LMFDB - Embedded newform 6045.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - x^{12} - 17 x^{11} + 14 x^{10} + 106 x^{9} - 68 x^{8} - 299 x^{7} + 141 x^{6} + 380 x^{5} + \cdots - 4 $ x^13 - x^12 - 17x^11 + 14x^10 + 106x^9 - 68x^8 - 299x^7 + 141x^6 + 380x^5 - 123x^4 - 186x^3 + 32x^2 + 20*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.62963$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62963 q^{2} -1.00000 q^{3} +4.91498 q^{4} +1.00000 q^{5} +2.62963 q^{6} -2.21047 q^{7} -7.66533 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62963 q^{2} -1.00000 q^{3} +4.91498 q^{4} +1.00000 q^{5} +2.62963 q^{6} -2.21047 q^{7} -7.66533 q^{8} +1.00000 q^{9} -2.62963 q^{10} +2.12563 q^{11} -4.91498 q^{12} -1.00000 q^{13} +5.81273 q^{14} -1.00000 q^{15} +10.3271 q^{16} +7.52696 q^{17} -2.62963 q^{18} +5.44910 q^{19} +4.91498 q^{20} +2.21047 q^{21} -5.58964 q^{22} -8.68068 q^{23} +7.66533 q^{24} +1.00000 q^{25} +2.62963 q^{26} -1.00000 q^{27} -10.8644 q^{28} -2.09570 q^{29} +2.62963 q^{30} +1.00000 q^{31} -11.8257 q^{32} -2.12563 q^{33} -19.7931 q^{34} -2.21047 q^{35} +4.91498 q^{36} -3.89434 q^{37} -14.3292 q^{38} +1.00000 q^{39} -7.66533 q^{40} -3.26488 q^{41} -5.81273 q^{42} -8.55928 q^{43} +10.4474 q^{44} +1.00000 q^{45} +22.8270 q^{46} +7.54854 q^{47} -10.3271 q^{48} -2.11383 q^{49} -2.62963 q^{50} -7.52696 q^{51} -4.91498 q^{52} +7.04672 q^{53} +2.62963 q^{54} +2.12563 q^{55} +16.9440 q^{56} -5.44910 q^{57} +5.51091 q^{58} -7.49193 q^{59} -4.91498 q^{60} -11.1222 q^{61} -2.62963 q^{62} -2.21047 q^{63} +10.4432 q^{64} -1.00000 q^{65} +5.58964 q^{66} -10.7836 q^{67} +36.9948 q^{68} +8.68068 q^{69} +5.81273 q^{70} +15.8127 q^{71} -7.66533 q^{72} -7.00511 q^{73} +10.2407 q^{74} -1.00000 q^{75} +26.7822 q^{76} -4.69865 q^{77} -2.62963 q^{78} +12.9055 q^{79} +10.3271 q^{80} +1.00000 q^{81} +8.58544 q^{82} -0.563266 q^{83} +10.8644 q^{84} +7.52696 q^{85} +22.5078 q^{86} +2.09570 q^{87} -16.2937 q^{88} -15.6908 q^{89} -2.62963 q^{90} +2.21047 q^{91} -42.6654 q^{92} -1.00000 q^{93} -19.8499 q^{94} +5.44910 q^{95} +11.8257 q^{96} +7.36527 q^{97} +5.55859 q^{98} +2.12563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - q^{2} - 13 q^{3} + 9 q^{4} + 13 q^{5} + q^{6} - 11 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - q^2 - 13 * q^3 + 9 * q^4 + 13 * q^5 + q^6 - 11 * q^7 - 6 * q^8 + 13 * q^9	\( 13 q - q^{2} - 13 q^{3} + 9 q^{4} + 13 q^{5} + q^{6} - 11 q^{7} - 6 q^{8} + 13 q^{9} - q^{10} + 4 q^{11} - 9 q^{12} - 13 q^{13} + q^{14} - 13 q^{15} + 9 q^{16} + 3 q^{17} - q^{18} - 2 q^{19} + 9 q^{20} + 11 q^{21} - 17 q^{22} - 9 q^{23} + 6 q^{24} + 13 q^{25} + q^{26} - 13 q^{27} - 30 q^{28} + 7 q^{29} + q^{30} + 13 q^{31} - 13 q^{32} - 4 q^{33} - 13 q^{34} - 11 q^{35} + 9 q^{36} - 7 q^{37} - 26 q^{38} + 13 q^{39} - 6 q^{40} - 13 q^{41} - q^{42} - 24 q^{43} - q^{44} + 13 q^{45} + 22 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} - q^{50} - 3 q^{51} - 9 q^{52} - 18 q^{53} + q^{54} + 4 q^{55} + 19 q^{56} + 2 q^{57} + 20 q^{58} - 26 q^{59} - 9 q^{60} - 12 q^{61} - q^{62} - 11 q^{63} - 2 q^{64} - 13 q^{65} + 17 q^{66} - 30 q^{67} + 23 q^{68} + 9 q^{69} + q^{70} - 3 q^{71} - 6 q^{72} - 5 q^{73} - 36 q^{74} - 13 q^{75} + 16 q^{76} - q^{78} - 9 q^{79} + 9 q^{80} + 13 q^{81} + 7 q^{82} - 35 q^{83} + 30 q^{84} + 3 q^{85} - 14 q^{86} - 7 q^{87} - 29 q^{88} + q^{89} - q^{90} + 11 q^{91} - 63 q^{92} - 13 q^{93} + 24 q^{94} - 2 q^{95} + 13 q^{96} - 33 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q - q^2 - 13 * q^3 + 9 * q^4 + 13 * q^5 + q^6 - 11 * q^7 - 6 * q^8 + 13 * q^9 - q^10 + 4 * q^11 - 9 * q^12 - 13 * q^13 + q^14 - 13 * q^15 + 9 * q^16 + 3 * q^17 - q^18 - 2 * q^19 + 9 * q^20 + 11 * q^21 - 17 * q^22 - 9 * q^23 + 6 * q^24 + 13 * q^25 + q^26 - 13 * q^27 - 30 * q^28 + 7 * q^29 + q^30 + 13 * q^31 - 13 * q^32 - 4 * q^33 - 13 * q^34 - 11 * q^35 + 9 * q^36 - 7 * q^37 - 26 * q^38 + 13 * q^39 - 6 * q^40 - 13 * q^41 - q^42 - 24 * q^43 - q^44 + 13 * q^45 + 22 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 - q^50 - 3 * q^51 - 9 * q^52 - 18 * q^53 + q^54 + 4 * q^55 + 19 * q^56 + 2 * q^57 + 20 * q^58 - 26 * q^59 - 9 * q^60 - 12 * q^61 - q^62 - 11 * q^63 - 2 * q^64 - 13 * q^65 + 17 * q^66 - 30 * q^67 + 23 * q^68 + 9 * q^69 + q^70 - 3 * q^71 - 6 * q^72 - 5 * q^73 - 36 * q^74 - 13 * q^75 + 16 * q^76 - q^78 - 9 * q^79 + 9 * q^80 + 13 * q^81 + 7 * q^82 - 35 * q^83 + 30 * q^84 + 3 * q^85 - 14 * q^86 - 7 * q^87 - 29 * q^88 + q^89 - q^90 + 11 * q^91 - 63 * q^92 - 13 * q^93 + 24 * q^94 - 2 * q^95 + 13 * q^96 - 33 * q^97 + q^98 + 4 * 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 $

$2$	−2.62963	−1.85943	−0.929716	−	0.368277i	$-0.879948\pi$
$2$	−2.62963	−1.85943	−0.929716	+	0.368277i	$0.879948\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.91498	2.45749
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.62963	1.07354
$7$	−2.21047	−0.835479	−0.417739	−	0.908567i	$-0.637177\pi$
$7$	−2.21047	−0.835479	−0.417739	+	0.908567i	$0.637177\pi$
$8$	−7.66533	−2.71010
$9$	1.00000	0.333333
$10$	−2.62963	−0.831563
$11$	2.12563	0.640903	0.320451	−	0.947265i	$-0.396165\pi$
$11$	2.12563	0.640903	0.320451	+	0.947265i	$0.396165\pi$
$12$	−4.91498	−1.41883
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.81273	1.55352
$15$	−1.00000	−0.258199
$16$	10.3271	2.58176
$17$	7.52696	1.82556	0.912778	−	0.408457i	$-0.133933\pi$
$17$	7.52696	1.82556	0.912778	+	0.408457i	$0.133933\pi$
$18$	−2.62963	−0.619811
$19$	5.44910	1.25011	0.625055	−	0.780581i	$-0.285077\pi$
$19$	5.44910	1.25011	0.625055	+	0.780581i	$0.285077\pi$
$20$	4.91498	1.09902
$21$	2.21047	0.482364
$22$	−5.58964	−1.19172
$23$	−8.68068	−1.81005	−0.905024	−	0.425361i	$-0.860147\pi$
$23$	−8.68068	−1.81005	−0.905024	+	0.425361i	$0.860147\pi$
$24$	7.66533	1.56468
$25$	1.00000	0.200000
$26$	2.62963	0.515714
$27$	−1.00000	−0.192450
$28$	−10.8644	−2.05318
$29$	−2.09570	−0.389161	−0.194580	−	0.980887i	$-0.562335\pi$
$29$	−2.09570	−0.389161	−0.194580	+	0.980887i	$0.562335\pi$
$30$	2.62963	0.480103
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−11.8257	−2.09051
$33$	−2.12563	−0.370025
$34$	−19.7931	−3.39450
