LMFDB - Embedded newform 4489.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4489,2,Mod(1,4489)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4489, 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("4489.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4489 = 67^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4489.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:	$35.8448454674$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.284630$ of defining polynomial
Character	$\chi$	$=$	4489.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51334 q^{2} -2.68251 q^{3} +4.31686 q^{4} -1.68251 q^{5} +6.74204 q^{6} +1.39788 q^{7} -5.82306 q^{8} +4.19584 q^{9} +O(q^{10})$	\(q-2.51334 q^{2} -2.68251 q^{3} +4.31686 q^{4} -1.68251 q^{5} +6.74204 q^{6} +1.39788 q^{7} -5.82306 q^{8} +4.19584 q^{9} +4.22871 q^{10} -4.74204 q^{11} -11.5800 q^{12} +5.97852 q^{13} -3.51334 q^{14} +4.51334 q^{15} +6.00158 q^{16} -4.30972 q^{17} -10.5456 q^{18} +4.64675 q^{19} -7.26315 q^{20} -3.74982 q^{21} +11.9184 q^{22} +1.07545 q^{23} +15.6204 q^{24} -2.16917 q^{25} -15.0260 q^{26} -3.20786 q^{27} +6.03445 q^{28} +2.39011 q^{29} -11.3435 q^{30} -2.69983 q^{31} -3.43788 q^{32} +12.7206 q^{33} +10.8318 q^{34} -2.35194 q^{35} +18.1129 q^{36} -3.75406 q^{37} -11.6788 q^{38} -16.0374 q^{39} +9.79734 q^{40} +0.453170 q^{41} +9.42455 q^{42} +4.16989 q^{43} -20.4708 q^{44} -7.05954 q^{45} -2.70298 q^{46} +0.0610313 q^{47} -16.0993 q^{48} -5.04594 q^{49} +5.45186 q^{50} +11.5609 q^{51} +25.8085 q^{52} -3.92879 q^{53} +8.06243 q^{54} +7.97852 q^{55} -8.13992 q^{56} -12.4649 q^{57} -6.00714 q^{58} +1.47547 q^{59} +19.4835 q^{60} -4.56900 q^{61} +6.78558 q^{62} +5.86528 q^{63} -3.36261 q^{64} -10.0589 q^{65} -31.9711 q^{66} -18.6045 q^{68} -2.88491 q^{69} +5.91121 q^{70} -0.793487 q^{71} -24.4326 q^{72} +3.14991 q^{73} +9.43522 q^{74} +5.81881 q^{75} +20.0594 q^{76} -6.62880 q^{77} +40.3075 q^{78} +0.102235 q^{79} -10.0977 q^{80} -3.98242 q^{81} -1.13897 q^{82} -13.7967 q^{83} -16.1874 q^{84} +7.25114 q^{85} -10.4803 q^{86} -6.41148 q^{87} +27.6132 q^{88} +15.3350 q^{89} +17.7430 q^{90} +8.35724 q^{91} +4.64259 q^{92} +7.24231 q^{93} -0.153392 q^{94} -7.81818 q^{95} +9.22214 q^{96} +16.5271 q^{97} +12.6821 q^{98} -19.8969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + q^{5} + 5 q^{6} - 2 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + q^5 + 5 * q^6 - 2 * q^7 - 9 * q^8 - 3 * q^9	\( 5 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + q^{5} + 5 q^{6} - 2 q^{7} - 9 q^{8} - 3 q^{9} + 7 q^{10} + 5 q^{11} - 12 q^{12} + 2 q^{13} - 3 q^{14} + 8 q^{15} + 6 q^{16} - 16 q^{17} - 21 q^{18} + 10 q^{19} - 8 q^{20} - 5 q^{21} + 24 q^{22} + 2 q^{23} + 16 q^{24} - 16 q^{25} - 19 q^{26} - q^{27} + 16 q^{28} - 12 q^{29} - 10 q^{30} + 16 q^{31} - 6 q^{32} + 7 q^{33} - 2 q^{34} - 7 q^{35} + 13 q^{36} + q^{37} - 18 q^{38} - 6 q^{39} + 7 q^{40} - 20 q^{41} + 9 q^{42} - q^{43} - 18 q^{44} - 16 q^{45} - 19 q^{46} + 11 q^{47} - 18 q^{48} - 21 q^{49} - 13 q^{50} + 15 q^{51} + 28 q^{52} - 17 q^{53} + 15 q^{54} + 12 q^{55} - 3 q^{56} - 8 q^{57} - 18 q^{58} + 14 q^{59} + 13 q^{60} + 19 q^{61} + 24 q^{62} + 10 q^{63} - 21 q^{64} - 4 q^{65} - 39 q^{66} - 15 q^{68} - 6 q^{69} + 6 q^{70} - 19 q^{71} - 21 q^{72} - 4 q^{73} + 18 q^{74} + 15 q^{75} - 14 q^{76} - 13 q^{77} + 46 q^{78} - 4 q^{79} - 12 q^{80} + q^{81} - 19 q^{82} - 36 q^{83} - 15 q^{84} - q^{85} - 18 q^{86} - 8 q^{87} + 24 q^{88} + 42 q^{89} + 9 q^{90} + 8 q^{91} - 38 q^{92} + 7 q^{93} + 2 q^{95} + 7 q^{96} + 27 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + q^5 + 5 * q^6 - 2 * q^7 - 9 * q^8 - 3 * q^9 + 7 * q^10 + 5 * q^11 - 12 * q^12 + 2 * q^13 - 3 * q^14 + 8 * q^15 + 6 * q^16 - 16 * q^17 - 21 * q^18 + 10 * q^19 - 8 * q^20 - 5 * q^21 + 24 * q^22 + 2 * q^23 + 16 * q^24 - 16 * q^25 - 19 * q^26 - q^27 + 16 * q^28 - 12 * q^29 - 10 * q^30 + 16 * q^31 - 6 * q^32 + 7 * q^33 - 2 * q^34 - 7 * q^35 + 13 * q^36 + q^37 - 18 * q^38 - 6 * q^39 + 7 * q^40 - 20 * q^41 + 9 * q^42 - q^43 - 18 * q^44 - 16 * q^45 - 19 * q^46 + 11 * q^47 - 18 * q^48 - 21 * q^49 - 13 * q^50 + 15 * q^51 + 28 * q^52 - 17 * q^53 + 15 * q^54 + 12 * q^55 - 3 * q^56 - 8 * q^57 - 18 * q^58 + 14 * q^59 + 13 * q^60 + 19 * q^61 + 24 * q^62 + 10 * q^63 - 21 * q^64 - 4 * q^65 - 39 * q^66 - 15 * q^68 - 6 * q^69 + 6 * q^70 - 19 * q^71 - 21 * q^72 - 4 * q^73 + 18 * q^74 + 15 * q^75 - 14 * q^76 - 13 * q^77 + 46 * q^78 - 4 * q^79 - 12 * q^80 + q^81 - 19 * q^82 - 36 * q^83 - 15 * q^84 - q^85 - 18 * q^86 - 8 * q^87 + 24 * q^88 + 42 * q^89 + 9 * q^90 + 8 * q^91 - 38 * q^92 + 7 * q^93 + 2 * q^95 + 7 * q^96 + 27 * q^97 - 15 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.51334	−1.77720	−0.888599	−	0.458685i	$-0.848321\pi$
$2$	−2.51334	−1.77720	−0.888599	+	0.458685i	$0.848321\pi$
$3$	−2.68251	−1.54875	−0.774373	−	0.632729i	$-0.781935\pi$
$3$	−2.68251	−1.54875	−0.774373	+	0.632729i	$0.781935\pi$
$4$	4.31686	2.15843
$5$	−1.68251	−0.752440	−0.376220	−	0.926530i	$-0.622776\pi$
$5$	−1.68251	−0.752440	−0.376220	+	0.926530i	$0.622776\pi$
$6$	6.74204	2.75243
$7$	1.39788	0.528348	0.264174	−	0.964475i	$-0.414901\pi$
$7$	1.39788	0.528348	0.264174	+	0.964475i	$0.414901\pi$
$8$	−5.82306	−2.05876
$9$	4.19584	1.39861
$10$	4.22871	1.33723
$11$	−4.74204	−1.42978	−0.714890	−	0.699237i	$-0.753523\pi$
$11$	−4.74204	−1.42978	−0.714890	+	0.699237i	$0.753523\pi$
$12$	−11.5800	−3.34286
$13$	5.97852	1.65814	0.829072	−	0.559142i	$-0.188869\pi$
$13$	5.97852	1.65814	0.829072	+	0.559142i	$0.188869\pi$
$14$	−3.51334	−0.938979
$15$	4.51334	1.16534
$16$	6.00158	1.50040
$17$	−4.30972	−1.04526	−0.522630	−	0.852559i	$-0.675049\pi$
$17$	−4.30972	−1.04526	−0.522630	+	0.852559i	$0.675049\pi$
$18$	−10.5456	−2.48561
$19$	4.64675	1.06604	0.533018	−	0.846104i	$-0.321058\pi$
$19$	4.64675	1.06604	0.533018	+	0.846104i	$0.321058\pi$
$20$	−7.26315	−1.62409
$21$	−3.74982	−0.818277
$22$	11.9184	2.54100
$23$	1.07545	0.224248	0.112124	−	0.993694i	$-0.464235\pi$
$23$	1.07545	0.224248	0.112124	+	0.993694i	$0.464235\pi$
$24$	15.6204	3.18850
$25$	−2.16917	−0.433834
$26$	−15.0260	−2.94685
$27$	−3.20786	−0.617353
$28$	6.03445	1.14040
