LMFDB - Embedded newform 841.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(1,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("841.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.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:	$6.71541880999$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.11973625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 15x^{3} + 13x^{2} - 27x + 9 $ x^6 - 2x^5 - 8x^4 + 15x^3 + 13x^2 - 27*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.94573$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.94573 q^{2} -2.27154 q^{3} +1.78585 q^{4} +3.21726 q^{5} +4.41979 q^{6} -2.53022 q^{7} +0.416673 q^{8} +2.15987 q^{9} -6.25991 q^{10} -1.12328 q^{11} -4.05663 q^{12} -1.54902 q^{13} +4.92311 q^{14} -7.30813 q^{15} -4.38244 q^{16} +4.41979 q^{17} -4.20253 q^{18} -4.91337 q^{19} +5.74556 q^{20} +5.74748 q^{21} +2.18560 q^{22} +2.47406 q^{23} -0.946487 q^{24} +5.35078 q^{25} +3.01398 q^{26} +1.90838 q^{27} -4.51860 q^{28} +14.2196 q^{30} +1.58761 q^{31} +7.69368 q^{32} +2.55158 q^{33} -8.59970 q^{34} -8.14037 q^{35} +3.85722 q^{36} +8.28372 q^{37} +9.56008 q^{38} +3.51866 q^{39} +1.34055 q^{40} -11.7882 q^{41} -11.1830 q^{42} +1.88390 q^{43} -2.00602 q^{44} +6.94888 q^{45} -4.81385 q^{46} -0.962649 q^{47} +9.95486 q^{48} -0.597997 q^{49} -10.4111 q^{50} -10.0397 q^{51} -2.76633 q^{52} +1.61810 q^{53} -3.71318 q^{54} -3.61390 q^{55} -1.05427 q^{56} +11.1609 q^{57} -13.3686 q^{59} -13.0512 q^{60} -1.92241 q^{61} -3.08905 q^{62} -5.46495 q^{63} -6.20492 q^{64} -4.98362 q^{65} -4.96468 q^{66} -3.02385 q^{67} +7.89309 q^{68} -5.61992 q^{69} +15.8389 q^{70} +4.14265 q^{71} +0.899961 q^{72} -3.79682 q^{73} -16.1178 q^{74} -12.1545 q^{75} -8.77456 q^{76} +2.84215 q^{77} -6.84635 q^{78} -13.2356 q^{79} -14.0994 q^{80} -10.8146 q^{81} +22.9366 q^{82} -9.70833 q^{83} +10.2642 q^{84} +14.2196 q^{85} -3.66555 q^{86} -0.468042 q^{88} +4.87979 q^{89} -13.5206 q^{90} +3.91937 q^{91} +4.41831 q^{92} -3.60630 q^{93} +1.87305 q^{94} -15.8076 q^{95} -17.4765 q^{96} -15.6150 q^{97} +1.16354 q^{98} -2.42615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 6 q^{9} - 15 q^{10} - 13 q^{11} + 4 q^{12} - 6 q^{13} + 6 q^{14} - 19 q^{15} + 4 q^{16} - 3 q^{17} - 17 q^{18} + 6 q^{19} - 5 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 6 * q^9 - 15 * q^10 - 13 * q^11 + 4 * q^12 - 6 * q^13 + 6 * q^14 - 19 * q^15 + 4 * q^16 - 3 * q^17 - 17 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 - 4 * q^22 - 5 * q^23 - 10 * q^24 + 6 * q^25 - 9 * q^26 + q^27 - 5 * q^28 + 26 * q^30 - 16 * q^31 - 33 * q^32 + 27 * q^33 - 4 * q^35 - 21 * q^36 + 10 * q^37 + 41 * q^38 - 17 * q^39 - 7 * q^40 - 30 * q^41 - 21 * q^42 + 2 * q^43 - 16 * q^44 + 16 * q^45 + 20 * q^46 - 5 * q^47 + 30 * q^48 - 12 * q^49 + 8 * q^50 - 23 * q^51 - 13 * q^53 + 19 * q^54 - 10 * q^55 - 16 * q^56 - 16 * q^57 - 17 * q^59 + 9 * q^60 + 4 * q^61 - 9 * q^63 + q^64 + 32 * q^65 + 8 * q^66 - 9 * q^67 - 16 * q^68 - 26 * q^69 + 28 * q^70 + 21 * q^72 - 9 * q^73 - 36 * q^74 - 7 * q^75 - 24 * q^76 - 13 * q^77 - 6 * q^79 + 5 * q^80 - 22 * q^81 + 19 * q^82 - 24 * q^83 + 26 * q^85 + 17 * q^86 + 21 * q^88 - 9 * q^89 + 16 * q^90 + 16 * q^91 - 23 * q^92 - 12 * q^93 - 37 * q^94 - 31 * q^95 - 37 * q^96 + 10 * q^97 + 42 * q^98 - 6 * q^99

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 $

$2$	−1.94573	−1.37584	−0.687918	−	0.725788i	$-0.741475\pi$
$2$	−1.94573	−1.37584	−0.687918	+	0.725788i	$0.741475\pi$
$3$	−2.27154	−1.31147	−0.655736	−	0.754990i	$-0.727642\pi$
$3$	−2.27154	−1.31147	−0.655736	+	0.754990i	$0.727642\pi$
$4$	1.78585	0.892926
$5$	3.21726	1.43880	0.719402	−	0.694594i	$-0.244416\pi$
$5$	3.21726	1.43880	0.719402	+	0.694594i	$0.244416\pi$
$6$	4.41979	1.80437
$7$	−2.53022	−0.956332	−0.478166	−	0.878269i	$-0.658698\pi$
$7$	−2.53022	−0.956332	−0.478166	+	0.878269i	$0.658698\pi$
$8$	0.416673	0.147316
$9$	2.15987	0.719958
$10$	−6.25991	−1.97956
$11$	−1.12328	−0.338683	−0.169341	−	0.985557i	$-0.554164\pi$
$11$	−1.12328	−0.338683	−0.169341	+	0.985557i	$0.554164\pi$
$12$	−4.05663	−1.17105
$13$	−1.54902	−0.429622	−0.214811	−	0.976656i	$-0.568914\pi$
$13$	−1.54902	−0.429622	−0.214811	+	0.976656i	$0.568914\pi$
$14$	4.92311	1.31576
$15$	−7.30813	−1.88695
$16$	−4.38244	−1.09561
$17$	4.41979	1.07196	0.535978	−	0.844232i	$-0.319943\pi$
$17$	4.41979	1.07196	0.535978	+	0.844232i	$0.319943\pi$
$18$	−4.20253	−0.990545
$19$	−4.91337	−1.12721	−0.563603	−	0.826046i	$-0.690585\pi$
$19$	−4.91337	−1.12721	−0.563603	+	0.826046i	$0.690585\pi$
$20$	5.74556	1.28475
$21$	5.74748	1.25420
$22$	2.18560	0.465972
$23$	2.47406	0.515877	0.257939	−	0.966161i	$-0.416957\pi$
$23$	2.47406	0.515877	0.257939	+	0.966161i	$0.416957\pi$
$24$	−0.946487	−0.193201
$25$	5.35078	1.07016
$26$	3.01398	0.591089
$27$	1.90838	0.367267
$28$	−4.51860	−0.853934
$29$	0	0
$29$	0	0
$30$	14.2196	2.59613
$31$	1.58761	0.285142	0.142571	−	0.989785i	$-0.454463\pi$
$31$	1.58761	0.285142	0.142571	+	0.989785i	$0.454463\pi$
$32$	7.69368	1.36006
$33$	2.55158	0.444173
$34$	−8.59970	−1.47484
$35$	−8.14037	−1.37597
$36$	3.85722	0.642869
$37$	8.28372	1.36183	0.680917	−	0.732360i	$-0.261581\pi$
$37$	8.28372	1.36183	0.680917	+	0.732360i	$0.261581\pi$
$38$	9.56008	1.55085
$39$	3.51866	0.563437
$40$	1.34055	0.211959
$41$	−11.7882	−1.84101	−0.920504	−	0.390733i	$-0.872222\pi$
$41$	−11.7882	−1.84101	−0.920504	+	0.390733i	$0.872222\pi$
$42$	−11.1830	−1.72558
$43$	1.88390	0.287292	0.143646	−	0.989629i	$-0.454117\pi$
$43$	1.88390	0.287292	0.143646	+	0.989629i	$0.454117\pi$
$44$	−2.00602	−0.302419
$45$	6.94888	1.03588
$46$	−4.81385	−0.709763
$47$	−0.962649	−0.140417	−0.0702084	−	0.997532i	$-0.522366\pi$
$47$	−0.962649	−0.140417	−0.0702084	+	0.997532i	$0.522366\pi$
$48$	9.95486	1.43686
$49$	−0.597997	−0.0854282
$50$	−10.4111	−1.47236
$51$	−10.0397	−1.40584
$52$	−2.76633	−0.383621
$53$	1.61810	0.222263	0.111132	−	0.993806i	$-0.464552\pi$
$53$	1.61810	0.222263	0.111132	+	0.993806i	$0.464552\pi$
