0.295659	−0.147830	−	0.989013i	$-0.547229\pi$
$113$	−3.14290	−0.295659	−0.147830	+	0.989013i	$0.547229\pi$
$114$	−3.41147	−0.319514
$115$	19.6117	1.82880
$116$	−2.83750	−0.263455
$117$	−0.977711	−0.0903894
$118$	−0.313148	−0.0288276
$119$	0	0
$120$	17.1138	1.56227
$121$	1.00000	0.0909091
$122$	−22.3405	−2.02261
$123$	1.22668	0.110606
$124$	0.921274	0.0827329
$125$	−10.5398	−0.942711
$126$	0	0
$127$	−0.445622	−0.0395426	−0.0197713	−	0.999805i	$-0.506294\pi$
$127$	−0.445622	−0.0395426	−0.0197713	+	0.999805i	$0.506294\pi$
$128$	−13.3405	−1.17914
$129$	3.41147	0.300364
$130$	0.664563	0.0582860
$131$	−12.0865	−1.05600	−0.528000	−	0.849245i	$-0.677058\pi$
$131$	−12.0865	−1.05600	−0.528000	+	0.849245i	$0.677058\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	−5.75877	−0.497482
$135$	15.4834	1.33260
$136$	−9.92902	−0.851406
$137$	−16.3482	−1.39672	−0.698362	−	0.715745i	$-0.746087\pi$
$137$	−16.3482	−1.39672	−0.698362	+	0.715745i	$0.746087\pi$
$138$	−36.8580	−3.13756
$139$	−20.7297	−1.75827	−0.879134	−	0.476575i	$-0.841878\pi$
$139$	−20.7297	−1.75827	−0.879134	+	0.476575i	$0.841878\pi$
$140$	0	0
$141$	−22.1138	−1.86232
$142$	15.2686	1.28131
$143$	−0.184793	−0.0154531
$144$	−24.2003	−2.01669
$145$	−19.1780	−1.59264
$146$	−0.184793	−0.0152935
$147$	0	0
$148$	−2.36959	−0.194779
$149$	−0.714193	−0.0585090	−0.0292545	−	0.999572i	$-0.509313\pi$
$149$	−0.714193	−0.0585090	−0.0292545	+	0.999572i	$0.509313\pi$
$150$	−2.24897	−0.183628
$151$	−9.54488	−0.776751	−0.388376	−	0.921501i	$-0.626964\pi$
$151$	−9.54488	−0.776751	−0.388376	+	0.921501i	$0.626964\pi$
$152$	1.95811	0.158824
$153$	−20.7469	−1.67729
$154$	0	0
$155$	6.22668	0.500139
$156$	−0.184793	−0.0147952
$157$	9.24123	0.737530	0.368765	−	0.929523i	$-0.379781\pi$
$157$	9.24123	0.737530	0.368765	+	0.929523i	$0.379781\pi$
$158$	−0.502059	−0.0399417
$159$	18.8726	1.49669
$160$	4.56212	0.360667
$161$	0	0
$162$	−4.78106	−0.375635
$163$	−8.80335	−0.689531	−0.344766	−	0.938689i	$-0.612042\pi$
$163$	−8.80335	−0.689531	−0.344766	+	0.938689i	$0.612042\pi$
$164$	0.147956	0.0115534
$165$	6.75877	0.526170
$166$	−5.14022	−0.398958
$167$	8.38238	0.648648	0.324324	−	0.945946i	$-0.394863\pi$
$167$	8.38238	0.648648	0.324324	+	0.945946i	$0.394863\pi$
$168$	0	0
$169$	−12.9659	−0.997373
$170$	14.1019	1.08157
$171$	4.09152	0.312886
$172$	0.411474	0.0313746
$173$	5.44562	0.414023	0.207012	−	0.978339i	$-0.433626\pi$
$173$	5.44562	0.414023	0.207012	+	0.978339i	$0.433626\pi$
$174$	36.0428	2.73240
$175$	0	0
$176$	−4.57398	−0.344777
$177$	0.588526	0.0442363
$178$	7.12836	0.534293
$179$	−10.0915	−0.754276	−0.377138	−	0.926157i	$-0.623092\pi$
$179$	−10.0915	−0.754276	−0.377138	+	0.926157i	$0.623092\pi$
$180$	4.31315	0.321483
$181$	19.8794	1.47762	0.738812	−	0.673912i	$-0.235387\pi$
$181$	19.8794	1.47762	0.738812	+	0.673912i	$0.235387\pi$
$182$	0	0
$183$	41.9864	3.10372
$184$	21.1557	1.55962
$185$	−16.0155	−1.17748
$186$	−11.7023	−0.858057
$187$	−3.92127	−0.286752
$188$	−2.66725	−0.194529
$189$	0	0
$190$	−2.78106	−0.201759
$191$	−25.3851	−1.83680	−0.918399	−	0.395654i	$-0.870518\pi$
$191$	−25.3851	−1.83680	−0.918399	+	0.395654i	$0.870518\pi$
$192$	17.7665	1.28219
$193$	−7.73143	−0.556520	−0.278260	−	0.960506i	$-0.589758\pi$
$193$	−7.73143	−0.556520	−0.278260	+	0.960506i	$0.589758\pi$
$194$	−20.1019	−1.44324
$195$	−1.24897	−0.0894406
$196$	0	0
$197$	−5.37464	−0.382927	−0.191464	−	0.981500i	$-0.561323\pi$
$197$	−5.37464	−0.382927	−0.191464	+	0.981500i	$0.561323\pi$
$198$	−8.10607	−0.576073
$199$	8.78106	0.622473	0.311236	−	0.950333i	$-0.399257\pi$
$199$	8.78106	0.622473	0.311236	+	0.950333i	$0.399257\pi$
$200$	1.29086	0.0912775
$201$	10.8229	0.763392
$202$	9.04189	0.636185
$203$	0	0
$204$	−3.92127	−0.274544
$205$	1.00000	0.0698430
$206$	−1.41147	−0.0983421
$207$	44.2053	3.07248
$208$	0.845237	0.0586066
$209$	0.773318	0.0534916
$210$	0	0
$211$	4.24123	0.291978	0.145989	−	0.989286i	$-0.453364\pi$
$211$	4.24123	0.291978	0.145989	+	0.989286i	$0.453364\pi$
$212$	2.27631	0.156338
$213$	−28.6955	−1.96619
$214$	15.8530	1.08369
$215$	2.78106	0.189667
$216$	16.7023	1.13645
$217$	0	0
$218$	−0.728741	−0.0493566
$219$	0.347296	0.0234681
$220$	0.815207	0.0549613
$221$	0.724622	0.0487434
$222$	30.0993	2.02013
$223$	−18.0351	−1.20772	−0.603859	−	0.797091i	$-0.706371\pi$
$223$	−18.0351	−1.20772	−0.603859	+	0.797091i	$0.706371\pi$
$224$	0	0
$225$	2.69728	0.179819
$226$	4.81521	0.320303
$227$	18.2053	1.20833	0.604165	−	0.796859i	$-0.293507\pi$
$227$	18.2053	1.20833	0.604165	+	0.796859i	$0.293507\pi$
$228$	0.773318	0.0512143
$229$	19.2412	1.27150	0.635748	−	0.771897i	$-0.280692\pi$
$229$	19.2412	1.27150	0.635748	+	0.771897i	$0.280692\pi$
$230$	−30.0469	−1.98124
$231$	0	0
$232$	−20.6878	−1.35822
$233$	9.32501	0.610902	0.305451	−	0.952208i	$-0.401193\pi$
$233$	9.32501	0.610902	0.305451	+	0.952208i	$0.401193\pi$