$29$	2.39011	0.443832	0.221916	−	0.975066i	$-0.428769\pi$
$29$	2.39011	0.443832	0.221916	+	0.975066i	$0.428769\pi$
$30$	−11.3435	−2.07104
$31$	−2.69983	−0.484903	−0.242452	−	0.970163i	$-0.577952\pi$
$31$	−2.69983	−0.484903	−0.242452	+	0.970163i	$0.577952\pi$
$32$	−3.43788	−0.607738
$33$	12.7206	2.21437
$34$	10.8318	1.85764
$35$	−2.35194	−0.397550
$36$	18.1129	3.01881
$37$	−3.75406	−0.617164	−0.308582	−	0.951198i	$-0.599854\pi$
$37$	−3.75406	−0.617164	−0.308582	+	0.951198i	$0.599854\pi$
$38$	−11.6788	−1.89456
$39$	−16.0374	−2.56804
$40$	9.79734	1.54910
$41$	0.453170	0.0707733	0.0353866	−	0.999374i	$-0.488734\pi$
$41$	0.453170	0.0707733	0.0353866	+	0.999374i	$0.488734\pi$
$42$	9.42455	1.45424
$43$	4.16989	0.635902	0.317951	−	0.948107i	$-0.397005\pi$
$43$	4.16989	0.635902	0.317951	+	0.948107i	$0.397005\pi$
$44$	−20.4708	−3.08608
$45$	−7.05954	−1.05237
$46$	−2.70298	−0.398533
$47$	0.0610313	0.00890234	0.00445117	−	0.999990i	$-0.498583\pi$
$47$	0.0610313	0.00890234	0.00445117	+	0.999990i	$0.498583\pi$
$48$	−16.0993	−2.32373
$49$	−5.04594	−0.720848
$50$	5.45186	0.771009
$51$	11.5609	1.61884
$52$	25.8085	3.57899
$53$	−3.92879	−0.539661	−0.269830	−	0.962908i	$-0.586968\pi$
$53$	−3.92879	−0.539661	−0.269830	+	0.962908i	$0.586968\pi$
$54$	8.06243	1.09716
$55$	7.97852	1.07582
$56$	−8.13992	−1.08774
$57$	−12.4649	−1.65102
$58$	−6.00714	−0.788776
$59$	1.47547	0.192090	0.0960450	−	0.995377i	$-0.469381\pi$
$59$	1.47547	0.192090	0.0960450	+	0.995377i	$0.469381\pi$
$60$	19.4835	2.51530
$61$	−4.56900	−0.585001	−0.292501	−	0.956265i	$-0.594487\pi$
$61$	−4.56900	−0.585001	−0.292501	+	0.956265i	$0.594487\pi$
$62$	6.78558	0.861769
$63$	5.86528	0.738955
$64$	−3.36261	−0.420326
$65$	−10.0589	−1.24765
$66$	−31.9711	−3.93537
$67$	0	0
$67$	0	0
$68$	−18.6045	−2.25612
$69$	−2.88491	−0.347303
$70$	5.91121	0.706525
$71$	−0.793487	−0.0941696	−0.0470848	−	0.998891i	$-0.514993\pi$
$71$	−0.793487	−0.0941696	−0.0470848	+	0.998891i	$0.514993\pi$
$72$	−24.4326	−2.87941
$73$	3.14991	0.368669	0.184334	−	0.982864i	$-0.440987\pi$
$73$	3.14991	0.368669	0.184334	+	0.982864i	$0.440987\pi$
$74$	9.43522	1.09682
$75$	5.81881	0.671899
$76$	20.0594	2.30097
$77$	−6.62880	−0.755422
$78$	40.3075	4.56392
$79$	0.102235	0.0115024	0.00575118	−	0.999983i	$-0.498169\pi$
$79$	0.102235	0.0115024	0.00575118	+	0.999983i	$0.498169\pi$
$80$	−10.0977	−1.12896
$81$	−3.98242	−0.442492
$82$	−1.13897	−0.125778
$83$	−13.7967	−1.51438	−0.757190	−	0.653195i	$-0.773428\pi$
$83$	−13.7967	−1.51438	−0.757190	+	0.653195i	$0.773428\pi$
$84$	−16.1874	−1.76619
$85$	7.25114	0.786496
$86$	−10.4803	−1.13012
$87$	−6.41148	−0.687382
$88$	27.6132	2.94358
$89$	15.3350	1.62551	0.812756	−	0.582604i	$-0.197966\pi$
$89$	15.3350	1.62551	0.812756	+	0.582604i	$0.197966\pi$
$90$	17.7430	1.87028
$91$	8.35724	0.876077
$92$	4.64259	0.484024
$93$	7.24231	0.750992
$94$	−0.153392	−0.0158212
$95$	−7.81818	−0.802129
$96$	9.22214	0.941231
$97$	16.5271	1.67808	0.839038	−	0.544073i	$-0.183119\pi$
$97$	16.5271	1.67808	0.839038	+	0.544073i	$0.183119\pi$
$98$	12.6821	1.28109
$99$	−19.8969	−1.99971
$100$	−9.36401	−0.936401
$101$	−7.63074	−0.759287	−0.379644	−	0.925133i	$-0.623953\pi$
$101$	−7.63074	−0.759287	−0.379644	+	0.925133i	$0.623953\pi$
$102$	−29.0563	−2.87701
$103$	−10.0267	−0.987958	−0.493979	−	0.869474i	$-0.664458\pi$
$103$	−10.0267	−0.987958	−0.493979	+	0.869474i	$0.664458\pi$
$104$	−34.8133	−3.41372
$105$	6.30909	0.615704
$106$	9.87437	0.959084
$107$	−6.27296	−0.606430	−0.303215	−	0.952922i	$-0.598060\pi$
$107$	−6.27296	−0.606430	−0.303215	+	0.952922i	$0.598060\pi$
$108$	−13.8479	−1.33251
$109$	−17.3770	−1.66441	−0.832206	−	0.554467i	$-0.812922\pi$
$109$	−17.3770	−1.66441	−0.832206	+	0.554467i	$0.812922\pi$
$110$	−20.0527	−1.91195
$111$	10.0703	0.955830
$112$	8.38948	0.792731
$113$	10.3602	0.974608	0.487304	−	0.873232i	$-0.337980\pi$
$113$	10.3602	0.974608	0.487304	+	0.873232i	$0.337980\pi$
$114$	31.3286	2.93419
$115$	−1.80946	−0.168733
$116$	10.3178	0.957980
$117$	25.0850	2.31910
$118$	−3.70836	−0.341382
$119$	−6.02446	−0.552262
$120$	−26.2814	−2.39915
$121$	11.4870	1.04427
$122$	11.4834	1.03966
$123$	−1.21563	−0.109610
$124$	−11.6548	−1.04663
$125$	12.0622	1.07887
$126$	−14.7414	−1.31327
$127$	20.7486	1.84114	0.920568	−	0.390582i	$-0.127726\pi$
$127$	20.7486	1.84114	0.920568	+	0.390582i	$0.127726\pi$
$128$	15.3271	1.35474
$129$	−11.1858	−0.984851
$130$	25.2814	2.21733
$131$	14.4334	1.26105	0.630527	−	0.776168i	$-0.282839\pi$
$131$	14.4334	1.26105	0.630527	+	0.776168i	$0.282839\pi$
$132$	54.9130	4.77956
$133$	6.49558	0.563238
$134$	0	0
$135$	5.39725	0.464521
$136$	25.0958	2.15194
$137$	5.17298	0.441958	0.220979	−	0.975279i	$-0.429075\pi$
$137$	5.17298	0.441958	0.220979	+	0.975279i	$0.429075\pi$
$138$	7.25076	0.617226
$139$	1.42311	0.120707	0.0603533	−	0.998177i	$-0.480777\pi$
$139$	1.42311	0.120707	0.0603533	+	0.998177i	$0.480777\pi$
$140$	−10.1530	−0.858085
$141$	−0.163717	−0.0137875
$142$	1.99430	0.167358
$143$	−28.3504	−2.37078
$144$	25.1817	2.09848
$145$	−4.02137	−0.333957
$146$	−7.91677	−0.655197
$147$	13.5358	1.11641
$148$	−16.2058	−1.33211
$149$	−7.92039	−0.648864	−0.324432	−	0.945909i	$-0.605173\pi$
$149$	−7.92039	−0.648864	−0.324432	+	0.945909i	$0.605173\pi$
$150$	−14.6246	−1.19410
$151$	−10.1152	−0.823164	−0.411582	−	0.911373i	$-0.635024\pi$
$151$	−10.1152	−0.823164	−0.411582	+	0.911373i	$0.635024\pi$
$152$	−27.0583	−2.19472
$153$	−18.0829	−1.46192
$154$	16.6604	1.34253
$155$	4.54248	0.364861
$156$	−69.2314	−5.54295
$157$	12.2369	0.976612	0.488306	−	0.872673i	$-0.337615\pi$
$157$	12.2369	0.976612	0.488306	+	0.872673i	$0.337615\pi$
$158$	−0.256952	−0.0204420
$159$	10.5390	0.835798
$160$	5.78426	0.457286
$161$	1.50335	0.118481
$162$	10.0092	0.786395
$163$	−8.70078	−0.681498	−0.340749	−	0.940154i	$-0.610681\pi$
$163$	−8.70078	−0.681498	−0.340749	+	0.940154i	$0.610681\pi$
$164$	1.95627	0.152759
$165$	−21.4024	−1.66618
$166$	34.6756	2.69135
$167$	15.0650	1.16577	0.582884	−	0.812555i	$-0.301924\pi$
$167$	15.0650	1.16577	0.582884	+	0.812555i	$0.301924\pi$
$168$	21.8354	1.68464
$169$	22.7427	1.74944
$170$	−18.2246	−1.39776
$171$	19.4970	1.49097
$172$	18.0008	1.37255