$54$	−3.71318	−0.505299
$55$	−3.61390	−0.487298
$56$	−1.05427	−0.140883
$57$	11.1609	1.47830
$58$	0	0
$59$	−13.3686	−1.74045	−0.870224	−	0.492657i	$-0.836026\pi$
$59$	−13.3686	−1.74045	−0.870224	+	0.492657i	$0.836026\pi$
$60$	−13.0512	−1.68491
$61$	−1.92241	−0.246140	−0.123070	−	0.992398i	$-0.539274\pi$
$61$	−1.92241	−0.246140	−0.123070	+	0.992398i	$0.539274\pi$
$62$	−3.08905	−0.392309
$63$	−5.46495	−0.688519
$64$	−6.20492	−0.775615
$65$	−4.98362	−0.618141
$66$	−4.96468	−0.611109
$67$	−3.02385	−0.369421	−0.184711	−	0.982793i	$-0.559135\pi$
$67$	−3.02385	−0.369421	−0.184711	+	0.982793i	$0.559135\pi$
$68$	7.89309	0.957177
$69$	−5.61992	−0.676559
$70$	15.8389	1.89312
$71$	4.14265	0.491642	0.245821	−	0.969315i	$-0.420942\pi$
$71$	4.14265	0.491642	0.245821	+	0.969315i	$0.420942\pi$
$72$	0.899961	0.106061
$73$	−3.79682	−0.444384	−0.222192	−	0.975003i	$-0.571321\pi$
$73$	−3.79682	−0.444384	−0.222192	+	0.975003i	$0.571321\pi$
$74$	−16.1178	−1.87366
$75$	−12.1545	−1.40348
$76$	−8.77456	−1.00651
$77$	2.84215	0.323893
$78$	−6.84635	−0.775197
$79$	−13.2356	−1.48913	−0.744563	−	0.667552i	$-0.767342\pi$
$79$	−13.2356	−1.48913	−0.744563	+	0.667552i	$0.767342\pi$
$80$	−14.0994	−1.57637
$81$	−10.8146	−1.20162
$82$	22.9366	2.53293
$83$	−9.70833	−1.06563	−0.532814	−	0.846232i	$-0.678865\pi$
$83$	−9.70833	−1.06563	−0.532814	+	0.846232i	$0.678865\pi$
$84$	10.2642	1.11991
$85$	14.2196	1.54233
$86$	−3.66555	−0.395267
$87$	0	0
$88$	−0.468042	−0.0498934
$89$	4.87979	0.517257	0.258628	−	0.965977i	$-0.416730\pi$
$89$	4.87979	0.517257	0.258628	+	0.965977i	$0.416730\pi$
$90$	−13.5206	−1.42520
$91$	3.91937	0.410861
$92$	4.41831	0.460640
$93$	−3.60630	−0.373956
$94$	1.87305	0.193190
$95$	−15.8076	−1.62183
$96$	−17.4765	−1.78368
$97$	−15.6150	−1.58546	−0.792731	−	0.609571i	$-0.791342\pi$
$97$	−15.6150	−1.58546	−0.792731	+	0.609571i	$0.791342\pi$
$98$	1.16354	0.117535
$99$	−2.42615	−0.243837
$100$	9.55570	0.955570
$101$	−11.3941	−1.13376	−0.566880	−	0.823800i	$-0.691850\pi$
$101$	−11.3941	−1.13376	−0.566880	+	0.823800i	$0.691850\pi$
$102$	19.5345	1.93421
$103$	7.38911	0.728070	0.364035	−	0.931385i	$-0.381399\pi$
$103$	7.38911	0.728070	0.364035	+	0.931385i	$0.381399\pi$
$104$	−0.645436	−0.0632902
$105$	18.4912	1.80455
$106$	−3.14838	−0.305798
$107$	−11.9202	−1.15237	−0.576183	−	0.817321i	$-0.695458\pi$
$107$	−11.9202	−1.15237	−0.576183	+	0.817321i	$0.695458\pi$
$108$	3.40808	0.327942
$109$	16.1719	1.54898	0.774492	−	0.632583i	$-0.218005\pi$
$109$	16.1719	1.54898	0.774492	+	0.632583i	$0.218005\pi$
$110$	7.03166	0.670442
$111$	−18.8168	−1.78601
$112$	11.0885	1.04777
$113$	−6.34816	−0.597184	−0.298592	−	0.954381i	$-0.596517\pi$
$113$	−6.34816	−0.597184	−0.298592	+	0.954381i	$0.596517\pi$
$114$	−21.7161	−2.03390
$115$	7.95970	0.742246
$116$	0	0
$117$	−3.34570	−0.309310
$118$	26.0117	2.39457
$119$	−11.1830	−1.02515
$120$	−3.04510	−0.277978
$121$	−9.73823	−0.885294
$122$	3.74049	0.338648
$123$	26.7773	2.41443
$124$	2.83523	0.254611
$125$	1.12854	0.100940
$126$	10.6333	0.947290
$127$	−17.8415	−1.58318	−0.791590	−	0.611053i	$-0.790746\pi$
$127$	−17.8415	−1.58318	−0.791590	+	0.611053i	$0.790746\pi$
$128$	−3.31428	−0.292943
$129$	−4.27934	−0.376775
$130$	9.69675	0.850461
$131$	0.574730	0.0502144	0.0251072	−	0.999685i	$-0.492007\pi$
$131$	0.574730	0.0502144	0.0251072	+	0.999685i	$0.492007\pi$
$132$	4.55674	0.396614
$133$	12.4319	1.07798
$134$	5.88358	0.508264
$135$	6.13974	0.528425
$136$	1.84161	0.157916
$137$	13.7829	1.17755	0.588774	−	0.808297i	$-0.299611\pi$
$137$	13.7829	1.17755	0.588774	+	0.808297i	$0.299611\pi$
$138$	10.9348	0.930834
$139$	10.6013	0.899192	0.449596	−	0.893232i	$-0.351568\pi$
$139$	10.6013	0.899192	0.449596	+	0.893232i	$0.351568\pi$
$140$	−14.5375	−1.22864
$141$	2.18669	0.184153
$142$	−8.06046	−0.676419
$143$	1.73999	0.145506
$144$	−9.46551	−0.788793
$145$	0	0
$146$	7.38758	0.611400
$147$	1.35837	0.112037
$148$	14.7935	1.21602
$149$	2.36656	0.193876	0.0969381	−	0.995290i	$-0.469095\pi$
$149$	2.36656	0.193876	0.0969381	+	0.995290i	$0.469095\pi$
$150$	23.6493	1.93096
$151$	9.74934	0.793390	0.396695	−	0.917950i	$-0.370157\pi$
$151$	9.74934	0.793390	0.396695	+	0.917950i	$0.370157\pi$
$152$	−2.04727	−0.166056
$153$	9.54619	0.771763
$154$	−5.53005	−0.445624
$155$	5.10774	0.410264
$156$	6.28381	0.503108
$157$	18.7547	1.49679	0.748396	−	0.663252i	$-0.230824\pi$
$157$	18.7547	1.49679	0.748396	+	0.663252i	$0.230824\pi$
$158$	25.7530	2.04879
$159$	−3.67557	−0.291492
$160$	24.7526	1.95686
$161$	−6.25991	−0.493350
$162$	21.0422	1.65323
$163$	−9.65226	−0.756023	−0.378012	−	0.925801i	$-0.623392\pi$
$163$	−9.65226	−0.756023	−0.378012	+	0.925801i	$0.623392\pi$
$164$	−21.0520	−1.64388
$165$	8.20910	0.639078
$166$	18.8898	1.46613
$167$	0.464845	0.0359708	0.0179854	−	0.999838i	$-0.494275\pi$
$167$	0.464845	0.0359708	0.0179854	+	0.999838i	$0.494275\pi$
$168$	2.39482	0.184764
$169$	−10.6005	−0.815425
$170$	−27.6675	−2.12200
$171$	−10.6123	−0.811541
$172$	3.36437	0.256530
$173$	−22.2914	−1.69478	−0.847392	−	0.530968i	$-0.821828\pi$
$173$	−22.2914	−1.69478	−0.847392	+	0.530968i	$0.821828\pi$
$174$	0	0
$175$	−13.5386	−1.02342
$176$	4.92272	0.371064
$177$	30.3673	2.28255
$178$	−9.49474	−0.711661
$179$	7.50994	0.561319	0.280660	−	0.959807i	$-0.409447\pi$
$179$	7.50994	0.561319	0.280660	+	0.959807i	$0.409447\pi$
$180$	12.4097	0.924963
$181$	−23.9371	−1.77923	−0.889615	−	0.456711i	$-0.849027\pi$
$181$	−23.9371	−1.77923	−0.889615	+	0.456711i	$0.849027\pi$
$182$	−7.62602	−0.565278
$183$	4.36683	0.322806
$184$	1.03087	0.0759971
$185$	26.6509	1.95941
$186$	7.01688	0.514503
$187$	−4.96468	−0.363053
$188$	−1.71915	−0.125382
$189$	−4.82861	−0.351229
$190$	30.7573	2.23137
$191$	−13.4059	−0.970016	−0.485008	−	0.874510i	$-0.661183\pi$
$191$	−13.4059	−0.970016	−0.485008	+	0.874510i	$0.661183\pi$
$192$	14.0947	1.01720
$193$	−12.7705	−0.919243	−0.459622	−	0.888115i	$-0.652015\pi$
$193$	−12.7705	−0.919243	−0.459622	+	0.888115i	$0.652015\pi$
$194$	30.3825	2.18134