$234$	1.49794	0.0979234
$235$	−18.0273	−1.17597
$236$	0.0709849	0.00462072
$237$	0.943563	0.0612910
$238$	0	0
$239$	11.1898	0.723811	0.361905	−	0.932215i	$-0.382126\pi$
$239$	11.1898	0.723811	0.361905	+	0.932215i	$0.382126\pi$
$240$	−30.9145	−1.99552
$241$	20.2044	1.30148	0.650740	−	0.759301i	$-0.274459\pi$
$241$	20.2044	1.30148	0.650740	+	0.759301i	$0.274459\pi$
$242$	−1.53209	−0.0984864
$243$	−10.8033	−0.693035
$244$	5.06418	0.324201
$245$	0	0
$246$	−1.87939	−0.119825
$247$	−0.142903	−0.00909273
$248$	6.71688	0.426522
$249$	9.66044	0.612206
$250$	16.1480	1.02129
$251$	−5.89218	−0.371911	−0.185956	−	0.982558i	$-0.559538\pi$
$251$	−5.89218	−0.371911	−0.185956	+	0.982558i	$0.559538\pi$
$252$	0	0
$253$	8.35504	0.525277
$254$	0.682733	0.0428385
$255$	−26.5030	−1.65968
$256$	8.09833	0.506145
$257$	−2.73648	−0.170697	−0.0853485	−	0.996351i	$-0.527200\pi$
$257$	−2.73648	−0.170697	−0.0853485	+	0.996351i	$0.527200\pi$
$258$	−5.22668	−0.325399
$259$	0	0
$260$	−0.150644	−0.00934256
$261$	−43.2276	−2.67572
$262$	18.5175	1.14402
$263$	6.19759	0.382160	0.191080	−	0.981575i	$-0.438801\pi$
$263$	6.19759	0.382160	0.191080	+	0.981575i	$0.438801\pi$
$264$	7.29086	0.448721
$265$	15.3851	0.945097
$266$	0	0
$267$	−13.3969	−0.819879
$268$	1.30541	0.0797404
$269$	−4.20945	−0.256654	−0.128327	−	0.991732i	$-0.540961\pi$
$269$	−4.20945	−0.256654	−0.128327	+	0.991732i	$0.540961\pi$
$270$	−23.7219	−1.44367
$271$	25.5817	1.55398	0.776989	−	0.629514i	$-0.216746\pi$
$271$	25.5817	1.55398	0.776989	+	0.629514i	$0.216746\pi$
$272$	17.9358	1.08752
$273$	0	0
$274$	25.0469	1.51314
$275$	0.509800	0.0307421
$276$	8.35504	0.502914
$277$	−15.3577	−0.922756	−0.461378	−	0.887204i	$-0.652645\pi$
$277$	−15.3577	−0.922756	−0.461378	+	0.887204i	$0.652645\pi$
$278$	31.7597	1.90482
$279$	14.0351	0.840258
$280$	0	0
$281$	19.2540	1.14860	0.574299	−	0.818645i	$-0.305275\pi$
$281$	19.2540	1.14860	0.574299	+	0.818645i	$0.305275\pi$
$282$	33.8803	2.01754
$283$	−27.0651	−1.60885	−0.804427	−	0.594052i	$-0.797527\pi$
$283$	−27.0651	−1.60885	−0.804427	+	0.594052i	$0.797527\pi$
$284$	−3.46110	−0.205379
$285$	5.22668	0.309602
$286$	0.283119	0.0167412
$287$	0	0
$288$	10.2831	0.605939
$289$	−1.62361	−0.0955063
$290$	29.3824	1.72539
$291$	37.7793	2.21466
$292$	0.0418891	0.00245137
$293$	4.03508	0.235732	0.117866	−	0.993030i	$-0.462395\pi$
$293$	4.03508	0.235732	0.117866	+	0.993030i	$0.462395\pi$
$294$	0	0
$295$	0.479771	0.0279333
$296$	−17.2763	−1.00417
$297$	6.59627	0.382754
$298$	1.09421	0.0633857
$299$	−1.54395	−0.0892888
$300$	0.509800	0.0294333
$301$	0	0
$302$	14.6236	0.841494
$303$	−16.9932	−0.976233
$304$	−3.53714	−0.202869
$305$	34.2276	1.95987
$306$	31.7861	1.81709
$307$	2.92902	0.167168	0.0835839	−	0.996501i	$-0.473363\pi$
$307$	2.92902	0.167168	0.0835839	+	0.996501i	$0.473363\pi$
$308$	0	0
$309$	2.65270	0.150907
$310$	−9.53983	−0.541826
$311$	15.6236	0.885934	0.442967	−	0.896538i	$-0.353926\pi$
$311$	15.6236	0.885934	0.442967	+	0.896538i	$0.353926\pi$
$312$	−1.34730	−0.0762756
$313$	−21.9760	−1.24215	−0.621077	−	0.783749i	$-0.713305\pi$
$313$	−21.9760	−1.24215	−0.621077	+	0.783749i	$0.713305\pi$
$314$	−14.1584	−0.799004
$315$	0	0
$316$	0.113808	0.00640218
$317$	−3.01186	−0.169163	−0.0845814	−	0.996417i	$-0.526955\pi$
$317$	−3.01186	−0.169163	−0.0845814	+	0.996417i	$0.526955\pi$
$318$	−28.9145	−1.62144
$319$	−8.17024	−0.457446
$320$	14.4834	0.809646
$321$	−29.7939	−1.66293
$322$	0	0
$323$	−3.03239	−0.168727
$324$	1.08378	0.0602099
$325$	−0.0942073	−0.00522568
$326$	13.4875	0.747004
$327$	1.36959	0.0757382
$328$	1.07873	0.0595627
$329$	0	0
$330$	−10.3550	−0.570026
$331$	27.4688	1.50982	0.754912	−	0.655826i	$-0.227679\pi$
$331$	27.4688	1.50982	0.754912	+	0.655826i	$0.227679\pi$
$332$	1.16519	0.0639482
$333$	−36.0993	−1.97823
$334$	−12.8425	−0.702713
$335$	8.82295	0.482049
$336$	0	0
$337$	17.2422	0.939240	0.469620	−	0.882869i	$-0.344391\pi$
$337$	17.2422	0.939240	0.469620	+	0.882869i	$0.344391\pi$
$338$	19.8648	1.08050
$339$	−9.04963	−0.491508
$340$	−3.19665	−0.173363
$341$	2.65270	0.143652
$342$	−6.26857	−0.338965
$343$	0	0
$344$	3.00000	0.161749
$345$	56.4698	3.04023
$346$	−8.34318	−0.448532
$347$	−11.4311	−0.613652	−0.306826	−	0.951766i	$-0.599267\pi$
$347$	−11.4311	−0.613652	−0.306826	+	0.951766i	$0.599267\pi$
$348$	−8.17024	−0.437971
$349$	28.3209	1.51598	0.757991	−	0.652265i	$-0.226181\pi$
$349$	28.3209	1.51598	0.757991	+	0.652265i	$0.226181\pi$
$350$	0	0
$351$	−1.21894	−0.0650622
$352$	1.94356	0.103592
$353$	16.4361	0.874807	0.437403	−	0.899265i	$-0.355898\pi$
$353$	16.4361	0.874807	0.437403	+	0.899265i	$0.355898\pi$
$354$	−0.901674	−0.0479234
$355$	−23.3928	−1.24156
$356$	−1.61587	−0.0856408
$357$	0	0
$358$	15.4611	0.817145
$359$	24.8631	1.31222	0.656112	−	0.754664i	$-0.272200\pi$
$359$	24.8631	1.31222	0.656112	+	0.754664i	$0.272200\pi$
$360$	31.4466	1.65738
$361$	−18.4020	−0.968525