$173$	15.9345	1.21148	0.605740	−	0.795662i	$-0.292877\pi$
$173$	15.9345	1.21148	0.605740	+	0.795662i	$0.292877\pi$
$174$	16.1142	1.22161
$175$	−3.03223	−0.229215
$176$	−28.4598	−2.14524
$177$	−3.95796	−0.297499
$178$	−38.5421	−2.88886
$179$	16.3710	1.22363	0.611815	−	0.791001i	$-0.290440\pi$
$179$	16.3710	1.22363	0.611815	+	0.791001i	$0.290440\pi$
$180$	−30.4751	−2.27148
$181$	−2.55356	−0.189804	−0.0949021	−	0.995487i	$-0.530254\pi$
$181$	−2.55356	−0.189804	−0.0949021	+	0.995487i	$0.530254\pi$
$182$	−21.0046	−1.55696
$183$	12.2564	0.906018
$184$	−6.26243	−0.461673
$185$	6.31623	0.464379
$186$	−18.2024	−1.33466
$187$	20.4369	1.49449
$188$	0.263464	0.0192151
$189$	−4.48420	−0.326177
$190$	19.6497	1.42554
$191$	−3.12299	−0.225971	−0.112986	−	0.993597i	$-0.536041\pi$
$191$	−3.12299	−0.225971	−0.112986	+	0.993597i	$0.536041\pi$
$192$	9.02022	0.650978
$193$	21.5176	1.54887	0.774436	−	0.632652i	$-0.218034\pi$
$193$	21.5176	1.54887	0.774436	+	0.632652i	$0.218034\pi$
$194$	−41.5383	−2.98227
$195$	26.9831	1.93230
$196$	−21.7826	−1.55590
$197$	15.2804	1.08868	0.544341	−	0.838864i	$-0.316780\pi$
$197$	15.2804	1.08868	0.544341	+	0.838864i	$0.316780\pi$
$198$	50.0076	3.55388
$199$	−14.2781	−1.01215	−0.506073	−	0.862491i	$-0.668903\pi$
$199$	−14.2781	−1.01215	−0.506073	+	0.862491i	$0.668903\pi$
$200$	12.6312	0.893161
$201$	0	0
$202$	19.1786	1.34940
$203$	3.34108	0.234497
$204$	49.9066	3.49416
$205$	−0.762462	−0.0532526
$206$	25.2004	1.75580
$207$	4.51244	0.313636
$208$	35.8806	2.48787
$209$	−22.0351	−1.52420
$210$	−15.8569	−1.09423
$211$	−9.85461	−0.678419	−0.339210	−	0.940711i	$-0.610160\pi$
$211$	−9.85461	−0.678419	−0.339210	+	0.940711i	$0.610160\pi$
$212$	−16.9601	−1.16482
$213$	2.12854	0.145845
$214$	15.7661	1.07775
$215$	−7.01587	−0.478478
$216$	18.6796	1.27098
$217$	−3.77403	−0.256198
$218$	43.6742	2.95799
$219$	−8.44964	−0.570974
$220$	34.4422	2.32209
$221$	−25.7658	−1.73319
$222$	−25.3100	−1.69870
$223$	−24.7970	−1.66053	−0.830266	−	0.557367i	$-0.811812\pi$
$223$	−24.7970	−1.66053	−0.830266	+	0.557367i	$0.811812\pi$
$224$	−4.80574	−0.321097
$225$	−9.10150	−0.606767
$226$	−26.0387	−1.73207
$227$	12.9495	0.859490	0.429745	−	0.902950i	$-0.358603\pi$
$227$	12.9495	0.859490	0.429745	+	0.902950i	$0.358603\pi$
$228$	−53.8094	−3.56361
$229$	3.86282	0.255262	0.127631	−	0.991822i	$-0.459263\pi$
$229$	3.86282	0.255262	0.127631	+	0.991822i	$0.459263\pi$
$230$	4.54778	0.299872
$231$	17.7818	1.16996
$232$	−13.9177	−0.913744
$233$	19.8030	1.29734	0.648670	−	0.761070i	$-0.275326\pi$
$233$	19.8030	1.29734	0.648670	+	0.761070i	$0.275326\pi$
$234$	−63.0469	−4.12151
$235$	−0.102686	−0.00669847
$236$	6.36941	0.414613
$237$	−0.274247	−0.0178142
$238$	15.1415	0.981478
$239$	−7.87943	−0.509678	−0.254839	−	0.966984i	$-0.582022\pi$
$239$	−7.87943	−0.509678	−0.254839	+	0.966984i	$0.582022\pi$
$240$	27.0872	1.74847
$241$	2.84067	0.182983	0.0914917	−	0.995806i	$-0.470836\pi$
$241$	2.84067	0.182983	0.0914917	+	0.995806i	$0.470836\pi$
$242$	−28.8707	−1.85588
$243$	20.3065	1.30266
$244$	−19.7238	−1.26268
$245$	8.48983	0.542395
$246$	3.05529	0.194798
$247$	27.7807	1.76764
$248$	15.7213	0.998301
$249$	37.0096	2.34539
$250$	−30.3163	−1.91737
$251$	1.69548	0.107018	0.0535088	−	0.998567i	$-0.482959\pi$
$251$	1.69548	0.107018	0.0535088	+	0.998567i	$0.482959\pi$
$252$	25.3196	1.59498
$253$	−5.09985	−0.320625
$254$	−52.1481	−3.27206
$255$	−19.4512	−1.21808
$256$	−31.7970	−1.98731
$257$	−0.415165	−0.0258973	−0.0129486	−	0.999916i	$-0.504122\pi$
$257$	−0.415165	−0.0258973	−0.0129486	+	0.999916i	$0.504122\pi$
$258$	28.1136	1.75027
$259$	−5.24772	−0.326077
$260$	−43.4229	−2.69298
$261$	10.0285	0.620749
$262$	−36.2760	−2.24114
$263$	−20.8569	−1.28609	−0.643045	−	0.765828i	$-0.722329\pi$
$263$	−20.8569	−1.28609	−0.643045	+	0.765828i	$0.722329\pi$
$264$	−74.0726	−4.55885
$265$	6.61022	0.406062
$266$	−16.3256	−1.00099
$267$	−41.1364	−2.51751
$268$	0	0
$269$	18.8401	1.14870	0.574352	−	0.818609i	$-0.305254\pi$
$269$	18.8401	1.14870	0.574352	+	0.818609i	$0.305254\pi$
$270$	−13.5651	−0.825546
$271$	−17.6469	−1.07197	−0.535986	−	0.844227i	$-0.680060\pi$
$271$	−17.6469	−1.07197	−0.535986	+	0.844227i	$0.680060\pi$
$272$	−25.8651	−1.56830
$273$	−22.4184	−1.35682
$274$	−13.0014	−0.785446
$275$	10.2863	0.620287
$276$	−12.4538	−0.749630
$277$	25.8388	1.55250	0.776251	−	0.630424i	$-0.217119\pi$
$277$	25.8388	1.55250	0.776251	+	0.630424i	$0.217119\pi$
$278$	−3.57675	−0.214519
$279$	−11.3281	−0.678193
$280$	13.6955	0.818461
$281$	−19.9322	−1.18906	−0.594529	−	0.804074i	$-0.702661\pi$
$281$	−19.9322	−1.18906	−0.594529	+	0.804074i	$0.702661\pi$
$282$	0.411476	0.0245030
$283$	6.10417	0.362855	0.181428	−	0.983404i	$-0.441928\pi$
$283$	6.10417	0.362855	0.181428	+	0.983404i	$0.441928\pi$
$284$	−3.42538	−0.203259
$285$	20.9723	1.24229
$286$	71.2542	4.21335
$287$	0.633476	0.0373929
$288$	−14.4248	−0.849991
$289$	1.57370	0.0925705
$290$	10.1071	0.593507
$291$	−44.3341	−2.59891
$292$	13.5977	0.795746
$293$	18.6910	1.09194	0.545969	−	0.837805i	$-0.316162\pi$
$293$	18.6910	1.09194	0.545969	+	0.837805i	$0.316162\pi$
$294$	−34.0199	−1.98408
$295$	−2.48249	−0.144536
$296$	21.8601	1.27059
$297$	15.2118	0.882679
$298$	19.9066	1.15316
$299$	6.42963	0.371835
$300$	25.1190	1.45025
$301$	5.82899	0.335978
$302$	25.4229	1.46292
$303$	20.4695	1.17594
$304$	27.8878	1.59948
$305$	7.68738	0.440178
$306$	45.4485	2.59812
$307$	−4.76872	−0.272165	−0.136083	−	0.990697i	$-0.543451\pi$
$307$	−4.76872	−0.272165	−0.136083	+	0.990697i	$0.543451\pi$
$308$	−28.6156	−1.63053
$309$	26.8966	1.53010
$310$	−11.4168	−0.648430
$311$	4.94753	0.280549	0.140274	−	0.990113i	$-0.455202\pi$
$311$	4.94753	0.280549	0.140274	+	0.990113i	$0.455202\pi$
$312$	93.3869	5.28699
$313$	−33.3091	−1.88274	−0.941371	−	0.337373i	$-0.890462\pi$
$313$	−33.3091	−1.88274	−0.941371	+	0.337373i	$0.890462\pi$
$314$	−30.7555	−1.73563
$315$	−9.86837	−0.556020
$316$	0.441336	0.0248271
$317$	9.03276	0.507330	0.253665	−	0.967292i	$-0.418364\pi$
$317$	9.03276	0.507330	0.253665	+	0.967292i	$0.418364\pi$
$318$	−26.4881	−1.48538
$319$	−11.3340	−0.634582
$320$	5.65761	0.316270
$321$	16.8273	0.939206
$322$	−3.77843	−0.210564
$323$	−20.0262	−1.11429