$35$	−2.21047	−0.373637
$36$	4.91498	0.819163
$37$	−3.89434	−0.640226	−0.320113	−	0.947379i	$-0.603721\pi$
$37$	−3.89434	−0.640226	−0.320113	+	0.947379i	$0.603721\pi$
$38$	−14.3292	−2.32450
$39$	1.00000	0.160128
$40$	−7.66533	−1.21199
$41$	−3.26488	−0.509889	−0.254944	−	0.966956i	$-0.582057\pi$
$41$	−3.26488	−0.509889	−0.254944	+	0.966956i	$0.582057\pi$
$42$	−5.81273	−0.896923
$43$	−8.55928	−1.30528	−0.652639	−	0.757669i	$-0.726338\pi$
$43$	−8.55928	−1.30528	−0.652639	+	0.757669i	$0.726338\pi$
$44$	10.4474	1.57501
$45$	1.00000	0.149071
$46$	22.8270	3.36566
$47$	7.54854	1.10107	0.550534	−	0.834813i	$-0.314424\pi$
$47$	7.54854	1.10107	0.550534	+	0.834813i	$0.314424\pi$
$48$	−10.3271	−1.49058
$49$	−2.11383	−0.301975
$50$	−2.62963	−0.371886
$51$	−7.52696	−1.05398
$52$	−4.91498	−0.681585
$53$	7.04672	0.967942	0.483971	−	0.875084i	$-0.339194\pi$
$53$	7.04672	0.967942	0.483971	+	0.875084i	$0.339194\pi$
$54$	2.62963	0.357848
$55$	2.12563	0.286620
$56$	16.9440	2.26423
$57$	−5.44910	−0.721751
$58$	5.51091	0.723619
$59$	−7.49193	−0.975366	−0.487683	−	0.873021i	$-0.662158\pi$
$59$	−7.49193	−0.975366	−0.487683	+	0.873021i	$0.662158\pi$
$60$	−4.91498	−0.634521
$61$	−11.1222	−1.42406	−0.712028	−	0.702151i	$-0.752223\pi$
$61$	−11.1222	−1.42406	−0.712028	+	0.702151i	$0.752223\pi$
$62$	−2.62963	−0.333964
$63$	−2.21047	−0.278493
$64$	10.4432	1.30540
$65$	−1.00000	−0.124035
$66$	5.58964	0.688037
$67$	−10.7836	−1.31743	−0.658715	−	0.752392i	$-0.728900\pi$
$67$	−10.7836	−1.31743	−0.658715	+	0.752392i	$0.728900\pi$
$68$	36.9948	4.48628
$69$	8.68068	1.04503
$70$	5.81273	0.694754
$71$	15.8127	1.87663	0.938313	−	0.345787i	$-0.112388\pi$
$71$	15.8127	1.87663	0.938313	+	0.345787i	$0.112388\pi$
$72$	−7.66533	−0.903367
$73$	−7.00511	−0.819886	−0.409943	−	0.912111i	$-0.634451\pi$
$73$	−7.00511	−0.819886	−0.409943	+	0.912111i	$0.634451\pi$
$74$	10.2407	1.19046
$75$	−1.00000	−0.115470
$76$	26.7822	3.07213
$77$	−4.69865	−0.535461
$78$	−2.62963	−0.297747
$79$	12.9055	1.45198	0.725990	−	0.687705i	$-0.241382\pi$
$79$	12.9055	1.45198	0.725990	+	0.687705i	$0.241382\pi$
$80$	10.3271	1.15460
$81$	1.00000	0.111111
$82$	8.58544	0.948103
$83$	−0.563266	−0.0618265	−0.0309133	−	0.999522i	$-0.509842\pi$
$83$	−0.563266	−0.0618265	−0.0309133	+	0.999522i	$0.509842\pi$
$84$	10.8644	1.18540
$85$	7.52696	0.816413
$86$	22.5078	2.42708
$87$	2.09570	0.224682
$88$	−16.2937	−1.73691
$89$	−15.6908	−1.66322	−0.831611	−	0.555358i	$-0.812581\pi$
$89$	−15.6908	−1.66322	−0.831611	+	0.555358i	$0.812581\pi$
$90$	−2.62963	−0.277188
$91$	2.21047	0.231720
$92$	−42.6654	−4.44817
$93$	−1.00000	−0.103695
$94$	−19.8499	−2.04736
$95$	5.44910	0.559066
$96$	11.8257	1.20696
$97$	7.36527	0.747830	0.373915	−	0.927463i	$-0.378015\pi$
$97$	7.36527	0.747830	0.373915	+	0.927463i	$0.378015\pi$
$98$	5.55859	0.561503
$99$	2.12563	0.213634
$100$	4.91498	0.491498
$101$	3.24134	0.322526	0.161263	−	0.986911i	$-0.448443\pi$
$101$	3.24134	0.322526	0.161263	+	0.986911i	$0.448443\pi$
$102$	19.7931	1.95981
$103$	−6.83537	−0.673509	−0.336754	−	0.941593i	$-0.609329\pi$
$103$	−6.83537	−0.673509	−0.336754	+	0.941593i	$0.609329\pi$
$104$	7.66533	0.751647
$105$	2.21047	0.215720
$106$	−18.5303	−1.79982
$107$	−7.94516	−0.768088	−0.384044	−	0.923315i	$-0.625469\pi$
$107$	−7.94516	−0.768088	−0.384044	+	0.923315i	$0.625469\pi$
$108$	−4.91498	−0.472944
$109$	9.66219	0.925470	0.462735	−	0.886497i	$-0.346868\pi$
$109$	9.66219	0.925470	0.462735	+	0.886497i	$0.346868\pi$
$110$	−5.58964	−0.532951
$111$	3.89434	0.369635
$112$	−22.8276	−2.15701
$113$	14.3973	1.35439	0.677193	−	0.735806i	$-0.263196\pi$
$113$	14.3973	1.35439	0.677193	+	0.735806i	$0.263196\pi$
$114$	14.3292	1.34205
$115$	−8.68068	−0.809478
$116$	−10.3003	−0.956359
$117$	−1.00000	−0.0924500
$118$	19.7010	1.81363
$119$	−16.6381	−1.52521
$120$	7.66533	0.699745
$121$	−6.48168	−0.589244
$122$	29.2474	2.64794
$123$	3.26488	0.294384
$124$	4.91498	0.441378
$125$	1.00000	0.0894427
$126$	5.81273	0.517839
$127$	−12.5002	−1.10921	−0.554605	−	0.832114i	$-0.687130\pi$
$127$	−12.5002	−1.10921	−0.554605	+	0.832114i	$0.687130\pi$
$128$	−3.81041	−0.336796
$129$	8.55928	0.753603
$130$	2.62963	0.230634
$131$	6.16707	0.538820	0.269410	−	0.963026i	$-0.413171\pi$
$131$	6.16707	0.538820	0.269410	+	0.963026i	$0.413171\pi$
$132$	−10.4474	−0.909333
$133$	−12.0451	−1.04444
$134$	28.3570	2.44967
$135$	−1.00000	−0.0860663
$136$	−57.6966	−4.94744
$137$	11.2995	0.965384	0.482692	−	0.875790i	$-0.339659\pi$
$137$	11.2995	0.965384	0.482692	+	0.875790i	$0.339659\pi$
$138$	−22.8270	−1.94317
$139$	−8.96768	−0.760629	−0.380314	−	0.924857i	$-0.624184\pi$
$139$	−8.96768	−0.760629	−0.380314	+	0.924857i	$0.624184\pi$
$140$	−10.8644	−0.918210
$141$	−7.54854	−0.635701
$142$	−41.5817	−3.48946
$143$	−2.12563	−0.177754
$144$	10.3271	0.860588
$145$	−2.09570	−0.174038
$146$	18.4209	1.52452
$147$	2.11383	0.174346
$148$	−19.1406	−1.57335
$149$	−17.9137	−1.46755	−0.733773	−	0.679395i	$-0.762242\pi$
$149$	−17.9137	−1.46755	−0.733773	+	0.679395i	$0.762242\pi$
$150$	2.62963	0.214709
$151$	−10.2887	−0.837284	−0.418642	−	0.908151i	$-0.637494\pi$
$151$	−10.2887	−0.837284	−0.418642	+	0.908151i	$0.637494\pi$
$152$	−41.7692	−3.38793
$153$	7.52696	0.608518
$154$	12.3557	0.995653
$155$	1.00000	0.0803219
$156$	4.91498	0.393513
$157$	1.47914	0.118048	0.0590241	−	0.998257i	$-0.481201\pi$
$157$	1.47914	0.118048	0.0590241	+	0.998257i	$0.481201\pi$
$158$	−33.9367	−2.69986
$159$	−7.04672	−0.558841
$160$	−11.8257	−0.934905
$161$	19.1884	1.51226
$162$	−2.62963	−0.206604
$163$	−19.6675	−1.54048	−0.770239	−	0.637756i	$-0.779863\pi$
$163$	−19.6675	−1.54048	−0.770239	+	0.637756i	$0.779863\pi$
$164$	−16.0468	−1.25305
$165$	−2.12563	−0.165480
$166$	1.48118	0.114962
$167$	12.5070	0.967821	0.483910	−	0.875118i	$-0.339216\pi$
$167$	12.5070	0.967821	0.483910	+	0.875118i	$0.339216\pi$
$168$	−16.9440	−1.30726
$169$	1.00000	0.0769231
$170$	−19.7931	−1.51807
$171$	5.44910	0.416703
$172$	−42.0687	−3.20771
$173$	−9.65682	−0.734195	−0.367097	−	0.930183i	$-0.619648\pi$
$173$	−9.65682	−0.734195	−0.367097	+	0.930183i	$0.619648\pi$
$174$	−5.51091	−0.417781