$195$	11.3205	0.810675
$196$	−1.06794	−0.0762811
$197$	−4.07710	−0.290481	−0.145241	−	0.989396i	$-0.546396\pi$
$197$	−4.07710	−0.290481	−0.145241	+	0.989396i	$0.546396\pi$
$198$	4.72063	0.335480
$199$	16.9678	1.20282	0.601409	−	0.798941i	$-0.294606\pi$
$199$	16.9678	1.20282	0.601409	+	0.798941i	$0.294606\pi$
$200$	2.22952	0.157651
$201$	6.86877	0.484486
$202$	22.1699	1.55987
$203$	0	0
$204$	−17.9294	−1.25531
$205$	−37.9258	−2.64885
$206$	−14.3772	−1.00171
$207$	5.34366	0.371410
$208$	6.78850	0.470698
$209$	5.51911	0.381765
$210$	−35.9787	−2.48277
$211$	−4.41621	−0.304024	−0.152012	−	0.988379i	$-0.548575\pi$
$211$	−4.41621	−0.304024	−0.152012	+	0.988379i	$0.548575\pi$
$212$	2.88969	0.198465
$213$	−9.41017	−0.644774
$214$	23.1934	1.58547
$215$	6.06100	0.413357
$216$	0.795168	0.0541044
$217$	−4.01699	−0.272691
$218$	−31.4660	−2.13115
$219$	8.62462	0.582798
$220$	−6.45389	−0.435121
$221$	−6.84635	−0.460536
$222$	36.6123	2.45725
$223$	−17.0683	−1.14298	−0.571488	−	0.820611i	$-0.693634\pi$
$223$	−17.0683	−1.14298	−0.571488	+	0.820611i	$0.693634\pi$
$224$	−19.4667	−1.30067
$225$	11.5570	0.770467
$226$	12.3518	0.821628
$227$	−9.78008	−0.649127	−0.324563	−	0.945864i	$-0.605217\pi$
$227$	−9.78008	−0.649127	−0.324563	+	0.945864i	$0.605217\pi$
$228$	19.9317	1.32001
$229$	3.43919	0.227268	0.113634	−	0.993523i	$-0.463751\pi$
$229$	3.43919	0.227268	0.113634	+	0.993523i	$0.463751\pi$
$230$	−15.4874	−1.02121
$231$	−6.45605	−0.424777
$232$	0	0
$233$	−4.39157	−0.287702	−0.143851	−	0.989599i	$-0.545949\pi$
$233$	−4.39157	−0.287702	−0.143851	+	0.989599i	$0.545949\pi$
$234$	6.50981	0.425560
$235$	−3.09709	−0.202032
$236$	−23.8744	−1.55409
$237$	30.0652	1.95295
$238$	21.7591	1.41043
$239$	17.6803	1.14364	0.571821	−	0.820378i	$-0.306237\pi$
$239$	17.6803	1.14364	0.571821	+	0.820378i	$0.306237\pi$
$240$	32.0274	2.06736
$241$	11.4068	0.734778	0.367389	−	0.930067i	$-0.380252\pi$
$241$	11.4068	0.734778	0.367389	+	0.930067i	$0.380252\pi$
$242$	18.9479	1.21802
$243$	18.8405	1.20862
$244$	−3.43315	−0.219785
$245$	−1.92391	−0.122914
$246$	−52.1014	−3.32186
$247$	7.61093	0.484272
$248$	0.661512	0.0420061
$249$	22.0528	1.39754
$250$	−2.19583	−0.138877
$251$	−25.5356	−1.61179	−0.805897	−	0.592056i	$-0.798317\pi$
$251$	−25.5356	−1.61179	−0.805897	+	0.592056i	$0.798317\pi$
$252$	−9.75960	−0.614797
$253$	−2.77907	−0.174719
$254$	34.7147	2.17820
$255$	−32.3004	−2.02273
$256$	18.8585	1.17866
$257$	0.178617	0.0111418	0.00557091	−	0.999984i	$-0.498227\pi$
$257$	0.178617	0.0111418	0.00557091	+	0.999984i	$0.498227\pi$
$258$	8.32643	0.518381
$259$	−20.9596	−1.30237
$260$	−8.90000	−0.551955
$261$	0	0
$262$	−1.11827	−0.0690869
$263$	−5.63230	−0.347303	−0.173651	−	0.984807i	$-0.555557\pi$
$263$	−5.63230	−0.347303	−0.173651	+	0.984807i	$0.555557\pi$
$264$	1.06317	0.0654338
$265$	5.20585	0.319793
$266$	−24.1891	−1.48313
$267$	−11.0846	−0.678367
$268$	−5.40014	−0.329866
$269$	1.94833	0.118792	0.0593958	−	0.998235i	$-0.481083\pi$
$269$	1.94833	0.118792	0.0593958	+	0.998235i	$0.481083\pi$
$270$	−11.9463	−0.727026
$271$	17.4418	1.05951	0.529756	−	0.848150i	$-0.322284\pi$
$271$	17.4418	1.05951	0.529756	+	0.848150i	$0.322284\pi$
$272$	−19.3694	−1.17444
$273$	−8.90298	−0.538833
$274$	−26.8177	−1.62011
$275$	−6.01044	−0.362443
$276$	−10.0363	−0.604117
$277$	−15.3445	−0.921964	−0.460982	−	0.887409i	$-0.652503\pi$
$277$	−15.3445	−0.921964	−0.460982	+	0.887409i	$0.652503\pi$
$278$	−20.6273	−1.23714
$279$	3.42903	0.205291
$280$	−3.39187	−0.202703
$281$	−13.2112	−0.788114	−0.394057	−	0.919086i	$-0.628929\pi$
$281$	−13.2112	−0.788114	−0.394057	+	0.919086i	$0.628929\pi$
$282$	−4.25470	−0.253364
$283$	−11.1563	−0.663170	−0.331585	−	0.943425i	$-0.607583\pi$
$283$	−11.1563	−0.663170	−0.331585	+	0.943425i	$0.607583\pi$
$284$	7.39816	0.439000
$285$	35.9076	2.12698
$286$	−3.38555	−0.200192
$287$	29.8267	1.76062
$288$	16.6174	0.979188
$289$	2.53452	0.149090
$290$	0	0
$291$	35.4700	2.07929
$292$	−6.78056	−0.396802
$293$	6.80277	0.397422	0.198711	−	0.980058i	$-0.436324\pi$
$293$	6.80277	0.397422	0.198711	+	0.980058i	$0.436324\pi$
$294$	−2.64302	−0.154144
$295$	−43.0104	−2.50416
$296$	3.45160	0.200620
$297$	−2.14365	−0.124387
$298$	−4.60468	−0.266742
$299$	−3.83238	−0.221632
$300$	−21.7061	−1.25320
$301$	−4.76668	−0.274747
$302$	−18.9695	−1.09157
$303$	25.8822	1.48689
$304$	21.5325	1.23498
$305$	−6.18491	−0.354147
$306$	−18.5743	−1.06182
$307$	16.1578	0.922176	0.461088	−	0.887354i	$-0.347459\pi$
$307$	16.1578	0.922176	0.461088	+	0.887354i	$0.347459\pi$
$308$	5.07567	0.289213
$309$	−16.7846	−0.954844
$310$	−9.93827	−0.564456
$311$	4.33954	0.246073	0.123036	−	0.992402i	$-0.460737\pi$
$311$	4.33954	0.246073	0.123036	+	0.992402i	$0.460737\pi$
$312$	1.46613	0.0830033
$313$	1.07340	0.0606724	0.0303362	−	0.999540i	$-0.490342\pi$
$313$	1.07340	0.0606724	0.0303362	+	0.999540i	$0.490342\pi$
$314$	−36.4916	−2.05934
$315$	−17.5822	−0.990644
$316$	−23.6369	−1.32968
$317$	−7.79415	−0.437763	−0.218882	−	0.975751i	$-0.570241\pi$
$317$	−7.79415	−0.437763	−0.218882	+	0.975751i	$0.570241\pi$
$318$	7.15166	0.401045
$319$	0	0
$320$	−19.9629	−1.11596
$321$	27.0771	1.51130
$322$	12.1801	0.678769
$323$	−21.7161	−1.20831
$324$	−19.3132	−1.07296
$325$	−8.28848	−0.459762
$326$	18.7807	1.04016
$327$	−36.7350	−2.03145
$328$	−4.91183	−0.271210
$329$	2.43571	0.134285
$330$	−15.9727	−0.879266
$331$	9.95716	0.547295	0.273648	−	0.961830i	$-0.411770\pi$
$331$	9.95716	0.547295	0.273648	+	0.961830i	$0.411770\pi$
$332$	−17.3377	−0.951527
$333$	17.8918	0.980464
$334$	−0.904461	−0.0494899
$335$	−9.72850	−0.531525
$336$	−25.1880	−1.37412
$337$	21.3599	1.16355	0.581774	−	0.813350i	$-0.302359\pi$
$337$	21.3599	1.16355	0.581774	+	0.813350i	$0.302359\pi$
$338$	20.6257	1.12189
$339$	14.4201	0.783191
$340$	25.3941	1.37719
$341$	−1.78333	−0.0965728
$342$	20.6486	1.11655
$343$	19.2246	1.03803
$344$	0.784970	0.0423227
$345$	−18.0807	−0.973435
$346$	43.3730	2.33174
$347$	26.9149	1.44487	0.722434	−	0.691440i	$-0.243023\pi$