$362$	−30.4570	−1.60078
$363$	2.87939	0.151129
$364$	0	0
$365$	0.283119	0.0148191
$366$	−64.3269	−3.36242
$367$	4.29860	0.224385	0.112193	−	0.993686i	$-0.464213\pi$
$367$	4.29860	0.224385	0.112193	+	0.993686i	$0.464213\pi$
$368$	−38.2158	−1.99213
$369$	2.25402	0.117340
$370$	24.5371	1.27563
$371$	0	0
$372$	2.65270	0.137536
$373$	−2.72967	−0.141337	−0.0706686	−	0.997500i	$-0.522513\pi$
$373$	−2.72967	−0.141337	−0.0706686	+	0.997500i	$0.522513\pi$
$374$	6.00774	0.310653
$375$	−30.3482	−1.56718
$376$	−19.4466	−1.00288
$377$	1.50980	0.0777587
$378$	0	0
$379$	−16.4584	−0.845412	−0.422706	−	0.906267i	$-0.638920\pi$
$379$	−16.4584	−0.845412	−0.422706	+	0.906267i	$0.638920\pi$
$380$	0.630415	0.0323396
$381$	−1.28312	−0.0657362
$382$	38.8922	1.98990
$383$	−7.85978	−0.401616	−0.200808	−	0.979631i	$-0.564357\pi$
$383$	−7.85978	−0.401616	−0.200808	+	0.979631i	$0.564357\pi$
$384$	−38.4124	−1.96022
$385$	0	0
$386$	11.8452	0.602907
$387$	6.26857	0.318649
$388$	4.55674	0.231334
$389$	9.64321	0.488930	0.244465	−	0.969658i	$-0.421388\pi$
$389$	9.64321	0.488930	0.244465	+	0.969658i	$0.421388\pi$
$390$	1.91353	0.0968955
$391$	−32.7624	−1.65687
$392$	0	0
$393$	−34.8016	−1.75551
$394$	8.23442	0.414844
$395$	0.769200	0.0387026
$396$	1.83750	0.0923377
$397$	−9.43376	−0.473467	−0.236733	−	0.971575i	$-0.576077\pi$
$397$	−9.43376	−0.473467	−0.236733	+	0.971575i	$0.576077\pi$
$398$	−13.4534	−0.674356
$399$	0	0
$400$	−2.33181	−0.116591
$401$	−18.2199	−0.909857	−0.454929	−	0.890528i	$-0.650335\pi$
$401$	−18.2199	−0.909857	−0.454929	+	0.890528i	$0.650335\pi$
$402$	−16.5817	−0.827021
$403$	−0.490200	−0.0244186
$404$	−2.04963	−0.101973
$405$	7.32501	0.363983
$406$	0	0
$407$	−6.82295	−0.338201
$408$	−28.5895	−1.41539
$409$	6.41147	0.317027	0.158513	−	0.987357i	$-0.449330\pi$
$409$	6.41147	0.317027	0.158513	+	0.987357i	$0.449330\pi$
$410$	−1.53209	−0.0756645
$411$	−47.0729	−2.32193
$412$	0.319955	0.0157631
$413$	0	0
$414$	−67.7265	−3.32858
$415$	7.87527	0.386582
$416$	−0.359156	−0.0176091
$417$	−59.6887	−2.92297
$418$	−1.18479	−0.0579501
$419$	1.62092	0.0791871	0.0395935	−	0.999216i	$-0.487394\pi$
$419$	1.62092	0.0791871	0.0395935	+	0.999216i	$0.487394\pi$
$420$	0	0
$421$	31.1489	1.51810	0.759052	−	0.651030i	$-0.225663\pi$
$421$	31.1489	1.51810	0.759052	+	0.651030i	$0.225663\pi$
$422$	−6.49794	−0.316315
$423$	−40.6340	−1.97569
$424$	16.5963	0.805986
$425$	−1.99907	−0.0969690
$426$	43.9641	2.13007
$427$	0	0
$428$	−3.59358	−0.173702
$429$	−0.532089	−0.0256895
$430$	−4.26083	−0.205475
$431$	34.2080	1.64774	0.823871	−	0.566777i	$-0.191810\pi$
$431$	34.2080	1.64774	0.823871	+	0.566777i	$0.191810\pi$
$432$	−30.1712	−1.45161
$433$	−20.4979	−0.985068	−0.492534	−	0.870293i	$-0.663929\pi$
$433$	−20.4979	−0.985068	−0.492534	+	0.870293i	$0.663929\pi$
$434$	0	0
$435$	−55.2208	−2.64764
$436$	0.165192	0.00791127
$437$	6.46110	0.309077
$438$	−0.532089	−0.0254242
$439$	31.3218	1.49491	0.747455	−	0.664313i	$-0.231276\pi$
$439$	31.3218	1.49491	0.747455	+	0.664313i	$0.231276\pi$
$440$	5.94356	0.283348
$441$	0	0
$442$	−1.11019	−0.0528061
$443$	−29.3979	−1.39673	−0.698367	−	0.715740i	$-0.746090\pi$
$443$	−29.3979	−1.39673	−0.698367	+	0.715740i	$0.746090\pi$
$444$	−6.82295	−0.323803
$445$	−10.9213	−0.517718
$446$	27.6313	1.30838
$447$	−2.05644	−0.0972661
$448$	0	0
$449$	−6.90074	−0.325666	−0.162833	−	0.986654i	$-0.552063\pi$
$449$	−6.90074	−0.325666	−0.162833	+	0.986654i	$0.552063\pi$
$450$	−4.13247	−0.194807
$451$	0.426022	0.0200606
$452$	−1.09152	−0.0513407
$453$	−27.4834	−1.29128
$454$	−27.8922	−1.30904
$455$	0	0
$456$	5.63816	0.264031
$457$	12.3746	0.578861	0.289431	−	0.957199i	$-0.406534\pi$
$457$	12.3746	0.578861	0.289431	+	0.957199i	$0.406534\pi$
$458$	−29.4793	−1.37748
$459$	−25.8658	−1.20731
$460$	6.81109	0.317569
$461$	20.0942	0.935881	0.467940	−	0.883760i	$-0.344996\pi$
$461$	20.0942	0.935881	0.467940	+	0.883760i	$0.344996\pi$
$462$	0	0
$463$	8.69190	0.403947	0.201974	−	0.979391i	$-0.435265\pi$
$463$	8.69190	0.403947	0.201974	+	0.979391i	$0.435265\pi$
$464$	37.3705	1.73488
$465$	17.9290	0.831438
$466$	−14.2867	−0.661820
$467$	4.76920	0.220692	0.110346	−	0.993893i	$-0.464804\pi$
$467$	4.76920	0.220692	0.110346	+	0.993893i	$0.464804\pi$
$468$	−0.339556	−0.0156960
$469$	0	0
$470$	27.6195	1.27399
$471$	26.6091	1.22608
$472$	0.517541	0.0238218
$473$	1.18479	0.0544768
$474$	−1.44562	−0.0663996
$475$	0.394238	0.0180889
$476$	0	0
$477$	34.6783	1.58781
$478$	−17.1438	−0.784141
$479$	−39.6141	−1.81001	−0.905007	−	0.425396i	$-0.860135\pi$
$479$	−39.6141	−1.81001	−0.905007	+	0.425396i	$0.860135\pi$
$480$	13.1361	0.599578
$481$	1.26083	0.0574889
$482$	−30.9549	−1.40996
$483$	0	0
$484$	0.347296	0.0157862
$485$	30.7980	1.39846
$486$	16.5517	0.750800
$487$	5.15570	0.233627	0.116813	−	0.993154i	$-0.462732\pi$
$487$	5.15570	0.233627	0.116813	+	0.993154i	$0.462732\pi$
