LMFDB - Embedded newform 1441.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29335 q^{2} +2.59523 q^{3} +3.25943 q^{4} +0.281199 q^{5} -5.95177 q^{6} -4.71795 q^{7} -2.88831 q^{8} +3.73524 q^{9} +O(q^{10})$	\(q-2.29335 q^{2} +2.59523 q^{3} +3.25943 q^{4} +0.281199 q^{5} -5.95177 q^{6} -4.71795 q^{7} -2.88831 q^{8} +3.73524 q^{9} -0.644885 q^{10} -1.00000 q^{11} +8.45899 q^{12} +1.91363 q^{13} +10.8199 q^{14} +0.729776 q^{15} +0.105032 q^{16} -3.77647 q^{17} -8.56619 q^{18} +7.73570 q^{19} +0.916548 q^{20} -12.2442 q^{21} +2.29335 q^{22} +9.13416 q^{23} -7.49584 q^{24} -4.92093 q^{25} -4.38862 q^{26} +1.90812 q^{27} -15.3778 q^{28} -2.69092 q^{29} -1.67363 q^{30} -2.71223 q^{31} +5.53575 q^{32} -2.59523 q^{33} +8.66075 q^{34} -1.32668 q^{35} +12.1748 q^{36} +11.2479 q^{37} -17.7406 q^{38} +4.96632 q^{39} -0.812189 q^{40} +7.75370 q^{41} +28.0802 q^{42} +0.287443 q^{43} -3.25943 q^{44} +1.05034 q^{45} -20.9478 q^{46} +7.01709 q^{47} +0.272583 q^{48} +15.2591 q^{49} +11.2854 q^{50} -9.80082 q^{51} +6.23735 q^{52} +6.07298 q^{53} -4.37597 q^{54} -0.281199 q^{55} +13.6269 q^{56} +20.0760 q^{57} +6.17120 q^{58} +1.04516 q^{59} +2.37866 q^{60} +1.72594 q^{61} +6.22007 q^{62} -17.6227 q^{63} -12.9054 q^{64} +0.538110 q^{65} +5.95177 q^{66} +3.00535 q^{67} -12.3091 q^{68} +23.7053 q^{69} +3.04254 q^{70} +9.41019 q^{71} -10.7885 q^{72} +1.80168 q^{73} -25.7954 q^{74} -12.7710 q^{75} +25.2140 q^{76} +4.71795 q^{77} -11.3895 q^{78} +3.95095 q^{79} +0.0295349 q^{80} -6.25371 q^{81} -17.7819 q^{82} -7.21069 q^{83} -39.9091 q^{84} -1.06194 q^{85} -0.659205 q^{86} -6.98356 q^{87} +2.88831 q^{88} +13.1047 q^{89} -2.40880 q^{90} -9.02842 q^{91} +29.7722 q^{92} -7.03886 q^{93} -16.0926 q^{94} +2.17527 q^{95} +14.3666 q^{96} -17.8476 q^{97} -34.9943 q^{98} -3.73524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * 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 $

$2$	−2.29335	−1.62164	−0.810820	−	0.585296i	$-0.800978\pi$
$2$	−2.29335	−1.62164	−0.810820	+	0.585296i	$0.800978\pi$
$3$	2.59523	1.49836	0.749180	−	0.662367i	$-0.230448\pi$
$3$	2.59523	1.49836	0.749180	+	0.662367i	$0.230448\pi$
$4$	3.25943	1.62972
$5$	0.281199	0.125756	0.0628779	−	0.998021i	$-0.479972\pi$
$5$	0.281199	0.125756	0.0628779	+	0.998021i	$0.479972\pi$
$6$	−5.95177	−2.42980
$7$	−4.71795	−1.78322	−0.891609	−	0.452806i	$-0.850423\pi$
$7$	−4.71795	−1.78322	−0.891609	+	0.452806i	$0.850423\pi$
$8$	−2.88831	−1.02117
$9$	3.73524	1.24508
$10$	−0.644885	−0.203931
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	8.45899	2.44190
$13$	1.91363	0.530746	0.265373	−	0.964146i	$-0.414505\pi$
$13$	1.91363	0.530746	0.265373	+	0.964146i	$0.414505\pi$
$14$	10.8199	2.89174
$15$	0.729776	0.188427
$16$	0.105032	0.0262580
$17$	−3.77647	−0.915929	−0.457964	−	0.888971i	$-0.651421\pi$
$17$	−3.77647	−0.915929	−0.457964	+	0.888971i	$0.651421\pi$
$18$	−8.56619	−2.01907
$19$	7.73570	1.77469	0.887346	−	0.461104i	$-0.152547\pi$
$19$	7.73570	1.77469	0.887346	+	0.461104i	$0.152547\pi$
$20$	0.916548	0.204946
$21$	−12.2442	−2.67190
$22$	2.29335	0.488943
$23$	9.13416	1.90460	0.952302	−	0.305157i	$-0.0987090\pi$
$23$	9.13416	1.90460	0.952302	+	0.305157i	$0.0987090\pi$
$24$	−7.49584	−1.53008
$25$	−4.92093	−0.984185
$26$	−4.38862	−0.860679
$27$	1.90812	0.367217
$28$	−15.3778	−2.90614
$29$	−2.69092	−0.499691	−0.249845	−	0.968286i	$-0.580380\pi$
$29$	−2.69092	−0.499691	−0.249845	+	0.968286i	$0.580380\pi$
$30$	−1.67363	−0.305561
$31$	−2.71223	−0.487130	−0.243565	−	0.969885i	$-0.578317\pi$
$31$	−2.71223	−0.487130	−0.243565	+	0.969885i	$0.578317\pi$
$32$	5.53575	0.978591
$33$	−2.59523	−0.451772
$34$	8.66075	1.48531
$35$	−1.32668	−0.224250
$36$	12.1748	2.02913
$37$	11.2479	1.84915	0.924575	−	0.380999i	$-0.124420\pi$
$37$	11.2479	1.84915	0.924575	+	0.380999i	$0.124420\pi$
$38$	−17.7406	−2.87791
$39$	4.96632	0.795248
$40$	−0.812189	−0.128418
$41$	7.75370	1.21092	0.605462	−	0.795874i	$-0.292988\pi$
$41$	7.75370	1.21092	0.605462	+	0.795874i	$0.292988\pi$
$42$	28.0802	4.33286
$43$	0.287443	0.0438346	0.0219173	−	0.999760i	$-0.493023\pi$
$43$	0.287443	0.0438346	0.0219173	+	0.999760i	$0.493023\pi$
$44$	−3.25943	−0.491378
$45$	1.05034	0.156576
$46$	−20.9478	−3.08858
$47$	7.01709	1.02355	0.511774	−	0.859120i	$-0.328989\pi$
$47$	7.01709	1.02355	0.511774	+	0.859120i	$0.328989\pi$
$48$	0.272583	0.0393440
$49$	15.2591	2.17987
$50$	11.2854	1.59599
$51$	−9.80082	−1.37239
$52$	6.23735	0.864965
$53$	6.07298	0.834187	0.417094	−	0.908864i	$-0.363049\pi$
$53$	6.07298	0.834187	0.417094	+	0.908864i	$0.363049\pi$
$54$	−4.37597	−0.595494
$55$	−0.281199	−0.0379168
$56$	13.6269	1.82097
$57$	20.0760	2.65913
$58$	6.17120	0.810319
$59$	1.04516	0.136069	0.0680343	−	0.997683i	$-0.478327\pi$
$59$	1.04516	0.136069	0.0680343	+	0.997683i	$0.478327\pi$
$60$	2.37866	0.307083
$61$	1.72594	0.220984	0.110492	−	0.993877i	$-0.464757\pi$
$61$	1.72594	0.220984	0.110492	+	0.993877i	$0.464757\pi$
$62$	6.22007	0.789950
$63$	−17.6227	−2.22025
$64$	−12.9054	−1.61318
$65$	0.538110	0.0667444
$66$	5.95177	0.732612
$67$	3.00535	0.367161	0.183581	−	0.983005i	$-0.441231\pi$
$67$	3.00535	0.367161	0.183581	+	0.983005i	$0.441231\pi$
$68$	−12.3091	−1.49270
$69$	23.7053	2.85378
$70$	3.04254	0.363653
$71$	9.41019	1.11678	0.558392	−	0.829577i	$-0.311418\pi$
$71$	9.41019	1.11678	0.558392	+	0.829577i	$0.311418\pi$
$72$	−10.7885	−1.27144
$73$	1.80168	0.210871	0.105435	−	0.994426i	$-0.466376\pi$
$73$	1.80168	0.210871	0.105435	+	0.994426i	$0.466376\pi$
$74$	−25.7954	−2.99866