$347$	26.9149	1.44487	0.722434	+	0.691440i	$0.243023\pi$
$348$	0	0
$349$	18.7783	1.00518	0.502591	−	0.864524i	$-0.332380\pi$
$349$	18.7783	1.00518	0.502591	+	0.864524i	$0.332380\pi$
$350$	26.3425	1.40806
$351$	−2.95612	−0.157786
$352$	−8.64218	−0.460630
$353$	29.5764	1.57419	0.787095	−	0.616831i	$-0.211584\pi$
$353$	29.5764	1.57419	0.787095	+	0.616831i	$0.211584\pi$
$354$	−59.0865	−3.14041
$355$	13.3280	0.707376
$356$	8.71458	0.461872
$357$	25.4026	1.34445
$358$	−14.6123	−0.772283
$359$	−20.2837	−1.07053	−0.535267	−	0.844683i	$-0.679789\pi$
$359$	−20.2837	−1.07053	−0.535267	+	0.844683i	$0.679789\pi$
$360$	2.89541	0.152602
$361$	5.14124	0.270592
$362$	46.5750	2.44793
$363$	22.1207	1.16104
$364$	6.99941	0.366869
$365$	−12.2154	−0.639382
$366$	−8.49667	−0.444128
$367$	16.9933	0.887044	0.443522	−	0.896263i	$-0.353729\pi$
$367$	16.9933	0.887044	0.443522	+	0.896263i	$0.353729\pi$
$368$	−10.8424	−0.565200
$369$	−25.4610	−1.32545
$370$	−51.8553	−2.69583
$371$	−4.09415	−0.212558
$372$	−6.44033	−0.333915
$373$	−10.4156	−0.539300	−0.269650	−	0.962958i	$-0.586908\pi$
$373$	−10.4156	−0.539300	−0.269650	+	0.962958i	$0.586908\pi$
$374$	9.65990	0.499502
$375$	−2.56352	−0.132380
$376$	−0.401110	−0.0206856
$377$	0	0
$378$	9.39515	0.483234
$379$	−22.8981	−1.17619	−0.588097	−	0.808790i	$-0.700123\pi$
$379$	−22.8981	−1.17619	−0.588097	+	0.808790i	$0.700123\pi$
$380$	−28.2301	−1.44817
$381$	40.5277	2.07630
$382$	26.0842	1.33458
$383$	−2.90269	−0.148320	−0.0741602	−	0.997246i	$-0.523628\pi$
$383$	−2.90269	−0.148320	−0.0741602	+	0.997246i	$0.523628\pi$
$384$	7.52849	0.384187
$385$	9.14395	0.466019
$386$	24.8480	1.26473
$387$	4.06899	0.206838
$388$	−27.8861	−1.41570
$389$	3.15385	0.159907	0.0799533	−	0.996799i	$-0.474523\pi$
$389$	3.15385	0.159907	0.0799533	+	0.996799i	$0.474523\pi$
$390$	−22.0265	−1.11536
$391$	10.9348	0.552998
$392$	−0.249169	−0.0125850
$393$	−1.30552	−0.0658548
$394$	7.93292	0.399655
$395$	−42.5826	−2.14256
$396$	−4.33275	−0.217729
$397$	21.2009	1.06404	0.532021	−	0.846731i	$-0.321433\pi$
$397$	21.2009	1.06404	0.532021	+	0.846731i	$0.321433\pi$
$398$	−33.0148	−1.65488
$399$	−28.2395	−1.41374
$400$	−23.4494	−1.17247
$401$	−4.29991	−0.214728	−0.107364	−	0.994220i	$-0.534241\pi$
$401$	−4.29991	−0.214728	−0.107364	+	0.994220i	$0.534241\pi$
$402$	−13.3648	−0.666573
$403$	−2.45924	−0.122503
$404$	−20.3483	−1.01236
$405$	−34.7933	−1.72889
$406$	0	0
$407$	−9.30497	−0.461230
$408$	−4.18327	−0.207103
$409$	−25.4982	−1.26081	−0.630403	−	0.776268i	$-0.717110\pi$
$409$	−25.4982	−1.26081	−0.630403	+	0.776268i	$0.717110\pi$
$410$	73.7931	3.64438
$411$	−31.3082	−1.54432
$412$	13.1959	0.650113
$413$	33.8255	1.66445
$414$	−10.3973	−0.511000
$415$	−31.2343	−1.53323
$416$	−11.9177	−0.584313
$417$	−24.0813	−1.17927
$418$	−10.7387	−0.525246
$419$	6.74628	0.329578	0.164789	−	0.986329i	$-0.447306\pi$
$419$	6.74628	0.329578	0.164789	+	0.986329i	$0.447306\pi$
$420$	33.0225	1.61133
$421$	34.5466	1.68370	0.841849	−	0.539713i	$-0.181467\pi$
$421$	34.5466	1.68370	0.841849	+	0.539713i	$0.181467\pi$
$422$	8.59273	0.418288
$423$	−2.07920	−0.101094
$424$	0.674219	0.0327430
$425$	23.6493	1.14716
$426$	18.3096	0.887104
$427$	4.86413	0.235392
$428$	−21.2877	−1.02898
$429$	−3.95246	−0.190826
$430$	−11.7930	−0.568711
$431$	9.87958	0.475882	0.237941	−	0.971280i	$-0.423527\pi$
$431$	9.87958	0.475882	0.237941	+	0.971280i	$0.423527\pi$
$432$	−8.36333	−0.402381
$433$	−3.20188	−0.153873	−0.0769363	−	0.997036i	$-0.524514\pi$
$433$	−3.20188	−0.153873	−0.0769363	+	0.997036i	$0.524514\pi$
$434$	7.81596	0.375178
$435$	0	0
$436$	28.8806	1.38313
$437$	−12.1560	−0.581500
$438$	−16.7811	−0.801834
$439$	6.41437	0.306141	0.153071	−	0.988215i	$-0.451084\pi$
$439$	6.41437	0.306141	0.153071	+	0.988215i	$0.451084\pi$
$440$	−1.50581	−0.0717869
$441$	−1.29160	−0.0615047
$442$	13.3211	0.633622
$443$	8.49949	0.403823	0.201911	−	0.979404i	$-0.435285\pi$
$443$	8.49949	0.403823	0.201911	+	0.979404i	$0.435285\pi$
$444$	−33.6040	−1.59477
$445$	15.6996	0.744231
$446$	33.2102	1.57255
$447$	−5.37573	−0.254263
$448$	15.6998	0.741746
$449$	−16.9423	−0.799555	−0.399778	−	0.916612i	$-0.630913\pi$
$449$	−16.9423	−0.799555	−0.399778	+	0.916612i	$0.630913\pi$
$450$	−22.4868	−1.06004
$451$	13.2415	0.623518
$452$	−11.3369	−0.533242
$453$	−22.1460	−1.04051
$454$	19.0294	0.893092
$455$	12.6096	0.591149
$456$	4.65045	0.217777
$457$	0.505911	0.0236655	0.0118328	−	0.999930i	$-0.496233\pi$
$457$	0.505911	0.0236655	0.0118328	+	0.999930i	$0.496233\pi$
$458$	−6.69173	−0.312684
$459$	8.43461	0.393694
$460$	14.2149	0.662771
$461$	−5.50088	−0.256201	−0.128101	−	0.991761i	$-0.540888\pi$
$461$	−5.50088	−0.256201	−0.128101	+	0.991761i	$0.540888\pi$
$462$	12.5617	0.584424
$463$	−6.56599	−0.305148	−0.152574	−	0.988292i	$-0.548756\pi$
$463$	−6.56599	−0.305148	−0.152574	+	0.988292i	$0.548756\pi$
$464$	0	0
$465$	−11.6024	−0.538050
$466$	8.54480	0.395830
$467$	4.47819	0.207226	0.103613	−	0.994618i	$-0.466960\pi$
$467$	4.47819	0.207226	0.103613	+	0.994618i	$0.466960\pi$
$468$	−5.97492	−0.276191
$469$	7.65099	0.353290
$470$	6.02610	0.277963
$471$	−42.6021	−1.96300
$472$	−5.57035	−0.256396
$473$	−2.11615	−0.0973008
$474$	−58.4988	−2.68694
$475$	−26.2904	−1.20628
$476$	−19.9712	−0.915380
$477$	3.49489	0.160020
$478$	−34.4010	−1.57347
$479$	−9.27693	−0.423874	−0.211937	−	0.977283i	$-0.567977\pi$
$479$	−9.27693	−0.423874	−0.211937	+	0.977283i	$0.567977\pi$
$480$	−56.2264	−2.56637
$481$	−12.8317	−0.585074
$482$	−22.1946	−1.01093
$483$	14.2196	0.647015
$484$	−17.3910	−0.790502
$485$	−50.2375	−2.28117
$486$	−36.6586	−1.66287
$487$	38.0837	1.72574	0.862869	−	0.505428i	$-0.168665\pi$
$487$	38.0837	1.72574	0.862869	+	0.505428i	$0.168665\pi$
$488$	−0.801018	−0.0362604
$489$	21.9254	0.991503
$490$	3.74341	0.169110
$491$	31.5938	1.42581	0.712904	−	0.701262i	$-0.247380\pi$
$491$	31.5938	1.42581	0.712904	+	0.701262i	$0.247380\pi$
$492$	47.8204	2.15591
$493$	0	0
$494$	−14.8088	−0.666279
$495$	−7.80557	−0.350834
$496$	−6.95758	−0.312405