$324$	−17.1916	−0.955088
$325$	−12.9684	−0.719359
$326$	21.8680	1.21116
$327$	46.6138	2.57775
$328$	−2.63884	−0.145705
$329$	0.0853143	0.00470353
$330$	53.7916	2.96113
$331$	−12.2565	−0.673678	−0.336839	−	0.941562i	$-0.609358\pi$
$331$	−12.2565	−0.673678	−0.336839	+	0.941562i	$0.609358\pi$
$332$	−59.5583	−3.26868
$333$	−15.7515	−0.863174
$334$	−37.8635	−2.07180
$335$	0	0
$336$	−22.5048	−1.22774
$337$	−0.455740	−0.0248258	−0.0124129	−	0.999923i	$-0.503951\pi$
$337$	−0.455740	−0.0248258	−0.0124129	+	0.999923i	$0.503951\pi$
$338$	−57.1602	−3.10910
$339$	−27.7914	−1.50942
$340$	31.3022	1.69760
$341$	12.8027	0.693305
$342$	−49.0026	−2.64976
$343$	−16.8387	−0.909207
$344$	−24.2815	−1.30917
$345$	4.85389	0.261325
$346$	−40.0489	−2.15304
$347$	22.7005	1.21863	0.609314	−	0.792929i	$-0.291445\pi$
$347$	22.7005	1.21863	0.609314	+	0.792929i	$0.291445\pi$
$348$	−27.6775	−1.48367
$349$	32.2359	1.72555	0.862774	−	0.505589i	$-0.168725\pi$
$349$	32.2359	1.72555	0.862774	+	0.505589i	$0.168725\pi$
$350$	7.62103	0.407361
$351$	−19.1783	−1.02366
$352$	16.3026	0.868931
$353$	−32.5926	−1.73473	−0.867364	−	0.497674i	$-0.834188\pi$
$353$	−32.5926	−1.73473	−0.867364	+	0.497674i	$0.834188\pi$
$354$	9.94769	0.528714
$355$	1.33505	0.0708570
$356$	66.1993	3.50856
$357$	16.1607	0.855313
$358$	−41.1460	−2.17463
$359$	−31.5448	−1.66487	−0.832437	−	0.554120i	$-0.813055\pi$
$359$	−31.5448	−1.66487	−0.832437	+	0.554120i	$0.813055\pi$
$360$	41.1081	2.16659
$361$	2.59226	0.136434
$362$	6.41795	0.337320
$363$	−30.8139	−1.61731
$364$	36.0771	1.89095
$365$	−5.29974	−0.277401
$366$	−30.8044	−1.61017
$367$	−19.3973	−1.01253	−0.506264	−	0.862378i	$-0.668974\pi$
$367$	−19.3973	−1.01253	−0.506264	+	0.862378i	$0.668974\pi$
$368$	6.45443	0.336460
$369$	1.90143	0.0989845
$370$	−15.8748	−0.825293
$371$	−5.49197	−0.285129
$372$	31.2640	1.62097
$373$	17.4411	0.903065	0.451533	−	0.892255i	$-0.350877\pi$
$373$	17.4411	0.903065	0.451533	+	0.892255i	$0.350877\pi$
$374$	−51.3648	−2.65601
$375$	−32.3569	−1.67090
$376$	−0.355389	−0.0183278
$377$	14.2893	0.735937
$378$	11.2703	0.579681
$379$	−21.4213	−1.10034	−0.550170	−	0.835053i	$-0.685437\pi$
$379$	−21.4213	−1.10034	−0.550170	+	0.835053i	$0.685437\pi$
$380$	−33.7500	−1.73134
$381$	−55.6582	−2.85145
$382$	7.84911	0.401596
$383$	−37.6659	−1.92464	−0.962319	−	0.271924i	$-0.912340\pi$
$383$	−37.6659	−1.92464	−0.962319	+	0.271924i	$0.912340\pi$
$384$	−41.1151	−2.09815
$385$	11.1530	0.568409
$386$	−54.0811	−2.75265
$387$	17.4962	0.889382
$388$	71.3454	3.62201
$389$	−20.0582	−1.01699	−0.508496	−	0.861065i	$-0.669798\pi$
$389$	−20.0582	−1.01699	−0.508496	+	0.861065i	$0.669798\pi$
$390$	−67.8176	−3.43408
$391$	−4.63491	−0.234397
$392$	29.3828	1.48406
$393$	−38.7177	−1.95305
$394$	−38.4048	−1.93480
$395$	−0.172012	−0.00865484
$396$	−85.8921	−4.31624
$397$	−11.8442	−0.594444	−0.297222	−	0.954808i	$-0.596060\pi$
$397$	−11.8442	−0.594444	−0.297222	+	0.954808i	$0.596060\pi$
$398$	35.8856	1.79878
$399$	−17.4244	−0.872313
$400$	−13.0185	−0.650923
$401$	23.7298	1.18501	0.592505	−	0.805567i	$-0.298139\pi$
$401$	23.7298	1.18501	0.592505	+	0.805567i	$0.298139\pi$
$402$	0	0
$403$	−16.1410	−0.804040
$404$	−32.9409	−1.63887
$405$	6.70046	0.332948
$406$	−8.39725	−0.416748
$407$	17.8019	0.882409
$408$	−67.3196	−3.33281
$409$	24.9620	1.23429	0.617145	−	0.786849i	$-0.288289\pi$
$409$	24.9620	1.23429	0.617145	+	0.786849i	$0.288289\pi$
$410$	1.91632	0.0946405
$411$	−13.8766	−0.684480
$412$	−43.2838	−2.13244
$413$	2.06253	0.101490
$414$	−11.3413	−0.557394
$415$	23.2130	1.13948
$416$	−20.5535	−1.00772
$417$	−3.81750	−0.186944
$418$	55.3816	2.70880
$419$	3.20317	0.156485	0.0782425	−	0.996934i	$-0.475069\pi$
$419$	3.20317	0.156485	0.0782425	+	0.996934i	$0.475069\pi$
$420$	27.2355	1.32896
$421$	−11.2318	−0.547404	−0.273702	−	0.961814i	$-0.588248\pi$
$421$	−11.2318	−0.547404	−0.273702	+	0.961814i	$0.588248\pi$
$422$	24.7679	1.20568
$423$	0.256078	0.0124509
$424$	22.8776	1.11103
$425$	9.34852	0.453470
$426$	−5.34973	−0.259195
$427$	−6.38691	−0.309084
$428$	−27.0795	−1.30894
$429$	76.0502	3.67174
$430$	17.6332	0.850350
$431$	−0.299510	−0.0144269	−0.00721345	−	0.999974i	$-0.502296\pi$
$431$	−0.299510	−0.0144269	−0.00721345	+	0.999974i	$0.502296\pi$
$432$	−19.2522	−0.926274
$433$	−7.14683	−0.343455	−0.171727	−	0.985145i	$-0.554935\pi$
$433$	−7.14683	−0.343455	−0.171727	+	0.985145i	$0.554935\pi$
$434$	9.48540	0.455314
$435$	10.7874	0.517214
$436$	−75.0140	−3.59252
$437$	4.99737	0.239056
$438$	21.2368	1.01473
$439$	−18.1442	−0.865976	−0.432988	−	0.901400i	$-0.642541\pi$
$439$	−18.1442	−0.865976	−0.432988	+	0.901400i	$0.642541\pi$
$440$	−46.4594	−2.21487
$441$	−21.1720	−1.00819
$442$	64.7581	3.08023
$443$	23.0158	1.09351	0.546757	−	0.837292i	$-0.315862\pi$
$443$	23.0158	1.09351	0.546757	+	0.837292i	$0.315862\pi$
$444$	43.4721	2.06309
$445$	−25.8013	−1.22310
$446$	62.3233	2.95109
$447$	21.2465	1.00492
$448$	−4.70051	−0.222078
$449$	−26.1717	−1.23512	−0.617559	−	0.786525i	$-0.711878\pi$
$449$	−26.1717	−1.23512	−0.617559	+	0.786525i	$0.711878\pi$
$450$	22.8751	1.07834
$451$	−2.14895	−0.101190
$452$	44.7237	2.10363
$453$	27.1341	1.27487
$454$	−32.5465	−1.52748
$455$	−14.0611	−0.659195
$456$	72.5840	3.39906
$457$	14.7470	0.689837	0.344919	−	0.938633i	$-0.387906\pi$
$457$	14.7470	0.689837	0.344919	+	0.938633i	$0.387906\pi$
$458$	−9.70856	−0.453651
$459$	13.8250	0.645295
$460$	−7.81119	−0.364199
$461$	−0.568681	−0.0264861	−0.0132431	−	0.999912i	$-0.504216\pi$
$461$	−0.568681	−0.0264861	−0.0132431	+	0.999912i	$0.504216\pi$
$462$	−44.6916	−2.07924
$463$	−26.1827	−1.21681	−0.608406	−	0.793626i	$-0.708191\pi$
$463$	−26.1827	−1.21681	−0.608406	+	0.793626i	$0.708191\pi$
$464$	14.3444	0.665923
$465$	−12.1852	−0.565077
$466$	−49.7717	−2.30563
$467$	−23.1393	−1.07076	−0.535380	−	0.844611i	$-0.679832\pi$
$467$	−23.1393	−1.07076	−0.535380	+	0.844611i	$0.679832\pi$
$468$	108.288	5.00563
$469$	0	0
$470$	0.258084	0.0119045
$471$	−32.8256	−1.51252
$472$	−8.59176	−0.395468
$473$	−19.7738	−0.909200
$474$	0.689275	0.0316594
$475$	−10.0796	−0.462483
$476$	−26.0068	−1.19202
$477$	−16.4846	−0.754778
$478$	19.8037	0.905798