$75$	−12.7710	−1.47466
$76$	25.2140	2.89224
$77$	4.71795	0.537661
$78$	−11.3895	−1.28961
$79$	3.95095	0.444516	0.222258	−	0.974988i	$-0.428657\pi$
$79$	3.95095	0.444516	0.222258	+	0.974988i	$0.428657\pi$
$80$	0.0295349	0.00330210
$81$	−6.25371	−0.694856
$82$	−17.7819	−1.96368
$83$	−7.21069	−0.791476	−0.395738	−	0.918363i	$-0.629511\pi$
$83$	−7.21069	−0.791476	−0.395738	+	0.918363i	$0.629511\pi$
$84$	−39.9091	−4.35444
$85$	−1.06194	−0.115183
$86$	−0.659205	−0.0710840
$87$	−6.98356	−0.748716
$88$	2.88831	0.307895
$89$	13.1047	1.38910	0.694550	−	0.719444i	$-0.255604\pi$
$89$	13.1047	1.38910	0.694550	+	0.719444i	$0.255604\pi$
$90$	−2.40880	−0.253910
$91$	−9.02842	−0.946436
$92$	29.7722	3.10396
$93$	−7.03886	−0.729896
$94$	−16.0926	−1.65983
$95$	2.17527	0.223178
$96$	14.3666	1.46628
$97$	−17.8476	−1.81215	−0.906074	−	0.423120i	$-0.860935\pi$
$97$	−17.8476	−1.81215	−0.906074	+	0.423120i	$0.860935\pi$
$98$	−34.9943	−3.53496
$99$	−3.73524	−0.375406
$100$	−16.0394	−1.60394
$101$	8.23021	0.818937	0.409468	−	0.912324i	$-0.365714\pi$
$101$	8.23021	0.818937	0.409468	+	0.912324i	$0.365714\pi$
$102$	22.4767	2.22552
$103$	−16.5081	−1.62660	−0.813298	−	0.581847i	$-0.802330\pi$
$103$	−16.5081	−1.62660	−0.813298	+	0.581847i	$0.802330\pi$
$104$	−5.52716	−0.541983
$105$	−3.44305	−0.336007
$106$	−13.9274	−1.35275
$107$	−12.2154	−1.18091	−0.590456	−	0.807070i	$-0.701052\pi$
$107$	−12.2154	−1.18091	−0.590456	+	0.807070i	$0.701052\pi$
$108$	6.21938	0.598460
$109$	−1.64547	−0.157608	−0.0788038	−	0.996890i	$-0.525110\pi$
$109$	−1.64547	−0.157608	−0.0788038	+	0.996890i	$0.525110\pi$
$110$	0.644885	0.0614874
$111$	29.1911	2.77069
$112$	−0.495537	−0.0468238
$113$	6.81133	0.640756	0.320378	−	0.947290i	$-0.396190\pi$
$113$	6.81133	0.640756	0.320378	+	0.947290i	$0.396190\pi$
$114$	−46.0411	−4.31214
$115$	2.56851	0.239515
$116$	−8.77086	−0.814354
$117$	7.14787	0.660821
$118$	−2.39692	−0.220654
$119$	17.8172	1.63330
$120$	−2.10782	−0.192417
$121$	1.00000	0.0909091
$122$	−3.95818	−0.358357
$123$	20.1227	1.81440
$124$	−8.84031	−0.793884
$125$	−2.78975	−0.249523
$126$	40.4149	3.60044
$127$	−4.54374	−0.403192	−0.201596	−	0.979469i	$-0.564613\pi$
$127$	−4.54374	−0.403192	−0.201596	+	0.979469i	$0.564613\pi$
$128$	18.5251	1.63741
$129$	0.745981	0.0656800
$130$	−1.23407	−0.108235
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−8.45899	−0.736260
$133$	−36.4967	−3.16466
$134$	−6.89229	−0.595403
$135$	0.536560	0.0461797
$136$	10.9076	0.935321
$137$	11.3341	0.968340	0.484170	−	0.874974i	$-0.339122\pi$
$137$	11.3341	0.968340	0.484170	+	0.874974i	$0.339122\pi$
$138$	−54.3644	−4.62780
$139$	3.87976	0.329077	0.164538	−	0.986371i	$-0.447387\pi$
$139$	3.87976	0.329077	0.164538	+	0.986371i	$0.447387\pi$
$140$	−4.32423	−0.365464
$141$	18.2110	1.53364
$142$	−21.5808	−1.81102
$143$	−1.91363	−0.160026
$144$	0.392320	0.0326933
$145$	−0.756682	−0.0628390
$146$	−4.13188	−0.341956
$147$	39.6009	3.26622
$148$	36.6619	3.01359
$149$	18.7850	1.53893	0.769463	−	0.638692i	$-0.220524\pi$
$149$	18.7850	1.53893	0.769463	+	0.638692i	$0.220524\pi$
$150$	29.2882	2.39137
$151$	0.153103	0.0124594	0.00622968	−	0.999981i	$-0.498017\pi$
$151$	0.153103	0.0124594	0.00622968	+	0.999981i	$0.498017\pi$
$152$	−22.3431	−1.81227
$153$	−14.1060	−1.14040
$154$	−10.8199	−0.871892
$155$	−0.762674	−0.0612594
$156$	16.1874	1.29603
$157$	−21.6506	−1.72790	−0.863951	−	0.503575i	$-0.832018\pi$
$157$	−21.6506	−1.72790	−0.863951	+	0.503575i	$0.832018\pi$
$158$	−9.06088	−0.720845
$159$	15.7608	1.24991
$160$	1.55664	0.123064
$161$	−43.0945	−3.39632
$162$	14.3419	1.12681
$163$	7.12788	0.558299	0.279150	−	0.960248i	$-0.409947\pi$
$163$	7.12788	0.558299	0.279150	+	0.960248i	$0.409947\pi$
$164$	25.2727	1.97346
$165$	−0.729776	−0.0568130
$166$	16.5366	1.28349
$167$	12.1770	0.942283	0.471142	−	0.882058i	$-0.343842\pi$
$167$	12.1770	0.942283	0.471142	+	0.882058i	$0.343842\pi$
$168$	35.3650	2.72847
$169$	−9.33802	−0.718309
$170$	2.43539	0.186786
$171$	28.8947	2.20963
$172$	0.936900	0.0714380
$173$	−0.905373	−0.0688343	−0.0344171	−	0.999408i	$-0.510957\pi$
$173$	−0.905373	−0.0688343	−0.0344171	+	0.999408i	$0.510957\pi$
$174$	16.0157	1.21415
$175$	23.2167	1.75502
$176$	−0.105032	−0.00791710
$177$	2.71244	0.203880
$178$	−30.0537	−2.25262
$179$	10.2399	0.765367	0.382684	−	0.923879i	$-0.375000\pi$
$179$	10.2399	0.765367	0.382684	+	0.923879i	$0.375000\pi$
$180$	3.42352	0.255174
$181$	16.6370	1.23662	0.618308	−	0.785936i	$-0.287818\pi$
$181$	16.6370	1.23662	0.618308	+	0.785936i	$0.287818\pi$
$182$	20.7053	1.53478
$183$	4.47922	0.331114
$184$	−26.3823	−1.94493
$185$	3.16291	0.232541
$186$	16.1425	1.18363
$187$	3.77647	0.276163
$188$	22.8717	1.66809
$189$	−9.00241	−0.654829
$190$	−4.98864	−0.361914
$191$	3.34395	0.241960	0.120980	−	0.992655i	$-0.461396\pi$
$191$	3.34395	0.241960	0.120980	+	0.992655i	$0.461396\pi$
$192$	−33.4927	−2.41712
$193$	23.3847	1.68327	0.841633	−	0.540049i	$-0.181594\pi$
$193$	23.3847	1.68327	0.841633	+	0.540049i	$0.181594\pi$
$194$	40.9307	2.93865
$195$	1.39652	0.100007
$196$	49.7359	3.55257
$197$	−22.4252	−1.59773	−0.798864	−	0.601511i	$-0.794566\pi$
$197$	−22.4252	−1.59773	−0.798864	+	0.601511i	$0.794566\pi$
$198$	8.56619	0.608773
$199$	−9.54885	−0.676900	−0.338450	−	0.940984i	$-0.609903\pi$
$199$	−9.54885	−0.676900	−0.338450	+	0.940984i	$0.609903\pi$
$200$	14.2132	1.00502
$201$	7.79957	0.550140
$202$	−18.8747	−1.32802
$203$	12.6956	0.891058
$204$	−31.9451	−2.23661
$205$	2.18033	0.152281
$206$	37.8589	2.63775