$497$	−10.4818	−0.470173
$498$	−42.9088	−1.92279
$499$	−21.0654	−0.943016	−0.471508	−	0.881862i	$-0.656290\pi$
$499$	−21.0654	−0.943016	−0.471508	+	0.881862i	$0.656290\pi$
$500$	2.01541	0.0901318
$501$	−1.05591	−0.0471746
$502$	49.6853	2.21757
$503$	−26.2365	−1.16983	−0.584915	−	0.811095i	$-0.698872\pi$
$503$	−26.2365	−1.16983	−0.584915	+	0.811095i	$0.698872\pi$
$504$	−2.27710	−0.101430
$505$	−36.6580	−1.63126
$506$	5.40732	0.240384
$507$	24.0795	1.06941
$508$	−31.8623	−1.41366
$509$	−20.9900	−0.930366	−0.465183	−	0.885215i	$-0.654011\pi$
$509$	−20.9900	−0.930366	−0.465183	+	0.885215i	$0.654011\pi$
$510$	62.8477	2.78294
$511$	9.60679	0.424979
$512$	−30.0650	−1.32870
$513$	−9.37656	−0.413985
$514$	−0.347540	−0.0153293
$515$	23.7727	1.04755
$516$	−7.64228	−0.336432
$517$	1.08133	0.0475567
$518$	40.7817	1.79184
$519$	50.6357	2.22266
$520$	−2.07654	−0.0910622
$521$	−37.4112	−1.63901	−0.819507	−	0.573069i	$-0.805753\pi$
$521$	−37.4112	−1.63901	−0.819507	+	0.573069i	$0.805753\pi$
$522$	0	0
$523$	17.4633	0.763618	0.381809	−	0.924241i	$-0.375301\pi$
$523$	17.4633	0.763618	0.381809	+	0.924241i	$0.375301\pi$
$524$	1.02638	0.0448378
$525$	30.7535	1.34219
$526$	10.9589	0.477832
$527$	7.01688	0.305660
$528$	−11.1821	−0.486640
$529$	−16.8790	−0.733871
$530$	−10.1292	−0.439983
$531$	−28.8746	−1.25305
$532$	22.2015	0.962559
$533$	18.2602	0.790937
$534$	21.5676	0.933323
$535$	−38.3503	−1.65803
$536$	−1.25995	−0.0544217
$537$	−17.0591	−0.736154
$538$	−3.79091	−0.163438
$539$	0.671721	0.0289331
$540$	10.9647	0.471845
$541$	5.69494	0.244845	0.122422	−	0.992478i	$-0.460934\pi$
$541$	5.69494	0.244845	0.122422	+	0.992478i	$0.460934\pi$
$542$	−33.9369	−1.45771
$543$	54.3740	2.33341
$544$	34.0044	1.45793
$545$	52.0292	2.22868
$546$	17.3228	0.741346
$547$	−26.1122	−1.11648	−0.558238	−	0.829681i	$-0.688522\pi$
$547$	−26.1122	−1.11648	−0.558238	+	0.829681i	$0.688522\pi$
$548$	24.6141	1.05146
$549$	−4.15217	−0.177210
$550$	11.6947	0.498663
$551$	0	0
$552$	−2.34167	−0.0996680
$553$	33.4891	1.42410
$554$	29.8563	1.26847
$555$	−60.5385	−2.56971
$556$	18.9324	0.802912
$557$	28.6514	1.21400	0.606998	−	0.794703i	$-0.292373\pi$
$557$	28.6514	1.21400	0.606998	+	0.794703i	$0.292373\pi$
$558$	−6.67195	−0.282446
$559$	−2.91820	−0.123427
$560$	35.6747	1.50753
$561$	11.2774	0.476134
$562$	25.7054	1.08432
$563$	2.23595	0.0942341	0.0471170	−	0.998889i	$-0.484997\pi$
$563$	2.23595	0.0942341	0.0471170	+	0.998889i	$0.484997\pi$
$564$	3.90511	0.164435
$565$	−20.4237	−0.859231
$566$	21.7070	0.912414
$567$	27.3632	1.14915
$568$	1.72613	0.0724268
$569$	14.6792	0.615385	0.307692	−	0.951486i	$-0.400443\pi$
$569$	14.6792	0.615385	0.307692	+	0.951486i	$0.400443\pi$
$570$	−69.8663	−2.92638
$571$	20.8600	0.872962	0.436481	−	0.899714i	$-0.356225\pi$
$571$	20.8600	0.872962	0.436481	+	0.899714i	$0.356225\pi$
$572$	3.10737	0.129926
$573$	30.4520	1.27215
$574$	−58.0347	−2.42232
$575$	13.2381	0.552069
$576$	−13.4018	−0.558410
$577$	22.4919	0.936348	0.468174	−	0.883636i	$-0.344912\pi$
$577$	22.4919	0.936348	0.468174	+	0.883636i	$0.344912\pi$
$578$	−4.93149	−0.205123
$579$	29.0087	1.20556
$580$	0	0
$581$	24.5642	1.01909
$582$	−69.0150	−2.86076
$583$	−1.81759	−0.0752767
$584$	−1.58203	−0.0654650
$585$	−10.7640	−0.445036
$586$	−13.2363	−0.546788
$587$	16.4960	0.680864	0.340432	−	0.940269i	$-0.389427\pi$
$587$	16.4960	0.680864	0.340432	+	0.940269i	$0.389427\pi$
$588$	2.42585	0.100040
$589$	−7.80050	−0.321414
$590$	83.6865	3.44532
$591$	9.26127	0.380958
$592$	−36.3029	−1.49204
$593$	−45.1022	−1.85212	−0.926062	−	0.377371i	$-0.876828\pi$
$593$	−45.1022	−1.85212	−0.926062	+	0.377371i	$0.876828\pi$
$594$	4.17095	0.171136
$595$	−35.9787	−1.47498
$596$	4.22633	0.173117
$597$	−38.5431	−1.57746
$598$	7.45676	0.304930
$599$	10.5711	0.431925	0.215963	−	0.976402i	$-0.430711\pi$
$599$	10.5711	0.431925	0.215963	+	0.976402i	$0.430711\pi$
$600$	−5.06444	−0.206755
$601$	−0.743399	−0.0303239	−0.0151619	−	0.999885i	$-0.504826\pi$
$601$	−0.743399	−0.0303239	−0.0151619	+	0.999885i	$0.504826\pi$
$602$	9.27465	0.378006
$603$	−6.53113	−0.265968
$604$	17.4109	0.708439
$605$	−31.3305	−1.27376
$606$	−50.3597	−2.04572
$607$	−32.6175	−1.32390	−0.661952	−	0.749546i	$-0.730272\pi$
$607$	−32.6175	−1.32390	−0.661952	+	0.749546i	$0.730272\pi$
$608$	−37.8019	−1.53307
$609$	0	0
$610$	12.0342	0.487248
$611$	1.49117	0.0603261
$612$	17.0481	0.689128
$613$	15.0054	0.606064	0.303032	−	0.952980i	$-0.402001\pi$
$613$	15.0054	0.606064	0.303032	+	0.952980i	$0.402001\pi$
$614$	−31.4387	−1.26876
$615$	86.1497	3.47389
$616$	1.18425	0.0477147
$617$	41.5249	1.67173	0.835864	−	0.548936i	$-0.184967\pi$
$617$	41.5249	1.67173	0.835864	+	0.548936i	$0.184967\pi$
$618$	32.6583	1.31371
$619$	−21.3783	−0.859268	−0.429634	−	0.903003i	$-0.641357\pi$
$619$	−21.3783	−0.859268	−0.429634	+	0.903003i	$0.641357\pi$
$620$	9.12168	0.366335
$621$	4.72144	0.189465
$622$	−8.44356	−0.338556
$623$	−12.3469	−0.494669
$624$	−15.4203	−0.617307
$625$	−23.1231	−0.924923
$626$	−2.08855	−0.0834752
$627$	−12.5369	−0.500674
$628$	33.4932	1.33652
$629$	36.6123	1.45983
$630$	34.2101	1.36296
$631$	22.2833	0.887085	0.443542	−	0.896253i	$-0.353722\pi$
$631$	22.2833	0.887085	0.443542	+	0.896253i	$0.353722\pi$
$632$	−5.51494	−0.219372
$633$	10.0316	0.398719
$634$	15.1653	0.602290
$635$	−57.4009	−2.27788
$636$	−6.56403	−0.260281
$637$	0.926312	0.0367018
$638$	0	0
$639$	8.94760	0.353962
$640$	−10.6629	−0.421488
$641$	−26.5934	−1.05038	−0.525188	−	0.850986i	$-0.676005\pi$
$641$	−26.5934	−1.05038	−0.525188	+	0.850986i	$0.676005\pi$
$642$	−52.6846	−2.07930
$643$	38.2237	1.50740	0.753699	−	0.657220i	$-0.228268\pi$
$643$	38.2237	1.50740	0.753699	+	0.657220i	$0.228268\pi$
$644$	−11.1793	−0.440525
$645$	−13.7678	−0.542106
$646$	42.2535	1.66244
$647$	32.8334	1.29081	0.645407	−	0.763839i	$-0.276688\pi$
$647$	32.8334	1.29081	0.645407	+	0.763839i	$0.276688\pi$
$648$	−4.50614	−0.177018
$649$	15.0168	0.589460
$650$	16.1271	0.632558
$651$	9.12473	0.357626