$175$	−2.21047	−0.167096
$176$	21.9515	1.65466
$177$	7.49193	0.563128
$178$	41.2611	3.09265
$179$	−4.12481	−0.308303	−0.154151	−	0.988047i	$-0.549264\pi$
$179$	−4.12481	−0.308303	−0.154151	+	0.988047i	$0.549264\pi$
$180$	4.91498	0.366341
$181$	0.683501	0.0508042	0.0254021	−	0.999677i	$-0.491913\pi$
$181$	0.683501	0.0508042	0.0254021	+	0.999677i	$0.491913\pi$
$182$	−5.81273	−0.430868
$183$	11.1222	0.822180
$184$	66.5403	4.90541
$185$	−3.89434	−0.286318
$186$	2.62963	0.192814
$187$	15.9996	1.17000
$188$	37.1009	2.70586
$189$	2.21047	0.160788
$190$	−14.3292	−1.03955
$191$	−17.0441	−1.23327	−0.616634	−	0.787250i	$-0.711504\pi$
$191$	−17.0441	−1.23327	−0.616634	+	0.787250i	$0.711504\pi$
$192$	−10.4432	−0.753674
$193$	−13.4744	−0.969912	−0.484956	−	0.874539i	$-0.661164\pi$
$193$	−13.4744	−0.969912	−0.484956	+	0.874539i	$0.661164\pi$
$194$	−19.3680	−1.39054
$195$	1.00000	0.0716115
$196$	−10.3894	−0.742101
$197$	14.5364	1.03568	0.517838	−	0.855479i	$-0.326737\pi$
$197$	14.5364	1.03568	0.517838	+	0.855479i	$0.326737\pi$
$198$	−5.58964	−0.397238
$199$	−0.516908	−0.0366427	−0.0183213	−	0.999832i	$-0.505832\pi$
$199$	−0.516908	−0.0366427	−0.0183213	+	0.999832i	$0.505832\pi$
$200$	−7.66533	−0.542020
$201$	10.7836	0.760619
$202$	−8.52355	−0.599715
$203$	4.63247	0.325136
$204$	−36.9948	−2.59016
$205$	−3.26488	−0.228029
$206$	17.9745	1.25234
$207$	−8.68068	−0.603349
$208$	−10.3271	−0.716052
$209$	11.5828	0.801199
$210$	−5.81273	−0.401116
$211$	−9.90357	−0.681790	−0.340895	−	0.940101i	$-0.610730\pi$
$211$	−9.90357	−0.681790	−0.340895	+	0.940101i	$0.610730\pi$
$212$	34.6345	2.37871
$213$	−15.8127	−1.08347
$214$	20.8929	1.42821
$215$	−8.55928	−0.583738
$216$	7.66533	0.521559
$217$	−2.21047	−0.150056
$218$	−25.4080	−1.72085
$219$	7.00511	0.473361
$220$	10.4474	0.704367
$221$	−7.52696	−0.506318
$222$	−10.2407	−0.687311
$223$	27.2453	1.82448	0.912241	−	0.409653i	$-0.134350\pi$
$223$	27.2453	1.82448	0.912241	+	0.409653i	$0.134350\pi$
$224$	26.1404	1.74658
$225$	1.00000	0.0666667
$226$	−37.8597	−2.51839
$227$	−0.765701	−0.0508214	−0.0254107	−	0.999677i	$-0.508089\pi$
$227$	−0.765701	−0.0508214	−0.0254107	+	0.999677i	$0.508089\pi$
$228$	−26.7822	−1.77370
$229$	20.4308	1.35010	0.675052	−	0.737770i	$-0.264121\pi$
$229$	20.4308	1.35010	0.675052	+	0.737770i	$0.264121\pi$
$230$	22.8270	1.50517
$231$	4.69865	0.309148
$232$	16.0642	1.05467
$233$	−16.7225	−1.09553	−0.547764	−	0.836633i	$-0.684521\pi$
$233$	−16.7225	−1.09553	−0.547764	+	0.836633i	$0.684521\pi$
$234$	2.62963	0.171905
$235$	7.54854	0.492412
$236$	−36.8227	−2.39695
$237$	−12.9055	−0.838301
$238$	43.7521	2.83603
$239$	24.4307	1.58029	0.790146	−	0.612918i	$-0.210005\pi$
$239$	24.4307	1.58029	0.790146	+	0.612918i	$0.210005\pi$
$240$	−10.3271	−0.666608
$241$	28.3634	1.82705	0.913525	−	0.406783i	$-0.133350\pi$
$241$	28.3634	1.82705	0.913525	+	0.406783i	$0.133350\pi$
$242$	17.0445	1.09566
$243$	−1.00000	−0.0641500
$244$	−54.6656	−3.49960
$245$	−2.11383	−0.135047
$246$	−8.58544	−0.547388
$247$	−5.44910	−0.346718
$248$	−7.66533	−0.486749
$249$	0.563266	0.0356956
$250$	−2.62963	−0.166313
$251$	−0.966398	−0.0609985	−0.0304992	−	0.999535i	$-0.509710\pi$
$251$	−0.966398	−0.0609985	−0.0304992	+	0.999535i	$0.509710\pi$
$252$	−10.8644	−0.684393
$253$	−18.4520	−1.16006
$254$	32.8708	2.06250
$255$	−7.52696	−0.471356
$256$	−10.8665	−0.679153
$257$	−3.47407	−0.216707	−0.108353	−	0.994112i	$-0.534558\pi$
$257$	−3.47407	−0.216707	−0.108353	+	0.994112i	$0.534558\pi$
$258$	−22.5078	−1.40127
$259$	8.60832	0.534895
$260$	−4.91498	−0.304814
$261$	−2.09570	−0.129720
$262$	−16.2171	−1.00190
$263$	7.45729	0.459836	0.229918	−	0.973210i	$-0.426154\pi$
$263$	7.45729	0.459836	0.229918	+	0.973210i	$0.426154\pi$
$264$	16.2937	1.00281
$265$	7.04672	0.432877
$266$	31.6741	1.94207
$267$	15.6908	0.960262
$268$	−53.0013	−3.23757
$269$	19.0989	1.16448	0.582241	−	0.813016i	$-0.302176\pi$
$269$	19.0989	1.16448	0.582241	+	0.813016i	$0.302176\pi$
$270$	2.62963	0.160034
$271$	−32.3722	−1.96647	−0.983235	−	0.182343i	$-0.941632\pi$
$271$	−32.3722	−1.96647	−0.983235	+	0.182343i	$0.941632\pi$
$272$	77.7313	4.71315
$273$	−2.21047	−0.133784
$274$	−29.7136	−1.79507
$275$	2.12563	0.128181
$276$	42.6654	2.56815
$277$	4.55430	0.273641	0.136821	−	0.990596i	$-0.456312\pi$
$277$	4.55430	0.273641	0.136821	+	0.990596i	$0.456312\pi$
$278$	23.5817	1.41434
$279$	1.00000	0.0598684
$280$	16.9440	1.01260
$281$	23.3322	1.39188	0.695940	−	0.718100i	$-0.254988\pi$
$281$	23.3322	1.39188	0.695940	+	0.718100i	$0.254988\pi$
$282$	19.8499	1.18204
$283$	−26.3041	−1.56361	−0.781807	−	0.623521i	$-0.785702\pi$
$283$	−26.3041	−1.56361	−0.781807	+	0.623521i	$0.785702\pi$
$284$	77.7192	4.61179
$285$	−5.44910	−0.322777
$286$	5.58964	0.330522
$287$	7.21692	0.426001
$288$	−11.8257	−0.696837
$289$	39.6551	2.33265
$290$	5.51091	0.323612
$291$	−7.36527	−0.431760
$292$	−34.4299	−2.01486
$293$	26.1433	1.52731	0.763654	−	0.645625i	$-0.223403\pi$
$293$	26.1433	1.52731	0.763654	+	0.645625i	$0.223403\pi$
$294$	−5.55859	−0.324184
$295$	−7.49193	−0.436197
$296$	29.8514	1.73508
$297$	−2.12563	−0.123342
$298$	47.1064	2.72880
$299$	8.68068	0.502017
$300$	−4.91498	−0.283766
$301$	18.9200	1.09053
$302$	27.0556	1.55687
$303$	−3.24134	−0.186210
$304$	56.2732	3.22749
$305$	−11.1222	−0.636858
$306$	−19.7931	−1.13150
$307$	18.9694	1.08264	0.541320	−	0.840816i	$-0.317925\pi$
$307$	18.9694	1.08264	0.541320	+	0.840816i	$0.317925\pi$
$308$	−23.0937	−1.31589
$309$	6.83537	0.388850
$310$	−2.62963	−0.149353
$311$	−22.2676	−1.26268	−0.631339	−	0.775507i	$-0.717494\pi$
$311$	−22.2676	−1.26268	−0.631339	+	0.775507i	$0.717494\pi$
$312$	−7.66533	−0.433964
$313$	14.0694	0.795249	0.397625	−	0.917548i	$-0.369835\pi$
$313$	14.0694	0.795249	0.397625	+	0.917548i	$0.369835\pi$
$314$	−3.88960	−0.219503
$315$	−2.21047	−0.124546
$316$	63.4302	3.56823
$317$	−14.6848	−0.824780	−0.412390	−	0.911008i	$-0.635306\pi$
$317$	−14.6848	−0.824780	−0.412390	+	0.911008i	$0.635306\pi$
$318$	18.5303	1.03913
$319$	−4.45468	−0.249414
$320$	10.4432	0.583794
$321$	7.94516	0.443456
$322$	−50.4584	−2.81194
$323$	41.0152	2.28215
$324$	4.91498	0.273054