$207$	34.1183	2.37138
$208$	0.200993	0.0139363
$209$	−7.73570	−0.535090
$210$	7.89610	0.544883
$211$	−3.55835	−0.244967	−0.122483	−	0.992471i	$-0.539086\pi$
$211$	−3.55835	−0.244967	−0.122483	+	0.992471i	$0.539086\pi$
$212$	19.7945	1.35949
$213$	24.4216	1.67334
$214$	28.0142	1.91501
$215$	0.0808285	0.00551246
$216$	−5.51124	−0.374992
$217$	12.7962	0.868659
$218$	3.77363	0.255583
$219$	4.67578	0.315960
$220$	−0.916548	−0.0617936
$221$	−7.22677	−0.486125
$222$	−66.9452	−4.49306
$223$	−15.4303	−1.03329	−0.516644	−	0.856201i	$-0.672819\pi$
$223$	−15.4303	−1.03329	−0.516644	+	0.856201i	$0.672819\pi$
$224$	−26.1174	−1.74504
$225$	−18.3808	−1.22539
$226$	−15.6207	−1.03908
$227$	3.65157	0.242363	0.121182	−	0.992630i	$-0.461332\pi$
$227$	3.65157	0.242363	0.121182	+	0.992630i	$0.461332\pi$
$228$	65.4362	4.33362
$229$	−26.7903	−1.77035	−0.885176	−	0.465256i	$-0.845962\pi$
$229$	−26.7903	−1.77035	−0.885176	+	0.465256i	$0.845962\pi$
$230$	−5.89049	−0.388407
$231$	12.2442	0.805609
$232$	7.77221	0.510271
$233$	−21.8606	−1.43213	−0.716067	−	0.698031i	$-0.754060\pi$
$233$	−21.8606	−1.43213	−0.716067	+	0.698031i	$0.754060\pi$
$234$	−16.3925	−1.07161
$235$	1.97320	0.128717
$236$	3.40663	0.221753
$237$	10.2536	0.666045
$238$	−40.8610	−2.64863
$239$	20.1220	1.30159	0.650794	−	0.759255i	$-0.274436\pi$
$239$	20.1220	1.30159	0.650794	+	0.759255i	$0.274436\pi$
$240$	0.0766499	0.00494773
$241$	2.77843	0.178974	0.0894872	−	0.995988i	$-0.471477\pi$
$241$	2.77843	0.178974	0.0894872	+	0.995988i	$0.471477\pi$
$242$	−2.29335	−0.147422
$243$	−21.9542	−1.40836
$244$	5.62559	0.360142
$245$	4.29083	0.274131
$246$	−46.1482	−2.94230
$247$	14.8033	0.941910
$248$	7.83375	0.497444
$249$	−18.7134	−1.18592
$250$	6.39786	0.404636
$251$	−5.90539	−0.372745	−0.186372	−	0.982479i	$-0.559673\pi$
$251$	−5.90539	−0.372745	−0.186372	+	0.982479i	$0.559673\pi$
$252$	−57.4399	−3.61838
$253$	−9.13416	−0.574260
$254$	10.4204	0.653832
$255$	−2.75598	−0.172586
$256$	−16.6737	−1.04210
$257$	−27.9676	−1.74457	−0.872287	−	0.488994i	$-0.837364\pi$
$257$	−27.9676	−1.74457	−0.872287	+	0.488994i	$0.837364\pi$
$258$	−1.71079	−0.106509
$259$	−53.0673	−3.29744
$260$	1.75393	0.108774
$261$	−10.0512	−0.622155
$262$	−2.29335	−0.141683
$263$	12.2507	0.755413	0.377707	−	0.925925i	$-0.376713\pi$
$263$	12.2507	0.755413	0.377707	+	0.925925i	$0.376713\pi$
$264$	7.49584	0.461337
$265$	1.70771	0.104904
$266$	83.6995	5.13194
$267$	34.0099	2.08137
$268$	9.79572	0.598369
$269$	19.8139	1.20808	0.604038	−	0.796956i	$-0.293558\pi$
$269$	19.8139	1.20808	0.604038	+	0.796956i	$0.293558\pi$
$270$	−1.23052	−0.0748869
$271$	10.3760	0.630296	0.315148	−	0.949043i	$-0.397946\pi$
$271$	10.3760	0.630296	0.315148	+	0.949043i	$0.397946\pi$
$272$	−0.396651	−0.0240505
$273$	−23.4309	−1.41810
$274$	−25.9931	−1.57030
$275$	4.92093	0.296743
$276$	77.2657	4.65085
$277$	7.68149	0.461536	0.230768	−	0.973009i	$-0.425876\pi$
$277$	7.68149	0.461536	0.230768	+	0.973009i	$0.425876\pi$
$278$	−8.89762	−0.533644
$279$	−10.1308	−0.606516
$280$	3.83187	0.228998
$281$	−11.0934	−0.661777	−0.330888	−	0.943670i	$-0.607348\pi$
$281$	−11.0934	−0.661777	−0.330888	+	0.943670i	$0.607348\pi$
$282$	−41.7641	−2.48702
$283$	−9.93802	−0.590754	−0.295377	−	0.955381i	$-0.595445\pi$
$283$	−9.93802	−0.590754	−0.295377	+	0.955381i	$0.595445\pi$
$284$	30.6719	1.82004
$285$	5.64533	0.334401
$286$	4.38862	0.259504
$287$	−36.5816	−2.15934
$288$	20.6773	1.21842
$289$	−2.73827	−0.161075
$290$	1.73533	0.101902
$291$	−46.3187	−2.71525
$292$	5.87245	0.343659
$293$	18.7157	1.09338	0.546690	−	0.837335i	$-0.315887\pi$
$293$	18.7157	1.09338	0.546690	+	0.837335i	$0.315887\pi$
$294$	−90.8185	−5.29664
$295$	0.293898	0.0171114
$296$	−32.4876	−1.88830
$297$	−1.90812	−0.110720
$298$	−43.0804	−2.49558
$299$	17.4794	1.01086
$300$	−41.6261	−2.40328
$301$	−1.35614	−0.0781667
$302$	−0.351119	−0.0202046
$303$	21.3593	1.22706
$304$	0.812497	0.0465999
$305$	0.485332	0.0277901
$306$	32.3500	1.84932
$307$	30.9048	1.76383	0.881916	−	0.471406i	$-0.156253\pi$
$307$	30.9048	1.76383	0.881916	+	0.471406i	$0.156253\pi$
$308$	15.3778	0.876234
$309$	−42.8425	−2.43722
$310$	1.74907	0.0993408
$311$	17.3892	0.986053	0.493027	−	0.870014i	$-0.335890\pi$
$311$	17.3892	0.986053	0.493027	+	0.870014i	$0.335890\pi$
$312$	−14.3443	−0.812085
$313$	−23.6434	−1.33640	−0.668202	−	0.743980i	$-0.732936\pi$
$313$	−23.6434	−1.33640	−0.668202	+	0.743980i	$0.732936\pi$
$314$	49.6522	2.80204
$315$	−4.95547	−0.279209
$316$	12.8778	0.724435
$317$	4.42026	0.248267	0.124133	−	0.992266i	$-0.460385\pi$
$317$	4.42026	0.248267	0.124133	+	0.992266i	$0.460385\pi$
$318$	−36.1449	−2.02691
$319$	2.69092	0.150662
$320$	−3.62899	−0.202867
$321$	−31.7019	−1.76943
$322$	98.8306	5.50762
$323$	−29.2137	−1.62549
$324$	−20.3835	−1.13242
$325$	−9.41684	−0.522352
$326$	−16.3467	−0.905360
$327$	−4.27038	−0.236153
$328$	−22.3951	−1.23656
$329$	−33.1063	−1.82521
$330$	1.67363	0.0921302
$331$	0.709655	0.0390062	0.0195031	−	0.999810i	$-0.493792\pi$
$331$	0.709655	0.0390062	0.0195031	+	0.999810i	$0.493792\pi$
$332$	−23.5027	−1.28988
$333$	42.0138	2.30234
$334$	−27.9260	−1.52804
$335$	0.845099	0.0461727
$336$	−1.28603	−0.0701589
$337$	−1.45977	−0.0795189	−0.0397595	−	0.999209i	$-0.512659\pi$
$337$	−1.45977	−0.0795189	−0.0397595	+	0.999209i	$0.512659\pi$
$338$	21.4153	1.16484
$339$	17.6770	0.960082
$340$	−3.46131	−0.187716
$341$	2.71223	0.146875
$342$	−66.2655	−3.58323
$343$	−38.9659	−2.10396
$344$	−0.830224	−0.0447627
$345$	6.66589	0.358880
$346$	2.07633	0.111624