$479$	13.0626	0.596847	0.298424	−	0.954434i	$-0.403539\pi$
$479$	13.0626	0.596847	0.298424	+	0.954434i	$0.403539\pi$
$480$	−15.5163	−0.708220
$481$	−22.4437	−1.02335
$482$	−7.13955	−0.325198
$483$	−4.03276	−0.183497
$484$	49.5877	2.25399
$485$	−27.8070	−1.26265
$486$	−51.0370	−2.31508
$487$	−10.6746	−0.483712	−0.241856	−	0.970312i	$-0.577756\pi$
$487$	−10.6746	−0.483712	−0.241856	+	0.970312i	$0.577756\pi$
$488$	26.6056	1.20438
$489$	23.3399	1.05547
$490$	−21.3378	−0.963943
$491$	−19.5414	−0.881890	−0.440945	−	0.897534i	$-0.645357\pi$
$491$	−19.5414	−0.881890	−0.440945	+	0.897534i	$0.645357\pi$
$492$	−5.24772	−0.236585
$493$	−10.3007	−0.463920
$494$	−69.8222	−3.14145
$495$	33.4766	1.50466
$496$	−16.2032	−0.727547
$497$	−1.10920	−0.0497543
$498$	−93.0176	−4.16822
$499$	−33.0146	−1.47794	−0.738968	−	0.673741i	$-0.764686\pi$
$499$	−33.0146	−1.47794	−0.738968	+	0.673741i	$0.764686\pi$
$500$	52.0708	2.32868
$501$	−40.4121	−1.80548
$502$	−4.26130	−0.190191
$503$	26.4236	1.17817	0.589086	−	0.808071i	$-0.299488\pi$
$503$	26.4236	1.17817	0.589086	+	0.808071i	$0.299488\pi$
$504$	−34.1538	−1.52133
$505$	12.8388	0.571318
$506$	12.8177	0.569814
$507$	−61.0076	−2.70944
$508$	89.5687	3.97397
$509$	−9.67944	−0.429033	−0.214517	−	0.976720i	$-0.568818\pi$
$509$	−9.67944	−0.429033	−0.214517	+	0.976720i	$0.568818\pi$
$510$	48.8875	2.16477
$511$	4.40318	0.194785
$512$	49.2624	2.17711
$513$	−14.9061	−0.658121
$514$	1.04345	0.0460246
$515$	16.8700	0.743379
$516$	−48.2874	−2.12573
$517$	−0.289413	−0.0127284
$518$	13.1893	0.579504
$519$	−42.7445	−1.87628
$520$	58.5736	2.56862
$521$	−22.0269	−0.965015	−0.482507	−	0.875892i	$-0.660274\pi$
$521$	−22.0269	−0.965015	−0.482507	+	0.875892i	$0.660274\pi$
$522$	−25.2050	−1.10319
$523$	−3.73030	−0.163115	−0.0815573	−	0.996669i	$-0.525989\pi$
$523$	−3.73030	−0.163115	−0.0815573	+	0.996669i	$0.525989\pi$
$524$	62.3071	2.72190
$525$	8.13399	0.354996
$526$	52.4204	2.28564
$527$	11.6355	0.506851
$528$	76.3435	3.32243
$529$	−21.8434	−0.949713
$530$	−16.6137	−0.721653
$531$	6.19085	0.268660
$532$	28.0405	1.21571
$533$	2.70929	0.117352
$534$	103.390	4.47410
$535$	10.5543	0.456302
$536$	0	0
$537$	−43.9154	−1.89509
$538$	−47.3516	−2.04147
$539$	23.9281	1.03065
$540$	23.2992	1.00264
$541$	−18.5357	−0.796913	−0.398457	−	0.917187i	$-0.630454\pi$
$541$	−18.5357	−0.796913	−0.398457	+	0.917187i	$0.630454\pi$
$542$	44.3525	1.90510
$543$	6.84993	0.293959
$544$	14.8163	0.635244
$545$	29.2369	1.25237
$546$	56.3449	2.41134
$547$	−0.451191	−0.0192915	−0.00964577	−	0.999953i	$-0.503070\pi$
$547$	−0.451191	−0.0192915	−0.00964577	+	0.999953i	$0.503070\pi$
$548$	22.3310	0.953935
$549$	−19.1708	−0.818191
$550$	−25.8529	−1.10237
$551$	11.1062	0.473141
$552$	16.7990	0.715014
$553$	0.142912	0.00607725
$554$	−64.9416	−2.75910
$555$	−16.9433	−0.719205
$556$	6.14337	0.260537
$557$	−16.4731	−0.697986	−0.348993	−	0.937125i	$-0.613476\pi$
$557$	−16.4731	−0.697986	−0.348993	+	0.937125i	$0.613476\pi$
$558$	28.4712	1.20528
$559$	24.9298	1.05442
$560$	−14.1154	−0.596483
$561$	−54.8221	−2.31459
$562$	50.0964	2.11319
$563$	23.1902	0.977350	0.488675	−	0.872466i	$-0.337480\pi$
$563$	23.1902	0.977350	0.488675	+	0.872466i	$0.337480\pi$
$564$	−0.706744	−0.0297593
$565$	−17.4312	−0.733334
$566$	−15.3418	−0.644866
$567$	−5.56694	−0.233790
$568$	4.62052	0.193873
$569$	−8.83077	−0.370205	−0.185103	−	0.982719i	$-0.559262\pi$
$569$	−8.83077	−0.370205	−0.185103	+	0.982719i	$0.559262\pi$
$570$	−52.7105	−2.20780
$571$	7.05006	0.295036	0.147518	−	0.989059i	$-0.452872\pi$
$571$	7.05006	0.295036	0.147518	+	0.989059i	$0.452872\pi$
$572$	−122.385	−5.11717
$573$	8.37743	0.349972
$574$	−1.59214	−0.0664546
$575$	−2.33284	−0.0972863
$576$	−14.1090	−0.587874
$577$	6.79012	0.282676	0.141338	−	0.989961i	$-0.454859\pi$
$577$	6.79012	0.282676	0.141338	+	0.989961i	$0.454859\pi$
$578$	−3.95524	−0.164516
$579$	−57.7212	−2.39881
$580$	−17.3597	−0.720823
$581$	−19.2860	−0.800119
$582$	111.427	4.61878
$583$	18.6305	0.771596
$584$	−18.3421	−0.759001
$585$	−42.2056	−1.74499
$586$	−46.9767	−1.94059
$587$	16.6114	0.685627	0.342813	−	0.939404i	$-0.388620\pi$
$587$	16.6114	0.685627	0.342813	+	0.939404i	$0.388620\pi$
$588$	58.4321	2.40970
$589$	−12.5454	−0.516925
$590$	6.23934	0.256869
$591$	−40.9898	−1.68609
$592$	−22.5303	−0.925990
$593$	10.8059	0.443743	0.221872	−	0.975076i	$-0.428783\pi$
$593$	10.8059	0.443743	0.221872	+	0.975076i	$0.428783\pi$
$594$	−38.2324	−1.56870
$595$	10.1362	0.415544
$596$	−34.1912	−1.40053
$597$	38.3010	1.56756
$598$	−16.1598	−0.660825
$599$	−14.7787	−0.603842	−0.301921	−	0.953333i	$-0.597628\pi$
$599$	−14.7787	−0.603842	−0.301921	+	0.953333i	$0.597628\pi$
$600$	−33.8833	−1.38328
$601$	−1.43722	−0.0586254	−0.0293127	−	0.999570i	$-0.509332\pi$
$601$	−1.43722	−0.0586254	−0.0293127	+	0.999570i	$0.509332\pi$
$602$	−14.6502	−0.597098
$603$	0	0
$604$	−43.6660	−1.77674
$605$	−19.3269	−0.785752
$606$	−51.4468	−2.08988
$607$	−2.58744	−0.105021	−0.0525104	−	0.998620i	$-0.516722\pi$
$607$	−2.58744	−0.105021	−0.0525104	+	0.998620i	$0.516722\pi$
$608$	−15.9750	−0.647871
$609$	−8.96246	−0.363177
$610$	−19.3210	−0.782284
$611$	0.364877	0.0147614
$612$	−78.0615	−3.15545
$613$	15.6826	0.633416	0.316708	−	0.948523i	$-0.397422\pi$
$613$	15.6826	0.633416	0.316708	+	0.948523i	$0.397422\pi$
$614$	11.9854	0.483691
$615$	2.04531	0.0824748
$616$	38.5999	1.55523
$617$	1.74861	0.0703963	0.0351981	−	0.999380i	$-0.488794\pi$
$617$	1.74861	0.0703963	0.0351981	+	0.999380i	$0.488794\pi$
$618$	−67.6003	−2.71928
$619$	20.7784	0.835156	0.417578	−	0.908641i	$-0.362879\pi$
$619$	20.7784	0.835156	0.417578	+	0.908641i	$0.362879\pi$
$620$	19.6093	0.787527
$621$	−3.44991	−0.138440
$622$	−12.4348	−0.498590
$623$	21.4365	0.858836
$624$	−96.2500	−3.85308
$625$	−9.44885	−0.377954
$626$	83.7170	3.34601
$627$	59.1093	2.36060
$628$	52.8251	2.10795
$629$	16.1790	0.645097
$630$	24.8025	0.988157
$631$	−5.99485	−0.238651	−0.119326	−	0.992855i	$-0.538073\pi$
$631$	−5.99485	−0.238651	−0.119326	+	0.992855i	$0.538073\pi$
$632$	−0.595322	−0.0236806
$633$	26.4351	1.05070
$634$	−22.7024	−0.901626
$635$	−34.9096	−1.38534
$636$	45.4955	1.80401
$637$	−30.1673	−1.19527
$638$	28.4861	1.12778