$488$	36.9222	1.67139
$489$	−25.3482	−1.14629
$490$	0	0
$491$	10.1925	0.459983	0.229991	−	0.973193i	$-0.426130\pi$
$491$	10.1925	0.459983	0.229991	+	0.973193i	$0.426130\pi$
$492$	0.426022	0.0192066
$493$	32.0378	1.44291
$494$	0.218941	0.00985061
$495$	12.4192	0.558202
$496$	−12.1334	−0.544806
$497$	0	0
$498$	−14.8007	−0.663233
$499$	5.88981	0.263664	0.131832	−	0.991272i	$-0.457914\pi$
$499$	5.88981	0.263664	0.131832	+	0.991272i	$0.457914\pi$
$500$	−3.66044	−0.163700
$501$	24.1361	1.07832
$502$	9.02734	0.402910
$503$	−12.8348	−0.572276	−0.286138	−	0.958188i	$-0.592372\pi$
$503$	−12.8348	−0.572276	−0.286138	+	0.958188i	$0.592372\pi$
$504$	0	0
$505$	−13.8530	−0.616449
$506$	−12.8007	−0.569059
$507$	−37.3337	−1.65805
$508$	−0.154763	−0.00686650
$509$	32.2131	1.42782	0.713910	−	0.700238i	$-0.246923\pi$
$509$	32.2131	1.42782	0.713910	+	0.700238i	$0.246923\pi$
$510$	40.6049	1.79802
$511$	0	0
$512$	14.2736	0.630811
$513$	5.10101	0.225215
$514$	4.19253	0.184925
$515$	2.16250	0.0952913
$516$	1.18479	0.0521576
$517$	−7.68004	−0.337768
$518$	0	0
$519$	15.6800	0.688278
$520$	−1.09833	−0.0481648
$521$	18.5280	0.811725	0.405863	−	0.913934i	$-0.366971\pi$
$521$	18.5280	0.811725	0.405863	+	0.913934i	$0.366971\pi$
$522$	66.2285	2.89874
$523$	−37.2422	−1.62849	−0.814243	−	0.580524i	$-0.802848\pi$
$523$	−37.2422	−1.62849	−0.814243	+	0.580524i	$0.802848\pi$
$524$	−4.19759	−0.183372
$525$	0	0
$526$	−9.49525	−0.414013
$527$	−10.4020	−0.453117
$528$	−13.1702	−0.573161
$529$	46.8066	2.03507
$530$	−23.5713	−1.02387
$531$	1.08141	0.0469294
$532$	0	0
$533$	−0.0787257	−0.00340999
$534$	20.5253	0.888216
$535$	−24.2882	−1.05007
$536$	9.51754	0.411095
$537$	−29.0574	−1.25392
$538$	6.44924	0.278047
$539$	0	0
$540$	5.37733	0.231403
$541$	36.1566	1.55449	0.777247	−	0.629195i	$-0.216615\pi$
$541$	36.1566	1.55449	0.777247	+	0.629195i	$0.216615\pi$
$542$	−39.1935	−1.68350
$543$	57.2404	2.45642
$544$	−7.62124	−0.326758
$545$	1.11650	0.0478254
$546$	0	0
$547$	12.7980	0.547202	0.273601	−	0.961843i	$-0.411785\pi$
$547$	12.7980	0.547202	0.273601	+	0.961843i	$0.411785\pi$
$548$	−5.67768	−0.242538
$549$	77.1498	3.29267
$550$	−0.781059	−0.0333045
$551$	−6.31820	−0.269164
$552$	60.9154	2.59273
$553$	0	0
$554$	23.5294	0.999668
$555$	−46.1147	−1.95746
$556$	−7.19934	−0.305320
$557$	−30.6587	−1.29905	−0.649525	−	0.760340i	$-0.725032\pi$
$557$	−30.6587	−1.29905	−0.649525	+	0.760340i	$0.725032\pi$
$558$	−21.5030	−0.910294
$559$	−0.218941	−0.00926021
$560$	0	0
$561$	−11.2909	−0.476700
$562$	−29.4989	−1.24433
$563$	−14.5047	−0.611302	−0.305651	−	0.952144i	$-0.598874\pi$
$563$	−14.5047	−0.611302	−0.305651	+	0.952144i	$0.598874\pi$
$564$	−7.68004	−0.323388
$565$	−7.37733	−0.310366
$566$	41.4662	1.74295
$567$	0	0
$568$	−25.2344	−1.05881
$569$	19.0051	0.796733	0.398367	−	0.917226i	$-0.369577\pi$
$569$	19.0051	0.796733	0.398367	+	0.917226i	$0.369577\pi$
$570$	−8.00774	−0.335407
$571$	−21.0009	−0.878862	−0.439431	−	0.898276i	$-0.644820\pi$
$571$	−21.0009	−0.878862	−0.439431	+	0.898276i	$0.644820\pi$
$572$	−0.0641778	−0.00268341
$573$	−73.0934	−3.05352
$574$	0	0
$575$	4.25940	0.177629
$576$	32.6459	1.36025
$577$	−5.18748	−0.215958	−0.107979	−	0.994153i	$-0.534438\pi$
$577$	−5.18748	−0.215958	−0.107979	+	0.994153i	$0.534438\pi$
$578$	2.48751	0.103467
$579$	−22.2618	−0.925167
$580$	−6.66044	−0.276560
$581$	0	0
$582$	−57.8813	−2.39926
$583$	6.55438	0.271455
$584$	0.305407	0.0126378
$585$	−2.29498	−0.0948857
$586$	−6.18210	−0.255380
$587$	8.33813	0.344151	0.172076	−	0.985084i	$-0.444953\pi$
$587$	8.33813	0.344151	0.172076	+	0.985084i	$0.444953\pi$
$588$	0	0
$589$	2.05138	0.0845258
$590$	−0.735051	−0.0302616
$591$	−15.4757	−0.636583
$592$	31.2080	1.28264
$593$	6.10195	0.250577	0.125288	−	0.992120i	$-0.460014\pi$
$593$	6.10195	0.250577	0.125288	+	0.992120i	$0.460014\pi$
$594$	−10.1061	−0.414657
$595$	0	0
$596$	−0.248037	−0.0101600
$597$	25.2841	1.03481
$598$	2.36547	0.0967311
$599$	−13.8503	−0.565907	−0.282954	−	0.959134i	$-0.591314\pi$
$599$	−13.8503	−0.565907	−0.282954	+	0.959134i	$0.591314\pi$
$600$	3.71688	0.151741
$601$	31.2695	1.27551	0.637755	−	0.770239i	$-0.279863\pi$
$601$	31.2695	1.27551	0.637755	+	0.770239i	$0.279863\pi$
$602$	0	0
$603$	19.8871	0.809866
$604$	−3.31490	−0.134881
$605$	2.34730	0.0954312
$606$	26.0351	1.05760
$607$	37.7962	1.53410	0.767051	−	0.641587i	$-0.221724\pi$
$607$	37.7962	1.53410	0.767051	+	0.641587i	$0.221724\pi$
$608$	1.50299	0.0609544
$609$	0	0
$610$	−52.4397	−2.12322
$611$	1.41921	0.0574153
$612$	−7.20533	−0.291258
$613$	21.1343	0.853608	0.426804	−	0.904344i	$-0.359639\pi$
$613$	21.1343	0.853608	0.426804	+	0.904344i	$0.359639\pi$
$614$	−4.48751	−0.181101
$615$	2.87939	0.116108
$616$	0	0
$617$	23.7743	0.957115	0.478558	−	0.878056i	$-0.341160\pi$
$617$	23.7743	0.957115	0.478558	+	0.878056i	$0.341160\pi$
$618$	−4.06418	−0.163485