$347$	−0.293106	−0.0157347	−0.00786737	−	0.999969i	$-0.502504\pi$
$347$	−0.293106	−0.0157347	−0.00786737	+	0.999969i	$0.502504\pi$
$348$	−22.7624	−1.22020
$349$	30.8214	1.64983	0.824916	−	0.565256i	$-0.191223\pi$
$349$	30.8214	1.64983	0.824916	+	0.565256i	$0.191223\pi$
$350$	−53.2439	−2.84601
$351$	3.65143	0.194899
$352$	−5.53575	−0.295056
$353$	−28.8749	−1.53686	−0.768428	−	0.639937i	$-0.778961\pi$
$353$	−28.8749	−1.53686	−0.768428	+	0.639937i	$0.778961\pi$
$354$	−6.22056	−0.330619
$355$	2.64613	0.140442
$356$	42.7140	2.26384
$357$	46.2398	2.44727
$358$	−23.4837	−1.24115
$359$	29.4641	1.55505	0.777527	−	0.628849i	$-0.216474\pi$
$359$	29.4641	1.55505	0.777527	+	0.628849i	$0.216474\pi$
$360$	−3.03372	−0.159891
$361$	40.8411	2.14953
$362$	−38.1543	−2.00535
$363$	2.59523	0.136214
$364$	−29.4275	−1.54242
$365$	0.506630	0.0265182
$366$	−10.2724	−0.536947
$367$	20.9596	1.09408	0.547041	−	0.837106i	$-0.315754\pi$
$367$	20.9596	1.09408	0.547041	+	0.837106i	$0.315754\pi$
$368$	0.959380	0.0500112
$369$	28.9619	1.50770
$370$	−7.25364	−0.377099
$371$	−28.6520	−1.48754
$372$	−22.9427	−1.18952
$373$	10.0616	0.520968	0.260484	−	0.965478i	$-0.416118\pi$
$373$	10.0616	0.520968	0.260484	+	0.965478i	$0.416118\pi$
$374$	−8.66075	−0.447837
$375$	−7.24006	−0.373875
$376$	−20.2675	−1.04522
$377$	−5.14942	−0.265209
$378$	20.6456	1.06190
$379$	−37.1517	−1.90836	−0.954178	−	0.299238i	$-0.903268\pi$
$379$	−37.1517	−1.90836	−0.954178	+	0.299238i	$0.903268\pi$
$380$	7.09014	0.363716
$381$	−11.7921	−0.604126
$382$	−7.66883	−0.392371
$383$	−23.4540	−1.19844	−0.599222	−	0.800583i	$-0.704524\pi$
$383$	−23.4540	−1.19844	−0.599222	+	0.800583i	$0.704524\pi$
$384$	48.0771	2.45342
$385$	1.32668	0.0676139
$386$	−53.6292	−2.72965
$387$	1.07367	0.0545776
$388$	−58.1730	−2.95329
$389$	0.189350	0.00960045	0.00480023	−	0.999988i	$-0.498472\pi$
$389$	0.189350	0.00960045	0.00480023	+	0.999988i	$0.498472\pi$
$390$	−3.20271	−0.162175
$391$	−34.4949	−1.74448
$392$	−44.0730	−2.22602
$393$	2.59523	0.130912
$394$	51.4287	2.59094
$395$	1.11100	0.0559005
$396$	−12.1748	−0.611805
$397$	−12.0872	−0.606638	−0.303319	−	0.952889i	$-0.598095\pi$
$397$	−12.0872	−0.606638	−0.303319	+	0.952889i	$0.598095\pi$
$398$	21.8988	1.09769
$399$	−94.7174	−4.74180
$400$	−0.516856	−0.0258428
$401$	−11.7293	−0.585735	−0.292868	−	0.956153i	$-0.594609\pi$
$401$	−11.7293	−0.585735	−0.292868	+	0.956153i	$0.594609\pi$
$402$	−17.8871	−0.892128
$403$	−5.19020	−0.258542
$404$	26.8258	1.33463
$405$	−1.75853	−0.0873822
$406$	−29.1154	−1.44498
$407$	−11.2479	−0.557540
$408$	28.3078	1.40145
$409$	−24.2817	−1.20065	−0.600326	−	0.799755i	$-0.704963\pi$
$409$	−24.2817	−1.20065	−0.600326	+	0.799755i	$0.704963\pi$
$410$	−5.00025	−0.246945
$411$	29.4147	1.45092
$412$	−53.8072	−2.65089
$413$	−4.93103	−0.242640
$414$	−78.2450	−3.84553
$415$	−2.02764	−0.0995327
$416$	10.5934	0.519383
$417$	10.0689	0.493075
$418$	17.7406	0.867723
$419$	13.1666	0.643232	0.321616	−	0.946870i	$-0.395774\pi$
$419$	13.1666	0.643232	0.321616	+	0.946870i	$0.395774\pi$
$420$	−11.2224	−0.547596
$421$	19.2883	0.940056	0.470028	−	0.882652i	$-0.344244\pi$
$421$	19.2883	0.940056	0.470028	+	0.882652i	$0.344244\pi$
$422$	8.16052	0.397248
$423$	26.2105	1.27440
$424$	−17.5406	−0.851849
$425$	18.5837	0.901444
$426$	−56.0073	−2.71356
$427$	−8.14291	−0.394063
$428$	−39.8154	−1.92455
$429$	−4.96632	−0.239776
$430$	−0.185368	−0.00893922
$431$	2.87707	0.138584	0.0692918	−	0.997596i	$-0.477926\pi$
$431$	2.87707	0.138584	0.0692918	+	0.997596i	$0.477926\pi$
$432$	0.200414	0.00964241
$433$	−0.494116	−0.0237457	−0.0118728	−	0.999930i	$-0.503779\pi$
$433$	−0.494116	−0.0237457	−0.0118728	+	0.999930i	$0.503779\pi$
$434$	−29.3460	−1.40865
$435$	−1.96377	−0.0941554
$436$	−5.36330	−0.256856
$437$	70.6591	3.38009
$438$	−10.7232	−0.512373
$439$	−3.82318	−0.182470	−0.0912352	−	0.995829i	$-0.529082\pi$
$439$	−3.82318	−0.182470	−0.0912352	+	0.995829i	$0.529082\pi$
$440$	0.812189	0.0387196
$441$	56.9963	2.71411
$442$	16.5735	0.788320
$443$	0.433596	0.0206007	0.0103004	−	0.999947i	$-0.496721\pi$
$443$	0.433596	0.0206007	0.0103004	+	0.999947i	$0.496721\pi$
$444$	95.1462	4.51544
$445$	3.68503	0.174687
$446$	35.3869	1.67562
$447$	48.7514	2.30586
$448$	60.8873	2.87665
$449$	−19.5141	−0.920930	−0.460465	−	0.887678i	$-0.652317\pi$
$449$	−19.5141	−0.920930	−0.460465	+	0.887678i	$0.652317\pi$
$450$	42.1536	1.98714
$451$	−7.75370	−0.365108
$452$	22.2011	1.04425
$453$	0.397339	0.0186686
$454$	−8.37430	−0.393026
$455$	−2.53878	−0.119020
$456$	−57.9856	−2.71543
$457$	−15.9609	−0.746617	−0.373309	−	0.927707i	$-0.621777\pi$
$457$	−15.9609	−0.746617	−0.373309	+	0.927707i	$0.621777\pi$
$458$	61.4394	2.87087
$459$	−7.20595	−0.336345
$460$	8.37189	0.390341
$461$	−36.4655	−1.69837	−0.849184	−	0.528097i	$-0.822906\pi$
$461$	−36.4655	−1.69837	−0.849184	+	0.528097i	$0.822906\pi$
$462$	−28.0802	−1.30641
$463$	−23.9184	−1.11158	−0.555791	−	0.831322i	$-0.687584\pi$
$463$	−23.9184	−1.11158	−0.555791	+	0.831322i	$0.687584\pi$
$464$	−0.282633	−0.0131209
$465$	−1.97932	−0.0917886
$466$	50.1339	2.32241
$467$	31.9339	1.47773	0.738863	−	0.673856i	$-0.235363\pi$
$467$	31.9339	1.47773	0.738863	+	0.673856i	$0.235363\pi$
$468$	23.2980	1.07695
$469$	−14.1791	−0.654729
$470$	−4.52522	−0.208733
$471$	−56.1883	−2.58902
$472$	−3.01875	−0.138949
$473$	−0.287443	−0.0132166
$474$	−23.5151	−1.08008
$475$	−38.0668	−1.74663
$476$	58.0740	2.66182
$477$	22.6840	1.03863
$478$	−46.1468	−2.11071
$479$	−6.03824	−0.275894	−0.137947	−	0.990440i	$-0.544050\pi$