$639$	−3.32935	−0.131707
$640$	−25.7880	−1.01936
$641$	21.2829	0.840625	0.420313	−	0.907379i	$-0.361920\pi$
$641$	21.2829	0.840625	0.420313	+	0.907379i	$0.361920\pi$
$642$	−42.2926	−1.66915
$643$	29.0051	1.14385	0.571925	−	0.820306i	$-0.306197\pi$
$643$	29.0051	1.14385	0.571925	+	0.820306i	$0.306197\pi$
$644$	6.48977	0.255733
$645$	18.8201	0.741041
$646$	50.3326	1.98031
$647$	−41.7185	−1.64012	−0.820061	−	0.572276i	$-0.806061\pi$
$647$	−41.7185	−1.64012	−0.820061	+	0.572276i	$0.806061\pi$
$648$	23.1899	0.910985
$649$	−6.99675	−0.274646
$650$	32.5940	1.27844
$651$	10.1239	0.396785
$652$	−37.5601	−1.47097
$653$	−24.1357	−0.944504	−0.472252	−	0.881464i	$-0.656559\pi$
$653$	−24.1357	−0.944504	−0.472252	+	0.881464i	$0.656559\pi$
$654$	−117.156	−4.58117
$655$	−24.2843	−0.948867
$656$	2.71974	0.106188
$657$	13.2165	0.515625
$658$	−0.214424	−0.00835911
$659$	19.2297	0.749081	0.374541	−	0.927211i	$-0.377800\pi$
$659$	19.2297	0.749081	0.374541	+	0.927211i	$0.377800\pi$
$660$	−92.3914	−3.59633
$661$	−11.8606	−0.461325	−0.230663	−	0.973034i	$-0.574089\pi$
$661$	−11.8606	−0.461325	−0.230663	+	0.973034i	$0.574089\pi$
$662$	30.8047	1.19726
$663$	69.1169	2.68428
$664$	80.3387	3.11775
$665$	−10.9289	−0.423803
$666$	39.5887	1.53403
$667$	2.57045	0.0995282
$668$	65.0337	2.51623
$669$	66.5182	2.57174
$670$	0	0
$671$	21.6664	0.836423
$672$	12.8914	0.497298
$673$	46.2235	1.78178	0.890892	−	0.454214i	$-0.150080\pi$
$673$	46.2235	1.78178	0.890892	+	0.454214i	$0.150080\pi$
$674$	1.14543	0.0441203
$675$	6.95839	0.267829
$676$	98.1773	3.77605
$677$	−17.3858	−0.668191	−0.334096	−	0.942539i	$-0.608431\pi$
$677$	−17.3858	−0.668191	−0.334096	+	0.942539i	$0.608431\pi$
$678$	69.8491	2.68254
$679$	23.1029	0.886608
$680$	−42.2238	−1.61921
$681$	−34.7372	−1.33113
$682$	−32.1775	−1.23214
$683$	−40.8433	−1.56283	−0.781413	−	0.624014i	$-0.785501\pi$
$683$	−40.8433	−1.56283	−0.781413	+	0.624014i	$0.785501\pi$
$684$	84.1660	3.21817
$685$	−8.70358	−0.332547
$686$	42.3214	1.61584
$687$	−10.3620	−0.395336
$688$	25.0259	0.954105
$689$	−23.4884	−0.894835
$690$	−12.1995	−0.464425
$691$	30.4785	1.15946	0.579729	−	0.814810i	$-0.303159\pi$
$691$	30.4785	1.15946	0.579729	+	0.814810i	$0.303159\pi$
$692$	68.7872	2.61490
$693$	−27.8134	−1.05654
$694$	−57.0541	−2.16574
$695$	−2.39439	−0.0908244
$696$	37.3344	1.41516
$697$	−1.95304	−0.0739765
$698$	−81.0197	−3.06664
$699$	−53.1218	−2.00925
$700$	−13.0897	−0.494746
$701$	−31.8917	−1.20453	−0.602267	−	0.798295i	$-0.705736\pi$
$701$	−31.8917	−1.20453	−0.602267	+	0.798295i	$0.705736\pi$
$702$	48.2015	1.81925
$703$	−17.4442	−0.657919
$704$	15.9456	0.600974
$705$	0.275455	0.0103742
$706$	81.9161	3.08295
$707$	−10.6668	−0.401168
$708$	−17.0860	−0.642131
$709$	−14.5892	−0.547909	−0.273954	−	0.961743i	$-0.588332\pi$
$709$	−14.5892	−0.547909	−0.273954	+	0.961743i	$0.588332\pi$
$710$	−3.35543	−0.125927
$711$	0.428963	0.0160874
$712$	−89.2969	−3.34654
$713$	−2.90354	−0.108738
$714$	−40.6172	−1.52006
$715$	47.6998	1.78387
$716$	70.6716	2.64112
$717$	21.1366	0.789362
$718$	79.2828	2.95881
$719$	33.9650	1.26668	0.633341	−	0.773873i	$-0.281683\pi$
$719$	33.9650	1.26668	0.633341	+	0.773873i	$0.281683\pi$
$720$	−42.3684	−1.57898
$721$	−14.0161	−0.521985
$722$	−6.51521	−0.242471
$723$	−7.62011	−0.283395
$724$	−11.0233	−0.409680
$725$	−5.18455	−0.192549
$726$	77.4458	2.87428
$727$	−29.7680	−1.10403	−0.552016	−	0.833833i	$-0.686141\pi$
$727$	−29.7680	−1.10403	−0.552016	+	0.833833i	$0.686141\pi$
$728$	−48.6647	−1.80363
$729$	−42.5250	−1.57500
$730$	13.3200	0.492996
$731$	−17.9711	−0.664684
$732$	52.9091	1.95558
$733$	22.8129	0.842613	0.421307	−	0.906918i	$-0.361572\pi$
$733$	22.8129	0.842613	0.421307	+	0.906918i	$0.361572\pi$
$734$	48.7519	1.79946
$735$	−22.7740	−0.840032
$736$	−3.69729	−0.136284
$737$	0	0
$738$	−4.77894	−0.175915
$739$	49.1768	1.80900	0.904499	−	0.426476i	$-0.140245\pi$
$739$	49.1768	1.80900	0.904499	+	0.426476i	$0.140245\pi$
$740$	27.2663	1.00233
$741$	−74.5219	−2.73763
$742$	13.8032	0.506730
$743$	−42.4170	−1.55613	−0.778065	−	0.628184i	$-0.783799\pi$
$743$	−42.4170	−1.55613	−0.778065	+	0.628184i	$0.783799\pi$
$744$	−42.1724	−1.54611
$745$	13.3261	0.488231
$746$	−43.8353	−1.60493
$747$	−57.8886	−2.11803
$748$	88.2233	3.22576
$749$	−8.76883	−0.320406
$750$	81.3237	2.96952
$751$	38.4534	1.40318	0.701592	−	0.712579i	$-0.252473\pi$
$751$	38.4534	1.40318	0.701592	+	0.712579i	$0.252473\pi$
$752$	0.366285	0.0133570
$753$	−4.54813	−0.165743
$754$	−35.9138	−1.30790
$755$	17.0189	0.619381
$756$	−19.3577	−0.704031
$757$	−17.6288	−0.640729	−0.320365	−	0.947294i	$-0.603805\pi$
$757$	−17.6288	−0.640729	−0.320365	+	0.947294i	$0.603805\pi$
$758$	53.8390	1.95552
$759$	13.6804	0.496567
$760$	45.5257	1.65139
$761$	−21.9266	−0.794838	−0.397419	−	0.917637i	$-0.630094\pi$
$761$	−21.9266	−0.794838	−0.397419	+	0.917637i	$0.630094\pi$
$762$	139.888	5.06760
$763$	−24.2909	−0.879389
$764$	−13.4815	−0.487744
$765$	30.4246	1.10001
$766$	94.6671	3.42046
$767$	8.82114	0.318513
$768$	85.2958	3.07785
$769$	−3.83938	−0.138451	−0.0692257	−	0.997601i	$-0.522053\pi$
$769$	−3.83938	−0.138451	−0.0692257	+	0.997601i	$0.522053\pi$
$770$	−28.0312	−1.01018
$771$	1.11368	0.0401083
$772$	92.8887	3.34314
$773$	0.591616	0.0212790	0.0106395	−	0.999943i	$-0.496613\pi$
$773$	0.591616	0.0212790	0.0106395	+	0.999943i	$0.496613\pi$
$774$	−43.9738	−1.58061
$775$	5.85638	0.210368
$776$	−96.2385	−3.45476
$777$	14.0770	0.505011
$778$	50.4130	1.80739
$779$	2.10577	0.0754469
$780$	116.482	4.17074
$781$	3.76275	0.134642
$782$	11.6491	0.416571
$783$	−7.66713	−0.274001
$784$	−30.2836	−1.08156
$785$	−20.5887	−0.734842
$786$	97.3107	3.47096
$787$	−29.1815	−1.04021	−0.520105	−	0.854103i	$-0.674107\pi$
$787$	−29.1815	−1.04021	−0.520105	+	0.854103i	$0.674107\pi$
$788$	65.9634	2.34985
$789$	55.9488	1.99183
$790$	0.432323	0.0153814
$791$	14.4823	0.514932
$792$	115.861	4.11693
$793$	−27.3159	−0.970016
$794$	29.7685	1.05644
$795$	−17.7320	−0.628888
$796$	−61.6365	−2.18465
$797$	−20.9705	−0.742812	−0.371406	−	0.928471i	$-0.621124\pi$
$797$	−20.9705	−0.742812	−0.371406	+	0.928471i	$0.621124\pi$
$798$	43.7935	1.55027
$799$	−0.263028	−0.00930526
$800$	7.45735	0.263657