$619$	13.5021	0.542694	0.271347	−	0.962482i	$-0.412531\pi$
$619$	13.5021	0.542694	0.271347	+	0.962482i	$0.412531\pi$
$620$	2.16250	0.0868482
$621$	55.1121	2.21157
$622$	−23.9368	−0.959776
$623$	0	0
$624$	2.43376	0.0974285
$625$	−27.2891	−1.09156
$626$	33.6691	1.34569
$627$	2.22668	0.0889251
$628$	3.20945	0.128071
$629$	26.7547	1.06678
$630$	0	0
$631$	−38.2354	−1.52213	−0.761063	−	0.648678i	$-0.775322\pi$
$631$	−38.2354	−1.52213	−0.761063	+	0.648678i	$0.775322\pi$
$632$	0.829755	0.0330059
$633$	12.2121	0.485389
$634$	4.61444	0.183263
$635$	−1.04601	−0.0415096
$636$	6.55438	0.259898
$637$	0	0
$638$	12.5175	0.495574
$639$	−52.7279	−2.08588
$640$	−31.3141	−1.23780
$641$	38.5553	1.52284	0.761422	−	0.648257i	$-0.224502\pi$
$641$	38.5553	1.52284	0.761422	+	0.648257i	$0.224502\pi$
$642$	45.6468	1.80154
$643$	19.2627	0.759647	0.379823	−	0.925059i	$-0.375985\pi$
$643$	19.2627	0.759647	0.379823	+	0.925059i	$0.375985\pi$
$644$	0	0
$645$	8.00774	0.315304
$646$	4.64590	0.182790
$647$	39.7844	1.56408	0.782042	−	0.623225i	$-0.214178\pi$
$647$	39.7844	1.56408	0.782042	+	0.623225i	$0.214178\pi$
$648$	7.90167	0.310407
$649$	0.204393	0.00802312
$650$	0.144334	0.00566124
$651$	0	0
$652$	−3.05737	−0.119736
$653$	4.76651	0.186528	0.0932640	−	0.995641i	$-0.470270\pi$
$653$	4.76651	0.186528	0.0932640	+	0.995641i	$0.470270\pi$
$654$	−2.09833	−0.0820510
$655$	−28.3705	−1.10853
$656$	−1.94862	−0.0760807
$657$	0.638156	0.0248968
$658$	0	0
$659$	−38.3550	−1.49410	−0.747050	−	0.664768i	$-0.768530\pi$
$659$	−38.3550	−1.49410	−0.747050	+	0.664768i	$0.768530\pi$
$660$	2.34730	0.0913684
$661$	−10.3628	−0.403065	−0.201533	−	0.979482i	$-0.564592\pi$
$661$	−10.3628	−0.403065	−0.201533	+	0.979482i	$0.564592\pi$
$662$	−42.0847	−1.63567
$663$	2.08647	0.0810316
$664$	8.49525	0.329680
$665$	0	0
$666$	55.3073	2.14311
$667$	−68.2627	−2.64314
$668$	2.91117	0.112637
$669$	−51.9299	−2.00773
$670$	−13.5175	−0.522228
$671$	14.5817	0.562921
$672$	0	0
$673$	−25.6168	−0.987455	−0.493728	−	0.869617i	$-0.664366\pi$
$673$	−25.6168	−0.987455	−0.493728	+	0.869617i	$0.664366\pi$
$674$	−26.4165	−1.01753
$675$	3.36278	0.129433
$676$	−4.50299	−0.173192
$677$	41.8375	1.60795	0.803973	−	0.594666i	$-0.202716\pi$
$677$	41.8375	1.60795	0.803973	+	0.594666i	$0.202716\pi$
$678$	13.8648	0.532476
$679$	0	0
$680$	−23.3063	−0.893757
$681$	52.4201	2.00874
$682$	−4.06418	−0.155625
$683$	−46.0428	−1.76178	−0.880890	−	0.473321i	$-0.843055\pi$
$683$	−46.0428	−1.76178	−0.880890	+	0.473321i	$0.843055\pi$
$684$	1.42097	0.0543321
$685$	−38.3741	−1.46620
$686$	0	0
$687$	55.4029	2.11375
$688$	−5.41921	−0.206606
$689$	−1.21120	−0.0461430
$690$	−86.5167	−3.29364
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	1.89124	0.0718943
$693$	0	0
$694$	17.5134	0.664800
$695$	−48.6587	−1.84573
$696$	−59.5681	−2.25792
$697$	−1.67055	−0.0632766
$698$	−43.3901	−1.64234
$699$	26.8503	1.01557
$700$	0	0
$701$	−32.8144	−1.23938	−0.619691	−	0.784846i	$-0.712742\pi$
$701$	−32.8144	−1.23938	−0.619691	+	0.784846i	$0.712742\pi$
$702$	1.86753	0.0704852
$703$	−5.27631	−0.199000
$704$	6.17024	0.232550
$705$	−51.9077	−1.95496
$706$	−25.1816	−0.947722
$707$	0	0
$708$	0.204393	0.00768156
$709$	7.40198	0.277987	0.138994	−	0.990293i	$-0.455613\pi$
$709$	7.40198	0.277987	0.138994	+	0.990293i	$0.455613\pi$
$710$	35.8399	1.34505
$711$	1.73379	0.0650223
$712$	−11.7811	−0.441514
$713$	22.1634	0.830027
$714$	0	0
$715$	−0.433763	−0.0162218
$716$	−3.50475	−0.130979
$717$	32.2199	1.20327
$718$	−38.0925	−1.42160
$719$	−14.1370	−0.527222	−0.263611	−	0.964629i	$-0.584914\pi$
$719$	−14.1370	−0.527222	−0.263611	+	0.964629i	$0.584914\pi$
$720$	−56.8052	−2.11701
$721$	0	0
$722$	28.1935	1.04925
$723$	58.1762	2.16360
$724$	6.90404	0.256587
$725$	−4.16519	−0.154691
$726$	−4.41147	−0.163725
$727$	15.2790	0.566667	0.283333	−	0.959021i	$-0.408560\pi$
$727$	15.2790	0.566667	0.283333	+	0.959021i	$0.408560\pi$
$728$	0	0
$729$	−40.4688	−1.49885
$730$	−0.433763	−0.0160543
$731$	−4.64590	−0.171835
$732$	14.5817	0.538956
$733$	1.34493	0.0496762	0.0248381	−	0.999691i	$-0.492093\pi$
$733$	1.34493	0.0496762	0.0248381	+	0.999691i	$0.492093\pi$
$734$	−6.58584	−0.243088
$735$	0	0
$736$	16.2385	0.598561
$737$	3.75877	0.138456
$738$	−3.45336	−0.127120
$739$	−25.6536	−0.943684	−0.471842	−	0.881683i	$-0.656411\pi$
$739$	−25.6536	−0.943684	−0.471842	+	0.881683i	$0.656411\pi$
$740$	−5.56212	−0.204468
$741$	−0.411474	−0.0151159
$742$	0	0
$743$	−6.08109	−0.223094	−0.111547	−	0.993759i	$-0.535580\pi$
$743$	−6.08109	−0.223094	−0.111547	+	0.993759i	$0.535580\pi$
$744$	19.3405	0.709057
$745$	−1.67642	−0.0614194
$746$	4.18210	0.153118
$747$	17.7510	0.649476
$748$	−1.36184	−0.0497940
$749$	0	0
$750$	46.4962	1.69780
$751$	20.8108	0.759396	0.379698	−	0.925111i	$-0.376028\pi$
$751$	20.8108	0.759396	0.379698	+	0.925111i	$0.376028\pi$
$752$	35.1284	1.28100
$753$	−16.9659	−0.618270