$479$	−6.03824	−0.275894	−0.137947	+	0.990440i	$0.544050\pi$
$480$	4.03986	0.184393
$481$	21.5244	0.981429
$482$	−6.37190	−0.290232
$483$	−111.840	−5.08891
$484$	3.25943	0.148156
$485$	−5.01871	−0.227888
$486$	50.3485	2.28386
$487$	−12.8430	−0.581970	−0.290985	−	0.956728i	$-0.593983\pi$
$487$	−12.8430	−0.581970	−0.290985	+	0.956728i	$0.593983\pi$
$488$	−4.98506	−0.225663
$489$	18.4985	0.836532
$490$	−9.84035	−0.444542
$491$	18.6600	0.842116	0.421058	−	0.907034i	$-0.361659\pi$
$491$	18.6600	0.842116	0.421058	+	0.907034i	$0.361659\pi$
$492$	65.5885	2.95696
$493$	10.1622	0.457681
$494$	−33.9490	−1.52744
$495$	−1.05034	−0.0472094
$496$	−0.284871	−0.0127911
$497$	−44.3968	−1.99147
$498$	42.9163	1.92313
$499$	29.3491	1.31385	0.656924	−	0.753957i	$-0.271857\pi$
$499$	29.3491	1.31385	0.656924	+	0.753957i	$0.271857\pi$
$500$	−9.09300	−0.406651
$501$	31.6021	1.41188
$502$	13.5431	0.604458
$503$	34.3816	1.53300	0.766500	−	0.642244i	$-0.221996\pi$
$503$	34.3816	1.53300	0.766500	+	0.642244i	$0.221996\pi$
$504$	50.8998	2.26726
$505$	2.31432	0.102986
$506$	20.9478	0.931242
$507$	−24.2343	−1.07628
$508$	−14.8100	−0.657088
$509$	−5.59034	−0.247787	−0.123894	−	0.992296i	$-0.539538\pi$
$509$	−5.59034	−0.247787	−0.123894	+	0.992296i	$0.539538\pi$
$510$	6.32041	0.279872
$511$	−8.50024	−0.376029
$512$	1.18816	0.0525099
$513$	14.7606	0.651698
$514$	64.1395	2.82907
$515$	−4.64207	−0.204554
$516$	2.43147	0.107040
$517$	−7.01709	−0.308611
$518$	121.702	5.34726
$519$	−2.34966	−0.103138
$520$	−1.55423	−0.0681575
$521$	−2.59655	−0.113757	−0.0568784	−	0.998381i	$-0.518115\pi$
$521$	−2.59655	−0.113757	−0.0568784	+	0.998381i	$0.518115\pi$
$522$	23.0509	1.00891
$523$	36.9088	1.61391	0.806955	−	0.590613i	$-0.201114\pi$
$523$	36.9088	1.61391	0.806955	+	0.590613i	$0.201114\pi$
$524$	3.25943	0.142389
$525$	60.2528	2.62965
$526$	−28.0952	−1.22501
$527$	10.2426	0.446176
$528$	−0.272583	−0.0118627
$529$	60.4329	2.62752
$530$	−3.91637	−0.170116
$531$	3.90393	0.169416
$532$	−118.958	−5.15750
$533$	14.8377	0.642693
$534$	−77.9964	−3.37523
$535$	−3.43497	−0.148507
$536$	−8.68037	−0.374935
$537$	26.5750	1.14679
$538$	−45.4401	−1.95906
$539$	−15.2591	−0.657255
$540$	1.74888	0.0752598
$541$	−20.6830	−0.889232	−0.444616	−	0.895721i	$-0.646660\pi$
$541$	−20.6830	−0.889232	−0.444616	+	0.895721i	$0.646660\pi$
$542$	−23.7957	−1.02211
$543$	43.1768	1.85289
$544$	−20.9056	−0.896320
$545$	−0.462704	−0.0198201
$546$	53.7351	2.29965
$547$	−39.8099	−1.70215	−0.851073	−	0.525047i	$-0.824048\pi$
$547$	−39.8099	−1.70215	−0.851073	+	0.525047i	$0.824048\pi$
$548$	36.9428	1.57812
$549$	6.44681	0.275143
$550$	−11.2854	−0.481210
$551$	−20.8161	−0.886797
$552$	−68.4682	−2.91420
$553$	−18.6404	−0.792669
$554$	−17.6163	−0.748445
$555$	8.20848	0.348431
$556$	12.6458	0.536301
$557$	−22.5385	−0.954988	−0.477494	−	0.878635i	$-0.658455\pi$
$557$	−22.5385	−0.954988	−0.477494	+	0.878635i	$0.658455\pi$
$558$	23.2334	0.983550
$559$	0.550059	0.0232650
$560$	−0.139344	−0.00588837
$561$	9.80082	0.413791
$562$	25.4410	1.07316
$563$	−31.4014	−1.32341	−0.661706	−	0.749763i	$-0.730167\pi$
$563$	−31.4014	−1.32341	−0.661706	+	0.749763i	$0.730167\pi$
$564$	59.3575	2.49940
$565$	1.91534	0.0805788
$566$	22.7913	0.957991
$567$	29.5047	1.23908
$568$	−27.1796	−1.14043
$569$	1.68384	0.0705903	0.0352952	−	0.999377i	$-0.488763\pi$
$569$	1.68384	0.0705903	0.0352952	+	0.999377i	$0.488763\pi$
$570$	−12.9467	−0.542277
$571$	−22.2513	−0.931189	−0.465594	−	0.884998i	$-0.654159\pi$
$571$	−22.2513	−0.931189	−0.465594	+	0.884998i	$0.654159\pi$
$572$	−6.23735	−0.260797
$573$	8.67833	0.362542
$574$	83.8942	3.50168
$575$	−44.9485	−1.87448
$576$	−48.2049	−2.00854
$577$	3.19967	0.133204	0.0666021	−	0.997780i	$-0.478784\pi$
$577$	3.19967	0.133204	0.0666021	+	0.997780i	$0.478784\pi$
$578$	6.27981	0.261206
$579$	60.6887	2.52214
$580$	−2.46635	−0.102410
$581$	34.0197	1.41137
$582$	106.225	4.40315
$583$	−6.07298	−0.251517
$584$	−5.20381	−0.215335
$585$	2.00997	0.0831021
$586$	−42.9215	−1.77307
$587$	20.5662	0.848858	0.424429	−	0.905461i	$-0.360475\pi$
$587$	20.5662	0.848858	0.424429	+	0.905461i	$0.360475\pi$
$588$	129.076	5.32302
$589$	−20.9810	−0.864506
$590$	−0.674010	−0.0277485
$591$	−58.1986	−2.39397
$592$	1.18140	0.0485551
$593$	−29.7853	−1.22313	−0.611567	−	0.791192i	$-0.709461\pi$
$593$	−29.7853	−1.22313	−0.611567	+	0.791192i	$0.709461\pi$
$594$	4.37597	0.179548
$595$	5.01017	0.205397
$596$	61.2284	2.50801
$597$	−24.7815	−1.01424
$598$	−40.0863	−1.63925
$599$	23.3136	0.952569	0.476284	−	0.879291i	$-0.341983\pi$
$599$	23.3136	0.952569	0.476284	+	0.879291i	$0.341983\pi$
$600$	36.8865	1.50589
$601$	−14.5973	−0.595438	−0.297719	−	0.954654i	$-0.596226\pi$
$601$	−14.5973	−0.595438	−0.297719	+	0.954654i	$0.596226\pi$
$602$	3.11010	0.126758
$603$	11.2257	0.457145
$604$	0.499030	0.0203052
$605$	0.281199	0.0114323
$606$	−48.9843	−1.98985
$607$	0.598100	0.0242761	0.0121381	−	0.999926i	$-0.496136\pi$
$607$	0.598100	0.0242761	0.0121381	+	0.999926i	$0.496136\pi$
$608$	42.8229	1.73670
$609$	32.9481	1.33512
$610$	−1.11303	−0.0450655
$611$	13.4281	0.543244
$612$	−45.9776	−1.85853
$613$	30.5921	1.23560	0.617802	−	0.786334i	$-0.288023\pi$
$613$	30.5921	1.23560	0.617802	+	0.786334i	$0.288023\pi$
$614$	−70.8755	−2.86030
$615$	5.65847	0.228171
$616$	−13.6269	−0.549044
$617$	13.3848	0.538851	0.269425	−	0.963021i	$-0.413166\pi$
$617$	13.3848	0.538851	0.269425	+	0.963021i	$0.413166\pi$
$618$	98.2526	3.95230
$619$	−30.9914	−1.24565	−0.622825	−	0.782361i	$-0.714015\pi$