$801$	64.3435	2.27346
$802$	−59.6410	−2.10600
$803$	−14.9370	−0.527115
$804$	0	0
$805$	−2.52940	−0.0891497
$806$	40.5677	1.42894
$807$	−50.5388	−1.77905
$808$	44.4343	1.56319
$809$	−53.2630	−1.87263	−0.936314	−	0.351164i	$-0.885786\pi$
$809$	−53.2630	−1.87263	−0.936314	+	0.351164i	$0.885786\pi$
$810$	−16.8405	−0.591715
$811$	−12.8855	−0.452472	−0.226236	−	0.974073i	$-0.572642\pi$
$811$	−12.8855	−0.452472	−0.226236	+	0.974073i	$0.572642\pi$
$812$	14.4230	0.506147
$813$	47.3379	1.66021
$814$	−44.7422	−1.56821
$815$	14.6391	0.512786
$816$	69.3834	2.42891
$817$	19.3764	0.677895
$818$	−62.7379	−2.19358
$819$	35.0657	1.22529
$820$	−3.29144	−0.114942
$821$	39.0630	1.36331	0.681654	−	0.731675i	$-0.261261\pi$
$821$	39.0630	1.36331	0.681654	+	0.731675i	$0.261261\pi$
$822$	34.8765	1.21646
$823$	−41.5271	−1.44754	−0.723772	−	0.690039i	$-0.757593\pi$
$823$	−41.5271	−1.44754	−0.723772	+	0.690039i	$0.757593\pi$
$824$	58.3859	2.03397
$825$	−27.5931	−0.960668
$826$	−5.18383	−0.180368
$827$	−37.9507	−1.31967	−0.659837	−	0.751409i	$-0.729375\pi$
$827$	−37.9507	−1.31967	−0.659837	+	0.751409i	$0.729375\pi$
$828$	19.4796	0.676962
$829$	−8.45897	−0.293792	−0.146896	−	0.989152i	$-0.546928\pi$
$829$	−8.45897	−0.293792	−0.146896	+	0.989152i	$0.546928\pi$
$830$	−58.3420	−2.02508
$831$	−69.3127	−2.40443
$832$	−20.1034	−0.696961
$833$	21.7466	0.753475
$834$	9.59466	0.332236
$835$	−25.3470	−0.877171
$836$	−95.1224	−3.28988
$837$	8.66067	0.299357
$838$	−8.05064	−0.278105
$839$	−22.4104	−0.773693	−0.386847	−	0.922144i	$-0.626436\pi$
$839$	−22.4104	−0.773693	−0.386847	+	0.922144i	$0.626436\pi$
$840$	−36.7382	−1.26759
$841$	−23.2874	−0.803014
$842$	28.2293	0.972846
$843$	53.4684	1.84155
$844$	−42.5410	−1.46432
$845$	−38.2648	−1.31635
$846$	−0.643610	−0.0221278
$847$	16.0574	0.551739
$848$	−23.5790	−0.809705
$849$	−16.3745	−0.561971
$850$	−23.4960	−0.805905
$851$	−4.03732	−0.138398
$852$	9.18860	0.314796
$853$	24.2639	0.830781	0.415390	−	0.909643i	$-0.363645\pi$
$853$	24.2639	0.830781	0.415390	+	0.909643i	$0.363645\pi$
$854$	16.0525	0.549304
$855$	−32.8039	−1.12187
$856$	36.5278	1.24849
$857$	−10.0938	−0.344797	−0.172398	−	0.985027i	$-0.555152\pi$
$857$	−10.0938	−0.344797	−0.172398	+	0.985027i	$0.555152\pi$
$858$	−191.140	−6.52541
$859$	−18.0626	−0.616287	−0.308143	−	0.951340i	$-0.599708\pi$
$859$	−18.0626	−0.616287	−0.308143	+	0.951340i	$0.599708\pi$
$860$	−30.2865	−1.03276
$861$	−1.69930	−0.0579121
$862$	0.752770	0.0256394
$863$	8.08627	0.275260	0.137630	−	0.990484i	$-0.456052\pi$
$863$	8.08627	0.275260	0.137630	+	0.990484i	$0.456052\pi$
$864$	11.0282	0.375189
$865$	−26.8100	−0.911567
$866$	17.9624	0.610387
$867$	−4.22146	−0.143368
$868$	−16.2920	−0.552985
$869$	−0.484804	−0.0164459
$870$	−27.1123	−0.919192
$871$	0	0
$872$	101.187	3.42663
$873$	69.3453	2.34698
$874$	−12.5601	−0.424850
$875$	16.8614	0.570021
$876$	−36.4760	−1.23241
$877$	42.1154	1.42214	0.711068	−	0.703123i	$-0.248212\pi$
$877$	42.1154	1.42214	0.711068	+	0.703123i	$0.248212\pi$
$878$	45.6025	1.53901
$879$	−50.1386	−1.69113
$880$	47.8838	1.61416
$881$	26.0329	0.877070	0.438535	−	0.898714i	$-0.355497\pi$
$881$	26.0329	0.877070	0.438535	+	0.898714i	$0.355497\pi$
$882$	53.2123	1.79175
$883$	−16.1649	−0.543991	−0.271996	−	0.962298i	$-0.587684\pi$
$883$	−16.1649	−0.543991	−0.271996	+	0.962298i	$0.587684\pi$
$884$	−111.227	−3.74098
$885$	6.65930	0.223850
$886$	−57.8465	−1.94339
$887$	2.88430	0.0968452	0.0484226	−	0.998827i	$-0.484581\pi$
$887$	2.88430	0.0968452	0.0484226	+	0.998827i	$0.484581\pi$
$888$	−58.6399	−1.96783
$889$	29.0039	0.972761
$890$	64.8474	2.17369
$891$	18.8848	0.632666
$892$	−107.045	−3.58414
$893$	0.283597	0.00949022
$894$	−53.3996	−1.78595
$895$	−27.5444	−0.920708
$896$	21.4254	0.715774
$897$	−17.2475	−0.575878
$898$	65.7782	2.19505
$899$	−6.45287	−0.215215
$900$	−39.2899	−1.30966
$901$	16.9320	0.564086
$902$	5.40104	0.179835
$903$	−15.6363	−0.520344
$904$	−60.3282	−2.00649
$905$	4.29637	0.142816
$906$	−68.1972	−2.26570
$907$	−6.40818	−0.212780	−0.106390	−	0.994324i	$-0.533929\pi$
$907$	−6.40818	−0.212780	−0.106390	+	0.994324i	$0.533929\pi$
$908$	55.9013	1.85515
$909$	−32.0174	−1.06195
$910$	35.3403	1.17152
$911$	2.86651	0.0949716	0.0474858	−	0.998872i	$-0.484879\pi$
$911$	2.86651	0.0949716	0.0474858	+	0.998872i	$0.484879\pi$
$912$	−74.8093	−2.47718
$913$	65.4243	2.16523
$914$	−37.0643	−1.22598
$915$	−20.6215	−0.681724
$916$	16.6753	0.550966
$917$	20.1761	0.666275
$918$	−34.7468	−1.14682
$919$	12.5942	0.415446	0.207723	−	0.978188i	$-0.433395\pi$
$919$	12.5942	0.415446	0.207723	+	0.978188i	$0.433395\pi$
$920$	10.5366	0.347381
$921$	12.7921	0.421515
$922$	1.42929	0.0470710
$923$	−4.74388	−0.156147
$924$	76.7616	2.52527
$925$	8.14320	0.267747
$926$	65.8059	2.16252
$927$	−42.0704	−1.38177
$928$	−8.21690	−0.269733
$929$	46.6121	1.52929	0.764647	−	0.644450i	$-0.222914\pi$
$929$	46.6121	1.52929	0.764647	+	0.644450i	$0.222914\pi$
$930$	30.6256	1.00425
$931$	−23.4472	−0.768451
$932$	85.4870	2.80022
$933$	−13.2718	−0.434499
$934$	58.1569	1.90295
$935$	−34.3852	−1.12452
$936$	−146.071	−4.77448
$937$	−51.8841	−1.69498	−0.847490	−	0.530811i	$-0.821887\pi$
$937$	−51.8841	−1.69498	−0.847490	+	0.530811i	$0.821887\pi$
$938$	0	0
$939$	89.3519	2.91589
$940$	−0.443280	−0.0144582
$941$	18.7575	0.611476	0.305738	−	0.952116i	$-0.401097\pi$
$941$	18.7575	0.611476	0.305738	+	0.952116i	$0.401097\pi$
$942$	82.5018	2.68805
$943$	0.487364	0.0158707
$944$	8.85516	0.288211
$945$	7.54469	0.245429
$946$	49.6982	1.61583
$947$	−45.6400	−1.48310	−0.741550	−	0.670898i	$-0.765909\pi$
$947$	−45.6400	−1.48310	−0.741550	+	0.670898i	$0.765909\pi$
$948$	−1.18389	−0.0384508
$949$	18.8318	0.611306
$950$	25.3334	0.821924
$951$	−24.2304	−0.785726
$952$	35.0808	1.13698
$953$	−18.7399	−0.607046	−0.303523	−	0.952824i	$-0.598163\pi$
$953$	−18.7399	−0.607046	−0.303523	+	0.952824i	$0.598163\pi$
$954$	41.4313	1.34139
$955$	5.25444	0.170030
$956$	−34.0144	−1.10010
$957$	30.4035	0.982806
$958$	−32.8308	−1.06072
$959$	7.23119	0.233507
$960$	−15.1766	−0.489822
$961$	−23.7109	−0.764869
$962$	56.4087	1.81869
$963$	−26.3204	−0.848161
$964$	12.2628	0.394957
$965$	−36.2036	−1.16543