$754$	−2.31315	−0.0842399
$755$	−22.4047	−0.815389
$756$	0	0
$757$	−5.25402	−0.190961	−0.0954804	−	0.995431i	$-0.530439\pi$
$757$	−5.25402	−0.190961	−0.0954804	+	0.995431i	$0.530439\pi$
$758$	25.2158	0.915877
$759$	24.0574	0.873227
$760$	4.59627	0.166724
$761$	−40.9813	−1.48557	−0.742786	−	0.669529i	$-0.766496\pi$
$761$	−40.9813	−1.48557	−0.742786	+	0.669529i	$0.766496\pi$
$762$	1.96585	0.0712153
$763$	0	0
$764$	−8.81614	−0.318957
$765$	−48.6991	−1.76072
$766$	12.0419	0.435091
$767$	−0.0377703	−0.00136381
$768$	23.3182	0.841423
$769$	47.5580	1.71499	0.857493	−	0.514496i	$-0.172021\pi$
$769$	47.5580	1.71499	0.857493	+	0.514496i	$0.172021\pi$
$770$	0	0
$771$	−7.87939	−0.283769
$772$	−2.68510	−0.0966388
$773$	20.4929	0.737078	0.368539	−	0.929612i	$-0.379858\pi$
$773$	20.4929	0.737078	0.368539	+	0.929612i	$0.379858\pi$
$774$	−9.60401	−0.345209
$775$	1.35235	0.0485778
$776$	33.2226	1.19262
$777$	0	0
$778$	−14.7743	−0.529683
$779$	0.329451	0.0118038
$780$	−0.433763	−0.0155312
$781$	−9.96585	−0.356606
$782$	50.1949	1.79497
$783$	−53.8931	−1.92598
$784$	0	0
$785$	21.6919	0.774217
$786$	53.3191	1.90183
$787$	−19.1206	−0.681576	−0.340788	−	0.940140i	$-0.610694\pi$
$787$	−19.1206	−0.681576	−0.340788	+	0.940140i	$0.610694\pi$
$788$	−1.86659	−0.0664946
$789$	17.8452	0.635307
$790$	−1.17848	−0.0419285
$791$	0	0
$792$	13.3969	0.476039
$793$	−2.69459	−0.0956878
$794$	14.4534	0.512931
$795$	44.2995	1.57114
$796$	3.04963	0.108091
$797$	−52.5144	−1.86015	−0.930077	−	0.367365i	$-0.880260\pi$
$797$	−52.5144	−1.86015	−0.930077	+	0.367365i	$0.880260\pi$
$798$	0	0
$799$	30.1156	1.06541
$800$	0.990829	0.0350311
$801$	−24.6168	−0.869792
$802$	27.9145	0.985694
$803$	0.120615	0.00425640
$804$	3.75877	0.132562
$805$	0	0
$806$	0.751030	0.0264539
$807$	−12.1206	−0.426666
$808$	−14.9436	−0.525713
$809$	40.6715	1.42993	0.714967	−	0.699159i	$-0.246442\pi$
$809$	40.6715	1.42993	0.714967	+	0.699159i	$0.246442\pi$
$810$	−11.2226	−0.394321
$811$	−20.5648	−0.722128	−0.361064	−	0.932541i	$-0.617586\pi$
$811$	−20.5648	−0.722128	−0.361064	+	0.932541i	$0.617586\pi$
$812$	0	0
$813$	73.6596	2.58336
$814$	10.4534	0.366390
$815$	−20.6641	−0.723831
$816$	51.6441	1.80791
$817$	0.916222	0.0320545
$818$	−9.82295	−0.343451
$819$	0	0
$820$	0.347296	0.0121281
$821$	6.36278	0.222062	0.111031	−	0.993817i	$-0.464585\pi$
$821$	6.36278	0.222062	0.111031	+	0.993817i	$0.464585\pi$
$822$	72.1198	2.51547
$823$	−2.50887	−0.0874536	−0.0437268	−	0.999044i	$-0.513923\pi$
$823$	−2.50887	−0.0874536	−0.0437268	+	0.999044i	$0.513923\pi$
$824$	2.33275	0.0812651
$825$	1.46791	0.0511061
$826$	0	0
$827$	−41.2645	−1.43491	−0.717453	−	0.696607i	$-0.754692\pi$
$827$	−41.2645	−1.43491	−0.717453	+	0.696607i	$0.754692\pi$
$828$	15.3523	0.533531
$829$	−46.7779	−1.62466	−0.812331	−	0.583196i	$-0.801802\pi$
$829$	−46.7779	−1.62466	−0.812331	+	0.583196i	$0.801802\pi$
$830$	−12.0656	−0.418803
$831$	−44.2208	−1.53400
$832$	−1.14022	−0.0395298
$833$	0	0
$834$	91.4484	3.16660
$835$	19.6759	0.680913
$836$	0.268571	0.00928871
$837$	17.4979	0.604817
$838$	−2.48339	−0.0857874
$839$	16.5439	0.571161	0.285580	−	0.958355i	$-0.407814\pi$
$839$	16.5439	0.571161	0.285580	+	0.958355i	$0.407814\pi$
$840$	0	0
$841$	37.7529	1.30182
$842$	−47.7229	−1.64464
$843$	55.4397	1.90945
$844$	1.47296	0.0507015
$845$	−30.4347	−1.04699
$846$	62.2550	2.14037
$847$	0	0
$848$	−29.9796	−1.02950
$849$	−77.9309	−2.67458
$850$	3.06275	0.105051
$851$	−57.0060	−1.95414
$852$	−9.96585	−0.341424
$853$	13.2163	0.452516	0.226258	−	0.974067i	$-0.427351\pi$
$853$	13.2163	0.452516	0.226258	+	0.974067i	$0.427351\pi$
$854$	0	0
$855$	9.60401	0.328450
$856$	−26.2003	−0.895507
$857$	−50.7211	−1.73260	−0.866300	−	0.499524i	$-0.833508\pi$
$857$	−50.7211	−1.73260	−0.866300	+	0.499524i	$0.833508\pi$
$858$	0.815207	0.0278307
$859$	55.1124	1.88041	0.940205	−	0.340609i	$-0.110633\pi$
$859$	55.1124	1.88041	0.940205	+	0.340609i	$0.110633\pi$
$860$	0.965852	0.0329353
$861$	0	0
$862$	−52.4097	−1.78508
$863$	10.5202	0.358113	0.179056	−	0.983839i	$-0.442696\pi$
$863$	10.5202	0.358113	0.179056	+	0.983839i	$0.442696\pi$
$864$	12.8203	0.436154
$865$	12.7825	0.434618
$866$	31.4047	1.06717
$867$	−4.67499	−0.158771
$868$	0	0
$869$	0.327696	0.0111163
$870$	84.6032	2.86832
$871$	−0.694593	−0.0235354
$872$	1.20439	0.0407859
$873$	69.4193	2.34949
$874$	−9.89899	−0.334838
$875$	0	0
$876$	0.120615	0.00407520
$877$	−39.6536	−1.33901	−0.669504	−	0.742808i	$-0.733493\pi$
$877$	−39.6536	−1.33901	−0.669504	+	0.742808i	$0.733493\pi$
$878$	−47.9878	−1.61951
$879$	11.6186	0.391884
$880$	−10.7365	−0.361927
$881$	25.0077	0.842532	0.421266	−	0.906937i	$-0.361586\pi$
$881$	25.0077	0.842532	0.421266	+	0.906937i	$0.361586\pi$
$882$	0	0
$883$	50.9341	1.71407	0.857034	−	0.515260i	$-0.172305\pi$
$883$	50.9341	1.71407	0.857034	+	0.515260i	$0.172305\pi$
$884$	0.251659	0.00846420
$885$	1.38144	0.0464368