$619$	−30.9914	−1.24565	−0.622825	+	0.782361i	$0.714015\pi$
$620$	−2.48588	−0.0998355
$621$	17.4291	0.699404
$622$	−39.8795	−1.59902
$623$	−61.8276	−2.47707
$624$	0.521623	0.0208816
$625$	23.8202	0.952807
$626$	54.2225	2.16717
$627$	−20.0760	−0.801757
$628$	−70.5685	−2.81599
$629$	−42.4775	−1.69369
$630$	11.3646	0.452777
$631$	−3.15523	−0.125608	−0.0628038	−	0.998026i	$-0.520004\pi$
$631$	−3.15523	−0.125608	−0.0628038	+	0.998026i	$0.520004\pi$
$632$	−11.4116	−0.453928
$633$	−9.23474	−0.367048
$634$	−10.1372	−0.402599
$635$	−1.27769	−0.0507037
$636$	51.3712	2.03700
$637$	29.2002	1.15696
$638$	−6.17120	−0.244320
$639$	35.1493	1.39049
$640$	5.20924	0.205913
$641$	−37.4841	−1.48053	−0.740267	−	0.672313i	$-0.765301\pi$
$641$	−37.4841	−1.48053	−0.740267	+	0.672313i	$0.765301\pi$
$642$	72.7035	2.86938
$643$	−16.7203	−0.659383	−0.329692	−	0.944089i	$-0.606945\pi$
$643$	−16.7203	−0.659383	−0.329692	+	0.944089i	$0.606945\pi$
$644$	−140.464	−5.53504
$645$	0.209769	0.00825964
$646$	66.9970	2.63596
$647$	−35.3518	−1.38982	−0.694911	−	0.719096i	$-0.744556\pi$
$647$	−35.3518	−1.38982	−0.694911	+	0.719096i	$0.744556\pi$
$648$	18.0627	0.709568
$649$	−1.04516	−0.0410262
$650$	21.5961	0.847067
$651$	33.2090	1.30156
$652$	23.2329	0.909869
$653$	−29.4459	−1.15231	−0.576153	−	0.817342i	$-0.695447\pi$
$653$	−29.4459	−1.15231	−0.576153	+	0.817342i	$0.695447\pi$
$654$	9.79346	0.382955
$655$	0.281199	0.0109873
$656$	0.814388	0.0317965
$657$	6.72971	0.262551
$658$	75.9242	2.95983
$659$	−4.37056	−0.170253	−0.0851264	−	0.996370i	$-0.527129\pi$
$659$	−4.37056	−0.170253	−0.0851264	+	0.996370i	$0.527129\pi$
$660$	−2.37866	−0.0925890
$661$	−14.4908	−0.563625	−0.281812	−	0.959469i	$-0.590936\pi$
$661$	−14.4908	−0.563625	−0.281812	+	0.959469i	$0.590936\pi$
$662$	−1.62748	−0.0632539
$663$	−18.7552	−0.728390
$664$	20.8267	0.808233
$665$	−10.2628	−0.397975
$666$	−96.3521	−3.73357
$667$	−24.5793	−0.951713
$668$	39.6900	1.53565
$669$	−40.0452	−1.54824
$670$	−1.93810	−0.0748755
$671$	−1.72594	−0.0666293
$672$	−67.7808	−2.61470
$673$	−8.72397	−0.336284	−0.168142	−	0.985763i	$-0.553777\pi$
$673$	−8.72397	−0.336284	−0.168142	+	0.985763i	$0.553777\pi$
$674$	3.34776	0.128951
$675$	−9.38971	−0.361410
$676$	−30.4366	−1.17064
$677$	−27.4394	−1.05458	−0.527291	−	0.849685i	$-0.676792\pi$
$677$	−27.4394	−1.05458	−0.527291	+	0.849685i	$0.676792\pi$
$678$	−40.5394	−1.55691
$679$	84.2040	3.23145
$680$	3.06721	0.117622
$681$	9.47667	0.363147
$682$	−6.22007	−0.238179
$683$	−16.6117	−0.635631	−0.317815	−	0.948153i	$-0.602949\pi$
$683$	−16.6117	−0.635631	−0.317815	+	0.948153i	$0.602949\pi$
$684$	94.1803	3.60107
$685$	3.18714	0.121774
$686$	89.3623	3.41187
$687$	−69.5271	−2.65262
$688$	0.0301907	0.00115101
$689$	11.6214	0.442741
$690$	−15.2872	−0.581973
$691$	2.06559	0.0785788	0.0392894	−	0.999228i	$-0.487491\pi$
$691$	2.06559	0.0785788	0.0392894	+	0.999228i	$0.487491\pi$
$692$	−2.95100	−0.112180
$693$	17.6227	0.669430
$694$	0.672193	0.0255161
$695$	1.09098	0.0413833
$696$	20.1707	0.764569
$697$	−29.2816	−1.10912
$698$	−70.6841	−2.67543
$699$	−56.7333	−2.14585
$700$	75.6733	2.86018
$701$	19.3780	0.731899	0.365949	−	0.930635i	$-0.380744\pi$
$701$	19.3780	0.731899	0.365949	+	0.930635i	$0.380744\pi$
$702$	−8.37400	−0.316056
$703$	87.0108	3.28167
$704$	12.9054	0.486392
$705$	5.12090	0.192864
$706$	66.2201	2.49223
$707$	−38.8298	−1.46034
$708$	8.84101	0.332266
$709$	44.7917	1.68219	0.841094	−	0.540888i	$-0.181912\pi$
$709$	44.7917	1.68219	0.841094	+	0.540888i	$0.181912\pi$
$710$	−6.06849	−0.227747
$711$	14.7577	0.553458
$712$	−37.8506	−1.41851
$713$	−24.7739	−0.927790
$714$	−106.044	−3.96859
$715$	−0.538110	−0.0201242
$716$	33.3763	1.24733
$717$	52.2214	1.95024
$718$	−67.5713	−2.52174
$719$	11.5863	0.432095	0.216047	−	0.976383i	$-0.430683\pi$
$719$	11.5863	0.432095	0.216047	+	0.976383i	$0.430683\pi$
$720$	0.110320	0.00411138
$721$	77.8846	2.90058
$722$	−93.6627	−3.48577
$723$	7.21067	0.268168
$724$	54.2271	2.01533
$725$	13.2418	0.491789
$726$	−5.95177	−0.220891
$727$	−4.65474	−0.172635	−0.0863174	−	0.996268i	$-0.527510\pi$
$727$	−4.65474	−0.172635	−0.0863174	+	0.996268i	$0.527510\pi$
$728$	26.0769	0.966474
$729$	−38.2151	−1.41537
$730$	−1.16188	−0.0430030
$731$	−1.08552	−0.0401494
$732$	14.5997	0.539621
$733$	32.5589	1.20259	0.601296	−	0.799027i	$-0.294651\pi$
$733$	32.5589	1.20259	0.601296	+	0.799027i	$0.294651\pi$
$734$	−48.0676	−1.77421
$735$	11.1357	0.410747
$736$	50.5644	1.86383
$737$	−3.00535	−0.110703
$738$	−66.4197	−2.44494
$739$	−0.993856	−0.0365596	−0.0182798	−	0.999833i	$-0.505819\pi$
$739$	−0.993856	−0.0365596	−0.0182798	+	0.999833i	$0.505819\pi$
$740$	10.3093	0.378977
$741$	38.4180	1.41132
$742$	65.7089	2.41225
$743$	−24.6731	−0.905167	−0.452584	−	0.891722i	$-0.649498\pi$
$743$	−24.6731	−0.905167	−0.452584	+	0.891722i	$0.649498\pi$
$744$	20.3304	0.745349
$745$	5.28231	0.193529
$746$	−23.0747	−0.844823
$747$	−26.9336	−0.985451
$748$	12.3091	0.450067
$749$	57.6319	2.10582
$750$	16.6039	0.606290
$751$	6.33138	0.231035	0.115518	−	0.993305i	$-0.463147\pi$
$751$	6.33138	0.231035	0.115518	+	0.993305i	$0.463147\pi$
$752$	0.737020	0.0268764
$753$	−15.3259	−0.558506
$754$	11.8094	0.430073
$755$	0.0430524	0.00156684
$756$	−29.3427	−1.06719
$757$	−9.13651	−0.332072	−0.166036	−	0.986120i	$-0.553097\pi$
$757$	−9.13651	−0.332072	−0.166036	+	0.986120i	$0.553097\pi$
$758$	85.2018	3.09467
$759$	−23.7053	−0.860447
$760$	−6.28285	−0.227903
$761$	−13.1478	−0.476609	−0.238305	−	0.971190i	$-0.576592\pi$