$652$	−17.2375	−0.675073
$653$	1.30358	0.0510131	0.0255066	−	0.999675i	$-0.491880\pi$
$653$	1.30358	0.0510131	0.0255066	+	0.999675i	$0.491880\pi$
$654$	71.4762	2.79494
$655$	1.84906	0.0722487
$656$	51.6611	2.01703
$657$	−8.20066	−0.319938
$658$	−4.73923	−0.184754
$659$	19.7479	0.769267	0.384634	−	0.923069i	$-0.374328\pi$
$659$	19.7479	0.769267	0.384634	+	0.923069i	$0.374328\pi$
$660$	14.6602	0.570649
$661$	−42.1752	−1.64042	−0.820212	−	0.572059i	$-0.806145\pi$
$661$	−42.1752	−1.64042	−0.820212	+	0.572059i	$0.806145\pi$
$662$	−19.3739	−0.752989
$663$	15.5517	0.603980
$664$	−4.04520	−0.156984
$665$	39.9967	1.55101
$666$	−34.8125	−1.34896
$667$	0	0
$668$	0.830144	0.0321192
$669$	38.7712	1.49898
$670$	18.9290	0.731291
$671$	2.15942	0.0833634
$672$	44.2193	1.70579
$673$	−41.6873	−1.60693	−0.803464	−	0.595353i	$-0.797012\pi$
$673$	−41.6873	−1.60693	−0.803464	+	0.595353i	$0.797012\pi$
$674$	−41.5605	−1.60085
$675$	10.2113	0.393033
$676$	−18.9310	−0.728114
$677$	24.5737	0.944443	0.472221	−	0.881480i	$-0.343452\pi$
$677$	24.5737	0.944443	0.472221	+	0.881480i	$0.343452\pi$
$678$	−28.0575	−1.07754
$679$	39.5093	1.51623
$680$	5.92493	0.227211
$681$	22.2158	0.851311
$682$	3.46988	0.132868
$683$	43.1311	1.65036	0.825182	−	0.564867i	$-0.191072\pi$
$683$	43.1311	1.65036	0.825182	+	0.564867i	$0.191072\pi$
$684$	−18.9519	−0.724646
$685$	44.3431	1.69426
$686$	−37.4058	−1.42816
$687$	−7.81225	−0.298056
$688$	−8.25607	−0.314760
$689$	−2.50648	−0.0954891
$690$	35.1802	1.33929
$691$	−41.0599	−1.56199	−0.780996	−	0.624536i	$-0.785288\pi$
$691$	−41.0599	−1.56199	−0.780996	+	0.624536i	$0.785288\pi$
$692$	−39.8091	−1.51332
$693$	6.13869	0.233190
$694$	−52.3691	−1.98790
$695$	34.1072	1.29376
$696$	0	0
$697$	−52.1014	−1.97348
$698$	−36.5375	−1.38297
$699$	9.97562	0.377313
$700$	−24.1780	−0.913842
$701$	1.11188	0.0419949	0.0209975	−	0.999780i	$-0.493316\pi$
$701$	1.11188	0.0419949	0.0209975	+	0.999780i	$0.493316\pi$
$702$	5.75180	0.217088
$703$	−40.7010	−1.53507
$704$	6.96989	0.262687
$705$	7.03516	0.264959
$706$	−57.5475	−2.16583
$707$	28.8297	1.08425
$708$	54.2315	2.03815
$709$	29.9385	1.12437	0.562183	−	0.827013i	$-0.309962\pi$
$709$	29.9385	1.12437	0.562183	+	0.827013i	$0.309962\pi$
$710$	−25.9326	−0.973234
$711$	−28.5873	−1.07211
$712$	2.03328	0.0762002
$713$	3.92783	0.147099
$714$	−49.4266	−1.84974
$715$	5.59801	0.209354
$716$	13.4116	0.501217
$717$	−40.1614	−1.49986
$718$	39.4666	1.47288
$719$	−5.03075	−0.187615	−0.0938076	−	0.995590i	$-0.529904\pi$
$719$	−5.03075	−0.187615	−0.0938076	+	0.995590i	$0.529904\pi$
$720$	−30.4530	−1.13492
$721$	−18.6961	−0.696277
$722$	−10.0034	−0.372290
$723$	−25.9110	−0.963640
$724$	−42.7481	−1.58872
$725$	0	0
$726$	−43.0409	−1.59740
$727$	−0.650727	−0.0241341	−0.0120671	−	0.999927i	$-0.503841\pi$
$727$	−0.650727	−0.0241341	−0.0120671	+	0.999927i	$0.503841\pi$
$728$	1.63309	0.0605265
$729$	−10.3533	−0.383455
$730$	23.7678	0.879685
$731$	8.32643	0.307964
$732$	7.79852	0.288242
$733$	−11.3833	−0.420451	−0.210225	−	0.977653i	$-0.567420\pi$
$733$	−11.3833	−0.420451	−0.210225	+	0.977653i	$0.567420\pi$
$734$	−33.0644	−1.22043
$735$	4.37024	0.161199
$736$	19.0346	0.701626
$737$	3.39664	0.125117
$738$	49.5402	1.82360
$739$	19.1778	0.705465	0.352732	−	0.935724i	$-0.385253\pi$
$739$	19.1778	0.705465	0.352732	+	0.935724i	$0.385253\pi$
$740$	47.5946	1.74961
$741$	−17.2885	−0.635109
$742$	7.96609	0.292444
$743$	−32.1621	−1.17991	−0.589956	−	0.807436i	$-0.700855\pi$
$743$	−32.1621	−1.17991	−0.589956	+	0.807436i	$0.700855\pi$
$744$	−1.50265	−0.0550898
$745$	7.61385	0.278950
$746$	20.2659	0.741988
$747$	−20.9688	−0.767208
$748$	−8.86618	−0.324180
$749$	30.1606	1.10205
$750$	4.98792	0.182133
$751$	38.3085	1.39790	0.698949	−	0.715172i	$-0.253652\pi$
$751$	38.3085	1.39790	0.698949	+	0.715172i	$0.253652\pi$
$752$	4.21875	0.153842
$753$	58.0051	2.11382
$754$	0	0
$755$	31.3662	1.14153
$756$	−8.62318	−0.313622
$757$	11.3624	0.412975	0.206487	−	0.978449i	$-0.433797\pi$
$757$	11.3624	0.412975	0.206487	+	0.978449i	$0.433797\pi$
$758$	44.5534	1.61825
$759$	6.31276	0.229139
$760$	−6.58660	−0.238921
$761$	−15.6194	−0.566205	−0.283102	−	0.959090i	$-0.591364\pi$
$761$	−15.6194	−0.566205	−0.283102	+	0.959090i	$0.591364\pi$
$762$	−78.8558	−2.85664
$763$	−40.9184	−1.48134
$764$	−23.9409	−0.866153
$765$	30.7126	1.11042
$766$	5.64784	0.204065
$767$	20.7083	0.747734
$768$	−42.8378	−1.54578
$769$	9.65324	0.348105	0.174052	−	0.984736i	$-0.444314\pi$
$769$	9.65324	0.348105	0.174052	+	0.984736i	$0.444314\pi$
$770$	−17.7916	−0.641166
$771$	−0.405735	−0.0146122
$772$	−22.8063	−0.820816
$773$	−15.7145	−0.565211	−0.282605	−	0.959236i	$-0.591199\pi$
$773$	−15.7145	−0.565211	−0.282605	+	0.959236i	$0.591199\pi$
$774$	−7.91713	−0.284576
$775$	8.49493	0.305147
$776$	−6.50635	−0.233564
$777$	47.6105	1.70802
$778$	−6.13653	−0.220005
$779$	57.9199	2.07519
$780$	20.2167	0.723873
$781$	−4.65337	−0.166511
$782$	−21.2762	−0.760835
$783$	0	0
$784$	2.62069	0.0935959
$785$	60.3389	2.15359
$786$	2.54019	0.0906055
$787$	5.12572	0.182712	0.0913560	−	0.995818i	$-0.470880\pi$
$787$	5.12572	0.182712	0.0913560	+	0.995818i	$0.470880\pi$
$788$	−7.28109	−0.259378
$789$	12.7940	0.455477
$790$	82.8540	2.94781
$791$	16.0622	0.571107
$792$	−1.01091	−0.0359212
$793$	2.97787	0.105747
$794$	−41.2511	−1.46395
$795$	−11.8253	−0.419400
$796$	30.3021	1.07403
$797$	40.5663	1.43693	0.718466	−	0.695562i	$-0.244844\pi$
$797$	40.5663	1.43693	0.718466	+	0.695562i	$0.244844\pi$
$798$	54.9464	1.94508
$799$	−4.25470	−0.150521
$800$	41.1672	1.45548
$801$	10.5397	0.372403
$802$	8.36646	0.295430
$803$	4.26491	0.150505
$804$	12.2666	0.432610
$805$	−20.1398	−0.709834
$806$	4.78501	0.168545
$807$	−4.42569	−0.155792
$808$	−4.74763	−0.167021
$809$	−31.0217	−1.09066	−0.545332	−	0.838220i	$-0.683597\pi$
$809$	−31.0217	−1.09066	−0.545332	+	0.838220i	$0.683597\pi$
$810$	67.6982	2.37867
$811$	−45.3970	−1.59410	−0.797052	−	0.603910i	$-0.793609\pi$
$811$	−45.3970	−1.59410	−0.797052	+	0.603910i	$0.793609\pi$