$325$	−1.00000	−0.0554700
$326$	51.7183	2.86441
$327$	−9.66219	−0.534321
$328$	25.0264	1.38185
$329$	−16.6858	−0.919918
$330$	5.58964	0.307700
$331$	−29.3126	−1.61117	−0.805583	−	0.592483i	$-0.798148\pi$
$331$	−29.3126	−1.61117	−0.805583	+	0.592483i	$0.798148\pi$
$332$	−2.76844	−0.151938
$333$	−3.89434	−0.213409
$334$	−32.8888	−1.79960
$335$	−10.7836	−0.589173
$336$	22.8276	1.24535
$337$	−18.0182	−0.981515	−0.490758	−	0.871296i	$-0.663280\pi$
$337$	−18.0182	−0.981515	−0.490758	+	0.871296i	$0.663280\pi$
$338$	−2.62963	−0.143033
$339$	−14.3973	−0.781955
$340$	36.9948	2.00633
$341$	2.12563	0.115110
$342$	−14.3292	−0.774832
$343$	20.1458	1.08777
$344$	65.6097	3.53744
$345$	8.68068	0.467352
$346$	25.3939	1.36519
$347$	15.7090	0.843302	0.421651	−	0.906758i	$-0.361451\pi$
$347$	15.7090	0.843302	0.421651	+	0.906758i	$0.361451\pi$
$348$	10.3003	0.552154
$349$	12.1950	0.652785	0.326393	−	0.945234i	$-0.394167\pi$
$349$	12.1950	0.652785	0.326393	+	0.945234i	$0.394167\pi$
$350$	5.81273	0.310703
$351$	1.00000	0.0533761
$352$	−25.1372	−1.33981
$353$	23.9784	1.27624	0.638120	−	0.769937i	$-0.279712\pi$
$353$	23.9784	1.27624	0.638120	+	0.769937i	$0.279712\pi$
$354$	−19.7010	−1.04710
$355$	15.8127	0.839253
$356$	−77.1200	−4.08735
$357$	16.6381	0.880582
$358$	10.8467	0.573268
$359$	−29.4055	−1.55196	−0.775980	−	0.630757i	$-0.782744\pi$
$359$	−29.4055	−1.55196	−0.775980	+	0.630757i	$0.782744\pi$
$360$	−7.66533	−0.403998
$361$	10.6927	0.562775
$362$	−1.79736	−0.0944670
$363$	6.48168	0.340200
$364$	10.8644	0.569450
$365$	−7.00511	−0.366664
$366$	−29.2474	−1.52879
$367$	−21.9579	−1.14619	−0.573097	−	0.819487i	$-0.694258\pi$
$367$	−21.9579	−1.14619	−0.573097	+	0.819487i	$0.694258\pi$
$368$	−89.6459	−4.67311
$369$	−3.26488	−0.169963
$370$	10.2407	0.532389
$371$	−15.5766	−0.808694
$372$	−4.91498	−0.254830
$373$	−19.9717	−1.03410	−0.517048	−	0.855956i	$-0.672969\pi$
$373$	−19.9717	−1.03410	−0.517048	+	0.855956i	$0.672969\pi$
$374$	−42.0730	−2.17554
$375$	−1.00000	−0.0516398
$376$	−57.8620	−2.98400
$377$	2.09570	0.107934
$378$	−5.81273	−0.298974
$379$	−24.3068	−1.24856	−0.624278	−	0.781202i	$-0.714607\pi$
$379$	−24.3068	−1.24856	−0.624278	+	0.781202i	$0.714607\pi$
$380$	26.7822	1.37390
$381$	12.5002	0.640402
$382$	44.8198	2.29318
$383$	−0.327918	−0.0167558	−0.00837792	−	0.999965i	$-0.502667\pi$
$383$	−0.327918	−0.0167558	−0.00837792	+	0.999965i	$0.502667\pi$
$384$	3.81041	0.194449
$385$	−4.69865	−0.239465
$386$	35.4329	1.80349
$387$	−8.55928	−0.435093
$388$	36.2001	1.83778
$389$	1.24670	0.0632102	0.0316051	−	0.999500i	$-0.489938\pi$
$389$	1.24670	0.0632102	0.0316051	+	0.999500i	$0.489938\pi$
$390$	−2.62963	−0.133157
$391$	−65.3391	−3.30434
$392$	16.2032	0.818384
$393$	−6.16707	−0.311088
$394$	−38.2254	−1.92577
$395$	12.9055	0.649346
$396$	10.4474	0.525004
$397$	−10.2081	−0.512330	−0.256165	−	0.966633i	$-0.582459\pi$
$397$	−10.2081	−0.512330	−0.256165	+	0.966633i	$0.582459\pi$
$398$	1.35928	0.0681345
$399$	12.0451	0.603008
$400$	10.3271	0.516353
$401$	10.2533	0.512027	0.256013	−	0.966673i	$-0.417591\pi$
$401$	10.2533	0.512027	0.256013	+	0.966673i	$0.417591\pi$
$402$	−28.3570	−1.41432
$403$	−1.00000	−0.0498135
$404$	15.9311	0.792604
$405$	1.00000	0.0496904
$406$	−12.1817	−0.604568
$407$	−8.27795	−0.410323
$408$	57.6966	2.85641
$409$	−20.7277	−1.02492	−0.512460	−	0.858711i	$-0.671266\pi$
$409$	−20.7277	−1.02492	−0.512460	+	0.858711i	$0.671266\pi$
$410$	8.58544	0.424005
$411$	−11.2995	−0.557365
$412$	−33.5957	−1.65514
$413$	16.5607	0.814898
$414$	22.8270	1.12189
$415$	−0.563266	−0.0276497
$416$	11.8257	0.579804
$417$	8.96768	0.439149
$418$	−30.4585	−1.48978
$419$	−39.9475	−1.95156	−0.975782	−	0.218744i	$-0.929804\pi$
$419$	−39.9475	−1.95156	−0.975782	+	0.218744i	$0.929804\pi$
$420$	10.8644	0.530129
$421$	−34.5619	−1.68444	−0.842222	−	0.539130i	$-0.818753\pi$
$421$	−34.5619	−1.68444	−0.842222	+	0.539130i	$0.818753\pi$
$422$	26.0428	1.26774
$423$	7.54854	0.367022
$424$	−54.0154	−2.62322
$425$	7.52696	0.365111
$426$	41.5817	2.01464
$427$	24.5854	1.18977
$428$	−39.0503	−1.88757
$429$	2.12563	0.102627
$430$	22.5078	1.08542
$431$	11.3935	0.548807	0.274403	−	0.961615i	$-0.411520\pi$
$431$	11.3935	0.548807	0.274403	+	0.961615i	$0.411520\pi$
$432$	−10.3271	−0.496861
$433$	21.6055	1.03829	0.519147	−	0.854685i	$-0.326250\pi$
$433$	21.6055	1.03829	0.519147	+	0.854685i	$0.326250\pi$
$434$	5.81273	0.279020
$435$	2.09570	0.100481
$436$	47.4895	2.27433
$437$	−47.3019	−2.26276
$438$	−18.4209	−0.880183
$439$	18.2905	0.872960	0.436480	−	0.899714i	$-0.356225\pi$
$439$	18.2905	0.872960	0.436480	+	0.899714i	$0.356225\pi$
$440$	−16.2937	−0.776771
$441$	−2.11383	−0.100658
$442$	19.7931	0.941464
$443$	−9.60399	−0.456300	−0.228150	−	0.973626i	$-0.573268\pi$
$443$	−9.60399	−0.456300	−0.228150	+	0.973626i	$0.573268\pi$
$444$	19.1406	0.908373
$445$	−15.6908	−0.743816
$446$	−71.6453	−3.39250
$447$	17.9137	0.847288
$448$	−23.0844	−1.09064
$449$	36.4378	1.71960	0.859802	−	0.510628i	$-0.170587\pi$
$449$	36.4378	1.71960	0.859802	+	0.510628i	$0.170587\pi$
$450$	−2.62963	−0.123962
$451$	−6.93994	−0.326789
$452$	70.7625	3.32839
$453$	10.2887	0.483406
$454$	2.01351	0.0944989
$455$	2.21047	0.103628
$456$	41.7692	1.95602
$457$	4.97904	0.232910	0.116455	−	0.993196i	$-0.462847\pi$
$457$	4.97904	0.232910	0.116455	+	0.993196i	$0.462847\pi$
$458$	−53.7255	−2.51043
$459$	−7.52696	−0.351328
$460$	−42.6654	−1.98928
$461$	1.77894	0.0828536	0.0414268	−	0.999142i	$-0.486810\pi$
$461$	1.77894	0.0828536	0.0414268	+	0.999142i	$0.486810\pi$
$462$	−12.3557	−0.574840
$463$	−8.94968	−0.415927	−0.207963	−	0.978137i	$-0.566683\pi$
$463$	−8.94968	−0.415927	−0.207963	+	0.978137i	$0.566683\pi$
$464$	−21.6424	−1.00472
$465$	−1.00000	−0.0463739
$466$	43.9741	2.03706
$467$	−30.2871	−1.40152	−0.700760	−	0.713397i	$-0.747156\pi$
$467$	−30.2871	−1.40152	−0.700760	+	0.713397i	$0.747156\pi$
$468$	−4.91498	−0.227195
$469$	23.8369	1.10069
$470$	−19.8499	−0.915607
$471$	−1.47914	−0.0681552
$472$	57.4281	2.64334
$473$	−18.1939	−0.836556
$474$	33.9367	1.55876
$475$	5.44910	0.250022
$476$	−81.7759	−3.74819
$477$	7.04672	0.322647
$478$	−64.2439	−2.93845