$966$	10.1357	0.326110
$967$	50.8675	1.63579	0.817895	−	0.575367i	$-0.195141\pi$
$967$	50.8675	1.63579	0.817895	+	0.575367i	$0.195141\pi$
$968$	−66.8894	−2.14991
$969$	53.7204	1.72575
$970$	69.8884	2.24398
$971$	−18.0987	−0.580816	−0.290408	−	0.956903i	$-0.593791\pi$
$971$	−18.0987	−0.580816	−0.290408	+	0.956903i	$0.593791\pi$
$972$	87.6602	2.81170
$973$	1.98933	0.0637750
$974$	26.8289	0.859652
$975$	34.7879	1.11410
$976$	−27.4213	−0.877733
$977$	−25.1943	−0.806038	−0.403019	−	0.915192i	$-0.632039\pi$
$977$	−25.1943	−0.806038	−0.403019	+	0.915192i	$0.632039\pi$
$978$	−58.6610	−1.87577
$979$	−72.7195	−2.32412
$980$	36.6494	1.17072
$981$	−72.9111	−2.32787
$982$	49.1141	1.56729
$983$	3.16103	0.100821	0.0504107	−	0.998729i	$-0.483947\pi$
$983$	3.16103	0.100821	0.0504107	+	0.998729i	$0.483947\pi$
$984$	7.07870	0.225661
$985$	−25.7094	−0.819168
$986$	25.8891	0.824477
$987$	−0.228856	−0.00728458
$988$	119.925	3.81534
$989$	4.48453	0.142600
$990$	−84.1381	−2.67408
$991$	3.73839	0.118754	0.0593770	−	0.998236i	$-0.481089\pi$
$991$	3.73839	0.118754	0.0593770	+	0.998236i	$0.481089\pi$
$992$	9.28169	0.294694
$993$	32.8781	1.04336
$994$	2.78779	0.0884233
$995$	24.0229	0.761579
$996$	159.765	5.06236
$997$	20.9772	0.664353	0.332177	−	0.943217i	$-0.392217\pi$
$997$	20.9772	0.664353	0.332177	+	0.943217i	$0.392217\pi$
$998$	82.9767	2.62658
$999$	12.0425	0.381008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4489.2.a.i.1.1		5
67.40	even	11		67.2.e.b.59.1	yes	10
67.62	even	11		67.2.e.b.25.1	✓	10
67.66	odd	2		4489.2.a.h.1.5		5
201.62	odd	22		603.2.u.a.226.1		10
201.107	odd	22		603.2.u.a.595.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.b.25.1	✓	10	67.62	even	11
67.2.e.b.59.1	yes	10	67.40	even	11
603.2.u.a.226.1		10	201.62	odd	22
603.2.u.a.595.1		10	201.107	odd	22
4489.2.a.h.1.5		5	67.66	odd	2
4489.2.a.i.1.1		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4489 = 67^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4489.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51334 q^{2} -2.68251 q^{3} +4.31686 q^{4} -1.68251 q^{5} +6.74204 q^{6} +1.39788 q^{7} -5.82306 q^{8} +4.19584 q^{9} +O(q^{10})\)	\(q-2.51334 q^{2} -2.68251 q^{3} +4.31686 q^{4} -1.68251 q^{5} +6.74204 q^{6} +1.39788 q^{7} -5.82306 q^{8} +4.19584 q^{9} +4.22871 q^{10} -4.74204 q^{11} -11.5800 q^{12} +5.97852 q^{13} -3.51334 q^{14} +4.51334 q^{15} +6.00158 q^{16} -4.30972 q^{17} -10.5456 q^{18} +4.64675 q^{19} -7.26315 q^{20} -3.74982 q^{21} +11.9184 q^{22} +1.07545 q^{23} +15.6204 q^{24} -2.16917 q^{25} -15.0260 q^{26} -3.20786 q^{27} +6.03445 q^{28} +2.39011 q^{29} -11.3435 q^{30} -2.69983 q^{31} -3.43788 q^{32} +12.7206 q^{33} +10.8318 q^{34} -2.35194 q^{35} +18.1129 q^{36} -3.75406 q^{37} -11.6788 q^{38} -16.0374 q^{39} +9.79734 q^{40} +0.453170 q^{41} +9.42455 q^{42} +4.16989 q^{43} -20.4708 q^{44} -7.05954 q^{45} -2.70298 q^{46} +0.0610313 q^{47} -16.0993 q^{48} -5.04594 q^{49} +5.45186 q^{50} +11.5609 q^{51} +25.8085 q^{52} -3.92879 q^{53} +8.06243 q^{54} +7.97852 q^{55} -8.13992 q^{56} -12.4649 q^{57} -6.00714 q^{58} +1.47547 q^{59} +19.4835 q^{60} -4.56900 q^{61} +6.78558 q^{62} +5.86528 q^{63} -3.36261 q^{64} -10.0589 q^{65} -31.9711 q^{66} -18.6045 q^{68} -2.88491 q^{69} +5.91121 q^{70} -0.793487 q^{71} -24.4326 q^{72} +3.14991 q^{73} +9.43522 q^{74} +5.81881 q^{75} +20.0594 q^{76} -6.62880 q^{77} +40.3075 q^{78} +0.102235 q^{79} -10.0977 q^{80} -3.98242 q^{81} -1.13897 q^{82} -13.7967 q^{83} -16.1874 q^{84} +7.25114 q^{85} -10.4803 q^{86} -6.41148 q^{87} +27.6132 q^{88} +15.3350 q^{89} +17.7430 q^{90} +8.35724 q^{91} +4.64259 q^{92} +7.24231 q^{93} -0.153392 q^{94} -7.81818 q^{95} +9.22214 q^{96} +16.5271 q^{97} +12.6821 q^{98} -19.8969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + q^{5} + 5 q^{6} - 2 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + q^5 + 5 * q^6 - 2 * q^7 - 9 * q^8 - 3 * q^9	\( 5 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + q^{5} + 5 q^{6} - 2 q^{7} - 9 q^{8} - 3 q^{9} + 7 q^{10} + 5 q^{11} - 12 q^{12} + 2 q^{13} - 3 q^{14} + 8 q^{15} + 6 q^{16} - 16 q^{17} - 21 q^{18} + 10 q^{19} - 8 q^{20} - 5 q^{21} + 24 q^{22} + 2 q^{23} + 16 q^{24} - 16 q^{25} - 19 q^{26} - q^{27} + 16 q^{28} - 12 q^{29} - 10 q^{30} + 16 q^{31} - 6 q^{32} + 7 q^{33} - 2 q^{34} - 7 q^{35} + 13 q^{36} + q^{37} - 18 q^{38} - 6 q^{39} + 7 q^{40} - 20 q^{41} + 9 q^{42} - q^{43} - 18 q^{44} - 16 q^{45} - 19 q^{46} + 11 q^{47} - 18 q^{48} - 21 q^{49} - 13 q^{50} + 15 q^{51} + 28 q^{52} - 17 q^{53} + 15 q^{54} + 12 q^{55} - 3 q^{56} - 8 q^{57} - 18 q^{58} + 14 q^{59} + 13 q^{60} + 19 q^{61} + 24 q^{62} + 10 q^{63} - 21 q^{64} - 4 q^{65} - 39 q^{66} - 15 q^{68} - 6 q^{69} + 6 q^{70} - 19 q^{71} - 21 q^{72} - 4 q^{73} + 18 q^{74} + 15 q^{75} - 14 q^{76} - 13 q^{77} + 46 q^{78} - 4 q^{79} - 12 q^{80} + q^{81} - 19 q^{82} - 36 q^{83} - 15 q^{84} - q^{85} - 18 q^{86} - 8 q^{87} + 24 q^{88} + 42 q^{89} + 9 q^{90} + 8 q^{91} - 38 q^{92} + 7 q^{93} + 2 q^{95} + 7 q^{96} + 27 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + q^5 + 5 * q^6 - 2 * q^7 - 9 * q^8 - 3 * q^9 + 7 * q^10 + 5 * q^11 - 12 * q^12 + 2 * q^13 - 3 * q^14 + 8 * q^15 + 6 * q^16 - 16 * q^17 - 21 * q^18 + 10 * q^19 - 8 * q^20 - 5 * q^21 + 24 * q^22 + 2 * q^23 + 16 * q^24 - 16 * q^25 - 19 * q^26 - q^27 + 16 * q^28 - 12 * q^29 - 10 * q^30 + 16 * q^31 - 6 * q^32 + 7 * q^33 - 2 * q^34 - 7 * q^35 + 13 * q^36 + q^37 - 18 * q^38 - 6 * q^39 + 7 * q^40 - 20 * q^41 + 9 * q^42 - q^43 - 18 * q^44 - 16 * q^45 - 19 * q^46 + 11 * q^47 - 18 * q^48 - 21 * q^49 - 13 * q^50 + 15 * q^51 + 28 * q^52 - 17 * q^53 + 15 * q^54 + 12 * q^55 - 3 * q^56 - 8 * q^57 - 18 * q^58 + 14 * q^59 + 13 * q^60 + 19 * q^61 + 24 * q^62 + 10 * q^63 - 21 * q^64 - 4 * q^65 - 39 * q^66 - 15 * q^68 - 6 * q^69 + 6 * q^70 - 19 * q^71 - 21 * q^72 - 4 * q^73 + 18 * q^74 + 15 * q^75 - 14 * q^76 - 13 * q^77 + 46 * q^78 - 4 * q^79 - 12 * q^80 + q^81 - 19 * q^82 - 36 * q^83 - 15 * q^84 - q^85 - 18 * q^86 - 8 * q^87 + 24 * q^88 + 42 * q^89 + 9 * q^90 + 8 * q^91 - 38 * q^92 + 7 * q^93 + 2 * q^95 + 7 * q^96 + 27 * q^97 - 15 * q^98 - 36 * q^99

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