$812$	0	0
$813$	−39.6196	−1.38952
$814$	18.1049	0.634577
$815$	−31.0538	−1.08777
$816$	43.9984	1.54025
$817$	−9.25630	−0.323837
$818$	49.6125	1.73466
$819$	8.46534	0.295803
$820$	−67.7298	−2.36523
$821$	−26.4086	−0.921665	−0.460833	−	0.887487i	$-0.652449\pi$
$821$	−26.4086	−0.921665	−0.460833	+	0.887487i	$0.652449\pi$
$822$	60.9173	2.12473
$823$	34.3735	1.19818	0.599092	−	0.800680i	$-0.295528\pi$
$823$	34.3735	1.19818	0.599092	+	0.800680i	$0.295528\pi$
$824$	3.07884	0.107257
$825$	13.6529	0.475334
$826$	−65.8153	−2.29001
$827$	40.3495	1.40309	0.701545	−	0.712626i	$-0.252494\pi$
$827$	40.3495	1.40309	0.701545	+	0.712626i	$0.252494\pi$
$828$	9.54299	0.331642
$829$	41.4695	1.44029	0.720147	−	0.693821i	$-0.244074\pi$
$829$	41.4695	1.44029	0.720147	+	0.693821i	$0.244074\pi$
$830$	60.7733	2.10947
$831$	34.8557	1.20913
$832$	9.61157	0.333221
$833$	−2.64302	−0.0915753
$834$	46.8556	1.62248
$835$	1.49553	0.0517549
$836$	9.85632	0.340888
$837$	3.02975	0.104723
$838$	−13.1264	−0.453445
$839$	−12.9838	−0.448250	−0.224125	−	0.974560i	$-0.571952\pi$
$839$	−12.9838	−0.448250	−0.224125	+	0.974560i	$0.571952\pi$
$840$	7.70476	0.265840
$841$	0	0
$842$	−67.2183	−2.31649
$843$	30.0097	1.03359
$844$	−7.88669	−0.271471
$845$	−34.1047	−1.17324
$846$	4.04556	0.139089
$847$	24.6399	0.846635
$848$	−7.09122	−0.243514
$849$	25.3418	0.869729
$850$	−46.0151	−1.57830
$851$	20.4944	0.702540
$852$	−16.8052	−0.575736
$853$	−8.15508	−0.279225	−0.139612	−	0.990206i	$-0.544586\pi$
$853$	−8.15508	−0.279225	−0.139612	+	0.990206i	$0.544586\pi$
$854$	−9.46426	−0.323860
$855$	−34.1425	−1.16765
$856$	−4.96681	−0.169762
$857$	−29.3691	−1.00323	−0.501615	−	0.865091i	$-0.667261\pi$
$857$	−29.3691	−1.00323	−0.501615	+	0.865091i	$0.667261\pi$
$858$	7.69040	0.262546
$859$	19.4101	0.662265	0.331133	−	0.943584i	$-0.392569\pi$
$859$	19.4101	0.662265	0.331133	+	0.943584i	$0.392569\pi$
$860$	10.8240	0.369097
$861$	−67.7525	−2.30900
$862$	−19.2230	−0.654736
$863$	−50.6162	−1.72300	−0.861498	−	0.507760i	$-0.830474\pi$
$863$	−50.6162	−1.72300	−0.861498	+	0.507760i	$0.830474\pi$
$864$	14.6824	0.499506
$865$	−71.7173	−2.43846
$866$	6.22999	0.211704
$867$	−5.75726	−0.195527
$868$	−7.17375	−0.243493
$869$	14.8674	0.504342
$870$	0	0
$871$	4.68401	0.158712
$872$	6.73838	0.228190
$873$	−33.7264	−1.14147
$874$	23.6522	0.800048
$875$	−2.85546	−0.0965321
$876$	15.4023	0.520395
$877$	35.1220	1.18598	0.592992	−	0.805208i	$-0.297946\pi$
$877$	35.1220	1.18598	0.592992	+	0.805208i	$0.297946\pi$
$878$	−12.4806	−0.421200
$879$	−15.4527	−0.521208
$880$	15.8377	0.533888
$881$	−32.1831	−1.08428	−0.542138	−	0.840289i	$-0.682385\pi$
$881$	−32.1831	−1.08428	−0.542138	+	0.840289i	$0.682385\pi$
$882$	2.51310	0.0846204
$883$	−46.8381	−1.57623	−0.788113	−	0.615530i	$-0.788942\pi$
$883$	−46.8381	−1.57623	−0.788113	+	0.615530i	$0.788942\pi$
$884$	−12.2266	−0.411224
$885$	97.6996	3.28414
$886$	−16.5377	−0.555594
$887$	6.85131	0.230045	0.115022	−	0.993363i	$-0.463306\pi$
$887$	6.85131	0.230045	0.115022	+	0.993363i	$0.463306\pi$
$888$	−7.84043	−0.263108
$889$	45.1429	1.51405
$890$	−30.5471	−1.02394
$891$	12.1478	0.406968
$892$	−30.4814	−1.02059
$893$	4.72985	0.158278
$894$	10.4597	0.349825
$895$	24.1614	0.807628
$896$	8.38584	0.280151
$897$	8.70538	0.290664
$898$	32.9650	1.10006
$899$	0	0
$900$	20.6391	0.687970
$901$	7.15166	0.238256
$902$	−25.7643	−0.857859
$903$	10.8277	0.360322
$904$	−2.64511	−0.0879749
$905$	−77.0119	−2.55996
$906$	43.0900	1.43157
$907$	12.2503	0.406764	0.203382	−	0.979099i	$-0.434807\pi$
$907$	12.2503	0.406764	0.203382	+	0.979099i	$0.434807\pi$
$908$	−17.4658	−0.579622
$909$	−24.6099	−0.816260
$910$	−24.5349	−0.813324
$911$	−19.8474	−0.657572	−0.328786	−	0.944404i	$-0.606640\pi$
$911$	−19.8474	−0.657572	−0.328786	+	0.944404i	$0.606640\pi$
$912$	−48.9119	−1.61964
$913$	10.9052	0.360910
$914$	−0.984364	−0.0325599
$915$	14.0493	0.464454
$916$	6.14189	0.202934
$917$	−1.45419	−0.0480217
$918$	−16.4115	−0.541659
$919$	−30.5383	−1.00736	−0.503682	−	0.863889i	$-0.668022\pi$
$919$	−30.5383	−1.00736	−0.503682	+	0.863889i	$0.668022\pi$
$920$	3.31659	0.109345
$921$	−36.7031	−1.20941
$922$	10.7032	0.352491
$923$	−6.41706	−0.211220
$924$	−11.5296	−0.379294
$925$	44.3243	1.45737
$926$	12.7756	0.419833
$927$	15.9595	0.524180
$928$	0	0
$929$	−8.90962	−0.292315	−0.146158	−	0.989261i	$-0.546691\pi$
$929$	−8.90962	−0.292315	−0.146158	+	0.989261i	$0.546691\pi$
$930$	22.5751	0.740268
$931$	2.93818	0.0962951
$932$	−7.84270	−0.256896
$933$	−9.85742	−0.322717
$934$	−8.71333	−0.285109
$935$	−15.9727	−0.522362
$936$	−1.39406	−0.0455663
$937$	15.3972	0.503006	0.251503	−	0.967857i	$-0.419075\pi$
$937$	15.3972	0.503006	0.251503	+	0.967857i	$0.419075\pi$
$938$	−14.8867	−0.486069
$939$	−2.43827	−0.0795701
$940$	−5.53095	−0.180400
$941$	46.5126	1.51627	0.758133	−	0.652100i	$-0.226112\pi$
$941$	46.5126	1.51627	0.758133	+	0.652100i	$0.226112\pi$
$942$	82.8920	2.70077
$943$	−29.1647	−0.949735
$944$	58.5872	1.90685
$945$	−15.5349	−0.505350
$946$	4.11746	0.133870
$947$	−31.2180	−1.01445	−0.507224	−	0.861814i	$-0.669328\pi$
$947$	−31.2180	−1.01445	−0.507224	+	0.861814i	$0.669328\pi$
$948$	53.6921	1.74384
$949$	5.88137	0.190917
$950$	51.1539	1.65965
$951$	17.7047	0.574114
$952$	−4.65966	−0.151021
$953$	−24.5654	−0.795752	−0.397876	−	0.917439i	$-0.630253\pi$
$953$	−24.5654	−0.795752	−0.397876	+	0.917439i	$0.630253\pi$
$954$	−6.80011	−0.220162
$955$	−43.1303	−1.39566
$956$	31.5744	1.02119
$957$	0	0
$958$	18.0504	0.583181
$959$	−34.8736	−1.12613
$960$	45.3463	1.46355
$961$	−28.4795	−0.918694
$962$	24.9669	0.804966
$963$	−25.7461	−0.829655
$964$	20.3709	0.656102
$965$	−41.0862	−1.32261
$966$	−27.6675	−0.890187
$967$	25.3774	0.816082	0.408041	−	0.912964i	$-0.366212\pi$
$967$	25.3774	0.816082	0.408041	+	0.912964i	$0.366212\pi$
$968$	−4.05766	−0.130418
$969$	49.3288	1.58467
$970$	97.7485	3.13852
$971$	11.0345	0.354115	0.177058	−	0.984200i	$-0.443342\pi$
$971$	11.0345	0.354115	0.177058	+	0.984200i	$0.443342\pi$