$479$	3.92023	0.179120	0.0895600	−	0.995981i	$-0.471454\pi$
$479$	3.92023	0.179120	0.0895600	+	0.995981i	$0.471454\pi$
$480$	11.8257	0.539768
$481$	3.89434	0.177567
$482$	−74.5855	−3.39727
$483$	−19.1884	−0.873102
$484$	−31.8573	−1.44806
$485$	7.36527	0.334440
$486$	2.62963	0.119283
$487$	−37.7511	−1.71067	−0.855333	−	0.518079i	$-0.826647\pi$
$487$	−37.7511	−1.71067	−0.855333	+	0.518079i	$0.826647\pi$
$488$	85.2556	3.85934
$489$	19.6675	0.889395
$490$	5.55859	0.251112
$491$	−23.0456	−1.04003	−0.520016	−	0.854156i	$-0.674074\pi$
$491$	−23.0456	−1.04003	−0.520016	+	0.854156i	$0.674074\pi$
$492$	16.0468	0.723446
$493$	−15.7742	−0.710435
$494$	14.3292	0.644699
$495$	2.12563	0.0955401
$496$	10.3271	0.463698
$497$	−34.9536	−1.56788
$498$	−1.48118	−0.0663735
$499$	−3.84490	−0.172121	−0.0860607	−	0.996290i	$-0.527428\pi$
$499$	−3.84490	−0.172121	−0.0860607	+	0.996290i	$0.527428\pi$
$500$	4.91498	0.219804
$501$	−12.5070	−0.558772
$502$	2.54127	0.113423
$503$	−10.5791	−0.471699	−0.235850	−	0.971790i	$-0.575787\pi$
$503$	−10.5791	−0.471699	−0.235850	+	0.971790i	$0.575787\pi$
$504$	16.9440	0.754744
$505$	3.24134	0.144238
$506$	48.5219	2.15706
$507$	−1.00000	−0.0444116
$508$	−61.4380	−2.72587
$509$	−2.12690	−0.0942733	−0.0471366	−	0.998888i	$-0.515010\pi$
$509$	−2.12690	−0.0942733	−0.0471366	+	0.998888i	$0.515010\pi$
$510$	19.7931	0.876455
$511$	15.4846	0.684997
$512$	36.1956	1.59964
$513$	−5.44910	−0.240584
$514$	9.13554	0.402951
$515$	−6.83537	−0.301202
$516$	42.0687	1.85197
$517$	16.0454	0.705677
$518$	−22.6367	−0.994602
$519$	9.65682	0.423887
$520$	7.66533	0.336147
$521$	−37.2076	−1.63010	−0.815048	−	0.579393i	$-0.803290\pi$
$521$	−37.2076	−1.63010	−0.815048	+	0.579393i	$0.803290\pi$
$522$	5.51091	0.241206
$523$	13.3878	0.585406	0.292703	−	0.956203i	$-0.405445\pi$
$523$	13.3878	0.585406	0.292703	+	0.956203i	$0.405445\pi$
$524$	30.3110	1.32414
$525$	2.21047	0.0964728
$526$	−19.6099	−0.855034
$527$	7.52696	0.327879
$528$	−21.9515	−0.955318
$529$	52.3543	2.27627
$530$	−18.5303	−0.804905
$531$	−7.49193	−0.325122
$532$	−59.2013	−2.56670
$533$	3.26488	0.141418
$534$	−41.2611	−1.78554
$535$	−7.94516	−0.343499
$536$	82.6601	3.57037
$537$	4.12481	0.177999
$538$	−50.2232	−2.16528
$539$	−4.49322	−0.193537
$540$	−4.91498	−0.211507
$541$	31.9856	1.37517	0.687584	−	0.726105i	$-0.258671\pi$
$541$	31.9856	1.37517	0.687584	+	0.726105i	$0.258671\pi$
$542$	85.1270	3.65652
$543$	−0.683501	−0.0293318
$544$	−89.0117	−3.81635
$545$	9.66219	0.413883
$546$	5.81273	0.248762
$547$	21.4921	0.918934	0.459467	−	0.888195i	$-0.348040\pi$
$547$	21.4921	0.918934	0.459467	+	0.888195i	$0.348040\pi$
$548$	55.5369	2.37242
$549$	−11.1222	−0.474686
$550$	−5.58964	−0.238343
$551$	−11.4197	−0.486494
$552$	−66.5403	−2.83214
$553$	−28.5272	−1.21310
$554$	−11.9761	−0.508818
$555$	3.89434	0.165306
$556$	−44.0760	−1.86924
$557$	−1.72057	−0.0729028	−0.0364514	−	0.999335i	$-0.511605\pi$
$557$	−1.72057	−0.0729028	−0.0364514	+	0.999335i	$0.511605\pi$
$558$	−2.62963	−0.111321
$559$	8.55928	0.362019
$560$	−22.8276	−0.964643
$561$	−15.9996	−0.675502
$562$	−61.3551	−2.58811
$563$	25.4226	1.07143	0.535717	−	0.844397i	$-0.320041\pi$
$563$	25.4226	1.07143	0.535717	+	0.844397i	$0.320041\pi$
$564$	−37.1009	−1.56223
$565$	14.3973	0.605700
$566$	69.1701	2.90743
$567$	−2.21047	−0.0928310
$568$	−121.210	−5.08585
$569$	−33.9777	−1.42442	−0.712210	−	0.701966i	$-0.752306\pi$
$569$	−33.9777	−1.42442	−0.712210	+	0.701966i	$0.752306\pi$
$570$	14.3292	0.600182
$571$	4.08245	0.170845	0.0854226	−	0.996345i	$-0.472776\pi$
$571$	4.08245	0.170845	0.0854226	+	0.996345i	$0.472776\pi$
$572$	−10.4474	−0.436830
$573$	17.0441	0.712028
$574$	−18.9779	−0.792120
$575$	−8.68068	−0.362010
$576$	10.4432	0.435134
$577$	3.08283	0.128340	0.0641699	−	0.997939i	$-0.479560\pi$
$577$	3.08283	0.128340	0.0641699	+	0.997939i	$0.479560\pi$
$578$	−104.278	−4.33741
$579$	13.4744	0.559979
$580$	−10.3003	−0.427697
$581$	1.24508	0.0516547
$582$	19.3680	0.802828
$583$	14.9787	0.620356
$584$	53.6964	2.22197
$585$	−1.00000	−0.0413449
$586$	−68.7474	−2.83993
$587$	−46.8623	−1.93421	−0.967107	−	0.254371i	$-0.918132\pi$
$587$	−46.8623	−1.93421	−0.967107	+	0.254371i	$0.918132\pi$
$588$	10.3894	0.428452
$589$	5.44910	0.224526
$590$	19.7010	0.811079
$591$	−14.5364	−0.597948
$592$	−40.2171	−1.65291
$593$	−19.9736	−0.820219	−0.410109	−	0.912036i	$-0.634509\pi$
$593$	−19.9736	−0.820219	−0.410109	+	0.912036i	$0.634509\pi$
$594$	5.58964	0.229346
$595$	−16.6381	−0.682096
$596$	−88.0454	−3.60648
$597$	0.516908	0.0211556
$598$	−22.8270	−0.933466
$599$	−33.8247	−1.38204	−0.691020	−	0.722835i	$-0.742838\pi$
$599$	−33.8247	−1.38204	−0.691020	+	0.722835i	$0.742838\pi$
$600$	7.66533	0.312936
$601$	3.10549	0.126675	0.0633377	−	0.997992i	$-0.479825\pi$
$601$	3.10549	0.126675	0.0633377	+	0.997992i	$0.479825\pi$
$602$	−49.7527	−2.02777
$603$	−10.7836	−0.439144
$604$	−50.5688	−2.05762
$605$	−6.48168	−0.263518
$606$	8.52355	0.346246
$607$	−17.8817	−0.725797	−0.362899	−	0.931829i	$-0.618213\pi$
$607$	−17.8817	−0.725797	−0.362899	+	0.931829i	$0.618213\pi$
$608$	−64.4396	−2.61337
$609$	−4.63247	−0.187717
$610$	29.2474	1.18419
$611$	−7.54854	−0.305381
$612$	36.9948	1.49543
$613$	15.2291	0.615099	0.307549	−	0.951532i	$-0.400491\pi$
$613$	15.2291	0.615099	0.307549	+	0.951532i	$0.400491\pi$
$614$	−49.8826	−2.01310
$615$	3.26488	0.131653
$616$	36.0167	1.45115
$617$	−44.0366	−1.77285	−0.886423	−	0.462877i	$-0.846817\pi$
$617$	−44.0366	−1.77285	−0.886423	+	0.462877i	$0.846817\pi$
$618$	−17.9745	−0.723041
$619$	14.3141	0.575331	0.287666	−	0.957731i	$-0.407121\pi$
$619$	14.3141	0.575331	0.287666	+	0.957731i	$0.407121\pi$
$620$	4.91498	0.197390
$621$	8.68068	0.348344
$622$	58.5555	2.34786
$623$	34.6840	1.38959
$624$	10.3271	0.413413
$625$	1.00000	0.0400000
$626$	−36.9974	−1.47871
$627$	−11.5828	−0.462572
$628$	7.26994	0.290102
$629$	−29.3126	−1.16877
$630$	5.81273	0.231585
$631$	−0.487438	−0.0194046	−0.00970230	−	0.999953i	$-0.503088\pi$
$631$	−0.487438	−0.0194046	−0.00970230	+	0.999953i	$0.503088\pi$
$632$	−98.9248	−3.93502
$633$	9.90357	0.393632
$634$	38.6156	1.53362
$635$	−12.5002	−0.496053