$761$	−13.1478	−0.476609	−0.238305	+	0.971190i	$0.576592\pi$
$762$	27.0433	0.979675
$763$	7.76325	0.281049
$764$	10.8994	0.394326
$765$	−3.96659	−0.143412
$766$	53.7882	1.94345
$767$	2.00005	0.0722178
$768$	−43.2720	−1.56145
$769$	−50.8048	−1.83207	−0.916034	−	0.401102i	$-0.868627\pi$
$769$	−50.8048	−1.83207	−0.916034	+	0.401102i	$0.868627\pi$
$770$	−3.04254	−0.109645
$771$	−72.5826	−2.61400
$772$	76.2208	2.74325
$773$	34.8943	1.25506	0.627530	−	0.778592i	$-0.284066\pi$
$773$	34.8943	1.25506	0.627530	+	0.778592i	$0.284066\pi$
$774$	−2.46229	−0.0885052
$775$	13.3467	0.479426
$776$	51.5494	1.85051
$777$	−137.722	−4.94075
$778$	−0.434246	−0.0155685
$779$	59.9803	2.14902
$780$	4.55187	0.162983
$781$	−9.41019	−0.336723
$782$	79.1087	2.82892
$783$	−5.13459	−0.183495
$784$	1.60269	0.0572391
$785$	−6.08811	−0.217294
$786$	−5.95177	−0.212293
$787$	22.1160	0.788349	0.394175	−	0.919036i	$-0.371030\pi$
$787$	22.1160	0.788349	0.394175	+	0.919036i	$0.371030\pi$
$788$	−73.0934	−2.60384
$789$	31.7935	1.13188
$790$	−2.54791	−0.0906505
$791$	−32.1355	−1.14261
$792$	10.7885	0.383354
$793$	3.30282	0.117286
$794$	27.7201	0.983748
$795$	4.43191	0.157184
$796$	−31.1238	−1.10315
$797$	−46.7936	−1.65752	−0.828758	−	0.559608i	$-0.810952\pi$
$797$	−46.7936	−1.65752	−0.828758	+	0.559608i	$0.810952\pi$
$798$	217.220	7.68950
$799$	−26.4998	−0.937497
$800$	−27.2410	−0.963115
$801$	48.9493	1.72954
$802$	26.8994	0.949851
$803$	−1.80168	−0.0635799
$804$	25.4222	0.896571
$805$	−12.1181	−0.427108
$806$	11.9029	0.419262
$807$	51.4217	1.81013
$808$	−23.7714	−0.836276
$809$	−3.84347	−0.135129	−0.0675647	−	0.997715i	$-0.521523\pi$
$809$	−3.84347	−0.135129	−0.0675647	+	0.997715i	$0.521523\pi$
$810$	4.03292	0.141702
$811$	18.2764	0.641770	0.320885	−	0.947118i	$-0.396020\pi$
$811$	18.2764	0.641770	0.320885	+	0.947118i	$0.396020\pi$
$812$	41.3805	1.45217
$813$	26.9281	0.944409
$814$	25.7954	0.904129
$815$	2.00435	0.0702093
$816$	−1.02940	−0.0360363
$817$	2.22357	0.0777929
$818$	55.6863	1.94703
$819$	−33.7233	−1.17839
$820$	7.10664	0.248175
$821$	4.42889	0.154569	0.0772846	−	0.997009i	$-0.475375\pi$
$821$	4.42889	0.154569	0.0772846	+	0.997009i	$0.475375\pi$
$822$	−67.4581	−2.35287
$823$	31.7806	1.10780	0.553901	−	0.832583i	$-0.313139\pi$
$823$	31.7806	1.10780	0.553901	+	0.832583i	$0.313139\pi$
$824$	47.6807	1.66103
$825$	12.7710	0.444628
$826$	11.3085	0.393475
$827$	2.98838	0.103916	0.0519580	−	0.998649i	$-0.483454\pi$
$827$	2.98838	0.103916	0.0519580	+	0.998649i	$0.483454\pi$
$828$	111.206	3.86468
$829$	7.18961	0.249706	0.124853	−	0.992175i	$-0.460154\pi$
$829$	7.18961	0.249706	0.124853	+	0.992175i	$0.460154\pi$
$830$	4.65007	0.161406
$831$	19.9353	0.691547
$832$	−24.6963	−0.856189
$833$	−57.6254	−1.99660
$834$	−23.0914	−0.799590
$835$	3.42415	0.118498
$836$	−25.2140	−0.872044
$837$	−5.17525	−0.178883
$838$	−30.1956	−1.04309
$839$	3.31630	0.114491	0.0572457	−	0.998360i	$-0.481768\pi$
$839$	3.31630	0.114491	0.0572457	+	0.998360i	$0.481768\pi$
$840$	9.94460	0.343121
$841$	−21.7590	−0.750309
$842$	−44.2348	−1.52443
$843$	−28.7900	−0.991579
$844$	−11.5982	−0.399226
$845$	−2.62584	−0.0903315
$846$	−60.1097	−2.06662
$847$	−4.71795	−0.162111
$848$	0.637858	0.0219041
$849$	−25.7915	−0.885162
$850$	−42.6189	−1.46182
$851$	102.741	3.52190
$852$	79.6007	2.72708
$853$	−6.97923	−0.238964	−0.119482	−	0.992836i	$-0.538123\pi$
$853$	−6.97923	−0.238964	−0.119482	+	0.992836i	$0.538123\pi$
$854$	18.6745	0.639029
$855$	8.12515	0.277874
$856$	35.2820	1.20591
$857$	−38.0811	−1.30083	−0.650413	−	0.759581i	$-0.725404\pi$
$857$	−38.0811	−1.30083	−0.650413	+	0.759581i	$0.725404\pi$
$858$	11.3895	0.388831
$859$	30.4877	1.04023	0.520113	−	0.854097i	$-0.325890\pi$
$859$	30.4877	1.04023	0.520113	+	0.854097i	$0.325890\pi$
$860$	0.263455	0.00898374
$861$	−94.9378	−3.23547
$862$	−6.59812	−0.224733
$863$	35.7615	1.21734	0.608669	−	0.793425i	$-0.291704\pi$
$863$	35.7615	1.21734	0.608669	+	0.793425i	$0.291704\pi$
$864$	10.5629	0.359356
$865$	−0.254590	−0.00865631
$866$	1.13318	0.0385070
$867$	−7.10646	−0.241348
$868$	41.7082	1.41567
$869$	−3.95095	−0.134027
$870$	4.50360	0.152686
$871$	5.75112	0.194869
$872$	4.75263	0.160944
$873$	−66.6650	−2.25627
$874$	−162.046	−5.48128
$875$	13.1619	0.444954
$876$	15.2404	0.514925
$877$	−45.5722	−1.53887	−0.769433	−	0.638728i	$-0.779461\pi$
$877$	−45.5722	−1.53887	−0.769433	+	0.638728i	$0.779461\pi$
$878$	8.76787	0.295901
$879$	48.5715	1.63828
$880$	−0.0295349	−0.000995621 0
$881$	21.5688	0.726671	0.363335	−	0.931658i	$-0.381638\pi$
$881$	21.5688	0.726671	0.363335	+	0.931658i	$0.381638\pi$
$882$	−130.712	−4.40131
$883$	24.6983	0.831164	0.415582	−	0.909556i	$-0.363578\pi$
$883$	24.6983	0.831164	0.415582	+	0.909556i	$0.363578\pi$
$884$	−23.5552	−0.792246
$885$	0.762734	0.0256390
$886$	−0.994384	−0.0334070
$887$	−31.6362	−1.06224	−0.531121	−	0.847296i	$-0.678229\pi$
$887$	−31.6362	−1.06224	−0.531121	+	0.847296i	$0.678229\pi$
$888$	−84.3129	−2.82935
$889$	21.4372	0.718979
$890$	−8.45106	−0.283280
$891$	6.25371	0.209507
$892$	−50.2939	−1.68396
$893$	54.2821	1.81648
$894$	−111.804	−3.73928
$895$	2.87945	0.0962494
$896$	−87.4008	−2.91985
$897$	45.3632	1.51463
$898$	44.7527	1.49342
$899$	7.29838	0.243414
$900$	−59.9111	−1.99704
$901$	−22.9344	−0.764056
$902$	17.7819	0.592073
$903$	−3.51950	−0.117122
$904$	−19.6732	−0.654322
$905$	4.67829	0.155512
$906$	−0.911235	−0.0302738
$907$	19.1385	0.635482	0.317741	−	0.948178i	$-0.397076\pi$
$907$	19.1385	0.635482	0.317741	+	0.948178i	$0.397076\pi$