$972$	33.6464	1.07921
$973$	−26.8237	−0.859927
$974$	−74.1005	−2.37433
$975$	18.8276	0.602965
$976$	8.42486	0.269673
$977$	−52.4730	−1.67876	−0.839380	−	0.543545i	$-0.817082\pi$
$977$	−52.4730	−1.67876	−0.839380	+	0.543545i	$0.817082\pi$
$978$	−42.6609	−1.36415
$979$	−5.48139	−0.175186
$980$	−3.43583	−0.109753
$981$	34.9292	1.11520
$982$	−61.4729	−1.96168
$983$	−46.0772	−1.46964	−0.734818	−	0.678265i	$-0.762732\pi$
$983$	−46.0772	−1.46964	−0.734818	+	0.678265i	$0.762732\pi$
$984$	11.1574	0.355685
$985$	−13.1171	−0.417945
$986$	0	0
$987$	−5.53280	−0.176111
$988$	13.5920	0.432419
$989$	4.66088	0.148207
$990$	15.1875	0.482690
$991$	0.807143	0.0256397	0.0128199	−	0.999918i	$-0.495919\pi$
$991$	0.807143	0.0256397	0.0128199	+	0.999918i	$0.495919\pi$
$992$	12.2145	0.387812
$993$	−22.6181	−0.717762
$994$	20.3947	0.646881
$995$	54.5900	1.73062
$996$	39.3831	1.24790
$997$	−30.6050	−0.969270	−0.484635	−	0.874716i	$-0.661048\pi$
$997$	−30.6050	−0.969270	−0.484635	+	0.874716i	$0.661048\pi$
$998$	40.9875	1.29744
$999$	15.8084	0.500157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.a.g.1.2	✓	6
3.2	odd	2		7569.2.a.bc.1.5		6
29.2	odd	28		841.2.e.l.236.3		72
29.3	odd	28		841.2.e.l.270.3		72
29.4	even	14		841.2.d.n.190.2		36
29.5	even	14		841.2.d.n.605.2		36
29.6	even	14		841.2.d.n.645.2		36
29.7	even	7		841.2.d.o.571.5		36
29.8	odd	28		841.2.e.l.267.3		72
29.9	even	14		841.2.d.n.574.5		36
29.10	odd	28		841.2.e.l.651.3		72
29.11	odd	28		841.2.e.l.63.3		72
29.12	odd	4		841.2.b.d.840.3		12
29.13	even	14		841.2.d.n.778.5		36
29.14	odd	28		841.2.e.l.196.10		72
29.15	odd	28		841.2.e.l.196.3		72
29.16	even	7		841.2.d.o.778.2		36
29.17	odd	4		841.2.b.d.840.10		12
29.18	odd	28		841.2.e.l.63.10		72
29.19	odd	28		841.2.e.l.651.10		72
29.20	even	7		841.2.d.o.574.2		36
29.21	odd	28		841.2.e.l.267.10		72
29.22	even	14		841.2.d.n.571.2		36
29.23	even	7		841.2.d.o.645.5		36
29.24	even	7		841.2.d.o.605.5		36
29.25	even	7		841.2.d.o.190.5		36
29.26	odd	28		841.2.e.l.270.10		72
29.27	odd	28		841.2.e.l.236.10		72
29.28	even	2		841.2.a.h.1.5	yes	6
87.86	odd	2		7569.2.a.y.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.2	✓	6	1.1	even	1	trivial
841.2.a.h.1.5	yes	6	29.28	even	2
841.2.b.d.840.3		12	29.12	odd	4
841.2.b.d.840.10		12	29.17	odd	4
841.2.d.n.190.2		36	29.4	even	14
841.2.d.n.571.2		36	29.22	even	14
841.2.d.n.574.5		36	29.9	even	14
841.2.d.n.605.2		36	29.5	even	14
841.2.d.n.645.2		36	29.6	even	14
841.2.d.n.778.5		36	29.13	even	14
841.2.d.o.190.5		36	29.25	even	7
841.2.d.o.571.5		36	29.7	even	7
841.2.d.o.574.2		36	29.20	even	7
841.2.d.o.605.5		36	29.24	even	7
841.2.d.o.645.5		36	29.23	even	7
841.2.d.o.778.2		36	29.16	even	7
841.2.e.l.63.3		72	29.11	odd	28
841.2.e.l.63.10		72	29.18	odd	28
841.2.e.l.196.3		72	29.15	odd	28
841.2.e.l.196.10		72	29.14	odd	28
841.2.e.l.236.3		72	29.2	odd	28
841.2.e.l.236.10		72	29.27	odd	28
841.2.e.l.267.3		72	29.8	odd	28
841.2.e.l.267.10		72	29.21	odd	28
841.2.e.l.270.3		72	29.3	odd	28
841.2.e.l.270.10		72	29.26	odd	28
841.2.e.l.651.3		72	29.10	odd	28
841.2.e.l.651.10		72	29.19	odd	28
7569.2.a.y.1.2		6	87.86	odd	2
7569.2.a.bc.1.5		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q-1.94573 q^{2} -2.27154 q^{3} +1.78585 q^{4} +3.21726 q^{5} +4.41979 q^{6} -2.53022 q^{7} +0.416673 q^{8} +2.15987 q^{9} -6.25991 q^{10} -1.12328 q^{11} -4.05663 q^{12} -1.54902 q^{13} +4.92311 q^{14} -7.30813 q^{15} -4.38244 q^{16} +4.41979 q^{17} -4.20253 q^{18} -4.91337 q^{19} +5.74556 q^{20} +5.74748 q^{21} +2.18560 q^{22} +2.47406 q^{23} -0.946487 q^{24} +5.35078 q^{25} +3.01398 q^{26} +1.90838 q^{27} -4.51860 q^{28} +14.2196 q^{30} +1.58761 q^{31} +7.69368 q^{32} +2.55158 q^{33} -8.59970 q^{34} -8.14037 q^{35} +3.85722 q^{36} +8.28372 q^{37} +9.56008 q^{38} +3.51866 q^{39} +1.34055 q^{40} -11.7882 q^{41} -11.1830 q^{42} +1.88390 q^{43} -2.00602 q^{44} +6.94888 q^{45} -4.81385 q^{46} -0.962649 q^{47} +9.95486 q^{48} -0.597997 q^{49} -10.4111 q^{50} -10.0397 q^{51} -2.76633 q^{52} +1.61810 q^{53} -3.71318 q^{54} -3.61390 q^{55} -1.05427 q^{56} +11.1609 q^{57} -13.3686 q^{59} -13.0512 q^{60} -1.92241 q^{61} -3.08905 q^{62} -5.46495 q^{63} -6.20492 q^{64} -4.98362 q^{65} -4.96468 q^{66} -3.02385 q^{67} +7.89309 q^{68} -5.61992 q^{69} +15.8389 q^{70} +4.14265 q^{71} +0.899961 q^{72} -3.79682 q^{73} -16.1178 q^{74} -12.1545 q^{75} -8.77456 q^{76} +2.84215 q^{77} -6.84635 q^{78} -13.2356 q^{79} -14.0994 q^{80} -10.8146 q^{81} +22.9366 q^{82} -9.70833 q^{83} +10.2642 q^{84} +14.2196 q^{85} -3.66555 q^{86} -0.468042 q^{88} +4.87979 q^{89} -13.5206 q^{90} +3.91937 q^{91} +4.41831 q^{92} -3.60630 q^{93} +1.87305 q^{94} -15.8076 q^{95} -17.4765 q^{96} -15.6150 q^{97} +1.16354 q^{98} -2.42615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 6 q^{9} - 15 q^{10} - 13 q^{11} + 4 q^{12} - 6 q^{13} + 6 q^{14} - 19 q^{15} + 4 q^{16} - 3 q^{17} - 17 q^{18} + 6 q^{19} - 5 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 6 * q^9 - 15 * q^10 - 13 * q^11 + 4 * q^12 - 6 * q^13 + 6 * q^14 - 19 * q^15 + 4 * q^16 - 3 * q^17 - 17 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 - 4 * q^22 - 5 * q^23 - 10 * q^24 + 6 * q^25 - 9 * q^26 + q^27 - 5 * q^28 + 26 * q^30 - 16 * q^31 - 33 * q^32 + 27 * q^33 - 4 * q^35 - 21 * q^36 + 10 * q^37 + 41 * q^38 - 17 * q^39 - 7 * q^40 - 30 * q^41 - 21 * q^42 + 2 * q^43 - 16 * q^44 + 16 * q^45 + 20 * q^46 - 5 * q^47 + 30 * q^48 - 12 * q^49 + 8 * q^50 - 23 * q^51 - 13 * q^53 + 19 * q^54 - 10 * q^55 - 16 * q^56 - 16 * q^57 - 17 * q^59 + 9 * q^60 + 4 * q^61 - 9 * q^63 + q^64 + 32 * q^65 + 8 * q^66 - 9 * q^67 - 16 * q^68 - 26 * q^69 + 28 * q^70 + 21 * q^72 - 9 * q^73 - 36 * q^74 - 7 * q^75 - 24 * q^76 - 13 * q^77 - 6 * q^79 + 5 * q^80 - 22 * q^81 + 19 * q^82 - 24 * q^83 + 26 * q^85 + 17 * q^86 + 21 * q^88 - 9 * q^89 + 16 * q^90 + 16 * q^91 - 23 * q^92 - 12 * q^93 - 37 * q^94 - 31 * q^95 - 37 * q^96 + 10 * q^97 + 42 * q^98 - 6 * q^99

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