$636$	−34.6345	−1.37335
$637$	2.11383	0.0837529
$638$	11.7142	0.463769
$639$	15.8127	0.625542
$640$	−3.81041	−0.150620
$641$	−9.58514	−0.378590	−0.189295	−	0.981920i	$-0.560620\pi$
$641$	−9.58514	−0.378590	−0.189295	+	0.981920i	$0.560620\pi$
$642$	−20.8929	−0.824576
$643$	5.06111	0.199591	0.0997953	−	0.995008i	$-0.468181\pi$
$643$	5.06111	0.199591	0.0997953	+	0.995008i	$0.468181\pi$
$644$	94.3105	3.71635
$645$	8.55928	0.337021
$646$	−107.855	−4.24349
$647$	30.1519	1.18539	0.592697	−	0.805426i	$-0.298063\pi$
$647$	30.1519	1.18539	0.592697	+	0.805426i	$0.298063\pi$
$648$	−7.66533	−0.301122
$649$	−15.9251	−0.625115
$650$	2.62963	0.103143
$651$	2.21047	0.0866351
$652$	−96.6653	−3.78571
$653$	−9.20905	−0.360378	−0.180189	−	0.983632i	$-0.557671\pi$
$653$	−9.20905	−0.360378	−0.180189	+	0.983632i	$0.557671\pi$
$654$	25.4080	0.993533
$655$	6.16707	0.240967
$656$	−33.7166	−1.31641
$657$	−7.00511	−0.273295
$658$	43.8776	1.71053
$659$	50.3142	1.95996	0.979981	−	0.199090i	$-0.0637986\pi$
$659$	50.3142	1.95996	0.979981	+	0.199090i	$0.0637986\pi$
$660$	−10.4474	−0.406666
$661$	−0.909741	−0.0353848	−0.0176924	−	0.999843i	$-0.505632\pi$
$661$	−0.909741	−0.0353848	−0.0176924	+	0.999843i	$0.505632\pi$
$662$	77.0814	2.99585
$663$	7.52696	0.292323
$664$	4.31762	0.167556
$665$	−12.0451	−0.467088
$666$	10.2407	0.396819
$667$	18.1921	0.704400
$668$	61.4716	2.37841
$669$	−27.2453	−1.05337
$670$	28.3570	1.09553
$671$	−23.6418	−0.912682
$672$	−26.1404	−1.00839
$673$	−1.62885	−0.0627874	−0.0313937	−	0.999507i	$-0.509995\pi$
$673$	−1.62885	−0.0627874	−0.0313937	+	0.999507i	$0.509995\pi$
$674$	47.3814	1.82506
$675$	−1.00000	−0.0384900
$676$	4.91498	0.189038
$677$	−1.43270	−0.0550632	−0.0275316	−	0.999621i	$-0.508765\pi$
$677$	−1.43270	−0.0550632	−0.0275316	+	0.999621i	$0.508765\pi$
$678$	37.8597	1.45399
$679$	−16.2807	−0.624796
$680$	−57.6966	−2.21256
$681$	0.765701	0.0293417
$682$	−5.58964	−0.214038
$683$	−26.4651	−1.01266	−0.506330	−	0.862340i	$-0.668998\pi$
$683$	−26.4651	−1.01266	−0.506330	+	0.862340i	$0.668998\pi$
$684$	26.7822	1.02404
$685$	11.2995	0.431733
$686$	−52.9762	−2.02264
$687$	−20.4308	−0.779483
$688$	−88.3921	−3.36992
$689$	−7.04672	−0.268459
$690$	−22.8270	−0.869010
$691$	29.1037	1.10716	0.553579	−	0.832797i	$-0.313262\pi$
$691$	29.1037	1.10716	0.553579	+	0.832797i	$0.313262\pi$
$692$	−47.4631	−1.80427
$693$	−4.69865	−0.178487
$694$	−41.3089	−1.56806
$695$	−8.96768	−0.340164
$696$	−16.0642	−0.608912
$697$	−24.5746	−0.930830
$698$	−32.0685	−1.21381
$699$	16.7225	0.632504
$700$	−10.8644	−0.410636
$701$	−27.0084	−1.02009	−0.510046	−	0.860147i	$-0.670372\pi$
$701$	−27.0084	−1.02009	−0.510046	+	0.860147i	$0.670372\pi$
$702$	−2.62963	−0.0992492
$703$	−21.2207	−0.800353
$704$	22.1985	0.836636
$705$	−7.54854	−0.284294
$706$	−63.0543	−2.37308
$707$	−7.16489	−0.269463
$708$	36.8227	1.38388
$709$	−21.1483	−0.794243	−0.397121	−	0.917766i	$-0.629991\pi$
$709$	−21.1483	−0.794243	−0.397121	+	0.917766i	$0.629991\pi$
$710$	−41.5817	−1.56053
$711$	12.9055	0.483994
$712$	120.275	4.50750
$713$	−8.68068	−0.325094
$714$	−43.7521	−1.63738
$715$	−2.12563	−0.0794942
$716$	−20.2733	−0.757651
$717$	−24.4307	−0.912382
$718$	77.3256	2.88577
$719$	15.4550	0.576373	0.288186	−	0.957574i	$-0.406948\pi$
$719$	15.4550	0.576373	0.288186	+	0.957574i	$0.406948\pi$
$720$	10.3271	0.384867
$721$	15.1094	0.562702
$722$	−28.1180	−1.04644
$723$	−28.3634	−1.05485
$724$	3.35939	0.124851
$725$	−2.09570	−0.0778322
$726$	−17.0445	−0.632579
$727$	−3.28540	−0.121849	−0.0609243	−	0.998142i	$-0.519405\pi$
$727$	−3.28540	−0.121849	−0.0609243	+	0.998142i	$0.519405\pi$
$728$	−16.9440	−0.627985
$729$	1.00000	0.0370370
$730$	18.4209	0.681787
$731$	−64.4253	−2.38286
$732$	54.6656	2.02050
$733$	−12.8114	−0.473199	−0.236600	−	0.971607i	$-0.576033\pi$
$733$	−12.8114	−0.473199	−0.236600	+	0.971607i	$0.576033\pi$
$734$	57.7413	2.13127
$735$	2.11383	0.0779697
$736$	102.655	3.78393
$737$	−22.9221	−0.844345
$738$	8.58544	0.316034
$739$	3.97303	0.146150	0.0730752	−	0.997326i	$-0.476719\pi$
$739$	3.97303	0.146150	0.0730752	+	0.997326i	$0.476719\pi$
$740$	−19.1406	−0.703623
$741$	5.44910	0.200178
$742$	40.9607	1.50371
$743$	−31.7559	−1.16501	−0.582506	−	0.812826i	$-0.697928\pi$
$743$	−31.7559	−1.16501	−0.582506	+	0.812826i	$0.697928\pi$
$744$	7.66533	0.281025
$745$	−17.9137	−0.656307
$746$	52.5183	1.92283
$747$	−0.563266	−0.0206088
$748$	78.6375	2.87527
$749$	17.5625	0.641721
$750$	2.62963	0.0960207
$751$	−33.2708	−1.21407	−0.607035	−	0.794675i	$-0.707641\pi$
$751$	−33.2708	−1.21407	−0.607035	+	0.794675i	$0.707641\pi$
$752$	77.9541	2.84269
$753$	0.966398	0.0352175
$754$	−5.51091	−0.200696
$755$	−10.2887	−0.374445
$756$	10.8644	0.395135
$757$	0.0133349	0.000484665 0	0.000242332	−	1.00000i	$-0.499923\pi$
$757$	0.0133349	0.000484665 0	0.000242332		1.00000i	$0.499923\pi$
$758$	63.9180	2.32161
$759$	18.4520	0.669764
$760$	−41.7692	−1.51513
$761$	−33.4879	−1.21394	−0.606968	−	0.794727i	$-0.707614\pi$
$761$	−33.4879	−1.21394	−0.606968	+	0.794727i	$0.707614\pi$
$762$	−32.8708	−1.19078
$763$	−21.3580	−0.773211
$764$	−83.7714	−3.03074
$765$	7.52696	0.272138
$766$	0.862305	0.0311564
$767$	7.49193	0.270518
$768$	10.8665	0.392109
$769$	−7.64138	−0.275555	−0.137778	−	0.990463i	$-0.543996\pi$
$769$	−7.64138	−0.275555	−0.137778	+	0.990463i	$0.543996\pi$
$770$	12.3557	0.445269
$771$	3.47407	0.125116
$772$	−66.2266	−2.38355
$773$	−39.7766	−1.43067	−0.715333	−	0.698784i	$-0.753725\pi$
$773$	−39.7766	−1.43067	−0.715333	+	0.698784i	$0.753725\pi$
$774$	22.5078	0.809025
$775$	1.00000	0.0359211
$776$	−56.4572	−2.02670
$777$	−8.60832	−0.308822
$778$	−3.27837	−0.117535
$779$	−17.7907	−0.637417
$780$	4.91498	0.175984
$781$	33.6121	1.20273
$782$	171.818	6.14420
$783$	2.09570	0.0748941
$784$	−21.8296	−0.779629
$785$	1.47914	0.0527928
$786$	16.2171	0.578447
$787$	−17.5516	−0.625648	−0.312824	−	0.949811i	$-0.601275\pi$
$787$	−17.5516	−0.625648	−0.312824	+	0.949811i	$0.601275\pi$
$788$	71.4461	2.54516
$789$	−7.45729	−0.265486
$790$	−33.9367	−1.20741
$791$	−31.8248	−1.13156
$792$	−16.2937	−0.578971
$793$	11.1222	0.394962
$794$	26.8436	0.952643