$908$	11.9020	0.394983
$909$	30.7418	1.01964
$910$	5.82230	0.193007
$911$	−9.58711	−0.317635	−0.158818	−	0.987308i	$-0.550768\pi$
$911$	−9.58711	−0.317635	−0.158818	+	0.987308i	$0.550768\pi$
$912$	2.10862	0.0698234
$913$	7.21069	0.238639
$914$	36.6037	1.21074
$915$	1.25955	0.0416395
$916$	−87.3211	−2.88517
$917$	−4.71795	−0.155801
$918$	16.5257	0.545430
$919$	−18.7872	−0.619733	−0.309867	−	0.950780i	$-0.600284\pi$
$919$	−18.7872	−0.619733	−0.309867	+	0.950780i	$0.600284\pi$
$920$	−7.41867	−0.244586
$921$	80.2053	2.64285
$922$	83.6280	2.75414
$923$	18.0076	0.592729
$924$	39.9091	1.31291
$925$	−55.3503	−1.81991
$926$	54.8531	1.80258
$927$	−61.6619	−2.02524
$928$	−14.8962	−0.488993
$929$	10.9349	0.358763	0.179381	−	0.983780i	$-0.442590\pi$
$929$	10.9349	0.358763	0.179381	+	0.983780i	$0.442590\pi$
$930$	4.53926	0.148848
$931$	118.040	3.86859
$932$	−71.2531	−2.33397
$933$	45.1291	1.47746
$934$	−73.2355	−2.39634
$935$	1.06194	0.0347291
$936$	−20.6453	−0.674812
$937$	−0.156151	−0.00510123	−0.00255061	−	0.999997i	$-0.500812\pi$
$937$	−0.156151	−0.00510123	−0.00255061	+	0.999997i	$0.500812\pi$
$938$	32.5175	1.06173
$939$	−61.3601	−2.00241
$940$	6.43150	0.209772
$941$	−22.6423	−0.738119	−0.369059	−	0.929406i	$-0.620320\pi$
$941$	−22.6423	−0.738119	−0.369059	+	0.929406i	$0.620320\pi$
$942$	128.859	4.19846
$943$	70.8236	2.30633
$944$	0.109776	0.00357289
$945$	−2.53146	−0.0823485
$946$	0.659205	0.0214326
$947$	56.5202	1.83666	0.918330	−	0.395815i	$-0.129538\pi$
$947$	56.5202	1.83666	0.918330	+	0.395815i	$0.129538\pi$
$948$	33.4210	1.08546
$949$	3.44775	0.111919
$950$	87.3004	2.83240
$951$	11.4716	0.371993
$952$	−51.4616	−1.66788
$953$	−17.4436	−0.565054	−0.282527	−	0.959259i	$-0.591173\pi$
$953$	−17.4436	−0.565054	−0.282527	+	0.959259i	$0.591173\pi$
$954$	−52.0223	−1.68428
$955$	0.940314	0.0304278
$956$	65.5864	2.12122
$957$	6.98356	0.225746
$958$	13.8478	0.447401
$959$	−53.4739	−1.72676
$960$	−9.41809	−0.303967
$961$	−23.6438	−0.762704
$962$	−49.3629	−1.59152
$963$	−45.6276	−1.47033
$964$	9.05610	0.291677
$965$	6.57574	0.211681
$966$	256.489	8.25239
$967$	23.2732	0.748416	0.374208	−	0.927345i	$-0.377915\pi$
$967$	23.2732	0.748416	0.374208	+	0.927345i	$0.377915\pi$
$968$	−2.88831	−0.0928339
$969$	−75.8163	−2.43557
$970$	11.5096	0.369552
$971$	−17.0540	−0.547290	−0.273645	−	0.961831i	$-0.588229\pi$
$971$	−17.0540	−0.547290	−0.273645	+	0.961831i	$0.588229\pi$
$972$	−71.5582	−2.29523
$973$	−18.3045	−0.586816
$974$	29.4533	0.943746
$975$	−24.4389	−0.782671
$976$	0.181279	0.00580261
$977$	−25.8638	−0.827458	−0.413729	−	0.910400i	$-0.635774\pi$
$977$	−25.8638	−0.827458	−0.413729	+	0.910400i	$0.635774\pi$
$978$	−42.4235	−1.35655
$979$	−13.1047	−0.418829
$980$	13.9857	0.446756
$981$	−6.14623	−0.196234
$982$	−42.7939	−1.36561
$983$	−37.8775	−1.20810	−0.604052	−	0.796945i	$-0.706448\pi$
$983$	−37.8775	−1.20810	−0.604052	+	0.796945i	$0.706448\pi$
$984$	−58.1206	−1.85282
$985$	−6.30593	−0.200924
$986$	−23.3054	−0.742194
$987$	−85.9186	−2.73482
$988$	48.2503	1.53505
$989$	2.62555	0.0834876
$990$	2.40880	0.0765567
$991$	35.2843	1.12084	0.560421	−	0.828208i	$-0.310639\pi$
$991$	35.2843	1.12084	0.560421	+	0.828208i	$0.310639\pi$
$992$	−15.0142	−0.476701
$993$	1.84172	0.0584452
$994$	101.817	3.22945
$995$	−2.68512	−0.0851241
$996$	−60.9951	−1.93270
$997$	16.7122	0.529280	0.264640	−	0.964347i	$-0.414747\pi$
$997$	16.7122	0.529280	0.264640	+	0.964347i	$0.414747\pi$
$998$	−67.3077	−2.13059
$999$	21.4624	0.679040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.3	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.3	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29335 q^{2} +2.59523 q^{3} +3.25943 q^{4} +0.281199 q^{5} -5.95177 q^{6} -4.71795 q^{7} -2.88831 q^{8} +3.73524 q^{9} +O(q^{10})\)	\(q-2.29335 q^{2} +2.59523 q^{3} +3.25943 q^{4} +0.281199 q^{5} -5.95177 q^{6} -4.71795 q^{7} -2.88831 q^{8} +3.73524 q^{9} -0.644885 q^{10} -1.00000 q^{11} +8.45899 q^{12} +1.91363 q^{13} +10.8199 q^{14} +0.729776 q^{15} +0.105032 q^{16} -3.77647 q^{17} -8.56619 q^{18} +7.73570 q^{19} +0.916548 q^{20} -12.2442 q^{21} +2.29335 q^{22} +9.13416 q^{23} -7.49584 q^{24} -4.92093 q^{25} -4.38862 q^{26} +1.90812 q^{27} -15.3778 q^{28} -2.69092 q^{29} -1.67363 q^{30} -2.71223 q^{31} +5.53575 q^{32} -2.59523 q^{33} +8.66075 q^{34} -1.32668 q^{35} +12.1748 q^{36} +11.2479 q^{37} -17.7406 q^{38} +4.96632 q^{39} -0.812189 q^{40} +7.75370 q^{41} +28.0802 q^{42} +0.287443 q^{43} -3.25943 q^{44} +1.05034 q^{45} -20.9478 q^{46} +7.01709 q^{47} +0.272583 q^{48} +15.2591 q^{49} +11.2854 q^{50} -9.80082 q^{51} +6.23735 q^{52} +6.07298 q^{53} -4.37597 q^{54} -0.281199 q^{55} +13.6269 q^{56} +20.0760 q^{57} +6.17120 q^{58} +1.04516 q^{59} +2.37866 q^{60} +1.72594 q^{61} +6.22007 q^{62} -17.6227 q^{63} -12.9054 q^{64} +0.538110 q^{65} +5.95177 q^{66} +3.00535 q^{67} -12.3091 q^{68} +23.7053 q^{69} +3.04254 q^{70} +9.41019 q^{71} -10.7885 q^{72} +1.80168 q^{73} -25.7954 q^{74} -12.7710 q^{75} +25.2140 q^{76} +4.71795 q^{77} -11.3895 q^{78} +3.95095 q^{79} +0.0295349 q^{80} -6.25371 q^{81} -17.7819 q^{82} -7.21069 q^{83} -39.9091 q^{84} -1.06194 q^{85} -0.659205 q^{86} -6.98356 q^{87} +2.88831 q^{88} +13.1047 q^{89} -2.40880 q^{90} -9.02842 q^{91} +29.7722 q^{92} -7.03886 q^{93} -16.0926 q^{94} +2.17527 q^{95} +14.3666 q^{96} -17.8476 q^{97} -34.9943 q^{98} -3.73524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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