$886$	45.0401	1.51315
$887$	32.0360	1.07566	0.537832	−	0.843052i	$-0.319243\pi$
$887$	32.0360	1.07566	0.537832	+	0.843052i	$0.319243\pi$
$888$	−49.7452	−1.66934
$889$	0	0
$890$	16.7324	0.560870
$891$	3.12061	0.104545
$892$	−6.26352	−0.209718
$893$	−5.93912	−0.198745
$894$	3.15064	0.105373
$895$	−23.6878	−0.791795
$896$	0	0
$897$	−4.44562	−0.148435
$898$	10.5725	0.352810
$899$	−21.6732	−0.722843
$900$	0.936756	0.0312252
$901$	−25.7015	−0.856242
$902$	−0.652704	−0.0217327
$903$	0	0
$904$	−7.95811	−0.264683
$905$	46.6628	1.55112
$906$	42.1070	1.39891
$907$	−16.4730	−0.546976	−0.273488	−	0.961875i	$-0.588177\pi$
$907$	−16.4730	−0.546976	−0.273488	+	0.961875i	$0.588177\pi$
$908$	6.32264	0.209824
$909$	−31.2249	−1.03567
$910$	0	0
$911$	−45.3979	−1.50410	−0.752049	−	0.659107i	$-0.770934\pi$
$911$	−45.3979	−1.50410	−0.752049	+	0.659107i	$0.770934\pi$
$912$	−10.1848	−0.337252
$913$	3.35504	0.111036
$914$	−18.9590	−0.627109
$915$	98.5545	3.25811
$916$	6.68241	0.220793
$917$	0	0
$918$	39.6287	1.30794
$919$	−12.3209	−0.406429	−0.203214	−	0.979134i	$-0.565139\pi$
$919$	−12.3209	−0.406429	−0.203214	+	0.979134i	$0.565139\pi$
$920$	49.6587	1.63720
$921$	8.43376	0.277902
$922$	−30.7861	−1.01389
$923$	1.84161	0.0606175
$924$	0	0
$925$	−3.47834	−0.114367
$926$	−13.3168	−0.437616
$927$	4.87433	0.160094
$928$	−15.8794	−0.521266
$929$	5.93313	0.194660	0.0973299	−	0.995252i	$-0.468970\pi$
$929$	5.93313	0.194660	0.0973299	+	0.995252i	$0.468970\pi$
$930$	−27.4688	−0.900739
$931$	0	0
$932$	3.23854	0.106082
$933$	44.9864	1.47279
$934$	−7.30684	−0.239087
$935$	−9.20439	−0.301016
$936$	−2.47565	−0.0809192
$937$	−45.0242	−1.47088	−0.735438	−	0.677593i	$-0.763023\pi$
$937$	−45.0242	−1.47088	−0.735438	+	0.677593i	$0.763023\pi$
$938$	0	0
$939$	−63.2772	−2.06497
$940$	−6.26083	−0.204206
$941$	−6.06242	−0.197629	−0.0988147	−	0.995106i	$-0.531505\pi$
$941$	−6.06242	−0.197629	−0.0988147	+	0.995106i	$0.531505\pi$
$942$	−40.7674	−1.32828
$943$	3.55943	0.115911
$944$	−0.934889	−0.0304280
$945$	0	0
$946$	−1.81521	−0.0590175
$947$	−18.9426	−0.615553	−0.307776	−	0.951459i	$-0.599585\pi$
$947$	−18.9426	−0.615553	−0.307776	+	0.951459i	$0.599585\pi$
$948$	0.327696	0.0106431
$949$	−0.0222887	−0.000723522 0
$950$	−0.604007	−0.0195966
$951$	−8.67230	−0.281219
$952$	0	0
$953$	−12.4970	−0.404818	−0.202409	−	0.979301i	$-0.564877\pi$
$953$	−12.4970	−0.404818	−0.202409	+	0.979301i	$0.564877\pi$
$954$	−53.1302	−1.72015
$955$	−59.5863	−1.92817
$956$	3.88619	0.125688
$957$	−23.5253	−0.760464
$958$	60.6923	1.96088
$959$	0	0
$960$	41.7033	1.34597
$961$	−23.9632	−0.773005
$962$	−1.93170	−0.0622806
$963$	−54.7461	−1.76417
$964$	7.01691	0.226000
$965$	−18.1480	−0.584203
$966$	0	0
$967$	−18.5294	−0.595865	−0.297933	−	0.954587i	$-0.596297\pi$
$967$	−18.5294	−0.595865	−0.297933	+	0.954587i	$0.596297\pi$
$968$	2.53209	0.0813844
$969$	−8.73143	−0.280494
$970$	−47.1852	−1.51503
$971$	41.4739	1.33096	0.665480	−	0.746415i	$-0.268227\pi$
$971$	41.4739	1.33096	0.665480	+	0.746415i	$0.268227\pi$
$972$	−3.75196	−0.120344
$973$	0	0
$974$	−7.89899	−0.253100
$975$	−0.271259	−0.00868724
$976$	−66.6965	−2.13490
$977$	−22.2321	−0.711267	−0.355633	−	0.934626i	$-0.615735\pi$
$977$	−22.2321	−0.711267	−0.355633	+	0.934626i	$0.615735\pi$
$978$	38.8357	1.24183
$979$	−4.65270	−0.148701
$980$	0	0
$981$	2.51661	0.0803491
$982$	−15.6159	−0.498322
$983$	35.4124	1.12948	0.564740	−	0.825269i	$-0.308976\pi$
$983$	35.4124	1.12948	0.564740	+	0.825269i	$0.308976\pi$
$984$	3.10607	0.0990178
$985$	−12.6159	−0.401975
$986$	−49.0847	−1.56318
$987$	0	0
$988$	−0.0496299	−0.00157894
$989$	9.89899	0.314769
$990$	−19.0273	−0.604729
$991$	45.5725	1.44766	0.723830	−	0.689979i	$-0.242380\pi$
$991$	45.5725	1.44766	0.723830	+	0.689979i	$0.242380\pi$
$992$	5.15570	0.163694
$993$	79.0934	2.50995
$994$	0	0
$995$	20.6117	0.653436
$996$	3.35504	0.106308
$997$	22.8367	0.723245	0.361622	−	0.932325i	$-0.382223\pi$
$997$	22.8367	0.723245	0.361622	+	0.932325i	$0.382223\pi$
$998$	−9.02372	−0.285641
$999$	−45.0060	−1.42393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.a.j.1.1		3
3.2	odd	2		4851.2.a.bj.1.3		3
4.3	odd	2		8624.2.a.ch.1.1		3
7.2	even	3		77.2.e.a.67.3	yes	6
7.3	odd	6		539.2.e.m.177.3		6
7.4	even	3		77.2.e.a.23.3	✓	6
7.5	odd	6		539.2.e.m.67.3		6
7.6	odd	2		539.2.a.g.1.1		3
11.10	odd	2		5929.2.a.x.1.3		3
21.2	odd	6		693.2.i.h.298.1		6
21.11	odd	6		693.2.i.h.100.1		6
21.20	even	2		4851.2.a.bk.1.3		3
28.11	odd	6		1232.2.q.m.177.3		6
28.23	odd	6		1232.2.q.m.529.3		6
28.27	even	2		8624.2.a.co.1.3		3
77.2	odd	30		847.2.n.f.81.1		24
77.4	even	15		847.2.n.g.632.3		24
77.9	even	15		847.2.n.g.81.3		24
77.16	even	15		847.2.n.g.487.1		24
77.18	odd	30		847.2.n.f.632.1		24
77.25	even	15		847.2.n.g.9.1		24
77.30	odd	30		847.2.n.f.130.1		24
77.32	odd	6		847.2.e.c.485.1		6
77.37	even	15		847.2.n.g.753.1		24