$795$	−7.04672	−0.249921
$796$	−2.54059	−0.0900489
$797$	15.8754	0.562336	0.281168	−	0.959659i	$-0.409278\pi$
$797$	15.8754	0.562336	0.281168	+	0.959659i	$0.409278\pi$
$798$	−31.6741	−1.12125
$799$	56.8175	2.01006
$800$	−11.8257	−0.418102
$801$	−15.6908	−0.554407
$802$	−26.9625	−0.952079
$803$	−14.8903	−0.525467
$804$	53.0013	1.86921
$805$	19.1884	0.676302
$806$	2.62963	0.0926249
$807$	−19.0989	−0.672314
$808$	−24.8460	−0.874078
$809$	−25.4449	−0.894594	−0.447297	−	0.894386i	$-0.647613\pi$
$809$	−25.4449	−0.894594	−0.447297	+	0.894386i	$0.647613\pi$
$810$	−2.62963	−0.0923959
$811$	41.5286	1.45827	0.729134	−	0.684371i	$-0.239923\pi$
$811$	41.5286	1.45827	0.729134	+	0.684371i	$0.239923\pi$
$812$	22.7685	0.799017
$813$	32.3722	1.13534
$814$	21.7680	0.762967
$815$	−19.6675	−0.688923
$816$	−77.7313	−2.72114
$817$	−46.6404	−1.63174
$818$	54.5063	1.90577
$819$	2.21047	0.0772400
$820$	−16.0468	−0.560379
$821$	−4.02340	−0.140417	−0.0702087	−	0.997532i	$-0.522367\pi$
$821$	−4.02340	−0.140417	−0.0702087	+	0.997532i	$0.522367\pi$
$822$	29.7136	1.03638
$823$	39.7202	1.38456	0.692280	−	0.721629i	$-0.256606\pi$
$823$	39.7202	1.38456	0.692280	+	0.721629i	$0.256606\pi$
$824$	52.3953	1.82528
$825$	−2.12563	−0.0740051
$826$	−43.5485	−1.51525
$827$	22.4231	0.779729	0.389864	−	0.920872i	$-0.372522\pi$
$827$	22.4231	0.779729	0.389864	+	0.920872i	$0.372522\pi$
$828$	−42.6654	−1.48272
$829$	−24.3492	−0.845682	−0.422841	−	0.906204i	$-0.638967\pi$
$829$	−24.3492	−0.845682	−0.422841	+	0.906204i	$0.638967\pi$
$830$	1.48118	0.0514127
$831$	−4.55430	−0.157987
$832$	−10.4432	−0.362054
$833$	−15.9107	−0.551273
$834$	−23.5817	−0.816568
$835$	12.5070	0.432823
$836$	56.9292	1.96894
$837$	−1.00000	−0.0345651
$838$	105.047	3.62880
$839$	21.2808	0.734694	0.367347	−	0.930084i	$-0.380266\pi$
$839$	21.2808	0.734694	0.367347	+	0.930084i	$0.380266\pi$
$840$	−16.9440	−0.584622
$841$	−24.6081	−0.848554
$842$	90.8852	3.13211
$843$	−23.3322	−0.803603
$844$	−48.6758	−1.67549
$845$	1.00000	0.0344010
$846$	−19.8499	−0.682453
$847$	14.3276	0.492301
$848$	72.7719	2.49900
$849$	26.3041	0.902753
$850$	−19.7931	−0.678899
$851$	33.8056	1.15884
$852$	−77.7192	−2.66262
$853$	23.2982	0.797716	0.398858	−	0.917013i	$-0.369407\pi$
$853$	23.2982	0.797716	0.398858	+	0.917013i	$0.369407\pi$
$854$	−64.6505	−2.21230
$855$	5.44910	0.186355
$856$	60.9022	2.08160
$857$	−1.95513	−0.0667858	−0.0333929	−	0.999442i	$-0.510631\pi$
$857$	−1.95513	−0.0667858	−0.0333929	+	0.999442i	$0.510631\pi$
$858$	−5.58964	−0.190827
$859$	−33.1842	−1.13223	−0.566115	−	0.824327i	$-0.691554\pi$
$859$	−33.1842	−1.13223	−0.566115	+	0.824327i	$0.691554\pi$
$860$	−42.0687	−1.43453
$861$	−7.21692	−0.245952
$862$	−29.9608	−1.02047
$863$	−50.3464	−1.71381	−0.856906	−	0.515472i	$-0.827617\pi$
$863$	−50.3464	−1.71381	−0.856906	+	0.515472i	$0.827617\pi$
$864$	11.8257	0.402319
$865$	−9.65682	−0.328342
$866$	−56.8146	−1.93064
$867$	−39.6551	−1.34676
$868$	−10.8644	−0.368762
$869$	27.4323	0.930578
$870$	−5.51091	−0.186837
$871$	10.7836	0.365390
$872$	−74.0639	−2.50812
$873$	7.36527	0.249277
$874$	124.387	4.20745
$875$	−2.21047	−0.0747275
$876$	34.4299	1.16328
$877$	28.3203	0.956309	0.478155	−	0.878276i	$-0.341306\pi$
$877$	28.3203	0.956309	0.478155	+	0.878276i	$0.341306\pi$
$878$	−48.0974	−1.62321
$879$	−26.1433	−0.881792
$880$	21.9515	0.739986
$881$	−31.4413	−1.05929	−0.529643	−	0.848221i	$-0.677674\pi$
$881$	−31.4413	−1.05929	−0.529643	+	0.848221i	$0.677674\pi$
$882$	5.55859	0.187168
$883$	−45.0836	−1.51718	−0.758591	−	0.651567i	$-0.774112\pi$
$883$	−45.0836	−1.51718	−0.758591	+	0.651567i	$0.774112\pi$
$884$	−36.9948	−1.24427
$885$	7.49193	0.251838
$886$	25.2550	0.848458
$887$	47.1025	1.58155	0.790774	−	0.612109i	$-0.209678\pi$
$887$	47.1025	1.58155	0.790774	+	0.612109i	$0.209678\pi$
$888$	−29.8514	−1.00175
$889$	27.6312	0.926721
$890$	41.2611	1.38307
$891$	2.12563	0.0712114
$892$	133.910	4.48365
$893$	41.1328	1.37646
$894$	−47.1064	−1.57547
$895$	−4.12481	−0.137877
$896$	8.42279	0.281386
$897$	−8.68068	−0.289840
$898$	−95.8180	−3.19749
$899$	−2.09570	−0.0698954
$900$	4.91498	0.163833
$901$	53.0404	1.76703
$902$	18.2495	0.607642
$903$	−18.9200	−0.629619
$904$	−110.360	−3.67052
$905$	0.683501	0.0227203
$906$	−27.0556	−0.898861
$907$	−19.9078	−0.661027	−0.330514	−	0.943801i	$-0.607222\pi$
$907$	−19.9078	−0.661027	−0.330514	+	0.943801i	$0.607222\pi$
$908$	−3.76341	−0.124893
$909$	3.24134	0.107509
$910$	−5.81273	−0.192690
$911$	−23.3483	−0.773563	−0.386782	−	0.922171i	$-0.626413\pi$
$911$	−23.3483	−0.773563	−0.386782	+	0.922171i	$0.626413\pi$
$912$	−56.2732	−1.86339
$913$	−1.19730	−0.0396248
$914$	−13.0931	−0.433080
$915$	11.1222	0.367690
$916$	100.417	3.31787
$917$	−13.6321	−0.450172
$918$	19.7931	0.653271
$919$	−42.3324	−1.39642	−0.698208	−	0.715895i	$-0.746019\pi$
$919$	−42.3324	−1.39642	−0.698208	+	0.715895i	$0.746019\pi$
$920$	66.5403	2.19377
$921$	−18.9694	−0.625063
$922$	−4.67797	−0.154061
$923$	−15.8127	−0.520482
$924$	23.0937	0.759729
$925$	−3.89434	−0.128045
$926$	23.5344	0.773388
$927$	−6.83537	−0.224503
$928$	24.7831	0.813546
$929$	−3.14836	−0.103294	−0.0516472	−	0.998665i	$-0.516447\pi$
$929$	−3.14836	−0.103294	−0.0516472	+	0.998665i	$0.516447\pi$
$930$	2.62963	0.0862291
$931$	−11.5185	−0.377502
$932$	−82.1908	−2.69225
$933$	22.2676	0.729007
$934$	79.6441	2.60603
$935$	15.9996	0.523241
$936$	7.66533	0.250549
$937$	21.2301	0.693558	0.346779	−	0.937947i	$-0.387275\pi$
$937$	21.2301	0.693558	0.346779	+	0.937947i	$0.387275\pi$
$938$	−62.6823	−2.04665
$939$	−14.0694	−0.459137
$940$	37.1009	1.21010
$941$	−45.5655	−1.48539	−0.742696	−	0.669629i	$-0.766453\pi$
$941$	−45.5655	−1.48539	−0.742696	+	0.669629i	$0.766453\pi$
$942$	3.88960	0.126730
$943$	28.3414	0.922923
$944$	−77.3695	−2.51816
$945$	2.21047	0.0719066
$946$	47.8433	1.55552
$947$	7.70866	0.250498	0.125249	−	0.992125i	$-0.460027\pi$
$947$	7.70866	0.250498	0.125249	+	0.992125i	$0.460027\pi$
$948$	−63.4302	−2.06012
$949$	7.00511	0.227395
$950$	−14.3292	−0.464899
$951$	14.6848	0.476187
$952$	127.537	4.13348
$953$	−36.9055	−1.19548	−0.597742	−	0.801688i	$-0.703935\pi$