77.39	odd	30		847.2.n.f.366.1		24
77.46	odd	30		847.2.n.f.807.3		24
77.51	odd	30		847.2.n.f.753.3		24
77.53	even	15		847.2.n.g.807.1		24
77.58	even	15		847.2.n.g.130.3		24
77.60	even	15		847.2.n.g.366.3		24
77.65	odd	6		847.2.e.c.606.1		6
77.72	odd	30		847.2.n.f.487.3		24
77.74	odd	30		847.2.n.f.9.3		24
77.76	even	2		5929.2.a.u.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.3	✓	6	7.4	even	3
77.2.e.a.67.3	yes	6	7.2	even	3
539.2.a.g.1.1		3	7.6	odd	2
539.2.a.j.1.1		3	1.1	even	1	trivial
539.2.e.m.67.3		6	7.5	odd	6
539.2.e.m.177.3		6	7.3	odd	6
693.2.i.h.100.1		6	21.11	odd	6
693.2.i.h.298.1		6	21.2	odd	6
847.2.e.c.485.1		6	77.32	odd	6
847.2.e.c.606.1		6	77.65	odd	6
847.2.n.f.9.3		24	77.74	odd	30
847.2.n.f.81.1		24	77.2	odd	30
847.2.n.f.130.1		24	77.30	odd	30
847.2.n.f.366.1		24	77.39	odd	30
847.2.n.f.487.3		24	77.72	odd	30
847.2.n.f.632.1		24	77.18	odd	30
847.2.n.f.753.3		24	77.51	odd	30
847.2.n.f.807.3		24	77.46	odd	30
847.2.n.g.9.1		24	77.25	even	15
847.2.n.g.81.3		24	77.9	even	15
847.2.n.g.130.3		24	77.58	even	15
847.2.n.g.366.3		24	77.60	even	15
847.2.n.g.487.1		24	77.16	even	15
847.2.n.g.632.3		24	77.4	even	15
847.2.n.g.753.1		24	77.37	even	15
847.2.n.g.807.1		24	77.53	even	15
1232.2.q.m.177.3		6	28.11	odd	6
1232.2.q.m.529.3		6	28.23	odd	6
4851.2.a.bj.1.3		3	3.2	odd	2
4851.2.a.bk.1.3		3	21.20	even	2
5929.2.a.u.1.3		3	77.76	even	2
5929.2.a.x.1.3		3	11.10	odd	2
8624.2.a.ch.1.1		3	4.3	odd	2
8624.2.a.co.1.3		3	28.27	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53209 q^{2} +2.87939 q^{3} +0.347296 q^{4} +2.34730 q^{5} -4.41147 q^{6} +2.53209 q^{8} +5.29086 q^{9} +O(q^{10})\)	\(q-1.53209 q^{2} +2.87939 q^{3} +0.347296 q^{4} +2.34730 q^{5} -4.41147 q^{6} +2.53209 q^{8} +5.29086 q^{9} -3.59627 q^{10} +1.00000 q^{11} +1.00000 q^{12} -0.184793 q^{13} +6.75877 q^{15} -4.57398 q^{16} -3.92127 q^{17} -8.10607 q^{18} +0.773318 q^{19} +0.815207 q^{20} -1.53209 q^{22} +8.35504 q^{23} +7.29086 q^{24} +0.509800 q^{25} +0.283119 q^{26} +6.59627 q^{27} -8.17024 q^{29} -10.3550 q^{30} +2.65270 q^{31} +1.94356 q^{32} +2.87939 q^{33} +6.00774 q^{34} +1.83750 q^{36} -6.82295 q^{37} -1.18479 q^{38} -0.532089 q^{39} +5.94356 q^{40} +0.426022 q^{41} +1.18479 q^{43} +0.347296 q^{44} +12.4192 q^{45} -12.8007 q^{46} -7.68004 q^{47} -13.1702 q^{48} -0.781059 q^{50} -11.2909 q^{51} -0.0641778 q^{52} +6.55438 q^{53} -10.1061 q^{54} +2.34730 q^{55} +2.22668 q^{57} +12.5175 q^{58} +0.204393 q^{59} +2.34730 q^{60} +14.5817 q^{61} -4.06418 q^{62} +6.17024 q^{64} -0.433763 q^{65} -4.41147 q^{66} +3.75877 q^{67} -1.36184 q^{68} +24.0574 q^{69} -9.96585 q^{71} +13.3969 q^{72} +0.120615 q^{73} +10.4534 q^{74} +1.46791 q^{75} +0.268571 q^{76} +0.815207 q^{78} +0.327696 q^{79} -10.7365 q^{80} +3.12061 q^{81} -0.652704 q^{82} +3.35504 q^{83} -9.20439 q^{85} -1.81521 q^{86} -23.5253 q^{87} +2.53209 q^{88} -4.65270 q^{89} -19.0273 q^{90} +2.90167 q^{92} +7.63816 q^{93} +11.7665 q^{94} +1.81521 q^{95} +5.59627 q^{96} +13.1206 q^{97} +5.29086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 6 q^{5} - 3 q^{6} + 3 q^{8}+O(q^{10}) \) 3 * q + 3 * q^3 + 6 * q^5 - 3 * q^6 + 3 * q^8	\( 3 q + 3 q^{3} + 6 q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 3 q^{13} + 9 q^{15} - 6 q^{16} - 3 q^{17} - 12 q^{18} + 9 q^{19} + 6 q^{20} + 6 q^{24} + 3 q^{25} + 9 q^{26} + 6 q^{27} - 3 q^{29} - 6 q^{30} + 9 q^{31} - 9 q^{32} + 3 q^{33} - 6 q^{34} + 3 q^{36} + 3 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{45} - 24 q^{46} - 3 q^{47} - 18 q^{48} + 15 q^{50} - 18 q^{51} + 9 q^{52} + 9 q^{53} - 18 q^{54} + 6 q^{55} + 15 q^{58} + 6 q^{60} + 12 q^{61} - 3 q^{62} - 3 q^{64} + 15 q^{65} - 3 q^{66} - 21 q^{68} + 21 q^{69} - 9 q^{71} + 12 q^{72} + 6 q^{73} + 18 q^{74} + 9 q^{75} - 9 q^{76} + 6 q^{78} - 3 q^{79} - 27 q^{80} + 15 q^{81} - 3 q^{82} - 15 q^{83} - 27 q^{85} - 9 q^{86} - 24 q^{87} + 3 q^{88} - 15 q^{89} - 36 q^{90} - 3 q^{92} + 6 q^{93} + 9 q^{95} + 3 q^{96} + 45 q^{97}+O(q^{100}) \) 3 * q + 3 * q^3 + 6 * q^5 - 3 * q^6 + 3 * q^8 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 3 * q^13 + 9 * q^15 - 6 * q^16 - 3 * q^17 - 12 * q^18 + 9 * q^19 + 6 * q^20 + 6 * q^24 + 3 * q^25 + 9 * q^26 + 6 * q^27 - 3 * q^29 - 6 * q^30 + 9 * q^31 - 9 * q^32 + 3 * q^33 - 6 * q^34 + 3 * q^36 + 3 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^45 - 24 * q^46 - 3 * q^47 - 18 * q^48 + 15 * q^50 - 18 * q^51 + 9 * q^52 + 9 * q^53 - 18 * q^54 + 6 * q^55 + 15 * q^58 + 6 * q^60 + 12 * q^61 - 3 * q^62 - 3 * q^64 + 15 * q^65 - 3 * q^66 - 21 * q^68 + 21 * q^69 - 9 * q^71 + 12 * q^72 + 6 * q^73 + 18 * q^74 + 9 * q^75 - 9 * q^76 + 6 * q^78 - 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 - 15 * q^83 - 27 * q^85 - 9 * q^86 - 24 * q^87 + 3 * q^88 - 15 * q^89 - 36 * q^90 - 3 * q^92 + 6 * q^93 + 9 * q^95 + 3 * q^96 + 45 * q^97

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