$953$	−36.9055	−1.19548	−0.597742	+	0.801688i	$0.703935\pi$
$954$	−18.5303	−0.599941
$955$	−17.0441	−0.551535
$956$	120.076	3.88355
$957$	4.45468	0.143999
$958$	−10.3088	−0.333061
$959$	−24.9773	−0.806558
$960$	−10.4432	−0.337053
$961$	1.00000	0.0322581
$962$	−10.2407	−0.330173
$963$	−7.94516	−0.256029
$964$	139.406	4.48995
$965$	−13.4744	−0.433758
$966$	50.4584	1.62347
$967$	25.0837	0.806637	0.403318	−	0.915060i	$-0.367857\pi$
$967$	25.0837	0.806637	0.403318	+	0.915060i	$0.367857\pi$
$968$	49.6842	1.59691
$969$	−41.0152	−1.31760
$970$	−19.3680	−0.621868
$971$	19.8809	0.638010	0.319005	−	0.947753i	$-0.396651\pi$
$971$	19.8809	0.638010	0.319005	+	0.947753i	$0.396651\pi$
$972$	−4.91498	−0.157648
$973$	19.8228	0.635489
$974$	99.2716	3.18087
$975$	1.00000	0.0320256
$976$	−114.860	−3.67658
$977$	59.7279	1.91086	0.955432	−	0.295211i	$-0.0953899\pi$
$977$	59.7279	1.91086	0.955432	+	0.295211i	$0.0953899\pi$
$978$	−51.7183	−1.65377
$979$	−33.3529	−1.06596
$980$	−10.3894	−0.331878
$981$	9.66219	0.308490
$982$	60.6014	1.93387
$983$	20.4687	0.652851	0.326426	−	0.945223i	$-0.394156\pi$
$983$	20.4687	0.652851	0.326426	+	0.945223i	$0.394156\pi$
$984$	−25.0264	−0.797812
$985$	14.5364	0.463168
$986$	41.4804	1.32101
$987$	16.6858	0.531115
$988$	−26.7822	−0.852056
$989$	74.3004	2.36262
$990$	−5.58964	−0.177650
$991$	−9.52790	−0.302664	−0.151332	−	0.988483i	$-0.548356\pi$
$991$	−9.52790	−0.302664	−0.151332	+	0.988483i	$0.548356\pi$
$992$	−11.8257	−0.375467
$993$	29.3126	0.930207
$994$	91.9151	2.91537
$995$	−0.516908	−0.0163871
$996$	2.76844	0.0877214
$997$	−17.2700	−0.546947	−0.273473	−	0.961880i	$-0.588173\pi$
$997$	−17.2700	−0.546947	−0.273473	+	0.961880i	$0.588173\pi$
$998$	10.1107	0.320048
$999$	3.89434	0.123212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.ba.1.1	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.ba.1.1	✓	13	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62963 q^{2} -1.00000 q^{3} +4.91498 q^{4} +1.00000 q^{5} +2.62963 q^{6} -2.21047 q^{7} -7.66533 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62963 q^{2} -1.00000 q^{3} +4.91498 q^{4} +1.00000 q^{5} +2.62963 q^{6} -2.21047 q^{7} -7.66533 q^{8} +1.00000 q^{9} -2.62963 q^{10} +2.12563 q^{11} -4.91498 q^{12} -1.00000 q^{13} +5.81273 q^{14} -1.00000 q^{15} +10.3271 q^{16} +7.52696 q^{17} -2.62963 q^{18} +5.44910 q^{19} +4.91498 q^{20} +2.21047 q^{21} -5.58964 q^{22} -8.68068 q^{23} +7.66533 q^{24} +1.00000 q^{25} +2.62963 q^{26} -1.00000 q^{27} -10.8644 q^{28} -2.09570 q^{29} +2.62963 q^{30} +1.00000 q^{31} -11.8257 q^{32} -2.12563 q^{33} -19.7931 q^{34} -2.21047 q^{35} +4.91498 q^{36} -3.89434 q^{37} -14.3292 q^{38} +1.00000 q^{39} -7.66533 q^{40} -3.26488 q^{41} -5.81273 q^{42} -8.55928 q^{43} +10.4474 q^{44} +1.00000 q^{45} +22.8270 q^{46} +7.54854 q^{47} -10.3271 q^{48} -2.11383 q^{49} -2.62963 q^{50} -7.52696 q^{51} -4.91498 q^{52} +7.04672 q^{53} +2.62963 q^{54} +2.12563 q^{55} +16.9440 q^{56} -5.44910 q^{57} +5.51091 q^{58} -7.49193 q^{59} -4.91498 q^{60} -11.1222 q^{61} -2.62963 q^{62} -2.21047 q^{63} +10.4432 q^{64} -1.00000 q^{65} +5.58964 q^{66} -10.7836 q^{67} +36.9948 q^{68} +8.68068 q^{69} +5.81273 q^{70} +15.8127 q^{71} -7.66533 q^{72} -7.00511 q^{73} +10.2407 q^{74} -1.00000 q^{75} +26.7822 q^{76} -4.69865 q^{77} -2.62963 q^{78} +12.9055 q^{79} +10.3271 q^{80} +1.00000 q^{81} +8.58544 q^{82} -0.563266 q^{83} +10.8644 q^{84} +7.52696 q^{85} +22.5078 q^{86} +2.09570 q^{87} -16.2937 q^{88} -15.6908 q^{89} -2.62963 q^{90} +2.21047 q^{91} -42.6654 q^{92} -1.00000 q^{93} -19.8499 q^{94} +5.44910 q^{95} +11.8257 q^{96} +7.36527 q^{97} +5.55859 q^{98} +2.12563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - q^{2} - 13 q^{3} + 9 q^{4} + 13 q^{5} + q^{6} - 11 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - q^2 - 13 * q^3 + 9 * q^4 + 13 * q^5 + q^6 - 11 * q^7 - 6 * q^8 + 13 * q^9	\( 13 q - q^{2} - 13 q^{3} + 9 q^{4} + 13 q^{5} + q^{6} - 11 q^{7} - 6 q^{8} + 13 q^{9} - q^{10} + 4 q^{11} - 9 q^{12} - 13 q^{13} + q^{14} - 13 q^{15} + 9 q^{16} + 3 q^{17} - q^{18} - 2 q^{19} + 9 q^{20} + 11 q^{21} - 17 q^{22} - 9 q^{23} + 6 q^{24} + 13 q^{25} + q^{26} - 13 q^{27} - 30 q^{28} + 7 q^{29} + q^{30} + 13 q^{31} - 13 q^{32} - 4 q^{33} - 13 q^{34} - 11 q^{35} + 9 q^{36} - 7 q^{37} - 26 q^{38} + 13 q^{39} - 6 q^{40} - 13 q^{41} - q^{42} - 24 q^{43} - q^{44} + 13 q^{45} + 22 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} - q^{50} - 3 q^{51} - 9 q^{52} - 18 q^{53} + q^{54} + 4 q^{55} + 19 q^{56} + 2 q^{57} + 20 q^{58} - 26 q^{59} - 9 q^{60} - 12 q^{61} - q^{62} - 11 q^{63} - 2 q^{64} - 13 q^{65} + 17 q^{66} - 30 q^{67} + 23 q^{68} + 9 q^{69} + q^{70} - 3 q^{71} - 6 q^{72} - 5 q^{73} - 36 q^{74} - 13 q^{75} + 16 q^{76} - q^{78} - 9 q^{79} + 9 q^{80} + 13 q^{81} + 7 q^{82} - 35 q^{83} + 30 q^{84} + 3 q^{85} - 14 q^{86} - 7 q^{87} - 29 q^{88} + q^{89} - q^{90} + 11 q^{91} - 63 q^{92} - 13 q^{93} + 24 q^{94} - 2 q^{95} + 13 q^{96} - 33 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q - q^2 - 13 * q^3 + 9 * q^4 + 13 * q^5 + q^6 - 11 * q^7 - 6 * q^8 + 13 * q^9 - q^10 + 4 * q^11 - 9 * q^12 - 13 * q^13 + q^14 - 13 * q^15 + 9 * q^16 + 3 * q^17 - q^18 - 2 * q^19 + 9 * q^20 + 11 * q^21 - 17 * q^22 - 9 * q^23 + 6 * q^24 + 13 * q^25 + q^26 - 13 * q^27 - 30 * q^28 + 7 * q^29 + q^30 + 13 * q^31 - 13 * q^32 - 4 * q^33 - 13 * q^34 - 11 * q^35 + 9 * q^36 - 7 * q^37 - 26 * q^38 + 13 * q^39 - 6 * q^40 - 13 * q^41 - q^42 - 24 * q^43 - q^44 + 13 * q^45 + 22 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 - q^50 - 3 * q^51 - 9 * q^52 - 18 * q^53 + q^54 + 4 * q^55 + 19 * q^56 + 2 * q^57 + 20 * q^58 - 26 * q^59 - 9 * q^60 - 12 * q^61 - q^62 - 11 * q^63 - 2 * q^64 - 13 * q^65 + 17 * q^66 - 30 * q^67 + 23 * q^68 + 9 * q^69 + q^70 - 3 * q^71 - 6 * q^72 - 5 * q^73 - 36 * q^74 - 13 * q^75 + 16 * q^76 - q^78 - 9 * q^79 + 9 * q^80 + 13 * q^81 + 7 * q^82 - 35 * q^83 + 30 * q^84 + 3 * q^85 - 14 * q^86 - 7 * q^87 - 29 * q^88 + q^89 - q^90 + 11 * q^91 - 63 * q^92 - 13 * q^93 + 24 * q^94 - 2 * q^95 + 13 * q^96 - 33 * q^97 + q^98 + 4 * q^99

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